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

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

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

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

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

Solution steps

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

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

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

\int 4 d x = 4 x

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

Simplify

= \frac{3}{x} + x^{2} + 4 x

Add a constant to the solution

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

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