integration of ln(sinx) ?

Question

anonymous · Answer

$$\int\limits_{}^{}\ln(sinx)$$

anonymous · Answer

You must remember the by parts rule right?

anonymous · Answer

yes i know.

anonymous · Answer

1*ln(sinx)

anonymous · Answer

Take 1 as the function to integrate and ln(sinx) to differentiate

anonymous · Answer

$$\int\limits_{}^{}u.v=u \int\limits_{}^{}v-\int\limits_{}^{}(du/dx.\int\limits_{}^{}vdx)$$

anonymous · Answer

is it right ?

anonymous · Answer

ah Yes it is 
U = ln sinx
V =1

anonymous · Answer

i got stuck up at $$x \ln sinx.\int\limits_{}^{}xcos x dx/sinx$$   i cant make substitution of sinx =t as x remains there

anonymous · Answer

okay
use by parts after substitution again

anonymous · Answer

$$x = sin^{-1}t$$

anonymous · Answer

trying ...

anonymous · Answer

$$x=\sin^{-1} t      $$ didnt work well ..it gets me more to intgrate

anonymous · Answer

yup okay I have to try it on my notebook

anonymous · Answer

thank you very much . sensei

anonymous · Answer

anonymous · Answer

ah I didn't get much ahead but see the integral scroll down a little

anonymous · Answer

This one was pretty tough. wondering why these questions are given to IIT aspirants

anonymous · Answer

lol

anonymous · Answer

Yea I know did you solve quadratic for IIT

anonymous · Answer

ah I still can't figure out how am I supposed to do them in 2 minutes I have posted a question go to my profile you will see

anonymous · Answer

question is quadratic related

anonymous · Answer