So Many Arctangents 2008 AIME I Problem 8
>> YOUR LINK HERE: ___ http://youtube.com/watch?v=ZQgD7m03v3I
Let's add up arctangents of reciprocals to get pi/4. • Your support is truly a huge encouragement. • Please take a second to subscribe in order to send us your valuable support and receive notifications for new videos! • Every subscriber and every like are wholeheartedly appreciated.","styleRuns":[{"startIndex":0,"length":280,"styleRunExtensions":{"styleRunColorMapExtension":{"colorMap":[{"key":"USER_INTERFACE_THEME_DARK","value":4294967295},{"key":"USER_INTERFACE_THEME_LIGHT","value":4279440147}]}},"fontFamilyName":"Roboto"}]},"headerRuns":[{"startIndex":0,"length":280,"headerMapping":"ATTRIBUTED_STRING_HEADER_MAPPING_UNSPECIFIED"}]}},{"itemSectionRenderer":{"contents":[{"continuationItemRenderer":{"trigger":"CONTINUATION_TRIGGER_ON_ITEM_SHOWN","continuationEndpoint":{"clickTrackingParams":"CM0BELsvGAIiEwjj6_Kv2M6LAxVObHoFHZJpGbc=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/next"}},"continuationCommand":{"token":"Eg0SC1pRZ0Q3bTAzdjNJGAYyJSIRIgtaUWdEN20wM3YzSTAAeAJCEGNvbW1lbnRzLXNlY3Rpb24%3D","request":"CONTINUATION_REQUEST_TYPE_WATCH_NEXT"}}}}],"trackingParams":"CM0BELsvGAIiEwjj6_Kv2M6LAxVObHoFHZJpGbc=","sectionIdentifier":"comment-item-section","targetId":"comments-section"}}],"trackingParams":"CMwBELovIhMI4-vyr9jOiwMVTmx6BR2SaRm3"}},"secondaryResults":{"secondaryResults":{"results":[{"compactVideoRenderer":{"videoId":"rrtSsKfSQ6o","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/rrtSsKfSQ6o/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG rs=AOn4CLDADwcqF_utuFIl8-0Oxwn8xOkBqg","width":168,"height":94},{"url":"https://i.ytimg.com/vi/rrtSsKfSQ6o/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg== rs=AOn4CLBuI44t1k2H3N-9dUWTCVe8nxfqJw","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"Quartic Polynomial and Real Roots (2018 AIME II Problem 6) by LetsSolveMathProblems 18,308 views 6 years ago 10 minutes, 46 seconds"}},"simpleText":"Quartic Polynomial and Real Roots (2018 AIME II Problem 6)"},"longBylineText":{"runs":[{"text":"LetsSolveMathProblems","navigationEndpoint":{"clickTrackingParams":"CMUBEKQwGAAiEwjj6_Kv2M6LAxVObHoFHZJpGbcyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@LetsSolveMathProblems","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCEI9wNw9a4cJfejeAU6J2wQ","canonicalBaseUrl":"/@LetsSolveMathProblems"}}}]},"publishedTimeText":{"simpleText":"6 years ago"},"viewCountText":{"simpleText":"18,308 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"10 minutes, 46 seconds"}},"simpleText":"10:46"},"navigationEndpoint":{"clickTrackingParams":"CMUBEKQwGAAiEwjj6_Kv2M6LAxVObHoFHZJpGbcyB3JlbGF0ZWRI8v7e6eb9gIRlmgEFCAEQ-B0=","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=rrtSsKfSQ6o","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"rrtSsKfSQ6o","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr4---sn-nvm-cxbz.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 id=aebb52b0a7d243aa ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=1407500 mt=1739931654 oweuc= pxtags=Cg4KAnR4Egg1MTM5MzE1OA rxtags=Cg4KAnR4Egg1MTM5MzE1NA%2CCg4KAnR4Egg1MTM5MzE1NQ%2CCg4KAnR4Egg1MTM5MzE1Ng%2CCg4KAnR4Egg1MTM5MzE1Nw%2CCg4KAnR4Egg1MTM5MzE1OA"}}}}},"shortBylineText":{"runs":[{"text":"LetsSolveMathProblems","navigationEndpoint":{"clickTrackingParams":"CMUBEKQwGAAiEwjj6_Kv2M6LAxVObHoFHZJpGbcyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@LetsSolveMathProblems","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCEI9wNw9a4cJfejeAU6J2wQ","canonicalBaseUrl":"/@LetsSolveMathProblems"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/ytc/AIdro_lzAS5eWeoT-6XJXlrDAeJoGv5RfgPRGYgEwdUDiiGlOp0=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"trackingParams":"CMUBEKQwGAAiEwjj6_Kv2M6LAxVObHoFHZJpGbdAqofJvorW1N2uAQ==","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"18K