1,1,370,0,0.418736," ","integrate((d*e*x+c*e)^3*(a+b*arctan(d*x+c)),x, algorithm=""maxima"")","\frac{1}{4} \, a d^{3} e^{3} x^{4} + a c d^{2} e^{3} x^{3} + \frac{3}{2} \, a c^{2} d e^{3} x^{2} + \frac{3}{2} \, {\left(x^{2} \arctan\left(d x + c\right) - d {\left(\frac{x}{d^{2}} + \frac{{\left(c^{2} - 1\right)} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d^{3}} - \frac{c \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{3}}\right)}\right)} b c^{2} d e^{3} + \frac{1}{2} \, {\left(2 \, x^{3} \arctan\left(d x + c\right) - d {\left(\frac{d x^{2} - 4 \, c x}{d^{3}} - \frac{2 \, {\left(c^{3} - 3 \, c\right)} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d^{4}} + \frac{{\left(3 \, c^{2} - 1\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{4}}\right)}\right)} b c d^{2} e^{3} + \frac{1}{12} \, {\left(3 \, x^{4} \arctan\left(d x + c\right) - d {\left(\frac{d^{2} x^{3} - 3 \, c d x^{2} + 3 \, {\left(3 \, c^{2} - 1\right)} x}{d^{4}} + \frac{3 \, {\left(c^{4} - 6 \, c^{2} + 1\right)} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d^{5}} - \frac{6 \, {\left(c^{3} - c\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{5}}\right)}\right)} b d^{3} e^{3} + a c^{3} e^{3} x + \frac{{\left(2 \, {\left(d x + c\right)} \arctan\left(d x + c\right) - \log\left({\left(d x + c\right)}^{2} + 1\right)\right)} b c^{3} e^{3}}{2 \, d}"," ",0,"1/4*a*d^3*e^3*x^4 + a*c*d^2*e^3*x^3 + 3/2*a*c^2*d*e^3*x^2 + 3/2*(x^2*arctan(d*x + c) - d*(x/d^2 + (c^2 - 1)*arctan((d^2*x + c*d)/d)/d^3 - c*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/d^3))*b*c^2*d*e^3 + 1/2*(2*x^3*arctan(d*x + c) - d*((d*x^2 - 4*c*x)/d^3 - 2*(c^3 - 3*c)*arctan((d^2*x + c*d)/d)/d^4 + (3*c^2 - 1)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/d^4))*b*c*d^2*e^3 + 1/12*(3*x^4*arctan(d*x + c) - d*((d^2*x^3 - 3*c*d*x^2 + 3*(3*c^2 - 1)*x)/d^4 + 3*(c^4 - 6*c^2 + 1)*arctan((d^2*x + c*d)/d)/d^5 - 6*(c^3 - c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/d^5))*b*d^3*e^3 + a*c^3*e^3*x + 1/2*(2*(d*x + c)*arctan(d*x + c) - log((d*x + c)^2 + 1))*b*c^3*e^3/d","B",0
2,1,238,0,0.420686," ","integrate((d*e*x+c*e)^2*(a+b*arctan(d*x+c)),x, algorithm=""maxima"")","\frac{1}{3} \, a d^{2} e^{2} x^{3} + a c d e^{2} x^{2} + {\left(x^{2} \arctan\left(d x + c\right) - d {\left(\frac{x}{d^{2}} + \frac{{\left(c^{2} - 1\right)} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d^{3}} - \frac{c \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{3}}\right)}\right)} b c d e^{2} + \frac{1}{6} \, {\left(2 \, x^{3} \arctan\left(d x + c\right) - d {\left(\frac{d x^{2} - 4 \, c x}{d^{3}} - \frac{2 \, {\left(c^{3} - 3 \, c\right)} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d^{4}} + \frac{{\left(3 \, c^{2} - 1\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{4}}\right)}\right)} b d^{2} e^{2} + a c^{2} e^{2} x + \frac{{\left(2 \, {\left(d x + c\right)} \arctan\left(d x + c\right) - \log\left({\left(d x + c\right)}^{2} + 1\right)\right)} b c^{2} e^{2}}{2 \, d}"," ",0,"1/3*a*d^2*e^2*x^3 + a*c*d*e^2*x^2 + (x^2*arctan(d*x + c) - d*(x/d^2 + (c^2 - 1)*arctan((d^2*x + c*d)/d)/d^3 - c*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/d^3))*b*c*d*e^2 + 1/6*(2*x^3*arctan(d*x + c) - d*((d*x^2 - 4*c*x)/d^3 - 2*(c^3 - 3*c)*arctan((d^2*x + c*d)/d)/d^4 + (3*c^2 - 1)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/d^4))*b*d^2*e^2 + a*c^2*e^2*x + 1/2*(2*(d*x + c)*arctan(d*x + c) - log((d*x + c)^2 + 1))*b*c^2*e^2/d","B",0
3,1,120,0,0.420003," ","integrate((d*e*x+c*e)*(a+b*arctan(d*x+c)),x, algorithm=""maxima"")","\frac{1}{2} \, a d e x^{2} + \frac{1}{2} \, {\left(x^{2} \arctan\left(d x + c\right) - d {\left(\frac{x}{d^{2}} + \frac{{\left(c^{2} - 1\right)} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d^{3}} - \frac{c \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{3}}\right)}\right)} b d e + a c e x + \frac{{\left(2 \, {\left(d x + c\right)} \arctan\left(d x + c\right) - \log\left({\left(d x + c\right)}^{2} + 1\right)\right)} b c e}{2 \, d}"," ",0,"1/2*a*d*e*x^2 + 1/2*(x^2*arctan(d*x + c) - d*(x/d^2 + (c^2 - 1)*arctan((d^2*x + c*d)/d)/d^3 - c*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/d^3))*b*d*e + a*c*e*x + 1/2*(2*(d*x + c)*arctan(d*x + c) - log((d*x + c)^2 + 1))*b*c*e/d","B",0
4,0,0,0,0.000000," ","integrate((a+b*arctan(d*x+c))/(d*e*x+c*e),x, algorithm=""maxima"")","2 \, b \int \frac{\arctan\left(d x + c\right)}{2 \, {\left(d e x + c e\right)}}\,{d x} + \frac{a \log\left(d e x + c e\right)}{d e}"," ",0,"2*b*integrate(1/2*arctan(d*x + c)/(d*e*x + c*e), x) + a*log(d*e*x + c*e)/(d*e)","F",0
5,1,92,0,0.315970," ","integrate((a+b*arctan(d*x+c))/(d*e*x+c*e)^2,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(d {\left(\frac{\log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{2} e^{2}} - \frac{2 \, \log\left(d x + c\right)}{d^{2} e^{2}}\right)} + \frac{2 \, \arctan\left(d x + c\right)}{d^{2} e^{2} x + c d e^{2}}\right)} b - \frac{a}{d^{2} e^{2} x + c d e^{2}}"," ",0,"-1/2*(d*(log(d^2*x^2 + 2*c*d*x + c^2 + 1)/(d^2*e^2) - 2*log(d*x + c)/(d^2*e^2)) + 2*arctan(d*x + c)/(d^2*e^2*x + c*d*e^2))*b - a/(d^2*e^2*x + c*d*e^2)","A",0
6,1,120,0,0.423664," ","integrate((a+b*arctan(d*x+c))/(d*e*x+c*e)^3,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(d {\left(\frac{1}{d^{3} e^{3} x + c d^{2} e^{3}} + \frac{\arctan\left(\frac{d^{2} x + c d}{d}\right)}{d^{2} e^{3}}\right)} + \frac{\arctan\left(d x + c\right)}{d^{3} e^{3} x^{2} + 2 \, c d^{2} e^{3} x + c^{2} d e^{3}}\right)} b - \frac{a}{2 \, {\left(d^{3} e^{3} x^{2} + 2 \, c d^{2} e^{3} x + c^{2} d e^{3}\right)}}"," ",0,"-1/2*(d*(1/(d^3*e^3*x + c*d^2*e^3) + arctan((d^2*x + c*d)/d)/(d^2*e^3)) + arctan(d*x + c)/(d^3*e^3*x^2 + 2*c*d^2*e^3*x + c^2*d*e^3))*b - 1/2*a/(d^3*e^3*x^2 + 2*c*d^2*e^3*x + c^2*d*e^3)","B",0
7,1,597,0,1.801954," ","integrate((d*e*x+c*e)^3*(a+b*arctan(d*x+c))^2,x, algorithm=""maxima"")","\frac{1}{4} \, a^{2} d^{3} e^{3} x^{4} + a^{2} c d^{2} e^{3} x^{3} + \frac{3}{2} \, a^{2} c^{2} d e^{3} x^{2} + 3 \, {\left(x^{2} \arctan\left(d x + c\right) - d {\left(\frac{x}{d^{2}} + \frac{{\left(c^{2} - 1\right)} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d^{3}} - \frac{c \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{3}}\right)}\right)} a b c^{2} d e^{3} + {\left(2 \, x^{3} \arctan\left(d x + c\right) - d {\left(\frac{d x^{2} - 4 \, c x}{d^{3}} - \frac{2 \, {\left(c^{3} - 3 \, c\right)} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d^{4}} + \frac{{\left(3 \, c^{2} - 1\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{4}}\right)}\right)} a b c d^{2} e^{3} + \frac{1}{6} \, {\left(3 \, x^{4} \arctan\left(d x + c\right) - d {\left(\frac{d^{2} x^{3} - 3 \, c d x^{2} + 3 \, {\left(3 \, c^{2} - 1\right)} x}{d^{4}} + \frac{3 \, {\left(c^{4} - 6 \, c^{2} + 1\right)} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d^{5}} - \frac{6 \, {\left(c^{3} - c\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{5}}\right)}\right)} a b d^{3} e^{3} + a^{2} c^{3} e^{3} x + \frac{{\left(2 \, {\left(d x + c\right)} \arctan\left(d x + c\right) - \log\left({\left(d x + c\right)}^{2} + 1\right)\right)} a b c^{3} e^{3}}{d} + \frac{b^{2} d^{2} e^{3} x^{2} + 2 \, b^{2} c d e^{3} x - 4 \, b^{2} e^{3} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right) + 3 \, {\left(b^{2} d^{4} e^{3} x^{4} + 4 \, b^{2} c d^{3} e^{3} x^{3} + 6 \, b^{2} c^{2} d^{2} e^{3} x^{2} + 4 \, b^{2} c^{3} d e^{3} x + {\left(b^{2} c^{4} - b^{2}\right)} e^{3}\right)} \arctan\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d^{3} e^{3} x^{3} + 3 \, b^{2} c d^{2} e^{3} x^{2} + 3 \, {\left(b^{2} c^{2} - b^{2}\right)} d e^{3} x + {\left(b^{2} c^{3} - 3 \, b^{2} c\right)} e^{3}\right)} \arctan\left(d x + c\right)}{12 \, d}"," ",0,"1/4*a^2*d^3*e^3*x^4 + a^2*c*d^2*e^3*x^3 + 3/2*a^2*c^2*d*e^3*x^2 + 3*(x^2*arctan(d*x + c) - d*(x/d^2 + (c^2 - 1)*arctan((d^2*x + c*d)/d)/d^3 - c*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/d^3))*a*b*c^2*d*e^3 + (2*x^3*arctan(d*x + c) - d*((d*x^2 - 4*c*x)/d^3 - 2*(c^3 - 3*c)*arctan((d^2*x + c*d)/d)/d^4 + (3*c^2 - 1)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/d^4))*a*b*c*d^2*e^3 + 1/6*(3*x^4*arctan(d*x + c) - d*((d^2*x^3 - 3*c*d*x^2 + 3*(3*c^2 - 1)*x)/d^4 + 3*(c^4 - 6*c^2 + 1)*arctan((d^2*x + c*d)/d)/d^5 - 6*(c^3 - c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/d^5))*a*b*d^3*e^3 + a^2*c^3*e^3*x + (2*(d*x + c)*arctan(d*x + c) - log((d*x + c)^2 + 1))*a*b*c^3*e^3/d + 1/12*(b^2*d^2*e^3*x^2 + 2*b^2*c*d*e^3*x - 4*b^2*e^3*log(d^2*x^2 + 2*c*d*x + c^2 + 1) + 3*(b^2*d^4*e^3*x^4 + 4*b^2*c*d^3*e^3*x^3 + 6*b^2*c^2*d^2*e^3*x^2 + 4*b^2*c^3*d*e^3*x + (b^2*c^4 - b^2)*e^3)*arctan(d*x + c)^2 - 2*(b^2*d^3*e^3*x^3 + 3*b^2*c*d^2*e^3*x^2 + 3*(b^2*c^2 - b^2)*d*e^3*x + (b^2*c^3 - 3*b^2*c)*e^3)*arctan(d*x + c))/d","B",0
8,0,0,0,0.000000," ","integrate((d*e*x+c*e)^2*(a+b*arctan(d*x+c))^2,x, algorithm=""maxima"")","\frac{3 \, b^{2} c^{4} e^{2} \arctan\left(d x + c\right)^{2} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{4 \, d} - \frac{1}{4} \, {\left(\frac{3 \, \arctan\left(d x + c\right) \arctan\left(\frac{d^{2} x + c d}{d}\right)^{2}}{d} - \frac{\arctan\left(\frac{d^{2} x + c d}{d}\right)^{3}}{d}\right)} b^{2} c^{4} e^{2} + \frac{1}{3} \, a^{2} d^{2} e^{2} x^{3} + 36 \, b^{2} d^{4} e^{2} \int \frac{x^{4} \arctan\left(d x + c\right)^{2}}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 3 \, b^{2} d^{4} e^{2} \int \frac{x^{4} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 144 \, b^{2} c d^{3} e^{2} \int \frac{x^{3} \arctan\left(d x + c\right)^{2}}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 4 \, b^{2} d^{4} e^{2} \int \frac{x^{4} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 12 \, b^{2} c d^{3} e^{2} \int \frac{x^{3} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 216 \, b^{2} c^{2} d^{2} e^{2} \int \frac{x^{2} \arctan\left(d x + c\right)^{2}}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 16 \, b^{2} c d^{3} e^{2} \int \frac{x^{3} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 18 \, b^{2} c^{2} d^{2} e^{2} \int \frac{x^{2} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 144 \, b^{2} c^{3} d e^{2} \int \frac{x \arctan\left(d x + c\right)^{2}}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 24 \, b^{2} c^{2} d^{2} e^{2} \int \frac{x^{2} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 12 \, b^{2} c^{3} d e^{2} \int \frac{x \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 12 \, b^{2} c^{3} d e^{2} \int \frac{x \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 3 \, b^{2} c^{4} e^{2} \int \frac{\log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + a^{2} c d e^{2} x^{2} + \frac{3 \, b^{2} c^{2} e^{2} \arctan\left(d x + c\right)^{2} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{4 \, d} - 8 \, b^{2} d^{3} e^{2} \int \frac{x^{3} \arctan\left(d x + c\right)}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} - 24 \, b^{2} c d^{2} e^{2} \int \frac{x^{2} \arctan\left(d x + c\right)}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} - 24 \, b^{2} c^{2} d e^{2} \int \frac{x \arctan\left(d x + c\right)}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} - \frac{1}{4} \, {\left(\frac{3 \, \arctan\left(d x + c\right) \arctan\left(\frac{d^{2} x + c d}{d}\right)^{2}}{d} - \frac{\arctan\left(\frac{d^{2} x + c d}{d}\right)^{3}}{d}\right)} b^{2} c^{2} e^{2} + 2 \, {\left(x^{2} \arctan\left(d x + c\right) - d {\left(\frac{x}{d^{2}} + \frac{{\left(c^{2} - 1\right)} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d^{3}} - \frac{c \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{3}}\right)}\right)} a b c d e^{2} + \frac{1}{3} \, {\left(2 \, x^{3} \arctan\left(d x + c\right) - d {\left(\frac{d x^{2} - 4 \, c x}{d^{3}} - \frac{2 \, {\left(c^{3} - 3 \, c\right)} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d^{4}} + \frac{{\left(3 \, c^{2} - 1\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{4}}\right)}\right)} a b d^{2} e^{2} + a^{2} c^{2} e^{2} x + 36 \, b^{2} d^{2} e^{2} \int \frac{x^{2} \arctan\left(d x + c\right)^{2}}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 3 \, b^{2} d^{2} e^{2} \int \frac{x^{2} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 72 \, b^{2} c d e^{2} \int \frac{x \arctan\left(d x + c\right)^{2}}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 6 \, b^{2} c d e^{2} \int \frac{x \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 3 \, b^{2} c^{2} e^{2} \int \frac{\log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + \frac{{\left(2 \, {\left(d x + c\right)} \arctan\left(d x + c\right) - \log\left({\left(d x + c\right)}^{2} + 1\right)\right)} a b c^{2} e^{2}}{d} + \frac{1}{12} \, {\left(b^{2} d^{2} e^{2} x^{3} + 3 \, b^{2} c d e^{2} x^{2} + 3 \, b^{2} c^{2} e^{2} x\right)} \arctan\left(d x + c\right)^{2} - \frac{1}{48} \, {\left(b^{2} d^{2} e^{2} x^{3} + 3 \, b^{2} c d e^{2} x^{2} + 3 \, b^{2} c^{2} e^{2} x\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}"," ",0,"3/4*b^2*c^4*e^2*arctan(d*x + c)^2*arctan((d^2*x + c*d)/d)/d - 1/4*(3*arctan(d*x + c)*arctan((d^2*x + c*d)/d)^2/d - arctan((d^2*x + c*d)/d)^3/d)*b^2*c^4*e^2 + 1/3*a^2*d^2*e^2*x^3 + 36*b^2*d^4*e^2*integrate(1/48*x^4*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 3*b^2*d^4*e^2*integrate(1/48*x^4*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 144*b^2*c*d^3*e^2*integrate(1/48*x^3*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 4*b^2*d^4*e^2*integrate(1/48*x^4*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 12*b^2*c*d^3*e^2*integrate(1/48*x^3*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 216*b^2*c^2*d^2*e^2*integrate(1/48*x^2*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 16*b^2*c*d^3*e^2*integrate(1/48*x^3*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 18*b^2*c^2*d^2*e^2*integrate(1/48*x^2*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 144*b^2*c^3*d*e^2*integrate(1/48*x*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 24*b^2*c^2*d^2*e^2*integrate(1/48*x^2*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 12*b^2*c^3*d*e^2*integrate(1/48*x*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 12*b^2*c^3*d*e^2*integrate(1/48*x*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 3*b^2*c^4*e^2*integrate(1/48*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + a^2*c*d*e^2*x^2 + 3/4*b^2*c^2*e^2*arctan(d*x + c)^2*arctan((d^2*x + c*d)/d)/d - 8*b^2*d^3*e^2*integrate(1/48*x^3*arctan(d*x + c)/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) - 24*b^2*c*d^2*e^2*integrate(1/48*x^2*arctan(d*x + c)/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) - 24*b^2*c^2*d*e^2*integrate(1/48*x*arctan(d*x + c)/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) - 1/4*(3*arctan(d*x + c)*arctan((d^2*x + c*d)/d)^2/d - arctan((d^2*x + c*d)/d)^3/d)*b^2*c^2*e^2 + 2*(x^2*arctan(d*x + c) - d*(x/d^2 + (c^2 - 1)*arctan((d^2*x + c*d)/d)/d^3 - c*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/d^3))*a*b*c*d*e^2 + 1/3*(2*x^3*arctan(d*x + c) - d*((d*x^2 - 4*c*x)/d^3 - 2*(c^3 - 3*c)*arctan((d^2*x + c*d)/d)/d^4 + (3*c^2 - 1)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/d^4))*a*b*d^2*e^2 + a^2*c^2*e^2*x + 36*b^2*d^2*e^2*integrate(1/48*x^2*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 3*b^2*d^2*e^2*integrate(1/48*x^2*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 72*b^2*c*d*e^2*integrate(1/48*x*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 6*b^2*c*d*e^2*integrate(1/48*x*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 3*b^2*c^2*e^2*integrate(1/48*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + (2*(d*x + c)*arctan(d*x + c) - log((d*x + c)^2 + 1))*a*b*c^2*e^2/d + 1/12*(b^2*d^2*e^2*x^3 + 3*b^2*c*d*e^2*x^2 + 3*b^2*c^2*e^2*x)*arctan(d*x + c)^2 - 1/48*(b^2*d^2*e^2*x^3 + 3*b^2*c*d*e^2*x^2 + 3*b^2*c^2*e^2*x)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2","F",0
9,1,218,0,1.488463," ","integrate((d*e*x+c*e)*(a+b*arctan(d*x+c))^2,x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} d e x^{2} + {\left(x^{2} \arctan\left(d x + c\right) - d {\left(\frac{x}{d^{2}} + \frac{{\left(c^{2} - 1\right)} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d^{3}} - \frac{c \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{3}}\right)}\right)} a b d e + a^{2} c e x + \frac{{\left(2 \, {\left(d x + c\right)} \arctan\left(d x + c\right) - \log\left({\left(d x + c\right)}^{2} + 1\right)\right)} a b c e}{d} + \frac{b^{2} e \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right) + {\left(b^{2} d^{2} e x^{2} + 2 \, b^{2} c d e x + {\left(b^{2} c^{2} + b^{2}\right)} e\right)} \arctan\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d e x + b^{2} c e\right)} \arctan\left(d x + c\right)}{2 \, d}"," ",0,"1/2*a^2*d*e*x^2 + (x^2*arctan(d*x + c) - d*(x/d^2 + (c^2 - 1)*arctan((d^2*x + c*d)/d)/d^3 - c*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/d^3))*a*b*d*e + a^2*c*e*x + (2*(d*x + c)*arctan(d*x + c) - log((d*x + c)^2 + 1))*a*b*c*e/d + 1/2*(b^2*e*log(d^2*x^2 + 2*c*d*x + c^2 + 1) + (b^2*d^2*e*x^2 + 2*b^2*c*d*e*x + (b^2*c^2 + b^2)*e)*arctan(d*x + c)^2 - 2*(b^2*d*e*x + b^2*c*e)*arctan(d*x + c))/d","B",0
10,0,0,0,0.000000," ","integrate((a+b*arctan(d*x+c))^2/(d*e*x+c*e),x, algorithm=""maxima"")","\frac{a^{2} \log\left(d e x + c e\right)}{d e} + \int \frac{12 \, b^{2} \arctan\left(d x + c\right)^{2} + b^{2} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2} + 32 \, a b \arctan\left(d x + c\right)}{16 \, {\left(d e x + c e\right)}}\,{d x}"," ",0,"a^2*log(d*e*x + c*e)/(d*e) + integrate(1/16*(12*b^2*arctan(d*x + c)^2 + b^2*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 + 32*a*b*arctan(d*x + c))/(d*e*x + c*e), x)","F",0
11,-1,0,0,0.000000," ","integrate((a+b*arctan(d*x+c))^2/(d*e*x+c*e)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
12,1,268,0,0.537694," ","integrate((a+b*arctan(d*x+c))^2/(d*e*x+c*e)^3,x, algorithm=""maxima"")","-{\left(d {\left(\frac{1}{d^{3} e^{3} x + c d^{2} e^{3}} + \frac{\arctan\left(\frac{d^{2} x + c d}{d}\right)}{d^{2} e^{3}}\right)} + \frac{\arctan\left(d x + c\right)}{d^{3} e^{3} x^{2} + 2 \, c d^{2} e^{3} x + c^{2} d e^{3}}\right)} a b - \frac{1}{2} \, {\left(2 \, d {\left(\frac{1}{d^{3} e^{3} x + c d^{2} e^{3}} + \frac{\arctan\left(\frac{d^{2} x + c d}{d}\right)}{d^{2} e^{3}}\right)} \arctan\left(d x + c\right) - \frac{\arctan\left(d x + c\right)^{2} - \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right) + 2 \, \log\left(d x + c\right)}{d e^{3}}\right)} b^{2} - \frac{b^{2} \arctan\left(d x + c\right)^{2}}{2 \, {\left(d^{3} e^{3} x^{2} + 2 \, c d^{2} e^{3} x + c^{2} d e^{3}\right)}} - \frac{a^{2}}{2 \, {\left(d^{3} e^{3} x^{2} + 2 \, c d^{2} e^{3} x + c^{2} d e^{3}\right)}}"," ",0,"-(d*(1/(d^3*e^3*x + c*d^2*e^3) + arctan((d^2*x + c*d)/d)/(d^2*e^3)) + arctan(d*x + c)/(d^3*e^3*x^2 + 2*c*d^2*e^3*x + c^2*d*e^3))*a*b - 1/2*(2*d*(1/(d^3*e^3*x + c*d^2*e^3) + arctan((d^2*x + c*d)/d)/(d^2*e^3))*arctan(d*x + c) - (arctan(d*x + c)^2 - log(d^2*x^2 + 2*c*d*x + c^2 + 1) + 2*log(d*x + c))/(d*e^3))*b^2 - 1/2*b^2*arctan(d*x + c)^2/(d^3*e^3*x^2 + 2*c*d^2*e^3*x + c^2*d*e^3) - 1/2*a^2/(d^3*e^3*x^2 + 2*c*d^2*e^3*x + c^2*d*e^3)","B",0
13,-1,0,0,0.000000," ","integrate((a+b*arctan(d*x+c))^2/(d*e*x+c*e)^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
14,1,534,0,0.510758," ","integrate((a+b*arctan(d*x+c))^2/(d*e*x+c*e)^5,x, algorithm=""maxima"")","\frac{1}{6} \, {\left(d {\left(\frac{3 \, d^{2} x^{2} + 6 \, c d x + 3 \, c^{2} - 1}{d^{5} e^{5} x^{3} + 3 \, c d^{4} e^{5} x^{2} + 3 \, c^{2} d^{3} e^{5} x + c^{3} d^{2} e^{5}} + \frac{3 \, \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d^{2} e^{5}}\right)} - \frac{3 \, \arctan\left(d x + c\right)}{d^{5} e^{5} x^{4} + 4 \, c d^{4} e^{5} x^{3} + 6 \, c^{2} d^{3} e^{5} x^{2} + 4 \, c^{3} d^{2} e^{5} x + c^{4} d e^{5}}\right)} a b + \frac{1}{12} \, {\left(2 \, d {\left(\frac{3 \, d^{2} x^{2} + 6 \, c d x + 3 \, c^{2} - 1}{d^{5} e^{5} x^{3} + 3 \, c d^{4} e^{5} x^{2} + 3 \, c^{2} d^{3} e^{5} x + c^{3} d^{2} e^{5}} + \frac{3 \, \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d^{2} e^{5}}\right)} \arctan\left(d x + c\right) - \frac{{\left(3 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2}\right)} \arctan\left(d x + c\right)^{2} - 4 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2}\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right) + 8 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2}\right)} \log\left(d x + c\right) + 1\right)} d^{2}}{d^{5} e^{5} x^{2} + 2 \, c d^{4} e^{5} x + c^{2} d^{3} e^{5}}\right)} b^{2} - \frac{b^{2} \arctan\left(d x + c\right)^{2}}{4 \, {\left(d^{5} e^{5} x^{4} + 4 \, c d^{4} e^{5} x^{3} + 6 \, c^{2} d^{3} e^{5} x^{2} + 4 \, c^{3} d^{2} e^{5} x + c^{4} d e^{5}\right)}} - \frac{a^{2}}{4 \, {\left(d^{5} e^{5} x^{4} + 4 \, c d^{4} e^{5} x^{3} + 6 \, c^{2} d^{3} e^{5} x^{2} + 4 \, c^{3} d^{2} e^{5} x + c^{4} d e^{5}\right)}}"," ",0,"1/6*(d*((3*d^2*x^2 + 6*c*d*x + 3*c^2 - 1)/(d^5*e^5*x^3 + 3*c*d^4*e^5*x^2 + 3*c^2*d^3*e^5*x + c^3*d^2*e^5) + 3*arctan((d^2*x + c*d)/d)/(d^2*e^5)) - 3*arctan(d*x + c)/(d^5*e^5*x^4 + 4*c*d^4*e^5*x^3 + 6*c^2*d^3*e^5*x^2 + 4*c^3*d^2*e^5*x + c^4*d*e^5))*a*b + 1/12*(2*d*((3*d^2*x^2 + 6*c*d*x + 3*c^2 - 1)/(d^5*e^5*x^3 + 3*c*d^4*e^5*x^2 + 3*c^2*d^3*e^5*x + c^3*d^2*e^5) + 3*arctan((d^2*x + c*d)/d)/(d^2*e^5))*arctan(d*x + c) - (3*(d^2*x^2 + 2*c*d*x + c^2)*arctan(d*x + c)^2 - 4*(d^2*x^2 + 2*c*d*x + c^2)*log(d^2*x^2 + 2*c*d*x + c^2 + 1) + 8*(d^2*x^2 + 2*c*d*x + c^2)*log(d*x + c) + 1)*d^2/(d^5*e^5*x^2 + 2*c*d^4*e^5*x + c^2*d^3*e^5))*b^2 - 1/4*b^2*arctan(d*x + c)^2/(d^5*e^5*x^4 + 4*c*d^4*e^5*x^3 + 6*c^2*d^3*e^5*x^2 + 4*c^3*d^2*e^5*x + c^4*d*e^5) - 1/4*a^2/(d^5*e^5*x^4 + 4*c*d^4*e^5*x^3 + 6*c^2*d^3*e^5*x^2 + 4*c^3*d^2*e^5*x + c^4*d*e^5)","B",0
15,0,0,0,0.000000," ","integrate((d*e*x+c*e)^2*(a+b*arctan(d*x+c))^3,x, algorithm=""maxima"")","\frac{7 \, b^{3} c^{4} e^{2} \arctan\left(d x + c\right)^{3} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{8 \, d} + \frac{3 \, a b^{2} c^{4} e^{2} \arctan\left(d x + c\right)^{2} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d} - {\left(\frac{3 \, \arctan\left(d x + c\right) \arctan\left(\frac{d^{2} x + c d}{d}\right)^{2}}{d} - \frac{\arctan\left(\frac{d^{2} x + c d}{d}\right)^{3}}{d}\right)} a b^{2} c^{4} e^{2} - \frac{7}{32} \, {\left(\frac{6 \, \arctan\left(d x + c\right)^{2} \arctan\left(\frac{d^{2} x + c d}{d}\right)^{2}}{d} - \frac{4 \, \arctan\left(d x + c\right) \arctan\left(\frac{d^{2} x + c d}{d}\right)^{3}}{d} + \frac{\arctan\left(\frac{d^{2} x + c d}{d}\right)^{4}}{d}\right)} b^{3} c^{4} e^{2} + \frac{1}{3} \, a^{3} d^{2} e^{2} x^{3} + \frac{7 \, b^{3} c^{2} e^{2} \arctan\left(d x + c\right)^{3} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{8 \, d} + 28 \, b^{3} d^{4} e^{2} \int \frac{x^{4} \arctan\left(d x + c\right)^{3}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 3 \, b^{3} d^{4} e^{2} \int \frac{x^{4} \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 96 \, a b^{2} d^{4} e^{2} \int \frac{x^{4} \arctan\left(d x + c\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 112 \, b^{3} c d^{3} e^{2} \int \frac{x^{3} \arctan\left(d x + c\right)^{3}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 4 \, b^{3} d^{4} e^{2} \int \frac{x^{4} \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 12 \, b^{3} c d^{3} e^{2} \int \frac{x^{3} \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 384 \, a b^{2} c d^{3} e^{2} \int \frac{x^{3} \arctan\left(d x + c\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 168 \, b^{3} c^{2} d^{2} e^{2} \int \frac{x^{2} \arctan\left(d x + c\right)^{3}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 16 \, b^{3} c d^{3} e^{2} \int \frac{x^{3} \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 18 \, b^{3} c^{2} d^{2} e^{2} \int \frac{x^{2} \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 576 \, a b^{2} c^{2} d^{2} e^{2} \int \frac{x^{2} \arctan\left(d x + c\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 112 \, b^{3} c^{3} d e^{2} \int \frac{x \arctan\left(d x + c\right)^{3}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 24 \, b^{3} c^{2} d^{2} e^{2} \int \frac{x^{2} \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 12 \, b^{3} c^{3} d e^{2} \int \frac{x \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 384 \, a b^{2} c^{3} d e^{2} \int \frac{x \arctan\left(d x + c\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 12 \, b^{3} c^{3} d e^{2} \int \frac{x \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 3 \, b^{3} c^{4} e^{2} \int \frac{\arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + a^{3} c d e^{2} x^{2} + \frac{3 \, a b^{2} c^{2} e^{2} \arctan\left(d x + c\right)^{2} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d} - 4 \, b^{3} d^{3} e^{2} \int \frac{x^{3} \arctan\left(d x + c\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + b^{3} d^{3} e^{2} \int \frac{x^{3} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} - 12 \, b^{3} c d^{2} e^{2} \int \frac{x^{2} \arctan\left(d x + c\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 3 \, b^{3} c d^{2} e^{2} \int \frac{x^{2} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} - 12 \, b^{3} c^{2} d e^{2} \int \frac{x \arctan\left(d x + c\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 3 \, b^{3} c^{2} d e^{2} \int \frac{x \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} - {\left(\frac{3 \, \arctan\left(d x + c\right) \arctan\left(\frac{d^{2} x + c d}{d}\right)^{2}}{d} - \frac{\arctan\left(\frac{d^{2} x + c d}{d}\right)^{3}}{d}\right)} a b^{2} c^{2} e^{2} - \frac{7}{32} \, {\left(\frac{6 \, \arctan\left(d x + c\right)^{2} \arctan\left(\frac{d^{2} x + c d}{d}\right)^{2}}{d} - \frac{4 \, \arctan\left(d x + c\right) \arctan\left(\frac{d^{2} x + c d}{d}\right)^{3}}{d} + \frac{\arctan\left(\frac{d^{2} x + c d}{d}\right)^{4}}{d}\right)} b^{3} c^{2} e^{2} + 3 \, {\left(x^{2} \arctan\left(d x + c\right) - d {\left(\frac{x}{d^{2}} + \frac{{\left(c^{2} - 1\right)} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d^{3}} - \frac{c \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{3}}\right)}\right)} a^{2} b c d e^{2} + \frac{1}{2} \, {\left(2 \, x^{3} \arctan\left(d x + c\right) - d {\left(\frac{d x^{2} - 4 \, c x}{d^{3}} - \frac{2 \, {\left(c^{3} - 3 \, c\right)} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d^{4}} + \frac{{\left(3 \, c^{2} - 1\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{4}}\right)}\right)} a^{2} b d^{2} e^{2} + a^{3} c^{2} e^{2} x + 28 \, b^{3} d^{2} e^{2} \int \frac{x^{2} \arctan\left(d x + c\right)^{3}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 3 \, b^{3} d^{2} e^{2} \int \frac{x^{2} \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 96 \, a b^{2} d^{2} e^{2} \int \frac{x^{2} \arctan\left(d x + c\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 56 \, b^{3} c d e^{2} \int \frac{x \arctan\left(d x + c\right)^{3}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 6 \, b^{3} c d e^{2} \int \frac{x \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 192 \, a b^{2} c d e^{2} \int \frac{x \arctan\left(d x + c\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 3 \, b^{3} c^{2} e^{2} \int \frac{\arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + \frac{3 \, {\left(2 \, {\left(d x + c\right)} \arctan\left(d x + c\right) - \log\left({\left(d x + c\right)}^{2} + 1\right)\right)} a^{2} b c^{2} e^{2}}{2 \, d} + \frac{1}{24} \, {\left(b^{3} d^{2} e^{2} x^{3} + 3 \, b^{3} c d e^{2} x^{2} + 3 \, b^{3} c^{2} e^{2} x\right)} \arctan\left(d x + c\right)^{3} - \frac{1}{32} \, {\left(b^{3} d^{2} e^{2} x^{3} + 3 \, b^{3} c d e^{2} x^{2} + 3 \, b^{3} c^{2} e^{2} x\right)} \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}"," ",0,"7/8*b^3*c^4*e^2*arctan(d*x + c)^3*arctan((d^2*x + c*d)/d)/d + 3*a*b^2*c^4*e^2*arctan(d*x + c)^2*arctan((d^2*x + c*d)/d)/d - (3*arctan(d*x + c)*arctan((d^2*x + c*d)/d)^2/d - arctan((d^2*x + c*d)/d)^3/d)*a*b^2*c^4*e^2 - 7/32*(6*arctan(d*x + c)^2*arctan((d^2*x + c*d)/d)^2/d - 4*arctan(d*x + c)*arctan((d^2*x + c*d)/d)^3/d + arctan((d^2*x + c*d)/d)^4/d)*b^3*c^4*e^2 + 1/3*a^3*d^2*e^2*x^3 + 7/8*b^3*c^2*e^2*arctan(d*x + c)^3*arctan((d^2*x + c*d)/d)/d + 28*b^3*d^4*e^2*integrate(1/32*x^4*arctan(d*x + c)^3/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 3*b^3*d^4*e^2*integrate(1/32*x^4*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 96*a*b^2*d^4*e^2*integrate(1/32*x^4*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 112*b^3*c*d^3*e^2*integrate(1/32*x^3*arctan(d*x + c)^3/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 4*b^3*d^4*e^2*integrate(1/32*x^4*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 12*b^3*c*d^3*e^2*integrate(1/32*x^3*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 384*a*b^2*c*d^3*e^2*integrate(1/32*x^3*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 168*b^3*c^2*d^2*e^2*integrate(1/32*x^2*arctan(d*x + c)^3/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 16*b^3*c*d^3*e^2*integrate(1/32*x^3*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 18*b^3*c^2*d^2*e^2*integrate(1/32*x^2*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 576*a*b^2*c^2*d^2*e^2*integrate(1/32*x^2*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 112*b^3*c^3*d*e^2*integrate(1/32*x*arctan(d*x + c)^3/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 24*b^3*c^2*d^2*e^2*integrate(1/32*x^2*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 12*b^3*c^3*d*e^2*integrate(1/32*x*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 384*a*b^2*c^3*d*e^2*integrate(1/32*x*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 12*b^3*c^3*d*e^2*integrate(1/32*x*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 3*b^3*c^4*e^2*integrate(1/32*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + a^3*c*d*e^2*x^2 + 3*a*b^2*c^2*e^2*arctan(d*x + c)^2*arctan((d^2*x + c*d)/d)/d - 4*b^3*d^3*e^2*integrate(1/32*x^3*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + b^3*d^3*e^2*integrate(1/32*x^3*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) - 12*b^3*c*d^2*e^2*integrate(1/32*x^2*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 3*b^3*c*d^2*e^2*integrate(1/32*x^2*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) - 12*b^3*c^2*d*e^2*integrate(1/32*x*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 3*b^3*c^2*d*e^2*integrate(1/32*x*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) - (3*arctan(d*x + c)*arctan((d^2*x + c*d)/d)^2/d - arctan((d^2*x + c*d)/d)^3/d)*a*b^2*c^2*e^2 - 7/32*(6*arctan(d*x + c)^2*arctan((d^2*x + c*d)/d)^2/d - 4*arctan(d*x + c)*arctan((d^2*x + c*d)/d)^3/d + arctan((d^2*x + c*d)/d)^4/d)*b^3*c^2*e^2 + 3*(x^2*arctan(d*x + c) - d*(x/d^2 + (c^2 - 1)*arctan((d^2*x + c*d)/d)/d^3 - c*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/d^3))*a^2*b*c*d*e^2 + 1/2*(2*x^3*arctan(d*x + c) - d*((d*x^2 - 4*c*x)/d^3 - 2*(c^3 - 3*c)*arctan((d^2*x + c*d)/d)/d^4 + (3*c^2 - 1)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/d^4))*a^2*b*d^2*e^2 + a^3*c^2*e^2*x + 28*b^3*d^2*e^2*integrate(1/32*x^2*arctan(d*x + c)^3/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 3*b^3*d^2*e^2*integrate(1/32*x^2*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 96*a*b^2*d^2*e^2*integrate(1/32*x^2*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 56*b^3*c*d*e^2*integrate(1/32*x*arctan(d*x + c)^3/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 6*b^3*c*d*e^2*integrate(1/32*x*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 192*a*b^2*c*d*e^2*integrate(1/32*x*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 3*b^3*c^2*e^2*integrate(1/32*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 3/2*(2*(d*x + c)*arctan(d*x + c) - log((d*x + c)^2 + 1))*a^2*b*c^2*e^2/d + 1/24*(b^3*d^2*e^2*x^3 + 3*b^3*c*d*e^2*x^2 + 3*b^3*c^2*e^2*x)*arctan(d*x + c)^3 - 1/32*(b^3*d^2*e^2*x^3 + 3*b^3*c*d*e^2*x^2 + 3*b^3*c^2*e^2*x)*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2","F",0
