1,0,0,0,0.565555," ","integrate(F^(c*(b*x+a))*sin(e*x+d)^n,x, algorithm=""fricas"")","{\rm integral}\left(F^{b c x + a c} \sin\left(e x + d\right)^{n}, x\right)"," ",0,"integral(F^(b*c*x + a*c)*sin(e*x + d)^n, x)","F",0
2,1,171,0,0.623266," ","integrate(F^(c*(b*x+a))*sin(e*x+d)^3,x, algorithm=""fricas"")","\frac{{\left(3 \, e^{3} \cos\left(e x + d\right)^{3} - 9 \, e^{3} \cos\left(e x + d\right) + 3 \, {\left(b^{2} c^{2} e \cos\left(e x + d\right)^{3} - b^{2} c^{2} e \cos\left(e x + d\right)\right)} \log\left(F\right)^{2} - {\left({\left(b^{3} c^{3} \cos\left(e x + d\right)^{2} - b^{3} c^{3}\right)} \log\left(F\right)^{3} + {\left(b c e^{2} \cos\left(e x + d\right)^{2} - 7 \, b c e^{2}\right)} \log\left(F\right)\right)} \sin\left(e x + d\right)\right)} F^{b c x + a c}}{b^{4} c^{4} \log\left(F\right)^{4} + 10 \, b^{2} c^{2} e^{2} \log\left(F\right)^{2} + 9 \, e^{4}}"," ",0,"(3*e^3*cos(e*x + d)^3 - 9*e^3*cos(e*x + d) + 3*(b^2*c^2*e*cos(e*x + d)^3 - b^2*c^2*e*cos(e*x + d))*log(F)^2 - ((b^3*c^3*cos(e*x + d)^2 - b^3*c^3)*log(F)^3 + (b*c*e^2*cos(e*x + d)^2 - 7*b*c*e^2)*log(F))*sin(e*x + d))*F^(b*c*x + a*c)/(b^4*c^4*log(F)^4 + 10*b^2*c^2*e^2*log(F)^2 + 9*e^4)","A",0
3,1,89,0,1.863579," ","integrate(F^(c*(b*x+a))*sin(e*x+d)^2,x, algorithm=""fricas"")","-\frac{{\left(2 \, b c e \cos\left(e x + d\right) \log\left(F\right) \sin\left(e x + d\right) + {\left(b^{2} c^{2} \cos\left(e x + d\right)^{2} - b^{2} c^{2}\right)} \log\left(F\right)^{2} - 2 \, e^{2}\right)} F^{b c x + a c}}{b^{3} c^{3} \log\left(F\right)^{3} + 4 \, b c e^{2} \log\left(F\right)}"," ",0,"-(2*b*c*e*cos(e*x + d)*log(F)*sin(e*x + d) + (b^2*c^2*cos(e*x + d)^2 - b^2*c^2)*log(F)^2 - 2*e^2)*F^(b*c*x + a*c)/(b^3*c^3*log(F)^3 + 4*b*c*e^2*log(F))","A",0
4,1,49,0,0.924965," ","integrate(F^(c*(b*x+a))*sin(e*x+d),x, algorithm=""fricas"")","\frac{{\left(b c \log\left(F\right) \sin\left(e x + d\right) - e \cos\left(e x + d\right)\right)} F^{b c x + a c}}{b^{2} c^{2} \log\left(F\right)^{2} + e^{2}}"," ",0,"(b*c*log(F)*sin(e*x + d) - e*cos(e*x + d))*F^(b*c*x + a*c)/(b^2*c^2*log(F)^2 + e^2)","A",0
5,0,0,0,0.846595," ","integrate(F^(c*(b*x+a))*csc(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(F^{b c x + a c} \csc\left(e x + d\right), x\right)"," ",0,"integral(F^(b*c*x + a*c)*csc(e*x + d), x)","F",0
6,0,0,0,0.951740," ","integrate(F^(c*(b*x+a))*csc(e*x+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(F^{b c x + a c} \csc\left(e x + d\right)^{2}, x\right)"," ",0,"integral(F^(b*c*x + a*c)*csc(e*x + d)^2, x)","F",0
7,0,0,0,0.643931," ","integrate(F^(c*(b*x+a))*csc(e*x+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(F^{b c x + a c} \csc\left(e x + d\right)^{3}, x\right)"," ",0,"integral(F^(b*c*x + a*c)*csc(e*x + d)^3, x)","F",0
8,0,0,0,3.497249," ","integrate(F^(c*(b*x+a))*csc(e*x+d)^4,x, algorithm=""fricas"")","{\rm integral}\left(F^{b c x + a c} \csc\left(e x + d\right)^{4}, x\right)"," ",0,"integral(F^(b*c*x + a*c)*csc(e*x + d)^4, x)","F",0
9,1,36,0,0.643644," ","integrate(exp(x)*sin(x)^4,x, algorithm=""fricas"")","\frac{4}{85} \, {\left(5 \, \cos\left(x\right)^{3} - 11 \, \cos\left(x\right)\right)} e^{x} \sin\left(x\right) + \frac{1}{85} \, {\left(5 \, \cos\left(x\right)^{4} - 22 \, \cos\left(x\right)^{2} + 41\right)} e^{x}"," ",0,"4/85*(5*cos(x)^3 - 11*cos(x))*e^x*sin(x) + 1/85*(5*cos(x)^4 - 22*cos(x)^2 + 41)*e^x","A",0
10,0,0,0,0.668897," ","integrate(F^(c*(b*x+a))*cos(e*x+d)^n,x, algorithm=""fricas"")","{\rm integral}\left(F^{b c x + a c} \cos\left(e x + d\right)^{n}, x\right)"," ",0,"integral(F^(b*c*x + a*c)*cos(e*x + d)^n, x)","F",0
11,1,142,0,2.091205," ","integrate(F^(c*(b*x+a))*cos(e*x+d)^3,x, algorithm=""fricas"")","\frac{{\left(b^{3} c^{3} \cos\left(e x + d\right)^{3} \log\left(F\right)^{3} + {\left(b c e^{2} \cos\left(e x + d\right)^{3} + 6 \, b c e^{2} \cos\left(e x + d\right)\right)} \log\left(F\right) + 3 \, {\left(b^{2} c^{2} e \cos\left(e x + d\right)^{2} \log\left(F\right)^{2} + e^{3} \cos\left(e x + d\right)^{2} + 2 \, e^{3}\right)} \sin\left(e x + d\right)\right)} F^{b c x + a c}}{b^{4} c^{4} \log\left(F\right)^{4} + 10 \, b^{2} c^{2} e^{2} \log\left(F\right)^{2} + 9 \, e^{4}}"," ",0,"(b^3*c^3*cos(e*x + d)^3*log(F)^3 + (b*c*e^2*cos(e*x + d)^3 + 6*b*c*e^2*cos(e*x + d))*log(F) + 3*(b^2*c^2*e*cos(e*x + d)^2*log(F)^2 + e^3*cos(e*x + d)^2 + 2*e^3)*sin(e*x + d))*F^(b*c*x + a*c)/(b^4*c^4*log(F)^4 + 10*b^2*c^2*e^2*log(F)^2 + 9*e^4)","A",0
12,1,78,0,0.711019," ","integrate(F^(c*(b*x+a))*cos(e*x+d)^2,x, algorithm=""fricas"")","\frac{{\left(b^{2} c^{2} \cos\left(e x + d\right)^{2} \log\left(F\right)^{2} + 2 \, b c e \cos\left(e x + d\right) \log\left(F\right) \sin\left(e x + d\right) + 2 \, e^{2}\right)} F^{b c x + a c}}{b^{3} c^{3} \log\left(F\right)^{3} + 4 \, b c e^{2} \log\left(F\right)}"," ",0,"(b^2*c^2*cos(e*x + d)^2*log(F)^2 + 2*b*c*e*cos(e*x + d)*log(F)*sin(e*x + d) + 2*e^2)*F^(b*c*x + a*c)/(b^3*c^3*log(F)^3 + 4*b*c*e^2*log(F))","A",0
13,1,48,0,0.727276," ","integrate(F^(c*(b*x+a))*cos(e*x+d),x, algorithm=""fricas"")","\frac{{\left(b c \cos\left(e x + d\right) \log\left(F\right) + e \sin\left(e x + d\right)\right)} F^{b c x + a c}}{b^{2} c^{2} \log\left(F\right)^{2} + e^{2}}"," ",0,"(b*c*cos(e*x + d)*log(F) + e*sin(e*x + d))*F^(b*c*x + a*c)/(b^2*c^2*log(F)^2 + e^2)","A",0
14,0,0,0,0.585707," ","integrate(F^(c*(b*x+a))*sec(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(F^{b c x + a c} \sec\left(e x + d\right), x\right)"," ",0,"integral(F^(b*c*x + a*c)*sec(e*x + d), x)","F",0
15,0,0,0,1.270361," ","integrate(F^(c*(b*x+a))*sec(e*x+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(F^{b c x + a c} \sec\left(e x + d\right)^{2}, x\right)"," ",0,"integral(F^(b*c*x + a*c)*sec(e*x + d)^2, x)","F",0
16,0,0,0,0.645198," ","integrate(F^(c*(b*x+a))*sec(e*x+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(F^{b c x + a c} \sec\left(e x + d\right)^{3}, x\right)"," ",0,"integral(F^(b*c*x + a*c)*sec(e*x + d)^3, x)","F",0
17,0,0,0,3.195773," ","integrate(F^(c*(b*x+a))*sec(e*x+d)^4,x, algorithm=""fricas"")","{\rm integral}\left(F^{b c x + a c} \sec\left(e x + d\right)^{4}, x\right)"," ",0,"integral(F^(b*c*x + a*c)*sec(e*x + d)^4, x)","F",0
18,1,36,0,0.643151," ","integrate(exp(x)*cos(x)^4,x, algorithm=""fricas"")","\frac{4}{85} \, {\left(5 \, \cos\left(x\right)^{3} + 6 \, \cos\left(x\right)\right)} e^{x} \sin\left(x\right) + \frac{1}{85} \, {\left(5 \, \cos\left(x\right)^{4} + 12 \, \cos\left(x\right)^{2} + 24\right)} e^{x}"," ",0,"4/85*(5*cos(x)^3 + 6*cos(x))*e^x*sin(x) + 1/85*(5*cos(x)^4 + 12*cos(x)^2 + 24)*e^x","A",0
19,0,0,0,0.721184," ","integrate(exp(c*(b*x+a))*tan(e*x+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(e^{\left(b c x + a c\right)} \tan\left(e x + d\right)^{3}, x\right)"," ",0,"integral(e^(b*c*x + a*c)*tan(e*x + d)^3, x)","F",0
20,0,0,0,0.736343," ","integrate(exp(c*(b*x+a))*tan(e*x+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(e^{\left(b c x + a c\right)} \tan\left(e x + d\right)^{2}, x\right)"," ",0,"integral(e^(b*c*x + a*c)*tan(e*x + d)^2, x)","F",0
21,0,0,0,1.022308," ","integrate(exp(c*(b*x+a))*tan(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(e^{\left(b c x + a c\right)} \tan\left(e x + d\right), x\right)"," ",0,"integral(e^(b*c*x + a*c)*tan(e*x + d), x)","F",0
22,0,0,0,0.577592," ","integrate(exp(c*(b*x+a))*cot(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\cot\left(e x + d\right) e^{\left(b c x + a c\right)}, x\right)"," ",0,"integral(cot(e*x + d)*e^(b*c*x + a*c), x)","F",0
23,0,0,0,0.402327," ","integrate(exp(c*(b*x+a))*cot(e*x+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\cot\left(e x + d\right)^{2} e^{\left(b c x + a c\right)}, x\right)"," ",0,"integral(cot(e*x + d)^2*e^(b*c*x + a*c), x)","F",0
24,0,0,0,0.416675," ","integrate(exp(c*(b*x+a))*cot(e*x+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\cot\left(e x + d\right)^{3} e^{\left(b c x + a c\right)}, x\right)"," ",0,"integral(cot(e*x + d)^3*e^(b*c*x + a*c), x)","F",0
25,0,0,0,0.758027," ","integrate(F^(b*x+a)*cot(1/2*c+1/4*pi+1/2*d*x),x, algorithm=""fricas"")","{\rm integral}\left(F^{b x + a} \cot\left(\frac{1}{4} \, \pi + \frac{1}{2} \, d x + \frac{1}{2} \, c\right), x\right)"," ",0,"integral(F^(b*x + a)*cot(1/4*pi + 1/2*d*x + 1/2*c), x)","F",0
26,0,0,0,1.551722," ","integrate(F^(c*(b*x+a))*sec(e*x+d)^n,x, algorithm=""fricas"")","{\rm integral}\left(F^{b c x + a c} \sec\left(e x + d\right)^{n}, x\right)"," ",0,"integral(F^(b*c*x + a*c)*sec(e*x + d)^n, x)","F",0
27,0,0,0,0.584565," ","integrate(F^(c*(b*x+a))*csc(e*x+d)^n,x, algorithm=""fricas"")","{\rm integral}\left(F^{b c x + a c} \csc\left(e x + d\right)^{n}, x\right)"," ",0,"integral(F^(b*c*x + a*c)*csc(e*x + d)^n, x)","F",0
28,1,130,0,0.896841," ","integrate(F^(c*(b*x+a))*(f*x)^m*sin(e*x+d),x, algorithm=""fricas"")","\frac{{\left(i \, b c \log\left(F\right) - e\right)} e^{\left(a c \log\left(F\right) - m \log\left(-\frac{b c \log\left(F\right) - i \, e}{f}\right) - i \, d\right)} \Gamma\left(m + 1, -b c x \log\left(F\right) + i \, e x\right) + {\left(-i \, b c \log\left(F\right) - e\right)} e^{\left(a c \log\left(F\right) - m \log\left(-\frac{b c \log\left(F\right) + i \, e}{f}\right) + i \, d\right)} \Gamma\left(m + 1, -b c x \log\left(F\right) - i \, e x\right)}{2 \, {\left(b^{2} c^{2} \log\left(F\right)^{2} + e^{2}\right)}}"," ",0,"1/2*((I*b*c*log(F) - e)*e^(a*c*log(F) - m*log(-(b*c*log(F) - I*e)/f) - I*d)*gamma(m + 1, -b*c*x*log(F) + I*e*x) + (-I*b*c*log(F) - e)*e^(a*c*log(F) - m*log(-(b*c*log(F) + I*e)/f) + I*d)*gamma(m + 1, -b*c*x*log(F) - I*e*x))/(b^2*c^2*log(F)^2 + e^2)","A",0
29,0,0,0,1.478262," ","integrate(F^(c*(b*x+a))*(f*x)^m/sin(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(f x\right)^{m} F^{b c x + a c}}{\sin\left(e x + d\right)}, x\right)"," ",0,"integral((f*x)^m*F^(b*c*x + a*c)/sin(e*x + d), x)","F",0
30,0,0,0,0.597369," ","integrate(F^(c*(b*x+a))*(f*x)^m/sin(e*x+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\left(f x\right)^{m} F^{b c x + a c}}{\cos\left(e x + d\right)^{2} - 1}, x\right)"," ",0,"integral(-(f*x)^m*F^(b*c*x + a*c)/(cos(e*x + d)^2 - 1), x)","F",0
31,1,26,0,0.563657," ","integrate(f*F^(c*(b*x+a))*(f*x)^(-2+m)*(e*x*cos(e*x+d)+(-1+m+b*c*x*log(F))*sin(e*x+d)),x, algorithm=""fricas"")","\left(f x\right)^{m - 2} F^{b c x + a c} f x \sin\left(e x + d\right)"," ",0,"(f*x)^(m - 2)*F^(b*c*x + a*c)*f*x*sin(e*x + d)","A",0
32,1,24,0,0.803828," ","integrate(f*F^(c*(b*x+a))*(f*x)^m*(e*x*cos(e*x+d)+(1+m+b*c*x*log(F))*sin(e*x+d)),x, algorithm=""fricas"")","\left(f x\right)^{m} F^{b c x + a c} f x \sin\left(e x + d\right)"," ",0,"(f*x)^m*F^(b*c*x + a*c)*f*x*sin(e*x + d)","A",0
33,1,22,0,0.654169," ","integrate(F^(c*(b*x+a))*(f*x)^m*(e*x*cos(e*x+d)+(m+b*c*x*log(F))*sin(e*x+d))/x,x, algorithm=""fricas"")","\left(f x\right)^{m} F^{b c x + a c} \sin\left(e x + d\right)"," ",0,"(f*x)^m*F^(b*c*x + a*c)*sin(e*x + d)","A",0
34,1,18,0,3.998177," ","integrate(F^(c*(b*x+a))*(e*x*cos(e*x+d)+(1+b*c*x*log(F))*sin(e*x+d)),x, algorithm=""fricas"")","F^{b c x + a c} x \sin\left(e x + d\right)"," ",0,"F^(b*c*x + a*c)*x*sin(e*x + d)","A",0
35,1,17,0,0.790242," ","integrate(F^(c*(b*x+a))*(e*cos(e*x+d)+b*c*log(F)*sin(e*x+d)),x, algorithm=""fricas"")","F^{b c x + a c} \sin\left(e x + d\right)"," ",0,"F^(b*c*x + a*c)*sin(e*x + d)","A",0
36,1,20,0,0.937875," ","integrate(F^(c*(b*x+a))*(e*x*cos(e*x+d)+(-1+b*c*x*log(F))*sin(e*x+d))/x^2,x, algorithm=""fricas"")","\frac{F^{b c x + a c} \sin\left(e x + d\right)}{x}"," ",0,"F^(b*c*x + a*c)*sin(e*x + d)/x","A",0
37,1,20,0,0.578723," ","integrate(F^(c*(b*x+a))*(e*x*cos(e*x+d)+(-2+b*c*x*log(F))*sin(e*x+d))/x^3,x, algorithm=""fricas"")","\frac{F^{b c x + a c} \sin\left(e x + d\right)}{x^{2}}"," ",0,"F^(b*c*x + a*c)*sin(e*x + d)/x^2","A",0
38,1,56,0,0.607023," ","integrate(exp(b*x+a)*cos(d*x+c)*sin(d*x+c),x, algorithm=""fricas"")","\frac{b \cos\left(d x + c\right) e^{\left(b x + a\right)} \sin\left(d x + c\right) - {\left(2 \, d \cos\left(d x + c\right)^{2} - d\right)} e^{\left(b x + a\right)}}{b^{2} + 4 \, d^{2}}"," ",0,"(b*cos(d*x + c)*e^(b*x + a)*sin(d*x + c) - (2*d*cos(d*x + c)^2 - d)*e^(b*x + a))/(b^2 + 4*d^2)","A",0
39,1,109,0,0.572927," ","integrate(exp(b*x+a)*cos(d*x+c)*sin(d*x+c)^2,x, algorithm=""fricas"")","\frac{{\left(b^{2} d + 3 \, d^{3} - 3 \, {\left(b^{2} d + d^{3}\right)} \cos\left(d x + c\right)^{2}\right)} e^{\left(b x + a\right)} \sin\left(d x + c\right) - {\left({\left(b^{3} + b d^{2}\right)} \cos\left(d x + c\right)^{3} - {\left(b^{3} + 3 \, b d^{2}\right)} \cos\left(d x + c\right)\right)} e^{\left(b x + a\right)}}{b^{4} + 10 \, b^{2} d^{2} + 9 \, d^{4}}"," ",0,"((b^2*d + 3*d^3 - 3*(b^2*d + d^3)*cos(d*x + c)^2)*e^(b*x + a)*sin(d*x + c) - ((b^3 + b*d^2)*cos(d*x + c)^3 - (b^3 + 3*b*d^2)*cos(d*x + c))*e^(b*x + a))/(b^4 + 10*b^2*d^2 + 9*d^4)","A",0
40,1,135,0,0.648147," ","integrate(exp(b*x+a)*cos(d*x+c)*sin(d*x+c)^3,x, algorithm=""fricas"")","-\frac{{\left({\left(b^{3} + 4 \, b d^{2}\right)} \cos\left(d x + c\right)^{3} - {\left(b^{3} + 10 \, b d^{2}\right)} \cos\left(d x + c\right)\right)} e^{\left(b x + a\right)} \sin\left(d x + c\right) - {\left(4 \, {\left(b^{2} d + 4 \, d^{3}\right)} \cos\left(d x + c\right)^{4} + b^{2} d + 10 \, d^{3} - {\left(5 \, b^{2} d + 32 \, d^{3}\right)} \cos\left(d x + c\right)^{2}\right)} e^{\left(b x + a\right)}}{b^{4} + 20 \, b^{2} d^{2} + 64 \, d^{4}}"," ",0,"-(((b^3 + 4*b*d^2)*cos(d*x + c)^3 - (b^3 + 10*b*d^2)*cos(d*x + c))*e^(b*x + a)*sin(d*x + c) - (4*(b^2*d + 4*d^3)*cos(d*x + c)^4 + b^2*d + 10*d^3 - (5*b^2*d + 32*d^3)*cos(d*x + c)^2)*e^(b*x + a))/(b^4 + 20*b^2*d^2 + 64*d^4)","A",0
41,1,98,0,0.894822," ","integrate(exp(b*x+a)*cos(d*x+c)^2*sin(d*x+c),x, algorithm=""fricas"")","\frac{{\left(2 \, b d^{2} + {\left(b^{3} + b d^{2}\right)} \cos\left(d x + c\right)^{2}\right)} e^{\left(b x + a\right)} \sin\left(d x + c\right) + {\left(2 \, b^{2} d \cos\left(d x + c\right) - 3 \, {\left(b^{2} d + d^{3}\right)} \cos\left(d x + c\right)^{3}\right)} e^{\left(b x + a\right)}}{b^{4} + 10 \, b^{2} d^{2} + 9 \, d^{4}}"," ",0,"((2*b*d^2 + (b^3 + b*d^2)*cos(d*x + c)^2)*e^(b*x + a)*sin(d*x + c) + (2*b^2*d*cos(d*x + c) - 3*(b^2*d + d^3)*cos(d*x + c)^3)*e^(b*x + a))/(b^4 + 10*b^2*d^2 + 9*d^4)","A",0
42,1,90,0,0.466093," ","integrate(exp(b*x+a)*cos(d*x+c)^2*sin(d*x+c)^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(2 \, b d \cos\left(d x + c\right)^{3} - b d \cos\left(d x + c\right)\right)} e^{\left(b x + a\right)} \sin\left(d x + c\right) + {\left(b^{2} \cos\left(d x + c\right)^{4} - b^{2} \cos\left(d x + c\right)^{2} - 2 \, d^{2}\right)} e^{\left(b x + a\right)}}{b^{3} + 16 \, b d^{2}}"," ",0,"-(2*(2*b*d*cos(d*x + c)^3 - b*d*cos(d*x + c))*e^(b*x + a)*sin(d*x + c) + (b^2*cos(d*x + c)^4 - b^2*cos(d*x + c)^2 - 2*d^2)*e^(b*x + a))/(b^3 + 16*b*d^2)","A",0
43,1,201,0,0.570306," ","integrate(exp(b*x+a)*cos(d*x+c)^2*sin(d*x+c)^3,x, algorithm=""fricas"")","\frac{{\left(2 \, b^{3} d^{2} + 26 \, b d^{4} - {\left(b^{5} + 10 \, b^{3} d^{2} + 9 \, b d^{4}\right)} \cos\left(d x + c\right)^{4} + {\left(b^{5} + 14 \, b^{3} d^{2} + 13 \, b d^{4}\right)} \cos\left(d x + c\right)^{2}\right)} e^{\left(b x + a\right)} \sin\left(d x + c\right) + {\left(5 \, {\left(b^{4} d + 10 \, b^{2} d^{3} + 9 \, d^{5}\right)} \cos\left(d x + c\right)^{5} - {\left(7 \, b^{4} d + 82 \, b^{2} d^{3} + 75 \, d^{5}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(b^{4} d + 13 \, b^{2} d^{3}\right)} \cos\left(d x + c\right)\right)} e^{\left(b x + a\right)}}{b^{6} + 35 \, b^{4} d^{2} + 259 \, b^{2} d^{4} + 225 \, d^{6}}"," ",0,"((2*b^3*d^2 + 26*b*d^4 - (b^5 + 10*b^3*d^2 + 9*b*d^4)*cos(d*x + c)^4 + (b^5 + 14*b^3*d^2 + 13*b*d^4)*cos(d*x + c)^2)*e^(b*x + a)*sin(d*x + c) + (5*(b^4*d + 10*b^2*d^3 + 9*d^5)*cos(d*x + c)^5 - (7*b^4*d + 82*b^2*d^3 + 75*d^5)*cos(d*x + c)^3 + 2*(b^4*d + 13*b^2*d^3)*cos(d*x + c))*e^(b*x + a))/(b^6 + 35*b^4*d^2 + 259*b^2*d^4 + 225*d^6)","A",0
44,1,114,0,0.584615," ","integrate(exp(b*x+a)*cos(d*x+c)^3*sin(d*x+c),x, algorithm=""fricas"")","\frac{{\left(6 \, b d^{2} \cos\left(d x + c\right) + {\left(b^{3} + 4 \, b d^{2}\right)} \cos\left(d x + c\right)^{3}\right)} e^{\left(b x + a\right)} \sin\left(d x + c\right) + {\left(3 \, b^{2} d \cos\left(d x + c\right)^{2} - 4 \, {\left(b^{2} d + 4 \, d^{3}\right)} \cos\left(d x + c\right)^{4} + 6 \, d^{3}\right)} e^{\left(b x + a\right)}}{b^{4} + 20 \, b^{2} d^{2} + 64 \, d^{4}}"," ",0,"((6*b*d^2*cos(d*x + c) + (b^3 + 4*b*d^2)*cos(d*x + c)^3)*e^(b*x + a)*sin(d*x + c) + (3*b^2*d*cos(d*x + c)^2 - 4*(b^2*d + 4*d^3)*cos(d*x + c)^4 + 6*d^3)*e^(b*x + a))/(b^4 + 20*b^2*d^2 + 64*d^4)","A",0
45,1,200,0,0.659925," ","integrate(exp(b*x+a)*cos(d*x+c)^3*sin(d*x+c)^2,x, algorithm=""fricas"")","\frac{{\left(6 \, b^{2} d^{3} + 30 \, d^{5} - 5 \, {\left(b^{4} d + 10 \, b^{2} d^{3} + 9 \, d^{5}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(b^{4} d + 6 \, b^{2} d^{3} + 5 \, d^{5}\right)} \cos\left(d x + c\right)^{2}\right)} e^{\left(b x + a\right)} \sin\left(d x + c\right) - {\left({\left(b^{5} + 10 \, b^{3} d^{2} + 9 \, b d^{4}\right)} \cos\left(d x + c\right)^{5} - {\left(b^{5} + 6 \, b^{3} d^{2} + 5 \, b d^{4}\right)} \cos\left(d x + c\right)^{3} - 6 \, {\left(b^{3} d^{2} + 5 \, b d^{4}\right)} \cos\left(d x + c\right)\right)} e^{\left(b x + a\right)}}{b^{6} + 35 \, b^{4} d^{2} + 259 \, b^{2} d^{4} + 225 \, d^{6}}"," ",0,"((6*b^2*d^3 + 30*d^5 - 5*(b^4*d + 10*b^2*d^3 + 9*d^5)*cos(d*x + c)^4 + 3*(b^4*d + 6*b^2*d^3 + 5*d^5)*cos(d*x + c)^2)*e^(b*x + a)*sin(d*x + c) - ((b^5 + 10*b^3*d^2 + 9*b*d^4)*cos(d*x + c)^5 - (b^5 + 6*b^3*d^2 + 5*b*d^4)*cos(d*x + c)^3 - 6*(b^3*d^2 + 5*b*d^4)*cos(d*x + c))*e^(b*x + a))/(b^6 + 35*b^4*d^2 + 259*b^2*d^4 + 225*d^6)","A",0
46,1,156,0,1.456114," ","integrate(exp(b*x+a)*cos(d*x+c)^3*sin(d*x+c)^3,x, algorithm=""fricas"")","-\frac{{\left({\left(b^{3} + 4 \, b d^{2}\right)} \cos\left(d x + c\right)^{5} - 6 \, b d^{2} \cos\left(d x + c\right) - {\left(b^{3} + 4 \, b d^{2}\right)} \cos\left(d x + c\right)^{3}\right)} e^{\left(b x + a\right)} \sin\left(d x + c\right) - 3 \, {\left(2 \, {\left(b^{2} d + 4 \, d^{3}\right)} \cos\left(d x + c\right)^{6} + b^{2} d \cos\left(d x + c\right)^{2} - 3 \, {\left(b^{2} d + 4 \, d^{3}\right)} \cos\left(d x + c\right)^{4} + 2 \, d^{3}\right)} e^{\left(b x + a\right)}}{b^{4} + 40 \, b^{2} d^{2} + 144 \, d^{4}}"," ",0,"-(((b^3 + 4*b*d^2)*cos(d*x + c)^5 - 6*b*d^2*cos(d*x + c) - (b^3 + 4*b*d^2)*cos(d*x + c)^3)*e^(b*x + a)*sin(d*x + c) - 3*(2*(b^2*d + 4*d^3)*cos(d*x + c)^6 + b^2*d*cos(d*x + c)^2 - 3*(b^2*d + 4*d^3)*cos(d*x + c)^4 + 2*d^3)*e^(b*x + a))/(b^4 + 40*b^2*d^2 + 144*d^4)","A",0
47,1,17,0,0.838842," ","integrate(exp(x)*x*sin(x),x, algorithm=""fricas"")","-\frac{1}{2} \, {\left(x - 1\right)} \cos\left(x\right) e^{x} + \frac{1}{2} \, x e^{x} \sin\left(x\right)"," ",0,"-1/2*(x - 1)*cos(x)*e^x + 1/2*x*e^x*sin(x)","A",0
48,1,26,0,1.579392," ","integrate(exp(x)*x^2*sin(x),x, algorithm=""fricas"")","-\frac{1}{2} \, {\left(x^{2} - 2 \, x + 1\right)} \cos\left(x\right) e^{x} + \frac{1}{2} \, {\left(x^{2} - 1\right)} e^{x} \sin\left(x\right)"," ",0,"-1/2*(x^2 - 2*x + 1)*cos(x)*e^x + 1/2*(x^2 - 1)*e^x*sin(x)","A",0
49,1,17,0,0.626890," ","integrate(exp(x)*x*cos(x),x, algorithm=""fricas"")","\frac{1}{2} \, x \cos\left(x\right) e^{x} + \frac{1}{2} \, {\left(x - 1\right)} e^{x} \sin\left(x\right)"," ",0,"1/2*x*cos(x)*e^x + 1/2*(x - 1)*e^x*sin(x)","A",0
50,1,26,0,0.657107," ","integrate(exp(x)*x^2*cos(x),x, algorithm=""fricas"")","\frac{1}{2} \, {\left(x^{2} - 1\right)} \cos\left(x\right) e^{x} + \frac{1}{2} \, {\left(x^{2} - 2 \, x + 1\right)} e^{x} \sin\left(x\right)"," ",0,"1/2*(x^2 - 1)*cos(x)*e^x + 1/2*(x^2 - 2*x + 1)*e^x*sin(x)","A",0
51,1,21,0,1.965016," ","integrate(exp(3*x)*(-5*cos(4*x)+2*sin(4*x)),x, algorithm=""fricas"")","-\frac{23}{25} \, \cos\left(4 \, x\right) e^{\left(3 \, x\right)} - \frac{14}{25} \, e^{\left(3 \, x\right)} \sin\left(4 \, x\right)"," ",0,"-23/25*cos(4*x)*e^(3*x) - 14/25*e^(3*x)*sin(4*x)","A",0
