What is the integral of 1/(5x-3) ?

The integral of 1/(5x-3) is 1/5 ln|5x-3|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/(5x-3)

\int \frac{1}{5 x - 3} d x

\frac{1}{5} ln ∣ 5 x - 3 ∣ + C

Solution steps

\int \frac{1}{5 x - 3} d x

Apply u-substitution

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

= \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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{5} ln ∣ u ∣

Substitute back

u = 5 x - 3

= \frac{1}{5} ln ∣ 5 x - 3 ∣

Add a constant to the solution

= \frac{1}{5} ln ∣ 5 x - 3 ∣ + C

\int sec^{4} (5 x) tan^{6} (5 x) d x

\frac{ln ( 1 + x )}{1 - x}

x^{2} - y^{2} + x y \frac{d y}{d x} = 0

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

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