Question

∫tan x dx

Answer 1

$\int\tan xdx=\int\frac{\sin x}{\cos x}dx\\ let\\ t=\cos x\\ dt=-\sin x dx\\ \int\frac{\sin x}{\cos x}dx=\int\frac{-dt}{t}=- \ln|t|+c=-\ln|\cos x|+c$

$\int\tan xdx=-\ln|cos x|+c$