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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

\frac{1}{9} sin^{3} (3 x) + C

Solution steps

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

Apply u-substitution

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

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

Apply u-substitution

: \int v^{2} d v

= \frac{1}{3} \cdot \int v^{2} d v

Apply the Power Rule

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

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

Substitute back

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

Simplify

\frac{1}{3} \cdot \frac{sin ^{3} ( 3 x )}{3} : \frac{1}{9} sin^{3} (3 x)

= \frac{1}{9} sin^{3} (3 x)

Add a constant to the solution

= \frac{1}{9} sin^{3} (3 x) + C

\int \frac{cos ( y )}{x + 3} d x

\int (x + 2) sin (x^{2} + 4 x + 8) d x

\int \frac{x ^{2} + cos ( x )}{x ^{3} + 3 sin ( x )} d x

\int x ln (4) d x

\int \frac{1}{8 sin ^{2} ( x ) cos ( x )} d x

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