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

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

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

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

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

Solution steps

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

Expand

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

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

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

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

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

Add a constant to the solution

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

\frac{d}{d t} (\frac{2 2}{3} t^{\frac{3}{2}})

x \to 0 + lim (\frac{x}{x})

f (x) = e^{3 x + 2}

\int \frac{1}{x ( ln ( x ) - 1 )} d x

\int (4 - 3 x)^{2} d x

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