integral of log(sinx)?*imp*test tmrw?

Question

plz plz solve it it will be really helpful plzzzzzzzzz i ahve a test tmrw......

Answer 1

this is going to be an complex function that does not have a closed form.... thus this is beyond the scope of usual calculus...

if you are dealing with such curves... i dont believe you would want to ask in yahoo answers...

it would be preferable to concentrate on simpler examples...

just for the heck of it... using a program...
∫ ln(sin x) dx = - x ln(1 - e^{2ix}) + x ln(sin x) + (i/2) (x² + LI_2(e^{2ix}) + C

where
LI_2(z) = Σ z^k/k² ... k = 1,2,3... ∞


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Answer 2

i dont believe that in calc 1 we ever learned to solve integrals of log functions.

Answer 3

set u = sin x

then use integration by parts of

integral { log u d(arcsin(u)) }