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+8)

Solution

\int \frac{1}{x + 8} d x

Solution

ln ∣ x + 8 ∣ + C

Solution steps

\int \frac{1}{x + 8} 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 + 8

= ln ∣ x + 8 ∣

Add a constant to the solution

= ln ∣ x + 8 ∣ + C

Popular Examples

integral from 0 to 1 of (2x)/((x^2+5)^2)

\int_{0}^{1} \frac{2 x}{( x ^{2} + 5 ) ^{2}} d x

integral from 0 to pi/4 of (sin(x))^4

\int_{0}^{\frac{π}{4}} (sin (x))^{4} d x

integral of (3u^{-2}-4u^2+1)

\int (3 u^{- 2} - 4 u^{2} + 1) d u

integral of (3x-2)^{20}

\int (3 x - 2)^{20} d x

tangent of f(x)=-6sqrt(x),\at x=4 tangent of

f (x) = - 6 x, at x = 4

Frequently Asked Questions (FAQ)

What is the integral of 1/(x+8) ?
The integral of 1/(x+8) is ln|x+8|+C