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

The integral of (1+3x)/((1-x)(3x-5)) is 2ln|x-1|-3ln|3x-5|+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)/((1-x)(3x-5))

\int \frac{1 + 3 x}{( 1 - x ) ( 3 x - 5 )} d x

2 ln ∣ x - 1 ∣ - 3 ln ∣ 3 x - 5 ∣ + C

Solution steps

\int \frac{1 + 3 x}{( 1 - x ) ( 3 x - 5 )} d x

Take the partial fraction of

\frac{1 + 3 x}{( 1 - x ) ( 3 x - 5 )} : \frac{2}{x - 1} - \frac{9}{3 x - 5}

= \int \frac{2}{x - 1} - \frac{9}{3 x - 5} d x

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{2}{x - 1} d x - \int \frac{9}{3 x - 5} d x

\int \frac{2}{x - 1} d x = 2 ln ∣ x - 1 ∣

\int \frac{9}{3 x - 5} d x = 3 ln ∣ 3 x - 5 ∣

= 2 ln ∣ x - 1 ∣ - 3 ln ∣ 3 x - 5 ∣

Add a constant to the solution

= 2 ln ∣ x - 1 ∣ - 3 ln ∣ 3 x - 5 ∣ + C

\int e^{7 t} d t

y = 5 + 5 x^{2} - 2 x^{3}, (2, 9)

\frac{d y}{d x} = y - y^{3}

(0, - 2), (- 2, - 2)

x \to 0 lim (2 cos (2 x))

What is the integral of (1+3x)/((1-x)(3x-5)) ?
The integral of (1+3x)/((1-x)(3x-5)) is 2ln|x-1|-3ln|3x-5|+C