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

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

\int \frac{ln ^{8} ( z )}{z} d z

\int (3 x^{2} ln (4 x) + x^{2}) d x

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

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

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