Integrating Exponential Functions - Solving by Parts

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SUMMARY

The discussion focuses on integrating the function (x^2)e^(-2a(x^2)) using integration by parts. Participants suggest using the integration by parts formula |udv = uv - |vdu, with the initial choice of u = x^2 and dv = e^(-2a(x^2)). However, a more effective approach is proposed, setting u = x and dv = xe^(-2ax^2)dx, which allows for a simpler integration through substitution. This method provides a clearer path to solving the integral.

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forty
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(x^2).e^(-2a(x^2))

how would i integrate this? By parts?

If so using |udv = uv - |vdu (hope that's right)

would i let u = x^2 and dv = e^(-2a(x^2)) ?

but how do I integrate dv = e^(-2a(x^2)) to find v ?

any help appreciated :)
 
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I think that integration by parts is the way to go, but there's more than one way to divide things up in this problem.

Try it this way:
u = x, dv = xe-2ax2dx

Now you have a dv that you have a hope of integrating (using an ordinary substitution).
 

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