Question

`int (e^x (1 + x))/(cos^2 (xe^x)) dx` equal

Options

• `- cot (e - x^x)`

• `tan (x - e^x) + c`

• `tan (e^x) + c`

• `cot (e^x) + c`

Answer 1

`tan (x - e^x) + c`

Explanation:

`int (e^x(1 + x))/(cos^2 (xe^x)) dx`, put `xe^x = t`

`(e^x + x - e^x)dx = dt`

or `e^x(1 + x) dx = dt`

`int (dt)/(cos^2t) = int sec^2 +  dt = tan t + c`

= `tan (xe^x) + c`