- #1
takarin
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Homework Statement
I'm getting different results when choosing my u & dv for Integration by Parts on the following integral:
[tex]\int 2x^3 e^x^2 dx [/tex]
(Note, the exponent on 'e' is x^2)
This yields the correct solution:
u = [tex]x^2[/tex]
dv = [tex]2x e^x^2 dx [/tex]
du = [tex]2xdx[/tex]
v = [tex]e^x^2[/tex]
However, I have tried using this instead (*)
u = [tex]2x^3[/tex]
dv = [tex]e^x^2 dx [/tex]
du = [tex]6x^2 dx[/tex]
v = [tex](e^x^2) / 2x[/tex]
and this is yielding the incorrect solution (see 3.)
Homework Equations
Integration by Parts:
[tex]\int udv = uv - \int vdu [/tex]
The Attempt at a Solution
The correct solution turns out to be
[tex] x^2 e^x^2 - e^x^2 + C[/tex]
When I use my other choice of variables (*), I get (using IBP)
[tex] \int 2x^3 e^x^2 dx = 2x^3 e^x^2 / 2x - \int e^x^2 / 2x * 6x^2 dx [/tex]
which leads to:
[tex]x^2 e^x^2 - 3/2 e^x^2 + C [/tex]
which is different from the other choice of variables.
I've looked over both choices of variables, and I don't know why the second choice (*) comes up with a different solution.
Thanks for the help!