en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/(x-7)

Solution

\int \frac{1}{x - 7} d x

Solution

ln ∣ x - 7 ∣ + C

Solution steps

\int \frac{1}{x - 7} d x

Apply u-substitution

: \int \frac{1}{u} d u

= \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = x - 7

= ln ∣ x - 7 ∣

Add a constant to the solution

= ln ∣ x - 7 ∣ + C

Graph

Popular Examples

integral of (6x-5)/(3x^2+5)

\int \frac{6 x - 5}{3 x ^{2} + 5} d x

y^'=(x^2y^4+2x^2)/(y^3)

y^{^{'}} = \frac{x ^{2} y ^{4} + 2 x ^{2}}{y ^{3}}

integral of (1+e^{2x})/(e^x)

\int \frac{1 + e ^{2 x}}{e ^{x}} d x

y^{^{'}} = - 2 x y

(dy)/(dx)=cot(1-2x^2)

\frac{d y}{d x} = cot (1 - 2 x^{2})

Frequently Asked Questions (FAQ)

What is the integral of 1/(x-7) ?
The integral of 1/(x-7) is ln|x-7|+C