$\int \frac{e^x(1+x)}{\cos ^2\left(x e^x\right)} d x=$

$-\cot \left(x e^x\right)$ $\tan \left(x e^x\right)$ $\tan \left(e^x\right)$ none of these

$\tan \left(x e^x\right)$

Put x ex = t    ∴ I = ∫sec2t dt = tan t + c = tan(x ex) + c; Hence (2) is the correct answer.