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- amyna

find intergal:
this is an interrogation by parts problem

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- amyna

find intergal:
this is an interrogation by parts problem

- schrodinger

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- amyna

|dw:1441854137872:dw|

- amyna

i got:
u=x^3
du=3x^2
dv=e^-x^2
v= i don't know lol

- freckles

\[u=x^2 \\ du=2x dx \\ \text{ now multiply both sides of } du=2x dx \text{ by } \frac{1}{2}x^2 \\ \text{ so we have } \\ \frac{1}{2}x^2 du=x^3 dx \\ \text{ but recall } x^2=u \\ \text{ so we have } \frac{1}{2}u du=x^3 dx\]
once I make this substitution then I would do integration by parts

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- freckles

or you could have actually went with the sub u=-x^2 instead

- amyna

ok i'll try and do this, and see what i get. thanks!

- amyna

ya i don't know what I'm doing! can i use integration by parts first?

- Jhannybean

this is an interrogation huh? ;)

- zepdrix

buhaha XD

- freckles

you could try integration by parts
but as you wrote earlier it is a little confusing to do
a substitution would make the integration by parts less confusing
--
what do you mean you don't know what you are doing?
like you couldn't do the substitution I gave you above ?

- amyna

ya where did you get the x^3 from?

- freckles

\[\int\limits x^3 e^{-x^2} dx \\ \text{ replace } x^2 \text{ with } u \\ \text{ replace } x^3 dx \text{ with } \frac{1}{2} u du \\ \text{ giving you } \\ \int\limits \frac{1}{2} u e^{-u} du\]

- freckles

did you read the third line ?

- freckles

\[u=x^2 \\ du=2x dx \\ \text{ now multiply both sides of } du=2x dx \text{ by } \frac{1}{2}x^2 \\ \text{ so we have } \\ \frac{1}{2}x^2 du=x^3 dx \\ \text{ but recall } x^2=u \\ \text{ so we have } \frac{1}{2}u du=x^3 dx\]
that third line said I multiplied both sides by 1/2x^2

- amyna

oh okay! thats more clear! Thanks!

- freckles

it was just a copy and paste of what I said earlier :p
\[\frac{1}{2}x^2 \cdot 2x dx =\frac{2}{2} x^3 dx=x^3 dx\]

- Jhannybean

where is this \(\dfrac{1}2x^2\) coming from...

- freckles

we have to write x^3 dx in terms of u

- freckles

that is where it comes from

- Jhannybean

Oh nevermind, it's to eliminate the 2 and to obtain x\(^3\) on the right side. Nvm.

- jacobciezki

Why are you girls still in her

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