## aditya.sinha 4 years ago integration of ln(sinx) ?

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

2. Ishaan94

You must remember the by parts rule right?

yes i know.

4. Ishaan94

1*ln(sinx)

5. Ishaan94

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

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

is it right ?

8. Ishaan94

ah Yes it is U = ln sinx V =1

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

10. Ishaan94

okay use by parts after substitution again

11. Ishaan94

$x = sin^{-1}t$

trying ...

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

14. Ishaan94

yup okay I have to try it on my notebook

thank you very much . sensei

16. Ishaan94
17. Ishaan94

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

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

19. Ishaan94

lol

20. Ishaan94

Yea I know did you solve quadratic for IIT

21. Ishaan94

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

22. Ishaan94