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

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

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

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

Solution steps

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

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

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

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

Simplify

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

Add a constant to the solution

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

\frac{d}{d x} (\frac{x ^{5}}{5 - x ^{4}})

- 2

\frac{d}{d x} (ln (x^{2} - 8 x))

x \to π lim (cos (tan (x)))

x \to \infty lim (x^{10})

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