What is the integral of (2u^2-2u^{-1}) ?

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

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integral of (2u^2-2u^{-1})

\int (2 u^{2} - 2 u^{- 1}) d u

\frac{2 u ^{3}}{3} - 2 ln ∣ u ∣ + C

Solution steps

\int 2 u^{2} - 2 u^{- 1} d u

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

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int 2 u^{2} d u = \frac{2 u ^{3}}{3}

\int \frac{2}{u} d u = 2 ln ∣ u ∣

= \frac{2 u ^{3}}{3} - 2 ln ∣ u ∣

Add a constant to the solution

= \frac{2 u ^{3}}{3} - 2 ln ∣ u ∣ + C

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