52,1,26,0,0.575160," ","integrate(sin(x)/exp(x)+exp(x)*sin(x),x, algorithm=""fricas"")","-\frac{1}{2} \, {\left(\cos\left(x\right) e^{\left(2 \, x\right)} - {\left(e^{\left(2 \, x\right)} - 1\right)} \sin\left(x\right) + \cos\left(x\right)\right)} e^{\left(-x\right)}"," ",0,"-1/2*(cos(x)*e^(2*x) - (e^(2*x) - 1)*sin(x) + cos(x))*e^(-x)","A",0
53,0,0,0,0.772399," ","integrate(F^(b*x+a)*cos(d*x+c)/(e+e*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{F^{b x + a} \cos\left(d x + c\right)}{e \sin\left(d x + c\right) + e}, x\right)"," ",0,"integral(F^(b*x + a)*cos(d*x + c)/(e*sin(d*x + c) + e), x)","F",0
54,0,0,0,0.753434," ","integrate(F^(b*x+a)*cos(d*x+c)/(e-e*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{F^{b x + a} \cos\left(d x + c\right)}{e \sin\left(d x + c\right) - e}, x\right)"," ",0,"integral(-F^(b*x + a)*cos(d*x + c)/(e*sin(d*x + c) - e), x)","F",0
55,0,0,0,0.678555," ","integrate(F^(b*x+a)*sin(d*x+c)/(e+e*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{F^{b x + a} \sin\left(d x + c\right)}{e \cos\left(d x + c\right) + e}, x\right)"," ",0,"integral(F^(b*x + a)*sin(d*x + c)/(e*cos(d*x + c) + e), x)","F",0
56,0,0,0,0.706624," ","integrate(F^(b*x+a)*sin(d*x+c)/(e-e*cos(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{F^{b x + a} \sin\left(d x + c\right)}{e \cos\left(d x + c\right) - e}, x\right)"," ",0,"integral(-F^(b*x + a)*sin(d*x + c)/(e*cos(d*x + c) - e), x)","F",0
57,1,30,0,0.669572," ","integrate(exp(x^2)*sin(b*x),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{\pi} {\left(\operatorname{erf}\left(\frac{1}{2} \, b + i \, x\right) - \operatorname{erf}\left(-\frac{1}{2} \, b + i \, x\right)\right)} e^{\left(\frac{1}{4} \, b^{2}\right)}"," ",0,"1/4*sqrt(pi)*(erf(1/2*b + I*x) - erf(-1/2*b + I*x))*e^(1/4*b^2)","A",0
58,1,32,0,0.766221," ","integrate(exp(x^2)*cos(b*x),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{\pi} {\left(-i \, \operatorname{erf}\left(\frac{1}{2} \, b + i \, x\right) - i \, \operatorname{erf}\left(-\frac{1}{2} \, b + i \, x\right)\right)} e^{\left(\frac{1}{4} \, b^{2}\right)}"," ",0,"1/4*sqrt(pi)*(-I*erf(1/2*b + I*x) - I*erf(-1/2*b + I*x))*e^(1/4*b^2)","A",0
59,1,45,0,0.640899," ","integrate(exp(x^2)*sin(b*x+a),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{\pi} {\left(\operatorname{erf}\left(-\frac{1}{2} \, b + i \, x\right) e^{\left(\frac{1}{4} \, b^{2} + i \, a\right)} - \operatorname{erf}\left(\frac{1}{2} \, b + i \, x\right) e^{\left(\frac{1}{4} \, b^{2} - i \, a\right)}\right)}"," ",0,"-1/4*sqrt(pi)*(erf(-1/2*b + I*x)*e^(1/4*b^2 + I*a) - erf(1/2*b + I*x)*e^(1/4*b^2 - I*a))","A",0
60,1,46,0,0.612867," ","integrate(exp(x^2)*cos(b*x+a),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{\pi} {\left(-i \, \operatorname{erf}\left(-\frac{1}{2} \, b + i \, x\right) e^{\left(\frac{1}{4} \, b^{2} + i \, a\right)} - i \, \operatorname{erf}\left(\frac{1}{2} \, b + i \, x\right) e^{\left(\frac{1}{4} \, b^{2} - i \, a\right)}\right)}"," ",0,"1/4*sqrt(pi)*(-I*erf(-1/2*b + I*x)*e^(1/4*b^2 + I*a) - I*erf(1/2*b + I*x)*e^(1/4*b^2 - I*a))","A",0
61,1,29,0,0.731843," ","integrate(exp(2*x^2)*x*cos(2*x^2),x, algorithm=""fricas"")","\frac{1}{8} \, \cos\left(2 \, x^{2}\right) e^{\left(2 \, x^{2}\right)} + \frac{1}{8} \, e^{\left(2 \, x^{2}\right)} \sin\left(2 \, x^{2}\right)"," ",0,"1/8*cos(2*x^2)*e^(2*x^2) + 1/8*e^(2*x^2)*sin(2*x^2)","A",0
62,1,5,0,2.287832," ","integrate(exp(x)*sin(exp(x)),x, algorithm=""fricas"")","-\cos\left(e^{x}\right)"," ",0,"-cos(e^x)","A",0
63,1,21,0,0.567336," ","integrate(exp(x)*csc(exp(x))*sec(exp(x)),x, algorithm=""fricas"")","-\frac{1}{2} \, \log\left(\cos\left(e^{x}\right)^{2}\right) + \frac{1}{2} \, \log\left(-\frac{1}{4} \, \cos\left(e^{x}\right)^{2} + \frac{1}{4}\right)"," ",0,"-1/2*log(cos(e^x)^2) + 1/2*log(-1/4*cos(e^x)^2 + 1/4)","B",0
64,1,3,0,0.761780," ","integrate(exp(x)*cos(exp(x)),x, algorithm=""fricas"")","\sin\left(e^{x}\right)"," ",0,"sin(e^x)","A",0
65,1,7,0,0.632744," ","integrate(exp(2*x)*cos(exp(2*x)),x, algorithm=""fricas"")","\frac{1}{2} \, \sin\left(e^{\left(2 \, x\right)}\right)"," ",0,"1/2*sin(e^(2*x))","A",0
66,1,7,0,0.680534," ","integrate(cos(exp(-2*x))/exp(2*x),x, algorithm=""fricas"")","-\frac{1}{2} \, \sin\left(e^{\left(-2 \, x\right)}\right)"," ",0,"-1/2*sin(e^(-2*x))","A",0
67,1,10,0,0.601475," ","integrate(exp(2*x)*cos(exp(x)),x, algorithm=""fricas"")","e^{x} \sin\left(e^{x}\right) + \cos\left(e^{x}\right)"," ",0,"e^x*sin(e^x) + cos(e^x)","A",0
68,1,42,0,0.992373," ","integrate(exp(-1+3*x)*cos(exp(-1+3*x))*sin(1+exp(-1+3*x)),x, algorithm=""fricas"")","-\frac{1}{6} \, \cos\left(1\right) \cos\left(e^{\left(3 \, x - 1\right)}\right)^{2} + \frac{1}{6} \, \cos\left(e^{\left(3 \, x - 1\right)}\right) \sin\left(1\right) \sin\left(e^{\left(3 \, x - 1\right)}\right) + \frac{1}{6} \, e^{\left(3 \, x - 1\right)} \sin\left(1\right)"," ",0,"-1/6*cos(1)*cos(e^(3*x - 1))^2 + 1/6*cos(e^(3*x - 1))*sin(1)*sin(e^(3*x - 1)) + 1/6*e^(3*x - 1)*sin(1)","A",0
69,1,12,0,1.103955," ","integrate(exp(x)*tan(exp(x)),x, algorithm=""fricas"")","-\frac{1}{2} \, \log\left(\frac{1}{\tan\left(e^{x}\right)^{2} + 1}\right)"," ",0,"-1/2*log(1/(tan(e^x)^2 + 1))","A",0
70,1,19,0,0.525727," ","integrate(exp(x)*sec(exp(x)),x, algorithm=""fricas"")","\frac{1}{2} \, \log\left(\sin\left(e^{x}\right) + 1\right) - \frac{1}{2} \, \log\left(-\sin\left(e^{x}\right) + 1\right)"," ",0,"1/2*log(sin(e^x) + 1) - 1/2*log(-sin(e^x) + 1)","B",0
71,1,5,0,1.097413," ","integrate(exp(x)*sec(exp(x))*tan(exp(x)),x, algorithm=""fricas"")","\frac{1}{\cos\left(e^{x}\right)}"," ",0,"1/cos(e^x)","A",0
72,1,10,0,0.755996," ","integrate(exp(x)*csc(exp(x))^2,x, algorithm=""fricas"")","-\frac{\cos\left(e^{x}\right)}{\sin\left(e^{x}\right)}"," ",0,"-cos(e^x)/sin(e^x)","A",0
73,1,30,0,1.192935," ","integrate(exp(x)*sin(b*x+a),x, algorithm=""fricas"")","-\frac{b \cos\left(b x + a\right) e^{x} - e^{x} \sin\left(b x + a\right)}{b^{2} + 1}"," ",0,"-(b*cos(b*x + a)*e^x - e^x*sin(b*x + a))/(b^2 + 1)","A",0
74,1,193,0,0.565786," ","integrate(exp(x)*sin(c*x^2+a),x, algorithm=""fricas"")","\frac{i \, \sqrt{2} \pi \sqrt{\frac{c}{\pi}} e^{\left(\frac{-4 i \, a c - i}{4 \, c}\right)} \operatorname{C}\left(\frac{\sqrt{2} {\left(2 \, c x + i\right)} \sqrt{\frac{c}{\pi}}}{2 \, c}\right) + i \, \sqrt{2} \pi \sqrt{\frac{c}{\pi}} e^{\left(\frac{4 i \, a c + i}{4 \, c}\right)} \operatorname{C}\left(-\frac{\sqrt{2} {\left(2 \, c x - i\right)} \sqrt{\frac{c}{\pi}}}{2 \, c}\right) + \sqrt{2} \pi \sqrt{\frac{c}{\pi}} e^{\left(\frac{-4 i \, a c - i}{4 \, c}\right)} \operatorname{S}\left(\frac{\sqrt{2} {\left(2 \, c x + i\right)} \sqrt{\frac{c}{\pi}}}{2 \, c}\right) - \sqrt{2} \pi \sqrt{\frac{c}{\pi}} e^{\left(\frac{4 i \, a c + i}{4 \, c}\right)} \operatorname{S}\left(-\frac{\sqrt{2} {\left(2 \, c x - i\right)} \sqrt{\frac{c}{\pi}}}{2 \, c}\right)}{4 \, c}"," ",0,"1/4*(I*sqrt(2)*pi*sqrt(c/pi)*e^(1/4*(-4*I*a*c - I)/c)*fresnel_cos(1/2*sqrt(2)*(2*c*x + I)*sqrt(c/pi)/c) + I*sqrt(2)*pi*sqrt(c/pi)*e^(1/4*(4*I*a*c + I)/c)*fresnel_cos(-1/2*sqrt(2)*(2*c*x - I)*sqrt(c/pi)/c) + sqrt(2)*pi*sqrt(c/pi)*e^(1/4*(-4*I*a*c - I)/c)*fresnel_sin(1/2*sqrt(2)*(2*c*x + I)*sqrt(c/pi)/c) - sqrt(2)*pi*sqrt(c/pi)*e^(1/4*(4*I*a*c + I)/c)*fresnel_sin(-1/2*sqrt(2)*(2*c*x - I)*sqrt(c/pi)/c))/c","B",0
75,1,229,0,0.870804," ","integrate(exp(x)*sin(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{i \, \sqrt{2} \pi \sqrt{\frac{c}{\pi}} e^{\left(\frac{i \, b^{2} - 4 i \, a c - 2 \, b - i}{4 \, c}\right)} \operatorname{C}\left(\frac{\sqrt{2} {\left(2 \, c x + b + i\right)} \sqrt{\frac{c}{\pi}}}{2 \, c}\right) + i \, \sqrt{2} \pi \sqrt{\frac{c}{\pi}} e^{\left(\frac{-i \, b^{2} + 4 i \, a c - 2 \, b + i}{4 \, c}\right)} \operatorname{C}\left(-\frac{\sqrt{2} {\left(2 \, c x + b - i\right)} \sqrt{\frac{c}{\pi}}}{2 \, c}\right) + \sqrt{2} \pi \sqrt{\frac{c}{\pi}} e^{\left(\frac{i \, b^{2} - 4 i \, a c - 2 \, b - i}{4 \, c}\right)} \operatorname{S}\left(\frac{\sqrt{2} {\left(2 \, c x + b + i\right)} \sqrt{\frac{c}{\pi}}}{2 \, c}\right) - \sqrt{2} \pi \sqrt{\frac{c}{\pi}} e^{\left(\frac{-i \, b^{2} + 4 i \, a c - 2 \, b + i}{4 \, c}\right)} \operatorname{S}\left(-\frac{\sqrt{2} {\left(2 \, c x + b - i\right)} \sqrt{\frac{c}{\pi}}}{2 \, c}\right)}{4 \, c}"," ",0,"1/4*(I*sqrt(2)*pi*sqrt(c/pi)*e^(1/4*(I*b^2 - 4*I*a*c - 2*b - I)/c)*fresnel_cos(1/2*sqrt(2)*(2*c*x + b + I)*sqrt(c/pi)/c) + I*sqrt(2)*pi*sqrt(c/pi)*e^(1/4*(-I*b^2 + 4*I*a*c - 2*b + I)/c)*fresnel_cos(-1/2*sqrt(2)*(2*c*x + b - I)*sqrt(c/pi)/c) + sqrt(2)*pi*sqrt(c/pi)*e^(1/4*(I*b^2 - 4*I*a*c - 2*b - I)/c)*fresnel_sin(1/2*sqrt(2)*(2*c*x + b + I)*sqrt(c/pi)/c) - sqrt(2)*pi*sqrt(c/pi)*e^(1/4*(-I*b^2 + 4*I*a*c - 2*b + I)/c)*fresnel_sin(-1/2*sqrt(2)*(2*c*x + b - I)*sqrt(c/pi)/c))/c","B",0
76,1,45,0,0.701502," ","integrate(exp(x^2)*sin(b*x+a),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{\pi} {\left(\operatorname{erf}\left(-\frac{1}{2} \, b + i \, x\right) e^{\left(\frac{1}{4} \, b^{2} + i \, a\right)} - \operatorname{erf}\left(\frac{1}{2} \, b + i \, x\right) e^{\left(\frac{1}{4} \, b^{2} - i \, a\right)}\right)}"," ",0,"-1/4*sqrt(pi)*(erf(-1/2*b + I*x)*e^(1/4*b^2 + I*a) - erf(1/2*b + I*x)*e^(1/4*b^2 - I*a))","A",0
77,1,66,0,0.711294," ","integrate(exp(x^2)*sin(c*x^2+a),x, algorithm=""fricas"")","\frac{\sqrt{\pi} {\left(c + i\right)} \sqrt{-i \, c - 1} \operatorname{erf}\left(\sqrt{-i \, c - 1} x\right) e^{\left(i \, a\right)} + \sqrt{\pi} {\left(c - i\right)} \sqrt{i \, c - 1} \operatorname{erf}\left(\sqrt{i \, c - 1} x\right) e^{\left(-i \, a\right)}}{4 \, {\left(c^{2} + 1\right)}}"," ",0,"1/4*(sqrt(pi)*(c + I)*sqrt(-I*c - 1)*erf(sqrt(-I*c - 1)*x)*e^(I*a) + sqrt(pi)*(c - I)*sqrt(I*c - 1)*erf(sqrt(I*c - 1)*x)*e^(-I*a))/(c^2 + 1)","A",0
78,1,161,0,2.070568," ","integrate(exp(x^2)*sin(c*x^2+b*x+a),x, algorithm=""fricas"")","-\frac{\sqrt{\pi} {\left(c - i\right)} \sqrt{i \, c - 1} \operatorname{erf}\left(-\frac{{\left(b c + 2 \, {\left(c^{2} + 1\right)} x - i \, b\right)} \sqrt{i \, c - 1}}{2 \, {\left(c^{2} + 1\right)}}\right) e^{\left(\frac{i \, b^{2} c - 4 i \, a c^{2} + b^{2} - 4 i \, a}{4 \, {\left(c^{2} + 1\right)}}\right)} - \sqrt{\pi} {\left(c + i\right)} \sqrt{-i \, c - 1} \operatorname{erf}\left(\frac{{\left(b c + 2 \, {\left(c^{2} + 1\right)} x + i \, b\right)} \sqrt{-i \, c - 1}}{2 \, {\left(c^{2} + 1\right)}}\right) e^{\left(\frac{-i \, b^{2} c + 4 i \, a c^{2} + b^{2} + 4 i \, a}{4 \, {\left(c^{2} + 1\right)}}\right)}}{4 \, {\left(c^{2} + 1\right)}}"," ",0,"-1/4*(sqrt(pi)*(c - I)*sqrt(I*c - 1)*erf(-1/2*(b*c + 2*(c^2 + 1)*x - I*b)*sqrt(I*c - 1)/(c^2 + 1))*e^(1/4*(I*b^2*c - 4*I*a*c^2 + b^2 - 4*I*a)/(c^2 + 1)) - sqrt(pi)*(c + I)*sqrt(-I*c - 1)*erf(1/2*(b*c + 2*(c^2 + 1)*x + I*b)*sqrt(-I*c - 1)/(c^2 + 1))*e^(1/4*(-I*b^2*c + 4*I*a*c^2 + b^2 + 4*I*a)/(c^2 + 1)))/(c^2 + 1)","A",0
79,1,265,0,0.728738," ","integrate(f^(b*x+a)*sin(f*x^2+d),x, algorithm=""fricas"")","\frac{i \, \sqrt{2} \pi \sqrt{\frac{f}{\pi}} e^{\left(\frac{-i \, b^{2} \log\left(f\right)^{2} + 4 \, a f \log\left(f\right) - 4 i \, d f}{4 \, f}\right)} \operatorname{C}\left(\frac{\sqrt{2} {\left(2 \, f x + i \, b \log\left(f\right)\right)} \sqrt{\frac{f}{\pi}}}{2 \, f}\right) + i \, \sqrt{2} \pi \sqrt{\frac{f}{\pi}} e^{\left(\frac{i \, b^{2} \log\left(f\right)^{2} + 4 \, a f \log\left(f\right) + 4 i \, d f}{4 \, f}\right)} \operatorname{C}\left(-\frac{\sqrt{2} {\left(2 \, f x - i \, b \log\left(f\right)\right)} \sqrt{\frac{f}{\pi}}}{2 \, f}\right) + \sqrt{2} \pi \sqrt{\frac{f}{\pi}} e^{\left(\frac{-i \, b^{2} \log\left(f\right)^{2} + 4 \, a f \log\left(f\right) - 4 i \, d f}{4 \, f}\right)} \operatorname{S}\left(\frac{\sqrt{2} {\left(2 \, f x + i \, b \log\left(f\right)\right)} \sqrt{\frac{f}{\pi}}}{2 \, f}\right) - \sqrt{2} \pi \sqrt{\frac{f}{\pi}} e^{\left(\frac{i \, b^{2} \log\left(f\right)^{2} + 4 \, a f \log\left(f\right) + 4 i \, d f}{4 \, f}\right)} \operatorname{S}\left(-\frac{\sqrt{2} {\left(2 \, f x - i \, b \log\left(f\right)\right)} \sqrt{\frac{f}{\pi}}}{2 \, f}\right)}{4 \, f}"," ",0,"1/4*(I*sqrt(2)*pi*sqrt(f/pi)*e^(1/4*(-I*b^2*log(f)^2 + 4*a*f*log(f) - 4*I*d*f)/f)*fresnel_cos(1/2*sqrt(2)*(2*f*x + I*b*log(f))*sqrt(f/pi)/f) + I*sqrt(2)*pi*sqrt(f/pi)*e^(1/4*(I*b^2*log(f)^2 + 4*a*f*log(f) + 4*I*d*f)/f)*fresnel_cos(-1/2*sqrt(2)*(2*f*x - I*b*log(f))*sqrt(f/pi)/f) + sqrt(2)*pi*sqrt(f/pi)*e^(1/4*(-I*b^2*log(f)^2 + 4*a*f*log(f) - 4*I*d*f)/f)*fresnel_sin(1/2*sqrt(2)*(2*f*x + I*b*log(f))*sqrt(f/pi)/f) - sqrt(2)*pi*sqrt(f/pi)*e^(1/4*(I*b^2*log(f)^2 + 4*a*f*log(f) + 4*I*d*f)/f)*fresnel_sin(-1/2*sqrt(2)*(2*f*x - I*b*log(f))*sqrt(f/pi)/f))/f","B",0
80,1,271,0,1.253978," ","integrate(f^(b*x+a)*sin(f*x^2+d)^2,x, algorithm=""fricas"")","-\frac{2 \, \pi b \sqrt{\frac{f}{\pi}} e^{\left(\frac{-i \, b^{2} \log\left(f\right)^{2} + 8 \, a f \log\left(f\right) - 16 i \, d f}{8 \, f}\right)} \operatorname{C}\left(\frac{{\left(4 \, f x + i \, b \log\left(f\right)\right)} \sqrt{\frac{f}{\pi}}}{2 \, f}\right) \log\left(f\right) - 2 \, \pi b \sqrt{\frac{f}{\pi}} e^{\left(\frac{i \, b^{2} \log\left(f\right)^{2} + 8 \, a f \log\left(f\right) + 16 i \, d f}{8 \, f}\right)} \operatorname{C}\left(-\frac{{\left(4 \, f x - i \, b \log\left(f\right)\right)} \sqrt{\frac{f}{\pi}}}{2 \, f}\right) \log\left(f\right) - 2 i \, \pi b \sqrt{\frac{f}{\pi}} e^{\left(\frac{-i \, b^{2} \log\left(f\right)^{2} + 8 \, a f \log\left(f\right) - 16 i \, d f}{8 \, f}\right)} \operatorname{S}\left(\frac{{\left(4 \, f x + i \, b \log\left(f\right)\right)} \sqrt{\frac{f}{\pi}}}{2 \, f}\right) \log\left(f\right) - 2 i \, \pi b \sqrt{\frac{f}{\pi}} e^{\left(\frac{i \, b^{2} \log\left(f\right)^{2} + 8 \, a f \log\left(f\right) + 16 i \, d f}{8 \, f}\right)} \operatorname{S}\left(-\frac{{\left(4 \, f x - i \, b \log\left(f\right)\right)} \sqrt{\frac{f}{\pi}}}{2 \, f}\right) \log\left(f\right) - 8 \, f f^{b x + a}}{16 \, b f \log\left(f\right)}"," ",0,"-1/16*(2*pi*b*sqrt(f/pi)*e^(1/8*(-I*b^2*log(f)^2 + 8*a*f*log(f) - 16*I*d*f)/f)*fresnel_cos(1/2*(4*f*x + I*b*log(f))*sqrt(f/pi)/f)*log(f) - 2*pi*b*sqrt(f/pi)*e^(1/8*(I*b^2*log(f)^2 + 8*a*f*log(f) + 16*I*d*f)/f)*fresnel_cos(-1/2*(4*f*x - I*b*log(f))*sqrt(f/pi)/f)*log(f) - 2*I*pi*b*sqrt(f/pi)*e^(1/8*(-I*b^2*log(f)^2 + 8*a*f*log(f) - 16*I*d*f)/f)*fresnel_sin(1/2*(4*f*x + I*b*log(f))*sqrt(f/pi)/f)*log(f) - 2*I*pi*b*sqrt(f/pi)*e^(1/8*(I*b^2*log(f)^2 + 8*a*f*log(f) + 16*I*d*f)/f)*fresnel_sin(-1/2*(4*f*x - I*b*log(f))*sqrt(f/pi)/f)*log(f) - 8*f*f^(b*x + a))/(b*f*log(f))","B",0
81,1,525,0,0.716182," ","integrate(f^(b*x+a)*sin(f*x^2+d)^3,x, algorithm=""fricas"")","\frac{-i \, \sqrt{6} \pi \sqrt{\frac{f}{\pi}} e^{\left(\frac{-i \, b^{2} \log\left(f\right)^{2} + 12 \, a f \log\left(f\right) - 36 i \, d f}{12 \, f}\right)} \operatorname{C}\left(\frac{\sqrt{6} {\left(6 \, f x + i \, b \log\left(f\right)\right)} \sqrt{\frac{f}{\pi}}}{6 \, f}\right) - i \, \sqrt{6} \pi \sqrt{\frac{f}{\pi}} e^{\left(\frac{i \, b^{2} \log\left(f\right)^{2} + 12 \, a f \log\left(f\right) + 36 i \, d f}{12 \, f}\right)} \operatorname{C}\left(-\frac{\sqrt{6} {\left(6 \, f x - i \, b \log\left(f\right)\right)} \sqrt{\frac{f}{\pi}}}{6 \, f}\right) + 9 i \, \sqrt{2} \pi \sqrt{\frac{f}{\pi}} e^{\left(\frac{-i \, b^{2} \log\left(f\right)^{2} + 4 \, a f \log\left(f\right) - 4 i \, d f}{4 \, f}\right)} \operatorname{C}\left(\frac{\sqrt{2} {\left(2 \, f x + i \, b \log\left(f\right)\right)} \sqrt{\frac{f}{\pi}}}{2 \, f}\right) + 9 i \, \sqrt{2} \pi \sqrt{\frac{f}{\pi}} e^{\left(\frac{i \, b^{2} \log\left(f\right)^{2} + 4 \, a f \log\left(f\right) + 4 i \, d f}{4 \, f}\right)} \operatorname{C}\left(-\frac{\sqrt{2} {\left(2 \, f x - i \, b \log\left(f\right)\right)} \sqrt{\frac{f}{\pi}}}{2 \, f}\right) - \sqrt{6} \pi \sqrt{\frac{f}{\pi}} e^{\left(\frac{-i \, b^{2} \log\left(f\right)^{2} + 12 \, a f \log\left(f\right) - 36 i \, d f}{12 \, f}\right)} \operatorname{S}\left(\frac{\sqrt{6} {\left(6 \, f x + i \, b \log\left(f\right)\right)} \sqrt{\frac{f}{\pi}}}{6 \, f}\right) + \sqrt{6} \pi \sqrt{\frac{f}{\pi}} e^{\left(\frac{i \, b^{2} \log\left(f\right)^{2} + 12 \, a f \log\left(f\right) + 36 i \, d f}{12 \, f}\right)} \operatorname{S}\left(-\frac{\sqrt{6} {\left(6 \, f x - i \, b \log\left(f\right)\right)} \sqrt{\frac{f}{\pi}}}{6 \, f}\right) + 9 \, \sqrt{2} \pi \sqrt{\frac{f}{\pi}} e^{\left(\frac{-i \, b^{2} \log\left(f\right)^{2} + 4 \, a f \log\left(f\right) - 4 i \, d f}{4 \, f}\right)} \operatorname{S}\left(\frac{\sqrt{2} {\left(2 \, f x + i \, b \log\left(f\right)\right)} \sqrt{\frac{f}{\pi}}}{2 \, f}\right) - 9 \, \sqrt{2} \pi \sqrt{\frac{f}{\pi}} e^{\left(\frac{i \, b^{2} \log\left(f\right)^{2} + 4 \, a f \log\left(f\right) + 4 i \, d f}{4 \, f}\right)} \operatorname{S}\left(-\frac{\sqrt{2} {\left(2 \, f x - i \, b \log\left(f\right)\right)} \sqrt{\frac{f}{\pi}}}{2 \, f}\right)}{48 \, f}"," ",0,"1/48*(-I*sqrt(6)*pi*sqrt(f/pi)*e^(1/12*(-I*b^2*log(f)^2 + 12*a*f*log(f) - 36*I*d*f)/f)*fresnel_cos(1/6*sqrt(6)*(6*f*x + I*b*log(f))*sqrt(f/pi)/f) - I*sqrt(6)*pi*sqrt(f/pi)*e^(1/12*(I*b^2*log(f)^2 + 12*a*f*log(f) + 36*I*d*f)/f)*fresnel_cos(-1/6*sqrt(6)*(6*f*x - I*b*log(f))*sqrt(f/pi)/f) + 9*I*sqrt(2)*pi*sqrt(f/pi)*e^(1/4*(-I*b^2*log(f)^2 + 4*a*f*log(f) - 4*I*d*f)/f)*fresnel_cos(1/2*sqrt(2)*(2*f*x + I*b*log(f))*sqrt(f/pi)/f) + 9*I*sqrt(2)*pi*sqrt(f/pi)*e^(1/4*(I*b^2*log(f)^2 + 4*a*f*log(f) + 4*I*d*f)/f)*fresnel_cos(-1/2*sqrt(2)*(2*f*x - I*b*log(f))*sqrt(f/pi)/f) - sqrt(6)*pi*sqrt(f/pi)*e^(1/12*(-I*b^2*log(f)^2 + 12*a*f*log(f) - 36*I*d*f)/f)*fresnel_sin(1/6*sqrt(6)*(6*f*x + I*b*log(f))*sqrt(f/pi)/f) + sqrt(6)*pi*sqrt(f/pi)*e^(1/12*(I*b^2*log(f)^2 + 12*a*f*log(f) + 36*I*d*f)/f)*fresnel_sin(-1/6*sqrt(6)*(6*f*x - I*b*log(f))*sqrt(f/pi)/f) + 9*sqrt(2)*pi*sqrt(f/pi)*e^(1/4*(-I*b^2*log(f)^2 + 4*a*f*log(f) - 4*I*d*f)/f)*fresnel_sin(1/2*sqrt(2)*(2*f*x + I*b*log(f))*sqrt(f/pi)/f) - 9*sqrt(2)*pi*sqrt(f/pi)*e^(1/4*(I*b^2*log(f)^2 + 4*a*f*log(f) + 4*I*d*f)/f)*fresnel_sin(-1/2*sqrt(2)*(2*f*x - I*b*log(f))*sqrt(f/pi)/f))/f","B",0
82,1,313,0,1.356743," ","integrate(f^(b*x+a)*sin(f*x^2+e*x+d),x, algorithm=""fricas"")","\frac{i \, \sqrt{2} \pi \sqrt{\frac{f}{\pi}} e^{\left(\frac{-i \, b^{2} \log\left(f\right)^{2} + i \, e^{2} - 4 i \, d f - 2 \, {\left(b e - 2 \, a f\right)} \log\left(f\right)}{4 \, f}\right)} \operatorname{C}\left(\frac{\sqrt{2} {\left(2 \, f x + i \, b \log\left(f\right) + e\right)} \sqrt{\frac{f}{\pi}}}{2 \, f}\right) + i \, \sqrt{2} \pi \sqrt{\frac{f}{\pi}} e^{\left(\frac{i \, b^{2} \log\left(f\right)^{2} - i \, e^{2} + 4 i \, d f - 2 \, {\left(b e - 2 \, a f\right)} \log\left(f\right)}{4 \, f}\right)} \operatorname{C}\left(-\frac{\sqrt{2} {\left(2 \, f x - i \, b \log\left(f\right) + e\right)} \sqrt{\frac{f}{\pi}}}{2 \, f}\right) + \sqrt{2} \pi \sqrt{\frac{f}{\pi}} e^{\left(\frac{-i \, b^{2} \log\left(f\right)^{2} + i \, e^{2} - 4 i \, d f - 2 \, {\left(b e - 2 \, a f\right)} \log\left(f\right)}{4 \, f}\right)} \operatorname{S}\left(\frac{\sqrt{2} {\left(2 \, f x + i \, b \log\left(f\right) + e\right)} \sqrt{\frac{f}{\pi}}}{2 \, f}\right) - \sqrt{2} \pi \sqrt{\frac{f}{\pi}} e^{\left(\frac{i \, b^{2} \log\left(f\right)^{2} - i \, e^{2} + 4 i \, d f - 2 \, {\left(b e - 2 \, a f\right)} \log\left(f\right)}{4 \, f}\right)} \operatorname{S}\left(-\frac{\sqrt{2} {\left(2 \, f x - i \, b \log\left(f\right) + e\right)} \sqrt{\frac{f}{\pi}}}{2 \, f}\right)}{4 \, f}"," ",0,"1/4*(I*sqrt(2)*pi*sqrt(f/pi)*e^(1/4*(-I*b^2*log(f)^2 + I*e^2 - 4*I*d*f - 2*(b*e - 2*a*f)*log(f))/f)*fresnel_cos(1/2*sqrt(2)*(2*f*x + I*b*log(f) + e)*sqrt(f/pi)/f) + I*sqrt(2)*pi*sqrt(f/pi)*e^(1/4*(I*b^2*log(f)^2 - I*e^2 + 4*I*d*f - 2*(b*e - 2*a*f)*log(f))/f)*fresnel_cos(-1/2*sqrt(2)*(2*f*x - I*b*log(f) + e)*sqrt(f/pi)/f) + sqrt(2)*pi*sqrt(f/pi)*e^(1/4*(-I*b^2*log(f)^2 + I*e^2 - 4*I*d*f - 2*(b*e - 2*a*f)*log(f))/f)*fresnel_sin(1/2*sqrt(2)*(2*f*x + I*b*log(f) + e)*sqrt(f/pi)/f) - sqrt(2)*pi*sqrt(f/pi)*e^(1/4*(I*b^2*log(f)^2 - I*e^2 + 4*I*d*f - 2*(b*e - 2*a*f)*log(f))/f)*fresnel_sin(-1/2*sqrt(2)*(2*f*x - I*b*log(f) + e)*sqrt(f/pi)/f))/f","B",0