views"}},"simpleText":"18K views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CMoBEP6YBBgFIhMI4-vyr9jOiwMVTmx6BR2SaRm3","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CMoBEP6YBBgFIhMI4-vyr9jOiwMVTmx6BR2SaRm3","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"rrtSsKfSQ6o","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CMoBEP6YBBgFIhMI4-vyr9jOiwMVTmx6BR2SaRm3","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["rrtSsKfSQ6o"],"params":"CAQ%3D"}},"videoIds":["rrtSsKfSQ6o"]}},{"clickTrackingParams":"CMoBEP6YBBgFIhMI4-vyr9jOiwMVTmx6BR2SaRm3","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CMsBELlqIhMI4-vyr9jOiwMVTmx6BR2SaRm3"}},"popupType":"TOAST"}}]}},"trackingParams":"CMoBEP6YBBgFIhMI4-vyr9jOiwMVTmx6BR2SaRm3"}},{"menuServiceItemDownloadRenderer":{"serviceEndpoint":{"clickTrackingParams":"CMkBENGqBRgGIhMI4-vyr9jOiwMVTmx6BR2SaRm3","offlineVideoEndpoint":{"videoId":"rrtSsKfSQ6o","onAddCommand":{"clickTrackingParams":"CMkBENGqBRgGIhMI4-vyr9jOiwMVTmx6BR2SaRm3","getDownloadActionCommand":{"videoId":"rrtSsKfSQ6o","params":"CAIQAA%3D%3D"}}}},"trackingParams":"CMkBENGqBRgGIhMI4-vyr9jOiwMVTmx6BR2SaRm3"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CMUBEKQwGAAiEwjj6_Kv2M6LAxVObHoFHZJpGbc=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"CgtycnRTc0tmU1E2bw%3D%3D","commands":[{"clickTrackingParams":"CMUBEKQwGAAiEwjj6_Kv2M6LAxVObHoFHZJpGbc=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CMgBEI5iIhMI4-vyr9jOiwMVTmx6BR2SaRm3","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CMUBEKQwGAAiEwjj6_Kv2M6LAxVObHoFHZJpGbc=","hasSeparator":true}}],"trackingParams":"CMUBEKQwGAAiEwjj6_Kv2M6LAxVObHoFHZJpGbc=","accessibility":{"accessibilityData":{"label":"Action menu"}},"targetId":"watch-related-menu-button"}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"10 minutes, 46 seconds"}},"simpleText":"10:46"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CMcBEPnnAxgBIhMI4-vyr9jOiwMVTmx6BR2SaRm3","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"rrtSsKfSQ6o","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CMcBEPnnAxgBIhMI4-vyr9jOiwMVTmx6BR2SaRm3","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"rrtSsKfSQ6o"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CMcBEPnnAxgBIhMI4-vyr9jOiwMVTmx6BR2SaRm3"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CMYBEMfsBBgCIhMI4-vyr9jOiwMVTmx6BR2SaRm3","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CMYBEMfsBBgCIhMI4-vyr9jOiwMVTmx6BR2SaRm3","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"rrtSsKfSQ6o","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CMYBEMfsBBgCIhMI4-vyr9jOiwMVTmx6BR2SaRm3","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["rrtSsKfSQ6o"],"params":"CAQ%3D"}},"videoIds":["rrtSsKfSQ6o"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CMYBEMfsBBgCIhMI4-vyr9jOiwMVTmx6BR2SaRm3"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"Quartic Polynomial and Real Roots (2018 AIME II Problem 6) - 10 minutes, 46 seconds - Go to channel - LetsSolveMathProblems - 18K views - 6 years ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"enableHoveredLogging":true,"enableOverlay":true}}}},{"compactVideoRenderer":{"videoId":"kPtnljDHjdk","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/kPtnljDHjdk/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG rs=AOn4CLDFMzh1y9GtAhmD71swPNg9ybCWvA","width":168,"height":94},{"url":"https://i.ytimg.com/vi/kPtnljDHjdk/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg== rs=AOn4CLAqva563lSqtnt1xoAfyAFWHZwfyA","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"2015 AIME I Problem 10 (Cubic Polynomial) by LetsSolveMathProblems 16,538 views 7 years ago 11 minutes, 1 second"}},"simpleText":"2015 AIME I Problem 10 (Cubic