What is the integral of (3x-2sqrt(x))/(sqrt(x)) ?

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

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integral of (3x-2sqrt(x))/(sqrt(x))

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

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

Solution steps

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

Simplify

\frac{3 x - 2 x}{x} : 3 x - 2

= \int 3 x - 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 d x - \int 2 d x

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

\int 2 d x = 2 x

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

Add a constant to the solution

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

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