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

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

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

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

Solution steps

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

Simplify

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

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

Apply the Power Rule

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

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

Add a constant to the solution

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

\frac{d}{d x} (\frac{( 3 x ^{2} - 5 )}{( 2 x ^{2} + 1 )})

f (x) = e^{x^{4}}

6 x \frac{d y}{d x} = 2 x e^{x} - 6 y + 6 x^{2}

\frac{\partial}{\partial x} (ln (x + 2))

\int x^{2} e^{5 x} d x

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