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

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

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

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

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

Solution steps

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

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 (t)

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

Add a constant to the solution

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

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