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) \cdot 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 \frac{( x - 1 )}{x ^{2} - x + 1} d x

x \to - \infty lim (e^{x} - 1)

x \to \frac{π}{4} lim (\frac{sec ^{2} ( x ) - 2 tan ( x )}{1 + cos ( 4 x )})

y^{^{''}} - (\frac{6}{x}) y^{^{'}} - (\frac{9}{x ^{2}}) y = 0

x \to - 2 + lim (\frac{- 2}{x ^{2} - 4})

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