I have the integral:
∫∞−∞e−x2dx
And I’d like to solve it using differentiation under the integral sign. I understand that I must convert e−x2 to e−x2g(x,t), where g(x,t) is just some term involving a new parameter t. I tried multiplying by e−2xt, which doesn’t really seem very logical, however, I just do not know what to put. How do I find the appropriate term to make the whole process work?
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