What is `int (e^(x) (1 + x))/(cos^(2) (xe^(x))) dx` equal to ?
where c is a constant of integration

Options

A. `xe^(x) + c`
B. `cos (xe^(x)) + c`
C. `tan (xe^(x)) + c`
D. `c "cosec"(xe^(x)) + c`

Answer

C

Explanation

Let `I = int (e^(x) (1 + x))/(cos^(2) (xe^(x))) dx`
Put, `xe^(x) = t rArr (dt)/(cos^(2)t) = int sec^(2) tdt = tan t + c`
where 'c' is a constant of integration
`= tan (xe^(x)) + c`