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Questions  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Integral Calculus
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Q)

Integrate : $\int e^x \bigg(\large\frac{2+\sin 2x}{1+ \cos 2x}\bigg)$$dx$

$(a)\;e^{x} \tan x +c \qquad(b)\;e^{x} \cot x +c \qquad(c)\;e^x\sin x +c \qquad (d)\;None$

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A)
$\int e^{x} \bigg(\large\frac{2+ 2 \sin x \cos x }{2 \cos^2 x}\bigg)$$dx$
=> $\int e^x (\sec^2 x+ \tan x)dx$
=> $\int e^x (\sec^2 x dx + \int e^x \tan x dx$
=> $\int e^x \sec^2 x dx +e^x . \tan x -\int e^x \sec^2 x dx+c$
$e^{x} \tan x +c$
Hence a is the correct answer.
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