Polynomial)"},"longBylineText":{"runs":[{"text":"LetsSolveMathProblems","navigationEndpoint":{"clickTrackingParams":"CL4BEKQwGAEiEwjj6_Kv2M6LAxVObHoFHZJpGbcyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@LetsSolveMathProblems","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCEI9wNw9a4cJfejeAU6J2wQ","canonicalBaseUrl":"/@LetsSolveMathProblems"}}}]},"publishedTimeText":{"simpleText":"7 years ago"},"viewCountText":{"simpleText":"16,538 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"11 minutes, 1 second"}},"simpleText":"11:01"},"navigationEndpoint":{"clickTrackingParams":"CL4BEKQwGAEiEwjj6_Kv2M6LAxVObHoFHZJpGbcyB3JlbGF0ZWRI8v7e6eb9gIRlmgEFCAEQ-B0=","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=kPtnljDHjdk","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"kPtnljDHjdk","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr1---sn-nvm-cxbz.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 id=90fb679630c78dd9 ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=1407500 mt=1739931654 oweuc= pxtags=Cg4KAnR4Egg1MTM5MzE1OA rxtags=Cg4KAnR4Egg1MTM5MzE1NA%2CCg4KAnR4Egg1MTM5MzE1NQ%2CCg4KAnR4Egg1MTM5MzE1Ng%2CCg4KAnR4Egg1MTM5MzE1Nw%2CCg4KAnR4Egg1MTM5MzE1OA"}}}}},"shortBylineText":{"runs":[{"text":"LetsSolveMathProblems","navigationEndpoint":{"clickTrackingParams":"CL4BEKQwGAEiEwjj6_Kv2M6LAxVObHoFHZJpGbcyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@LetsSolveMathProblems","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCEI9wNw9a4cJfejeAU6J2wQ","canonicalBaseUrl":"/@LetsSolveMathProblems"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/ytc/AIdro_lzAS5eWeoT-6XJXlrDAeJoGv5RfgPRGYgEwdUDiiGlOp0=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"trackingParams":"CL4BEKQwGAEiEwjj6_Kv2M6LAxVObHoFHZJpGbdA2ZuehuPy2f2QAQ==","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"16K views"}},"simpleText":"16K views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CMMBEP6YBBgFIhMI4-vyr9jOiwMVTmx6BR2SaRm3","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CMMBEP6YBBgFIhMI4-vyr9jOiwMVTmx6BR2SaRm3","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"kPtnljDHjdk","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CMMBEP6YBBgFIhMI4-vyr9jOiwMVTmx6BR2SaRm3","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["kPtnljDHjdk"],"params":"CAQ%3D"}},"videoIds":["kPtnljDHjdk"]}},{"clickTrackingParams":"CMMBEP6YBBgFIhMI4-vyr9jOiwMVTmx6BR2SaRm3","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CMQBELlqIhMI4-vyr9jOiwMVTmx6BR2SaRm3"}},"popupType":"TOAST"}}]}},"trackingParams":"CMMBEP6YBBgFIhMI4-vyr9jOiwMVTmx6BR2SaRm3"}},{"menuServiceItemDownloadRenderer":{"serviceEndpoint":{"clickTrackingParams":"CMIBENGqBRgGIhMI4-vyr9jOiwMVTmx6BR2SaRm3","offlineVideoEndpoint":{"videoId":"kPtnljDHjdk","onAddCommand":{"clickTrackingParams":"CMIBENGqBRgGIhMI4-vyr9jOiwMVTmx6BR2SaRm3","getDownloadActionCommand":{"videoId":"kPtnljDHjdk","params":"CAIQAA%3D%3D"}}}},"trackingParams":"CMIBENGqBRgGIhMI4-vyr9jOiwMVTmx6BR2SaRm3"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CL4BEKQwGAEiEwjj6_Kv2M6LAxVObHoFHZJpGbc=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"CgtrUHRubGpESGpkaw%3D%3D","commands":[{"clickTrackingParams":"CL4BEKQwGAEiEwjj6_Kv2M6LAxVObHoFHZJpGbc=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CMEBEI5iIhMI4-vyr9jOiwMVTmx6BR2SaRm3","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CL4BEKQwGAEiEwjj6_Kv2M6LAxVObHoFHZJpGbc=","hasSeparator":true}}],"trackingParams":"CL4BEKQwGAEiEwjj6_Kv2M6LAxVObHoFHZJpGbc=","accessibility":{"accessibilityData":{"label":"Action menu"}}}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"11 minutes, 1 