If $\int e^x(1+x) \sec ^2\left(x e^x\right) d x=f(x)+$ Constant, then $f(x)$ is equal to
Answer & explanation
Correct answer: option 4
We have,
$\int e^x(1+x) \sec ^2\left(x e^x\right) d x$
$=\int \sec ^2\left(x e^x\right) d\left(x e^x\right)=\tan \left(x e^x\right)+C$
∴ $f(x)=\tan \left(x e^x\right)$