1,1,87,94,0.051365,"\text{Not used}","int((a + b*x^3)*(c + d*x^3)^4,x)","x^4\,\left(\frac{b\,c^4}{4}+a\,d\,c^3\right)+x^{13}\,\left(\frac{a\,d^4}{13}+\frac{4\,b\,c\,d^3}{13}\right)+\frac{b\,d^4\,x^{16}}{16}+a\,c^4\,x+\frac{2\,c^2\,d\,x^7\,\left(3\,a\,d+2\,b\,c\right)}{7}+\frac{c\,d^2\,x^{10}\,\left(2\,a\,d+3\,b\,c\right)}{5}","Not used",1,"x^4*((b*c^4)/4 + a*c^3*d) + x^13*((a*d^4)/13 + (4*b*c*d^3)/13) + (b*d^4*x^16)/16 + a*c^4*x + (2*c^2*d*x^7*(3*a*d + 2*b*c))/7 + (c*d^2*x^10*(2*a*d + 3*b*c))/5","B"
2,1,66,70,0.034014,"\text{Not used}","int((a + b*x^3)*(c + d*x^3)^3,x)","x^4\,\left(\frac{b\,c^3}{4}+\frac{3\,a\,d\,c^2}{4}\right)+x^{10}\,\left(\frac{a\,d^3}{10}+\frac{3\,b\,c\,d^2}{10}\right)+\frac{b\,d^3\,x^{13}}{13}+a\,c^3\,x+\frac{3\,c\,d\,x^7\,\left(a\,d+b\,c\right)}{7}","Not used",1,"x^4*((b*c^3)/4 + (3*a*c^2*d)/4) + x^10*((a*d^3)/10 + (3*b*c*d^2)/10) + (b*d^3*x^13)/13 + a*c^3*x + (3*c*d*x^7*(a*d + b*c))/7","B"
3,1,48,50,0.047528,"\text{Not used}","int((a + b*x^3)*(c + d*x^3)^2,x)","x^4\,\left(\frac{b\,c^2}{4}+\frac{a\,d\,c}{2}\right)+x^7\,\left(\frac{a\,d^2}{7}+\frac{2\,b\,c\,d}{7}\right)+\frac{b\,d^2\,x^{10}}{10}+a\,c^2\,x","Not used",1,"x^4*((b*c^2)/4 + (a*c*d)/2) + x^7*((a*d^2)/7 + (2*b*c*d)/7) + (b*d^2*x^10)/10 + a*c^2*x","B"
4,1,25,28,0.036637,"\text{Not used}","int((a + b*x^3)*(c + d*x^3),x)","\frac{b\,d\,x^7}{7}+\left(\frac{a\,d}{4}+\frac{b\,c}{4}\right)\,x^4+a\,c\,x","Not used",1,"x^4*((a*d)/4 + (b*c)/4) + a*c*x + (b*d*x^7)/7","B"
5,1,123,144,1.383055,"\text{Not used}","int((a + b*x^3)/(c + d*x^3),x)","\frac{b\,x}{d}+\frac{\ln\left(d^{1/3}\,x+c^{1/3}\right)\,\left(a\,d-b\,c\right)}{3\,c^{2/3}\,d^{4/3}}-\frac{\ln\left(c^{1/3}-2\,d^{1/3}\,x+\sqrt{3}\,c^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(a\,d-b\,c\right)}{3\,c^{2/3}\,d^{4/3}}+\frac{\ln\left(2\,d^{1/3}\,x-c^{1/3}+\sqrt{3}\,c^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(a\,d-b\,c\right)}{3\,c^{2/3}\,d^{4/3}}","Not used",1,"(b*x)/d + (log(d^(1/3)*x + c^(1/3))*(a*d - b*c))/(3*c^(2/3)*d^(4/3)) - (log(3^(1/2)*c^(1/3)*1i - 2*d^(1/3)*x + c^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(a*d - b*c))/(3*c^(2/3)*d^(4/3)) + (log(3^(1/2)*c^(1/3)*1i + 2*d^(1/3)*x - c^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(a*d - b*c))/(3*c^(2/3)*d^(4/3))","B"
6,1,143,169,1.398291,"\text{Not used}","int((a + b*x^3)/(c + d*x^3)^2,x)","\frac{\ln\left(d^{1/3}\,x+c^{1/3}\right)\,\left(2\,a\,d+b\,c\right)}{9\,c^{5/3}\,d^{4/3}}-\frac{\ln\left(c^{1/3}-2\,d^{1/3}\,x+\sqrt{3}\,c^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(2\,a\,d+b\,c\right)}{9\,c^{5/3}\,d^{4/3}}+\frac{\ln\left(2\,d^{1/3}\,x-c^{1/3}+\sqrt{3}\,c^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(2\,a\,d+b\,c\right)}{9\,c^{5/3}\,d^{4/3}}+\frac{x\,\left(a\,d-b\,c\right)}{3\,c\,d\,\left(d\,x^3+c\right)}","Not used",1,"(log(d^(1/3)*x + c^(1/3))*(2*a*d + b*c))/(9*c^(5/3)*d^(4/3)) - (log(3^(1/2)*c^(1/3)*1i - 2*d^(1/3)*x + c^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(2*a*d + b*c))/(9*c^(5/3)*d^(4/3)) + (log(3^(1/2)*c^(1/3)*1i + 2*d^(1/3)*x - c^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(2*a*d + b*c))/(9*c^(5/3)*d^(4/3)) + (x*(a*d - b*c))/(3*c*d*(c + d*x^3))","B"
7,1,173,197,1.395706,"\text{Not used}","int((a + b*x^3)/(c + d*x^3)^3,x)","\frac{\frac{x^4\,\left(5\,a\,d+b\,c\right)}{18\,c^2}+\frac{x\,\left(4\,a\,d-b\,c\right)}{9\,c\,d}}{c^2+2\,c\,d\,x^3+d^2\,x^6}+\frac{\ln\left(d^{1/3}\,x+c^{1/3}\right)\,\left(5\,a\,d+b\,c\right)}{27\,c^{8/3}\,d^{4/3}}-\frac{\ln\left(c^{1/3}-2\,d^{1/3}\,x+\sqrt{3}\,c^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(5\,a\,d+b\,c\right)}{27\,c^{8/3}\,d^{4/3}}+\frac{\ln\left(2\,d^{1/3}\,x-c^{1/3}+\sqrt{3}\,c^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(5\,a\,d+b\,c\right)}{27\,c^{8/3}\,d^{4/3}}","Not used",1,"((x^4*(5*a*d + b*c))/(18*c^2) + (x*(4*a*d - b*c))/(9*c*d))/(c^2 + d^2*x^6 + 2*c*d*x^3) + (log(d^(1/3)*x + c^(1/3))*(5*a*d + b*c))/(27*c^(8/3)*d^(4/3)) - (log(3^(1/2)*c^(1/3)*1i - 2*d^(1/3)*x + c^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(5*a*d + b*c))/(27*c^(8/3)*d^(4/3)) + (log(3^(1/2)*c^(1/3)*1i + 2*d^(1/3)*x - c^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(5*a*d + b*c))/(27*c^(8/3)*d^(4/3))","B"
8,1,116,122,1.198956,"\text{Not used}","int((a + b*x^3)^2*(c + d*x^3)^3,x)","x^7\,\left(\frac{3\,a^2\,c\,d^2}{7}+\frac{6\,a\,b\,c^2\,d}{7}+\frac{b^2\,c^3}{7}\right)+x^{10}\,\left(\frac{a^2\,d^3}{10}+\frac{3\,a\,b\,c\,d^2}{5}+\frac{3\,b^2\,c^2\,d}{10}\right)+a^2\,c^3\,x+\frac{b^2\,d^3\,x^{16}}{16}+\frac{a\,c^2\,x^4\,\left(3\,a\,d+2\,b\,c\right)}{4}+\frac{b\,d^2\,x^{13}\,\left(2\,a\,d+3\,b\,c\right)}{13}","Not used",1,"x^7*((b^2*c^3)/7 + (3*a^2*c*d^2)/7 + (6*a*b*c^2*d)/7) + x^10*((a^2*d^3)/10 + (3*b^2*c^2*d)/10 + (3*a*b*c*d^2)/5) + a^2*c^3*x + (b^2*d^3*x^16)/16 + (a*c^2*x^4*(3*a*d + 2*b*c))/4 + (b*d^2*x^13*(2*a*d + 3*b*c))/13","B"
9,1,75,82,0.042283,"\text{Not used}","int((a + b*x^3)^2*(c + d*x^3)^2,x)","x^7\,\left(\frac{a^2\,d^2}{7}+\frac{4\,a\,b\,c\,d}{7}+\frac{b^2\,c^2}{7}\right)+a^2\,c^2\,x+\frac{b^2\,d^2\,x^{13}}{13}+\frac{a\,c\,x^4\,\left(a\,d+b\,c\right)}{2}+\frac{b\,d\,x^{10}\,\left(a\,d+b\,c\right)}{5}","Not used",1,"x^7*((a^2*d^2)/7 + (b^2*c^2)/7 + (4*a*b*c*d)/7) + a^2*c^2*x + (b^2*d^2*x^13)/13 + (a*c*x^4*(a*d + b*c))/2 + (b*d*x^10*(a*d + b*c))/5","B"
10,1,48,50,0.044812,"\text{Not used}","int((a + b*x^3)^2*(c + d*x^3),x)","x^4\,\left(\frac{d\,a^2}{4}+\frac{b\,c\,a}{2}\right)+x^7\,\left(\frac{c\,b^2}{7}+\frac{2\,a\,d\,b}{7}\right)+\frac{b^2\,d\,x^{10}}{10}+a^2\,c\,x","Not used",1,"x^4*((a^2*d)/4 + (a*b*c)/2) + x^7*((b^2*c)/7 + (2*a*b*d)/7) + (b^2*d*x^10)/10 + a^2*c*x","B"
11,1,152,173,1.385540,"\text{Not used}","int((a + b*x^3)^2/(c + d*x^3),x)","\frac{b^2\,x^4}{4\,d}-x\,\left(\frac{b^2\,c}{d^2}-\frac{2\,a\,b}{d}\right)+\frac{\ln\left(d^{1/3}\,x+c^{1/3}\right)\,{\left(a\,d-b\,c\right)}^2}{3\,c^{2/3}\,d^{7/3}}+\frac{\ln\left(2\,d^{1/3}\,x-c^{1/3}+\sqrt{3}\,c^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)\,{\left(a\,d-b\,c\right)}^2}{c^{2/3}\,d^{7/3}}-\frac{\ln\left(c^{1/3}-2\,d^{1/3}\,x+\sqrt{3}\,c^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(a\,d-b\,c\right)}^2}{3\,c^{2/3}\,d^{7/3}}","Not used",1,"(b^2*x^4)/(4*d) - x*((b^2*c)/d^2 - (2*a*b)/d) + (log(d^(1/3)*x + c^(1/3))*(a*d - b*c)^2)/(3*c^(2/3)*d^(7/3)) + (log(3^(1/2)*c^(1/3)*1i + 2*d^(1/3)*x - c^(1/3))*((3^(1/2)*1i)/6 - 1/6)*(a*d - b*c)^2)/(c^(2/3)*d^(7/3)) - (log(3^(1/2)*c^(1/3)*1i - 2*d^(1/3)*x + c^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(a*d - b*c)^2)/(3*c^(2/3)*d^(7/3))","B"
12,1,191,203,1.411660,"\text{Not used}","int((a + b*x^3)^2/(c + d*x^3)^2,x)","\frac{b^2\,x}{d^2}+\frac{x\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}{3\,c\,\left(d^3\,x^3+c\,d^2\right)}+\frac{2\,\ln\left(d^{1/3}\,x+c^{1/3}\right)\,\left(a\,d-b\,c\right)\,\left(a\,d+2\,b\,c\right)}{9\,c^{5/3}\,d^{7/3}}+\frac{2\,\ln\left(2\,d^{1/3}\,x-c^{1/3}+\sqrt{3}\,c^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(a\,d-b\,c\right)\,\left(a\,d+2\,b\,c\right)}{9\,c^{5/3}\,d^{7/3}}-\frac{2\,\ln\left(c^{1/3}-2\,d^{1/3}\,x+\sqrt{3}\,c^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(a\,d-b\,c\right)\,\left(a\,d+2\,b\,c\right)}{9\,c^{5/3}\,d^{7/3}}","Not used",1,"(b^2*x)/d^2 + (x*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/(3*c*(c*d^2 + d^3*x^3)) + (2*log(d^(1/3)*x + c^(1/3))*(a*d - b*c)*(a*d + 2*b*c))/(9*c^(5/3)*d^(7/3)) + (2*log(3^(1/2)*c^(1/3)*1i + 2*d^(1/3)*x - c^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(a*d - b*c)*(a*d + 2*b*c))/(9*c^(5/3)*d^(7/3)) - (2*log(3^(1/2)*c^(1/3)*1i - 2*d^(1/3)*x + c^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(a*d - b*c)*(a*d + 2*b*c))/(9*c^(5/3)*d^(7/3))","B"
13,1,249,258,1.428212,"\text{Not used}","int((a + b*x^3)^2/(c + d*x^3)^3,x)","\frac{\ln\left(d^{1/3}\,x+c^{1/3}\right)\,\left(5\,a^2\,d^2+2\,a\,b\,c\,d+2\,b^2\,c^2\right)}{27\,c^{8/3}\,d^{7/3}}-\frac{\frac{2\,x\,\left(-2\,a^2\,d^2+a\,b\,c\,d+b^2\,c^2\right)}{9\,c\,d^2}-\frac{x^4\,\left(5\,a^2\,d^2+2\,a\,b\,c\,d-7\,b^2\,c^2\right)}{18\,c^2\,d}}{c^2+2\,c\,d\,x^3+d^2\,x^6}+\frac{\ln\left(2\,d^{1/3}\,x-c^{1/3}+\sqrt{3}\,c^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(5\,a^2\,d^2+2\,a\,b\,c\,d+2\,b^2\,c^2\right)}{27\,c^{8/3}\,d^{7/3}}-\frac{\ln\left(c^{1/3}-2\,d^{1/3}\,x+\sqrt{3}\,c^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(5\,a^2\,d^2+2\,a\,b\,c\,d+2\,b^2\,c^2\right)}{27\,c^{8/3}\,d^{7/3}}","Not used",1,"(log(d^(1/3)*x + c^(1/3))*(5*a^2*d^2 + 2*b^2*c^2 + 2*a*b*c*d))/(27*c^(8/3)*d^(7/3)) - ((2*x*(b^2*c^2 - 2*a^2*d^2 + a*b*c*d))/(9*c*d^2) - (x^4*(5*a^2*d^2 - 7*b^2*c^2 + 2*a*b*c*d))/(18*c^2*d))/(c^2 + d^2*x^6 + 2*c*d*x^3) + (log(3^(1/2)*c^(1/3)*1i + 2*d^(1/3)*x - c^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(5*a^2*d^2 + 2*b^2*c^2 + 2*a*b*c*d))/(27*c^(8/3)*d^(7/3)) - (log(3^(1/2)*c^(1/3)*1i - 2*d^(1/3)*x + c^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(5*a^2*d^2 + 2*b^2*c^2 + 2*a*b*c*d))/(27*c^(8/3)*d^(7/3))","B"
14,1,250,252,1.430236,"\text{Not used}","int((c + d*x^3)^4/(a + b*x^3),x)","x\,\left(\frac{4\,c^3\,d}{b}-\frac{a\,\left(\frac{a\,\left(\frac{a\,d^4}{b^2}-\frac{4\,c\,d^3}{b}\right)}{b}+\frac{6\,c^2\,d^2}{b}\right)}{b}\right)-x^7\,\left(\frac{a\,d^4}{7\,b^2}-\frac{4\,c\,d^3}{7\,b}\right)+x^4\,\left(\frac{a\,\left(\frac{a\,d^4}{b^2}-\frac{4\,c\,d^3}{b}\right)}{4\,b}+\frac{3\,c^2\,d^2}{2\,b}\right)+\frac{d^4\,x^{10}}{10\,b}+\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,{\left(a\,d-b\,c\right)}^4}{3\,a^{2/3}\,b^{13/3}}+\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)\,{\left(a\,d-b\,c\right)}^4}{a^{2/3}\,b^{13/3}}-\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(a\,d-b\,c\right)}^4}{3\,a^{2/3}\,b^{13/3}}","Not used",1,"x*((4*c^3*d)/b - (a*((a*((a*d^4)/b^2 - (4*c*d^3)/b))/b + (6*c^2*d^2)/b))/b) - x^7*((a*d^4)/(7*b^2) - (4*c*d^3)/(7*b)) + x^4*((a*((a*d^4)/b^2 - (4*c*d^3)/b))/(4*b) + (3*c^2*d^2)/(2*b)) + (d^4*x^10)/(10*b) + (log(b^(1/3)*x + a^(1/3))*(a*d - b*c)^4)/(3*a^(2/3)*b^(13/3)) + (log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/6 - 1/6)*(a*d - b*c)^4)/(a^(2/3)*b^(13/3)) - (log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(a*d - b*c)^4)/(3*a^(2/3)*b^(13/3))","B"
15,1,192,208,1.401591,"\text{Not used}","int((c + d*x^3)^3/(a + b*x^3),x)","x\,\left(\frac{3\,c^2\,d}{b}+\frac{a\,\left(\frac{a\,d^3}{b^2}-\frac{3\,c\,d^2}{b}\right)}{b}\right)-x^4\,\left(\frac{a\,d^3}{4\,b^2}-\frac{3\,c\,d^2}{4\,b}\right)+\frac{d^3\,x^7}{7\,b}-\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,{\left(a\,d-b\,c\right)}^3}{3\,a^{2/3}\,b^{10/3}}-\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(a\,d-b\,c\right)}^3}{3\,a^{2/3}\,b^{10/3}}+\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)\,{\left(a\,d-b\,c\right)}^3}{a^{2/3}\,b^{10/3}}","Not used",1,"x*((3*c^2*d)/b + (a*((a*d^3)/b^2 - (3*c*d^2)/b))/b) - x^4*((a*d^3)/(4*b^2) - (3*c*d^2)/(4*b)) + (d^3*x^7)/(7*b) - (log(b^(1/3)*x + a^(1/3))*(a*d - b*c)^3)/(3*a^(2/3)*b^(10/3)) - (log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(a*d - b*c)^3)/(3*a^(2/3)*b^(10/3)) + (log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/6 + 1/6)*(a*d - b*c)^3)/(a^(2/3)*b^(10/3))","B"
16,1,152,173,1.375365,"\text{Not used}","int((c + d*x^3)^2/(a + b*x^3),x)","\frac{d^2\,x^4}{4\,b}-x\,\left(\frac{a\,d^2}{b^2}-\frac{2\,c\,d}{b}\right)+\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,{\left(a\,d-b\,c\right)}^2}{3\,a^{2/3}\,b^{7/3}}+\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)\,{\left(a\,d-b\,c\right)}^2}{a^{2/3}\,b^{7/3}}-\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(a\,d-b\,c\right)}^2}{3\,a^{2/3}\,b^{7/3}}","Not used",1,"(d^2*x^4)/(4*b) - x*((a*d^2)/b^2 - (2*c*d)/b) + (log(b^(1/3)*x + a^(1/3))*(a*d - b*c)^2)/(3*a^(2/3)*b^(7/3)) + (log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/6 - 1/6)*(a*d - b*c)^2)/(a^(2/3)*b^(7/3)) - (log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(a*d - b*c)^2)/(3*a^(2/3)*b^(7/3))","B"
17,1,123,145,1.378635,"\text{Not used}","int((c + d*x^3)/(a + b*x^3),x)","\frac{d\,x}{b}-\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(a\,d-b\,c\right)}{3\,a^{2/3}\,b^{4/3}}+\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(a\,d-b\,c\right)}{3\,a^{2/3}\,b^{4/3}}-\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(a\,d-b\,c\right)}{3\,a^{2/3}\,b^{4/3}}","Not used",1,"(d*x)/b - (log(b^(1/3)*x + a^(1/3))*(a*d - b*c))/(3*a^(2/3)*b^(4/3)) + (log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(a*d - b*c))/(3*a^(2/3)*b^(4/3)) - (log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(a*d - b*c))/(3*a^(2/3)*b^(4/3))","B"
18,1,1364,288,7.704521,"\text{Not used}","int(1/((a + b*x^3)*(c + d*x^3)),x)","\ln\left(\frac{{\left(-\frac{b^2}{a^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}\,\left(9\,a^2\,b^4\,d^6+9\,b^6\,c^2\,d^4-18\,a\,b^5\,c\,d^5-9\,b^3\,d^3\,\left(x+a\,c\,{\left(-\frac{b^2}{a^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}\right)\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(-\frac{b^2}{a^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}\right)}{3}-6\,b^5\,d^5\,x\right)\,{\left(-\frac{b^2}{27\,a^5\,d^3-81\,a^4\,b\,c\,d^2+81\,a^3\,b^2\,c^2\,d-27\,a^2\,b^3\,c^3}\right)}^{1/3}+\ln\left(\frac{{\left(\frac{d^2}{c^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}\,\left(9\,a^2\,b^4\,d^6+9\,b^6\,c^2\,d^4-18\,a\,b^5\,c\,d^5-9\,b^3\,d^3\,\left(x+a\,c\,{\left(\frac{d^2}{c^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}\right)\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(\frac{d^2}{c^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}\right)}{3}-6\,b^5\,d^5\,x\right)\,{\left(-\frac{d^2}{-27\,a^3\,c^2\,d^3+81\,a^2\,b\,c^3\,d^2-81\,a\,b^2\,c^4\,d+27\,b^3\,c^5}\right)}^{1/3}+\frac{\ln\left(6\,b^5\,d^5\,x+\frac{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(-\frac{b^2}{a^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}\,\left(\frac{{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(81\,b^3\,d^3\,x\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4+\frac{81\,a\,b^3\,c\,d^3\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(-\frac{b^2}{a^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}}{2}\right)\,{\left(-\frac{b^2}{a^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}}{36}-9\,a^2\,b^4\,d^6-9\,b^6\,c^2\,d^4+18\,a\,b^5\,c\,d^5\right)}{6}\right)\,{\left(-\frac{b^2}{27\,a^5\,d^3-81\,a^4\,b\,c\,d^2+81\,a^3\,b^2\,c^2\,d-27\,a^2\,b^3\,c^3}\right)}^{1/3}\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}-\frac{\ln\left(6\,b^5\,d^5\,x-\frac{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(-\frac{b^2}{a^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}\,\left(\frac{{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(81\,b^3\,d^3\,x\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4-\frac{81\,a\,b^3\,c\,d^3\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(-\frac{b^2}{a^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}}{2}\right)\,{\left(-\frac{b^2}{a^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}}{36}-9\,a^2\,b^4\,d^6-9\,b^6\,c^2\,d^4+18\,a\,b^5\,c\,d^5\right)}{6}\right)\,{\left(-\frac{b^2}{27\,a^5\,d^3-81\,a^4\,b\,c\,d^2+81\,a^3\,b^2\,c^2\,d-27\,a^2\,b^3\,c^3}\right)}^{1/3}\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}+\frac{\ln\left(6\,b^5\,d^5\,x+\frac{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(\frac{d^2}{c^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}\,\left(\frac{{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(81\,b^3\,d^3\,x\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4+\frac{81\,a\,b^3\,c\,d^3\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(\frac{d^2}{c^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}}{2}\right)\,{\left(\frac{d^2}{c^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}}{36}-9\,a^2\,b^4\,d^6-9\,b^6\,c^2\,d^4+18\,a\,b^5\,c\,d^5\right)}{6}\right)\,{\left(-\frac{d^2}{-27\,a^3\,c^2\,d^3+81\,a^2\,b\,c^3\,d^2-81\,a\,b^2\,c^4\,d+27\,b^3\,c^5}\right)}^{1/3}\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}-\frac{\ln\left(6\,b^5\,d^5\,x-\frac{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(\frac{d^2}{c^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}\,\left(\frac{{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(81\,b^3\,d^3\,x\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4-\frac{81\,a\,b^3\,c\,d^3\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(\frac{d^2}{c^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}}{2}\right)\,{\left(\frac{d^2}{c^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}}{36}-9\,a^2\,b^4\,d^6-9\,b^6\,c^2\,d^4+18\,a\,b^5\,c\,d^5\right)}{6}\right)\,{\left(-\frac{d^2}{-27\,a^3\,c^2\,d^3+81\,a^2\,b\,c^3\,d^2-81\,a\,b^2\,c^4\,d+27\,b^3\,c^5}\right)}^{1/3}\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}","Not used",1,"log(((-b^2/(a^2*(a*d - b*c)^3))^(1/3)*(9*a^2*b^4*d^6 + 9*b^6*c^2*d^4 - 18*a*b^5*c*d^5 - 9*b^3*d^3*(x + a*c*(-b^2/(a^2*(a*d - b*c)^3))^(1/3))*(a*d + b*c)*(a*d - b*c)^4*(-b^2/(a^2*(a*d - b*c)^3))^(2/3)))/3 - 6*b^5*d^5*x)*(-b^2/(27*a^5*d^3 - 27*a^2*b^3*c^3 + 81*a^3*b^2*c^2*d - 81*a^4*b*c*d^2))^(1/3) + log(((d^2/(c^2*(a*d - b*c)^3))^(1/3)*(9*a^2*b^4*d^6 + 9*b^6*c^2*d^4 - 18*a*b^5*c*d^5 - 9*b^3*d^3*(x + a*c*(d^2/(c^2*(a*d - b*c)^3))^(1/3))*(a*d + b*c)*(a*d - b*c)^4*(d^2/(c^2*(a*d - b*c)^3))^(2/3)))/3 - 6*b^5*d^5*x)*(-d^2/(27*b^3*c^5 - 27*a^3*c^2*d^3 + 81*a^2*b*c^3*d^2 - 81*a*b^2*c^4*d))^(1/3) + (log(6*b^5*d^5*x + ((3^(1/2)*1i - 1)*(-b^2/(a^2*(a*d - b*c)^3))^(1/3)*(((3^(1/2)*1i - 1)^2*(81*b^3*d^3*x*(a*d + b*c)*(a*d - b*c)^4 + (81*a*b^3*c*d^3*(3^(1/2)*1i - 1)*(a*d + b*c)*(a*d - b*c)^4*(-b^2/(a^2*(a*d - b*c)^3))^(1/3))/2)*(-b^2/(a^2*(a*d - b*c)^3))^(2/3))/36 - 9*a^2*b^4*d^6 - 9*b^6*c^2*d^4 + 18*a*b^5*c*d^5))/6)*(-b^2/(27*a^5*d^3 - 27*a^2*b^3*c^3 + 81*a^3*b^2*c^2*d - 81*a^4*b*c*d^2))^(1/3)*(3^(1/2)*1i - 1))/2 - (log(6*b^5*d^5*x - ((3^(1/2)*1i + 1)*(-b^2/(a^2*(a*d - b*c)^3))^(1/3)*(((3^(1/2)*1i + 1)^2*(81*b^3*d^3*x*(a*d + b*c)*(a*d - b*c)^4 - (81*a*b^3*c*d^3*(3^(1/2)*1i + 1)*(a*d + b*c)*(a*d - b*c)^4*(-b^2/(a^2*(a*d - b*c)^3))^(1/3))/2)*(-b^2/(a^2*(a*d - b*c)^3))^(2/3))/36 - 9*a^2*b^4*d^6 - 9*b^6*c^2*d^4 + 18*a*b^5*c*d^5))/6)*(-b^2/(27*a^5*d^3 - 27*a^2*b^3*c^3 + 81*a^3*b^2*c^2*d - 81*a^4*b*c*d^2))^(1/3)*(3^(1/2)*1i + 1))/2 + (log(6*b^5*d^5*x + ((3^(1/2)*1i - 1)*(d^2/(c^2*(a*d - b*c)^3))^(1/3)*(((3^(1/2)*1i - 1)^2*(81*b^3*d^3*x*(a*d + b*c)*(a*d - b*c)^4 + (81*a*b^3*c*d^3*(3^(1/2)*1i - 1)*(a*d + b*c)*(a*d - b*c)^4*(d^2/(c^2*(a*d - b*c)^3))^(1/3))/2)*(d^2/(c^2*(a*d - b*c)^3))^(2/3))/36 - 9*a^2*b^4*d^6 - 9*b^6*c^2*d^4 + 18*a*b^5*c*d^5))/6)*(-d^2/(27*b^3*c^5 - 27*a^3*c^2*d^3 + 81*a^2*b*c^3*d^2 - 81*a*b^2*c^4*d))^(1/3)*(3^(1/2)*1i - 1))/2 - (log(6*b^5*d^5*x - ((3^(1/2)*1i + 1)*(d^2/(c^2*(a*d - b*c)^3))^(1/3)*(((3^(1/2)*1i + 1)^2*(81*b^3*d^3*x*(a*d + b*c)*(a*d - b*c)^4 - (81*a*b^3*c*d^3*(3^(1/2)*1i + 1)*(a*d + b*c)*(a*d - b*c)^4*(d^2/(c^2*(a*d - b*c)^3))^(1/3))/2)*(d^2/(c^2*(a*d - b*c)^3))^(2/3))/36 - 9*a^2*b^4*d^6 - 9*b^6*c^2*d^4 + 18*a*b^5*c*d^5))/6)*(-d^2/(27*b^3*c^5 - 27*a^3*c^2*d^3 + 81*a^2*b*c^3*d^2 - 81*a*b^2*c^4*d))^(1/3)*(3^(1/2)*1i + 1))/2","B"
19,1,2589,346,16.806580,"\text{Not used}","int(1/((a + b*x^3)*(c + d*x^3)^2),x)","\ln\left(\frac{\left(\frac{\left(\frac{27\,b^3\,d^3\,x\,{\left(a\,d-b\,c\right)}^3\,\left(-2\,a^2\,d^2+3\,a\,b\,c\,d+3\,b^2\,c^2\right)}{c}+\frac{27\,a\,b^3\,c^4\,d^3\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^5\,{\left(\frac{d^2\,{\left(2\,a\,d-5\,b\,c\right)}^3}{c^5\,{\left(a\,d-b\,c\right)}^6}\right)}^{1/3}}{b\,c^4-a\,c^3\,d}\right)\,{\left(\frac{d^2\,{\left(2\,a\,d-5\,b\,c\right)}^3}{c^5\,{\left(a\,d-b\,c\right)}^6}\right)}^{2/3}}{81}-\frac{b^4\,d^4\,\left(8\,a^3\,d^3-52\,a^2\,b\,c\,d^2+98\,a\,b^2\,c^2\,d-27\,b^3\,c^3\right)}{3\,b\,c^4-3\,a\,c^3\,d}\right)\,{\left(\frac{d^2\,{\left(2\,a\,d-5\,b\,c\right)}^3}{c^5\,{\left(a\,d-b\,c\right)}^6}\right)}^{1/3}}{9}+\frac{2\,b^6\,d^5\,x\,\left(4\,a^3\,d^3-30\,a^2\,b\,c\,d^2+84\,a\,b^2\,c^2\,d-85\,b^3\,c^3\right)}{9\,c^3\,{\left(a\,d-b\,c\right)}^4}\right)\,{\left(\frac{8\,a^3\,d^5-60\,a^2\,b\,c\,d^4+150\,a\,b^2\,c^2\,d^3-125\,b^3\,c^3\,d^2}{729\,a^6\,c^5\,d^6-4374\,a^5\,b\,c^6\,d^5+10935\,a^4\,b^2\,c^7\,d^4-14580\,a^3\,b^3\,c^8\,d^3+10935\,a^2\,b^4\,c^9\,d^2-4374\,a\,b^5\,c^{10}\,d+729\,b^6\,c^{11}}\right)}^{1/3}+\ln\left(\frac{\left(\frac{\left(\frac{27\,b^3\,d^3\,x\,{\left(a\,d-b\,c\right)}^3\,\left(-2\,a^2\,d^2+3\,a\,b\,c\,d+3\,b^2\,c^2\right)}{c}+\frac{81\,a\,b^3\,c^4\,d^3\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^5\,{\left(\frac{b^5}{a^2\,{\left(a\,d-b\,c\right)}^6}\right)}^{1/3}}{b\,c^4-a\,c^3\,d}\right)\,{\left(\frac{b^5}{a^2\,{\left(a\,d-b\,c\right)}^6}\right)}^{2/3}}{9}-\frac{b^4\,d^4\,\left(8\,a^3\,d^3-52\,a^2\,b\,c\,d^2+98\,a\,b^2\,c^2\,d-27\,b^3\,c^3\right)}{3\,b\,c^4-3\,a\,c^3\,d}\right)\,{\left(\frac{b^5}{a^2\,{\left(a\,d-b\,c\right)}^6}\right)}^{1/3}}{3}+\frac{2\,b^6\,d^5\,x\,\left(4\,a^3\,d^3-30\,a^2\,b\,c\,d^2+84\,a\,b^2\,c^2\,d-85\,b^3\,c^3\right)}{9\,c^3\,{\left(a\,d-b\,c\right)}^4}\right)\,{\left(\frac{b^5}{27\,a^8\,d^6-162\,a^7\,b\,c\,d^5+405\,a^6\,b^2\,c^2\,d^4-540\,a^5\,b^3\,c^3\,d^3+405\,a^4\,b^4\,c^4\,d^2-162\,a^3\,b^5\,c^5\,d+27\,a^2\,b^6\,c^6}\right)}^{1/3}+\frac{\ln\left(\frac{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(\frac{{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(\frac{27\,b^3\,d^3\,x\,{\left(a\,d-b\,c\right)}^3\,\left(-2\,a^2\,d^2+3\,a\,b\,c\,d+3\,b^2\,c^2\right)}{c}+\frac{27\,a\,b^3\,c^4\,d^3\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^5\,{\left(\frac{d^2\,{\left(2\,a\,d-5\,b\,c\right)}^3}{c^5\,{\left(a\,d-b\,c\right)}^6}\right)}^{1/3}}{2\,\left(b\,c^4-a\,c^3\,d\right)}\right)\,{\left(\frac{d^2\,{\left(2\,a\,d-5\,b\,c\right)}^3}{c^5\,{\left(a\,d-b\,c\right)}^6}\right)}^{2/3}}{324}-\frac{b^4\,d^4\,\left(8\,a^3\,d^3-52\,a^2\,b\,c\,d^2+98\,a\,b^2\,c^2\,d-27\,b^3\,c^3\right)}{3\,b\,c^4-3\,a\,c^3\,d}\right)\,{\left(\frac{d^2\,{\left(2\,a\,d-5\,b\,c\right)}^3}{c^5\,{\left(a\,d-b\,c\right)}^6}\right)}^{1/3}}{18}+\frac{2\,b^6\,d^5\,x\,\left(4\,a^3\,d^3-30\,a^2\,b\,c\,d^2+84\,a\,b^2\,c^2\,d-85\,b^3\,c^3\right)}{9\,c^3\,{\left(a\,d-b\,c\right)}^4}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(\frac{8\,a^3\,d^5-60\,a^2\,b\,c\,d^4+150\,a\,b^2\,c^2\,d^3-125\,b^3\,c^3\,d^2}{729\,a^6\,c^5\,d^6-4374\,a^5\,b\,c^6\,d^5+10935\,a^4\,b^2\,c^7\,d^4-14580\,a^3\,b^3\,c^8\,d^3+10935\,a^2\,b^4\,c^9\,d^2-4374\,a\,b^5\,c^{10}\,d+729\,b^6\,c^{11}}\right)}^{1/3}}{2}-\frac{\ln\left(\frac{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(\frac{{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(\frac{27\,b^3\,d^3\,x\,{\left(a\,d-b\,c\right)}^3\,\left(-2\,a^2\,d^2+3\,a\,b\,c\,d+3\,b^2\,c^2\right)}{c}-\frac{27\,a\,b^3\,c^4\,d^3\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^5\,{\left(\frac{d^2\,{\left(2\,a\,d-5\,b\,c\right)}^3}{c^5\,{\left(a\,d-b\,c\right)}^6}\right)}^{1/3}}{2\,\left(b\,c^4-a\,c^3\,d\right)}\right)\,{\left(\frac{d^2\,{\left(2\,a\,d-5\,b\,c\right)}^3}{c^5\,{\left(a\,d-b\,c\right)}^6}\right)}^{2/3}}{324}-\frac{b^4\,d^4\,\left(8\,a^3\,d^3-52\,a^2\,b\,c\,d^2+98\,a\,b^2\,c^2\,d-27\,b^3\,c^3\right)}{3\,b\,c^4-3\,a\,c^3\,d}\right)\,{\left(\frac{d^2\,{\left(2\,a\,d-5\,b\,c\right)}^3}{c^5\,{\left(a\,d-b\,c\right)}^6}\right)}^{1/3}}{18}-\frac{2\,b^6\,d^5\,x\,\left(4\,a^3\,d^3-30\,a^2\,b\,c\,d^2+84\,a\,b^2\,c^2\,d-85\,b^3\,c^3\right)}{9\,c^3\,{\left(a\,d-b\,c\right)}^4}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(\frac{8\,a^3\,d^5-60\,a^2\,b\,c\,d^4+150\,a\,b^2\,c^2\,d^3-125\,b^3\,c^3\,d^2}{729\,a^6\,c^5\,d^6-4374\,a^5\,b\,c^6\,d^5+10935\,a^4\,b^2\,c^7\,d^4-14580\,a^3\,b^3\,c^8\,d^3+10935\,a^2\,b^4\,c^9\,d^2-4374\,a\,b^5\,c^{10}\,d+729\,b^6\,c^{11}}\right)}^{1/3}}{2}+\frac{\ln\left(\frac{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(\frac{{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(\frac{27\,b^3\,d^3\,x\,{\left(a\,d-b\,c\right)}^3\,\left(-2\,a^2\,d^2+3\,a\,b\,c\,d+3\,b^2\,c^2\right)}{c}+\frac{81\,a\,b^3\,c^4\,d^3\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^5\,{\left(\frac{b^5}{a^2\,{\left(a\,d-b\,c\right)}^6}\right)}^{1/3}}{2\,\left(b\,c^4-a\,c^3\,d\right)}\right)\,{\left(\frac{b^5}{a^2\,{\left(a\,d-b\,c\right)}^6}\right)}^{2/3}}{36}-\frac{b^4\,d^4\,\left(8\,a^3\,d^3-52\,a^2\,b\,c\,d^2+98\,a\,b^2\,c^2\,d-27\,b^3\,c^3\right)}{3\,b\,c^4-3\,a\,c^3\,d}\right)\,{\left(\frac{b^5}{a^2\,{\left(a\,d-b\,c\right)}^6}\right)}^{1/3}}{6}+\frac{2\,b^6\,d^5\,x\,\left(4\,a^3\,d^3-30\,a^2\,b\,c\,d^2+84\,a\,b^2\,c^2\,d-85\,b^3\,c^3\right)}{9\,c^3\,{\left(a\,d-b\,c\right)}^4}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(\frac{b^5}{27\,a^8\,d^6-162\,a^7\,b\,c\,d^5+405\,a^6\,b^2\,c^2\,d^4-540\,a^5\,b^3\,c^3\,d^3+405\,a^4\,b^4\,c^4\,d^2-162\,a^3\,b^5\,c^5\,d+27\,a^2\,b^6\,c^6}\right)}^{1/3}}{2}-\frac{\ln\left(\frac{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(\frac{{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(\frac{27\,b^3\,d^3\,x\,{\left(a\,d-b\,c\right)}^3\,\left(-2\,a^2\,d^2+3\,a\,b\,c\,d+3\,b^2\,c^2\right)}{c}-\frac{81\,a\,b^3\,c^4\,d^3\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^5\,{\left(\frac{b^5}{a^2\,{\left(a\,d-b\,c\right)}^6}\right)}^{1/3}}{2\,\left(b\,c^4-a\,c^3\,d\right)}\right)\,{\left(\frac{b^5}{a^2\,{\left(a\,d-b\,c\right)}^6}\right)}^{2/3}}{36}-\frac{b^4\,d^4\,\left(8\,a^3\,d^3-52\,a^2\,b\,c\,d^2+98\,a\,b^2\,c^2\,d-27\,b^3\,c^3\right)}{3\,b\,c^4-3\,a\,c^3\,d}\right)\,{\left(\frac{b^5}{a^2\,{\left(a\,d-b\,c\right)}^6}\right)}^{1/3}}{6}-\frac{2\,b^6\,d^5\,x\,\left(4\,a^3\,d^3-30\,a^2\,b\,c\,d^2+84\,a\,b^2\,c^2\,d-85\,b^3\,c^3\right)}{9\,c^3\,{\left(a\,d-b\,c\right)}^4}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(\frac{b^5}{27\,a^8\,d^6-162\,a^7\,b\,c\,d^5+405\,a^6\,b^2\,c^2\,d^4-540\,a^5\,b^3\,c^3\,d^3+405\,a^4\,b^4\,c^4\,d^2-162\,a^3\,b^5\,c^5\,d+27\,a^2\,b^6\,c^6}\right)}^{1/3}}{2}+\frac{d\,x}{3\,c\,\left(d\,x^3+c\right)\,\left(a\,d-b\,c\right)}","Not used",1,"log((((((27*b^3*d^3*x*(a*d - b*c)^3*(3*b^2*c^2 - 2*a^2*d^2 + 3*a*b*c*d))/c + (27*a*b^3*c^4*d^3*(a*d + b*c)*(a*d - b*c)^5*((d^2*(2*a*d - 5*b*c)^3)/(c^5*(a*d - b*c)^6))^(1/3))/(b*c^4 - a*c^3*d))*((d^2*(2*a*d - 5*b*c)^3)/(c^5*(a*d - b*c)^6))^(2/3))/81 - (b^4*d^4*(8*a^3*d^3 - 27*b^3*c^3 + 98*a*b^2*c^2*d - 52*a^2*b*c*d^2))/(3*b*c^4 - 3*a*c^3*d))*((d^2*(2*a*d - 5*b*c)^3)/(c^5*(a*d - b*c)^6))^(1/3))/9 + (2*b^6*d^5*x*(4*a^3*d^3 - 85*b^3*c^3 + 84*a*b^2*c^2*d - 30*a^2*b*c*d^2))/(9*c^3*(a*d - b*c)^4))*((8*a^3*d^5 - 125*b^3*c^3*d^2 + 150*a*b^2*c^2*d^3 - 60*a^2*b*c*d^4)/(729*b^6*c^11 + 729*a^6*c^5*d^6 - 4374*a^5*b*c^6*d^5 + 10935*a^2*b^4*c^9*d^2 - 14580*a^3*b^3*c^8*d^3 + 10935*a^4*b^2*c^7*d^4 - 4374*a*b^5*c^10*d))^(1/3) + log((((((27*b^3*d^3*x*(a*d - b*c)^3*(3*b^2*c^2 - 2*a^2*d^2 + 3*a*b*c*d))/c + (81*a*b^3*c^4*d^3*(a*d + b*c)*(a*d - b*c)^5*(b^5/(a^2*(a*d - b*c)^6))^(1/3))/(b*c^4 - a*c^3*d))*(b^5/(a^2*(a*d - b*c)^6))^(2/3))/9 - (b^4*d^4*(8*a^3*d^3 - 27*b^3*c^3 + 98*a*b^2*c^2*d - 52*a^2*b*c*d^2))/(3*b*c^4 - 3*a*c^3*d))*(b^5/(a^2*(a*d - b*c)^6))^(1/3))/3 + (2*b^6*d^5*x*(4*a^3*d^3 - 85*b^3*c^3 + 84*a*b^2*c^2*d - 30*a^2*b*c*d^2))/(9*c^3*(a*d - b*c)^4))*(b^5/(27*a^8*d^6 + 27*a^2*b^6*c^6 - 162*a^3*b^5*c^5*d + 405*a^4*b^4*c^4*d^2 - 540*a^5*b^3*c^3*d^3 + 405*a^6*b^2*c^2*d^4 - 162*a^7*b*c*d^5))^(1/3) + (log(((3^(1/2)*1i - 1)*(((3^(1/2)*1i - 1)^2*((27*b^3*d^3*x*(a*d - b*c)^3*(3*b^2*c^2 - 2*a^2*d^2 + 3*a*b*c*d))/c + (27*a*b^3*c^4*d^3*(3^(1/2)*1i - 1)*(a*d + b*c)*(a*d - b*c)^5*((d^2*(2*a*d - 5*b*c)^3)/(c^5*(a*d - b*c)^6))^(1/3))/(2*(b*c^4 - a*c^3*d)))*((d^2*(2*a*d - 5*b*c)^3)/(c^5*(a*d - b*c)^6))^(2/3))/324 - (b^4*d^4*(8*a^3*d^3 - 27*b^3*c^3 + 98*a*b^2*c^2*d - 52*a^2*b*c*d^2))/(3*b*c^4 - 3*a*c^3*d))*((d^2*(2*a*d - 5*b*c)^3)/(c^5*(a*d - b*c)^6))^(1/3))/18 + (2*b^6*d^5*x*(4*a^3*d^3 - 85*b^3*c^3 + 84*a*b^2*c^2*d - 30*a^2*b*c*d^2))/(9*c^3*(a*d - b*c)^4))*(3^(1/2)*1i - 1)*((8*a^3*d^5 - 125*b^3*c^3*d^2 + 150*a*b^2*c^2*d^3 - 60*a^2*b*c*d^4)/(729*b^6*c^11 + 729*a^6*c^5*d^6 - 4374*a^5*b*c^6*d^5 + 10935*a^2*b^4*c^9*d^2 - 14580*a^3*b^3*c^8*d^3 + 10935*a^4*b^2*c^7*d^4 - 4374*a*b^5*c^10*d))^(1/3))/2 - (log(((3^(1/2)*1i + 1)*(((3^(1/2)*1i + 1)^2*((27*b^3*d^3*x*(a*d - b*c)^3*(3*b^2*c^2 - 2*a^2*d^2 + 3*a*b*c*d))/c - (27*a*b^3*c^4*d^3*(3^(1/2)*1i + 1)*(a*d + b*c)*(a*d - b*c)^5*((d^2*(2*a*d - 5*b*c)^3)/(c^5*(a*d - b*c)^6))^(1/3))/(2*(b*c^4 - a*c^3*d)))*((d^2*(2*a*d - 5*b*c)^3)/(c^5*(a*d - b*c)^6))^(2/3))/324 - (b^4*d^4*(8*a^3*d^3 - 27*b^3*c^3 + 98*a*b^2*c^2*d - 52*a^2*b*c*d^2))/(3*b*c^4 - 3*a*c^3*d))*((d^2*(2*a*d - 5*b*c)^3)/(c^5*(a*d - b*c)^6))^(1/3))/18 - (2*b^6*d^5*x*(4*a^3*d^3 - 85*b^3*c^3 + 84*a*b^2*c^2*d - 30*a^2*b*c*d^2))/(9*c^3*(a*d - b*c)^4))*(3^(1/2)*1i + 1)*((8*a^3*d^5 - 125*b^3*c^3*d^2 + 150*a*b^2*c^2*d^3 - 60*a^2*b*c*d^4)/(729*b^6*c^11 + 729*a^6*c^5*d^6 - 4374*a^5*b*c^6*d^5 + 10935*a^2*b^4*c^9*d^2 - 14580*a^3*b^3*c^8*d^3 + 10935*a^4*b^2*c^7*d^4 - 4374*a*b^5*c^10*d))^(1/3))/2 + (log(((3^(1/2)*1i - 1)*(((3^(1/2)*1i - 1)^2*((27*b^3*d^3*x*(a*d - b*c)^3*(3*b^2*c^2 - 2*a^2*d^2 + 3*a*b*c*d))/c + (81*a*b^3*c^4*d^3*(3^(1/2)*1i - 1)*(a*d + b*c)*(a*d - b*c)^5*(b^5/(a^2*(a*d - b*c)^6))^(1/3))/(2*(b*c^4 - a*c^3*d)))*(b^5/(a^2*(a*d - b*c)^6))^(2/3))/36 - (b^4*d^4*(8*a^3*d^3 - 27*b^3*c^3 + 98*a*b^2*c^2*d - 52*a^2*b*c*d^2))/(3*b*c^4 - 3*a*c^3*d))*(b^5/(a^2*(a*d - b*c)^6))^(1/3))/6 + (2*b^6*d^5*x*(4*a^3*d^3 - 85*b^3*c^3 + 84*a*b^2*c^2*d - 30*a^2*b*c*d^2))/(9*c^3*(a*d - b*c)^4))*(3^(1/2)*1i - 1)*(b^5/(27*a^8*d^6 + 27*a^2*b^6*c^6 - 162*a^3*b^5*c^5*d + 405*a^4*b^4*c^4*d^2 - 540*a^5*b^3*c^3*d^3 + 405*a^6*b^2*c^2*d^4 - 162*a^7*b*c*d^5))^(1/3))/2 - (log(((3^(1/2)*1i + 1)*(((3^(1/2)*1i + 1)^2*((27*b^3*d^3*x*(a*d - b*c)^3*(3*b^2*c^2 - 2*a^2*d^2 + 3*a*b*c*d))/c - (81*a*b^3*c^4*d^3*(3^(1/2)*1i + 1)*(a*d + b*c)*(a*d - b*c)^5*(b^5/(a^2*(a*d - b*c)^6))^(1/3))/(2*(b*c^4 - a*c^3*d)))*(b^5/(a^2*(a*d - b*c)^6))^(2/3))/36 - (b^4*d^4*(8*a^3*d^3 - 27*b^3*c^3 + 98*a*b^2*c^2*d - 52*a^2*b*c*d^2))/(3*b*c^4 - 3*a*c^3*d))*(b^5/(a^2*(a*d - b*c)^6))^(1/3))/6 - (2*b^6*d^5*x*(4*a^3*d^3 - 85*b^3*c^3 + 84*a*b^2*c^2*d - 30*a^2*b*c*d^2))/(9*c^3*(a*d - b*c)^4))*(3^(1/2)*1i + 1)*(b^5/(27*a^8*d^6 + 27*a^2*b^6*c^6 - 162*a^3*b^5*c^5*d + 405*a^4*b^4*c^4*d^2 - 540*a^5*b^3*c^3*d^3 + 405*a^6*b^2*c^2*d^4 - 162*a^7*b*c*d^5))^(1/3))/2 + (d*x)/(3*c*(c + d*x^3)*(a*d - b*c))","B"
20,1,416,320,0.389932,"\text{Not used}","int((c + d*x^3)^5/(a + b*x^3)^2,x)","x\,\left(\frac{10\,c^3\,d^2}{b^2}-\frac{2\,a\,\left(\frac{2\,a\,\left(\frac{2\,a\,d^5}{b^3}-\frac{5\,c\,d^4}{b^2}\right)}{b}-\frac{a^2\,d^5}{b^4}+\frac{10\,c^2\,d^3}{b^2}\right)}{b}+\frac{a^2\,\left(\frac{2\,a\,d^5}{b^3}-\frac{5\,c\,d^4}{b^2}\right)}{b^2}\right)-x^7\,\left(\frac{2\,a\,d^5}{7\,b^3}-\frac{5\,c\,d^4}{7\,b^2}\right)+x^4\,\left(\frac{a\,\left(\frac{2\,a\,d^5}{b^3}-\frac{5\,c\,d^4}{b^2}\right)}{2\,b}-\frac{a^2\,d^5}{4\,b^4}+\frac{5\,c^2\,d^3}{2\,b^2}\right)+\frac{d^5\,x^{10}}{10\,b^2}-\frac{x\,\left(a^5\,d^5-5\,a^4\,b\,c\,d^4+10\,a^3\,b^2\,c^2\,d^3-10\,a^2\,b^3\,c^3\,d^2+5\,a\,b^4\,c^4\,d-b^5\,c^5\right)}{3\,a\,\left(b^6\,x^3+a\,b^5\right)}+\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,{\left(a\,d-b\,c\right)}^4\,\left(13\,a\,d+2\,b\,c\right)}{9\,a^{5/3}\,b^{16/3}}-\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(a\,d-b\,c\right)}^4\,\left(13\,a\,d+2\,b\,c\right)}{9\,a^{5/3}\,b^{16/3}}+\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(a\,d-b\,c\right)}^4\,\left(13\,a\,d+2\,b\,c\right)}{9\,a^{5/3}\,b^{16/3}}","Not used",1,"x*((10*c^3*d^2)/b^2 - (2*a*((2*a*((2*a*d^5)/b^3 - (5*c*d^4)/b^2))/b - (a^2*d^5)/b^4 + (10*c^2*d^3)/b^2))/b + (a^2*((2*a*d^5)/b^3 - (5*c*d^4)/b^2))/b^2) - x^7*((2*a*d^5)/(7*b^3) - (5*c*d^4)/(7*b^2)) + x^4*((a*((2*a*d^5)/b^3 - (5*c*d^4)/b^2))/(2*b) - (a^2*d^5)/(4*b^4) + (5*c^2*d^3)/(2*b^2)) + (d^5*x^10)/(10*b^2) - (x*(a^5*d^5 - b^5*c^5 - 10*a^2*b^3*c^3*d^2 + 10*a^3*b^2*c^2*d^3 + 5*a*b^4*c^4*d - 5*a^4*b*c*d^4))/(3*a*(a*b^5 + b^6*x^3)) + (log(b^(1/3)*x + a^(1/3))*(a*d - b*c)^4*(13*a*d + 2*b*c))/(9*a^(5/3)*b^(16/3)) - (log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(a*d - b*c)^4*(13*a*d + 2*b*c))/(9*a^(5/3)*b^(16/3)) + (log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(a*d - b*c)^4*(13*a*d + 2*b*c))/(9*a^(5/3)*b^(16/3))","B"
21,1,302,267,1.493050,"\text{Not used}","int((c + d*x^3)^4/(a + b*x^3)^2,x)","x\,\left(\frac{2\,a\,\left(\frac{2\,a\,d^4}{b^3}-\frac{4\,c\,d^3}{b^2}\right)}{b}-\frac{a^2\,d^4}{b^4}+\frac{6\,c^2\,d^2}{b^2}\right)-x^4\,\left(\frac{a\,d^4}{2\,b^3}-\frac{c\,d^3}{b^2}\right)+\frac{d^4\,x^7}{7\,b^2}+\frac{x\,\left(a^4\,d^4-4\,a^3\,b\,c\,d^3+6\,a^2\,b^2\,c^2\,d^2-4\,a\,b^3\,c^3\,d+b^4\,c^4\right)}{3\,a\,\left(b^5\,x^3+a\,b^4\right)}-\frac{2\,\ln\left(b^{1/3}\,x+a^{1/3}\right)\,{\left(a\,d-b\,c\right)}^3\,\left(5\,a\,d+b\,c\right)}{9\,a^{5/3}\,b^{13/3}}+\frac{2\,\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(a\,d-b\,c\right)}^3\,\left(5\,a\,d+b\,c\right)}{9\,a^{5/3}\,b^{13/3}}-\frac{2\,\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(a\,d-b\,c\right)}^3\,\left(5\,a\,d+b\,c\right)}{9\,a^{5/3}\,b^{13/3}}","Not used",1,"x*((2*a*((2*a*d^4)/b^3 - (4*c*d^3)/b^2))/b - (a^2*d^4)/b^4 + (6*c^2*d^2)/b^2) - x^4*((a*d^4)/(2*b^3) - (c*d^3)/b^2) + (d^4*x^7)/(7*b^2) + (x*(a^4*d^4 + b^4*c^4 + 6*a^2*b^2*c^2*d^2 - 4*a*b^3*c^3*d - 4*a^3*b*c*d^3))/(3*a*(a*b^4 + b^5*x^3)) - (2*log(b^(1/3)*x + a^(1/3))*(a*d - b*c)^3*(5*a*d + b*c))/(9*a^(5/3)*b^(13/3)) + (2*log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(a*d - b*c)^3*(5*a*d + b*c))/(9*a^(5/3)*b^(13/3)) - (2*log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(a*d - b*c)^3*(5*a*d + b*c))/(9*a^(5/3)*b^(13/3))","B"
22,1,240,234,0.296094,"\text{Not used}","int((c + d*x^3)^3/(a + b*x^3)^2,x)","\frac{d^3\,x^4}{4\,b^2}-x\,\left(\frac{2\,a\,d^3}{b^3}-\frac{3\,c\,d^2}{b^2}\right)-\frac{x\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)}{3\,a\,\left(b^4\,x^3+a\,b^3\right)}+\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(7\,a\,d+2\,b\,c\right)}{9\,a^{5/3}\,b^{10/3}}-\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(7\,a\,d+2\,b\,c\right)}{9\,a^{5/3}\,b^{10/3}}+\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(7\,a\,d+2\,b\,c\right)}{9\,a^{5/3}\,b^{10/3}}","Not used",1,"(d^3*x^4)/(4*b^2) - x*((2*a*d^3)/b^3 - (3*c*d^2)/b^2) - (x*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))/(3*a*(a*b^3 + b^4*x^3)) + (log(b^(1/3)*x + a^(1/3))*(a*d - b*c)^2*(7*a*d + 2*b*c))/(9*a^(5/3)*b^(10/3)) - (log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(a*d - b*c)^2*(7*a*d + 2*b*c))/(9*a^(5/3)*b^(10/3)) + (log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(a*d - b*c)^2*(7*a*d + 2*b*c))/(9*a^(5/3)*b^(10/3))","B"
23,1,191,203,1.467075,"\text{Not used}","int((c + d*x^3)^2/(a + b*x^3)^2,x)","\frac{d^2\,x}{b^2}+\frac{x\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}{3\,a\,\left(b^3\,x^3+a\,b^2\right)}-\frac{2\,\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(a\,d-b\,c\right)\,\left(2\,a\,d+b\,c\right)}{9\,a^{5/3}\,b^{7/3}}-\frac{2\,\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(a\,d-b\,c\right)\,\left(2\,a\,d+b\,c\right)}{9\,a^{5/3}\,b^{7/3}}+\frac{2\,\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(a\,d-b\,c\right)\,\left(2\,a\,d+b\,c\right)}{9\,a^{5/3}\,b^{7/3}}","Not used",1,"(d^2*x)/b^2 + (x*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/(3*a*(a*b^2 + b^3*x^3)) - (2*log(b^(1/3)*x + a^(1/3))*(a*d - b*c)*(2*a*d + b*c))/(9*a^(5/3)*b^(7/3)) - (2*log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(a*d - b*c)*(2*a*d + b*c))/(9*a^(5/3)*b^(7/3)) + (2*log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(a*d - b*c)*(2*a*d + b*c))/(9*a^(5/3)*b^(7/3))","B"
24,1,143,169,1.427793,"\text{Not used}","int((c + d*x^3)/(a + b*x^3)^2,x)","\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(a\,d+2\,b\,c\right)}{9\,a^{5/3}\,b^{4/3}}-\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(a\,d+2\,b\,c\right)}{9\,a^{5/3}\,b^{4/3}}+\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(a\,d+2\,b\,c\right)}{9\,a^{5/3}\,b^{4/3}}-\frac{x\,\left(a\,d-b\,c\right)}{3\,a\,b\,\left(b\,x^3+a\right)}","Not used",1,"(log(b^(1/3)*x + a^(1/3))*(a*d + 2*b*c))/(9*a^(5/3)*b^(4/3)) - (log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(a*d + 2*b*c))/(9*a^(5/3)*b^(4/3)) + (log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(a*d + 2*b*c))/(9*a^(5/3)*b^(4/3)) - (x*(a*d - b*c))/(3*a*b*(a + b*x^3))","B"
25,1,2492,346,15.929928,"\text{Not used}","int(1/((a + b*x^3)^2*(c + d*x^3)),x)","\ln\left(\frac{\left(\frac{\left(\frac{27\,b^3\,d^3\,x\,{\left(a\,d-b\,c\right)}^3\,\left(3\,a^2\,d^2+3\,a\,b\,c\,d-2\,b^2\,c^2\right)}{a}+27\,a\,b^3\,c\,d^3\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(-\frac{b^2\,{\left(5\,a\,d-2\,b\,c\right)}^3}{a^5\,{\left(a\,d-b\,c\right)}^6}\right)}^{1/3}\right)\,{\left(-\frac{b^2\,{\left(5\,a\,d-2\,b\,c\right)}^3}{a^5\,{\left(a\,d-b\,c\right)}^6}\right)}^{2/3}}{81}-\frac{b^4\,d^4\,\left(27\,a^3\,d^3-98\,a^2\,b\,c\,d^2+52\,a\,b^2\,c^2\,d-8\,b^3\,c^3\right)}{3\,a^4\,d-3\,a^3\,b\,c}\right)\,{\left(-\frac{b^2\,{\left(5\,a\,d-2\,b\,c\right)}^3}{a^5\,{\left(a\,d-b\,c\right)}^6}\right)}^{1/3}}{9}+\frac{2\,b^5\,d^6\,x\,\left(85\,a^3\,d^3-84\,a^2\,b\,c\,d^2+30\,a\,b^2\,c^2\,d-4\,b^3\,c^3\right)}{9\,a^3\,{\left(a\,d-b\,c\right)}^4}\right)\,{\left(\frac{-125\,a^3\,b^2\,d^3+150\,a^2\,b^3\,c\,d^2-60\,a\,b^4\,c^2\,d+8\,b^5\,c^3}{729\,a^{11}\,d^6-4374\,a^{10}\,b\,c\,d^5+10935\,a^9\,b^2\,c^2\,d^4-14580\,a^8\,b^3\,c^3\,d^3+10935\,a^7\,b^4\,c^4\,d^2-4374\,a^6\,b^5\,c^5\,d+729\,a^5\,b^6\,c^6}\right)}^{1/3}+\ln\left(\frac{\left(\frac{\left(\frac{27\,b^3\,d^3\,x\,{\left(a\,d-b\,c\right)}^3\,\left(3\,a^2\,d^2+3\,a\,b\,c\,d-2\,b^2\,c^2\right)}{a}+81\,a\,b^3\,c\,d^3\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(\frac{d^5}{c^2\,{\left(a\,d-b\,c\right)}^6}\right)}^{1/3}\right)\,{\left(\frac{d^5}{c^2\,{\left(a\,d-b\,c\right)}^6}\right)}^{2/3}}{9}-\frac{b^4\,d^4\,\left(27\,a^3\,d^3-98\,a^2\,b\,c\,d^2+52\,a\,b^2\,c^2\,d-8\,b^3\,c^3\right)}{3\,a^4\,d-3\,a^3\,b\,c}\right)\,{\left(\frac{d^5}{c^2\,{\left(a\,d-b\,c\right)}^6}\right)}^{1/3}}{3}+\frac{2\,b^5\,d^6\,x\,\left(85\,a^3\,d^3-84\,a^2\,b\,c\,d^2+30\,a\,b^2\,c^2\,d-4\,b^3\,c^3\right)}{9\,a^3\,{\left(a\,d-b\,c\right)}^4}\right)\,{\left(\frac{d^5}{27\,a^6\,c^2\,d^6-162\,a^5\,b\,c^3\,d^5+405\,a^4\,b^2\,c^4\,d^4-540\,a^3\,b^3\,c^5\,d^3+405\,a^2\,b^4\,c^6\,d^2-162\,a\,b^5\,c^7\,d+27\,b^6\,c^8}\right)}^{1/3}+\frac{\ln\left(\frac{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(\frac{{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(\frac{27\,b^3\,d^3\,x\,{\left(a\,d-b\,c\right)}^3\,\left(3\,a^2\,d^2+3\,a\,b\,c\,d-2\,b^2\,c^2\right)}{a}+\frac{27\,a\,b^3\,c\,d^3\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(-\frac{b^2\,{\left(5\,a\,d-2\,b\,c\right)}^3}{a^5\,{\left(a\,d-b\,c\right)}^6}\right)}^{1/3}}{2}\right)\,{\left(-\frac{b^2\,{\left(5\,a\,d-2\,b\,c\right)}^3}{a^5\,{\left(a\,d-b\,c\right)}^6}\right)}^{2/3}}{324}-\frac{b^4\,d^4\,\left(27\,a^3\,d^3-98\,a^2\,b\,c\,d^2+52\,a\,b^2\,c^2\,d-8\,b^3\,c^3\right)}{3\,a^4\,d-3\,a^3\,b\,c}\right)\,{\left(-\frac{b^2\,{\left(5\,a\,d-2\,b\,c\right)}^3}{a^5\,{\left(a\,d-b\,c\right)}^6}\right)}^{1/3}}{18}+\frac{2\,b^5\,d^6\,x\,\left(85\,a^3\,d^3-84\,a^2\,b\,c\,d^2+30\,a\,b^2\,c^2\,d-4\,b^3\,c^3\right)}{9\,a^3\,{\left(a\,d-b\,c\right)}^4}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(\frac{-125\,a^3\,b^2\,d^3+150\,a^2\,b^3\,c\,d^2-60\,a\,b^4\,c^2\,d+8\,b^5\,c^3}{729\,a^{11}\,d^6-4374\,a^{10}\,b\,c\,d^5+10935\,a^9\,b^2\,c^2\,d^4-14580\,a^8\,b^3\,c^3\,d^3+10935\,a^7\,b^4\,c^4\,d^2-4374\,a^6\,b^5\,c^5\,d+729\,a^5\,b^6\,c^6}\right)}^{1/3}}{2}-\frac{\ln\left(\frac{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(\frac{{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(\frac{27\,b^3\,d^3\,x\,{\left(a\,d-b\,c\right)}^3\,\left(3\,a^2\,d^2+3\,a\,b\,c\,d-2\,b^2\,c^2\right)}{a}-\frac{27\,a\,b^3\,c\,d^3\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(-\frac{b^2\,{\left(5\,a\,d-2\,b\,c\right)}^3}{a^5\,{\left(a\,d-b\,c\right)}^6}\right)}^{1/3}}{2}\right)\,{\left(-\frac{b^2\,{\left(5\,a\,d-2\,b\,c\right)}^3}{a^5\,{\left(a\,d-b\,c\right)}^6}\right)}^{2/3}}{324}-\frac{b^4\,d^4\,\left(27\,a^3\,d^3-98\,a^2\,b\,c\,d^2+52\,a\,b^2\,c^2\,d-8\,b^3\,c^3\right)}{3\,a^4\,d-3\,a^3\,b\,c}\right)\,{\left(-\frac{b^2\,{\left(5\,a\,d-2\,b\,c\right)}^3}{a^5\,{\left(a\,d-b\,c\right)}^6}\right)}^{1/3}}{18}-\frac{2\,b^5\,d^6\,x\,\left(85\,a^3\,d^3-84\,a^2\,b\,c\,d^2+30\,a\,b^2\,c^2\,d-4\,b^3\,c^3\right)}{9\,a^3\,{\left(a\,d-b\,c\right)}^4}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(\frac{-125\,a^3\,b^2\,d^3+150\,a^2\,b^3\,c\,d^2-60\,a\,b^4\,c^2\,d+8\,b^5\,c^3}{729\,a^{11}\,d^6-4374\,a^{10}\,b\,c\,d^5+10935\,a^9\,b^2\,c^2\,d^4-14580\,a^8\,b^3\,c^3\,d^3+10935\,a^7\,b^4\,c^4\,d^2-4374\,a^6\,b^5\,c^5\,d+729\,a^5\,b^6\,c^6}\right)}^{1/3}}{2}+\frac{\ln\left(\frac{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(\frac{{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(\frac{27\,b^3\,d^3\,x\,{\left(a\,d-b\,c\right)}^3\,\left(3\,a^2\,d^2+3\,a\,b\,c\,d-2\,b^2\,c^2\right)}{a}+\frac{81\,a\,b^3\,c\,d^3\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(\frac{d^5}{c^2\,{\left(a\,d-b\,c\right)}^6}\right)}^{1/3}}{2}\right)\,{\left(\frac{d^5}{c^2\,{\left(a\,d-b\,c\right)}^6}\right)}^{2/3}}{36}-\frac{b^4\,d^4\,\left(27\,a^3\,d^3-98\,a^2\,b\,c\,d^2+52\,a\,b^2\,c^2\,d-8\,b^3\,c^3\right)}{3\,a^4\,d-3\,a^3\,b\,c}\right)\,{\left(\frac{d^5}{c^2\,{\left(a\,d-b\,c\right)}^6}\right)}^{1/3}}{6}+\frac{2\,b^5\,d^6\,x\,\left(85\,a^3\,d^3-84\,a^2\,b\,c\,d^2+30\,a\,b^2\,c^2\,d-4\,b^3\,c^3\right)}{9\,a^3\,{\left(a\,d-b\,c\right)}^4}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(\frac{d^5}{27\,a^6\,c^2\,d^6-162\,a^5\,b\,c^3\,d^5+405\,a^4\,b^2\,c^4\,d^4-540\,a^3\,b^3\,c^5\,d^3+405\,a^2\,b^4\,c^6\,d^2-162\,a\,b^5\,c^7\,d+27\,b^6\,c^8}\right)}^{1/3}}{2}-\frac{\ln\left(\frac{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(\frac{{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(\frac{27\,b^3\,d^3\,x\,{\left(a\,d-b\,c\right)}^3\,\left(3\,a^2\,d^2+3\,a\,b\,c\,d-2\,b^2\,c^2\right)}{a}-\frac{81\,a\,b^3\,c\,d^3\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(\frac{d^5}{c^2\,{\left(a\,d-b\,c\right)}^6}\right)}^{1/3}}{2}\right)\,{\left(\frac{d^5}{c^2\,{\left(a\,d-b\,c\right)}^6}\right)}^{2/3}}{36}-\frac{b^4\,d^4\,\left(27\,a^3\,d^3-98\,a^2\,b\,c\,d^2+52\,a\,b^2\,c^2\,d-8\,b^3\,c^3\right)}{3\,a^4\,d-3\,a^3\,b\,c}\right)\,{\left(\frac{d^5}{c^2\,{\left(a\,d-b\,c\right)}^6}\right)}^{1/3}}{6}-\frac{2\,b^5\,d^6\,x\,\left(85\,a^3\,d^3-84\,a^2\,b\,c\,d^2+30\,a\,b^2\,c^2\,d-4\,b^3\,c^3\right)}{9\,a^3\,{\left(a\,d-b\,c\right)}^4}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(\frac{d^5}{27\,a^6\,c^2\,d^6-162\,a^5\,b\,c^3\,d^5+405\,a^4\,b^2\,c^4\,d^4-540\,a^3\,b^3\,c^5\,d^3+405\,a^2\,b^4\,c^6\,d^2-162\,a\,b^5\,c^7\,d+27\,b^6\,c^8}\right)}^{1/3}}{2}-\frac{b\,x}{3\,a\,\left(b\,x^3+a\right)\,\left(a\,d-b\,c\right)}","Not used",1,"log((((((27*b^3*d^3*x*(a*d - b*c)^3*(3*a^2*d^2 - 2*b^2*c^2 + 3*a*b*c*d))/a + 27*a*b^3*c*d^3*(a*d + b*c)*(a*d - b*c)^4*(-(b^2*(5*a*d - 2*b*c)^3)/(a^5*(a*d - b*c)^6))^(1/3))*(-(b^2*(5*a*d - 2*b*c)^3)/(a^5*(a*d - b*c)^6))^(2/3))/81 - (b^4*d^4*(27*a^3*d^3 - 8*b^3*c^3 + 52*a*b^2*c^2*d - 98*a^2*b*c*d^2))/(3*a^4*d - 3*a^3*b*c))*(-(b^2*(5*a*d - 2*b*c)^3)/(a^5*(a*d - b*c)^6))^(1/3))/9 + (2*b^5*d^6*x*(85*a^3*d^3 - 4*b^3*c^3 + 30*a*b^2*c^2*d - 84*a^2*b*c*d^2))/(9*a^3*(a*d - b*c)^4))*((8*b^5*c^3 - 125*a^3*b^2*d^3 + 150*a^2*b^3*c*d^2 - 60*a*b^4*c^2*d)/(729*a^11*d^6 + 729*a^5*b^6*c^6 - 4374*a^6*b^5*c^5*d + 10935*a^7*b^4*c^4*d^2 - 14580*a^8*b^3*c^3*d^3 + 10935*a^9*b^2*c^2*d^4 - 4374*a^10*b*c*d^5))^(1/3) + log((((((27*b^3*d^3*x*(a*d - b*c)^3*(3*a^2*d^2 - 2*b^2*c^2 + 3*a*b*c*d))/a + 81*a*b^3*c*d^3*(a*d + b*c)*(a*d - b*c)^4*(d^5/(c^2*(a*d - b*c)^6))^(1/3))*(d^5/(c^2*(a*d - b*c)^6))^(2/3))/9 - (b^4*d^4*(27*a^3*d^3 - 8*b^3*c^3 + 52*a*b^2*c^2*d - 98*a^2*b*c*d^2))/(3*a^4*d - 3*a^3*b*c))*(d^5/(c^2*(a*d - b*c)^6))^(1/3))/3 + (2*b^5*d^6*x*(85*a^3*d^3 - 4*b^3*c^3 + 30*a*b^2*c^2*d - 84*a^2*b*c*d^2))/(9*a^3*(a*d - b*c)^4))*(d^5/(27*b^6*c^8 + 27*a^6*c^2*d^6 - 162*a^5*b*c^3*d^5 + 405*a^2*b^4*c^6*d^2 - 540*a^3*b^3*c^5*d^3 + 405*a^4*b^2*c^4*d^4 - 162*a*b^5*c^7*d))^(1/3) + (log(((3^(1/2)*1i - 1)*(((3^(1/2)*1i - 1)^2*((27*b^3*d^3*x*(a*d - b*c)^3*(3*a^2*d^2 - 2*b^2*c^2 + 3*a*b*c*d))/a + (27*a*b^3*c*d^3*(3^(1/2)*1i - 1)*(a*d + b*c)*(a*d - b*c)^4*(-(b^2*(5*a*d - 2*b*c)^3)/(a^5*(a*d - b*c)^6))^(1/3))/2)*(-(b^2*(5*a*d - 2*b*c)^3)/(a^5*(a*d - b*c)^6))^(2/3))/324 - (b^4*d^4*(27*a^3*d^3 - 8*b^3*c^3 + 52*a*b^2*c^2*d - 98*a^2*b*c*d^2))/(3*a^4*d - 3*a^3*b*c))*(-(b^2*(5*a*d - 2*b*c)^3)/(a^5*(a*d - b*c)^6))^(1/3))/18 + (2*b^5*d^6*x*(85*a^3*d^3 - 4*b^3*c^3 + 30*a*b^2*c^2*d - 84*a^2*b*c*d^2))/(9*a^3*(a*d - b*c)^4))*(3^(1/2)*1i - 1)*((8*b^5*c^3 - 125*a^3*b^2*d^3 + 150*a^2*b^3*c*d^2 - 60*a*b^4*c^2*d)/(729*a^11*d^6 + 729*a^5*b^6*c^6 - 4374*a^6*b^5*c^5*d + 10935*a^7*b^4*c^4*d^2 - 14580*a^8*b^3*c^3*d^3 + 10935*a^9*b^2*c^2*d^4 - 4374*a^10*b*c*d^5))^(1/3))/2 - (log(((3^(1/2)*1i + 1)*(((3^(1/2)*1i + 1)^2*((27*b^3*d^3*x*(a*d - b*c)^3*(3*a^2*d^2 - 2*b^2*c^2 + 3*a*b*c*d))/a - (27*a*b^3*c*d^3*(3^(1/2)*1i + 1)*(a*d + b*c)*(a*d - b*c)^4*(-(b^2*(5*a*d - 2*b*c)^3)/(a^5*(a*d - b*c)^6))^(1/3))/2)*(-(b^2*(5*a*d - 2*b*c)^3)/(a^5*(a*d - b*c)^6))^(2/3))/324 - (b^4*d^4*(27*a^3*d^3 - 8*b^3*c^3 + 52*a*b^2*c^2*d - 98*a^2*b*c*d^2))/(3*a^4*d - 3*a^3*b*c))*(-(b^2*(5*a*d - 2*b*c)^3)/(a^5*(a*d - b*c)^6))^(1/3))/18 - (2*b^5*d^6*x*(85*a^3*d^3 - 4*b^3*c^3 + 30*a*b^2*c^2*d - 84*a^2*b*c*d^2))/(9*a^3*(a*d - b*c)^4))*(3^(1/2)*1i + 1)*((8*b^5*c^3 - 125*a^3*b^2*d^3 + 150*a^2*b^3*c*d^2 - 60*a*b^4*c^2*d)/(729*a^11*d^6 + 729*a^5*b^6*c^6 - 4374*a^6*b^5*c^5*d + 10935*a^7*b^4*c^4*d^2 - 14580*a^8*b^3*c^3*d^3 + 10935*a^9*b^2*c^2*d^4 - 4374*a^10*b*c*d^5))^(1/3))/2 + (log(((3^(1/2)*1i - 1)*(((3^(1/2)*1i - 1)^2*((27*b^3*d^3*x*(a*d - b*c)^3*(3*a^2*d^2 - 2*b^2*c^2 + 3*a*b*c*d))/a + (81*a*b^3*c*d^3*(3^(1/2)*1i - 1)*(a*d + b*c)*(a*d - b*c)^4*(d^5/(c^2*(a*d - b*c)^6))^(1/3))/2)*(d^5/(c^2*(a*d - b*c)^6))^(2/3))/36 - (b^4*d^4*(27*a^3*d^3 - 8*b^3*c^3 + 52*a*b^2*c^2*d - 98*a^2*b*c*d^2))/(3*a^4*d - 3*a^3*b*c))*(d^5/(c^2*(a*d - b*c)^6))^(1/3))/6 + (2*b^5*d^6*x*(85*a^3*d^3 - 4*b^3*c^3 + 30*a*b^2*c^2*d - 84*a^2*b*c*d^2))/(9*a^3*(a*d - b*c)^4))*(3^(1/2)*1i - 1)*(d^5/(27*b^6*c^8 + 27*a^6*c^2*d^6 - 162*a^5*b*c^3*d^5 + 405*a^2*b^4*c^6*d^2 - 540*a^3*b^3*c^5*d^3 + 405*a^4*b^2*c^4*d^4 - 162*a*b^5*c^7*d))^(1/3))/2 - (log(((3^(1/2)*1i + 1)*(((3^(1/2)*1i + 1)^2*((27*b^3*d^3*x*(a*d - b*c)^3*(3*a^2*d^2 - 2*b^2*c^2 + 3*a*b*c*d))/a - (81*a*b^3*c*d^3*(3^(1/2)*1i + 1)*(a*d + b*c)*(a*d - b*c)^4*(d^5/(c^2*(a*d - b*c)^6))^(1/3))/2)*(d^5/(c^2*(a*d - b*c)^6))^(2/3))/36 - (b^4*d^4*(27*a^3*d^3 - 8*b^3*c^3 + 52*a*b^2*c^2*d - 98*a^2*b*c*d^2))/(3*a^4*d - 3*a^3*b*c))*(d^5/(c^2*(a*d - b*c)^6))^(1/3))/6 - (2*b^5*d^6*x*(85*a^3*d^3 - 4*b^3*c^3 + 30*a*b^2*c^2*d - 84*a^2*b*c*d^2))/(9*a^3*(a*d - b*c)^4))*(3^(1/2)*1i + 1)*(d^5/(27*b^6*c^8 + 27*a^6*c^2*d^6 - 162*a^5*b*c^3*d^5 + 405*a^2*b^4*c^6*d^2 - 540*a^3*b^3*c^5*d^3 + 405*a^4*b^2*c^4*d^4 - 162*a*b^5*c^7*d))^(1/3))/2 - (b*x)/(3*a*(a + b*x^3)*(a*d - b*c))","B"
26,1,3637,419,24.310089,"\text{Not used}","int(1/((a + b*x^3)^2*(c + d*x^3)^2),x)","\frac{\frac{x\,\left(a^2\,d^2+b^2\,c^2\right)}{3\,a\,c\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}+\frac{b\,d\,x^4\,\left(a\,d+b\,c\right)}{3\,a\,c\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}}{b\,d\,x^6+\left(a\,d+b\,c\right)\,x^3+a\,c}+\ln\left(\frac{2\,\left(\frac{4\,\left(\frac{54\,b^3\,d^3\,x\,{\left(a\,d-b\,c\right)}^2\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2-3\,a\,b^2\,c^2\,d+b^3\,c^3\right)}{a\,c}+54\,a\,b^3\,c\,d^3\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(\frac{b^5\,{\left(4\,a\,d-b\,c\right)}^3}{a^5\,{\left(a\,d-b\,c\right)}^9}\right)}^{1/3}\right)\,{\left(\frac{b^5\,{\left(4\,a\,d-b\,c\right)}^3}{a^5\,{\left(a\,d-b\,c\right)}^9}\right)}^{2/3}}{81}-\frac{8\,b^4\,d^4\,\left(a^6\,d^6-11\,a^5\,b\,c\,d^5+37\,a^4\,b^2\,c^2\,d^4-27\,a^3\,b^3\,c^3\,d^3+37\,a^2\,b^4\,c^4\,d^2-11\,a\,b^5\,c^5\,d+b^6\,c^6\right)}{3\,a^3\,c^3\,{\left(a\,d-b\,c\right)}^4}\right)\,{\left(\frac{b^5\,{\left(4\,a\,d-b\,c\right)}^3}{a^5\,{\left(a\,d-b\,c\right)}^9}\right)}^{1/3}}{9}-\frac{16\,b^6\,d^6\,x\,\left(4\,a^6\,d^6-49\,a^5\,b\,c\,d^5+268\,a^4\,b^2\,c^2\,d^4-608\,a^3\,b^3\,c^3\,d^3+268\,a^2\,b^4\,c^4\,d^2-49\,a\,b^5\,c^5\,d+4\,b^6\,c^6\right)}{27\,a^3\,c^3\,{\left(a\,d-b\,c\right)}^8}\right)\,{\left(-\frac{-512\,a^3\,b^5\,d^3+384\,a^2\,b^6\,c\,d^2-96\,a\,b^7\,c^2\,d+8\,b^8\,c^3}{729\,a^{14}\,d^9-6561\,a^{13}\,b\,c\,d^8+26244\,a^{12}\,b^2\,c^2\,d^7-61236\,a^{11}\,b^3\,c^3\,d^6+91854\,a^{10}\,b^4\,c^4\,d^5-91854\,a^9\,b^5\,c^5\,d^4+61236\,a^8\,b^6\,c^6\,d^3-26244\,a^7\,b^7\,c^7\,d^2+6561\,a^6\,b^8\,c^8\,d-729\,a^5\,b^9\,c^9}\right)}^{1/3}+\ln\left(\frac{2\,\left(\frac{4\,\left(\frac{54\,b^3\,d^3\,x\,{\left(a\,d-b\,c\right)}^2\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2-3\,a\,b^2\,c^2\,d+b^3\,c^3\right)}{a\,c}+54\,a\,b^3\,c\,d^3\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(\frac{d^5\,{\left(a\,d-4\,b\,c\right)}^3}{c^5\,{\left(a\,d-b\,c\right)}^9}\right)}^{1/3}\right)\,{\left(\frac{d^5\,{\left(a\,d-4\,b\,c\right)}^3}{c^5\,{\left(a\,d-b\,c\right)}^9}\right)}^{2/3}}{81}-\frac{8\,b^4\,d^4\,\left(a^6\,d^6-11\,a^5\,b\,c\,d^5+37\,a^4\,b^2\,c^2\,d^4-27\,a^3\,b^3\,c^3\,d^3+37\,a^2\,b^4\,c^4\,d^2-11\,a\,b^5\,c^5\,d+b^6\,c^6\right)}{3\,a^3\,c^3\,{\left(a\,d-b\,c\right)}^4}\right)\,{\left(\frac{d^5\,{\left(a\,d-4\,b\,c\right)}^3}{c^5\,{\left(a\,d-b\,c\right)}^9}\right)}^{1/3}}{9}-\frac{16\,b^6\,d^6\,x\,\left(4\,a^6\,d^6-49\,a^5\,b\,c\,d^5+268\,a^4\,b^2\,c^2\,d^4-608\,a^3\,b^3\,c^3\,d^3+268\,a^2\,b^4\,c^4\,d^2-49\,a\,b^5\,c^5\,d+4\,b^6\,c^6\right)}{27\,a^3\,c^3\,{\left(a\,d-b\,c\right)}^8}\right)\,{\left(-\frac{8\,a^3\,d^8-96\,a^2\,b\,c\,d^7+384\,a\,b^2\,c^2\,d^6-512\,b^3\,c^3\,d^5}{-729\,a^9\,c^5\,d^9+6561\,a^8\,b\,c^6\,d^8-26244\,a^7\,b^2\,c^7\,d^7+61236\,a^6\,b^3\,c^8\,d^6-91854\,a^5\,b^4\,c^9\,d^5+91854\,a^4\,b^5\,c^{10}\,d^4-61236\,a^3\,b^6\,c^{11}\,d^3+26244\,a^2\,b^7\,c^{12}\,d^2-6561\,a\,b^8\,c^{13}\,d+729\,b^9\,c^{14}}\right)}^{1/3}+\frac{\ln\left(\frac{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(\frac{{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(\frac{54\,b^3\,d^3\,x\,{\left(a\,d-b\,c\right)}^2\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2-3\,a\,b^2\,c^2\,d+b^3\,c^3\right)}{a\,c}+27\,a\,b^3\,c\,d^3\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(\frac{b^5\,{\left(4\,a\,d-b\,c\right)}^3}{a^5\,{\left(a\,d-b\,c\right)}^9}\right)}^{1/3}\right)\,{\left(\frac{b^5\,{\left(4\,a\,d-b\,c\right)}^3}{a^5\,{\left(a\,d-b\,c\right)}^9}\right)}^{2/3}}{81}-\frac{8\,b^4\,d^4\,\left(a^6\,d^6-11\,a^5\,b\,c\,d^5+37\,a^4\,b^2\,c^2\,d^4-27\,a^3\,b^3\,c^3\,d^3+37\,a^2\,b^4\,c^4\,d^2-11\,a\,b^5\,c^5\,d+b^6\,c^6\right)}{3\,a^3\,c^3\,{\left(a\,d-b\,c\right)}^4}\right)\,{\left(\frac{b^5\,{\left(4\,a\,d-b\,c\right)}^3}{a^5\,{\left(a\,d-b\,c\right)}^9}\right)}^{1/3}}{9}-\frac{16\,b^6\,d^6\,x\,\left(4\,a^6\,d^6-49\,a^5\,b\,c\,d^5+268\,a^4\,b^2\,c^2\,d^4-608\,a^3\,b^3\,c^3\,d^3+268\,a^2\,b^4\,c^4\,d^2-49\,a\,b^5\,c^5\,d+4\,b^6\,c^6\right)}{27\,a^3\,c^3\,{\left(a\,d-b\,c\right)}^8}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(-\frac{-512\,a^3\,b^5\,d^3+384\,a^2\,b^6\,c\,d^2-96\,a\,b^7\,c^2\,d+8\,b^8\,c^3}{729\,a^{14}\,d^9-6561\,a^{13}\,b\,c\,d^8+26244\,a^{12}\,b^2\,c^2\,d^7-61236\,a^{11}\,b^3\,c^3\,d^6+91854\,a^{10}\,b^4\,c^4\,d^5-91854\,a^9\,b^5\,c^5\,d^4+61236\,a^8\,b^6\,c^6\,d^3-26244\,a^7\,b^7\,c^7\,d^2+6561\,a^6\,b^8\,c^8\,d-729\,a^5\,b^9\,c^9}\right)}^{1/3}}{2}-\frac{\ln\left(\frac{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(\frac{{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(\frac{54\,b^3\,d^3\,x\,{\left(a\,d-b\,c\right)}^2\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2-3\,a\,b^2\,c^2\,d+b^3\,c^3\right)}{a\,c}-27\,a\,b^3\,c\,d^3\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(\frac{b^5\,{\left(4\,a\,d-b\,c\right)}^3}{a^5\,{\left(a\,d-b\,c\right)}^9}\right)}^{1/3}\right)\,{\left(\frac{b^5\,{\left(4\,a\,d-b\,c\right)}^3}{a^5\,{\left(a\,d-b\,c\right)}^9}\right)}^{2/3}}{81}-\frac{8\,b^4\,d^4\,\left(a^6\,d^6-11\,a^5\,b\,c\,d^5+37\,a^4\,b^2\,c^2\,d^4-27\,a^3\,b^3\,c^3\,d^3+37\,a^2\,b^4\,c^4\,d^2-11\,a\,b^5\,c^5\,d+b^6\,c^6\right)}{3\,a^3\,c^3\,{\left(a\,d-b\,c\right)}^4}\right)\,{\left(\frac{b^5\,{\left(4\,a\,d-b\,c\right)}^3}{a^5\,{\left(a\,d-b\,c\right)}^9}\right)}^{1/3}}{9}+\frac{16\,b^6\,d^6\,x\,\left(4\,a^6\,d^6-49\,a^5\,b\,c\,d^5+268\,a^4\,b^2\,c^2\,d^4-608\,a^3\,b^3\,c^3\,d^3+268\,a^2\,b^4\,c^4\,d^2-49\,a\,b^5\,c^5\,d+4\,b^6\,c^6\right)}{27\,a^3\,c^3\,{\left(a\,d-b\,c\right)}^8}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(-\frac{-512\,a^3\,b^5\,d^3+384\,a^2\,b^6\,c\,d^2-96\,a\,b^7\,c^2\,d+8\,b^8\,c^3}{729\,a^{14}\,d^9-6561\,a^{13}\,b\,c\,d^8+26244\,a^{12}\,b^2\,c^2\,d^7-61236\,a^{11}\,b^3\,c^3\,d^6+91854\,a^{10}\,b^4\,c^4\,d^5-91854\,a^9\,b^5\,c^5\,d^4+61236\,a^8\,b^6\,c^6\,d^3-26244\,a^7\,b^7\,c^7\,d^2+6561\,a^6\,b^8\,c^8\,d-729\,a^5\,b^9\,c^9}\right)}^{1/3}}{2}+\frac{\ln\left(\frac{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(\frac{{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(\frac{54\,b^3\,d^3\,x\,{\left(a\,d-b\,c\right)}^2\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2-3\,a\,b^2\,c^2\,d+b^3\,c^3\right)}{a\,c}+27\,a\,b^3\,c\,d^3\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(\frac{d^5\,{\left(a\,d-4\,b\,c\right)}^3}{c^5\,{\left(a\,d-b\,c\right)}^9}\right)}^{1/3}\right)\,{\left(\frac{d^5\,{\left(a\,d-4\,b\,c\right)}^3}{c^5\,{\left(a\,d-b\,c\right)}^9}\right)}^{2/3}}{81}-\frac{8\,b^4\,d^4\,\left(a^6\,d^6-11\,a^5\,b\,c\,d^5+37\,a^4\,b^2\,c^2\,d^4-27\,a^3\,b^3\,c^3\,d^3+37\,a^2\,b^4\,c^4\,d^2-11\,a\,b^5\,c^5\,d+b^6\,c^6\right)}{3\,a^3\,c^3\,{\left(a\,d-b\,c\right)}^4}\right)\,{\left(\frac{d^5\,{\left(a\,d-4\,b\,c\right)}^3}{c^5\,{\left(a\,d-b\,c\right)}^9}\right)}^{1/3}}{9}-\frac{16\,b^6\,d^6\,x\,\left(4\,a^6\,d^6-49\,a^5\,b\,c\,d^5+268\,a^4\,b^2\,c^2\,d^4-608\,a^3\,b^3\,c^3\,d^3+268\,a^2\,b^4\,c^4\,d^2-49\,a\,b^5\,c^5\,d+4\,b^6\,c^6\right)}{27\,a^3\,c^3\,{\left(a\,d-b\,c\right)}^8}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(-\frac{8\,a^3\,d^8-96\,a^2\,b\,c\,d^7+384\,a\,b^2\,c^2\,d^6-512\,b^3\,c^3\,d^5}{-729\,a^9\,c^5\,d^9+6561\,a^8\,b\,c^6\,d^8-26244\,a^7\,b^2\,c^7\,d^7+61236\,a^6\,b^3\,c^8\,d^6-91854\,a^5\,b^4\,c^9\,d^5+91854\,a^4\,b^5\,c^{10}\,d^4-61236\,a^3\,b^6\,c^{11}\,d^3+26244\,a^2\,b^7\,c^{12}\,d^2-6561\,a\,b^8\,c^{13}\,d+729\,b^9\,c^{14}}\right)}^{1/3}}{2}-\frac{\ln\left(\frac{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(\frac{{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(\frac{54\,b^3\,d^3\,x\,{\left(a\,d-b\,c\right)}^2\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2-3\,a\,b^2\,c^2\,d+b^3\,c^3\right)}{a\,c}-27\,a\,b^3\,c\,d^3\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(\frac{d^5\,{\left(a\,d-4\,b\,c\right)}^3}{c^5\,{\left(a\,d-b\,c\right)}^9}\right)}^{1/3}\right)\,{\left(\frac{d^5\,{\left(a\,d-4\,b\,c\right)}^3}{c^5\,{\left(a\,d-b\,c\right)}^9}\right)}^{2/3}}{81}-\frac{8\,b^4\,d^4\,\left(a^6\,d^6-11\,a^5\,b\,c\,d^5+37\,a^4\,b^2\,c^2\,d^4-27\,a^3\,b^3\,c^3\,d^3+37\,a^2\,b^4\,c^4\,d^2-11\,a\,b^5\,c^5\,d+b^6\,c^6\right)}{3\,a^3\,c^3\,{\left(a\,d-b\,c\right)}^4}\right)\,{\left(\frac{d^5\,{\left(a\,d-4\,b\,c\right)}^3}{c^5\,{\left(a\,d-b\,c\right)}^9}\right)}^{1/3}}{9}+\frac{16\,b^6\,d^6\,x\,\left(4\,a^6\,d^6-49\,a^5\,b\,c\,d^5+268\,a^4\,b^2\,c^2\,d^4-608\,a^3\,b^3\,c^3\,d^3+268\,a^2\,b^4\,c^4\,d^2-49\,a\,b^5\,c^5\,d+4\,b^6\,c^6\right)}{27\,a^3\,c^3\,{\left(a\,d-b\,c\right)}^8}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(-\frac{8\,a^3\,d^8-96\,a^2\,b\,c\,d^7+384\,a\,b^2\,c^2\,d^6-512\,b^3\,c^3\,d^5}{-729\,a^9\,c^5\,d^9+6561\,a^8\,b\,c^6\,d^8-26244\,a^7\,b^2\,c^7\,d^7+61236\,a^6\,b^3\,c^8\,d^6-91854\,a^5\,b^4\,c^9\,d^5+91854\,a^4\,b^5\,c^{10}\,d^4-61236\,a^3\,b^6\,c^{11}\,d^3+26244\,a^2\,b^7\,c^{12}\,d^2-6561\,a\,b^8\,c^{13}\,d+729\,b^9\,c^{14}}\right)}^{1/3}}{2}","Not used",1,"((x*(a^2*d^2 + b^2*c^2))/(3*a*c*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) + (b*d*x^4*(a*d + b*c))/(3*a*c*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)))/(a*c + x^3*(a*d + b*c) + b*d*x^6) + log((2*((4*((54*b^3*d^3*x*(a*d - b*c)^2*(a^3*d^3 + b^3*c^3 - 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))/(a*c) + 54*a*b^3*c*d^3*(a*d + b*c)*(a*d - b*c)^4*((b^5*(4*a*d - b*c)^3)/(a^5*(a*d - b*c)^9))^(1/3))*((b^5*(4*a*d - b*c)^3)/(a^5*(a*d - b*c)^9))^(2/3))/81 - (8*b^4*d^4*(a^6*d^6 + b^6*c^6 + 37*a^2*b^4*c^4*d^2 - 27*a^3*b^3*c^3*d^3 + 37*a^4*b^2*c^2*d^4 - 11*a*b^5*c^5*d - 11*a^5*b*c*d^5))/(3*a^3*c^3*(a*d - b*c)^4))*((b^5*(4*a*d - b*c)^3)/(a^5*(a*d - b*c)^9))^(1/3))/9 - (16*b^6*d^6*x*(4*a^6*d^6 + 4*b^6*c^6 + 268*a^2*b^4*c^4*d^2 - 608*a^3*b^3*c^3*d^3 + 268*a^4*b^2*c^2*d^4 - 49*a*b^5*c^5*d - 49*a^5*b*c*d^5))/(27*a^3*c^3*(a*d - b*c)^8))*(-(8*b^8*c^3 - 512*a^3*b^5*d^3 + 384*a^2*b^6*c*d^2 - 96*a*b^7*c^2*d)/(729*a^14*d^9 - 729*a^5*b^9*c^9 + 6561*a^6*b^8*c^8*d - 26244*a^7*b^7*c^7*d^2 + 61236*a^8*b^6*c^6*d^3 - 91854*a^9*b^5*c^5*d^4 + 91854*a^10*b^4*c^4*d^5 - 61236*a^11*b^3*c^3*d^6 + 26244*a^12*b^2*c^2*d^7 - 6561*a^13*b*c*d^8))^(1/3) + log((2*((4*((54*b^3*d^3*x*(a*d - b*c)^2*(a^3*d^3 + b^3*c^3 - 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))/(a*c) + 54*a*b^3*c*d^3*(a*d + b*c)*(a*d - b*c)^4*((d^5*(a*d - 4*b*c)^3)/(c^5*(a*d - b*c)^9))^(1/3))*((d^5*(a*d - 4*b*c)^3)/(c^5*(a*d - b*c)^9))^(2/3))/81 - (8*b^4*d^4*(a^6*d^6 + b^6*c^6 + 37*a^2*b^4*c^4*d^2 - 27*a^3*b^3*c^3*d^3 + 37*a^4*b^2*c^2*d^4 - 11*a*b^5*c^5*d - 11*a^5*b*c*d^5))/(3*a^3*c^3*(a*d - b*c)^4))*((d^5*(a*d - 4*b*c)^3)/(c^5*(a*d - b*c)^9))^(1/3))/9 - (16*b^6*d^6*x*(4*a^6*d^6 + 4*b^6*c^6 + 268*a^2*b^4*c^4*d^2 - 608*a^3*b^3*c^3*d^3 + 268*a^4*b^2*c^2*d^4 - 49*a*b^5*c^5*d - 49*a^5*b*c*d^5))/(27*a^3*c^3*(a*d - b*c)^8))*(-(8*a^3*d^8 - 512*b^3*c^3*d^5 + 384*a*b^2*c^2*d^6 - 96*a^2*b*c*d^7)/(729*b^9*c^14 - 729*a^9*c^5*d^9 + 6561*a^8*b*c^6*d^8 + 26244*a^2*b^7*c^12*d^2 - 61236*a^3*b^6*c^11*d^3 + 91854*a^4*b^5*c^10*d^4 - 91854*a^5*b^4*c^9*d^5 + 61236*a^6*b^3*c^8*d^6 - 26244*a^7*b^2*c^7*d^7 - 6561*a*b^8*c^13*d))^(1/3) + (log(((3^(1/2)*1i - 1)*(((3^(1/2)*1i - 1)^2*((54*b^3*d^3*x*(a*d - b*c)^2*(a^3*d^3 + b^3*c^3 - 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))/(a*c) + 27*a*b^3*c*d^3*(3^(1/2)*1i - 1)*(a*d + b*c)*(a*d - b*c)^4*((b^5*(4*a*d - b*c)^3)/(a^5*(a*d - b*c)^9))^(1/3))*((b^5*(4*a*d - b*c)^3)/(a^5*(a*d - b*c)^9))^(2/3))/81 - (8*b^4*d^4*(a^6*d^6 + b^6*c^6 + 37*a^2*b^4*c^4*d^2 - 27*a^3*b^3*c^3*d^3 + 37*a^4*b^2*c^2*d^4 - 11*a*b^5*c^5*d - 11*a^5*b*c*d^5))/(3*a^3*c^3*(a*d - b*c)^4))*((b^5*(4*a*d - b*c)^3)/(a^5*(a*d - b*c)^9))^(1/3))/9 - (16*b^6*d^6*x*(4*a^6*d^6 + 4*b^6*c^6 + 268*a^2*b^4*c^4*d^2 - 608*a^3*b^3*c^3*d^3 + 268*a^4*b^2*c^2*d^4 - 49*a*b^5*c^5*d - 49*a^5*b*c*d^5))/(27*a^3*c^3*(a*d - b*c)^8))*(3^(1/2)*1i - 1)*(-(8*b^8*c^3 - 512*a^3*b^5*d^3 + 384*a^2*b^6*c*d^2 - 96*a*b^7*c^2*d)/(729*a^14*d^9 - 729*a^5*b^9*c^9 + 6561*a^6*b^8*c^8*d - 26244*a^7*b^7*c^7*d^2 + 61236*a^8*b^6*c^6*d^3 - 91854*a^9*b^5*c^5*d^4 + 91854*a^10*b^4*c^4*d^5 - 61236*a^11*b^3*c^3*d^6 + 26244*a^12*b^2*c^2*d^7 - 6561*a^13*b*c*d^8))^(1/3))/2 - (log(((3^(1/2)*1i + 1)*(((3^(1/2)*1i + 1)^2*((54*b^3*d^3*x*(a*d - b*c)^2*(a^3*d^3 + b^3*c^3 - 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))/(a*c) - 27*a*b^3*c*d^3*(3^(1/2)*1i + 1)*(a*d + b*c)*(a*d - b*c)^4*((b^5*(4*a*d - b*c)^3)/(a^5*(a*d - b*c)^9))^(1/3))*((b^5*(4*a*d - b*c)^3)/(a^5*(a*d - b*c)^9))^(2/3))/81 - (8*b^4*d^4*(a^6*d^6 + b^6*c^6 + 37*a^2*b^4*c^4*d^2 - 27*a^3*b^3*c^3*d^3 + 37*a^4*b^2*c^2*d^4 - 11*a*b^5*c^5*d - 11*a^5*b*c*d^5))/(3*a^3*c^3*(a*d - b*c)^4))*((b^5*(4*a*d - b*c)^3)/(a^5*(a*d - b*c)^9))^(1/3))/9 + (16*b^6*d^6*x*(4*a^6*d^6 + 4*b^6*c^6 + 268*a^2*b^4*c^4*d^2 - 608*a^3*b^3*c^3*d^3 + 268*a^4*b^2*c^2*d^4 - 49*a*b^5*c^5*d - 49*a^5*b*c*d^5))/(27*a^3*c^3*(a*d - b*c)^8))*(3^(1/2)*1i + 1)*(-(8*b^8*c^3 - 512*a^3*b^5*d^3 + 384*a^2*b^6*c*d^2 - 96*a*b^7*c^2*d)/(729*a^14*d^9 - 729*a^5*b^9*c^9 + 6561*a^6*b^8*c^8*d - 26244*a^7*b^7*c^7*d^2 + 61236*a^8*b^6*c^6*d^3 - 91854*a^9*b^5*c^5*d^4 + 91854*a^10*b^4*c^4*d^5 - 61236*a^11*b^3*c^3*d^6 + 26244*a^12*b^2*c^2*d^7 - 6561*a^13*b*c*d^8))^(1/3))/2 + (log(((3^(1/2)*1i - 1)*(((3^(1/2)*1i - 1)^2*((54*b^3*d^3*x*(a*d - b*c)^2*(a^3*d^3 + b^3*c^3 - 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))/(a*c) + 27*a*b^3*c*d^3*(3^(1/2)*1i - 1)*(a*d + b*c)*(a*d - b*c)^4*((d^5*(a*d - 4*b*c)^3)/(c^5*(a*d - b*c)^9))^(1/3))*((d^5*(a*d - 4*b*c)^3)/(c^5*(a*d - b*c)^9))^(2/3))/81 - (8*b^4*d^4*(a^6*d^6 + b^6*c^6 + 37*a^2*b^4*c^4*d^2 - 27*a^3*b^3*c^3*d^3 + 37*a^4*b^2*c^2*d^4 - 11*a*b^5*c^5*d - 11*a^5*b*c*d^5))/(3*a^3*c^3*(a*d - b*c)^4))*((d^5*(a*d - 4*b*c)^3)/(c^5*(a*d - b*c)^9))^(1/3))/9 - (16*b^6*d^6*x*(4*a^6*d^6 + 4*b^6*c^6 + 268*a^2*b^4*c^4*d^2 - 608*a^3*b^3*c^3*d^3 + 268*a^4*b^2*c^2*d^4 - 49*a*b^5*c^5*d - 49*a^5*b*c*d^5))/(27*a^3*c^3*(a*d - b*c)^8))*(3^(1/2)*1i - 1)*(-(8*a^3*d^8 - 512*b^3*c^3*d^5 + 384*a*b^2*c^2*d^6 - 96*a^2*b*c*d^7)/(729*b^9*c^14 - 729*a^9*c^5*d^9 + 6561*a^8*b*c^6*d^8 + 26244*a^2*b^7*c^12*d^2 - 61236*a^3*b^6*c^11*d^3 + 91854*a^4*b^5*c^10*d^4 - 91854*a^5*b^4*c^9*d^5 + 61236*a^6*b^3*c^8*d^6 - 26244*a^7*b^2*c^7*d^7 - 6561*a*b^8*c^13*d))^(1/3))/2 - (log(((3^(1/2)*1i + 1)*(((3^(1/2)*1i + 1)^2*((54*b^3*d^3*x*(a*d - b*c)^2*(a^3*d^3 + b^3*c^3 - 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))/(a*c) - 27*a*b^3*c*d^3*(3^(1/2)*1i + 1)*(a*d + b*c)*(a*d - b*c)^4*((d^5*(a*d - 4*b*c)^3)/(c^5*(a*d - b*c)^9))^(1/3))*((d^5*(a*d - 4*b*c)^3)/(c^5*(a*d - b*c)^9))^(2/3))/81 - (8*b^4*d^4*(a^6*d^6 + b^6*c^6 + 37*a^2*b^4*c^4*d^2 - 27*a^3*b^3*c^3*d^3 + 37*a^4*b^2*c^2*d^4 - 11*a*b^5*c^5*d - 11*a^5*b*c*d^5))/(3*a^3*c^3*(a*d - b*c)^4))*((d^5*(a*d - 4*b*c)^3)/(c^5*(a*d - b*c)^9))^(1/3))/9 + (16*b^6*d^6*x*(4*a^6*d^6 + 4*b^6*c^6 + 268*a^2*b^4*c^4*d^2 - 608*a^3*b^3*c^3*d^3 + 268*a^4*b^2*c^2*d^4 - 49*a*b^5*c^5*d - 49*a^5*b*c*d^5))/(27*a^3*c^3*(a*d - b*c)^8))*(3^(1/2)*1i + 1)*(-(8*a^3*d^8 - 512*b^3*c^3*d^5 + 384*a*b^2*c^2*d^6 - 96*a^2*b*c*d^7)/(729*b^9*c^14 - 729*a^9*c^5*d^9 + 6561*a^8*b*c^6*d^8 + 26244*a^2*b^7*c^12*d^2 - 61236*a^3*b^6*c^11*d^3 + 91854*a^4*b^5*c^10*d^4 - 91854*a^5*b^4*c^9*d^5 + 61236*a^6*b^3*c^8*d^6 - 26244*a^7*b^2*c^7*d^7 - 6561*a*b^8*c^13*d))^(1/3))/2","B"
27,0,-1,112,0.000000,"\text{Not used}","int((a + b*x^3)^(2/3)*(a - b*x^3),x)","\int {\left(b\,x^3+a\right)}^{2/3}\,\left(a-b\,x^3\right) \,d x","Not used",1,"int((a + b*x^3)^(2/3)*(a - b*x^3), x)","F"
28,0,-1,91,0.000000,"\text{Not used}","int((a - b*x^3)/(a + b*x^3)^(1/3),x)","\int \frac{a-b\,x^3}{{\left(b\,x^3+a\right)}^{1/3}} \,d x","Not used",1,"int((a - b*x^3)/(a + b*x^3)^(1/3), x)","F"
29,0,-1,85,0.000000,"\text{Not used}","int((a - b*x^3)/(a + b*x^3)^(4/3),x)","\int \frac{a-b\,x^3}{{\left(b\,x^3+a\right)}^{4/3}} \,d x","Not used",1,"int((a - b*x^3)/(a + b*x^3)^(4/3), x)","F"
30,1,27,47,1.347893,"\text{Not used}","int((a - b*x^3)/(a + b*x^3)^(7/3),x)","\frac{x\,\left(b\,x^3+a\right)+a\,x}{2\,a\,{\left(b\,x^3+a\right)}^{4/3}}","Not used",1,"(x*(a + b*x^3) + a*x)/(2*a*(a + b*x^3)^(4/3))","B"
31,1,44,55,1.424746,"\text{Not used}","int((a - b*x^3)/(a + b*x^3)^(10/3),x)","\frac{15\,x\,{\left(b\,x^3+a\right)}^2+8\,a^2\,x+5\,a\,x\,\left(b\,x^3+a\right)}{28\,a^2\,{\left(b\,x^3+a\right)}^{7/3}}","Not used",1,"(15*x*(a + b*x^3)^2 + 8*a^2*x + 5*a*x*(a + b*x^3))/(28*a^2*(a + b*x^3)^(7/3))","B"
32,1,58,74,1.390977,"\text{Not used}","int((a - b*x^3)/(a + b*x^3)^(13/3),x)","\frac{x}{5\,{\left(b\,x^3+a\right)}^{10/3}}+\frac{18\,x}{35\,a^3\,{\left(b\,x^3+a\right)}^{1/3}}+\frac{6\,x}{35\,a^2\,{\left(b\,x^3+a\right)}^{4/3}}+\frac{4\,x}{35\,a\,{\left(b\,x^3+a\right)}^{7/3}}","Not used",1,"x/(5*(a + b*x^3)^(10/3)) + (18*x)/(35*a^3*(a + b*x^3)^(1/3)) + (6*x)/(35*a^2*(a + b*x^3)^(4/3)) + (4*x)/(35*a*(a + b*x^3)^(7/3))","B"
33,1,73,93,1.371472,"\text{Not used}","int((a - b*x^3)/(a + b*x^3)^(16/3),x)","\frac{2\,x}{13\,{\left(b\,x^3+a\right)}^{13/3}}+\frac{891\,x}{1820\,a^4\,{\left(b\,x^3+a\right)}^{1/3}}+\frac{297\,x}{1820\,a^3\,{\left(b\,x^3+a\right)}^{4/3}}+\frac{99\,x}{910\,a^2\,{\left(b\,x^3+a\right)}^{7/3}}+\frac{11\,x}{130\,a\,{\left(b\,x^3+a\right)}^{10/3}}","Not used",1,"(2*x)/(13*(a + b*x^3)^(13/3)) + (891*x)/(1820*a^4*(a + b*x^3)^(1/3)) + (297*x)/(1820*a^3*(a + b*x^3)^(4/3)) + (99*x)/(910*a^2*(a + b*x^3)^(7/3)) + (11*x)/(130*a*(a + b*x^3)^(10/3))","B"
34,0,-1,483,0.000000,"\text{Not used}","int((a + b*x^3)^(7/3)/(a - b*x^3),x)","\int \frac{{\left(b\,x^3+a\right)}^{7/3}}{a-b\,x^3} \,d x","Not used",1,"int((a + b*x^3)^(7/3)/(a - b*x^3), x)","F"
35,0,-1,464,0.000000,"\text{Not used}","int((a + b*x^3)^(4/3)/(a - b*x^3),x)","\int \frac{{\left(b\,x^3+a\right)}^{4/3}}{a-b\,x^3} \,d x","Not used",1,"int((a + b*x^3)^(4/3)/(a - b*x^3), x)","F"
36,0,-1,398,0.000000,"\text{Not used}","int((a + b*x^3)^(1/3)/(a - b*x^3),x)","\int \frac{{\left(b\,x^3+a\right)}^{1/3}}{a-b\,x^3} \,d x","Not used",1,"int((a + b*x^3)^(1/3)/(a - b*x^3), x)","F"
37,0,-1,452,0.000000,"\text{Not used}","int(1/((a + b*x^3)^(2/3)*(a - b*x^3)),x)","\int \frac{1}{{\left(b\,x^3+a\right)}^{2/3}\,\left(a-b\,x^3\right)} \,d x","Not used",1,"int(1/((a + b*x^3)^(2/3)*(a - b*x^3)), x)","F"
38,0,-1,473,0.000000,"\text{Not used}","int(1/((a + b*x^3)^(5/3)*(a - b*x^3)),x)","\int \frac{1}{{\left(b\,x^3+a\right)}^{5/3}\,\left(a-b\,x^3\right)} \,d x","Not used",1,"int(1/((a + b*x^3)^(5/3)*(a - b*x^3)), x)","F"
39,0,-1,492,0.000000,"\text{Not used}","int(1/((a + b*x^3)^(8/3)*(a - b*x^3)),x)","\int \frac{1}{{\left(b\,x^3+a\right)}^{8/3}\,\left(a-b\,x^3\right)} \,d x","Not used",1,"int(1/((a + b*x^3)^(8/3)*(a - b*x^3)), x)","F"
40,0,-1,139,0.000000,"\text{Not used}","int((a + b*x^3)^(2/3)*(a - b*x^3)^2,x)","\int {\left(b\,x^3+a\right)}^{2/3}\,{\left(a-b\,x^3\right)}^2 \,d x","Not used",1,"int((a + b*x^3)^(2/3)*(a - b*x^3)^2, x)","F"
41,0,-1,120,0.000000,"\text{Not used}","int((a - b*x^3)^2/(a + b*x^3)^(1/3),x)","\int \frac{{\left(a-b\,x^3\right)}^2}{{\left(b\,x^3+a\right)}^{1/3}} \,d x","Not used",1,"int((a - b*x^3)^2/(a + b*x^3)^(1/3), x)","F"
42,0,-1,113,0.000000,"\text{Not used}","int((a - b*x^3)^2/(a + b*x^3)^(4/3),x)","\int \frac{{\left(a-b\,x^3\right)}^2}{{\left(b\,x^3+a\right)}^{4/3}} \,d x","Not used",1,"int((a - b*x^3)^2/(a + b*x^3)^(4/3), x)","F"
43,0,-1,110,0.000000,"\text{Not used}","int((a - b*x^3)^2/(a + b*x^3)^(7/3),x)","\int \frac{{\left(a-b\,x^3\right)}^2}{{\left(b\,x^3+a\right)}^{7/3}} \,d x","Not used",1,"int((a - b*x^3)^2/(a + b*x^3)^(7/3), x)","F"
44,1,44,76,1.431784,"\text{Not used}","int((a - b*x^3)^2/(a + b*x^3)^(10/3),x)","\frac{4\,x\,{\left(b\,x^3+a\right)}^2+4\,a^2\,x-a\,x\,\left(b\,x^3+a\right)}{7\,a\,{\left(b\,x^3+a\right)}^{7/3}}","Not used",1,"(4*x*(a + b*x^3)^2 + 4*a^2*x - a*x*(a + b*x^3))/(7*a*(a + b*x^3)^(7/3))","B"
45,1,56,105,1.388976,"\text{Not used}","int((a - b*x^3)^2/(a + b*x^3)^(13/3),x)","\frac{69\,x}{140\,a^2\,{\left(b\,x^3+a\right)}^{1/3}}-\frac{2\,x}{35\,{\left(b\,x^3+a\right)}^{7/3}}+\frac{23\,x}{140\,a\,{\left(b\,x^3+a\right)}^{4/3}}+\frac{2\,a\,x}{5\,{\left(b\,x^3+a\right)}^{10/3}}","Not used",1,"(69*x)/(140*a^2*(a + b*x^3)^(1/3)) - (2*x)/(35*(a + b*x^3)^(7/3)) + (23*x)/(140*a*(a + b*x^3)^(4/3)) + (2*a*x)/(5*(a + b*x^3)^(10/3))","B"
46,1,71,98,1.436315,"\text{Not used}","int((a - b*x^3)^2/(a + b*x^3)^(16/3),x)","\frac{423\,x}{910\,a^3\,{\left(b\,x^3+a\right)}^{1/3}}-\frac{2\,x}{65\,{\left(b\,x^3+a\right)}^{10/3}}+\frac{141\,x}{910\,a^2\,{\left(b\,x^3+a\right)}^{4/3}}+\frac{47\,x}{455\,a\,{\left(b\,x^3+a\right)}^{7/3}}+\frac{4\,a\,x}{13\,{\left(b\,x^3+a\right)}^{13/3}}","Not used",1,"(423*x)/(910*a^3*(a + b*x^3)^(1/3)) - (2*x)/(65*(a + b*x^3)^(10/3)) + (141*x)/(910*a^2*(a + b*x^3)^(4/3)) + (47*x)/(455*a*(a + b*x^3)^(7/3)) + (4*a*x)/(13*(a + b*x^3)^(13/3))","B"
47,1,86,117,1.427487,"\text{Not used}","int((a - b*x^3)^2/(a + b*x^3)^(19/3),x)","\frac{81\,x}{182\,a^4\,{\left(b\,x^3+a\right)}^{1/3}}-\frac{x}{52\,{\left(b\,x^3+a\right)}^{13/3}}+\frac{27\,x}{182\,a^3\,{\left(b\,x^3+a\right)}^{4/3}}+\frac{9\,x}{91\,a^2\,{\left(b\,x^3+a\right)}^{7/3}}+\frac{x}{13\,a\,{\left(b\,x^3+a\right)}^{10/3}}+\frac{a\,x}{4\,{\left(b\,x^3+a\right)}^{16/3}}","Not used",1,"(81*x)/(182*a^4*(a + b*x^3)^(1/3)) - x/(52*(a + b*x^3)^(13/3)) + (27*x)/(182*a^3*(a + b*x^3)^(4/3)) + (9*x)/(91*a^2*(a + b*x^3)^(7/3)) + x/(13*a*(a + b*x^3)^(10/3)) + (a*x)/(4*(a + b*x^3)^(16/3))","B"
48,0,-1,94,0.000000,"\text{Not used}","int((a + b*x^3)^(4/3)*(a - b*x^3)^2,x)","\int {\left(b\,x^3+a\right)}^{4/3}\,{\left(a-b\,x^3\right)}^2 \,d x","Not used",1,"int((a + b*x^3)^(4/3)*(a - b*x^3)^2, x)","F"
49,0,-1,94,0.000000,"\text{Not used}","int((a + b*x^3)^(1/3)*(a - b*x^3)^2,x)","\int {\left(b\,x^3+a\right)}^{1/3}\,{\left(a-b\,x^3\right)}^2 \,d x","Not used",1,"int((a + b*x^3)^(1/3)*(a - b*x^3)^2, x)","F"
50,0,-1,94,0.000000,"\text{Not used}","int((a - b*x^3)^2/(a + b*x^3)^(2/3),x)","\int \frac{{\left(a-b\,x^3\right)}^2}{{\left(b\,x^3+a\right)}^{2/3}} \,d x","Not used",1,"int((a - b*x^3)^2/(a + b*x^3)^(2/3), x)","F"
51,0,-1,74,0.000000,"\text{Not used}","int((a - b*x^3)^2/(a + b*x^3)^(5/3),x)","\int \frac{{\left(a-b\,x^3\right)}^2}{{\left(b\,x^3+a\right)}^{5/3}} \,d x","Not used",1,"int((a - b*x^3)^2/(a + b*x^3)^(5/3), x)","F"
52,0,-1,74,0.000000,"\text{Not used}","int((a - b*x^3)^2/(a + b*x^3)^(8/3),x)","\int \frac{{\left(a-b\,x^3\right)}^2}{{\left(b\,x^3+a\right)}^{8/3}} \,d x","Not used",1,"int((a - b*x^3)^2/(a + b*x^3)^(8/3), x)","F"
53,0,-1,77,0.000000,"\text{Not used}","int((a - b*x^3)^2/(a + b*x^3)^(11/3),x)","\int \frac{{\left(a-b\,x^3\right)}^2}{{\left(b\,x^3+a\right)}^{11/3}} \,d x","Not used",1,"int((a - b*x^3)^2/(a + b*x^3)^(11/3), x)","F"
54,0,-1,93,0.000000,"\text{Not used}","int((a - b*x^3)^2/(a + b*x^3)^(14/3),x)","\int \frac{{\left(a-b\,x^3\right)}^2}{{\left(b\,x^3+a\right)}^{14/3}} \,d x","Not used",1,"int((a - b*x^3)^2/(a + b*x^3)^(14/3), x)","F"
55,0,-1,93,0.000000,"\text{Not used}","int((a - b*x^3)^2/(a + b*x^3)^(17/3),x)","\int \frac{{\left(a-b\,x^3\right)}^2}{{\left(b\,x^3+a\right)}^{17/3}} \,d x","Not used",1,"int((a - b*x^3)^2/(a + b*x^3)^(17/3), x)","F"
56,0,-1,174,0.000000,"\text{Not used}","int((a + b*x^3)^(5/3)*(c + d*x^3),x)","\int {\left(b\,x^3+a\right)}^{5/3}\,\left(d\,x^3+c\right) \,d x","Not used",1,"int((a + b*x^3)^(5/3)*(c + d*x^3), x)","F"
57,0,-1,141,0.000000,"\text{Not used}","int((a + b*x^3)^(2/3)*(c + d*x^3),x)","\int {\left(b\,x^3+a\right)}^{2/3}\,\left(d\,x^3+c\right) \,d x","Not used",1,"int((a + b*x^3)^(2/3)*(c + d*x^3), x)","F"
58,0,-1,111,0.000000,"\text{Not used}","int((c + d*x^3)/(a + b*x^3)^(1/3),x)","\int \frac{d\,x^3+c}{{\left(b\,x^3+a\right)}^{1/3}} \,d x","Not used",1,"int((c + d*x^3)/(a + b*x^3)^(1/3), x)","F"
59,0,-1,99,0.000000,"\text{Not used}","int((c + d*x^3)/(a + b*x^3)^(4/3),x)","\int \frac{d\,x^3+c}{{\left(b\,x^3+a\right)}^{4/3}} \,d x","Not used",1,"int((c + d*x^3)/(a + b*x^3)^(4/3), x)","F"
60,1,33,47,1.370057,"\text{Not used}","int((c + d*x^3)/(a + b*x^3)^(7/3),x)","\frac{4\,a\,c\,x+a\,d\,x^4+3\,b\,c\,x^4}{4\,a^2\,{\left(b\,x^3+a\right)}^{4/3}}","Not used",1,"(4*a*c*x + a*d*x^4 + 3*b*c*x^4)/(4*a^2*(a + b*x^3)^(4/3))","B"
61,1,87,91,1.424096,"\text{Not used}","int((c + d*x^3)/(a + b*x^3)^(10/3),x)","\frac{3\,a\,d\,x\,{\left(b\,x^3+a\right)}^2-4\,a^3\,d\,x+18\,b\,c\,x\,{\left(b\,x^3+a\right)}^2+a^2\,d\,x\,\left(b\,x^3+a\right)+4\,a^2\,b\,c\,x+6\,a\,b\,c\,x\,\left(b\,x^3+a\right)}{28\,a^3\,b\,{\left(b\,x^3+a\right)}^{7/3}}","Not used",1,"(3*a*d*x*(a + b*x^3)^2 - 4*a^3*d*x + 18*b*c*x*(a + b*x^3)^2 + a^2*d*x*(a + b*x^3) + 4*a^2*b*c*x + 6*a*b*c*x*(a + b*x^3))/(28*a^3*b*(a + b*x^3)^(7/3))","B"
62,1,105,121,1.460403,"\text{Not used}","int((c + d*x^3)/(a + b*x^3)^(13/3),x)","\frac{x\,\left(\frac{c}{10\,a}-\frac{d}{10\,b}\right)}{{\left(b\,x^3+a\right)}^{10/3}}+\frac{x\,\left(a\,d+9\,b\,c\right)}{70\,a^2\,b\,{\left(b\,x^3+a\right)}^{7/3}}+\frac{x\,\left(3\,a\,d+27\,b\,c\right)}{140\,a^3\,b\,{\left(b\,x^3+a\right)}^{4/3}}+\frac{x\,\left(9\,a\,d+81\,b\,c\right)}{140\,a^4\,b\,{\left(b\,x^3+a\right)}^{1/3}}","Not used",1,"(x*(c/(10*a) - d/(10*b)))/(a + b*x^3)^(10/3) + (x*(a*d + 9*b*c))/(70*a^2*b*(a + b*x^3)^(7/3)) + (x*(3*a*d + 27*b*c))/(140*a^3*b*(a + b*x^3)^(4/3)) + (x*(9*a*d + 81*b*c))/(140*a^4*b*(a + b*x^3)^(1/3))","B"
63,1,132,151,1.453127,"\text{Not used}","int((c + d*x^3)/(a + b*x^3)^(16/3),x)","\frac{x\,\left(\frac{c}{13\,a}-\frac{d}{13\,b}\right)}{{\left(b\,x^3+a\right)}^{13/3}}+\frac{x\,\left(a\,d+12\,b\,c\right)}{130\,a^2\,b\,{\left(b\,x^3+a\right)}^{10/3}}+\frac{x\,\left(9\,a\,d+108\,b\,c\right)}{910\,a^3\,b\,{\left(b\,x^3+a\right)}^{7/3}}+\frac{x\,\left(27\,a\,d+324\,b\,c\right)}{1820\,a^4\,b\,{\left(b\,x^3+a\right)}^{4/3}}+\frac{x\,\left(81\,a\,d+972\,b\,c\right)}{1820\,a^5\,b\,{\left(b\,x^3+a\right)}^{1/3}}","Not used",1,"(x*(c/(13*a) - d/(13*b)))/(a + b*x^3)^(13/3) + (x*(a*d + 12*b*c))/(130*a^2*b*(a + b*x^3)^(10/3)) + (x*(9*a*d + 108*b*c))/(910*a^3*b*(a + b*x^3)^(7/3)) + (x*(27*a*d + 324*b*c))/(1820*a^4*b*(a + b*x^3)^(4/3)) + (x*(81*a*d + 972*b*c))/(1820*a^5*b*(a + b*x^3)^(1/3))","B"
64,0,-1,85,0.000000,"\text{Not used}","int((a + b*x^3)^(7/3)*(c + d*x^3),x)","\int {\left(b\,x^3+a\right)}^{7/3}\,\left(d\,x^3+c\right) \,d x","Not used",1,"int((a + b*x^3)^(7/3)*(c + d*x^3), x)","F"
65,0,-1,83,0.000000,"\text{Not used}","int((a + b*x^3)^(4/3)*(c + d*x^3),x)","\int {\left(b\,x^3+a\right)}^{4/3}\,\left(d\,x^3+c\right) \,d x","Not used",1,"int((a + b*x^3)^(4/3)*(c + d*x^3), x)","F"
66,0,-1,82,0.000000,"\text{Not used}","int((a + b*x^3)^(1/3)*(c + d*x^3),x)","\int {\left(b\,x^3+a\right)}^{1/3}\,\left(d\,x^3+c\right) \,d x","Not used",1,"int((a + b*x^3)^(1/3)*(c + d*x^3), x)","F"
67,0,-1,82,0.000000,"\text{Not used}","int((c + d*x^3)/(a + b*x^3)^(2/3),x)","\int \frac{d\,x^3+c}{{\left(b\,x^3+a\right)}^{2/3}} \,d x","Not used",1,"int((c + d*x^3)/(a + b*x^3)^(2/3), x)","F"
68,0,-1,93,0.000000,"\text{Not used}","int((c + d*x^3)/(a + b*x^3)^(5/3),x)","\int \frac{d\,x^3+c}{{\left(b\,x^3+a\right)}^{5/3}} \,d x","Not used",1,"int((c + d*x^3)/(a + b*x^3)^(5/3), x)","F"
69,0,-1,94,0.000000,"\text{Not used}","int((c + d*x^3)/(a + b*x^3)^(8/3),x)","\int \frac{d\,x^3+c}{{\left(b\,x^3+a\right)}^{8/3}} \,d x","Not used",1,"int((c + d*x^3)/(a + b*x^3)^(8/3), x)","F"
70,0,-1,262,0.000000,"\text{Not used}","int((a + b*x^3)^(5/3)*(c + d*x^3)^2,x)","\int {\left(b\,x^3+a\right)}^{5/3}\,{\left(d\,x^3+c\right)}^2 \,d x","Not used",1,"int((a + b*x^3)^(5/3)*(c + d*x^3)^2, x)","F"
71,0,-1,219,0.000000,"\text{Not used}","int((a + b*x^3)^(2/3)*(c + d*x^3)^2,x)","\int {\left(b\,x^3+a\right)}^{2/3}\,{\left(d\,x^3+c\right)}^2 \,d x","Not used",1,"int((a + b*x^3)^(2/3)*(c + d*x^3)^2, x)","F"
72,0,-1,175,0.000000,"\text{Not used}","int((c + d*x^3)^2/(a + b*x^3)^(1/3),x)","\int \frac{{\left(d\,x^3+c\right)}^2}{{\left(b\,x^3+a\right)}^{1/3}} \,d x","Not used",1,"int((c + d*x^3)^2/(a + b*x^3)^(1/3), x)","F"
73,0,-1,159,0.000000,"\text{Not used}","int((c + d*x^3)^2/(a + b*x^3)^(4/3),x)","\int \frac{{\left(d\,x^3+c\right)}^2}{{\left(b\,x^3+a\right)}^{4/3}} \,d x","Not used",1,"int((c + d*x^3)^2/(a + b*x^3)^(4/3), x)","F"
74,0,-1,152,0.000000,"\text{Not used}","int((c + d*x^3)^2/(a + b*x^3)^(7/3),x)","\int \frac{{\left(d\,x^3+c\right)}^2}{{\left(b\,x^3+a\right)}^{7/3}} \,d x","Not used",1,"int((c + d*x^3)^2/(a + b*x^3)^(7/3), x)","F"
75,1,148,78,1.426527,"\text{Not used}","int((c + d*x^3)^2/(a + b*x^3)^(10/3),x)","\frac{2\,a^4\,d^2\,x+2\,a^2\,d^2\,x\,{\left(b\,x^3+a\right)}^2+9\,b^2\,c^2\,x\,{\left(b\,x^3+a\right)}^2+2\,a^2\,b^2\,c^2\,x-4\,a^3\,d^2\,x\,\left(b\,x^3+a\right)+3\,a\,b^2\,c^2\,x\,\left(b\,x^3+a\right)-4\,a^3\,b\,c\,d\,x+3\,a\,b\,c\,d\,x\,{\left(b\,x^3+a\right)}^2+a^2\,b\,c\,d\,x\,\left(b\,x^3+a\right)}{14\,a^3\,b^2\,{\left(b\,x^3+a\right)}^{7/3}}","Not used",1,"(2*a^4*d^2*x + 2*a^2*d^2*x*(a + b*x^3)^2 + 9*b^2*c^2*x*(a + b*x^3)^2 + 2*a^2*b^2*c^2*x - 4*a^3*d^2*x*(a + b*x^3) + 3*a*b^2*c^2*x*(a + b*x^3) - 4*a^3*b*c*d*x + 3*a*b*c*d*x*(a + b*x^3)^2 + a^2*b*c*d*x*(a + b*x^3))/(14*a^3*b^2*(a + b*x^3)^(7/3))","B"
76,1,176,174,1.450108,"\text{Not used}","int((c + d*x^3)^2/(a + b*x^3)^(13/3),x)","\frac{x\,\left(\frac{c^2}{10\,a}+\frac{a\,\left(\frac{d^2}{10\,b}-\frac{c\,d}{5\,a}\right)}{b}\right)}{{\left(b\,x^3+a\right)}^{10/3}}-\frac{x\,\left(\frac{d^2}{7\,b^2}-\frac{-a^2\,d^2+2\,a\,b\,c\,d+9\,b^2\,c^2}{70\,a^2\,b^2}\right)}{{\left(b\,x^3+a\right)}^{7/3}}+\frac{x\,\left(2\,a^2\,d^2+6\,a\,b\,c\,d+27\,b^2\,c^2\right)}{140\,a^3\,b^2\,{\left(b\,x^3+a\right)}^{4/3}}+\frac{x\,\left(6\,a^2\,d^2+18\,a\,b\,c\,d+81\,b^2\,c^2\right)}{140\,a^4\,b^2\,{\left(b\,x^3+a\right)}^{1/3}}","Not used",1,"(x*(c^2/(10*a) + (a*(d^2/(10*b) - (c*d)/(5*a)))/b))/(a + b*x^3)^(10/3) - (x*(d^2/(7*b^2) - (9*b^2*c^2 - a^2*d^2 + 2*a*b*c*d)/(70*a^2*b^2)))/(a + b*x^3)^(7/3) + (x*(2*a^2*d^2 + 27*b^2*c^2 + 6*a*b*c*d))/(140*a^3*b^2*(a + b*x^3)^(4/3)) + (x*(6*a^2*d^2 + 81*b^2*c^2 + 18*a*b*c*d))/(140*a^4*b^2*(a + b*x^3)^(1/3))","B"
77,1,217,211,1.430413,"\text{Not used}","int((c + d*x^3)^2/(a + b*x^3)^(16/3),x)","\frac{x\,\left(\frac{c^2}{13\,a}+\frac{a\,\left(\frac{d^2}{13\,b}-\frac{2\,c\,d}{13\,a}\right)}{b}\right)}{{\left(b\,x^3+a\right)}^{13/3}}-\frac{x\,\left(\frac{d^2}{10\,b^2}-\frac{-a^2\,d^2+2\,a\,b\,c\,d+12\,b^2\,c^2}{130\,a^2\,b^2}\right)}{{\left(b\,x^3+a\right)}^{10/3}}+\frac{x\,\left(2\,a^2\,d^2+9\,a\,b\,c\,d+54\,b^2\,c^2\right)}{455\,a^3\,b^2\,{\left(b\,x^3+a\right)}^{7/3}}+\frac{x\,\left(6\,a^2\,d^2+27\,a\,b\,c\,d+162\,b^2\,c^2\right)}{910\,a^4\,b^2\,{\left(b\,x^3+a\right)}^{4/3}}+\frac{x\,\left(18\,a^2\,d^2+81\,a\,b\,c\,d+486\,b^2\,c^2\right)}{910\,a^5\,b^2\,{\left(b\,x^3+a\right)}^{1/3}}","Not used",1,"(x*(c^2/(13*a) + (a*(d^2/(13*b) - (2*c*d)/(13*a)))/b))/(a + b*x^3)^(13/3) - (x*(d^2/(10*b^2) - (12*b^2*c^2 - a^2*d^2 + 2*a*b*c*d)/(130*a^2*b^2)))/(a + b*x^3)^(10/3) + (x*(2*a^2*d^2 + 54*b^2*c^2 + 9*a*b*c*d))/(455*a^3*b^2*(a + b*x^3)^(7/3)) + (x*(6*a^2*d^2 + 162*b^2*c^2 + 27*a*b*c*d))/(910*a^4*b^2*(a + b*x^3)^(4/3)) + (x*(18*a^2*d^2 + 486*b^2*c^2 + 81*a*b*c*d))/(910*a^5*b^2*(a + b*x^3)^(1/3))","B"
78,1,257,253,1.481123,"\text{Not used}","int((c + d*x^3)^2/(a + b*x^3)^(19/3),x)","\frac{x\,\left(\frac{c^2}{16\,a}+\frac{a\,\left(\frac{d^2}{16\,b}-\frac{c\,d}{8\,a}\right)}{b}\right)}{{\left(b\,x^3+a\right)}^{16/3}}-\frac{x\,\left(\frac{d^2}{13\,b^2}-\frac{-a^2\,d^2+2\,a\,b\,c\,d+15\,b^2\,c^2}{208\,a^2\,b^2}\right)}{{\left(b\,x^3+a\right)}^{13/3}}+\frac{x\,\left(a^2\,d^2+6\,a\,b\,c\,d+45\,b^2\,c^2\right)}{520\,a^3\,b^2\,{\left(b\,x^3+a\right)}^{10/3}}+\frac{x\,\left(9\,a^2\,d^2+54\,a\,b\,c\,d+405\,b^2\,c^2\right)}{3640\,a^4\,b^2\,{\left(b\,x^3+a\right)}^{7/3}}+\frac{x\,\left(27\,a^2\,d^2+162\,a\,b\,c\,d+1215\,b^2\,c^2\right)}{7280\,a^5\,b^2\,{\left(b\,x^3+a\right)}^{4/3}}+\frac{x\,\left(81\,a^2\,d^2+486\,a\,b\,c\,d+3645\,b^2\,c^2\right)}{7280\,a^6\,b^2\,{\left(b\,x^3+a\right)}^{1/3}}","Not used",1,"(x*(c^2/(16*a) + (a*(d^2/(16*b) - (c*d)/(8*a)))/b))/(a + b*x^3)^(16/3) - (x*(d^2/(13*b^2) - (15*b^2*c^2 - a^2*d^2 + 2*a*b*c*d)/(208*a^2*b^2)))/(a + b*x^3)^(13/3) + (x*(a^2*d^2 + 45*b^2*c^2 + 6*a*b*c*d))/(520*a^3*b^2*(a + b*x^3)^(10/3)) + (x*(9*a^2*d^2 + 405*b^2*c^2 + 54*a*b*c*d))/(3640*a^4*b^2*(a + b*x^3)^(7/3)) + (x*(27*a^2*d^2 + 1215*b^2*c^2 + 162*a*b*c*d))/(7280*a^5*b^2*(a + b*x^3)^(4/3)) + (x*(81*a^2*d^2 + 3645*b^2*c^2 + 486*a*b*c*d))/(7280*a^6*b^2*(a + b*x^3)^(1/3))","B"
79,0,-1,135,0.000000,"\text{Not used}","int((a + b*x^3)^(7/3)*(c + d*x^3)^2,x)","\int {\left(b\,x^3+a\right)}^{7/3}\,{\left(d\,x^3+c\right)}^2 \,d x","Not used",1,"int((a + b*x^3)^(7/3)*(c + d*x^3)^2, x)","F"
80,0,-1,133,0.000000,"\text{Not used}","int((a + b*x^3)^(4/3)*(c + d*x^3)^2,x)","\int {\left(b\,x^3+a\right)}^{4/3}\,{\left(d\,x^3+c\right)}^2 \,d x","Not used",1,"int((a + b*x^3)^(4/3)*(c + d*x^3)^2, x)","F"
81,0,-1,131,0.000000,"\text{Not used}","int((a + b*x^3)^(1/3)*(c + d*x^3)^2,x)","\int {\left(b\,x^3+a\right)}^{1/3}\,{\left(d\,x^3+c\right)}^2 \,d x","Not used",1,"int((a + b*x^3)^(1/3)*(c + d*x^3)^2, x)","F"
82,0,-1,132,0.000000,"\text{Not used}","int((c + d*x^3)^2/(a + b*x^3)^(2/3),x)","\int \frac{{\left(d\,x^3+c\right)}^2}{{\left(b\,x^3+a\right)}^{2/3}} \,d x","Not used",1,"int((c + d*x^3)^2/(a + b*x^3)^(2/3), x)","F"
83,0,-1,146,0.000000,"\text{Not used}","int((c + d*x^3)^2/(a + b*x^3)^(5/3),x)","\int \frac{{\left(d\,x^3+c\right)}^2}{{\left(b\,x^3+a\right)}^{5/3}} \,d x","Not used",1,"int((c + d*x^3)^2/(a + b*x^3)^(5/3), x)","F"
84,0,-1,147,0.000000,"\text{Not used}","int((c + d*x^3)^2/(a + b*x^3)^(8/3),x)","\int \frac{{\left(d\,x^3+c\right)}^2}{{\left(b\,x^3+a\right)}^{8/3}} \,d x","Not used",1,"int((c + d*x^3)^2/(a + b*x^3)^(8/3), x)","F"
85,1,271,109,1.556228,"\text{Not used}","int((a + b*x^3)^3/(c + d*x^3)^(13/3),x)","\frac{x\,\left(\frac{a^3}{10\,c}-\frac{c\,\left(\frac{c\,\left(\frac{b^3}{10\,d}-\frac{3\,a\,b^2}{10\,c}\right)}{d}+\frac{3\,a^2\,b}{10\,c}\right)}{d}\right)}{{\left(d\,x^3+c\right)}^{10/3}}-\frac{x\,\left(\frac{b^3}{4\,d^3}-\frac{27\,a^3\,d^3+9\,a^2\,b\,c\,d^2+6\,a\,b^2\,c^2\,d-7\,b^3\,c^3}{140\,c^3\,d^3}\right)}{{\left(d\,x^3+c\right)}^{4/3}}+\frac{x\,\left(\frac{c\,\left(\frac{b^3}{7\,d^2}-\frac{b^2\,\left(3\,a\,d-b\,c\right)}{7\,c\,d^2}\right)}{d}+\frac{9\,a^3\,d^3+3\,a^2\,b\,c\,d^2-3\,a\,b^2\,c^2\,d+b^3\,c^3}{70\,c^2\,d^3}\right)}{{\left(d\,x^3+c\right)}^{7/3}}+\frac{x\,\left(81\,a^3\,d^3+27\,a^2\,b\,c\,d^2+18\,a\,b^2\,c^2\,d+14\,b^3\,c^3\right)}{140\,c^4\,d^3\,{\left(d\,x^3+c\right)}^{1/3}}","Not used",1,"(x*(a^3/(10*c) - (c*((c*(b^3/(10*d) - (3*a*b^2)/(10*c)))/d + (3*a^2*b)/(10*c)))/d))/(c + d*x^3)^(10/3) - (x*(b^3/(4*d^3) - (27*a^3*d^3 - 7*b^3*c^3 + 6*a*b^2*c^2*d + 9*a^2*b*c*d^2)/(140*c^3*d^3)))/(c + d*x^3)^(4/3) + (x*((c*(b^3/(7*d^2) - (b^2*(3*a*d - b*c))/(7*c*d^2)))/d + (9*a^3*d^3 + b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2)/(70*c^2*d^3)))/(c + d*x^3)^(7/3) + (x*(81*a^3*d^3 + 14*b^3*c^3 + 18*a*b^2*c^2*d + 27*a^2*b*c*d^2))/(140*c^4*d^3*(c + d*x^3)^(1/3))","B"
86,0,-1,331,0.000000,"\text{Not used}","int((a + b*x^3)^(8/3)/(c + d*x^3),x)","\int \frac{{\left(b\,x^3+a\right)}^{8/3}}{d\,x^3+c} \,d x","Not used",1,"int((a + b*x^3)^(8/3)/(c + d*x^3), x)","F"
87,0,-1,273,0.000000,"\text{Not used}","int((a + b*x^3)^(5/3)/(c + d*x^3),x)","\int \frac{{\left(b\,x^3+a\right)}^{5/3}}{d\,x^3+c} \,d x","Not used",1,"int((a + b*x^3)^(5/3)/(c + d*x^3), x)","F"
88,0,-1,233,0.000000,"\text{Not used}","int((a + b*x^3)^(2/3)/(c + d*x^3),x)","\int \frac{{\left(b\,x^3+a\right)}^{2/3}}{d\,x^3+c} \,d x","Not used",1,"int((a + b*x^3)^(2/3)/(c + d*x^3), x)","F"
89,0,-1,148,0.000000,"\text{Not used}","int(1/((a + b*x^3)^(1/3)*(c + d*x^3)),x)","\int \frac{1}{{\left(b\,x^3+a\right)}^{1/3}\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int(1/((a + b*x^3)^(1/3)*(c + d*x^3)), x)","F"
90,0,-1,179,0.000000,"\text{Not used}","int(1/((a + b*x^3)^(4/3)*(c + d*x^3)),x)","\int \frac{1}{{\left(b\,x^3+a\right)}^{4/3}\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int(1/((a + b*x^3)^(4/3)*(c + d*x^3)), x)","F"
91,0,-1,226,0.000000,"\text{Not used}","int(1/((a + b*x^3)^(7/3)*(c + d*x^3)),x)","\int \frac{1}{{\left(b\,x^3+a\right)}^{7/3}\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int(1/((a + b*x^3)^(7/3)*(c + d*x^3)), x)","F"
92,0,-1,280,0.000000,"\text{Not used}","int(1/((a + b*x^3)^(10/3)*(c + d*x^3)),x)","\int \frac{1}{{\left(b\,x^3+a\right)}^{10/3}\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int(1/((a + b*x^3)^(10/3)*(c + d*x^3)), x)","F"
93,0,-1,60,0.000000,"\text{Not used}","int((a + b*x^3)^(4/3)/(c + d*x^3),x)","\int \frac{{\left(b\,x^3+a\right)}^{4/3}}{d\,x^3+c} \,d x","Not used",1,"int((a + b*x^3)^(4/3)/(c + d*x^3), x)","F"
94,0,-1,59,0.000000,"\text{Not used}","int((a + b*x^3)^(1/3)/(c + d*x^3),x)","\int \frac{{\left(b\,x^3+a\right)}^{1/3}}{d\,x^3+c} \,d x","Not used",1,"int((a + b*x^3)^(1/3)/(c + d*x^3), x)","F"
95,0,-1,59,0.000000,"\text{Not used}","int(1/((a + b*x^3)^(2/3)*(c + d*x^3)),x)","\int \frac{1}{{\left(b\,x^3+a\right)}^{2/3}\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int(1/((a + b*x^3)^(2/3)*(c + d*x^3)), x)","F"
96,0,-1,62,0.000000,"\text{Not used}","int(1/((a + b*x^3)^(5/3)*(c + d*x^3)),x)","\int \frac{1}{{\left(b\,x^3+a\right)}^{5/3}\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int(1/((a + b*x^3)^(5/3)*(c + d*x^3)), x)","F"
97,0,-1,62,0.000000,"\text{Not used}","int(1/((a + b*x^3)^(8/3)*(c + d*x^3)),x)","\int \frac{1}{{\left(b\,x^3+a\right)}^{8/3}\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int(1/((a + b*x^3)^(8/3)*(c + d*x^3)), x)","F"
98,0,-1,351,0.000000,"\text{Not used}","int((a + b*x^3)^(8/3)/(c + d*x^3)^2,x)","\int \frac{{\left(b\,x^3+a\right)}^{8/3}}{{\left(d\,x^3+c\right)}^2} \,d x","Not used",1,"int((a + b*x^3)^(8/3)/(c + d*x^3)^2, x)","F"
99,0,-1,301,0.000000,"\text{Not used}","int((a + b*x^3)^(5/3)/(c + d*x^3)^2,x)","\int \frac{{\left(b\,x^3+a\right)}^{5/3}}{{\left(d\,x^3+c\right)}^2} \,d x","Not used",1,"int((a + b*x^3)^(5/3)/(c + d*x^3)^2, x)","F"
100,0,-1,182,0.000000,"\text{Not used}","int((a + b*x^3)^(2/3)/(c + d*x^3)^2,x)","\int \frac{{\left(b\,x^3+a\right)}^{2/3}}{{\left(d\,x^3+c\right)}^2} \,d x","Not used",1,"int((a + b*x^3)^(2/3)/(c + d*x^3)^2, x)","F"
101,0,-1,217,0.000000,"\text{Not used}","int(1/((a + b*x^3)^(1/3)*(c + d*x^3)^2),x)","\int \frac{1}{{\left(b\,x^3+a\right)}^{1/3}\,{\left(d\,x^3+c\right)}^2} \,d x","Not used",1,"int(1/((a + b*x^3)^(1/3)*(c + d*x^3)^2), x)","F"
102,0,-1,261,0.000000,"\text{Not used}","int(1/((a + b*x^3)^(4/3)*(c + d*x^3)^2),x)","\int \frac{1}{{\left(b\,x^3+a\right)}^{4/3}\,{\left(d\,x^3+c\right)}^2} \,d x","Not used",1,"int(1/((a + b*x^3)^(4/3)*(c + d*x^3)^2), x)","F"
103,0,-1,324,0.000000,"\text{Not used}","int(1/((a + b*x^3)^(7/3)*(c + d*x^3)^2),x)","\int \frac{1}{{\left(b\,x^3+a\right)}^{7/3}\,{\left(d\,x^3+c\right)}^2} \,d x","Not used",1,"int(1/((a + b*x^3)^(7/3)*(c + d*x^3)^2), x)","F"
104,0,-1,60,0.000000,"\text{Not used}","int((a + b*x^3)^(4/3)/(c + d*x^3)^2,x)","\int \frac{{\left(b\,x^3+a\right)}^{4/3}}{{\left(d\,x^3+c\right)}^2} \,d x","Not used",1,"int((a + b*x^3)^(4/3)/(c + d*x^3)^2, x)","F"
105,0,-1,59,0.000000,"\text{Not used}","int((a + b*x^3)^(1/3)/(c + d*x^3)^2,x)","\int \frac{{\left(b\,x^3+a\right)}^{1/3}}{{\left(d\,x^3+c\right)}^2} \,d x","Not used",1,"int((a + b*x^3)^(1/3)/(c + d*x^3)^2, x)","F"