second"}},"simpleText":"11:01"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CMABEPnnAxgBIhMI4-vyr9jOiwMVTmx6BR2SaRm3","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"kPtnljDHjdk","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CMABEPnnAxgBIhMI4-vyr9jOiwMVTmx6BR2SaRm3","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"kPtnljDHjdk"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CMABEPnnAxgBIhMI4-vyr9jOiwMVTmx6BR2SaRm3"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CL8BEMfsBBgCIhMI4-vyr9jOiwMVTmx6BR2SaRm3","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CL8BEMfsBBgCIhMI4-vyr9jOiwMVTmx6BR2SaRm3","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"kPtnljDHjdk","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CL8BEMfsBBgCIhMI4-vyr9jOiwMVTmx6BR2SaRm3","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["kPtnljDHjdk"],"params":"CAQ%3D"}},"videoIds":["kPtnljDHjdk"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CL8BEMfsBBgCIhMI4-vyr9jOiwMVTmx6BR2SaRm3"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"2015 AIME I Problem 10 (Cubic Polynomial) - 11 minutes, 1 second - Go to channel - LetsSolveMathProblems - 16K views - 7 years ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"enableHoveredLogging":true,"enableOverlay":true}}}},{"compactVideoRenderer":{"videoId":"qn7z9T-dezw","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/qn7z9T-dezw/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG rs=AOn4CLD22wQ5iTr5Td_B1xPQHqMw-L6ovg","width":168,"height":94},{"url":"https://i.ytimg.com/vi/qn7z9T-dezw/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg== rs=AOn4CLAoNx-W2MA47y0kTxgN25Xx8rUd0w","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"What is this Product?!!: MIT Integration Bee (15) by LetsSolveMathProblems 255,354 views 7 years ago 17 minutes"}},"simpleText":"What is this Product?!!: MIT Integration Bee (15)"},"longBylineText":{"runs":[{"text":"LetsSolveMathProblems","navigationEndpoint":{"clickTrackingParams":"CLcBEKQwGAIiEwjj6_Kv2M6LAxVObHoFHZJpGbcyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@LetsSolveMathProblems","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCEI9wNw9a4cJfejeAU6J2wQ","canonicalBaseUrl":"/@LetsSolveMathProblems"}}}]},"publishedTimeText":{"simpleText":"7 years ago"},"viewCountText":{"simpleText":"255,354 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"17 minutes, 24 seconds"}},"simpleText":"17:24"},"navigationEndpoint":{"clickTrackingParams":"CLcBEKQwGAIiEwjj6_Kv2M6LAxVObHoFHZJpGbcyB3JlbGF0ZWRI8v7e6eb9gIRlmgEFCAEQ-B0=","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=qn7z9T-dezw","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"qn7z9T-dezw","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr4---sn-uxaxiv0nxx5q-nv4l.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 id=aa7ef3f53f9d7b3c ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=1335000 mt=1739931654 oweuc= pxtags=Cg4KAnR4Egg1MTM5MzE1OA rxtags=Cg4KAnR4Egg1MTM5MzE1NA%2CCg4KAnR4Egg1MTM5MzE1NQ%2CCg4KAnR4Egg1MTM5MzE1Ng%2CCg4KAnR4Egg1MTM5MzE1Nw%2CCg4KAnR4Egg1MTM5MzE1OA"}}}}},"shortBylineText":{"runs":[{"text":"LetsSolveMathProblems","navigationEndpoint":{"clickTrackingParams":"CLcBEKQwGAIiEwjj6_Kv2M6LAxVObHoFHZJpGbcyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@LetsSolveMathProblems","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCEI9wNw9a4cJfejeAU6J2wQ","canonicalBaseUrl":"/@LetsSolveMathProblems"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/ytc/AIdro_lzAS5eWeoT-6XJXlrDAeJoGv5RfgPRGYgEwdUDiiGlOp0=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"trackingParams":"CLcBEKQwGAIiEwjj6_Kv2M6LAxVObHoFHZJpGbdAvPb1_NP-vL-qAQ==","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"255K views"}},"simpleText":"255K