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

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

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

- \frac{cos ^{3} ( x )}{3} + C

Solution steps

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

Apply u-substitution

: \int - u^{2} d u

= \int - u^{2} d u

Take the constant out:

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

= - \int u^{2} d u

Apply the Power Rule

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

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

Substitute back

u = cos (x)

= - \frac{cos ^{3} ( x )}{3}

Add a constant to the solution

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

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

\int \frac{1}{4 x + 3 x} d x

\int \frac{x ^{4}}{1 + x ^{2}} d x

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

\int \frac{2 x ^{3}}{x + 1} d x

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