I'm computing the indefinite integral of $\log(\sin(x))$; this is the my solution with integration by substitution:
$$ \begin{align} &\int\log(\sin(x))dx\\ = &\int\log(y)\frac{1}{\cos(x)}dy \\ = &\frac{1}{\cos(x)}\int\log(y)dy \\ = &\frac{1}{\cos(x)}(y\log(y)-y) \\ = &\tan(x)\log(\sin(x))-\tan(x) \end{align} $$
Because I did the substitution $y=\sin(x), dy=\cos(x)dx\rightarrow dx=\frac{dy}{\cos(x)}$.
Wolfram online gives a different result; where is the my error?