What is the integral of 2/(3x-5) ?

The integral of 2/(3x-5) is 2/3 ln|3x-5|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 2/(3x-5)

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

\frac{2}{3} ln ∣ 3 x - 5 ∣ + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{3 u} d u

= 2 \cdot \int \frac{1}{3 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}{3} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 2 \cdot \frac{1}{3} ln ∣ u ∣

Substitute back

u = 3 x - 5

= 2 \cdot \frac{1}{3} ln ∣ 3 x - 5 ∣

Simplify

2 \cdot \frac{1}{3} ln ∣ 3 x - 5 ∣ : \frac{2}{3} ln ∣ 3 x - 5 ∣

= \frac{2}{3} ln ∣ 3 x - 5 ∣

Add a constant to the solution

= \frac{2}{3} ln ∣ 3 x - 5 ∣ + C

\int (sec (x) tan (x) + 4 x) d x

\int \frac{2 x ^{2}}{6 x ^{3} + 1} d x

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

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