What is the integral of (4x-3)/(sqrt(x)) ?

The integral of (4x-3)/(sqrt(x)) is 8/3 x^{3/2}-6sqrt(x)+C

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integral of (4x-3)/(sqrt(x))

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

\frac{8}{3} x^{\frac{3}{2}} - 6 x + C

Solution steps

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

Expand

\frac{4 x - 3}{x} : 4 x - \frac{3}{x}

= \int 4 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 4 x d x - \int \frac{3}{x} d x

\int 4 x d x = \frac{8}{3} x^{\frac{3}{2}}

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

= \frac{8}{3} x^{\frac{3}{2}} - 6 x

Add a constant to the solution

= \frac{8}{3} x^{\frac{3}{2}} - 6 x + C

y = ln (5 + 2 x + x^{3})

\int \frac{1}{cos ^{2} ( a y )} d y

\frac{\partial}{\partial x} (8 x^{2} + y^{2} - 9 y)

f (x) = x^{2} + 3 x + 1, at x = 4

x \to 0 lim (ln (0))

What is the integral of (4x-3)/(sqrt(x)) ?
The integral of (4x-3)/(sqrt(x)) is 8/3 x^{3/2}-6sqrt(x)+C