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

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

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

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

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

Solution steps

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

n = 0 \sum \infty n^{2} e^{- n}

\frac{d}{d x} (- \frac{3}{3 x + 2})

\int_{- 14}^{1} x 49 - x^{2} d x

e^{t} sin (9 t)

\frac{d}{d x} (sin (\frac{π x}{2}))

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