Q. $\int \sin x(1+\cos x)^{9} d x=\ldots \ldots+ c$

KCETKCET 2022 Report Error

A

$(1+\cos x)^{10}$

B

$-\frac{(1+\cos x)^{10}}{10}$

C

$\left(-1+\frac{\cos x}{10}\right)^{10}$

D

$9(\cos x-1)^{8}$

Solution:

$I=-\int(1+\cos x)^{9}(-\sin x) d x\, -\int(1+\cos x)^{9} d(1+\cos x)$
$=-\frac{(1+\cos x)^{10}}{10}$

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