If ∫ex(1+x)sec2⁡xexdx=f(x)+ Constant, then f (x) is equal to

A
$\cos (x e^{x})$
B
$\sin (x e^{x})$
C
$2 \tan^{- 1} x$
D
$t a n (x e^{x})$

Solution:

We have,

$\begin{array}{l} \int e^{x} (1 + x) \sec^{2} (x e^{x}) d x \\ = \int \sec^{2} (x e^{x}) d (x e^{x}) = \tan (x e^{x}) + C \\ ∴ f (x) = \tan (x e^{x}) \end{array}$

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