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Killer C4 integral

Im stuck on this integrals, can someone help?

1. (x^3)(e^x^2)

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Original post by Alex-Torres
Im stuck on this integrals, can someone help?

1. (x^3)(e^x^2)


IBP with u=x^2
Original post by Alex-Torres
Im stuck on this integrals, can someone help?

1. (x^3)(e^x^2)

long ass integration by parts
Reply 3
Original post by TenOfThem
IBP with u=x^2


If u= x^2, what does dv/dx equal? :s-smilie:
Original post by joeymr
If u= x^2, what does dv/dx equal? :s-smilie:


xex2xe^{x^2}
Reply 5
Original post by joeymr
If u= x^2, what does dv/dx equal? :s-smilie:


Try integration by parts, not by substitution

Edit- Just realised that you're doing it by parts and not subbing something in sorry
(edited 9 years ago)
Original post by Alex-Torres
Im stuck on this integrals, can someone help?

1. (x^3)(e^x^2)


You could always use integration by substitution, with u = x^2, because then (1/2)du = xdx, and you just have to integrate [u(e^u)]/2 du - which you then do by parts :tongue:.
(edited 9 years ago)
Reply 7
Original post by rs232
Try integration by parts, not by substitution


I am using IBP :smile:

Let u= x^2 and dv/dx= xe^x^2
du/dx= 2x and v= (I have no idea :colondollar:)
Original post by joeymr
I am using IBP :smile:

Let u= x^2 and dv/dx= xe^x^2
du/dx= 2x and v= (I have no idea :colondollar:)


try my above method and see if that helps :smile:
Reply 9
Original post by CTArsenal
try my above method and see if that helps :smile:


Thanks- just had a look at noticed that when you rearranged your du/dx= 2x to get it to =dx, you left the x with the dx to give xdx= du/2. I'm probably being extremely thick here but how can you do that? I've finished C4 and i've never done that before :colondollar: ive always been taught to take everything over with the du to get dx on its own?
(edited 9 years ago)
Original post by joeymr
I am using IBP :smile:

Let u= x^2 and dv/dx= xe^x^2
du/dx= 2x and v= (I have no idea :colondollar:)


Do you know what the differential of ex2e^{x^2} is
Could someone check my answer please

Spoiler

Reply 12
Original post by TenOfThem
Do you know what the differential of ex2e^{x^2} is


2xe^(x^2)?
Original post by Davelittle
Could someone check my answer please

Spoiler



Surely you could check the answer yourself by differentiating it :biggrin:
Original post by joeymr
2xe^(x^2)?


So you know what v is
Original post by joeymr
Thanks- just had a look at noticed that when you rearranged your du/dx= 2x to get it to =dx, you left the x with the dx to give xdx= du/2. I'm probably being extremely thick here but how can you do that? I've finished C4 and i've never done that before :colondollar:


It's just making it simpler to substitute in, for instance if you have dy/dx = 2x, dy = 2xdx; the differential becomes an integral, which takes you back to y = x^2 (+C).

You're allowed to manipulate it like that, for instance xdx = 1/2 du is the same as x^2/2 = u/2 (+C.. but let's ignore the constant here), which brings you back to your original integral when you multiply both sides by two. The integers are just a constant, it doesn't make much difference how you manipulate them as long as you stay thorough throughout.
(edited 9 years ago)
Original post by CTArsenal
It's just making it simpler to substitute in, for instance if you have dy/dx = 2x, dy = 2xdx; the differential becomes an integral, which takes you back to y = x^2 (+C).

You're allowed to manipulate it like that, for instance xdx = 1/2 du is the same as x^2/2 = u/2 (+C.. but let's ignore the constant here), which brings you back to your original integral when you multiply both sides by two. The integers are just a constant, it doesn't make much difference how you manipulate them as long as you stay thorough throughout.


Hey I done it your way and it worked, but when I done it the other way you end up doing IBP twice and I got an extra term on my answer :\... The second integration I had was x(e^(x^2))... I ended up getting for this integral 0.5e^(x^2)-(1\(4x^2))(e^(x^2) +c

Please try and make sense of that aha :frown::confused:

Posted from TSR Mobile
(edited 9 years ago)
Reply 17
Original post by Davelittle
Could someone check my answer please

Spoiler



I believe that you're right; that's what I got too :biggrin:.
Original post by Hac
I believe that you're right; that's what I got too :biggrin:.


Wolfram alpha confirms it as well :biggrin: :biggrin: :biggrin:
Original post by Branny101
Hey I done it your way and it worked, but when I done it the other way you end up doing IBP twice and I got an extra term on my answer :\... The second integration I had was x(e^(x^2))... I ended up getting for this integral 0.5e^(x^2)-(1\(4x^2))(e^(x^2) +c

Please try and make sense of that aha :frown::confused:

Posted from TSR Mobile


The other way is more doing it all in one go in my opinion, it's the same method just done quicker. If you spot good substitutions in any question, use them straight away before attempting integration by parts - that's if the question needs it (generally you end up using just the one method).

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