Question

calcII
show that for any integer n>=0, we have int{0,1}(lnx)^ndx=(-1)^n(n!)

Answer 1

its straight forward... I almost finished it and accidentally the page got refreshed! :( too late (gotta sleep)
use the substitution \(\ln x=-u\implies x=e^{-u}\)
you'd keep getting integration by parts that will keep giving you \(n(n-1)(n-2)\ldots\)
the \((-1)^n\) shows up right after the substitution.

Answer 2

that's why you keep on hitting post every few lines. atleast that's what i do.

Answer 3

my biological CPU is shutting down..

Answer 4

but thanks, i'll try to solve it from here.

Answer 5

ya, you should go to bed.

Answer 6

hey experiment do you think you help explain the rest of this to me?

Answer 7

where do you need help?

Answer 8

i don't really understand what electro did there.

Answer 9

this is pretty staring forward.