perm filename INTEG[ALI,HPM] blob
sn#254009 filedate 1976-12-14 generic text, type C, neo UTF8
COMMENT ⊗ VALID 00002 PAGES
C REC PAGE DESCRIPTION
C00001 00001
C00002 00002
C00025 ENDMK
C⊗;
(D29) SIN(X)
(C30) TAYLOR(%,X,0,10);
3 5 7 9
X X X X
(D30)/T/ X - -- + --- - ---- + ------ + . . .
6 120 5040 362880
(C31) POWERSERIES(D29,X,0);
INF
==== I1 2 I1 + 1
\ (- 1) X
(D31) > -----------------
/ (2 I1 + 1)!
====
I1 = 0
(C36) TAYLOR(SIN(D30),X,0,10);
3 5 7 9
X X 8 X 13 X
(D36)/T/ X - -- + -- - ---- + ----- + . . .
3 10 315 2520
(C37) TAYLOR(SIN(SIN(X)),X,0,10);
3 5 7 9
X X 8 X 13 X
(D37)/T/ X - -- + -- - ---- + ----- + . . .
3 10 315 2520
(C60) TAN(X);
(D60) TAN(X)
(C61) INTEGRATE(D60);
(C62) INTEGRATE(D60,X);
(D62) LOG(SEC(X))
(C65) INTEGRATE(SEC(X),X);
(D65) LOG(TAN(X) + SEC(X))
(C80) INTEGRATE(LOG(X),X);
(D80) X LOG(X) - X
(C81) INTEGRATE(LOG(1/X),X);
(D81) X - X LOG(X)
(C82) INTEGRATE(LOG(X↑2),X);
(D82) 2 (X LOG(X) - X)
(C83) INTEGRATE(COS(X)↑2,X);
(C86) RATSIMP(%);
SIN(2 X) + 2 X
(D86) --------------
4
(C87) TRIGEXPAND(%);
2 COS(X) SIN(X) + 2 X
(D87) ---------------------
4
(C7) integrate(e↑(-2*x) ,x);
1
(D7) - -------------
2 X
2 E LOG(E)
(C8) integrate(e↑(-x),x);
1
(D8) - ---------
X
E LOG(E)
(C9) diff(e↑x,x);
X
(D9) E LOG(E)
(C20) INTEGRATE(COT(X),X);
(D20) LOG(SIN(X))
(C23) INTEGRATE(ATAN(X),X);
2
LOG(X + 1)
(D23) X ATAN(X) - -----------
2
(C24) INTEGRATE(TAN(X)↑2,X);
(D24) TAN(X) - X
(C26) INTEGRATE(LOG(SECX),X);
(D26) LOG(SECX) X
4 2 6 6
- 17 TAN (O) - 30 TAN (O) - 15) (X - O) /(90 TAN (O))
14 12 10 8 6
+ (45 TAN (O) + 105 TAN (O) + 77 TAN (O) + 17 TAN (O) + 17 TAN (O)
4 2 7 7
+ 77 TAN (O) + 105 TAN (O) + 45) (X - O) /(315 TAN (O))
16 14 12 10
+ (315 TAN (O) + 840 TAN (O) + 756 TAN (O) + 248 TAN (O)
6 4 2 8
- 248 TAN (O) - 756 TAN (O) - 840 TAN (O) - 315) (X - O)
8 18 16 14
/(2520 TAN (O)) + (315 TAN (O) + 945 TAN (O) + 1008 TAN (O)
12 10 8 6
+ 440 TAN (O) + 62 TAN (O) + 62 TAN (O) + 440 TAN (O)
4 2 9 9
+ 1008 TAN (O) + 945 TAN (O) + 315) (X - O) /(2835 TAN (O))
20 18 16 14
+ (2835 TAN (O) + 9450 TAN (O) + 11655 TAN (O) + 6360 TAN (O)
12 8 6 4
+ 1382 TAN (O) - 1382 TAN (O) - 6360 TAN (O) - 11655 TAN (O)
2 10 10
- 9450 TAN (O) - 2835) (X - O) /(28350 TAN (O)) + . . .
(C40) POWERSERIES (LOG(TAN(X)),X,0 ) ;
Is I3 zero or nonzero?
NONZERO;
INF
==== I3 - 1 4 I3 - 2 2 I3
\ (- 1) 2 BERN(2 I3) X
(D40) 2 ( > --------------------------------------)
/ I3 (2 I3)!
