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

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

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

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

- \frac{5}{2 x ^{2}} - \frac{5}{x} + 5 ln ∣ x ∣ + C

Solution steps

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

\int \frac{5}{x ^{3}} d x = - \frac{5}{2 x ^{2}}

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

\int \frac{5}{x} d x = 5 ln ∣ x ∣

= - \frac{5}{2 x ^{2}} - \frac{5}{x} + 5 ln ∣ x ∣

Add a constant to the solution

= - \frac{5}{2 x ^{2}} - \frac{5}{x} + 5 ln ∣ x ∣ + C

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