$\int \frac{e^{x} (x + 1)}{c o s^{2} (x e^{x})} d x$ is equal to

t a n (x e^{x}) + c

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s e c (x e^{x}) t a n (x e^{x}) + c

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- t a n (x e^{x}) + c

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none of these

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Solution

The correct option is A $t a n (x e^{x}) + c$
Given,

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

substitute $u = x e^{x} ⟹ d u = (x + 1) e^{x} d x$

$= \int \frac{1}{{cos}^{2} (u)} d u$

$= tan (u)$

$= tan (x e^{x}) + C$

Suggest Corrections

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

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$\int \frac{e^{x} (x - 1) (x - l n x)}{x^{2}} d x$ is equal to

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