;;;Test TILU: ~/x22may-2-mrg: ;;;Test TILU: ~/x1t21may-1-mrg: ;;; (VERSION D "4.2.0 THE on Wed May 15 18:16:31 PDT 1996") ;;; ;;; format: generally free format lisp expressions delimited by () ;;; (<(our index number)> ) ;;; ;;; abbreviations in the input include: ;;; N, M, P are assumed to be positive integers; ;;; N or M followed by a single digit are assumed to be positive integers; ;;; INF means positive real infinity, MINF is negative real infinity; ;;; PI, TWOPI and HALFPI are multiples of 3.14159...; ;;; PM_ meaning plus or minus one, NLT0 is integer<0. ;;; Input looks like (INTEGRATE x) ;;; or (INTEGRATE x ) ;;; There are 2169 examples in this file ;;; We can do these at about 6.5 milliseconds average. ((4 9 1) (INTEGRATE (EXPT X -1) X)) ((5 11 2) (INTEGRATE (EXP X) X)) ((6 12 3) (INTEGRATE (EXP (* A X)) X)) ((7 12 3) (INTEGRATE (EXP (* 1 X)) X)) ((8 12 3) (INTEGRATE (EXP X) X)) ((9 13 4) (INTEGRATE (EXPT B (* A X)) X)) ((10 13 4) (INTEGRATE (EXPT 1 (* A X)) X)) ((11 13 4) (INTEGRATE (EXPT B (* 1 X)) X)) ((12 13 4) (INTEGRATE (EXPT B X) X)) ((13 14 5) (INTEGRATE (LOG X) X)) ((14 15 6) (INTEGRATE (EXPT A X) X)) ((15 15 6) (INTEGRATE (EXPT 1 X) X)) ((16 16 7) (INTEGRATE (EXPT (+ (EXPT A 2) (EXPT X 2)) -1) X)) ((17 16 7) (INTEGRATE (EXPT (+ (EXPT 1 2) (EXPT X 2)) -1) X)) ((18 17 8) (INTEGRATE (EXPT (+ (EXPT A 2) (* -1 (EXPT X 2))) -1) X)) ((19 17 8) (INTEGRATE (EXPT (+ (EXPT 1 2) (* -1 (EXPT X 2))) -1) X)) ((20 18 9) (INTEGRATE (EXPT (+ (EXPT A 2) (* -1 (EXPT X 2))) -1) X)) ((21 18 9) (INTEGRATE (EXPT (+ (EXPT 1 2) (* -1 (EXPT X 2))) -1) X)) ((22 19 10) (INTEGRATE (EXPT (+ (* -1 (EXPT A 2)) (EXPT X 2)) -1) X)) ((23 19 10) (INTEGRATE (EXPT (+ (* -1 (EXPT 1 2)) (EXPT X 2)) -1) X)) ((24 20 11) (INTEGRATE (EXPT (+ (* -1 (EXPT A 2)) (EXPT X 2)) -1) X)) ((25 20 11) (INTEGRATE (EXPT (+ (* -1 (EXPT 1 2)) (EXPT X 2)) -1) X)) ((26 21 12) (INTEGRATE (EXPT (+ (EXPT A 2) (* -1 (EXPT X 2))) -1/2) X)) ((27 21 12) (INTEGRATE (EXPT (+ (EXPT 1 2) (* -1 (EXPT X 2))) -1/2) X)) ((28 22 13) (INTEGRATE (EXPT (+ (EXPT A 2) (* -1 (EXPT X 2))) -1/2) X)) ((29 22 13) (INTEGRATE (EXPT (+ (EXPT 1 2) (* -1 (EXPT X 2))) -1/2) X)) ((30 23 14) (INTEGRATE (EXPT (+ (* (EXPT A 2) PM_) (EXPT X 2)) -1/2) X)) ((31 23 14) (INTEGRATE (EXPT (+ (* (EXPT 1 2) PM_) (EXPT X 2)) -1/2) X)) ((32 24 15) (INTEGRATE (EXPT (* X (EXPT (+ (* -1 (EXPT A 2)) (EXPT X 2)) 1/2)) -1) X)) ((33 24 15) (INTEGRATE (EXPT (* X (EXPT (+ (* -1 (EXPT 1 2)) (EXPT X 2)) 1/2)) -1) X)) ((34 25 16) (INTEGRATE (EXPT (* X (EXPT (+ (EXPT A 2) (* PM_ (EXPT X 2))) 1/2)) -1) X)) ((35 25 16) (INTEGRATE (EXPT (* X (EXPT (+ (EXPT 1 2) (* PM_ (EXPT X 2))) 1/2)) -1) X)) ((36 26 17) (INTEGRATE (EXPT (+ A (* B