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

\int - cos (x) (2 x + 1) d x

\frac{d}{d x} (\frac{ln ( x )}{x ^{9}})

sec (t)

x \to 0 - lim (- \frac{6}{x ^{7}})

\int 0.1 e^{- \frac{x}{10}} d x

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