====
I3 = 0
INF
==== I3 - 1 2 I3 - 1 2 I3
\ (- 1) 2 BERN(2 I3) X
- 2 > --------------------------------------
/ I3 (2 I3)!
====
I3 = 0
(C41) INTEGRATE(%,X);
DIFF2 FASL DSK MAXOUT being loaded
loading done
INF
/ ==== I3 - 1 4 I3 - 2 2 I3
[ \ (- 1) 2 BERN(2 I3) X
(D41) 2 I > -------------------------------------- dX
] / I3 (2 I3)!
/ ====
I3 = 0
INF
/ ==== I3 - 1 2 I3 - 1 2 I3
[ \ (- 1) 2 BERN(2 I3) X
- 2 I > -------------------------------------- dX
] / I3 (2 I3)!
/ ====
I3 = 0
(C42) INTEGRATE(LOG(TAN(X)),X);
/
[
(D42) I LOG(TAN(X)) dX
]
/
(C43) ↑Z
42337) .IOT 1,1 :SEND JPG HOW CAN YOU FORCE INTEGRATE TO APPLY ITSE!
LF THRU AN INFINITE SUMMATION↑C
*$P
CHANGEVAR(D42,X=ATAN(Y),Y);
CHANGV FASL DSK MAXOUT being loaded
loading done
/
[ LOG(Y)
(D43) I ------ dY
] 2
/ Y + 1
(C44) %,INTEGRATE;
/
[ LOG(Y)
(D44) I ------ dY
] 2
/ Y + 1
(C45)
πππππMESSAGE FROM JPG HACTRN
JPG@MC 02:38:53
Just SUM(INTEGRATE(FIRST(summ),X),i,ll,ul);
↑Z
42337) .IOT 1,1 :SEND JPG BUT WHAT IF THE SUM TO BE INTEGRATED WAS !
GENERATED BY POWERSERIES?↑C
*$P
πππππMESSAGE FROM JPG HACTRN
JPG@MC 02:41:19
So, how does that change things?
↑Z
42337) .IOT 1,1 :SEND JPG I SEE. SOUNDS LIKE A KLUDGE.↑C
*$P
πππππMESSAGE FROM JPG HACTRN
JPG@MC 02:42:19
Yes, I suppose so. DIFF currently has that rule but not INTEGRATE.
DIFF(LOG(TAN(X),X);
Unbalanced matchfix operator
DIFF ( LOG ( TAN ( X ) , X ) **$**
Please rephrase or edit
(C45) DIFF(LOG(TAN(X)),X);
2
SEC (X)
(D45) -------
TAN(X)
(C46) TRIG(%);
2
SEC (X)
(D46) TRIG(-------)
TAN(X)
(C47) TRIGREDUCE(D45);
(D47) 2 CSC(2 X)
(C48) TRIGEXPAND(D45);
2
SEC (X)
(D48) -------
TAN(X)
(C49) TRIGEXPAND(D47);
(D49) CSC(X) SEC(X)
(C50) INTEGRATE(%);
WRONG NUMBER OF ARGS TO INTEGRATE
(C51) INTEGRATE(%,X);
LOG(SIN(X) + 1) LOG(SIN(X) - 1)
(D51) - --------------- + LOG(SIN(X)) - ---------------
2 2
(C52) LOGCONTRACT(%);
LOGCON FASL DSK MAXOUT being loaded
loading done
4 2
SIN (X) - 2 SIN (X) + 1
LOG(-----------------------)
4
SIN (X)
(D52) - ----------------------------
4
(C53) FACTOR(%);
4 2
SIN (X) - 2 SIN (X) + 1
LOG(-----------------------)
4
SIN (X)
(D53) - ----------------------------
4
(C54) FACTOR(PART(%,1,1,1));
2 2
(SIN(X) - 1) (SIN(X) + 1)
(D54) ---------------------------
4
SIN (X)
(C55) SUBSTINPART(%,D53,1,1,1);
PART FELL OFF END
(C56) SUBSTINPART(D53,D54,1,1,1);
4 2
SIN (X) - 2 SIN (X) + 1
LOG(-----------------------)
4
2 SIN (X) 2
(SIN(X) + 1) (SIN(X) - ----------------------------)
4
(D56) ------------------------------------------------------
4
SIN (X)
(C57) SUBSTINPART(D54,D53,1,1,1);
PART FELL OFF END
(C58)