# Indefinite integral of fraction? [duplicate]

How to integrate $$\int\frac{1}{x^{14}+1}dx$$ I've tried to use partial fraction decomposition but it doesn't work

• Are you sure no bounds? – jamie Apr 23 '20 at 13:38
• @jamie yep, I need to find indefinite integral of this – Limenal Apr 23 '20 at 13:40
• the indefinite integral doesn't have a closed form, however if you are integrating in the whole $\mathbb{R}$ then you can use the residue theorem to find a closed form for it value – Masacroso Apr 23 '20 at 13:40
• @Masacroso So, any "simple" methods (like from algebra) will not work? – Limenal Apr 23 '20 at 13:44

The integrand is the sum of a geometric series with common ratio $$-x^{14}$$, so your integral equals
$$\int 1 - x^{14} + x^{28} - x^{42} + \cdots \; dx$$
$$= x - \frac{x^{15}}{15} + \frac{x^{29}}{29} - \cdots.$$