e^ x ( x + ^2 x ) ,dx is equal to - Vidyadip

MCQ

$\int {{e^{\sin x}}\left( {\sin x + {{\sec }^2}x} \right)} \,dx$ is equal to

✓
${e^{\sin x}}.\tan x + C$
B
${e^{\sin x}}.\sec x + C$
C
${e^{\sin x}}.\cot x + C$
D
None of these

✓

Answer

Correct option: A.

${e^{\sin x}}.\tan x + C$

a
$\begin{array}{l}
\int {{e^{\sin x}}\left( {\cos x\tan x + {{\sec }^2}x} \right)} \,dx\\
= {e^{\sin x}}\tan x + C
\end{array}$

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