Question

`int (e^x(1 +x))/cos^2(e^x x) dx` equals ______.

Options

• − cot (e^xx) + C

• tan (xe^x) + C

• tan (e^x) + C

• cot (e^x) + C

Answer 1

`int (e^x(1 +x))/cos^2(e^x x) dx` equals tan (xe^x) + C.

Explanation:

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

Put xe^x = t 

⇒ `(e^x *1 + e^x x) dx = dt`

e^x (1 + x) dx = dt

`I = int dt/(cos^2 t) = sec^2` t dt

= tan t + C

= tan (xe^x) + C