Question

1/(x+x²)dx(1,+∞)是发散还是收敛？

Answer 1

∫<1, +∞>[1/(x+x²)]dx = ∫<1, +∞>[1/x-1/(1+x)]dx
= ln[x/(x+1)]<1, +∞> = lim<x→+∞>ln[x/(x+1)] + ln2
= 0 + ln2 = ln2 , 积分收敛。

Answer 2

0<1/(x+x^2)<1/x^2，而1/x^2收敛，所以原来积分收敛