What is the integral of (4w-11)/(2w^2+7w-4) ?

The integral of (4w-11)/(2w^2+7w-4) is -ln|2w-1|+3ln|w+4|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (4w-11)/(2w^2+7w-4)

\int \frac{4 w - 11}{2 w ^{2} + 7 w - 4} d w

- ln ∣ 2 w - 1 ∣ + 3 ln ∣ w + 4 ∣ + C

Solution steps

\int \frac{4 w - 11}{2 w ^{2} + 7 w - 4} d w

Take the partial fraction of

\frac{4 w - 11}{2 w ^{2} + 7 w - 4} : - \frac{2}{2 w - 1} + \frac{3}{w + 4}

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

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 w - 1} d w + \int \frac{3}{w + 4} d w

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

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

= - ln ∣ 2 w - 1 ∣ + 3 ln ∣ w + 4 ∣

Add a constant to the solution

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

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

\int_{- 1}^{1} 1 1^{x} d x

\int x^{\frac{1}{3}} + 6 d x

\frac{d}{d x} (- e^{- 3 x})

e^{2 t}

What is the integral of (4w-11)/(2w^2+7w-4) ?
The integral of (4w-11)/(2w^2+7w-4) is -ln|2w-1|+3ln|w+4|+C