What is the integral of (-5x^{-2}+x) ?

The integral of (-5x^{-2}+x) is 5/x+(x^2)/2+C

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integral of (-5x^{-2}+x)

\int (- 5 x^{- 2} + x) d x

\frac{5}{x} + \frac{x ^{2}}{2} + C

Solution steps

\int - 5 x^{- 2} + x d x

5 x^{- 2} = \frac{5}{x ^{2}}

= \int - \frac{5}{x ^{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 \frac{5}{x ^{2}} d x + \int x d x

\int \frac{5}{x ^{2}} d x = - \frac{5}{x}

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

= - (- \frac{5}{x}) + \frac{x ^{2}}{2}

Simplify

= \frac{5}{x} + \frac{x ^{2}}{2}

Add a constant to the solution

= \frac{5}{x} + \frac{x ^{2}}{2} + C

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What is the integral of (-5x^{-2}+x) ?
The integral of (-5x^{-2}+x) is 5/x+(x^2)/2+C