What is the integral from 0 to 3 of 1/((x-1)) ?

The integral from 0 to 3 of 1/((x-1)) 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 3 of 1/((x-1))

\int_{0}^{3} \frac{1}{( x - 1 )} d x

diverges

Solution steps

\int_{0}^{3} \frac{1}{x - 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{1}{x - 1} d x + \int_{1}^{3} \frac{1}{x - 1} d x

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

diverges

If part of the expression diverges, then entire expression diverges

= diverges

\int_{0}^{5} 2.5 x d x

\int_{x}^{x^{3}} \frac{y}{x} d y

\int_{1}^{\infty} \frac{1}{x ^{m}} d x

\int_{2}^{6} 6 x d x

\int_{0}^{x} t^{2} e^{t^{2}} d t

What is the integral from 0 to 3 of 1/((x-1)) ?
The integral from 0 to 3 of 1/((x-1)) is diverges