https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-7/v/antiderivatives-and-indefinite-integrals 2020-07-26T09:23:46Z Antiderivatives and indefinite integrals What's the opposite of a derivative?  It's something called the "indefinite integral". Sal Khan video https://cdn.kastatic.org/googleusercontent/6cQ_nKo3eeyc6ImA7ekRRBCA5xhm6OjRNsElD7N5emNSybeLvYlE8YmQUPoM5rBbW5XOSu9-nBnkM4Kod8wJTbR5qA Antiderivatives and indefinite integrals What's the opposite of a derivative?  It's something called the "indefinite integral". https://cdn.kastatic.org/ka-youtube-converted/MMv-027KEqU.mp4/MMv-027KEqU.mp4 223 Integration as an inverse process of differentiation https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-7/e/antiderivatives 2026-04-08T00:54:09.631945657Z Antiderivatives and indefinite integrals Test your skills at finding antiderivatives. Tomer Gal exercise https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-8a/v/indefinite-integrals-of-x-raised-to-a-power 2020-07-26T09:23:47Z Reverse power rule Can you find a function whose derivative is x^n? Sal Khan video https://cdn.kastatic.org/googleusercontent/w2ki56wz2hvFEh8sEsYfFo6hkFK0RoediG0G_V0u0E8ZdM1jvXJEXROEy3W1NtSM4MrhseOfe_ma1fmIjSbzT4w Reverse power rule Can you find a function whose derivative is x^n? https://cdn.kastatic.org/ka-youtube-converted/QxbJsg-Vdms.mp4/QxbJsg-Vdms.mp4 348 Integration as an inverse process of differentiation https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-8a/e/intro-to-integration 2025-03-12T14:20:10.072734823Z Reverse power rule For example, find the indefinite integral of t². Tomer Gal exercise https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-8a/e/basic-integration 2025-05-05T08:14:25.350149109Z Reverse power rule: negative and fractional powers For example, find the indefinite integral of x^(-2)  or x^(3/4). Tomer Gal exercise https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-8a/e/integration 2025-05-05T08:14:25.350149109Z Reverse power rule: sums & multiples Find the indefinite integrals of polynomials. Tomer Gal exercise https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-8b/v/basic-trig-and-exponential-antiderivatives 2021-02-07T17:14:01Z Indefinite integrals of sin(x), cos(x), and eˣ ∫sin(x)dx=-cos(x)+C, ∫cos(x)dx=sin(x)+C, and ∫eˣdx=eˣ+C. Learn why this is so and see worked examples. Sal Khan video https://cdn.kastatic.org/googleusercontent/Is3CtgB0HwOe3bseTfwBnJrJkuxBiuVASEjHoGLB41nH_075Jj12HIZhnMt-ZtsGMsg2DJrU2cP5JkSI3u1_JDm6mg Indefinite integrals of sin(x), cos(x), and eˣ ∫sin(x)dx=-cos(x)+C, ∫cos(x)dx=sin(x)+C, and ∫eˣdx=eˣ+C. Learn why this is so and see worked examples. https://cdn.kastatic.org/ka-youtube-converted/hXg-6YgAARk.mp4/hXg-6YgAARk.mp4 244 Integration as an inverse process of differentiation https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-8b/e/integrating-sin-cos 2025-03-12T14:20:10.072734823Z Indefinite integrals: sin & cos For example, find the indefinite integral of 5cos(x). Tomer Gal exercise https://www.khanacademy.org/math/ka-math-class-12/x6f66cbee9a2f805b:integrals-ncert-new/x6f66cbee9a2f805b:integration-as-an-inverse-process-of-differentiation/v/graphs-of-indefinite-integrals 2020-07-26T09:23:45Z Graphs of indefinite integrals More practice identifying the graph of the antiderivative of a function. video https://cdn.kastatic.org/googleusercontent/e0gN1EmunRbNv0cSJ0QHD47d85O-C_5s5jX3HXADBZQEH4rgQB-qDd33_5yEVsv55KSWinVwV8Gl3VpH-_QZ8O6G Graphs of indefinite integrals More practice identifying the graph of the antiderivative of a function. https://cdn.kastatic.org/ka-youtube-converted/Gn3mJOC1wK8.mp4/Gn3mJOC1wK8.mp4 246 Integration as an inverse process of differentiation https://www.khanacademy.org/math/integral-calculus/ic-integration/ic-reverse-power-rule/v/antiderivative-of-hairier-expression 2021-02-07T17:14:01Z Rewriting before integrating: challenge problem In this example, we find the antiderivative an expression which is not so simple.  Sal Khan video https://cdn.kastatic.org/googleusercontent/D_EsY5BUhsuX0oT4zJOsDr14uC4JLqLqgGag4l8llFFWRD7dG3F3JOiR7OMSPQgqfoRVx7U1b3ags8bunswA5hpW Rewriting before integrating: challenge problem In this example, we find the antiderivative an expression which is not so simple.  https://cdn.kastatic.org/ka-youtube-converted/cBi4a1iSaPk.mp4/cBi4a1iSaPk.mp4 376 Integration as an inverse process of differentiation https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-8b/v/antiderivative-of-x-1 2021-02-07T17:14:01Z Indefinite integral of 1/x In differential ​calculus we learned that the derivative of ln(x) is 1/x. Integration goes the other way: the integral (or antiderivative) of 1/x should be a function whose derivative is 1/x. As we just saw, this is ln(x). However, if x is negative then ln(x) is undefined! The solution is quite simple: the antiderivative of 1/x is ln(|x|). Sal Khan video https://cdn.kastatic.org/googleusercontent/OBL4ZZcRYxyaaLfpt4aeWQEqRsqC0cu0pD-FO3FncYnJgYQrTDIzyeZL8zUJBQDlqppDSUbbTMg653Ga1p2VUEB1Sg Indefinite integral of 1/x In differential ​calculus we learned that the derivative of ln(x) is 1/x. Integration goes the other way: the integral (or antiderivative) of 1/x should be a function whose derivative is 1/x. As we just saw, this is ln(x). However, if x is negative then ln(x) is undefined! The solution is quite simple: the antiderivative of 1/x is ln(|x|). https://cdn.kastatic.org/ka-youtube-converted/sPPjk4aXzmQ.mp4/sPPjk4aXzmQ.mp4 455 Integration as an inverse process of differentiation https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-8b/e/indefinite-integrals-of-e-x-1-x 2025-05-05T08:14:25.350149109Z Indefinite integrals: eˣ & 1/x For example, find the indefinite integral of 4eˣ-3/x. Tomer Gal exercise https://www.khanacademy.org/math/integral-calculus/ic-integration/ic-common-indefinite-integrals/e/integrating-trig-functions 2025-05-05T08:14:25.350149109Z Integrating trig functions . Tomer Gal exercise https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-8b/a/common-integrals-review 2021-04-29T07:58:15Z Common integrals review Review the integration rules for all the common function types. article