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

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

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

\frac{x ^{2}}{2} - 2 x - \frac{1}{x} + C

Solution steps

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

Expand

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

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

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

\int 2 d x = 2 x

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

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

Add a constant to the solution

= \frac{x ^{2}}{2} - 2 x - \frac{1}{x} + C

\int \frac{1}{4 - u ^{2}} d u

\int 9 - 3 x d x

\int x^{4} ln (1 + x) d x

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

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