What is the integral of-x^{-3}+x-1 ?

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

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integral of-x^{-3}+x-1

\int - x^{- 3} + x - 1 d x

\frac{1}{2 x ^{2}} + \frac{x ^{2}}{2} - x + C

Solution steps

\int - x^{- 3} + x - 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 x^{- 3} d x + \int x d x - \int 1 d x

\int x^{- 3} d x = - \frac{1}{2 x ^{2}}

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

\int 1 d x = x

= - (- \frac{1}{2 x ^{2}}) + \frac{x ^{2}}{2} - x

Simplify

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

Add a constant to the solution

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

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