83,1,327,0,0.800555," ","integrate(f^(b*x+a)*sin(f*x^2+e*x+d)^2,x, algorithm=""fricas"")","-\frac{2 \, \pi b \sqrt{\frac{f}{\pi}} e^{\left(\frac{-i \, b^{2} \log\left(f\right)^{2} + 4 i \, e^{2} - 16 i \, d f - 4 \, {\left(b e - 2 \, a f\right)} \log\left(f\right)}{8 \, f}\right)} \operatorname{C}\left(\frac{{\left(4 \, f x + i \, b \log\left(f\right) + 2 \, e\right)} \sqrt{\frac{f}{\pi}}}{2 \, f}\right) \log\left(f\right) - 2 \, \pi b \sqrt{\frac{f}{\pi}} e^{\left(\frac{i \, b^{2} \log\left(f\right)^{2} - 4 i \, e^{2} + 16 i \, d f - 4 \, {\left(b e - 2 \, a f\right)} \log\left(f\right)}{8 \, f}\right)} \operatorname{C}\left(-\frac{{\left(4 \, f x - i \, b \log\left(f\right) + 2 \, e\right)} \sqrt{\frac{f}{\pi}}}{2 \, f}\right) \log\left(f\right) - 2 i \, \pi b \sqrt{\frac{f}{\pi}} e^{\left(\frac{-i \, b^{2} \log\left(f\right)^{2} + 4 i \, e^{2} - 16 i \, d f - 4 \, {\left(b e - 2 \, a f\right)} \log\left(f\right)}{8 \, f}\right)} \operatorname{S}\left(\frac{{\left(4 \, f x + i \, b \log\left(f\right) + 2 \, e\right)} \sqrt{\frac{f}{\pi}}}{2 \, f}\right) \log\left(f\right) - 2 i \, \pi b \sqrt{\frac{f}{\pi}} e^{\left(\frac{i \, b^{2} \log\left(f\right)^{2} - 4 i \, e^{2} + 16 i \, d f - 4 \, {\left(b e - 2 \, a f\right)} \log\left(f\right)}{8 \, f}\right)} \operatorname{S}\left(-\frac{{\left(4 \, f x - i \, b \log\left(f\right) + 2 \, e\right)} \sqrt{\frac{f}{\pi}}}{2 \, f}\right) \log\left(f\right) - 8 \, f f^{b x + a}}{16 \, b f \log\left(f\right)}"," ",0,"-1/16*(2*pi*b*sqrt(f/pi)*e^(1/8*(-I*b^2*log(f)^2 + 4*I*e^2 - 16*I*d*f - 4*(b*e - 2*a*f)*log(f))/f)*fresnel_cos(1/2*(4*f*x + I*b*log(f) + 2*e)*sqrt(f/pi)/f)*log(f) - 2*pi*b*sqrt(f/pi)*e^(1/8*(I*b^2*log(f)^2 - 4*I*e^2 + 16*I*d*f - 4*(b*e - 2*a*f)*log(f))/f)*fresnel_cos(-1/2*(4*f*x - I*b*log(f) + 2*e)*sqrt(f/pi)/f)*log(f) - 2*I*pi*b*sqrt(f/pi)*e^(1/8*(-I*b^2*log(f)^2 + 4*I*e^2 - 16*I*d*f - 4*(b*e - 2*a*f)*log(f))/f)*fresnel_sin(1/2*(4*f*x + I*b*log(f) + 2*e)*sqrt(f/pi)/f)*log(f) - 2*I*pi*b*sqrt(f/pi)*e^(1/8*(I*b^2*log(f)^2 - 4*I*e^2 + 16*I*d*f - 4*(b*e - 2*a*f)*log(f))/f)*fresnel_sin(-1/2*(4*f*x - I*b*log(f) + 2*e)*sqrt(f/pi)/f)*log(f) - 8*f*f^(b*x + a))/(b*f*log(f))","B",0
84,1,629,0,1.563725," ","integrate(f^(b*x+a)*sin(f*x^2+e*x+d)^3,x, algorithm=""fricas"")","\frac{-i \, \sqrt{6} \pi \sqrt{\frac{f}{\pi}} e^{\left(\frac{-i \, b^{2} \log\left(f\right)^{2} + 9 i \, e^{2} - 36 i \, d f - 6 \, {\left(b e - 2 \, a f\right)} \log\left(f\right)}{12 \, f}\right)} \operatorname{C}\left(\frac{\sqrt{6} {\left(6 \, f x + i \, b \log\left(f\right) + 3 \, e\right)} \sqrt{\frac{f}{\pi}}}{6 \, f}\right) - i \, \sqrt{6} \pi \sqrt{\frac{f}{\pi}} e^{\left(\frac{i \, b^{2} \log\left(f\right)^{2} - 9 i \, e^{2} + 36 i \, d f - 6 \, {\left(b e - 2 \, a f\right)} \log\left(f\right)}{12 \, f}\right)} \operatorname{C}\left(-\frac{\sqrt{6} {\left(6 \, f x - i \, b \log\left(f\right) + 3 \, e\right)} \sqrt{\frac{f}{\pi}}}{6 \, f}\right) + 9 i \, \sqrt{2} \pi \sqrt{\frac{f}{\pi}} e^{\left(\frac{-i \, b^{2} \log\left(f\right)^{2} + i \, e^{2} - 4 i \, d f - 2 \, {\left(b e - 2 \, a f\right)} \log\left(f\right)}{4 \, f}\right)} \operatorname{C}\left(\frac{\sqrt{2} {\left(2 \, f x + i \, b \log\left(f\right) + e\right)} \sqrt{\frac{f}{\pi}}}{2 \, f}\right) + 9 i \, \sqrt{2} \pi \sqrt{\frac{f}{\pi}} e^{\left(\frac{i \, b^{2} \log\left(f\right)^{2} - i \, e^{2} + 4 i \, d f - 2 \, {\left(b e - 2 \, a f\right)} \log\left(f\right)}{4 \, f}\right)} \operatorname{C}\left(-\frac{\sqrt{2} {\left(2 \, f x - i \, b \log\left(f\right) + e\right)} \sqrt{\frac{f}{\pi}}}{2 \, f}\right) - \sqrt{6} \pi \sqrt{\frac{f}{\pi}} e^{\left(\frac{-i \, b^{2} \log\left(f\right)^{2} + 9 i \, e^{2} - 36 i \, d f - 6 \, {\left(b e - 2 \, a f\right)} \log\left(f\right)}{12 \, f}\right)} \operatorname{S}\left(\frac{\sqrt{6} {\left(6 \, f x + i \, b \log\left(f\right) + 3 \, e\right)} \sqrt{\frac{f}{\pi}}}{6 \, f}\right) + \sqrt{6} \pi \sqrt{\frac{f}{\pi}} e^{\left(\frac{i \, b^{2} \log\left(f\right)^{2} - 9 i \, e^{2} + 36 i \, d f - 6 \, {\left(b e - 2 \, a f\right)} \log\left(f\right)}{12 \, f}\right)} \operatorname{S}\left(-\frac{\sqrt{6} {\left(6 \, f x - i \, b \log\left(f\right) + 3 \, e\right)} \sqrt{\frac{f}{\pi}}}{6 \, f}\right) + 9 \, \sqrt{2} \pi \sqrt{\frac{f}{\pi}} e^{\left(\frac{-i \, b^{2} \log\left(f\right)^{2} + i \, e^{2} - 4 i \, d f - 2 \, {\left(b e - 2 \, a f\right)} \log\left(f\right)}{4 \, f}\right)} \operatorname{S}\left(\frac{\sqrt{2} {\left(2 \, f x + i \, b \log\left(f\right) + e\right)} \sqrt{\frac{f}{\pi}}}{2 \, f}\right) - 9 \, \sqrt{2} \pi \sqrt{\frac{f}{\pi}} e^{\left(\frac{i \, b^{2} \log\left(f\right)^{2} - i \, e^{2} + 4 i \, d f - 2 \, {\left(b e - 2 \, a f\right)} \log\left(f\right)}{4 \, f}\right)} \operatorname{S}\left(-\frac{\sqrt{2} {\left(2 \, f x - i \, b \log\left(f\right) + e\right)} \sqrt{\frac{f}{\pi}}}{2 \, f}\right)}{48 \, f}"," ",0,"1/48*(-I*sqrt(6)*pi*sqrt(f/pi)*e^(1/12*(-I*b^2*log(f)^2 + 9*I*e^2 - 36*I*d*f - 6*(b*e - 2*a*f)*log(f))/f)*fresnel_cos(1/6*sqrt(6)*(6*f*x + I*b*log(f) + 3*e)*sqrt(f/pi)/f) - I*sqrt(6)*pi*sqrt(f/pi)*e^(1/12*(I*b^2*log(f)^2 - 9*I*e^2 + 36*I*d*f - 6*(b*e - 2*a*f)*log(f))/f)*fresnel_cos(-1/6*sqrt(6)*(6*f*x - I*b*log(f) + 3*e)*sqrt(f/pi)/f) + 9*I*sqrt(2)*pi*sqrt(f/pi)*e^(1/4*(-I*b^2*log(f)^2 + I*e^2 - 4*I*d*f - 2*(b*e - 2*a*f)*log(f))/f)*fresnel_cos(1/2*sqrt(2)*(2*f*x + I*b*log(f) + e)*sqrt(f/pi)/f) + 9*I*sqrt(2)*pi*sqrt(f/pi)*e^(1/4*(I*b^2*log(f)^2 - I*e^2 + 4*I*d*f - 2*(b*e - 2*a*f)*log(f))/f)*fresnel_cos(-1/2*sqrt(2)*(2*f*x - I*b*log(f) + e)*sqrt(f/pi)/f) - sqrt(6)*pi*sqrt(f/pi)*e^(1/12*(-I*b^2*log(f)^2 + 9*I*e^2 - 36*I*d*f - 6*(b*e - 2*a*f)*log(f))/f)*fresnel_sin(1/6*sqrt(6)*(6*f*x + I*b*log(f) + 3*e)*sqrt(f/pi)/f) + sqrt(6)*pi*sqrt(f/pi)*e^(1/12*(I*b^2*log(f)^2 - 9*I*e^2 + 36*I*d*f - 6*(b*e - 2*a*f)*log(f))/f)*fresnel_sin(-1/6*sqrt(6)*(6*f*x - I*b*log(f) + 3*e)*sqrt(f/pi)/f) + 9*sqrt(2)*pi*sqrt(f/pi)*e^(1/4*(-I*b^2*log(f)^2 + I*e^2 - 4*I*d*f - 2*(b*e - 2*a*f)*log(f))/f)*fresnel_sin(1/2*sqrt(2)*(2*f*x + I*b*log(f) + e)*sqrt(f/pi)/f) - 9*sqrt(2)*pi*sqrt(f/pi)*e^(1/4*(I*b^2*log(f)^2 - I*e^2 + 4*I*d*f - 2*(b*e - 2*a*f)*log(f))/f)*fresnel_sin(-1/2*sqrt(2)*(2*f*x - I*b*log(f) + e)*sqrt(f/pi)/f))/f","B",0
85,1,144,0,0.940766," ","integrate(f^(c*x^2+a)*sin(e*x+d),x, algorithm=""fricas"")","\frac{i \, \sqrt{\pi} \sqrt{-c \log\left(f\right)} \operatorname{erf}\left(\frac{{\left(2 \, c x \log\left(f\right) + i \, e\right)} \sqrt{-c \log\left(f\right)}}{2 \, c \log\left(f\right)}\right) e^{\left(\frac{4 \, a c \log\left(f\right)^{2} + 4 i \, c d \log\left(f\right) + e^{2}}{4 \, c \log\left(f\right)}\right)} - i \, \sqrt{\pi} \sqrt{-c \log\left(f\right)} \operatorname{erf}\left(\frac{{\left(2 \, c x \log\left(f\right) - i \, e\right)} \sqrt{-c \log\left(f\right)}}{2 \, c \log\left(f\right)}\right) e^{\left(\frac{4 \, a c \log\left(f\right)^{2} - 4 i \, c d \log\left(f\right) + e^{2}}{4 \, c \log\left(f\right)}\right)}}{4 \, c \log\left(f\right)}"," ",0,"1/4*(I*sqrt(pi)*sqrt(-c*log(f))*erf(1/2*(2*c*x*log(f) + I*e)*sqrt(-c*log(f))/(c*log(f)))*e^(1/4*(4*a*c*log(f)^2 + 4*I*c*d*log(f) + e^2)/(c*log(f))) - I*sqrt(pi)*sqrt(-c*log(f))*erf(1/2*(2*c*x*log(f) - I*e)*sqrt(-c*log(f))/(c*log(f)))*e^(1/4*(4*a*c*log(f)^2 - 4*I*c*d*log(f) + e^2)/(c*log(f))))/(c*log(f))","A",0
86,1,161,0,0.481867," ","integrate(f^(c*x^2+a)*sin(e*x+d)^2,x, algorithm=""fricas"")","-\frac{2 \, \sqrt{\pi} \sqrt{-c \log\left(f\right)} f^{a} \operatorname{erf}\left(\sqrt{-c \log\left(f\right)} x\right) - \sqrt{\pi} \sqrt{-c \log\left(f\right)} \operatorname{erf}\left(\frac{{\left(c x \log\left(f\right) + i \, e\right)} \sqrt{-c \log\left(f\right)}}{c \log\left(f\right)}\right) e^{\left(\frac{a c \log\left(f\right)^{2} + 2 i \, c d \log\left(f\right) + e^{2}}{c \log\left(f\right)}\right)} - \sqrt{\pi} \sqrt{-c \log\left(f\right)} \operatorname{erf}\left(\frac{{\left(c x \log\left(f\right) - i \, e\right)} \sqrt{-c \log\left(f\right)}}{c \log\left(f\right)}\right) e^{\left(\frac{a c \log\left(f\right)^{2} - 2 i \, c d \log\left(f\right) + e^{2}}{c \log\left(f\right)}\right)}}{8 \, c \log\left(f\right)}"," ",0,"-1/8*(2*sqrt(pi)*sqrt(-c*log(f))*f^a*erf(sqrt(-c*log(f))*x) - sqrt(pi)*sqrt(-c*log(f))*erf((c*x*log(f) + I*e)*sqrt(-c*log(f))/(c*log(f)))*e^((a*c*log(f)^2 + 2*I*c*d*log(f) + e^2)/(c*log(f))) - sqrt(pi)*sqrt(-c*log(f))*erf((c*x*log(f) - I*e)*sqrt(-c*log(f))/(c*log(f)))*e^((a*c*log(f)^2 - 2*I*c*d*log(f) + e^2)/(c*log(f))))/(c*log(f))","A",0
87,1,282,0,0.623278," ","integrate(f^(c*x^2+a)*sin(e*x+d)^3,x, algorithm=""fricas"")","\frac{-i \, \sqrt{\pi} \sqrt{-c \log\left(f\right)} \operatorname{erf}\left(\frac{{\left(2 \, c x \log\left(f\right) + 3 i \, e\right)} \sqrt{-c \log\left(f\right)}}{2 \, c \log\left(f\right)}\right) e^{\left(\frac{4 \, a c \log\left(f\right)^{2} + 12 i \, c d \log\left(f\right) + 9 \, e^{2}}{4 \, c \log\left(f\right)}\right)} + 3 i \, \sqrt{\pi} \sqrt{-c \log\left(f\right)} \operatorname{erf}\left(\frac{{\left(2 \, c x \log\left(f\right) + i \, e\right)} \sqrt{-c \log\left(f\right)}}{2 \, c \log\left(f\right)}\right) e^{\left(\frac{4 \, a c \log\left(f\right)^{2} + 4 i \, c d \log\left(f\right) + e^{2}}{4 \, c \log\left(f\right)}\right)} - 3 i \, \sqrt{\pi} \sqrt{-c \log\left(f\right)} \operatorname{erf}\left(\frac{{\left(2 \, c x \log\left(f\right) - i \, e\right)} \sqrt{-c \log\left(f\right)}}{2 \, c \log\left(f\right)}\right) e^{\left(\frac{4 \, a c \log\left(f\right)^{2} - 4 i \, c d \log\left(f\right) + e^{2}}{4 \, c \log\left(f\right)}\right)} + i \, \sqrt{\pi} \sqrt{-c \log\left(f\right)} \operatorname{erf}\left(\frac{{\left(2 \, c x \log\left(f\right) - 3 i \, e\right)} \sqrt{-c \log\left(f\right)}}{2 \, c \log\left(f\right)}\right) e^{\left(\frac{4 \, a c \log\left(f\right)^{2} - 12 i \, c d \log\left(f\right) + 9 \, e^{2}}{4 \, c \log\left(f\right)}\right)}}{16 \, c \log\left(f\right)}"," ",0,"1/16*(-I*sqrt(pi)*sqrt(-c*log(f))*erf(1/2*(2*c*x*log(f) + 3*I*e)*sqrt(-c*log(f))/(c*log(f)))*e^(1/4*(4*a*c*log(f)^2 + 12*I*c*d*log(f) + 9*e^2)/(c*log(f))) + 3*I*sqrt(pi)*sqrt(-c*log(f))*erf(1/2*(2*c*x*log(f) + I*e)*sqrt(-c*log(f))/(c*log(f)))*e^(1/4*(4*a*c*log(f)^2 + 4*I*c*d*log(f) + e^2)/(c*log(f))) - 3*I*sqrt(pi)*sqrt(-c*log(f))*erf(1/2*(2*c*x*log(f) - I*e)*sqrt(-c*log(f))/(c*log(f)))*e^(1/4*(4*a*c*log(f)^2 - 4*I*c*d*log(f) + e^2)/(c*log(f))) + I*sqrt(pi)*sqrt(-c*log(f))*erf(1/2*(2*c*x*log(f) - 3*I*e)*sqrt(-c*log(f))/(c*log(f)))*e^(1/4*(4*a*c*log(f)^2 - 12*I*c*d*log(f) + 9*e^2)/(c*log(f))))/(c*log(f))","A",0
88,1,107,0,0.762095," ","integrate(f^(c*x^2+a)*sin(f*x^2+d),x, algorithm=""fricas"")","\frac{\sqrt{\pi} {\left(i \, c \log\left(f\right) + f\right)} \sqrt{-c \log\left(f\right) - i \, f} \operatorname{erf}\left(\sqrt{-c \log\left(f\right) - i \, f} x\right) e^{\left(a \log\left(f\right) + i \, d\right)} + \sqrt{\pi} {\left(-i \, c \log\left(f\right) + f\right)} \sqrt{-c \log\left(f\right) + i \, f} \operatorname{erf}\left(\sqrt{-c \log\left(f\right) + i \, f} x\right) e^{\left(a \log\left(f\right) - i \, d\right)}}{4 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}"," ",0,"1/4*(sqrt(pi)*(I*c*log(f) + f)*sqrt(-c*log(f) - I*f)*erf(sqrt(-c*log(f) - I*f)*x)*e^(a*log(f) + I*d) + sqrt(pi)*(-I*c*log(f) + f)*sqrt(-c*log(f) + I*f)*erf(sqrt(-c*log(f) + I*f)*x)*e^(a*log(f) - I*d))/(c^2*log(f)^2 + f^2)","A",0
89,1,169,0,0.719284," ","integrate(f^(c*x^2+a)*sin(f*x^2+d)^2,x, algorithm=""fricas"")","-\frac{2 \, \sqrt{\pi} {\left(c^{2} \log\left(f\right)^{2} + 4 \, f^{2}\right)} \sqrt{-c \log\left(f\right)} f^{a} \operatorname{erf}\left(\sqrt{-c \log\left(f\right)} x\right) - \sqrt{\pi} {\left(c^{2} \log\left(f\right)^{2} - 2 i \, c f \log\left(f\right)\right)} \sqrt{-c \log\left(f\right) - 2 i \, f} \operatorname{erf}\left(\sqrt{-c \log\left(f\right) - 2 i \, f} x\right) e^{\left(a \log\left(f\right) + 2 i \, d\right)} - \sqrt{\pi} {\left(c^{2} \log\left(f\right)^{2} + 2 i \, c f \log\left(f\right)\right)} \sqrt{-c \log\left(f\right) + 2 i \, f} \operatorname{erf}\left(\sqrt{-c \log\left(f\right) + 2 i \, f} x\right) e^{\left(a \log\left(f\right) - 2 i \, d\right)}}{8 \, {\left(c^{3} \log\left(f\right)^{3} + 4 \, c f^{2} \log\left(f\right)\right)}}"," ",0,"-1/8*(2*sqrt(pi)*(c^2*log(f)^2 + 4*f^2)*sqrt(-c*log(f))*f^a*erf(sqrt(-c*log(f))*x) - sqrt(pi)*(c^2*log(f)^2 - 2*I*c*f*log(f))*sqrt(-c*log(f) - 2*I*f)*erf(sqrt(-c*log(f) - 2*I*f)*x)*e^(a*log(f) + 2*I*d) - sqrt(pi)*(c^2*log(f)^2 + 2*I*c*f*log(f))*sqrt(-c*log(f) + 2*I*f)*erf(sqrt(-c*log(f) + 2*I*f)*x)*e^(a*log(f) - 2*I*d))/(c^3*log(f)^3 + 4*c*f^2*log(f))","A",0
90,1,315,0,0.595229," ","integrate(f^(c*x^2+a)*sin(f*x^2+d)^3,x, algorithm=""fricas"")","\frac{\sqrt{\pi} {\left(-i \, c^{3} \log\left(f\right)^{3} - 3 \, c^{2} f \log\left(f\right)^{2} - i \, c f^{2} \log\left(f\right) - 3 \, f^{3}\right)} \sqrt{-c \log\left(f\right) - 3 i \, f} \operatorname{erf}\left(\sqrt{-c \log\left(f\right) - 3 i \, f} x\right) e^{\left(a \log\left(f\right) + 3 i \, d\right)} + \sqrt{\pi} {\left(3 i \, c^{3} \log\left(f\right)^{3} + 3 \, c^{2} f \log\left(f\right)^{2} + 27 i \, c f^{2} \log\left(f\right) + 27 \, f^{3}\right)} \sqrt{-c \log\left(f\right) - i \, f} \operatorname{erf}\left(\sqrt{-c \log\left(f\right) - i \, f} x\right) e^{\left(a \log\left(f\right) + i \, d\right)} + \sqrt{\pi} {\left(-3 i \, c^{3} \log\left(f\right)^{3} + 3 \, c^{2} f \log\left(f\right)^{2} - 27 i \, c f^{2} \log\left(f\right) + 27 \, f^{3}\right)} \sqrt{-c \log\left(f\right) + i \, f} \operatorname{erf}\left(\sqrt{-c \log\left(f\right) + i \, f} x\right) e^{\left(a \log\left(f\right) - i \, d\right)} + \sqrt{\pi} {\left(i \, c^{3} \log\left(f\right)^{3} - 3 \, c^{2} f \log\left(f\right)^{2} + i \, c f^{2} \log\left(f\right) - 3 \, f^{3}\right)} \sqrt{-c \log\left(f\right) + 3 i \, f} \operatorname{erf}\left(\sqrt{-c \log\left(f\right) + 3 i \, f} x\right) e^{\left(a \log\left(f\right) - 3 i \, d\right)}}{16 \, {\left(c^{4} \log\left(f\right)^{4} + 10 \, c^{2} f^{2} \log\left(f\right)^{2} + 9 \, f^{4}\right)}}"," ",0,"1/16*(sqrt(pi)*(-I*c^3*log(f)^3 - 3*c^2*f*log(f)^2 - I*c*f^2*log(f) - 3*f^3)*sqrt(-c*log(f) - 3*I*f)*erf(sqrt(-c*log(f) - 3*I*f)*x)*e^(a*log(f) + 3*I*d) + sqrt(pi)*(3*I*c^3*log(f)^3 + 3*c^2*f*log(f)^2 + 27*I*c*f^2*log(f) + 27*f^3)*sqrt(-c*log(f) - I*f)*erf(sqrt(-c*log(f) - I*f)*x)*e^(a*log(f) + I*d) + sqrt(pi)*(-3*I*c^3*log(f)^3 + 3*c^2*f*log(f)^2 - 27*I*c*f^2*log(f) + 27*f^3)*sqrt(-c*log(f) + I*f)*erf(sqrt(-c*log(f) + I*f)*x)*e^(a*log(f) - I*d) + sqrt(pi)*(I*c^3*log(f)^3 - 3*c^2*f*log(f)^2 + I*c*f^2*log(f) - 3*f^3)*sqrt(-c*log(f) + 3*I*f)*erf(sqrt(-c*log(f) + 3*I*f)*x)*e^(a*log(f) - 3*I*d))/(c^4*log(f)^4 + 10*c^2*f^2*log(f)^2 + 9*f^4)","B",0
91,1,299,0,0.738326," ","integrate(f^(c*x^2+a)*sin(f*x^2+e*x+d),x, algorithm=""fricas"")","\frac{\sqrt{\pi} {\left(i \, c \log\left(f\right) + f\right)} \sqrt{-c \log\left(f\right) - i \, f} \operatorname{erf}\left(\frac{{\left(2 \, c^{2} x \log\left(f\right)^{2} + 2 \, f^{2} x + i \, c e \log\left(f\right) + e f\right)} \sqrt{-c \log\left(f\right) - i \, f}}{2 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}\right) e^{\left(\frac{4 \, a c^{2} \log\left(f\right)^{3} + 4 i \, c^{2} d \log\left(f\right)^{2} - i \, e^{2} f + 4 i \, d f^{2} + {\left(c e^{2} + 4 \, a f^{2}\right)} \log\left(f\right)}{4 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}\right)} + \sqrt{\pi} {\left(-i \, c \log\left(f\right) + f\right)} \sqrt{-c \log\left(f\right) + i \, f} \operatorname{erf}\left(\frac{{\left(2 \, c^{2} x \log\left(f\right)^{2} + 2 \, f^{2} x - i \, c e \log\left(f\right) + e f\right)} \sqrt{-c \log\left(f\right) + i \, f}}{2 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}\right) e^{\left(\frac{4 \, a c^{2} \log\left(f\right)^{3} - 4 i \, c^{2} d \log\left(f\right)^{2} + i \, e^{2} f - 4 i \, d f^{2} + {\left(c e^{2} + 4 \, a f^{2}\right)} \log\left(f\right)}{4 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}\right)}}{4 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}"," ",0,"1/4*(sqrt(pi)*(I*c*log(f) + f)*sqrt(-c*log(f) - I*f)*erf(1/2*(2*c^2*x*log(f)^2 + 2*f^2*x + I*c*e*log(f) + e*f)*sqrt(-c*log(f) - I*f)/(c^2*log(f)^2 + f^2))*e^(1/4*(4*a*c^2*log(f)^3 + 4*I*c^2*d*log(f)^2 - I*e^2*f + 4*I*d*f^2 + (c*e^2 + 4*a*f^2)*log(f))/(c^2*log(f)^2 + f^2)) + sqrt(pi)*(-I*c*log(f) + f)*sqrt(-c*log(f) + I*f)*erf(1/2*(2*c^2*x*log(f)^2 + 2*f^2*x - I*c*e*log(f) + e*f)*sqrt(-c*log(f) + I*f)/(c^2*log(f)^2 + f^2))*e^(1/4*(4*a*c^2*log(f)^3 - 4*I*c^2*d*log(f)^2 + I*e^2*f - 4*I*d*f^2 + (c*e^2 + 4*a*f^2)*log(f))/(c^2*log(f)^2 + f^2)))/(c^2*log(f)^2 + f^2)","B",0
92,1,363,0,0.698199," ","integrate(f^(c*x^2+a)*sin(f*x^2+e*x+d)^2,x, algorithm=""fricas"")","-\frac{2 \, \sqrt{\pi} {\left(c^{2} \log\left(f\right)^{2} + 4 \, f^{2}\right)} \sqrt{-c \log\left(f\right)} f^{a} \operatorname{erf}\left(\sqrt{-c \log\left(f\right)} x\right) - \sqrt{\pi} {\left(c^{2} \log\left(f\right)^{2} - 2 i \, c f \log\left(f\right)\right)} \sqrt{-c \log\left(f\right) - 2 i \, f} \operatorname{erf}\left(\frac{{\left(c^{2} x \log\left(f\right)^{2} + 4 \, f^{2} x + i \, c e \log\left(f\right) + 2 \, e f\right)} \sqrt{-c \log\left(f\right) - 2 i \, f}}{c^{2} \log\left(f\right)^{2} + 4 \, f^{2}}\right) e^{\left(\frac{a c^{2} \log\left(f\right)^{3} + 2 i \, c^{2} d \log\left(f\right)^{2} - 2 i \, e^{2} f + 8 i \, d f^{2} + {\left(c e^{2} + 4 \, a f^{2}\right)} \log\left(f\right)}{c^{2} \log\left(f\right)^{2} + 4 \, f^{2}}\right)} - \sqrt{\pi} {\left(c^{2} \log\left(f\right)^{2} + 2 i \, c f \log\left(f\right)\right)} \sqrt{-c \log\left(f\right) + 2 i \, f} \operatorname{erf}\left(\frac{{\left(c^{2} x \log\left(f\right)^{2} + 4 \, f^{2} x - i \, c e \log\left(f\right) + 2 \, e f\right)} \sqrt{-c \log\left(f\right) + 2 i \, f}}{c^{2} \log\left(f\right)^{2} + 4 \, f^{2}}\right) e^{\left(\frac{a c^{2} \log\left(f\right)^{3} - 2 i \, c^{2} d \log\left(f\right)^{2} + 2 i \, e^{2} f - 8 i \, d f^{2} + {\left(c e^{2} + 4 \, a f^{2}\right)} \log\left(f\right)}{c^{2} \log\left(f\right)^{2} + 4 \, f^{2}}\right)}}{8 \, {\left(c^{3} \log\left(f\right)^{3} + 4 \, c f^{2} \log\left(f\right)\right)}}"," ",0,"-1/8*(2*sqrt(pi)*(c^2*log(f)^2 + 4*f^2)*sqrt(-c*log(f))*f^a*erf(sqrt(-c*log(f))*x) - sqrt(pi)*(c^2*log(f)^2 - 2*I*c*f*log(f))*sqrt(-c*log(f) - 2*I*f)*erf((c^2*x*log(f)^2 + 4*f^2*x + I*c*e*log(f) + 2*e*f)*sqrt(-c*log(f) - 2*I*f)/(c^2*log(f)^2 + 4*f^2))*e^((a*c^2*log(f)^3 + 2*I*c^2*d*log(f)^2 - 2*I*e^2*f + 8*I*d*f^2 + (c*e^2 + 4*a*f^2)*log(f))/(c^2*log(f)^2 + 4*f^2)) - sqrt(pi)*(c^2*log(f)^2 + 2*I*c*f*log(f))*sqrt(-c*log(f) + 2*I*f)*erf((c^2*x*log(f)^2 + 4*f^2*x - I*c*e*log(f) + 2*e*f)*sqrt(-c*log(f) + 2*I*f)/(c^2*log(f)^2 + 4*f^2))*e^((a*c^2*log(f)^3 - 2*I*c^2*d*log(f)^2 + 2*I*e^2*f - 8*I*d*f^2 + (c*e^2 + 4*a*f^2)*log(f))/(c^2*log(f)^2 + 4*f^2)))/(c^3*log(f)^3 + 4*c*f^2*log(f))","B",0
