What is the integral of sin^2(x)os(x) ?

The integral of sin^2(x)os(x) is d/3 sin^3(x)+C

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integral of sin^2(x)os(x)

\int sin^{2} (x) d cos (x) d x

\frac{d}{3} sin^{3} (x) + C

Solution steps

\int sin^{2} (x) d cos (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= d \cdot \int sin^{2} (x) cos (x) d x

Apply u-substitution

= d \cdot \int u^{2} d u

Apply the Power Rule

= d \frac{u ^{3}}{3}

Substitute back

u = sin (x)

= d \frac{sin ^{3} ( x )}{3}

Simplify

d \frac{sin ^{3} ( x )}{3} : \frac{d}{3} sin^{3} (x)

= \frac{d}{3} sin^{3} (x)

Add a constant to the solution

= \frac{d}{3} sin^{3} (x) + C

What is the integral of sin^2(x)os(x) ?
The integral of sin^2(x)os(x) is d/3 sin^3(x)+C