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

The integral of (4-x)/(x^3) is -2/(x^2)+1/x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (4-x)/(x^3)

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

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

Solution steps

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

Expand

\frac{4 - x}{x ^{3}} : \frac{4}{x ^{3}} - \frac{1}{x ^{2}}

= \int \frac{4}{x ^{3}} - \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 \frac{4}{x ^{3}} d x - \int \frac{1}{x ^{2}} d x

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

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

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

Simplify

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

Add a constant to the solution

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

What is the integral of (4-x)/(x^3) ?
The integral of (4-x)/(x^3) is -2/(x^2)+1/x+C