1,1,755,0,0.652572," ","integrate(x^2*cosh(c*x^2+b*x+a),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \cosh\left(c x^{2} + b x + a\right) + \frac{{\left(\frac{\sqrt{\pi} {\left(2 \, c x + b\right)} b^{3} {\left(\operatorname{erf}\left(\frac{1}{2} \, \sqrt{-\frac{{\left(2 \, c x + b\right)}^{2}}{c}}\right) - 1\right)}}{\sqrt{-\frac{{\left(2 \, c x + b\right)}^{2}}{c}} c^{\frac{7}{2}}} - \frac{6 \, b^{2} e^{\left(\frac{{\left(2 \, c x + b\right)}^{2}}{4 \, c}\right)}}{c^{\frac{5}{2}}} - \frac{12 \, {\left(2 \, c x + b\right)}^{3} b \Gamma\left(\frac{3}{2}, -\frac{{\left(2 \, c x + b\right)}^{2}}{4 \, c}\right)}{\left(-\frac{{\left(2 \, c x + b\right)}^{2}}{c}\right)^{\frac{3}{2}} c^{\frac{7}{2}}} + \frac{8 \, \Gamma\left(2, -\frac{{\left(2 \, c x + b\right)}^{2}}{4 \, c}\right)}{c^{\frac{3}{2}}}\right)} b e^{\left(a - \frac{b^{2}}{4 \, c}\right)}}{96 \, \sqrt{c}} - \frac{1}{96} \, {\left(\frac{\sqrt{\pi} {\left(2 \, c x + b\right)} b^{4} {\left(\operatorname{erf}\left(\frac{1}{2} \, \sqrt{-\frac{{\left(2 \, c x + b\right)}^{2}}{c}}\right) - 1\right)}}{\sqrt{-\frac{{\left(2 \, c x + b\right)}^{2}}{c}} c^{\frac{9}{2}}} - \frac{8 \, b^{3} e^{\left(\frac{{\left(2 \, c x + b\right)}^{2}}{4 \, c}\right)}}{c^{\frac{7}{2}}} - \frac{24 \, {\left(2 \, c x + b\right)}^{3} b^{2} \Gamma\left(\frac{3}{2}, -\frac{{\left(2 \, c x + b\right)}^{2}}{4 \, c}\right)}{\left(-\frac{{\left(2 \, c x + b\right)}^{2}}{c}\right)^{\frac{3}{2}} c^{\frac{9}{2}}} + \frac{32 \, b \Gamma\left(2, -\frac{{\left(2 \, c x + b\right)}^{2}}{4 \, c}\right)}{c^{\frac{5}{2}}} - \frac{16 \, {\left(2 \, c x + b\right)}^{5} \Gamma\left(\frac{5}{2}, -\frac{{\left(2 \, c x + b\right)}^{2}}{4 \, c}\right)}{\left(-\frac{{\left(2 \, c x + b\right)}^{2}}{c}\right)^{\frac{5}{2}} c^{\frac{9}{2}}}\right)} \sqrt{c} e^{\left(a - \frac{b^{2}}{4 \, c}\right)} - \frac{{\left(\frac{\sqrt{\pi} {\left(2 \, c x + b\right)} b^{3} {\left(\operatorname{erf}\left(\frac{1}{2} \, \sqrt{\frac{{\left(2 \, c x + b\right)}^{2}}{c}}\right) - 1\right)}}{\sqrt{\frac{{\left(2 \, c x + b\right)}^{2}}{c}} \left(-c\right)^{\frac{7}{2}}} + \frac{6 \, b^{2} c e^{\left(-\frac{{\left(2 \, c x + b\right)}^{2}}{4 \, c}\right)}}{\left(-c\right)^{\frac{7}{2}}} - \frac{12 \, {\left(2 \, c x + b\right)}^{3} b \Gamma\left(\frac{3}{2}, \frac{{\left(2 \, c x + b\right)}^{2}}{4 \, c}\right)}{\left(\frac{{\left(2 \, c x + b\right)}^{2}}{c}\right)^{\frac{3}{2}} \left(-c\right)^{\frac{7}{2}}} + \frac{8 \, c^{2} \Gamma\left(2, \frac{{\left(2 \, c x + b\right)}^{2}}{4 \, c}\right)}{\left(-c\right)^{\frac{7}{2}}}\right)} b e^{\left(-a + \frac{b^{2}}{4 \, c}\right)}}{96 \, \sqrt{-c}} - \frac{{\left(\frac{\sqrt{\pi} {\left(2 \, c x + b\right)} b^{4} {\left(\operatorname{erf}\left(\frac{1}{2} \, \sqrt{\frac{{\left(2 \, c x + b\right)}^{2}}{c}}\right) - 1\right)}}{\sqrt{\frac{{\left(2 \, c x + b\right)}^{2}}{c}} \left(-c\right)^{\frac{9}{2}}} + \frac{8 \, b^{3} c e^{\left(-\frac{{\left(2 \, c x + b\right)}^{2}}{4 \, c}\right)}}{\left(-c\right)^{\frac{9}{2}}} - \frac{24 \, {\left(2 \, c x + b\right)}^{3} b^{2} \Gamma\left(\frac{3}{2}, \frac{{\left(2 \, c x + b\right)}^{2}}{4 \, c}\right)}{\left(\frac{{\left(2 \, c x + b\right)}^{2}}{c}\right)^{\frac{3}{2}} \left(-c\right)^{\frac{9}{2}}} + \frac{32 \, b c^{2} \Gamma\left(2, \frac{{\left(2 \, c x + b\right)}^{2}}{4 \, c}\right)}{\left(-c\right)^{\frac{9}{2}}} - \frac{16 \, {\left(2 \, c x + b\right)}^{5} \Gamma\left(\frac{5}{2}, \frac{{\left(2 \, c x + b\right)}^{2}}{4 \, c}\right)}{\left(\frac{{\left(2 \, c x + b\right)}^{2}}{c}\right)^{\frac{5}{2}} \left(-c\right)^{\frac{9}{2}}}\right)} c e^{\left(-a + \frac{b^{2}}{4 \, c}\right)}}{96 \, \sqrt{-c}}"," ",0,"1/3*x^3*cosh(c*x^2 + b*x + a) + 1/96*(sqrt(pi)*(2*c*x + b)*b^3*(erf(1/2*sqrt(-(2*c*x + b)^2/c)) - 1)/(sqrt(-(2*c*x + b)^2/c)*c^(7/2)) - 6*b^2*e^(1/4*(2*c*x + b)^2/c)/c^(5/2) - 12*(2*c*x + b)^3*b*gamma(3/2, -1/4*(2*c*x + b)^2/c)/((-(2*c*x + b)^2/c)^(3/2)*c^(7/2)) + 8*gamma(2, -1/4*(2*c*x + b)^2/c)/c^(3/2))*b*e^(a - 1/4*b^2/c)/sqrt(c) - 1/96*(sqrt(pi)*(2*c*x + b)*b^4*(erf(1/2*sqrt(-(2*c*x + b)^2/c)) - 1)/(sqrt(-(2*c*x + b)^2/c)*c^(9/2)) - 8*b^3*e^(1/4*(2*c*x + b)^2/c)/c^(7/2) - 24*(2*c*x + b)^3*b^2*gamma(3/2, -1/4*(2*c*x + b)^2/c)/((-(2*c*x + b)^2/c)^(3/2)*c^(9/2)) + 32*b*gamma(2, -1/4*(2*c*x + b)^2/c)/c^(5/2) - 16*(2*c*x + b)^5*gamma(5/2, -1/4*(2*c*x + b)^2/c)/((-(2*c*x + b)^2/c)^(5/2)*c^(9/2)))*sqrt(c)*e^(a - 1/4*b^2/c) - 1/96*(sqrt(pi)*(2*c*x + b)*b^3*(erf(1/2*sqrt((2*c*x + b)^2/c)) - 1)/(sqrt((2*c*x + b)^2/c)*(-c)^(7/2)) + 6*b^2*c*e^(-1/4*(2*c*x + b)^2/c)/(-c)^(7/2) - 12*(2*c*x + b)^3*b*gamma(3/2, 1/4*(2*c*x + b)^2/c)/(((2*c*x + b)^2/c)^(3/2)*(-c)^(7/2)) + 8*c^2*gamma(2, 1/4*(2*c*x + b)^2/c)/(-c)^(7/2))*b*e^(-a + 1/4*b^2/c)/sqrt(-c) - 1/96*(sqrt(pi)*(2*c*x + b)*b^4*(erf(1/2*sqrt((2*c*x + b)^2/c)) - 1)/(sqrt((2*c*x + b)^2/c)*(-c)^(9/2)) + 8*b^3*c*e^(-1/4*(2*c*x + b)^2/c)/(-c)^(9/2) - 24*(2*c*x + b)^3*b^2*gamma(3/2, 1/4*(2*c*x + b)^2/c)/(((2*c*x + b)^2/c)^(3/2)*(-c)^(9/2)) + 32*b*c^2*gamma(2, 1/4*(2*c*x + b)^2/c)/(-c)^(9/2) - 16*(2*c*x + b)^5*gamma(5/2, 1/4*(2*c*x + b)^2/c)/(((2*c*x + b)^2/c)^(5/2)*(-c)^(9/2)))*c*e^(-a + 1/4*b^2/c)/sqrt(-c)","B",0
2,1,611,0,0.611471," ","integrate(x*cosh(c*x^2+b*x+a),x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \cosh\left(c x^{2} + b x + a\right) - \frac{{\left(\frac{\sqrt{\pi} {\left(2 \, c x + b\right)} b^{2} {\left(\operatorname{erf}\left(\frac{1}{2} \, \sqrt{-\frac{{\left(2 \, c x + b\right)}^{2}}{c}}\right) - 1\right)}}{\sqrt{-\frac{{\left(2 \, c x + b\right)}^{2}}{c}} c^{\frac{5}{2}}} - \frac{4 \, b e^{\left(\frac{{\left(2 \, c x + b\right)}^{2}}{4 \, c}\right)}}{c^{\frac{3}{2}}} - \frac{4 \, {\left(2 \, c x + b\right)}^{3} \Gamma\left(\frac{3}{2}, -\frac{{\left(2 \, c x + b\right)}^{2}}{4 \, c}\right)}{\left(-\frac{{\left(2 \, c x + b\right)}^{2}}{c}\right)^{\frac{3}{2}} c^{\frac{5}{2}}}\right)} b e^{\left(a - \frac{b^{2}}{4 \, c}\right)}}{32 \, \sqrt{c}} + \frac{1}{32} \, {\left(\frac{\sqrt{\pi} {\left(2 \, c x + b\right)} b^{3} {\left(\operatorname{erf}\left(\frac{1}{2} \, \sqrt{-\frac{{\left(2 \, c x + b\right)}^{2}}{c}}\right) - 1\right)}}{\sqrt{-\frac{{\left(2 \, c x + b\right)}^{2}}{c}} c^{\frac{7}{2}}} - \frac{6 \, b^{2} e^{\left(\frac{{\left(2 \, c x + b\right)}^{2}}{4 \, c}\right)}}{c^{\frac{5}{2}}} - \frac{12 \, {\left(2 \, c x + b\right)}^{3} b \Gamma\left(\frac{3}{2}, -\frac{{\left(2 \, c x + b\right)}^{2}}{4 \, c}\right)}{\left(-\frac{{\left(2 \, c x + b\right)}^{2}}{c}\right)^{\frac{3}{2}} c^{\frac{7}{2}}} + \frac{8 \, \Gamma\left(2, -\frac{{\left(2 \, c x + b\right)}^{2}}{4 \, c}\right)}{c^{\frac{3}{2}}}\right)} \sqrt{c} e^{\left(a - \frac{b^{2}}{4 \, c}\right)} - \frac{{\left(\frac{\sqrt{\pi} {\left(2 \, c x + b\right)} b^{2} {\left(\operatorname{erf}\left(\frac{1}{2} \, \sqrt{\frac{{\left(2 \, c x + b\right)}^{2}}{c}}\right) - 1\right)}}{\sqrt{\frac{{\left(2 \, c x + b\right)}^{2}}{c}} \left(-c\right)^{\frac{5}{2}}} + \frac{4 \, b c e^{\left(-\frac{{\left(2 \, c x + b\right)}^{2}}{4 \, c}\right)}}{\left(-c\right)^{\frac{5}{2}}} - \frac{4 \, {\left(2 \, c x + b\right)}^{3} \Gamma\left(\frac{3}{2}, \frac{{\left(2 \, c x + b\right)}^{2}}{4 \, c}\right)}{\left(\frac{{\left(2 \, c x + b\right)}^{2}}{c}\right)^{\frac{3}{2}} \left(-c\right)^{\frac{5}{2}}}\right)} b e^{\left(-a + \frac{b^{2}}{4 \, c}\right)}}{32 \, \sqrt{-c}} - \frac{{\left(\frac{\sqrt{\pi} {\left(2 \, c x + b\right)} b^{3} {\left(\operatorname{erf}\left(\frac{1}{2} \, \sqrt{\frac{{\left(2 \, c x + b\right)}^{2}}{c}}\right) - 1\right)}}{\sqrt{\frac{{\left(2 \, c x + b\right)}^{2}}{c}} \left(-c\right)^{\frac{7}{2}}} + \frac{6 \, b^{2} c e^{\left(-\frac{{\left(2 \, c x + b\right)}^{2}}{4 \, c}\right)}}{\left(-c\right)^{\frac{7}{2}}} - \frac{12 \, {\left(2 \, c x + b\right)}^{3} b \Gamma\left(\frac{3}{2}, \frac{{\left(2 \, c x + b\right)}^{2}}{4 \, c}\right)}{\left(\frac{{\left(2 \, c x + b\right)}^{2}}{c}\right)^{\frac{3}{2}} \left(-c\right)^{\frac{7}{2}}} + \frac{8 \, c^{2} \Gamma\left(2, \frac{{\left(2 \, c x + b\right)}^{2}}{4 \, c}\right)}{\left(-c\right)^{\frac{7}{2}}}\right)} c e^{\left(-a + \frac{b^{2}}{4 \, c}\right)}}{32 \, \sqrt{-c}}"," ",0,"1/2*x^2*cosh(c*x^2 + b*x + a) - 1/32*(sqrt(pi)*(2*c*x + b)*b^2*(erf(1/2*sqrt(-(2*c*x + b)^2/c)) - 1)/(sqrt(-(2*c*x + b)^2/c)*c^(5/2)) - 4*b*e^(1/4*(2*c*x + b)^2/c)/c^(3/2) - 4*(2*c*x + b)^3*gamma(3/2, -1/4*(2*c*x + b)^2/c)/((-(2*c*x + b)^2/c)^(3/2)*c^(5/2)))*b*e^(a - 1/4*b^2/c)/sqrt(c) + 1/32*(sqrt(pi)*(2*c*x + b)*b^3*(erf(1/2*sqrt(-(2*c*x + b)^2/c)) - 1)/(sqrt(-(2*c*x + b)^2/c)*c^(7/2)) - 6*b^2*e^(1/4*(2*c*x + b)^2/c)/c^(5/2) - 12*(2*c*x + b)^3*b*gamma(3/2, -1/4*(2*c*x + b)^2/c)/((-(2*c*x + b)^2/c)^(3/2)*c^(7/2)) + 8*gamma(2, -1/4*(2*c*x + b)^2/c)/c^(3/2))*sqrt(c)*e^(a - 1/4*b^2/c) - 1/32*(sqrt(pi)*(2*c*x + b)*b^2*(erf(1/2*sqrt((2*c*x + b)^2/c)) - 1)/(sqrt((2*c*x + b)^2/c)*(-c)^(5/2)) + 4*b*c*e^(-1/4*(2*c*x + b)^2/c)/(-c)^(5/2) - 4*(2*c*x + b)^3*gamma(3/2, 1/4*(2*c*x + b)^2/c)/(((2*c*x + b)^2/c)^(3/2)*(-c)^(5/2)))*b*e^(-a + 1/4*b^2/c)/sqrt(-c) - 1/32*(sqrt(pi)*(2*c*x + b)*b^3*(erf(1/2*sqrt((2*c*x + b)^2/c)) - 1)/(sqrt((2*c*x + b)^2/c)*(-c)^(7/2)) + 6*b^2*c*e^(-1/4*(2*c*x + b)^2/c)/(-c)^(7/2) - 12*(2*c*x + b)^3*b*gamma(3/2, 1/4*(2*c*x + b)^2/c)/(((2*c*x + b)^2/c)^(3/2)*(-c)^(7/2)) + 8*c^2*gamma(2, 1/4*(2*c*x + b)^2/c)/(-c)^(7/2))*c*e^(-a + 1/4*b^2/c)/sqrt(-c)","B",0
3,1,464,0,0.545636," ","integrate(cosh(c*x^2+b*x+a),x, algorithm=""maxima"")","\frac{{\left(\frac{\sqrt{\pi} {\left(2 \, c x + b\right)} b {\left(\operatorname{erf}\left(\frac{1}{2} \, \sqrt{-\frac{{\left(2 \, c x + b\right)}^{2}}{c}}\right) - 1\right)}}{\sqrt{-\frac{{\left(2 \, c x + b\right)}^{2}}{c}} c^{\frac{3}{2}}} - \frac{2 \, e^{\left(\frac{{\left(2 \, c x + b\right)}^{2}}{4 \, c}\right)}}{\sqrt{c}}\right)} b e^{\left(a - \frac{b^{2}}{4 \, c}\right)}}{8 \, \sqrt{c}} - \frac{1}{8} \, {\left(\frac{\sqrt{\pi} {\left(2 \, c x + b\right)} b^{2} {\left(\operatorname{erf}\left(\frac{1}{2} \, \sqrt{-\frac{{\left(2 \, c x + b\right)}^{2}}{c}}\right) - 1\right)}}{\sqrt{-\frac{{\left(2 \, c x + b\right)}^{2}}{c}} c^{\frac{5}{2}}} - \frac{4 \, b e^{\left(\frac{{\left(2 \, c x + b\right)}^{2}}{4 \, c}\right)}}{c^{\frac{3}{2}}} - \frac{4 \, {\left(2 \, c x + b\right)}^{3} \Gamma\left(\frac{3}{2}, -\frac{{\left(2 \, c x + b\right)}^{2}}{4 \, c}\right)}{\left(-\frac{{\left(2 \, c x + b\right)}^{2}}{c}\right)^{\frac{3}{2}} c^{\frac{5}{2}}}\right)} \sqrt{c} e^{\left(a - \frac{b^{2}}{4 \, c}\right)} - \frac{{\left(\frac{\sqrt{\pi} {\left(2 \, c x + b\right)} b {\left(\operatorname{erf}\left(\frac{1}{2} \, \sqrt{\frac{{\left(2 \, c x + b\right)}^{2}}{c}}\right) - 1\right)}}{\sqrt{\frac{{\left(2 \, c x + b\right)}^{2}}{c}} \left(-c\right)^{\frac{3}{2}}} + \frac{2 \, c e^{\left(-\frac{{\left(2 \, c x + b\right)}^{2}}{4 \, c}\right)}}{\left(-c\right)^{\frac{3}{2}}}\right)} b e^{\left(-a + \frac{b^{2}}{4 \, c}\right)}}{8 \, \sqrt{-c}} - \frac{{\left(\frac{\sqrt{\pi} {\left(2 \, c x + b\right)} b^{2} {\left(\operatorname{erf}\left(\frac{1}{2} \, \sqrt{\frac{{\left(2 \, c x + b\right)}^{2}}{c}}\right) - 1\right)}}{\sqrt{\frac{{\left(2 \, c x + b\right)}^{2}}{c}} \left(-c\right)^{\frac{5}{2}}} + \frac{4 \, b c e^{\left(-\frac{{\left(2 \, c x + b\right)}^{2}}{4 \, c}\right)}}{\left(-c\right)^{\frac{5}{2}}} - \frac{4 \, {\left(2 \, c x + b\right)}^{3} \Gamma\left(\frac{3}{2}, \frac{{\left(2 \, c x + b\right)}^{2}}{4 \, c}\right)}{\left(\frac{{\left(2 \, c x + b\right)}^{2}}{c}\right)^{\frac{3}{2}} \left(-c\right)^{\frac{5}{2}}}\right)} c e^{\left(-a + \frac{b^{2}}{4 \, c}\right)}}{8 \, \sqrt{-c}} + x \cosh\left(c x^{2} + b x + a\right)"," ",0,"1/8*(sqrt(pi)*(2*c*x + b)*b*(erf(1/2*sqrt(-(2*c*x + b)^2/c)) - 1)/(sqrt(-(2*c*x + b)^2/c)*c^(3/2)) - 2*e^(1/4*(2*c*x + b)^2/c)/sqrt(c))*b*e^(a - 1/4*b^2/c)/sqrt(c) - 1/8*(sqrt(pi)*(2*c*x + b)*b^2*(erf(1/2*sqrt(-(2*c*x + b)^2/c)) - 1)/(sqrt(-(2*c*x + b)^2/c)*c^(5/2)) - 4*b*e^(1/4*(2*c*x + b)^2/c)/c^(3/2) - 4*(2*c*x + b)^3*gamma(3/2, -1/4*(2*c*x + b)^2/c)/((-(2*c*x + b)^2/c)^(3/2)*c^(5/2)))*sqrt(c)*e^(a - 1/4*b^2/c) - 1/8*(sqrt(pi)*(2*c*x + b)*b*(erf(1/2*sqrt((2*c*x + b)^2/c)) - 1)/(sqrt((2*c*x + b)^2/c)*(-c)^(3/2)) + 2*c*e^(-1/4*(2*c*x + b)^2/c)/(-c)^(3/2))*b*e^(-a + 1/4*b^2/c)/sqrt(-c) - 1/8*(sqrt(pi)*(2*c*x + b)*b^2*(erf(1/2*sqrt((2*c*x + b)^2/c)) - 1)/(sqrt((2*c*x + b)^2/c)*(-c)^(5/2)) + 4*b*c*e^(-1/4*(2*c*x + b)^2/c)/(-c)^(5/2) - 4*(2*c*x + b)^3*gamma(3/2, 1/4*(2*c*x + b)^2/c)/(((2*c*x + b)^2/c)^(3/2)*(-c)^(5/2)))*c*e^(-a + 1/4*b^2/c)/sqrt(-c) + x*cosh(c*x^2 + b*x + a)","B",0
4,0,0,0,0.000000," ","integrate(cosh(c*x^2+b*x+a)/x,x, algorithm=""maxima"")","\int \frac{\cosh\left(c x^{2} + b x + a\right)}{x}\,{d x}"," ",0,"integrate(cosh(c*x^2 + b*x + a)/x, x)","F",0
5,0,0,0,0.000000," ","integrate(cosh(c*x^2+b*x+a)/x^2-b*sinh(c*x^2+b*x+a)/x,x, algorithm=""maxima"")","\int -\frac{b \sinh\left(c x^{2} + b x + a\right)}{x} + \frac{\cosh\left(c x^{2} + b x + a\right)}{x^{2}}\,{d x}"," ",0,"integrate(-b*sinh(c*x^2 + b*x + a)/x + cosh(c*x^2 + b*x + a)/x^2, x)","F",0
