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Algebraic manipulation of integral

  • Thread starter dirk_mec1
  • Start date
  • #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?
 

Answers and Replies

  • #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.
 

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