# Integral of Ln(Sinx)/Sinx

• Jan 10th 2010, 10:03 AM
parkhid
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 .

$\displaystyle Integral of Ln(sin(x)) / sin(x)$
• Jan 10th 2010, 10:10 AM
TWiX
Quote:

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?
• Jan 10th 2010, 11:04 AM
parkhid
yes. this links has solved the integral by semi numbers.

any other ideas ?
• Jan 10th 2010, 12:11 PM
mr fantastic
Quote:

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

any other ideas ?

• Jan 10th 2010, 01:39 PM
rshekhar.in
Quote:

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...
• Jan 10th 2010, 02:18 PM
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.
• Jan 11th 2010, 12:44 AM
parkhid
Quote:

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 ?
• Jan 11th 2010, 02:18 AM
mr fantastic
Quote:

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

Quote:

Originally Posted by mr fantastic