106,0,-1,59,0.000000,"\text{Not used}","int(1/((a + b*x^3)^(2/3)*(c + d*x^3)^2),x)","\int \frac{1}{{\left(b\,x^3+a\right)}^{2/3}\,{\left(d\,x^3+c\right)}^2} \,d x","Not used",1,"int(1/((a + b*x^3)^(2/3)*(c + d*x^3)^2), x)","F"
107,0,-1,62,0.000000,"\text{Not used}","int(1/((a + b*x^3)^(5/3)*(c + d*x^3)^2),x)","\int \frac{1}{{\left(b\,x^3+a\right)}^{5/3}\,{\left(d\,x^3+c\right)}^2} \,d x","Not used",1,"int(1/((a + b*x^3)^(5/3)*(c + d*x^3)^2), x)","F"
108,0,-1,62,0.000000,"\text{Not used}","int(1/((a + b*x^3)^(8/3)*(c + d*x^3)^2),x)","\int \frac{1}{{\left(b\,x^3+a\right)}^{8/3}\,{\left(d\,x^3+c\right)}^2} \,d x","Not used",1,"int(1/((a + b*x^3)^(8/3)*(c + d*x^3)^2), x)","F"
109,0,-1,541,0.000000,"\text{Not used}","int((a + b*x^3)^(14/3)/(c + d*x^3)^3,x)","\int \frac{{\left(b\,x^3+a\right)}^{14/3}}{{\left(d\,x^3+c\right)}^3} \,d x","Not used",1,"int((a + b*x^3)^(14/3)/(c + d*x^3)^3, x)","F"
110,0,-1,458,0.000000,"\text{Not used}","int((a + b*x^3)^(11/3)/(c + d*x^3)^3,x)","\int \frac{{\left(b\,x^3+a\right)}^{11/3}}{{\left(d\,x^3+c\right)}^3} \,d x","Not used",1,"int((a + b*x^3)^(11/3)/(c + d*x^3)^3, x)","F"
111,0,-1,391,0.000000,"\text{Not used}","int((a + b*x^3)^(8/3)/(c + d*x^3)^3,x)","\int \frac{{\left(b\,x^3+a\right)}^{8/3}}{{\left(d\,x^3+c\right)}^3} \,d x","Not used",1,"int((a + b*x^3)^(8/3)/(c + d*x^3)^3, x)","F"
112,0,-1,217,0.000000,"\text{Not used}","int((a + b*x^3)^(5/3)/(c + d*x^3)^3,x)","\int \frac{{\left(b\,x^3+a\right)}^{5/3}}{{\left(d\,x^3+c\right)}^3} \,d x","Not used",1,"int((a + b*x^3)^(5/3)/(c + d*x^3)^3, x)","F"
113,0,-1,267,0.000000,"\text{Not used}","int((a + b*x^3)^(2/3)/(c + d*x^3)^3,x)","\int \frac{{\left(b\,x^3+a\right)}^{2/3}}{{\left(d\,x^3+c\right)}^3} \,d x","Not used",1,"int((a + b*x^3)^(2/3)/(c + d*x^3)^3, x)","F"
114,0,-1,307,0.000000,"\text{Not used}","int(1/((a + b*x^3)^(1/3)*(c + d*x^3)^3),x)","\int \frac{1}{{\left(b\,x^3+a\right)}^{1/3}\,{\left(d\,x^3+c\right)}^3} \,d x","Not used",1,"int(1/((a + b*x^3)^(1/3)*(c + d*x^3)^3), x)","F"
115,0,-1,377,0.000000,"\text{Not used}","int(1/((a + b*x^3)^(4/3)*(c + d*x^3)^3),x)","\int \frac{1}{{\left(b\,x^3+a\right)}^{4/3}\,{\left(d\,x^3+c\right)}^3} \,d x","Not used",1,"int(1/((a + b*x^3)^(4/3)*(c + d*x^3)^3), x)","F"
116,0,-1,463,0.000000,"\text{Not used}","int(1/((a + b*x^3)^(7/3)*(c + d*x^3)^3),x)","\int \frac{1}{{\left(b\,x^3+a\right)}^{7/3}\,{\left(d\,x^3+c\right)}^3} \,d x","Not used",1,"int(1/((a + b*x^3)^(7/3)*(c + d*x^3)^3), x)","F"
117,0,-1,60,0.000000,"\text{Not used}","int((a + b*x^3)^(4/3)/(c + d*x^3)^3,x)","\int \frac{{\left(b\,x^3+a\right)}^{4/3}}{{\left(d\,x^3+c\right)}^3} \,d x","Not used",1,"int((a + b*x^3)^(4/3)/(c + d*x^3)^3, x)","F"
118,0,-1,59,0.000000,"\text{Not used}","int((a + b*x^3)^(1/3)/(c + d*x^3)^3,x)","\int \frac{{\left(b\,x^3+a\right)}^{1/3}}{{\left(d\,x^3+c\right)}^3} \,d x","Not used",1,"int((a + b*x^3)^(1/3)/(c + d*x^3)^3, x)","F"
119,0,-1,59,0.000000,"\text{Not used}","int(1/((a + b*x^3)^(2/3)*(c + d*x^3)^3),x)","\int \frac{1}{{\left(b\,x^3+a\right)}^{2/3}\,{\left(d\,x^3+c\right)}^3} \,d x","Not used",1,"int(1/((a + b*x^3)^(2/3)*(c + d*x^3)^3), x)","F"
120,0,-1,62,0.000000,"\text{Not used}","int(1/((a + b*x^3)^(5/3)*(c + d*x^3)^3),x)","\int \frac{1}{{\left(b\,x^3+a\right)}^{5/3}\,{\left(d\,x^3+c\right)}^3} \,d x","Not used",1,"int(1/((a + b*x^3)^(5/3)*(c + d*x^3)^3), x)","F"
121,0,-1,62,0.000000,"\text{Not used}","int(1/((a + b*x^3)^(8/3)*(c + d*x^3)^3),x)","\int \frac{1}{{\left(b\,x^3+a\right)}^{8/3}\,{\left(d\,x^3+c\right)}^3} \,d x","Not used",1,"int(1/((a + b*x^3)^(8/3)*(c + d*x^3)^3), x)","F"
122,0,-1,155,0.000000,"\text{Not used}","int((a + b*x^3)^(7/4)/(c + d*x^3)^(37/12),x)","\int \frac{{\left(b\,x^3+a\right)}^{7/4}}{{\left(d\,x^3+c\right)}^{37/12}} \,d x","Not used",1,"int((a + b*x^3)^(7/4)/(c + d*x^3)^(37/12), x)","F"
123,0,-1,155,0.000000,"\text{Not used}","int((a + b*x^3)^(5/4)/(c + d*x^3)^(31/12),x)","\int \frac{{\left(b\,x^3+a\right)}^{5/4}}{{\left(d\,x^3+c\right)}^{31/12}} \,d x","Not used",1,"int((a + b*x^3)^(5/4)/(c + d*x^3)^(31/12), x)","F"
124,0,-1,122,0.000000,"\text{Not used}","int((a + b*x^3)^(3/4)/(c + d*x^3)^(25/12),x)","\int \frac{{\left(b\,x^3+a\right)}^{3/4}}{{\left(d\,x^3+c\right)}^{25/12}} \,d x","Not used",1,"int((a + b*x^3)^(3/4)/(c + d*x^3)^(25/12), x)","F"
125,0,-1,122,0.000000,"\text{Not used}","int((a + b*x^3)^(1/4)/(c + d*x^3)^(19/12),x)","\int \frac{{\left(b\,x^3+a\right)}^{1/4}}{{\left(d\,x^3+c\right)}^{19/12}} \,d x","Not used",1,"int((a + b*x^3)^(1/4)/(c + d*x^3)^(19/12), x)","F"
126,0,-1,87,0.000000,"\text{Not used}","int(1/((a + b*x^3)^(1/4)*(c + d*x^3)^(13/12)),x)","\int \frac{1}{{\left(b\,x^3+a\right)}^{1/4}\,{\left(d\,x^3+c\right)}^{13/12}} \,d x","Not used",1,"int(1/((a + b*x^3)^(1/4)*(c + d*x^3)^(13/12)), x)","F"
127,0,-1,87,0.000000,"\text{Not used}","int(1/((a + b*x^3)^(3/4)*(c + d*x^3)^(7/12)),x)","\int \frac{1}{{\left(b\,x^3+a\right)}^{3/4}\,{\left(d\,x^3+c\right)}^{7/12}} \,d x","Not used",1,"int(1/((a + b*x^3)^(3/4)*(c + d*x^3)^(7/12)), x)","F"
128,0,-1,87,0.000000,"\text{Not used}","int(1/((a + b*x^3)^(5/4)*(c + d*x^3)^(1/12)),x)","\int \frac{1}{{\left(b\,x^3+a\right)}^{5/4}\,{\left(d\,x^3+c\right)}^{1/12}} \,d x","Not used",1,"int(1/((a + b*x^3)^(5/4)*(c + d*x^3)^(1/12)), x)","F"
129,0,-1,121,0.000000,"\text{Not used}","int((c + d*x^3)^(5/12)/(a + b*x^3)^(7/4),x)","\int \frac{{\left(d\,x^3+c\right)}^{5/12}}{{\left(b\,x^3+a\right)}^{7/4}} \,d x","Not used",1,"int((c + d*x^3)^(5/12)/(a + b*x^3)^(7/4), x)","F"
130,0,-1,121,0.000000,"\text{Not used}","int((c + d*x^3)^(11/12)/(a + b*x^3)^(9/4),x)","\int \frac{{\left(d\,x^3+c\right)}^{11/12}}{{\left(b\,x^3+a\right)}^{9/4}} \,d x","Not used",1,"int((c + d*x^3)^(11/12)/(a + b*x^3)^(9/4), x)","F"
131,0,-1,153,0.000000,"\text{Not used}","int((c + d*x^3)^(17/12)/(a + b*x^3)^(11/4),x)","\int \frac{{\left(d\,x^3+c\right)}^{17/12}}{{\left(b\,x^3+a\right)}^{11/4}} \,d x","Not used",1,"int((c + d*x^3)^(17/12)/(a + b*x^3)^(11/4), x)","F"
132,0,-1,153,0.000000,"\text{Not used}","int((c + d*x^3)^(23/12)/(a + b*x^3)^(13/4),x)","\int \frac{{\left(d\,x^3+c\right)}^{23/12}}{{\left(b\,x^3+a\right)}^{13/4}} \,d x","Not used",1,"int((c + d*x^3)^(23/12)/(a + b*x^3)^(13/4), x)","F"
133,0,-1,79,0.000000,"\text{Not used}","int((a + b*x^3)^m*(c + d*x^3)^p,x)","\int {\left(b\,x^3+a\right)}^m\,{\left(d\,x^3+c\right)}^p \,d x","Not used",1,"int((a + b*x^3)^m*(c + d*x^3)^p, x)","F"
134,0,-1,167,0.000000,"\text{Not used}","int((a + b*x^3)^2*(c + d*x^3)^q,x)","\int {\left(b\,x^3+a\right)}^2\,{\left(d\,x^3+c\right)}^q \,d x","Not used",1,"int((a + b*x^3)^2*(c + d*x^3)^q, x)","F"
135,0,-1,84,0.000000,"\text{Not used}","int((a + b*x^3)*(c + d*x^3)^q,x)","\int \left(b\,x^3+a\right)\,{\left(d\,x^3+c\right)}^q \,d x","Not used",1,"int((a + b*x^3)*(c + d*x^3)^q, x)","F"
136,0,-1,57,0.000000,"\text{Not used}","int((c + d*x^3)^q/(a + b*x^3),x)","\int \frac{{\left(d\,x^3+c\right)}^q}{b\,x^3+a} \,d x","Not used",1,"int((c + d*x^3)^q/(a + b*x^3), x)","F"
137,0,-1,57,0.000000,"\text{Not used}","int((c + d*x^3)^q/(a + b*x^3)^2,x)","\int \frac{{\left(d\,x^3+c\right)}^q}{{\left(b\,x^3+a\right)}^2} \,d x","Not used",1,"int((c + d*x^3)^q/(a + b*x^3)^2, x)","F"
138,0,-1,298,0.000000,"\text{Not used}","int((a + b*x^3)^m*(c + d*x^3)^3,x)","\int {\left(b\,x^3+a\right)}^m\,{\left(d\,x^3+c\right)}^3 \,d x","Not used",1,"int((a + b*x^3)^m*(c + d*x^3)^3, x)","F"
139,0,-1,176,0.000000,"\text{Not used}","int((a + b*x^3)^m*(c + d*x^3)^2,x)","\int {\left(b\,x^3+a\right)}^m\,{\left(d\,x^3+c\right)}^2 \,d x","Not used",1,"int((a + b*x^3)^m*(c + d*x^3)^2, x)","F"
140,0,-1,93,0.000000,"\text{Not used}","int((a + b*x^3)^m*(c + d*x^3),x)","\int {\left(b\,x^3+a\right)}^m\,\left(d\,x^3+c\right) \,d x","Not used",1,"int((a + b*x^3)^m*(c + d*x^3), x)","F"
141,1,41,44,1.345735,"\text{Not used}","int((a + b*x^3)^m,x)","\frac{x\,{\left(b\,x^3+a\right)}^m\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{3},-m;\ \frac{4}{3};\ -\frac{b\,x^3}{a}\right)}{{\left(\frac{b\,x^3}{a}+1\right)}^m}","Not used",1,"(x*(a + b*x^3)^m*hypergeom([1/3, -m], 4/3, -(b*x^3)/a))/((b*x^3)/a + 1)^m","B"
142,0,-1,57,0.000000,"\text{Not used}","int((a + b*x^3)^m/(c + d*x^3),x)","\int \frac{{\left(b\,x^3+a\right)}^m}{d\,x^3+c} \,d x","Not used",1,"int((a + b*x^3)^m/(c + d*x^3), x)","F"
143,0,-1,57,0.000000,"\text{Not used}","int((a + b*x^3)^m/(c + d*x^3)^2,x)","\int \frac{{\left(b\,x^3+a\right)}^m}{{\left(d\,x^3+c\right)}^2} \,d x","Not used",1,"int((a + b*x^3)^m/(c + d*x^3)^2, x)","F"
144,0,-1,57,0.000000,"\text{Not used}","int((a + b*x^3)^m/(c + d*x^3)^3,x)","\int \frac{{\left(b\,x^3+a\right)}^m}{{\left(d\,x^3+c\right)}^3} \,d x","Not used",1,"int((a + b*x^3)^m/(c + d*x^3)^3, x)","F"
145,1,131,53,1.904657,"\text{Not used}","int((a + b*x^3)^((b*c)/(3*a*d - 3*b*c) - 1)/(c + d*x^3)^((a*d)/(3*a*d - 3*b*c) + 1),x)","\frac{x\,{\left(b\,x^3+a\right)}^{\frac{b\,c}{3\,a\,d-3\,b\,c}-1}+\frac{x^4\,{\left(b\,x^3+a\right)}^{\frac{b\,c}{3\,a\,d-3\,b\,c}-1}\,\left(a\,d+b\,c\right)}{a\,c}+\frac{b\,d\,x^7\,{\left(b\,x^3+a\right)}^{\frac{b\,c}{3\,a\,d-3\,b\,c}-1}}{a\,c}}{{\left(d\,x^3+c\right)}^{\frac{a\,d}{3\,a\,d-3\,b\,c}+1}}","Not used",1,"(x*(a + b*x^3)^((b*c)/(3*a*d - 3*b*c) - 1) + (x^4*(a + b*x^3)^((b*c)/(3*a*d - 3*b*c) - 1)*(a*d + b*c))/(a*c) + (b*d*x^7*(a + b*x^3)^((b*c)/(3*a*d - 3*b*c) - 1))/(a*c))/(c + d*x^3)^((a*d)/(3*a*d - 3*b*c) + 1)","B"
146,1,88,94,1.303492,"\text{Not used}","int((a + b*x^4)*(c + d*x^4)^4,x)","x^5\,\left(\frac{b\,c^4}{5}+\frac{4\,a\,d\,c^3}{5}\right)+x^{17}\,\left(\frac{a\,d^4}{17}+\frac{4\,b\,c\,d^3}{17}\right)+\frac{b\,d^4\,x^{21}}{21}+a\,c^4\,x+\frac{2\,c^2\,d\,x^9\,\left(3\,a\,d+2\,b\,c\right)}{9}+\frac{2\,c\,d^2\,x^{13}\,\left(2\,a\,d+3\,b\,c\right)}{13}","Not used",1,"x^5*((b*c^4)/5 + (4*a*c^3*d)/5) + x^17*((a*d^4)/17 + (4*b*c*d^3)/17) + (b*d^4*x^21)/21 + a*c^4*x + (2*c^2*d*x^9*(3*a*d + 2*b*c))/9 + (2*c*d^2*x^13*(2*a*d + 3*b*c))/13","B"
147,1,66,70,1.242011,"\text{Not used}","int((a + b*x^4)*(c + d*x^4)^3,x)","x^5\,\left(\frac{b\,c^3}{5}+\frac{3\,a\,d\,c^2}{5}\right)+x^{13}\,\left(\frac{a\,d^3}{13}+\frac{3\,b\,c\,d^2}{13}\right)+\frac{b\,d^3\,x^{17}}{17}+a\,c^3\,x+\frac{c\,d\,x^9\,\left(a\,d+b\,c\right)}{3}","Not used",1,"x^5*((b*c^3)/5 + (3*a*c^2*d)/5) + x^13*((a*d^3)/13 + (3*b*c*d^2)/13) + (b*d^3*x^17)/17 + a*c^3*x + (c*d*x^9*(a*d + b*c))/3","B"
148,1,48,50,0.048466,"\text{Not used}","int((a + b*x^4)*(c + d*x^4)^2,x)","x^5\,\left(\frac{b\,c^2}{5}+\frac{2\,a\,d\,c}{5}\right)+x^9\,\left(\frac{a\,d^2}{9}+\frac{2\,b\,c\,d}{9}\right)+\frac{b\,d^2\,x^{13}}{13}+a\,c^2\,x","Not used",1,"x^5*((b*c^2)/5 + (2*a*c*d)/5) + x^9*((a*d^2)/9 + (2*b*c*d)/9) + (b*d^2*x^13)/13 + a*c^2*x","B"
149,1,25,28,0.035696,"\text{Not used}","int((a + b*x^4)*(c + d*x^4),x)","\frac{b\,d\,x^9}{9}+\left(\frac{a\,d}{5}+\frac{b\,c}{5}\right)\,x^5+a\,c\,x","Not used",1,"x^5*((a*d)/5 + (b*c)/5) + a*c*x + (b*d*x^9)/9","B"
150,1,720,223,1.479511,"\text{Not used}","int((a + b*x^4)/(c + d*x^4),x)","\frac{b\,x}{d}-\frac{\mathrm{atan}\left(\frac{\frac{\left(x\,\left(4\,a^2\,d^3-8\,a\,b\,c\,d^2+4\,b^2\,c^2\,d\right)-\frac{\left(16\,b\,c^2\,d^2-16\,a\,c\,d^3\right)\,\left(a\,d-b\,c\right)}{4\,{\left(-c\right)}^{3/4}\,d^{5/4}}\right)\,\left(a\,d-b\,c\right)\,1{}\mathrm{i}}{4\,{\left(-c\right)}^{3/4}\,d^{5/4}}+\frac{\left(x\,\left(4\,a^2\,d^3-8\,a\,b\,c\,d^2+4\,b^2\,c^2\,d\right)+\frac{\left(16\,b\,c^2\,d^2-16\,a\,c\,d^3\right)\,\left(a\,d-b\,c\right)}{4\,{\left(-c\right)}^{3/4}\,d^{5/4}}\right)\,\left(a\,d-b\,c\right)\,1{}\mathrm{i}}{4\,{\left(-c\right)}^{3/4}\,d^{5/4}}}{\frac{\left(x\,\left(4\,a^2\,d^3-8\,a\,b\,c\,d^2+4\,b^2\,c^2\,d\right)-\frac{\left(16\,b\,c^2\,d^2-16\,a\,c\,d^3\right)\,\left(a\,d-b\,c\right)}{4\,{\left(-c\right)}^{3/4}\,d^{5/4}}\right)\,\left(a\,d-b\,c\right)}{4\,{\left(-c\right)}^{3/4}\,d^{5/4}}-\frac{\left(x\,\left(4\,a^2\,d^3-8\,a\,b\,c\,d^2+4\,b^2\,c^2\,d\right)+\frac{\left(16\,b\,c^2\,d^2-16\,a\,c\,d^3\right)\,\left(a\,d-b\,c\right)}{4\,{\left(-c\right)}^{3/4}\,d^{5/4}}\right)\,\left(a\,d-b\,c\right)}{4\,{\left(-c\right)}^{3/4}\,d^{5/4}}}\right)\,\left(a\,d-b\,c\right)\,1{}\mathrm{i}}{2\,{\left(-c\right)}^{3/4}\,d^{5/4}}-\frac{\mathrm{atan}\left(\frac{\frac{\left(x\,\left(4\,a^2\,d^3-8\,a\,b\,c\,d^2+4\,b^2\,c^2\,d\right)-\frac{\left(16\,b\,c^2\,d^2-16\,a\,c\,d^3\right)\,\left(a\,d-b\,c\right)\,1{}\mathrm{i}}{4\,{\left(-c\right)}^{3/4}\,d^{5/4}}\right)\,\left(a\,d-b\,c\right)}{4\,{\left(-c\right)}^{3/4}\,d^{5/4}}+\frac{\left(x\,\left(4\,a^2\,d^3-8\,a\,b\,c\,d^2+4\,b^2\,c^2\,d\right)+\frac{\left(16\,b\,c^2\,d^2-16\,a\,c\,d^3\right)\,\left(a\,d-b\,c\right)\,1{}\mathrm{i}}{4\,{\left(-c\right)}^{3/4}\,d^{5/4}}\right)\,\left(a\,d-b\,c\right)}{4\,{\left(-c\right)}^{3/4}\,d^{5/4}}}{\frac{\left(x\,\left(4\,a^2\,d^3-8\,a\,b\,c\,d^2+4\,b^2\,c^2\,d\right)-\frac{\left(16\,b\,c^2\,d^2-16\,a\,c\,d^3\right)\,\left(a\,d-b\,c\right)\,1{}\mathrm{i}}{4\,{\left(-c\right)}^{3/4}\,d^{5/4}}\right)\,\left(a\,d-b\,c\right)\,1{}\mathrm{i}}{4\,{\left(-c\right)}^{3/4}\,d^{5/4}}-\frac{\left(x\,\left(4\,a^2\,d^3-8\,a\,b\,c\,d^2+4\,b^2\,c^2\,d\right)+\frac{\left(16\,b\,c^2\,d^2-16\,a\,c\,d^3\right)\,\left(a\,d-b\,c\right)\,1{}\mathrm{i}}{4\,{\left(-c\right)}^{3/4}\,d^{5/4}}\right)\,\left(a\,d-b\,c\right)\,1{}\mathrm{i}}{4\,{\left(-c\right)}^{3/4}\,d^{5/4}}}\right)\,\left(a\,d-b\,c\right)}{2\,{\left(-c\right)}^{3/4}\,d^{5/4}}","Not used",1,"(b*x)/d - (atan((((x*(4*a^2*d^3 + 4*b^2*c^2*d - 8*a*b*c*d^2) - ((16*b*c^2*d^2 - 16*a*c*d^3)*(a*d - b*c))/(4*(-c)^(3/4)*d^(5/4)))*(a*d - b*c)*1i)/(4*(-c)^(3/4)*d^(5/4)) + ((x*(4*a^2*d^3 + 4*b^2*c^2*d - 8*a*b*c*d^2) + ((16*b*c^2*d^2 - 16*a*c*d^3)*(a*d - b*c))/(4*(-c)^(3/4)*d^(5/4)))*(a*d - b*c)*1i)/(4*(-c)^(3/4)*d^(5/4)))/(((x*(4*a^2*d^3 + 4*b^2*c^2*d - 8*a*b*c*d^2) - ((16*b*c^2*d^2 - 16*a*c*d^3)*(a*d - b*c))/(4*(-c)^(3/4)*d^(5/4)))*(a*d - b*c))/(4*(-c)^(3/4)*d^(5/4)) - ((x*(4*a^2*d^3 + 4*b^2*c^2*d - 8*a*b*c*d^2) + ((16*b*c^2*d^2 - 16*a*c*d^3)*(a*d - b*c))/(4*(-c)^(3/4)*d^(5/4)))*(a*d - b*c))/(4*(-c)^(3/4)*d^(5/4))))*(a*d - b*c)*1i)/(2*(-c)^(3/4)*d^(5/4)) - (atan((((x*(4*a^2*d^3 + 4*b^2*c^2*d - 8*a*b*c*d^2) - ((16*b*c^2*d^2 - 16*a*c*d^3)*(a*d - b*c)*1i)/(4*(-c)^(3/4)*d^(5/4)))*(a*d - b*c))/(4*(-c)^(3/4)*d^(5/4)) + ((x*(4*a^2*d^3 + 4*b^2*c^2*d - 8*a*b*c*d^2) + ((16*b*c^2*d^2 - 16*a*c*d^3)*(a*d - b*c)*1i)/(4*(-c)^(3/4)*d^(5/4)))*(a*d - b*c))/(4*(-c)^(3/4)*d^(5/4)))/(((x*(4*a^2*d^3 + 4*b^2*c^2*d - 8*a*b*c*d^2) - ((16*b*c^2*d^2 - 16*a*c*d^3)*(a*d - b*c)*1i)/(4*(-c)^(3/4)*d^(5/4)))*(a*d - b*c)*1i)/(4*(-c)^(3/4)*d^(5/4)) - ((x*(4*a^2*d^3 + 4*b^2*c^2*d - 8*a*b*c*d^2) + ((16*b*c^2*d^2 - 16*a*c*d^3)*(a*d - b*c)*1i)/(4*(-c)^(3/4)*d^(5/4)))*(a*d - b*c)*1i)/(4*(-c)^(3/4)*d^(5/4))))*(a*d - b*c))/(2*(-c)^(3/4)*d^(5/4))","B"
151,1,740,245,1.520458,"\text{Not used}","int((a + b*x^4)/(c + d*x^4)^2,x)","\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{x\,\left(9\,a^2\,d^3+6\,a\,b\,c\,d^2+b^2\,c^2\,d\right)}{4\,c^2}-\frac{\left(3\,a\,d+b\,c\right)\,\left(12\,a\,d^3+4\,b\,c\,d^2\right)\,1{}\mathrm{i}}{16\,{\left(-c\right)}^{7/4}\,d^{5/4}}\right)\,\left(3\,a\,d+b\,c\right)}{16\,{\left(-c\right)}^{7/4}\,d^{5/4}}+\frac{\left(\frac{x\,\left(9\,a^2\,d^3+6\,a\,b\,c\,d^2+b^2\,c^2\,d\right)}{4\,c^2}+\frac{\left(3\,a\,d+b\,c\right)\,\left(12\,a\,d^3+4\,b\,c\,d^2\right)\,1{}\mathrm{i}}{16\,{\left(-c\right)}^{7/4}\,d^{5/4}}\right)\,\left(3\,a\,d+b\,c\right)}{16\,{\left(-c\right)}^{7/4}\,d^{5/4}}}{\frac{\left(\frac{x\,\left(9\,a^2\,d^3+6\,a\,b\,c\,d^2+b^2\,c^2\,d\right)}{4\,c^2}-\frac{\left(3\,a\,d+b\,c\right)\,\left(12\,a\,d^3+4\,b\,c\,d^2\right)\,1{}\mathrm{i}}{16\,{\left(-c\right)}^{7/4}\,d^{5/4}}\right)\,\left(3\,a\,d+b\,c\right)\,1{}\mathrm{i}}{16\,{\left(-c\right)}^{7/4}\,d^{5/4}}-\frac{\left(\frac{x\,\left(9\,a^2\,d^3+6\,a\,b\,c\,d^2+b^2\,c^2\,d\right)}{4\,c^2}+\frac{\left(3\,a\,d+b\,c\right)\,\left(12\,a\,d^3+4\,b\,c\,d^2\right)\,1{}\mathrm{i}}{16\,{\left(-c\right)}^{7/4}\,d^{5/4}}\right)\,\left(3\,a\,d+b\,c\right)\,1{}\mathrm{i}}{16\,{\left(-c\right)}^{7/4}\,d^{5/4}}}\right)\,\left(3\,a\,d+b\,c\right)}{8\,{\left(-c\right)}^{7/4}\,d^{5/4}}+\frac{x\,\left(a\,d-b\,c\right)}{4\,c\,d\,\left(d\,x^4+c\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{x\,\left(9\,a^2\,d^3+6\,a\,b\,c\,d^2+b^2\,c^2\,d\right)}{4\,c^2}-\frac{\left(3\,a\,d+b\,c\right)\,\left(12\,a\,d^3+4\,b\,c\,d^2\right)}{16\,{\left(-c\right)}^{7/4}\,d^{5/4}}\right)\,\left(3\,a\,d+b\,c\right)\,1{}\mathrm{i}}{16\,{\left(-c\right)}^{7/4}\,d^{5/4}}+\frac{\left(\frac{x\,\left(9\,a^2\,d^3+6\,a\,b\,c\,d^2+b^2\,c^2\,d\right)}{4\,c^2}+\frac{\left(3\,a\,d+b\,c\right)\,\left(12\,a\,d^3+4\,b\,c\,d^2\right)}{16\,{\left(-c\right)}^{7/4}\,d^{5/4}}\right)\,\left(3\,a\,d+b\,c\right)\,1{}\mathrm{i}}{16\,{\left(-c\right)}^{7/4}\,d^{5/4}}}{\frac{\left(\frac{x\,\left(9\,a^2\,d^3+6\,a\,b\,c\,d^2+b^2\,c^2\,d\right)}{4\,c^2}-\frac{\left(3\,a\,d+b\,c\right)\,\left(12\,a\,d^3+4\,b\,c\,d^2\right)}{16\,{\left(-c\right)}^{7/4}\,d^{5/4}}\right)\,\left(3\,a\,d+b\,c\right)}{16\,{\left(-c\right)}^{7/4}\,d^{5/4}}-\frac{\left(\frac{x\,\left(9\,a^2\,d^3+6\,a\,b\,c\,d^2+b^2\,c^2\,d\right)}{4\,c^2}+\frac{\left(3\,a\,d+b\,c\right)\,\left(12\,a\,d^3+4\,b\,c\,d^2\right)}{16\,{\left(-c\right)}^{7/4}\,d^{5/4}}\right)\,\left(3\,a\,d+b\,c\right)}{16\,{\left(-c\right)}^{7/4}\,d^{5/4}}}\right)\,\left(3\,a\,d+b\,c\right)\,1{}\mathrm{i}}{8\,{\left(-c\right)}^{7/4}\,d^{5/4}}","Not used",1,"(atan(((((x*(9*a^2*d^3 + b^2*c^2*d + 6*a*b*c*d^2))/(4*c^2) - ((3*a*d + b*c)*(12*a*d^3 + 4*b*c*d^2))/(16*(-c)^(7/4)*d^(5/4)))*(3*a*d + b*c)*1i)/(16*(-c)^(7/4)*d^(5/4)) + (((x*(9*a^2*d^3 + b^2*c^2*d + 6*a*b*c*d^2))/(4*c^2) + ((3*a*d + b*c)*(12*a*d^3 + 4*b*c*d^2))/(16*(-c)^(7/4)*d^(5/4)))*(3*a*d + b*c)*1i)/(16*(-c)^(7/4)*d^(5/4)))/((((x*(9*a^2*d^3 + b^2*c^2*d + 6*a*b*c*d^2))/(4*c^2) - ((3*a*d + b*c)*(12*a*d^3 + 4*b*c*d^2))/(16*(-c)^(7/4)*d^(5/4)))*(3*a*d + b*c))/(16*(-c)^(7/4)*d^(5/4)) - (((x*(9*a^2*d^3 + b^2*c^2*d + 6*a*b*c*d^2))/(4*c^2) + ((3*a*d + b*c)*(12*a*d^3 + 4*b*c*d^2))/(16*(-c)^(7/4)*d^(5/4)))*(3*a*d + b*c))/(16*(-c)^(7/4)*d^(5/4))))*(3*a*d + b*c)*1i)/(8*(-c)^(7/4)*d^(5/4)) + (atan(((((x*(9*a^2*d^3 + b^2*c^2*d + 6*a*b*c*d^2))/(4*c^2) - ((3*a*d + b*c)*(12*a*d^3 + 4*b*c*d^2)*1i)/(16*(-c)^(7/4)*d^(5/4)))*(3*a*d + b*c))/(16*(-c)^(7/4)*d^(5/4)) + (((x*(9*a^2*d^3 + b^2*c^2*d + 6*a*b*c*d^2))/(4*c^2) + ((3*a*d + b*c)*(12*a*d^3 + 4*b*c*d^2)*1i)/(16*(-c)^(7/4)*d^(5/4)))*(3*a*d + b*c))/(16*(-c)^(7/4)*d^(5/4)))/((((x*(9*a^2*d^3 + b^2*c^2*d + 6*a*b*c*d^2))/(4*c^2) - ((3*a*d + b*c)*(12*a*d^3 + 4*b*c*d^2)*1i)/(16*(-c)^(7/4)*d^(5/4)))*(3*a*d + b*c)*1i)/(16*(-c)^(7/4)*d^(5/4)) - (((x*(9*a^2*d^3 + b^2*c^2*d + 6*a*b*c*d^2))/(4*c^2) + ((3*a*d + b*c)*(12*a*d^3 + 4*b*c*d^2)*1i)/(16*(-c)^(7/4)*d^(5/4)))*(3*a*d + b*c)*1i)/(16*(-c)^(7/4)*d^(5/4))))*(3*a*d + b*c))/(8*(-c)^(7/4)*d^(5/4)) + (x*(a*d - b*c))/(4*c*d*(c + d*x^4))","B"
152,1,762,273,1.581157,"\text{Not used}","int((a + b*x^4)/(c + d*x^4)^3,x)","\frac{\frac{x^5\,\left(7\,a\,d+b\,c\right)}{32\,c^2}+\frac{x\,\left(11\,a\,d-3\,b\,c\right)}{32\,c\,d}}{c^2+2\,c\,d\,x^4+d^2\,x^8}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{9\,x\,\left(49\,a^2\,d^3+14\,a\,b\,c\,d^2+b^2\,c^2\,d\right)}{256\,c^4}-\frac{9\,\left(7\,a\,d+b\,c\right)\,\left(7\,a\,d^3+b\,c\,d^2\right)}{256\,{\left(-c\right)}^{15/4}\,d^{5/4}}\right)\,\left(7\,a\,d+b\,c\right)\,3{}\mathrm{i}}{128\,{\left(-c\right)}^{11/4}\,d^{5/4}}+\frac{\left(\frac{9\,x\,\left(49\,a^2\,d^3+14\,a\,b\,c\,d^2+b^2\,c^2\,d\right)}{256\,c^4}+\frac{9\,\left(7\,a\,d+b\,c\right)\,\left(7\,a\,d^3+b\,c\,d^2\right)}{256\,{\left(-c\right)}^{15/4}\,d^{5/4}}\right)\,\left(7\,a\,d+b\,c\right)\,3{}\mathrm{i}}{128\,{\left(-c\right)}^{11/4}\,d^{5/4}}}{\frac{3\,\left(\frac{9\,x\,\left(49\,a^2\,d^3+14\,a\,b\,c\,d^2+b^2\,c^2\,d\right)}{256\,c^4}-\frac{9\,\left(7\,a\,d+b\,c\right)\,\left(7\,a\,d^3+b\,c\,d^2\right)}{256\,{\left(-c\right)}^{15/4}\,d^{5/4}}\right)\,\left(7\,a\,d+b\,c\right)}{128\,{\left(-c\right)}^{11/4}\,d^{5/4}}-\frac{3\,\left(\frac{9\,x\,\left(49\,a^2\,d^3+14\,a\,b\,c\,d^2+b^2\,c^2\,d\right)}{256\,c^4}+\frac{9\,\left(7\,a\,d+b\,c\right)\,\left(7\,a\,d^3+b\,c\,d^2\right)}{256\,{\left(-c\right)}^{15/4}\,d^{5/4}}\right)\,\left(7\,a\,d+b\,c\right)}{128\,{\left(-c\right)}^{11/4}\,d^{5/4}}}\right)\,\left(7\,a\,d+b\,c\right)\,3{}\mathrm{i}}{64\,{\left(-c\right)}^{11/4}\,d^{5/4}}-\frac{3\,\mathrm{atan}\left(\frac{\frac{3\,\left(\frac{9\,x\,\left(49\,a^2\,d^3+14\,a\,b\,c\,d^2+b^2\,c^2\,d\right)}{256\,c^4}-\frac{\left(7\,a\,d+b\,c\right)\,\left(7\,a\,d^3+b\,c\,d^2\right)\,9{}\mathrm{i}}{256\,{\left(-c\right)}^{15/4}\,d^{5/4}}\right)\,\left(7\,a\,d+b\,c\right)}{128\,{\left(-c\right)}^{11/4}\,d^{5/4}}+\frac{3\,\left(\frac{9\,x\,\left(49\,a^2\,d^3+14\,a\,b\,c\,d^2+b^2\,c^2\,d\right)}{256\,c^4}+\frac{\left(7\,a\,d+b\,c\right)\,\left(7\,a\,d^3+b\,c\,d^2\right)\,9{}\mathrm{i}}{256\,{\left(-c\right)}^{15/4}\,d^{5/4}}\right)\,\left(7\,a\,d+b\,c\right)}{128\,{\left(-c\right)}^{11/4}\,d^{5/4}}}{\frac{\left(\frac{9\,x\,\left(49\,a^2\,d^3+14\,a\,b\,c\,d^2+b^2\,c^2\,d\right)}{256\,c^4}-\frac{\left(7\,a\,d+b\,c\right)\,\left(7\,a\,d^3+b\,c\,d^2\right)\,9{}\mathrm{i}}{256\,{\left(-c\right)}^{15/4}\,d^{5/4}}\right)\,\left(7\,a\,d+b\,c\right)\,3{}\mathrm{i}}{128\,{\left(-c\right)}^{11/4}\,d^{5/4}}-\frac{\left(\frac{9\,x\,\left(49\,a^2\,d^3+14\,a\,b\,c\,d^2+b^2\,c^2\,d\right)}{256\,c^4}+\frac{\left(7\,a\,d+b\,c\right)\,\left(7\,a\,d^3+b\,c\,d^2\right)\,9{}\mathrm{i}}{256\,{\left(-c\right)}^{15/4}\,d^{5/4}}\right)\,\left(7\,a\,d+b\,c\right)\,3{}\mathrm{i}}{128\,{\left(-c\right)}^{11/4}\,d^{5/4}}}\right)\,\left(7\,a\,d+b\,c\right)}{64\,{\left(-c\right)}^{11/4}\,d^{5/4}}","Not used",1,"((x^5*(7*a*d + b*c))/(32*c^2) + (x*(11*a*d - 3*b*c))/(32*c*d))/(c^2 + d^2*x^8 + 2*c*d*x^4) - (atan(((((9*x*(49*a^2*d^3 + b^2*c^2*d + 14*a*b*c*d^2))/(256*c^4) - (9*(7*a*d + b*c)*(7*a*d^3 + b*c*d^2))/(256*(-c)^(15/4)*d^(5/4)))*(7*a*d + b*c)*3i)/(128*(-c)^(11/4)*d^(5/4)) + (((9*x*(49*a^2*d^3 + b^2*c^2*d + 14*a*b*c*d^2))/(256*c^4) + (9*(7*a*d + b*c)*(7*a*d^3 + b*c*d^2))/(256*(-c)^(15/4)*d^(5/4)))*(7*a*d + b*c)*3i)/(128*(-c)^(11/4)*d^(5/4)))/((3*((9*x*(49*a^2*d^3 + b^2*c^2*d + 14*a*b*c*d^2))/(256*c^4) - (9*(7*a*d + b*c)*(7*a*d^3 + b*c*d^2))/(256*(-c)^(15/4)*d^(5/4)))*(7*a*d + b*c))/(128*(-c)^(11/4)*d^(5/4)) - (3*((9*x*(49*a^2*d^3 + b^2*c^2*d + 14*a*b*c*d^2))/(256*c^4) + (9*(7*a*d + b*c)*(7*a*d^3 + b*c*d^2))/(256*(-c)^(15/4)*d^(5/4)))*(7*a*d + b*c))/(128*(-c)^(11/4)*d^(5/4))))*(7*a*d + b*c)*3i)/(64*(-c)^(11/4)*d^(5/4)) - (3*atan(((3*((9*x*(49*a^2*d^3 + b^2*c^2*d + 14*a*b*c*d^2))/(256*c^4) - ((7*a*d + b*c)*(7*a*d^3 + b*c*d^2)*9i)/(256*(-c)^(15/4)*d^(5/4)))*(7*a*d + b*c))/(128*(-c)^(11/4)*d^(5/4)) + (3*((9*x*(49*a^2*d^3 + b^2*c^2*d + 14*a*b*c*d^2))/(256*c^4) + ((7*a*d + b*c)*(7*a*d^3 + b*c*d^2)*9i)/(256*(-c)^(15/4)*d^(5/4)))*(7*a*d + b*c))/(128*(-c)^(11/4)*d^(5/4)))/((((9*x*(49*a^2*d^3 + b^2*c^2*d + 14*a*b*c*d^2))/(256*c^4) - ((7*a*d + b*c)*(7*a*d^3 + b*c*d^2)*9i)/(256*(-c)^(15/4)*d^(5/4)))*(7*a*d + b*c)*3i)/(128*(-c)^(11/4)*d^(5/4)) - (((9*x*(49*a^2*d^3 + b^2*c^2*d + 14*a*b*c*d^2))/(256*c^4) + ((7*a*d + b*c)*(7*a*d^3 + b*c*d^2)*9i)/(256*(-c)^(15/4)*d^(5/4)))*(7*a*d + b*c)*3i)/(128*(-c)^(11/4)*d^(5/4))))*(7*a*d + b*c))/(64*(-c)^(11/4)*d^(5/4))","B"
153,1,146,154,0.066891,"\text{Not used}","int((a + b*x^4)^2*(c + d*x^4)^4,x)","x^9\,\left(\frac{2\,a^2\,c^2\,d^2}{3}+\frac{8\,a\,b\,c^3\,d}{9}+\frac{b^2\,c^4}{9}\right)+x^{17}\,\left(\frac{a^2\,d^4}{17}+\frac{8\,a\,b\,c\,d^3}{17}+\frac{6\,b^2\,c^2\,d^2}{17}\right)+a^2\,c^4\,x+\frac{b^2\,d^4\,x^{25}}{25}+\frac{2\,a\,c^3\,x^5\,\left(2\,a\,d+b\,c\right)}{5}+\frac{2\,b\,d^3\,x^{21}\,\left(a\,d+2\,b\,c\right)}{21}+\frac{4\,c\,d\,x^{13}\,\left(a^2\,d^2+3\,a\,b\,c\,d+b^2\,c^2\right)}{13}","Not used",1,"x^9*((b^2*c^4)/9 + (2*a^2*c^2*d^2)/3 + (8*a*b*c^3*d)/9) + x^17*((a^2*d^4)/17 + (6*b^2*c^2*d^2)/17 + (8*a*b*c*d^3)/17) + a^2*c^4*x + (b^2*d^4*x^25)/25 + (2*a*c^3*x^5*(2*a*d + b*c))/5 + (2*b*d^3*x^21*(a*d + 2*b*c))/21 + (4*c*d*x^13*(a^2*d^2 + b^2*c^2 + 3*a*b*c*d))/13","B"
154,1,116,122,1.297175,"\text{Not used}","int((a + b*x^4)^2*(c + d*x^4)^3,x)","x^9\,\left(\frac{a^2\,c\,d^2}{3}+\frac{2\,a\,b\,c^2\,d}{3}+\frac{b^2\,c^3}{9}\right)+x^{13}\,\left(\frac{a^2\,d^3}{13}+\frac{6\,a\,b\,c\,d^2}{13}+\frac{3\,b^2\,c^2\,d}{13}\right)+a^2\,c^3\,x+\frac{b^2\,d^3\,x^{21}}{21}+\frac{a\,c^2\,x^5\,\left(3\,a\,d+2\,b\,c\right)}{5}+\frac{b\,d^2\,x^{17}\,\left(2\,a\,d+3\,b\,c\right)}{17}","Not used",1,"x^9*((b^2*c^3)/9 + (a^2*c*d^2)/3 + (2*a*b*c^2*d)/3) + x^13*((a^2*d^3)/13 + (3*b^2*c^2*d)/13 + (6*a*b*c*d^2)/13) + a^2*c^3*x + (b^2*d^3*x^21)/21 + (a*c^2*x^5*(3*a*d + 2*b*c))/5 + (b*d^2*x^17*(2*a*d + 3*b*c))/17","B"
155,1,75,82,0.046204,"\text{Not used}","int((a + b*x^4)^2*(c + d*x^4)^2,x)","x^9\,\left(\frac{a^2\,d^2}{9}+\frac{4\,a\,b\,c\,d}{9}+\frac{b^2\,c^2}{9}\right)+a^2\,c^2\,x+\frac{b^2\,d^2\,x^{17}}{17}+\frac{2\,a\,c\,x^5\,\left(a\,d+b\,c\right)}{5}+\frac{2\,b\,d\,x^{13}\,\left(a\,d+b\,c\right)}{13}","Not used",1,"x^9*((a^2*d^2)/9 + (b^2*c^2)/9 + (4*a*b*c*d)/9) + a^2*c^2*x + (b^2*d^2*x^17)/17 + (2*a*c*x^5*(a*d + b*c))/5 + (2*b*d*x^13*(a*d + b*c))/13","B"
156,1,48,50,0.044982,"\text{Not used}","int((a + b*x^4)^2*(c + d*x^4),x)","x^5\,\left(\frac{d\,a^2}{5}+\frac{2\,b\,c\,a}{5}\right)+x^9\,\left(\frac{c\,b^2}{9}+\frac{2\,a\,d\,b}{9}\right)+\frac{b^2\,d\,x^{13}}{13}+a^2\,c\,x","Not used",1,"x^5*((a^2*d)/5 + (2*a*b*c)/5) + x^9*((b^2*c)/9 + (2*a*b*d)/9) + (b^2*d*x^13)/13 + a^2*c*x","B"
157,1,1081,253,1.484553,"\text{Not used}","int((a + b*x^4)^2/(c + d*x^4),x)","\frac{b^2\,x^5}{5\,d}-x\,\left(\frac{b^2\,c}{d^2}-\frac{2\,a\,b}{d}\right)+\frac{\mathrm{atan}\left(\frac{\frac{{\left(a\,d-b\,c\right)}^2\,\left(\frac{x\,\left(a^4\,d^4-4\,a^3\,b\,c\,d^3+6\,a^2\,b^2\,c^2\,d^2-4\,a\,b^3\,c^3\,d+b^4\,c^4\right)}{d}-\frac{{\left(a\,d-b\,c\right)}^2\,\left(4\,a^2\,c\,d^3-8\,a\,b\,c^2\,d^2+4\,b^2\,c^3\,d\right)}{4\,{\left(-c\right)}^{3/4}\,d^{9/4}}\right)\,1{}\mathrm{i}}{{\left(-c\right)}^{3/4}\,d^{9/4}}+\frac{{\left(a\,d-b\,c\right)}^2\,\left(\frac{x\,\left(a^4\,d^4-4\,a^3\,b\,c\,d^3+6\,a^2\,b^2\,c^2\,d^2-4\,a\,b^3\,c^3\,d+b^4\,c^4\right)}{d}+\frac{{\left(a\,d-b\,c\right)}^2\,\left(4\,a^2\,c\,d^3-8\,a\,b\,c^2\,d^2+4\,b^2\,c^3\,d\right)}{4\,{\left(-c\right)}^{3/4}\,d^{9/4}}\right)\,1{}\mathrm{i}}{{\left(-c\right)}^{3/4}\,d^{9/4}}}{\frac{{\left(a\,d-b\,c\right)}^2\,\left(\frac{x\,\left(a^4\,d^4-4\,a^3\,b\,c\,d^3+6\,a^2\,b^2\,c^2\,d^2-4\,a\,b^3\,c^3\,d+b^4\,c^4\right)}{d}-\frac{{\left(a\,d-b\,c\right)}^2\,\left(4\,a^2\,c\,d^3-8\,a\,b\,c^2\,d^2+4\,b^2\,c^3\,d\right)}{4\,{\left(-c\right)}^{3/4}\,d^{9/4}}\right)}{{\left(-c\right)}^{3/4}\,d^{9/4}}-\frac{{\left(a\,d-b\,c\right)}^2\,\left(\frac{x\,\left(a^4\,d^4-4\,a^3\,b\,c\,d^3+6\,a^2\,b^2\,c^2\,d^2-4\,a\,b^3\,c^3\,d+b^4\,c^4\right)}{d}+\frac{{\left(a\,d-b\,c\right)}^2\,\left(4\,a^2\,c\,d^3-8\,a\,b\,c^2\,d^2+4\,b^2\,c^3\,d\right)}{4\,{\left(-c\right)}^{3/4}\,d^{9/4}}\right)}{{\left(-c\right)}^{3/4}\,d^{9/4}}}\right)\,{\left(a\,d-b\,c\right)}^2\,1{}\mathrm{i}}{2\,{\left(-c\right)}^{3/4}\,d^{9/4}}+\frac{\mathrm{atan}\left(\frac{\frac{{\left(a\,d-b\,c\right)}^2\,\left(\frac{x\,\left(a^4\,d^4-4\,a^3\,b\,c\,d^3+6\,a^2\,b^2\,c^2\,d^2-4\,a\,b^3\,c^3\,d+b^4\,c^4\right)}{d}-\frac{{\left(a\,d-b\,c\right)}^2\,\left(4\,a^2\,c\,d^3-8\,a\,b\,c^2\,d^2+4\,b^2\,c^3\,d\right)\,1{}\mathrm{i}}{4\,{\left(-c\right)}^{3/4}\,d^{9/4}}\right)}{{\left(-c\right)}^{3/4}\,d^{9/4}}+\frac{{\left(a\,d-b\,c\right)}^2\,\left(\frac{x\,\left(a^4\,d^4-4\,a^3\,b\,c\,d^3+6\,a^2\,b^2\,c^2\,d^2-4\,a\,b^3\,c^3\,d+b^4\,c^4\right)}{d}+\frac{{\left(a\,d-b\,c\right)}^2\,\left(4\,a^2\,c\,d^3-8\,a\,b\,c^2\,d^2+4\,b^2\,c^3\,d\right)\,1{}\mathrm{i}}{4\,{\left(-c\right)}^{3/4}\,d^{9/4}}\right)}{{\left(-c\right)}^{3/4}\,d^{9/4}}}{\frac{{\left(a\,d-b\,c\right)}^2\,\left(\frac{x\,\left(a^4\,d^4-4\,a^3\,b\,c\,d^3+6\,a^2\,b^2\,c^2\,d^2-4\,a\,b^3\,c^3\,d+b^4\,c^4\right)}{d}-\frac{{\left(a\,d-b\,c\right)}^2\,\left(4\,a^2\,c\,d^3-8\,a\,b\,c^2\,d^2+4\,b^2\,c^3\,d\right)\,1{}\mathrm{i}}{4\,{\left(-c\right)}^{3/4}\,d^{9/4}}\right)\,1{}\mathrm{i}}{{\left(-c\right)}^{3/4}\,d^{9/4}}-\frac{{\left(a\,d-b\,c\right)}^2\,\left(\frac{x\,\left(a^4\,d^4-4\,a^3\,b\,c\,d^3+6\,a^2\,b^2\,c^2\,d^2-4\,a\,b^3\,c^3\,d+b^4\,c^4\right)}{d}+\frac{{\left(a\,d-b\,c\right)}^2\,\left(4\,a^2\,c\,d^3-8\,a\,b\,c^2\,d^2+4\,b^2\,c^3\,d\right)\,1{}\mathrm{i}}{4\,{\left(-c\right)}^{3/4}\,d^{9/4}}\right)\,1{}\mathrm{i}}{{\left(-c\right)}^{3/4}\,d^{9/4}}}\right)\,{\left(a\,d-b\,c\right)}^2}{2\,{\left(-c\right)}^{3/4}\,d^{9/4}}","Not used",1,"(b^2*x^5)/(5*d) - x*((b^2*c)/d^2 - (2*a*b)/d) + (atan((((a*d - b*c)^2*((x*(a^4*d^4 + b^4*c^4 + 6*a^2*b^2*c^2*d^2 - 4*a*b^3*c^3*d - 4*a^3*b*c*d^3))/d - ((a*d - b*c)^2*(4*a^2*c*d^3 + 4*b^2*c^3*d - 8*a*b*c^2*d^2))/(4*(-c)^(3/4)*d^(9/4)))*1i)/((-c)^(3/4)*d^(9/4)) + ((a*d - b*c)^2*((x*(a^4*d^4 + b^4*c^4 + 6*a^2*b^2*c^2*d^2 - 4*a*b^3*c^3*d - 4*a^3*b*c*d^3))/d + ((a*d - b*c)^2*(4*a^2*c*d^3 + 4*b^2*c^3*d - 8*a*b*c^2*d^2))/(4*(-c)^(3/4)*d^(9/4)))*1i)/((-c)^(3/4)*d^(9/4)))/(((a*d - b*c)^2*((x*(a^4*d^4 + b^4*c^4 + 6*a^2*b^2*c^2*d^2 - 4*a*b^3*c^3*d - 4*a^3*b*c*d^3))/d - ((a*d - b*c)^2*(4*a^2*c*d^3 + 4*b^2*c^3*d - 8*a*b*c^2*d^2))/(4*(-c)^(3/4)*d^(9/4))))/((-c)^(3/4)*d^(9/4)) - ((a*d - b*c)^2*((x*(a^4*d^4 + b^4*c^4 + 6*a^2*b^2*c^2*d^2 - 4*a*b^3*c^3*d - 4*a^3*b*c*d^3))/d + ((a*d - b*c)^2*(4*a^2*c*d^3 + 4*b^2*c^3*d - 8*a*b*c^2*d^2))/(4*(-c)^(3/4)*d^(9/4))))/((-c)^(3/4)*d^(9/4))))*(a*d - b*c)^2*1i)/(2*(-c)^(3/4)*d^(9/4)) + (atan((((a*d - b*c)^2*((x*(a^4*d^4 + b^4*c^4 + 6*a^2*b^2*c^2*d^2 - 4*a*b^3*c^3*d - 4*a^3*b*c*d^3))/d - ((a*d - b*c)^2*(4*a^2*c*d^3 + 4*b^2*c^3*d - 8*a*b*c^2*d^2)*1i)/(4*(-c)^(3/4)*d^(9/4))))/((-c)^(3/4)*d^(9/4)) + ((a*d - b*c)^2*((x*(a^4*d^4 + b^4*c^4 + 6*a^2*b^2*c^2*d^2 - 4*a*b^3*c^3*d - 4*a^3*b*c*d^3))/d + ((a*d - b*c)^2*(4*a^2*c*d^3 + 4*b^2*c^3*d - 8*a*b*c^2*d^2)*1i)/(4*(-c)^(3/4)*d^(9/4))))/((-c)^(3/4)*d^(9/4)))/(((a*d - b*c)^2*((x*(a^4*d^4 + b^4*c^4 + 6*a^2*b^2*c^2*d^2 - 4*a*b^3*c^3*d - 4*a^3*b*c*d^3))/d - ((a*d - b*c)^2*(4*a^2*c*d^3 + 4*b^2*c^3*d - 8*a*b*c^2*d^2)*1i)/(4*(-c)^(3/4)*d^(9/4)))*1i)/((-c)^(3/4)*d^(9/4)) - ((a*d - b*c)^2*((x*(a^4*d^4 + b^4*c^4 + 6*a^2*b^2*c^2*d^2 - 4*a*b^3*c^3*d - 4*a^3*b*c*d^3))/d + ((a*d - b*c)^2*(4*a^2*c*d^3 + 4*b^2*c^3*d - 8*a*b*c^2*d^2)*1i)/(4*(-c)^(3/4)*d^(9/4)))*1i)/((-c)^(3/4)*d^(9/4))))*(a*d - b*c)^2)/(2*(-c)^(3/4)*d^(9/4))","B"
158,1,1254,291,1.536213,"\text{Not used}","int((a + b*x^4)^2/(c + d*x^4)^2,x)","\frac{b^2\,x}{d^2}+\frac{x\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}{4\,c\,\left(d^3\,x^4+c\,d^2\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{x\,\left(9\,a^4\,d^4+12\,a^3\,b\,c\,d^3-26\,a^2\,b^2\,c^2\,d^2-20\,a\,b^3\,c^3\,d+25\,b^4\,c^4\right)}{4\,c^2\,d}-\frac{\left(a\,d-b\,c\right)\,\left(3\,a\,d+5\,b\,c\right)\,\left(12\,a^2\,d^3+8\,a\,b\,c\,d^2-20\,b^2\,c^2\,d\right)}{16\,{\left(-c\right)}^{7/4}\,d^{9/4}}\right)\,\left(a\,d-b\,c\right)\,\left(3\,a\,d+5\,b\,c\right)\,1{}\mathrm{i}}{16\,{\left(-c\right)}^{7/4}\,d^{9/4}}+\frac{\left(\frac{x\,\left(9\,a^4\,d^4+12\,a^3\,b\,c\,d^3-26\,a^2\,b^2\,c^2\,d^2-20\,a\,b^3\,c^3\,d+25\,b^4\,c^4\right)}{4\,c^2\,d}+\frac{\left(a\,d-b\,c\right)\,\left(3\,a\,d+5\,b\,c\right)\,\left(12\,a^2\,d^3+8\,a\,b\,c\,d^2-20\,b^2\,c^2\,d\right)}{16\,{\left(-c\right)}^{7/4}\,d^{9/4}}\right)\,\left(a\,d-b\,c\right)\,\left(3\,a\,d+5\,b\,c\right)\,1{}\mathrm{i}}{16\,{\left(-c\right)}^{7/4}\,d^{9/4}}}{\frac{\left(\frac{x\,\left(9\,a^4\,d^4+12\,a^3\,b\,c\,d^3-26\,a^2\,b^2\,c^2\,d^2-20\,a\,b^3\,c^3\,d+25\,b^4\,c^4\right)}{4\,c^2\,d}-\frac{\left(a\,d-b\,c\right)\,\left(3\,a\,d+5\,b\,c\right)\,\left(12\,a^2\,d^3+8\,a\,b\,c\,d^2-20\,b^2\,c^2\,d\right)}{16\,{\left(-c\right)}^{7/4}\,d^{9/4}}\right)\,\left(a\,d-b\,c\right)\,\left(3\,a\,d+5\,b\,c\right)}{16\,{\left(-c\right)}^{7/4}\,d^{9/4}}-\frac{\left(\frac{x\,\left(9\,a^4\,d^4+12\,a^3\,b\,c\,d^3-26\,a^2\,b^2\,c^2\,d^2-20\,a\,b^3\,c^3\,d+25\,b^4\,c^4\right)}{4\,c^2\,d}+\frac{\left(a\,d-b\,c\right)\,\left(3\,a\,d+5\,b\,c\right)\,\left(12\,a^2\,d^3+8\,a\,b\,c\,d^2-20\,b^2\,c^2\,d\right)}{16\,{\left(-c\right)}^{7/4}\,d^{9/4}}\right)\,\left(a\,d-b\,c\right)\,\left(3\,a\,d+5\,b\,c\right)}{16\,{\left(-c\right)}^{7/4}\,d^{9/4}}}\right)\,\left(a\,d-b\,c\right)\,\left(3\,a\,d+5\,b\,c\right)\,1{}\mathrm{i}}{8\,{\left(-c\right)}^{7/4}\,d^{9/4}}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{x\,\left(9\,a^4\,d^4+12\,a^3\,b\,c\,d^3-26\,a^2\,b^2\,c^2\,d^2-20\,a\,b^3\,c^3\,d+25\,b^4\,c^4\right)}{4\,c^2\,d}-\frac{\left(a\,d-b\,c\right)\,\left(3\,a\,d+5\,b\,c\right)\,\left(12\,a^2\,d^3+8\,a\,b\,c\,d^2-20\,b^2\,c^2\,d\right)\,1{}\mathrm{i}}{16\,{\left(-c\right)}^{7/4}\,d^{9/4}}\right)\,\left(a\,d-b\,c\right)\,\left(3\,a\,d+5\,b\,c\right)}{16\,{\left(-c\right)}^{7/4}\,d^{9/4}}+\frac{\left(\frac{x\,\left(9\,a^4\,d^4+12\,a^3\,b\,c\,d^3-26\,a^2\,b^2\,c^2\,d^2-20\,a\,b^3\,c^3\,d+25\,b^4\,c^4\right)}{4\,c^2\,d}+\frac{\left(a\,d-b\,c\right)\,\left(3\,a\,d+5\,b\,c\right)\,\left(12\,a^2\,d^3+8\,a\,b\,c\,d^2-20\,b^2\,c^2\,d\right)\,1{}\mathrm{i}}{16\,{\left(-c\right)}^{7/4}\,d^{9/4}}\right)\,\left(a\,d-b\,c\right)\,\left(3\,a\,d+5\,b\,c\right)}{16\,{\left(-c\right)}^{7/4}\,d^{9/4}}}{\frac{\left(\frac{x\,\left(9\,a^4\,d^4+12\,a^3\,b\,c\,d^3-26\,a^2\,b^2\,c^2\,d^2-20\,a\,b^3\,c^3\,d+25\,b^4\,c^4\right)}{4\,c^2\,d}-\frac{\left(a\,d-b\,c\right)\,\left(3\,a\,d+5\,b\,c\right)\,\left(12\,a^2\,d^3+8\,a\,b\,c\,d^2-20\,b^2\,c^2\,d\right)\,1{}\mathrm{i}}{16\,{\left(-c\right)}^{7/4}\,d^{9/4}}\right)\,\left(a\,d-b\,c\right)\,\left(3\,a\,d+5\,b\,c\right)\,1{}\mathrm{i}}{16\,{\left(-c\right)}^{7/4}\,d^{9/4}}-\frac{\left(\frac{x\,\left(9\,a^4\,d^4+12\,a^3\,b\,c\,d^3-26\,a^2\,b^2\,c^2\,d^2-20\,a\,b^3\,c^3\,d+25\,b^4\,c^4\right)}{4\,c^2\,d}+\frac{\left(a\,d-b\,c\right)\,\left(3\,a\,d+5\,b\,c\right)\,\left(12\,a^2\,d^3+8\,a\,b\,c\,d^2-20\,b^2\,c^2\,d\right)\,1{}\mathrm{i}}{16\,{\left(-c\right)}^{7/4}\,d^{9/4}}\right)\,\left(a\,d-b\,c\right)\,\left(3\,a\,d+5\,b\,c\right)\,1{}\mathrm{i}}{16\,{\left(-c\right)}^{7/4}\,d^{9/4}}}\right)\,\left(a\,d-b\,c\right)\,\left(3\,a\,d+5\,b\,c\right)}{8\,{\left(-c\right)}^{7/4}\,d^{9/4}}","Not used",1,"(b^2*x)/d^2 + (x*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/(4*c*(c*d^2 + d^3*x^4)) + (atan(((((x*(9*a^4*d^4 + 25*b^4*c^4 - 26*a^2*b^2*c^2*d^2 - 20*a*b^3*c^3*d + 12*a^3*b*c*d^3))/(4*c^2*d) - ((a*d - b*c)*(3*a*d + 5*b*c)*(12*a^2*d^3 - 20*b^2*c^2*d + 8*a*b*c*d^2))/(16*(-c)^(7/4)*d^(9/4)))*(a*d - b*c)*(3*a*d + 5*b*c)*1i)/(16*(-c)^(7/4)*d^(9/4)) + (((x*(9*a^4*d^4 + 25*b^4*c^4 - 26*a^2*b^2*c^2*d^2 - 20*a*b^3*c^3*d + 12*a^3*b*c*d^3))/(4*c^2*d) + ((a*d - b*c)*(3*a*d + 5*b*c)*(12*a^2*d^3 - 20*b^2*c^2*d + 8*a*b*c*d^2))/(16*(-c)^(7/4)*d^(9/4)))*(a*d - b*c)*(3*a*d + 5*b*c)*1i)/(16*(-c)^(7/4)*d^(9/4)))/((((x*(9*a^4*d^4 + 25*b^4*c^4 - 26*a^2*b^2*c^2*d^2 - 20*a*b^3*c^3*d + 12*a^3*b*c*d^3))/(4*c^2*d) - ((a*d - b*c)*(3*a*d + 5*b*c)*(12*a^2*d^3 - 20*b^2*c^2*d + 8*a*b*c*d^2))/(16*(-c)^(7/4)*d^(9/4)))*(a*d - b*c)*(3*a*d + 5*b*c))/(16*(-c)^(7/4)*d^(9/4)) - (((x*(9*a^4*d^4 + 25*b^4*c^4 - 26*a^2*b^2*c^2*d^2 - 20*a*b^3*c^3*d + 12*a^3*b*c*d^3))/(4*c^2*d) + ((a*d - b*c)*(3*a*d + 5*b*c)*(12*a^2*d^3 - 20*b^2*c^2*d + 8*a*b*c*d^2))/(16*(-c)^(7/4)*d^(9/4)))*(a*d - b*c)*(3*a*d + 5*b*c))/(16*(-c)^(7/4)*d^(9/4))))*(a*d - b*c)*(3*a*d + 5*b*c)*1i)/(8*(-c)^(7/4)*d^(9/4)) + (atan(((((x*(9*a^4*d^4 + 25*b^4*c^4 - 26*a^2*b^2*c^2*d^2 - 20*a*b^3*c^3*d + 12*a^3*b*c*d^3))/(4*c^2*d) - ((a*d - b*c)*(3*a*d + 5*b*c)*(12*a^2*d^3 - 20*b^2*c^2*d + 8*a*b*c*d^2)*1i)/(16*(-c)^(7/4)*d^(9/4)))*(a*d - b*c)*(3*a*d + 5*b*c))/(16*(-c)^(7/4)*d^(9/4)) + (((x*(9*a^4*d^4 + 25*b^4*c^4 - 26*a^2*b^2*c^2*d^2 - 20*a*b^3*c^3*d + 12*a^3*b*c*d^3))/(4*c^2*d) + ((a*d - b*c)*(3*a*d + 5*b*c)*(12*a^2*d^3 - 20*b^2*c^2*d + 8*a*b*c*d^2)*1i)/(16*(-c)^(7/4)*d^(9/4)))*(a*d - b*c)*(3*a*d + 5*b*c))/(16*(-c)^(7/4)*d^(9/4)))/((((x*(9*a^4*d^4 + 25*b^4*c^4 - 26*a^2*b^2*c^2*d^2 - 20*a*b^3*c^3*d + 12*a^3*b*c*d^3))/(4*c^2*d) - ((a*d - b*c)*(3*a*d + 5*b*c)*(12*a^2*d^3 - 20*b^2*c^2*d + 8*a*b*c*d^2)*1i)/(16*(-c)^(7/4)*d^(9/4)))*(a*d - b*c)*(3*a*d + 5*b*c)*1i)/(16*(-c)^(7/4)*d^(9/4)) - (((x*(9*a^4*d^4 + 25*b^4*c^4 - 26*a^2*b^2*c^2*d^2 - 20*a*b^3*c^3*d + 12*a^3*b*c*d^3))/(4*c^2*d) + ((a*d - b*c)*(3*a*d + 5*b*c)*(12*a^2*d^3 - 20*b^2*c^2*d + 8*a*b*c*d^2)*1i)/(16*(-c)^(7/4)*d^(9/4)))*(a*d - b*c)*(3*a*d + 5*b*c)*1i)/(16*(-c)^(7/4)*d^(9/4))))*(a*d - b*c)*(3*a*d + 5*b*c))/(8*(-c)^(7/4)*d^(9/4))","B"
159,1,1401,349,1.660069,"\text{Not used}","int((a + b*x^4)^2/(c + d*x^4)^3,x)","-\frac{\frac{x\,\left(-11\,a^2\,d^2+6\,a\,b\,c\,d+5\,b^2\,c^2\right)}{32\,c\,d^2}-\frac{x^5\,\left(7\,a^2\,d^2+2\,a\,b\,c\,d-9\,b^2\,c^2\right)}{32\,c^2\,d}}{c^2+2\,c\,d\,x^4+d^2\,x^8}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\left(21\,a^2\,d^2+6\,a\,b\,c\,d+5\,b^2\,c^2\right)\,\left(21\,a^2\,d^3+6\,a\,b\,c\,d^2+5\,b^2\,c^2\,d\right)}{256\,{\left(-c\right)}^{15/4}\,d^{9/4}}-\frac{x\,\left(441\,a^4\,d^4+252\,a^3\,b\,c\,d^3+246\,a^2\,b^2\,c^2\,d^2+60\,a\,b^3\,c^3\,d+25\,b^4\,c^4\right)}{256\,c^4\,d}\right)\,\left(21\,a^2\,d^2+6\,a\,b\,c\,d+5\,b^2\,c^2\right)\,1{}\mathrm{i}}{128\,{\left(-c\right)}^{11/4}\,d^{9/4}}-\frac{\left(\frac{\left(21\,a^2\,d^2+6\,a\,b\,c\,d+5\,b^2\,c^2\right)\,\left(21\,a^2\,d^3+6\,a\,b\,c\,d^2+5\,b^2\,c^2\,d\right)}{256\,{\left(-c\right)}^{15/4}\,d^{9/4}}+\frac{x\,\left(441\,a^4\,d^4+252\,a^3\,b\,c\,d^3+246\,a^2\,b^2\,c^2\,d^2+60\,a\,b^3\,c^3\,d+25\,b^4\,c^4\right)}{256\,c^4\,d}\right)\,\left(21\,a^2\,d^2+6\,a\,b\,c\,d+5\,b^2\,c^2\right)\,1{}\mathrm{i}}{128\,{\left(-c\right)}^{11/4}\,d^{9/4}}}{\frac{\left(\frac{\left(21\,a^2\,d^2+6\,a\,b\,c\,d+5\,b^2\,c^2\right)\,\left(21\,a^2\,d^3+6\,a\,b\,c\,d^2+5\,b^2\,c^2\,d\right)}{256\,{\left(-c\right)}^{15/4}\,d^{9/4}}-\frac{x\,\left(441\,a^4\,d^4+252\,a^3\,b\,c\,d^3+246\,a^2\,b^2\,c^2\,d^2+60\,a\,b^3\,c^3\,d+25\,b^4\,c^4\right)}{256\,c^4\,d}\right)\,\left(21\,a^2\,d^2+6\,a\,b\,c\,d+5\,b^2\,c^2\right)}{128\,{\left(-c\right)}^{11/4}\,d^{9/4}}+\frac{\left(\frac{\left(21\,a^2\,d^2+6\,a\,b\,c\,d+5\,b^2\,c^2\right)\,\left(21\,a^2\,d^3+6\,a\,b\,c\,d^2+5\,b^2\,c^2\,d\right)}{256\,{\left(-c\right)}^{15/4}\,d^{9/4}}+\frac{x\,\left(441\,a^4\,d^4+252\,a^3\,b\,c\,d^3+246\,a^2\,b^2\,c^2\,d^2+60\,a\,b^3\,c^3\,d+25\,b^4\,c^4\right)}{256\,c^4\,d}\right)\,\left(21\,a^2\,d^2+6\,a\,b\,c\,d+5\,b^2\,c^2\right)}{128\,{\left(-c\right)}^{11/4}\,d^{9/4}}}\right)\,\left(21\,a^2\,d^2+6\,a\,b\,c\,d+5\,b^2\,c^2\right)\,1{}\mathrm{i}}{64\,{\left(-c\right)}^{11/4}\,d^{9/4}}-\frac{\mathrm{atan}\left(\frac{\frac{\left(-\frac{x\,\left(441\,a^4\,d^4+252\,a^3\,b\,c\,d^3+246\,a^2\,b^2\,c^2\,d^2+60\,a\,b^3\,c^3\,d+25\,b^4\,c^4\right)}{256\,c^4\,d}+\frac{\left(21\,a^2\,d^2+6\,a\,b\,c\,d+5\,b^2\,c^2\right)\,\left(21\,a^2\,d^3+6\,a\,b\,c\,d^2+5\,b^2\,c^2\,d\right)\,1{}\mathrm{i}}{256\,{\left(-c\right)}^{15/4}\,d^{9/4}}\right)\,\left(21\,a^2\,d^2+6\,a\,b\,c\,d+5\,b^2\,c^2\right)}{128\,{\left(-c\right)}^{11/4}\,d^{9/4}}-\frac{\left(\frac{x\,\left(441\,a^4\,d^4+252\,a^3\,b\,c\,d^3+246\,a^2\,b^2\,c^2\,d^2+60\,a\,b^3\,c^3\,d+25\,b^4\,c^4\right)}{256\,c^4\,d}+\frac{\left(21\,a^2\,d^2+6\,a\,b\,c\,d+5\,b^2\,c^2\right)\,\left(21\,a^2\,d^3+6\,a\,b\,c\,d^2+5\,b^2\,c^2\,d\right)\,1{}\mathrm{i}}{256\,{\left(-c\right)}^{15/4}\,d^{9/4}}\right)\,\left(21\,a^2\,d^2+6\,a\,b\,c\,d+5\,b^2\,c^2\right)}{128\,{\left(-c\right)}^{11/4}\,d^{9/4}}}{\frac{\left(-\frac{x\,\left(441\,a^4\,d^4+252\,a^3\,b\,c\,d^3+246\,a^2\,b^2\,c^2\,d^2+60\,a\,b^3\,c^3\,d+25\,b^4\,c^4\right)}{256\,c^4\,d}+\frac{\left(21\,a^2\,d^2+6\,a\,b\,c\,d+5\,b^2\,c^2\right)\,\left(21\,a^2\,d^3+6\,a\,b\,c\,d^2+5\,b^2\,c^2\,d\right)\,1{}\mathrm{i}}{256\,{\left(-c\right)}^{15/4}\,d^{9/4}}\right)\,\left(21\,a^2\,d^2+6\,a\,b\,c\,d+5\,b^2\,c^2\right)\,1{}\mathrm{i}}{128\,{\left(-c\right)}^{11/4}\,d^{9/4}}+\frac{\left(\frac{x\,\left(441\,a^4\,d^4+252\,a^3\,b\,c\,d^3+246\,a^2\,b^2\,c^2\,d^2+60\,a\,b^3\,c^3\,d+25\,b^4\,c^4\right)}{256\,c^4\,d}+\frac{\left(21\,a^2\,d^2+6\,a\,b\,c\,d+5\,b^2\,c^2\right)\,\left(21\,a^2\,d^3+6\,a\,b\,c\,d^2+5\,b^2\,c^2\,d\right)\,1{}\mathrm{i}}{256\,{\left(-c\right)}^{15/4}\,d^{9/4}}\right)\,\left(21\,a^2\,d^2+6\,a\,b\,c\,d+5\,b^2\,c^2\right)\,1{}\mathrm{i}}{128\,{\left(-c\right)}^{11/4}\,d^{9/4}}}\right)\,\left(21\,a^2\,d^2+6\,a\,b\,c\,d+5\,b^2\,c^2\right)}{64\,{\left(-c\right)}^{11/4}\,d^{9/4}}","Not used",1,"- ((x*(5*b^2*c^2 - 11*a^2*d^2 + 6*a*b*c*d))/(32*c*d^2) - (x^5*(7*a^2*d^2 - 9*b^2*c^2 + 2*a*b*c*d))/(32*c^2*d))/(c^2 + d^2*x^8 + 2*c*d*x^4) - (atan((((((21*a^2*d^2 + 5*b^2*c^2 + 6*a*b*c*d)*(21*a^2*d^3 + 5*b^2*c^2*d + 6*a*b*c*d^2))/(256*(-c)^(15/4)*d^(9/4)) - (x*(441*a^4*d^4 + 25*b^4*c^4 + 246*a^2*b^2*c^2*d^2 + 60*a*b^3*c^3*d + 252*a^3*b*c*d^3))/(256*c^4*d))*(21*a^2*d^2 + 5*b^2*c^2 + 6*a*b*c*d)*1i)/(128*(-c)^(11/4)*d^(9/4)) - ((((21*a^2*d^2 + 5*b^2*c^2 + 6*a*b*c*d)*(21*a^2*d^3 + 5*b^2*c^2*d + 6*a*b*c*d^2))/(256*(-c)^(15/4)*d^(9/4)) + (x*(441*a^4*d^4 + 25*b^4*c^4 + 246*a^2*b^2*c^2*d^2 + 60*a*b^3*c^3*d + 252*a^3*b*c*d^3))/(256*c^4*d))*(21*a^2*d^2 + 5*b^2*c^2 + 6*a*b*c*d)*1i)/(128*(-c)^(11/4)*d^(9/4)))/(((((21*a^2*d^2 + 5*b^2*c^2 + 6*a*b*c*d)*(21*a^2*d^3 + 5*b^2*c^2*d + 6*a*b*c*d^2))/(256*(-c)^(15/4)*d^(9/4)) - (x*(441*a^4*d^4 + 25*b^4*c^4 + 246*a^2*b^2*c^2*d^2 + 60*a*b^3*c^3*d + 252*a^3*b*c*d^3))/(256*c^4*d))*(21*a^2*d^2 + 5*b^2*c^2 + 6*a*b*c*d))/(128*(-c)^(11/4)*d^(9/4)) + ((((21*a^2*d^2 + 5*b^2*c^2 + 6*a*b*c*d)*(21*a^2*d^3 + 5*b^2*c^2*d + 6*a*b*c*d^2))/(256*(-c)^(15/4)*d^(9/4)) + (x*(441*a^4*d^4 + 25*b^4*c^4 + 246*a^2*b^2*c^2*d^2 + 60*a*b^3*c^3*d + 252*a^3*b*c*d^3))/(256*c^4*d))*(21*a^2*d^2 + 5*b^2*c^2 + 6*a*b*c*d))/(128*(-c)^(11/4)*d^(9/4))))*(21*a^2*d^2 + 5*b^2*c^2 + 6*a*b*c*d)*1i)/(64*(-c)^(11/4)*d^(9/4)) - (atan((((((21*a^2*d^2 + 5*b^2*c^2 + 6*a*b*c*d)*(21*a^2*d^3 + 5*b^2*c^2*d + 6*a*b*c*d^2)*1i)/(256*(-c)^(15/4)*d^(9/4)) - (x*(441*a^4*d^4 + 25*b^4*c^4 + 246*a^2*b^2*c^2*d^2 + 60*a*b^3*c^3*d + 252*a^3*b*c*d^3))/(256*c^4*d))*(21*a^2*d^2 + 5*b^2*c^2 + 6*a*b*c*d))/(128*(-c)^(11/4)*d^(9/4)) - ((((21*a^2*d^2 + 5*b^2*c^2 + 6*a*b*c*d)*(21*a^2*d^3 + 5*b^2*c^2*d + 6*a*b*c*d^2)*1i)/(256*(-c)^(15/4)*d^(9/4)) + (x*(441*a^4*d^4 + 25*b^4*c^4 + 246*a^2*b^2*c^2*d^2 + 60*a*b^3*c^3*d + 252*a^3*b*c*d^3))/(256*c^4*d))*(21*a^2*d^2 + 5*b^2*c^2 + 6*a*b*c*d))/(128*(-c)^(11/4)*d^(9/4)))/(((((21*a^2*d^2 + 5*b^2*c^2 + 6*a*b*c*d)*(21*a^2*d^3 + 5*b^2*c^2*d + 6*a*b*c*d^2)*1i)/(256*(-c)^(15/4)*d^(9/4)) - (x*(441*a^4*d^4 + 25*b^4*c^4 + 246*a^2*b^2*c^2*d^2 + 60*a*b^3*c^3*d + 252*a^3*b*c*d^3))/(256*c^4*d))*(21*a^2*d^2 + 5*b^2*c^2 + 6*a*b*c*d)*1i)/(128*(-c)^(11/4)*d^(9/4)) + ((((21*a^2*d^2 + 5*b^2*c^2 + 6*a*b*c*d)*(21*a^2*d^3 + 5*b^2*c^2*d + 6*a*b*c*d^2)*1i)/(256*(-c)^(15/4)*d^(9/4)) + (x*(441*a^4*d^4 + 25*b^4*c^4 + 246*a^2*b^2*c^2*d^2 + 60*a*b^3*c^3*d + 252*a^3*b*c*d^3))/(256*c^4*d))*(21*a^2*d^2 + 5*b^2*c^2 + 6*a*b*c*d)*1i)/(128*(-c)^(11/4)*d^(9/4))))*(21*a^2*d^2 + 5*b^2*c^2 + 6*a*b*c*d))/(64*(-c)^(11/4)*d^(9/4))","B"
160,1,1822,332,1.514910,"\text{Not used}","int((c + d*x^4)^4/(a + b*x^4),x)","x\,\left(\frac{4\,c^3\,d}{b}-\frac{a\,\left(\frac{a\,\left(\frac{a\,d^4}{b^2}-\frac{4\,c\,d^3}{b}\right)}{b}+\frac{6\,c^2\,d^2}{b}\right)}{b}\right)-x^9\,\left(\frac{a\,d^4}{9\,b^2}-\frac{4\,c\,d^3}{9\,b}\right)+x^5\,\left(\frac{a\,\left(\frac{a\,d^4}{b^2}-\frac{4\,c\,d^3}{b}\right)}{5\,b}+\frac{6\,c^2\,d^2}{5\,b}\right)+\frac{d^4\,x^{13}}{13\,b}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{4\,x\,\left(a^8\,d^8-8\,a^7\,b\,c\,d^7+28\,a^6\,b^2\,c^2\,d^6-56\,a^5\,b^3\,c^3\,d^5+70\,a^4\,b^4\,c^4\,d^4-56\,a^3\,b^5\,c^5\,d^3+28\,a^2\,b^6\,c^6\,d^2-8\,a\,b^7\,c^7\,d+b^8\,c^8\right)}{b^5}-\frac{4\,{\left(a\,d-b\,c\right)}^4\,\left(a^5\,d^4-4\,a^4\,b\,c\,d^3+6\,a^3\,b^2\,c^2\,d^2-4\,a^2\,b^3\,c^3\,d+a\,b^4\,c^4\right)}{{\left(-a\right)}^{3/4}\,b^{21/4}}\right)\,{\left(a\,d-b\,c\right)}^4\,1{}\mathrm{i}}{4\,{\left(-a\right)}^{3/4}\,b^{17/4}}+\frac{\left(\frac{4\,x\,\left(a^8\,d^8-8\,a^7\,b\,c\,d^7+28\,a^6\,b^2\,c^2\,d^6-56\,a^5\,b^3\,c^3\,d^5+70\,a^4\,b^4\,c^4\,d^4-56\,a^3\,b^5\,c^5\,d^3+28\,a^2\,b^6\,c^6\,d^2-8\,a\,b^7\,c^7\,d+b^8\,c^8\right)}{b^5}+\frac{4\,{\left(a\,d-b\,c\right)}^4\,\left(a^5\,d^4-4\,a^4\,b\,c\,d^3+6\,a^3\,b^2\,c^2\,d^2-4\,a^2\,b^3\,c^3\,d+a\,b^4\,c^4\right)}{{\left(-a\right)}^{3/4}\,b^{21/4}}\right)\,{\left(a\,d-b\,c\right)}^4\,1{}\mathrm{i}}{4\,{\left(-a\right)}^{3/4}\,b^{17/4}}}{\frac{\left(\frac{4\,x\,\left(a^8\,d^8-8\,a^7\,b\,c\,d^7+28\,a^6\,b^2\,c^2\,d^6-56\,a^5\,b^3\,c^3\,d^5+70\,a^4\,b^4\,c^4\,d^4-56\,a^3\,b^5\,c^5\,d^3+28\,a^2\,b^6\,c^6\,d^2-8\,a\,b^7\,c^7\,d+b^8\,c^8\right)}{b^5}-\frac{4\,{\left(a\,d-b\,c\right)}^4\,\left(a^5\,d^4-4\,a^4\,b\,c\,d^3+6\,a^3\,b^2\,c^2\,d^2-4\,a^2\,b^3\,c^3\,d+a\,b^4\,c^4\right)}{{\left(-a\right)}^{3/4}\,b^{21/4}}\right)\,{\left(a\,d-b\,c\right)}^4}{4\,{\left(-a\right)}^{3/4}\,b^{17/4}}-\frac{\left(\frac{4\,x\,\left(a^8\,d^8-8\,a^7\,b\,c\,d^7+28\,a^6\,b^2\,c^2\,d^6-56\,a^5\,b^3\,c^3\,d^5+70\,a^4\,b^4\,c^4\,d^4-56\,a^3\,b^5\,c^5\,d^3+28\,a^2\,b^6\,c^6\,d^2-8\,a\,b^7\,c^7\,d+b^8\,c^8\right)}{b^5}+\frac{4\,{\left(a\,d-b\,c\right)}^4\,\left(a^5\,d^4-4\,a^4\,b\,c\,d^3+6\,a^3\,b^2\,c^2\,d^2-4\,a^2\,b^3\,c^3\,d+a\,b^4\,c^4\right)}{{\left(-a\right)}^{3/4}\,b^{21/4}}\right)\,{\left(a\,d-b\,c\right)}^4}{4\,{\left(-a\right)}^{3/4}\,b^{17/4}}}\right)\,{\left(a\,d-b\,c\right)}^4\,1{}\mathrm{i}}{2\,{\left(-a\right)}^{3/4}\,b^{17/4}}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{4\,x\,\left(a^8\,d^8-8\,a^7\,b\,c\,d^7+28\,a^6\,b^2\,c^2\,d^6-56\,a^5\,b^3\,c^3\,d^5+70\,a^4\,b^4\,c^4\,d^4-56\,a^3\,b^5\,c^5\,d^3+28\,a^2\,b^6\,c^6\,d^2-8\,a\,b^7\,c^7\,d+b^8\,c^8\right)}{b^5}-\frac{{\left(a\,d-b\,c\right)}^4\,\left(a^5\,d^4-4\,a^4\,b\,c\,d^3+6\,a^3\,b^2\,c^2\,d^2-4\,a^2\,b^3\,c^3\,d+a\,b^4\,c^4\right)\,4{}\mathrm{i}}{{\left(-a\right)}^{3/4}\,b^{21/4}}\right)\,{\left(a\,d-b\,c\right)}^4}{4\,{\left(-a\right)}^{3/4}\,b^{17/4}}+\frac{\left(\frac{4\,x\,\left(a^8\,d^8-8\,a^7\,b\,c\,d^7+28\,a^6\,b^2\,c^2\,d^6-56\,a^5\,b^3\,c^3\,d^5+70\,a^4\,b^4\,c^4\,d^4-56\,a^3\,b^5\,c^5\,d^3+28\,a^2\,b^6\,c^6\,d^2-8\,a\,b^7\,c^7\,d+b^8\,c^8\right)}{b^5}+\frac{{\left(a\,d-b\,c\right)}^4\,\left(a^5\,d^4-4\,a^4\,b\,c\,d^3+6\,a^3\,b^2\,c^2\,d^2-4\,a^2\,b^3\,c^3\,d+a\,b^4\,c^4\right)\,4{}\mathrm{i}}{{\left(-a\right)}^{3/4}\,b^{21/4}}\right)\,{\left(a\,d-b\,c\right)}^4}{4\,{\left(-a\right)}^{3/4}\,b^{17/4}}}{\frac{\left(\frac{4\,x\,\left(a^8\,d^8-8\,a^7\,b\,c\,d^7+28\,a^6\,b^2\,c^2\,d^6-56\,a^5\,b^3\,c^3\,d^5+70\,a^4\,b^4\,c^4\,d^4-56\,a^3\,b^5\,c^5\,d^3+28\,a^2\,b^6\,c^6\,d^2-8\,a\,b^7\,c^7\,d+b^8\,c^8\right)}{b^5}-\frac{{\left(a\,d-b\,c\right)}^4\,\left(a^5\,d^4-4\,a^4\,b\,c\,d^3+6\,a^3\,b^2\,c^2\,d^2-4\,a^2\,b^3\,c^3\,d+a\,b^4\,c^4\right)\,4{}\mathrm{i}}{{\left(-a\right)}^{3/4}\,b^{21/4}}\right)\,{\left(a\,d-b\,c\right)}^4\,1{}\mathrm{i}}{4\,{\left(-a\right)}^{3/4}\,b^{17/4}}-\frac{\left(\frac{4\,x\,\left(a^8\,d^8-8\,a^7\,b\,c\,d^7+28\,a^6\,b^2\,c^2\,d^6-56\,a^5\,b^3\,c^3\,d^5+70\,a^4\,b^4\,c^4\,d^4-56\,a^3\,b^5\,c^5\,d^3+28\,a^2\,b^6\,c^6\,d^2-8\,a\,b^7\,c^7\,d+b^8\,c^8\right)}{b^5}+\frac{{\left(a\,d-b\,c\right)}^4\,\left(a^5\,d^4-4\,a^4\,b\,c\,d^3+6\,a^3\,b^2\,c^2\,d^2-4\,a^2\,b^3\,c^3\,d+a\,b^4\,c^4\right)\,4{}\mathrm{i}}{{\left(-a\right)}^{3/4}\,b^{21/4}}\right)\,{\left(a\,d-b\,c\right)}^4\,1{}\mathrm{i}}{4\,{\left(-a\right)}^{3/4}\,b^{17/4}}}\right)\,{\left(a\,d-b\,c\right)}^4}{2\,{\left(-a\right)}^{3/4}\,b^{17/4}}","Not used",1,"x*((4*c^3*d)/b - (a*((a*((a*d^4)/b^2 - (4*c*d^3)/b))/b + (6*c^2*d^2)/b))/b) - x^9*((a*d^4)/(9*b^2) - (4*c*d^3)/(9*b)) + x^5*((a*((a*d^4)/b^2 - (4*c*d^3)/b))/(5*b) + (6*c^2*d^2)/(5*b)) + (d^4*x^13)/(13*b) + (atan(((((4*x*(a^8*d^8 + b^8*c^8 + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a*b^7*c^7*d - 8*a^7*b*c*d^7))/b^5 - (4*(a*d - b*c)^4*(a^5*d^4 + a*b^4*c^4 - 4*a^2*b^3*c^3*d + 6*a^3*b^2*c^2*d^2 - 4*a^4*b*c*d^3))/((-a)^(3/4)*b^(21/4)))*(a*d - b*c)^4*1i)/(4*(-a)^(3/4)*b^(17/4)) + (((4*x*(a^8*d^8 + b^8*c^8 + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a*b^7*c^7*d - 8*a^7*b*c*d^7))/b^5 + (4*(a*d - b*c)^4*(a^5*d^4 + a*b^4*c^4 - 4*a^2*b^3*c^3*d + 6*a^3*b^2*c^2*d^2 - 4*a^4*b*c*d^3))/((-a)^(3/4)*b^(21/4)))*(a*d - b*c)^4*1i)/(4*(-a)^(3/4)*b^(17/4)))/((((4*x*(a^8*d^8 + b^8*c^8 + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a*b^7*c^7*d - 8*a^7*b*c*d^7))/b^5 - (4*(a*d - b*c)^4*(a^5*d^4 + a*b^4*c^4 - 4*a^2*b^3*c^3*d + 6*a^3*b^2*c^2*d^2 - 4*a^4*b*c*d^3))/((-a)^(3/4)*b^(21/4)))*(a*d - b*c)^4)/(4*(-a)^(3/4)*b^(17/4)) - (((4*x*(a^8*d^8 + b^8*c^8 + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a*b^7*c^7*d - 8*a^7*b*c*d^7))/b^5 + (4*(a*d - b*c)^4*(a^5*d^4 + a*b^4*c^4 - 4*a^2*b^3*c^3*d + 6*a^3*b^2*c^2*d^2 - 4*a^4*b*c*d^3))/((-a)^(3/4)*b^(21/4)))*(a*d - b*c)^4)/(4*(-a)^(3/4)*b^(17/4))))*(a*d - b*c)^4*1i)/(2*(-a)^(3/4)*b^(17/4)) + (atan(((((4*x*(a^8*d^8 + b^8*c^8 + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a*b^7*c^7*d - 8*a^7*b*c*d^7))/b^5 - ((a*d - b*c)^4*(a^5*d^4 + a*b^4*c^4 - 4*a^2*b^3*c^3*d + 6*a^3*b^2*c^2*d^2 - 4*a^4*b*c*d^3)*4i)/((-a)^(3/4)*b^(21/4)))*(a*d - b*c)^4)/(4*(-a)^(3/4)*b^(17/4)) + (((4*x*(a^8*d^8 + b^8*c^8 + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a*b^7*c^7*d - 8*a^7*b*c*d^7))/b^5 + ((a*d - b*c)^4*(a^5*d^4 + a*b^4*c^4 - 4*a^2*b^3*c^3*d + 6*a^3*b^2*c^2*d^2 - 4*a^4*b*c*d^3)*4i)/((-a)^(3/4)*b^(21/4)))*(a*d - b*c)^4)/(4*(-a)^(3/4)*b^(17/4)))/((((4*x*(a^8*d^8 + b^8*c^8 + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a*b^7*c^7*d - 8*a^7*b*c*d^7))/b^5 - ((a*d - b*c)^4*(a^5*d^4 + a*b^4*c^4 - 4*a^2*b^3*c^3*d + 6*a^3*b^2*c^2*d^2 - 4*a^4*b*c*d^3)*4i)/((-a)^(3/4)*b^(21/4)))*(a*d - b*c)^4*1i)/(4*(-a)^(3/4)*b^(17/4)) - (((4*x*(a^8*d^8 + b^8*c^8 + 28*a^2*b^6*c^6*d^2 - 56*a^3*b^5*c^5*d^3 + 70*a^4*b^4*c^4*d^4 - 56*a^5*b^3*c^3*d^5 + 28*a^6*b^2*c^2*d^6 - 8*a*b^7*c^7*d - 8*a^7*b*c*d^7))/b^5 + ((a*d - b*c)^4*(a^5*d^4 + a*b^4*c^4 - 4*a^2*b^3*c^3*d + 6*a^3*b^2*c^2*d^2 - 4*a^4*b*c*d^3)*4i)/((-a)^(3/4)*b^(21/4)))*(a*d - b*c)^4*1i)/(4*(-a)^(3/4)*b^(17/4))))*(a*d - b*c)^4)/(2*(-a)^(3/4)*b^(17/4))","B"
161,1,1433,288,1.487785,"\text{Not used}","int((c + d*x^4)^3/(a + b*x^4),x)","x\,\left(\frac{3\,c^2\,d}{b}+\frac{a\,\left(\frac{a\,d^3}{b^2}-\frac{3\,c\,d^2}{b}\right)}{b}\right)-x^5\,\left(\frac{a\,d^3}{5\,b^2}-\frac{3\,c\,d^2}{5\,b}\right)+\frac{d^3\,x^9}{9\,b}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{x\,\left(a^6\,d^6-6\,a^5\,b\,c\,d^5+15\,a^4\,b^2\,c^2\,d^4-20\,a^3\,b^3\,c^3\,d^3+15\,a^2\,b^4\,c^4\,d^2-6\,a\,b^5\,c^5\,d+b^6\,c^6\right)}{b^3}-\frac{{\left(a\,d-b\,c\right)}^3\,\left(4\,a^4\,d^3-12\,a^3\,b\,c\,d^2+12\,a^2\,b^2\,c^2\,d-4\,a\,b^3\,c^3\right)}{4\,{\left(-a\right)}^{3/4}\,b^{13/4}}\right)\,{\left(a\,d-b\,c\right)}^3\,1{}\mathrm{i}}{{\left(-a\right)}^{3/4}\,b^{13/4}}+\frac{\left(\frac{x\,\left(a^6\,d^6-6\,a^5\,b\,c\,d^5+15\,a^4\,b^2\,c^2\,d^4-20\,a^3\,b^3\,c^3\,d^3+15\,a^2\,b^4\,c^4\,d^2-6\,a\,b^5\,c^5\,d+b^6\,c^6\right)}{b^3}+\frac{{\left(a\,d-b\,c\right)}^3\,\left(4\,a^4\,d^3-12\,a^3\,b\,c\,d^2+12\,a^2\,b^2\,c^2\,d-4\,a\,b^3\,c^3\right)}{4\,{\left(-a\right)}^{3/4}\,b^{13/4}}\right)\,{\left(a\,d-b\,c\right)}^3\,1{}\mathrm{i}}{{\left(-a\right)}^{3/4}\,b^{13/4}}}{\frac{\left(\frac{x\,\left(a^6\,d^6-6\,a^5\,b\,c\,d^5+15\,a^4\,b^2\,c^2\,d^4-20\,a^3\,b^3\,c^3\,d^3+15\,a^2\,b^4\,c^4\,d^2-6\,a\,b^5\,c^5\,d+b^6\,c^6\right)}{b^3}-\frac{{\left(a\,d-b\,c\right)}^3\,\left(4\,a^4\,d^3-12\,a^3\,b\,c\,d^2+12\,a^2\,b^2\,c^2\,d-4\,a\,b^3\,c^3\right)}{4\,{\left(-a\right)}^{3/4}\,b^{13/4}}\right)\,{\left(a\,d-b\,c\right)}^3}{{\left(-a\right)}^{3/4}\,b^{13/4}}-\frac{\left(\frac{x\,\left(a^6\,d^6-6\,a^5\,b\,c\,d^5+15\,a^4\,b^2\,c^2\,d^4-20\,a^3\,b^3\,c^3\,d^3+15\,a^2\,b^4\,c^4\,d^2-6\,a\,b^5\,c^5\,d+b^6\,c^6\right)}{b^3}+\frac{{\left(a\,d-b\,c\right)}^3\,\left(4\,a^4\,d^3-12\,a^3\,b\,c\,d^2+12\,a^2\,b^2\,c^2\,d-4\,a\,b^3\,c^3\right)}{4\,{\left(-a\right)}^{3/4}\,b^{13/4}}\right)\,{\left(a\,d-b\,c\right)}^3}{{\left(-a\right)}^{3/4}\,b^{13/4}}}\right)\,{\left(a\,d-b\,c\right)}^3\,1{}\mathrm{i}}{2\,{\left(-a\right)}^{3/4}\,b^{13/4}}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{x\,\left(a^6\,d^6-6\,a^5\,b\,c\,d^5+15\,a^4\,b^2\,c^2\,d^4-20\,a^3\,b^3\,c^3\,d^3+15\,a^2\,b^4\,c^4\,d^2-6\,a\,b^5\,c^5\,d+b^6\,c^6\right)}{b^3}-\frac{{\left(a\,d-b\,c\right)}^3\,\left(4\,a^4\,d^3-12\,a^3\,b\,c\,d^2+12\,a^2\,b^2\,c^2\,d-4\,a\,b^3\,c^3\right)\,1{}\mathrm{i}}{4\,{\left(-a\right)}^{3/4}\,b^{13/4}}\right)\,{\left(a\,d-b\,c\right)}^3}{{\left(-a\right)}^{3/4}\,b^{13/4}}+\frac{\left(\frac{x\,\left(a^6\,d^6-6\,a^5\,b\,c\,d^5+15\,a^4\,b^2\,c^2\,d^4-20\,a^3\,b^3\,c^3\,d^3+15\,a^2\,b^4\,c^4\,d^2-6\,a\,b^5\,c^5\,d+b^6\,c^6\right)}{b^3}+\frac{{\left(a\,d-b\,c\right)}^3\,\left(4\,a^4\,d^3-12\,a^3\,b\,c\,d^2+12\,a^2\,b^2\,c^2\,d-4\,a\,b^3\,c^3\right)\,1{}\mathrm{i}}{4\,{\left(-a\right)}^{3/4}\,b^{13/4}}\right)\,{\left(a\,d-b\,c\right)}^3}{{\left(-a\right)}^{3/4}\,b^{13/4}}}{\frac{\left(\frac{x\,\left(a^6\,d^6-6\,a^5\,b\,c\,d^5+15\,a^4\,b^2\,c^2\,d^4-20\,a^3\,b^3\,c^3\,d^3+15\,a^2\,b^4\,c^4\,d^2-6\,a\,b^5\,c^5\,d+b^6\,c^6\right)}{b^3}-\frac{{\left(a\,d-b\,c\right)}^3\,\left(4\,a^4\,d^3-12\,a^3\,b\,c\,d^2+12\,a^2\,b^2\,c^2\,d-4\,a\,b^3\,c^3\right)\,1{}\mathrm{i}}{4\,{\left(-a\right)}^{3/4}\,b^{13/4}}\right)\,{\left(a\,d-b\,c\right)}^3\,1{}\mathrm{i}}{{\left(-a\right)}^{3/4}\,b^{13/4}}-\frac{\left(\frac{x\,\left(a^6\,d^6-6\,a^5\,b\,c\,d^5+15\,a^4\,b^2\,c^2\,d^4-20\,a^3\,b^3\,c^3\,d^3+15\,a^2\,b^4\,c^4\,d^2-6\,a\,b^5\,c^5\,d+b^6\,c^6\right)}{b^3}+\frac{{\left(a\,d-b\,c\right)}^3\,\left(4\,a^4\,d^3-12\,a^3\,b\,c\,d^2+12\,a^2\,b^2\,c^2\,d-4\,a\,b^3\,c^3\right)\,1{}\mathrm{i}}{4\,{\left(-a\right)}^{3/4}\,b^{13/4}}\right)\,{\left(a\,d-b\,c\right)}^3\,1{}\mathrm{i}}{{\left(-a\right)}^{3/4}\,b^{13/4}}}\right)\,{\left(a\,d-b\,c\right)}^3}{2\,{\left(-a\right)}^{3/4}\,b^{13/4}}","Not used",1,"x*((3*c^2*d)/b + (a*((a*d^3)/b^2 - (3*c*d^2)/b))/b) - x^5*((a*d^3)/(5*b^2) - (3*c*d^2)/(5*b)) + (d^3*x^9)/(9*b) - (atan(((((x*(a^6*d^6 + b^6*c^6 + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a*b^5*c^5*d - 6*a^5*b*c*d^5))/b^3 - ((a*d - b*c)^3*(4*a^4*d^3 - 4*a*b^3*c^3 + 12*a^2*b^2*c^2*d - 12*a^3*b*c*d^2))/(4*(-a)^(3/4)*b^(13/4)))*(a*d - b*c)^3*1i)/((-a)^(3/4)*b^(13/4)) + (((x*(a^6*d^6 + b^6*c^6 + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a*b^5*c^5*d - 6*a^5*b*c*d^5))/b^3 + ((a*d - b*c)^3*(4*a^4*d^3 - 4*a*b^3*c^3 + 12*a^2*b^2*c^2*d - 12*a^3*b*c*d^2))/(4*(-a)^(3/4)*b^(13/4)))*(a*d - b*c)^3*1i)/((-a)^(3/4)*b^(13/4)))/((((x*(a^6*d^6 + b^6*c^6 + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a*b^5*c^5*d - 6*a^5*b*c*d^5))/b^3 - ((a*d - b*c)^3*(4*a^4*d^3 - 4*a*b^3*c^3 + 12*a^2*b^2*c^2*d - 12*a^3*b*c*d^2))/(4*(-a)^(3/4)*b^(13/4)))*(a*d - b*c)^3)/((-a)^(3/4)*b^(13/4)) - (((x*(a^6*d^6 + b^6*c^6 + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a*b^5*c^5*d - 6*a^5*b*c*d^5))/b^3 + ((a*d - b*c)^3*(4*a^4*d^3 - 4*a*b^3*c^3 + 12*a^2*b^2*c^2*d - 12*a^3*b*c*d^2))/(4*(-a)^(3/4)*b^(13/4)))*(a*d - b*c)^3)/((-a)^(3/4)*b^(13/4))))*(a*d - b*c)^3*1i)/(2*(-a)^(3/4)*b^(13/4)) - (atan(((((x*(a^6*d^6 + b^6*c^6 + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a*b^5*c^5*d - 6*a^5*b*c*d^5))/b^3 - ((a*d - b*c)^3*(4*a^4*d^3 - 4*a*b^3*c^3 + 12*a^2*b^2*c^2*d - 12*a^3*b*c*d^2)*1i)/(4*(-a)^(3/4)*b^(13/4)))*(a*d - b*c)^3)/((-a)^(3/4)*b^(13/4)) + (((x*(a^6*d^6 + b^6*c^6 + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a*b^5*c^5*d - 6*a^5*b*c*d^5))/b^3 + ((a*d - b*c)^3*(4*a^4*d^3 - 4*a*b^3*c^3 + 12*a^2*b^2*c^2*d - 12*a^3*b*c*d^2)*1i)/(4*(-a)^(3/4)*b^(13/4)))*(a*d - b*c)^3)/((-a)^(3/4)*b^(13/4)))/((((x*(a^6*d^6 + b^6*c^6 + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a*b^5*c^5*d - 6*a^5*b*c*d^5))/b^3 - ((a*d - b*c)^3*(4*a^4*d^3 - 4*a*b^3*c^3 + 12*a^2*b^2*c^2*d - 12*a^3*b*c*d^2)*1i)/(4*(-a)^(3/4)*b^(13/4)))*(a*d - b*c)^3*1i)/((-a)^(3/4)*b^(13/4)) - (((x*(a^6*d^6 + b^6*c^6 + 15*a^2*b^4*c^4*d^2 - 20*a^3*b^3*c^3*d^3 + 15*a^4*b^2*c^2*d^4 - 6*a*b^5*c^5*d - 6*a^5*b*c*d^5))/b^3 + ((a*d - b*c)^3*(4*a^4*d^3 - 4*a*b^3*c^3 + 12*a^2*b^2*c^2*d - 12*a^3*b*c*d^2)*1i)/(4*(-a)^(3/4)*b^(13/4)))*(a*d - b*c)^3*1i)/((-a)^(3/4)*b^(13/4))))*(a*d - b*c)^3)/(2*(-a)^(3/4)*b^(13/4))","B"
162,1,1081,253,1.466121,"\text{Not used}","int((c + d*x^4)^2/(a + b*x^4),x)","\frac{d^2\,x^5}{5\,b}-x\,\left(\frac{a\,d^2}{b^2}-\frac{2\,c\,d}{b}\right)+\frac{\mathrm{atan}\left(\frac{\frac{{\left(a\,d-b\,c\right)}^2\,\left(\frac{x\,\left(a^4\,d^4-4\,a^3\,b\,c\,d^3+6\,a^2\,b^2\,c^2\,d^2-4\,a\,b^3\,c^3\,d+b^4\,c^4\right)}{b}-\frac{{\left(a\,d-b\,c\right)}^2\,\left(4\,a^3\,b\,d^2-8\,a^2\,b^2\,c\,d+4\,a\,b^3\,c^2\right)}{4\,{\left(-a\right)}^{3/4}\,b^{9/4}}\right)\,1{}\mathrm{i}}{{\left(-a\right)}^{3/4}\,b^{9/4}}+\frac{{\left(a\,d-b\,c\right)}^2\,\left(\frac{x\,\left(a^4\,d^4-4\,a^3\,b\,c\,d^3+6\,a^2\,b^2\,c^2\,d^2-4\,a\,b^3\,c^3\,d+b^4\,c^4\right)}{b}+\frac{{\left(a\,d-b\,c\right)}^2\,\left(4\,a^3\,b\,d^2-8\,a^2\,b^2\,c\,d+4\,a\,b^3\,c^2\right)}{4\,{\left(-a\right)}^{3/4}\,b^{9/4}}\right)\,1{}\mathrm{i}}{{\left(-a\right)}^{3/4}\,b^{9/4}}}{\frac{{\left(a\,d-b\,c\right)}^2\,\left(\frac{x\,\left(a^4\,d^4-4\,a^3\,b\,c\,d^3+6\,a^2\,b^2\,c^2\,d^2-4\,a\,b^3\,c^3\,d+b^4\,c^4\right)}{b}-\frac{{\left(a\,d-b\,c\right)}^2\,\left(4\,a^3\,b\,d^2-8\,a^2\,b^2\,c\,d+4\,a\,b^3\,c^2\right)}{4\,{\left(-a\right)}^{3/4}\,b^{9/4}}\right)}{{\left(-a\right)}^{3/4}\,b^{9/4}}-\frac{{\left(a\,d-b\,c\right)}^2\,\left(\frac{x\,\left(a^4\,d^4-4\,a^3\,b\,c\,d^3+6\,a^2\,b^2\,c^2\,d^2-4\,a\,b^3\,c^3\,d+b^4\,c^4\right)}{b}+\frac{{\left(a\,d-b\,c\right)}^2\,\left(4\,a^3\,b\,d^2-8\,a^2\,b^2\,c\,d+4\,a\,b^3\,c^2\right)}{4\,{\left(-a\right)}^{3/4}\,b^{9/4}}\right)}{{\left(-a\right)}^{3/4}\,b^{9/4}}}\right)\,{\left(a\,d-b\,c\right)}^2\,1{}\mathrm{i}}{2\,{\left(-a\right)}^{3/4}\,b^{9/4}}+\frac{\mathrm{atan}\left(\frac{\frac{{\left(a\,d-b\,c\right)}^2\,\left(\frac{x\,\left(a^4\,d^4-4\,a^3\,b\,c\,d^3+6\,a^2\,b^2\,c^2\,d^2-4\,a\,b^3\,c^3\,d+b^4\,c^4\right)}{b}-\frac{{\left(a\,d-b\,c\right)}^2\,\left(4\,a^3\,b\,d^2-8\,a^2\,b^2\,c\,d+4\,a\,b^3\,c^2\right)\,1{}\mathrm{i}}{4\,{\left(-a\right)}^{3/4}\,b^{9/4}}\right)}{{\left(-a\right)}^{3/4}\,b^{9/4}}+\frac{{\left(a\,d-b\,c\right)}^2\,\left(\frac{x\,\left(a^4\,d^4-4\,a^3\,b\,c\,d^3+6\,a^2\,b^2\,c^2\,d^2-4\,a\,b^3\,c^3\,d+b^4\,c^4\right)}{b}+\frac{{\left(a\,d-b\,c\right)}^2\,\left(4\,a^3\,b\,d^2-8\,a^2\,b^2\,c\,d+4\,a\,b^3\,c^2\right)\,1{}\mathrm{i}}{4\,{\left(-a\right)}^{3/4}\,b^{9/4}}\right)}{{\left(-a\right)}^{3/4}\,b^{9/4}}}{\frac{{\left(a\,d-b\,c\right)}^2\,\left(\frac{x\,\left(a^4\,d^4-4\,a^3\,b\,c\,d^3+6\,a^2\,b^2\,c^2\,d^2-4\,a\,b^3\,c^3\,d+b^4\,c^4\right)}{b}-\frac{{\left(a\,d-b\,c\right)}^2\,\left(4\,a^3\,b\,d^2-8\,a^2\,b^2\,c\,d+4\,a\,b^3\,c^2\right)\,1{}\mathrm{i}}{4\,{\left(-a\right)}^{3/4}\,b^{9/4}}\right)\,1{}\mathrm{i}}{{\left(-a\right)}^{3/4}\,b^{9/4}}-\frac{{\left(a\,d-b\,c\right)}^2\,\left(\frac{x\,\left(a^4\,d^4-4\,a^3\,b\,c\,d^3+6\,a^2\,b^2\,c^2\,d^2-4\,a\,b^3\,c^3\,d+b^4\,c^4\right)}{b}+\frac{{\left(a\,d-b\,c\right)}^2\,\left(4\,a^3\,b\,d^2-8\,a^2\,b^2\,c\,d+4\,a\,b^3\,c^2\right)\,1{}\mathrm{i}}{4\,{\left(-a\right)}^{3/4}\,b^{9/4}}\right)\,1{}\mathrm{i}}{{\left(-a\right)}^{3/4}\,b^{9/4}}}\right)\,{\left(a\,d-b\,c\right)}^2}{2\,{\left(-a\right)}^{3/4}\,b^{9/4}}","Not used",1,"(d^2*x^5)/(5*b) - x*((a*d^2)/b^2 - (2*c*d)/b) + (atan((((a*d - b*c)^2*((x*(a^4*d^4 + b^4*c^4 + 6*a^2*b^2*c^2*d^2 - 4*a*b^3*c^3*d - 4*a^3*b*c*d^3))/b - ((a*d - b*c)^2*(4*a*b^3*c^2 + 4*a^3*b*d^2 - 8*a^2*b^2*c*d))/(4*(-a)^(3/4)*b^(9/4)))*1i)/((-a)^(3/4)*b^(9/4)) + ((a*d - b*c)^2*((x*(a^4*d^4 + b^4*c^4 + 6*a^2*b^2*c^2*d^2 - 4*a*b^3*c^3*d - 4*a^3*b*c*d^3))/b + ((a*d - b*c)^2*(4*a*b^3*c^2 + 4*a^3*b*d^2 - 8*a^2*b^2*c*d))/(4*(-a)^(3/4)*b^(9/4)))*1i)/((-a)^(3/4)*b^(9/4)))/(((a*d - b*c)^2*((x*(a^4*d^4 + b^4*c^4 + 6*a^2*b^2*c^2*d^2 - 4*a*b^3*c^3*d - 4*a^3*b*c*d^3))/b - ((a*d - b*c)^2*(4*a*b^3*c^2 + 4*a^3*b*d^2 - 8*a^2*b^2*c*d))/(4*(-a)^(3/4)*b^(9/4))))/((-a)^(3/4)*b^(9/4)) - ((a*d - b*c)^2*((x*(a^4*d^4 + b^4*c^4 + 6*a^2*b^2*c^2*d^2 - 4*a*b^3*c^3*d - 4*a^3*b*c*d^3))/b + ((a*d - b*c)^2*(4*a*b^3*c^2 + 4*a^3*b*d^2 - 8*a^2*b^2*c*d))/(4*(-a)^(3/4)*b^(9/4))))/((-a)^(3/4)*b^(9/4))))*(a*d - b*c)^2*1i)/(2*(-a)^(3/4)*b^(9/4)) + (atan((((a*d - b*c)^2*((x*(a^4*d^4 + b^4*c^4 + 6*a^2*b^2*c^2*d^2 - 4*a*b^3*c^3*d - 4*a^3*b*c*d^3))/b - ((a*d - b*c)^2*(4*a*b^3*c^2 + 4*a^3*b*d^2 - 8*a^2*b^2*c*d)*1i)/(4*(-a)^(3/4)*b^(9/4))))/((-a)^(3/4)*b^(9/4)) + ((a*d - b*c)^2*((x*(a^4*d^4 + b^4*c^4 + 6*a^2*b^2*c^2*d^2 - 4*a*b^3*c^3*d - 4*a^3*b*c*d^3))/b + ((a*d - b*c)^2*(4*a*b^3*c^2 + 4*a^3*b*d^2 - 8*a^2*b^2*c*d)*1i)/(4*(-a)^(3/4)*b^(9/4))))/((-a)^(3/4)*b^(9/4)))/(((a*d - b*c)^2*((x*(a^4*d^4 + b^4*c^4 + 6*a^2*b^2*c^2*d^2 - 4*a*b^3*c^3*d - 4*a^3*b*c*d^3))/b - ((a*d - b*c)^2*(4*a*b^3*c^2 + 4*a^3*b*d^2 - 8*a^2*b^2*c*d)*1i)/(4*(-a)^(3/4)*b^(9/4)))*1i)/((-a)^(3/4)*b^(9/4)) - ((a*d - b*c)^2*((x*(a^4*d^4 + b^4*c^4 + 6*a^2*b^2*c^2*d^2 - 4*a*b^3*c^3*d - 4*a^3*b*c*d^3))/b + ((a*d - b*c)^2*(4*a*b^3*c^2 + 4*a^3*b*d^2 - 8*a^2*b^2*c*d)*1i)/(4*(-a)^(3/4)*b^(9/4)))*1i)/((-a)^(3/4)*b^(9/4))))*(a*d - b*c)^2)/(2*(-a)^(3/4)*b^(9/4))","B"
163,1,720,223,0.220644,"\text{Not used}","int((c + d*x^4)/(a + b*x^4),x)","\frac{d\,x}{b}-\frac{\mathrm{atan}\left(\frac{\frac{\left(x\,\left(4\,a^2\,b\,d^2-8\,a\,b^2\,c\,d+4\,b^3\,c^2\right)-\frac{\left(16\,a^2\,b^2\,d-16\,a\,b^3\,c\right)\,\left(a\,d-b\,c\right)}{4\,{\left(-a\right)}^{3/4}\,b^{5/4}}\right)\,\left(a\,d-b\,c\right)\,1{}\mathrm{i}}{4\,{\left(-a\right)}^{3/4}\,b^{5/4}}+\frac{\left(x\,\left(4\,a^2\,b\,d^2-8\,a\,b^2\,c\,d+4\,b^3\,c^2\right)+\frac{\left(16\,a^2\,b^2\,d-16\,a\,b^3\,c\right)\,\left(a\,d-b\,c\right)}{4\,{\left(-a\right)}^{3/4}\,b^{5/4}}\right)\,\left(a\,d-b\,c\right)\,1{}\mathrm{i}}{4\,{\left(-a\right)}^{3/4}\,b^{5/4}}}{\frac{\left(x\,\left(4\,a^2\,b\,d^2-8\,a\,b^2\,c\,d+4\,b^3\,c^2\right)-\frac{\left(16\,a^2\,b^2\,d-16\,a\,b^3\,c\right)\,\left(a\,d-b\,c\right)}{4\,{\left(-a\right)}^{3/4}\,b^{5/4}}\right)\,\left(a\,d-b\,c\right)}{4\,{\left(-a\right)}^{3/4}\,b^{5/4}}-\frac{\left(x\,\left(4\,a^2\,b\,d^2-8\,a\,b^2\,c\,d+4\,b^3\,c^2\right)+\frac{\left(16\,a^2\,b^2\,d-16\,a\,b^3\,c\right)\,\left(a\,d-b\,c\right)}{4\,{\left(-a\right)}^{3/4}\,b^{5/4}}\right)\,\left(a\,d-b\,c\right)}{4\,{\left(-a\right)}^{3/4}\,b^{5/4}}}\right)\,\left(a\,d-b\,c\right)\,1{}\mathrm{i}}{2\,{\left(-a\right)}^{3/4}\,b^{5/4}}-\frac{\mathrm{atan}\left(\frac{\frac{\left(x\,\left(4\,a^2\,b\,d^2-8\,a\,b^2\,c\,d+4\,b^3\,c^2\right)-\frac{\left(16\,a^2\,b^2\,d-16\,a\,b^3\,c\right)\,\left(a\,d-b\,c\right)\,1{}\mathrm{i}}{4\,{\left(-a\right)}^{3/4}\,b^{5/4}}\right)\,\left(a\,d-b\,c\right)}{4\,{\left(-a\right)}^{3/4}\,b^{5/4}}+\frac{\left(x\,\left(4\,a^2\,b\,d^2-8\,a\,b^2\,c\,d+4\,b^3\,c^2\right)+\frac{\left(16\,a^2\,b^2\,d-16\,a\,b^3\,c\right)\,\left(a\,d-b\,c\right)\,1{}\mathrm{i}}{4\,{\left(-a\right)}^{3/4}\,b^{5/4}}\right)\,\left(a\,d-b\,c\right)}{4\,{\left(-a\right)}^{3/4}\,b^{5/4}}}{\frac{\left(x\,\left(4\,a^2\,b\,d^2-8\,a\,b^2\,c\,d+4\,b^3\,c^2\right)-\frac{\left(16\,a^2\,b^2\,d-16\,a\,b^3\,c\right)\,\left(a\,d-b\,c\right)\,1{}\mathrm{i}}{4\,{\left(-a\right)}^{3/4}\,b^{5/4}}\right)\,\left(a\,d-b\,c\right)\,1{}\mathrm{i}}{4\,{\left(-a\right)}^{3/4}\,b^{5/4}}-\frac{\left(x\,\left(4\,a^2\,b\,d^2-8\,a\,b^2\,c\,d+4\,b^3\,c^2\right)+\frac{\left(16\,a^2\,b^2\,d-16\,a\,b^3\,c\right)\,\left(a\,d-b\,c\right)\,1{}\mathrm{i}}{4\,{\left(-a\right)}^{3/4}\,b^{5/4}}\right)\,\left(a\,d-b\,c\right)\,1{}\mathrm{i}}{4\,{\left(-a\right)}^{3/4}\,b^{5/4}}}\right)\,\left(a\,d-b\,c\right)}{2\,{\left(-a\right)}^{3/4}\,b^{5/4}}","Not used",1,"(d*x)/b - (atan((((x*(4*b^3*c^2 + 4*a^2*b*d^2 - 8*a*b^2*c*d) - ((16*a^2*b^2*d - 16*a*b^3*c)*(a*d - b*c))/(4*(-a)^(3/4)*b^(5/4)))*(a*d - b*c)*1i)/(4*(-a)^(3/4)*b^(5/4)) + ((x*(4*b^3*c^2 + 4*a^2*b*d^2 - 8*a*b^2*c*d) + ((16*a^2*b^2*d - 16*a*b^3*c)*(a*d - b*c))/(4*(-a)^(3/4)*b^(5/4)))*(a*d - b*c)*1i)/(4*(-a)^(3/4)*b^(5/4)))/(((x*(4*b^3*c^2 + 4*a^2*b*d^2 - 8*a*b^2*c*d) - ((16*a^2*b^2*d - 16*a*b^3*c)*(a*d - b*c))/(4*(-a)^(3/4)*b^(5/4)))*(a*d - b*c))/(4*(-a)^(3/4)*b^(5/4)) - ((x*(4*b^3*c^2 + 4*a^2*b*d^2 - 8*a*b^2*c*d) + ((16*a^2*b^2*d - 16*a*b^3*c)*(a*d - b*c))/(4*(-a)^(3/4)*b^(5/4)))*(a*d - b*c))/(4*(-a)^(3/4)*b^(5/4))))*(a*d - b*c)*1i)/(2*(-a)^(3/4)*b^(5/4)) - (atan((((x*(4*b^3*c^2 + 4*a^2*b*d^2 - 8*a*b^2*c*d) - ((16*a^2*b^2*d - 16*a*b^3*c)*(a*d - b*c)*1i)/(4*(-a)^(3/4)*b^(5/4)))*(a*d - b*c))/(4*(-a)^(3/4)*b^(5/4)) + ((x*(4*b^3*c^2 + 4*a^2*b*d^2 - 8*a*b^2*c*d) + ((16*a^2*b^2*d - 16*a*b^3*c)*(a*d - b*c)*1i)/(4*(-a)^(3/4)*b^(5/4)))*(a*d - b*c))/(4*(-a)^(3/4)*b^(5/4)))/(((x*(4*b^3*c^2 + 4*a^2*b*d^2 - 8*a*b^2*c*d) - ((16*a^2*b^2*d - 16*a*b^3*c)*(a*d - b*c)*1i)/(4*(-a)^(3/4)*b^(5/4)))*(a*d - b*c)*1i)/(4*(-a)^(3/4)*b^(5/4)) - ((x*(4*b^3*c^2 + 4*a^2*b*d^2 - 8*a*b^2*c*d) + ((16*a^2*b^2*d - 16*a*b^3*c)*(a*d - b*c)*1i)/(4*(-a)^(3/4)*b^(5/4)))*(a*d - b*c)*1i)/(4*(-a)^(3/4)*b^(5/4))))*(a*d - b*c))/(2*(-a)^(3/4)*b^(5/4))","B"
164,1,6153,449,2.755465,"\text{Not used}","int(1/((a + b*x^4)*(c + d*x^4)),x)","-2\,\mathrm{atan}\left(\frac{b^3\,d^3\,x-\frac{128\,b^{10}\,c^7\,x}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}-\frac{128\,a^7\,b^3\,d^7\,x}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}-\frac{768\,a^2\,b^8\,c^5\,d^2\,x}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}+\frac{384\,a^3\,b^7\,c^4\,d^3\,x}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}+\frac{384\,a^4\,b^6\,c^3\,d^4\,x}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}-\frac{768\,a^5\,b^5\,c^2\,d^5\,x}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}+\frac{512\,a\,b^9\,c^6\,d\,x}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}+\frac{512\,a^6\,b^4\,c\,d^6\,x}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}}{{\left(-\frac{b^3}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}\right)}^{1/4}\,\left(\frac{b^3\,\left(512\,a^8\,c\,d^7-2560\,a^7\,b\,c^2\,d^6+4608\,a^6\,b^2\,c^3\,d^5-2560\,a^5\,b^3\,c^4\,d^4-2560\,a^4\,b^4\,c^5\,d^3+4608\,a^3\,b^5\,c^6\,d^2-2560\,a^2\,b^6\,c^7\,d+512\,a\,b^7\,c^8\right)}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}+2\,a^2\,b^2\,d^4+2\,b^4\,c^2\,d^2-4\,a\,b^3\,c\,d^3\right)}\right)\,{\left(-\frac{b^3}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}\right)}^{1/4}-2\,\mathrm{atan}\left(\frac{b^3\,d^3\,x-\frac{128\,a^7\,d^{10}\,x}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}-\frac{128\,b^7\,c^7\,d^3\,x}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}-\frac{768\,a^2\,b^5\,c^5\,d^5\,x}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}+\frac{384\,a^3\,b^4\,c^4\,d^6\,x}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}+\frac{384\,a^4\,b^3\,c^3\,d^7\,x}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}-\frac{768\,a^5\,b^2\,c^2\,d^8\,x}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}+\frac{512\,a^6\,b\,c\,d^9\,x}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}+\frac{512\,a\,b^6\,c^6\,d^4\,x}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}}{{\left(-\frac{d^3}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}\right)}^{1/4}\,\left(\frac{d^3\,\left(512\,a^8\,c\,d^7-2560\,a^7\,b\,c^2\,d^6+4608\,a^6\,b^2\,c^3\,d^5-2560\,a^5\,b^3\,c^4\,d^4-2560\,a^4\,b^4\,c^5\,d^3+4608\,a^3\,b^5\,c^6\,d^2-2560\,a^2\,b^6\,c^7\,d+512\,a\,b^7\,c^8\right)}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}+2\,a^2\,b^2\,d^4+2\,b^4\,c^2\,d^2-4\,a\,b^3\,c\,d^3\right)}\right)\,{\left(-\frac{d^3}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}\right)}^{1/4}-\mathrm{atan}\left(\frac{\left({\left(-\frac{d^3}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}\right)}^{1/4}\,\left({\left(-\frac{d^3}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}\right)}^{3/4}\,\left({\left(-\frac{d^3}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}\right)}^{1/4}\,\left(4096\,a^8\,b^4\,c\,d^{11}-20480\,a^7\,b^5\,c^2\,d^{10}+36864\,a^6\,b^6\,c^3\,d^9-20480\,a^5\,b^7\,c^4\,d^8-20480\,a^4\,b^8\,c^5\,d^7+36864\,a^3\,b^9\,c^6\,d^6-20480\,a^2\,b^{10}\,c^7\,d^5+4096\,a\,b^{11}\,c^8\,d^4\right)+x\,\left(1024\,a^7\,b^4\,d^{11}-4096\,a^6\,b^5\,c\,d^{10}+6144\,a^5\,b^6\,c^2\,d^9-3072\,a^4\,b^7\,c^3\,d^8-3072\,a^3\,b^8\,c^4\,d^7+6144\,a^2\,b^9\,c^5\,d^6-4096\,a\,b^{10}\,c^6\,d^5+1024\,b^{11}\,c^7\,d^4\right)\right)-16\,a^2\,b^6\,d^8-16\,b^8\,c^2\,d^6+32\,a\,b^7\,c\,d^7\right)+8\,b^7\,d^7\,x\right)\,{\left(-\frac{d^3}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}\right)}^{1/4}\,1{}\mathrm{i}-\left({\left(-\frac{d^3}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}\right)}^{1/4}\,\left({\left(-\frac{d^3}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}\right)}^{3/4}\,\left({\left(-\frac{d^3}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}\right)}^{1/4}\,\left(4096\,a^8\,b^4\,c\,d^{11}-20480\,a^7\,b^5\,c^2\,d^{10}+36864\,a^6\,b^6\,c^3\,d^9-20480\,a^5\,b^7\,c^4\,d^8-20480\,a^4\,b^8\,c^5\,d^7+36864\,a^3\,b^9\,c^6\,d^6-20480\,a^2\,b^{10}\,c^7\,d^5+4096\,a\,b^{11}\,c^8\,d^4\right)-x\,\left(1024\,a^7\,b^4\,d^{11}-4096\,a^6\,b^5\,c\,d^{10}+6144\,a^5\,b^6\,c^2\,d^9-3072\,a^4\,b^7\,c^3\,d^8-3072\,a^3\,b^8\,c^4\,d^7+6144\,a^2\,b^9\,c^5\,d^6-4096\,a\,b^{10}\,c^6\,d^5+1024\,b^{11}\,c^7\,d^4\right)\right)-16\,a^2\,b^6\,d^8-16\,b^8\,c^2\,d^6+32\,a\,b^7\,c\,d^7\right)-8\,b^7\,d^7\,x\right)\,{\left(-\frac{d^3}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}\right)}^{1/4}\,1{}\mathrm{i}}{\left({\left(-\frac{d^3}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}\right)}^{1/4}\,\left({\left(-\frac{d^3}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}\right)}^{3/4}\,\left({\left(-\frac{d^3}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}\right)}^{1/4}\,\left(4096\,a^8\,b^4\,c\,d^{11}-20480\,a^7\,b^5\,c^2\,d^{10}+36864\,a^6\,b^6\,c^3\,d^9-20480\,a^5\,b^7\,c^4\,d^8-20480\,a^4\,b^8\,c^5\,d^7+36864\,a^3\,b^9\,c^6\,d^6-20480\,a^2\,b^{10}\,c^7\,d^5+4096\,a\,b^{11}\,c^8\,d^4\right)+x\,\left(1024\,a^7\,b^4\,d^{11}-4096\,a^6\,b^5\,c\,d^{10}+6144\,a^5\,b^6\,c^2\,d^9-3072\,a^4\,b^7\,c^3\,d^8-3072\,a^3\,b^8\,c^4\,d^7+6144\,a^2\,b^9\,c^5\,d^6-4096\,a\,b^{10}\,c^6\,d^5+1024\,b^{11}\,c^7\,d^4\right)\right)-16\,a^2\,b^6\,d^8-16\,b^8\,c^2\,d^6+32\,a\,b^7\,c\,d^7\right)+8\,b^7\,d^7\,x\right)\,{\left(-\frac{d^3}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}\right)}^{1/4}+\left({\left(-\frac{d^3}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}\right)}^{1/4}\,\left({\left(-\frac{d^3}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}\right)}^{3/4}\,\left({\left(-\frac{d^3}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}\right)}^{1/4}\,\left(4096\,a^8\,b^4\,c\,d^{11}-20480\,a^7\,b^5\,c^2\,d^{10}+36864\,a^6\,b^6\,c^3\,d^9-20480\,a^5\,b^7\,c^4\,d^8-20480\,a^4\,b^8\,c^5\,d^7+36864\,a^3\,b^9\,c^6\,d^6-20480\,a^2\,b^{10}\,c^7\,d^5+4096\,a\,b^{11}\,c^8\,d^4\right)-x\,\left(1024\,a^7\,b^4\,d^{11}-4096\,a^6\,b^5\,c\,d^{10}+6144\,a^5\,b^6\,c^2\,d^9-3072\,a^4\,b^7\,c^3\,d^8-3072\,a^3\,b^8\,c^4\,d^7+6144\,a^2\,b^9\,c^5\,d^6-4096\,a\,b^{10}\,c^6\,d^5+1024\,b^{11}\,c^7\,d^4\right)\right)-16\,a^2\,b^6\,d^8-16\,b^8\,c^2\,d^6+32\,a\,b^7\,c\,d^7\right)-8\,b^7\,d^7\,x\right)\,{\left(-\frac{d^3}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}\right)}^{1/4}}\right)\,{\left(-\frac{d^3}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}\right)}^{1/4}\,2{}\mathrm{i}-\mathrm{atan}\left(\frac{\left({\left(-\frac{b^3}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}\right)}^{1/4}\,\left({\left(-\frac{b^3}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}\right)}^{3/4}\,\left({\left(-\frac{b^3}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}\right)}^{1/4}\,\left(4096\,a^8\,b^4\,c\,d^{11}-20480\,a^7\,b^5\,c^2\,d^{10}+36864\,a^6\,b^6\,c^3\,d^9-20480\,a^5\,b^7\,c^4\,d^8-20480\,a^4\,b^8\,c^5\,d^7+36864\,a^3\,b^9\,c^6\,d^6-20480\,a^2\,b^{10}\,c^7\,d^5+4096\,a\,b^{11}\,c^8\,d^4\right)+x\,\left(1024\,a^7\,b^4\,d^{11}-4096\,a^6\,b^5\,c\,d^{10}+6144\,a^5\,b^6\,c^2\,d^9-3072\,a^4\,b^7\,c^3\,d^8-3072\,a^3\,b^8\,c^4\,d^7+6144\,a^2\,b^9\,c^5\,d^6-4096\,a\,b^{10}\,c^6\,d^5+1024\,b^{11}\,c^7\,d^4\right)\right)-16\,a^2\,b^6\,d^8-16\,b^8\,c^2\,d^6+32\,a\,b^7\,c\,d^7\right)+8\,b^7\,d^7\,x\right)\,{\left(-\frac{b^3}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}\right)}^{1/4}\,1{}\mathrm{i}-\left({\left(-\frac{b^3}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}\right)}^{1/4}\,\left({\left(-\frac{b^3}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}\right)}^{3/4}\,\left({\left(-\frac{b^3}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}\right)}^{1/4}\,\left(4096\,a^8\,b^4\,c\,d^{11}-20480\,a^7\,b^5\,c^2\,d^{10}+36864\,a^6\,b^6\,c^3\,d^9-20480\,a^5\,b^7\,c^4\,d^8-20480\,a^4\,b^8\,c^5\,d^7+36864\,a^3\,b^9\,c^6\,d^6-20480\,a^2\,b^{10}\,c^7\,d^5+4096\,a\,b^{11}\,c^8\,d^4\right)-x\,\left(1024\,a^7\,b^4\,d^{11}-4096\,a^6\,b^5\,c\,d^{10}+6144\,a^5\,b^6\,c^2\,d^9-3072\,a^4\,b^7\,c^3\,d^8-3072\,a^3\,b^8\,c^4\,d^7+6144\,a^2\,b^9\,c^5\,d^6-4096\,a\,b^{10}\,c^6\,d^5+1024\,b^{11}\,c^7\,d^4\right)\right)-16\,a^2\,b^6\,d^8-16\,b^8\,c^2\,d^6+32\,a\,b^7\,c\,d^7\right)-8\,b^7\,d^7\,x\right)\,{\left(-\frac{b^3}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}\right)}^{1/4}\,1{}\mathrm{i}}{\left({\left(-\frac{b^3}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}\right)}^{1/4}\,\left({\left(-\frac{b^3}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}\right)}^{3/4}\,\left({\left(-\frac{b^3}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}\right)}^{1/4}\,\left(4096\,a^8\,b^4\,c\,d^{11}-20480\,a^7\,b^5\,c^2\,d^{10}+36864\,a^6\,b^6\,c^3\,d^9-20480\,a^5\,b^7\,c^4\,d^8-20480\,a^4\,b^8\,c^5\,d^7+36864\,a^3\,b^9\,c^6\,d^6-20480\,a^2\,b^{10}\,c^7\,d^5+4096\,a\,b^{11}\,c^8\,d^4\right)+x\,\left(1024\,a^7\,b^4\,d^{11}-4096\,a^6\,b^5\,c\,d^{10}+6144\,a^5\,b^6\,c^2\,d^9-3072\,a^4\,b^7\,c^3\,d^8-3072\,a^3\,b^8\,c^4\,d^7+6144\,a^2\,b^9\,c^5\,d^6-4096\,a\,b^{10}\,c^6\,d^5+1024\,b^{11}\,c^7\,d^4\right)\right)-16\,a^2\,b^6\,d^8-16\,b^8\,c^2\,d^6+32\,a\,b^7\,c\,d^7\right)+8\,b^7\,d^7\,x\right)\,{\left(-\frac{b^3}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}\right)}^{1/4}+\left({\left(-\frac{b^3}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}\right)}^{1/4}\,\left({\left(-\frac{b^3}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}\right)}^{3/4}\,\left({\left(-\frac{b^3}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}\right)}^{1/4}\,\left(4096\,a^8\,b^4\,c\,d^{11}-20480\,a^7\,b^5\,c^2\,d^{10}+36864\,a^6\,b^6\,c^3\,d^9-20480\,a^5\,b^7\,c^4\,d^8-20480\,a^4\,b^8\,c^5\,d^7+36864\,a^3\,b^9\,c^6\,d^6-20480\,a^2\,b^{10}\,c^7\,d^5+4096\,a\,b^{11}\,c^8\,d^4\right)-x\,\left(1024\,a^7\,b^4\,d^{11}-4096\,a^6\,b^5\,c\,d^{10}+6144\,a^5\,b^6\,c^2\,d^9-3072\,a^4\,b^7\,c^3\,d^8-3072\,a^3\,b^8\,c^4\,d^7+6144\,a^2\,b^9\,c^5\,d^6-4096\,a\,b^{10}\,c^6\,d^5+1024\,b^{11}\,c^7\,d^4\right)\right)-16\,a^2\,b^6\,d^8-16\,b^8\,c^2\,d^6+32\,a\,b^7\,c\,d^7\right)-8\,b^7\,d^7\,x\right)\,{\left(-\frac{b^3}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}\right)}^{1/4}}\right)\,{\left(-\frac{b^3}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}\right)}^{1/4}\,2{}\mathrm{i}","Not used",1,"- atan((((-d^3/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d))^(1/4)*((-d^3/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d))^(3/4)*((-d^3/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d))^(1/4)*(4096*a*b^11*c^8*d^4 + 4096*a^8*b^4*c*d^11 - 20480*a^2*b^10*c^7*d^5 + 36864*a^3*b^9*c^6*d^6 - 20480*a^4*b^8*c^5*d^7 - 20480*a^5*b^7*c^4*d^8 + 36864*a^6*b^6*c^3*d^9 - 20480*a^7*b^5*c^2*d^10) + x*(1024*a^7*b^4*d^11 + 1024*b^11*c^7*d^4 - 4096*a*b^10*c^6*d^5 - 4096*a^6*b^5*c*d^10 + 6144*a^2*b^9*c^5*d^6 - 3072*a^3*b^8*c^4*d^7 - 3072*a^4*b^7*c^3*d^8 + 6144*a^5*b^6*c^2*d^9)) - 16*a^2*b^6*d^8 - 16*b^8*c^2*d^6 + 32*a*b^7*c*d^7) + 8*b^7*d^7*x)*(-d^3/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d))^(1/4)*1i - ((-d^3/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d))^(1/4)*((-d^3/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d))^(3/4)*((-d^3/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d))^(1/4)*(4096*a*b^11*c^8*d^4 + 4096*a^8*b^4*c*d^11 - 20480*a^2*b^10*c^7*d^5 + 36864*a^3*b^9*c^6*d^6 - 20480*a^4*b^8*c^5*d^7 - 20480*a^5*b^7*c^4*d^8 + 36864*a^6*b^6*c^3*d^9 - 20480*a^7*b^5*c^2*d^10) - x*(1024*a^7*b^4*d^11 + 1024*b^11*c^7*d^4 - 4096*a*b^10*c^6*d^5 - 4096*a^6*b^5*c*d^10 + 6144*a^2*b^9*c^5*d^6 - 3072*a^3*b^8*c^4*d^7 - 3072*a^4*b^7*c^3*d^8 + 6144*a^5*b^6*c^2*d^9)) - 16*a^2*b^6*d^8 - 16*b^8*c^2*d^6 + 32*a*b^7*c*d^7) - 8*b^7*d^7*x)*(-d^3/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d))^(1/4)*1i)/(((-d^3/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d))^(1/4)*((-d^3/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d))^(3/4)*((-d^3/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d))^(1/4)*(4096*a*b^11*c^8*d^4 + 4096*a^8*b^4*c*d^11 - 20480*a^2*b^10*c^7*d^5 + 36864*a^3*b^9*c^6*d^6 - 20480*a^4*b^8*c^5*d^7 - 20480*a^5*b^7*c^4*d^8 + 36864*a^6*b^6*c^3*d^9 - 20480*a^7*b^5*c^2*d^10) + x*(1024*a^7*b^4*d^11 + 1024*b^11*c^7*d^4 - 4096*a*b^10*c^6*d^5 - 4096*a^6*b^5*c*d^10 + 6144*a^2*b^9*c^5*d^6 - 3072*a^3*b^8*c^4*d^7 - 3072*a^4*b^7*c^3*d^8 + 6144*a^5*b^6*c^2*d^9)) - 16*a^2*b^6*d^8 - 16*b^8*c^2*d^6 + 32*a*b^7*c*d^7) + 8*b^7*d^7*x)*(-d^3/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d))^(1/4) + ((-d^3/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d))^(1/4)*((-d^3/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d))^(3/4)*((-d^3/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d))^(1/4)*(4096*a*b^11*c^8*d^4 + 4096*a^8*b^4*c*d^11 - 20480*a^2*b^10*c^7*d^5 + 36864*a^3*b^9*c^6*d^6 - 20480*a^4*b^8*c^5*d^7 - 20480*a^5*b^7*c^4*d^8 + 36864*a^6*b^6*c^3*d^9 - 20480*a^7*b^5*c^2*d^10) - x*(1024*a^7*b^4*d^11 + 1024*b^11*c^7*d^4 - 4096*a*b^10*c^6*d^5 - 4096*a^6*b^5*c*d^10 + 6144*a^2*b^9*c^5*d^6 - 3072*a^3*b^8*c^4*d^7 - 3072*a^4*b^7*c^3*d^8 + 6144*a^5*b^6*c^2*d^9)) - 16*a^2*b^6*d^8 - 16*b^8*c^2*d^6 + 32*a*b^7*c*d^7) - 8*b^7*d^7*x)*(-d^3/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d))^(1/4)))*(-d^3/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d))^(1/4)*2i - atan((((-b^3/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3))^(1/4)*((-b^3/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3))^(3/4)*((-b^3/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3))^(1/4)*(4096*a*b^11*c^8*d^4 + 4096*a^8*b^4*c*d^11 - 20480*a^2*b^10*c^7*d^5 + 36864*a^3*b^9*c^6*d^6 - 20480*a^4*b^8*c^5*d^7 - 20480*a^5*b^7*c^4*d^8 + 36864*a^6*b^6*c^3*d^9 - 20480*a^7*b^5*c^2*d^10) + x*(1024*a^7*b^4*d^11 + 1024*b^11*c^7*d^4 - 4096*a*b^10*c^6*d^5 - 4096*a^6*b^5*c*d^10 + 6144*a^2*b^9*c^5*d^6 - 3072*a^3*b^8*c^4*d^7 - 3072*a^4*b^7*c^3*d^8 + 6144*a^5*b^6*c^2*d^9)) - 16*a^2*b^6*d^8 - 16*b^8*c^2*d^6 + 32*a*b^7*c*d^7) + 8*b^7*d^7*x)*(-b^3/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3))^(1/4)*1i - ((-b^3/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3))^(1/4)*((-b^3/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3))^(3/4)*((-b^3/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3))^(1/4)*(4096*a*b^11*c^8*d^4 + 4096*a^8*b^4*c*d^11 - 20480*a^2*b^10*c^7*d^5 + 36864*a^3*b^9*c^6*d^6 - 20480*a^4*b^8*c^5*d^7 - 20480*a^5*b^7*c^4*d^8 + 36864*a^6*b^6*c^3*d^9 - 20480*a^7*b^5*c^2*d^10) - x*(1024*a^7*b^4*d^11 + 1024*b^11*c^7*d^4 - 4096*a*b^10*c^6*d^5 - 4096*a^6*b^5*c*d^10 + 6144*a^2*b^9*c^5*d^6 - 3072*a^3*b^8*c^4*d^7 - 3072*a^4*b^7*c^3*d^8 + 6144*a^5*b^6*c^2*d^9)) - 16*a^2*b^6*d^8 - 16*b^8*c^2*d^6 + 32*a*b^7*c*d^7) - 8*b^7*d^7*x)*(-b^3/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3))^(1/4)*1i)/(((-b^3/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3))^(1/4)*((-b^3/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3))^(3/4)*((-b^3/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3))^(1/4)*(4096*a*b^11*c^8*d^4 + 4096*a^8*b^4*c*d^11 - 20480*a^2*b^10*c^7*d^5 + 36864*a^3*b^9*c^6*d^6 - 20480*a^4*b^8*c^5*d^7 - 20480*a^5*b^7*c^4*d^8 + 36864*a^6*b^6*c^3*d^9 - 20480*a^7*b^5*c^2*d^10) + x*(1024*a^7*b^4*d^11 + 1024*b^11*c^7*d^4 - 4096*a*b^10*c^6*d^5 - 4096*a^6*b^5*c*d^10 + 6144*a^2*b^9*c^5*d^6 - 3072*a^3*b^8*c^4*d^7 - 3072*a^4*b^7*c^3*d^8 + 6144*a^5*b^6*c^2*d^9)) - 16*a^2*b^6*d^8 - 16*b^8*c^2*d^6 + 32*a*b^7*c*d^7) + 8*b^7*d^7*x)*(-b^3/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3))^(1/4) + ((-b^3/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3))^(1/4)*((-b^3/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3))^(3/4)*((-b^3/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3))^(1/4)*(4096*a*b^11*c^8*d^4 + 4096*a^8*b^4*c*d^11 - 20480*a^2*b^10*c^7*d^5 + 36864*a^3*b^9*c^6*d^6 - 20480*a^4*b^8*c^5*d^7 - 20480*a^5*b^7*c^4*d^8 + 36864*a^6*b^6*c^3*d^9 - 20480*a^7*b^5*c^2*d^10) - x*(1024*a^7*b^4*d^11 + 1024*b^11*c^7*d^4 - 4096*a*b^10*c^6*d^5 - 4096*a^6*b^5*c*d^10 + 6144*a^2*b^9*c^5*d^6 - 3072*a^3*b^8*c^4*d^7 - 3072*a^4*b^7*c^3*d^8 + 6144*a^5*b^6*c^2*d^9)) - 16*a^2*b^6*d^8 - 16*b^8*c^2*d^6 + 32*a*b^7*c*d^7) - 8*b^7*d^7*x)*(-b^3/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3))^(1/4)))*(-b^3/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3))^(1/4)*2i - 2*atan((b^3*d^3*x - (128*b^10*c^7*x)/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3) - (128*a^7*b^3*d^7*x)/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3) - (768*a^2*b^8*c^5*d^2*x)/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3) + (384*a^3*b^7*c^4*d^3*x)/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3) + (384*a^4*b^6*c^3*d^4*x)/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3) - (768*a^5*b^5*c^2*d^5*x)/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3) + (512*a*b^9*c^6*d*x)/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3) + (512*a^6*b^4*c*d^6*x)/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3))/((-b^3/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3))^(1/4)*((b^3*(512*a*b^7*c^8 + 512*a^8*c*d^7 - 2560*a^2*b^6*c^7*d - 2560*a^7*b*c^2*d^6 + 4608*a^3*b^5*c^6*d^2 - 2560*a^4*b^4*c^5*d^3 - 2560*a^5*b^3*c^4*d^4 + 4608*a^6*b^2*c^3*d^5))/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3) + 2*a^2*b^2*d^4 + 2*b^4*c^2*d^2 - 4*a*b^3*c*d^3)))*(-b^3/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3))^(1/4) - 2*atan((b^3*d^3*x - (128*a^7*d^10*x)/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d) - (128*b^7*c^7*d^3*x)/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d) - (768*a^2*b^5*c^5*d^5*x)/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d) + (384*a^3*b^4*c^4*d^6*x)/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d) + (384*a^4*b^3*c^3*d^7*x)/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d) - (768*a^5*b^2*c^2*d^8*x)/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d) + (512*a^6*b*c*d^9*x)/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d) + (512*a*b^6*c^6*d^4*x)/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d))/((-d^3/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d))^(1/4)*((d^3*(512*a*b^7*c^8 + 512*a^8*c*d^7 - 2560*a^2*b^6*c^7*d - 2560*a^7*b*c^2*d^6 + 4608*a^3*b^5*c^6*d^2 - 2560*a^4*b^4*c^5*d^3 - 2560*a^5*b^3*c^4*d^4 + 4608*a^6*b^2*c^3*d^5))/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d) + 2*a^2*b^2*d^4 + 2*b^4*c^2*d^2 - 4*a*b^3*c*d^3)))*(-d^3/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d))^(1/4)","B"
