What is the integral of 1/(3x-10) ?

The integral of 1/(3x-10) is 1/3 ln|3x-10|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/(3x-10)

\int \frac{1}{3 x - 10} d x

\frac{1}{3} ln ∣ 3 x - 10 ∣ + C

Solution steps

\int \frac{1}{3 x - 10} d x

Apply u-substitution

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

= \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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{3} ln ∣ u ∣

Substitute back

u = 3 x - 10

= \frac{1}{3} ln ∣ 3 x - 10 ∣

Add a constant to the solution

= \frac{1}{3} ln ∣ 3 x - 10 ∣ + C

\int 3 x e^{8 x^{2}} d x

\int 50 - \frac{20}{x + 5} d x

\int 10 sin (1000 π x) d x

\int sec^{2} (x) 2 + tan (x) d x

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

What is the integral of 1/(3x-10) ?
The integral of 1/(3x-10) is 1/3 ln|3x-10|+C