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

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

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

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

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

Solution steps

\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

\frac{d}{d x} (x^{s i n (2 x)})

\frac{d}{d x} (sin^{2} (x) - cos^{2} (x) sin^{2} (x))

\frac{\partial}{\partial x} (x y^{2})

f (x) = 10 x, (1, 10)

y = arccos (4 x^{2})

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