165,1,21975,513,4.003916,"\text{Not used}","int(1/((a + b*x^4)*(c + d*x^4)^2),x)","2\,\mathrm{atan}\left(\frac{{\left(-\frac{81\,a^4\,d^7-756\,a^3\,b\,c\,d^6+2646\,a^2\,b^2\,c^2\,d^5-4116\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{65536\,a^8\,c^7\,d^8-524288\,a^7\,b\,c^8\,d^7+1835008\,a^6\,b^2\,c^9\,d^6-3670016\,a^5\,b^3\,c^{10}\,d^5+4587520\,a^4\,b^4\,c^{11}\,d^4-3670016\,a^3\,b^5\,c^{12}\,d^3+1835008\,a^2\,b^6\,c^{13}\,d^2-524288\,a\,b^7\,c^{14}\,d+65536\,b^8\,c^{15}}\right)}^{1/4}\,\left({\left(-\frac{81\,a^4\,d^7-756\,a^3\,b\,c\,d^6+2646\,a^2\,b^2\,c^2\,d^5-4116\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{65536\,a^8\,c^7\,d^8-524288\,a^7\,b\,c^8\,d^7+1835008\,a^6\,b^2\,c^9\,d^6-3670016\,a^5\,b^3\,c^{10}\,d^5+4587520\,a^4\,b^4\,c^{11}\,d^4-3670016\,a^3\,b^5\,c^{12}\,d^3+1835008\,a^2\,b^6\,c^{13}\,d^2-524288\,a\,b^7\,c^{14}\,d+65536\,b^8\,c^{15}}\right)}^{1/4}\,\left(\frac{\left(\frac{81\,a^4\,b^7\,d^{10}}{16}-\frac{675\,a^3\,b^8\,c\,d^9}{16}+\frac{1971\,a^2\,b^9\,c^2\,d^8}{16}-\frac{2145\,a\,b^{10}\,c^3\,d^7}{16}+28\,b^{11}\,c^4\,d^6\right)\,1{}\mathrm{i}}{-a^3\,c^4\,d^3+3\,a^2\,b\,c^5\,d^2-3\,a\,b^2\,c^6\,d+b^3\,c^7}+{\left(-\frac{81\,a^4\,d^7-756\,a^3\,b\,c\,d^6+2646\,a^2\,b^2\,c^2\,d^5-4116\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{65536\,a^8\,c^7\,d^8-524288\,a^7\,b\,c^8\,d^7+1835008\,a^6\,b^2\,c^9\,d^6-3670016\,a^5\,b^3\,c^{10}\,d^5+4587520\,a^4\,b^4\,c^{11}\,d^4-3670016\,a^3\,b^5\,c^{12}\,d^3+1835008\,a^2\,b^6\,c^{13}\,d^2-524288\,a\,b^7\,c^{14}\,d+65536\,b^8\,c^{15}}\right)}^{3/4}\,\left(\frac{{\left(-\frac{81\,a^4\,d^7-756\,a^3\,b\,c\,d^6+2646\,a^2\,b^2\,c^2\,d^5-4116\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{65536\,a^8\,c^7\,d^8-524288\,a^7\,b\,c^8\,d^7+1835008\,a^6\,b^2\,c^9\,d^6-3670016\,a^5\,b^3\,c^{10}\,d^5+4587520\,a^4\,b^4\,c^{11}\,d^4-3670016\,a^3\,b^5\,c^{12}\,d^3+1835008\,a^2\,b^6\,c^{13}\,d^2-524288\,a\,b^7\,c^{14}\,d+65536\,b^8\,c^{15}}\right)}^{1/4}\,\left(3072\,a^{11}\,b^4\,c^4\,d^{14}-28672\,a^{10}\,b^5\,c^5\,d^{13}+114688\,a^9\,b^6\,c^6\,d^{12}-253952\,a^8\,b^7\,c^7\,d^{11}+329728\,a^7\,b^8\,c^8\,d^{10}-229376\,a^6\,b^9\,c^9\,d^9+28672\,a^5\,b^{10}\,c^{10}\,d^8+90112\,a^4\,b^{11}\,c^{11}\,d^7-78848\,a^3\,b^{12}\,c^{12}\,d^6+28672\,a^2\,b^{13}\,c^{13}\,d^5-4096\,a\,b^{14}\,c^{14}\,d^4\right)}{-a^3\,c^4\,d^3+3\,a^2\,b\,c^5\,d^2-3\,a\,b^2\,c^6\,d+b^3\,c^7}-\frac{x\,\left(36864\,a^{13}\,b^4\,c^2\,d^{17}-466944\,a^{12}\,b^5\,c^3\,d^{16}+2609152\,a^{11}\,b^6\,c^4\,d^{15}-8486912\,a^{10}\,b^7\,c^5\,d^{14}+17833984\,a^9\,b^8\,c^6\,d^{13}-25280512\,a^8\,b^9\,c^7\,d^{12}+24190976\,a^7\,b^{10}\,c^8\,d^{11}-14516224\,a^6\,b^{11}\,c^9\,d^{10}+3362816\,a^5\,b^{12}\,c^{10}\,d^9+2809856\,a^4\,b^{13}\,c^{11}\,d^8-3469312\,a^3\,b^{14}\,c^{12}\,d^7+1835008\,a^2\,b^{15}\,c^{13}\,d^6-524288\,a\,b^{16}\,c^{14}\,d^5+65536\,b^{17}\,c^{15}\,d^4\right)\,1{}\mathrm{i}}{64\,\left(a^6\,c^4\,d^6-6\,a^5\,b\,c^5\,d^5+15\,a^4\,b^2\,c^6\,d^4-20\,a^3\,b^3\,c^7\,d^3+15\,a^2\,b^4\,c^8\,d^2-6\,a\,b^5\,c^9\,d+b^6\,c^{10}\right)}\right)\,1{}\mathrm{i}\right)+\frac{x\,\left(81\,a^4\,b^9\,d^{11}-756\,a^3\,b^{10}\,c\,d^{10}+2790\,a^2\,b^{11}\,c^2\,d^9-4788\,a\,b^{12}\,c^3\,d^8+3185\,b^{13}\,c^4\,d^7\right)}{64\,\left(a^6\,c^4\,d^6-6\,a^5\,b\,c^5\,d^5+15\,a^4\,b^2\,c^6\,d^4-20\,a^3\,b^3\,c^7\,d^3+15\,a^2\,b^4\,c^8\,d^2-6\,a\,b^5\,c^9\,d+b^6\,c^{10}\right)}\right)-{\left(-\frac{81\,a^4\,d^7-756\,a^3\,b\,c\,d^6+2646\,a^2\,b^2\,c^2\,d^5-4116\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{65536\,a^8\,c^7\,d^8-524288\,a^7\,b\,c^8\,d^7+1835008\,a^6\,b^2\,c^9\,d^6-3670016\,a^5\,b^3\,c^{10}\,d^5+4587520\,a^4\,b^4\,c^{11}\,d^4-3670016\,a^3\,b^5\,c^{12}\,d^3+1835008\,a^2\,b^6\,c^{13}\,d^2-524288\,a\,b^7\,c^{14}\,d+65536\,b^8\,c^{15}}\right)}^{1/4}\,\left({\left(-\frac{81\,a^4\,d^7-756\,a^3\,b\,c\,d^6+2646\,a^2\,b^2\,c^2\,d^5-4116\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{65536\,a^8\,c^7\,d^8-524288\,a^7\,b\,c^8\,d^7+1835008\,a^6\,b^2\,c^9\,d^6-3670016\,a^5\,b^3\,c^{10}\,d^5+4587520\,a^4\,b^4\,c^{11}\,d^4-3670016\,a^3\,b^5\,c^{12}\,d^3+1835008\,a^2\,b^6\,c^{13}\,d^2-524288\,a\,b^7\,c^{14}\,d+65536\,b^8\,c^{15}}\right)}^{1/4}\,\left(\frac{\left(\frac{81\,a^4\,b^7\,d^{10}}{16}-\frac{675\,a^3\,b^8\,c\,d^9}{16}+\frac{1971\,a^2\,b^9\,c^2\,d^8}{16}-\frac{2145\,a\,b^{10}\,c^3\,d^7}{16}+28\,b^{11}\,c^4\,d^6\right)\,1{}\mathrm{i}}{-a^3\,c^4\,d^3+3\,a^2\,b\,c^5\,d^2-3\,a\,b^2\,c^6\,d+b^3\,c^7}+{\left(-\frac{81\,a^4\,d^7-756\,a^3\,b\,c\,d^6+2646\,a^2\,b^2\,c^2\,d^5-4116\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{65536\,a^8\,c^7\,d^8-524288\,a^7\,b\,c^8\,d^7+1835008\,a^6\,b^2\,c^9\,d^6-3670016\,a^5\,b^3\,c^{10}\,d^5+4587520\,a^4\,b^4\,c^{11}\,d^4-3670016\,a^3\,b^5\,c^{12}\,d^3+1835008\,a^2\,b^6\,c^{13}\,d^2-524288\,a\,b^7\,c^{14}\,d+65536\,b^8\,c^{15}}\right)}^{3/4}\,\left(\frac{{\left(-\frac{81\,a^4\,d^7-756\,a^3\,b\,c\,d^6+2646\,a^2\,b^2\,c^2\,d^5-4116\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{65536\,a^8\,c^7\,d^8-524288\,a^7\,b\,c^8\,d^7+1835008\,a^6\,b^2\,c^9\,d^6-3670016\,a^5\,b^3\,c^{10}\,d^5+4587520\,a^4\,b^4\,c^{11}\,d^4-3670016\,a^3\,b^5\,c^{12}\,d^3+1835008\,a^2\,b^6\,c^{13}\,d^2-524288\,a\,b^7\,c^{14}\,d+65536\,b^8\,c^{15}}\right)}^{1/4}\,\left(3072\,a^{11}\,b^4\,c^4\,d^{14}-28672\,a^{10}\,b^5\,c^5\,d^{13}+114688\,a^9\,b^6\,c^6\,d^{12}-253952\,a^8\,b^7\,c^7\,d^{11}+329728\,a^7\,b^8\,c^8\,d^{10}-229376\,a^6\,b^9\,c^9\,d^9+28672\,a^5\,b^{10}\,c^{10}\,d^8+90112\,a^4\,b^{11}\,c^{11}\,d^7-78848\,a^3\,b^{12}\,c^{12}\,d^6+28672\,a^2\,b^{13}\,c^{13}\,d^5-4096\,a\,b^{14}\,c^{14}\,d^4\right)}{-a^3\,c^4\,d^3+3\,a^2\,b\,c^5\,d^2-3\,a\,b^2\,c^6\,d+b^3\,c^7}+\frac{x\,\left(36864\,a^{13}\,b^4\,c^2\,d^{17}-466944\,a^{12}\,b^5\,c^3\,d^{16}+2609152\,a^{11}\,b^6\,c^4\,d^{15}-8486912\,a^{10}\,b^7\,c^5\,d^{14}+17833984\,a^9\,b^8\,c^6\,d^{13}-25280512\,a^8\,b^9\,c^7\,d^{12}+24190976\,a^7\,b^{10}\,c^8\,d^{11}-14516224\,a^6\,b^{11}\,c^9\,d^{10}+3362816\,a^5\,b^{12}\,c^{10}\,d^9+2809856\,a^4\,b^{13}\,c^{11}\,d^8-3469312\,a^3\,b^{14}\,c^{12}\,d^7+1835008\,a^2\,b^{15}\,c^{13}\,d^6-524288\,a\,b^{16}\,c^{14}\,d^5+65536\,b^{17}\,c^{15}\,d^4\right)\,1{}\mathrm{i}}{64\,\left(a^6\,c^4\,d^6-6\,a^5\,b\,c^5\,d^5+15\,a^4\,b^2\,c^6\,d^4-20\,a^3\,b^3\,c^7\,d^3+15\,a^2\,b^4\,c^8\,d^2-6\,a\,b^5\,c^9\,d+b^6\,c^{10}\right)}\right)\,1{}\mathrm{i}\right)-\frac{x\,\left(81\,a^4\,b^9\,d^{11}-756\,a^3\,b^{10}\,c\,d^{10}+2790\,a^2\,b^{11}\,c^2\,d^9-4788\,a\,b^{12}\,c^3\,d^8+3185\,b^{13}\,c^4\,d^7\right)}{64\,\left(a^6\,c^4\,d^6-6\,a^5\,b\,c^5\,d^5+15\,a^4\,b^2\,c^6\,d^4-20\,a^3\,b^3\,c^7\,d^3+15\,a^2\,b^4\,c^8\,d^2-6\,a\,b^5\,c^9\,d+b^6\,c^{10}\right)}\right)}{{\left(-\frac{81\,a^4\,d^7-756\,a^3\,b\,c\,d^6+2646\,a^2\,b^2\,c^2\,d^5-4116\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{65536\,a^8\,c^7\,d^8-524288\,a^7\,b\,c^8\,d^7+1835008\,a^6\,b^2\,c^9\,d^6-3670016\,a^5\,b^3\,c^{10}\,d^5+4587520\,a^4\,b^4\,c^{11}\,d^4-3670016\,a^3\,b^5\,c^{12}\,d^3+1835008\,a^2\,b^6\,c^{13}\,d^2-524288\,a\,b^7\,c^{14}\,d+65536\,b^8\,c^{15}}\right)}^{1/4}\,\left({\left(-\frac{81\,a^4\,d^7-756\,a^3\,b\,c\,d^6+2646\,a^2\,b^2\,c^2\,d^5-4116\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{65536\,a^8\,c^7\,d^8-524288\,a^7\,b\,c^8\,d^7+1835008\,a^6\,b^2\,c^9\,d^6-3670016\,a^5\,b^3\,c^{10}\,d^5+4587520\,a^4\,b^4\,c^{11}\,d^4-3670016\,a^3\,b^5\,c^{12}\,d^3+1835008\,a^2\,b^6\,c^{13}\,d^2-524288\,a\,b^7\,c^{14}\,d+65536\,b^8\,c^{15}}\right)}^{1/4}\,\left(\frac{\left(\frac{81\,a^4\,b^7\,d^{10}}{16}-\frac{675\,a^3\,b^8\,c\,d^9}{16}+\frac{1971\,a^2\,b^9\,c^2\,d^8}{16}-\frac{2145\,a\,b^{10}\,c^3\,d^7}{16}+28\,b^{11}\,c^4\,d^6\right)\,1{}\mathrm{i}}{-a^3\,c^4\,d^3+3\,a^2\,b\,c^5\,d^2-3\,a\,b^2\,c^6\,d+b^3\,c^7}+{\left(-\frac{81\,a^4\,d^7-756\,a^3\,b\,c\,d^6+2646\,a^2\,b^2\,c^2\,d^5-4116\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{65536\,a^8\,c^7\,d^8-524288\,a^7\,b\,c^8\,d^7+1835008\,a^6\,b^2\,c^9\,d^6-3670016\,a^5\,b^3\,c^{10}\,d^5+4587520\,a^4\,b^4\,c^{11}\,d^4-3670016\,a^3\,b^5\,c^{12}\,d^3+1835008\,a^2\,b^6\,c^{13}\,d^2-524288\,a\,b^7\,c^{14}\,d+65536\,b^8\,c^{15}}\right)}^{3/4}\,\left(\frac{{\left(-\frac{81\,a^4\,d^7-756\,a^3\,b\,c\,d^6+2646\,a^2\,b^2\,c^2\,d^5-4116\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{65536\,a^8\,c^7\,d^8-524288\,a^7\,b\,c^8\,d^7+1835008\,a^6\,b^2\,c^9\,d^6-3670016\,a^5\,b^3\,c^{10}\,d^5+4587520\,a^4\,b^4\,c^{11}\,d^4-3670016\,a^3\,b^5\,c^{12}\,d^3+1835008\,a^2\,b^6\,c^{13}\,d^2-524288\,a\,b^7\,c^{14}\,d+65536\,b^8\,c^{15}}\right)}^{1/4}\,\left(3072\,a^{11}\,b^4\,c^4\,d^{14}-28672\,a^{10}\,b^5\,c^5\,d^{13}+114688\,a^9\,b^6\,c^6\,d^{12}-253952\,a^8\,b^7\,c^7\,d^{11}+329728\,a^7\,b^8\,c^8\,d^{10}-229376\,a^6\,b^9\,c^9\,d^9+28672\,a^5\,b^{10}\,c^{10}\,d^8+90112\,a^4\,b^{11}\,c^{11}\,d^7-78848\,a^3\,b^{12}\,c^{12}\,d^6+28672\,a^2\,b^{13}\,c^{13}\,d^5-4096\,a\,b^{14}\,c^{14}\,d^4\right)}{-a^3\,c^4\,d^3+3\,a^2\,b\,c^5\,d^2-3\,a\,b^2\,c^6\,d+b^3\,c^7}-\frac{x\,\left(36864\,a^{13}\,b^4\,c^2\,d^{17}-466944\,a^{12}\,b^5\,c^3\,d^{16}+2609152\,a^{11}\,b^6\,c^4\,d^{15}-8486912\,a^{10}\,b^7\,c^5\,d^{14}+17833984\,a^9\,b^8\,c^6\,d^{13}-25280512\,a^8\,b^9\,c^7\,d^{12}+24190976\,a^7\,b^{10}\,c^8\,d^{11}-14516224\,a^6\,b^{11}\,c^9\,d^{10}+3362816\,a^5\,b^{12}\,c^{10}\,d^9+2809856\,a^4\,b^{13}\,c^{11}\,d^8-3469312\,a^3\,b^{14}\,c^{12}\,d^7+1835008\,a^2\,b^{15}\,c^{13}\,d^6-524288\,a\,b^{16}\,c^{14}\,d^5+65536\,b^{17}\,c^{15}\,d^4\right)\,1{}\mathrm{i}}{64\,\left(a^6\,c^4\,d^6-6\,a^5\,b\,c^5\,d^5+15\,a^4\,b^2\,c^6\,d^4-20\,a^3\,b^3\,c^7\,d^3+15\,a^2\,b^4\,c^8\,d^2-6\,a\,b^5\,c^9\,d+b^6\,c^{10}\right)}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}+\frac{x\,\left(81\,a^4\,b^9\,d^{11}-756\,a^3\,b^{10}\,c\,d^{10}+2790\,a^2\,b^{11}\,c^2\,d^9-4788\,a\,b^{12}\,c^3\,d^8+3185\,b^{13}\,c^4\,d^7\right)\,1{}\mathrm{i}}{64\,\left(a^6\,c^4\,d^6-6\,a^5\,b\,c^5\,d^5+15\,a^4\,b^2\,c^6\,d^4-20\,a^3\,b^3\,c^7\,d^3+15\,a^2\,b^4\,c^8\,d^2-6\,a\,b^5\,c^9\,d+b^6\,c^{10}\right)}\right)+{\left(-\frac{81\,a^4\,d^7-756\,a^3\,b\,c\,d^6+2646\,a^2\,b^2\,c^2\,d^5-4116\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{65536\,a^8\,c^7\,d^8-524288\,a^7\,b\,c^8\,d^7+1835008\,a^6\,b^2\,c^9\,d^6-3670016\,a^5\,b^3\,c^{10}\,d^5+4587520\,a^4\,b^4\,c^{11}\,d^4-3670016\,a^3\,b^5\,c^{12}\,d^3+1835008\,a^2\,b^6\,c^{13}\,d^2-524288\,a\,b^7\,c^{14}\,d+65536\,b^8\,c^{15}}\right)}^{1/4}\,\left({\left(-\frac{81\,a^4\,d^7-756\,a^3\,b\,c\,d^6+2646\,a^2\,b^2\,c^2\,d^5-4116\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{65536\,a^8\,c^7\,d^8-524288\,a^7\,b\,c^8\,d^7+1835008\,a^6\,b^2\,c^9\,d^6-3670016\,a^5\,b^3\,c^{10}\,d^5+4587520\,a^4\,b^4\,c^{11}\,d^4-3670016\,a^3\,b^5\,c^{12}\,d^3+1835008\,a^2\,b^6\,c^{13}\,d^2-524288\,a\,b^7\,c^{14}\,d+65536\,b^8\,c^{15}}\right)}^{1/4}\,\left(\frac{\left(\frac{81\,a^4\,b^7\,d^{10}}{16}-\frac{675\,a^3\,b^8\,c\,d^9}{16}+\frac{1971\,a^2\,b^9\,c^2\,d^8}{16}-\frac{2145\,a\,b^{10}\,c^3\,d^7}{16}+28\,b^{11}\,c^4\,d^6\right)\,1{}\mathrm{i}}{-a^3\,c^4\,d^3+3\,a^2\,b\,c^5\,d^2-3\,a\,b^2\,c^6\,d+b^3\,c^7}+{\left(-\frac{81\,a^4\,d^7-756\,a^3\,b\,c\,d^6+2646\,a^2\,b^2\,c^2\,d^5-4116\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{65536\,a^8\,c^7\,d^8-524288\,a^7\,b\,c^8\,d^7+1835008\,a^6\,b^2\,c^9\,d^6-3670016\,a^5\,b^3\,c^{10}\,d^5+4587520\,a^4\,b^4\,c^{11}\,d^4-3670016\,a^3\,b^5\,c^{12}\,d^3+1835008\,a^2\,b^6\,c^{13}\,d^2-524288\,a\,b^7\,c^{14}\,d+65536\,b^8\,c^{15}}\right)}^{3/4}\,\left(\frac{{\left(-\frac{81\,a^4\,d^7-756\,a^3\,b\,c\,d^6+2646\,a^2\,b^2\,c^2\,d^5-4116\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{65536\,a^8\,c^7\,d^8-524288\,a^7\,b\,c^8\,d^7+1835008\,a^6\,b^2\,c^9\,d^6-3670016\,a^5\,b^3\,c^{10}\,d^5+4587520\,a^4\,b^4\,c^{11}\,d^4-3670016\,a^3\,b^5\,c^{12}\,d^3+1835008\,a^2\,b^6\,c^{13}\,d^2-524288\,a\,b^7\,c^{14}\,d+65536\,b^8\,c^{15}}\right)}^{1/4}\,\left(3072\,a^{11}\,b^4\,c^4\,d^{14}-28672\,a^{10}\,b^5\,c^5\,d^{13}+114688\,a^9\,b^6\,c^6\,d^{12}-253952\,a^8\,b^7\,c^7\,d^{11}+329728\,a^7\,b^8\,c^8\,d^{10}-229376\,a^6\,b^9\,c^9\,d^9+28672\,a^5\,b^{10}\,c^{10}\,d^8+90112\,a^4\,b^{11}\,c^{11}\,d^7-78848\,a^3\,b^{12}\,c^{12}\,d^6+28672\,a^2\,b^{13}\,c^{13}\,d^5-4096\,a\,b^{14}\,c^{14}\,d^4\right)}{-a^3\,c^4\,d^3+3\,a^2\,b\,c^5\,d^2-3\,a\,b^2\,c^6\,d+b^3\,c^7}+\frac{x\,\left(36864\,a^{13}\,b^4\,c^2\,d^{17}-466944\,a^{12}\,b^5\,c^3\,d^{16}+2609152\,a^{11}\,b^6\,c^4\,d^{15}-8486912\,a^{10}\,b^7\,c^5\,d^{14}+17833984\,a^9\,b^8\,c^6\,d^{13}-25280512\,a^8\,b^9\,c^7\,d^{12}+24190976\,a^7\,b^{10}\,c^8\,d^{11}-14516224\,a^6\,b^{11}\,c^9\,d^{10}+3362816\,a^5\,b^{12}\,c^{10}\,d^9+2809856\,a^4\,b^{13}\,c^{11}\,d^8-3469312\,a^3\,b^{14}\,c^{12}\,d^7+1835008\,a^2\,b^{15}\,c^{13}\,d^6-524288\,a\,b^{16}\,c^{14}\,d^5+65536\,b^{17}\,c^{15}\,d^4\right)\,1{}\mathrm{i}}{64\,\left(a^6\,c^4\,d^6-6\,a^5\,b\,c^5\,d^5+15\,a^4\,b^2\,c^6\,d^4-20\,a^3\,b^3\,c^7\,d^3+15\,a^2\,b^4\,c^8\,d^2-6\,a\,b^5\,c^9\,d+b^6\,c^{10}\right)}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}-\frac{x\,\left(81\,a^4\,b^9\,d^{11}-756\,a^3\,b^{10}\,c\,d^{10}+2790\,a^2\,b^{11}\,c^2\,d^9-4788\,a\,b^{12}\,c^3\,d^8+3185\,b^{13}\,c^4\,d^7\right)\,1{}\mathrm{i}}{64\,\left(a^6\,c^4\,d^6-6\,a^5\,b\,c^5\,d^5+15\,a^4\,b^2\,c^6\,d^4-20\,a^3\,b^3\,c^7\,d^3+15\,a^2\,b^4\,c^8\,d^2-6\,a\,b^5\,c^9\,d+b^6\,c^{10}\right)}\right)}\right)\,{\left(-\frac{81\,a^4\,d^7-756\,a^3\,b\,c\,d^6+2646\,a^2\,b^2\,c^2\,d^5-4116\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{65536\,a^8\,c^7\,d^8-524288\,a^7\,b\,c^8\,d^7+1835008\,a^6\,b^2\,c^9\,d^6-3670016\,a^5\,b^3\,c^{10}\,d^5+4587520\,a^4\,b^4\,c^{11}\,d^4-3670016\,a^3\,b^5\,c^{12}\,d^3+1835008\,a^2\,b^6\,c^{13}\,d^2-524288\,a\,b^7\,c^{14}\,d+65536\,b^8\,c^{15}}\right)}^{1/4}+2\,\mathrm{atan}\left(\frac{{\left(-\frac{b^7}{256\,a^{11}\,d^8-2048\,a^{10}\,b\,c\,d^7+7168\,a^9\,b^2\,c^2\,d^6-14336\,a^8\,b^3\,c^3\,d^5+17920\,a^7\,b^4\,c^4\,d^4-14336\,a^6\,b^5\,c^5\,d^3+7168\,a^5\,b^6\,c^6\,d^2-2048\,a^4\,b^7\,c^7\,d+256\,a^3\,b^8\,c^8}\right)}^{1/4}\,\left({\left(-\frac{b^7}{256\,a^{11}\,d^8-2048\,a^{10}\,b\,c\,d^7+7168\,a^9\,b^2\,c^2\,d^6-14336\,a^8\,b^3\,c^3\,d^5+17920\,a^7\,b^4\,c^4\,d^4-14336\,a^6\,b^5\,c^5\,d^3+7168\,a^5\,b^6\,c^6\,d^2-2048\,a^4\,b^7\,c^7\,d+256\,a^3\,b^8\,c^8}\right)}^{1/4}\,\left({\left(-\frac{b^7}{256\,a^{11}\,d^8-2048\,a^{10}\,b\,c\,d^7+7168\,a^9\,b^2\,c^2\,d^6-14336\,a^8\,b^3\,c^3\,d^5+17920\,a^7\,b^4\,c^4\,d^4-14336\,a^6\,b^5\,c^5\,d^3+7168\,a^5\,b^6\,c^6\,d^2-2048\,a^4\,b^7\,c^7\,d+256\,a^3\,b^8\,c^8}\right)}^{3/4}\,\left(\frac{{\left(-\frac{b^7}{256\,a^{11}\,d^8-2048\,a^{10}\,b\,c\,d^7+7168\,a^9\,b^2\,c^2\,d^6-14336\,a^8\,b^3\,c^3\,d^5+17920\,a^7\,b^4\,c^4\,d^4-14336\,a^6\,b^5\,c^5\,d^3+7168\,a^5\,b^6\,c^6\,d^2-2048\,a^4\,b^7\,c^7\,d+256\,a^3\,b^8\,c^8}\right)}^{1/4}\,\left(3072\,a^{11}\,b^4\,c^4\,d^{14}-28672\,a^{10}\,b^5\,c^5\,d^{13}+114688\,a^9\,b^6\,c^6\,d^{12}-253952\,a^8\,b^7\,c^7\,d^{11}+329728\,a^7\,b^8\,c^8\,d^{10}-229376\,a^6\,b^9\,c^9\,d^9+28672\,a^5\,b^{10}\,c^{10}\,d^8+90112\,a^4\,b^{11}\,c^{11}\,d^7-78848\,a^3\,b^{12}\,c^{12}\,d^6+28672\,a^2\,b^{13}\,c^{13}\,d^5-4096\,a\,b^{14}\,c^{14}\,d^4\right)}{-a^3\,c^4\,d^3+3\,a^2\,b\,c^5\,d^2-3\,a\,b^2\,c^6\,d+b^3\,c^7}-\frac{x\,\left(36864\,a^{13}\,b^4\,c^2\,d^{17}-466944\,a^{12}\,b^5\,c^3\,d^{16}+2609152\,a^{11}\,b^6\,c^4\,d^{15}-8486912\,a^{10}\,b^7\,c^5\,d^{14}+17833984\,a^9\,b^8\,c^6\,d^{13}-25280512\,a^8\,b^9\,c^7\,d^{12}+24190976\,a^7\,b^{10}\,c^8\,d^{11}-14516224\,a^6\,b^{11}\,c^9\,d^{10}+3362816\,a^5\,b^{12}\,c^{10}\,d^9+2809856\,a^4\,b^{13}\,c^{11}\,d^8-3469312\,a^3\,b^{14}\,c^{12}\,d^7+1835008\,a^2\,b^{15}\,c^{13}\,d^6-524288\,a\,b^{16}\,c^{14}\,d^5+65536\,b^{17}\,c^{15}\,d^4\right)\,1{}\mathrm{i}}{64\,\left(a^6\,c^4\,d^6-6\,a^5\,b\,c^5\,d^5+15\,a^4\,b^2\,c^6\,d^4-20\,a^3\,b^3\,c^7\,d^3+15\,a^2\,b^4\,c^8\,d^2-6\,a\,b^5\,c^9\,d+b^6\,c^{10}\right)}\right)\,1{}\mathrm{i}+\frac{\left(\frac{81\,a^4\,b^7\,d^{10}}{16}-\frac{675\,a^3\,b^8\,c\,d^9}{16}+\frac{1971\,a^2\,b^9\,c^2\,d^8}{16}-\frac{2145\,a\,b^{10}\,c^3\,d^7}{16}+28\,b^{11}\,c^4\,d^6\right)\,1{}\mathrm{i}}{-a^3\,c^4\,d^3+3\,a^2\,b\,c^5\,d^2-3\,a\,b^2\,c^6\,d+b^3\,c^7}\right)+\frac{x\,\left(81\,a^4\,b^9\,d^{11}-756\,a^3\,b^{10}\,c\,d^{10}+2790\,a^2\,b^{11}\,c^2\,d^9-4788\,a\,b^{12}\,c^3\,d^8+3185\,b^{13}\,c^4\,d^7\right)}{64\,\left(a^6\,c^4\,d^6-6\,a^5\,b\,c^5\,d^5+15\,a^4\,b^2\,c^6\,d^4-20\,a^3\,b^3\,c^7\,d^3+15\,a^2\,b^4\,c^8\,d^2-6\,a\,b^5\,c^9\,d+b^6\,c^{10}\right)}\right)-{\left(-\frac{b^7}{256\,a^{11}\,d^8-2048\,a^{10}\,b\,c\,d^7+7168\,a^9\,b^2\,c^2\,d^6-14336\,a^8\,b^3\,c^3\,d^5+17920\,a^7\,b^4\,c^4\,d^4-14336\,a^6\,b^5\,c^5\,d^3+7168\,a^5\,b^6\,c^6\,d^2-2048\,a^4\,b^7\,c^7\,d+256\,a^3\,b^8\,c^8}\right)}^{1/4}\,\left({\left(-\frac{b^7}{256\,a^{11}\,d^8-2048\,a^{10}\,b\,c\,d^7+7168\,a^9\,b^2\,c^2\,d^6-14336\,a^8\,b^3\,c^3\,d^5+17920\,a^7\,b^4\,c^4\,d^4-14336\,a^6\,b^5\,c^5\,d^3+7168\,a^5\,b^6\,c^6\,d^2-2048\,a^4\,b^7\,c^7\,d+256\,a^3\,b^8\,c^8}\right)}^{1/4}\,\left({\left(-\frac{b^7}{256\,a^{11}\,d^8-2048\,a^{10}\,b\,c\,d^7+7168\,a^9\,b^2\,c^2\,d^6-14336\,a^8\,b^3\,c^3\,d^5+17920\,a^7\,b^4\,c^4\,d^4-14336\,a^6\,b^5\,c^5\,d^3+7168\,a^5\,b^6\,c^6\,d^2-2048\,a^4\,b^7\,c^7\,d+256\,a^3\,b^8\,c^8}\right)}^{3/4}\,\left(\frac{{\left(-\frac{b^7}{256\,a^{11}\,d^8-2048\,a^{10}\,b\,c\,d^7+7168\,a^9\,b^2\,c^2\,d^6-14336\,a^8\,b^3\,c^3\,d^5+17920\,a^7\,b^4\,c^4\,d^4-14336\,a^6\,b^5\,c^5\,d^3+7168\,a^5\,b^6\,c^6\,d^2-2048\,a^4\,b^7\,c^7\,d+256\,a^3\,b^8\,c^8}\right)}^{1/4}\,\left(3072\,a^{11}\,b^4\,c^4\,d^{14}-28672\,a^{10}\,b^5\,c^5\,d^{13}+114688\,a^9\,b^6\,c^6\,d^{12}-253952\,a^8\,b^7\,c^7\,d^{11}+329728\,a^7\,b^8\,c^8\,d^{10}-229376\,a^6\,b^9\,c^9\,d^9+28672\,a^5\,b^{10}\,c^{10}\,d^8+90112\,a^4\,b^{11}\,c^{11}\,d^7-78848\,a^3\,b^{12}\,c^{12}\,d^6+28672\,a^2\,b^{13}\,c^{13}\,d^5-4096\,a\,b^{14}\,c^{14}\,d^4\right)}{-a^3\,c^4\,d^3+3\,a^2\,b\,c^5\,d^2-3\,a\,b^2\,c^6\,d+b^3\,c^7}+\frac{x\,\left(36864\,a^{13}\,b^4\,c^2\,d^{17}-466944\,a^{12}\,b^5\,c^3\,d^{16}+2609152\,a^{11}\,b^6\,c^4\,d^{15}-8486912\,a^{10}\,b^7\,c^5\,d^{14}+17833984\,a^9\,b^8\,c^6\,d^{13}-25280512\,a^8\,b^9\,c^7\,d^{12}+24190976\,a^7\,b^{10}\,c^8\,d^{11}-14516224\,a^6\,b^{11}\,c^9\,d^{10}+3362816\,a^5\,b^{12}\,c^{10}\,d^9+2809856\,a^4\,b^{13}\,c^{11}\,d^8-3469312\,a^3\,b^{14}\,c^{12}\,d^7+1835008\,a^2\,b^{15}\,c^{13}\,d^6-524288\,a\,b^{16}\,c^{14}\,d^5+65536\,b^{17}\,c^{15}\,d^4\right)\,1{}\mathrm{i}}{64\,\left(a^6\,c^4\,d^6-6\,a^5\,b\,c^5\,d^5+15\,a^4\,b^2\,c^6\,d^4-20\,a^3\,b^3\,c^7\,d^3+15\,a^2\,b^4\,c^8\,d^2-6\,a\,b^5\,c^9\,d+b^6\,c^{10}\right)}\right)\,1{}\mathrm{i}+\frac{\left(\frac{81\,a^4\,b^7\,d^{10}}{16}-\frac{675\,a^3\,b^8\,c\,d^9}{16}+\frac{1971\,a^2\,b^9\,c^2\,d^8}{16}-\frac{2145\,a\,b^{10}\,c^3\,d^7}{16}+28\,b^{11}\,c^4\,d^6\right)\,1{}\mathrm{i}}{-a^3\,c^4\,d^3+3\,a^2\,b\,c^5\,d^2-3\,a\,b^2\,c^6\,d+b^3\,c^7}\right)-\frac{x\,\left(81\,a^4\,b^9\,d^{11}-756\,a^3\,b^{10}\,c\,d^{10}+2790\,a^2\,b^{11}\,c^2\,d^9-4788\,a\,b^{12}\,c^3\,d^8+3185\,b^{13}\,c^4\,d^7\right)}{64\,\left(a^6\,c^4\,d^6-6\,a^5\,b\,c^5\,d^5+15\,a^4\,b^2\,c^6\,d^4-20\,a^3\,b^3\,c^7\,d^3+15\,a^2\,b^4\,c^8\,d^2-6\,a\,b^5\,c^9\,d+b^6\,c^{10}\right)}\right)}{{\left(-\frac{b^7}{256\,a^{11}\,d^8-2048\,a^{10}\,b\,c\,d^7+7168\,a^9\,b^2\,c^2\,d^6-14336\,a^8\,b^3\,c^3\,d^5+17920\,a^7\,b^4\,c^4\,d^4-14336\,a^6\,b^5\,c^5\,d^3+7168\,a^5\,b^6\,c^6\,d^2-2048\,a^4\,b^7\,c^7\,d+256\,a^3\,b^8\,c^8}\right)}^{1/4}\,\left({\left(-\frac{b^7}{256\,a^{11}\,d^8-2048\,a^{10}\,b\,c\,d^7+7168\,a^9\,b^2\,c^2\,d^6-14336\,a^8\,b^3\,c^3\,d^5+17920\,a^7\,b^4\,c^4\,d^4-14336\,a^6\,b^5\,c^5\,d^3+7168\,a^5\,b^6\,c^6\,d^2-2048\,a^4\,b^7\,c^7\,d+256\,a^3\,b^8\,c^8}\right)}^{1/4}\,\left({\left(-\frac{b^7}{256\,a^{11}\,d^8-2048\,a^{10}\,b\,c\,d^7+7168\,a^9\,b^2\,c^2\,d^6-14336\,a^8\,b^3\,c^3\,d^5+17920\,a^7\,b^4\,c^4\,d^4-14336\,a^6\,b^5\,c^5\,d^3+7168\,a^5\,b^6\,c^6\,d^2-2048\,a^4\,b^7\,c^7\,d+256\,a^3\,b^8\,c^8}\right)}^{3/4}\,\left(\frac{{\left(-\frac{b^7}{256\,a^{11}\,d^8-2048\,a^{10}\,b\,c\,d^7+7168\,a^9\,b^2\,c^2\,d^6-14336\,a^8\,b^3\,c^3\,d^5+17920\,a^7\,b^4\,c^4\,d^4-14336\,a^6\,b^5\,c^5\,d^3+7168\,a^5\,b^6\,c^6\,d^2-2048\,a^4\,b^7\,c^7\,d+256\,a^3\,b^8\,c^8}\right)}^{1/4}\,\left(3072\,a^{11}\,b^4\,c^4\,d^{14}-28672\,a^{10}\,b^5\,c^5\,d^{13}+114688\,a^9\,b^6\,c^6\,d^{12}-253952\,a^8\,b^7\,c^7\,d^{11}+329728\,a^7\,b^8\,c^8\,d^{10}-229376\,a^6\,b^9\,c^9\,d^9+28672\,a^5\,b^{10}\,c^{10}\,d^8+90112\,a^4\,b^{11}\,c^{11}\,d^7-78848\,a^3\,b^{12}\,c^{12}\,d^6+28672\,a^2\,b^{13}\,c^{13}\,d^5-4096\,a\,b^{14}\,c^{14}\,d^4\right)}{-a^3\,c^4\,d^3+3\,a^2\,b\,c^5\,d^2-3\,a\,b^2\,c^6\,d+b^3\,c^7}-\frac{x\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24288\,a\,b^7\,c^{14}\,d+65536\,b^8\,c^{15}}\right)}^{1/4}\,\left(\frac{\frac{81\,a^4\,b^7\,d^{10}}{16}-\frac{675\,a^3\,b^8\,c\,d^9}{16}+\frac{1971\,a^2\,b^9\,c^2\,d^8}{16}-\frac{2145\,a\,b^{10}\,c^3\,d^7}{16}+28\,b^{11}\,c^4\,d^6}{-a^3\,c^4\,d^3+3\,a^2\,b\,c^5\,d^2-3\,a\,b^2\,c^6\,d+b^3\,c^7}+{\left(-\frac{81\,a^4\,d^7-756\,a^3\,b\,c\,d^6+2646\,a^2\,b^2\,c^2\,d^5-4116\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{65536\,a^8\,c^7\,d^8-524288\,a^7\,b\,c^8\,d^7+1835008\,a^6\,b^2\,c^9\,d^6-3670016\,a^5\,b^3\,c^{10}\,d^5+4587520\,a^4\,b^4\,c^{11}\,d^4-3670016\,a^3\,b^5\,c^{12}\,d^3+1835008\,a^2\,b^6\,c^{13}\,d^2-524288\,a\,b^7\,c^{14}\,d+65536\,b^8\,c^{15}}\right)}^{3/4}\,\left(\frac{{\left(-\frac{81\,a^4\,d^7-756\,a^3\,b\,c\,d^6+2646\,a^2\,b^2\,c^2\,d^5-4116\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{65536\,a^8\,c^7\,d^8-524288\,a^7\,b\,c^8\,d^7+1835008\,a^6\,b^2\,c^9\,d^6-3670016\,a^5\,b^3\,c^{10}\,d^5+4587520\,a^4\,b^4\,c^{11}\,d^4-3670016\,a^3\,b^5\,c^{12}\,d^3+1835008\,a^2\,b^6\,c^{13}\,d^2-524288\,a\,b^7\,c^{14}\,d+65536\,b^8\,c^{15}}\right)}^{1/4}\,\left(3072\,a^{11}\,b^4\,c^4\,d^{14}-28672\,a^{10}\,b^5\,c^5\,d^{13}+114688\,a^9\,b^6\,c^6\,d^{12}-253952\,a^8\,b^7\,c^7\,d^{11}+329728\,a^7\,b^8\,c^8\,d^{10}-229376\,a^6\,b^9\,c^9\,d^9+28672\,a^5\,b^{10}\,c^{10}\,d^8+90112\,a^4\,b^{11}\,c^{11}\,d^7-78848\,a^3\,b^{12}\,c^{12}\,d^6+28672\,a^2\,b^{13}\,c^{13}\,d^5-4096\,a\,b^{14}\,c^{14}\,d^4\right)}{-a^3\,c^4\,d^3+3\,a^2\,b\,c^5\,d^2-3\,a\,b^2\,c^6\,d+b^3\,c^7}-\frac{x\,\left(36864\,a^{13}\,b^4\,c^2\,d^{17}-466944\,a^{12}\,b^5\,c^3\,d^{16}+2609152\,a^{11}\,b^6\,c^4\,d^{15}-8486912\,a^{10}\,b^7\,c^5\,d^{14}+17833984\,a^9\,b^8\,c^6\,d^{13}-25280512\,a^8\,b^9\,c^7\,d^{12}+24190976\,a^7\,b^{10}\,c^8\,d^{11}-14516224\,a^6\,b^{11}\,c^9\,d^{10}+3362816\,a^5\,b^{12}\,c^{10}\,d^9+2809856\,a^4\,b^{13}\,c^{11}\,d^8-3469312\,a^3\,b^{14}\,c^{12}\,d^7+1835008\,a^2\,b^{15}\,c^{13}\,d^6-524288\,a\,b^{16}\,c^{14}\,d^5+65536\,b^{17}\,c^{15}\,d^4\right)}{64\,\left(a^6\,c^4\,d^6-6\,a^5\,b\,c^5\,d^5+15\,a^4\,b^2\,c^6\,d^4-20\,a^3\,b^3\,c^7\,d^3+15\,a^2\,b^4\,c^8\,d^2-6\,a\,b^5\,c^9\,d+b^6\,c^{10}\right)}\right)\right)\,1{}\mathrm{i}-\frac{x\,\left(81\,a^4\,b^9\,d^{11}-756\,a^3\,b^{10}\,c\,d^{10}+2790\,a^2\,b^{11}\,c^2\,d^9-4788\,a\,b^{12}\,c^3\,d^8+3185\,b^{13}\,c^4\,d^7\right)\,1{}\mathrm{i}}{64\,\left(a^6\,c^4\,d^6-6\,a^5\,b\,c^5\,d^5+15\,a^4\,b^2\,c^6\,d^4-20\,a^3\,b^3\,c^7\,d^3+15\,a^2\,b^4\,c^8\,d^2-6\,a\,b^5\,c^9\,d+b^6\,c^{10}\right)}\right)-{\left(-\frac{81\,a^4\,d^7-756\,a^3\,b\,c\,d^6+2646\,a^2\,b^2\,c^2\,d^5-4116\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{65536\,a^8\,c^7\,d^8-524288\,a^7\,b\,c^8\,d^7+1835008\,a^6\,b^2\,c^9\,d^6-3670016\,a^5\,b^3\,c^{10}\,d^5+4587520\,a^4\,b^4\,c^{11}\,d^4-3670016\,a^3\,b^5\,c^{12}\,d^3+1835008\,a^2\,b^6\,c^{13}\,d^2-524288\,a\,b^7\,c^{14}\,d+65536\,b^8\,c^{15}}\right)}^{1/4}\,\left({\left(-\frac{81\,a^4\,d^7-756\,a^3\,b\,c\,d^6+2646\,a^2\,b^2\,c^2\,d^5-4116\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{65536\,a^8\,c^7\,d^8-524288\,a^7\,b\,c^8\,d^7+1835008\,a^6\,b^2\,c^9\,d^6-3670016\,a^5\,b^3\,c^{10}\,d^5+4587520\,a^4\,b^4\,c^{11}\,d^4-3670016\,a^3\,b^5\,c^{12}\,d^3+1835008\,a^2\,b^6\,c^{13}\,d^2-524288\,a\,b^7\,c^{14}\,d+65536\,b^8\,c^{15}}\right)}^{1/4}\,\left(\frac{\frac{81\,a^4\,b^7\,d^{10}}{16}-\frac{675\,a^3\,b^8\,c\,d^9}{16}+\frac{1971\,a^2\,b^9\,c^2\,d^8}{16}-\frac{2145\,a\,b^{10}\,c^3\,d^7}{16}+28\,b^{11}\,c^4\,d^6}{-a^3\,c^4\,d^3+3\,a^2\,b\,c^5\,d^2-3\,a\,b^2\,c^6\,d+b^3\,c^7}+{\left(-\frac{81\,a^4\,d^7-756\,a^3\,b\,c\,d^6+2646\,a^2\,b^2\,c^2\,d^5-4116\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{65536\,a^8\,c^7\,d^8-524288\,a^7\,b\,c^8\,d^7+1835008\,a^6\,b^2\,c^9\,d^6-3670016\,a^5\,b^3\,c^{10}\,d^5+4587520\,a^4\,b^4\,c^{11}\,d^4-3670016\,a^3\,b^5\,c^{12}\,d^3+1835008\,a^2\,b^6\,c^{13}\,d^2-524288\,a\,b^7\,c^{14}\,d+65536\,b^8\,c^{15}}\right)}^{3/4}\,\left(\frac{{\left(-\frac{81\,a^4\,d^7-756\,a^3\,b\,c\,d^6+2646\,a^2\,b^2\,c^2\,d^5-4116\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{65536\,a^8\,c^7\,d^8-524288\,a^7\,b\,c^8\,d^7+1835008\,a^6\,b^2\,c^9\,d^6-3670016\,a^5\,b^3\,c^{10}\,d^5+4587520\,a^4\,b^4\,c^{11}\,d^4-3670016\,a^3\,b^5\,c^{12}\,d^3+1835008\,a^2\,b^6\,c^{13}\,d^2-524288\,a\,b^7\,c^{14}\,d+65536\,b^8\,c^{15}}\right)}^{1/4}\,\left(3072\,a^{11}\,b^4\,c^4\,d^{14}-28672\,a^{10}\,b^5\,c^5\,d^{13}+114688\,a^9\,b^6\,c^6\,d^{12}-253952\,a^8\,b^7\,c^7\,d^{11}+329728\,a^7\,b^8\,c^8\,d^{10}-229376\,a^6\,b^9\,c^9\,d^9+28672\,a^5\,b^{10}\,c^{10}\,d^8+90112\,a^4\,b^{11}\,c^{11}\,d^7-78848\,a^3\,b^{12}\,c^{12}\,d^6+28672\,a^2\,b^{13}\,c^{13}\,d^5-4096\,a\,b^{14}\,c^{14}\,d^4\right)}{-a^3\,c^4\,d^3+3\,a^2\,b\,c^5\,d^2-3\,a\,b^2\,c^6\,d+b^3\,c^7}+\frac{x\,\left(36864\,a^{13}\,b^4\,c^2\,d^{17}-466944\,a^{12}\,b^5\,c^3\,d^{16}+2609152\,a^{11}\,b^6\,c^4\,d^{15}-8486912\,a^{10}\,b^7\,c^5\,d^{14}+17833984\,a^9\,b^8\,c^6\,d^{13}-25280512\,a^8\,b^9\,c^7\,d^{12}+24190976\,a^7\,b^{10}\,c^8\,d^{11}-14516224\,a^6\,b^{11}\,c^9\,d^{10}+3362816\,a^5\,b^{12}\,c^{10}\,d^9+2809856\,a^4\,b^{13}\,c^{11}\,d^8-3469312\,a^3\,b^{14}\,c^{12}\,d^7+1835008\,a^2\,b^{15}\,c^{13}\,d^6-524288\,a\,b^{16}\,c^{14}\,d^5+65536\,b^{17}\,c^{15}\,d^4\right)}{64\,\left(a^6\,c^4\,d^6-6\,a^5\,b\,c^5\,d^5+15\,a^4\,b^2\,c^6\,d^4-20\,a^3\,b^3\,c^7\,d^3+15\,a^2\,b^4\,c^8\,d^2-6\,a\,b^5\,c^9\,d+b^6\,c^{10}\right)}\right)\right)\,1{}\mathrm{i}+\frac{x\,\left(81\,a^4\,b^9\,d^{11}-756\,a^3\,b^{10}\,c\,d^{10}+2790\,a^2\,b^{11}\,c^2\,d^9-4788\,a\,b^{12}\,c^3\,d^8+3185\,b^{13}\,c^4\,d^7\right)\,1{}\mathrm{i}}{64\,\left(a^6\,c^4\,d^6-6\,a^5\,b\,c^5\,d^5+15\,a^4\,b^2\,c^6\,d^4-20\,a^3\,b^3\,c^7\,d^3+15\,a^2\,b^4\,c^8\,d^2-6\,a\,b^5\,c^9\,d+b^6\,c^{10}\right)}\right)}{{\left(-\frac{81\,a^4\,d^7-756\,a^3\,b\,c\,d^6+2646\,a^2\,b^2\,c^2\,d^5-4116\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{65536\,a^8\,c^7\,d^8-524288\,a^7\,b\,c^8\,d^7+1835008\,a^6\,b^2\,c^9\,d^6-3670016\,a^5\,b^3\,c^{10}\,d^5+4587520\,a^4\,b^4\,c^{11}\,d^4-3670016\,a^3\,b^5\,c^{12}\,d^3+1835008\,a^2\,b^6\,c^{13}\,d^2-524288\,a\,b^7\,c^{14}\,d+65536\,b^8\,c^{15}}\right)}^{1/4}\,\left({\left(-\frac{81\,a^4\,d^7-756\,a^3\,b\,c\,d^6+2646\,a^2\,b^2\,c^2\,d^5-4116\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{65536\,a^8\,c^7\,d^8-524288\,a^7\,b\,c^8\,d^7+1835008\,a^6\,b^2\,c^9\,d^6-3670016\,a^5\,b^3\,c^{10}\,d^5+4587520\,a^4\,b^4\,c^{11}\,d^4-3670016\,a^3\,b^5\,c^{12}\,d^3+1835008\,a^2\,b^6\,c^{13}\,d^2-524288\,a\,b^7\,c^{14}\,d+65536\,b^8\,c^{15}}\right)}^{1/4}\,\left(\frac{\frac{81\,a^4\,b^7\,d^{10}}{16}-\frac{675\,a^3\,b^8\,c\,d^9}{16}+\frac{1971\,a^2\,b^9\,c^2\,d^8}{16}-\frac{2145\,a\,b^{10}\,c^3\,d^7}{16}+28\,b^{11}\,c^4\,d^6}{-a^3\,c^4\,d^3+3\,a^2\,b\,c^5\,d^2-3\,a\,b^2\,c^6\,d+b^3\,c^7}+{\left(-\frac{81\,a^4\,d^7-756\,a^3\,b\,c\,d^6+2646\,a^2\,b^2\,c^2\,d^5-4116\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{65536\,a^8\,c^7\,d^8-524288\,a^7\,b\,c^8\,d^7+1835008\,a^6\,b^2\,c^9\,d^6-3670016\,a^5\,b^3\,c^{10}\,d^5+4587520\,a^4\,b^4\,c^{11}\,d^4-3670016\,a^3\,b^5\,c^{12}\,d^3+1835008\,a^2\,b^6\,c^{13}\,d^2-524288\,a\,b^7\,c^{14}\,d+65536\,b^8\,c^{15}}\right)}^{3/4}\,\left(\frac{{\left(-\frac{81\,a^4\,d^7-756\,a^3\,b\,c\,d^6+2646\,a^2\,b^2\,c^2\,d^5-4116\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{65536\,a^8\,c^7\,d^8-524288\,a^7\,b\,c^8\,d^7+1835008\,a^6\,b^2\,c^9\,d^6-3670016\,a^5\,b^3\,c^{10}\,d^5+4587520\,a^4\,b^4\,c^{11}\,d^4-3670016\,a^3\,b^5\,c^{12}\,d^3+1835008\,a^2\,b^6\,c^{13}\,d^2-524288\,a\,b^7\,c^{14}\,d+65536\,b^8\,c^{15}}\right)}^{1/4}\,\left(3072\,a^{11}\,b^4\,c^4\,d^{14}-28672\,a^{10}\,b^5\,c^5\,d^{13}+114688\,a^9\,b^6\,c^6\,d^{12}-253952\,a^8\,b^7\,c^7\,d^{11}+329728\,a^7\,b^8\,c^8\,d^{10}-229376\,a^6\,b^9\,c^9\,d^9+28672\,a^5\,b^{10}\,c^{10}\,d^8+90112\,a^4\,b^{11}\,c^{11}\,d^7-78848\,a^3\,b^{12}\,c^{12}\,d^6+28672\,a^2\,b^{13}\,c^{13}\,d^5-4096\,a\,b^{14}\,c^{14}\,d^4\right)}{-a^3\,c^4\,d^3+3\,a^2\,b\,c^5\,d^2-3\,a\,b^2\,c^6\,d+b^3\,c^7}-\frac{x\,\left(36864\,a^{13}\,b^4\,c^2\,d^{17}-466944\,a^{12}\,b^5\,c^3\,d^{16}+2609152\,a^{11}\,b^6\,c^4\,d^{15}-8486912\,a^{10}\,b^7\,c^5\,d^{14}+17833984\,a^9\,b^8\,c^6\,d^{13}-25280512\,a^8\,b^9\,c^7\,d^{12}+24190976\,a^7\,b^{10}\,c^8\,d^{11}-14516224\,a^6\,b^{11}\,c^9\,d^{10}+3362816\,a^5\,b^{12}\,c^{10}\,d^9+2809856\,a^4\,b^{13}\,c^{11}\,d^8-3469312\,a^3\,b^{14}\,c^{12}\,d^7+1835008\,a^2\,b^{15}\,c^{13}\,d^6-524288\,a\,b^{16}\,c^{14}\,d^5+65536\,b^{17}\,c^{15}\,d^4\right)}{64\,\left(a^6\,c^4\,d^6-6\,a^5\,b\,c^5\,d^5+15\,a^4\,b^2\,c^6\,d^4-20\,a^3\,b^3\,c^7\,d^3+15\,a^2\,b^4\,c^8\,d^2-6\,a\,b^5\,c^9\,d+b^6\,c^{10}\right)}\right)\right)-\frac{x\,\left(81\,a^4\,b^9\,d^{11}-756\,a^3\,b^{10}\,c\,d^{10}+2790\,a^2\,b^{11}\,c^2\,d^9-4788\,a\,b^{12}\,c^3\,d^8+3185\,b^{13}\,c^4\,d^7\right)}{64\,\left(a^6\,c^4\,d^6-6\,a^5\,b\,c^5\,d^5+15\,a^4\,b^2\,c^6\,d^4-20\,a^3\,b^3\,c^7\,d^3+15\,a^2\,b^4\,c^8\,d^2-6\,a\,b^5\,c^9\,d+b^6\,c^{10}\right)}\right)+{\left(-\frac{81\,a^4\,d^7-756\,a^3\,b\,c\,d^6+2646\,a^2\,b^2\,c^2\,d^5-4116\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{65536\,a^8\,c^7\,d^8-524288\,a^7\,b\,c^8\,d^7+1835008\,a^6\,b^2\,c^9\,d^6-3670016\,a^5\,b^3\,c^{10}\,d^5+4587520\,a^4\,b^4\,c^{11}\,d^4-3670016\,a^3\,b^5\,c^{12}\,d^3+1835008\,a^2\,b^6\,c^{13}\,d^2-524288\,a\,b^7\,c^{14}\,d+65536\,b^8\,c^{15}}\right)}^{1/4}\,\left({\left(-\frac{81\,a^4\,d^7-756\,a^3\,b\,c\,d^6+2646\,a^2\,b^2\,c^2\,d^5-4116\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{65536\,a^8\,c^7\,d^8-524288\,a^7\,b\,c^8\,d^7+1835008\,a^6\,b^2\,c^9\,d^6-3670016\,a^5\,b^3\,c^{10}\,d^5+4587520\,a^4\,b^4\,c^{11}\,d^4-3670016\,a^3\,b^5\,c^{12}\,d^3+1835008\,a^2\,b^6\,c^{13}\,d^2-524288\,a\,b^7\,c^{14}\,d+65536\,b^8\,c^{15}}\right)}^{1/4}\,\left(\frac{\frac{81\,a^4\,b^7\,d^{10}}{16}-\frac{675\,a^3\,b^8\,c\,d^9}{16}+\frac{1971\,a^2\,b^9\,c^2\,d^8}{16}-\frac{2145\,a\,b^{10}\,c^3\,d^7}{16}+28\,b^{11}\,c^4\,d^6}{-a^3\,c^4\,d^3+3\,a^2\,b\,c^5\,d^2-3\,a\,b^2\,c^6\,d+b^3\,c^7}+{\left(-\frac{81\,a^4\,d^7-756\,a^3\,b\,c\,d^6+2646\,a^2\,b^2\,c^2\,d^5-4116\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{65536\,a^8\,c^7\,d^8-524288\,a^7\,b\,c^8\,d^7+1835008\,a^6\,b^2\,c^9\,d^6-3670016\,a^5\,b^3\,c^{10}\,d^5+4587520\,a^4\,b^4\,c^{11}\,d^4-3670016\,a^3\,b^5\,c^{12}\,d^3+1835008\,a^2\,b^6\,c^{13}\,d^2-524288\,a\,b^7\,c^{14}\,d+65536\,b^8\,c^{15}}\right)}^{3/4}\,\left(\frac{{\left(-\frac{81\,a^4\,d^7-756\,a^3\,b\,c\,d^6+2646\,a^2\,b^2\,c^2\,d^5-4116\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{65536\,a^8\,c^7\,d^8-524288\,a^7\,b\,c^8\,d^7+1835008\,a^6\,b^2\,c^9\,d^6-3670016\,a^5\,b^3\,c^{10}\,d^5+4587520\,a^4\,b^4\,c^{11}\,d^4-3670016\,a^3\,b^5\,c^{12}\,d^3+1835008\,a^2\,b^6\,c^{13}\,d^2-524288\,a\,b^7\,c^{14}\,d+65536\,b^8\,c^{15}}\right)}^{1/4}\,\left(3072\,a^{11}\,b^4\,c^4\,d^{14}-28672\,a^{10}\,b^5\,c^5\,d^{13}+114688\,a^9\,b^6\,c^6\,d^{12}-253952\,a^8\,b^7\,c^7\,d^{11}+329728\,a^7\,b^8\,c^8\,d^{10}-229376\,a^6\,b^9\,c^9\,d^9+28672\,a^5\,b^{10}\,c^{10}\,d^8+90112\,a^4\,b^{11}\,c^{11}\,d^7-78848\,a^3\,b^{12}\,c^{12}\,d^6+28672\,a^2\,b^{13}\,c^{13}\,d^5-4096\,a\,b^{14}\,c^{14}\,d^4\right)}{-a^3\,c^4\,d^3+3\,a^2\,b\,c^5\,d^2-3\,a\,b^2\,c^6\,d+b^3\,c^7}+\frac{x\,\left(36864\,a^{13}\,b^4\,c^2\,d^{17}-466944\,a^{12}\,b^5\,c^3\,d^{16}+2609152\,a^{11}\,b^6\,c^4\,d^{15}-8486912\,a^{10}\,b^7\,c^5\,d^{14}+17833984\,a^9\,b^8\,c^6\,d^{13}-25280512\,a^8\,b^9\,c^7\,d^{12}+24190976\,a^7\,b^{10}\,c^8\,d^{11}-14516224\,a^6\,b^{11}\,c^9\,d^{10}+3362816\,a^5\,b^{12}\,c^{10}\,d^9+2809856\,a^4\,b^{13}\,c^{11}\,d^8-3469312\,a^3\,b^{14}\,c^{12}\,d^7+1835008\,a^2\,b^{15}\,c^{13}\,d^6-524288\,a\,b^{16}\,c^{14}\,d^5+65536\,b^{17}\,c^{15}\,d^4\right)}{64\,\left(a^6\,c^4\,d^6-6\,a^5\,b\,c^5\,d^5+15\,a^4\,b^2\,c^6\,d^4-20\,a^3\,b^3\,c^7\,d^3+15\,a^2\,b^4\,c^8\,d^2-6\,a\,b^5\,c^9\,d+b^6\,c^{10}\right)}\right)\right)+\frac{x\,\left(81\,a^4\,b^9\,d^{11}-756\,a^3\,b^{10}\,c\,d^{10}+2790\,a^2\,b^{11}\,c^2\,d^9-4788\,a\,b^{12}\,c^3\,d^8+3185\,b^{13}\,c^4\,d^7\right)}{64\,\left(a^6\,c^4\,d^6-6\,a^5\,b\,c^5\,d^5+15\,a^4\,b^2\,c^6\,d^4-20\,a^3\,b^3\,c^7\,d^3+15\,a^2\,b^4\,c^8\,d^2-6\,a\,b^5\,c^9\,d+b^6\,c^{10}\right)}\right)}\right)\,{\left(-\frac{81\,a^4\,d^7-756\,a^3\,b\,c\,d^6+2646\,a^2\,b^2\,c^2\,d^5-4116\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{65536\,a^8\,c^7\,d^8-524288\,a^7\,b\,c^8\,d^7+1835008\,a^6\,b^2\,c^9\,d^6-3670016\,a^5\,b^3\,c^{10}\,d^5+4587520\,a^4\,b^4\,c^{11}\,d^4-3670016\,a^3\,b^5\,c^{12}\,d^3+1835008\,a^2\,b^6\,c^{13}\,d^2-524288\,a\,b^7\,c^{14}\,d+65536\,b^8\,c^{15}}\right)}^{1/4}\,2{}\mathrm{i}-\mathrm{atan}\left(\frac{{\left(-\frac{b^7}{256\,a^{11}\,d^8-2048\,a^{10}\,b\,c\,d^7+7168\,a^9\,b^2\,c^2\,d^6-14336\,a^8\,b^3\,c^3\,d^5+17920\,a^7\,b^4\,c^4\,d^4-14336\,a^6\,b^5\,c^5\,d^3+7168\,a^5\,b^6\,c^6\,d^2-2048\,a^4\,b^7\,c^7\,d+256\,a^3\,b^8\,c^8}\right)}^{1/4}\,\left({\left(-\frac{b^7}{256\,a^{11}\,d^8-2048\,a^{10}\,b\,c\,d^7+7168\,a^9\,b^2\,c^2\,d^6-14336\,a^8\,b^3\,c^3\,d^5+17920\,a^7\,b^4\,c^4\,d^4-14336\,a^6\,b^5\,c^5\,d^3+7168\,a^5\,b^6\,c^6\,d^2-2048\,a^4\,b^7\,c^7\,d+256\,a^3\,b^8\,c^8}\right)}^{1/4}\,\left({\left(-\frac{b^7}{256\,a^{11}\,d^8-2048\,a^{10}\,b\,c\,d^7+7168\,a^9\,b^2\,c^2\,d^6-14336\,a^8\,b^3\,c^3\,d^5+17920\,a^7\,b^4\,c^4\,d^4-14336\,a^6\,b^5\,c^5\,d^3+7168\,a^5\,b^6\,c^6\,d^2-2048\,a^4\,b^7\,c^7\,d+256\,a^3\,b^8\,c^8}\right)}^{3/4}\,\left(\frac{{\left(-\frac{b^7}{256\,a^{11}\,d^8-2048\,a^{10}\,b\,c\,d^7+7168\,a^9\,b^2\,c^2\,d^6-14336\,a^8\,b^3\,c^3\,d^5+17920\,a^7\,b^4\,c^4\,d^4-14336\,a^6\,b^5\,c^5\,d^3+7168\,a^5\,b^6\,c^6\,d^2-2048\,a^4\,b^7\,c^7\,d+256\,a^3\,b^8\,c^8}\right)}^{1/4}\,\left(3072\,a^{11}\,b^4\,c^4\,d^{14}-28672\,a^{10}\,b^5\,c^5\,d^{13}+114688\,a^9\,b^6\,c^6\,d^{12}-253952\,a^8\,b^7\,c^7\,d^{11}+329728\,a^7\,b^8\,c^8\,d^{10}-229376\,a^6\,b^9\,c^9\,d^9+28672\,a^5\,b^{10}\,c^{10}\,d^8+90112\,a^4\,b^{11}\,c^{11}\,d^7-78848\,a^3\,b^{12}\,c^{12}\,d^6+28672\,a^2\,b^{13}\,c^{13}\,d^5-4096\,a\,b^{14}\,c^{14}\,d^4\right)}{-a^3\,c^4\,d^3+3\,a^2\,b\,c^5\,d^2-3\,a\,b^2\,c^6\,d+b^3\,c^7}-\frac{x\,\left(36864\,a^{13}\,b^4\,c^2\,d^{17}-466944\,a^{12}\,b^5\,c^3\,d^{16}+2609152\,a^{11}\,b^6\,c^4\,d^{15}-8486912\,a^{10}\,b^7\,c^5\,d^{14}+17833984\,a^9\,b^8\,c^6\,d^{13}-25280512\,a^8\,b^9\,c^7\,d^{12}+24190976\,a^7\,b^{10}\,c^8\,d^{11}-14516224\,a^6\,b^{11}\,c^9\,d^{10}+3362816\,a^5\,b^{12}\,c^{10}\,d^9+2809856\,a^4\,b^{13}\,c^{11}\,d^8-3469312\,a^3\,b^{14}\,c^{12}\,d^7+1835008\,a^2\,b^{15}\,c^{13}\,d^6-524288\,a\,b^{16}\,c^{14}\,d^5+65536\,b^{17}\,c^{15}\,d^4\right)}{64\,\left(a^6\,c^4\,d^6-6\,a^5\,b\,c^5\,d^5+15\,a^4\,b^2\,c^6\,d^4-20\,a^3\,b^3\,c^7\,d^3+15\,a^2\,b^4\,c^8\,d^2-6\,a\,b^5\,c^9\,d+b^6\,c^{10}\right)}\right)+\frac{\frac{81\,a^4\,b^7\,d^{10}}{16}-\frac{675\,a^3\,b^8\,c\,d^9}{16}+\frac{1971\,a^2\,b^9\,c^2\,d^8}{16}-\frac{2145\,a\,b^{10}\,c^3\,d^7}{16}+28\,b^{11}\,c^4\,d^6}{-a^3\,c^4\,d^3+3\,a^2\,b\,c^5\,d^2-3\,a\,b^2\,c^6\,d+b^3\,c^7}\right)\,1{}\mathrm{i}-\frac{x\,\left(81\,a^4\,b^9\,d^{11}-756\,a^3\,b^{10}\,c\,d^{10}+2790\,a^2\,b^{11}\,c^2\,d^9-4788\,a\,b^{12}\,c^3\,d^8+3185\,b^{13}\,c^4\,d^7\right)\,1{}\mathrm{i}}{64\,\left(a^6\,c^4\,d^6-6\,a^5\,b\,c^5\,d^5+15\,a^4\,b^2\,c^6\,d^4-20\,a^3\,b^3\,c^7\,d^3+15\,a^2\,b^4\,c^8\,d^2-6\,a\,b^5\,c^9\,d+b^6\,c^{10}\right)}\right)-{\left(-\frac{b^7}{256\,a^{11}\,d^8-2048\,a^{10}\,b\,c\,d^7+7168\,a^9\,b^2\,c^2\,d^6-14336\,a^8\,b^3\,c^3\,d^5+17920\,a^7\,b^4\,c^4\,d^4-14336\,a^6\,b^5\,c^5\,d^3+7168\,a^5\,b^6\,c^6\,d^2-2048\,a^4\,b^7\,c^7\,d+256\,a^3\,b^8\,c^8}\right)}^{1/4}\,\left({\left(-\frac{b^7}{256\,a^{11}\,d^8-2048\,a^{10}\,b\,c\,d^7+7168\,a^9\,b^2\,c^2\,d^6-14336\,a^8\,b^3\,c^3\,d^5+17920\,a^7\,b^4\,c^4\,d^4-14336\,a^6\,b^5\,c^5\,d^3+7168\,a^5\,b^6\,c^6\,d^2-2048\,a^4\,b^7\,c^7\,d+256\,a^3\,b^8\,c^8}\right)}^{1/4}\,\left({\left(-\frac{b^7}{256\,a^{11}\,d^8-2048\,a^{10}\,b\,c\,d^7+7168\,a^9\,b^2\,c^2\,d^6-14336\,a^8\,b^3\,c^3\,d^5+17920\,a^7\,b^4\,c^4\,d^4-14336\,a^6\,b^5\,c^5\,d^3+7168\,a^5\,b^6\,c^6\,d^2-2048\,a^4\,b^7\,c^7\,d+256\,a^3\,b^8\,c^8}\right)}^{3/4}\,\left(\frac{{\left(-\frac{b^7}{256\,a^{11}\,d^8-2048\,a^{10}\,b\,c\,d^7+7168\,a^9\,b^2\,c^2\,d^6-14336\,a^8\,b^3\,c^3\,d^5+17920\,a^7\,b^4\,c^4\,d^4-14336\,a^6\,b^5\,c^5\,d^3+7168\,a^5\,b^6\,c^6\,d^2-2048\,a^4\,b^7\,c^7\,d+256\,a^3\,b^8\,c^8}\right)}^{1/4}\,\left(3072\,a^{11}\,b^4\,c^4\,d^{14}-28672\,a^{10}\,b^5\,c^5\,d^{13}+114688\,a^9\,b^6\,c^6\,d^{12}-253952\,a^8\,b^7\,c^7\,d^{11}+329728\,a^7\,b^8\,c^8\,d^{10}-229376\,a^6\,b^9\,c^9\,d^9+28672\,a^5\,b^{10}\,c^{10}\,d^8+90112\,a^4\,b^{11}\,c^{11}\,d^7-78848\,a^3\,b^{12}\,c^{12}\,d^6+28672\,a^2\,b^{13}\,c^{13}\,d^5-4096\,a\,b^{14}\,c^{14}\,d^4\right)}{-a^3\,c^4\,d^3+3\,a^2\,b\,c^5\,d^2-3\,a\,b^2\,c^6\,d+b^3\,c^7}+\frac{x\,\left(36864\,a^{13}\,b^4\,c^2\,d^{17}-466944\,a^{12}\,b^5\,c^3\,d^{16}+2609152\,a^{11}\,b^6\,c^4\,d^{15}-8486912\,a^{10}\,b^7\,c^5\,d^{14}+17833984\,a^9\,b^8\,c^6\,d^{13}-25280512\,a^8\,b^9\,c^7\,d^{12}+24190976\,a^7\,b^{10}\,c^8\,d^{11}-14516224\,a^6\,b^{11}\,c^9\,d^{10}+3362816\,a^5\,b^{12}\,c^{10}\,d^9+2809856\,a^4\,b^{13}\,c^{11}\,d^8-3469312\,a^3\,b^{14}\,c^{12}\,d^7+1835008\,a^2\,b^{15}\,c^{13}\,d^6-524288\,a\,b^{16}\,c^{14}\,d^5+65536\,b^{17}\,c^{15}\,d^4\right)}{64\,\left(a^6\,c^4\,d^6-6\,a^5\,b\,c^5\,d^5+15\,a^4\,b^2\,c^6\,d^4-20\,a^3\,b^3\,c^7\,d^3+15\,a^2\,b^4\,c^8\,d^2-6\,a\,b^5\,c^9\,d+b^6\,c^{10}\right)}\right)+\frac{\frac{81\,a^4\,b^7\,d^{10}}{16}-\frac{675\,a^3\,b^8\,c\,d^9}{16}+\frac{1971\,a^2\,b^9\,c^2\,d^8}{16}-\frac{2145\,a\,b^{10}\,c^3\,d^7}{16}+28\,b^{11}\,c^4\,d^6}{-a^3\,c^4\,d^3+3\,a^2\,b\,c^5\,d^2-3\,a\,b^2\,c^6\,d+b^3\,c^7}\right)\,1{}\mathrm{i}+\frac{x\,\left(81\,a^4\,b^9\,d^{11}-756\,a^3\,b^{10}\,c\,d^{10}+2790\,a^2\,b^{11}\,c^2\,d^9-4788\,a\,b^{12}\,c^3\,d^8+3185\,b^{13}\,c^4\,d^7\right)\,1{}\mathrm{i}}{64\,\left(a^6\,c^4\,d^6-6\,a^5\,b\,c^5\,d^5+15\,a^4\,b^2\,c^6\,d^4-20\,a^3\,b^3\,c^7\,d^3+15\,a^2\,b^4\,c^8\,d^2-6\,a\,b^5\,c^9\,d+b^6\,c^{10}\right)}\right)}{{\left(-\frac{b^7}{256\,a^{11}\,d^8-2048\,a^{10}\,b\,c\,d^7+7168\,a^9\,b^2\,c^2\,d^6-14336\,a^8\,b^3\,c^3\,d^5+17920\,a^7\,b^4\,c^4\,d^4-14336\,a^6\,b^5\,c^5\,d^3+7168\,a^5\,b^6\,c^6\,d^2-2048\,a^4\,b^7\,c^7\,d+256\,a^3\,b^8\,c^8}\right)}^{1/4}\,\left({\left(-\frac{b^7}{256\,a^{11}\,d^8-2048\,a^{10}\,b\,c\,d^7+7168\,a^9\,b^2\,c^2\,d^6-14336\,a^8\,b^3\,c^3\,d^5+17920\,a^7\,b^4\,c^4\,d^4-14336\,a^6\,b^5\,c^5\,d^3+7168\,a^5\,b^6\,c^6\,d^2-2048\,a^4\,b^7\,c^7\,d+256\,a^3\,b^8\,c^8}\right)}^{1/4}\,\left({\left(-\frac{b^7}{256\,a^{11}\,d^8-2048\,a^{10}\,b\,c\,d^7+7168\,a^9\,b^2\,c^2\,d^6-14336\,a^8\,b^3\,c^3\,d^5+17920\,a^7\,b^4\,c^4\,d^4-14336\,a^6\,b^5\,c^5\,d^3+7168\,a^5\,b^6\,c^6\,d^2-2048\,a^4\,b^7\,c^7\,d+256\,a^3\,b^8\,c^8}\right)}^{3/4}\,\left(\frac{{\left(-\frac{b^7}{256\,a^{11}\,d^8-2048\,a^{10}\,b\,c\,d^7+7168\,a^9\,b^2\,c^2\,d^6-14336\,a^8\,b^3\,c^3\,d^5+17920\,a^7\,b^4\,c^4\,d^4-14336\,a^6\,b^5\,c^5\,d^3+7168\,a^5\,b^6\,c^6\,d^2-2048\,a^4\,b^7\,c^7\,d+256\,a^3\,b^8\,c^8}\right)}^{1/4}\,\left(3072\,a^{11}\,b^4\,c^4\,d^{14}-28672\,a^{10}\,b^5\,c^5\,d^{13}+114688\,a^9\,b^6\,c^6\,d^{12}-253952\,a^8\,b^7\,c^7\,d^{11}+329728\,a^7\,b^8\,c^8\,d^{10}-229376\,a^6\,b^9\,c^9\,d^9+28672\,a^5\,b^{10}\,c^{10}\,d^8+90112\,a^4\,b^{11}\,c^{11}\,d^7-78848\,a^3\,b^{12}\,c^{12}\,d^6+28672\,a^2\,b^{13}\,c^{13}\,d^5-4096\,a\,b^{14}\,c^{14}\,d^4\right)}{-a^3\,c^4\,d^3+3\,a^2\,b\,c^5\,d^2-3\,a\,b^2\,c^6\,d+b^3\,c^7}-\frac{x\,\left(36864\,a^{13}\,b^4\,c^2\,d^{17}-466944\,a^{12}\,b^5\,c^3\,d^{16}+2609152\,a^{11}\,b^6\,c^4\,d^{15}-8486912\,a^{10}\,b^7\,c^5\,d^{14}+17833984\,a^9\,b^8\,c^6\,d^{13}-25280512\,a^8\,b^9\,c^7\,d^{12}+24190976\,a^7\,b^{10}\,c^8\,d^{11}-14516224\,a^6\,b^{11}\,c^9\,d^{10}+3362816\,a^5\,b^{12}\,c^{10}\,d^9+2809856\,a^4\,b^{13}\,c^{11}\,d^8-3469312\,a^3\,b^{14}\,c^{12}\,d^7+1835008\,a^2\,b^{15}\,c^{13}\,d^6-524288\,a\,b^{16}\,c^{14}\,d^5+65536\,b^{17}\,c^{15}\,d^4\right)}{64\,\left(a^6\,c^4\,d^6-6\,a^5\,b\,c^5\,d^5+15\,a^4\,b^2\,c^6\,d^4-20\,a^3\,b^3\,c^7\,d^3+15\,a^2\,b^4\,c^8\,d^2-6\,a\,b^5\,c^9\,d+b^6\,c^{10}\right)}\right)+\frac{\frac{81\,a^4\,b^7\,d^{10}}{16}-\frac{675\,a^3\,b^8\,c\,d^9}{16}+\frac{1971\,a^2\,b^9\,c^2\,d^8}{16}-\frac{2145\,a\,b^{10}\,c^3\,d^7}{16}+28\,b^{11}\,c^4\,d^6}{-a^3\,c^4\,d^3+3\,a^2\,b\,c^5\,d^2-3\,a\,b^2\,c^6\,d+b^3\,c^7}\right)-\frac{x\,\left(81\,a^4\,b^9\,d^{11}-756\,a^3\,b^{10}\,c\,d^{10}+2790\,a^2\,b^{11}\,c^2\,d^9-4788\,a\,b^{12}\,c^3\,d^8+3185\,b^{13}\,c^4\,d^7\right)}{64\,\left(a^6\,c^4\,d^6-6\,a^5\,b\,c^5\,d^5+15\,a^4\,b^2\,c^6\,d^4-20\,a^3\,b^3\,c^7\,d^3+15\,a^2\,b^4\,c^8\,d^2-6\,a\,b^5\,c^9\,d+b^6\,c^{10}\right)}\right)+{\left(-\frac{b^7}{256\,a^{11}\,d^8-2048\,a^{10}\,b\,c\,d^7+7168\,a^9\,b^2\,c^2\,d^6-14336\,a^8\,b^3\,c^3\,d^5+17920\,a^7\,b^4\,c^4\,d^4-14336\,a^6\,b^5\,c^5\,d^3+7168\,a^5\,b^6\,c^6\,d^2-2048\,a^4\,b^7\,c^7\,d+256\,a^3\,b^8\,c^8}\right)}^{1/4}\,\left({\left(-\frac{b^7}{256\,a^{11}\,d^8-2048\,a^{10}\,b\,c\,d^7+7168\,a^9\,b^2\,c^2\,d^6-14336\,a^8\,b^3\,c^3\,d^5+17920\,a^7\,b^4\,c^4\,d^4-14336\,a^6\,b^5\,c^5\,d^3+7168\,a^5\,b^6\,c^6\,d^2-2048\,a^4\,b^7\,c^7\,d+256\,a^3\,b^8\,c^8}\right)}^{1/4}\,\left({\left(-\frac{b^7}{256\,a^{11}\,d^8-2048\,a^{10}\,b\,c\,d^7+7168\,a^9\,b^2\,c^2\,d^6-14336\,a^8\,b^3\,c^3\,d^5+17920\,a^7\,b^4\,c^4\,d^4-14336\,a^6\,b^5\,c^5\,d^3+7168\,a^5\,b^6\,c^6\,d^2-2048\,a^4\,b^7\,c^7\,d+256\,a^3\,b^8\,c^8}\right)}^{3/4}\,\left(\frac{{\left(-\frac{b^7}{256\,a^{11}\,d^8-2048\,a^{10}\,b\,c\,d^7+7168\,a^9\,b^2\,c^2\,d^6-14336\,a^8\,b^3\,c^3\,d^5+17920\,a^7\,b^4\,c^4\,d^4-14336\,a^6\,b^5\,c^5\,d^3+7168\,a^5\,b^6\,c^6\,d^2-2048\,a^4\,b^7\,c^7\,d+256\,a^3\,b^8\,c^8}\right)}^{1/4}\,\left(3072\,a^{11}\,b^4\,c^4\,d^{14}-28672\,a^{10}\,b^5\,c^5\,d^{13}+114688\,a^9\,b^6\,c^6\,d^{12}-253952\,a^8\,b^7\,c^7\,d^{11}+329728\,a^7\,b^8\,c^8\,d^{10}-229376\,a^6\,b^9\,c^9\,d^9+28672\,a^5\,b^{10}\,c^{10}\,d^8+90112\,a^4\,b^{11}\,c^{11}\,d^7-78848\,a^3\,b^{12}\,c^{12}\,d^6+28672\,a^2\,b^{13}\,c^{13}\,d^5-4096\,a\,b^{14}\,c^{14}\,d^4\right)}{-a^3\,c^4\,d^3+3\,a^2\,b\,c^5\,d^2-3\,a\,b^2\,c^6\,d+b^3\,c^7}+\frac{x\,\left(36864\,a^{13}\,b^4\,c^2\,d^{17}-466944\,a^{12}\,b^5\,c^3\,d^{16}+2609152\,a^{11}\,b^6\,c^4\,d^{15}-8486912\,a^{10}\,b^7\,c^5\,d^{14}+17833984\,a^9\,b^8\,c^6\,d^{13}-25280512\,a^8\,b^9\,c^7\,d^{12}+24190976\,a^7\,b^{10}\,c^8\,d^{11}-14516224\,a^6\,b^{11}\,c^9\,d^{10}+3362816\,a^5\,b^{12}\,c^{10}\,d^9+2809856\,a^4\,b^{13}\,c^{11}\,d^8-3469312\,a^3\,b^{14}\,c^{12}\,d^7+1835008\,a^2\,b^{15}\,c^{13}\,d^6-524288\,a\,b^{16}\,c^{14}\,d^5+65536\,b^{17}\,c^{15}\,d^4\right)}{64\,\left(a^6\,c^4\,d^6-6\,a^5\,b\,c^5\,d^5+15\,a^4\,b^2\,c^6\,d^4-20\,a^3\,b^3\,c^7\,d^3+15\,a^2\,b^4\,c^8\,d^2-6\,a\,b^5\,c^9\,d+b^6\,c^{10}\right)}\right)+\frac{\frac{81\,a^4\,b^7\,d^{10}}{16}-\frac{675\,a^3\,b^8\,c\,d^9}{16}+\frac{1971\,a^2\,b^9\,c^2\,d^8}{16}-\frac{2145\,a\,b^{10}\,c^3\,d^7}{16}+28\,b^{11}\,c^4\,d^6}{-a^3\,c^4\,d^3+3\,a^2\,b\,c^5\,d^2-3\,a\,b^2\,c^6\,d+b^3\,c^7}\right)+\frac{x\,\left(81\,a^4\,b^9\,d^{11}-756\,a^3\,b^{10}\,c\,d^{10}+2790\,a^2\,b^{11}\,c^2\,d^9-4788\,a\,b^{12}\,c^3\,d^8+3185\,b^{13}\,c^4\,d^7\right)}{64\,\left(a^6\,c^4\,d^6-6\,a^5\,b\,c^5\,d^5+15\,a^4\,b^2\,c^6\,d^4-20\,a^3\,b^3\,c^7\,d^3+15\,a^2\,b^4\,c^8\,d^2-6\,a\,b^5\,c^9\,d+b^6\,c^{10}\right)}\right)}\right)\,{\left(-\frac{b^7}{256\,a^{11}\,d^8-2048\,a^{10}\,b\,c\,d^7+7168\,a^9\,b^2\,c^2\,d^6-14336\,a^8\,b^3\,c^3\,d^5+17920\,a^7\,b^4\,c^4\,d^4-14336\,a^6\,b^5\,c^5\,d^3+7168\,a^5\,b^6\,c^6\,d^2-2048\,a^4\,b^7\,c^7\,d+256\,a^3\,b^8\,c^8}\right)}^{1/4}\,2{}\mathrm{i}","Not used",1,"2*atan(((-(81*a^4*d^7 + 2401*b^4*c^4*d^3 - 4116*a*b^3*c^3*d^4 + 2646*a^2*b^2*c^2*d^5 - 756*a^3*b*c*d^6)/(65536*b^8*c^15 + 65536*a^8*c^7*d^8 - 524288*a^7*b*c^8*d^7 + 1835008*a^2*b^6*c^13*d^2 - 3670016*a^3*b^5*c^12*d^3 + 4587520*a^4*b^4*c^11*d^4 - 3670016*a^5*b^3*c^10*d^5 + 1835008*a^6*b^2*c^9*d^6 - 524288*a*b^7*c^14*d))^(1/4)*((-(81*a^4*d^7 + 2401*b^4*c^4*d^3 - 4116*a*b^3*c^3*d^4 + 2646*a^2*b^2*c^2*d^5 - 756*a^3*b*c*d^6)/(65536*b^8*c^15 + 65536*a^8*c^7*d^8 - 524288*a^7*b*c^8*d^7 + 1835008*a^2*b^6*c^13*d^2 - 3670016*a^3*b^5*c^12*d^3 + 4587520*a^4*b^4*c^11*d^4 - 3670016*a^5*b^3*c^10*d^5 + 1835008*a^6*b^2*c^9*d^6 - 524288*a*b^7*c^14*d))^(1/4)*((((81*a^4*b^7*d^10)/16 + 28*b^11*c^4*d^6 - (2145*a*b^10*c^3*d^7)/16 - (675*a^3*b^8*c*d^9)/16 + (1971*a^2*b^9*c^2*d^8)/16)*1i)/(b^3*c^7 - a^3*c^4*d^3 + 3*a^2*b*c^5*d^2 - 3*a*b^2*c^6*d) + (-(81*a^4*d^7 + 2401*b^4*c^4*d^3 - 4116*a*b^3*c^3*d^4 + 2646*a^2*b^2*c^2*d^5 - 756*a^3*b*c*d^6)/(65536*b^8*c^15 + 65536*a^8*c^7*d^8 - 524288*a^7*b*c^8*d^7 + 1835008*a^2*b^6*c^13*d^2 - 3670016*a^3*b^5*c^12*d^3 + 4587520*a^4*b^4*c^11*d^4 - 3670016*a^5*b^3*c^10*d^5 + 1835008*a^6*b^2*c^9*d^6 - 524288*a*b^7*c^14*d))^(3/4)*(((-(81*a^4*d^7 + 2401*b^4*c^4*d^3 - 4116*a*b^3*c^3*d^4 + 2646*a^2*b^2*c^2*d^5 - 756*a^3*b*c*d^6)/(65536*b^8*c^15 + 65536*a^8*c^7*d^8 - 524288*a^7*b*c^8*d^7 + 1835008*a^2*b^6*c^13*d^2 - 3670016*a^3*b^5*c^12*d^3 + 4587520*a^4*b^4*c^11*d^4 - 3670016*a^5*b^3*c^10*d^5 + 1835008*a^6*b^2*c^9*d^6 - 524288*a*b^7*c^14*d))^(1/4)*(28672*a^2*b^13*c^13*d^5 - 4096*a*b^14*c^14*d^4 - 78848*a^3*b^12*c^12*d^6 + 90112*a^4*b^11*c^11*d^7 + 28672*a^5*b^10*c^10*d^8 - 229376*a^6*b^9*c^9*d^9 + 329728*a^7*b^8*c^8*d^10 - 253952*a^8*b^7*c^7*d^11 + 114688*a^9*b^6*c^6*d^12 - 28672*a^10*b^5*c^5*d^13 + 3072*a^11*b^4*c^4*d^14))/(b^3*c^7 - a^3*c^4*d^3 + 3*a^2*b*c^5*d^2 - 3*a*b^2*c^6*d) - (x*(65536*b^17*c^15*d^4 - 524288*a*b^16*c^14*d^5 + 1835008*a^2*b^15*c^13*d^6 - 3469312*a^3*b^14*c^12*d^7 + 2809856*a^4*b^13*c^11*d^8 + 3362816*a^5*b^12*c^10*d^9 - 14516224*a^6*b^11*c^9*d^10 + 24190976*a^7*b^10*c^8*d^11 - 25280512*a^8*b^9*c^7*d^12 + 17833984*a^9*b^8*c^6*d^13 - 8486912*a^10*b^7*c^5*d^14 + 2609152*a^11*b^6*c^4*d^15 - 466944*a^12*b^5*c^3*d^16 + 36864*a^13*b^4*c^2*d^17)*1i)/(64*(b^6*c^10 + a^6*c^4*d^6 - 6*a^5*b*c^5*d^5 + 15*a^2*b^4*c^8*d^2 - 20*a^3*b^3*c^7*d^3 + 15*a^4*b^2*c^6*d^4 - 6*a*b^5*c^9*d)))*1i) + (x*(81*a^4*b^9*d^11 + 3185*b^13*c^4*d^7 - 4788*a*b^12*c^3*d^8 - 756*a^3*b^10*c*d^10 + 2790*a^2*b^11*c^2*d^9))/(64*(b^6*c^10 + a^6*c^4*d^6 - 6*a^5*b*c^5*d^5 + 15*a^2*b^4*c^8*d^2 - 20*a^3*b^3*c^7*d^3 + 15*a^4*b^2*c^6*d^4 - 6*a*b^5*c^9*d))) - (-(81*a^4*d^7 + 2401*b^4*c^4*d^3 - 4116*a*b^3*c^3*d^4 + 2646*a^2*b^2*c^2*d^5 - 756*a^3*b*c*d^6)/(65536*b^8*c^15 + 65536*a^8*c^7*d^8 - 524288*a^7*b*c^8*d^7 + 1835008*a^2*b^6*c^13*d^2 - 3670016*a^3*b^5*c^12*d^3 + 4587520*a^4*b^4*c^11*d^4 - 3670016*a^5*b^3*c^10*d^5 + 1835008*a^6*b^2*c^9*d^6 - 524288*a*b^7*c^14*d))^(1/4)*((-(81*a^4*d^7 + 2401*b^4*c^4*d^3 - 4116*a*b^3*c^3*d^4 + 2646*a^2*b^2*c^2*d^5 - 756*a^3*b*c*d^6)/(65536*b^8*c^15 + 65536*a^8*c^7*d^8 - 524288*a^7*b*c^8*d^7 + 1835008*a^2*b^6*c^13*d^2 - 3670016*a^3*b^5*c^12*d^3 + 4587520*a^4*b^4*c^11*d^4 - 3670016*a^5*b^3*c^10*d^5 + 1835008*a^6*b^2*c^9*d^6 - 524288*a*b^7*c^14*d))^(1/4)*((((81*a^4*b^7*d^10)/16 + 28*b^11*c^4*d^6 - (2145*a*b^10*c^3*d^7)/16 - (675*a^3*b^8*c*d^9)/16 + (1971*a^2*b^9*c^2*d^8)/16)*1i)/(b^3*c^7 - a^3*c^4*d^3 + 3*a^2*b*c^5*d^2 - 3*a*b^2*c^6*d) + (-(81*a^4*d^7 + 2401*b^4*c^4*d^3 - 4116*a*b^3*c^3*d^4 + 2646*a^2*b^2*c^2*d^5 - 756*a^3*b*c*d^6)/(65536*b^8*c^15 + 65536*a^8*c^7*d^8 - 524288*a^7*b*c^8*d^7 + 1835008*a^2*b^6*c^13*d^2 - 3670016*a^3*b^5*c^12*d^3 + 4587520*a^4*b^4*c^11*d^4 - 3670016*a^5*b^3*c^10*d^5 + 1835008*a^6*b^2*c^9*d^6 - 524288*a*b^7*c^14*d))^(3/4)*(((-(81*a^4*d^7 + 2401*b^4*c^4*d^3 - 4116*a*b^3*c^3*d^4 + 2646*a^2*b^2*c^2*d^5 - 756*a^3*b*c*d^6)/(65536*b^8*c^15 + 65536*a^8*c^7*d^8 - 524288*a^7*b*c^8*d^7 + 1835008*a^2*b^6*c^13*d^2 - 3670016*a^3*b^5*c^12*d^3 + 4587520*a^4*b^4*c^11*d^4 - 3670016*a^5*b^3*c^10*d^5 + 1835008*a^6*b^2*c^9*d^6 - 524288*a*b^7*c^14*d))^(1/4)*(28672*a^2*b^13*c^13*d^5 - 4096*a*b^14*c^14*d^4 - 78848*a^3*b^12*c^12*d^6 + 90112*a^4*b^11*c^11*d^7 + 28672*a^5*b^10*c^10*d^8 - 229376*a^6*b^9*c^9*d^9 + 329728*a^7*b^8*c^8*d^10 - 253952*a^8*b^7*c^7*d^11 + 114688*a^9*b^6*c^6*d^12 - 28672*a^10*b^5*c^5*d^13 + 3072*a^11*b^4*c^4*d^14))/(b^3*c^7 - a^3*c^4*d^3 + 3*a^2*b*c^5*d^2 - 3*a*b^2*c^6*d) + (x*(65536*b^17*c^15*d^4 - 524288*a*b^16*c^14*d^5 + 1835008*a^2*b^15*c^13*d^6 - 3469312*a^3*b^14*c^12*d^7 + 2809856*a^4*b^13*c^11*d^8 + 3362816*a^5*b^12*c^10*d^9 - 14516224*a^6*b^11*c^9*d^10 + 24190976*a^7*b^10*c^8*d^11 - 25280512*a^8*b^9*c^7*d^12 + 17833984*a^9*b^8*c^6*d^13 - 8486912*a^10*b^7*c^5*d^14 + 2609152*a^11*b^6*c^4*d^15 - 466944*a^12*b^5*c^3*d^16 + 36864*a^13*b^4*c^2*d^17)*1i)/(64*(b^6*c^10 + a^6*c^4*d^6 - 6*a^5*b*c^5*d^5 + 15*a^2*b^4*c^8*d^2 - 20*a^3*b^3*c^7*d^3 + 15*a^4*b^2*c^6*d^4 - 6*a*b^5*c^9*d)))*1i) - (x*(81*a^4*b^9*d^11 + 3185*b^13*c^4*d^7 - 4788*a*b^12*c^3*d^8 - 756*a^3*b^10*c*d^10 + 2790*a^2*b^11*c^2*d^9))/(64*(b^6*c^10 + a^6*c^4*d^6 - 6*a^5*b*c^5*d^5 + 15*a^2*b^4*c^8*d^2 - 20*a^3*b^3*c^7*d^3 + 15*a^4*b^2*c^6*d^4 - 6*a*b^5*c^9*d))))/((-(81*a^4*d^7 + 2401*b^4*c^4*d^3 - 4116*a*b^3*c^3*d^4 + 2646*a^2*b^2*c^2*d^5 - 756*a^3*b*c*d^6)/(65536*b^8*c^15 + 65536*a^8*c^7*d^8 - 524288*a^7*b*c^8*d^7 + 1835008*a^2*b^6*c^13*d^2 - 3670016*a^3*b^5*c^12*d^3 + 4587520*a^4*b^4*c^11*d^4 - 3670016*a^5*b^3*c^10*d^5 + 1835008*a^6*b^2*c^9*d^6 - 524288*a*b^7*c^14*d))^(1/4)*((-(81*a^4*d^7 + 2401*b^4*c^4*d^3 - 4116*a*b^3*c^3*d^4 + 2646*a^2*b^2*c^2*d^5 - 756*a^3*b*c*d^6)/(65536*b^8*c^15 + 65536*a^8*c^7*d^8 - 524288*a^7*b*c^8*d^7 + 1835008*a^2*b^6*c^13*d^2 - 3670016*a^3*b^5*c^12*d^3 + 4587520*a^4*b^4*c^11*d^4 - 3670016*a^5*b^3*c^10*d^5 + 1835008*a^6*b^2*c^9*d^6 - 524288*a*b^7*c^14*d))^(1/4)*((((81*a^4*b^7*d^10)/16 + 28*b^11*c^4*d^6 - (2145*a*b^10*c^3*d^7)/16 - (675*a^3*b^8*c*d^9)/16 + (1971*a^2*b^9*c^2*d^8)/16)*1i)/(b^3*c^7 - a^3*c^4*d^3 + 3*a^2*b*c^5*d^2 - 3*a*b^2*c^6*d) + (-(81*a^4*d^7 + 2401*b^4*c^4*d^3 - 4116*a*b^3*c^3*d^4 + 2646*a^2*b^2*c^2*d^5 - 756*a^3*b*c*d^6)/(65536*b^8*c^15 + 65536*a^8*c^7*d^8 - 524288*a^7*b*c^8*d^7 + 1835008*a^2*b^6*c^13*d^2 - 3670016*a^3*b^5*c^12*d^3 + 4587520*a^4*b^4*c^11*d^4 - 3670016*a^5*b^3*c^10*d^5 + 1835008*a^6*b^2*c^9*d^6 - 524288*a*b^7*c^14*d))^(3/4)*(((-(81*a^4*d^7 + 2401*b^4*c^4*d^3 - 4116*a*b^3*c^3*d^4 + 2646*a^2*b^2*c^2*d^5 - 756*a^3*b*c*d^6)/(65536*b^8*c^15 + 65536*a^8*c^7*d^8 - 524288*a^7*b*c^8*d^7 + 1835008*a^2*b^6*c^13*d^2 - 3670016*a^3*b^5*c^12*d^3 + 4587520*a^4*b^4*c^11*d^4 - 3670016*a^5*b^3*c^10*d^5 + 1835008*a^6*b^2*c^9*d^6 - 524288*a*b^7*c^14*d))^(1/4)*(28672*a^2*b^13*c^13*d^5 - 4096*a*b^14*c^14*d^4 - 78848*a^3*b^12*c^12*d^6 + 90112*a^4*b^11*c^11*d^7 + 28672*a^5*b^10*c^10*d^8 - 229376*a^6*b^9*c^9*d^9 + 329728*a^7*b^8*c^8*d^10 - 253952*a^8*b^7*c^7*d^11 + 114688*a^9*b^6*c^6*d^12 - 28672*a^10*b^5*c^5*d^13 + 3072*a^11*b^4*c^4*d^14))/(b^3*c^7 - a^3*c^4*d^3 + 3*a^2*b*c^5*d^2 - 3*a*b^2*c^6*d) - (x*(65536*b^17*c^15*d^4 - 524288*a*b^16*c^14*d^5 + 1835008*a^2*b^15*c^13*d^6 - 3469312*a^3*b^14*c^12*d^7 + 2809856*a^4*b^13*c^11*d^8 + 3362816*a^5*b^12*c^10*d^9 - 14516224*a^6*b^11*c^9*d^10 + 24190976*a^7*b^10*c^8*d^11 - 25280512*a^8*b^9*c^7*d^12 + 17833984*a^9*b^8*c^6*d^13 - 8486912*a^10*b^7*c^5*d^14 + 2609152*a^11*b^6*c^4*d^15 - 466944*a^12*b^5*c^3*d^16 + 36864*a^13*b^4*c^2*d^17)*1i)/(64*(b^6*c^10 + a^6*c^4*d^6 - 6*a^5*b*c^5*d^5 + 15*a^2*b^4*c^8*d^2 - 20*a^3*b^3*c^7*d^3 + 15*a^4*b^2*c^6*d^4 - 6*a*b^5*c^9*d)))*1i)*1i + (x*(81*a^4*b^9*d^11 + 3185*b^13*c^4*d^7 - 4788*a*b^12*c^3*d^8 - 756*a^3*b^10*c*d^10 + 2790*a^2*b^11*c^2*d^9)*1i)/(64*(b^6*c^10 + a^6*c^4*d^6 - 6*a^5*b*c^5*d^5 + 15*a^2*b^4*c^8*d^2 - 20*a^3*b^3*c^7*d^3 + 15*a^4*b^2*c^6*d^4 - 6*a*b^5*c^9*d))) + (-(81*a^4*d^7 + 2401*b^4*c^4*d^3 - 4116*a*b^3*c^3*d^4 + 2646*a^2*b^2*c^2*d^5 - 756*a^3*b*c*d^6)/(65536*b^8*c^15 + 65536*a^8*c^7*d^8 - 524288*a^7*b*c^8*d^7 + 1835008*a^2*b^6*c^13*d^2 - 3670016*a^3*b^5*c^12*d^3 + 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2646*a^2*b^2*c^2*d^5 - 756*a^3*b*c*d^6)/(65536*b^8*c^15 + 65536*a^8*c^7*d^8 - 524288*a^7*b*c^8*d^7 + 1835008*a^2*b^6*c^13*d^2 - 3670016*a^3*b^5*c^12*d^3 + 4587520*a^4*b^4*c^11*d^4 - 3670016*a^5*b^3*c^10*d^5 + 1835008*a^6*b^2*c^9*d^6 - 524288*a*b^7*c^14*d))^(1/4)*(28672*a^2*b^13*c^13*d^5 - 4096*a*b^14*c^14*d^4 - 78848*a^3*b^12*c^12*d^6 + 90112*a^4*b^11*c^11*d^7 + 28672*a^5*b^10*c^10*d^8 - 229376*a^6*b^9*c^9*d^9 + 329728*a^7*b^8*c^8*d^10 - 253952*a^8*b^7*c^7*d^11 + 114688*a^9*b^6*c^6*d^12 - 28672*a^10*b^5*c^5*d^13 + 3072*a^11*b^4*c^4*d^14))/(b^3*c^7 - a^3*c^4*d^3 + 3*a^2*b*c^5*d^2 - 3*a*b^2*c^6*d) + (x*(65536*b^17*c^15*d^4 - 524288*a*b^16*c^14*d^5 + 1835008*a^2*b^15*c^13*d^6 - 3469312*a^3*b^14*c^12*d^7 + 2809856*a^4*b^13*c^11*d^8 + 3362816*a^5*b^12*c^10*d^9 - 14516224*a^6*b^11*c^9*d^10 + 24190976*a^7*b^10*c^8*d^11 - 25280512*a^8*b^9*c^7*d^12 + 17833984*a^9*b^8*c^6*d^13 - 8486912*a^10*b^7*c^5*d^14 + 2609152*a^11*b^6*c^4*d^15 - 466944*a^12*b^5*c^3*d^16 + 36864*a^13*b^4*c^2*d^17)*1i)/(64*(b^6*c^10 + a^6*c^4*d^6 - 6*a^5*b*c^5*d^5 + 15*a^2*b^4*c^8*d^2 - 20*a^3*b^3*c^7*d^3 + 15*a^4*b^2*c^6*d^4 - 6*a*b^5*c^9*d)))*1i)*1i - (x*(81*a^4*b^9*d^11 + 3185*b^13*c^4*d^7 - 4788*a*b^12*c^3*d^8 - 756*a^3*b^10*c*d^10 + 2790*a^2*b^11*c^2*d^9)*1i)/(64*(b^6*c^10 + a^6*c^4*d^6 - 6*a^5*b*c^5*d^5 + 15*a^2*b^4*c^8*d^2 - 20*a^3*b^3*c^7*d^3 + 15*a^4*b^2*c^6*d^4 - 6*a*b^5*c^9*d)))))*(-(81*a^4*d^7 + 2401*b^4*c^4*d^3 - 4116*a*b^3*c^3*d^4 + 2646*a^2*b^2*c^2*d^5 - 756*a^3*b*c*d^6)/(65536*b^8*c^15 + 65536*a^8*c^7*d^8 - 524288*a^7*b*c^8*d^7 + 1835008*a^2*b^6*c^13*d^2 - 3670016*a^3*b^5*c^12*d^3 + 4587520*a^4*b^4*c^11*d^4 - 3670016*a^5*b^3*c^10*d^5 + 1835008*a^6*b^2*c^9*d^6 - 524288*a*b^7*c^14*d))^(1/4) - atan(((-(81*a^4*d^7 + 2401*b^4*c^4*d^3 - 4116*a*b^3*c^3*d^4 + 2646*a^2*b^2*c^2*d^5 - 756*a^3*b*c*d^6)/(65536*b^8*c^15 + 65536*a^8*c^7*d^8 - 524288*a^7*b*c^8*d^7 + 1835008*a^2*b^6*c^13*d^2 - 3670016*a^3*b^5*c^12*d^3 + 4587520*a^4*b^4*c^11*d^4 - 3670016*a^5*b^3*c^10*d^5 + 1835008*a^6*b^2*c^9*d^6 - 524288*a*b^7*c^14*d))^(1/4)*((-(81*a^4*d^7 + 2401*b^4*c^4*d^3 - 4116*a*b^3*c^3*d^4 + 2646*a^2*b^2*c^2*d^5 - 756*a^3*b*c*d^6)/(65536*b^8*c^15 + 65536*a^8*c^7*d^8 - 524288*a^7*b*c^8*d^7 + 1835008*a^2*b^6*c^13*d^2 - 3670016*a^3*b^5*c^12*d^3 + 4587520*a^4*b^4*c^11*d^4 - 3670016*a^5*b^3*c^10*d^5 + 1835008*a^6*b^2*c^9*d^6 - 524288*a*b^7*c^14*d))^(1/4)*(((81*a^4*b^7*d^10)/16 + 28*b^11*c^4*d^6 - (2145*a*b^10*c^3*d^7)/16 - (675*a^3*b^8*c*d^9)/16 + (1971*a^2*b^9*c^2*d^8)/16)/(b^3*c^7 - a^3*c^4*d^3 + 3*a^2*b*c^5*d^2 - 3*a*b^2*c^6*d) + (-(81*a^4*d^7 + 2401*b^4*c^4*d^3 - 4116*a*b^3*c^3*d^4 + 2646*a^2*b^2*c^2*d^5 - 756*a^3*b*c*d^6)/(65536*b^8*c^15 + 65536*a^8*c^7*d^8 - 524288*a^7*b*c^8*d^7 + 1835008*a^2*b^6*c^13*d^2 - 3670016*a^3*b^5*c^12*d^3 + 4587520*a^4*b^4*c^11*d^4 - 3670016*a^5*b^3*c^10*d^5 + 1835008*a^6*b^2*c^9*d^6 - 524288*a*b^7*c^14*d))^(3/4)*(((-(81*a^4*d^7 + 2401*b^4*c^4*d^3 - 4116*a*b^3*c^3*d^4 + 2646*a^2*b^2*c^2*d^5 - 756*a^3*b*c*d^6)/(65536*b^8*c^15 + 65536*a^8*c^7*d^8 - 524288*a^7*b*c^8*d^7 + 1835008*a^2*b^6*c^13*d^2 - 3670016*a^3*b^5*c^12*d^3 + 4587520*a^4*b^4*c^11*d^4 - 3670016*a^5*b^3*c^10*d^5 + 1835008*a^6*b^2*c^9*d^6 - 524288*a*b^7*c^14*d))^(1/4)*(28672*a^2*b^13*c^13*d^5 - 4096*a*b^14*c^14*d^4 - 78848*a^3*b^12*c^12*d^6 + 90112*a^4*b^11*c^11*d^7 + 28672*a^5*b^10*c^10*d^8 - 229376*a^6*b^9*c^9*d^9 + 329728*a^7*b^8*c^8*d^10 - 253952*a^8*b^7*c^7*d^11 + 114688*a^9*b^6*c^6*d^12 - 28672*a^10*b^5*c^5*d^13 + 3072*a^11*b^4*c^4*d^14))/(b^3*c^7 - a^3*c^4*d^3 + 3*a^2*b*c^5*d^2 - 3*a*b^2*c^6*d) - (x*(65536*b^17*c^15*d^4 - 524288*a*b^16*c^14*d^5 + 1835008*a^2*b^15*c^13*d^6 - 3469312*a^3*b^14*c^12*d^7 + 2809856*a^4*b^13*c^11*d^8 + 3362816*a^5*b^12*c^10*d^9 - 14516224*a^6*b^11*c^9*d^10 + 24190976*a^7*b^10*c^8*d^11 - 25280512*a^8*b^9*c^7*d^12 + 17833984*a^9*b^8*c^6*d^13 - 8486912*a^10*b^7*c^5*d^14 + 2609152*a^11*b^6*c^4*d^15 - 466944*a^12*b^5*c^3*d^16 + 36864*a^13*b^4*c^2*d^17))/(64*(b^6*c^10 + a^6*c^4*d^6 - 6*a^5*b*c^5*d^5 + 15*a^2*b^4*c^8*d^2 - 20*a^3*b^3*c^7*d^3 + 15*a^4*b^2*c^6*d^4 - 6*a*b^5*c^9*d))))*1i - (x*(81*a^4*b^9*d^11 + 3185*b^13*c^4*d^7 - 4788*a*b^12*c^3*d^8 - 756*a^3*b^10*c*d^10 + 2790*a^2*b^11*c^2*d^9)*1i)/(64*(b^6*c^10 + a^6*c^4*d^6 - 6*a^5*b*c^5*d^5 + 15*a^2*b^4*c^8*d^2 - 20*a^3*b^3*c^7*d^3 + 15*a^4*b^2*c^6*d^4 - 6*a*b^5*c^9*d))) - (-(81*a^4*d^7 + 2401*b^4*c^4*d^3 - 4116*a*b^3*c^3*d^4 + 2646*a^2*b^2*c^2*d^5 - 756*a^3*b*c*d^6)/(65536*b^8*c^15 + 65536*a^8*c^7*d^8 - 524288*a^7*b*c^8*d^7 + 1835008*a^2*b^6*c^13*d^2 - 3670016*a^3*b^5*c^12*d^3 + 4587520*a^4*b^4*c^11*d^4 - 3670016*a^5*b^3*c^10*d^5 + 1835008*a^6*b^2*c^9*d^6 - 524288*a*b^7*c^14*d))^(1/4)*((-(81*a^4*d^7 + 2401*b^4*c^4*d^3 - 4116*a*b^3*c^3*d^4 + 2646*a^2*b^2*c^2*d^5 - 756*a^3*b*c*d^6)/(65536*b^8*c^15 + 65536*a^8*c^7*d^8 - 524288*a^7*b*c^8*d^7 + 1835008*a^2*b^6*c^13*d^2 - 3670016*a^3*b^5*c^12*d^3 + 4587520*a^4*b^4*c^11*d^4 - 3670016*a^5*b^3*c^10*d^5 + 1835008*a^6*b^2*c^9*d^6 - 524288*a*b^7*c^14*d))^(1/4)*(((81*a^4*b^7*d^10)/16 + 28*b^11*c^4*d^6 - (2145*a*b^10*c^3*d^7)/16 - (675*a^3*b^8*c*d^9)/16 + (1971*a^2*b^9*c^2*d^8)/16)/(b^3*c^7 - a^3*c^4*d^3 + 3*a^2*b*c^5*d^2 - 3*a*b^2*c^6*d) + (-(81*a^4*d^7 + 2401*b^4*c^4*d^3 - 4116*a*b^3*c^3*d^4 + 2646*a^2*b^2*c^2*d^5 - 756*a^3*b*c*d^6)/(65536*b^8*c^15 + 65536*a^8*c^7*d^8 - 524288*a^7*b*c^8*d^7 + 1835008*a^2*b^6*c^13*d^2 - 3670016*a^3*b^5*c^12*d^3 + 4587520*a^4*b^4*c^11*d^4 - 3670016*a^5*b^3*c^10*d^5 + 1835008*a^6*b^2*c^9*d^6 - 524288*a*b^7*c^14*d))^(3/4)*(((-(81*a^4*d^7 + 2401*b^4*c^4*d^3 - 4116*a*b^3*c^3*d^4 + 2646*a^2*b^2*c^2*d^5 - 756*a^3*b*c*d^6)/(65536*b^8*c^15 + 65536*a^8*c^7*d^8 - 524288*a^7*b*c^8*d^7 + 1835008*a^2*b^6*c^13*d^2 - 3670016*a^3*b^5*c^12*d^3 + 4587520*a^4*b^4*c^11*d^4 - 3670016*a^5*b^3*c^10*d^5 + 1835008*a^6*b^2*c^9*d^6 - 524288*a*b^7*c^14*d))^(1/4)*(28672*a^2*b^13*c^13*d^5 - 4096*a*b^14*c^14*d^4 - 78848*a^3*b^12*c^12*d^6 + 90112*a^4*b^11*c^11*d^7 + 28672*a^5*b^10*c^10*d^8 - 229376*a^6*b^9*c^9*d^9 + 329728*a^7*b^8*c^8*d^10 - 253952*a^8*b^7*c^7*d^11 + 114688*a^9*b^6*c^6*d^12 - 28672*a^10*b^5*c^5*d^13 + 3072*a^11*b^4*c^4*d^14))/(b^3*c^7 - a^3*c^4*d^3 + 3*a^2*b*c^5*d^2 - 3*a*b^2*c^6*d) + (x*(65536*b^17*c^15*d^4 - 524288*a*b^16*c^14*d^5 + 1835008*a^2*b^15*c^13*d^6 - 3469312*a^3*b^14*c^12*d^7 + 2809856*a^4*b^13*c^11*d^8 + 3362816*a^5*b^12*c^10*d^9 - 14516224*a^6*b^11*c^9*d^10 + 24190976*a^7*b^10*c^8*d^11 - 25280512*a^8*b^9*c^7*d^12 + 17833984*a^9*b^8*c^6*d^13 - 8486912*a^10*b^7*c^5*d^14 + 2609152*a^11*b^6*c^4*d^15 - 466944*a^12*b^5*c^3*d^16 + 36864*a^13*b^4*c^2*d^17))/(64*(b^6*c^10 + a^6*c^4*d^6 - 6*a^5*b*c^5*d^5 + 15*a^2*b^4*c^8*d^2 - 20*a^3*b^3*c^7*d^3 + 15*a^4*b^2*c^6*d^4 - 6*a*b^5*c^9*d))))*1i + (x*(81*a^4*b^9*d^11 + 3185*b^13*c^4*d^7 - 4788*a*b^12*c^3*d^8 - 756*a^3*b^10*c*d^10 + 2790*a^2*b^11*c^2*d^9)*1i)/(64*(b^6*c^10 + a^6*c^4*d^6 - 6*a^5*b*c^5*d^5 + 15*a^2*b^4*c^8*d^2 - 20*a^3*b^3*c^7*d^3 + 15*a^4*b^2*c^6*d^4 - 6*a*b^5*c^9*d))))/((-(81*a^4*d^7 + 2401*b^4*c^4*d^3 - 4116*a*b^3*c^3*d^4 + 2646*a^2*b^2*c^2*d^5 - 756*a^3*b*c*d^6)/(65536*b^8*c^15 + 65536*a^8*c^7*d^8 - 524288*a^7*b*c^8*d^7 + 1835008*a^2*b^6*c^13*d^2 - 3670016*a^3*b^5*c^12*d^3 + 4587520*a^4*b^4*c^11*d^4 - 3670016*a^5*b^3*c^10*d^5 + 1835008*a^6*b^2*c^9*d^6 - 524288*a*b^7*c^14*d))^(1/4)*((-(81*a^4*d^7 + 2401*b^4*c^4*d^3 - 4116*a*b^3*c^3*d^4 + 2646*a^2*b^2*c^2*d^5 - 756*a^3*b*c*d^6)/(65536*b^8*c^15 + 65536*a^8*c^7*d^8 - 524288*a^7*b*c^8*d^7 + 1835008*a^2*b^6*c^13*d^2 - 3670016*a^3*b^5*c^12*d^3 + 4587520*a^4*b^4*c^11*d^4 - 3670016*a^5*b^3*c^10*d^5 + 1835008*a^6*b^2*c^9*d^6 - 524288*a*b^7*c^14*d))^(1/4)*(((81*a^4*b^7*d^10)/16 + 28*b^11*c^4*d^6 - (2145*a*b^10*c^3*d^7)/16 - (675*a^3*b^8*c*d^9)/16 + (1971*a^2*b^9*c^2*d^8)/16)/(b^3*c^7 - a^3*c^4*d^3 + 3*a^2*b*c^5*d^2 - 3*a*b^2*c^6*d) + (-(81*a^4*d^7 + 2401*b^4*c^4*d^3 - 4116*a*b^3*c^3*d^4 + 2646*a^2*b^2*c^2*d^5 - 756*a^3*b*c*d^6)/(65536*b^8*c^15 + 65536*a^8*c^7*d^8 - 524288*a^7*b*c^8*d^7 + 1835008*a^2*b^6*c^13*d^2 - 3670016*a^3*b^5*c^12*d^3 + 4587520*a^4*b^4*c^11*d^4 - 3670016*a^5*b^3*c^10*d^5 + 1835008*a^6*b^2*c^9*d^6 - 524288*a*b^7*c^14*d))^(3/4)*(((-(81*a^4*d^7 + 2401*b^4*c^4*d^3 - 4116*a*b^3*c^3*d^4 + 2646*a^2*b^2*c^2*d^5 - 756*a^3*b*c*d^6)/(65536*b^8*c^15 + 65536*a^8*c^7*d^8 - 524288*a^7*b*c^8*d^7 + 1835008*a^2*b^6*c^13*d^2 - 3670016*a^3*b^5*c^12*d^3 + 4587520*a^4*b^4*c^11*d^4 - 3670016*a^5*b^3*c^10*d^5 + 1835008*a^6*b^2*c^9*d^6 - 524288*a*b^7*c^14*d))^(1/4)*(28672*a^2*b^13*c^13*d^5 - 4096*a*b^14*c^14*d^4 - 78848*a^3*b^12*c^12*d^6 + 90112*a^4*b^11*c^11*d^7 + 28672*a^5*b^10*c^10*d^8 - 229376*a^6*b^9*c^9*d^9 + 329728*a^7*b^8*c^8*d^10 - 253952*a^8*b^7*c^7*d^11 + 114688*a^9*b^6*c^6*d^12 - 28672*a^10*b^5*c^5*d^13 + 3072*a^11*b^4*c^4*d^14))/(b^3*c^7 - a^3*c^4*d^3 + 3*a^2*b*c^5*d^2 - 3*a*b^2*c^6*d) - (x*(65536*b^17*c^15*d^4 - 524288*a*b^16*c^14*d^5 + 1835008*a^2*b^15*c^13*d^6 - 3469312*a^3*b^14*c^12*d^7 + 2809856*a^4*b^13*c^11*d^8 + 3362816*a^5*b^12*c^10*d^9 - 14516224*a^6*b^11*c^9*d^10 + 24190976*a^7*b^10*c^8*d^11 - 25280512*a^8*b^9*c^7*d^12 + 17833984*a^9*b^8*c^6*d^13 - 8486912*a^10*b^7*c^5*d^14 + 2609152*a^11*b^6*c^4*d^15 - 466944*a^12*b^5*c^3*d^16 + 36864*a^13*b^4*c^2*d^17))/(64*(b^6*c^10 + a^6*c^4*d^6 - 6*a^5*b*c^5*d^5 + 15*a^2*b^4*c^8*d^2 - 20*a^3*b^3*c^7*d^3 + 15*a^4*b^2*c^6*d^4 - 6*a*b^5*c^9*d)))) - (x*(81*a^4*b^9*d^11 + 3185*b^13*c^4*d^7 - 4788*a*b^12*c^3*d^8 - 756*a^3*b^10*c*d^10 + 2790*a^2*b^11*c^2*d^9))/(64*(b^6*c^10 + a^6*c^4*d^6 - 6*a^5*b*c^5*d^5 + 15*a^2*b^4*c^8*d^2 - 20*a^3*b^3*c^7*d^3 + 15*a^4*b^2*c^6*d^4 - 6*a*b^5*c^9*d))) + (-(81*a^4*d^7 + 2401*b^4*c^4*d^3 - 4116*a*b^3*c^3*d^4 + 2646*a^2*b^2*c^2*d^5 - 756*a^3*b*c*d^6)/(65536*b^8*c^15 + 65536*a^8*c^7*d^8 - 524288*a^7*b*c^8*d^7 + 1835008*a^2*b^6*c^13*d^2 - 3670016*a^3*b^5*c^12*d^3 + 4587520*a^4*b^4*c^11*d^4 - 3670016*a^5*b^3*c^10*d^5 + 1835008*a^6*b^2*c^9*d^6 - 524288*a*b^7*c^14*d))^(1/4)*((-(81*a^4*d^7 + 2401*b^4*c^4*d^3 - 4116*a*b^3*c^3*d^4 + 2646*a^2*b^2*c^2*d^5 - 756*a^3*b*c*d^6)/(65536*b^8*c^15 + 65536*a^8*c^7*d^8 - 524288*a^7*b*c^8*d^7 + 1835008*a^2*b^6*c^13*d^2 - 3670016*a^3*b^5*c^12*d^3 + 4587520*a^4*b^4*c^11*d^4 - 3670016*a^5*b^3*c^10*d^5 + 1835008*a^6*b^2*c^9*d^6 - 524288*a*b^7*c^14*d))^(1/4)*(((81*a^4*b^7*d^10)/16 + 28*b^11*c^4*d^6 - (2145*a*b^10*c^3*d^7)/16 - (675*a^3*b^8*c*d^9)/16 + (1971*a^2*b^9*c^2*d^8)/16)/(b^3*c^7 - a^3*c^4*d^3 + 3*a^2*b*c^5*d^2 - 3*a*b^2*c^6*d) + (-(81*a^4*d^7 + 2401*b^4*c^4*d^3 - 4116*a*b^3*c^3*d^4 + 2646*a^2*b^2*c^2*d^5 - 756*a^3*b*c*d^6)/(65536*b^8*c^15 + 65536*a^8*c^7*d^8 - 524288*a^7*b*c^8*d^7 + 1835008*a^2*b^6*c^13*d^2 - 3670016*a^3*b^5*c^12*d^3 + 4587520*a^4*b^4*c^11*d^4 - 3670016*a^5*b^3*c^10*d^5 + 1835008*a^6*b^2*c^9*d^6 - 524288*a*b^7*c^14*d))^(3/4)*(((-(81*a^4*d^7 + 2401*b^4*c^4*d^3 - 4116*a*b^3*c^3*d^4 + 2646*a^2*b^2*c^2*d^5 - 756*a^3*b*c*d^6)/(65536*b^8*c^15 + 65536*a^8*c^7*d^8 - 524288*a^7*b*c^8*d^7 + 1835008*a^2*b^6*c^13*d^2 - 3670016*a^3*b^5*c^12*d^3 + 4587520*a^4*b^4*c^11*d^4 - 3670016*a^5*b^3*c^10*d^5 + 1835008*a^6*b^2*c^9*d^6 - 524288*a*b^7*c^14*d))^(1/4)*(28672*a^2*b^13*c^13*d^5 - 4096*a*b^14*c^14*d^4 - 78848*a^3*b^12*c^12*d^6 + 90112*a^4*b^11*c^11*d^7 + 28672*a^5*b^10*c^10*d^8 - 229376*a^6*b^9*c^9*d^9 + 329728*a^7*b^8*c^8*d^10 - 253952*a^8*b^7*c^7*d^11 + 114688*a^9*b^6*c^6*d^12 - 28672*a^10*b^5*c^5*d^13 + 3072*a^11*b^4*c^4*d^14))/(b^3*c^7 - a^3*c^4*d^3 + 3*a^2*b*c^5*d^2 - 3*a*b^2*c^6*d) + (x*(65536*b^17*c^15*d^4 - 524288*a*b^16*c^14*d^5 + 1835008*a^2*b^15*c^13*d^6 - 3469312*a^3*b^14*c^12*d^7 + 2809856*a^4*b^13*c^11*d^8 + 3362816*a^5*b^12*c^10*d^9 - 14516224*a^6*b^11*c^9*d^10 + 24190976*a^7*b^10*c^8*d^11 - 25280512*a^8*b^9*c^7*d^12 + 17833984*a^9*b^8*c^6*d^13 - 8486912*a^10*b^7*c^5*d^14 + 2609152*a^11*b^6*c^4*d^15 - 466944*a^12*b^5*c^3*d^16 + 36864*a^13*b^4*c^2*d^17))/(64*(b^6*c^10 + a^6*c^4*d^6 - 6*a^5*b*c^5*d^5 + 15*a^2*b^4*c^8*d^2 - 20*a^3*b^3*c^7*d^3 + 15*a^4*b^2*c^6*d^4 - 6*a*b^5*c^9*d)))) + (x*(81*a^4*b^9*d^11 + 3185*b^13*c^4*d^7 - 4788*a*b^12*c^3*d^8 - 756*a^3*b^10*c*d^10 + 2790*a^2*b^11*c^2*d^9))/(64*(b^6*c^10 + a^6*c^4*d^6 - 6*a^5*b*c^5*d^5 + 15*a^2*b^4*c^8*d^2 - 20*a^3*b^3*c^7*d^3 + 15*a^4*b^2*c^6*d^4 - 6*a*b^5*c^9*d)))))*(-(81*a^4*d^7 + 2401*b^4*c^4*d^3 - 4116*a*b^3*c^3*d^4 + 2646*a^2*b^2*c^2*d^5 - 756*a^3*b*c*d^6)/(65536*b^8*c^15 + 65536*a^8*c^7*d^8 - 524288*a^7*b*c^8*d^7 + 1835008*a^2*b^6*c^13*d^2 - 3670016*a^3*b^5*c^12*d^3 + 4587520*a^4*b^4*c^11*d^4 - 3670016*a^5*b^3*c^10*d^5 + 1835008*a^6*b^2*c^9*d^6 - 524288*a*b^7*c^14*d))^(1/4)*2i - atan(((-b^7/(256*a^11*d^8 + 256*a^3*b^8*c^8 - 2048*a^4*b^7*c^7*d + 7168*a^5*b^6*c^6*d^2 - 14336*a^6*b^5*c^5*d^3 + 17920*a^7*b^4*c^4*d^4 - 14336*a^8*b^3*c^3*d^5 + 7168*a^9*b^2*c^2*d^6 - 2048*a^10*b*c*d^7))^(1/4)*((-b^7/(256*a^11*d^8 + 256*a^3*b^8*c^8 - 2048*a^4*b^7*c^7*d + 7168*a^5*b^6*c^6*d^2 - 14336*a^6*b^5*c^5*d^3 + 17920*a^7*b^4*c^4*d^4 - 14336*a^8*b^3*c^3*d^5 + 7168*a^9*b^2*c^2*d^6 - 2048*a^10*b*c*d^7))^(1/4)*((-b^7/(256*a^11*d^8 + 256*a^3*b^8*c^8 - 2048*a^4*b^7*c^7*d + 7168*a^5*b^6*c^6*d^2 - 14336*a^6*b^5*c^5*d^3 + 17920*a^7*b^4*c^4*d^4 - 14336*a^8*b^3*c^3*d^5 + 7168*a^9*b^2*c^2*d^6 - 2048*a^10*b*c*d^7))^(3/4)*(((-b^7/(256*a^11*d^8 + 256*a^3*b^8*c^8 - 2048*a^4*b^7*c^7*d + 7168*a^5*b^6*c^6*d^2 - 14336*a^6*b^5*c^5*d^3 + 17920*a^7*b^4*c^4*d^4 - 14336*a^8*b^3*c^3*d^5 + 7168*a^9*b^2*c^2*d^6 - 2048*a^10*b*c*d^7))^(1/4)*(28672*a^2*b^13*c^13*d^5 - 4096*a*b^14*c^14*d^4 - 78848*a^3*b^12*c^12*d^6 + 90112*a^4*b^11*c^11*d^7 + 28672*a^5*b^10*c^10*d^8 - 229376*a^6*b^9*c^9*d^9 + 329728*a^7*b^8*c^8*d^10 - 253952*a^8*b^7*c^7*d^11 + 114688*a^9*b^6*c^6*d^12 - 28672*a^10*b^5*c^5*d^13 + 3072*a^11*b^4*c^4*d^14))/(b^3*c^7 - a^3*c^4*d^3 + 3*a^2*b*c^5*d^2 - 3*a*b^2*c^6*d) - (x*(65536*b^17*c^15*d^4 - 524288*a*b^16*c^14*d^5 + 1835008*a^2*b^15*c^13*d^6 - 3469312*a^3*b^14*c^12*d^7 + 2809856*a^4*b^13*c^11*d^8 + 3362816*a^5*b^12*c^10*d^9 - 14516224*a^6*b^11*c^9*d^10 + 24190976*a^7*b^10*c^8*d^11 - 25280512*a^8*b^9*c^7*d^12 + 17833984*a^9*b^8*c^6*d^13 - 8486912*a^10*b^7*c^5*d^14 + 2609152*a^11*b^6*c^4*d^15 - 466944*a^12*b^5*c^3*d^16 + 36864*a^13*b^4*c^2*d^17))/(64*(b^6*c^10 + a^6*c^4*d^6 - 6*a^5*b*c^5*d^5 + 15*a^2*b^4*c^8*d^2 - 20*a^3*b^3*c^7*d^3 + 15*a^4*b^2*c^6*d^4 - 6*a*b^5*c^9*d))) + ((81*a^4*b^7*d^10)/16 + 28*b^11*c^4*d^6 - (2145*a*b^10*c^3*d^7)/16 - (675*a^3*b^8*c*d^9)/16 + (1971*a^2*b^9*c^2*d^8)/16)/(b^3*c^7 - a^3*c^4*d^3 + 3*a^2*b*c^5*d^2 - 3*a*b^2*c^6*d))*1i - (x*(81*a^4*b^9*d^11 + 3185*b^13*c^4*d^7 - 4788*a*b^12*c^3*d^8 - 756*a^3*b^10*c*d^10 + 2790*a^2*b^11*c^2*d^9)*1i)/(64*(b^6*c^10 + a^6*c^4*d^6 - 6*a^5*b*c^5*d^5 + 15*a^2*b^4*c^8*d^2 - 20*a^3*b^3*c^7*d^3 + 15*a^4*b^2*c^6*d^4 - 6*a*b^5*c^9*d))) - (-b^7/(256*a^11*d^8 + 256*a^3*b^8*c^8 - 2048*a^4*b^7*c^7*d + 7168*a^5*b^6*c^6*d^2 - 14336*a^6*b^5*c^5*d^3 + 17920*a^7*b^4*c^4*d^4 - 14336*a^8*b^3*c^3*d^5 + 7168*a^9*b^2*c^2*d^6 - 2048*a^10*b*c*d^7))^(1/4)*((-b^7/(256*a^11*d^8 + 256*a^3*b^8*c^8 - 2048*a^4*b^7*c^7*d + 7168*a^5*b^6*c^6*d^2 - 14336*a^6*b^5*c^5*d^3 + 17920*a^7*b^4*c^4*d^4 - 14336*a^8*b^3*c^3*d^5 + 7168*a^9*b^2*c^2*d^6 - 2048*a^10*b*c*d^7))^(1/4)*((-b^7/(256*a^11*d^8 + 256*a^3*b^8*c^8 - 2048*a^4*b^7*c^7*d + 7168*a^5*b^6*c^6*d^2 - 14336*a^6*b^5*c^5*d^3 + 17920*a^7*b^4*c^4*d^4 - 14336*a^8*b^3*c^3*d^5 + 7168*a^9*b^2*c^2*d^6 - 2048*a^10*b*c*d^7))^(3/4)*(((-b^7/(256*a^11*d^8 + 256*a^3*b^8*c^8 - 2048*a^4*b^7*c^7*d + 7168*a^5*b^6*c^6*d^2 - 14336*a^6*b^5*c^5*d^3 + 17920*a^7*b^4*c^4*d^4 - 14336*a^8*b^3*c^3*d^5 + 7168*a^9*b^2*c^2*d^6 - 2048*a^10*b*c*d^7))^(1/4)*(28672*a^2*b^13*c^13*d^5 - 4096*a*b^14*c^14*d^4 - 78848*a^3*b^12*c^12*d^6 + 90112*a^4*b^11*c^11*d^7 + 28672*a^5*b^10*c^10*d^8 - 229376*a^6*b^9*c^9*d^9 + 329728*a^7*b^8*c^8*d^10 - 253952*a^8*b^7*c^7*d^11 + 114688*a^9*b^6*c^6*d^12 - 28672*a^10*b^5*c^5*d^13 + 3072*a^11*b^4*c^4*d^14))/(b^3*c^7 - a^3*c^4*d^3 + 3*a^2*b*c^5*d^2 - 3*a*b^2*c^6*d) + (x*(65536*b^17*c^15*d^4 - 524288*a*b^16*c^14*d^5 + 1835008*a^2*b^15*c^13*d^6 - 3469312*a^3*b^14*c^12*d^7 + 2809856*a^4*b^13*c^11*d^8 + 3362816*a^5*b^12*c^10*d^9 - 14516224*a^6*b^11*c^9*d^10 + 24190976*a^7*b^10*c^8*d^11 - 25280512*a^8*b^9*c^7*d^12 + 17833984*a^9*b^8*c^6*d^13 - 8486912*a^10*b^7*c^5*d^14 + 2609152*a^11*b^6*c^4*d^15 - 466944*a^12*b^5*c^3*d^16 + 36864*a^13*b^4*c^2*d^17))/(64*(b^6*c^10 + a^6*c^4*d^6 - 6*a^5*b*c^5*d^5 + 15*a^2*b^4*c^8*d^2 - 20*a^3*b^3*c^7*d^3 + 15*a^4*b^2*c^6*d^4 - 6*a*b^5*c^9*d))) + ((81*a^4*b^7*d^10)/16 + 28*b^11*c^4*d^6 - (2145*a*b^10*c^3*d^7)/16 - (675*a^3*b^8*c*d^9)/16 + (1971*a^2*b^9*c^2*d^8)/16)/(b^3*c^7 - a^3*c^4*d^3 + 3*a^2*b*c^5*d^2 - 3*a*b^2*c^6*d))*1i + (x*(81*a^4*b^9*d^11 + 3185*b^13*c^4*d^7 - 4788*a*b^12*c^3*d^8 - 756*a^3*b^10*c*d^10 + 2790*a^2*b^11*c^2*d^9)*1i)/(64*(b^6*c^10 + a^6*c^4*d^6 - 6*a^5*b*c^5*d^5 + 15*a^2*b^4*c^8*d^2 - 20*a^3*b^3*c^7*d^3 + 15*a^4*b^2*c^6*d^4 - 6*a*b^5*c^9*d))))/((-b^7/(256*a^11*d^8 + 256*a^3*b^8*c^8 - 2048*a^4*b^7*c^7*d + 7168*a^5*b^6*c^6*d^2 - 14336*a^6*b^5*c^5*d^3 + 17920*a^7*b^4*c^4*d^4 - 14336*a^8*b^3*c^3*d^5 + 7168*a^9*b^2*c^2*d^6 - 2048*a^10*b*c*d^7))^(1/4)*((-b^7/(256*a^11*d^8 + 256*a^3*b^8*c^8 - 2048*a^4*b^7*c^7*d + 7168*a^5*b^6*c^6*d^2 - 14336*a^6*b^5*c^5*d^3 + 17920*a^7*b^4*c^4*d^4 - 14336*a^8*b^3*c^3*d^5 + 7168*a^9*b^2*c^2*d^6 - 2048*a^10*b*c*d^7))^(1/4)*((-b^7/(256*a^11*d^8 + 256*a^3*b^8*c^8 - 2048*a^4*b^7*c^7*d + 7168*a^5*b^6*c^6*d^2 - 14336*a^6*b^5*c^5*d^3 + 17920*a^7*b^4*c^4*d^4 - 14336*a^8*b^3*c^3*d^5 + 7168*a^9*b^2*c^2*d^6 - 2048*a^10*b*c*d^7))^(3/4)*(((-b^7/(256*a^11*d^8 + 256*a^3*b^8*c^8 - 2048*a^4*b^7*c^7*d + 7168*a^5*b^6*c^6*d^2 - 14336*a^6*b^5*c^5*d^3 + 17920*a^7*b^4*c^4*d^4 - 14336*a^8*b^3*c^3*d^5 + 7168*a^9*b^2*c^2*d^6 - 2048*a^10*b*c*d^7))^(1/4)*(28672*a^2*b^13*c^13*d^5 - 4096*a*b^14*c^14*d^4 - 78848*a^3*b^12*c^12*d^6 + 90112*a^4*b^11*c^11*d^7 + 28672*a^5*b^10*c^10*d^8 - 229376*a^6*b^9*c^9*d^9 + 329728*a^7*b^8*c^8*d^10 - 253952*a^8*b^7*c^7*d^11 + 114688*a^9*b^6*c^6*d^12 - 28672*a^10*b^5*c^5*d^13 + 3072*a^11*b^4*c^4*d^14))/(b^3*c^7 - a^3*c^4*d^3 + 3*a^2*b*c^5*d^2 - 3*a*b^2*c^6*d) - (x*(65536*b^17*c^15*d^4 - 524288*a*b^16*c^14*d^5 + 1835008*a^2*b^15*c^13*d^6 - 3469312*a^3*b^14*c^12*d^7 + 2809856*a^4*b^13*c^11*d^8 + 3362816*a^5*b^12*c^10*d^9 - 14516224*a^6*b^11*c^9*d^10 + 24190976*a^7*b^10*c^8*d^11 - 25280512*a^8*b^9*c^7*d^12 + 17833984*a^9*b^8*c^6*d^13 - 8486912*a^10*b^7*c^5*d^14 + 2609152*a^11*b^6*c^4*d^15 - 466944*a^12*b^5*c^3*d^16 + 36864*a^13*b^4*c^2*d^17))/(64*(b^6*c^10 + a^6*c^4*d^6 - 6*a^5*b*c^5*d^5 + 15*a^2*b^4*c^8*d^2 - 20*a^3*b^3*c^7*d^3 + 15*a^4*b^2*c^6*d^4 - 6*a*b^5*c^9*d))) + ((81*a^4*b^7*d^10)/16 + 28*b^11*c^4*d^6 - (2145*a*b^10*c^3*d^7)/16 - (675*a^3*b^8*c*d^9)/16 + (1971*a^2*b^9*c^2*d^8)/16)/(b^3*c^7 - a^3*c^4*d^3 + 3*a^2*b*c^5*d^2 - 3*a*b^2*c^6*d)) - (x*(81*a^4*b^9*d^11 + 3185*b^13*c^4*d^7 - 4788*a*b^12*c^3*d^8 - 756*a^3*b^10*c*d^10 + 2790*a^2*b^11*c^2*d^9))/(64*(b^6*c^10 + a^6*c^4*d^6 - 6*a^5*b*c^5*d^5 + 15*a^2*b^4*c^8*d^2 - 20*a^3*b^3*c^7*d^3 + 15*a^4*b^2*c^6*d^4 - 6*a*b^5*c^9*d))) + (-b^7/(256*a^11*d^8 + 256*a^3*b^8*c^8 - 2048*a^4*b^7*c^7*d + 7168*a^5*b^6*c^6*d^2 - 14336*a^6*b^5*c^5*d^3 + 17920*a^7*b^4*c^4*d^4 - 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3*a^2*b*c^5*d^2 - 3*a*b^2*c^6*d) + (x*(65536*b^17*c^15*d^4 - 524288*a*b^16*c^14*d^5 + 1835008*a^2*b^15*c^13*d^6 - 3469312*a^3*b^14*c^12*d^7 + 2809856*a^4*b^13*c^11*d^8 + 3362816*a^5*b^12*c^10*d^9 - 14516224*a^6*b^11*c^9*d^10 + 24190976*a^7*b^10*c^8*d^11 - 25280512*a^8*b^9*c^7*d^12 + 17833984*a^9*b^8*c^6*d^13 - 8486912*a^10*b^7*c^5*d^14 + 2609152*a^11*b^6*c^4*d^15 - 466944*a^12*b^5*c^3*d^16 + 36864*a^13*b^4*c^2*d^17))/(64*(b^6*c^10 + a^6*c^4*d^6 - 6*a^5*b*c^5*d^5 + 15*a^2*b^4*c^8*d^2 - 20*a^3*b^3*c^7*d^3 + 15*a^4*b^2*c^6*d^4 - 6*a*b^5*c^9*d))) + ((81*a^4*b^7*d^10)/16 + 28*b^11*c^4*d^6 - (2145*a*b^10*c^3*d^7)/16 - (675*a^3*b^8*c*d^9)/16 + (1971*a^2*b^9*c^2*d^8)/16)/(b^3*c^7 - a^3*c^4*d^3 + 3*a^2*b*c^5*d^2 - 3*a*b^2*c^6*d)) + (x*(81*a^4*b^9*d^11 + 3185*b^13*c^4*d^7 - 4788*a*b^12*c^3*d^8 - 756*a^3*b^10*c*d^10 + 2790*a^2*b^11*c^2*d^9))/(64*(b^6*c^10 + a^6*c^4*d^6 - 6*a^5*b*c^5*d^5 + 15*a^2*b^4*c^8*d^2 - 20*a^3*b^3*c^7*d^3 + 15*a^4*b^2*c^6*d^4 - 6*a*b^5*c^9*d)))))*(-b^7/(256*a^11*d^8 + 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2048*a^10*b*c*d^7))^(1/4)*(28672*a^2*b^13*c^13*d^5 - 4096*a*b^14*c^14*d^4 - 78848*a^3*b^12*c^12*d^6 + 90112*a^4*b^11*c^11*d^7 + 28672*a^5*b^10*c^10*d^8 - 229376*a^6*b^9*c^9*d^9 + 329728*a^7*b^8*c^8*d^10 - 253952*a^8*b^7*c^7*d^11 + 114688*a^9*b^6*c^6*d^12 - 28672*a^10*b^5*c^5*d^13 + 3072*a^11*b^4*c^4*d^14))/(b^3*c^7 - a^3*c^4*d^3 + 3*a^2*b*c^5*d^2 - 3*a*b^2*c^6*d) - (x*(65536*b^17*c^15*d^4 - 524288*a*b^16*c^14*d^5 + 1835008*a^2*b^15*c^13*d^6 - 3469312*a^3*b^14*c^12*d^7 + 2809856*a^4*b^13*c^11*d^8 + 3362816*a^5*b^12*c^10*d^9 - 14516224*a^6*b^11*c^9*d^10 + 24190976*a^7*b^10*c^8*d^11 - 25280512*a^8*b^9*c^7*d^12 + 17833984*a^9*b^8*c^6*d^13 - 8486912*a^10*b^7*c^5*d^14 + 2609152*a^11*b^6*c^4*d^15 - 466944*a^12*b^5*c^3*d^16 + 36864*a^13*b^4*c^2*d^17)*1i)/(64*(b^6*c^10 + a^6*c^4*d^6 - 6*a^5*b*c^5*d^5 + 15*a^2*b^4*c^8*d^2 - 20*a^3*b^3*c^7*d^3 + 15*a^4*b^2*c^6*d^4 - 6*a*b^5*c^9*d)))*1i + (((81*a^4*b^7*d^10)/16 + 28*b^11*c^4*d^6 - (2145*a*b^10*c^3*d^7)/16 - (675*a^3*b^8*c*d^9)/16 + 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15*a^4*b^2*c^6*d^4 - 6*a*b^5*c^9*d)))*1i + (((81*a^4*b^7*d^10)/16 + 28*b^11*c^4*d^6 - (2145*a*b^10*c^3*d^7)/16 - (675*a^3*b^8*c*d^9)/16 + (1971*a^2*b^9*c^2*d^8)/16)*1i)/(b^3*c^7 - a^3*c^4*d^3 + 3*a^2*b*c^5*d^2 - 3*a*b^2*c^6*d)) - (x*(81*a^4*b^9*d^11 + 3185*b^13*c^4*d^7 - 4788*a*b^12*c^3*d^8 - 756*a^3*b^10*c*d^10 + 2790*a^2*b^11*c^2*d^9))/(64*(b^6*c^10 + a^6*c^4*d^6 - 6*a^5*b*c^5*d^5 + 15*a^2*b^4*c^8*d^2 - 20*a^3*b^3*c^7*d^3 + 15*a^4*b^2*c^6*d^4 - 6*a*b^5*c^9*d))))/((-b^7/(256*a^11*d^8 + 256*a^3*b^8*c^8 - 2048*a^4*b^7*c^7*d + 7168*a^5*b^6*c^6*d^2 - 14336*a^6*b^5*c^5*d^3 + 17920*a^7*b^4*c^4*d^4 - 14336*a^8*b^3*c^3*d^5 + 7168*a^9*b^2*c^2*d^6 - 2048*a^10*b*c*d^7))^(1/4)*((-b^7/(256*a^11*d^8 + 256*a^3*b^8*c^8 - 2048*a^4*b^7*c^7*d + 7168*a^5*b^6*c^6*d^2 - 14336*a^6*b^5*c^5*d^3 + 17920*a^7*b^4*c^4*d^4 - 14336*a^8*b^3*c^3*d^5 + 7168*a^9*b^2*c^2*d^6 - 2048*a^10*b*c*d^7))^(1/4)*((-b^7/(256*a^11*d^8 + 256*a^3*b^8*c^8 - 2048*a^4*b^7*c^7*d + 7168*a^5*b^6*c^6*d^2 - 14336*a^6*b^5*c^5*d^3 + 17920*a^7*b^4*c^4*d^4 - 14336*a^8*b^3*c^3*d^5 + 7168*a^9*b^2*c^2*d^6 - 2048*a^10*b*c*d^7))^(3/4)*(((-b^7/(256*a^11*d^8 + 256*a^3*b^8*c^8 - 2048*a^4*b^7*c^7*d + 7168*a^5*b^6*c^6*d^2 - 14336*a^6*b^5*c^5*d^3 + 17920*a^7*b^4*c^4*d^4 - 14336*a^8*b^3*c^3*d^5 + 7168*a^9*b^2*c^2*d^6 - 2048*a^10*b*c*d^7))^(1/4)*(28672*a^2*b^13*c^13*d^5 - 4096*a*b^14*c^14*d^4 - 78848*a^3*b^12*c^12*d^6 + 90112*a^4*b^11*c^11*d^7 + 28672*a^5*b^10*c^10*d^8 - 229376*a^6*b^9*c^9*d^9 + 329728*a^7*b^8*c^8*d^10 - 253952*a^8*b^7*c^7*d^11 + 114688*a^9*b^6*c^6*d^12 - 28672*a^10*b^5*c^5*d^13 + 3072*a^11*b^4*c^4*d^14))/(b^3*c^7 - a^3*c^4*d^3 + 3*a^2*b*c^5*d^2 - 3*a*b^2*c^6*d) - (x*(65536*b^17*c^15*d^4 - 524288*a*b^16*c^14*d^5 + 1835008*a^2*b^15*c^13*d^6 - 3469312*a^3*b^14*c^12*d^7 + 2809856*a^4*b^13*c^11*d^8 + 3362816*a^5*b^12*c^10*d^9 - 14516224*a^6*b^11*c^9*d^10 + 24190976*a^7*b^10*c^8*d^11 - 25280512*a^8*b^9*c^7*d^12 + 17833984*a^9*b^8*c^6*d^13 - 8486912*a^10*b^7*c^5*d^14 + 2609152*a^11*b^6*c^4*d^15 - 466944*a^12*b^5*c^3*d^16 + 36864*a^13*b^4*c^2*d^17)*1i)/(64*(b^6*c^10 + a^6*c^4*d^6 - 6*a^5*b*c^5*d^5 + 15*a^2*b^4*c^8*d^2 - 20*a^3*b^3*c^7*d^3 + 15*a^4*b^2*c^6*d^4 - 6*a*b^5*c^9*d)))*1i + (((81*a^4*b^7*d^10)/16 + 28*b^11*c^4*d^6 - (2145*a*b^10*c^3*d^7)/16 - (675*a^3*b^8*c*d^9)/16 + (1971*a^2*b^9*c^2*d^8)/16)*1i)/(b^3*c^7 - a^3*c^4*d^3 + 3*a^2*b*c^5*d^2 - 3*a*b^2*c^6*d))*1i + (x*(81*a^4*b^9*d^11 + 3185*b^13*c^4*d^7 - 4788*a*b^12*c^3*d^8 - 756*a^3*b^10*c*d^10 + 2790*a^2*b^11*c^2*d^9)*1i)/(64*(b^6*c^10 + a^6*c^4*d^6 - 6*a^5*b*c^5*d^5 + 15*a^2*b^4*c^8*d^2 - 20*a^3*b^3*c^7*d^3 + 15*a^4*b^2*c^6*d^4 - 6*a*b^5*c^9*d))) + (-b^7/(256*a^11*d^8 + 256*a^3*b^8*c^8 - 2048*a^4*b^7*c^7*d + 7168*a^5*b^6*c^6*d^2 - 14336*a^6*b^5*c^5*d^3 + 17920*a^7*b^4*c^4*d^4 - 14336*a^8*b^3*c^3*d^5 + 7168*a^9*b^2*c^2*d^6 - 2048*a^10*b*c*d^7))^(1/4)*((-b^7/(256*a^11*d^8 + 256*a^3*b^8*c^8 - 2048*a^4*b^7*c^7*d + 7168*a^5*b^6*c^6*d^2 - 14336*a^6*b^5*c^5*d^3 + 17920*a^7*b^4*c^4*d^4 - 14336*a^8*b^3*c^3*d^5 + 7168*a^9*b^2*c^2*d^6 - 2048*a^10*b*c*d^7))^(1/4)*((-b^7/(256*a^11*d^8 + 256*a^3*b^8*c^8 - 2048*a^4*b^7*c^7*d + 7168*a^5*b^6*c^6*d^2 - 14336*a^6*b^5*c^5*d^3 + 17920*a^7*b^4*c^4*d^4 - 14336*a^8*b^3*c^3*d^5 + 7168*a^9*b^2*c^2*d^6 - 2048*a^10*b*c*d^7))^(3/4)*(((-b^7/(256*a^11*d^8 + 256*a^3*b^8*c^8 - 2048*a^4*b^7*c^7*d + 7168*a^5*b^6*c^6*d^2 - 14336*a^6*b^5*c^5*d^3 + 17920*a^7*b^4*c^4*d^4 - 14336*a^8*b^3*c^3*d^5 + 7168*a^9*b^2*c^2*d^6 - 2048*a^10*b*c*d^7))^(1/4)*(28672*a^2*b^13*c^13*d^5 - 4096*a*b^14*c^14*d^4 - 78848*a^3*b^12*c^12*d^6 + 90112*a^4*b^11*c^11*d^7 + 28672*a^5*b^10*c^10*d^8 - 229376*a^6*b^9*c^9*d^9 + 329728*a^7*b^8*c^8*d^10 - 253952*a^8*b^7*c^7*d^11 + 114688*a^9*b^6*c^6*d^12 - 28672*a^10*b^5*c^5*d^13 + 3072*a^11*b^4*c^4*d^14))/(b^3*c^7 - a^3*c^4*d^3 + 3*a^2*b*c^5*d^2 - 3*a*b^2*c^6*d) + (x*(65536*b^17*c^15*d^4 - 524288*a*b^16*c^14*d^5 + 1835008*a^2*b^15*c^13*d^6 - 3469312*a^3*b^14*c^12*d^7 + 2809856*a^4*b^13*c^11*d^8 + 3362816*a^5*b^12*c^10*d^9 - 14516224*a^6*b^11*c^9*d^10 + 24190976*a^7*b^10*c^8*d^11 - 25280512*a^8*b^9*c^7*d^12 + 17833984*a^9*b^8*c^6*d^13 - 8486912*a^10*b^7*c^5*d^14 + 2609152*a^11*b^6*c^4*d^15 - 466944*a^12*b^5*c^3*d^16 + 36864*a^13*b^4*c^2*d^17)*1i)/(64*(b^6*c^10 + a^6*c^4*d^6 - 6*a^5*b*c^5*d^5 + 15*a^2*b^4*c^8*d^2 - 20*a^3*b^3*c^7*d^3 + 15*a^4*b^2*c^6*d^4 - 6*a*b^5*c^9*d)))*1i + (((81*a^4*b^7*d^10)/16 + 28*b^11*c^4*d^6 - (2145*a*b^10*c^3*d^7)/16 - (675*a^3*b^8*c*d^9)/16 + (1971*a^2*b^9*c^2*d^8)/16)*1i)/(b^3*c^7 - a^3*c^4*d^3 + 3*a^2*b*c^5*d^2 - 3*a*b^2*c^6*d))*1i - (x*(81*a^4*b^9*d^11 + 3185*b^13*c^4*d^7 - 4788*a*b^12*c^3*d^8 - 756*a^3*b^10*c*d^10 + 2790*a^2*b^11*c^2*d^9)*1i)/(64*(b^6*c^10 + a^6*c^4*d^6 - 6*a^5*b*c^5*d^5 + 15*a^2*b^4*c^8*d^2 - 20*a^3*b^3*c^7*d^3 + 15*a^4*b^2*c^6*d^4 - 6*a*b^5*c^9*d)))))*(-b^7/(256*a^11*d^8 + 256*a^3*b^8*c^8 - 2048*a^4*b^7*c^7*d + 7168*a^5*b^6*c^6*d^2 - 14336*a^6*b^5*c^5*d^3 + 17920*a^7*b^4*c^4*d^4 - 14336*a^8*b^3*c^3*d^5 + 7168*a^9*b^2*c^2*d^6 - 2048*a^10*b*c*d^7))^(1/4) + (d*x)/(4*c*(c + d*x^4)*(a*d - b*c))","B"
166,1,2490,407,1.706574,"\text{Not used}","int((c + d*x^4)^5/(a + b*x^4)^2,x)","x\,\left(\frac{10\,c^3\,d^2}{b^2}-\frac{2\,a\,\left(\frac{2\,a\,\left(\frac{2\,a\,d^5}{b^3}-\frac{5\,c\,d^4}{b^2}\right)}{b}-\frac{a^2\,d^5}{b^4}+\frac{10\,c^2\,d^3}{b^2}\right)}{b}+\frac{a^2\,\left(\frac{2\,a\,d^5}{b^3}-\frac{5\,c\,d^4}{b^2}\right)}{b^2}\right)-x^9\,\left(\frac{2\,a\,d^5}{9\,b^3}-\frac{5\,c\,d^4}{9\,b^2}\right)+x^5\,\left(\frac{2\,a\,\left(\frac{2\,a\,d^5}{b^3}-\frac{5\,c\,d^4}{b^2}\right)}{5\,b}-\frac{a^2\,d^5}{5\,b^4}+\frac{2\,c^2\,d^3}{b^2}\right)+\frac{d^5\,x^{13}}{13\,b^2}-\frac{x\,\left(a^5\,d^5-5\,a^4\,b\,c\,d^4+10\,a^3\,b^2\,c^2\,d^3-10\,a^2\,b^3\,c^3\,d^2+5\,a\,b^4\,c^4\,d-b^5\,c^5\right)}{4\,a\,\left(b^6\,x^4+a\,b^5\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{x\,\left(289\,a^{10}\,d^{10}-2210\,a^9\,b\,c\,d^9+7285\,a^8\,b^2\,c^2\,d^8-13400\,a^7\,b^3\,c^3\,d^7+14770\,a^6\,b^4\,c^4\,d^6-9548\,a^5\,b^5\,c^5\,d^5+3010\,a^4\,b^6\,c^6\,d^4+40\,a^3\,b^7\,c^7\,d^3-275\,a^2\,b^8\,c^8\,d^2+30\,a\,b^9\,c^9\,d+9\,b^{10}\,c^{10}\right)}{4\,a^2\,b^7}-\frac{{\left(a\,d-b\,c\right)}^4\,\left(17\,a\,d+3\,b\,c\right)\,\left(17\,a^5\,d^5-65\,a^4\,b\,c\,d^4+90\,a^3\,b^2\,c^2\,d^3-50\,a^2\,b^3\,c^3\,d^2+5\,a\,b^4\,c^4\,d+3\,b^5\,c^5\right)}{4\,{\left(-a\right)}^{7/4}\,b^{29/4}}\right)\,{\left(a\,d-b\,c\right)}^4\,\left(17\,a\,d+3\,b\,c\right)\,1{}\mathrm{i}}{16\,{\left(-a\right)}^{7/4}\,b^{21/4}}+\frac{\left(\frac{x\,\left(289\,a^{10}\,d^{10}-2210\,a^9\,b\,c\,d^9+7285\,a^8\,b^2\,c^2\,d^8-13400\,a^7\,b^3\,c^3\,d^7+14770\,a^6\,b^4\,c^4\,d^6-9548\,a^5\,b^5\,c^5\,d^5+3010\,a^4\,b^6\,c^6\,d^4+40\,a^3\,b^7\,c^7\,d^3-275\,a^2\,b^8\,c^8\,d^2+30\,a\,b^9\,c^9\,d+9\,b^{10}\,c^{10}\right)}{4\,a^2\,b^7}+\frac{{\left(a\,d-b\,c\right)}^4\,\left(17\,a\,d+3\,b\,c\right)\,\left(17\,a^5\,d^5-65\,a^4\,b\,c\,d^4+90\,a^3\,b^2\,c^2\,d^3-50\,a^2\,b^3\,c^3\,d^2+5\,a\,b^4\,c^4\,d+3\,b^5\,c^5\right)}{4\,{\left(-a\right)}^{7/4}\,b^{29/4}}\right)\,{\left(a\,d-b\,c\right)}^4\,\left(17\,a\,d+3\,b\,c\right)\,1{}\mathrm{i}}{16\,{\left(-a\right)}^{7/4}\,b^{21/4}}}{\frac{\left(\frac{x\,\left(289\,a^{10}\,d^{10}-2210\,a^9\,b\,c\,d^9+7285\,a^8\,b^2\,c^2\,d^8-13400\,a^7\,b^3\,c^3\,d^7+14770\,a^6\,b^4\,c^4\,d^6-9548\,a^5\,b^5\,c^5\,d^5+3010\,a^4\,b^6\,c^6\,d^4+40\,a^3\,b^7\,c^7\,d^3-275\,a^2\,b^8\,c^8\,d^2+30\,a\,b^9\,c^9\,d+9\,b^{10}\,c^{10}\right)}{4\,a^2\,b^7}-\frac{{\left(a\,d-b\,c\right)}^4\,\left(17\,a\,d+3\,b\,c\right)\,\left(17\,a^5\,d^5-65\,a^4\,b\,c\,d^4+90\,a^3\,b^2\,c^2\,d^3-50\,a^2\,b^3\,c^3\,d^2+5\,a\,b^4\,c^4\,d+3\,b^5\,c^5\right)}{4\,{\left(-a\right)}^{7/4}\,b^{29/4}}\right)\,{\left(a\,d-b\,c\right)}^4\,\left(17\,a\,d+3\,b\,c\right)}{16\,{\left(-a\right)}^{7/4}\,b^{21/4}}-\frac{\left(\frac{x\,\left(289\,a^{10}\,d^{10}-2210\,a^9\,b\,c\,d^9+7285\,a^8\,b^2\,c^2\,d^8-13400\,a^7\,b^3\,c^3\,d^7+14770\,a^6\,b^4\,c^4\,d^6-9548\,a^5\,b^5\,c^5\,d^5+3010\,a^4\,b^6\,c^6\,d^4+40\,a^3\,b^7\,c^7\,d^3-275\,a^2\,b^8\,c^8\,d^2+30\,a\,b^9\,c^9\,d+9\,b^{10}\,c^{10}\right)}{4\,a^2\,b^7}+\frac{{\left(a\,d-b\,c\right)}^4\,\left(17\,a\,d+3\,b\,c\right)\,\left(17\,a^5\,d^5-65\,a^4\,b\,c\,d^4+90\,a^3\,b^2\,c^2\,d^3-50\,a^2\,b^3\,c^3\,d^2+5\,a\,b^4\,c^4\,d+3\,b^5\,c^5\right)}{4\,{\left(-a\right)}^{7/4}\,b^{29/4}}\right)\,{\left(a\,d-b\,c\right)}^4\,\left(17\,a\,d+3\,b\,c\right)}{16\,{\left(-a\right)}^{7/4}\,b^{21/4}}}\right)\,{\left(a\,d-b\,c\right)}^4\,\left(17\,a\,d+3\,b\,c\right)\,1{}\mathrm{i}}{8\,{\left(-a\right)}^{7/4}\,b^{21/4}}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{x\,\left(289\,a^{10}\,d^{10}-2210\,a^9\,b\,c\,d^9+7285\,a^8\,b^2\,c^2\,d^8-13400\,a^7\,b^3\,c^3\,d^7+14770\,a^6\,b^4\,c^4\,d^6-9548\,a^5\,b^5\,c^5\,d^5+3010\,a^4\,b^6\,c^6\,d^4+40\,a^3\,b^7\,c^7\,d^3-275\,a^2\,b^8\,c^8\,d^2+30\,a\,b^9\,c^9\,d+9\,b^{10}\,c^{10}\right)}{4\,a^2\,b^7}-\frac{{\left(a\,d-b\,c\right)}^4\,\left(17\,a\,d+3\,b\,c\right)\,\left(17\,a^5\,d^5-65\,a^4\,b\,c\,d^4+90\,a^3\,b^2\,c^2\,d^3-50\,a^2\,b^3\,c^3\,d^2+5\,a\,b^4\,c^4\,d+3\,b^5\,c^5\right)\,1{}\mathrm{i}}{4\,{\left(-a\right)}^{7/4}\,b^{29/4}}\right)\,{\left(a\,d-b\,c\right)}^4\,\left(17\,a\,d+3\,b\,c\right)}{16\,{\left(-a\right)}^{7/4}\,b^{21/4}}+\frac{\left(\frac{x\,\left(289\,a^{10}\,d^{10}-2210\,a^9\,b\,c\,d^9+7285\,a^8\,b^2\,c^2\,d^8-13400\,a^7\,b^3\,c^3\,d^7+14770\,a^6\,b^4\,c^4\,d^6-9548\,a^5\,b^5\,c^5\,d^5+3010\,a^4\,b^6\,c^6\,d^4+40\,a^3\,b^7\,c^7\,d^3-275\,a^2\,b^8\,c^8\,d^2+30\,a\,b^9\,c^9\,d+9\,b^{10}\,c^{10}\right)}{4\,a^2\,b^7}+\frac{{\left(a\,d-b\,c\right)}^4\,\left(17\,a\,d+3\,b\,c\right)\,\left(17\,a^5\,d^5-65\,a^4\,b\,c\,d^4+90\,a^3\,b^2\,c^2\,d^3-50\,a^2\,b^3\,c^3\,d^2+5\,a\,b^4\,c^4\,d+3\,b^5\,c^5\right)\,1{}\mathrm{i}}{4\,{\left(-a\right)}^{7/4}\,b^{29/4}}\right)\,{\left(a\,d-b\,c\right)}^4\,\left(17\,a\,d+3\,b\,c\right)}{16\,{\left(-a\right)}^{7/4}\,b^{21/4}}}{\frac{\left(\frac{x\,\left(289\,a^{10}\,d^{10}-2210\,a^9\,b\,c\,d^9+7285\,a^8\,b^2\,c^2\,d^8-13400\,a^7\,b^3\,c^3\,d^7+14770\,a^6\,b^4\,c^4\,d^6-9548\,a^5\,b^5\,c^5\,d^5+3010\,a^4\,b^6\,c^6\,d^4+40\,a^3\,b^7\,c^7\,d^3-275\,a^2\,b^8\,c^8\,d^2+30\,a\,b^9\,c^9\,d+9\,b^{10}\,c^{10}\right)}{4\,a^2\,b^7}-\frac{{\left(a\,d-b\,c\right)}^4\,\left(17\,a\,d+3\,b\,c\right)\,\left(17\,a^5\,d^5-65\,a^4\,b\,c\,d^4+90\,a^3\,b^2\,c^2\,d^3-50\,a^2\,b^3\,c^3\,d^2+5\,a\,b^4\,c^4\,d+3\,b^5\,c^5\right)\,1{}\mathrm{i}}{4\,{\left(-a\right)}^{7/4}\,b^{29/4}}\right)\,{\left(a\,d-b\,c\right)}^4\,\left(17\,a\,d+3\,b\,c\right)\,1{}\mathrm{i}}{16\,{\left(-a\right)}^{7/4}\,b^{21/4}}-\frac{\left(\frac{x\,\left(289\,a^{10}\,d^{10}-2210\,a^9\,b\,c\,d^9+7285\,a^8\,b^2\,c^2\,d^8-13400\,a^7\,b^3\,c^3\,d^7+14770\,a^6\,b^4\,c^4\,d^6-9548\,a^5\,b^5\,c^5\,d^5+3010\,a^4\,b^6\,c^6\,d^4+40\,a^3\,b^7\,c^7\,d^3-275\,a^2\,b^8\,c^8\,d^2+30\,a\,b^9\,c^9\,d+9\,b^{10}\,c^{10}\right)}{4\,a^2\,b^7}+\frac{{\left(a\,d-b\,c\right)}^4\,\left(17\,a\,d+3\,b\,c\right)\,\left(17\,a^5\,d^5-65\,a^4\,b\,c\,d^4+90\,a^3\,b^2\,c^2\,d^3-50\,a^2\,b^3\,c^3\,d^2+5\,a\,b^4\,c^4\,d+3\,b^5\,c^5\right)\,1{}\mathrm{i}}{4\,{\left(-a\right)}^{7/4}\,b^{29/4}}\right)\,{\left(a\,d-b\,c\right)}^4\,\left(17\,a\,d+3\,b\,c\right)\,1{}\mathrm{i}}{16\,{\left(-a\right)}^{7/4}\,b^{21/4}}}\right)\,{\left(a\,d-b\,c\right)}^4\,\left(17\,a\,d+3\,b\,c\right)}{8\,{\left(-a\right)}^{7/4}\,b^{21/4}}","Not used",1,"x*((10*c^3*d^2)/b^2 - (2*a*((2*a*((2*a*d^5)/b^3 - (5*c*d^4)/b^2))/b - (a^2*d^5)/b^4 + (10*c^2*d^3)/b^2))/b + (a^2*((2*a*d^5)/b^3 - (5*c*d^4)/b^2))/b^2) - x^9*((2*a*d^5)/(9*b^3) - (5*c*d^4)/(9*b^2)) + x^5*((2*a*((2*a*d^5)/b^3 - (5*c*d^4)/b^2))/(5*b) - (a^2*d^5)/(5*b^4) + (2*c^2*d^3)/b^2) + (d^5*x^13)/(13*b^2) - (x*(a^5*d^5 - b^5*c^5 - 10*a^2*b^3*c^3*d^2 + 10*a^3*b^2*c^2*d^3 + 5*a*b^4*c^4*d - 5*a^4*b*c*d^4))/(4*a*(a*b^5 + b^6*x^4)) + (atan(((((x*(289*a^10*d^10 + 9*b^10*c^10 - 275*a^2*b^8*c^8*d^2 + 40*a^3*b^7*c^7*d^3 + 3010*a^4*b^6*c^6*d^4 - 9548*a^5*b^5*c^5*d^5 + 14770*a^6*b^4*c^4*d^6 - 13400*a^7*b^3*c^3*d^7 + 7285*a^8*b^2*c^2*d^8 + 30*a*b^9*c^9*d - 2210*a^9*b*c*d^9))/(4*a^2*b^7) - ((a*d - b*c)^4*(17*a*d + 3*b*c)*(17*a^5*d^5 + 3*b^5*c^5 - 50*a^2*b^3*c^3*d^2 + 90*a^3*b^2*c^2*d^3 + 5*a*b^4*c^4*d - 65*a^4*b*c*d^4))/(4*(-a)^(7/4)*b^(29/4)))*(a*d - b*c)^4*(17*a*d + 3*b*c)*1i)/(16*(-a)^(7/4)*b^(21/4)) + (((x*(289*a^10*d^10 + 9*b^10*c^10 - 275*a^2*b^8*c^8*d^2 + 40*a^3*b^7*c^7*d^3 + 3010*a^4*b^6*c^6*d^4 - 9548*a^5*b^5*c^5*d^5 + 14770*a^6*b^4*c^4*d^6 - 13400*a^7*b^3*c^3*d^7 + 7285*a^8*b^2*c^2*d^8 + 30*a*b^9*c^9*d - 2210*a^9*b*c*d^9))/(4*a^2*b^7) + ((a*d - b*c)^4*(17*a*d + 3*b*c)*(17*a^5*d^5 + 3*b^5*c^5 - 50*a^2*b^3*c^3*d^2 + 90*a^3*b^2*c^2*d^3 + 5*a*b^4*c^4*d - 65*a^4*b*c*d^4))/(4*(-a)^(7/4)*b^(29/4)))*(a*d - b*c)^4*(17*a*d + 3*b*c)*1i)/(16*(-a)^(7/4)*b^(21/4)))/((((x*(289*a^10*d^10 + 9*b^10*c^10 - 275*a^2*b^8*c^8*d^2 + 40*a^3*b^7*c^7*d^3 + 3010*a^4*b^6*c^6*d^4 - 9548*a^5*b^5*c^5*d^5 + 14770*a^6*b^4*c^4*d^6 - 13400*a^7*b^3*c^3*d^7 + 7285*a^8*b^2*c^2*d^8 + 30*a*b^9*c^9*d - 2210*a^9*b*c*d^9))/(4*a^2*b^7) - ((a*d - b*c)^4*(17*a*d + 3*b*c)*(17*a^5*d^5 + 3*b^5*c^5 - 50*a^2*b^3*c^3*d^2 + 90*a^3*b^2*c^2*d^3 + 5*a*b^4*c^4*d - 65*a^4*b*c*d^4))/(4*(-a)^(7/4)*b^(29/4)))*(a*d - b*c)^4*(17*a*d + 3*b*c))/(16*(-a)^(7/4)*b^(21/4)) - (((x*(289*a^10*d^10 + 9*b^10*c^10 - 275*a^2*b^8*c^8*d^2 + 40*a^3*b^7*c^7*d^3 + 3010*a^4*b^6*c^6*d^4 - 9548*a^5*b^5*c^5*d^5 + 14770*a^6*b^4*c^4*d^6 - 13400*a^7*b^3*c^3*d^7 + 7285*a^8*b^2*c^2*d^8 + 30*a*b^9*c^9*d - 2210*a^9*b*c*d^9))/(4*a^2*b^7) + ((a*d - b*c)^4*(17*a*d + 3*b*c)*(17*a^5*d^5 + 3*b^5*c^5 - 50*a^2*b^3*c^3*d^2 + 90*a^3*b^2*c^2*d^3 + 5*a*b^4*c^4*d - 65*a^4*b*c*d^4))/(4*(-a)^(7/4)*b^(29/4)))*(a*d - b*c)^4*(17*a*d + 3*b*c))/(16*(-a)^(7/4)*b^(21/4))))*(a*d - b*c)^4*(17*a*d + 3*b*c)*1i)/(8*(-a)^(7/4)*b^(21/4)) + (atan(((((x*(289*a^10*d^10 + 9*b^10*c^10 - 275*a^2*b^8*c^8*d^2 + 40*a^3*b^7*c^7*d^3 + 3010*a^4*b^6*c^6*d^4 - 9548*a^5*b^5*c^5*d^5 + 14770*a^6*b^4*c^4*d^6 - 13400*a^7*b^3*c^3*d^7 + 7285*a^8*b^2*c^2*d^8 + 30*a*b^9*c^9*d - 2210*a^9*b*c*d^9))/(4*a^2*b^7) - ((a*d - b*c)^4*(17*a*d + 3*b*c)*(17*a^5*d^5 + 3*b^5*c^5 - 50*a^2*b^3*c^3*d^2 + 90*a^3*b^2*c^2*d^3 + 5*a*b^4*c^4*d - 65*a^4*b*c*d^4)*1i)/(4*(-a)^(7/4)*b^(29/4)))*(a*d - b*c)^4*(17*a*d + 3*b*c))/(16*(-a)^(7/4)*b^(21/4)) + (((x*(289*a^10*d^10 + 9*b^10*c^10 - 275*a^2*b^8*c^8*d^2 + 40*a^3*b^7*c^7*d^3 + 3010*a^4*b^6*c^6*d^4 - 9548*a^5*b^5*c^5*d^5 + 14770*a^6*b^4*c^4*d^6 - 13400*a^7*b^3*c^3*d^7 + 7285*a^8*b^2*c^2*d^8 + 30*a*b^9*c^9*d - 2210*a^9*b*c*d^9))/(4*a^2*b^7) + ((a*d - b*c)^4*(17*a*d + 3*b*c)*(17*a^5*d^5 + 3*b^5*c^5 - 50*a^2*b^3*c^3*d^2 + 90*a^3*b^2*c^2*d^3 + 5*a*b^4*c^4*d - 65*a^4*b*c*d^4)*1i)/(4*(-a)^(7/4)*b^(29/4)))*(a*d - b*c)^4*(17*a*d + 3*b*c))/(16*(-a)^(7/4)*b^(21/4)))/((((x*(289*a^10*d^10 + 9*b^10*c^10 - 275*a^2*b^8*c^8*d^2 + 40*a^3*b^7*c^7*d^3 + 3010*a^4*b^6*c^6*d^4 - 9548*a^5*b^5*c^5*d^5 + 14770*a^6*b^4*c^4*d^6 - 13400*a^7*b^3*c^3*d^7 + 7285*a^8*b^2*c^2*d^8 + 30*a*b^9*c^9*d - 2210*a^9*b*c*d^9))/(4*a^2*b^7) - ((a*d - b*c)^4*(17*a*d + 3*b*c)*(17*a^5*d^5 + 3*b^5*c^5 - 50*a^2*b^3*c^3*d^2 + 90*a^3*b^2*c^2*d^3 + 5*a*b^4*c^4*d - 65*a^4*b*c*d^4)*1i)/(4*(-a)^(7/4)*b^(29/4)))*(a*d - b*c)^4*(17*a*d + 3*b*c)*1i)/(16*(-a)^(7/4)*b^(21/4)) - (((x*(289*a^10*d^10 + 9*b^10*c^10 - 275*a^2*b^8*c^8*d^2 + 40*a^3*b^7*c^7*d^3 + 3010*a^4*b^6*c^6*d^4 - 9548*a^5*b^5*c^5*d^5 + 14770*a^6*b^4*c^4*d^6 - 13400*a^7*b^3*c^3*d^7 + 7285*a^8*b^2*c^2*d^8 + 30*a*b^9*c^9*d - 2210*a^9*b*c*d^9))/(4*a^2*b^7) + ((a*d - b*c)^4*(17*a*d + 3*b*c)*(17*a^5*d^5 + 3*b^5*c^5 - 50*a^2*b^3*c^3*d^2 + 90*a^3*b^2*c^2*d^3 + 5*a*b^4*c^4*d - 65*a^4*b*c*d^4)*1i)/(4*(-a)^(7/4)*b^(29/4)))*(a*d - b*c)^4*(17*a*d + 3*b*c)*1i)/(16*(-a)^(7/4)*b^(21/4))))*(a*d - b*c)^4*(17*a*d + 3*b*c))/(8*(-a)^(7/4)*b^(21/4))","B"
