Mathematics

# Solve:$\int {{{\sin }^3}x.{{\cos }^2}xdx}$.

##### SOLUTION
$\displaystyle\int \sin^3x(\cos^2x)dx$

$\displaystyle\int \sin x(\sin^2x)(\cos^2x)dx$
$\Rightarrow \displaystyle\int \sin x(1-\cos^2x)(\cos^2x)dx$

$\Rightarrow \displaystyle\int \sin x\cos^2xdx-\displaystyle\int \sin x\cos^4xdx$

Put $\cos x=t$
$-\sin xdx=dt$
$\Rightarrow -\displaystyle\int t^2dt+\displaystyle\int t^4dt$
$\Rightarrow -\dfrac{t^3}{3}+\dfrac{t^5}{5}+c$
$\displaystyle\int \sin^3x\cos xdx=\dfrac{\cos^5x}{5}-\dfrac{\cos^3x}{3}+c$.

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

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