What is the integral of (x^2-7x+2)/(x^2) ?

The integral of (x^2-7x+2)/(x^2) is x-7ln|x|-2/x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (x^2-7x+2)/(x^2)

\int \frac{x ^{2} - 7 x + 2}{x ^{2}} d x

x - 7 ln ∣ x ∣ - \frac{2}{x} + C

Solution steps

\int \frac{x ^{2} - 7 x + 2}{x ^{2}} d x

Expand

\frac{x ^{2} - 7 x + 2}{x ^{2}} : 1 - \frac{7}{x} + \frac{2}{x ^{2}}

= \int 1 - \frac{7}{x} + \frac{2}{x ^{2}} 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 1 d x - \int \frac{7}{x} d x + \int \frac{2}{x ^{2}} d x

\int 1 d x = x

\int \frac{7}{x} d x = 7 ln ∣ x ∣

\int \frac{2}{x ^{2}} d x = - \frac{2}{x}

= x - 7 ln ∣ x ∣ - \frac{2}{x}

Add a constant to the solution

= x - 7 ln ∣ x ∣ - \frac{2}{x} + C

\int \frac{4}{1 - 2 x} d x

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

\int \frac{1}{m} d m

\int \frac{y}{1 + 2 y ^{2}} d y

\int e^{- 5 t} t d t

What is the integral of (x^2-7x+2)/(x^2) ?
The integral of (x^2-7x+2)/(x^2) is x-7ln|x|-2/x+C