i have to integrate (ln x)(ln x)/ e^5t [in a variation of parameters problem] and have looked everywhere to see if Ln x multiplied by itself can be shortened to something like ln x^2 or some other reasonable thing but can't find such a rule anywhere. do i have to do this the long way with integration by parts? not even sure what to do with three things in integration by parts.
nicksauce
Aug3-08, 02:48 PM
Is it e^5t or e^5x?. If it's the latter I don't believe there's a closed form solution, but if it's the former, then it's more doable.
Let u = lnx, du= dx/x, dv=lnxdx, v = xlnx - x (Verify this by IBP). Then all the integrals are doable.
And yes, there are no identities to simplify ln(x)^2.
eagleswings
Aug3-08, 04:28 PM
yes actually it is e^5x. all the t's that go into the integral have to change to x. but perhaps i can start with what you gave me - thanks!
nicksauce
Aug3-08, 05:05 PM
You can see what the integral is here
http://integrals.wolfram.com/index.jsp?expr=ln(x)*ln(x)*exp(-5x)&random=false
But it's not very pretty.
eagleswings
Aug8-08, 07:54 PM
man, i can'te even read that one. it's got symbols i haven't seen used, maybe they are just variables, but unusual ones. maybe i learn that next year! sigh.