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

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

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

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

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

Solution steps

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

\frac{d}{d x} (24 x)

\frac{\partial}{\partial x} (\frac{x y}{6 x + 7 y})

\int x^{2} + 2 x - 8 d x

\int \frac{cos ( \frac{1}{x ^{2}} )}{x ^{3}} d x

\int_{0}^{9} f (x) d x

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