# Thread: Finding an integral from a derivative.

1. ## Finding an integral from a derivative.

Differentiate $tan^{-1}(cos x)$ and hence evaluate $\int_0^\pi sin \frac{dx}{(2-sin^{2}x)}$

2. Originally Posted by nerdzor
Differentiate $\tan^{-1}(\cos x)$ and hence evaluate $\int_0^\pi {\color{red}\sin x} \frac{dx}{(2 - \sin^{2}x)}$
You have a made a typo (see the red).

Can you differentiate the given function? Note that $1 + \cos^2 x = 2 - \sin^2 x$ using the Pythagorean Identity. So the derivative of the function is equal to the integrand. What does that tell you ....?