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

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

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

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

- \frac{1}{x ^{2}} + ln ∣ x ∣ + C

Solution steps

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

Simplify

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

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

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

\int \frac{1}{x} d x = ln ∣ x ∣

= - \frac{1}{x ^{2}} + ln ∣ x ∣

Add a constant to the solution

= - \frac{1}{x ^{2}} + ln ∣ x ∣ + C

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