Evaluate: `int1/(sinx+cosx)\ dx`

Explanation

Let `I=int(frac{sin ^{2} x+cos ^{2} x}{sin x cos x}) d x`
`
=int(frac{sin ^{2} x}{sin x cos x}+frac{cos ^{2} x}{sin x cos x} d x) `
`
=int(tan x+cot x) d x`
`
=log sec x+(-log {cosec} x)+C`
`
=log |frac{sec x}{ {cosec x}|+C=log |tan x|+C`