# S.O.S. Mathematics CyberBoard

Your Resource for mathematics help on the web!
 It is currently Fri, 30 Sep 2016 22:55:27 UTC

 All times are UTC [ DST ]

 Page 1 of 1 [ 2 posts ]
 Print view Previous topic | Next topic
Author Message
 Post subject: Advanced Math IntegralPosted: Tue, 14 Oct 2008 00:38:54 UTC
 Senior Member

Joined: Thu, 11 Sep 2008 01:59:14 UTC
Posts: 73
[Integral from 0 to infinity] of [ln(x) * e^(-3x)]

Have fun!

Hint: Exponential integral Ei(x)

Top

 Post subject: Posted: Sun, 29 Mar 2009 01:31:20 UTC
 Member

Joined: Sat, 21 Feb 2009 21:40:14 UTC
Posts: 22
Location: ncsu soph

No need to use Ei. Just use the first Euler-Mascheroni integral , which is proven as follows:

from the integral definition of the gamma function, so as z goes to 1

. Using the Weierstrauss product and logarithmically differentiating

Simply allowing z to go to 0 gives , being the Euler-Mascheroni constant. So,

Now consider integrals of the form ; substitute , giving which after evaluating and simplifying is

which is the solution for all n>0. To answer your question specifically,

Top

 Display posts from previous: All posts1 day7 days2 weeks1 month3 months6 months1 year Sort by AuthorPost timeSubject AscendingDescending
 Page 1 of 1 [ 2 posts ]

 All times are UTC [ DST ]

#### Who is online

Users browsing this forum: No registered users

 You cannot post new topics in this forumYou cannot reply to topics in this forumYou cannot edit your posts in this forumYou cannot delete your posts in this forum

Search for:
 Jump to:  Select a forum ------------------ High School and College Mathematics    Algebra    Geometry and Trigonometry    Calculus    Matrix and Linear Algebra    Differential Equations    Probability and Statistics    Proposed Problems Applications    Physics, Chemistry, Engineering, etc.    Computer Science    Math for Business and Economics Advanced Mathematics    Foundations    Algebra and Number Theory    Analysis and Topology    Applied Mathematics    Other Topics in Advanced Mathematics Other Topics    Administrator Announcements    Comments and Suggestions for S.O.S. Math    Posting Math Formulas with LaTeX    Miscellaneous