What is the integral of (sin(x))^3(cos(x)) ?

The integral of (sin(x))^3(cos(x)) is (sin^4(x))/4+C

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integral of (sin(x))^3(cos(x))

\int (sin (x))^{3} (cos (x)) d x

\frac{sin ^{4} ( x )}{4} + C

Solution steps

\int (sin (x))^{3} cos (x) d x

Simplify

= \int sin^{3} (x) cos (x) d x

Apply u-substitution

: \int u^{3} d u

= \int u^{3} d u

Apply the Power Rule

: \frac{u ^{4}}{4}

= \frac{u ^{4}}{4}

Substitute back

u = sin (x)

= \frac{sin ^{4} ( x )}{4}

Add a constant to the solution

= \frac{sin ^{4} ( x )}{4} + C

x \to - 1 lim (\frac{1}{x + 1})

x \to 0 lim (e^{7 x})

\int arccos (7 x) d x

n = 0 \sum \infty n + 2

\frac{d x}{d t} = - 2 x - 3 x^{2}

What is the integral of (sin(x))^3(cos(x)) ?
The integral of (sin(x))^3(cos(x)) is (sin^4(x))/4+C