6,1,834,0,0.661324," ","integrate(x^2*cosh(-c*x^2+b*x+a),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \cosh\left(c x^{2} - b x - a\right) - \frac{{\left(\frac{\sqrt{\pi} {\left(2 \, c x - b\right)} b^{3} {\left(\operatorname{erf}\left(\frac{1}{2} \, \sqrt{\frac{{\left(2 \, c x - b\right)}^{2}}{c}}\right) - 1\right)}}{\sqrt{\frac{{\left(2 \, c x - b\right)}^{2}}{c}} \left(-c\right)^{\frac{7}{2}}} - \frac{6 \, b^{2} c e^{\left(-\frac{{\left(2 \, c x - b\right)}^{2}}{4 \, c}\right)}}{\left(-c\right)^{\frac{7}{2}}} - \frac{12 \, {\left(2 \, c x - b\right)}^{3} b \Gamma\left(\frac{3}{2}, \frac{{\left(2 \, c x - b\right)}^{2}}{4 \, c}\right)}{\left(\frac{{\left(2 \, c x - b\right)}^{2}}{c}\right)^{\frac{3}{2}} \left(-c\right)^{\frac{7}{2}}} - \frac{8 \, c^{2} \Gamma\left(2, \frac{{\left(2 \, c x - b\right)}^{2}}{4 \, c}\right)}{\left(-c\right)^{\frac{7}{2}}}\right)} b e^{\left(a + \frac{b^{2}}{4 \, c}\right)}}{96 \, \sqrt{-c}} - \frac{{\left(\frac{\sqrt{\pi} {\left(2 \, c x - b\right)} b^{4} {\left(\operatorname{erf}\left(\frac{1}{2} \, \sqrt{\frac{{\left(2 \, c x - b\right)}^{2}}{c}}\right) - 1\right)}}{\sqrt{\frac{{\left(2 \, c x - b\right)}^{2}}{c}} \left(-c\right)^{\frac{9}{2}}} - \frac{8 \, b^{3} c e^{\left(-\frac{{\left(2 \, c x - b\right)}^{2}}{4 \, c}\right)}}{\left(-c\right)^{\frac{9}{2}}} - \frac{24 \, {\left(2 \, c x - b\right)}^{3} b^{2} \Gamma\left(\frac{3}{2}, \frac{{\left(2 \, c x - b\right)}^{2}}{4 \, c}\right)}{\left(\frac{{\left(2 \, c x - b\right)}^{2}}{c}\right)^{\frac{3}{2}} \left(-c\right)^{\frac{9}{2}}} - \frac{32 \, b c^{2} \Gamma\left(2, \frac{{\left(2 \, c x - b\right)}^{2}}{4 \, c}\right)}{\left(-c\right)^{\frac{9}{2}}} - \frac{16 \, {\left(2 \, c x - b\right)}^{5} \Gamma\left(\frac{5}{2}, \frac{{\left(2 \, c x - b\right)}^{2}}{4 \, c}\right)}{\left(\frac{{\left(2 \, c x - b\right)}^{2}}{c}\right)^{\frac{5}{2}} \left(-c\right)^{\frac{9}{2}}}\right)} c e^{\left(a + \frac{b^{2}}{4 \, c}\right)}}{96 \, \sqrt{-c}} + \frac{{\left(\frac{\sqrt{\pi} {\left(2 \, c x - b\right)} b^{3} {\left(\operatorname{erf}\left(\frac{1}{2} \, \sqrt{-\frac{{\left(2 \, c x - b\right)}^{2}}{c}}\right) - 1\right)}}{\sqrt{-\frac{{\left(2 \, c x - b\right)}^{2}}{c}} c^{\frac{7}{2}}} + \frac{6 \, b^{2} e^{\left(\frac{{\left(2 \, c x - b\right)}^{2}}{4 \, c}\right)}}{c^{\frac{5}{2}}} - \frac{12 \, {\left(2 \, c x - b\right)}^{3} b \Gamma\left(\frac{3}{2}, -\frac{{\left(2 \, c x - b\right)}^{2}}{4 \, c}\right)}{\left(-\frac{{\left(2 \, c x - b\right)}^{2}}{c}\right)^{\frac{3}{2}} c^{\frac{7}{2}}} - \frac{8 \, \Gamma\left(2, -\frac{{\left(2 \, c x - b\right)}^{2}}{4 \, c}\right)}{c^{\frac{3}{2}}}\right)} b e^{\left(-a - \frac{b^{2}}{4 \, c}\right)}}{96 \, \sqrt{c}} - \frac{1}{96} \, {\left(\frac{\sqrt{\pi} {\left(2 \, c x - b\right)} b^{4} {\left(\operatorname{erf}\left(\frac{1}{2} \, \sqrt{-\frac{{\left(2 \, c x - b\right)}^{2}}{c}}\right) - 1\right)}}{\sqrt{-\frac{{\left(2 \, c x - b\right)}^{2}}{c}} c^{\frac{9}{2}}} + \frac{8 \, b^{3} e^{\left(\frac{{\left(2 \, c x - b\right)}^{2}}{4 \, c}\right)}}{c^{\frac{7}{2}}} - \frac{24 \, {\left(2 \, c x - b\right)}^{3} b^{2} \Gamma\left(\frac{3}{2}, -\frac{{\left(2 \, c x - b\right)}^{2}}{4 \, c}\right)}{\left(-\frac{{\left(2 \, c x - b\right)}^{2}}{c}\right)^{\frac{3}{2}} c^{\frac{9}{2}}} - \frac{32 \, b \Gamma\left(2, -\frac{{\left(2 \, c x - b\right)}^{2}}{4 \, c}\right)}{c^{\frac{5}{2}}} - \frac{16 \, {\left(2 \, c x - b\right)}^{5} \Gamma\left(\frac{5}{2}, -\frac{{\left(2 \, c x - b\right)}^{2}}{4 \, c}\right)}{\left(-\frac{{\left(2 \, c x - b\right)}^{2}}{c}\right)^{\frac{5}{2}} c^{\frac{9}{2}}}\right)} \sqrt{c} e^{\left(-a - \frac{b^{2}}{4 \, c}\right)}"," ",0,"1/3*x^3*cosh(c*x^2 - b*x - a) - 1/96*(sqrt(pi)*(2*c*x - b)*b^3*(erf(1/2*sqrt((2*c*x - b)^2/c)) - 1)/(sqrt((2*c*x - b)^2/c)*(-c)^(7/2)) - 6*b^2*c*e^(-1/4*(2*c*x - b)^2/c)/(-c)^(7/2) - 12*(2*c*x - b)^3*b*gamma(3/2, 1/4*(2*c*x - b)^2/c)/(((2*c*x - b)^2/c)^(3/2)*(-c)^(7/2)) - 8*c^2*gamma(2, 1/4*(2*c*x - b)^2/c)/(-c)^(7/2))*b*e^(a + 1/4*b^2/c)/sqrt(-c) - 1/96*(sqrt(pi)*(2*c*x - b)*b^4*(erf(1/2*sqrt((2*c*x - b)^2/c)) - 1)/(sqrt((2*c*x - b)^2/c)*(-c)^(9/2)) - 8*b^3*c*e^(-1/4*(2*c*x - b)^2/c)/(-c)^(9/2) - 24*(2*c*x - b)^3*b^2*gamma(3/2, 1/4*(2*c*x - b)^2/c)/(((2*c*x - b)^2/c)^(3/2)*(-c)^(9/2)) - 32*b*c^2*gamma(2, 1/4*(2*c*x - b)^2/c)/(-c)^(9/2) - 16*(2*c*x - b)^5*gamma(5/2, 1/4*(2*c*x - b)^2/c)/(((2*c*x - b)^2/c)^(5/2)*(-c)^(9/2)))*c*e^(a + 1/4*b^2/c)/sqrt(-c) + 1/96*(sqrt(pi)*(2*c*x - b)*b^3*(erf(1/2*sqrt(-(2*c*x - b)^2/c)) - 1)/(sqrt(-(2*c*x - b)^2/c)*c^(7/2)) + 6*b^2*e^(1/4*(2*c*x - b)^2/c)/c^(5/2) - 12*(2*c*x - b)^3*b*gamma(3/2, -1/4*(2*c*x - b)^2/c)/((-(2*c*x - b)^2/c)^(3/2)*c^(7/2)) - 8*gamma(2, -1/4*(2*c*x - b)^2/c)/c^(3/2))*b*e^(-a - 1/4*b^2/c)/sqrt(c) - 1/96*(sqrt(pi)*(2*c*x - b)*b^4*(erf(1/2*sqrt(-(2*c*x - b)^2/c)) - 1)/(sqrt(-(2*c*x - b)^2/c)*c^(9/2)) + 8*b^3*e^(1/4*(2*c*x - b)^2/c)/c^(7/2) - 24*(2*c*x - b)^3*b^2*gamma(3/2, -1/4*(2*c*x - b)^2/c)/((-(2*c*x - b)^2/c)^(3/2)*c^(9/2)) - 32*b*gamma(2, -1/4*(2*c*x - b)^2/c)/c^(5/2) - 16*(2*c*x - b)^5*gamma(5/2, -1/4*(2*c*x - b)^2/c)/((-(2*c*x - b)^2/c)^(5/2)*c^(9/2)))*sqrt(c)*e^(-a - 1/4*b^2/c)","B",0
7,1,674,0,0.628922," ","integrate(x*cosh(-c*x^2+b*x+a),x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \cosh\left(c x^{2} - b x - a\right) + \frac{{\left(\frac{\sqrt{\pi} {\left(2 \, c x - b\right)} b^{2} {\left(\operatorname{erf}\left(\frac{1}{2} \, \sqrt{\frac{{\left(2 \, c x - b\right)}^{2}}{c}}\right) - 1\right)}}{\sqrt{\frac{{\left(2 \, c x - b\right)}^{2}}{c}} \left(-c\right)^{\frac{5}{2}}} - \frac{4 \, b c e^{\left(-\frac{{\left(2 \, c x - b\right)}^{2}}{4 \, c}\right)}}{\left(-c\right)^{\frac{5}{2}}} - \frac{4 \, {\left(2 \, c x - b\right)}^{3} \Gamma\left(\frac{3}{2}, \frac{{\left(2 \, c x - b\right)}^{2}}{4 \, c}\right)}{\left(\frac{{\left(2 \, c x - b\right)}^{2}}{c}\right)^{\frac{3}{2}} \left(-c\right)^{\frac{5}{2}}}\right)} b e^{\left(a + \frac{b^{2}}{4 \, c}\right)}}{32 \, \sqrt{-c}} + \frac{{\left(\frac{\sqrt{\pi} {\left(2 \, c x - b\right)} b^{3} {\left(\operatorname{erf}\left(\frac{1}{2} \, \sqrt{\frac{{\left(2 \, c x - b\right)}^{2}}{c}}\right) - 1\right)}}{\sqrt{\frac{{\left(2 \, c x - b\right)}^{2}}{c}} \left(-c\right)^{\frac{7}{2}}} - \frac{6 \, b^{2} c e^{\left(-\frac{{\left(2 \, c x - b\right)}^{2}}{4 \, c}\right)}}{\left(-c\right)^{\frac{7}{2}}} - \frac{12 \, {\left(2 \, c x - b\right)}^{3} b \Gamma\left(\frac{3}{2}, \frac{{\left(2 \, c x - b\right)}^{2}}{4 \, c}\right)}{\left(\frac{{\left(2 \, c x - b\right)}^{2}}{c}\right)^{\frac{3}{2}} \left(-c\right)^{\frac{7}{2}}} - \frac{8 \, c^{2} \Gamma\left(2, \frac{{\left(2 \, c x - b\right)}^{2}}{4 \, c}\right)}{\left(-c\right)^{\frac{7}{2}}}\right)} c e^{\left(a + \frac{b^{2}}{4 \, c}\right)}}{32 \, \sqrt{-c}} + \frac{{\left(\frac{\sqrt{\pi} {\left(2 \, c x - b\right)} b^{2} {\left(\operatorname{erf}\left(\frac{1}{2} \, \sqrt{-\frac{{\left(2 \, c x - b\right)}^{2}}{c}}\right) - 1\right)}}{\sqrt{-\frac{{\left(2 \, c x - b\right)}^{2}}{c}} c^{\frac{5}{2}}} + \frac{4 \, b e^{\left(\frac{{\left(2 \, c x - b\right)}^{2}}{4 \, c}\right)}}{c^{\frac{3}{2}}} - \frac{4 \, {\left(2 \, c x - b\right)}^{3} \Gamma\left(\frac{3}{2}, -\frac{{\left(2 \, c x - b\right)}^{2}}{4 \, c}\right)}{\left(-\frac{{\left(2 \, c x - b\right)}^{2}}{c}\right)^{\frac{3}{2}} c^{\frac{5}{2}}}\right)} b