93,1,711,0,0.757042," ","integrate(f^(c*x^2+a)*sin(f*x^2+e*x+d)^3,x, algorithm=""fricas"")","\frac{\sqrt{\pi} {\left(-i \, c^{3} \log\left(f\right)^{3} - 3 \, c^{2} f \log\left(f\right)^{2} - i \, c f^{2} \log\left(f\right) - 3 \, f^{3}\right)} \sqrt{-c \log\left(f\right) - 3 i \, f} \operatorname{erf}\left(\frac{{\left(2 \, c^{2} x \log\left(f\right)^{2} + 18 \, f^{2} x + 3 i \, c e \log\left(f\right) + 9 \, e f\right)} \sqrt{-c \log\left(f\right) - 3 i \, f}}{2 \, {\left(c^{2} \log\left(f\right)^{2} + 9 \, f^{2}\right)}}\right) e^{\left(\frac{4 \, a c^{2} \log\left(f\right)^{3} + 12 i \, c^{2} d \log\left(f\right)^{2} - 27 i \, e^{2} f + 108 i \, d f^{2} + 9 \, {\left(c e^{2} + 4 \, a f^{2}\right)} \log\left(f\right)}{4 \, {\left(c^{2} \log\left(f\right)^{2} + 9 \, f^{2}\right)}}\right)} + \sqrt{\pi} {\left(i \, c^{3} \log\left(f\right)^{3} - 3 \, c^{2} f \log\left(f\right)^{2} + i \, c f^{2} \log\left(f\right) - 3 \, f^{3}\right)} \sqrt{-c \log\left(f\right) + 3 i \, f} \operatorname{erf}\left(\frac{{\left(2 \, c^{2} x \log\left(f\right)^{2} + 18 \, f^{2} x - 3 i \, c e \log\left(f\right) + 9 \, e f\right)} \sqrt{-c \log\left(f\right) + 3 i \, f}}{2 \, {\left(c^{2} \log\left(f\right)^{2} + 9 \, f^{2}\right)}}\right) e^{\left(\frac{4 \, a c^{2} \log\left(f\right)^{3} - 12 i \, c^{2} d \log\left(f\right)^{2} + 27 i \, e^{2} f - 108 i \, d f^{2} + 9 \, {\left(c e^{2} + 4 \, a f^{2}\right)} \log\left(f\right)}{4 \, {\left(c^{2} \log\left(f\right)^{2} + 9 \, f^{2}\right)}}\right)} + \sqrt{\pi} {\left(3 i \, c^{3} \log\left(f\right)^{3} + 3 \, c^{2} f \log\left(f\right)^{2} + 27 i \, c f^{2} \log\left(f\right) + 27 \, f^{3}\right)} \sqrt{-c \log\left(f\right) - i \, f} \operatorname{erf}\left(\frac{{\left(2 \, c^{2} x \log\left(f\right)^{2} + 2 \, f^{2} x + i \, c e \log\left(f\right) + e f\right)} \sqrt{-c \log\left(f\right) - i \, f}}{2 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}\right) e^{\left(\frac{4 \, a c^{2} \log\left(f\right)^{3} + 4 i \, c^{2} d \log\left(f\right)^{2} - i \, e^{2} f + 4 i \, d f^{2} + {\left(c e^{2} + 4 \, a f^{2}\right)} \log\left(f\right)}{4 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}\right)} + \sqrt{\pi} {\left(-3 i \, c^{3} \log\left(f\right)^{3} + 3 \, c^{2} f \log\left(f\right)^{2} - 27 i \, c f^{2} \log\left(f\right) + 27 \, f^{3}\right)} \sqrt{-c \log\left(f\right) + i \, f} \operatorname{erf}\left(\frac{{\left(2 \, c^{2} x \log\left(f\right)^{2} + 2 \, f^{2} x - i \, c e \log\left(f\right) + e f\right)} \sqrt{-c \log\left(f\right) + i \, f}}{2 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}\right) e^{\left(\frac{4 \, a c^{2} \log\left(f\right)^{3} - 4 i \, c^{2} d \log\left(f\right)^{2} + i \, e^{2} f - 4 i \, d f^{2} + {\left(c e^{2} + 4 \, a f^{2}\right)} \log\left(f\right)}{4 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}\right)}}{16 \, {\left(c^{4} \log\left(f\right)^{4} + 10 \, c^{2} f^{2} \log\left(f\right)^{2} + 9 \, f^{4}\right)}}"," ",0,"1/16*(sqrt(pi)*(-I*c^3*log(f)^3 - 3*c^2*f*log(f)^2 - I*c*f^2*log(f) - 3*f^3)*sqrt(-c*log(f) - 3*I*f)*erf(1/2*(2*c^2*x*log(f)^2 + 18*f^2*x + 3*I*c*e*log(f) + 9*e*f)*sqrt(-c*log(f) - 3*I*f)/(c^2*log(f)^2 + 9*f^2))*e^(1/4*(4*a*c^2*log(f)^3 + 12*I*c^2*d*log(f)^2 - 27*I*e^2*f + 108*I*d*f^2 + 9*(c*e^2 + 4*a*f^2)*log(f))/(c^2*log(f)^2 + 9*f^2)) + sqrt(pi)*(I*c^3*log(f)^3 - 3*c^2*f*log(f)^2 + I*c*f^2*log(f) - 3*f^3)*sqrt(-c*log(f) + 3*I*f)*erf(1/2*(2*c^2*x*log(f)^2 + 18*f^2*x - 3*I*c*e*log(f) + 9*e*f)*sqrt(-c*log(f) + 3*I*f)/(c^2*log(f)^2 + 9*f^2))*e^(1/4*(4*a*c^2*log(f)^3 - 12*I*c^2*d*log(f)^2 + 27*I*e^2*f - 108*I*d*f^2 + 9*(c*e^2 + 4*a*f^2)*log(f))/(c^2*log(f)^2 + 9*f^2)) + sqrt(pi)*(3*I*c^3*log(f)^3 + 3*c^2*f*log(f)^2 + 27*I*c*f^2*log(f) + 27*f^3)*sqrt(-c*log(f) - I*f)*erf(1/2*(2*c^2*x*log(f)^2 + 2*f^2*x + I*c*e*log(f) + e*f)*sqrt(-c*log(f) - I*f)/(c^2*log(f)^2 + f^2))*e^(1/4*(4*a*c^2*log(f)^3 + 4*I*c^2*d*log(f)^2 - I*e^2*f + 4*I*d*f^2 + (c*e^2 + 4*a*f^2)*log(f))/(c^2*log(f)^2 + f^2)) + sqrt(pi)*(-3*I*c^3*log(f)^3 + 3*c^2*f*log(f)^2 - 27*I*c*f^2*log(f) + 27*f^3)*sqrt(-c*log(f) + I*f)*erf(1/2*(2*c^2*x*log(f)^2 + 2*f^2*x - I*c*e*log(f) + e*f)*sqrt(-c*log(f) + I*f)/(c^2*log(f)^2 + f^2))*e^(1/4*(4*a*c^2*log(f)^3 - 4*I*c^2*d*log(f)^2 + I*e^2*f - 4*I*d*f^2 + (c*e^2 + 4*a*f^2)*log(f))/(c^2*log(f)^2 + f^2)))/(c^4*log(f)^4 + 10*c^2*f^2*log(f)^2 + 9*f^4)","B",0
94,1,178,0,1.315598," ","integrate(f^(c*x^2+b*x+a)*sin(e*x+d),x, algorithm=""fricas"")","\frac{i \, \sqrt{\pi} \sqrt{-c \log\left(f\right)} \operatorname{erf}\left(\frac{{\left({\left(2 \, c x + b\right)} \log\left(f\right) + i \, e\right)} \sqrt{-c \log\left(f\right)}}{2 \, c \log\left(f\right)}\right) e^{\left(-\frac{{\left(b^{2} - 4 \, a c\right)} \log\left(f\right)^{2} - e^{2} - {\left(4 i \, c d - 2 i \, b e\right)} \log\left(f\right)}{4 \, c \log\left(f\right)}\right)} - i \, \sqrt{\pi} \sqrt{-c \log\left(f\right)} \operatorname{erf}\left(\frac{{\left({\left(2 \, c x + b\right)} \log\left(f\right) - i \, e\right)} \sqrt{-c \log\left(f\right)}}{2 \, c \log\left(f\right)}\right) e^{\left(-\frac{{\left(b^{2} - 4 \, a c\right)} \log\left(f\right)^{2} - e^{2} - {\left(-4 i \, c d + 2 i \, b e\right)} \log\left(f\right)}{4 \, c \log\left(f\right)}\right)}}{4 \, c \log\left(f\right)}"," ",0,"1/4*(I*sqrt(pi)*sqrt(-c*log(f))*erf(1/2*((2*c*x + b)*log(f) + I*e)*sqrt(-c*log(f))/(c*log(f)))*e^(-1/4*((b^2 - 4*a*c)*log(f)^2 - e^2 - (4*I*c*d - 2*I*b*e)*log(f))/(c*log(f))) - I*sqrt(pi)*sqrt(-c*log(f))*erf(1/2*((2*c*x + b)*log(f) - I*e)*sqrt(-c*log(f))/(c*log(f)))*e^(-1/4*((b^2 - 4*a*c)*log(f)^2 - e^2 - (-4*I*c*d + 2*I*b*e)*log(f))/(c*log(f))))/(c*log(f))","A",0
95,1,224,0,0.716050," ","integrate(f^(c*x^2+b*x+a)*sin(e*x+d)^2,x, algorithm=""fricas"")","\frac{\sqrt{\pi} \sqrt{-c \log\left(f\right)} \operatorname{erf}\left(\frac{{\left({\left(2 \, c x + b\right)} \log\left(f\right) + 2 i \, e\right)} \sqrt{-c \log\left(f\right)}}{2 \, c \log\left(f\right)}\right) e^{\left(-\frac{{\left(b^{2} - 4 \, a c\right)} \log\left(f\right)^{2} - 4 \, e^{2} - {\left(8 i \, c d - 4 i \, b e\right)} \log\left(f\right)}{4 \, c \log\left(f\right)}\right)} + \sqrt{\pi} \sqrt{-c \log\left(f\right)} \operatorname{erf}\left(\frac{{\left({\left(2 \, c x + b\right)} \log\left(f\right) - 2 i \, e\right)} \sqrt{-c \log\left(f\right)}}{2 \, c \log\left(f\right)}\right) e^{\left(-\frac{{\left(b^{2} - 4 \, a c\right)} \log\left(f\right)^{2} - 4 \, e^{2} - {\left(-8 i \, c d + 4 i \, b e\right)} \log\left(f\right)}{4 \, c \log\left(f\right)}\right)} - \frac{2 \, \sqrt{\pi} \sqrt{-c \log\left(f\right)} \operatorname{erf}\left(\frac{{\left(2 \, c x + b\right)} \sqrt{-c \log\left(f\right)}}{2 \, c}\right)}{f^{\frac{b^{2} - 4 \, a c}{4 \, c}}}}{8 \, c \log\left(f\right)}"," ",0,"1/8*(sqrt(pi)*sqrt(-c*log(f))*erf(1/2*((2*c*x + b)*log(f) + 2*I*e)*sqrt(-c*log(f))/(c*log(f)))*e^(-1/4*((b^2 - 4*a*c)*log(f)^2 - 4*e^2 - (8*I*c*d - 4*I*b*e)*log(f))/(c*log(f))) + sqrt(pi)*sqrt(-c*log(f))*erf(1/2*((2*c*x + b)*log(f) - 2*I*e)*sqrt(-c*log(f))/(c*log(f)))*e^(-1/4*((b^2 - 4*a*c)*log(f)^2 - 4*e^2 - (-8*I*c*d + 4*I*b*e)*log(f))/(c*log(f))) - 2*sqrt(pi)*sqrt(-c*log(f))*erf(1/2*(2*c*x + b)*sqrt(-c*log(f))/c)/f^(1/4*(b^2 - 4*a*c)/c))/(c*log(f))","A",0
96,1,346,0,1.038759," ","integrate(f^(c*x^2+b*x+a)*sin(e*x+d)^3,x, algorithm=""fricas"")","\frac{3 i \, \sqrt{\pi} \sqrt{-c \log\left(f\right)} \operatorname{erf}\left(\frac{{\left({\left(2 \, c x + b\right)} \log\left(f\right) + i \, e\right)} \sqrt{-c \log\left(f\right)}}{2 \, c \log\left(f\right)}\right) e^{\left(-\frac{{\left(b^{2} - 4 \, a c\right)} \log\left(f\right)^{2} - e^{2} - {\left(4 i \, c d - 2 i \, b e\right)} \log\left(f\right)}{4 \, c \log\left(f\right)}\right)} - 3 i \, \sqrt{\pi} \sqrt{-c \log\left(f\right)} \operatorname{erf}\left(\frac{{\left({\left(2 \, c x + b\right)} \log\left(f\right) - i \, e\right)} \sqrt{-c \log\left(f\right)}}{2 \, c \log\left(f\right)}\right) e^{\left(-\frac{{\left(b^{2} - 4 \, a c\right)} \log\left(f\right)^{2} - e^{2} - {\left(-4 i \, c d + 2 i \, b e\right)} \log\left(f\right)}{4 \, c \log\left(f\right)}\right)} - i \, \sqrt{\pi} \sqrt{-c \log\left(f\right)} \operatorname{erf}\left(\frac{{\left({\left(2 \, c x + b\right)} \log\left(f\right) + 3 i \, e\right)} \sqrt{-c \log\left(f\right)}}{2 \, c \log\left(f\right)}\right) e^{\left(-\frac{{\left(b^{2} - 4 \, a c\right)} \log\left(f\right)^{2} - 9 \, e^{2} - {\left(12 i \, c d - 6 i \, b e\right)} \log\left(f\right)}{4 \, c \log\left(f\right)}\right)} + i \, \sqrt{\pi} \sqrt{-c \log\left(f\right)} \operatorname{erf}\left(\frac{{\left({\left(2 \, c x + b\right)} \log\left(f\right) - 3 i \, e\right)} \sqrt{-c \log\left(f\right)}}{2 \, c \log\left(f\right)}\right) e^{\left(-\frac{{\left(b^{2} - 4 \, a c\right)} \log\left(f\right)^{2} - 9 \, e^{2} - {\left(-12 i \, c d + 6 i \, b e\right)} \log\left(f\right)}{4 \, c \log\left(f\right)}\right)}}{16 \, c \log\left(f\right)}"," ",0,"1/16*(3*I*sqrt(pi)*sqrt(-c*log(f))*erf(1/2*((2*c*x + b)*log(f) + I*e)*sqrt(-c*log(f))/(c*log(f)))*e^(-1/4*((b^2 - 4*a*c)*log(f)^2 - e^2 - (4*I*c*d - 2*I*b*e)*log(f))/(c*log(f))) - 3*I*sqrt(pi)*sqrt(-c*log(f))*erf(1/2*((2*c*x + b)*log(f) - I*e)*sqrt(-c*log(f))/(c*log(f)))*e^(-1/4*((b^2 - 4*a*c)*log(f)^2 - e^2 - (-4*I*c*d + 2*I*b*e)*log(f))/(c*log(f))) - I*sqrt(pi)*sqrt(-c*log(f))*erf(1/2*((2*c*x + b)*log(f) + 3*I*e)*sqrt(-c*log(f))/(c*log(f)))*e^(-1/4*((b^2 - 4*a*c)*log(f)^2 - 9*e^2 - (12*I*c*d - 6*I*b*e)*log(f))/(c*log(f))) + I*sqrt(pi)*sqrt(-c*log(f))*erf(1/2*((2*c*x + b)*log(f) - 3*I*e)*sqrt(-c*log(f))/(c*log(f)))*e^(-1/4*((b^2 - 4*a*c)*log(f)^2 - 9*e^2 - (-12*I*c*d + 6*I*b*e)*log(f))/(c*log(f))))/(c*log(f))","A",0
97,1,309,0,0.821215," ","integrate(f^(c*x^2+b*x+a)*sin(f*x^2+d),x, algorithm=""fricas"")","\frac{\sqrt{\pi} {\left(i \, c \log\left(f\right) + f\right)} \sqrt{-c \log\left(f\right) - i \, f} \operatorname{erf}\left(\frac{{\left(2 \, f^{2} x - i \, b f \log\left(f\right) + {\left(2 \, c^{2} x + b c\right)} \log\left(f\right)^{2}\right)} \sqrt{-c \log\left(f\right) - i \, f}}{2 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}\right) e^{\left(\frac{4 \, a f^{2} \log\left(f\right) - {\left(b^{2} c - 4 \, a c^{2}\right)} \log\left(f\right)^{3} + 4 i \, d f^{2} + {\left(4 i \, c^{2} d + i \, b^{2} f\right)} \log\left(f\right)^{2}}{4 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}\right)} + \sqrt{\pi} {\left(-i \, c \log\left(f\right) + f\right)} \sqrt{-c \log\left(f\right) + i \, f} \operatorname{erf}\left(\frac{{\left(2 \, f^{2} x + i \, b f \log\left(f\right) + {\left(2 \, c^{2} x + b c\right)} \log\left(f\right)^{2}\right)} \sqrt{-c \log\left(f\right) + i \, f}}{2 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}\right) e^{\left(\frac{4 \, a f^{2} \log\left(f\right) - {\left(b^{2} c - 4 \, a c^{2}\right)} \log\left(f\right)^{3} - 4 i \, d f^{2} + {\left(-4 i \, c^{2} d - i \, b^{2} f\right)} \log\left(f\right)^{2}}{4 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}\right)}}{4 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}"," ",0,"1/4*(sqrt(pi)*(I*c*log(f) + f)*sqrt(-c*log(f) - I*f)*erf(1/2*(2*f^2*x - I*b*f*log(f) + (2*c^2*x + b*c)*log(f)^2)*sqrt(-c*log(f) - I*f)/(c^2*log(f)^2 + f^2))*e^(1/4*(4*a*f^2*log(f) - (b^2*c - 4*a*c^2)*log(f)^3 + 4*I*d*f^2 + (4*I*c^2*d + I*b^2*f)*log(f)^2)/(c^2*log(f)^2 + f^2)) + sqrt(pi)*(-I*c*log(f) + f)*sqrt(-c*log(f) + I*f)*erf(1/2*(2*f^2*x + I*b*f*log(f) + (2*c^2*x + b*c)*log(f)^2)*sqrt(-c*log(f) + I*f)/(c^2*log(f)^2 + f^2))*e^(1/4*(4*a*f^2*log(f) - (b^2*c - 4*a*c^2)*log(f)^3 - 4*I*d*f^2 + (-4*I*c^2*d - I*b^2*f)*log(f)^2)/(c^2*log(f)^2 + f^2)))/(c^2*log(f)^2 + f^2)","B",0
98,1,400,0,0.960677," ","integrate(f^(c*x^2+b*x+a)*sin(f*x^2+d)^2,x, algorithm=""fricas"")","\frac{\sqrt{\pi} {\left(c^{2} \log\left(f\right)^{2} - 2 i \, c f \log\left(f\right)\right)} \sqrt{-c \log\left(f\right) - 2 i \, f} \operatorname{erf}\left(\frac{{\left(8 \, f^{2} x - 2 i \, b f \log\left(f\right) + {\left(2 \, c^{2} x + b c\right)} \log\left(f\right)^{2}\right)} \sqrt{-c \log\left(f\right) - 2 i \, f}}{2 \, {\left(c^{2} \log\left(f\right)^{2} + 4 \, f^{2}\right)}}\right) e^{\left(\frac{16 \, a f^{2} \log\left(f\right) - {\left(b^{2} c - 4 \, a c^{2}\right)} \log\left(f\right)^{3} + 32 i \, d f^{2} + {\left(8 i \, c^{2} d + 2 i \, b^{2} f\right)} \log\left(f\right)^{2}}{4 \, {\left(c^{2} \log\left(f\right)^{2} + 4 \, f^{2}\right)}}\right)} + \sqrt{\pi} {\left(c^{2} \log\left(f\right)^{2} + 2 i \, c f \log\left(f\right)\right)} \sqrt{-c \log\left(f\right) + 2 i \, f} \operatorname{erf}\left(\frac{{\left(8 \, f^{2} x + 2 i \, b f \log\left(f\right) + {\left(2 \, c^{2} x + b c\right)} \log\left(f\right)^{2}\right)} \sqrt{-c \log\left(f\right) + 2 i \, f}}{2 \, {\left(c^{2} \log\left(f\right)^{2} + 4 \, f^{2}\right)}}\right) e^{\left(\frac{16 \, a f^{2} \log\left(f\right) - {\left(b^{2} c - 4 \, a c^{2}\right)} \log\left(f\right)^{3} - 32 i \, d f^{2} + {\left(-8 i \, c^{2} d - 2 i \, b^{2} f\right)} \log\left(f\right)^{2}}{4 \, {\left(c^{2} \log\left(f\right)^{2} + 4 \, f^{2}\right)}}\right)} - \frac{2 \, \sqrt{\pi} {\left(c^{2} \log\left(f\right)^{2} + 4 \, f^{2}\right)} \sqrt{-c \log\left(f\right)} \operatorname{erf}\left(\frac{{\left(2 \, c x + b\right)} \sqrt{-c \log\left(f\right)}}{2 \, c}\right)}{f^{\frac{b^{2} - 4 \, a c}{4 \, c}}}}{8 \, {\left(c^{3} \log\left(f\right)^{3} + 4 \, c f^{2} \log\left(f\right)\right)}}"," ",0,"1/8*(sqrt(pi)*(c^2*log(f)^2 - 2*I*c*f*log(f))*sqrt(-c*log(f) - 2*I*f)*erf(1/2*(8*f^2*x - 2*I*b*f*log(f) + (2*c^2*x + b*c)*log(f)^2)*sqrt(-c*log(f) - 2*I*f)/(c^2*log(f)^2 + 4*f^2))*e^(1/4*(16*a*f^2*log(f) - (b^2*c - 4*a*c^2)*log(f)^3 + 32*I*d*f^2 + (8*I*c^2*d + 2*I*b^2*f)*log(f)^2)/(c^2*log(f)^2 + 4*f^2)) + sqrt(pi)*(c^2*log(f)^2 + 2*I*c*f*log(f))*sqrt(-c*log(f) + 2*I*f)*erf(1/2*(8*f^2*x + 2*I*b*f*log(f) + (2*c^2*x + b*c)*log(f)^2)*sqrt(-c*log(f) + 2*I*f)/(c^2*log(f)^2 + 4*f^2))*e^(1/4*(16*a*f^2*log(f) - (b^2*c - 4*a*c^2)*log(f)^3 - 32*I*d*f^2 + (-8*I*c^2*d - 2*I*b^2*f)*log(f)^2)/(c^2*log(f)^2 + 4*f^2)) - 2*sqrt(pi)*(c^2*log(f)^2 + 4*f^2)*sqrt(-c*log(f))*erf(1/2*(2*c*x + b)*sqrt(-c*log(f))/c)/f^(1/4*(b^2 - 4*a*c)/c))/(c^3*log(f)^3 + 4*c*f^2*log(f))","B",0
99,1,727,0,1.996152," ","integrate(f^(c*x^2+b*x+a)*sin(f*x^2+d)^3,x, algorithm=""fricas"")","\frac{\sqrt{\pi} {\left(-i \, c^{3} \log\left(f\right)^{3} - 3 \, c^{2} f \log\left(f\right)^{2} - i \, c f^{2} \log\left(f\right) - 3 \, f^{3}\right)} \sqrt{-c \log\left(f\right) - 3 i \, f} \operatorname{erf}\left(\frac{{\left(18 \, f^{2} x - 3 i \, b f \log\left(f\right) + {\left(2 \, c^{2} x + b c\right)} \log\left(f\right)^{2}\right)} \sqrt{-c \log\left(f\right) - 3 i \, f}}{2 \, {\left(c^{2} \log\left(f\right)^{2} + 9 \, f^{2}\right)}}\right) e^{\left(\frac{36 \, a f^{2} \log\left(f\right) - {\left(b^{2} c - 4 \, a c^{2}\right)} \log\left(f\right)^{3} + 108 i \, d f^{2} + {\left(12 i \, c^{2} d + 3 i \, b^{2} f\right)} \log\left(f\right)^{2}}{4 \, {\left(c^{2} \log\left(f\right)^{2} + 9 \, f^{2}\right)}}\right)} + \sqrt{\pi} {\left(i \, c^{3} \log\left(f\right)^{3} - 3 \, c^{2} f \log\left(f\right)^{2} + i \, c f^{2} \log\left(f\right) - 3 \, f^{3}\right)} \sqrt{-c \log\left(f\right) + 3 i \, f} \operatorname{erf}\left(\frac{{\left(18 \, f^{2} x + 3 i \, b f \log\left(f\right) + {\left(2 \, c^{2} x + b c\right)} \log\left(f\right)^{2}\right)} \sqrt{-c \log\left(f\right) + 3 i \, f}}{2 \, {\left(c^{2} \log\left(f\right)^{2} + 9 \, f^{2}\right)}}\right) e^{\left(\frac{36 \, a f^{2} \log\left(f\right) - {\left(b^{2} c - 4 \, a c^{2}\right)} \log\left(f\right)^{3} - 108 i \, d f^{2} + {\left(-12 i \, c^{2} d - 3 i \, b^{2} f\right)} \log\left(f\right)^{2}}{4 \, {\left(c^{2} \log\left(f\right)^{2} + 9 \, f^{2}\right)}}\right)} + \sqrt{\pi} {\left(3 i \, c^{3} \log\left(f\right)^{3} + 3 \, c^{2} f \log\left(f\right)^{2} + 27 i \, c f^{2} \log\left(f\right) + 27 \, f^{3}\right)} \sqrt{-c \log\left(f\right) - i \, f} \operatorname{erf}\left(\frac{{\left(2 \, f^{2} x - i \, b f \log\left(f\right) + {\left(2 \, c^{2} x + b c\right)} \log\left(f\right)^{2}\right)} \sqrt{-c \log\left(f\right) - i \, f}}{2 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}\right) e^{\left(\frac{4 \, a f^{2} \log\left(f\right) - {\left(b^{2} c - 4 \, a c^{2}\right)} \log\left(f\right)^{3} + 4 i \, d f^{2} + {\left(4 i \, c^{2} d + i \, b^{2} f\right)} \log\left(f\right)^{2}}{4 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}\right)} + \sqrt{\pi} {\left(-3 i \, c^{3} \log\left(f\right)^{3} + 3 \, c^{2} f \log\left(f\right)^{2} - 27 i \, c f^{2} \log\left(f\right) + 27 \, f^{3}\right)} \sqrt{-c \log\left(f\right) + i \, f} \operatorname{erf}\left(\frac{{\left(2 \, f^{2} x + i \, b f \log\left(f\right) + {\left(2 \, c^{2} x + b c\right)} \log\left(f\right)^{2}\right)} \sqrt{-c \log\left(f\right) + i \, f}}{2 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}\right) e^{\left(\frac{4 \, a f^{2} \log\left(f\right) - {\left(b^{2} c - 4 \, a c^{2}\right)} \log\left(f\right)^{3} - 4 i \, d f^{2} + {\left(-4 i \, c^{2} d - i \, b^{2} f\right)} \log\left(f\right)^{2}}{4 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}\right)}}{16 \, {\left(c^{4} \log\left(f\right)^{4} + 10 \, c^{2} f^{2} \log\left(f\right)^{2} + 9 \, f^{4}\right)}}"," ",0,"1/16*(sqrt(pi)*(-I*c^3*log(f)^3 - 3*c^2*f*log(f)^2 - I*c*f^2*log(f) - 3*f^3)*sqrt(-c*log(f) - 3*I*f)*erf(1/2*(18*f^2*x - 3*I*b*f*log(f) + (2*c^2*x + b*c)*log(f)^2)*sqrt(-c*log(f) - 3*I*f)/(c^2*log(f)^2 + 9*f^2))*e^(1/4*(36*a*f^2*log(f) - (b^2*c - 4*a*c^2)*log(f)^3 + 108*I*d*f^2 + (12*I*c^2*d + 3*I*b^2*f)*log(f)^2)/(c^2*log(f)^2 + 9*f^2)) + sqrt(pi)*(I*c^3*log(f)^3 - 3*c^2*f*log(f)^2 + I*c*f^2*log(f) - 3*f^3)*sqrt(-c*log(f) + 3*I*f)*erf(1/2*(18*f^2*x + 3*I*b*f*log(f) + (2*c^2*x + b*c)*log(f)^2)*sqrt(-c*log(f) + 3*I*f)/(c^2*log(f)^2 + 9*f^2))*e^(1/4*(36*a*f^2*log(f) - (b^2*c - 4*a*c^2)*log(f)^3 - 108*I*d*f^2 + (-12*I*c^2*d - 3*I*b^2*f)*log(f)^2)/(c^2*log(f)^2 + 9*f^2)) + sqrt(pi)*(3*I*c^3*log(f)^3 + 3*c^2*f*log(f)^2 + 27*I*c*f^2*log(f) + 27*f^3)*sqrt(-c*log(f) - I*f)*erf(1/2*(2*f^2*x - I*b*f*log(f) + (2*c^2*x + b*c)*log(f)^2)*sqrt(-c*log(f) - I*f)/(c^2*log(f)^2 + f^2))*e^(1/4*(4*a*f^2*log(f) - (b^2*c - 4*a*c^2)*log(f)^3 + 4*I*d*f^2 + (4*I*c^2*d + I*b^2*f)*log(f)^2)/(c^2*log(f)^2 + f^2)) + sqrt(pi)*(-3*I*c^3*log(f)^3 + 3*c^2*f*log(f)^2 - 27*I*c*f^2*log(f) + 27*f^3)*sqrt(-c*log(f) + I*f)*erf(1/2*(2*f^2*x + I*b*f*log(f) + (2*c^2*x + b*c)*log(f)^2)*sqrt(-c*log(f) + I*f)/(c^2*log(f)^2 + f^2))*e^(1/4*(4*a*f^2*log(f) - (b^2*c - 4*a*c^2)*log(f)^3 - 4*I*d*f^2 + (-4*I*c^2*d - I*b^2*f)*log(f)^2)/(c^2*log(f)^2 + f^2)))/(c^4*log(f)^4 + 10*c^2*f^2*log(f)^2 + 9*f^4)","B",0
100,1,375,0,1.035383," ","integrate(f^(c*x^2+b*x+a)*sin(f*x^2+e*x+d),x, algorithm=""fricas"")","\frac{\sqrt{\pi} {\left(i \, c \log\left(f\right) + f\right)} \sqrt{-c \log\left(f\right) - i \, f} \operatorname{erf}\left(\frac{{\left(2 \, f^{2} x + {\left(2 \, c^{2} x + b c\right)} \log\left(f\right)^{2} + e f + {\left(i \, c e - i \, b f\right)} \log\left(f\right)\right)} \sqrt{-c \log\left(f\right) - i \, f}}{2 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}\right) e^{\left(-\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} \log\left(f\right)^{3} + i \, e^{2} f - 4 i \, d f^{2} - {\left(4 i \, c^{2} d - 2 i \, b c e + i \, b^{2} f\right)} \log\left(f\right)^{2} - {\left(c e^{2} - 2 \, b e f + 4 \, a f^{2}\right)} \log\left(f\right)}{4 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}\right)} + \sqrt{\pi} {\left(-i \, c \log\left(f\right) + f\right)} \sqrt{-c \log\left(f\right) + i \, f} \operatorname{erf}\left(\frac{{\left(2 \, f^{2} x + {\left(2 \, c^{2} x + b c\right)} \log\left(f\right)^{2} + e f + {\left(-i \, c e + i \, b f\right)} \log\left(f\right)\right)} \sqrt{-c \log\left(f\right) + i \, f}}{2 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}\right) e^{\left(-\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} \log\left(f\right)^{3} - i \, e^{2} f + 4 i \, d f^{2} - {\left(-4 i \, c^{2} d + 2 i \, b c e - i \, b^{2} f\right)} \log\left(f\right)^{2} - {\left(c e^{2} - 2 \, b e f + 4 \, a f^{2}\right)} \log\left(f\right)}{4 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}\right)}}{4 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}"," ",0,"1/4*(sqrt(pi)*(I*c*log(f) + f)*sqrt(-c*log(f) - I*f)*erf(1/2*(2*f^2*x + (2*c^2*x + b*c)*log(f)^2 + e*f + (I*c*e - I*b*f)*log(f))*sqrt(-c*log(f) - I*f)/(c^2*log(f)^2 + f^2))*e^(-1/4*((b^2*c - 4*a*c^2)*log(f)^3 + I*e^2*f - 4*I*d*f^2 - (4*I*c^2*d - 2*I*b*c*e + I*b^2*f)*log(f)^2 - (c*e^2 - 2*b*e*f + 4*a*f^2)*log(f))/(c^2*log(f)^2 + f^2)) + sqrt(pi)*(-I*c*log(f) + f)*sqrt(-c*log(f) + I*f)*erf(1/2*(2*f^2*x + (2*c^2*x + b*c)*log(f)^2 + e*f + (-I*c*e + I*b*f)*log(f))*sqrt(-c*log(f) + I*f)/(c^2*log(f)^2 + f^2))*e^(-1/4*((b^2*c - 4*a*c^2)*log(f)^3 - I*e^2*f + 4*I*d*f^2 - (-4*I*c^2*d + 2*I*b*c*e - I*b^2*f)*log(f)^2 - (c*e^2 - 2*b*e*f + 4*a*f^2)*log(f))/(c^2*log(f)^2 + f^2)))/(c^2*log(f)^2 + f^2)","B",0
