







The divisors (aliquot parts) of a positive integer 
20191031 

From Kenneth: Is there a fast and simple method that can be used to determine the aliquot parts, whole, positive numbers that can divide into another whole, positive number? Answered by Harley Weston. 





Partitions into distinct parts 
20150919 

From Brian: Looking for a formula where I can type in a number, 17 for example, and using the numbers 1 through 17 (1, 2, 3, 4 etc....), to come up with all possible combinations, when added, that will equal 17. And each number can only be used once. I've tried a few search engines but my computer stares at me blankly and scratches its head :/. Answered by Chris Fisher. 





The integral of sqrt(x) * ln(x) 
20091012 

From Oana: Hi! Can you tell me please how much is : ∫ (√x * ln x) ? Answered by Penny Nom. 





Integration 
20081017 

From hazela: integration of
x sinx cosnx Answered by Harley Weston. 





Integration by parts 
20080130 

From seth: hi i really dont understand integr
ation by parts. for example, the integral(t^2sintdt. i have u=t^2 and v'=sint also u'=t^/3 v=cost
for the formula i have uvintegralvu' dx this is all well and good but i cant get it right. Answered by Harley Weston. 





Integration 
20070202 

From Jenna: How do I integrate ( ln(x) ) / ( x^2 ) ? Answered by Penny Nom and Claude Tardif. 





Can one divide a circle into 4.5 parts 
20060330 

From Chris: If it is possible, can one divide a circle into say, 4.5 parts (with 4 equal parts and a half part)?
Or for that matter, for any integer, n, into n/2 parts as above?] Answered by Walter Whiteley. 





Integrating e^x sin(x) 
20030503 

From Lech: I am having trouble integrating the following expression by parts: ex sin(x) I used the integrator at http://www.integrals.com/ to find the solution, ? 1/2 ex cos(x) + 1/2 ex sin(x). This is easy to confirm by differentiation, however I am confounded as how to arrive at the answer. Answered by Penny Nom and Claude Tardif. 





Dividing a circle 
20011017 

From Ahmeen: I am having a hard time figuring out how a circle can be divided into 11 equal parts with only 4 cut allowed? My teacher gave this to us and I still can't cut my pie into eleven equal parts with only four cuts. Answered by Walter Whiteley. 





Integration by parts 
20010409 

From A student: how do you integrate x tan^{1}x dx, i know it can be done by integration by parts maybe, but i'm not sure.... Answered by Claude Tardif and Harley Weston. 





Two integrals 
20010403 

From Jim: I'm having trouble with these integrals. Can you help me out? 1)the integral of:
x^{5} arctan x dx 2)the integral of:
2x^{5} + 9x^{4} + 19x^{3} + 13x^{2}  5x  25  dx x^{4} + 4x^{3} + 5x^{2} Answered by Claude Tardif. 





Congruent parts of congruent figures 
20000310 

From Erica: Yesterday, I recieved a test problem asking to prove two line segments equal. Here is the problem as I was given it: Given: paralleogram ABCD AE is perpendicular to DB CF is perpendicular to DB Prove: AE is equal to CF I answered the problem as follows: . . . Answered by Walter Whiteley. 

