What is the integral of cos(3x)sin^4(3x) ?

The integral of cos(3x)sin^4(3x) is 1/15 sin^5(3x)+C

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integral of cos(3x)sin^4(3x)

\int cos (3 x) sin^{4} (3 x) d x

\frac{1}{15} sin^{5} (3 x) + C

Solution steps

\int cos (3 x) sin^{4} (3 x) d x

Apply u-substitution

: \int cos (u) sin^{4} (u) \frac{1}{3} d u

= \int cos (u) sin^{4} (u) \frac{1}{3} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{3} \cdot \int cos (u) sin^{4} (u) d u

Apply u-substitution

: \int v^{4} d v

= \frac{1}{3} \cdot \int v^{4} d v

Apply the Power Rule

: \frac{v ^{5}}{5}

= \frac{1}{3} \cdot \frac{v ^{5}}{5}

Substitute back

= \frac{1}{3} \cdot \frac{sin ^{5} ( 3 x )}{5}

Simplify

\frac{1}{3} \cdot \frac{sin ^{5} ( 3 x )}{5} : \frac{1}{15} sin^{5} (3 x)

= \frac{1}{15} sin^{5} (3 x)

Add a constant to the solution

= \frac{1}{15} sin^{5} (3 x) + C

\frac{d y}{d x} = (4 x - 1) (y + 5)

\int (x + 2) (x - 2) d x

\int \frac{x}{1} (1) d x

\frac{1}{1 + x}, 2

(x e^{- x^{2}})^{^{'}}

What is the integral of cos(3x)sin^4(3x) ?
The integral of cos(3x)sin^4(3x) is 1/15 sin^5(3x)+C