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) \cdot 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

\frac{7}{x + 4}

\int x^{3} e^{x^{4} + 5} d x

y + y^{4} = (y^{6} + 3 x) y^{^{'}}

cos (x) y^{^{'}} - sin (x) y = 0

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