views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CLwBEP6YBBgFIhMI4-vyr9jOiwMVTmx6BR2SaRm3","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CLwBEP6YBBgFIhMI4-vyr9jOiwMVTmx6BR2SaRm3","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"qn7z9T-dezw","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CLwBEP6YBBgFIhMI4-vyr9jOiwMVTmx6BR2SaRm3","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["qn7z9T-dezw"],"params":"CAQ%3D"}},"videoIds":["qn7z9T-dezw"]}},{"clickTrackingParams":"CLwBEP6YBBgFIhMI4-vyr9jOiwMVTmx6BR2SaRm3","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CL0BELlqIhMI4-vyr9jOiwMVTmx6BR2SaRm3"}},"popupType":"TOAST"}}]}},"trackingParams":"CLwBEP6YBBgFIhMI4-vyr9jOiwMVTmx6BR2SaRm3"}},{"menuServiceItemDownloadRenderer":{"serviceEndpoint":{"clickTrackingParams":"CLsBENGqBRgGIhMI4-vyr9jOiwMVTmx6BR2SaRm3","offlineVideoEndpoint":{"videoId":"qn7z9T-dezw","onAddCommand":{"clickTrackingParams":"CLsBENGqBRgGIhMI4-vyr9jOiwMVTmx6BR2SaRm3","getDownloadActionCommand":{"videoId":"qn7z9T-dezw","params":"CAIQAA%3D%3D"}}}},"trackingParams":"CLsBENGqBRgGIhMI4-vyr9jOiwMVTmx6BR2SaRm3"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CLcBEKQwGAIiEwjj6_Kv2M6LAxVObHoFHZJpGbc=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"Cgtxbjd6OVQtZGV6dw%3D%3D","commands":[{"clickTrackingParams":"CLcBEKQwGAIiEwjj6_Kv2M6LAxVObHoFHZJpGbc=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CLoBEI5iIhMI4-vyr9jOiwMVTmx6BR2SaRm3","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CLcBEKQwGAIiEwjj6_Kv2M6LAxVObHoFHZJpGbc=","hasSeparator":true}}],"trackingParams":"CLcBEKQwGAIiEwjj6_Kv2M6LAxVObHoFHZJpGbc=","accessibility":{"accessibilityData":{"label":"Action menu"}}}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"17 minutes, 24 seconds"}},"simpleText":"17:24"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CLkBEPnnAxgBIhMI4-vyr9jOiwMVTmx6BR2SaRm3","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"qn7z9T-dezw","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CLkBEPnnAxgBIhMI4-vyr9jOiwMVTmx6BR2SaRm3","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"qn7z9T-dezw"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CLkBEPnnAxgBIhMI4-vyr9jOiwMVTmx6BR2SaRm3"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CLgBEMfsBBgCIhMI4-vyr9jOiwMVTmx6BR2SaRm3","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CLgBEMfsBBgCIhMI4-vyr9jOiwMVTmx6BR2SaRm3","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"qn7z9T-dezw","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CLgBEMfsBBgCIhMI4-vyr9jOiwMVTmx6BR2SaRm3","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["qn7z9T-dezw"],"params":"CAQ%3D"}},"videoIds":["qn7z9T-dezw"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CLgBEMfsBBgCIhMI4-vyr9jOiwMVTmx6BR2SaRm3"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"What is this Product?!!: MIT Integration Bee (15) - 17 minutes - Go to channel - LetsSolveMathProblems - 255K views - 7 years ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"enableHoveredLogging":true,"enableOverlay":true}}}},{"compactVideoRenderer":{"videoId":"t24yRy3gocU","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/t24yRy3gocU/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG rs=AOn4CLCYyVErfKu8BDW6TvgvRdlOa1bzug","width":168,"height":94},{"url":"https://i.ytimg.com/vi/t24yRy3gocU/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg== rs=AOn4CLA_K1Ad59lZxGgCPbYCy2nzAuIXXA","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"Integrate 1/(1+x^3) by Prime Newtons 156,583 views 2 months ago 24 minutes"}},"simpleText":"Integrate 1/(1+x^3)"},"longBylineText":{"runs":[{"text":"Prime Newtons","navigationEndpoint":{"clickTrackingParams":"CLABEKQwGAMiEwjj6_Kv2M6LAxVObHoFHZJpGbcyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@PrimeNewtons","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCQ3jbVA0UCuBJfqTWxOb1aQ","canonicalBaseUrl":"/@PrimeNewtons"}}}]},"publishedTimeText":{"simpleText":"2 months ago"},"viewCountText":{"simpleText":"156,583 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"24 minutes, 56 seconds"}},"simpleText":"24:56"},"navigationEndpoint":{"clickTrackingParams":"CLABEKQwGAMiEwjj6_Kv2M6LAxVObHoFHZJpGbcyB3JlbGF0ZWRI8v7e6eb9gIRlmgEFCAEQ-B0=","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=t24yRy3gocU","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"t24yRy3gocU","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr2---sn-nvm-cxbz.