The value of e^ sin ⁡x sin ⁡2 xdx is

Question

Accepted Answer

Correct answer: D. (d) : Let I= e^ sin ⁡x sin ⁡2 xdx= e^ sin ⁡x2 sin ⁡x cos ⁡ xdx Put e^ sin ⁡x=t ⇒ sin ⁡x= log ⁡t ⇒e^ sin ⁡x cos ⁡ xdx= dt ∴I= 2 log ⁡t dt=2( log ⁡t t- 1t tdt) =2 [t log ⁡t-t ]+C=2(e^ sin ⁡x sin ⁡x-e^ sin ⁡x)+C =2e^ sin ⁡x ( sin ⁡x-1 )+C

$The value of \int e^{sin x} sin 2 xdx is$

Solution

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