Question

integration of ln(sinx) ?

Answer 1

any one helping me the integration of ln(sinx) plz ?

Answer 2

so i took u=lnsinx

dv=1

by parts

lnsinx * x- ∫x cosx/sinx

x*lnsinx-(cosx/sinx * x^2/2 - ∫ x^2/2 * sinx(-sinx) -cosx*cosx/sin^2

x*lnsinx- x^2/2 *cosx/sinx +1/2 ∫1/sin^2dx

x*lnsinx- x^2/2 *cosx/sinx +1/2 ∫ cosec^x+

x*lnsinx- x^2/2 *cosx/sinx +1/2(-cotx)+C

x*lnsinx- x^2/2 *cosx/sinx -1/2 cotx +C

:O

Answer 3

that was a try and its a tough one :P

Answer 4

I have never understood this site, it makes simple things so complicated.