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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 3/(2x-3)

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

\frac{3}{2} ln ∣ 2 x - 3 ∣ + C

Solution steps

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

Take the constant out:

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

= 3 \cdot \int \frac{1}{2 x - 3} d x

Apply u-substitution

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

= 3 \cdot \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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 3 \cdot \frac{1}{2} ln ∣ u ∣

Substitute back

u = 2 x - 3

= 3 \cdot \frac{1}{2} ln ∣ 2 x - 3 ∣

Simplify

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

= \frac{3}{2} ln ∣ 2 x - 3 ∣

Add a constant to the solution

= \frac{3}{2} ln ∣ 2 x - 3 ∣ + C

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

\int \frac{1}{e ^{40 x} - 1} d x

\int \frac{sec ^{5} ( x )}{csc ( x )} d x

\int x^{3} e^{\frac{- x}{3}} d x

\int \frac{π x}{2} d x