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

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

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

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

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