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

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

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

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

\frac{2 x ^{3}}{3} - 2 ln ∣ x ∣ + C

Solution steps

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

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

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

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

\int \frac{2}{x} d x = 2 ln ∣ x ∣

= \frac{2 x ^{3}}{3} - 2 ln ∣ x ∣

Add a constant to the solution

= \frac{2 x ^{3}}{3} - 2 ln ∣ x ∣ + C

\frac{\partial}{\partial y} (6 x y - 12)

\frac{\partial}{\partial x} (2 x^{2} + 3 x y)

\int \frac{1}{100} d x

\frac{1}{( s + 1 ) ^{2} + 5}

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