Mathematics - Indefinite Integration Question with Solution | TestHub

$\int \frac{5\tan x}{\tan x-2}dx=\int \frac{5\sin x}{\sin x-2\cos x}dx$ $\Rightarrow \int \left[\frac{2(\cos x+2\sin x)+(\sin x-2\cos x)}{\sin x-2\cos x}\right]dx$ $=2\int \left(\frac{\cos x+2\sin x}{\sin x-2\cos x}\right)dx+\int dx+k$ $=2\log |\sin x-2\cos x|+x+k\therefore a=2$