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

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

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

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

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

Solution steps

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

Expand

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

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

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

\int \frac{2}{x} d x = 4 x

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

Add a constant to the solution

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

\frac{1}{( s ) ( s + 2 ) ( s + 3 )}

y^{^{'}} = \frac{e ^{x - y}}{1 + e ^{x}}, y (1) = 0

y = \frac{6 x ^{2} + 2 x + 8}{x}

\int \frac{1 + sin ( x )}{cos ( x )} d x

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