101,1,468,0,1.644689," ","integrate(f^(c*x^2+b*x+a)*sin(f*x^2+e*x+d)^2,x, algorithm=""fricas"")","\frac{\sqrt{\pi} {\left(c^{2} \log\left(f\right)^{2} - 2 i \, c f \log\left(f\right)\right)} \sqrt{-c \log\left(f\right) - 2 i \, f} \operatorname{erf}\left(\frac{{\left(8 \, f^{2} x + {\left(2 \, c^{2} x + b c\right)} \log\left(f\right)^{2} + 4 \, e f + {\left(2 i \, c e - 2 i \, b f\right)} \log\left(f\right)\right)} \sqrt{-c \log\left(f\right) - 2 i \, f}}{2 \, {\left(c^{2} \log\left(f\right)^{2} + 4 \, f^{2}\right)}}\right) e^{\left(-\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} \log\left(f\right)^{3} + 8 i \, e^{2} f - 32 i \, d f^{2} - {\left(8 i \, c^{2} d - 4 i \, b c e + 2 i \, b^{2} f\right)} \log\left(f\right)^{2} - 4 \, {\left(c e^{2} - 2 \, b e f + 4 \, a f^{2}\right)} \log\left(f\right)}{4 \, {\left(c^{2} \log\left(f\right)^{2} + 4 \, f^{2}\right)}}\right)} + \sqrt{\pi} {\left(c^{2} \log\left(f\right)^{2} + 2 i \, c f \log\left(f\right)\right)} \sqrt{-c \log\left(f\right) + 2 i \, f} \operatorname{erf}\left(\frac{{\left(8 \, f^{2} x + {\left(2 \, c^{2} x + b c\right)} \log\left(f\right)^{2} + 4 \, e f + {\left(-2 i \, c e + 2 i \, b f\right)} \log\left(f\right)\right)} \sqrt{-c \log\left(f\right) + 2 i \, f}}{2 \, {\left(c^{2} \log\left(f\right)^{2} + 4 \, f^{2}\right)}}\right) e^{\left(-\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} \log\left(f\right)^{3} - 8 i \, e^{2} f + 32 i \, d f^{2} - {\left(-8 i \, c^{2} d + 4 i \, b c e - 2 i \, b^{2} f\right)} \log\left(f\right)^{2} - 4 \, {\left(c e^{2} - 2 \, b e f + 4 \, a f^{2}\right)} \log\left(f\right)}{4 \, {\left(c^{2} \log\left(f\right)^{2} + 4 \, f^{2}\right)}}\right)} - \frac{2 \, \sqrt{\pi} {\left(c^{2} \log\left(f\right)^{2} + 4 \, f^{2}\right)} \sqrt{-c \log\left(f\right)} \operatorname{erf}\left(\frac{{\left(2 \, c x + b\right)} \sqrt{-c \log\left(f\right)}}{2 \, c}\right)}{f^{\frac{b^{2} - 4 \, a c}{4 \, c}}}}{8 \, {\left(c^{3} \log\left(f\right)^{3} + 4 \, c f^{2} \log\left(f\right)\right)}}"," ",0,"1/8*(sqrt(pi)*(c^2*log(f)^2 - 2*I*c*f*log(f))*sqrt(-c*log(f) - 2*I*f)*erf(1/2*(8*f^2*x + (2*c^2*x + b*c)*log(f)^2 + 4*e*f + (2*I*c*e - 2*I*b*f)*log(f))*sqrt(-c*log(f) - 2*I*f)/(c^2*log(f)^2 + 4*f^2))*e^(-1/4*((b^2*c - 4*a*c^2)*log(f)^3 + 8*I*e^2*f - 32*I*d*f^2 - (8*I*c^2*d - 4*I*b*c*e + 2*I*b^2*f)*log(f)^2 - 4*(c*e^2 - 2*b*e*f + 4*a*f^2)*log(f))/(c^2*log(f)^2 + 4*f^2)) + sqrt(pi)*(c^2*log(f)^2 + 2*I*c*f*log(f))*sqrt(-c*log(f) + 2*I*f)*erf(1/2*(8*f^2*x + (2*c^2*x + b*c)*log(f)^2 + 4*e*f + (-2*I*c*e + 2*I*b*f)*log(f))*sqrt(-c*log(f) + 2*I*f)/(c^2*log(f)^2 + 4*f^2))*e^(-1/4*((b^2*c - 4*a*c^2)*log(f)^3 - 8*I*e^2*f + 32*I*d*f^2 - (-8*I*c^2*d + 4*I*b*c*e - 2*I*b^2*f)*log(f)^2 - 4*(c*e^2 - 2*b*e*f + 4*a*f^2)*log(f))/(c^2*log(f)^2 + 4*f^2)) - 2*sqrt(pi)*(c^2*log(f)^2 + 4*f^2)*sqrt(-c*log(f))*erf(1/2*(2*c*x + b)*sqrt(-c*log(f))/c)/f^(1/4*(b^2 - 4*a*c)/c))/(c^3*log(f)^3 + 4*c*f^2*log(f))","B",0
102,1,861,0,0.869849," ","integrate(f^(c*x^2+b*x+a)*sin(f*x^2+e*x+d)^3,x, algorithm=""fricas"")","\frac{\sqrt{\pi} {\left(-i \, c^{3} \log\left(f\right)^{3} - 3 \, c^{2} f \log\left(f\right)^{2} - i \, c f^{2} \log\left(f\right) - 3 \, f^{3}\right)} \sqrt{-c \log\left(f\right) - 3 i \, f} \operatorname{erf}\left(\frac{{\left(18 \, f^{2} x + {\left(2 \, c^{2} x + b c\right)} \log\left(f\right)^{2} + 9 \, e f + {\left(3 i \, c e - 3 i \, b f\right)} \log\left(f\right)\right)} \sqrt{-c \log\left(f\right) - 3 i \, f}}{2 \, {\left(c^{2} \log\left(f\right)^{2} + 9 \, f^{2}\right)}}\right) e^{\left(-\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} \log\left(f\right)^{3} + 27 i \, e^{2} f - 108 i \, d f^{2} - {\left(12 i \, c^{2} d - 6 i \, b c e + 3 i \, b^{2} f\right)} \log\left(f\right)^{2} - 9 \, {\left(c e^{2} - 2 \, b e f + 4 \, a f^{2}\right)} \log\left(f\right)}{4 \, {\left(c^{2} \log\left(f\right)^{2} + 9 \, f^{2}\right)}}\right)} + \sqrt{\pi} {\left(3 i \, c^{3} \log\left(f\right)^{3} + 3 \, c^{2} f \log\left(f\right)^{2} + 27 i \, c f^{2} \log\left(f\right) + 27 \, f^{3}\right)} \sqrt{-c \log\left(f\right) - i \, f} \operatorname{erf}\left(\frac{{\left(2 \, f^{2} x + {\left(2 \, c^{2} x + b c\right)} \log\left(f\right)^{2} + e f + {\left(i \, c e - i \, b f\right)} \log\left(f\right)\right)} \sqrt{-c \log\left(f\right) - i \, f}}{2 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}\right) e^{\left(-\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} \log\left(f\right)^{3} + i \, e^{2} f - 4 i \, d f^{2} - {\left(4 i \, c^{2} d - 2 i \, b c e + i \, b^{2} f\right)} \log\left(f\right)^{2} - {\left(c e^{2} - 2 \, b e f + 4 \, a f^{2}\right)} \log\left(f\right)}{4 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}\right)} + \sqrt{\pi} {\left(-3 i \, c^{3} \log\left(f\right)^{3} + 3 \, c^{2} f \log\left(f\right)^{2} - 27 i \, c f^{2} \log\left(f\right) + 27 \, f^{3}\right)} \sqrt{-c \log\left(f\right) + i \, f} \operatorname{erf}\left(\frac{{\left(2 \, f^{2} x + {\left(2 \, c^{2} x + b c\right)} \log\left(f\right)^{2} + e f + {\left(-i \, c e + i \, b f\right)} \log\left(f\right)\right)} \sqrt{-c \log\left(f\right) + i \, f}}{2 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}\right) e^{\left(-\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} \log\left(f\right)^{3} - i \, e^{2} f + 4 i \, d f^{2} - {\left(-4 i \, c^{2} d + 2 i \, b c e - i \, b^{2} f\right)} \log\left(f\right)^{2} - {\left(c e^{2} - 2 \, b e f + 4 \, a f^{2}\right)} \log\left(f\right)}{4 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}\right)} + \sqrt{\pi} {\left(i \, c^{3} \log\left(f\right)^{3} - 3 \, c^{2} f \log\left(f\right)^{2} + i \, c f^{2} \log\left(f\right) - 3 \, f^{3}\right)} \sqrt{-c \log\left(f\right) + 3 i \, f} \operatorname{erf}\left(\frac{{\left(18 \, f^{2} x + {\left(2 \, c^{2} x + b c\right)} \log\left(f\right)^{2} + 9 \, e f + {\left(-3 i \, c e + 3 i \, b f\right)} \log\left(f\right)\right)} \sqrt{-c \log\left(f\right) + 3 i \, f}}{2 \, {\left(c^{2} \log\left(f\right)^{2} + 9 \, f^{2}\right)}}\right) e^{\left(-\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} \log\left(f\right)^{3} - 27 i \, e^{2} f + 108 i \, d f^{2} - {\left(-12 i \, c^{2} d + 6 i \, b c e - 3 i \, b^{2} f\right)} \log\left(f\right)^{2} - 9 \, {\left(c e^{2} - 2 \, b e f + 4 \, a f^{2}\right)} \log\left(f\right)}{4 \, {\left(c^{2} \log\left(f\right)^{2} + 9 \, f^{2}\right)}}\right)}}{16 \, {\left(c^{4} \log\left(f\right)^{4} + 10 \, c^{2} f^{2} \log\left(f\right)^{2} + 9 \, f^{4}\right)}}"," ",0,"1/16*(sqrt(pi)*(-I*c^3*log(f)^3 - 3*c^2*f*log(f)^2 - I*c*f^2*log(f) - 3*f^3)*sqrt(-c*log(f) - 3*I*f)*erf(1/2*(18*f^2*x + (2*c^2*x + b*c)*log(f)^2 + 9*e*f + (3*I*c*e - 3*I*b*f)*log(f))*sqrt(-c*log(f) - 3*I*f)/(c^2*log(f)^2 + 9*f^2))*e^(-1/4*((b^2*c - 4*a*c^2)*log(f)^3 + 27*I*e^2*f - 108*I*d*f^2 - (12*I*c^2*d - 6*I*b*c*e + 3*I*b^2*f)*log(f)^2 - 9*(c*e^2 - 2*b*e*f + 4*a*f^2)*log(f))/(c^2*log(f)^2 + 9*f^2)) + sqrt(pi)*(3*I*c^3*log(f)^3 + 3*c^2*f*log(f)^2 + 27*I*c*f^2*log(f) + 27*f^3)*sqrt(-c*log(f) - I*f)*erf(1/2*(2*f^2*x + (2*c^2*x + b*c)*log(f)^2 + e*f + (I*c*e - I*b*f)*log(f))*sqrt(-c*log(f) - I*f)/(c^2*log(f)^2 + f^2))*e^(-1/4*((b^2*c - 4*a*c^2)*log(f)^3 + I*e^2*f - 4*I*d*f^2 - (4*I*c^2*d - 2*I*b*c*e + I*b^2*f)*log(f)^2 - (c*e^2 - 2*b*e*f + 4*a*f^2)*log(f))/(c^2*log(f)^2 + f^2)) + sqrt(pi)*(-3*I*c^3*log(f)^3 + 3*c^2*f*log(f)^2 - 27*I*c*f^2*log(f) + 27*f^3)*sqrt(-c*log(f) + I*f)*erf(1/2*(2*f^2*x + (2*c^2*x + b*c)*log(f)^2 + e*f + (-I*c*e + I*b*f)*log(f))*sqrt(-c*log(f) + I*f)/(c^2*log(f)^2 + f^2))*e^(-1/4*((b^2*c - 4*a*c^2)*log(f)^3 - I*e^2*f + 4*I*d*f^2 - (-4*I*c^2*d + 2*I*b*c*e - I*b^2*f)*log(f)^2 - (c*e^2 - 2*b*e*f + 4*a*f^2)*log(f))/(c^2*log(f)^2 + f^2)) + sqrt(pi)*(I*c^3*log(f)^3 - 3*c^2*f*log(f)^2 + I*c*f^2*log(f) - 3*f^3)*sqrt(-c*log(f) + 3*I*f)*erf(1/2*(18*f^2*x + (2*c^2*x + b*c)*log(f)^2 + 9*e*f + (-3*I*c*e + 3*I*b*f)*log(f))*sqrt(-c*log(f) + 3*I*f)/(c^2*log(f)^2 + 9*f^2))*e^(-1/4*((b^2*c - 4*a*c^2)*log(f)^3 - 27*I*e^2*f + 108*I*d*f^2 - (-12*I*c^2*d + 6*I*b*c*e - 3*I*b^2*f)*log(f)^2 - 9*(c*e^2 - 2*b*e*f + 4*a*f^2)*log(f))/(c^2*log(f)^2 + 9*f^2)))/(c^4*log(f)^4 + 10*c^2*f^2*log(f)^2 + 9*f^4)","B",0
103,1,379,0,0.637153," ","integrate(f^(c*x^2+b*x+a)*sin(e*x^2+b*x+a),x, algorithm=""fricas"")","\frac{\sqrt{\pi} {\left(i \, c \log\left(f\right) + e\right)} \sqrt{-c \log\left(f\right) - i \, e} \operatorname{erf}\left(\frac{{\left(2 \, e^{2} x + {\left(2 \, c^{2} x + b c\right)} \log\left(f\right)^{2} + b e + {\left(i \, b c - i \, b e\right)} \log\left(f\right)\right)} \sqrt{-c \log\left(f\right) - i \, e}}{2 \, {\left(c^{2} \log\left(f\right)^{2} + e^{2}\right)}}\right) e^{\left(-\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} \log\left(f\right)^{3} + i \, b^{2} e - 4 i \, a e^{2} - {\left(-2 i \, b^{2} c + 4 i \, a c^{2} + i \, b^{2} e\right)} \log\left(f\right)^{2} - {\left(b^{2} c - 2 \, b^{2} e + 4 \, a e^{2}\right)} \log\left(f\right)}{4 \, {\left(c^{2} \log\left(f\right)^{2} + e^{2}\right)}}\right)} + \sqrt{\pi} {\left(-i \, c \log\left(f\right) + e\right)} \sqrt{-c \log\left(f\right) + i \, e} \operatorname{erf}\left(\frac{{\left(2 \, e^{2} x + {\left(2 \, c^{2} x + b c\right)} \log\left(f\right)^{2} + b e + {\left(-i \, b c + i \, b e\right)} \log\left(f\right)\right)} \sqrt{-c \log\left(f\right) + i \, e}}{2 \, {\left(c^{2} \log\left(f\right)^{2} + e^{2}\right)}}\right) e^{\left(-\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} \log\left(f\right)^{3} - i \, b^{2} e + 4 i \, a e^{2} - {\left(2 i \, b^{2} c - 4 i \, a c^{2} - i \, b^{2} e\right)} \log\left(f\right)^{2} - {\left(b^{2} c - 2 \, b^{2} e + 4 \, a e^{2}\right)} \log\left(f\right)}{4 \, {\left(c^{2} \log\left(f\right)^{2} + e^{2}\right)}}\right)}}{4 \, {\left(c^{2} \log\left(f\right)^{2} + e^{2}\right)}}"," ",0,"1/4*(sqrt(pi)*(I*c*log(f) + e)*sqrt(-c*log(f) - I*e)*erf(1/2*(2*e^2*x + (2*c^2*x + b*c)*log(f)^2 + b*e + (I*b*c - I*b*e)*log(f))*sqrt(-c*log(f) - I*e)/(c^2*log(f)^2 + e^2))*e^(-1/4*((b^2*c - 4*a*c^2)*log(f)^3 + I*b^2*e - 4*I*a*e^2 - (-2*I*b^2*c + 4*I*a*c^2 + I*b^2*e)*log(f)^2 - (b^2*c - 2*b^2*e + 4*a*e^2)*log(f))/(c^2*log(f)^2 + e^2)) + sqrt(pi)*(-I*c*log(f) + e)*sqrt(-c*log(f) + I*e)*erf(1/2*(2*e^2*x + (2*c^2*x + b*c)*log(f)^2 + b*e + (-I*b*c + I*b*e)*log(f))*sqrt(-c*log(f) + I*e)/(c^2*log(f)^2 + e^2))*e^(-1/4*((b^2*c - 4*a*c^2)*log(f)^3 - I*b^2*e + 4*I*a*e^2 - (2*I*b^2*c - 4*I*a*c^2 - I*b^2*e)*log(f)^2 - (b^2*c - 2*b^2*e + 4*a*e^2)*log(f))/(c^2*log(f)^2 + e^2)))/(c^2*log(f)^2 + e^2)","B",0
104,1,28,0,0.942102," ","integrate(exp(x)*cos(b*x+a),x, algorithm=""fricas"")","\frac{b e^{x} \sin\left(b x + a\right) + \cos\left(b x + a\right) e^{x}}{b^{2} + 1}"," ",0,"(b*e^x*sin(b*x + a) + cos(b*x + a)*e^x)/(b^2 + 1)","A",0
105,1,193,0,2.089702," ","integrate(exp(x)*cos(c*x^2+a),x, algorithm=""fricas"")","\frac{\sqrt{2} \pi \sqrt{\frac{c}{\pi}} e^{\left(\frac{-4 i \, a c - i}{4 \, c}\right)} \operatorname{C}\left(\frac{\sqrt{2} {\left(2 \, c x + i\right)} \sqrt{\frac{c}{\pi}}}{2 \, c}\right) - \sqrt{2} \pi \sqrt{\frac{c}{\pi}} e^{\left(\frac{4 i \, a c + i}{4 \, c}\right)} \operatorname{C}\left(-\frac{\sqrt{2} {\left(2 \, c x - i\right)} \sqrt{\frac{c}{\pi}}}{2 \, c}\right) - i \, \sqrt{2} \pi \sqrt{\frac{c}{\pi}} e^{\left(\frac{-4 i \, a c - i}{4 \, c}\right)} \operatorname{S}\left(\frac{\sqrt{2} {\left(2 \, c x + i\right)} \sqrt{\frac{c}{\pi}}}{2 \, c}\right) - i \, \sqrt{2} \pi \sqrt{\frac{c}{\pi}} e^{\left(\frac{4 i \, a c + i}{4 \, c}\right)} \operatorname{S}\left(-\frac{\sqrt{2} {\left(2 \, c x - i\right)} \sqrt{\frac{c}{\pi}}}{2 \, c}\right)}{4 \, c}"," ",0,"1/4*(sqrt(2)*pi*sqrt(c/pi)*e^(1/4*(-4*I*a*c - I)/c)*fresnel_cos(1/2*sqrt(2)*(2*c*x + I)*sqrt(c/pi)/c) - sqrt(2)*pi*sqrt(c/pi)*e^(1/4*(4*I*a*c + I)/c)*fresnel_cos(-1/2*sqrt(2)*(2*c*x - I)*sqrt(c/pi)/c) - I*sqrt(2)*pi*sqrt(c/pi)*e^(1/4*(-4*I*a*c - I)/c)*fresnel_sin(1/2*sqrt(2)*(2*c*x + I)*sqrt(c/pi)/c) - I*sqrt(2)*pi*sqrt(c/pi)*e^(1/4*(4*I*a*c + I)/c)*fresnel_sin(-1/2*sqrt(2)*(2*c*x - I)*sqrt(c/pi)/c))/c","B",0
106,1,229,0,2.074251," ","integrate(exp(x)*cos(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{\sqrt{2} \pi \sqrt{\frac{c}{\pi}} e^{\left(\frac{i \, b^{2} - 4 i \, a c - 2 \, b - i}{4 \, c}\right)} \operatorname{C}\left(\frac{\sqrt{2} {\left(2 \, c x + b + i\right)} \sqrt{\frac{c}{\pi}}}{2 \, c}\right) - \sqrt{2} \pi \sqrt{\frac{c}{\pi}} e^{\left(\frac{-i \, b^{2} + 4 i \, a c - 2 \, b + i}{4 \, c}\right)} \operatorname{C}\left(-\frac{\sqrt{2} {\left(2 \, c x + b - i\right)} \sqrt{\frac{c}{\pi}}}{2 \, c}\right) - i \, \sqrt{2} \pi \sqrt{\frac{c}{\pi}} e^{\left(\frac{i \, b^{2} - 4 i \, a c - 2 \, b - i}{4 \, c}\right)} \operatorname{S}\left(\frac{\sqrt{2} {\left(2 \, c x + b + i\right)} \sqrt{\frac{c}{\pi}}}{2 \, c}\right) - i \, \sqrt{2} \pi \sqrt{\frac{c}{\pi}} e^{\left(\frac{-i \, b^{2} + 4 i \, a c - 2 \, b + i}{4 \, c}\right)} \operatorname{S}\left(-\frac{\sqrt{2} {\left(2 \, c x + b - i\right)} \sqrt{\frac{c}{\pi}}}{2 \, c}\right)}{4 \, c}"," ",0,"1/4*(sqrt(2)*pi*sqrt(c/pi)*e^(1/4*(I*b^2 - 4*I*a*c - 2*b - I)/c)*fresnel_cos(1/2*sqrt(2)*(2*c*x + b + I)*sqrt(c/pi)/c) - sqrt(2)*pi*sqrt(c/pi)*e^(1/4*(-I*b^2 + 4*I*a*c - 2*b + I)/c)*fresnel_cos(-1/2*sqrt(2)*(2*c*x + b - I)*sqrt(c/pi)/c) - I*sqrt(2)*pi*sqrt(c/pi)*e^(1/4*(I*b^2 - 4*I*a*c - 2*b - I)/c)*fresnel_sin(1/2*sqrt(2)*(2*c*x + b + I)*sqrt(c/pi)/c) - I*sqrt(2)*pi*sqrt(c/pi)*e^(1/4*(-I*b^2 + 4*I*a*c - 2*b + I)/c)*fresnel_sin(-1/2*sqrt(2)*(2*c*x + b - I)*sqrt(c/pi)/c))/c","B",0
107,1,46,0,1.689029," ","integrate(exp(x^2)*cos(b*x+a),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{\pi} {\left(-i \, \operatorname{erf}\left(-\frac{1}{2} \, b + i \, x\right) e^{\left(\frac{1}{4} \, b^{2} + i \, a\right)} - i \, \operatorname{erf}\left(\frac{1}{2} \, b + i \, x\right) e^{\left(\frac{1}{4} \, b^{2} - i \, a\right)}\right)}"," ",0,"1/4*sqrt(pi)*(-I*erf(-1/2*b + I*x)*e^(1/4*b^2 + I*a) - I*erf(1/2*b + I*x)*e^(1/4*b^2 - I*a))","A",0
108,1,70,0,0.901249," ","integrate(exp(x^2)*cos(c*x^2+a),x, algorithm=""fricas"")","\frac{\sqrt{\pi} {\left(i \, c - 1\right)} \sqrt{-i \, c - 1} \operatorname{erf}\left(\sqrt{-i \, c - 1} x\right) e^{\left(i \, a\right)} + \sqrt{\pi} \sqrt{i \, c - 1} {\left(-i \, c - 1\right)} \operatorname{erf}\left(\sqrt{i \, c - 1} x\right) e^{\left(-i \, a\right)}}{4 \, {\left(c^{2} + 1\right)}}"," ",0,"1/4*(sqrt(pi)*(I*c - 1)*sqrt(-I*c - 1)*erf(sqrt(-I*c - 1)*x)*e^(I*a) + sqrt(pi)*sqrt(I*c - 1)*(-I*c - 1)*erf(sqrt(I*c - 1)*x)*e^(-I*a))/(c^2 + 1)","A",0
109,1,164,0,1.854367," ","integrate(exp(x^2)*cos(c*x^2+b*x+a),x, algorithm=""fricas"")","\frac{\sqrt{\pi} {\left(i \, c + 1\right)} \sqrt{i \, c - 1} \operatorname{erf}\left(-\frac{{\left(b c + 2 \, {\left(c^{2} + 1\right)} x - i \, b\right)} \sqrt{i \, c - 1}}{2 \, {\left(c^{2} + 1\right)}}\right) e^{\left(\frac{i \, b^{2} c - 4 i \, a c^{2} + b^{2} - 4 i \, a}{4 \, {\left(c^{2} + 1\right)}}\right)} + \sqrt{\pi} {\left(i \, c - 1\right)} \sqrt{-i \, c - 1} \operatorname{erf}\left(\frac{{\left(b c + 2 \, {\left(c^{2} + 1\right)} x + i \, b\right)} \sqrt{-i \, c - 1}}{2 \, {\left(c^{2} + 1\right)}}\right) e^{\left(\frac{-i \, b^{2} c + 4 i \, a c^{2} + b^{2} + 4 i \, a}{4 \, {\left(c^{2} + 1\right)}}\right)}}{4 \, {\left(c^{2} + 1\right)}}"," ",0,"1/4*(sqrt(pi)*(I*c + 1)*sqrt(I*c - 1)*erf(-1/2*(b*c + 2*(c^2 + 1)*x - I*b)*sqrt(I*c - 1)/(c^2 + 1))*e^(1/4*(I*b^2*c - 4*I*a*c^2 + b^2 - 4*I*a)/(c^2 + 1)) + sqrt(pi)*(I*c - 1)*sqrt(-I*c - 1)*erf(1/2*(b*c + 2*(c^2 + 1)*x + I*b)*sqrt(-I*c - 1)/(c^2 + 1))*e^(1/4*(-I*b^2*c + 4*I*a*c^2 + b^2 + 4*I*a)/(c^2 + 1)))/(c^2 + 1)","A",0
110,1,265,0,0.688713," ","integrate(f^(b*x+a)*cos(f*x^2+d),x, algorithm=""fricas"")","\frac{\sqrt{2} \pi \sqrt{\frac{f}{\pi}} e^{\left(\frac{-i \, b^{2} \log\left(f\right)^{2} + 4 \, a f \log\left(f\right) - 4 i \, d f}{4 \, f}\right)} \operatorname{C}\left(\frac{\sqrt{2} {\left(2 \, f x + i \, b \log\left(f\right)\right)} \sqrt{\frac{f}{\pi}}}{2 \, f}\right) - \sqrt{2} \pi \sqrt{\frac{f}{\pi}} e^{\left(\frac{i \, b^{2} \log\left(f\right)^{2} + 4 \, a f \log\left(f\right) + 4 i \, d f}{4 \, f}\right)} \operatorname{C}\left(-\frac{\sqrt{2} {\left(2 \, f x - i \, b \log\left(f\right)\right)} \sqrt{\frac{f}{\pi}}}{2 \, f}\right) - i \, \sqrt{2} \pi \sqrt{\frac{f}{\pi}} e^{\left(\frac{-i \, b^{2} \log\left(f\right)^{2} + 4 \, a f \log\left(f\right) - 4 i \, d f}{4 \, f}\right)} \operatorname{S}\left(\frac{\sqrt{2} {\left(2 \, f x + i \, b \log\left(f\right)\right)} \sqrt{\frac{f}{\pi}}}{2 \, f}\right) - i \, \sqrt{2} \pi \sqrt{\frac{f}{\pi}} e^{\left(\frac{i \, b^{2} \log\left(f\right)^{2} + 4 \, a f \log\left(f\right) + 4 i \, d f}{4 \, f}\right)} \operatorname{S}\left(-\frac{\sqrt{2} {\left(2 \, f x - i \, b \log\left(f\right)\right)} \sqrt{\frac{f}{\pi}}}{2 \, f}\right)}{4 \, f}"," ",0,"1/4*(sqrt(2)*pi*sqrt(f/pi)*e^(1/4*(-I*b^2*log(f)^2 + 4*a*f*log(f) - 4*I*d*f)/f)*fresnel_cos(1/2*sqrt(2)*(2*f*x + I*b*log(f))*sqrt(f/pi)/f) - sqrt(2)*pi*sqrt(f/pi)*e^(1/4*(I*b^2*log(f)^2 + 4*a*f*log(f) + 4*I*d*f)/f)*fresnel_cos(-1/2*sqrt(2)*(2*f*x - I*b*log(f))*sqrt(f/pi)/f) - I*sqrt(2)*pi*sqrt(f/pi)*e^(1/4*(-I*b^2*log(f)^2 + 4*a*f*log(f) - 4*I*d*f)/f)*fresnel_sin(1/2*sqrt(2)*(2*f*x + I*b*log(f))*sqrt(f/pi)/f) - I*sqrt(2)*pi*sqrt(f/pi)*e^(1/4*(I*b^2*log(f)^2 + 4*a*f*log(f) + 4*I*d*f)/f)*fresnel_sin(-1/2*sqrt(2)*(2*f*x - I*b*log(f))*sqrt(f/pi)/f))/f","B",0
111,1,271,0,0.865193," ","integrate(f^(b*x+a)*cos(f*x^2+d)^2,x, algorithm=""fricas"")","\frac{2 \, \pi b \sqrt{\frac{f}{\pi}} e^{\left(\frac{-i \, b^{2} \log\left(f\right)^{2} + 8 \, a f \log\left(f\right) - 16 i \, d f}{8 \, f}\right)} \operatorname{C}\left(\frac{{\left(4 \, f x + i \, b \log\left(f\right)\right)} \sqrt{\frac{f}{\pi}}}{2 \, f}\right) \log\left(f\right) - 2 \, \pi b \sqrt{\frac{f}{\pi}} e^{\left(\frac{i \, b^{2} \log\left(f\right)^{2} + 8 \, a f \log\left(f\right) + 16 i \, d f}{8 \, f}\right)} \operatorname{C}\left(-\frac{{\left(4 \, f x - i \, b \log\left(f\right)\right)} \sqrt{\frac{f}{\pi}}}{2 \, f}\right) \log\left(f\right) - 2 i \, \pi b \sqrt{\frac{f}{\pi}} e^{\left(\frac{-i \, b^{2} \log\left(f\right)^{2} + 8 \, a f \log\left(f\right) - 16 i \, d f}{8 \, f}\right)} \operatorname{S}\left(\frac{{\left(4 \, f x + i \, b \log\left(f\right)\right)} \sqrt{\frac{f}{\pi}}}{2 \, f}\right) \log\left(f\right) - 2 i \, \pi b \sqrt{\frac{f}{\pi}} e^{\left(\frac{i \, b^{2} \log\left(f\right)^{2} + 8 \, a f \log\left(f\right) + 16 i \, d f}{8 \, f}\right)} \operatorname{S}\left(-\frac{{\left(4 \, f x - i \, b \log\left(f\right)\right)} \sqrt{\frac{f}{\pi}}}{2 \, f}\right) \log\left(f\right) + 8 \, f f^{b x + a}}{16 \, b f \log\left(f\right)}"," ",0,"1/16*(2*pi*b*sqrt(f/pi)*e^(1/8*(-I*b^2*log(f)^2 + 8*a*f*log(f) - 16*I*d*f)/f)*fresnel_cos(1/2*(4*f*x + I*b*log(f))*sqrt(f/pi)/f)*log(f) - 2*pi*b*sqrt(f/pi)*e^(1/8*(I*b^2*log(f)^2 + 8*a*f*log(f) + 16*I*d*f)/f)*fresnel_cos(-1/2*(4*f*x - I*b*log(f))*sqrt(f/pi)/f)*log(f) - 2*I*pi*b*sqrt(f/pi)*e^(1/8*(-I*b^2*log(f)^2 + 8*a*f*log(f) - 16*I*d*f)/f)*fresnel_sin(1/2*(4*f*x + I*b*log(f))*sqrt(f/pi)/f)*log(f) - 2*I*pi*b*sqrt(f/pi)*e^(1/8*(I*b^2*log(f)^2 + 8*a*f*log(f) + 16*I*d*f)/f)*fresnel_sin(-1/2*(4*f*x - I*b*log(f))*sqrt(f/pi)/f)*log(f) + 8*f*f^(b*x + a))/(b*f*log(f))","B",0
