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

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

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

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

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

Solution steps

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

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 (x)

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

Add a constant to the solution

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

3 x^{- 3} (x^{4} - 3 x^{3} + 10 x - 9)

\int \frac{1}{x ^{2} + z ^{2}} d x

\int \frac{9 e ^{x}}{e ^{x} - 1} d x

\frac{\partial}{\partial x} (x^{4} + 5 x^{2} y)

y^{^{''}} - 7 y^{^{'}} + 10 y = 0

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