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 id=b76e32472de0a1c5 ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=1407500 mt=1739931654 oweuc= pxtags=Cg4KAnR4Egg1MTM5MzE1OA rxtags=Cg4KAnR4Egg1MTM5MzE1NA%2CCg4KAnR4Egg1MTM5MzE1NQ%2CCg4KAnR4Egg1MTM5MzE1Ng%2CCg4KAnR4Egg1MTM5MzE1Nw%2CCg4KAnR4Egg1MTM5MzE1OA"}}}}},"shortBylineText":{"runs":[{"text":"Prime Newtons","navigationEndpoint":{"clickTrackingParams":"CLABEKQwGAMiEwjj6_Kv2M6LAxVObHoFHZJpGbcyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@PrimeNewtons","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCQ3jbVA0UCuBJfqTWxOb1aQ","canonicalBaseUrl":"/@PrimeNewtons"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/wxfmE3GxAAG8F4wC1QF7V5Ob9xo4MXGGnn0V-c5WeVtVFe7RrCf68SCsQT8cMPhw6sgPYbmDiqs=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"ownerBadges":[{"metadataBadgeRenderer":{"icon":{"iconType":"CHECK_CIRCLE_THICK"},"style":"BADGE_STYLE_TYPE_VERIFIED","tooltip":"Verified","trackingParams":"CLABEKQwGAMiEwjj6_Kv2M6LAxVObHoFHZJpGbc=","accessibilityData":{"label":"Verified"}}}],"trackingParams":"CLABEKQwGAMiEwjj6_Kv2M6LAxVObHoFHZJpGbdAxcOC7_LIjLe3AQ==","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"156K views"}},"simpleText":"156K views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CLUBEP6YBBgHIhMI4-vyr9jOiwMVTmx6BR2SaRm3","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CLUBEP6YBBgHIhMI4-vyr9jOiwMVTmx6BR2SaRm3","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"t24yRy3gocU","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CLUBEP6YBBgHIhMI4-vyr9jOiwMVTmx6BR2SaRm3","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["t24yRy3gocU"],"params":"CAQ%3D"}},"videoIds":["t24yRy3gocU"]}},{"clickTrackingParams":"CLUBEP6YBBgHIhMI4-vyr9jOiwMVTmx6BR2SaRm3","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CLYBELlqIhMI4-vyr9jOiwMVTmx6BR2SaRm3"}},"popupType":"TOAST"}}]}},"trackingParams":"CLUBEP6YBBgHIhMI4-vyr9jOiwMVTmx6BR2SaRm3"}},{"menuServiceItemDownloadRenderer":{"serviceEndpoint":{"clickTrackingParams":"CLQBENGqBRgIIhMI4-vyr9jOiwMVTmx6BR2SaRm3","offlineVideoEndpoint":{"videoId":"t24yRy3gocU","onAddCommand":{"clickTrackingParams":"CLQBENGqBRgIIhMI4-vyr9jOiwMVTmx6BR2SaRm3","getDownloadActionCommand":{"videoId":"t24yRy3gocU","params":"CAIQAA%3D%3D"}}}},"trackingParams":"CLQBENGqBRgIIhMI4-vyr9jOiwMVTmx6BR2SaRm3"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CLABEKQwGAMiEwjj6_Kv2M6LAxVObHoFHZJpGbc=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"Cgt0MjR5UnkzZ29jVQ%3D%3D","commands":[{"clickTrackingParams":"CLABEKQwGAMiEwjj6_Kv2M6LAxVObHoFHZJpGbc=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CLMBEI5iIhMI4-vyr9jOiwMVTmx6BR2SaRm3","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CLABEKQwGAMiEwjj6_Kv2M6LAxVObHoFHZJpGbc=","hasSeparator":true}}],"trackingParams":"CLABEKQwGAMiEwjj6_Kv2M6LAxVObHoFHZJpGbc=","accessibility":{"accessibilityData":{"label":"Action menu"}}}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"24 minutes, 56 seconds"}},"simpleText":"24:56"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CLIBEPnnAxgCIhMI4-vyr9jOiwMVTmx6BR2SaRm3","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"t24yRy3gocU","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CLIBEPnnAxgCIhMI4-vyr9jOiwMVTmx6BR2SaRm3","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"t24yRy3gocU"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CLIBEPnnAxgCIhMI4-vyr9jOiwMVTmx6BR2SaRm3"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CLEBEMfsBBgDIhMI4-vyr9jOiwMVTmx6BR2SaRm3","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CLEBEMfsBBgDIhMI4-vyr9jOiwMVTmx6BR2SaRm3","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"t24yRy3gocU","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CLEBEMfsBBgDIhMI4-vyr9jOiwMVTmx6BR2SaRm3","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["t24yRy3gocU"],"params":"CAQ%3D"}},"videoIds":["t24yRy3gocU"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CLEBEMfsBBgDIhMI4-vyr9jOiwMVTmx6BR2SaRm3"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"Integrate 