I have this integral that I want to solve for homework: $\int \frac{x}{\cos\left(x\right)}\mathrm{d}x$.
After some research, I found out that I can use a half-angle substitution to solve similar questions. I know what to substitute for $\mathrm{d}x$ and for $\sec(x)$ but I don't know what to substitute for the $x$ remaining.
Typing in Symbolab $$\int \frac{x}{\cos\left(x\right)}\,dx$$ gives as a result $$-\log \left(\left|1-\tan ^2\left(\frac{x}{2}\right)\right|\right)+C$$ which is totally wrong.
Doing the same using https://www.integral-calculator.com/# gives, just as Wolfram Alpha $$i \left(\text{Li}_2\left(-i e^{i x}\right)-\text{Li}_2\left(i e^{i x}\right)\right)+x \left(\log \left(1-i e^{i x}\right)-\log \left(1+i e^{i x}\right)\right)$$ as Chase Ryan Taylor already reported in comments.