Made the substitution, but now how to integrate?

**phys251** · June 18th 2012, 04:55 AM

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?

**BobP** · June 18th 2012, 07:35 AM

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

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

**phys251** · June 19th 2012, 05:22 AM

Oh! Durr, trig identities! Thanks.

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Made the substitution, but now how to integrate?

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