1,1,227,0,0.201748," ","integrate(x^2*sin(c*x^2+b*x+a),x, algorithm=""giac"")","-\frac{-\frac{i \, \sqrt{2} \sqrt{\pi} {\left(b^{2} + 2 i \, c\right)} \operatorname{erf}\left(-\frac{1}{4} \, \sqrt{2} {\left(2 \, x + \frac{b}{c}\right)} {\left(-\frac{i \, c}{{\left| c \right|}} + 1\right)} \sqrt{{\left| c \right|}}\right) e^{\left(-\frac{i \, b^{2} - 4 i \, a c}{4 \, c}\right)}}{{\left(-\frac{i \, c}{{\left| c \right|}} + 1\right)} \sqrt{{\left| c \right|}}} - 2 i \, {\left(c {\left(2 i \, x + \frac{i \, b}{c}\right)} - 2 i \, b\right)} e^{\left(i \, c x^{2} + i \, b x + i \, a\right)}}{16 \, c^{2}} - \frac{\frac{i \, \sqrt{2} \sqrt{\pi} {\left(b^{2} - 2 i \, c\right)} \operatorname{erf}\left(-\frac{1}{4} \, \sqrt{2} {\left(2 \, x + \frac{b}{c}\right)} {\left(\frac{i \, c}{{\left| c \right|}} + 1\right)} \sqrt{{\left| c \right|}}\right) e^{\left(-\frac{-i \, b^{2} + 4 i \, a c}{4 \, c}\right)}}{{\left(\frac{i \, c}{{\left| c \right|}} + 1\right)} \sqrt{{\left| c \right|}}} - 2 i \, {\left(c {\left(2 i \, x + \frac{i \, b}{c}\right)} - 2 i \, b\right)} e^{\left(-i \, c x^{2} - i \, b x - i \, a\right)}}{16 \, c^{2}}"," ",0,"-1/16*(-I*sqrt(2)*sqrt(pi)*(b^2 + 2*I*c)*erf(-1/4*sqrt(2)*(2*x + b/c)*(-I*c/abs(c) + 1)*sqrt(abs(c)))*e^(-1/4*(I*b^2 - 4*I*a*c)/c)/((-I*c/abs(c) + 1)*sqrt(abs(c))) - 2*I*(c*(2*I*x + I*b/c) - 2*I*b)*e^(I*c*x^2 + I*b*x + I*a))/c^2 - 1/16*(I*sqrt(2)*sqrt(pi)*(b^2 - 2*I*c)*erf(-1/4*sqrt(2)*(2*x + b/c)*(I*c/abs(c) + 1)*sqrt(abs(c)))*e^(-1/4*(-I*b^2 + 4*I*a*c)/c)/((I*c/abs(c) + 1)*sqrt(abs(c))) - 2*I*(c*(2*I*x + I*b/c) - 2*I*b)*e^(-I*c*x^2 - I*b*x - I*a))/c^2","C",0
2,1,183,0,1.220313," ","integrate(x*sin(c*x^2+b*x+a),x, algorithm=""giac"")","-\frac{\frac{i \, \sqrt{2} \sqrt{\pi} b \operatorname{erf}\left(-\frac{1}{4} \, \sqrt{2} {\left(2 \, x + \frac{b}{c}\right)} {\left(-\frac{i \, c}{{\left| c \right|}} + 1\right)} \sqrt{{\left| c \right|}}\right) e^{\left(-\frac{i \, b^{2} - 4 i \, a c}{4 \, c}\right)}}{{\left(-\frac{i \, c}{{\left| c \right|}} + 1\right)} \sqrt{{\left| c \right|}}} + 2 \, e^{\left(i \, c x^{2} + i \, b x + i \, a\right)}}{8 \, c} - \frac{-\frac{i \, \sqrt{2} \sqrt{\pi} b \operatorname{erf}\left(-\frac{1}{4} \, \sqrt{2} {\left(2 \, x + \frac{b}{c}\right)} {\left(\frac{i \, c}{{\left| c \right|}} + 1\right)} \sqrt{{\left| c \right|}}\right) e^{\left(-\frac{-i \, b^{2} + 4 i \, a c}{4 \, c}\right)}}{{\left(\frac{i \, c}{{\left| c \right|}} + 1\right)} \sqrt{{\left| c \right|}}} + 2 \, e^{\left(-i \, c x^{2} - i \, b x - i \, a\right)}}{8 \, c}"," ",0,"-1/8*(I*sqrt(2)*sqrt(pi)*b*erf(-1/4*sqrt(2)*(2*x + b/c)*(-I*c/abs(c) + 1)*sqrt(abs(c)))*e^(-1/4*(I*b^2 - 4*I*a*c)/c)/((-I*c/abs(c) + 1)*sqrt(abs(c))) + 2*e^(I*c*x^2 + I*b*x + I*a))/c - 1/8*(-I*sqrt(2)*sqrt(pi)*b*erf(-1/4*sqrt(2)*(2*x + b/c)*(I*c/abs(c) + 1)*sqrt(abs(c)))*e^(-1/4*(-I*b^2 + 4*I*a*c)/c)/((I*c/abs(c) + 1)*sqrt(abs(c))) + 2*e^(-I*c*x^2 - I*b*x - I*a))/c","C",0
3,1,135,0,0.191623," ","integrate(sin(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{i \, \sqrt{2} \sqrt{\pi} \operatorname{erf}\left(-\frac{1}{4} \, \sqrt{2} {\left(2 \, x + \frac{b}{c}\right)} {\left(-\frac{i \, c}{{\left| c \right|}} + 1\right)} \sqrt{{\left| c \right|}}\right) e^{\left(-\frac{i \, b^{2} - 4 i \, a c}{4 \, c}\right)}}{4 \, {\left(-\frac{i \, c}{{\left| c \right|}} + 1\right)} \sqrt{{\left| c \right|}}} - \frac{i \, \sqrt{2} \sqrt{\pi} \operatorname{erf}\left(-\frac{1}{4} \, \sqrt{2} {\left(2 \, x + \frac{b}{c}\right)} {\left(\frac{i \, c}{{\left| c \right|}} + 1\right)} \sqrt{{\left| c \right|}}\right) e^{\left(-\frac{-i \, b^{2} + 4 i \, a c}{4 \, c}\right)}}{4 \, {\left(\frac{i \, c}{{\left| c \right|}} + 1\right)} \sqrt{{\left| c \right|}}}"," ",0,"1/4*I*sqrt(2)*sqrt(pi)*erf(-1/4*sqrt(2)*(2*x + b/c)*(-I*c/abs(c) + 1)*sqrt(abs(c)))*e^(-1/4*(I*b^2 - 4*I*a*c)/c)/((-I*c/abs(c) + 1)*sqrt(abs(c))) - 1/4*I*sqrt(2)*sqrt(pi)*erf(-1/4*sqrt(2)*(2*x + b/c)*(I*c/abs(c) + 1)*sqrt(abs(c)))*e^(-1/4*(-I*b^2 + 4*I*a*c)/c)/((I*c/abs(c) + 1)*sqrt(abs(c)))","C",0
4,0,0,0,0.000000," ","integrate(sin(c*x^2+b*x+a)/x,x, algorithm=""giac"")","\int \frac{\sin\left(c x^{2} + b x + a\right)}{x}\,{d x}"," ",0,"integrate(sin(c*x^2 + b*x + a)/x, x)","F",0
5,0,0,0,0.000000," ","integrate(-b*cos(c*x^2+b*x+a)/x+sin(c*x^2+b*x+a)/x^2,x, algorithm=""giac"")","\int -\frac{b \cos\left(c x^{2} + b x + a\right)}{x} + \frac{\sin\left(c x^{2} + b x + a\right)}{x^{2}}\,{d x}"," ",0,"integrate(-b*cos(c*x^2 + b*x + a)/x + sin(c*x^2 + b*x + a)/x^2, x)","F",0
