how do you show that intergrate from o to infinity of exp (-r^2) over (r^4 + a^4) is less than pi over ( (2)^(0.5) a^3)
given that integrate from o to infinity of 1/ (x^2 +a^2 ) dx is pi over (2a)
Since whenever r>0, it follows that . Substitute r=ax into that second integral to see that it is equal to . The integral can be evaluated (by contour integration, or by partial fractions), and it is equal to .
Putting that all together, you get . That is better than what was asked for, because it has an extra 2 in the denominator. But I don't see any way of getting this result by using the given hint about .