112,1,525,0,1.024583," ","integrate(f^(b*x+a)*cos(f*x^2+d)^3,x, algorithm=""fricas"")","\frac{\sqrt{6} \pi \sqrt{\frac{f}{\pi}} e^{\left(\frac{-i \, b^{2} \log\left(f\right)^{2} + 12 \, a f \log\left(f\right) - 36 i \, d f}{12 \, f}\right)} \operatorname{C}\left(\frac{\sqrt{6} {\left(6 \, f x + i \, b \log\left(f\right)\right)} \sqrt{\frac{f}{\pi}}}{6 \, f}\right) - \sqrt{6} \pi \sqrt{\frac{f}{\pi}} e^{\left(\frac{i \, b^{2} \log\left(f\right)^{2} + 12 \, a f \log\left(f\right) + 36 i \, d f}{12 \, f}\right)} \operatorname{C}\left(-\frac{\sqrt{6} {\left(6 \, f x - i \, b \log\left(f\right)\right)} \sqrt{\frac{f}{\pi}}}{6 \, f}\right) + 9 \, \sqrt{2} \pi \sqrt{\frac{f}{\pi}} e^{\left(\frac{-i \, b^{2} \log\left(f\right)^{2} + 4 \, a f \log\left(f\right) - 4 i \, d f}{4 \, f}\right)} \operatorname{C}\left(\frac{\sqrt{2} {\left(2 \, f x + i \, b \log\left(f\right)\right)} \sqrt{\frac{f}{\pi}}}{2 \, f}\right) - 9 \, \sqrt{2} \pi \sqrt{\frac{f}{\pi}} e^{\left(\frac{i \, b^{2} \log\left(f\right)^{2} + 4 \, a f \log\left(f\right) + 4 i \, d f}{4 \, f}\right)} \operatorname{C}\left(-\frac{\sqrt{2} {\left(2 \, f x - i \, b \log\left(f\right)\right)} \sqrt{\frac{f}{\pi}}}{2 \, f}\right) - i \, \sqrt{6} \pi \sqrt{\frac{f}{\pi}} e^{\left(\frac{-i \, b^{2} \log\left(f\right)^{2} + 12 \, a f \log\left(f\right) - 36 i \, d f}{12 \, f}\right)} \operatorname{S}\left(\frac{\sqrt{6} {\left(6 \, f x + i \, b \log\left(f\right)\right)} \sqrt{\frac{f}{\pi}}}{6 \, f}\right) - i \, \sqrt{6} \pi \sqrt{\frac{f}{\pi}} e^{\left(\frac{i \, b^{2} \log\left(f\right)^{2} + 12 \, a f \log\left(f\right) + 36 i \, d f}{12 \, f}\right)} \operatorname{S}\left(-\frac{\sqrt{6} {\left(6 \, f x - i \, b \log\left(f\right)\right)} \sqrt{\frac{f}{\pi}}}{6 \, f}\right) - 9 i \, \sqrt{2} \pi \sqrt{\frac{f}{\pi}} e^{\left(\frac{-i \, b^{2} \log\left(f\right)^{2} + 4 \, a f \log\left(f\right) - 4 i \, d f}{4 \, f}\right)} \operatorname{S}\left(\frac{\sqrt{2} {\left(2 \, f x + i \, b \log\left(f\right)\right)} \sqrt{\frac{f}{\pi}}}{2 \, f}\right) - 9 i \, \sqrt{2} \pi \sqrt{\frac{f}{\pi}} e^{\left(\frac{i \, b^{2} \log\left(f\right)^{2} + 4 \, a f \log\left(f\right) + 4 i \, d f}{4 \, f}\right)} \operatorname{S}\left(-\frac{\sqrt{2} {\left(2 \, f x - i \, b \log\left(f\right)\right)} \sqrt{\frac{f}{\pi}}}{2 \, f}\right)}{48 \, f}"," ",0,"1/48*(sqrt(6)*pi*sqrt(f/pi)*e^(1/12*(-I*b^2*log(f)^2 + 12*a*f*log(f) - 36*I*d*f)/f)*fresnel_cos(1/6*sqrt(6)*(6*f*x + I*b*log(f))*sqrt(f/pi)/f) - sqrt(6)*pi*sqrt(f/pi)*e^(1/12*(I*b^2*log(f)^2 + 12*a*f*log(f) + 36*I*d*f)/f)*fresnel_cos(-1/6*sqrt(6)*(6*f*x - I*b*log(f))*sqrt(f/pi)/f) + 9*sqrt(2)*pi*sqrt(f/pi)*e^(1/4*(-I*b^2*log(f)^2 + 4*a*f*log(f) - 4*I*d*f)/f)*fresnel_cos(1/2*sqrt(2)*(2*f*x + I*b*log(f))*sqrt(f/pi)/f) - 9*sqrt(2)*pi*sqrt(f/pi)*e^(1/4*(I*b^2*log(f)^2 + 4*a*f*log(f) + 4*I*d*f)/f)*fresnel_cos(-1/2*sqrt(2)*(2*f*x - I*b*log(f))*sqrt(f/pi)/f) - I*sqrt(6)*pi*sqrt(f/pi)*e^(1/12*(-I*b^2*log(f)^2 + 12*a*f*log(f) - 36*I*d*f)/f)*fresnel_sin(1/6*sqrt(6)*(6*f*x + I*b*log(f))*sqrt(f/pi)/f) - I*sqrt(6)*pi*sqrt(f/pi)*e^(1/12*(I*b^2*log(f)^2 + 12*a*f*log(f) + 36*I*d*f)/f)*fresnel_sin(-1/6*sqrt(6)*(6*f*x - I*b*log(f))*sqrt(f/pi)/f) - 9*I*sqrt(2)*pi*sqrt(f/pi)*e^(1/4*(-I*b^2*log(f)^2 + 4*a*f*log(f) - 4*I*d*f)/f)*fresnel_sin(1/2*sqrt(2)*(2*f*x + I*b*log(f))*sqrt(f/pi)/f) - 9*I*sqrt(2)*pi*sqrt(f/pi)*e^(1/4*(I*b^2*log(f)^2 + 4*a*f*log(f) + 4*I*d*f)/f)*fresnel_sin(-1/2*sqrt(2)*(2*f*x - I*b*log(f))*sqrt(f/pi)/f))/f","B",0
113,1,313,0,1.722802," ","integrate(f^(b*x+a)*cos(f*x^2+e*x+d),x, algorithm=""fricas"")","\frac{\sqrt{2} \pi \sqrt{\frac{f}{\pi}} e^{\left(\frac{-i \, b^{2} \log\left(f\right)^{2} + i \, e^{2} - 4 i \, d f - 2 \, {\left(b e - 2 \, a f\right)} \log\left(f\right)}{4 \, f}\right)} \operatorname{C}\left(\frac{\sqrt{2} {\left(2 \, f x + i \, b \log\left(f\right) + e\right)} \sqrt{\frac{f}{\pi}}}{2 \, f}\right) - \sqrt{2} \pi \sqrt{\frac{f}{\pi}} e^{\left(\frac{i \, b^{2} \log\left(f\right)^{2} - i \, e^{2} + 4 i \, d f - 2 \, {\left(b e - 2 \, a f\right)} \log\left(f\right)}{4 \, f}\right)} \operatorname{C}\left(-\frac{\sqrt{2} {\left(2 \, f x - i \, b \log\left(f\right) + e\right)} \sqrt{\frac{f}{\pi}}}{2 \, f}\right) - i \, \sqrt{2} \pi \sqrt{\frac{f}{\pi}} e^{\left(\frac{-i \, b^{2} \log\left(f\right)^{2} + i \, e^{2} - 4 i \, d f - 2 \, {\left(b e - 2 \, a f\right)} \log\left(f\right)}{4 \, f}\right)} \operatorname{S}\left(\frac{\sqrt{2} {\left(2 \, f x + i \, b \log\left(f\right) + e\right)} \sqrt{\frac{f}{\pi}}}{2 \, f}\right) - i \, \sqrt{2} \pi \sqrt{\frac{f}{\pi}} e^{\left(\frac{i \, b^{2} \log\left(f\right)^{2} - i \, e^{2} + 4 i \, d f - 2 \, {\left(b e - 2 \, a f\right)} \log\left(f\right)}{4 \, f}\right)} \operatorname{S}\left(-\frac{\sqrt{2} {\left(2 \, f x - i \, b \log\left(f\right) + e\right)} \sqrt{\frac{f}{\pi}}}{2 \, f}\right)}{4 \, f}"," ",0,"1/4*(sqrt(2)*pi*sqrt(f/pi)*e^(1/4*(-I*b^2*log(f)^2 + I*e^2 - 4*I*d*f - 2*(b*e - 2*a*f)*log(f))/f)*fresnel_cos(1/2*sqrt(2)*(2*f*x + I*b*log(f) + e)*sqrt(f/pi)/f) - sqrt(2)*pi*sqrt(f/pi)*e^(1/4*(I*b^2*log(f)^2 - I*e^2 + 4*I*d*f - 2*(b*e - 2*a*f)*log(f))/f)*fresnel_cos(-1/2*sqrt(2)*(2*f*x - I*b*log(f) + e)*sqrt(f/pi)/f) - I*sqrt(2)*pi*sqrt(f/pi)*e^(1/4*(-I*b^2*log(f)^2 + I*e^2 - 4*I*d*f - 2*(b*e - 2*a*f)*log(f))/f)*fresnel_sin(1/2*sqrt(2)*(2*f*x + I*b*log(f) + e)*sqrt(f/pi)/f) - I*sqrt(2)*pi*sqrt(f/pi)*e^(1/4*(I*b^2*log(f)^2 - I*e^2 + 4*I*d*f - 2*(b*e - 2*a*f)*log(f))/f)*fresnel_sin(-1/2*sqrt(2)*(2*f*x - I*b*log(f) + e)*sqrt(f/pi)/f))/f","B",0
114,1,327,0,0.761717," ","integrate(f^(b*x+a)*cos(f*x^2+e*x+d)^2,x, algorithm=""fricas"")","\frac{2 \, \pi b \sqrt{\frac{f}{\pi}} e^{\left(\frac{-i \, b^{2} \log\left(f\right)^{2} + 4 i \, e^{2} - 16 i \, d f - 4 \, {\left(b e - 2 \, a f\right)} \log\left(f\right)}{8 \, f}\right)} \operatorname{C}\left(\frac{{\left(4 \, f x + i \, b \log\left(f\right) + 2 \, e\right)} \sqrt{\frac{f}{\pi}}}{2 \, f}\right) \log\left(f\right) - 2 \, \pi b \sqrt{\frac{f}{\pi}} e^{\left(\frac{i \, b^{2} \log\left(f\right)^{2} - 4 i \, e^{2} + 16 i \, d f - 4 \, {\left(b e - 2 \, a f\right)} \log\left(f\right)}{8 \, f}\right)} \operatorname{C}\left(-\frac{{\left(4 \, f x - i \, b \log\left(f\right) + 2 \, e\right)} \sqrt{\frac{f}{\pi}}}{2 \, f}\right) \log\left(f\right) - 2 i \, \pi b \sqrt{\frac{f}{\pi}} e^{\left(\frac{-i \, b^{2} \log\left(f\right)^{2} + 4 i \, e^{2} - 16 i \, d f - 4 \, {\left(b e - 2 \, a f\right)} \log\left(f\right)}{8 \, f}\right)} \operatorname{S}\left(\frac{{\left(4 \, f x + i \, b \log\left(f\right) + 2 \, e\right)} \sqrt{\frac{f}{\pi}}}{2 \, f}\right) \log\left(f\right) - 2 i \, \pi b \sqrt{\frac{f}{\pi}} e^{\left(\frac{i \, b^{2} \log\left(f\right)^{2} - 4 i \, e^{2} + 16 i \, d f - 4 \, {\left(b e - 2 \, a f\right)} \log\left(f\right)}{8 \, f}\right)} \operatorname{S}\left(-\frac{{\left(4 \, f x - i \, b \log\left(f\right) + 2 \, e\right)} \sqrt{\frac{f}{\pi}}}{2 \, f}\right) \log\left(f\right) + 8 \, f f^{b x + a}}{16 \, b f \log\left(f\right)}"," ",0,"1/16*(2*pi*b*sqrt(f/pi)*e^(1/8*(-I*b^2*log(f)^2 + 4*I*e^2 - 16*I*d*f - 4*(b*e - 2*a*f)*log(f))/f)*fresnel_cos(1/2*(4*f*x + I*b*log(f) + 2*e)*sqrt(f/pi)/f)*log(f) - 2*pi*b*sqrt(f/pi)*e^(1/8*(I*b^2*log(f)^2 - 4*I*e^2 + 16*I*d*f - 4*(b*e - 2*a*f)*log(f))/f)*fresnel_cos(-1/2*(4*f*x - I*b*log(f) + 2*e)*sqrt(f/pi)/f)*log(f) - 2*I*pi*b*sqrt(f/pi)*e^(1/8*(-I*b^2*log(f)^2 + 4*I*e^2 - 16*I*d*f - 4*(b*e - 2*a*f)*log(f))/f)*fresnel_sin(1/2*(4*f*x + I*b*log(f) + 2*e)*sqrt(f/pi)/f)*log(f) - 2*I*pi*b*sqrt(f/pi)*e^(1/8*(I*b^2*log(f)^2 - 4*I*e^2 + 16*I*d*f - 4*(b*e - 2*a*f)*log(f))/f)*fresnel_sin(-1/2*(4*f*x - I*b*log(f) + 2*e)*sqrt(f/pi)/f)*log(f) + 8*f*f^(b*x + a))/(b*f*log(f))","B",0
115,1,629,0,1.558349," ","integrate(f^(b*x+a)*cos(f*x^2+e*x+d)^3,x, algorithm=""fricas"")","\frac{\sqrt{6} \pi \sqrt{\frac{f}{\pi}} e^{\left(\frac{-i \, b^{2} \log\left(f\right)^{2} + 9 i \, e^{2} - 36 i \, d f - 6 \, {\left(b e - 2 \, a f\right)} \log\left(f\right)}{12 \, f}\right)} \operatorname{C}\left(\frac{\sqrt{6} {\left(6 \, f x + i \, b \log\left(f\right) + 3 \, e\right)} \sqrt{\frac{f}{\pi}}}{6 \, f}\right) - \sqrt{6} \pi \sqrt{\frac{f}{\pi}} e^{\left(\frac{i \, b^{2} \log\left(f\right)^{2} - 9 i \, e^{2} + 36 i \, d f - 6 \, {\left(b e - 2 \, a f\right)} \log\left(f\right)}{12 \, f}\right)} \operatorname{C}\left(-\frac{\sqrt{6} {\left(6 \, f x - i \, b \log\left(f\right) + 3 \, e\right)} \sqrt{\frac{f}{\pi}}}{6 \, f}\right) + 9 \, \sqrt{2} \pi \sqrt{\frac{f}{\pi}} e^{\left(\frac{-i \, b^{2} \log\left(f\right)^{2} + i \, e^{2} - 4 i \, d f - 2 \, {\left(b e - 2 \, a f\right)} \log\left(f\right)}{4 \, f}\right)} \operatorname{C}\left(\frac{\sqrt{2} {\left(2 \, f x + i \, b \log\left(f\right) + e\right)} \sqrt{\frac{f}{\pi}}}{2 \, f}\right) - 9 \, \sqrt{2} \pi \sqrt{\frac{f}{\pi}} e^{\left(\frac{i \, b^{2} \log\left(f\right)^{2} - i \, e^{2} + 4 i \, d f - 2 \, {\left(b e - 2 \, a f\right)} \log\left(f\right)}{4 \, f}\right)} \operatorname{C}\left(-\frac{\sqrt{2} {\left(2 \, f x - i \, b \log\left(f\right) + e\right)} \sqrt{\frac{f}{\pi}}}{2 \, f}\right) - i \, \sqrt{6} \pi \sqrt{\frac{f}{\pi}} e^{\left(\frac{-i \, b^{2} \log\left(f\right)^{2} + 9 i \, e^{2} - 36 i \, d f - 6 \, {\left(b e - 2 \, a f\right)} \log\left(f\right)}{12 \, f}\right)} \operatorname{S}\left(\frac{\sqrt{6} {\left(6 \, f x + i \, b \log\left(f\right) + 3 \, e\right)} \sqrt{\frac{f}{\pi}}}{6 \, f}\right) - i \, \sqrt{6} \pi \sqrt{\frac{f}{\pi}} e^{\left(\frac{i \, b^{2} \log\left(f\right)^{2} - 9 i \, e^{2} + 36 i \, d f - 6 \, {\left(b e - 2 \, a f\right)} \log\left(f\right)}{12 \, f}\right)} \operatorname{S}\left(-\frac{\sqrt{6} {\left(6 \, f x - i \, b \log\left(f\right) + 3 \, e\right)} \sqrt{\frac{f}{\pi}}}{6 \, f}\right) - 9 i \, \sqrt{2} \pi \sqrt{\frac{f}{\pi}} e^{\left(\frac{-i \, b^{2} \log\left(f\right)^{2} + i \, e^{2} - 4 i \, d f - 2 \, {\left(b e - 2 \, a f\right)} \log\left(f\right)}{4 \, f}\right)} \operatorname{S}\left(\frac{\sqrt{2} {\left(2 \, f x + i \, b \log\left(f\right) + e\right)} \sqrt{\frac{f}{\pi}}}{2 \, f}\right) - 9 i \, \sqrt{2} \pi \sqrt{\frac{f}{\pi}} e^{\left(\frac{i \, b^{2} \log\left(f\right)^{2} - i \, e^{2} + 4 i \, d f - 2 \, {\left(b e - 2 \, a f\right)} \log\left(f\right)}{4 \, f}\right)} \operatorname{S}\left(-\frac{\sqrt{2} {\left(2 \, f x - i \, b \log\left(f\right) + e\right)} \sqrt{\frac{f}{\pi}}}{2 \, f}\right)}{48 \, f}"," ",0,"1/48*(sqrt(6)*pi*sqrt(f/pi)*e^(1/12*(-I*b^2*log(f)^2 + 9*I*e^2 - 36*I*d*f - 6*(b*e - 2*a*f)*log(f))/f)*fresnel_cos(1/6*sqrt(6)*(6*f*x + I*b*log(f) + 3*e)*sqrt(f/pi)/f) - sqrt(6)*pi*sqrt(f/pi)*e^(1/12*(I*b^2*log(f)^2 - 9*I*e^2 + 36*I*d*f - 6*(b*e - 2*a*f)*log(f))/f)*fresnel_cos(-1/6*sqrt(6)*(6*f*x - I*b*log(f) + 3*e)*sqrt(f/pi)/f) + 9*sqrt(2)*pi*sqrt(f/pi)*e^(1/4*(-I*b^2*log(f)^2 + I*e^2 - 4*I*d*f - 2*(b*e - 2*a*f)*log(f))/f)*fresnel_cos(1/2*sqrt(2)*(2*f*x + I*b*log(f) + e)*sqrt(f/pi)/f) - 9*sqrt(2)*pi*sqrt(f/pi)*e^(1/4*(I*b^2*log(f)^2 - I*e^2 + 4*I*d*f - 2*(b*e - 2*a*f)*log(f))/f)*fresnel_cos(-1/2*sqrt(2)*(2*f*x - I*b*log(f) + e)*sqrt(f/pi)/f) - I*sqrt(6)*pi*sqrt(f/pi)*e^(1/12*(-I*b^2*log(f)^2 + 9*I*e^2 - 36*I*d*f - 6*(b*e - 2*a*f)*log(f))/f)*fresnel_sin(1/6*sqrt(6)*(6*f*x + I*b*log(f) + 3*e)*sqrt(f/pi)/f) - I*sqrt(6)*pi*sqrt(f/pi)*e^(1/12*(I*b^2*log(f)^2 - 9*I*e^2 + 36*I*d*f - 6*(b*e - 2*a*f)*log(f))/f)*fresnel_sin(-1/6*sqrt(6)*(6*f*x - I*b*log(f) + 3*e)*sqrt(f/pi)/f) - 9*I*sqrt(2)*pi*sqrt(f/pi)*e^(1/4*(-I*b^2*log(f)^2 + I*e^2 - 4*I*d*f - 2*(b*e - 2*a*f)*log(f))/f)*fresnel_sin(1/2*sqrt(2)*(2*f*x + I*b*log(f) + e)*sqrt(f/pi)/f) - 9*I*sqrt(2)*pi*sqrt(f/pi)*e^(1/4*(I*b^2*log(f)^2 - I*e^2 + 4*I*d*f - 2*(b*e - 2*a*f)*log(f))/f)*fresnel_sin(-1/2*sqrt(2)*(2*f*x - I*b*log(f) + e)*sqrt(f/pi)/f))/f","B",0
116,1,142,0,0.815565," ","integrate(f^(c*x^2+a)*cos(e*x+d),x, algorithm=""fricas"")","-\frac{\sqrt{\pi} \sqrt{-c \log\left(f\right)} \operatorname{erf}\left(\frac{{\left(2 \, c x \log\left(f\right) + i \, e\right)} \sqrt{-c \log\left(f\right)}}{2 \, c \log\left(f\right)}\right) e^{\left(\frac{4 \, a c \log\left(f\right)^{2} + 4 i \, c d \log\left(f\right) + e^{2}}{4 \, c \log\left(f\right)}\right)} + \sqrt{\pi} \sqrt{-c \log\left(f\right)} \operatorname{erf}\left(\frac{{\left(2 \, c x \log\left(f\right) - i \, e\right)} \sqrt{-c \log\left(f\right)}}{2 \, c \log\left(f\right)}\right) e^{\left(\frac{4 \, a c \log\left(f\right)^{2} - 4 i \, c d \log\left(f\right) + e^{2}}{4 \, c \log\left(f\right)}\right)}}{4 \, c \log\left(f\right)}"," ",0,"-1/4*(sqrt(pi)*sqrt(-c*log(f))*erf(1/2*(2*c*x*log(f) + I*e)*sqrt(-c*log(f))/(c*log(f)))*e^(1/4*(4*a*c*log(f)^2 + 4*I*c*d*log(f) + e^2)/(c*log(f))) + sqrt(pi)*sqrt(-c*log(f))*erf(1/2*(2*c*x*log(f) - I*e)*sqrt(-c*log(f))/(c*log(f)))*e^(1/4*(4*a*c*log(f)^2 - 4*I*c*d*log(f) + e^2)/(c*log(f))))/(c*log(f))","A",0
117,1,159,0,0.619097," ","integrate(f^(c*x^2+a)*cos(e*x+d)^2,x, algorithm=""fricas"")","-\frac{2 \, \sqrt{\pi} \sqrt{-c \log\left(f\right)} f^{a} \operatorname{erf}\left(\sqrt{-c \log\left(f\right)} x\right) + \sqrt{\pi} \sqrt{-c \log\left(f\right)} \operatorname{erf}\left(\frac{{\left(c x \log\left(f\right) + i \, e\right)} \sqrt{-c \log\left(f\right)}}{c \log\left(f\right)}\right) e^{\left(\frac{a c \log\left(f\right)^{2} + 2 i \, c d \log\left(f\right) + e^{2}}{c \log\left(f\right)}\right)} + \sqrt{\pi} \sqrt{-c \log\left(f\right)} \operatorname{erf}\left(\frac{{\left(c x \log\left(f\right) - i \, e\right)} \sqrt{-c \log\left(f\right)}}{c \log\left(f\right)}\right) e^{\left(\frac{a c \log\left(f\right)^{2} - 2 i \, c d \log\left(f\right) + e^{2}}{c \log\left(f\right)}\right)}}{8 \, c \log\left(f\right)}"," ",0,"-1/8*(2*sqrt(pi)*sqrt(-c*log(f))*f^a*erf(sqrt(-c*log(f))*x) + sqrt(pi)*sqrt(-c*log(f))*erf((c*x*log(f) + I*e)*sqrt(-c*log(f))/(c*log(f)))*e^((a*c*log(f)^2 + 2*I*c*d*log(f) + e^2)/(c*log(f))) + sqrt(pi)*sqrt(-c*log(f))*erf((c*x*log(f) - I*e)*sqrt(-c*log(f))/(c*log(f)))*e^((a*c*log(f)^2 - 2*I*c*d*log(f) + e^2)/(c*log(f))))/(c*log(f))","A",0
118,1,280,0,1.362584," ","integrate(f^(c*x^2+a)*cos(e*x+d)^3,x, algorithm=""fricas"")","-\frac{\sqrt{\pi} \sqrt{-c \log\left(f\right)} \operatorname{erf}\left(\frac{{\left(2 \, c x \log\left(f\right) + 3 i \, e\right)} \sqrt{-c \log\left(f\right)}}{2 \, c \log\left(f\right)}\right) e^{\left(\frac{4 \, a c \log\left(f\right)^{2} + 12 i \, c d \log\left(f\right) + 9 \, e^{2}}{4 \, c \log\left(f\right)}\right)} + 3 \, \sqrt{\pi} \sqrt{-c \log\left(f\right)} \operatorname{erf}\left(\frac{{\left(2 \, c x \log\left(f\right) + i \, e\right)} \sqrt{-c \log\left(f\right)}}{2 \, c \log\left(f\right)}\right) e^{\left(\frac{4 \, a c \log\left(f\right)^{2} + 4 i \, c d \log\left(f\right) + e^{2}}{4 \, c \log\left(f\right)}\right)} + 3 \, \sqrt{\pi} \sqrt{-c \log\left(f\right)} \operatorname{erf}\left(\frac{{\left(2 \, c x \log\left(f\right) - i \, e\right)} \sqrt{-c \log\left(f\right)}}{2 \, c \log\left(f\right)}\right) e^{\left(\frac{4 \, a c \log\left(f\right)^{2} - 4 i \, c d \log\left(f\right) + e^{2}}{4 \, c \log\left(f\right)}\right)} + \sqrt{\pi} \sqrt{-c \log\left(f\right)} \operatorname{erf}\left(\frac{{\left(2 \, c x \log\left(f\right) - 3 i \, e\right)} \sqrt{-c \log\left(f\right)}}{2 \, c \log\left(f\right)}\right) e^{\left(\frac{4 \, a c \log\left(f\right)^{2} - 12 i \, c d \log\left(f\right) + 9 \, e^{2}}{4 \, c \log\left(f\right)}\right)}}{16 \, c \log\left(f\right)}"," ",0,"-1/16*(sqrt(pi)*sqrt(-c*log(f))*erf(1/2*(2*c*x*log(f) + 3*I*e)*sqrt(-c*log(f))/(c*log(f)))*e^(1/4*(4*a*c*log(f)^2 + 12*I*c*d*log(f) + 9*e^2)/(c*log(f))) + 3*sqrt(pi)*sqrt(-c*log(f))*erf(1/2*(2*c*x*log(f) + I*e)*sqrt(-c*log(f))/(c*log(f)))*e^(1/4*(4*a*c*log(f)^2 + 4*I*c*d*log(f) + e^2)/(c*log(f))) + 3*sqrt(pi)*sqrt(-c*log(f))*erf(1/2*(2*c*x*log(f) - I*e)*sqrt(-c*log(f))/(c*log(f)))*e^(1/4*(4*a*c*log(f)^2 - 4*I*c*d*log(f) + e^2)/(c*log(f))) + sqrt(pi)*sqrt(-c*log(f))*erf(1/2*(2*c*x*log(f) - 3*I*e)*sqrt(-c*log(f))/(c*log(f)))*e^(1/4*(4*a*c*log(f)^2 - 12*I*c*d*log(f) + 9*e^2)/(c*log(f))))/(c*log(f))","A",0
119,1,109,0,2.292560," ","integrate(f^(c*x^2+a)*cos(f*x^2+d),x, algorithm=""fricas"")","-\frac{\sqrt{\pi} {\left(c \log\left(f\right) - i \, f\right)} \sqrt{-c \log\left(f\right) - i \, f} \operatorname{erf}\left(\sqrt{-c \log\left(f\right) - i \, f} x\right) e^{\left(a \log\left(f\right) + i \, d\right)} + \sqrt{\pi} {\left(c \log\left(f\right) + i \, f\right)} \sqrt{-c \log\left(f\right) + i \, f} \operatorname{erf}\left(\sqrt{-c \log\left(f\right) + i \, f} x\right) e^{\left(a \log\left(f\right) - i \, d\right)}}{4 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}"," ",0,"-1/4*(sqrt(pi)*(c*log(f) - I*f)*sqrt(-c*log(f) - I*f)*erf(sqrt(-c*log(f) - I*f)*x)*e^(a*log(f) + I*d) + sqrt(pi)*(c*log(f) + I*f)*sqrt(-c*log(f) + I*f)*erf(sqrt(-c*log(f) + I*f)*x)*e^(a*log(f) - I*d))/(c^2*log(f)^2 + f^2)","A",0
120,1,167,0,1.707112," ","integrate(f^(c*x^2+a)*cos(f*x^2+d)^2,x, algorithm=""fricas"")","-\frac{2 \, \sqrt{\pi} {\left(c^{2} \log\left(f\right)^{2} + 4 \, f^{2}\right)} \sqrt{-c \log\left(f\right)} f^{a} \operatorname{erf}\left(\sqrt{-c \log\left(f\right)} x\right) + \sqrt{\pi} {\left(c^{2} \log\left(f\right)^{2} - 2 i \, c f \log\left(f\right)\right)} \sqrt{-c \log\left(f\right) - 2 i \, f} \operatorname{erf}\left(\sqrt{-c \log\left(f\right) - 2 i \, f} x\right) e^{\left(a \log\left(f\right) + 2 i \, d\right)} + \sqrt{\pi} {\left(c^{2} \log\left(f\right)^{2} + 2 i \, c f \log\left(f\right)\right)} \sqrt{-c \log\left(f\right) + 2 i \, f} \operatorname{erf}\left(\sqrt{-c \log\left(f\right) + 2 i \, f} x\right) e^{\left(a \log\left(f\right) - 2 i \, d\right)}}{8 \, {\left(c^{3} \log\left(f\right)^{3} + 4 \, c f^{2} \log\left(f\right)\right)}}"," ",0,"-1/8*(2*sqrt(pi)*(c^2*log(f)^2 + 4*f^2)*sqrt(-c*log(f))*f^a*erf(sqrt(-c*log(f))*x) + sqrt(pi)*(c^2*log(f)^2 - 2*I*c*f*log(f))*sqrt(-c*log(f) - 2*I*f)*erf(sqrt(-c*log(f) - 2*I*f)*x)*e^(a*log(f) + 2*I*d) + sqrt(pi)*(c^2*log(f)^2 + 2*I*c*f*log(f))*sqrt(-c*log(f) + 2*I*f)*erf(sqrt(-c*log(f) + 2*I*f)*x)*e^(a*log(f) - 2*I*d))/(c^3*log(f)^3 + 4*c*f^2*log(f))","A",0
121,1,311,0,0.630926," ","integrate(f^(c*x^2+a)*cos(f*x^2+d)^3,x, algorithm=""fricas"")","-\frac{\sqrt{\pi} {\left(c^{3} \log\left(f\right)^{3} - 3 i \, c^{2} f \log\left(f\right)^{2} + c f^{2} \log\left(f\right) - 3 i \, f^{3}\right)} \sqrt{-c \log\left(f\right) - 3 i \, f} \operatorname{erf}\left(\sqrt{-c \log\left(f\right) - 3 i \, f} x\right) e^{\left(a \log\left(f\right) + 3 i \, d\right)} + \sqrt{\pi} {\left(3 \, c^{3} \log\left(f\right)^{3} - 3 i \, c^{2} f \log\left(f\right)^{2} + 27 \, c f^{2} \log\left(f\right) - 27 i \, f^{3}\right)} \sqrt{-c \log\left(f\right) - i \, f} \operatorname{erf}\left(\sqrt{-c \log\left(f\right) - i \, f} x\right) e^{\left(a \log\left(f\right) + i \, d\right)} + \sqrt{\pi} {\left(3 \, c^{3} \log\left(f\right)^{3} + 3 i \, c^{2} f \log\left(f\right)^{2} + 27 \, c f^{2} \log\left(f\right) + 27 i \, f^{3}\right)} \sqrt{-c \log\left(f\right) + i \, f} \operatorname{erf}\left(\sqrt{-c \log\left(f\right) + i \, f} x\right) e^{\left(a \log\left(f\right) - i \, d\right)} + \sqrt{\pi} {\left(c^{3} \log\left(f\right)^{3} + 3 i \, c^{2} f \log\left(f\right)^{2} + c f^{2} \log\left(f\right) + 3 i \, f^{3}\right)} \sqrt{-c \log\left(f\right) + 3 i \, f} \operatorname{erf}\left(\sqrt{-c \log\left(f\right) + 3 i \, f} x\right) e^{\left(a \log\left(f\right) - 3 i \, d\right)}}{16 \, {\left(c^{4} \log\left(f\right)^{4} + 10 \, c^{2} f^{2} \log\left(f\right)^{2} + 9 \, f^{4}\right)}}"," ",0,"-1/16*(sqrt(pi)*(c^3*log(f)^3 - 3*I*c^2*f*log(f)^2 + c*f^2*log(f) - 3*I*f^3)*sqrt(-c*log(f) - 3*I*f)*erf(sqrt(-c*log(f) - 3*I*f)*x)*e^(a*log(f) + 3*I*d) + sqrt(pi)*(3*c^3*log(f)^3 - 3*I*c^2*f*log(f)^2 + 27*c*f^2*log(f) - 27*I*f^3)*sqrt(-c*log(f) - I*f)*erf(sqrt(-c*log(f) - I*f)*x)*e^(a*log(f) + I*d) + sqrt(pi)*(3*c^3*log(f)^3 + 3*I*c^2*f*log(f)^2 + 27*c*f^2*log(f) + 27*I*f^3)*sqrt(-c*log(f) + I*f)*erf(sqrt(-c*log(f) + I*f)*x)*e^(a*log(f) - I*d) + sqrt(pi)*(c^3*log(f)^3 + 3*I*c^2*f*log(f)^2 + c*f^2*log(f) + 3*I*f^3)*sqrt(-c*log(f) + 3*I*f)*erf(sqrt(-c*log(f) + 3*I*f)*x)*e^(a*log(f) - 3*I*d))/(c^4*log(f)^4 + 10*c^2*f^2*log(f)^2 + 9*f^4)","B",0
