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

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

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 x/(2-x)

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

2 ln (2) - 1

Decimal Notation

0.38629 \dots

Solution steps

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

\frac{x}{2 - x} = \frac{2}{2 - x} - 1

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

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

= 2 ln (2) - 1

\int_{0}^{2} 2 x ln (1 + x) d x

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

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

\int_{- \infty}^{0} \frac{3}{9 + x ^{2}} d x

\int_{0}^{1} x y^{2} d x

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