# Made the substitution, but now how to integrate?

• June 18th 2012, 04:55 AM
phys251
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?
• June 18th 2012, 07:35 AM
BobP
Re: Made the substitution, but now how to integrate?
$1+\tan^{2}A=\sec^{2}A,$

$\frac{1}{\sec^{2}A}=\cos^{2}A=\frac{1}{2}(1+\cos2A ).$
• June 19th 2012, 05:22 AM
phys251
Re: Made the substitution, but now how to integrate?
Oh! Durr, trig identities! Thanks.