What is the integral of (2x^{-2}+4) ?

The integral of (2x^{-2}+4) is -2/x+4x+C

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integral of (2x^{-2}+4)

\int (2 x^{- 2} + 4) d x

- \frac{2}{x} + 4 x + C

Solution steps

\int 2 x^{- 2} + 4 d x

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

= \int \frac{2}{x ^{2}} + 4 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 ^{2}} d x + \int 4 d x

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

\int 4 d x = 4 x

= - \frac{2}{x} + 4 x

Add a constant to the solution

= - \frac{2}{x} + 4 x + C

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