What is the integral of csc^2(x)cot^3(x) ?

The integral of csc^2(x)cot^3(x) is -(cot^4(x))/4+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of csc^2(x)cot^3(x)

\int csc^{2} (x) cot^{3} (x) d x

- \frac{cot ^{4} ( x )}{4} + C

Solution steps

\int csc^{2} (x) cot^{3} (x) d x

Apply u-substitution

= \int - u^{3} d u

Take the constant out:

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

= - \int u^{3} d u

Apply the Power Rule

= - \frac{u ^{4}}{4}

Substitute back

u = cot (x)

= - \frac{cot ^{4} ( x )}{4}

Add a constant to the solution

= - \frac{cot ^{4} ( x )}{4} + C

What is the integral of csc^2(x)cot^3(x) ?
The integral of csc^2(x)cot^3(x) is -(cot^4(x))/4+C