What is the integral of (4/x+9/(x^7)) ?

The integral of (4/x+9/(x^7)) is 4ln|x|-3/(2x^6)+C

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integral of (4/x+9/(x^7))

\int (\frac{4}{x} + \frac{9}{x ^{7}}) d x

4 ln ∣ x ∣ - \frac{3}{2 x ^{6}} + C

Solution steps

\int \frac{4}{x} + \frac{9}{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{4}{x} d x + \int \frac{9}{x ^{7}} d x

\int \frac{4}{x} d x = 4 ln ∣ x ∣

\int \frac{9}{x ^{7}} d x = - \frac{3}{2 x ^{6}}

= 4 ln ∣ x ∣ - \frac{3}{2 x ^{6}}

Add a constant to the solution

= 4 ln ∣ x ∣ - \frac{3}{2 x ^{6}} + C

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What is the integral of (4/x+9/(x^7)) ?
The integral of (4/x+9/(x^7)) is 4ln|x|-3/(2x^6)+C