Question

\[\int \sin(x) \ln (\tan(x)) dx\]

Answer 1

@Kainui

Answer 2

Interesting problem, my first guess is that there's something involving this fact\[\Large \int\limits \tan x dx = -\ln(\sin x)\]

Answer 3

Ok I solved it. You need to do integration by parts and what I just mentioned although involves sine, ln, and tangent is only a coincidental set of stuff.

Would you like a hint?

Answer 4

Hint:
\[\int\frac{1}{\sin(x)}\,dx=\ln|\csc(x)-\cot(x)|+C\]

Answer 5

I solved it.

Answer 6

Cool.