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

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

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

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

\frac{sin ^{6} ( x )}{6} + C

Solution steps

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

Simplify

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

Apply u-substitution

: \int u^{5} d u

= \int u^{5} d u

Apply the Power Rule

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

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

Substitute back

u = sin (x)

= \frac{sin ^{6} ( x )}{6}

Add a constant to the solution

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

\int e^{- \frac{5 x}{6}} d x

n = 1 \sum \infty 7 (0.9)^{n - 1}

f (x) = (3 x^{2} + 1)^{3}

\frac{d}{d x} (\frac{x}{z})

\int_{0}^{2 π} sin^{2} (11 x) d x

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