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aljabar/node_modules/algebrite/tests/integral.coffee

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CoffeeScript
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test_integral = ->
run_test [
"clearall",
"",
"tty=1",
"",
"integral(x^2+x)-(1/2*x^2+1/3*x^3)",
"0",
#1
"integral(A,X)",
"A*X",
#4
"integral(A+B,X)-(A*X+B*X)",
"0",
#9
"integral(1/X,X)",
"log(X)",
#11
"integral(exp(X),X)",
"exp(X)",
#12
"integral(exp(A*X),X)-exp(A*X)/A",
"0",
#14
"integral(log(X),X)-X*log(X)+X",
"0",
#15
"integral(3^X*log(3),X)",
"3^X",
#16
"integral(1/(3+x^2),x)-3^(-1/2)*arctan(3^(-1/2)*x)",
"0",
#17
"integral(1/(a-x^2),x)-a^(-1/2)*arctanh(a^(-1/2)*x)",
"0",
#19
"integral(1/sqrt(a-x^2),x)-arcsin(a^(-1/2)*x)",
"0",
#20
"integral(1/sqrt(a+x^2),x)-(log(x+(a+x^2)^(1/2)))",
"0",
#27
"integral(1/(a+b*x),x)-(log(a+b*x)/b)",
"0",
#28
"integral(1/(A+B*X)^2,X)+1/B*1/(A+B*X)",
"0",
#29
"integral(1/(a+b*x)^3,x)+1/2*1/b*(a+b*x)^(-2)",
"0",
#30
"integral(X/(A+B*X),X)+A*B^(-2)*log(A+B*X)-X/B",
"0",
#31
"integral(X/(A+B*X)^2,X)-1/B^2*(log(A+B*X)+A/(A+B*X))",
"0",
#33
"integral(X^2/(A+B*X),X)-1/B^2*(1/2*(A+B*X)^2-2*A*(A+B*X)+A^2*log(A+B*X))",
"0",
#34
"integral(X^2/(A+B*X)^2,X)-1/B^3*(A+B*X-2*A*log(A+B*X)-A^2/(A+B*X))",
"0",
#35
"integral(X^2/(A+B*X)^3,X)-1/B^3*(log(A+B*X)+2*A/(A+B*X)-1/2*A^2/(A+B*X)^2)",
"0",
#37
"integral(1/X*1/(A+B*X),X)+1/A*log((A+B*X)/X)",
"0",
#38
"integral(1/X*1/(A+B*X)^2,X)-1/A*1/(A+B*X)+1/A^2*log((A+B*X)/X)",
"0",
#39
"integral(1/X*1/(A+B*X)^3,X)-1/A^3*(1/2*((2*A+B*X)/(A+B*X))^2+log(X/(A+B*X)))",
"0",
#40
"integral(1/X^2*1/(A+B*X),X)+1/(A*X)-B/A^2*log((A+B*X)/X)",
"0",
#41
"integral(1/X^3*1/(A+B*X),X)-(2*B*X-A)/(2*A^2*X^2)-B^2/A^3*log(X/(A+B*X))",
"0",
#42
"integral(1/X^2*1/(A+B*X)^2,X)+(A+2*B*X)/(A^2*X*(A+B*X))-2*B/A^3*log((A+B*X)/X)",
"0",
#60
"integral(1/(2+3*X^2),X)-1/sqrt(6)*arctan(1/2*X*sqrt(6))",
"0",
"integral(1/(-2-3*X^2),X)-1/sqrt(6)*arctan(-1/2*X*sqrt(6))",
"0",
#61
"integral(1/(2-3*X^2),X)-1/2*1/sqrt(6)*log((2+X*sqrt(6))/(2-X*sqrt(6)))",
"0",
"integral(1/(-2+3*X^2),X)-1/2*1/sqrt(6)*log((-2+X*sqrt(6))/(-2-X*sqrt(6)))",