16,0,0,0,0.000000," ","integrate((d*e*x+c*e)*(a+b*arctan(d*x+c))^3,x, algorithm=""maxima"")","\frac{1}{2} \, a^{3} d e x^{2} + \frac{3}{2} \, {\left(x^{2} \arctan\left(d x + c\right) - d {\left(\frac{x}{d^{2}} + \frac{{\left(c^{2} - 1\right)} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d^{3}} - \frac{c \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{3}}\right)}\right)} a^{2} b d e + a^{3} c e x + \frac{3 \, {\left(2 \, {\left(d x + c\right)} \arctan\left(d x + c\right) - \log\left({\left(d x + c\right)}^{2} + 1\right)\right)} a^{2} b c e}{2 \, d} + \frac{8 \, {\left(b^{3} d^{2} e x^{2} + 2 \, b^{3} c d e x + {\left(b^{3} c^{2} + b^{3}\right)} e\right)} \arctan\left(d x + c\right)^{3} + 12 \, {\left(a b^{2} d^{2} e x^{2} + {\left(2 \, a b^{2} c - b^{3}\right)} d e x\right)} \arctan\left(d x + c\right)^{2} - 3 \, {\left(a b^{2} d^{2} e x^{2} + {\left(2 \, a b^{2} c - b^{3}\right)} d e x\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2} + {\left(\frac{16 \, b^{3} c^{3} e \arctan\left(d x + c\right)^{3} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d} + \frac{72 \, a b^{2} c^{3} e \arctan\left(d x + c\right)^{2} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d} - 24 \, {\left(\frac{3 \, \arctan\left(d x + c\right) \arctan\left(\frac{d^{2} x + c d}{d}\right)^{2}}{d} - \frac{\arctan\left(\frac{d^{2} x + c d}{d}\right)^{3}}{d}\right)} a b^{2} c^{3} e - 4 \, {\left(\frac{6 \, \arctan\left(d x + c\right)^{2} \arctan\left(\frac{d^{2} x + c d}{d}\right)^{2}}{d} - \frac{4 \, \arctan\left(d x + c\right) \arctan\left(\frac{d^{2} x + c d}{d}\right)^{3}}{d} + \frac{\arctan\left(\frac{d^{2} x + c d}{d}\right)^{4}}{d}\right)} b^{3} c^{3} e - \frac{12 \, b^{3} c^{2} e \arctan\left(d x + c\right)^{2} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d} + \frac{16 \, b^{3} c e \arctan\left(d x + c\right)^{3} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d} + 16 \, b^{3} d^{3} e \int \frac{x^{3} \arctan\left(d x + c\right)^{3}}{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\,{d x} + 72 \, a b^{2} d^{3} e \int \frac{x^{3} \arctan\left(d x + c\right)^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\,{d x} + 48 \, b^{3} c d^{2} e \int \frac{x^{2} \arctan\left(d x + c\right)^{3}}{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\,{d x} + 6 \, a b^{2} d^{3} e \int \frac{x^{3} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\,{d x} + 216 \, a b^{2} c d^{2} e \int \frac{x^{2} \arctan\left(d x + c\right)^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\,{d x} + 48 \, b^{3} c^{2} d e \int \frac{x \arctan\left(d x + c\right)^{3}}{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\,{d x} + 12 \, a b^{2} d^{3} e \int \frac{x^{3} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\,{d x} + 18 \, a b^{2} c d^{2} e \int \frac{x^{2} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\,{d x} + 216 \, a b^{2} c^{2} d e \int \frac{x \arctan\left(d x + c\right)^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\,{d x} + 36 \, a b^{2} c d^{2} e \int \frac{x^{2} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\,{d x} + 18 \, a b^{2} c^{2} d e \int \frac{x \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\,{d x} + 24 \, a b^{2} c^{2} d e \int \frac{x \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\,{d x} + 6 \, a b^{2} c^{3} e \int \frac{\log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\,{d x} + 4 \, {\left(\frac{3 \, \arctan\left(d x + c\right) \arctan\left(\frac{d^{2} x + c d}{d}\right)^{2}}{d} - \frac{\arctan\left(\frac{d^{2} x + c d}{d}\right)^{3}}{d}\right)} b^{3} c^{2} e + \frac{72 \, a b^{2} c e \arctan\left(d x + c\right)^{2} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d} - 12 \, b^{3} d^{2} e \int \frac{x^{2} \arctan\left(d x + c\right)^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\,{d x} - 3 \, b^{3} d^{2} e \int \frac{x^{2} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\,{d x} - 24 \, a b^{2} d^{2} e \int \frac{x^{2} \arctan\left(d x + c\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\,{d x} - 24 \, b^{3} c d e \int \frac{x \arctan\left(d x + c\right)^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\,{d x} - 12 \, b^{3} d^{2} e \int \frac{x^{2} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\,{d x} - 6 \, b^{3} c d e \int \frac{x \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\,{d x} - 48 \, a b^{2} c d e \int \frac{x \arctan\left(d x + c\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\,{d x} - 12 \, b^{3} c d e \int \frac{x \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\,{d x} - 3 \, b^{3} c^{2} e \int \frac{\log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\,{d x} - 24 \, {\left(\frac{3 \, \arctan\left(d x + c\right) \arctan\left(\frac{d^{2} x + c d}{d}\right)^{2}}{d} - \frac{\arctan\left(\frac{d^{2} x + c d}{d}\right)^{3}}{d}\right)} a b^{2} c e - 4 \, {\left(\frac{6 \, \arctan\left(d x + c\right)^{2} \arctan\left(\frac{d^{2} x + c d}{d}\right)^{2}}{d} - \frac{4 \, \arctan\left(d x + c\right) \arctan\left(\frac{d^{2} x + c d}{d}\right)^{3}}{d} + \frac{\arctan\left(\frac{d^{2} x + c d}{d}\right)^{4}}{d}\right)} b^{3} c e - \frac{12 \, b^{3} e \arctan\left(d x + c\right)^{2} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d} + 16 \, b^{3} d e \int \frac{x \arctan\left(d x + c\right)^{3}}{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\,{d x} + 72 \, a b^{2} d e \int \frac{x \arctan\left(d x + c\right)^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\,{d x} + 6 \, a b^{2} d e \int \frac{x \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\,{d x} + 24 \, b^{3} d e \int \frac{x \arctan\left(d x + c\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\,{d x} + 6 \, a b^{2} c e \int \frac{\log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\,{d x} + 4 \, {\left(\frac{3 \, \arctan\left(d x + c\right) \arctan\left(\frac{d^{2} x + c d}{d}\right)^{2}}{d} - \frac{\arctan\left(\frac{d^{2} x + c d}{d}\right)^{3}}{d}\right)} b^{3} e - 3 \, b^{3} e \int \frac{\log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2} + 1}\,{d x}\right)} d}{32 \, d}"," ",0,"1/2*a^3*d*e*x^2 + 3/2*(x^2*arctan(d*x + c) - d*(x/d^2 + (c^2 - 1)*arctan((d^2*x + c*d)/d)/d^3 - c*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/d^3))*a^2*b*d*e + a^3*c*e*x + 3/2*(2*(d*x + c)*arctan(d*x + c) - log((d*x + c)^2 + 1))*a^2*b*c*e/d + 1/32*(8*(b^3*d^2*e*x^2 + 2*b^3*c*d*e*x + (b^3*c^2 + b^3)*e)*arctan(d*x + c)^3 + 12*(a*b^2*d^2*e*x^2 + (2*a*b^2*c - b^3)*d*e*x)*arctan(d*x + c)^2 - 3*(a*b^2*d^2*e*x^2 + (2*a*b^2*c - b^3)*d*e*x)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 + 4*(4*b^3*c^3*e*arctan(d*x + c)^3*arctan((d^2*x + c*d)/d)/d + 18*a*b^2*c^3*e*arctan(d*x + c)^2*arctan((d^2*x + c*d)/d)/d - 6*(3*arctan(d*x + c)*arctan((d^2*x + c*d)/d)^2/d - arctan((d^2*x + c*d)/d)^3/d)*a*b^2*c^3*e - (6*arctan(d*x + c)^2*arctan((d^2*x + c*d)/d)^2/d - 4*arctan(d*x + c)*arctan((d^2*x + c*d)/d)^3/d + arctan((d^2*x + c*d)/d)^4/d)*b^3*c^3*e - 3*b^3*c^2*e*arctan(d*x + c)^2*arctan((d^2*x + c*d)/d)/d + 4*b^3*c*e*arctan(d*x + c)^3*arctan((d^2*x + c*d)/d)/d + 128*b^3*d^3*e*integrate(1/32*x^3*arctan(d*x + c)^3/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 576*a*b^2*d^3*e*integrate(1/32*x^3*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 384*b^3*c*d^2*e*integrate(1/32*x^2*arctan(d*x + c)^3/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 48*a*b^2*d^3*e*integrate(1/32*x^3*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 1728*a*b^2*c*d^2*e*integrate(1/32*x^2*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 384*b^3*c^2*d*e*integrate(1/32*x*arctan(d*x + c)^3/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 96*a*b^2*d^3*e*integrate(1/32*x^3*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 144*a*b^2*c*d^2*e*integrate(1/32*x^2*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 1728*a*b^2*c^2*d*e*integrate(1/32*x*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 288*a*b^2*c*d^2*e*integrate(1/32*x^2*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 144*a*b^2*c^2*d*e*integrate(1/32*x*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 192*a*b^2*c^2*d*e*integrate(1/32*x*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 48*a*b^2*c^3*e*integrate(1/32*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + (3*arctan(d*x + c)*arctan((d^2*x + c*d)/d)^2/d - arctan((d^2*x + c*d)/d)^3/d)*b^3*c^2*e + 18*a*b^2*c*e*arctan(d*x + c)^2*arctan((d^2*x + c*d)/d)/d - 96*b^3*d^2*e*integrate(1/32*x^2*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) - 24*b^3*d^2*e*integrate(1/32*x^2*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) - 192*a*b^2*d^2*e*integrate(1/32*x^2*arctan(d*x + c)/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) - 192*b^3*c*d*e*integrate(1/32*x*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) - 96*b^3*d^2*e*integrate(1/32*x^2*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) - 48*b^3*c*d*e*integrate(1/32*x*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) - 384*a*b^2*c*d*e*integrate(1/32*x*arctan(d*x + c)/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) - 96*b^3*c*d*e*integrate(1/32*x*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) - 24*b^3*c^2*e*integrate(1/32*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) - 6*(3*arctan(d*x + c)*arctan((d^2*x + c*d)/d)^2/d - arctan((d^2*x + c*d)/d)^3/d)*a*b^2*c*e - (6*arctan(d*x + c)^2*arctan((d^2*x + c*d)/d)^2/d - 4*arctan(d*x + c)*arctan((d^2*x + c*d)/d)^3/d + arctan((d^2*x + c*d)/d)^4/d)*b^3*c*e - 3*b^3*e*arctan(d*x + c)^2*arctan((d^2*x + c*d)/d)/d + 128*b^3*d*e*integrate(1/32*x*arctan(d*x + c)^3/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 576*a*b^2*d*e*integrate(1/32*x*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 48*a*b^2*d*e*integrate(1/32*x*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 192*b^3*d*e*integrate(1/32*x*arctan(d*x + c)/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 48*a*b^2*c*e*integrate(1/32*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + (3*arctan(d*x + c)*arctan((d^2*x + c*d)/d)^2/d - arctan((d^2*x + c*d)/d)^3/d)*b^3*e - 24*b^3*e*integrate(1/32*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x))*d)/d","F",0
17,0,0,0,0.000000," ","integrate((a+b*arctan(d*x+c))^3/(d*e*x+c*e),x, algorithm=""maxima"")","\frac{a^{3} \log\left(d e x + c e\right)}{d e} + \int \frac{28 \, b^{3} \arctan\left(d x + c\right)^{3} + 3 \, b^{3} \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2} + 96 \, a b^{2} \arctan\left(d x + c\right)^{2} + 96 \, a^{2} b \arctan\left(d x + c\right)}{32 \, {\left(d e x + c e\right)}}\,{d x}"," ",0,"a^3*log(d*e*x + c*e)/(d*e) + integrate(1/32*(28*b^3*arctan(d*x + c)^3 + 3*b^3*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 + 96*a*b^2*arctan(d*x + c)^2 + 96*a^2*b*arctan(d*x + c))/(d*e*x + c*e), x)","F",0
18,0,0,0,0.000000," ","integrate((a+b*arctan(d*x+c))^3/(d*e*x+c*e)^2,x, algorithm=""maxima"")","-\frac{3}{2} \, {\left(d {\left(\frac{\log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{2} e^{2}} - \frac{2 \, \log\left(d x + c\right)}{d^{2} e^{2}}\right)} + \frac{2 \, \arctan\left(d x + c\right)}{d^{2} e^{2} x + c d e^{2}}\right)} a^{2} b - \frac{a^{3}}{d^{2} e^{2} x + c d e^{2}} - \frac{\frac{15}{2} \, b^{3} \arctan\left(d x + c\right)^{3} - \frac{21}{8} \, b^{3} \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2} - {\left(d^{2} e^{2} x + c d e^{2}\right)} \int \frac{196 \, {\left(b^{3} d^{2} x^{2} + 2 \, b^{3} c d x + b^{3} c^{2} + b^{3}\right)} \arctan\left(d x + c\right)^{3} + 12 \, {\left(64 \, a b^{2} d^{2} x^{2} + 64 \, a b^{2} c^{2} + 15 \, b^{3} c + 64 \, a b^{2} + {\left(128 \, a b^{2} c + 15 \, b^{3}\right)} d x\right)} \arctan\left(d x + c\right)^{2} - 84 \, {\left(b^{3} d^{2} x^{2} + 2 \, b^{3} c d x + b^{3} c^{2}\right)} \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right) - 21 \, {\left(b^{3} d x + b^{3} c - {\left(b^{3} d^{2} x^{2} + 2 \, b^{3} c d x + b^{3} c^{2} + b^{3}\right)} \arctan\left(d x + c\right)\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{8 \, {\left(d^{4} e^{2} x^{4} + 4 \, c d^{3} e^{2} x^{3} + {\left(6 \, c^{2} + 1\right)} d^{2} e^{2} x^{2} + 2 \, {\left(2 \, c^{3} + c\right)} d e^{2} x + {\left(c^{4} + c^{2}\right)} e^{2}\right)}}\,{d x}}{32 \, {\left(d^{2} e^{2} x + c d e^{2}\right)}}"," ",0,"-3/2*(d*(log(d^2*x^2 + 2*c*d*x + c^2 + 1)/(d^2*e^2) - 2*log(d*x + c)/(d^2*e^2)) + 2*arctan(d*x + c)/(d^2*e^2*x + c*d*e^2))*a^2*b - a^3/(d^2*e^2*x + c*d*e^2) - 1/32*(4*b^3*arctan(d*x + c)^3 - 3*b^3*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 - 32*(d^2*e^2*x + c*d*e^2)*integrate(1/32*(28*(b^3*d^2*x^2 + 2*b^3*c*d*x + b^3*c^2 + b^3)*arctan(d*x + c)^3 + 12*(8*a*b^2*d^2*x^2 + 8*a*b^2*c^2 + b^3*c + 8*a*b^2 + (16*a*b^2*c + b^3)*d*x)*arctan(d*x + c)^2 - 12*(b^3*d^2*x^2 + 2*b^3*c*d*x + b^3*c^2)*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1) - 3*(b^3*d*x + b^3*c - (b^3*d^2*x^2 + 2*b^3*c*d*x + b^3*c^2 + b^3)*arctan(d*x + c))*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2)/(d^4*e^2*x^4 + 4*c*d^3*e^2*x^3 + (6*c^2 + 1)*d^2*e^2*x^2 + 2*(2*c^3 + c)*d*e^2*x + (c^4 + c^2)*e^2), x))/(d^2*e^2*x + c*d*e^2)","F",0
19,0,0,0,0.000000," ","integrate((a+b*arctan(d*x+c))^3/(d*e*x+c*e)^3,x, algorithm=""maxima"")","-\frac{3}{2} \, {\left(d {\left(\frac{1}{d^{3} e^{3} x + c d^{2} e^{3}} + \frac{\arctan\left(\frac{d^{2} x + c d}{d}\right)}{d^{2} e^{3}}\right)} + \frac{\arctan\left(d x + c\right)}{d^{3} e^{3} x^{2} + 2 \, c d^{2} e^{3} x + c^{2} d e^{3}}\right)} a^{2} b - \frac{3}{2} \, {\left(2 \, d {\left(\frac{1}{d^{3} e^{3} x + c d^{2} e^{3}} + \frac{\arctan\left(\frac{d^{2} x + c d}{d}\right)}{d^{2} e^{3}}\right)} \arctan\left(d x + c\right) - \frac{\arctan\left(d x + c\right)^{2} - \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right) + 2 \, \log\left(d x + c\right)}{d e^{3}}\right)} a b^{2} - \frac{3 \, a b^{2} \arctan\left(d x + c\right)^{2}}{2 \, {\left(d^{3} e^{3} x^{2} + 2 \, c d^{2} e^{3} x + c^{2} d e^{3}\right)}} - \frac{\frac{1}{4} \, {\left(48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} \arctan\left(d x + c\right)^{3} + 84 \, {\left(d x + c\right)} \arctan\left(d x + c\right)^{2} - 9 \, {\left(d x + c\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2} - 4 \, {\left(d^{3} e^{3} x^{2} + 2 \, c d^{2} e^{3} x + c^{2} d e^{3}\right)} \int \frac{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} \arctan\left(d x + c\right)^{3} + 60 \, {\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(3 \, c^{2} + 1\right)} d x + c\right)} \arctan\left(d x + c\right)^{2} + 9 \, {\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + c^{3} + {\left(3 \, c^{2} + 1\right)} d x + c\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2} + 168 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2}\right)} \arctan\left(d x + c\right) - 36 \, {\left(d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{4 \, {\left(d^{5} e^{3} x^{5} + 5 \, c d^{4} e^{3} x^{4} + {\left(10 \, c^{2} + 1\right)} d^{3} e^{3} x^{3} + {\left(10 \, c^{3} + 3 \, c\right)} d^{2} e^{3} x^{2} + {\left(5 \, c^{4} + 3 \, c^{2}\right)} d e^{3} x + {\left(c^{5} + c^{3}\right)} e^{3}\right)}}\,{d x}\right)} b^{3}}{32 \, {\left(d^{3} e^{3} x^{2} + 2 \, c d^{2} e^{3} x + c^{2} d e^{3}\right)}} - \frac{a^{3}}{2 \, {\left(d^{3} e^{3} x^{2} + 2 \, c d^{2} e^{3} x + c^{2} d e^{3}\right)}}"," ",0,"-3/2*(d*(1/(d^3*e^3*x + c*d^2*e^3) + arctan((d^2*x + c*d)/d)/(d^2*e^3)) + arctan(d*x + c)/(d^3*e^3*x^2 + 2*c*d^2*e^3*x + c^2*d*e^3))*a^2*b - 3/2*(2*d*(1/(d^3*e^3*x + c*d^2*e^3) + arctan((d^2*x + c*d)/d)/(d^2*e^3))*arctan(d*x + c) - (arctan(d*x + c)^2 - log(d^2*x^2 + 2*c*d*x + c^2 + 1) + 2*log(d*x + c))/(d*e^3))*a*b^2 - 3/2*a*b^2*arctan(d*x + c)^2/(d^3*e^3*x^2 + 2*c*d^2*e^3*x + c^2*d*e^3) - 1/32*(8*(d^2*x^2 + 2*c*d*x + c^2 + 1)*arctan(d*x + c)^3 + 12*(d*x + c)*arctan(d*x + c)^2 - 3*(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 - 32*(d^3*e^3*x^2 + 2*c*d^2*e^3*x + c^2*d*e^3)*integrate(1/32*(16*(d^2*x^2 + 2*c*d*x + c^2 + 1)*arctan(d*x + c)^3 + 12*(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (3*c^2 + 1)*d*x + c)*arctan(d*x + c)^2 + 3*(d^3*x^3 + 3*c*d^2*x^2 + c^3 + (3*c^2 + 1)*d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 + 24*(d^2*x^2 + 2*c*d*x + c^2)*arctan(d*x + c) - 12*(d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3)*log(d^2*x^2 + 2*c*d*x + c^2 + 1))/(d^5*e^3*x^5 + 5*c*d^4*e^3*x^4 + (10*c^2 + 1)*d^3*e^3*x^3 + (10*c^3 + 3*c)*d^2*e^3*x^2 + (5*c^4 + 3*c^2)*d*e^3*x + (c^5 + c^3)*e^3), x))*b^3/(d^3*e^3*x^2 + 2*c*d^2*e^3*x + c^2*d*e^3) - 1/2*a^3/(d^3*e^3*x^2 + 2*c*d^2*e^3*x + c^2*d*e^3)","F",0
20,-1,0,0,0.000000," ","integrate((a+b*arctan(d*x+c))^3/(d*e*x+c*e)^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
21,1,44,0,0.455675," ","integrate(arctan(1+x)/(2+2*x),x, algorithm=""maxima"")","-\frac{1}{4} \, \arctan\left(x + 1, 0\right) \log\left(x^{2} + 2 \, x + 2\right) + \frac{1}{2} \, \arctan\left(x + 1\right) \log\left({\left| x + 1 \right|}\right) - \frac{1}{4} i \, {\rm Li}_2\left(i \, x + i + 1\right) + \frac{1}{4} i \, {\rm Li}_2\left(-i \, x - i + 1\right)"," ",0,"-1/4*arctan2(x + 1, 0)*log(x^2 + 2*x + 2) + 1/2*arctan(x + 1)*log(abs(x + 1)) - 1/4*I*dilog(I*x + I + 1) + 1/4*I*dilog(-I*x - I + 1)","B",0
22,1,123,0,0.486111," ","integrate(arctan(b*x+a)/(a*d/b+d*x),x, algorithm=""maxima"")","\frac{\arctan\left(b x + a\right) \log\left(d x + \frac{a d}{b}\right)}{d} - \frac{\arctan\left(\frac{b^{2} x + a b}{b}\right) \log\left(d x + \frac{a d}{b}\right)}{d} - \frac{\arctan\left(b x + a, 0\right) \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right) - 2 \, \arctan\left(b x + a\right) \log\left({\left| b x + a \right|}\right) + i \, {\rm Li}_2\left(i \, b x + i \, a + 1\right) - i \, {\rm Li}_2\left(-i \, b x - i \, a + 1\right)}{2 \, d}"," ",0,"arctan(b*x + a)*log(d*x + a*d/b)/d - arctan((b^2*x + a*b)/b)*log(d*x + a*d/b)/d - 1/2*(arctan2(b*x + a, 0)*log(b^2*x^2 + 2*a*b*x + a^2 + 1) - 2*arctan(b*x + a)*log(abs(b*x + a)) + I*dilog(I*b*x + I*a + 1) - I*dilog(-I*b*x - I*a + 1))/d","B",0
23,-2,0,0,0.000000," ","integrate((b*x+a)^2*arctan(b*x+a)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
24,1,346,0,0.427542," ","integrate((f*x+e)^3*(a+b*arctan(d*x+c)),x, algorithm=""maxima"")","\frac{1}{4} \, a f^{3} x^{4} + a e f^{2} x^{3} + \frac{3}{2} \, a e^{2} f x^{2} + \frac{3}{2} \, {\left(x^{2} \arctan\left(d x + c\right) - d {\left(\frac{x}{d^{2}} + \frac{{\left(c^{2} - 1\right)} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d^{3}} - \frac{c \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{3}}\right)}\right)} b e^{2} f + \frac{1}{2} \, {\left(2 \, x^{3} \arctan\left(d x + c\right) - d {\left(\frac{d x^{2} - 4 \, c x}{d^{3}} - \frac{2 \, {\left(c^{3} - 3 \, c\right)} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d^{4}} + \frac{{\left(3 \, c^{2} - 1\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{4}}\right)}\right)} b e f^{2} + \frac{1}{12} \, {\left(3 \, x^{4} \arctan\left(d x + c\right) - d {\left(\frac{d^{2} x^{3} - 3 \, c d x^{2} + 3 \, {\left(3 \, c^{2} - 1\right)} x}{d^{4}} + \frac{3 \, {\left(c^{4} - 6 \, c^{2} + 1\right)} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d^{5}} - \frac{6 \, {\left(c^{3} - c\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{5}}\right)}\right)} b f^{3} + a e^{3} x + \frac{{\left(2 \, {\left(d x + c\right)} \arctan\left(d x + c\right) - \log\left({\left(d x + c\right)}^{2} + 1\right)\right)} b e^{3}}{2 \, d}"," ",0,"1/4*a*f^3*x^4 + a*e*f^2*x^3 + 3/2*a*e^2*f*x^2 + 3/2*(x^2*arctan(d*x + c) - d*(x/d^2 + (c^2 - 1)*arctan((d^2*x + c*d)/d)/d^3 - c*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/d^3))*b*e^2*f + 1/2*(2*x^3*arctan(d*x + c) - d*((d*x^2 - 4*c*x)/d^3 - 2*(c^3 - 3*c)*arctan((d^2*x + c*d)/d)/d^4 + (3*c^2 - 1)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/d^4))*b*e*f^2 + 1/12*(3*x^4*arctan(d*x + c) - d*((d^2*x^3 - 3*c*d*x^2 + 3*(3*c^2 - 1)*x)/d^4 + 3*(c^4 - 6*c^2 + 1)*arctan((d^2*x + c*d)/d)/d^5 - 6*(c^3 - c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/d^5))*b*f^3 + a*e^3*x + 1/2*(2*(d*x + c)*arctan(d*x + c) - log((d*x + c)^2 + 1))*b*e^3/d","A",0
25,1,220,0,0.426790," ","integrate((f*x+e)^2*(a+b*arctan(d*x+c)),x, algorithm=""maxima"")","\frac{1}{3} \, a f^{2} x^{3} + a e f x^{2} + {\left(x^{2} \arctan\left(d x + c\right) - d {\left(\frac{x}{d^{2}} + \frac{{\left(c^{2} - 1\right)} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d^{3}} - \frac{c \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{3}}\right)}\right)} b e f + \frac{1}{6} \, {\left(2 \, x^{3} \arctan\left(d x + c\right) - d {\left(\frac{d x^{2} - 4 \, c x}{d^{3}} - \frac{2 \, {\left(c^{3} - 3 \, c\right)} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d^{4}} + \frac{{\left(3 \, c^{2} - 1\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{4}}\right)}\right)} b f^{2} + a e^{2} x + \frac{{\left(2 \, {\left(d x + c\right)} \arctan\left(d x + c\right) - \log\left({\left(d x + c\right)}^{2} + 1\right)\right)} b e^{2}}{2 \, d}"," ",0,"1/3*a*f^2*x^3 + a*e*f*x^2 + (x^2*arctan(d*x + c) - d*(x/d^2 + (c^2 - 1)*arctan((d^2*x + c*d)/d)/d^3 - c*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/d^3))*b*e*f + 1/6*(2*x^3*arctan(d*x + c) - d*((d*x^2 - 4*c*x)/d^3 - 2*(c^3 - 3*c)*arctan((d^2*x + c*d)/d)/d^4 + (3*c^2 - 1)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/d^4))*b*f^2 + a*e^2*x + 1/2*(2*(d*x + c)*arctan(d*x + c) - log((d*x + c)^2 + 1))*b*e^2/d","A",0
26,1,116,0,0.420160," ","integrate((f*x+e)*(a+b*arctan(d*x+c)),x, algorithm=""maxima"")","\frac{1}{2} \, a f x^{2} + \frac{1}{2} \, {\left(x^{2} \arctan\left(d x + c\right) - d {\left(\frac{x}{d^{2}} + \frac{{\left(c^{2} - 1\right)} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d^{3}} - \frac{c \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{3}}\right)}\right)} b f + a e x + \frac{{\left(2 \, {\left(d x + c\right)} \arctan\left(d x + c\right) - \log\left({\left(d x + c\right)}^{2} + 1\right)\right)} b e}{2 \, d}"," ",0,"1/2*a*f*x^2 + 1/2*(x^2*arctan(d*x + c) - d*(x/d^2 + (c^2 - 1)*arctan((d^2*x + c*d)/d)/d^3 - c*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/d^3))*b*f + a*e*x + 1/2*(2*(d*x + c)*arctan(d*x + c) - log((d*x + c)^2 + 1))*b*e/d","A",0
27,1,36,0,0.317389," ","integrate(a+b*arctan(d*x+c),x, algorithm=""maxima"")","a x + \frac{{\left(2 \, {\left(d x + c\right)} \arctan\left(d x + c\right) - \log\left({\left(d x + c\right)}^{2} + 1\right)\right)} b}{2 \, d}"," ",0,"a*x + 1/2*(2*(d*x + c)*arctan(d*x + c) - log((d*x + c)^2 + 1))*b/d","A",0
28,0,0,0,0.000000," ","integrate((a+b*arctan(d*x+c))/(f*x+e),x, algorithm=""maxima"")","2 \, b \int \frac{\arctan\left(d x + c\right)}{2 \, {\left(f x + e\right)}}\,{d x} + \frac{a \log\left(f x + e\right)}{f}"," ",0,"2*b*integrate(1/2*arctan(d*x + c)/(f*x + e), x) + a*log(f*x + e)/f","F",0
29,1,177,0,0.417418," ","integrate((a+b*arctan(d*x+c))/(f*x+e)^2,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(d {\left(\frac{2 \, {\left(d^{2} e - c d f\right)} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{{\left(d^{2} e^{2} f - 2 \, c d e f^{2} + {\left(c^{2} + 1\right)} f^{3}\right)} d} - \frac{\log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{2} e^{2} - 2 \, c d e f + {\left(c^{2} + 1\right)} f^{2}} + \frac{2 \, \log\left(f x + e\right)}{d^{2} e^{2} - 2 \, c d e f + {\left(c^{2} + 1\right)} f^{2}}\right)} - \frac{2 \, \arctan\left(d x + c\right)}{f^{2} x + e f}\right)} b - \frac{a}{f^{2} x + e f}"," ",0,"1/2*(d*(2*(d^2*e - c*d*f)*arctan((d^2*x + c*d)/d)/((d^2*e^2*f - 2*c*d*e*f^2 + (c^2 + 1)*f^3)*d) - log(d^2*x^2 + 2*c*d*x + c^2 + 1)/(d^2*e^2 - 2*c*d*e*f + (c^2 + 1)*f^2) + 2*log(f*x + e)/(d^2*e^2 - 2*c*d*e*f + (c^2 + 1)*f^2)) - 2*arctan(d*x + c)/(f^2*x + e*f))*b - a/(f^2*x + e*f)","A",0
30,1,409,0,0.426529," ","integrate((a+b*arctan(d*x+c))/(f*x+e)^3,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(d {\left(\frac{{\left(d^{2} e - c d f\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{4} e^{4} - 4 \, c d^{3} e^{3} f + 2 \, {\left(3 \, c^{2} + 1\right)} d^{2} e^{2} f^{2} - 4 \, {\left(c^{3} + c\right)} d e f^{3} + {\left(c^{4} + 2 \, c^{2} + 1\right)} f^{4}} - \frac{2 \, {\left(d^{2} e - c d f\right)} \log\left(f x + e\right)}{d^{4} e^{4} - 4 \, c d^{3} e^{3} f + 2 \, {\left(3 \, c^{2} + 1\right)} d^{2} e^{2} f^{2} - 4 \, {\left(c^{3} + c\right)} d e f^{3} + {\left(c^{4} + 2 \, c^{2} + 1\right)} f^{4}} - \frac{{\left(d^{4} e^{2} - 2 \, c d^{3} e f + {\left(c^{2} - 1\right)} d^{2} f^{2}\right)} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{{\left(d^{4} e^{4} f - 4 \, c d^{3} e^{3} f^{2} + 2 \, {\left(3 \, c^{2} + 1\right)} d^{2} e^{2} f^{3} - 4 \, {\left(c^{3} + c\right)} d e f^{4} + {\left(c^{4} + 2 \, c^{2} + 1\right)} f^{5}\right)} d} + \frac{1}{d^{2} e^{3} - 2 \, c d e^{2} f + {\left(c^{2} + 1\right)} e f^{2} + {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + {\left(c^{2} + 1\right)} f^{3}\right)} x}\right)} + \frac{\arctan\left(d x + c\right)}{f^{3} x^{2} + 2 \, e f^{2} x + e^{2} f}\right)} b - \frac{a}{2 \, {\left(f^{3} x^{2} + 2 \, e f^{2} x + e^{2} f\right)}}"," ",0,"-1/2*(d*((d^2*e - c*d*f)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/(d^4*e^4 - 4*c*d^3*e^3*f + 2*(3*c^2 + 1)*d^2*e^2*f^2 - 4*(c^3 + c)*d*e*f^3 + (c^4 + 2*c^2 + 1)*f^4) - 2*(d^2*e - c*d*f)*log(f*x + e)/(d^4*e^4 - 4*c*d^3*e^3*f + 2*(3*c^2 + 1)*d^2*e^2*f^2 - 4*(c^3 + c)*d*e*f^3 + (c^4 + 2*c^2 + 1)*f^4) - (d^4*e^2 - 2*c*d^3*e*f + (c^2 - 1)*d^2*f^2)*arctan((d^2*x + c*d)/d)/((d^4*e^4*f - 4*c*d^3*e^3*f^2 + 2*(3*c^2 + 1)*d^2*e^2*f^3 - 4*(c^3 + c)*d*e*f^4 + (c^4 + 2*c^2 + 1)*f^5)*d) + 1/(d^2*e^3 - 2*c*d*e^2*f + (c^2 + 1)*e*f^2 + (d^2*e^2*f - 2*c*d*e*f^2 + (c^2 + 1)*f^3)*x)) + arctan(d*x + c)/(f^3*x^2 + 2*e*f^2*x + e^2*f))*b - 1/2*a/(f^3*x^2 + 2*e*f^2*x + e^2*f)","A",0
31,0,0,0,0.000000," ","integrate((f*x+e)^2*(a+b*arctan(d*x+c))^2,x, algorithm=""maxima"")","\frac{3 \, b^{2} c^{2} e^{2} \arctan\left(d x + c\right)^{2} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{4 \, d} - \frac{1}{4} \, {\left(\frac{3 \, \arctan\left(d x + c\right) \arctan\left(\frac{d^{2} x + c d}{d}\right)^{2}}{d} - \frac{\arctan\left(\frac{d^{2} x + c d}{d}\right)^{3}}{d}\right)} b^{2} c^{2} e^{2} + \frac{1}{3} \, a^{2} f^{2} x^{3} + 36 \, b^{2} d^{2} f^{2} \int \frac{x^{4} \arctan\left(d x + c\right)^{2}}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 3 \, b^{2} d^{2} f^{2} \int \frac{x^{4} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 72 \, b^{2} d^{2} e f \int \frac{x^{3} \arctan\left(d x + c\right)^{2}}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 72 \, b^{2} c d f^{2} \int \frac{x^{3} \arctan\left(d x + c\right)^{2}}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 4 \, b^{2} d^{2} f^{2} \int \frac{x^{4} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 6 \, b^{2} d^{2} e f \int \frac{x^{3} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 6 \, b^{2} c d f^{2} \int \frac{x^{3} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 36 \, b^{2} d^{2} e^{2} \int \frac{x^{2} \arctan\left(d x + c\right)^{2}}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 144 \, b^{2} c d e f \int \frac{x^{2} \arctan\left(d x + c\right)^{2}}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 36 \, b^{2} c^{2} f^{2} \int \frac{x^{2} \arctan\left(d x + c\right)^{2}}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 12 \, b^{2} d^{2} e f \int \frac{x^{3} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 4 \, b^{2} c d f^{2} \int \frac{x^{3} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 3 \, b^{2} d^{2} e^{2} \int \frac{x^{2} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 12 \, b^{2} c d e f \int \frac{x^{2} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 3 \, b^{2} c^{2} f^{2} \int \frac{x^{2} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 72 \, b^{2} c d e^{2} \int \frac{x \arctan\left(d x + c\right)^{2}}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 72 \, b^{2} c^{2} e f \int \frac{x \arctan\left(d x + c\right)^{2}}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 12 \, b^{2} d^{2} e^{2} \int \frac{x^{2} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 12 \, b^{2} c d e f \int \frac{x^{2} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 6 \, b^{2} c d e^{2} \int \frac{x \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 6 \, b^{2} c^{2} e f \int \frac{x \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 12 \, b^{2} c d e^{2} \int \frac{x \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 3 \, b^{2} c^{2} e^{2} \int \frac{\log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + a^{2} e f x^{2} + \frac{3 \, b^{2} e^{2} \arctan\left(d x + c\right)^{2} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{4 \, d} - 8 \, b^{2} d f^{2} \int \frac{x^{3} \arctan\left(d x + c\right)}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} - 24 \, b^{2} d e f \int \frac{x^{2} \arctan\left(d x + c\right)}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} - 24 \, b^{2} d e^{2} \int \frac{x \arctan\left(d x + c\right)}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} - \frac{1}{4} \, {\left(\frac{3 \, \arctan\left(d x + c\right) \arctan\left(\frac{d^{2} x + c d}{d}\right)^{2}}{d} - \frac{\arctan\left(\frac{d^{2} x + c d}{d}\right)^{3}}{d}\right)} b^{2} e^{2} + 2 \, {\left(x^{2} \arctan\left(d x + c\right) - d {\left(\frac{x}{d^{2}} + \frac{{\left(c^{2} - 1\right)} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d^{3}} - \frac{c \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{3}}\right)}\right)} a b e f + \frac{1}{3} \, {\left(2 \, x^{3} \arctan\left(d x + c\right) - d {\left(\frac{d x^{2} - 4 \, c x}{d^{3}} - \frac{2 \, {\left(c^{3} - 3 \, c\right)} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d^{4}} + \frac{{\left(3 \, c^{2} - 1\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{4}}\right)}\right)} a b f^{2} + a^{2} e^{2} x + 36 \, b^{2} f^{2} \int \frac{x^{2} \arctan\left(d x + c\right)^{2}}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 3 \, b^{2} f^{2} \int \frac{x^{2} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 72 \, b^{2} e f \int \frac{x \arctan\left(d x + c\right)^{2}}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 6 \, b^{2} e f \int \frac{x \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 3 \, b^{2} e^{2} \int \frac{\log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + \frac{{\left(2 \, {\left(d x + c\right)} \arctan\left(d x + c\right) - \log\left({\left(d x + c\right)}^{2} + 1\right)\right)} a b e^{2}}{d} + \frac{1}{12} \, {\left(b^{2} f^{2} x^{3} + 3 \, b^{2} e f x^{2} + 3 \, b^{2} e^{2} x\right)} \arctan\left(d x + c\right)^{2} - \frac{1}{48} \, {\left(b^{2} f^{2} x^{3} + 3 \, b^{2} e f x^{2} + 3 \, b^{2} e^{2} x\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}"," ",0,"3/4*b^2*c^2*e^2*arctan(d*x + c)^2*arctan((d^2*x + c*d)/d)/d - 1/4*(3*arctan(d*x + c)*arctan((d^2*x + c*d)/d)^2/d - arctan((d^2*x + c*d)/d)^3/d)*b^2*c^2*e^2 + 1/3*a^2*f^2*x^3 + 36*b^2*d^2*f^2*integrate(1/48*x^4*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 3*b^2*d^2*f^2*integrate(1/48*x^4*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 72*b^2*d^2*e*f*integrate(1/48*x^3*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 72*b^2*c*d*f^2*integrate(1/48*x^3*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 4*b^2*d^2*f^2*integrate(1/48*x^4*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 6*b^2*d^2*e*f*integrate(1/48*x^3*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 6*b^2*c*d*f^2*integrate(1/48*x^3*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 36*b^2*d^2*e^2*integrate(1/48*x^2*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 144*b^2*c*d*e*f*integrate(1/48*x^2*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 36*b^2*c^2*f^2*integrate(1/48*x^2*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 12*b^2*d^2*e*f*integrate(1/48*x^3*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 4*b^2*c*d*f^2*integrate(1/48*x^3*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 3*b^2*d^2*e^2*integrate(1/48*x^2*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 12*b^2*c*d*e*f*integrate(1/48*x^2*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 3*b^2*c^2*f^2*integrate(1/48*x^2*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 72*b^2*c*d*e^2*integrate(1/48*x*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 72*b^2*c^2*e*f*integrate(1/48*x*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 12*b^2*d^2*e^2*integrate(1/48*x^2*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 12*b^2*c*d*e*f*integrate(1/48*x^2*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 6*b^2*c*d*e^2*integrate(1/48*x*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 6*b^2*c^2*e*f*integrate(1/48*x*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 12*b^2*c*d*e^2*integrate(1/48*x*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 3*b^2*c^2*e^2*integrate(1/48*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + a^2*e*f*x^2 + 3/4*b^2*e^2*arctan(d*x + c)^2*arctan((d^2*x + c*d)/d)/d - 8*b^2*d*f^2*integrate(1/48*x^3*arctan(d*x + c)/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) - 24*b^2*d*e*f*integrate(1/48*x^2*arctan(d*x + c)/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) - 24*b^2*d*e^2*integrate(1/48*x*arctan(d*x + c)/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) - 1/4*(3*arctan(d*x + c)*arctan((d^2*x + c*d)/d)^2/d - arctan((d^2*x + c*d)/d)^3/d)*b^2*e^2 + 2*(x^2*arctan(d*x + c) - d*(x/d^2 + (c^2 - 1)*arctan((d^2*x + c*d)/d)/d^3 - c*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/d^3))*a*b*e*f + 1/3*(2*x^3*arctan(d*x + c) - d*((d*x^2 - 4*c*x)/d^3 - 2*(c^3 - 3*c)*arctan((d^2*x + c*d)/d)/d^4 + (3*c^2 - 1)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/d^4))*a*b*f^2 + a^2*e^2*x + 36*b^2*f^2*integrate(1/48*x^2*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 3*b^2*f^2*integrate(1/48*x^2*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 72*b^2*e*f*integrate(1/48*x*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 6*b^2*e*f*integrate(1/48*x*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 3*b^2*e^2*integrate(1/48*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + (2*(d*x + c)*arctan(d*x + c) - log((d*x + c)^2 + 1))*a*b*e^2/d + 1/12*(b^2*f^2*x^3 + 3*b^2*e*f*x^2 + 3*b^2*e^2*x)*arctan(d*x + c)^2 - 1/48*(b^2*f^2*x^3 + 3*b^2*e*f*x^2 + 3*b^2*e^2*x)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2","F",0
