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

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

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

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

Solution steps

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

Expand

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

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

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

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

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

Simplify

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

Add a constant to the solution

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

\int e^{(x)^{2}} d x

\int e^{- x} + e^{- 2 x} d x

\int (arctan (x))^{2} x d x

\int (x^{3} - 3 e^{x}) d x

\int (12 - x)^{2} d x

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