1/(1+x^3) - 24 minutes - Go to channel - Prime Newtons - 156K views - 2 months ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"movingThumbnailDetails":{"thumbnails":[{"url":"https://i.ytimg.com/an_webp/t24yRy3gocU/mqdefault_6s.webp?du=3000 sqp=CObx1L0G rs=AOn4CLBRcOjjgH02xY0dE1B-TtYLfGsBqQ","width":320,"height":180}],"logAsMovingThumbnail":true},"enableHoveredLogging":true,"enableOverlay":true}}}},{"compactVideoRenderer":{"videoId":"82Nzy7Cgq1M","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/82Nzy7Cgq1M/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG rs=AOn4CLAISukwzigHGiR3CZqVpc4g06xeXg","width":168,"height":94},{"url":"https://i.ytimg.com/vi/82Nzy7Cgq1M/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg== rs=AOn4CLBAfxqt6BZFQkBFZt4329qNEOF6NA","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"AIME: HARD Logarithm/Series Problem (2007 II Problem 12) by LetsSolveMathProblems 30,990 views 6 years ago 12 minutes, 45 seconds"}},"simpleText":"AIME: HARD Logarithm/Series Problem (2007 II Problem 12)"},"longBylineText":{"runs":[{"text":"LetsSolveMathProblems","navigationEndpoint":{"clickTrackingParams":"CKkBEKQwGAQiEwjj6_Kv2M6LAxVObHoFHZJpGbcyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@LetsSolveMathProblems","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCEI9wNw9a4cJfejeAU6J2wQ","canonicalBaseUrl":"/@LetsSolveMathProblems"}}}]},"publishedTimeText":{"simpleText":"6 years ago"},"viewCountText":{"simpleText":"30,990 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"12 minutes, 45 seconds"}},"simpleText":"12:45"},"navigationEndpoint":{"clickTrackingParams":"CKkBEKQwGAQiEwjj6_Kv2M6LAxVObHoFHZJpGbcyB3JlbGF0ZWRI8v7e6eb9gIRlmgEFCAEQ-B0=","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=82Nzy7Cgq1M","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"82Nzy7Cgq1M","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr4---sn-uxaxiv0nxx5q-nv4l.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 id=f36373cbb0a0ab53 ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=1335000 mt=1739931654 oweuc= pxtags=Cg4KAnR4Egg1MTM5MzE1OA rxtags=Cg4KAnR4Egg1MTM5MzE1NA%2CCg4KAnR4Egg1MTM5MzE1NQ%2CCg4KAnR4Egg1MTM5MzE1Ng%2CCg4KAnR4Egg1MTM5MzE1Nw%2CCg4KAnR4Egg1MTM5MzE1OA"}}}}},"shortBylineText":{"runs":[{"text":"LetsSolveMathProblems","navigationEndpoint":{"clickTrackingParams":"CKkBEKQwGAQiEwjj6_Kv2M6LAxVObHoFHZJpGbcyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@LetsSolveMathProblems","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCEI9wNw9a4cJfejeAU6J2wQ","canonicalBaseUrl":"/@LetsSolveMathProblems"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/ytc/AIdro_lzAS5eWeoT-6XJXlrDAeJoGv5RfgPRGYgEwdUDiiGlOp0=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"trackingParams":"CKkBEKQwGAQiEwjj6_Kv2M6LAxVObHoFHZJpGbdA09aChbv53LHzAQ==","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"30K views"}},"simpleText":"30K views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CK4BEP6YBBgFIhMI4-vyr9jOiwMVTmx6BR2SaRm3","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CK4BEP6YBBgFIhMI4-vyr9jOiwMVTmx6BR2SaRm3","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"82Nzy7Cgq1M","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CK4BEP6YBBgFIhMI4-vyr9jOiwMVTmx6BR2SaRm3","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["82Nzy7Cgq1M"],"params":"CAQ%3D"}},"videoIds":["82Nzy7Cgq1M"]}},{"clickTrackingParams":"CK4BEP6YBBgFIhMI4-vyr9jOiwMVTmx6BR2SaRm3","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CK8BELlqIhMI4-vyr9jOiwMVTmx6BR2SaRm3"}},"popupType":"TOAST"}}]}},"