- #1

- 761

- 13

## Homework Statement

[tex]

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

[/tex]

## The Attempt at a Solution

Can anyone give me a hint as to what to do?

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter dirk_mec1
- Start date

- #1

- 761

- 13

[tex]

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

[/tex]

Can anyone give me a hint as to what to do?

- #2

Cyosis

Homework Helper

- 1,495

- 0

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

[tex]\int_0^1 \frac{\arctan(y)}{y\sqrt{1-y^2}}\ dy - \int_0^1 \frac{\arctan{y}}{y}\ dy [/tex]

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

Share: