Question Number 148567 by mathmax by abdo last updated on 29/Jul/21

find ∫_0 ^∞ ((x^2 logx)/((x^2 +1)^3 ))dx

Answered by Ar Brandon last updated on 29/Jul/21

Ω=∫_0 ^∞ ((x^2 logx)/((x^2 +1)^3 ))dx =∫_0 ^1 ((x^2 logx)/((x^2 +1)^3 ))dx+∫_1 ^∞ ((x^2 logx)/((x^2 +1)^3 ))dx =∫_0 ^1 ((x^2 logx)/((x^2 +1)^3 ))dx−∫_0 ^1 ((x^2 logx)/((x^2 +1)^3 ))dx=0