Constructing Antiderivatives Analytically Indefinite Integrals

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We can find symbolic formulas for many antiderivatives based on memorizing various derivative facts. These formulas can be written using indefinite integrals. Along with the Fundamental Theorem of Calculus, they can be used to solve many applied word problems. Infinite Powers, How Calculus Reveals the Secrets of the Universe: https://amzn.to/37PBMjb. • Calculus problems and solutions • 🔴 Calculus 1, Lesson 1.1: Linear Functions (3Blue1Brown SoME2): • Calculus 1, Lesson 1.2: Exponential F... • 🔴 Calculus 1, Lesson 1.2: Exponential Functions: • Calculus 1, Lesson 1.1: Linear Functi... • 🔴 Calculus 1, Lesson 1.3: Quadratic Functions, Transformations of Functions, and Function Composition: • Calculus 1, Lesson 1.3: Quadratic Fun... • 🔴 Calculus 1, Lesson 1.4: Logarithmic Functions (Intro to Horizontal Compressions Inverse Functions): • Calculus 1, Lesson 1.4: Logarithmic F... • 🔴 Calculus 1, Lesson 1.5: Trigonometric Functions and Inverse Trigonometric Functions: • Calculus 1, Lesson 1.5: Trigonometric... • 🔴 AP Calculus AB Exam Review: Practice Exam Problems Solutions (Multiple Choice, No Calculator): • AP Calculus AB Exam Review 2025: Prac... • 🔴 AP Calculus AB Exam Review: Free Response Practice Exam Problems Solutions: • AP Calculus AB Exam Review 2025: Free... • 🔴 AP Calculus BC Exam Review: Practice Exam (30 Question Multiple Choice, No Calculator): • AP Calculus BC Exam Review 2025: Prac... • 🔴 AP Calculus BC Exam Review: Free Response Practice Exam Problems Solutions: • AP Calculus BC Exam Review 2025: Free... • 🔴 Calculus 1 Exam 1 Review Problems and Solutions (Precalculus, Limits, Continuity, Derivatives): • Calculus 1 Exam 1 Review Problems and... • 🔴 Calculus 1 Course, Lecture 1: The Big Ideas (Rates Areas, the Infinity Principle Circular Area): • Calculus 1 Course, Lecture 1: The Big... • 🔴 Calculus 1 Course Lecture Playlist: • Calculus 1 Course Lectures • #antiderivative #antiderivatives #calculus • Links and resources • =============================== • 🔴 Subscribe to Bill Kinney Math: https://www.youtube.com/user/billkinn... • 🔴 Subscribe to my Math Blog, Infinity is Really Big: https://infinityisreallybig.com/ • 🔴 Follow me on Twitter: / billkinneymath • 🔴 Follow me on Instagram: / billkinneymath • 🔴 You can support me by buying Infinite Powers, How Calculus Reveals the Secrets of the Universe , by Steven Strogatz, or anything else you want to buy, starting from this link: https://amzn.to/3eXEmuA. • 🔴 Check out my artist son Tyler Kinney's website: https://www.tylertkinney.co/ • (0:00) Identify antiderivatives of f(x)=1/x • (7:50) Antiderivatives to memorize • (16:23) Integral of 4sin(3t) • (19:07) Integral of 6e^(-2t) • (20:21) Integral of (x^2 + sqrt(x))/x • (22:55) Integral of 1/(1+25x^2) • (24:38) Find the average value of sqrt(x)=x^(1/2) on [4,9] and graphically interpret • (28:48) Find the area between y=x^2 and y=2-x^2 • (31:54) Given the velocity, find the position • (36:44) Total cost of drilling a well, given the fixed costs and marginal costs (per meter) • • AMAZON ASSOCIATE • As an Amazon Associate I earn from qualifying purchases.

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