General

[quote=ulti25]Oh, thank you, I guess there wasn't any error, you just went a step further than me and factored/combined fractions. I was being lazy.

I had assumed I made an error but couldn't see one and it had been bugging me[/quote]

Oooh I thought you forgot about the [(1+x^2)] in the denominator part, just a reminder hehe ^^

[quote=Oyster]I believe the final answer is (1/2)[ e^(x^2) / (1+x^2)].
I took a pic of the scrap work: http://i.imgur.com/i047p.png
Hope this helps.[/quote]

Oh, thank you, I guess there wasn't any error, you just went a step further than me and factored/combined fractions. I was being lazy.

I had assumed I made an error but couldn't see one and it had been bugging me

I don't even...

[quote=ulti25] Last integral easily simplifies to 1/2*e^(x^2) [/quote]

I believe the final answer is (1/2)[ e^(x^2) / (1+x^2)].
I took a pic of the scrap work: http://i.imgur.com/i047p.png
Hope this helps.

omg ew calculus

Lol I didn't learn this yet.

[quote=Benighted]Have you tried integration by parts?

I doubt your teacher/book would be as evil as to force you to do this problem with integration by parts...but might as well try it? lol

edit: derp...dude above me just made your day 10x worse.

oh. hey, i think the guy above me's mistake was that he used x^2*e^(x^2) instead of x^3*e^(x^2) for u.
ouch. that's such a simple error from the beginning. lol[/quote]

Nope, one x was used for dv for it to integrate to v.

Neat, didn't know you could write the integral on this forum.

Use integration by parts:
∫ ( u dv ) = uv - ∫ (v du)

∫ ( x^3)(e^(x^2)) / (x^2 + 1)^2 dx

Let's let dv = x / (x^2 + 1)^2 dx since that seems like the most complicated thing we can easily (hopefully) integrate.
v = - 1/2(x^2 + 1)

That leaves us with u = x^2*e^(x^2) which we can differentiate using the product rule to be (2x*e^(x^2) + 2xe^(x^2)*x^2 )

So what do we have?

∫ ( x^3)(e^(x^2)) / (x^2 + 1)^2 dx = -(x^2*e^(x^2))/2(x^2 + 1) + ∫ 1/2(x^2+1) * [ (2x*e^(x^2) + 2xe^(x^2)*x^2 ]

I really don't feel like writing down the steps to simplify the last integral, but if you multiply the products with v and then combine, you'll find that you can factor out (x^2 + 1) from 2xe^(x^2) + 2xe^(x^2)x^2 and cancel the denominator.

∫ ( x^3)(e^(x^2)) / (x^2 + 1)^2 dx = -(x^2*e^(x^2))/2(x^2 + 1) + ∫x*e^(x^2)

Last integral easily simplifies to 1/2*e^(x^2)

EDIT:

Seems the above was correct after all, but I got lazy in the end and didn't combine terms. Thanks to Oyster!

[quote=silkym39]Whoa! how'd u get that integration symbol on basil? o.o[/quote]

Wikipedia'd and copy-paste

Whoa! how'd u get that integration symbol on basil? o.o