What is the integral of (arccot(sqrt(x)))/(sqrt(x)) ?

The integral of (arccot(sqrt(x)))/(sqrt(x)) is 2sqrt(x)arccot(sqrt(x))+ln|x+1|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (arccot(sqrt(x)))/(sqrt(x))

\int \frac{arccot ( x )}{x} d x

2 x arccot (x) + ln ∣ x + 1 ∣ + C

Solution steps

\int \frac{arccot ( x )}{x} d x

Apply Integration By Parts

= 2 x arccot (x) - \int - \frac{1}{x + 1} d x

\int - \frac{1}{x + 1} d x = - ln ∣ x + 1 ∣

= 2 x arccot (x) - (- ln ∣ x + 1 ∣)

Simplify

= 2 x arccot (x) + ln ∣ x + 1 ∣

Add a constant to the solution

= 2 x arccot (x) + ln ∣ x + 1 ∣ + C

What is the integral of (arccot(sqrt(x)))/(sqrt(x)) ?
The integral of (arccot(sqrt(x)))/(sqrt(x)) is 2sqrt(x)arccot(sqrt(x))+ln|x+1|+C