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