Integration Problem

[bubbblybubbbles]

My physical chemistry class has turned into a math class, and it's been a few too many years since I've taken calculus for me to be sure of myself.

Here's what I'm trying to integrate followed by the solution given by the Mathematica Online Integrator.

Comments

[ex_beshenov]

The right answer is a^3/4.

[bubbblybubbbles]

Woohoo! I guess my skills are not so rusty :) Thanks for the help!

[ex_beshenov]

?

It's the answer you get from the Mathematica integrator.

[bubbblybubbbles]

Oh wait a second; I misread your answer. Apparently both my math and reading skills need some work :) Thank you, again!

[sans_galois]

Natural number e?

[bubbblybubbbles]

Ahhh. I've never been allowed to use math software for homework before, so I know nothing about its quirks. This is good to know since every function in PChem seems to have "e" in it. Thanks for the help and the good info!

[nevermore_x]

I get a^3/4, similar to the first commentor and the result you obtained from Mathematica.
But, I have not done such an integral in quite a long time...

[bubbblybubbbles]

Yeah, I haven't done these in a long time either. It's too easy to lose constants with so many integrations by parts. Thanks for the help! I kind of figured the computer was right...

[nevermore_x]

Indeed, but I rarely rely on technology alone. If you were still having trouble, I would suggest working backward from the correst result.

[kray_zemli]

Mathematica solution is correct :-)

You may somehow use the fact (that is derived of integration by parts), that integral (0..inf) of xn*e-x is equal to factorial of n.