What is the integral of (3x-5)/(sqrt(x)) ?

The integral of (3x-5)/(sqrt(x)) is 2x^{3/2}-10sqrt(x)+C

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integral of (3x-5)/(sqrt(x))

\int \frac{3 x - 5}{x} d x

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

Solution steps

\int \frac{3 x - 5}{x} d x

Expand

\frac{3 x - 5}{x} : 3 x - \frac{5}{x}

= \int 3 x - \frac{5}{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{5}{x} d x

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

\int \frac{5}{x} d x = 10 x

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

Add a constant to the solution

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

\frac{d y}{d x} = 0.72 - \frac{9 y}{1000}, y (0) = 80

\int_{- 1}^{1} x (x^{2} + 9)^{3} d x

y \frac{d y}{d x} + 8 x^{3} = 4

\int_{0}^{3} \frac{2 x - 1}{x + 1} d x

What is the integral of (3x-5)/(sqrt(x)) ?
The integral of (3x-5)/(sqrt(x)) is 2x^{3/2}-10sqrt(x)+C