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

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

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

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

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

Solution steps

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

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

\int 2 d x = 2 x

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

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

Simplify

= \frac{3}{2 x ^{2}} + 2 x - \frac{3}{x}

Add a constant to the solution

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

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