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

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

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

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

Solution steps

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

Simplify

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

\frac{d}{d x} (x^{2} - x - ln (x))

\int_{- 1}^{2} (8 - x^{2}) d x

\frac{\partial}{\partial x} ((5 x + 9 y)^{10})

\frac{d}{d x} (3 cos (4 x))

\frac{\partial}{\partial t} (4 e^{s i n (x + 3 c t)})

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