What is the integral of cos^{12}(x)sin(x) ?

The integral of cos^{12}(x)sin(x) is -(cos^{13}(x))/(13)+C

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integral of cos^{12}(x)sin(x)

\int cos^{12} (x) sin (x) d x

- \frac{cos ^{13} ( x )}{13} + C

Solution steps

\int cos^{12} (x) sin (x) d x

Apply u-substitution

: \int - u^{12} d u

= \int - u^{12} d u

Take the constant out:

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

= - \int u^{12} d u

Apply the Power Rule

: \frac{u ^{13}}{13}

= - \frac{u ^{13}}{13}

Substitute back

u = cos (x)

= - \frac{cos ^{13} ( x )}{13}

Add a constant to the solution

= - \frac{cos ^{13} ( x )}{13} + C

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

y = e^{x}, y = e^{3 x}, x = 0, x = ln (4)

\int_{0}^{1} 7 cos (4 x) d x

\int \frac{2}{x} - \frac{3}{x ^{4}} d x

\frac{d}{d x} y + 3 y = 0

What is the integral of cos^{12}(x)sin(x) ?
The integral of cos^{12}(x)sin(x) is -(cos^{13}(x))/(13)+C