6,1,229,0,0.180243," ","integrate(x^2*sin(-c*x^2+b*x+a),x, algorithm=""giac"")","-\frac{\frac{i \, \sqrt{2} \sqrt{\pi} {\left(b^{2} + 2 i \, c\right)} \operatorname{erf}\left(-\frac{1}{4} \, \sqrt{2} {\left(2 \, x - \frac{b}{c}\right)} {\left(-\frac{i \, c}{{\left| c \right|}} + 1\right)} \sqrt{{\left| c \right|}}\right) e^{\left(-\frac{i \, b^{2} + 4 i \, a c}{4 \, c}\right)}}{{\left(-\frac{i \, c}{{\left| c \right|}} + 1\right)} \sqrt{{\left| c \right|}}} - 2 i \, {\left(c {\left(-2 i \, x + \frac{i \, b}{c}\right)} - 2 i \, b\right)} e^{\left(i \, c x^{2} - i \, b x - i \, a\right)}}{16 \, c^{2}} - \frac{-\frac{i \, \sqrt{2} \sqrt{\pi} {\left(b^{2} - 2 i \, c\right)} \operatorname{erf}\left(-\frac{1}{4} \, \sqrt{2} {\left(2 \, x - \frac{b}{c}\right)} {\left(\frac{i \, c}{{\left| c \right|}} + 1\right)} \sqrt{{\left| c \right|}}\right) e^{\left(-\frac{-i \, b^{2} - 4 i \, a c}{4 \, c}\right)}}{{\left(\frac{i \, c}{{\left| c \right|}} + 1\right)} \sqrt{{\left| c \right|}}} - 2 i \, {\left(c {\left(-2 i \, x + \frac{i \, b}{c}\right)} - 2 i \, b\right)} e^{\left(-i \, c x^{2} + i \, b x + i \, a\right)}}{16 \, c^{2}}"," ",0,"-1/16*(I*sqrt(2)*sqrt(pi)*(b^2 + 2*I*c)*erf(-1/4*sqrt(2)*(2*x - b/c)*(-I*c/abs(c) + 1)*sqrt(abs(c)))*e^(-1/4*(I*b^2 + 4*I*a*c)/c)/((-I*c/abs(c) + 1)*sqrt(abs(c))) - 2*I*(c*(-2*I*x + I*b/c) - 2*I*b)*e^(I*c*x^2 - I*b*x - I*a))/c^2 - 1/16*(-I*sqrt(2)*sqrt(pi)*(b^2 - 2*I*c)*erf(-1/4*sqrt(2)*(2*x - b/c)*(I*c/abs(c) + 1)*sqrt(abs(c)))*e^(-1/4*(-I*b^2 - 4*I*a*c)/c)/((I*c/abs(c) + 1)*sqrt(abs(c))) - 2*I*(c*(-2*I*x + I*b/c) - 2*I*b)*e^(-I*c*x^2 + I*b*x + I*a))/c^2","C",0
7,1,185,0,0.207687," ","integrate(x*sin(-c*x^2+b*x+a),x, algorithm=""giac"")","-\frac{\frac{i \, \sqrt{2} \sqrt{\pi} b \operatorname{erf}\left(-\frac{1}{4} \, \sqrt{2} {\left(2 \, x - \frac{b}{c}\right)} {\left(-\frac{i \, c}{{\left| c \right|}} + 1\right)} \sqrt{{\left| c \right|}}\right) e^{\left(-\frac{i \, b^{2} + 4 i \, a c}{4 \, c}\right)}}{{\left(-\frac{i \, c}{{\left| c \right|}} + 1\right)} \sqrt{{\left| c \right|}}} - 2 \, e^{\left(i \, c x^{2} - i \, b x - i \, a\right)}}{8 \, c} - \frac{-\frac{i \, \sqrt{2} \sqrt{\pi} b \operatorname{erf}\left(-\frac{1}{4} \, \sqrt{2} {\left(2 \, x - \frac{b}{c}\right)} {\left(\frac{i \, c}{{\left| c \right|}} + 1\right)} \sqrt{{\left| c \right|}}\right) e^{\left(-\frac{-i \, b^{2} - 4 i \, a c}{4 \, c}\right)}}{{\left(\frac{i \, c}{{\left| c \right|}} + 1\right)} \sqrt{{\left| c \right|}}} - 2 \, e^{\left(-i \, c x^{2} + i \, b x + i \, a\right)}}{8 \, c}"," ",0,"-1/8*(I*sqrt(2)*sqrt(pi)*b*erf(-1/4*sqrt(2)*(2*x - b/c)*(-I*c/abs(c) + 1)*sqrt(abs(c)))*e^(-1/4*(I*b^2 + 4*I*a*c)/c)/((-I*c/abs(c) + 1)*sqrt(abs(c))) - 2*e^(I*c*x^2 - I*b*x - I*a))/c - 1/8*(-I*sqrt(2)*sqrt(pi)*b*erf(-1/4*sqrt(2)*(2*x - b/c)*(I*c/abs(c) + 1)*sqrt(abs(c)))*e^(-1/4*(-I*b^2 - 4*I*a*c)/c)/((I*c/abs(c) + 1)*sqrt(abs(c))) - 2*e^(-I*c*x^2 + I*b*x + I*a))/c","C",0
8,1,137,0,0.263865," ","integrate(sin(-c*x^2+b*x+a),x, algorithm=""giac"")","-\frac{i \, \sqrt{2} \sqrt{\pi} \operatorname{erf}\left(-\frac{1}{4} \, \sqrt{2} {\left(2 \, x - \frac{b}{c}\right)} {\left(-\frac{i \, c}{{\left| c \right|}} + 1\right)} \sqrt{{\left| c \right|}}\right) e^{\left(-\frac{i \, b^{2} + 4 i \, a c}{4 \, c}\right)}}{4 \, {\left(-\frac{i \, c}{{\left| c \right|}} + 1\right)} \sqrt{{\left| c \right|}}} + \frac{i \, \sqrt{2} \sqrt{\pi} \operatorname{erf}\left(-\frac{1}{4} \, \sqrt{2} {\left(2 \, x - \frac{b}{c}\right)} {\left(\frac{i \, c}{{\left| c \right|}} + 1\right)} \sqrt{{\left| c \right|}}\right) e^{\left(-\frac{-i \, b^{2} - 4 i \, a c}{4 \, c}\right)}}{4 \, {\left(\frac{i \, c}{{\left| c \right|}} + 1\right)} \sqrt{{\left| c \right|}}}"," ",0,"-1/4*I*sqrt(2)*sqrt(pi)*erf(-1/4*sqrt(2)*(2*x - b/c)*(-I*c/abs(c) + 1)*sqrt(abs(c)))*e^(-1/4*(I*b^2 + 4*I*a*c)/c)/((-I*c/abs(c) + 1)*sqrt(abs(c))) + 1/4*I*sqrt(2)*sqrt(pi)*erf(-1/4*sqrt(2)*(2*x - b/c)*(I*c/abs(c) + 1)*sqrt(abs(c)))*e^(-1/4*(-I*b^2 - 4*I*a*c)/c)/((I*c/abs(c) + 1)*sqrt(abs(c)))","C",0
9,0,0,0,0.000000," ","integrate(sin(-c*x^2+b*x+a)/x,x, algorithm=""giac"")","\int \frac{\sin\left(-c x^{2} + b x + a\right)}{x}\,{d x}"," ",0,"integrate(sin(-c*x^2 + b*x + a)/x, x)","F",0
10,0,0,0,0.000000," ","integrate(-b*cos(-c*x^2+b*x+a)/x+sin(-c*x^2+b*x+a)/x^2,x, algorithm=""giac"")","\int -\frac{b \cos\left(-c x^{2} + b x + a\right)}{x} + \frac{\sin\left(-c x^{2} + b x + a\right)}{x^{2}}\,{d x}"," ",0,"integrate(-b*cos(-c*x^2 + b*x + a)/x + sin(-c*x^2 + b*x + a)/x^2, x)","F",0
