Question

Find `int (sin^2 x - cos^2 x)/(sin xcosx) dx`

Answer 1

`int (sin^2x)/(sin x cos x) dx - int (cos^2x)/(sin x cos x) dx`

`= int tanxdx - int cot xdx`

`= ln|sec x| - ln|sin x| + C`

`=ln |(sec x)/(sin x)| + C`

`= ln|1/(sin x cosx)| + C`

`= ln|2/(2sinxcosx)| + C`

`= ln|2cosec2x| + C`