# Thread: Made the substitution, but now how to integrate?

1. ## Made the substitution, but now how to integrate?

Hi all.

I started with this equation:

$\frac {dy}{dx}=tan^2(x+y)$

I made the substitution $u = x+y$ and am now looking at this:

$\frac {du}{tan^2u+1} = dx$

How the heck do I integrate that left side?

2. ## Re: Made the substitution, but now how to integrate?

$1+\tan^{2}A=\sec^{2}A,$

$\frac{1}{\sec^{2}A}=\cos^{2}A=\frac{1}{2}(1+\cos2A ).$

3. ## Re: Made the substitution, but now how to integrate?

Oh! Durr, trig identities! Thanks.