What is the integral of cos^{15}(x)sin(x) ?

The integral of cos^{15}(x)sin(x) is -(cos^{16}(x))/(16)+C

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integral of cos^{15}(x)sin(x)

\int cos^{15} (x) sin (x) d x

- \frac{cos ^{16} ( x )}{16} + C

Solution steps

\int cos^{15} (x) sin (x) d x

Apply u-substitution

: \int - u^{15} d u

= \int - u^{15} d u

Take the constant out:

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

= - \int u^{15} d u

Apply the Power Rule

: \frac{u ^{16}}{16}

= - \frac{u ^{16}}{16}

Substitute back

u = cos (x)

= - \frac{cos ^{16} ( x )}{16}

Add a constant to the solution

= - \frac{cos ^{16} ( x )}{16} + C

\int \frac{x}{4 x ^{2} - 4 x + 5} d x

x \to \infty lim (2 (x))

f (x) = - 6 e^{- 6 x}

- y^{3} \frac{d y}{d x} = x^{5} - 7 x^{2} + 3 x

s^{^{'}}

What is the integral of cos^{15}(x)sin(x) ?
The integral of cos^{15}(x)sin(x) is -(cos^{16}(x))/(16)+C