"0",
#63
"integral(X/(A+B*X^2),X)-1/2*1/B*log(A+B*X^2)",
"0",
#64
"integral(X^2/(A+B*X^2),X)-X/B+A/B*integral(1/(A+B*X^2),X)",
"0",
#65
"integral(1/(A+B*X^2)^2,X)-X/(2*A*(A+B*X^2))-1/2*1/A*integral(1/(A+B*X^2),X)",
"0",
#70
"integral(1/X*1/(A+B*X^2),X)-1/2*1/A*log(X^2/(A+B*X^2))",
"0",
#71
"integral(1/X^2*1/(A+B*X^2),X)+1/(A*X)+B/A*integral(1/(A+B*X^2),X)",
"0",
#74
"integral(1/(A+B*X^3),X)-1/3*1/A*(A/B)^(1/3)*(1/2*log(((A/B)^(1/3)+X)^3/(A+B*X^3))+sqrt(3)*arctan((2*X-(A/B)^(1/3))*(A/B)^(-1/3)/sqrt(3)))",
"0",
#76
"integral(X^2/(A+B*X^3),X)-1/3*1/B*log(A+B*X^3)",
"0",
# commenting this out because the definite integral of this one
# between 0 and pi was incorrect AND the indefinite integral
# became incorrect after I avoided having roots in the denominator
# when doing multiplications. The two things combined made me
# think to eliminate this test.
#77
#"integral(1/(2+3*X^4),X)-1/2*1/2*(2/3/4)^(1/4)*(1/2*log((X^2+2*(2/3/4)^(1/4)*X+2*(2/3/4)^(1/2))/(X^2-2*(2/3/4)^(1/4)*X+2*(2/3/4)^(1/2)))+arctan(2*(2/3/4)^(1/4)*X/(2*(2/3/4)^(1/2)-X^2)))",
#"0",
# commenting this out because the definite integral of this one
# between 0 and pi was incorrect AND the indefinite integral
# became incorrect after I avoided having roots in the denominator
# when doing multiplications. The two things combined made me
# think to eliminate this test.
#78
#"integral(1/(2-3*X^4),X)-1/2*(2/3)^(1/4)/2*(1/2*log((X+(2/3)^(1/4))/(X-(2/3)^(1/4)))+arctan(X*(2/3)^(-1/4)))",
#"0",
#79
"integral(X/(2+3*X^4),X)-1/2*1/3*1/sqrt(2/3)*arctan(X^2/sqrt(2/3))",
"0",
#80
"integral(X/(2-3*X^4),X)+1/4*1/3*sqrt(3/2)*log((X^2-sqrt(2/3))/(X^2+sqrt(2/3)))",
"0",
# commenting this out because the definite integral of this one
# between 0 and pi was incorrect AND the indefinite integral
# became incorrect after I avoided having roots in the denominator
# when doing multiplications. The two things combined made me
# think to eliminate this test.
#81
#"integral(X^2/(2+3*X^4),X)-1/4*1/3*(2/3/4)^(-1/4)*(1/2*log((X^2-2*(2/3/4)^(1/4)*X+2*sqrt(2/3/4))/(X^2+2*(2/3/4)^(1/4)*X+2*sqrt(2/3/4)))+arctan(2*(2/3/4)^(1/4)*X/(2*sqrt(2/3/4)-X^2)))",
