What is the integral of cos^2(5y)sin(5y) ?

The integral of cos^2(5y)sin(5y) is -1/15 cos^3(5y)+C

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integral of cos^2(5y)sin(5y)

\int cos^{2} (5 y) sin (5 y) d y

- \frac{1}{15} cos^{3} (5 y) + C

Solution steps

\int cos^{2} (5 y) sin (5 y) d y

Apply u-substitution

: \int cos^{2} (u) sin (u) \frac{1}{5} d u

= \int cos^{2} (u) sin (u) \frac{1}{5} d u

Take the constant out:

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

= \frac{1}{5} \cdot \int cos^{2} (u) sin (u) d u

Apply u-substitution

: \int - v^{2} d v

= \frac{1}{5} \cdot \int - v^{2} d v

Take the constant out:

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

= \frac{1}{5} (- \int v^{2} d v)

Apply the Power Rule

: \frac{v ^{3}}{3}

= \frac{1}{5} (- \frac{v ^{3}}{3})

Substitute back

= \frac{1}{5} (- \frac{cos ^{3} ( 5 y )}{3})

Simplify

\frac{1}{5} (- \frac{cos ^{3} ( 5 y )}{3}) : - \frac{1}{15} cos^{3} (5 y)

= - \frac{1}{15} cos^{3} (5 y)

Add a constant to the solution

= - \frac{1}{15} cos^{3} (5 y) + C

\int_{- 3}^{\infty} e^{- x} d x

\frac{1}{1 - x}

\frac{\partial}{\partial z} (- 9 z cos (3 x + yz))

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

\frac{d y}{d x} = 2 y (1 - y)

What is the integral of cos^2(5y)sin(5y) ?
The integral of cos^2(5y)sin(5y) is -1/15 cos^3(5y)+C