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

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

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integral of 1/(x^5)+1

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

- \frac{1}{4 x ^{4}} + x + C

Solution steps

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

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

\int 1 d x = x

= - \frac{1}{4 x ^{4}} + x

Add a constant to the solution

= - \frac{1}{4 x ^{4}} + x + C

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