11,1,75,0,0.133767," ","integrate(x^2*sin(1/4+x+x^2),x, algorithm=""giac"")","-\left(\frac{1}{32} i + \frac{3}{32}\right) \, \sqrt{2} \sqrt{\pi} \operatorname{erf}\left(\left(\frac{1}{4} i - \frac{1}{4}\right) \, \sqrt{2} {\left(2 \, x + 1\right)}\right) + \left(\frac{1}{32} i - \frac{3}{32}\right) \, \sqrt{2} \sqrt{\pi} \operatorname{erf}\left(-\left(\frac{1}{4} i + \frac{1}{4}\right) \, \sqrt{2} {\left(2 \, x + 1\right)}\right) - \frac{1}{8} i \, {\left(-2 i \, x + i\right)} e^{\left(i \, x^{2} + i \, x + \frac{1}{4} i\right)} - \frac{1}{8} i \, {\left(-2 i \, x + i\right)} e^{\left(-i \, x^{2} - i \, x - \frac{1}{4} i\right)}"," ",0,"-(1/32*I + 3/32)*sqrt(2)*sqrt(pi)*erf((1/4*I - 1/4)*sqrt(2)*(2*x + 1)) + (1/32*I - 3/32)*sqrt(2)*sqrt(pi)*erf(-(1/4*I + 1/4)*sqrt(2)*(2*x + 1)) - 1/8*I*(-2*I*x + I)*e^(I*x^2 + I*x + 1/4*I) - 1/8*I*(-2*I*x + I)*e^(-I*x^2 - I*x - 1/4*I)","C",0
12,1,65,0,0.183916," ","integrate(x*sin(1/4+x+x^2),x, algorithm=""giac"")","-\left(\frac{1}{16} i - \frac{1}{16}\right) \, \sqrt{2} \sqrt{\pi} \operatorname{erf}\left(\left(\frac{1}{4} i - \frac{1}{4}\right) \, \sqrt{2} {\left(2 \, x + 1\right)}\right) + \left(\frac{1}{16} i + \frac{1}{16}\right) \, \sqrt{2} \sqrt{\pi} \operatorname{erf}\left(-\left(\frac{1}{4} i + \frac{1}{4}\right) \, \sqrt{2} {\left(2 \, x + 1\right)}\right) - \frac{1}{4} \, e^{\left(i \, x^{2} + i \, x + \frac{1}{4} i\right)} - \frac{1}{4} \, e^{\left(-i \, x^{2} - i \, x - \frac{1}{4} i\right)}"," ",0,"-(1/16*I - 1/16)*sqrt(2)*sqrt(pi)*erf((1/4*I - 1/4)*sqrt(2)*(2*x + 1)) + (1/16*I + 1/16)*sqrt(2)*sqrt(pi)*erf(-(1/4*I + 1/4)*sqrt(2)*(2*x + 1)) - 1/4*e^(I*x^2 + I*x + 1/4*I) - 1/4*e^(-I*x^2 - I*x - 1/4*I)","C",0
13,1,39,0,1.230553," ","integrate(sin(1/4+x+x^2),x, algorithm=""giac"")","\left(\frac{1}{8} i - \frac{1}{8}\right) \, \sqrt{2} \sqrt{\pi} \operatorname{erf}\left(\left(\frac{1}{4} i - \frac{1}{4}\right) \, \sqrt{2} {\left(2 \, x + 1\right)}\right) - \left(\frac{1}{8} i + \frac{1}{8}\right) \, \sqrt{2} \sqrt{\pi} \operatorname{erf}\left(-\left(\frac{1}{4} i + \frac{1}{4}\right) \, \sqrt{2} {\left(2 \, x + 1\right)}\right)"," ",0,"(1/8*I - 1/8)*sqrt(2)*sqrt(pi)*erf((1/4*I - 1/4)*sqrt(2)*(2*x + 1)) - (1/8*I + 1/8)*sqrt(2)*sqrt(pi)*erf(-(1/4*I + 1/4)*sqrt(2)*(2*x + 1))","C",0
14,0,0,0,0.000000," ","integrate(sin(1/4+x+x^2)/x,x, algorithm=""giac"")","\int \frac{\sin\left(x^{2} + x + \frac{1}{4}\right)}{x}\,{d x}"," ",0,"integrate(sin(x^2 + x + 1/4)/x, x)","F",0
15,0,0,0,0.000000," ","integrate(sin(1/4+x+x^2)/x^2,x, algorithm=""giac"")","\int \frac{\sin\left(x^{2} + x + \frac{1}{4}\right)}{x^{2}}\,{d x}"," ",0,"integrate(sin(x^2 + x + 1/4)/x^2, x)","F",0
16,1,214,0,0.224796," ","integrate(x^2*sin(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{1}{6} \, x^{3} - \frac{{\left(c {\left(-2 i \, x - \frac{i \, b}{c}\right)} + 2 i \, b\right)} e^{\left(2 i \, c x^{2} + 2 i \, b x + 2 i \, a\right)} - \frac{\sqrt{\pi} {\left(b^{2} + i \, c\right)} \operatorname{erf}\left(-\frac{1}{2} \, \sqrt{c} {\left(2 \, x + \frac{b}{c}\right)} {\left(-\frac{i \, c}{{\left| c \right|}} + 1\right)}\right) e^{\left(-\frac{i \, b^{2} - 4 i \, a c}{2 \, c}\right)}}{\sqrt{c} {\left(-\frac{i \, c}{{\left| c \right|}} + 1\right)}}}{32 \, c^{2}} - \frac{{\left(c {\left(2 i \, x + \frac{i \, b}{c}\right)} - 2 i \, b\right)} e^{\left(-2 i \, c x^{2} - 2 i \, b x - 2 i \, a\right)} - \frac{\sqrt{\pi} {\left(b^{2} - i \, c\right)} \operatorname{erf}\left(-\frac{1}{2} \, \sqrt{c} {\left(2 \, x + \frac{b}{c}\right)} {\left(\frac{i \, c}{{\left| c \right|}} + 1\right)}\right) e^{\left(-\frac{-i \, b^{2} + 4 i \, a c}{2 \, c}\right)}}{\sqrt{c} {\left(\frac{i \, c}{{\left| c \right|}} + 1\right)}}}{32 \, c^{2}}"," ",0,"1/6*x^3 - 1/32*((c*(-2*I*x - I*b/c) + 2*I*b)*e^(2*I*c*x^2 + 2*I*b*x + 2*I*a) - sqrt(pi)*(b^2 + I*c)*erf(-1/2*sqrt(c)*(2*x + b/c)*(-I*c/abs(c) + 1))*e^(-1/2*(I*b^2 - 4*I*a*c)/c)/(sqrt(c)*(-I*c/abs(c) + 1)))/c^2 - 1/32*((c*(2*I*x + I*b/c) - 2*I*b)*e^(-2*I*c*x^2 - 2*I*b*x - 2*I*a) - sqrt(pi)*(b^2 - I*c)*erf(-1/2*sqrt(c)*(2*x + b/c)*(I*c/abs(c) + 1))*e^(-1/2*(-I*b^2 + 4*I*a*c)/c)/(sqrt(c)*(I*c/abs(c) + 1)))/c^2","C",0
