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

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

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

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

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

Solution steps

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

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 (t)

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

Add a constant to the solution

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

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\int 2 e^{5} d x

\int (x^{3} - 2) d x

\frac{d}{d x} ((3 x + 1)^{4})

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