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

The integral of (2/(sqrt(x))+(sqrt(x))/2) is 4sqrt(x)+1/3 x^{3/2}+C

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integral of (2/(sqrt(x))+(sqrt(x))/2)

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

4 x + \frac{1}{3} x^{\frac{3}{2}} + C

Solution steps

\int \frac{2}{x} + \frac{x}{2} 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{2}{x} d x + \int \frac{x}{2} d x

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

\int \frac{x}{2} d x = \frac{1}{3} x^{\frac{3}{2}}

= 4 x + \frac{1}{3} x^{\frac{3}{2}}

Add a constant to the solution

= 4 x + \frac{1}{3} x^{\frac{3}{2}} + C

\int \frac{( 4 + 3 x ^{2} )}{x ^{3}} d x

x \to 16 lim (x)

\frac{\partial}{\partial x} (sin (\frac{1}{1 + y}))

\int_{0}^{4 - x^{2}} x^{2} y d y

\frac{\partial}{\partial x} (x + 5 y)

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