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

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

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

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

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

Solution steps

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

Apply u-substitution

: \int u^{2} d u

= \int u^{2} d u

Apply the Power Rule

: \frac{u ^{3}}{3}

= \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

x \to 1 lim (1 + x)

\int \frac{x \cdot ( arctan ( x ) )}{( 1 + x ^{2} ) ^{2}} d x

t^{4} - 8 t

- 9

\int cot (\frac{θ}{9}) d θ

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