32,0,0,0,0.000000," ","integrate((f*x+e)*(a+b*arctan(d*x+c))^2,x, algorithm=""maxima"")","\frac{3 \, b^{2} c^{2} e \arctan\left(d x + c\right)^{2} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{4 \, d} - \frac{1}{4} \, {\left(\frac{3 \, \arctan\left(d x + c\right) \arctan\left(\frac{d^{2} x + c d}{d}\right)^{2}}{d} - \frac{\arctan\left(\frac{d^{2} x + c d}{d}\right)^{3}}{d}\right)} b^{2} c^{2} e + 12 \, b^{2} d^{2} f \int \frac{x^{3} \arctan\left(d x + c\right)^{2}}{16 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + b^{2} d^{2} f \int \frac{x^{3} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{16 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 12 \, b^{2} d^{2} e \int \frac{x^{2} \arctan\left(d x + c\right)^{2}}{16 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 24 \, b^{2} c d f \int \frac{x^{2} \arctan\left(d x + c\right)^{2}}{16 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 2 \, b^{2} d^{2} f \int \frac{x^{3} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{16 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + b^{2} d^{2} e \int \frac{x^{2} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{16 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 2 \, b^{2} c d f \int \frac{x^{2} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{16 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 24 \, b^{2} c d e \int \frac{x \arctan\left(d x + c\right)^{2}}{16 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 12 \, b^{2} c^{2} f \int \frac{x \arctan\left(d x + c\right)^{2}}{16 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 4 \, b^{2} d^{2} e \int \frac{x^{2} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{16 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 2 \, b^{2} c d f \int \frac{x^{2} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{16 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 2 \, b^{2} c d e \int \frac{x \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{16 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + b^{2} c^{2} f \int \frac{x \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{16 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 4 \, b^{2} c d e \int \frac{x \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{16 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + b^{2} c^{2} e \int \frac{\log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{16 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + \frac{1}{2} \, a^{2} f x^{2} + \frac{3 \, b^{2} e \arctan\left(d x + c\right)^{2} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{4 \, d} - 4 \, b^{2} d f \int \frac{x^{2} \arctan\left(d x + c\right)}{16 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} - 8 \, b^{2} d e \int \frac{x \arctan\left(d x + c\right)}{16 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} - \frac{1}{4} \, {\left(\frac{3 \, \arctan\left(d x + c\right) \arctan\left(\frac{d^{2} x + c d}{d}\right)^{2}}{d} - \frac{\arctan\left(\frac{d^{2} x + c d}{d}\right)^{3}}{d}\right)} b^{2} e + {\left(x^{2} \arctan\left(d x + c\right) - d {\left(\frac{x}{d^{2}} + \frac{{\left(c^{2} - 1\right)} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d^{3}} - \frac{c \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{3}}\right)}\right)} a b f + a^{2} e x + 12 \, b^{2} f \int \frac{x \arctan\left(d x + c\right)^{2}}{16 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + b^{2} f \int \frac{x \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{16 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + b^{2} e \int \frac{\log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{16 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + \frac{{\left(2 \, {\left(d x + c\right)} \arctan\left(d x + c\right) - \log\left({\left(d x + c\right)}^{2} + 1\right)\right)} a b e}{d} + \frac{1}{8} \, {\left(b^{2} f x^{2} + 2 \, b^{2} e x\right)} \arctan\left(d x + c\right)^{2} - \frac{1}{32} \, {\left(b^{2} f x^{2} + 2 \, b^{2} e x\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}"," ",0,"3/4*b^2*c^2*e*arctan(d*x + c)^2*arctan((d^2*x + c*d)/d)/d - 1/4*(3*arctan(d*x + c)*arctan((d^2*x + c*d)/d)^2/d - arctan((d^2*x + c*d)/d)^3/d)*b^2*c^2*e + 12*b^2*d^2*f*integrate(1/16*x^3*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + b^2*d^2*f*integrate(1/16*x^3*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 12*b^2*d^2*e*integrate(1/16*x^2*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 24*b^2*c*d*f*integrate(1/16*x^2*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 2*b^2*d^2*f*integrate(1/16*x^3*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + b^2*d^2*e*integrate(1/16*x^2*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 2*b^2*c*d*f*integrate(1/16*x^2*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 24*b^2*c*d*e*integrate(1/16*x*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 12*b^2*c^2*f*integrate(1/16*x*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 4*b^2*d^2*e*integrate(1/16*x^2*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 2*b^2*c*d*f*integrate(1/16*x^2*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 2*b^2*c*d*e*integrate(1/16*x*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + b^2*c^2*f*integrate(1/16*x*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 4*b^2*c*d*e*integrate(1/16*x*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + b^2*c^2*e*integrate(1/16*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 1/2*a^2*f*x^2 + 3/4*b^2*e*arctan(d*x + c)^2*arctan((d^2*x + c*d)/d)/d - 4*b^2*d*f*integrate(1/16*x^2*arctan(d*x + c)/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) - 8*b^2*d*e*integrate(1/16*x*arctan(d*x + c)/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) - 1/4*(3*arctan(d*x + c)*arctan((d^2*x + c*d)/d)^2/d - arctan((d^2*x + c*d)/d)^3/d)*b^2*e + (x^2*arctan(d*x + c) - d*(x/d^2 + (c^2 - 1)*arctan((d^2*x + c*d)/d)/d^3 - c*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/d^3))*a*b*f + a^2*e*x + 12*b^2*f*integrate(1/16*x*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + b^2*f*integrate(1/16*x*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + b^2*e*integrate(1/16*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + (2*(d*x + c)*arctan(d*x + c) - log((d*x + c)^2 + 1))*a*b*e/d + 1/8*(b^2*f*x^2 + 2*b^2*e*x)*arctan(d*x + c)^2 - 1/32*(b^2*f*x^2 + 2*b^2*e*x)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2","F",0
33,0,0,0,0.000000," ","integrate((a+b*arctan(d*x+c))^2,x, algorithm=""maxima"")","\frac{1}{16} \, {\left(\frac{12 \, c^{2} \arctan\left(d x + c\right)^{2} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d} - 4 \, {\left(\frac{3 \, \arctan\left(d x + c\right) \arctan\left(\frac{d^{2} x + c d}{d}\right)^{2}}{d} - \frac{\arctan\left(\frac{d^{2} x + c d}{d}\right)^{3}}{d}\right)} c^{2} + 4 \, x \arctan\left(d x + c\right)^{2} + 192 \, d^{2} \int \frac{x^{2} \arctan\left(d x + c\right)^{2}}{16 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 16 \, d^{2} \int \frac{x^{2} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{16 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 384 \, c d \int \frac{x \arctan\left(d x + c\right)^{2}}{16 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 64 \, d^{2} \int \frac{x^{2} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{16 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 32 \, c d \int \frac{x \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{16 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 64 \, c d \int \frac{x \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{16 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 16 \, c^{2} \int \frac{\log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{16 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} - x \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2} + \frac{12 \, \arctan\left(d x + c\right)^{2} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d} - \frac{12 \, \arctan\left(d x + c\right) \arctan\left(\frac{d^{2} x + c d}{d}\right)^{2}}{d} + \frac{4 \, \arctan\left(\frac{d^{2} x + c d}{d}\right)^{3}}{d} - 128 \, d \int \frac{x \arctan\left(d x + c\right)}{16 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 16 \, \int \frac{\log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{16 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x}\right)} b^{2} + a^{2} x + \frac{{\left(2 \, {\left(d x + c\right)} \arctan\left(d x + c\right) - \log\left({\left(d x + c\right)}^{2} + 1\right)\right)} a b}{d}"," ",0,"1/16*(12*c^2*arctan(d*x + c)^2*arctan((d^2*x + c*d)/d)/d - 4*(3*arctan(d*x + c)*arctan((d^2*x + c*d)/d)^2/d - arctan((d^2*x + c*d)/d)^3/d)*c^2 + 4*x*arctan(d*x + c)^2 + 192*d^2*integrate(1/16*x^2*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 16*d^2*integrate(1/16*x^2*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 384*c*d*integrate(1/16*x*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 64*d^2*integrate(1/16*x^2*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 32*c*d*integrate(1/16*x*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 64*c*d*integrate(1/16*x*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 16*c^2*integrate(1/16*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) - x*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 + 12*arctan(d*x + c)^2*arctan((d^2*x + c*d)/d)/d - 12*arctan(d*x + c)*arctan((d^2*x + c*d)/d)^2/d + 4*arctan((d^2*x + c*d)/d)^3/d - 128*d*integrate(1/16*x*arctan(d*x + c)/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 16*integrate(1/16*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x))*b^2 + a^2*x + (2*(d*x + c)*arctan(d*x + c) - log((d*x + c)^2 + 1))*a*b/d","F",0
34,0,0,0,0.000000," ","integrate((a+b*arctan(d*x+c))^2/(f*x+e),x, algorithm=""maxima"")","\frac{a^{2} \log\left(f x + e\right)}{f} + \int \frac{12 \, b^{2} \arctan\left(d x + c\right)^{2} + b^{2} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2} + 32 \, a b \arctan\left(d x + c\right)}{16 \, {\left(f x + e\right)}}\,{d x}"," ",0,"a^2*log(f*x + e)/f + integrate(1/16*(12*b^2*arctan(d*x + c)^2 + b^2*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 + 32*a*b*arctan(d*x + c))/(f*x + e), x)","F",0
35,0,0,0,0.000000," ","integrate((a+b*arctan(d*x+c))^2/(f*x+e)^2,x, algorithm=""maxima"")","{\left(d {\left(\frac{2 \, {\left(d^{2} e - c d f\right)} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{{\left(d^{2} e^{2} f - 2 \, c d e f^{2} + {\left(c^{2} + 1\right)} f^{3}\right)} d} - \frac{\log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{2} e^{2} - 2 \, c d e f + {\left(c^{2} + 1\right)} f^{2}} + \frac{2 \, \log\left(f x + e\right)}{d^{2} e^{2} - 2 \, c d e f + {\left(c^{2} + 1\right)} f^{2}}\right)} - \frac{2 \, \arctan\left(d x + c\right)}{f^{2} x + e f}\right)} a b - \frac{\frac{1}{4} \, {\left(28 \, \arctan\left(d x + c\right)^{2} - 4 \, {\left(f^{2} x + e f\right)} \int \frac{36 \, {\left(d^{2} f x^{2} + 2 \, c d f x + {\left(c^{2} + 1\right)} f\right)} \arctan\left(d x + c\right)^{2} + 3 \, {\left(d^{2} f x^{2} + 2 \, c d f x + {\left(c^{2} + 1\right)} f\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2} + 56 \, {\left(d f x + d e\right)} \arctan\left(d x + c\right) - 12 \, {\left(d^{2} f x^{2} + c d e + {\left(d^{2} e + c d f\right)} x\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{4 \, {\left(d^{2} f^{3} x^{4} + {\left(c^{2} + 1\right)} e^{2} f + 2 \, {\left(d^{2} e f^{2} + c d f^{3}\right)} x^{3} + {\left(d^{2} e^{2} f + 4 \, c d e f^{2} + {\left(c^{2} + 1\right)} f^{3}\right)} x^{2} + 2 \, {\left(c d e^{2} f + {\left(c^{2} + 1\right)} e f^{2}\right)} x\right)}}\,{d x} - 3 \, \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}\right)} b^{2}}{16 \, {\left(f^{2} x + e f\right)}} - \frac{a^{2}}{f^{2} x + e f}"," ",0,"(d*(2*(d^2*e - c*d*f)*arctan((d^2*x + c*d)/d)/((d^2*e^2*f - 2*c*d*e*f^2 + (c^2 + 1)*f^3)*d) - log(d^2*x^2 + 2*c*d*x + c^2 + 1)/(d^2*e^2 - 2*c*d*e*f + (c^2 + 1)*f^2) + 2*log(f*x + e)/(d^2*e^2 - 2*c*d*e*f + (c^2 + 1)*f^2)) - 2*arctan(d*x + c)/(f^2*x + e*f))*a*b - 1/16*(4*arctan(d*x + c)^2 - 16*(f^2*x + e*f)*integrate(1/16*(12*(d^2*f*x^2 + 2*c*d*f*x + (c^2 + 1)*f)*arctan(d*x + c)^2 + (d^2*f*x^2 + 2*c*d*f*x + (c^2 + 1)*f)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 + 8*(d*f*x + d*e)*arctan(d*x + c) - 4*(d^2*f*x^2 + c*d*e + (d^2*e + c*d*f)*x)*log(d^2*x^2 + 2*c*d*x + c^2 + 1))/(d^2*f^3*x^4 + (c^2 + 1)*e^2*f + 2*(d^2*e*f^2 + c*d*f^3)*x^3 + (d^2*e^2*f + 4*c*d*e*f^2 + (c^2 + 1)*f^3)*x^2 + 2*(c*d*e^2*f + (c^2 + 1)*e*f^2)*x), x) - log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2)*b^2/(f^2*x + e*f) - a^2/(f^2*x + e*f)","F",0
36,0,0,0,0.000000," ","integrate((f*x+e)^2*(a+b*arctan(d*x+c))^3,x, algorithm=""maxima"")","\frac{7 \, b^{3} c^{2} e^{2} \arctan\left(d x + c\right)^{3} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{8 \, d} + \frac{3 \, a b^{2} c^{2} e^{2} \arctan\left(d x + c\right)^{2} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d} - {\left(\frac{3 \, \arctan\left(d x + c\right) \arctan\left(\frac{d^{2} x + c d}{d}\right)^{2}}{d} - \frac{\arctan\left(\frac{d^{2} x + c d}{d}\right)^{3}}{d}\right)} a b^{2} c^{2} e^{2} - \frac{7}{32} \, {\left(\frac{6 \, \arctan\left(d x + c\right)^{2} \arctan\left(\frac{d^{2} x + c d}{d}\right)^{2}}{d} - \frac{4 \, \arctan\left(d x + c\right) \arctan\left(\frac{d^{2} x + c d}{d}\right)^{3}}{d} + \frac{\arctan\left(\frac{d^{2} x + c d}{d}\right)^{4}}{d}\right)} b^{3} c^{2} e^{2} + \frac{1}{3} \, a^{3} f^{2} x^{3} + \frac{7 \, b^{3} e^{2} \arctan\left(d x + c\right)^{3} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{8 \, d} + 28 \, b^{3} d^{2} f^{2} \int \frac{x^{4} \arctan\left(d x + c\right)^{3}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 3 \, b^{3} d^{2} f^{2} \int \frac{x^{4} \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 96 \, a b^{2} d^{2} f^{2} \int \frac{x^{4} \arctan\left(d x + c\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 56 \, b^{3} d^{2} e f \int \frac{x^{3} \arctan\left(d x + c\right)^{3}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 56 \, b^{3} c d f^{2} \int \frac{x^{3} \arctan\left(d x + c\right)^{3}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 4 \, b^{3} d^{2} f^{2} \int \frac{x^{4} \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 6 \, b^{3} d^{2} e f \int \frac{x^{3} \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 6 \, b^{3} c d f^{2} \int \frac{x^{3} \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 192 \, a b^{2} d^{2} e f \int \frac{x^{3} \arctan\left(d x + c\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 192 \, a b^{2} c d f^{2} \int \frac{x^{3} \arctan\left(d x + c\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 28 \, b^{3} d^{2} e^{2} \int \frac{x^{2} \arctan\left(d x + c\right)^{3}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 112 \, b^{3} c d e f \int \frac{x^{2} \arctan\left(d x + c\right)^{3}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 28 \, b^{3} c^{2} f^{2} \int \frac{x^{2} \arctan\left(d x + c\right)^{3}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 12 \, b^{3} d^{2} e f \int \frac{x^{3} \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 4 \, b^{3} c d f^{2} \int \frac{x^{3} \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 3 \, b^{3} d^{2} e^{2} \int \frac{x^{2} \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 12 \, b^{3} c d e f \int \frac{x^{2} \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 3 \, b^{3} c^{2} f^{2} \int \frac{x^{2} \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 96 \, a b^{2} d^{2} e^{2} \int \frac{x^{2} \arctan\left(d x + c\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 384 \, a b^{2} c d e f \int \frac{x^{2} \arctan\left(d x + c\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 96 \, a b^{2} c^{2} f^{2} \int \frac{x^{2} \arctan\left(d x + c\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 56 \, b^{3} c d e^{2} \int \frac{x \arctan\left(d x + c\right)^{3}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 56 \, b^{3} c^{2} e f \int \frac{x \arctan\left(d x + c\right)^{3}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 12 \, b^{3} d^{2} e^{2} \int \frac{x^{2} \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 12 \, b^{3} c d e f \int \frac{x^{2} \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 6 \, b^{3} c d e^{2} \int \frac{x \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 6 \, b^{3} c^{2} e f \int \frac{x \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 192 \, a b^{2} c d e^{2} \int \frac{x \arctan\left(d x + c\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 192 \, a b^{2} c^{2} e f \int \frac{x \arctan\left(d x + c\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 12 \, b^{3} c d e^{2} \int \frac{x \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 3 \, b^{3} c^{2} e^{2} \int \frac{\arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + a^{3} e f x^{2} + \frac{3 \, a b^{2} e^{2} \arctan\left(d x + c\right)^{2} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d} - 4 \, b^{3} d f^{2} \int \frac{x^{3} \arctan\left(d x + c\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + b^{3} d f^{2} \int \frac{x^{3} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} - 12 \, b^{3} d e f \int \frac{x^{2} \arctan\left(d x + c\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 3 \, b^{3} d e f \int \frac{x^{2} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} - 12 \, b^{3} d e^{2} \int \frac{x \arctan\left(d x + c\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 3 \, b^{3} d e^{2} \int \frac{x \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} - {\left(\frac{3 \, \arctan\left(d x + c\right) \arctan\left(\frac{d^{2} x + c d}{d}\right)^{2}}{d} - \frac{\arctan\left(\frac{d^{2} x + c d}{d}\right)^{3}}{d}\right)} a b^{2} e^{2} - \frac{7}{32} \, {\left(\frac{6 \, \arctan\left(d x + c\right)^{2} \arctan\left(\frac{d^{2} x + c d}{d}\right)^{2}}{d} - \frac{4 \, \arctan\left(d x + c\right) \arctan\left(\frac{d^{2} x + c d}{d}\right)^{3}}{d} + \frac{\arctan\left(\frac{d^{2} x + c d}{d}\right)^{4}}{d}\right)} b^{3} e^{2} + 3 \, {\left(x^{2} \arctan\left(d x + c\right) - d {\left(\frac{x}{d^{2}} + \frac{{\left(c^{2} - 1\right)} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d^{3}} - \frac{c \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{3}}\right)}\right)} a^{2} b e f + \frac{1}{2} \, {\left(2 \, x^{3} \arctan\left(d x + c\right) - d {\left(\frac{d x^{2} - 4 \, c x}{d^{3}} - \frac{2 \, {\left(c^{3} - 3 \, c\right)} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d^{4}} + \frac{{\left(3 \, c^{2} - 1\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{4}}\right)}\right)} a^{2} b f^{2} + a^{3} e^{2} x + 28 \, b^{3} f^{2} \int \frac{x^{2} \arctan\left(d x + c\right)^{3}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 3 \, b^{3} f^{2} \int \frac{x^{2} \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 96 \, a b^{2} f^{2} \int \frac{x^{2} \arctan\left(d x + c\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 56 \, b^{3} e f \int \frac{x \arctan\left(d x + c\right)^{3}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 6 \, b^{3} e f \int \frac{x \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 192 \, a b^{2} e f \int \frac{x \arctan\left(d x + c\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 3 \, b^{3} e^{2} \int \frac{\arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + \frac{3 \, {\left(2 \, {\left(d x + c\right)} \arctan\left(d x + c\right) - \log\left({\left(d x + c\right)}^{2} + 1\right)\right)} a^{2} b e^{2}}{2 \, d} + \frac{1}{24} \, {\left(b^{3} f^{2} x^{3} + 3 \, b^{3} e f x^{2} + 3 \, b^{3} e^{2} x\right)} \arctan\left(d x + c\right)^{3} - \frac{1}{32} \, {\left(b^{3} f^{2} x^{3} + 3 \, b^{3} e f x^{2} + 3 \, b^{3} e^{2} x\right)} \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}"," ",0,"7/8*b^3*c^2*e^2*arctan(d*x + c)^3*arctan((d^2*x + c*d)/d)/d + 3*a*b^2*c^2*e^2*arctan(d*x + c)^2*arctan((d^2*x + c*d)/d)/d - (3*arctan(d*x + c)*arctan((d^2*x + c*d)/d)^2/d - arctan((d^2*x + c*d)/d)^3/d)*a*b^2*c^2*e^2 - 7/32*(6*arctan(d*x + c)^2*arctan((d^2*x + c*d)/d)^2/d - 4*arctan(d*x + c)*arctan((d^2*x + c*d)/d)^3/d + arctan((d^2*x + c*d)/d)^4/d)*b^3*c^2*e^2 + 1/3*a^3*f^2*x^3 + 7/8*b^3*e^2*arctan(d*x + c)^3*arctan((d^2*x + c*d)/d)/d + 28*b^3*d^2*f^2*integrate(1/32*x^4*arctan(d*x + c)^3/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 3*b^3*d^2*f^2*integrate(1/32*x^4*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 96*a*b^2*d^2*f^2*integrate(1/32*x^4*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 56*b^3*d^2*e*f*integrate(1/32*x^3*arctan(d*x + c)^3/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 56*b^3*c*d*f^2*integrate(1/32*x^3*arctan(d*x + c)^3/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 4*b^3*d^2*f^2*integrate(1/32*x^4*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 6*b^3*d^2*e*f*integrate(1/32*x^3*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 6*b^3*c*d*f^2*integrate(1/32*x^3*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 192*a*b^2*d^2*e*f*integrate(1/32*x^3*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 192*a*b^2*c*d*f^2*integrate(1/32*x^3*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 28*b^3*d^2*e^2*integrate(1/32*x^2*arctan(d*x + c)^3/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 112*b^3*c*d*e*f*integrate(1/32*x^2*arctan(d*x + c)^3/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 28*b^3*c^2*f^2*integrate(1/32*x^2*arctan(d*x + c)^3/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 12*b^3*d^2*e*f*integrate(1/32*x^3*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 4*b^3*c*d*f^2*integrate(1/32*x^3*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 3*b^3*d^2*e^2*integrate(1/32*x^2*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 12*b^3*c*d*e*f*integrate(1/32*x^2*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 3*b^3*c^2*f^2*integrate(1/32*x^2*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 96*a*b^2*d^2*e^2*integrate(1/32*x^2*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 384*a*b^2*c*d*e*f*integrate(1/32*x^2*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 96*a*b^2*c^2*f^2*integrate(1/32*x^2*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 56*b^3*c*d*e^2*integrate(1/32*x*arctan(d*x + c)^3/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 56*b^3*c^2*e*f*integrate(1/32*x*arctan(d*x + c)^3/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 12*b^3*d^2*e^2*integrate(1/32*x^2*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 12*b^3*c*d*e*f*integrate(1/32*x^2*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 6*b^3*c*d*e^2*integrate(1/32*x*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 6*b^3*c^2*e*f*integrate(1/32*x*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 192*a*b^2*c*d*e^2*integrate(1/32*x*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 192*a*b^2*c^2*e*f*integrate(1/32*x*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 12*b^3*c*d*e^2*integrate(1/32*x*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 3*b^3*c^2*e^2*integrate(1/32*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + a^3*e*f*x^2 + 3*a*b^2*e^2*arctan(d*x + c)^2*arctan((d^2*x + c*d)/d)/d - 4*b^3*d*f^2*integrate(1/32*x^3*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + b^3*d*f^2*integrate(1/32*x^3*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) - 12*b^3*d*e*f*integrate(1/32*x^2*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 3*b^3*d*e*f*integrate(1/32*x^2*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) - 12*b^3*d*e^2*integrate(1/32*x*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 3*b^3*d*e^2*integrate(1/32*x*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) - (3*arctan(d*x + c)*arctan((d^2*x + c*d)/d)^2/d - arctan((d^2*x + c*d)/d)^3/d)*a*b^2*e^2 - 7/32*(6*arctan(d*x + c)^2*arctan((d^2*x + c*d)/d)^2/d - 4*arctan(d*x + c)*arctan((d^2*x + c*d)/d)^3/d + arctan((d^2*x + c*d)/d)^4/d)*b^3*e^2 + 3*(x^2*arctan(d*x + c) - d*(x/d^2 + (c^2 - 1)*arctan((d^2*x + c*d)/d)/d^3 - c*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/d^3))*a^2*b*e*f + 1/2*(2*x^3*arctan(d*x + c) - d*((d*x^2 - 4*c*x)/d^3 - 2*(c^3 - 3*c)*arctan((d^2*x + c*d)/d)/d^4 + (3*c^2 - 1)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/d^4))*a^2*b*f^2 + a^3*e^2*x + 28*b^3*f^2*integrate(1/32*x^2*arctan(d*x + c)^3/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 3*b^3*f^2*integrate(1/32*x^2*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 96*a*b^2*f^2*integrate(1/32*x^2*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 56*b^3*e*f*integrate(1/32*x*arctan(d*x + c)^3/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 6*b^3*e*f*integrate(1/32*x*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 192*a*b^2*e*f*integrate(1/32*x*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 3*b^3*e^2*integrate(1/32*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 3/2*(2*(d*x + c)*arctan(d*x + c) - log((d*x + c)^2 + 1))*a^2*b*e^2/d + 1/24*(b^3*f^2*x^3 + 3*b^3*e*f*x^2 + 3*b^3*e^2*x)*arctan(d*x + c)^3 - 1/32*(b^3*f^2*x^3 + 3*b^3*e*f*x^2 + 3*b^3*e^2*x)*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2","F",0
37,0,0,0,0.000000," ","integrate((f*x+e)*(a+b*arctan(d*x+c))^3,x, algorithm=""maxima"")","\frac{7 \, b^{3} c^{2} e \arctan\left(d x + c\right)^{3} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{8 \, d} + \frac{3 \, a b^{2} c^{2} e \arctan\left(d x + c\right)^{2} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d} - {\left(\frac{3 \, \arctan\left(d x + c\right) \arctan\left(\frac{d^{2} x + c d}{d}\right)^{2}}{d} - \frac{\arctan\left(\frac{d^{2} x + c d}{d}\right)^{3}}{d}\right)} a b^{2} c^{2} e - \frac{7}{32} \, {\left(\frac{6 \, \arctan\left(d x + c\right)^{2} \arctan\left(\frac{d^{2} x + c d}{d}\right)^{2}}{d} - \frac{4 \, \arctan\left(d x + c\right) \arctan\left(\frac{d^{2} x + c d}{d}\right)^{3}}{d} + \frac{\arctan\left(\frac{d^{2} x + c d}{d}\right)^{4}}{d}\right)} b^{3} c^{2} e + \frac{7 \, b^{3} e \arctan\left(d x + c\right)^{3} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{8 \, d} + 56 \, b^{3} d^{2} f \int \frac{x^{3} \arctan\left(d x + c\right)^{3}}{64 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 6 \, b^{3} d^{2} f \int \frac{x^{3} \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{64 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 192 \, a b^{2} d^{2} f \int \frac{x^{3} \arctan\left(d x + c\right)^{2}}{64 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 56 \, b^{3} d^{2} e \int \frac{x^{2} \arctan\left(d x + c\right)^{3}}{64 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 112 \, b^{3} c d f \int \frac{x^{2} \arctan\left(d x + c\right)^{3}}{64 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 12 \, b^{3} d^{2} f \int \frac{x^{3} \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{64 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 6 \, b^{3} d^{2} e \int \frac{x^{2} \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{64 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 12 \, b^{3} c d f \int \frac{x^{2} \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{64 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 192 \, a b^{2} d^{2} e \int \frac{x^{2} \arctan\left(d x + c\right)^{2}}{64 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 384 \, a b^{2} c d f \int \frac{x^{2} \arctan\left(d x + c\right)^{2}}{64 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 112 \, b^{3} c d e \int \frac{x \arctan\left(d x + c\right)^{3}}{64 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 56 \, b^{3} c^{2} f \int \frac{x \arctan\left(d x + c\right)^{3}}{64 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 24 \, b^{3} d^{2} e \int \frac{x^{2} \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{64 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 12 \, b^{3} c d f \int \frac{x^{2} \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{64 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 12 \, b^{3} c d e \int \frac{x \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{64 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 6 \, b^{3} c^{2} f \int \frac{x \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{64 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 384 \, a b^{2} c d e \int \frac{x \arctan\left(d x + c\right)^{2}}{64 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 192 \, a b^{2} c^{2} f \int \frac{x \arctan\left(d x + c\right)^{2}}{64 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 24 \, b^{3} c d e \int \frac{x \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{64 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 6 \, b^{3} c^{2} e \int \frac{\arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{64 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + \frac{1}{2} \, a^{3} f x^{2} + \frac{3 \, a b^{2} e \arctan\left(d x + c\right)^{2} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d} - 12 \, b^{3} d f \int \frac{x^{2} \arctan\left(d x + c\right)^{2}}{64 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 3 \, b^{3} d f \int \frac{x^{2} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{64 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} - 24 \, b^{3} d e \int \frac{x \arctan\left(d x + c\right)^{2}}{64 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 6 \, b^{3} d e \int \frac{x \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{64 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} - {\left(\frac{3 \, \arctan\left(d x + c\right) \arctan\left(\frac{d^{2} x + c d}{d}\right)^{2}}{d} - \frac{\arctan\left(\frac{d^{2} x + c d}{d}\right)^{3}}{d}\right)} a b^{2} e - \frac{7}{32} \, {\left(\frac{6 \, \arctan\left(d x + c\right)^{2} \arctan\left(\frac{d^{2} x + c d}{d}\right)^{2}}{d} - \frac{4 \, \arctan\left(d x + c\right) \arctan\left(\frac{d^{2} x + c d}{d}\right)^{3}}{d} + \frac{\arctan\left(\frac{d^{2} x + c d}{d}\right)^{4}}{d}\right)} b^{3} e + \frac{3}{2} \, {\left(x^{2} \arctan\left(d x + c\right) - d {\left(\frac{x}{d^{2}} + \frac{{\left(c^{2} - 1\right)} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d^{3}} - \frac{c \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{3}}\right)}\right)} a^{2} b f + a^{3} e x + 56 \, b^{3} f \int \frac{x \arctan\left(d x + c\right)^{3}}{64 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 6 \, b^{3} f \int \frac{x \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{64 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 192 \, a b^{2} f \int \frac{x \arctan\left(d x + c\right)^{2}}{64 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 6 \, b^{3} e \int \frac{\arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{64 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + \frac{3 \, {\left(2 \, {\left(d x + c\right)} \arctan\left(d x + c\right) - \log\left({\left(d x + c\right)}^{2} + 1\right)\right)} a^{2} b e}{2 \, d} + \frac{1}{16} \, {\left(b^{3} f x^{2} + 2 \, b^{3} e x\right)} \arctan\left(d x + c\right)^{3} - \frac{3}{64} \, {\left(b^{3} f x^{2} + 2 \, b^{3} e x\right)} \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}"," ",0,"7/8*b^3*c^2*e*arctan(d*x + c)^3*arctan((d^2*x + c*d)/d)/d + 3*a*b^2*c^2*e*arctan(d*x + c)^2*arctan((d^2*x + c*d)/d)/d - (3*arctan(d*x + c)*arctan((d^2*x + c*d)/d)^2/d - arctan((d^2*x + c*d)/d)^3/d)*a*b^2*c^2*e - 7/32*(6*arctan(d*x + c)^2*arctan((d^2*x + c*d)/d)^2/d - 4*arctan(d*x + c)*arctan((d^2*x + c*d)/d)^3/d + arctan((d^2*x + c*d)/d)^4/d)*b^3*c^2*e + 7/8*b^3*e*arctan(d*x + c)^3*arctan((d^2*x + c*d)/d)/d + 56*b^3*d^2*f*integrate(1/64*x^3*arctan(d*x + c)^3/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 6*b^3*d^2*f*integrate(1/64*x^3*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 192*a*b^2*d^2*f*integrate(1/64*x^3*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 56*b^3*d^2*e*integrate(1/64*x^2*arctan(d*x + c)^3/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 112*b^3*c*d*f*integrate(1/64*x^2*arctan(d*x + c)^3/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 12*b^3*d^2*f*integrate(1/64*x^3*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 6*b^3*d^2*e*integrate(1/64*x^2*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 12*b^3*c*d*f*integrate(1/64*x^2*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 192*a*b^2*d^2*e*integrate(1/64*x^2*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 384*a*b^2*c*d*f*integrate(1/64*x^2*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 112*b^3*c*d*e*integrate(1/64*x*arctan(d*x + c)^3/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 56*b^3*c^2*f*integrate(1/64*x*arctan(d*x + c)^3/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 24*b^3*d^2*e*integrate(1/64*x^2*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 12*b^3*c*d*f*integrate(1/64*x^2*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 12*b^3*c*d*e*integrate(1/64*x*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 6*b^3*c^2*f*integrate(1/64*x*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 384*a*b^2*c*d*e*integrate(1/64*x*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 192*a*b^2*c^2*f*integrate(1/64*x*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 24*b^3*c*d*e*integrate(1/64*x*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 6*b^3*c^2*e*integrate(1/64*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 1/2*a^3*f*x^2 + 3*a*b^2*e*arctan(d*x + c)^2*arctan((d^2*x + c*d)/d)/d - 12*b^3*d*f*integrate(1/64*x^2*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 3*b^3*d*f*integrate(1/64*x^2*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) - 24*b^3*d*e*integrate(1/64*x*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 6*b^3*d*e*integrate(1/64*x*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) - (3*arctan(d*x + c)*arctan((d^2*x + c*d)/d)^2/d - arctan((d^2*x + c*d)/d)^3/d)*a*b^2*e - 7/32*(6*arctan(d*x + c)^2*arctan((d^2*x + c*d)/d)^2/d - 4*arctan(d*x + c)*arctan((d^2*x + c*d)/d)^3/d + arctan((d^2*x + c*d)/d)^4/d)*b^3*e + 3/2*(x^2*arctan(d*x + c) - d*(x/d^2 + (c^2 - 1)*arctan((d^2*x + c*d)/d)/d^3 - c*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/d^3))*a^2*b*f + a^3*e*x + 56*b^3*f*integrate(1/64*x*arctan(d*x + c)^3/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 6*b^3*f*integrate(1/64*x*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 192*a*b^2*f*integrate(1/64*x*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 6*b^3*e*integrate(1/64*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 3/2*(2*(d*x + c)*arctan(d*x + c) - log((d*x + c)^2 + 1))*a^2*b*e/d + 1/16*(b^3*f*x^2 + 2*b^3*e*x)*arctan(d*x + c)^3 - 3/64*(b^3*f*x^2 + 2*b^3*e*x)*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2","F",0
