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

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

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

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

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

Solution steps

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

Expand

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

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

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

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

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

Add a constant to the solution

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

\int 6 + y (y + 2)^{2} d y

\frac{d}{d x} (6 x^{4} sin (x))

\frac{\partial}{\partial x} (4 x^{2} - 8 x y^{4} + 7 a y^{5} - 3)

sin (x + 1)

\frac{d}{d x} (- \frac{1}{2} cot (x))

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