en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

integral of ((x+9))/x

Solution

\int \frac{( x + 9 )}{x} d x

Solution

x + 9 ln ∣ x ∣ + C

Solution steps

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

Expand

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

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int 1 d x = x

\int \frac{9}{x} d x = 9 ln ∣ x ∣

= x + 9 ln ∣ x ∣

Add a constant to the solution

= x + 9 ln ∣ x ∣ + C

Graph

Popular Examples

integral of (81)/(x^2)

\int \frac{81}{x ^{2}} d x

integral of (z^2+5)^3z

\int (z^{2} + 5)^{3} z d z

integral of (x^2-1)sin(x)

\int (x^{2} - 1) sin (x) d x

integral of y^3sqrt(y^4+5)

\int y^{3} y^{4} + 5 d y

integral of (x^7+2x)^5

\int (x^{7} + 2 x)^{5} d x

Frequently Asked Questions (FAQ)

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