en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/(a+x)

Solution

\int \frac{1}{a + x} d x

Solution

ln ∣ a + x ∣ + C

Solution steps

\int \frac{1}{a + x} 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 = a + x

= ln ∣ a + x ∣

Add a constant to the solution

= ln ∣ a + x ∣ + C

Graph

Popular Examples

integral from 0 to 2 of-x^2-x+13

\int_{0}^{2} - x^{2} - x + 13 d x

integral of (pi-x)sin(nx)

\int (π - x) sin (n x) d x

((1-2ln(x))/(x^3))^'

(\frac{1 - 2 ln ( x )}{x ^{3}})^{^{'}}

integral of (e^x)/(4-e^{2x)}

\int \frac{e ^{x}}{4 - e ^{2 x}} d x

derivative of (-2x^2+x+4)/(x^2+4x-1)derivative of

\frac{- 2 x ^{2} + x + 4}{x ^{2} + 4 x - 1}

Frequently Asked Questions (FAQ)

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