en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x/(x-20)

Solution

\int \frac{x}{x - 20} d x

Solution

x - 20 + 20 ln ∣ x - 20 ∣ + C

Solution steps

\int \frac{x}{x - 20} d x

Apply u-substitution

: \int \frac{u + 20}{u} d u

= \int \frac{u + 20}{u} d u

Expand

\frac{u + 20}{u} : 1 + \frac{20}{u}

= \int 1 + \frac{20}{u} d u

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 u + \int \frac{20}{u} d u

\int 1 d u = u

\int \frac{20}{u} d u = 20 ln ∣ u ∣

= u + 20 ln ∣ u ∣

Substitute back

u = x - 20

= x - 20 + 20 ln ∣ x - 20 ∣

Add a constant to the solution

= x - 20 + 20 ln ∣ x - 20 ∣ + C

Popular Examples

maclaurin 1/(1+\frac{1){1+x}}maclaurin

\frac{1}{1 + \frac{1}{1 + x}}

derivative of 1/3 t^3-4t^2+16t+7 derivative of

\frac{1}{3} t^{3} - 4 t^{2} + 16 t + 7

limit as x approaches 0 of log_{2}(x)

x \to 0 lim (lo g_{2} (x))

integral of (x+6y)

\int (x + 6 y) d y

integral of (2sqrt(x))

\int (2 x) d x

Frequently Asked Questions (FAQ)

What is the integral of x/(x-20) ?
The integral of x/(x-20) is x-20+20ln|x-20|+C