What is the integral of (5x+sqrt(3x))/(x^2) ?

The integral of (5x+sqrt(3x))/(x^2) is 5ln|x|-(2sqrt(3))/(sqrt(x))+C

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integral of (5x+sqrt(3x))/(x^2)

\int \frac{5 x + 3 x}{x ^{2}} d x

5 ln ∣ x ∣ - \frac{2 3}{x} + C

Solution steps

\int \frac{5 x + 3 x}{x ^{2}} d x

Expand

\frac{5 x + 3 x}{x ^{2}} : \frac{5}{x} + \frac{3}{x ^{3}}

= \int \frac{5}{x} + \frac{3}{x ^{3}} 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{5}{x} d x + \int \frac{3}{x ^{3}} d x

\int \frac{5}{x} d x = 5 ln ∣ x ∣

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

= 5 ln ∣ x ∣ - \frac{2 3}{x}

Add a constant to the solution

= 5 ln ∣ x ∣ - \frac{2 3}{x} + C

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What is the integral of (5x+sqrt(3x))/(x^2) ?
The integral of (5x+sqrt(3x))/(x^2) is 5ln|x|-(2sqrt(3))/(sqrt(x))+C