e^{\left(-a - \frac{b^{2}}{4 \, c}\right)}}{32 \, \sqrt{c}} - \frac{1}{32} \, {\left(\frac{\sqrt{\pi} {\left(2 \, c x - b\right)} b^{3} {\left(\operatorname{erf}\left(\frac{1}{2} \, \sqrt{-\frac{{\left(2 \, c x - b\right)}^{2}}{c}}\right) - 1\right)}}{\sqrt{-\frac{{\left(2 \, c x - b\right)}^{2}}{c}} c^{\frac{7}{2}}} + \frac{6 \, b^{2} e^{\left(\frac{{\left(2 \, c x - b\right)}^{2}}{4 \, c}\right)}}{c^{\frac{5}{2}}} - \frac{12 \, {\left(2 \, c x - b\right)}^{3} b \Gamma\left(\frac{3}{2}, -\frac{{\left(2 \, c x - b\right)}^{2}}{4 \, c}\right)}{\left(-\frac{{\left(2 \, c x - b\right)}^{2}}{c}\right)^{\frac{3}{2}} c^{\frac{7}{2}}} - \frac{8 \, \Gamma\left(2, -\frac{{\left(2 \, c x - b\right)}^{2}}{4 \, c}\right)}{c^{\frac{3}{2}}}\right)} \sqrt{c} e^{\left(-a - \frac{b^{2}}{4 \, c}\right)}"," ",0,"1/2*x^2*cosh(c*x^2 - b*x - a) + 1/32*(sqrt(pi)*(2*c*x - b)*b^2*(erf(1/2*sqrt((2*c*x - b)^2/c)) - 1)/(sqrt((2*c*x - b)^2/c)*(-c)^(5/2)) - 4*b*c*e^(-1/4*(2*c*x - b)^2/c)/(-c)^(5/2) - 4*(2*c*x - b)^3*gamma(3/2, 1/4*(2*c*x - b)^2/c)/(((2*c*x - b)^2/c)^(3/2)*(-c)^(5/2)))*b*e^(a + 1/4*b^2/c)/sqrt(-c) + 1/32*(sqrt(pi)*(2*c*x - b)*b^3*(erf(1/2*sqrt((2*c*x - b)^2/c)) - 1)/(sqrt((2*c*x - b)^2/c)*(-c)^(7/2)) - 6*b^2*c*e^(-1/4*(2*c*x - b)^2/c)/(-c)^(7/2) - 12*(2*c*x - b)^3*b*gamma(3/2, 1/4*(2*c*x - b)^2/c)/(((2*c*x - b)^2/c)^(3/2)*(-c)^(7/2)) - 8*c^2*gamma(2, 1/4*(2*c*x - b)^2/c)/(-c)^(7/2))*c*e^(a + 1/4*b^2/c)/sqrt(-c) + 1/32*(sqrt(pi)*(2*c*x - b)*b^2*(erf(1/2*sqrt(-(2*c*x - b)^2/c)) - 1)/(sqrt(-(2*c*x - b)^2/c)*c^(5/2)) + 4*b*e^(1/4*(2*c*x - b)^2/c)/c^(3/2) - 4*(2*c*x - b)^3*gamma(3/2, -1/4*(2*c*x - b)^2/c)/((-(2*c*x - b)^2/c)^(3/2)*c^(5/2)))*b*e^(-a - 1/4*b^2/c)/sqrt(c) - 1/32*(sqrt(pi)*(2*c*x - b)*b^3*(erf(1/2*sqrt(-(2*c*x - b)^2/c)) - 1)/(sqrt(-(2*c*x - b)^2/c)*c^(7/2)) + 6*b^2*e^(1/4*(2*c*x - b)^2/c)/c^(5/2) - 12*(2*c*x - b)^3*b*gamma(3/2, -1/4*(2*c*x - b)^2/c)/((-(2*c*x - b)^2/c)^(3/2)*c^(7/2)) - 8*gamma(2, -1/4*(2*c*x - b)^2/c)/c^(3/2))*sqrt(c)*e^(-a - 1/4*b^2/c)","B",0
8,1,511,0,0.650083," ","integrate(cosh(-c*x^2+b*x+a),x, algorithm=""maxima"")","-\frac{{\left(\frac{\sqrt{\pi} {\left(2 \, c x - b\right)} b {\left(\operatorname{erf}\left(\frac{1}{2} \, \sqrt{\frac{{\left(2 \, c x - b\right)}^{2}}{c}}\right) - 1\right)}}{\sqrt{\frac{{\left(2 \, c x - b\right)}^{2}}{c}} \left(-c\right)^{\frac{3}{2}}} - \frac{2 \, c e^{\left(-\frac{{\left(2 \, c x - b\right)}^{2}}{4 \, c}\right)}}{\left(-c\right)^{\frac{3}{2}}}\right)} b e^{\left(a + \frac{b^{2}}{4 \, c}\right)}}{8 \, \sqrt{-c}} - \frac{{\left(\frac{\sqrt{\pi} {\left(2 \, c x - b\right)} b^{2} {\left(\operatorname{erf}\left(\frac{1}{2} \, \sqrt{\frac{{\left(2 \, c x - b\right)}^{2}}{c}}\right) - 1\right)}}{\sqrt{\frac{{\left(2 \, c x - b\right)}^{2}}{c}} \left(-c\right)^{\frac{5}{2}}} - \frac{4 \, b c e^{\left(-\frac{{\left(2 \, c x - b\right)}^{2}}{4 \, c}\right)}}{\left(-c\right)^{\frac{5}{2}}} - \frac{4 \, {\left(2 \, c x - b\right)}^{3} \Gamma\left(\frac{3}{2}, \frac{{\left(2 \, c x - b\right)}^{2}}{4 \, c}\right)}{\left(\frac{{\left(2 \, c x - b\right)}^{2}}{c}\right)^{\frac{3}{2}} \left(-c\right)^{\frac{5}{2}}}\right)} c e^{\left(a + \frac{b^{2}}{4 \, c}\right)}}{8 \, \sqrt{-c}} + \frac{{\left(\frac{\sqrt{\pi} {\left(2 \, c x - b\right)} b {\left(\operatorname{erf}\left(\frac{1}{2} \, \sqrt{-\frac{{\left(2 \, c x - b\right)}^{2}}{c}}\right) - 1\right)}}{\sqrt{-\frac{{\left(2 \, c x - b\right)}^{2}}{c}} c^{\frac{3}{2}}} + \frac{2 \, e^{\left(\frac{{\left(2 \, c x - b\right)}^{2}}{4 \, c}\right)}}{\sqrt{c}}\right)} b e^{\left(-a - \frac{b^{2}}{4 \, c}\right)}}{8 \, \sqrt{c}} - \frac{1}{8} \, {\left(\frac{\sqrt{\pi} {\left(2 \, c x - b\right)} b^{2} {\left(\operatorname{erf}\left(\frac{1}{2} \, \sqrt{-\frac{{\left(2 \, c x - b\right)}^{2}}{c}}\right) - 1\right)}}{\sqrt{-\frac{{\left(2 \, c x - b\right)}^{2}}{c}} c^{\frac{5}{2}}} + \frac{4 \, b e^{\left(\frac{{\left(2 \, c x - b\right)}^{2}}{4 \, c}\right)}}{c^{\frac{3}{2}}} - \frac{4 \, {\left(2 \, c x - b\right)}^{3} \Gamma\left(\frac{3}{2}, -\frac{{\left(2 \, c x - b\right)}^{2}}{4 \, c}\right)}{\left(-\frac{{\left(2 \, c x - b\right)}^{2}}{c}\right)^{\frac{3}{2}} c^{\frac{5}{2}}}\right)} \sqrt{c} e^{\left(-a - \frac{b^{2}}{4 \, c}\right)} + x \cosh\left(c x^{2} - b x - a\right)"," ",0,"-1/8*(sqrt(pi)*(2*c*x - b)*b*(erf(1/2*sqrt((2*c*x - b)^2/c)) - 1)/(sqrt((2*c*x - b)^2/c)*(-c)^(3/2)) - 2*c*e^(-1/4*(2*c*x - b)^2/c)/(-c)^(3/2))*b*e^(a + 1/4*b^2/c)/sqrt(-c) - 1/8*(sqrt(pi)*(2*c*x - b)*b^2*(erf(1/2*sqrt((2*c*x - b)^2/c)) - 1)/(sqrt((2*c*x - b)^2/c)*(-c)^(5/2)) - 4*b*c*e^(-1/4*(2*c*x - b)^2/c)/(-c)^(5/2) - 4*(2*c*x - b)^3*gamma(3/2, 1/4*(2*c*x - b)^2/c)/(((2*c*x - b)^2/c)^(3/2)*(-c)^(5/2)))*c*e^(a + 1/4*b^2/c)/sqrt(-c) + 1/8*(sqrt(pi)*(2*c*x - b)*b*(erf(1/2*sqrt(-(2*c*x - b)^2/c)) - 1)/(sqrt(-(2*c*x - b)^2/c)*c^(3/2)) + 2*e^(1/4*(2*c*x - b)^2/c)/sqrt(c))*b*e^(-a - 1/4*b^2/c)/sqrt(c) - 1/8*(sqrt(pi)*(2*c*x - b)*b^2*(erf(1/2*sqrt(-(2*c*x - b)^2/c)) - 1)/(sqrt(-(2*c*x - b)^2/c)*c^(5/2)) + 4*b*e^(1/4*(2*c*x - b)^2/c)/c^(3/2) - 4*(2*c*x - b)^3*gamma(3/2, -1/4*(2*c*x - b)^2/c)/((-(2*c*x - b)^2/c)^(3/2)*c^(5/2)))*sqrt(c)*e^(-a - 1/4*b^2/c) + x*cosh(c*x^2 - b*x - a)","B",0
9,0,0,0,0.000000," ","integrate(cosh(-c*x^2+b*x+a)/x,x, algorithm=""maxima"")","\int \frac{\cosh\left(c x^{2} - b x - a\right)}{x}\,{d x}"," ",0,"integrate(cosh(c*x^2 - b*x - a)/x, x)","F",0
10,0,0,0,0.000000," ","integrate(cosh(-c*x^2+b*x+a)/x^2-b*sinh(-c*x^2+b*x+a)/x,x, algorithm=""maxima"")","\int \frac{b \sinh\left(c x^{2} - b x - a\right)}{x} + \frac{\cosh\left(c x^{2} - b x - a\right)}{x^{2}}\,{d x}"," ",0,"integrate(b*sinh(c*x^2 - b*x - a)/x + cosh(c*x^2 - b*x - a)/x^2, x)","F",0
11,1,183,0,0.445110," ","integrate(x^2*cosh(1/4+x+x^2),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \cosh\left(x^{2} + x + \frac{1}{4}\right) - \frac{{\left(2 \, x + 1\right)}^{5} \Gamma\left(\frac{5}{2}, \frac{1}{4} \, {\left(2 \, x + 1\right)}^{2}\right)}{6 \, {\left({\left(2 \, x + 1\right)}^{2}\right)}^{\frac{5}{2}}} + \frac{{\left(2 \, x + 1\right)}^{5} \Gamma\left(\frac{5}{2}, -\frac{1}{4} \, {\left(2 \, x + 1\right)}^{2}\right)}{6 \, \left(-{\left(2 \, x + 1\right)}^{2}\right)^{\frac{5}{2}}} - \frac{{\left(2 \, x + 1\right)}^{3} \Gamma\left(\frac{3}{2}, \frac{1}{4} \, {\left(2 \, x + 1\right)}^{2}\right)}{8 \, {\left({\left(2 \, x + 1\right)}^{2}\right)}^{\frac{3}{2}}} + \frac{{\left(2 \, x + 1\right)}^{3} \Gamma\left(\frac{3}{2}, -\frac{1}{4} \, {\left(2 \, x + 1\right)}^{2}\right)}{8 \, \left(-{\left(2 \, x + 1\right)}^{2}\right)^{\frac{3}{2}}} + \frac{1}{48} \, e^{\left(\frac{1}{4} \, {\left(2 \, x + 1\right)}^{2}\right)} + \frac{1}{48} \, e^{\left(-\frac{1}{4} \, {\left(2 \, x + 1\right)}^{2}\right)} + \frac{1}{4} \, \Gamma\left(2, \frac{1}{4} \, {\left(2 \, x + 1\right)}^{2}\right) - \frac{1}{4} \, \Gamma\left(2, -\frac{1}{4} \, {\left(2 \, x + 1\right)}^{2}\right)"," ",0,"1/3*x^3*cosh(x^2 + x + 1/4) - 1/6*(2*x + 1)^5*gamma(5/2, 1/4*(2*x + 1)^2)/((2*x + 1)^2)^(5/2) + 1/6*(2*x + 1)^5*gamma(5/2, -1/4*(2*x + 1)^2)/(-(2*x + 1)^2)^(5/2) - 1/8*(2*x + 1)^3*gamma(3/2, 1/4*(2*x + 1)^2)/((2*x + 1)^2)^(3/2) + 1/8*(2*x + 1)^3*gamma(3/2, -1/4*(2*x + 1)^2)/(-(2*x + 1)^2)^(3/2) + 1/48*e^(1/4*(2*x + 1)^2) + 1/48*e^(-1/4*(2*x + 1)^2) + 1/4*gamma(2, 1/4*(2*x + 1)^2) - 1/4*gamma(2, -1/4*(2*x + 1)^2)","B",0
