What is the integral of (8/x-5/(x^2)+6/(x^3)) ?

The integral of (8/x-5/(x^2)+6/(x^3)) is 8ln|x|+5/x-3/(x^2)+C

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integral of (8/x-5/(x^2)+6/(x^3))

\int (\frac{8}{x} - \frac{5}{x ^{2}} + \frac{6}{x ^{3}}) d x

8 ln ∣ x ∣ + \frac{5}{x} - \frac{3}{x ^{2}} + C

Solution steps

\int \frac{8}{x} - \frac{5}{x ^{2}} + \frac{6}{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{8}{x} d x - \int \frac{5}{x ^{2}} d x + \int \frac{6}{x ^{3}} d x

\int \frac{8}{x} d x = 8 ln ∣ x ∣

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

\int \frac{6}{x ^{3}} d x = - \frac{3}{x ^{2}}

= 8 ln ∣ x ∣ - (- \frac{5}{x}) - \frac{3}{x ^{2}}

Simplify

= 8 ln ∣ x ∣ + \frac{5}{x} - \frac{3}{x ^{2}}

Add a constant to the solution

= 8 ln ∣ x ∣ + \frac{5}{x} - \frac{3}{x ^{2}} + C

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What is the integral of (8/x-5/(x^2)+6/(x^3)) ?
The integral of (8/x-5/(x^2)+6/(x^3)) is 8ln|x|+5/x-3/(x^2)+C