Question

Evaluate \[\int\limits_{0}^{∞}(1+x^2)^2e^{-x} dx\] in terms of the gamma function

Answer 1

expand \[(1+x^2)^2\]

get ...

\[\Gamma(1)+2\Gamma(3)+\Gamma(5)=29\]

Answer 2

brilliant

Answer 3

Evaluate \[\int\limits_{0}^{1} [{1-x^2 \over 1+x^2}]^{1/2} dx\] in terms of the gamma function