#"0",
# commenting this out because the definite integral of this one
# between 0 and pi was incorrect AND the indefinite integral
# became incorrect after I avoided having roots in the denominator
# when doing multiplications. The two things combined made me
# think to eliminate this test.
#82
#"integral(X^2/(2-3*X^4),X)+1/4*1/3*(2/3)^(-1/4)*(log((X-(2/3)^(1/4))/(X+(2/3)^(1/4)))+2*arctan(X*(2/3)^(-1/4)))",
#"0",
#83
"integral(X^3/(A+B*X^4),X)-1/4*1/B*log(A+B*X^4)",
"0",
#124
"integral(sqrt(A+B*X),X)-2/3/B*sqrt((A+B*X)^3)",
"0",
#125
"integral(X*sqrt(A+B*X),X)+2*(2*A-3*B*X)*sqrt((A+B*X)^3)/15*B^(-2)",
"0",
#126
"integral(X^2*sqrt(A+B*X),X)-2*(8*A^2-12*A*B*X+15*B^2*X^2)*sqrt((A+B*X)^3)/105*B^(-3)",
"0",
#128
"integral(sqrt(A+B*X)/X,X)-2*sqrt(A+B*X)-A*integral(1/X*1/sqrt(A+B*X),X)",
"0",
#129
"integral(sqrt(A+B*X)/X^2,X)+sqrt(A+B*X)/X-B/2*integral(1/X*1/sqrt(A+B*X),X)",
"0",
#131
"integral(1/sqrt(A+B*X),X)-2*sqrt(A+B*X)/B",
"0",
#132
"integral(X/sqrt(A+B*X),X)+2/3*(2*A-B*X)*sqrt(A+B*X)/B^2",
"0",
#133
"integral(X^2/sqrt(A+B*X),X)-2/15*(8*A^2-4*A*B*X+3*B^2*X^2)*sqrt(A+B*X)/B^3",
"0",
#134
"integral(1/X*1/sqrt(2+B*X),X)-1/sqrt(2)*log((sqrt(2+B*X)-sqrt(2))/(sqrt(2+B*X)+sqrt(2)))",
"0",
#136
"integral(1/X*1/sqrt(-2+B*X),X)-2/sqrt(2)*arctan(sqrt((-2+B*X)/2))",
"0",
#137
"integral(1/X^2*1/sqrt(A+B*X),X)+sqrt(A+B*X)/A/X+1/2*B/A*integral(1/X*1/sqrt(A+B*X),X)",
"0",
#156
"integral(sqrt(X^2+A),X)-1/2*(X*sqrt(X^2+A)+A*log(X+sqrt(X^2+A)))",
"0",
#157
"integral(1/sqrt(X^2+A),X)-log(X+sqrt(X^2+A))",
"0",
#158
"integral(1/X*1/sqrt(X^2-2),X)-arcsec(X/sqrt(2))/sqrt(2)",
"0",
#159
"integral(1/X*1/sqrt(X^2+2),X)+1/sqrt(2)*log((sqrt(2)+sqrt(X^2+2))/X)",
"0",
#160
"integral(sqrt(X^2+2)/X,X)-sqrt(X^2+2)+sqrt(2)*log((sqrt(2)+sqrt(X^2+2))/X)",
"0",
#161
"integral(sqrt(X^2-2)/X,X)-sqrt(X^2-2)+sqrt(2)*arcsec(X/sqrt(2))",
"0",
#162
"integral(X/sqrt(X^2+A),X)-sqrt(X^2+A)",
"0",
#163
"integral(X*sqrt(X^2+A),X)-1/3*sqrt((X^2+A)^3)",
"0",
#164 fails after Jan 2017 changes to abs/mag
#"integral(sqrt((X^2+A)^3),X)-1/4*(X*sqrt((X^2+A)^3)+3/2*A*X*sqrt(X^2+A)+3/2*A^2*log(X+sqrt(X^2+A)))",
