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

The integral of x^{1/2}-3x^{-1/2} is 2/3 x^{3/2}-6x^{1/2}+C

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integral of x^{1/2}-3x^{-1/2}

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

\frac{2}{3} x^{\frac{3}{2}} - 6 x^{\frac{1}{2}} + C

Solution steps

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

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

\int 3 x^{- \frac{1}{2}} d x = 6 x^{\frac{1}{2}}

= \frac{2}{3} x^{\frac{3}{2}} - 6 x^{\frac{1}{2}}

Add a constant to the solution

= \frac{2}{3} x^{\frac{3}{2}} - 6 x^{\frac{1}{2}} + C

What is the integral of x^{1/2}-3x^{-1/2} ?
The integral of x^{1/2}-3x^{-1/2} is 2/3 x^{3/2}-6x^{1/2}+C