Chapter 4 - Integrals - 4.5 The Substitution Rule - 4.5 Exercises - Page 346: 8

$-\frac{cos(x^3)}{3} +C$

Evaluate the Integral using substitution: $\int x^2sin(x^3)dx$ Substitution Rule: $\int f(g(x))g’(x)dx = \int f(u)du$ $u= x^3$ $du =3x^2$ Solve the integral in terms of $u$: $\int \frac{sin(u)}{3}du$ $\frac{1}{3}\int sin(u)du $ $-\frac{1}{3}cos(u) +C$ Substitute for $u$: $-\frac{cos(x^3)}{3} +C$