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

The integral of (3x-2)/(2x+5) is 3/2 x+15/4-19/4 ln|2x+5|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (3x-2)/(2x+5)

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

\frac{3}{2} x + \frac{15}{4} - \frac{19}{4} ln ∣ 2 x + 5 ∣ + C

Solution steps

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

Expand

\frac{3 x - 2}{2 x + 5} : \frac{3 x}{2 x + 5} - \frac{2}{2 x + 5}

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int \frac{3 x}{2 x + 5} d x = \frac{3}{4} (2 x + 5 - 5 ln ∣ 2 x + 5 ∣)

\int \frac{2}{2 x + 5} d x = ln ∣ 2 x + 5 ∣

= \frac{3}{4} (2 x + 5 - 5 ln ∣ 2 x + 5 ∣) - ln ∣ 2 x + 5 ∣

Simplify

\frac{3}{4} (2 x + 5 - 5 ln ∣ 2 x + 5 ∣) - ln ∣ 2 x + 5 ∣ : \frac{3}{2} x + \frac{15}{4} - \frac{19}{4} ln ∣ 2 x + 5 ∣

= \frac{3}{2} x + \frac{15}{4} - \frac{19}{4} ln ∣ 2 x + 5 ∣

Add a constant to the solution

= \frac{3}{2} x + \frac{15}{4} - \frac{19}{4} ln ∣ 2 x + 5 ∣ + C

\int sec (x) (9 sec (x) + 5 tan (x)) d x

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

\int \frac{2 x ^{2} - 4 x + 3}{( x - 1 ) ^{2}} d x

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

\int (8 t + 2) e^{- t} d t

What is the integral of (3x-2)/(2x+5) ?
The integral of (3x-2)/(2x+5) is 3/2 x+15/4-19/4 ln|2x+5|+C