What is the integral of cos^{11}(x)sin(x) ?

The integral of cos^{11}(x)sin(x) is -(cos^{12}(x))/(12)+C

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integral of cos^{11}(x)sin(x)

\int cos^{11} (x) sin (x) d x

- \frac{cos ^{12} ( x )}{12} + C

Solution steps

\int cos^{11} (x) sin (x) d x

Apply u-substitution

: \int - u^{11} d u

= \int - u^{11} d u

Take the constant out:

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

= - \int u^{11} d u

Apply the Power Rule

: \frac{u ^{12}}{12}

= - \frac{u ^{12}}{12}

Substitute back

u = cos (x)

= - \frac{cos ^{12} ( x )}{12}

Add a constant to the solution

= - \frac{cos ^{12} ( x )}{12} + C

2 (\frac{1}{s - 3})

\int e^{2 y} cos (3 y) d y

\frac{\partial}{\partial x} (3 x cos (x) cos (y))

x - 6

\int \frac{x ^{4}}{5 - x ^{5}} d x

What is the integral of cos^{11}(x)sin(x) ?
The integral of cos^{11}(x)sin(x) is -(cos^{12}(x))/(12)+C