# Homework Help: Calculus Substitution Rule Problem Check

1. Nov 30, 2008

### aeonsky

1. The problem statement, all variables and given/known data

Evaluate the indefinite integral...

$\int x^2 (x^3+5)^9 dx$

2. Relevant equations

$\int f(g(x))g'(x)dx = \int f(u)du$

3. The attempt at a solution

$u = x^3+5$

$du = x^2dx$

Does that look right?

And one more...

1. The problem statement, all variables and given/known data

Evaluate the indefinite integral...

$\int x/(x^2+1)^2$

2. Relevant equations

$\int f(g(x))g'(x)dx = \int f(u)du$

3. The attempt at a solution

$u = x^2+1$

$du = 1/2 dx$

$(-1)/2(x^2+1) + C$