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{d ^{2}}{d x ^{2}} (\frac{3 x - 2}{2 x + 5})

θ \to 0 lim (\frac{sin ( θ )}{θ})

\frac{d}{d x} (ln (x + 10))

\int 12 t (3 t^{2} - 1)^{3} d t

e^{- 3 x} + e^{4 x}

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