If the integral ∫ex1+sin x cos xcos2 xdx is the of the

If the integral $\int e^{x} \frac{1 + s i n x c o s x}{c o s^{2} x} d x$ is the of the form $\int e^{x}$ [f(x) + f'(x)]dx then the appropriate f(x) would be -

$s e c^{2} x$

$s i n x . c o s x$

$t a n x$

$s e c x$

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Right Answer is: C

SOLUTION

We can approach this problem by simplifying the given expression

$\int e^{x} \frac{1 + s i n x c o s x}{c o s^{2} x} d x$

$= \int e^{x} (s e c^{2} x + t a n x)$

or $\int e^{x} (t a n x + s e c^{2} x)$

On comparing this with $\int e^{x}$ [f(x) + f'(x)] we see that $s e c^{2} x$ is the derivative of $t a n x$

So f(x) should be $t a n x$

If the integral ∫ex1+sin x cos xcos2 xdx is the of the

Right Answer is: C

SOLUTION

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