167,1,2043,357,0.302463,"\text{Not used}","int((c + d*x^4)^4/(a + b*x^4)^2,x)","x\,\left(\frac{2\,a\,\left(\frac{2\,a\,d^4}{b^3}-\frac{4\,c\,d^3}{b^2}\right)}{b}-\frac{a^2\,d^4}{b^4}+\frac{6\,c^2\,d^2}{b^2}\right)-x^5\,\left(\frac{2\,a\,d^4}{5\,b^3}-\frac{4\,c\,d^3}{5\,b^2}\right)+\frac{d^4\,x^9}{9\,b^2}+\frac{x\,\left(a^4\,d^4-4\,a^3\,b\,c\,d^3+6\,a^2\,b^2\,c^2\,d^2-4\,a\,b^3\,c^3\,d+b^4\,c^4\right)}{4\,a\,\left(b^5\,x^4+a\,b^4\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{x\,\left(169\,a^8\,d^8-936\,a^7\,b\,c\,d^7+2076\,a^6\,b^2\,c^2\,d^6-2264\,a^5\,b^3\,c^3\,d^5+1110\,a^4\,b^4\,c^4\,d^4-24\,a^3\,b^5\,c^5\,d^3-164\,a^2\,b^6\,c^6\,d^2+24\,a\,b^7\,c^7\,d+9\,b^8\,c^8\right)}{4\,a^2\,b^5}-\frac{{\left(a\,d-b\,c\right)}^3\,\left(13\,a\,d+3\,b\,c\right)\,\left(-13\,a^4\,d^4+36\,a^3\,b\,c\,d^3-30\,a^2\,b^2\,c^2\,d^2+4\,a\,b^3\,c^3\,d+3\,b^4\,c^4\right)}{4\,{\left(-a\right)}^{7/4}\,b^{21/4}}\right)\,{\left(a\,d-b\,c\right)}^3\,\left(13\,a\,d+3\,b\,c\right)\,1{}\mathrm{i}}{16\,{\left(-a\right)}^{7/4}\,b^{17/4}}+\frac{\left(\frac{x\,\left(169\,a^8\,d^8-936\,a^7\,b\,c\,d^7+2076\,a^6\,b^2\,c^2\,d^6-2264\,a^5\,b^3\,c^3\,d^5+1110\,a^4\,b^4\,c^4\,d^4-24\,a^3\,b^5\,c^5\,d^3-164\,a^2\,b^6\,c^6\,d^2+24\,a\,b^7\,c^7\,d+9\,b^8\,c^8\right)}{4\,a^2\,b^5}+\frac{{\left(a\,d-b\,c\right)}^3\,\left(13\,a\,d+3\,b\,c\right)\,\left(-13\,a^4\,d^4+36\,a^3\,b\,c\,d^3-30\,a^2\,b^2\,c^2\,d^2+4\,a\,b^3\,c^3\,d+3\,b^4\,c^4\right)}{4\,{\left(-a\right)}^{7/4}\,b^{21/4}}\right)\,{\left(a\,d-b\,c\right)}^3\,\left(13\,a\,d+3\,b\,c\right)\,1{}\mathrm{i}}{16\,{\left(-a\right)}^{7/4}\,b^{17/4}}}{\frac{\left(\frac{x\,\left(169\,a^8\,d^8-936\,a^7\,b\,c\,d^7+2076\,a^6\,b^2\,c^2\,d^6-2264\,a^5\,b^3\,c^3\,d^5+1110\,a^4\,b^4\,c^4\,d^4-24\,a^3\,b^5\,c^5\,d^3-164\,a^2\,b^6\,c^6\,d^2+24\,a\,b^7\,c^7\,d+9\,b^8\,c^8\right)}{4\,a^2\,b^5}-\frac{{\left(a\,d-b\,c\right)}^3\,\left(13\,a\,d+3\,b\,c\right)\,\left(-13\,a^4\,d^4+36\,a^3\,b\,c\,d^3-30\,a^2\,b^2\,c^2\,d^2+4\,a\,b^3\,c^3\,d+3\,b^4\,c^4\right)}{4\,{\left(-a\right)}^{7/4}\,b^{21/4}}\right)\,{\left(a\,d-b\,c\right)}^3\,\left(13\,a\,d+3\,b\,c\right)}{16\,{\left(-a\right)}^{7/4}\,b^{17/4}}-\frac{\left(\frac{x\,\left(169\,a^8\,d^8-936\,a^7\,b\,c\,d^7+2076\,a^6\,b^2\,c^2\,d^6-2264\,a^5\,b^3\,c^3\,d^5+1110\,a^4\,b^4\,c^4\,d^4-24\,a^3\,b^5\,c^5\,d^3-164\,a^2\,b^6\,c^6\,d^2+24\,a\,b^7\,c^7\,d+9\,b^8\,c^8\right)}{4\,a^2\,b^5}+\frac{{\left(a\,d-b\,c\right)}^3\,\left(13\,a\,d+3\,b\,c\right)\,\left(-13\,a^4\,d^4+36\,a^3\,b\,c\,d^3-30\,a^2\,b^2\,c^2\,d^2+4\,a\,b^3\,c^3\,d+3\,b^4\,c^4\right)}{4\,{\left(-a\right)}^{7/4}\,b^{21/4}}\right)\,{\left(a\,d-b\,c\right)}^3\,\left(13\,a\,d+3\,b\,c\right)}{16\,{\left(-a\right)}^{7/4}\,b^{17/4}}}\right)\,{\left(a\,d-b\,c\right)}^3\,\left(13\,a\,d+3\,b\,c\right)\,1{}\mathrm{i}}{8\,{\left(-a\right)}^{7/4}\,b^{17/4}}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{x\,\left(169\,a^8\,d^8-936\,a^7\,b\,c\,d^7+2076\,a^6\,b^2\,c^2\,d^6-2264\,a^5\,b^3\,c^3\,d^5+1110\,a^4\,b^4\,c^4\,d^4-24\,a^3\,b^5\,c^5\,d^3-164\,a^2\,b^6\,c^6\,d^2+24\,a\,b^7\,c^7\,d+9\,b^8\,c^8\right)}{4\,a^2\,b^5}-\frac{{\left(a\,d-b\,c\right)}^3\,\left(13\,a\,d+3\,b\,c\right)\,\left(-13\,a^4\,d^4+36\,a^3\,b\,c\,d^3-30\,a^2\,b^2\,c^2\,d^2+4\,a\,b^3\,c^3\,d+3\,b^4\,c^4\right)\,1{}\mathrm{i}}{4\,{\left(-a\right)}^{7/4}\,b^{21/4}}\right)\,{\left(a\,d-b\,c\right)}^3\,\left(13\,a\,d+3\,b\,c\right)}{16\,{\left(-a\right)}^{7/4}\,b^{17/4}}+\frac{\left(\frac{x\,\left(169\,a^8\,d^8-936\,a^7\,b\,c\,d^7+2076\,a^6\,b^2\,c^2\,d^6-2264\,a^5\,b^3\,c^3\,d^5+1110\,a^4\,b^4\,c^4\,d^4-24\,a^3\,b^5\,c^5\,d^3-164\,a^2\,b^6\,c^6\,d^2+24\,a\,b^7\,c^7\,d+9\,b^8\,c^8\right)}{4\,a^2\,b^5}+\frac{{\left(a\,d-b\,c\right)}^3\,\left(13\,a\,d+3\,b\,c\right)\,\left(-13\,a^4\,d^4+36\,a^3\,b\,c\,d^3-30\,a^2\,b^2\,c^2\,d^2+4\,a\,b^3\,c^3\,d+3\,b^4\,c^4\right)\,1{}\mathrm{i}}{4\,{\left(-a\right)}^{7/4}\,b^{21/4}}\right)\,{\left(a\,d-b\,c\right)}^3\,\left(13\,a\,d+3\,b\,c\right)}{16\,{\left(-a\right)}^{7/4}\,b^{17/4}}}{\frac{\left(\frac{x\,\left(169\,a^8\,d^8-936\,a^7\,b\,c\,d^7+2076\,a^6\,b^2\,c^2\,d^6-2264\,a^5\,b^3\,c^3\,d^5+1110\,a^4\,b^4\,c^4\,d^4-24\,a^3\,b^5\,c^5\,d^3-164\,a^2\,b^6\,c^6\,d^2+24\,a\,b^7\,c^7\,d+9\,b^8\,c^8\right)}{4\,a^2\,b^5}-\frac{{\left(a\,d-b\,c\right)}^3\,\left(13\,a\,d+3\,b\,c\right)\,\left(-13\,a^4\,d^4+36\,a^3\,b\,c\,d^3-30\,a^2\,b^2\,c^2\,d^2+4\,a\,b^3\,c^3\,d+3\,b^4\,c^4\right)\,1{}\mathrm{i}}{4\,{\left(-a\right)}^{7/4}\,b^{21/4}}\right)\,{\left(a\,d-b\,c\right)}^3\,\left(13\,a\,d+3\,b\,c\right)\,1{}\mathrm{i}}{16\,{\left(-a\right)}^{7/4}\,b^{17/4}}-\frac{\left(\frac{x\,\left(169\,a^8\,d^8-936\,a^7\,b\,c\,d^7+2076\,a^6\,b^2\,c^2\,d^6-2264\,a^5\,b^3\,c^3\,d^5+1110\,a^4\,b^4\,c^4\,d^4-24\,a^3\,b^5\,c^5\,d^3-164\,a^2\,b^6\,c^6\,d^2+24\,a\,b^7\,c^7\,d+9\,b^8\,c^8\right)}{4\,a^2\,b^5}+\frac{{\left(a\,d-b\,c\right)}^3\,\left(13\,a\,d+3\,b\,c\right)\,\left(-13\,a^4\,d^4+36\,a^3\,b\,c\,d^3-30\,a^2\,b^2\,c^2\,d^2+4\,a\,b^3\,c^3\,d+3\,b^4\,c^4\right)\,1{}\mathrm{i}}{4\,{\left(-a\right)}^{7/4}\,b^{21/4}}\right)\,{\left(a\,d-b\,c\right)}^3\,\left(13\,a\,d+3\,b\,c\right)\,1{}\mathrm{i}}{16\,{\left(-a\right)}^{7/4}\,b^{17/4}}}\right)\,{\left(a\,d-b\,c\right)}^3\,\left(13\,a\,d+3\,b\,c\right)}{8\,{\left(-a\right)}^{7/4}\,b^{17/4}}","Not used",1,"x*((2*a*((2*a*d^4)/b^3 - (4*c*d^3)/b^2))/b - (a^2*d^4)/b^4 + (6*c^2*d^2)/b^2) - x^5*((2*a*d^4)/(5*b^3) - (4*c*d^3)/(5*b^2)) + (d^4*x^9)/(9*b^2) + (x*(a^4*d^4 + b^4*c^4 + 6*a^2*b^2*c^2*d^2 - 4*a*b^3*c^3*d - 4*a^3*b*c*d^3))/(4*a*(a*b^4 + b^5*x^4)) + (atan(((((x*(169*a^8*d^8 + 9*b^8*c^8 - 164*a^2*b^6*c^6*d^2 - 24*a^3*b^5*c^5*d^3 + 1110*a^4*b^4*c^4*d^4 - 2264*a^5*b^3*c^3*d^5 + 2076*a^6*b^2*c^2*d^6 + 24*a*b^7*c^7*d - 936*a^7*b*c*d^7))/(4*a^2*b^5) - ((a*d - b*c)^3*(13*a*d + 3*b*c)*(3*b^4*c^4 - 13*a^4*d^4 - 30*a^2*b^2*c^2*d^2 + 4*a*b^3*c^3*d + 36*a^3*b*c*d^3))/(4*(-a)^(7/4)*b^(21/4)))*(a*d - b*c)^3*(13*a*d + 3*b*c)*1i)/(16*(-a)^(7/4)*b^(17/4)) + (((x*(169*a^8*d^8 + 9*b^8*c^8 - 164*a^2*b^6*c^6*d^2 - 24*a^3*b^5*c^5*d^3 + 1110*a^4*b^4*c^4*d^4 - 2264*a^5*b^3*c^3*d^5 + 2076*a^6*b^2*c^2*d^6 + 24*a*b^7*c^7*d - 936*a^7*b*c*d^7))/(4*a^2*b^5) + ((a*d - b*c)^3*(13*a*d + 3*b*c)*(3*b^4*c^4 - 13*a^4*d^4 - 30*a^2*b^2*c^2*d^2 + 4*a*b^3*c^3*d + 36*a^3*b*c*d^3))/(4*(-a)^(7/4)*b^(21/4)))*(a*d - b*c)^3*(13*a*d + 3*b*c)*1i)/(16*(-a)^(7/4)*b^(17/4)))/((((x*(169*a^8*d^8 + 9*b^8*c^8 - 164*a^2*b^6*c^6*d^2 - 24*a^3*b^5*c^5*d^3 + 1110*a^4*b^4*c^4*d^4 - 2264*a^5*b^3*c^3*d^5 + 2076*a^6*b^2*c^2*d^6 + 24*a*b^7*c^7*d - 936*a^7*b*c*d^7))/(4*a^2*b^5) - ((a*d - b*c)^3*(13*a*d + 3*b*c)*(3*b^4*c^4 - 13*a^4*d^4 - 30*a^2*b^2*c^2*d^2 + 4*a*b^3*c^3*d + 36*a^3*b*c*d^3))/(4*(-a)^(7/4)*b^(21/4)))*(a*d - b*c)^3*(13*a*d + 3*b*c))/(16*(-a)^(7/4)*b^(17/4)) - (((x*(169*a^8*d^8 + 9*b^8*c^8 - 164*a^2*b^6*c^6*d^2 - 24*a^3*b^5*c^5*d^3 + 1110*a^4*b^4*c^4*d^4 - 2264*a^5*b^3*c^3*d^5 + 2076*a^6*b^2*c^2*d^6 + 24*a*b^7*c^7*d - 936*a^7*b*c*d^7))/(4*a^2*b^5) + ((a*d - b*c)^3*(13*a*d + 3*b*c)*(3*b^4*c^4 - 13*a^4*d^4 - 30*a^2*b^2*c^2*d^2 + 4*a*b^3*c^3*d + 36*a^3*b*c*d^3))/(4*(-a)^(7/4)*b^(21/4)))*(a*d - b*c)^3*(13*a*d + 3*b*c))/(16*(-a)^(7/4)*b^(17/4))))*(a*d - b*c)^3*(13*a*d + 3*b*c)*1i)/(8*(-a)^(7/4)*b^(17/4)) + (atan(((((x*(169*a^8*d^8 + 9*b^8*c^8 - 164*a^2*b^6*c^6*d^2 - 24*a^3*b^5*c^5*d^3 + 1110*a^4*b^4*c^4*d^4 - 2264*a^5*b^3*c^3*d^5 + 2076*a^6*b^2*c^2*d^6 + 24*a*b^7*c^7*d - 936*a^7*b*c*d^7))/(4*a^2*b^5) - ((a*d - b*c)^3*(13*a*d + 3*b*c)*(3*b^4*c^4 - 13*a^4*d^4 - 30*a^2*b^2*c^2*d^2 + 4*a*b^3*c^3*d + 36*a^3*b*c*d^3)*1i)/(4*(-a)^(7/4)*b^(21/4)))*(a*d - b*c)^3*(13*a*d + 3*b*c))/(16*(-a)^(7/4)*b^(17/4)) + (((x*(169*a^8*d^8 + 9*b^8*c^8 - 164*a^2*b^6*c^6*d^2 - 24*a^3*b^5*c^5*d^3 + 1110*a^4*b^4*c^4*d^4 - 2264*a^5*b^3*c^3*d^5 + 2076*a^6*b^2*c^2*d^6 + 24*a*b^7*c^7*d - 936*a^7*b*c*d^7))/(4*a^2*b^5) + ((a*d - b*c)^3*(13*a*d + 3*b*c)*(3*b^4*c^4 - 13*a^4*d^4 - 30*a^2*b^2*c^2*d^2 + 4*a*b^3*c^3*d + 36*a^3*b*c*d^3)*1i)/(4*(-a)^(7/4)*b^(21/4)))*(a*d - b*c)^3*(13*a*d + 3*b*c))/(16*(-a)^(7/4)*b^(17/4)))/((((x*(169*a^8*d^8 + 9*b^8*c^8 - 164*a^2*b^6*c^6*d^2 - 24*a^3*b^5*c^5*d^3 + 1110*a^4*b^4*c^4*d^4 - 2264*a^5*b^3*c^3*d^5 + 2076*a^6*b^2*c^2*d^6 + 24*a*b^7*c^7*d - 936*a^7*b*c*d^7))/(4*a^2*b^5) - ((a*d - b*c)^3*(13*a*d + 3*b*c)*(3*b^4*c^4 - 13*a^4*d^4 - 30*a^2*b^2*c^2*d^2 + 4*a*b^3*c^3*d + 36*a^3*b*c*d^3)*1i)/(4*(-a)^(7/4)*b^(21/4)))*(a*d - b*c)^3*(13*a*d + 3*b*c)*1i)/(16*(-a)^(7/4)*b^(17/4)) - (((x*(169*a^8*d^8 + 9*b^8*c^8 - 164*a^2*b^6*c^6*d^2 - 24*a^3*b^5*c^5*d^3 + 1110*a^4*b^4*c^4*d^4 - 2264*a^5*b^3*c^3*d^5 + 2076*a^6*b^2*c^2*d^6 + 24*a*b^7*c^7*d - 936*a^7*b*c*d^7))/(4*a^2*b^5) + ((a*d - b*c)^3*(13*a*d + 3*b*c)*(3*b^4*c^4 - 13*a^4*d^4 - 30*a^2*b^2*c^2*d^2 + 4*a*b^3*c^3*d + 36*a^3*b*c*d^3)*1i)/(4*(-a)^(7/4)*b^(21/4)))*(a*d - b*c)^3*(13*a*d + 3*b*c)*1i)/(16*(-a)^(7/4)*b^(17/4))))*(a*d - b*c)^3*(13*a*d + 3*b*c))/(8*(-a)^(7/4)*b^(17/4))","B"
168,1,1616,317,1.530290,"\text{Not used}","int((c + d*x^4)^3/(a + b*x^4)^2,x)","\frac{d^3\,x^5}{5\,b^2}-x\,\left(\frac{2\,a\,d^3}{b^3}-\frac{3\,c\,d^2}{b^2}\right)-\frac{x\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)}{4\,a\,\left(b^4\,x^4+a\,b^3\right)}+\frac{\mathrm{atan}\left(\frac{\frac{{\left(a\,d-b\,c\right)}^2\,\left(3\,a\,d+b\,c\right)\,\left(\frac{9\,x\,\left(9\,a^6\,d^6-30\,a^5\,b\,c\,d^5+31\,a^4\,b^2\,c^2\,d^4-4\,a^3\,b^3\,c^3\,d^3-9\,a^2\,b^4\,c^4\,d^2+2\,a\,b^5\,c^5\,d+b^6\,c^6\right)}{4\,a^2\,b^3}-\frac{3\,{\left(a\,d-b\,c\right)}^2\,\left(3\,a\,d+b\,c\right)\,\left(36\,a^3\,d^3-60\,a^2\,b\,c\,d^2+12\,a\,b^2\,c^2\,d+12\,b^3\,c^3\right)}{16\,{\left(-a\right)}^{7/4}\,b^{13/4}}\right)\,3{}\mathrm{i}}{16\,{\left(-a\right)}^{7/4}\,b^{13/4}}+\frac{{\left(a\,d-b\,c\right)}^2\,\left(3\,a\,d+b\,c\right)\,\left(\frac{9\,x\,\left(9\,a^6\,d^6-30\,a^5\,b\,c\,d^5+31\,a^4\,b^2\,c^2\,d^4-4\,a^3\,b^3\,c^3\,d^3-9\,a^2\,b^4\,c^4\,d^2+2\,a\,b^5\,c^5\,d+b^6\,c^6\right)}{4\,a^2\,b^3}+\frac{3\,{\left(a\,d-b\,c\right)}^2\,\left(3\,a\,d+b\,c\right)\,\left(36\,a^3\,d^3-60\,a^2\,b\,c\,d^2+12\,a\,b^2\,c^2\,d+12\,b^3\,c^3\right)}{16\,{\left(-a\right)}^{7/4}\,b^{13/4}}\right)\,3{}\mathrm{i}}{16\,{\left(-a\right)}^{7/4}\,b^{13/4}}}{\frac{3\,{\left(a\,d-b\,c\right)}^2\,\left(3\,a\,d+b\,c\right)\,\left(\frac{9\,x\,\left(9\,a^6\,d^6-30\,a^5\,b\,c\,d^5+31\,a^4\,b^2\,c^2\,d^4-4\,a^3\,b^3\,c^3\,d^3-9\,a^2\,b^4\,c^4\,d^2+2\,a\,b^5\,c^5\,d+b^6\,c^6\right)}{4\,a^2\,b^3}-\frac{3\,{\left(a\,d-b\,c\right)}^2\,\left(3\,a\,d+b\,c\right)\,\left(36\,a^3\,d^3-60\,a^2\,b\,c\,d^2+12\,a\,b^2\,c^2\,d+12\,b^3\,c^3\right)}{16\,{\left(-a\right)}^{7/4}\,b^{13/4}}\right)}{16\,{\left(-a\right)}^{7/4}\,b^{13/4}}-\frac{3\,{\left(a\,d-b\,c\right)}^2\,\left(3\,a\,d+b\,c\right)\,\left(\frac{9\,x\,\left(9\,a^6\,d^6-30\,a^5\,b\,c\,d^5+31\,a^4\,b^2\,c^2\,d^4-4\,a^3\,b^3\,c^3\,d^3-9\,a^2\,b^4\,c^4\,d^2+2\,a\,b^5\,c^5\,d+b^6\,c^6\right)}{4\,a^2\,b^3}+\frac{3\,{\left(a\,d-b\,c\right)}^2\,\left(3\,a\,d+b\,c\right)\,\left(36\,a^3\,d^3-60\,a^2\,b\,c\,d^2+12\,a\,b^2\,c^2\,d+12\,b^3\,c^3\right)}{16\,{\left(-a\right)}^{7/4}\,b^{13/4}}\right)}{16\,{\left(-a\right)}^{7/4}\,b^{13/4}}}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(3\,a\,d+b\,c\right)\,3{}\mathrm{i}}{8\,{\left(-a\right)}^{7/4}\,b^{13/4}}+\frac{3\,\mathrm{atan}\left(\frac{\frac{3\,{\left(a\,d-b\,c\right)}^2\,\left(3\,a\,d+b\,c\right)\,\left(\frac{9\,x\,\left(9\,a^6\,d^6-30\,a^5\,b\,c\,d^5+31\,a^4\,b^2\,c^2\,d^4-4\,a^3\,b^3\,c^3\,d^3-9\,a^2\,b^4\,c^4\,d^2+2\,a\,b^5\,c^5\,d+b^6\,c^6\right)}{4\,a^2\,b^3}-\frac{{\left(a\,d-b\,c\right)}^2\,\left(3\,a\,d+b\,c\right)\,\left(36\,a^3\,d^3-60\,a^2\,b\,c\,d^2+12\,a\,b^2\,c^2\,d+12\,b^3\,c^3\right)\,3{}\mathrm{i}}{16\,{\left(-a\right)}^{7/4}\,b^{13/4}}\right)}{16\,{\left(-a\right)}^{7/4}\,b^{13/4}}+\frac{3\,{\left(a\,d-b\,c\right)}^2\,\left(3\,a\,d+b\,c\right)\,\left(\frac{9\,x\,\left(9\,a^6\,d^6-30\,a^5\,b\,c\,d^5+31\,a^4\,b^2\,c^2\,d^4-4\,a^3\,b^3\,c^3\,d^3-9\,a^2\,b^4\,c^4\,d^2+2\,a\,b^5\,c^5\,d+b^6\,c^6\right)}{4\,a^2\,b^3}+\frac{{\left(a\,d-b\,c\right)}^2\,\left(3\,a\,d+b\,c\right)\,\left(36\,a^3\,d^3-60\,a^2\,b\,c\,d^2+12\,a\,b^2\,c^2\,d+12\,b^3\,c^3\right)\,3{}\mathrm{i}}{16\,{\left(-a\right)}^{7/4}\,b^{13/4}}\right)}{16\,{\left(-a\right)}^{7/4}\,b^{13/4}}}{\frac{{\left(a\,d-b\,c\right)}^2\,\left(3\,a\,d+b\,c\right)\,\left(\frac{9\,x\,\left(9\,a^6\,d^6-30\,a^5\,b\,c\,d^5+31\,a^4\,b^2\,c^2\,d^4-4\,a^3\,b^3\,c^3\,d^3-9\,a^2\,b^4\,c^4\,d^2+2\,a\,b^5\,c^5\,d+b^6\,c^6\right)}{4\,a^2\,b^3}-\frac{{\left(a\,d-b\,c\right)}^2\,\left(3\,a\,d+b\,c\right)\,\left(36\,a^3\,d^3-60\,a^2\,b\,c\,d^2+12\,a\,b^2\,c^2\,d+12\,b^3\,c^3\right)\,3{}\mathrm{i}}{16\,{\left(-a\right)}^{7/4}\,b^{13/4}}\right)\,3{}\mathrm{i}}{16\,{\left(-a\right)}^{7/4}\,b^{13/4}}-\frac{{\left(a\,d-b\,c\right)}^2\,\left(3\,a\,d+b\,c\right)\,\left(\frac{9\,x\,\left(9\,a^6\,d^6-30\,a^5\,b\,c\,d^5+31\,a^4\,b^2\,c^2\,d^4-4\,a^3\,b^3\,c^3\,d^3-9\,a^2\,b^4\,c^4\,d^2+2\,a\,b^5\,c^5\,d+b^6\,c^6\right)}{4\,a^2\,b^3}+\frac{{\left(a\,d-b\,c\right)}^2\,\left(3\,a\,d+b\,c\right)\,\left(36\,a^3\,d^3-60\,a^2\,b\,c\,d^2+12\,a\,b^2\,c^2\,d+12\,b^3\,c^3\right)\,3{}\mathrm{i}}{16\,{\left(-a\right)}^{7/4}\,b^{13/4}}\right)\,3{}\mathrm{i}}{16\,{\left(-a\right)}^{7/4}\,b^{13/4}}}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(3\,a\,d+b\,c\right)}{8\,{\left(-a\right)}^{7/4}\,b^{13/4}}","Not used",1,"(d^3*x^5)/(5*b^2) - x*((2*a*d^3)/b^3 - (3*c*d^2)/b^2) - (x*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))/(4*a*(a*b^3 + b^4*x^4)) + (atan((((a*d - b*c)^2*(3*a*d + b*c)*((9*x*(9*a^6*d^6 + b^6*c^6 - 9*a^2*b^4*c^4*d^2 - 4*a^3*b^3*c^3*d^3 + 31*a^4*b^2*c^2*d^4 + 2*a*b^5*c^5*d - 30*a^5*b*c*d^5))/(4*a^2*b^3) - (3*(a*d - b*c)^2*(3*a*d + b*c)*(36*a^3*d^3 + 12*b^3*c^3 + 12*a*b^2*c^2*d - 60*a^2*b*c*d^2))/(16*(-a)^(7/4)*b^(13/4)))*3i)/(16*(-a)^(7/4)*b^(13/4)) + ((a*d - b*c)^2*(3*a*d + b*c)*((9*x*(9*a^6*d^6 + b^6*c^6 - 9*a^2*b^4*c^4*d^2 - 4*a^3*b^3*c^3*d^3 + 31*a^4*b^2*c^2*d^4 + 2*a*b^5*c^5*d - 30*a^5*b*c*d^5))/(4*a^2*b^3) + (3*(a*d - b*c)^2*(3*a*d + b*c)*(36*a^3*d^3 + 12*b^3*c^3 + 12*a*b^2*c^2*d - 60*a^2*b*c*d^2))/(16*(-a)^(7/4)*b^(13/4)))*3i)/(16*(-a)^(7/4)*b^(13/4)))/((3*(a*d - b*c)^2*(3*a*d + b*c)*((9*x*(9*a^6*d^6 + b^6*c^6 - 9*a^2*b^4*c^4*d^2 - 4*a^3*b^3*c^3*d^3 + 31*a^4*b^2*c^2*d^4 + 2*a*b^5*c^5*d - 30*a^5*b*c*d^5))/(4*a^2*b^3) - (3*(a*d - b*c)^2*(3*a*d + b*c)*(36*a^3*d^3 + 12*b^3*c^3 + 12*a*b^2*c^2*d - 60*a^2*b*c*d^2))/(16*(-a)^(7/4)*b^(13/4))))/(16*(-a)^(7/4)*b^(13/4)) - (3*(a*d - b*c)^2*(3*a*d + b*c)*((9*x*(9*a^6*d^6 + b^6*c^6 - 9*a^2*b^4*c^4*d^2 - 4*a^3*b^3*c^3*d^3 + 31*a^4*b^2*c^2*d^4 + 2*a*b^5*c^5*d - 30*a^5*b*c*d^5))/(4*a^2*b^3) + (3*(a*d - b*c)^2*(3*a*d + b*c)*(36*a^3*d^3 + 12*b^3*c^3 + 12*a*b^2*c^2*d - 60*a^2*b*c*d^2))/(16*(-a)^(7/4)*b^(13/4))))/(16*(-a)^(7/4)*b^(13/4))))*(a*d - b*c)^2*(3*a*d + b*c)*3i)/(8*(-a)^(7/4)*b^(13/4)) + (3*atan(((3*(a*d - b*c)^2*(3*a*d + b*c)*((9*x*(9*a^6*d^6 + b^6*c^6 - 9*a^2*b^4*c^4*d^2 - 4*a^3*b^3*c^3*d^3 + 31*a^4*b^2*c^2*d^4 + 2*a*b^5*c^5*d - 30*a^5*b*c*d^5))/(4*a^2*b^3) - ((a*d - b*c)^2*(3*a*d + b*c)*(36*a^3*d^3 + 12*b^3*c^3 + 12*a*b^2*c^2*d - 60*a^2*b*c*d^2)*3i)/(16*(-a)^(7/4)*b^(13/4))))/(16*(-a)^(7/4)*b^(13/4)) + (3*(a*d - b*c)^2*(3*a*d + b*c)*((9*x*(9*a^6*d^6 + b^6*c^6 - 9*a^2*b^4*c^4*d^2 - 4*a^3*b^3*c^3*d^3 + 31*a^4*b^2*c^2*d^4 + 2*a*b^5*c^5*d - 30*a^5*b*c*d^5))/(4*a^2*b^3) + ((a*d - b*c)^2*(3*a*d + b*c)*(36*a^3*d^3 + 12*b^3*c^3 + 12*a*b^2*c^2*d - 60*a^2*b*c*d^2)*3i)/(16*(-a)^(7/4)*b^(13/4))))/(16*(-a)^(7/4)*b^(13/4)))/(((a*d - b*c)^2*(3*a*d + b*c)*((9*x*(9*a^6*d^6 + b^6*c^6 - 9*a^2*b^4*c^4*d^2 - 4*a^3*b^3*c^3*d^3 + 31*a^4*b^2*c^2*d^4 + 2*a*b^5*c^5*d - 30*a^5*b*c*d^5))/(4*a^2*b^3) - ((a*d - b*c)^2*(3*a*d + b*c)*(36*a^3*d^3 + 12*b^3*c^3 + 12*a*b^2*c^2*d - 60*a^2*b*c*d^2)*3i)/(16*(-a)^(7/4)*b^(13/4)))*3i)/(16*(-a)^(7/4)*b^(13/4)) - ((a*d - b*c)^2*(3*a*d + b*c)*((9*x*(9*a^6*d^6 + b^6*c^6 - 9*a^2*b^4*c^4*d^2 - 4*a^3*b^3*c^3*d^3 + 31*a^4*b^2*c^2*d^4 + 2*a*b^5*c^5*d - 30*a^5*b*c*d^5))/(4*a^2*b^3) + ((a*d - b*c)^2*(3*a*d + b*c)*(36*a^3*d^3 + 12*b^3*c^3 + 12*a*b^2*c^2*d - 60*a^2*b*c*d^2)*3i)/(16*(-a)^(7/4)*b^(13/4)))*3i)/(16*(-a)^(7/4)*b^(13/4))))*(a*d - b*c)^2*(3*a*d + b*c))/(8*(-a)^(7/4)*b^(13/4))","B"
169,1,1254,291,0.298500,"\text{Not used}","int((c + d*x^4)^2/(a + b*x^4)^2,x)","\frac{d^2\,x}{b^2}+\frac{x\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}{4\,a\,\left(b^3\,x^4+a\,b^2\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(a\,d-b\,c\right)\,\left(5\,a\,d+3\,b\,c\right)\,\left(\frac{x\,\left(25\,a^4\,d^4-20\,a^3\,b\,c\,d^3-26\,a^2\,b^2\,c^2\,d^2+12\,a\,b^3\,c^3\,d+9\,b^4\,c^4\right)}{4\,a^2\,b}-\frac{\left(a\,d-b\,c\right)\,\left(5\,a\,d+3\,b\,c\right)\,\left(-20\,a^2\,b\,d^2+8\,a\,b^2\,c\,d+12\,b^3\,c^2\right)}{16\,{\left(-a\right)}^{7/4}\,b^{9/4}}\right)\,1{}\mathrm{i}}{16\,{\left(-a\right)}^{7/4}\,b^{9/4}}+\frac{\left(a\,d-b\,c\right)\,\left(5\,a\,d+3\,b\,c\right)\,\left(\frac{x\,\left(25\,a^4\,d^4-20\,a^3\,b\,c\,d^3-26\,a^2\,b^2\,c^2\,d^2+12\,a\,b^3\,c^3\,d+9\,b^4\,c^4\right)}{4\,a^2\,b}+\frac{\left(a\,d-b\,c\right)\,\left(5\,a\,d+3\,b\,c\right)\,\left(-20\,a^2\,b\,d^2+8\,a\,b^2\,c\,d+12\,b^3\,c^2\right)}{16\,{\left(-a\right)}^{7/4}\,b^{9/4}}\right)\,1{}\mathrm{i}}{16\,{\left(-a\right)}^{7/4}\,b^{9/4}}}{\frac{\left(a\,d-b\,c\right)\,\left(5\,a\,d+3\,b\,c\right)\,\left(\frac{x\,\left(25\,a^4\,d^4-20\,a^3\,b\,c\,d^3-26\,a^2\,b^2\,c^2\,d^2+12\,a\,b^3\,c^3\,d+9\,b^4\,c^4\right)}{4\,a^2\,b}-\frac{\left(a\,d-b\,c\right)\,\left(5\,a\,d+3\,b\,c\right)\,\left(-20\,a^2\,b\,d^2+8\,a\,b^2\,c\,d+12\,b^3\,c^2\right)}{16\,{\left(-a\right)}^{7/4}\,b^{9/4}}\right)}{16\,{\left(-a\right)}^{7/4}\,b^{9/4}}-\frac{\left(a\,d-b\,c\right)\,\left(5\,a\,d+3\,b\,c\right)\,\left(\frac{x\,\left(25\,a^4\,d^4-20\,a^3\,b\,c\,d^3-26\,a^2\,b^2\,c^2\,d^2+12\,a\,b^3\,c^3\,d+9\,b^4\,c^4\right)}{4\,a^2\,b}+\frac{\left(a\,d-b\,c\right)\,\left(5\,a\,d+3\,b\,c\right)\,\left(-20\,a^2\,b\,d^2+8\,a\,b^2\,c\,d+12\,b^3\,c^2\right)}{16\,{\left(-a\right)}^{7/4}\,b^{9/4}}\right)}{16\,{\left(-a\right)}^{7/4}\,b^{9/4}}}\right)\,\left(a\,d-b\,c\right)\,\left(5\,a\,d+3\,b\,c\right)\,1{}\mathrm{i}}{8\,{\left(-a\right)}^{7/4}\,b^{9/4}}+\frac{\mathrm{atan}\left(\frac{\frac{\left(a\,d-b\,c\right)\,\left(5\,a\,d+3\,b\,c\right)\,\left(\frac{x\,\left(25\,a^4\,d^4-20\,a^3\,b\,c\,d^3-26\,a^2\,b^2\,c^2\,d^2+12\,a\,b^3\,c^3\,d+9\,b^4\,c^4\right)}{4\,a^2\,b}-\frac{\left(a\,d-b\,c\right)\,\left(5\,a\,d+3\,b\,c\right)\,\left(-20\,a^2\,b\,d^2+8\,a\,b^2\,c\,d+12\,b^3\,c^2\right)\,1{}\mathrm{i}}{16\,{\left(-a\right)}^{7/4}\,b^{9/4}}\right)}{16\,{\left(-a\right)}^{7/4}\,b^{9/4}}+\frac{\left(a\,d-b\,c\right)\,\left(5\,a\,d+3\,b\,c\right)\,\left(\frac{x\,\left(25\,a^4\,d^4-20\,a^3\,b\,c\,d^3-26\,a^2\,b^2\,c^2\,d^2+12\,a\,b^3\,c^3\,d+9\,b^4\,c^4\right)}{4\,a^2\,b}+\frac{\left(a\,d-b\,c\right)\,\left(5\,a\,d+3\,b\,c\right)\,\left(-20\,a^2\,b\,d^2+8\,a\,b^2\,c\,d+12\,b^3\,c^2\right)\,1{}\mathrm{i}}{16\,{\left(-a\right)}^{7/4}\,b^{9/4}}\right)}{16\,{\left(-a\right)}^{7/4}\,b^{9/4}}}{\frac{\left(a\,d-b\,c\right)\,\left(5\,a\,d+3\,b\,c\right)\,\left(\frac{x\,\left(25\,a^4\,d^4-20\,a^3\,b\,c\,d^3-26\,a^2\,b^2\,c^2\,d^2+12\,a\,b^3\,c^3\,d+9\,b^4\,c^4\right)}{4\,a^2\,b}-\frac{\left(a\,d-b\,c\right)\,\left(5\,a\,d+3\,b\,c\right)\,\left(-20\,a^2\,b\,d^2+8\,a\,b^2\,c\,d+12\,b^3\,c^2\right)\,1{}\mathrm{i}}{16\,{\left(-a\right)}^{7/4}\,b^{9/4}}\right)\,1{}\mathrm{i}}{16\,{\left(-a\right)}^{7/4}\,b^{9/4}}-\frac{\left(a\,d-b\,c\right)\,\left(5\,a\,d+3\,b\,c\right)\,\left(\frac{x\,\left(25\,a^4\,d^4-20\,a^3\,b\,c\,d^3-26\,a^2\,b^2\,c^2\,d^2+12\,a\,b^3\,c^3\,d+9\,b^4\,c^4\right)}{4\,a^2\,b}+\frac{\left(a\,d-b\,c\right)\,\left(5\,a\,d+3\,b\,c\right)\,\left(-20\,a^2\,b\,d^2+8\,a\,b^2\,c\,d+12\,b^3\,c^2\right)\,1{}\mathrm{i}}{16\,{\left(-a\right)}^{7/4}\,b^{9/4}}\right)\,1{}\mathrm{i}}{16\,{\left(-a\right)}^{7/4}\,b^{9/4}}}\right)\,\left(a\,d-b\,c\right)\,\left(5\,a\,d+3\,b\,c\right)}{8\,{\left(-a\right)}^{7/4}\,b^{9/4}}","Not used",1,"(d^2*x)/b^2 + (x*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/(4*a*(a*b^2 + b^3*x^4)) + (atan((((a*d - b*c)*(5*a*d + 3*b*c)*((x*(25*a^4*d^4 + 9*b^4*c^4 - 26*a^2*b^2*c^2*d^2 + 12*a*b^3*c^3*d - 20*a^3*b*c*d^3))/(4*a^2*b) - ((a*d - b*c)*(5*a*d + 3*b*c)*(12*b^3*c^2 - 20*a^2*b*d^2 + 8*a*b^2*c*d))/(16*(-a)^(7/4)*b^(9/4)))*1i)/(16*(-a)^(7/4)*b^(9/4)) + ((a*d - b*c)*(5*a*d + 3*b*c)*((x*(25*a^4*d^4 + 9*b^4*c^4 - 26*a^2*b^2*c^2*d^2 + 12*a*b^3*c^3*d - 20*a^3*b*c*d^3))/(4*a^2*b) + ((a*d - b*c)*(5*a*d + 3*b*c)*(12*b^3*c^2 - 20*a^2*b*d^2 + 8*a*b^2*c*d))/(16*(-a)^(7/4)*b^(9/4)))*1i)/(16*(-a)^(7/4)*b^(9/4)))/(((a*d - b*c)*(5*a*d + 3*b*c)*((x*(25*a^4*d^4 + 9*b^4*c^4 - 26*a^2*b^2*c^2*d^2 + 12*a*b^3*c^3*d - 20*a^3*b*c*d^3))/(4*a^2*b) - ((a*d - b*c)*(5*a*d + 3*b*c)*(12*b^3*c^2 - 20*a^2*b*d^2 + 8*a*b^2*c*d))/(16*(-a)^(7/4)*b^(9/4))))/(16*(-a)^(7/4)*b^(9/4)) - ((a*d - b*c)*(5*a*d + 3*b*c)*((x*(25*a^4*d^4 + 9*b^4*c^4 - 26*a^2*b^2*c^2*d^2 + 12*a*b^3*c^3*d - 20*a^3*b*c*d^3))/(4*a^2*b) + ((a*d - b*c)*(5*a*d + 3*b*c)*(12*b^3*c^2 - 20*a^2*b*d^2 + 8*a*b^2*c*d))/(16*(-a)^(7/4)*b^(9/4))))/(16*(-a)^(7/4)*b^(9/4))))*(a*d - b*c)*(5*a*d + 3*b*c)*1i)/(8*(-a)^(7/4)*b^(9/4)) + (atan((((a*d - b*c)*(5*a*d + 3*b*c)*((x*(25*a^4*d^4 + 9*b^4*c^4 - 26*a^2*b^2*c^2*d^2 + 12*a*b^3*c^3*d - 20*a^3*b*c*d^3))/(4*a^2*b) - ((a*d - b*c)*(5*a*d + 3*b*c)*(12*b^3*c^2 - 20*a^2*b*d^2 + 8*a*b^2*c*d)*1i)/(16*(-a)^(7/4)*b^(9/4))))/(16*(-a)^(7/4)*b^(9/4)) + ((a*d - b*c)*(5*a*d + 3*b*c)*((x*(25*a^4*d^4 + 9*b^4*c^4 - 26*a^2*b^2*c^2*d^2 + 12*a*b^3*c^3*d - 20*a^3*b*c*d^3))/(4*a^2*b) + ((a*d - b*c)*(5*a*d + 3*b*c)*(12*b^3*c^2 - 20*a^2*b*d^2 + 8*a*b^2*c*d)*1i)/(16*(-a)^(7/4)*b^(9/4))))/(16*(-a)^(7/4)*b^(9/4)))/(((a*d - b*c)*(5*a*d + 3*b*c)*((x*(25*a^4*d^4 + 9*b^4*c^4 - 26*a^2*b^2*c^2*d^2 + 12*a*b^3*c^3*d - 20*a^3*b*c*d^3))/(4*a^2*b) - ((a*d - b*c)*(5*a*d + 3*b*c)*(12*b^3*c^2 - 20*a^2*b*d^2 + 8*a*b^2*c*d)*1i)/(16*(-a)^(7/4)*b^(9/4)))*1i)/(16*(-a)^(7/4)*b^(9/4)) - ((a*d - b*c)*(5*a*d + 3*b*c)*((x*(25*a^4*d^4 + 9*b^4*c^4 - 26*a^2*b^2*c^2*d^2 + 12*a*b^3*c^3*d - 20*a^3*b*c*d^3))/(4*a^2*b) + ((a*d - b*c)*(5*a*d + 3*b*c)*(12*b^3*c^2 - 20*a^2*b*d^2 + 8*a*b^2*c*d)*1i)/(16*(-a)^(7/4)*b^(9/4)))*1i)/(16*(-a)^(7/4)*b^(9/4))))*(a*d - b*c)*(5*a*d + 3*b*c))/(8*(-a)^(7/4)*b^(9/4))","B"
170,1,740,245,1.533420,"\text{Not used}","int((c + d*x^4)/(a + b*x^4)^2,x)","\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{x\,\left(a^2\,b\,d^2+6\,a\,b^2\,c\,d+9\,b^3\,c^2\right)}{4\,a^2}-\frac{\left(a\,d+3\,b\,c\right)\,\left(12\,c\,b^3+4\,a\,d\,b^2\right)\,1{}\mathrm{i}}{16\,{\left(-a\right)}^{7/4}\,b^{5/4}}\right)\,\left(a\,d+3\,b\,c\right)}{16\,{\left(-a\right)}^{7/4}\,b^{5/4}}+\frac{\left(\frac{x\,\left(a^2\,b\,d^2+6\,a\,b^2\,c\,d+9\,b^3\,c^2\right)}{4\,a^2}+\frac{\left(a\,d+3\,b\,c\right)\,\left(12\,c\,b^3+4\,a\,d\,b^2\right)\,1{}\mathrm{i}}{16\,{\left(-a\right)}^{7/4}\,b^{5/4}}\right)\,\left(a\,d+3\,b\,c\right)}{16\,{\left(-a\right)}^{7/4}\,b^{5/4}}}{\frac{\left(\frac{x\,\left(a^2\,b\,d^2+6\,a\,b^2\,c\,d+9\,b^3\,c^2\right)}{4\,a^2}-\frac{\left(a\,d+3\,b\,c\right)\,\left(12\,c\,b^3+4\,a\,d\,b^2\right)\,1{}\mathrm{i}}{16\,{\left(-a\right)}^{7/4}\,b^{5/4}}\right)\,\left(a\,d+3\,b\,c\right)\,1{}\mathrm{i}}{16\,{\left(-a\right)}^{7/4}\,b^{5/4}}-\frac{\left(\frac{x\,\left(a^2\,b\,d^2+6\,a\,b^2\,c\,d+9\,b^3\,c^2\right)}{4\,a^2}+\frac{\left(a\,d+3\,b\,c\right)\,\left(12\,c\,b^3+4\,a\,d\,b^2\right)\,1{}\mathrm{i}}{16\,{\left(-a\right)}^{7/4}\,b^{5/4}}\right)\,\left(a\,d+3\,b\,c\right)\,1{}\mathrm{i}}{16\,{\left(-a\right)}^{7/4}\,b^{5/4}}}\right)\,\left(a\,d+3\,b\,c\right)}{8\,{\left(-a\right)}^{7/4}\,b^{5/4}}-\frac{x\,\left(a\,d-b\,c\right)}{4\,a\,b\,\left(b\,x^4+a\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{x\,\left(a^2\,b\,d^2+6\,a\,b^2\,c\,d+9\,b^3\,c^2\right)}{4\,a^2}-\frac{\left(a\,d+3\,b\,c\right)\,\left(12\,c\,b^3+4\,a\,d\,b^2\right)}{16\,{\left(-a\right)}^{7/4}\,b^{5/4}}\right)\,\left(a\,d+3\,b\,c\right)\,1{}\mathrm{i}}{16\,{\left(-a\right)}^{7/4}\,b^{5/4}}+\frac{\left(\frac{x\,\left(a^2\,b\,d^2+6\,a\,b^2\,c\,d+9\,b^3\,c^2\right)}{4\,a^2}+\frac{\left(a\,d+3\,b\,c\right)\,\left(12\,c\,b^3+4\,a\,d\,b^2\right)}{16\,{\left(-a\right)}^{7/4}\,b^{5/4}}\right)\,\left(a\,d+3\,b\,c\right)\,1{}\mathrm{i}}{16\,{\left(-a\right)}^{7/4}\,b^{5/4}}}{\frac{\left(\frac{x\,\left(a^2\,b\,d^2+6\,a\,b^2\,c\,d+9\,b^3\,c^2\right)}{4\,a^2}-\frac{\left(a\,d+3\,b\,c\right)\,\left(12\,c\,b^3+4\,a\,d\,b^2\right)}{16\,{\left(-a\right)}^{7/4}\,b^{5/4}}\right)\,\left(a\,d+3\,b\,c\right)}{16\,{\left(-a\right)}^{7/4}\,b^{5/4}}-\frac{\left(\frac{x\,\left(a^2\,b\,d^2+6\,a\,b^2\,c\,d+9\,b^3\,c^2\right)}{4\,a^2}+\frac{\left(a\,d+3\,b\,c\right)\,\left(12\,c\,b^3+4\,a\,d\,b^2\right)}{16\,{\left(-a\right)}^{7/4}\,b^{5/4}}\right)\,\left(a\,d+3\,b\,c\right)}{16\,{\left(-a\right)}^{7/4}\,b^{5/4}}}\right)\,\left(a\,d+3\,b\,c\right)\,1{}\mathrm{i}}{8\,{\left(-a\right)}^{7/4}\,b^{5/4}}","Not used",1,"(atan(((((x*(9*b^3*c^2 + a^2*b*d^2 + 6*a*b^2*c*d))/(4*a^2) - ((a*d + 3*b*c)*(12*b^3*c + 4*a*b^2*d))/(16*(-a)^(7/4)*b^(5/4)))*(a*d + 3*b*c)*1i)/(16*(-a)^(7/4)*b^(5/4)) + (((x*(9*b^3*c^2 + a^2*b*d^2 + 6*a*b^2*c*d))/(4*a^2) + ((a*d + 3*b*c)*(12*b^3*c + 4*a*b^2*d))/(16*(-a)^(7/4)*b^(5/4)))*(a*d + 3*b*c)*1i)/(16*(-a)^(7/4)*b^(5/4)))/((((x*(9*b^3*c^2 + a^2*b*d^2 + 6*a*b^2*c*d))/(4*a^2) - ((a*d + 3*b*c)*(12*b^3*c + 4*a*b^2*d))/(16*(-a)^(7/4)*b^(5/4)))*(a*d + 3*b*c))/(16*(-a)^(7/4)*b^(5/4)) - (((x*(9*b^3*c^2 + a^2*b*d^2 + 6*a*b^2*c*d))/(4*a^2) + ((a*d + 3*b*c)*(12*b^3*c + 4*a*b^2*d))/(16*(-a)^(7/4)*b^(5/4)))*(a*d + 3*b*c))/(16*(-a)^(7/4)*b^(5/4))))*(a*d + 3*b*c)*1i)/(8*(-a)^(7/4)*b^(5/4)) + (atan(((((x*(9*b^3*c^2 + a^2*b*d^2 + 6*a*b^2*c*d))/(4*a^2) - ((a*d + 3*b*c)*(12*b^3*c + 4*a*b^2*d)*1i)/(16*(-a)^(7/4)*b^(5/4)))*(a*d + 3*b*c))/(16*(-a)^(7/4)*b^(5/4)) + (((x*(9*b^3*c^2 + a^2*b*d^2 + 6*a*b^2*c*d))/(4*a^2) + ((a*d + 3*b*c)*(12*b^3*c + 4*a*b^2*d)*1i)/(16*(-a)^(7/4)*b^(5/4)))*(a*d + 3*b*c))/(16*(-a)^(7/4)*b^(5/4)))/((((x*(9*b^3*c^2 + a^2*b*d^2 + 6*a*b^2*c*d))/(4*a^2) - ((a*d + 3*b*c)*(12*b^3*c + 4*a*b^2*d)*1i)/(16*(-a)^(7/4)*b^(5/4)))*(a*d + 3*b*c)*1i)/(16*(-a)^(7/4)*b^(5/4)) - (((x*(9*b^3*c^2 + a^2*b*d^2 + 6*a*b^2*c*d))/(4*a^2) + ((a*d + 3*b*c)*(12*b^3*c + 4*a*b^2*d)*1i)/(16*(-a)^(7/4)*b^(5/4)))*(a*d + 3*b*c)*1i)/(16*(-a)^(7/4)*b^(5/4))))*(a*d + 3*b*c))/(8*(-a)^(7/4)*b^(5/4)) - (x*(a*d - b*c))/(4*a*b*(a + b*x^4))","B"
171,1,21975,513,3.816546,"\text{Not used}","int(1/((a + b*x^4)^2*(c + d*x^4)),x)","2\,\mathrm{atan}\left(\frac{\left({\left(-\frac{2401\,a^4\,b^3\,d^4-4116\,a^3\,b^4\,c\,d^3+2646\,a^2\,b^5\,c^2\,d^2-756\,a\,b^6\,c^3\,d+81\,b^7\,c^4}{65536\,a^{15}\,d^8-524288\,a^{14}\,b\,c\,d^7+1835008\,a^{13}\,b^2\,c^2\,d^6-3670016\,a^{12}\,b^3\,c^3\,d^5+4587520\,a^{11}\,b^4\,c^4\,d^4-3670016\,a^{10}\,b^5\,c^5\,d^3+1835008\,a^9\,b^6\,c^6\,d^2-524288\,a^8\,b^7\,c^7\,d+65536\,a^7\,b^8\,c^8}\right)}^{1/4}\,\left(\frac{\left(28\,a^4\,b^6\,d^{11}-\frac{2145\,a^3\,b^7\,c\,d^{10}}{16}+\frac{1971\,a^2\,b^8\,c^2\,d^9}{16}-\frac{675\,a\,b^9\,c^3\,d^8}{16}+\frac{81\,b^{10}\,c^4\,d^7}{16}\right)\,1{}\mathrm{i}}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-a^4\,b^3\,c^3}+{\left(-\frac{2401\,a^4\,b^3\,d^4-4116\,a^3\,b^4\,c\,d^3+2646\,a^2\,b^5\,c^2\,d^2-756\,a\,b^6\,c^3\,d+81\,b^7\,c^4}{65536\,a^{15}\,d^8-524288\,a^{14}\,b\,c\,d^7+1835008\,a^{13}\,b^2\,c^2\,d^6-3670016\,a^{12}\,b^3\,c^3\,d^5+4587520\,a^{11}\,b^4\,c^4\,d^4-3670016\,a^{10}\,b^5\,c^5\,d^3+1835008\,a^9\,b^6\,c^6\,d^2-524288\,a^8\,b^7\,c^7\,d+65536\,a^7\,b^8\,c^8}\right)}^{3/4}\,\left(\frac{{\left(-\frac{2401\,a^4\,b^3\,d^4-4116\,a^3\,b^4\,c\,d^3+2646\,a^2\,b^5\,c^2\,d^2-756\,a\,b^6\,c^3\,d+81\,b^7\,c^4}{65536\,a^{15}\,d^8-524288\,a^{14}\,b\,c\,d^7+1835008\,a^{13}\,b^2\,c^2\,d^6-3670016\,a^{12}\,b^3\,c^3\,d^5+4587520\,a^{11}\,b^4\,c^4\,d^4-3670016\,a^{10}\,b^5\,c^5\,d^3+1835008\,a^9\,b^6\,c^6\,d^2-524288\,a^8\,b^7\,c^7\,d+65536\,a^7\,b^8\,c^8}\right)}^{1/4}\,\left(-4096\,a^{14}\,b^4\,c\,d^{14}+28672\,a^{13}\,b^5\,c^2\,d^{13}-78848\,a^{12}\,b^6\,c^3\,d^{12}+90112\,a^{11}\,b^7\,c^4\,d^{11}+28672\,a^{10}\,b^8\,c^5\,d^{10}-229376\,a^9\,b^9\,c^6\,d^9+329728\,a^8\,b^{10}\,c^7\,d^8-253952\,a^7\,b^{11}\,c^8\,d^7+114688\,a^6\,b^{12}\,c^9\,d^6-28672\,a^5\,b^{13}\,c^{10}\,d^5+3072\,a^4\,b^{14}\,c^{11}\,d^4\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-a^4\,b^3\,c^3}-\frac{x\,\left(65536\,a^{15}\,b^4\,d^{17}-524288\,a^{14}\,b^5\,c\,d^{16}+1835008\,a^{13}\,b^6\,c^2\,d^{15}-3469312\,a^{12}\,b^7\,c^3\,d^{14}+2809856\,a^{11}\,b^8\,c^4\,d^{13}+3362816\,a^{10}\,b^9\,c^5\,d^{12}-14516224\,a^9\,b^{10}\,c^6\,d^{11}+24190976\,a^8\,b^{11}\,c^7\,d^{10}-25280512\,a^7\,b^{12}\,c^8\,d^9+17833984\,a^6\,b^{13}\,c^9\,d^8-8486912\,a^5\,b^{14}\,c^{10}\,d^7+2609152\,a^4\,b^{15}\,c^{11}\,d^6-466944\,a^3\,b^{16}\,c^{12}\,d^5+36864\,a^2\,b^{17}\,c^{13}\,d^4\right)\,1{}\mathrm{i}}{64\,\left(a^{10}\,d^6-6\,a^9\,b\,c\,d^5+15\,a^8\,b^2\,c^2\,d^4-20\,a^7\,b^3\,c^3\,d^3+15\,a^6\,b^4\,c^4\,d^2-6\,a^5\,b^5\,c^5\,d+a^4\,b^6\,c^6\right)}\right)\,1{}\mathrm{i}\right)+\frac{x\,\left(3185\,a^4\,b^7\,d^{13}-4788\,a^3\,b^8\,c\,d^{12}+2790\,a^2\,b^9\,c^2\,d^{11}-756\,a\,b^{10}\,c^3\,d^{10}+81\,b^{11}\,c^4\,d^9\right)}{64\,\left(a^{10}\,d^6-6\,a^9\,b\,c\,d^5+15\,a^8\,b^2\,c^2\,d^4-20\,a^7\,b^3\,c^3\,d^3+15\,a^6\,b^4\,c^4\,d^2-6\,a^5\,b^5\,c^5\,d+a^4\,b^6\,c^6\right)}\right)\,{\left(-\frac{2401\,a^4\,b^3\,d^4-4116\,a^3\,b^4\,c\,d^3+2646\,a^2\,b^5\,c^2\,d^2-756\,a\,b^6\,c^3\,d+81\,b^7\,c^4}{65536\,a^{15}\,d^8-524288\,a^{14}\,b\,c\,d^7+1835008\,a^{13}\,b^2\,c^2\,d^6-3670016\,a^{12}\,b^3\,c^3\,d^5+4587520\,a^{11}\,b^4\,c^4\,d^4-3670016\,a^{10}\,b^5\,c^5\,d^3+1835008\,a^9\,b^6\,c^6\,d^2-524288\,a^8\,b^7\,c^7\,d+65536\,a^7\,b^8\,c^8}\right)}^{1/4}-\left({\left(-\frac{2401\,a^4\,b^3\,d^4-4116\,a^3\,b^4\,c\,d^3+2646\,a^2\,b^5\,c^2\,d^2-756\,a\,b^6\,c^3\,d+81\,b^7\,c^4}{65536\,a^{15}\,d^8-524288\,a^{14}\,b\,c\,d^7+1835008\,a^{13}\,b^2\,c^2\,d^6-3670016\,a^{12}\,b^3\,c^3\,d^5+4587520\,a^{11}\,b^4\,c^4\,d^4-3670016\,a^{10}\,b^5\,c^5\,d^3+1835008\,a^9\,b^6\,c^6\,d^2-524288\,a^8\,b^7\,c^7\,d+65536\,a^7\,b^8\,c^8}\right)}^{1/4}\,\left(\frac{\left(28\,a^4\,b^6\,d^{11}-\frac{2145\,a^3\,b^7\,c\,d^{10}}{16}+\frac{1971\,a^2\,b^8\,c^2\,d^9}{16}-\frac{675\,a\,b^9\,c^3\,d^8}{16}+\frac{81\,b^{10}\,c^4\,d^7}{16}\right)\,1{}\mathrm{i}}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-a^4\,b^3\,c^3}+{\left(-\frac{2401\,a^4\,b^3\,d^4-4116\,a^3\,b^4\,c\,d^3+2646\,a^2\,b^5\,c^2\,d^2-756\,a\,b^6\,c^3\,d+81\,b^7\,c^4}{65536\,a^{15}\,d^8-524288\,a^{14}\,b\,c\,d^7+1835008\,a^{13}\,b^2\,c^2\,d^6-3670016\,a^{12}\,b^3\,c^3\,d^5+4587520\,a^{11}\,b^4\,c^4\,d^4-3670016\,a^{10}\,b^5\,c^5\,d^3+1835008\,a^9\,b^6\,c^6\,d^2-524288\,a^8\,b^7\,c^7\,d+65536\,a^7\,b^8\,c^8}\right)}^{3/4}\,\left(\frac{{\left(-\frac{2401\,a^4\,b^3\,d^4-4116\,a^3\,b^4\,c\,d^3+2646\,a^2\,b^5\,c^2\,d^2-756\,a\,b^6\,c^3\,d+81\,b^7\,c^4}{65536\,a^{15}\,d^8-524288\,a^{14}\,b\,c\,d^7+1835008\,a^{13}\,b^2\,c^2\,d^6-3670016\,a^{12}\,b^3\,c^3\,d^5+4587520\,a^{11}\,b^4\,c^4\,d^4-3670016\,a^{10}\,b^5\,c^5\,d^3+1835008\,a^9\,b^6\,c^6\,d^2-524288\,a^8\,b^7\,c^7\,d+65536\,a^7\,b^8\,c^8}\right)}^{1/4}\,\left(-4096\,a^{14}\,b^4\,c\,d^{14}+28672\,a^{13}\,b^5\,c^2\,d^{13}-78848\,a^{12}\,b^6\,c^3\,d^{12}+90112\,a^{11}\,b^7\,c^4\,d^{11}+28672\,a^{10}\,b^8\,c^5\,d^{10}-229376\,a^9\,b^9\,c^6\,d^9+329728\,a^8\,b^{10}\,c^7\,d^8-253952\,a^7\,b^{11}\,c^8\,d^7+114688\,a^6\,b^{12}\,c^9\,d^6-28672\,a^5\,b^{13}\,c^{10}\,d^5+3072\,a^4\,b^{14}\,c^{11}\,d^4\right)}{a^7\,d^3-3\,a^6\,b\,c\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frac{\left(28\,a^4\,b^6\,d^{11}-\frac{2145\,a^3\,b^7\,c\,d^{10}}{16}+\frac{1971\,a^2\,b^8\,c^2\,d^9}{16}-\frac{675\,a\,b^9\,c^3\,d^8}{16}+\frac{81\,b^{10}\,c^4\,d^7}{16}\right)\,1{}\mathrm{i}}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-a^4\,b^3\,c^3}+{\left(-\frac{2401\,a^4\,b^3\,d^4-4116\,a^3\,b^4\,c\,d^3+2646\,a^2\,b^5\,c^2\,d^2-756\,a\,b^6\,c^3\,d+81\,b^7\,c^4}{65536\,a^{15}\,d^8-524288\,a^{14}\,b\,c\,d^7+1835008\,a^{13}\,b^2\,c^2\,d^6-3670016\,a^{12}\,b^3\,c^3\,d^5+4587520\,a^{11}\,b^4\,c^4\,d^4-3670016\,a^{10}\,b^5\,c^5\,d^3+1835008\,a^9\,b^6\,c^6\,d^2-524288\,a^8\,b^7\,c^7\,d+65536\,a^7\,b^8\,c^8}\right)}^{3/4}\,\left(\frac{{\left(-\frac{2401\,a^4\,b^3\,d^4-4116\,a^3\,b^4\,c\,d^3+2646\,a^2\,b^5\,c^2\,d^2-756\,a\,b^6\,c^3\,d+81\,b^7\,c^4}{65536\,a^{15}\,d^8-524288\,a^{14}\,b\,c\,d^7+1835008\,a^{13}\,b^2\,c^2\,d^6-3670016\,a^{12}\,b^3\,c^3\,d^5+4587520\,a^{11}\,b^4\,c^4\,d^4-3670016\,a^{10}\,b^5\,c^5\,d^3+1835008\,a^9\,b^6\,c^6\,d^2-524288\,a^8\,b^7\,c^7\,d+65536\,a^7\,b^8\,c^8}\right)}^{1/4}\,\left(-4096\,a^{14}\,b^4\,c\,d^{14}+28672\,a^{13}\,b^5\,c^2\,d^{13}-78848\,a^{12}\,b^6\,c^3\,d^{12}+90112\,a^{11}\,b^7\,c^4\,d^{11}+28672\,a^{10}\,b^8\,c^5\,d^{10}-229376\,a^9\,b^9\,c^6\,d^9+329728\,a^8\,b^{10}\,c^7\,d^8-253952\,a^7\,b^{11}\,c^8\,d^7+114688\,a^6\,b^{12}\,c^9\,d^6-28672\,a^5\,b^{13}\,c^{10}\,d^5+3072\,a^4\,b^{14}\,c^{11}\,d^4\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-a^4\,b^3\,c^3}+\frac{x\,\left(65536\,a^{15}\,b^4\,d^{17}-524288\,a^{14}\,b^5\,c\,d^{16}+1835008\,a^{13}\,b^6\,c^2\,d^{15}-3469312\,a^{12}\,b^7\,c^3\,d^{14}+2809856\,a^{11}\,b^8\,c^4\,d^{13}+3362816\,a^{10}\,b^9\,c^5\,d^{12}-14516224\,a^9\,b^{10}\,c^6\,d^{11}+24190976\,a^8\,b^{11}\,c^7\,d^{10}-25280512\,a^7\,b^{12}\,c^8\,d^9+17833984\,a^6\,b^{13}\,c^9\,d^8-8486912\,a^5\,b^{14}\,c^{10}\,d^7+2609152\,a^4\,b^{15}\,c^{11}\,d^6-466944\,a^3\,b^{16}\,c^{12}\,d^5+36864\,a^2\,b^{17}\,c^{13}\,d^4\right)\,1{}\mathrm{i}}{64\,\left(a^{10}\,d^6-6\,a^9\,b\,c\,d^5+15\,a^8\,b^2\,c^2\,d^4-20\,a^7\,b^3\,c^3\,d^3+15\,a^6\,b^4\,c^4\,d^2-6\,a^5\,b^5\,c^5\,d+a^4\,b^6\,c^6\right)}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}-\frac{x\,\left(3185\,a^4\,b^7\,d^{13}-4788\,a^3\,b^8\,c\,d^{12}+2790\,a^2\,b^9\,c^2\,d^{11}-756\,a\,b^{10}\,c^3\,d^{10}+81\,b^{11}\,c^4\,d^9\right)\,1{}\mathrm{i}}{64\,\left(a^{10}\,d^6-6\,a^9\,b\,c\,d^5+15\,a^8\,b^2\,c^2\,d^4-20\,a^7\,b^3\,c^3\,d^3+15\,a^6\,b^4\,c^4\,d^2-6\,a^5\,b^5\,c^5\,d+a^4\,b^6\,c^6\right)}\right)\,{\left(-\frac{2401\,a^4\,b^3\,d^4-4116\,a^3\,b^4\,c\,d^3+2646\,a^2\,b^5\,c^2\,d^2-756\,a\,b^6\,c^3\,d+81\,b^7\,c^4}{65536\,a^{15}\,d^8-524288\,a^{14}\,b\,c\,d^7+1835008\,a^{13}\,b^2\,c^2\,d^6-3670016\,a^{12}\,b^3\,c^3\,d^5+4587520\,a^{11}\,b^4\,c^4\,d^4-3670016\,a^{10}\,b^5\,c^5\,d^3+1835008\,a^9\,b^6\,c^6\,d^2-524288\,a^8\,b^7\,c^7\,d+65536\,a^7\,b^8\,c^8}\right)}^{1/4}}\right)\,{\left(-\frac{2401\,a^4\,b^3\,d^4-4116\,a^3\,b^4\,c\,d^3+2646\,a^2\,b^5\,c^2\,d^2-756\,a\,b^6\,c^3\,d+81\,b^7\,c^4}{65536\,a^{15}\,d^8-524288\,a^{14}\,b\,c\,d^7+1835008\,a^{13}\,b^2\,c^2\,d^6-3670016\,a^{12}\,b^3\,c^3\,d^5+4587520\,a^{11}\,b^4\,c^4\,d^4-3670016\,a^{10}\,b^5\,c^5\,d^3+1835008\,a^9\,b^6\,c^6\,d^2-524288\,a^8\,b^7\,c^7\,d+65536\,a^7\,b^8\,c^8}\right)}^{1/4}+2\,\mathrm{atan}\left(\frac{{\left(-\frac{d^7}{256\,a^8\,c^3\,d^8-2048\,a^7\,b\,c^4\,d^7+7168\,a^6\,b^2\,c^5\,d^6-14336\,a^5\,b^3\,c^6\,d^5+17920\,a^4\,b^4\,c^7\,d^4-14336\,a^3\,b^5\,c^8\,d^3+7168\,a^2\,b^6\,c^9\,d^2-2048\,a\,b^7\,c^{10}\,d+256\,b^8\,c^{11}}\right)}^{1/4}\,\left({\left(-\frac{d^7}{256\,a^8\,c^3\,d^8-2048\,a^7\,b\,c^4\,d^7+7168\,a^6\,b^2\,c^5\,d^6-14336\,a^5\,b^3\,c^6\,d^5+17920\,a^4\,b^4\,c^7\,d^4-14336\,a^3\,b^5\,c^8\,d^3+7168\,a^2\,b^6\,c^9\,d^2-2048\,a\,b^7\,c^{10}\,d+256\,b^8\,c^{11}}\right)}^{1/4}\,\left({\left(-\frac{d^7}{256\,a^8\,c^3\,d^8-2048\,a^7\,b\,c^4\,d^7+7168\,a^6\,b^2\,c^5\,d^6-14336\,a^5\,b^3\,c^6\,d^5+17920\,a^4\,b^4\,c^7\,d^4-14336\,a^3\,b^5\,c^8\,d^3+7168\,a^2\,b^6\,c^9\,d^2-2048\,a\,b^7\,c^{10}\,d+256\,b^8\,c^{11}}\right)}^{3/4}\,\left(\frac{{\left(-\frac{d^7}{256\,a^8\,c^3\,d^8-2048\,a^7\,b\,c^4\,d^7+7168\,a^6\,b^2\,c^5\,d^6-14336\,a^5\,b^3\,c^6\,d^5+17920\,a^4\,b^4\,c^7\,d^4-14336\,a^3\,b^5\,c^8\,d^3+7168\,a^2\,b^6\,c^9\,d^2-2048\,a\,b^7\,c^{10}\,d+256\,b^8\,c^{11}}\right)}^{1/4}\,\left(-4096\,a^{14}\,b^4\,c\,d^{14}+28672\,a^{13}\,b^5\,c^2\,d^{13}-78848\,a^{12}\,b^6\,c^3\,d^{12}+90112\,a^{11}\,b^7\,c^4\,d^{11}+28672\,a^{10}\,b^8\,c^5\,d^{10}-229376\,a^9\,b^9\,c^6\,d^9+329728\,a^8\,b^{10}\,c^7\,d^8-253952\,a^7\,b^{11}\,c^8\,d^7+114688\,a^6\,b^{12}\,c^9\,d^6-28672\,a^5\,b^{13}\,c^{10}\,d^5+3072\,a^4\,b^{14}\,c^{11}\,d^4\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-a^4\,b^3\,c^3}-\frac{x\,\left(65536\,a^{15}\,b^4\,d^{17}-524288\,a^{14}\,b^5\,c\,d^{16}+1835008\,a^{13}\,b^6\,c^2\,d^{15}-3469312\,a^{12}\,b^7\,c^3\,d^{14}+2809856\,a^{11}\,b^8\,c^4\,d^{13}+3362816\,a^{10}\,b^9\,c^5\,d^{12}-14516224\,a^9\,b^{10}\,c^6\,d^{11}+24190976\,a^8\,b^{11}\,c^7\,d^{10}-25280512\,a^7\,b^{12}\,c^8\,d^9+17833984\,a^6\,b^{13}\,c^9\,d^8-84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5536\,a^{15}\,b^4\,d^{17}-524288\,a^{14}\,b^5\,c\,d^{16}+1835008\,a^{13}\,b^6\,c^2\,d^{15}-3469312\,a^{12}\,b^7\,c^3\,d^{14}+2809856\,a^{11}\,b^8\,c^4\,d^{13}+3362816\,a^{10}\,b^9\,c^5\,d^{12}-14516224\,a^9\,b^{10}\,c^6\,d^{11}+24190976\,a^8\,b^{11}\,c^7\,d^{10}-25280512\,a^7\,b^{12}\,c^8\,d^9+17833984\,a^6\,b^{13}\,c^9\,d^8-8486912\,a^5\,b^{14}\,c^{10}\,d^7+2609152\,a^4\,b^{15}\,c^{11}\,d^6-466944\,a^3\,b^{16}\,c^{12}\,d^5+36864\,a^2\,b^{17}\,c^{13}\,d^4\right)\,1{}\mathrm{i}}{64\,\left(a^{10}\,d^6-6\,a^9\,b\,c\,d^5+15\,a^8\,b^2\,c^2\,d^4-20\,a^7\,b^3\,c^3\,d^3+15\,a^6\,b^4\,c^4\,d^2-6\,a^5\,b^5\,c^5\,d+a^4\,b^6\,c^6\right)}\right)\,1{}\mathrm{i}+\frac{\left(28\,a^4\,b^6\,d^{11}-\frac{2145\,a^3\,b^7\,c\,d^{10}}{16}+\frac{1971\,a^2\,b^8\,c^2\,d^9}{16}-\frac{675\,a\,b^9\,c^3\,d^8}{16}+\frac{81\,b^{10}\,c^4\,d^7}{16}\right)\,1{}\mathrm{i}}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-a^4\,b^3\,c^3}\right)\,1{}\mathrm{i}+\frac{x\,\left(3185\,a^4\,b^7\,d^{13}-4788\,a^3\,b^8\,c\,d^{12}+2790\,a^2\,b^9\,c^2\,d^{11}-756\,a\,b^{10}\,c^3\,d^{10}+81\,b^{11}\,c^4\,d^9\right)\,1{}\mathrm{i}}{64\,\left(a^{10}\,d^6-6\,a^9\,b\,c\,d^5+15\,a^8\,b^2\,c^2\,d^4-20\,a^7\,b^3\,c^3\,d^3+15\,a^6\,b^4\,c^4\,d^2-6\,a^5\,b^5\,c^5\,d+a^4\,b^6\,c^6\right)}\right)+{\left(-\frac{d^7}{256\,a^8\,c^3\,d^8-2048\,a^7\,b\,c^4\,d^7+7168\,a^6\,b^2\,c^5\,d^6-14336\,a^5\,b^3\,c^6\,d^5+17920\,a^4\,b^4\,c^7\,d^4-14336\,a^3\,b^5\,c^8\,d^3+7168\,a^2\,b^6\,c^9\,d^2-2048\,a\,b^7\,c^{10}\,d+256\,b^8\,c^{11}}\right)}^{1/4}\,\left({\left(-\frac{d^7}{256\,a^8\,c^3\,d^8-2048\,a^7\,b\,c^4\,d^7+7168\,a^6\,b^2\,c^5\,d^6-14336\,a^5\,b^3\,c^6\,d^5+17920\,a^4\,b^4\,c^7\,d^4-14336\,a^3\,b^5\,c^8\,d^3+7168\,a^2\,b^6\,c^9\,d^2-2048\,a\,b^7\,c^{10}\,d+256\,b^8\,c^{11}}\right)}^{1/4}\,\left({\left(-\frac{d^7}{256\,a^8\,c^3\,d^8-2048\,a^7\,b\,c^4\,d^7+7168\,a^6\,b^2\,c^5\,d^6-14336\,a^5\,b^3\,c^6\,d^5+17920\,a^4\,b^4\,c^7\,d^4-14336\,a^3\,b^5\,c^8\,d^3+7168\,a^2\,b^6\,c^9\,d^2-2048\,a\,b^7\,c^{10}\,d+256\,b^8\,c^{11}}\right)}^{3/4}\,\left(\frac{{\left(-\frac{d^7}{256\,a^8\,c^3\,d^8-2048\,a^7\,b\,c^4\,d^7+7168\,a^6\,b^2\,c^5\,d^6-14336\,a^5\,b^3\,c^6\,d^5+17920\,a^4\,b^4\,c^7\,d^4-14336\,a^3\,b^5\,c^8\,d^3+7168\,a^2\,b^6\,c^9\,d^2-2048\,a\,b^7\,c^{10}\,d+256\,b^8\,c^{11}}\right)}^{1/4}\,\left(-4096\,a^{14}\,b^4\,c\,d^{14}+28672\,a^{13}\,b^5\,c^2\,d^{13}-78848\,a^{12}\,b^6\,c^3\,d^{12}+90112\,a^{11}\,b^7\,c^4\,d^{11}+28672\,a^{10}\,b^8\,c^5\,d^{10}-229376\,a^9\,b^9\,c^6\,d^9+329728\,a^8\,b^{10}\,c^7\,d^8-253952\,a^7\,b^{11}\,c^8\,d^7+114688\,a^6\,b^{12}\,c^9\,d^6-28672\,a^5\,b^{13}\,c^{10}\,d^5+3072\,a^4\,b^{14}\,c^{11}\,d^4\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-a^4\,b^3\,c^3}+\frac{x\,\left(65536\,a^{15}\,b^4\,d^{17}-524288\,a^{14}\,b^5\,c\,d^{16}+1835008\,a^{13}\,b^6\,c^2\,d^{15}-3469312\,a^{12}\,b^7\,c^3\,d^{14}+2809856\,a^{11}\,b^8\,c^4\,d^{13}+3362816\,a^{10}\,b^9\,c^5\,d^{12}-14516224\,a^9\,b^{10}\,c^6\,d^{11}+24190976\,a^8\,b^{11}\,c^7\,d^{10}-25280512\,a^7\,b^{12}\,c^8\,d^9+17833984\,a^6\,b^{13}\,c^9\,d^8-8486912\,a^5\,b^{14}\,c^{10}\,d^7+2609152\,a^4\,b^{15}\,c^{11}\,d^6-466944\,a^3\,b^{16}\,c^{12}\,d^5+36864\,a^2\,b^{17}\,c^{13}\,d^4\right)\,1{}\mathrm{i}}{64\,\left(a^{10}\,d^6-6\,a^9\,b\,c\,d^5+15\,a^8\,b^2\,c^2\,d^4-20\,a^7\,b^3\,c^3\,d^3+15\,a^6\,b^4\,c^4\,d^2-6\,a^5\,b^5\,c^5\,d+a^4\,b^6\,c^6\right)}\right)\,1{}\mathrm{i}+\frac{\left(28\,a^4\,b^6\,d^{11}-\frac{2145\,a^3\,b^7\,c\,d^{10}}{16}+\frac{1971\,a^2\,b^8\,c^2\,d^9}{16}-\frac{675\,a\,b^9\,c^3\,d^8}{16}+\frac{81\,b^{10}\,c^4\,d^7}{16}\right)\,1{}\mathrm{i}}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-a^4\,b^3\,c^3}\right)\,1{}\mathrm{i}-\frac{x\,\left(3185\,a^4\,b^7\,d^{13}-4788\,a^3\,b^8\,c\,d^{12}+2790\,a^2\,b^9\,c^2\,d^{11}-756\,a\,b^{10}\,c^3\,d^{10}+81\,b^{11}\,c^4\,d^9\right)\,1{}\mathrm{i}}{64\,\left(a^{10}\,d^6-6\,a^9\,b\,c\,d^5+15\,a^8\,b^2\,c^2\,d^4-20\,a^7\,b^3\,c^3\,d^3+15\,a^6\,b^4\,c^4\,d^2-6\,a^5\,b^5\,c^5\,d+a^4\,b^6\,c^6\right)}\right)}\right)\,{\left(-\frac{d^7}{256\,a^8\,c^3\,d^8-2048\,a^7\,b\,c^4\,d^7+7168\,a^6\,b^2\,c^5\,d^6-14336\,a^5\,b^3\,c^6\,d^5+17920\,a^4\,b^4\,c^7\,d^4-14336\,a^3\,b^5\,c^8\,d^3+7168\,a^2\,b^6\,c^9\,d^2-2048\,a\,b^7\,c^{10}\,d+256\,b^8\,c^{11}}\right)}^{1/4}-\frac{b\,x}{4\,a\,\left(b\,x^4+a\right)\,\left(a\,d-b\,c\right)}-\mathrm{atan}\left(\frac{\left({\left(-\frac{2401\,a^4\,b^3\,d^4-4116\,a^3\,b^4\,c\,d^3+2646\,a^2\,b^5\,c^2\,d^2-756\,a\,b^6\,c^3\,d+81\,b^7\,c^4}{65536\,a^{15}\,d^8-524288\,a^{14}\,b\,c\,d^7+1835008\,a^{13}\,b^2\,c^2\,d^6-3670016\,a^{12}\,b^3\,c^3\,d^5+4587520\,a^{11}\,b^4\,c^4\,d^4-3670016\,a^{10}\,b^5\,c^5\,d^3+1835008\,a^9\,b^6\,c^6\,d^2-524288\,a^8\,b^7\,c^7\,d+65536\,a^7\,b^8\,c^8}\right)}^{1/4}\,\left(\frac{28\,a^4\,b^6\,d^{11}-\frac{2145\,a^3\,b^7\,c\,d^{10}}{16}+\frac{1971\,a^2\,b^8\,c^2\,d^9}{16}-\frac{675\,a\,b^9\,c^3\,d^8}{16}+\frac{81\,b^{10}\,c^4\,d^7}{16}}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-a^4\,b^3\,c^3}+{\left(-\frac{2401\,a^4\,b^3\,d^4-4116\,a^3\,b^4\,c\,d^3+2646\,a^2\,b^5\,c^2\,d^2-756\,a\,b^6\,c^3\,d+81\,b^7\,c^4}{65536\,a^{15}\,d^8-524288\,a^{14}\,b\,c\,d^7+1835008\,a^{13}\,b^2\,c^2\,d^6-3670016\,a^{12}\,b^3\,c^3\,d^5+4587520\,a^{11}\,b^4\,c^4\,d^4-3670016\,a^{10}\,b^5\,c^5\,d^3+1835008\,a^9\,b^6\,c^6\,d^2-524288\,a^8\,b^7\,c^7\,d+65536\,a^7\,b^8\,c^8}\right)}^{3/4}\,\left(\frac{{\left(-\frac{2401\,a^4\,b^3\,d^4-4116\,a^3\,b^4\,c\,d^3+2646\,a^2\,b^5\,c^2\,d^2-756\,a\,b^6\,c^3\,d+81\,b^7\,c^4}{65536\,a^{15}\,d^8-524288\,a^{14}\,b\,c\,d^7+1835008\,a^{13}\,b^2\,c^2\,d^6-3670016\,a^{12}\,b^3\,c^3\,d^5+4587520\,a^{11}\,b^4\,c^4\,d^4-3670016\,a^{10}\,b^5\,c^5\,d^3+1835008\,a^9\,b^6\,c^6\,d^2-524288\,a^8\,b^7\,c^7\,d+65536\,a^7\,b^8\,c^8}\right)}^{1/4}\,\left(-4096\,a^{14}\,b^4\,c\,d^{14}+28672\,a^{13}\,b^5\,c^2\,d^{13}-78848\,a^{12}\,b^6\,c^3\,d^{12}+90112\,a^{11}\,b^7\,c^4\,d^{11}+28672\,a^{10}\,b^8\,c^5\,d^{10}-229376\,a^9\,b^9\,c^6\,d^9+329728\,a^8\,b^{10}\,c^7\,d^8-253952\,a^7\,b^{11}\,c^8\,d^7+114688\,a^6\,b^{12}\,c^9\,d^6-28672\,a^5\,b^{13}\,c^{10}\,d^5+3072\,a^4\,b^{14}\,c^{11}\,d^4\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-a^4\,b^3\,c^3}-\frac{x\,\left(65536\,a^{15}\,b^4\,d^{17}-524288\,a^{14}\,b^5\,c\,d^{16}+1835008\,a^{13}\,b^6\,c^2\,d^{15}-3469312\,a^{12}\,b^7\,c^3\,d^{14}+2809856\,a^{11}\,b^8\,c^4\,d^{13}+3362816\,a^{10}\,b^9\,c^5\,d^{12}-14516224\,a^9\,b^{10}\,c^6\,d^{11}+24190976\,a^8\,b^{11}\,c^7\,d^{10}-25280512\,a^7\,b^{12}\,c^8\,d^9+17833984\,a^6\,b^{13}\,c^9\,d^8-8486912\,a^5\,b^{14}\,c^{10}\,d^7+2609152\,a^4\,b^{15}\,c^{11}\,d^6-466944\,a^3\,b^{16}\,c^{12}\,d^5+36864\,a^2\,b^{17}\,c^{13}\,d^4\right)}{64\,\left(a^{10}\,d^6-6\,a^9\,b\,c\,d^5+15\,a^8\,b^2\,c^2\,d^4-20\,a^7\,b^3\,c^3\,d^3+15\,a^6\,b^4\,c^4\,d^2-6\,a^5\,b^5\,c^5\,d+a^4\,b^6\,c^6\right)}\right)\right)\,1{}\mathrm{i}-\frac{x\,\left(3185\,a^4\,b^7\,d^{13}-4788\,a^3\,b^8\,c\,d^{12}+2790\,a^2\,b^9\,c^2\,d^{11}-756\,a\,b^{10}\,c^3\,d^{10}+81\,b^{11}\,c^4\,d^9\right)\,1{}\mathrm{i}}{64\,\left(a^{10}\,d^6-6\,a^9\,b\,c\,d^5+15\,a^8\,b^2\,c^2\,d^4-20\,a^7\,b^3\,c^3\,d^3+15\,a^6\,b^4\,c^4\,d^2-6\,a^5\,b^5\,c^5\,d+a^4\,b^6\,c^6\right)}\right)\,{\left(-\frac{2401\,a^4\,b^3\,d^4-4116\,a^3\,b^4\,c\,d^3+2646\,a^2\,b^5\,c^2\,d^2-756\,a\,b^6\,c^3\,d+81\,b^7\,c^4}{65536\,a^{15}\,d^8-524288\,a^{14}\,b\,c\,d^7+1835008\,a^{13}\,b^2\,c^2\,d^6-3670016\,a^{12}\,b^3\,c^3\,d^5+4587520\,a^{11}\,b^4\,c^4\,d^4-3670016\,a^{10}\,b^5\,c^5\,d^3+1835008\,a^9\,b^6\,c^6\,d^2-524288\,a^8\,b^7\,c^7\,d+65536\,a^7\,b^8\,c^8}\right)}^{1/4}-\left({\left(-\frac{2401\,a^4\,b^3\,d^4-4116\,a^3\,b^4\,c\,d^3+2646\,a^2\,b^5\,c^2\,d^2-756\,a\,b^6\,c^3\,d+81\,b^7\,c^4}{65536\,a^{15}\,d^8-524288\,a^{14}\,b\,c\,d^7+1835008\,a^{13}\,b^2\,c^2\,d^6-3670016\,a^{12}\,b^3\,c^3\,d^5+4587520\,a^{11}\,b^4\,c^4\,d^4-3670016\,a^{10}\,b^5\,c^5\,d^3+1835008\,a^9\,b^6\,c^6\,d^2-524288\,a^8\,b^7\,c^7\,d+65536\,a^7\,b^8\,c^8}\right)}^{1/4}\,\left(\frac{28\,a^4\,b^6\,d^{11}-\frac{2145\,a^3\,b^7\,c\,d^{10}}{16}+\frac{1971\,a^2\,b^8\,c^2\,d^9}{16}-\frac{675\,a\,b^9\,c^3\,d^8}{16}+\frac{81\,b^{10}\,c^4\,d^7}{16}}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-a^4\,b^3\,c^3}+{\left(-\frac{2401\,a^4\,b^3\,d^4-4116\,a^3\,b^4\,c\,d^3+2646\,a^2\,b^5\,c^2\,d^2-756\,a\,b^6\,c^3\,d+81\,b^7\,c^4}{65536\,a^{15}\,d^8-524288\,a^{14}\,b\,c\,d^7+1835008\,a^{13}\,b^2\,c^2\,d^6-3670016\,a^{12}\,b^3\,c^3\,d^5+4587520\,a^{11}\,b^4\,c^4\,d^4-3670016\,a^{10}\,b^5\,c^5\,d^3+1835008\,a^9\,b^6\,c^6\,d^2-524288\,a^8\,b^7\,c^7\,d+65536\,a^7\,b^8\,c^8}\right)}^{3/4}\,\left(\frac{{\left(-\frac{2401\,a^4\,b^3\,d^4-4116\,a^3\,b^4\,c\,d^3+2646\,a^2\,b^5\,c^2\,d^2-756\,a\,b^6\,c^3\,d+81\,b^7\,c^4}{65536\,a^{15}\,d^8-524288\,a^{14}\,b\,c\,d^7+1835008\,a^{13}\,b^2\,c^2\,d^6-3670016\,a^{12}\,b^3\,c^3\,d^5+4587520\,a^{11}\,b^4\,c^4\,d^4-3670016\,a^{10}\,b^5\,c^5\,d^3+1835008\,a^9\,b^6\,c^6\,d^2-524288\,a^8\,b^7\,c^7\,d+65536\,a^7\,b^8\,c^8}\right)}^{1/4}\,\left(-4096\,a^{14}\,b^4\,c\,d^{14}+28672\,a^{13}\,b^5\,c^2\,d^{13}-78848\,a^{12}\,b^6\,c^3\,d^{12}+90112\,a^{11}\,b^7\,c^4\,d^{11}+28672\,a^{10}\,b^8\,c^5\,d^{10}-229376\,a^9\,b^9\,c^6\,d^9+329728\,a^8\,b^{10}\,c^7\,d^8-253952\,a^7\,b^{11}\,c^8\,d^7+114688\,a^6\,b^{12}\,c^9\,d^6-28672\,a^5\,b^{13}\,c^{10}\,d^5+3072\,a^4\,b^{14}\,c^{11}\,d^4\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-a^4\,b^3\,c^3}+\frac{x\,\left(65536\,a^{15}\,b^4\,d^{17}-524288\,a^{14}\,b^5\,c\,d^{16}+1835008\,a^{13}\,b^6\,c^2\,d^{15}-3469312\,a^{12}\,b^7\,c^3\,d^{14}+2809856\,a^{11}\,b^8\,c^4\,d^{13}+3362816\,a^{10}\,b^9\,c^5\,d^{12}-14516224\,a^9\,b^{10}\,c^6\,d^{11}+24190976\,a^8\,b^{11}\,c^7\,d^{10}-25280512\,a^7\,b^{12}\,c^8\,d^9+17833984\,a^6\,b^{13}\,c^9\,d^8-8486912\,a^5\,b^{14}\,c^{10}\,d^7+2609152\,a^4\,b^{15}\,c^{11}\,d^6-466944\,a^3\,b^{16}\,c^{12}\,d^5+36864\,a^2\,b^{17}\,c^{13}\,d^4\right)}{64\,\left(a^{10}\,d^6-6\,a^9\,b\,c\,d^5+15\,a^8\,b^2\,c^2\,d^4-20\,a^7\,b^3\,c^3\,d^3+15\,a^6\,b^4\,c^4\,d^2-6\,a^5\,b^5\,c^5\,d+a^4\,b^6\,c^6\right)}\right)\right)\,1{}\mathrm{i}+\frac{x\,\left(3185\,a^4\,b^7\,d^{13}-4788\,a^3\,b^8\,c\,d^{12}+2790\,a^2\,b^9\,c^2\,d^{11}-756\,a\,b^{10}\,c^3\,d^{10}+81\,b^{11}\,c^4\,d^9\right)\,1{}\mathrm{i}}{64\,\left(a^{10}\,d^6-6\,a^9\,b\,c\,d^5+15\,a^8\,b^2\,c^2\,d^4-20\,a^7\,b^3\,c^3\,d^3+15\,a^6\,b^4\,c^4\,d^2-6\,a^5\,b^5\,c^5\,d+a^4\,b^6\,c^6\right)}\right)\,{\left(-\frac{2401\,a^4\,b^3\,d^4-4116\,a^3\,b^4\,c\,d^3+2646\,a^2\,b^5\,c^2\,d^2-756\,a\,b^6\,c^3\,d+81\,b^7\,c^4}{65536\,a^{15}\,d^8-524288\,a^{14}\,b\,c\,d^7+1835008\,a^{13}\,b^2\,c^2\,d^6-3670016\,a^{12}\,b^3\,c^3\,d^5+4587520\,a^{11}\,b^4\,c^4\,d^4-3670016\,a^{10}\,b^5\,c^5\,d^3+1835008\,a^9\,b^6\,c^6\,d^2-524288\,a^8\,b^7\,c^7\,d+65536\,a^7\,b^8\,c^8}\right)}^{1/4}}{\left({\left(-\frac{2401\,a^4\,b^3\,d^4-4116\,a^3\,b^4\,c\,d^3+2646\,a^2\,b^5\,c^2\,d^2-756\,a\,b^6\,c^3\,d+81\,b^7\,c^4}{65536\,a^{15}\,d^8-524288\,a^{14}\,b\,c\,d^7+1835008\,a^{13}\,b^2\,c^2\,d^6-3670016\,a^{12}\,b^3\,c^3\,d^5+4587520\,a^{11}\,b^4\,c^4\,d^4-3670016\,a^{10}\,b^5\,c^5\,d^3+1835008\,a^9\,b^6\,c^6\,d^2-524288\,a^8\,b^7\,c^7\,d+65536\,a^7\,b^8\,c^8}\right)}^{1/4}\,\left(\frac{28\,a^4\,b^6\,d^{11}-\frac{2145\,a^3\,b^7\,c\,d^{10}}{16}+\frac{1971\,a^2\,b^8\,c^2\,d^9}{16}-\frac{675\,a\,b^9\,c^3\,d^8}{16}+\frac{81\,b^{10}\,c^4\,d^7}{16}}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-a^4\,b^3\,c^3}+{\left(-\frac{2401\,a^4\,b^3\,d^4-4116\,a^3\,b^4\,c\,d^3+2646\,a^2\,b^5\,c^2\,d^2-756\,a\,b^6\,c^3\,d+81\,b^7\,c^4}{65536\,a^{15}\,d^8-524288\,a^{14}\,b\,c\,d^7+1835008\,a^{13}\,b^2\,c^2\,d^6-3670016\,a^{12}\,b^3\,c^3\,d^5+4587520\,a^{11}\,b^4\,c^4\,d^4-3670016\,a^{10}\,b^5\,c^5\,d^3+1835008\,a^9\,b^6\,c^6\,d^2-524288\,a^8\,b^7\,c^7\,d+65536\,a^7\,b^8\,c^8}\right)}^{3/4}\,\left(\frac{{\left(-\frac{2401\,a^4\,b^3\,d^4-4116\,a^3\,b^4\,c\,d^3+2646\,a^2\,b^5\,c^2\,d^2-756\,a\,b^6\,c^3\,d+81\,b^7\,c^4}{65536\,a^{15}\,d^8-524288\,a^{14}\,b\,c\,d^7+1835008\,a^{13}\,b^2\,c^2\,d^6-3670016\,a^{12}\,b^3\,c^3\,d^5+4587520\,a^{11}\,b^4\,c^4\,d^4-3670016\,a^{10}\,b^5\,c^5\,d^3+1835008\,a^9\,b^6\,c^6\,d^2-524288\,a^8\,b^7\,c^7\,d+65536\,a^7\,b^8\,c^8}\right)}^{1/4}\,\left(-4096\,a^{14}\,b^4\,c\,d^{14}+28672\,a^{13}\,b^5\,c^2\,d^{13}-78848\,a^{12}\,b^6\,c^3\,d^{12}+90112\,a^{11}\,b^7\,c^4\,d^{11}+28672\,a^{10}\,b^8\,c^5\,d^{10}-229376\,a^9\,b^9\,c^6\,d^9+329728\,a^8\,b^{10}\,c^7\,d^8-253952\,a^7\,b^{11}\,c^8\,d^7+114688\,a^6\,b^{12}\,c^9\,d^6-28672\,a^5\,b^{13}\,c^{10}\,d^5+3072\,a^4\,b^{14}\,c^{11}\,d^4\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-a^4\,b^3\,c^3}-\frac{x\,\left(65536\,a^{15}\,b^4\,d^{17}-524288\,a^{14}\,b^5\,c\,d^{16}+1835008\,a^{13}\,b^6\,c^2\,d^{15}-3469312\,a^{12}\,b^7\,c^3\,d^{14}+2809856\,a^{11}\,b^8\,c^4\,d^{13}+3362816\,a^{10}\,b^9\,c^5\,d^{12}-14516224\,a^9\,b^{10}\,c^6\,d^{11}+24190976\,a^8\,b^{11}\,c^7\,d^{10}-25280512\,a^7\,b^{12}\,c^8\,d^9+17833984\,a^6\,b^{13}\,c^9\,d^8-8486912\,a^5\,b^{14}\,c^{10}\,d^7+2609152\,a^4\,b^{15}\,c^{11}\,d^6-466944\,a^3\,b^{16}\,c^{12}\,d^5+36864\,a^2\,b^{17}\,c^{13}\,d^4\right)}{64\,\left(a^{10}\,d^6-6\,a^9\,b\,c\,d^5+15\,a^8\,b^2\,c^2\,d^4-20\,a^7\,b^3\,c^3\,d^3+15\,a^6\,b^4\,c^4\,d^2-6\,a^5\,b^5\,c^5\,d+a^4\,b^6\,c^6\right)}\right)\right)-\frac{x\,\left(3185\,a^4\,b^7\,d^{13}-4788\,a^3\,b^8\,c\,d^{12}+2790\,a^2\,b^9\,c^2\,d^{11}-756\,a\,b^{10}\,c^3\,d^{10}+81\,b^{11}\,c^4\,d^9\right)}{64\,\left(a^{10}\,d^6-6\,a^9\,b\,c\,d^5+15\,a^8\,b^2\,c^2\,d^4-20\,a^7\,b^3\,c^3\,d^3+15\,a^6\,b^4\,c^4\,d^2-6\,a^5\,b^5\,c^5\,d+a^4\,b^6\,c^6\right)}\right)\,{\left(-\frac{2401\,a^4\,b^3\,d^4-4116\,a^3\,b^4\,c\,d^3+2646\,a^2\,b^5\,c^2\,d^2-756\,a\,b^6\,c^3\,d+81\,b^7\,c^4}{65536\,a^{15}\,d^8-524288\,a^{14}\,b\,c\,d^7+1835008\,a^{13}\,b^2\,c^2\,d^6-3670016\,a^{12}\,b^3\,c^3\,d^5+4587520\,a^{11}\,b^4\,c^4\,d^4-3670016\,a^{10}\,b^5\,c^5\,d^3+1835008\,a^9\,b^6\,c^6\,d^2-524288\,a^8\,b^7\,c^7\,d+65536\,a^7\,b^8\,c^8}\right)}^{1/4}+\left({\left(-\frac{2401\,a^4\,b^3\,d^4-4116\,a^3\,b^4\,c\,d^3+2646\,a^2\,b^5\,c^2\,d^2-756\,a\,b^6\,c^3\,d+81\,b^7\,c^4}{65536\,a^{15}\,d^8-524288\,a^{14}\,b\,c\,d^7+1835008\,a^{13}\,b^2\,c^2\,d^6-3670016\,a^{12}\,b^3\,c^3\,d^5+4587520\,a^{11}\,b^4\,c^4\,d^4-3670016\,a^{10}\,b^5\,c^5\,d^3+1835008\,a^9\,b^6\,c^6\,d^2-524288\,a^8\,b^7\,c^7\,d+65536\,a^7\,b^8\,c^8}\right)}^{1/4}\,\left(\frac{28\,a^4\,b^6\,d^{11}-\frac{2145\,a^3\,b^7\,c\,d^{10}}{16}+\frac{1971\,a^2\,b^8\,c^2\,d^9}{16}-\frac{675\,a\,b^9\,c^3\,d^8}{16}+\frac{81\,b^{10}\,c^4\,d^7}{16}}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-a^4\,b^3\,c^3}+{\left(-\frac{2401\,a^4\,b^3\,d^4-4116\,a^3\,b^4\,c\,d^3+2646\,a^2\,b^5\,c^2\,d^2-756\,a\,b^6\,c^3\,d+81\,b^7\,c^4}{65536\,a^{15}\,d^8-524288\,a^{14}\,b\,c\,d^7+1835008\,a^{13}\,b^2\,c^2\,d^6-3670016\,a^{12}\,b^3\,c^3\,d^5+4587520\,a^{11}\,b^4\,c^4\,d^4-3670016\,a^{10}\,b^5\,c^5\,d^3+1835008\,a^9\,b^6\,c^6\,d^2-524288\,a^8\,b^7\,c^7\,d+65536\,a^7\,b^8\,c^8}\right)}^{3/4}\,\left(\frac{{\left(-\frac{2401\,a^4\,b^3\,d^4-4116\,a^3\,b^4\,c\,d^3+2646\,a^2\,b^5\,c^2\,d^2-756\,a\,b^6\,c^3\,d+81\,b^7\,c^4}{65536\,a^{15}\,d^8-524288\,a^{14}\,b\,c\,d^7+1835008\,a^{13}\,b^2\,c^2\,d^6-3670016\,a^{12}\,b^3\,c^3\,d^5+4587520\,a^{11}\,b^4\,c^4\,d^4-3670016\,a^{10}\,b^5\,c^5\,d^3+1835008\,a^9\,b^6\,c^6\,d^2-524288\,a^8\,b^7\,c^7\,d+65536\,a^7\,b^8\,c^8}\right)}^{1/4}\,\left(-4096\,a^{14}\,b^4\,c\,d^{14}+28672\,a^{13}\,b^5\,c^2\,d^{13}-78848\,a^{12}\,b^6\,c^3\,d^{12}+90112\,a^{11}\,b^7\,c^4\,d^{11}+28672\,a^{10}\,b^8\,c^5\,d^{10}-229376\,a^9\,b^9\,c^6\,d^9+329728\,a^8\,b^{10}\,c^7\,d^8-253952\,a^7\,b^{11}\,c^8\,d^7+114688\,a^6\,b^{12}\,c^9\,d^6-28672\,a^5\,b^{13}\,c^{10}\,d^5+3072\,a^4\,b^{14}\,c^{11}\,d^4\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-a^4\,b^3\,c^3}+\frac{x\,\left(65536\,a^{15}\,b^4\,d^{17}-524288\,a^{14}\,b^5\,c\,d^{16}+1835008\,a^{13}\,b^6\,c^2\,d^{15}-3469312\,a^{12}\,b^7\,c^3\,d^{14}+2809856\,a^{11}\,b^8\,c^4\,d^{13}+3362816\,a^{10}\,b^9\,c^5\,d^{12}-14516224\,a^9\,b^{10}\,c^6\,d^{11}+24190976\,a^8\,b^{11}\,c^7\,d^{10}-25280512\,a^7\,b^{12}\,c^8\,d^9+17833984\,a^6\,b^{13}\,c^9\,d^8-8486912\,a^5\,b^{14}\,c^{10}\,d^7+2609152\,a^4\,b^{15}\,c^{11}\,d^6-466944\,a^3\,b^{16}\,c^{12}\,d^5+36864\,a^2\,b^{17}\,c^{13}\,d^4\right)}{64\,\left(a^{10}\,d^6-6\,a^9\,b\,c\,d^5+15\,a^8\,b^2\,c^2\,d^4-20\,a^7\,b^3\,c^3\,d^3+15\,a^6\,b^4\,c^4\,d^2-6\,a^5\,b^5\,c^5\,d+a^4\,b^6\,c^6\right)}\right)\right)+\frac{x\,\left(3185\,a^4\,b^7\,d^{13}-4788\,a^3\,b^8\,c\,d^{12}+2790\,a^2\,b^9\,c^2\,d^{11}-756\,a\,b^{10}\,c^3\,d^{10}+81\,b^{11}\,c^4\,d^9\right)}{64\,\left(a^{10}\,d^6-6\,a^9\,b\,c\,d^5+15\,a^8\,b^2\,c^2\,d^4-20\,a^7\,b^3\,c^3\,d^3+15\,a^6\,b^4\,c^4\,d^2-6\,a^5\,b^5\,c^5\,d+a^4\,b^6\,c^6\right)}\right)\,{\left(-\frac{2401\,a^4\,b^3\,d^4-4116\,a^3\,b^4\,c\,d^3+2646\,a^2\,b^5\,c^2\,d^2-756\,a\,b^6\,c^3\,d+81\,b^7\,c^4}{65536\,a^{15}\,d^8-524288\,a^{14}\,b\,c\,d^7+1835008\,a^{13}\,b^2\,c^2\,d^6-3670016\,a^{12}\,b^3\,c^3\,d^5+4587520\,a^{11}\,b^4\,c^4\,d^4-3670016\,a^{10}\,b^5\,c^5\,d^3+1835008\,a^9\,b^6\,c^6\,d^2-524288\,a^8\,b^7\,c^7\,d+65536\,a^7\,b^8\,c^8}\right)}^{1/4}}\right)\,{\left(-\frac{2401\,a^4\,b^3\,d^4-4116\,a^3\,b^4\,c\,d^3+2646\,a^2\,b^5\,c^2\,d^2-756\,a\,b^6\,c^3\,d+81\,b^7\,c^4}{65536\,a^{15}\,d^8-524288\,a^{14}\,b\,c\,d^7+1835008\,a^{13}\,b^2\,c^2\,d^6-3670016\,a^{12}\,b^3\,c^3\,d^5+4587520\,a^{11}\,b^4\,c^4\,d^4-3670016\,a^{10}\,b^5\,c^5\,d^3+1835008\,a^9\,b^6\,c^6\,d^2-524288\,a^8\,b^7\,c^7\,d+65536\,a^7\,b^8\,c^8}\right)}^{1/4}\,2{}\mathrm{i}-\mathrm{atan}\left(\frac{{\left(-\frac{d^7}{256\,a^8\,c^3\,d^8-2048\,a^7\,b\,c^4\,d^7+7168\,a^6\,b^2\,c^5\,d^6-14336\,a^5\,b^3\,c^6\,d^5+17920\,a^4\,b^4\,c^7\,d^4-14336\,a^3\,b^5\,c^8\,d^3+7168\,a^2\,b^6\,c^9\,d^2-2048\,a\,b^7\,c^{10}\,d+256\,b^8\,c^{11}}\right)}^{1/4}\,\left({\left(-\frac{d^7}{256\,a^8\,c^3\,d^8-2048\,a^7\,b\,c^4\,d^7+7168\,a^6\,b^2\,c^5\,d^6-14336\,a^5\,b^3\,c^6\,d^5+17920\,a^4\,b^4\,c^7\,d^4-14336\,a^3\,b^5\,c^8\,d^3+7168\,a^2\,b^6\,c^9\,d^2-2048\,a\,b^7\,c^{10}\,d+256\,b^8\,c^{11}}\right)}^{1/4}\,\left({\left(-\frac{d^7}{256\,a^8\,c^3\,d^8-2048\,a^7\,b\,c^4\,d^7+7168\,a^6\,b^2\,c^5\,d^6-14336\,a^5\,b^3\,c^6\,d^5+17920\,a^4\,b^4\,c^7\,d^4-14336\,a^3\,b^5\,c^8\,d^3+7168\,a^2\,b^6\,c^9\,d^2-2048\,a\,b^7\,c^{10}\,d+256\,b^8\,c^{11}}\right)}^{3/4}\,\left(\frac{{\left(-\frac{d^7}{256\,a^8\,c^3\,d^8-2048\,a^7\,b\,c^4\,d^7+7168\,a^6\,b^2\,c^5\,d^6-14336\,a^5\,b^3\,c^6\,d^5+17920\,a^4\,b^4\,c^7\,d^4-14336\,a^3\,b^5\,c^8\,d^3+7168\,a^2\,b^6\,c^9\,d^2-2048\,a\,b^7\,c^{10}\,d+256\,b^8\,c^{11}}\right)}^{1/4}\,\left(-4096\,a^{14}\,b^4\,c\,d^{14}+28672\,a^{13}\,b^5\,c^2\,d^{13}-78848\,a^{12}\,b^6\,c^3\,d^{12}+90112\,a^{11}\,b^7\,c^4\,d^{11}+28672\,a^{10}\,b^8\,c^5\,d^{10}-229376\,a^9\,b^9\,c^6\,d^9+329728\,a^8\,b^{10}\,c^7\,d^8-253952\,a^7\,b^{11}\,c^8\,d^7+114688\,a^6\,b^{12}\,c^9\,d^6-28672\,a^5\,b^{13}\,c^{10}\,d^5+3072\,a^4\,b^{14}\,c^{11}\,d^4\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-a^4\,b^3\,c^3}-\frac{x\,\left(65536\,a^{15}\,b^4\,d^{17}-524288\,a^{14}\,b^5\,c\,d^{16}+1835008\,a^{13}\,b^6\,c^2\,d^{15}-3469312\,a^{12}\,b^7\,c^3\,d^{14}+2809856\,a^{11}\,b^8\,c^4\,d^{13}+3362816\,a^{10}\,b^9\,c^5\,d^{12}-14516224\,a^9\,b^{10}\,c^6\,d^{11}+24190976\,a^8\,b^{11}\,c^7\,d^{10}-25280512\,a^7\,b^{12}\,c^8\,d^9+17833984\,a^6\,b^{13}\,c^9\,d^8-8486912\,a^5\,b^{14}\,c^{10}\,d^7+2609152\,a^4\,b^{15}\,c^{11}\,d^6-466944\,a^3\,b^{16}\,c^{12}\,d^5+36864\,a^2\,b^{17}\,c^{13}\,d^4\right)}{64\,\left(a^{10}\,d^6-6\,a^9\,b\,c\,d^5+15\,a^8\,b^2\,c^2\,d^4-20\,a^7\,b^3\,c^3\,d^3+15\,a^6\,b^4\,c^4\,d^2-6\,a^5\,b^5\,c^5\,d+a^4\,b^6\,c^6\right)}\right)+\frac{28\,a^4\,b^6\,d^{11}-\frac{2145\,a^3\,b^7\,c\,d^{10}}{16}+\frac{1971\,a^2\,b^8\,c^2\,d^9}{16}-\frac{675\,a\,b^9\,c^3\,d^8}{16}+\frac{81\,b^{10}\,c^4\,d^7}{16}}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-a^4\,b^3\,c^3}\right)\,1{}\mathrm{i}-\frac{x\,\left(3185\,a^4\,b^7\,d^{13}-4788\,a^3\,b^8\,c\,d^{12}+2790\,a^2\,b^9\,c^2\,d^{11}-756\,a\,b^{10}\,c^3\,d^{10}+81\,b^{11}\,c^4\,d^9\right)\,1{}\mathrm{i}}{64\,\left(a^{10}\,d^6-6\,a^9\,b\,c\,d^5+15\,a^8\,b^2\,c^2\,d^4-20\,a^7\,b^3\,c^3\,d^3+15\,a^6\,b^4\,c^4\,d^2-6\,a^5\,b^5\,c^5\,d+a^4\,b^6\,c^6\right)}\right)-{\left(-\frac{d^7}{256\,a^8\,c^3\,d^8-2048\,a^7\,b\,c^4\,d^7+7168\,a^6\,b^2\,c^5\,d^6-14336\,a^5\,b^3\,c^6\,d^5+17920\,a^4\,b^4\,c^7\,d^4-14336\,a^3\,b^5\,c^8\,d^3+7168\,a^2\,b^6\,c^9\,d^2-2048\,a\,b^7\,c^{10}\,d+256\,b^8\,c^{11}}\right)}^{1/4}\,\left({\left(-\frac{d^7}{256\,a^8\,c^3\,d^8-2048\,a^7\,b\,c^4\,d^7+7168\,a^6\,b^2\,c^5\,d^6-14336\,a^5\,b^3\,c^6\,d^5+17920\,a^4\,b^4\,c^7\,d^4-14336\,a^3\,b^5\,c^8\,d^3+7168\,a^2\,b^6\,c^9\,d^2-2048\,a\,b^7\,c^{10}\,d+256\,b^8\,c^{11}}\right)}^{1/4}\,\left({\left(-\frac{d^7}{256\,a^8\,c^3\,d^8-2048\,a^7\,b\,c^4\,d^7+7168\,a^6\,b^2\,c^5\,d^6-14336\,a^5\,b^3\,c^6\,d^5+17920\,a^4\,b^4\,c^7\,d^4-14336\,a^3\,b^5\,c^8\,d^3+7168\,a^2\,b^6\,c^9\,d^2-2048\,a\,b^7\,c^{10}\,d+256\,b^8\,c^{11}}\right)}^{3/4}\,\left(\frac{{\left(-\frac{d^7}{256\,a^8\,c^3\,d^8-2048\,a^7\,b\,c^4\,d^7+7168\,a^6\,b^2\,c^5\,d^6-14336\,a^5\,b^3\,c^6\,d^5+17920\,a^4\,b^4\,c^7\,d^4-14336\,a^3\,b^5\,c^8\,d^3+7168\,a^2\,b^6\,c^9\,d^2-2048\,a\,b^7\,c^{10}\,d+256\,b^8\,c^{11}}\right)}^{1/4}\,\left(-4096\,a^{14}\,b^4\,c\,d^{14}+28672\,a^{13}\,b^5\,c^2\,d^{13}-78848\,a^{12}\,b^6\,c^3\,d^{12}+90112\,a^{11}\,b^7\,c^4\,d^{11}+28672\,a^{10}\,b^8\,c^5\,d^{10}-229376\,a^9\,b^9\,c^6\,d^9+329728\,a^8\,b^{10}\,c^7\,d^8-253952\,a^7\,b^{11}\,c^8\,d^7+114688\,a^6\,b^{12}\,c^9\,d^6-28672\,a^5\,b^{13}\,c^{10}\,d^5+3072\,a^4\,b^{14}\,c^{11}\,d^4\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-a^4\,b^3\,c^3}+\frac{x\,\left(65536\,a^{15}\,b^4\,d^{17}-524288\,a^{14}\,b^5\,c\,d^{16}+1835008\,a^{13}\,b^6\,c^2\,d^{15}-3469312\,a^{12}\,b^7\,c^3\,d^{14}+2809856\,a^{11}\,b^8\,c^4\,d^{13}+3362816\,a^{10}\,b^9\,c^5\,d^{12}-14516224\,a^9\,b^{10}\,c^6\,d^{11}+24190976\,a^8\,b^{11}\,c^7\,d^{10}-25280512\,a^7\,b^{12}\,c^8\,d^9+17833984\,a^6\,b^{13}\,c^9\,d^8-8486912\,a^5\,b^{14}\,c^{10}\,d^7+2609152\,a^4\,b^{15}\,c^{11}\,d^6-466944\,a^3\,b^{16}\,c^{12}\,d^5+36864\,a^2\,b^{17}\,c^{13}\,d^4\right)}{64\,\left(a^{10}\,d^6-6\,a^9\,b\,c\,d^5+15\,a^8\,b^2\,c^2\,d^4-20\,a^7\,b^3\,c^3\,d^3+15\,a^6\,b^4\,c^4\,d^2-6\,a^5\,b^5\,c^5\,d+a^4\,b^6\,c^6\right)}\right)+\frac{28\,a^4\,b^6\,d^{11}-\frac{2145\,a^3\,b^7\,c\,d^{10}}{16}+\frac{1971\,a^2\,b^8\,c^2\,d^9}{16}-\frac{675\,a\,b^9\,c^3\,d^8}{16}+\frac{81\,b^{10}\,c^4\,d^7}{16}}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-a^4\,b^3\,c^3}\right)\,1{}\mathrm{i}+\frac{x\,\left(3185\,a^4\,b^7\,d^{13}-4788\,a^3\,b^8\,c\,d^{12}+2790\,a^2\,b^9\,c^2\,d^{11}-756\,a\,b^{10}\,c^3\,d^{10}+81\,b^{11}\,c^4\,d^9\right)\,1{}\mathrm{i}}{64\,\left(a^{10}\,d^6-6\,a^9\,b\,c\,d^5+15\,a^8\,b^2\,c^2\,d^4-20\,a^7\,b^3\,c^3\,d^3+15\,a^6\,b^4\,c^4\,d^2-6\,a^5\,b^5\,c^5\,d+a^4\,b^6\,c^6\right)}\right)}{{\left(-\frac{d^7}{256\,a^8\,c^3\,d^8-2048\,a^7\,b\,c^4\,d^7+7168\,a^6\,b^2\,c^5\,d^6-14336\,a^5\,b^3\,c^6\,d^5+17920\,a^4\,b^4\,c^7\,d^4-14336\,a^3\,b^5\,c^8\,d^3+7168\,a^2\,b^6\,c^9\,d^2-2048\,a\,b^7\,c^{10}\,d+256\,b^8\,c^{11}}\right)}^{1/4}\,\left({\left(-\frac{d^7}{256\,a^8\,c^3\,d^8-2048\,a^7\,b\,c^4\,d^7+7168\,a^6\,b^2\,c^5\,d^6-14336\,a^5\,b^3\,c^6\,d^5+17920\,a^4\,b^4\,c^7\,d^4-14336\,a^3\,b^5\,c^8\,d^3+7168\,a^2\,b^6\,c^9\,d^2-2048\,a\,b^7\,c^{10}\,d+256\,b^8\,c^{11}}\right)}^{1/4}\,\left({\left(-\frac{d^7}{256\,a^8\,c^3\,d^8-2048\,a^7\,b\,c^4\,d^7+7168\,a^6\,b^2\,c^5\,d^6-14336\,a^5\,b^3\,c^6\,d^5+17920\,a^4\,b^4\,c^7\,d^4-14336\,a^3\,b^5\,c^8\,d^3+7168\,a^2\,b^6\,c^9\,d^2-2048\,a\,b^7\,c^{10}\,d+256\,b^8\,c^{11}}\right)}^{3/4}\,\left(\frac{{\left(-\frac{d^7}{256\,a^8\,c^3\,d^8-2048\,a^7\,b\,c^4\,d^7+7168\,a^6\,b^2\,c^5\,d^6-14336\,a^5\,b^3\,c^6\,d^5+17920\,a^4\,b^4\,c^7\,d^4-14336\,a^3\,b^5\,c^8\,d^3+7168\,a^2\,b^6\,c^9\,d^2-2048\,a\,b^7\,c^{10}\,d+256\,b^8\,c^{11}}\right)}^{1/4}\,\left(-4096\,a^{14}\,b^4\,c\,d^{14}+28672\,a^{13}\,b^5\,c^2\,d^{13}-78848\,a^{12}\,b^6\,c^3\,d^{12}+90112\,a^{11}\,b^7\,c^4\,d^{11}+28672\,a^{10}\,b^8\,c^5\,d^{10}-229376\,a^9\,b^9\,c^6\,d^9+329728\,a^8\,b^{10}\,c^7\,d^8-253952\,a^7\,b^{11}\,c^8\,d^7+114688\,a^6\,b^{12}\,c^9\,d^6-28672\,a^5\,b^{13}\,c^{10}\,d^5+3072\,a^4\,b^{14}\,c^{11}\,d^4\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-a^4\,b^3\,c^3}-\frac{x\,\left(65536\,a^{15}\,b^4\,d^{17}-524288\,a^{14}\,b^5\,c\,d^{16}+1835008\,a^{13}\,b^6\,c^2\,d^{15}-3469312\,a^{12}\,b^7\,c^3\,d^{14}+2809856\,a^{11}\,b^8\,c^4\,d^{13}+3362816\,a^{10}\,b^9\,c^5\,d^{12}-14516224\,a^9\,b^{10}\,c^6\,d^{11}+24190976\,a^8\,b^{11}\,c^7\,d^{10}-25280512\,a^7\,b^{12}\,c^8\,d^9+17833984\,a^6\,b^{13}\,c^9\,d^8-8486912\,a^5\,b^{14}\,c^{10}\,d^7+2609152\,a^4\,b^{15}\,c^{11}\,d^6-466944\,a^3\,b^{16}\,c^{12}\,d^5+36864\,a^2\,b^{17}\,c^{13}\,d^4\right)}{64\,\left(a^{10}\,d^6-6\,a^9\,b\,c\,d^5+15\,a^8\,b^2\,c^2\,d^4-20\,a^7\,b^3\,c^3\,d^3+15\,a^6\,b^4\,c^4\,d^2-6\,a^5\,b^5\,c^5\,d+a^4\,b^6\,c^6\right)}\right)+\frac{28\,a^4\,b^6\,d^{11}-\frac{2145\,a^3\,b^7\,c\,d^{10}}{16}+\frac{1971\,a^2\,b^8\,c^2\,d^9}{16}-\frac{675\,a\,b^9\,c^3\,d^8}{16}+\frac{81\,b^{10}\,c^4\,d^7}{16}}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-a^4\,b^3\,c^3}\right)-\frac{x\,\left(3185\,a^4\,b^7\,d^{13}-4788\,a^3\,b^8\,c\,d^{12}+2790\,a^2\,b^9\,c^2\,d^{11}-756\,a\,b^{10}\,c^3\,d^{10}+81\,b^{11}\,c^4\,d^9\right)}{64\,\left(a^{10}\,d^6-6\,a^9\,b\,c\,d^5+15\,a^8\,b^2\,c^2\,d^4-20\,a^7\,b^3\,c^3\,d^3+15\,a^6\,b^4\,c^4\,d^2-6\,a^5\,b^5\,c^5\,d+a^4\,b^6\,c^6\right)}\right)+{\left(-\frac{d^7}{256\,a^8\,c^3\,d^8-2048\,a^7\,b\,c^4\,d^7+7168\,a^6\,b^2\,c^5\,d^6-14336\,a^5\,b^3\,c^6\,d^5+17920\,a^4\,b^4\,c^7\,d^4-14336\,a^3\,b^5\,c^8\,d^3+7168\,a^2\,b^6\,c^9\,d^2-2048\,a\,b^7\,c^{10}\,d+256\,b^8\,c^{11}}\right)}^{1/4}\,\left({\left(-\frac{d^7}{256\,a^8\,c^3\,d^8-2048\,a^7\,b\,c^4\,d^7+7168\,a^6\,b^2\,c^5\,d^6-14336\,a^5\,b^3\,c^6\,d^5+17920\,a^4\,b^4\,c^7\,d^4-14336\,a^3\,b^5\,c^8\,d^3+7168\,a^2\,b^6\,c^9\,d^2-2048\,a\,b^7\,c^{10}\,d+256\,b^8\,c^{11}}\right)}^{1/4}\,\left({\left(-\frac{d^7}{256\,a^8\,c^3\,d^8-2048\,a^7\,b\,c^4\,d^7+7168\,a^6\,b^2\,c^5\,d^6-14336\,a^5\,b^3\,c^6\,d^5+17920\,a^4\,b^4\,c^7\,d^4-14336\,a^3\,b^5\,c^8\,d^3+7168\,a^2\,b^6\,c^9\,d^2-2048\,a\,b^7\,c^{10}\,d+256\,b^8\,c^{11}}\right)}^{3/4}\,\left(\frac{{\left(-\frac{d^7}{256\,a^8\,c^3\,d^8-2048\,a^7\,b\,c^4\,d^7+7168\,a^6\,b^2\,c^5\,d^6-14336\,a^5\,b^3\,c^6\,d^5+17920\,a^4\,b^4\,c^7\,d^4-14336\,a^3\,b^5\,c^8\,d^3+7168\,a^2\,b^6\,c^9\,d^2-2048\,a\,b^7\,c^{10}\,d+256\,b^8\,c^{11}}\right)}^{1/4}\,\left(-4096\,a^{14}\,b^4\,c\,d^{14}+28672\,a^{13}\,b^5\,c^2\,d^{13}-78848\,a^{12}\,b^6\,c^3\,d^{12}+90112\,a^{11}\,b^7\,c^4\,d^{11}+28672\,a^{10}\,b^8\,c^5\,d^{10}-229376\,a^9\,b^9\,c^6\,d^9+329728\,a^8\,b^{10}\,c^7\,d^8-253952\,a^7\,b^{11}\,c^8\,d^7+114688\,a^6\,b^{12}\,c^9\,d^6-28672\,a^5\,b^{13}\,c^{10}\,d^5+3072\,a^4\,b^{14}\,c^{11}\,d^4\right)}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-a^4\,b^3\,c^3}+\frac{x\,\left(65536\,a^{15}\,b^4\,d^{17}-524288\,a^{14}\,b^5\,c\,d^{16}+1835008\,a^{13}\,b^6\,c^2\,d^{15}-3469312\,a^{12}\,b^7\,c^3\,d^{14}+2809856\,a^{11}\,b^8\,c^4\,d^{13}+3362816\,a^{10}\,b^9\,c^5\,d^{12}-14516224\,a^9\,b^{10}\,c^6\,d^{11}+24190976\,a^8\,b^{11}\,c^7\,d^{10}-25280512\,a^7\,b^{12}\,c^8\,d^9+17833984\,a^6\,b^{13}\,c^9\,d^8-8486912\,a^5\,b^{14}\,c^{10}\,d^7+2609152\,a^4\,b^{15}\,c^{11}\,d^6-466944\,a^3\,b^{16}\,c^{12}\,d^5+36864\,a^2\,b^{17}\,c^{13}\,d^4\right)}{64\,\left(a^{10}\,d^6-6\,a^9\,b\,c\,d^5+15\,a^8\,b^2\,c^2\,d^4-20\,a^7\,b^3\,c^3\,d^3+15\,a^6\,b^4\,c^4\,d^2-6\,a^5\,b^5\,c^5\,d+a^4\,b^6\,c^6\right)}\right)+\frac{28\,a^4\,b^6\,d^{11}-\frac{2145\,a^3\,b^7\,c\,d^{10}}{16}+\frac{1971\,a^2\,b^8\,c^2\,d^9}{16}-\frac{675\,a\,b^9\,c^3\,d^8}{16}+\frac{81\,b^{10}\,c^4\,d^7}{16}}{a^7\,d^3-3\,a^6\,b\,c\,d^2+3\,a^5\,b^2\,c^2\,d-a^4\,b^3\,c^3}\right)+\frac{x\,\left(3185\,a^4\,b^7\,d^{13}-4788\,a^3\,b^8\,c\,d^{12}+2790\,a^2\,b^9\,c^2\,d^{11}-756\,a\,b^{10}\,c^3\,d^{10}+81\,b^{11}\,c^4\,d^9\right)}{64\,\left(a^{10}\,d^6-6\,a^9\,b\,c\,d^5+15\,a^8\,b^2\,c^2\,d^4-20\,a^7\,b^3\,c^3\,d^3+15\,a^6\,b^4\,c^4\,d^2-6\,a^5\,b^5\,c^5\,d+a^4\,b^6\,c^6\right)}\right)}\right)\,{\left(-\frac{d^7}{256\,a^8\,c^3\,d^8-2048\,a^7\,b\,c^4\,d^7+7168\,a^6\,b^2\,c^5\,d^6-14336\,a^5\,b^3\,c^6\,d^5+17920\,a^4\,b^4\,c^7\,d^4-14336\,a^3\,b^5\,c^8\,d^3+7168\,a^2\,b^6\,c^9\,d^2-2048\,a\,b^7\,c^{10}\,d+256\,b^8\,c^{11}}\right)}^{1/4}\,2{}\mathrm{i}","Not used",1,"2*atan((((-(81*b^7*c^4 + 2401*a^4*b^3*d^4 - 4116*a^3*b^4*c*d^3 + 2646*a^2*b^5*c^2*d^2 - 756*a*b^6*c^3*d)/(65536*a^15*d^8 + 65536*a^7*b^8*c^8 - 524288*a^8*b^7*c^7*d + 1835008*a^9*b^6*c^6*d^2 - 3670016*a^10*b^5*c^5*d^3 + 4587520*a^11*b^4*c^4*d^4 - 3670016*a^12*b^3*c^3*d^5 + 1835008*a^13*b^2*c^2*d^6 - 524288*a^14*b*c*d^7))^(1/4)*(((28*a^4*b^6*d^11 + (81*b^10*c^4*d^7)/16 - (675*a*b^9*c^3*d^8)/16 - (2145*a^3*b^7*c*d^10)/16 + (1971*a^2*b^8*c^2*d^9)/16)*1i)/(a^7*d^3 - a^4*b^3*c^3 + 3*a^5*b^2*c^2*d - 3*a^6*b*c*d^2) + (-(81*b^7*c^4 + 2401*a^4*b^3*d^4 - 4116*a^3*b^4*c*d^3 + 2646*a^2*b^5*c^2*d^2 - 756*a*b^6*c^3*d)/(65536*a^15*d^8 + 65536*a^7*b^8*c^8 - 524288*a^8*b^7*c^7*d + 1835008*a^9*b^6*c^6*d^2 - 3670016*a^10*b^5*c^5*d^3 + 4587520*a^11*b^4*c^4*d^4 - 3670016*a^12*b^3*c^3*d^5 + 1835008*a^13*b^2*c^2*d^6 - 524288*a^14*b*c*d^7))^(3/4)*(((-(81*b^7*c^4 + 2401*a^4*b^3*d^4 - 4116*a^3*b^4*c*d^3 + 2646*a^2*b^5*c^2*d^2 - 756*a*b^6*c^3*d)/(65536*a^15*d^8 + 65536*a^7*b^8*c^8 - 524288*a^8*b^7*c^7*d + 1835008*a^9*b^6*c^6*d^2 - 3670016*a^10*b^5*c^5*d^3 + 4587520*a^11*b^4*c^4*d^4 - 3670016*a^12*b^3*c^3*d^5 + 1835008*a^13*b^2*c^2*d^6 - 524288*a^14*b*c*d^7))^(1/4)*(3072*a^4*b^14*c^11*d^4 - 4096*a^14*b^4*c*d^14 - 28672*a^5*b^13*c^10*d^5 + 114688*a^6*b^12*c^9*d^6 - 253952*a^7*b^11*c^8*d^7 + 329728*a^8*b^10*c^7*d^8 - 229376*a^9*b^9*c^6*d^9 + 28672*a^10*b^8*c^5*d^10 + 90112*a^11*b^7*c^4*d^11 - 78848*a^12*b^6*c^3*d^12 + 28672*a^13*b^5*c^2*d^13))/(a^7*d^3 - a^4*b^3*c^3 + 3*a^5*b^2*c^2*d - 3*a^6*b*c*d^2) - (x*(65536*a^15*b^4*d^17 - 524288*a^14*b^5*c*d^16 + 36864*a^2*b^17*c^13*d^4 - 466944*a^3*b^16*c^12*d^5 + 2609152*a^4*b^15*c^11*d^6 - 8486912*a^5*b^14*c^10*d^7 + 17833984*a^6*b^13*c^9*d^8 - 25280512*a^7*b^12*c^8*d^9 + 24190976*a^8*b^11*c^7*d^10 - 14516224*a^9*b^10*c^6*d^11 + 3362816*a^10*b^9*c^5*d^12 + 2809856*a^11*b^8*c^4*d^13 - 3469312*a^12*b^7*c^3*d^14 + 1835008*a^13*b^6*c^2*d^15)*1i)/(64*(a^10*d^6 + a^4*b^6*c^6 - 6*a^5*b^5*c^5*d + 15*a^6*b^4*c^4*d^2 - 20*a^7*b^3*c^3*d^3 + 15*a^8*b^2*c^2*d^4 - 6*a^9*b*c*d^5)))*1i) + (x*(3185*a^4*b^7*d^13 + 81*b^11*c^4*d^9 - 756*a*b^10*c^3*d^10 - 4788*a^3*b^8*c*d^12 + 2790*a^2*b^9*c^2*d^11))/(64*(a^10*d^6 + a^4*b^6*c^6 - 6*a^5*b^5*c^5*d + 15*a^6*b^4*c^4*d^2 - 20*a^7*b^3*c^3*d^3 + 15*a^8*b^2*c^2*d^4 - 6*a^9*b*c*d^5)))*(-(81*b^7*c^4 + 2401*a^4*b^3*d^4 - 4116*a^3*b^4*c*d^3 + 2646*a^2*b^5*c^2*d^2 - 756*a*b^6*c^3*d)/(65536*a^15*d^8 + 65536*a^7*b^8*c^8 - 524288*a^8*b^7*c^7*d + 1835008*a^9*b^6*c^6*d^2 - 3670016*a^10*b^5*c^5*d^3 + 4587520*a^11*b^4*c^4*d^4 - 3670016*a^12*b^3*c^3*d^5 + 1835008*a^13*b^2*c^2*d^6 - 524288*a^14*b*c*d^7))^(1/4) - ((-(81*b^7*c^4 + 2401*a^4*b^3*d^4 - 4116*a^3*b^4*c*d^3 + 2646*a^2*b^5*c^2*d^2 - 756*a*b^6*c^3*d)/(65536*a^15*d^8 + 65536*a^7*b^8*c^8 - 524288*a^8*b^7*c^7*d + 1835008*a^9*b^6*c^6*d^2 - 3670016*a^10*b^5*c^5*d^3 + 4587520*a^11*b^4*c^4*d^4 - 3670016*a^12*b^3*c^3*d^5 + 1835008*a^13*b^2*c^2*d^6 - 524288*a^14*b*c*d^7))^(1/4)*(((28*a^4*b^6*d^11 + (81*b^10*c^4*d^7)/16 - (675*a*b^9*c^3*d^8)/16 - (2145*a^3*b^7*c*d^10)/16 + (1971*a^2*b^8*c^2*d^9)/16)*1i)/(a^7*d^3 - a^4*b^3*c^3 + 3*a^5*b^2*c^2*d - 3*a^6*b*c*d^2) + (-(81*b^7*c^4 + 2401*a^4*b^3*d^4 - 4116*a^3*b^4*c*d^3 + 2646*a^2*b^5*c^2*d^2 - 756*a*b^6*c^3*d)/(65536*a^15*d^8 + 65536*a^7*b^8*c^8 - 524288*a^8*b^7*c^7*d + 1835008*a^9*b^6*c^6*d^2 - 3670016*a^10*b^5*c^5*d^3 + 4587520*a^11*b^4*c^4*d^4 - 3670016*a^12*b^3*c^3*d^5 + 1835008*a^13*b^2*c^2*d^6 - 524288*a^14*b*c*d^7))^(3/4)*(((-(81*b^7*c^4 + 2401*a^4*b^3*d^4 - 4116*a^3*b^4*c*d^3 + 2646*a^2*b^5*c^2*d^2 - 756*a*b^6*c^3*d)/(65536*a^15*d^8 + 65536*a^7*b^8*c^8 - 524288*a^8*b^7*c^7*d + 1835008*a^9*b^6*c^6*d^2 - 3670016*a^10*b^5*c^5*d^3 + 4587520*a^11*b^4*c^4*d^4 - 3670016*a^12*b^3*c^3*d^5 + 1835008*a^13*b^2*c^2*d^6 - 524288*a^14*b*c*d^7))^(1/4)*(3072*a^4*b^14*c^11*d^4 - 4096*a^14*b^4*c*d^14 - 28672*a^5*b^13*c^10*d^5 + 114688*a^6*b^12*c^9*d^6 - 253952*a^7*b^11*c^8*d^7 + 329728*a^8*b^10*c^7*d^8 - 229376*a^9*b^9*c^6*d^9 + 28672*a^10*b^8*c^5*d^10 + 90112*a^11*b^7*c^4*d^11 - 78848*a^12*b^6*c^3*d^12 + 28672*a^13*b^5*c^2*d^13))/(a^7*d^3 - a^4*b^3*c^3 + 3*a^5*b^2*c^2*d - 3*a^6*b*c*d^2) + (x*(65536*a^15*b^4*d^17 - 524288*a^14*b^5*c*d^16 + 36864*a^2*b^17*c^13*d^4 - 466944*a^3*b^16*c^12*d^5 + 2609152*a^4*b^15*c^11*d^6 - 8486912*a^5*b^14*c^10*d^7 + 17833984*a^6*b^13*c^9*d^8 - 25280512*a^7*b^12*c^8*d^9 + 24190976*a^8*b^11*c^7*d^10 - 14516224*a^9*b^10*c^6*d^11 + 3362816*a^10*b^9*c^5*d^12 + 2809856*a^11*b^8*c^4*d^13 - 3469312*a^12*b^7*c^3*d^14 + 1835008*a^13*b^6*c^2*d^15)*1i)/(64*(a^10*d^6 + a^4*b^6*c^6 - 6*a^5*b^5*c^5*d + 15*a^6*b^4*c^4*d^2 - 20*a^7*b^3*c^3*d^3 + 15*a^8*b^2*c^2*d^4 - 6*a^9*b*c*d^5)))*1i) - (x*(3185*a^4*b^7*d^13 + 81*b^11*c^4*d^9 - 756*a*b^10*c^3*d^10 - 4788*a^3*b^8*c*d^12 + 2790*a^2*b^9*c^2*d^11))/(64*(a^10*d^6 + a^4*b^6*c^6 - 6*a^5*b^5*c^5*d + 15*a^6*b^4*c^4*d^2 - 20*a^7*b^3*c^3*d^3 + 15*a^8*b^2*c^2*d^4 - 6*a^9*b*c*d^5)))*(-(81*b^7*c^4 + 2401*a^4*b^3*d^4 - 4116*a^3*b^4*c*d^3 + 2646*a^2*b^5*c^2*d^2 - 756*a*b^6*c^3*d)/(65536*a^15*d^8 + 65536*a^7*b^8*c^8 - 524288*a^8*b^7*c^7*d + 1835008*a^9*b^6*c^6*d^2 - 3670016*a^10*b^5*c^5*d^3 + 4587520*a^11*b^4*c^4*d^4 - 3670016*a^12*b^3*c^3*d^5 + 1835008*a^13*b^2*c^2*d^6 - 524288*a^14*b*c*d^7))^(1/4))/(((-(81*b^7*c^4 + 2401*a^4*b^3*d^4 - 4116*a^3*b^4*c*d^3 + 2646*a^2*b^5*c^2*d^2 - 756*a*b^6*c^3*d)/(65536*a^15*d^8 + 65536*a^7*b^8*c^8 - 524288*a^8*b^7*c^7*d + 1835008*a^9*b^6*c^6*d^2 - 3670016*a^10*b^5*c^5*d^3 + 4587520*a^11*b^4*c^4*d^4 - 3670016*a^12*b^3*c^3*d^5 + 1835008*a^13*b^2*c^2*d^6 - 524288*a^14*b*c*d^7))^(1/4)*(((28*a^4*b^6*d^11 + (81*b^10*c^4*d^7)/16 - (675*a*b^9*c^3*d^8)/16 - (2145*a^3*b^7*c*d^10)/16 + (1971*a^2*b^8*c^2*d^9)/16)*1i)/(a^7*d^3 - a^4*b^3*c^3 + 3*a^5*b^2*c^2*d - 3*a^6*b*c*d^2) + (-(81*b^7*c^4 + 2401*a^4*b^3*d^4 - 4116*a^3*b^4*c*d^3 + 2646*a^2*b^5*c^2*d^2 - 756*a*b^6*c^3*d)/(65536*a^15*d^8 + 65536*a^7*b^8*c^8 - 524288*a^8*b^7*c^7*d + 1835008*a^9*b^6*c^6*d^2 - 3670016*a^10*b^5*c^5*d^3 + 4587520*a^11*b^4*c^4*d^4 - 3670016*a^12*b^3*c^3*d^5 + 1835008*a^13*b^2*c^2*d^6 - 524288*a^14*b*c*d^7))^(3/4)*(((-(81*b^7*c^4 + 2401*a^4*b^3*d^4 - 4116*a^3*b^4*c*d^3 + 2646*a^2*b^5*c^2*d^2 - 756*a*b^6*c^3*d)/(65536*a^15*d^8 + 65536*a^7*b^8*c^8 - 524288*a^8*b^7*c^7*d + 1835008*a^9*b^6*c^6*d^2 - 3670016*a^10*b^5*c^5*d^3 + 4587520*a^11*b^4*c^4*d^4 - 3670016*a^12*b^3*c^3*d^5 + 1835008*a^13*b^2*c^2*d^6 - 524288*a^14*b*c*d^7))^(1/4)*(3072*a^4*b^14*c^11*d^4 - 4096*a^14*b^4*c*d^14 - 28672*a^5*b^13*c^10*d^5 + 114688*a^6*b^12*c^9*d^6 - 253952*a^7*b^11*c^8*d^7 + 329728*a^8*b^10*c^7*d^8 - 229376*a^9*b^9*c^6*d^9 + 28672*a^10*b^8*c^5*d^10 + 90112*a^11*b^7*c^4*d^11 - 78848*a^12*b^6*c^3*d^12 + 28672*a^13*b^5*c^2*d^13))/(a^7*d^3 - a^4*b^3*c^3 + 3*a^5*b^2*c^2*d - 3*a^6*b*c*d^2) - (x*(65536*a^15*b^4*d^17 - 524288*a^14*b^5*c*d^16 + 36864*a^2*b^17*c^13*d^4 - 466944*a^3*b^16*c^12*d^5 + 2609152*a^4*b^15*c^11*d^6 - 8486912*a^5*b^14*c^10*d^7 + 17833984*a^6*b^13*c^9*d^8 - 25280512*a^7*b^12*c^8*d^9 + 24190976*a^8*b^11*c^7*d^10 - 14516224*a^9*b^10*c^6*d^11 + 3362816*a^10*b^9*c^5*d^12 + 2809856*a^11*b^8*c^4*d^13 - 3469312*a^12*b^7*c^3*d^14 + 1835008*a^13*b^6*c^2*d^15)*1i)/(64*(a^10*d^6 + a^4*b^6*c^6 - 6*a^5*b^5*c^5*d + 15*a^6*b^4*c^4*d^2 - 20*a^7*b^3*c^3*d^3 + 15*a^8*b^2*c^2*d^4 - 6*a^9*b*c*d^5)))*1i)*1i + (x*(3185*a^4*b^7*d^13 + 81*b^11*c^4*d^9 - 756*a*b^10*c^3*d^10 - 4788*a^3*b^8*c*d^12 + 2790*a^2*b^9*c^2*d^11)*1i)/(64*(a^10*d^6 + a^4*b^6*c^6 - 6*a^5*b^5*c^5*d + 15*a^6*b^4*c^4*d^2 - 20*a^7*b^3*c^3*d^3 + 15*a^8*b^2*c^2*d^4 - 6*a^9*b*c*d^5)))*(-(81*b^7*c^4 + 2401*a^4*b^3*d^4 - 4116*a^3*b^4*c*d^3 + 2646*a^2*b^5*c^2*d^2 - 756*a*b^6*c^3*d)/(65536*a^15*d^8 + 65536*a^7*b^8*c^8 - 524288*a^8*b^7*c^7*d + 1835008*a^9*b^6*c^6*d^2 - 3670016*a^10*b^5*c^5*d^3 + 4587520*a^11*b^4*c^4*d^4 - 3670016*a^12*b^3*c^3*d^5 + 1835008*a^13*b^2*c^2*d^6 - 524288*a^14*b*c*d^7))^(1/4) + ((-(81*b^7*c^4 + 2401*a^4*b^3*d^4 - 4116*a^3*b^4*c*d^3 + 2646*a^2*b^5*c^2*d^2 - 756*a*b^6*c^3*d)/(65536*a^15*d^8 + 65536*a^7*b^8*c^8 - 524288*a^8*b^7*c^7*d + 1835008*a^9*b^6*c^6*d^2 - 3670016*a^10*b^5*c^5*d^3 + 4587520*a^11*b^4*c^4*d^4 - 3670016*a^12*b^3*c^3*d^5 + 1835008*a^13*b^2*c^2*d^6 - 524288*a^14*b*c*d^7))^(1/4)*(((28*a^4*b^6*d^11 + (81*b^10*c^4*d^7)/16 - (675*a*b^9*c^3*d^8)/16 - (2145*a^3*b^7*c*d^10)/16 + (1971*a^2*b^8*c^2*d^9)/16)*1i)/(a^7*d^3 - a^4*b^3*c^3 + 3*a^5*b^2*c^2*d - 3*a^6*b*c*d^2) + (-(81*b^7*c^4 + 2401*a^4*b^3*d^4 - 4116*a^3*b^4*c*d^3 + 2646*a^2*b^5*c^2*d^2 - 756*a*b^6*c^3*d)/(65536*a^15*d^8 + 65536*a^7*b^8*c^8 - 524288*a^8*b^7*c^7*d + 1835008*a^9*b^6*c^6*d^2 - 3670016*a^10*b^5*c^5*d^3 + 4587520*a^11*b^4*c^4*d^4 - 3670016*a^12*b^3*c^3*d^5 + 1835008*a^13*b^2*c^2*d^6 - 524288*a^14*b*c*d^7))^(3/4)*(((-(81*b^7*c^4 + 2401*a^4*b^3*d^4 - 4116*a^3*b^4*c*d^3 + 2646*a^2*b^5*c^2*d^2 - 756*a*b^6*c^3*d)/(65536*a^15*d^8 + 65536*a^7*b^8*c^8 - 524288*a^8*b^7*c^7*d + 1835008*a^9*b^6*c^6*d^2 - 3670016*a^10*b^5*c^5*d^3 + 4587520*a^11*b^4*c^4*d^4 - 3670016*a^12*b^3*c^3*d^5 + 1835008*a^13*b^2*c^2*d^6 - 524288*a^14*b*c*d^7))^(1/4)*(3072*a^4*b^14*c^11*d^4 - 4096*a^14*b^4*c*d^14 - 28672*a^5*b^13*c^10*d^5 + 114688*a^6*b^12*c^9*d^6 - 253952*a^7*b^11*c^8*d^7 + 329728*a^8*b^10*c^7*d^8 - 229376*a^9*b^9*c^6*d^9 + 28672*a^10*b^8*c^5*d^10 + 90112*a^11*b^7*c^4*d^11 - 78848*a^12*b^6*c^3*d^12 + 28672*a^13*b^5*c^2*d^13))/(a^7*d^3 - a^4*b^3*c^3 + 3*a^5*b^2*c^2*d - 3*a^6*b*c*d^2) + (x*(65536*a^15*b^4*d^17 - 524288*a^14*b^5*c*d^16 + 36864*a^2*b^17*c^13*d^4 - 466944*a^3*b^16*c^12*d^5 + 2609152*a^4*b^15*c^11*d^6 - 8486912*a^5*b^14*c^10*d^7 + 17833984*a^6*b^13*c^9*d^8 - 25280512*a^7*b^12*c^8*d^9 + 24190976*a^8*b^11*c^7*d^10 - 14516224*a^9*b^10*c^6*d^11 + 3362816*a^10*b^9*c^5*d^12 + 2809856*a^11*b^8*c^4*d^13 - 3469312*a^12*b^7*c^3*d^14 + 1835008*a^13*b^6*c^2*d^15)*1i)/(64*(a^10*d^6 + a^4*b^6*c^6 - 6*a^5*b^5*c^5*d + 15*a^6*b^4*c^4*d^2 - 20*a^7*b^3*c^3*d^3 + 15*a^8*b^2*c^2*d^4 - 6*a^9*b*c*d^5)))*1i)*1i - (x*(3185*a^4*b^7*d^13 + 81*b^11*c^4*d^9 - 756*a*b^10*c^3*d^10 - 4788*a^3*b^8*c*d^12 + 2790*a^2*b^9*c^2*d^11)*1i)/(64*(a^10*d^6 + a^4*b^6*c^6 - 6*a^5*b^5*c^5*d + 15*a^6*b^4*c^4*d^2 - 20*a^7*b^3*c^3*d^3 + 15*a^8*b^2*c^2*d^4 - 6*a^9*b*c*d^5)))*(-(81*b^7*c^4 + 2401*a^4*b^3*d^4 - 4116*a^3*b^4*c*d^3 + 2646*a^2*b^5*c^2*d^2 - 756*a*b^6*c^3*d)/(65536*a^15*d^8 + 65536*a^7*b^8*c^8 - 524288*a^8*b^7*c^7*d + 1835008*a^9*b^6*c^6*d^2 - 3670016*a^10*b^5*c^5*d^3 + 4587520*a^11*b^4*c^4*d^4 - 3670016*a^12*b^3*c^3*d^5 + 1835008*a^13*b^2*c^2*d^6 - 524288*a^14*b*c*d^7))^(1/4)))*(-(81*b^7*c^4 + 2401*a^4*b^3*d^4 - 4116*a^3*b^4*c*d^3 + 2646*a^2*b^5*c^2*d^2 - 756*a*b^6*c^3*d)/(65536*a^15*d^8 + 65536*a^7*b^8*c^8 - 524288*a^8*b^7*c^7*d + 1835008*a^9*b^6*c^6*d^2 - 3670016*a^10*b^5*c^5*d^3 + 4587520*a^11*b^4*c^4*d^4 - 3670016*a^12*b^3*c^3*d^5 + 1835008*a^13*b^2*c^2*d^6 - 524288*a^14*b*c*d^7))^(1/4) - atan((((-(81*b^7*c^4 + 2401*a^4*b^3*d^4 - 4116*a^3*b^4*c*d^3 + 2646*a^2*b^5*c^2*d^2 - 756*a*b^6*c^3*d)/(65536*a^15*d^8 + 65536*a^7*b^8*c^8 - 524288*a^8*b^7*c^7*d + 1835008*a^9*b^6*c^6*d^2 - 3670016*a^10*b^5*c^5*d^3 + 4587520*a^11*b^4*c^4*d^4 - 3670016*a^12*b^3*c^3*d^5 + 1835008*a^13*b^2*c^2*d^6 - 524288*a^14*b*c*d^7))^(1/4)*((28*a^4*b^6*d^11 + (81*b^10*c^4*d^7)/16 - (675*a*b^9*c^3*d^8)/16 - (2145*a^3*b^7*c*d^10)/16 + (1971*a^2*b^8*c^2*d^9)/16)/(a^7*d^3 - a^4*b^3*c^3 + 3*a^5*b^2*c^2*d - 3*a^6*b*c*d^2) + (-(81*b^7*c^4 + 2401*a^4*b^3*d^4 - 4116*a^3*b^4*c*d^3 + 2646*a^2*b^5*c^2*d^2 - 756*a*b^6*c^3*d)/(65536*a^15*d^8 + 65536*a^7*b^8*c^8 - 524288*a^8*b^7*c^7*d + 1835008*a^9*b^6*c^6*d^2 - 3670016*a^10*b^5*c^5*d^3 + 4587520*a^11*b^4*c^4*d^4 - 3670016*a^12*b^3*c^3*d^5 + 1835008*a^13*b^2*c^2*d^6 - 524288*a^14*b*c*d^7))^(3/4)*(((-(81*b^7*c^4 + 2401*a^4*b^3*d^4 - 4116*a^3*b^4*c*d^3 + 2646*a^2*b^5*c^2*d^2 - 756*a*b^6*c^3*d)/(65536*a^15*d^8 + 65536*a^7*b^8*c^8 - 524288*a^8*b^7*c^7*d + 1835008*a^9*b^6*c^6*d^2 - 3670016*a^10*b^5*c^5*d^3 + 4587520*a^11*b^4*c^4*d^4 - 3670016*a^12*b^3*c^3*d^5 + 1835008*a^13*b^2*c^2*d^6 - 524288*a^14*b*c*d^7))^(1/4)*(3072*a^4*b^14*c^11*d^4 - 4096*a^14*b^4*c*d^14 - 28672*a^5*b^13*c^10*d^5 + 114688*a^6*b^12*c^9*d^6 - 253952*a^7*b^11*c^8*d^7 + 329728*a^8*b^10*c^7*d^8 - 229376*a^9*b^9*c^6*d^9 + 28672*a^10*b^8*c^5*d^10 + 90112*a^11*b^7*c^4*d^11 - 78848*a^12*b^6*c^3*d^12 + 28672*a^13*b^5*c^2*d^13))/(a^7*d^3 - a^4*b^3*c^3 + 3*a^5*b^2*c^2*d - 3*a^6*b*c*d^2) - (x*(65536*a^15*b^4*d^17 - 524288*a^14*b^5*c*d^16 + 36864*a^2*b^17*c^13*d^4 - 466944*a^3*b^16*c^12*d^5 + 2609152*a^4*b^15*c^11*d^6 - 8486912*a^5*b^14*c^10*d^7 + 17833984*a^6*b^13*c^9*d^8 - 25280512*a^7*b^12*c^8*d^9 + 24190976*a^8*b^11*c^7*d^10 - 14516224*a^9*b^10*c^6*d^11 + 3362816*a^10*b^9*c^5*d^12 + 2809856*a^11*b^8*c^4*d^13 - 3469312*a^12*b^7*c^3*d^14 + 1835008*a^13*b^6*c^2*d^15))/(64*(a^10*d^6 + a^4*b^6*c^6 - 6*a^5*b^5*c^5*d + 15*a^6*b^4*c^4*d^2 - 20*a^7*b^3*c^3*d^3 + 15*a^8*b^2*c^2*d^4 - 6*a^9*b*c*d^5))))*1i - (x*(3185*a^4*b^7*d^13 + 81*b^11*c^4*d^9 - 756*a*b^10*c^3*d^10 - 4788*a^3*b^8*c*d^12 + 2790*a^2*b^9*c^2*d^11)*1i)/(64*(a^10*d^6 + a^4*b^6*c^6 - 6*a^5*b^5*c^5*d + 15*a^6*b^4*c^4*d^2 - 20*a^7*b^3*c^3*d^3 + 15*a^8*b^2*c^2*d^4 - 6*a^9*b*c*d^5)))*(-(81*b^7*c^4 + 2401*a^4*b^3*d^4 - 4116*a^3*b^4*c*d^3 + 2646*a^2*b^5*c^2*d^2 - 756*a*b^6*c^3*d)/(65536*a^15*d^8 + 65536*a^7*b^8*c^8 - 524288*a^8*b^7*c^7*d + 1835008*a^9*b^6*c^6*d^2 - 3670016*a^10*b^5*c^5*d^3 + 4587520*a^11*b^4*c^4*d^4 - 3670016*a^12*b^3*c^3*d^5 + 1835008*a^13*b^2*c^2*d^6 - 524288*a^14*b*c*d^7))^(1/4) - ((-(81*b^7*c^4 + 2401*a^4*b^3*d^4 - 4116*a^3*b^4*c*d^3 + 2646*a^2*b^5*c^2*d^2 - 756*a*b^6*c^3*d)/(65536*a^15*d^8 + 65536*a^7*b^8*c^8 - 524288*a^8*b^7*c^7*d + 1835008*a^9*b^6*c^6*d^2 - 3670016*a^10*b^5*c^5*d^3 + 4587520*a^11*b^4*c^4*d^4 - 3670016*a^12*b^3*c^3*d^5 + 1835008*a^13*b^2*c^2*d^6 - 524288*a^14*b*c*d^7))^(1/4)*((28*a^4*b^6*d^11 + (81*b^10*c^4*d^7)/16 - (675*a*b^9*c^3*d^8)/16 - (2145*a^3*b^7*c*d^10)/16 + (1971*a^2*b^8*c^2*d^9)/16)/(a^7*d^3 - a^4*b^3*c^3 + 3*a^5*b^2*c^2*d - 3*a^6*b*c*d^2) + (-(81*b^7*c^4 + 2401*a^4*b^3*d^4 - 4116*a^3*b^4*c*d^3 + 2646*a^2*b^5*c^2*d^2 - 756*a*b^6*c^3*d)/(65536*a^15*d^8 + 65536*a^7*b^8*c^8 - 524288*a^8*b^7*c^7*d + 1835008*a^9*b^6*c^6*d^2 - 3670016*a^10*b^5*c^5*d^3 + 4587520*a^11*b^4*c^4*d^4 - 3670016*a^12*b^3*c^3*d^5 + 1835008*a^13*b^2*c^2*d^6 - 524288*a^14*b*c*d^7))^(3/4)*(((-(81*b^7*c^4 + 2401*a^4*b^3*d^4 - 4116*a^3*b^4*c*d^3 + 2646*a^2*b^5*c^2*d^2 - 756*a*b^6*c^3*d)/(65536*a^15*d^8 + 65536*a^7*b^8*c^8 - 524288*a^8*b^7*c^7*d + 1835008*a^9*b^6*c^6*d^2 - 3670016*a^10*b^5*c^5*d^3 + 4587520*a^11*b^4*c^4*d^4 - 3670016*a^12*b^3*c^3*d^5 + 1835008*a^13*b^2*c^2*d^6 - 524288*a^14*b*c*d^7))^(1/4)*(3072*a^4*b^14*c^11*d^4 - 4096*a^14*b^4*c*d^14 - 28672*a^5*b^13*c^10*d^5 + 114688*a^6*b^12*c^9*d^6 - 253952*a^7*b^11*c^8*d^7 + 329728*a^8*b^10*c^7*d^8 - 229376*a^9*b^9*c^6*d^9 + 28672*a^10*b^8*c^5*d^10 + 90112*a^11*b^7*c^4*d^11 - 78848*a^12*b^6*c^3*d^12 + 28672*a^13*b^5*c^2*d^13))/(a^7*d^3 - a^4*b^3*c^3 + 3*a^5*b^2*c^2*d - 3*a^6*b*c*d^2) + (x*(65536*a^15*b^4*d^17 - 524288*a^14*b^5*c*d^16 + 36864*a^2*b^17*c^13*d^4 - 466944*a^3*b^16*c^12*d^5 + 2609152*a^4*b^15*c^11*d^6 - 8486912*a^5*b^14*c^10*d^7 + 17833984*a^6*b^13*c^9*d^8 - 25280512*a^7*b^12*c^8*d^9 + 24190976*a^8*b^11*c^7*d^10 - 14516224*a^9*b^10*c^6*d^11 + 3362816*a^10*b^9*c^5*d^12 + 2809856*a^11*b^8*c^4*d^13 - 3469312*a^12*b^7*c^3*d^14 + 1835008*a^13*b^6*c^2*d^15))/(64*(a^10*d^6 + a^4*b^6*c^6 - 6*a^5*b^5*c^5*d + 15*a^6*b^4*c^4*d^2 - 20*a^7*b^3*c^3*d^3 + 15*a^8*b^2*c^2*d^4 - 6*a^9*b*c*d^5))))*1i + (x*(3185*a^4*b^7*d^13 + 81*b^11*c^4*d^9 - 756*a*b^10*c^3*d^10 - 4788*a^3*b^8*c*d^12 + 2790*a^2*b^9*c^2*d^11)*1i)/(64*(a^10*d^6 + a^4*b^6*c^6 - 6*a^5*b^5*c^5*d + 15*a^6*b^4*c^4*d^2 - 20*a^7*b^3*c^3*d^3 + 15*a^8*b^2*c^2*d^4 - 6*a^9*b*c*d^5)))*(-(81*b^7*c^4 + 2401*a^4*b^3*d^4 - 4116*a^3*b^4*c*d^3 + 2646*a^2*b^5*c^2*d^2 - 756*a*b^6*c^3*d)/(65536*a^15*d^8 + 65536*a^7*b^8*c^8 - 524288*a^8*b^7*c^7*d + 1835008*a^9*b^6*c^6*d^2 - 3670016*a^10*b^5*c^5*d^3 + 4587520*a^11*b^4*c^4*d^4 - 3670016*a^12*b^3*c^3*d^5 + 1835008*a^13*b^2*c^2*d^6 - 524288*a^14*b*c*d^7))^(1/4))/(((-(81*b^7*c^4 + 2401*a^4*b^3*d^4 - 4116*a^3*b^4*c*d^3 + 2646*a^2*b^5*c^2*d^2 - 756*a*b^6*c^3*d)/(65536*a^15*d^8 + 65536*a^7*b^8*c^8 - 524288*a^8*b^7*c^7*d + 1835008*a^9*b^6*c^6*d^2 - 3670016*a^10*b^5*c^5*d^3 + 4587520*a^11*b^4*c^4*d^4 - 3670016*a^12*b^3*c^3*d^5 + 1835008*a^13*b^2*c^2*d^6 - 524288*a^14*b*c*d^7))^(1/4)*((28*a^4*b^6*d^11 + (81*b^10*c^4*d^7)/16 - (675*a*b^9*c^3*d^8)/16 - (2145*a^3*b^7*c*d^10)/16 + (1971*a^2*b^8*c^2*d^9)/16)/(a^7*d^3 - a^4*b^3*c^3 + 3*a^5*b^2*c^2*d - 3*a^6*b*c*d^2) + (-(81*b^7*c^4 + 2401*a^4*b^3*d^4 - 4116*a^3*b^4*c*d^3 + 2646*a^2*b^5*c^2*d^2 - 756*a*b^6*c^3*d)/(65536*a^15*d^8 + 65536*a^7*b^8*c^8 - 524288*a^8*b^7*c^7*d + 1835008*a^9*b^6*c^6*d^2 - 3670016*a^10*b^5*c^5*d^3 + 4587520*a^11*b^4*c^4*d^4 - 3670016*a^12*b^3*c^3*d^5 + 1835008*a^13*b^2*c^2*d^6 - 524288*a^14*b*c*d^7))^(3/4)*(((-(81*b^7*c^4 + 2401*a^4*b^3*d^4 - 4116*a^3*b^4*c*d^3 + 2646*a^2*b^5*c^2*d^2 - 756*a*b^6*c^3*d)/(65536*a^15*d^8 + 65536*a^7*b^8*c^8 - 524288*a^8*b^7*c^7*d + 1835008*a^9*b^6*c^6*d^2 - 3670016*a^10*b^5*c^5*d^3 + 4587520*a^11*b^4*c^4*d^4 - 3670016*a^12*b^3*c^3*d^5 + 1835008*a^13*b^2*c^2*d^6 - 524288*a^14*b*c*d^7))^(1/4)*(3072*a^4*b^14*c^11*d^4 - 4096*a^14*b^4*c*d^14 - 28672*a^5*b^13*c^10*d^5 + 114688*a^6*b^12*c^9*d^6 - 253952*a^7*b^11*c^8*d^7 + 329728*a^8*b^10*c^7*d^8 - 229376*a^9*b^9*c^6*d^9 + 28672*a^10*b^8*c^5*d^10 + 90112*a^11*b^7*c^4*d^11 - 78848*a^12*b^6*c^3*d^12 + 28672*a^13*b^5*c^2*d^13))/(a^7*d^3 - a^4*b^3*c^3 + 3*a^5*b^2*c^2*d - 3*a^6*b*c*d^2) - (x*(65536*a^15*b^4*d^17 - 524288*a^14*b^5*c*d^16 + 36864*a^2*b^17*c^13*d^4 - 466944*a^3*b^16*c^12*d^5 + 2609152*a^4*b^15*c^11*d^6 - 8486912*a^5*b^14*c^10*d^7 + 17833984*a^6*b^13*c^9*d^8 - 25280512*a^7*b^12*c^8*d^9 + 24190976*a^8*b^11*c^7*d^10 - 14516224*a^9*b^10*c^6*d^11 + 3362816*a^10*b^9*c^5*d^12 + 2809856*a^11*b^8*c^4*d^13 - 3469312*a^12*b^7*c^3*d^14 + 1835008*a^13*b^6*c^2*d^15))/(64*(a^10*d^6 + a^4*b^6*c^6 - 6*a^5*b^5*c^5*d + 15*a^6*b^4*c^4*d^2 - 20*a^7*b^3*c^3*d^3 + 15*a^8*b^2*c^2*d^4 - 6*a^9*b*c*d^5)))) - (x*(3185*a^4*b^7*d^13 + 81*b^11*c^4*d^9 - 756*a*b^10*c^3*d^10 - 4788*a^3*b^8*c*d^12 + 2790*a^2*b^9*c^2*d^11))/(64*(a^10*d^6 + a^4*b^6*c^6 - 6*a^5*b^5*c^5*d + 15*a^6*b^4*c^4*d^2 - 20*a^7*b^3*c^3*d^3 + 15*a^8*b^2*c^2*d^4 - 6*a^9*b*c*d^5)))*(-(81*b^7*c^4 + 2401*a^4*b^3*d^4 - 4116*a^3*b^4*c*d^3 + 2646*a^2*b^5*c^2*d^2 - 756*a*b^6*c^3*d)/(65536*a^15*d^8 + 65536*a^7*b^8*c^8 - 524288*a^8*b^7*c^7*d + 1835008*a^9*b^6*c^6*d^2 - 3670016*a^10*b^5*c^5*d^3 + 4587520*a^11*b^4*c^4*d^4 - 3670016*a^12*b^3*c^3*d^5 + 1835008*a^13*b^2*c^2*d^6 - 524288*a^14*b*c*d^7))^(1/4) + ((-(81*b^7*c^4 + 2401*a^4*b^3*d^4 - 4116*a^3*b^4*c*d^3 + 2646*a^2*b^5*c^2*d^2 - 756*a*b^6*c^3*d)/(65536*a^15*d^8 + 65536*a^7*b^8*c^8 - 524288*a^8*b^7*c^7*d + 1835008*a^9*b^6*c^6*d^2 - 3670016*a^10*b^5*c^5*d^3 + 4587520*a^11*b^4*c^4*d^4 - 3670016*a^12*b^3*c^3*d^5 + 1835008*a^13*b^2*c^2*d^6 - 524288*a^14*b*c*d^7))^(1/4)*((28*a^4*b^6*d^11 + (81*b^10*c^4*d^7)/16 - (675*a*b^9*c^3*d^8)/16 - (2145*a^3*b^7*c*d^10)/16 + (1971*a^2*b^8*c^2*d^9)/16)/(a^7*d^3 - a^4*b^3*c^3 + 3*a^5*b^2*c^2*d - 3*a^6*b*c*d^2) + (-(81*b^7*c^4 + 2401*a^4*b^3*d^4 - 4116*a^3*b^4*c*d^3 + 2646*a^2*b^5*c^2*d^2 - 756*a*b^6*c^3*d)/(65536*a^15*d^8 + 65536*a^7*b^8*c^8 - 524288*a^8*b^7*c^7*d + 1835008*a^9*b^6*c^6*d^2 - 3670016*a^10*b^5*c^5*d^3 + 4587520*a^11*b^4*c^4*d^4 - 3670016*a^12*b^3*c^3*d^5 + 1835008*a^13*b^2*c^2*d^6 - 524288*a^14*b*c*d^7))^(3/4)*(((-(81*b^7*c^4 + 2401*a^4*b^3*d^4 - 4116*a^3*b^4*c*d^3 + 2646*a^2*b^5*c^2*d^2 - 756*a*b^6*c^3*d)/(65536*a^15*d^8 + 65536*a^7*b^8*c^8 - 524288*a^8*b^7*c^7*d + 1835008*a^9*b^6*c^6*d^2 - 3670016*a^10*b^5*c^5*d^3 + 4587520*a^11*b^4*c^4*d^4 - 3670016*a^12*b^3*c^3*d^5 + 1835008*a^13*b^2*c^2*d^6 - 524288*a^14*b*c*d^7))^(1/4)*(3072*a^4*b^14*c^11*d^4 - 4096*a^14*b^4*c*d^14 - 28672*a^5*b^13*c^10*d^5 + 114688*a^6*b^12*c^9*d^6 - 253952*a^7*b^11*c^8*d^7 + 329728*a^8*b^10*c^7*d^8 - 229376*a^9*b^9*c^6*d^9 + 28672*a^10*b^8*c^5*d^10 + 90112*a^11*b^7*c^4*d^11 - 78848*a^12*b^6*c^3*d^12 + 28672*a^13*b^5*c^2*d^13))/(a^7*d^3 - a^4*b^3*c^3 + 3*a^5*b^2*c^2*d - 3*a^6*b*c*d^2) + (x*(65536*a^15*b^4*d^17 - 524288*a^14*b^5*c*d^16 + 36864*a^2*b^17*c^13*d^4 - 466944*a^3*b^16*c^12*d^5 + 2609152*a^4*b^15*c^11*d^6 - 8486912*a^5*b^14*c^10*d^7 + 17833984*a^6*b^13*c^9*d^8 - 25280512*a^7*b^12*c^8*d^9 + 24190976*a^8*b^11*c^7*d^10 - 14516224*a^9*b^10*c^6*d^11 + 3362816*a^10*b^9*c^5*d^12 + 2809856*a^11*b^8*c^4*d^13 - 3469312*a^12*b^7*c^3*d^14 + 1835008*a^13*b^6*c^2*d^15))/(64*(a^10*d^6 + a^4*b^6*c^6 - 6*a^5*b^5*c^5*d + 15*a^6*b^4*c^4*d^2 - 20*a^7*b^3*c^3*d^3 + 15*a^8*b^2*c^2*d^4 - 6*a^9*b*c*d^5)))) + (x*(3185*a^4*b^7*d^13 + 81*b^11*c^4*d^9 - 756*a*b^10*c^3*d^10 - 4788*a^3*b^8*c*d^12 + 2790*a^2*b^9*c^2*d^11))/(64*(a^10*d^6 + a^4*b^6*c^6 - 6*a^5*b^5*c^5*d + 15*a^6*b^4*c^4*d^2 - 20*a^7*b^3*c^3*d^3 + 15*a^8*b^2*c^2*d^4 - 6*a^9*b*c*d^5)))*(-(81*b^7*c^4 + 2401*a^4*b^3*d^4 - 4116*a^3*b^4*c*d^3 + 2646*a^2*b^5*c^2*d^2 - 756*a*b^6*c^3*d)/(65536*a^15*d^8 + 65536*a^7*b^8*c^8 - 524288*a^8*b^7*c^7*d + 1835008*a^9*b^6*c^6*d^2 - 3670016*a^10*b^5*c^5*d^3 + 4587520*a^11*b^4*c^4*d^4 - 3670016*a^12*b^3*c^3*d^5 + 1835008*a^13*b^2*c^2*d^6 - 524288*a^14*b*c*d^7))^(1/4)))*(-(81*b^7*c^4 + 2401*a^4*b^3*d^4 - 4116*a^3*b^4*c*d^3 + 2646*a^2*b^5*c^2*d^2 - 756*a*b^6*c^3*d)/(65536*a^15*d^8 + 65536*a^7*b^8*c^8 - 524288*a^8*b^7*c^7*d + 1835008*a^9*b^6*c^6*d^2 - 3670016*a^10*b^5*c^5*d^3 + 4587520*a^11*b^4*c^4*d^4 - 3670016*a^12*b^3*c^3*d^5 + 1835008*a^13*b^2*c^2*d^6 - 524288*a^14*b*c*d^7))^(1/4)*2i - atan(((-d^7/(256*b^8*c^11 + 256*a^8*c^3*d^8 - 2048*a^7*b*c^4*d^7 + 7168*a^2*b^6*c^9*d^2 - 14336*a^3*b^5*c^8*d^3 + 17920*a^4*b^4*c^7*d^4 - 14336*a^5*b^3*c^6*d^5 + 7168*a^6*b^2*c^5*d^6 - 2048*a*b^7*c^10*d))^(1/4)*((-d^7/(256*b^8*c^11 + 256*a^8*c^3*d^8 - 2048*a^7*b*c^4*d^7 + 7168*a^2*b^6*c^9*d^2 - 14336*a^3*b^5*c^8*d^3 + 17920*a^4*b^4*c^7*d^4 - 14336*a^5*b^3*c^6*d^5 + 7168*a^6*b^2*c^5*d^6 - 2048*a*b^7*c^10*d))^(1/4)*((-d^7/(256*b^8*c^11 + 256*a^8*c^3*d^8 - 2048*a^7*b*c^4*d^7 + 7168*a^2*b^6*c^9*d^2 - 14336*a^3*b^5*c^8*d^3 + 17920*a^4*b^4*c^7*d^4 - 14336*a^5*b^3*c^6*d^5 + 7168*a^6*b^2*c^5*d^6 - 2048*a*b^7*c^10*d))^(3/4)*(((-d^7/(256*b^8*c^11 + 256*a^8*c^3*d^8 - 2048*a^7*b*c^4*d^7 + 7168*a^2*b^6*c^9*d^2 - 14336*a^3*b^5*c^8*d^3 + 17920*a^4*b^4*c^7*d^4 - 14336*a^5*b^3*c^6*d^5 + 7168*a^6*b^2*c^5*d^6 - 2048*a*b^7*c^10*d))^(1/4)*(3072*a^4*b^14*c^11*d^4 - 4096*a^14*b^4*c*d^14 - 28672*a^5*b^13*c^10*d^5 + 114688*a^6*b^12*c^9*d^6 - 253952*a^7*b^11*c^8*d^7 + 329728*a^8*b^10*c^7*d^8 - 229376*a^9*b^9*c^6*d^9 + 28672*a^10*b^8*c^5*d^10 + 90112*a^11*b^7*c^4*d^11 - 78848*a^12*b^6*c^3*d^12 + 28672*a^13*b^5*c^2*d^13))/(a^7*d^3 - a^4*b^3*c^3 + 3*a^5*b^2*c^2*d - 3*a^6*b*c*d^2) - (x*(65536*a^15*b^4*d^17 - 524288*a^14*b^5*c*d^16 + 36864*a^2*b^17*c^13*d^4 - 466944*a^3*b^16*c^12*d^5 + 2609152*a^4*b^15*c^11*d^6 - 8486912*a^5*b^14*c^10*d^7 + 17833984*a^6*b^13*c^9*d^8 - 25280512*a^7*b^12*c^8*d^9 + 24190976*a^8*b^11*c^7*d^10 - 14516224*a^9*b^10*c^6*d^11 + 3362816*a^10*b^9*c^5*d^12 + 2809856*a^11*b^8*c^4*d^13 - 3469312*a^12*b^7*c^3*d^14 + 1835008*a^13*b^6*c^2*d^15))/(64*(a^10*d^6 + a^4*b^6*c^6 - 6*a^5*b^5*c^5*d + 15*a^6*b^4*c^4*d^2 - 20*a^7*b^3*c^3*d^3 + 15*a^8*b^2*c^2*d^4 - 6*a^9*b*c*d^5))) + (28*a^4*b^6*d^11 + (81*b^10*c^4*d^7)/16 - (675*a*b^9*c^3*d^8)/16 - (2145*a^3*b^7*c*d^10)/16 + (1971*a^2*b^8*c^2*d^9)/16)/(a^7*d^3 - a^4*b^3*c^3 + 3*a^5*b^2*c^2*d - 3*a^6*b*c*d^2))*1i - (x*(3185*a^4*b^7*d^13 + 81*b^11*c^4*d^9 - 756*a*b^10*c^3*d^10 - 4788*a^3*b^8*c*d^12 + 2790*a^2*b^9*c^2*d^11)*1i)/(64*(a^10*d^6 + a^4*b^6*c^6 - 6*a^5*b^5*c^5*d + 15*a^6*b^4*c^4*d^2 - 20*a^7*b^3*c^3*d^3 + 15*a^8*b^2*c^2*d^4 - 6*a^9*b*c*d^5))) - (-d^7/(256*b^8*c^11 + 256*a^8*c^3*d^8 - 2048*a^7*b*c^4*d^7 + 7168*a^2*b^6*c^9*d^2 - 14336*a^3*b^5*c^8*d^3 + 17920*a^4*b^4*c^7*d^4 - 14336*a^5*b^3*c^6*d^5 + 7168*a^6*b^2*c^5*d^6 - 2048*a*b^7*c^10*d))^(1/4)*((-d^7/(256*b^8*c^11 + 256*a^8*c^3*d^8 - 2048*a^7*b*c^4*d^7 + 7168*a^2*b^6*c^9*d^2 - 14336*a^3*b^5*c^8*d^3 + 17920*a^4*b^4*c^7*d^4 - 14336*a^5*b^3*c^6*d^5 + 7168*a^6*b^2*c^5*d^6 - 2048*a*b^7*c^10*d))^(1/4)*((-d^7/(256*b^8*c^11 + 256*a^8*c^3*d^8 - 2048*a^7*b*c^4*d^7 + 7168*a^2*b^6*c^9*d^2 - 14336*a^3*b^5*c^8*d^3 + 17920*a^4*b^4*c^7*d^4 - 14336*a^5*b^3*c^6*d^5 + 7168*a^6*b^2*c^5*d^6 - 2048*a*b^7*c^10*d))^(3/4)*(((-d^7/(256*b^8*c^11 + 256*a^8*c^3*d^8 - 2048*a^7*b*c^4*d^7 + 7168*a^2*b^6*c^9*d^2 - 14336*a^3*b^5*c^8*d^3 + 17920*a^4*b^4*c^7*d^4 - 14336*a^5*b^3*c^6*d^5 + 7168*a^6*b^2*c^5*d^6 - 2048*a*b^7*c^10*d))^(1/4)*(3072*a^4*b^14*c^11*d^4 - 4096*a^14*b^4*c*d^14 - 28672*a^5*b^13*c^10*d^5 + 114688*a^6*b^12*c^9*d^6 - 253952*a^7*b^11*c^8*d^7 + 329728*a^8*b^10*c^7*d^8 - 229376*a^9*b^9*c^6*d^9 + 28672*a^10*b^8*c^5*d^10 + 90112*a^11*b^7*c^4*d^11 - 78848*a^12*b^6*c^3*d^12 + 28672*a^13*b^5*c^2*d^13))/(a^7*d^3 - a^4*b^3*c^3 + 3*a^5*b^2*c^2*d - 3*a^6*b*c*d^2) + (x*(65536*a^15*b^4*d^17 - 524288*a^14*b^5*c*d^16 + 36864*a^2*b^17*c^13*d^4 - 466944*a^3*b^16*c^12*d^5 + 2609152*a^4*b^15*c^11*d^6 - 8486912*a^5*b^14*c^10*d^7 + 17833984*a^6*b^13*c^9*d^8 - 25280512*a^7*b^12*c^8*d^9 + 24190976*a^8*b^11*c^7*d^10 - 14516224*a^9*b^10*c^6*d^11 + 3362816*a^10*b^9*c^5*d^12 + 2809856*a^11*b^8*c^4*d^13 - 3469312*a^12*b^7*c^3*d^14 + 1835008*a^13*b^6*c^2*d^15))/(64*(a^10*d^6 + a^4*b^6*c^6 - 6*a^5*b^5*c^5*d + 15*a^6*b^4*c^4*d^2 - 20*a^7*b^3*c^3*d^3 + 15*a^8*b^2*c^2*d^4 - 6*a^9*b*c*d^5))) + (28*a^4*b^6*d^11 + (81*b^10*c^4*d^7)/16 - (675*a*b^9*c^3*d^8)/16 - (2145*a^3*b^7*c*d^10)/16 + (1971*a^2*b^8*c^2*d^9)/16)/(a^7*d^3 - a^4*b^3*c^3 + 3*a^5*b^2*c^2*d - 3*a^6*b*c*d^2))*1i + (x*(3185*a^4*b^7*d^13 + 81*b^11*c^4*d^9 - 756*a*b^10*c^3*d^10 - 4788*a^3*b^8*c*d^12 + 2790*a^2*b^9*c^2*d^11)*1i)/(64*(a^10*d^6 + a^4*b^6*c^6 - 6*a^5*b^5*c^5*d + 15*a^6*b^4*c^4*d^2 - 20*a^7*b^3*c^3*d^3 + 15*a^8*b^2*c^2*d^4 - 6*a^9*b*c*d^5))))/((-d^7/(256*b^8*c^11 + 256*a^8*c^3*d^8 - 2048*a^7*b*c^4*d^7 + 7168*a^2*b^6*c^9*d^2 - 14336*a^3*b^5*c^8*d^3 + 17920*a^4*b^4*c^7*d^4 - 14336*a^5*b^3*c^6*d^5 + 7168*a^6*b^2*c^5*d^6 - 2048*a*b^7*c^10*d))^(1/4)*((-d^7/(256*b^8*c^11 + 256*a^8*c^3*d^8 - 2048*a^7*b*c^4*d^7 + 7168*a^2*b^6*c^9*d^2 - 14336*a^3*b^5*c^8*d^3 + 17920*a^4*b^4*c^7*d^4 - 14336*a^5*b^3*c^6*d^5 + 7168*a^6*b^2*c^5*d^6 - 2048*a*b^7*c^10*d))^(1/4)*((-d^7/(256*b^8*c^11 + 256*a^8*c^3*d^8 - 2048*a^7*b*c^4*d^7 + 7168*a^2*b^6*c^9*d^2 - 14336*a^3*b^5*c^8*d^3 + 17920*a^4*b^4*c^7*d^4 - 14336*a^5*b^3*c^6*d^5 + 7168*a^6*b^2*c^5*d^6 - 2048*a*b^7*c^10*d))^(3/4)*(((-d^7/(256*b^8*c^11 + 256*a^8*c^3*d^8 - 2048*a^7*b*c^4*d^7 + 7168*a^2*b^6*c^9*d^2 - 14336*a^3*b^5*c^8*d^3 + 17920*a^4*b^4*c^7*d^4 - 14336*a^5*b^3*c^6*d^5 + 7168*a^6*b^2*c^5*d^6 - 2048*a*b^7*c^10*d))^(1/4)*(3072*a^4*b^14*c^11*d^4 - 4096*a^14*b^4*c*d^14 - 28672*a^5*b^13*c^10*d^5 + 114688*a^6*b^12*c^9*d^6 - 253952*a^7*b^11*c^8*d^7 + 329728*a^8*b^10*c^7*d^8 - 229376*a^9*b^9*c^6*d^9 + 28672*a^10*b^8*c^5*d^10 + 90112*a^11*b^7*c^4*d^11 - 78848*a^12*b^6*c^3*d^12 + 28672*a^13*b^5*c^2*d^13))/(a^7*d^3 - a^4*b^3*c^3 + 3*a^5*b^2*c^2*d - 3*a^6*b*c*d^2) - (x*(65536*a^15*b^4*d^17 - 524288*a^14*b^5*c*d^16 + 36864*a^2*b^17*c^13*d^4 - 466944*a^3*b^16*c^12*d^5 + 2609152*a^4*b^15*c^11*d^6 - 8486912*a^5*b^14*c^10*d^7 + 17833984*a^6*b^13*c^9*d^8 - 25280512*a^7*b^12*c^8*d^9 + 24190976*a^8*b^11*c^7*d^10 - 14516224*a^9*b^10*c^6*d^11 + 3362816*a^10*b^9*c^5*d^12 + 2809856*a^11*b^8*c^4*d^13 - 3469312*a^12*b^7*c^3*d^14 + 1835008*a^13*b^6*c^2*d^15))/(64*(a^10*d^6 + a^4*b^6*c^6 - 6*a^5*b^5*c^5*d + 15*a^6*b^4*c^4*d^2 - 20*a^7*b^3*c^3*d^3 + 15*a^8*b^2*c^2*d^4 - 6*a^9*b*c*d^5))) + (28*a^4*b^6*d^11 + (81*b^10*c^4*d^7)/16 - (675*a*b^9*c^3*d^8)/16 - (2145*a^3*b^7*c*d^10)/16 + (1971*a^2*b^8*c^2*d^9)/16)/(a^7*d^3 - a^4*b^3*c^3 + 3*a^5*b^2*c^2*d - 3*a^6*b*c*d^2)) - (x*(3185*a^4*b^7*d^13 + 81*b^11*c^4*d^9 - 756*a*b^10*c^3*d^10 - 4788*a^3*b^8*c*d^12 + 2790*a^2*b^9*c^2*d^11))/(64*(a^10*d^6 + a^4*b^6*c^6 - 6*a^5*b^5*c^5*d + 15*a^6*b^4*c^4*d^2 - 20*a^7*b^3*c^3*d^3 + 15*a^8*b^2*c^2*d^4 - 6*a^9*b*c*d^5))) + (-d^7/(256*b^8*c^11 + 256*a^8*c^3*d^8 - 2048*a^7*b*c^4*d^7 + 7168*a^2*b^6*c^9*d^2 - 14336*a^3*b^5*c^8*d^3 + 17920*a^4*b^4*c^7*d^4 - 14336*a^5*b^3*c^6*d^5 + 7168*a^6*b^2*c^5*d^6 - 2048*a*b^7*c^10*d))^(1/4)*((-d^7/(256*b^8*c^11 + 256*a^8*c^3*d^8 - 2048*a^7*b*c^4*d^7 + 7168*a^2*b^6*c^9*d^2 - 14336*a^3*b^5*c^8*d^3 + 17920*a^4*b^4*c^7*d^4 - 14336*a^5*b^3*c^6*d^5 + 7168*a^6*b^2*c^5*d^6 - 2048*a*b^7*c^10*d))^(1/4)*((-d^7/(256*b^8*c^11 + 256*a^8*c^3*d^8 - 2048*a^7*b*c^4*d^7 + 7168*a^2*b^6*c^9*d^2 - 14336*a^3*b^5*c^8*d^3 + 17920*a^4*b^4*c^7*d^4 - 14336*a^5*b^3*c^6*d^5 + 7168*a^6*b^2*c^5*d^6 - 2048*a*b^7*c^10*d))^(3/4)*(((-d^7/(256*b^8*c^11 + 256*a^8*c^3*d^8 - 2048*a^7*b*c^4*d^7 + 7168*a^2*b^6*c^9*d^2 - 14336*a^3*b^5*c^8*d^3 + 17920*a^4*b^4*c^7*d^4 - 14336*a^5*b^3*c^6*d^5 + 7168*a^6*b^2*c^5*d^6 - 2048*a*b^7*c^10*d))^(1/4)*(3072*a^4*b^14*c^11*d^4 - 4096*a^14*b^4*c*d^14 - 28672*a^5*b^13*c^10*d^5 + 114688*a^6*b^12*c^9*d^6 - 253952*a^7*b^11*c^8*d^7 + 329728*a^8*b^10*c^7*d^8 - 229376*a^9*b^9*c^6*d^9 + 28672*a^10*b^8*c^5*d^10 + 90112*a^11*b^7*c^4*d^11 - 78848*a^12*b^6*c^3*d^12 + 28672*a^13*b^5*c^2*d^13))/(a^7*d^3 - a^4*b^3*c^3 + 3*a^5*b^2*c^2*d - 3*a^6*b*c*d^2) + (x*(65536*a^15*b^4*d^17 - 524288*a^14*b^5*c*d^16 + 36864*a^2*b^17*c^13*d^4 - 466944*a^3*b^16*c^12*d^5 + 2609152*a^4*b^15*c^11*d^6 - 8486912*a^5*b^14*c^10*d^7 + 17833984*a^6*b^13*c^9*d^8 - 25280512*a^7*b^12*c^8*d^9 + 24190976*a^8*b^11*c^7*d^10 - 14516224*a^9*b^10*c^6*d^11 + 3362816*a^10*b^9*c^5*d^12 + 2809856*a^11*b^8*c^4*d^13 - 3469312*a^12*b^7*c^3*d^14 + 1835008*a^13*b^6*c^2*d^15))/(64*(a^10*d^6 + a^4*b^6*c^6 - 6*a^5*b^5*c^5*d + 15*a^6*b^4*c^4*d^2 - 20*a^7*b^3*c^3*d^3 + 15*a^8*b^2*c^2*d^4 - 6*a^9*b*c*d^5))) + (28*a^4*b^6*d^11 + (81*b^10*c^4*d^7)/16 - (675*a*b^9*c^3*d^8)/16 - (2145*a^3*b^7*c*d^10)/16 + (1971*a^2*b^8*c^2*d^9)/16)/(a^7*d^3 - a^4*b^3*c^3 + 3*a^5*b^2*c^2*d - 3*a^6*b*c*d^2)) + (x*(3185*a^4*b^7*d^13 + 81*b^11*c^4*d^9 - 756*a*b^10*c^3*d^10 - 4788*a^3*b^8*c*d^12 + 2790*a^2*b^9*c^2*d^11))/(64*(a^10*d^6 + a^4*b^6*c^6 - 6*a^5*b^5*c^5*d + 15*a^6*b^4*c^4*d^2 - 20*a^7*b^3*c^3*d^3 + 15*a^8*b^2*c^2*d^4 - 6*a^9*b*c*d^5)))))*(-d^7/(256*b^8*c^11 + 256*a^8*c^3*d^8 - 2048*a^7*b*c^4*d^7 + 7168*a^2*b^6*c^9*d^2 - 14336*a^3*b^5*c^8*d^3 + 17920*a^4*b^4*c^7*d^4 - 14336*a^5*b^3*c^6*d^5 + 7168*a^6*b^2*c^5*d^6 - 2048*a*b^7*c^10*d))^(1/4)*2i + 2*atan(((-d^7/(256*b^8*c^11 + 256*a^8*c^3*d^8 - 2048*a^7*b*c^4*d^7 + 7168*a^2*b^6*c^9*d^2 - 14336*a^3*b^5*c^8*d^3 + 17920*a^4*b^4*c^7*d^4 - 14336*a^5*b^3*c^6*d^5 + 7168*a^6*b^2*c^5*d^6 - 2048*a*b^7*c^10*d))^(1/4)*((-d^7/(256*b^8*c^11 + 256*a^8*c^3*d^8 - 2048*a^7*b*c^4*d^7 + 7168*a^2*b^6*c^9*d^2 - 14336*a^3*b^5*c^8*d^3 + 17920*a^4*b^4*c^7*d^4 - 14336*a^5*b^3*c^6*d^5 + 7168*a^6*b^2*c^5*d^6 - 2048*a*b^7*c^10*d))^(1/4)*((-d^7/(256*b^8*c^11 + 256*a^8*c^3*d^8 - 2048*a^7*b*c^4*d^7 + 7168*a^2*b^6*c^9*d^2 - 14336*a^3*b^5*c^8*d^3 + 17920*a^4*b^4*c^7*d^4 - 14336*a^5*b^3*c^6*d^5 + 7168*a^6*b^2*c^5*d^6 - 2048*a*b^7*c^10*d))^(3/4)*(((-d^7/(256*b^8*c^11 + 256*a^8*c^3*d^8 - 2048*a^7*b*c^4*d^7 + 7168*a^2*b^6*c^9*d^2 - 14336*a^3*b^5*c^8*d^3 + 17920*a^4*b^4*c^7*d^4 - 14336*a^5*b^3*c^6*d^5 + 7168*a^6*b^2*c^5*d^6 - 2048*a*b^7*c^10*d))^(1/4)*(3072*a^4*b^14*c^11*d^4 - 4096*a^14*b^4*c*d^14 - 28672*a^5*b^13*c^10*d^5 + 114688*a^6*b^12*c^9*d^6 - 253952*a^7*b^11*c^8*d^7 + 329728*a^8*b^10*c^7*d^8 - 229376*a^9*b^9*c^6*d^9 + 28672*a^10*b^8*c^5*d^10 + 90112*a^11*b^7*c^4*d^11 - 78848*a^12*b^6*c^3*d^12 + 28672*a^13*b^5*c^2*d^13))/(a^7*d^3 - a^4*b^3*c^3 + 3*a^5*b^2*c^2*d - 3*a^6*b*c*d^2) - (x*(65536*a^15*b^4*d^17 - 524288*a^14*b^5*c*d^16 + 36864*a^2*b^17*c^13*d^4 - 466944*a^3*b^16*c^12*d^5 + 2609152*a^4*b^15*c^11*d^6 - 8486912*a^5*b^14*c^10*d^7 + 17833984*a^6*b^13*c^9*d^8 - 25280512*a^7*b^12*c^8*d^9 + 24190976*a^8*b^11*c^7*d^10 - 14516224*a^9*b^10*c^6*d^11 + 3362816*a^10*b^9*c^5*d^12 + 2809856*a^11*b^8*c^4*d^13 - 3469312*a^12*b^7*c^3*d^14 + 1835008*a^13*b^6*c^2*d^15)*1i)/(64*(a^10*d^6 + a^4*b^6*c^6 - 6*a^5*b^5*c^5*d + 15*a^6*b^4*c^4*d^2 - 20*a^7*b^3*c^3*d^3 + 15*a^8*b^2*c^2*d^4 - 6*a^9*b*c*d^5)))*1i + ((28*a^4*b^6*d^11 + (81*b^10*c^4*d^7)/16 - (675*a*b^9*c^3*d^8)/16 - (2145*a^3*b^7*c*d^10)/16 + 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2048*a^7*b*c^4*d^7 + 7168*a^2*b^6*c^9*d^2 - 14336*a^3*b^5*c^8*d^3 + 17920*a^4*b^4*c^7*d^4 - 14336*a^5*b^3*c^6*d^5 + 7168*a^6*b^2*c^5*d^6 - 2048*a*b^7*c^10*d))^(1/4)*(3072*a^4*b^14*c^11*d^4 - 4096*a^14*b^4*c*d^14 - 28672*a^5*b^13*c^10*d^5 + 114688*a^6*b^12*c^9*d^6 - 253952*a^7*b^11*c^8*d^7 + 329728*a^8*b^10*c^7*d^8 - 229376*a^9*b^9*c^6*d^9 + 28672*a^10*b^8*c^5*d^10 + 90112*a^11*b^7*c^4*d^11 - 78848*a^12*b^6*c^3*d^12 + 28672*a^13*b^5*c^2*d^13))/(a^7*d^3 - a^4*b^3*c^3 + 3*a^5*b^2*c^2*d - 3*a^6*b*c*d^2) + (x*(65536*a^15*b^4*d^17 - 524288*a^14*b^5*c*d^16 + 36864*a^2*b^17*c^13*d^4 - 466944*a^3*b^16*c^12*d^5 + 2609152*a^4*b^15*c^11*d^6 - 8486912*a^5*b^14*c^10*d^7 + 17833984*a^6*b^13*c^9*d^8 - 25280512*a^7*b^12*c^8*d^9 + 24190976*a^8*b^11*c^7*d^10 - 14516224*a^9*b^10*c^6*d^11 + 3362816*a^10*b^9*c^5*d^12 + 2809856*a^11*b^8*c^4*d^13 - 3469312*a^12*b^7*c^3*d^14 + 1835008*a^13*b^6*c^2*d^15)*1i)/(64*(a^10*d^6 + a^4*b^6*c^6 - 6*a^5*b^5*c^5*d + 15*a^6*b^4*c^4*d^2 - 20*a^7*b^3*c^3*d^3 + 15*a^8*b^2*c^2*d^4 - 6*a^9*b*c*d^5)))*1i + ((28*a^4*b^6*d^11 + (81*b^10*c^4*d^7)/16 - (675*a*b^9*c^3*d^8)/16 - (2145*a^3*b^7*c*d^10)/16 + (1971*a^2*b^8*c^2*d^9)/16)*1i)/(a^7*d^3 - a^4*b^3*c^3 + 3*a^5*b^2*c^2*d - 3*a^6*b*c*d^2)) - (x*(3185*a^4*b^7*d^13 + 81*b^11*c^4*d^9 - 756*a*b^10*c^3*d^10 - 4788*a^3*b^8*c*d^12 + 2790*a^2*b^9*c^2*d^11))/(64*(a^10*d^6 + a^4*b^6*c^6 - 6*a^5*b^5*c^5*d + 15*a^6*b^4*c^4*d^2 - 20*a^7*b^3*c^3*d^3 + 15*a^8*b^2*c^2*d^4 - 6*a^9*b*c*d^5))))/((-d^7/(256*b^8*c^11 + 256*a^8*c^3*d^8 - 2048*a^7*b*c^4*d^7 + 7168*a^2*b^6*c^9*d^2 - 14336*a^3*b^5*c^8*d^3 + 17920*a^4*b^4*c^7*d^4 - 14336*a^5*b^3*c^6*d^5 + 7168*a^6*b^2*c^5*d^6 - 2048*a*b^7*c^10*d))^(1/4)*((-d^7/(256*b^8*c^11 + 256*a^8*c^3*d^8 - 2048*a^7*b*c^4*d^7 + 7168*a^2*b^6*c^9*d^2 - 14336*a^3*b^5*c^8*d^3 + 17920*a^4*b^4*c^7*d^4 - 14336*a^5*b^3*c^6*d^5 + 7168*a^6*b^2*c^5*d^6 - 2048*a*b^7*c^10*d))^(1/4)*((-d^7/(256*b^8*c^11 + 256*a^8*c^3*d^8 - 2048*a^7*b*c^4*d^7 + 7168*a^2*b^6*c^9*d^2 - 14336*a^3*b^5*c^8*d^3 + 17920*a^4*b^4*c^7*d^4 - 14336*a^5*b^3*c^6*d^5 + 7168*a^6*b^2*c^5*d^6 - 2048*a*b^7*c^10*d))^(3/4)*(((-d^7/(256*b^8*c^11 + 256*a^8*c^3*d^8 - 2048*a^7*b*c^4*d^7 + 7168*a^2*b^6*c^9*d^2 - 14336*a^3*b^5*c^8*d^3 + 17920*a^4*b^4*c^7*d^4 - 14336*a^5*b^3*c^6*d^5 + 7168*a^6*b^2*c^5*d^6 - 2048*a*b^7*c^10*d))^(1/4)*(3072*a^4*b^14*c^11*d^4 - 4096*a^14*b^4*c*d^14 - 28672*a^5*b^13*c^10*d^5 + 114688*a^6*b^12*c^9*d^6 - 253952*a^7*b^11*c^8*d^7 + 329728*a^8*b^10*c^7*d^8 - 229376*a^9*b^9*c^6*d^9 + 28672*a^10*b^8*c^5*d^10 + 90112*a^11*b^7*c^4*d^11 - 78848*a^12*b^6*c^3*d^12 + 28672*a^13*b^5*c^2*d^13))/(a^7*d^3 - a^4*b^3*c^3 + 3*a^5*b^2*c^2*d - 3*a^6*b*c*d^2) - (x*(65536*a^15*b^4*d^17 - 524288*a^14*b^5*c*d^16 + 36864*a^2*b^17*c^13*d^4 - 466944*a^3*b^16*c^12*d^5 + 2609152*a^4*b^15*c^11*d^6 - 8486912*a^5*b^14*c^10*d^7 + 17833984*a^6*b^13*c^9*d^8 - 25280512*a^7*b^12*c^8*d^9 + 24190976*a^8*b^11*c^7*d^10 - 14516224*a^9*b^10*c^6*d^11 + 3362816*a^10*b^9*c^5*d^12 + 2809856*a^11*b^8*c^4*d^13 - 3469312*a^12*b^7*c^3*d^14 + 1835008*a^13*b^6*c^2*d^15)*1i)/(64*(a^10*d^6 + a^4*b^6*c^6 - 6*a^5*b^5*c^5*d + 15*a^6*b^4*c^4*d^2 - 20*a^7*b^3*c^3*d^3 + 15*a^8*b^2*c^2*d^4 - 6*a^9*b*c*d^5)))*1i + ((28*a^4*b^6*d^11 + (81*b^10*c^4*d^7)/16 - (675*a*b^9*c^3*d^8)/16 - (2145*a^3*b^7*c*d^10)/16 + (1971*a^2*b^8*c^2*d^9)/16)*1i)/(a^7*d^3 - a^4*b^3*c^3 + 3*a^5*b^2*c^2*d - 3*a^6*b*c*d^2))*1i + (x*(3185*a^4*b^7*d^13 + 81*b^11*c^4*d^9 - 756*a*b^10*c^3*d^10 - 4788*a^3*b^8*c*d^12 + 2790*a^2*b^9*c^2*d^11)*1i)/(64*(a^10*d^6 + a^4*b^6*c^6 - 6*a^5*b^5*c^5*d + 15*a^6*b^4*c^4*d^2 - 20*a^7*b^3*c^3*d^3 + 15*a^8*b^2*c^2*d^4 - 6*a^9*b*c*d^5))) + (-d^7/(256*b^8*c^11 + 256*a^8*c^3*d^8 - 2048*a^7*b*c^4*d^7 + 7168*a^2*b^6*c^9*d^2 - 14336*a^3*b^5*c^8*d^3 + 17920*a^4*b^4*c^7*d^4 - 14336*a^5*b^3*c^6*d^5 + 7168*a^6*b^2*c^5*d^6 - 2048*a*b^7*c^10*d))^(1/4)*((-d^7/(256*b^8*c^11 + 256*a^8*c^3*d^8 - 2048*a^7*b*c^4*d^7 + 7168*a^2*b^6*c^9*d^2 - 14336*a^3*b^5*c^8*d^3 + 17920*a^4*b^4*c^7*d^4 - 14336*a^5*b^3*c^6*d^5 + 7168*a^6*b^2*c^5*d^6 - 2048*a*b^7*c^10*d))^(1/4)*((-d^7/(256*b^8*c^11 + 256*a^8*c^3*d^8 - 2048*a^7*b*c^4*d^7 + 7168*a^2*b^6*c^9*d^2 - 14336*a^3*b^5*c^8*d^3 + 17920*a^4*b^4*c^7*d^4 - 14336*a^5*b^3*c^6*d^5 + 7168*a^6*b^2*c^5*d^6 - 2048*a*b^7*c^10*d))^(3/4)*(((-d^7/(256*b^8*c^11 + 256*a^8*c^3*d^8 - 2048*a^7*b*c^4*d^7 + 7168*a^2*b^6*c^9*d^2 - 14336*a^3*b^5*c^8*d^3 + 17920*a^4*b^4*c^7*d^4 - 14336*a^5*b^3*c^6*d^5 + 7168*a^6*b^2*c^5*d^6 - 2048*a*b^7*c^10*d))^(1/4)*(3072*a^4*b^14*c^11*d^4 - 4096*a^14*b^4*c*d^14 - 28672*a^5*b^13*c^10*d^5 + 114688*a^6*b^12*c^9*d^6 - 253952*a^7*b^11*c^8*d^7 + 329728*a^8*b^10*c^7*d^8 - 229376*a^9*b^9*c^6*d^9 + 28672*a^10*b^8*c^5*d^10 + 90112*a^11*b^7*c^4*d^11 - 78848*a^12*b^6*c^3*d^12 + 28672*a^13*b^5*c^2*d^13))/(a^7*d^3 - a^4*b^3*c^3 + 3*a^5*b^2*c^2*d - 3*a^6*b*c*d^2) + (x*(65536*a^15*b^4*d^17 - 524288*a^14*b^5*c*d^16 + 36864*a^2*b^17*c^13*d^4 - 466944*a^3*b^16*c^12*d^5 + 2609152*a^4*b^15*c^11*d^6 - 8486912*a^5*b^14*c^10*d^7 + 17833984*a^6*b^13*c^9*d^8 - 25280512*a^7*b^12*c^8*d^9 + 24190976*a^8*b^11*c^7*d^10 - 14516224*a^9*b^10*c^6*d^11 + 3362816*a^10*b^9*c^5*d^12 + 2809856*a^11*b^8*c^4*d^13 - 3469312*a^12*b^7*c^3*d^14 + 1835008*a^13*b^6*c^2*d^15)*1i)/(64*(a^10*d^6 + a^4*b^6*c^6 - 6*a^5*b^5*c^5*d + 15*a^6*b^4*c^4*d^2 - 20*a^7*b^3*c^3*d^3 + 15*a^8*b^2*c^2*d^4 - 6*a^9*b*c*d^5)))*1i + ((28*a^4*b^6*d^11 + (81*b^10*c^4*d^7)/16 - (675*a*b^9*c^3*d^8)/16 - (2145*a^3*b^7*c*d^10)/16 + (1971*a^2*b^8*c^2*d^9)/16)*1i)/(a^7*d^3 - a^4*b^3*c^3 + 3*a^5*b^2*c^2*d - 3*a^6*b*c*d^2))*1i - (x*(3185*a^4*b^7*d^13 + 81*b^11*c^4*d^9 - 756*a*b^10*c^3*d^10 - 4788*a^3*b^8*c*d^12 + 2790*a^2*b^9*c^2*d^11)*1i)/(64*(a^10*d^6 + a^4*b^6*c^6 - 6*a^5*b^5*c^5*d + 15*a^6*b^4*c^4*d^2 - 20*a^7*b^3*c^3*d^3 + 15*a^8*b^2*c^2*d^4 - 6*a^9*b*c*d^5)))))*(-d^7/(256*b^8*c^11 + 256*a^8*c^3*d^8 - 2048*a^7*b*c^4*d^7 + 7168*a^2*b^6*c^9*d^2 - 14336*a^3*b^5*c^8*d^3 + 17920*a^4*b^4*c^7*d^4 - 14336*a^5*b^3*c^6*d^5 + 7168*a^6*b^2*c^5*d^6 - 2048*a*b^7*c^10*d))^(1/4) - (b*x)/(4*a*(a + b*x^4)*(a*d - b*c))","B"
172,1,37266,596,5.616689,"\text{Not used}","int(1/((a + b*x^4)^2*(c + d*x^4)^2),x)","\frac{\frac{x\,\left(a^2\,d^2+b^2\,c^2\right)}{4\,a\,c\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}+\frac{b\,d\,x^5\,\left(a\,d+b\,c\right)}{4\,a\,c\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}}{b\,d\,x^8+\left(a\,d+b\,c\right)\,x^4+a\,c}-\mathrm{atan}\left(\frac{{\left(-\frac{81\,a^4\,d^{11}-1188\,a^3\,b\,c\,d^{10}+6534\,a^2\,b^2\,c^2\,d^9-15972\,a\,b^3\,c^3\,d^8+14641\,b^4\,c^4\,d^7}{65536\,a^{12}\,c^7\,d^{12}-786432\,a^{11}\,b\,c^8\,d^{11}+4325376\,a^{10}\,b^2\,c^9\,d^{10}-14417920\,a^9\,b^3\,c^{10}\,d^9+32440320\,a^8\,b^4\,c^{11}\,d^8-51904512\,a^7\,b^5\,c^{12}\,d^7+60555264\,a^6\,b^6\,c^{13}\,d^6-51904512\,a^5\,b^7\,c^{14}\,d^5+32440320\,a^4\,b^8\,c^{15}\,d^4-14417920\,a^3\,b^9\,c^{16}\,d^3+4325376\,a^2\,b^{10}\,c^{17}\,d^2-786432\,a\,b^{11}\,c^{18}\,d+65536\,b^{12}\,c^{19}}\right)}^{1/4}\,\left({\left(-\frac{81\,a^4\,d^{11}-1188\,a^3\,b\,c\,d^{10}+6534\,a^2\,b^2\,c^2\,d^9-15972\,a\,b^3\,c^3\,d^8+14641\,b^4\,c^4\,d^7}{65536\,a^{12}\,c^7\,d^{12}-786432\,a^{11}\,b\,c^8\,d^{11}+4325376\,a^{10}\,b^2\,c^9\,d^{10}-14417920\,a^9\,b^3\,c^{10}\,d^9+32440320\,a^8\,b^4\,c^{11}\,d^8-51904512\,a^7\,b^5\,c^{12}\,d^7+60555264\,a^6\,b^6\,c^{13}\,d^6-51904512\,a^5\,b^7\,c^{14}\,d^5+32440320\,a^4\,b^8\,c^{15}\,d^4-14417920\,a^3\,b^9\,c^{16}\,d^3+4325376\,a^2\,b^{10}\,c^{17}\,d^2-786432\,a\,b^{11}\,c^{18}\,d+65536\,b^{12}\,c^{19}}\right)}^{1/4}\,\left(\frac{\frac{891\,a^8\,b^7\,d^{15}}{64}-\frac{3105\,a^7\,b^8\,c\,d^{14}}{16}+\frac{31509\,a^6\,b^9\,c^2\,d^{13}}{32}-\frac{33069\,a^5\,b^{10}\,c^3\,d^{12}}{16}+\frac{60307\,a^4\,b^{11}\,c^4\,d^{11}}{32}-\frac{33069\,a^3\,b^{12}\,c^5\,d^{10}}{16}+\frac{31509\,a^2\,b^{13}\,c^6\,d^9}{32}-\frac{3105\,a\,b^{14}\,c^7\,d^8}{16}+\frac{891\,b^{15}\,c^8\,d^7}{64}}{a^{12}\,c^4\,d^8-8\,a^{11}\,b\,c^5\,d^7+28\,a^{10}\,b^2\,c^6\,d^6-56\,a^9\,b^3\,c^7\,d^5+70\,a^8\,b^4\,c^8\,d^4-56\,a^7\,b^5\,c^9\,d^3+28\,a^6\,b^6\,c^{10}\,d^2-8\,a^5\,b^7\,c^{11}\,d+a^4\,b^8\,c^{12}}+{\left(-\frac{81\,a^4\,d^{11}-1188\,a^3\,b\,c\,d^{10}+6534\,a^2\,b^2\,c^2\,d^9-15972\,a\,b^3\,c^3\,d^8+14641\,b^4\,c^4\,d^7}{65536\,a^{12}\,c^7\,d^{12}-786432\,a^{11}\,b\,c^8\,d^{11}+4325376\,a^{10}\,b^2\,c^9\,d^{10}-14417920\,a^9\,b^3\,c^{10}\,d^9+32440320\,a^8\,b^4\,c^{11}\,d^8-51904512\,a^7\,b^5\,c^{12}\,d^7+60555264\,a^6\,b^6\,c^{13}\,d^6-51904512\,a^5\,b^7\,c^{14}\,d^5+32440320\,a^4\,b^8\,c^{15}\,d^4-14417920\,a^3\,b^9\,c^{16}\,d^3+4325376\,a^2\,b^{10}\,c^{17}\,d^2-786432\,a\,b^{11}\,c^{18}\,d+65536\,b^{12}\,c^{19}}\right)}^{3/4}\,\left(\frac{x\,\left(589824\,a^{21}\,b^4\,c^2\,d^{23}-11403264\,a^{20}\,b^5\,c^3\,d^{22}+98762752\,a^{19}\,b^6\,c^4\,d^{21}-510394368\,a^{18}\,b^7\,c^5\,d^{20}+1766916096\,a^{17}\,b^8\,c^6\,d^{19}-4344840192\,a^{16}\,b^9\,c^7\,d^{18}+7796490240\,a^{15}\,b^{10}\,c^8\,d^{17}-10168369152\,a^{14}\,b^{11}\,c^9\,d^{16}+9007726592\,a^{13}\,b^{12}\,c^{10}\,d^{15}-3635478528\,a^{12}\,b^{13}\,c^{11}\,d^{14}-3635478528\,a^{11}\,b^{14}\,c^{12}\,d^{13}+9007726592\,a^{10}\,b^{15}\,c^{13}\,d^{12}-10168369152\,a^9\,b^{16}\,c^{14}\,d^{11}+7796490240\,a^8\,b^{17}\,c^{15}\,d^{10}-4344840192\,a^7\,b^{18}\,c^{16}\,d^9+1766916096\,a^6\,b^{19}\,c^{17}\,d^8-510394368\,a^5\,b^{20}\,c^{18}\,d^7+98762752\,a^4\,b^{21}\,c^{19}\,d^6-11403264\,a^3\,b^{22}\,c^{20}\,d^5+589824\,a^2\,b^{23}\,c^{21}\,d^4\right)}{1024\,\left(a^{16}\,c^4\,d^{12}-12\,a^{15}\,b\,c^5\,d^{11}+66\,a^{14}\,b^2\,c^6\,d^{10}-220\,a^{13}\,b^3\,c^7\,d^9+495\,a^{12}\,b^4\,c^8\,d^8-792\,a^{11}\,b^5\,c^9\,d^7+924\,a^{10}\,b^6\,c^{10}\,d^6-792\,a^9\,b^7\,c^{11}\,d^5+495\,a^8\,b^8\,c^{12}\,d^4-220\,a^7\,b^9\,c^{13}\,d^3+66\,a^6\,b^{10}\,c^{14}\,d^2-12\,a^5\,b^{11}\,c^{15}\,d+a^4\,b^{12}\,c^{16}\right)}+\frac{{\left(-\frac{81\,a^4\,d^{11}-1188\,a^3\,b\,c\,d^{10}+6534\,a^2\,b^2\,c^2\,d^9-15972\,a\,b^3\,c^3\,d^8+14641\,b^4\,c^4\,d^7}{65536\,a^{12}\,c^7\,d^{12}-786432\,a^{11}\,b\,c^8\,d^{11}+4325376\,a^{10}\,b^2\,c^9\,d^{10}-14417920\,a^9\,b^3\,c^{10}\,d^9+32440320\,a^8\,b^4\,c^{11}\,d^8-51904512\,a^7\,b^5\,c^{12}\,d^7+60555264\,a^6\,b^6\,c^{13}\,d^6-51904512\,a^5\,b^7\,c^{14}\,d^5+32440320\,a^4\,b^8\,c^{15}\,d^4-14417920\,a^3\,b^9\,c^{16}\,d^3+4325376\,a^2\,b^{10}\,c^{17}\,d^2-786432\,a\,b^{11}\,c^{18}\,d+65536\,b^{12}\,c^{19}}\right)}^{1/4}\,\left(3072\,a^{19}\,b^4\,c^4\,d^{19}-45056\,a^{18}\,b^5\,c^5\,d^{18}+292864\,a^{17}\,b^6\,c^6\,d^{17}-1115136\,a^{16}\,b^7\,c^7\,d^{16}+2745344\,a^{15}\,b^8\,c^8\,d^{15}-4483072\,a^{14}\,b^9\,c^9\,d^{14}+4595712\,a^{13}\,b^{10}\,c^{10}\,d^{13}-1993728\,a^{12}\,b^{11}\,c^{11}\,d^{12}-1993728\,a^{11}\,b^{12}\,c^{12}\,d^{11}+4595712\,a^{10}\,b^{13}\,c^{13}\,d^{10}-4483072\,a^9\,b^{14}\,c^{14}\,d^9+2745344\,a^8\,b^{15}\,c^{15}\,d^8-1115136\,a^7\,b^{16}\,c^{16}\,d^7+292864\,a^6\,b^{17}\,c^{17}\,d^6-45056\,a^5\,b^{18}\,c^{18}\,d^5+3072\,a^4\,b^{19}\,c^{19}\,d^4\right)}{a^{12}\,c^4\,d^8-8\,a^{11}\,b\,c^5\,d^7+28\,a^{10}\,b^2\,c^6\,d^6-56\,a^9\,b^3\,c^7\,d^5+70\,a^8\,b^4\,c^8\,d^4-56\,a^7\,b^5\,c^9\,d^3+28\,a^6\,b^6\,c^{10}\,d^2-8\,a^5\,b^7\,c^{11}\,d+a^4\,b^8\,c^{12}}\right)\right)\,1{}\mathrm{i}+\frac{x\,\left(9801\,a^8\,b^9\,d^{17}-149094\,a^7\,b^{10}\,c\,d^{16}+1001520\,a^6\,b^{11}\,c^2\,d^{15}-3484602\,a^5\,b^{12}\,c^3\,d^{14}+5769038\,a^4\,b^{13}\,c^4\,d^{13}-3484602\,a^3\,b^{14}\,c^5\,d^{12}+1001520\,a^2\,b^{15}\,c^6\,d^{11}-149094\,a\,b^{16}\,c^7\,d^{10}+9801\,b^{17}\,c^8\,d^9\right)\,1{}\mathrm{i}}{1024\,\left(a^{16}\,c^4\,d^{12}-12\,a^{15}\,b\,c^5\,d^{11}+66\,a^{14}\,b^2\,c^6\,d^{10}-220\,a^{13}\,b^3\,c^7\,d^9+495\,a^{12}\,b^4\,c^8\,d^8-792\,a^{11}\,b^5\,c^9\,d^7+924\,a^{10}\,b^6\,c^{10}\,d^6-792\,a^9\,b^7\,c^{11}\,d^5+495\,a^8\,b^8\,c^{12}\,d^4-220\,a^7\,b^9\,c^{13}\,d^3+66\,a^6\,b^{10}\,c^{14}\,d^2-12\,a^5\,b^{11}\,c^{15}\,d+a^4\,b^{12}\,c^{16}\right)}\right)-{\left(-\frac{81\,a^4\,d^{11}-1188\,a^3\,b\,c\,d^{10}+6534\,a^2\,b^2\,c^2\,d^9-15972\,a\,b^3\,c^3\,d^8+14641\,b^4\,c^4\,d^7}{65536\,a^{12}\,c^7\,d^{12}-786432\,a^{11}\,b\,c^8\,d^{11}+4325376\,a^{10}\,b^2\,c^9\,d^{10}-14417920\,a^9\,b^3\,c^{10}\,d^9+32440320\,a^8\,b^4\,c^{11}\,d^8-51904512\,a^7\,b^5\,c^{12}\,d^7+60555264\,a^6\,b^6\,c^{13}\,d^6-51904512\,a^5\,b^7\,c^{14}\,d^5+32440320\,a^4\,b^8\,c^{15}\,d^4-14417920\,a^3\,b^9\,c^{16}\,d^3+4325376\,a^2\,b^{10}\,c^{17}\,d^2-786432\,a\,b^{11}\,c^{18}\,d+65536\,b^{12}\,c^{19}}\right)}^{1/4}\,\left({\left(-\frac{81\,a^4\,d^{11}-1188\,a^3\,b\,c\,d^{10}+6534\,a^2\,b^2\,c^2\,d^9-15972\,a\,b^3\,c^3\,d^8+14641\,b^4\,c^4\,d^7}{65536\,a^{12}\,c^7\,d^{12}-786432\,a^{11}\,b\,c^8\,d^{11}+4325376\,a^{10}\,b^2\,c^9\,d^{10}-14417920\,a^9\,b^3\,c^{10}\,d^9+32440320\,a^8\,b^4\,c^{11}\,d^8-51904512\,a^7\,b^5\,c^{12}\,d^7+60555264\,a^6\,b^6\,c^{13}\,d^6-51904512\,a^5\,b^7\,c^{14}\,d^5+32440320\,a^4\,b^8\,c^{15}\,d^4-14417920\,a^3\,b^9\,c^{16}\,d^3+4325376\,a^2\,b^{10}\,c^{17}\,d^2-786432\,a\,b^{11}\,c^{18}\,d+65536\,b^{12}\,c^{19}}\right)}^{1/4}\,\left(\frac{\frac{891\,a^8\,b^7\,d^{15}}{64}-\frac{3105\,a^7\,b^8\,c\,d^{14}}{16}+\frac{31509\,a^6\,b^9\,c^2\,d^{13}}{32}-\frac{33069\,a^5\,b^{10}\,c^3\,d^{12}}{16}+\frac{60307\,a^4\,b^{11}\,c^4\,d^{11}}{32}-\frac{33069\,a^3\,b^{12}\,c^5\,d^{10}}{16}+\frac{31509\,a^2\,b^{13}\,c^6\,d^9}{32}-\frac{3105\,a\,b^{14}\,c^7\,d^8}{16}+\frac{891\,b^{15}\,c^8\,d^7}{64}}{a^{12}\,c^4\,d^8-8\,a^{11}\,b\,c^5\,d^7+28\,a^{10}\,b^2\,c^6\,d^6-56\,a^9\,b^3\,c^7\,d^5+70\,a^8\,b^4\,c^8\,d^4-56\,a^7\,b^5\,c^9\,d^3+28\,a^6\,b^6\,c^{10}\,d^2-8\,a^5\,b^7\,c^{11}\,d+a^4\,b^8\,c^{12}}-{\left(-\frac{81\,a^4\,d^{11}-1188\,a^3\,b\,c\,d^{10}+6534\,a^2\,b^2\,c^2\,d^9-15972\,a\,b^3\,c^3\,d^8+14641\,b^4\,c^4\,d^7}{65536\,a^{12}\,c^7\,d^{12}-786432\,a^{11}\,b\,c^8\,d^{11}+4325376\,a^{10}\,b^2\,c^9\,d^{10}-14417920\,a^9\,b^3\,c^{10}\,d^9+32440320\,a^8\,b^4\,c^{11}\,d^8-51904512\,a^7\,b^5\,c^{12}\,d^7+60555264\,a^6\,b^6\,c^{13}\,d^6-51904512\,a^5\,b^7\,c^{14}\,d^5+32440320\,a^4\,b^8\,c^{15}\,d^4-14417920\,a^3\,b^9\,c^{16}\,d^3+4325376\,a^2\,b^{10}\,c^{17}\,d^2-786432\,a\,b^{11}\,c^{18}\,d+65536\,b^{12}\,c^{19}}\right)}^{3/4}\,\left(\frac{x\,\left(589824\,a^{21}\,b^4\,c^2\,d^{23}-11403264\,a^{20}\,b^5\,c^3\,d^{22}+98762752\,a^{19}\,b^6\,c^4\,d^{21}-510394368\,a^{18}\,b^7\,c^5\,d^{20}+1766916096\,a^{17}\,b^8\,c^6\,d^{19}-4344840192\,a^{16}\,b^9\,c^7\,d^{18}+7796490240\,a^{15}\,b^{10}\,c^8\,d^{17}-10168369152\,a^{14}\,b^{11}\,c^9\,d^{16}+9007726592\,a^{13}\,b^{12}\,c^{10}\,d^{15}-3635478528\,a^{12}\,b^{13}\,c^{11}\,d^{14}-3635478528\,a^{11}\,b^{14}\,c^{12}\,d^{13}+9007726592\,a^{10}\,b^{15}\,c^{13}\,d^{12}-10168369152\,a^9\,b^{16}\,c^{14}\,d^{11}+7796490240\,a^8\,b^{17}\,c^{15}\,d^{10}-4344840192\,a^7\,b^{18}\,c^{16}\,d^9+1766916096\,a^6\,b^{19}\,c^{17}\,d^8-510394368\,a^5\,b^{20}\,c^{18}\,d^7+98762752\,a^4\,b^{21}\,c^{19}\,d^6-11403264\,a^3\,b^{22}\,c^{20}\,d^5+589824\,a^2\,b^{23}\,c^{21}\,d^4\right)}{1024\,\left(a^{16}\,c^4\,d^{12}-12\,a^{15}\,b\,c^5\,d^{11}+66\,a^{14}\,b^2\,c^6\,d^{10}-220\,a^{13}\,b^3\,c^7\,d^9+495\,a^{12}\,b^4\,c^8\,d^8-792\,a^{11}\,b^5\,c^9\,d^7+924\,a^{10}\,b^6\,c^{10}\,d^6-792\,a^9\,b^7\,c^{11}\,d^5+495\,a^8\,b^8\,c^{12}\,d^4-220\,a^7\,b^9\,c^{13}\,d^3+66\,a^6\,b^{10}\,c^{14}\,d^2-12\,a^5\,b^{11}\,c^{15}\,d+a^4\,b^{12}\,c^{16}\right)}-\frac{{\left(-\frac{81\,a^4\,d^{11}-1188\,a^3\,b\,c\,d^{10}+6534\,a^2\,b^2\,c^2\,d^9-15972\,a\,b^3\,c^3\,d^8+14641\,b^4\,c^4\,d^7}{65536\,a^{12}\,c^7\,d^{12}-786432\,a^{11}\,b\,c^8\,d^{11}+4325376\,a^{10}\,b^2\,c^9\,d^{10}-14417920\,a^9\,b^3\,c^{10}\,d^9+32440320\,a^8\,b^4\,c^{11}\,d^8-51904512\,a^7\,b^5\,c^{12}\,d^7+60555264\,a^6\,b^6\,c^{13}\,d^6-51904512\,a^5\,b^7\,c^{14}\,d^5+32440320\,a^4\,b^8\,c^{15}\,d^4-14417920\,a^3\,b^9\,c^{16}\,d^3+4325376\,a^2\,b^{10}\,c^{17}\,d^2-786432\,a\,b^{11}\,c^{18}\,d+65536\,b^{12}\,c^{19}}\right)}^{1/4}\,\left(3072\,a^{19}\,b^4\,c^4\,d^{19}-45056\,a^{18}\,b^5\,c^5\,d^{18}+292864\,a^{17}\,b^6\,c^6\,d^{17}-1115136\,a^{16}\,b^7\,c^7\,d^{16}+2745344\,a^{15}\,b^8\,c^8\,d^{15}-4483072\,a^{14}\,b^9\,c^9\,d^{14}+4595712\,a^{13}\,b^{10}\,c^{10}\,d^{13}-1993728\,a^{12}\,b^{11}\,c^{11}\,d^{12}-1993728\,a^{11}\,b^{12}\,c^{12}\,d^{11}+4595712\,a^{10}\,b^{13}\,c^{13}\,d^{10}-4483072\,a^9\,b^{14}\,c^{14}\,d^9+2745344\,a^8\,b^{15}\,c^{15}\,d^8-1115136\,a^7\,b^{16}\,c^{16}\,d^7+292864\,a^6\,b^{17}\,c^{17}\,d^6-45056\,a^5\,b^{18}\,c^{18}\,d^5+3072\,a^4\,b^{19}\,c^{19}\,d^4\right)}{a^{12}\,c^4\,d^8-8\,a^{11}\,b\,c^5\,d^7+28\,a^{10}\,b^2\,c^6\,d^6-56\,a^9\,b^3\,c^7\,d^5+70\,a^8\,b^4\,c^8\,d^4-56\,a^7\,b^5\,c^9\,d^3+28\,a^6\,b^6\,c^{10}\,d^2-8\,a^5\,b^7\,c^{11}\,d+a^4\,b^8\,c^{12}}\right)\right)\,1{}\mathrm{i}-\frac{x\,\left(9801\,a^8\,b^9\,d^{17}-149094\,a^7\,b^{10}\,c\,d^{16}+1001520\,a^6\,b^{11}\,c^2\,d^{15}-3484602\,a^5\,b^{12}\,c^3\,d^{14}+5769038\,a^4\,b^{13}\,c^4\,d^{13}-3484602\,a^3\,b^{14}\,c^5\,d^{12}+1001520\,a^2\,b^{15}\,c^6\,d^{11}-149094\,a\,b^{16}\,c^7\,d^{10}+9801\,b^{17}\,c^8\,d^9\right)\,1{}\mathrm{i}}{1024\,\left(a^{16}\,c^4\,d^{12}-12\,a^{15}\,b\,c^5\,d^{11}+66\,a^{14}\,b^2\,c^6\,d^{10}-220\,a^{13}\,b^3\,c^7\,d^9+495\,a^{12}\,b^4\,c^8\,d^8-792\,a^{11}\,b^5\,c^9\,d^7+924\,a^{10}\,b^6\,c^{10}\,d^6-792\,a^9\,b^7\,c^{11}\,d^5+495\,a^8\,b^8\,c^{12}\,d^4-220\,a^7\,b^9\,c^{13}\,d^3+66\,a^6\,b^{10}\,c^{14}\,d^2-12\,a^5\,b^{11}\,c^{15}\,d+a^4\,b^{12}\,c^{16}\right)}\right)}{{\left(-\frac{81\,a^4\,d^{11}-1188\,a^3\,b\,c\,d^{10}+6534\,a^2\,b^2\,c^2\,d^9-15972\,a\,b^3\,c^3\,d^8+14641\,b^4\,c^4\,d^7}{65536\,a^{12}\,c^7\,d^{12}-786432\,a^{11}\,b\,c^8\,d^{11}+4325376\,a^{10}\,b^2\,c^9\,d^{10}-14417920\,a^9\,b^3\,c^{10}\,d^9+32440320\,a^8\,b^4\,c^{11}\,d^8-51904512\,a^7\,b^5\,c^{12}\,d^7+60555264\,a^6\,b^6\,c^{13}\,d^6-51904512\,a^5\,b^7\,c^{14}\,d^5+32440320\,a^4\,b^8\,c^{15}\,d^4-14417920\,a^3\,b^9\,c^{16}\,d^3+4325376\,a^2\,b^{10}\,c^{17}\,d^2-786432\,a\,b^{11}\,c^{18}\,d+65536\,b^{12}\,c^{19}}\right)}^{1/4}\,\left({\left(-\frac{81\,a^4\,d^{11}-1188\,a^3\,b\,c\,d^{10}+6534\,a^2\,b^2\,c^2\,d^9-15972\,a\,b^3\,c^3\,d^8+14641\,b^4\,c^4\,d^7}{65536\,a^{12}\,c^7\,d^{12}-786432\,a^{11}\,b\,c^8\,d^{11}+4325376\,a^{10}\,b^2\,c^9\,d^{10}-14417920\,a^9\,b^3\,c^{10}\,d^9+32440320\,a^8\,b^4\,c^{11}\,d^8-51904512\,a^7\,b^5\,c^{12}\,d^7+60555264\,a^6\,b^6\,c^{13}\,d^6-51904512\,a^5\,b^7\,c^{14}\,d^5+32440320\,a^4\,b^8\,c^{15}\,d^4-14417920\,a^3\,b^9\,c^{16}\,d^3+4325376\,a^2\,b^{10}\,c^{17}\,d^2-786432\,a\,b^{11}\,c^{18}\,d+65536\,b^{12}\,c^{19}}\right)}^{1/4}\,\left(\frac{\frac{891\,a^8\,b^7\,d^{15}}{64}-\frac{3105\,a^7\,b^8\,c\,d^{14}}{16}+\frac{31509\,a^6\,b^9\,c^2\,d^{13}}{32}-\frac{33069\,a^5\,b^{10}\,c^3\,d^{12}}{16}+\frac{60307\,a^4\,b^{11}\,c^4\,d^{11}}{32}-\frac{33069\,a^3\,b^{12}\,c^5\,d^{10}}{16}+\frac{31509\,a^2\,b^{13}\,c^6\,d^9}{32}-\frac{3105\,a\,b^{14}\,c^7\,d^8}{16}+\frac{891\,b^{15}\,c^8\,d^7}{64}}{a^{12}\,c^4\,d^8-8\,a^{11}\,b\,c^5\,d^7+28\,a^{10}\,b^2\,c^6\,d^6-56\,a^9\,b^3\,c^7\,d^5+70\,a^8\,b^4\,c^8\,d^4-56\,a^7\,b^5\,c^9\,d^3+28\,a^6\,b^6\,c^{10}\,d^2-8\,a^5\,b^7\,c^{11}\,d+a^4\,b^8\,c^{12}}+{\left(-\frac{81\,a^4\,d^{11}-1188\,a^3\,b\,c\,d^{10}+6534\,a^2\,b^2\,c^2\,d^9-15972\,a\,b^3\,c^3\,d^8+14641\,b^4\,c^4\,d^7}{65536\,a^{12}\,c^7\,d^{12}-786432\,a^{11}\,b\,c^8\,d^{11}+4325376\,a^{10}\,b^2\,c^9\,d^{10}-14417920\,a^9\,b^3\,c^{10}\,d^9+32440320\,a^8\,b^4\,c^{11}\,d^8-51904512\,a^7\,b^5\,c^{12}\,d^7+60555264\,a^6\,b^6\,c^{13}\,d^6-51904512\,a^5\,b^7\,c^{14}\,d^5+32440320\,a^4\,b^8\,c^{15}\,d^4-14417920\,a^3\,b^9\,c^{16}\,d^3+4325376\,a^2\,b^{10}\,c^{17}\,d^2-786432\,a\,b^{11}\,c^{18}\,d+65536\,b^{12}\,c^{19}}\right)}^{3/4}\,\left(\frac{x\,\left(589824\,a^{21}\,b^4\,c^2\,d^{23}-11403264\,a^{20}\,b^5\,c^3\,d^{22}+98762752\,a^{19}\,b^6\,c^4\,d^{21}-510394368\,a^{18}\,b^7\,c^5\,d^{20}+1766916096\,a^{17}\,b^8\,c^6\,d^{19}-4344840192\,a^{16}\,b^9\,c^7\,d^{18}+7796490240\,a^{15}\,b^{10}\,c^8\,d^{17}-10168369152\,a^{14}\,b^{11}\,c^9\,d^{16}+9007726592\,a^{13}\,b^{12}\,c^{10}\,d^{15}-3635478528\,a^{12}\,b^{13}\,c^{11}\,d^{14}-3635478528\,a^{11}\,b^{14}\,c^{12}\,d^{13}+9007726592\,a^{10}\,b^{15}\,c^{13}\,d^{12}-10168369152\,a^9\,b^{16}\,c^{14}\,d^{11}+7796490240\,a^8\,b^{17}\,c^{15}\,d^{10}-4344840192\,a^7\,b^{18}\,c^{16}\,d^9+1766916096\,a^6\,b^{19}\,c^{17}\,d^8-510394368\,a^5\,b^{20}\,c^{18}\,d^7+98762752\,a^4\,b^{21}\,c^{19}\,d^6-11403264\,a^3\,b^{22}\,c^{20}\,d^5+589824\,a^2\,b^{23}\,c^{21}\,d^4\right)}{1024\,\left(a^{16}\,c^4\,d^{12}-12\,a^{15}\,b\,c^5\,d^{11}+66\,a^{14}\,b^2\,c^6\,d^{10}-220\,a^{13}\,b^3\,c^7\,d^9+495\,a^{12}\,b^4\,c^8\,d^8-792\,a^{11}\,b^5\,c^9\,d^7+924\,a^{10}\,b^6\,c^{10}\,d^6-792\,a^9\,b^7\,c^{11}\,d^5+495\,a^8\,b^8\,c^{12}\,d^4-220\,a^7\,b^9\,c^{13}\,d^3+66\,a^6\,b^{10}\,c^{14}\,d^2-12\,a^5\,b^{11}\,c^{15}\,d+a^4\,b^{12}\,c^{16}\right)}+\frac{{\left(-\frac{81\,a^4\,d^{11}-1188\,a^3\,b\,c\,d^{10}+6534\,a^2\,b^2\,c^2\,d^9-15972\,a\,b^3\,c^3\,d^8+14641\,b^4\,c^4\,d^7}{65536\,a^{12}\,c^7\,d^{12}-786432\,a^{11}\,b\,c^8\,d^{11}+4325376\,a^{10}\,b^2\,c^9\,d^{10}-14417920\,a^9\,b^3\,c^{10}\,d^9+32440320\,a^8\,b^4\,c^{11}\,d^8-51904512\,a^7\,b^5\,c^{12}\,d^7+60555264\,a^6\,b^6\,c^{13}\,d^6-51904512\,a^5\,b^7\,c^{14}\,d^5+32440320\,a^4\,b^8\,c^{15}\,d^4-14417920\,a^3\,b^9\,c^{16}\,d^3+4325376\,a^2\,b^{10}\,c^{17}\,d^2-786432\,a\,b^{11}\,c^{18}\,d+65536\,b^{12}\,c^{19}}\right)}^{1/4}\,\left(3072\,a^{19}\,b^4\,c^4\,d^{19}-45056\,a^{18}\,b^5\,c^5\,d^{18}+292864\,a^{17}\,b^6\,c^6\,d^{17}-1115136\,a^{16}\,b^7\,c^7\,d^{16}+2745344\,a^{15}\,b^8\,c^8\,d^{15}-4483072\,a^{14}\,b^9\,c^9\,d^{14}+4595712\,a^{13}\,b^{10}\,c^{10}\,d^{13}-1993728\,a^{12}\,b^{11}\,c^{11}\,d^{12}-1993728\,a^{11}\,b^{12}\,c^{12}\,d^{11}+4595712\,a^{10}\,b^{13}\,c^{13}\,d^{10}-4483072\,a^9\,b^{14}\,c^{14}\,d^9+2745344\,a^8\,b^{15}\,c^{15}\,d^8-1115136\,a^7\,b^{16}\,c^{16}\,d^7+292864\,a^6\,b^{17}\,c^{17}\,d^6-45056\,a^5\,b^{18}\,c^{18}\,d^5+3072\,a^4\,b^{19}\,c^{19}\,d^4\right)}{a^{12}\,c^4\,d^8-8\,a^{11}\,b\,c^5\,d^7+28\,a^{10}\,b^2\,c^6\,d^6-56\,a^9\,b^3\,c^7\,d^5+70\,a^8\,b^4\,c^8\,d^4-56\,a^7\,b^5\,c^9\,d^3+28\,a^6\,b^6\,c^{10}\,d^2-8\,a^5\,b^7\,c^{11}\,d+a^4\,b^8\,c^{12}}\right)\right)+\frac{x\,\left(9801\,a^8\,b^9\,d^{17}-149094\,a^7\,b^{10}\,c\,d^{16}+1001520\,a^6\,b^{11}\,c^2\,d^{15}-3484602\,a^5\,b^{12}\,c^3\,d^{14}+5769038\,a^4\,b^{13}\,c^4\,d^{13}-3484602\,a^3\,b^{14}\,c^5\,d^{12}+1001520\,a^2\,b^{15}\,c^6\,d^{11}-149094\,a\,b^{16}\,c^7\,d^{10}+9801\,b^{17}\,c^8\,d^9\right)}{1024\,\left(a^{16}\,c^4\,d^{12}-12\,a^{15}\,b\,c^5\,d^{11}+66\,a^{14}\,b^2\,c^6\,d^{10}-220\,a^{13}\,b^3\,c^7\,d^9+495\,a^{12}\,b^4\,c^8\,d^8-792\,a^{11}\,b^5\,c^9\,d^7+924\,a^{10}\,b^6\,c^{10}\,d^6-792\,a^9\,b^7\,c^{11}\,d^5+495\,a^8\,b^8\,c^{12}\,d^4-220\,a^7\,b^9\,c^{13}\,d^3+66\,a^6\,b^{10}\,c^{14}\,d^2-12\,a^5\,b^{11}\,c^{15}\,d+a^4\,b^{12}\,c^{16}\right)}\right)+{\left(-\frac{81\,a^4\,d^{11}-1188\,a^3\,b\,c\,d^{10}+6534\,a^2\,b^2\,c^2\,d^9-15972\,a\,b^3\,c^3\,d^8+14641\,b^4\,c^4\,d^7}{65536\,a^{12}\,c^7\,d^{12}-786432\,a^{11}\,b\,c^8\,d^{11}+4325376\,a^{10}\,b^2\,c^9\,d^{10}-14417920\,a^9\,b^3\,c^{10}\,d^9+32440320\,a^8\,b^4\,c^{11}\,d^8-51904512\,a^7\,b^5\,c^{12}\,d^7+60555264\,a^6\,b^6\,c^{13}\,d^6-51904512\,a^5\,b^7\,c^{14}\,d^5+32440320\,a^4\,b^8\,c^{15}\,d^4-14417920\,a^3\,b^9\,c^{16}\,d^3+4325376\,a^2\,b^{10}\,c^{17}\,d^2-786432\,a\,b^{11}\,c^{18}\,d+65536\,b^{12}\,c^{19}}\right)}^{1/4}\,\left({\left(-\frac{81\,a^4\,d^{11}-1188\,a^3\,b\,c\,d^{10}+6534\,a^2\,b^2\,c^2\,d^9-15972\,a\,b^3\,c^3\,d^8+14641\,b^4\,c^4\,d^7}{65536\,a^{12}\,c^7\,d^{12}-786432\,a^{11}\,b\,c^8\,d^{11}+4325376\,a^{10}\,b^2\,c^9\,d^{10}-14417920\,a^9\,b^3\,c^{10}\,d^9+32440320\,a^8\,b^4\,c^{11}\,d^8-51904512\,a^7\,b^5\,c^{12}\,d^7+60555264\,a^6\,b^6\,c^{13}\,d^6-51904512\,a^5\,b^7\,c^{14}\,d^5+32440320\,a^4\,b^8\,c^{15}\,d^4-14417920\,a^3\,b^9\,c^{16}\,d^3+4325376\,a^2\,b^{10}\,c^{17}\,d^2-786432\,a\,b^{11}\,c^{18}\,d+65536\,b^{12}\,c^{19}}\right)}^{1/4}\,\left(\frac{\frac{891\,a^8\,b^7\,d^{15}}{64}-\frac{3105\,a^7\,b^8\,c\,d^{14}}{16}+\frac{31509\,a^6\,b^9\,c^2\,d^{13}}{32}-\frac{33069\,a^5\,b^{10}\,c^3\,d^{12}}{16}+\frac{60307\,a^4\,b^{11}\,c^4\,d^{11}}{32}-\frac{33069\,a^3\,b^{12}\,c^5\,d^{10}}{16}+\frac{31509\,a^2\,b^{13}\,c^6\,d^9}{32}-\frac{3105\,a\,b^{14}\,c^7\,d^8}{16}+\frac{891\,b^{15}\,c^8\,d^7}{64}}{a^{12}\,c^4\,d^8-8\,a^{11}\,b\,c^5\,d^7+28\,a^{10}\,b^2\,c^6\,d^6-56\,a^9\,b^3\,c^7\,d^5+70\,a^8\,b^4\,c^8\,d^4-56\,a^7\,b^5\,c^9\,d^3+28\,a^6\,b^6\,c^{10}\,d^2-8\,a^5\,b^7\,c^{11}\,d+a^4\,b^8\,c^{12}}-{\left(-\frac{81\,a^4\,d^{11}-1188\,a^3\,b\,c\,d^{10}+6534\,a^2\,b^2\,c^2\,d^9-15972\,a\,b^3\,c^3\,d^8+14641\,b^4\,c^4\,d^7}{65536\,a^{12}\,c^7\,d^{12}-786432\,a^{11}\,b\,c^8\,d^{11}+4325376\,a^{10}\,b^2\,c^9\,d^{10}-14417920\,a^9\,b^3\,c^{10}\,d^9+32440320\,a^8\,b^4\,c^{11}\,d^8-51904512\,a^7\,b^5\,c^{12}\,d^7+60555264\,a^6\,b^6\,c^{13}\,d^6-51904512\,a^5\,b^7\,c^{14}\,d^5+32440320\,a^4\,b^8\,c^{15}\,d^4-14417920\,a^3\,b^9\,c^{16}\,d^3+4325376\,a^2\,b^{10}\,c^{17}\,d^2-786432\,a\,b^{11}\,c^{18}\,d+65536\,b^{12}\,c^{19}}\right)}^{3/4}\,\left(\frac{x\,\left(589824\,a^{21}\,b^4\,c^2\,d^{23}-11403264\,a^{20}\,b^5\,c^3\,d^{22}+98762752\,a^{19}\,b^6\,c^4\,d^{21}-510394368\,a^{18}\,b^7\,c^5\,d^{20}+1766916096\,a^{17}\,b^8\,c^6\,d^{19}-4344840192\,a^{16}\,b^9\,c^7\,d^{18}+7796490240\,a^{15}\,b^{10}\,c^8\,d^{17}-10168369152\,a^{14}\,b^{11}\,c^9\,d^{16}+9007726592\,a^{13}\,b^{12}\,c^{10}\,d^{15}-3635478528\,a^{12}\,b^{13}\,c^{11}\,d^{14}-3635478528\,a^{11}\,b^{14}\,c^{12}\,d^{13}+9007726592\,a^{10}\,b^{15}\,c^{13}\,d^{12}-10168369152\,a^9\,b^{16}\,c^{14}\,d^{11}+7796490240\,a^8\,b^{17}\,c^{15}\,d^{10}-4344840192\,a^7\,b^{18}\,c^{16}\,d^9+1766916096\,a^6\,b^{19}\,c^{17}\,d^8-510394368\,a^5\,b^{20}\,c^{18}\,d^7+98762752\,a^4\,b^{21}\,c^{19}\,d^6-11403264\,a^3\,b^{22}\,c^{20}\,d^5+589824\,a^2\,b^{23}\,c^{21}\,d^4\right)}{1024\,\left(a^{16}\,c^4\,d^{12}-12\,a^{15}\,b\,c^5\,d^{11}+66\,a^{14}\,b^2\,c^6\,d^{10}-220\,a^{13}\,b^3\,c^7\,d^9+495\,a^{12}\,b^4\,c^8\,d^8-792\,a^{11}\,b^5\,c^9\,d^7+924\,a^{10}\,b^6\,c^{10}\,d^6-792\,a^9\,b^7\,c^{11}\,d^5+495\,a^8\,b^8\,c^{12}\,d^4-220\,a^7\,b^9\,c^{13}\,d^3+66\,a^6\,b^{10}\,c^{14}\,d^2-12\,a^5\,b^{11}\,c^{15}\,d+a^4\,b^{12}\,c^{16}\right)}-\frac{{\left(-\frac{81\,a^4\,d^{11}-1188\,a^3\,b\,c\,d^{10}+6534\,a^2\,b^2\,c^2\,d^9-15972\,a\,b^3\,c^3\,d^8+14641\,b^4\,c^4\,d^7}{65536\,a^{12}\,c^7\,d^{12}-786432\,a^{11}\,b\,c^8\,d^{11}+4325376\,a^{10}\,b^2\,c^9\,d^{10}-14417920\,a^9\,b^3\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4-14417920\,a^3\,b^9\,c^{16}\,d^3+4325376\,a^2\,b^{10}\,c^{17}\,d^2-786432\,a\,b^{11}\,c^{18}\,d+65536\,b^{12}\,c^{19}}\right)}^{1/4}\,\left(3072\,a^{19}\,b^4\,c^4\,d^{19}-45056\,a^{18}\,b^5\,c^5\,d^{18}+292864\,a^{17}\,b^6\,c^6\,d^{17}-1115136\,a^{16}\,b^7\,c^7\,d^{16}+2745344\,a^{15}\,b^8\,c^8\,d^{15}-4483072\,a^{14}\,b^9\,c^9\,d^{14}+4595712\,a^{13}\,b^{10}\,c^{10}\,d^{13}-1993728\,a^{12}\,b^{11}\,c^{11}\,d^{12}-1993728\,a^{11}\,b^{12}\,c^{12}\,d^{11}+4595712\,a^{10}\,b^{13}\,c^{13}\,d^{10}-4483072\,a^9\,b^{14}\,c^{14}\,d^9+2745344\,a^8\,b^{15}\,c^{15}\,d^8-1115136\,a^7\,b^{16}\,c^{16}\,d^7+292864\,a^6\,b^{17}\,c^{17}\,d^6-45056\,a^5\,b^{18}\,c^{18}\,d^5+3072\,a^4\,b^{19}\,c^{19}\,d^4\right)}{a^{12}\,c^4\,d^8-8\,a^{11}\,b\,c^5\,d^7+28\,a^{10}\,b^2\,c^6\,d^6-56\,a^9\,b^3\,c^7\,d^5+70\,a^8\,b^4\,c^8\,d^4-56\,a^7\,b^5\,c^9\,d^3+28\,a^6\,b^6\,c^{10}\,d^2-8\,a^5\,b^7\,c^{11}\,d+a^4\,b^8\,c^{12}}+\frac{x\,\left(589824\,a^{21}\,b^4\,c^2\,d^{23}-11403264\,a^{20}\,b^5\,c^3\,d^{22}+98762752\,a^{19}\,b^6\,c^4\,d^{21}-510394368\,a^{18}\,b^7\,c^5\,d^{20}+1766916096\,a^{17}\,b^8\,c^6\,d^{19}-4344840192\,a^{16}\,b^9\,c^7\,d^{18}+7796490240\,a^{15}\,b^{10}\,c^8\,d^{17}-10168369152\,a^{14}\,b^{11}\,c^9\,d^{16}+9007726592\,a^{13}\,b^{12}\,c^{10}\,d^{15}-3635478528\,a^{12}\,b^{13}\,c^{11}\,d^{14}-3635478528\,a^{11}\,b^{14}\,c^{12}\,d^{13}+9007726592\,a^{10}\,b^{15}\,c^{13}\,d^{12}-10168369152\,a^9\,b^{16}\,c^{14}\,d^{11}+7796490240\,a^8\,b^{17}\,c^{15}\,d^{10}-4344840192\,a^7\,b^{18}\,c^{16}\,d^9+1766916096\,a^6\,b^{19}\,c^{17}\,d^8-510394368\,a^5\,b^{20}\,c^{18}\,d^7+98762752\,a^4\,b^{21}\,c^{19}\,d^6-11403264\,a^3\,b^{22}\,c^{20}\,d^5+589824\,a^2\,b^{23}\,c^{21}\,d^4\right)\,1{}\mathrm{i}}{1024\,\left(a^{16}\,c^4\,d^{12}-12\,a^{15}\,b\,c^5\,d^{11}+66\,a^{14}\,b^2\,c^6\,d^{10}-220\,a^{13}\,b^3\,c^7\,d^9+495\,a^{12}\,b^4\,c^8\,d^8-792\,a^{11}\,b^5\,c^9\,d^7+924\,a^{10}\,b^6\,c^{10}\,d^6-792\,a^9\,b^7\,c^{11}\,d^5+495\,a^8\,b^8\,c^{12}\,d^4-220\,a^7\,b^9\,c^{13}\,d^3+66\,a^6\,b^{10}\,c^{14}\,d^2-12\,a^5\,b^{11}\,c^{15}\,d+a^4\,b^{12}\,c^{16}\right)}\right)\,1{}\mathrm{i}\right)-\frac{x\,\left(9801\,a^8\,b^9\,d^{17}-149094\,a^7\,b^{10}\,c\,d^{16}+1001520\,a^6\,b^{11}\,c^2\,d^{15}-3484602\,a^5\,b^{12}\,c^3\,d^{14}+5769038\,a^4\,b^{13}\,c^4\,d^{13}-3484602\,a^3\,b^{14}\,c^5\,d^{12}+1001520\,a^2\,b^{15}\,c^6\,d^{11}-149094\,a\,b^{16}\,c^7\,d^{10}+9801\,b^{17}\,c^8\,d^9\right)}{1024\,\left(a^{16}\,c^4\,d^{12}-12\,a^{15}\,b\,c^5\,d^{11}+66\,a^{14}\,b^2\,c^6\,d^{10}-220\,a^{13}\,b^3\,c^7\,d^9+495\,a^{12}\,b^4\,c^8\,d^8-792\,a^{11}\,b^5\,c^9\,d^7+924\,a^{10}\,b^6\,c^{10}\,d^6-792\,a^9\,b^7\,c^{11}\,d^5+495\,a^8\,b^8\,c^{12}\,d^4-220\,a^7\,b^9\,c^{13}\,d^3+66\,a^6\,b^{10}\,c^{14}\,d^2-12\,a^5\,b^{11}\,c^{15}\,d+a^4\,b^{12}\,c^{16}\right)}\right)-{\left(-\frac{81\,a^4\,d^{11}-1188\,a^3\,b\,c\,d^{10}+6534\,a^2\,b^2\,c^2\,d^9-15972\,a\,b^3\,c^3\,d^8+14641\,b^4\,c^4\,d^7}{65536\,a^{12}\,c^7\,d^{12}-786432\,a^{11}\,b\,c^8\,d^{11}+4325376\,a^{10}\,b^2\,c^9\,d^{10}-14417920\,a^9\,b^3\,c^{10}\,d^9+32440320\,a^8\,b^4\,c^{11}\,d^8-51904512\,a^7\,b^5\,c^{12}\,d^7+60555264\,a^6\,b^6\,c^{13}\,d^6-51904512\,a^5\,b^7\,c^{14}\,d^5+32440320\,a^4\,b^8\,c^{15}\,d^4-14417920\,a^3\,b^9\,c^{16}\,d^3+4325376\,a^2\,b^{10}\,c^{17}\,d^2-786432\,a\,b^{11}\,c^{18}\,d+65536\,b^{12}\,c^{19}}\right)}^{1/4}\,\left({\left(-\frac{81\,a^4\,d^{11}-1188\,a^3\,b\,c\,d^{10}+6534\,a^2\,b^2\,c^2\,d^9-15972\,a\,b^3\,c^3\,d^8+14641\,b^4\,c^4\,d^7}{65536\,a^{12}\,c^7\,d^{12}-786432\,a^{11}\,b\,c^8\,d^{11}+4325376\,a^{10}\,b^2\,c^9\,d^{10}-14417920\,a^9\,b^3\,c^{10}\,d^9+32440320\,a^8\,b^4\,c^{11}\,d^8-51904512\,a^7\,b^5\,c^{12}\,d^7+60555264\,a^6\,b^6\,c^{13}\,d^6-51904512\,a^5\,b^7\,c^{14}\,d^5+32440320\,a^4\,b^8\,c^{15}\,d^4-14417920\,a^3\,b^9\,c^{16}\,d^3+4325376\,a^2\,b^{10}\,c^{17}\,d^2-786432\,a\,b^{11}\,c^{18}\,d+65536\,b^{12}\,c^{19}}\right)}^{1/4}\,\left(\frac{\left(\frac{891\,a^8\,b^7\,d^{15}}{64}-\frac{3105\,a^7\,b^8\,c\,d^{14}}{16}+\frac{31509\,a^6\,b^9\,c^2\,d^{13}}{32}-\frac{33069\,a^5\,b^{10}\,c^3\,d^{12}}{16}+\frac{60307\,a^4\,b^{11}\,c^4\,d^{11}}{32}-\frac{33069\,a^3\,b^{12}\,c^5\,d^{10}}{16}+\frac{31509\,a^2\,b^{13}\,c^6\,d^9}{32}-\frac{3105\,a\,b^{14}\,c^7\,d^8}{16}+\frac{891\,b^{15}\,c^8\,d^7}{64}\right)\,1{}\mathrm{i}}{a^{12}\,c^4\,d^8-8\,a^{11}\,b\,c^5\,d^7+28\,a^{10}\,b^2\,c^6\,d^6-56\,a^9\,b^3\,c^7\,d^5+70\,a^8\,b^4\,c^8\,d^4-56\,a^7\,b^5\,c^9\,d^3+28\,a^6\,b^6\,c^{10}\,d^2-8\,a^5\,b^7\,c^{11}\,d+a^4\,b^8\,c^{12}}-{\left(-\frac{81\,a^4\,d^{11}-1188\,a^3\,b\,c\,d^{10}+6534\,a^2\,b^2\,c^2\,d^9-15972\,a\,b^3\,c^3\,d^8+14641\,b^4\,c^4\,d^7}{65536\,a^{12}\,c^7\,d^{12}-786432\,a^{11}\,b\,c^8\,d^{11}+4325376\,a^{10}\,b^2\,c^9\,d^{10}-14417920\,a^9\,b^3\,c^{10}\,d^9+32440320\,a^8\,b^4\,c^{11}\,d^8-51904512\,a^7\,b^5\,c^{12}\,d^7+60555264\,a^6\,b^6\,c^{13}\,d^6-51904512\,a^5\,b^7\,c^{14}\,d^5+32440320\,a^4\,b^8\,c^{15}\,d^4-14417920\,a^3\,b^9\,c^{16}\,d^3+4325376\,a^2\,b^{10}\,c^{17}\,d^2-786432\,a\,b^{11}\,c^{18}\,d+65536\,b^{12}\,c^{19}}\right)}^{3/4}\,\left(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^{12}\,c^7\,d^{12}-786432\,a^{11}\,b\,c^8\,d^{11}+4325376\,a^{10}\,b^2\,c^9\,d^{10}-14417920\,a^9\,b^3\,c^{10}\,d^9+32440320\,a^8\,b^4\,c^{11}\,d^8-51904512\,a^7\,b^5\,c^{12}\,d^7+60555264\,a^6\,b^6\,c^{13}\,d^6-51904512\,a^5\,b^7\,c^{14}\,d^5+32440320\,a^4\,b^8\,c^{15}\,d^4-14417920\,a^3\,b^9\,c^{16}\,d^3+4325376\,a^2\,b^{10}\,c^{17}\,d^2-786432\,a\,b^{11}\,c^{18}\,d+65536\,b^{12}\,c^{19}}\right)}^{3/4}\,\left(\frac{{\left(-\frac{81\,a^4\,d^{11}-1188\,a^3\,b\,c\,d^{10}+6534\,a^2\,b^2\,c^2\,d^9-15972\,a\,b^3\,c^3\,d^8+14641\,b^4\,c^4\,d^7}{65536\,a^{12}\,c^7\,d^{12}-786432\,a^{11}\,b\,c^8\,d^{11}+4325376\,a^{10}\,b^2\,c^9\,d^{10}-14417920\,a^9\,b^3\,c^{10}\,d^9+32440320\,a^8\,b^4\,c^{11}\,d^8-51904512\,a^7\,b^5\,c^{12}\,d^7+60555264\,a^6\,b^6\,c^{13}\,d^6-51904512\,a^5\,b^7\,c^{14}\,d^5+32440320\,a^4\,b^8\,c^{15}\,d^4-14417920\,a^3\,b^9\,c^{16}\,d^3+4325376\,a^2\,b^{10}\,c^{17}\,d^2-786432\,a\,b^{11}\,c^{18}\,d+65536\,b^{12}\,c^{19}}\right)}^{1/4}\,\left(3072\,a^{19}\,b^4\,c^4\,d^{19}-45056\,a^{18}\,b^5\,c^5\,d^{18}+292864\,a^{17}\,b^6\,c^6\,d^{17}-1115136\,a^{16}\,b^7\,c^7\,d^{16}+2745344\,a^{15}\,b^8\,c^8\,d^{15}-4483072\,a^{14}\,b^9\,c^9\,d^{14}+4595712\,a^{13}\,b^{10}\,c^{10}\,d^{13}-1993728\,a^{12}\,b^{11}\,c^{11}\,d^{12}-1993728\,a^{11}\,b^{12}\,c^{12}\,d^{11}+4595712\,a^{10}\,b^{13}\,c^{13}\,d^{10}-4483072\,a^9\,b^{14}\,c^{14}\,d^9+2745344\,a^8\,b^{15}\,c^{15}\,d^8-1115136\,a^7\,b^{16}\,c^{16}\,d^7+292864\,a^6\,b^{17}\,c^{17}\,d^6-45056\,a^5\,b^{18}\,c^{18}\,d^5+3072\,a^4\,b^{19}\,c^{19}\,d^4\right)}{a^{12}\,c^4\,d^8-8\,a^{11}\,b\,c^5\,d^7+28\,a^{10}\,b^2\,c^6\,d^6-56\,a^9\,b^3\,c^7\,d^5+70\,a^8\,b^4\,c^8\,d^4-56\,a^7\,b^5\,c^9\,d^3+28\,a^6\,b^6\,c^{10}\,d^2-8\,a^5\,b^7\,c^{11}\,d+a^4\,b^8\,c^{12}}+\frac{x\,\left(589824\,a^{21}\,b^4\,c^2\,d^{23}-11403264\,a^{20}\,b^5\,c^3\,d^{22}+98762752\,a^{19}\,b^6\,c^4\,d^{21}-510394368\,a^{18}\,b^7\,c^5\,d^{20}+1766916096\,a^{17}\,b^8\,c^6\,d^{19}-4344840192\,a^{16}\,b^9\,c^7\,d^{18}+7796490240\,a^{15}\,b^{10}\,c^8\,d^{17}-10168369152\,a^{14}\,b^{11}\,c^9\,d^{16}+9007726592\,a^{13}\,b^{12}\,c^{10}\,d^{15}-3635478528\,a^{12}\,b^{13}\,c^{11}\,d^{14}-3635478528\,a^{11}\,b^{14}\,c^{12}\,d^{13}+9007726592\,a^{10}\,b^{15}\,c^{13}\,d^{12}-10168369152\,a^9\,b^{16}\,c^{14}\,d^{11}+7796490240\,a^8\,b^{17}\,c^{15}\,d^{10}-4344840192\,a^7\,b^{18}\,c^{16}\,d^9+1766916096\,a^6\,b^{19}\,c^{17}\,d^8-510394368\,a^5\,b^{20}\,c^{18}\,d^7+98762752\,a^4\,b^{21}\,c^{19}\,d^6-11403264\,a^3\,b^{22}\,c^{20}\,d^5+589824\,a^2\,b^{23}\,c^{21}\,d^4\right)\,1{}\mathrm{i}}{1024\,\left(a^{16}\,c^4\,d^{12}-12\,a^{15}\,b\,c^5\,d^{11}+66\,a^{14}\,b^2\,c^6\,d^{10}-220\,a^{13}\,b^3\,c^7\,d^9+495\,a^{12}\,b^4\,c^8\,d^8-792\,a^{11}\,b^5\,c^9\,d^7+924\,a^{10}\,b^6\,c^{10}\,d^6-792\,a^9\,b^7\,c^{11}\,d^5+495\,a^8\,b^8\,c^{12}\,d^4-220\,a^7\,b^9\,c^{13}\,d^3+66\,a^6\,b^{10}\,c^{14}\,d^2-12\,a^5\,b^{11}\,c^{15}\,d+a^4\,b^{12}\,c^{16}\right)}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}-\frac{x\,\left(9801\,a^8\,b^9\,d^{17}-149094\,a^7\,b^{10}\,c\,d^{16}+1001520\,a^6\,b^{11}\,c^2\,d^{15}-3484602\,a^5\,b^{12}\,c^3\,d^{14}+5769038\,a^4\,b^{13}\,c^4\,d^{13}-3484602\,a^3\,b^{14}\,c^5\,d^{12}+1001520\,a^2\,b^{15}\,c^6\,d^{11}-149094\,a\,b^{16}\,c^7\,d^{10}+9801\,b^{17}\,c^8\,d^9\right)\,1{}\mathrm{i}}{1024\,\left(a^{16}\,c^4\,d^{12}-12\,a^{15}\,b\,c^5\,d^{11}+66\,a^{14}\,b^2\,c^6\,d^{10}-220\,a^{13}\,b^3\,c^7\,d^9+495\,a^{12}\,b^4\,c^8\,d^8-792\,a^{11}\,b^5\,c^9\,d^7+924\,a^{10}\,b^6\,c^{10}\,d^6-792\,a^9\,b^7\,c^{11}\,d^5+495\,a^8\,b^8\,c^{12}\,d^4-220\,a^7\,b^9\,c^{13}\,d^3+66\,a^6\,b^{10}\,c^{14}\,d^2-12\,a^5\,b^{11}\,c^{15}\,d+a^4\,b^{12}\,c^{16}\right)}\right)+{\left(-\frac{81\,a^4\,d^{11}-1188\,a^3\,b\,c\,d^{10}+6534\,a^2\,b^2\,c^2\,d^9-15972\,a\,b^3\,c^3\,d^8+14641\,b^4\,c^4\,d^7}{65536\,a^{12}\,c^7\,d^{12}-786432\,a^{11}\,b\,c^8\,d^{11}+4325376\,a^{10}\,b^2\,c^9\,d^{10}-14417920\,a^9\,b^3\,c^{10}\,d^9+32440320\,a^8\,b^4\,c^{11}\,d^8-51904512\,a^7\,b^5\,c^{12}\,d^7+60555264\,a^6\,b^6\,c^{13}\,d^6-51904512\,a^5\,b^7\,c^{14}\,d^5+32440320\,a^4\,b^8\,c^{15}\,d^4-14417920\,a^3\,b^9\,c^{16}\,d^3+4325376\,a^2\,b^{10}\,c^{17}\,d^2-786432\,a\,b^{11}\,c^{18}\,d+65536\,b^{12}\,c^{19}}\right)}^{1/4}\,\left({\left(-\frac{81\,a^4\,d^{11}-1188\,a^3\,b\,c\,d^{10}+6534\,a^2\,b^2\,c^2\,d^9-15972\,a\,b^3\,c^3\,d^8+14641\,b^4\,c^4\,d^7}{65536\,a^{12}\,c^7\,d^{12}-786432\,a^{11}\,b\,c^8\,d^{11}+4325376\,a^{10}\,b^2\,c^9\,d^{10}-14417920\,a^9\,b^3\,c^{10}\,d^9+32440320\,a^8\,b^4\,c^{11}\,d^8-51904512\,a^7\,b^5\,c^{12}\,d^7+60555264\,a^6\,b^6\,c^{13}\,d^6-51904512\,a^5\,b^7\,c^{14}\,d^5+32440320\,a^4\,b^8\,c^{15}\,d^4-14417920\,a^3\,b^9\,c^{16}\,d^3+4325376\,a^2\,b^{10}\,c^{17}\,d^2-786432\,a\,b^{11}\,c^{18}\,d+65536\,b^{12}\,c^{19}}\right)}^{1/4}\,\left(\frac{\left(\frac{891\,a^8\,b^7\,d^{15}}{64}-\frac{3105\,a^7\,b^8\,c\,d^{14}}{16}+\frac{31509\,a^6\,b^9\,c^2\,d^{13}}{32}-\frac{33069\,a^5\,b^{10}\,c^3\,d^{12}}{16}+\frac{60307\,a^4\,b^{11}\,c^4\,d^{11}}{32}-\frac{33069\,a^3\,b^{12}\,c^5\,d^{10}}{16}+\frac{31509\,a^2\,b^{13}\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d^4-56\,a^7\,b^5\,c^9\,d^3+28\,a^6\,b^6\,c^{10}\,d^2-8\,a^5\,b^7\,c^{11}\,d+a^4\,b^8\,c^{12}}\right)+\frac{x\,\left(9801\,a^8\,b^9\,d^{17}-149094\,a^7\,b^{10}\,c\,d^{16}+1001520\,a^6\,b^{11}\,c^2\,d^{15}-3484602\,a^5\,b^{12}\,c^3\,d^{14}+5769038\,a^4\,b^{13}\,c^4\,d^{13}-3484602\,a^3\,b^{14}\,c^5\,d^{12}+1001520\,a^2\,b^{15}\,c^6\,d^{11}-149094\,a\,b^{16}\,c^7\,d^{10}+9801\,b^{17}\,c^8\,d^9\right)}{1024\,\left(a^{16}\,c^4\,d^{12}-12\,a^{15}\,b\,c^5\,d^{11}+66\,a^{14}\,b^2\,c^6\,d^{10}-220\,a^{13}\,b^3\,c^7\,d^9+495\,a^{12}\,b^4\,c^8\,d^8-792\,a^{11}\,b^5\,c^9\,d^7+924\,a^{10}\,b^6\,c^{10}\,d^6-792\,a^9\,b^7\,c^{11}\,d^5+495\,a^8\,b^8\,c^{12}\,d^4-220\,a^7\,b^9\,c^{13}\,d^3+66\,a^6\,b^{10}\,c^{14}\,d^2-12\,a^5\,b^{11}\,c^{15}\,d+a^4\,b^{12}\,c^{16}\right)}\right)-{\left(-\frac{14641\,a^4\,b^7\,d^4-15972\,a^3\,b^8\,c\,d^3+6534\,a^2\,b^9\,c^2\,d^2-1188\,a\,b^{10}\,c^3\,d+81\,b^{11}\,c^4}{65536\,a^{19}\,d^{12}-786432\,a^{18}\,b\,c\,d^{11}+4325376\,a^{17}\,b^2\,c^2\,d^{10}-14417920\,a^{16}\,b^3\,c^3\,d^9+32440320\,a^{15}\,b^4\,c^4\,d^8-51904512\,a^{14}\,b^5\,c^5\,d^7+60555264\,a^{13}\,b^6\,c^6\,d^6-51904512\,a^{12}\,b^7\,c^7\,d^5+32440320\,a^{11}\,b^8\,c^8\,d^4-14417920\,a^{10}\,b^9\,c^9\,d^3+4325376\,a^9\,b^{10}\,c^{10}\,d^2-786432\,a^8\,b^{11}\,c^{11}\,d+65536\,a^7\,b^{12}\,c^{12}}\right)}^{1/4}\,\left({\left(-\frac{14641\,a^4\,b^7\,d^4-15972\,a^3\,b^8\,c\,d^3+6534\,a^2\,b^9\,c^2\,d^2-1188\,a\,b^{10}\,c^3\,d+81\,b^{11}\,c^4}{65536\,a^{19}\,d^{12}-786432\,a^{18}\,b\,c\,d^{11}+4325376\,a^{17}\,b^2\,c^2\,d^{10}-14417920\,a^{16}\,b^3\,c^3\,d^9+32440320\,a^{15}\,b^4\,c^4\,d^8-51904512\,a^{14}\,b^5\,c^5\,d^7+60555264\,a^{13}\,b^6\,c^6\,d^6-51904512\,a^{12}\,b^7\,c^7\,d^5+32440320\,a^{11}\,b^8\,c^8\,d^4-14417920\,a^{10}\,b^9\,c^9\,d^3+4325376\,a^9\,b^{10}\,c^{10}\,d^2-786432\,a^8\,b^{11}\,c^{11}\,d+65536\,a^7\,b^{12}\,c^{12}}\right)}^{1/4}\,\left({\left(-\frac{14641\,a^4\,b^7\,d^4-15972\,a^3\,b^8\,c\,d^3+6534\,a^2\,b^9\,c^2\,d^2-1188\,a\,b^{10}\,c^3\,d+81\,b^{11}\,c^4}{65536\,a^{19}\,d^{12}-786432\,a^{18}\,b\,c\,d^{11}+4325376\,a^{17}\,b^2\,c^2\,d^{10}-14417920\,a^{16}\,b^3\,c^3\,d^9+32440320\,a^{15}\,b^4\,c^4\,d^8-51904512\,a^{14}\,b^5\,c^5\,d^7+60555264\,a^{13}\,b^6\,c^6\,d^6-51904512\,a^{12}\,b^7\,c^7\,d^5+32440320\,a^{11}\,b^8\,c^8\,d^4-14417920\,a^{10}\,b^9\,c^9\,d^3+4325376\,a^9\,b^{10}\,c^{10}\,d^2-786432\,a^8\,b^{11}\,c^{11}\,d+65536\,a^7\,b^{12}\,c^{12}}\right)}^{3/4}\,\left(\frac{x\,\left(589824\,a^{21}\,b^4\,c^2\,d^{23}-11403264\,a^{20}\,b^5\,c^3\,d^{22}+98762752\,a^{19}\,b^6\,c^4\,d^{21}-510394368\,a^{18}\,b^7\,c^5\,d^{20}+1766916096\,a^{17}\,b^8\,c^6\,d^{19}-4344840192\,a^{16}\,b^9\,c^7\,d^{18}+7796490240\,a^{15}\,b^{10}\,c^8\,d^{17}-10168369152\,a^{14}\,b^{11}\,c^9\,d^{16}+9007726592\,a^{13}\,b^{12}\,c^{10}\,d^{15}-3635478528\,a^{12}\,b^{13}\,c^{11}\,d^{14}-3635478528\,a^{11}\,b^{14}\,c^{12}\,d^{13}+9007726592\,a^{10}\,b^{15}\,c^{13}\,d^{12}-10168369152\,a^9\,b^{16}\,c^{14}\,d^{11}+7796490240\,a^8\,b^{17}\,c^{15}\,d^{10}-4344840192\,a^7\,b^{18}\,c^{16}\,d^9+1766916096\,a^6\,b^{19}\,c^{17}\,d^8-510394368\,a^5\,b^{20}\,c^{18}\,d^7+98762752\,a^4\,b^{21}\,c^{19}\,d^6-11403264\,a^3\,b^{22}\,c^{20}\,d^5+589824\,a^2\,b^{23}\,c^{21}\,d^4\right)}{1024\,\left(a^{16}\,c^4\,d^{12}-12\,a^{15}\,b\,c^5\,d^{11}+66\,a^{14}\,b^2\,c^6\,d^{10}-220\,a^{13}\,b^3\,c^7\,d^9+495\,a^{12}\,b^4\,c^8\,d^8-792\,a^{11}\,b^5\,c^9\,d^7+924\,a^{10}\,b^6\,c^{10}\,d^6-792\,a^9\,b^7\,c^{11}\,d^5+495\,a^8\,b^8\,c^{12}\,d^4-220\,a^7\,b^9\,c^{13}\,d^3+66\,a^6\,b^{10}\,c^{14}\,d^2-12\,a^5\,b^{11}\,c^{15}\,d+a^4\,b^{12}\,c^{16}\right)}-\frac{{\left(-\frac{14641\,a^4\,b^7\,d^4-15972\,a^3\,b^8\,c\,d^3+6534\,a^2\,b^9\,c^2\,d^2-1188\,a\,b^{10}\,c^3\,d+81\,b^{11}\,c^4}{65536\,a^{19}\,d^{12}-786432\,a^{18}\,b\,c\,d^{11}+4325376\,a^{17}\,b^2\,c^2\,d^{10}-14417920\,a^{16}\,b^3\,c^3\,d^9+32440320\,a^{15}\,b^4\,c^4\,d^8-51904512\,a^{14}\,b^5\,c^5\,d^7+60555264\,a^{13}\,b^6\,c^6\,d^6-51904512\,a^{12}\,b^7\,c^7\,d^5+32440320\,a^{11}\,b^8\,c^8\,d^4-14417920\,a^{10}\,b^9\,c^9\,d^3+4325376\,a^9\,b^{10}\,c^{10}\,d^2-786432\,a^8\,b^{11}\,c^{11}\,d+65536\,a^7\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(3072\,a^{19}\,b^4\,c^4\,d^{19}-45056\,a^{18}\,b^5\,c^5\,d^{18}+292864\,a^{17}\,b^6\,c^6\,d^{17}-1115136\,a^{16}\,b^7\,c^7\,d^{16}+2745344\,a^{15}\,b^8\,c^8\,d^{15}-4483072\,a^{14}\,b^9\,c^9\,d^{14}+4595712\,a^{13}\,b^{10}\,c^{10}\,d^{13}-1993728\,a^{12}\,b^{11}\,c^{11}\,d^{12}-1993728\,a^{11}\,b^{12}\,c^{12}\,d^{11}+4595712\,a^{10}\,b^{13}\,c^{13}\,d^{10}-4483072\,a^9\,b^{14}\,c^{14}\,d^9+2745344\,a^8\,b^{15}\,c^{15}\,d^8-1115136\,a^7\,b^{16}\,c^{16}\,d^7+292864\,a^6\,b^{17}\,c^{17}\,d^6-45056\,a^5\,b^{18}\,c^{18}\,d^5+3072\,a^4\,b^{19}\,c^{19}\,d^4\right)}{a^{12}\,c^4\,d^8-8\,a^{11}\,b\,c^5\,d^7+28\,a^{10}\,b^2\,c^6\,d^6-56\,a^9\,b^3\,c^7\,d^5+70\,a^8\,b^4\,c^8\,d^4-56\,a^7\,b^5\,c^9\,d^3+28\,a^6\,b^6\,c^{10}\,d^2-8\,a^5\,b^7\,c^{11}\,d+a^4\,b^8\,c^{12}}\right)-\frac{\frac{891\,a^8\,b^7\,d^{15}}{64}-\frac{3105\,a^7\,b^8\,c\,d^{14}}{16}+\frac{31509\,a^6\,b^9\,c^2\,d^{13}}{32}-\frac{33069\,a^5\,b^{10}\,c^3\,d^{12}}{16}+\frac{60307\,a^4\,b^{11}\,c^4\,d^{11}}{32}-\frac{33069\,a^3\,b^{12}\,c^5\,d^{10}}{16}+\frac{31509\,a^2\,b^{13}\,c^6\,d^9}{32}-\frac{3105\,a\,b^{14}\,c^7\,d^8}{16}+\frac{891\,b^{15}\,c^8\,d^7}{64}}{a^{12}\,c^4\,d^8-8\,a^{11}\,b\,c^5\,d^7+28\,a^{10}\,b^2\,c^6\,d^6-56\,a^9\,b^3\,c^7\,d^5+70\,a^8\,b^4\,c^8\,d^4-56\,a^7\,b^5\,c^9\,d^3+28\,a^6\,b^6\,c^{10}\,d^2-8\,a^5\,b^7\,c^{11}\,d+a^4\,b^8\,c^{12}}\right)+\frac{x\,\left(9801\,a^8\,b^9\,d^{17}-149094\,a^7\,b^{10}\,c\,d^{16}+1001520\,a^6\,b^{11}\,c^2\,d^{15}-3484602\,a^5\,b^{12}\,c^3\,d^{14}+5769038\,a^4\,b^{13}\,c^4\,d^{13}-3484602\,a^3\,b^{14}\,c^5\,d^{12}+1001520\,a^2\,b^{15}\,c^6\,d^{11}-149094\,a\,b^{16}\,c^7\,d^{10}+9801\,b^{17}\,c^8\,d^9\right)}{1024\,\left(a^{16}\,c^4\,d^{12}-12\,a^{15}\,b\,c^5\,d^{11}+66\,a^{14}\,b^2\,c^6\,d^{10}-220\,a^{13}\,b^3\,c^7\,d^9+495\,a^{12}\,b^4\,c^8\,d^8-792\,a^{11}\,b^5\,c^9\,d^7+924\,a^{10}\,b^6\,c^{10}\,d^6-792\,a^9\,b^7\,c^{11}\,d^5+495\,a^8\,b^8\,c^{12}\,d^4-220\,a^7\,b^9\,c^{13}\,d^3+66\,a^6\,b^{10}\,c^{14}\,d^2-12\,a^5\,b^{11}\,c^{15}\,d+a^4\,b^{12}\,c^{16}\right)}\right)}\right)\,{\left(-\frac{14641\,a^4\,b^7\,d^4-15972\,a^3\,b^8\,c\,d^3+6534\,a^2\,b^9\,c^2\,d^2-1188\,a\,b^{10}\,c^3\,d+81\,b^{11}\,c^4}{65536\,a^{19}\,d^{12}-786432\,a^{18}\,b\,c\,d^{11}+4325376\,a^{17}\,b^2\,c^2\,d^{10}-14417920\,a^{16}\,b^3\,c^3\,d^9+32440320\,a^{15}\,b^4\,c^4\,d^8-51904512\,a^{14}\,b^5\,c^5\,d^7+60555264\,a^{13}\,b^6\,c^6\,d^6-51904512\,a^{12}\,b^7\,c^7\,d^5+32440320\,a^{11}\,b^8\,c^8\,d^4-14417920\,a^{10}\,b^9\,c^9\,d^3+4325376\,a^9\,b^{10}\,c^{10}\,d^2-786432\,a^8\,b^{11}\,c^{11}\,d+65536\,a^7\,b^{12}\,c^{12}}\right)}^{1/4}\,2{}\mathrm{i}+2\,\mathrm{atan}\left(\frac{{\left(-\frac{14641\,a^4\,b^7\,d^4-15972\,a^3\,b^8\,c\,d^3+6534\,a^2\,b^9\,c^2\,d^2-1188\,a\,b^{10}\,c^3\,d+81\,b^{11}\,c^4}{65536\,a^{19}\,d^{12}-786432\,a^{18}\,b\,c\,d^{11}+4325376\,a^{17}\,b^2\,c^2\,d^{10}-14417920\,a^{16}\,b^3\,c^3\,d^9+32440320\,a^{15}\,b^4\,c^4\,d^8-51904512\,a^{14}\,b^5\,c^5\,d^7+60555264\,a^{13}\,b^6\,c^6\,d^6-51904512\,a^{12}\,b^7\,c^7\,d^5+32440320\,a^{11}\,b^8\,c^8\,d^4-14417920\,a^{10}\,b^9\,c^9\,d^3+4325376\,a^9\,b^{10}\,c^{10}\,d^2-786432\,a^8\,b^{11}\,c^{11}\,d+65536\,a^7\,b^{12}\,c^{12}}\right)}^{1/4}\,\left({\left(-\frac{14641\,a^4\,b^7\,d^4-15972\,a^3\,b^8\,c\,d^3+6534\,a^2\,b^9\,c^2\,d^2-1188\,a\,b^{10}\,c^3\,d+81\,b^{11}\,c^4}{65536\,a^{19}\,d^{12}-786432\,a^{18}\,b\,c\,d^{11}+4325376\,a^{17}\,b^2\,c^2\,d^{10}-14417920\,a^{16}\,b^3\,c^3\,d^9+32440320\,a^{15}\,b^4\,c^4\,d^8-51904512\,a^{14}\,b^5\,c^5\,d^7+60555264\,a^{13}\,b^6\,c^6\,d^6-51904512\,a^{12}\,b^7\,c^7\,d^5+32440320\,a^{11}\,b^8\,c^8\,d^4-14417920\,a^{10}\,b^9\,c^9\,d^3+4325376\,a^9\,b^{10}\,c^{10}\,d^2-786432\,a^8\,b^{11}\,c^{11}\,d+65536\,a^7\,b^{12}\,c^{12}}\right)}^{1/4}\,\left({\left(-\frac{14641\,a^4\,b^7\,d^4-15972\,a^3\,b^8\,c\,d^3+6534\,a^2\,b^9\,c^2\,d^2-1188\,a\,b^{10}\,c^3\,d+81\,b^{11}\,c^4}{65536\,a^{19}\,d^{12}-786432\,a^{18}\,b\,c\,d^{11}+4325376\,a^{17}\,b^2\,c^2\,d^{10}-14417920\,a^{16}\,b^3\,c^3\,d^9+32440320\,a^{15}\,b^4\,c^4\,d^8-51904512\,a^{14}\,b^5\,c^5\,d^7+60555264\,a^{13}\,b^6\,c^6\,d^6-51904512\,a^{12}\,b^7\,c^7\,d^5+32440320\,a^{11}\,b^8\,c^8\,d^4-14417920\,a^{10}\,b^9\,c^9\,d^3+4325376\,a^9\,b^{10}\,c^{10}\,d^2-786432\,a^8\,b^{11}\,c^{11}\,d+65536\,a^7\,b^{12}\,c^{12}}\right)}^{3/4}\,\left(\frac{{\left(-\frac{14641\,a^4\,b^7\,d^4-15972\,a^3\,b^8\,c\,d^3+6534\,a^2\,b^9\,c^2\,d^2-1188\,a\,b^{10}\,c^3\,d+81\,b^{11}\,c^4}{65536\,a^{19}\,d^{12}-786432\,a^{18}\,b\,c\,d^{11}+4325376\,a^{17}\,b^2\,c^2\,d^{10}-14417920\,a^{16}\,b^3\,c^3\,d^9+32440320\,a^{15}\,b^4\,c^4\,d^8-51904512\,a^{14}\,b^5\,c^5\,d^7+60555264\,a^{13}\,b^6\,c^6\,d^6-51904512\,a^{12}\,b^7\,c^7\,d^5+32440320\,a^{11}\,b^8\,c^8\,d^4-14417920\,a^{10}\,b^9\,c^9\,d^3+4325376\,a^9\,b^{10}\,c^{10}\,d^2-786432\,a^8\,b^{11}\,c^{11}\,d+65536\,a^7\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(3072\,a^{19}\,b^4\,c^4\,d^{19}-45056\,a^{18}\,b^5\,c^5\,d^{18}+292864\,a^{17}\,b^6\,c^6\,d^{17}-1115136\,a^{16}\,b^7\,c^7\,d^{16}+2745344\,a^{15}\,b^8\,c^8\,d^{15}-4483072\,a^{14}\,b^9\,c^9\,d^{14}+4595712\,a^{13}\,b^{10}\,c^{10}\,d^{13}-1993728\,a^{12}\,b^{11}\,c^{11}\,d^{12}-1993728\,a^{11}\,b^{12}\,c^{12}\,d^{11}+4595712\,a^{10}\,b^{13}\,c^{13}\,d^{10}-4483072\,a^9\,b^{14}\,c^{14}\,d^9+2745344\,a^8\,b^{15}\,c^{15}\,d^8-1115136\,a^7\,b^{16}\,c^{16}\,d^7+292864\,a^6\,b^{17}\,c^{17}\,d^6-45056\,a^5\,b^{18}\,c^{18}\,d^5+3072\,a^4\,b^{19}\,c^{19}\,d^4\right)}{a^{12}\,c^4\,d^8-8\,a^{11}\,b\,c^5\,d^7+28\,a^{10}\,b^2\,c^6\,d^6-56\,a^9\,b^3\,c^7\,d^5+70\,a^8\,b^4\,c^8\,d^4-56\,a^7\,b^5\,c^9\,d^3+28\,a^6\,b^6\,c^{10}\,d^2-8\,a^5\,b^7\,c^{11}\,d+a^4\,b^8\,c^{12}}+\frac{x\,\left(589824\,a^{21}\,b^4\,c^2\,d^{23}-11403264\,a^{20}\,b^5\,c^3\,d^{22}+98762752\,a^{19}\,b^6\,c^4\,d^{21}-510394368\,a^{18}\,b^7\,c^5\,d^{20}+1766916096\,a^{17}\,b^8\,c^6\,d^{19}-4344840192\,a^{16}\,b^9\,c^7\,d^{18}+7796490240\,a^{15}\,b^{10}\,c^8\,d^{17}-10168369152\,a^{14}\,b^{11}\,c^9\,d^{16}+900772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\,b^{11}\,c^{11}\,d^{12}-1993728\,a^{11}\,b^{12}\,c^{12}\,d^{11}+4595712\,a^{10}\,b^{13}\,c^{13}\,d^{10}-4483072\,a^9\,b^{14}\,c^{14}\,d^9+2745344\,a^8\,b^{15}\,c^{15}\,d^8-1115136\,a^7\,b^{16}\,c^{16}\,d^7+292864\,a^6\,b^{17}\,c^{17}\,d^6-45056\,a^5\,b^{18}\,c^{18}\,d^5+3072\,a^4\,b^{19}\,c^{19}\,d^4\right)}{a^{12}\,c^4\,d^8-8\,a^{11}\,b\,c^5\,d^7+28\,a^{10}\,b^2\,c^6\,d^6-56\,a^9\,b^3\,c^7\,d^5+70\,a^8\,b^4\,c^8\,d^4-56\,a^7\,b^5\,c^9\,d^3+28\,a^6\,b^6\,c^{10}\,d^2-8\,a^5\,b^7\,c^{11}\,d+a^4\,b^8\,c^{12}}+\frac{x\,\left(589824\,a^{21}\,b^4\,c^2\,d^{23}-11403264\,a^{20}\,b^5\,c^3\,d^{22}+98762752\,a^{19}\,b^6\,c^4\,d^{21}-510394368\,a^{18}\,b^7\,c^5\,d^{20}+1766916096\,a^{17}\,b^8\,c^6\,d^{19}-4344840192\,a^{16}\,b^9\,c^7\,d^{18}+7796490240\,a^{15}\,b^{10}\,c^8\,d^{17}-10168369152\,a^{14}\,b^{11}\,c^9\,d^{16}+9007726592\,a^{13}\,b^{12}\,c^{10}\,d^{15}-3635478528\,a^{12}\,b^{13}\,c^{11}\,d^{14}-3635478528\,a^{11}\,b^{14}\,c^{12}\,d^{13}+9007726592\,a^{10}\,b^{15}\,c^{13}\,d^{12}-10168369152\,a^9\,b^{16}\,c^{14}\,d^{11}+7796490240\,a^8\,b^{17}\,c^{15}\,d^{10}-4344840192\,a^7\,b^{18}\,c^{16}\,d^9+1766916096\,a^6\,b^{19}\,c^{17}\,d^8-510394368\,a^5\,b^{20}\,c^{18}\,d^7+98762752\,a^4\,b^{21}\,c^{19}\,d^6-11403264\,a^3\,b^{22}\,c^{20}\,d^5+589824\,a^2\,b^{23}\,c^{21}\,d^4\right)\,1{}\mathrm{i}}{1024\,\left(a^{16}\,c^4\,d^{12}-12\,a^{15}\,b\,c^5\,d^{11}+66\,a^{14}\,b^2\,c^6\,d^{10}-220\,a^{13}\,b^3\,c^7\,d^9+495\,a^{12}\,b^4\,c^8\,d^8-792\,a^{11}\,b^5\,c^9\,d^7+924\,a^{10}\,b^6\,c^{10}\,d^6-792\,a^9\,b^7\,c^{11}\,d^5+495\,a^8\,b^8\,c^{12}\,d^4-220\,a^7\,b^9\,c^{13}\,d^3+66\,a^6\,b^{10}\,c^{14}\,d^2-12\,a^5\,b^{11}\,c^{15}\,d+a^4\,b^{12}\,c^{16}\right)}\right)\,1{}\mathrm{i}+\frac{\left(\frac{891\,a^8\,b^7\,d^{15}}{64}-\frac{3105\,a^7\,b^8\,c\,d^{14}}{16}+\frac{31509\,a^6\,b^9\,c^2\,d^{13}}{32}-\frac{33069\,a^5\,b^{10}\,c^3\,d^{12}}{16}+\frac{60307\,a^4\,b^{11}\,c^4\,d^{11}}{32}-\frac{33069\,a^3\,b^{12}\,c^5\,d^{10}}{16}+\frac{31509\,a^2\,b^{13}\,c^6\,d^9}{32}-\frac{3105\,a\,b^{14}\,c^7\,d^8}{16}+\frac{891\,b^{15}\,c^8\,d^7}{64}\right)\,1{}\mathrm{i}}{a^{12}\,c^4\,d^8-8\,a^{11}\,b\,c^5\,d^7+28\,a^{10}\,b^2\,c^6\,d^6-56\,a^9\,b^3\,c^7\,d^5+70\,a^8\,b^4\,c^8\,d^4-56\,a^7\,b^5\,c^9\,d^3+28\,a^6\,b^6\,c^{10}\,d^2-8\,a^5\,b^7\,c^{11}\,d+a^4\,b^8\,c^{12}}\right)\,1{}\mathrm{i}-\frac{x\,\left(9801\,a^8\,b^9\,d^{17}-149094\,a^7\,b^{10}\,c\,d^{16}+1001520\,a^6\,b^{11}\,c^2\,d^{15}-3484602\,a^5\,b^{12}\,c^3\,d^{14}+5769038\,a^4\,b^{13}\,c^4\,d^{13}-3484602\,a^3\,b^{14}\,c^5\,d^{12}+1001520\,a^2\,b^{15}\,c^6\,d^{11}-149094\,a\,b^{16}\,c^7\,d^{10}+9801\,b^{17}\,c^8\,d^9\right)\,1{}\mathrm{i}}{1024\,\left(a^{16}\,c^4\,d^{12}-12\,a^{15}\,b\,c^5\,d^{11}+66\,a^{14}\,b^2\,c^6\,d^{10}-220\,a^{13}\,b^3\,c^7\,d^9+495\,a^{12}\,b^4\,c^8\,d^8-792\,a^{11}\,b^5\,c^9\,d^7+924\,a^{10}\,b^6\,c^{10}\,d^6-792\,a^9\,b^7\,c^{11}\,d^5+495\,a^8\,b^8\,c^{12}\,d^4-220\,a^7\,b^9\,c^{13}\,d^3+66\,a^6\,b^{10}\,c^{14}\,d^2-12\,a^5\,b^{11}\,c^{15}\,d+a^4\,b^{12}\,c^{16}\right)}\right)-{\left(-\frac{14641\,a^4\,b^7\,d^4-15972\,a^3\,b^8\,c\,d^3+6534\,a^2\,b^9\,c^2\,d^2-1188\,a\,b^{10}\,c^3\,d+81\,b^{11}\,c^4}{65536\,a^{19}\,d^{12}-786432\,a^{18}\,b\,c\,d^{11}+4325376\,a^{17}\,b^2\,c^2\,d^{10}-14417920\,a^{16}\,b^3\,c^3\,d^9+32440320\,a^{15}\,b^4\,c^4\,d^8-51904512\,a^{14}\,b^5\,c^5\,d^7+60555264\,a^{13}\,b^6\,c^6\,d^6-51904512\,a^{12}\,b^7\,c^7\,d^5+32440320\,a^{11}\,b^8\,c^8\,d^4-14417920\,a^{10}\,b^9\,c^9\,d^3+4325376\,a^9\,b^{10}\,c^{10}\,d^2-786432\,a^8\,b^{11}\,c^{11}\,d+65536\,a^7\,b^{12}\,c^{12}}\right)}^{1/4}\,\left({\left(-\frac{14641\,a^4\,b^7\,d^4-15972\,a^3\,b^8\,c\,d^3+6534\,a^2\,b^9\,c^2\,d^2-1188\,a\,b^{10}\,c^3\,d+81\,b^{11}\,c^4}{65536\,a^{19}\,d^{12}-786432\,a^{18}\,b\,c\,d^{11}+4325376\,a^{17}\,b^2\,c^2\,d^{10}-14417920\,a^{16}\,b^3\,c^3\,d^9+32440320\,a^{15}\,b^4\,c^4\,d^8-51904512\,a^{14}\,b^5\,c^5\,d^7+60555264\,a^{13}\,b^6\,c^6\,d^6-51904512\,a^{12}\,b^7\,c^7\,d^5+32440320\,a^{11}\,b^8\,c^8\,d^4-14417920\,a^{10}\,b^9\,c^9\,d^3+4325376\,a^9\,b^{10}\,c^{10}\,d^2-786432\,a^8\,b^{11}\,c^{11}\,d+65536\,a^7\,b^{12}\,c^{12}}\right)}^{1/4}\,\left({\left(-\frac{14641\,a^4\,b^7\,d^4-15972\,a^3\,b^8\,c\,d^3+6534\,a^2\,b^9\,c^2\,d^2-1188\,a\,b^{10}\,c^3\,d+81\,b^{11}\,c^4}{65536\,a^{19}\,d^{12}-786432\,a^{18}\,b\,c\,d^{11}+4325376\,a^{17}\,b^2\,c^2\,d^{10}-14417920\,a^{16}\,b^3\,c^3\,d^9+32440320\,a^{15}\,b^4\,c^4\,d^8-51904512\,a^{14}\,b^5\,c^5\,d^7+60555264\,a^{13}\,b^6\,c^6\,d^6-51904512\,a^{12}\,b^7\,c^7\,d^5+32440320\,a^{11}\,b^8\,c^8\,d^4-14417920\,a^{10}\,b^9\,c^9\,d^3+4325376\,a^9\,b^{10}\,c^{10}\,d^2-786432\,a^8\,b^{11}\,c^{11}\,d+65536\,a^7\,b^{12}\,c^{12}}\right)}^{3/4}\,\left(-\frac{{\left(-\frac{14641\,a^4\,b^7\,d^4-15972\,a^3\,b^8\,c\,d^3+6534\,a^2\,b^9\,c^2\,d^2-1188\,a\,b^{10}\,c^3\,d+81\,b^{11}\,c^4}{65536\,a^{19}\,d^{12}-786432\,a^{18}\,b\,c\,d^{11}+4325376\,a^{17}\,b^2\,c^2\,d^{10}-14417920\,a^{16}\,b^3\,c^3\,d^9+32440320\,a^{15}\,b^4\,c^4\,d^8-51904512\,a^{14}\,b^5\,c^5\,d^7+60555264\,a^{13}\,b^6\,c^6\,d^6-51904512\,a^{12}\,b^7\,c^7\,d^5+32440320\,a^{11}\,b^8\,c^8\,d^4-14417920\,a^{10}\,b^9\,c^9\,d^3+4325376\,a^9\,b^{10}\,c^{10}\,d^2-786432\,a^8\,b^{11}\,c^{11}\,d+65536\,a^7\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(3072\,a^{19}\,b^4\,c^4\,d^{19}-45056\,a^{18}\,b^5\,c^5\,d^{18}+292864\,a^{17}\,b^6\,c^6\,d^{17}-1115136\,a^{16}\,b^7\,c^7\,d^{16}+2745344\,a^{15}\,b^8\,c^8\,d^{15}-4483072\,a^{14}\,b^9\,c^9\,d^{14}+4595712\,a^{13}\,b^{10}\,c^{10}\,d^{13}-1993728\,a^{12}\,b^{11}\,c^{11}\,d^{12}-1993728\,a^{11}\,b^{12}\,c^{12}\,d^{11}+4595712\,a^{10}\,b^{13}\,c^{13}\,d^{10}-4483072\,a^9\,b^{14}\,c^{14}\,d^9+2745344\,a^8\,b^{15}\,c^{15}\,d^8-1115136\,a^7\,b^{16}\,c^{16}\,d^7+292864\,a^6\,b^{17}\,c^{17}\,d^6-45056\,a^5\,b^{18}\,c^{18}\,d^5+3072\,a^4\,b^{19}\,c^{19}\,d^4\right)}{a^{12}\,c^4\,d^8-8\,a^{11}\,b\,c^5\,d^7+28\,a^{10}\,b^2\,c^6\,d^6-56\,a^9\,b^3\,c^7\,d^5+70\,a^8\,b^4\,c^8\,d^4-56\,a^7\,b^5\,c^9\,d^3+28\,a^6\,b^6\,c^{10}\,d^2-8\,a^5\,b^7\,c^{11}\,d+a^4\,b^8\,c^{12}}+\frac{x\,\left(589824\,a^{21}\,b^4\,c^2\,d^{23}-11403264\,a^{20}\,b^5\,c^3\,d^{22}+98762752\,a^{19}\,b^6\,c^4\,d^{21}-510394368\,a^{18}\,b^7\,c^5\,d^{20}+1766916096\,a^{17}\,b^8\,c^6\,d^{19}-4344840192\,a^{16}\,b^9\,c^7\,d^{18}+7796490240\,a^{15}\,b^{10}\,c^8\,d^{17}-10168369152\,a^{14}\,b^{11}\,c^9\,d^{16}+9007726592\,a^{13}\,b^{12}\,c^{10}\,d^{15}-3635478528\,a^{12}\,b^{13}\,c^{11}\,d^{14}-3635478528\,a^{11}\,b^{14}\,c^{12}\,d^{13}+9007726592\,a^{10}\,b^{15}\,c^{13}\,d^{12}-10168369152\,a^9\,b^{16}\,c^{14}\,d^{11}+7796490240\,a^8\,b^{17}\,c^{15}\,d^{10}-4344840192\,a^7\,b^{18}\,c^{16}\,d^9+1766916096\,a^6\,b^{19}\,c^{17}\,d^8-510394368\,a^5\,b^{20}\,c^{18}\,d^7+98762752\,a^4\,b^{21}\,c^{19}\,d^6-11403264\,a^3\,b^{22}\,c^{20}\,d^5+589824\,a^2\,b^{23}\,c^{21}\,d^4\right)\,1{}\mathrm{i}}{1024\,\left(a^{16}\,c^4\,d^{12}-12\,a^{15}\,b\,c^5\,d^{11}+66\,a^{14}\,b^2\,c^6\,d^{10}-220\,a^{13}\,b^3\,c^7\,d^9+495\,a^{12}\,b^4\,c^8\,d^8-792\,a^{11}\,b^5\,c^9\,d^7+924\,a^{10}\,b^6\,c^{10}\,d^6-792\,a^9\,b^7\,c^{11}\,d^5+495\,a^8\,b^8\,c^{12}\,d^4-220\,a^7\,b^9\,c^{13}\,d^3+66\,a^6\,b^{10}\,c^{14}\,d^2-12\,a^5\,b^{11}\,c^{15}\,d+a^4\,b^{12}\,c^{16}\right)}\right)\,1{}\mathrm{i}-\frac{\left(\frac{891\,a^8\,b^7\,d^{15}}{64}-\frac{3105\,a^7\,b^8\,c\,d^{14}}{16}+\frac{31509\,a^6\,b^9\,c^2\,d^{13}}{32}-\frac{33069\,a^5\,b^{10}\,c^3\,d^{12}}{16}+\frac{60307\,a^4\,b^{11}\,c^4\,d^{11}}{32}-\frac{33069\,a^3\,b^{12}\,c^5\,d^{10}}{16}+\frac{31509\,a^2\,b^{13}\,c^6\,d^9}{32}-\frac{3105\,a\,b^{14}\,c^7\,d^8}{16}+\frac{891\,b^{15}\,c^8\,d^7}{64}\right)\,1{}\mathrm{i}}{a^{12}\,c^4\,d^8-8\,a^{11}\,b\,c^5\,d^7+28\,a^{10}\,b^2\,c^6\,d^6-56\,a^9\,b^3\,c^7\,d^5+70\,a^8\,b^4\,c^8\,d^4-56\,a^7\,b^5\,c^9\,d^3+28\,a^6\,b^6\,c^{10}\,d^2-8\,a^5\,b^7\,c^{11}\,d+a^4\,b^8\,c^{12}}\right)\,1{}\mathrm{i}-\frac{x\,\left(9801\,a^8\,b^9\,d^{17}-149094\,a^7\,b^{10}\,c\,d^{16}+1001520\,a^6\,b^{11}\,c^2\,d^{15}-3484602\,a^5\,b^{12}\,c^3\,d^{14}+5769038\,a^4\,b^{13}\,c^4\,d^{13}-3484602\,a^3\,b^{14}\,c^5\,d^{12}+1001520\,a^2\,b^{15}\,c^6\,d^{11}-149094\,a\,b^{16}\,c^7\,d^{10}+9801\,b^{17}\,c^8\,d^9\right)\,1{}\mathrm{i}}{1024\,\left(a^{16}\,c^4\,d^{12}-12\,a^{15}\,b\,c^5\,d^{11}+66\,a^{14}\,b^2\,c^6\,d^{10}-220\,a^{13}\,b^3\,c^7\,d^9+495\,a^{12}\,b^4\,c^8\,d^8-792\,a^{11}\,b^5\,c^9\,d^7+924\,a^{10}\,b^6\,c^{10}\,d^6-792\,a^9\,b^7\,c^{11}\,d^5+495\,a^8\,b^8\,c^{12}\,d^4-220\,a^7\,b^9\,c^{13}\,d^3+66\,a^6\,b^{10}\,c^{14}\,d^2-12\,a^5\,b^{11}\,c^{15}\,d+a^4\,b^{12}\,c^{16}\right)}\right)}\right)\,{\left(-\frac{14641\,a^4\,b^7\,d^4-15972\,a^3\,b^8\,c\,d^3+6534\,a^2\,b^9\,c^2\,d^2-1188\,a\,b^{10}\,c^3\,d+81\,b^{11}\,c^4}{65536\,a^{19}\,d^{12}-786432\,a^{18}\,b\,c\,d^{11}+4325376\,a^{17}\,b^2\,c^2\,d^{10}-14417920\,a^{16}\,b^3\,c^3\,d^9+32440320\,a^{15}\,b^4\,c^4\,d^8-51904512\,a^{14}\,b^5\,c^5\,d^7+60555264\,a^{13}\,b^6\,c^6\,d^6-51904512\,a^{12}\,b^7\,c^7\,d^5+32440320\,a^{11}\,b^8\,c^8\,d^4-14417920\,a^{10}\,b^9\,c^9\,d^3+4325376\,a^9\,b^{10}\,c^{10}\,d^2-786432\,a^8\,b^{11}\,c^{11}\,d+65536\,a^7\,b^{12}\,c^{12}}\right)}^{1/4}","Not used",1,"((x*(a^2*d^2 + b^2*c^2))/(4*a*c*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) + (b*d*x^5*(a*d + b*c))/(4*a*c*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)))/(a*c + x^4*(a*d + b*c) + b*d*x^8) - atan(((-(81*a^4*d^11 + 14641*b^4*c^4*d^7 - 15972*a*b^3*c^3*d^8 + 6534*a^2*b^2*c^2*d^9 - 1188*a^3*b*c*d^10)/(65536*b^12*c^19 + 65536*a^12*c^7*d^12 - 786432*a^11*b*c^8*d^11 + 4325376*a^2*b^10*c^17*d^2 - 14417920*a^3*b^9*c^16*d^3 + 32440320*a^4*b^8*c^15*d^4 - 51904512*a^5*b^7*c^14*d^5 + 60555264*a^6*b^6*c^13*d^6 - 51904512*a^7*b^5*c^12*d^7 + 32440320*a^8*b^4*c^11*d^8 - 14417920*a^9*b^3*c^10*d^9 + 4325376*a^10*b^2*c^9*d^10 - 786432*a*b^11*c^18*d))^(1/4)*((-(81*a^4*d^11 + 14641*b^4*c^4*d^7 - 15972*a*b^3*c^3*d^8 + 6534*a^2*b^2*c^2*d^9 - 1188*a^3*b*c*d^10)/(65536*b^12*c^19 + 65536*a^12*c^7*d^12 - 786432*a^11*b*c^8*d^11 + 4325376*a^2*b^10*c^17*d^2 - 14417920*a^3*b^9*c^16*d^3 + 32440320*a^4*b^8*c^15*d^4 - 51904512*a^5*b^7*c^14*d^5 + 60555264*a^6*b^6*c^13*d^6 - 51904512*a^7*b^5*c^12*d^7 + 32440320*a^8*b^4*c^11*d^8 - 14417920*a^9*b^3*c^10*d^9 + 4325376*a^10*b^2*c^9*d^10 - 786432*a*b^11*c^18*d))^(1/4)*(((891*a^8*b^7*d^15)/64 + (891*b^15*c^8*d^7)/64 - (3105*a*b^14*c^7*d^8)/16 - (3105*a^7*b^8*c*d^14)/16 + (31509*a^2*b^13*c^6*d^9)/32 - (33069*a^3*b^12*c^5*d^10)/16 + (60307*a^4*b^11*c^4*d^11)/32 - (33069*a^5*b^10*c^3*d^12)/16 + (31509*a^6*b^9*c^2*d^13)/32)/(a^4*b^8*c^12 + a^12*c^4*d^8 - 8*a^5*b^7*c^11*d - 8*a^11*b*c^5*d^7 + 28*a^6*b^6*c^10*d^2 - 56*a^7*b^5*c^9*d^3 + 70*a^8*b^4*c^8*d^4 - 56*a^9*b^3*c^7*d^5 + 28*a^10*b^2*c^6*d^6) + (-(81*a^4*d^11 + 14641*b^4*c^4*d^7 - 15972*a*b^3*c^3*d^8 + 6534*a^2*b^2*c^2*d^9 - 1188*a^3*b*c*d^10)/(65536*b^12*c^19 + 65536*a^12*c^7*d^12 - 786432*a^11*b*c^8*d^11 + 4325376*a^2*b^10*c^17*d^2 - 14417920*a^3*b^9*c^16*d^3 + 32440320*a^4*b^8*c^15*d^4 - 51904512*a^5*b^7*c^14*d^5 + 60555264*a^6*b^6*c^13*d^6 - 51904512*a^7*b^5*c^12*d^7 + 32440320*a^8*b^4*c^11*d^8 - 14417920*a^9*b^3*c^10*d^9 + 4325376*a^10*b^2*c^9*d^10 - 786432*a*b^11*c^18*d))^(3/4)*((x*(589824*a^2*b^23*c^21*d^4 - 11403264*a^3*b^22*c^20*d^5 + 98762752*a^4*b^21*c^19*d^6 - 510394368*a^5*b^20*c^18*d^7 + 1766916096*a^6*b^19*c^17*d^8 - 4344840192*a^7*b^18*c^16*d^9 + 7796490240*a^8*b^17*c^15*d^10 - 10168369152*a^9*b^16*c^14*d^11 + 9007726592*a^10*b^15*c^13*d^12 - 3635478528*a^11*b^14*c^12*d^13 - 3635478528*a^12*b^13*c^11*d^14 + 9007726592*a^13*b^12*c^10*d^15 - 10168369152*a^14*b^11*c^9*d^16 + 7796490240*a^15*b^10*c^8*d^17 - 4344840192*a^16*b^9*c^7*d^18 + 1766916096*a^17*b^8*c^6*d^19 - 510394368*a^18*b^7*c^5*d^20 + 98762752*a^19*b^6*c^4*d^21 - 11403264*a^20*b^5*c^3*d^22 + 589824*a^21*b^4*c^2*d^23))/(1024*(a^4*b^12*c^16 + a^16*c^4*d^12 - 12*a^5*b^11*c^15*d - 12*a^15*b*c^5*d^11 + 66*a^6*b^10*c^14*d^2 - 220*a^7*b^9*c^13*d^3 + 495*a^8*b^8*c^12*d^4 - 792*a^9*b^7*c^11*d^5 + 924*a^10*b^6*c^10*d^6 - 792*a^11*b^5*c^9*d^7 + 495*a^12*b^4*c^8*d^8 - 220*a^13*b^3*c^7*d^9 + 66*a^14*b^2*c^6*d^10)) + ((-(81*a^4*d^11 + 14641*b^4*c^4*d^7 - 15972*a*b^3*c^3*d^8 + 6534*a^2*b^2*c^2*d^9 - 1188*a^3*b*c*d^10)/(65536*b^12*c^19 + 65536*a^12*c^7*d^12 - 786432*a^11*b*c^8*d^11 + 4325376*a^2*b^10*c^17*d^2 - 14417920*a^3*b^9*c^16*d^3 + 32440320*a^4*b^8*c^15*d^4 - 51904512*a^5*b^7*c^14*d^5 + 60555264*a^6*b^6*c^13*d^6 - 51904512*a^7*b^5*c^12*d^7 + 32440320*a^8*b^4*c^11*d^8 - 14417920*a^9*b^3*c^10*d^9 + 4325376*a^10*b^2*c^9*d^10 - 786432*a*b^11*c^18*d))^(1/4)*(3072*a^4*b^19*c^19*d^4 - 45056*a^5*b^18*c^18*d^5 + 292864*a^6*b^17*c^17*d^6 - 1115136*a^7*b^16*c^16*d^7 + 2745344*a^8*b^15*c^15*d^8 - 4483072*a^9*b^14*c^14*d^9 + 4595712*a^10*b^13*c^13*d^10 - 1993728*a^11*b^12*c^12*d^11 - 1993728*a^12*b^11*c^11*d^12 + 4595712*a^13*b^10*c^10*d^13 - 4483072*a^14*b^9*c^9*d^14 + 2745344*a^15*b^8*c^8*d^15 - 1115136*a^16*b^7*c^7*d^16 + 292864*a^17*b^6*c^6*d^17 - 45056*a^18*b^5*c^5*d^18 + 3072*a^19*b^4*c^4*d^19))/(a^4*b^8*c^12 + a^12*c^4*d^8 - 8*a^5*b^7*c^11*d - 8*a^11*b*c^5*d^7 + 28*a^6*b^6*c^10*d^2 - 56*a^7*b^5*c^9*d^3 + 70*a^8*b^4*c^8*d^4 - 56*a^9*b^3*c^7*d^5 + 28*a^10*b^2*c^6*d^6)))*1i + (x*(9801*a^8*b^9*d^17 + 9801*b^17*c^8*d^9 - 149094*a*b^16*c^7*d^10 - 149094*a^7*b^10*c*d^16 + 1001520*a^2*b^15*c^6*d^11 - 3484602*a^3*b^14*c^5*d^12 + 5769038*a^4*b^13*c^4*d^13 - 3484602*a^5*b^12*c^3*d^14 + 1001520*a^6*b^11*c^2*d^15)*1i)/(1024*(a^4*b^12*c^16 + a^16*c^4*d^12 - 12*a^5*b^11*c^15*d - 12*a^15*b*c^5*d^11 + 66*a^6*b^10*c^14*d^2 - 220*a^7*b^9*c^13*d^3 + 495*a^8*b^8*c^12*d^4 - 792*a^9*b^7*c^11*d^5 + 924*a^10*b^6*c^10*d^6 - 792*a^11*b^5*c^9*d^7 + 495*a^12*b^4*c^8*d^8 - 220*a^13*b^3*c^7*d^9 + 66*a^14*b^2*c^6*d^10))) - (-(81*a^4*d^11 + 14641*b^4*c^4*d^7 - 15972*a*b^3*c^3*d^8 + 6534*a^2*b^2*c^2*d^9 - 1188*a^3*b*c*d^10)/(65536*b^12*c^19 + 65536*a^12*c^7*d^12 - 786432*a^11*b*c^8*d^11 + 4325376*a^2*b^10*c^17*d^2 - 14417920*a^3*b^9*c^16*d^3 + 32440320*a^4*b^8*c^15*d^4 - 51904512*a^5*b^7*c^14*d^5 + 60555264*a^6*b^6*c^13*d^6 - 51904512*a^7*b^5*c^12*d^7 + 32440320*a^8*b^4*c^11*d^8 - 14417920*a^9*b^3*c^10*d^9 + 4325376*a^10*b^2*c^9*d^10 - 786432*a*b^11*c^18*d))^(1/4)*((-(81*a^4*d^11 + 14641*b^4*c^4*d^7 - 15972*a*b^3*c^3*d^8 + 6534*a^2*b^2*c^2*d^9 - 1188*a^3*b*c*d^10)/(65536*b^12*c^19 + 65536*a^12*c^7*d^12 - 786432*a^11*b*c^8*d^11 + 4325376*a^2*b^10*c^17*d^2 - 14417920*a^3*b^9*c^16*d^3 + 32440320*a^4*b^8*c^15*d^4 - 51904512*a^5*b^7*c^14*d^5 + 60555264*a^6*b^6*c^13*d^6 - 51904512*a^7*b^5*c^12*d^7 + 32440320*a^8*b^4*c^11*d^8 - 14417920*a^9*b^3*c^10*d^9 + 4325376*a^10*b^2*c^9*d^10 - 786432*a*b^11*c^18*d))^(1/4)*(((891*a^8*b^7*d^15)/64 + (891*b^15*c^8*d^7)/64 - (3105*a*b^14*c^7*d^8)/16 - (3105*a^7*b^8*c*d^14)/16 + (31509*a^2*b^13*c^6*d^9)/32 - (33069*a^3*b^12*c^5*d^10)/16 + (60307*a^4*b^11*c^4*d^11)/32 - (33069*a^5*b^10*c^3*d^12)/16 + (31509*a^6*b^9*c^2*d^13)/32)/(a^4*b^8*c^12 + a^12*c^4*d^8 - 8*a^5*b^7*c^11*d - 8*a^11*b*c^5*d^7 + 28*a^6*b^6*c^10*d^2 - 56*a^7*b^5*c^9*d^3 + 70*a^8*b^4*c^8*d^4 - 56*a^9*b^3*c^7*d^5 + 28*a^10*b^2*c^6*d^6) - (-(81*a^4*d^11 + 14641*b^4*c^4*d^7 - 15972*a*b^3*c^3*d^8 + 6534*a^2*b^2*c^2*d^9 - 1188*a^3*b*c*d^10)/(65536*b^12*c^19 + 65536*a^12*c^7*d^12 - 786432*a^11*b*c^8*d^11 + 4325376*a^2*b^10*c^17*d^2 - 14417920*a^3*b^9*c^16*d^3 + 32440320*a^4*b^8*c^15*d^4 - 51904512*a^5*b^7*c^14*d^5 + 60555264*a^6*b^6*c^13*d^6 - 51904512*a^7*b^5*c^12*d^7 + 32440320*a^8*b^4*c^11*d^8 - 14417920*a^9*b^3*c^10*d^9 + 4325376*a^10*b^2*c^9*d^10 - 786432*a*b^11*c^18*d))^(3/4)*((x*(589824*a^2*b^23*c^21*d^4 - 11403264*a^3*b^22*c^20*d^5 + 98762752*a^4*b^21*c^19*d^6 - 510394368*a^5*b^20*c^18*d^7 + 1766916096*a^6*b^19*c^17*d^8 - 4344840192*a^7*b^18*c^16*d^9 + 7796490240*a^8*b^17*c^15*d^10 - 10168369152*a^9*b^16*c^14*d^11 + 9007726592*a^10*b^15*c^13*d^12 - 3635478528*a^11*b^14*c^12*d^13 - 3635478528*a^12*b^13*c^11*d^14 + 9007726592*a^13*b^12*c^10*d^15 - 10168369152*a^14*b^11*c^9*d^16 + 7796490240*a^15*b^10*c^8*d^17 - 4344840192*a^16*b^9*c^7*d^18 + 1766916096*a^17*b^8*c^6*d^19 - 510394368*a^18*b^7*c^5*d^20 + 98762752*a^19*b^6*c^4*d^21 - 11403264*a^20*b^5*c^3*d^22 + 589824*a^21*b^4*c^2*d^23))/(1024*(a^4*b^12*c^16 + a^16*c^4*d^12 - 12*a^5*b^11*c^15*d - 12*a^15*b*c^5*d^11 + 66*a^6*b^10*c^14*d^2 - 220*a^7*b^9*c^13*d^3 + 495*a^8*b^8*c^12*d^4 - 792*a^9*b^7*c^11*d^5 + 924*a^10*b^6*c^10*d^6 - 792*a^11*b^5*c^9*d^7 + 495*a^12*b^4*c^8*d^8 - 220*a^13*b^3*c^7*d^9 + 66*a^14*b^2*c^6*d^10)) - ((-(81*a^4*d^11 + 14641*b^4*c^4*d^7 - 15972*a*b^3*c^3*d^8 + 6534*a^2*b^2*c^2*d^9 - 1188*a^3*b*c*d^10)/(65536*b^12*c^19 + 65536*a^12*c^7*d^12 - 786432*a^11*b*c^8*d^11 + 4325376*a^2*b^10*c^17*d^2 - 14417920*a^3*b^9*c^16*d^3 + 32440320*a^4*b^8*c^15*d^4 - 51904512*a^5*b^7*c^14*d^5 + 60555264*a^6*b^6*c^13*d^6 - 51904512*a^7*b^5*c^12*d^7 + 32440320*a^8*b^4*c^11*d^8 - 14417920*a^9*b^3*c^10*d^9 + 4325376*a^10*b^2*c^9*d^10 - 786432*a*b^11*c^18*d))^(1/4)*(3072*a^4*b^19*c^19*d^4 - 45056*a^5*b^18*c^18*d^5 + 292864*a^6*b^17*c^17*d^6 - 1115136*a^7*b^16*c^16*d^7 + 2745344*a^8*b^15*c^15*d^8 - 4483072*a^9*b^14*c^14*d^9 + 4595712*a^10*b^13*c^13*d^10 - 1993728*a^11*b^12*c^12*d^11 - 1993728*a^12*b^11*c^11*d^12 + 4595712*a^13*b^10*c^10*d^13 - 4483072*a^14*b^9*c^9*d^14 + 2745344*a^15*b^8*c^8*d^15 - 1115136*a^16*b^7*c^7*d^16 + 292864*a^17*b^6*c^6*d^17 - 45056*a^18*b^5*c^5*d^18 + 3072*a^19*b^4*c^4*d^19))/(a^4*b^8*c^12 + a^12*c^4*d^8 - 8*a^5*b^7*c^11*d - 8*a^11*b*c^5*d^7 + 28*a^6*b^6*c^10*d^2 - 56*a^7*b^5*c^9*d^3 + 70*a^8*b^4*c^8*d^4 - 56*a^9*b^3*c^7*d^5 + 28*a^10*b^2*c^6*d^6)))*1i - (x*(9801*a^8*b^9*d^17 + 9801*b^17*c^8*d^9 - 149094*a*b^16*c^7*d^10 - 149094*a^7*b^10*c*d^16 + 1001520*a^2*b^15*c^6*d^11 - 3484602*a^3*b^14*c^5*d^12 + 5769038*a^4*b^13*c^4*d^13 - 3484602*a^5*b^12*c^3*d^14 + 1001520*a^6*b^11*c^2*d^15)*1i)/(1024*(a^4*b^12*c^16 + a^16*c^4*d^12 - 12*a^5*b^11*c^15*d - 12*a^15*b*c^5*d^11 + 66*a^6*b^10*c^14*d^2 - 220*a^7*b^9*c^13*d^3 + 495*a^8*b^8*c^12*d^4 - 792*a^9*b^7*c^11*d^5 + 924*a^10*b^6*c^10*d^6 - 792*a^11*b^5*c^9*d^7 + 495*a^12*b^4*c^8*d^8 - 220*a^13*b^3*c^7*d^9 + 66*a^14*b^2*c^6*d^10))))/((-(81*a^4*d^11 + 14641*b^4*c^4*d^7 - 15972*a*b^3*c^3*d^8 + 6534*a^2*b^2*c^2*d^9 - 1188*a^3*b*c*d^10)/(65536*b^12*c^19 + 65536*a^12*c^7*d^12 - 786432*a^11*b*c^8*d^11 + 4325376*a^2*b^10*c^17*d^2 - 14417920*a^3*b^9*c^16*d^3 + 32440320*a^4*b^8*c^15*d^4 - 51904512*a^5*b^7*c^14*d^5 + 60555264*a^6*b^6*c^13*d^6 - 51904512*a^7*b^5*c^12*d^7 + 32440320*a^8*b^4*c^11*d^8 - 14417920*a^9*b^3*c^10*d^9 + 4325376*a^10*b^2*c^9*d^10 - 786432*a*b^11*c^18*d))^(1/4)*((-(81*a^4*d^11 + 14641*b^4*c^4*d^7 - 15972*a*b^3*c^3*d^8 + 6534*a^2*b^2*c^2*d^9 - 1188*a^3*b*c*d^10)/(65536*b^12*c^19 + 65536*a^12*c^7*d^12 - 786432*a^11*b*c^8*d^11 + 4325376*a^2*b^10*c^17*d^2 - 14417920*a^3*b^9*c^16*d^3 + 32440320*a^4*b^8*c^15*d^4 - 51904512*a^5*b^7*c^14*d^5 + 60555264*a^6*b^6*c^13*d^6 - 51904512*a^7*b^5*c^12*d^7 + 32440320*a^8*b^4*c^11*d^8 - 14417920*a^9*b^3*c^10*d^9 + 4325376*a^10*b^2*c^9*d^10 - 786432*a*b^11*c^18*d))^(1/4)*(((891*a^8*b^7*d^15)/64 + (891*b^15*c^8*d^7)/64 - (3105*a*b^14*c^7*d^8)/16 - (3105*a^7*b^8*c*d^14)/16 + (31509*a^2*b^13*c^6*d^9)/32 - (33069*a^3*b^12*c^5*d^10)/16 + (60307*a^4*b^11*c^4*d^11)/32 - (33069*a^5*b^10*c^3*d^12)/16 + (31509*a^6*b^9*c^2*d^13)/32)/(a^4*b^8*c^12 + a^12*c^4*d^8 - 8*a^5*b^7*c^11*d - 8*a^11*b*c^5*d^7 + 28*a^6*b^6*c^10*d^2 - 56*a^7*b^5*c^9*d^3 + 70*a^8*b^4*c^8*d^4 - 56*a^9*b^3*c^7*d^5 + 28*a^10*b^2*c^6*d^6) + (-(81*a^4*d^11 + 14641*b^4*c^4*d^7 - 15972*a*b^3*c^3*d^8 + 6534*a^2*b^2*c^2*d^9 - 1188*a^3*b*c*d^10)/(65536*b^12*c^19 + 65536*a^12*c^7*d^12 - 786432*a^11*b*c^8*d^11 + 4325376*a^2*b^10*c^17*d^2 - 14417920*a^3*b^9*c^16*d^3 + 32440320*a^4*b^8*c^15*d^4 - 51904512*a^5*b^7*c^14*d^5 + 60555264*a^6*b^6*c^13*d^6 - 51904512*a^7*b^5*c^12*d^7 + 32440320*a^8*b^4*c^11*d^8 - 14417920*a^9*b^3*c^10*d^9 + 4325376*a^10*b^2*c^9*d^10 - 786432*a*b^11*c^18*d))^(3/4)*((x*(589824*a^2*b^23*c^21*d^4 - 11403264*a^3*b^22*c^20*d^5 + 98762752*a^4*b^21*c^19*d^6 - 510394368*a^5*b^20*c^18*d^7 + 1766916096*a^6*b^19*c^17*d^8 - 4344840192*a^7*b^18*c^16*d^9 + 7796490240*a^8*b^17*c^15*d^10 - 10168369152*a^9*b^16*c^14*d^11 + 9007726592*a^10*b^15*c^13*d^12 - 3635478528*a^11*b^14*c^12*d^13 - 3635478528*a^12*b^13*c^11*d^14 + 9007726592*a^13*b^12*c^10*d^15 - 10168369152*a^14*b^11*c^9*d^16 + 7796490240*a^15*b^10*c^8*d^17 - 4344840192*a^16*b^9*c^7*d^18 + 1766916096*a^17*b^8*c^6*d^19 - 510394368*a^18*b^7*c^5*d^20 + 98762752*a^19*b^6*c^4*d^21 - 11403264*a^20*b^5*c^3*d^22 + 589824*a^21*b^4*c^2*d^23))/(1024*(a^4*b^12*c^16 + a^16*c^4*d^12 - 12*a^5*b^11*c^15*d - 12*a^15*b*c^5*d^11 + 66*a^6*b^10*c^14*d^2 - 220*a^7*b^9*c^13*d^3 + 495*a^8*b^8*c^12*d^4 - 792*a^9*b^7*c^11*d^5 + 924*a^10*b^6*c^10*d^6 - 792*a^11*b^5*c^9*d^7 + 495*a^12*b^4*c^8*d^8 - 220*a^13*b^3*c^7*d^9 + 66*a^14*b^2*c^6*d^10)) + ((-(81*a^4*d^11 + 14641*b^4*c^4*d^7 - 15972*a*b^3*c^3*d^8 + 6534*a^2*b^2*c^2*d^9 - 1188*a^3*b*c*d^10)/(65536*b^12*c^19 + 65536*a^12*c^7*d^12 - 786432*a^11*b*c^8*d^11 + 4325376*a^2*b^10*c^17*d^2 - 14417920*a^3*b^9*c^16*d^3 + 32440320*a^4*b^8*c^15*d^4 - 51904512*a^5*b^7*c^14*d^5 + 60555264*a^6*b^6*c^13*d^6 - 51904512*a^7*b^5*c^12*d^7 + 32440320*a^8*b^4*c^11*d^8 - 14417920*a^9*b^3*c^10*d^9 + 4325376*a^10*b^2*c^9*d^10 - 786432*a*b^11*c^18*d))^(1/4)*(3072*a^4*b^19*c^19*d^4 - 45056*a^5*b^18*c^18*d^5 + 292864*a^6*b^17*c^17*d^6 - 1115136*a^7*b^16*c^16*d^7 + 2745344*a^8*b^15*c^15*d^8 - 4483072*a^9*b^14*c^14*d^9 + 4595712*a^10*b^13*c^13*d^10 - 1993728*a^11*b^12*c^12*d^11 - 1993728*a^12*b^11*c^11*d^12 + 4595712*a^13*b^10*c^10*d^13 - 4483072*a^14*b^9*c^9*d^14 + 2745344*a^15*b^8*c^8*d^15 - 1115136*a^16*b^7*c^7*d^16 + 292864*a^17*b^6*c^6*d^17 - 45056*a^18*b^5*c^5*d^18 + 3072*a^19*b^4*c^4*d^19))/(a^4*b^8*c^12 + a^12*c^4*d^8 - 8*a^5*b^7*c^11*d - 8*a^11*b*c^5*d^7 + 28*a^6*b^6*c^10*d^2 - 56*a^7*b^5*c^9*d^3 + 70*a^8*b^4*c^8*d^4 - 56*a^9*b^3*c^7*d^5 + 28*a^10*b^2*c^6*d^6))) + (x*(9801*a^8*b^9*d^17 + 9801*b^17*c^8*d^9 - 149094*a*b^16*c^7*d^10 - 149094*a^7*b^10*c*d^16 + 1001520*a^2*b^15*c^6*d^11 - 3484602*a^3*b^14*c^5*d^12 + 5769038*a^4*b^13*c^4*d^13 - 3484602*a^5*b^12*c^3*d^14 + 1001520*a^6*b^11*c^2*d^15))/(1024*(a^4*b^12*c^16 + a^16*c^4*d^12 - 12*a^5*b^11*c^15*d - 12*a^15*b*c^5*d^11 + 66*a^6*b^10*c^14*d^2 - 220*a^7*b^9*c^13*d^3 + 495*a^8*b^8*c^12*d^4 - 792*a^9*b^7*c^11*d^5 + 924*a^10*b^6*c^10*d^6 - 792*a^11*b^5*c^9*d^7 + 495*a^12*b^4*c^8*d^8 - 220*a^13*b^3*c^7*d^9 + 66*a^14*b^2*c^6*d^10))) + (-(81*a^4*d^11 + 14641*b^4*c^4*d^7 - 15972*a*b^3*c^3*d^8 + 6534*a^2*b^2*c^2*d^9 - 1188*a^3*b*c*d^10)/(65536*b^12*c^19 + 65536*a^12*c^7*d^12 - 786432*a^11*b*c^8*d^11 + 4325376*a^2*b^10*c^17*d^2 - 14417920*a^3*b^9*c^16*d^3 + 32440320*a^4*b^8*c^15*d^4 - 51904512*a^5*b^7*c^14*d^5 + 60555264*a^6*b^6*c^13*d^6 - 51904512*a^7*b^5*c^12*d^7 + 32440320*a^8*b^4*c^11*d^8 - 14417920*a^9*b^3*c^10*d^9 + 4325376*a^10*b^2*c^9*d^10 - 786432*a*b^11*c^18*d))^(1/4)*((-(81*a^4*d^11 + 14641*b^4*c^4*d^7 - 15972*a*b^3*c^3*d^8 + 6534*a^2*b^2*c^2*d^9 - 1188*a^3*b*c*d^10)/(65536*b^12*c^19 + 65536*a^12*c^7*d^12 - 786432*a^11*b*c^8*d^11 + 4325376*a^2*b^10*c^17*d^2 - 14417920*a^3*b^9*c^16*d^3 + 32440320*a^4*b^8*c^15*d^4 - 51904512*a^5*b^7*c^14*d^5 + 60555264*a^6*b^6*c^13*d^6 - 51904512*a^7*b^5*c^12*d^7 + 32440320*a^8*b^4*c^11*d^8 - 14417920*a^9*b^3*c^10*d^9 + 4325376*a^10*b^2*c^9*d^10 - 786432*a*b^11*c^18*d))^(1/4)*(((891*a^8*b^7*d^15)/64 + (891*b^15*c^8*d^7)/64 - (3105*a*b^14*c^7*d^8)/16 - (3105*a^7*b^8*c*d^14)/16 + (31509*a^2*b^13*c^6*d^9)/32 - (33069*a^3*b^12*c^5*d^10)/16 + (60307*a^4*b^11*c^4*d^11)/32 - (33069*a^5*b^10*c^3*d^12)/16 + (31509*a^6*b^9*c^2*d^13)/32)/(a^4*b^8*c^12 + a^12*c^4*d^8 - 8*a^5*b^7*c^11*d - 8*a^11*b*c^5*d^7 + 28*a^6*b^6*c^10*d^2 - 56*a^7*b^5*c^9*d^3 + 70*a^8*b^4*c^8*d^4 - 56*a^9*b^3*c^7*d^5 + 28*a^10*b^2*c^6*d^6) - (-(81*a^4*d^11 + 14641*b^4*c^4*d^7 - 15972*a*b^3*c^3*d^8 + 6534*a^2*b^2*c^2*d^9 - 1188*a^3*b*c*d^10)/(65536*b^12*c^19 + 65536*a^12*c^7*d^12 - 786432*a^11*b*c^8*d^11 + 4325376*a^2*b^10*c^17*d^2 - 14417920*a^3*b^9*c^16*d^3 + 32440320*a^4*b^8*c^15*d^4 - 51904512*a^5*b^7*c^14*d^5 + 60555264*a^6*b^6*c^13*d^6 - 51904512*a^7*b^5*c^12*d^7 + 32440320*a^8*b^4*c^11*d^8 - 14417920*a^9*b^3*c^10*d^9 + 4325376*a^10*b^2*c^9*d^10 - 786432*a*b^11*c^18*d))^(3/4)*((x*(589824*a^2*b^23*c^21*d^4 - 11403264*a^3*b^22*c^20*d^5 + 98762752*a^4*b^21*c^19*d^6 - 510394368*a^5*b^20*c^18*d^7 + 1766916096*a^6*b^19*c^17*d^8 - 4344840192*a^7*b^18*c^16*d^9 + 7796490240*a^8*b^17*c^15*d^10 - 10168369152*a^9*b^16*c^14*d^11 + 9007726592*a^10*b^15*c^13*d^12 - 3635478528*a^11*b^14*c^12*d^13 - 3635478528*a^12*b^13*c^11*d^14 + 9007726592*a^13*b^12*c^10*d^15 - 10168369152*a^14*b^11*c^9*d^16 + 7796490240*a^15*b^10*c^8*d^17 - 4344840192*a^16*b^9*c^7*d^18 + 1766916096*a^17*b^8*c^6*d^19 - 510394368*a^18*b^7*c^5*d^20 + 98762752*a^19*b^6*c^4*d^21 - 11403264*a^20*b^5*c^3*d^22 + 589824*a^21*b^4*c^2*d^23))/(1024*(a^4*b^12*c^16 + a^16*c^4*d^12 - 12*a^5*b^11*c^15*d - 12*a^15*b*c^5*d^11 + 66*a^6*b^10*c^14*d^2 - 220*a^7*b^9*c^13*d^3 + 495*a^8*b^8*c^12*d^4 - 792*a^9*b^7*c^11*d^5 + 924*a^10*b^6*c^10*d^6 - 792*a^11*b^5*c^9*d^7 + 495*a^12*b^4*c^8*d^8 - 220*a^13*b^3*c^7*d^9 + 66*a^14*b^2*c^6*d^10)) - ((-(81*a^4*d^11 + 14641*b^4*c^4*d^7 - 15972*a*b^3*c^3*d^8 + 6534*a^2*b^2*c^2*d^9 - 1188*a^3*b*c*d^10)/(65536*b^12*c^19 + 65536*a^12*c^7*d^12 - 786432*a^11*b*c^8*d^11 + 4325376*a^2*b^10*c^17*d^2 - 14417920*a^3*b^9*c^16*d^3 + 32440320*a^4*b^8*c^15*d^4 - 51904512*a^5*b^7*c^14*d^5 + 60555264*a^6*b^6*c^13*d^6 - 51904512*a^7*b^5*c^12*d^7 + 32440320*a^8*b^4*c^11*d^8 - 14417920*a^9*b^3*c^10*d^9 + 4325376*a^10*b^2*c^9*d^10 - 786432*a*b^11*c^18*d))^(1/4)*(3072*a^4*b^19*c^19*d^4 - 45056*a^5*b^18*c^18*d^5 + 292864*a^6*b^17*c^17*d^6 - 1115136*a^7*b^16*c^16*d^7 + 2745344*a^8*b^15*c^15*d^8 - 4483072*a^9*b^14*c^14*d^9 + 4595712*a^10*b^13*c^13*d^10 - 1993728*a^11*b^12*c^12*d^11 - 1993728*a^12*b^11*c^11*d^12 + 4595712*a^13*b^10*c^10*d^13 - 4483072*a^14*b^9*c^9*d^14 + 2745344*a^15*b^8*c^8*d^15 - 1115136*a^16*b^7*c^7*d^16 + 292864*a^17*b^6*c^6*d^17 - 45056*a^18*b^5*c^5*d^18 + 3072*a^19*b^4*c^4*d^19))/(a^4*b^8*c^12 + a^12*c^4*d^8 - 8*a^5*b^7*c^11*d - 8*a^11*b*c^5*d^7 + 28*a^6*b^6*c^10*d^2 - 56*a^7*b^5*c^9*d^3 + 70*a^8*b^4*c^8*d^4 - 56*a^9*b^3*c^7*d^5 + 28*a^10*b^2*c^6*d^6))) - (x*(9801*a^8*b^9*d^17 + 9801*b^17*c^8*d^9 - 149094*a*b^16*c^7*d^10 - 149094*a^7*b^10*c*d^16 + 1001520*a^2*b^15*c^6*d^11 - 3484602*a^3*b^14*c^5*d^12 + 5769038*a^4*b^13*c^4*d^13 - 3484602*a^5*b^12*c^3*d^14 + 1001520*a^6*b^11*c^2*d^15))/(1024*(a^4*b^12*c^16 + a^16*c^4*d^12 - 12*a^5*b^11*c^15*d - 12*a^15*b*c^5*d^11 + 66*a^6*b^10*c^14*d^2 - 220*a^7*b^9*c^13*d^3 + 495*a^8*b^8*c^12*d^4 - 792*a^9*b^7*c^11*d^5 + 924*a^10*b^6*c^10*d^6 - 792*a^11*b^5*c^9*d^7 + 495*a^12*b^4*c^8*d^8 - 220*a^13*b^3*c^7*d^9 + 66*a^14*b^2*c^6*d^10)))))*(-(81*a^4*d^11 + 14641*b^4*c^4*d^7 - 15972*a*b^3*c^3*d^8 + 6534*a^2*b^2*c^2*d^9 - 1188*a^3*b*c*d^10)/(65536*b^12*c^19 + 65536*a^12*c^7*d^12 - 786432*a^11*b*c^8*d^11 + 4325376*a^2*b^10*c^17*d^2 - 14417920*a^3*b^9*c^16*d^3 + 32440320*a^4*b^8*c^15*d^4 - 51904512*a^5*b^7*c^14*d^5 + 60555264*a^6*b^6*c^13*d^6 - 51904512*a^7*b^5*c^12*d^7 + 32440320*a^8*b^4*c^11*d^8 - 14417920*a^9*b^3*c^10*d^9 + 4325376*a^10*b^2*c^9*d^10 - 786432*a*b^11*c^18*d))^(1/4)*2i + 2*atan(((-(81*a^4*d^11 + 14641*b^4*c^4*d^7 - 15972*a*b^3*c^3*d^8 + 6534*a^2*b^2*c^2*d^9 - 1188*a^3*b*c*d^10)/(65536*b^12*c^19 + 65536*a^12*c^7*d^12 - 786432*a^11*b*c^8*d^11 + 4325376*a^2*b^10*c^17*d^2 - 14417920*a^3*b^9*c^16*d^3 + 32440320*a^4*b^8*c^15*d^4 - 51904512*a^5*b^7*c^14*d^5 + 60555264*a^6*b^6*c^13*d^6 - 51904512*a^7*b^5*c^12*d^7 + 32440320*a^8*b^4*c^11*d^8 - 14417920*a^9*b^3*c^10*d^9 + 4325376*a^10*b^2*c^9*d^10 - 786432*a*b^11*c^18*d))^(1/4)*((-(81*a^4*d^11 + 14641*b^4*c^4*d^7 - 15972*a*b^3*c^3*d^8 + 6534*a^2*b^2*c^2*d^9 - 1188*a^3*b*c*d^10)/(65536*b^12*c^19 + 65536*a^12*c^7*d^12 - 786432*a^11*b*c^8*d^11 + 4325376*a^2*b^10*c^17*d^2 - 14417920*a^3*b^9*c^16*d^3 + 32440320*a^4*b^8*c^15*d^4 - 51904512*a^5*b^7*c^14*d^5 + 60555264*a^6*b^6*c^13*d^6 - 51904512*a^7*b^5*c^12*d^7 + 32440320*a^8*b^4*c^11*d^8 - 14417920*a^9*b^3*c^10*d^9 + 4325376*a^10*b^2*c^9*d^10 - 786432*a*b^11*c^18*d))^(1/4)*((((891*a^8*b^7*d^15)/64 + (891*b^15*c^8*d^7)/64 - (3105*a*b^14*c^7*d^8)/16 - (3105*a^7*b^8*c*d^14)/16 + (31509*a^2*b^13*c^6*d^9)/32 - (33069*a^3*b^12*c^5*d^10)/16 + (60307*a^4*b^11*c^4*d^11)/32 - (33069*a^5*b^10*c^3*d^12)/16 + (31509*a^6*b^9*c^2*d^13)/32)*1i)/(a^4*b^8*c^12 + a^12*c^4*d^8 - 8*a^5*b^7*c^11*d - 8*a^11*b*c^5*d^7 + 28*a^6*b^6*c^10*d^2 - 56*a^7*b^5*c^9*d^3 + 70*a^8*b^4*c^8*d^4 - 56*a^9*b^3*c^7*d^5 + 28*a^10*b^2*c^6*d^6) + (-(81*a^4*d^11 + 14641*b^4*c^4*d^7 - 15972*a*b^3*c^3*d^8 + 6534*a^2*b^2*c^2*d^9 - 1188*a^3*b*c*d^10)/(65536*b^12*c^19 + 65536*a^12*c^7*d^12 - 786432*a^11*b*c^8*d^11 + 4325376*a^2*b^10*c^17*d^2 - 14417920*a^3*b^9*c^16*d^3 + 32440320*a^4*b^8*c^15*d^4 - 51904512*a^5*b^7*c^14*d^5 + 60555264*a^6*b^6*c^13*d^6 - 51904512*a^7*b^5*c^12*d^7 + 32440320*a^8*b^4*c^11*d^8 - 14417920*a^9*b^3*c^10*d^9 + 4325376*a^10*b^2*c^9*d^10 - 786432*a*b^11*c^18*d))^(3/4)*((x*(589824*a^2*b^23*c^21*d^4 - 11403264*a^3*b^22*c^20*d^5 + 98762752*a^4*b^21*c^19*d^6 - 510394368*a^5*b^20*c^18*d^7 + 1766916096*a^6*b^19*c^17*d^8 - 4344840192*a^7*b^18*c^16*d^9 + 7796490240*a^8*b^17*c^15*d^10 - 10168369152*a^9*b^16*c^14*d^11 + 9007726592*a^10*b^15*c^13*d^12 - 3635478528*a^11*b^14*c^12*d^13 - 3635478528*a^12*b^13*c^11*d^14 + 9007726592*a^13*b^12*c^10*d^15 - 10168369152*a^14*b^11*c^9*d^16 + 7796490240*a^15*b^10*c^8*d^17 - 4344840192*a^16*b^9*c^7*d^18 + 1766916096*a^17*b^8*c^6*d^19 - 510394368*a^18*b^7*c^5*d^20 + 98762752*a^19*b^6*c^4*d^21 - 11403264*a^20*b^5*c^3*d^22 + 589824*a^21*b^4*c^2*d^23)*1i)/(1024*(a^4*b^12*c^16 + a^16*c^4*d^12 - 12*a^5*b^11*c^15*d - 12*a^15*b*c^5*d^11 + 66*a^6*b^10*c^14*d^2 - 220*a^7*b^9*c^13*d^3 + 495*a^8*b^8*c^12*d^4 - 792*a^9*b^7*c^11*d^5 + 924*a^10*b^6*c^10*d^6 - 792*a^11*b^5*c^9*d^7 + 495*a^12*b^4*c^8*d^8 - 220*a^13*b^3*c^7*d^9 + 66*a^14*b^2*c^6*d^10)) + ((-(81*a^4*d^11 + 14641*b^4*c^4*d^7 - 15972*a*b^3*c^3*d^8 + 6534*a^2*b^2*c^2*d^9 - 1188*a^3*b*c*d^10)/(65536*b^12*c^19 + 65536*a^12*c^7*d^12 - 786432*a^11*b*c^8*d^11 + 4325376*a^2*b^10*c^17*d^2 - 14417920*a^3*b^9*c^16*d^3 + 32440320*a^4*b^8*c^15*d^4 - 51904512*a^5*b^7*c^14*d^5 + 60555264*a^6*b^6*c^13*d^6 - 51904512*a^7*b^5*c^12*d^7 + 32440320*a^8*b^4*c^11*d^8 - 14417920*a^9*b^3*c^10*d^9 + 4325376*a^10*b^2*c^9*d^10 - 786432*a*b^11*c^18*d))^(1/4)*(3072*a^4*b^19*c^19*d^4 - 45056*a^5*b^18*c^18*d^5 + 292864*a^6*b^17*c^17*d^6 - 1115136*a^7*b^16*c^16*d^7 + 