What is the integral from 5 to 7 of 1/(x-2) ?

The integral from 5 to 7 of 1/(x-2) is ln(5)-ln(3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 5 to 7 of 1/(x-2)

\int_{5}^{7} \frac{1}{x - 2} d x

ln (5) - ln (3)

Decimal

0.51082 \dots

Solution steps

\int_{5}^{7} \frac{1}{x - 2} d x

Apply u-substitution

= \int_{3}^{5} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{3}^{5}

Compute the boundaries:

ln (5) - ln (3)

= ln (5) - ln (3)

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

\int_{1}^{2} (\frac{x}{2} - \frac{6}{x}) d x

\int_{0}^{1} x^{2} cos (π x) d x

\int_{0}^{4} 2 x - (2 x - 4) d x

\int_{x}^{2} ln (t) d t

What is the integral from 5 to 7 of 1/(x-2) ?
The integral from 5 to 7 of 1/(x-2) is ln(5)-ln(3)