122,1,301,0,0.816671," ","integrate(f^(c*x^2+a)*cos(f*x^2+e*x+d),x, algorithm=""fricas"")","-\frac{\sqrt{\pi} {\left(c \log\left(f\right) - i \, f\right)} \sqrt{-c \log\left(f\right) - i \, f} \operatorname{erf}\left(\frac{{\left(2 \, c^{2} x \log\left(f\right)^{2} + 2 \, f^{2} x + i \, c e \log\left(f\right) + e f\right)} \sqrt{-c \log\left(f\right) - i \, f}}{2 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}\right) e^{\left(\frac{4 \, a c^{2} \log\left(f\right)^{3} + 4 i \, c^{2} d \log\left(f\right)^{2} - i \, e^{2} f + 4 i \, d f^{2} + {\left(c e^{2} + 4 \, a f^{2}\right)} \log\left(f\right)}{4 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}\right)} + \sqrt{\pi} {\left(c \log\left(f\right) + i \, f\right)} \sqrt{-c \log\left(f\right) + i \, f} \operatorname{erf}\left(\frac{{\left(2 \, c^{2} x \log\left(f\right)^{2} + 2 \, f^{2} x - i \, c e \log\left(f\right) + e f\right)} \sqrt{-c \log\left(f\right) + i \, f}}{2 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}\right) e^{\left(\frac{4 \, a c^{2} \log\left(f\right)^{3} - 4 i \, c^{2} d \log\left(f\right)^{2} + i \, e^{2} f - 4 i \, d f^{2} + {\left(c e^{2} + 4 \, a f^{2}\right)} \log\left(f\right)}{4 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}\right)}}{4 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}"," ",0,"-1/4*(sqrt(pi)*(c*log(f) - I*f)*sqrt(-c*log(f) - I*f)*erf(1/2*(2*c^2*x*log(f)^2 + 2*f^2*x + I*c*e*log(f) + e*f)*sqrt(-c*log(f) - I*f)/(c^2*log(f)^2 + f^2))*e^(1/4*(4*a*c^2*log(f)^3 + 4*I*c^2*d*log(f)^2 - I*e^2*f + 4*I*d*f^2 + (c*e^2 + 4*a*f^2)*log(f))/(c^2*log(f)^2 + f^2)) + sqrt(pi)*(c*log(f) + I*f)*sqrt(-c*log(f) + I*f)*erf(1/2*(2*c^2*x*log(f)^2 + 2*f^2*x - I*c*e*log(f) + e*f)*sqrt(-c*log(f) + I*f)/(c^2*log(f)^2 + f^2))*e^(1/4*(4*a*c^2*log(f)^3 - 4*I*c^2*d*log(f)^2 + I*e^2*f - 4*I*d*f^2 + (c*e^2 + 4*a*f^2)*log(f))/(c^2*log(f)^2 + f^2)))/(c^2*log(f)^2 + f^2)","B",0
123,1,361,0,1.508085," ","integrate(f^(c*x^2+a)*cos(f*x^2+e*x+d)^2,x, algorithm=""fricas"")","-\frac{2 \, \sqrt{\pi} {\left(c^{2} \log\left(f\right)^{2} + 4 \, f^{2}\right)} \sqrt{-c \log\left(f\right)} f^{a} \operatorname{erf}\left(\sqrt{-c \log\left(f\right)} x\right) + \sqrt{\pi} {\left(c^{2} \log\left(f\right)^{2} - 2 i \, c f \log\left(f\right)\right)} \sqrt{-c \log\left(f\right) - 2 i \, f} \operatorname{erf}\left(\frac{{\left(c^{2} x \log\left(f\right)^{2} + 4 \, f^{2} x + i \, c e \log\left(f\right) + 2 \, e f\right)} \sqrt{-c \log\left(f\right) - 2 i \, f}}{c^{2} \log\left(f\right)^{2} + 4 \, f^{2}}\right) e^{\left(\frac{a c^{2} \log\left(f\right)^{3} + 2 i \, c^{2} d \log\left(f\right)^{2} - 2 i \, e^{2} f + 8 i \, d f^{2} + {\left(c e^{2} + 4 \, a f^{2}\right)} \log\left(f\right)}{c^{2} \log\left(f\right)^{2} + 4 \, f^{2}}\right)} + \sqrt{\pi} {\left(c^{2} \log\left(f\right)^{2} + 2 i \, c f \log\left(f\right)\right)} \sqrt{-c \log\left(f\right) + 2 i \, f} \operatorname{erf}\left(\frac{{\left(c^{2} x \log\left(f\right)^{2} + 4 \, f^{2} x - i \, c e \log\left(f\right) + 2 \, e f\right)} \sqrt{-c \log\left(f\right) + 2 i \, f}}{c^{2} \log\left(f\right)^{2} + 4 \, f^{2}}\right) e^{\left(\frac{a c^{2} \log\left(f\right)^{3} - 2 i \, c^{2} d \log\left(f\right)^{2} + 2 i \, e^{2} f - 8 i \, d f^{2} + {\left(c e^{2} + 4 \, a f^{2}\right)} \log\left(f\right)}{c^{2} \log\left(f\right)^{2} + 4 \, f^{2}}\right)}}{8 \, {\left(c^{3} \log\left(f\right)^{3} + 4 \, c f^{2} \log\left(f\right)\right)}}"," ",0,"-1/8*(2*sqrt(pi)*(c^2*log(f)^2 + 4*f^2)*sqrt(-c*log(f))*f^a*erf(sqrt(-c*log(f))*x) + sqrt(pi)*(c^2*log(f)^2 - 2*I*c*f*log(f))*sqrt(-c*log(f) - 2*I*f)*erf((c^2*x*log(f)^2 + 4*f^2*x + I*c*e*log(f) + 2*e*f)*sqrt(-c*log(f) - 2*I*f)/(c^2*log(f)^2 + 4*f^2))*e^((a*c^2*log(f)^3 + 2*I*c^2*d*log(f)^2 - 2*I*e^2*f + 8*I*d*f^2 + (c*e^2 + 4*a*f^2)*log(f))/(c^2*log(f)^2 + 4*f^2)) + sqrt(pi)*(c^2*log(f)^2 + 2*I*c*f*log(f))*sqrt(-c*log(f) + 2*I*f)*erf((c^2*x*log(f)^2 + 4*f^2*x - I*c*e*log(f) + 2*e*f)*sqrt(-c*log(f) + 2*I*f)/(c^2*log(f)^2 + 4*f^2))*e^((a*c^2*log(f)^3 - 2*I*c^2*d*log(f)^2 + 2*I*e^2*f - 8*I*d*f^2 + (c*e^2 + 4*a*f^2)*log(f))/(c^2*log(f)^2 + 4*f^2)))/(c^3*log(f)^3 + 4*c*f^2*log(f))","B",0
124,1,707,0,0.933486," ","integrate(f^(c*x^2+a)*cos(f*x^2+e*x+d)^3,x, algorithm=""fricas"")","-\frac{\sqrt{\pi} {\left(c^{3} \log\left(f\right)^{3} - 3 i \, c^{2} f \log\left(f\right)^{2} + c f^{2} \log\left(f\right) - 3 i \, f^{3}\right)} \sqrt{-c \log\left(f\right) - 3 i \, f} \operatorname{erf}\left(\frac{{\left(2 \, c^{2} x \log\left(f\right)^{2} + 18 \, f^{2} x + 3 i \, c e \log\left(f\right) + 9 \, e f\right)} \sqrt{-c \log\left(f\right) - 3 i \, f}}{2 \, {\left(c^{2} \log\left(f\right)^{2} + 9 \, f^{2}\right)}}\right) e^{\left(\frac{4 \, a c^{2} \log\left(f\right)^{3} + 12 i \, c^{2} d \log\left(f\right)^{2} - 27 i \, e^{2} f + 108 i \, d f^{2} + 9 \, {\left(c e^{2} + 4 \, a f^{2}\right)} \log\left(f\right)}{4 \, {\left(c^{2} \log\left(f\right)^{2} + 9 \, f^{2}\right)}}\right)} + \sqrt{\pi} {\left(c^{3} \log\left(f\right)^{3} + 3 i \, c^{2} f \log\left(f\right)^{2} + c f^{2} \log\left(f\right) + 3 i \, f^{3}\right)} \sqrt{-c \log\left(f\right) + 3 i \, f} \operatorname{erf}\left(\frac{{\left(2 \, c^{2} x \log\left(f\right)^{2} + 18 \, f^{2} x - 3 i \, c e \log\left(f\right) + 9 \, e f\right)} \sqrt{-c \log\left(f\right) + 3 i \, f}}{2 \, {\left(c^{2} \log\left(f\right)^{2} + 9 \, f^{2}\right)}}\right) e^{\left(\frac{4 \, a c^{2} \log\left(f\right)^{3} - 12 i \, c^{2} d \log\left(f\right)^{2} + 27 i \, e^{2} f - 108 i \, d f^{2} + 9 \, {\left(c e^{2} + 4 \, a f^{2}\right)} \log\left(f\right)}{4 \, {\left(c^{2} \log\left(f\right)^{2} + 9 \, f^{2}\right)}}\right)} + \sqrt{\pi} {\left(3 \, c^{3} \log\left(f\right)^{3} - 3 i \, c^{2} f \log\left(f\right)^{2} + 27 \, c f^{2} \log\left(f\right) - 27 i \, f^{3}\right)} \sqrt{-c \log\left(f\right) - i \, f} \operatorname{erf}\left(\frac{{\left(2 \, c^{2} x \log\left(f\right)^{2} + 2 \, f^{2} x + i \, c e \log\left(f\right) + e f\right)} \sqrt{-c \log\left(f\right) - i \, f}}{2 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}\right) e^{\left(\frac{4 \, a c^{2} \log\left(f\right)^{3} + 4 i \, c^{2} d \log\left(f\right)^{2} - i \, e^{2} f + 4 i \, d f^{2} + {\left(c e^{2} + 4 \, a f^{2}\right)} \log\left(f\right)}{4 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}\right)} + \sqrt{\pi} {\left(3 \, c^{3} \log\left(f\right)^{3} + 3 i \, c^{2} f \log\left(f\right)^{2} + 27 \, c f^{2} \log\left(f\right) + 27 i \, f^{3}\right)} \sqrt{-c \log\left(f\right) + i \, f} \operatorname{erf}\left(\frac{{\left(2 \, c^{2} x \log\left(f\right)^{2} + 2 \, f^{2} x - i \, c e \log\left(f\right) + e f\right)} \sqrt{-c \log\left(f\right) + i \, f}}{2 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}\right) e^{\left(\frac{4 \, a c^{2} \log\left(f\right)^{3} - 4 i \, c^{2} d \log\left(f\right)^{2} + i \, e^{2} f - 4 i \, d f^{2} + {\left(c e^{2} + 4 \, a f^{2}\right)} \log\left(f\right)}{4 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}\right)}}{16 \, {\left(c^{4} \log\left(f\right)^{4} + 10 \, c^{2} f^{2} \log\left(f\right)^{2} + 9 \, f^{4}\right)}}"," ",0,"-1/16*(sqrt(pi)*(c^3*log(f)^3 - 3*I*c^2*f*log(f)^2 + c*f^2*log(f) - 3*I*f^3)*sqrt(-c*log(f) - 3*I*f)*erf(1/2*(2*c^2*x*log(f)^2 + 18*f^2*x + 3*I*c*e*log(f) + 9*e*f)*sqrt(-c*log(f) - 3*I*f)/(c^2*log(f)^2 + 9*f^2))*e^(1/4*(4*a*c^2*log(f)^3 + 12*I*c^2*d*log(f)^2 - 27*I*e^2*f + 108*I*d*f^2 + 9*(c*e^2 + 4*a*f^2)*log(f))/(c^2*log(f)^2 + 9*f^2)) + sqrt(pi)*(c^3*log(f)^3 + 3*I*c^2*f*log(f)^2 + c*f^2*log(f) + 3*I*f^3)*sqrt(-c*log(f) + 3*I*f)*erf(1/2*(2*c^2*x*log(f)^2 + 18*f^2*x - 3*I*c*e*log(f) + 9*e*f)*sqrt(-c*log(f) + 3*I*f)/(c^2*log(f)^2 + 9*f^2))*e^(1/4*(4*a*c^2*log(f)^3 - 12*I*c^2*d*log(f)^2 + 27*I*e^2*f - 108*I*d*f^2 + 9*(c*e^2 + 4*a*f^2)*log(f))/(c^2*log(f)^2 + 9*f^2)) + sqrt(pi)*(3*c^3*log(f)^3 - 3*I*c^2*f*log(f)^2 + 27*c*f^2*log(f) - 27*I*f^3)*sqrt(-c*log(f) - I*f)*erf(1/2*(2*c^2*x*log(f)^2 + 2*f^2*x + I*c*e*log(f) + e*f)*sqrt(-c*log(f) - I*f)/(c^2*log(f)^2 + f^2))*e^(1/4*(4*a*c^2*log(f)^3 + 4*I*c^2*d*log(f)^2 - I*e^2*f + 4*I*d*f^2 + (c*e^2 + 4*a*f^2)*log(f))/(c^2*log(f)^2 + f^2)) + sqrt(pi)*(3*c^3*log(f)^3 + 3*I*c^2*f*log(f)^2 + 27*c*f^2*log(f) + 27*I*f^3)*sqrt(-c*log(f) + I*f)*erf(1/2*(2*c^2*x*log(f)^2 + 2*f^2*x - I*c*e*log(f) + e*f)*sqrt(-c*log(f) + I*f)/(c^2*log(f)^2 + f^2))*e^(1/4*(4*a*c^2*log(f)^3 - 4*I*c^2*d*log(f)^2 + I*e^2*f - 4*I*d*f^2 + (c*e^2 + 4*a*f^2)*log(f))/(c^2*log(f)^2 + f^2)))/(c^4*log(f)^4 + 10*c^2*f^2*log(f)^2 + 9*f^4)","B",0
125,1,176,0,0.724687," ","integrate(f^(c*x^2+b*x+a)*cos(e*x+d),x, algorithm=""fricas"")","-\frac{\sqrt{\pi} \sqrt{-c \log\left(f\right)} \operatorname{erf}\left(\frac{{\left({\left(2 \, c x + b\right)} \log\left(f\right) + i \, e\right)} \sqrt{-c \log\left(f\right)}}{2 \, c \log\left(f\right)}\right) e^{\left(-\frac{{\left(b^{2} - 4 \, a c\right)} \log\left(f\right)^{2} - e^{2} - {\left(4 i \, c d - 2 i \, b e\right)} \log\left(f\right)}{4 \, c \log\left(f\right)}\right)} + \sqrt{\pi} \sqrt{-c \log\left(f\right)} \operatorname{erf}\left(\frac{{\left({\left(2 \, c x + b\right)} \log\left(f\right) - i \, e\right)} \sqrt{-c \log\left(f\right)}}{2 \, c \log\left(f\right)}\right) e^{\left(-\frac{{\left(b^{2} - 4 \, a c\right)} \log\left(f\right)^{2} - e^{2} - {\left(-4 i \, c d + 2 i \, b e\right)} \log\left(f\right)}{4 \, c \log\left(f\right)}\right)}}{4 \, c \log\left(f\right)}"," ",0,"-1/4*(sqrt(pi)*sqrt(-c*log(f))*erf(1/2*((2*c*x + b)*log(f) + I*e)*sqrt(-c*log(f))/(c*log(f)))*e^(-1/4*((b^2 - 4*a*c)*log(f)^2 - e^2 - (4*I*c*d - 2*I*b*e)*log(f))/(c*log(f))) + sqrt(pi)*sqrt(-c*log(f))*erf(1/2*((2*c*x + b)*log(f) - I*e)*sqrt(-c*log(f))/(c*log(f)))*e^(-1/4*((b^2 - 4*a*c)*log(f)^2 - e^2 - (-4*I*c*d + 2*I*b*e)*log(f))/(c*log(f))))/(c*log(f))","A",0
126,1,224,0,0.779812," ","integrate(f^(c*x^2+b*x+a)*cos(e*x+d)^2,x, algorithm=""fricas"")","-\frac{\sqrt{\pi} \sqrt{-c \log\left(f\right)} \operatorname{erf}\left(\frac{{\left({\left(2 \, c x + b\right)} \log\left(f\right) + 2 i \, e\right)} \sqrt{-c \log\left(f\right)}}{2 \, c \log\left(f\right)}\right) e^{\left(-\frac{{\left(b^{2} - 4 \, a c\right)} \log\left(f\right)^{2} - 4 \, e^{2} - {\left(8 i \, c d - 4 i \, b e\right)} \log\left(f\right)}{4 \, c \log\left(f\right)}\right)} + \sqrt{\pi} \sqrt{-c \log\left(f\right)} \operatorname{erf}\left(\frac{{\left({\left(2 \, c x + b\right)} \log\left(f\right) - 2 i \, e\right)} \sqrt{-c \log\left(f\right)}}{2 \, c \log\left(f\right)}\right) e^{\left(-\frac{{\left(b^{2} - 4 \, a c\right)} \log\left(f\right)^{2} - 4 \, e^{2} - {\left(-8 i \, c d + 4 i \, b e\right)} \log\left(f\right)}{4 \, c \log\left(f\right)}\right)} + \frac{2 \, \sqrt{\pi} \sqrt{-c \log\left(f\right)} \operatorname{erf}\left(\frac{{\left(2 \, c x + b\right)} \sqrt{-c \log\left(f\right)}}{2 \, c}\right)}{f^{\frac{b^{2} - 4 \, a c}{4 \, c}}}}{8 \, c \log\left(f\right)}"," ",0,"-1/8*(sqrt(pi)*sqrt(-c*log(f))*erf(1/2*((2*c*x + b)*log(f) + 2*I*e)*sqrt(-c*log(f))/(c*log(f)))*e^(-1/4*((b^2 - 4*a*c)*log(f)^2 - 4*e^2 - (8*I*c*d - 4*I*b*e)*log(f))/(c*log(f))) + sqrt(pi)*sqrt(-c*log(f))*erf(1/2*((2*c*x + b)*log(f) - 2*I*e)*sqrt(-c*log(f))/(c*log(f)))*e^(-1/4*((b^2 - 4*a*c)*log(f)^2 - 4*e^2 - (-8*I*c*d + 4*I*b*e)*log(f))/(c*log(f))) + 2*sqrt(pi)*sqrt(-c*log(f))*erf(1/2*(2*c*x + b)*sqrt(-c*log(f))/c)/f^(1/4*(b^2 - 4*a*c)/c))/(c*log(f))","A",0
127,1,344,0,0.772824," ","integrate(f^(c*x^2+b*x+a)*cos(e*x+d)^3,x, algorithm=""fricas"")","-\frac{3 \, \sqrt{\pi} \sqrt{-c \log\left(f\right)} \operatorname{erf}\left(\frac{{\left({\left(2 \, c x + b\right)} \log\left(f\right) + i \, e\right)} \sqrt{-c \log\left(f\right)}}{2 \, c \log\left(f\right)}\right) e^{\left(-\frac{{\left(b^{2} - 4 \, a c\right)} \log\left(f\right)^{2} - e^{2} - {\left(4 i \, c d - 2 i \, b e\right)} \log\left(f\right)}{4 \, c \log\left(f\right)}\right)} + 3 \, \sqrt{\pi} \sqrt{-c \log\left(f\right)} \operatorname{erf}\left(\frac{{\left({\left(2 \, c x + b\right)} \log\left(f\right) - i \, e\right)} \sqrt{-c \log\left(f\right)}}{2 \, c \log\left(f\right)}\right) e^{\left(-\frac{{\left(b^{2} - 4 \, a c\right)} \log\left(f\right)^{2} - e^{2} - {\left(-4 i \, c d + 2 i \, b e\right)} \log\left(f\right)}{4 \, c \log\left(f\right)}\right)} + \sqrt{\pi} \sqrt{-c \log\left(f\right)} \operatorname{erf}\left(\frac{{\left({\left(2 \, c x + b\right)} \log\left(f\right) + 3 i \, e\right)} \sqrt{-c \log\left(f\right)}}{2 \, c \log\left(f\right)}\right) e^{\left(-\frac{{\left(b^{2} - 4 \, a c\right)} \log\left(f\right)^{2} - 9 \, e^{2} - {\left(12 i \, c d - 6 i \, b e\right)} \log\left(f\right)}{4 \, c \log\left(f\right)}\right)} + \sqrt{\pi} \sqrt{-c \log\left(f\right)} \operatorname{erf}\left(\frac{{\left({\left(2 \, c x + b\right)} \log\left(f\right) - 3 i \, e\right)} \sqrt{-c \log\left(f\right)}}{2 \, c \log\left(f\right)}\right) e^{\left(-\frac{{\left(b^{2} - 4 \, a c\right)} \log\left(f\right)^{2} - 9 \, e^{2} - {\left(-12 i \, c d + 6 i \, b e\right)} \log\left(f\right)}{4 \, c \log\left(f\right)}\right)}}{16 \, c \log\left(f\right)}"," ",0,"-1/16*(3*sqrt(pi)*sqrt(-c*log(f))*erf(1/2*((2*c*x + b)*log(f) + I*e)*sqrt(-c*log(f))/(c*log(f)))*e^(-1/4*((b^2 - 4*a*c)*log(f)^2 - e^2 - (4*I*c*d - 2*I*b*e)*log(f))/(c*log(f))) + 3*sqrt(pi)*sqrt(-c*log(f))*erf(1/2*((2*c*x + b)*log(f) - I*e)*sqrt(-c*log(f))/(c*log(f)))*e^(-1/4*((b^2 - 4*a*c)*log(f)^2 - e^2 - (-4*I*c*d + 2*I*b*e)*log(f))/(c*log(f))) + sqrt(pi)*sqrt(-c*log(f))*erf(1/2*((2*c*x + b)*log(f) + 3*I*e)*sqrt(-c*log(f))/(c*log(f)))*e^(-1/4*((b^2 - 4*a*c)*log(f)^2 - 9*e^2 - (12*I*c*d - 6*I*b*e)*log(f))/(c*log(f))) + sqrt(pi)*sqrt(-c*log(f))*erf(1/2*((2*c*x + b)*log(f) - 3*I*e)*sqrt(-c*log(f))/(c*log(f)))*e^(-1/4*((b^2 - 4*a*c)*log(f)^2 - 9*e^2 - (-12*I*c*d + 6*I*b*e)*log(f))/(c*log(f))))/(c*log(f))","A",0
128,1,311,0,0.722206," ","integrate(f^(c*x^2+b*x+a)*cos(f*x^2+d),x, algorithm=""fricas"")","-\frac{\sqrt{\pi} {\left(c \log\left(f\right) - i \, f\right)} \sqrt{-c \log\left(f\right) - i \, f} \operatorname{erf}\left(\frac{{\left(2 \, f^{2} x - i \, b f \log\left(f\right) + {\left(2 \, c^{2} x + b c\right)} \log\left(f\right)^{2}\right)} \sqrt{-c \log\left(f\right) - i \, f}}{2 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}\right) e^{\left(\frac{4 \, a f^{2} \log\left(f\right) - {\left(b^{2} c - 4 \, a c^{2}\right)} \log\left(f\right)^{3} + 4 i \, d f^{2} + {\left(4 i \, c^{2} d + i \, b^{2} f\right)} \log\left(f\right)^{2}}{4 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}\right)} + \sqrt{\pi} {\left(c \log\left(f\right) + i \, f\right)} \sqrt{-c \log\left(f\right) + i \, f} \operatorname{erf}\left(\frac{{\left(2 \, f^{2} x + i \, b f \log\left(f\right) + {\left(2 \, c^{2} x + b c\right)} \log\left(f\right)^{2}\right)} \sqrt{-c \log\left(f\right) + i \, f}}{2 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}\right) e^{\left(\frac{4 \, a f^{2} \log\left(f\right) - {\left(b^{2} c - 4 \, a c^{2}\right)} \log\left(f\right)^{3} - 4 i \, d f^{2} + {\left(-4 i \, c^{2} d - i \, b^{2} f\right)} \log\left(f\right)^{2}}{4 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}\right)}}{4 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}"," ",0,"-1/4*(sqrt(pi)*(c*log(f) - I*f)*sqrt(-c*log(f) - I*f)*erf(1/2*(2*f^2*x - I*b*f*log(f) + (2*c^2*x + b*c)*log(f)^2)*sqrt(-c*log(f) - I*f)/(c^2*log(f)^2 + f^2))*e^(1/4*(4*a*f^2*log(f) - (b^2*c - 4*a*c^2)*log(f)^3 + 4*I*d*f^2 + (4*I*c^2*d + I*b^2*f)*log(f)^2)/(c^2*log(f)^2 + f^2)) + sqrt(pi)*(c*log(f) + I*f)*sqrt(-c*log(f) + I*f)*erf(1/2*(2*f^2*x + I*b*f*log(f) + (2*c^2*x + b*c)*log(f)^2)*sqrt(-c*log(f) + I*f)/(c^2*log(f)^2 + f^2))*e^(1/4*(4*a*f^2*log(f) - (b^2*c - 4*a*c^2)*log(f)^3 - 4*I*d*f^2 + (-4*I*c^2*d - I*b^2*f)*log(f)^2)/(c^2*log(f)^2 + f^2)))/(c^2*log(f)^2 + f^2)","B",0
129,1,400,0,0.721990," ","integrate(f^(c*x^2+b*x+a)*cos(f*x^2+d)^2,x, algorithm=""fricas"")","-\frac{\sqrt{\pi} {\left(c^{2} \log\left(f\right)^{2} - 2 i \, c f \log\left(f\right)\right)} \sqrt{-c \log\left(f\right) - 2 i \, f} \operatorname{erf}\left(\frac{{\left(8 \, f^{2} x - 2 i \, b f \log\left(f\right) + {\left(2 \, c^{2} x + b c\right)} \log\left(f\right)^{2}\right)} \sqrt{-c \log\left(f\right) - 2 i \, f}}{2 \, {\left(c^{2} \log\left(f\right)^{2} + 4 \, f^{2}\right)}}\right) e^{\left(\frac{16 \, a f^{2} \log\left(f\right) - {\left(b^{2} c - 4 \, a c^{2}\right)} \log\left(f\right)^{3} + 32 i \, d f^{2} + {\left(8 i \, c^{2} d + 2 i \, b^{2} f\right)} \log\left(f\right)^{2}}{4 \, {\left(c^{2} \log\left(f\right)^{2} + 4 \, f^{2}\right)}}\right)} + \sqrt{\pi} {\left(c^{2} \log\left(f\right)^{2} + 2 i \, c f \log\left(f\right)\right)} \sqrt{-c \log\left(f\right) + 2 i \, f} \operatorname{erf}\left(\frac{{\left(8 \, f^{2} x + 2 i \, b f \log\left(f\right) + {\left(2 \, c^{2} x + b c\right)} \log\left(f\right)^{2}\right)} \sqrt{-c \log\left(f\right) + 2 i \, f}}{2 \, {\left(c^{2} \log\left(f\right)^{2} + 4 \, f^{2}\right)}}\right) e^{\left(\frac{16 \, a f^{2} \log\left(f\right) - {\left(b^{2} c - 4 \, a c^{2}\right)} \log\left(f\right)^{3} - 32 i \, d f^{2} + {\left(-8 i \, c^{2} d - 2 i \, b^{2} f\right)} \log\left(f\right)^{2}}{4 \, {\left(c^{2} \log\left(f\right)^{2} + 4 \, f^{2}\right)}}\right)} + \frac{2 \, \sqrt{\pi} {\left(c^{2} \log\left(f\right)^{2} + 4 \, f^{2}\right)} \sqrt{-c \log\left(f\right)} \operatorname{erf}\left(\frac{{\left(2 \, c x + b\right)} \sqrt{-c \log\left(f\right)}}{2 \, c}\right)}{f^{\frac{b^{2} - 4 \, a c}{4 \, c}}}}{8 \, {\left(c^{3} \log\left(f\right)^{3} + 4 \, c f^{2} \log\left(f\right)\right)}}"," ",0,"-1/8*(sqrt(pi)*(c^2*log(f)^2 - 2*I*c*f*log(f))*sqrt(-c*log(f) - 2*I*f)*erf(1/2*(8*f^2*x - 2*I*b*f*log(f) + (2*c^2*x + b*c)*log(f)^2)*sqrt(-c*log(f) - 2*I*f)/(c^2*log(f)^2 + 4*f^2))*e^(1/4*(16*a*f^2*log(f) - (b^2*c - 4*a*c^2)*log(f)^3 + 32*I*d*f^2 + (8*I*c^2*d + 2*I*b^2*f)*log(f)^2)/(c^2*log(f)^2 + 4*f^2)) + sqrt(pi)*(c^2*log(f)^2 + 2*I*c*f*log(f))*sqrt(-c*log(f) + 2*I*f)*erf(1/2*(8*f^2*x + 2*I*b*f*log(f) + (2*c^2*x + b*c)*log(f)^2)*sqrt(-c*log(f) + 2*I*f)/(c^2*log(f)^2 + 4*f^2))*e^(1/4*(16*a*f^2*log(f) - (b^2*c - 4*a*c^2)*log(f)^3 - 32*I*d*f^2 + (-8*I*c^2*d - 2*I*b^2*f)*log(f)^2)/(c^2*log(f)^2 + 4*f^2)) + 2*sqrt(pi)*(c^2*log(f)^2 + 4*f^2)*sqrt(-c*log(f))*erf(1/2*(2*c*x + b)*sqrt(-c*log(f))/c)/f^(1/4*(b^2 - 4*a*c)/c))/(c^3*log(f)^3 + 4*c*f^2*log(f))","B",0
