What is the integral of sqrt(x)+1/(sqrt(x)) ?

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

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integral of sqrt(x)+1/(sqrt(x))

\int x + \frac{1}{x} d x

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

Solution steps

\int x + \frac{1}{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 x d x + \int \frac{1}{x} d x

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

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

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

Add a constant to the solution

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

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

(0, 2), (4, - 2)

\frac{x}{x ^{2} - 6}

\int \frac{1}{16 sin ^{2} ( x )} d x

81 y^{^{''}} + 18 y^{^{'}} + y = 0

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