What is the integral of (1+3x+7x^2-2x^3)/(x^2) ?

The integral of (1+3x+7x^2-2x^3)/(x^2) is -1/x+3ln|x|+7x-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 (1+3x+7x^2-2x^3)/(x^2)

\int \frac{1 + 3 x + 7 x ^{2} - 2 x ^{3}}{x ^{2}} d x

- \frac{1}{x} + 3 ln ∣ x ∣ + 7 x - x^{2} + C

Solution steps

\int \frac{1 + 3 x + 7 x ^{2} - 2 x ^{3}}{x ^{2}} d x

Expand

\frac{1 + 3 x + 7 x ^{2} - 2 x ^{3}}{x ^{2}} : \frac{1}{x ^{2}} + \frac{3}{x} + 7 - 2 x

= \int \frac{1}{x ^{2}} + \frac{3}{x} + 7 - 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 \frac{1}{x ^{2}} d x + \int \frac{3}{x} d x + \int 7 d x - \int 2 x d x

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

\int \frac{3}{x} d x = 3 ln ∣ x ∣

\int 7 d x = 7 x

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

= - \frac{1}{x} + 3 ln ∣ x ∣ + 7 x - x^{2}

Add a constant to the solution

= - \frac{1}{x} + 3 ln ∣ x ∣ + 7 x - x^{2} + C

\int 0.75 (1 - x^{2}) d x

\int ln^{x} (d) x d x

\int 21 x e^{- 11 x^{2}} d x

\int \frac{x + y}{x - y} d x

\int 6 x x - 8 d x

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