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

The integral of (3/(sqrt(x))-(xsqrt(x))/4) is 6sqrt(x)-1/10 x^{5/2}+C

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

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

6 x - \frac{1}{10} x^{\frac{5}{2}} + C

Solution steps

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

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

\int \frac{x x}{4} d x = \frac{1}{10} x^{\frac{5}{2}}

= 6 x - \frac{1}{10} x^{\frac{5}{2}}

Add a constant to the solution

= 6 x - \frac{1}{10} x^{\frac{5}{2}} + C

z^{^{'}}

\frac{d}{d x} (y^{2} + x^{2})

x^{2} (\frac{d y}{d x}) = y - x y

y = 4 - x^{2}, (1, 2)

\frac{d y}{d x} = \frac{y}{y + x}

What is the integral of (3/(sqrt(x))-(xsqrt(x))/4) ?
The integral of (3/(sqrt(x))-(xsqrt(x))/4) is 6sqrt(x)-1/10 x^{5/2}+C