What is the integral of (sin^3(x)cos(x)) ?

The integral of (sin^3(x)cos(x)) is (sin^4(x))/4+C

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integral of (sin^3(x)cos(x))

\int (sin^{3} (x) cos (x)) d x

\frac{sin ^{4} ( x )}{4} + C

Solution steps

\int sin^{3} (x) cos (x) d x

Apply u-substitution

: \int u^{3} d u

= \int u^{3} d u

Apply the Power Rule

: \frac{u ^{4}}{4}

= \frac{u ^{4}}{4}

Substitute back

u = sin (x)

= \frac{sin ^{4} ( x )}{4}

Add a constant to the solution

= \frac{sin ^{4} ( x )}{4} + C

\int e^{- \frac{2 r}{a}} r^{2} d r

f (x) = x^{3}, at - 5

\int - x sin (n x) d x

\frac{d}{d x} (\frac{1}{x} ln (x))

y^{^{''}} - 6 y^{^{'}} + 9 y = 3 x e^{3 x}

What is the integral of (sin^3(x)cos(x)) ?
The integral of (sin^3(x)cos(x)) is (sin^4(x))/4+C