e x sin x ( sin x + 2 cos x ) ? d x =

Question

$\int e^{x} \sin x (\sin x + 2 \cos x) d x =$

Smart Achievers · Accepted Answer

(1)

Ans. $e^{x} \sin^{2} x + C$

Explanation :

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

$= \int e^{x} \sin^{2} x d x + \int e^{x} 2 \sin x \cos x d x$

$= \int e^{x} \sin^{2} x d x + \int e^{x} \sin 2 x d x$

$= e^{x} \sin^{2} x - \int e^{x} 2 \sin x \cos x d x + \int e^{x} \sin 2 x d x + C$

$= e^{x} \sin^{2} x - \int e^{x} \sin 2 x d x + \int e^{x} \sin 2 x d x + C$

$= e^{x} \sin^{2} x + C$

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