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+14)

Solution

\int \frac{x}{x + 14} d x

Solution

x + 14 - 14 ln ∣ x + 14 ∣ + C

Solution steps

\int \frac{x}{x + 14} d x

Apply u-substitution

: \int \frac{u - 14}{u} d u

= \int \frac{u - 14}{u} d u

Expand

\frac{u - 14}{u} : 1 - \frac{14}{u}

= \int 1 - \frac{14}{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{14}{u} d u

\int 1 d u = u

\int \frac{14}{u} d u = 14 ln ∣ u ∣

= u - 14 ln ∣ u ∣

Substitute back

u = x + 14

= x + 14 - 14 ln ∣ x + 14 ∣

Add a constant to the solution

= x + 14 - 14 ln ∣ x + 14 ∣ + C

Graph

Popular Examples

integral of (2x)/(5x^2-3)

\int \frac{2 x}{5 x ^{2} - 3} d x

integral of (sinh(5x)+cosh(3x))

\int (sinh (5 x) + cosh (3 x)) d x

integral of tan^3(7x)

\int tan^{3} (7 x) d x

integral of 10xln(7x)

\int 10 x ln (7 x) d x

integral of 2/(x^2-2x+5)

\int \frac{2}{x ^{2} - 2 x + 5} d x

Frequently Asked Questions (FAQ)

What is the integral of x/(x+14) ?
The integral of x/(x+14) is x+14-14ln|x+14|+C