Question

definite integral: [(ln(x))^4 / 2x ]dx upper limit e^2 and lower limit 1.

Do I use substitution and how do I do this?

Answer 1

sub u = lnx
du = 1/x dx

Answer 2

Ya a u-sub will work really nicely for this one,
maybe this picture will help a little bit.
I rearranged things so you can see how your u-sub will get plugged in.

Answer 3

Wow, once you know what you're doing it becomes VERY easy! Wish I had more time to practice but unfortunately time is limited :(
Thanks so much for your help!
Once i replaced (1/x dx) with du and integrated 1/2 u^4 the answer is
ln^5/10 + C

Answer 4

Cool, looks good! :)

Answer 5

When I sub in the limits I get [ln(e^2)^5) - ln(1)^5/10)
lne^10 - ln^5/10
does this make sense?

Answer 6

The exponent ( the 5 ) is being applied to the log, not to the contents of the log.

First simply ln(e^2) and ln(1) before you apply the 5th power to them.

Answer 7

ok that makes sense
lne^2=2 and ln(1) is 0
so then it becomes
(2)^5/10 - (0)^5/10
= 5/2

Answer 8

Mmm ya that looks good!

Answer 9

Appreciate the help!

Answer 10

Ooo wolfram is coming up with 32/5.. Lemme see where we goofed up..

Answer 11

Err 16/5* hmm

Answer 12

Yep I got it.

Answer 13

Hmm your answer looks correct, I don't know where 16/5 is coming from.. weirdddd :U

Answer 14

32/10 = 16/5 I think it's ok. My answer must have been incorrect as (2)^5 = 32