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

The integral of (x^2-2)/(sqrt(x)) is 2/5 x^{5/2}-4sqrt(x)+C

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integral of (x^2-2)/(sqrt(x))

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

\frac{2}{5} x^{\frac{5}{2}} - 4 x + C

Solution steps

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

Expand

\frac{x ^{2} - 2}{x} : x^{\frac{3}{2}} - \frac{2}{x}

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

\int x^{\frac{3}{2}} d x = \frac{2}{5} x^{\frac{5}{2}}

\int \frac{2}{x} d x = 4 x

= \frac{2}{5} x^{\frac{5}{2}} - 4 x

Add a constant to the solution

= \frac{2}{5} x^{\frac{5}{2}} - 4 x + C

\frac{150000}{( 4 x + 75 ) ^{2}}

π^{7} + 3 x

(x + 1)^{2} (2 - x)^{2}

\frac{\partial}{\partial x} (cos^{7} (x^{4} y^{9}))

n = 1 \sum \infty (1 + \frac{1}{n})^{- n}

What is the integral of (x^2-2)/(sqrt(x)) ?
The integral of (x^2-2)/(sqrt(x)) is 2/5 x^{5/2}-4sqrt(x)+C