- #1
csinger1
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Substitution method with Integration by Parts?
Evaluate the integral...
∫x^3[e^(-x^2)]dx
∫udv=uv-∫vdu
I first tried using integration by parts setting u and dv equal to anything and everything. This seemed to make it more complicated so I decided to use the substitution method setting y=-x^2 and dy=-2xdx and finally -1/2dy=xdx to give me
1/2∫ye^ydy
From here i used integration by parts with u=y, du=dy, v=e^y and dv=e^y dy to get
1/2(ye^y-∫e^y dy) = 1/2(ye^y-e^y)
and then
1/2[-x^2e^(-x^2)-e^(-x^2)]
This problem got really confusing with all the variables and I just want to make sure that I'm not way off base with my methods and solution.
Thanks in advance for any input!
Homework Statement
Evaluate the integral...
∫x^3[e^(-x^2)]dx
Homework Equations
∫udv=uv-∫vdu
The Attempt at a Solution
I first tried using integration by parts setting u and dv equal to anything and everything. This seemed to make it more complicated so I decided to use the substitution method setting y=-x^2 and dy=-2xdx and finally -1/2dy=xdx to give me
1/2∫ye^ydy
From here i used integration by parts with u=y, du=dy, v=e^y and dv=e^y dy to get
1/2(ye^y-∫e^y dy) = 1/2(ye^y-e^y)
and then
1/2[-x^2e^(-x^2)-e^(-x^2)]
This problem got really confusing with all the variables and I just want to make sure that I'm not way off base with my methods and solution.
Thanks in advance for any input!