12,1,123,0,0.472464," ","integrate(x*cosh(1/4+x+x^2),x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \cosh\left(x^{2} + x + \frac{1}{4}\right) + \frac{{\left(2 \, x + 1\right)}^{3} \Gamma\left(\frac{3}{2}, \frac{1}{4} \, {\left(2 \, x + 1\right)}^{2}\right)}{4 \, {\left({\left(2 \, x + 1\right)}^{2}\right)}^{\frac{3}{2}}} - \frac{{\left(2 \, x + 1\right)}^{3} \Gamma\left(\frac{3}{2}, -\frac{1}{4} \, {\left(2 \, x + 1\right)}^{2}\right)}{4 \, \left(-{\left(2 \, x + 1\right)}^{2}\right)^{\frac{3}{2}}} - \frac{1}{16} \, e^{\left(\frac{1}{4} \, {\left(2 \, x + 1\right)}^{2}\right)} - \frac{1}{16} \, e^{\left(-\frac{1}{4} \, {\left(2 \, x + 1\right)}^{2}\right)} - \frac{1}{4} \, \Gamma\left(2, \frac{1}{4} \, {\left(2 \, x + 1\right)}^{2}\right) + \frac{1}{4} \, \Gamma\left(2, -\frac{1}{4} \, {\left(2 \, x + 1\right)}^{2}\right)"," ",0,"1/2*x^2*cosh(x^2 + x + 1/4) + 1/4*(2*x + 1)^3*gamma(3/2, 1/4*(2*x + 1)^2)/((2*x + 1)^2)^(3/2) - 1/4*(2*x + 1)^3*gamma(3/2, -1/4*(2*x + 1)^2)/(-(2*x + 1)^2)^(3/2) - 1/16*e^(1/4*(2*x + 1)^2) - 1/16*e^(-1/4*(2*x + 1)^2) - 1/4*gamma(2, 1/4*(2*x + 1)^2) + 1/4*gamma(2, -1/4*(2*x + 1)^2)","B",0
13,1,94,0,0.431589," ","integrate(cosh(1/4+x+x^2),x, algorithm=""maxima"")","-\frac{{\left(2 \, x + 1\right)}^{3} \Gamma\left(\frac{3}{2}, \frac{1}{4} \, {\left(2 \, x + 1\right)}^{2}\right)}{2 \, {\left({\left(2 \, x + 1\right)}^{2}\right)}^{\frac{3}{2}}} + \frac{{\left(2 \, x + 1\right)}^{3} \Gamma\left(\frac{3}{2}, -\frac{1}{4} \, {\left(2 \, x + 1\right)}^{2}\right)}{2 \, \left(-{\left(2 \, x + 1\right)}^{2}\right)^{\frac{3}{2}}} + x \cosh\left(x^{2} + x + \frac{1}{4}\right) + \frac{1}{4} \, e^{\left(\frac{1}{4} \, {\left(2 \, x + 1\right)}^{2}\right)} + \frac{1}{4} \, e^{\left(-\frac{1}{4} \, {\left(2 \, x + 1\right)}^{2}\right)}"," ",0,"-1/2*(2*x + 1)^3*gamma(3/2, 1/4*(2*x + 1)^2)/((2*x + 1)^2)^(3/2) + 1/2*(2*x + 1)^3*gamma(3/2, -1/4*(2*x + 1)^2)/(-(2*x + 1)^2)^(3/2) + x*cosh(x^2 + x + 1/4) + 1/4*e^(1/4*(2*x + 1)^2) + 1/4*e^(-1/4*(2*x + 1)^2)","B",0
14,0,0,0,0.000000," ","integrate(cosh(1/4+x+x^2)/x,x, algorithm=""maxima"")","\int \frac{\cosh\left(x^{2} + x + \frac{1}{4}\right)}{x}\,{d x}"," ",0,"integrate(cosh(x^2 + x + 1/4)/x, x)","F",0
15,0,0,0,0.000000," ","integrate(cosh(1/4+x+x^2)/x^2,x, algorithm=""maxima"")","\int \frac{\cosh\left(x^{2} + x + \frac{1}{4}\right)}{x^{2}}\,{d x}"," ",0,"integrate(cosh(x^2 + x + 1/4)/x^2, x)","F",0
16,1,294,0,0.471956," ","integrate(x^2*cosh(c*x^2+b*x+a)^2,x, algorithm=""maxima"")","\frac{1}{6} \, x^{3} + \frac{\sqrt{2} {\left(\frac{\sqrt{\pi} {\left(2 \, c x + b\right)} b^{2} {\left(\operatorname{erf}\left(\sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(2 \, c x + b\right)}^{2}}{c}}\right) - 1\right)}}{\sqrt{-\frac{{\left(2 \, c x + b\right)}^{2}}{c}} c^{\frac{5}{2}}} - \frac{2 \, \sqrt{2} b e^{\left(\frac{{\left(2 \, c x + b\right)}^{2}}{2 \, c}\right)}}{c^{\frac{3}{2}}} - \frac{2 \, {\left(2 \, c x + b\right)}^{3} \Gamma\left(\frac{3}{2}, -\frac{{\left(2 \, c x + b\right)}^{2}}{2 \, c}\right)}{\left(-\frac{{\left(2 \, c x + b\right)}^{2}}{c}\right)^{\frac{3}{2}} c^{\frac{5}{2}}}\right)} e^{\left(2 \, a - \frac{b^{2}}{2 \, c}\right)}}{64 \, \sqrt{c}} - \frac{\sqrt{2} {\left(\frac{\sqrt{\pi} {\left(2 \, c x + b\right)} b^{2} {\left(\operatorname{erf}\left(\sqrt{\frac{1}{2}} \sqrt{\frac{{\left(2 \, c x + b\right)}^{2}}{c}}\right) - 1\right)}}{\sqrt{\frac{{\left(2 \, c x + b\right)}^{2}}{c}} \left(-c\right)^{\frac{5}{2}}} + \frac{2 \, \sqrt{2} b c e^{\left(-\frac{{\left(2 \, c x + b\right)}^{2}}{2 \, c}\right)}}{\left(-c\right)^{\frac{5}{2}}} - \frac{2 \, {\left(2 \, c x + b\right)}^{3} \Gamma\left(\frac{3}{2}, \frac{{\left(2 \, c x + b\right)}^{2}}{2 \, c}\right)}{\left(\frac{{\left(2 \, c x + b\right)}^{2}}{c}\right)^{\frac{3}{2}} \left(-c\right)^{\frac{5}{2}}}\right)} e^{\left(-2 \, a + \frac{b^{2}}{2 \, c}\right)}}{64 \, \sqrt{-c}}"," ",0,"1/6*x^3 + 1/64*sqrt(2)*(sqrt(pi)*(2*c*x + b)*b^2*(erf(sqrt(1/2)*sqrt(-(2*c*x + b)^2/c)) - 1)/(sqrt(-(2*c*x + b)^2/c)*c^(5/2)) - 2*sqrt(2)*b*e^(1/2*(2*c*x + b)^2/c)/c^(3/2) - 2*(2*c*x + b)^3*gamma(3/2, -1/2*(2*c*x + b)^2/c)/((-(2*c*x + b)^2/c)^(3/2)*c^(5/2)))*e^(2*a - 1/2*b^2/c)/sqrt(c) - 1/64*sqrt(2)*(sqrt(pi)*(2*c*x + b)*b^2*(erf(sqrt(1/2)*sqrt((2*c*x + b)^2/c)) - 1)/(sqrt((2*c*x + b)^2/c)*(-c)^(5/2)) + 2*sqrt(2)*b*c*e^(-1/2*(2*c*x + b)^2/c)/(-c)^(5/2) - 2*(2*c*x + b)^3*gamma(3/2, 1/2*(2*c*x + b)^2/c)/(((2*c*x + b)^2/c)^(3/2)*(-c)^(5/2)))*e^(-2*a + 1/2*b^2/c)/sqrt(-c)","A",0
17,1,200,0,0.427701," ","integrate(x*cosh(c*x^2+b*x+a)^2,x, algorithm=""maxima"")","\frac{1}{4} \, x^{2} - \frac{\sqrt{2} {\left(\frac{\sqrt{\pi} {\left(2 \, c x + b\right)} b {\left(\operatorname{erf}\left(\sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(2 \, c x + b\right)}^{2}}{c}}\right) - 1\right)}}{\sqrt{-\frac{{\left(2 \, c x + b\right)}^{2}}{c}} c^{\frac{3}{2}}} - \frac{\sqrt{2} e^{\left(\frac{{\left(2 \, c x + b\right)}^{2}}{2 \, c}\right)}}{\sqrt{c}}\right)} e^{\left(2 \, a - \frac{b^{2}}{2 \, c}\right)}}{32 \, \sqrt{c}} - \frac{\sqrt{2} {\left(\frac{\sqrt{\pi} {\left(2 \, c x + b\right)} b {\left(\operatorname{erf}\left(\sqrt{\frac{1}{2}} \sqrt{\frac{{\left(2 \, c x + b\right)}^{2}}{c}}\right) - 1\right)}}{\sqrt{\frac{{\left(2 \, c x + b\right)}^{2}}{c}} \left(-c\right)^{\frac{3}{2}}} + \frac{\sqrt{2} c e^{\left(-\frac{{\left(2 \, c x + b\right)}^{2}}{2 \, c}\right)}}{\left(-c\right)^{\frac{3}{2}}}\right)} e^{\left(-2 \, a + \frac{b^{2}}{2 \, c}\right)}}{32 \, \sqrt{-c}}"," ",0,"1/4*x^2 - 1/32*sqrt(2)*(sqrt(pi)*(2*c*x + b)*b*(erf(sqrt(1/2)*sqrt(-(2*c*x + b)^2/c)) - 1)/(sqrt(-(2*c*x + b)^2/c)*c^(3/2)) - sqrt(2)*e^(1/2*(2*c*x + b)^2/c)/sqrt(c))*e^(2*a - 1/2*b^2/c)/sqrt(c) - 1/32*sqrt(2)*(sqrt(pi)*(2*c*x + b)*b*(erf(sqrt(1/2)*sqrt((2*c*x + b)^2/c)) - 1)/(sqrt((2*c*x + b)^2/c)*(-c)^(3/2)) + sqrt(2)*c*e^(-1/2*(2*c*x + b)^2/c)/(-c)^(3/2))*e^(-2*a + 1/2*b^2/c)/sqrt(-c)","A",0
18,1,96,0,0.402842," ","integrate(cosh(c*x^2+b*x+a)^2,x, algorithm=""maxima"")","\frac{\sqrt{2} \sqrt{\pi} \operatorname{erf}\left(\sqrt{2} \sqrt{-c} x - \frac{\sqrt{2} b}{2 \, \sqrt{-c}}\right) e^{\left(2 \, a - \frac{b^{2}}{2 \, c}\right)}}{16 \, \sqrt{-c}} + \frac{\sqrt{2} \sqrt{\pi} \operatorname{erf}\left(\sqrt{2} \sqrt{c} x + \frac{\sqrt{2} b}{2 \, \sqrt{c}}\right) e^{\left(-2 \, a + \frac{b^{2}}{2 \, c}\right)}}{16 \, \sqrt{c}} + \frac{1}{2} \, x"," ",0,"1/16*sqrt(2)*sqrt(pi)*erf(sqrt(2)*sqrt(-c)*x - 1/2*sqrt(2)*b/sqrt(-c))*e^(2*a - 1/2*b^2/c)/sqrt(-c) + 1/16*sqrt(2)*sqrt(pi)*erf(sqrt(2)*sqrt(c)*x + 1/2*sqrt(2)*b/sqrt(c))*e^(-2*a + 1/2*b^2/c)/sqrt(c) + 1/2*x","A",0
