Problem: Calculate the integral
Feynman’s method: Solve the following equation for $t$
and calculate $I(0)$.
The trick here is to differentiate $I(t)$ under the integral sign and solve the differential equation.
And here is the differential equation for $I(t)$
which can be solved by integration, using the substitution method.
We can find the constant $C$ by computing $I(+\infty)$
The final solution for $I(t)$ is
We can now calculate the original integral