What is the integral of cos(x)sin^5(x) ?

The integral of cos(x)sin^5(x) is (sin^6(x))/6+C

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integral of cos(x)sin^5(x)

\int cos (x) sin^{5} (x) d x

\frac{sin ^{6} ( x )}{6} + C

Solution steps

\int cos (x) sin^{5} (x) d x

Apply u-substitution

: \int u^{5} d u

= \int u^{5} d u

Apply the Power Rule

: \frac{u ^{6}}{6}

= \frac{u ^{6}}{6}

Substitute back

u = sin (x)

= \frac{sin ^{6} ( x )}{6}

Add a constant to the solution

= \frac{sin ^{6} ( x )}{6} + C

3 - x, - 4 \leq x \leq 2

\frac{d}{d x} ((1 - x^{2})^{\frac{1}{3}})

\frac{2}{x ^{7}}

e^{\frac{- x}{2}}

\frac{\partial}{\partial x} (x^{2} + sin (y) - 0.4)

What is the integral of cos(x)sin^5(x) ?
The integral of cos(x)sin^5(x) is (sin^6(x))/6+C