What is the integral of (1/(2x+5)) ?

The integral of (1/(2x+5)) is 1/2 ln|2x+5|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (1/(2x+5))

\int (\frac{1}{2 x + 5}) d x

\frac{1}{2} ln ∣ 2 x + 5 ∣ + C

Solution steps

\int \frac{1}{2 x + 5} d x

Apply u-substitution

: \int \frac{1}{2 u} d u

= \int \frac{1}{2 u} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{2} ln ∣ u ∣

Substitute back

u = 2 x + 5

= \frac{1}{2} ln ∣ 2 x + 5 ∣

Add a constant to the solution

= \frac{1}{2} ln ∣ 2 x + 5 ∣ + C

5 x^{^{''}} + 50 x = 10

\int x (5 x^{2} + \frac{2}{3})^{4} d x

\frac{d}{d x} (- 5 x^{3} + x^{2} - 3 x - 3)

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

\int \frac{2 x + 7}{x ^{2} + 2 x - 4} d x

What is the integral of (1/(2x+5)) ?
The integral of (1/(2x+5)) is 1/2 ln|2x+5|+C