Question

Evaluate `int e^x [(cosx - sin x)/sin^2 x]dx`

Answer 1

`I = inte^x [cosx/sin^2x - sinx/sin^2x]dx`

`= int e^x[(cotx.cosecx, -cosecx),(f'(x), f(x))]`

∵ `int e^x[f(x) + f'(x)]dx  = e^x f(x) + C`

`:. I = -e^x.cosec x + C`