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

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

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integral of x^{-1}-2x^{-2}+1

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

ln ∣ x ∣ + \frac{2}{x} + x + C

Solution steps

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

\int x^{- 1} d x = ln ∣ x ∣

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

\int 1 d x = x

= ln ∣ x ∣ - (- \frac{2}{x}) + x

Simplify

= ln ∣ x ∣ + \frac{2}{x} + x

Add a constant to the solution

= ln ∣ x ∣ + \frac{2}{x} + x + C

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