What is the integral of (5/x+(12)/(x^5)) ?

The integral of (5/x+(12)/(x^5)) is 5ln|x|-3/(x^4)+C

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integral of (5/x+(12)/(x^5))

\int (\frac{5}{x} + \frac{12}{x ^{5}}) d x

5 ln ∣ x ∣ - \frac{3}{x ^{4}} + C

Solution steps

\int \frac{5}{x} + \frac{12}{x ^{5}} 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{12}{x ^{5}} d x

\int \frac{5}{x} d x = 5 ln ∣ x ∣

\int \frac{12}{x ^{5}} d x = - \frac{3}{x ^{4}}

= 5 ln ∣ x ∣ - \frac{3}{x ^{4}}

Add a constant to the solution

= 5 ln ∣ x ∣ - \frac{3}{x ^{4}} + C

What is the integral of (5/x+(12)/(x^5)) ?
The integral of (5/x+(12)/(x^5)) is 5ln|x|-3/(x^4)+C