What is the integral of (4x-11)/((2x-1)(x+4)) ?

The integral of (4x-11)/((2x-1)(x+4)) is -ln|2x-1|+3ln|x+4|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (4x-11)/((2x-1)(x+4))

\int \frac{4 x - 11}{( 2 x - 1 ) ( x + 4 )} d x

- ln ∣ 2 x - 1 ∣ + 3 ln ∣ x + 4 ∣ + C

Solution steps

\int \frac{4 x - 11}{( 2 x - 1 ) ( x + 4 )} d x

Take the partial fraction of

\frac{4 x - 11}{( 2 x - 1 ) ( x + 4 )} : - \frac{2}{2 x - 1} + \frac{3}{x + 4}

= \int - \frac{2}{2 x - 1} + \frac{3}{x + 4} 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}{2 x - 1} d x + \int \frac{3}{x + 4} d x

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

\int \frac{3}{x + 4} d x = 3 ln ∣ x + 4 ∣

= - ln ∣ 2 x - 1 ∣ + 3 ln ∣ x + 4 ∣

Add a constant to the solution

= - ln ∣ 2 x - 1 ∣ + 3 ln ∣ x + 4 ∣ + C

\frac{d}{d x} (6 x^{2} + 5 x - 6)

\int \frac{1}{4} x d x

\frac{( 6 s + 3 )}{s ^{2}}

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

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

What is the integral of (4x-11)/((2x-1)(x+4)) ?
The integral of (4x-11)/((2x-1)(x+4)) is -ln|2x-1|+3ln|x+4|+C