What is the integral of 4cos^2(θ)sin(θ) ?

The integral of 4cos^2(θ)sin(θ) is -4/3 cos^3(θ)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 4cos^2(θ)sin(θ)

\int 4 cos^{2} (θ) sin (θ) d θ

- \frac{4}{3} cos^{3} (θ) + C

Solution steps

\int 4 cos^{2} (θ) sin (θ) d θ

Take the constant out:

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

= 4 \cdot \int cos^{2} (θ) sin (θ) d θ

Apply u-substitution

: \int - u^{2} d u

= 4 \cdot \int - u^{2} d u

Take the constant out:

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

= 4 (- \int u^{2} d u)

Apply the Power Rule

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

= 4 (- \frac{u ^{3}}{3})

Substitute back

u = cos (θ)

= 4 (- \frac{cos ^{3} ( θ )}{3})

Simplify

4 (- \frac{cos ^{3} ( θ )}{3}) : - \frac{4}{3} cos^{3} (θ)

= - \frac{4}{3} cos^{3} (θ)

Add a constant to the solution

= - \frac{4}{3} cos^{3} (θ) + C

\int \frac{2}{( t ^{2} - 4 ) ^{2}} d t

\int \frac{1}{( x ) ^{\frac{3}{2}}} d x

\int (sin^{2} (4 x) + cos^{2} (4 x)) d x

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

\int \frac{1}{x ^{2} + 11} d x

What is the integral of 4cos^2(θ)sin(θ) ?
The integral of 4cos^2(θ)sin(θ) is -4/3 cos^3(θ)+C