Calculus Substitution Rule Problem Check

[aeonsky]

Homework Statement

Evaluate the indefinite integral...

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

Homework Equations

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

The Attempt at a Solution

u = x^3+5

du = x^2dx

So my answer is...

Does that look right?

And one more...

Homework Statement

Evaluate the indefinite integral...

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

Homework Equations

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

The Attempt at a Solution

u = x^2+1

du = 1/2 dx

So my answer is...

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

Does that look right?

 

[VeeEight]

Since you are solving indefinite integrals, to check your answer simply differentiate and see if it is same as the function under the integral.