#"0",
#"integral(sqrt((X^2-A)^3),X)-1/4*(X*sqrt((X^2-A)^3)-3/2*A*X*sqrt(X^2-A)+3/2*A^2*log(X+sqrt(X^2-A)))",
#"0",
#165 fails after Jan 2017 changes to abs/mag
#"integral(1/sqrt((X^2+A)^3),X)-X/A/sqrt(X^2+A)",
#"0",
#166 fails after Jan 2017 changes to abs/mag
#"integral(X/sqrt((X^2+A)^3),X)+1/sqrt(X^2+A)",
#"0",
#167 fails after Jan 2017 changes to abs/mag
#"integral(X*sqrt((X^2+A)^3),X)-1/5*sqrt((X^2+A)^5)",
#"0",
#168
"integral(X^2*sqrt(X^2+A),X)-1/4*X*sqrt((X^2+A)^3)+1/8*A*X*sqrt(X^2+A)+1/8*A^2*log(X+sqrt(X^2+A))",
"0",
#169
"integral(X^3*sqrt(X^2+7),X)-(1/5*X^2-2/15*7)*sqrt((X^2+7)^3)",
"0",
#170
"integral(X^3*sqrt(X^2-7),X)-(sqrt((X^2-7)^5)/5+7*sqrt((X^2-7)^3)/3)",
"0",
#171
"integral(X^2/sqrt(X^2+A),X)-1/2*X*sqrt(X^2+A)+1/2*A*log(X+sqrt(X^2+A))",
"0",
#172
"integral(X^3/sqrt(X^2+A),X)-1/3*sqrt((X^2+A)^3)+A*sqrt(X^2+A)",
"0",
#173
"integral(1/X^2*1/sqrt(X^2+A),X)+sqrt(X^2+A)/A/X",
"0",
#174
"integral(1/X^3*1/sqrt(X^2+2),X)+1/2*sqrt(X^2+2)/2/X^2-1/2*log((sqrt(2)+sqrt(X^2+2))/X)/(sqrt(2)^3)",
"0",
#175
"integral(1/X^3*1/sqrt(X^2-2),X)-1/2*sqrt(X^2-2)/2/X^2-1/2*1/(2^(3/2))*arcsec(X/(2^(1/2)))",
"0",
#176+
"integral(X^2*sqrt((X^2+2^2)^3),X)\
-1/6*X*sqrt((X^2+2^2)^5)\
+1/24*(2^2)*X*sqrt((X^2+2^2)^3)\
+1/16*(2^4)X*sqrt(X^2+2^2)\
+1/16*(2^6)*log(X+sqrt(X^2+2^2))",
"0",
#176-
"integral(X^2*sqrt((X^2-2^2)^3),X)\
-1/6*X*sqrt((X^2-2^2)^5)\
-1/24*(2^2)*X*sqrt((X^2-2^2)^3)\
+1/16*(2^4)X*sqrt(X^2-2^2)\
-1/16*(2^6)*log(X+sqrt(X^2-2^2))",
"0",
#177+
"integral(X^3*sqrt((X^2+7^2)^3),X)\
-1/7*sqrt((X^2+7^2)^7)\
+1/5*(7^2)*sqrt((X^2+7^2)^5)",
"0",
#177-
"integral(X^3*sqrt((X^2-7^2)^3),X)\
-1/7*sqrt((X^2-7^2)^7)\
-1/5*(7^2)*sqrt((X^2-7^2)^5)",
"0",
#196
"simplify(integral(1/(X-A)/sqrt(X^2-A^2),X)+sqrt(X^2-A^2)/A/(X-A))",
"0",
"simplify(1/(X-A)/sqrt(X^2-A^2)-d(integral(1/(X-A)/sqrt(X^2-A^2),X),X))",
"0",
#197
"integral(1/(X+A)/sqrt(X^2-A^2),X)-sqrt(X^2-A^2)/A/(X+A)",
"0",
"simplify(1/(X+A)/sqrt(X^2-A^2)-d(integral(1/(X+A)/sqrt(X^2-A^2),X),X))",
"0",
#200
"integral(sqrt(7-X^2),X)-1/2*(X*sqrt(7-X^2)+7*arcsin(X/sqrt(7)))",
"0",
#201
