What is the integral of (5/x-3/(x^4)) ?

The integral of (5/x-3/(x^4)) is 5ln|x|+1/(x^3)+C

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integral of (5/x-3/(x^4))

\int (\frac{5}{x} - \frac{3}{x ^{4}}) d x

5 ln ∣ x ∣ + \frac{1}{x ^{3}} + C

Solution steps

\int \frac{5}{x} - \frac{3}{x ^{4}} 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} d x - \int \frac{3}{x ^{4}} d x

\int \frac{5}{x} d x = 5 ln ∣ x ∣

\int \frac{3}{x ^{4}} d x = - \frac{1}{x ^{3}}

= 5 ln ∣ x ∣ - (- \frac{1}{x ^{3}})

Simplify

= 5 ln ∣ x ∣ + \frac{1}{x ^{3}}

Add a constant to the solution

= 5 ln ∣ x ∣ + \frac{1}{x ^{3}} + C

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What is the integral of (5/x-3/(x^4)) ?
The integral of (5/x-3/(x^4)) is 5ln|x|+1/(x^3)+C