2745344*a^8*b^15*c^15*d^8 - 4483072*a^9*b^14*c^14*d^9 + 4595712*a^10*b^13*c^13*d^10 - 1993728*a^11*b^12*c^12*d^11 - 1993728*a^12*b^11*c^11*d^12 + 4595712*a^13*b^10*c^10*d^13 - 4483072*a^14*b^9*c^9*d^14 + 2745344*a^15*b^8*c^8*d^15 - 1115136*a^16*b^7*c^7*d^16 + 292864*a^17*b^6*c^6*d^17 - 45056*a^18*b^5*c^5*d^18 + 3072*a^19*b^4*c^4*d^19))/(a^4*b^8*c^12 + a^12*c^4*d^8 - 8*a^5*b^7*c^11*d - 8*a^11*b*c^5*d^7 + 28*a^6*b^6*c^10*d^2 - 56*a^7*b^5*c^9*d^3 + 70*a^8*b^4*c^8*d^4 - 56*a^9*b^3*c^7*d^5 + 28*a^10*b^2*c^6*d^6))*1i) - (x*(9801*a^8*b^9*d^17 + 9801*b^17*c^8*d^9 - 149094*a*b^16*c^7*d^10 - 149094*a^7*b^10*c*d^16 + 1001520*a^2*b^15*c^6*d^11 - 3484602*a^3*b^14*c^5*d^12 + 5769038*a^4*b^13*c^4*d^13 - 3484602*a^5*b^12*c^3*d^14 + 1001520*a^6*b^11*c^2*d^15))/(1024*(a^4*b^12*c^16 + a^16*c^4*d^12 - 12*a^5*b^11*c^15*d - 12*a^15*b*c^5*d^11 + 66*a^6*b^10*c^14*d^2 - 220*a^7*b^9*c^13*d^3 + 495*a^8*b^8*c^12*d^4 - 792*a^9*b^7*c^11*d^5 + 924*a^10*b^6*c^10*d^6 - 792*a^11*b^5*c^9*d^7 + 495*a^12*b^4*c^8*d^8 - 220*a^13*b^3*c^7*d^9 + 66*a^14*b^2*c^6*d^10))) - (-(81*a^4*d^11 + 14641*b^4*c^4*d^7 - 15972*a*b^3*c^3*d^8 + 6534*a^2*b^2*c^2*d^9 - 1188*a^3*b*c*d^10)/(65536*b^12*c^19 + 65536*a^12*c^7*d^12 - 786432*a^11*b*c^8*d^11 + 4325376*a^2*b^10*c^17*d^2 - 14417920*a^3*b^9*c^16*d^3 + 32440320*a^4*b^8*c^15*d^4 - 51904512*a^5*b^7*c^14*d^5 + 60555264*a^6*b^6*c^13*d^6 - 51904512*a^7*b^5*c^12*d^7 + 32440320*a^8*b^4*c^11*d^8 - 14417920*a^9*b^3*c^10*d^9 + 4325376*a^10*b^2*c^9*d^10 - 786432*a*b^11*c^18*d))^(1/4)*((-(81*a^4*d^11 + 14641*b^4*c^4*d^7 - 15972*a*b^3*c^3*d^8 + 6534*a^2*b^2*c^2*d^9 - 1188*a^3*b*c*d^10)/(65536*b^12*c^19 + 65536*a^12*c^7*d^12 - 786432*a^11*b*c^8*d^11 + 4325376*a^2*b^10*c^17*d^2 - 14417920*a^3*b^9*c^16*d^3 + 32440320*a^4*b^8*c^15*d^4 - 51904512*a^5*b^7*c^14*d^5 + 60555264*a^6*b^6*c^13*d^6 - 51904512*a^7*b^5*c^12*d^7 + 32440320*a^8*b^4*c^11*d^8 - 14417920*a^9*b^3*c^10*d^9 + 4325376*a^10*b^2*c^9*d^10 - 786432*a*b^11*c^18*d))^(1/4)*((((891*a^8*b^7*d^15)/64 + (891*b^15*c^8*d^7)/64 - (3105*a*b^14*c^7*d^8)/16 - (3105*a^7*b^8*c*d^14)/16 + (31509*a^2*b^13*c^6*d^9)/32 - (33069*a^3*b^12*c^5*d^10)/16 + (60307*a^4*b^11*c^4*d^11)/32 - (33069*a^5*b^10*c^3*d^12)/16 + (31509*a^6*b^9*c^2*d^13)/32)*1i)/(a^4*b^8*c^12 + a^12*c^4*d^8 - 8*a^5*b^7*c^11*d - 8*a^11*b*c^5*d^7 + 28*a^6*b^6*c^10*d^2 - 56*a^7*b^5*c^9*d^3 + 70*a^8*b^4*c^8*d^4 - 56*a^9*b^3*c^7*d^5 + 28*a^10*b^2*c^6*d^6) - (-(81*a^4*d^11 + 14641*b^4*c^4*d^7 - 15972*a*b^3*c^3*d^8 + 6534*a^2*b^2*c^2*d^9 - 1188*a^3*b*c*d^10)/(65536*b^12*c^19 + 65536*a^12*c^7*d^12 - 786432*a^11*b*c^8*d^11 + 4325376*a^2*b^10*c^17*d^2 - 14417920*a^3*b^9*c^16*d^3 + 32440320*a^4*b^8*c^15*d^4 - 51904512*a^5*b^7*c^14*d^5 + 60555264*a^6*b^6*c^13*d^6 - 51904512*a^7*b^5*c^12*d^7 + 32440320*a^8*b^4*c^11*d^8 - 14417920*a^9*b^3*c^10*d^9 + 4325376*a^10*b^2*c^9*d^10 - 786432*a*b^11*c^18*d))^(3/4)*((x*(589824*a^2*b^23*c^21*d^4 - 11403264*a^3*b^22*c^20*d^5 + 98762752*a^4*b^21*c^19*d^6 - 510394368*a^5*b^20*c^18*d^7 + 1766916096*a^6*b^19*c^17*d^8 - 4344840192*a^7*b^18*c^16*d^9 + 7796490240*a^8*b^17*c^15*d^10 - 10168369152*a^9*b^16*c^14*d^11 + 9007726592*a^10*b^15*c^13*d^12 - 3635478528*a^11*b^14*c^12*d^13 - 3635478528*a^12*b^13*c^11*d^14 + 9007726592*a^13*b^12*c^10*d^15 - 10168369152*a^14*b^11*c^9*d^16 + 7796490240*a^15*b^10*c^8*d^17 - 4344840192*a^16*b^9*c^7*d^18 + 1766916096*a^17*b^8*c^6*d^19 - 510394368*a^18*b^7*c^5*d^20 + 98762752*a^19*b^6*c^4*d^21 - 11403264*a^20*b^5*c^3*d^22 + 589824*a^21*b^4*c^2*d^23)*1i)/(1024*(a^4*b^12*c^16 + a^16*c^4*d^12 - 12*a^5*b^11*c^15*d - 12*a^15*b*c^5*d^11 + 66*a^6*b^10*c^14*d^2 - 220*a^7*b^9*c^13*d^3 + 495*a^8*b^8*c^12*d^4 - 792*a^9*b^7*c^11*d^5 + 924*a^10*b^6*c^10*d^6 - 792*a^11*b^5*c^9*d^7 + 495*a^12*b^4*c^8*d^8 - 220*a^13*b^3*c^7*d^9 + 66*a^14*b^2*c^6*d^10)) - ((-(81*a^4*d^11 + 14641*b^4*c^4*d^7 - 15972*a*b^3*c^3*d^8 + 6534*a^2*b^2*c^2*d^9 - 1188*a^3*b*c*d^10)/(65536*b^12*c^19 + 65536*a^12*c^7*d^12 - 786432*a^11*b*c^8*d^11 + 4325376*a^2*b^10*c^17*d^2 - 14417920*a^3*b^9*c^16*d^3 + 32440320*a^4*b^8*c^15*d^4 - 51904512*a^5*b^7*c^14*d^5 + 60555264*a^6*b^6*c^13*d^6 - 51904512*a^7*b^5*c^12*d^7 + 32440320*a^8*b^4*c^11*d^8 - 14417920*a^9*b^3*c^10*d^9 + 4325376*a^10*b^2*c^9*d^10 - 786432*a*b^11*c^18*d))^(1/4)*(3072*a^4*b^19*c^19*d^4 - 45056*a^5*b^18*c^18*d^5 + 292864*a^6*b^17*c^17*d^6 - 1115136*a^7*b^16*c^16*d^7 + 2745344*a^8*b^15*c^15*d^8 - 4483072*a^9*b^14*c^14*d^9 + 4595712*a^10*b^13*c^13*d^10 - 1993728*a^11*b^12*c^12*d^11 - 1993728*a^12*b^11*c^11*d^12 + 4595712*a^13*b^10*c^10*d^13 - 4483072*a^14*b^9*c^9*d^14 + 2745344*a^15*b^8*c^8*d^15 - 1115136*a^16*b^7*c^7*d^16 + 292864*a^17*b^6*c^6*d^17 - 45056*a^18*b^5*c^5*d^18 + 3072*a^19*b^4*c^4*d^19))/(a^4*b^8*c^12 + a^12*c^4*d^8 - 8*a^5*b^7*c^11*d - 8*a^11*b*c^5*d^7 + 28*a^6*b^6*c^10*d^2 - 56*a^7*b^5*c^9*d^3 + 70*a^8*b^4*c^8*d^4 - 56*a^9*b^3*c^7*d^5 + 28*a^10*b^2*c^6*d^6))*1i) + (x*(9801*a^8*b^9*d^17 + 9801*b^17*c^8*d^9 - 149094*a*b^16*c^7*d^10 - 149094*a^7*b^10*c*d^16 + 1001520*a^2*b^15*c^6*d^11 - 3484602*a^3*b^14*c^5*d^12 + 5769038*a^4*b^13*c^4*d^13 - 3484602*a^5*b^12*c^3*d^14 + 1001520*a^6*b^11*c^2*d^15))/(1024*(a^4*b^12*c^16 + a^16*c^4*d^12 - 12*a^5*b^11*c^15*d - 12*a^15*b*c^5*d^11 + 66*a^6*b^10*c^14*d^2 - 220*a^7*b^9*c^13*d^3 + 495*a^8*b^8*c^12*d^4 - 792*a^9*b^7*c^11*d^5 + 924*a^10*b^6*c^10*d^6 - 792*a^11*b^5*c^9*d^7 + 495*a^12*b^4*c^8*d^8 - 220*a^13*b^3*c^7*d^9 + 66*a^14*b^2*c^6*d^10))))/((-(81*a^4*d^11 + 14641*b^4*c^4*d^7 - 15972*a*b^3*c^3*d^8 + 6534*a^2*b^2*c^2*d^9 - 1188*a^3*b*c*d^10)/(65536*b^12*c^19 + 65536*a^12*c^7*d^12 - 786432*a^11*b*c^8*d^11 + 4325376*a^2*b^10*c^17*d^2 - 14417920*a^3*b^9*c^16*d^3 + 32440320*a^4*b^8*c^15*d^4 - 51904512*a^5*b^7*c^14*d^5 + 60555264*a^6*b^6*c^13*d^6 - 51904512*a^7*b^5*c^12*d^7 + 32440320*a^8*b^4*c^11*d^8 - 14417920*a^9*b^3*c^10*d^9 + 4325376*a^10*b^2*c^9*d^10 - 786432*a*b^11*c^18*d))^(1/4)*((-(81*a^4*d^11 + 14641*b^4*c^4*d^7 - 15972*a*b^3*c^3*d^8 + 6534*a^2*b^2*c^2*d^9 - 1188*a^3*b*c*d^10)/(65536*b^12*c^19 + 65536*a^12*c^7*d^12 - 786432*a^11*b*c^8*d^11 + 4325376*a^2*b^10*c^17*d^2 - 14417920*a^3*b^9*c^16*d^3 + 32440320*a^4*b^8*c^15*d^4 - 51904512*a^5*b^7*c^14*d^5 + 60555264*a^6*b^6*c^13*d^6 - 51904512*a^7*b^5*c^12*d^7 + 32440320*a^8*b^4*c^11*d^8 - 14417920*a^9*b^3*c^10*d^9 + 4325376*a^10*b^2*c^9*d^10 - 786432*a*b^11*c^18*d))^(1/4)*((((891*a^8*b^7*d^15)/64 + (891*b^15*c^8*d^7)/64 - (3105*a*b^14*c^7*d^8)/16 - (3105*a^7*b^8*c*d^14)/16 + (31509*a^2*b^13*c^6*d^9)/32 - (33069*a^3*b^12*c^5*d^10)/16 + (60307*a^4*b^11*c^4*d^11)/32 - (33069*a^5*b^10*c^3*d^12)/16 + (31509*a^6*b^9*c^2*d^13)/32)*1i)/(a^4*b^8*c^12 + a^12*c^4*d^8 - 8*a^5*b^7*c^11*d - 8*a^11*b*c^5*d^7 + 28*a^6*b^6*c^10*d^2 - 56*a^7*b^5*c^9*d^3 + 70*a^8*b^4*c^8*d^4 - 56*a^9*b^3*c^7*d^5 + 28*a^10*b^2*c^6*d^6) + (-(81*a^4*d^11 + 14641*b^4*c^4*d^7 - 15972*a*b^3*c^3*d^8 + 6534*a^2*b^2*c^2*d^9 - 1188*a^3*b*c*d^10)/(65536*b^12*c^19 + 65536*a^12*c^7*d^12 - 786432*a^11*b*c^8*d^11 + 4325376*a^2*b^10*c^17*d^2 - 14417920*a^3*b^9*c^16*d^3 + 32440320*a^4*b^8*c^15*d^4 - 51904512*a^5*b^7*c^14*d^5 + 60555264*a^6*b^6*c^13*d^6 - 51904512*a^7*b^5*c^12*d^7 + 32440320*a^8*b^4*c^11*d^8 - 14417920*a^9*b^3*c^10*d^9 + 4325376*a^10*b^2*c^9*d^10 - 786432*a*b^11*c^18*d))^(3/4)*((x*(589824*a^2*b^23*c^21*d^4 - 11403264*a^3*b^22*c^20*d^5 + 98762752*a^4*b^21*c^19*d^6 - 510394368*a^5*b^20*c^18*d^7 + 1766916096*a^6*b^19*c^17*d^8 - 4344840192*a^7*b^18*c^16*d^9 + 7796490240*a^8*b^17*c^15*d^10 - 10168369152*a^9*b^16*c^14*d^11 + 9007726592*a^10*b^15*c^13*d^12 - 3635478528*a^11*b^14*c^12*d^13 - 3635478528*a^12*b^13*c^11*d^14 + 9007726592*a^13*b^12*c^10*d^15 - 10168369152*a^14*b^11*c^9*d^16 + 7796490240*a^15*b^10*c^8*d^17 - 4344840192*a^16*b^9*c^7*d^18 + 1766916096*a^17*b^8*c^6*d^19 - 510394368*a^18*b^7*c^5*d^20 + 98762752*a^19*b^6*c^4*d^21 - 11403264*a^20*b^5*c^3*d^22 + 589824*a^21*b^4*c^2*d^23)*1i)/(1024*(a^4*b^12*c^16 + a^16*c^4*d^12 - 12*a^5*b^11*c^15*d - 12*a^15*b*c^5*d^11 + 66*a^6*b^10*c^14*d^2 - 220*a^7*b^9*c^13*d^3 + 495*a^8*b^8*c^12*d^4 - 792*a^9*b^7*c^11*d^5 + 924*a^10*b^6*c^10*d^6 - 792*a^11*b^5*c^9*d^7 + 495*a^12*b^4*c^8*d^8 - 220*a^13*b^3*c^7*d^9 + 66*a^14*b^2*c^6*d^10)) + ((-(81*a^4*d^11 + 14641*b^4*c^4*d^7 - 15972*a*b^3*c^3*d^8 + 6534*a^2*b^2*c^2*d^9 - 1188*a^3*b*c*d^10)/(65536*b^12*c^19 + 65536*a^12*c^7*d^12 - 786432*a^11*b*c^8*d^11 + 4325376*a^2*b^10*c^17*d^2 - 14417920*a^3*b^9*c^16*d^3 + 32440320*a^4*b^8*c^15*d^4 - 51904512*a^5*b^7*c^14*d^5 + 60555264*a^6*b^6*c^13*d^6 - 51904512*a^7*b^5*c^12*d^7 + 32440320*a^8*b^4*c^11*d^8 - 14417920*a^9*b^3*c^10*d^9 + 4325376*a^10*b^2*c^9*d^10 - 786432*a*b^11*c^18*d))^(1/4)*(3072*a^4*b^19*c^19*d^4 - 45056*a^5*b^18*c^18*d^5 + 292864*a^6*b^17*c^17*d^6 - 1115136*a^7*b^16*c^16*d^7 + 2745344*a^8*b^15*c^15*d^8 - 4483072*a^9*b^14*c^14*d^9 + 4595712*a^10*b^13*c^13*d^10 - 1993728*a^11*b^12*c^12*d^11 - 1993728*a^12*b^11*c^11*d^12 + 4595712*a^13*b^10*c^10*d^13 - 4483072*a^14*b^9*c^9*d^14 + 2745344*a^15*b^8*c^8*d^15 - 1115136*a^16*b^7*c^7*d^16 + 292864*a^17*b^6*c^6*d^17 - 45056*a^18*b^5*c^5*d^18 + 3072*a^19*b^4*c^4*d^19))/(a^4*b^8*c^12 + a^12*c^4*d^8 - 8*a^5*b^7*c^11*d - 8*a^11*b*c^5*d^7 + 28*a^6*b^6*c^10*d^2 - 56*a^7*b^5*c^9*d^3 + 70*a^8*b^4*c^8*d^4 - 56*a^9*b^3*c^7*d^5 + 28*a^10*b^2*c^6*d^6))*1i)*1i - (x*(9801*a^8*b^9*d^17 + 9801*b^17*c^8*d^9 - 149094*a*b^16*c^7*d^10 - 149094*a^7*b^10*c*d^16 + 1001520*a^2*b^15*c^6*d^11 - 3484602*a^3*b^14*c^5*d^12 + 5769038*a^4*b^13*c^4*d^13 - 3484602*a^5*b^12*c^3*d^14 + 1001520*a^6*b^11*c^2*d^15)*1i)/(1024*(a^4*b^12*c^16 + a^16*c^4*d^12 - 12*a^5*b^11*c^15*d - 12*a^15*b*c^5*d^11 + 66*a^6*b^10*c^14*d^2 - 220*a^7*b^9*c^13*d^3 + 495*a^8*b^8*c^12*d^4 - 792*a^9*b^7*c^11*d^5 + 924*a^10*b^6*c^10*d^6 - 792*a^11*b^5*c^9*d^7 + 495*a^12*b^4*c^8*d^8 - 220*a^13*b^3*c^7*d^9 + 66*a^14*b^2*c^6*d^10))) + (-(81*a^4*d^11 + 14641*b^4*c^4*d^7 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(33069*a^3*b^12*c^5*d^10)/16 + (60307*a^4*b^11*c^4*d^11)/32 - (33069*a^5*b^10*c^3*d^12)/16 + (31509*a^6*b^9*c^2*d^13)/32)*1i)/(a^4*b^8*c^12 + a^12*c^4*d^8 - 8*a^5*b^7*c^11*d - 8*a^11*b*c^5*d^7 + 28*a^6*b^6*c^10*d^2 - 56*a^7*b^5*c^9*d^3 + 70*a^8*b^4*c^8*d^4 - 56*a^9*b^3*c^7*d^5 + 28*a^10*b^2*c^6*d^6) - (-(81*a^4*d^11 + 14641*b^4*c^4*d^7 - 15972*a*b^3*c^3*d^8 + 6534*a^2*b^2*c^2*d^9 - 1188*a^3*b*c*d^10)/(65536*b^12*c^19 + 65536*a^12*c^7*d^12 - 786432*a^11*b*c^8*d^11 + 4325376*a^2*b^10*c^17*d^2 - 14417920*a^3*b^9*c^16*d^3 + 32440320*a^4*b^8*c^15*d^4 - 51904512*a^5*b^7*c^14*d^5 + 60555264*a^6*b^6*c^13*d^6 - 51904512*a^7*b^5*c^12*d^7 + 32440320*a^8*b^4*c^11*d^8 - 14417920*a^9*b^3*c^10*d^9 + 4325376*a^10*b^2*c^9*d^10 - 786432*a*b^11*c^18*d))^(3/4)*((x*(589824*a^2*b^23*c^21*d^4 - 11403264*a^3*b^22*c^20*d^5 + 98762752*a^4*b^21*c^19*d^6 - 510394368*a^5*b^20*c^18*d^7 + 1766916096*a^6*b^19*c^17*d^8 - 4344840192*a^7*b^18*c^16*d^9 + 7796490240*a^8*b^17*c^15*d^10 - 10168369152*a^9*b^16*c^14*d^11 + 9007726592*a^10*b^15*c^13*d^12 - 3635478528*a^11*b^14*c^12*d^13 - 3635478528*a^12*b^13*c^11*d^14 + 9007726592*a^13*b^12*c^10*d^15 - 10168369152*a^14*b^11*c^9*d^16 + 7796490240*a^15*b^10*c^8*d^17 - 4344840192*a^16*b^9*c^7*d^18 + 1766916096*a^17*b^8*c^6*d^19 - 510394368*a^18*b^7*c^5*d^20 + 98762752*a^19*b^6*c^4*d^21 - 11403264*a^20*b^5*c^3*d^22 + 589824*a^21*b^4*c^2*d^23)*1i)/(1024*(a^4*b^12*c^16 + a^16*c^4*d^12 - 12*a^5*b^11*c^15*d - 12*a^15*b*c^5*d^11 + 66*a^6*b^10*c^14*d^2 - 220*a^7*b^9*c^13*d^3 + 495*a^8*b^8*c^12*d^4 - 792*a^9*b^7*c^11*d^5 + 924*a^10*b^6*c^10*d^6 - 792*a^11*b^5*c^9*d^7 + 495*a^12*b^4*c^8*d^8 - 220*a^13*b^3*c^7*d^9 + 66*a^14*b^2*c^6*d^10)) - ((-(81*a^4*d^11 + 14641*b^4*c^4*d^7 - 15972*a*b^3*c^3*d^8 + 6534*a^2*b^2*c^2*d^9 - 1188*a^3*b*c*d^10)/(65536*b^12*c^19 + 65536*a^12*c^7*d^12 - 786432*a^11*b*c^8*d^11 + 4325376*a^2*b^10*c^17*d^2 - 14417920*a^3*b^9*c^16*d^3 + 32440320*a^4*b^8*c^15*d^4 - 51904512*a^5*b^7*c^14*d^5 + 60555264*a^6*b^6*c^13*d^6 - 51904512*a^7*b^5*c^12*d^7 + 32440320*a^8*b^4*c^11*d^8 - 14417920*a^9*b^3*c^10*d^9 + 4325376*a^10*b^2*c^9*d^10 - 786432*a*b^11*c^18*d))^(1/4)*(3072*a^4*b^19*c^19*d^4 - 45056*a^5*b^18*c^18*d^5 + 292864*a^6*b^17*c^17*d^6 - 1115136*a^7*b^16*c^16*d^7 + 2745344*a^8*b^15*c^15*d^8 - 4483072*a^9*b^14*c^14*d^9 + 4595712*a^10*b^13*c^13*d^10 - 1993728*a^11*b^12*c^12*d^11 - 1993728*a^12*b^11*c^11*d^12 + 4595712*a^13*b^10*c^10*d^13 - 4483072*a^14*b^9*c^9*d^14 + 2745344*a^15*b^8*c^8*d^15 - 1115136*a^16*b^7*c^7*d^16 + 292864*a^17*b^6*c^6*d^17 - 45056*a^18*b^5*c^5*d^18 + 3072*a^19*b^4*c^4*d^19))/(a^4*b^8*c^12 + a^12*c^4*d^8 - 8*a^5*b^7*c^11*d - 8*a^11*b*c^5*d^7 + 28*a^6*b^6*c^10*d^2 - 56*a^7*b^5*c^9*d^3 + 70*a^8*b^4*c^8*d^4 - 56*a^9*b^3*c^7*d^5 + 28*a^10*b^2*c^6*d^6))*1i)*1i + (x*(9801*a^8*b^9*d^17 + 9801*b^17*c^8*d^9 - 149094*a*b^16*c^7*d^10 - 149094*a^7*b^10*c*d^16 + 1001520*a^2*b^15*c^6*d^11 - 3484602*a^3*b^14*c^5*d^12 + 5769038*a^4*b^13*c^4*d^13 - 3484602*a^5*b^12*c^3*d^14 + 1001520*a^6*b^11*c^2*d^15)*1i)/(1024*(a^4*b^12*c^16 + a^16*c^4*d^12 - 12*a^5*b^11*c^15*d - 12*a^15*b*c^5*d^11 + 66*a^6*b^10*c^14*d^2 - 220*a^7*b^9*c^13*d^3 + 495*a^8*b^8*c^12*d^4 - 792*a^9*b^7*c^11*d^5 + 924*a^10*b^6*c^10*d^6 - 792*a^11*b^5*c^9*d^7 + 495*a^12*b^4*c^8*d^8 - 220*a^13*b^3*c^7*d^9 + 66*a^14*b^2*c^6*d^10)))))*(-(81*a^4*d^11 + 14641*b^4*c^4*d^7 - 15972*a*b^3*c^3*d^8 + 6534*a^2*b^2*c^2*d^9 - 1188*a^3*b*c*d^10)/(65536*b^12*c^19 + 65536*a^12*c^7*d^12 - 786432*a^11*b*c^8*d^11 + 4325376*a^2*b^10*c^17*d^2 - 14417920*a^3*b^9*c^16*d^3 + 32440320*a^4*b^8*c^15*d^4 - 51904512*a^5*b^7*c^14*d^5 + 60555264*a^6*b^6*c^13*d^6 - 51904512*a^7*b^5*c^12*d^7 + 32440320*a^8*b^4*c^11*d^8 - 14417920*a^9*b^3*c^10*d^9 + 4325376*a^10*b^2*c^9*d^10 - 786432*a*b^11*c^18*d))^(1/4) - atan(((-(81*b^11*c^4 + 14641*a^4*b^7*d^4 - 15972*a^3*b^8*c*d^3 + 6534*a^2*b^9*c^2*d^2 - 1188*a*b^10*c^3*d)/(65536*a^19*d^12 + 65536*a^7*b^12*c^12 - 786432*a^8*b^11*c^11*d + 4325376*a^9*b^10*c^10*d^2 - 14417920*a^10*b^9*c^9*d^3 + 32440320*a^11*b^8*c^8*d^4 - 51904512*a^12*b^7*c^7*d^5 + 60555264*a^13*b^6*c^6*d^6 - 51904512*a^14*b^5*c^5*d^7 + 32440320*a^15*b^4*c^4*d^8 - 14417920*a^16*b^3*c^3*d^9 + 4325376*a^17*b^2*c^2*d^10 - 786432*a^18*b*c*d^11))^(1/4)*((-(81*b^11*c^4 + 14641*a^4*b^7*d^4 - 15972*a^3*b^8*c*d^3 + 6534*a^2*b^9*c^2*d^2 - 1188*a*b^10*c^3*d)/(65536*a^19*d^12 + 65536*a^7*b^12*c^12 - 786432*a^8*b^11*c^11*d + 4325376*a^9*b^10*c^10*d^2 - 14417920*a^10*b^9*c^9*d^3 + 32440320*a^11*b^8*c^8*d^4 - 51904512*a^12*b^7*c^7*d^5 + 60555264*a^13*b^6*c^6*d^6 - 51904512*a^14*b^5*c^5*d^7 + 32440320*a^15*b^4*c^4*d^8 - 14417920*a^16*b^3*c^3*d^9 + 4325376*a^17*b^2*c^2*d^10 - 786432*a^18*b*c*d^11))^(1/4)*((-(81*b^11*c^4 + 14641*a^4*b^7*d^4 - 15972*a^3*b^8*c*d^3 + 6534*a^2*b^9*c^2*d^2 - 1188*a*b^10*c^3*d)/(65536*a^19*d^12 + 65536*a^7*b^12*c^12 - 786432*a^8*b^11*c^11*d + 4325376*a^9*b^10*c^10*d^2 - 14417920*a^10*b^9*c^9*d^3 + 32440320*a^11*b^8*c^8*d^4 - 51904512*a^12*b^7*c^7*d^5 + 60555264*a^13*b^6*c^6*d^6 - 51904512*a^14*b^5*c^5*d^7 + 32440320*a^15*b^4*c^4*d^8 - 14417920*a^16*b^3*c^3*d^9 + 4325376*a^17*b^2*c^2*d^10 - 786432*a^18*b*c*d^11))^(3/4)*((x*(589824*a^2*b^23*c^21*d^4 - 11403264*a^3*b^22*c^20*d^5 + 98762752*a^4*b^21*c^19*d^6 - 510394368*a^5*b^20*c^18*d^7 + 1766916096*a^6*b^19*c^17*d^8 - 4344840192*a^7*b^18*c^16*d^9 + 7796490240*a^8*b^17*c^15*d^10 - 10168369152*a^9*b^16*c^14*d^11 + 9007726592*a^10*b^15*c^13*d^12 - 3635478528*a^11*b^14*c^12*d^13 - 3635478528*a^12*b^13*c^11*d^14 + 9007726592*a^13*b^12*c^10*d^15 - 10168369152*a^14*b^11*c^9*d^16 + 7796490240*a^15*b^10*c^8*d^17 - 4344840192*a^16*b^9*c^7*d^18 + 1766916096*a^17*b^8*c^6*d^19 - 510394368*a^18*b^7*c^5*d^20 + 98762752*a^19*b^6*c^4*d^21 - 11403264*a^20*b^5*c^3*d^22 + 589824*a^21*b^4*c^2*d^23))/(1024*(a^4*b^12*c^16 + a^16*c^4*d^12 - 12*a^5*b^11*c^15*d - 12*a^15*b*c^5*d^11 + 66*a^6*b^10*c^14*d^2 - 220*a^7*b^9*c^13*d^3 + 495*a^8*b^8*c^12*d^4 - 792*a^9*b^7*c^11*d^5 + 924*a^10*b^6*c^10*d^6 - 792*a^11*b^5*c^9*d^7 + 495*a^12*b^4*c^8*d^8 - 220*a^13*b^3*c^7*d^9 + 66*a^14*b^2*c^6*d^10)) + ((-(81*b^11*c^4 + 14641*a^4*b^7*d^4 - 15972*a^3*b^8*c*d^3 + 6534*a^2*b^9*c^2*d^2 - 1188*a*b^10*c^3*d)/(65536*a^19*d^12 + 65536*a^7*b^12*c^12 - 786432*a^8*b^11*c^11*d + 4325376*a^9*b^10*c^10*d^2 - 14417920*a^10*b^9*c^9*d^3 + 32440320*a^11*b^8*c^8*d^4 - 51904512*a^12*b^7*c^7*d^5 + 60555264*a^13*b^6*c^6*d^6 - 51904512*a^14*b^5*c^5*d^7 + 32440320*a^15*b^4*c^4*d^8 - 14417920*a^16*b^3*c^3*d^9 + 4325376*a^17*b^2*c^2*d^10 - 786432*a^18*b*c*d^11))^(1/4)*(3072*a^4*b^19*c^19*d^4 - 45056*a^5*b^18*c^18*d^5 + 292864*a^6*b^17*c^17*d^6 - 1115136*a^7*b^16*c^16*d^7 + 2745344*a^8*b^15*c^15*d^8 - 4483072*a^9*b^14*c^14*d^9 + 4595712*a^10*b^13*c^13*d^10 - 1993728*a^11*b^12*c^12*d^11 - 1993728*a^12*b^11*c^11*d^12 + 4595712*a^13*b^10*c^10*d^13 - 4483072*a^14*b^9*c^9*d^14 + 2745344*a^15*b^8*c^8*d^15 - 1115136*a^16*b^7*c^7*d^16 + 292864*a^17*b^6*c^6*d^17 - 45056*a^18*b^5*c^5*d^18 + 3072*a^19*b^4*c^4*d^19))/(a^4*b^8*c^12 + a^12*c^4*d^8 - 8*a^5*b^7*c^11*d - 8*a^11*b*c^5*d^7 + 28*a^6*b^6*c^10*d^2 - 56*a^7*b^5*c^9*d^3 + 70*a^8*b^4*c^8*d^4 - 56*a^9*b^3*c^7*d^5 + 28*a^10*b^2*c^6*d^6)) + ((891*a^8*b^7*d^15)/64 + (891*b^15*c^8*d^7)/64 - (3105*a*b^14*c^7*d^8)/16 - (3105*a^7*b^8*c*d^14)/16 + (31509*a^2*b^13*c^6*d^9)/32 - (33069*a^3*b^12*c^5*d^10)/16 + (60307*a^4*b^11*c^4*d^11)/32 - (33069*a^5*b^10*c^3*d^12)/16 + (31509*a^6*b^9*c^2*d^13)/32)/(a^4*b^8*c^12 + a^12*c^4*d^8 - 8*a^5*b^7*c^11*d - 8*a^11*b*c^5*d^7 + 28*a^6*b^6*c^10*d^2 - 56*a^7*b^5*c^9*d^3 + 70*a^8*b^4*c^8*d^4 - 56*a^9*b^3*c^7*d^5 + 28*a^10*b^2*c^6*d^6))*1i + (x*(9801*a^8*b^9*d^17 + 9801*b^17*c^8*d^9 - 149094*a*b^16*c^7*d^10 - 149094*a^7*b^10*c*d^16 + 1001520*a^2*b^15*c^6*d^11 - 3484602*a^3*b^14*c^5*d^12 + 5769038*a^4*b^13*c^4*d^13 - 3484602*a^5*b^12*c^3*d^14 + 1001520*a^6*b^11*c^2*d^15)*1i)/(1024*(a^4*b^12*c^16 + a^16*c^4*d^12 - 12*a^5*b^11*c^15*d - 12*a^15*b*c^5*d^11 + 66*a^6*b^10*c^14*d^2 - 220*a^7*b^9*c^13*d^3 + 495*a^8*b^8*c^12*d^4 - 792*a^9*b^7*c^11*d^5 + 924*a^10*b^6*c^10*d^6 - 792*a^11*b^5*c^9*d^7 + 495*a^12*b^4*c^8*d^8 - 220*a^13*b^3*c^7*d^9 + 66*a^14*b^2*c^6*d^10))) + (-(81*b^11*c^4 + 14641*a^4*b^7*d^4 - 15972*a^3*b^8*c*d^3 + 6534*a^2*b^9*c^2*d^2 - 1188*a*b^10*c^3*d)/(65536*a^19*d^12 + 65536*a^7*b^12*c^12 - 786432*a^8*b^11*c^11*d + 4325376*a^9*b^10*c^10*d^2 - 14417920*a^10*b^9*c^9*d^3 + 32440320*a^11*b^8*c^8*d^4 - 51904512*a^12*b^7*c^7*d^5 + 60555264*a^13*b^6*c^6*d^6 - 51904512*a^14*b^5*c^5*d^7 + 32440320*a^15*b^4*c^4*d^8 - 14417920*a^16*b^3*c^3*d^9 + 4325376*a^17*b^2*c^2*d^10 - 786432*a^18*b*c*d^11))^(1/4)*((-(81*b^11*c^4 + 14641*a^4*b^7*d^4 - 15972*a^3*b^8*c*d^3 + 6534*a^2*b^9*c^2*d^2 - 1188*a*b^10*c^3*d)/(65536*a^19*d^12 + 65536*a^7*b^12*c^12 - 786432*a^8*b^11*c^11*d + 4325376*a^9*b^10*c^10*d^2 - 14417920*a^10*b^9*c^9*d^3 + 32440320*a^11*b^8*c^8*d^4 - 51904512*a^12*b^7*c^7*d^5 + 60555264*a^13*b^6*c^6*d^6 - 51904512*a^14*b^5*c^5*d^7 + 32440320*a^15*b^4*c^4*d^8 - 14417920*a^16*b^3*c^3*d^9 + 4325376*a^17*b^2*c^2*d^10 - 786432*a^18*b*c*d^11))^(1/4)*((-(81*b^11*c^4 + 14641*a^4*b^7*d^4 - 15972*a^3*b^8*c*d^3 + 6534*a^2*b^9*c^2*d^2 - 1188*a*b^10*c^3*d)/(65536*a^19*d^12 + 65536*a^7*b^12*c^12 - 786432*a^8*b^11*c^11*d + 4325376*a^9*b^10*c^10*d^2 - 14417920*a^10*b^9*c^9*d^3 + 32440320*a^11*b^8*c^8*d^4 - 51904512*a^12*b^7*c^7*d^5 + 60555264*a^13*b^6*c^6*d^6 - 51904512*a^14*b^5*c^5*d^7 + 32440320*a^15*b^4*c^4*d^8 - 14417920*a^16*b^3*c^3*d^9 + 4325376*a^17*b^2*c^2*d^10 - 786432*a^18*b*c*d^11))^(3/4)*((x*(589824*a^2*b^23*c^21*d^4 - 11403264*a^3*b^22*c^20*d^5 + 98762752*a^4*b^21*c^19*d^6 - 510394368*a^5*b^20*c^18*d^7 + 1766916096*a^6*b^19*c^17*d^8 - 4344840192*a^7*b^18*c^16*d^9 + 7796490240*a^8*b^17*c^15*d^10 - 10168369152*a^9*b^16*c^14*d^11 + 9007726592*a^10*b^15*c^13*d^12 - 3635478528*a^11*b^14*c^12*d^13 - 3635478528*a^12*b^13*c^11*d^14 + 9007726592*a^13*b^12*c^10*d^15 - 10168369152*a^14*b^11*c^9*d^16 + 7796490240*a^15*b^10*c^8*d^17 - 4344840192*a^16*b^9*c^7*d^18 + 1766916096*a^17*b^8*c^6*d^19 - 510394368*a^18*b^7*c^5*d^20 + 98762752*a^19*b^6*c^4*d^21 - 11403264*a^20*b^5*c^3*d^22 + 589824*a^21*b^4*c^2*d^23))/(1024*(a^4*b^12*c^16 + a^16*c^4*d^12 - 12*a^5*b^11*c^15*d - 12*a^15*b*c^5*d^11 + 66*a^6*b^10*c^14*d^2 - 220*a^7*b^9*c^13*d^3 + 495*a^8*b^8*c^12*d^4 - 792*a^9*b^7*c^11*d^5 + 924*a^10*b^6*c^10*d^6 - 792*a^11*b^5*c^9*d^7 + 495*a^12*b^4*c^8*d^8 - 220*a^13*b^3*c^7*d^9 + 66*a^14*b^2*c^6*d^10)) - ((-(81*b^11*c^4 + 14641*a^4*b^7*d^4 - 15972*a^3*b^8*c*d^3 + 6534*a^2*b^9*c^2*d^2 - 1188*a*b^10*c^3*d)/(65536*a^19*d^12 + 65536*a^7*b^12*c^12 - 786432*a^8*b^11*c^11*d + 4325376*a^9*b^10*c^10*d^2 - 14417920*a^10*b^9*c^9*d^3 + 32440320*a^11*b^8*c^8*d^4 - 51904512*a^12*b^7*c^7*d^5 + 60555264*a^13*b^6*c^6*d^6 - 51904512*a^14*b^5*c^5*d^7 + 32440320*a^15*b^4*c^4*d^8 - 14417920*a^16*b^3*c^3*d^9 + 4325376*a^17*b^2*c^2*d^10 - 786432*a^18*b*c*d^11))^(1/4)*(3072*a^4*b^19*c^19*d^4 - 45056*a^5*b^18*c^18*d^5 + 292864*a^6*b^17*c^17*d^6 - 1115136*a^7*b^16*c^16*d^7 + 2745344*a^8*b^15*c^15*d^8 - 4483072*a^9*b^14*c^14*d^9 + 4595712*a^10*b^13*c^13*d^10 - 1993728*a^11*b^12*c^12*d^11 - 1993728*a^12*b^11*c^11*d^12 + 4595712*a^13*b^10*c^10*d^13 - 4483072*a^14*b^9*c^9*d^14 + 2745344*a^15*b^8*c^8*d^15 - 1115136*a^16*b^7*c^7*d^16 + 292864*a^17*b^6*c^6*d^17 - 45056*a^18*b^5*c^5*d^18 + 3072*a^19*b^4*c^4*d^19))/(a^4*b^8*c^12 + a^12*c^4*d^8 - 8*a^5*b^7*c^11*d - 8*a^11*b*c^5*d^7 + 28*a^6*b^6*c^10*d^2 - 56*a^7*b^5*c^9*d^3 + 70*a^8*b^4*c^8*d^4 - 56*a^9*b^3*c^7*d^5 + 28*a^10*b^2*c^6*d^6)) - ((891*a^8*b^7*d^15)/64 + (891*b^15*c^8*d^7)/64 - (3105*a*b^14*c^7*d^8)/16 - (3105*a^7*b^8*c*d^14)/16 + (31509*a^2*b^13*c^6*d^9)/32 - (33069*a^3*b^12*c^5*d^10)/16 + (60307*a^4*b^11*c^4*d^11)/32 - (33069*a^5*b^10*c^3*d^12)/16 + (31509*a^6*b^9*c^2*d^13)/32)/(a^4*b^8*c^12 + a^12*c^4*d^8 - 8*a^5*b^7*c^11*d - 8*a^11*b*c^5*d^7 + 28*a^6*b^6*c^10*d^2 - 56*a^7*b^5*c^9*d^3 + 70*a^8*b^4*c^8*d^4 - 56*a^9*b^3*c^7*d^5 + 28*a^10*b^2*c^6*d^6))*1i + (x*(9801*a^8*b^9*d^17 + 9801*b^17*c^8*d^9 - 149094*a*b^16*c^7*d^10 - 149094*a^7*b^10*c*d^16 + 1001520*a^2*b^15*c^6*d^11 - 3484602*a^3*b^14*c^5*d^12 + 5769038*a^4*b^13*c^4*d^13 - 3484602*a^5*b^12*c^3*d^14 + 1001520*a^6*b^11*c^2*d^15)*1i)/(1024*(a^4*b^12*c^16 + a^16*c^4*d^12 - 12*a^5*b^11*c^15*d - 12*a^15*b*c^5*d^11 + 66*a^6*b^10*c^14*d^2 - 220*a^7*b^9*c^13*d^3 + 495*a^8*b^8*c^12*d^4 - 792*a^9*b^7*c^11*d^5 + 924*a^10*b^6*c^10*d^6 - 792*a^11*b^5*c^9*d^7 + 495*a^12*b^4*c^8*d^8 - 220*a^13*b^3*c^7*d^9 + 66*a^14*b^2*c^6*d^10))))/((-(81*b^11*c^4 + 14641*a^4*b^7*d^4 - 15972*a^3*b^8*c*d^3 + 6534*a^2*b^9*c^2*d^2 - 1188*a*b^10*c^3*d)/(65536*a^19*d^12 + 65536*a^7*b^12*c^12 - 786432*a^8*b^11*c^11*d + 4325376*a^9*b^10*c^10*d^2 - 14417920*a^10*b^9*c^9*d^3 + 32440320*a^11*b^8*c^8*d^4 - 51904512*a^12*b^7*c^7*d^5 + 60555264*a^13*b^6*c^6*d^6 - 51904512*a^14*b^5*c^5*d^7 + 32440320*a^15*b^4*c^4*d^8 - 14417920*a^16*b^3*c^3*d^9 + 4325376*a^17*b^2*c^2*d^10 - 786432*a^18*b*c*d^11))^(1/4)*((-(81*b^11*c^4 + 14641*a^4*b^7*d^4 - 15972*a^3*b^8*c*d^3 + 6534*a^2*b^9*c^2*d^2 - 1188*a*b^10*c^3*d)/(65536*a^19*d^12 + 65536*a^7*b^12*c^12 - 786432*a^8*b^11*c^11*d + 4325376*a^9*b^10*c^10*d^2 - 14417920*a^10*b^9*c^9*d^3 + 32440320*a^11*b^8*c^8*d^4 - 51904512*a^12*b^7*c^7*d^5 + 60555264*a^13*b^6*c^6*d^6 - 51904512*a^14*b^5*c^5*d^7 + 32440320*a^15*b^4*c^4*d^8 - 14417920*a^16*b^3*c^3*d^9 + 4325376*a^17*b^2*c^2*d^10 - 786432*a^18*b*c*d^11))^(1/4)*((-(81*b^11*c^4 + 14641*a^4*b^7*d^4 - 15972*a^3*b^8*c*d^3 + 6534*a^2*b^9*c^2*d^2 - 1188*a*b^10*c^3*d)/(65536*a^19*d^12 + 65536*a^7*b^12*c^12 - 786432*a^8*b^11*c^11*d + 4325376*a^9*b^10*c^10*d^2 - 14417920*a^10*b^9*c^9*d^3 + 32440320*a^11*b^8*c^8*d^4 - 51904512*a^12*b^7*c^7*d^5 + 60555264*a^13*b^6*c^6*d^6 - 51904512*a^14*b^5*c^5*d^7 + 32440320*a^15*b^4*c^4*d^8 - 14417920*a^16*b^3*c^3*d^9 + 4325376*a^17*b^2*c^2*d^10 - 786432*a^18*b*c*d^11))^(3/4)*((x*(589824*a^2*b^23*c^21*d^4 - 11403264*a^3*b^22*c^20*d^5 + 98762752*a^4*b^21*c^19*d^6 - 510394368*a^5*b^20*c^18*d^7 + 1766916096*a^6*b^19*c^17*d^8 - 4344840192*a^7*b^18*c^16*d^9 + 7796490240*a^8*b^17*c^15*d^10 - 10168369152*a^9*b^16*c^14*d^11 + 9007726592*a^10*b^15*c^13*d^12 - 3635478528*a^11*b^14*c^12*d^13 - 3635478528*a^12*b^13*c^11*d^14 + 9007726592*a^13*b^12*c^10*d^15 - 10168369152*a^14*b^11*c^9*d^16 + 7796490240*a^15*b^10*c^8*d^17 - 4344840192*a^16*b^9*c^7*d^18 + 1766916096*a^17*b^8*c^6*d^19 - 510394368*a^18*b^7*c^5*d^20 + 98762752*a^19*b^6*c^4*d^21 - 11403264*a^20*b^5*c^3*d^22 + 589824*a^21*b^4*c^2*d^23))/(1024*(a^4*b^12*c^16 + a^16*c^4*d^12 - 12*a^5*b^11*c^15*d - 12*a^15*b*c^5*d^11 + 66*a^6*b^10*c^14*d^2 - 220*a^7*b^9*c^13*d^3 + 495*a^8*b^8*c^12*d^4 - 792*a^9*b^7*c^11*d^5 + 924*a^10*b^6*c^10*d^6 - 792*a^11*b^5*c^9*d^7 + 495*a^12*b^4*c^8*d^8 - 220*a^13*b^3*c^7*d^9 + 66*a^14*b^2*c^6*d^10)) + ((-(81*b^11*c^4 + 14641*a^4*b^7*d^4 - 15972*a^3*b^8*c*d^3 + 6534*a^2*b^9*c^2*d^2 - 1188*a*b^10*c^3*d)/(65536*a^19*d^12 + 65536*a^7*b^12*c^12 - 786432*a^8*b^11*c^11*d + 4325376*a^9*b^10*c^10*d^2 - 14417920*a^10*b^9*c^9*d^3 + 32440320*a^11*b^8*c^8*d^4 - 51904512*a^12*b^7*c^7*d^5 + 60555264*a^13*b^6*c^6*d^6 - 51904512*a^14*b^5*c^5*d^7 + 32440320*a^15*b^4*c^4*d^8 - 14417920*a^16*b^3*c^3*d^9 + 4325376*a^17*b^2*c^2*d^10 - 786432*a^18*b*c*d^11))^(1/4)*(3072*a^4*b^19*c^19*d^4 - 45056*a^5*b^18*c^18*d^5 + 292864*a^6*b^17*c^17*d^6 - 1115136*a^7*b^16*c^16*d^7 + 2745344*a^8*b^15*c^15*d^8 - 4483072*a^9*b^14*c^14*d^9 + 4595712*a^10*b^13*c^13*d^10 - 1993728*a^11*b^12*c^12*d^11 - 1993728*a^12*b^11*c^11*d^12 + 4595712*a^13*b^10*c^10*d^13 - 4483072*a^14*b^9*c^9*d^14 + 2745344*a^15*b^8*c^8*d^15 - 1115136*a^16*b^7*c^7*d^16 + 292864*a^17*b^6*c^6*d^17 - 45056*a^18*b^5*c^5*d^18 + 3072*a^19*b^4*c^4*d^19))/(a^4*b^8*c^12 + a^12*c^4*d^8 - 8*a^5*b^7*c^11*d - 8*a^11*b*c^5*d^7 + 28*a^6*b^6*c^10*d^2 - 56*a^7*b^5*c^9*d^3 + 70*a^8*b^4*c^8*d^4 - 56*a^9*b^3*c^7*d^5 + 28*a^10*b^2*c^6*d^6)) + ((891*a^8*b^7*d^15)/64 + (891*b^15*c^8*d^7)/64 - (3105*a*b^14*c^7*d^8)/16 - (3105*a^7*b^8*c*d^14)/16 + (31509*a^2*b^13*c^6*d^9)/32 - (33069*a^3*b^12*c^5*d^10)/16 + (60307*a^4*b^11*c^4*d^11)/32 - (33069*a^5*b^10*c^3*d^12)/16 + (31509*a^6*b^9*c^2*d^13)/32)/(a^4*b^8*c^12 + a^12*c^4*d^8 - 8*a^5*b^7*c^11*d - 8*a^11*b*c^5*d^7 + 28*a^6*b^6*c^10*d^2 - 56*a^7*b^5*c^9*d^3 + 70*a^8*b^4*c^8*d^4 - 56*a^9*b^3*c^7*d^5 + 28*a^10*b^2*c^6*d^6)) + (x*(9801*a^8*b^9*d^17 + 9801*b^17*c^8*d^9 - 149094*a*b^16*c^7*d^10 - 149094*a^7*b^10*c*d^16 + 1001520*a^2*b^15*c^6*d^11 - 3484602*a^3*b^14*c^5*d^12 + 5769038*a^4*b^13*c^4*d^13 - 3484602*a^5*b^12*c^3*d^14 + 1001520*a^6*b^11*c^2*d^15))/(1024*(a^4*b^12*c^16 + a^16*c^4*d^12 - 12*a^5*b^11*c^15*d - 12*a^15*b*c^5*d^11 + 66*a^6*b^10*c^14*d^2 - 220*a^7*b^9*c^13*d^3 + 495*a^8*b^8*c^12*d^4 - 792*a^9*b^7*c^11*d^5 + 924*a^10*b^6*c^10*d^6 - 792*a^11*b^5*c^9*d^7 + 495*a^12*b^4*c^8*d^8 - 220*a^13*b^3*c^7*d^9 + 66*a^14*b^2*c^6*d^10))) - (-(81*b^11*c^4 + 14641*a^4*b^7*d^4 - 15972*a^3*b^8*c*d^3 + 6534*a^2*b^9*c^2*d^2 - 1188*a*b^10*c^3*d)/(65536*a^19*d^12 + 65536*a^7*b^12*c^12 - 786432*a^8*b^11*c^11*d + 4325376*a^9*b^10*c^10*d^2 - 14417920*a^10*b^9*c^9*d^3 + 32440320*a^11*b^8*c^8*d^4 - 51904512*a^12*b^7*c^7*d^5 + 60555264*a^13*b^6*c^6*d^6 - 51904512*a^14*b^5*c^5*d^7 + 32440320*a^15*b^4*c^4*d^8 - 14417920*a^16*b^3*c^3*d^9 + 4325376*a^17*b^2*c^2*d^10 - 786432*a^18*b*c*d^11))^(1/4)*((-(81*b^11*c^4 + 14641*a^4*b^7*d^4 - 15972*a^3*b^8*c*d^3 + 6534*a^2*b^9*c^2*d^2 - 1188*a*b^10*c^3*d)/(65536*a^19*d^12 + 65536*a^7*b^12*c^12 - 786432*a^8*b^11*c^11*d + 4325376*a^9*b^10*c^10*d^2 - 14417920*a^10*b^9*c^9*d^3 + 32440320*a^11*b^8*c^8*d^4 - 51904512*a^12*b^7*c^7*d^5 + 60555264*a^13*b^6*c^6*d^6 - 51904512*a^14*b^5*c^5*d^7 + 32440320*a^15*b^4*c^4*d^8 - 14417920*a^16*b^3*c^3*d^9 + 4325376*a^17*b^2*c^2*d^10 - 786432*a^18*b*c*d^11))^(1/4)*((-(81*b^11*c^4 + 14641*a^4*b^7*d^4 - 15972*a^3*b^8*c*d^3 + 6534*a^2*b^9*c^2*d^2 - 1188*a*b^10*c^3*d)/(65536*a^19*d^12 + 65536*a^7*b^12*c^12 - 786432*a^8*b^11*c^11*d + 4325376*a^9*b^10*c^10*d^2 - 14417920*a^10*b^9*c^9*d^3 + 32440320*a^11*b^8*c^8*d^4 - 51904512*a^12*b^7*c^7*d^5 + 60555264*a^13*b^6*c^6*d^6 - 51904512*a^14*b^5*c^5*d^7 + 32440320*a^15*b^4*c^4*d^8 - 14417920*a^16*b^3*c^3*d^9 + 4325376*a^17*b^2*c^2*d^10 - 786432*a^18*b*c*d^11))^(3/4)*((x*(589824*a^2*b^23*c^21*d^4 - 11403264*a^3*b^22*c^20*d^5 + 98762752*a^4*b^21*c^19*d^6 - 510394368*a^5*b^20*c^18*d^7 + 1766916096*a^6*b^19*c^17*d^8 - 4344840192*a^7*b^18*c^16*d^9 + 7796490240*a^8*b^17*c^15*d^10 - 10168369152*a^9*b^16*c^14*d^11 + 9007726592*a^10*b^15*c^13*d^12 - 3635478528*a^11*b^14*c^12*d^13 - 3635478528*a^12*b^13*c^11*d^14 + 9007726592*a^13*b^12*c^10*d^15 - 10168369152*a^14*b^11*c^9*d^16 + 7796490240*a^15*b^10*c^8*d^17 - 4344840192*a^16*b^9*c^7*d^18 + 1766916096*a^17*b^8*c^6*d^19 - 510394368*a^18*b^7*c^5*d^20 + 98762752*a^19*b^6*c^4*d^21 - 11403264*a^20*b^5*c^3*d^22 + 589824*a^21*b^4*c^2*d^23))/(1024*(a^4*b^12*c^16 + a^16*c^4*d^12 - 12*a^5*b^11*c^15*d - 12*a^15*b*c^5*d^11 + 66*a^6*b^10*c^14*d^2 - 220*a^7*b^9*c^13*d^3 + 495*a^8*b^8*c^12*d^4 - 792*a^9*b^7*c^11*d^5 + 924*a^10*b^6*c^10*d^6 - 792*a^11*b^5*c^9*d^7 + 495*a^12*b^4*c^8*d^8 - 220*a^13*b^3*c^7*d^9 + 66*a^14*b^2*c^6*d^10)) - ((-(81*b^11*c^4 + 14641*a^4*b^7*d^4 - 15972*a^3*b^8*c*d^3 + 6534*a^2*b^9*c^2*d^2 - 1188*a*b^10*c^3*d)/(65536*a^19*d^12 + 65536*a^7*b^12*c^12 - 786432*a^8*b^11*c^11*d + 4325376*a^9*b^10*c^10*d^2 - 14417920*a^10*b^9*c^9*d^3 + 32440320*a^11*b^8*c^8*d^4 - 51904512*a^12*b^7*c^7*d^5 + 60555264*a^13*b^6*c^6*d^6 - 51904512*a^14*b^5*c^5*d^7 + 32440320*a^15*b^4*c^4*d^8 - 14417920*a^16*b^3*c^3*d^9 + 4325376*a^17*b^2*c^2*d^10 - 786432*a^18*b*c*d^11))^(1/4)*(3072*a^4*b^19*c^19*d^4 - 45056*a^5*b^18*c^18*d^5 + 292864*a^6*b^17*c^17*d^6 - 1115136*a^7*b^16*c^16*d^7 + 2745344*a^8*b^15*c^15*d^8 - 4483072*a^9*b^14*c^14*d^9 + 4595712*a^10*b^13*c^13*d^10 - 1993728*a^11*b^12*c^12*d^11 - 1993728*a^12*b^11*c^11*d^12 + 4595712*a^13*b^10*c^10*d^13 - 4483072*a^14*b^9*c^9*d^14 + 2745344*a^15*b^8*c^8*d^15 - 1115136*a^16*b^7*c^7*d^16 + 292864*a^17*b^6*c^6*d^17 - 45056*a^18*b^5*c^5*d^18 + 3072*a^19*b^4*c^4*d^19))/(a^4*b^8*c^12 + a^12*c^4*d^8 - 8*a^5*b^7*c^11*d - 8*a^11*b*c^5*d^7 + 28*a^6*b^6*c^10*d^2 - 56*a^7*b^5*c^9*d^3 + 70*a^8*b^4*c^8*d^4 - 56*a^9*b^3*c^7*d^5 + 28*a^10*b^2*c^6*d^6)) - ((891*a^8*b^7*d^15)/64 + (891*b^15*c^8*d^7)/64 - (3105*a*b^14*c^7*d^8)/16 - (3105*a^7*b^8*c*d^14)/16 + (31509*a^2*b^13*c^6*d^9)/32 - (33069*a^3*b^12*c^5*d^10)/16 + (60307*a^4*b^11*c^4*d^11)/32 - (33069*a^5*b^10*c^3*d^12)/16 + (31509*a^6*b^9*c^2*d^13)/32)/(a^4*b^8*c^12 + a^12*c^4*d^8 - 8*a^5*b^7*c^11*d - 8*a^11*b*c^5*d^7 + 28*a^6*b^6*c^10*d^2 - 56*a^7*b^5*c^9*d^3 + 70*a^8*b^4*c^8*d^4 - 56*a^9*b^3*c^7*d^5 + 28*a^10*b^2*c^6*d^6)) + (x*(9801*a^8*b^9*d^17 + 9801*b^17*c^8*d^9 - 149094*a*b^16*c^7*d^10 - 149094*a^7*b^10*c*d^16 + 1001520*a^2*b^15*c^6*d^11 - 3484602*a^3*b^14*c^5*d^12 + 5769038*a^4*b^13*c^4*d^13 - 3484602*a^5*b^12*c^3*d^14 + 1001520*a^6*b^11*c^2*d^15))/(1024*(a^4*b^12*c^16 + a^16*c^4*d^12 - 12*a^5*b^11*c^15*d - 12*a^15*b*c^5*d^11 + 66*a^6*b^10*c^14*d^2 - 220*a^7*b^9*c^13*d^3 + 495*a^8*b^8*c^12*d^4 - 792*a^9*b^7*c^11*d^5 + 924*a^10*b^6*c^10*d^6 - 792*a^11*b^5*c^9*d^7 + 495*a^12*b^4*c^8*d^8 - 220*a^13*b^3*c^7*d^9 + 66*a^14*b^2*c^6*d^10)))))*(-(81*b^11*c^4 + 14641*a^4*b^7*d^4 - 15972*a^3*b^8*c*d^3 + 6534*a^2*b^9*c^2*d^2 - 1188*a*b^10*c^3*d)/(65536*a^19*d^12 + 65536*a^7*b^12*c^12 - 786432*a^8*b^11*c^11*d + 4325376*a^9*b^10*c^10*d^2 - 14417920*a^10*b^9*c^9*d^3 + 32440320*a^11*b^8*c^8*d^4 - 51904512*a^12*b^7*c^7*d^5 + 60555264*a^13*b^6*c^6*d^6 - 51904512*a^14*b^5*c^5*d^7 + 32440320*a^15*b^4*c^4*d^8 - 14417920*a^16*b^3*c^3*d^9 + 4325376*a^17*b^2*c^2*d^10 - 786432*a^18*b*c*d^11))^(1/4)*2i + 2*atan(((-(81*b^11*c^4 + 14641*a^4*b^7*d^4 - 15972*a^3*b^8*c*d^3 + 6534*a^2*b^9*c^2*d^2 - 1188*a*b^10*c^3*d)/(65536*a^19*d^12 + 65536*a^7*b^12*c^12 - 786432*a^8*b^11*c^11*d + 4325376*a^9*b^10*c^10*d^2 - 14417920*a^10*b^9*c^9*d^3 + 32440320*a^11*b^8*c^8*d^4 - 51904512*a^12*b^7*c^7*d^5 + 60555264*a^13*b^6*c^6*d^6 - 51904512*a^14*b^5*c^5*d^7 + 32440320*a^15*b^4*c^4*d^8 - 14417920*a^16*b^3*c^3*d^9 + 4325376*a^17*b^2*c^2*d^10 - 786432*a^18*b*c*d^11))^(1/4)*((-(81*b^11*c^4 + 14641*a^4*b^7*d^4 - 15972*a^3*b^8*c*d^3 + 6534*a^2*b^9*c^2*d^2 - 1188*a*b^10*c^3*d)/(65536*a^19*d^12 + 65536*a^7*b^12*c^12 - 786432*a^8*b^11*c^11*d + 4325376*a^9*b^10*c^10*d^2 - 14417920*a^10*b^9*c^9*d^3 + 32440320*a^11*b^8*c^8*d^4 - 51904512*a^12*b^7*c^7*d^5 + 60555264*a^13*b^6*c^6*d^6 - 51904512*a^14*b^5*c^5*d^7 + 32440320*a^15*b^4*c^4*d^8 - 14417920*a^16*b^3*c^3*d^9 + 4325376*a^17*b^2*c^2*d^10 - 786432*a^18*b*c*d^11))^(1/4)*((-(81*b^11*c^4 + 14641*a^4*b^7*d^4 - 15972*a^3*b^8*c*d^3 + 6534*a^2*b^9*c^2*d^2 - 1188*a*b^10*c^3*d)/(65536*a^19*d^12 + 65536*a^7*b^12*c^12 - 786432*a^8*b^11*c^11*d + 4325376*a^9*b^10*c^10*d^2 - 14417920*a^10*b^9*c^9*d^3 + 32440320*a^11*b^8*c^8*d^4 - 51904512*a^12*b^7*c^7*d^5 + 60555264*a^13*b^6*c^6*d^6 - 51904512*a^14*b^5*c^5*d^7 + 32440320*a^15*b^4*c^4*d^8 - 14417920*a^16*b^3*c^3*d^9 + 4325376*a^17*b^2*c^2*d^10 - 786432*a^18*b*c*d^11))^(3/4)*((x*(589824*a^2*b^23*c^21*d^4 - 11403264*a^3*b^22*c^20*d^5 + 98762752*a^4*b^21*c^19*d^6 - 510394368*a^5*b^20*c^18*d^7 + 1766916096*a^6*b^19*c^17*d^8 - 4344840192*a^7*b^18*c^16*d^9 + 7796490240*a^8*b^17*c^15*d^10 - 10168369152*a^9*b^16*c^14*d^11 + 9007726592*a^10*b^15*c^13*d^12 - 3635478528*a^11*b^14*c^12*d^13 - 3635478528*a^12*b^13*c^11*d^14 + 9007726592*a^13*b^12*c^10*d^15 - 10168369152*a^14*b^11*c^9*d^16 + 7796490240*a^15*b^10*c^8*d^17 - 4344840192*a^16*b^9*c^7*d^18 + 1766916096*a^17*b^8*c^6*d^19 - 510394368*a^18*b^7*c^5*d^20 + 98762752*a^19*b^6*c^4*d^21 - 11403264*a^20*b^5*c^3*d^22 + 589824*a^21*b^4*c^2*d^23)*1i)/(1024*(a^4*b^12*c^16 + a^16*c^4*d^12 - 12*a^5*b^11*c^15*d - 12*a^15*b*c^5*d^11 + 66*a^6*b^10*c^14*d^2 - 220*a^7*b^9*c^13*d^3 + 495*a^8*b^8*c^12*d^4 - 792*a^9*b^7*c^11*d^5 + 924*a^10*b^6*c^10*d^6 - 792*a^11*b^5*c^9*d^7 + 495*a^12*b^4*c^8*d^8 - 220*a^13*b^3*c^7*d^9 + 66*a^14*b^2*c^6*d^10)) + ((-(81*b^11*c^4 + 14641*a^4*b^7*d^4 - 15972*a^3*b^8*c*d^3 + 6534*a^2*b^9*c^2*d^2 - 1188*a*b^10*c^3*d)/(65536*a^19*d^12 + 65536*a^7*b^12*c^12 - 786432*a^8*b^11*c^11*d + 4325376*a^9*b^10*c^10*d^2 - 14417920*a^10*b^9*c^9*d^3 + 32440320*a^11*b^8*c^8*d^4 - 51904512*a^12*b^7*c^7*d^5 + 60555264*a^13*b^6*c^6*d^6 - 51904512*a^14*b^5*c^5*d^7 + 32440320*a^15*b^4*c^4*d^8 - 14417920*a^16*b^3*c^3*d^9 + 4325376*a^17*b^2*c^2*d^10 - 786432*a^18*b*c*d^11))^(1/4)*(3072*a^4*b^19*c^19*d^4 - 45056*a^5*b^18*c^18*d^5 + 292864*a^6*b^17*c^17*d^6 - 1115136*a^7*b^16*c^16*d^7 + 2745344*a^8*b^15*c^15*d^8 - 4483072*a^9*b^14*c^14*d^9 + 4595712*a^10*b^13*c^13*d^10 - 1993728*a^11*b^12*c^12*d^11 - 1993728*a^12*b^11*c^11*d^12 + 4595712*a^13*b^10*c^10*d^13 - 4483072*a^14*b^9*c^9*d^14 + 2745344*a^15*b^8*c^8*d^15 - 1115136*a^16*b^7*c^7*d^16 + 292864*a^17*b^6*c^6*d^17 - 45056*a^18*b^5*c^5*d^18 + 3072*a^19*b^4*c^4*d^19))/(a^4*b^8*c^12 + a^12*c^4*d^8 - 8*a^5*b^7*c^11*d - 8*a^11*b*c^5*d^7 + 28*a^6*b^6*c^10*d^2 - 56*a^7*b^5*c^9*d^3 + 70*a^8*b^4*c^8*d^4 - 56*a^9*b^3*c^7*d^5 + 28*a^10*b^2*c^6*d^6))*1i + (((891*a^8*b^7*d^15)/64 + (891*b^15*c^8*d^7)/64 - (3105*a*b^14*c^7*d^8)/16 - (3105*a^7*b^8*c*d^14)/16 + (31509*a^2*b^13*c^6*d^9)/32 - (33069*a^3*b^12*c^5*d^10)/16 + (60307*a^4*b^11*c^4*d^11)/32 - (33069*a^5*b^10*c^3*d^12)/16 + (31509*a^6*b^9*c^2*d^13)/32)*1i)/(a^4*b^8*c^12 + a^12*c^4*d^8 - 8*a^5*b^7*c^11*d - 8*a^11*b*c^5*d^7 + 28*a^6*b^6*c^10*d^2 - 56*a^7*b^5*c^9*d^3 + 70*a^8*b^4*c^8*d^4 - 56*a^9*b^3*c^7*d^5 + 28*a^10*b^2*c^6*d^6)) - (x*(9801*a^8*b^9*d^17 + 9801*b^17*c^8*d^9 - 149094*a*b^16*c^7*d^10 - 149094*a^7*b^10*c*d^16 + 1001520*a^2*b^15*c^6*d^11 - 3484602*a^3*b^14*c^5*d^12 + 5769038*a^4*b^13*c^4*d^13 - 3484602*a^5*b^12*c^3*d^14 + 1001520*a^6*b^11*c^2*d^15))/(1024*(a^4*b^12*c^16 + a^16*c^4*d^12 - 12*a^5*b^11*c^15*d - 12*a^15*b*c^5*d^11 + 66*a^6*b^10*c^14*d^2 - 220*a^7*b^9*c^13*d^3 + 495*a^8*b^8*c^12*d^4 - 792*a^9*b^7*c^11*d^5 + 924*a^10*b^6*c^10*d^6 - 792*a^11*b^5*c^9*d^7 + 495*a^12*b^4*c^8*d^8 - 220*a^13*b^3*c^7*d^9 + 66*a^14*b^2*c^6*d^10))) + (-(81*b^11*c^4 + 14641*a^4*b^7*d^4 - 15972*a^3*b^8*c*d^3 + 6534*a^2*b^9*c^2*d^2 - 1188*a*b^10*c^3*d)/(65536*a^19*d^12 + 65536*a^7*b^12*c^12 - 786432*a^8*b^11*c^11*d + 4325376*a^9*b^10*c^10*d^2 - 14417920*a^10*b^9*c^9*d^3 + 32440320*a^11*b^8*c^8*d^4 - 51904512*a^12*b^7*c^7*d^5 + 60555264*a^13*b^6*c^6*d^6 - 51904512*a^14*b^5*c^5*d^7 + 32440320*a^15*b^4*c^4*d^8 - 14417920*a^16*b^3*c^3*d^9 + 4325376*a^17*b^2*c^2*d^10 - 786432*a^18*b*c*d^11))^(1/4)*((-(81*b^11*c^4 + 14641*a^4*b^7*d^4 - 15972*a^3*b^8*c*d^3 + 6534*a^2*b^9*c^2*d^2 - 1188*a*b^10*c^3*d)/(65536*a^19*d^12 + 65536*a^7*b^12*c^12 - 786432*a^8*b^11*c^11*d + 4325376*a^9*b^10*c^10*d^2 - 14417920*a^10*b^9*c^9*d^3 + 32440320*a^11*b^8*c^8*d^4 - 51904512*a^12*b^7*c^7*d^5 + 60555264*a^13*b^6*c^6*d^6 - 51904512*a^14*b^5*c^5*d^7 + 32440320*a^15*b^4*c^4*d^8 - 14417920*a^16*b^3*c^3*d^9 + 4325376*a^17*b^2*c^2*d^10 - 786432*a^18*b*c*d^11))^(1/4)*((-(81*b^11*c^4 + 14641*a^4*b^7*d^4 - 15972*a^3*b^8*c*d^3 + 6534*a^2*b^9*c^2*d^2 - 1188*a*b^10*c^3*d)/(65536*a^19*d^12 + 65536*a^7*b^12*c^12 - 786432*a^8*b^11*c^11*d + 4325376*a^9*b^10*c^10*d^2 - 14417920*a^10*b^9*c^9*d^3 + 32440320*a^11*b^8*c^8*d^4 - 51904512*a^12*b^7*c^7*d^5 + 60555264*a^13*b^6*c^6*d^6 - 51904512*a^14*b^5*c^5*d^7 + 32440320*a^15*b^4*c^4*d^8 - 14417920*a^16*b^3*c^3*d^9 + 4325376*a^17*b^2*c^2*d^10 - 786432*a^18*b*c*d^11))^(3/4)*((x*(589824*a^2*b^23*c^21*d^4 - 11403264*a^3*b^22*c^20*d^5 + 98762752*a^4*b^21*c^19*d^6 - 510394368*a^5*b^20*c^18*d^7 + 1766916096*a^6*b^19*c^17*d^8 - 4344840192*a^7*b^18*c^16*d^9 + 7796490240*a^8*b^17*c^15*d^10 - 10168369152*a^9*b^16*c^14*d^11 + 9007726592*a^10*b^15*c^13*d^12 - 3635478528*a^11*b^14*c^12*d^13 - 3635478528*a^12*b^13*c^11*d^14 + 9007726592*a^13*b^12*c^10*d^15 - 10168369152*a^14*b^11*c^9*d^16 + 7796490240*a^15*b^10*c^8*d^17 - 4344840192*a^16*b^9*c^7*d^18 + 1766916096*a^17*b^8*c^6*d^19 - 510394368*a^18*b^7*c^5*d^20 + 98762752*a^19*b^6*c^4*d^21 - 11403264*a^20*b^5*c^3*d^22 + 589824*a^21*b^4*c^2*d^23)*1i)/(1024*(a^4*b^12*c^16 + a^16*c^4*d^12 - 12*a^5*b^11*c^15*d - 12*a^15*b*c^5*d^11 + 66*a^6*b^10*c^14*d^2 - 220*a^7*b^9*c^13*d^3 + 495*a^8*b^8*c^12*d^4 - 792*a^9*b^7*c^11*d^5 + 924*a^10*b^6*c^10*d^6 - 792*a^11*b^5*c^9*d^7 + 495*a^12*b^4*c^8*d^8 - 220*a^13*b^3*c^7*d^9 + 66*a^14*b^2*c^6*d^10)) - ((-(81*b^11*c^4 + 14641*a^4*b^7*d^4 - 15972*a^3*b^8*c*d^3 + 6534*a^2*b^9*c^2*d^2 - 1188*a*b^10*c^3*d)/(65536*a^19*d^12 + 65536*a^7*b^12*c^12 - 786432*a^8*b^11*c^11*d + 4325376*a^9*b^10*c^10*d^2 - 14417920*a^10*b^9*c^9*d^3 + 32440320*a^11*b^8*c^8*d^4 - 51904512*a^12*b^7*c^7*d^5 + 60555264*a^13*b^6*c^6*d^6 - 51904512*a^14*b^5*c^5*d^7 + 32440320*a^15*b^4*c^4*d^8 - 14417920*a^16*b^3*c^3*d^9 + 4325376*a^17*b^2*c^2*d^10 - 786432*a^18*b*c*d^11))^(1/4)*(3072*a^4*b^19*c^19*d^4 - 45056*a^5*b^18*c^18*d^5 + 292864*a^6*b^17*c^17*d^6 - 1115136*a^7*b^16*c^16*d^7 + 2745344*a^8*b^15*c^15*d^8 - 4483072*a^9*b^14*c^14*d^9 + 4595712*a^10*b^13*c^13*d^10 - 1993728*a^11*b^12*c^12*d^11 - 1993728*a^12*b^11*c^11*d^12 + 4595712*a^13*b^10*c^10*d^13 - 4483072*a^14*b^9*c^9*d^14 + 2745344*a^15*b^8*c^8*d^15 - 1115136*a^16*b^7*c^7*d^16 + 292864*a^17*b^6*c^6*d^17 - 45056*a^18*b^5*c^5*d^18 + 3072*a^19*b^4*c^4*d^19))/(a^4*b^8*c^12 + a^12*c^4*d^8 - 8*a^5*b^7*c^11*d - 8*a^11*b*c^5*d^7 + 28*a^6*b^6*c^10*d^2 - 56*a^7*b^5*c^9*d^3 + 70*a^8*b^4*c^8*d^4 - 56*a^9*b^3*c^7*d^5 + 28*a^10*b^2*c^6*d^6))*1i - (((891*a^8*b^7*d^15)/64 + (891*b^15*c^8*d^7)/64 - (3105*a*b^14*c^7*d^8)/16 - (3105*a^7*b^8*c*d^14)/16 + (31509*a^2*b^13*c^6*d^9)/32 - (33069*a^3*b^12*c^5*d^10)/16 + (60307*a^4*b^11*c^4*d^11)/32 - (33069*a^5*b^10*c^3*d^12)/16 + (31509*a^6*b^9*c^2*d^13)/32)*1i)/(a^4*b^8*c^12 + a^12*c^4*d^8 - 8*a^5*b^7*c^11*d - 8*a^11*b*c^5*d^7 + 28*a^6*b^6*c^10*d^2 - 56*a^7*b^5*c^9*d^3 + 70*a^8*b^4*c^8*d^4 - 56*a^9*b^3*c^7*d^5 + 28*a^10*b^2*c^6*d^6)) - (x*(9801*a^8*b^9*d^17 + 9801*b^17*c^8*d^9 - 149094*a*b^16*c^7*d^10 - 149094*a^7*b^10*c*d^16 + 1001520*a^2*b^15*c^6*d^11 - 3484602*a^3*b^14*c^5*d^12 + 5769038*a^4*b^13*c^4*d^13 - 3484602*a^5*b^12*c^3*d^14 + 1001520*a^6*b^11*c^2*d^15))/(1024*(a^4*b^12*c^16 + a^16*c^4*d^12 - 12*a^5*b^11*c^15*d - 12*a^15*b*c^5*d^11 + 66*a^6*b^10*c^14*d^2 - 220*a^7*b^9*c^13*d^3 + 495*a^8*b^8*c^12*d^4 - 792*a^9*b^7*c^11*d^5 + 924*a^10*b^6*c^10*d^6 - 792*a^11*b^5*c^9*d^7 + 495*a^12*b^4*c^8*d^8 - 220*a^13*b^3*c^7*d^9 + 66*a^14*b^2*c^6*d^10))))/((-(81*b^11*c^4 + 14641*a^4*b^7*d^4 - 15972*a^3*b^8*c*d^3 + 6534*a^2*b^9*c^2*d^2 - 1188*a*b^10*c^3*d)/(65536*a^19*d^12 + 65536*a^7*b^12*c^12 - 786432*a^8*b^11*c^11*d + 4325376*a^9*b^10*c^10*d^2 - 14417920*a^10*b^9*c^9*d^3 + 32440320*a^11*b^8*c^8*d^4 - 51904512*a^12*b^7*c^7*d^5 + 60555264*a^13*b^6*c^6*d^6 - 51904512*a^14*b^5*c^5*d^7 + 32440320*a^15*b^4*c^4*d^8 - 14417920*a^16*b^3*c^3*d^9 + 4325376*a^17*b^2*c^2*d^10 - 786432*a^18*b*c*d^11))^(1/4)*((-(81*b^11*c^4 + 14641*a^4*b^7*d^4 - 15972*a^3*b^8*c*d^3 + 6534*a^2*b^9*c^2*d^2 - 1188*a*b^10*c^3*d)/(65536*a^19*d^12 + 65536*a^7*b^12*c^12 - 786432*a^8*b^11*c^11*d + 4325376*a^9*b^10*c^10*d^2 - 14417920*a^10*b^9*c^9*d^3 + 32440320*a^11*b^8*c^8*d^4 - 51904512*a^12*b^7*c^7*d^5 + 60555264*a^13*b^6*c^6*d^6 - 51904512*a^14*b^5*c^5*d^7 + 32440320*a^15*b^4*c^4*d^8 - 14417920*a^16*b^3*c^3*d^9 + 4325376*a^17*b^2*c^2*d^10 - 786432*a^18*b*c*d^11))^(1/4)*((-(81*b^11*c^4 + 14641*a^4*b^7*d^4 - 15972*a^3*b^8*c*d^3 + 6534*a^2*b^9*c^2*d^2 - 1188*a*b^10*c^3*d)/(65536*a^19*d^12 + 65536*a^7*b^12*c^12 - 786432*a^8*b^11*c^11*d + 4325376*a^9*b^10*c^10*d^2 - 14417920*a^10*b^9*c^9*d^3 + 32440320*a^11*b^8*c^8*d^4 - 51904512*a^12*b^7*c^7*d^5 + 60555264*a^13*b^6*c^6*d^6 - 51904512*a^14*b^5*c^5*d^7 + 32440320*a^15*b^4*c^4*d^8 - 14417920*a^16*b^3*c^3*d^9 + 4325376*a^17*b^2*c^2*d^10 - 786432*a^18*b*c*d^11))^(3/4)*((x*(589824*a^2*b^23*c^21*d^4 - 11403264*a^3*b^22*c^20*d^5 + 98762752*a^4*b^21*c^19*d^6 - 510394368*a^5*b^20*c^18*d^7 + 1766916096*a^6*b^19*c^17*d^8 - 4344840192*a^7*b^18*c^16*d^9 + 7796490240*a^8*b^17*c^15*d^10 - 10168369152*a^9*b^16*c^14*d^11 + 9007726592*a^10*b^15*c^13*d^12 - 3635478528*a^11*b^14*c^12*d^13 - 3635478528*a^12*b^13*c^11*d^14 + 9007726592*a^13*b^12*c^10*d^15 - 10168369152*a^14*b^11*c^9*d^16 + 7796490240*a^15*b^10*c^8*d^17 - 4344840192*a^16*b^9*c^7*d^18 + 1766916096*a^17*b^8*c^6*d^19 - 510394368*a^18*b^7*c^5*d^20 + 98762752*a^19*b^6*c^4*d^21 - 11403264*a^20*b^5*c^3*d^22 + 589824*a^21*b^4*c^2*d^23)*1i)/(1024*(a^4*b^12*c^16 + a^16*c^4*d^12 - 12*a^5*b^11*c^15*d - 12*a^15*b*c^5*d^11 + 66*a^6*b^10*c^14*d^2 - 220*a^7*b^9*c^13*d^3 + 495*a^8*b^8*c^12*d^4 - 792*a^9*b^7*c^11*d^5 + 924*a^10*b^6*c^10*d^6 - 792*a^11*b^5*c^9*d^7 + 495*a^12*b^4*c^8*d^8 - 220*a^13*b^3*c^7*d^9 + 66*a^14*b^2*c^6*d^10)) + ((-(81*b^11*c^4 + 14641*a^4*b^7*d^4 - 15972*a^3*b^8*c*d^3 + 6534*a^2*b^9*c^2*d^2 - 1188*a*b^10*c^3*d)/(65536*a^19*d^12 + 65536*a^7*b^12*c^12 - 786432*a^8*b^11*c^11*d + 4325376*a^9*b^10*c^10*d^2 - 14417920*a^10*b^9*c^9*d^3 + 32440320*a^11*b^8*c^8*d^4 - 51904512*a^12*b^7*c^7*d^5 + 60555264*a^13*b^6*c^6*d^6 - 51904512*a^14*b^5*c^5*d^7 + 32440320*a^15*b^4*c^4*d^8 - 14417920*a^16*b^3*c^3*d^9 + 4325376*a^17*b^2*c^2*d^10 - 786432*a^18*b*c*d^11))^(1/4)*(3072*a^4*b^19*c^19*d^4 - 45056*a^5*b^18*c^18*d^5 + 292864*a^6*b^17*c^17*d^6 - 1115136*a^7*b^16*c^16*d^7 + 2745344*a^8*b^15*c^15*d^8 - 4483072*a^9*b^14*c^14*d^9 + 4595712*a^10*b^13*c^13*d^10 - 1993728*a^11*b^12*c^12*d^11 - 1993728*a^12*b^11*c^11*d^12 + 4595712*a^13*b^10*c^10*d^13 - 4483072*a^14*b^9*c^9*d^14 + 2745344*a^15*b^8*c^8*d^15 - 1115136*a^16*b^7*c^7*d^16 + 292864*a^17*b^6*c^6*d^17 - 45056*a^18*b^5*c^5*d^18 + 3072*a^19*b^4*c^4*d^19))/(a^4*b^8*c^12 + a^12*c^4*d^8 - 8*a^5*b^7*c^11*d - 8*a^11*b*c^5*d^7 + 28*a^6*b^6*c^10*d^2 - 56*a^7*b^5*c^9*d^3 + 70*a^8*b^4*c^8*d^4 - 56*a^9*b^3*c^7*d^5 + 28*a^10*b^2*c^6*d^6))*1i + (((891*a^8*b^7*d^15)/64 + (891*b^15*c^8*d^7)/64 - (3105*a*b^14*c^7*d^8)/16 - (3105*a^7*b^8*c*d^14)/16 + (31509*a^2*b^13*c^6*d^9)/32 - (33069*a^3*b^12*c^5*d^10)/16 + (60307*a^4*b^11*c^4*d^11)/32 - (33069*a^5*b^10*c^3*d^12)/16 + (31509*a^6*b^9*c^2*d^13)/32)*1i)/(a^4*b^8*c^12 + a^12*c^4*d^8 - 8*a^5*b^7*c^11*d - 8*a^11*b*c^5*d^7 + 28*a^6*b^6*c^10*d^2 - 56*a^7*b^5*c^9*d^3 + 70*a^8*b^4*c^8*d^4 - 56*a^9*b^3*c^7*d^5 + 28*a^10*b^2*c^6*d^6))*1i - (x*(9801*a^8*b^9*d^17 + 9801*b^17*c^8*d^9 - 149094*a*b^16*c^7*d^10 - 149094*a^7*b^10*c*d^16 + 1001520*a^2*b^15*c^6*d^11 - 3484602*a^3*b^14*c^5*d^12 + 5769038*a^4*b^13*c^4*d^13 - 3484602*a^5*b^12*c^3*d^14 + 1001520*a^6*b^11*c^2*d^15)*1i)/(1024*(a^4*b^12*c^16 + a^16*c^4*d^12 - 12*a^5*b^11*c^15*d - 12*a^15*b*c^5*d^11 + 66*a^6*b^10*c^14*d^2 - 220*a^7*b^9*c^13*d^3 + 495*a^8*b^8*c^12*d^4 - 792*a^9*b^7*c^11*d^5 + 924*a^10*b^6*c^10*d^6 - 792*a^11*b^5*c^9*d^7 + 495*a^12*b^4*c^8*d^8 - 220*a^13*b^3*c^7*d^9 + 66*a^14*b^2*c^6*d^10))) - (-(81*b^11*c^4 + 14641*a^4*b^7*d^4 - 15972*a^3*b^8*c*d^3 + 6534*a^2*b^9*c^2*d^2 - 1188*a*b^10*c^3*d)/(65536*a^19*d^12 + 65536*a^7*b^12*c^12 - 786432*a^8*b^11*c^11*d + 4325376*a^9*b^10*c^10*d^2 - 14417920*a^10*b^9*c^9*d^3 + 32440320*a^11*b^8*c^8*d^4 - 51904512*a^12*b^7*c^7*d^5 + 60555264*a^13*b^6*c^6*d^6 - 51904512*a^14*b^5*c^5*d^7 + 32440320*a^15*b^4*c^4*d^8 - 14417920*a^16*b^3*c^3*d^9 + 4325376*a^17*b^2*c^2*d^10 - 786432*a^18*b*c*d^11))^(1/4)*((-(81*b^11*c^4 + 14641*a^4*b^7*d^4 - 15972*a^3*b^8*c*d^3 + 6534*a^2*b^9*c^2*d^2 - 1188*a*b^10*c^3*d)/(65536*a^19*d^12 + 65536*a^7*b^12*c^12 - 786432*a^8*b^11*c^11*d + 4325376*a^9*b^10*c^10*d^2 - 14417920*a^10*b^9*c^9*d^3 + 32440320*a^11*b^8*c^8*d^4 - 51904512*a^12*b^7*c^7*d^5 + 60555264*a^13*b^6*c^6*d^6 - 51904512*a^14*b^5*c^5*d^7 + 32440320*a^15*b^4*c^4*d^8 - 14417920*a^16*b^3*c^3*d^9 + 4325376*a^17*b^2*c^2*d^10 - 786432*a^18*b*c*d^11))^(1/4)*((-(81*b^11*c^4 + 14641*a^4*b^7*d^4 - 15972*a^3*b^8*c*d^3 + 6534*a^2*b^9*c^2*d^2 - 1188*a*b^10*c^3*d)/(65536*a^19*d^12 + 65536*a^7*b^12*c^12 - 786432*a^8*b^11*c^11*d + 4325376*a^9*b^10*c^10*d^2 - 14417920*a^10*b^9*c^9*d^3 + 32440320*a^11*b^8*c^8*d^4 - 51904512*a^12*b^7*c^7*d^5 + 60555264*a^13*b^6*c^6*d^6 - 51904512*a^14*b^5*c^5*d^7 + 32440320*a^15*b^4*c^4*d^8 - 14417920*a^16*b^3*c^3*d^9 + 4325376*a^17*b^2*c^2*d^10 - 786432*a^18*b*c*d^11))^(3/4)*((x*(589824*a^2*b^23*c^21*d^4 - 11403264*a^3*b^22*c^20*d^5 + 98762752*a^4*b^21*c^19*d^6 - 510394368*a^5*b^20*c^18*d^7 + 1766916096*a^6*b^19*c^17*d^8 - 4344840192*a^7*b^18*c^16*d^9 + 7796490240*a^8*b^17*c^15*d^10 - 10168369152*a^9*b^16*c^14*d^11 + 9007726592*a^10*b^15*c^13*d^12 - 3635478528*a^11*b^14*c^12*d^13 - 3635478528*a^12*b^13*c^11*d^14 + 9007726592*a^13*b^12*c^10*d^15 - 10168369152*a^14*b^11*c^9*d^16 + 7796490240*a^15*b^10*c^8*d^17 - 4344840192*a^16*b^9*c^7*d^18 + 1766916096*a^17*b^8*c^6*d^19 - 510394368*a^18*b^7*c^5*d^20 + 98762752*a^19*b^6*c^4*d^21 - 11403264*a^20*b^5*c^3*d^22 + 589824*a^21*b^4*c^2*d^23)*1i)/(1024*(a^4*b^12*c^16 + a^16*c^4*d^12 - 12*a^5*b^11*c^15*d - 12*a^15*b*c^5*d^11 + 66*a^6*b^10*c^14*d^2 - 220*a^7*b^9*c^13*d^3 + 495*a^8*b^8*c^12*d^4 - 792*a^9*b^7*c^11*d^5 + 924*a^10*b^6*c^10*d^6 - 792*a^11*b^5*c^9*d^7 + 495*a^12*b^4*c^8*d^8 - 220*a^13*b^3*c^7*d^9 + 66*a^14*b^2*c^6*d^10)) - ((-(81*b^11*c^4 + 14641*a^4*b^7*d^4 - 15972*a^3*b^8*c*d^3 + 6534*a^2*b^9*c^2*d^2 - 1188*a*b^10*c^3*d)/(65536*a^19*d^12 + 65536*a^7*b^12*c^12 - 786432*a^8*b^11*c^11*d + 4325376*a^9*b^10*c^10*d^2 - 14417920*a^10*b^9*c^9*d^3 + 32440320*a^11*b^8*c^8*d^4 - 51904512*a^12*b^7*c^7*d^5 + 60555264*a^13*b^6*c^6*d^6 - 51904512*a^14*b^5*c^5*d^7 + 32440320*a^15*b^4*c^4*d^8 - 14417920*a^16*b^3*c^3*d^9 + 4325376*a^17*b^2*c^2*d^10 - 786432*a^18*b*c*d^11))^(1/4)*(3072*a^4*b^19*c^19*d^4 - 45056*a^5*b^18*c^18*d^5 + 292864*a^6*b^17*c^17*d^6 - 1115136*a^7*b^16*c^16*d^7 + 2745344*a^8*b^15*c^15*d^8 - 4483072*a^9*b^14*c^14*d^9 + 4595712*a^10*b^13*c^13*d^10 - 1993728*a^11*b^12*c^12*d^11 - 1993728*a^12*b^11*c^11*d^12 + 4595712*a^13*b^10*c^10*d^13 - 4483072*a^14*b^9*c^9*d^14 + 2745344*a^15*b^8*c^8*d^15 - 1115136*a^16*b^7*c^7*d^16 + 292864*a^17*b^6*c^6*d^17 - 45056*a^18*b^5*c^5*d^18 + 3072*a^19*b^4*c^4*d^19))/(a^4*b^8*c^12 + a^12*c^4*d^8 - 8*a^5*b^7*c^11*d - 8*a^11*b*c^5*d^7 + 28*a^6*b^6*c^10*d^2 - 56*a^7*b^5*c^9*d^3 + 70*a^8*b^4*c^8*d^4 - 56*a^9*b^3*c^7*d^5 + 28*a^10*b^2*c^6*d^6))*1i - (((891*a^8*b^7*d^15)/64 + (891*b^15*c^8*d^7)/64 - (3105*a*b^14*c^7*d^8)/16 - (3105*a^7*b^8*c*d^14)/16 + (31509*a^2*b^13*c^6*d^9)/32 - (33069*a^3*b^12*c^5*d^10)/16 + (60307*a^4*b^11*c^4*d^11)/32 - (33069*a^5*b^10*c^3*d^12)/16 + (31509*a^6*b^9*c^2*d^13)/32)*1i)/(a^4*b^8*c^12 + a^12*c^4*d^8 - 8*a^5*b^7*c^11*d - 8*a^11*b*c^5*d^7 + 28*a^6*b^6*c^10*d^2 - 56*a^7*b^5*c^9*d^3 + 70*a^8*b^4*c^8*d^4 - 56*a^9*b^3*c^7*d^5 + 28*a^10*b^2*c^6*d^6))*1i - (x*(9801*a^8*b^9*d^17 + 9801*b^17*c^8*d^9 - 149094*a*b^16*c^7*d^10 - 149094*a^7*b^10*c*d^16 + 1001520*a^2*b^15*c^6*d^11 - 3484602*a^3*b^14*c^5*d^12 + 5769038*a^4*b^13*c^4*d^13 - 3484602*a^5*b^12*c^3*d^14 + 1001520*a^6*b^11*c^2*d^15)*1i)/(1024*(a^4*b^12*c^16 + a^16*c^4*d^12 - 12*a^5*b^11*c^15*d - 12*a^15*b*c^5*d^11 + 66*a^6*b^10*c^14*d^2 - 220*a^7*b^9*c^13*d^3 + 495*a^8*b^8*c^12*d^4 - 792*a^9*b^7*c^11*d^5 + 924*a^10*b^6*c^10*d^6 - 792*a^11*b^5*c^9*d^7 + 495*a^12*b^4*c^8*d^8 - 220*a^13*b^3*c^7*d^9 + 66*a^14*b^2*c^6*d^10)))))*(-(81*b^11*c^4 + 14641*a^4*b^7*d^4 - 15972*a^3*b^8*c*d^3 + 6534*a^2*b^9*c^2*d^2 - 1188*a*b^10*c^3*d)/(65536*a^19*d^12 + 65536*a^7*b^12*c^12 - 786432*a^8*b^11*c^11*d + 4325376*a^9*b^10*c^10*d^2 - 14417920*a^10*b^9*c^9*d^3 + 32440320*a^11*b^8*c^8*d^4 - 51904512*a^12*b^7*c^7*d^5 + 60555264*a^13*b^6*c^6*d^6 - 51904512*a^14*b^5*c^5*d^7 + 32440320*a^15*b^4*c^4*d^8 - 14417920*a^16*b^3*c^3*d^9 + 4325376*a^17*b^2*c^2*d^10 - 786432*a^18*b*c*d^11))^(1/4)","B"
173,0,-1,321,0.000000,"\text{Not used}","int((a - b*x^4)^(5/2)/(c - d*x^4),x)","\int \frac{{\left(a-b\,x^4\right)}^{5/2}}{c-d\,x^4} \,d x","Not used",1,"int((a - b*x^4)^(5/2)/(c - d*x^4), x)","F"
174,0,-1,277,0.000000,"\text{Not used}","int((a - b*x^4)^(3/2)/(c - d*x^4),x)","\int \frac{{\left(a-b\,x^4\right)}^{3/2}}{c-d\,x^4} \,d x","Not used",1,"int((a - b*x^4)^(3/2)/(c - d*x^4), x)","F"
175,0,-1,240,0.000000,"\text{Not used}","int((a - b*x^4)^(1/2)/(c - d*x^4),x)","\int \frac{\sqrt{a-b\,x^4}}{c-d\,x^4} \,d x","Not used",1,"int((a - b*x^4)^(1/2)/(c - d*x^4), x)","F"
176,0,-1,162,0.000000,"\text{Not used}","int(1/((a - b*x^4)^(1/2)*(c - d*x^4)),x)","\int \frac{1}{\sqrt{a-b\,x^4}\,\left(c-d\,x^4\right)} \,d x","Not used",1,"int(1/((a - b*x^4)^(1/2)*(c - d*x^4)), x)","F"
177,0,-1,281,0.000000,"\text{Not used}","int(1/((a - b*x^4)^(3/2)*(c - d*x^4)),x)","\int \frac{1}{{\left(a-b\,x^4\right)}^{3/2}\,\left(c-d\,x^4\right)} \,d x","Not used",1,"int(1/((a - b*x^4)^(3/2)*(c - d*x^4)), x)","F"
178,0,-1,334,0.000000,"\text{Not used}","int(1/((a - b*x^4)^(5/2)*(c - d*x^4)),x)","\int \frac{1}{{\left(a-b\,x^4\right)}^{5/2}\,\left(c-d\,x^4\right)} \,d x","Not used",1,"int(1/((a - b*x^4)^(5/2)*(c - d*x^4)), x)","F"
179,0,-1,926,0.000000,"\text{Not used}","int((a + b*x^4)^(3/2)/(c + d*x^4),x)","\int \frac{{\left(b\,x^4+a\right)}^{3/2}}{d\,x^4+c} \,d x","Not used",1,"int((a + b*x^4)^(3/2)/(c + d*x^4), x)","F"
180,0,-1,881,0.000000,"\text{Not used}","int((a + b*x^4)^(1/2)/(c + d*x^4),x)","\int \frac{\sqrt{b\,x^4+a}}{d\,x^4+c} \,d x","Not used",1,"int((a + b*x^4)^(1/2)/(c + d*x^4), x)","F"
181,0,-1,742,0.000000,"\text{Not used}","int(1/((a + b*x^4)^(1/2)*(c + d*x^4)),x)","\int \frac{1}{\sqrt{b\,x^4+a}\,\left(d\,x^4+c\right)} \,d x","Not used",1,"int(1/((a + b*x^4)^(1/2)*(c + d*x^4)), x)","F"
182,0,-1,913,0.000000,"\text{Not used}","int(1/((a + b*x^4)^(3/2)*(c + d*x^4)),x)","\int \frac{1}{{\left(b\,x^4+a\right)}^{3/2}\,\left(d\,x^4+c\right)} \,d x","Not used",1,"int(1/((a + b*x^4)^(3/2)*(c + d*x^4)), x)","F"
183,0,-1,976,0.000000,"\text{Not used}","int(1/((a + b*x^4)^(5/2)*(c + d*x^4)),x)","\int \frac{1}{{\left(b\,x^4+a\right)}^{5/2}\,\left(d\,x^4+c\right)} \,d x","Not used",1,"int(1/((a + b*x^4)^(5/2)*(c + d*x^4)), x)","F"
184,0,-1,426,0.000000,"\text{Not used}","int((a - b*x^4)^(7/2)/(c - d*x^4)^2,x)","\int \frac{{\left(a-b\,x^4\right)}^{7/2}}{{\left(c-d\,x^4\right)}^2} \,d x","Not used",1,"int((a - b*x^4)^(7/2)/(c - d*x^4)^2, x)","F"
185,0,-1,365,0.000000,"\text{Not used}","int((a - b*x^4)^(5/2)/(c - d*x^4)^2,x)","\int \frac{{\left(a-b\,x^4\right)}^{5/2}}{{\left(c-d\,x^4\right)}^2} \,d x","Not used",1,"int((a - b*x^4)^(5/2)/(c - d*x^4)^2, x)","F"
186,0,-1,309,0.000000,"\text{Not used}","int((a - b*x^4)^(3/2)/(c - d*x^4)^2,x)","\int \frac{{\left(a-b\,x^4\right)}^{3/2}}{{\left(c-d\,x^4\right)}^2} \,d x","Not used",1,"int((a - b*x^4)^(3/2)/(c - d*x^4)^2, x)","F"
187,0,-1,276,0.000000,"\text{Not used}","int((a - b*x^4)^(1/2)/(c - d*x^4)^2,x)","\int \frac{\sqrt{a-b\,x^4}}{{\left(c-d\,x^4\right)}^2} \,d x","Not used",1,"int((a - b*x^4)^(1/2)/(c - d*x^4)^2, x)","F"
188,0,-1,310,0.000000,"\text{Not used}","int(1/((a - b*x^4)^(1/2)*(c - d*x^4)^2),x)","\int \frac{1}{\sqrt{a-b\,x^4}\,{\left(c-d\,x^4\right)}^2} \,d x","Not used",1,"int(1/((a - b*x^4)^(1/2)*(c - d*x^4)^2), x)","F"
189,0,-1,362,0.000000,"\text{Not used}","int(1/((a - b*x^4)^(3/2)*(c - d*x^4)^2),x)","\int \frac{1}{{\left(a-b\,x^4\right)}^{3/2}\,{\left(c-d\,x^4\right)}^2} \,d x","Not used",1,"int(1/((a - b*x^4)^(3/2)*(c - d*x^4)^2), x)","F"
190,0,-1,439,0.000000,"\text{Not used}","int(1/((a - b*x^4)^(5/2)*(c - d*x^4)^2),x)","\int \frac{1}{{\left(a-b\,x^4\right)}^{5/2}\,{\left(c-d\,x^4\right)}^2} \,d x","Not used",1,"int(1/((a - b*x^4)^(5/2)*(c - d*x^4)^2), x)","F"
191,0,-1,103,0.000000,"\text{Not used}","int((a + b*x^4)^(1/2)/(a*c - b*c*x^4),x)","\int \frac{\sqrt{b\,x^4+a}}{a\,c-b\,c\,x^4} \,d x","Not used",1,"int((a + b*x^4)^(1/2)/(a*c - b*c*x^4), x)","F"
192,0,-1,116,0.000000,"\text{Not used}","int((a - b*x^4)^(1/2)/(a*c + b*c*x^4),x)","\int \frac{\sqrt{a-b\,x^4}}{b\,c\,x^4+a\,c} \,d x","Not used",1,"int((a - b*x^4)^(1/2)/(a*c + b*c*x^4), x)","F"
193,0,-1,211,0.000000,"\text{Not used}","int((a + b*x^4)^(7/4)/(c + d*x^4),x)","\int \frac{{\left(b\,x^4+a\right)}^{7/4}}{d\,x^4+c} \,d x","Not used",1,"int((a + b*x^4)^(7/4)/(c + d*x^4), x)","F"
194,0,-1,173,0.000000,"\text{Not used}","int((a + b*x^4)^(3/4)/(c + d*x^4),x)","\int \frac{{\left(b\,x^4+a\right)}^{3/4}}{d\,x^4+c} \,d x","Not used",1,"int((a + b*x^4)^(3/4)/(c + d*x^4), x)","F"
195,0,-1,105,0.000000,"\text{Not used}","int(1/((a + b*x^4)^(1/4)*(c + d*x^4)),x)","\int \frac{1}{{\left(b\,x^4+a\right)}^{1/4}\,\left(d\,x^4+c\right)} \,d x","Not used",1,"int(1/((a + b*x^4)^(1/4)*(c + d*x^4)), x)","F"
196,0,-1,134,0.000000,"\text{Not used}","int(1/((a + b*x^4)^(5/4)*(c + d*x^4)),x)","\int \frac{1}{{\left(b\,x^4+a\right)}^{5/4}\,\left(d\,x^4+c\right)} \,d x","Not used",1,"int(1/((a + b*x^4)^(5/4)*(c + d*x^4)), x)","F"
197,0,-1,180,0.000000,"\text{Not used}","int(1/((a + b*x^4)^(9/4)*(c + d*x^4)),x)","\int \frac{1}{{\left(b\,x^4+a\right)}^{9/4}\,\left(d\,x^4+c\right)} \,d x","Not used",1,"int(1/((a + b*x^4)^(9/4)*(c + d*x^4)), x)","F"
198,0,-1,233,0.000000,"\text{Not used}","int(1/((a + b*x^4)^(13/4)*(c + d*x^4)),x)","\int \frac{1}{{\left(b\,x^4+a\right)}^{13/4}\,\left(d\,x^4+c\right)} \,d x","Not used",1,"int(1/((a + b*x^4)^(13/4)*(c + d*x^4)), x)","F"
199,0,-1,316,0.000000,"\text{Not used}","int((a + b*x^4)^(9/4)/(c + d*x^4),x)","\int \frac{{\left(b\,x^4+a\right)}^{9/4}}{d\,x^4+c} \,d x","Not used",1,"int((a + b*x^4)^(9/4)/(c + d*x^4), x)","F"
200,0,-1,274,0.000000,"\text{Not used}","int((a + b*x^4)^(5/4)/(c + d*x^4),x)","\int \frac{{\left(b\,x^4+a\right)}^{5/4}}{d\,x^4+c} \,d x","Not used",1,"int((a + b*x^4)^(5/4)/(c + d*x^4), x)","F"
201,0,-1,166,0.000000,"\text{Not used}","int((a + b*x^4)^(1/4)/(c + d*x^4),x)","\int \frac{{\left(b\,x^4+a\right)}^{1/4}}{d\,x^4+c} \,d x","Not used",1,"int((a + b*x^4)^(1/4)/(c + d*x^4), x)","F"
202,0,-1,259,0.000000,"\text{Not used}","int(1/((a + b*x^4)^(3/4)*(c + d*x^4)),x)","\int \frac{1}{{\left(b\,x^4+a\right)}^{3/4}\,\left(d\,x^4+c\right)} \,d x","Not used",1,"int(1/((a + b*x^4)^(3/4)*(c + d*x^4)), x)","F"
203,0,-1,304,0.000000,"\text{Not used}","int(1/((a + b*x^4)^(7/4)*(c + d*x^4)),x)","\int \frac{1}{{\left(b\,x^4+a\right)}^{7/4}\,\left(d\,x^4+c\right)} \,d x","Not used",1,"int(1/((a + b*x^4)^(7/4)*(c + d*x^4)), x)","F"
204,0,-1,357,0.000000,"\text{Not used}","int(1/((a + b*x^4)^(11/4)*(c + d*x^4)),x)","\int \frac{1}{{\left(b\,x^4+a\right)}^{11/4}\,\left(d\,x^4+c\right)} \,d x","Not used",1,"int(1/((a + b*x^4)^(11/4)*(c + d*x^4)), x)","F"
205,0,-1,280,0.000000,"\text{Not used}","int((a + b*x^4)^(11/4)/(c + d*x^4)^2,x)","\int \frac{{\left(b\,x^4+a\right)}^{11/4}}{{\left(d\,x^4+c\right)}^2} \,d x","Not used",1,"int((a + b*x^4)^(11/4)/(c + d*x^4)^2, x)","F"
206,0,-1,230,0.000000,"\text{Not used}","int((a + b*x^4)^(7/4)/(c + d*x^4)^2,x)","\int \frac{{\left(b\,x^4+a\right)}^{7/4}}{{\left(d\,x^4+c\right)}^2} \,d x","Not used",1,"int((a + b*x^4)^(7/4)/(c + d*x^4)^2, x)","F"
207,0,-1,135,0.000000,"\text{Not used}","int((a + b*x^4)^(3/4)/(c + d*x^4)^2,x)","\int \frac{{\left(b\,x^4+a\right)}^{3/4}}{{\left(d\,x^4+c\right)}^2} \,d x","Not used",1,"int((a + b*x^4)^(3/4)/(c + d*x^4)^2, x)","F"
208,0,-1,162,0.000000,"\text{Not used}","int(1/((a + b*x^4)^(1/4)*(c + d*x^4)^2),x)","\int \frac{1}{{\left(b\,x^4+a\right)}^{1/4}\,{\left(d\,x^4+c\right)}^2} \,d x","Not used",1,"int(1/((a + b*x^4)^(1/4)*(c + d*x^4)^2), x)","F"
209,0,-1,205,0.000000,"\text{Not used}","int(1/((a + b*x^4)^(5/4)*(c + d*x^4)^2),x)","\int \frac{1}{{\left(b\,x^4+a\right)}^{5/4}\,{\left(d\,x^4+c\right)}^2} \,d x","Not used",1,"int(1/((a + b*x^4)^(5/4)*(c + d*x^4)^2), x)","F"
210,0,-1,266,0.000000,"\text{Not used}","int(1/((a + b*x^4)^(9/4)*(c + d*x^4)^2),x)","\int \frac{1}{{\left(b\,x^4+a\right)}^{9/4}\,{\left(d\,x^4+c\right)}^2} \,d x","Not used",1,"int(1/((a + b*x^4)^(9/4)*(c + d*x^4)^2), x)","F"
211,0,-1,353,0.000000,"\text{Not used}","int((a + b*x^4)^(9/4)/(c + d*x^4)^2,x)","\int \frac{{\left(b\,x^4+a\right)}^{9/4}}{{\left(d\,x^4+c\right)}^2} \,d x","Not used",1,"int((a + b*x^4)^(9/4)/(c + d*x^4)^2, x)","F"
212,0,-1,298,0.000000,"\text{Not used}","int((a + b*x^4)^(5/4)/(c + d*x^4)^2,x)","\int \frac{{\left(b\,x^4+a\right)}^{5/4}}{{\left(d\,x^4+c\right)}^2} \,d x","Not used",1,"int((a + b*x^4)^(5/4)/(c + d*x^4)^2, x)","F"
213,0,-1,308,0.000000,"\text{Not used}","int((a + b*x^4)^(1/4)/(c + d*x^4)^2,x)","\int \frac{{\left(b\,x^4+a\right)}^{1/4}}{{\left(d\,x^4+c\right)}^2} \,d x","Not used",1,"int((a + b*x^4)^(1/4)/(c + d*x^4)^2, x)","F"
214,0,-1,330,0.000000,"\text{Not used}","int(1/((a + b*x^4)^(3/4)*(c + d*x^4)^2),x)","\int \frac{1}{{\left(b\,x^4+a\right)}^{3/4}\,{\left(d\,x^4+c\right)}^2} \,d x","Not used",1,"int(1/((a + b*x^4)^(3/4)*(c + d*x^4)^2), x)","F"
215,0,-1,390,0.000000,"\text{Not used}","int(1/((a + b*x^4)^(7/4)*(c + d*x^4)^2),x)","\int \frac{1}{{\left(b\,x^4+a\right)}^{7/4}\,{\left(d\,x^4+c\right)}^2} \,d x","Not used",1,"int(1/((a + b*x^4)^(7/4)*(c + d*x^4)^2), x)","F"
216,0,-1,53,0.000000,"\text{Not used}","int(1/((x^4 + 1)^(1/4)*(x^4 + 2)),x)","\int \frac{1}{{\left(x^4+1\right)}^{1/4}\,\left(x^4+2\right)} \,d x","Not used",1,"int(1/((x^4 + 1)^(1/4)*(x^4 + 2)), x)","F"
217,0,-1,57,0.000000,"\text{Not used}","int(1/((a + b*x^4)^(1/4)*(a - x^4*(a - b))),x)","\int \frac{1}{{\left(b\,x^4+a\right)}^{1/4}\,\left(a-x^4\,\left(a-b\right)\right)} \,d x","Not used",1,"int(1/((a + b*x^4)^(1/4)*(a - x^4*(a - b))), x)","F"
218,0,-1,79,0.000000,"\text{Not used}","int((a + b*x^4)^p*(c + d*x^4)^q,x)","\int {\left(b\,x^4+a\right)}^p\,{\left(d\,x^4+c\right)}^q \,d x","Not used",1,"int((a + b*x^4)^p*(c + d*x^4)^q, x)","F"
219,0,-1,176,0.000000,"\text{Not used}","int((a + b*x^4)^2*(c + d*x^4)^q,x)","\int {\left(b\,x^4+a\right)}^2\,{\left(d\,x^4+c\right)}^q \,d x","Not used",1,"int((a + b*x^4)^2*(c + d*x^4)^q, x)","F"
220,0,-1,93,0.000000,"\text{Not used}","int((a + b*x^4)*(c + d*x^4)^q,x)","\int \left(b\,x^4+a\right)\,{\left(d\,x^4+c\right)}^q \,d x","Not used",1,"int((a + b*x^4)*(c + d*x^4)^q, x)","F"
221,0,-1,57,0.000000,"\text{Not used}","int((c + d*x^4)^q/(a + b*x^4),x)","\int \frac{{\left(d\,x^4+c\right)}^q}{b\,x^4+a} \,d x","Not used",1,"int((c + d*x^4)^q/(a + b*x^4), x)","F"
222,0,-1,57,0.000000,"\text{Not used}","int((c + d*x^4)^q/(a + b*x^4)^2,x)","\int \frac{{\left(d\,x^4+c\right)}^q}{{\left(b\,x^4+a\right)}^2} \,d x","Not used",1,"int((c + d*x^4)^q/(a + b*x^4)^2, x)","F"
223,0,-1,545,0.000000,"\text{Not used}","int(1/((a + b*x^5)^(1/5)*(c + d*x^5)),x)","\int \frac{1}{{\left(b\,x^5+a\right)}^{1/5}\,\left(d\,x^5+c\right)} \,d x","Not used",1,"int(1/((a + b*x^5)^(1/5)*(c + d*x^5)), x)","F"
224,1,173,143,2.593303,"\text{Not used}","int((a + b/x)^(1/2)*(c + d/x)^3,x)","{\left(a+\frac{b}{x}\right)}^{3/2}\,\left(\frac{6\,a\,d^3-6\,b\,c\,d^2}{3\,b^2}-\frac{4\,a\,d^3}{3\,b^2}\right)+\sqrt{a+\frac{b}{x}}\,\left(2\,a\,\left(\frac{6\,a\,d^3-6\,b\,c\,d^2}{b^2}-\frac{4\,a\,d^3}{b^2}\right)-\frac{6\,d\,{\left(a\,d-b\,c\right)}^2}{b^2}+\frac{2\,a^2\,d^3}{b^2}\right)+c^3\,x\,\sqrt{a+\frac{b}{x}}-\frac{2\,d^3\,{\left(a+\frac{b}{x}\right)}^{5/2}}{5\,b^2}-\frac{c^2\,\mathrm{atan}\left(\frac{\sqrt{a+\frac{b}{x}}\,1{}\mathrm{i}}{\sqrt{a}}\right)\,\left(6\,a\,d+b\,c\right)\,1{}\mathrm{i}}{\sqrt{a}}","Not used",1,"(a + b/x)^(3/2)*((6*a*d^3 - 6*b*c*d^2)/(3*b^2) - (4*a*d^3)/(3*b^2)) + (a + b/x)^(1/2)*(2*a*((6*a*d^3 - 6*b*c*d^2)/b^2 - (4*a*d^3)/b^2) - (6*d*(a*d - b*c)^2)/b^2 + (2*a^2*d^3)/b^2) + c^3*x*(a + b/x)^(1/2) - (2*d^3*(a + b/x)^(5/2))/(5*b^2) - (c^2*atan(((a + b/x)^(1/2)*1i)/a^(1/2))*(6*a*d + b*c)*1i)/a^(1/2)","B"
225,1,99,99,1.900953,"\text{Not used}","int((a + b/x)^(1/2)*(c + d/x)^2,x)","\left(\frac{4\,a\,d^2-4\,b\,c\,d}{b}-\frac{4\,a\,d^2}{b}\right)\,\sqrt{a+\frac{b}{x}}+c^2\,x\,\sqrt{a+\frac{b}{x}}-\frac{2\,d^2\,{\left(a+\frac{b}{x}\right)}^{3/2}}{3\,b}-\frac{c\,\mathrm{atan}\left(\frac{\sqrt{a+\frac{b}{x}}\,1{}\mathrm{i}}{\sqrt{a}}\right)\,\left(4\,a\,d+b\,c\right)\,1{}\mathrm{i}}{\sqrt{a}}","Not used",1,"((4*a*d^2 - 4*b*c*d)/b - (4*a*d^2)/b)*(a + b/x)^(1/2) + c^2*x*(a + b/x)^(1/2) - (2*d^2*(a + b/x)^(3/2))/(3*b) - (c*atan(((a + b/x)^(1/2)*1i)/a^(1/2))*(4*a*d + b*c)*1i)/a^(1/2)","B"
226,1,92,74,1.961791,"\text{Not used}","int((a + b/x)^(1/2)*(c + d/x),x)","2\,\sqrt{a}\,d\,\mathrm{atanh}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)-2\,d\,\sqrt{a+\frac{b}{x}}+c\,x\,\sqrt{a\,x^2+b\,x}\,\sqrt{\frac{1}{x^2}}+\frac{b\,c\,x\,\ln\left(\frac{\frac{b}{2}+a\,x+\sqrt{a}\,\sqrt{a\,x^2+b\,x}}{\sqrt{a}}\right)\,\sqrt{\frac{1}{x^2}}}{2\,\sqrt{a}}","Not used",1,"2*a^(1/2)*d*atanh((a + b/x)^(1/2)/a^(1/2)) - 2*d*(a + b/x)^(1/2) + c*x*(b*x + a*x^2)^(1/2)*(1/x^2)^(1/2) + (b*c*x*log((b/2 + a*x + a^(1/2)*(b*x + a*x^2)^(1/2))/a^(1/2))*(1/x^2)^(1/2))/(2*a^(1/2))","B"
227,1,58,39,0.076223,"\text{Not used}","int((a + b/x)^(1/2),x)","x\,\sqrt{a\,x^2+b\,x}\,\sqrt{\frac{1}{x^2}}+\frac{b\,x\,\ln\left(\frac{\frac{b}{2}+a\,x+\sqrt{a}\,\sqrt{a\,x^2+b\,x}}{\sqrt{a}}\right)\,\sqrt{\frac{1}{x^2}}}{2\,\sqrt{a}}","Not used",1,"x*(b*x + a*x^2)^(1/2)*(1/x^2)^(1/2) + (b*x*log((b/2 + a*x + a^(1/2)*(b*x + a*x^2)^(1/2))/a^(1/2))*(1/x^2)^(1/2))/(2*a^(1/2))","B"
228,1,149,104,1.631362,"\text{Not used}","int((a + b/x)^(1/2)/(c + d/x),x)","\frac{x\,\sqrt{a+\frac{b}{x}}}{c}+\frac{\ln\left(\sqrt{a+\frac{b}{x}}-\sqrt{a}\right)\,\left(a\,d-\frac{b\,c}{2}\right)}{\sqrt{a}\,c^2}-\frac{\ln\left(\sqrt{a+\frac{b}{x}}+\sqrt{a}\right)\,\left(2\,a\,d-b\,c\right)}{2\,\sqrt{a}\,c^2}-\frac{\mathrm{atan}\left(\frac{b^4\,d^3\,\sqrt{a+\frac{b}{x}}\,\sqrt{a\,d^2-b\,c\,d}\,4{}\mathrm{i}}{4\,a\,b^4\,d^4-4\,b^5\,c\,d^3}\right)\,\sqrt{a\,d^2-b\,c\,d}\,2{}\mathrm{i}}{c^2}","Not used",1,"(x*(a + b/x)^(1/2))/c - (atan((b^4*d^3*(a + b/x)^(1/2)*(a*d^2 - b*c*d)^(1/2)*4i)/(4*a*b^4*d^4 - 4*b^5*c*d^3))*(a*d^2 - b*c*d)^(1/2)*2i)/c^2 + (log((a + b/x)^(1/2) - a^(1/2))*(a*d - (b*c)/2))/(a^(1/2)*c^2) - (log((a + b/x)^(1/2) + a^(1/2))*(2*a*d - b*c))/(2*a^(1/2)*c^2)","B"
229,1,1195,147,2.263353,"\text{Not used}","int((a + b/x)^(1/2)/(c + d/x)^2,x)","-\frac{\frac{2\,b\,d\,{\left(a+\frac{b}{x}\right)}^{3/2}}{c^2}-\frac{b\,\sqrt{a+\frac{b}{x}}\,\left(2\,a\,d-b\,c\right)}{c^2}}{\left(a+\frac{b}{x}\right)\,\left(2\,a\,d-b\,c\right)-d\,{\left(a+\frac{b}{x}\right)}^2-a^2\,d+a\,b\,c}-\frac{\mathrm{atanh}\left(\frac{8\,b^5\,d^3\,\sqrt{a+\frac{b}{x}}}{\sqrt{a}\,\left(8\,b^5\,d^3-\frac{2\,b^6\,c\,d^2}{a}\right)}+\frac{2\,b^6\,d^2\,\sqrt{a+\frac{b}{x}}}{a^{3/2}\,\left(\frac{2\,b^6\,d^2}{a}-\frac{8\,b^5\,d^3}{c}\right)}\right)\,\left(4\,a\,d-b\,c\right)}{\sqrt{a}\,c^3}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{d\,\left(a\,d-b\,c\right)}\,\left(\frac{4\,\sqrt{a+\frac{b}{x}}\,\left(16\,a^2\,b^2\,d^5-16\,a\,b^3\,c\,d^4+5\,b^4\,c^2\,d^3\right)}{c^4}-\frac{\left(\frac{2\,\left(2\,b^4\,c^7\,d^2-4\,a\,b^3\,c^6\,d^3\right)}{c^6}-\frac{2\,\left(2\,b^3\,c^7\,d^2-4\,a\,b^2\,c^6\,d^3\right)\,\sqrt{a+\frac{b}{x}}\,\sqrt{d\,\left(a\,d-b\,c\right)}\,\left(4\,a\,d-3\,b\,c\right)}{c^4\,\left(b\,c^4-a\,c^3\,d\right)}\right)\,\sqrt{d\,\left(a\,d-b\,c\right)}\,\left(4\,a\,d-3\,b\,c\right)}{2\,\left(b\,c^4-a\,c^3\,d\right)}\right)\,\left(4\,a\,d-3\,b\,c\right)\,1{}\mathrm{i}}{2\,\left(b\,c^4-a\,c^3\,d\right)}+\frac{\sqrt{d\,\left(a\,d-b\,c\right)}\,\left(\frac{4\,\sqrt{a+\frac{b}{x}}\,\left(16\,a^2\,b^2\,d^5-16\,a\,b^3\,c\,d^4+5\,b^4\,c^2\,d^3\right)}{c^4}+\frac{\left(\frac{2\,\left(2\,b^4\,c^7\,d^2-4\,a\,b^3\,c^6\,d^3\right)}{c^6}+\frac{2\,\left(2\,b^3\,c^7\,d^2-4\,a\,b^2\,c^6\,d^3\right)\,\sqrt{a+\frac{b}{x}}\,\sqrt{d\,\left(a\,d-b\,c\right)}\,\left(4\,a\,d-3\,b\,c\right)}{c^4\,\left(b\,c^4-a\,c^3\,d\right)}\right)\,\sqrt{d\,\left(a\,d-b\,c\right)}\,\left(4\,a\,d-3\,b\,c\right)}{2\,\left(b\,c^4-a\,c^3\,d\right)}\right)\,\left(4\,a\,d-3\,b\,c\right)\,1{}\mathrm{i}}{2\,\left(b\,c^4-a\,c^3\,d\right)}}{\frac{4\,\left(16\,a^2\,b^3\,d^5-16\,a\,b^4\,c\,d^4+3\,b^5\,c^2\,d^3\right)}{c^6}-\frac{\sqrt{d\,\left(a\,d-b\,c\right)}\,\left(\frac{4\,\sqrt{a+\frac{b}{x}}\,\left(16\,a^2\,b^2\,d^5-16\,a\,b^3\,c\,d^4+5\,b^4\,c^2\,d^3\right)}{c^4}-\frac{\left(\frac{2\,\left(2\,b^4\,c^7\,d^2-4\,a\,b^3\,c^6\,d^3\right)}{c^6}-\frac{2\,\left(2\,b^3\,c^7\,d^2-4\,a\,b^2\,c^6\,d^3\right)\,\sqrt{a+\frac{b}{x}}\,\sqrt{d\,\left(a\,d-b\,c\right)}\,\left(4\,a\,d-3\,b\,c\right)}{c^4\,\left(b\,c^4-a\,c^3\,d\right)}\right)\,\sqrt{d\,\left(a\,d-b\,c\right)}\,\left(4\,a\,d-3\,b\,c\right)}{2\,\left(b\,c^4-a\,c^3\,d\right)}\right)\,\left(4\,a\,d-3\,b\,c\right)}{2\,\left(b\,c^4-a\,c^3\,d\right)}+\frac{\sqrt{d\,\left(a\,d-b\,c\right)}\,\left(\frac{4\,\sqrt{a+\frac{b}{x}}\,\left(16\,a^2\,b^2\,d^5-16\,a\,b^3\,c\,d^4+5\,b^4\,c^2\,d^3\right)}{c^4}+\frac{\left(\frac{2\,\left(2\,b^4\,c^7\,d^2-4\,a\,b^3\,c^6\,d^3\right)}{c^6}+\frac{2\,\left(2\,b^3\,c^7\,d^2-4\,a\,b^2\,c^6\,d^3\right)\,\sqrt{a+\frac{b}{x}}\,\sqrt{d\,\left(a\,d-b\,c\right)}\,\left(4\,a\,d-3\,b\,c\right)}{c^4\,\left(b\,c^4-a\,c^3\,d\right)}\right)\,\sqrt{d\,\left(a\,d-b\,c\right)}\,\left(4\,a\,d-3\,b\,c\right)}{2\,\left(b\,c^4-a\,c^3\,d\right)}\right)\,\left(4\,a\,d-3\,b\,c\right)}{2\,\left(b\,c^4-a\,c^3\,d\right)}}\right)\,\sqrt{d\,\left(a\,d-b\,c\right)}\,\left(4\,a\,d-3\,b\,c\right)\,1{}\mathrm{i}}{b\,c^4-a\,c^3\,d}","Not used",1,"- ((2*b*d*(a + b/x)^(3/2))/c^2 - (b*(a + b/x)^(1/2)*(2*a*d - b*c))/c^2)/((a + b/x)*(2*a*d - b*c) - d*(a + b/x)^2 - a^2*d + a*b*c) - (atanh((8*b^5*d^3*(a + b/x)^(1/2))/(a^(1/2)*(8*b^5*d^3 - (2*b^6*c*d^2)/a)) + (2*b^6*d^2*(a + b/x)^(1/2))/(a^(3/2)*((2*b^6*d^2)/a - (8*b^5*d^3)/c)))*(4*a*d - b*c))/(a^(1/2)*c^3) - (atan((((d*(a*d - b*c))^(1/2)*((4*(a + b/x)^(1/2)*(16*a^2*b^2*d^5 + 5*b^4*c^2*d^3 - 16*a*b^3*c*d^4))/c^4 - (((2*(2*b^4*c^7*d^2 - 4*a*b^3*c^6*d^3))/c^6 - (2*(2*b^3*c^7*d^2 - 4*a*b^2*c^6*d^3)*(a + b/x)^(1/2)*(d*(a*d - b*c))^(1/2)*(4*a*d - 3*b*c))/(c^4*(b*c^4 - a*c^3*d)))*(d*(a*d - b*c))^(1/2)*(4*a*d - 3*b*c))/(2*(b*c^4 - a*c^3*d)))*(4*a*d - 3*b*c)*1i)/(2*(b*c^4 - a*c^3*d)) + ((d*(a*d - b*c))^(1/2)*((4*(a + b/x)^(1/2)*(16*a^2*b^2*d^5 + 5*b^4*c^2*d^3 - 16*a*b^3*c*d^4))/c^4 + (((2*(2*b^4*c^7*d^2 - 4*a*b^3*c^6*d^3))/c^6 + (2*(2*b^3*c^7*d^2 - 4*a*b^2*c^6*d^3)*(a + b/x)^(1/2)*(d*(a*d - b*c))^(1/2)*(4*a*d - 3*b*c))/(c^4*(b*c^4 - a*c^3*d)))*(d*(a*d - b*c))^(1/2)*(4*a*d - 3*b*c))/(2*(b*c^4 - a*c^3*d)))*(4*a*d - 3*b*c)*1i)/(2*(b*c^4 - a*c^3*d)))/((4*(16*a^2*b^3*d^5 + 3*b^5*c^2*d^3 - 16*a*b^4*c*d^4))/c^6 - ((d*(a*d - b*c))^(1/2)*((4*(a + b/x)^(1/2)*(16*a^2*b^2*d^5 + 5*b^4*c^2*d^3 - 16*a*b^3*c*d^4))/c^4 - (((2*(2*b^4*c^7*d^2 - 4*a*b^3*c^6*d^3))/c^6 - (2*(2*b^3*c^7*d^2 - 4*a*b^2*c^6*d^3)*(a + b/x)^(1/2)*(d*(a*d - b*c))^(1/2)*(4*a*d - 3*b*c))/(c^4*(b*c^4 - a*c^3*d)))*(d*(a*d - b*c))^(1/2)*(4*a*d - 3*b*c))/(2*(b*c^4 - a*c^3*d)))*(4*a*d - 3*b*c))/(2*(b*c^4 - a*c^3*d)) + ((d*(a*d - b*c))^(1/2)*((4*(a + b/x)^(1/2)*(16*a^2*b^2*d^5 + 5*b^4*c^2*d^3 - 16*a*b^3*c*d^4))/c^4 + (((2*(2*b^4*c^7*d^2 - 4*a*b^3*c^6*d^3))/c^6 + (2*(2*b^3*c^7*d^2 - 4*a*b^2*c^6*d^3)*(a + b/x)^(1/2)*(d*(a*d - b*c))^(1/2)*(4*a*d - 3*b*c))/(c^4*(b*c^4 - a*c^3*d)))*(d*(a*d - b*c))^(1/2)*(4*a*d - 3*b*c))/(2*(b*c^4 - a*c^3*d)))*(4*a*d - 3*b*c))/(2*(b*c^4 - a*c^3*d))))*(d*(a*d - b*c))^(1/2)*(4*a*d - 3*b*c)*1i)/(b*c^4 - a*c^3*d)","B"
230,1,1895,213,3.729476,"\text{Not used}","int((a + b/x)^(1/2)/(c + d/x)^3,x)","\frac{\ln\left(\sqrt{a+\frac{b}{x}}\,\sqrt{d\,{\left(a\,d-b\,c\right)}^3}-a^2\,d^2-b^2\,c^2+2\,a\,b\,c\,d\right)\,\sqrt{d\,{\left(a\,d-b\,c\right)}^3}\,\left(3\,a^2\,d^2-5\,a\,b\,c\,d+\frac{15\,b^2\,c^2}{8}\right)}{-a^3\,c^4\,d^3+3\,a^2\,b\,c^5\,d^2-3\,a\,b^2\,c^6\,d+b^3\,c^7}-\frac{\frac{b\,\sqrt{a+\frac{b}{x}}\,\left(12\,a^2\,d^2-17\,a\,b\,c\,d+4\,b^2\,c^2\right)}{4\,c^3}+\frac{b\,{\left(a+\frac{b}{x}\right)}^{5/2}\,\left(12\,a\,d^3-11\,b\,c\,d^2\right)}{4\,c^3\,\left(a\,d-b\,c\right)}-\frac{d\,{\left(a+\frac{b}{x}\right)}^{3/2}\,\left(24\,a^2\,b\,d^2-40\,a\,b^2\,c\,d+17\,b^3\,c^2\right)}{4\,c^3\,\left(a\,d-b\,c\right)}}{{\left(a+\frac{b}{x}\right)}^2\,\left(3\,a\,d^2-2\,b\,c\,d\right)-\left(a+\frac{b}{x}\right)\,\left(3\,a^2\,d^2-4\,a\,b\,c\,d+b^2\,c^2\right)-d^2\,{\left(a+\frac{b}{x}\right)}^3+a^3\,d^2+a\,b^2\,c^2-2\,a^2\,b\,c\,d}-\frac{\ln\left(\sqrt{a+\frac{b}{x}}\,\sqrt{d\,{\left(a\,d-b\,c\right)}^3}+a^2\,d^2+b^2\,c^2-2\,a\,b\,c\,d\right)\,\sqrt{d\,{\left(a\,d-b\,c\right)}^3}\,\left(24\,a^2\,d^2-40\,a\,b\,c\,d+15\,b^2\,c^2\right)}{8\,\left(-a^3\,c^4\,d^3+3\,a^2\,b\,c^5\,d^2-3\,a\,b^2\,c^6\,d+b^3\,c^7\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\sqrt{a+\frac{b}{x}}\,\left(1152\,a^4\,b^2\,d^7-3264\,a^3\,b^3\,c\,d^6+3296\,a^2\,b^4\,c^2\,d^5-1424\,a\,b^5\,c^3\,d^4+241\,b^6\,c^4\,d^3\right)}{8\,\left(a^2\,c^6\,d^2-2\,a\,b\,c^7\,d+b^2\,c^8\right)}-\frac{\left(6\,a\,d-b\,c\right)\,\left(\frac{-12\,a^3\,b^3\,c^8\,d^5+29\,a^2\,b^4\,c^9\,d^4-21\,a\,b^5\,c^{10}\,d^3+4\,b^6\,c^{11}\,d^2}{a^2\,c^9\,d^2-2\,a\,b\,c^{10}\,d+b^2\,c^{11}}-\frac{\sqrt{a+\frac{b}{x}}\,\left(6\,a\,d-b\,c\right)\,\left(-128\,a^3\,b^2\,c^8\,d^5+320\,a^2\,b^3\,c^9\,d^4-256\,a\,b^4\,c^{10}\,d^3+64\,b^5\,c^{11}\,d^2\right)}{16\,\sqrt{a}\,c^4\,\left(a^2\,c^6\,d^2-2\,a\,b\,c^7\,d+b^2\,c^8\right)}\right)}{2\,\sqrt{a}\,c^4}\right)\,\left(6\,a\,d-b\,c\right)\,1{}\mathrm{i}}{2\,\sqrt{a}\,c^4}+\frac{\left(\frac{\sqrt{a+\frac{b}{x}}\,\left(1152\,a^4\,b^2\,d^7-3264\,a^3\,b^3\,c\,d^6+3296\,a^2\,b^4\,c^2\,d^5-1424\,a\,b^5\,c^3\,d^4+241\,b^6\,c^4\,d^3\right)}{8\,\left(a^2\,c^6\,d^2-2\,a\,b\,c^7\,d+b^2\,c^8\right)}+\frac{\left(6\,a\,d-b\,c\right)\,\left(\frac{-12\,a^3\,b^3\,c^8\,d^5+29\,a^2\,b^4\,c^9\,d^4-21\,a\,b^5\,c^{10}\,d^3+4\,b^6\,c^{11}\,d^2}{a^2\,c^9\,d^2-2\,a\,b\,c^{10}\,d+b^2\,c^{11}}+\frac{\sqrt{a+\frac{b}{x}}\,\left(6\,a\,d-b\,c\right)\,\left(-128\,a^3\,b^2\,c^8\,d^5+320\,a^2\,b^3\,c^9\,d^4-256\,a\,b^4\,c^{10}\,d^3+64\,b^5\,c^{11}\,d^2\right)}{16\,\sqrt{a}\,c^4\,\left(a^2\,c^6\,d^2-2\,a\,b\,c^7\,d+b^2\,c^8\right)}\right)}{2\,\sqrt{a}\,c^4}\right)\,\left(6\,a\,d-b\,c\right)\,1{}\mathrm{i}}{2\,\sqrt{a}\,c^4}}{\frac{216\,a^4\,b^3\,d^7-594\,a^3\,b^4\,c\,d^6+558\,a^2\,b^5\,c^2\,d^5-\frac{805\,a\,b^6\,c^3\,d^4}{4}+\frac{165\,b^7\,c^4\,d^3}{8}}{a^2\,c^9\,d^2-2\,a\,b\,c^{10}\,d+b^2\,c^{11}}-\frac{\left(\frac{\sqrt{a+\frac{b}{x}}\,\left(1152\,a^4\,b^2\,d^7-3264\,a^3\,b^3\,c\,d^6+3296\,a^2\,b^4\,c^2\,d^5-1424\,a\,b^5\,c^3\,d^4+241\,b^6\,c^4\,d^3\right)}{8\,\left(a^2\,c^6\,d^2-2\,a\,b\,c^7\,d+b^2\,c^8\right)}-\frac{\left(6\,a\,d-b\,c\right)\,\left(\frac{-12\,a^3\,b^3\,c^8\,d^5+29\,a^2\,b^4\,c^9\,d^4-21\,a\,b^5\,c^{10}\,d^3+4\,b^6\,c^{11}\,d^2}{a^2\,c^9\,d^2-2\,a\,b\,c^{10}\,d+b^2\,c^{11}}-\frac{\sqrt{a+\frac{b}{x}}\,\left(6\,a\,d-b\,c\right)\,\left(-128\,a^3\,b^2\,c^8\,d^5+320\,a^2\,b^3\,c^9\,d^4-256\,a\,b^4\,c^{10}\,d^3+64\,b^5\,c^{11}\,d^2\right)}{16\,\sqrt{a}\,c^4\,\left(a^2\,c^6\,d^2-2\,a\,b\,c^7\,d+b^2\,c^8\right)}\right)}{2\,\sqrt{a}\,c^4}\right)\,\left(6\,a\,d-b\,c\right)}{2\,\sqrt{a}\,c^4}+\frac{\left(\frac{\sqrt{a+\frac{b}{x}}\,\left(1152\,a^4\,b^2\,d^7-3264\,a^3\,b^3\,c\,d^6+3296\,a^2\,b^4\,c^2\,d^5-1424\,a\,b^5\,c^3\,d^4+241\,b^6\,c^4\,d^3\right)}{8\,\left(a^2\,c^6\,d^2-2\,a\,b\,c^7\,d+b^2\,c^8\right)}+\frac{\left(6\,a\,d-b\,c\right)\,\left(\frac{-12\,a^3\,b^3\,c^8\,d^5+29\,a^2\,b^4\,c^9\,d^4-21\,a\,b^5\,c^{10}\,d^3+4\,b^6\,c^{11}\,d^2}{a^2\,c^9\,d^2-2\,a\,b\,c^{10}\,d+b^2\,c^{11}}+\frac{\sqrt{a+\frac{b}{x}}\,\left(6\,a\,d-b\,c\right)\,\left(-128\,a^3\,b^2\,c^8\,d^5+320\,a^2\,b^3\,c^9\,d^4-256\,a\,b^4\,c^{10}\,d^3+64\,b^5\,c^{11}\,d^2\right)}{16\,\sqrt{a}\,c^4\,\left(a^2\,c^6\,d^2-2\,a\,b\,c^7\,d+b^2\,c^8\right)}\right)}{2\,\sqrt{a}\,c^4}\right)\,\left(6\,a\,d-b\,c\right)}{2\,\sqrt{a}\,c^4}}\right)\,\left(6\,a\,d-b\,c\right)\,1{}\mathrm{i}}{\sqrt{a}\,c^4}","Not used",1,"(log((a + b/x)^(1/2)*(d*(a*d - b*c)^3)^(1/2) - a^2*d^2 - b^2*c^2 + 2*a*b*c*d)*(d*(a*d - b*c)^3)^(1/2)*(3*a^2*d^2 + (15*b^2*c^2)/8 - 5*a*b*c*d))/(b^3*c^7 - a^3*c^4*d^3 + 3*a^2*b*c^5*d^2 - 3*a*b^2*c^6*d) - ((b*(a + b/x)^(1/2)*(12*a^2*d^2 + 4*b^2*c^2 - 17*a*b*c*d))/(4*c^3) + (b*(a + b/x)^(5/2)*(12*a*d^3 - 11*b*c*d^2))/(4*c^3*(a*d - b*c)) - (d*(a + b/x)^(3/2)*(17*b^3*c^2 + 24*a^2*b*d^2 - 40*a*b^2*c*d))/(4*c^3*(a*d - b*c)))/((a + b/x)^2*(3*a*d^2 - 2*b*c*d) - (a + b/x)*(3*a^2*d^2 + b^2*c^2 - 4*a*b*c*d) - d^2*(a + b/x)^3 + a^3*d^2 + a*b^2*c^2 - 2*a^2*b*c*d) - (log((a + b/x)^(1/2)*(d*(a*d - b*c)^3)^(1/2) + a^2*d^2 + b^2*c^2 - 2*a*b*c*d)*(d*(a*d - b*c)^3)^(1/2)*(24*a^2*d^2 + 15*b^2*c^2 - 40*a*b*c*d))/(8*(b^3*c^7 - a^3*c^4*d^3 + 3*a^2*b*c^5*d^2 - 3*a*b^2*c^6*d)) - (atan((((((a + b/x)^(1/2)*(1152*a^4*b^2*d^7 + 241*b^6*c^4*d^3 - 1424*a*b^5*c^3*d^4 - 3264*a^3*b^3*c*d^6 + 3296*a^2*b^4*c^2*d^5))/(8*(b^2*c^8 + a^2*c^6*d^2 - 2*a*b*c^7*d)) - ((6*a*d - b*c)*((4*b^6*c^11*d^2 - 21*a*b^5*c^10*d^3 + 29*a^2*b^4*c^9*d^4 - 12*a^3*b^3*c^8*d^5)/(b^2*c^11 + a^2*c^9*d^2 - 2*a*b*c^10*d) - ((a + b/x)^(1/2)*(6*a*d - b*c)*(64*b^5*c^11*d^2 - 256*a*b^4*c^10*d^3 + 320*a^2*b^3*c^9*d^4 - 128*a^3*b^2*c^8*d^5))/(16*a^(1/2)*c^4*(b^2*c^8 + a^2*c^6*d^2 - 2*a*b*c^7*d))))/(2*a^(1/2)*c^4))*(6*a*d - b*c)*1i)/(2*a^(1/2)*c^4) + ((((a + b/x)^(1/2)*(1152*a^4*b^2*d^7 + 241*b^6*c^4*d^3 - 1424*a*b^5*c^3*d^4 - 3264*a^3*b^3*c*d^6 + 3296*a^2*b^4*c^2*d^5))/(8*(b^2*c^8 + a^2*c^6*d^2 - 2*a*b*c^7*d)) + ((6*a*d - b*c)*((4*b^6*c^11*d^2 - 21*a*b^5*c^10*d^3 + 29*a^2*b^4*c^9*d^4 - 12*a^3*b^3*c^8*d^5)/(b^2*c^11 + a^2*c^9*d^2 - 2*a*b*c^10*d) + ((a + b/x)^(1/2)*(6*a*d - b*c)*(64*b^5*c^11*d^2 - 256*a*b^4*c^10*d^3 + 320*a^2*b^3*c^9*d^4 - 128*a^3*b^2*c^8*d^5))/(16*a^(1/2)*c^4*(b^2*c^8 + a^2*c^6*d^2 - 2*a*b*c^7*d))))/(2*a^(1/2)*c^4))*(6*a*d - b*c)*1i)/(2*a^(1/2)*c^4))/((216*a^4*b^3*d^7 + (165*b^7*c^4*d^3)/8 - (805*a*b^6*c^3*d^4)/4 - 594*a^3*b^4*c*d^6 + 558*a^2*b^5*c^2*d^5)/(b^2*c^11 + a^2*c^9*d^2 - 2*a*b*c^10*d) - ((((a + b/x)^(1/2)*(1152*a^4*b^2*d^7 + 241*b^6*c^4*d^3 - 1424*a*b^5*c^3*d^4 - 3264*a^3*b^3*c*d^6 + 3296*a^2*b^4*c^2*d^5))/(8*(b^2*c^8 + a^2*c^6*d^2 - 2*a*b*c^7*d)) - ((6*a*d - b*c)*((4*b^6*c^11*d^2 - 21*a*b^5*c^10*d^3 + 29*a^2*b^4*c^9*d^4 - 12*a^3*b^3*c^8*d^5)/(b^2*c^11 + a^2*c^9*d^2 - 2*a*b*c^10*d) - ((a + b/x)^(1/2)*(6*a*d - b*c)*(64*b^5*c^11*d^2 - 256*a*b^4*c^10*d^3 + 320*a^2*b^3*c^9*d^4 - 128*a^3*b^2*c^8*d^5))/(16*a^(1/2)*c^4*(b^2*c^8 + a^2*c^6*d^2 - 2*a*b*c^7*d))))/(2*a^(1/2)*c^4))*(6*a*d - b*c))/(2*a^(1/2)*c^4) + ((((a + b/x)^(1/2)*(1152*a^4*b^2*d^7 + 241*b^6*c^4*d^3 - 1424*a*b^5*c^3*d^4 - 3264*a^3*b^3*c*d^6 + 3296*a^2*b^4*c^2*d^5))/(8*(b^2*c^8 + a^2*c^6*d^2 - 2*a*b*c^7*d)) + ((6*a*d - b*c)*((4*b^6*c^11*d^2 - 21*a*b^5*c^10*d^3 + 29*a^2*b^4*c^9*d^4 - 12*a^3*b^3*c^8*d^5)/(b^2*c^11 + a^2*c^9*d^2 - 2*a*b*c^10*d) + ((a + b/x)^(1/2)*(6*a*d - b*c)*(64*b^5*c^11*d^2 - 256*a*b^4*c^10*d^3 + 320*a^2*b^3*c^9*d^4 - 128*a^3*b^2*c^8*d^5))/(16*a^(1/2)*c^4*(b^2*c^8 + a^2*c^6*d^2 - 2*a*b*c^7*d))))/(2*a^(1/2)*c^4))*(6*a*d - b*c))/(2*a^(1/2)*c^4)))*(6*a*d - b*c)*1i)/(a^(1/2)*c^4)","B"
231,1,327,164,3.878150,"\text{Not used}","int((a + b/x)^(3/2)*(c + d/x)^3,x)","{\left(a+\frac{b}{x}\right)}^{5/2}\,\left(\frac{6\,a\,d^3-6\,b\,c\,d^2}{5\,b^2}-\frac{4\,a\,d^3}{5\,b^2}\right)+\sqrt{a+\frac{b}{x}}\,\left(\frac{2\,{\left(a\,d-b\,c\right)}^3}{b^2}+2\,a\,\left(2\,a\,\left(\frac{6\,a\,d^3-6\,b\,c\,d^2}{b^2}-\frac{4\,a\,d^3}{b^2}\right)-\frac{6\,d\,{\left(a\,d-b\,c\right)}^2}{b^2}+\frac{2\,a^2\,d^3}{b^2}\right)-a^2\,\left(\frac{6\,a\,d^3-6\,b\,c\,d^2}{b^2}-\frac{4\,a\,d^3}{b^2}\right)\right)+{\left(a+\frac{b}{x}\right)}^{3/2}\,\left(\frac{2\,a\,\left(\frac{6\,a\,d^3-6\,b\,c\,d^2}{b^2}-\frac{4\,a\,d^3}{b^2}\right)}{3}-\frac{2\,d\,{\left(a\,d-b\,c\right)}^2}{b^2}+\frac{2\,a^2\,d^3}{3\,b^2}\right)-\frac{2\,d^3\,{\left(a+\frac{b}{x}\right)}^{7/2}}{7\,b^2}+a\,c^3\,x\,\sqrt{a+\frac{b}{x}}-2\,c^2\,\mathrm{atan}\left(\frac{2\,c^2\,\sqrt{a+\frac{b}{x}}\,\left(2\,a\,d+b\,c\right)\,\sqrt{-\frac{9\,a}{4}}}{6\,d\,a^2\,c^2+3\,b\,a\,c^3}\right)\,\left(2\,a\,d+b\,c\right)\,\sqrt{-\frac{9\,a}{4}}","Not used",1,"(a + b/x)^(5/2)*((6*a*d^3 - 6*b*c*d^2)/(5*b^2) - (4*a*d^3)/(5*b^2)) + (a + b/x)^(1/2)*((2*(a*d - b*c)^3)/b^2 + 2*a*(2*a*((6*a*d^3 - 6*b*c*d^2)/b^2 - (4*a*d^3)/b^2) - (6*d*(a*d - b*c)^2)/b^2 + (2*a^2*d^3)/b^2) - a^2*((6*a*d^3 - 6*b*c*d^2)/b^2 - (4*a*d^3)/b^2)) + (a + b/x)^(3/2)*((2*a*((6*a*d^3 - 6*b*c*d^2)/b^2 - (4*a*d^3)/b^2))/3 - (2*d*(a*d - b*c)^2)/b^2 + (2*a^2*d^3)/(3*b^2)) - (2*d^3*(a + b/x)^(7/2))/(7*b^2) + a*c^3*x*(a + b/x)^(1/2) - 2*c^2*atan((2*c^2*(a + b/x)^(1/2)*(2*a*d + b*c)*(-(9*a)/4)^(1/2))/(6*a^2*c^2*d + 3*a*b*c^3))*(2*a*d + b*c)*(-(9*a)/4)^(1/2)","B"
232,1,197,126,2.578953,"\text{Not used}","int((a + b/x)^(3/2)*(c + d/x)^2,x)","\sqrt{a+\frac{b}{x}}\,\left(2\,a\,\left(\frac{4\,a\,d^2-4\,b\,c\,d}{b}-\frac{4\,a\,d^2}{b}\right)-\frac{2\,{\left(a\,d-b\,c\right)}^2}{b}+\frac{2\,a^2\,d^2}{b}\right)+\left(\frac{4\,a\,d^2-4\,b\,c\,d}{3\,b}-\frac{4\,a\,d^2}{3\,b}\right)\,{\left(a+\frac{b}{x}\right)}^{3/2}-\frac{2\,d^2\,{\left(a+\frac{b}{x}\right)}^{5/2}}{5\,b}+a\,c^2\,x\,\sqrt{a+\frac{b}{x}}-2\,c\,\mathrm{atan}\left(\frac{2\,c\,\sqrt{a+\frac{b}{x}}\,\left(4\,a\,d+3\,b\,c\right)\,\sqrt{-\frac{a}{4}}}{4\,d\,a^2\,c+3\,b\,a\,c^2}\right)\,\left(4\,a\,d+3\,b\,c\right)\,\sqrt{-\frac{a}{4}}","Not used",1,"(a + b/x)^(1/2)*(2*a*((4*a*d^2 - 4*b*c*d)/b - (4*a*d^2)/b) - (2*(a*d - b*c)^2)/b + (2*a^2*d^2)/b) + ((4*a*d^2 - 4*b*c*d)/(3*b) - (4*a*d^2)/(3*b))*(a + b/x)^(3/2) - (2*d^2*(a + b/x)^(5/2))/(5*b) + a*c^2*x*(a + b/x)^(1/2) - 2*c*atan((2*c*(a + b/x)^(1/2)*(4*a*d + 3*b*c)*(-a/4)^(1/2))/(3*a*b*c^2 + 4*a^2*c*d))*(4*a*d + 3*b*c)*(-a/4)^(1/2)","B"
233,1,81,100,2.512001,"\text{Not used}","int((a + b/x)^(3/2)*(c + d/x),x)","2\,a^{3/2}\,d\,\mathrm{atanh}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)-\frac{2\,d\,{\left(a+\frac{b}{x}\right)}^{3/2}}{3}-2\,a\,d\,\sqrt{a+\frac{b}{x}}-\frac{2\,c\,x\,{\left(a+\frac{b}{x}\right)}^{3/2}\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{2},-\frac{1}{2};\ \frac{1}{2};\ -\frac{a\,x}{b}\right)}{{\left(\frac{a\,x}{b}+1\right)}^{3/2}}","Not used",1,"2*a^(3/2)*d*atanh((a + b/x)^(1/2)/a^(1/2)) - (2*d*(a + b/x)^(3/2))/3 - 2*a*d*(a + b/x)^(1/2) - (2*c*x*(a + b/x)^(3/2)*hypergeom([-3/2, -1/2], 1/2, -(a*x)/b))/((a*x)/b + 1)^(3/2)","B"
234,1,34,54,1.501010,"\text{Not used}","int((a + b/x)^(3/2),x)","-\frac{2\,x\,{\left(a+\frac{b}{x}\right)}^{3/2}\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{2},-\frac{1}{2};\ \frac{1}{2};\ -\frac{a\,x}{b}\right)}{{\left(\frac{a\,x}{b}+1\right)}^{3/2}}","Not used",1,"-(2*x*(a + b/x)^(3/2)*hypergeom([-3/2, -1/2], 1/2, -(a*x)/b))/((a*x)/b + 1)^(3/2)","B"
235,1,556,106,1.684469,"\text{Not used}","int((a + b/x)^(3/2)/(c + d/x),x)","\frac{a\,x\,\sqrt{a+\frac{b}{x}}}{c}-\frac{\sqrt{a}\,\mathrm{atanh}\left(\frac{58\,a^{3/2}\,b^6\,d^2\,\sqrt{a+\frac{b}{x}}}{58\,a^2\,b^6\,d^2-24\,a\,b^7\,c\,d-\frac{46\,a^3\,b^5\,d^3}{c}+\frac{12\,a^4\,b^4\,d^4}{c^2}}+\frac{46\,a^{5/2}\,b^5\,d^3\,\sqrt{a+\frac{b}{x}}}{46\,a^3\,b^5\,d^3-58\,a^2\,b^6\,c\,d^2-\frac{12\,a^4\,b^4\,d^4}{c}+24\,a\,b^7\,c^2\,d}+\frac{12\,a^{7/2}\,b^4\,d^4\,\sqrt{a+\frac{b}{x}}}{12\,a^4\,b^4\,d^4-46\,a^3\,b^5\,c\,d^3+58\,a^2\,b^6\,c^2\,d^2-24\,a\,b^7\,c^3\,d}-\frac{24\,\sqrt{a}\,b^7\,c\,d\,\sqrt{a+\frac{b}{x}}}{58\,a^2\,b^6\,d^2-24\,a\,b^7\,c\,d-\frac{46\,a^3\,b^5\,d^3}{c}+\frac{12\,a^4\,b^4\,d^4}{c^2}}\right)\,\left(2\,a\,d-3\,b\,c\right)}{c^2}+\frac{2\,\mathrm{atanh}\left(\frac{12\,a^2\,b^4\,d^2\,\sqrt{a+\frac{b}{x}}\,\sqrt{a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d}}{12\,a^4\,b^4\,d^4-40\,a^3\,b^5\,c\,d^3+44\,a^2\,b^6\,c^2\,d^2-16\,a\,b^7\,c^3\,d}+\frac{16\,a\,b^5\,d\,\sqrt{a+\frac{b}{x}}\,\sqrt{a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d}}{40\,a^3\,b^5\,d^3-44\,a^2\,b^6\,c\,d^2-\frac{12\,a^4\,b^4\,d^4}{c}+16\,a\,b^7\,c^2\,d}\right)\,\sqrt{d\,{\left(a\,d-b\,c\right)}^3}}{c^2\,d}","Not used",1,"(a*x*(a + b/x)^(1/2))/c - (a^(1/2)*atanh((58*a^(3/2)*b^6*d^2*(a + b/x)^(1/2))/(58*a^2*b^6*d^2 - 24*a*b^7*c*d - (46*a^3*b^5*d^3)/c + (12*a^4*b^4*d^4)/c^2) + (46*a^(5/2)*b^5*d^3*(a + b/x)^(1/2))/(46*a^3*b^5*d^3 - 58*a^2*b^6*c*d^2 - (12*a^4*b^4*d^4)/c + 24*a*b^7*c^2*d) + (12*a^(7/2)*b^4*d^4*(a + b/x)^(1/2))/(12*a^4*b^4*d^4 - 46*a^3*b^5*c*d^3 + 58*a^2*b^6*c^2*d^2 - 24*a*b^7*c^3*d) - (24*a^(1/2)*b^7*c*d*(a + b/x)^(1/2))/(58*a^2*b^6*d^2 - 24*a*b^7*c*d - (46*a^3*b^5*d^3)/c + (12*a^4*b^4*d^4)/c^2))*(2*a*d - 3*b*c))/c^2 + (2*atanh((12*a^2*b^4*d^2*(a + b/x)^(1/2)*(a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3)^(1/2))/(12*a^4*b^4*d^4 - 40*a^3*b^5*c*d^3 + 44*a^2*b^6*c^2*d^2 - 16*a*b^7*c^3*d) + (16*a*b^5*d*(a + b/x)^(1/2)*(a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3)^(1/2))/(40*a^3*b^5*d^3 - 44*a^2*b^6*c*d^2 - (12*a^4*b^4*d^4)/c + 16*a*b^7*c^2*d))*(d*(a*d - b*c)^3)^(1/2))/(c^2*d)","B"
236,1,448,156,2.164629,"\text{Not used}","int((a + b/x)^(3/2)/(c + d/x)^2,x)","\frac{\mathrm{atanh}\left(\frac{8\,a^2\,b^5\,d^2\,\sqrt{a+\frac{b}{x}}\,\sqrt{a\,d^2-b\,c\,d}}{8\,a^3\,b^5\,d^3-10\,a^2\,b^6\,c\,d^2+2\,a\,b^7\,c^2\,d}-\frac{2\,a\,b^6\,d\,\sqrt{a+\frac{b}{x}}\,\sqrt{a\,d^2-b\,c\,d}}{2\,a\,b^7\,c\,d-10\,a^2\,b^6\,d^2+\frac{8\,a^3\,b^5\,d^3}{c}}\right)\,\sqrt{d\,\left(a\,d-b\,c\right)}\,\left(4\,a\,d-b\,c\right)}{c^3\,d}-\frac{\sqrt{a}\,\mathrm{atanh}\left(\frac{6\,\sqrt{a}\,b^7\,d\,\sqrt{a+\frac{b}{x}}}{6\,a\,b^7\,d-\frac{14\,a^2\,b^6\,d^2}{c}+\frac{8\,a^3\,b^5\,d^3}{c^2}}-\frac{14\,a^{3/2}\,b^6\,d^2\,\sqrt{a+\frac{b}{x}}}{6\,a\,b^7\,c\,d-14\,a^2\,b^6\,d^2+\frac{8\,a^3\,b^5\,d^3}{c}}+\frac{8\,a^{5/2}\,b^5\,d^3\,\sqrt{a+\frac{b}{x}}}{8\,a^3\,b^5\,d^3-14\,a^2\,b^6\,c\,d^2+6\,a\,b^7\,c^2\,d}\right)\,\left(4\,a\,d-3\,b\,c\right)}{c^3}-\frac{\frac{2\,\left(a\,b^2\,c-a^2\,b\,d\right)\,\sqrt{a+\frac{b}{x}}}{c^2}+\frac{b\,{\left(a+\frac{b}{x}\right)}^{3/2}\,\left(2\,a\,d-b\,c\right)}{c^2}}{\left(a+\frac{b}{x}\right)\,\left(2\,a\,d-b\,c\right)-d\,{\left(a+\frac{b}{x}\right)}^2-a^2\,d+a\,b\,c}","Not used",1,"(atanh((8*a^2*b^5*d^2*(a + b/x)^(1/2)*(a*d^2 - b*c*d)^(1/2))/(8*a^3*b^5*d^3 - 10*a^2*b^6*c*d^2 + 2*a*b^7*c^2*d) - (2*a*b^6*d*(a + b/x)^(1/2)*(a*d^2 - b*c*d)^(1/2))/(2*a*b^7*c*d - 10*a^2*b^6*d^2 + (8*a^3*b^5*d^3)/c))*(d*(a*d - b*c))^(1/2)*(4*a*d - b*c))/(c^3*d) - (a^(1/2)*atanh((6*a^(1/2)*b^7*d*(a + b/x)^(1/2))/(6*a*b^7*d - (14*a^2*b^6*d^2)/c + (8*a^3*b^5*d^3)/c^2) - (14*a^(3/2)*b^6*d^2*(a + b/x)^(1/2))/(6*a*b^7*c*d - 14*a^2*b^6*d^2 + (8*a^3*b^5*d^3)/c) + (8*a^(5/2)*b^5*d^3*(a + b/x)^(1/2))/(8*a^3*b^5*d^3 - 14*a^2*b^6*c*d^2 + 6*a*b^7*c^2*d))*(4*a*d - 3*b*c))/c^3 - ((2*(a*b^2*c - a^2*b*d)*(a + b/x)^(1/2))/c^2 + (b*(a + b/x)^(3/2)*(2*a*d - b*c))/c^2)/((a + b/x)*(2*a*d - b*c) - d*(a + b/x)^2 - a^2*d + a*b*c)","B"
