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## Homework Statement

[tex]\int \frac{26 dx}{{(169x^2+1)}^2}[/tex] <= the whole denominator is supposed to be squared...

## The Attempt at a Solution

So I converted the thing in the denominator so that it has a square root:

[tex]\int \frac{26 dx}{{\sqrt{169x^2+1}}^4}[/tex]

Looking at the denominator, I realized I should do an inverse substitution:

13x=tan(t)

dx=sec

^{2}(t)*dt/13

I subbed that in to the equation before and got:

[tex]\int \frac{26 * sec^2(t) * dt}{13*sec^4(t)}[/tex]

Simplifying which, I get:

2[tex]\int cos^2(t) dt[/tex]

Then I tried doing integration by parts, but I got nowhere - I kept getting cos^2 again... Please help me, this question frustrates me. Thanks in advance!

(Sidenote: I finally got my formulas all pretty, yay!)