How to integrate $$\int\frac{1}{x^{14}+1}dx$$ I've tried to use partial fraction decomposition but it doesn't work
Asked
Active
Viewed 57 times
0
-
1Are 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 – Apr 23 '20 at 13:40
-
@Masacroso So, any "simple" methods (like from algebra) will not work? – Limenal Apr 23 '20 at 13:44
1 Answers
0
The integrand is the sum of a geometric series with common ratio $-x^{14}$, so your integral equals
$$\int 1 - x^{14} + x^{28} - x^{42} + \cdots \; dx $$
$$= x - \frac{x^{15}}{15} + \frac{x^{29}}{29} - \cdots.$$
That's probably as good as you're going to do. (Plus constant.)
B. Goddard
- 33,728