Little Help with a Calc Question

[americanangel]

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Okay I'm stuck on this for my calc II class...
integral of (x^3)(e^-x^2) and integral of (x^3)(2+x)^(5/2)
I know both are integration by parts but nothing is working!!! Somebody please help!!!

 

[Athomeonarock]

www.quickmath.com

the best site ever

 

[americanangel]

Great site but i need to show work?? Any ideas how to get the answer?

 

[Cerberus]

damn, its been too long since calc two. Looks like integration by parts and substitution though.

 

[americanangel]

yeah that is what i was thinking but i keep getting these freaky integrals that dont match the real answer!!!

thanks for the reply

any ideas welcome!!!

 

[Cerberus]

Ok, i'll do the first one.

int(x^3)(e^-x^2)dx

let u=x^2

then

int[u*x*e^(-u)dx]
and dx = du*1/(2x)

so

int[u*x*e^(-u)(1/(2x)du) = 1/2*int[u*e^(-u)du]

by integration by parts:

1/2*int[u*e^(-u)du] = 1/2[-u*e^(-u) - int[1*e^(-u)du] = -1/2*u*e^(-u) + 1/2e^(-u) = -1/2*x^2*e^(-x^2) + 1/2e^(-x^2) = e^(-x^2)*(1-x^2)/2

 

[americanangel]

oh cool...that found my mistake...i did u=x instead of x^2
why i did that I dont know but at least I straightened that out!!!

thanks so much for that!!!
i really appreciate it!!!

 

[kels]

For the second one, just substitute u=x+2. So you'll have (u-2)^3*u^(5/2). Expand the first term (u-2)^3 and you'll get something slight messy, but then you can multiply tern by term with u^(5/2), so you'll have a long polynomial with terms like u^(11/2). Then you can integrate those individually, like 12/13*u^(13/12).