# Homework Help: Algebraic manipulation of integral

1. Apr 10, 2009

### dirk_mec1

1. The problem statement, all variables and given/known data

$$\int_0^{\frac{\pi}{2}} \frac{\cos(x)}{1+\sin^2(x)} \ln(1+\cos(x))\ dx$$

3. The attempt at a solution
Can anyone give me a hint as to what to do?

2. Apr 14, 2009

### Cyosis

Re: integral

Using y=sin(x) followed by partial integration and some algebraic manipulation you can get to the following integral:

$$\int_0^1 \frac{\arctan(y)}{y\sqrt{1-y^2}}\ dy - \int_0^1 \frac{\arctan{y}}{y}\ dy$$

You know the first integral from a previous question you asked and the second integral is equal to Catalan's constant.