What is the integral of 7/x+1/(3x^7) ?

The integral of 7/x+1/(3x^7) is 7ln|x|-1/(18x^6)+C

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integral of 7/x+1/(3x^7)

\int \frac{7}{x} + \frac{1}{3 x ^{7}} d x

7 ln ∣ x ∣ - \frac{1}{18 x ^{6}} + C

Solution steps

\int \frac{7}{x} + \frac{1}{3 x ^{7}} 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{1}{3 x ^{7}} d x

\int \frac{7}{x} d x = 7 ln ∣ x ∣

\int \frac{1}{3 x ^{7}} d x = - \frac{1}{18 x ^{6}}

= 7 ln ∣ x ∣ - \frac{1}{18 x ^{6}}

Add a constant to the solution

= 7 ln ∣ x ∣ - \frac{1}{18 x ^{6}} + C

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What is the integral of 7/x+1/(3x^7) ?
The integral of 7/x+1/(3x^7) is 7ln|x|-1/(18x^6)+C