What is the integral of arccoth(x) ?

The integral of arccoth(x) is xarccoth(x)+1/2 ln|1-x^2|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of arccoth(x)

\int arccoth (x) d x

x arccoth (x) + \frac{1}{2} ln 1 - x^{2} + C

Solution steps

\int arccoth (x) d x

Apply Integration By Parts

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

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

\int \frac{x}{1 - x ^{2}} d x = - \frac{1}{2} ln 1 - x^{2}

= x arccoth (x) - (- \frac{1}{2} ln 1 - x^{2})

Simplify

= x arccoth (x) + \frac{1}{2} ln 1 - x^{2}

Add a constant to the solution

= x arccoth (x) + \frac{1}{2} ln 1 - x^{2} + C

\int x^{2} cos (4 x^{3} - 1) d x

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

\int \frac{6 x ^{2} + x - 3}{x ^{3} - x} d x

\int \frac{1}{9 t ^{2} + 4} d t

\int \frac{3 sin ( x ) + 2}{2 sin ( x ) + 3} d x

What is the integral of arccoth(x) ?
The integral of arccoth(x) is xarccoth(x)+1/2 ln|1-x^2|+C