let-j-e-i2pi-3-and-P-x-1-jx-n-1-jx-n-with-n-integr-natural-1-find-roots-of-P-x-2-factorize-P-x-inside-C-x-3-calculate-0-1-P-x-dx-4-decompose-inside-C-x-the-fraction-F-x-1-

Question Number 52449 by maxmathsup by imad last updated on 07/Jan/19

l e t j = e^{\frac{i 2 π}{3}} a n d P (x) = {(1 + j x)}^{n} - {(1 - j x)}^{n} w i t h n i n t e g r n a t u r a l

1) f i n d r o o t s o f P (x)

2) f a c t o r i z e P (x) i n s i d e C [x]

3) c a l c u l a t e \int_{0}^{1} P (x) d x .

4) d e c o m p o s e i n s i d e C (x) t h e f r a c t i o n F (x) = \frac{1}{P (x)}