What is the integral of 1/(2-3y) ?

The integral of 1/(2-3y) is -1/3 ln|2-3y|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/(2-3y)

\int \frac{1}{2 - 3 y} d y

- \frac{1}{3} ln ∣ 2 - 3 y ∣ + C

Solution steps

\int \frac{1}{2 - 3 y} d y

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 = 2 - 3 y

= - \frac{1}{3} ln ∣ 2 - 3 y ∣

Add a constant to the solution

= - \frac{1}{3} ln ∣ 2 - 3 y ∣ + C

\int sin (a \cdot x) \cdot sin (b \cdot x) d x

\int \frac{r}{16 - 9 r ^{2}} d r

\int \frac{100}{25 x ^{2} + 36} d x

\int sin (x) (tan (x) + cot (x)) d x

\int x^{3} 4 x^{2} - 9 d x