19,0,0,0,0.000000," ","integrate(cosh(c*x^2+b*x+a)^2/x,x, algorithm=""maxima"")","\frac{1}{4} \, \int \frac{e^{\left(2 \, c x^{2} + 2 \, b x + 2 \, a\right)}}{x}\,{d x} + \frac{1}{4} \, \int \frac{e^{\left(-2 \, c x^{2} - 2 \, b x - 2 \, a\right)}}{x}\,{d x} + \frac{1}{2} \, \log\left(x\right)"," ",0,"1/4*integrate(e^(2*c*x^2 + 2*b*x + 2*a)/x, x) + 1/4*integrate(e^(-2*c*x^2 - 2*b*x - 2*a)/x, x) + 1/2*log(x)","F",0
20,1,322,0,0.493401," ","integrate(x^2*cosh(-c*x^2+b*x+a)^2,x, algorithm=""maxima"")","\frac{1}{6} \, x^{3} - \frac{\sqrt{2} {\left(\frac{\sqrt{\pi} {\left(2 \, c x - b\right)} b^{2} {\left(\operatorname{erf}\left(\sqrt{\frac{1}{2}} \sqrt{\frac{{\left(2 \, c x - b\right)}^{2}}{c}}\right) - 1\right)}}{\sqrt{\frac{{\left(2 \, c x - b\right)}^{2}}{c}} \left(-c\right)^{\frac{5}{2}}} - \frac{2 \, \sqrt{2} b c e^{\left(-\frac{{\left(2 \, c x - b\right)}^{2}}{2 \, c}\right)}}{\left(-c\right)^{\frac{5}{2}}} - \frac{2 \, {\left(2 \, c x - b\right)}^{3} \Gamma\left(\frac{3}{2}, \frac{{\left(2 \, c x - b\right)}^{2}}{2 \, c}\right)}{\left(\frac{{\left(2 \, c x - b\right)}^{2}}{c}\right)^{\frac{3}{2}} \left(-c\right)^{\frac{5}{2}}}\right)} e^{\left(2 \, a + \frac{b^{2}}{2 \, c}\right)}}{64 \, \sqrt{-c}} + \frac{\sqrt{2} {\left(\frac{\sqrt{\pi} {\left(2 \, c x - b\right)} b^{2} {\left(\operatorname{erf}\left(\sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(2 \, c x - b\right)}^{2}}{c}}\right) - 1\right)}}{\sqrt{-\frac{{\left(2 \, c x - b\right)}^{2}}{c}} c^{\frac{5}{2}}} + \frac{2 \, \sqrt{2} b e^{\left(\frac{{\left(2 \, c x - b\right)}^{2}}{2 \, c}\right)}}{c^{\frac{3}{2}}} - \frac{2 \, {\left(2 \, c x - b\right)}^{3} \Gamma\left(\frac{3}{2}, -\frac{{\left(2 \, c x - b\right)}^{2}}{2 \, c}\right)}{\left(-\frac{{\left(2 \, c x - b\right)}^{2}}{c}\right)^{\frac{3}{2}} c^{\frac{5}{2}}}\right)} e^{\left(-2 \, a - \frac{b^{2}}{2 \, c}\right)}}{64 \, \sqrt{c}}"," ",0,"1/6*x^3 - 1/64*sqrt(2)*(sqrt(pi)*(2*c*x - b)*b^2*(erf(sqrt(1/2)*sqrt((2*c*x - b)^2/c)) - 1)/(sqrt((2*c*x - b)^2/c)*(-c)^(5/2)) - 2*sqrt(2)*b*c*e^(-1/2*(2*c*x - b)^2/c)/(-c)^(5/2) - 2*(2*c*x - b)^3*gamma(3/2, 1/2*(2*c*x - b)^2/c)/(((2*c*x - b)^2/c)^(3/2)*(-c)^(5/2)))*e^(2*a + 1/2*b^2/c)/sqrt(-c) + 1/64*sqrt(2)*(sqrt(pi)*(2*c*x - b)*b^2*(erf(sqrt(1/2)*sqrt(-(2*c*x - b)^2/c)) - 1)/(sqrt(-(2*c*x - b)^2/c)*c^(5/2)) + 2*sqrt(2)*b*e^(1/2*(2*c*x - b)^2/c)/c^(3/2) - 2*(2*c*x - b)^3*gamma(3/2, -1/2*(2*c*x - b)^2/c)/((-(2*c*x - b)^2/c)^(3/2)*c^(5/2)))*e^(-2*a - 1/2*b^2/c)/sqrt(c)","A",0
21,1,216,0,0.434852," ","integrate(x*cosh(-c*x^2+b*x+a)^2,x, algorithm=""maxima"")","\frac{1}{4} \, x^{2} + \frac{\sqrt{2} {\left(\frac{\sqrt{\pi} {\left(2 \, c x - b\right)} b {\left(\operatorname{erf}\left(\sqrt{\frac{1}{2}} \sqrt{\frac{{\left(2 \, c x - b\right)}^{2}}{c}}\right) - 1\right)}}{\sqrt{\frac{{\left(2 \, c x - b\right)}^{2}}{c}} \left(-c\right)^{\frac{3}{2}}} - \frac{\sqrt{2} c e^{\left(-\frac{{\left(2 \, c x - b\right)}^{2}}{2 \, c}\right)}}{\left(-c\right)^{\frac{3}{2}}}\right)} e^{\left(2 \, a + \frac{b^{2}}{2 \, c}\right)}}{32 \, \sqrt{-c}} + \frac{\sqrt{2} {\left(\frac{\sqrt{\pi} {\left(2 \, c x - b\right)} b {\left(\operatorname{erf}\left(\sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(2 \, c x - b\right)}^{2}}{c}}\right) - 1\right)}}{\sqrt{-\frac{{\left(2 \, c x - b\right)}^{2}}{c}} c^{\frac{3}{2}}} + \frac{\sqrt{2} e^{\left(\frac{{\left(2 \, c x - b\right)}^{2}}{2 \, c}\right)}}{\sqrt{c}}\right)} e^{\left(-2 \, a - \frac{b^{2}}{2 \, c}\right)}}{32 \, \sqrt{c}}"," ",0,"1/4*x^2 + 1/32*sqrt(2)*(sqrt(pi)*(2*c*x - b)*b*(erf(sqrt(1/2)*sqrt((2*c*x - b)^2/c)) - 1)/(sqrt((2*c*x - b)^2/c)*(-c)^(3/2)) - sqrt(2)*c*e^(-1/2*(2*c*x - b)^2/c)/(-c)^(3/2))*e^(2*a + 1/2*b^2/c)/sqrt(-c) + 1/32*sqrt(2)*(sqrt(pi)*(2*c*x - b)*b*(erf(sqrt(1/2)*sqrt(-(2*c*x - b)^2/c)) - 1)/(sqrt(-(2*c*x - b)^2/c)*c^(3/2)) + sqrt(2)*e^(1/2*(2*c*x - b)^2/c)/sqrt(c))*e^(-2*a - 1/2*b^2/c)/sqrt(c)","A",0
22,1,96,0,0.395068," ","integrate(cosh(-c*x^2+b*x+a)^2,x, algorithm=""maxima"")","\frac{\sqrt{2} \sqrt{\pi} \operatorname{erf}\left(\sqrt{2} \sqrt{c} x - \frac{\sqrt{2} b}{2 \, \sqrt{c}}\right) e^{\left(2 \, a + \frac{b^{2}}{2 \, c}\right)}}{16 \, \sqrt{c}} + \frac{\sqrt{2} \sqrt{\pi} \operatorname{erf}\left(\sqrt{2} \sqrt{-c} x + \frac{\sqrt{2} b}{2 \, \sqrt{-c}}\right) e^{\left(-2 \, a - \frac{b^{2}}{2 \, c}\right)}}{16 \, \sqrt{-c}} + \frac{1}{2} \, x"," ",0,"1/16*sqrt(2)*sqrt(pi)*erf(sqrt(2)*sqrt(c)*x - 1/2*sqrt(2)*b/sqrt(c))*e^(2*a + 1/2*b^2/c)/sqrt(c) + 1/16*sqrt(2)*sqrt(pi)*erf(sqrt(2)*sqrt(-c)*x + 1/2*sqrt(2)*b/sqrt(-c))*e^(-2*a - 1/2*b^2/c)/sqrt(-c) + 1/2*x","A",0
23,0,0,0,0.000000," ","integrate(cosh(-c*x^2+b*x+a)^2/x,x, algorithm=""maxima"")","\frac{1}{4} \, \int \frac{e^{\left(2 \, c x^{2} - 2 \, b x - 2 \, a\right)}}{x}\,{d x} + \frac{1}{4} \, \int \frac{e^{\left(-2 \, c x^{2} + 2 \, b x + 2 \, a\right)}}{x}\,{d x} + \frac{1}{2} \, \log\left(x\right)"," ",0,"1/4*integrate(e^(2*c*x^2 - 2*b*x - 2*a)/x, x) + 1/4*integrate(e^(-2*c*x^2 + 2*b*x + 2*a)/x, x) + 1/2*log(x)","F",0
24,1,113,0,0.442680," ","integrate(x^2*cosh(1/4+x+x^2)^2,x, algorithm=""maxima"")","\frac{1}{6} \, x^{3} + \frac{1}{32} \, {\left(2 \, x e^{\frac{1}{2}} - e^{\frac{1}{2}}\right)} e^{\left(2 \, x^{2} + 2 \, x\right)} - \frac{1}{64} i \, \sqrt{2} {\left(-\frac{2 i \, {\left(2 \, x + 1\right)}^{3} \Gamma\left(\frac{3}{2}, \frac{1}{2} \, {\left(2 \, x + 1\right)}^{2}\right)}{{\left({\left(2 \, x + 1\right)}^{2}\right)}^{\frac{3}{2}}} + \frac{i \, \sqrt{\pi} {\left(2 \, x + 1\right)} {\left(\operatorname{erf}\left(\sqrt{\frac{1}{2}} \sqrt{{\left(2 \, x + 1\right)}^{2}}\right) - 1\right)}}{\sqrt{{\left(2 \, x + 1\right)}^{2}}} + 2 i \, \sqrt{2} e^{\left(-\frac{1}{2} \, {\left(2 \, x + 1\right)}^{2}\right)}\right)}"," ",0,"1/6*x^3 + 1/32*(2*x*e^(1/2) - e^(1/2))*e^(2*x^2 + 2*x) - 1/64*I*sqrt(2)*(-2*I*(2*x + 1)^3*gamma(3/2, 1/2*(2*x + 1)^2)/((2*x + 1)^2)^(3/2) + I*sqrt(pi)*(2*x + 1)*(erf(sqrt(1/2)*sqrt((2*x + 1)^2)) - 1)/sqrt((2*x + 1)^2) + 2*I*sqrt(2)*e^(-1/2*(2*x + 1)^2))","C",0