38,0,0,0,0.000000," ","integrate((a+b*arctan(d*x+c))^3,x, algorithm=""maxima"")","\frac{7 \, b^{3} c^{2} \arctan\left(d x + c\right)^{3} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{8 \, d} + \frac{1}{8} \, b^{3} x \arctan\left(d x + c\right)^{3} + \frac{3 \, a b^{2} c^{2} \arctan\left(d x + c\right)^{2} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d} - \frac{3}{32} \, b^{3} x \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2} - {\left(\frac{3 \, \arctan\left(d x + c\right) \arctan\left(\frac{d^{2} x + c d}{d}\right)^{2}}{d} - \frac{\arctan\left(\frac{d^{2} x + c d}{d}\right)^{3}}{d}\right)} a b^{2} c^{2} - \frac{7}{32} \, {\left(\frac{6 \, \arctan\left(d x + c\right)^{2} \arctan\left(\frac{d^{2} x + c d}{d}\right)^{2}}{d} - \frac{4 \, \arctan\left(d x + c\right) \arctan\left(\frac{d^{2} x + c d}{d}\right)^{3}}{d} + \frac{\arctan\left(\frac{d^{2} x + c d}{d}\right)^{4}}{d}\right)} b^{3} c^{2} + \frac{7 \, b^{3} \arctan\left(d x + c\right)^{3} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{8 \, d} + 28 \, b^{3} d^{2} \int \frac{x^{2} \arctan\left(d x + c\right)^{3}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 3 \, b^{3} d^{2} \int \frac{x^{2} \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 96 \, a b^{2} d^{2} \int \frac{x^{2} \arctan\left(d x + c\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 56 \, b^{3} c d \int \frac{x \arctan\left(d x + c\right)^{3}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 12 \, b^{3} d^{2} \int \frac{x^{2} \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 6 \, b^{3} c d \int \frac{x \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 192 \, a b^{2} c d \int \frac{x \arctan\left(d x + c\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 12 \, b^{3} c d \int \frac{x \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 3 \, b^{3} c^{2} \int \frac{\arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + \frac{3 \, a b^{2} \arctan\left(d x + c\right)^{2} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d} - 12 \, b^{3} d \int \frac{x \arctan\left(d x + c\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + 3 \, b^{3} d \int \frac{x \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} - {\left(\frac{3 \, \arctan\left(d x + c\right) \arctan\left(\frac{d^{2} x + c d}{d}\right)^{2}}{d} - \frac{\arctan\left(\frac{d^{2} x + c d}{d}\right)^{3}}{d}\right)} a b^{2} - \frac{7}{32} \, {\left(\frac{6 \, \arctan\left(d x + c\right)^{2} \arctan\left(\frac{d^{2} x + c d}{d}\right)^{2}}{d} - \frac{4 \, \arctan\left(d x + c\right) \arctan\left(\frac{d^{2} x + c d}{d}\right)^{3}}{d} + \frac{\arctan\left(\frac{d^{2} x + c d}{d}\right)^{4}}{d}\right)} b^{3} + a^{3} x + 3 \, b^{3} \int \frac{\arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x} + \frac{3 \, {\left(2 \, {\left(d x + c\right)} \arctan\left(d x + c\right) - \log\left({\left(d x + c\right)}^{2} + 1\right)\right)} a^{2} b}{2 \, d}"," ",0,"7/8*b^3*c^2*arctan(d*x + c)^3*arctan((d^2*x + c*d)/d)/d + 1/8*b^3*x*arctan(d*x + c)^3 + 3*a*b^2*c^2*arctan(d*x + c)^2*arctan((d^2*x + c*d)/d)/d - 3/32*b^3*x*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 - (3*arctan(d*x + c)*arctan((d^2*x + c*d)/d)^2/d - arctan((d^2*x + c*d)/d)^3/d)*a*b^2*c^2 - 7/32*(6*arctan(d*x + c)^2*arctan((d^2*x + c*d)/d)^2/d - 4*arctan(d*x + c)*arctan((d^2*x + c*d)/d)^3/d + arctan((d^2*x + c*d)/d)^4/d)*b^3*c^2 + 7/8*b^3*arctan(d*x + c)^3*arctan((d^2*x + c*d)/d)/d + 28*b^3*d^2*integrate(1/32*x^2*arctan(d*x + c)^3/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 3*b^3*d^2*integrate(1/32*x^2*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 96*a*b^2*d^2*integrate(1/32*x^2*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 56*b^3*c*d*integrate(1/32*x*arctan(d*x + c)^3/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 12*b^3*d^2*integrate(1/32*x^2*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 6*b^3*c*d*integrate(1/32*x*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 192*a*b^2*c*d*integrate(1/32*x*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 12*b^3*c*d*integrate(1/32*x*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 3*b^3*c^2*integrate(1/32*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 3*a*b^2*arctan(d*x + c)^2*arctan((d^2*x + c*d)/d)/d - 12*b^3*d*integrate(1/32*x*arctan(d*x + c)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 3*b^3*d*integrate(1/32*x*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) - (3*arctan(d*x + c)*arctan((d^2*x + c*d)/d)^2/d - arctan((d^2*x + c*d)/d)^3/d)*a*b^2 - 7/32*(6*arctan(d*x + c)^2*arctan((d^2*x + c*d)/d)^2/d - 4*arctan(d*x + c)*arctan((d^2*x + c*d)/d)^3/d + arctan((d^2*x + c*d)/d)^4/d)*b^3 + a^3*x + 3*b^3*integrate(1/32*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2/(d^2*x^2 + 2*c*d*x + c^2 + 1), x) + 3/2*(2*(d*x + c)*arctan(d*x + c) - log((d*x + c)^2 + 1))*a^2*b/d","F",0
39,0,0,0,0.000000," ","integrate((a+b*arctan(d*x+c))^3/(f*x+e),x, algorithm=""maxima"")","\frac{a^{3} \log\left(f x + e\right)}{f} + \int \frac{28 \, b^{3} \arctan\left(d x + c\right)^{3} + 3 \, b^{3} \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2} + 96 \, a b^{2} \arctan\left(d x + c\right)^{2} + 96 \, a^{2} b \arctan\left(d x + c\right)}{32 \, {\left(f x + e\right)}}\,{d x}"," ",0,"a^3*log(f*x + e)/f + integrate(1/32*(28*b^3*arctan(d*x + c)^3 + 3*b^3*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 + 96*a*b^2*arctan(d*x + c)^2 + 96*a^2*b*arctan(d*x + c))/(f*x + e), x)","F",0
40,0,0,0,0.000000," ","integrate((a+b*arctan(d*x+c))^3/(f*x+e)^2,x, algorithm=""maxima"")","\frac{3}{2} \, {\left(d {\left(\frac{2 \, {\left(d^{2} e - c d f\right)} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{{\left(d^{2} e^{2} f - 2 \, c d e f^{2} + {\left(c^{2} + 1\right)} f^{3}\right)} d} - \frac{\log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{2} e^{2} - 2 \, c d e f + {\left(c^{2} + 1\right)} f^{2}} + \frac{2 \, \log\left(f x + e\right)}{d^{2} e^{2} - 2 \, c d e f + {\left(c^{2} + 1\right)} f^{2}}\right)} - \frac{2 \, \arctan\left(d x + c\right)}{f^{2} x + e f}\right)} a^{2} b - \frac{a^{3}}{f^{2} x + e f} - \frac{\frac{15}{2} \, b^{3} \arctan\left(d x + c\right)^{3} - \frac{21}{8} \, b^{3} \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2} - {\left(f^{2} x + e f\right)} \int \frac{196 \, {\left(b^{3} d^{2} f x^{2} + 2 \, b^{3} c d f x + {\left(b^{3} c^{2} + b^{3}\right)} f\right)} \arctan\left(d x + c\right)^{3} + 12 \, {\left(64 \, a b^{2} d^{2} f x^{2} + 15 \, b^{3} d e + {\left(128 \, a b^{2} c + 15 \, b^{3}\right)} d f x + 64 \, {\left(a b^{2} c^{2} + a b^{2}\right)} f\right)} \arctan\left(d x + c\right)^{2} - 84 \, {\left(b^{3} d^{2} f x^{2} + b^{3} c d e + {\left(b^{3} d^{2} e + b^{3} c d f\right)} x\right)} \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right) - 21 \, {\left(b^{3} d f x + b^{3} d e - {\left(b^{3} d^{2} f x^{2} + 2 \, b^{3} c d f x + {\left(b^{3} c^{2} + b^{3}\right)} f\right)} \arctan\left(d x + c\right)\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{8 \, {\left(d^{2} f^{3} x^{4} + {\left(c^{2} + 1\right)} e^{2} f + 2 \, {\left(d^{2} e f^{2} + c d f^{3}\right)} x^{3} + {\left(d^{2} e^{2} f + 4 \, c d e f^{2} + {\left(c^{2} + 1\right)} f^{3}\right)} x^{2} + 2 \, {\left(c d e^{2} f + {\left(c^{2} + 1\right)} e f^{2}\right)} x\right)}}\,{d x}}{32 \, {\left(f^{2} x + e f\right)}}"," ",0,"3/2*(d*(2*(d^2*e - c*d*f)*arctan((d^2*x + c*d)/d)/((d^2*e^2*f - 2*c*d*e*f^2 + (c^2 + 1)*f^3)*d) - log(d^2*x^2 + 2*c*d*x + c^2 + 1)/(d^2*e^2 - 2*c*d*e*f + (c^2 + 1)*f^2) + 2*log(f*x + e)/(d^2*e^2 - 2*c*d*e*f + (c^2 + 1)*f^2)) - 2*arctan(d*x + c)/(f^2*x + e*f))*a^2*b - a^3/(f^2*x + e*f) - 1/32*(4*b^3*arctan(d*x + c)^3 - 3*b^3*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 - 32*(f^2*x + e*f)*integrate(1/32*(28*(b^3*d^2*f*x^2 + 2*b^3*c*d*f*x + (b^3*c^2 + b^3)*f)*arctan(d*x + c)^3 + 12*(8*a*b^2*d^2*f*x^2 + b^3*d*e + (16*a*b^2*c + b^3)*d*f*x + 8*(a*b^2*c^2 + a*b^2)*f)*arctan(d*x + c)^2 - 12*(b^3*d^2*f*x^2 + b^3*c*d*e + (b^3*d^2*e + b^3*c*d*f)*x)*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1) - 3*(b^3*d*f*x + b^3*d*e - (b^3*d^2*f*x^2 + 2*b^3*c*d*f*x + (b^3*c^2 + b^3)*f)*arctan(d*x + c))*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2)/(d^2*f^3*x^4 + (c^2 + 1)*e^2*f + 2*(d^2*e*f^2 + c*d*f^3)*x^3 + (d^2*e^2*f + 4*c*d*e*f^2 + (c^2 + 1)*f^3)*x^2 + 2*(c*d*e^2*f + (c^2 + 1)*e*f^2)*x), x))/(f^2*x + e*f)","F",0
41,-1,0,0,0.000000," ","integrate((f*x+e)^m*(a+b*arctan(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
42,0,0,0,0.000000," ","integrate((f*x+e)^m*(a+b*arctan(d*x+c))^2,x, algorithm=""maxima"")","\frac{{\left(f x + e\right)}^{m + 1} a^{2}}{f {\left(m + 1\right)}} + \frac{7 \, {\left(b^{2} f x + b^{2} e\right)} {\left(f x + e\right)}^{m} \arctan\left(d x + c\right)^{2} - \frac{3}{4} \, {\left(b^{2} f x + b^{2} e\right)} {\left(f x + e\right)}^{m} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2} + {\left(f m + f\right)} \int \frac{36 \, {\left({\left(b^{2} c^{2} + b^{2}\right)} f m + {\left(b^{2} d^{2} f m + b^{2} d^{2} f\right)} x^{2} + {\left(b^{2} c^{2} + b^{2}\right)} f + 2 \, {\left(b^{2} c d f m + b^{2} c d f\right)} x\right)} {\left(f x + e\right)}^{m} \arctan\left(d x + c\right)^{2} + 3 \, {\left({\left(b^{2} c^{2} + b^{2}\right)} f m + {\left(b^{2} d^{2} f m + b^{2} d^{2} f\right)} x^{2} + {\left(b^{2} c^{2} + b^{2}\right)} f + 2 \, {\left(b^{2} c d f m + b^{2} c d f\right)} x\right)} {\left(f x + e\right)}^{m} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2} - 8 \, {\left(7 \, b^{2} d e - 16 \, {\left(a b c^{2} + a b\right)} f m - 16 \, {\left(a b d^{2} f m + a b d^{2} f\right)} x^{2} - 16 \, {\left(a b c^{2} + a b\right)} f - {\left(32 \, a b c d f m + {\left(32 \, a b c - 7 \, b^{2}\right)} d f\right)} x\right)} {\left(f x + e\right)}^{m} \arctan\left(d x + c\right) + 12 \, {\left(b^{2} d^{2} f x^{2} + b^{2} c d e + {\left(b^{2} d^{2} e + b^{2} c d f\right)} x\right)} {\left(f x + e\right)}^{m} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{4 \, {\left({\left(c^{2} + 1\right)} f m + {\left(d^{2} f m + d^{2} f\right)} x^{2} + {\left(c^{2} + 1\right)} f + 2 \, {\left(c d f m + c d f\right)} x\right)}}\,{d x}}{16 \, {\left(f m + f\right)}}"," ",0,"(f*x + e)^(m + 1)*a^2/(f*(m + 1)) + 1/16*(4*(b^2*f*x + b^2*e)*(f*x + e)^m*arctan(d*x + c)^2 - (b^2*f*x + b^2*e)*(f*x + e)^m*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 + 16*(f*m + f)*integrate(1/16*(12*((b^2*c^2 + b^2)*f*m + (b^2*d^2*f*m + b^2*d^2*f)*x^2 + (b^2*c^2 + b^2)*f + 2*(b^2*c*d*f*m + b^2*c*d*f)*x)*(f*x + e)^m*arctan(d*x + c)^2 + ((b^2*c^2 + b^2)*f*m + (b^2*d^2*f*m + b^2*d^2*f)*x^2 + (b^2*c^2 + b^2)*f + 2*(b^2*c*d*f*m + b^2*c*d*f)*x)*(f*x + e)^m*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 - 8*(b^2*d*e - 4*(a*b*c^2 + a*b)*f*m - 4*(a*b*d^2*f*m + a*b*d^2*f)*x^2 - 4*(a*b*c^2 + a*b)*f - (8*a*b*c*d*f*m + (8*a*b*c - b^2)*d*f)*x)*(f*x + e)^m*arctan(d*x + c) + 4*(b^2*d^2*f*x^2 + b^2*c*d*e + (b^2*d^2*e + b^2*c*d*f)*x)*(f*x + e)^m*log(d^2*x^2 + 2*c*d*x + c^2 + 1))/((c^2 + 1)*f*m + (d^2*f*m + d^2*f)*x^2 + (c^2 + 1)*f + 2*(c*d*f*m + c*d*f)*x), x))/(f*m + f)","F",0
43,0,0,0,0.000000," ","integrate((f*x+e)^m*(a+b*arctan(d*x+c))^3,x, algorithm=""maxima"")","\frac{{\left(f x + e\right)}^{m + 1} a^{3}}{f {\left(m + 1\right)}} + \frac{4 \, {\left(b^{3} f x + b^{3} e\right)} {\left(f x + e\right)}^{m} \arctan\left(d x + c\right)^{3} - 3 \, {\left(b^{3} f x + b^{3} e\right)} {\left(f x + e\right)}^{m} \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2} + {\left(f m + f\right)} \int \frac{28 \, {\left({\left(b^{3} c^{2} + b^{3}\right)} f m + {\left(b^{3} d^{2} f m + b^{3} d^{2} f\right)} x^{2} + {\left(b^{3} c^{2} + b^{3}\right)} f + 2 \, {\left(b^{3} c d f m + b^{3} c d f\right)} x\right)} {\left(f x + e\right)}^{m} \arctan\left(d x + c\right)^{3} - 12 \, {\left(b^{3} d e - 8 \, {\left(a b^{2} c^{2} + a b^{2}\right)} f m - 8 \, {\left(a b^{2} d^{2} f m + a b^{2} d^{2} f\right)} x^{2} - 8 \, {\left(a b^{2} c^{2} + a b^{2}\right)} f - {\left(16 \, a b^{2} c d f m + {\left(16 \, a b^{2} c - b^{3}\right)} d f\right)} x\right)} {\left(f x + e\right)}^{m} \arctan\left(d x + c\right)^{2} + 12 \, {\left(b^{3} d^{2} f x^{2} + b^{3} c d e + {\left(b^{3} d^{2} e + b^{3} c d f\right)} x\right)} {\left(f x + e\right)}^{m} \arctan\left(d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right) + 96 \, {\left({\left(a^{2} b c^{2} + a^{2} b\right)} f m + {\left(a^{2} b d^{2} f m + a^{2} b d^{2} f\right)} x^{2} + {\left(a^{2} b c^{2} + a^{2} b\right)} f + 2 \, {\left(a^{2} b c d f m + a^{2} b c d f\right)} x\right)} {\left(f x + e\right)}^{m} \arctan\left(d x + c\right) + 3 \, {\left({\left({\left(b^{3} c^{2} + b^{3}\right)} f m + {\left(b^{3} d^{2} f m + b^{3} d^{2} f\right)} x^{2} + {\left(b^{3} c^{2} + b^{3}\right)} f + 2 \, {\left(b^{3} c d f m + b^{3} c d f\right)} x\right)} {\left(f x + e\right)}^{m} \arctan\left(d x + c\right) + {\left(b^{3} d f x + b^{3} d e\right)} {\left(f x + e\right)}^{m}\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}}{{\left(c^{2} + 1\right)} f m + {\left(d^{2} f m + d^{2} f\right)} x^{2} + {\left(c^{2} + 1\right)} f + 2 \, {\left(c d f m + c d f\right)} x}\,{d x}}{32 \, {\left(f m + f\right)}}"," ",0,"(f*x + e)^(m + 1)*a^3/(f*(m + 1)) + 1/32*(4*(b^3*f*x + b^3*e)*(f*x + e)^m*arctan(d*x + c)^3 - 3*(b^3*f*x + b^3*e)*(f*x + e)^m*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 + 32*(f*m + f)*integrate(1/32*(28*((b^3*c^2 + b^3)*f*m + (b^3*d^2*f*m + b^3*d^2*f)*x^2 + (b^3*c^2 + b^3)*f + 2*(b^3*c*d*f*m + b^3*c*d*f)*x)*(f*x + e)^m*arctan(d*x + c)^3 - 12*(b^3*d*e - 8*(a*b^2*c^2 + a*b^2)*f*m - 8*(a*b^2*d^2*f*m + a*b^2*d^2*f)*x^2 - 8*(a*b^2*c^2 + a*b^2)*f - (16*a*b^2*c*d*f*m + (16*a*b^2*c - b^3)*d*f)*x)*(f*x + e)^m*arctan(d*x + c)^2 + 12*(b^3*d^2*f*x^2 + b^3*c*d*e + (b^3*d^2*e + b^3*c*d*f)*x)*(f*x + e)^m*arctan(d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1) + 96*((a^2*b*c^2 + a^2*b)*f*m + (a^2*b*d^2*f*m + a^2*b*d^2*f)*x^2 + (a^2*b*c^2 + a^2*b)*f + 2*(a^2*b*c*d*f*m + a^2*b*c*d*f)*x)*(f*x + e)^m*arctan(d*x + c) + 3*(((b^3*c^2 + b^3)*f*m + (b^3*d^2*f*m + b^3*d^2*f)*x^2 + (b^3*c^2 + b^3)*f + 2*(b^3*c*d*f*m + b^3*c*d*f)*x)*(f*x + e)^m*arctan(d*x + c) + (b^3*d*f*x + b^3*d*e)*(f*x + e)^m)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2)/((c^2 + 1)*f*m + (d^2*f*m + d^2*f)*x^2 + (c^2 + 1)*f + 2*(c*d*f*m + c*d*f)*x), x))/(f*m + f)","F",0
44,1,104,0,0.409179," ","integrate(x^3*arctan(b*x+a),x, algorithm=""maxima"")","\frac{1}{4} \, x^{4} \arctan\left(b x + a\right) - \frac{1}{12} \, b {\left(\frac{b^{2} x^{3} - 3 \, a b x^{2} + 3 \, {\left(3 \, a^{2} - 1\right)} x}{b^{4}} + \frac{3 \, {\left(a^{4} - 6 \, a^{2} + 1\right)} \arctan\left(\frac{b^{2} x + a b}{b}\right)}{b^{5}} - \frac{6 \, {\left(a^{3} - a\right)} \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}{b^{5}}\right)}"," ",0,"1/4*x^4*arctan(b*x + a) - 1/12*b*((b^2*x^3 - 3*a*b*x^2 + 3*(3*a^2 - 1)*x)/b^4 + 3*(a^4 - 6*a^2 + 1)*arctan((b^2*x + a*b)/b)/b^5 - 6*(a^3 - a)*log(b^2*x^2 + 2*a*b*x + a^2 + 1)/b^5)","A",0
45,1,85,0,0.412262," ","integrate(x^2*arctan(b*x+a),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \arctan\left(b x + a\right) - \frac{1}{6} \, b {\left(\frac{b x^{2} - 4 \, a x}{b^{3}} - \frac{2 \, {\left(a^{3} - 3 \, a\right)} \arctan\left(\frac{b^{2} x + a b}{b}\right)}{b^{4}} + \frac{{\left(3 \, a^{2} - 1\right)} \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}{b^{4}}\right)}"," ",0,"1/3*x^3*arctan(b*x + a) - 1/6*b*((b*x^2 - 4*a*x)/b^3 - 2*(a^3 - 3*a)*arctan((b^2*x + a*b)/b)/b^4 + (3*a^2 - 1)*log(b^2*x^2 + 2*a*b*x + a^2 + 1)/b^4)","A",0
46,1,68,0,0.409623," ","integrate(x*arctan(b*x+a),x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \arctan\left(b x + a\right) - \frac{1}{2} \, b {\left(\frac{x}{b^{2}} + \frac{{\left(a^{2} - 1\right)} \arctan\left(\frac{b^{2} x + a b}{b}\right)}{b^{3}} - \frac{a \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}{b^{3}}\right)}"," ",0,"1/2*x^2*arctan(b*x + a) - 1/2*b*(x/b^2 + (a^2 - 1)*arctan((b^2*x + a*b)/b)/b^3 - a*log(b^2*x^2 + 2*a*b*x + a^2 + 1)/b^3)","A",0
47,1,31,0,0.309483," ","integrate(arctan(b*x+a),x, algorithm=""maxima"")","\frac{2 \, {\left(b x + a\right)} \arctan\left(b x + a\right) - \log\left({\left(b x + a\right)}^{2} + 1\right)}{2 \, b}"," ",0,"1/2*(2*(b*x + a)*arctan(b*x + a) - log((b*x + a)^2 + 1))/b","A",0
48,1,134,0,0.469823," ","integrate(arctan(b*x+a)/x,x, algorithm=""maxima"")","-\frac{1}{2} \, \arctan\left(\frac{b x}{a^{2} + 1}, -\frac{a b x}{a^{2} + 1}\right) \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right) + \frac{1}{2} \, \arctan\left(b x + a\right) \log\left(\frac{b^{2} x^{2}}{a^{2} + 1}\right) + \arctan\left(b x + a\right) \log\left(x\right) - \arctan\left(\frac{b^{2} x + a b}{b}\right) \log\left(x\right) - \frac{1}{2} i \, {\rm Li}_2\left(\frac{i \, b x + i \, a + 1}{i \, a + 1}\right) + \frac{1}{2} i \, {\rm Li}_2\left(\frac{i \, b x + i \, a - 1}{i \, a - 1}\right)"," ",0,"-1/2*arctan2(b*x/(a^2 + 1), -a*b*x/(a^2 + 1))*log(b^2*x^2 + 2*a*b*x + a^2 + 1) + 1/2*arctan(b*x + a)*log(b^2*x^2/(a^2 + 1)) + arctan(b*x + a)*log(x) - arctan((b^2*x + a*b)/b)*log(x) - 1/2*I*dilog((I*b*x + I*a + 1)/(I*a + 1)) + 1/2*I*dilog((I*b*x + I*a - 1)/(I*a - 1))","A",0
49,1,77,0,0.411067," ","integrate(arctan(b*x+a)/x^2,x, algorithm=""maxima"")","-\frac{1}{2} \, b {\left(\frac{2 \, a \arctan\left(\frac{b^{2} x + a b}{b}\right)}{a^{2} + 1} + \frac{\log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}{a^{2} + 1} - \frac{2 \, \log\left(x\right)}{a^{2} + 1}\right)} - \frac{\arctan\left(b x + a\right)}{x}"," ",0,"-1/2*b*(2*a*arctan((b^2*x + a*b)/b)/(a^2 + 1) + log(b^2*x^2 + 2*a*b*x + a^2 + 1)/(a^2 + 1) - 2*log(x)/(a^2 + 1)) - arctan(b*x + a)/x","A",0
50,1,112,0,0.408707," ","integrate(arctan(b*x+a)/x^3,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\frac{{\left(a^{2} - 1\right)} b \arctan\left(\frac{b^{2} x + a b}{b}\right)}{a^{4} + 2 \, a^{2} + 1} + \frac{a b \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}{a^{4} + 2 \, a^{2} + 1} - \frac{2 \, a b \log\left(x\right)}{a^{4} + 2 \, a^{2} + 1} - \frac{1}{{\left(a^{2} + 1\right)} x}\right)} b - \frac{\arctan\left(b x + a\right)}{2 \, x^{2}}"," ",0,"1/2*((a^2 - 1)*b*arctan((b^2*x + a*b)/b)/(a^4 + 2*a^2 + 1) + a*b*log(b^2*x^2 + 2*a*b*x + a^2 + 1)/(a^4 + 2*a^2 + 1) - 2*a*b*log(x)/(a^4 + 2*a^2 + 1) - 1/((a^2 + 1)*x))*b - 1/2*arctan(b*x + a)/x^2","A",0
51,1,165,0,0.414721," ","integrate(arctan(b*x+a)/x^4,x, algorithm=""maxima"")","-\frac{1}{6} \, {\left(\frac{2 \, {\left(a^{3} - 3 \, a\right)} b^{2} \arctan\left(\frac{b^{2} x + a b}{b}\right)}{a^{6} + 3 \, a^{4} + 3 \, a^{2} + 1} + \frac{{\left(3 \, a^{2} - 1\right)} b^{2} \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}{a^{6} + 3 \, a^{4} + 3 \, a^{2} + 1} - \frac{2 \, {\left(3 \, a^{2} - 1\right)} b^{2} \log\left(x\right)}{a^{6} + 3 \, a^{4} + 3 \, a^{2} + 1} - \frac{4 \, a b x - a^{2} - 1}{{\left(a^{4} + 2 \, a^{2} + 1\right)} x^{2}}\right)} b - \frac{\arctan\left(b x + a\right)}{3 \, x^{3}}"," ",0,"-1/6*(2*(a^3 - 3*a)*b^2*arctan((b^2*x + a*b)/b)/(a^6 + 3*a^4 + 3*a^2 + 1) + (3*a^2 - 1)*b^2*log(b^2*x^2 + 2*a*b*x + a^2 + 1)/(a^6 + 3*a^4 + 3*a^2 + 1) - 2*(3*a^2 - 1)*b^2*log(x)/(a^6 + 3*a^4 + 3*a^2 + 1) - (4*a*b*x - a^2 - 1)/((a^4 + 2*a^2 + 1)*x^2))*b - 1/3*arctan(b*x + a)/x^3","A",0
52,0,0,0,0.000000," ","integrate(arctan(b*x+a)/(d*x^3+c),x, algorithm=""maxima"")","\int \frac{\arctan\left(b x + a\right)}{d x^{3} + c}\,{d x}"," ",0,"integrate(arctan(b*x + a)/(d*x^3 + c), x)","F",0
53,1,8520,0,5.931175," ","integrate(arctan(b*x+a)/(d*x^2+c),x, algorithm=""maxima"")","\frac{b {\left(\frac{8 \, \arctan\left(\frac{d x}{\sqrt{c d}}\right) \arctan\left(\frac{b^{2} x + a b}{b}\right)}{b} - \frac{4 \, \arctan\left(\frac{\sqrt{d} x}{\sqrt{c}}\right) \arctan\left(\frac{2 \, a b^{2} c d + {\left(a b^{3} c + {\left(a^{3} + a\right)} b d + {\left(b^{4} c + {\left(a^{2} + 3\right)} b^{2} d\right)} x\right)} \sqrt{c} \sqrt{d} + {\left(3 \, b^{3} c d + {\left(a^{2} + 1\right)} b d^{2}\right)} x}{b^{4} c^{2} + 2 \, {\left(a^{2} + 3\right)} b^{2} c d + {\left(a^{4} + 2 \, a^{2} + 1\right)} d^{2} + 4 \, {\left(b^{3} c + {\left(a^{2} + 1\right)} b d\right)} \sqrt{c} \sqrt{d}}, \frac{{\left(a^{2} + 3\right)} b^{2} c d + {\left(a^{4} + 2 \, a^{2} + 1\right)} d^{2} + {\left(2 \, a b^{2} d x + b^{3} c + 3 \, {\left(a^{2} + 1\right)} b d\right)} \sqrt{c} \sqrt{d} + {\left(a b^{3} c d + {\left(a^{3} + a\right)} b d^{2}\right)} x}{b^{4} c^{2} + 2 \, {\left(a^{2} + 3\right)} b^{2} c d + {\left(a^{4} + 2 \, a^{2} + 1\right)} d^{2} + 4 \, {\left(b^{3} c + {\left(a^{2} + 1\right)} b d\right)} \sqrt{c} \sqrt{d}}\right) + 4 \, \arctan\left(\frac{\sqrt{d} x}{\sqrt{c}}\right) \arctan\left(\frac{2 \, a b^{2} c d - {\left(a b^{3} c + {\left(a^{3} + a\right)} b d + {\left(b^{4} c + {\left(a^{2} + 3\right)} b^{2} d\right)} x\right)} \sqrt{c} \sqrt{d} + {\left(3 \, b^{3} c d + {\left(a^{2} + 1\right)} b d^{2}\right)} x}{b^{4} c^{2} + 2 \, {\left(a^{2} + 3\right)} b^{2} c d + {\left(a^{4} + 2 \, a^{2} + 1\right)} d^{2} - 4 \, {\left(b^{3} c + {\left(a^{2} + 1\right)} b d\right)} \sqrt{c} \sqrt{d}}, \frac{{\left(a^{2} + 3\right)} b^{2} c d + {\left(a^{4} + 2 \, a^{2} + 1\right)} d^{2} - {\left(2 \, a b^{2} d x + b^{3} c + 3 \, {\left(a^{2} + 1\right)} b d\right)} \sqrt{c} \sqrt{d} + {\left(a b^{3} c d + {\left(a^{3} + a\right)} b d^{2}\right)} x}{b^{4} c^{2} + 2 \, {\left(a^{2} + 3\right)} b^{2} c d + {\left(a^{4} + 2 \, a^{2} + 1\right)} d^{2} - 4 \, {\left(b^{3} c + {\left(a^{2} + 1\right)} b d\right)} \sqrt{c} \sqrt{d}}\right) + \log\left(d x^{2} + c\right) \log\left(\frac{{\left(a^{2} + 1\right)} b^{22} c^{11} d + 11 \, {\left(a^{4} + 22 \, a^{2} + 21\right)} b^{20} c^{10} d^{2} + 55 \, {\left(a^{6} + 39 \, a^{4} + 171 \, a^{2} + 133\right)} b^{18} c^{9} d^{3} + 33 \, {\left(5 \, a^{8} + 260 \, a^{6} + 1870 \, a^{4} + 3876 \, a^{2} + 2261\right)} b^{16} c^{8} d^{4} + 330 \, {\left(a^{10} + 61 \, a^{8} + 570 \, a^{6} + 1802 \, a^{4} + 2261 \, a^{2} + 969\right)} b^{14} c^{7} d^{5} + 22 \, {\left(21 \, a^{12} + 1386 \, a^{10} + 15015 \, a^{8} + 60060 \, a^{6} + 109395 \, a^{4} + 92378 \, a^{2} + 29393\right)} b^{12} c^{6} d^{6} + 22 \, {\left(21 \, a^{14} + 1407 \, a^{12} + 16401 \, a^{10} + 75075 \, a^{8} + 169455 \, a^{6} + 201773 \, a^{4} + 121771 \, a^{2} + 29393\right)} b^{10} c^{5} d^{7} + 330 \, {\left(a^{16} + 64 \, a^{14} + 756 \, a^{12} + 3696 \, a^{10} + 9438 \, a^{8} + 13728 \, a^{6} + 11492 \, a^{4} + 5168 \, a^{2} + 969\right)} b^{8} c^{4} d^{8} + 33 \, {\left(5 \, a^{18} + 285 \, a^{16} + 3220 \, a^{14} + 15876 \, a^{12} + 42966 \, a^{10} + 70070 \, a^{8} + 70980 \, a^{6} + 43860 \, a^{4} + 15181 \, a^{2} + 2261\right)} b^{6} c^{3} d^{9} + 55 \, {\left(a^{20} + 46 \, a^{18} + 465 \, a^{16} + 2184 \, a^{14} + 5922 \, a^{12} + 10164 \, a^{10} + 11466 \, a^{8} + 8520 \, a^{6} + 4029 \, a^{4} + 1102 \, a^{2} + 133\right)} b^{4} c^{2} d^{10} + 11 \, {\left(a^{22} + 31 \, a^{20} + 255 \, a^{18} + 1065 \, a^{16} + 2730 \, a^{14} + 4662 \, a^{12} + 5502 \, a^{10} + 4530 \, a^{8} + 2565 \, a^{6} + 955 \, a^{4} + 211 \, a^{2} + 21\right)} b^{2} c d^{11} + {\left(a^{24} + 12 \, a^{22} + 66 \, a^{20} + 220 \, a^{18} + 495 \, a^{16} + 792 \, a^{14} + 924 \, a^{12} + 792 \, a^{10} + 495 \, a^{8} + 220 \, a^{6} + 66 \, a^{4} + 12 \, a^{2} + 1\right)} d^{12} + {\left(b^{24} c^{11} d + 11 \, {\left(a^{2} + 21\right)} b^{22} c^{10} d^{2} + 55 \, {\left(a^{4} + 38 \, a^{2} + 133\right)} b^{20} c^{9} d^{3} + 33 \, {\left(5 \, a^{6} + 255 \, a^{4} + 1615 \, a^{2} + 2261\right)} b^{18} c^{8} d^{4} + 330 \, {\left(a^{8} + 60 \, a^{6} + 510 \, a^{4} + 1292 \, a^{2} + 969\right)} b^{16} c^{7} d^{5} + 22 \, {\left(21 \, a^{10} + 1365 \, a^{8} + 13650 \, a^{6} + 46410 \, a^{4} + 62985 \, a^{2} + 29393\right)} b^{14} c^{6} d^{6} + 22 \, {\left(21 \, a^{12} + 1386 \, a^{10} + 15015 \, a^{8} + 60060 \, a^{6} + 109395 \, a^{4} + 92378 \, a^{2} + 29393\right)} b^{12} c^{5} d^{7} + 330 \, {\left(a^{14} + 63 \, a^{12} + 693 \, a^{10} + 3003 \, a^{8} + 6435 \, a^{6} + 7293 \, a^{4} + 4199 \, a^{2} + 969\right)} b^{10} c^{4} d^{8} + 33 \, {\left(5 \, a^{16} + 280 \, a^{14} + 2940 \, a^{12} + 12936 \, a^{10} + 30030 \, a^{8} + 40040 \, a^{6} + 30940 \, a^{4} + 12920 \, a^{2} + 2261\right)} b^{8} c^{3} d^{9} + 55 \, {\left(a^{18} + 45 \, a^{16} + 420 \, a^{14} + 1764 \, a^{12} + 4158 \, a^{10} + 6006 \, a^{8} + 5460 \, a^{6} + 3060 \, a^{4} + 969 \, a^{2} + 133\right)} b^{6} c^{2} d^{10} + 11 \, {\left(a^{20} + 30 \, a^{18} + 225 \, a^{16} + 840 \, a^{14} + 1890 \, a^{12} + 2772 \, a^{10} + 2730 \, a^{8} + 1800 \, a^{6} + 765 \, a^{4} + 190 \, a^{2} + 21\right)} b^{4} c d^{11} + {\left(a^{22} + 11 \, a^{20} + 55 \, a^{18} + 165 \, a^{16} + 330 \, a^{14} + 462 \, a^{12} + 462 \, a^{10} + 330 \, a^{8} + 165 \, a^{6} + 55 \, a^{4} + 11 \, a^{2} + 1\right)} b^{2} d^{12}\right)} x^{2} + 2 \, {\left(11 \, {\left(a^{2} + 1\right)} b^{21} c^{10} d + 110 \, {\left(a^{4} + 8 \, a^{2} + 7\right)} b^{19} c^{9} d^{2} + 33 \, {\left(15 \, a^{6} + 205 \, a^{4} + 589 \, a^{2} + 399\right)} b^{17} c^{8} d^{3} + 264 \, {\left(5 \, a^{8} + 90 \, a^{6} + 408 \, a^{4} + 646 \, a^{2} + 323\right)} b^{15} c^{7} d^{4} + 110 \, {\left(21 \, a^{10} + 441 \, a^{8} + 2562 \, a^{6} + 6018 \, a^{4} + 6137 \, a^{2} + 2261\right)} b^{13} c^{6} d^{5} + 4 \, {\left(693 \, a^{12} + 15708 \, a^{10} + 105105 \, a^{8} + 308880 \, a^{6} + 449735 \, a^{4} + 319124 \, a^{2} + 88179\right)} b^{11} c^{5} d^{6} + 110 \, {\left(21 \, a^{14} + 483 \, a^{12} + 3465 \, a^{10} + 11583 \, a^{8} + 20735 \, a^{6} + 20553 \, a^{4} + 10659 \, a^{2} + 2261\right)} b^{9} c^{4} d^{7} + 264 \, {\left(5 \, a^{16} + 110 \, a^{14} + 798 \, a^{12} + 2838 \, a^{10} + 5720 \, a^{8} + 6890 \, a^{6} + 4930 \, a^{4} + 1938 \, a^{2} + 323\right)} b^{7} c^{3} d^{8} + 33 \, {\left(15 \, a^{18} + 295 \, a^{16} + 2044 \, a^{14} + 7308 \, a^{12} + 15554 \, a^{10} + 20930 \, a^{8} + 18060 \, a^{6} + 9724 \, a^{4} + 2983 \, a^{2} + 399\right)} b^{5} c^{2} d^{9} + 110 \, {\left(a^{20} + 16 \, a^{18} + 99 \, a^{16} + 336 \, a^{14} + 714 \, a^{12} + 1008 \, a^{10} + 966 \, a^{8} + 624 \, a^{6} + 261 \, a^{4} + 64 \, a^{2} + 7\right)} b^{3} c d^{10} + 11 \, {\left(a^{22} + 11 \, a^{20} + 55 \, a^{18} + 165 \, a^{16} + 330 \, a^{14} + 462 \, a^{12} + 462 \, a^{10} + 330 \, a^{8} + 165 \, a^{6} + 55 \, a^{4} + 11 \, a^{2} + 1\right)} b d^{11} + {\left(11 \, b^{23} c^{10} d + 110 \, {\left(a^{2} + 7\right)} b^{21} c^{9} d^{2} + 33 \, {\left(15 \, a^{4} + 190 \, a^{2} + 399\right)} b^{19} c^{8} d^{3} + 264 \, {\left(5 \, a^{6} + 85 \, a^{4} + 323 \, a^{2} + 323\right)} b^{17} c^{7} d^{4} + 110 \, {\left(21 \, a^{8} + 420 \, a^{6} + 2142 \, a^{4} + 3876 \, a^{2} + 2261\right)} b^{15} c^{6} d^{5} + 4 \, {\left(693 \, a^{10} + 15015 \, a^{8} + 90090 \, a^{6} + 218790 \, a^{4} + 230945 \, a^{2} + 88179\right)} b^{13} c^{5} d^{6} + 110 \, {\left(21 \, a^{12} + 462 \, a^{10} + 3003 \, a^{8} + 8580 \, a^{6} + 12155 \, a^{4} + 8398 \, a^{2} + 2261\right)} b^{11} c^{4} d^{7} + 264 \, {\left(5 \, a^{14} + 105 \, a^{12} + 693 \, a^{10} + 2145 \, a^{8} + 3575 \, a^{6} + 3315 \, a^{4} + 1615 \, a^{2} + 323\right)} b^{9} c^{3} d^{8} + 33 \, {\left(15 \, a^{16} + 280 \, a^{14} + 1764 \, a^{12} + 5544 \, a^{10} + 10010 \, a^{8} + 10920 \, a^{6} + 7140 \, a^{4} + 2584 \, a^{2} + 399\right)} b^{7} c^{2} d^{9} + 110 \, {\left(a^{18} + 15 \, a^{16} + 84 \, a^{14} + 252 \, a^{12} + 462 \, a^{10} + 546 \, a^{8} + 420 \, a^{6} + 204 \, a^{4} + 57 \, a^{2} + 7\right)} b^{5} c d^{10} + 11 \, {\left(a^{20} + 10 \, a^{18} + 45 \, a^{16} + 120 \, a^{14} + 210 \, a^{12} + 252 \, a^{10} + 210 \, a^{8} + 120 \, a^{6} + 45 \, a^{4} + 10 \, a^{2} + 1\right)} b^{3} d^{11}\right)} x^{2} + 2 \, {\left(11 \, a b^{22} c^{10} d + 110 \, {\left(a^{3} + 7 \, a\right)} b^{20} c^{9} d^{2} + 33 \, {\left(15 \, a^{5} + 190 \, a^{3} + 399 \, a\right)} b^{18} c^{8} d^{3} + 264 \, {\left(5 \, a^{7} + 85 \, a^{5} + 323 \, a^{3} + 323 \, a\right)} b^{16} c^{7} d^{4} + 110 \, {\left(21 \, a^{9} + 420 \, a^{7} + 2142 \, a^{5} + 3876 \, a^{3} + 2261 \, a\right)} b^{14} c^{6} d^{5} + 4 \, {\left(693 \, a^{11} + 15015 \, a^{9} + 90090 \, a^{7} + 218790 \, a^{5} + 230945 \, a^{3} + 88179 \, a\right)} b^{12} c^{5} d^{6} + 110 \, {\left(21 \, a^{13} + 462 \, a^{11} + 3003 \, a^{9} + 8580 \, a^{7} + 12155 \, a^{5} + 8398 \, a^{3} + 2261 \, a\right)} b^{10} c^{4} d^{7} + 264 \, {\left(5 \, a^{15} + 105 \, a^{13} + 693 \, a^{11} + 2145 \, a^{9} + 3575 \, a^{7} + 3315 \, a^{5} + 1615 \, a^{3} + 323 \, a\right)} b^{8} c^{3} d^{8} + 33 \, {\left(15 \, a^{17} + 280 \, a^{15} + 1764 \, a^{13} + 5544 \, a^{11} + 10010 \, a^{9} + 10920 \, a^{7} + 7140 \, a^{5} + 2584 \, a^{3} + 399 \, a\right)} b^{6} c^{2} d^{9} + 110 \, {\left(a^{19} + 15 \, a^{17} + 84 \, a^{15} + 252 \, a^{13} + 462 \, a^{11} + 546 \, a^{9} + 420 \, a^{7} + 204 \, a^{5} + 57 \, a^{3} + 7 \, a\right)} b^{4} c d^{10} + 11 \, {\left(a^{21} + 10 \, a^{19} + 45 \, a^{17} + 120 \, a^{15} + 210 \, a^{13} + 252 \, a^{11} + 210 \, a^{9} + 120 \, a^{7} + 45 \, a^{5} + 10 \, a^{3} + a\right)} b^{2} d^{11}\right)} x\right)} \sqrt{c} \sqrt{d} + 2 \, {\left(a b^{23} c^{11} d + 11 \, {\left(a^{3} + 21 \, a\right)} b^{21} c^{10} d^{2} + 55 \, {\left(a^{5} + 38 \, a^{3} + 133 \, a\right)} b^{19} c^{9} d^{3} + 33 \, {\left(5 \, a^{7} + 255 \, a^{5} + 1615 \, a^{3} + 2261 \, a\right)} b^{17} c^{8} d^{4} + 330 \, {\left(a^{9} + 60 \, a^{7} + 510 \, a^{5} + 1292 \, a^{3} + 969 \, a\right)} b^{15} c^{7} d^{5} + 22 \, {\left(21 \, a^{11} + 1365 \, a^{9} + 13650 \, a^{7} + 46410 \, a^{5} + 62985 \, a^{3} + 29393 \, a\right)} b^{13} c^{6} d^{6} + 22 \, {\left(21 \, a^{13} + 1386 \, a^{11} + 15015 \, a^{9} + 60060 \, a^{7} + 109395 \, a^{5} + 92378 \, a^{3} + 29393 \, a\right)} b^{11} c^{5} d^{7} + 330 \, {\left(a^{15} + 63 \, a^{13} + 693 \, a^{11} + 3003 \, a^{9} + 6435 \, a^{7} + 7293 \, a^{5} + 4199 \, a^{3} + 969 \, a\right)} b^{9} c^{4} d^{8} + 33 \, {\left(5 \, a^{17} + 280 \, a^{15} + 2940 \, a^{13} + 12936 \, a^{11} + 30030 \, a^{9} + 40040 \, a^{7} + 30940 \, a^{5} + 12920 \, a^{3} + 2261 \, a\right)} b^{7} c^{3} d^{9} + 55 \, {\left(a^{19} + 45 \, a^{17} + 420 \, a^{15} + 1764 \, a^{13} + 4158 \, a^{11} + 6006 \, a^{9} + 5460 \, a^{7} + 3060 \, a^{5} + 969 \, a^{3} + 133 \, a\right)} b^{5} c^{2} d^{10} + 11 \, {\left(a^{21} + 30 \, a^{19} + 225 \, a^{17} + 840 \, a^{15} + 1890 \, a^{13} + 2772 \, a^{11} + 2730 \, a^{9} + 1800 \, a^{7} + 765 \, a^{5} + 190 \, a^{3} + 21 \, a\right)} b^{3} c d^{11} + {\left(a^{23} + 11 \, a^{21} + 55 \, a^{19} + 165 \, a^{17} + 330 \, a^{15} + 462 \, a^{13} + 462 \, a^{11} + 330 \, a^{9} + 165 \, a^{7} + 55 \, a^{5} + 11 \, a^{3} + a\right)} b d^{12}\right)} x}{b^{24} c^{12} + 12 \, {\left(a^{2} + 23\right)} b^{22} c^{11} d + 66 \, {\left(a^{4} + 42 \, a^{2} + 161\right)} b^{20} c^{10} d^{2} + 44 \, {\left(5 \, a^{6} + 285 \, a^{4} + 1995 \, a^{2} + 3059\right)} b^{18} c^{9} d^{3} + 99 \, {\left(5 \, a^{8} + 340 \, a^{6} + 3230 \, a^{4} + 9044 \, a^{2} + 7429\right)} b^{16} c^{8} d^{4} + 264 \, {\left(3 \, a^{10} + 225 \, a^{8} + 2550 \, a^{6} + 9690 \, a^{4} + 14535 \, a^{2} + 7429\right)} b^{14} c^{7} d^{5} + 4 \, {\left(231 \, a^{12} + 18018 \, a^{10} + 225225 \, a^{8} + 1021020 \, a^{6} + 2078505 \, a^{4} + 1939938 \, a^{2} + 676039\right)} b^{12} c^{6} d^{6} + 264 \, {\left(3 \, a^{14} + 231 \, a^{12} + 3003 \, a^{10} + 15015 \, a^{8} + 36465 \, a^{6} + 46189 \, a^{4} + 29393 \, a^{2} + 7429\right)} b^{10} c^{5} d^{7} + 99 \, {\left(5 \, a^{16} + 360 \, a^{14} + 4620 \, a^{12} + 24024 \, a^{10} + 64350 \, a^{8} + 97240 \, a^{6} + 83980 \, a^{4} + 38760 \, a^{2} + 7429\right)} b^{8} c^{4} d^{8} + 44 \, {\left(5 \, a^{18} + 315 \, a^{16} + 3780 \, a^{14} + 19404 \, a^{12} + 54054 \, a^{10} + 90090 \, a^{8} + 92820 \, a^{6} + 58140 \, a^{4} + 20349 \, a^{2} + 3059\right)} b^{6} c^{3} d^{9} + 66 \, {\left(a^{20} + 50 \, a^{18} + 525 \, a^{16} + 2520 \, a^{14} + 6930 \, a^{12} + 12012 \, a^{10} + 13650 \, a^{8} + 10200 \, a^{6} + 4845 \, a^{4} + 1330 \, a^{2} + 161\right)} b^{4} c^{2} d^{10} + 12 \, {\left(a^{22} + 33 \, a^{20} + 275 \, a^{18} + 1155 \, a^{16} + 2970 \, a^{14} + 5082 \, a^{12} + 6006 \, a^{10} + 4950 \, a^{8} + 2805 \, a^{6} + 1045 \, a^{4} + 231 \, a^{2} + 23\right)} b^{2} c d^{11} + {\left(a^{24} + 12 \, a^{22} + 66 \, a^{20} + 220 \, a^{18} + 495 \, a^{16} + 792 \, a^{14} + 924 \, a^{12} + 792 \, a^{10} + 495 \, a^{8} + 220 \, a^{6} + 66 \, a^{4} + 12 \, a^{2} + 1\right)} d^{12} + 8 \, {\left(3 \, b^{23} c^{11} + 11 \, {\left(3 \, a^{2} + 23\right)} b^{21} c^{10} d + 33 \, {\left(5 \, a^{4} + 70 \, a^{2} + 161\right)} b^{19} c^{9} d^{2} + 99 \, {\left(5 \, a^{6} + 95 \, a^{4} + 399 \, a^{2} + 437\right)} b^{17} c^{8} d^{3} + 22 \, {\left(45 \, a^{8} + 1020 \, a^{6} + 5814 \, a^{4} + 11628 \, a^{2} + 7429\right)} b^{15} c^{7} d^{4} + 6 \, {\left(231 \, a^{10} + 5775 \, a^{8} + 39270 \, a^{6} + 106590 \, a^{4} + 124355 \, a^{2} + 52003\right)} b^{13} c^{6} d^{5} + 6 \, {\left(231 \, a^{12} + 6006 \, a^{10} + 45045 \, a^{8} + 145860 \, a^{6} + 230945 \, a^{4} + 176358 \, a^{2} + 52003\right)} b^{11} c^{5} d^{6} + 22 \, {\left(45 \, a^{14} + 1155 \, a^{12} + 9009 \, a^{10} + 32175 \, a^{8} + 60775 \, a^{6} + 62985 \, a^{4} + 33915 \, a^{2} + 7429\right)} b^{9} c^{4} d^{7} + 99 \, {\left(5 \, a^{16} + 120 \, a^{14} + 924 \, a^{12} + 3432 \, a^{10} + 7150 \, a^{8} + 8840 \, a^{6} + 6460 \, a^{4} + 2584 \, a^{2} + 437\right)} b^{7} c^{3} d^{8} + 33 \, {\left(5 \, a^{18} + 105 \, a^{16} + 756 \, a^{14} + 2772 \, a^{12} + 6006 \, a^{10} + 8190 \, a^{8} + 7140 \, a^{6} + 3876 \, a^{4} + 1197 \, a^{2} + 161\right)} b^{5} c^{2} d^{9} + 11 \, {\left(3 \, a^{20} + 50 \, a^{18} + 315 \, a^{16} + 1080 \, a^{14} + 2310 \, a^{12} + 3276 \, a^{10} + 3150 \, a^{8} + 2040 \, a^{6} + 855 \, a^{4} + 210 \, a^{2} + 23\right)} b^{3} c d^{10} + 3 \, {\left(a^{22} + 11 \, a^{20} + 55 \, a^{18} + 165 \, a^{16} + 330 \, a^{14} + 462 \, a^{12} + 462 \, a^{10} + 330 \, a^{8} + 165 \, a^{6} + 55 \, a^{4} + 11 \, a^{2} + 1\right)} b d^{11}\right)} \sqrt{c} \sqrt{d}}\right) - \log\left(d x^{2} + c\right) \log\left(\frac{{\left(a^{2} + 1\right)} b^{22} c^{11} d + 11 \, {\left(a^{4} + 22 \, a^{2} + 21\right)} b^{20} c^{10} d^{2} + 55 \, {\left(a^{6} + 39 \, a^{4} + 171 \, a^{2} + 133\right)} b^{18} c^{9} d^{3} + 33 \, {\left(5 \, a^{8} + 260 \, a^{6} + 1870 \, a^{4} + 3876 \, a^{2} + 2261\right)} b^{16} c^{8} d^{4} + 330 \, {\left(a^{10} + 61 \, a^{8} + 570 \, a^{6} + 1802 \, a^{4} + 2261 \, a^{2} + 969\right)} b^{14} c^{7} d^{5} + 22 \, {\left(21 \, a^{12} + 1386 \, a^{10} + 15015 \, a^{8} + 60060 \, a^{6} + 109395 \, a^{4} + 92378 \, a^{2} + 29393\right)} b^{12} c^{6} d^{6} + 22 \, {\left(21 \, a^{14} + 1407 \, a^{12} + 16401 \, a^{10} + 75075 \, a^{8} + 169455 \, a^{6} + 201773 \, a^{4} + 121771 \, a^{2} + 29393\right)} b^{10} c^{5} d^{7} + 330 \, {\left(a^{16} + 64 \, a^{14} + 756 \, a^{12} + 3696 \, a^{10} + 9438 \, a^{8} + 13728 \, a^{6} + 11492 \, a^{4} + 5168 \, a^{2} + 969\right)} b^{8} c^{4} d^{8} + 33 \, {\left(5 \, a^{18} + 285 \, a^{16} + 3220 \, a^{14} + 15876 \, a^{12} + 42966 \, a^{10} + 70070 \, a^{8} + 70980 \, a^{6} + 43860 \, a^{4} + 15181 \, a^{2} + 2261\right)} b^{6} c^{3} d^{9} + 55 \, {\left(a^{20} + 46 \, a^{18} + 465 \, a^{16} + 2184 \, a^{14} + 5922 \, a^{12} + 10164 \, a^{10} + 11466 \, a^{8} + 8520 \, a^{6} + 4029 \, a^{4} + 1102 \, a^{2} + 133\right)} b^{4} c^{2} d^{10} + 11 \, {\left(a^{22} + 31 \, a^{20} + 255 \, a^{18} + 1065 \, a^{16} + 2730 \, a^{14} + 4662 \, a^{12} + 5502 \, a^{10} + 4530 \, a^{8} + 2565 \, a^{6} + 955 \, a^{4} + 211 \, a^{2} + 21\right)} b^{2} c d^{11} + {\left(a^{24} + 12 \, a^{22} + 66 \, a^{20} + 220 \, a^{18} + 495 \, a^{16} + 792 \, a^{14} + 924 \, a^{12} + 792 \, a^{10} + 495 \, a^{8} + 220 \, a^{6} + 66 \, a^{4} + 12 \, a^{2} + 1\right)} d^{12} + {\left(b^{24} c^{11} d + 11 \, {\left(a^{2} + 21\right)} b^{22} c^{10} d^{2} + 55 \, {\left(a^{4} + 38 \, a^{2} + 133\right)} b^{20} c^{9} d^{3} + 33 \, {\left(5 \, a^{6} + 255 \, a^{4} + 1615 \, a^{2} + 2261\right)} b^{18} c^{8} d^{4} + 330 \, {\left(a^{8} + 60 \, a^{6} + 510 \, a^{4} + 1292 \, a^{2} + 969\right)} b^{16} c^{7} d^{5} + 22 \, {\left(21 \, a^{10} + 1365 \, a^{8} + 13650 \, a^{6} + 46410 \, a^{4} + 62985 \, a^{2} + 29393\right)} b^{14} c^{6} d^{6} + 22 \, {\left(21 \, a^{12} + 1386 \, a^{10} + 15015 \, a^{8} + 60060 \, a^{6} + 109395 \, a^{4} + 92378 \, a^{2} + 29393\right)} b^{12} c^{5} d^{7} + 330 \, {\left(a^{14} + 63 \, a^{12} + 693 \, a^{10} + 3003 \, a^{8} + 6435 \, a^{6} + 7293 \, a^{4} + 4199 \, a^{2} + 969\right)} b^{10} c^{4} d^{8} + 33 \, {\left(5 \, a^{16} + 280 \, a^{14} + 2940 \, a^{12} + 12936 \, a^{10} + 30030 \, a^{8} + 40040 \, a^{6} + 30940 \, a^{4} + 12920 \, a^{2} + 2261\right)} b^{8} c^{3} d^{9} + 55 \, {\left(a^{18} + 45 \, a^{16} + 420 \, a^{14} + 1764 \, a^{12} + 4158 \, a^{10} + 6006 \, a^{8} + 5460 \, a^{6} + 3060 \, a^{4} + 969 \, a^{2} + 133\right)} b^{6} c^{2} d^{10} + 11 \, {\left(a^{20} + 30 \, a^{18} + 225 \, a^{16} + 840 \, a^{14} + 1890 \, a^{12} + 2772 \, a^{10} + 2730 \, a^{8} + 1800 \, a^{6} + 765 \, a^{4} + 190 \, a^{2} + 21\right)} b^{4} c d^{11} + {\left(a^{22} + 11 \, a^{20} + 55 \, a^{18} + 165 \, a^{16} + 330 \, a^{14} + 462 \, a^{12} + 462 \, a^{10} + 330 \, a^{8} + 165 \, a^{6} + 55 \, a^{4} + 11 \, a^{2} + 1\right)} b^{2} d^{12}\right)} x^{2} - 2 \, {\left(11 \, {\left(a^{2} + 1\right)} b^{21} c^{10} d + 110 \, {\left(a^{4} + 8 \, a^{2} + 7\right)} b^{19} c^{9} d^{2} + 33 \, {\left(15 \, a^{6} + 205 \, a^{4} + 589 \, a^{2} + 399\right)} b^{17} c^{8} d^{3} + 264 \, {\left(5 \, a^{8} + 90 \, a^{6} + 408 \, a^{4} + 646 \, a^{2} + 323\right)} b^{15} c^{7} d^{4} + 110 \, {\left(21 \, a^{10} + 441 \, a^{8} + 2562 \, a^{6} + 6018 \, a^{4} + 6137 \, a^{2} + 2261\right)} b^{13} c^{6} d^{5} + 4 \, {\left(693 \, a^{12} + 15708 \, a^{10} + 105105 \, a^{8} + 308880 \, a^{6} + 449735 \, a^{4} + 319124 \, a^{2} + 88179\right)} b^{11} c^{5} d^{6} + 110 \, {\left(21 \, a^{14} + 483 \, a^{12} + 3465 \, a^{10} + 11583 \, a^{8} + 20735 \, a^{6} + 20553 \, a^{4} + 10659 \, a^{2} + 2261\right)} b^{9} c^{4} d^{7} + 264 \, {\left(5 \, a^{16} + 110 \, a^{14} + 798 \, a^{12} + 2838 \, a^{10} + 5720 \, a^{8} + 6890 \, a^{6} + 4930 \, a^{4} + 1938 \, a^{2} + 323\right)} b^{7} c^{3} d^{8} + 33 \, {\left(15 \, a^{18} + 295 \, a^{16} + 2044 \, a^{14} + 7308 \, a^{12} + 15554 \, a^{10} + 20930 \, a^{8} + 18060 \, a^{6} + 9724 \, a^{4} + 2983 \, a^{2} + 399\right)} b^{5} c^{2} d^{9} + 110 \, {\left(a^{20} + 16 \, a^{18} + 99 \, a^{16} + 336 \, a^{14} + 714 \, a^{12} + 1008 \, a^{10} + 966 \, a^{8} + 624 \, a^{6} + 261 \, a^{4} + 64 \, a^{2} + 7\right)} b^{3} c d^{10} + 11 \, {\left(a^{22} + 11 \, a^{20} + 55 \, a^{18} + 165 \, a^{16} + 330 \, a^{14} + 462 \, a^{12} + 462 \, a^{10} + 330 \, a^{8} + 165 \, a^{6} + 55 \, a^{4} + 11 \, a^{2} + 1\right)} b d^{11} + {\left(11 \, b^{23} c^{10} d + 110 \, {\left(a^{2} + 7\right)} b^{21} c^{9} d^{2} + 33 \, {\left(15 \, a^{4} + 190 \, a^{2} + 399\right)} b^{19} c^{8} d^{3} + 264 \, {\left(5 \, a^{6} + 85 \, a^{4} + 323 \, a^{2} + 323\right)} b^{17} c^{7} d^{4} + 110 \, {\left(21 \, a^{8} + 420 \, a^{6} + 2142 \, a^{4} + 3876 \, a^{2} + 2261\right)} b^{15} c^{6} d^{5} + 4 \, {\left(693 \, a^{10} + 15015 \, a^{8} + 90090 \, a^{6} + 218790 \, a^{4} + 230945 \, a^{2} + 88179\right)} b^{13} c^{5} d^{6} + 110 \, {\left(21 \, a^{12} + 462 \, a^{10} + 3003 \, a^{8} + 8580 \, a^{6} + 12155 \, a^{4} + 8398 \, a^{2} + 2261\right)} b^{11} c^{4} d^{7} + 264 \, {\left(5 \, a^{14} + 105 \, a^{12} + 693 \, a^{10} + 2145 \, a^{8} + 3575 \, a^{6} + 3315 \, a^{4} + 1615 \, a^{2} + 323\right)} b^{9} c^{3} d^{8} + 33 \, {\left(15 \, a^{16} + 280 \, a^{14} + 1764 \, a^{12} + 5544 \, a^{10} + 10010 \, a^{8} + 10920 \, a^{6} + 7140 \, a^{4} + 2584 \, a^{2} + 399\right)} b^{7} c^{2} d^{9} + 110 \, {\left(a^{18} + 15 \, a^{16} + 84 \, a^{14} + 252 \, a^{12} + 462 \, a^{10} + 546 \, a^{8} + 420 \, a^{6} + 204 \, a^{4} + 57 \, a^{2} + 7\right)} b^{5} c d^{10} + 11 \, {\left(a^{20} + 10 \, a^{18} + 45 \, a^{16} + 120 \, a^{14} + 210 \, a^{12} + 252 \, a^{10} + 210 \, a^{8} + 120 \, a^{6} + 45 \, a^{4} + 10 \, a^{2} + 1\right)} b^{3} d^{11}\right)} x^{2} + 2 \, {\left(11 \, a b^{22} c^{10} d + 110 \, {\left(a^{3} + 7 \, a\right)} b^{20} c^{9} d^{2} + 33 \, {\left(15 \, a^{5} + 190 \, a^{3} + 399 \, a\right)} b^{18} c^{8} d^{3} + 264 \, {\left(5 \, a^{7} + 85 \, a^{5} + 323 \, a^{3} + 323 \, a\right)} b^{16} c^{7} d^{4} + 110 \, {\left(21 \, a^{9} + 420 \, a^{7} + 2142 \, a^{5} + 3876 \, a^{3} + 2261 \, a\right)} b^{14} c^{6} d^{5} + 4 \, {\left(693 \, a^{11} + 15015 \, a^{9} + 90090 \, a^{7} + 218790 \, a^{5} + 230945 \, a^{3} + 88179 \, a\right)} b^{12} c^{5} d^{6} + 110 \, {\left(21 \, a^{13} + 462 \, a^{11} + 3003 \, a^{9} + 8580 \, a^{7} + 12155 \, a^{5} + 8398 \, a^{3} + 2261 \, a\right)} b^{10} c^{4} d^{7} + 264 \, {\left(5 \, a^{15} + 105 \, a^{13} + 693 \, a^{11} + 2145 \, a^{9} + 3575 \, a^{7} + 3315 \, a^{5} + 1615 \, a^{3} + 323 \, a\right)} b^{8} c^{3} d^{8} + 33 \, {\left(15 \, a^{17} + 280 \, a^{15} + 1764 \, a^{13} + 5544 \, a^{11} + 10010 \, a^{9} + 10920 \, a^{7} + 7140 \, a^{5} + 2584 \, a^{3} + 399 \, a\right)} b^{6} c^{2} d^{9} + 110 \, {\left(a^{19} + 15 \, a^{17} + 84 \, a^{15} + 252 \, a^{13} + 462 \, a^{11} + 546 \, a^{9} + 420 \, a^{7} + 204 \, a^{5} + 57 \, a^{3} + 7 \, a\right)} b^{4} c d^{10} + 11 \, {\left(a^{21} + 10 \, a^{19} + 45 \, a^{17} + 120 \, a^{15} + 210 \, a^{13} + 252 \, a^{11} + 210 \, a^{9} + 120 \, a^{7} + 45 \, a^{5} + 10 \, a^{3} + a\right)} b^{2} d^{11}\right)} x\right)} \sqrt{c} \sqrt{d} + 2 \, {\left(a b^{23} c^{11} d + 11 \, {\left(a^{3} + 21 \, a\right)} b^{21} c^{10} d^{2} + 55 \, {\left(a^{5} + 38 \, a^{3} + 133 \, a\right)} b^{19} c^{9} d^{3} + 33 \, {\left(5 \, a^{7} + 255 \, a^{5} + 1615 \, a^{3} + 2261 \, a\right)} b^{17} c^{8} d^{4} + 330 \, {\left(a^{9} + 60 \, a^{7} + 510 \, a^{5} + 1292 \, a^{3} + 969 \, a\right)} b^{15} c^{7} d^{5} + 22 \, {\left(21 \, a^{11} + 1365 \, a^{9} + 13650 \, a^{7} + 46410 \, a^{5} + 62985 \, a^{3} + 29393 \, a\right)} b^{13} c^{6} d^{6} + 22 \, {\left(21 \, a^{13} + 1386 \, a^{11} + 15015 \, a^{9} + 60060 \, a^{7} + 109395 \, a^{5} + 92378 \, a^{3} + 29393 \, a\right)} b^{11} c^{5} d^{7} + 330 \, {\left(a^{15} + 63 \, a^{13} + 693 \, a^{11} + 3003 \, a^{9} + 6435 \, a^{7} + 7293 \, a^{5} + 4199 \, a^{3} + 969 \, a\right)} b^{9} c^{4} d^{8} + 33 \, {\left(5 \, a^{17} + 280 \, a^{15} + 2940 \, a^{13} + 12936 \, a^{11} + 30030 \, a^{9} + 40040 \, a^{7} + 30940 \, a^{5} + 12920 \, a^{3} + 2261 \, a\right)} b^{7} c^{3} d^{9} + 55 \, {\left(a^{19} + 45 \, a^{17} + 420 \, a^{15} + 1764 \, a^{13} + 4158 \, a^{11} + 6006 \, a^{9} + 5460 \, a^{7} + 3060 \, a^{5} + 969 \, a^{3} + 133 \, a\right)} b^{5} c^{2} d^{10} + 11 \, {\left(a^{21} + 30 \, a^{19} + 225 \, a^{17} + 840 \, a^{15} + 1890 \, a^{13} + 2772 \, a^{11} + 2730 \, a^{9} + 1800 \, a^{7} + 765 \, a^{5} + 190 \, a^{3} + 21 \, a\right)} b^{3} c d^{11} + {\left(a^{23} + 11 \, a^{21} + 55 \, a^{19} + 165 \, a^{17} + 330 \, a^{15} + 462 \, a^{13} + 462 \, a^{11} + 330 \, a^{9} + 165 \, a^{7} + 55 \, a^{5} + 11 \, a^{3} + a\right)} b d^{12}\right)} x}{b^{24} c^{12} + 12 \, {\left(a^{2} + 23\right)} b^{22} c^{11} d + 66 \, {\left(a^{4} + 42 \, a^{2} + 161\right)} b^{20} c^{10} d^{2} + 44 \, {\left(5 \, a^{6} + 285 \, a^{4} + 1995 \, a^{2} + 3059\right)} b^{18} c^{9} d^{3} + 99 \, {\left(5 \, a^{8} + 340 \, a^{6} + 3230 \, a^{4} + 9044 \, a^{2} + 7429\right)} b^{16} c^{8} d^{4} + 264 \, {\left(3 \, a^{10} + 225 \, a^{8} + 2550 \, a^{6} + 9690 \, a^{4} + 14535 \, a^{2} + 7429\right)} b^{14} c^{7} d^{5} + 4 \, {\left(231 \, a^{12} + 18018 \, a^{10} + 225225 \, a^{8} + 1021020 \, a^{6} + 2078505 \, a^{4} + 1939938 \, a^{2} + 676039\right)} b^{12} c^{6} d^{6} + 264 \, {\left(3 \, a^{14} + 231 \, a^{12} + 3003 \, a^{10} + 15015 \, a^{8} + 36465 \, a^{6} + 46189 \, a^{4} + 29393 \, a^{2} + 7429\right)} b^{10} c^{5} d^{7} + 99 \, {\left(5 \, a^{16} + 360 \, a^{14} + 4620 \, a^{12} + 24024 \, a^{10} + 64350 \, a^{8} + 97240 \, a^{6} + 83980 \, a^{4} + 38760 \, a^{2} + 7429\right)} b^{8} c^{4} d^{8} + 44 \, {\left(5 \, a^{18} + 315 \, a^{16} + 3780 \, a^{14} + 19404 \, a^{12} + 54054 \, a^{10} + 90090 \, a^{8} + 92820 \, a^{6} + 58140 \, a^{4} + 20349 \, a^{2} + 3059\right)} b^{6} c^{3} d^{9} + 66 \, {\left(a^{20} + 50 \, a^{18} + 525 \, a^{16} + 2520 \, a^{14} + 6930 \, a^{12} + 12012 \, a^{10} + 13650 \, a^{8} + 10200 \, a^{6} + 4845 \, a^{4} + 1330 \, a^{2} + 161\right)} b^{4} c^{2} d^{10} + 12 \, {\left(a^{22} + 33 \, a^{20} + 275 \, a^{18} + 1155 \, a^{16} + 2970 \, a^{14} + 5082 \, a^{12} + 6006 \, a^{10} + 4950 \, a^{8} + 2805 \, a^{6} + 1045 \, a^{4} + 231 \, a^{2} + 23\right)} b^{2} c d^{11} + {\left(a^{24} + 12 \, a^{22} + 66 \, a^{20} + 220 \, a^{18} + 495 \, a^{16} + 792 \, a^{14} + 924 \, a^{12} + 792 \, a^{10} + 495 \, a^{8} + 220 \, a^{6} + 66 \, a^{4} + 12 \, a^{2} + 1\right)} d^{12} - 8 \, {\left(3 \, b^{23} c^{11} + 11 \, {\left(3 \, a^{2} + 23\right)} b^{21} c^{10} d + 33 \, {\left(5 \, a^{4} + 70 \, a^{2} + 161\right)} b^{19} c^{9} d^{2} + 99 \, {\left(5 \, a^{6} + 95 \, a^{4} + 399 \, a^{2} + 437\right)} b^{17} c^{8} d^{3} + 22 \, {\left(45 \, a^{8} + 1020 \, a^{6} + 5814 \, a^{4} + 11628 \, a^{2} + 7429\right)} b^{15} c^{7} d^{4} + 6 \, {\left(231 \, a^{10} + 5775 \, a^{8} + 39270 \, a^{6} + 106590 \, a^{4} + 124355 \, a^{2} + 52003\right)} b^{13} c^{6} d^{5} + 6 \, {\left(231 \, a^{12} + 6006 \, a^{10} + 45045 \, a^{8} + 145860 \, a^{6} + 230945 \, a^{4} + 176358 \, a^{2} + 52003\right)} b^{11} c^{5} d^{6} + 22 \, {\left(45 \, a^{14} + 1155 \, a^{12} + 9009 \, a^{10} + 32175 \, a^{8} + 60775 \, a^{6} + 62985 \, a^{4} + 33915 \, a^{2} + 7429\right)} b^{9} c^{4} d^{7} + 99 \, {\left(5 \, a^{16} + 120 \, a^{14} + 924 \, a^{12} + 3432 \, a^{10} + 7150 \, a^{8} + 8840 \, a^{6} + 6460 \, a^{4} + 2584 \, a^{2} + 437\right)} b^{7} c^{3} d^{8} + 33 \, {\left(5 \, a^{18} + 105 \, a^{16} + 756 \, a^{14} + 2772 \, a^{12} + 6006 \, a^{10} + 8190 \, a^{8} + 7140 \, a^{6} + 3876 \, a^{4} + 1197 \, a^{2} + 161\right)} b^{5} c^{2} d^{9} + 11 \, {\left(3 \, a^{20} + 50 \, a^{18} + 315 \, a^{16} + 1080 \, a^{14} + 2310 \, a^{12} + 3276 \, a^{10} + 3150 \, a^{8} + 2040 \, a^{6} + 855 \, a^{4} + 210 \, a^{2} + 23\right)} b^{3} c d^{10} + 3 \, {\left(a^{22} + 11 \, a^{20} + 55 \, a^{18} + 165 \, a^{16} + 330 \, a^{14} + 462 \, a^{12} + 462 \, a^{10} + 330 \, a^{8} + 165 \, a^{6} + 55 \, a^{4} + 11 \, a^{2} + 1\right)} b d^{11}\right)} \sqrt{c} \sqrt{d}}\right) + 2 \, {\rm Li}_2\left(\frac{{\left(a + i\right)} b d x + b^{2} c + {\left(i \, b^{2} x + {\left(-i \, a + 1\right)} b\right)} \sqrt{c} \sqrt{d}}{b^{2} c + 2 \, {\left(-i \, a + 1\right)} b \sqrt{c} \sqrt{d} - {\left(a^{2} + 2 i \, a - 1\right)} d}\right) - 2 \, {\rm Li}_2\left(\frac{{\left(a + i\right)} b d x + b^{2} c - {\left(i \, b^{2} x + {\left(-i \, a + 1\right)} b\right)} \sqrt{c} \sqrt{d}}{b^{2} c - 2 \, {\left(-i \, a + 1\right)} b \sqrt{c} \sqrt{d} - {\left(a^{2} + 2 i \, a - 1\right)} d}\right) - 2 \, {\rm Li}_2\left(\frac{{\left(a - i\right)} b d x + b^{2} c + {\left(i \, b^{2} x + {\left(-i \, a - 1\right)} b\right)} \sqrt{c} \sqrt{d}}{b^{2} c + 2 \, {\left(-i \, a - 1\right)} b \sqrt{c} \sqrt{d} - {\left(a^{2} - 2 i \, a - 1\right)} d}\right) + 2 \, {\rm Li}_2\left(\frac{{\left(a - i\right)} b d x + b^{2} c - {\left(i \, b^{2} x + {\left(-i \, a - 1\right)} b\right)} \sqrt{c} \sqrt{d}}{b^{2} c - 2 \, {\left(-i \, a - 1\right)} b \sqrt{c} \sqrt{d} - {\left(a^{2} - 2 i \, a - 1\right)} d}\right)}{b}\right)}}{8 \, \sqrt{c d}} + \frac{\arctan\left(b x + a\right) \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d}} - \frac{\arctan\left(\frac{d x}{\sqrt{c d}}\right) \arctan\left(\frac{b^{2} x + a b}{b}\right)}{\sqrt{c d}}"," ",0,"1/8*b*(8*arctan(d*x/sqrt(c*d))*arctan((b^2*x + a*b)/b)/b - (4*arctan(sqrt(d)*x/sqrt(c))*arctan2((2*a*b^2*c*d + (a*b^3*c + (a^3 + a)*b*d + (b^4*c + (a^2 + 3)*b^2*d)*x)*sqrt(c)*sqrt(d) + (3*b^3*c*d + (a^2 + 1)*b*d^2)*x)/(b^4*c^2 + 2*(a^2 + 3)*b^2*c*d + (a^4 + 2*a^2 + 1)*d^2 + 4*(b^3*c + (a^2 + 1)*b*d)*sqrt(c)*sqrt(d)), ((a^2 + 3)*b^2*c*d + (a^4 + 2*a^2 + 1)*d^2 + (2*a*b^2*d*x + b^3*c + 3*(a^2 + 1)*b*d)*sqrt(c)*sqrt(d) + (a*b^3*c*d + (a^3 + a)*b*d^2)*x)/(b^4*c^2 + 2*(a^2 + 3)*b^2*c*d + (a^4 + 2*a^2 + 1)*d^2 + 4*(b^3*c + (a^2 + 1)*b*d)*sqrt(c)*sqrt(d))) + 4*arctan(sqrt(d)*x/sqrt(c))*arctan2((2*a*b^2*c*d - (a*b^3*c + (a^3 + a)*b*d + (b^4*c + (a^2 + 3)*b^2*d)*x)*sqrt(c)*sqrt(d) + (3*b^3*c*d + (a^2 + 1)*b*d^2)*x)/(b^4*c^2 + 2*(a^2 + 3)*b^2*c*d + (a^4 + 2*a^2 + 1)*d^2 - 4*(b^3*c + (a^2 + 1)*b*d)*sqrt(c)*sqrt(d)), ((a^2 + 3)*b^2*c*d + (a^4 + 2*a^2 + 1)*d^2 - (2*a*b^2*d*x + b^3*c + 3*(a^2 + 1)*b*d)*sqrt(c)*sqrt(d) + (a*b^3*c*d + (a^3 + a)*b*d^2)*x)/(b^4*c^2 + 2*(a^2 + 3)*b^2*c*d + (a^4 + 2*a^2 + 1)*d^2 - 4*(b^3*c + (a^2 + 1)*b*d)*sqrt(c)*sqrt(d))) + log(d*x^2 + c)*log(((a^2 + 1)*b^22*c^11*d + 11*(a^4 + 22*a^2 + 21)*b^20*c^10*d^2 + 55*(a^6 + 39*a^4 + 171*a^2 + 133)*b^18*c^9*d^3 + 33*(5*a^8 + 260*a^6 + 1870*a^4 + 3876*a^2 + 2261)*b^16*c^8*d^4 + 330*(a^10 + 61*a^8 + 570*a^6 + 1802*a^4 + 2261*a^2 + 969)*b^14*c^7*d^5 + 22*(21*a^12 + 1386*a^10 + 15015*a^8 + 60060*a^6 + 109395*a^4 + 92378*a^2 + 29393)*b^12*c^6*d^6 + 22*(21*a^14 + 1407*a^12 + 16401*a^10 + 75075*a^8 + 169455*a^6 + 201773*a^4 + 121771*a^2 + 29393)*b^10*c^5*d^7 + 330*(a^16 + 64*a^14 + 756*a^12 + 3696*a^10 + 9438*a^8 + 13728*a^6 + 11492*a^4 + 5168*a^2 + 969)*b^8*c^4*d^8 + 33*(5*a^18 + 285*a^16 + 3220*a^14 + 15876*a^12 + 42966*a^10 + 70070*a^8 + 70980*a^6 + 43860*a^4 + 15181*a^2 + 2261)*b^6*c^3*d^9 + 55*(a^20 + 46*a^18 + 465*a^16 + 2184*a^14 + 5922*a^12 + 10164*a^10 + 11466*a^8 + 8520*a^6 + 4029*a^4 + 1102*a^2 + 133)*b^4*c^2*d^10 + 11*(a^22 + 31*a^20 + 255*a^18 + 1065*a^16 + 2730*a^14 + 4662*a^12 + 5502*a^10 + 4530*a^8 + 2565*a^6 + 955*a^4 + 211*a^2 + 21)*b^2*c*d^11 + (a^24 + 12*a^22 + 66*a^20 + 220*a^18 + 495*a^16 + 792*a^14 + 924*a^12 + 792*a^10 + 495*a^8 + 220*a^6 + 66*a^4 + 12*a^2 + 1)*d^12 + (b^24*c^11*d + 11*(a^2 + 21)*b^22*c^10*d^2 + 55*(a^4 + 38*a^2 + 133)*b^20*c^9*d^3 + 33*(5*a^6 + 255*a^4 + 1615*a^2 + 2261)*b^18*c^8*d^4 + 330*(a^8 + 60*a^6 + 510*a^4 + 1292*a^2 + 969)*b^16*c^7*d^5 + 22*(21*a^10 + 1365*a^8 + 13650*a^6 + 46410*a^4 + 62985*a^2 + 29393)*b^14*c^6*d^6 + 22*(21*a^12 + 1386*a^10 + 15015*a^8 + 60060*a^6 + 109395*a^4 + 92378*a^2 + 29393)*b^12*c^5*d^7 + 330*(a^14 + 63*a^12 + 693*a^10 + 3003*a^8 + 6435*a^6 + 7293*a^4 + 4199*a^2 + 969)*b^10*c^4*d^8 + 33*(5*a^16 + 280*a^14 + 2940*a^12 + 12936*a^10 + 30030*a^8 + 40040*a^6 + 30940*a^4 + 12920*a^2 + 2261)*b^8*c^3*d^9 + 55*(a^18 + 45*a^16 + 420*a^14 + 1764*a^12 + 4158*a^10 + 6006*a^8 + 5460*a^6 + 3060*a^4 + 969*a^2 + 133)*b^6*c^2*d^10 + 11*(a^20 + 30*a^18 + 225*a^16 + 840*a^14 + 1890*a^12 + 2772*a^10 + 2730*a^8 + 1800*a^6 + 765*a^4 + 190*a^2 + 21)*b^4*c*d^11 + (a^22 + 11*a^20 + 55*a^18 + 165*a^16 + 330*a^14 + 462*a^12 + 462*a^10 + 330*a^8 + 165*a^6 + 55*a^4 + 11*a^2 + 1)*b^2*d^12)*x^2 + 2*(11*(a^2 + 1)*b^21*c^10*d + 110*(a^4 + 8*a^2 + 7)*b^19*c^9*d^2 + 33*(15*a^6 + 205*a^4 + 589*a^2 + 399)*b^17*c^8*d^3 + 264*(5*a^8 + 90*a^6 + 408*a^4 + 646*a^2 + 323)*b^15*c^7*d^4 + 110*(21*a^10 + 441*a^8 + 2562*a^6 + 6018*a^4 + 6137*a^2 + 2261)*b^13*c^6*d^5 + 4*(693*a^12 + 15708*a^10 + 105105*a^8 + 308880*a^6 + 449735*a^4 + 319124*a^2 + 88179)*b^11*c^5*d^6 + 110*(21*a^14 + 483*a^12 + 3465*a^10 + 11583*a^8 + 20735*a^6 + 20553*a^4 + 10659*a^2 + 2261)*b^9*c^4*d^7 + 264*(5*a^16 + 110*a^14 + 798*a^12 + 2838*a^10 + 5720*a^8 + 6890*a^6 + 4930*a^4 + 1938*a^2 + 323)*b^7*c^3*d^8 + 33*(15*a^18 + 295*a^16 + 2044*a^14 + 7308*a^12 + 15554*a^10 + 20930*a^8 + 18060*a^6 + 9724*a^4 + 2983*a^2 + 399)*b^5*c^2*d^9 + 110*(a^20 + 16*a^18 + 99*a^16 + 336*a^14 + 714*a^12 + 1008*a^10 + 966*a^8 + 624*a^6 + 261*a^4 + 64*a^2 + 7)*b^3*c*d^10 + 11*(a^22 + 11*a^20 + 55*a^18 + 165*a^16 + 330*a^14 + 462*a^12 + 462*a^10 + 330*a^8 + 165*a^6 + 55*a^4 + 11*a^2 + 1)*b*d^11 + (11*b^23*c^10*d + 110*(a^2 + 7)*b^21*c^9*d^2 + 33*(15*a^4 + 190*a^2 + 399)*b^19*c^8*d^3 + 264*(5*a^6 + 85*a^4 + 323*a^2 + 323)*b^17*c^7*d^4 + 110*(21*a^8 + 420*a^6 + 2142*a^4 + 3876*a^2 + 2261)*b^15*c^6*d^5 + 4*(693*a^10 + 15015*a^8 + 90090*a^6 + 218790*a^4 + 230945*a^2 + 88179)*b^13*c^5*d^6 + 110*(21*a^12 + 462*a^10 + 3003*a^8 + 8580*a^6 + 12155*a^4 + 8398*a^2 + 2261)*b^11*c^4*d^7 + 264*(5*a^14 + 105*a^12 + 693*a^10 + 2145*a^8 + 3575*a^6 + 3315*a^4 + 1615*a^2 + 323)*b^9*c^3*d^8 + 33*(15*a^16 + 280*a^14 + 1764*a^12 + 5544*a^10 + 10010*a^8 + 10920*a^6 + 7140*a^4 + 2584*a^2 + 399)*b^7*c^2*d^9 + 110*(a^18 + 15*a^16 + 84*a^14 + 252*a^12 + 462*a^10 + 546*a^8 + 420*a^6 + 204*a^4 + 57*a^2 + 7)*b^5*c*d^10 + 11*(a^20 + 10*a^18 + 45*a^16 + 120*a^14 + 210*a^12 + 252*a^10 + 210*a^8 + 120*a^6 + 45*a^4 + 10*a^2 + 1)*b^3*d^11)*x^2 + 2*(11*a*b^22*c^10*d + 110*(a^3 + 7*a)*b^20*c^9*d^2 + 33*(15*a^5 + 190*a^3 + 399*a)*b^18*c^8*d^3 + 264*(5*a^7 + 85*a^5 + 323*a^3 + 323*a)*b^16*c^7*d^4 + 110*(21*a^9 + 420*a^7 + 2142*a^5 + 3876*a^3 + 2261*a)*b^14*c^6*d^5 + 4*(693*a^11 + 15015*a^9 + 90090*a^7 + 218790*a^5 + 230945*a^3 + 88179*a)*b^12*c^5*d^6 + 110*(21*a^13 + 462*a^11 + 3003*a^9 + 8580*a^7 + 12155*a^5 + 8398*a^3 + 2261*a)*b^10*c^4*d^7 + 264*(5*a^15 + 105*a^13 + 693*a^11 + 2145*a^9 + 3575*a^7 + 3315*a^5 + 1615*a^3 + 323*a)*b^8*c^3*d^8 + 33*(15*a^17 + 280*a^15 + 1764*a^13 + 5544*a^11 + 10010*a^9 + 10920*a^7 + 7140*a^5 + 2584*a^3 + 399*a)*b^6*c^2*d^9 + 110*(a^19 + 15*a^17 + 84*a^15 + 252*a^13 + 462*a^11 + 546*a^9 + 420*a^7 + 204*a^5 + 57*a^3 + 7*a)*b^4*c*d^10 + 11*(a^21 + 10*a^19 + 45*a^17 + 120*a^15 + 210*a^13 + 252*a^11 + 210*a^9 + 120*a^7 + 45*a^5 + 10*a^3 + a)*b^2*d^11)*x)*sqrt(c)*sqrt(d) + 2*(a*b^23*c^11*d + 11*(a^3 + 21*a)*b^21*c^10*d^2 + 55*(a^5 + 38*a^3 + 133*a)*b^19*c^9*d^3 + 33*(5*a^7 + 255*a^5 + 1615*a^3 + 2261*a)*b^17*c^8*d^4 + 330*(a^9 + 60*a^7 + 510*a^5 + 1292*a^3 + 969*a)*b^15*c^7*d^5 + 22*(21*a^11 + 1365*a^9 + 13650*a^7 + 46410*a^5 + 62985*a^3 + 29393*a)*b^13*c^6*d^6 + 22*(21*a^13 + 1386*a^11 + 15015*a^9 + 60060*a^7 + 109395*a^5 + 92378*a^3 + 29393*a)*b^11*c^5*d^7 + 330*(a^15 + 63*a^13 + 693*a^11 + 3003*a^9 + 6435*a^7 + 7293*a^5 + 4199*a^3 + 969*a)*b^9*c^4*d^8 + 33*(5*a^17 + 280*a^15 + 2940*a^13 + 12936*a^11 + 30030*a^9 + 40040*a^7 + 30940*a^5 + 12920*a^3 + 2261*a)*b^7*c^3*d^9 + 55*(a^19 + 45*a^17 + 420*a^15 + 1764*a^13 + 4158*a^11 + 6006*a^9 + 5460*a^7 + 3060*a^5 + 969*a^3 + 133*a)*b^5*c^2*d^10 + 11*(a^21 + 30*a^19 + 225*a^17 + 840*a^15 + 1890*a^13 + 2772*a^11 + 2730*a^9 + 1800*a^7 + 765*a^5 + 190*a^3 + 21*a)*b^3*c*d^11 + (a^23 + 11*a^21 + 55*a^19 + 165*a^17 + 330*a^15 + 462*a^13 + 462*a^11 + 330*a^9 + 165*a^7 + 55*a^5 + 11*a^3 + a)*b*d^12)*x)/(b^24*c^12 + 12*(a^2 + 23)*b^22*c^11*d + 66*(a^4 + 42*a^2 + 161)*b^20*c^10*d^2 + 44*(5*a^6 + 285*a^4 + 1995*a^2 + 3059)*b^18*c^9*d^3 + 99*(5*a^8 + 340*a^6 + 3230*a^4 + 9044*a^2 + 7429)*b^16*c^8*d^4 + 264*(3*a^10 + 225*a^8 + 2550*a^6 + 9690*a^4 + 14535*a^2 + 7429)*b^14*c^7*d^5 + 4*(231*a^12 + 18018*a^10 + 225225*a^8 + 1021020*a^6 + 2078505*a^4 + 1939938*a^2 + 676039)*b^12*c^6*d^6 + 264*(3*a^14 + 231*a^12 + 3003*a^10 + 15015*a^8 + 36465*a^6 + 46189*a^4 + 29393*a^2 + 7429)*b^10*c^5*d^7 + 99*(5*a^16 + 360*a^14 + 4620*a^12 + 24024*a^10 + 64350*a^8 + 97240*a^6 + 83980*a^4 + 38760*a^2 + 7429)*b^8*c^4*d^8 + 44*(5*a^18 + 315*a^16 + 3780*a^14 + 19404*a^12 + 54054*a^10 + 90090*a^8 + 92820*a^6 + 58140*a^4 + 20349*a^2 + 3059)*b^6*c^3*d^9 + 66*(a^20 + 50*a^18 + 525*a^16 + 2520*a^14 + 6930*a^12 + 12012*a^10 + 13650*a^8 + 10200*a^6 + 4845*a^4 + 1330*a^2 + 161)*b^4*c^2*d^10 + 12*(a^22 + 33*a^20 + 275*a^18 + 1155*a^16 + 2970*a^14 + 5082*a^12 + 6006*a^10 + 4950*a^8 + 2805*a^6 + 1045*a^4 + 231*a^2 + 23)*b^2*c*d^11 + (a^24 + 12*a^22 + 66*a^20 + 220*a^18 + 495*a^16 + 792*a^14 + 924*a^12 + 792*a^10 + 495*a^8 + 220*a^6 + 66*a^4 + 12*a^2 + 1)*d^12 + 8*(3*b^23*c^11 + 11*(3*a^2 + 23)*b^21*c^10*d + 33*(5*a^4 + 70*a^2 + 161)*b^19*c^9*d^2 + 99*(5*a^6 + 95*a^4 + 399*a^2 + 437)*b^17*c^8*d^3 + 22*(45*a^8 + 1020*a^6 + 5814*a^4 + 11628*a^2 + 7429)*b^15*c^7*d^4 + 6*(231*a^10 + 5775*a^8 + 39270*a^6 + 106590*a^4 + 124355*a^2 + 52003)*b^13*c^6*d^5 + 6*(231*a^12 + 6006*a^10 + 45045*a^8 + 145860*a^6 + 230945*a^4 + 176358*a^2 + 52003)*b^11*c^5*d^6 + 22*(45*a^14 + 1155*a^12 + 9009*a^10 + 32175*a^8 + 60775*a^6 + 62985*a^4 + 33915*a^2 + 7429)*b^9*c^4*d^7 + 99*(5*a^16 + 120*a^14 + 924*a^12 + 3432*a^10 + 7150*a^8 + 8840*a^6 + 6460*a^4 + 2584*a^2 + 437)*b^7*c^3*d^8 + 33*(5*a^18 + 105*a^16 + 756*a^14 + 2772*a^12 + 6006*a^10 + 8190*a^8 + 7140*a^6 + 3876*a^4 + 1197*a^2 + 161)*b^5*c^2*d^9 + 11*(3*a^20 + 50*a^18 + 315*a^16 + 1080*a^14 + 2310*a^12 + 3276*a^10 + 3150*a^8 + 2040*a^6 + 855*a^4 + 210*a^2 + 23)*b^3*c*d^10 + 3*(a^22 + 11*a^20 + 55*a^18 + 165*a^16 + 330*a^14 + 462*a^12 + 462*a^10 + 330*a^8 + 165*a^6 + 55*a^4 + 11*a^2 + 1)*b*d^11)*sqrt(c)*sqrt(d))) - log(d*x^2 + c)*log(((a^2 + 1)*b^22*c^11*d + 11*(a^4 + 22*a^2 + 21)*b^20*c^10*d^2 + 55*(a^6 + 39*a^4 + 171*a^2 + 133)*b^18*c^9*d^3 + 33*(5*a^8 + 260*a^6 + 1870*a^4 + 3876*a^2 + 2261)*b^16*c^8*d^4 + 330*(a^10 + 61*a^8 + 570*a^6 + 1802*a^4 + 2261*a^2 + 969)*b^14*c^7*d^5 + 22*(21*a^12 + 1386*a^10 + 15015*a^8 + 60060*a^6 + 109395*a^4 + 92378*a^2 + 29393)*b^12*c^6*d^6 + 22*(21*a^14 + 1407*a^12 + 16401*a^10 + 75075*a^8 + 169455*a^6 + 201773*a^4 + 121771*a^2 + 29393)*b^10*c^5*d^7 + 330*(a^16 + 64*a^14 + 756*a^12 + 3696*a^10 + 9438*a^8 + 13728*a^6 + 11492*a^4 + 5168*a^2 + 969)*b^8*c^4*d^8 + 33*(5*a^18 + 285*a^16 + 3220*a^14 + 15876*a^12 + 42966*a^10 + 70070*a^8 + 70980*a^6 + 43860*a^4 + 15181*a^2 + 2261)*b^6*c^3*d^9 + 55*(a^20 + 46*a^18 + 465*a^16 + 2184*a^14 + 5922*a^12 + 10164*a^10 + 11466*a^8 + 8520*a^6 + 4029*a^4 + 1102*a^2 + 133)*b^4*c^2*d^10 + 11*(a^22 + 31*a^20 + 255*a^18 + 1065*a^16 + 2730*a^14 + 4662*a^12 + 5502*a^10 + 4530*a^8 + 2565*a^6 + 955*a^4 + 211*a^2 + 21)*b^2*c*d^11 + (a^24 + 12*a^22 + 66*a^20 + 220*a^18 + 495*a^16 + 792*a^14 + 924*a^12 + 792*a^10 + 495*a^8 + 220*a^6 + 66*a^4 + 12*a^2 + 1)*d^12 + (b^24*c^11*d + 11*(a^2 + 21)*b^22*c^10*d^2 + 55*(a^4 + 38*a^2 + 133)*b^20*c^9*d^3 + 33*(5*a^6 + 255*a^4 + 1615*a^2 + 2261)*b^18*c^8*d^4 + 330*(a^8 + 60*a^6 + 510*a^4 + 1292*a^2 + 969)*b^16*c^7*d^5 + 22*(21*a^10 + 1365*a^8 + 13650*a^6 + 46410*a^4 + 62985*a^2 + 29393)*b^14*c^6*d^6 + 22*(21*a^12 + 1386*a^10 + 15015*a^8 + 60060*a^6 + 109395*a^4 + 92378*a^2 + 29393)*b^12*c^5*d^7 + 330*(a^14 + 63*a^12 + 693*a^10 + 3003*a^8 + 6435*a^6 + 7293*a^4 + 4199*a^2 + 969)*b^10*c^4*d^8 + 33*(5*a^16 + 280*a^14 + 2940*a^12 + 12936*a^10 + 30030*a^8 + 40040*a^6 + 30940*a^4 + 12920*a^2 + 2261)*b^8*c^3*d^9 + 55*(a^18 + 45*a^16 + 420*a^14 + 1764*a^12 + 4158*a^10 + 6006*a^8 + 5460*a^6 + 3060*a^4 + 969*a^2 + 133)*b^6*c^2*d^10 + 11*(a^20 + 30*a^18 + 225*a^16 + 840*a^14 + 1890*a^12 + 2772*a^10 + 2730*a^8 + 1800*a^6 + 765*a^4 + 190*a^2 + 21)*b^4*c*d^11 + (a^22 + 11*a^20 + 55*a^18 + 165*a^16 + 330*a^14 + 462*a^12 + 462*a^10 + 330*a^8 + 165*a^6 + 55*a^4 + 11*a^2 + 1)*b^2*d^12)*x^2 - 2*(11*(a^2 + 1)*b^21*c^10*d + 110*(a^4 + 8*a^2 + 7)*b^19*c^9*d^2 + 33*(15*a^6 + 205*a^4 + 589*a^2 + 399)*b^17*c^8*d^3 + 264*(5*a^8 + 90*a^6 + 408*a^4 + 646*a^2 + 323)*b^15*c^7*d^4 + 110*(21*a^10 + 441*a^8 + 2562*a^6 + 6018*a^4 + 6137*a^2 + 2261)*b^13*c^6*d^5 + 4*(693*a^12 + 15708*a^10 + 105105*a^8 + 308880*a^6 + 449735*a^4 + 319124*a^2 + 88179)*b^11*c^5*d^6 + 110*(21*a^14 + 483*a^12 + 3465*a^10 + 11583*a^8 + 20735*a^6 + 20553*a^4 + 10659*a^2 + 2261)*b^9*c^4*d^7 + 264*(5*a^16 + 110*a^14 + 798*a^12 + 2838*a^10 + 5720*a^8 + 6890*a^6 + 4930*a^4 + 1938*a^2 + 323)*b^7*c^3*d^8 + 33*(15*a^18 + 295*a^16 + 2044*a^14 + 7308*a^12 + 15554*a^10 + 20930*a^8 + 18060*a^6 + 9724*a^4 + 2983*a^2 + 399)*b^5*c^2*d^9 + 110*(a^20 + 16*a^18 + 99*a^16 + 336*a^14 + 714*a^12 + 1008*a^10 + 966*a^8 + 624*a^6 + 261*a^4 + 64*a^2 + 7)*b^3*c*d^10 + 11*(a^22 + 11*a^20 + 55*a^18 + 165*a^16 + 330*a^14 + 462*a^12 + 462*a^10 + 330*a^8 + 165*a^6 + 55*a^4 + 11*a^2 + 1)*b*d^11 + (11*b^23*c^10*d + 110*(a^2 + 7)*b^21*c^9*d^2 + 33*(15*a^4 + 190*a^2 + 399)*b^19*c^8*d^3 + 264*(5*a^6 + 85*a^4 + 323*a^2 + 323)*b^17*c^7*d^4 + 110*(21*a^8 + 420*a^6 + 2142*a^4 + 3876*a^2 + 2261)*b^15*c^6*d^5 + 4*(693*a^10 + 15015*a^8 + 90090*a^6 + 218790*a^4 + 230945*a^2 + 88179)*b^13*c^5*d^6 + 110*(21*a^12 + 462*a^10 + 3003*a^8 + 8580*a^6 + 12155*a^4 + 8398*a^2 + 2261)*b^11*c^4*d^7 + 264*(5*a^14 + 105*a^12 + 693*a^10 + 2145*a^8 + 3575*a^6 + 3315*a^4 + 1615*a^2 + 323)*b^9*c^3*d^8 + 33*(15*a^16 + 280*a^14 + 1764*a^12 + 5544*a^10 + 10010*a^8 + 10920*a^6 + 7140*a^4 + 2584*a^2 + 399)*b^7*c^2*d^9 + 110*(a^18 + 15*a^16 + 84*a^14 + 252*a^12 + 462*a^10 + 546*a^8 + 420*a^6 + 204*a^4 + 57*a^2 + 7)*b^5*c*d^10 + 11*(a^20 + 10*a^18 + 45*a^16 + 120*a^14 + 210*a^12 + 252*a^10 + 210*a^8 + 120*a^6 + 45*a^4 + 10*a^2 + 1)*b^3*d^11)*x^2 + 2*(11*a*b^22*c^10*d + 110*(a^3 + 7*a)*b^20*c^9*d^2 + 33*(15*a^5 + 190*a^3 + 399*a)*b^18*c^8*d^3 + 264*(5*a^7 + 85*a^5 + 323*a^3 + 323*a)*b^16*c^7*d^4 + 110*(21*a^9 + 420*a^7 + 2142*a^5 + 3876*a^3 + 2261*a)*b^14*c^6*d^5 + 4*(693*a^11 + 15015*a^9 + 90090*a^7 + 218790*a^5 + 230945*a^3 + 88179*a)*b^12*c^5*d^6 + 110*(21*a^13 + 462*a^11 + 3003*a^9 + 8580*a^7 + 12155*a^5 + 8398*a^3 + 2261*a)*b^10*c^4*d^7 + 264*(5*a^15 + 105*a^13 + 693*a^11 + 2145*a^9 + 3575*a^7 + 3315*a^5 + 1615*a^3 + 323*a)*b^8*c^3*d^8 + 33*(15*a^17 + 280*a^15 + 1764*a^13 + 5544*a^11 + 10010*a^9 + 10920*a^7 + 7140*a^5 + 2584*a^3 + 399*a)*b^6*c^2*d^9 + 110*(a^19 + 15*a^17 + 84*a^15 + 252*a^13 + 462*a^11 + 546*a^9 + 420*a^7 + 204*a^5 + 57*a^3 + 7*a)*b^4*c*d^10 + 11*(a^21 + 10*a^19 + 45*a^17 + 120*a^15 + 210*a^13 + 252*a^11 + 210*a^9 + 120*a^7 + 45*a^5 + 10*a^3 + a)*b^2*d^11)*x)*sqrt(c)*sqrt(d) + 2*(a*b^23*c^11*d + 11*(a^3 + 21*a)*b^21*c^10*d^2 + 55*(a^5 + 38*a^3 + 133*a)*b^19*c^9*d^3 + 33*(5*a^7 + 255*a^5 + 1615*a^3 + 2261*a)*b^17*c^8*d^4 + 330*(a^9 + 60*a^7 + 510*a^5 + 1292*a^3 + 969*a)*b^15*c^7*d^5 + 22*(21*a^11 + 1365*a^9 + 13650*a^7 + 46410*a^5 + 62985*a^3 + 29393*a)*b^13*c^6*d^6 + 22*(21*a^13 + 1386*a^11 + 15015*a^9 + 60060*a^7 + 109395*a^5 + 92378*a^3 + 29393*a)*b^11*c^5*d^7 + 330*(a^15 + 63*a^13 + 693*a^11 + 3003*a^9 + 6435*a^7 + 7293*a^5 + 4199*a^3 + 969*a)*b^9*c^4*d^8 + 33*(5*a^17 + 280*a^15 + 2940*a^13 + 12936*a^11 + 30030*a^9 + 40040*a^7 + 30940*a^5 + 12920*a^3 + 2261*a)*b^7*c^3*d^9 + 55*(a^19 + 45*a^17 + 420*a^15 + 1764*a^13 + 4158*a^11 + 6006*a^9 + 5460*a^7 + 3060*a^5 + 969*a^3 + 133*a)*b^5*c^2*d^10 + 11*(a^21 + 30*a^19 + 225*a^17 + 840*a^15 + 1890*a^13 + 2772*a^11 + 2730*a^9 + 1800*a^7 + 765*a^5 + 190*a^3 + 21*a)*b^3*c*d^11 + (a^23 + 11*a^21 + 55*a^19 + 165*a^17 + 330*a^15 + 462*a^13 + 462*a^11 + 330*a^9 + 165*a^7 + 55*a^5 + 11*a^3 + a)*b*d^12)*x)/(b^24*c^12 + 12*(a^2 + 23)*b^22*c^11*d + 66*(a^4 + 42*a^2 + 161)*b^20*c^10*d^2 + 44*(5*a^6 + 285*a^4 + 1995*a^2 + 3059)*b^18*c^9*d^3 + 99*(5*a^8 + 340*a^6 + 3230*a^4 + 9044*a^2 + 7429)*b^16*c^8*d^4 + 264*(3*a^10 + 225*a^8 + 2550*a^6 + 9690*a^4 + 14535*a^2 + 7429)*b^14*c^7*d^5 + 4*(231*a^12 + 18018*a^10 + 225225*a^8 + 1021020*a^6 + 2078505*a^4 + 1939938*a^2 + 676039)*b^12*c^6*d^6 + 264*(3*a^14 + 231*a^12 + 3003*a^10 + 15015*a^8 + 36465*a^6 + 46189*a^4 + 29393*a^2 + 7429)*b^10*c^5*d^7 + 99*(5*a^16 + 360*a^14 + 4620*a^12 + 24024*a^10 + 64350*a^8 + 97240*a^6 + 83980*a^4 + 38760*a^2 + 7429)*b^8*c^4*d^8 + 44*(5*a^18 + 315*a^16 + 3780*a^14 + 19404*a^12 + 54054*a^10 + 90090*a^8 + 92820*a^6 + 58140*a^4 + 20349*a^2 + 3059)*b^6*c^3*d^9 + 66*(a^20 + 50*a^18 + 525*a^16 + 2520*a^14 + 6930*a^12 + 12012*a^10 + 13650*a^8 + 10200*a^6 + 4845*a^4 + 1330*a^2 + 161)*b^4*c^2*d^10 + 12*(a^22 + 33*a^20 + 275*a^18 + 1155*a^16 + 2970*a^14 + 5082*a^12 + 6006*a^10 + 4950*a^8 + 2805*a^6 + 1045*a^4 + 231*a^2 + 23)*b^2*c*d^11 + (a^24 + 12*a^22 + 66*a^20 + 220*a^18 + 495*a^16 + 792*a^14 + 924*a^12 + 792*a^10 + 495*a^8 + 220*a^6 + 66*a^4 + 12*a^2 + 1)*d^12 - 8*(3*b^23*c^11 + 11*(3*a^2 + 23)*b^21*c^10*d + 33*(5*a^4 + 70*a^2 + 161)*b^19*c^9*d^2 + 99*(5*a^6 + 95*a^4 + 399*a^2 + 437)*b^17*c^8*d^3 + 22*(45*a^8 + 1020*a^6 + 5814*a^4 + 11628*a^2 + 7429)*b^15*c^7*d^4 + 6*(231*a^10 + 5775*a^8 + 39270*a^6 + 106590*a^4 + 124355*a^2 + 52003)*b^13*c^6*d^5 + 6*(231*a^12 + 6006*a^10 + 45045*a^8 + 145860*a^6 + 230945*a^4 + 176358*a^2 + 52003)*b^11*c^5*d^6 + 22*(45*a^14 + 1155*a^12 + 9009*a^10 + 32175*a^8 + 60775*a^6 + 62985*a^4 + 33915*a^2 + 7429)*b^9*c^4*d^7 + 99*(5*a^16 + 120*a^14 + 924*a^12 + 3432*a^10 + 7150*a^8 + 8840*a^6 + 6460*a^4 + 2584*a^2 + 437)*b^7*c^3*d^8 + 33*(5*a^18 + 105*a^16 + 756*a^14 + 2772*a^12 + 6006*a^10 + 8190*a^8 + 7140*a^6 + 3876*a^4 + 1197*a^2 + 161)*b^5*c^2*d^9 + 11*(3*a^20 + 50*a^18 + 315*a^16 + 1080*a^14 + 2310*a^12 + 3276*a^10 + 3150*a^8 + 2040*a^6 + 855*a^4 + 210*a^2 + 23)*b^3*c*d^10 + 3*(a^22 + 11*a^20 + 55*a^18 + 165*a^16 + 330*a^14 + 462*a^12 + 462*a^10 + 330*a^8 + 165*a^6 + 55*a^4 + 11*a^2 + 1)*b*d^11)*sqrt(c)*sqrt(d))) + 2*dilog(((a + I)*b*d*x + b^2*c + (I*b^2*x + (-I*a + 1)*b)*sqrt(c)*sqrt(d))/(b^2*c + 2*(-I*a + 1)*b*sqrt(c)*sqrt(d) - (a^2 + 2*I*a - 1)*d)) - 2*dilog(((a + I)*b*d*x + b^2*c - (I*b^2*x + (-I*a + 1)*b)*sqrt(c)*sqrt(d))/(b^2*c - 2*(-I*a + 1)*b*sqrt(c)*sqrt(d) - (a^2 + 2*I*a - 1)*d)) - 2*dilog(((a - I)*b*d*x + b^2*c + (I*b^2*x + (-I*a - 1)*b)*sqrt(c)*sqrt(d))/(b^2*c + 2*(-I*a - 1)*b*sqrt(c)*sqrt(d) - (a^2 - 2*I*a - 1)*d)) + 2*dilog(((a - I)*b*d*x + b^2*c - (I*b^2*x + (-I*a - 1)*b)*sqrt(c)*sqrt(d))/(b^2*c - 2*(-I*a - 1)*b*sqrt(c)*sqrt(d) - (a^2 - 2*I*a - 1)*d)))/b)/sqrt(c*d) + arctan(b*x + a)*arctan(d*x/sqrt(c*d))/sqrt(c*d) - arctan(d*x/sqrt(c*d))*arctan((b^2*x + a*b)/b)/sqrt(c*d)","B",0
