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I don't know how to start and solve this integral. Can you help me? $$\int \dfrac{dx}{1+x^{7}}$$

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    Using [this search](https://approach0.xyz/search/?q=%24%5Cint%20%5Cdfrac%7Bdx%7D%7B1%2Bx%5E%7B7%7D%7D%24&p=1) or [this search](https://approach0.xyz/search/?q=%24%5Cint%20%5Cdfrac%7B1%7D%7B1%2Bx%5E%7B7%7D%7D%20dx%24&p=1) in Approach0 you can find a few similar question which might help you with this one. For example, [Evaluate the integral $\int \frac{dx}{1+x^5}$](http://math.stackexchange.com/q/2014388). – 2017-01-14

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Start by partial fraction decomposition (e.g. https://en.wikipedia.org/wiki/Partial_fraction_decomposition).

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    How do you propose to factor...? – 2017-01-13
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    Just can just write done the seven seventh roots of $-1$ explicit, e.g. using Eulers formula. – 2017-01-13
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    And the result is logarithms of complex numbers. IMO, very inelegant. (pst, see the comment above on the main post) – 2017-01-13
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    @SimpleArt Probably means a comment linking to [Evaluate $\int\frac1{1+x^n}dx$ for $n\in\mathbb R$](http://math.stackexchange.com/q/1999869). (It was added automatically with a vote to close as a duplicate and it was removed after [the question was closed](http://math.stackexchange.com/posts/2096666/revisions).) – 2017-01-14