1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Indefinite integral & series

  1. Jul 9, 2011 #1
    1. The problem statement, all variables and given/known data

    The problem is divided into two sections:

    a) does the improper integral: 2ln(x)/x^7 (from 1 to infinity) Converge or diverge? If it converges, to what value?

    b) Determine whether the series: sigma n=1 to infinity (2ln(n)/n^7) converges or diverges.

    2. Relevant equations

    Integration by parts?

    3. The attempt at a solution

    For the first part, I made the limit as c--> infinity, and took out the 2, then I simply integrated by parts where:

    u = ln(x) du= 1/x dx dv= x^7 dx v = (x^8)/8

    and ended up with: I = 1/4 lim c--> inf (x^8*ln(x) + (x^8)/8) from 1 to c

    When I work it out, I get it Diverges, as the end result is infinity... But it's supposed to converge...

    As for the second part, I assumed that they were similar where I could use the integral series test (ending up with the same result as the first part) to get the answer, but again, the answer lead to convergence....

    Am I using the correct techniques?

  2. jcsd
  3. Jul 9, 2011 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    How did you integrate 2ln(x)/x7 ? That's the same as 2(x-7)ln(x)

    I would expect the anti-derivative to have x-6 in it, not x8 !
  4. Jul 9, 2011 #3
    Thank you! That was it, didn't take the proper dv -- took x^7 as oppose to 1/x^7 giving x^-7.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook