What is the integral of (7/x-5/(x^6)) ?

The integral of (7/x-5/(x^6)) is 7ln|x|+1/(x^5)+C

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integral of (7/x-5/(x^6))

\int (\frac{7}{x} - \frac{5}{x ^{6}}) d x

7 ln ∣ x ∣ + \frac{1}{x ^{5}} + C

Solution steps

\int \frac{7}{x} - \frac{5}{x ^{6}} 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{7}{x} d x - \int \frac{5}{x ^{6}} d x

\int \frac{7}{x} d x = 7 ln ∣ x ∣

\int \frac{5}{x ^{6}} d x = - \frac{1}{x ^{5}}

= 7 ln ∣ x ∣ - (- \frac{1}{x ^{5}})

Simplify

= 7 ln ∣ x ∣ + \frac{1}{x ^{5}}

Add a constant to the solution

= 7 ln ∣ x ∣ + \frac{1}{x ^{5}} + C

What is the integral of (7/x-5/(x^6)) ?
The integral of (7/x-5/(x^6)) is 7ln|x|+1/(x^5)+C