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

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

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

\int (3 x^{\frac{1}{2}} - x^{- 2} + 2) d x

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

Solution steps

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

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

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

\int 2 d x = 2 x

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

Simplify

= 2 x^{\frac{3}{2}} + \frac{1}{x} + 2 x

Add a constant to the solution

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

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