Tuesday, 14 March 2017

calculus - Integrate intfracln(sinx)sin2x,mathrmdx.



I'm having trouble evaluating the integral




ln(sinx)sin2xdx.



I tried u-substitution and integration by parts but they didn't work.


Answer



Here is a start. using integration by parts,




udv=uvvdu.





Let



u=ln(sin(x))u=cos(x)sin(x)=cot(x),v=dxsin2x=cot(x).



Can you finish it now?


No comments:

Post a Comment

real analysis - How to find limhrightarrow0fracsin(ha)h

How to find limh0sin(ha)h without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...