Integrating Exponential Functions - Solving by Parts

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To integrate the function (x^2)e^(-2a(x^2)), integration by parts is suggested as a viable method. The proposed approach involves setting u = x and dv = xe^(-2a(x^2))dx, allowing for a more manageable integration of dv. This substitution facilitates the use of ordinary integration techniques, such as substitution, to solve for v. The discussion emphasizes the flexibility in choosing u and dv to simplify the integration process. Overall, integration by parts is confirmed as an effective strategy for this problem.
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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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