17,1,170,0,0.416137," ","integrate(x*sin(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{1}{4} \, x^{2} - \frac{\frac{\sqrt{\pi} b \operatorname{erf}\left(-\frac{1}{2} \, \sqrt{c} {\left(2 \, x + \frac{b}{c}\right)} {\left(-\frac{i \, c}{{\left| c \right|}} + 1\right)}\right) e^{\left(-\frac{i \, b^{2} - 4 i \, a c}{2 \, c}\right)}}{\sqrt{c} {\left(-\frac{i \, c}{{\left| c \right|}} + 1\right)}} - i \, e^{\left(2 i \, c x^{2} + 2 i \, b x + 2 i \, a\right)}}{16 \, c} - \frac{\frac{\sqrt{\pi} b \operatorname{erf}\left(-\frac{1}{2} \, \sqrt{c} {\left(2 \, x + \frac{b}{c}\right)} {\left(\frac{i \, c}{{\left| c \right|}} + 1\right)}\right) e^{\left(-\frac{-i \, b^{2} + 4 i \, a c}{2 \, c}\right)}}{\sqrt{c} {\left(\frac{i \, c}{{\left| c \right|}} + 1\right)}} + i \, e^{\left(-2 i \, c x^{2} - 2 i \, b x - 2 i \, a\right)}}{16 \, c}"," ",0,"1/4*x^2 - 1/16*(sqrt(pi)*b*erf(-1/2*sqrt(c)*(2*x + b/c)*(-I*c/abs(c) + 1))*e^(-1/2*(I*b^2 - 4*I*a*c)/c)/(sqrt(c)*(-I*c/abs(c) + 1)) - I*e^(2*I*c*x^2 + 2*I*b*x + 2*I*a))/c - 1/16*(sqrt(pi)*b*erf(-1/2*sqrt(c)*(2*x + b/c)*(I*c/abs(c) + 1))*e^(-1/2*(-I*b^2 + 4*I*a*c)/c)/(sqrt(c)*(I*c/abs(c) + 1)) + I*e^(-2*I*c*x^2 - 2*I*b*x - 2*I*a))/c","C",0
18,1,122,0,0.794150," ","integrate(sin(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{1}{2} \, x + \frac{\sqrt{\pi} \operatorname{erf}\left(-\frac{1}{2} \, \sqrt{c} {\left(2 \, x + \frac{b}{c}\right)} {\left(-\frac{i \, c}{{\left| c \right|}} + 1\right)}\right) e^{\left(-\frac{i \, b^{2} - 4 i \, a c}{2 \, c}\right)}}{8 \, \sqrt{c} {\left(-\frac{i \, c}{{\left| c \right|}} + 1\right)}} + \frac{\sqrt{\pi} \operatorname{erf}\left(-\frac{1}{2} \, \sqrt{c} {\left(2 \, x + \frac{b}{c}\right)} {\left(\frac{i \, c}{{\left| c \right|}} + 1\right)}\right) e^{\left(-\frac{-i \, b^{2} + 4 i \, a c}{2 \, c}\right)}}{8 \, \sqrt{c} {\left(\frac{i \, c}{{\left| c \right|}} + 1\right)}}"," ",0,"1/2*x + 1/8*sqrt(pi)*erf(-1/2*sqrt(c)*(2*x + b/c)*(-I*c/abs(c) + 1))*e^(-1/2*(I*b^2 - 4*I*a*c)/c)/(sqrt(c)*(-I*c/abs(c) + 1)) + 1/8*sqrt(pi)*erf(-1/2*sqrt(c)*(2*x + b/c)*(I*c/abs(c) + 1))*e^(-1/2*(-I*b^2 + 4*I*a*c)/c)/(sqrt(c)*(I*c/abs(c) + 1))","C",0
19,0,0,0,0.000000," ","integrate(sin(c*x^2+b*x+a)^2/x,x, algorithm=""giac"")","\int \frac{\sin\left(c x^{2} + b x + a\right)^{2}}{x}\,{d x}"," ",0,"integrate(sin(c*x^2 + b*x + a)^2/x, x)","F",0
20,1,216,0,0.923823," ","integrate(x^2*sin(-c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{1}{6} \, x^{3} - \frac{{\left(c {\left(-2 i \, x + \frac{i \, b}{c}\right)} - 2 i \, b\right)} e^{\left(2 i \, c x^{2} - 2 i \, b x - 2 i \, a\right)} - \frac{\sqrt{\pi} {\left(b^{2} + i \, c\right)} \operatorname{erf}\left(-\frac{1}{2} \, \sqrt{c} {\left(2 \, x - \frac{b}{c}\right)} {\left(-\frac{i \, c}{{\left| c \right|}} + 1\right)}\right) e^{\left(-\frac{i \, b^{2} + 4 i \, a c}{2 \, c}\right)}}{\sqrt{c} {\left(-\frac{i \, c}{{\left| c \right|}} + 1\right)}}}{32 \, c^{2}} - \frac{{\left(c {\left(2 i \, x - \frac{i \, b}{c}\right)} + 2 i \, b\right)} e^{\left(-2 i \, c x^{2} + 2 i \, b x + 2 i \, a\right)} - \frac{\sqrt{\pi} {\left(b^{2} - i \, c\right)} \operatorname{erf}\left(-\frac{1}{2} \, \sqrt{c} {\left(2 \, x - \frac{b}{c}\right)} {\left(\frac{i \, c}{{\left| c \right|}} + 1\right)}\right) e^{\left(-\frac{-i \, b^{2} - 4 i \, a c}{2 \, c}\right)}}{\sqrt{c} {\left(\frac{i \, c}{{\left| c \right|}} + 1\right)}}}{32 \, c^{2}}"," ",0,"1/6*x^3 - 1/32*((c*(-2*I*x + I*b/c) - 2*I*b)*e^(2*I*c*x^2 - 2*I*b*x - 2*I*a) - sqrt(pi)*(b^2 + I*c)*erf(-1/2*sqrt(c)*(2*x - b/c)*(-I*c/abs(c) + 1))*e^(-1/2*(I*b^2 + 4*I*a*c)/c)/(sqrt(c)*(-I*c/abs(c) + 1)))/c^2 - 1/32*((c*(2*I*x - I*b/c) + 2*I*b)*e^(-2*I*c*x^2 + 2*I*b*x + 2*I*a) - sqrt(pi)*(b^2 - I*c)*erf(-1/2*sqrt(c)*(2*x - b/c)*(I*c/abs(c) + 1))*e^(-1/2*(-I*b^2 - 4*I*a*c)/c)/(sqrt(c)*(I*c/abs(c) + 1)))/c^2","C",0
21,1,172,0,0.237009," ","integrate(x*sin(-c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{1}{4} \, x^{2} + \frac{\frac{\sqrt{\pi} b \operatorname{erf}\left(-\frac{1}{2} \, \sqrt{c} {\left(2 \, x - \frac{b}{c}\right)} {\left(-\frac{i \, c}{{\left| c \right|}} + 1\right)}\right) e^{\left(-\frac{i \, b^{2} + 4 i \, a c}{2 \, c}\right)}}{\sqrt{c} {\left(-\frac{i \, c}{{\left| c \right|}} + 1\right)}} + i \, e^{\left(2 i \, c x^{2} - 2 i \, b x - 2 i \, a\right)}}{16 \, c} + \frac{\frac{\sqrt{\pi} b \operatorname{erf}\left(-\frac{1}{2} \, \sqrt{c} {\left(2 \, x - \frac{b}{c}\right)} {\left(\frac{i \, c}{{\left| c \right|}} + 1\right)}\right) e^{\left(-\frac{-i \, b^{2} - 4 i \, a c}{2 \, c}\right)}}{\sqrt{c} {\left(\frac{i \, c}{{\left| c \right|}} + 1\right)}} - i \, e^{\left(-2 i \, c x^{2} + 2 i \, b x + 2 i \, a\right)}}{16 \, c}"," ",0,"1/4*x^2 + 1/16*(sqrt(pi)*b*erf(-1/2*sqrt(c)*(2*x - b/c)*(-I*c/abs(c) + 1))*e^(-1/2*(I*b^2 + 4*I*a*c)/c)/(sqrt(c)*(-I*c/abs(c) + 1)) + I*e^(2*I*c*x^2 - 2*I*b*x - 2*I*a))/c + 1/16*(sqrt(pi)*b*erf(-1/2*sqrt(c)*(2*x - b/c)*(I*c/abs(c) + 1))*e^(-1/2*(-I*b^2 - 4*I*a*c)/c)/(sqrt(c)*(I*c/abs(c) + 1)) - I*e^(-2*I*c*x^2 + 2*I*b*x + 2*I*a))/c","C",0
