What is the integral from 0 to pi/2 of x/(x^2-1) ?

The integral from 0 to pi/2 of x/(x^2-1) is diverges

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 0 to pi/2 of x/(x^2-1)

\int_{0}^{\frac{π}{2}} \frac{x}{x ^{2} - 1} d x

diverges

Solution steps

\int_{0}^{\frac{π}{2}} \frac{x}{x ^{2} - 1} d x

Find undefined (singularity) points:

x = 1

If exist

b, a < b < c, f (b) =

undefined

, \int_{a}^{c} f (x) d x = \int_{a}^{b} f (x) d x + \int_{b}^{c} f (x) d x

= \int_{0}^{1} \frac{x}{x ^{2} - 1} d x + \int_{1}^{\frac{π}{2}} \frac{x}{x ^{2} - 1} d x

\int_{0}^{1} \frac{x}{x ^{2} - 1} d x =

diverges

If part of the expression diverges, then entire expression diverges

= diverges

What is the integral from 0 to pi/2 of x/(x^2-1) ?
The integral from 0 to pi/2 of x/(x^2-1) is diverges