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

The integral of cos^4(θ)sin(θ) is -(cos^5(θ))/5+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of cos^4(θ)sin(θ)

\int cos^{4} (θ) sin (θ) d θ

- \frac{cos ^{5} ( θ )}{5} + C

Solution steps

\int cos^{4} (θ) sin (θ) d θ

Apply u-substitution

: \int - u^{4} d u

= \int - u^{4} d u

Take the constant out:

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

= - \int u^{4} d u

Apply the Power Rule

: \frac{u ^{5}}{5}

= - \frac{u ^{5}}{5}

Substitute back

u = cos (θ)

= - \frac{cos ^{5} ( θ )}{5}

Add a constant to the solution

= - \frac{cos ^{5} ( θ )}{5} + C

\frac{d}{d x} (ln (3 x^{2} - 2 x))

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

\int (x + 3) 4 - x^{2} d x

ln (15)

x \to 9 lim (ln (x - 9))

What is the integral of cos^4(θ)sin(θ) ?
The integral of cos^4(θ)sin(θ) is -(cos^5(θ))/5+C