"integral(1/sqrt(7-X^2),X)-arcsin(X/sqrt(7))",
"0",
#202
"integral(1/X*1/sqrt(7-X^2),X)+1/sqrt(7)*log((sqrt(7)+sqrt(7-X^2))/X)",
"0",
#203
"integral(sqrt(7-X^2)/X,X)\
-sqrt(7-X^2)+sqrt(7)*log((sqrt(7)+sqrt(7-X^2))/X)",
"0",
#204
"integral(X/sqrt(A-X^2),X)\
+sqrt(A-X^2)",
"0",
#205
"integral(X*sqrt(A-X^2),X)\
+1/3*sqrt((A-X^2)^3)",
"0",
#210
"integral(X^2*sqrt(7-X^2),X)\
+1/4*X*sqrt((7-X^2)^3)\
-7/8*(X*sqrt(7-X^2)+7*arcsin(X/sqrt(7)))",
"0",
#211
"integral(X^3*sqrt(7-X^2),X)\
-(-1/5*X^2-2/15*7)*sqrt((7-X^2)^3)",
"0",
#214
"integral(X^2/sqrt(7-X^2),X)\
+X/2*sqrt(7-X^2)\
-7/2*arcsin(X/sqrt(7))",
"0",
#215
"integral(1/X^2*1/sqrt(7-X^2),X)\
+sqrt(7-X^2)/7/X",
"0",
#216
"integral(sqrt(7-X^2)/X^2,X)\
+sqrt(7-X^2)/X\
+arcsin(X/sqrt(7))",
"0",
#217
"integral(sqrt(7-X^2)/X^3,X)\
+1/2*sqrt(7-X^2)/X^2\
-1/2*log((sqrt(7)+sqrt(7-X^2))/X)/sqrt(7)",
"0",
#218
"integral(sqrt(7-X^2)/X^4,X)\
+1/3*sqrt((7-X^2)^3)/7/X^3",
"0",
#273
"integral(sqrt(7*X^2+C),X)-X*sqrt(7*X^2+C)/2-C*log(X*sqrt(7)+sqrt(7*X^2+C))/2/sqrt(7)",
"0",
#274
"integral(sqrt(-7*X^2+C),X)-X*sqrt(-7*X^2+C)/2-C*arcsin(X*sqrt(7/C))/2/sqrt(7)",
"0",
#290
"integral(sin(A*X),X)+cos(A*X)/A",
"0",
#291
"integral(cos(A*X),X)-sin(A*X)/A",
"0",
#292
"integral(tan(A*X),X)+log(cos(A*X))/A",
"0",
#293
"integral(1/tan(A*X),X)-log(sin(A*X))/A",
"0",
#294
"integral(1/cos(A*X),X)-log(tan(pi/4+A*X/2))/A",
"0",
#295
"integral(1/sin(A*X),X)-log(tan(A*X/2))/A",
"0",
#296
"integral(sin(A*X)^2,X)-X/2+sin(2*A*X)/(4*A)",
"0",
#297
"integral(sin(A*X)^3,X)+cos(A*X)*(sin(A*X)^2+2)/(3*A)",
"0",
#298
"integral(sin(A*X)^4,X)-3/8*X+sin(2*A*X)/(4*A)-sin(4*A*X)/(32*A)",
"0",
#302
"integral(cos(A*X)^2,X)-X/2-sin(2*A*X)/(4*A)",
"0",
#303
"integral(cos(A*X)^3,X)-sin(A*X)*(cos(A*X)^2+2)/(3*A)",
"0",
#304
"integral(cos(A*X)^4,X)-3/8*X-sin(2*A*X)/(4*A)-sin(4*A*X)/(32*A)",
"0",
#308
"integral((1/sin(A*X))^2,X)+1/A*1/tan(A*X)",
"0",
#312
"integral((1/cos(A*X))^2,X)-tan(A*X)/A",
"0",
#318
"integral(sin(A*X)*cos(A*X),X)-sin(A*X)^2/(2*A)",
"0",
#320
"integral(sin(A*X)^2*cos(A*X)^2,X)+sin(4*A*X)/(32*A)-X/8",
"0",
#326
