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

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

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

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

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

Solution steps

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

Expand

\frac{2 - x}{x ^{2}} : \frac{2}{x ^{2}} - \frac{1}{x ^{\frac{3}{2}}}

= \int \frac{2}{x ^{2}} - \frac{1}{x ^{\frac{3}{2}}} 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{2}{x ^{2}} d x - \int \frac{1}{x ^{\frac{3}{2}}} d x

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

\int \frac{1}{x ^{\frac{3}{2}}} d x = - \frac{2}{x}

= - \frac{2}{x} - (- \frac{2}{x})

Simplify

= - \frac{2}{x} + \frac{2}{x}

Add a constant to the solution

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

\frac{d}{d y} ((x^{2} + y^{2} + z^{2})^{- \frac{1}{2}})

\int 54 - 18 z - 6 z^{2} + 2 z^{3} d z

\int_{0}^{1} 2 x 5^{x} d x

v^{\frac{3}{2}} (v + c e^{x})

(y + x cos^{2} (\frac{y}{x})) d x - x d y = 0

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