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

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

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

diverges

Solution steps

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

Find undefined (singularity) points:

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

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

diverges

If part of the expression diverges, then entire expression diverges

= diverges

\int_{3}^{5} \frac{1}{x ^{2} - 3 x + 2} d x

\int_{0}^{2} x^{3} - 5 x^{2} + 6 x d x

\int_{1}^{2} 6 x^{4} d x

\int_{0}^{\frac{π}{6}} x cos (x) d x

\int_{0}^{\frac{π}{2}} 5 sin (x) d x

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