What is the integral of (9/x-4/(x^3)) ?

The integral of (9/x-4/(x^3)) is 9ln|x|+2/(x^2)+C

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integral of (9/x-4/(x^3))

\int (\frac{9}{x} - \frac{4}{x ^{3}}) d x

9 ln ∣ x ∣ + \frac{2}{x ^{2}} + C

Solution steps

\int \frac{9}{x} - \frac{4}{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{9}{x} d x - \int \frac{4}{x ^{3}} d x

\int \frac{9}{x} d x = 9 ln ∣ x ∣

\int \frac{4}{x ^{3}} d x = - \frac{2}{x ^{2}}

= 9 ln ∣ x ∣ - (- \frac{2}{x ^{2}})

Simplify

= 9 ln ∣ x ∣ + \frac{2}{x ^{2}}

Add a constant to the solution

= 9 ln ∣ x ∣ + \frac{2}{x ^{2}} + C

What is the integral of (9/x-4/(x^3)) ?
The integral of (9/x-4/(x^3)) is 9ln|x|+2/(x^2)+C