What is the integral of 2/(x^5)+1/x ?

The integral of 2/(x^5)+1/x is -1/(2x^4)+ln|x|+C

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integral of 2/(x^5)+1/x

\int \frac{2}{x ^{5}} + \frac{1}{x} d x

- \frac{1}{2 x ^{4}} + ln ∣ x ∣ + C

Solution steps

\int \frac{2}{x ^{5}} + \frac{1}{x} 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{2}{x ^{5}} d x + \int \frac{1}{x} d x

\int \frac{2}{x ^{5}} d x = - \frac{1}{2 x ^{4}}

\int \frac{1}{x} d x = ln ∣ x ∣

= - \frac{1}{2 x ^{4}} + ln ∣ x ∣

Add a constant to the solution

= - \frac{1}{2 x ^{4}} + ln ∣ x ∣ + C

\int \frac{cos ( 6 x )}{cos ^{2} ( 3 x )} d x

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What is the integral of 2/(x^5)+1/x ?
The integral of 2/(x^5)+1/x is -1/(2x^4)+ln|x|+C