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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (4/(x^2)-3/(x^3))

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

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

Solution steps

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

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

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

= - \frac{4}{x} - (- \frac{3}{2 x ^{2}})

Simplify

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

Add a constant to the solution

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

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