What is the integral of cot(x)csc^3(x) ?

The integral of cot(x)csc^3(x) is -(csc^3(x))/3+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of cot(x)csc^3(x)

\int cot (x) csc^{3} (x) d x

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

Solution steps

\int cot (x) csc^{3} (x) d x

Apply u-substitution

= \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}

Substitute back

u = csc (x)

= - \frac{csc ^{3} ( x )}{3}

Add a constant to the solution

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

What is the integral of cot(x)csc^3(x) ?
The integral of cot(x)csc^3(x) is -(csc^3(x))/3+C