## anonymous 4 years ago integration of ln(sinx) ?

1. anonymous

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

2. anonymous

You must remember the by parts rule right?

3. anonymous

yes i know.

4. anonymous

1*ln(sinx)

5. anonymous

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

6. anonymous

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

7. anonymous

is it right ?

8. anonymous

ah Yes it is U = ln sinx V =1

9. anonymous

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. anonymous

okay use by parts after substitution again

11. anonymous

$x = sin^{-1}t$

12. anonymous

trying ...

13. anonymous

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

14. anonymous

yup okay I have to try it on my notebook

15. anonymous

thank you very much . sensei

16. anonymous
17. anonymous

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

18. anonymous

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

19. anonymous

lol

20. anonymous

Yea I know did you solve quadratic for IIT

21. anonymous

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. anonymous