What is the integral of (3x^{1/2}-x^{(-2)/3}+7) ?

The integral of (3x^{1/2}-x^{(-2)/3}+7) is 2x^{3/2}-3x^{1/3}+7x+C

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integral of (3x^{1/2}-x^{(-2)/3}+7)

\int (3 x^{\frac{1}{2}} - x^{\frac{- 2}{3}} + 7) d x

2 x^{\frac{3}{2}} - 3 x^{\frac{1}{3}} + 7 x + C

Solution steps

\int 3 x^{\frac{1}{2}} - x^{\frac{- 2}{3}} + 7 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^{\frac{- 2}{3}} d x + \int 7 d x

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

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

\int 7 d x = 7 x

= 2 x^{\frac{3}{2}} - 3 x^{\frac{1}{3}} + 7 x

Add a constant to the solution

= 2 x^{\frac{3}{2}} - 3 x^{\frac{1}{3}} + 7 x + C

What is the integral of (3x^{1/2}-x^{(-2)/3}+7) ?
The integral of (3x^{1/2}-x^{(-2)/3}+7) is 2x^{3/2}-3x^{1/3}+7x+C