237,1,1664,209,3.471846,"\text{Not used}","int((a + b/x)^(3/2)/(c + d/x)^3,x)","-\frac{\frac{3\,\sqrt{a+\frac{b}{x}}\,\left(4\,a^3\,b\,d^2-7\,a^2\,b^2\,c\,d+3\,a\,b^3\,c^2\right)}{4\,c^3}-\frac{{\left(a+\frac{b}{x}\right)}^{3/2}\,\left(24\,a^2\,b\,d^2-24\,a\,b^2\,c\,d+5\,b^3\,c^2\right)}{4\,c^3}+\frac{3\,b\,{\left(a+\frac{b}{x}\right)}^{5/2}\,\left(4\,a\,d^2-b\,c\,d\right)}{4\,c^3}}{{\left(a+\frac{b}{x}\right)}^2\,\left(3\,a\,d^2-2\,b\,c\,d\right)-\left(a+\frac{b}{x}\right)\,\left(3\,a^2\,d^2-4\,a\,b\,c\,d+b^2\,c^2\right)-d^2\,{\left(a+\frac{b}{x}\right)}^3+a^3\,d^2+a\,b^2\,c^2-2\,a^2\,b\,c\,d}-\frac{3\,\sqrt{a}\,\mathrm{atanh}\left(\frac{27\,\sqrt{a}\,b^7\,d\,\sqrt{a+\frac{b}{x}}}{8\,\left(\frac{27\,a\,b^7\,d}{8}-\frac{27\,a^2\,b^6\,d^2}{4\,c}\right)}+\frac{27\,a^{3/2}\,b^6\,d^2\,\sqrt{a+\frac{b}{x}}}{4\,\left(\frac{27\,a^2\,b^6\,d^2}{4}-\frac{27\,a\,b^7\,c\,d}{8}\right)}\right)\,\left(2\,a\,d-b\,c\right)}{c^4}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\sqrt{a+\frac{b}{x}}\,\left(1152\,a^4\,b^2\,d^5-1728\,a^3\,b^3\,c\,d^4+864\,a^2\,b^4\,c^2\,d^3-144\,a\,b^5\,c^3\,d^2+9\,b^6\,c^4\,d\right)}{8\,c^6}-\frac{3\,\sqrt{d\,\left(a\,d-b\,c\right)}\,\left(\frac{9\,a\,b^4\,c^9\,d^2-12\,a^2\,b^3\,c^8\,d^3}{c^9}-\frac{3\,\left(64\,b^3\,c^9\,d^2-128\,a\,b^2\,c^8\,d^3\right)\,\sqrt{a+\frac{b}{x}}\,\sqrt{d\,\left(a\,d-b\,c\right)}\,\left(8\,a^2\,d^2-8\,a\,b\,c\,d+b^2\,c^2\right)}{64\,c^6\,\left(a\,c^4\,d^2-b\,c^5\,d\right)}\right)\,\left(8\,a^2\,d^2-8\,a\,b\,c\,d+b^2\,c^2\right)}{8\,\left(a\,c^4\,d^2-b\,c^5\,d\right)}\right)\,\sqrt{d\,\left(a\,d-b\,c\right)}\,\left(8\,a^2\,d^2-8\,a\,b\,c\,d+b^2\,c^2\right)\,3{}\mathrm{i}}{8\,\left(a\,c^4\,d^2-b\,c^5\,d\right)}+\frac{\left(\frac{\sqrt{a+\frac{b}{x}}\,\left(1152\,a^4\,b^2\,d^5-1728\,a^3\,b^3\,c\,d^4+864\,a^2\,b^4\,c^2\,d^3-144\,a\,b^5\,c^3\,d^2+9\,b^6\,c^4\,d\right)}{8\,c^6}+\frac{3\,\sqrt{d\,\left(a\,d-b\,c\right)}\,\left(\frac{9\,a\,b^4\,c^9\,d^2-12\,a^2\,b^3\,c^8\,d^3}{c^9}+\frac{3\,\left(64\,b^3\,c^9\,d^2-128\,a\,b^2\,c^8\,d^3\right)\,\sqrt{a+\frac{b}{x}}\,\sqrt{d\,\left(a\,d-b\,c\right)}\,\left(8\,a^2\,d^2-8\,a\,b\,c\,d+b^2\,c^2\right)}{64\,c^6\,\left(a\,c^4\,d^2-b\,c^5\,d\right)}\right)\,\left(8\,a^2\,d^2-8\,a\,b\,c\,d+b^2\,c^2\right)}{8\,\left(a\,c^4\,d^2-b\,c^5\,d\right)}\right)\,\sqrt{d\,\left(a\,d-b\,c\right)}\,\left(8\,a^2\,d^2-8\,a\,b\,c\,d+b^2\,c^2\right)\,3{}\mathrm{i}}{8\,\left(a\,c^4\,d^2-b\,c^5\,d\right)}}{\frac{216\,a^5\,b^3\,d^5-378\,a^4\,b^4\,c\,d^4+216\,a^3\,b^5\,c^2\,d^3-\frac{189\,a^2\,b^6\,c^3\,d^2}{4}+\frac{27\,a\,b^7\,c^4\,d}{8}}{c^9}-\frac{3\,\left(\frac{\sqrt{a+\frac{b}{x}}\,\left(1152\,a^4\,b^2\,d^5-1728\,a^3\,b^3\,c\,d^4+864\,a^2\,b^4\,c^2\,d^3-144\,a\,b^5\,c^3\,d^2+9\,b^6\,c^4\,d\right)}{8\,c^6}-\frac{3\,\sqrt{d\,\left(a\,d-b\,c\right)}\,\left(\frac{9\,a\,b^4\,c^9\,d^2-12\,a^2\,b^3\,c^8\,d^3}{c^9}-\frac{3\,\left(64\,b^3\,c^9\,d^2-128\,a\,b^2\,c^8\,d^3\right)\,\sqrt{a+\frac{b}{x}}\,\sqrt{d\,\left(a\,d-b\,c\right)}\,\left(8\,a^2\,d^2-8\,a\,b\,c\,d+b^2\,c^2\right)}{64\,c^6\,\left(a\,c^4\,d^2-b\,c^5\,d\right)}\right)\,\left(8\,a^2\,d^2-8\,a\,b\,c\,d+b^2\,c^2\right)}{8\,\left(a\,c^4\,d^2-b\,c^5\,d\right)}\right)\,\sqrt{d\,\left(a\,d-b\,c\right)}\,\left(8\,a^2\,d^2-8\,a\,b\,c\,d+b^2\,c^2\right)}{8\,\left(a\,c^4\,d^2-b\,c^5\,d\right)}+\frac{3\,\left(\frac{\sqrt{a+\frac{b}{x}}\,\left(1152\,a^4\,b^2\,d^5-1728\,a^3\,b^3\,c\,d^4+864\,a^2\,b^4\,c^2\,d^3-144\,a\,b^5\,c^3\,d^2+9\,b^6\,c^4\,d\right)}{8\,c^6}+\frac{3\,\sqrt{d\,\left(a\,d-b\,c\right)}\,\left(\frac{9\,a\,b^4\,c^9\,d^2-12\,a^2\,b^3\,c^8\,d^3}{c^9}+\frac{3\,\left(64\,b^3\,c^9\,d^2-128\,a\,b^2\,c^8\,d^3\right)\,\sqrt{a+\frac{b}{x}}\,\sqrt{d\,\left(a\,d-b\,c\right)}\,\left(8\,a^2\,d^2-8\,a\,b\,c\,d+b^2\,c^2\right)}{64\,c^6\,\left(a\,c^4\,d^2-b\,c^5\,d\right)}\right)\,\left(8\,a^2\,d^2-8\,a\,b\,c\,d+b^2\,c^2\right)}{8\,\left(a\,c^4\,d^2-b\,c^5\,d\right)}\right)\,\sqrt{d\,\left(a\,d-b\,c\right)}\,\left(8\,a^2\,d^2-8\,a\,b\,c\,d+b^2\,c^2\right)}{8\,\left(a\,c^4\,d^2-b\,c^5\,d\right)}}\right)\,\sqrt{d\,\left(a\,d-b\,c\right)}\,\left(8\,a^2\,d^2-8\,a\,b\,c\,d+b^2\,c^2\right)\,3{}\mathrm{i}}{4\,\left(a\,c^4\,d^2-b\,c^5\,d\right)}","Not used",1,"- ((3*(a + b/x)^(1/2)*(3*a*b^3*c^2 + 4*a^3*b*d^2 - 7*a^2*b^2*c*d))/(4*c^3) - ((a + b/x)^(3/2)*(5*b^3*c^2 + 24*a^2*b*d^2 - 24*a*b^2*c*d))/(4*c^3) + (3*b*(a + b/x)^(5/2)*(4*a*d^2 - b*c*d))/(4*c^3))/((a + b/x)^2*(3*a*d^2 - 2*b*c*d) - (a + b/x)*(3*a^2*d^2 + b^2*c^2 - 4*a*b*c*d) - d^2*(a + b/x)^3 + a^3*d^2 + a*b^2*c^2 - 2*a^2*b*c*d) - (3*a^(1/2)*atanh((27*a^(1/2)*b^7*d*(a + b/x)^(1/2))/(8*((27*a*b^7*d)/8 - (27*a^2*b^6*d^2)/(4*c))) + (27*a^(3/2)*b^6*d^2*(a + b/x)^(1/2))/(4*((27*a^2*b^6*d^2)/4 - (27*a*b^7*c*d)/8)))*(2*a*d - b*c))/c^4 - (atan((((((a + b/x)^(1/2)*(9*b^6*c^4*d + 1152*a^4*b^2*d^5 - 144*a*b^5*c^3*d^2 - 1728*a^3*b^3*c*d^4 + 864*a^2*b^4*c^2*d^3))/(8*c^6) - (3*(d*(a*d - b*c))^(1/2)*((9*a*b^4*c^9*d^2 - 12*a^2*b^3*c^8*d^3)/c^9 - (3*(64*b^3*c^9*d^2 - 128*a*b^2*c^8*d^3)*(a + b/x)^(1/2)*(d*(a*d - b*c))^(1/2)*(8*a^2*d^2 + b^2*c^2 - 8*a*b*c*d))/(64*c^6*(a*c^4*d^2 - b*c^5*d)))*(8*a^2*d^2 + b^2*c^2 - 8*a*b*c*d))/(8*(a*c^4*d^2 - b*c^5*d)))*(d*(a*d - b*c))^(1/2)*(8*a^2*d^2 + b^2*c^2 - 8*a*b*c*d)*3i)/(8*(a*c^4*d^2 - b*c^5*d)) + ((((a + b/x)^(1/2)*(9*b^6*c^4*d + 1152*a^4*b^2*d^5 - 144*a*b^5*c^3*d^2 - 1728*a^3*b^3*c*d^4 + 864*a^2*b^4*c^2*d^3))/(8*c^6) + (3*(d*(a*d - b*c))^(1/2)*((9*a*b^4*c^9*d^2 - 12*a^2*b^3*c^8*d^3)/c^9 + (3*(64*b^3*c^9*d^2 - 128*a*b^2*c^8*d^3)*(a + b/x)^(1/2)*(d*(a*d - b*c))^(1/2)*(8*a^2*d^2 + b^2*c^2 - 8*a*b*c*d))/(64*c^6*(a*c^4*d^2 - b*c^5*d)))*(8*a^2*d^2 + b^2*c^2 - 8*a*b*c*d))/(8*(a*c^4*d^2 - b*c^5*d)))*(d*(a*d - b*c))^(1/2)*(8*a^2*d^2 + b^2*c^2 - 8*a*b*c*d)*3i)/(8*(a*c^4*d^2 - b*c^5*d)))/((216*a^5*b^3*d^5 - 378*a^4*b^4*c*d^4 - (189*a^2*b^6*c^3*d^2)/4 + 216*a^3*b^5*c^2*d^3 + (27*a*b^7*c^4*d)/8)/c^9 - (3*(((a + b/x)^(1/2)*(9*b^6*c^4*d + 1152*a^4*b^2*d^5 - 144*a*b^5*c^3*d^2 - 1728*a^3*b^3*c*d^4 + 864*a^2*b^4*c^2*d^3))/(8*c^6) - (3*(d*(a*d - b*c))^(1/2)*((9*a*b^4*c^9*d^2 - 12*a^2*b^3*c^8*d^3)/c^9 - (3*(64*b^3*c^9*d^2 - 128*a*b^2*c^8*d^3)*(a + b/x)^(1/2)*(d*(a*d - b*c))^(1/2)*(8*a^2*d^2 + b^2*c^2 - 8*a*b*c*d))/(64*c^6*(a*c^4*d^2 - b*c^5*d)))*(8*a^2*d^2 + b^2*c^2 - 8*a*b*c*d))/(8*(a*c^4*d^2 - b*c^5*d)))*(d*(a*d - b*c))^(1/2)*(8*a^2*d^2 + b^2*c^2 - 8*a*b*c*d))/(8*(a*c^4*d^2 - b*c^5*d)) + (3*(((a + b/x)^(1/2)*(9*b^6*c^4*d + 1152*a^4*b^2*d^5 - 144*a*b^5*c^3*d^2 - 1728*a^3*b^3*c*d^4 + 864*a^2*b^4*c^2*d^3))/(8*c^6) + (3*(d*(a*d - b*c))^(1/2)*((9*a*b^4*c^9*d^2 - 12*a^2*b^3*c^8*d^3)/c^9 + (3*(64*b^3*c^9*d^2 - 128*a*b^2*c^8*d^3)*(a + b/x)^(1/2)*(d*(a*d - b*c))^(1/2)*(8*a^2*d^2 + b^2*c^2 - 8*a*b*c*d))/(64*c^6*(a*c^4*d^2 - b*c^5*d)))*(8*a^2*d^2 + b^2*c^2 - 8*a*b*c*d))/(8*(a*c^4*d^2 - b*c^5*d)))*(d*(a*d - b*c))^(1/2)*(8*a^2*d^2 + b^2*c^2 - 8*a*b*c*d))/(8*(a*c^4*d^2 - b*c^5*d))))*(d*(a*d - b*c))^(1/2)*(8*a^2*d^2 + b^2*c^2 - 8*a*b*c*d)*3i)/(4*(a*c^4*d^2 - b*c^5*d))","B"
238,1,487,198,6.048739,"\text{Not used}","int((a + b/x)^(5/2)*(c + d/x)^3,x)","{\left(a+\frac{b}{x}\right)}^{7/2}\,\left(\frac{6\,a\,d^3-6\,b\,c\,d^2}{7\,b^2}-\frac{4\,a\,d^3}{7\,b^2}\right)-\sqrt{a+\frac{b}{x}}\,\left(a^2\,\left(2\,a\,\left(\frac{6\,a\,d^3-6\,b\,c\,d^2}{b^2}-\frac{4\,a\,d^3}{b^2}\right)-\frac{6\,d\,{\left(a\,d-b\,c\right)}^2}{b^2}+\frac{2\,a^2\,d^3}{b^2}\right)-2\,a\,\left(\frac{2\,{\left(a\,d-b\,c\right)}^3}{b^2}+2\,a\,\left(2\,a\,\left(\frac{6\,a\,d^3-6\,b\,c\,d^2}{b^2}-\frac{4\,a\,d^3}{b^2}\right)-\frac{6\,d\,{\left(a\,d-b\,c\right)}^2}{b^2}+\frac{2\,a^2\,d^3}{b^2}\right)-a^2\,\left(\frac{6\,a\,d^3-6\,b\,c\,d^2}{b^2}-\frac{4\,a\,d^3}{b^2}\right)\right)\right)+{\left(a+\frac{b}{x}\right)}^{3/2}\,\left(\frac{2\,{\left(a\,d-b\,c\right)}^3}{3\,b^2}+\frac{2\,a\,\left(2\,a\,\left(\frac{6\,a\,d^3-6\,b\,c\,d^2}{b^2}-\frac{4\,a\,d^3}{b^2}\right)-\frac{6\,d\,{\left(a\,d-b\,c\right)}^2}{b^2}+\frac{2\,a^2\,d^3}{b^2}\right)}{3}-\frac{a^2\,\left(\frac{6\,a\,d^3-6\,b\,c\,d^2}{b^2}-\frac{4\,a\,d^3}{b^2}\right)}{3}\right)+{\left(a+\frac{b}{x}\right)}^{5/2}\,\left(\frac{2\,a\,\left(\frac{6\,a\,d^3-6\,b\,c\,d^2}{b^2}-\frac{4\,a\,d^3}{b^2}\right)}{5}-\frac{6\,d\,{\left(a\,d-b\,c\right)}^2}{5\,b^2}+\frac{2\,a^2\,d^3}{5\,b^2}\right)-\frac{2\,d^3\,{\left(a+\frac{b}{x}\right)}^{9/2}}{9\,b^2}+a^2\,c^3\,x\,\sqrt{a+\frac{b}{x}}-a^{3/2}\,c^2\,\mathrm{atan}\left(\frac{\sqrt{a+\frac{b}{x}}\,1{}\mathrm{i}}{\sqrt{a}}\right)\,\left(6\,a\,d+5\,b\,c\right)\,1{}\mathrm{i}","Not used",1,"(a + b/x)^(7/2)*((6*a*d^3 - 6*b*c*d^2)/(7*b^2) - (4*a*d^3)/(7*b^2)) - (a + b/x)^(1/2)*(a^2*(2*a*((6*a*d^3 - 6*b*c*d^2)/b^2 - (4*a*d^3)/b^2) - (6*d*(a*d - b*c)^2)/b^2 + (2*a^2*d^3)/b^2) - 2*a*((2*(a*d - b*c)^3)/b^2 + 2*a*(2*a*((6*a*d^3 - 6*b*c*d^2)/b^2 - (4*a*d^3)/b^2) - (6*d*(a*d - b*c)^2)/b^2 + (2*a^2*d^3)/b^2) - a^2*((6*a*d^3 - 6*b*c*d^2)/b^2 - (4*a*d^3)/b^2))) + (a + b/x)^(3/2)*((2*(a*d - b*c)^3)/(3*b^2) + (2*a*(2*a*((6*a*d^3 - 6*b*c*d^2)/b^2 - (4*a*d^3)/b^2) - (6*d*(a*d - b*c)^2)/b^2 + (2*a^2*d^3)/b^2))/3 - (a^2*((6*a*d^3 - 6*b*c*d^2)/b^2 - (4*a*d^3)/b^2))/3) + (a + b/x)^(5/2)*((2*a*((6*a*d^3 - 6*b*c*d^2)/b^2 - (4*a*d^3)/b^2))/5 - (6*d*(a*d - b*c)^2)/(5*b^2) + (2*a^2*d^3)/(5*b^2)) - (2*d^3*(a + b/x)^(9/2))/(9*b^2) + a^2*c^3*x*(a + b/x)^(1/2) - a^(3/2)*c^2*atan(((a + b/x)^(1/2)*1i)/a^(1/2))*(6*a*d + 5*b*c)*1i","B"
239,1,271,152,3.791177,"\text{Not used}","int((a + b/x)^(5/2)*(c + d/x)^2,x)","{\left(a+\frac{b}{x}\right)}^{3/2}\,\left(\frac{2\,a\,\left(\frac{4\,a\,d^2-4\,b\,c\,d}{b}-\frac{4\,a\,d^2}{b}\right)}{3}-\frac{2\,{\left(a\,d-b\,c\right)}^2}{3\,b}+\frac{2\,a^2\,d^2}{3\,b}\right)+\left(\frac{4\,a\,d^2-4\,b\,c\,d}{5\,b}-\frac{4\,a\,d^2}{5\,b}\right)\,{\left(a+\frac{b}{x}\right)}^{5/2}-\sqrt{a+\frac{b}{x}}\,\left(a^2\,\left(\frac{4\,a\,d^2-4\,b\,c\,d}{b}-\frac{4\,a\,d^2}{b}\right)-2\,a\,\left(2\,a\,\left(\frac{4\,a\,d^2-4\,b\,c\,d}{b}-\frac{4\,a\,d^2}{b}\right)-\frac{2\,{\left(a\,d-b\,c\right)}^2}{b}+\frac{2\,a^2\,d^2}{b}\right)\right)-\frac{2\,d^2\,{\left(a+\frac{b}{x}\right)}^{7/2}}{7\,b}+a^2\,c^2\,x\,\sqrt{a+\frac{b}{x}}-a^{3/2}\,c\,\mathrm{atan}\left(\frac{\sqrt{a+\frac{b}{x}}\,1{}\mathrm{i}}{\sqrt{a}}\right)\,\left(4\,a\,d+5\,b\,c\right)\,1{}\mathrm{i}","Not used",1,"(a + b/x)^(3/2)*((2*a*((4*a*d^2 - 4*b*c*d)/b - (4*a*d^2)/b))/3 - (2*(a*d - b*c)^2)/(3*b) + (2*a^2*d^2)/(3*b)) + ((4*a*d^2 - 4*b*c*d)/(5*b) - (4*a*d^2)/(5*b))*(a + b/x)^(5/2) - (a + b/x)^(1/2)*(a^2*((4*a*d^2 - 4*b*c*d)/b - (4*a*d^2)/b) - 2*a*(2*a*((4*a*d^2 - 4*b*c*d)/b - (4*a*d^2)/b) - (2*(a*d - b*c)^2)/b + (2*a^2*d^2)/b)) - (2*d^2*(a + b/x)^(7/2))/(7*b) + a^2*c^2*x*(a + b/x)^(1/2) - a^(3/2)*c*atan(((a + b/x)^(1/2)*1i)/a^(1/2))*(4*a*d + 5*b*c)*1i","B"
240,1,99,125,3.479977,"\text{Not used}","int((a + b/x)^(5/2)*(c + d/x),x)","-\frac{2\,d\,{\left(a+\frac{b}{x}\right)}^{5/2}}{5}-2\,a^2\,d\,\sqrt{a+\frac{b}{x}}-\frac{2\,a\,d\,{\left(a+\frac{b}{x}\right)}^{3/2}}{3}-\frac{2\,c\,x\,{\left(a+\frac{b}{x}\right)}^{5/2}\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{2},-\frac{3}{2};\ -\frac{1}{2};\ -\frac{a\,x}{b}\right)}{3\,{\left(\frac{a\,x}{b}+1\right)}^{5/2}}-a^{5/2}\,d\,\mathrm{atan}\left(\frac{\sqrt{a+\frac{b}{x}}\,1{}\mathrm{i}}{\sqrt{a}}\right)\,2{}\mathrm{i}","Not used",1,"- (2*d*(a + b/x)^(5/2))/5 - 2*a^2*d*(a + b/x)^(1/2) - a^(5/2)*d*atan(((a + b/x)^(1/2)*1i)/a^(1/2))*2i - (2*a*d*(a + b/x)^(3/2))/3 - (2*c*x*(a + b/x)^(5/2)*hypergeom([-5/2, -3/2], -1/2, -(a*x)/b))/(3*((a*x)/b + 1)^(5/2))","B"
241,1,34,71,1.629988,"\text{Not used}","int((a + b/x)^(5/2),x)","-\frac{2\,x\,{\left(a+\frac{b}{x}\right)}^{5/2}\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{2},-\frac{3}{2};\ -\frac{1}{2};\ -\frac{a\,x}{b}\right)}{3\,{\left(\frac{a\,x}{b}+1\right)}^{5/2}}","Not used",1,"-(2*x*(a + b/x)^(5/2)*hypergeom([-5/2, -3/2], -1/2, -(a*x)/b))/(3*((a*x)/b + 1)^(5/2))","B"
242,1,1427,134,2.156038,"\text{Not used}","int((a + b/x)^(5/2)/(c + d/x),x)","\frac{a^2\,b\,d\,\sqrt{a+\frac{b}{x}}}{c\,\left(d\,\left(a+\frac{b}{x}\right)-a\,d\right)}-\frac{2\,b^2\,\sqrt{a+\frac{b}{x}}}{d}+\frac{\mathrm{atan}\left(\frac{a^3\,b^5\,\sqrt{a+\frac{b}{x}}\,\sqrt{a^5\,d^8-5\,a^4\,b\,c\,d^7+10\,a^3\,b^2\,c^2\,d^6-10\,a^2\,b^3\,c^3\,d^5+5\,a\,b^4\,c^4\,d^4-b^5\,c^5\,d^3}\,160{}\mathrm{i}}{448\,a^3\,b^8\,c^3\,d-340\,a^6\,b^5\,d^4-128\,a^2\,b^9\,c^4+740\,a^5\,b^6\,c\,d^3+\frac{16\,a\,b^{10}\,c^5}{d}-796\,a^4\,b^7\,c^2\,d^2+\frac{60\,a^7\,b^4\,d^5}{c}}-\frac{a^2\,b^6\,\sqrt{a+\frac{b}{x}}\,\sqrt{a^5\,d^8-5\,a^4\,b\,c\,d^7+10\,a^3\,b^2\,c^2\,d^6-10\,a^2\,b^3\,c^3\,d^5+5\,a\,b^4\,c^4\,d^4-b^5\,c^5\,d^3}\,80{}\mathrm{i}}{16\,a\,b^{10}\,c^4+740\,a^5\,b^6\,d^4-128\,a^2\,b^9\,c^3\,d-796\,a^4\,b^7\,c\,d^3+448\,a^3\,b^8\,c^2\,d^2-\frac{340\,a^6\,b^5\,d^5}{c}+\frac{60\,a^7\,b^4\,d^6}{c^2}}-\frac{a^4\,b^4\,\sqrt{a+\frac{b}{x}}\,\sqrt{a^5\,d^8-5\,a^4\,b\,c\,d^7+10\,a^3\,b^2\,c^2\,d^6-10\,a^2\,b^3\,c^3\,d^5+5\,a\,b^4\,c^4\,d^4-b^5\,c^5\,d^3}\,60{}\mathrm{i}}{448\,a^3\,b^8\,c^4+60\,a^7\,b^4\,d^4-796\,a^4\,b^7\,c^3\,d-340\,a^6\,b^5\,c\,d^3+\frac{16\,a\,b^{10}\,c^6}{d^2}+740\,a^5\,b^6\,c^2\,d^2-\frac{128\,a^2\,b^9\,c^5}{d}}+\frac{a\,b^7\,c\,\sqrt{a+\frac{b}{x}}\,\sqrt{a^5\,d^8-5\,a^4\,b\,c\,d^7+10\,a^3\,b^2\,c^2\,d^6-10\,a^2\,b^3\,c^3\,d^5+5\,a\,b^4\,c^4\,d^4-b^5\,c^5\,d^3}\,16{}\mathrm{i}}{740\,a^5\,b^6\,d^5-796\,a^4\,b^7\,c\,d^4-128\,a^2\,b^9\,c^3\,d^2+448\,a^3\,b^8\,c^2\,d^3-\frac{340\,a^6\,b^5\,d^6}{c}+\frac{60\,a^7\,b^4\,d^7}{c^2}+16\,a\,b^{10}\,c^4\,d}\right)\,\sqrt{d^3\,{\left(a\,d-b\,c\right)}^5}\,2{}\mathrm{i}}{c^2\,d^3}+\frac{\mathrm{atan}\left(\frac{b^9\,c^3\,\sqrt{a+\frac{b}{x}}\,\sqrt{a^3}\,40{}\mathrm{i}}{40\,a^2\,b^9\,c^3-790\,a^5\,b^6\,d^3-256\,a^3\,b^8\,c^2\,d+696\,a^4\,b^7\,c\,d^2+\frac{370\,a^6\,b^5\,d^4}{c}-\frac{60\,a^7\,b^4\,d^5}{c^2}}+\frac{a\,b^8\,c^2\,\sqrt{a+\frac{b}{x}}\,\sqrt{a^3}\,256{}\mathrm{i}}{256\,a^3\,b^8\,c^2+790\,a^5\,b^6\,d^2-\frac{40\,a^2\,b^9\,c^3}{d}-\frac{370\,a^6\,b^5\,d^3}{c}+\frac{60\,a^7\,b^4\,d^4}{c^2}-696\,a^4\,b^7\,c\,d}+\frac{a^3\,b^6\,d^2\,\sqrt{a+\frac{b}{x}}\,\sqrt{a^3}\,790{}\mathrm{i}}{256\,a^3\,b^8\,c^2+790\,a^5\,b^6\,d^2-\frac{40\,a^2\,b^9\,c^3}{d}-\frac{370\,a^6\,b^5\,d^3}{c}+\frac{60\,a^7\,b^4\,d^4}{c^2}-696\,a^4\,b^7\,c\,d}-\frac{a^4\,b^5\,d^3\,\sqrt{a+\frac{b}{x}}\,\sqrt{a^3}\,370{}\mathrm{i}}{256\,a^3\,b^8\,c^3-370\,a^6\,b^5\,d^3-696\,a^4\,b^7\,c^2\,d+790\,a^5\,b^6\,c\,d^2-\frac{40\,a^2\,b^9\,c^4}{d}+\frac{60\,a^7\,b^4\,d^4}{c}}+\frac{a^5\,b^4\,d^4\,\sqrt{a+\frac{b}{x}}\,\sqrt{a^3}\,60{}\mathrm{i}}{256\,a^3\,b^8\,c^4+60\,a^7\,b^4\,d^4-696\,a^4\,b^7\,c^3\,d-370\,a^6\,b^5\,c\,d^3+790\,a^5\,b^6\,c^2\,d^2-\frac{40\,a^2\,b^9\,c^5}{d}}-\frac{a^2\,b^7\,c\,d\,\sqrt{a+\frac{b}{x}}\,\sqrt{a^3}\,696{}\mathrm{i}}{256\,a^3\,b^8\,c^2+790\,a^5\,b^6\,d^2-\frac{40\,a^2\,b^9\,c^3}{d}-\frac{370\,a^6\,b^5\,d^3}{c}+\frac{60\,a^7\,b^4\,d^4}{c^2}-696\,a^4\,b^7\,c\,d}\right)\,\left(2\,a\,d-5\,b\,c\right)\,\sqrt{a^3}\,1{}\mathrm{i}}{c^2}","Not used",1,"(atan((a^3*b^5*(a + b/x)^(1/2)*(a^5*d^8 - b^5*c^5*d^3 + 5*a*b^4*c^4*d^4 - 10*a^2*b^3*c^3*d^5 + 10*a^3*b^2*c^2*d^6 - 5*a^4*b*c*d^7)^(1/2)*160i)/(448*a^3*b^8*c^3*d - 340*a^6*b^5*d^4 - 128*a^2*b^9*c^4 + 740*a^5*b^6*c*d^3 + (16*a*b^10*c^5)/d - 796*a^4*b^7*c^2*d^2 + (60*a^7*b^4*d^5)/c) - (a^2*b^6*(a + b/x)^(1/2)*(a^5*d^8 - b^5*c^5*d^3 + 5*a*b^4*c^4*d^4 - 10*a^2*b^3*c^3*d^5 + 10*a^3*b^2*c^2*d^6 - 5*a^4*b*c*d^7)^(1/2)*80i)/(16*a*b^10*c^4 + 740*a^5*b^6*d^4 - 128*a^2*b^9*c^3*d - 796*a^4*b^7*c*d^3 + 448*a^3*b^8*c^2*d^2 - (340*a^6*b^5*d^5)/c + (60*a^7*b^4*d^6)/c^2) - (a^4*b^4*(a + b/x)^(1/2)*(a^5*d^8 - b^5*c^5*d^3 + 5*a*b^4*c^4*d^4 - 10*a^2*b^3*c^3*d^5 + 10*a^3*b^2*c^2*d^6 - 5*a^4*b*c*d^7)^(1/2)*60i)/(448*a^3*b^8*c^4 + 60*a^7*b^4*d^4 - 796*a^4*b^7*c^3*d - 340*a^6*b^5*c*d^3 + (16*a*b^10*c^6)/d^2 + 740*a^5*b^6*c^2*d^2 - (128*a^2*b^9*c^5)/d) + (a*b^7*c*(a + b/x)^(1/2)*(a^5*d^8 - b^5*c^5*d^3 + 5*a*b^4*c^4*d^4 - 10*a^2*b^3*c^3*d^5 + 10*a^3*b^2*c^2*d^6 - 5*a^4*b*c*d^7)^(1/2)*16i)/(740*a^5*b^6*d^5 - 796*a^4*b^7*c*d^4 - 128*a^2*b^9*c^3*d^2 + 448*a^3*b^8*c^2*d^3 - (340*a^6*b^5*d^6)/c + (60*a^7*b^4*d^7)/c^2 + 16*a*b^10*c^4*d))*(d^3*(a*d - b*c)^5)^(1/2)*2i)/(c^2*d^3) - (2*b^2*(a + b/x)^(1/2))/d + (atan((b^9*c^3*(a + b/x)^(1/2)*(a^3)^(1/2)*40i)/(40*a^2*b^9*c^3 - 790*a^5*b^6*d^3 - 256*a^3*b^8*c^2*d + 696*a^4*b^7*c*d^2 + (370*a^6*b^5*d^4)/c - (60*a^7*b^4*d^5)/c^2) + (a*b^8*c^2*(a + b/x)^(1/2)*(a^3)^(1/2)*256i)/(256*a^3*b^8*c^2 + 790*a^5*b^6*d^2 - (40*a^2*b^9*c^3)/d - (370*a^6*b^5*d^3)/c + (60*a^7*b^4*d^4)/c^2 - 696*a^4*b^7*c*d) + (a^3*b^6*d^2*(a + b/x)^(1/2)*(a^3)^(1/2)*790i)/(256*a^3*b^8*c^2 + 790*a^5*b^6*d^2 - (40*a^2*b^9*c^3)/d - (370*a^6*b^5*d^3)/c + (60*a^7*b^4*d^4)/c^2 - 696*a^4*b^7*c*d) - (a^4*b^5*d^3*(a + b/x)^(1/2)*(a^3)^(1/2)*370i)/(256*a^3*b^8*c^3 - 370*a^6*b^5*d^3 - 696*a^4*b^7*c^2*d + 790*a^5*b^6*c*d^2 - (40*a^2*b^9*c^4)/d + (60*a^7*b^4*d^4)/c) + (a^5*b^4*d^4*(a + b/x)^(1/2)*(a^3)^(1/2)*60i)/(256*a^3*b^8*c^4 + 60*a^7*b^4*d^4 - 696*a^4*b^7*c^3*d - 370*a^6*b^5*c*d^3 + 790*a^5*b^6*c^2*d^2 - (40*a^2*b^9*c^5)/d) - (a^2*b^7*c*d*(a + b/x)^(1/2)*(a^3)^(1/2)*696i)/(256*a^3*b^8*c^2 + 790*a^5*b^6*d^2 - (40*a^2*b^9*c^3)/d - (370*a^6*b^5*d^3)/c + (60*a^7*b^4*d^4)/c^2 - 696*a^4*b^7*c*d))*(2*a*d - 5*b*c)*(a^3)^(1/2)*1i)/c^2 + (a^2*b*d*(a + b/x)^(1/2))/(c*(d*(a + b/x) - a*d))","B"
243,1,1153,166,2.311369,"\text{Not used}","int((a + b/x)^(5/2)/(c + d/x)^2,x)","\frac{\frac{\sqrt{a+\frac{b}{x}}\,\left(2\,a^3\,b\,d^2-3\,a^2\,b^2\,c\,d+a\,b^3\,c^2\right)}{c^2\,d}-\frac{b\,{\left(a+\frac{b}{x}\right)}^{3/2}\,\left(2\,a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}{c^2\,d}}{\left(a+\frac{b}{x}\right)\,\left(2\,a\,d-b\,c\right)-d\,{\left(a+\frac{b}{x}\right)}^2-a^2\,d+a\,b\,c}-\frac{\mathrm{atanh}\left(\frac{10\,b^9\,\sqrt{a+\frac{b}{x}}\,\sqrt{a^3}}{10\,a^2\,b^9+\frac{32\,a^3\,b^8\,d}{c}-\frac{132\,a^4\,b^7\,d^2}{c^2}+\frac{130\,a^5\,b^6\,d^3}{c^3}-\frac{40\,a^6\,b^5\,d^4}{c^4}}+\frac{32\,a\,b^8\,\sqrt{a+\frac{b}{x}}\,\sqrt{a^3}}{32\,a^3\,b^8+\frac{10\,a^2\,b^9\,c}{d}-\frac{132\,a^4\,b^7\,d}{c}+\frac{130\,a^5\,b^6\,d^2}{c^2}-\frac{40\,a^6\,b^5\,d^3}{c^3}}-\frac{132\,a^2\,b^7\,d\,\sqrt{a+\frac{b}{x}}\,\sqrt{a^3}}{32\,a^3\,b^8\,c-132\,a^4\,b^7\,d+\frac{10\,a^2\,b^9\,c^2}{d}+\frac{130\,a^5\,b^6\,d^2}{c}-\frac{40\,a^6\,b^5\,d^3}{c^2}}+\frac{130\,a^3\,b^6\,d^2\,\sqrt{a+\frac{b}{x}}\,\sqrt{a^3}}{32\,a^3\,b^8\,c^2+130\,a^5\,b^6\,d^2+\frac{10\,a^2\,b^9\,c^3}{d}-\frac{40\,a^6\,b^5\,d^3}{c}-132\,a^4\,b^7\,c\,d}-\frac{40\,a^4\,b^5\,d^3\,\sqrt{a+\frac{b}{x}}\,\sqrt{a^3}}{32\,a^3\,b^8\,c^3-40\,a^6\,b^5\,d^3-132\,a^4\,b^7\,c^2\,d+130\,a^5\,b^6\,c\,d^2+\frac{10\,a^2\,b^9\,c^4}{d}}\right)\,\left(4\,a\,d-5\,b\,c\right)\,\sqrt{a^3}}{c^3}+\frac{\mathrm{atanh}\left(\frac{30\,a^3\,b^6\,\sqrt{a+\frac{b}{x}}\,\sqrt{a^3\,d^6-3\,a^2\,b\,c\,d^5+3\,a\,b^2\,c^2\,d^4-b^3\,c^3\,d^3}}{14\,a^2\,b^9\,c^3+110\,a^5\,b^6\,d^3-4\,a^3\,b^8\,c^2\,d-82\,a^4\,b^7\,c\,d^2+\frac{2\,a\,b^{10}\,c^4}{d}-\frac{40\,a^6\,b^5\,d^4}{c}}+\frac{18\,a^2\,b^7\,\sqrt{a+\frac{b}{x}}\,\sqrt{a^3\,d^6-3\,a^2\,b\,c\,d^5+3\,a\,b^2\,c^2\,d^4-b^3\,c^3\,d^3}}{2\,a\,b^{10}\,c^3-82\,a^4\,b^7\,d^3+14\,a^2\,b^9\,c^2\,d-4\,a^3\,b^8\,c\,d^2+\frac{110\,a^5\,b^6\,d^4}{c}-\frac{40\,a^6\,b^5\,d^5}{c^2}}+\frac{40\,a^4\,b^5\,\sqrt{a+\frac{b}{x}}\,\sqrt{a^3\,d^6-3\,a^2\,b\,c\,d^5+3\,a\,b^2\,c^2\,d^4-b^3\,c^3\,d^3}}{4\,a^3\,b^8\,c^3+40\,a^6\,b^5\,d^3+82\,a^4\,b^7\,c^2\,d-110\,a^5\,b^6\,c\,d^2-\frac{2\,a\,b^{10}\,c^5}{d^2}-\frac{14\,a^2\,b^9\,c^4}{d}}-\frac{2\,a\,b^8\,\sqrt{a+\frac{b}{x}}\,\sqrt{a^3\,d^6-3\,a^2\,b\,c\,d^5+3\,a\,b^2\,c^2\,d^4-b^3\,c^3\,d^3}}{4\,a^3\,b^8\,d^3-14\,a^2\,b^9\,c\,d^2+\frac{82\,a^4\,b^7\,d^4}{c}-\frac{110\,a^5\,b^6\,d^5}{c^2}+\frac{40\,a^6\,b^5\,d^6}{c^3}-2\,a\,b^{10}\,c^2\,d}\right)\,\sqrt{d^3\,{\left(a\,d-b\,c\right)}^3}\,\left(4\,a\,d+b\,c\right)}{c^3\,d^3}","Not used",1,"(((a + b/x)^(1/2)*(a*b^3*c^2 + 2*a^3*b*d^2 - 3*a^2*b^2*c*d))/(c^2*d) - (b*(a + b/x)^(3/2)*(2*a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/(c^2*d))/((a + b/x)*(2*a*d - b*c) - d*(a + b/x)^2 - a^2*d + a*b*c) - (atanh((10*b^9*(a + b/x)^(1/2)*(a^3)^(1/2))/(10*a^2*b^9 + (32*a^3*b^8*d)/c - (132*a^4*b^7*d^2)/c^2 + (130*a^5*b^6*d^3)/c^3 - (40*a^6*b^5*d^4)/c^4) + (32*a*b^8*(a + b/x)^(1/2)*(a^3)^(1/2))/(32*a^3*b^8 + (10*a^2*b^9*c)/d - (132*a^4*b^7*d)/c + (130*a^5*b^6*d^2)/c^2 - (40*a^6*b^5*d^3)/c^3) - (132*a^2*b^7*d*(a + b/x)^(1/2)*(a^3)^(1/2))/(32*a^3*b^8*c - 132*a^4*b^7*d + (10*a^2*b^9*c^2)/d + (130*a^5*b^6*d^2)/c - (40*a^6*b^5*d^3)/c^2) + (130*a^3*b^6*d^2*(a + b/x)^(1/2)*(a^3)^(1/2))/(32*a^3*b^8*c^2 + 130*a^5*b^6*d^2 + (10*a^2*b^9*c^3)/d - (40*a^6*b^5*d^3)/c - 132*a^4*b^7*c*d) - (40*a^4*b^5*d^3*(a + b/x)^(1/2)*(a^3)^(1/2))/(32*a^3*b^8*c^3 - 40*a^6*b^5*d^3 - 132*a^4*b^7*c^2*d + 130*a^5*b^6*c*d^2 + (10*a^2*b^9*c^4)/d))*(4*a*d - 5*b*c)*(a^3)^(1/2))/c^3 + (atanh((30*a^3*b^6*(a + b/x)^(1/2)*(a^3*d^6 - b^3*c^3*d^3 + 3*a*b^2*c^2*d^4 - 3*a^2*b*c*d^5)^(1/2))/(14*a^2*b^9*c^3 + 110*a^5*b^6*d^3 - 4*a^3*b^8*c^2*d - 82*a^4*b^7*c*d^2 + (2*a*b^10*c^4)/d - (40*a^6*b^5*d^4)/c) + (18*a^2*b^7*(a + b/x)^(1/2)*(a^3*d^6 - b^3*c^3*d^3 + 3*a*b^2*c^2*d^4 - 3*a^2*b*c*d^5)^(1/2))/(2*a*b^10*c^3 - 82*a^4*b^7*d^3 + 14*a^2*b^9*c^2*d - 4*a^3*b^8*c*d^2 + (110*a^5*b^6*d^4)/c - (40*a^6*b^5*d^5)/c^2) + (40*a^4*b^5*(a + b/x)^(1/2)*(a^3*d^6 - b^3*c^3*d^3 + 3*a*b^2*c^2*d^4 - 3*a^2*b*c*d^5)^(1/2))/(4*a^3*b^8*c^3 + 40*a^6*b^5*d^3 + 82*a^4*b^7*c^2*d - 110*a^5*b^6*c*d^2 - (2*a*b^10*c^5)/d^2 - (14*a^2*b^9*c^4)/d) - (2*a*b^8*(a + b/x)^(1/2)*(a^3*d^6 - b^3*c^3*d^3 + 3*a*b^2*c^2*d^4 - 3*a^2*b*c*d^5)^(1/2))/(4*a^3*b^8*d^3 - 14*a^2*b^9*c*d^2 + (82*a^4*b^7*d^4)/c - (110*a^5*b^6*d^5)/c^2 + (40*a^6*b^5*d^6)/c^3 - 2*a*b^10*c^2*d))*(d^3*(a*d - b*c)^3)^(1/2)*(4*a*d + b*c))/(c^3*d^3)","B"
244,1,1476,237,3.438983,"\text{Not used}","int((a + b/x)^(5/2)/(c + d/x)^3,x)","\frac{\ln\left(-\frac{1728\,a^8\,b^3\,d^6-4752\,a^7\,b^4\,c\,d^5+4464\,a^6\,b^5\,c^2\,d^4-1450\,a^5\,b^6\,c^3\,d^3-59\,a^4\,b^7\,c^4\,d^2+64\,a^3\,b^8\,c^5\,d+5\,a^2\,b^9\,c^6}{16\,c^9\,d}-\frac{\left(\frac{\sqrt{a+\frac{b}{x}}\,\left(1152\,a^6\,b^2\,d^6-2496\,a^5\,b^3\,c\,d^5+1760\,a^4\,b^4\,c^2\,d^4-400\,a^3\,b^5\,c^3\,d^3-15\,a^2\,b^6\,c^4\,d^2+14\,a\,b^7\,c^5\,d+b^8\,c^6\right)}{8\,c^6\,d}-\frac{\left(\frac{192\,a^3\,b^3\,c^8\,d^4-208\,a^2\,b^4\,c^9\,d^3+16\,a\,b^5\,c^{10}\,d^2}{16\,c^9\,d}-\frac{\left(64\,b^3\,c^9\,d^3-128\,a\,b^2\,c^8\,d^4\right)\,\sqrt{a+\frac{b}{x}}\,\sqrt{d^3\,\left(a\,d-b\,c\right)}\,\left(-3\,a^2\,d^2+a\,b\,c\,d+\frac{b^2\,c^2}{8}\right)}{8\,c^{10}\,d^4}\right)\,\sqrt{d^3\,\left(a\,d-b\,c\right)}\,\left(-3\,a^2\,d^2+a\,b\,c\,d+\frac{b^2\,c^2}{8}\right)}{c^4\,d^3}\right)\,\sqrt{d^3\,\left(a\,d-b\,c\right)}\,\left(-3\,a^2\,d^2+a\,b\,c\,d+\frac{b^2\,c^2}{8}\right)}{c^4\,d^3}\right)\,\sqrt{d^3\,\left(a\,d-b\,c\right)}\,\left(-3\,a^2\,d^2+a\,b\,c\,d+\frac{b^2\,c^2}{8}\right)}{c^4\,d^3}-\frac{\frac{{\left(a+\frac{b}{x}\right)}^{3/2}\,\left(-24\,a^3\,b\,d^3+32\,a^2\,b^2\,c\,d^2-9\,a\,b^3\,c^2\,d+b^4\,c^3\right)}{4\,c^3\,d}-\frac{b\,{\left(a+\frac{b}{x}\right)}^{5/2}\,\left(-12\,a^2\,d^2+7\,a\,b\,c\,d+b^2\,c^2\right)}{4\,c^3}+\frac{b\,\sqrt{a+\frac{b}{x}}\,\left(12\,a^4\,d^3-25\,a^3\,b\,c\,d^2+14\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3\right)}{4\,c^3\,d}}{{\left(a+\frac{b}{x}\right)}^2\,\left(3\,a\,d^2-2\,b\,c\,d\right)-\left(a+\frac{b}{x}\right)\,\left(3\,a^2\,d^2-4\,a\,b\,c\,d+b^2\,c^2\right)-d^2\,{\left(a+\frac{b}{x}\right)}^3+a^3\,d^2+a\,b^2\,c^2-2\,a^2\,b\,c\,d}-\frac{\ln\left(\frac{\left(\frac{\sqrt{a+\frac{b}{x}}\,\left(1152\,a^6\,b^2\,d^6-2496\,a^5\,b^3\,c\,d^5+1760\,a^4\,b^4\,c^2\,d^4-400\,a^3\,b^5\,c^3\,d^3-15\,a^2\,b^6\,c^4\,d^2+14\,a\,b^7\,c^5\,d+b^8\,c^6\right)}{8\,c^6\,d}+\frac{\left(\frac{192\,a^3\,b^3\,c^8\,d^4-208\,a^2\,b^4\,c^9\,d^3+16\,a\,b^5\,c^{10}\,d^2}{16\,c^9\,d}+\frac{\left(64\,b^3\,c^9\,d^3-128\,a\,b^2\,c^8\,d^4\right)\,\sqrt{a+\frac{b}{x}}\,\sqrt{d^3\,\left(a\,d-b\,c\right)}\,\left(-24\,a^2\,d^2+8\,a\,b\,c\,d+b^2\,c^2\right)}{64\,c^{10}\,d^4}\right)\,\sqrt{d^3\,\left(a\,d-b\,c\right)}\,\left(-24\,a^2\,d^2+8\,a\,b\,c\,d+b^2\,c^2\right)}{8\,c^4\,d^3}\right)\,\sqrt{d^3\,\left(a\,d-b\,c\right)}\,\left(-24\,a^2\,d^2+8\,a\,b\,c\,d+b^2\,c^2\right)}{8\,c^4\,d^3}-\frac{1728\,a^8\,b^3\,d^6-4752\,a^7\,b^4\,c\,d^5+4464\,a^6\,b^5\,c^2\,d^4-1450\,a^5\,b^6\,c^3\,d^3-59\,a^4\,b^7\,c^4\,d^2+64\,a^3\,b^8\,c^5\,d+5\,a^2\,b^9\,c^6}{16\,c^9\,d}\right)\,\sqrt{d^3\,\left(a\,d-b\,c\right)}\,\left(-24\,a^2\,d^2+8\,a\,b\,c\,d+b^2\,c^2\right)}{8\,c^4\,d^3}+\frac{\mathrm{atan}\left(\frac{b^9\,\sqrt{a+\frac{b}{x}}\,\sqrt{a^3}\,5{}\mathrm{i}}{8\,\left(\frac{5\,a^2\,b^9}{8}+\frac{8\,a^3\,b^8\,d}{c}-\frac{159\,a^4\,b^7\,d^2}{8\,c^2}+\frac{45\,a^5\,b^6\,d^3}{4\,c^3}\right)}+\frac{a\,b^8\,\sqrt{a+\frac{b}{x}}\,\sqrt{a^3}\,8{}\mathrm{i}}{8\,a^3\,b^8+\frac{5\,a^2\,b^9\,c}{8\,d}-\frac{159\,a^4\,b^7\,d}{8\,c}+\frac{45\,a^5\,b^6\,d^2}{4\,c^2}}-\frac{a^2\,b^7\,d\,\sqrt{a+\frac{b}{x}}\,\sqrt{a^3}\,159{}\mathrm{i}}{8\,\left(8\,a^3\,b^8\,c-\frac{159\,a^4\,b^7\,d}{8}+\frac{5\,a^2\,b^9\,c^2}{8\,d}+\frac{45\,a^5\,b^6\,d^2}{4\,c}\right)}+\frac{a^3\,b^6\,d^2\,\sqrt{a+\frac{b}{x}}\,\sqrt{a^3}\,45{}\mathrm{i}}{4\,\left(8\,a^3\,b^8\,c^2+\frac{45\,a^5\,b^6\,d^2}{4}+\frac{5\,a^2\,b^9\,c^3}{8\,d}-\frac{159\,a^4\,b^7\,c\,d}{8}\right)}\right)\,\left(6\,a\,d-5\,b\,c\right)\,\sqrt{a^3}\,1{}\mathrm{i}}{c^4}","Not used",1,"(atan((b^9*(a + b/x)^(1/2)*(a^3)^(1/2)*5i)/(8*((5*a^2*b^9)/8 + (8*a^3*b^8*d)/c - (159*a^4*b^7*d^2)/(8*c^2) + (45*a^5*b^6*d^3)/(4*c^3))) + (a*b^8*(a + b/x)^(1/2)*(a^3)^(1/2)*8i)/(8*a^3*b^8 + (5*a^2*b^9*c)/(8*d) - (159*a^4*b^7*d)/(8*c) + (45*a^5*b^6*d^2)/(4*c^2)) - (a^2*b^7*d*(a + b/x)^(1/2)*(a^3)^(1/2)*159i)/(8*(8*a^3*b^8*c - (159*a^4*b^7*d)/8 + (5*a^2*b^9*c^2)/(8*d) + (45*a^5*b^6*d^2)/(4*c))) + (a^3*b^6*d^2*(a + b/x)^(1/2)*(a^3)^(1/2)*45i)/(4*(8*a^3*b^8*c^2 + (45*a^5*b^6*d^2)/4 + (5*a^2*b^9*c^3)/(8*d) - (159*a^4*b^7*c*d)/8)))*(6*a*d - 5*b*c)*(a^3)^(1/2)*1i)/c^4 - (((a + b/x)^(3/2)*(b^4*c^3 - 24*a^3*b*d^3 + 32*a^2*b^2*c*d^2 - 9*a*b^3*c^2*d))/(4*c^3*d) - (b*(a + b/x)^(5/2)*(b^2*c^2 - 12*a^2*d^2 + 7*a*b*c*d))/(4*c^3) + (b*(a + b/x)^(1/2)*(12*a^4*d^3 - a*b^3*c^3 + 14*a^2*b^2*c^2*d - 25*a^3*b*c*d^2))/(4*c^3*d))/((a + b/x)^2*(3*a*d^2 - 2*b*c*d) - (a + b/x)*(3*a^2*d^2 + b^2*c^2 - 4*a*b*c*d) - d^2*(a + b/x)^3 + a^3*d^2 + a*b^2*c^2 - 2*a^2*b*c*d) + (log(- (5*a^2*b^9*c^6 + 1728*a^8*b^3*d^6 + 64*a^3*b^8*c^5*d - 4752*a^7*b^4*c*d^5 - 59*a^4*b^7*c^4*d^2 - 1450*a^5*b^6*c^3*d^3 + 4464*a^6*b^5*c^2*d^4)/(16*c^9*d) - ((((a + b/x)^(1/2)*(b^8*c^6 + 1152*a^6*b^2*d^6 - 2496*a^5*b^3*c*d^5 - 15*a^2*b^6*c^4*d^2 - 400*a^3*b^5*c^3*d^3 + 1760*a^4*b^4*c^2*d^4 + 14*a*b^7*c^5*d))/(8*c^6*d) - (((16*a*b^5*c^10*d^2 - 208*a^2*b^4*c^9*d^3 + 192*a^3*b^3*c^8*d^4)/(16*c^9*d) - ((64*b^3*c^9*d^3 - 128*a*b^2*c^8*d^4)*(a + b/x)^(1/2)*(d^3*(a*d - b*c))^(1/2)*((b^2*c^2)/8 - 3*a^2*d^2 + a*b*c*d))/(8*c^10*d^4))*(d^3*(a*d - b*c))^(1/2)*((b^2*c^2)/8 - 3*a^2*d^2 + a*b*c*d))/(c^4*d^3))*(d^3*(a*d - b*c))^(1/2)*((b^2*c^2)/8 - 3*a^2*d^2 + a*b*c*d))/(c^4*d^3))*(d^3*(a*d - b*c))^(1/2)*((b^2*c^2)/8 - 3*a^2*d^2 + a*b*c*d))/(c^4*d^3) - (log(((((a + b/x)^(1/2)*(b^8*c^6 + 1152*a^6*b^2*d^6 - 2496*a^5*b^3*c*d^5 - 15*a^2*b^6*c^4*d^2 - 400*a^3*b^5*c^3*d^3 + 1760*a^4*b^4*c^2*d^4 + 14*a*b^7*c^5*d))/(8*c^6*d) + (((16*a*b^5*c^10*d^2 - 208*a^2*b^4*c^9*d^3 + 192*a^3*b^3*c^8*d^4)/(16*c^9*d) + ((64*b^3*c^9*d^3 - 128*a*b^2*c^8*d^4)*(a + b/x)^(1/2)*(d^3*(a*d - b*c))^(1/2)*(b^2*c^2 - 24*a^2*d^2 + 8*a*b*c*d))/(64*c^10*d^4))*(d^3*(a*d - b*c))^(1/2)*(b^2*c^2 - 24*a^2*d^2 + 8*a*b*c*d))/(8*c^4*d^3))*(d^3*(a*d - b*c))^(1/2)*(b^2*c^2 - 24*a^2*d^2 + 8*a*b*c*d))/(8*c^4*d^3) - (5*a^2*b^9*c^6 + 1728*a^8*b^3*d^6 + 64*a^3*b^8*c^5*d - 4752*a^7*b^4*c*d^5 - 59*a^4*b^7*c^4*d^2 - 1450*a^5*b^6*c^3*d^3 + 4464*a^6*b^5*c^2*d^4)/(16*c^9*d))*(d^3*(a*d - b*c))^(1/2)*(b^2*c^2 - 24*a^2*d^2 + 8*a*b*c*d))/(8*c^4*d^3)","B"
245,1,107,126,1.726566,"\text{Not used}","int((c + d/x)^3/(a + b/x)^(1/2),x)","\sqrt{a+\frac{b}{x}}\,\left(\frac{6\,a\,d^3-6\,b\,c\,d^2}{b^2}-\frac{4\,a\,d^3}{b^2}\right)-\frac{2\,d^3\,{\left(a+\frac{b}{x}\right)}^{3/2}}{3\,b^2}+\frac{c^3\,x\,\sqrt{a+\frac{b}{x}}}{a}-\frac{c^2\,\mathrm{atan}\left(\frac{\sqrt{a+\frac{b}{x}}\,1{}\mathrm{i}}{\sqrt{a}}\right)\,\left(6\,a\,d-b\,c\right)\,1{}\mathrm{i}}{a^{3/2}}","Not used",1,"(a + b/x)^(1/2)*((6*a*d^3 - 6*b*c*d^2)/b^2 - (4*a*d^3)/b^2) - (2*d^3*(a + b/x)^(3/2))/(3*b^2) + (c^3*x*(a + b/x)^(1/2))/a - (c^2*atan(((a + b/x)^(1/2)*1i)/a^(1/2))*(6*a*d - b*c)*1i)/a^(3/2)","B"
246,1,63,73,1.620958,"\text{Not used}","int((c + d/x)^2/(a + b/x)^(1/2),x)","\frac{c^2\,x\,\sqrt{a+\frac{b}{x}}}{a}-\frac{2\,d^2\,\sqrt{a+\frac{b}{x}}}{b}+\frac{c\,\mathrm{atanh}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)\,\left(4\,a\,d-b\,c\right)}{a^{3/2}}","Not used",1,"(c^2*x*(a + b/x)^(1/2))/a - (2*d^2*(a + b/x)^(1/2))/b + (c*atanh((a + b/x)^(1/2)/a^(1/2))*(4*a*d - b*c))/a^(3/2)","B"
247,1,88,51,1.977093,"\text{Not used}","int((c + d/x)/(a + b/x)^(1/2),x)","\frac{2\,d\,\mathrm{atanh}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{\sqrt{a}}+\frac{2\,c\,x\,\left(\frac{3\,\sqrt{b}\,\sqrt{b+a\,x}}{2\,a\,x}+\frac{b^{3/2}\,\mathrm{asin}\left(\frac{\sqrt{a}\,\sqrt{x}\,1{}\mathrm{i}}{\sqrt{b}}\right)\,3{}\mathrm{i}}{2\,a^{3/2}\,x^{3/2}}\right)\,\sqrt{\frac{a\,x}{b}+1}}{3\,\sqrt{a+\frac{b}{x}}}","Not used",1,"(2*d*atanh((a + b/x)^(1/2)/a^(1/2)))/a^(1/2) + (2*c*x*((3*b^(1/2)*(b + a*x)^(1/2))/(2*a*x) + (b^(3/2)*asin((a^(1/2)*x^(1/2)*1i)/b^(1/2))*3i)/(2*a^(3/2)*x^(3/2)))*((a*x)/b + 1)^(1/2))/(3*(a + b/x)^(1/2))","B"
248,1,66,43,1.441247,"\text{Not used}","int(1/(a + b/x)^(1/2),x)","\frac{2\,x\,\left(\frac{3\,\sqrt{b}\,\sqrt{b+a\,x}}{2\,a\,x}+\frac{b^{3/2}\,\mathrm{asin}\left(\frac{\sqrt{a}\,\sqrt{x}\,1{}\mathrm{i}}{\sqrt{b}}\right)\,3{}\mathrm{i}}{2\,a^{3/2}\,x^{3/2}}\right)\,\sqrt{\frac{a\,x}{b}+1}}{3\,\sqrt{a+\frac{b}{x}}}","Not used",1,"(2*x*((3*b^(1/2)*(b + a*x)^(1/2))/(2*a*x) + (b^(3/2)*asin((a^(1/2)*x^(1/2)*1i)/b^(1/2))*3i)/(2*a^(3/2)*x^(3/2)))*((a*x)/b + 1)^(1/2))/(3*(a + b/x)^(1/2))","B"
249,1,1183,108,1.982492,"\text{Not used}","int(1/((a + b/x)^(1/2)*(c + d/x)),x)","\frac{x\,\sqrt{a+\frac{b}{x}}}{a\,c}-\frac{\mathrm{atanh}\left(\frac{12\,b^4\,d^4\,\sqrt{a+\frac{b}{x}}}{\sqrt{a^3}\,\left(\frac{12\,b^4\,d^4}{a}+\frac{10\,b^5\,c\,d^3}{a^2}+\frac{2\,b^6\,c^2\,d^2}{a^3}\right)}+\frac{10\,b^5\,d^3\,\sqrt{a+\frac{b}{x}}}{\sqrt{a^3}\,\left(\frac{10\,b^5\,d^3}{a}+\frac{12\,b^4\,d^4}{c}+\frac{2\,b^6\,c\,d^2}{a^2}\right)}+\frac{2\,b^6\,d^2\,\sqrt{a+\frac{b}{x}}}{\sqrt{a^3}\,\left(\frac{2\,b^6\,d^2}{a}+\frac{10\,b^5\,d^3}{c}+\frac{12\,a\,b^4\,d^4}{c^2}\right)}\right)\,\left(2\,a\,d+b\,c\right)}{c^2\,\sqrt{a^3}}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\left(\frac{2\,\left(2\,a^2\,b^3\,c^4\,d^3+2\,a\,b^4\,c^5\,d^2\right)}{a^2\,c^3}-\frac{2\,\left(4\,a^2\,b^3\,c^5\,d^2-8\,a^3\,b^2\,c^4\,d^3\right)\,\sqrt{a+\frac{b}{x}}\,\sqrt{a\,d^4-b\,c\,d^3}}{a^2\,c^2\,\left(b\,c^3-a\,c^2\,d\right)}\right)\,\sqrt{a\,d^4-b\,c\,d^3}}{b\,c^3-a\,c^2\,d}-\frac{2\,\sqrt{a+\frac{b}{x}}\,\left(8\,a^2\,b^2\,d^5+4\,a\,b^3\,c\,d^4+b^4\,c^2\,d^3\right)}{a^2\,c^2}\right)\,\sqrt{a\,d^4-b\,c\,d^3}\,1{}\mathrm{i}}{b\,c^3-a\,c^2\,d}-\frac{\left(\frac{\left(\frac{2\,\left(2\,a^2\,b^3\,c^4\,d^3+2\,a\,b^4\,c^5\,d^2\right)}{a^2\,c^3}+\frac{2\,\left(4\,a^2\,b^3\,c^5\,d^2-8\,a^3\,b^2\,c^4\,d^3\right)\,\sqrt{a+\frac{b}{x}}\,\sqrt{a\,d^4-b\,c\,d^3}}{a^2\,c^2\,\left(b\,c^3-a\,c^2\,d\right)}\right)\,\sqrt{a\,d^4-b\,c\,d^3}}{b\,c^3-a\,c^2\,d}+\frac{2\,\sqrt{a+\frac{b}{x}}\,\left(8\,a^2\,b^2\,d^5+4\,a\,b^3\,c\,d^4+b^4\,c^2\,d^3\right)}{a^2\,c^2}\right)\,\sqrt{a\,d^4-b\,c\,d^3}\,1{}\mathrm{i}}{b\,c^3-a\,c^2\,d}}{\frac{\left(\frac{\left(\frac{2\,\left(2\,a^2\,b^3\,c^4\,d^3+2\,a\,b^4\,c^5\,d^2\right)}{a^2\,c^3}-\frac{2\,\left(4\,a^2\,b^3\,c^5\,d^2-8\,a^3\,b^2\,c^4\,d^3\right)\,\sqrt{a+\frac{b}{x}}\,\sqrt{a\,d^4-b\,c\,d^3}}{a^2\,c^2\,\left(b\,c^3-a\,c^2\,d\right)}\right)\,\sqrt{a\,d^4-b\,c\,d^3}}{b\,c^3-a\,c^2\,d}-\frac{2\,\sqrt{a+\frac{b}{x}}\,\left(8\,a^2\,b^2\,d^5+4\,a\,b^3\,c\,d^4+b^4\,c^2\,d^3\right)}{a^2\,c^2}\right)\,\sqrt{a\,d^4-b\,c\,d^3}}{b\,c^3-a\,c^2\,d}-\frac{4\,\left(c\,b^4\,d^4+2\,a\,b^3\,d^5\right)}{a^2\,c^3}+\frac{\left(\frac{\left(\frac{2\,\left(2\,a^2\,b^3\,c^4\,d^3+2\,a\,b^4\,c^5\,d^2\right)}{a^2\,c^3}+\frac{2\,\left(4\,a^2\,b^3\,c^5\,d^2-8\,a^3\,b^2\,c^4\,d^3\right)\,\sqrt{a+\frac{b}{x}}\,\sqrt{a\,d^4-b\,c\,d^3}}{a^2\,c^2\,\left(b\,c^3-a\,c^2\,d\right)}\right)\,\sqrt{a\,d^4-b\,c\,d^3}}{b\,c^3-a\,c^2\,d}+\frac{2\,\sqrt{a+\frac{b}{x}}\,\left(8\,a^2\,b^2\,d^5+4\,a\,b^3\,c\,d^4+b^4\,c^2\,d^3\right)}{a^2\,c^2}\right)\,\sqrt{a\,d^4-b\,c\,d^3}}{b\,c^3-a\,c^2\,d}}\right)\,\sqrt{a\,d^4-b\,c\,d^3}\,2{}\mathrm{i}}{b\,c^3-a\,c^2\,d}","Not used",1,"(x*(a + b/x)^(1/2))/(a*c) - (atan(((((((2*(2*a*b^4*c^5*d^2 + 2*a^2*b^3*c^4*d^3))/(a^2*c^3) - (2*(4*a^2*b^3*c^5*d^2 - 8*a^3*b^2*c^4*d^3)*(a + b/x)^(1/2)*(a*d^4 - b*c*d^3)^(1/2))/(a^2*c^2*(b*c^3 - a*c^2*d)))*(a*d^4 - b*c*d^3)^(1/2))/(b*c^3 - a*c^2*d) - (2*(a + b/x)^(1/2)*(8*a^2*b^2*d^5 + b^4*c^2*d^3 + 4*a*b^3*c*d^4))/(a^2*c^2))*(a*d^4 - b*c*d^3)^(1/2)*1i)/(b*c^3 - a*c^2*d) - (((((2*(2*a*b^4*c^5*d^2 + 2*a^2*b^3*c^4*d^3))/(a^2*c^3) + (2*(4*a^2*b^3*c^5*d^2 - 8*a^3*b^2*c^4*d^3)*(a + b/x)^(1/2)*(a*d^4 - b*c*d^3)^(1/2))/(a^2*c^2*(b*c^3 - a*c^2*d)))*(a*d^4 - b*c*d^3)^(1/2))/(b*c^3 - a*c^2*d) + (2*(a + b/x)^(1/2)*(8*a^2*b^2*d^5 + b^4*c^2*d^3 + 4*a*b^3*c*d^4))/(a^2*c^2))*(a*d^4 - b*c*d^3)^(1/2)*1i)/(b*c^3 - a*c^2*d))/((((((2*(2*a*b^4*c^5*d^2 + 2*a^2*b^3*c^4*d^3))/(a^2*c^3) - (2*(4*a^2*b^3*c^5*d^2 - 8*a^3*b^2*c^4*d^3)*(a + b/x)^(1/2)*(a*d^4 - b*c*d^3)^(1/2))/(a^2*c^2*(b*c^3 - a*c^2*d)))*(a*d^4 - b*c*d^3)^(1/2))/(b*c^3 - a*c^2*d) - (2*(a + b/x)^(1/2)*(8*a^2*b^2*d^5 + b^4*c^2*d^3 + 4*a*b^3*c*d^4))/(a^2*c^2))*(a*d^4 - b*c*d^3)^(1/2))/(b*c^3 - a*c^2*d) - (4*(2*a*b^3*d^5 + b^4*c*d^4))/(a^2*c^3) + (((((2*(2*a*b^4*c^5*d^2 + 2*a^2*b^3*c^4*d^3))/(a^2*c^3) + (2*(4*a^2*b^3*c^5*d^2 - 8*a^3*b^2*c^4*d^3)*(a + b/x)^(1/2)*(a*d^4 - b*c*d^3)^(1/2))/(a^2*c^2*(b*c^3 - a*c^2*d)))*(a*d^4 - b*c*d^3)^(1/2))/(b*c^3 - a*c^2*d) + (2*(a + b/x)^(1/2)*(8*a^2*b^2*d^5 + b^4*c^2*d^3 + 4*a*b^3*c*d^4))/(a^2*c^2))*(a*d^4 - b*c*d^3)^(1/2))/(b*c^3 - a*c^2*d)))*(a*d^4 - b*c*d^3)^(1/2)*2i)/(b*c^3 - a*c^2*d) - (atanh((12*b^4*d^4*(a + b/x)^(1/2))/((a^3)^(1/2)*((12*b^4*d^4)/a + (10*b^5*c*d^3)/a^2 + (2*b^6*c^2*d^2)/a^3)) + (10*b^5*d^3*(a + b/x)^(1/2))/((a^3)^(1/2)*((10*b^5*d^3)/a + (12*b^4*d^4)/c + (2*b^6*c*d^2)/a^2)) + (2*b^6*d^2*(a + b/x)^(1/2))/((a^3)^(1/2)*((2*b^6*d^2)/a + (10*b^5*d^3)/c + (12*a*b^4*d^4)/c^2)))*(2*a*d + b*c))/(c^2*(a^3)^(1/2))","B"
250,1,3813,172,3.535578,"\text{Not used}","int(1/((a + b/x)^(1/2)*(c + d/x)^2),x)","\frac{\frac{\sqrt{a+\frac{b}{x}}\,\left(2\,a^2\,b\,d^2-2\,a\,b^2\,c\,d+b^3\,c^2\right)}{c^2\,\left(a^2\,d-a\,b\,c\right)}+\frac{d\,{\left(a+\frac{b}{x}\right)}^{3/2}\,\left(b^2\,c-2\,a\,b\,d\right)}{c^2\,\left(a^2\,d-a\,b\,c\right)}}{\left(a+\frac{b}{x}\right)\,\left(2\,a\,d-b\,c\right)-d\,{\left(a+\frac{b}{x}\right)}^2-a^2\,d+a\,b\,c}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{2\,\sqrt{a+\frac{b}{x}}\,\left(32\,a^4\,b^2\,d^7-64\,a^3\,b^3\,c\,d^6+26\,a^2\,b^4\,c^2\,d^5+6\,a\,b^5\,c^3\,d^4+b^6\,c^4\,d^3\right)}{a^4\,c^4\,d^2-2\,a^3\,b\,c^5\,d+a^2\,b^2\,c^6}+\frac{\left(\frac{8\,a^4\,b^3\,c^6\,d^5-16\,a^3\,b^4\,c^7\,d^4+4\,a^2\,b^5\,c^8\,d^3+4\,a\,b^6\,c^9\,d^2}{a^4\,c^6\,d^2-2\,a^3\,b\,c^7\,d+a^2\,b^2\,c^8}+\frac{\sqrt{a+\frac{b}{x}}\,\left(4\,a\,d+b\,c\right)\,\left(-8\,a^5\,b^2\,c^6\,d^5+20\,a^4\,b^3\,c^7\,d^4-16\,a^3\,b^4\,c^8\,d^3+4\,a^2\,b^5\,c^9\,d^2\right)}{c^3\,\sqrt{a^3}\,\left(a^4\,c^4\,d^2-2\,a^3\,b\,c^5\,d+a^2\,b^2\,c^6\right)}\right)\,\left(4\,a\,d+b\,c\right)}{2\,c^3\,\sqrt{a^3}}\right)\,\left(4\,a\,d+b\,c\right)\,1{}\mathrm{i}}{2\,c^3\,\sqrt{a^3}}+\frac{\left(\frac{2\,\sqrt{a+\frac{b}{x}}\,\left(32\,a^4\,b^2\,d^7-64\,a^3\,b^3\,c\,d^6+26\,a^2\,b^4\,c^2\,d^5+6\,a\,b^5\,c^3\,d^4+b^6\,c^4\,d^3\right)}{a^4\,c^4\,d^2-2\,a^3\,b\,c^5\,d+a^2\,b^2\,c^6}-\frac{\left(\frac{8\,a^4\,b^3\,c^6\,d^5-16\,a^3\,b^4\,c^7\,d^4+4\,a^2\,b^5\,c^8\,d^3+4\,a\,b^6\,c^9\,d^2}{a^4\,c^6\,d^2-2\,a^3\,b\,c^7\,d+a^2\,b^2\,c^8}-\frac{\sqrt{a+\frac{b}{x}}\,\left(4\,a\,d+b\,c\right)\,\left(-8\,a^5\,b^2\,c^6\,d^5+20\,a^4\,b^3\,c^7\,d^4-16\,a^3\,b^4\,c^8\,d^3+4\,a^2\,b^5\,c^9\,d^2\right)}{c^3\,\sqrt{a^3}\,\left(a^4\,c^4\,d^2-2\,a^3\,b\,c^5\,d+a^2\,b^2\,c^6\right)}\right)\,\left(4\,a\,d+b\,c\right)}{2\,c^3\,\sqrt{a^3}}\right)\,\left(4\,a\,d+b\,c\right)\,1{}\mathrm{i}}{2\,c^3\,\sqrt{a^3}}}{\frac{2\,\left(32\,a^3\,b^3\,d^7-48\,a^2\,b^4\,c\,d^6+6\,a\,b^5\,c^2\,d^5+5\,b^6\,c^3\,d^4\right)}{a^4\,c^6\,d^2-2\,a^3\,b\,c^7\,d+a^2\,b^2\,c^8}-\frac{\left(\frac{2\,\sqrt{a+\frac{b}{x}}\,\left(32\,a^4\,b^2\,d^7-64\,a^3\,b^3\,c\,d^6+26\,a^2\,b^4\,c^2\,d^5+6\,a\,b^5\,c^3\,d^4+b^6\,c^4\,d^3\right)}{a^4\,c^4\,d^2-2\,a^3\,b\,c^5\,d+a^2\,b^2\,c^6}+\frac{\left(\frac{8\,a^4\,b^3\,c^6\,d^5-16\,a^3\,b^4\,c^7\,d^4+4\,a^2\,b^5\,c^8\,d^3+4\,a\,b^6\,c^9\,d^2}{a^4\,c^6\,d^2-2\,a^3\,b\,c^7\,d+a^2\,b^2\,c^8}+\frac{\sqrt{a+\frac{b}{x}}\,\left(4\,a\,d+b\,c\right)\,\left(-8\,a^5\,b^2\,c^6\,d^5+20\,a^4\,b^3\,c^7\,d^4-16\,a^3\,b^4\,c^8\,d^3+4\,a^2\,b^5\,c^9\,d^2\right)}{c^3\,\sqrt{a^3}\,\left(a^4\,c^4\,d^2-2\,a^3\,b\,c^5\,d+a^2\,b^2\,c^6\right)}\right)\,\left(4\,a\,d+b\,c\right)}{2\,c^3\,\sqrt{a^3}}\right)\,\left(4\,a\,d+b\,c\right)}{2\,c^3\,\sqrt{a^3}}+\frac{\left(\frac{2\,\sqrt{a+\frac{b}{x}}\,\left(32\,a^4\,b^2\,d^7-64\,a^3\,b^3\,c\,d^6+26\,a^2\,b^4\,c^2\,d^5+6\,a\,b^5\,c^3\,d^4+b^6\,c^4\,d^3\right)}{a^4\,c^4\,d^2-2\,a^3\,b\,c^5\,d+a^2\,b^2\,c^6}-\frac{\left(\frac{8\,a^4\,b^3\,c^6\,d^5-16\,a^3\,b^4\,c^7\,d^4+4\,a^2\,b^5\,c^8\,d^3+4\,a\,b^6\,c^9\,d^2}{a^4\,c^6\,d^2-2\,a^3\,b\,c^7\,d+a^2\,b^2\,c^8}-\frac{\sqrt{a+\frac{b}{x}}\,\left(4\,a\,d+b\,c\right)\,\left(-8\,a^5\,b^2\,c^6\,d^5+20\,a^4\,b^3\,c^7\,d^4-16\,a^3\,b^4\,c^8\,d^3+4\,a^2\,b^5\,c^9\,d^2\right)}{c^3\,\sqrt{a^3}\,\left(a^4\,c^4\,d^2-2\,a^3\,b\,c^5\,d+a^2\,b^2\,c^6\right)}\right)\,\left(4\,a\,d+b\,c\right)}{2\,c^3\,\sqrt{a^3}}\right)\,\left(4\,a\,d+b\,c\right)}{2\,c^3\,\sqrt{a^3}}}\right)\,\left(4\,a\,d+b\,c\right)\,1{}\mathrm{i}}{c^3\,\sqrt{a^3}}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{d^3\,{\left(a\,d-b\,c\right)}^3}\,\left(4\,a\,d-5\,b\,c\right)\,\left(\frac{2\,\sqrt{a+\frac{b}{x}}\,\left(32\,a^4\,b^2\,d^7-64\,a^3\,b^3\,c\,d^6+26\,a^2\,b^4\,c^2\,d^5+6\,a\,b^5\,c^3\,d^4+b^6\,c^4\,d^3\right)}{a^4\,c^4\,d^2-2\,a^3\,b\,c^5\,d+a^2\,b^2\,c^6}+\frac{\sqrt{d^3\,{\left(a\,d-b\,c\right)}^3}\,\left(4\,a\,d-5\,b\,c\right)\,\left(\frac{8\,a^4\,b^3\,c^6\,d^5-16\,a^3\,b^4\,c^7\,d^4+4\,a^2\,b^5\,c^8\,d^3+4\,a\,b^6\,c^9\,d^2}{a^4\,c^6\,d^2-2\,a^3\,b\,c^7\,d+a^2\,b^2\,c^8}+\frac{\sqrt{d^3\,{\left(a\,d-b\,c\right)}^3}\,\sqrt{a+\frac{b}{x}}\,\left(4\,a\,d-5\,b\,c\right)\,\left(-8\,a^5\,b^2\,c^6\,d^5+20\,a^4\,b^3\,c^7\,d^4-16\,a^3\,b^4\,c^8\,d^3+4\,a^2\,b^5\,c^9\,d^2\right)}{\left(a^4\,c^4\,d^2-2\,a^3\,b\,c^5\,d+a^2\,b^2\,c^6\right)\,\left(-a^3\,c^3\,d^3+3\,a^2\,b\,c^4\,d^2-3\,a\,b^2\,c^5\,d+b^3\,c^6\right)}\right)}{2\,\left(-a^3\,c^3\,d^3+3\,a^2\,b\,c^4\,d^2-3\,a\,b^2\,c^5\,d+b^3\,c^6\right)}\right)\,1{}\mathrm{i}}{2\,\left(-a^3\,c^3\,d^3+3\,a^2\,b\,c^4\,d^2-3\,a\,b^2\,c^5\,d+b^3\,c^6\right)}+\frac{\sqrt{d^3\,{\left(a\,d-b\,c\right)}^3}\,\left(4\,a\,d-5\,b\,c\right)\,\left(\frac{2\,\sqrt{a+\frac{b}{x}}\,\left(32\,a^4\,b^2\,d^7-64\,a^3\,b^3\,c\,d^6+26\,a^2\,b^4\,c^2\,d^5+6\,a\,b^5\,c^3\,d^4+b^6\,c^4\,d^3\right)}{a^4\,c^4\,d^2-2\,a^3\,b\,c^5\,d+a^2\,b^2\,c^6}-\frac{\sqrt{d^3\,{\left(a\,d-b\,c\right)}^3}\,\left(4\,a\,d-5\,b\,c\right)\,\left(\frac{8\,a^4\,b^3\,c^6\,d^5-16\,a^3\,b^4\,c^7\,d^4+4\,a^2\,b^5\,c^8\,d^3+4\,a\,b^6\,c^9\,d^2}{a^4\,c^6\,d^2-2\,a^3\,b\,c^7\,d+a^2\,b^2\,c^8}-\frac{\sqrt{d^3\,{\left(a\,d-b\,c\right)}^3}\,\sqrt{a+\frac{b}{x}}\,\left(4\,a\,d-5\,b\,c\right)\,\left(-8\,a^5\,b^2\,c^6\,d^5+20\,a^4\,b^3\,c^7\,d^4-16\,a^3\,b^4\,c^8\,d^3+4\,a^2\,b^5\,c^9\,d^2\right)}{\left(a^4\,c^4\,d^2-2\,a^3\,b\,c^5\,d+a^2\,b^2\,c^6\right)\,\left(-a^3\,c^3\,d^3+3\,a^2\,b\,c^4\,d^2-3\,a\,b^2\,c^5\,d+b^3\,c^6\right)}\right)}{2\,\left(-a^3\,c^3\,d^3+3\,a^2\,b\,c^4\,d^2-3\,a\,b^2\,c^5\,d+b^3\,c^6\right)}\right)\,1{}\mathrm{i}}{2\,\left(-a^3\,c^3\,d^3+3\,a^2\,b\,c^4\,d^2-3\,a\,b^2\,c^5\,d+b^3\,c^6\right)}}{\frac{2\,\left(32\,a^3\,b^3\,d^7-48\,a^2\,b^4\,c\,d^6+6\,a\,b^5\,c^2\,d^5+5\,b^6\,c^3\,d^4\right)}{a^4\,c^6\,d^2-2\,a^3\,b\,c^7\,d+a^2\,b^2\,c^8}-\frac{\sqrt{d^3\,{\left(a\,d-b\,c\right)}^3}\,\left(4\,a\,d-5\,b\,c\right)\,\left(\frac{2\,\sqrt{a+\frac{b}{x}}\,\left(32\,a^4\,b^2\,d^7-64\,a^3\,b^3\,c\,d^6+26\,a^2\,b^4\,c^2\,d^5+6\,a\,b^5\,c^3\,d^4+b^6\,c^4\,d^3\right)}{a^4\,c^4\,d^2-2\,a^3\,b\,c^5\,d+a^2\,b^2\,c^6}+\frac{\sqrt{d^3\,{\left(a\,d-b\,c\right)}^3}\,\left(4\,a\,d-5\,b\,c\right)\,\left(\frac{8\,a^4\,b^3\,c^6\,d^5-16\,a^3\,b^4\,c^7\,d^4+4\,a^2\,b^5\,c^8\,d^3+4\,a\,b^6\,c^9\,d^2}{a^4\,c^6\,d^2-2\,a^3\,b\,c^7\,d+a^2\,b^2\,c^8}+\frac{\sqrt{d^3\,{\left(a\,d-b\,c\right)}^3}\,\sqrt{a+\frac{b}{x}}\,\left(4\,a\,d-5\,b\,c\right)\,\left(-8\,a^5\,b^2\,c^6\,d^5+20\,a^4\,b^3\,c^7\,d^4-16\,a^3\,b^4\,c^8\,d^3+4\,a^2\,b^5\,c^9\,d^2\right)}{\left(a^4\,c^4\,d^2-2\,a^3\,b\,c^5\,d+a^2\,b^2\,c^6\right)\,\left(-a^3\,c^3\,d^3+3\,a^2\,b\,c^4\,d^2-3\,a\,b^2\,c^5\,d+b^3\,c^6\right)}\right)}{2\,\left(-a^3\,c^3\,d^3+3\,a^2\,b\,c^4\,d^2-3\,a\,b^2\,c^5\,d+b^3\,c^6\right)}\right)}{2\,\left(-a^3\,c^3\,d^3+3\,a^2\,b\,c^4\,d^2-3\,a\,b^2\,c^5\,d+b^3\,c^6\right)}+\frac{\sqrt{d^3\,{\left(a\,d-b\,c\right)}^3}\,\left(4\,a\,d-5\,b\,c\right)\,\left(\frac{2\,\sqrt{a+\frac{b}{x}}\,\left(32\,a^4\,b^2\,d^7-64\,a^3\,b^3\,c\,d^6+26\,a^2\,b^4\,c^2\,d^5+6\,a\,b^5\,c^3\,d^4+b^6\,c^4\,d^3\right)}{a^4\,c^4\,d^2-2\,a^3\,b\,c^5\,d+a^2\,b^2\,c^6}-\frac{\sqrt{d^3\,{\left(a\,d-b\,c\right)}^3}\,\left(4\,a\,d-5\,b\,c\right)\,\left(\frac{8\,a^4\,b^3\,c^6\,d^5-16\,a^3\,b^4\,c^7\,d^4+4\,a^2\,b^5\,c^8\,d^3+4\,a\,b^6\,c^9\,d^2}{a^4\,c^6\,d^2-2\,a^3\,b\,c^7\,d+a^2\,b^2\,c^8}-\frac{\sqrt{d^3\,{\left(a\,d-b\,c\right)}^3}\,\sqrt{a+\frac{b}{x}}\,\left(4\,a\,d-5\,b\,c\right)\,\left(-8\,a^5\,b^2\,c^6\,d^5+20\,a^4\,b^3\,c^7\,d^4-16\,a^3\,b^4\,c^8\,d^3+4\,a^2\,b^5\,c^9\,d^2\right)}{\left(a^4\,c^4\,d^2-2\,a^3\,b\,c^5\,d+a^2\,b^2\,c^6\right)\,\left(-a^3\,c^3\,d^3+3\,a^2\,b\,c^4\,d^2-3\,a\,b^2\,c^5\,d+b^3\,c^6\right)}\right)}{2\,\left(-a^3\,c^3\,d^3+3\,a^2\,b\,c^4\,d^2-3\,a\,b^2\,c^5\,d+b^3\,c^6\right)}\right)}{2\,\left(-a^3\,c^3\,d^3+3\,a^2\,b\,c^4\,d^2-3\,a\,b^2\,c^5\,d+b^3\,c^6\right)}}\right)\,\sqrt{d^3\,{\left(a\,d-b\,c\right)}^3}\,\left(4\,a\,d-5\,b\,c\right)\,1{}\mathrm{i}}{-a^3\,c^3\,d^3+3\,a^2\,b\,c^4\,d^2-3\,a\,b^2\,c^5\,d+b^3\,c^6}","Not used",1,"(((a + b/x)^(1/2)*(b^3*c^2 + 2*a^2*b*d^2 - 2*a*b^2*c*d))/(c^2*(a^2*d - a*b*c)) + (d*(a + b/x)^(3/2)*(b^2*c - 2*a*b*d))/(c^2*(a^2*d - a*b*c)))/((a + b/x)*(2*a*d - b*c) - d*(a + b/x)^2 - a^2*d + a*b*c) - (atan(((((2*(a + b/x)^(1/2)*(32*a^4*b^2*d^7 + b^6*c^4*d^3 + 6*a*b^5*c^3*d^4 - 64*a^3*b^3*c*d^6 + 26*a^2*b^4*c^2*d^5))/(a^2*b^2*c^6 + a^4*c^4*d^2 - 2*a^3*b*c^5*d) + (((4*a*b^6*c^9*d^2 + 4*a^2*b^5*c^8*d^3 - 16*a^3*b^4*c^7*d^4 + 8*a^4*b^3*c^6*d^5)/(a^2*b^2*c^8 + a^4*c^6*d^2 - 2*a^3*b*c^7*d) + ((a + b/x)^(1/2)*(4*a*d + b*c)*(4*a^2*b^5*c^9*d^2 - 16*a^3*b^4*c^8*d^3 + 20*a^4*b^3*c^7*d^4 - 8*a^5*b^2*c^6*d^5))/(c^3*(a^3)^(1/2)*(a^2*b^2*c^6 + a^4*c^4*d^2 - 2*a^3*b*c^5*d)))*(4*a*d + b*c))/(2*c^3*(a^3)^(1/2)))*(4*a*d + b*c)*1i)/(2*c^3*(a^3)^(1/2)) + (((2*(a + b/x)^(1/2)*(32*a^4*b^2*d^7 + b^6*c^4*d^3 + 6*a*b^5*c^3*d^4 - 64*a^3*b^3*c*d^6 + 26*a^2*b^4*c^2*d^5))/(a^2*b^2*c^6 + a^4*c^4*d^2 - 2*a^3*b*c^5*d) - (((4*a*b^6*c^9*d^2 + 4*a^2*b^5*c^8*d^3 - 16*a^3*b^4*c^7*d^4 + 8*a^4*b^3*c^6*d^5)/(a^2*b^2*c^8 + a^4*c^6*d^2 - 2*a^3*b*c^7*d) - ((a + b/x)^(1/2)*(4*a*d + b*c)*(4*a^2*b^5*c^9*d^2 - 16*a^3*b^4*c^8*d^3 + 20*a^4*b^3*c^7*d^4 - 8*a^5*b^2*c^6*d^5))/(c^3*(a^3)^(1/2)*(a^2*b^2*c^6 + a^4*c^4*d^2 - 2*a^3*b*c^5*d)))*(4*a*d + b*c))/(2*c^3*(a^3)^(1/2)))*(4*a*d + b*c)*1i)/(2*c^3*(a^3)^(1/2)))/((2*(32*a^3*b^3*d^7 + 5*b^6*c^3*d^4 + 6*a*b^5*c^2*d^5 - 48*a^2*b^4*c*d^6))/(a^2*b^2*c^8 + a^4*c^6*d^2 - 2*a^3*b*c^7*d) - (((2*(a + b/x)^(1/2)*(32*a^4*b^2*d^7 + b^6*c^4*d^3 + 6*a*b^5*c^3*d^4 - 64*a^3*b^3*c*d^6 + 26*a^2*b^4*c^2*d^5))/(a^2*b^2*c^6 + a^4*c^4*d^2 - 2*a^3*b*c^5*d) + (((4*a*b^6*c^9*d^2 + 4*a^2*b^5*c^8*d^3 - 16*a^3*b^4*c^7*d^4 + 8*a^4*b^3*c^6*d^5)/(a^2*b^2*c^8 + a^4*c^6*d^2 - 2*a^3*b*c^7*d) + ((a + b/x)^(1/2)*(4*a*d + b*c)*(4*a^2*b^5*c^9*d^2 - 16*a^3*b^4*c^8*d^3 + 20*a^4*b^3*c^7*d^4 - 8*a^5*b^2*c^6*d^5))/(c^3*(a^3)^(1/2)*(a^2*b^2*c^6 + a^4*c^4*d^2 - 2*a^3*b*c^5*d)))*(4*a*d + b*c))/(2*c^3*(a^3)^(1/2)))*(4*a*d + b*c))/(2*c^3*(a^3)^(1/2)) + (((2*(a + b/x)^(1/2)*(32*a^4*b^2*d^7 + b^6*c^4*d^3 + 6*a*b^5*c^3*d^4 - 64*a^3*b^3*c*d^6 + 26*a^2*b^4*c^2*d^5))/(a^2*b^2*c^6 + a^4*c^4*d^2 - 2*a^3*b*c^5*d) - (((4*a*b^6*c^9*d^2 + 4*a^2*b^5*c^8*d^3 - 16*a^3*b^4*c^7*d^4 + 8*a^4*b^3*c^6*d^5)/(a^2*b^2*c^8 + a^4*c^6*d^2 - 2*a^3*b*c^7*d) - ((a + b/x)^(1/2)*(4*a*d + b*c)*(4*a^2*b^5*c^9*d^2 - 16*a^3*b^4*c^8*d^3 + 20*a^4*b^3*c^7*d^4 - 8*a^5*b^2*c^6*d^5))/(c^3*(a^3)^(1/2)*(a^2*b^2*c^6 + a^4*c^4*d^2 - 2*a^3*b*c^5*d)))*(4*a*d + b*c))/(2*c^3*(a^3)^(1/2)))*(4*a*d + b*c))/(2*c^3*(a^3)^(1/2))))*(4*a*d + b*c)*1i)/(c^3*(a^3)^(1/2)) - (atan((((d^3*(a*d - b*c)^3)^(1/2)*(4*a*d - 5*b*c)*((2*(a + b/x)^(1/2)*(32*a^4*b^2*d^7 + b^6*c^4*d^3 + 6*a*b^5*c^3*d^4 - 64*a^3*b^3*c*d^6 + 26*a^2*b^4*c^2*d^5))/(a^2*b^2*c^6 + a^4*c^4*d^2 - 2*a^3*b*c^5*d) + ((d^3*(a*d - b*c)^3)^(1/2)*(4*a*d - 5*b*c)*((4*a*b^6*c^9*d^2 + 4*a^2*b^5*c^8*d^3 - 16*a^3*b^4*c^7*d^4 + 8*a^4*b^3*c^6*d^5)/(a^2*b^2*c^8 + a^4*c^6*d^2 - 2*a^3*b*c^7*d) + ((d^3*(a*d - b*c)^3)^(1/2)*(a + b/x)^(1/2)*(4*a*d - 5*b*c)*(4*a^2*b^5*c^9*d^2 - 16*a^3*b^4*c^8*d^3 + 20*a^4*b^3*c^7*d^4 - 8*a^5*b^2*c^6*d^5))/((a^2*b^2*c^6 + a^4*c^4*d^2 - 2*a^3*b*c^5*d)*(b^3*c^6 - a^3*c^3*d^3 + 3*a^2*b*c^4*d^2 - 3*a*b^2*c^5*d))))/(2*(b^3*c^6 - a^3*c^3*d^3 + 3*a^2*b*c^4*d^2 - 3*a*b^2*c^5*d)))*1i)/(2*(b^3*c^6 - a^3*c^3*d^3 + 3*a^2*b*c^4*d^2 - 3*a*b^2*c^5*d)) + ((d^3*(a*d - b*c)^3)^(1/2)*(4*a*d - 5*b*c)*((2*(a + b/x)^(1/2)*(32*a^4*b^2*d^7 + b^6*c^4*d^3 + 6*a*b^5*c^3*d^4 - 64*a^3*b^3*c*d^6 + 26*a^2*b^4*c^2*d^5))/(a^2*b^2*c^6 + a^4*c^4*d^2 - 2*a^3*b*c^5*d) - ((d^3*(a*d - b*c)^3)^(1/2)*(4*a*d - 5*b*c)*((4*a*b^6*c^9*d^2 + 4*a^2*b^5*c^8*d^3 - 16*a^3*b^4*c^7*d^4 + 8*a^4*b^3*c^6*d^5)/(a^2*b^2*c^8 + a^4*c^6*d^2 - 2*a^3*b*c^7*d) - ((d^3*(a*d - b*c)^3)^(1/2)*(a + b/x)^(1/2)*(4*a*d - 5*b*c)*(4*a^2*b^5*c^9*d^2 - 16*a^3*b^4*c^8*d^3 + 20*a^4*b^3*c^7*d^4 - 8*a^5*b^2*c^6*d^5))/((a^2*b^2*c^6 + a^4*c^4*d^2 - 2*a^3*b*c^5*d)*(b^3*c^6 - a^3*c^3*d^3 + 3*a^2*b*c^4*d^2 - 3*a*b^2*c^5*d))))/(2*(b^3*c^6 - a^3*c^3*d^3 + 3*a^2*b*c^4*d^2 - 3*a*b^2*c^5*d)))*1i)/(2*(b^3*c^6 - a^3*c^3*d^3 + 3*a^2*b*c^4*d^2 - 3*a*b^2*c^5*d)))/((2*(32*a^3*b^3*d^7 + 5*b^6*c^3*d^4 + 6*a*b^5*c^2*d^5 - 48*a^2*b^4*c*d^6))/(a^2*b^2*c^8 + a^4*c^6*d^2 - 2*a^3*b*c^7*d) - ((d^3*(a*d - b*c)^3)^(1/2)*(4*a*d - 5*b*c)*((2*(a + b/x)^(1/2)*(32*a^4*b^2*d^7 + b^6*c^4*d^3 + 6*a*b^5*c^3*d^4 - 64*a^3*b^3*c*d^6 + 26*a^2*b^4*c^2*d^5))/(a^2*b^2*c^6 + a^4*c^4*d^2 - 2*a^3*b*c^5*d) + ((d^3*(a*d - b*c)^3)^(1/2)*(4*a*d - 5*b*c)*((4*a*b^6*c^9*d^2 + 4*a^2*b^5*c^8*d^3 - 16*a^3*b^4*c^7*d^4 + 8*a^4*b^3*c^6*d^5)/(a^2*b^2*c^8 + a^4*c^6*d^2 - 2*a^3*b*c^7*d) + ((d^3*(a*d - b*c)^3)^(1/2)*(a + b/x)^(1/2)*(4*a*d - 5*b*c)*(4*a^2*b^5*c^9*d^2 - 16*a^3*b^4*c^8*d^3 + 20*a^4*b^3*c^7*d^4 - 8*a^5*b^2*c^6*d^5))/((a^2*b^2*c^6 + a^4*c^4*d^2 - 2*a^3*b*c^5*d)*(b^3*c^6 - a^3*c^3*d^3 + 3*a^2*b*c^4*d^2 - 3*a*b^2*c^5*d))))/(2*(b^3*c^6 - a^3*c^3*d^3 + 3*a^2*b*c^4*d^2 - 3*a*b^2*c^5*d))))/(2*(b^3*c^6 - a^3*c^3*d^3 + 3*a^2*b*c^4*d^2 - 3*a*b^2*c^5*d)) + ((d^3*(a*d - b*c)^3)^(1/2)*(4*a*d - 5*b*c)*((2*(a + b/x)^(1/2)*(32*a^4*b^2*d^7 + b^6*c^4*d^3 + 6*a*b^5*c^3*d^4 - 64*a^3*b^3*c*d^6 + 26*a^2*b^4*c^2*d^5))/(a^2*b^2*c^6 + a^4*c^4*d^2 - 2*a^3*b*c^5*d) - ((d^3*(a*d - b*c)^3)^(1/2)*(4*a*d - 5*b*c)*((4*a*b^6*c^9*d^2 + 4*a^2*b^5*c^8*d^3 - 16*a^3*b^4*c^7*d^4 + 8*a^4*b^3*c^6*d^5)/(a^2*b^2*c^8 + a^4*c^6*d^2 - 2*a^3*b*c^7*d) - ((d^3*(a*d - b*c)^3)^(1/2)*(a + b/x)^(1/2)*(4*a*d - 5*b*c)*(4*a^2*b^5*c^9*d^2 - 16*a^3*b^4*c^8*d^3 + 20*a^4*b^3*c^7*d^4 - 8*a^5*b^2*c^6*d^5))/((a^2*b^2*c^6 + a^4*c^4*d^2 - 2*a^3*b*c^5*d)*(b^3*c^6 - a^3*c^3*d^3 + 3*a^2*b*c^4*d^2 - 3*a*b^2*c^5*d))))/(2*(b^3*c^6 - a^3*c^3*d^3 + 3*a^2*b*c^4*d^2 - 3*a*b^2*c^5*d))))/(2*(b^3*c^6 - a^3*c^3*d^3 + 3*a^2*b*c^4*d^2 - 3*a*b^2*c^5*d))))*(d^3*(a*d - b*c)^3)^(1/2)*(4*a*d - 5*b*c)*1i)/(b^3*c^6 - a^3*c^3*d^3 + 3*a^2*b*c^4*d^2 - 3*a*b^2*c^5*d)","B"
251,1,2890,250,5.479290,"\text{Not used}","int(1/((a + b/x)^(1/2)*(c + d/x)^3),x)","\frac{\ln\left(\sqrt{d^3\,{\left(a\,d-b\,c\right)}^5}\,\sqrt{a+\frac{b}{x}}-a^3\,d^4+b^3\,c^3\,d-3\,a\,b^2\,c^2\,d^2+3\,a^2\,b\,c\,d^3\right)\,\sqrt{d^3\,{\left(a\,d-b\,c\right)}^5}\,\left(3\,a^2\,d^2-7\,a\,b\,c\,d+\frac{35\,b^2\,c^2}{8}\right)}{-a^5\,c^4\,d^5+5\,a^4\,b\,c^5\,d^4-10\,a^3\,b^2\,c^6\,d^3+10\,a^2\,b^3\,c^7\,d^2-5\,a\,b^4\,c^8\,d+b^5\,c^9}-\frac{\frac{b\,{\left(a+\frac{b}{x}\right)}^{5/2}\,\left(12\,a^2\,d^4-19\,a\,b\,c\,d^3+4\,b^2\,c^2\,d^2\right)}{4\,a\,c^3\,{\left(a\,d-b\,c\right)}^2}-\frac{\sqrt{a+\frac{b}{x}}\,\left(-12\,a^3\,b\,d^3+25\,a^2\,b^2\,c\,d^2-12\,a\,b^3\,c^2\,d+4\,b^4\,c^3\right)}{4\,a\,c^3\,\left(a\,d-b\,c\right)}+\frac{d\,{\left(a+\frac{b}{x}\right)}^{3/2}\,\left(-24\,a^3\,b\,d^3+56\,a^2\,b^2\,c\,d^2-37\,a\,b^3\,c^2\,d+8\,b^4\,c^3\right)}{4\,c^3\,\left(a^2\,d-a\,b\,c\right)\,\left(a\,d-b\,c\right)}}{{\left(a+\frac{b}{x}\right)}^2\,\left(3\,a\,d^2-2\,b\,c\,d\right)-\left(a+\frac{b}{x}\right)\,\left(3\,a^2\,d^2-4\,a\,b\,c\,d+b^2\,c^2\right)-d^2\,{\left(a+\frac{b}{x}\right)}^3+a^3\,d^2+a\,b^2\,c^2-2\,a^2\,b\,c\,d}-\frac{\ln\left(\sqrt{d^3\,{\left(a\,d-b\,c\right)}^5}\,\sqrt{a+\frac{b}{x}}+a^3\,d^4-b^3\,c^3\,d+3\,a\,b^2\,c^2\,d^2-3\,a^2\,b\,c\,d^3\right)\,\sqrt{d^3\,{\left(a\,d-b\,c\right)}^5}\,\left(24\,a^2\,d^2-56\,a\,b\,c\,d+35\,b^2\,c^2\right)}{8\,\left(-a^5\,c^4\,d^5+5\,a^4\,b\,c^5\,d^4-10\,a^3\,b^2\,c^6\,d^3+10\,a^2\,b^3\,c^7\,d^2-5\,a\,b^4\,c^8\,d+b^5\,c^9\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\sqrt{a+\frac{b}{x}}\,\left(1152\,a^6\,b^2\,d^9-4800\,a^5\,b^3\,c\,d^8+7520\,a^4\,b^4\,c^2\,d^7-5136\,a^3\,b^5\,c^3\,d^6+1129\,a^2\,b^6\,c^4\,d^5+128\,a\,b^7\,c^5\,d^4+16\,b^8\,c^6\,d^3\right)}{8\,\left(a^6\,c^6\,d^4-4\,a^5\,b\,c^7\,d^3+6\,a^4\,b^2\,c^8\,d^2-4\,a^3\,b^3\,c^9\,d+a^2\,b^4\,c^{10}\right)}-\frac{\left(\frac{12\,a^6\,b^3\,c^8\,d^7-49\,a^5\,b^4\,c^9\,d^6+74\,a^4\,b^5\,c^{10}\,d^5-45\,a^3\,b^6\,c^{11}\,d^4+4\,a^2\,b^7\,c^{12}\,d^3+4\,a\,b^8\,c^{13}\,d^2}{a^6\,c^9\,d^4-4\,a^5\,b\,c^{10}\,d^3+6\,a^4\,b^2\,c^{11}\,d^2-4\,a^3\,b^3\,c^{12}\,d+a^2\,b^4\,c^{13}}-\frac{\sqrt{a+\frac{b}{x}}\,\left(6\,a\,d+b\,c\right)\,\left(-128\,a^7\,b^2\,c^8\,d^7+576\,a^6\,b^3\,c^9\,d^6-1024\,a^5\,b^4\,c^{10}\,d^5+896\,a^4\,b^5\,c^{11}\,d^4-384\,a^3\,b^6\,c^{12}\,d^3+64\,a^2\,b^7\,c^{13}\,d^2\right)}{16\,c^4\,\sqrt{a^3}\,\left(a^6\,c^6\,d^4-4\,a^5\,b\,c^7\,d^3+6\,a^4\,b^2\,c^8\,d^2-4\,a^3\,b^3\,c^9\,d+a^2\,b^4\,c^{10}\right)}\right)\,\left(6\,a\,d+b\,c\right)}{2\,c^4\,\sqrt{a^3}}\right)\,\left(6\,a\,d+b\,c\right)\,1{}\mathrm{i}}{2\,c^4\,\sqrt{a^3}}+\frac{\left(\frac{\sqrt{a+\frac{b}{x}}\,\left(1152\,a^6\,b^2\,d^9-4800\,a^5\,b^3\,c\,d^8+7520\,a^4\,b^4\,c^2\,d^7-5136\,a^3\,b^5\,c^3\,d^6+1129\,a^2\,b^6\,c^4\,d^5+128\,a\,b^7\,c^5\,d^4+16\,b^8\,c^6\,d^3\right)}{8\,\left(a^6\,c^6\,d^4-4\,a^5\,b\,c^7\,d^3+6\,a^4\,b^2\,c^8\,d^2-4\,a^3\,b^3\,c^9\,d+a^2\,b^4\,c^{10}\right)}+\frac{\left(\frac{12\,a^6\,b^3\,c^8\,d^7-49\,a^5\,b^4\,c^9\,d^6+74\,a^4\,b^5\,c^{10}\,d^5-45\,a^3\,b^6\,c^{11}\,d^4+4\,a^2\,b^7\,c^{12}\,d^3+4\,a\,b^8\,c^{13}\,d^2}{a^6\,c^9\,d^4-4\,a^5\,b\,c^{10}\,d^3+6\,a^4\,b^2\,c^{11}\,d^2-4\,a^3\,b^3\,c^{12}\,d+a^2\,b^4\,c^{13}}+\frac{\sqrt{a+\frac{b}{x}}\,\left(6\,a\,d+b\,c\right)\,\left(-128\,a^7\,b^2\,c^8\,d^7+576\,a^6\,b^3\,c^9\,d^6-1024\,a^5\,b^4\,c^{10}\,d^5+896\,a^4\,b^5\,c^{11}\,d^4-384\,a^3\,b^6\,c^{12}\,d^3+64\,a^2\,b^7\,c^{13}\,d^2\right)}{16\,c^4\,\sqrt{a^3}\,\left(a^6\,c^6\,d^4-4\,a^5\,b\,c^7\,d^3+6\,a^4\,b^2\,c^8\,d^2-4\,a^3\,b^3\,c^9\,d+a^2\,b^4\,c^{10}\right)}\right)\,\left(6\,a\,d+b\,c\right)}{2\,c^4\,\sqrt{a^3}}\right)\,\left(6\,a\,d+b\,c\right)\,1{}\mathrm{i}}{2\,c^4\,\sqrt{a^3}}}{\frac{216\,a^5\,b^3\,d^9-810\,a^4\,b^4\,c\,d^8+1044\,a^3\,b^5\,c^2\,d^7-\frac{1877\,a^2\,b^6\,c^3\,d^6}{4}-\frac{49\,a\,b^7\,c^4\,d^5}{8}+\frac{35\,b^8\,c^5\,d^4}{2}}{a^6\,c^9\,d^4-4\,a^5\,b\,c^{10}\,d^3+6\,a^4\,b^2\,c^{11}\,d^2-4\,a^3\,b^3\,c^{12}\,d+a^2\,b^4\,c^{13}}+\frac{\left(\frac{\sqrt{a+\frac{b}{x}}\,\left(1152\,a^6\,b^2\,d^9-4800\,a^5\,b^3\,c\,d^8+7520\,a^4\,b^4\,c^2\,d^7-5136\,a^3\,b^5\,c^3\,d^6+1129\,a^2\,b^6\,c^4\,d^5+128\,a\,b^7\,c^5\,d^4+16\,b^8\,c^6\,d^3\right)}{8\,\left(a^6\,c^6\,d^4-4\,a^5\,b\,c^7\,d^3+6\,a^4\,b^2\,c^8\,d^2-4\,a^3\,b^3\,c^9\,d+a^2\,b^4\,c^{10}\right)}-\frac{\left(\frac{12\,a^6\,b^3\,c^8\,d^7-49\,a^5\,b^4\,c^9\,d^6+74\,a^4\,b^5\,c^{10}\,d^5-45\,a^3\,b^6\,c^{11}\,d^4+4\,a^2\,b^7\,c^{12}\,d^3+4\,a\,b^8\,c^{13}\,d^2}{a^6\,c^9\,d^4-4\,a^5\,b\,c^{10}\,d^3+6\,a^4\,b^2\,c^{11}\,d^2-4\,a^3\,b^3\,c^{12}\,d+a^2\,b^4\,c^{13}}-\frac{\sqrt{a+\frac{b}{x}}\,\left(6\,a\,d+b\,c\right)\,\left(-128\,a^7\,b^2\,c^8\,d^7+576\,a^6\,b^3\,c^9\,d^6-1024\,a^5\,b^4\,c^{10}\,d^5+896\,a^4\,b^5\,c^{11}\,d^4-384\,a^3\,b^6\,c^{12}\,d^3+64\,a^2\,b^7\,c^{13}\,d^2\right)}{16\,c^4\,\sqrt{a^3}\,\left(a^6\,c^6\,d^4-4\,a^5\,b\,c^7\,d^3+6\,a^4\,b^2\,c^8\,d^2-4\,a^3\,b^3\,c^9\,d+a^2\,b^4\,c^{10}\right)}\right)\,\left(6\,a\,d+b\,c\right)}{2\,c^4\,\sqrt{a^3}}\right)\,\left(6\,a\,d+b\,c\right)}{2\,c^4\,\sqrt{a^3}}-\frac{\left(\frac{\sqrt{a+\frac{b}{x}}\,\left(1152\,a^6\,b^2\,d^9-4800\,a^5\,b^3\,c\,d^8+7520\,a^4\,b^4\,c^2\,d^7-5136\,a^3\,b^5\,c^3\,d^6+1129\,a^2\,b^6\,c^4\,d^5+128\,a\,b^7\,c^5\,d^4+16\,b^8\,c^6\,d^3\right)}{8\,\left(a^6\,c^6\,d^4-4\,a^5\,b\,c^7\,d^3+6\,a^4\,b^2\,c^8\,d^2-4\,a^3\,b^3\,c^9\,d+a^2\,b^4\,c^{10}\right)}+\frac{\left(\frac{12\,a^6\,b^3\,c^8\,d^7-49\,a^5\,b^4\,c^9\,d^6+74\,a^4\,b^5\,c^{10}\,d^5-45\,a^3\,b^6\,c^{11}\,d^4+4\,a^2\,b^7\,c^{12}\,d^3+4\,a\,b^8\,c^{13}\,d^2}{a^6\,c^9\,d^4-4\,a^5\,b\,c^{10}\,d^3+6\,a^4\,b^2\,c^{11}\,d^2-4\,a^3\,b^3\,c^{12}\,d+a^2\,b^4\,c^{13}}+\frac{\sqrt{a+\frac{b}{x}}\,\left(6\,a\,d+b\,c\right)\,\left(-128\,a^7\,b^2\,c^8\,d^7+576\,a^6\,b^3\,c^9\,d^6-1024\,a^5\,b^4\,c^{10}\,d^5+896\,a^4\,b^5\,c^{11}\,d^4-384\,a^3\,b^6\,c^{12}\,d^3+64\,a^2\,b^7\,c^{13}\,d^2\right)}{16\,c^4\,\sqrt{a^3}\,\left(a^6\,c^6\,d^4-4\,a^5\,b\,c^7\,d^3+6\,a^4\,b^2\,c^8\,d^2-4\,a^3\,b^3\,c^9\,d+a^2\,b^4\,c^{10}\right)}\right)\,\left(6\,a\,d+b\,c\right)}{2\,c^4\,\sqrt{a^3}}\right)\,\left(6\,a\,d+b\,c\right)}{2\,c^4\,\sqrt{a^3}}}\right)\,\left(6\,a\,d+b\,c\right)\,1{}\mathrm{i}}{c^4\,\sqrt{a^3}}","Not used",1,"(log((d^3*(a*d - b*c)^5)^(1/2)*(a + b/x)^(1/2) - a^3*d^4 + b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3)*(d^3*(a*d - b*c)^5)^(1/2)*(3*a^2*d^2 + (35*b^2*c^2)/8 - 7*a*b*c*d))/(b^5*c^9 - a^5*c^4*d^5 + 5*a^4*b*c^5*d^4 + 10*a^2*b^3*c^7*d^2 - 10*a^3*b^2*c^6*d^3 - 5*a*b^4*c^8*d) - ((b*(a + b/x)^(5/2)*(12*a^2*d^4 + 4*b^2*c^2*d^2 - 19*a*b*c*d^3))/(4*a*c^3*(a*d - b*c)^2) - ((a + b/x)^(1/2)*(4*b^4*c^3 - 12*a^3*b*d^3 + 25*a^2*b^2*c*d^2 - 12*a*b^3*c^2*d))/(4*a*c^3*(a*d - b*c)) + (d*(a + b/x)^(3/2)*(8*b^4*c^3 - 24*a^3*b*d^3 + 56*a^2*b^2*c*d^2 - 37*a*b^3*c^2*d))/(4*c^3*(a^2*d - a*b*c)*(a*d - b*c)))/((a + b/x)^2*(3*a*d^2 - 2*b*c*d) - (a + b/x)*(3*a^2*d^2 + b^2*c^2 - 4*a*b*c*d) - d^2*(a + b/x)^3 + a^3*d^2 + a*b^2*c^2 - 2*a^2*b*c*d) - (log((d^3*(a*d - b*c)^5)^(1/2)*(a + b/x)^(1/2) + a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3)*(d^3*(a*d - b*c)^5)^(1/2)*(24*a^2*d^2 + 35*b^2*c^2 - 56*a*b*c*d))/(8*(b^5*c^9 - a^5*c^4*d^5 + 5*a^4*b*c^5*d^4 + 10*a^2*b^3*c^7*d^2 - 10*a^3*b^2*c^6*d^3 - 5*a*b^4*c^8*d)) - (atan((((((a + b/x)^(1/2)*(1152*a^6*b^2*d^9 + 16*b^8*c^6*d^3 + 128*a*b^7*c^5*d^4 - 4800*a^5*b^3*c*d^8 + 1129*a^2*b^6*c^4*d^5 - 5136*a^3*b^5*c^3*d^6 + 7520*a^4*b^4*c^2*d^7))/(8*(a^2*b^4*c^10 + a^6*c^6*d^4 - 4*a^3*b^3*c^9*d - 4*a^5*b*c^7*d^3 + 6*a^4*b^2*c^8*d^2)) - (((4*a*b^8*c^13*d^2 + 4*a^2*b^7*c^12*d^3 - 45*a^3*b^6*c^11*d^4 + 74*a^4*b^5*c^10*d^5 - 49*a^5*b^4*c^9*d^6 + 12*a^6*b^3*c^8*d^7)/(a^2*b^4*c^13 + a^6*c^9*d^4 - 4*a^3*b^3*c^12*d - 4*a^5*b*c^10*d^3 + 6*a^4*b^2*c^11*d^2) - ((a + b/x)^(1/2)*(6*a*d + b*c)*(64*a^2*b^7*c^13*d^2 - 384*a^3*b^6*c^12*d^3 + 896*a^4*b^5*c^11*d^4 - 1024*a^5*b^4*c^10*d^5 + 576*a^6*b^3*c^9*d^6 - 128*a^7*b^2*c^8*d^7))/(16*c^4*(a^3)^(1/2)*(a^2*b^4*c^10 + a^6*c^6*d^4 - 4*a^3*b^3*c^9*d - 4*a^5*b*c^7*d^3 + 6*a^4*b^2*c^8*d^2)))*(6*a*d + b*c))/(2*c^4*(a^3)^(1/2)))*(6*a*d + b*c)*1i)/(2*c^4*(a^3)^(1/2)) + ((((a + b/x)^(1/2)*(1152*a^6*b^2*d^9 + 16*b^8*c^6*d^3 + 128*a*b^7*c^5*d^4 - 4800*a^5*b^3*c*d^8 + 1129*a^2*b^6*c^4*d^5 - 5136*a^3*b^5*c^3*d^6 + 7520*a^4*b^4*c^2*d^7))/(8*(a^2*b^4*c^10 + a^6*c^6*d^4 - 4*a^3*b^3*c^9*d - 4*a^5*b*c^7*d^3 + 6*a^4*b^2*c^8*d^2)) + (((4*a*b^8*c^13*d^2 + 4*a^2*b^7*c^12*d^3 - 45*a^3*b^6*c^11*d^4 + 74*a^4*b^5*c^10*d^5 - 49*a^5*b^4*c^9*d^6 + 12*a^6*b^3*c^8*d^7)/(a^2*b^4*c^13 + a^6*c^9*d^4 - 4*a^3*b^3*c^12*d - 4*a^5*b*c^10*d^3 + 6*a^4*b^2*c^11*d^2) + ((a + b/x)^(1/2)*(6*a*d + b*c)*(64*a^2*b^7*c^13*d^2 - 384*a^3*b^6*c^12*d^3 + 896*a^4*b^5*c^11*d^4 - 1024*a^5*b^4*c^10*d^5 + 576*a^6*b^3*c^9*d^6 - 128*a^7*b^2*c^8*d^7))/(16*c^4*(a^3)^(1/2)*(a^2*b^4*c^10 + a^6*c^6*d^4 - 4*a^3*b^3*c^9*d - 4*a^5*b*c^7*d^3 + 6*a^4*b^2*c^8*d^2)))*(6*a*d + b*c))/(2*c^4*(a^3)^(1/2)))*(6*a*d + b*c)*1i)/(2*c^4*(a^3)^(1/2)))/((216*a^5*b^3*d^9 + (35*b^8*c^5*d^4)/2 - (49*a*b^7*c^4*d^5)/8 - 810*a^4*b^4*c*d^8 - (1877*a^2*b^6*c^3*d^6)/4 + 1044*a^3*b^5*c^2*d^7)/(a^2*b^4*c^13 + a^6*c^9*d^4 - 4*a^3*b^3*c^12*d - 4*a^5*b*c^10*d^3 + 6*a^4*b^2*c^11*d^2) + ((((a + b/x)^(1/2)*(1152*a^6*b^2*d^9 + 16*b^8*c^6*d^3 + 128*a*b^7*c^5*d^4 - 4800*a^5*b^3*c*d^8 + 1129*a^2*b^6*c^4*d^5 - 5136*a^3*b^5*c^3*d^6 + 7520*a^4*b^4*c^2*d^7))/(8*(a^2*b^4*c^10 + a^6*c^6*d^4 - 4*a^3*b^3*c^9*d - 4*a^5*b*c^7*d^3 + 6*a^4*b^2*c^8*d^2)) - (((4*a*b^8*c^13*d^2 + 4*a^2*b^7*c^12*d^3 - 45*a^3*b^6*c^11*d^4 + 74*a^4*b^5*c^10*d^5 - 49*a^5*b^4*c^9*d^6 + 12*a^6*b^3*c^8*d^7)/(a^2*b^4*c^13 + a^6*c^9*d^4 - 4*a^3*b^3*c^12*d - 4*a^5*b*c^10*d^3 + 6*a^4*b^2*c^11*d^2) - ((a + b/x)^(1/2)*(6*a*d + b*c)*(64*a^2*b^7*c^13*d^2 - 384*a^3*b^6*c^12*d^3 + 896*a^4*b^5*c^11*d^4 - 1024*a^5*b^4*c^10*d^5 + 576*a^6*b^3*c^9*d^6 - 128*a^7*b^2*c^8*d^7))/(16*c^4*(a^3)^(1/2)*(a^2*b^4*c^10 + a^6*c^6*d^4 - 4*a^3*b^3*c^9*d - 4*a^5*b*c^7*d^3 + 6*a^4*b^2*c^8*d^2)))*(6*a*d + b*c))/(2*c^4*(a^3)^(1/2)))*(6*a*d + b*c))/(2*c^4*(a^3)^(1/2)) - ((((a + b/x)^(1/2)*(1152*a^6*b^2*d^9 + 16*b^8*c^6*d^3 + 128*a*b^7*c^5*d^4 - 4800*a^5*b^3*c*d^8 + 1129*a^2*b^6*c^4*d^5 - 5136*a^3*b^5*c^3*d^6 + 7520*a^4*b^4*c^2*d^7))/(8*(a^2*b^4*c^10 + a^6*c^6*d^4 - 4*a^3*b^3*c^9*d - 4*a^5*b*c^7*d^3 + 6*a^4*b^2*c^8*d^2)) + (((4*a*b^8*c^13*d^2 + 4*a^2*b^7*c^12*d^3 - 45*a^3*b^6*c^11*d^4 + 74*a^4*b^5*c^10*d^5 - 49*a^5*b^4*c^9*d^6 + 12*a^6*b^3*c^8*d^7)/(a^2*b^4*c^13 + a^6*c^9*d^4 - 4*a^3*b^3*c^12*d - 4*a^5*b*c^10*d^3 + 6*a^4*b^2*c^11*d^2) + ((a + b/x)^(1/2)*(6*a*d + b*c)*(64*a^2*b^7*c^13*d^2 - 384*a^3*b^6*c^12*d^3 + 896*a^4*b^5*c^11*d^4 - 1024*a^5*b^4*c^10*d^5 + 576*a^6*b^3*c^9*d^6 - 128*a^7*b^2*c^8*d^7))/(16*c^4*(a^3)^(1/2)*(a^2*b^4*c^10 + a^6*c^6*d^4 - 4*a^3*b^3*c^9*d - 4*a^5*b*c^7*d^3 + 6*a^4*b^2*c^8*d^2)))*(6*a*d + b*c))/(2*c^4*(a^3)^(1/2)))*(6*a*d + b*c))/(2*c^4*(a^3)^(1/2))))*(6*a*d + b*c)*1i)/(c^4*(a^3)^(1/2))","B"
252,1,172,132,1.908482,"\text{Not used}","int((c + d/x)^3/(a + b/x)^(3/2),x)","\frac{\frac{2\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)}{a}-\frac{\left(a+\frac{b}{x}\right)\,\left(2\,a^3\,d^3-6\,a^2\,b\,c\,d^2+6\,a\,b^2\,c^2\,d-3\,b^3\,c^3\right)}{a^2}}{b^2\,{\left(a+\frac{b}{x}\right)}^{3/2}-a\,b^2\,\sqrt{a+\frac{b}{x}}}-\frac{2\,d^3\,\sqrt{a+\frac{b}{x}}}{b^2}+\frac{3\,c^2\,\mathrm{atanh}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)\,\left(2\,a\,d-b\,c\right)}{a^{5/2}}","Not used",1,"((2*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))/a - ((a + b/x)*(2*a^3*d^3 - 3*b^3*c^3 + 6*a*b^2*c^2*d - 6*a^2*b*c*d^2))/a^2)/(b^2*(a + b/x)^(3/2) - a*b^2*(a + b/x)^(1/2)) - (2*d^3*(a + b/x)^(1/2))/b^2 + (3*c^2*atanh((a + b/x)^(1/2)/a^(1/2))*(2*a*d - b*c))/a^(5/2)","B"
253,1,120,94,1.834401,"\text{Not used}","int((c + d/x)^2/(a + b/x)^(3/2),x)","\frac{c\,\mathrm{atanh}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)\,\left(4\,a\,d-3\,b\,c\right)}{a^{5/2}}-\frac{\frac{2\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}{a}-\frac{\left(a+\frac{b}{x}\right)\,\left(2\,a^2\,d^2-4\,a\,b\,c\,d+3\,b^2\,c^2\right)}{a^2}}{b\,{\left(a+\frac{b}{x}\right)}^{3/2}-a\,b\,\sqrt{a+\frac{b}{x}}}","Not used",1,"(c*atanh((a + b/x)^(1/2)/a^(1/2))*(4*a*d - 3*b*c))/a^(5/2) - ((2*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/a - ((a + b/x)*(2*a^2*d^2 + 3*b^2*c^2 - 4*a*b*c*d))/a^2)/(b*(a + b/x)^(3/2) - a*b*(a + b/x)^(1/2))","B"
254,1,71,76,2.438139,"\text{Not used}","int((c + d/x)/(a + b/x)^(3/2),x)","\frac{2\,d\,\mathrm{atanh}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{3/2}}-\frac{2\,d}{a\,\sqrt{a+\frac{b}{x}}}+\frac{2\,c\,x\,{\left(\frac{a\,x}{b}+1\right)}^{3/2}\,{{}}_2{\mathrm{F}}_1\left(\frac{3}{2},\frac{5}{2};\ \frac{7}{2};\ -\frac{a\,x}{b}\right)}{5\,{\left(a+\frac{b}{x}\right)}^{3/2}}","Not used",1,"(2*d*atanh((a + b/x)^(1/2)/a^(1/2)))/a^(3/2) - (2*d)/(a*(a + b/x)^(1/2)) + (2*c*x*((a*x)/b + 1)^(3/2)*hypergeom([3/2, 5/2], 7/2, -(a*x)/b))/(5*(a + b/x)^(3/2))","B"
255,1,34,60,1.868403,"\text{Not used}","int(1/(a + b/x)^(3/2),x)","\frac{2\,x\,{\left(\frac{a\,x}{b}+1\right)}^{3/2}\,{{}}_2{\mathrm{F}}_1\left(\frac{3}{2},\frac{5}{2};\ \frac{7}{2};\ -\frac{a\,x}{b}\right)}{5\,{\left(a+\frac{b}{x}\right)}^{3/2}}","Not used",1,"(2*x*((a*x)/b + 1)^(3/2)*hypergeom([3/2, 5/2], 7/2, -(a*x)/b))/(5*(a + b/x)^(3/2))","B"
256,1,3000,147,2.683765,"\text{Not used}","int(1/((a + b/x)^(3/2)*(c + d/x)),x)","-\frac{\frac{2\,b^2}{a^2\,d-a\,b\,c}+\frac{b\,\left(a+\frac{b}{x}\right)\,\left(a\,d-3\,b\,c\right)}{a^2\,c\,\left(a\,d-b\,c\right)}}{a\,\sqrt{a+\frac{b}{x}}-{\left(a+\frac{b}{x}\right)}^{3/2}}-\frac{\mathrm{atanh}\left(\frac{54\,a^5\,b^{11}\,c^{10}\,d^2\,\sqrt{a+\frac{b}{x}}}{\sqrt{a^5}\,\left(-60\,a^{10}\,b^4\,c^3\,d^9+110\,a^9\,b^5\,c^4\,d^8+120\,a^8\,b^6\,c^5\,d^7-366\,a^7\,b^7\,c^6\,d^6+124\,a^6\,b^8\,c^7\,d^5+234\,a^5\,b^9\,c^8\,d^4-216\,a^4\,b^{10}\,c^9\,d^3+54\,a^3\,b^{11}\,c^{10}\,d^2\right)}-\frac{216\,a^6\,b^{10}\,c^9\,d^3\,\sqrt{a+\frac{b}{x}}}{\sqrt{a^5}\,\left(-60\,a^{10}\,b^4\,c^3\,d^9+110\,a^9\,b^5\,c^4\,d^8+120\,a^8\,b^6\,c^5\,d^7-366\,a^7\,b^7\,c^6\,d^6+124\,a^6\,b^8\,c^7\,d^5+234\,a^5\,b^9\,c^8\,d^4-216\,a^4\,b^{10}\,c^9\,d^3+54\,a^3\,b^{11}\,c^{10}\,d^2\right)}+\frac{234\,a^7\,b^9\,c^8\,d^4\,\sqrt{a+\frac{b}{x}}}{\sqrt{a^5}\,\left(-60\,a^{10}\,b^4\,c^3\,d^9+110\,a^9\,b^5\,c^4\,d^8+120\,a^8\,b^6\,c^5\,d^7-366\,a^7\,b^7\,c^6\,d^6+124\,a^6\,b^8\,c^7\,d^5+234\,a^5\,b^9\,c^8\,d^4-216\,a^4\,b^{10}\,c^9\,d^3+54\,a^3\,b^{11}\,c^{10}\,d^2\right)}+\frac{124\,a^8\,b^8\,c^7\,d^5\,\sqrt{a+\frac{b}{x}}}{\sqrt{a^5}\,\left(-60\,a^{10}\,b^4\,c^3\,d^9+110\,a^9\,b^5\,c^4\,d^8+120\,a^8\,b^6\,c^5\,d^7-366\,a^7\,b^7\,c^6\,d^6+124\,a^6\,b^8\,c^7\,d^5+234\,a^5\,b^9\,c^8\,d^4-216\,a^4\,b^{10}\,c^9\,d^3+54\,a^3\,b^{11}\,c^{10}\,d^2\right)}-\frac{366\,a^9\,b^7\,c^6\,d^6\,\sqrt{a+\frac{b}{x}}}{\sqrt{a^5}\,\left(-60\,a^{10}\,b^4\,c^3\,d^9+110\,a^9\,b^5\,c^4\,d^8+120\,a^8\,b^6\,c^5\,d^7-366\,a^7\,b^7\,c^6\,d^6+124\,a^6\,b^8\,c^7\,d^5+234\,a^5\,b^9\,c^8\,d^4-216\,a^4\,b^{10}\,c^9\,d^3+54\,a^3\,b^{11}\,c^{10}\,d^2\right)}+\frac{120\,a^{10}\,b^6\,c^5\,d^7\,\sqrt{a+\frac{b}{x}}}{\sqrt{a^5}\,\left(-60\,a^{10}\,b^4\,c^3\,d^9+110\,a^9\,b^5\,c^4\,d^8+120\,a^8\,b^6\,c^5\,d^7-366\,a^7\,b^7\,c^6\,d^6+124\,a^6\,b^8\,c^7\,d^5+234\,a^5\,b^9\,c^8\,d^4-216\,a^4\,b^{10}\,c^9\,d^3+54\,a^3\,b^{11}\,c^{10}\,d^2\right)}+\frac{110\,a^{11}\,b^5\,c^4\,d^8\,\sqrt{a+\frac{b}{x}}}{\sqrt{a^5}\,\left(-60\,a^{10}\,b^4\,c^3\,d^9+110\,a^9\,b^5\,c^4\,d^8+120\,a^8\,b^6\,c^5\,d^7-366\,a^7\,b^7\,c^6\,d^6+124\,a^6\,b^8\,c^7\,d^5+234\,a^5\,b^9\,c^8\,d^4-216\,a^4\,b^{10}\,c^9\,d^3+54\,a^3\,b^{11}\,c^{10}\,d^2\right)}-\frac{60\,a^{12}\,b^4\,c^3\,d^9\,\sqrt{a+\frac{b}{x}}}{\sqrt{a^5}\,\left(-60\,a^{10}\,b^4\,c^3\,d^9+110\,a^9\,b^5\,c^4\,d^8+120\,a^8\,b^6\,c^5\,d^7-366\,a^7\,b^7\,c^6\,d^6+124\,a^6\,b^8\,c^7\,d^5+234\,a^5\,b^9\,c^8\,d^4-216\,a^4\,b^{10}\,c^9\,d^3+54\,a^3\,b^{11}\,c^{10}\,d^2\right)}\right)\,\left(2\,a\,d+3\,b\,c\right)}{c^2\,\sqrt{a^5}}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{d^5\,{\left(a\,d-b\,c\right)}^3}\,\left(\sqrt{a+\frac{b}{x}}\,\left(-16\,a^{13}\,b^2\,c^3\,d^{10}+40\,a^{12}\,b^3\,c^4\,d^9-2\,a^{11}\,b^4\,c^5\,d^8-62\,a^{10}\,b^5\,c^6\,d^7+20\,a^9\,b^6\,c^7\,d^6+68\,a^8\,b^7\,c^8\,d^5-66\,a^7\,b^8\,c^9\,d^4+18\,a^6\,b^9\,c^{10}\,d^3\right)+\frac{\sqrt{d^5\,{\left(a\,d-b\,c\right)}^3}\,\left(64\,a^9\,b^8\,c^{11}\,d^3-12\,a^8\,b^9\,c^{12}\,d^2-132\,a^{10}\,b^7\,c^{10}\,d^4+128\,a^{11}\,b^6\,c^9\,d^5-52\,a^{12}\,b^5\,c^8\,d^6+4\,a^{14}\,b^3\,c^6\,d^8+\frac{\sqrt{d^5\,{\left(a\,d-b\,c\right)}^3}\,\sqrt{a+\frac{b}{x}}\,\left(16\,a^{16}\,b^2\,c^7\,d^8-88\,a^{15}\,b^3\,c^8\,d^7+200\,a^{14}\,b^4\,c^9\,d^6-240\,a^{13}\,b^5\,c^{10}\,d^5+160\,a^{12}\,b^6\,c^{11}\,d^4-56\,a^{11}\,b^7\,c^{12}\,d^3+8\,a^{10}\,b^8\,c^{13}\,d^2\right)}{c^2\,{\left(a\,d-b\,c\right)}^3}\right)}{c^2\,{\left(a\,d-b\,c\right)}^3}\right)\,1{}\mathrm{i}}{c^2\,{\left(a\,d-b\,c\right)}^3}+\frac{\sqrt{d^5\,{\left(a\,d-b\,c\right)}^3}\,\left(\sqrt{a+\frac{b}{x}}\,\left(-16\,a^{13}\,b^2\,c^3\,d^{10}+40\,a^{12}\,b^3\,c^4\,d^9-2\,a^{11}\,b^4\,c^5\,d^8-62\,a^{10}\,b^5\,c^6\,d^7+20\,a^9\,b^6\,c^7\,d^6+68\,a^8\,b^7\,c^8\,d^5-66\,a^7\,b^8\,c^9\,d^4+18\,a^6\,b^9\,c^{10}\,d^3\right)+\frac{\sqrt{d^5\,{\left(a\,d-b\,c\right)}^3}\,\left(12\,a^8\,b^9\,c^{12}\,d^2-64\,a^9\,b^8\,c^{11}\,d^3+132\,a^{10}\,b^7\,c^{10}\,d^4-128\,a^{11}\,b^6\,c^9\,d^5+52\,a^{12}\,b^5\,c^8\,d^6-4\,a^{14}\,b^3\,c^6\,d^8+\frac{\sqrt{d^5\,{\left(a\,d-b\,c\right)}^3}\,\sqrt{a+\frac{b}{x}}\,\left(16\,a^{16}\,b^2\,c^7\,d^8-88\,a^{15}\,b^3\,c^8\,d^7+200\,a^{14}\,b^4\,c^9\,d^6-240\,a^{13}\,b^5\,c^{10}\,d^5+160\,a^{12}\,b^6\,c^{11}\,d^4-56\,a^{11}\,b^7\,c^{12}\,d^3+8\,a^{10}\,b^8\,c^{13}\,d^2\right)}{c^2\,{\left(a\,d-b\,c\right)}^3}\right)}{c^2\,{\left(a\,d-b\,c\right)}^3}\right)\,1{}\mathrm{i}}{c^2\,{\left(a\,d-b\,c\right)}^3}}{36\,a^6\,b^8\,c^7\,d^5-96\,a^7\,b^7\,c^6\,d^6+64\,a^8\,b^6\,c^5\,d^7+24\,a^9\,b^5\,c^4\,d^8-36\,a^{10}\,b^4\,c^3\,d^9+8\,a^{11}\,b^3\,c^2\,d^{10}-\frac{\sqrt{d^5\,{\left(a\,d-b\,c\right)}^3}\,\left(\sqrt{a+\frac{b}{x}}\,\left(-16\,a^{13}\,b^2\,c^3\,d^{10}+40\,a^{12}\,b^3\,c^4\,d^9-2\,a^{11}\,b^4\,c^5\,d^8-62\,a^{10}\,b^5\,c^6\,d^7+20\,a^9\,b^6\,c^7\,d^6+68\,a^8\,b^7\,c^8\,d^5-66\,a^7\,b^8\,c^9\,d^4+18\,a^6\,b^9\,c^{10}\,d^3\right)+\frac{\sqrt{d^5\,{\left(a\,d-b\,c\right)}^3}\,\left(64\,a^9\,b^8\,c^{11}\,d^3-12\,a^8\,b^9\,c^{12}\,d^2-132\,a^{10}\,b^7\,c^{10}\,d^4+128\,a^{11}\,b^6\,c^9\,d^5-52\,a^{12}\,b^5\,c^8\,d^6+4\,a^{14}\,b^3\,c^6\,d^8+\frac{\sqrt{d^5\,{\left(a\,d-b\,c\right)}^3}\,\sqrt{a+\frac{b}{x}}\,\left(16\,a^{16}\,b^2\,c^7\,d^8-88\,a^{15}\,b^3\,c^8\,d^7+200\,a^{14}\,b^4\,c^9\,d^6-240\,a^{13}\,b^5\,c^{10}\,d^5+160\,a^{12}\,b^6\,c^{11}\,d^4-56\,a^{11}\,b^7\,c^{12}\,d^3+8\,a^{10}\,b^8\,c^{13}\,d^2\right)}{c^2\,{\left(a\,d-b\,c\right)}^3}\right)}{c^2\,{\left(a\,d-b\,c\right)}^3}\right)}{c^2\,{\left(a\,d-b\,c\right)}^3}+\frac{\sqrt{d^5\,{\left(a\,d-b\,c\right)}^3}\,\left(\sqrt{a+\frac{b}{x}}\,\left(-16\,a^{13}\,b^2\,c^3\,d^{10}+40\,a^{12}\,b^3\,c^4\,d^9-2\,a^{11}\,b^4\,c^5\,d^8-62\,a^{10}\,b^5\,c^6\,d^7+20\,a^9\,b^6\,c^7\,d^6+68\,a^8\,b^7\,c^8\,d^5-66\,a^7\,b^8\,c^9\,d^4+18\,a^6\,b^9\,c^{10}\,d^3\right)+\frac{\sqrt{d^5\,{\left(a\,d-b\,c\right)}^3}\,\left(12\,a^8\,b^9\,c^{12}\,d^2-64\,a^9\,b^8\,c^{11}\,d^3+132\,a^{10}\,b^7\,c^{10}\,d^4-128\,a^{11}\,b^6\,c^9\,d^5+52\,a^{12}\,b^5\,c^8\,d^6-4\,a^{14}\,b^3\,c^6\,d^8+\frac{\sqrt{d^5\,{\left(a\,d-b\,c\right)}^3}\,\sqrt{a+\frac{b}{x}}\,\left(16\,a^{16}\,b^2\,c^7\,d^8-88\,a^{15}\,b^3\,c^8\,d^7+200\,a^{14}\,b^4\,c^9\,d^6-240\,a^{13}\,b^5\,c^{10}\,d^5+160\,a^{12}\,b^6\,c^{11}\,d^4-56\,a^{11}\,b^7\,c^{12}\,d^3+8\,a^{10}\,b^8\,c^{13}\,d^2\right)}{c^2\,{\left(a\,d-b\,c\right)}^3}\right)}{c^2\,{\left(a\,d-b\,c\right)}^3}\right)}{c^2\,{\left(a\,d-b\,c\right)}^3}}\right)\,\sqrt{d^5\,{\left(a\,d-b\,c\right)}^3}\,2{}\mathrm{i}}{c^2\,{\left(a\,d-b\,c\right)}^3}","Not used",1,"(atan((((d^5*(a*d - b*c)^3)^(1/2)*((a + b/x)^(1/2)*(18*a^6*b^9*c^10*d^3 - 66*a^7*b^8*c^9*d^4 + 68*a^8*b^7*c^8*d^5 + 20*a^9*b^6*c^7*d^6 - 62*a^10*b^5*c^6*d^7 - 2*a^11*b^4*c^5*d^8 + 40*a^12*b^3*c^4*d^9 - 16*a^13*b^2*c^3*d^10) + ((d^5*(a*d - b*c)^3)^(1/2)*(64*a^9*b^8*c^11*d^3 - 12*a^8*b^9*c^12*d^2 - 132*a^10*b^7*c^10*d^4 + 128*a^11*b^6*c^9*d^5 - 52*a^12*b^5*c^8*d^6 + 4*a^14*b^3*c^6*d^8 + ((d^5*(a*d - b*c)^3)^(1/2)*(a + b/x)^(1/2)*(8*a^10*b^8*c^13*d^2 - 56*a^11*b^7*c^12*d^3 + 160*a^12*b^6*c^11*d^4 - 240*a^13*b^5*c^10*d^5 + 200*a^14*b^4*c^9*d^6 - 88*a^15*b^3*c^8*d^7 + 16*a^16*b^2*c^7*d^8))/(c^2*(a*d - b*c)^3)))/(c^2*(a*d - b*c)^3))*1i)/(c^2*(a*d - b*c)^3) + ((d^5*(a*d - b*c)^3)^(1/2)*((a + b/x)^(1/2)*(18*a^6*b^9*c^10*d^3 - 66*a^7*b^8*c^9*d^4 + 68*a^8*b^7*c^8*d^5 + 20*a^9*b^6*c^7*d^6 - 62*a^10*b^5*c^6*d^7 - 2*a^11*b^4*c^5*d^8 + 40*a^12*b^3*c^4*d^9 - 16*a^13*b^2*c^3*d^10) + ((d^5*(a*d - b*c)^3)^(1/2)*(12*a^8*b^9*c^12*d^2 - 64*a^9*b^8*c^11*d^3 + 132*a^10*b^7*c^10*d^4 - 128*a^11*b^6*c^9*d^5 + 52*a^12*b^5*c^8*d^6 - 4*a^14*b^3*c^6*d^8 + ((d^5*(a*d - b*c)^3)^(1/2)*(a + b/x)^(1/2)*(8*a^10*b^8*c^13*d^2 - 56*a^11*b^7*c^12*d^3 + 160*a^12*b^6*c^11*d^4 - 240*a^13*b^5*c^10*d^5 + 200*a^14*b^4*c^9*d^6 - 88*a^15*b^3*c^8*d^7 + 16*a^16*b^2*c^7*d^8))/(c^2*(a*d - b*c)^3)))/(c^2*(a*d - b*c)^3))*1i)/(c^2*(a*d - b*c)^3))/(36*a^6*b^8*c^7*d^5 - 96*a^7*b^7*c^6*d^6 + 64*a^8*b^6*c^5*d^7 + 24*a^9*b^5*c^4*d^8 - 36*a^10*b^4*c^3*d^9 + 8*a^11*b^3*c^2*d^10 - ((d^5*(a*d - b*c)^3)^(1/2)*((a + b/x)^(1/2)*(18*a^6*b^9*c^10*d^3 - 66*a^7*b^8*c^9*d^4 + 68*a^8*b^7*c^8*d^5 + 20*a^9*b^6*c^7*d^6 - 62*a^10*b^5*c^6*d^7 - 2*a^11*b^4*c^5*d^8 + 40*a^12*b^3*c^4*d^9 - 16*a^13*b^2*c^3*d^10) + ((d^5*(a*d - b*c)^3)^(1/2)*(64*a^9*b^8*c^11*d^3 - 12*a^8*b^9*c^12*d^2 - 132*a^10*b^7*c^10*d^4 + 128*a^11*b^6*c^9*d^5 - 52*a^12*b^5*c^8*d^6 + 4*a^14*b^3*c^6*d^8 + ((d^5*(a*d - b*c)^3)^(1/2)*(a + b/x)^(1/2)*(8*a^10*b^8*c^13*d^2 - 56*a^11*b^7*c^12*d^3 + 160*a^12*b^6*c^11*d^4 - 240*a^13*b^5*c^10*d^5 + 200*a^14*b^4*c^9*d^6 - 88*a^15*b^3*c^8*d^7 + 16*a^16*b^2*c^7*d^8))/(c^2*(a*d - b*c)^3)))/(c^2*(a*d - b*c)^3)))/(c^2*(a*d - b*c)^3) + ((d^5*(a*d - b*c)^3)^(1/2)*((a + b/x)^(1/2)*(18*a^6*b^9*c^10*d^3 - 66*a^7*b^8*c^9*d^4 + 68*a^8*b^7*c^8*d^5 + 20*a^9*b^6*c^7*d^6 - 62*a^10*b^5*c^6*d^7 - 2*a^11*b^4*c^5*d^8 + 40*a^12*b^3*c^4*d^9 - 16*a^13*b^2*c^3*d^10) + ((d^5*(a*d - b*c)^3)^(1/2)*(12*a^8*b^9*c^12*d^2 - 64*a^9*b^8*c^11*d^3 + 132*a^10*b^7*c^10*d^4 - 128*a^11*b^6*c^9*d^5 + 52*a^12*b^5*c^8*d^6 - 4*a^14*b^3*c^6*d^8 + ((d^5*(a*d - b*c)^3)^(1/2)*(a + b/x)^(1/2)*(8*a^10*b^8*c^13*d^2 - 56*a^11*b^7*c^12*d^3 + 160*a^12*b^6*c^11*d^4 - 240*a^13*b^5*c^10*d^5 + 200*a^14*b^4*c^9*d^6 - 88*a^15*b^3*c^8*d^7 + 16*a^16*b^2*c^7*d^8))/(c^2*(a*d - b*c)^3)))/(c^2*(a*d - b*c)^3)))/(c^2*(a*d - b*c)^3)))*(d^5*(a*d - b*c)^3)^(1/2)*2i)/(c^2*(a*d - b*c)^3) - (atanh((54*a^5*b^11*c^10*d^2*(a + b/x)^(1/2))/((a^5)^(1/2)*(54*a^3*b^11*c^10*d^2 - 216*a^4*b^10*c^9*d^3 + 234*a^5*b^9*c^8*d^4 + 124*a^6*b^8*c^7*d^5 - 366*a^7*b^7*c^6*d^6 + 120*a^8*b^6*c^5*d^7 + 110*a^9*b^5*c^4*d^8 - 60*a^10*b^4*c^3*d^9)) - (216*a^6*b^10*c^9*d^3*(a + b/x)^(1/2))/((a^5)^(1/2)*(54*a^3*b^11*c^10*d^2 - 216*a^4*b^10*c^9*d^3 + 234*a^5*b^9*c^8*d^4 + 124*a^6*b^8*c^7*d^5 - 366*a^7*b^7*c^6*d^6 + 120*a^8*b^6*c^5*d^7 + 110*a^9*b^5*c^4*d^8 - 60*a^10*b^4*c^3*d^9)) + (234*a^7*b^9*c^8*d^4*(a + b/x)^(1/2))/((a^5)^(1/2)*(54*a^3*b^11*c^10*d^2 - 216*a^4*b^10*c^9*d^3 + 234*a^5*b^9*c^8*d^4 + 124*a^6*b^8*c^7*d^5 - 366*a^7*b^7*c^6*d^6 + 120*a^8*b^6*c^5*d^7 + 110*a^9*b^5*c^4*d^8 - 60*a^10*b^4*c^3*d^9)) + (124*a^8*b^8*c^7*d^5*(a + b/x)^(1/2))/((a^5)^(1/2)*(54*a^3*b^11*c^10*d^2 - 216*a^4*b^10*c^9*d^3 + 234*a^5*b^9*c^8*d^4 + 124*a^6*b^8*c^7*d^5 - 366*a^7*b^7*c^6*d^6 + 120*a^8*b^6*c^5*d^7 + 110*a^9*b^5*c^4*d^8 - 60*a^10*b^4*c^3*d^9)) - (366*a^9*b^7*c^6*d^6*(a + b/x)^(1/2))/((a^5)^(1/2)*(54*a^3*b^11*c^10*d^2 - 216*a^4*b^10*c^9*d^3 + 234*a^5*b^9*c^8*d^4 + 124*a^6*b^8*c^7*d^5 - 366*a^7*b^7*c^6*d^6 + 120*a^8*b^6*c^5*d^7 + 110*a^9*b^5*c^4*d^8 - 60*a^10*b^4*c^3*d^9)) + (120*a^10*b^6*c^5*d^7*(a + b/x)^(1/2))/((a^5)^(1/2)*(54*a^3*b^11*c^10*d^2 - 216*a^4*b^10*c^9*d^3 + 234*a^5*b^9*c^8*d^4 + 124*a^6*b^8*c^7*d^5 - 366*a^7*b^7*c^6*d^6 + 120*a^8*b^6*c^5*d^7 + 110*a^9*b^5*c^4*d^8 - 60*a^10*b^4*c^3*d^9)) + (110*a^11*b^5*c^4*d^8*(a + b/x)^(1/2))/((a^5)^(1/2)*(54*a^3*b^11*c^10*d^2 - 216*a^4*b^10*c^9*d^3 + 234*a^5*b^9*c^8*d^4 + 124*a^6*b^8*c^7*d^5 - 366*a^7*b^7*c^6*d^6 + 120*a^8*b^6*c^5*d^7 + 110*a^9*b^5*c^4*d^8 - 60*a^10*b^4*c^3*d^9)) - (60*a^12*b^4*c^3*d^9*(a + b/x)^(1/2))/((a^5)^(1/2)*(54*a^3*b^11*c^10*d^2 - 216*a^4*b^10*c^9*d^3 + 234*a^5*b^9*c^8*d^4 + 124*a^6*b^8*c^7*d^5 - 366*a^7*b^7*c^6*d^6 + 120*a^8*b^6*c^5*d^7 + 110*a^9*b^5*c^4*d^8 - 60*a^10*b^4*c^3*d^9)))*(2*a*d + 3*b*c))/(c^2*(a^5)^(1/2)) - ((2*b^2)/(a^2*d - a*b*c) + (b*(a + b/x)*(a*d - 3*b*c))/(a^2*c*(a*d - b*c)))/(a*(a + b/x)^(1/2) - (a + b/x)^(3/2))","B"
257,1,4274,224,6.202481,"\text{Not used}","int(1/((a + b/x)^(3/2)*(c + d/x)^2),x)","\frac{\frac{2\,b^3}{a^2\,d-a\,b\,c}+\frac{b\,{\left(a+\frac{b}{x}\right)}^2\,\left(2\,a^2\,d^3-2\,a\,b\,c\,d^2+3\,b^2\,c^2\,d\right)}{c^2\,{\left(a^2\,d-a\,b\,c\right)}^2}-\frac{b\,\left(a+\frac{b}{x}\right)\,\left(2\,a\,d-b\,c\right)\,\left(a^2\,d^2-a\,b\,c\,d+3\,b^2\,c^2\right)}{c^2\,{\left(a^2\,d-a\,b\,c\right)}^2}}{d\,{\left(a+\frac{b}{x}\right)}^{5/2}+\sqrt{a+\frac{b}{x}}\,\left(a^2\,d-a\,b\,c\right)-{\left(a+\frac{b}{x}\right)}^{3/2}\,\left(2\,a\,d-b\,c\right)}+\frac{\mathrm{atan}\left(\frac{-a^{10}\,b^{14}\,c^{14}\,\sqrt{a+\frac{b}{x}}\,27{}\mathrm{i}-a^{12}\,b^{12}\,c^{12}\,d^2\,\sqrt{a+\frac{b}{x}}\,441{}\mathrm{i}+a^{13}\,b^{11}\,c^{11}\,d^3\,\sqrt{a+\frac{b}{x}}\,35{}\mathrm{i}+a^{14}\,b^{10}\,c^{10}\,d^4\,\sqrt{a+\frac{b}{x}}\,1694{}\mathrm{i}-a^{15}\,b^9\,c^9\,d^5\,\sqrt{a+\frac{b}{x}}\,3073{}\mathrm{i}+a^{16}\,b^8\,c^8\,d^6\,\sqrt{a+\frac{b}{x}}\,1316{}\mathrm{i}+a^{17}\,b^7\,c^7\,d^7\,\sqrt{a+\frac{b}{x}}\,2561{}\mathrm{i}-a^{18}\,b^6\,c^6\,d^8\,\sqrt{a+\frac{b}{x}}\,4375{}\mathrm{i}+a^{19}\,b^5\,c^5\,d^9\,\sqrt{a+\frac{b}{x}}\,2996{}\mathrm{i}-a^{20}\,b^4\,c^4\,d^{10}\,\sqrt{a+\frac{b}{x}}\,1015{}\mathrm{i}+a^{21}\,b^3\,c^3\,d^{11}\,\sqrt{a+\frac{b}{x}}\,140{}\mathrm{i}+a^{11}\,b^{13}\,c^{13}\,d\,\sqrt{a+\frac{b}{x}}\,189{}\mathrm{i}}{a^5\,\sqrt{a^5}\,\left(a^5\,\left(a^5\,\left(140\,a^4\,b^3\,c^3\,d^{11}-1015\,a^3\,b^4\,c^4\,d^{10}+2996\,a^2\,b^5\,c^5\,d^9-4375\,a\,b^6\,c^6\,d^8+2561\,b^7\,c^7\,d^7\right)-441\,b^{12}\,c^{12}\,d^2+35\,a\,b^{11}\,c^{11}\,d^3+1694\,a^2\,b^{10}\,c^{10}\,d^4-3073\,a^3\,b^9\,c^9\,d^5+1316\,a^4\,b^8\,c^8\,d^6\right)-27\,a^3\,b^{14}\,c^{14}+189\,a^4\,b^{13}\,c^{13}\,d\right)}\right)\,\left(4\,a\,d+3\,b\,c\right)\,1{}\mathrm{i}}{c^3\,\sqrt{a^5}}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{d^5\,{\left(a\,d-b\,c\right)}^5}\,\left(4\,a\,d-7\,b\,c\right)\,\left(\sqrt{a+\frac{b}{x}}\,\left(64\,a^{18}\,b^2\,c^6\,d^{15}-576\,a^{17}\,b^3\,c^7\,d^{14}+2228\,a^{16}\,b^4\,c^8\,d^{13}-4768\,a^{15}\,b^5\,c^9\,d^{12}+5960\,a^{14}\,b^6\,c^{10}\,d^{11}-3976\,a^{13}\,b^7\,c^{11}\,d^{10}+578\,a^{12}\,b^8\,c^{12}\,d^9+1004\,a^{11}\,b^9\,c^{13}\,d^8-442\,a^{10}\,b^{10}\,c^{14}\,d^7-320\,a^9\,b^{11}\,c^{15}\,d^6+362\,a^8\,b^{12}\,c^{16}\,d^5-132\,a^7\,b^{13}\,c^{17}\,d^4+18\,a^6\,b^{14}\,c^{18}\,d^3\right)-\frac{\sqrt{d^5\,{\left(a\,d-b\,c\right)}^5}\,\left(4\,a\,d-7\,b\,c\right)\,\left(12\,a^8\,b^{14}\,c^{21}\,d^2-116\,a^9\,b^{13}\,c^{20}\,d^3+484\,a^{10}\,b^{12}\,c^{19}\,d^4-1128\,a^{11}\,b^{11}\,c^{18}\,d^5+1560\,a^{12}\,b^{10}\,c^{17}\,d^6-1176\,a^{13}\,b^9\,c^{16}\,d^7+168\,a^{14}\,b^8\,c^{15}\,d^8+576\,a^{15}\,b^7\,c^{14}\,d^9-612\,a^{16}\,b^6\,c^{13}\,d^{10}+300\,a^{17}\,b^5\,c^{12}\,d^{11}-76\,a^{18}\,b^4\,c^{11}\,d^{12}+8\,a^{19}\,b^3\,c^{10}\,d^{13}-\frac{\sqrt{d^5\,{\left(a\,d-b\,c\right)}^5}\,\sqrt{a+\frac{b}{x}}\,\left(4\,a\,d-7\,b\,c\right)\,\left(-16\,a^{21}\,b^2\,c^{12}\,d^{13}+168\,a^{20}\,b^3\,c^{13}\,d^{12}-800\,a^{19}\,b^4\,c^{14}\,d^{11}+2280\,a^{18}\,b^5\,c^{15}\,d^{10}-4320\,a^{17}\,b^6\,c^{16}\,d^9+5712\,a^{16}\,b^7\,c^{17}\,d^8-5376\,a^{15}\,b^8\,c^{18}\,d^7+3600\,a^{14}\,b^9\,c^{19}\,d^6-1680\,a^{13}\,b^{10}\,c^{20}\,d^5+520\,a^{12}\,b^{11}\,c^{21}\,d^4-96\,a^{11}\,b^{12}\,c^{22}\,d^3+8\,a^{10}\,b^{13}\,c^{23}\,d^2\right)}{2\,\left(-a^5\,c^3\,d^5+5\,a^4\,b\,c^4\,d^4-10\,a^3\,b^2\,c^5\,d^3+10\,a^2\,b^3\,c^6\,d^2-5\,a\,b^4\,c^7\,d+b^5\,c^8\right)}\right)}{2\,\left(-a^5\,c^3\,d^5+5\,a^4\,b\,c^4\,d^4-10\,a^3\,b^2\,c^5\,d^3+10\,a^2\,b^3\,c^6\,d^2-5\,a\,b^4\,c^7\,d+b^5\,c^8\right)}\right)\,1{}\mathrm{i}}{2\,\left(-a^5\,c^3\,d^5+5\,a^4\,b\,c^4\,d^4-10\,a^3\,b^2\,c^5\,d^3+10\,a^2\,b^3\,c^6\,d^2-5\,a\,b^4\,c^7\,d+b^5\,c^8\right)}+\frac{\sqrt{d^5\,{\left(a\,d-b\,c\right)}^5}\,\left(4\,a\,d-7\,b\,c\right)\,\left(\sqrt{a+\frac{b}{x}}\,\left(64\,a^{18}\,b^2\,c^6\,d^{15}-576\,a^{17}\,b^3\,c^7\,d^{14}+2228\,a^{16}\,b^4\,c^8\,d^{13}-4768\,a^{15}\,b^5\,c^9\,d^{12}+5960\,a^{14}\,b^6\,c^{10}\,d^{11}-3976\,a^{13}\,b^7\,c^{11}\,d^{10}+578\,a^{12}\,b^8\,c^{12}\,d^9+1004\,a^{11}\,b^9\,c^{13}\,d^8-442\,a^{10}\,b^{10}\,c^{14}\,d^7-320\,a^9\,b^{11}\,c^{15}\,d^6+362\,a^8\,b^{12}\,c^{16}\,d^5-132\,a^7\,b^{13}\,c^{17}\,d^4+18\,a^6\,b^{14}\,c^{18}\,d^3\right)+\frac{\sqrt{d^5\,{\left(a\,d-b\,c\right)}^5}\,\left(4\,a\,d-7\,b\,c\right)\,\left(12\,a^8\,b^{14}\,c^{21}\,d^2-116\,a^9\,b^{13}\,c^{20}\,d^3+484\,a^{10}\,b^{12}\,c^{19}\,d^4-1128\,a^{11}\,b^{11}\,c^{18}\,d^5+1560\,a^{12}\,b^{10}\,c^{17}\,d^6-1176\,a^{13}\,b^9\,c^{16}\,d^7+168\,a^{14}\,b^8\,c^{15}\,d^8+576\,a^{15}\,b^7\,c^{14}\,d^9-612\,a^{16}\,b^6\,c^{13}\,d^{10}+300\,a^{17}\,b^5\,c^{12}\,d^{11}-76\,a^{18}\,b^4\,c^{11}\,d^{12}+8\,a^{19}\,b^3\,c^{10}\,d^{13}+\frac{\sqrt{d^5\,{\left(a\,d-b\,c\right)}^5}\,\sqrt{a+\frac{b}{x}}\,\left(4\,a\,d-7\,b\,c\right)\,\left(-16\,a^{21}\,b^2\,c^{12}\,d^{13}+168\,a^{20}\,b^3\,c^{13}\,d^{12}-800\,a^{19}\,b^4\,c^{14}\,d^{11}+2280\,a^{18}\,b^5\,c^{15}\,d^{10}-4320\,a^{17}\,b^6\,c^{16}\,d^9+5712\,a^{16}\,b^7\,c^{17}\,d^8-5376\,a^{15}\,b^8\,c^{18}\,d^7+3600\,a^{14}\,b^9\,c^{19}\,d^6-1680\,a^{13}\,b^{10}\,c^{20}\,d^5+520\,a^{12}\,b^{11}\,c^{21}\,d^4-96\,a^{11}\,b^{12}\,c^{22}\,d^3+8\,a^{10}\,b^{13}\,c^{23}\,d^2\right)}{2\,\left(-a^5\,c^3\,d^5+5\,a^4\,b\,c^4\,d^4-10\,a^3\,b^2\,c^5\,d^3+10\,a^2\,b^3\,c^6\,d^2-5\,a\,b^4\,c^7\,d+b^5\,c^8\right)}\right)}{2\,\left(-a^5\,c^3\,d^5+5\,a^4\,b\,c^4\,d^4-10\,a^3\,b^2\,c^5\,d^3+10\,a^2\,b^3\,c^6\,d^2-5\,a\,b^4\,c^7\,d+b^5\,c^8\right)}\right)\,1{}\mathrm{i}}{2\,\left(-a^5\,c^3\,d^5+5\,a^4\,b\,c^4\,d^4-10\,a^3\,b^2\,c^5\,d^3+10\,a^2\,b^3\,c^6\,d^2-5\,a\,b^4\,c^7\,d+b^5\,c^8\right)}}{\frac{\sqrt{d^5\,{\left(a\,d-b\,c\right)}^5}\,\left(4\,a\,d-7\,b\,c\right)\,\left(\sqrt{a+\frac{b}{x}}\,\left(64\,a^{18}\,b^2\,c^6\,d^{15}-576\,a^{17}\,b^3\,c^7\,d^{14}+2228\,a^{16}\,b^4\,c^8\,d^{13}-4768\,a^{15}\,b^5\,c^9\,d^{12}+5960\,a^{14}\,b^6\,c^{10}\,d^{11}-3976\,a^{13}\,b^7\,c^{11}\,d^{10}+578\,a^{12}\,b^8\,c^{12}\,d^9+1004\,a^{11}\,b^9\,c^{13}\,d^8-442\,a^{10}\,b^{10}\,c^{14}\,d^7-320\,a^9\,b^{11}\,c^{15}\,d^6+362\,a^8\,b^{12}\,c^{16}\,d^5-132\,a^7\,b^{13}\,c^{17}\,d^4+18\,a^6\,b^{14}\,c^{18}\,d^3\right)-\frac{\sqrt{d^5\,{\left(a\,d-b\,c\right)}^5}\,\left(4\,a\,d-7\,b\,c\right)\,\left(12\,a^8\,b^{14}\,c^{21}\,d^2-116\,a^9\,b^{13}\,c^{20}\,d^3+484\,a^{10}\,b^{12}\,c^{19}\,d^4-1128\,a^{11}\,b^{11}\,c^{18}\,d^5+1560\,a^{12}\,b^{10}\,c^{17}\,d^6-1176\,a^{13}\,b^9\,c^{16}\,d^7+168\,a^{14}\,b^8\,c^{15}\,d^8+576\,a^{15}\,b^7\,c^{14}\,d^9-612\,a^{16}\,b^6\,c^{13}\,d^{10}+300\,a^{17}\,b^5\,c^{12}\,d^{11}-76\,a^{18}\,b^4\,c^{11}\,d^{12}+8\,a^{19}\,b^3\,c^{10}\,d^{13}-\frac{\sqrt{d^5\,{\left(a\,d-b\,c\right)}^5}\,\sqrt{a+\frac{b}{x}}\,\left(4\,a\,d-7\,b\,c\right)\,\left(-16\,a^{21}\,b^2\,c^{12}\,d^{13}+168\,a^{20}\,b^3\,c^{13}\,d^{12}-800\,a^{19}\,b^4\,c^{14}\,d^{11}+2280\,a^{18}\,b^5\,c^{15}\,d^{10}-4320\,a^{17}\,b^6\,c^{16}\,d^9+5712\,a^{16}\,b^7\,c^{17}\,d^8-5376\,a^{15}\,b^8\,c^{18}\,d^7+3600\,a^{14}\,b^9\,c^{19}\,d^6-1680\,a^{13}\,b^{10}\,c^{20}\,d^5+520\,a^{12}\,b^{11}\,c^{21}\,d^4-96\,a^{11}\,b^{12}\,c^{22}\,d^3+8\,a^{10}\,b^{13}\,c^{23}\,d^2\right)}{2\,\left(-a^5\,c^3\,d^5+5\,a^4\,b\,c^4\,d^4-10\,a^3\,b^2\,c^5\,d^3+10\,a^2\,b^3\,c^6\,d^2-5\,a\,b^4\,c^7\,d+b^5\,c^8\right)}\right)}{2\,\left(-a^5\,c^3\,d^5+5\,a^4\,b\,c^4\,d^4-10\,a^3\,b^2\,c^5\,d^3+10\,a^2\,b^3\,c^6\,d^2-5\,a\,b^4\,c^7\,d+b^5\,c^8\right)}\right)}{2\,\left(-a^5\,c^3\,d^5+5\,a^4\,b\,c^4\,d^4-10\,a^3\,b^2\,c^5\,d^3+10\,a^2\,b^3\,c^6\,d^2-5\,a\,b^4\,c^7\,d+b^5\,c^8\right)}-\frac{\sqrt{d^5\,{\left(a\,d-b\,c\right)}^5}\,\left(4\,a\,d-7\,b\,c\right)\,\left(\sqrt{a+\frac{b}{x}}\,\left(64\,a^{18}\,b^2\,c^6\,d^{15}-576\,a^{17}\,b^3\,c^7\,d^{14}+2228\,a^{16}\,b^4\,c^8\,d^{13}-4768\,a^{15}\,b^5\,c^9\,d^{12}+5960\,a^{14}\,b^6\,c^{10}\,d^{11}-3976\,a^{13}\,b^7\,c^{11}\,d^{10}+578\,a^{12}\,b^8\,c^{12}\,d^9+1004\,a^{11}\,b^9\,c^{13}\,d^8-442\,a^{10}\,b^{10}\,c^{14}\,d^7-320\,a^9\,b^{11}\,c^{15}\,d^6+362\,a^8\,b^{12}\,c^{16}\,d^5-132\,a^7\,b^{13}\,c^{17}\,d^4+18\,a^6\,b^{14}\,c^{18}\,d^3\right)+\frac{\sqrt{d^5\,{\left(a\,d-b\,c\right)}^5}\,\left(4\,a\,d-7\,b\,c\right)\,\left(12\,a^8\,b^{14}\,c^{21}\,d^2-116\,a^9\,b^{13}\,c^{20}\,d^3+484\,a^{10}\,b^{12}\,c^{19}\,d^4-1128\,a^{11}\,b^{11}\,c^{18}\,d^5+1560\,a^{12}\,b^{10}\,c^{17}\,d^6-1176\,a^{13}\,b^9\,c^{16}\,d^7+168\,a^{14}\,b^8\,c^{15}\,d^8+576\,a^{15}\,b^7\,c^{14}\,d^9-612\,a^{16}\,b^6\,c^{13}\,d^{10}+300\,a^{17}\,b^5\,c^{12}\,d^{11}-76\,a^{18}\,b^4\,c^{11}\,d^{12}+8\,a^{19}\,b^3\,c^{10}\,d^{13}+\frac{\sqrt{d^5\,{\left(a\,d-b\,c\right)}^5}\,\sqrt{a+\frac{b}{x}}\,\left(4\,a\,d-7\,b\,c\right)\,\left(-16\,a^{21}\,b^2\,c^{12}\,d^{13}+168\,a^{20}\,b^3\,c^{13}\,d^{12}-800\,a^{19}\,b^4\,c^{14}\,d^{11}+2280\,a^{18}\,b^5\,c^{15}\,d^{10}-4320\,a^{17}\,b^6\,c^{16}\,d^9+5712\,a^{16}\,b^7\,c^{17}\,d^8-5376\,a^{15}\,b^8\,c^{18}\,d^7+3600\,a^{14}\,b^9\,c^{19}\,d^6-1680\,a^{13}\,b^{10}\,c^{20}\,d^5+520\,a^{12}\,b^{11}\,c^{21}\,d^4-96\,a^{11}\,b^{12}\,c^{22}\,d^3+8\,a^{10}\,b^{13}\,c^{23}\,d^2\right)}{2\,\left(-a^5\,c^3\,d^5+5\,a^4\,b\,c^4\,d^4-10\,a^3\,b^2\,c^5\,d^3+10\,a^2\,b^3\,c^6\,d^2-5\,a\,b^4\,c^7\,d+b^5\,c^8\right)}\right)}{2\,\left(-a^5\,c^3\,d^5+5\,a^4\,b\,c^4\,d^4-10\,a^3\,b^2\,c^5\,d^3+10\,a^2\,b^3\,c^6\,d^2-5\,a\,b^4\,c^7\,d+b^5\,c^8\right)}\right)}{2\,\left(-a^5\,c^3\,d^5+5\,a^4\,b\,c^4\,d^4-10\,a^3\,b^2\,c^5\,d^3+10\,a^2\,b^3\,c^6\,d^2-5\,a\,b^4\,c^7\,d+b^5\,c^8\right)}-126\,a^6\,b^{13}\,c^{14}\,d^5+744\,a^7\,b^{12}\,c^{13}\,d^6-1742\,a^8\,b^{11}\,c^{12}\,d^7+1756\,a^9\,b^{10}\,c^{11}\,d^8+322\,a^{10}\,b^9\,c^{10}\,d^9-3248\,a^{11}\,b^8\,c^9\,d^{10}+4606\,a^{12}\,b^7\,c^8\,d^{11}-3668\,a^{13}\,b^6\,c^7\,d^{12}+1804\,a^{14}\,b^5\,c^6\,d^{13}-512\,a^{15}\,b^4\,c^5\,d^{14}+64\,a^{16}\,b^3\,c^4\,d^{15}}\right)\,\sqrt{d^5\,{\left(a\,d-b\,c\right)}^5}\,\left(4\,a\,d-7\,b\,c\right)\,1{}\mathrm{i}}{-a^5\,c^3\,d^5+5\,a^4\,b\,c^4\,d^4-10\,a^3\,b^2\,c^5\,d^3+10\,a^2\,b^3\,c^6\,d^2-5\,a\,b^4\,c^7\,d+b^5\,c^8}","Not used",1,"((2*b^3)/(a^2*d - a*b*c) + (b*(a + b/x)^2*(2*a^2*d^3 + 3*b^2*c^2*d - 2*a*b*c*d^2))/(c^2*(a^2*d - a*b*c)^2) - (b*(a + b/x)*(2*a*d - b*c)*(a^2*d^2 + 3*b^2*c^2 - a*b*c*d))/(c^2*(a^2*d - a*b*c)^2))/(d*(a + b/x)^(5/2) + (a + b/x)^(1/2)*(a^2*d - a*b*c) - (a + b/x)^(3/2)*(2*a*d - b*c)) + (atan((a^13*b^11*c^11*d^3*(a + b/x)^(1/2)*35i - a^12*b^12*c^12*d^2*(a + b/x)^(1/2)*441i - a^10*b^14*c^14*(a + b/x)^(1/2)*27i + a^14*b^10*c^10*d^4*(a + b/x)^(1/2)*1694i - a^15*b^9*c^9*d^5*(a + b/x)^(1/2)*3073i + a^16*b^8*c^8*d^6*(a + b/x)^(1/2)*1316i + a^17*b^7*c^7*d^7*(a + b/x)^(1/2)*2561i - a^18*b^6*c^6*d^8*(a + b/x)^(1/2)*4375i + a^19*b^5*c^5*d^9*(a + b/x)^(1/2)*2996i - a^20*b^4*c^4*d^10*(a + b/x)^(1/2)*1015i + a^21*b^3*c^3*d^11*(a + b/x)^(1/2)*140i + a^11*b^13*c^13*d*(a + b/x)^(1/2)*189i)/(a^5*(a^5)^(1/2)*(a^5*(a^5*(2561*b^7*c^7*d^7 - 4375*a*b^6*c^6*d^8 + 2996*a^2*b^5*c^5*d^9 - 1015*a^3*b^4*c^4*d^10 + 140*a^4*b^3*c^3*d^11) - 441*b^12*c^12*d^2 + 35*a*b^11*c^11*d^3 + 1694*a^2*b^10*c^10*d^4 - 3073*a^3*b^9*c^9*d^5 + 1316*a^4*b^8*c^8*d^6) - 27*a^3*b^14*c^14 + 189*a^4*b^13*c^13*d)))*(4*a*d + 3*b*c)*1i)/(c^3*(a^5)^(1/2)) - (atan((((d^5*(a*d - b*c)^5)^(1/2)*(4*a*d - 7*b*c)*((a + b/x)^(1/2)*(18*a^6*b^14*c^18*d^3 - 132*a^7*b^13*c^17*d^4 + 362*a^8*b^12*c^16*d^5 - 320*a^9*b^11*c^15*d^6 - 442*a^10*b^10*c^14*d^7 + 1004*a^11*b^9*c^13*d^8 + 578*a^12*b^8*c^12*d^9 - 3976*a^13*b^7*c^11*d^10 + 5960*a^14*b^6*c^10*d^11 - 4768*a^15*b^5*c^9*d^12 + 2228*a^16*b^4*c^8*d^13 - 576*a^17*b^3*c^7*d^14 + 64*a^18*b^2*c^6*d^15) - ((d^5*(a*d - b*c)^5)^(1/2)*(4*a*d - 7*b*c)*(12*a^8*b^14*c^21*d^2 - 116*a^9*b^13*c^20*d^3 + 484*a^10*b^12*c^19*d^4 - 1128*a^11*b^11*c^18*d^5 + 1560*a^12*b^10*c^17*d^6 - 1176*a^13*b^9*c^16*d^7 + 168*a^14*b^8*c^15*d^8 + 576*a^15*b^7*c^14*d^9 - 612*a^16*b^6*c^13*d^10 + 300*a^17*b^5*c^12*d^11 - 76*a^18*b^4*c^11*d^12 + 8*a^19*b^3*c^10*d^13 - ((d^5*(a*d - b*c)^5)^(1/2)*(a + b/x)^(1/2)*(4*a*d - 7*b*c)*(8*a^10*b^13*c^23*d^2 - 96*a^11*b^12*c^22*d^3 + 520*a^12*b^11*c^21*d^4 - 1680*a^13*b^10*c^20*d^5 + 3600*a^14*b^9*c^19*d^6 - 5376*a^15*b^8*c^18*d^7 + 5712*a^16*b^7*c^17*d^8 - 4320*a^17*b^6*c^16*d^9 + 2280*a^18*b^5*c^15*d^10 - 800*a^19*b^4*c^14*d^11 + 168*a^20*b^3*c^13*d^12 - 16*a^21*b^2*c^12*d^13))/(2*(b^5*c^8 - a^5*c^3*d^5 + 5*a^4*b*c^4*d^4 + 10*a^2*b^3*c^6*d^2 - 10*a^3*b^2*c^5*d^3 - 5*a*b^4*c^7*d))))/(2*(b^5*c^8 - a^5*c^3*d^5 + 5*a^4*b*c^4*d^4 + 10*a^2*b^3*c^6*d^2 - 10*a^3*b^2*c^5*d^3 - 5*a*b^4*c^7*d)))*1i)/(2*(b^5*c^8 - a^5*c^3*d^5 + 5*a^4*b*c^4*d^4 + 10*a^2*b^3*c^6*d^2 - 10*a^3*b^2*c^5*d^3 - 5*a*b^4*c^7*d)) + ((d^5*(a*d - b*c)^5)^(1/2)*(4*a*d - 7*b*c)*((a + b/x)^(1/2)*(18*a^6*b^14*c^18*d^3 - 132*a^7*b^13*c^17*d^4 + 362*a^8*b^12*c^16*d^5 - 320*a^9*b^11*c^15*d^6 - 442*a^10*b^10*c^14*d^7 + 1004*a^11*b^9*c^13*d^8 + 578*a^12*b^8*c^12*d^9 - 3976*a^13*b^7*c^11*d^10 + 5960*a^14*b^6*c^10*d^11 - 4768*a^15*b^5*c^9*d^12 + 2228*a^16*b^4*c^8*d^13 - 576*a^17*b^3*c^7*d^14 + 64*a^18*b^2*c^6*d^15) + ((d^5*(a*d - b*c)^5)^(1/2)*(4*a*d - 7*b*c)*(12*a^8*b^14*c^21*d^2 - 116*a^9*b^13*c^20*d^3 + 484*a^10*b^12*c^19*d^4 - 1128*a^11*b^11*c^18*d^5 + 1560*a^12*b^10*c^17*d^6 - 1176*a^13*b^9*c^16*d^7 + 168*a^14*b^8*c^15*d^8 + 576*a^15*b^7*c^14*d^9 - 612*a^16*b^6*c^13*d^10 + 300*a^17*b^5*c^12*d^11 - 76*a^18*b^4*c^11*d^12 + 8*a^19*b^3*c^10*d^13 + ((d^5*(a*d - b*c)^5)^(1/2)*(a + b/x)^(1/2)*(4*a*d - 7*b*c)*(8*a^10*b^13*c^23*d^2 - 96*a^11*b^12*c^22*d^3 + 520*a^12*b^11*c^21*d^4 - 1680*a^13*b^10*c^20*d^5 + 3600*a^14*b^9*c^19*d^6 - 5376*a^15*b^8*c^18*d^7 + 5712*a^16*b^7*c^17*d^8 - 4320*a^17*b^6*c^16*d^9 + 2280*a^18*b^5*c^15*d^10 - 800*a^19*b^4*c^14*d^11 + 168*a^20*b^3*c^13*d^12 - 16*a^21*b^2*c^12*d^13))/(2*(b^5*c^8 - a^5*c^3*d^5 + 5*a^4*b*c^4*d^4 + 10*a^2*b^3*c^6*d^2 - 10*a^3*b^2*c^5*d^3 - 5*a*b^4*c^7*d))))/(2*(b^5*c^8 - a^5*c^3*d^5 + 5*a^4*b*c^4*d^4 + 10*a^2*b^3*c^6*d^2 - 10*a^3*b^2*c^5*d^3 - 5*a*b^4*c^7*d)))*1i)/(2*(b^5*c^8 - a^5*c^3*d^5 + 5*a^4*b*c^4*d^4 + 10*a^2*b^3*c^6*d^2 - 10*a^3*b^2*c^5*d^3 - 5*a*b^4*c^7*d)))/(((d^5*(a*d - b*c)^5)^(1/2)*(4*a*d - 7*b*c)*((a + b/x)^(1/2)*(18*a^6*b^14*c^18*d^3 - 132*a^7*b^13*c^17*d^4 + 362*a^8*b^12*c^16*d^5 - 320*a^9*b^11*c^15*d^6 - 442*a^10*b^10*c^14*d^7 + 1004*a^11*b^9*c^13*d^8 + 578*a^12*b^8*c^12*d^9 - 3976*a^13*b^7*c^11*d^10 + 5960*a^14*b^6*c^10*d^11 - 4768*a^15*b^5*c^9*d^12 + 2228*a^16*b^4*c^8*d^13 - 576*a^17*b^3*c^7*d^14 + 64*a^18*b^2*c^6*d^15) - ((d^5*(a*d - b*c)^5)^(1/2)*(4*a*d - 7*b*c)*(12*a^8*b^14*c^21*d^2 - 116*a^9*b^13*c^20*d^3 + 484*a^10*b^12*c^19*d^4 - 1128*a^11*b^11*c^18*d^5 + 1560*a^12*b^10*c^17*d^6 - 1176*a^13*b^9*c^16*d^7 + 168*a^14*b^8*c^15*d^8 + 576*a^15*b^7*c^14*d^9 - 612*a^16*b^6*c^13*d^10 + 300*a^17*b^5*c^12*d^11 - 76*a^18*b^4*c^11*d^12 + 8*a^19*b^3*c^10*d^13 - ((d^5*(a*d - b*c)^5)^(1/2)*(a + b/x)^(1/2)*(4*a*d - 7*b*c)*(8*a^10*b^13*c^23*d^2 - 96*a^11*b^12*c^22*d^3 + 520*a^12*b^11*c^21*d^4 - 1680*a^13*b^10*c^20*d^5 + 3600*a^14*b^9*c^19*d^6 - 5376*a^15*b^8*c^18*d^7 + 5712*a^16*b^7*c^17*d^8 - 4320*a^17*b^6*c^16*d^9 + 2280*a^18*b^5*c^15*d^10 - 800*a^19*b^4*c^14*d^11 + 168*a^20*b^3*c^13*d^12 - 16*a^21*b^2*c^12*d^13))/(2*(b^5*c^8 - a^5*c^3*d^5 + 5*a^4*b*c^4*d^4 + 10*a^2*b^3*c^6*d^2 - 10*a^3*b^2*c^5*d^3 - 5*a*b^4*c^7*d))))/(2*(b^5*c^8 - a^5*c^3*d^5 + 5*a^4*b*c^4*d^4 + 10*a^2*b^3*c^6*d^2 - 10*a^3*b^2*c^5*d^3 - 5*a*b^4*c^7*d))))/(2*(b^5*c^8 - a^5*c^3*d^5 + 5*a^4*b*c^4*d^4 + 10*a^2*b^3*c^6*d^2 - 10*a^3*b^2*c^5*d^3 - 5*a*b^4*c^7*d)) - ((d^5*(a*d - b*c)^5)^(1/2)*(4*a*d - 7*b*c)*((a + b/x)^(1/2)*(18*a^6*b^14*c^18*d^3 - 132*a^7*b^13*c^17*d^4 + 362*a^8*b^12*c^16*d^5 - 320*a^9*b^11*c^15*d^6 - 442*a^10*b^10*c^14*d^7 + 1004*a^11*b^9*c^13*d^8 + 578*a^12*b^8*c^12*d^9 - 3976*a^13*b^7*c^11*d^10 + 5960*a^14*b^6*c^10*d^11 - 4768*a^15*b^5*c^9*d^12 + 2228*a^16*b^4*c^8*d^13 - 576*a^17*b^3*c^7*d^14 + 64*a^18*b^2*c^6*d^15) + ((d^5*(a*d - b*c)^5)^(1/2)*(4*a*d - 7*b*c)*(12*a^8*b^14*c^21*d^2 - 116*a^9*b^13*c^20*d^3 + 484*a^10*b^12*c^19*d^4 - 1128*a^11*b^11*c^18*d^5 + 1560*a^12*b^10*c^17*d^6 - 1176*a^13*b^9*c^16*d^7 + 168*a^14*b^8*c^15*d^8 + 576*a^15*b^7*c^14*d^9 - 612*a^16*b^6*c^13*d^10 + 300*a^17*b^5*c^12*d^11 - 76*a^18*b^4*c^11*d^12 + 8*a^19*b^3*c^10*d^13 + ((d^5*(a*d - b*c)^5)^(1/2)*(a + b/x)^(1/2)*(4*a*d - 7*b*c)*(8*a^10*b^13*c^23*d^2 - 96*a^11*b^12*c^22*d^3 + 520*a^12*b^11*c^21*d^4 - 1680*a^13*b^10*c^20*d^5 + 3600*a^14*b^9*c^19*d^6 - 5376*a^15*b^8*c^18*d^7 + 5712*a^16*b^7*c^17*d^8 - 4320*a^17*b^6*c^16*d^9 + 2280*a^18*b^5*c^15*d^10 - 800*a^19*b^4*c^14*d^11 + 168*a^20*b^3*c^13*d^12 - 16*a^21*b^2*c^12*d^13))/(2*(b^5*c^8 - a^5*c^3*d^5 + 5*a^4*b*c^4*d^4 + 10*a^2*b^3*c^6*d^2 - 10*a^3*b^2*c^5*d^3 - 5*a*b^4*c^7*d))))/(2*(b^5*c^8 - a^5*c^3*d^5 + 5*a^4*b*c^4*d^4 + 10*a^2*b^3*c^6*d^2 - 10*a^3*b^2*c^5*d^3 - 5*a*b^4*c^7*d))))/(2*(b^5*c^8 - a^5*c^3*d^5 + 5*a^4*b*c^4*d^4 + 10*a^2*b^3*c^6*d^2 - 10*a^3*b^2*c^5*d^3 - 5*a*b^4*c^7*d)) - 126*a^6*b^13*c^14*d^5 + 744*a^7*b^12*c^13*d^6 - 1742*a^8*b^11*c^12*d^7 + 1756*a^9*b^10*c^11*d^8 + 322*a^10*b^9*c^10*d^9 - 3248*a^11*b^8*c^9*d^10 + 4606*a^12*b^7*c^8*d^11 - 3668*a^13*b^6*c^7*d^12 + 1804*a^14*b^5*c^6*d^13 - 512*a^15*b^4*c^5*d^14 + 64*a^16*b^3*c^4*d^15))*(d^5*(a*d - b*c)^5)^(1/2)*(4*a*d - 7*b*c)*1i)/(b^5*c^8 - a^5*c^3*d^5 + 5*a^4*b*c^4*d^4 + 10*a^2*b^3*c^6*d^2 - 10*a^3*b^2*c^5*d^3 - 5*a*b^4*c^7*d)","B"
