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#1




Integration by parts shortcut
I need to integrate x^4*e^(2x)....any suggestions?

#2




Tabular integration by parts. Here's how it works: Write down the derivatives of alongside the antiderivatives of :
Now form the alternating sum of the products of the k(th) entry in the first column with the (k+1)th entry in the second column until such products are not possible: which in turn simplifies to . This is the required antiderivative. 
#3




What he said.

#6




Tabular integration is sometimes taught at the AP Calculus BC level, and is mentioned in the Wikipedia entry on integration by parts. It is merely a bookkeeping method for a recursive integration. (Bookkeeping, by the way, is one of the few words which have three consecutive double letter pairs.) Thus the method is valid for any integrand that is the product of two functions, one of which has an n(th) derivative that is zero, and the other has n successive antiderivatives.
Incidentally, this is a method by which one can easily prove the formula for the CDF of a gamma distribution. 
#7




Quote:
(it's probably been done before, but we're undergrads, and it's good practice ). 
#10




Isnt that tabular method just a more organized way of doing nested uvint(vdu) over and over again until du is 1?

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