22,1,124,0,0.587003," ","integrate(sin(-c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{1}{2} \, x + \frac{\sqrt{\pi} \operatorname{erf}\left(-\frac{1}{2} \, \sqrt{c} {\left(2 \, x - \frac{b}{c}\right)} {\left(-\frac{i \, c}{{\left| c \right|}} + 1\right)}\right) e^{\left(-\frac{i \, b^{2} + 4 i \, a c}{2 \, c}\right)}}{8 \, \sqrt{c} {\left(-\frac{i \, c}{{\left| c \right|}} + 1\right)}} + \frac{\sqrt{\pi} \operatorname{erf}\left(-\frac{1}{2} \, \sqrt{c} {\left(2 \, x - \frac{b}{c}\right)} {\left(\frac{i \, c}{{\left| c \right|}} + 1\right)}\right) e^{\left(-\frac{-i \, b^{2} - 4 i \, a c}{2 \, c}\right)}}{8 \, \sqrt{c} {\left(\frac{i \, c}{{\left| c \right|}} + 1\right)}}"," ",0,"1/2*x + 1/8*sqrt(pi)*erf(-1/2*sqrt(c)*(2*x - b/c)*(-I*c/abs(c) + 1))*e^(-1/2*(I*b^2 + 4*I*a*c)/c)/(sqrt(c)*(-I*c/abs(c) + 1)) + 1/8*sqrt(pi)*erf(-1/2*sqrt(c)*(2*x - b/c)*(I*c/abs(c) + 1))*e^(-1/2*(-I*b^2 - 4*I*a*c)/c)/(sqrt(c)*(I*c/abs(c) + 1))","C",0
23,0,0,0,0.000000," ","integrate(sin(-c*x^2+b*x+a)^2/x,x, algorithm=""giac"")","\int \frac{\sin\left(-c x^{2} + b x + a\right)^{2}}{x}\,{d x}"," ",0,"integrate(sin(-c*x^2 + b*x + a)^2/x, x)","F",0
24,1,64,0,0.716699," ","integrate(x^2*sin(1/4+x+x^2)^2,x, algorithm=""giac"")","\frac{1}{6} \, x^{3} - \frac{1}{32} \, {\left(-2 i \, x + i\right)} e^{\left(2 i \, x^{2} + 2 i \, x + \frac{1}{2} i\right)} - \frac{1}{32} \, {\left(2 i \, x - i\right)} e^{\left(-2 i \, x^{2} - 2 i \, x - \frac{1}{2} i\right)} + \frac{1}{32} i \, \sqrt{\pi} \operatorname{erf}\left(\left(i - 1\right) \, x + \frac{1}{2} i - \frac{1}{2}\right) - \frac{1}{32} i \, \sqrt{\pi} \operatorname{erf}\left(-\left(i + 1\right) \, x - \frac{1}{2} i - \frac{1}{2}\right)"," ",0,"1/6*x^3 - 1/32*(-2*I*x + I)*e^(2*I*x^2 + 2*I*x + 1/2*I) - 1/32*(2*I*x - I)*e^(-2*I*x^2 - 2*I*x - 1/2*I) + 1/32*I*sqrt(pi)*erf((I - 1)*x + 1/2*I - 1/2) - 1/32*I*sqrt(pi)*erf(-(I + 1)*x - 1/2*I - 1/2)","C",0
25,1,54,0,0.189941," ","integrate(x*sin(1/4+x+x^2)^2,x, algorithm=""giac"")","\frac{1}{4} \, x^{2} - \left(\frac{1}{32} i + \frac{1}{32}\right) \, \sqrt{\pi} \operatorname{erf}\left(\left(i - 1\right) \, x + \frac{1}{2} i - \frac{1}{2}\right) + \left(\frac{1}{32} i - \frac{1}{32}\right) \, \sqrt{\pi} \operatorname{erf}\left(-\left(i + 1\right) \, x - \frac{1}{2} i - \frac{1}{2}\right) + \frac{1}{16} i \, e^{\left(2 i \, x^{2} + 2 i \, x + \frac{1}{2} i\right)} - \frac{1}{16} i \, e^{\left(-2 i \, x^{2} - 2 i \, x - \frac{1}{2} i\right)}"," ",0,"1/4*x^2 - (1/32*I + 1/32)*sqrt(pi)*erf((I - 1)*x + 1/2*I - 1/2) + (1/32*I - 1/32)*sqrt(pi)*erf(-(I + 1)*x - 1/2*I - 1/2) + 1/16*I*e^(2*I*x^2 + 2*I*x + 1/2*I) - 1/16*I*e^(-2*I*x^2 - 2*I*x - 1/2*I)","C",0
26,1,26,0,0.172911," ","integrate(sin(1/4+x+x^2)^2,x, algorithm=""giac"")","\left(\frac{1}{16} i + \frac{1}{16}\right) \, \sqrt{\pi} \operatorname{erf}\left(\left(i - 1\right) \, x + \frac{1}{2} i - \frac{1}{2}\right) - \left(\frac{1}{16} i - \frac{1}{16}\right) \, \sqrt{\pi} \operatorname{erf}\left(-\left(i + 1\right) \, x - \frac{1}{2} i - \frac{1}{2}\right) + \frac{1}{2} \, x"," ",0,"(1/16*I + 1/16)*sqrt(pi)*erf((I - 1)*x + 1/2*I - 1/2) - (1/16*I - 1/16)*sqrt(pi)*erf(-(I + 1)*x - 1/2*I - 1/2) + 1/2*x","C",0
27,0,0,0,0.000000," ","integrate(sin(1/4+x+x^2)^2/x,x, algorithm=""giac"")","\int \frac{\sin\left(x^{2} + x + \frac{1}{4}\right)^{2}}{x}\,{d x}"," ",0,"integrate(sin(x^2 + x + 1/4)^2/x, x)","F",0
28,0,0,0,0.000000," ","integrate(sin(1/4+x+x^2)^2/x^2,x, algorithm=""giac"")","\int \frac{\sin\left(x^{2} + x + \frac{1}{4}\right)^{2}}{x^{2}}\,{d x}"," ",0,"integrate(sin(x^2 + x + 1/4)^2/x^2, x)","F",0
29,1,569,0,0.391144," ","integrate((e*x+d)^2*sin(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{i \, \sqrt{2} \sqrt{\pi} d^{2} \operatorname{erf}\left(-\frac{1}{4} \, \sqrt{2} {\left(2 \, x + \frac{b}{c}\right)} {\left(-\frac{i \, c}{{\left| c \right|}} + 1\right)} \sqrt{{\left| c \right|}}\right) e^{\left(-\frac{i \, b^{2} - 4 i \, a c}{4 \, c}\right)}}{4 \, {\left(-\frac{i \, c}{{\left| c \right|}} + 1\right)} \sqrt{{\left| c \right|}}} - \frac{i \, \sqrt{2} \sqrt{\pi} d^{2} \operatorname{erf}\left(-\frac{1}{4} \, \sqrt{2} {\left(2 \, x + \frac{b}{c}\right)} {\left(\frac{i \, c}{{\left| c \right|}} + 1\right)} \sqrt{{\left| c \right|}}\right) e^{\left(-\frac{-i \, b^{2} + 4 i \, a c}{4 \, c}\right)}}{4 \, {\left(\frac{i \, c}{{\left| c \right|}} + 1\right)} \sqrt{{\left| c \right|}}} - \frac{\frac{i \, \sqrt{2} \sqrt{\pi} b d \operatorname{erf}\left(-\frac{1}{4} \, \sqrt{2} {\left(2 \, x + \frac{b}{c}\right)} {\left(-\frac{i \, c}{{\left| c \right|}} + 1\right)} \sqrt{{\left| c \right|}}\right) e^{\left(-\frac{i \, b^{2} - 4 i \, a c - 4 \, c}{4 \, c}\right)}}{{\left(-\frac{i \, c}{{\left| c \right|}} + 1\right)} \sqrt{{\left| c \right|}}} + 2 \, d e^{\left(i \, c x^{2} + i \, b x + i \, a + 1\right)}}{4 \, c} - \frac{-\frac{i \, \sqrt{2} \sqrt{\pi} b d \operatorname{erf}\left(-\frac{1}{4} \, \sqrt{2} {\left(2 \, x + \frac{b}{c}\right)} {\left(\frac{i \, c}{{\left| c \right|}} + 1\right)} \sqrt{{\left| c \right|}}\right) e^{\left(-\frac{-i \, b^{2} + 4 i \, a c - 4 \, c}{4 \, c}\right)}}{{\left(\frac{i \, c}{{\left| c \right|}} + 1\right)} \sqrt{{\left| c \right|}}} + 2 \, d e^{\left(-i \, c x^{2} - i \, b x - i \, a + 1\right)}}{4 \, c} - \frac{-\frac{i \, \sqrt{2} \sqrt{\pi} {\left(b^{2} + 2 i \, c\right)} \operatorname{erf}\left(-\frac{1}{4} \, \sqrt{2} {\left(2 \, x + \frac{b}{c}\right)} {\left(-\frac{i \, c}{{\left| c \right|}} + 1\right)} \sqrt{{\left| c \right|}}\right) e^{\left(-\frac{i \, b^{2} - 4 i \, a c - 8 \, c}{4 \, c}\right)}}{{\left(-\frac{i \, c}{{\left| c \right|}} + 1\right)} \sqrt{{\left| c \right|}}} - 2 i \, {\left(c {\left(2 i \, x + \frac{i \, b}{c}\right)} - 2 i \, b\right)} e^{\left(i \, c x^{2} + i \, b x + i \, a + 2\right)}}{16 \, c^{2}} - \frac{\frac{i \, \sqrt{2} \sqrt{\pi} {\left(b^{2} - 2 i \, c\right)} \operatorname{erf}\left(-\frac{1}{4} \, \sqrt{2} {\left(2 \, x + \frac{b}{c}\right)} {\left(\frac{i \, c}{{\left| c \right|}} + 1\right)} \sqrt{{\left| c \right|}}\right) e^{\left(-\frac{-i \, b^{2} + 4 i \, a c - 8 \, c}{4 \, c}\right)}}{{\left(\frac{i \, c}{{\left| c \right|}} + 1\right)} \sqrt{{\left| c \right|}}} - 2 i \, {\left(c {\left(2 i \, x + \frac{i \, b}{c}\right)} - 2 i \, b\right)} e^{\left(-i \, c x^{2} - i \, b x - i \, a + 2\right)}}{16 \, c^{2}}"," ",0,"1/4*I*sqrt(2)*sqrt(pi)*d^2*erf(-1/4*sqrt(2)*(2*x + b/c)*(-I*c/abs(c) + 1)*sqrt(abs(c)))*e^(-1/4*(I*b^2 - 4*I*a*c)/c)/((-I*c/abs(c) + 1)*sqrt(abs(c))) - 1/4*I*sqrt(2)*sqrt(pi)*d^2*erf(-1/4*sqrt(2)*(2*x + b/c)*(I*c/abs(c) + 1)*sqrt(abs(c)))*e^(-1/4*(-I*b^2 + 4*I*a*c)/c)/((I*c/abs(c) + 1)*sqrt(abs(c))) - 1/4*(I*sqrt(2)*sqrt(pi)*b*d*erf(-1/4*sqrt(2)*(2*x + b/c)*(-I*c/abs(c) + 1)*sqrt(abs(c)))*e^(-1/4*(I*b^2 - 4*I*a*c - 4*c)/c)/((-I*c/abs(c) + 1)*sqrt(abs(c))) + 2*d*e^(I*c*x^2 + I*b*x + I*a + 1))/c - 1/4*(-I*sqrt(2)*sqrt(pi)*b*d*erf(-1/4*sqrt(2)*(2*x + b/c)*(I*c/abs(c) + 1)*sqrt(abs(c)))*e^(-1/4*(-I*b^2 + 4*I*a*c - 4*c)/c)/((I*c/abs(c) + 1)*sqrt(abs(c))) + 2*d*e^(-I*c*x^2 - I*b*x - I*a + 1))/c - 1/16*(-I*sqrt(2)*sqrt(pi)*(b^2 + 2*I*c)*erf(-1/4*sqrt(2)*(2*x + b/c)*(-I*c/abs(c) + 1)*sqrt(abs(c)))*e^(-1/4*(I*b^2 - 4*I*a*c - 8*c)/c)/((-I*c/abs(c) + 1)*sqrt(abs(c))) - 2*I*(c*(2*I*x + I*b/c) - 2*I*b)*e^(I*c*x^2 + I*b*x + I*a + 2))/c^2 - 1/16*(I*sqrt(2)*sqrt(pi)*(b^2 - 2*I*c)*erf(-1/4*sqrt(2)*(2*x + b/c)*(I*c/abs(c) + 1)*sqrt(abs(c)))*e^(-1/4*(-I*b^2 + 4*I*a*c - 8*c)/c)/((I*c/abs(c) + 1)*sqrt(abs(c))) - 2*I*(c*(2*I*x + I*b/c) - 2*I*b)*e^(-I*c*x^2 - I*b*x - I*a + 2))/c^2","C",0
30,1,327,0,0.191468," ","integrate((e*x+d)*sin(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{i \, \sqrt{2} \sqrt{\pi} d \operatorname{erf}\left(-\frac{1}{4} \, \sqrt{2} {\left(2 \, x + \frac{b}{c}\right)} {\left(-\frac{i \, c}{{\left| c \right|}} + 1\right)} \sqrt{{\left| c \right|}}\right) e^{\left(-\frac{i \, b^{2} - 4 i \, a c}{4 \, c}\right)}}{4 \, {\left(-\frac{i \, c}{{\left| c \right|}} + 1\right)} \sqrt{{\left| c \right|}}} - \frac{i \, \sqrt{2} \sqrt{\pi} d \operatorname{erf}\left(-\frac{1}{4} \, \sqrt{2} {\left(2 \, x + \frac{b}{c}\right)} {\left(\frac{i \, c}{{\left| c \right|}} + 1\right)} \sqrt{{\left| c \right|}}\right) e^{\left(-\frac{-i \, b^{2} + 4 i \, a c}{4 \, c}\right)}}{4 \, {\left(\frac{i \, c}{{\left| c \right|}} + 1\right)} \sqrt{{\left| c \right|}}} - \frac{\frac{i \, \sqrt{2} \sqrt{\pi} b \operatorname{erf}\left(-\frac{1}{4} \, \sqrt{2} {\left(2 \, x + \frac{b}{c}\right)} {\left(-\frac{i \, c}{{\left| c \right|}} + 1\right)} \sqrt{{\left| c \right|}}\right) e^{\left(-\frac{i \, b^{2} - 4 i \, a c - 4 \, c}{4 \, c}\right)}}{{\left(-\frac{i \, c}{{\left| c \right|}} + 1\right)} \sqrt{{\left| c \right|}}} + 2 \, e^{\left(i \, c x^{2} + i \, b x + i \, a + 1\right)}}{8 \, c} - \frac{-\frac{i \, \sqrt{2} \sqrt{\pi} b \operatorname{erf}\left(-\frac{1}{4} \, \sqrt{2} {\left(2 \, x + \frac{b}{c}\right)} {\left(\frac{i \, c}{{\left| c \right|}} + 1\right)} \sqrt{{\left| c \right|}}\right) e^{\left(-\frac{-i \, b^{2} + 