Question

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

• A. $(1+\cos x)^{10}$
• B. $-\frac{(1+\cos x)^{10}}{10}$
• C. $\left(-1+\frac{\cos x}{10}\right)^{10}$
• D. $9(\cos x-1)^{8}$

Answer 1

Answer: (B)

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