# Problem integrating

I'm supposed to integrate w/w^4 + 1

The two ideas I'd come up with was trying to substitute w^4+1 with u but that results in a 0 in the numerator.

Then I thought maybe I have to put w/w^4+1 into the 1/1+w^2 form and integrate into 1/k tan^-1kx + C but I'm not sure how to keep the original function while making the w^4 a w^2.

Help please? Am I at least going in the right direction with any of these ideas?

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dx
Homework Helper
Gold Member
Use integration by parts. You'll have to do it twice.

EDIT: Mark44's way is better, ignore this.

Mark44
Mentor
You're going in the right direction thinking of tan-1(x).

An ordinary substitution should do the trick: u = x2, so du = 2xdx. Then your integrand becomes roughly du/(u2 + 1). Notice the parentheses I added to make clear what the denominator is. You'll also need to add the right constant multiplier in the numerator, since I omitted it.

Does that mean I can substitute just the variable and leave the "+ 1"? That is substitute u as w^2 getting u^2 = u^4?

dx
Homework Helper
Gold Member
You mean u2 = w4.

Mark44
Mentor
Yes. The substitution is u = w2, so u2 = w4, and du = 2wdw.

Oh, yeah. Typo. That's what I meant.

Awesome, thanks for the help.