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Posted: 3/9/2013 3:45:43 AM EDT
[#1]
I have a project on patterns in integration:
I have to prove a general equation for the integral of (x^n)(e^x) dx Feel like giving it a shot? |
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Posted: 3/9/2013 4:01:52 AM EDT
[#2]
¦xnex =xnex-ex(xn-1/n-1)+ex(xn-2/n-2)-ex(xn-3/n-3).....
So to sum, I you use a -12 term to get the alternating plus minus. |
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Posted: 3/9/2013 4:40:01 AM EDT
[#3]
I don't see where your denominators are coming from. Using integration by parts (reduction formula) they shouldn't be there.
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Posted: 3/9/2013 9:15:40 AM EDT
[#4]
Quoted:
I don't see where your denominators are coming from. Using integration by parts (reduction formula) they shouldn't be there. maybe he meant multiply instead of divide After 2 integrations int(x^n*e^x)=x^n*e^x-nx^(n-1)*e^x+int(n-1)x^(n-2)e^xdx) basically, you need to do enough integrations to find yourself a pattern. Then see what happens when you've subtracted n-1 from n (i.e. you have x^(n-(n-1)) finally in your 2nd to last integral) so that you can see how it ends. Then write it in sum form. |
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Posted: 3/10/2013 5:10:59 AM EDT
[#5]
Quoted:
int(x^n*e^x)=x^n*e^x-nx^(n-1)*e^x+int(n-1)x^(n-2)e^xdx) That's what I got. |
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