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

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

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

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

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

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

\frac{d}{d x} (5 x e^{- x})

\int_{- 4}^{- 1} - \frac{4}{x ^{3}} d x

y^{^{'}} + 3 y = e^{t}

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