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

The integral of cos^2(t)sin(t) is -(cos^3(t))/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(t)sin(t)

integral

cos^{2} (t) sin (t)

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

Solution steps

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

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 (t)

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

Add a constant to the solution

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

((sin (x))^{2}) ((cos^{2} (x))^{2})

\frac{1}{36 + x ^{2}}

(x^{2}) sin (x)

\frac{e}{( e ^{x} ) ^{2}}

\frac{( 1 + x ) ^{2}}{( x ( 1 + x ^{2} ) )}

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