"integral(sin(A*X)/cos(A*X)/cos(A*X),X)-1/(A*cos(A*X))",
"0",
#327
"integral(sin(A*X)^2/cos(A*X),X)+sin(A*X)/A-log(tan(pi/4+A*X/2))/A",
"0",
#328
"integral(cos(A*X)/sin(A*X)^2,X)+1/(A*sin(A*X))",
"0",
#329
"integral(1/sin(A*X)/cos(A*X),X)-log(tan(A*X))/A",
"0",
#330
"integral(1/sin(A*X)/cos(A*X)^2,X)-(1/cos(A*X)+log(tan(A*X/2)))/A",
"0",
#332
"integral(1/sin(A*X)^2/cos(A*X),X)-(log(tan(pi/4+A*X/2))-1/sin(A*X))/A",
"0",
#333
"integral(1/sin(A*X)^2/cos(A*X)^2,X)+2/(A*tan(2*A*X))",
"0",
#335
"integral(sin(A+B*X),X)+cos(A+B*X)/B",
"0",
#336
"integral(cos(A+B*X),X)-sin(A+B*X)/B",
"0",
#337+
"integral(1/(1+sin(A*X)),X)+tan(pi/4-A*X/2)/A",
"0",
#337b+
"integral(1/(B+B*sin(A*X)),X)+tan(pi/4-A*X/2)/A/B",
"0",
#337-
"integral(1/(1-sin(A*X)),X)-tan(pi/4+A*X/2)/A",
"0",
#337b-
"integral(1/(B-B*sin(A*X)),X)-tan(pi/4+A*X/2)/A/B",
"0",
#338
"integral(1/(1+cos(A*X)),X)-tan(A*X/2)/A",
"0",
#339
"integral(1/(1-cos(A*X)),X)+1/(A*tan(A*X/2))",
"0",
#340
"integral(1/(A+B*sin(X)),X)-1/sqrt(B^2-A^2)*log((A*tan(X/2)+B-sqrt(B^2-A^2))/(A*tan(X/2)+B+sqrt(B^2-A^2)))",
"0",
#341
"integral(1/(A+B*cos(X)),X)-1/sqrt(B^2-A^2)*log((sqrt(B^2-A^2)*tan(X/2)+A+B)/(sqrt(B^2-A^2)*tan(X/2)-A-B))",
"0",
#389
"x*sin(A*x)-d(integral(x*sin(A*x)))",
"0",
#390
"x^2*sin(A*x)-d(integral(x^2*sin(A*x)))",
"0",
#393
"x*cos(A*x)-d(integral(x*cos(A*x)))",
"0",
#394
"x^2*cos(A*x)-d(integral(x^2*cos(A*x)))",
"0",
#441
"integral(arcsin(A*X),X)-X*arcsin(A*X)-sqrt(1-A^2*X^2)/A",
"0",
#442
"integral(arccos(A*X),X)-X*arccos(A*X)+sqrt(1-A^2*X^2)/A",
"0",
#443
"integral(arctan(A*X),X)-X*arctan(A*X)+log(1+A^2*X^2)/(2*A)",
"0",
#485
"integral(log(X),X)-X*log(X)+X",
"0",
#485a
"integral(log(A*X),X)-X*log(A*X)+X",
"0",
#486
"integral(X*log(X),X)-1/2*X^2*log(X)+1/4*X^2",
"0",
#486a
"integral(X*log(A*X),X)-1/2*X^2*log(A*X)+1/4*X^2",
"0",
#487
"integral(X^2*log(A*X),X)-1/3*X^3*log(A*X)+X^3/9",
"0",
#489
"integral(log(X)^2,X)-X*log(X)^2+2*X*log(X)-2*X",
"0",
#493
"integral(1/X*1/log(A*X),X)-log(log(A*X))",
"0",
#499
"integral(log(A*X+B),X)-(A*X+B)*log(A*X+B)/A+X",
"0",
#500
"integral(log(A*X+B)/X^2,X)-A*log(X)/B+(A*X+B)*log(A*X+B)/B/X",
