What is the integral of sin(3z)cos^2(3z) ?

The integral of sin(3z)cos^2(3z) is -1/9 cos^3(3z)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sin(3z)cos^2(3z)

\int sin (3 z) cos^{2} (3 z) d z

- \frac{1}{9} cos^{3} (3 z) + C

Solution steps

\int sin (3 z) cos^{2} (3 z) d z

Apply u-substitution

: \int sin (u) cos^{2} (u) \frac{1}{3} d u

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

Apply u-substitution

: \int - v^{2} d v

= \frac{1}{3} \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}{3} (- \int v^{2} d v)

Apply the Power Rule

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

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

Substitute back

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

Simplify

\frac{1}{3} (- \frac{cos ^{3} ( 3 z )}{3}) : - \frac{1}{9} cos^{3} (3 z)

= - \frac{1}{9} cos^{3} (3 z)

Add a constant to the solution

= - \frac{1}{9} cos^{3} (3 z) + C

\int x sec^{2} (x^{2}) d x

n = 0 \sum \infty (\frac{1}{5})^{n}

12 arcsin (e^{\frac{x}{2}})

\frac{7 x}{8}

\frac{d y}{d x} + 5 y = 0, y (0) = 2

What is the integral of sin(3z)cos^2(3z) ?
The integral of sin(3z)cos^2(3z) is -1/9 cos^3(3z)+C