What is the integral of (-5x^{-2}+1) ?

The integral of (-5x^{-2}+1) is 5/x+x+C

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integral of (-5x^{-2}+1)

\int (- 5 x^{- 2} + 1) d x

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

Solution steps

\int - 5 x^{- 2} + 1 d x

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

= \int - \frac{5}{x ^{2}} + 1 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 1 d x

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

\int 1 d x = x

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

Simplify

= \frac{5}{x} + x

Add a constant to the solution

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