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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

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

Solution steps

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

Simplify

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

Apply u-substitution

= \int u^{2} d u

Apply the Power Rule

= \frac{u ^{3}}{3}

Substitute back

u = sin (x)

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

Add a constant to the solution

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

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