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+9)

Solution

\int \frac{1}{x + 9} d x

Solution

ln ∣ x + 9 ∣ + C

Solution steps

\int \frac{1}{x + 9} 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 + 9

= ln ∣ x + 9 ∣

Add a constant to the solution

= ln ∣ x + 9 ∣ + C

Popular Examples

derivative of xarcsin(x+sqrt(1-x^2))

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

y^{''}+8y^'+41y=0,y(0)=2,y^'(0)=-7

y^{^{''}} + 8 y^{^{'}} + 41 y = 0, y (0) = 2, y^{^{'}} (0) = - 7

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

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

derivative of ((x+1/x)^3)

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

derivative of (x^2/(x^2-16))

\frac{d}{d x} (\frac{x ^{2}}{x ^{2} - 16})

Frequently Asked Questions (FAQ)

What is the integral of 1/(x+9) ?
The integral of 1/(x+9) is ln|x+9|+C