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

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

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

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

3 ln ∣ x ∣ - \frac{5}{x} + C

Solution steps

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

\int \frac{3}{x} d x = 3 ln ∣ x ∣

\int \frac{5}{x ^{2}} d x = - \frac{5}{x}

= 3 ln ∣ x ∣ - \frac{5}{x}

Add a constant to the solution

= 3 ln ∣ x ∣ - \frac{5}{x} + C

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