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

Apply the Power Rule

= \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

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