What is the integral of cos^5(x)sin(x) ?

The integral of cos^5(x)sin(x) is -(cos^6(x))/6+C

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integral of cos^5(x)sin(x)

\int cos^{5} (x) sin (x) d x

- \frac{cos ^{6} ( x )}{6} + C

Solution steps

\int cos^{5} (x) sin (x) d x

Apply u-substitution

: \int - u^{5} d u

= \int - u^{5} d u

Take the constant out:

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

= - \int u^{5} d u

Apply the Power Rule

: \frac{u ^{6}}{6}

= - \frac{u ^{6}}{6}

Substitute back

u = cos (x)

= - \frac{cos ^{6} ( x )}{6}

Add a constant to the solution

= - \frac{cos ^{6} ( x )}{6} + C

z

\int \frac{12}{3 x + x x} d x

(3 + 3 x^{2}) \frac{d y}{d x} + 2 x y = 2 x y^{4}

f (x) = ln (2)

\int 3 e^{4} d x

What is the integral of cos^5(x)sin(x) ?
The integral of cos^5(x)sin(x) is -(cos^6(x))/6+C