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",
  ]