What is the integral of (-3x^3+2x^{-2}-6) ?

The integral of (-3x^3+2x^{-2}-6) is -(3x^4)/4-2/x-6x+C

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integral of (-3x^3+2x^{-2}-6)

\int (- 3 x^{3} + 2 x^{- 2} - 6) d x

- \frac{3 x ^{4}}{4} - \frac{2}{x} - 6 x + C

Solution steps

\int - 3 x^{3} + 2 x^{- 2} - 6 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 x^{- 2} d x - \int 6 d x

\int 3 x^{3} d x = \frac{3 x ^{4}}{4}

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

\int 6 d x = 6 x

= - \frac{3 x ^{4}}{4} - \frac{2}{x} - 6 x

Add a constant to the solution

= - \frac{3 x ^{4}}{4} - \frac{2}{x} - 6 x + C

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What is the integral of (-3x^3+2x^{-2}-6) ?
The integral of (-3x^3+2x^{-2}-6) is -(3x^4)/4-2/x-6x+C