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

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

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

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

Solution steps

\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

\int \frac{12 x ^{3}}{x ^{4} + 7} d x

y = x^{3}, at x = - 1

f (x) = \frac{2 x}{sin ( x ) + cos ( x )}

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

x \to 2 lim (\frac{3}{x})

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