What is the integral of ((x^3-2sqrt(x))/x) ?

The integral of ((x^3-2sqrt(x))/x) is (x^3)/3-4sqrt(x)+C

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integral of ((x^3-2sqrt(x))/x)

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

\frac{x ^{3}}{3} - 4 x + C

Solution steps

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

Expand

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

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

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

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

= \frac{x ^{3}}{3} - 4 x

Add a constant to the solution

= \frac{x ^{3}}{3} - 4 x + C

y = - \frac{1}{2 x ^{3}}, (2, - \frac{1}{16})

x \to 0 lim (2 x ln (1 - x^{2}))

\frac{d}{d x} (\frac{3 x + 6}{2 x + 3})

y^{^{''}} + 80 y^{^{'}} + 1200 y = 0

\frac{\partial}{\partial x} (4 cos (3 x))

What is the integral of ((x^3-2sqrt(x))/x) ?
The integral of ((x^3-2sqrt(x))/x) is (x^3)/3-4sqrt(x)+C