# Homework Help: Indefinite integral and anti-derivative

1. Jan 25, 2010

### hover

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

Find the indefinite integral of 16x^2+36+1/(16x^2+36) with respect to x

2. Relevant equations

Anything possible to take an anti-derivative

3. The attempt at a solution

I have absolutely no idea on how to deal with this problem. I can take an anti-derivative of the first 2 terms just fine but that fraction term just messes with me. I don't know how to take it on. It kind of looks like 1/(1+x^2) which would have an anti-derivative of arctan(x) but I really don't know how to handle this.

Thanks for the help

2. Jan 25, 2010

### Char. Limit

If it looks like 1/(1+x^2), then maybe you should make it look more like such by factoring things out, and do a trig substitution.

Also, have you tried using partial fractions?

3. Jan 25, 2010

### hover

I've tried a bunch of ways to try to solve this. Of my whole homework set, this is the only one I can't get. I just don't see how to break apart that fraction.

4. Jan 25, 2010

### Staff: Mentor

You can't break apart that fraction. You need to make it look like 1/(a^2 + u^2), which has an antiderivative of arctan(u/a) + C.