54,1,284,0,0.530293," ","integrate(arctan(b*x+a)/(d*x+c),x, algorithm=""maxima"")","\frac{\arctan\left(b x + a\right) \log\left(d x + c\right)}{d} - \frac{\arctan\left(\frac{b^{2} x + a b}{b}\right) \log\left(d x + c\right)}{d} - \frac{\arctan\left(\frac{b d^{2} x + b c d}{b^{2} c^{2} - 2 \, a b c d + {\left(a^{2} + 1\right)} d^{2}}, \frac{b^{2} c^{2} - a b c d + {\left(b^{2} c d - a b d^{2}\right)} x}{b^{2} c^{2} - 2 \, a b c d + {\left(a^{2} + 1\right)} d^{2}}\right) \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right) - \arctan\left(b x + a\right) \log\left(\frac{b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}}{b^{2} c^{2} - 2 \, a b c d + {\left(a^{2} + 1\right)} d^{2}}\right) + i \, {\rm Li}_2\left(\frac{i \, b d x + {\left(i \, a + 1\right)} d}{-i \, b c + {\left(i \, a + 1\right)} d}\right) - i \, {\rm Li}_2\left(\frac{i \, b d x + {\left(i \, a - 1\right)} d}{-i \, b c + {\left(i \, a - 1\right)} d}\right)}{2 \, d}"," ",0,"arctan(b*x + a)*log(d*x + c)/d - arctan((b^2*x + a*b)/b)*log(d*x + c)/d - 1/2*(arctan2((b*d^2*x + b*c*d)/(b^2*c^2 - 2*a*b*c*d + (a^2 + 1)*d^2), (b^2*c^2 - a*b*c*d + (b^2*c*d - a*b*d^2)*x)/(b^2*c^2 - 2*a*b*c*d + (a^2 + 1)*d^2))*log(b^2*x^2 + 2*a*b*x + a^2 + 1) - arctan(b*x + a)*log((b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)/(b^2*c^2 - 2*a*b*c*d + (a^2 + 1)*d^2)) + I*dilog((I*b*d*x + (I*a + 1)*d)/(-I*b*c + (I*a + 1)*d)) - I*dilog((I*b*d*x + (I*a - 1)*d)/(-I*b*c + (I*a - 1)*d)))/d","B",0
55,1,284,0,0.551729," ","integrate(arctan(b*x+a)/(c+d/x),x, algorithm=""maxima"")","-\frac{b d \arctan\left(b x + a\right) \log\left(-\frac{b^{2} c^{2} x^{2} + 2 \, b^{2} c d x + b^{2} d^{2}}{2 \, a b c d - b^{2} d^{2} - {\left(a^{2} + 1\right)} c^{2}}\right) + i \, b d {\rm Li}_2\left(-\frac{i \, b c x + {\left(i \, a - 1\right)} c}{{\left(-i \, a + 1\right)} c + i \, b d}\right) - i \, b d {\rm Li}_2\left(-\frac{i \, b c x + {\left(i \, a + 1\right)} c}{{\left(-i \, a - 1\right)} c + i \, b d}\right) - 2 \, {\left(b c x + a c\right)} \arctan\left(b x + a\right) - {\left(b d \arctan\left(-\frac{b c^{2} x + b c d}{2 \, a b c d - b^{2} d^{2} - {\left(a^{2} + 1\right)} c^{2}}, \frac{a b c d - b^{2} d^{2} + {\left(a b c^{2} - b^{2} c d\right)} x}{2 \, a b c d - b^{2} d^{2} - {\left(a^{2} + 1\right)} c^{2}}\right) - c\right)} \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}{2 \, b c^{2}}"," ",0,"-1/2*(b*d*arctan(b*x + a)*log(-(b^2*c^2*x^2 + 2*b^2*c*d*x + b^2*d^2)/(2*a*b*c*d - b^2*d^2 - (a^2 + 1)*c^2)) + I*b*d*dilog(-(I*b*c*x + (I*a - 1)*c)/((-I*a + 1)*c + I*b*d)) - I*b*d*dilog(-(I*b*c*x + (I*a + 1)*c)/((-I*a - 1)*c + I*b*d)) - 2*(b*c*x + a*c)*arctan(b*x + a) - (b*d*arctan2(-(b*c^2*x + b*c*d)/(2*a*b*c*d - b^2*d^2 - (a^2 + 1)*c^2), (a*b*c*d - b^2*d^2 + (a*b*c^2 - b^2*c*d)*x)/(2*a*b*c*d - b^2*d^2 - (a^2 + 1)*c^2)) - c)*log(b^2*x^2 + 2*a*b*x + a^2 + 1))/(b*c^2)","A",0
56,1,8518,0,1.349219," ","integrate(arctan(b*x+a)/(c+d/x^2),x, algorithm=""maxima"")","-{\left(\frac{d \arctan\left(\frac{c x}{\sqrt{c d}}\right)}{\sqrt{c d} c} - \frac{x}{c}\right)} \arctan\left(b x + a\right) + \frac{8 \, a c \arctan\left(b x + a\right) + {\left(4 \, b \arctan\left(\frac{\sqrt{c} x}{\sqrt{d}}\right) \arctan\left(\frac{2 \, a b^{2} c d + {\left(a b^{3} d + {\left(a^{3} + a\right)} b c + {\left(b^{4} d + {\left(a^{2} + 3\right)} b^{2} c\right)} x\right)} \sqrt{c} \sqrt{d} + {\left(3 \, b^{3} c d + {\left(a^{2} + 1\right)} b c^{2}\right)} x}{b^{4} d^{2} + 2 \, {\left(a^{2} + 3\right)} b^{2} c d + {\left(a^{4} + 2 \, a^{2} + 1\right)} c^{2} + 4 \, {\left(b^{3} d + {\left(a^{2} + 1\right)} b c\right)} \sqrt{c} \sqrt{d}}, \frac{{\left(a^{2} + 3\right)} b^{2} c d + {\left(a^{4} + 2 \, a^{2} + 1\right)} c^{2} + {\left(2 \, a b^{2} c x + b^{3} d + 3 \, {\left(a^{2} + 1\right)} b c\right)} \sqrt{c} \sqrt{d} + {\left(a b^{3} c d + {\left(a^{3} + a\right)} b c^{2}\right)} x}{b^{4} d^{2} + 2 \, {\left(a^{2} + 3\right)} b^{2} c d + {\left(a^{4} + 2 \, a^{2} + 1\right)} c^{2} + 4 \, {\left(b^{3} d + {\left(a^{2} + 1\right)} b c\right)} \sqrt{c} \sqrt{d}}\right) + 4 \, b \arctan\left(\frac{\sqrt{c} x}{\sqrt{d}}\right) \arctan\left(\frac{2 \, a b^{2} c d - {\left(a b^{3} d + {\left(a^{3} + a\right)} b c + {\left(b^{4} d + {\left(a^{2} + 3\right)} b^{2} c\right)} x\right)} \sqrt{c} \sqrt{d} + {\left(3 \, b^{3} c d + {\left(a^{2} + 1\right)} b c^{2}\right)} x}{b^{4} d^{2} + 2 \, {\left(a^{2} + 3\right)} b^{2} c d + {\left(a^{4} + 2 \, a^{2} + 1\right)} c^{2} - 4 \, {\left(b^{3} d + {\left(a^{2} + 1\right)} b c\right)} \sqrt{c} \sqrt{d}}, \frac{{\left(a^{2} + 3\right)} b^{2} c d + {\left(a^{4} + 2 \, a^{2} + 1\right)} c^{2} - {\left(2 \, a b^{2} c x + b^{3} d + 3 \, {\left(a^{2} + 1\right)} b c\right)} \sqrt{c} \sqrt{d} + {\left(a b^{3} c d + {\left(a^{3} + a\right)} b c^{2}\right)} x}{b^{4} d^{2} + 2 \, {\left(a^{2} + 3\right)} b^{2} c d + {\left(a^{4} + 2 \, a^{2} + 1\right)} c^{2} - 4 \, {\left(b^{3} d + {\left(a^{2} + 1\right)} b c\right)} \sqrt{c} \sqrt{d}}\right) + b \log\left(c x^{2} + d\right) \log\left(\frac{{\left(a^{2} + 1\right)} b^{22} c d^{11} + 11 \, {\left(a^{4} + 22 \, a^{2} + 21\right)} b^{20} c^{2} d^{10} + 55 \, {\left(a^{6} + 39 \, a^{4} + 171 \, a^{2} + 133\right)} b^{18} c^{3} d^{9} + 33 \, {\left(5 \, a^{8} + 260 \, a^{6} + 1870 \, a^{4} + 3876 \, a^{2} + 2261\right)} b^{16} c^{4} d^{8} + 330 \, {\left(a^{10} + 61 \, a^{8} + 570 \, a^{6} + 1802 \, a^{4} + 2261 \, a^{2} + 969\right)} b^{14} c^{5} d^{7} + 22 \, {\left(21 \, a^{12} + 1386 \, a^{10} + 15015 \, a^{8} + 60060 \, a^{6} + 109395 \, a^{4} + 92378 \, a^{2} + 29393\right)} b^{12} c^{6} d^{6} + 22 \, {\left(21 \, a^{14} + 1407 \, a^{12} + 16401 \, a^{10} + 75075 \, a^{8} + 169455 \, a^{6} + 201773 \, a^{4} + 121771 \, a^{2} + 29393\right)} b^{10} c^{7} d^{5} + 330 \, {\left(a^{16} + 64 \, a^{14} + 756 \, a^{12} + 3696 \, a^{10} + 9438 \, a^{8} + 13728 \, a^{6} + 11492 \, a^{4} + 5168 \, a^{2} + 969\right)} b^{8} c^{8} d^{4} + 33 \, {\left(5 \, a^{18} + 285 \, a^{16} + 3220 \, a^{14} + 15876 \, a^{12} + 42966 \, a^{10} + 70070 \, a^{8} + 70980 \, a^{6} + 43860 \, a^{4} + 15181 \, a^{2} + 2261\right)} b^{6} c^{9} d^{3} + 55 \, {\left(a^{20} + 46 \, a^{18} + 465 \, a^{16} + 2184 \, a^{14} + 5922 \, a^{12} + 10164 \, a^{10} + 11466 \, a^{8} + 8520 \, a^{6} + 4029 \, a^{4} + 1102 \, a^{2} + 133\right)} b^{4} c^{10} d^{2} + 11 \, {\left(a^{22} + 31 \, a^{20} + 255 \, a^{18} + 1065 \, a^{16} + 2730 \, a^{14} + 4662 \, a^{12} + 5502 \, a^{10} + 4530 \, a^{8} + 2565 \, a^{6} + 955 \, a^{4} + 211 \, a^{2} + 21\right)} b^{2} c^{11} d + {\left(a^{24} + 12 \, a^{22} + 66 \, a^{20} + 220 \, a^{18} + 495 \, a^{16} + 792 \, a^{14} + 924 \, a^{12} + 792 \, a^{10} + 495 \, a^{8} + 220 \, a^{6} + 66 \, a^{4} + 12 \, a^{2} + 1\right)} c^{12} + {\left(b^{24} c d^{11} + 11 \, {\left(a^{2} + 21\right)} b^{22} c^{2} d^{10} + 55 \, {\left(a^{4} + 38 \, a^{2} + 133\right)} b^{20} c^{3} d^{9} + 33 \, {\left(5 \, a^{6} + 255 \, a^{4} + 1615 \, a^{2} + 2261\right)} b^{18} c^{4} d^{8} + 330 \, {\left(a^{8} + 60 \, a^{6} + 510 \, a^{4} + 1292 \, a^{2} + 969\right)} b^{16} c^{5} d^{7} + 22 \, {\left(21 \, a^{10} + 1365 \, a^{8} + 13650 \, a^{6} + 46410 \, a^{4} + 62985 \, a^{2} + 29393\right)} b^{14} c^{6} d^{6} + 22 \, {\left(21 \, a^{12} + 1386 \, a^{10} + 15015 \, a^{8} + 60060 \, a^{6} + 109395 \, a^{4} + 92378 \, a^{2} + 29393\right)} b^{12} c^{7} d^{5} + 330 \, {\left(a^{14} + 63 \, a^{12} + 693 \, a^{10} + 3003 \, a^{8} + 6435 \, a^{6} + 7293 \, a^{4} + 4199 \, a^{2} + 969\right)} b^{10} c^{8} d^{4} + 33 \, {\left(5 \, a^{16} + 280 \, a^{14} + 2940 \, a^{12} + 12936 \, a^{10} + 30030 \, a^{8} + 40040 \, a^{6} + 30940 \, a^{4} + 12920 \, a^{2} + 2261\right)} b^{8} c^{9} d^{3} + 55 \, {\left(a^{18} + 45 \, a^{16} + 420 \, a^{14} + 1764 \, a^{12} + 4158 \, a^{10} + 6006 \, a^{8} + 5460 \, a^{6} + 3060 \, a^{4} + 969 \, a^{2} + 133\right)} b^{6} c^{10} d^{2} + 11 \, {\left(a^{20} + 30 \, a^{18} + 225 \, a^{16} + 840 \, a^{14} + 1890 \, a^{12} + 2772 \, a^{10} + 2730 \, a^{8} + 1800 \, a^{6} + 765 \, a^{4} + 190 \, a^{2} + 21\right)} b^{4} c^{11} d + {\left(a^{22} + 11 \, a^{20} + 55 \, a^{18} + 165 \, a^{16} + 330 \, a^{14} + 462 \, a^{12} + 462 \, a^{10} + 330 \, a^{8} + 165 \, a^{6} + 55 \, a^{4} + 11 \, a^{2} + 1\right)} b^{2} c^{12}\right)} x^{2} + 2 \, {\left(11 \, {\left(a^{2} + 1\right)} b^{21} c d^{10} + 110 \, {\left(a^{4} + 8 \, a^{2} + 7\right)} b^{19} c^{2} d^{9} + 33 \, {\left(15 \, a^{6} + 205 \, a^{4} + 589 \, a^{2} + 399\right)} b^{17} c^{3} d^{8} + 264 \, {\left(5 \, a^{8} + 90 \, a^{6} + 408 \, a^{4} + 646 \, a^{2} + 323\right)} b^{15} c^{4} d^{7} + 110 \, {\left(21 \, a^{10} + 441 \, a^{8} + 2562 \, a^{6} + 6018 \, a^{4} + 6137 \, a^{2} + 2261\right)} b^{13} c^{5} d^{6} + 4 \, {\left(693 \, a^{12} + 15708 \, a^{10} + 105105 \, a^{8} + 308880 \, a^{6} + 449735 \, a^{4} + 319124 \, a^{2} + 88179\right)} b^{11} c^{6} d^{5} + 110 \, {\left(21 \, a^{14} + 483 \, a^{12} + 3465 \, a^{10} + 11583 \, a^{8} + 20735 \, a^{6} + 20553 \, a^{4} + 10659 \, a^{2} + 2261\right)} b^{9} c^{7} d^{4} + 264 \, {\left(5 \, a^{16} + 110 \, a^{14} + 798 \, a^{12} + 2838 \, a^{10} + 5720 \, a^{8} + 6890 \, a^{6} + 4930 \, a^{4} + 1938 \, a^{2} + 323\right)} b^{7} c^{8} d^{3} + 33 \, {\left(15 \, a^{18} + 295 \, a^{16} + 2044 \, a^{14} + 7308 \, a^{12} + 15554 \, a^{10} + 20930 \, a^{8} + 18060 \, a^{6} + 9724 \, a^{4} + 2983 \, a^{2} + 399\right)} b^{5} c^{9} d^{2} + 110 \, {\left(a^{20} + 16 \, a^{18} + 99 \, a^{16} + 336 \, a^{14} + 714 \, a^{12} + 1008 \, a^{10} + 966 \, a^{8} + 624 \, a^{6} + 261 \, a^{4} + 64 \, a^{2} + 7\right)} b^{3} c^{10} d + 11 \, {\left(a^{22} + 11 \, a^{20} + 55 \, a^{18} + 165 \, a^{16} + 330 \, a^{14} + 462 \, a^{12} + 462 \, a^{10} + 330 \, a^{8} + 165 \, a^{6} + 55 \, a^{4} + 11 \, a^{2} + 1\right)} b c^{11} + {\left(11 \, b^{23} c d^{10} + 110 \, {\left(a^{2} + 7\right)} b^{21} c^{2} d^{9} + 33 \, {\left(15 \, a^{4} + 190 \, a^{2} + 399\right)} b^{19} c^{3} d^{8} + 264 \, {\left(5 \, a^{6} + 85 \, a^{4} + 323 \, a^{2} + 323\right)} b^{17} c^{4} d^{7} + 110 \, {\left(21 \, a^{8} + 420 \, a^{6} + 2142 \, a^{4} + 3876 \, a^{2} + 2261\right)} b^{15} c^{5} d^{6} + 4 \, {\left(693 \, a^{10} + 15015 \, a^{8} + 90090 \, a^{6} + 218790 \, a^{4} + 230945 \, a^{2} + 88179\right)} b^{13} c^{6} d^{5} + 110 \, {\left(21 \, a^{12} + 462 \, a^{10} + 3003 \, a^{8} + 8580 \, a^{6} + 12155 \, a^{4} + 8398 \, a^{2} + 2261\right)} b^{11} c^{7} d^{4} + 264 \, {\left(5 \, a^{14} + 105 \, a^{12} + 693 \, a^{10} + 2145 \, a^{8} + 3575 \, a^{6} + 3315 \, a^{4} + 1615 \, a^{2} + 323\right)} b^{9} c^{8} d^{3} + 33 \, {\left(15 \, a^{16} + 280 \, a^{14} + 1764 \, a^{12} + 5544 \, a^{10} + 10010 \, a^{8} + 10920 \, a^{6} + 7140 \, a^{4} + 2584 \, a^{2} + 399\right)} b^{7} c^{9} d^{2} + 110 \, {\left(a^{18} + 15 \, a^{16} + 84 \, a^{14} + 252 \, a^{12} + 462 \, a^{10} + 546 \, a^{8} + 420 \, a^{6} + 204 \, a^{4} + 57 \, a^{2} + 7\right)} b^{5} c^{10} d + 11 \, {\left(a^{20} + 10 \, a^{18} + 45 \, a^{16} + 120 \, a^{14} + 210 \, a^{12} + 252 \, a^{10} + 210 \, a^{8} + 120 \, a^{6} + 45 \, a^{4} + 10 \, a^{2} + 1\right)} b^{3} c^{11}\right)} x^{2} + 2 \, {\left(11 \, a b^{22} c d^{10} + 110 \, {\left(a^{3} + 7 \, a\right)} b^{20} c^{2} d^{9} + 33 \, {\left(15 \, a^{5} + 190 \, a^{3} + 399 \, a\right)} b^{18} c^{3} d^{8} + 264 \, {\left(5 \, a^{7} + 85 \, a^{5} + 323 \, a^{3} + 323 \, a\right)} b^{16} c^{4} d^{7} + 110 \, {\left(21 \, a^{9} + 420 \, a^{7} + 2142 \, a^{5} + 3876 \, a^{3} + 2261 \, a\right)} b^{14} c^{5} d^{6} + 4 \, {\left(693 \, a^{11} + 15015 \, a^{9} + 90090 \, a^{7} + 218790 \, a^{5} + 230945 \, a^{3} + 88179 \, a\right)} b^{12} c^{6} d^{5} + 110 \, {\left(21 \, a^{13} + 462 \, a^{11} + 3003 \, a^{9} + 8580 \, a^{7} + 12155 \, a^{5} + 8398 \, a^{3} + 2261 \, a\right)} b^{10} c^{7} d^{4} + 264 \, {\left(5 \, a^{15} + 105 \, a^{13} + 693 \, a^{11} + 2145 \, a^{9} + 3575 \, a^{7} + 3315 \, a^{5} + 1615 \, a^{3} + 323 \, a\right)} b^{8} c^{8} d^{3} + 33 \, {\left(15 \, a^{17} + 280 \, a^{15} + 1764 \, a^{13} + 5544 \, a^{11} + 10010 \, a^{9} + 10920 \, a^{7} + 7140 \, a^{5} + 2584 \, a^{3} + 399 \, a\right)} b^{6} c^{9} d^{2} + 110 \, {\left(a^{19} + 15 \, a^{17} + 84 \, a^{15} + 252 \, a^{13} + 462 \, a^{11} + 546 \, a^{9} + 420 \, a^{7} + 204 \, a^{5} + 57 \, a^{3} + 7 \, a\right)} b^{4} c^{10} d + 11 \, {\left(a^{21} + 10 \, a^{19} + 45 \, a^{17} + 120 \, a^{15} + 210 \, a^{13} + 252 \, a^{11} + 210 \, a^{9} + 120 \, a^{7} + 45 \, a^{5} + 10 \, a^{3} + a\right)} b^{2} c^{11}\right)} x\right)} \sqrt{c} \sqrt{d} + 2 \, {\left(a b^{23} c d^{11} + 11 \, {\left(a^{3} + 21 \, a\right)} b^{21} c^{2} d^{10} + 55 \, {\left(a^{5} + 38 \, a^{3} + 133 \, a\right)} b^{19} c^{3} d^{9} + 33 \, {\left(5 \, a^{7} + 255 \, a^{5} + 1615 \, a^{3} + 2261 \, a\right)} b^{17} c^{4} d^{8} + 330 \, {\left(a^{9} + 60 \, a^{7} + 510 \, a^{5} + 1292 \, a^{3} + 969 \, a\right)} b^{15} c^{5} d^{7} + 22 \, {\left(21 \, a^{11} + 1365 \, a^{9} + 13650 \, a^{7} + 46410 \, a^{5} + 62985 \, a^{3} + 29393 \, a\right)} b^{13} c^{6} d^{6} + 22 \, {\left(21 \, a^{13} + 1386 \, a^{11} + 15015 \, a^{9} + 60060 \, a^{7} + 109395 \, a^{5} + 92378 \, a^{3} + 29393 \, a\right)} b^{11} c^{7} d^{5} + 330 \, {\left(a^{15} + 63 \, a^{13} + 693 \, a^{11} + 3003 \, a^{9} + 6435 \, a^{7} + 7293 \, a^{5} + 4199 \, a^{3} + 969 \, a\right)} b^{9} c^{8} d^{4} + 33 \, {\left(5 \, a^{17} + 280 \, a^{15} + 2940 \, a^{13} + 12936 \, a^{11} + 30030 \, a^{9} + 40040 \, a^{7} + 30940 \, a^{5} + 12920 \, a^{3} + 2261 \, a\right)} b^{7} c^{9} d^{3} + 55 \, {\left(a^{19} + 45 \, a^{17} + 420 \, a^{15} + 1764 \, a^{13} + 4158 \, a^{11} + 6006 \, a^{9} + 5460 \, a^{7} + 3060 \, a^{5} + 969 \, a^{3} + 133 \, a\right)} b^{5} c^{10} d^{2} + 11 \, {\left(a^{21} + 30 \, a^{19} + 225 \, a^{17} + 840 \, a^{15} + 1890 \, a^{13} + 2772 \, a^{11} + 2730 \, a^{9} + 1800 \, a^{7} + 765 \, a^{5} + 190 \, a^{3} + 21 \, a\right)} b^{3} c^{11} d + {\left(a^{23} + 11 \, a^{21} + 55 \, a^{19} + 165 \, a^{17} + 330 \, a^{15} + 462 \, a^{13} + 462 \, a^{11} + 330 \, a^{9} + 165 \, a^{7} + 55 \, a^{5} + 11 \, a^{3} + a\right)} b c^{12}\right)} x}{b^{24} d^{12} + 12 \, {\left(a^{2} + 23\right)} b^{22} c d^{11} + 66 \, {\left(a^{4} + 42 \, a^{2} + 161\right)} b^{20} c^{2} d^{10} + 44 \, {\left(5 \, a^{6} + 285 \, a^{4} + 1995 \, a^{2} + 3059\right)} b^{18} c^{3} d^{9} + 99 \, {\left(5 \, a^{8} + 340 \, a^{6} + 3230 \, a^{4} + 9044 \, a^{2} + 7429\right)} b^{16} c^{4} d^{8} + 264 \, {\left(3 \, a^{10} + 225 \, a^{8} + 2550 \, a^{6} + 9690 \, a^{4} + 14535 \, a^{2} + 7429\right)} b^{14} c^{5} d^{7} + 4 \, {\left(231 \, a^{12} + 18018 \, a^{10} + 225225 \, a^{8} + 1021020 \, a^{6} + 2078505 \, a^{4} + 1939938 \, a^{2} + 676039\right)} b^{12} c^{6} d^{6} + 264 \, {\left(3 \, a^{14} + 231 \, a^{12} + 3003 \, a^{10} + 15015 \, a^{8} + 36465 \, a^{6} + 46189 \, a^{4} + 29393 \, a^{2} + 7429\right)} b^{10} c^{7} d^{5} + 99 \, {\left(5 \, a^{16} + 360 \, a^{14} + 4620 \, a^{12} + 24024 \, a^{10} + 64350 \, a^{8} + 97240 \, a^{6} + 83980 \, a^{4} + 38760 \, a^{2} + 7429\right)} b^{8} c^{8} d^{4} + 44 \, {\left(5 \, a^{18} + 315 \, a^{16} + 3780 \, a^{14} + 19404 \, a^{12} + 54054 \, a^{10} + 90090 \, a^{8} + 92820 \, a^{6} + 58140 \, a^{4} + 20349 \, a^{2} + 3059\right)} b^{6} c^{9} d^{3} + 66 \, {\left(a^{20} + 50 \, a^{18} + 525 \, a^{16} + 2520 \, a^{14} + 6930 \, a^{12} + 12012 \, a^{10} + 13650 \, a^{8} + 10200 \, a^{6} + 4845 \, a^{4} + 1330 \, a^{2} + 161\right)} b^{4} c^{10} d^{2} + 12 \, {\left(a^{22} + 33 \, a^{20} + 275 \, a^{18} + 1155 \, a^{16} + 2970 \, a^{14} + 5082 \, a^{12} + 6006 \, a^{10} + 4950 \, a^{8} + 2805 \, a^{6} + 1045 \, a^{4} + 231 \, a^{2} + 23\right)} b^{2} c^{11} d + {\left(a^{24} + 12 \, a^{22} + 66 \, a^{20} + 220 \, a^{18} + 495 \, a^{16} + 792 \, a^{14} + 924 \, a^{12} + 792 \, a^{10} + 495 \, a^{8} + 220 \, a^{6} + 66 \, a^{4} + 12 \, a^{2} + 1\right)} c^{12} + 8 \, {\left(3 \, b^{23} d^{11} + 11 \, {\left(3 \, a^{2} + 23\right)} b^{21} c d^{10} + 33 \, {\left(5 \, a^{4} + 70 \, a^{2} + 161\right)} b^{19} c^{2} d^{9} + 99 \, {\left(5 \, a^{6} + 95 \, a^{4} + 399 \, a^{2} + 437\right)} b^{17} c^{3} d^{8} + 22 \, {\left(45 \, a^{8} + 1020 \, a^{6} + 5814 \, a^{4} + 11628 \, a^{2} + 7429\right)} b^{15} c^{4} d^{7} + 6 \, {\left(231 \, a^{10} + 5775 \, a^{8} + 39270 \, a^{6} + 106590 \, a^{4} + 124355 \, a^{2} + 52003\right)} b^{13} c^{5} d^{6} + 6 \, {\left(231 \, a^{12} + 6006 \, a^{10} + 45045 \, a^{8} + 145860 \, a^{6} + 230945 \, a^{4} + 176358 \, a^{2} + 52003\right)} b^{11} c^{6} d^{5} + 22 \, {\left(45 \, a^{14} + 1155 \, a^{12} + 9009 \, a^{10} + 32175 \, a^{8} + 60775 \, a^{6} + 62985 \, a^{4} + 33915 \, a^{2} + 7429\right)} b^{9} c^{7} d^{4} + 99 \, {\left(5 \, a^{16} + 120 \, a^{14} + 924 \, a^{12} + 3432 \, a^{10} + 7150 \, a^{8} + 8840 \, a^{6} + 6460 \, a^{4} + 2584 \, a^{2} + 437\right)} b^{7} c^{8} d^{3} + 33 \, {\left(5 \, a^{18} + 105 \, a^{16} + 756 \, a^{14} + 2772 \, a^{12} + 6006 \, a^{10} + 8190 \, a^{8} + 7140 \, a^{6} + 3876 \, a^{4} + 1197 \, a^{2} + 161\right)} b^{5} c^{9} d^{2} + 11 \, {\left(3 \, a^{20} + 50 \, a^{18} + 315 \, a^{16} + 1080 \, a^{14} + 2310 \, a^{12} + 3276 \, a^{10} + 3150 \, a^{8} + 2040 \, a^{6} + 855 \, a^{4} + 210 \, a^{2} + 23\right)} b^{3} c^{10} d + 3 \, {\left(a^{22} + 11 \, a^{20} + 55 \, a^{18} + 165 \, a^{16} + 330 \, a^{14} + 462 \, a^{12} + 462 \, a^{10} + 330 \, a^{8} + 165 \, a^{6} + 55 \, a^{4} + 11 \, a^{2} + 1\right)} b c^{11}\right)} \sqrt{c} \sqrt{d}}\right) - b \log\left(c x^{2} + d\right) \log\left(\frac{{\left(a^{2} + 1\right)} b^{22} c d^{11} + 11 \, {\left(a^{4} + 22 \, a^{2} + 21\right)} b^{20} c^{2} d^{10} + 55 \, {\left(a^{6} + 39 \, a^{4} + 171 \, a^{2} + 133\right)} b^{18} c^{3} d^{9} + 33 \, {\left(5 \, a^{8} + 260 \, a^{6} + 1870 \, a^{4} + 3876 \, a^{2} + 2261\right)} b^{16} c^{4} d^{8} + 330 \, {\left(a^{10} + 61 \, a^{8} + 570 \, a^{6} + 1802 \, a^{4} + 2261 \, a^{2} + 969\right)} b^{14} c^{5} d^{7} + 22 \, {\left(21 \, a^{12} + 1386 \, a^{10} + 15015 \, a^{8} + 60060 \, a^{6} + 109395 \, a^{4} + 92378 \, a^{2} + 29393\right)} b^{12} c^{6} d^{6} + 22 \, {\left(21 \, a^{14} + 1407 \, a^{12} + 16401 \, a^{10} + 75075 \, a^{8} + 169455 \, a^{6} + 201773 \, a^{4} + 121771 \, a^{2} + 29393\right)} b^{10} c^{7} d^{5} + 330 \, {\left(a^{16} + 64 \, a^{14} + 756 \, a^{12} + 3696 \, a^{10} + 9438 \, a^{8} + 13728 \, a^{6} + 11492 \, a^{4} + 5168 \, a^{2} + 969\right)} b^{8} c^{8} d^{4} + 33 \, {\left(5 \, a^{18} + 285 \, a^{16} + 3220 \, a^{14} + 15876 \, a^{12} + 42966 \, a^{10} + 70070 \, a^{8} + 70980 \, a^{6} + 43860 \, a^{4} + 15181 \, a^{2} + 2261\right)} b^{6} c^{9} d^{3} + 55 \, {\left(a^{20} + 46 \, a^{18} + 465 \, a^{16} + 2184 \, a^{14} + 5922 \, a^{12} + 10164 \, a^{10} + 11466 \, a^{8} + 8520 \, a^{6} + 4029 \, a^{4} + 1102 \, a^{2} + 133\right)} b^{4} c^{10} d^{2} + 11 \, {\left(a^{22} + 31 \, a^{20} + 255 \, a^{18} + 1065 \, a^{16} + 2730 \, a^{14} + 4662 \, a^{12} + 5502 \, a^{10} + 4530 \, a^{8} + 2565 \, a^{6} + 955 \, a^{4} + 211 \, a^{2} + 21\right)} b^{2} c^{11} d + {\left(a^{24} + 12 \, a^{22} + 66 \, a^{20} + 220 \, a^{18} + 495 \, a^{16} + 792 \, a^{14} + 924 \, a^{12} + 792 \, a^{10} + 495 \, a^{8} + 220 \, a^{6} + 66 \, a^{4} + 12 \, a^{2} + 1\right)} c^{12} + {\left(b^{24} c d^{11} + 11 \, {\left(a^{2} + 21\right)} b^{22} c^{2} d^{10} + 55 \, {\left(a^{4} + 38 \, a^{2} + 133\right)} b^{20} c^{3} d^{9} + 33 \, {\left(5 \, a^{6} + 255 \, a^{4} + 1615 \, a^{2} + 2261\right)} b^{18} c^{4} d^{8} + 330 \, {\left(a^{8} + 60 \, a^{6} + 510 \, a^{4} + 1292 \, a^{2} + 969\right)} b^{16} c^{5} d^{7} + 22 \, {\left(21 \, a^{10} + 1365 \, a^{8} + 13650 \, a^{6} + 46410 \, a^{4} + 62985 \, a^{2} + 29393\right)} b^{14} c^{6} d^{6} + 22 \, {\left(21 \, a^{12} + 1386 \, a^{10} + 15015 \, a^{8} + 60060 \, a^{6} + 109395 \, a^{4} + 92378 \, a^{2} + 29393\right)} b^{12} c^{7} d^{5} + 330 \, {\left(a^{14} + 63 \, a^{12} + 693 \, a^{10} + 3003 \, a^{8} + 6435 \, a^{6} + 7293 \, a^{4} + 4199 \, a^{2} + 969\right)} b^{10} c^{8} d^{4} + 33 \, {\left(5 \, a^{16} + 280 \, a^{14} + 2940 \, a^{12} + 12936 \, a^{10} + 30030 \, a^{8} + 40040 \, a^{6} + 30940 \, a^{4} + 12920 \, a^{2} + 2261\right)} b^{8} c^{9} d^{3} + 55 \, {\left(a^{18} + 45 \, a^{16} + 420 \, a^{14} + 1764 \, a^{12} + 4158 \, a^{10} + 6006 \, a^{8} + 5460 \, a^{6} + 3060 \, a^{4} + 969 \, a^{2} + 133\right)} b^{6} c^{10} d^{2} + 11 \, {\left(a^{20} + 30 \, a^{18} + 225 \, a^{16} + 840 \, a^{14} + 1890 \, a^{12} + 2772 \, a^{10} + 2730 \, a^{8} + 1800 \, a^{6} + 765 \, a^{4} + 190 \, a^{2} + 21\right)} b^{4} c^{11} d + {\left(a^{22} + 11 \, a^{20} + 55 \, a^{18} + 165 \, a^{16} + 330 \, a^{14} + 462 \, a^{12} + 462 \, a^{10} + 330 \, a^{8} + 165 \, a^{6} + 55 \, a^{4} + 11 \, a^{2} + 1\right)} b^{2} c^{12}\right)} x^{2} - 2 \, {\left(11 \, {\left(a^{2} + 1\right)} b^{21} c d^{10} + 110 \, {\left(a^{4} + 8 \, a^{2} + 7\right)} b^{19} c^{2} d^{9} + 33 \, {\left(15 \, a^{6} + 205 \, a^{4} + 589 \, a^{2} + 399\right)} b^{17} c^{3} d^{8} + 264 \, {\left(5 \, a^{8} + 90 \, a^{6} + 408 \, a^{4} + 646 \, a^{2} + 323\right)} b^{15} c^{4} d^{7} + 110 \, {\left(21 \, a^{10} + 441 \, a^{8} + 2562 \, a^{6} + 6018 \, a^{4} + 6137 \, a^{2} + 2261\right)} b^{13} c^{5} d^{6} + 4 \, {\left(693 \, a^{12} + 15708 \, a^{10} + 105105 \, a^{8} + 308880 \, a^{6} + 449735 \, a^{4} + 319124 \, a^{2} + 88179\right)} b^{11} c^{6} d^{5} + 110 \, {\left(21 \, a^{14} + 483 \, a^{12} + 3465 \, a^{10} + 11583 \, a^{8} + 20735 \, a^{6} + 20553 \, a^{4} + 10659 \, a^{2} + 2261\right)} b^{9} c^{7} d^{4} + 264 \, {\left(5 \, a^{16} + 110 \, a^{14} + 798 \, a^{12} + 2838 \, a^{10} + 5720 \, a^{8} + 6890 \, a^{6} + 4930 \, a^{4} + 1938 \, a^{2} + 323\right)} b^{7} c^{8} d^{3} + 33 \, {\left(15 \, a^{18} + 295 \, a^{16} + 2044 \, a^{14} + 7308 \, a^{12} + 15554 \, a^{10} + 20930 \, a^{8} + 18060 \, a^{6} + 9724 \, a^{4} + 2983 \, a^{2} + 399\right)} b^{5} c^{9} d^{2} + 110 \, {\left(a^{20} + 16 \, a^{18} + 99 \, a^{16} + 336 \, a^{14} + 714 \, a^{12} + 1008 \, a^{10} + 966 \, a^{8} + 624 \, a^{6} + 261 \, a^{4} + 64 \, a^{2} + 7\right)} b^{3} c^{10} d + 11 \, {\left(a^{22} + 11 \, a^{20} + 55 \, a^{18} + 165 \, a^{16} + 330 \, a^{14} + 462 \, a^{12} + 462 \, a^{10} + 330 \, a^{8} + 165 \, a^{6} + 55 \, a^{4} + 11 \, a^{2} + 1\right)} b c^{11} + {\left(11 \, b^{23} c d^{10} + 110 \, {\left(a^{2} + 7\right)} b^{21} c^{2} d^{9} + 33 \, {\left(15 \, a^{4} + 190 \, a^{2} + 399\right)} b^{19} c^{3} d^{8} + 264 \, {\left(5 \, a^{6} + 85 \, a^{4} + 323 \, a^{2} + 323\right)} b^{17} c^{4} d^{7} + 110 \, {\left(21 \, a^{8} + 420 \, a^{6} + 2142 \, a^{4} + 3876 \, a^{2} + 2261\right)} b^{15} c^{5} d^{6} + 4 \, {\left(693 \, a^{10} + 15015 \, a^{8} + 90090 \, a^{6} + 218790 \, a^{4} + 230945 \, a^{2} + 88179\right)} b^{13} c^{6} d^{5} + 110 \, {\left(21 \, a^{12} + 462 \, a^{10} + 3003 \, a^{8} + 8580 \, a^{6} + 12155 \, a^{4} + 8398 \, a^{2} + 2261\right)} b^{11} c^{7} d^{4} + 264 \, {\left(5 \, a^{14} + 105 \, a^{12} + 693 \, a^{10} + 2145 \, a^{8} + 3575 \, a^{6} + 3315 \, a^{4} + 1615 \, a^{2} + 323\right)} b^{9} c^{8} d^{3} + 33 \, {\left(15 \, a^{16} + 280 \, a^{14} + 1764 \, a^{12} + 5544 \, a^{10} + 10010 \, a^{8} + 10920 \, a^{6} + 7140 \, a^{4} + 2584 \, a^{2} + 399\right)} b^{7} c^{9} d^{2} + 110 \, {\left(a^{18} + 15 \, a^{16} + 84 \, a^{14} + 252 \, a^{12} + 462 \, a^{10} + 546 \, a^{8} + 420 \, a^{6} + 204 \, a^{4} + 57 \, a^{2} + 7\right)} b^{5} c^{10} d + 11 \, {\left(a^{20} + 10 \, a^{18} + 45 \, a^{16} + 120 \, a^{14} + 210 \, a^{12} + 252 \, a^{10} + 210 \, a^{8} + 120 \, a^{6} + 45 \, a^{4} + 10 \, a^{2} + 1\right)} b^{3} c^{11}\right)} x^{2} + 2 \, {\left(11 \, a b^{22} c d^{10} + 110 \, {\left(a^{3} + 7 \, a\right)} b^{20} c^{2} d^{9} + 33 \, {\left(15 \, a^{5} + 190 \, a^{3} + 399 \, a\right)} b^{18} c^{3} d^{8} + 264 \, {\left(5 \, a^{7} + 85 \, a^{5} + 323 \, a^{3} + 323 \, a\right)} b^{16} c^{4} d^{7} + 110 \, {\left(21 \, a^{9} + 420 \, a^{7} + 2142 \, a^{5} + 3876 \, a^{3} + 2261 \, a\right)} b^{14} c^{5} d^{6} + 4 \, {\left(693 \, a^{11} + 15015 \, a^{9} + 90090 \, a^{7} + 218790 \, a^{5} + 230945 \, a^{3} + 88179 \, a\right)} b^{12} c^{6} d^{5} + 110 \, {\left(21 \, a^{13} + 462 \, a^{11} + 3003 \, a^{9} + 8580 \, a^{7} + 12155 \, a^{5} + 8398 \, a^{3} + 2261 \, a\right)} b^{10} c^{7} d^{4} + 264 \, {\left(5 \, a^{15} + 105 \, a^{13} + 693 \, a^{11} + 2145 \, a^{9} + 3575 \, a^{7} + 3315 \, a^{5} + 1615 \, a^{3} + 323 \, a\right)} b^{8} c^{8} d^{3} + 33 \, {\left(15 \, a^{17} + 280 \, a^{15} + 1764 \, a^{13} + 5544 \, a^{11} + 10010 \, a^{9} + 10920 \, a^{7} + 7140 \, a^{5} + 2584 \, a^{3} + 399 \, a\right)} b^{6} c^{9} d^{2} + 110 \, {\left(a^{19} + 15 \, a^{17} + 84 \, a^{15} + 252 \, a^{13} + 462 \, a^{11} + 546 \, a^{9} + 420 \, a^{7} + 204 \, a^{5} + 57 \, a^{3} + 7 \, a\right)} b^{4} c^{10} d + 11 \, {\left(a^{21} + 10 \, a^{19} + 45 \, a^{17} + 120 \, a^{15} + 210 \, a^{13} + 252 \, a^{11} + 210 \, a^{9} + 120 \, a^{7} + 45 \, a^{5} + 10 \, a^{3} + a\right)} b^{2} c^{11}\right)} x\right)} \sqrt{c} \sqrt{d} + 2 \, {\left(a b^{23} c d^{11} + 11 \, {\left(a^{3} + 21 \, a\right)} b^{21} c^{2} d^{10} + 55 \, {\left(a^{5} + 38 \, a^{3} + 133 \, a\right)} b^{19} c^{3} d^{9} + 33 \, {\left(5 \, a^{7} + 255 \, a^{5} + 1615 \, a^{3} + 2261 \, a\right)} b^{17} c^{4} d^{8} + 330 \, {\left(a^{9} + 60 \, a^{7} + 510 \, a^{5} + 1292 \, a^{3} + 969 \, a\right)} b^{15} c^{5} d^{7} + 22 \, {\left(21 \, a^{11} + 1365 \, a^{9} + 13650 \, a^{7} + 46410 \, a^{5} + 62985 \, a^{3} + 29393 \, a\right)} b^{13} c^{6} d^{6} + 22 \, {\left(21 \, a^{13} + 1386 \, a^{11} + 15015 \, a^{9} + 60060 \, a^{7} + 109395 \, a^{5} + 92378 \, a^{3} + 29393 \, a\right)} b^{11} c^{7} d^{5} + 330 \, {\left(a^{15} + 63 \, a^{13} + 693 \, a^{11} + 3003 \, a^{9} + 6435 \, a^{7} + 7293 \, a^{5} + 4199 \, a^{3} + 969 \, a\right)} b^{9} c^{8} d^{4} + 33 \, {\left(5 \, a^{17} + 280 \, a^{15} + 2940 \, a^{13} + 12936 \, a^{11} + 30030 \, a^{9} + 40040 \, a^{7} + 30940 \, a^{5} + 12920 \, a^{3} + 2261 \, a\right)} b^{7} c^{9} d^{3} + 55 \, {\left(a^{19} + 45 \, a^{17} + 420 \, a^{15} + 1764 \, a^{13} + 4158 \, a^{11} + 6006 \, a^{9} + 5460 \, a^{7} + 3060 \, a^{5} + 969 \, a^{3} + 133 \, a\right)} b^{5} c^{10} d^{2} + 11 \, {\left(a^{21} + 30 \, a^{19} + 225 \, a^{17} + 840 \, a^{15} + 1890 \, a^{13} + 2772 \, a^{11} + 2730 \, a^{9} + 1800 \, a^{7} + 765 \, a^{5} + 190 \, a^{3} + 21 \, a\right)} b^{3} c^{11} d + {\left(a^{23} + 11 \, a^{21} + 55 \, a^{19} + 165 \, a^{17} + 330 \, a^{15} + 462 \, a^{13} + 462 \, a^{11} + 330 \, a^{9} + 165 \, a^{7} + 55 \, a^{5} + 11 \, a^{3} + a\right)} b c^{12}\right)} x}{b^{24} d^{12} + 12 \, {\left(a^{2} + 23\right)} b^{22} c d^{11} + 66 \, {\left(a^{4} + 42 \, a^{2} + 161\right)} b^{20} c^{2} d^{10} + 44 \, {\left(5 \, a^{6} + 285 \, a^{4} + 1995 \, a^{2} + 3059\right)} b^{18} c^{3} d^{9} + 99 \, {\left(5 \, a^{8} + 340 \, a^{6} + 3230 \, a^{4} + 9044 \, a^{2} + 7429\right)} b^{16} c^{4} d^{8} + 264 \, {\left(3 \, a^{10} + 225 \, a^{8} + 2550 \, a^{6} + 9690 \, a^{4} + 14535 \, a^{2} + 7429\right)} b^{14} c^{5} d^{7} + 4 \, {\left(231 \, a^{12} + 18018 \, a^{10} + 225225 \, a^{8} + 1021020 \, a^{6} + 2078505 \, a^{4} + 1939938 \, a^{2} + 676039\right)} b^{12} c^{6} d^{6} + 264 \, {\left(3 \, a^{14} + 231 \, a^{12} + 3003 \, a^{10} + 15015 \, a^{8} + 36465 \, a^{6} + 46189 \, a^{4} + 29393 \, a^{2} + 7429\right)} b^{10} c^{7} d^{5} + 99 \, {\left(5 \, a^{16} + 360 \, a^{14} + 4620 \, a^{12} + 24024 \, a^{10} + 64350 \, a^{8} + 97240 \, a^{6} + 83980 \, a^{4} + 38760 \, a^{2} + 7429\right)} b^{8} c^{8} d^{4} + 44 \, {\left(5 \, a^{18} + 315 \, a^{16} + 3780 \, a^{14} + 19404 \, a^{12} + 54054 \, a^{10} + 90090 \, a^{8} + 92820 \, a^{6} + 58140 \, a^{4} + 20349 \, a^{2} + 3059\right)} b^{6} c^{9} d^{3} + 66 \, {\left(a^{20} + 50 \, a^{18} + 525 \, a^{16} + 2520 \, a^{14} + 6930 \, a^{12} + 12012 \, a^{10} + 13650 \, a^{8} + 10200 \, a^{6} + 4845 \, a^{4} + 1330 \, a^{2} + 161\right)} b^{4} c^{10} d^{2} + 12 \, {\left(a^{22} + 33 \, a^{20} + 275 \, a^{18} + 1155 \, a^{16} + 2970 \, a^{14} + 5082 \, a^{12} + 6006 \, a^{10} + 4950 \, a^{8} + 2805 \, a^{6} + 1045 \, a^{4} + 231 \, a^{2} + 23\right)} b^{2} c^{11} d + {\left(a^{24} + 12 \, a^{22} + 66 \, a^{20} + 220 \, a^{18} + 495 \, a^{16} + 792 \, a^{14} + 924 \, a^{12} + 792 \, a^{10} + 495 \, a^{8} + 220 \, a^{6} + 66 \, a^{4} + 12 \, a^{2} + 1\right)} c^{12} - 8 \, {\left(3 \, b^{23} d^{11} + 11 \, {\left(3 \, a^{2} + 23\right)} b^{21} c d^{10} + 33 \, {\left(5 \, a^{4} + 70 \, a^{2} + 161\right)} b^{19} c^{2} d^{9} + 99 \, {\left(5 \, a^{6} + 95 \, a^{4} + 399 \, a^{2} + 437\right)} b^{17} c^{3} d^{8} + 22 \, {\left(45 \, a^{8} + 1020 \, a^{6} + 5814 \, a^{4} + 11628 \, a^{2} + 7429\right)} b^{15} c^{4} d^{7} + 6 \, {\left(231 \, a^{10} + 5775 \, a^{8} + 39270 \, a^{6} + 106590 \, a^{4} + 124355 \, a^{2} + 52003\right)} b^{13} c^{5} d^{6} + 6 \, {\left(231 \, a^{12} + 6006 \, a^{10} + 45045 \, a^{8} + 145860 \, a^{6} + 230945 \, a^{4} + 176358 \, a^{2} + 52003\right)} b^{11} c^{6} d^{5} + 22 \, {\left(45 \, a^{14} + 1155 \, a^{12} + 9009 \, a^{10} + 32175 \, a^{8} + 60775 \, a^{6} + 62985 \, a^{4} + 33915 \, a^{2} + 7429\right)} b^{9} c^{7} d^{4} + 99 \, {\left(5 \, a^{16} + 120 \, a^{14} + 924 \, a^{12} + 3432 \, a^{10} + 7150 \, a^{8} + 8840 \, a^{6} + 6460 \, a^{4} + 2584 \, a^{2} + 437\right)} b^{7} c^{8} d^{3} + 33 \, {\left(5 \, a^{18} + 105 \, a^{16} + 756 \, a^{14} + 2772 \, a^{12} + 6006 \, a^{10} + 8190 \, a^{8} + 7140 \, a^{6} + 3876 \, a^{4} + 1197 \, a^{2} + 161\right)} b^{5} c^{9} d^{2} + 11 \, {\left(3 \, a^{20} + 50 \, a^{18} + 315 \, a^{16} + 1080 \, a^{14} + 2310 \, a^{12} + 3276 \, a^{10} + 3150 \, a^{8} + 2040 \, a^{6} + 855 \, a^{4} + 210 \, a^{2} + 23\right)} b^{3} c^{10} d + 3 \, {\left(a^{22} + 11 \, a^{20} + 55 \, a^{18} + 165 \, a^{16} + 330 \, a^{14} + 462 \, a^{12} + 462 \, a^{10} + 330 \, a^{8} + 165 \, a^{6} + 55 \, a^{4} + 11 \, a^{2} + 1\right)} b c^{11}\right)} \sqrt{c} \sqrt{d}}\right) + 2 \, b {\rm Li}_2\left(\frac{{\left(a + i\right)} b c x + b^{2} d + {\left(i \, b^{2} x + {\left(-i \, a + 1\right)} b\right)} \sqrt{c} \sqrt{d}}{2 \, {\left(-i \, a + 1\right)} b \sqrt{c} \sqrt{d} + b^{2} d - {\left(a^{2} + 2 i \, a - 1\right)} c}\right) - 2 \, b {\rm Li}_2\left(-\frac{{\left(a + i\right)} b c x + b^{2} d - {\left(i \, b^{2} x + {\left(-i \, a + 1\right)} b\right)} \sqrt{c} \sqrt{d}}{2 \, {\left(-i \, a + 1\right)} b \sqrt{c} \sqrt{d} - b^{2} d + {\left(a^{2} + 2 i \, a - 1\right)} c}\right) - 2 \, b {\rm Li}_2\left(\frac{{\left(a - i\right)} b c x + b^{2} d + {\left(i \, b^{2} x + {\left(-i \, a - 1\right)} b\right)} \sqrt{c} \sqrt{d}}{2 \, {\left(-i \, a - 1\right)} b \sqrt{c} \sqrt{d} + b^{2} d - {\left(a^{2} - 2 i \, a - 1\right)} c}\right) + 2 \, b {\rm Li}_2\left(-\frac{{\left(a - i\right)} b c x + b^{2} d - {\left(i \, b^{2} x + {\left(-i \, a - 1\right)} b\right)} \sqrt{c} \sqrt{d}}{2 \, {\left(-i \, a - 1\right)} b \sqrt{c} \sqrt{d} - b^{2} d + {\left(a^{2} - 2 i \, a - 1\right)} c}\right)\right)} \sqrt{c} \sqrt{d} - 4 \, c \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}{8 \, b c^{2}}"," ",0,"-(d*arctan(c*x/sqrt(c*d))/(sqrt(c*d)*c) - x/c)*arctan(b*x + a) + 1/8*(8*a*c*arctan(b*x + a) + (4*b*arctan(sqrt(c)*x/sqrt(d))*arctan2((2*a*b^2*c*d + (a*b^3*d + (a^3 + a)*b*c + (b^4*d + (a^2 + 3)*b^2*c)*x)*sqrt(c)*sqrt(d) + (3*b^3*c*d + (a^2 + 1)*b*c^2)*x)/(b^4*d^2 + 2*(a^2 + 3)*b^2*c*d + (a^4 + 2*a^2 + 1)*c^2 + 4*(b^3*d + (a^2 + 1)*b*c)*sqrt(c)*sqrt(d)), ((a^2 + 3)*b^2*c*d + (a^4 + 2*a^2 + 1)*c^2 + (2*a*b^2*c*x + b^3*d + 3*(a^2 + 1)*b*c)*sqrt(c)*sqrt(d) + (a*b^3*c*d + (a^3 + a)*b*c^2)*x)/(b^4*d^2 + 2*(a^2 + 3)*b^2*c*d + (a^4 + 2*a^2 + 1)*c^2 + 4*(b^3*d + (a^2 + 1)*b*c)*sqrt(c)*sqrt(d))) + 4*b*arctan(sqrt(c)*x/sqrt(d))*arctan2((2*a*b^2*c*d - (a*b^3*d + (a^3 + a)*b*c + (b^4*d + (a^2 + 3)*b^2*c)*x)*sqrt(c)*sqrt(d) + (3*b^3*c*d + (a^2 + 1)*b*c^2)*x)/(b^4*d^2 + 2*(a^2 + 3)*b^2*c*d + (a^4 + 2*a^2 + 1)*c^2 - 4*(b^3*d + (a^2 + 1)*b*c)*sqrt(c)*sqrt(d)), ((a^2 + 3)*b^2*c*d + (a^4 + 2*a^2 + 1)*c^2 - (2*a*b^2*c*x + b^3*d + 3*(a^2 + 1)*b*c)*sqrt(c)*sqrt(d) + (a*b^3*c*d + (a^3 + a)*b*c^2)*x)/(b^4*d^2 + 2*(a^2 + 3)*b^2*c*d + (a^4 + 2*a^2 + 1)*c^2 - 4*(b^3*d + (a^2 + 1)*b*c)*sqrt(c)*sqrt(d))) + b*log(c*x^2 + d)*log(((a^2 + 1)*b^22*c*d^11 + 11*(a^4 + 22*a^2 + 21)*b^20*c^2*d^10 + 55*(a^6 + 39*a^4 + 171*a^2 + 133)*b^18*c^3*d^9 + 33*(5*a^8 + 260*a^6 + 1870*a^4 + 3876*a^2 + 2261)*b^16*c^4*d^8 + 330*(a^10 + 61*a^8 + 570*a^6 + 1802*a^4 + 2261*a^2 + 969)*b^14*c^5*d^7 + 22*(21*a^12 + 1386*a^10 + 15015*a^8 + 60060*a^6 + 109395*a^4 + 92378*a^2 + 29393)*b^12*c^6*d^6 + 22*(21*a^14 + 1407*a^12 + 16401*a^10 + 75075*a^8 + 169455*a^6 + 201773*a^4 + 121771*a^2 + 29393)*b^10*c^7*d^5 + 330*(a^16 + 64*a^14 + 756*a^12 + 3696*a^10 + 9438*a^8 + 13728*a^6 + 11492*a^4 + 5168*a^2 + 969)*b^8*c^8*d^4 + 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12920*a^2 + 2261)*b^8*c^9*d^3 + 55*(a^18 + 45*a^16 + 420*a^14 + 1764*a^12 + 4158*a^10 + 6006*a^8 + 5460*a^6 + 3060*a^4 + 969*a^2 + 133)*b^6*c^10*d^2 + 11*(a^20 + 30*a^18 + 225*a^16 + 840*a^14 + 1890*a^12 + 2772*a^10 + 2730*a^8 + 1800*a^6 + 765*a^4 + 190*a^2 + 21)*b^4*c^11*d + (a^22 + 11*a^20 + 55*a^18 + 165*a^16 + 330*a^14 + 462*a^12 + 462*a^10 + 330*a^8 + 165*a^6 + 55*a^4 + 11*a^2 + 1)*b^2*c^12)*x^2 - 2*(11*(a^2 + 1)*b^21*c*d^10 + 110*(a^4 + 8*a^2 + 7)*b^19*c^2*d^9 + 33*(15*a^6 + 205*a^4 + 589*a^2 + 399)*b^17*c^3*d^8 + 264*(5*a^8 + 90*a^6 + 408*a^4 + 646*a^2 + 323)*b^15*c^4*d^7 + 110*(21*a^10 + 441*a^8 + 2562*a^6 + 6018*a^4 + 6137*a^2 + 2261)*b^13*c^5*d^6 + 4*(693*a^12 + 15708*a^10 + 105105*a^8 + 308880*a^6 + 449735*a^4 + 319124*a^2 + 88179)*b^11*c^6*d^5 + 110*(21*a^14 + 483*a^12 + 3465*a^10 + 11583*a^8 + 20735*a^6 + 20553*a^4 + 10659*a^2 + 2261)*b^9*c^7*d^4 + 264*(5*a^16 + 110*a^14 + 798*a^12 + 2838*a^10 + 5720*a^8 + 6890*a^6 + 4930*a^4 + 1938*a^2 + 323)*b^7*c^8*d^3 + 33*(15*a^18 + 295*a^16 + 2044*a^14 + 7308*a^12 + 15554*a^10 + 20930*a^8 + 18060*a^6 + 9724*a^4 + 2983*a^2 + 399)*b^5*c^9*d^2 + 110*(a^20 + 16*a^18 + 99*a^16 + 336*a^14 + 714*a^12 + 1008*a^10 + 966*a^8 + 624*a^6 + 261*a^4 + 64*a^2 + 7)*b^3*c^10*d + 11*(a^22 + 11*a^20 + 55*a^18 + 165*a^16 + 330*a^14 + 462*a^12 + 462*a^10 + 330*a^8 + 165*a^6 + 55*a^4 + 11*a^2 + 1)*b*c^11 + (11*b^23*c*d^10 + 110*(a^2 + 7)*b^21*c^2*d^9 + 33*(15*a^4 + 190*a^2 + 399)*b^19*c^3*d^8 + 264*(5*a^6 + 85*a^4 + 323*a^2 + 323)*b^17*c^4*d^7 + 110*(21*a^8 + 420*a^6 + 2142*a^4 + 3876*a^2 + 2261)*b^15*c^5*d^6 + 4*(693*a^10 + 15015*a^8 + 90090*a^6 + 218790*a^4 + 230945*a^2 + 88179)*b^13*c^6*d^5 + 110*(21*a^12 + 462*a^10 + 3003*a^8 + 8580*a^6 + 12155*a^4 + 8398*a^2 + 2261)*b^11*c^7*d^4 + 264*(5*a^14 + 105*a^12 + 693*a^10 + 2145*a^8 + 3575*a^6 + 3315*a^4 + 1615*a^2 + 323)*b^9*c^8*d^3 + 33*(15*a^16 + 280*a^14 + 1764*a^12 + 5544*a^10 + 10010*a^8 + 10920*a^6 + 7140*a^4 + 2584*a^2 + 399)*b^7*c^9*d^2 + 110*(a^18 + 15*a^16 + 84*a^14 + 252*a^12 + 462*a^10 + 546*a^8 + 420*a^6 + 204*a^4 + 57*a^2 + 7)*b^5*c^10*d + 11*(a^20 + 10*a^18 + 45*a^16 + 120*a^14 + 210*a^12 + 252*a^10 + 210*a^8 + 120*a^6 + 45*a^4 + 10*a^2 + 1)*b^3*c^11)*x^2 + 2*(11*a*b^22*c*d^10 + 110*(a^3 + 7*a)*b^20*c^2*d^9 + 33*(15*a^5 + 190*a^3 + 399*a)*b^18*c^3*d^8 + 264*(5*a^7 + 85*a^5 + 323*a^3 + 323*a)*b^16*c^4*d^7 + 110*(21*a^9 + 420*a^7 + 2142*a^5 + 3876*a^3 + 2261*a)*b^14*c^5*d^6 + 4*(693*a^11 + 15015*a^9 + 90090*a^7 + 218790*a^5 + 230945*a^3 + 88179*a)*b^12*c^6*d^5 + 110*(21*a^13 + 462*a^11 + 3003*a^9 + 8580*a^7 + 12155*a^5 + 8398*a^3 + 2261*a)*b^10*c^7*d^4 + 264*(5*a^15 + 105*a^13 + 693*a^11 + 2145*a^9 + 3575*a^7 + 3315*a^5 + 1615*a^3 + 323*a)*b^8*c^8*d^3 + 33*(15*a^17 + 280*a^15 + 1764*a^13 + 5544*a^11 + 10010*a^9 + 10920*a^7 + 7140*a^5 + 2584*a^3 + 399*a)*b^6*c^9*d^2 + 110*(a^19 + 15*a^17 + 84*a^15 + 252*a^13 + 462*a^11 + 546*a^9 + 420*a^7 + 204*a^5 + 57*a^3 + 7*a)*b^4*c^10*d + 11*(a^21 + 10*a^19 + 45*a^17 + 120*a^15 + 210*a^13 + 252*a^11 + 210*a^9 + 120*a^7 + 45*a^5 + 10*a^3 + a)*b^2*c^11)*x)*sqrt(c)*sqrt(d) + 2*(a*b^23*c*d^11 + 11*(a^3 + 21*a)*b^21*c^2*d^10 + 55*(a^5 + 38*a^3 + 133*a)*b^19*c^3*d^9 + 33*(5*a^7 + 255*a^5 + 1615*a^3 + 2261*a)*b^17*c^4*d^8 + 330*(a^9 + 60*a^7 + 510*a^5 + 1292*a^3 + 969*a)*b^15*c^5*d^7 + 22*(21*a^11 + 1365*a^9 + 13650*a^7 + 46410*a^5 + 62985*a^3 + 29393*a)*b^13*c^6*d^6 + 22*(21*a^13 + 1386*a^11 + 15015*a^9 + 60060*a^7 + 109395*a^5 + 92378*a^3 + 29393*a)*b^11*c^7*d^5 + 330*(a^15 + 63*a^13 + 693*a^11 + 3003*a^9 + 6435*a^7 + 7293*a^5 + 4199*a^3 + 969*a)*b^9*c^8*d^4 + 33*(5*a^17 + 280*a^15 + 2940*a^13 + 12936*a^11 + 30030*a^9 + 40040*a^7 + 30940*a^5 + 12920*a^3 + 2261*a)*b^7*c^9*d^3 + 55*(a^19 + 45*a^17 + 420*a^15 + 1764*a^13 + 4158*a^11 + 6006*a^9 + 5460*a^7 + 3060*a^5 + 969*a^3 + 133*a)*b^5*c^10*d^2 + 11*(a^21 + 30*a^19 + 225*a^17 + 840*a^15 + 1890*a^13 + 2772*a^11 + 2730*a^9 + 1800*a^7 + 765*a^5 + 190*a^3 + 21*a)*b^3*c^11*d + (a^23 + 11*a^21 + 55*a^19 + 165*a^17 + 330*a^15 + 462*a^13 + 462*a^11 + 330*a^9 + 165*a^7 + 55*a^5 + 11*a^3 + a)*b*c^12)*x)/(b^24*d^12 + 12*(a^2 + 23)*b^22*c*d^11 + 66*(a^4 + 42*a^2 + 161)*b^20*c^2*d^10 + 44*(5*a^6 + 285*a^4 + 1995*a^2 + 3059)*b^18*c^3*d^9 + 99*(5*a^8 + 340*a^6 + 3230*a^4 + 9044*a^2 + 7429)*b^16*c^4*d^8 + 264*(3*a^10 + 225*a^8 + 2550*a^6 + 9690*a^4 + 14535*a^2 + 7429)*b^14*c^5*d^7 + 4*(231*a^12 + 18018*a^10 + 225225*a^8 + 1021020*a^6 + 2078505*a^4 + 1939938*a^2 + 676039)*b^12*c^6*d^6 + 264*(3*a^14 + 231*a^12 + 3003*a^10 + 15015*a^8 + 36465*a^6 + 46189*a^4 + 29393*a^2 + 7429)*b^10*c^7*d^5 + 99*(5*a^16 + 360*a^14 + 4620*a^12 + 24024*a^10 + 64350*a^8 + 97240*a^6 + 83980*a^4 + 38760*a^2 + 7429)*b^8*c^8*d^4 + 44*(5*a^18 + 315*a^16 + 3780*a^14 + 19404*a^12 + 54054*a^10 + 90090*a^8 + 92820*a^6 + 58140*a^4 + 20349*a^2 + 3059)*b^6*c^9*d^3 + 66*(a^20 + 50*a^18 + 525*a^16 + 2520*a^14 + 6930*a^12 + 12012*a^10 + 13650*a^8 + 10200*a^6 + 4845*a^4 + 1330*a^2 + 161)*b^4*c^10*d^2 + 12*(a^22 + 33*a^20 + 275*a^18 + 1155*a^16 + 2970*a^14 + 5082*a^12 + 6006*a^10 + 4950*a^8 + 2805*a^6 + 1045*a^4 + 231*a^2 + 23)*b^2*c^11*d + (a^24 + 12*a^22 + 66*a^20 + 220*a^18 + 495*a^16 + 792*a^14 + 924*a^12 + 792*a^10 + 495*a^8 + 220*a^6 + 66*a^4 + 12*a^2 + 1)*c^12 - 8*(3*b^23*d^11 + 11*(3*a^2 + 23)*b^21*c*d^10 + 33*(5*a^4 + 70*a^2 + 161)*b^19*c^2*d^9 + 99*(5*a^6 + 95*a^4 + 399*a^2 + 437)*b^17*c^3*d^8 + 22*(45*a^8 + 1020*a^6 + 5814*a^4 + 11628*a^2 + 7429)*b^15*c^4*d^7 + 6*(231*a^10 + 5775*a^8 + 39270*a^6 + 106590*a^4 + 124355*a^2 + 52003)*b^13*c^5*d^6 + 6*(231*a^12 + 6006*a^10 + 45045*a^8 + 145860*a^6 + 230945*a^4 + 176358*a^2 + 52003)*b^11*c^6*d^5 + 22*(45*a^14 + 1155*a^12 + 9009*a^10 + 32175*a^8 + 60775*a^6 + 62985*a^4 + 33915*a^2 + 7429)*b^9*c^7*d^4 + 99*(5*a^16 + 120*a^14 + 924*a^12 + 3432*a^10 + 7150*a^8 + 8840*a^6 + 6460*a^4 + 2584*a^2 + 437)*b^7*c^8*d^3 + 33*(5*a^18 + 105*a^16 + 756*a^14 + 2772*a^12 + 6006*a^10 + 8190*a^8 + 7140*a^6 + 3876*a^4 + 1197*a^2 + 161)*b^5*c^9*d^2 + 11*(3*a^20 + 50*a^18 + 315*a^16 + 1080*a^14 + 2310*a^12 + 3276*a^10 + 3150*a^8 + 2040*a^6 + 855*a^4 + 210*a^2 + 23)*b^3*c^10*d + 3*(a^22 + 11*a^20 + 55*a^18 + 165*a^16 + 330*a^14 + 462*a^12 + 462*a^10 + 330*a^8 + 165*a^6 + 55*a^4 + 11*a^2 + 1)*b*c^11)*sqrt(c)*sqrt(d))) + 2*b*dilog(((a + I)*b*c*x + b^2*d + (I*b^2*x + (-I*a + 1)*b)*sqrt(c)*sqrt(d))/(2*(-I*a + 1)*b*sqrt(c)*sqrt(d) + b^2*d - (a^2 + 2*I*a - 1)*c)) - 2*b*dilog(-((a + I)*b*c*x + b^2*d - (I*b^2*x + (-I*a + 1)*b)*sqrt(c)*sqrt(d))/(2*(-I*a + 1)*b*sqrt(c)*sqrt(d) - b^2*d + (a^2 + 2*I*a - 1)*c)) - 2*b*dilog(((a - I)*b*c*x + b^2*d + (I*b^2*x + (-I*a - 1)*b)*sqrt(c)*sqrt(d))/(2*(-I*a - 1)*b*sqrt(c)*sqrt(d) + b^2*d - (a^2 - 2*I*a - 1)*c)) + 2*b*dilog(-((a - I)*b*c*x + b^2*d - (I*b^2*x + (-I*a - 1)*b)*sqrt(c)*sqrt(d))/(2*(-I*a - 1)*b*sqrt(c)*sqrt(d) - b^2*d + (a^2 - 2*I*a - 1)*c)))*sqrt(c)*sqrt(d) - 4*c*log(b^2*x^2 + 2*a*b*x + a^2 + 1))/(b*c^2)","B",0
57,0,0,0,0.000000," ","integrate(arctan(b*x+a)/(c+d/x^3),x, algorithm=""maxima"")","\int \frac{\arctan\left(b x + a\right)}{c + \frac{d}{x^{3}}}\,{d x}"," ",0,"integrate(arctan(b*x + a)/(c + d/x^3), x)","F",0
58,0,0,0,0.000000," ","integrate(arctan(b*x+a)/(c+d*x^(1/2)),x, algorithm=""maxima"")","\int \frac{\arctan\left(b x + a\right)}{d \sqrt{x} + c}\,{d x}"," ",0,"integrate(arctan(b*x + a)/(d*sqrt(x) + c), x)","F",0
59,0,0,0,0.000000," ","integrate(arctan(b*x+a)/(c+d/x^(1/2)),x, algorithm=""maxima"")","\int \frac{\arctan\left(b x + a\right)}{c + \frac{d}{\sqrt{x}}}\,{d x}"," ",0,"integrate(arctan(b*x + a)/(c + d/sqrt(x)), x)","F",0
60,1,328,0,0.546336," ","integrate(arctan(b*x+a)/(x^2+1),x, algorithm=""maxima"")","\frac{1}{8} \, b {\left(\frac{8 \, \arctan\left(x\right) \arctan\left(\frac{b^{2} x + a b}{b}\right)}{b} - \frac{4 \, \arctan\left(x\right) \arctan\left(\frac{a b + {\left(b^{2} + b\right)} x}{a^{2} + b^{2} + 2 \, b + 1}, \frac{a b x + a^{2} + b + 1}{a^{2} + b^{2} + 2 \, b + 1}\right) - 4 \, \arctan\left(x\right) \arctan\left(\frac{a b + {\left(b^{2} - b\right)} x}{a^{2} + b^{2} - 2 \, b + 1}, \frac{a b x + a^{2} - b + 1}{a^{2} + b^{2} - 2 \, b + 1}\right) + \log\left(x^{2} + 1\right) \log\left(\frac{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}{a^{2} + b^{2} + 2 \, b + 1}\right) - \log\left(x^{2} + 1\right) \log\left(\frac{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}{a^{2} + b^{2} - 2 \, b + 1}\right) + 2 \, {\rm Li}_2\left(-\frac{i \, b x - b}{i \, a + b + 1}\right) - 2 \, {\rm Li}_2\left(-\frac{i \, b x - b}{i \, a + b - 1}\right) + 2 \, {\rm Li}_2\left(\frac{i \, b x + b}{-i \, a + b + 1}\right) - 2 \, {\rm Li}_2\left(\frac{i \, b x + b}{-i \, a + b - 1}\right)}{b}\right)} + \arctan\left(b x + a\right) \arctan\left(x\right) - \arctan\left(x\right) \arctan\left(\frac{b^{2} x + a b}{b}\right)"," ",0,"1/8*b*(8*arctan(x)*arctan((b^2*x + a*b)/b)/b - (4*arctan(x)*arctan2((a*b + (b^2 + b)*x)/(a^2 + b^2 + 2*b + 1), (a*b*x + a^2 + b + 1)/(a^2 + b^2 + 2*b + 1)) - 4*arctan(x)*arctan2((a*b + (b^2 - b)*x)/(a^2 + b^2 - 2*b + 1), (a*b*x + a^2 - b + 1)/(a^2 + b^2 - 2*b + 1)) + log(x^2 + 1)*log((b^2*x^2 + 2*a*b*x + a^2 + 1)/(a^2 + b^2 + 2*b + 1)) - log(x^2 + 1)*log((b^2*x^2 + 2*a*b*x + a^2 + 1)/(a^2 + b^2 - 2*b + 1)) + 2*dilog(-(I*b*x - b)/(I*a + b + 1)) - 2*dilog(-(I*b*x - b)/(I*a + b - 1)) + 2*dilog((I*b*x + b)/(-I*a + b + 1)) - 2*dilog((I*b*x + b)/(-I*a + b - 1)))/b) + arctan(b*x + a)*arctan(x) - arctan(x)*arctan((b^2*x + a*b)/b)","A",0
61,1,14300,0,2.839920," ","integrate(arctan(e*x+d)/(b*x^2+a),x, algorithm=""maxima"")","\frac{e {\left(\frac{8 \, \arctan\left(\frac{b x}{\sqrt{a b}}\right) \arctan\left(\frac{e^{2} x + d e}{e}\right)}{e} - \frac{4 \, \arctan\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \arctan\left(\frac{2 \, a b d e^{2} + {\left(a d e^{3} + {\left(b d^{3} + b d\right)} e + {\left(a e^{4} + {\left(b d^{2} + 3 \, b\right)} e^{2}\right)} x\right)} \sqrt{a} \sqrt{b} + {\left(3 \, a b e^{3} + {\left(b^{2} d^{2} + b^{2}\right)} e\right)} x}{b^{2} d^{4} + a^{2} e^{4} + 2 \, b^{2} d^{2} + 2 \, {\left(a b d^{2} + 3 \, a b\right)} e^{2} + 4 \, {\left(a e^{3} + {\left(b d^{2} + b\right)} e\right)} \sqrt{a} \sqrt{b} + b^{2}}, \frac{b^{2} d^{4} + 2 \, b^{2} d^{2} + {\left(a b d^{2} + 3 \, a b\right)} e^{2} + {\left(2 \, b d e^{2} x + a e^{3} + 3 \, {\left(b d^{2} + b\right)} e\right)} \sqrt{a} \sqrt{b} + b^{2} + {\left(a b d e^{3} + {\left(b^{2} d^{3} + b^{2} d\right)} e\right)} x}{b^{2} d^{4} + a^{2} e^{4} + 2 \, b^{2} d^{2} + 2 \, {\left(a b d^{2} + 3 \, a b\right)} e^{2} + 4 \, {\left(a e^{3} + {\left(b d^{2} + b\right)} e\right)} \sqrt{a} \sqrt{b} + b^{2}}\right) + 4 \, \arctan\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \arctan\left(\frac{2 \, a b d e^{2} - {\left(a d e^{3} + {\left(b d^{3} + b d\right)} e + {\left(a e^{4} + {\left(b d^{2} + 3 \, b\right)} e^{2}\right)} x\right)} \sqrt{a} \sqrt{b} + {\left(3 \, a b e^{3} + {\left(b^{2} d^{2} + b^{2}\right)} e\right)} x}{b^{2} d^{4} + a^{2} e^{4} + 2 \, b^{2} d^{2} + 2 \, {\left(a b d^{2} + 3 \, a b\right)} e^{2} - 4 \, {\left(a e^{3} + {\left(b d^{2} + b\right)} e\right)} \sqrt{a} \sqrt{b} + b^{2}}, \frac{b^{2} d^{4} + 2 \, b^{2} d^{2} + {\left(a b d^{2} + 3 \, a b\right)} e^{2} - {\left(2 \, b d e^{2} x + a e^{3} + 3 \, {\left(b d^{2} + b\right)} e\right)} \sqrt{a} \sqrt{b} + b^{2} + {\left(a b d e^{3} + {\left(b^{2} d^{3} + b^{2} d\right)} e\right)} x}{b^{2} d^{4} + a^{2} e^{4} + 2 \, b^{2} d^{2} + 2 \, {\left(a b d^{2} + 3 \, a b\right)} e^{2} - 4 \, {\left(a e^{3} + {\left(b d^{2} + b\right)} e\right)} \sqrt{a} \sqrt{b} + b^{2}}\right) + \log\left(b x^{2} + a\right) \log\left(\frac{b^{12} d^{24} + 12 \, b^{12} d^{22} + 66 \, b^{12} d^{20} + 220 \, b^{12} d^{18} + 495 \, b^{12} d^{16} + 792 \, b^{12} d^{14} + 924 \, b^{12} d^{12} + {\left(a^{11} b d^{2} + a^{11} b\right)} e^{22} + 792 \, b^{12} d^{10} + 11 \, {\left(a^{10} b^{2} d^{4} + 22 \, a^{10} b^{2} d^{2} + 21 \, a^{10} b^{2}\right)} e^{20} + 495 \, b^{12} d^{8} + 55 \, {\left(a^{9} b^{3} d^{6} + 39 \, a^{9} b^{3} d^{4} + 171 \, a^{9} b^{3} d^{2} + 133 \, a^{9} b^{3}\right)} e^{18} + 220 \, b^{12} d^{6} + 33 \, {\left(5 \, a^{8} b^{4} d^{8} + 260 \, a^{8} b^{4} d^{6} + 1870 \, a^{8} b^{4} d^{4} + 3876 \, a^{8} b^{4} d^{2} + 2261 \, a^{8} b^{4}\right)} e^{16} + 66 \, b^{12} d^{4} + 330 \, {\left(a^{7} b^{5} d^{10} + 61 \, a^{7} b^{5} d^{8} + 570 \, a^{7} b^{5} d^{6} + 1802 \, a^{7} b^{5} d^{4} + 2261 \, a^{7} b^{5} d^{2} + 969 \, a^{7} b^{5}\right)} e^{14} + 12 \, b^{12} d^{2} + 22 \, {\left(21 \, a^{6} b^{6} d^{12} + 1386 \, a^{6} b^{6} d^{10} + 15015 \, a^{6} b^{6} d^{8} + 60060 \, a^{6} b^{6} d^{6} + 109395 \, a^{6} b^{6} d^{4} + 92378 \, a^{6} b^{6} d^{2} + 29393 \, a^{6} b^{6}\right)} e^{12} + b^{12} + 22 \, {\left(21 \, a^{5} b^{7} d^{14} + 1407 \, a^{5} b^{7} d^{12} + 16401 \, a^{5} b^{7} d^{10} + 75075 \, a^{5} b^{7} d^{8} + 169455 \, a^{5} b^{7} d^{6} + 201773 \, a^{5} b^{7} d^{4} + 121771 \, a^{5} b^{7} d^{2} + 29393 \, a^{5} b^{7}\right)} e^{10} + 330 \, {\left(a^{4} b^{8} d^{16} + 64 \, a^{4} b^{8} d^{14} + 756 \, a^{4} b^{8} d^{12} + 3696 \, a^{4} b^{8} d^{10} + 9438 \, a^{4} b^{8} d^{8} + 13728 \, a^{4} b^{8} d^{6} + 11492 \, a^{4} b^{8} d^{4} + 5168 \, a^{4} b^{8} d^{2} + 969 \, a^{4} b^{8}\right)} e^{8} + 33 \, {\left(5 \, a^{3} b^{9} d^{18} + 285 \, a^{3} b^{9} d^{16} + 3220 \, a^{3} b^{9} d^{14} + 15876 \, a^{3} b^{9} d^{12} + 42966 \, a^{3} b^{9} d^{10} + 70070 \, a^{3} b^{9} d^{8} + 70980 \, a^{3} b^{9} d^{6} + 43860 \, a^{3} b^{9} d^{4} + 15181 \, a^{3} b^{9} d^{2} + 2261 \, a^{3} b^{9}\right)} e^{6} + 55 \, {\left(a^{2} b^{10} d^{20} + 46 \, a^{2} b^{10} d^{18} + 465 \, a^{2} b^{10} d^{16} + 2184 \, a^{2} b^{10} d^{14} + 5922 \, a^{2} b^{10} d^{12} + 10164 \, a^{2} b^{10} d^{10} + 11466 \, a^{2} b^{10} d^{8} + 8520 \, a^{2} b^{10} d^{6} + 4029 \, a^{2} b^{10} d^{4} + 1102 \, a^{2} b^{10} d^{2} + 133 \, a^{2} b^{10}\right)} e^{4} + 11 \, {\left(a b^{11} d^{22} + 31 \, a b^{11} d^{20} + 255 \, a b^{11} d^{18} + 1065 \, a b^{11} d^{16} + 2730 \, a b^{11} d^{14} + 4662 \, a b^{11} d^{12} + 5502 \, a b^{11} d^{10} + 4530 \, a b^{11} d^{8} + 2565 \, a b^{11} d^{6} + 955 \, a b^{11} d^{4} + 211 \, a b^{11} d^{2} + 21 \, a b^{11}\right)} e^{2} + {\left(a^{11} b e^{24} + 11 \, {\left(a^{10} b^{2} d^{2} + 21 \, a^{10} b^{2}\right)} e^{22} + 55 \, {\left(a^{9} b^{3} d^{4} + 38 \, a^{9} b^{3} d^{2} + 133 \, a^{9} b^{3}\right)} e^{20} + 33 \, {\left(5 \, a^{8} b^{4} d^{6} + 255 \, a^{8} b^{4} d^{4} + 1615 \, a^{8} b^{4} d^{2} + 2261 \, a^{8} b^{4}\right)} e^{18} + 330 \, {\left(a^{7} b^{5} d^{8} + 60 \, a^{7} b^{5} d^{6} + 510 \, a^{7} b^{5} d^{4} + 1292 \, a^{7} b^{5} d^{2} + 969 \, a^{7} b^{5}\right)} e^{16} + 22 \, {\left(21 \, a^{6} b^{6} d^{10} + 1365 \, a^{6} b^{6} d^{8} + 13650 \, a^{6} b^{6} d^{6} + 46410 \, a^{6} b^{6} d^{4} + 62985 \, a^{6} b^{6} d^{2} + 29393 \, a^{6} b^{6}\right)} e^{14} + 22 \, {\left(21 \, a^{5} b^{7} d^{12} + 1386 \, a^{5} b^{7} d^{10} + 15015 \, a^{5} b^{7} d^{8} + 60060 \, a^{5} b^{7} d^{6} + 109395 \, a^{5} b^{7} d^{4} + 92378 \, a^{5} b^{7} d^{2} + 29393 \, a^{5} b^{7}\right)} e^{12} + 330 \, {\left(a^{4} b^{8} d^{14} + 63 \, a^{4} b^{8} d^{12} + 693 \, a^{4} b^{8} d^{10} + 3003 \, a^{4} b^{8} d^{8} + 6435 \, a^{4} b^{8} d^{6} + 7293 \, a^{4} b^{8} d^{4} + 4199 \, a^{4} b^{8} d^{2} + 969 \, a^{4} b^{8}\right)} e^{10} + 33 \, {\left(5 \, a^{3} b^{9} d^{16} + 280 \, a^{3} b^{9} d^{14} + 2940 \, a^{3} b^{9} d^{12} + 12936 \, a^{3} b^{9} d^{10} + 30030 \, a^{3} b^{9} d^{8} + 40040 \, a^{3} b^{9} d^{6} + 30940 \, a^{3} b^{9} d^{4} + 12920 \, a^{3} b^{9} d^{2} + 2261 \, a^{3} b^{9}\right)} e^{8} + 55 \, {\left(a^{2} b^{10} d^{18} + 45 \, a^{2} b^{10} d^{16} + 420 \, a^{2} b^{10} d^{14} + 1764 \, a^{2} b^{10} d^{12} + 4158 \, a^{2} b^{10} d^{10} + 6006 \, a^{2} b^{10} d^{8} + 5460 \, a^{2} b^{10} d^{6} + 3060 \, a^{2} b^{10} d^{4} + 969 \, a^{2} b^{10} d^{2} + 133 \, a^{2} b^{10}\right)} e^{6} + 11 \, {\left(a b^{11} d^{20} + 30 \, a b^{11} d^{18} + 225 \, a b^{11} d^{16} + 840 \, a b^{11} d^{14} + 1890 \, a b^{11} d^{12} + 2772 \, a b^{11} d^{10} + 2730 \, a b^{11} d^{8} + 1800 \, a b^{11} d^{6} + 765 \, a b^{11} d^{4} + 190 \, a b^{11} d^{2} + 21 \, a b^{11}\right)} e^{4} + {\left(b^{12} d^{22} + 11 \, b^{12} d^{20} + 55 \, b^{12} d^{18} + 165 \, b^{12} d^{16} + 330 \, b^{12} d^{14} + 462 \, b^{12} d^{12} + 462 \, b^{12} d^{10} + 330 \, b^{12} d^{8} + 165 \, b^{12} d^{6} + 55 \, b^{12} d^{4} + 11 \, b^{12} d^{2} + b^{12}\right)} e^{2}\right)} x^{2} + 2 \, {\left(11 \, {\left(a^{10} b d^{2} + a^{10} b\right)} e^{21} + 110 \, {\left(a^{9} b^{2} d^{4} + 8 \, a^{9} b^{2} d^{2} + 7 \, a^{9} b^{2}\right)} e^{19} + 33 \, {\left(15 \, a^{8} b^{3} d^{6} + 205 \, a^{8} b^{3} d^{4} + 589 \, a^{8} b^{3} d^{2} + 399 \, a^{8} b^{3}\right)} e^{17} + 264 \, {\left(5 \, a^{7} b^{4} d^{8} + 90 \, a^{7} b^{4} d^{6} + 408 \, a^{7} b^{4} d^{4} + 646 \, a^{7} b^{4} d^{2} + 323 \, a^{7} b^{4}\right)} e^{15} + 110 \, {\left(21 \, a^{6} b^{5} d^{10} + 441 \, a^{6} b^{5} d^{8} + 2562 \, a^{6} b^{5} d^{6} + 6018 \, a^{6} b^{5} d^{4} + 6137 \, a^{6} b^{5} d^{2} + 2261 \, a^{6} b^{5}\right)} e^{13} + 4 \, {\left(693 \, a^{5} b^{6} d^{12} + 15708 \, a^{5} b^{6} d^{10} + 105105 \, a^{5} b^{6} d^{8} + 308880 \, a^{5} b^{6} d^{6} + 449735 \, a^{5} b^{6} d^{4} + 319124 \, a^{5} b^{6} d^{2} + 88179 \, a^{5} b^{6}\right)} e^{11} + 110 \, {\left(21 \, a^{4} b^{7} d^{14} + 483 \, a^{4} b^{7} d^{12} + 3465 \, a^{4} b^{7} d^{10} + 11583 \, a^{4} b^{7} d^{8} + 20735 \, a^{4} b^{7} d^{6} + 20553 \, a^{4} b^{7} d^{4} + 10659 \, a^{4} b^{7} d^{2} + 2261 \, a^{4} b^{7}\right)} e^{9} + 264 \, {\left(5 \, a^{3} b^{8} d^{16} + 110 \, a^{3} b^{8} d^{14} + 798 \, a^{3} b^{8} d^{12} + 2838 \, a^{3} b^{8} d^{10} + 5720 \, a^{3} b^{8} d^{8} + 6890 \, a^{3} b^{8} d^{6} + 4930 \, a^{3} b^{8} d^{4} + 1938 \, a^{3} b^{8} d^{2} + 323 \, a^{3} b^{8}\right)} e^{7} + 33 \, {\left(15 \, a^{2} b^{9} d^{18} + 295 \, a^{2} b^{9} d^{16} + 2044 \, a^{2} b^{9} d^{14} + 7308 \, a^{2} b^{9} d^{12} + 15554 \, a^{2} b^{9} d^{10} + 20930 \, a^{2} b^{9} d^{8} + 18060 \, a^{2} b^{9} d^{6} + 9724 \, a^{2} b^{9} d^{4} + 2983 \, a^{2} b^{9} d^{2} + 399 \, a^{2} b^{9}\right)} e^{5} + 110 \, {\left(a b^{10} d^{20} + 16 \, a b^{10} d^{18} + 99 \, a b^{10} d^{16} + 336 \, a b^{10} d^{14} + 714 \, a b^{10} d^{12} + 1008 \, a b^{10} d^{10} + 966 \, a b^{10} d^{8} + 624 \, a b^{10} d^{6} + 261 \, a b^{10} d^{4} + 64 \, a b^{10} d^{2} + 7 \, a b^{10}\right)} e^{3} + {\left(11 \, a^{10} b e^{23} + 110 \, {\left(a^{9} b^{2} d^{2} + 7 \, a^{9} b^{2}\right)} e^{21} + 33 \, {\left(15 \, a^{8} b^{3} d^{4} + 190 \, a^{8} b^{3} d^{2} + 399 \, a^{8} b^{3}\right)} e^{19} + 264 \, {\left(5 \, a^{7} b^{4} d^{6} + 85 \, a^{7} b^{4} d^{4} + 323 \, a^{7} b^{4} d^{2} + 323 \, a^{7} b^{4}\right)} e^{17} + 110 \, {\left(21 \, a^{6} b^{5} d^{8} + 420 \, a^{6} b^{5} d^{6} + 2142 \, a^{6} b^{5} d^{4} + 3876 \, a^{6} b^{5} d^{2} + 2261 \, a^{6} b^{5}\right)} e^{15} + 4 \, {\left(693 \, a^{5} b^{6} d^{10} + 15015 \, a^{5} b^{6} d^{8} + 90090 \, a^{5} b^{6} d^{6} + 218790 \, a^{5} b^{6} d^{4} + 230945 \, a^{5} b^{6} d^{2} + 88179 \, a^{5} b^{6}\right)} e^{13} + 110 \, {\left(21 \, a^{4} b^{7} d^{12} + 462 \, a^{4} b^{7} d^{10} + 3003 \, a^{4} b^{7} d^{8} + 8580 \, a^{4} b^{7} d^{6} + 12155 \, a^{4} b^{7} d^{4} + 8398 \, a^{4} b^{7} d^{2} + 2261 \, a^{4} b^{7}\right)} e^{11} + 264 \, {\left(5 \, a^{3} b^{8} d^{14} + 105 \, a^{3} b^{8} d^{12} + 693 \, a^{3} b^{8} d^{10} + 2145 \, a^{3} b^{8} d^{8} + 3575 \, a^{3} b^{8} d^{6} + 3315 \, a^{3} b^{8} d^{4} + 1615 \, a^{3} b^{8} d^{2} + 323 \, a^{3} b^{8}\right)} e^{9} + 33 \, {\left(15 \, a^{2} b^{9} d^{16} + 280 \, a^{2} b^{9} d^{14} + 1764 \, a^{2} b^{9} d^{12} + 5544 \, a^{2} b^{9} d^{10} + 10010 \, a^{2} b^{9} d^{8} + 10920 \, a^{2} b^{9} d^{6} + 7140 \, a^{2} b^{9} d^{4} + 2584 \, a^{2} b^{9} d^{2} + 399 \, a^{2} b^{9}\right)} e^{7} + 110 \, {\left(a b^{10} d^{18} + 15 \, a b^{10} d^{16} + 84 \, a b^{10} d^{14} + 252 \, a b^{10} d^{12} + 462 \, a b^{10} d^{10} + 546 \, a b^{10} d^{8} + 420 \, a b^{10} d^{6} + 204 \, a b^{10} d^{4} + 57 \, a b^{10} d^{2} + 7 \, a b^{10}\right)} e^{5} + 11 \, {\left(b^{11} d^{20} + 10 \, b^{11} d^{18} + 45 \, b^{11} d^{16} + 120 \, b^{11} d^{14} + 210 \, b^{11} d^{12} + 252 \, b^{11} d^{10} + 210 \, b^{11} d^{8} + 120 \, b^{11} d^{6} + 45 \, b^{11} d^{4} + 10 \, b^{11} d^{2} + b^{11}\right)} e^{3}\right)} x^{2} + 11 \, {\left(b^{11} d^{22} + 11 \, b^{11} d^{20} + 55 \, b^{11} d^{18} + 165 \, b^{11} d^{16} + 330 \, b^{11} d^{14} + 462 \, b^{11} d^{12} + 462 \, b^{11} d^{10} + 330 \, b^{11} d^{8} + 165 \, b^{11} d^{6} + 55 \, b^{11} d^{4} + 11 \, b^{11} d^{2} + b^{11}\right)} e + 2 \, {\left(11 \, a^{10} b d e^{22} + 110 \, {\left(a^{9} b^{2} d^{3} + 7 \, a^{9} b^{2} d\right)} e^{20} + 33 \, {\left(15 \, a^{8} b^{3} d^{5} + 190 \, a^{8} b^{3} d^{3} + 399 \, a^{8} b^{3} d\right)} e^{18} + 264 \, {\left(5 \, a^{7} b^{4} d^{7} + 85 \, a^{7} b^{4} d^{5} + 323 \, a^{7} b^{4} d^{3} + 323 \, a^{7} b^{4} d\right)} e^{16} + 110 \, {\left(21 \, a^{6} b^{5} d^{9} + 420 \, a^{6} b^{5} d^{7} + 2142 \, a^{6} b^{5} d^{5} + 3876 \, a^{6} b^{5} d^{3} + 2261 \, a^{6} b^{5} d\right)} e^{14} + 4 \, {\left(693 \, a^{5} b^{6} d^{11} + 15015 \, a^{5} b^{6} d^{9} + 90090 \, a^{5} b^{6} d^{7} + 218790 \, a^{5} b^{6} d^{5} + 230945 \, a^{5} b^{6} d^{3} + 88179 \, a^{5} b^{6} d\right)} e^{12} + 110 \, {\left(21 \, a^{4} b^{7} d^{13} + 462 \, a^{4} b^{7} d^{11} + 3003 \, a^{4} b^{7} d^{9} + 8580 \, a^{4} b^{7} d^{7} + 12155 \, a^{4} b^{7} d^{5} + 8398 \, a^{4} b^{7} d^{3} + 2261 \, a^{4} b^{7} d\right)} e^{10} + 264 \, {\left(5 \, a^{3} b^{8} d^{15} + 105 \, a^{3} b^{8} d^{13} + 693 \, a^{3} b^{8} d^{11} + 2145 \, a^{3} b^{8} d^{9} + 3575 \, a^{3} b^{8} d^{7} + 3315 \, a^{3} b^{8} d^{5} + 1615 \, a^{3} b^{8} d^{3} + 323 \, a^{3} b^{8} d\right)} e^{8} + 33 \, {\left(15 \, a^{2} b^{9} d^{17} + 280 \, a^{2} b^{9} d^{15} + 1764 \, a^{2} b^{9} d^{13} + 5544 \, a^{2} b^{9} d^{11} + 10010 \, a^{2} b^{9} d^{9} + 10920 \, a^{2} b^{9} d^{7} + 7140 \, a^{2} b^{9} d^{5} + 2584 \, a^{2} b^{9} d^{3} + 399 \, a^{2} b^{9} d\right)} e^{6} + 110 \, {\left(a b^{10} d^{19} + 15 \, a b^{10} d^{17} + 84 \, a b^{10} d^{15} + 252 \, a b^{10} d^{13} + 462 \, a b^{10} d^{11} + 546 \, a b^{10} d^{9} + 420 \, a b^{10} d^{7} + 204 \, a b^{10} d^{5} + 57 \, a b^{10} d^{3} + 7 \, a b^{10} d\right)} e^{4} + 11 \, {\left(b^{11} d^{21} + 10 \, b^{11} d^{19} + 45 \, b^{11} d^{17} + 120 \, b^{11} d^{15} + 210 \, b^{11} d^{13} + 252 \, b^{11} d^{11} + 210 \, b^{11} d^{9} + 120 \, b^{11} d^{7} + 45 \, b^{11} d^{5} + 10 \, b^{11} d^{3} + b^{11} d\right)} e^{2}\right)} x\right)} \sqrt{a} \sqrt{b} + 2 \, {\left(a^{11} b d e^{23} + 11 \, {\left(a^{10} b^{2} d^{3} + 21 \, a^{10} b^{2} d\right)} e^{21} + 55 \, {\left(a^{9} b^{3} d^{5} + 38 \, a^{9} b^{3} d^{3} + 133 \, a^{9} b^{3} d\right)} e^{19} + 33 \, {\left(5 \, a^{8} b^{4} d^{7} + 255 \, a^{8} b^{4} d^{5} + 1615 \, a^{8} b^{4} d^{3} + 2261 \, a^{8} b^{4} d\right)} e^{17} + 330 \, {\left(a^{7} b^{5} d^{9} + 60 \, a^{7} b^{5} d^{7} + 510 \, a^{7} b^{5} d^{5} + 1292 \, a^{7} b^{5} d^{3} + 969 \, a^{7} b^{5} d\right)} e^{15} + 22 \, {\left(21 \, a^{6} b^{6} d^{11} + 1365 \, a^{6} b^{6} d^{9} + 13650 \, a^{6} b^{6} d^{7} + 46410 \, a^{6} b^{6} d^{5} + 62985 \, a^{6} b^{6} d^{3} + 29393 \, a^{6} b^{6} d\right)} e^{13} + 22 \, {\left(21 \, a^{5} b^{7} d^{13} + 1386 \, a^{5} b^{7} d^{11} + 15015 \, a^{5} b^{7} d^{9} + 60060 \, a^{5} b^{7} d^{7} + 109395 \, a^{5} b^{7} d^{5} + 92378 \, a^{5} b^{7} d^{3} + 29393 \, a^{5} b^{7} d\right)} e^{11} + 330 \, {\left(a^{4} b^{8} d^{15} + 63 \, a^{4} b^{8} d^{13} + 693 \, a^{4} b^{8} d^{11} + 3003 \, a^{4} b^{8} d^{9} + 6435 \, a^{4} b^{8} d^{7} + 7293 \, a^{4} b^{8} d^{5} + 4199 \, a^{4} b^{8} d^{3} + 969 \, a^{4} b^{8} d\right)} e^{9} + 33 \, {\left(5 \, a^{3} b^{9} d^{17} + 280 \, a^{3} b^{9} d^{15} + 2940 \, a^{3} b^{9} d^{13} + 12936 \, a^{3} b^{9} d^{11} + 30030 \, a^{3} b^{9} d^{9} + 40040 \, a^{3} b^{9} d^{7} + 30940 \, a^{3} b^{9} d^{5} + 12920 \, a^{3} b^{9} d^{3} + 2261 \, a^{3} b^{9} d\right)} e^{7} + 55 \, {\left(a^{2} b^{10} d^{19} + 45 \, a^{2} b^{10} d^{17} + 420 \, a^{2} b^{10} d^{15} + 1764 \, a^{2} b^{10} d^{13} + 4158 \, a^{2} b^{10} d^{11} + 6006 \, a^{2} b^{10} d^{9} + 5460 \, a^{2} b^{10} d^{7} + 3060 \, a^{2} b^{10} d^{5} + 969 \, a^{2} b^{10} d^{3} + 133 \, a^{2} b^{10} d\right)} e^{5} + 11 \, {\left(a b^{11} d^{21} + 30 \, a b^{11} d^{19} + 225 \, a b^{11} d^{17} + 840 \, a b^{11} d^{15} + 1890 \, a b^{11} d^{13} + 2772 \, a b^{11} d^{11} + 2730 \, a b^{11} d^{9} + 1800 \, a b^{11} d^{7} + 765 \, a b^{11} d^{5} + 190 \, a b^{11} d^{3} + 21 \, a b^{11} d\right)} e^{3} + {\left(b^{12} d^{23} + 11 \, b^{12} d^{21} + 55 \, b^{12} d^{19} + 165 \, b^{12} d^{17} + 330 \, b^{12} d^{15} + 462 \, b^{12} d^{13} + 462 \, b^{12} d^{11} + 330 \, b^{12} d^{9} + 165 \, b^{12} d^{7} + 55 \, b^{12} d^{5} + 11 \, b^{12} d^{3} + b^{12} d\right)} e\right)} x}{b^{12} d^{24} + a^{12} e^{24} + 12 \, b^{12} d^{22} + 66 \, b^{12} d^{20} + 220 \, b^{12} d^{18} + 495 \, b^{12} d^{16} + 792 \, b^{12} d^{14} + 924 \, b^{12} d^{12} + 12 \, {\left(a^{11} b d^{2} + 23 \, a^{11} b\right)} e^{22} + 792 \, b^{12} d^{10} + 66 \, {\left(a^{10} b^{2} d^{4} + 42 \, a^{10} b^{2} d^{2} + 161 \, a^{10} b^{2}\right)} e^{20} + 495 \, b^{12} d^{8} + 44 \, {\left(5 \, a^{9} b^{3} d^{6} + 285 \, a^{9} b^{3} d^{4} + 1995 \, a^{9} b^{3} d^{2} + 3059 \, a^{9} b^{3}\right)} e^{18} + 220 \, b^{12} d^{6} + 99 \, {\left(5 \, a^{8} b^{4} d^{8} + 340 \, a^{8} b^{4} d^{6} + 3230 \, a^{8} b^{4} d^{4} + 9044 \, a^{8} b^{4} d^{2} + 7429 \, a^{8} b^{4}\right)} e^{16} + 66 \, b^{12} d^{4} + 264 \, {\left(3 \, a^{7} b^{5} d^{10} + 225 \, a^{7} b^{5} d^{8} + 2550 \, a^{7} b^{5} d^{6} + 9690 \, a^{7} b^{5} d^{4} + 14535 \, a^{7} b^{5} d^{2} + 7429 \, a^{7} b^{5}\right)} e^{14} + 12 \, b^{12} d^{2} + 4 \, {\left(231 \, a^{6} b^{6} d^{12} + 18018 \, a^{6} b^{6} d^{10} + 225225 \, a^{6} b^{6} d^{8} + 1021020 \, a^{6} b^{6} d^{6} + 2078505 \, a^{6} b^{6} d^{4} + 1939938 \, a^{6} b^{6} d^{2} + 676039 \, a^{6} b^{6}\right)} e^{12} + b^{12} + 264 \, {\left(3 \, a^{5} b^{7} d^{14} + 231 \, a^{5} b^{7} d^{12} + 3003 \, a^{5} b^{7} d^{10} + 15015 \, a^{5} b^{7} d^{8} + 36465 \, a^{5} b^{7} d^{6} + 46189 \, a^{5} b^{7} d^{4} + 29393 \, a^{5} b^{7} d^{2} + 7429 \, a^{5} b^{7}\right)} e^{10} + 99 \, {\left(5 \, a^{4} b^{8} d^{16} + 360 \, a^{4} b^{8} d^{14} + 4620 \, a^{4} b^{8} d^{12} + 24024 \, a^{4} b^{8} d^{10} + 64350 \, a^{4} b^{8} d^{8} + 97240 \, a^{4} b^{8} d^{6} + 83980 \, a^{4} b^{8} d^{4} + 38760 \, a^{4} b^{8} d^{2} + 7429 \, a^{4} b^{8}\right)} e^{8} + 44 \, {\left(5 \, a^{3} b^{9} d^{18} + 315 \, a^{3} b^{9} d^{16} + 3780 \, a^{3} b^{9} d^{14} + 19404 \, a^{3} b^{9} d^{12} + 54054 \, a^{3} b^{9} d^{10} + 90090 \, a^{3} b^{9} d^{8} + 92820 \, a^{3} b^{9} d^{6} + 58140 \, a^{3} b^{9} d^{4} + 20349 \, a^{3} b^{9} d^{2} + 3059 \, a^{3} b^{9}\right)} e^{6} + 66 \, {\left(a^{2} b^{10} d^{20} + 50 \, a^{2} b^{10} d^{18} + 525 \, a^{2} b^{10} d^{16} + 2520 \, a^{2} b^{10} d^{14} + 6930 \, a^{2} b^{10} d^{12} + 12012 \, a^{2} b^{10} d^{10} + 13650 \, a^{2} b^{10} d^{8} + 10200 \, a^{2} b^{10} d^{6} + 4845 \, a^{2} b^{10} d^{4} + 1330 \, a^{2} b^{10} d^{2} + 161 \, a^{2} b^{10}\right)} e^{4} + 12 \, {\left(a b^{11} d^{22} + 33 \, a b^{11} d^{20} + 275 \, a b^{11} d^{18} + 1155 \, a b^{11} d^{16} + 2970 \, a b^{11} d^{14} + 5082 \, a b^{11} d^{12} + 