What is the integral of cos(t)sin^4(t) ?

The integral of cos(t)sin^4(t) is (sin^5(t))/5+C

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integral of cos(t)sin^4(t)

\int cos (t) sin^{4} (t) d t

\frac{sin ^{5} ( t )}{5} + C

Solution steps

\int cos (t) sin^{4} (t) d t

Apply u-substitution

: \int u^{4} d u

= \int u^{4} d u

Apply the Power Rule

: \frac{u ^{5}}{5}

= \frac{u ^{5}}{5}

Substitute back

u = sin (t)

= \frac{sin ^{5} ( t )}{5}

Add a constant to the solution

= \frac{sin ^{5} ( t )}{5} + C

\int \frac{x ^{4} + x - 81}{x ^{2} + 9} d x

\frac{\partial}{\partial x} (x z ln (x + 2 y + 3 z))

\frac{d}{d x} (e^{- 5})

\frac{\partial}{\partial y} (e^{x} sin (yz))

\frac{d}{d x} (5 x^{2} - 3 x)

What is the integral of cos(t)sin^4(t) ?
The integral of cos(t)sin^4(t) is (sin^5(t))/5+C