130,1,723,0,0.925917," ","integrate(f^(c*x^2+b*x+a)*cos(f*x^2+d)^3,x, algorithm=""fricas"")","-\frac{\sqrt{\pi} {\left(c^{3} \log\left(f\right)^{3} - 3 i \, c^{2} f \log\left(f\right)^{2} + c f^{2} \log\left(f\right) - 3 i \, f^{3}\right)} \sqrt{-c \log\left(f\right) - 3 i \, f} \operatorname{erf}\left(\frac{{\left(18 \, f^{2} x - 3 i \, b f \log\left(f\right) + {\left(2 \, c^{2} x + b c\right)} \log\left(f\right)^{2}\right)} \sqrt{-c \log\left(f\right) - 3 i \, f}}{2 \, {\left(c^{2} \log\left(f\right)^{2} + 9 \, f^{2}\right)}}\right) e^{\left(\frac{36 \, a f^{2} \log\left(f\right) - {\left(b^{2} c - 4 \, a c^{2}\right)} \log\left(f\right)^{3} + 108 i \, d f^{2} + {\left(12 i \, c^{2} d + 3 i \, b^{2} f\right)} \log\left(f\right)^{2}}{4 \, {\left(c^{2} \log\left(f\right)^{2} + 9 \, f^{2}\right)}}\right)} + \sqrt{\pi} {\left(c^{3} \log\left(f\right)^{3} + 3 i \, c^{2} f \log\left(f\right)^{2} + c f^{2} \log\left(f\right) + 3 i \, f^{3}\right)} \sqrt{-c \log\left(f\right) + 3 i \, f} \operatorname{erf}\left(\frac{{\left(18 \, f^{2} x + 3 i \, b f \log\left(f\right) + {\left(2 \, c^{2} x + b c\right)} \log\left(f\right)^{2}\right)} \sqrt{-c \log\left(f\right) + 3 i \, f}}{2 \, {\left(c^{2} \log\left(f\right)^{2} + 9 \, f^{2}\right)}}\right) e^{\left(\frac{36 \, a f^{2} \log\left(f\right) - {\left(b^{2} c - 4 \, a c^{2}\right)} \log\left(f\right)^{3} - 108 i \, d f^{2} + {\left(-12 i \, c^{2} d - 3 i \, b^{2} f\right)} \log\left(f\right)^{2}}{4 \, {\left(c^{2} \log\left(f\right)^{2} + 9 \, f^{2}\right)}}\right)} + \sqrt{\pi} {\left(3 \, c^{3} \log\left(f\right)^{3} - 3 i \, c^{2} f \log\left(f\right)^{2} + 27 \, c f^{2} \log\left(f\right) - 27 i \, f^{3}\right)} \sqrt{-c \log\left(f\right) - i \, f} \operatorname{erf}\left(\frac{{\left(2 \, f^{2} x - i \, b f \log\left(f\right) + {\left(2 \, c^{2} x + b c\right)} \log\left(f\right)^{2}\right)} \sqrt{-c \log\left(f\right) - i \, f}}{2 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}\right) e^{\left(\frac{4 \, a f^{2} \log\left(f\right) - {\left(b^{2} c - 4 \, a c^{2}\right)} \log\left(f\right)^{3} + 4 i \, d f^{2} + {\left(4 i \, c^{2} d + i \, b^{2} f\right)} \log\left(f\right)^{2}}{4 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}\right)} + \sqrt{\pi} {\left(3 \, c^{3} \log\left(f\right)^{3} + 3 i \, c^{2} f \log\left(f\right)^{2} + 27 \, c f^{2} \log\left(f\right) + 27 i \, f^{3}\right)} \sqrt{-c \log\left(f\right) + i \, f} \operatorname{erf}\left(\frac{{\left(2 \, f^{2} x + i \, b f \log\left(f\right) + {\left(2 \, c^{2} x + b c\right)} \log\left(f\right)^{2}\right)} \sqrt{-c \log\left(f\right) + i \, f}}{2 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}\right) e^{\left(\frac{4 \, a f^{2} \log\left(f\right) - {\left(b^{2} c - 4 \, a c^{2}\right)} \log\left(f\right)^{3} - 4 i \, d f^{2} + {\left(-4 i \, c^{2} d - i \, b^{2} f\right)} \log\left(f\right)^{2}}{4 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}\right)}}{16 \, {\left(c^{4} \log\left(f\right)^{4} + 10 \, c^{2} f^{2} \log\left(f\right)^{2} + 9 \, f^{4}\right)}}"," ",0,"-1/16*(sqrt(pi)*(c^3*log(f)^3 - 3*I*c^2*f*log(f)^2 + c*f^2*log(f) - 3*I*f^3)*sqrt(-c*log(f) - 3*I*f)*erf(1/2*(18*f^2*x - 3*I*b*f*log(f) + (2*c^2*x + b*c)*log(f)^2)*sqrt(-c*log(f) - 3*I*f)/(c^2*log(f)^2 + 9*f^2))*e^(1/4*(36*a*f^2*log(f) - (b^2*c - 4*a*c^2)*log(f)^3 + 108*I*d*f^2 + (12*I*c^2*d + 3*I*b^2*f)*log(f)^2)/(c^2*log(f)^2 + 9*f^2)) + sqrt(pi)*(c^3*log(f)^3 + 3*I*c^2*f*log(f)^2 + c*f^2*log(f) + 3*I*f^3)*sqrt(-c*log(f) + 3*I*f)*erf(1/2*(18*f^2*x + 3*I*b*f*log(f) + (2*c^2*x + b*c)*log(f)^2)*sqrt(-c*log(f) + 3*I*f)/(c^2*log(f)^2 + 9*f^2))*e^(1/4*(36*a*f^2*log(f) - (b^2*c - 4*a*c^2)*log(f)^3 - 108*I*d*f^2 + (-12*I*c^2*d - 3*I*b^2*f)*log(f)^2)/(c^2*log(f)^2 + 9*f^2)) + sqrt(pi)*(3*c^3*log(f)^3 - 3*I*c^2*f*log(f)^2 + 27*c*f^2*log(f) - 27*I*f^3)*sqrt(-c*log(f) - I*f)*erf(1/2*(2*f^2*x - I*b*f*log(f) + (2*c^2*x + b*c)*log(f)^2)*sqrt(-c*log(f) - I*f)/(c^2*log(f)^2 + f^2))*e^(1/4*(4*a*f^2*log(f) - (b^2*c - 4*a*c^2)*log(f)^3 + 4*I*d*f^2 + (4*I*c^2*d + I*b^2*f)*log(f)^2)/(c^2*log(f)^2 + f^2)) + sqrt(pi)*(3*c^3*log(f)^3 + 3*I*c^2*f*log(f)^2 + 27*c*f^2*log(f) + 27*I*f^3)*sqrt(-c*log(f) + I*f)*erf(1/2*(2*f^2*x + I*b*f*log(f) + (2*c^2*x + b*c)*log(f)^2)*sqrt(-c*log(f) + I*f)/(c^2*log(f)^2 + f^2))*e^(1/4*(4*a*f^2*log(f) - (b^2*c - 4*a*c^2)*log(f)^3 - 4*I*d*f^2 + (-4*I*c^2*d - I*b^2*f)*log(f)^2)/(c^2*log(f)^2 + f^2)))/(c^4*log(f)^4 + 10*c^2*f^2*log(f)^2 + 9*f^4)","B",0
131,1,377,0,0.712567," ","integrate(f^(c*x^2+b*x+a)*cos(f*x^2+e*x+d),x, algorithm=""fricas"")","-\frac{\sqrt{\pi} {\left(c \log\left(f\right) - i \, f\right)} \sqrt{-c \log\left(f\right) - i \, f} \operatorname{erf}\left(\frac{{\left(2 \, f^{2} x + {\left(2 \, c^{2} x + b c\right)} \log\left(f\right)^{2} + e f + {\left(i \, c e - i \, b f\right)} \log\left(f\right)\right)} \sqrt{-c \log\left(f\right) - i \, f}}{2 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}\right) e^{\left(-\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} \log\left(f\right)^{3} + i \, e^{2} f - 4 i \, d f^{2} - {\left(4 i \, c^{2} d - 2 i \, b c e + i \, b^{2} f\right)} \log\left(f\right)^{2} - {\left(c e^{2} - 2 \, b e f + 4 \, a f^{2}\right)} \log\left(f\right)}{4 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}\right)} + \sqrt{\pi} {\left(c \log\left(f\right) + i \, f\right)} \sqrt{-c \log\left(f\right) + i \, f} \operatorname{erf}\left(\frac{{\left(2 \, f^{2} x + {\left(2 \, c^{2} x + b c\right)} \log\left(f\right)^{2} + e f + {\left(-i \, c e + i \, b f\right)} \log\left(f\right)\right)} \sqrt{-c \log\left(f\right) + i \, f}}{2 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}\right) e^{\left(-\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} \log\left(f\right)^{3} - i \, e^{2} f + 4 i \, d f^{2} - {\left(-4 i \, c^{2} d + 2 i \, b c e - i \, b^{2} f\right)} \log\left(f\right)^{2} - {\left(c e^{2} - 2 \, b e f + 4 \, a f^{2}\right)} \log\left(f\right)}{4 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}\right)}}{4 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}"," ",0,"-1/4*(sqrt(pi)*(c*log(f) - I*f)*sqrt(-c*log(f) - I*f)*erf(1/2*(2*f^2*x + (2*c^2*x + b*c)*log(f)^2 + e*f + (I*c*e - I*b*f)*log(f))*sqrt(-c*log(f) - I*f)/(c^2*log(f)^2 + f^2))*e^(-1/4*((b^2*c - 4*a*c^2)*log(f)^3 + I*e^2*f - 4*I*d*f^2 - (4*I*c^2*d - 2*I*b*c*e + I*b^2*f)*log(f)^2 - (c*e^2 - 2*b*e*f + 4*a*f^2)*log(f))/(c^2*log(f)^2 + f^2)) + sqrt(pi)*(c*log(f) + I*f)*sqrt(-c*log(f) + I*f)*erf(1/2*(2*f^2*x + (2*c^2*x + b*c)*log(f)^2 + e*f + (-I*c*e + I*b*f)*log(f))*sqrt(-c*log(f) + I*f)/(c^2*log(f)^2 + f^2))*e^(-1/4*((b^2*c - 4*a*c^2)*log(f)^3 - I*e^2*f + 4*I*d*f^2 - (-4*I*c^2*d + 2*I*b*c*e - I*b^2*f)*log(f)^2 - (c*e^2 - 2*b*e*f + 4*a*f^2)*log(f))/(c^2*log(f)^2 + f^2)))/(c^2*log(f)^2 + f^2)","B",0
132,1,468,0,0.679385," ","integrate(f^(c*x^2+b*x+a)*cos(f*x^2+e*x+d)^2,x, algorithm=""fricas"")","-\frac{\sqrt{\pi} {\left(c^{2} \log\left(f\right)^{2} - 2 i \, c f \log\left(f\right)\right)} \sqrt{-c \log\left(f\right) - 2 i \, f} \operatorname{erf}\left(\frac{{\left(8 \, f^{2} x + {\left(2 \, c^{2} x + b c\right)} \log\left(f\right)^{2} + 4 \, e f + {\left(2 i \, c e - 2 i \, b f\right)} \log\left(f\right)\right)} \sqrt{-c \log\left(f\right) - 2 i \, f}}{2 \, {\left(c^{2} \log\left(f\right)^{2} + 4 \, f^{2}\right)}}\right) e^{\left(-\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} \log\left(f\right)^{3} + 8 i \, e^{2} f - 32 i \, d f^{2} - {\left(8 i \, c^{2} d - 4 i \, b c e + 2 i \, b^{2} f\right)} \log\left(f\right)^{2} - 4 \, {\left(c e^{2} - 2 \, b e f + 4 \, a f^{2}\right)} \log\left(f\right)}{4 \, {\left(c^{2} \log\left(f\right)^{2} + 4 \, f^{2}\right)}}\right)} + \sqrt{\pi} {\left(c^{2} \log\left(f\right)^{2} + 2 i \, c f \log\left(f\right)\right)} \sqrt{-c \log\left(f\right) + 2 i \, f} \operatorname{erf}\left(\frac{{\left(8 \, f^{2} x + {\left(2 \, c^{2} x + b c\right)} \log\left(f\right)^{2} + 4 \, e f + {\left(-2 i \, c e + 2 i \, b f\right)} \log\left(f\right)\right)} \sqrt{-c \log\left(f\right) + 2 i \, f}}{2 \, {\left(c^{2} \log\left(f\right)^{2} + 4 \, f^{2}\right)}}\right) e^{\left(-\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} \log\left(f\right)^{3} - 8 i \, e^{2} f + 32 i \, d f^{2} - {\left(-8 i \, c^{2} d + 4 i \, b c e - 2 i \, b^{2} f\right)} \log\left(f\right)^{2} - 4 \, {\left(c e^{2} - 2 \, b e f + 4 \, a f^{2}\right)} \log\left(f\right)}{4 \, {\left(c^{2} \log\left(f\right)^{2} + 4 \, f^{2}\right)}}\right)} + \frac{2 \, \sqrt{\pi} {\left(c^{2} \log\left(f\right)^{2} + 4 \, f^{2}\right)} \sqrt{-c \log\left(f\right)} \operatorname{erf}\left(\frac{{\left(2 \, c x + b\right)} \sqrt{-c \log\left(f\right)}}{2 \, c}\right)}{f^{\frac{b^{2} - 4 \, a c}{4 \, c}}}}{8 \, {\left(c^{3} \log\left(f\right)^{3} + 4 \, c f^{2} \log\left(f\right)\right)}}"," ",0,"-1/8*(sqrt(pi)*(c^2*log(f)^2 - 2*I*c*f*log(f))*sqrt(-c*log(f) - 2*I*f)*erf(1/2*(8*f^2*x + (2*c^2*x + b*c)*log(f)^2 + 4*e*f + (2*I*c*e - 2*I*b*f)*log(f))*sqrt(-c*log(f) - 2*I*f)/(c^2*log(f)^2 + 4*f^2))*e^(-1/4*((b^2*c - 4*a*c^2)*log(f)^3 + 8*I*e^2*f - 32*I*d*f^2 - (8*I*c^2*d - 4*I*b*c*e + 2*I*b^2*f)*log(f)^2 - 4*(c*e^2 - 2*b*e*f + 4*a*f^2)*log(f))/(c^2*log(f)^2 + 4*f^2)) + sqrt(pi)*(c^2*log(f)^2 + 2*I*c*f*log(f))*sqrt(-c*log(f) + 2*I*f)*erf(1/2*(8*f^2*x + (2*c^2*x + b*c)*log(f)^2 + 4*e*f + (-2*I*c*e + 2*I*b*f)*log(f))*sqrt(-c*log(f) + 2*I*f)/(c^2*log(f)^2 + 4*f^2))*e^(-1/4*((b^2*c - 4*a*c^2)*log(f)^3 - 8*I*e^2*f + 32*I*d*f^2 - (-8*I*c^2*d + 4*I*b*c*e - 2*I*b^2*f)*log(f)^2 - 4*(c*e^2 - 2*b*e*f + 4*a*f^2)*log(f))/(c^2*log(f)^2 + 4*f^2)) + 2*sqrt(pi)*(c^2*log(f)^2 + 4*f^2)*sqrt(-c*log(f))*erf(1/2*(2*c*x + b)*sqrt(-c*log(f))/c)/f^(1/4*(b^2 - 4*a*c)/c))/(c^3*log(f)^3 + 4*c*f^2*log(f))","B",0
133,1,857,0,0.925820," ","integrate(f^(c*x^2+b*x+a)*cos(f*x^2+e*x+d)^3,x, algorithm=""fricas"")","-\frac{\sqrt{\pi} {\left(c^{3} \log\left(f\right)^{3} - 3 i \, c^{2} f \log\left(f\right)^{2} + c f^{2} \log\left(f\right) - 3 i \, f^{3}\right)} \sqrt{-c \log\left(f\right) - 3 i \, f} \operatorname{erf}\left(\frac{{\left(18 \, f^{2} x + {\left(2 \, c^{2} x + b c\right)} \log\left(f\right)^{2} + 9 \, e f + {\left(3 i \, c e - 3 i \, b f\right)} \log\left(f\right)\right)} \sqrt{-c \log\left(f\right) - 3 i \, f}}{2 \, {\left(c^{2} \log\left(f\right)^{2} + 9 \, f^{2}\right)}}\right) e^{\left(-\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} \log\left(f\right)^{3} + 27 i \, e^{2} f - 108 i \, d f^{2} - {\left(12 i \, c^{2} d - 6 i \, b c e + 3 i \, b^{2} f\right)} \log\left(f\right)^{2} - 9 \, {\left(c e^{2} - 2 \, b e f + 4 \, a f^{2}\right)} \log\left(f\right)}{4 \, {\left(c^{2} \log\left(f\right)^{2} + 9 \, f^{2}\right)}}\right)} + \sqrt{\pi} {\left(3 \, c^{3} \log\left(f\right)^{3} - 3 i \, c^{2} f \log\left(f\right)^{2} + 27 \, c f^{2} \log\left(f\right) - 27 i \, f^{3}\right)} \sqrt{-c \log\left(f\right) - i \, f} \operatorname{erf}\left(\frac{{\left(2 \, f^{2} x + {\left(2 \, c^{2} x + b c\right)} \log\left(f\right)^{2} + e f + {\left(i \, c e - i \, b f\right)} \log\left(f\right)\right)} \sqrt{-c \log\left(f\right) - i \, f}}{2 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}\right) e^{\left(-\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} \log\left(f\right)^{3} + i \, e^{2} f - 4 i \, d f^{2} - {\left(4 i \, c^{2} d - 2 i \, b c e + i \, b^{2} f\right)} \log\left(f\right)^{2} - {\left(c e^{2} - 2 \, b e f + 4 \, a f^{2}\right)} \log\left(f\right)}{4 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}\right)} + \sqrt{\pi} {\left(3 \, c^{3} \log\left(f\right)^{3} + 3 i \, c^{2} f \log\left(f\right)^{2} + 27 \, c f^{2} \log\left(f\right) + 27 i \, f^{3}\right)} \sqrt{-c \log\left(f\right) + i \, f} \operatorname{erf}\left(\frac{{\left(2 \, f^{2} x + {\left(2 \, c^{2} x + b c\right)} \log\left(f\right)^{2} + e f + {\left(-i \, c e + i \, b f\right)} \log\left(f\right)\right)} \sqrt{-c \log\left(f\right) + i \, f}}{2 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}\right) e^{\left(-\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} \log\left(f\right)^{3} - i \, e^{2} f + 4 i \, d f^{2} - {\left(-4 i \, c^{2} d + 2 i \, b c e - i \, b^{2} f\right)} \log\left(f\right)^{2} - {\left(c e^{2} - 2 \, b e f + 4 \, a f^{2}\right)} \log\left(f\right)}{4 \, {\left(c^{2} \log\left(f\right)^{2} + f^{2}\right)}}\right)} + \sqrt{\pi} {\left(c^{3} \log\left(f\right)^{3} + 3 i \, c^{2} f \log\left(f\right)^{2} + c f^{2} \log\left(f\right) + 3 i \, f^{3}\right)} \sqrt{-c \log\left(f\right) + 3 i \, f} \operatorname{erf}\left(\frac{{\left(18 \, f^{2} x + {\left(2 \, c^{2} x + b c\right)} \log\left(f\right)^{2} + 9 \, e f + {\left(-3 i \, c e + 3 i \, b f\right)} \log\left(f\right)\right)} \sqrt{-c \log\left(f\right) + 3 i \, f}}{2 \, {\left(c^{2} \log\left(f\right)^{2} + 9 \, f^{2}\right)}}\right) e^{\left(-\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} \log\left(f\right)^{3} - 27 i \, e^{2} f + 108 i \, d f^{2} - {\left(-12 i \, c^{2} d + 6 i \, b c e - 3 i \, b^{2} f\right)} \log\left(f\right)^{2} - 9 \, {\left(c e^{2} - 2 \, b e f + 4 \, a f^{2}\right)} \log\left(f\right)}{4 \, {\left(c^{2} \log\left(f\right)^{2} + 9 \, f^{2}\right)}}\right)}}{16 \, {\left(c^{4} \log\left(f\right)^{4} + 10 \, c^{2} f^{2} \log\left(f\right)^{2} + 9 \, f^{4}\right)}}"," ",0,"-1/16*(sqrt(pi)*(c^3*log(f)^3 - 3*I*c^2*f*log(f)^2 + c*f^2*log(f) - 3*I*f^3)*sqrt(-c*log(f) - 3*I*f)*erf(1/2*(18*f^2*x + (2*c^2*x + b*c)*log(f)^2 + 9*e*f + (3*I*c*e - 3*I*b*f)*log(f))*sqrt(-c*log(f) - 3*I*f)/(c^2*log(f)^2 + 9*f^2))*e^(-1/4*((b^2*c - 4*a*c^2)*log(f)^3 + 27*I*e^2*f - 108*I*d*f^2 - (12*I*c^2*d - 6*I*b*c*e + 3*I*b^2*f)*log(f)^2 - 9*(c*e^2 - 2*b*e*f + 4*a*f^2)*log(f))/(c^2*log(f)^2 + 9*f^2)) + sqrt(pi)*(3*c^3*log(f)^3 - 3*I*c^2*f*log(f)^2 + 27*c*f^2*log(f) - 27*I*f^3)*sqrt(-c*log(f) - I*f)*erf(1/2*(2*f^2*x + (2*c^2*x + b*c)*log(f)^2 + e*f + (I*c*e - I*b*f)*log(f))*sqrt(-c*log(f) - I*f)/(c^2*log(f)^2 + f^2))*e^(-1/4*((b^2*c - 4*a*c^2)*log(f)^3 + I*e^2*f - 4*I*d*f^2 - (4*I*c^2*d - 2*I*b*c*e + I*b^2*f)*log(f)^2 - (c*e^2 - 2*b*e*f + 4*a*f^2)*log(f))/(c^2*log(f)^2 + f^2)) + sqrt(pi)*(3*c^3*log(f)^3 + 3*I*c^2*f*log(f)^2 + 27*c*f^2*log(f) + 27*I*f^3)*sqrt(-c*log(f) + I*f)*erf(1/2*(2*f^2*x + (2*c^2*x + b*c)*log(f)^2 + e*f + (-I*c*e + I*b*f)*log(f))*sqrt(-c*log(f) + I*f)/(c^2*log(f)^2 + f^2))*e^(-1/4*((b^2*c - 4*a*c^2)*log(f)^3 - I*e^2*f + 4*I*d*f^2 - (-4*I*c^2*d + 2*I*b*c*e - I*b^2*f)*log(f)^2 - (c*e^2 - 2*b*e*f + 4*a*f^2)*log(f))/(c^2*log(f)^2 + f^2)) + sqrt(pi)*(c^3*log(f)^3 + 3*I*c^2*f*log(f)^2 + c*f^2*log(f) + 3*I*f^3)*sqrt(-c*log(f) + 3*I*f)*erf(1/2*(18*f^2*x + (2*c^2*x + b*c)*log(f)^2 + 9*e*f + (-3*I*c*e + 3*I*b*f)*log(f))*sqrt(-c*log(f) + 3*I*f)/(c^2*log(f)^2 + 9*f^2))*e^(-1/4*((b^2*c - 4*a*c^2)*log(f)^3 - 27*I*e^2*f + 108*I*d*f^2 - (-12*I*c^2*d + 6*I*b*c*e - 3*I*b^2*f)*log(f)^2 - 9*(c*e^2 - 2*b*e*f + 4*a*f^2)*log(f))/(c^2*log(f)^2 + 9*f^2)))/(c^4*log(f)^4 + 10*c^2*f^2*log(f)^2 + 9*f^4)","B",0
134,1,381,0,2.131061," ","integrate(f^(c*x^2+b*x+a)*cos(e*x^2+b*x+a),x, algorithm=""fricas"")","-\frac{\sqrt{\pi} {\left(c \log\left(f\right) - i \, e\right)} \sqrt{-c \log\left(f\right) - i \, e} \operatorname{erf}\left(\frac{{\left(2 \, e^{2} x + {\left(2 \, c^{2} x + b c\right)} \log\left(f\right)^{2} + b e + {\left(i \, b c - i \, b e\right)} \log\left(f\right)\right)} \sqrt{-c \log\left(f\right) - i \, e}}{2 \, {\left(c^{2} \log\left(f\right)^{2} + e^{2}\right)}}\right) e^{\left(-\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} \log\left(f\right)^{3} + i \, b^{2} e - 4 i \, a e^{2} - {\left(-2 i \, b^{2} c + 4 i \, a c^{2} + i \, b^{2} e\right)} \log\left(f\right)^{2} - {\left(b^{2} c - 2 \, b^{2} e + 4 \, a e^{2}\right)} \log\left(f\right)}{4 \, {\left(c^{2} \log\left(f\right)^{2} + e^{2}\right)}}\right)} + \sqrt{\pi} {\left(c \log\left(f\right) + i \, e\right)} \sqrt{-c \log\left(f\right) + i \, e} \operatorname{erf}\left(\frac{{\left(2 \, e^{2} x + {\left(2 \, c^{2} x + b c\right)} \log\left(f\right)^{2} + b e + {\left(-i \, b c + i \, b e\right)} \log\left(f\right)\right)} \sqrt{-c \log\left(f\right) + i \, e}}{2 \, {\left(c^{2} \log\left(f\right)^{2} + e^{2}\right)}}\right) e^{\left(-\frac{{\left(b^{2} c - 4 \, a c^{2}\right)} \log\left(f\right)^{3} - i \, b^{2} e + 4 i \, a e^{2} - {\left(2 i \, b^{2} c - 4 i \, a c^{2} - i \, b^{2} e\right)} \log\left(f\right)^{2} - {\left(b^{2} c - 2 \, b^{2} e + 4 \, a e^{2}\right)} \log\left(f\right)}{4 \, {\left(c^{2} \log\left(f\right)^{2} + e^{2}\right)}}\right)}}{4 \, {\left(c^{2} \log\left(f\right)^{2} + e^{2}\right)}}"," ",0,"-1/4*(sqrt(pi)*(c*log(f) - I*e)*sqrt(-c*log(f) - I*e)*erf(1/2*(2*e^2*x + (2*c^2*x + b*c)*log(f)^2 + b*e + (I*b*c - I*b*e)*log(f))*sqrt(-c*log(f) - I*e)/(c^2*log(f)^2 + e^2))*e^(-1/4*((b^2*c - 4*a*c^2)*log(f)^3 + I*b^2*e - 4*I*a*e^2 - (-2*I*b^2*c + 4*I*a*c^2 + I*b^2*e)*log(f)^2 - (b^2*c - 2*b^2*e + 4*a*e^2)*log(f))/(c^2*log(f)^2 + e^2)) + sqrt(pi)*(c*log(f) + I*e)*sqrt(-c*log(f) + I*e)*erf(1/2*(2*e^2*x + (2*c^2*x + b*c)*log(f)^2 + b*e + (-I*b*c + I*b*e)*log(f))*sqrt(-c*log(f) + I*e)/(c^2*log(f)^2 + e^2))*e^(-1/4*((b^2*c - 4*a*c^2)*log(f)^3 - I*b^2*e + 4*I*a*e^2 - (2*I*b^2*c - 4*I*a*c^2 - I*b^2*e)*log(f)^2 - (b^2*c - 2*b^2*e + 4*a*e^2)*log(f))/(c^2*log(f)^2 + e^2)))/(c^2*log(f)^2 + e^2)","B",0
135,1,256,0,0.714608," ","integrate(F^(c*(b*x+a))*(f+f*sin(e*x+d))^2,x, algorithm=""fricas"")","-\frac{{\left(2 \, b^{3} c^{3} e f^{2} \cos\left(e x + d\right) \log\left(F\right)^{3} + 8 \, b c e^{3} f^{2} \cos\left(e x + d\right) \log\left(F\right) - 6 \, e^{4} f^{2} + {\left(b^{4} c^{4} f^{2} \cos\left(e x + d\right)^{2} - 2 \, b^{4} c^{4} f^{2}\right)} \log\left(F\right)^{4} + {\left(b^{2} c^{2} e^{2} f^{2} \cos\left(e x + d\right)^{2} - 8 \, b^{2} c^{2} e^{2} f^{2}\right)} \log\left(F\right)^{2} - 2 \, {\left(b^{4} c^{4} f^{2} \log\left(F\right)^{4} - b^{3} c^{3} e f^{2} \cos\left(e x + d\right) \log\left(F\right)^{3} + 4 \, b^{2} c^{2} e^{2} f^{2} \log\left(F\right)^{2} - b c e^{3} f^{2} \cos\left(e x + d\right) \log\left(F\right)\right)} \sin\left(e x + d\right)\right)} F^{b c x + a c}}{b^{5} c^{5} \log\left(F\right)^{5} + 5 \, b^{3} c^{3} e^{2} \log\left(F\right)^{3} + 4 \, b c e^{4} \log\left(F\right)}"," ",0,"-(2*b^3*c^3*e*f^2*cos(e*x + d)*log(F)^3 + 8*b*c*e^3*f^2*cos(e*x + d)*log(F) - 6*e^4*f^2 + (b^4*c^4*f^2*cos(e*x + d)^2 - 2*b^4*c^4*f^2)*log(F)^4 + (b^2*c^2*e^2*f^2*cos(e*x + d)^2 - 8*b^2*c^2*e^2*f^2)*log(F)^2 - 2*(b^4*c^4*f^2*log(F)^4 - b^3*c^3*e*f^2*cos(e*x + d)*log(F)^3 + 4*b^2*c^2*e^2*f^2*log(F)^2 - b*c*e^3*f^2*cos(e*x + d)*log(F))*sin(e*x + d))*F^(b*c*x + a*c)/(b^5*c^5*log(F)^5 + 5*b^3*c^3*e^2*log(F)^3 + 4*b*c*e^4*log(F))","A",0
136,1,83,0,0.651584," ","integrate(F^(c*(b*x+a))*(f+f*sin(e*x+d)),x, algorithm=""fricas"")","\frac{{\left(b^{2} c^{2} f \log\left(F\right)^{2} \sin\left(e x + d\right) + b^{2} c^{2} f \log\left(F\right)^{2} - b c e f \cos\left(e x + d\right) \log\left(F\right) + e^{2} f\right)} F^{b c x + a c}}{b^{3} c^{3} \log\left(F\right)^{3} + b c e^{2} \log\left(F\right)}"," ",0,"(b^2*c^2*f*log(F)^2*sin(e*x + d) + b^2*c^2*f*log(F)^2 - b*c*e*f*cos(e*x + d)*log(F) + e^2*f)*F^(b*c*x + a*c)/(b^3*c^3*log(F)^3 + b*c*e^2*log(F))","A",0
137,0,0,0,0.768483," ","integrate(F^(c*(b*x+a))/(f+f*sin(e*x+d)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{F^{b c x + a c}}{f \sin\left(e x + d\right) + f}, x\right)"," ",0,"integral(F^(b*c*x + a*c)/(f*sin(e*x + d) + f), x)","F",0
138,0,0,0,0.599522," ","integrate(F^(c*(b*x+a))/(f+f*sin(e*x+d))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{F^{b c x + a c}}{f^{2} \cos\left(e x + d\right)^{2} - 2 \, f^{2} \sin\left(e x + d\right) - 2 \, f^{2}}, x\right)"," ",0,"integral(-F^(b*c*x + a*c)/(f^2*cos(e*x + d)^2 - 2*f^2*sin(e*x + d) - 2*f^2), x)","F",0
139,1,242,0,1.386742," ","integrate(F^(c*(b*x+a))*(f+f*cos(e*x+d))^2,x, algorithm=""fricas"")","\frac{{\left(6 \, e^{4} f^{2} + {\left(b^{4} c^{4} f^{2} \cos\left(e x + d\right)^{2} + 2 \, b^{4} c^{4} f^{2} \cos\left(e x + d\right) + b^{4} c^{4} f^{2}\right)} \log\left(F\right)^{4} + {\left(b^{2} c^{2} e^{2} f^{2} \cos\left(e x + d\right)^{2} + 8 \, b^{2} c^{2} e^{2} f^{2} \cos\left(e x + d\right) + 7 \, b^{2} c^{2} e^{2} f^{2}\right)} \log\left(F\right)^{2} + 2 \, {\left({\left(b^{3} c^{3} e f^{2} \cos\left(e x + d\right) + b^{3} c^{3} e f^{2}\right)} \log\left(F\right)^{3} + {\left(b c e^{3} f^{2} \cos\left(e x + d\right) + 4 \, b c e^{3} f^{2}\right)} \log\left(F\right)\right)} \sin\left(e x + d\right)\right)} F^{b c x + a c}}{b^{5} c^{5} \log\left(F\right)^{5} + 5 \, b^{3} c^{3} e^{2} \log\left(F\right)^{3} + 4 \, b c e^{4} \log\left(F\right)}"," ",0,"(6*e^4*f^2 + (b^4*c^4*f^2*cos(e*x + d)^2 + 2*b^4*c^4*f^2*cos(e*x + d) + b^4*c^4*f^2)*log(F)^4 + (b^2*c^2*e^2*f^2*cos(e*x + d)^2 + 8*b^2*c^2*e^2*f^2*cos(e*x + d) + 7*b^2*c^2*e^2*f^2)*log(F)^2 + 2*((b^3*c^3*e*f^2*cos(e*x + d) + b^3*c^3*e*f^2)*log(F)^3 + (b*c*e^3*f^2*cos(e*x + d) + 4*b*c*e^3*f^2)*log(F))*sin(e*x + d))*F^(b*c*x + a*c)/(b^5*c^5*log(F)^5 + 5*b^3*c^3*e^2*log(F)^3 + 4*b*c*e^4*log(F))","A",0
140,1,80,0,0.699449," ","integrate(F^(c*(b*x+a))*(f+f*cos(e*x+d)),x, algorithm=""fricas"")","\frac{{\left(b c e f \log\left(F\right) \sin\left(e x + d\right) + e^{2} f + {\left(b^{2} c^{2} f \cos\left(e x + d\right) + b^{2} c^{2} f\right)} \log\left(F\right)^{2}\right)} F^{b c x + a c}}{b^{3} c^{3} \log\left(F\right)^{3} + b c e^{2} \log\left(F\right)}"," ",0,"(b*c*e*f*log(F)*sin(e*x + d) + e^2*f + (b^2*c^2*f*cos(e*x + d) + b^2*c^2*f)*log(F)^2)*F^(b*c*x + a*c)/(b^3*c^3*log(F)^3 + b*c*e^2*log(F))","A",0
141,0,0,0,0.564623," ","integrate(F^(c*(b*x+a))/(f+f*cos(e*x+d)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{F^{b c x + a c}}{f \cos\left(e x + d\right) + f}, x\right)"," ",0,"integral(F^(b*c*x + a*c)/(f*cos(e*x + d) + f), x)","F",0
142,0,0,0,0.599474," ","integrate(F^(c*(b*x+a))/(f+f*cos(e*x+d))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{F^{b c x + a c}}{f^{2} \cos\left(e x + d\right)^{2} + 2 \, f^{2} \cos\left(e x + d\right) + f^{2}}, x\right)"," ",0,"integral(F^(b*c*x + a*c)/(f^2*cos(e*x + d)^2 + 2*f^2*cos(e*x + d) + f^2), x)","F",0
