Mathematics

# Solve:$\int {\sin x\left( {2 + 5x} \right)} dx$

##### SOLUTION
$\displaystyle\int \sin x(2+5x)dx=\displaystyle\int (2\sin x+5x\sin x)dx$

$=\displaystyle\int 2\sin xdx+\displaystyle\int 5x\sin xdx$

$=-2\cos x+5\left[x\displaystyle\int \sin x dx-\displaystyle\int\left\{\dfrac{d}{dx}(x)\displaystyle\int \sin x dx\right\}dx\right]$

$=-2\cos x+5\left[x(-\cos x)-\displaystyle\int (-\cos x)dx\right]$
$=-2\cos x+5\left[-x\cos x+\displaystyle\int\cos xdx\right]$

$=-2\cos x-5x\cos x+5\sin x+c$

$\displaystyle\int \sin x(2+5x)dx=5\sin x-2\cos x-5x\cos x+c$.

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

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