trackingParams":"CK4BEP6YBBgFIhMI4-vyr9jOiwMVTmx6BR2SaRm3"}},{"menuServiceItemDownloadRenderer":{"serviceEndpoint":{"clickTrackingParams":"CK0BENGqBRgGIhMI4-vyr9jOiwMVTmx6BR2SaRm3","offlineVideoEndpoint":{"videoId":"82Nzy7Cgq1M","onAddCommand":{"clickTrackingParams":"CK0BENGqBRgGIhMI4-vyr9jOiwMVTmx6BR2SaRm3","getDownloadActionCommand":{"videoId":"82Nzy7Cgq1M","params":"CAIQAA%3D%3D"}}}},"trackingParams":"CK0BENGqBRgGIhMI4-vyr9jOiwMVTmx6BR2SaRm3"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CKkBEKQwGAQiEwjj6_Kv2M6LAxVObHoFHZJpGbc=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"Cgs4Mk56eTdDZ3ExTQ%3D%3D","commands":[{"clickTrackingParams":"CKkBEKQwGAQiEwjj6_Kv2M6LAxVObHoFHZJpGbc=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CKwBEI5iIhMI4-vyr9jOiwMVTmx6BR2SaRm3","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CKkBEKQwGAQiEwjj6_Kv2M6LAxVObHoFHZJpGbc=","hasSeparator":true}}],"trackingParams":"CKkBEKQwGAQiEwjj6_Kv2M6LAxVObHoFHZJpGbc=","accessibility":{"accessibilityData":{"label":"Action menu"}}}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"12 minutes, 45 seconds"}},"simpleText":"12:45"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CKsBEPnnAxgBIhMI4-vyr9jOiwMVTmx6BR2SaRm3","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"82Nzy7Cgq1M","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CKsBEPnnAxgBIhMI4-vyr9jOiwMVTmx6BR2SaRm3","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"82Nzy7Cgq1M"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CKsBEPnnAxgBIhMI4-vyr9jOiwMVTmx6BR2SaRm3"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CKoBEMfsBBgCIhMI4-vyr9jOiwMVTmx6BR2SaRm3","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CKoBEMfsBBgCIhMI4-vyr9jOiwMVTmx6BR2SaRm3","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"82Nzy7Cgq1M","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CKoBEMfsBBgCIhMI4-vyr9jOiwMVTmx6BR2SaRm3","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["82Nzy7Cgq1M"],"params":"CAQ%3D"}},"videoIds":["82Nzy7Cgq1M"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CKoBEMfsBBgCIhMI4-vyr9jOiwMVTmx6BR2SaRm3"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"AIME: HARD Logarithm/Series Problem (2007 II Problem 12) - 12 minutes, 45 seconds - Go to channel - LetsSolveMathProblems - 30K views - 6 years ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"enableHoveredLogging":true,"enableOverlay":true}}}},{"lockupViewModel":{"contentImage":{"collectionThumbnailViewModel":{"primaryThumbnail":{"thumbnailViewModel":{"image":{"sources":[{"url":"https://i.ytimg.com/vi/FudmfolONYU/hqdefault.jpg?sqp=-oaymwEWCKgBEF5IWvKriqkDCQgBFQAAiEIYAQ== rs=AOn4CLA-IR1F4XNcLYbWt_DQQT36HFPpRQ","width":168,"height":94},{"url":"https://i.ytimg.com/vi/FudmfolONYU/hqdefault.jpg?sqp=-oaymwEXCNACELwBSFryq4qpAwkIARUAAIhCGAE= rs=AOn4CLDvd0435uk93pT3q_25E0tQBERDFA","width":336,"height":188}]},"overlays":[{"thumbnailOverlayBadgeViewModel":{"thumbnailBadges":[{"thumbnailBadgeViewModel":{"icon":{"sources":[{"clientResource":{"imageName":"PLAYLISTS"}}]},"text":"31 videos","badgeStyle":"THUMBNAIL_OVERLAY_BADGE_STYLE_DEFAULT","backgroundColor":{"lightTheme":3355443,"darkTheme":3355443}}}],"position":"THUMBNAIL_OVERLAY_BADGE_POSITION_BOTTOM_END"}},{"thumbnailHoverOverlayViewModel":{"icon":{"sources":[{"clientResource":{"imageName":"PLAY_ALL"}}]},"text":{"content":"Play all","styleRuns":[{"startIndex":0,"length":8}]},"style":"THUMBNAIL_HOVER_OVERLAY_STYLE_COVER"}}],"backgroundColor":{"lightTheme":4210752,"darkTheme":4210752}}},"stackColor":{"lightTheme":10066329,"darkTheme":9211020}}},"metadata":{"lockupMetadataViewModel":{"title":{"content":"AIME (American Invitational Mathematical Examination)"},"metadata":{"contentMetadataViewModel":{"metadataRows":[{"metadataParts":[{"text":{"content":"LetsSolveMathProblems
#############################
![](http://youtor.org/essay_main.png)