6006 \, a b^{11} d^{10} + 4950 \, a b^{11} d^{8} + 2805 \, a b^{11} d^{6} + 1045 \, a b^{11} d^{4} + 231 \, a b^{11} d^{2} + 23 \, a b^{11}\right)} e^{2} + 8 \, {\left(3 \, a^{11} e^{23} + 11 \, {\left(3 \, a^{10} b d^{2} + 23 \, a^{10} b\right)} e^{21} + 33 \, {\left(5 \, a^{9} b^{2} d^{4} + 70 \, a^{9} b^{2} d^{2} + 161 \, a^{9} b^{2}\right)} e^{19} + 99 \, {\left(5 \, a^{8} b^{3} d^{6} + 95 \, a^{8} b^{3} d^{4} + 399 \, a^{8} b^{3} d^{2} + 437 \, a^{8} b^{3}\right)} e^{17} + 22 \, {\left(45 \, a^{7} b^{4} d^{8} + 1020 \, a^{7} b^{4} d^{6} + 5814 \, a^{7} b^{4} d^{4} + 11628 \, a^{7} b^{4} d^{2} + 7429 \, a^{7} b^{4}\right)} e^{15} + 6 \, {\left(231 \, a^{6} b^{5} d^{10} + 5775 \, a^{6} b^{5} d^{8} + 39270 \, a^{6} b^{5} d^{6} + 106590 \, a^{6} b^{5} d^{4} + 124355 \, a^{6} b^{5} d^{2} + 52003 \, a^{6} b^{5}\right)} e^{13} + 6 \, {\left(231 \, a^{5} b^{6} d^{12} + 6006 \, a^{5} b^{6} d^{10} + 45045 \, a^{5} b^{6} d^{8} + 145860 \, a^{5} b^{6} d^{6} + 230945 \, a^{5} b^{6} d^{4} + 176358 \, a^{5} b^{6} d^{2} + 52003 \, a^{5} b^{6}\right)} e^{11} + 22 \, {\left(45 \, a^{4} b^{7} d^{14} + 1155 \, a^{4} b^{7} d^{12} + 9009 \, a^{4} b^{7} d^{10} + 32175 \, a^{4} b^{7} d^{8} + 60775 \, a^{4} b^{7} d^{6} + 62985 \, a^{4} b^{7} d^{4} + 33915 \, a^{4} b^{7} d^{2} + 7429 \, a^{4} b^{7}\right)} e^{9} + 99 \, {\left(5 \, a^{3} b^{8} d^{16} + 120 \, a^{3} b^{8} d^{14} + 924 \, a^{3} b^{8} d^{12} + 3432 \, a^{3} b^{8} d^{10} + 7150 \, a^{3} b^{8} d^{8} + 8840 \, a^{3} b^{8} d^{6} + 6460 \, a^{3} b^{8} d^{4} + 2584 \, a^{3} b^{8} d^{2} + 437 \, a^{3} b^{8}\right)} e^{7} + 33 \, {\left(5 \, a^{2} b^{9} d^{18} + 105 \, a^{2} b^{9} d^{16} + 756 \, a^{2} b^{9} d^{14} + 2772 \, a^{2} b^{9} d^{12} + 6006 \, a^{2} b^{9} d^{10} + 8190 \, a^{2} b^{9} d^{8} + 7140 \, a^{2} b^{9} d^{6} + 3876 \, a^{2} b^{9} d^{4} + 1197 \, a^{2} b^{9} d^{2} + 161 \, a^{2} b^{9}\right)} e^{5} + 11 \, {\left(3 \, a b^{10} d^{20} + 50 \, a b^{10} d^{18} + 315 \, a b^{10} d^{16} + 1080 \, a b^{10} d^{14} + 2310 \, a b^{10} d^{12} + 3276 \, a b^{10} d^{10} + 3150 \, a b^{10} d^{8} + 2040 \, a b^{10} d^{6} + 855 \, a b^{10} d^{4} + 210 \, a b^{10} d^{2} + 23 \, a b^{10}\right)} e^{3} + 3 \, {\left(b^{11} d^{22} + 11 \, b^{11} d^{20} + 55 \, b^{11} d^{18} + 165 \, b^{11} d^{16} + 330 \, b^{11} d^{14} + 462 \, b^{11} d^{12} + 462 \, b^{11} d^{10} + 330 \, b^{11} d^{8} + 165 \, b^{11} d^{6} + 55 \, b^{11} d^{4} + 11 \, b^{11} d^{2} + b^{11}\right)} e\right)} \sqrt{a} \sqrt{b}}\right) - \log\left(b x^{2} + a\right) \log\left(\frac{b^{12} d^{24} + 12 \, b^{12} d^{22} + 66 \, b^{12} d^{20} + 220 \, b^{12} d^{18} + 495 \, b^{12} d^{16} + 792 \, b^{12} d^{14} + 924 \, b^{12} d^{12} + {\left(a^{11} b d^{2} + a^{11} b\right)} e^{22} + 792 \, b^{12} d^{10} + 11 \, {\left(a^{10} b^{2} d^{4} + 22 \, a^{10} b^{2} d^{2} + 21 \, a^{10} b^{2}\right)} e^{20} + 495 \, b^{12} d^{8} + 55 \, {\left(a^{9} b^{3} d^{6} + 39 \, a^{9} b^{3} d^{4} + 171 \, a^{9} b^{3} d^{2} + 133 \, a^{9} b^{3}\right)} e^{18} + 220 \, b^{12} d^{6} + 33 \, {\left(5 \, a^{8} b^{4} d^{8} + 260 \, a^{8} b^{4} d^{6} + 1870 \, a^{8} b^{4} d^{4} + 3876 \, a^{8} b^{4} d^{2} + 2261 \, a^{8} b^{4}\right)} e^{16} + 66 \, b^{12} d^{4} + 330 \, {\left(a^{7} b^{5} d^{10} + 61 \, a^{7} b^{5} d^{8} + 570 \, a^{7} b^{5} d^{6} + 1802 \, a^{7} b^{5} d^{4} + 2261 \, a^{7} b^{5} d^{2} + 969 \, a^{7} b^{5}\right)} e^{14} + 12 \, b^{12} d^{2} + 22 \, {\left(21 \, a^{6} b^{6} d^{12} + 1386 \, a^{6} b^{6} d^{10} + 15015 \, a^{6} b^{6} d^{8} + 60060 \, a^{6} b^{6} d^{6} + 109395 \, a^{6} b^{6} d^{4} + 92378 \, a^{6} b^{6} d^{2} + 29393 \, a^{6} b^{6}\right)} e^{12} + b^{12} + 22 \, {\left(21 \, a^{5} b^{7} d^{14} + 1407 \, a^{5} b^{7} d^{12} + 16401 \, a^{5} b^{7} d^{10} + 75075 \, a^{5} b^{7} d^{8} + 169455 \, a^{5} b^{7} d^{6} + 201773 \, a^{5} b^{7} d^{4} + 121771 \, a^{5} b^{7} d^{2} + 29393 \, a^{5} b^{7}\right)} e^{10} + 330 \, {\left(a^{4} b^{8} d^{16} + 64 \, a^{4} b^{8} d^{14} + 756 \, a^{4} b^{8} d^{12} + 3696 \, a^{4} b^{8} d^{10} + 9438 \, a^{4} b^{8} d^{8} + 13728 \, a^{4} b^{8} d^{6} + 11492 \, a^{4} b^{8} d^{4} + 5168 \, a^{4} b^{8} d^{2} + 969 \, a^{4} b^{8}\right)} e^{8} + 33 \, {\left(5 \, a^{3} b^{9} d^{18} + 285 \, a^{3} b^{9} d^{16} + 3220 \, a^{3} b^{9} d^{14} + 15876 \, a^{3} b^{9} d^{12} + 42966 \, a^{3} b^{9} d^{10} + 70070 \, a^{3} b^{9} d^{8} + 70980 \, a^{3} b^{9} d^{6} + 43860 \, a^{3} b^{9} d^{4} + 15181 \, a^{3} b^{9} d^{2} + 2261 \, a^{3} b^{9}\right)} e^{6} + 55 \, {\left(a^{2} b^{10} d^{20} + 46 \, a^{2} b^{10} d^{18} + 465 \, a^{2} b^{10} d^{16} + 2184 \, a^{2} b^{10} d^{14} + 5922 \, a^{2} b^{10} d^{12} + 10164 \, a^{2} b^{10} d^{10} + 11466 \, a^{2} b^{10} d^{8} + 8520 \, a^{2} b^{10} d^{6} + 4029 \, a^{2} b^{10} d^{4} + 1102 \, a^{2} b^{10} d^{2} + 133 \, a^{2} b^{10}\right)} e^{4} + 11 \, {\left(a b^{11} d^{22} + 31 \, a b^{11} d^{20} + 255 \, a b^{11} d^{18} + 1065 \, a b^{11} d^{16} + 2730 \, a b^{11} d^{14} + 4662 \, a b^{11} d^{12} + 5502 \, a b^{11} d^{10} + 4530 \, a b^{11} d^{8} + 2565 \, a b^{11} d^{6} + 955 \, a b^{11} d^{4} + 211 \, a b^{11} d^{2} + 21 \, a b^{11}\right)} e^{2} + {\left(a^{11} b e^{24} + 11 \, {\left(a^{10} b^{2} d^{2} + 21 \, a^{10} b^{2}\right)} e^{22} + 55 \, {\left(a^{9} b^{3} d^{4} + 38 \, a^{9} b^{3} d^{2} + 133 \, a^{9} b^{3}\right)} e^{20} + 33 \, {\left(5 \, a^{8} b^{4} d^{6} + 255 \, a^{8} b^{4} d^{4} + 1615 \, a^{8} b^{4} d^{2} + 2261 \, a^{8} b^{4}\right)} e^{18} + 330 \, {\left(a^{7} b^{5} d^{8} + 60 \, a^{7} b^{5} d^{6} + 510 \, a^{7} b^{5} d^{4} + 1292 \, a^{7} b^{5} d^{2} + 969 \, a^{7} b^{5}\right)} e^{16} + 22 \, {\left(21 \, a^{6} b^{6} d^{10} + 1365 \, a^{6} b^{6} d^{8} + 13650 \, a^{6} b^{6} d^{6} + 46410 \, a^{6} b^{6} d^{4} + 62985 \, a^{6} b^{6} d^{2} + 29393 \, a^{6} b^{6}\right)} e^{14} + 22 \, {\left(21 \, a^{5} b^{7} d^{12} + 1386 \, a^{5} b^{7} d^{10} + 15015 \, a^{5} b^{7} d^{8} + 60060 \, a^{5} b^{7} d^{6} + 109395 \, a^{5} b^{7} d^{4} + 92378 \, a^{5} b^{7} d^{2} + 29393 \, a^{5} b^{7}\right)} e^{12} + 330 \, {\left(a^{4} b^{8} d^{14} + 63 \, a^{4} b^{8} d^{12} + 693 \, a^{4} b^{8} d^{10} + 3003 \, a^{4} b^{8} d^{8} + 6435 \, a^{4} b^{8} d^{6} + 7293 \, a^{4} b^{8} d^{4} + 4199 \, a^{4} b^{8} d^{2} + 969 \, a^{4} b^{8}\right)} e^{10} + 33 \, {\left(5 \, a^{3} b^{9} d^{16} + 280 \, a^{3} b^{9} d^{14} + 2940 \, a^{3} b^{9} d^{12} + 12936 \, a^{3} b^{9} d^{10} + 30030 \, a^{3} b^{9} d^{8} + 40040 \, a^{3} b^{9} d^{6} + 30940 \, a^{3} b^{9} d^{4} + 12920 \, a^{3} b^{9} d^{2} + 2261 \, a^{3} b^{9}\right)} e^{8} + 55 \, {\left(a^{2} b^{10} d^{18} + 45 \, a^{2} b^{10} d^{16} + 420 \, a^{2} b^{10} d^{14} + 1764 \, a^{2} b^{10} d^{12} + 4158 \, a^{2} b^{10} d^{10} + 6006 \, a^{2} b^{10} d^{8} + 5460 \, a^{2} b^{10} d^{6} + 3060 \, a^{2} b^{10} d^{4} + 969 \, a^{2} b^{10} d^{2} + 133 \, a^{2} b^{10}\right)} e^{6} + 11 \, {\left(a b^{11} d^{20} + 30 \, a b^{11} d^{18} + 225 \, a b^{11} d^{16} + 840 \, a b^{11} d^{14} + 1890 \, a b^{11} d^{12} + 2772 \, a b^{11} d^{10} + 2730 \, a b^{11} d^{8} + 1800 \, a b^{11} d^{6} + 765 \, a b^{11} d^{4} + 190 \, a b^{11} d^{2} + 21 \, a b^{11}\right)} e^{4} + {\left(b^{12} d^{22} + 11 \, b^{12} d^{20} + 55 \, b^{12} d^{18} + 165 \, b^{12} d^{16} + 330 \, b^{12} d^{14} + 462 \, b^{12} d^{12} + 462 \, b^{12} d^{10} + 330 \, b^{12} d^{8} + 165 \, b^{12} d^{6} + 55 \, b^{12} d^{4} + 11 \, b^{12} d^{2} + b^{12}\right)} e^{2}\right)} x^{2} - 2 \, {\left(11 \, {\left(a^{10} b d^{2} + a^{10} b\right)} e^{21} + 110 \, {\left(a^{9} b^{2} d^{4} + 8 \, a^{9} b^{2} d^{2} + 7 \, a^{9} b^{2}\right)} e^{19} + 33 \, {\left(15 \, a^{8} b^{3} d^{6} + 205 \, a^{8} b^{3} d^{4} + 589 \, a^{8} b^{3} d^{2} + 399 \, a^{8} b^{3}\right)} e^{17} + 264 \, {\left(5 \, a^{7} b^{4} d^{8} + 90 \, a^{7} b^{4} d^{6} + 408 \, a^{7} b^{4} d^{4} + 646 \, a^{7} b^{4} d^{2} + 323 \, a^{7} b^{4}\right)} e^{15} + 110 \, {\left(21 \, a^{6} b^{5} d^{10} + 441 \, a^{6} b^{5} d^{8} + 2562 \, a^{6} b^{5} d^{6} + 6018 \, a^{6} b^{5} d^{4} + 6137 \, a^{6} b^{5} d^{2} + 2261 \, a^{6} b^{5}\right)} e^{13} + 4 \, {\left(693 \, a^{5} b^{6} d^{12} + 15708 \, a^{5} b^{6} d^{10} + 105105 \, a^{5} b^{6} d^{8} + 308880 \, a^{5} b^{6} d^{6} + 449735 \, a^{5} b^{6} d^{4} + 319124 \, a^{5} b^{6} d^{2} + 88179 \, a^{5} b^{6}\right)} e^{11} + 110 \, {\left(21 \, a^{4} b^{7} d^{14} + 483 \, a^{4} b^{7} d^{12} + 3465 \, a^{4} b^{7} d^{10} + 11583 \, a^{4} b^{7} d^{8} + 20735 \, a^{4} b^{7} d^{6} + 20553 \, a^{4} b^{7} d^{4} + 10659 \, a^{4} b^{7} d^{2} + 2261 \, a^{4} b^{7}\right)} e^{9} + 264 \, {\left(5 \, a^{3} b^{8} d^{16} + 110 \, a^{3} b^{8} d^{14} + 798 \, a^{3} b^{8} d^{12} + 2838 \, a^{3} b^{8} d^{10} + 5720 \, a^{3} b^{8} d^{8} + 6890 \, a^{3} b^{8} d^{6} + 4930 \, a^{3} b^{8} d^{4} + 1938 \, a^{3} b^{8} d^{2} + 323 \, a^{3} b^{8}\right)} e^{7} + 33 \, {\left(15 \, a^{2} b^{9} d^{18} + 295 \, a^{2} b^{9} d^{16} + 2044 \, a^{2} b^{9} d^{14} + 7308 \, a^{2} b^{9} d^{12} + 15554 \, a^{2} b^{9} d^{10} + 20930 \, a^{2} b^{9} d^{8} + 18060 \, a^{2} b^{9} d^{6} + 9724 \, a^{2} b^{9} d^{4} + 2983 \, a^{2} b^{9} d^{2} + 399 \, a^{2} b^{9}\right)} e^{5} + 110 \, {\left(a b^{10} d^{20} + 16 \, a b^{10} d^{18} + 99 \, a b^{10} d^{16} + 336 \, a b^{10} d^{14} + 714 \, a b^{10} d^{12} + 1008 \, a b^{10} d^{10} + 966 \, a b^{10} d^{8} + 624 \, a b^{10} d^{6} + 261 \, a b^{10} d^{4} + 64 \, a b^{10} d^{2} + 7 \, a b^{10}\right)} e^{3} + {\left(11 \, a^{10} b e^{23} + 110 \, {\left(a^{9} b^{2} d^{2} + 7 \, a^{9} b^{2}\right)} e^{21} + 33 \, {\left(15 \, a^{8} b^{3} d^{4} + 190 \, a^{8} b^{3} d^{2} + 399 \, a^{8} b^{3}\right)} e^{19} + 264 \, {\left(5 \, a^{7} b^{4} d^{6} + 85 \, a^{7} b^{4} d^{4} + 323 \, a^{7} b^{4} d^{2} + 323 \, a^{7} b^{4}\right)} e^{17} + 110 \, {\left(21 \, a^{6} b^{5} d^{8} + 420 \, a^{6} b^{5} d^{6} + 2142 \, a^{6} b^{5} d^{4} + 3876 \, a^{6} b^{5} d^{2} + 2261 \, a^{6} b^{5}\right)} e^{15} + 4 \, {\left(693 \, a^{5} b^{6} d^{10} + 15015 \, a^{5} b^{6} d^{8} + 90090 \, a^{5} b^{6} d^{6} + 218790 \, a^{5} b^{6} d^{4} + 230945 \, a^{5} b^{6} d^{2} + 88179 \, a^{5} b^{6}\right)} e^{13} + 110 \, {\left(21 \, a^{4} b^{7} d^{12} + 462 \, a^{4} b^{7} d^{10} + 3003 \, a^{4} b^{7} d^{8} + 8580 \, a^{4} b^{7} d^{6} + 12155 \, a^{4} b^{7} d^{4} + 8398 \, a^{4} b^{7} d^{2} + 2261 \, a^{4} b^{7}\right)} e^{11} + 264 \, {\left(5 \, a^{3} b^{8} d^{14} + 105 \, a^{3} b^{8} d^{12} + 693 \, a^{3} b^{8} d^{10} + 2145 \, a^{3} b^{8} d^{8} + 3575 \, a^{3} b^{8} d^{6} + 3315 \, a^{3} b^{8} d^{4} + 1615 \, a^{3} b^{8} d^{2} + 323 \, a^{3} b^{8}\right)} e^{9} + 33 \, {\left(15 \, a^{2} b^{9} d^{16} + 280 \, a^{2} b^{9} d^{14} + 1764 \, a^{2} b^{9} d^{12} + 5544 \, a^{2} b^{9} d^{10} + 10010 \, a^{2} b^{9} d^{8} + 10920 \, a^{2} b^{9} d^{6} + 7140 \, a^{2} b^{9} d^{4} + 2584 \, a^{2} b^{9} d^{2} + 399 \, a^{2} b^{9}\right)} e^{7} + 110 \, {\left(a b^{10} d^{18} + 15 \, a b^{10} d^{16} + 84 \, a b^{10} d^{14} + 252 \, a b^{10} d^{12} + 462 \, a b^{10} d^{10} + 546 \, a b^{10} d^{8} + 420 \, a b^{10} d^{6} + 204 \, a b^{10} d^{4} + 57 \, a b^{10} d^{2} + 7 \, a b^{10}\right)} e^{5} + 11 \, {\left(b^{11} d^{20} + 10 \, b^{11} d^{18} + 45 \, b^{11} d^{16} + 120 \, b^{11} d^{14} + 210 \, b^{11} d^{12} + 252 \, b^{11} d^{10} + 210 \, b^{11} d^{8} + 120 \, b^{11} d^{6} + 45 \, b^{11} d^{4} + 10 \, b^{11} d^{2} + b^{11}\right)} e^{3}\right)} x^{2} + 11 \, {\left(b^{11} d^{22} + 11 \, b^{11} d^{20} + 55 \, b^{11} d^{18} + 165 \, b^{11} d^{16} + 330 \, b^{11} d^{14} + 462 \, b^{11} d^{12} + 462 \, b^{11} d^{10} + 330 \, b^{11} d^{8} + 165 \, b^{11} d^{6} + 55 \, b^{11} d^{4} + 11 \, b^{11} d^{2} + b^{11}\right)} e + 2 \, {\left(11 \, a^{10} b d e^{22} + 110 \, {\left(a^{9} b^{2} d^{3} + 7 \, a^{9} b^{2} d\right)} e^{20} + 33 \, {\left(15 \, a^{8} b^{3} d^{5} + 190 \, a^{8} b^{3} d^{3} + 399 \, a^{8} b^{3} d\right)} e^{18} + 264 \, {\left(5 \, a^{7} b^{4} d^{7} + 85 \, a^{7} b^{4} d^{5} + 323 \, a^{7} b^{4} d^{3} + 323 \, a^{7} b^{4} d\right)} e^{16} + 110 \, {\left(21 \, a^{6} b^{5} d^{9} + 420 \, a^{6} b^{5} d^{7} + 2142 \, a^{6} b^{5} d^{5} + 3876 \, a^{6} b^{5} d^{3} + 2261 \, a^{6} b^{5} d\right)} e^{14} + 4 \, {\left(693 \, a^{5} b^{6} d^{11} + 15015 \, a^{5} b^{6} d^{9} + 90090 \, a^{5} b^{6} d^{7} + 218790 \, a^{5} b^{6} d^{5} + 230945 \, a^{5} b^{6} d^{3} + 88179 \, a^{5} b^{6} d\right)} e^{12} + 110 \, {\left(21 \, a^{4} b^{7} d^{13} + 462 \, a^{4} b^{7} d^{11} + 3003 \, a^{4} b^{7} d^{9} + 8580 \, a^{4} b^{7} d^{7} + 12155 \, a^{4} b^{7} d^{5} + 8398 \, a^{4} b^{7} d^{3} + 2261 \, a^{4} b^{7} d\right)} e^{10} + 264 \, {\left(5 \, a^{3} b^{8} d^{15} + 105 \, a^{3} b^{8} d^{13} + 693 \, a^{3} b^{8} d^{11} + 2145 \, a^{3} b^{8} d^{9} + 3575 \, a^{3} b^{8} d^{7} + 3315 \, a^{3} b^{8} d^{5} + 1615 \, a^{3} b^{8} d^{3} + 323 \, a^{3} b^{8} d\right)} e^{8} + 33 \, {\left(15 \, a^{2} b^{9} d^{17} + 280 \, a^{2} b^{9} d^{15} + 1764 \, a^{2} b^{9} d^{13} + 5544 \, a^{2} b^{9} d^{11} + 10010 \, a^{2} b^{9} d^{9} + 10920 \, a^{2} b^{9} d^{7} + 7140 \, a^{2} b^{9} d^{5} + 2584 \, a^{2} b^{9} d^{3} + 399 \, a^{2} b^{9} d\right)} e^{6} + 110 \, {\left(a b^{10} d^{19} + 15 \, a b^{10} d^{17} + 84 \, a b^{10} d^{15} + 252 \, a b^{10} d^{13} + 462 \, a b^{10} d^{11} + 546 \, a b^{10} d^{9} + 420 \, a b^{10} d^{7} + 204 \, a b^{10} d^{5} + 57 \, a b^{10} d^{3} + 7 \, a b^{10} d\right)} e^{4} + 11 \, {\left(b^{11} d^{21} + 10 \, b^{11} d^{19} + 45 \, b^{11} d^{17} + 120 \, b^{11} d^{15} + 210 \, b^{11} d^{13} + 252 \, b^{11} d^{11} + 210 \, b^{11} d^{9} + 120 \, b^{11} d^{7} + 45 \, b^{11} d^{5} + 10 \, b^{11} d^{3} + b^{11} d\right)} e^{2}\right)} x\right)} \sqrt{a} \sqrt{b} + 2 \, {\left(a^{11} b d e^{23} + 11 \, {\left(a^{10} b^{2} d^{3} + 21 \, a^{10} b^{2} d\right)} e^{21} + 55 \, {\left(a^{9} b^{3} d^{5} + 38 \, a^{9} b^{3} d^{3} + 133 \, a^{9} b^{3} d\right)} e^{19} + 33 \, {\left(5 \, a^{8} b^{4} d^{7} + 255 \, a^{8} b^{4} d^{5} + 1615 \, a^{8} b^{4} d^{3} + 2261 \, a^{8} b^{4} d\right)} e^{17} + 330 \, {\left(a^{7} b^{5} d^{9} + 60 \, a^{7} b^{5} d^{7} + 510 \, a^{7} b^{5} d^{5} + 1292 \, a^{7} b^{5} d^{3} + 969 \, a^{7} b^{5} d\right)} e^{15} + 22 \, {\left(21 \, a^{6} b^{6} d^{11} + 1365 \, a^{6} b^{6} d^{9} + 13650 \, a^{6} b^{6} d^{7} + 46410 \, a^{6} b^{6} d^{5} + 62985 \, a^{6} b^{6} d^{3} + 29393 \, a^{6} b^{6} d\right)} e^{13} + 22 \, {\left(21 \, a^{5} b^{7} d^{13} + 1386 \, a^{5} b^{7} d^{11} + 15015 \, a^{5} b^{7} d^{9} + 60060 \, a^{5} b^{7} d^{7} + 109395 \, a^{5} b^{7} d^{5} + 92378 \, a^{5} b^{7} d^{3} + 29393 \, a^{5} b^{7} d\right)} e^{11} + 330 \, {\left(a^{4} b^{8} d^{15} + 63 \, a^{4} b^{8} d^{13} + 693 \, a^{4} b^{8} d^{11} + 3003 \, a^{4} b^{8} d^{9} + 6435 \, a^{4} b^{8} d^{7} + 7293 \, a^{4} b^{8} d^{5} + 4199 \, a^{4} b^{8} d^{3} + 969 \, a^{4} b^{8} d\right)} e^{9} + 33 \, {\left(5 \, a^{3} b^{9} d^{17} + 280 \, a^{3} b^{9} d^{15} + 2940 \, a^{3} b^{9} d^{13} + 12936 \, a^{3} b^{9} d^{11} + 30030 \, a^{3} b^{9} d^{9} + 40040 \, a^{3} b^{9} d^{7} + 30940 \, a^{3} b^{9} d^{5} + 12920 \, a^{3} b^{9} d^{3} + 2261 \, a^{3} b^{9} d\right)} e^{7} + 55 \, {\left(a^{2} b^{10} d^{19} + 45 \, a^{2} b^{10} d^{17} + 420 \, a^{2} b^{10} d^{15} + 1764 \, a^{2} b^{10} d^{13} + 4158 \, a^{2} b^{10} d^{11} + 6006 \, a^{2} b^{10} d^{9} + 5460 \, a^{2} b^{10} d^{7} + 3060 \, a^{2} b^{10} d^{5} + 969 \, a^{2} b^{10} d^{3} + 133 \, a^{2} b^{10} d\right)} e^{5} + 11 \, {\left(a b^{11} d^{21} + 30 \, a b^{11} d^{19} + 225 \, a b^{11} d^{17} + 840 \, a b^{11} d^{15} + 1890 \, a b^{11} d^{13} + 2772 \, a b^{11} d^{11} + 2730 \, a b^{11} d^{9} + 1800 \, a b^{11} d^{7} + 765 \, a b^{11} d^{5} + 190 \, a b^{11} d^{3} + 21 \, a b^{11} d\right)} e^{3} + {\left(b^{12} d^{23} + 11 \, b^{12} d^{21} + 55 \, b^{12} d^{19} + 165 \, b^{12} d^{17} + 330 \, b^{12} d^{15} + 462 \, b^{12} d^{13} + 462 \, b^{12} d^{11} + 330 \, b^{12} d^{9} + 165 \, b^{12} d^{7} + 55 \, b^{12} d^{5} + 11 \, b^{12} d^{3} + b^{12} d\right)} e\right)} x}{b^{12} d^{24} + a^{12} e^{24} + 12 \, b^{12} d^{22} + 66 \, b^{12} d^{20} + 220 \, b^{12} d^{18} + 495 \, b^{12} d^{16} + 792 \, b^{12} d^{14} + 924 \, b^{12} d^{12} + 12 \, {\left(a^{11} b d^{2} + 23 \, a^{11} b\right)} e^{22} + 792 \, b^{12} d^{10} + 66 \, {\left(a^{10} b^{2} d^{4} + 42 \, a^{10} b^{2} d^{2} + 161 \, a^{10} b^{2}\right)} e^{20} + 495 \, b^{12} d^{8} + 44 \, {\left(5 \, a^{9} b^{3} d^{6} + 285 \, a^{9} b^{3} d^{4} + 1995 \, a^{9} b^{3} d^{2} + 3059 \, a^{9} b^{3}\right)} e^{18} + 220 \, b^{12} d^{6} + 99 \, {\left(5 \, a^{8} b^{4} d^{8} + 340 \, a^{8} b^{4} d^{6} + 3230 \, a^{8} b^{4} d^{4} + 9044 \, a^{8} b^{4} d^{2} + 7429 \, a^{8} b^{4}\right)} e^{16} + 66 \, b^{12} d^{4} + 264 \, {\left(3 \, a^{7} b^{5} d^{10} + 225 \, a^{7} b^{5} d^{8} + 2550 \, a^{7} b^{5} d^{6} + 9690 \, a^{7} b^{5} d^{4} + 14535 \, a^{7} b^{5} d^{2} + 7429 \, a^{7} b^{5}\right)} e^{14} + 12 \, b^{12} d^{2} + 4 \, {\left(231 \, a^{6} b^{6} d^{12} + 18018 \, a^{6} b^{6} d^{10} + 225225 \, a^{6} b^{6} d^{8} + 1021020 \, a^{6} b^{6} d^{6} + 2078505 \, a^{6} b^{6} d^{4} + 1939938 \, a^{6} b^{6} d^{2} + 676039 \, a^{6} b^{6}\right)} e^{12} + b^{12} + 264 \, {\left(3 \, a^{5} b^{7} d^{14} + 231 \, a^{5} b^{7} d^{12} + 3003 \, a^{5} b^{7} d^{10} + 15015 \, a^{5} b^{7} d^{8} + 36465 \, a^{5} b^{7} d^{6} + 46189 \, a^{5} b^{7} d^{4} + 29393 \, a^{5} b^{7} d^{2} + 7429 \, a^{5} b^{7}\right)} e^{10} + 99 \, {\left(5 \, a^{4} b^{8} d^{16} + 360 \, a^{4} b^{8} d^{14} + 4620 \, a^{4} b^{8} d^{12} + 24024 \, a^{4} b^{8} d^{10} + 64350 \, a^{4} b^{8} d^{8} + 97240 \, a^{4} b^{8} d^{6} + 83980 \, a^{4} b^{8} d^{4} + 38760 \, a^{4} b^{8} d^{2} + 7429 \, a^{4} b^{8}\right)} e^{8} + 44 \, {\left(5 \, a^{3} b^{9} d^{18} + 315 \, a^{3} b^{9} d^{16} + 3780 \, a^{3} b^{9} d^{14} + 19404 \, a^{3} b^{9} d^{12} + 54054 \, a^{3} b^{9} d^{10} + 90090 \, a^{3} b^{9} d^{8} + 92820 \, a^{3} b^{9} d^{6} + 58140 \, a^{3} b^{9} d^{4} + 20349 \, a^{3} b^{9} d^{2} + 3059 \, a^{3} b^{9}\right)} e^{6} + 66 \, {\left(a^{2} b^{10} d^{20} + 50 \, a^{2} b^{10} d^{18} + 525 \, a^{2} b^{10} d^{16} + 2520 \, a^{2} b^{10} d^{14} + 6930 \, a^{2} b^{10} d^{12} + 12012 \, a^{2} b^{10} d^{10} + 13650 \, a^{2} b^{10} d^{8} + 10200 \, a^{2} b^{10} d^{6} + 4845 \, a^{2} b^{10} d^{4} + 1330 \, a^{2} b^{10} d^{2} + 161 \, a^{2} b^{10}\right)} e^{4} + 12 \, {\left(a b^{11} d^{22} + 33 \, a b^{11} d^{20} + 275 \, a b^{11} d^{18} + 1155 \, a b^{11} d^{16} + 2970 \, a b^{11} d^{14} + 5082 \, a b^{11} d^{12} + 6006 \, a b^{11} d^{10} + 4950 \, a b^{11} d^{8} + 2805 \, a b^{11} d^{6} + 1045 \, a b^{11} d^{4} + 231 \, a b^{11} d^{2} + 23 \, a b^{11}\right)} e^{2} - 8 \, {\left(3 \, a^{11} e^{23} + 11 \, {\left(3 \, a^{10} b d^{2} + 23 \, a^{10} b\right)} e^{21} + 33 \, {\left(5 \, a^{9} b^{2} d^{4} + 70 \, a^{9} b^{2} d^{2} + 161 \, a^{9} b^{2}\right)} e^{19} + 99 \, {\left(5 \, a^{8} b^{3} d^{6} + 95 \, a^{8} b^{3} d^{4} + 399 \, a^{8} b^{3} d^{2} + 437 \, a^{8} b^{3}\right)} e^{17} + 22 \, {\left(45 \, a^{7} b^{4} d^{8} + 1020 \, a^{7} b^{4} d^{6} + 5814 \, a^{7} b^{4} d^{4} + 11628 \, a^{7} b^{4} d^{2} + 7429 \, a^{7} b^{4}\right)} e^{15} + 6 \, {\left(231 \, a^{6} b^{5} d^{10} + 5775 \, a^{6} b^{5} d^{8} + 39270 \, a^{6} b^{5} d^{6} + 106590 \, a^{6} b^{5} d^{4} + 124355 \, a^{6} b^{5} d^{2} + 52003 \, a^{6} b^{5}\right)} e^{13} + 6 \, {\left(231 \, a^{5} b^{6} d^{12} + 6006 \, a^{5} b^{6} d^{10} + 45045 \, a^{5} b^{6} d^{8} + 145860 \, a^{5} b^{6} d^{6} + 230945 \, a^{5} b^{6} d^{4} + 176358 \, a^{5} b^{6} d^{2} + 52003 \, a^{5} b^{6}\right)} e^{11} + 22 \, {\left(45 \, a^{4} b^{7} d^{14} + 1155 \, a^{4} b^{7} d^{12} + 9009 \, a^{4} b^{7} d^{10} + 32175 \, a^{4} b^{7} d^{8} + 60775 \, a^{4} b^{7} d^{6} + 62985 \, a^{4} b^{7} d^{4} + 33915 \, a^{4} b^{7} d^{2} + 7429 \, a^{4} b^{7}\right)} e^{9} + 99 \, {\left(5 \, a^{3} b^{8} d^{16} + 120 \, a^{3} b^{8} d^{14} + 924 \, a^{3} b^{8} d^{12} + 3432 \, a^{3} b^{8} d^{10} + 7150 \, a^{3} b^{8} d^{8} + 8840 \, a^{3} b^{8} d^{6} + 6460 \, a^{3} b^{8} d^{4} + 2584 \, a^{3} b^{8} d^{2} + 437 \, a^{3} b^{8}\right)} e^{7} + 33 \, {\left(5 \, a^{2} b^{9} d^{18} + 105 \, a^{2} b^{9} d^{16} + 756 \, a^{2} b^{9} d^{14} + 2772 \, a^{2} b^{9} d^{12} + 6006 \, a^{2} b^{9} d^{10} + 8190 \, a^{2} b^{9} d^{8} + 7140 \, a^{2} b^{9} d^{6} + 3876 \, a^{2} b^{9} d^{4} + 1197 \, a^{2} b^{9} d^{2} + 161 \, a^{2} b^{9}\right)} e^{5} + 11 \, {\left(3 \, a b^{10} d^{20} + 50 \, a b^{10} d^{18} + 315 \, a b^{10} d^{16} + 1080 \, a b^{10} d^{14} + 2310 \, a b^{10} d^{12} + 3276 \, a b^{10} d^{10} + 3150 \, a b^{10} d^{8} + 2040 \, a b^{10} d^{6} + 855 \, a b^{10} d^{4} + 210 \, a b^{10} d^{2} + 23 \, a b^{10}\right)} e^{3} + 3 \, {\left(b^{11} d^{22} + 11 \, b^{11} d^{20} + 55 \, b^{11} d^{18} + 165 \, b^{11} d^{16} + 330 \, b^{11} d^{14} + 462 \, b^{11} d^{12} + 462 \, b^{11} d^{10} + 330 \, b^{11} d^{8} + 165 \, b^{11} d^{6} + 55 \, b^{11} d^{4} + 11 \, b^{11} d^{2} + b^{11}\right)} e\right)} \sqrt{a} \sqrt{b}}\right) + 2 \, {\rm Li}_2\left(-\frac{a e^{2} + {\left(b d + i \, b\right)} e x + {\left(i \, e^{2} x + {\left(-i \, d + 1\right)} e\right)} \sqrt{a} \sqrt{b}}{b d^{2} - 2 \, \sqrt{a} \sqrt{b} {\left(-i \, d + 1\right)} e - a e^{2} + 2 i \, b d - b}\right) - 2 \, {\rm Li}_2\left(-\frac{a e^{2} + {\left(b d + i \, b\right)} e x - {\left(i \, e^{2} x + {\left(-i \, d + 1\right)} e\right)} \sqrt{a} \sqrt{b}}{b d^{2} + 2 \, \sqrt{a} \sqrt{b} {\left(-i \, d + 1\right)} e - a e^{2} + 2 i \, b d - b}\right) - 2 \, {\rm Li}_2\left(-\frac{a e^{2} + {\left(b d - i \, b\right)} e x + {\left(i \, e^{2} x + {\left(-i \, d - 1\right)} e\right)} \sqrt{a} \sqrt{b}}{b d^{2} - 2 \, \sqrt{a} \sqrt{b} {\left(-i \, d - 1\right)} e - a e^{2} - 2 i \, b d - b}\right) + 2 \, {\rm Li}_2\left(-\frac{a e^{2} + {\left(b d - i \, b\right)} e x - {\left(i \, e^{2} x + {\left(-i \, d - 1\right)} e\right)} \sqrt{a} \sqrt{b}}{b d^{2} + 2 \, \sqrt{a} \sqrt{b} {\left(-i \, d - 1\right)} e - a e^{2} - 2 i \, b d - b}\right)}{e}\right)}}{8 \, \sqrt{a b}} + \frac{\arctan\left(e x + d\right) \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}} - \frac{\arctan\left(\frac{b x}{\sqrt{a b}}\right) \arctan\left(\frac{e^{2} x + d e}{e}\right)}{\sqrt{a b}}"," ",0,"1/8*e*(8*arctan(b*x/sqrt(a*b))*arctan((e^2*x + d*e)/e)/e - (4*arctan(sqrt(b)*x/sqrt(a))*arctan2((2*a*b*d*e^2 + (a*d*e^3 + (b*d^3 + b*d)*e + (a*e^4 + (b*d^2 + 3*b)*e^2)*x)*sqrt(a)*sqrt(b) + (3*a*b*e^3 + (b^2*d^2 + b^2)*e)*x)/(b^2*d^4 + a^2*e^4 + 2*b^2*d^2 + 2*(a*b*d^2 + 3*a*b)*e^2 + 4*(a*e^3 + (b*d^2 + b)*e)*sqrt(a)*sqrt(b) + b^2), (b^2*d^4 + 2*b^2*d^2 + (a*b*d^2 + 3*a*b)*e^2 + (2*b*d*e^2*x + a*e^3 + 3*(b*d^2 + b)*e)*sqrt(a)*sqrt(b) + b^2 + (a*b*d*e^3 + (b^2*d^3 + b^2*d)*e)*x)/(b^2*d^4 + a^2*e^4 + 2*b^2*d^2 + 2*(a*b*d^2 + 3*a*b)*e^2 + 4*(a*e^3 + (b*d^2 + b)*e)*sqrt(a)*sqrt(b) + b^2)) + 4*arctan(sqrt(b)*x/sqrt(a))*arctan2((2*a*b*d*e^2 - (a*d*e^3 + (b*d^3 + b*d)*e + (a*e^4 + (b*d^2 + 3*b)*e^2)*x)*sqrt(a)*sqrt(b) + (3*a*b*e^3 + (b^2*d^2 + b^2)*e)*x)/(b^2*d^4 + a^2*e^4 + 2*b^2*d^2 + 2*(a*b*d^2 + 3*a*b)*e^2 - 4*(a*e^3 + (b*d^2 + b)*e)*sqrt(a)*sqrt(b) + b^2), (b^2*d^4 + 2*b^2*d^2 + (a*b*d^2 + 3*a*b)*e^2 - (2*b*d*e^2*x + a*e^3 + 3*(b*d^2 + b)*e)*sqrt(a)*sqrt(b) + b^2 + (a*b*d*e^3 + (b^2*d^3 + b^2*d)*e)*x)/(b^2*d^4 + a^2*e^4 + 2*b^2*d^2 + 2*(a*b*d^2 + 3*a*b)*e^2 - 4*(a*e^3 + (b*d^2 + b)*e)*sqrt(a)*sqrt(b) + b^2)) + log(b*x^2 + a)*log((b^12*d^24 + 12*b^12*d^22 + 66*b^12*d^20 + 220*b^12*d^18 + 495*b^12*d^16 + 792*b^12*d^14 + 924*b^12*d^12 + (a^11*b*d^2 + a^11*b)*e^22 + 792*b^12*d^10 + 11*(a^10*b^2*d^4 + 22*a^10*b^2*d^2 + 21*a^10*b^2)*e^20 + 495*b^12*d^8 + 55*(a^9*b^3*d^6 + 39*a^9*b^3*d^4 + 171*a^9*b^3*d^2 + 133*a^9*b^3)*e^18 + 220*b^12*d^6 + 33*(5*a^8*b^4*d^8 + 260*a^8*b^4*d^6 + 1870*a^8*b^4*d^4 + 3876*a^8*b^4*d^2 + 2261*a^8*b^4)*e^16 + 66*b^12*d^4 + 330*(a^7*b^5*d^10 + 61*a^7*b^5*d^8 + 570*a^7*b^5*d^6 + 1802*a^7*b^5*d^4 + 2261*a^7*b^5*d^2 + 969*a^7*b^5)*e^14 + 12*b^12*d^2 + 22*(21*a^6*b^6*d^12 + 1386*a^6*b^6*d^10 + 15015*a^6*b^6*d^8 + 60060*a^6*b^6*d^6 + 109395*a^6*b^6*d^4 + 92378*a^6*b^6*d^2 + 29393*a^6*b^6)*e^12 + b^12 + 22*(21*a^5*b^7*d^14 + 1407*a^5*b^7*d^12 + 16401*a^5*b^7*d^10 + 75075*a^5*b^7*d^8 + 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45*b^11*d^17 + 120*b^11*d^15 + 210*b^11*d^13 + 252*b^11*d^11 + 210*b^11*d^9 + 120*b^11*d^7 + 45*b^11*d^5 + 10*b^11*d^3 + b^11*d)*e^2)*x)*sqrt(a)*sqrt(b) + 2*(a^11*b*d*e^23 + 11*(a^10*b^2*d^3 + 21*a^10*b^2*d)*e^21 + 55*(a^9*b^3*d^5 + 38*a^9*b^3*d^3 + 133*a^9*b^3*d)*e^19 + 33*(5*a^8*b^4*d^7 + 255*a^8*b^4*d^5 + 1615*a^8*b^4*d^3 + 2261*a^8*b^4*d)*e^17 + 330*(a^7*b^5*d^9 + 60*a^7*b^5*d^7 + 510*a^7*b^5*d^5 + 1292*a^7*b^5*d^3 + 969*a^7*b^5*d)*e^15 + 22*(21*a^6*b^6*d^11 + 1365*a^6*b^6*d^9 + 13650*a^6*b^6*d^7 + 46410*a^6*b^6*d^5 + 62985*a^6*b^6*d^3 + 29393*a^6*b^6*d)*e^13 + 22*(21*a^5*b^7*d^13 + 1386*a^5*b^7*d^11 + 15015*a^5*b^7*d^9 + 60060*a^5*b^7*d^7 + 109395*a^5*b^7*d^5 + 92378*a^5*b^7*d^3 + 29393*a^5*b^7*d)*e^11 + 330*(a^4*b^8*d^15 + 63*a^4*b^8*d^13 + 693*a^4*b^8*d^11 + 3003*a^4*b^8*d^9 + 6435*a^4*b^8*d^7 + 7293*a^4*b^8*d^5 + 4199*a^4*b^8*d^3 + 969*a^4*b^8*d)*e^9 + 33*(5*a^3*b^9*d^17 + 280*a^3*b^9*d^15 + 2940*a^3*b^9*d^13 + 12936*a^3*b^9*d^11 + 30030*a^3*b^9*d^9 + 40040*a^3*b^9*d^7 + 30940*a^3*b^9*d^5 + 12920*a^3*b^9*d^3 + 2261*a^3*b^9*d)*e^7 + 55*(a^2*b^10*d^19 + 45*a^2*b^10*d^17 + 420*a^2*b^10*d^15 + 1764*a^2*b^10*d^13 + 4158*a^2*b^10*d^11 + 6006*a^2*b^10*d^9 + 5460*a^2*b^10*d^7 + 3060*a^2*b^10*d^5 + 969*a^2*b^10*d^3 + 133*a^2*b^10*d)*e^5 + 11*(a*b^11*d^21 + 30*a*b^11*d^19 + 225*a*b^11*d^17 + 840*a*b^11*d^15 + 1890*a*b^11*d^13 + 2772*a*b^11*d^11 + 2730*a*b^11*d^9 + 1800*a*b^11*d^7 + 765*a*b^11*d^5 + 190*a*b^11*d^3 + 21*a*b^11*d)*e^3 + (b^12*d^23 + 11*b^12*d^21 + 55*b^12*d^19 + 165*b^12*d^17 + 330*b^12*d^15 + 462*b^12*d^13 + 462*b^12*d^11 + 330*b^12*d^9 + 165*b^12*d^7 + 55*b^12*d^5 + 11*b^12*d^3 + b^12*d)*e)*x)/(b^12*d^24 + a^12*e^24 + 12*b^12*d^22 + 66*b^12*d^20 + 220*b^12*d^18 + 495*b^12*d^16 + 792*b^12*d^14 + 924*b^12*d^12 + 12*(a^11*b*d^2 + 23*a^11*b)*e^22 + 792*b^12*d^10 + 66*(a^10*b^2*d^4 + 42*a^10*b^2*d^2 + 161*a^10*b^2)*e^20 + 495*b^12*d^8 + 44*(5*a^9*b^3*d^6 + 285*a^9*b^3*d^4 + 1995*a^9*b^3*d^2 + 3059*a^9*b^3)*e^18 + 220*b^12*d^6 + 99*(5*a^8*b^4*d^8 + 340*a^8*b^4*d^6 + 3230*a^8*b^4*d^4 + 9044*a^8*b^4*d^2 + 7429*a^8*b^4)*e^16 + 66*b^12*d^4 + 264*(3*a^7*b^5*d^10 + 225*a^7*b^5*d^8 + 2550*a^7*b^5*d^6 + 9690*a^7*b^5*d^4 + 14535*a^7*b^5*d^2 + 7429*a^7*b^5)*e^14 + 12*b^12*d^2 + 4*(231*a^6*b^6*d^12 + 18018*a^6*b^6*d^10 + 225225*a^6*b^6*d^8 + 1021020*a^6*b^6*d^6 + 2078505*a^6*b^6*d^4 + 1939938*a^6*b^6*d^2 + 676039*a^6*b^6)*e^12 + b^12 + 264*(3*a^5*b^7*d^14 + 231*a^5*b^7*d^12 + 3003*a^5*b^7*d^10 + 15015*a^5*b^7*d^8 + 36465*a^5*b^7*d^6 + 46189*a^5*b^7*d^4 + 29393*a^5*b^7*d^2 + 7429*a^5*b^7)*e^10 + 99*(5*a^4*b^8*d^16 + 360*a^4*b^8*d^14 + 4620*a^4*b^8*d^12 + 24024*a^4*b^8*d^10 + 64350*a^4*b^8*d^8 + 97240*a^4*b^8*d^6 + 83980*a^4*b^8*d^4 + 38760*a^4*b^8*d^2 + 7429*a^4*b^8)*e^8 + 44*(5*a^3*b^9*d^18 + 315*a^3*b^9*d^16 + 3780*a^3*b^9*d^14 + 19404*a^3*b^9*d^12 + 54054*a^3*b^9*d^10 + 90090*a^3*b^9*d^8 + 92820*a^3*b^9*d^6 + 58140*a^3*b^9*d^4 + 20349*a^3*b^9*d^2 + 3059*a^3*b^9)*e^6 + 66*(a^2*b^10*d^20 + 50*a^2*b^10*d^18 + 525*a^2*b^10*d^16 + 2520*a^2*b^10*d^14 + 6930*a^2*b^10*d^12 + 12012*a^2*b^10*d^10 + 13650*a^2*b^10*d^8 + 10200*a^2*b^10*d^6 + 4845*a^2*b^10*d^4 + 1330*a^2*b^10*d^2 + 161*a^2*b^10)*e^4 + 12*(a*b^11*d^22 + 33*a*b^11*d^20 + 275*a*b^11*d^18 + 1155*a*b^11*d^16 + 2970*a*b^11*d^14 + 5082*a*b^11*d^12 + 6006*a*b^11*d^10 + 4950*a*b^11*d^8 + 2805*a*b^11*d^6 + 1045*a*b^11*d^4 + 231*a*b^11*d^2 + 23*a*b^11)*e^2 - 8*(3*a^11*e^23 + 11*(3*a^10*b*d^2 + 23*a^10*b)*e^21 + 33*(5*a^9*b^2*d^4 + 70*a^9*b^2*d^2 + 161*a^9*b^2)*e^19 + 99*(5*a^8*b^3*d^6 + 95*a^8*b^3*d^4 + 399*a^8*b^3*d^2 + 437*a^8*b^3)*e^17 + 22*(45*a^7*b^4*d^8 + 1020*a^7*b^4*d^6 + 5814*a^7*b^4*d^4 + 11628*a^7*b^4*d^2 + 7429*a^7*b^4)*e^15 + 6*(231*a^6*b^5*d^10 + 5775*a^6*b^5*d^8 + 39270*a^6*b^5*d^6 + 106590*a^6*b^5*d^4 + 124355*a^6*b^5*d^2 + 52003*a^6*b^5)*e^13 + 6*(231*a^5*b^6*d^12 + 6006*a^5*b^6*d^10 + 45045*a^5*b^6*d^8 + 145860*a^5*b^6*d^6 + 230945*a^5*b^6*d^4 + 176358*a^5*b^6*d^2 + 52003*a^5*b^6)*e^11 + 22*(45*a^4*b^7*d^14 + 1155*a^4*b^7*d^12 + 9009*a^4*b^7*d^10 + 32175*a^4*b^7*d^8 + 60775*a^4*b^7*d^6 + 62985*a^4*b^7*d^4 + 33915*a^4*b^7*d^2 + 7429*a^4*b^7)*e^9 + 99*(5*a^3*b^8*d^16 + 120*a^3*b^8*d^14 + 924*a^3*b^8*d^12 + 3432*a^3*b^8*d^10 + 7150*a^3*b^8*d^8 + 8840*a^3*b^8*d^6 + 6460*a^3*b^8*d^4 + 2584*a^3*b^8*d^2 + 437*a^3*b^8)*e^7 + 33*(5*a^2*b^9*d^18 + 105*a^2*b^9*d^16 + 756*a^2*b^9*d^14 + 2772*a^2*b^9*d^12 + 6006*a^2*b^9*d^10 + 8190*a^2*b^9*d^8 + 7140*a^2*b^9*d^6 + 3876*a^2*b^9*d^4 + 1197*a^2*b^9*d^2 + 161*a^2*b^9)*e^5 + 11*(3*a*b^10*d^20 + 50*a*b^10*d^18 + 315*a*b^10*d^16 + 1080*a*b^10*d^14 + 2310*a*b^10*d^12 + 3276*a*b^10*d^10 + 3150*a*b^10*d^8 + 2040*a*b^10*d^6 + 855*a*b^10*d^4 + 210*a*b^10*d^2 + 23*a*b^10)*e^3 + 3*(b^11*d^22 + 11*b^11*d^20 + 55*b^11*d^18 + 165*b^11*d^16 + 330*b^11*d^14 + 462*b^11*d^12 + 462*b^11*d^10 + 330*b^11*d^8 + 165*b^11*d^6 + 55*b^11*d^4 + 11*b^11*d^2 + b^11)*e)*sqrt(a)*sqrt(b))) + 2*dilog(-(a*e^2 + (b*d + I*b)*e*x + (I*e^2*x + (-I*d + 1)*e)*sqrt(a)*sqrt(b))/(b*d^2 - 2*sqrt(a)*sqrt(b)*(-I*d + 1)*e - a*e^2 + 2*I*b*d - b)) - 2*dilog(-(a*e^2 + (b*d + I*b)*e*x - (I*e^2*x + (-I*d + 1)*e)*sqrt(a)*sqrt(b))/(b*d^2 + 2*sqrt(a)*sqrt(b)*(-I*d + 1)*e - a*e^2 + 2*I*b*d - b)) - 2*dilog(-(a*e^2 + (b*d - I*b)*e*x + (I*e^2*x + (-I*d - 1)*e)*sqrt(a)*sqrt(b))/(b*d^2 - 2*sqrt(a)*sqrt(b)*(-I*d - 1)*e - a*e^2 - 2*I*b*d - b)) + 2*dilog(-(a*e^2 + (b*d - I*b)*e*x - (I*e^2*x + (-I*d - 1)*e)*sqrt(a)*sqrt(b))/(b*d^2 + 2*sqrt(a)*sqrt(b)*(-I*d - 1)*e - a*e^2 - 2*I*b*d - b)))/e)/sqrt(a*b) + arctan(e*x + d)*arctan(b*x/sqrt(a*b))/sqrt(a*b) - arctan(b*x/sqrt(a*b))*arctan((e^2*x + d*e)/e)/sqrt(a*b)","B",0
62,-2,0,0,0.000000," ","integrate(arctan(e*x+d)/(c*x^2+b*x+a),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
63,0,0,0,0.000000," ","integrate(arctan(b*x+a)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\arctan\left(b x + a\right)}{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}\,{d x}"," ",0,"integrate(arctan(b*x + a)/sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1), x)","F",0
64,0,0,0,0.000000," ","integrate(arctan(b*x+a)/((a^2+1)*c+2*a*b*c*x+c*x^2*b^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\arctan\left(b x + a\right)}{\sqrt{b^{2} c x^{2} + 2 \, a b c x + {\left(a^{2} + 1\right)} c}}\,{d x}"," ",0,"integrate(arctan(b*x + a)/sqrt(b^2*c*x^2 + 2*a*b*c*x + (a^2 + 1)*c), x)","F",0
65,0,0,0,0.000000," ","integrate(arctan(b*x+a)/(b^2*x^2+2*a*b*x+a^2+1)^(1/3),x, algorithm=""maxima"")","\int \frac{\arctan\left(b x + a\right)}{{\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(arctan(b*x + a)/(b^2*x^2 + 2*a*b*x + a^2 + 1)^(1/3), x)","F",0
66,0,0,0,0.000000," ","integrate(arctan(b*x+a)/((a^2+1)*c+2*a*b*c*x+c*x^2*b^2)^(1/3),x, algorithm=""maxima"")","\int \frac{\arctan\left(b x + a\right)}{{\left(b^{2} c x^{2} + 2 \, a b c x + {\left(a^{2} + 1\right)} c\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(arctan(b*x + a)/(b^2*c*x^2 + 2*a*b*c*x + (a^2 + 1)*c)^(1/3), x)","F",0
67,0,0,0,0.000000," ","integrate((b*x+a)^2*arctan(b*x+a)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b x + a\right)}^{2} \arctan\left(b x + a\right)}{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}\,{d x}"," ",0,"integrate((b*x + a)^2*arctan(b*x + a)/sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1), x)","F",0
68,0,0,0,0.000000," ","integrate((b*x+a)^2*arctan(b*x+a)/((a^2+1)*c+2*a*b*c*x+c*x^2*b^2)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b x + a\right)}^{2} \arctan\left(b x + a\right)}{\sqrt{b^{2} c x^{2} + 2 \, a b c x + {\left(a^{2} + 1\right)} c}}\,{d x}"," ",0,"integrate((b*x + a)^2*arctan(b*x + a)/sqrt(b^2*c*x^2 + 2*a*b*c*x + (a^2 + 1)*c), x)","F",0
69,0,0,0,0.000000," ","integrate((b*x+a)^2*arctan(b*x+a)/(b^2*x^2+2*a*b*x+a^2+1)^(1/3),x, algorithm=""maxima"")","\int \frac{{\left(b x + a\right)}^{2} \arctan\left(b x + a\right)}{{\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((b*x + a)^2*arctan(b*x + a)/(b^2*x^2 + 2*a*b*x + a^2 + 1)^(1/3), x)","F",0
70,0,0,0,0.000000," ","integrate((b*x+a)^2*arctan(b*x+a)/((a^2+1)*c+2*a*b*c*x+c*x^2*b^2)^(1/3),x, algorithm=""maxima"")","\int \frac{{\left(b x + a\right)}^{2} \arctan\left(b x + a\right)}{{\left(b^{2} c x^{2} + 2 \, a b c x + {\left(a^{2} + 1\right)} c\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((b*x + a)^2*arctan(b*x + a)/(b^2*c*x^2 + 2*a*b*c*x + (a^2 + 1)*c)^(1/3), x)","F",0
