What is the integral from 2 to 3 of (x+1)/(x^2-x) ?

The integral from 2 to 3 of (x+1)/(x^2-x) is -ln(3)+3ln(2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 2 to 3 of (x+1)/(x^2-x)

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

- ln (3) + 3 ln (2)

Decimal Notation

0.98082 \dots

Solution steps

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

Take the partial fraction of

\frac{x + 1}{x ^{2} - x} : - \frac{1}{x} + \frac{2}{x - 1}

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

\int_{2}^{3} \frac{1}{x} d x = ln (3) - ln (2)

\int_{2}^{3} \frac{2}{x - 1} d x = 2 ln (2)

= - (ln (3) - ln (2)) + 2 ln (2)

Simplify

= - ln (3) + 3 ln (2)

x \to 1 lim (\frac{3 x + 2}{4 x - 5})

\frac{\partial}{\partial x} (10 - (3 x^{2} + 3 y^{2}))

\frac{d}{d x} (3 x^{2} - 4 x + 1)

\int \frac{3}{e ^{\frac{t}{2}}} d t

\int e^{x^{6}} d x

What is the integral from 2 to 3 of (x+1)/(x^2-x) ?
The integral from 2 to 3 of (x+1)/(x^2-x) is -ln(3)+3ln(2)