What is the integral of (sin^9(x))cos(x) ?

The integral of (sin^9(x))cos(x) is (sin^{10}(x))/(10)+C

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integral of (sin^9(x))cos(x)

\int (sin^{9} (x)) cos (x) d x

\frac{sin ^{10} ( x )}{10} + C

Solution steps

\int sin^{9} (x) cos (x) d x

Apply u-substitution

: \int u^{9} d u

= \int u^{9} d u

Apply the Power Rule

: \frac{u ^{10}}{10}

= \frac{u ^{10}}{10}

Substitute back

u = sin (x)

= \frac{sin ^{10} ( x )}{10}

Add a constant to the solution

= \frac{sin ^{10} ( x )}{10} + C

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What is the integral of (sin^9(x))cos(x) ?
The integral of (sin^9(x))cos(x) is (sin^{10}(x))/(10)+C