What is the integral of (-x^{-3}+4x^{-2}-3) ?

The integral of (-x^{-3}+4x^{-2}-3) is 1/(2x^2)-4/x-3x+C

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integral of (-x^{-3}+4x^{-2}-3)

\int (- x^{- 3} + 4 x^{- 2} - 3) d x

\frac{1}{2 x ^{2}} - \frac{4}{x} - 3 x + C

Solution steps

\int - x^{- 3} + 4 x^{- 2} - 3 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 4 x^{- 2} d x - \int 3 d x

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

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

\int 3 d x = 3 x

= - (- \frac{1}{2 x ^{2}}) - \frac{4}{x} - 3 x

Simplify

= \frac{1}{2 x ^{2}} - \frac{4}{x} - 3 x

Add a constant to the solution

= \frac{1}{2 x ^{2}} - \frac{4}{x} - 3 x + C

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What is the integral of (-x^{-3}+4x^{-2}-3) ?
The integral of (-x^{-3}+4x^{-2}-3) is 1/(2x^2)-4/x-3x+C