What is the integral of ((6x-3)/(sqrt(x))) ?

The integral of ((6x-3)/(sqrt(x))) is 4x^{3/2}-6sqrt(x)+C

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integral of ((6x-3)/(sqrt(x)))

\int (\frac{6 x - 3}{x}) d x

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

Solution steps

\int \frac{6 x - 3}{x} d x

Expand

\frac{6 x - 3}{x} : 6 x - \frac{3}{x}

= \int 6 x - \frac{3}{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 6 x d x - \int \frac{3}{x} d x

\int 6 x d x = 4 x^{\frac{3}{2}}

\int \frac{3}{x} d x = 6 x

= 4 x^{\frac{3}{2}} - 6 x

Add a constant to the solution

= 4 x^{\frac{3}{2}} - 6 x + C

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

\int \frac{1}{x ^{\frac{3}{4}} - x ^{\frac{1}{4}}} d x

What is the integral of ((6x-3)/(sqrt(x))) ?
The integral of ((6x-3)/(sqrt(x))) is 4x^{3/2}-6sqrt(x)+C