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

x \to \frac{π}{2} lim (\frac{csc ( 4 x )}{csc ( 2 x )})

f (x) = \frac{2 x - 1}{x + 5}, at x = 1

x \to - \infty lim (\frac{4 x ^{6}}{x ^{3} - 8})

θ \to \frac{π}{3} lim (\frac{tan ( θ )}{sin ^{2} ( θ )})

\int \frac{x ^{2}}{( x + 1 ) ^{50}} d x

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