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can ANYONE solve this integral?

flood

Diamond Member
Oct 17, 1999
4,213
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integral of e ot the power of t spuared times e to the power of t
it looks like:
S(e^(t^2)) (e^t) dt
S representing the integral sign

I need to get it down to something with no integrals.
 

flood

Diamond Member
Oct 17, 1999
4,213
0
0
Integration by parts is the idela way to do this, but I've done it several times and it still hasnt worked.

The method that I tried to use is:
S(e garbage) = stuff - S(e garbage)

2(S(e garbage) ) = stuff

S(e garbage) = (1/2) stuff

but what happens is you have to do partial integration twice, and so the "S(e garbage)" comes out to be positive on the right side.
 

DAM

Diamond Member
Jan 10, 2000
6,102
1
76
u = e^t

du = e^t dt


replace your substitution


new problem is S u^2 du


i hope you know how to do that problem




dam()
 

flood

Diamond Member
Oct 17, 1999
4,213
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DAM-

that would work if it was
[e^t]^2

but its e^(t^2)

which can be rewritten as [e^t]^t
hmm... havent look at it that way before
 

flood

Diamond Member
Oct 17, 1999
4,213
0
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Gatsby-
the integrator gave me a real messy answer with "Erfi" in it
I have no idea what "Erfi" means
 

DAM

Diamond Member
Jan 10, 2000
6,102
1
76
u = e^t^2
du = 2te^t^2

v = e^t
dv = e^tdt

the integral becomes: (e^t^2)(e^t) - S (e^t)(2e^t^2)dt

which can be written as: (e^t^2)(e^t) - 2S (e^t^3)dt


then use u subs

u = t
du = dt

integral becomes: (e^u^2)(e^u) - 2S (e^u^3)dt

and just take the derivative of (e^u^2)




dam()




(e^u^2)(e^u) - 2S (e^u)(e^u^
 

flood

Diamond Member
Oct 17, 1999
4,213
0
0
DAM-
how'd you get from u = e^t^2 to du = 2t3^t^2 ?

derivitive of u = (e^t^2) 2t dt
 

flood

Diamond Member
Oct 17, 1999
4,213
0
0
DAM-
you selected a u and a v
what youre supposed to do is select a u and a dv
 

DAM

Diamond Member
Jan 10, 2000
6,102
1
76
you selected a u and a v
what youre supposed to do is select a u and a dv



i posted this:

u = e^t^2
du = 2te^t^2

v = e^t
dv = e^tdt


original problem:

S(e^(t^2)) (e^t) dt


now what do you mind asking again your question cause i dont understand?




dam()



 

perry

Diamond Member
Apr 7, 2000
4,018
1
0
And it'll probably require multiple integration by parts or integration by parts and a substitution if you can figure it out.

First integration by parts:
dv = e^t u = e^[t^2]
v = e^t du = 2*t*e[t^2]

So:
e^[t^2] * e^t - S(e^t * 2 * t * e^[t^2] dt) =
e^[t^2] * e^t - 2 * S(t * e^[t^2 + t] dt)

Second starts to get really messy, which is why I think you need substitution. I worked the second out, but it won't help too much. Gots ta get back to my own work..

Edit: That's probably wrong, but who knows. I haven't take a math course in a while.
 

flood

Diamond Member
Oct 17, 1999
4,213
0
0
when you do integration by parts, you take the integral you start with
and break it into two pieces: a u and a dv
you take the derivitive of u to get your du
you take the integral of dv to get v
you do no select v or du
you get those from the other parts. you select only the u and dv.

when you did:
u = e^t^2
du = 2te^t^2

v = e^t
dv = e^tdt

you choose the parts of the original problem to be u and v
(or u and dv)
 

hendon

Senior member
Oct 9, 2000
373
0
0
The integral cannot be done by hand, in particular, the integral of e^(t^2) dt cannot be formed from any of the elementary functions that we know.

Using the integrator that was mentioned earlier in the thread, I think you get something involving an 'erfi'...
check out this website for the definition... some complex stuff :p

http://mathworld.wolfram.com/Erfi.html
 

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