1. ## Integral of Ln(Sinx)/Sinx

Hi . What should am I Do With this Integral .
I have working on it for hours . but i can't find the way .

$\displaystyle Integral of Ln(sin(x)) / sin(x)$

2. Originally Posted by parkhid
Hi . What should am I Do With this Integral .
I have working on it for hours . but i can't find the way .

$\displaystyle Integral of Ln(sin(x)) / sin(x)$
its integration has unelementary function:
integrate ln(sinx) / sin(x) - Wolfram|Alpha

Do you post all informations of your problem?

3. yes. this links has solved the integral by semi numbers.

any other ideas ?

4. Originally Posted by parkhid
yes. this links has solved the integral by semi numbers.

any other ideas ?

5. Originally Posted by parkhid
Hi . What should am I Do With this Integral .
I have working on it for hours . but i can't find the way .

$\displaystyle Integral of Ln(sin(x)) / sin(x)$
I am not good in maths but i suppose it can be done by

$\displaystyle Let v=log(sinx)$
$\displaystyle \frac{dv}{dx}=\frac{1}{sinx}$
$\displaystyle dv . sinx = dx$

Substitute and integrate...

6. The derivative of $\displaystyle ln(sin(x))=\frac{1}{tan(x)}$

$\displaystyle \int\frac{ln(sin(x))}{sin(x)}dx$

An indefinite form for this is hard to come by. Parts, substitution, etc will not work too well.

7. Originally Posted by galactus
The derivative of $\displaystyle ln(sin(x))=\frac{1}{tan(x)}$

$\displaystyle \int\frac{ln(sin(x))}{sin(x)}dx$

An indefinite form for this is hard to come by. Parts, substitution, etc will not work too well.
So What should am i do ? It has been solved by poly logarithmic functions.
but isn't there any way ?

8. Originally Posted by parkhid
So What should am i do ? It has been solved by poly logarithmic functions.
but isn't there any way ?
Originally Posted by mr fantastic