What is the integral of cos(x)sin^7(x) ?

The integral of cos(x)sin^7(x) is (sin^8(x))/8+C

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integral of cos(x)sin^7(x)

\int cos (x) sin^{7} (x) d x

\frac{sin ^{8} ( x )}{8} + C

Solution steps

\int cos (x) sin^{7} (x) d x

Apply u-substitution

: \int u^{7} d u

= \int u^{7} d u

Apply the Power Rule

: \frac{u ^{8}}{8}

= \frac{u ^{8}}{8}

Substitute back

u = sin (x)

= \frac{sin ^{8} ( x )}{8}

Add a constant to the solution

= \frac{sin ^{8} ( x )}{8} + C

\int (3 x^{2} - 4 x + 1) d x

\frac{d}{d y} (2 k q y (y^{2} + d^{2})^{- \frac{3}{2}})

\int π^{4} x^{2} d x

\frac{d}{d x} (\frac{3 x ^{4}}{e ^{x}})

3 y^{2} = 2 y (x^{4} - x) \frac{d y}{d x} - 3

What is the integral of cos(x)sin^7(x) ?
The integral of cos(x)sin^7(x) is (sin^8(x))/8+C