What is the integral of 2/(5x-8) ?

The integral of 2/(5x-8) is 2/5 ln|5x-8|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 2/(5x-8)

\int \frac{2}{5 x - 8} d x

\frac{2}{5} ln ∣ 5 x - 8 ∣ + C

Solution steps

\int \frac{2}{5 x - 8} d x

Take the constant out:

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

= 2 \cdot \int \frac{1}{5 x - 8} d x

Apply u-substitution

: \int \frac{1}{5 u} d u

= 2 \cdot \int \frac{1}{5 u} d u

Take the constant out:

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

= 2 \cdot \frac{1}{5} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 2 \cdot \frac{1}{5} ln ∣ u ∣

Substitute back

u = 5 x - 8

= 2 \cdot \frac{1}{5} ln ∣ 5 x - 8 ∣

Simplify

2 \cdot \frac{1}{5} ln ∣ 5 x - 8 ∣ : \frac{2}{5} ln ∣ 5 x - 8 ∣

= \frac{2}{5} ln ∣ 5 x - 8 ∣

Add a constant to the solution

= \frac{2}{5} ln ∣ 5 x - 8 ∣ + C

\int \frac{( x ^{3} - 4 x - 10 )}{( x ^{2} - x - 6 )} d x

\int \frac{5}{( t ^{2} + 1 ) ^{\frac{3}{2}}} d t

\frac{d}{d x} (- \frac{7}{x ^{4}})

y = \frac{x}{x - 1}

\int_{0}^{1} 1 - x^{\frac{2}{5}} d x