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

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

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

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

- \frac{1}{x} - ln ∣ x ∣ + 2 x + C

Solution steps

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

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

\int x^{- 1} d x = ln ∣ x ∣

\int 2 d x = 2 x

= - \frac{1}{x} - ln ∣ x ∣ + 2 x

Add a constant to the solution

= - \frac{1}{x} - ln ∣ x ∣ + 2 x + C

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