[微積] 一題看起來像微積分卻考在ODE的題目

[bjiyxo (若自礌)]

Integral from 0 to Infinity[e^(-t^2-9/t^2)]dt
他給的hint是令I(x)=Integral from 0 to Infinity[e^(-t^2-x^2/t^2)]dt
and find I'(x). Integral from 0 to Infinity[e^(-t^2)]dt=(pi^0.5)/2

請問大家會怎麼去解這一題呢?

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