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

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

Popular >

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

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

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

Solution steps

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

Apply u-substitution

: \int u^{2} d u

= \int u^{2} d u

Apply the Power Rule

: \frac{u ^{3}}{3}

= \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

\int \frac{x ^{2} - 2 x + 4}{x ^{2}} d x

\int x tan (x) tan (x) d x

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

\int 14 sin (x) - 5 cos (x) d x

\int \frac{x}{2 x ^{2} - 4 x - 7} d x

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