X)) N) X)) ((37 26 17) (INTEGRATE (EXPT (+ A (* 1 X)) N) X)) ((38 26 17) (INTEGRATE (EXPT (+ A X) N) X)) ((39 26 17) (INTEGRATE (EXPT (+ 1 (* B X)) N) X)) ((40 26 17) (INTEGRATE (EXPT (+ A (* B X)) 2) X)) ((41 26 17) (INTEGRATE (EXPT (+ A (* B X)) 3) X)) ((42 27 18) (INTEGRATE (* X (EXPT (+ A (* B X)) N)) X)) ((43 27 18) (INTEGRATE (* X (EXPT (+ A (* 1 X)) N)) X)) ((44 27 18) (INTEGRATE (* X (EXPT (+ A X) N)) X)) ((45 27 18) (INTEGRATE (* X (EXPT (+ 1 (* B X)) N)) X)) ((46 27 18) (INTEGRATE (* X (EXPT (+ A (* B X)) 2)) X)) ((47 27 18) (INTEGRATE (* X (EXPT (+ A (* B X)) 3)) X)) ((78 32 23) (INTEGRATE (EXPT (+ A (* B X)) -1) X)) ((79 32 23) (INTEGRATE (EXPT (+ A (* 1 X)) -1) X)) ((80 32 23) (INTEGRATE (EXPT (+ A X) -1) X)) ((81 32 23) (INTEGRATE (EXPT (+ 1 (* B X)) -1) X)) ((82 33 24) (INTEGRATE (EXPT (+ A (* B X)) -2) X)) ((83 33 24) (INTEGRATE (EXPT (+ A (* 1 X)) -2) X)) ((84 33 24) (INTEGRATE (EXPT (+ A X) -2) X)) ((85 33 24) (INTEGRATE (EXPT (+ 1 (* B X)) -2) X)) ((86 34 25) (INTEGRATE (EXPT (+ A (* B X)) -3) X)) ((87 34 25) (INTEGRATE (EXPT (+ A (* 1 X)) -3) X)) ((88 34 25) (INTEGRATE (EXPT (+ A X) -3) X)) ((89 34 25) (INTEGRATE (EXPT (+ 1 (* B X)) -3) X)) ((90 35 26) (INTEGRATE (* X (EXPT (+ A (* B X)) -1)) X)) ((91 35 26) (INTEGRATE (* X (EXPT (+ A (* 1 X)) -1)) X)) ((92 35 26) (INTEGRATE (* X (EXPT (+ A X) -1)) X)) ((93 35 26) (INTEGRATE (* X (EXPT (+ 1 (* B X)) -1)) X)) ((94 36 27) (INTEGRATE (* X (EXPT (+ A (* B X)) -1)) X)) ((95 36 27) (INTEGRATE (* X (EXPT (+ A (* 1 X)) -1)) X)) ((96 36 27) (INTEGRATE (* X (EXPT (+ A X) -1)) X)) ((97 36 27) (INTEGRATE (* X (EXPT (+ 1 (* B X)) -1)) X)) ((98 37 28) (INTEGRATE (* X (EXPT (EXPT (+ A (* B X)) 2) -1)) X)) ((99 37 28) (INTEGRATE (* X (EXPT (EXPT (+ A (* 1 X)) 2) -1)) X)) ((100 37 28) (INTEGRATE (* X (EXPT (EXPT (+ A X) 2) -1)) X)) ((101 37 28) (INTEGRATE (* X (EXPT (EXPT (+ 1 (* B X)) 2) -1)) X)) ((102 38 29) (INTEGRATE (* X (EXPT (EXPT (+ A (* B X)) N) -1)) X)) ((103 38 29) (INTEGRATE (* X (EXPT (EXPT (+ A (* 1 X)) N) -1)) X)) ((104 38 29) (INTEGRATE (* X (EXPT (EXPT (+ A X) N) -1)) X)) ((105 38 29) (INTEGRATE (* X (EXPT (EXPT (+ 1 (* B X)) N) -1)) X)) ((106 38 29) (INTEGRATE (* X (EXPT (EXPT (+ A (* B X)) 2) -1)) X)) ((107 38 29) (INTEGRATE (* X (EXPT (EXPT (+ A (* B X)) 3) -1)) X)) ((108 39 30) (INTEGRATE (* (EXPT X 2) (EXPT (+ A (* B X)) -1)) X)) ((109 39 30) (INTEGRATE (* (EXPT X 2) (EXPT (+ A (* 1 X)) -1)) X)) ((110 39 30) (INTEGRATE (* (EXPT X 2) (EXPT (+ A X) -1)) X)) ((111 39 30) (INTEGRATE (* (EXPT X 2) (EXPT (+ 1 (* B X)) -1)) X)) ((112 40 31) (INTEGRATE (* (EXPT X 2) (EXPT (EXPT (+ A (* B X)) 2) -1)) X)) ((113 40 31) (INTEGRATE (* (EXPT X 2) (EXPT (EXPT (+ A (* 