Indefinite integral and anti-derivative

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Homework Statement

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

Homework Equations

Anything possible to take an anti-derivative

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

 

[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?

 

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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.

 

[Mark44]

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.