What is the integral of cos^{10}(x)sin(x) ?

The integral of cos^{10}(x)sin(x) is -(cos^{11}(x))/(11)+C

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integral of cos^{10}(x)sin(x)

\int cos^{10} (x) sin (x) d x

- \frac{cos ^{11} ( x )}{11} + C

Solution steps

\int cos^{10} (x) sin (x) d x

Apply u-substitution

: \int - u^{10} d u

= \int - u^{10} d u

Take the constant out:

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

= - \int u^{10} d u

Apply the Power Rule

: \frac{u ^{11}}{11}

= - \frac{u ^{11}}{11}

Substitute back

u = cos (x)

= - \frac{cos ^{11} ( x )}{11}

Add a constant to the solution

= - \frac{cos ^{11} ( x )}{11} + C

\int sin (x) + 2 d x

f (x) = 3 e^{x} cos (x)

(x - 1)^{2} sin (\frac{1}{x - 1})

\int \frac{1}{( 4 - x ^{2} ) ^{\frac{1}{2}}} d x

\frac{d}{d x} (\frac{- 1}{x ^{2} + y ^{2}})

What is the integral of cos^{10}(x)sin(x) ?
The integral of cos^{10}(x)sin(x) is -(cos^{11}(x))/(11)+C