$\int \frac{e^x(1+x)}{\cos ^2\left(x e^x\right)} d x$ is equal to:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $\tan \left(x e^x\right)+c$, where c is a constant
$I=\int\frac{e^x(1+x)}{\cos^2(xe^x)}dx$
let $y=xe^x$
$dy=e^x(1+x)dx$
$⇒I=\int\sec^2ydy=\tan y+c$
$=\tan(xe^x)+c$