25,1,121,0,0.458534," ","integrate(x*cosh(1/4+x+x^2)^2,x, algorithm=""maxima"")","\frac{1}{4} \, x^{2} - \frac{1}{32} \, \sqrt{2} {\left(\frac{\sqrt{\pi} {\left(2 \, x + 1\right)} {\left(\operatorname{erf}\left(\sqrt{\frac{1}{2}} \sqrt{-{\left(2 \, x + 1\right)}^{2}}\right) - 1\right)}}{\sqrt{-{\left(2 \, x + 1\right)}^{2}}} - \sqrt{2} e^{\left(\frac{1}{2} \, {\left(2 \, x + 1\right)}^{2}\right)}\right)} - \frac{1}{32} i \, \sqrt{2} {\left(-\frac{i \, \sqrt{\pi} {\left(2 \, x + 1\right)} {\left(\operatorname{erf}\left(\sqrt{\frac{1}{2}} \sqrt{{\left(2 \, x + 1\right)}^{2}}\right) - 1\right)}}{\sqrt{{\left(2 \, x + 1\right)}^{2}}} - i \, \sqrt{2} e^{\left(-\frac{1}{2} \, {\left(2 \, x + 1\right)}^{2}\right)}\right)}"," ",0,"1/4*x^2 - 1/32*sqrt(2)*(sqrt(pi)*(2*x + 1)*(erf(sqrt(1/2)*sqrt(-(2*x + 1)^2)) - 1)/sqrt(-(2*x + 1)^2) - sqrt(2)*e^(1/2*(2*x + 1)^2)) - 1/32*I*sqrt(2)*(-I*sqrt(pi)*(2*x + 1)*(erf(sqrt(1/2)*sqrt((2*x + 1)^2)) - 1)/sqrt((2*x + 1)^2) - I*sqrt(2)*e^(-1/2*(2*x + 1)^2))","C",0
26,1,45,0,0.416497," ","integrate(cosh(1/4+x+x^2)^2,x, algorithm=""maxima"")","\frac{1}{16} \, \sqrt{2} \sqrt{\pi} \operatorname{erf}\left(\sqrt{2} x + \frac{1}{2} \, \sqrt{2}\right) - \frac{1}{16} i \, \sqrt{2} \sqrt{\pi} \operatorname{erf}\left(i \, \sqrt{2} x + \frac{1}{2} i \, \sqrt{2}\right) + \frac{1}{2} \, x"," ",0,"1/16*sqrt(2)*sqrt(pi)*erf(sqrt(2)*x + 1/2*sqrt(2)) - 1/16*I*sqrt(2)*sqrt(pi)*erf(I*sqrt(2)*x + 1/2*I*sqrt(2)) + 1/2*x","C",0
27,0,0,0,0.000000," ","integrate(cosh(1/4+x+x^2)^2/x,x, algorithm=""maxima"")","\frac{1}{4} \, \int \frac{e^{\left(2 \, x^{2} + 2 \, x + \frac{1}{2}\right)}}{x}\,{d x} + \frac{1}{4} \, \int \frac{e^{\left(-2 \, x^{2} - 2 \, x - \frac{1}{2}\right)}}{x}\,{d x} + \frac{1}{2} \, \log\left(x\right)"," ",0,"1/4*integrate(e^(2*x^2 + 2*x + 1/2)/x, x) + 1/4*integrate(e^(-2*x^2 - 2*x - 1/2)/x, x) + 1/2*log(x)","F",0
28,1,536,0,0.575686," ","integrate((e*x+d)^2*cosh(c*x^2+b*x+a),x, algorithm=""maxima"")","\frac{\sqrt{\pi} d^{2} \operatorname{erf}\left(\sqrt{-c} x - \frac{b}{2 \, \sqrt{-c}}\right) e^{\left(a - \frac{b^{2}}{4 \, c}\right)}}{4 \, \sqrt{-c}} + \frac{\sqrt{\pi} d^{2} \operatorname{erf}\left(\sqrt{c} x + \frac{b}{2 \, \sqrt{c}}\right) e^{\left(-a + \frac{b^{2}}{4 \, c}\right)}}{4 \, \sqrt{c}} - \frac{{\left(\frac{\sqrt{\pi} {\left(2 \, c x + b\right)} b {\left(\operatorname{erf}\left(\frac{1}{2} \, \sqrt{-\frac{{\left(2 \, c x + b\right)}^{2}}{c}}\right) - 1\right)}}{\sqrt{-\frac{{\left(2 \, c x + b\right)}^{2}}{c}} c^{\frac{3}{2}}} - \frac{2 \, e^{\left(\frac{{\left(2 \, c x + b\right)}^{2}}{4 \, c}\right)}}{\sqrt{c}}\right)} d e e^{\left(a - \frac{b^{2}}{4 \, c}\right)}}{4 \, \sqrt{c}} + \frac{{\left(\frac{\sqrt{\pi} {\left(2 \, c x + b\right)} b^{2} {\left(\operatorname{erf}\left(\frac{1}{2} \, \sqrt{-\frac{{\left(2 \, c x + b\right)}^{2}}{c}}\right) - 1\right)}}{\sqrt{-\frac{{\left(2 \, c x + b\right)}^{2}}{c}} c^{\frac{5}{2}}} - \frac{4 \, b e^{\left(\frac{{\left(2 \, c x + b\right)}^{2}}{4 \, c}\right)}}{c^{\frac{3}{2}}} - \frac{4 \, {\left(2 \, c x + b\right)}^{3} \Gamma\left(\frac{3}{2}, -\frac{{\left(2 \, c x + b\right)}^{2}}{4 \, c}\right)}{\left(-\frac{{\left(2 \, c x + b\right)}^{2}}{c}\right)^{\frac{3}{2}} c^{\frac{5}{2}}}\right)} e^{2} e^{\left(a - \frac{b^{2}}{4 \, c}\right)}}{16 \, \sqrt{c}} - \frac{{\left(\frac{\sqrt{\pi} {\left(2 \, c x + b\right)} b {\left(\operatorname{erf}\left(\frac{1}{2} \, \sqrt{\frac{{\left(2 \, c x + b\right)}^{2}}{c}}\right) - 1\right)}}{\sqrt{\frac{{\left(2 \, c x + b\right)}^{2}}{c}} \left(-c\right)^{\frac{3}{2}}} + \frac{2 \, c e^{\left(-\frac{{\left(2 \, c x + b\right)}^{2}}{4 \, c}\right)}}{\left(-c\right)^{\frac{3}{2}}}\right)} d e e^{\left(-a + \frac{b^{2}}{4 \, c}\right)}}{4 \, \sqrt{-c}} - \frac{{\left(\frac{\sqrt{\pi} {\left(2 \, c x + b\right)} b^{2} {\left(\operatorname{erf}\left(\frac{1}{2} \, \sqrt{\frac{{\left(2 \, c x + b\right)}^{2}}{c}}\right) - 1\right)}}{\sqrt{\frac{{\left(2 \, c x + b\right)}^{2}}{c}} \left(-c\right)^{\frac{5}{2}}} + \frac{4 \, b c e^{\left(-\frac{{\left(2 \, c x + b\right)}^{2}}{4 \, c}\right)}}{\left(-c\right)^{\frac{5}{2}}} - \frac{4 \, {\left(2 \, c x + b\right)}^{3} \Gamma\left(\frac{3}{2}, \frac{{\left(2 \, c x + b\right)}^{2}}{4 \, c}\right)}{\left(\frac{{\left(2 \, c x + b\right)}^{2}}{c}\right)^{\frac{3}{2}} \left(-c\right)^{\frac{5}{2}}}\right)} e^{2} e^{\left(-a + \frac{b^{2}}{4 \, c}\right)}}{16 \, \sqrt{-c}}"," ",0,"1/4*sqrt(pi)*d^2*erf(sqrt(-c)*x - 1/2*b/sqrt(-c))*e^(a - 1/4*b^2/c)/sqrt(-c) + 1/4*sqrt(pi)*d^2*erf(sqrt(c)*x + 1/2*b/sqrt(c))*e^(-a + 1/4*b^2/c)/sqrt(c) - 1/4*(sqrt(pi)*(2*c*x + b)*b*(erf(1/2*sqrt(-(2*c*x + b)^2/c)) - 1)/(sqrt(-(2*c*x + b)^2/c)*c^(3/2)) - 2*e^(1/4*(2*c*x + b)^2/c)/sqrt(c))*d*e*e^(a - 1/4*b^2/c)/sqrt(c) + 1/16*(sqrt(pi)*(2*c*x + b)*b^2*(erf(1/2*sqrt(-(2*c*x + b)^2/c)) - 1)/(sqrt(-(2*c*x + b)^2/c)*c^(5/2)) - 4*b*e^(1/4*(2*c*x + b)^2/c)/c^(3/2) - 4*(2*c*x + b)^3*gamma(3/2, -1/4*(2*c*x + b)^2/c)/((-(2*c*x + b)^2/c)^(3/2)*c^(5/2)))*e^2*e^(a - 1/4*b^2/c)/sqrt(c) - 1/4*(sqrt(pi)*(2*c*x + b)*b*(erf(1/2*sqrt((2*c*x + b)^2/c)) - 1)/(sqrt((2*c*x + b)^2/c)*(-c)^(3/2)) + 2*c*e^(-1/4*(2*c*x + b)^2/c)/(-c)^(3/2))*d*e*e^(-a + 1/4*b^2/c)/sqrt(-c) - 1/16*(sqrt(pi)*(2*c*x + b)*b^2*(erf(1/2*sqrt((2*c*x + b)^2/c)) - 1)/(sqrt((2*c*x + b)^2/c)*(-c)^(5/2)) + 4*b*c*e^(-1/4*(2*c*x + b)^2/c)/(-c)^(5/2) - 4*(2*c*x + b)^3*gamma(3/2, 1/4*(2*c*x + b)^2/c)/(((2*c*x + b)^2/c)^(3/2)*(-c)^(5/2)))*e^2*e^(-a + 1/4*b^2/c)/sqrt(-c)","B",0
29,1,254,0,0.441814," ","integrate((e*x+d)*cosh(c*x^2+b*x+a),x, algorithm=""maxima"")","\frac{\sqrt{\pi} d \operatorname{erf}\left(\sqrt{-c} x - \frac{b}{2 \, \sqrt{-c}}\right) e^{\left(a - \frac{b^{2}}{4 \, c}\right)}}{4 \, \sqrt{-c}} + \frac{\sqrt{\pi} d \operatorname{erf}\left(\sqrt{c} x + \frac{b}{2 \, \sqrt{c}}\right) e^{\left(-a + \frac{b^{2}}{4 \, c}\right)}}{4 \, \sqrt{c}} - \frac{{\left(\frac{\sqrt{\pi} {\left(2 \, c x + b\right)} b {\left(\operatorname{erf}\left(\frac{1}{2} \, \sqrt{-\frac{{\left(2 \, c x + b\right)}^{2}}{c}}\right) - 1\right)}}{\sqrt{-\frac{{\left(2 \, c x + b\right)}^{2}}{c}} c^{\frac{3}{2}}} - \frac{2 \, e^{\left(\frac{{\left(2 \, c x + b\right)}^{2}}{4 \, c}\right)}}{\sqrt{c}}\right)} e e^{\left(a - \frac{b^{2}}{4 \, c}\right)}}{8 \, \sqrt{c}} - \frac{{\left(\frac{\sqrt{\pi} {\left(2 \, c x + b\right)} b {\left(\operatorname{erf}\left(\frac{1}{2} \, \sqrt{\frac{{\left(2 \, c x + b\right)}^{2}}{c}}\right) - 1\right)}}{\sqrt{\frac{{\left(2 \, c x + b\right)}^{2}}{c}} \left(-c\right)^{\frac{3}{2}}} + \frac{2 \, c e^{\left(-\frac{{\left(2 \, c x + b\right)}^{2}}{4 \, c}\right)}}{\left(-c\right)^{\frac{3}{2}}}\right)} e e^{\left(-a + \frac{b^{2}}{4 \, c}\right)}}{8 \, \sqrt{-c}}"," ",0,"1/4*sqrt(pi)*d*erf(sqrt(-c)*x - 1/2*b/sqrt(-c))*e^(a - 1/4*b^2/c)/sqrt(-c) + 1/4*sqrt(pi)*d*erf(sqrt(c)*x + 1/2*b/sqrt(c))*e^(-a + 1/4*b^2/c)/sqrt(c) - 1/8*(sqrt(pi)*(2*c*x + b)*b*(erf(1/2*sqrt(-(2*c*x + b)^2/c)) - 1)/(sqrt(-(2*c*x + b)^2/c)*c^(3/2)) - 2*e^(1/4*(2*c*x + b)^2/c)/sqrt(c))*e*e^(a - 1/4*b^2/c)/sqrt(c) - 1/8*(sqrt(pi)*(2*c*x + b)*b*(erf(1/2*sqrt((2*c*x + b)^2/c)) - 1)/(sqrt((2*c*x + b)^2/c)*(-c)^(3/2)) + 2*c*e^(-1/4*(2*c*x + b)^2/c)/(-c)^(3/2))*e*e^(-a + 1/4*b^2/c)/sqrt(-c)","B",0
