When integrating by parts (formula:http://imgur.com/ayjjQ)
How do you decide which is the correct choice for u and which is the correct choice for dv?

Question

When integrating by parts (formula:http://imgur.com/ayjjQ) 
How do you decide which is the correct choice for u and which is the correct choice for dv?

anonymous · Answer

Here's an example problem: $$\int\limits_{}^{}e ^{2x}sinx dx$$

zarkon · Answer

experience is a big help :)

I usually try to get rid of logs  (U=log  gets rid of them)

and I try to reduce polynomials

zarkon · Answer

that one requires parts twice...it doesn't matter the order you do it

u=e^{2x} or u=sin(x) will both work

anonymous · Answer

So... guess until you start to get some intuition?

zarkon · Answer

well...not totally.  The two examples I mentions are a good place to start.

if after you do parts once and the problem looks more complicated than the original the n try the other way

anonymous · Answer

oh, ok thaanks. ou can use either choice for dv and u on all problem or only some?

zarkon · Answer

sure...though one way might lead to a simple solution and the other could be in infinite regression into madness  ;)

zarkon · Answer

for example

$$\int x\sin(x)dx$$

$$u=x$$ will lead to a simple solution

$$u=\sin(x)$$ will take you further away from the solution