What is the integral of sqrt(x)+1/(2sqrt(x)) ?

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

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integral of sqrt(x)+1/(2sqrt(x))

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

\frac{d y}{d x} = (x - 5) e^{- 2 y}

\frac{d}{d x} (- 2 tan (2 x))

x \to 2 lim (\frac{x ^{2} + 3}{\frac{1}{x}})

\frac{d y}{d t} = \frac{t e ^{t}}{y 4 + y ^{2}}

f (x) = \frac{e ^{x} + 1}{e ^{x} - 1}

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