What is the integral of (cot(x))^4 ?

The integral of (cot(x))^4 is -1/3 cot^3(x)+x+cot(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (cot(x))^4

\int (cot (x))^{4} d x

- \frac{1}{3} cot^{3} (x) + x + cot (x) + C

Solution steps

\int (cot (x))^{4} d x

Simplify

= \int cot^{4} (x) d x

Apply Integral Reduction

= - \frac{cot ^{3} ( x )}{3} - \int cot^{2} (x) d x

\int cot^{2} (x) d x = - x - cot (x)

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

Simplify

- \frac{cot ^{3} ( x )}{3} - (- x - cot (x)) : - \frac{1}{3} cot^{3} (x) + x + cot (x)

= - \frac{1}{3} cot^{3} (x) + x + cot (x)

Add a constant to the solution

= - \frac{1}{3} cot^{3} (x) + x + cot (x) + C

\int \frac{x ^{2}}{4 x ^{2} - 9} d x

\int x (π - x) sin (n x) d x

\int \frac{x ^{3} + 3 x ^{2} + 2 x + 5}{x + 2} d x

\int sin (\frac{π}{6} x) d x

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

What is the integral of (cot(x))^4 ?
The integral of (cot(x))^4 is -1/3 cot^3(x)+x+cot(x)+C