What is the integral of cos^1(x)sin^2(x) ?

The integral of cos^1(x)sin^2(x) is (sin^3(x))/3+C

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integral of cos^1(x)sin^2(x)

\int cos^{1} (x) sin^{2} (x) d x

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

Solution steps

\int cos^{1} (x) sin^{2} (x) d x

Simplify

sin^{2} (x) : sin (x) sin (x)

= \int cos^{1} (x) sin (x) sin (x) d x

Simplify

cos^{1} (x) sin (x) sin (x) : sin^{2} (x) cos (x)

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

Apply u-substitution

= \int u^{2} d u

Apply the Power Rule

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

Substitute back

u = sin (x)

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

Add a constant to the solution

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

What is the integral of cos^1(x)sin^2(x) ?
The integral of cos^1(x)sin^2(x) is (sin^3(x))/3+C