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Topic: It's teatime at the End of the Universe ...
Replies: 2   Last Post: Oct 23, 2011 8:03 AM

 Messages: [ Previous | Next ]
 clicliclic@freenet.de Posts: 1,245 Registered: 4/26/08
It's teatime at the End of the Universe ...
Posted: Oct 15, 2011 4:09 AM

... today the Restaurant at the End of the Universe is offering free
the cheeef! ... you look like you want one? ... help yourself, Sir ...

(m + 1)*(a*d - b*c)*(a*f - b*e)
*INT((A + B*x)*(a + b*x)^m*(c + d*x)^n*(e + f*x)^p, x)
- INT(((m + 1)*(A*(a*d*f - (c*f + d*e)*b) + B*b*c*e) - (A*b - B*a)
*((n + 1)*d*e + (p + 1)*c*f) - (m + n + p + 3)*(A*b - B*a)*d*f*x)
*(a + b*x)^(m + 1)*(c + d*x)^n*(e + f*x)^p, x)
- (A*b - B*a)
*(a + b*x)^(m + 1)*(c + d*x)^(n + 1)*(e + f*x)^(p + 1) = 0

(m + n + p + 2)*d*f
*INT((A + B*x)*(a + b*x)^m*(c + d*x)^n*(e + f*x)^p, x)
- INT(((m + n + p + 2)*A*a*d*f - B*(m*b*c*e
+ ((n + 1)*d*e + (p + 1)*c*f)*a) + ((m + n + p + 2)*A*b*d*f
+ B*(m*a*d*f - ((m + n + 1)*e*d + (m + p + 1)*c*f)*b))*x)
*(a + b*x)^(m - 1)*(c + d*x)^n*(e + f*x)^p, x)
- B*(a + b*x)^m*(c + d*x)^(n + 1)*(e + f*x)^(p + 1) = 0

(m + 1)*(a*f - b*e)*b
*INT((A + B*x)*(a + b*x)^m*(c + d*x)^n*(e + f*x)^p, x)
- INT(((m + 1)*(A*f - B*e)*b*c + (A*b - B*a)*(n*d*e + (p + 1)*c*f)
+ ((m + 1)*(A*f - B*e)*b + (n + p + 1)*(A*b - B*a)*f)*d*x)
*(a + b*x)^(m + 1)*(c + d*x)^(n - 1)*(e + f*x)^p, x)
+ (A*b - B*a)*(a + b*x)^(m + 1)*(c + d*x)^n*(e + f*x)^(p + 1) = 0

... they say you are aiming to be the first to draw a three-dimensional
domain-map - that's something! ... fresh snaaacks! ... free cookies
made by the cheeef! .... Want one too? ... note that the next four
require a*d - b*c = 0 ...

(m + n + 1)*(a*f - b*e)*INT((a + b*x)^m*(c + d*x)^n*(e + f*x)^p, x)
- (m + n + p + 2)*f*INT((a + b*x)^(m + 1)*(c + d*x)^n*(e + f*x)^p, x)
+ (a + b*x)^(m + 1)*(c + d*x)^n*(e + f*x)^(p + 1) = 0

(p + 1)*(c*f - d*e)*INT((a + b*x)^m*(c + d*x)^n*(e + f*x)^p, x)
+ (m + n + p + 2)*d*INT((a + b*x)^m*(c + d*x)^n*(e + f*x)^(p + 1), x)
- (a + b*x)^m*(c + d*x)^(n + 1)*(e + f*x)^(p + 1) = 0

(m + n + 1)*b*INT((a + b*x)^m*(c + d*x)^n*(e + f*x)^p, x)
+ p*f*INT((a + b*x)^(m + 1)*(c + d*x)^n*(e + f*x)^(p - 1), x)
- (a + b*x)^(m + 1)*(c + d*x)^n*(e + f*x)^p = 0

b*INT((a + b*x)^m*(c + d*x)^n*(e + f*x)^p, x)
- d*INT((a + b*x)^(m + 1)*(c + d*x)^(n - 1)*(e + f*x)^p, x) = 0

... that last one looks especially yummy ... unfortunately we have only
one today ... fresh snaaacks! ... free cookies made by the cheeef! ...
hungry for a snack? ... the next two require a*d - b*c = c*f - d*e = 0
...

(m + n + p + 1)*f*INT((a + b*x)^m*(c + d*x)^n*(e + f*x)^p, x)
- (a + b*x)^m*(c + d*x)^n*(e + f*x)^(p + 1) = 0

f*INT((a + b*x)^m*(c + d*x)^n/(e + f*x)^(m + n + 1), x)
- (a + b*x)^m*(c + d*x)^n/(e + f*x)^(m + n)*LN(e + f*x) = 0

... nonrecursive creations are a real strength of our chef ... fresh
snaaacks! ... free cookies at the End of the Universe ...

Martin.

Date Subject Author
10/15/11 clicliclic@freenet.de
10/22/11 Albert D. Rich
10/23/11 clicliclic@freenet.de