What is the integral of 10-1.5x^{1/2} ?

The integral of 10-1.5x^{1/2} is 10x-x^{3/2}+C

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integral of 10-1.5x^{1/2}

\int 10 - 1.5 x^{\frac{1}{2}} d x

10 x - x^{\frac{3}{2}} + C

Solution steps

\int 10 - 1.5 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 10 d x - \int 1.5 x^{\frac{1}{2}} d x

\int 10 d x = 10 x

\int 1.5 x^{\frac{1}{2}} d x = x^{\frac{3}{2}}

= 10 x - x^{\frac{3}{2}}

Add a constant to the solution

= 10 x - x^{\frac{3}{2}} + C

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What is the integral of 10-1.5x^{1/2} ?
The integral of 10-1.5x^{1/2} is 10x-x^{3/2}+C