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

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

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integral of (4+sqrt(x))/(x^2)

\int \frac{4 + x}{x ^{2}} d x

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

Solution steps

\int \frac{4 + x}{x ^{2}} d x

Expand

\frac{4 + x}{x ^{2}} : \frac{4}{x ^{2}} + \frac{1}{x ^{\frac{3}{2}}}

= \int \frac{4}{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{4}{x ^{2}} d x + \int \frac{1}{x ^{\frac{3}{2}}} d x

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

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

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

Add a constant to the solution

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

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