## Monday Math 73

Find .

Here, we use the geometric series: as  for , we have  for 
.
Now, we can find via integration by parts or by a table of integrals (see #3 here) that
, so
 (as  for any p>0).
Thus
.

### 3 Responses to “Monday Math 73”

1. Avertedd Says:

У автора очень приятный слог

2. Monday Math 75 « Twisted One 151’s Weblog Says:

[…] then, is ? Note first that . Thus: . Reversing order of integration, . Now, as , , and so Now, I previously showed that ; thus […]

3. Monday Math 80 « Twisted One 151’s Weblog Says:

[…] and one without. [More] Solution 1 (polylogarithm): We integrate directly in y: We showed here a way to find that . So now, we need to find . Making the substitution u=-x, we get . This is a […]