What is the integral of (x^3+4x^2-3x+2)/(x^2) ?

The integral of (x^3+4x^2-3x+2)/(x^2) is (x^2)/2+4x-3ln|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^3+4x^2-3x+2)/(x^2)

integral

\frac{x ^{3} + 4 x ^{2} - 3 x + 2}{x ^{2}}

\frac{x ^{2}}{2} + 4 x - 3 ln ∣ x ∣ - \frac{2}{x} + C

Solution steps

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

Expand

\frac{x ^{3} + 4 x ^{2} - 3 x + 2}{x ^{2}} : x + 4 - \frac{3}{x} + \frac{2}{x ^{2}}

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

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

\int 4 d x = 4 x

\int \frac{3}{x} d x = 3 ln ∣ x ∣

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

= \frac{x ^{2}}{2} + 4 x - 3 ln ∣ x ∣ - \frac{2}{x}

Add a constant to the solution

= \frac{x ^{2}}{2} + 4 x - 3 ln ∣ x ∣ - \frac{2}{x} + C

\frac{x ^{- 2}}{- 2}

3 x^{2} + 8 x + 3

\frac{x - 2}{x + 2}

\frac{1}{( y ^{2} + 1 ) ^{2}}

\frac{1}{2 sin ^{2} ( x )}

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