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

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

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

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

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

Solution steps

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

Simplify

= \int sin^{2} (x) cos (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 0 lim (\frac{0}{2 x ^{2}})

\frac{d y}{d t} = sin (t) - y, y (0) = - 1

(x + 1)^{\frac{2}{3}} \frac{d y}{d x} = y^{\frac{1}{3}}

f (x) = \frac{x}{x ^{2} + 49}

\int_{0}^{1} \frac{4}{1 + t ^{2}} d t

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