Evaluate: `int((x+1)e^x)/(cos^2(x e^x))dx`

Explanation

Let `1 = int (e^(x) (1 + x))/(cos^(2) (xe^(x)))dx`
Take ` x ' . e^(x) = t `
Differentiating equation (i) w.r.t.x,
` rArr x'e^(x) . 1 = (dt)/(dx) " "` (using chain rule )
` rArr e^(x) . (x + 1) = (dt)/(dx)`
`rArr e^(x) (x + 1) dx = dt `
` therefore 1= int (dt)/(cos^(2)t)`
` int sec^(2) t. dt`
` tan t + C `
`therefore int (e^(x) (1 + x))/(cos^(2) (xe^(x)))dx= tan (x'e^(x)) + C `