2006-06-18 08:45:45 · 9 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
What?
If u=x^x
du/u=(1+ln(x))dx
Interal exp(x^x)dx=integral exp(u)du
Analytical solution for this indefinite integral is dificult.
2006-06-18 08:57:04 · answer #1 · answered by Edward 7 · 0⤊ 0⤋
mathematician is right: It can't be written as an elementary function.
As this maybe seems to be a big problem, it isn't. Remember exp(x) is just an abbreviation for something complicated like sum over (-1)^n x^n/n!. You can of course integrate that sum term by term and get a infinite sum for your integral. Give that a appropriate name and call it an "elementary function" and the problem sounds harmless.
Of course you have to think about things like convergence of the resulting sum, but you silently assume that when you integrate elementary functions.
2006-06-18 18:11:24 · answer #2 · answered by Wonko der Verständige 5 · 0⤊ 0⤋
x^x is a real function for x>0 and a definite integral involving two positive integration limits for x exists. Same is true for exp(x^x).
However, x^x is a complex spiral for x<0, and a definite integral involving real integration limits for x<0 does not exist. exp(x^x) fails the same test for the same reason.
2006-06-18 21:44:17 · answer #3 · answered by none2perdy 4 · 0⤊ 0⤋
This is a continuous function, so there is an answer, but unfortunately I cannot find it using standard integration techniques. So you have to go to numerical methods. But you have to give me the limits. There are two methods I know, called 'Trapozoidal rule' and 'Siemens rule'. But those are approximations, but well accurate. There may be more numerical methods. Calculators and Computers use numerical methods, so you will see you'll get the answer in famous casio fx991ms calculator for above integration if given with limits...
2006-06-19 05:20:13 · answer #4 · answered by Azmil M. 2 · 0⤊ 0⤋
It probably can't be done in terms of elementary functions.
2006-06-18 15:57:58 · answer #5 · answered by musiclover 5 · 0⤊ 0⤋
This won't be possible in terms of elementary functions.
2006-06-18 16:48:33 · answer #6 · answered by mathematician 7 · 0⤊ 0⤋
int e^x dx = ex
int e^2x dx = 1/2e2x
2006-06-18 17:38:42 · answer #7 · answered by i want to talk 2 · 0⤊ 0⤋
http://answers.yahoo.com/question/index;_ylt=AlGU2aCUSyBUM1HAQQImTMbsy6IX?qid=1006052508880
I don't agree with the answer that was chosen, but you can look at what others have put down.
2006-06-19 16:12:35 · answer #8 · answered by Anonymous · 0⤊ 0⤋
Mathematica can't do it. It probably doesn't exist.
2006-06-18 16:12:12 · answer #9 · answered by blahb31 6 · 0⤊ 0⤋