What is the integral from 0 to 5 of x/(x^2-2) ?

The integral from 0 to 5 of x/(x^2-2) is diverges

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 5 of x/(x^2-2)

\int_{0}^{5} \frac{x}{x ^{2} - 2} d x

diverges

Solution steps

\int_{0}^{5} \frac{x}{x ^{2} - 2} d x

Find undefined (singularity) points:

x = 2

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}^{2} \frac{x}{x ^{2} - 2} d x + \int_{2}^{5} \frac{x}{x ^{2} - 2} d x

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

diverges

If part of the expression diverges, then entire expression diverges

= diverges

\int_{1.5}^{2} \frac{3}{8} x^{2} d x

\int_{1}^{\infty} \frac{c}{x ^{3}} d x

\int_{0}^{3} \frac{10}{x ^{2} - 2 x} d x

\int_{4}^{6} \frac{1}{x ln ( 1.5 )} d x

\int_{1}^{5} x^{3} ln (x) d x

What is the integral from 0 to 5 of x/(x^2-2) ?
The integral from 0 to 5 of x/(x^2-2) is diverges