Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §5.4 Indefinite Integrals and Substitutions, #33 · Calculus · Techniques of integration

True or false, when … is an antiderivative of …: (a) …

True or false, when $f$ is an antiderivative of $v$ :
(a) $\int v (u (x)) d x = f (u (x)) + C$
(b) $\int v^{2} (x) d x = \frac{1}{3} f^{3} (x) + C$
(c) $\int v (x) (d u / d x) d x = f (u (x)) + C$
(d) $\int v (x) (d v / d x) d x = \frac{1}{2} f^{2} (x) + C$

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §5.4 Indefinite Integrals and Substitutions, #33

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