How can I integrate (x^2)(e^x)Sinx dx efficiently?

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To integrate (x^2)(e^x)Sinx dx efficiently, the recommended approach is to use integration by parts, specifically differentiating x^2. The process involves performing four partial integrations, which can be complex but manageable. Some participants express frustration over the lack of a shorter method for this integration. Despite the challenges, the consensus is that the integration can be completed with practice. Overall, the discussion emphasizes the necessity of multiple integration steps to solve the problem.
Yegor
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I have no idea. How to integrate
(x^2)(e^x)Sinx dx ?
 
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It's fairly simple, I can think of a couple of ways to do it off the top of my head but I would suggest using by-parts and differentiating x^2 out as the most obvious.
 
There are 4 partial integrations that need to be done in all...They're not difficult,but anyway,if you ran into trouble,please complain.

Daniel.
 
I have ran through it. I just expected that i don't see shorter way. I didn't wanted to have such a practise in partial intregration. There really are 4 several integrations (some of them many times). thank You all!
 

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