Integration by Parts: Solve x^2exp(-3x)dx

[cogs24]

hi guys
just doing some revision and I am stuck on this question

*integral sign* x^2 . exponential ^ -3x . dx

I know i have to use integration by parts, but i just can't seem to get it out
any ideas?
thanx

 

[dextercioby]

HINT:Take dv=e^{-3x} \ dx and u=x^2.

U'll figure out what to do next.

Daniel.

 

[cogs24]

but, what is the integral of exponential ^ -3x?

 

[cogs24]

is it -1/3 *exponential* ^ -3x?

 

[dextercioby]

Yes,as you can check by differentiation.

Daniel.

 

[Jameson]

The tabular method would work great on this question. Are you familiar with this?

 

[cogs24]

ok, once i sub u, du, v and dv into the integral by parts formula, i have to assign, u and dv again to:
-1/3 exponential ^ -3x and 2x

so is dv assigned to the exponential again, like in the first case?

 

[cogs24]

no, i am not aware of the tabular method, sorry

 

[cogs24]

ok, I've got my answer, unfortunately i don't kow if its right, we don't get solutions for this exercise

-1/3 *exponential* ^ -3x . x^2 - 1/9*exponential*^-3x . 2x - 2/27*exponential*^-3x

 

[whozum]

Maple agrees, good job.

 

[dextercioby]

Surely,you must add an arbitrary constant wrt "x" to your solution.

Daniel.

 

[cogs24]

arbitary constant would be + c

 

[Jameson]

In case you were interested in this method, http://marauder.millersville.edu/~bikenaga/calculus/parts/partspf.html is a link to the explanation. If one of the two terms will eventually differentiate to zero, this method is much less time consuming.

Jameson

 

[cogs24]

i see, thanks for that link, i will probably apply this method from now on