30,0,0,0,0.000000," ","integrate(cosh(c*x^2+b*x+a)/(e*x+d),x, algorithm=""maxima"")","\int \frac{\cosh\left(c x^{2} + b x + a\right)}{e x + d}\,{d x}"," ",0,"integrate(cosh(c*x^2 + b*x + a)/(e*x + d), x)","F",0
31,1,603,0,0.666780," ","integrate((e*x+d)^2*cosh(c*x^2+b*x+a)^2,x, algorithm=""maxima"")","\frac{1}{16} \, {\left(\frac{\sqrt{2} \sqrt{\pi} \operatorname{erf}\left(\sqrt{2} \sqrt{-c} x - \frac{\sqrt{2} b}{2 \, \sqrt{-c}}\right) e^{\left(2 \, a - \frac{b^{2}}{2 \, c}\right)}}{\sqrt{-c}} + \frac{\sqrt{2} \sqrt{\pi} \operatorname{erf}\left(\sqrt{2} \sqrt{c} x + \frac{\sqrt{2} b}{2 \, \sqrt{c}}\right) e^{\left(-2 \, a + \frac{b^{2}}{2 \, c}\right)}}{\sqrt{c}} + 8 \, x\right)} d^{2} + \frac{1}{16} \, {\left(8 \, x^{2} - \frac{\sqrt{2} {\left(\frac{\sqrt{\pi} {\left(2 \, c x + b\right)} b {\left(\operatorname{erf}\left(\sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(2 \, c x + b\right)}^{2}}{c}}\right) - 1\right)}}{\sqrt{-\frac{{\left(2 \, c x + b\right)}^{2}}{c}} c^{\frac{3}{2}}} - \frac{\sqrt{2} e^{\left(\frac{{\left(2 \, c x + b\right)}^{2}}{2 \, c}\right)}}{\sqrt{c}}\right)} e^{\left(2 \, a - \frac{b^{2}}{2 \, c}\right)}}{\sqrt{c}} - \frac{\sqrt{2} {\left(\frac{\sqrt{\pi} {\left(2 \, c x + b\right)} b {\left(\operatorname{erf}\left(\sqrt{\frac{1}{2}} \sqrt{\frac{{\left(2 \, c x + b\right)}^{2}}{c}}\right) - 1\right)}}{\sqrt{\frac{{\left(2 \, c x + b\right)}^{2}}{c}} \left(-c\right)^{\frac{3}{2}}} + \frac{\sqrt{2} c e^{\left(-\frac{{\left(2 \, c x + b\right)}^{2}}{2 \, c}\right)}}{\left(-c\right)^{\frac{3}{2}}}\right)} e^{\left(-2 \, a + \frac{b^{2}}{2 \, c}\right)}}{\sqrt{-c}}\right)} d e + \frac{1}{192} \, {\left(32 \, x^{3} + \frac{3 \, \sqrt{2} {\left(\frac{\sqrt{\pi} {\left(2 \, c x + b\right)} b^{2} {\left(\operatorname{erf}\left(\sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(2 \, c x + b\right)}^{2}}{c}}\right) - 1\right)}}{\sqrt{-\frac{{\left(2 \, c x + b\right)}^{2}}{c}} c^{\frac{5}{2}}} - \frac{2 \, \sqrt{2} b e^{\left(\frac{{\left(2 \, c x + b\right)}^{2}}{2 \, c}\right)}}{c^{\frac{3}{2}}} - \frac{2 \, {\left(2 \, c x + b\right)}^{3} \Gamma\left(\frac{3}{2}, -\frac{{\left(2 \, c x + b\right)}^{2}}{2 \, c}\right)}{\left(-\frac{{\left(2 \, c x + b\right)}^{2}}{c}\right)^{\frac{3}{2}} c^{\frac{5}{2}}}\right)} e^{\left(2 \, a - \frac{b^{2}}{2 \, c}\right)}}{\sqrt{c}} - \frac{3 \, \sqrt{2} {\left(\frac{\sqrt{\pi} {\left(2 \, c x + b\right)} b^{2} {\left(\operatorname{erf}\left(\sqrt{\frac{1}{2}} \sqrt{\frac{{\left(2 \, c x + b\right)}^{2}}{c}}\right) - 1\right)}}{\sqrt{\frac{{\left(2 \, c x + b\right)}^{2}}{c}} \left(-c\right)^{\frac{5}{2}}} + \frac{2 \, \sqrt{2} b c e^{\left(-\frac{{\left(2 \, c x + b\right)}^{2}}{2 \, c}\right)}}{\left(-c\right)^{\frac{5}{2}}} - \frac{2 \, {\left(2 \, c x + b\right)}^{3} \Gamma\left(\frac{3}{2}, \frac{{\left(2 \, c x + b\right)}^{2}}{2 \, c}\right)}{\left(\frac{{\left(2 \, c x + b\right)}^{2}}{c}\right)^{\frac{3}{2}} \left(-c\right)^{\frac{5}{2}}}\right)} e^{\left(-2 \, a + \frac{b^{2}}{2 \, c}\right)}}{\sqrt{-c}}\right)} e^{2}"," ",0,"1/16*(sqrt(2)*sqrt(pi)*erf(sqrt(2)*sqrt(-c)*x - 1/2*sqrt(2)*b/sqrt(-c))*e^(2*a - 1/2*b^2/c)/sqrt(-c) + sqrt(2)*sqrt(pi)*erf(sqrt(2)*sqrt(c)*x + 1/2*sqrt(2)*b/sqrt(c))*e^(-2*a + 1/2*b^2/c)/sqrt(c) + 8*x)*d^2 + 1/16*(8*x^2 - sqrt(2)*(sqrt(pi)*(2*c*x + b)*b*(erf(sqrt(1/2)*sqrt(-(2*c*x + b)^2/c)) - 1)/(sqrt(-(2*c*x + b)^2/c)*c^(3/2)) - sqrt(2)*e^(1/2*(2*c*x + b)^2/c)/sqrt(c))*e^(2*a - 1/2*b^2/c)/sqrt(c) - sqrt(2)*(sqrt(pi)*(2*c*x + b)*b*(erf(sqrt(1/2)*sqrt((2*c*x + b)^2/c)) - 1)/(sqrt((2*c*x + b)^2/c)*(-c)^(3/2)) + sqrt(2)*c*e^(-1/2*(2*c*x + b)^2/c)/(-c)^(3/2))*e^(-2*a + 1/2*b^2/c)/sqrt(-c))*d*e + 1/192*(32*x^3 + 3*sqrt(2)*(sqrt(pi)*(2*c*x + b)*b^2*(erf(sqrt(1/2)*sqrt(-(2*c*x + b)^2/c)) - 1)/(sqrt(-(2*c*x + b)^2/c)*c^(5/2)) - 2*sqrt(2)*b*e^(1/2*(2*c*x + b)^2/c)/c^(3/2) - 2*(2*c*x + b)^3*gamma(3/2, -1/2*(2*c*x + b)^2/c)/((-(2*c*x + b)^2/c)^(3/2)*c^(5/2)))*e^(2*a - 1/2*b^2/c)/sqrt(c) - 3*sqrt(2)*(sqrt(pi)*(2*c*x + b)*b^2*(erf(sqrt(1/2)*sqrt((2*c*x + b)^2/c)) - 1)/(sqrt((2*c*x + b)^2/c)*(-c)^(5/2)) + 2*sqrt(2)*b*c*e^(-1/2*(2*c*x + b)^2/c)/(-c)^(5/2) - 2*(2*c*x + b)^3*gamma(3/2, 1/2*(2*c*x + b)^2/c)/(((2*c*x + b)^2/c)^(3/2)*(-c)^(5/2)))*e^(-2*a + 1/2*b^2/c)/sqrt(-c))*e^2","B",0
32,1,301,0,0.537312," ","integrate((e*x+d)*cosh(c*x^2+b*x+a)^2,x, algorithm=""maxima"")","\frac{1}{16} \, {\left(\frac{\sqrt{2} \sqrt{\pi} \operatorname{erf}\left(\sqrt{2} \sqrt{-c} x - \frac{\sqrt{2} b}{2 \, \sqrt{-c}}\right) e^{\left(2 \, a - \frac{b^{2}}{2 \, c}\right)}}{\sqrt{-c}} + \frac{\sqrt{2} \sqrt{\pi} \operatorname{erf}\left(\sqrt{2} \sqrt{c} x + \frac{\sqrt{2} b}{2 \, \sqrt{c}}\right) e^{\left(-2 \, a + \frac{b^{2}}{2 \, c}\right)}}{\sqrt{c}} + 8 \, x\right)} d + \frac{1}{32} \, {\left(8 \, x^{2} - \frac{\sqrt{2} {\left(\frac{\sqrt{\pi} {\left(2 \, c x + b\right)} b {\left(\operatorname{erf}\left(\sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(2 \, c x + b\right)}^{2}}{c}}\right) - 1\right)}}{\sqrt{-\frac{{\left(2 \, c x + b\right)}^{2}}{c}} c^{\frac{3}{2}}} - \frac{\sqrt{2} e^{\left(\frac{{\left(2 \, c x + b\right)}^{2}}{2 \, c}\right)}}{\sqrt{c}}\right)} e^{\left(2 \, a - \frac{b^{2}}{2 \, c}\right)}}{\sqrt{c}} - \frac{\sqrt{2} {\left(\frac{\sqrt{\pi} {\left(2 \, c x + b\right)} b {\left(\operatorname{erf}\left(\sqrt{\frac{1}{2}} \sqrt{\frac{{\left(2 \, c x + b\right)}^{2}}{c}}\right) - 1\right)}}{\sqrt{\frac{{\left(2 \, c x + b\right)}^{2}}{c}} \left(-c\right)^{\frac{3}{2}}} + \frac{\sqrt{2} c e^{\left(-\frac{{\left(2 \, c x + b\right)}^{2}}{2 \, c}\right)}}{\left(-c\right)^{\frac{3}{2}}}\right)} e^{\left(-2 \, a + \frac{b^{2}}{2 \, c}\right)}}{\sqrt{-c}}\right)} e"," ",0,"1/16*(sqrt(2)*sqrt(pi)*erf(sqrt(2)*sqrt(-c)*x - 1/2*sqrt(2)*b/sqrt(-c))*e^(2*a - 1/2*b^2/c)/sqrt(-c) + sqrt(2)*sqrt(pi)*erf(sqrt(2)*sqrt(c)*x + 1/2*sqrt(2)*b/sqrt(c))*e^(-2*a + 1/2*b^2/c)/sqrt(c) + 8*x)*d + 1/32*(8*x^2 - sqrt(2)*(sqrt(pi)*(2*c*x + b)*b*(erf(sqrt(1/2)*sqrt(-(2*c*x + b)^2/c)) - 1)/(sqrt(-(2*c*x + b)^2/c)*c^(3/2)) - sqrt(2)*e^(1/2*(2*c*x + b)^2/c)/sqrt(c))*e^(2*a - 1/2*b^2/c)/sqrt(c) - sqrt(2)*(sqrt(pi)*(2*c*x + b)*b*(erf(sqrt(1/2)*sqrt((2*c*x + b)^2/c)) - 1)/(sqrt((2*c*x + b)^2/c)*(-c)^(3/2)) + sqrt(2)*c*e^(-1/2*(2*c*x + b)^2/c)/(-c)^(3/2))*e^(-2*a + 1/2*b^2/c)/sqrt(-c))*e","B",0
33,0,0,0,0.000000," ","integrate(cosh(c*x^2+b*x+a)^2/(e*x+d),x, algorithm=""maxima"")","\frac{\log\left(e x + d\right)}{2 \, e} + \frac{1}{4} \, \int \frac{e^{\left(2 \, c x^{2} + 2 \, b x + 2 \, a\right)}}{e x + d}\,{d x} + \frac{1}{4} \, \int \frac{e^{\left(-2 \, c x^{2} - 2 \, b x\right)}}{e x e^{\left(2 \, a\right)} + d e^{\left(2 \, a\right)}}\,{d x}"," ",0,"1/2*log(e*x + d)/e + 1/4*integrate(e^(2*c*x^2 + 2*b*x + 2*a)/(e*x + d), x) + 1/4*integrate(e^(-2*c*x^2 - 2*b*x)/(e*x*e^(2*a) + d*e^(2*a)), x)","F",0
