What is the integral of sin(x)cos^8(x) ?

The integral of sin(x)cos^8(x) is -(cos^9(x))/9+C

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integral of sin(x)cos^8(x)

\int sin (x) cos^{8} (x) d x

- \frac{cos ^{9} ( x )}{9} + C

Solution steps

\int sin (x) cos^{8} (x) d x

Apply u-substitution

= \int - u^{8} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int u^{8} d u

Apply the Power Rule

= - \frac{u ^{9}}{9}

Substitute back

u = cos (x)

= - \frac{cos ^{9} ( x )}{9}

Add a constant to the solution

= - \frac{cos ^{9} ( x )}{9} + C

What is the integral of sin(x)cos^8(x) ?
The integral of sin(x)cos^8(x) is -(cos^9(x))/9+C