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

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

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

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

- \frac{cos ^{8} ( y )}{8} + C

Solution steps

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

Apply u-substitution

: \int - u^{7} d u

= \int - u^{7} d u

Take the constant out:

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

= - \int u^{7} d u

Apply the Power Rule

: \frac{u ^{8}}{8}

= - \frac{u ^{8}}{8}

Substitute back

u = cos (y)

= - \frac{cos ^{8} ( y )}{8}

Add a constant to the solution

= - \frac{cos ^{8} ( y )}{8} + C

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