Answer
$-\frac{cos(x^3)}{3} +C$
Work Step by Step
Evaluate the Integral using substitution: $\int x^2sin(x^3)dx$
Substitution Rule: $\int f(g(x))gā(x)dx = \int f(u)du$
$u= x^3$
$du =3x^2$
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 $u$:
$-\frac{cos(x^3)}{3} +C$