How can integration by parts simplify this integral?

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The integral from r to R of e^(-2r/a)*r^2 dr can be simplified using integration by parts twice. By setting u = r^2 and dv = e^(-2r/a) dr, the first integration yields a new integral involving e^(-2r/a). The second application of integration by parts will further simplify the integral to one that only includes e^(-2r/a). Attention to signs and integration limits is crucial throughout the process. This method effectively streamlines the calculation of the integral.
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from r to R e^(-2r/a)*r^2 dr

Thanks
 
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starbaj12 said:
from r to R e^(-2r/a)*r^2 dr

Thanks

U're one lazy dude... Two times part integration,pay attention to signs and integration limits.
Daniel.
 
Looks pretty standard to me.

Use "integration by parts", twice.

If you let u= r2 and dv= e-2r/a, then du= 2r dr and
v= -a/2 e-2r/a

Now you have an integral of e-2r/ar and integrating by parts again will give you an integral with just e-2r/a.
 

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