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

.

Advertisements

Tags: Geometric Series, Integration, Math, Monday Math

May 26, 2009 at 12:01 am |

У автора очень приятный слог

June 8, 2009 at 12:24 am |

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

July 13, 2009 at 12:05 am |

[…] 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 […]