What is the integral of (28x^3-56x^2+3)/(x^2-2x) ?

The integral of (28x^3-56x^2+3)/(x^2-2x) is 14x^2-3(1/2 ln|x|-1/2 ln|x-2|)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (28x^3-56x^2+3)/(x^2-2x)

\int \frac{28 x ^{3} - 56 x ^{2} + 3}{x ^{2} - 2 x} d x

14 x^{2} - 3 (\frac{1}{2} ln ∣ x ∣ - \frac{1}{2} ln ∣ x - 2 ∣) + C

Solution steps

\int \frac{28 x ^{3} - 56 x ^{2} + 3}{x ^{2} - 2 x} d x

Long division

\frac{28 x ^{3} - 56 x ^{2} + 3}{x ^{2} - 2 x} : 28 x + \frac{3}{x ^{2} - 2 x}

= \int 28 x + \frac{3}{x ^{2} - 2 x} 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 28 x d x + \int \frac{3}{x ^{2} - 2 x} d x

\int 28 x d x = 14 x^{2}

\int \frac{3}{x ^{2} - 2 x} d x = - 3 (\frac{1}{2} ln ∣ x ∣ - \frac{1}{2} ln ∣ x - 2 ∣)

= 14 x^{2} - 3 (\frac{1}{2} ln ∣ x ∣ - \frac{1}{2} ln ∣ x - 2 ∣)

Add a constant to the solution

= 14 x^{2} - 3 (\frac{1}{2} ln ∣ x ∣ - \frac{1}{2} ln ∣ x - 2 ∣) + C

\int u^{8} d u

\frac{d}{d x} (x^{8} (x - 2)^{7})

\int ln (ln (x)) d x

\frac{d}{d x} (cot (x) + tan (x))

f (x) = x^{2}, (1, 1)

What is the integral of (28x^3-56x^2+3)/(x^2-2x) ?
The integral of (28x^3-56x^2+3)/(x^2-2x) is 14x^2-3(1/2 ln|x|-1/2 ln|x-2|)+C