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

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

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

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

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

Solution steps

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

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 (x)

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

Add a constant to the solution

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

\int_{0}^{3} (x + 1) d x

f (x) = x^{2} - 6 x

\frac{d}{d x} (\frac{1}{2} arctan (\frac{x}{2}))

\frac{\partial}{\partial x} (\frac{( x - y )}{( z - y )})

y = \frac{x ^{2} + 32 x}{8}

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