4 i \, a c - 4 \, c}{4 \, c}\right)}}{{\left(\frac{i \, c}{{\left| c \right|}} + 1\right)} \sqrt{{\left| c \right|}}} + 2 \, e^{\left(-i \, c x^{2} - i \, b x - i \, a + 1\right)}}{8 \, c}"," ",0,"1/4*I*sqrt(2)*sqrt(pi)*d*erf(-1/4*sqrt(2)*(2*x + b/c)*(-I*c/abs(c) + 1)*sqrt(abs(c)))*e^(-1/4*(I*b^2 - 4*I*a*c)/c)/((-I*c/abs(c) + 1)*sqrt(abs(c))) - 1/4*I*sqrt(2)*sqrt(pi)*d*erf(-1/4*sqrt(2)*(2*x + b/c)*(I*c/abs(c) + 1)*sqrt(abs(c)))*e^(-1/4*(-I*b^2 + 4*I*a*c)/c)/((I*c/abs(c) + 1)*sqrt(abs(c))) - 1/8*(I*sqrt(2)*sqrt(pi)*b*erf(-1/4*sqrt(2)*(2*x + b/c)*(-I*c/abs(c) + 1)*sqrt(abs(c)))*e^(-1/4*(I*b^2 - 4*I*a*c - 4*c)/c)/((-I*c/abs(c) + 1)*sqrt(abs(c))) + 2*e^(I*c*x^2 + I*b*x + I*a + 1))/c - 1/8*(-I*sqrt(2)*sqrt(pi)*b*erf(-1/4*sqrt(2)*(2*x + b/c)*(I*c/abs(c) + 1)*sqrt(abs(c)))*e^(-1/4*(-I*b^2 + 4*I*a*c - 4*c)/c)/((I*c/abs(c) + 1)*sqrt(abs(c))) + 2*e^(-I*c*x^2 - I*b*x - I*a + 1))/c","C",0
31,1,135,0,0.193960," ","integrate(sin(c*x^2+b*x+a),x, algorithm=""giac"")","\frac{i \, \sqrt{2} \sqrt{\pi} \operatorname{erf}\left(-\frac{1}{4} \, \sqrt{2} {\left(2 \, x + \frac{b}{c}\right)} {\left(-\frac{i \, c}{{\left| c \right|}} + 1\right)} \sqrt{{\left| c \right|}}\right) e^{\left(-\frac{i \, b^{2} - 4 i \, a c}{4 \, c}\right)}}{4 \, {\left(-\frac{i \, c}{{\left| c \right|}} + 1\right)} \sqrt{{\left| c \right|}}} - \frac{i \, \sqrt{2} \sqrt{\pi} \operatorname{erf}\left(-\frac{1}{4} \, \sqrt{2} {\left(2 \, x + \frac{b}{c}\right)} {\left(\frac{i \, c}{{\left| c \right|}} + 1\right)} \sqrt{{\left| c \right|}}\right) e^{\left(-\frac{-i \, b^{2} + 4 i \, a c}{4 \, c}\right)}}{4 \, {\left(\frac{i \, c}{{\left| c \right|}} + 1\right)} \sqrt{{\left| c \right|}}}"," ",0,"1/4*I*sqrt(2)*sqrt(pi)*erf(-1/4*sqrt(2)*(2*x + b/c)*(-I*c/abs(c) + 1)*sqrt(abs(c)))*e^(-1/4*(I*b^2 - 4*I*a*c)/c)/((-I*c/abs(c) + 1)*sqrt(abs(c))) - 1/4*I*sqrt(2)*sqrt(pi)*erf(-1/4*sqrt(2)*(2*x + b/c)*(I*c/abs(c) + 1)*sqrt(abs(c)))*e^(-1/4*(-I*b^2 + 4*I*a*c)/c)/((I*c/abs(c) + 1)*sqrt(abs(c)))","C",0
32,0,0,0,0.000000," ","integrate(sin(c*x^2+b*x+a)/(e*x+d),x, algorithm=""giac"")","\int \frac{\sin\left(c x^{2} + b x + a\right)}{e x + d}\,{d x}"," ",0,"integrate(sin(c*x^2 + b*x + a)/(e*x + d), x)","F",0
33,1,538,0,0.570132," ","integrate((e*x+d)^2*sin(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{1}{6} \, x^{3} e^{2} + \frac{1}{2} \, d x^{2} e + \frac{1}{2} \, d^{2} x + \frac{\sqrt{\pi} d^{2} \operatorname{erf}\left(-\frac{1}{2} \, \sqrt{c} {\left(2 \, x + \frac{b}{c}\right)} {\left(-\frac{i \, c}{{\left| c \right|}} + 1\right)}\right) e^{\left(-\frac{i \, b^{2} - 4 i \, a c}{2 \, c}\right)}}{8 \, \sqrt{c} {\left(-\frac{i \, c}{{\left| c \right|}} + 1\right)}} + \frac{\sqrt{\pi} d^{2} \operatorname{erf}\left(-\frac{1}{2} \, \sqrt{c} {\left(2 \, x + \frac{b}{c}\right)} {\left(\frac{i \, c}{{\left| c \right|}} + 1\right)}\right) e^{\left(-\frac{-i \, b^{2} + 4 i \, a c}{2 \, c}\right)}}{8 \, \sqrt{c} {\left(\frac{i \, c}{{\left| c \right|}} + 1\right)}} - \frac{\frac{\sqrt{\pi} b d \operatorname{erf}\left(-\frac{1}{2} \, \sqrt{c} {\left(2 \, x + \frac{b}{c}\right)} {\left(-\frac{i \, c}{{\left| c \right|}} + 1\right)}\right) e^{\left(-\frac{i \, b^{2} - 4 i \, a c - 2 \, c}{2 \, c}\right)}}{\sqrt{c} {\left(-\frac{i \, c}{{\left| c \right|}} + 1\right)}} - i \, d e^{\left(2 i \, c x^{2} + 2 i \, b x + 2 i \, a + 1\right)}}{8 \, c} - \frac{\frac{\sqrt{\pi} b d \operatorname{erf}\left(-\frac{1}{2} \, \sqrt{c} {\left(2 \, x + \frac{b}{c}\right)} {\left(\frac{i \, c}{{\left| c \right|}} + 1\right)}\right) e^{\left(-\frac{-i \, b^{2} + 4 i \, a c - 2 \, c}{2 \, c}\right)}}{\sqrt{c} {\left(\frac{i \, c}{{\left| c \right|}} + 1\right)}} + i \, d e^{\left(-2 i \, c x^{2} - 2 i \, b x - 2 i \, a + 1\right)}}{8 \, c} - \frac{{\left(c {\left(-2 i \, x - \frac{i \, b}{c}\right)} + 2 i \, b\right)} e^{\left(2 i \, c x^{2} + 2 i \, b x + 2 i \, a + 2\right)} - \frac{\sqrt{\pi} {\left(b^{2} + i \, c\right)} \operatorname{erf}\left(-\frac{1}{2} \, \sqrt{c} {\left(2 \, x + \frac{b}{c}\right)} {\left(-\frac{i \, c}{{\left| c \right|}} + 1\right)}\right) e^{\left(-\frac{i \, b^{2} - 4 i \, a c - 4 \, c}{2 \, c}\right)}}{\sqrt{c} {\left(-\frac{i \, c}{{\left| c \right|}} + 1\right)}}}{32 \, c^{2}} - \frac{{\left(c {\left(2 i \, x + \frac{i \, b}{c}\right)} - 2 i \, b\right)} e^{\left(-2 i \, c x^{2} - 2 i \, b x - 2 i \, a + 2\right)} - \frac{\sqrt{\pi} {\left(b^{2} - i \, c\right)} \operatorname{erf}\left(-\frac{1}{2} \, \sqrt{c} {\left(2 \, x + \frac{b}{c}\right)} {\left(\frac{i \, c}{{\left| c \right|}} + 1\right)}\right) e^{\left(-\frac{-i \, b^{2} + 4 i \, a c - 4 \, c}{2 \, c}\right)}}{\sqrt{c} {\left(\frac{i \, c}{{\left| c \right|}} + 1\right)}}}{32 \, c^{2}}"," ",0,"1/6*x^3*e^2 + 1/2*d*x^2*e + 1/2*d^2*x + 1/8*sqrt(pi)*d^2*erf(-1/2*sqrt(c)*(2*x + b/c)*(-I*c/abs(c) + 1))*e^(-1/2*(I*b^2 - 4*I*a*c)/c)/(sqrt(c)*(-I*c/abs(c) + 1)) + 1/8*sqrt(pi)*d^2*erf(-1/2*sqrt(c)*(2*x + b/c)*(I*c/abs(c) + 1))*e^(-1/2*(-I*b^2 + 4*I*a*c)/c)/(sqrt(c)*(I*c/abs(c) + 1)) - 1/8*(sqrt(pi)*b*d*erf(-1/2*sqrt(c)*(2*x + b/c)*(-I*c/abs(c) + 1))*e^(-1/2*(I*b^2 - 4*I*a*c - 2*c)/c)/(sqrt(c)*(-I*c/abs(c) + 1)) - I*d*e^(2*I*c*x^2 + 2*I*b*x + 2*I*a + 1))/c - 1/8*(sqrt(pi)*b*d*erf(-1/2*sqrt(c)*(2*x + b/c)*(I*c/abs(c) + 1))*e^(-1/2*(-I*b^2 + 4*I*a*c - 2*c)/c)/(sqrt(c)*(I*c/abs(c) + 1)) + I*d*e^(-2*I*c*x^2 - 2*I*b*x - 2*I*a + 1))/c - 1/32*((c*(-2*I*x - I*b/c) + 2*I*b)*e^(2*I*c*x^2 + 2*I*b*x + 2*I*a + 2) - sqrt(pi)*(b^2 + I*c)*erf(-1/2*sqrt(c)*(2*x + b/c)*(-I*c/abs(c) + 1))*e^(-1/2*(I*b^2 - 4*I*a*c - 4*c)/c)/(sqrt(c)*(-I*c/abs(c) + 1)))/c^2 - 1/32*((c*(2*I*x + I*b/c) - 2*I*b)*e^(-2*I*c*x^2 - 2*I*b*x - 2*I*a + 2) - sqrt(pi)*(b^2 - I*c)*erf(-1/2*sqrt(c)*(2*x + b/c)*(I*c/abs(c) + 1))*e^(-1/2*(-I*b^2 + 4*I*a*c - 4*c)/c)/(sqrt(c)*(I*c/abs(c) + 1)))/c^2","C",0
34,1,304,0,1.340340," ","integrate((e*x+d)*sin(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{1}{4} \, x^{2} e + \frac{1}{2} \, d x + \frac{\sqrt{\pi} d \operatorname{erf}\left(-\frac{1}{2} \, \sqrt{c} {\left(2 \, x + \frac{b}{c}\right)} {\left(-\frac{i \, c}{{\left| c \right|}} + 1\right)}\right) e^{\left(-\frac{i \, b^{2} - 4 i \, a c}{2 \, c}\right)}}{8 \, \sqrt{c} {\left(-\frac{i \, c}{{\left| c \right|}} + 1\right)}} + \frac{\sqrt{\pi} d \operatorname{erf}\left(-\frac{1}{2} \, \sqrt{c} {\left(2 \, x + \frac{b}{c}\right)} {\left(\frac{i \, c}{{\left| c \right|}} + 1\right)}\right) e^{\left(-\frac{-i \, b^{2} + 4 i \, a c}{2 \, c}\right)}}{8 \, \sqrt{c} {\left(\frac{i \, c}{{\left| c \right|}} + 1\right)}} - \frac{\frac{\sqrt{\pi} b \operatorname{erf}\left(-\frac{1}{2} \, \sqrt{c} {\left(2 \, x + \frac{b}{c}\right)} {\left(-\frac{i \, c}{{\left| c \right|}} + 1\right)}\right) e^{\left(-\frac{i \, b^{2} - 4 i \, a c - 2 \, c}{2 \, c}\right)}}{\sqrt{c} {\left(-\frac{i \, c}{{\left| c \right|}} + 1\right)}} - i \, e^{\left(2 i \, c x^{2} + 2 i \, b x + 2 i \, a + 1\right)}}{16 \, c} - \frac{\frac{\sqrt{\pi} b \operatorname{erf}\left(-\frac{1}{2} \, \sqrt{c} {\left(2 \, x + \frac{b}{c}\right)} {\left(\frac{i \, c}{{\left| c \right|}} + 1\right)}\right) e^{\left(-\frac{-i \, b^{2} + 4 i \, a c - 2 \, c}{2 \, c}\right)}}{\sqrt{c} {\left(\frac{i \, c}{{\left| c \right|}} + 1\right)}} + i \, e^{\left(-2 i \, c x^{2} - 2 i \, b x - 2 i \, a + 1\right)}}{16 \, c}"," ",0,"1/4*x^2*e + 1/2*d*x + 1/8*sqrt(pi)*d*erf(-1/2*sqrt(c)*(2*x + b/c)*(-I*c/abs(c) + 1))*e^(-1/2*(I*b^2 - 4*I*a*c)/c)/(sqrt(c)*(-I*c/abs(c) + 1)) + 1/8*sqrt(pi)*d*erf(-1/2*sqrt(c)*(2*x + b/c)*(I*c/abs(c) + 1))*e^(-1/2*(-I*b^2 + 4*I*a*c)/c)/(sqrt(c)*(I*c/abs(c) + 1)) - 1/16*(sqrt(pi)*b*erf(-1/2*sqrt(c)*(2*x + b/c)*(-I*c/abs(c) + 1))*e^(-1/2*(I*b^2 - 4*I*a*c - 2*c)/c)/(sqrt(c)*(-I*c/abs(c) + 1)) - I*e^(2*I*c*x^2 + 2*I*b*x + 2*I*a + 1))/c - 1/16*(sqrt(pi)*b*erf(-1/2*sqrt(c)*(2*x + b/c)*(I*c/abs(c) + 1))*e^(-1/2*(-I*b^2 + 4*I*a*c - 2*c)/c)/(sqrt(c)*(I*c/abs(c) + 1)) + I*e^(-2*I*c*x^2 - 2*I*b*x - 2*I*a + 1))/c","C",0
35,1,122,0,0.268990," ","integrate(sin(c*x^2+b*x+a)^2,x, algorithm=""giac"")","\frac{1}{2} \, x + \frac{\sqrt{\pi} \operatorname{erf}\left(-\frac{1}{2} \, \sqrt{c} {\left(2 \, x + \frac{b}{c}\right)} {\left(-\frac{i \, c}{{\left| c \right|}} + 1\right)}\right) e^{\left(-\frac{i \, b^{2} - 4 i \, a c}{2 \, c}\right)}}{8 \, \sqrt{c} {\left(-\frac{i \, c}{{\left| c \right|}} + 1\right)}} + \frac{\sqrt{\pi} \operatorname{erf}\left(-\frac{1}{2} \, \sqrt{c} {\left(2 \, x + \frac{b}{c}\right)} {\left(\frac{i \, c}{{\left| c \right|}} + 1\right)}\right) e^{\left(-\frac{-i \, b^{2} + 4 i \, a c}{2 \, c}\right)}}{8 \, \sqrt{c} {\left(\frac{i \, c}{{\left| c \right|}} + 1\right)}}"," ",0,"1/2*x + 1/8*sqrt(pi)*erf(-1/2*sqrt(c)*(2*x + b/c)*(-I*c/abs(c) + 1))*e^(-1/2*(I*b^2 - 4*I*a*c)/c)/(sqrt(c)*(-I*c/abs(c) + 1)) + 1/8*sqrt(pi)*erf(-1/2*sqrt(c)*(2*x + b/c)*(I*c/abs(c) + 1))*e^(-1/2*(-I*b^2 + 4*I*a*c)/c)/(sqrt(c)*(I*c/abs(c) + 1))","C",0
36,0,0,0,0.000000," ","integrate(sin(c*x^2+b*x+a)^2/(e*x+d),x, algorithm=""giac"")","\int \frac{\sin\left(c x^{2} + b x + a\right)^{2}}{e x + d}\,{d x}"," ",0,"integrate(sin(c*x^2 + b*x + a)^2/(e*x + d), x)","F",0
