Evaluate: `intx\ ((sec2x-1)/(sec2x+1))\ dx`

Explanation

`int x(frac{sec 2 x-1}{sec 2 x+1}) d x`
`
=int x(frac{1-cos 2 x}{1+cos 2 x}) d x`
`
=int x tan ^{2} x d x`
`
=int x(sec ^{2} x-1) d x`
`
=int x sec ^{2} x d x-int d x`
`
=x int sec ^{2} x d x-int tan x d x-x+c`
`
=x tan x-log |sec x|-x+c`
`