1 X)) 2) -1)) X)) ((114 40 31) (INTEGRATE (* (EXPT X 2) (EXPT (EXPT (+ A X) 2) -1)) X)) ((115 40 31) (INTEGRATE (* (EXPT X 2) (EXPT (EXPT (+ 1 (* B X)) 2) -1)) X)) ((116 41 32) (INTEGRATE (* (EXPT X 2) (EXPT (EXPT (+ A (* B X)) 3) -1)) X)) ((117 41 32) (INTEGRATE (* (EXPT X 2) (EXPT (EXPT (+ A (* 1 X)) 3) -1)) X)) ((118 41 32) (INTEGRATE (* (EXPT X 2) (EXPT (EXPT (+ 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-1)) X)) ((198 61 52) (INTEGRATE (* X (EXPT (* (EXPT (+ A (* B X)) 2) (+ C (* 1 X))) -1)) X)) ((199 61 52) (INTEGRATE (* X (EXPT (* (EXPT (+ A (* B X)) 2) (+ C X)) -1)) X)) ((200 61 52) (INTEGRATE (* X (EXPT (* (EXPT (+ A (* B X)) 2) (+ 1 (* D X))) -1)) X)) ((201 61 52) (INTEGRATE (* X (EXPT (* (EXPT (+ A (* 1 X)) 2) (+ C (* D X))) -1)) X)) ((202 61 52) (INTEGRATE (* X (EXPT (* (EXPT (+ A X) 2) (+ C (* D X))) -1)) X)) ((203 61 52) (INTEGRATE (* X (EXPT (* (EXPT (+ 1 (* B X)) 2) (+ C (* D X))) -1)) X)) ((204 62 53) (INTEGRATE (* (EXPT X 2) (EXPT (* (EXPT (+ A (* B X)) 2) (+ C (* D X))) -1)) X)) ((205 62 53) (INTEGRATE (* (EXPT X 2) (EXPT (* (EXPT (+ A (* B X)) 2) (+ C (* 1 X))) -1)) X)) ((206 62 53) (INTEGRATE (* (EXPT X 2) (EXPT (* (EXPT (+ A (* B X)) 2) (+ C X)) -1)) X)) ((207 62 53) (INTEGRATE (* (EXPT X 2) (EXPT (* (EXPT (+ A (* B X)) 2) (+ 1 (* D X))) -1)) X)) ((208 62 53) (INTEGRATE (* (EXPT X 2) (EXPT (* (EXPT (+ A (* 1 X)) 2) (+ C (* D X))) -1)) X)) ((209 62 53) (INTEGRATE (* 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INF)) ((111 904 35) (INTEGRATE (* (+ (TANH X) (* C (TANH (* 1 X)))) (EXPT X -1)) X 0 INF)) ((115 905 36) (INTEGRATE (* (+ (TANH (* A X)) (* C (TANH X))) (EXPT X -1)) X 0 INF)) ((118 905 36) (INTEGRATE (* (+ (TANH (* 1 X)) (* C (TANH X))) (EXPT X -1)) X 0 INF)) ((120 906 37) (INTEGRATE (* (+ (SECH X) (* Q (SECH (* B X)))) (EXPT X -1)) X 0 INF)) ((123 906 37) (INTEGRATE (* (+ (SECH X) (* Q (SECH (* 1 X)))) (EXPT X -1)) X 0 INF)) ((125 907 38) (INTEGRATE (* (+ (SECH (* A X)) (* Q (SECH X))) (EXPT X -1)) X 0 INF)) ((128 907 38) (INTEGRATE (* (+ (SECH (* 1 X)) (* Q (SECH X))) (EXPT X -1)) X 0 INF)) #| entries 2835,2836,2837,2838,2839,2841,2842,2844,2845,2847,2848,2851,2852, 2999,3000, 3149 deleted because the (sole) message no-more-integrals-in-table really means "we can't do this one at all". Entries 3241 and 3243 deleted because, after simplification, the provisos were all impossible to satisfy. Entries 2902, 2903,2904,2905 deleted because they were not integrable but seemed to be so, because of one bug. (same bug tan[x]/x 0 inf). Entry 2901 deleted because gave inf as an answer. Adamchik says 66 and 67 diverge. I don't know why, and the integrals (taken from G&R) dont show divergence. |#