Integration by Parts: Help Needed with x^2 e^x^3 dx

[bondgirl007]

Homework Statement

Integrate x^2 e^x^3 dx

Homework Equations

I = uv - integral of u'v

The Attempt at a Solution

I don't know where to begin this question at all and have been stuck on it for the past half hour. Any help would be really appreciated. :(

 

[Dick]

e^x^3 can mean either e^(x^3) or (e^x)^3. Use parentheses! (If not TeX). If it's the former then d(x^3)=3*x^2, suggest a u substitution.

 

[bondgirl007]

Sorry about that. I'll try again.

 

[bondgirl007]

I'm not sure how to use the tags here so I'll just post a picture.
http://img231.imageshack.us/img231/1954/52551832cl9.png

 

[olgranpappy]

that doesn't really help...

 

[bondgirl007]

That's how it is in my textbook though.

 

[Dick]

Ok, we'll guess. I think it probably means e^(x^3). Can you suggest a u substitution?

 

[olgranpappy]

...in which case, you don't need to "integrate by parts". you just need the substitution which was suggested.

(which bond girl are you? Ursella Andress?)

 

[bondgirl007]

Here's what I have done
u = x^2
v = 3x^2 e^(x^3)
du = 2x dx
dv = e^(x^3)2x dx

I = x^2 3x^2 e^(x^3) - integral of 3x^2 e^(x^3)

I'm not sure how to integrate the 3x^2 e^(x^3).

 

[olgranpappy]

use the substitution y=x^3 and that's it. just "change variables" not "integrate by parts".

 

[bondgirl007]

I'll try that - thanks!