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

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

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

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

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

Solution steps

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

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

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

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

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

Add a constant to the solution

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

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