"0",
#554
"integral(sinh(X),X)-cosh(X)",
"0",
#555
"integral(cosh(X),X)-sinh(X)",
"0",
#556
"integral(tanh(X),X)-log(cosh(X))",
"0",
#560
"integral(X*sinh(X),X)-X*cosh(X)+sinh(X)",
"0",
#562
"integral(X*cosh(X),X)-X*sinh(X)+cosh(X)",
"0",
#566
"integral(sinh(X)^2,X)-sinh(2*X)/4+X/2",
"0",
#569
"integral(tanh(X)^2,X)-X+tanh(X)",
"0",
#572
"integral(cosh(X)^2,X)-sinh(2*X)/4-X/2",
"0",
# test integral(exp(a*x^2))
"integral(exp(a*x^2))+i*sqrt(pi)*erf(i*sqrt(a)*x)/sqrt(a)/2",
"0",
"integral(exp(-x^2))-sqrt(pi)*erf(x)/2",
"0",
# before abs/mag changes of Jan 2017
# this integral gave the more compact result of:
# sqrt(pi/3)*erf(sqrt(3)*x)/2
# but the new given one is still correct
"integral(exp(-3*x^2))-pi^(1/2)*erf(3^(1/2)*x)/(2*3^(1/2))",
"0",
"integral(1/x*1/(a+log(x)),x)-log(a+log(x))",
"0",
"integral(exp(a*x+b*x))",
"exp((a+b)*x)/(a+b)",
"integral(x*exp(a*x))",
"-exp(a*x)/(a^2)+x*exp(a*x)/a",
"derivative",
"x*exp(a*x)",
"integral(x*exp(a*x+b))",
"-exp(a*x+b)/(a^2)+x*exp(a*x+b)/a",
"derivative",
"x*exp(a*x+b)",
"integral(x*exp(-a*x+b))",
"-exp(-a*x+b)/(a^2)-x*exp(-a*x+b)/a",
"derivative",
"x*exp(-a*x+b)",
"integral(x^2*exp(a*x))",
"2*exp(a*x)/(a^3)-2*x*exp(a*x)/(a^2)+x^2*exp(a*x)/a",
"derivative",
"x^2*exp(a*x)",
"integral(x^2*exp(a*x+b))",
"2*exp(a*x+b)/(a^3)-2*x*exp(a*x+b)/(a^2)+x^2*exp(a*x+b)/a",
"derivative",
"x^2*exp(a*x+b)",
"integral(x^3*exp(a*x))",
"-6*exp(a*x)/(a^4)+6*x*exp(a*x)/(a^3)-3*x^2*exp(a*x)/(a^2)+x^3*exp(a*x)/a",
"derivative",
"x^3*exp(a*x)",
"integral(x^3*exp(a*x+b))",
"-6*exp(a*x+b)/(a^4)+6*x*exp(a*x+b)/(a^3)-3*x^2*exp(a*x+b)/(a^2)+x^3*exp(a*x+b)/a",
"derivative",
"x^3*exp(a*x+b)",
# here
"integral(sqrt(a*x^2+b))",
"Stop: integral: sorry, could not find a solution",
"integral(x^2*(1-x^2)^(3/2))-(x*sqrt(1-x^2)*(-8*x^4+14*x^2-3)+3*arcsin(x))/48",
"0",
"integral(x^4*(1-x^2)^(3/2))-(-x*sqrt(1-x^2)*(16*x^6-24*x^4+2*x^2+3)+3*arcsin(x))/128",
"0",
"integral(x^2*(1-x^2)^(5/2))-(x*sqrt(1-x^2)*(48*x^6-136*x^4+118*x^2-15)+15*arcsin(x))/384",
"0",
]
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