So, me and my friends are still thinking about this one:
Evaluate ∫(1/(1+x^5))dx.
Note that –1 = –1(cos0°+i sin0°)
∴the roots of the equation x^5+1 = 0 are
(–1)^(1/5) (cos((0°+360k°)/5)+i sin((0°+360k°)/5)) , where k = 0, 1, 2, 3, 4
= –1(cos0°+i sin0°) , –1(cos72°+i...