258,1,8936,320,9.487895,"\text{Not used}","int(1/((a + b/x)^(3/2)*(c + d/x)^3),x)","\frac{\frac{2\,b^4}{a^2\,d-a\,b\,c}+\frac{b\,\left(a+\frac{b}{x}\right)\,\left(12\,a^4\,d^4-33\,a^3\,b\,c\,d^3+24\,a^2\,b^2\,c^2\,d^2-40\,a\,b^3\,c^3\,d+12\,b^4\,c^4\right)}{4\,a\,c^3\,\left(a^2\,d-a\,b\,c\right)\,\left(a\,d-b\,c\right)}+\frac{3\,b\,{\left(a+\frac{b}{x}\right)}^3\,\left(4\,a^3\,d^5-9\,a^2\,b\,c\,d^4+4\,a\,b^2\,c^2\,d^3-4\,b^3\,c^3\,d^2\right)}{4\,a\,c^3\,\left(a^2\,d-a\,b\,c\right)\,{\left(a\,d-b\,c\right)}^2}-\frac{b\,{\left(a+\frac{b}{x}\right)}^2\,\left(24\,a^4\,d^5-72\,a^3\,b\,c\,d^4+65\,a^2\,b^2\,c^2\,d^3-56\,a\,b^3\,c^3\,d^2+24\,b^4\,c^4\,d\right)}{4\,a\,c^3\,\left(a^2\,d-a\,b\,c\right)\,{\left(a\,d-b\,c\right)}^2}}{{\left(a+\frac{b}{x}\right)}^{3/2}\,\left(3\,a^2\,d^2-4\,a\,b\,c\,d+b^2\,c^2\right)-{\left(a+\frac{b}{x}\right)}^{5/2}\,\left(3\,a\,d^2-2\,b\,c\,d\right)+d^2\,{\left(a+\frac{b}{x}\right)}^{7/2}-\sqrt{a+\frac{b}{x}}\,\left(a^3\,d^2-2\,a^2\,b\,c\,d+a\,b^2\,c^2\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\sqrt{a+\frac{b}{x}}\,\left(-147456\,a^{23}\,b^2\,c^9\,d^{20}+2138112\,a^{22}\,b^3\,c^{10}\,d^{19}-14340096\,a^{21}\,b^4\,c^{11}\,d^{18}+58816512\,a^{20}\,b^5\,c^{12}\,d^{17}-164257920\,a^{19}\,b^6\,c^{13}\,d^{16}+328809600\,a^{18}\,b^7\,c^{14}\,d^{15}-482904576\,a^{17}\,b^8\,c^{15}\,d^{14}+521961984\,a^{16}\,b^9\,c^{16}\,d^{13}-407418624\,a^{15}\,b^{10}\,c^{17}\,d^{12}+216610560\,a^{14}\,b^{11}\,c^{18}\,d^{11}-65382912\,a^{13}\,b^{12}\,c^{19}\,d^{10}+1276416\,a^{12}\,b^{13}\,c^{20}\,d^9+6007680\,a^{11}\,b^{14}\,c^{21}\,d^8-137088\,a^{10}\,b^{15}\,c^{22}\,d^7-1751040\,a^9\,b^{16}\,c^{23}\,d^6+903168\,a^8\,b^{17}\,c^{24}\,d^5-202752\,a^7\,b^{18}\,c^{25}\,d^4+18432\,a^6\,b^{19}\,c^{26}\,d^3\right)-\frac{3\,\sqrt{d^5\,{\left(a\,d-b\,c\right)}^7}\,\left(8\,a^2\,d^2-24\,a\,b\,c\,d+21\,b^2\,c^2\right)\,\left(12288\,a^8\,b^{19}\,c^{30}\,d^2-172032\,a^9\,b^{18}\,c^{29}\,d^3+1081344\,a^{10}\,b^{17}\,c^{28}\,d^4-3996672\,a^{11}\,b^{16}\,c^{27}\,d^5+9449472\,a^{12}\,b^{15}\,c^{26}\,d^6-14112768\,a^{13}\,b^{14}\,c^{25}\,d^7+10407936\,a^{14}\,b^{13}\,c^{24}\,d^8+6454272\,a^{15}\,b^{12}\,c^{23}\,d^9-30007296\,a^{16}\,b^{11}\,c^{22}\,d^{10}+45551616\,a^{17}\,b^{10}\,c^{21}\,d^{11}-44064768\,a^{18}\,b^9\,c^{20}\,d^{12}+30096384\,a^{19}\,b^8\,c^{19}\,d^{13}-14831616\,a^{20}\,b^7\,c^{18}\,d^{14}+5203968\,a^{21}\,b^6\,c^{17}\,d^{15}-1241088\,a^{22}\,b^5\,c^{16}\,d^{16}+181248\,a^{23}\,b^4\,c^{15}\,d^{17}-12288\,a^{24}\,b^3\,c^{14}\,d^{18}-\frac{3\,\sqrt{d^5\,{\left(a\,d-b\,c\right)}^7}\,\sqrt{a+\frac{b}{x}}\,\left(8\,a^2\,d^2-24\,a\,b\,c\,d+21\,b^2\,c^2\right)\,\left(16384\,a^{26}\,b^2\,c^{17}\,d^{18}-253952\,a^{25}\,b^3\,c^{18}\,d^{17}+1843200\,a^{24}\,b^4\,c^{19}\,d^{16}-8314880\,a^{23}\,b^5\,c^{20}\,d^{15}+26091520\,a^{22}\,b^6\,c^{21}\,d^{14}-60383232\,a^{21}\,b^7\,c^{22}\,d^{13}+106602496\,a^{20}\,b^8\,c^{23}\,d^{12}-146432000\,a^{19}\,b^9\,c^{24}\,d^{11}+158146560\,a^{18}\,b^{10}\,c^{25}\,d^{10}-134717440\,a^{17}\,b^{11}\,c^{26}\,d^9+90202112\,a^{16}\,b^{12}\,c^{27}\,d^8-46964736\,a^{15}\,b^{13}\,c^{28}\,d^7+18636800\,a^{14}\,b^{14}\,c^{29}\,d^6-5447680\,a^{13}\,b^{15}\,c^{30}\,d^5+1105920\,a^{12}\,b^{16}\,c^{31}\,d^4-139264\,a^{11}\,b^{17}\,c^{32}\,d^3+8192\,a^{10}\,b^{18}\,c^{33}\,d^2\right)}{8\,\left(-a^7\,c^4\,d^7+7\,a^6\,b\,c^5\,d^6-21\,a^5\,b^2\,c^6\,d^5+35\,a^4\,b^3\,c^7\,d^4-35\,a^3\,b^4\,c^8\,d^3+21\,a^2\,b^5\,c^9\,d^2-7\,a\,b^6\,c^{10}\,d+b^7\,c^{11}\right)}\right)}{8\,\left(-a^7\,c^4\,d^7+7\,a^6\,b\,c^5\,d^6-21\,a^5\,b^2\,c^6\,d^5+35\,a^4\,b^3\,c^7\,d^4-35\,a^3\,b^4\,c^8\,d^3+21\,a^2\,b^5\,c^9\,d^2-7\,a\,b^6\,c^{10}\,d+b^7\,c^{11}\right)}\right)\,\sqrt{d^5\,{\left(a\,d-b\,c\right)}^7}\,\left(8\,a^2\,d^2-24\,a\,b\,c\,d+21\,b^2\,c^2\right)\,3{}\mathrm{i}}{8\,\left(-a^7\,c^4\,d^7+7\,a^6\,b\,c^5\,d^6-21\,a^5\,b^2\,c^6\,d^5+35\,a^4\,b^3\,c^7\,d^4-35\,a^3\,b^4\,c^8\,d^3+21\,a^2\,b^5\,c^9\,d^2-7\,a\,b^6\,c^{10}\,d+b^7\,c^{11}\right)}+\frac{\left(\sqrt{a+\frac{b}{x}}\,\left(-147456\,a^{23}\,b^2\,c^9\,d^{20}+2138112\,a^{22}\,b^3\,c^{10}\,d^{19}-14340096\,a^{21}\,b^4\,c^{11}\,d^{18}+58816512\,a^{20}\,b^5\,c^{12}\,d^{17}-164257920\,a^{19}\,b^6\,c^{13}\,d^{16}+328809600\,a^{18}\,b^7\,c^{14}\,d^{15}-482904576\,a^{17}\,b^8\,c^{15}\,d^{14}+521961984\,a^{16}\,b^9\,c^{16}\,d^{13}-407418624\,a^{15}\,b^{10}\,c^{17}\,d^{12}+216610560\,a^{14}\,b^{11}\,c^{18}\,d^{11}-65382912\,a^{13}\,b^{12}\,c^{19}\,d^{10}+1276416\,a^{12}\,b^{13}\,c^{20}\,d^9+6007680\,a^{11}\,b^{14}\,c^{21}\,d^8-137088\,a^{10}\,b^{15}\,c^{22}\,d^7-1751040\,a^9\,b^{16}\,c^{23}\,d^6+903168\,a^8\,b^{17}\,c^{24}\,d^5-202752\,a^7\,b^{18}\,c^{25}\,d^4+18432\,a^6\,b^{19}\,c^{26}\,d^3\right)+\frac{3\,\sqrt{d^5\,{\left(a\,d-b\,c\right)}^7}\,\left(8\,a^2\,d^2-24\,a\,b\,c\,d+21\,b^2\,c^2\right)\,\left(12288\,a^8\,b^{19}\,c^{30}\,d^2-172032\,a^9\,b^{18}\,c^{29}\,d^3+1081344\,a^{10}\,b^{17}\,c^{28}\,d^4-3996672\,a^{11}\,b^{16}\,c^{27}\,d^5+9449472\,a^{12}\,b^{15}\,c^{26}\,d^6-14112768\,a^{13}\,b^{14}\,c^{25}\,d^7+10407936\,a^{14}\,b^{13}\,c^{24}\,d^8+6454272\,a^{15}\,b^{12}\,c^{23}\,d^9-30007296\,a^{16}\,b^{11}\,c^{22}\,d^{10}+45551616\,a^{17}\,b^{10}\,c^{21}\,d^{11}-44064768\,a^{18}\,b^9\,c^{20}\,d^{12}+30096384\,a^{19}\,b^8\,c^{19}\,d^{13}-14831616\,a^{20}\,b^7\,c^{18}\,d^{14}+5203968\,a^{21}\,b^6\,c^{17}\,d^{15}-1241088\,a^{22}\,b^5\,c^{16}\,d^{16}+181248\,a^{23}\,b^4\,c^{15}\,d^{17}-12288\,a^{24}\,b^3\,c^{14}\,d^{18}+\frac{3\,\sqrt{d^5\,{\left(a\,d-b\,c\right)}^7}\,\sqrt{a+\frac{b}{x}}\,\left(8\,a^2\,d^2-24\,a\,b\,c\,d+21\,b^2\,c^2\right)\,\left(16384\,a^{26}\,b^2\,c^{17}\,d^{18}-253952\,a^{25}\,b^3\,c^{18}\,d^{17}+1843200\,a^{24}\,b^4\,c^{19}\,d^{16}-8314880\,a^{23}\,b^5\,c^{20}\,d^{15}+26091520\,a^{22}\,b^6\,c^{21}\,d^{14}-60383232\,a^{21}\,b^7\,c^{22}\,d^{13}+106602496\,a^{20}\,b^8\,c^{23}\,d^{12}-146432000\,a^{19}\,b^9\,c^{24}\,d^{11}+158146560\,a^{18}\,b^{10}\,c^{25}\,d^{10}-134717440\,a^{17}\,b^{11}\,c^{26}\,d^9+90202112\,a^{16}\,b^{12}\,c^{27}\,d^8-46964736\,a^{15}\,b^{13}\,c^{28}\,d^7+18636800\,a^{14}\,b^{14}\,c^{29}\,d^6-5447680\,a^{13}\,b^{15}\,c^{30}\,d^5+1105920\,a^{12}\,b^{16}\,c^{31}\,d^4-139264\,a^{11}\,b^{17}\,c^{32}\,d^3+8192\,a^{10}\,b^{18}\,c^{33}\,d^2\right)}{8\,\left(-a^7\,c^4\,d^7+7\,a^6\,b\,c^5\,d^6-21\,a^5\,b^2\,c^6\,d^5+35\,a^4\,b^3\,c^7\,d^4-35\,a^3\,b^4\,c^8\,d^3+21\,a^2\,b^5\,c^9\,d^2-7\,a\,b^6\,c^{10}\,d+b^7\,c^{11}\right)}\right)}{8\,\left(-a^7\,c^4\,d^7+7\,a^6\,b\,c^5\,d^6-21\,a^5\,b^2\,c^6\,d^5+35\,a^4\,b^3\,c^7\,d^4-35\,a^3\,b^4\,c^8\,d^3+21\,a^2\,b^5\,c^9\,d^2-7\,a\,b^6\,c^{10}\,d+b^7\,c^{11}\right)}\right)\,\sqrt{d^5\,{\left(a\,d-b\,c\right)}^7}\,\left(8\,a^2\,d^2-24\,a\,b\,c\,d+21\,b^2\,c^2\right)\,3{}\mathrm{i}}{8\,\left(-a^7\,c^4\,d^7+7\,a^6\,b\,c^5\,d^6-21\,a^5\,b^2\,c^6\,d^5+35\,a^4\,b^3\,c^7\,d^4-35\,a^3\,b^4\,c^8\,d^3+21\,a^2\,b^5\,c^9\,d^2-7\,a\,b^6\,c^{10}\,d+b^7\,c^{11}\right)}}{290304\,a^6\,b^{18}\,c^{21}\,d^5-2654208\,a^7\,b^{17}\,c^{20}\,d^6+10675584\,a^8\,b^{16}\,c^{19}\,d^7-23497344\,a^9\,b^{15}\,c^{18}\,d^8+23604480\,a^{10}\,b^{14}\,c^{17}\,d^9+24731136\,a^{11}\,b^{13}\,c^{16}\,d^{10}-148172544\,a^{12}\,b^{12}\,c^{15}\,d^{11}+320101632\,a^{13}\,b^{11}\,c^{14}\,d^{12}-452086272\,a^{14}\,b^{10}\,c^{13}\,d^{13}+459302400\,a^{15}\,b^9\,c^{12}\,d^{14}-343108224\,a^{16}\,b^8\,c^{11}\,d^{15}+187373952\,a^{17}\,b^7\,c^{10}\,d^{16}-72873216\,a^{18}\,b^6\,c^9\,d^{17}+19132416\,a^{19}\,b^5\,c^8\,d^{18}-3041280\,a^{20}\,b^4\,c^7\,d^{19}+221184\,a^{21}\,b^3\,c^6\,d^{20}-\frac{3\,\left(\sqrt{a+\frac{b}{x}}\,\left(-147456\,a^{23}\,b^2\,c^9\,d^{20}+2138112\,a^{22}\,b^3\,c^{10}\,d^{19}-14340096\,a^{21}\,b^4\,c^{11}\,d^{18}+58816512\,a^{20}\,b^5\,c^{12}\,d^{17}-164257920\,a^{19}\,b^6\,c^{13}\,d^{16}+328809600\,a^{18}\,b^7\,c^{14}\,d^{15}-482904576\,a^{17}\,b^8\,c^{15}\,d^{14}+521961984\,a^{16}\,b^9\,c^{16}\,d^{13}-407418624\,a^{15}\,b^{10}\,c^{17}\,d^{12}+216610560\,a^{14}\,b^{11}\,c^{18}\,d^{11}-65382912\,a^{13}\,b^{12}\,c^{19}\,d^{10}+1276416\,a^{12}\,b^{13}\,c^{20}\,d^9+6007680\,a^{11}\,b^{14}\,c^{21}\,d^8-137088\,a^{10}\,b^{15}\,c^{22}\,d^7-1751040\,a^9\,b^{16}\,c^{23}\,d^6+903168\,a^8\,b^{17}\,c^{24}\,d^5-202752\,a^7\,b^{18}\,c^{25}\,d^4+18432\,a^6\,b^{19}\,c^{26}\,d^3\right)-\frac{3\,\sqrt{d^5\,{\left(a\,d-b\,c\right)}^7}\,\left(8\,a^2\,d^2-24\,a\,b\,c\,d+21\,b^2\,c^2\right)\,\left(12288\,a^8\,b^{19}\,c^{30}\,d^2-172032\,a^9\,b^{18}\,c^{29}\,d^3+1081344\,a^{10}\,b^{17}\,c^{28}\,d^4-3996672\,a^{11}\,b^{16}\,c^{27}\,d^5+9449472\,a^{12}\,b^{15}\,c^{26}\,d^6-14112768\,a^{13}\,b^{14}\,c^{25}\,d^7+10407936\,a^{14}\,b^{13}\,c^{24}\,d^8+6454272\,a^{15}\,b^{12}\,c^{23}\,d^9-30007296\,a^{16}\,b^{11}\,c^{22}\,d^{10}+45551616\,a^{17}\,b^{10}\,c^{21}\,d^{11}-44064768\,a^{18}\,b^9\,c^{20}\,d^{12}+30096384\,a^{19}\,b^8\,c^{19}\,d^{13}-14831616\,a^{20}\,b^7\,c^{18}\,d^{14}+5203968\,a^{21}\,b^6\,c^{17}\,d^{15}-1241088\,a^{22}\,b^5\,c^{16}\,d^{16}+181248\,a^{23}\,b^4\,c^{15}\,d^{17}-12288\,a^{24}\,b^3\,c^{14}\,d^{18}-\frac{3\,\sqrt{d^5\,{\left(a\,d-b\,c\right)}^7}\,\sqrt{a+\frac{b}{x}}\,\left(8\,a^2\,d^2-24\,a\,b\,c\,d+21\,b^2\,c^2\right)\,\left(16384\,a^{26}\,b^2\,c^{17}\,d^{18}-253952\,a^{25}\,b^3\,c^{18}\,d^{17}+1843200\,a^{24}\,b^4\,c^{19}\,d^{16}-8314880\,a^{23}\,b^5\,c^{20}\,d^{15}+26091520\,a^{22}\,b^6\,c^{21}\,d^{14}-60383232\,a^{21}\,b^7\,c^{22}\,d^{13}+106602496\,a^{20}\,b^8\,c^{23}\,d^{12}-146432000\,a^{19}\,b^9\,c^{24}\,d^{11}+158146560\,a^{18}\,b^{10}\,c^{25}\,d^{10}-134717440\,a^{17}\,b^{11}\,c^{26}\,d^9+90202112\,a^{16}\,b^{12}\,c^{27}\,d^8-46964736\,a^{15}\,b^{13}\,c^{28}\,d^7+18636800\,a^{14}\,b^{14}\,c^{29}\,d^6-5447680\,a^{13}\,b^{15}\,c^{30}\,d^5+1105920\,a^{12}\,b^{16}\,c^{31}\,d^4-139264\,a^{11}\,b^{17}\,c^{32}\,d^3+8192\,a^{10}\,b^{18}\,c^{33}\,d^2\right)}{8\,\left(-a^7\,c^4\,d^7+7\,a^6\,b\,c^5\,d^6-21\,a^5\,b^2\,c^6\,d^5+35\,a^4\,b^3\,c^7\,d^4-35\,a^3\,b^4\,c^8\,d^3+21\,a^2\,b^5\,c^9\,d^2-7\,a\,b^6\,c^{10}\,d+b^7\,c^{11}\right)}\right)}{8\,\left(-a^7\,c^4\,d^7+7\,a^6\,b\,c^5\,d^6-21\,a^5\,b^2\,c^6\,d^5+35\,a^4\,b^3\,c^7\,d^4-35\,a^3\,b^4\,c^8\,d^3+21\,a^2\,b^5\,c^9\,d^2-7\,a\,b^6\,c^{10}\,d+b^7\,c^{11}\right)}\right)\,\sqrt{d^5\,{\left(a\,d-b\,c\right)}^7}\,\left(8\,a^2\,d^2-24\,a\,b\,c\,d+21\,b^2\,c^2\right)}{8\,\left(-a^7\,c^4\,d^7+7\,a^6\,b\,c^5\,d^6-21\,a^5\,b^2\,c^6\,d^5+35\,a^4\,b^3\,c^7\,d^4-35\,a^3\,b^4\,c^8\,d^3+21\,a^2\,b^5\,c^9\,d^2-7\,a\,b^6\,c^{10}\,d+b^7\,c^{11}\right)}+\frac{3\,\left(\sqrt{a+\frac{b}{x}}\,\left(-147456\,a^{23}\,b^2\,c^9\,d^{20}+2138112\,a^{22}\,b^3\,c^{10}\,d^{19}-14340096\,a^{21}\,b^4\,c^{11}\,d^{18}+58816512\,a^{20}\,b^5\,c^{12}\,d^{17}-164257920\,a^{19}\,b^6\,c^{13}\,d^{16}+328809600\,a^{18}\,b^7\,c^{14}\,d^{15}-482904576\,a^{17}\,b^8\,c^{15}\,d^{14}+521961984\,a^{16}\,b^9\,c^{16}\,d^{13}-407418624\,a^{15}\,b^{10}\,c^{17}\,d^{12}+216610560\,a^{14}\,b^{11}\,c^{18}\,d^{11}-65382912\,a^{13}\,b^{12}\,c^{19}\,d^{10}+1276416\,a^{12}\,b^{13}\,c^{20}\,d^9+6007680\,a^{11}\,b^{14}\,c^{21}\,d^8-137088\,a^{10}\,b^{15}\,c^{22}\,d^7-1751040\,a^9\,b^{16}\,c^{23}\,d^6+903168\,a^8\,b^{17}\,c^{24}\,d^5-202752\,a^7\,b^{18}\,c^{25}\,d^4+18432\,a^6\,b^{19}\,c^{26}\,d^3\right)+\frac{3\,\sqrt{d^5\,{\left(a\,d-b\,c\right)}^7}\,\left(8\,a^2\,d^2-24\,a\,b\,c\,d+21\,b^2\,c^2\right)\,\left(12288\,a^8\,b^{19}\,c^{30}\,d^2-172032\,a^9\,b^{18}\,c^{29}\,d^3+1081344\,a^{10}\,b^{17}\,c^{28}\,d^4-3996672\,a^{11}\,b^{16}\,c^{27}\,d^5+9449472\,a^{12}\,b^{15}\,c^{26}\,d^6-14112768\,a^{13}\,b^{14}\,c^{25}\,d^7+10407936\,a^{14}\,b^{13}\,c^{24}\,d^8+6454272\,a^{15}\,b^{12}\,c^{23}\,d^9-30007296\,a^{16}\,b^{11}\,c^{22}\,d^{10}+45551616\,a^{17}\,b^{10}\,c^{21}\,d^{11}-44064768\,a^{18}\,b^9\,c^{20}\,d^{12}+30096384\,a^{19}\,b^8\,c^{19}\,d^{13}-14831616\,a^{20}\,b^7\,c^{18}\,d^{14}+5203968\,a^{21}\,b^6\,c^{17}\,d^{15}-1241088\,a^{22}\,b^5\,c^{16}\,d^{16}+181248\,a^{23}\,b^4\,c^{15}\,d^{17}-12288\,a^{24}\,b^3\,c^{14}\,d^{18}+\frac{3\,\sqrt{d^5\,{\left(a\,d-b\,c\right)}^7}\,\sqrt{a+\frac{b}{x}}\,\left(8\,a^2\,d^2-24\,a\,b\,c\,d+21\,b^2\,c^2\right)\,\left(16384\,a^{26}\,b^2\,c^{17}\,d^{18}-253952\,a^{25}\,b^3\,c^{18}\,d^{17}+1843200\,a^{24}\,b^4\,c^{19}\,d^{16}-8314880\,a^{23}\,b^5\,c^{20}\,d^{15}+26091520\,a^{22}\,b^6\,c^{21}\,d^{14}-60383232\,a^{21}\,b^7\,c^{22}\,d^{13}+106602496\,a^{20}\,b^8\,c^{23}\,d^{12}-146432000\,a^{19}\,b^9\,c^{24}\,d^{11}+158146560\,a^{18}\,b^{10}\,c^{25}\,d^{10}-134717440\,a^{17}\,b^{11}\,c^{26}\,d^9+90202112\,a^{16}\,b^{12}\,c^{27}\,d^8-46964736\,a^{15}\,b^{13}\,c^{28}\,d^7+18636800\,a^{14}\,b^{14}\,c^{29}\,d^6-5447680\,a^{13}\,b^{15}\,c^{30}\,d^5+1105920\,a^{12}\,b^{16}\,c^{31}\,d^4-139264\,a^{11}\,b^{17}\,c^{32}\,d^3+8192\,a^{10}\,b^{18}\,c^{33}\,d^2\right)}{8\,\left(-a^7\,c^4\,d^7+7\,a^6\,b\,c^5\,d^6-21\,a^5\,b^2\,c^6\,d^5+35\,a^4\,b^3\,c^7\,d^4-35\,a^3\,b^4\,c^8\,d^3+21\,a^2\,b^5\,c^9\,d^2-7\,a\,b^6\,c^{10}\,d+b^7\,c^{11}\right)}\right)}{8\,\left(-a^7\,c^4\,d^7+7\,a^6\,b\,c^5\,d^6-21\,a^5\,b^2\,c^6\,d^5+35\,a^4\,b^3\,c^7\,d^4-35\,a^3\,b^4\,c^8\,d^3+21\,a^2\,b^5\,c^9\,d^2-7\,a\,b^6\,c^{10}\,d+b^7\,c^{11}\right)}\right)\,\sqrt{d^5\,{\left(a\,d-b\,c\right)}^7}\,\left(8\,a^2\,d^2-24\,a\,b\,c\,d+21\,b^2\,c^2\right)}{8\,\left(-a^7\,c^4\,d^7+7\,a^6\,b\,c^5\,d^6-21\,a^5\,b^2\,c^6\,d^5+35\,a^4\,b^3\,c^7\,d^4-35\,a^3\,b^4\,c^8\,d^3+21\,a^2\,b^5\,c^9\,d^2-7\,a\,b^6\,c^{10}\,d+b^7\,c^{11}\right)}}\right)\,\sqrt{d^5\,{\left(a\,d-b\,c\right)}^7}\,\left(8\,a^2\,d^2-24\,a\,b\,c\,d+21\,b^2\,c^2\right)\,3{}\mathrm{i}}{4\,\left(-a^7\,c^4\,d^7+7\,a^6\,b\,c^5\,d^6-21\,a^5\,b^2\,c^6\,d^5+35\,a^4\,b^3\,c^7\,d^4-35\,a^3\,b^4\,c^8\,d^3+21\,a^2\,b^5\,c^9\,d^2-7\,a\,b^6\,c^{10}\,d+b^7\,c^{11}\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(2\,a\,d+b\,c\right)\,\left(\sqrt{a+\frac{b}{x}}\,\left(-147456\,a^{23}\,b^2\,c^9\,d^{20}+2138112\,a^{22}\,b^3\,c^{10}\,d^{19}-14340096\,a^{21}\,b^4\,c^{11}\,d^{18}+58816512\,a^{20}\,b^5\,c^{12}\,d^{17}-164257920\,a^{19}\,b^6\,c^{13}\,d^{16}+328809600\,a^{18}\,b^7\,c^{14}\,d^{15}-482904576\,a^{17}\,b^8\,c^{15}\,d^{14}+521961984\,a^{16}\,b^9\,c^{16}\,d^{13}-407418624\,a^{15}\,b^{10}\,c^{17}\,d^{12}+216610560\,a^{14}\,b^{11}\,c^{18}\,d^{11}-65382912\,a^{13}\,b^{12}\,c^{19}\,d^{10}+1276416\,a^{12}\,b^{13}\,c^{20}\,d^9+6007680\,a^{11}\,b^{14}\,c^{21}\,d^8-137088\,a^{10}\,b^{15}\,c^{22}\,d^7-1751040\,a^9\,b^{16}\,c^{23}\,d^6+903168\,a^8\,b^{17}\,c^{24}\,d^5-202752\,a^7\,b^{18}\,c^{25}\,d^4+18432\,a^6\,b^{19}\,c^{26}\,d^3\right)-\frac{3\,\left(2\,a\,d+b\,c\right)\,\left(12288\,a^8\,b^{19}\,c^{30}\,d^2-172032\,a^9\,b^{18}\,c^{29}\,d^3+1081344\,a^{10}\,b^{17}\,c^{28}\,d^4-3996672\,a^{11}\,b^{16}\,c^{27}\,d^5+9449472\,a^{12}\,b^{15}\,c^{26}\,d^6-14112768\,a^{13}\,b^{14}\,c^{25}\,d^7+10407936\,a^{14}\,b^{13}\,c^{24}\,d^8+6454272\,a^{15}\,b^{12}\,c^{23}\,d^9-30007296\,a^{16}\,b^{11}\,c^{22}\,d^{10}+45551616\,a^{17}\,b^{10}\,c^{21}\,d^{11}-44064768\,a^{18}\,b^9\,c^{20}\,d^{12}+30096384\,a^{19}\,b^8\,c^{19}\,d^{13}-14831616\,a^{20}\,b^7\,c^{18}\,d^{14}+5203968\,a^{21}\,b^6\,c^{17}\,d^{15}-1241088\,a^{22}\,b^5\,c^{16}\,d^{16}+181248\,a^{23}\,b^4\,c^{15}\,d^{17}-12288\,a^{24}\,b^3\,c^{14}\,d^{18}-\frac{3\,\sqrt{a+\frac{b}{x}}\,\left(2\,a\,d+b\,c\right)\,\left(16384\,a^{26}\,b^2\,c^{17}\,d^{18}-253952\,a^{25}\,b^3\,c^{18}\,d^{17}+1843200\,a^{24}\,b^4\,c^{19}\,d^{16}-8314880\,a^{23}\,b^5\,c^{20}\,d^{15}+26091520\,a^{22}\,b^6\,c^{21}\,d^{14}-60383232\,a^{21}\,b^7\,c^{22}\,d^{13}+106602496\,a^{20}\,b^8\,c^{23}\,d^{12}-146432000\,a^{19}\,b^9\,c^{24}\,d^{11}+158146560\,a^{18}\,b^{10}\,c^{25}\,d^{10}-134717440\,a^{17}\,b^{11}\,c^{26}\,d^9+90202112\,a^{16}\,b^{12}\,c^{27}\,d^8-46964736\,a^{15}\,b^{13}\,c^{28}\,d^7+18636800\,a^{14}\,b^{14}\,c^{29}\,d^6-5447680\,a^{13}\,b^{15}\,c^{30}\,d^5+1105920\,a^{12}\,b^{16}\,c^{31}\,d^4-139264\,a^{11}\,b^{17}\,c^{32}\,d^3+8192\,a^{10}\,b^{18}\,c^{33}\,d^2\right)}{2\,c^4\,\sqrt{a^5}}\right)}{2\,c^4\,\sqrt{a^5}}\right)\,3{}\mathrm{i}}{2\,c^4\,\sqrt{a^5}}+\frac{\left(2\,a\,d+b\,c\right)\,\left(\sqrt{a+\frac{b}{x}}\,\left(-147456\,a^{23}\,b^2\,c^9\,d^{20}+2138112\,a^{22}\,b^3\,c^{10}\,d^{19}-14340096\,a^{21}\,b^4\,c^{11}\,d^{18}+58816512\,a^{20}\,b^5\,c^{12}\,d^{17}-164257920\,a^{19}\,b^6\,c^{13}\,d^{16}+328809600\,a^{18}\,b^7\,c^{14}\,d^{15}-482904576\,a^{17}\,b^8\,c^{15}\,d^{14}+521961984\,a^{16}\,b^9\,c^{16}\,d^{13}-407418624\,a^{15}\,b^{10}\,c^{17}\,d^{12}+216610560\,a^{14}\,b^{11}\,c^{18}\,d^{11}-65382912\,a^{13}\,b^{12}\,c^{19}\,d^{10}+1276416\,a^{12}\,b^{13}\,c^{20}\,d^9+6007680\,a^{11}\,b^{14}\,c^{21}\,d^8-137088\,a^{10}\,b^{15}\,c^{22}\,d^7-1751040\,a^9\,b^{16}\,c^{23}\,d^6+903168\,a^8\,b^{17}\,c^{24}\,d^5-202752\,a^7\,b^{18}\,c^{25}\,d^4+18432\,a^6\,b^{19}\,c^{26}\,d^3\right)+\frac{3\,\left(2\,a\,d+b\,c\right)\,\left(12288\,a^8\,b^{19}\,c^{30}\,d^2-172032\,a^9\,b^{18}\,c^{29}\,d^3+1081344\,a^{10}\,b^{17}\,c^{28}\,d^4-3996672\,a^{11}\,b^{16}\,c^{27}\,d^5+9449472\,a^{12}\,b^{15}\,c^{26}\,d^6-14112768\,a^{13}\,b^{14}\,c^{25}\,d^7+10407936\,a^{14}\,b^{13}\,c^{24}\,d^8+6454272\,a^{15}\,b^{12}\,c^{23}\,d^9-30007296\,a^{16}\,b^{11}\,c^{22}\,d^{10}+45551616\,a^{17}\,b^{10}\,c^{21}\,d^{11}-44064768\,a^{18}\,b^9\,c^{20}\,d^{12}+30096384\,a^{19}\,b^8\,c^{19}\,d^{13}-14831616\,a^{20}\,b^7\,c^{18}\,d^{14}+5203968\,a^{21}\,b^6\,c^{17}\,d^{15}-1241088\,a^{22}\,b^5\,c^{16}\,d^{16}+181248\,a^{23}\,b^4\,c^{15}\,d^{17}-12288\,a^{24}\,b^3\,c^{14}\,d^{18}+\frac{3\,\sqrt{a+\frac{b}{x}}\,\left(2\,a\,d+b\,c\right)\,\left(16384\,a^{26}\,b^2\,c^{17}\,d^{18}-253952\,a^{25}\,b^3\,c^{18}\,d^{17}+1843200\,a^{24}\,b^4\,c^{19}\,d^{16}-8314880\,a^{23}\,b^5\,c^{20}\,d^{15}+26091520\,a^{22}\,b^6\,c^{21}\,d^{14}-60383232\,a^{21}\,b^7\,c^{22}\,d^{13}+106602496\,a^{20}\,b^8\,c^{23}\,d^{12}-146432000\,a^{19}\,b^9\,c^{24}\,d^{11}+158146560\,a^{18}\,b^{10}\,c^{25}\,d^{10}-134717440\,a^{17}\,b^{11}\,c^{26}\,d^9+90202112\,a^{16}\,b^{12}\,c^{27}\,d^8-46964736\,a^{15}\,b^{13}\,c^{28}\,d^7+18636800\,a^{14}\,b^{14}\,c^{29}\,d^6-5447680\,a^{13}\,b^{15}\,c^{30}\,d^5+1105920\,a^{12}\,b^{16}\,c^{31}\,d^4-139264\,a^{11}\,b^{17}\,c^{32}\,d^3+8192\,a^{10}\,b^{18}\,c^{33}\,d^2\right)}{2\,c^4\,\sqrt{a^5}}\right)}{2\,c^4\,\sqrt{a^5}}\right)\,3{}\mathrm{i}}{2\,c^4\,\sqrt{a^5}}}{290304\,a^6\,b^{18}\,c^{21}\,d^5-2654208\,a^7\,b^{17}\,c^{20}\,d^6+10675584\,a^8\,b^{16}\,c^{19}\,d^7-23497344\,a^9\,b^{15}\,c^{18}\,d^8+23604480\,a^{10}\,b^{14}\,c^{17}\,d^9+24731136\,a^{11}\,b^{13}\,c^{16}\,d^{10}-148172544\,a^{12}\,b^{12}\,c^{15}\,d^{11}+320101632\,a^{13}\,b^{11}\,c^{14}\,d^{12}-452086272\,a^{14}\,b^{10}\,c^{13}\,d^{13}+459302400\,a^{15}\,b^9\,c^{12}\,d^{14}-343108224\,a^{16}\,b^8\,c^{11}\,d^{15}+187373952\,a^{17}\,b^7\,c^{10}\,d^{16}-72873216\,a^{18}\,b^6\,c^9\,d^{17}+19132416\,a^{19}\,b^5\,c^8\,d^{18}-3041280\,a^{20}\,b^4\,c^7\,d^{19}+221184\,a^{21}\,b^3\,c^6\,d^{20}-\frac{3\,\left(2\,a\,d+b\,c\right)\,\left(\sqrt{a+\frac{b}{x}}\,\left(-147456\,a^{23}\,b^2\,c^9\,d^{20}+2138112\,a^{22}\,b^3\,c^{10}\,d^{19}-14340096\,a^{21}\,b^4\,c^{11}\,d^{18}+58816512\,a^{20}\,b^5\,c^{12}\,d^{17}-164257920\,a^{19}\,b^6\,c^{13}\,d^{16}+328809600\,a^{18}\,b^7\,c^{14}\,d^{15}-482904576\,a^{17}\,b^8\,c^{15}\,d^{14}+521961984\,a^{16}\,b^9\,c^{16}\,d^{13}-407418624\,a^{15}\,b^{10}\,c^{17}\,d^{12}+216610560\,a^{14}\,b^{11}\,c^{18}\,d^{11}-65382912\,a^{13}\,b^{12}\,c^{19}\,d^{10}+1276416\,a^{12}\,b^{13}\,c^{20}\,d^9+6007680\,a^{11}\,b^{14}\,c^{21}\,d^8-137088\,a^{10}\,b^{15}\,c^{22}\,d^7-1751040\,a^9\,b^{16}\,c^{23}\,d^6+903168\,a^8\,b^{17}\,c^{24}\,d^5-202752\,a^7\,b^{18}\,c^{25}\,d^4+18432\,a^6\,b^{19}\,c^{26}\,d^3\right)-\frac{3\,\left(2\,a\,d+b\,c\right)\,\left(12288\,a^8\,b^{19}\,c^{30}\,d^2-172032\,a^9\,b^{18}\,c^{29}\,d^3+1081344\,a^{10}\,b^{17}\,c^{28}\,d^4-3996672\,a^{11}\,b^{16}\,c^{27}\,d^5+9449472\,a^{12}\,b^{15}\,c^{26}\,d^6-14112768\,a^{13}\,b^{14}\,c^{25}\,d^7+10407936\,a^{14}\,b^{13}\,c^{24}\,d^8+6454272\,a^{15}\,b^{12}\,c^{23}\,d^9-30007296\,a^{16}\,b^{11}\,c^{22}\,d^{10}+45551616\,a^{17}\,b^{10}\,c^{21}\,d^{11}-44064768\,a^{18}\,b^9\,c^{20}\,d^{12}+30096384\,a^{19}\,b^8\,c^{19}\,d^{13}-14831616\,a^{20}\,b^7\,c^{18}\,d^{14}+5203968\,a^{21}\,b^6\,c^{17}\,d^{15}-1241088\,a^{22}\,b^5\,c^{16}\,d^{16}+181248\,a^{23}\,b^4\,c^{15}\,d^{17}-12288\,a^{24}\,b^3\,c^{14}\,d^{18}-\frac{3\,\sqrt{a+\frac{b}{x}}\,\left(2\,a\,d+b\,c\right)\,\left(16384\,a^{26}\,b^2\,c^{17}\,d^{18}-253952\,a^{25}\,b^3\,c^{18}\,d^{17}+1843200\,a^{24}\,b^4\,c^{19}\,d^{16}-8314880\,a^{23}\,b^5\,c^{20}\,d^{15}+26091520\,a^{22}\,b^6\,c^{21}\,d^{14}-60383232\,a^{21}\,b^7\,c^{22}\,d^{13}+106602496\,a^{20}\,b^8\,c^{23}\,d^{12}-146432000\,a^{19}\,b^9\,c^{24}\,d^{11}+158146560\,a^{18}\,b^{10}\,c^{25}\,d^{10}-134717440\,a^{17}\,b^{11}\,c^{26}\,d^9+90202112\,a^{16}\,b^{12}\,c^{27}\,d^8-46964736\,a^{15}\,b^{13}\,c^{28}\,d^7+18636800\,a^{14}\,b^{14}\,c^{29}\,d^6-5447680\,a^{13}\,b^{15}\,c^{30}\,d^5+1105920\,a^{12}\,b^{16}\,c^{31}\,d^4-139264\,a^{11}\,b^{17}\,c^{32}\,d^3+8192\,a^{10}\,b^{18}\,c^{33}\,d^2\right)}{2\,c^4\,\sqrt{a^5}}\right)}{2\,c^4\,\sqrt{a^5}}\right)}{2\,c^4\,\sqrt{a^5}}+\frac{3\,\left(2\,a\,d+b\,c\right)\,\left(\sqrt{a+\frac{b}{x}}\,\left(-147456\,a^{23}\,b^2\,c^9\,d^{20}+2138112\,a^{22}\,b^3\,c^{10}\,d^{19}-14340096\,a^{21}\,b^4\,c^{11}\,d^{18}+58816512\,a^{20}\,b^5\,c^{12}\,d^{17}-164257920\,a^{19}\,b^6\,c^{13}\,d^{16}+328809600\,a^{18}\,b^7\,c^{14}\,d^{15}-482904576\,a^{17}\,b^8\,c^{15}\,d^{14}+521961984\,a^{16}\,b^9\,c^{16}\,d^{13}-407418624\,a^{15}\,b^{10}\,c^{17}\,d^{12}+216610560\,a^{14}\,b^{11}\,c^{18}\,d^{11}-65382912\,a^{13}\,b^{12}\,c^{19}\,d^{10}+1276416\,a^{12}\,b^{13}\,c^{20}\,d^9+6007680\,a^{11}\,b^{14}\,c^{21}\,d^8-137088\,a^{10}\,b^{15}\,c^{22}\,d^7-1751040\,a^9\,b^{16}\,c^{23}\,d^6+903168\,a^8\,b^{17}\,c^{24}\,d^5-202752\,a^7\,b^{18}\,c^{25}\,d^4+18432\,a^6\,b^{19}\,c^{26}\,d^3\right)+\frac{3\,\left(2\,a\,d+b\,c\right)\,\left(12288\,a^8\,b^{19}\,c^{30}\,d^2-172032\,a^9\,b^{18}\,c^{29}\,d^3+1081344\,a^{10}\,b^{17}\,c^{28}\,d^4-3996672\,a^{11}\,b^{16}\,c^{27}\,d^5+9449472\,a^{12}\,b^{15}\,c^{26}\,d^6-14112768\,a^{13}\,b^{14}\,c^{25}\,d^7+10407936\,a^{14}\,b^{13}\,c^{24}\,d^8+6454272\,a^{15}\,b^{12}\,c^{23}\,d^9-30007296\,a^{16}\,b^{11}\,c^{22}\,d^{10}+45551616\,a^{17}\,b^{10}\,c^{21}\,d^{11}-44064768\,a^{18}\,b^9\,c^{20}\,d^{12}+30096384\,a^{19}\,b^8\,c^{19}\,d^{13}-14831616\,a^{20}\,b^7\,c^{18}\,d^{14}+5203968\,a^{21}\,b^6\,c^{17}\,d^{15}-1241088\,a^{22}\,b^5\,c^{16}\,d^{16}+181248\,a^{23}\,b^4\,c^{15}\,d^{17}-12288\,a^{24}\,b^3\,c^{14}\,d^{18}+\frac{3\,\sqrt{a+\frac{b}{x}}\,\left(2\,a\,d+b\,c\right)\,\left(16384\,a^{26}\,b^2\,c^{17}\,d^{18}-253952\,a^{25}\,b^3\,c^{18}\,d^{17}+1843200\,a^{24}\,b^4\,c^{19}\,d^{16}-8314880\,a^{23}\,b^5\,c^{20}\,d^{15}+26091520\,a^{22}\,b^6\,c^{21}\,d^{14}-60383232\,a^{21}\,b^7\,c^{22}\,d^{13}+106602496\,a^{20}\,b^8\,c^{23}\,d^{12}-146432000\,a^{19}\,b^9\,c^{24}\,d^{11}+158146560\,a^{18}\,b^{10}\,c^{25}\,d^{10}-134717440\,a^{17}\,b^{11}\,c^{26}\,d^9+90202112\,a^{16}\,b^{12}\,c^{27}\,d^8-46964736\,a^{15}\,b^{13}\,c^{28}\,d^7+18636800\,a^{14}\,b^{14}\,c^{29}\,d^6-5447680\,a^{13}\,b^{15}\,c^{30}\,d^5+1105920\,a^{12}\,b^{16}\,c^{31}\,d^4-139264\,a^{11}\,b^{17}\,c^{32}\,d^3+8192\,a^{10}\,b^{18}\,c^{33}\,d^2\right)}{2\,c^4\,\sqrt{a^5}}\right)}{2\,c^4\,\sqrt{a^5}}\right)}{2\,c^4\,\sqrt{a^5}}}\right)\,\left(2\,a\,d+b\,c\right)\,3{}\mathrm{i}}{c^4\,\sqrt{a^5}}","Not used",1,"((2*b^4)/(a^2*d - a*b*c) + (b*(a + b/x)*(12*a^4*d^4 + 12*b^4*c^4 + 24*a^2*b^2*c^2*d^2 - 40*a*b^3*c^3*d - 33*a^3*b*c*d^3))/(4*a*c^3*(a^2*d - a*b*c)*(a*d - b*c)) + (3*b*(a + b/x)^3*(4*a^3*d^5 - 4*b^3*c^3*d^2 + 4*a*b^2*c^2*d^3 - 9*a^2*b*c*d^4))/(4*a*c^3*(a^2*d - a*b*c)*(a*d - b*c)^2) - (b*(a + b/x)^2*(24*a^4*d^5 + 24*b^4*c^4*d - 56*a*b^3*c^3*d^2 + 65*a^2*b^2*c^2*d^3 - 72*a^3*b*c*d^4))/(4*a*c^3*(a^2*d - a*b*c)*(a*d - b*c)^2))/((a + b/x)^(3/2)*(3*a^2*d^2 + b^2*c^2 - 4*a*b*c*d) - (a + b/x)^(5/2)*(3*a*d^2 - 2*b*c*d) + d^2*(a + b/x)^(7/2) - (a + b/x)^(1/2)*(a^3*d^2 + a*b^2*c^2 - 2*a^2*b*c*d)) + (atan(((((a + b/x)^(1/2)*(18432*a^6*b^19*c^26*d^3 - 202752*a^7*b^18*c^25*d^4 + 903168*a^8*b^17*c^24*d^5 - 1751040*a^9*b^16*c^23*d^6 - 137088*a^10*b^15*c^22*d^7 + 6007680*a^11*b^14*c^21*d^8 + 1276416*a^12*b^13*c^20*d^9 - 65382912*a^13*b^12*c^19*d^10 + 216610560*a^14*b^11*c^18*d^11 - 407418624*a^15*b^10*c^17*d^12 + 521961984*a^16*b^9*c^16*d^13 - 482904576*a^17*b^8*c^15*d^14 + 328809600*a^18*b^7*c^14*d^15 - 164257920*a^19*b^6*c^13*d^16 + 58816512*a^20*b^5*c^12*d^17 - 14340096*a^21*b^4*c^11*d^18 + 2138112*a^22*b^3*c^10*d^19 - 147456*a^23*b^2*c^9*d^20) - (3*(d^5*(a*d - b*c)^7)^(1/2)*(8*a^2*d^2 + 21*b^2*c^2 - 24*a*b*c*d)*(12288*a^8*b^19*c^30*d^2 - 172032*a^9*b^18*c^29*d^3 + 1081344*a^10*b^17*c^28*d^4 - 3996672*a^11*b^16*c^27*d^5 + 9449472*a^12*b^15*c^26*d^6 - 14112768*a^13*b^14*c^25*d^7 + 10407936*a^14*b^13*c^24*d^8 + 6454272*a^15*b^12*c^23*d^9 - 30007296*a^16*b^11*c^22*d^10 + 45551616*a^17*b^10*c^21*d^11 - 44064768*a^18*b^9*c^20*d^12 + 30096384*a^19*b^8*c^19*d^13 - 14831616*a^20*b^7*c^18*d^14 + 5203968*a^21*b^6*c^17*d^15 - 1241088*a^22*b^5*c^16*d^16 + 181248*a^23*b^4*c^15*d^17 - 12288*a^24*b^3*c^14*d^18 - (3*(d^5*(a*d - b*c)^7)^(1/2)*(a + b/x)^(1/2)*(8*a^2*d^2 + 21*b^2*c^2 - 24*a*b*c*d)*(8192*a^10*b^18*c^33*d^2 - 139264*a^11*b^17*c^32*d^3 + 1105920*a^12*b^16*c^31*d^4 - 5447680*a^13*b^15*c^30*d^5 + 18636800*a^14*b^14*c^29*d^6 - 46964736*a^15*b^13*c^28*d^7 + 90202112*a^16*b^12*c^27*d^8 - 134717440*a^17*b^11*c^26*d^9 + 158146560*a^18*b^10*c^25*d^10 - 146432000*a^19*b^9*c^24*d^11 + 106602496*a^20*b^8*c^23*d^12 - 60383232*a^21*b^7*c^22*d^13 + 26091520*a^22*b^6*c^21*d^14 - 8314880*a^23*b^5*c^20*d^15 + 1843200*a^24*b^4*c^19*d^16 - 253952*a^25*b^3*c^18*d^17 + 16384*a^26*b^2*c^17*d^18))/(8*(b^7*c^11 - a^7*c^4*d^7 + 7*a^6*b*c^5*d^6 + 21*a^2*b^5*c^9*d^2 - 35*a^3*b^4*c^8*d^3 + 35*a^4*b^3*c^7*d^4 - 21*a^5*b^2*c^6*d^5 - 7*a*b^6*c^10*d))))/(8*(b^7*c^11 - a^7*c^4*d^7 + 7*a^6*b*c^5*d^6 + 21*a^2*b^5*c^9*d^2 - 35*a^3*b^4*c^8*d^3 + 35*a^4*b^3*c^7*d^4 - 21*a^5*b^2*c^6*d^5 - 7*a*b^6*c^10*d)))*(d^5*(a*d - b*c)^7)^(1/2)*(8*a^2*d^2 + 21*b^2*c^2 - 24*a*b*c*d)*3i)/(8*(b^7*c^11 - a^7*c^4*d^7 + 7*a^6*b*c^5*d^6 + 21*a^2*b^5*c^9*d^2 - 35*a^3*b^4*c^8*d^3 + 35*a^4*b^3*c^7*d^4 - 21*a^5*b^2*c^6*d^5 - 7*a*b^6*c^10*d)) + (((a + b/x)^(1/2)*(18432*a^6*b^19*c^26*d^3 - 202752*a^7*b^18*c^25*d^4 + 903168*a^8*b^17*c^24*d^5 - 1751040*a^9*b^16*c^23*d^6 - 137088*a^10*b^15*c^22*d^7 + 6007680*a^11*b^14*c^21*d^8 + 1276416*a^12*b^13*c^20*d^9 - 65382912*a^13*b^12*c^19*d^10 + 216610560*a^14*b^11*c^18*d^11 - 407418624*a^15*b^10*c^17*d^12 + 521961984*a^16*b^9*c^16*d^13 - 482904576*a^17*b^8*c^15*d^14 + 328809600*a^18*b^7*c^14*d^15 - 164257920*a^19*b^6*c^13*d^16 + 58816512*a^20*b^5*c^12*d^17 - 14340096*a^21*b^4*c^11*d^18 + 2138112*a^22*b^3*c^10*d^19 - 147456*a^23*b^2*c^9*d^20) + (3*(d^5*(a*d - b*c)^7)^(1/2)*(8*a^2*d^2 + 21*b^2*c^2 - 24*a*b*c*d)*(12288*a^8*b^19*c^30*d^2 - 172032*a^9*b^18*c^29*d^3 + 1081344*a^10*b^17*c^28*d^4 - 3996672*a^11*b^16*c^27*d^5 + 9449472*a^12*b^15*c^26*d^6 - 14112768*a^13*b^14*c^25*d^7 + 10407936*a^14*b^13*c^24*d^8 + 6454272*a^15*b^12*c^23*d^9 - 30007296*a^16*b^11*c^22*d^10 + 45551616*a^17*b^10*c^21*d^11 - 44064768*a^18*b^9*c^20*d^12 + 30096384*a^19*b^8*c^19*d^13 - 14831616*a^20*b^7*c^18*d^14 + 5203968*a^21*b^6*c^17*d^15 - 1241088*a^22*b^5*c^16*d^16 + 181248*a^23*b^4*c^15*d^17 - 12288*a^24*b^3*c^14*d^18 + (3*(d^5*(a*d - b*c)^7)^(1/2)*(a + b/x)^(1/2)*(8*a^2*d^2 + 21*b^2*c^2 - 24*a*b*c*d)*(8192*a^10*b^18*c^33*d^2 - 139264*a^11*b^17*c^32*d^3 + 1105920*a^12*b^16*c^31*d^4 - 5447680*a^13*b^15*c^30*d^5 + 18636800*a^14*b^14*c^29*d^6 - 46964736*a^15*b^13*c^28*d^7 + 90202112*a^16*b^12*c^27*d^8 - 134717440*a^17*b^11*c^26*d^9 + 158146560*a^18*b^10*c^25*d^10 - 146432000*a^19*b^9*c^24*d^11 + 106602496*a^20*b^8*c^23*d^12 - 60383232*a^21*b^7*c^22*d^13 + 26091520*a^22*b^6*c^21*d^14 - 8314880*a^23*b^5*c^20*d^15 + 1843200*a^24*b^4*c^19*d^16 - 253952*a^25*b^3*c^18*d^17 + 16384*a^26*b^2*c^17*d^18))/(8*(b^7*c^11 - a^7*c^4*d^7 + 7*a^6*b*c^5*d^6 + 21*a^2*b^5*c^9*d^2 - 35*a^3*b^4*c^8*d^3 + 35*a^4*b^3*c^7*d^4 - 21*a^5*b^2*c^6*d^5 - 7*a*b^6*c^10*d))))/(8*(b^7*c^11 - a^7*c^4*d^7 + 7*a^6*b*c^5*d^6 + 21*a^2*b^5*c^9*d^2 - 35*a^3*b^4*c^8*d^3 + 35*a^4*b^3*c^7*d^4 - 21*a^5*b^2*c^6*d^5 - 7*a*b^6*c^10*d)))*(d^5*(a*d - b*c)^7)^(1/2)*(8*a^2*d^2 + 21*b^2*c^2 - 24*a*b*c*d)*3i)/(8*(b^7*c^11 - a^7*c^4*d^7 + 7*a^6*b*c^5*d^6 + 21*a^2*b^5*c^9*d^2 - 35*a^3*b^4*c^8*d^3 + 35*a^4*b^3*c^7*d^4 - 21*a^5*b^2*c^6*d^5 - 7*a*b^6*c^10*d)))/(290304*a^6*b^18*c^21*d^5 - 2654208*a^7*b^17*c^20*d^6 + 10675584*a^8*b^16*c^19*d^7 - 23497344*a^9*b^15*c^18*d^8 + 23604480*a^10*b^14*c^17*d^9 + 24731136*a^11*b^13*c^16*d^10 - 148172544*a^12*b^12*c^15*d^11 + 320101632*a^13*b^11*c^14*d^12 - 452086272*a^14*b^10*c^13*d^13 + 459302400*a^15*b^9*c^12*d^14 - 343108224*a^16*b^8*c^11*d^15 + 187373952*a^17*b^7*c^10*d^16 - 72873216*a^18*b^6*c^9*d^17 + 19132416*a^19*b^5*c^8*d^18 - 3041280*a^20*b^4*c^7*d^19 + 221184*a^21*b^3*c^6*d^20 - (3*((a + b/x)^(1/2)*(18432*a^6*b^19*c^26*d^3 - 202752*a^7*b^18*c^25*d^4 + 903168*a^8*b^17*c^24*d^5 - 1751040*a^9*b^16*c^23*d^6 - 137088*a^10*b^15*c^22*d^7 + 6007680*a^11*b^14*c^21*d^8 + 1276416*a^12*b^13*c^20*d^9 - 65382912*a^13*b^12*c^19*d^10 + 216610560*a^14*b^11*c^18*d^11 - 407418624*a^15*b^10*c^17*d^12 + 521961984*a^16*b^9*c^16*d^13 - 482904576*a^17*b^8*c^15*d^14 + 328809600*a^18*b^7*c^14*d^15 - 164257920*a^19*b^6*c^13*d^16 + 58816512*a^20*b^5*c^12*d^17 - 14340096*a^21*b^4*c^11*d^18 + 2138112*a^22*b^3*c^10*d^19 - 147456*a^23*b^2*c^9*d^20) - (3*(d^5*(a*d - b*c)^7)^(1/2)*(8*a^2*d^2 + 21*b^2*c^2 - 24*a*b*c*d)*(12288*a^8*b^19*c^30*d^2 - 172032*a^9*b^18*c^29*d^3 + 1081344*a^10*b^17*c^28*d^4 - 3996672*a^11*b^16*c^27*d^5 + 9449472*a^12*b^15*c^26*d^6 - 14112768*a^13*b^14*c^25*d^7 + 10407936*a^14*b^13*c^24*d^8 + 6454272*a^15*b^12*c^23*d^9 - 30007296*a^16*b^11*c^22*d^10 + 45551616*a^17*b^10*c^21*d^11 - 44064768*a^18*b^9*c^20*d^12 + 30096384*a^19*b^8*c^19*d^13 - 14831616*a^20*b^7*c^18*d^14 + 5203968*a^21*b^6*c^17*d^15 - 1241088*a^22*b^5*c^16*d^16 + 181248*a^23*b^4*c^15*d^17 - 12288*a^24*b^3*c^14*d^18 - (3*(d^5*(a*d - b*c)^7)^(1/2)*(a + b/x)^(1/2)*(8*a^2*d^2 + 21*b^2*c^2 - 24*a*b*c*d)*(8192*a^10*b^18*c^33*d^2 - 139264*a^11*b^17*c^32*d^3 + 1105920*a^12*b^16*c^31*d^4 - 5447680*a^13*b^15*c^30*d^5 + 18636800*a^14*b^14*c^29*d^6 - 46964736*a^15*b^13*c^28*d^7 + 90202112*a^16*b^12*c^27*d^8 - 134717440*a^17*b^11*c^26*d^9 + 158146560*a^18*b^10*c^25*d^10 - 146432000*a^19*b^9*c^24*d^11 + 106602496*a^20*b^8*c^23*d^12 - 60383232*a^21*b^7*c^22*d^13 + 26091520*a^22*b^6*c^21*d^14 - 8314880*a^23*b^5*c^20*d^15 + 1843200*a^24*b^4*c^19*d^16 - 253952*a^25*b^3*c^18*d^17 + 16384*a^26*b^2*c^17*d^18))/(8*(b^7*c^11 - a^7*c^4*d^7 + 7*a^6*b*c^5*d^6 + 21*a^2*b^5*c^9*d^2 - 35*a^3*b^4*c^8*d^3 + 35*a^4*b^3*c^7*d^4 - 21*a^5*b^2*c^6*d^5 - 7*a*b^6*c^10*d))))/(8*(b^7*c^11 - a^7*c^4*d^7 + 7*a^6*b*c^5*d^6 + 21*a^2*b^5*c^9*d^2 - 35*a^3*b^4*c^8*d^3 + 35*a^4*b^3*c^7*d^4 - 21*a^5*b^2*c^6*d^5 - 7*a*b^6*c^10*d)))*(d^5*(a*d - b*c)^7)^(1/2)*(8*a^2*d^2 + 21*b^2*c^2 - 24*a*b*c*d))/(8*(b^7*c^11 - a^7*c^4*d^7 + 7*a^6*b*c^5*d^6 + 21*a^2*b^5*c^9*d^2 - 35*a^3*b^4*c^8*d^3 + 35*a^4*b^3*c^7*d^4 - 21*a^5*b^2*c^6*d^5 - 7*a*b^6*c^10*d)) + (3*((a + b/x)^(1/2)*(18432*a^6*b^19*c^26*d^3 - 202752*a^7*b^18*c^25*d^4 + 903168*a^8*b^17*c^24*d^5 - 1751040*a^9*b^16*c^23*d^6 - 137088*a^10*b^15*c^22*d^7 + 6007680*a^11*b^14*c^21*d^8 + 1276416*a^12*b^13*c^20*d^9 - 65382912*a^13*b^12*c^19*d^10 + 216610560*a^14*b^11*c^18*d^11 - 407418624*a^15*b^10*c^17*d^12 + 521961984*a^16*b^9*c^16*d^13 - 482904576*a^17*b^8*c^15*d^14 + 328809600*a^18*b^7*c^14*d^15 - 164257920*a^19*b^6*c^13*d^16 + 58816512*a^20*b^5*c^12*d^17 - 14340096*a^21*b^4*c^11*d^18 + 2138112*a^22*b^3*c^10*d^19 - 147456*a^23*b^2*c^9*d^20) + (3*(d^5*(a*d - b*c)^7)^(1/2)*(8*a^2*d^2 + 21*b^2*c^2 - 24*a*b*c*d)*(12288*a^8*b^19*c^30*d^2 - 172032*a^9*b^18*c^29*d^3 + 1081344*a^10*b^17*c^28*d^4 - 3996672*a^11*b^16*c^27*d^5 + 9449472*a^12*b^15*c^26*d^6 - 14112768*a^13*b^14*c^25*d^7 + 10407936*a^14*b^13*c^24*d^8 + 6454272*a^15*b^12*c^23*d^9 - 30007296*a^16*b^11*c^22*d^10 + 45551616*a^17*b^10*c^21*d^11 - 44064768*a^18*b^9*c^20*d^12 + 30096384*a^19*b^8*c^19*d^13 - 14831616*a^20*b^7*c^18*d^14 + 5203968*a^21*b^6*c^17*d^15 - 1241088*a^22*b^5*c^16*d^16 + 181248*a^23*b^4*c^15*d^17 - 12288*a^24*b^3*c^14*d^18 + (3*(d^5*(a*d - b*c)^7)^(1/2)*(a + b/x)^(1/2)*(8*a^2*d^2 + 21*b^2*c^2 - 24*a*b*c*d)*(8192*a^10*b^18*c^33*d^2 - 139264*a^11*b^17*c^32*d^3 + 1105920*a^12*b^16*c^31*d^4 - 5447680*a^13*b^15*c^30*d^5 + 18636800*a^14*b^14*c^29*d^6 - 46964736*a^15*b^13*c^28*d^7 + 90202112*a^16*b^12*c^27*d^8 - 134717440*a^17*b^11*c^26*d^9 + 158146560*a^18*b^10*c^25*d^10 - 146432000*a^19*b^9*c^24*d^11 + 106602496*a^20*b^8*c^23*d^12 - 60383232*a^21*b^7*c^22*d^13 + 26091520*a^22*b^6*c^21*d^14 - 8314880*a^23*b^5*c^20*d^15 + 1843200*a^24*b^4*c^19*d^16 - 253952*a^25*b^3*c^18*d^17 + 16384*a^26*b^2*c^17*d^18))/(8*(b^7*c^11 - a^7*c^4*d^7 + 7*a^6*b*c^5*d^6 + 21*a^2*b^5*c^9*d^2 - 35*a^3*b^4*c^8*d^3 + 35*a^4*b^3*c^7*d^4 - 21*a^5*b^2*c^6*d^5 - 7*a*b^6*c^10*d))))/(8*(b^7*c^11 - a^7*c^4*d^7 + 7*a^6*b*c^5*d^6 + 21*a^2*b^5*c^9*d^2 - 35*a^3*b^4*c^8*d^3 + 35*a^4*b^3*c^7*d^4 - 21*a^5*b^2*c^6*d^5 - 7*a*b^6*c^10*d)))*(d^5*(a*d - b*c)^7)^(1/2)*(8*a^2*d^2 + 21*b^2*c^2 - 24*a*b*c*d))/(8*(b^7*c^11 - a^7*c^4*d^7 + 7*a^6*b*c^5*d^6 + 21*a^2*b^5*c^9*d^2 - 35*a^3*b^4*c^8*d^3 + 35*a^4*b^3*c^7*d^4 - 21*a^5*b^2*c^6*d^5 - 7*a*b^6*c^10*d))))*(d^5*(a*d - b*c)^7)^(1/2)*(8*a^2*d^2 + 21*b^2*c^2 - 24*a*b*c*d)*3i)/(4*(b^7*c^11 - a^7*c^4*d^7 + 7*a^6*b*c^5*d^6 + 21*a^2*b^5*c^9*d^2 - 35*a^3*b^4*c^8*d^3 + 35*a^4*b^3*c^7*d^4 - 21*a^5*b^2*c^6*d^5 - 7*a*b^6*c^10*d)) + (atan((((2*a*d + b*c)*((a + b/x)^(1/2)*(18432*a^6*b^19*c^26*d^3 - 202752*a^7*b^18*c^25*d^4 + 903168*a^8*b^17*c^24*d^5 - 1751040*a^9*b^16*c^23*d^6 - 137088*a^10*b^15*c^22*d^7 + 6007680*a^11*b^14*c^21*d^8 + 1276416*a^12*b^13*c^20*d^9 - 65382912*a^13*b^12*c^19*d^10 + 216610560*a^14*b^11*c^18*d^11 - 407418624*a^15*b^10*c^17*d^12 + 521961984*a^16*b^9*c^16*d^13 - 482904576*a^17*b^8*c^15*d^14 + 328809600*a^18*b^7*c^14*d^15 - 164257920*a^19*b^6*c^13*d^16 + 58816512*a^20*b^5*c^12*d^17 - 14340096*a^21*b^4*c^11*d^18 + 2138112*a^22*b^3*c^10*d^19 - 147456*a^23*b^2*c^9*d^20) - (3*(2*a*d + b*c)*(12288*a^8*b^19*c^30*d^2 - 172032*a^9*b^18*c^29*d^3 + 1081344*a^10*b^17*c^28*d^4 - 3996672*a^11*b^16*c^27*d^5 + 9449472*a^12*b^15*c^26*d^6 - 14112768*a^13*b^14*c^25*d^7 + 10407936*a^14*b^13*c^24*d^8 + 6454272*a^15*b^12*c^23*d^9 - 30007296*a^16*b^11*c^22*d^10 + 45551616*a^17*b^10*c^21*d^11 - 44064768*a^18*b^9*c^20*d^12 + 30096384*a^19*b^8*c^19*d^13 - 14831616*a^20*b^7*c^18*d^14 + 5203968*a^21*b^6*c^17*d^15 - 1241088*a^22*b^5*c^16*d^16 + 181248*a^23*b^4*c^15*d^17 - 12288*a^24*b^3*c^14*d^18 - (3*(a + b/x)^(1/2)*(2*a*d + b*c)*(8192*a^10*b^18*c^33*d^2 - 139264*a^11*b^17*c^32*d^3 + 1105920*a^12*b^16*c^31*d^4 - 5447680*a^13*b^15*c^30*d^5 + 18636800*a^14*b^14*c^29*d^6 - 46964736*a^15*b^13*c^28*d^7 + 90202112*a^16*b^12*c^27*d^8 - 134717440*a^17*b^11*c^26*d^9 + 158146560*a^18*b^10*c^25*d^10 - 146432000*a^19*b^9*c^24*d^11 + 106602496*a^20*b^8*c^23*d^12 - 60383232*a^21*b^7*c^22*d^13 + 26091520*a^22*b^6*c^21*d^14 - 8314880*a^23*b^5*c^20*d^15 + 1843200*a^24*b^4*c^19*d^16 - 253952*a^25*b^3*c^18*d^17 + 16384*a^26*b^2*c^17*d^18))/(2*c^4*(a^5)^(1/2))))/(2*c^4*(a^5)^(1/2)))*3i)/(2*c^4*(a^5)^(1/2)) + ((2*a*d + b*c)*((a + b/x)^(1/2)*(18432*a^6*b^19*c^26*d^3 - 202752*a^7*b^18*c^25*d^4 + 903168*a^8*b^17*c^24*d^5 - 1751040*a^9*b^16*c^23*d^6 - 137088*a^10*b^15*c^22*d^7 + 6007680*a^11*b^14*c^21*d^8 + 1276416*a^12*b^13*c^20*d^9 - 65382912*a^13*b^12*c^19*d^10 + 216610560*a^14*b^11*c^18*d^11 - 407418624*a^15*b^10*c^17*d^12 + 521961984*a^16*b^9*c^16*d^13 - 482904576*a^17*b^8*c^15*d^14 + 328809600*a^18*b^7*c^14*d^15 - 164257920*a^19*b^6*c^13*d^16 + 58816512*a^20*b^5*c^12*d^17 - 14340096*a^21*b^4*c^11*d^18 + 2138112*a^22*b^3*c^10*d^19 - 147456*a^23*b^2*c^9*d^20) + (3*(2*a*d + b*c)*(12288*a^8*b^19*c^30*d^2 - 172032*a^9*b^18*c^29*d^3 + 1081344*a^10*b^17*c^28*d^4 - 3996672*a^11*b^16*c^27*d^5 + 9449472*a^12*b^15*c^26*d^6 - 14112768*a^13*b^14*c^25*d^7 + 10407936*a^14*b^13*c^24*d^8 + 6454272*a^15*b^12*c^23*d^9 - 30007296*a^16*b^11*c^22*d^10 + 45551616*a^17*b^10*c^21*d^11 - 44064768*a^18*b^9*c^20*d^12 + 30096384*a^19*b^8*c^19*d^13 - 14831616*a^20*b^7*c^18*d^14 + 5203968*a^21*b^6*c^17*d^15 - 1241088*a^22*b^5*c^16*d^16 + 181248*a^23*b^4*c^15*d^17 - 12288*a^24*b^3*c^14*d^18 + (3*(a + b/x)^(1/2)*(2*a*d + b*c)*(8192*a^10*b^18*c^33*d^2 - 139264*a^11*b^17*c^32*d^3 + 1105920*a^12*b^16*c^31*d^4 - 5447680*a^13*b^15*c^30*d^5 + 18636800*a^14*b^14*c^29*d^6 - 46964736*a^15*b^13*c^28*d^7 + 90202112*a^16*b^12*c^27*d^8 - 134717440*a^17*b^11*c^26*d^9 + 158146560*a^18*b^10*c^25*d^10 - 146432000*a^19*b^9*c^24*d^11 + 106602496*a^20*b^8*c^23*d^12 - 60383232*a^21*b^7*c^22*d^13 + 26091520*a^22*b^6*c^21*d^14 - 8314880*a^23*b^5*c^20*d^15 + 1843200*a^24*b^4*c^19*d^16 - 253952*a^25*b^3*c^18*d^17 + 16384*a^26*b^2*c^17*d^18))/(2*c^4*(a^5)^(1/2))))/(2*c^4*(a^5)^(1/2)))*3i)/(2*c^4*(a^5)^(1/2)))/(290304*a^6*b^18*c^21*d^5 - 2654208*a^7*b^17*c^20*d^6 + 10675584*a^8*b^16*c^19*d^7 - 23497344*a^9*b^15*c^18*d^8 + 23604480*a^10*b^14*c^17*d^9 + 24731136*a^11*b^13*c^16*d^10 - 148172544*a^12*b^12*c^15*d^11 + 320101632*a^13*b^11*c^14*d^12 - 452086272*a^14*b^10*c^13*d^13 + 459302400*a^15*b^9*c^12*d^14 - 343108224*a^16*b^8*c^11*d^15 + 187373952*a^17*b^7*c^10*d^16 - 72873216*a^18*b^6*c^9*d^17 + 19132416*a^19*b^5*c^8*d^18 - 3041280*a^20*b^4*c^7*d^19 + 221184*a^21*b^3*c^6*d^20 - (3*(2*a*d + b*c)*((a + b/x)^(1/2)*(18432*a^6*b^19*c^26*d^3 - 202752*a^7*b^18*c^25*d^4 + 903168*a^8*b^17*c^24*d^5 - 1751040*a^9*b^16*c^23*d^6 - 137088*a^10*b^15*c^22*d^7 + 6007680*a^11*b^14*c^21*d^8 + 1276416*a^12*b^13*c^20*d^9 - 65382912*a^13*b^12*c^19*d^10 + 216610560*a^14*b^11*c^18*d^11 - 407418624*a^15*b^10*c^17*d^12 + 521961984*a^16*b^9*c^16*d^13 - 482904576*a^17*b^8*c^15*d^14 + 328809600*a^18*b^7*c^14*d^15 - 164257920*a^19*b^6*c^13*d^16 + 58816512*a^20*b^5*c^12*d^17 - 14340096*a^21*b^4*c^11*d^18 + 2138112*a^22*b^3*c^10*d^19 - 147456*a^23*b^2*c^9*d^20) - (3*(2*a*d + b*c)*(12288*a^8*b^19*c^30*d^2 - 172032*a^9*b^18*c^29*d^3 + 1081344*a^10*b^17*c^28*d^4 - 3996672*a^11*b^16*c^27*d^5 + 9449472*a^12*b^15*c^26*d^6 - 14112768*a^13*b^14*c^25*d^7 + 10407936*a^14*b^13*c^24*d^8 + 6454272*a^15*b^12*c^23*d^9 - 30007296*a^16*b^11*c^22*d^10 + 45551616*a^17*b^10*c^21*d^11 - 44064768*a^18*b^9*c^20*d^12 + 30096384*a^19*b^8*c^19*d^13 - 14831616*a^20*b^7*c^18*d^14 + 5203968*a^21*b^6*c^17*d^15 - 1241088*a^22*b^5*c^16*d^16 + 181248*a^23*b^4*c^15*d^17 - 12288*a^24*b^3*c^14*d^18 - (3*(a + b/x)^(1/2)*(2*a*d + b*c)*(8192*a^10*b^18*c^33*d^2 - 139264*a^11*b^17*c^32*d^3 + 1105920*a^12*b^16*c^31*d^4 - 5447680*a^13*b^15*c^30*d^5 + 18636800*a^14*b^14*c^29*d^6 - 46964736*a^15*b^13*c^28*d^7 + 90202112*a^16*b^12*c^27*d^8 - 134717440*a^17*b^11*c^26*d^9 + 158146560*a^18*b^10*c^25*d^10 - 146432000*a^19*b^9*c^24*d^11 + 106602496*a^20*b^8*c^23*d^12 - 60383232*a^21*b^7*c^22*d^13 + 26091520*a^22*b^6*c^21*d^14 - 8314880*a^23*b^5*c^20*d^15 + 1843200*a^24*b^4*c^19*d^16 - 253952*a^25*b^3*c^18*d^17 + 16384*a^26*b^2*c^17*d^18))/(2*c^4*(a^5)^(1/2))))/(2*c^4*(a^5)^(1/2))))/(2*c^4*(a^5)^(1/2)) + (3*(2*a*d + b*c)*((a + b/x)^(1/2)*(18432*a^6*b^19*c^26*d^3 - 202752*a^7*b^18*c^25*d^4 + 903168*a^8*b^17*c^24*d^5 - 1751040*a^9*b^16*c^23*d^6 - 137088*a^10*b^15*c^22*d^7 + 6007680*a^11*b^14*c^21*d^8 + 1276416*a^12*b^13*c^20*d^9 - 65382912*a^13*b^12*c^19*d^10 + 216610560*a^14*b^11*c^18*d^11 - 407418624*a^15*b^10*c^17*d^12 + 521961984*a^16*b^9*c^16*d^13 - 482904576*a^17*b^8*c^15*d^14 + 328809600*a^18*b^7*c^14*d^15 - 164257920*a^19*b^6*c^13*d^16 + 58816512*a^20*b^5*c^12*d^17 - 14340096*a^21*b^4*c^11*d^18 + 2138112*a^22*b^3*c^10*d^19 - 147456*a^23*b^2*c^9*d^20) + (3*(2*a*d + b*c)*(12288*a^8*b^19*c^30*d^2 - 172032*a^9*b^18*c^29*d^3 + 1081344*a^10*b^17*c^28*d^4 - 3996672*a^11*b^16*c^27*d^5 + 9449472*a^12*b^15*c^26*d^6 - 14112768*a^13*b^14*c^25*d^7 + 10407936*a^14*b^13*c^24*d^8 + 6454272*a^15*b^12*c^23*d^9 - 30007296*a^16*b^11*c^22*d^10 + 45551616*a^17*b^10*c^21*d^11 - 44064768*a^18*b^9*c^20*d^12 + 30096384*a^19*b^8*c^19*d^13 - 14831616*a^20*b^7*c^18*d^14 + 5203968*a^21*b^6*c^17*d^15 - 1241088*a^22*b^5*c^16*d^16 + 181248*a^23*b^4*c^15*d^17 - 12288*a^24*b^3*c^14*d^18 + (3*(a + b/x)^(1/2)*(2*a*d + b*c)*(8192*a^10*b^18*c^33*d^2 - 139264*a^11*b^17*c^32*d^3 + 1105920*a^12*b^16*c^31*d^4 - 5447680*a^13*b^15*c^30*d^5 + 18636800*a^14*b^14*c^29*d^6 - 46964736*a^15*b^13*c^28*d^7 + 90202112*a^16*b^12*c^27*d^8 - 134717440*a^17*b^11*c^26*d^9 + 158146560*a^18*b^10*c^25*d^10 - 146432000*a^19*b^9*c^24*d^11 + 106602496*a^20*b^8*c^23*d^12 - 60383232*a^21*b^7*c^22*d^13 + 26091520*a^22*b^6*c^21*d^14 - 8314880*a^23*b^5*c^20*d^15 + 1843200*a^24*b^4*c^19*d^16 - 253952*a^25*b^3*c^18*d^17 + 16384*a^26*b^2*c^17*d^18))/(2*c^4*(a^5)^(1/2))))/(2*c^4*(a^5)^(1/2))))/(2*c^4*(a^5)^(1/2))))*(2*a*d + b*c)*3i)/(c^4*(a^5)^(1/2))","B"
259,1,194,143,2.049828,"\text{Not used}","int((c + d/x)^3/(a + b/x)^(5/2),x)","\frac{\frac{2\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)}{3\,a}+\frac{{\left(a+\frac{b}{x}\right)}^2\,\left(2\,a^3\,d^3-6\,a\,b^2\,c^2\,d+5\,b^3\,c^3\right)}{a^3}-\frac{2\,\left(a+\frac{b}{x}\right)\,\left(4\,a^3\,d^3-3\,a^2\,b\,c\,d^2-6\,a\,b^2\,c^2\,d+5\,b^3\,c^3\right)}{3\,a^2}}{b^2\,{\left(a+\frac{b}{x}\right)}^{5/2}-a\,b^2\,{\left(a+\frac{b}{x}\right)}^{3/2}}+\frac{c^2\,\mathrm{atanh}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)\,\left(6\,a\,d-5\,b\,c\right)}{a^{7/2}}","Not used",1,"((2*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))/(3*a) + ((a + b/x)^2*(2*a^3*d^3 + 5*b^3*c^3 - 6*a*b^2*c^2*d))/a^3 - (2*(a + b/x)*(4*a^3*d^3 + 5*b^3*c^3 - 6*a*b^2*c^2*d - 3*a^2*b*c*d^2))/(3*a^2))/(b^2*(a + b/x)^(5/2) - a*b^2*(a + b/x)^(3/2)) + (c^2*atanh((a + b/x)^(1/2)/a^(1/2))*(6*a*d - 5*b*c))/a^(7/2)","B"
260,1,144,122,2.219442,"\text{Not used}","int((c + d/x)^2/(a + b/x)^(5/2),x)","\frac{\frac{2\,\left(a+\frac{b}{x}\right)\,\left(a^2\,d^2+4\,a\,b\,c\,d-5\,b^2\,c^2\right)}{3\,a^2}-\frac{2\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}{3\,a}+\frac{b\,{\left(a+\frac{b}{x}\right)}^2\,\left(5\,b\,c^2-4\,a\,c\,d\right)}{a^3}}{b\,{\left(a+\frac{b}{x}\right)}^{5/2}-a\,b\,{\left(a+\frac{b}{x}\right)}^{3/2}}+\frac{c\,\mathrm{atanh}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)\,\left(4\,a\,d-5\,b\,c\right)}{a^{7/2}}","Not used",1,"((2*(a + b/x)*(a^2*d^2 - 5*b^2*c^2 + 4*a*b*c*d))/(3*a^2) - (2*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/(3*a) + (b*(a + b/x)^2*(5*b*c^2 - 4*a*c*d))/a^3)/(b*(a + b/x)^(5/2) - a*b*(a + b/x)^(3/2)) + (c*atanh((a + b/x)^(1/2)/a^(1/2))*(4*a*d - 5*b*c))/a^(7/2)","B"
261,1,87,103,2.910028,"\text{Not used}","int((c + d/x)/(a + b/x)^(5/2),x)","\frac{2\,d\,\mathrm{atanh}\left(\frac{\sqrt{a+\frac{b}{x}}}{\sqrt{a}}\right)}{a^{5/2}}-\frac{\frac{2\,d}{3\,a}+\frac{2\,d\,\left(a+\frac{b}{x}\right)}{a^2}}{{\left(a+\frac{b}{x}\right)}^{3/2}}+\frac{2\,c\,x\,{\left(\frac{a\,x}{b}+1\right)}^{5/2}\,{{}}_2{\mathrm{F}}_1\left(\frac{5}{2},\frac{7}{2};\ \frac{9}{2};\ -\frac{a\,x}{b}\right)}{7\,{\left(a+\frac{b}{x}\right)}^{5/2}}","Not used",1,"(2*d*atanh((a + b/x)^(1/2)/a^(1/2)))/a^(5/2) - ((2*d)/(3*a) + (2*d*(a + b/x))/a^2)/(a + b/x)^(3/2) + (2*c*x*((a*x)/b + 1)^(5/2)*hypergeom([5/2, 7/2], 9/2, -(a*x)/b))/(7*(a + b/x)^(5/2))","B"
262,1,34,79,1.721817,"\text{Not used}","int(1/(a + b/x)^(5/2),x)","\frac{2\,x\,{\left(\frac{a\,x}{b}+1\right)}^{5/2}\,{{}}_2{\mathrm{F}}_1\left(\frac{5}{2},\frac{7}{2};\ \frac{9}{2};\ -\frac{a\,x}{b}\right)}{7\,{\left(a+\frac{b}{x}\right)}^{5/2}}","Not used",1,"(2*x*((a*x)/b + 1)^(5/2)*hypergeom([5/2, 7/2], 9/2, -(a*x)/b))/(7*(a + b/x)^(5/2))","B"
263,1,5387,201,4.622138,"\text{Not used}","int(1/((a + b/x)^(5/2)*(c + d/x)),x)","-\frac{\frac{2\,b^2}{3\,\left(a^2\,d-a\,b\,c\right)}+\frac{2\,b^2\,\left(a+\frac{b}{x}\right)\,\left(8\,a\,d-5\,b\,c\right)}{3\,{\left(a^2\,d-a\,b\,c\right)}^2}+\frac{b\,{\left(a+\frac{b}{x}\right)}^2\,\left(a^2\,d^2-8\,a\,b\,c\,d+5\,b^2\,c^2\right)}{a^2\,c\,\left(a^2\,d-a\,b\,c\right)\,\left(a\,d-b\,c\right)}}{a\,{\left(a+\frac{b}{x}\right)}^{3/2}-{\left(a+\frac{b}{x}\right)}^{5/2}}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\sqrt{a+\frac{b}{x}}\,\left(16\,a^{21}\,b^2\,c^3\,d^{15}-88\,a^{20}\,b^3\,c^4\,d^{14}+130\,a^{19}\,b^4\,c^5\,d^{13}+180\,a^{18}\,b^5\,c^6\,d^{12}-750\,a^{17}\,b^6\,c^7\,d^{11}+336\,a^{16}\,b^7\,c^8\,d^{10}+2108\,a^{15}\,b^8\,c^9\,d^9-5160\,a^{14}\,b^9\,c^{10}\,d^8+6060\,a^{13}\,b^{10}\,c^{11}\,d^7-4280\,a^{12}\,b^{11}\,c^{12}\,d^6+1858\,a^{11}\,b^{12}\,c^{13}\,d^5-460\,a^{10}\,b^{13}\,c^{14}\,d^4+50\,a^9\,b^{14}\,c^{15}\,d^3\right)-\frac{\left(2\,a\,d+5\,b\,c\right)\,\left(20\,a^{12}\,b^{14}\,c^{17}\,d^2-212\,a^{13}\,b^{13}\,c^{16}\,d^3+1012\,a^{14}\,b^{12}\,c^{15}\,d^4-2860\,a^{15}\,b^{11}\,c^{14}\,d^5+5288\,a^{16}\,b^{10}\,c^{13}\,d^6-6664\,a^{17}\,b^9\,c^{12}\,d^7+5768\,a^{18}\,b^8\,c^{11}\,d^8-3352\,a^{19}\,b^7\,c^{10}\,d^9+1220\,a^{20}\,b^6\,c^9\,d^{10}-228\,a^{21}\,b^5\,c^8\,d^{11}+4\,a^{22}\,b^4\,c^7\,d^{12}+4\,a^{23}\,b^3\,c^6\,d^{13}-\frac{\sqrt{a+\frac{b}{x}}\,\left(2\,a\,d+5\,b\,c\right)\,\left(-16\,a^{26}\,b^2\,c^7\,d^{13}+168\,a^{25}\,b^3\,c^8\,d^{12}-800\,a^{24}\,b^4\,c^9\,d^{11}+2280\,a^{23}\,b^5\,c^{10}\,d^{10}-4320\,a^{22}\,b^6\,c^{11}\,d^9+5712\,a^{21}\,b^7\,c^{12}\,d^8-5376\,a^{20}\,b^8\,c^{13}\,d^7+3600\,a^{19}\,b^9\,c^{14}\,d^6-1680\,a^{18}\,b^{10}\,c^{15}\,d^5+520\,a^{17}\,b^{11}\,c^{16}\,d^4-96\,a^{16}\,b^{12}\,c^{17}\,d^3+8\,a^{15}\,b^{13}\,c^{18}\,d^2\right)}{2\,c^2\,\sqrt{a^7}}\right)}{2\,c^2\,\sqrt{a^7}}\right)\,\left(2\,a\,d+5\,b\,c\right)\,1{}\mathrm{i}}{2\,c^2\,\sqrt{a^7}}+\frac{\left(\sqrt{a+\frac{b}{x}}\,\left(16\,a^{21}\,b^2\,c^3\,d^{15}-88\,a^{20}\,b^3\,c^4\,d^{14}+130\,a^{19}\,b^4\,c^5\,d^{13}+180\,a^{18}\,b^5\,c^6\,d^{12}-750\,a^{17}\,b^6\,c^7\,d^{11}+336\,a^{16}\,b^7\,c^8\,d^{10}+2108\,a^{15}\,b^8\,c^9\,d^9-5160\,a^{14}\,b^9\,c^{10}\,d^8+6060\,a^{13}\,b^{10}\,c^{11}\,d^7-4280\,a^{12}\,b^{11}\,c^{12}\,d^6+1858\,a^{11}\,b^{12}\,c^{13}\,d^5-460\,a^{10}\,b^{13}\,c^{14}\,d^4+50\,a^9\,b^{14}\,c^{15}\,d^3\right)+\frac{\left(2\,a\,d+5\,b\,c\right)\,\left(20\,a^{12}\,b^{14}\,c^{17}\,d^2-212\,a^{13}\,b^{13}\,c^{16}\,d^3+1012\,a^{14}\,b^{12}\,c^{15}\,d^4-2860\,a^{15}\,b^{11}\,c^{14}\,d^5+5288\,a^{16}\,b^{10}\,c^{13}\,d^6-6664\,a^{17}\,b^9\,c^{12}\,d^7+5768\,a^{18}\,b^8\,c^{11}\,d^8-3352\,a^{19}\,b^7\,c^{10}\,d^9+1220\,a^{20}\,b^6\,c^9\,d^{10}-228\,a^{21}\,b^5\,c^8\,d^{11}+4\,a^{22}\,b^4\,c^7\,d^{12}+4\,a^{23}\,b^3\,c^6\,d^{13}+\frac{\sqrt{a+\frac{b}{x}}\,\left(2\,a\,d+5\,b\,c\right)\,\left(-16\,a^{26}\,b^2\,c^7\,d^{13}+168\,a^{25}\,b^3\,c^8\,d^{12}-800\,a^{24}\,b^4\,c^9\,d^{11}+2280\,a^{23}\,b^5\,c^{10}\,d^{10}-4320\,a^{22}\,b^6\,c^{11}\,d^9+5712\,a^{21}\,b^7\,c^{12}\,d^8-5376\,a^{20}\,b^8\,c^{13}\,d^7+3600\,a^{19}\,b^9\,c^{14}\,d^6-1680\,a^{18}\,b^{10}\,c^{15}\,d^5+520\,a^{17}\,b^{11}\,c^{16}\,d^4-96\,a^{16}\,b^{12}\,c^{17}\,d^3+8\,a^{15}\,b^{13}\,c^{18}\,d^2\right)}{2\,c^2\,\sqrt{a^7}}\right)}{2\,c^2\,\sqrt{a^7}}\right)\,\left(2\,a\,d+5\,b\,c\right)\,1{}\mathrm{i}}{2\,c^2\,\sqrt{a^7}}}{100\,a^9\,b^{12}\,c^{11}\,d^6-720\,a^{10}\,b^{11}\,c^{10}\,d^7+2176\,a^{11}\,b^{10}\,c^9\,d^8-3528\,a^{12}\,b^9\,c^8\,d^9+3192\,a^{13}\,b^8\,c^7\,d^{10}-1400\,a^{14}\,b^7\,c^6\,d^{11}+264\,a^{16}\,b^5\,c^4\,d^{13}-92\,a^{17}\,b^4\,c^3\,d^{14}+8\,a^{18}\,b^3\,c^2\,d^{15}+\frac{\left(\sqrt{a+\frac{b}{x}}\,\left(16\,a^{21}\,b^2\,c^3\,d^{15}-88\,a^{20}\,b^3\,c^4\,d^{14}+130\,a^{19}\,b^4\,c^5\,d^{13}+180\,a^{18}\,b^5\,c^6\,d^{12}-750\,a^{17}\,b^6\,c^7\,d^{11}+336\,a^{16}\,b^7\,c^8\,d^{10}+2108\,a^{15}\,b^8\,c^9\,d^9-5160\,a^{14}\,b^9\,c^{10}\,d^8+6060\,a^{13}\,b^{10}\,c^{11}\,d^7-4280\,a^{12}\,b^{11}\,c^{12}\,d^6+1858\,a^{11}\,b^{12}\,c^{13}\,d^5-460\,a^{10}\,b^{13}\,c^{14}\,d^4+50\,a^9\,b^{14}\,c^{15}\,d^3\right)-\frac{\left(2\,a\,d+5\,b\,c\right)\,\left(20\,a^{12}\,b^{14}\,c^{17}\,d^2-212\,a^{13}\,b^{13}\,c^{16}\,d^3+1012\,a^{14}\,b^{12}\,c^{15}\,d^4-2860\,a^{15}\,b^{11}\,c^{14}\,d^5+5288\,a^{16}\,b^{10}\,c^{13}\,d^6-6664\,a^{17}\,b^9\,c^{12}\,d^7+5768\,a^{18}\,b^8\,c^{11}\,d^8-3352\,a^{19}\,b^7\,c^{10}\,d^9+1220\,a^{20}\,b^6\,c^9\,d^{10}-228\,a^{21}\,b^5\,c^8\,d^{11}+4\,a^{22}\,b^4\,c^7\,d^{12}+4\,a^{23}\,b^3\,c^6\,d^{13}-\frac{\sqrt{a+\frac{b}{x}}\,\left(2\,a\,d+5\,b\,c\right)\,\left(-16\,a^{26}\,b^2\,c^7\,d^{13}+168\,a^{25}\,b^3\,c^8\,d^{12}-800\,a^{24}\,b^4\,c^9\,d^{11}+2280\,a^{23}\,b^5\,c^{10}\,d^{10}-4320\,a^{22}\,b^6\,c^{11}\,d^9+5712\,a^{21}\,b^7\,c^{12}\,d^8-5376\,a^{20}\,b^8\,c^{13}\,d^7+3600\,a^{19}\,b^9\,c^{14}\,d^6-1680\,a^{18}\,b^{10}\,c^{15}\,d^5+520\,a^{17}\,b^{11}\,c^{16}\,d^4-96\,a^{16}\,b^{12}\,c^{17}\,d^3+8\,a^{15}\,b^{13}\,c^{18}\,d^2\right)}{2\,c^2\,\sqrt{a^7}}\right)}{2\,c^2\,\sqrt{a^7}}\right)\,\left(2\,a\,d+5\,b\,c\right)}{2\,c^2\,\sqrt{a^7}}-\frac{\left(\sqrt{a+\frac{b}{x}}\,\left(16\,a^{21}\,b^2\,c^3\,d^{15}-88\,a^{20}\,b^3\,c^4\,d^{14}+130\,a^{19}\,b^4\,c^5\,d^{13}+180\,a^{18}\,b^5\,c^6\,d^{12}-750\,a^{17}\,b^6\,c^7\,d^{11}+336\,a^{16}\,b^7\,c^8\,d^{10}+2108\,a^{15}\,b^8\,c^9\,d^9-5160\,a^{14}\,b^9\,c^{10}\,d^8+6060\,a^{13}\,b^{10}\,c^{11}\,d^7-4280\,a^{12}\,b^{11}\,c^{12}\,d^6+1858\,a^{11}\,b^{12}\,c^{13}\,d^5-460\,a^{10}\,b^{13}\,c^{14}\,d^4+50\,a^9\,b^{14}\,c^{15}\,d^3\right)+\frac{\left(2\,a\,d+5\,b\,c\right)\,\left(20\,a^{12}\,b^{14}\,c^{17}\,d^2-212\,a^{13}\,b^{13}\,c^{16}\,d^3+1012\,a^{14}\,b^{12}\,c^{15}\,d^4-2860\,a^{15}\,b^{11}\,c^{14}\,d^5+5288\,a^{16}\,b^{10}\,c^{13}\,d^6-6664\,a^{17}\,b^9\,c^{12}\,d^7+5768\,a^{18}\,b^8\,c^{11}\,d^8-3352\,a^{19}\,b^7\,c^{10}\,d^9+1220\,a^{20}\,b^6\,c^9\,d^{10}-228\,a^{21}\,b^5\,c^8\,d^{11}+4\,a^{22}\,b^4\,c^7\,d^{12}+4\,a^{23}\,b^3\,c^6\,d^{13}+\frac{\sqrt{a+\frac{b}{x}}\,\left(2\,a\,d+5\,b\,c\right)\,\left(-16\,a^{26}\,b^2\,c^7\,d^{13}+168\,a^{25}\,b^3\,c^8\,d^{12}-800\,a^{24}\,b^4\,c^9\,d^{11}+2280\,a^{23}\,b^5\,c^{10}\,d^{10}-4320\,a^{22}\,b^6\,c^{11}\,d^9+5712\,a^{21}\,b^7\,c^{12}\,d^8-5376\,a^{20}\,b^8\,c^{13}\,d^7+3600\,a^{19}\,b^9\,c^{14}\,d^6-1680\,a^{18}\,b^{10}\,c^{15}\,d^5+520\,a^{17}\,b^{11}\,c^{16}\,d^4-96\,a^{16}\,b^{12}\,c^{17}\,d^3+8\,a^{15}\,b^{13}\,c^{18}\,d^2\right)}{2\,c^2\,\sqrt{a^7}}\right)}{2\,c^2\,\sqrt{a^7}}\right)\,\left(2\,a\,d+5\,b\,c\right)}{2\,c^2\,\sqrt{a^7}}}\right)\,\left(2\,a\,d+5\,b\,c\right)\,1{}\mathrm{i}}{c^2\,\sqrt{a^7}}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{d^7\,{\left(a\,d-b\,c\right)}^5}\,\left(\sqrt{a+\frac{b}{x}}\,\left(16\,a^{21}\,b^2\,c^3\,d^{15}-88\,a^{20}\,b^3\,c^4\,d^{14}+130\,a^{19}\,b^4\,c^5\,d^{13}+180\,a^{18}\,b^5\,c^6\,d^{12}-750\,a^{17}\,b^6\,c^7\,d^{11}+336\,a^{16}\,b^7\,c^8\,d^{10}+2108\,a^{15}\,b^8\,c^9\,d^9-5160\,a^{14}\,b^9\,c^{10}\,d^8+6060\,a^{13}\,b^{10}\,c^{11}\,d^7-4280\,a^{12}\,b^{11}\,c^{12}\,d^6+1858\,a^{11}\,b^{12}\,c^{13}\,d^5-460\,a^{10}\,b^{13}\,c^{14}\,d^4+50\,a^9\,b^{14}\,c^{15}\,d^3\right)+\frac{\sqrt{d^7\,{\left(a\,d-b\,c\right)}^5}\,\left(20\,a^{12}\,b^{14}\,c^{17}\,d^2-212\,a^{13}\,b^{13}\,c^{16}\,d^3+1012\,a^{14}\,b^{12}\,c^{15}\,d^4-2860\,a^{15}\,b^{11}\,c^{14}\,d^5+5288\,a^{16}\,b^{10}\,c^{13}\,d^6-6664\,a^{17}\,b^9\,c^{12}\,d^7+5768\,a^{18}\,b^8\,c^{11}\,d^8-3352\,a^{19}\,b^7\,c^{10}\,d^9+1220\,a^{20}\,b^6\,c^9\,d^{10}-228\,a^{21}\,b^5\,c^8\,d^{11}+4\,a^{22}\,b^4\,c^7\,d^{12}+4\,a^{23}\,b^3\,c^6\,d^{13}+\frac{\sqrt{d^7\,{\left(a\,d-b\,c\right)}^5}\,\sqrt{a+\frac{b}{x}}\,\left(-16\,a^{26}\,b^2\,c^7\,d^{13}+168\,a^{25}\,b^3\,c^8\,d^{12}-800\,a^{24}\,b^4\,c^9\,d^{11}+2280\,a^{23}\,b^5\,c^{10}\,d^{10}-4320\,a^{22}\,b^6\,c^{11}\,d^9+5712\,a^{21}\,b^7\,c^{12}\,d^8-5376\,a^{20}\,b^8\,c^{13}\,d^7+3600\,a^{19}\,b^9\,c^{14}\,d^6-1680\,a^{18}\,b^{10}\,c^{15}\,d^5+520\,a^{17}\,b^{11}\,c^{16}\,d^4-96\,a^{16}\,b^{12}\,c^{17}\,d^3+8\,a^{15}\,b^{13}\,c^{18}\,d^2\right)}{c^2\,{\left(a\,d-b\,c\right)}^5}\right)}{c^2\,{\left(a\,d-b\,c\right)}^5}\right)\,1{}\mathrm{i}}{c^2\,{\left(a\,d-b\,c\right)}^5}+\frac{\sqrt{d^7\,{\left(a\,d-b\,c\right)}^5}\,\left(\sqrt{a+\frac{b}{x}}\,\left(16\,a^{21}\,b^2\,c^3\,d^{15}-88\,a^{20}\,b^3\,c^4\,d^{14}+130\,a^{19}\,b^4\,c^5\,d^{13}+180\,a^{18}\,b^5\,c^6\,d^{12}-750\,a^{17}\,b^6\,c^7\,d^{11}+336\,a^{16}\,b^7\,c^8\,d^{10}+2108\,a^{15}\,b^8\,c^9\,d^9-5160\,a^{14}\,b^9\,c^{10}\,d^8+6060\,a^{13}\,b^{10}\,c^{11}\,d^7-4280\,a^{12}\,b^{11}\,c^{12}\,d^6+1858\,a^{11}\,b^{12}\,c^{13}\,d^5-460\,a^{10}\,b^{13}\,c^{14}\,d^4+50\,a^9\,b^{14}\,c^{15}\,d^3\right)-\frac{\sqrt{d^7\,{\left(a\,d-b\,c\right)}^5}\,\left(20\,a^{12}\,b^{14}\,c^{17}\,d^2-212\,a^{13}\,b^{13}\,c^{16}\,d^3+1012\,a^{14}\,b^{12}\,c^{15}\,d^4-2860\,a^{15}\,b^{11}\,c^{14}\,d^5+5288\,a^{16}\,b^{10}\,c^{13}\,d^6-6664\,a^{17}\,b^9\,c^{12}\,d^7+5768\,a^{18}\,b^8\,c^{11}\,d^8-3352\,a^{19}\,b^7\,c^{10}\,d^9+1220\,a^{20}\,b^6\,c^9\,d^{10}-228\,a^{21}\,b^5\,c^8\,d^{11}+4\,a^{22}\,b^4\,c^7\,d^{12}+4\,a^{23}\,b^3\,c^6\,d^{13}-\frac{\sqrt{d^7\,{\left(a\,d-b\,c\right)}^5}\,\sqrt{a+\frac{b}{x}}\,\left(-16\,a^{26}\,b^2\,c^7\,d^{13}+168\,a^{25}\,b^3\,c^8\,d^{12}-800\,a^{24}\,b^4\,c^9\,d^{11}+2280\,a^{23}\,b^5\,c^{10}\,d^{10}-4320\,a^{22}\,b^6\,c^{11}\,d^9+5712\,a^{21}\,b^7\,c^{12}\,d^8-5376\,a^{20}\,b^8\,c^{13}\,d^7+3600\,a^{19}\,b^9\,c^{14}\,d^6-1680\,a^{18}\,b^{10}\,c^{15}\,d^5+520\,a^{17}\,b^{11}\,c^{16}\,d^4-96\,a^{16}\,b^{12}\,c^{17}\,d^3+8\,a^{15}\,b^{13}\,c^{18}\,d^2\right)}{c^2\,{\left(a\,d-b\,c\right)}^5}\right)}{c^2\,{\left(a\,d-b\,c\right)}^5}\right)\,1{}\mathrm{i}}{c^2\,{\left(a\,d-b\,c\right)}^5}}{\frac{\sqrt{d^7\,{\left(a\,d-b\,c\right)}^5}\,\left(\sqrt{a+\frac{b}{x}}\,\left(16\,a^{21}\,b^2\,c^3\,d^{15}-88\,a^{20}\,b^3\,c^4\,d^{14}+130\,a^{19}\,b^4\,c^5\,d^{13}+180\,a^{18}\,b^5\,c^6\,d^{12}-750\,a^{17}\,b^6\,c^7\,d^{11}+336\,a^{16}\,b^7\,c^8\,d^{10}+2108\,a^{15}\,b^8\,c^9\,d^9-5160\,a^{14}\,b^9\,c^{10}\,d^8+6060\,a^{13}\,b^{10}\,c^{11}\,d^7-4280\,a^{12}\,b^{11}\,c^{12}\,d^6+1858\,a^{11}\,b^{12}\,c^{13}\,d^5-460\,a^{10}\,b^{13}\,c^{14}\,d^4+50\,a^9\,b^{14}\,c^{15}\,d^3\right)-\frac{\sqrt{d^7\,{\left(a\,d-b\,c\right)}^5}\,\left(20\,a^{12}\,b^{14}\,c^{17}\,d^2-212\,a^{13}\,b^{13}\,c^{16}\,d^3+1012\,a^{14}\,b^{12}\,c^{15}\,d^4-2860\,a^{15}\,b^{11}\,c^{14}\,d^5+5288\,a^{16}\,b^{10}\,c^{13}\,d^6-6664\,a^{17}\,b^9\,c^{12}\,d^7+5768\,a^{18}\,b^8\,c^{11}\,d^8-3352\,a^{19}\,b^7\,c^{10}\,d^9+1220\,a^{20}\,b^6\,c^9\,d^{10}-228\,a^{21}\,b^5\,c^8\,d^{11}+4\,a^{22}\,b^4\,c^7\,d^{12}+4\,a^{23}\,b^3\,c^6\,d^{13}-\frac{\sqrt{d^7\,{\left(a\,d-b\,c\right)}^5}\,\sqrt{a+\frac{b}{x}}\,\left(-16\,a^{26}\,b^2\,c^7\,d^{13}+168\,a^{25}\,b^3\,c^8\,d^{12}-800\,a^{24}\,b^4\,c^9\,d^{11}+2280\,a^{23}\,b^5\,c^{10}\,d^{10}-4320\,a^{22}\,b^6\,c^{11}\,d^9+5712\,a^{21}\,b^7\,c^{12}\,d^8-5376\,a^{20}\,b^8\,c^{13}\,d^7+3600\,a^{19}\,b^9\,c^{14}\,d^6-1680\,a^{18}\,b^{10}\,c^{15}\,d^5+520\,a^{17}\,b^{11}\,c^{16}\,d^4-96\,a^{16}\,b^{12}\,c^{17}\,d^3+8\,a^{15}\,b^{13}\,c^{18}\,d^2\right)}{c^2\,{\left(a\,d-b\,c\right)}^5}\right)}{c^2\,{\left(a\,d-b\,c\right)}^5}\right)}{c^2\,{\left(a\,d-b\,c\right)}^5}-\frac{\sqrt{d^7\,{\left(a\,d-b\,c\right)}^5}\,\left(\sqrt{a+\frac{b}{x}}\,\left(16\,a^{21}\,b^2\,c^3\,d^{15}-88\,a^{20}\,b^3\,c^4\,d^{14}+130\,a^{19}\,b^4\,c^5\,d^{13}+180\,a^{18}\,b^5\,c^6\,d^{12}-750\,a^{17}\,b^6\,c^7\,d^{11}+336\,a^{16}\,b^7\,c^8\,d^{10}+2108\,a^{15}\,b^8\,c^9\,d^9-5160\,a^{14}\,b^9\,c^{10}\,d^8+6060\,a^{13}\,b^{10}\,c^{11}\,d^7-4280\,a^{12}\,b^{11}\,c^{12}\,d^6+1858\,a^{11}\,b^{12}\,c^{13}\,d^5-460\,a^{10}\,b^{13}\,c^{14}\,d^4+50\,a^9\,b^{14}\,c^{15}\,d^3\right)+\frac{\sqrt{d^7\,{\left(a\,d-b\,c\right)}^5}\,\left(20\,a^{12}\,b^{14}\,c^{17}\,d^2-212\,a^{13}\,b^{13}\,c^{16}\,d^3+1012\,a^{14}\,b^{12}\,c^{15}\,d^4-2860\,a^{15}\,b^{11}\,c^{14}\,d^5+5288\,a^{16}\,b^{10}\,c^{13}\,d^6-6664\,a^{17}\,b^9\,c^{12}\,d^7+5768\,a^{18}\,b^8\,c^{11}\,d^8-3352\,a^{19}\,b^7\,c^{10}\,d^9+1220\,a^{20}\,b^6\,c^9\,d^{10}-228\,a^{21}\,b^5\,c^8\,d^{11}+4\,a^{22}\,b^4\,c^7\,d^{12}+4\,a^{23}\,b^3\,c^6\,d^{13}+\frac{\sqrt{d^7\,{\left(a\,d-b\,c\right)}^5}\,\sqrt{a+\frac{b}{x}}\,\left(-16\,a^{26}\,b^2\,c^7\,d^{13}+168\,a^{25}\,b^3\,c^8\,d^{12}-800\,a^{24}\,b^4\,c^9\,d^{11}+2280\,a^{23}\,b^5\,c^{10}\,d^{10}-4320\,a^{22}\,b^6\,c^{11}\,d^9+5712\,a^{21}\,b^7\,c^{12}\,d^8-5376\,a^{20}\,b^8\,c^{13}\,d^7+3600\,a^{19}\,b^9\,c^{14}\,d^6-1680\,a^{18}\,b^{10}\,c^{15}\,d^5+520\,a^{17}\,b^{11}\,c^{16}\,d^4-96\,a^{16}\,b^{12}\,c^{17}\,d^3+8\,a^{15}\,b^{13}\,c^{18}\,d^2\right)}{c^2\,{\left(a\,d-b\,c\right)}^5}\right)}{c^2\,{\left(a\,d-b\,c\right)}^5}\right)}{c^2\,{\left(a\,d-b\,c\right)}^5}+100\,a^9\,b^{12}\,c^{11}\,d^6-720\,a^{10}\,b^{11}\,c^{10}\,d^7+2176\,a^{11}\,b^{10}\,c^9\,d^8-3528\,a^{12}\,b^9\,c^8\,d^9+3192\,a^{13}\,b^8\,c^7\,d^{10}-1400\,a^{14}\,b^7\,c^6\,d^{11}+264\,a^{16}\,b^5\,c^4\,d^{13}-92\,a^{17}\,b^4\,c^3\,d^{14}+8\,a^{18}\,b^3\,c^2\,d^{15}}\right)\,\sqrt{d^7\,{\left(a\,d-b\,c\right)}^5}\,2{}\mathrm{i}}{c^2\,{\left(a\,d-b\,c\right)}^5}","Not used",1,"- ((2*b^2)/(3*(a^2*d - a*b*c)) + (2*b^2*(a + b/x)*(8*a*d - 5*b*c))/(3*(a^2*d - a*b*c)^2) + (b*(a + b/x)^2*(a^2*d^2 + 5*b^2*c^2 - 8*a*b*c*d))/(a^2*c*(a^2*d - a*b*c)*(a*d - b*c)))/(a*(a + b/x)^(3/2) - (a + b/x)^(5/2)) - (atan(((((a + b/x)^(1/2)*(50*a^9*b^14*c^15*d^3 - 460*a^10*b^13*c^14*d^4 + 1858*a^11*b^12*c^13*d^5 - 4280*a^12*b^11*c^12*d^6 + 6060*a^13*b^10*c^11*d^7 - 5160*a^14*b^9*c^10*d^8 + 2108*a^15*b^8*c^9*d^9 + 336*a^16*b^7*c^8*d^10 - 750*a^17*b^6*c^7*d^11 + 180*a^18*b^5*c^6*d^12 + 130*a^19*b^4*c^5*d^13 - 88*a^20*b^3*c^4*d^14 + 16*a^21*b^2*c^3*d^15) - ((2*a*d + 5*b*c)*(20*a^12*b^14*c^17*d^2 - 212*a^13*b^13*c^16*d^3 + 1012*a^14*b^12*c^15*d^4 - 2860*a^15*b^11*c^14*d^5 + 5288*a^16*b^10*c^13*d^6 - 6664*a^17*b^9*c^12*d^7 + 5768*a^18*b^8*c^11*d^8 - 3352*a^19*b^7*c^10*d^9 + 1220*a^20*b^6*c^9*d^10 - 228*a^21*b^5*c^8*d^11 + 4*a^22*b^4*c^7*d^12 + 4*a^23*b^3*c^6*d^13 - ((a + b/x)^(1/2)*(2*a*d + 5*b*c)*(8*a^15*b^13*c^18*d^2 - 96*a^16*b^12*c^17*d^3 + 520*a^17*b^11*c^16*d^4 - 1680*a^18*b^10*c^15*d^5 + 3600*a^19*b^9*c^14*d^6 - 5376*a^20*b^8*c^13*d^7 + 5712*a^21*b^7*c^12*d^8 - 4320*a^22*b^6*c^11*d^9 + 2280*a^23*b^5*c^10*d^10 - 800*a^24*b^4*c^9*d^11 + 168*a^25*b^3*c^8*d^12 - 16*a^26*b^2*c^7*d^13))/(2*c^2*(a^7)^(1/2))))/(2*c^2*(a^7)^(1/2)))*(2*a*d + 5*b*c)*1i)/(2*c^2*(a^7)^(1/2)) + (((a + b/x)^(1/2)*(50*a^9*b^14*c^15*d^3 - 460*a^10*b^13*c^14*d^4 + 1858*a^11*b^12*c^13*d^5 - 4280*a^12*b^11*c^12*d^6 + 6060*a^13*b^10*c^11*d^7 - 5160*a^14*b^9*c^10*d^8 + 2108*a^15*b^8*c^9*d^9 + 336*a^16*b^7*c^8*d^10 - 750*a^17*b^6*c^7*d^11 + 180*a^18*b^5*c^6*d^12 + 130*a^19*b^4*c^5*d^13 - 88*a^20*b^3*c^4*d^14 + 16*a^21*b^2*c^3*d^15) + ((2*a*d + 5*b*c)*(20*a^12*b^14*c^17*d^2 - 212*a^13*b^13*c^16*d^3 + 1012*a^14*b^12*c^15*d^4 - 2860*a^15*b^11*c^14*d^5 + 5288*a^16*b^10*c^13*d^6 - 6664*a^17*b^9*c^12*d^7 + 5768*a^18*b^8*c^11*d^8 - 3352*a^19*b^7*c^10*d^9 + 1220*a^20*b^6*c^9*d^10 - 228*a^21*b^5*c^8*d^11 + 4*a^22*b^4*c^7*d^12 + 4*a^23*b^3*c^6*d^13 + ((a + b/x)^(1/2)*(2*a*d + 5*b*c)*(8*a^15*b^13*c^18*d^2 - 96*a^16*b^12*c^17*d^3 + 520*a^17*b^11*c^16*d^4 - 1680*a^18*b^10*c^15*d^5 + 3600*a^19*b^9*c^14*d^6 - 5376*a^20*b^8*c^13*d^7 + 5712*a^21*b^7*c^12*d^8 - 4320*a^22*b^6*c^11*d^9 + 2280*a^23*b^5*c^10*d^10 - 800*a^24*b^4*c^9*d^11 + 168*a^25*b^3*c^8*d^12 - 16*a^26*b^2*c^7*d^13))/(2*c^2*(a^7)^(1/2))))/(2*c^2*(a^7)^(1/2)))*(2*a*d + 5*b*c)*1i)/(2*c^2*(a^7)^(1/2)))/(100*a^9*b^12*c^11*d^6 - 720*a^10*b^11*c^10*d^7 + 2176*a^11*b^10*c^9*d^8 - 3528*a^12*b^9*c^8*d^9 + 3192*a^13*b^8*c^7*d^10 - 1400*a^14*b^7*c^6*d^11 + 264*a^16*b^5*c^4*d^13 - 92*a^17*b^4*c^3*d^14 + 8*a^18*b^3*c^2*d^15 + (((a + b/x)^(1/2)*(50*a^9*b^14*c^15*d^3 - 460*a^10*b^13*c^14*d^4 + 1858*a^11*b^12*c^13*d^5 - 4280*a^12*b^11*c^12*d^6 + 6060*a^13*b^10*c^11*d^7 - 5160*a^14*b^9*c^10*d^8 + 2108*a^15*b^8*c^9*d^9 + 336*a^16*b^7*c^8*d^10 - 750*a^17*b^6*c^7*d^11 + 180*a^18*b^5*c^6*d^12 + 130*a^19*b^4*c^5*d^13 - 88*a^20*b^3*c^4*d^14 + 16*a^21*b^2*c^3*d^15) - ((2*a*d + 5*b*c)*(20*a^12*b^14*c^17*d^2 - 212*a^13*b^13*c^16*d^3 + 1012*a^14*b^12*c^15*d^4 - 2860*a^15*b^11*c^14*d^5 + 5288*a^16*b^10*c^13*d^6 - 6664*a^17*b^9*c^12*d^7 + 5768*a^18*b^8*c^11*d^8 - 3352*a^19*b^7*c^10*d^9 + 1220*a^20*b^6*c^9*d^10 - 228*a^21*b^5*c^8*d^11 + 4*a^22*b^4*c^7*d^12 + 4*a^23*b^3*c^6*d^13 - ((a + b/x)^(1/2)*(2*a*d + 5*b*c)*(8*a^15*b^13*c^18*d^2 - 96*a^16*b^12*c^17*d^3 + 520*a^17*b^11*c^16*d^4 - 1680*a^18*b^10*c^15*d^5 + 3600*a^19*b^9*c^14*d^6 - 5376*a^20*b^8*c^13*d^7 + 5712*a^21*b^7*c^12*d^8 - 4320*a^22*b^6*c^11*d^9 + 2280*a^23*b^5*c^10*d^10 - 800*a^24*b^4*c^9*d^11 + 168*a^25*b^3*c^8*d^12 - 16*a^26*b^2*c^7*d^13))/(2*c^2*(a^7)^(1/2))))/(2*c^2*(a^7)^(1/2)))*(2*a*d + 5*b*c))/(2*c^2*(a^7)^(1/2)) - (((a + b/x)^(1/2)*(50*a^9*b^14*c^15*d^3 - 460*a^10*b^13*c^14*d^4 + 1858*a^11*b^12*c^13*d^5 - 4280*a^12*b^11*c^12*d^6 + 6060*a^13*b^10*c^11*d^7 - 5160*a^14*b^9*c^10*d^8 + 2108*a^15*b^8*c^9*d^9 + 336*a^16*b^7*c^8*d^10 - 750*a^17*b^6*c^7*d^11 + 180*a^18*b^5*c^6*d^12 + 130*a^19*b^4*c^5*d^13 - 88*a^20*b^3*c^4*d^14 + 16*a^21*b^2*c^3*d^15) + ((2*a*d + 5*b*c)*(20*a^12*b^14*c^17*d^2 - 212*a^13*b^13*c^16*d^3 + 1012*a^14*b^12*c^15*d^4 - 2860*a^15*b^11*c^14*d^5 + 5288*a^16*b^10*c^13*d^6 - 6664*a^17*b^9*c^12*d^7 + 5768*a^18*b^8*c^11*d^8 - 3352*a^19*b^7*c^10*d^9 + 1220*a^20*b^6*c^9*d^10 - 228*a^21*b^5*c^8*d^11 + 4*a^22*b^4*c^7*d^12 + 4*a^23*b^3*c^6*d^13 + ((a + b/x)^(1/2)*(2*a*d + 5*b*c)*(8*a^15*b^13*c^18*d^2 - 96*a^16*b^12*c^17*d^3 + 520*a^17*b^11*c^16*d^4 - 1680*a^18*b^10*c^15*d^5 + 3600*a^19*b^9*c^14*d^6 - 5376*a^20*b^8*c^13*d^7 + 5712*a^21*b^7*c^12*d^8 - 4320*a^22*b^6*c^11*d^9 + 2280*a^23*b^5*c^10*d^10 - 800*a^24*b^4*c^9*d^11 + 168*a^25*b^3*c^8*d^12 - 16*a^26*b^2*c^7*d^13))/(2*c^2*(a^7)^(1/2))))/(2*c^2*(a^7)^(1/2)))*(2*a*d + 5*b*c))/(2*c^2*(a^7)^(1/2))))*(2*a*d + 5*b*c)*1i)/(c^2*(a^7)^(1/2)) - (atan((((d^7*(a*d - b*c)^5)^(1/2)*((a + b/x)^(1/2)*(50*a^9*b^14*c^15*d^3 - 460*a^10*b^13*c^14*d^4 + 1858*a^11*b^12*c^13*d^5 - 4280*a^12*b^11*c^12*d^6 + 6060*a^13*b^10*c^11*d^7 - 5160*a^14*b^9*c^10*d^8 + 2108*a^15*b^8*c^9*d^9 + 336*a^16*b^7*c^8*d^10 - 750*a^17*b^6*c^7*d^11 + 180*a^18*b^5*c^6*d^12 + 130*a^19*b^4*c^5*d^13 - 88*a^20*b^3*c^4*d^14 + 16*a^21*b^2*c^3*d^15) + ((d^7*(a*d - b*c)^5)^(1/2)*(20*a^12*b^14*c^17*d^2 - 212*a^13*b^13*c^16*d^3 + 1012*a^14*b^12*c^15*d^4 - 2860*a^15*b^11*c^14*d^5 + 5288*a^16*b^10*c^13*d^6 - 6664*a^17*b^9*c^12*d^7 + 5768*a^18*b^8*c^11*d^8 - 3352*a^19*b^7*c^10*d^9 + 1220*a^20*b^6*c^9*d^10 - 228*a^21*b^5*c^8*d^11 + 4*a^22*b^4*c^7*d^12 + 4*a^23*b^3*c^6*d^13 + ((d^7*(a*d - b*c)^5)^(1/2)*(a + b/x)^(1/2)*(8*a^15*b^13*c^18*d^2 - 96*a^16*b^12*c^17*d^3 + 520*a^17*b^11*c^16*d^4 - 1680*a^18*b^10*c^15*d^5 + 3600*a^19*b^9*c^14*d^6 - 5376*a^20*b^8*c^13*d^7 + 5712*a^21*b^7*c^12*d^8 - 4320*a^22*b^6*c^11*d^9 + 2280*a^23*b^5*c^10*d^10 - 800*a^24*b^4*c^9*d^11 + 168*a^25*b^3*c^8*d^12 - 16*a^26*b^2*c^7*d^13))/(c^2*(a*d - b*c)^5)))/(c^2*(a*d - b*c)^5))*1i)/(c^2*(a*d - b*c)^5) + ((d^7*(a*d - b*c)^5)^(1/2)*((a + b/x)^(1/2)*(50*a^9*b^14*c^15*d^3 - 460*a^10*b^13*c^14*d^4 + 1858*a^11*b^12*c^13*d^5 - 4280*a^12*b^11*c^12*d^6 + 6060*a^13*b^10*c^11*d^7 - 5160*a^14*b^9*c^10*d^8 + 2108*a^15*b^8*c^9*d^9 + 336*a^16*b^7*c^8*d^10 - 750*a^17*b^6*c^7*d^11 + 180*a^18*b^5*c^6*d^12 + 130*a^19*b^4*c^5*d^13 - 88*a^20*b^3*c^4*d^14 + 16*a^21*b^2*c^3*d^15) - ((d^7*(a*d - b*c)^5)^(1/2)*(20*a^12*b^14*c^17*d^2 - 212*a^13*b^13*c^16*d^3 + 1012*a^14*b^12*c^15*d^4 - 2860*a^15*b^11*c^14*d^5 + 5288*a^16*b^10*c^13*d^6 - 6664*a^17*b^9*c^12*d^7 + 5768*a^18*b^8*c^11*d^8 - 3352*a^19*b^7*c^10*d^9 + 1220*a^20*b^6*c^9*d^10 - 228*a^21*b^5*c^8*d^11 + 4*a^22*b^4*c^7*d^12 + 4*a^23*b^3*c^6*d^13 - ((d^7*(a*d - b*c)^5)^(1/2)*(a + b/x)^(1/2)*(8*a^15*b^13*c^18*d^2 - 96*a^16*b^12*c^17*d^3 + 520*a^17*b^11*c^16*d^4 - 1680*a^18*b^10*c^15*d^5 + 3600*a^19*b^9*c^14*d^6 - 5376*a^20*b^8*c^13*d^7 + 5712*a^21*b^7*c^12*d^8 - 4320*a^22*b^6*c^11*d^9 + 2280*a^23*b^5*c^10*d^10 - 800*a^24*b^4*c^9*d^11 + 168*a^25*b^3*c^8*d^12 - 16*a^26*b^2*c^7*d^13))/(c^2*(a*d - b*c)^5)))/(c^2*(a*d - b*c)^5))*1i)/(c^2*(a*d - b*c)^5))/(((d^7*(a*d - b*c)^5)^(1/2)*((a + b/x)^(1/2)*(50*a^9*b^14*c^15*d^3 - 460*a^10*b^13*c^14*d^4 + 1858*a^11*b^12*c^13*d^5 - 4280*a^12*b^11*c^12*d^6 + 6060*a^13*b^10*c^11*d^7 - 5160*a^14*b^9*c^10*d^8 + 2108*a^15*b^8*c^9*d^9 + 336*a^16*b^7*c^8*d^10 - 750*a^17*b^6*c^7*d^11 + 180*a^18*b^5*c^6*d^12 + 130*a^19*b^4*c^5*d^13 - 88*a^20*b^3*c^4*d^14 + 16*a^21*b^2*c^3*d^15) - ((d^7*(a*d - b*c)^5)^(1/2)*(20*a^12*b^14*c^17*d^2 - 212*a^13*b^13*c^16*d^3 + 1012*a^14*b^12*c^15*d^4 - 2860*a^15*b^11*c^14*d^5 + 5288*a^16*b^10*c^13*d^6 - 6664*a^17*b^9*c^12*d^7 + 5768*a^18*b^8*c^11*d^8 - 3352*a^19*b^7*c^10*d^9 + 1220*a^20*b^6*c^9*d^10 - 228*a^21*b^5*c^8*d^11 + 4*a^22*b^4*c^7*d^12 + 4*a^23*b^3*c^6*d^13 - ((d^7*(a*d - b*c)^5)^(1/2)*(a + b/x)^(1/2)*(8*a^15*b^13*c^18*d^2 - 96*a^16*b^12*c^17*d^3 + 520*a^17*b^11*c^16*d^4 - 1680*a^18*b^10*c^15*d^5 + 3600*a^19*b^9*c^14*d^6 - 5376*a^20*b^8*c^13*d^7 + 5712*a^21*b^7*c^12*d^8 - 4320*a^22*b^6*c^11*d^9 + 2280*a^23*b^5*c^10*d^10 - 800*a^24*b^4*c^9*d^11 + 168*a^25*b^3*c^8*d^12 - 16*a^26*b^2*c^7*d^13))/(c^2*(a*d - b*c)^5)))/(c^2*(a*d - b*c)^5)))/(c^2*(a*d - b*c)^5) - ((d^7*(a*d - b*c)^5)^(1/2)*((a + b/x)^(1/2)*(50*a^9*b^14*c^15*d^3 - 460*a^10*b^13*c^14*d^4 + 1858*a^11*b^12*c^13*d^5 - 4280*a^12*b^11*c^12*d^6 + 6060*a^13*b^10*c^11*d^7 - 5160*a^14*b^9*c^10*d^8 + 2108*a^15*b^8*c^9*d^9 + 336*a^16*b^7*c^8*d^10 - 750*a^17*b^6*c^7*d^11 + 180*a^18*b^5*c^6*d^12 + 130*a^19*b^4*c^5*d^13 - 88*a^20*b^3*c^4*d^14 + 16*a^21*b^2*c^3*d^15) + ((d^7*(a*d - b*c)^5)^(1/2)*(20*a^12*b^14*c^17*d^2 - 212*a^13*b^13*c^16*d^3 + 1012*a^14*b^12*c^15*d^4 - 2860*a^15*b^11*c^14*d^5 + 5288*a^16*b^10*c^13*d^6 - 6664*a^17*b^9*c^12*d^7 + 5768*a^18*b^8*c^11*d^8 - 3352*a^19*b^7*c^10*d^9 + 1220*a^20*b^6*c^9*d^10 - 228*a^21*b^5*c^8*d^11 + 4*a^22*b^4*c^7*d^12 + 4*a^23*b^3*c^6*d^13 + ((d^7*(a*d - b*c)^5)^(1/2)*(a + b/x)^(1/2)*(8*a^15*b^13*c^18*d^2 - 96*a^16*b^12*c^17*d^3 + 520*a^17*b^11*c^16*d^4 - 1680*a^18*b^10*c^15*d^5 + 3600*a^19*b^9*c^14*d^6 - 5376*a^20*b^8*c^13*d^7 + 5712*a^21*b^7*c^12*d^8 - 4320*a^22*b^6*c^11*d^9 + 2280*a^23*b^5*c^10*d^10 - 800*a^24*b^4*c^9*d^11 + 168*a^25*b^3*c^8*d^12 - 16*a^26*b^2*c^7*d^13))/(c^2*(a*d - b*c)^5)))/(c^2*(a*d - b*c)^5)))/(c^2*(a*d - b*c)^5) + 100*a^9*b^12*c^11*d^6 - 720*a^10*b^11*c^10*d^7 + 2176*a^11*b^10*c^9*d^8 - 3528*a^12*b^9*c^8*d^9 + 3192*a^13*b^8*c^7*d^10 - 1400*a^14*b^7*c^6*d^11 + 264*a^16*b^5*c^4*d^13 - 92*a^17*b^4*c^3*d^14 + 8*a^18*b^3*c^2*d^15))*(d^7*(a*d - b*c)^5)^(1/2)*2i)/(c^2*(a*d - b*c)^5)","B"
264,1,5789,287,8.728554,"\text{Not used}","int(1/((a + b/x)^(5/2)*(c + d/x)^2),x)","\frac{\frac{2\,b^3}{3\,\left(a^2\,d-a\,b\,c\right)}+\frac{10\,b^3\,\left(a+\frac{b}{x}\right)\,\left(2\,a\,d-b\,c\right)}{3\,{\left(a^2\,d-a\,b\,c\right)}^2}-\frac{b\,{\left(a+\frac{b}{x}\right)}^2\,\left(6\,a^4\,d^4-12\,a^3\,b\,c\,d^3+64\,a^2\,b^2\,c^2\,d^2-58\,a\,b^3\,c^3\,d+15\,b^4\,c^4\right)}{3\,c^2\,{\left(a^2\,d-a\,b\,c\right)}^3}+\frac{b\,{\left(a+\frac{b}{x}\right)}^3\,\left(2\,a\,d-b\,c\right)\,\left(a^2\,d^3-a\,b\,c\,d^2+5\,b^2\,c^2\,d\right)}{c^2\,{\left(a^2\,d-a\,b\,c\right)}^3}}{d\,{\left(a+\frac{b}{x}\right)}^{7/2}+{\left(a+\frac{b}{x}\right)}^{3/2}\,\left(a^2\,d-a\,b\,c\right)-{\left(a+\frac{b}{x}\right)}^{5/2}\,\left(2\,a\,d-b\,c\right)}+\frac{\mathrm{atan}\left(\frac{a^{15}\,b^{19}\,c^{19}\,\sqrt{a+\frac{b}{x}}\,125{}\mathrm{i}+a^{17}\,b^{17}\,c^{17}\,d^2\,\sqrt{a+\frac{b}{x}}\,10440{}\mathrm{i}-a^{18}\,b^{16}\,c^{16}\,d^3\,\sqrt{a+\frac{b}{x}}\,37776{}\mathrm{i}+a^{19}\,b^{15}\,c^{15}\,d^4\,\sqrt{a+\frac{b}{x}}\,87276{}\mathrm{i}-a^{20}\,b^{14}\,c^{14}\,d^5\,\sqrt{a+\frac{b}{x}}\,126720{}\mathrm{i}+a^{21}\,b^{13}\,c^{13}\,d^6\,\sqrt{a+\frac{b}{x}}\,91560{}\mathrm{i}+a^{22}\,b^{12}\,c^{12}\,d^7\,\sqrt{a+\frac{b}{x}}\,40965{}\mathrm{i}-a^{23}\,b^{11}\,c^{11}\,d^8\,\sqrt{a+\frac{b}{x}}\,184563{}\mathrm{i}+a^{24}\,b^{10}\,c^{10}\,d^9\,\sqrt{a+\frac{b}{x}}\,212608{}\mathrm{i}-a^{25}\,b^9\,c^9\,d^{10}\,\sqrt{a+\frac{b}{x}}\,107740{}\mathrm{i}-a^{26}\,b^8\,c^8\,d^{11}\,\sqrt{a+\frac{b}{x}}\,19530{}\mathrm{i}+a^{27}\,b^7\,c^7\,d^{12}\,\sqrt{a+\frac{b}{x}}\,71070{}\mathrm{i}-a^{28}\,b^6\,c^6\,d^{13}\,\sqrt{a+\frac{b}{x}}\,52836{}\mathrm{i}+a^{29}\,b^5\,c^5\,d^{14}\,\sqrt{a+\frac{b}{x}}\,20916{}\mathrm{i}-a^{30}\,b^4\,c^4\,d^{15}\,\sqrt{a+\frac{b}{x}}\,4515{}\mathrm{i}+a^{31}\,b^3\,c^3\,d^{16}\,\sqrt{a+\frac{b}{x}}\,420{}\mathrm{i}-a^{16}\,b^{18}\,c^{18}\,d\,\sqrt{a+\frac{b}{x}}\,1700{}\mathrm{i}}{a^7\,\sqrt{a^7}\,\left(a^7\,\left(a^7\,\left(420\,a^7\,b^3\,c^3\,d^{16}-4515\,a^6\,b^4\,c^4\,d^{15}+20916\,a^5\,b^5\,c^5\,d^{14}-52836\,a^4\,b^6\,c^6\,d^{13}+71070\,a^3\,b^7\,c^7\,d^{12}-19530\,a^2\,b^8\,c^8\,d^{11}-107740\,a\,b^9\,c^9\,d^{10}+212608\,b^{10}\,c^{10}\,d^9\right)+10440\,b^{17}\,c^{17}\,d^2-37776\,a\,b^{16}\,c^{16}\,d^3+87276\,a^2\,b^{15}\,c^{15}\,d^4-126720\,a^3\,b^{14}\,c^{14}\,d^5+91560\,a^4\,b^{13}\,c^{13}\,d^6+40965\,a^5\,b^{12}\,c^{12}\,d^7-184563\,a^6\,b^{11}\,c^{11}\,d^8\right)+125\,a^5\,b^{19}\,c^{19}-1700\,a^6\,b^{18}\,c^{18}\,d\right)}\right)\,\left(4\,a\,d+5\,b\,c\right)\,1{}\mathrm{i}}{c^3\,\sqrt{a^7}}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{d^7\,{\left(a\,d-b\,c\right)}^7}\,\left(\sqrt{a+\frac{b}{x}}\,\left(64\,a^{26}\,b^2\,c^6\,d^{20}-832\,a^{25}\,b^3\,c^7\,d^{19}+4820\,a^{24}\,b^4\,c^8\,d^{18}-16240\,a^{23}\,b^5\,c^9\,d^{17}+34490\,a^{22}\,b^6\,c^{10}\,d^{16}-45430\,a^{21}\,b^7\,c^{11}\,d^{15}+29414\,a^{20}\,b^8\,c^{12}\,d^{14}+10670\,a^{19}\,b^9\,c^{13}\,d^{13}-39550\,a^{18}\,b^{10}\,c^{14}\,d^{12}+25730\,a^{17}\,b^{11}\,c^{15}\,d^{11}+19048\,a^{16}\,b^{12}\,c^{16}\,d^{10}-53852\,a^{15}\,b^{13}\,c^{17}\,d^9+55510\,a^{14}\,b^{14}\,c^{18}\,d^8-35210\,a^{13}\,b^{15}\,c^{19}\,d^7+14830\,a^{12}\,b^{16}\,c^{20}\,d^6-4082\,a^{11}\,b^{17}\,c^{21}\,d^5+670\,a^{10}\,b^{18}\,c^{22}\,d^4-50\,a^9\,b^{19}\,c^{23}\,d^3\right)-\frac{\sqrt{d^7\,{\left(a\,d-b\,c\right)}^7}\,\left(4\,a\,d-9\,b\,c\right)\,\left(304\,a^{13}\,b^{18}\,c^{25}\,d^3-20\,a^{12}\,b^{19}\,c^{26}\,d^2-2144\,a^{14}\,b^{17}\,c^{24}\,d^4+9280\,a^{15}\,b^{16}\,c^{23}\,d^5-27476\,a^{16}\,b^{15}\,c^{22}\,d^6+58688\,a^{17}\,b^{14}\,c^{21}\,d^7-92840\,a^{18}\,b^{13}\,c^{20}\,d^8+109648\,a^{19}\,b^{12}\,c^{19}\,d^9-95700\,a^{20}\,b^{11}\,c^{18}\,d^{10}+59312\,a^{21}\,b^{10}\,c^{17}\,d^{11}-23056\,a^{22}\,b^9\,c^{16}\,d^{12}+2528\,a^{23}\,b^8\,c^{15}\,d^{13}+2996\,a^{24}\,b^7\,c^{14}\,d^{14}-2080\,a^{25}\,b^6\,c^{13}\,d^{15}+664\,a^{26}\,b^5\,c^{12}\,d^{16}-112\,a^{27}\,b^4\,c^{11}\,d^{17}+8\,a^{28}\,b^3\,c^{10}\,d^{18}+\frac{\sqrt{d^7\,{\left(a\,d-b\,c\right)}^7}\,\sqrt{a+\frac{b}{x}}\,\left(4\,a\,d-9\,b\,c\right)\,\left(16\,a^{31}\,b^2\,c^{12}\,d^{18}-248\,a^{30}\,b^3\,c^{13}\,d^{17}+1800\,a^{29}\,b^4\,c^{14}\,d^{16}-8120\,a^{28}\,b^5\,c^{15}\,d^{15}+25480\,a^{27}\,b^6\,c^{16}\,d^{14}-58968\,a^{26}\,b^7\,c^{17}\,d^{13}+104104\,a^{25}\,b^8\,c^{18}\,d^{12}-143000\,a^{24}\,b^9\,c^{19}\,d^{11}+154440\,a^{23}\,b^{10}\,c^{20}\,d^{10}-131560\,a^{22}\,b^{11}\,c^{21}\,d^9+88088\,a^{21}\,b^{12}\,c^{22}\,d^8-45864\,a^{20}\,b^{13}\,c^{23}\,d^7+18200\,a^{19}\,b^{14}\,c^{24}\,d^6-5320\,a^{18}\,b^{15}\,c^{25}\,d^5+1080\,a^{17}\,b^{16}\,c^{26}\,d^4-136\,a^{16}\,b^{17}\,c^{27}\,d^3+8\,a^{15}\,b^{18}\,c^{28}\,d^2\right)}{2\,\left(-a^7\,c^3\,d^7+7\,a^6\,b\,c^4\,d^6-21\,a^5\,b^2\,c^5\,d^5+35\,a^4\,b^3\,c^6\,d^4-35\,a^3\,b^4\,c^7\,d^3+21\,a^2\,b^5\,c^8\,d^2-7\,a\,b^6\,c^9\,d+b^7\,c^{10}\right)}\right)}{2\,\left(-a^7\,c^3\,d^7+7\,a^6\,b\,c^4\,d^6-21\,a^5\,b^2\,c^5\,d^5+35\,a^4\,b^3\,c^6\,d^4-35\,a^3\,b^4\,c^7\,d^3+21\,a^2\,b^5\,c^8\,d^2-7\,a\,b^6\,c^9\,d+b^7\,c^{10}\right)}\right)\,\left(4\,a\,d-9\,b\,c\right)\,1{}\mathrm{i}}{2\,\left(-a^7\,c^3\,d^7+7\,a^6\,b\,c^4\,d^6-21\,a^5\,b^2\,c^5\,d^5+35\,a^4\,b^3\,c^6\,d^4-35\,a^3\,b^4\,c^7\,d^3+21\,a^2\,b^5\,c^8\,d^2-7\,a\,b^6\,c^9\,d+b^7\,c^{10}\right)}+\frac{\sqrt{d^7\,{\left(a\,d-b\,c\right)}^7}\,\left(\sqrt{a+\frac{b}{x}}\,\left(64\,a^{26}\,b^2\,c^6\,d^{20}-832\,a^{25}\,b^3\,c^7\,d^{19}+4820\,a^{24}\,b^4\,c^8\,d^{18}-16240\,a^{23}\,b^5\,c^9\,d^{17}+34490\,a^{22}\,b^6\,c^{10}\,d^{16}-45430\,a^{21}\,b^7\,c^{11}\,d^{15}+29414\,a^{20}\,b^8\,c^{12}\,d^{14}+10670\,a^{19}\,b^9\,c^{13}\,d^{13}-39550\,a^{18}\,b^{10}\,c^{14}\,d^{12}+25730\,a^{17}\,b^{11}\,c^{15}\,d^{11}+19048\,a^{16}\,b^{12}\,c^{16}\,d^{10}-53852\,a^{15}\,b^{13}\,c^{17}\,d^9+55510\,a^{14}\,b^{14}\,c^{18}\,d^8-35210\,a^{13}\,b^{15}\,c^{19}\,d^7+14830\,a^{12}\,b^{16}\,c^{20}\,d^6-4082\,a^{11}\,b^{17}\,c^{21}\,d^5+670\,a^{10}\,b^{18}\,c^{22}\,d^4-50\,a^9\,b^{19}\,c^{23}\,d^3\right)-\frac{\sqrt{d^7\,{\left(a\,d-b\,c\right)}^7}\,\left(4\,a\,d-9\,b\,c\right)\,\left(20\,a^{12}\,b^{19}\,c^{26}\,d^2-304\,a^{13}\,b^{18}\,c^{25}\,d^3+2144\,a^{14}\,b^{17}\,c^{24}\,d^4-9280\,a^{15}\,b^{16}\,c^{23}\,d^5+27476\,a^{16}\,b^{15}\,c^{22}\,d^6-58688\,a^{17}\,b^{14}\,c^{21}\,d^7+92840\,a^{18}\,b^{13}\,c^{20}\,d^8-109648\,a^{19}\,b^{12}\,c^{19}\,d^9+95700\,a^{20}\,b^{11}\,c^{18}\,d^{10}-59312\,a^{21}\,b^{10}\,c^{17}\,d^{11}+23056\,a^{22}\,b^9\,c^{16}\,d^{12}-2528\,a^{23}\,b^8\,c^{15}\,d^{13}-2996\,a^{24}\,b^7\,c^{14}\,d^{14}+2080\,a^{25}\,b^6\,c^{13}\,d^{15}-664\,a^{26}\,b^5\,c^{12}\,d^{16}+112\,a^{27}\,b^4\,c^{11}\,d^{17}-8\,a^{28}\,b^3\,c^{10}\,d^{18}+\frac{\sqrt{d^7\,{\left(a\,d-b\,c\right)}^7}\,\sqrt{a+\frac{b}{x}}\,\left(4\,a\,d-9\,b\,c\right)\,\left(16\,a^{31}\,b^2\,c^{12}\,d^{18}-248\,a^{30}\,b^3\,c^{13}\,d^{17}+1800\,a^{29}\,b^4\,c^{14}\,d^{16}-8120\,a^{28}\,b^5\,c^{15}\,d^{15}+25480\,a^{27}\,b^6\,c^{16}\,d^{14}-58968\,a^{26}\,b^7\,c^{17}\,d^{13}+104104\,a^{25}\,b^8\,c^{18}\,d^{12}-143000\,a^{24}\,b^9\,c^{19}\,d^{11}+154440\,a^{23}\,b^{10}\,c^{20}\,d^{10}-131560\,a^{22}\,b^{11}\,c^{21}\,d^9+88088\,a^{21}\,b^{12}\,c^{22}\,d^8-45864\,a^{20}\,b^{13}\,c^{23}\,d^7+18200\,a^{19}\,b^{14}\,c^{24}\,d^6-5320\,a^{18}\,b^{15}\,c^{25}\,d^5+1080\,a^{17}\,b^{16}\,c^{26}\,d^4-136\,a^{16}\,b^{17}\,c^{27}\,d^3+8\,a^{15}\,b^{18}\,c^{28}\,d^2\right)}{2\,\left(-a^7\,c^3\,d^7+7\,a^6\,b\,c^4\,d^6-21\,a^5\,b^2\,c^5\,d^5+35\,a^4\,b^3\,c^6\,d^4-35\,a^3\,b^4\,c^7\,d^3+21\,a^2\,b^5\,c^8\,d^2-7\,a\,b^6\,c^9\,d+b^7\,c^{10}\right)}\right)}{2\,\left(-a^7\,c^3\,d^7+7\,a^6\,b\,c^4\,d^6-21\,a^5\,b^2\,c^5\,d^5+35\,a^4\,b^3\,c^6\,d^4-35\,a^3\,b^4\,c^7\,d^3+21\,a^2\,b^5\,c^8\,d^2-7\,a\,b^6\,c^9\,d+b^7\,c^{10}\right)}\right)\,\left(4\,a\,d-9\,b\,c\right)\,1{}\mathrm{i}}{2\,\left(-a^7\,c^3\,d^7+7\,a^6\,b\,c^4\,d^6-21\,a^5\,b^2\,c^5\,d^5+35\,a^4\,b^3\,c^6\,d^4-35\,a^3\,b^4\,c^7\,d^3+21\,a^2\,b^5\,c^8\,d^2-7\,a\,b^6\,c^9\,d+b^7\,c^{10}\right)}}{4880\,a^{10}\,b^{16}\,c^{17}\,d^7-450\,a^9\,b^{17}\,c^{18}\,d^6-23428\,a^{11}\,b^{15}\,c^{16}\,d^8+65234\,a^{12}\,b^{14}\,c^{15}\,d^9-115136\,a^{13}\,b^{13}\,c^{14}\,d^{10}+129800\,a^{14}\,b^{12}\,c^{13}\,d^{11}-83040\,a^{15}\,b^{11}\,c^{12}\,d^{12}+5916\,a^{16}\,b^{10}\,c^{11}\,d^{13}+45702\,a^{17}\,b^9\,c^{10}\,d^{14}-51528\,a^{18}\,b^8\,c^9\,d^{15}+32500\,a^{19}\,b^7\,c^8\,d^{16}-13790\,a^{20}\,b^6\,c^7\,d^{17}+4012\,a^{21}\,b^5\,c^6\,d^{18}-736\,a^{22}\,b^4\,c^5\,d^{19}+64\,a^{23}\,b^3\,c^4\,d^{20}+\frac{\sqrt{d^7\,{\left(a\,d-b\,c\right)}^7}\,\left(\sqrt{a+\frac{b}{x}}\,\left(64\,a^{26}\,b^2\,c^6\,d^{20}-832\,a^{25}\,b^3\,c^7\,d^{19}+4820\,a^{24}\,b^4\,c^8\,d^{18}-16240\,a^{23}\,b^5\,c^9\,d^{17}+34490\,a^{22}\,b^6\,c^{10}\,d^{16}-45430\,a^{21}\,b^7\,c^{11}\,d^{15}+29414\,a^{20}\,b^8\,c^{12}\,d^{14}+10670\,a^{19}\,b^9\,c^{13}\,d^{13}-39550\,a^{18}\,b^{10}\,c^{14}\,d^{12}+25730\,a^{17}\,b^{11}\,c^{15}\,d^{11}+19048\,a^{16}\,b^{12}\,c^{16}\,d^{10}-53852\,a^{15}\,b^{13}\,c^{17}\,d^9+55510\,a^{14}\,b^{14}\,c^{18}\,d^8-35210\,a^{13}\,b^{15}\,c^{19}\,d^7+14830\,a^{12}\,b^{16}\,c^{20}\,d^6-4082\,a^{11}\,b^{17}\,c^{21}\,d^5+670\,a^{10}\,b^{18}\,c^{22}\,d^4-50\,a^9\,b^{19}\,c^{23}\,d^3\right)-\frac{\sqrt{d^7\,{\left(a\,d-b\,c\right)}^7}\,\left(4\,a\,d-9\,b\,c\right)\,\left(304\,a^{13}\,b^{18}\,c^{25}\,d^3-20\,a^{12}\,b^{19}\,c^{26}\,d^2-2144\,a^{14}\,b^{17}\,c^{24}\,d^4+9280\,a^{15}\,b^{16}\,c^{23}\,d^5-27476\,a^{16}\,b^{15}\,c^{22}\,d^6+58688\,a^{17}\,b^{14}\,c^{21}\,d^7-92840\,a^{18}\,b^{13}\,c^{20}\,d^8+109648\,a^{19}\,b^{12}\,c^{19}\,d^9-95700\,a^{20}\,b^{11}\,c^{18}\,d^{10}+59312\,a^{21}\,b^{10}\,c^{17}\,d^{11}-23056\,a^{22}\,b^9\,c^{16}\,d^{12}+2528\,a^{23}\,b^8\,c^{15}\,d^{13}+2996\,a^{24}\,b^7\,c^{14}\,d^{14}-2080\,a^{25}\,b^6\,c^{13}\,d^{15}+664\,a^{26}\,b^5\,c^{12}\,d^{16}-112\,a^{27}\,b^4\,c^{11}\,d^{17}+8\,a^{28}\,b^3\,c^{10}\,d^{18}+\frac{\sqrt{d^7\,{\left(a\,d-b\,c\right)}^7}\,\sqrt{a+\frac{b}{x}}\,\left(4\,a\,d-9\,b\,c\right)\,\left(16\,a^{31}\,b^2\,c^{12}\,d^{18}-248\,a^{30}\,b^3\,c^{13}\,d^{17}+1800\,a^{29}\,b^4\,c^{14}\,d^{16}-8120\,a^{28}\,b^5\,c^{15}\,d^{15}+25480\,a^{27}\,b^6\,c^{16}\,d^{14}-58968\,a^{26}\,b^7\,c^{17}\,d^{13}+104104\,a^{25}\,b^8\,c^{18}\,d^{12}-143000\,a^{24}\,b^9\,c^{19}\,d^{11}+154440\,a^{23}\,b^{10}\,c^{20}\,d^{10}-131560\,a^{22}\,b^{11}\,c^{21}\,d^9+88088\,a^{21}\,b^{12}\,c^{22}\,d^8-45864\,a^{20}\,b^{13}\,c^{23}\,d^7+18200\,a^{19}\,b^{14}\,c^{24}\,d^6-5320\,a^{18}\,b^{15}\,c^{25}\,d^5+1080\,a^{17}\,b^{16}\,c^{26}\,d^4-136\,a^{16}\,b^{17}\,c^{27}\,d^3+8\,a^{15}\,b^{18}\,c^{28}\,d^2\right)}{2\,\left(-a^7\,c^3\,d^7+7\,a^6\,b\,c^4\,d^6-21\,a^5\,b^2\,c^5\,d^5+35\,a^4\,b^3\,c^6\,d^4-35\,a^3\,b^4\,c^7\,d^3+21\,a^2\,b^5\,c^8\,d^2-7\,a\,b^6\,c^9\,d+b^7\,c^{10}\right)}\right)}{2\,\left(-a^7\,c^3\,d^7+7\,a^6\,b\,c^4\,d^6-21\,a^5\,b^2\,c^5\,d^5+35\,a^4\,b^3\,c^6\,d^4-35\,a^3\,b^4\,c^7\,d^3+21\,a^2\,b^5\,c^8\,d^2-7\,a\,b^6\,c^9\,d+b^7\,c^{10}\right)}\right)\,\left(4\,a\,d-9\,b\,c\right)}{2\,\left(-a^7\,c^3\,d^7+7\,a^6\,b\,c^4\,d^6-21\,a^5\,b^2\,c^5\,d^5+35\,a^4\,b^3\,c^6\,d^4-35\,a^3\,b^4\,c^7\,d^3+21\,a^2\,b^5\,c^8\,d^2-7\,a\,b^6\,c^9\,d+b^7\,c^{10}\right)}-\frac{\sqrt{d^7\,{\left(a\,d-b\,c\right)}^7}\,\left(\sqrt{a+\frac{b}{x}}\,\left(64\,a^{26}\,b^2\,c^6\,d^{20}-832\,a^{25}\,b^3\,c^7\,d^{19}+4820\,a^{24}\,b^4\,c^8\,d^{18}-16240\,a^{23}\,b^5\,c^9\,d^{17}+34490\,a^{22}\,b^6\,c^{10}\,d^{16}-45430\,a^{21}\,b^7\,c^{11}\,d^{15}+29414\,a^{20}\,b^8\,c^{12}\,d^{14}+10670\,a^{19}\,b^9\,c^{13}\,d^{13}-39550\,a^{18}\,b^{10}\,c^{14}\,d^{12}+25730\,a^{17}\,b^{11}\,c^{15}\,d^{11}+19048\,a^{16}\,b^{12}\,c^{16}\,d^{10}-53852\,a^{15}\,b^{13}\,c^{17}\,d^9+55510\,a^{14}\,b^{14}\,c^{18}\,d^8-35210\,a^{13}\,b^{15}\,c^{19}\,d^7+14830\,a^{12}\,b^{16}\,c^{20}\,d^6-4082\,a^{11}\,b^{17}\,c^{21}\,d^5+670\,a^{10}\,b^{18}\,c^{22}\,d^4-50\,a^9\,b^{19}\,c^{23}\,d^3\right)-\frac{\sqrt{d^7\,{\left(a\,d-b\,c\right)}^7}\,\left(4\,a\,d-9\,b\,c\right)\,\left(20\,a^{12}\,b^{19}\,c^{26}\,d^2-304\,a^{13}\,b^{18}\,c^{25}\,d^3+2144\,a^{14}\,b^{17}\,c^{24}\,d^4-9280\,a^{15}\,b^{16}\,c^{23}\,d^5+27476\,a^{16}\,b^{15}\,c^{22}\,d^6-58688\,a^{17}\,b^{14}\,c^{21}\,d^7+92840\,a^{18}\,b^{13}\,c^{20}\,d^8-109648\,a^{19}\,b^{12}\,c^{19}\,d^9+95700\,a^{20}\,b^{11}\,c^{18}\,d^{10}-59312\,a^{21}\,b^{10}\,c^{17}\,d^{11}+23056\,a^{22}\,b^9\,c^{16}\,d^{12}-2528\,a^{23}\,b^8\,c^{15}\,d^{13}-2996\,a^{24}\,b^7\,c^{14}\,d^{14}+2080\,a^{25}\,b^6\,c^{13}\,d^{15}-664\,a^{26}\,b^5\,c^{12}\,d^{16}+112\,a^{27}\,b^4\,c^{11}\,d^{17}-8\,a^{28}\,b^3\,c^{10}\,d^{18}+\frac{\sqrt{d^7\,{\left(a\,d-b\,c\right)}^7}\,\sqrt{a+\frac{b}{x}}\,\left(4\,a\,d-9\,b\,c\right)\,\left(16\,a^{31}\,b^2\,c^{12}\,d^{18}-248\,a^{30}\,b^3\,c^{13}\,d^{17}+1800\,a^{29}\,b^4\,c^{14}\,d^{16}-8120\,a^{28}\,b^5\,c^{15}\,d^{15}+25480\,a^{27}\,b^6\,c^{16}\,d^{14}-58968\,a^{26}\,b^7\,c^{17}\,d^{13}+104104\,a^{25}\,b^8\,c^{18}\,d^{12}-143000\,a^{24}\,b^9\,c^{19}\,d^{11}+154440\,a^{23}\,b^{10}\,c^{20}\,d^{10}-131560\,a^{22}\,b^{11}\,c^{21}\,d^9+88088\,a^{21}\,b^{12}\,c^{22}\,d^8-45864\,a^{20}\,b^{13}\,c^{23}\,d^7+18200\,a^{19}\,b^{14}\,c^{24}\,d^6-5320\,a^{18}\,b^{15}\,c^{25}\,d^5+1080\,a^{17}\,b^{16}\,c^{26}\,d^4-136\,a^{16}\,b^{17}\,c^{27}\,d^3+8\,a^{15}\,b^{18}\,c^{28}\,d^2\right)}{2\,\left(-a^7\,c^3\,d^7+7\,a^6\,b\,c^4\,d^6-21\,a^5\,b^2\,c^5\,d^5+35\,a^4\,b^3\,c^6\,d^4-35\,a^3\,b^4\,c^7\,d^3+21\,a^2\,b^5\,c^8\,d^2-7\,a\,b^6\,c^9\,d+b^7\,c^{10}\right)}\right)}{2\,\left(-a^7\,c^3\,d^7+7\,a^6\,b\,c^4\,d^6-21\,a^5\,b^2\,c^5\,d^5+35\,a^4\,b^3\,c^6\,d^4-35\,a^3\,b^4\,c^7\,d^3+21\,a^2\,b^5\,c^8\,d^2-7\,a\,b^6\,c^9\,d+b^7\,c^{10}\right)}\right)\,\left(4\,a\,d-9\,b\,c\right)}{2\,\left(-a^7\,c^3\,d^7+7\,a^6\,b\,c^4\,d^6-21\,a^5\,b^2\,c^5\,d^5+35\,a^4\,b^3\,c^6\,d^4-35\,a^3\,b^4\,c^7\,d^3+21\,a^2\,b^5\,c^8\,d^2-7\,a\,b^6\,c^9\,d+b^7\,c^{10}\right)}}\right)\,\sqrt{d^7\,{\left(a\,d-b\,c\right)}^7}\,\left(4\,a\,d-9\,b\,c\right)\,1{}\mathrm{i}}{-a^7\,c^3\,d^7+7\,a^6\,b\,c^4\,d^6-21\,a^5\,b^2\,c^5\,d^5+35\,a^4\,b^3\,c^6\,d^4-35\,a^3\,b^4\,c^7\,d^3+21\,a^2\,b^5\,c^8\,d^2-7\,a\,b^6\,c^9\,d+b^7\,c^{10}}","Not used",1,"((2*b^3)/(3*(a^2*d - a*b*c)) + (10*b^3*(a + b/x)*(2*a*d - b*c))/(3*(a^2*d - a*b*c)^2) - (b*(a + b/x)^2*(6*a^4*d^4 + 15*b^4*c^4 + 64*a^2*b^2*c^2*d^2 - 58*a*b^3*c^3*d - 12*a^3*b*c*d^3))/(3*c^2*(a^2*d - a*b*c)^3) + (b*(a + b/x)^3*(2*a*d - b*c)*(a^2*d^3 + 5*b^2*c^2*d - a*b*c*d^2))/(c^2*(a^2*d - a*b*c)^3))/(d*(a + b/x)^(7/2) + (a + b/x)^(3/2)*(a^2*d - a*b*c) - (a + b/x)^(5/2)*(2*a*d - b*c)) + (atan((a^15*b^19*c^19*(a + b/x)^(1/2)*125i + a^17*b^17*c^17*d^2*(a + b/x)^(1/2)*10440i - a^18*b^16*c^16*d^3*(a + b/x)^(1/2)*37776i + a^19*b^15*c^15*d^4*(a + b/x)^(1/2)*87276i - a^20*b^14*c^14*d^5*(a + b/x)^(1/2)*126720i + a^21*b^13*c^13*d^6*(a + b/x)^(1/2)*91560i + a^22*b^12*c^12*d^7*(a + b/x)^(1/2)*40965i - a^23*b^11*c^11*d^8*(a + b/x)^(1/2)*184563i + a^24*b^10*c^10*d^9*(a + b/x)^(1/2)*212608i - a^25*b^9*c^9*d^10*(a + b/x)^(1/2)*107740i - a^26*b^8*c^8*d^11*(a + b/x)^(1/2)*19530i + a^27*b^7*c^7*d^12*(a + b/x)^(1/2)*71070i - a^28*b^6*c^6*d^13*(a + b/x)^(1/2)*52836i + a^29*b^5*c^5*d^14*(a + b/x)^(1/2)*20916i - a^30*b^4*c^4*d^15*(a + b/x)^(1/2)*4515i + a^31*b^3*c^3*d^16*(a + b/x)^(1/2)*420i - a^16*b^18*c^18*d*(a + b/x)^(1/2)*1700i)/(a^7*(a^7)^(1/2)*(a^7*(a^7*(212608*b^10*c^10*d^9 - 107740*a*b^9*c^9*d^10 - 19530*a^2*b^8*c^8*d^11 + 71070*a^3*b^7*c^7*d^12 - 52836*a^4*b^6*c^6*d^13 + 20916*a^5*b^5*c^5*d^14 - 4515*a^6*b^4*c^4*d^15 + 420*a^7*b^3*c^3*d^16) + 10440*b^17*c^17*d^2 - 37776*a*b^16*c^16*d^3 + 87276*a^2*b^15*c^15*d^4 - 126720*a^3*b^14*c^14*d^5 + 91560*a^4*b^13*c^13*d^6 + 40965*a^5*b^12*c^12*d^7 - 184563*a^6*b^11*c^11*d^8) + 125*a^5*b^19*c^19 - 1700*a^6*b^18*c^18*d)))*(4*a*d + 5*b*c)*1i)/(c^3*(a^7)^(1/2)) - (atan((((d^7*(a*d - b*c)^7)^(1/2)*((a + b/x)^(1/2)*(670*a^10*b^18*c^22*d^4 - 50*a^9*b^19*c^23*d^3 - 4082*a^11*b^17*c^21*d^5 + 14830*a^12*b^16*c^20*d^6 - 35210*a^13*b^15*c^19*d^7 + 55510*a^14*b^14*c^18*d^8 - 53852*a^15*b^13*c^17*d^9 + 19048*a^16*b^12*c^16*d^10 + 25730*a^17*b^11*c^15*d^11 - 39550*a^18*b^10*c^14*d^12 + 10670*a^19*b^9*c^13*d^13 + 29414*a^20*b^8*c^12*d^14 - 45430*a^21*b^7*c^11*d^15 + 34490*a^22*b^6*c^10*d^16 - 16240*a^23*b^5*c^9*d^17 + 4820*a^24*b^4*c^8*d^18 - 832*a^25*b^3*c^7*d^19 + 64*a^26*b^2*c^6*d^20) - ((d^7*(a*d - b*c)^7)^(1/2)*(4*a*d - 9*b*c)*(304*a^13*b^18*c^25*d^3 - 20*a^12*b^19*c^26*d^2 - 2144*a^14*b^17*c^24*d^4 + 9280*a^15*b^16*c^23*d^5 - 27476*a^16*b^15*c^22*d^6 + 58688*a^17*b^14*c^21*d^7 - 92840*a^18*b^13*c^20*d^8 + 109648*a^19*b^12*c^19*d^9 - 95700*a^20*b^11*c^18*d^10 + 59312*a^21*b^10*c^17*d^11 - 23056*a^22*b^9*c^16*d^12 + 2528*a^23*b^8*c^15*d^13 + 2996*a^24*b^7*c^14*d^14 - 2080*a^25*b^6*c^13*d^15 + 664*a^26*b^5*c^12*d^16 - 112*a^27*b^4*c^11*d^17 + 8*a^28*b^3*c^10*d^18 + ((d^7*(a*d - b*c)^7)^(1/2)*(a + b/x)^(1/2)*(4*a*d - 9*b*c)*(8*a^15*b^18*c^28*d^2 - 136*a^16*b^17*c^27*d^3 + 1080*a^17*b^16*c^26*d^4 - 5320*a^18*b^15*c^25*d^5 + 18200*a^19*b^14*c^24*d^6 - 45864*a^20*b^13*c^23*d^7 + 88088*a^21*b^12*c^22*d^8 - 131560*a^22*b^11*c^21*d^9 + 154440*a^23*b^10*c^20*d^10 - 143000*a^24*b^9*c^19*d^11 + 104104*a^25*b^8*c^18*d^12 - 58968*a^26*b^7*c^17*d^13 + 25480*a^27*b^6*c^16*d^14 - 8120*a^28*b^5*c^15*d^15 + 1800*a^29*b^4*c^14*d^16 - 248*a^30*b^3*c^13*d^17 + 16*a^31*b^2*c^12*d^18))/(2*(b^7*c^10 - a^7*c^3*d^7 + 7*a^6*b*c^4*d^6 + 21*a^2*b^5*c^8*d^2 - 35*a^3*b^4*c^7*d^3 + 35*a^4*b^3*c^6*d^4 - 21*a^5*b^2*c^5*d^5 - 7*a*b^6*c^9*d))))/(2*(b^7*c^10 - a^7*c^3*d^7 + 7*a^6*b*c^4*d^6 + 21*a^2*b^5*c^8*d^2 - 35*a^3*b^4*c^7*d^3 + 35*a^4*b^3*c^6*d^4 - 21*a^5*b^2*c^5*d^5 - 7*a*b^6*c^9*d)))*(4*a*d - 9*b*c)*1i)/(2*(b^7*c^10 - a^7*c^3*d^7 + 7*a^6*b*c^4*d^6 + 21*a^2*b^5*c^8*d^2 - 35*a^3*b^4*c^7*d^3 + 35*a^4*b^3*c^6*d^4 - 21*a^5*b^2*c^5*d^5 - 7*a*b^6*c^9*d)) + ((d^7*(a*d - b*c)^7)^(1/2)*((a + b/x)^(1/2)*(670*a^10*b^18*c^22*d^4 - 50*a^9*b^19*c^23*d^3 - 4082*a^11*b^17*c^21*d^5 + 14830*a^12*b^16*c^20*d^6 - 35210*a^13*b^15*c^19*d^7 + 55510*a^14*b^14*c^18*d^8 - 53852*a^15*b^13*c^17*d^9 + 19048*a^16*b^12*c^16*d^10 + 25730*a^17*b^11*c^15*d^11 - 39550*a^18*b^10*c^14*d^12 + 10670*a^19*b^9*c^13*d^13 + 29414*a^20*b^8*c^12*d^14 - 45430*a^21*b^7*c^11*d^15 + 34490*a^22*b^6*c^10*d^16 - 16240*a^23*b^5*c^9*d^17 + 4820*a^24*b^4*c^8*d^18 - 832*a^25*b^3*c^7*d^19 + 64*a^26*b^2*c^6*d^20) - ((d^7*(a*d - b*c)^7)^(1/2)*(4*a*d - 9*b*c)*(20*a^12*b^19*c^26*d^2 - 304*a^13*b^18*c^25*d^3 + 2144*a^14*b^17*c^24*d^4 - 9280*a^15*b^16*c^23*d^5 + 27476*a^16*b^15*c^22*d^6 - 58688*a^17*b^14*c^21*d^7 + 92840*a^18*b^13*c^20*d^8 - 109648*a^19*b^12*c^19*d^9 + 95700*a^20*b^11*c^18*d^10 - 59312*a^21*b^10*c^17*d^11 + 23056*a^22*b^9*c^16*d^12 - 2528*a^23*b^8*c^15*d^13 - 2996*a^24*b^7*c^14*d^14 + 2080*a^25*b^6*c^13*d^15 - 664*a^26*b^5*c^12*d^16 + 112*a^27*b^4*c^11*d^17 - 8*a^28*b^3*c^10*d^18 + ((d^7*(a*d - b*c)^7)^(1/2)*(a + b/x)^(1/2)*(4*a*d - 9*b*c)*(8*a^15*b^18*c^28*d^2 - 136*a^16*b^17*c^27*d^3 + 1080*a^17*b^16*c^26*d^4 - 5320*a^18*b^15*c^25*d^5 + 18200*a^19*b^14*c^24*d^6 - 45864*a^20*b^13*c^23*d^7 + 88088*a^21*b^12*c^22*d^8 - 131560*a^22*b^11*c^21*d^9 + 154440*a^23*b^10*c^20*d^10 - 143000*a^24*b^9*c^19*d^11 + 104104*a^25*b^8*c^18*d^12 - 58968*a^26*b^7*c^17*d^13 + 25480*a^27*b^6*c^16*d^14 - 8120*a^28*b^5*c^15*d^15 + 1800*a^29*b^4*c^14*d^16 - 248*a^30*b^3*c^13*d^17 + 16*a^31*b^2*c^12*d^18))/(2*(b^7*c^10 - a^7*c^3*d^7 + 7*a^6*b*c^4*d^6 + 21*a^2*b^5*c^8*d^2 - 35*a^3*b^4*c^7*d^3 + 35*a^4*b^3*c^6*d^4 - 21*a^5*b^2*c^5*d^5 - 7*a*b^6*c^9*d))))/(2*(b^7*c^10 - a^7*c^3*d^7 + 7*a^6*b*c^4*d^6 + 21*a^2*b^5*c^8*d^2 - 35*a^3*b^4*c^7*d^3 + 35*a^4*b^3*c^6*d^4 - 21*a^5*b^2*c^5*d^5 - 7*a*b^6*c^9*d)))*(4*a*d - 9*b*c)*1i)/(2*(b^7*c^10 - a^7*c^3*d^7 + 7*a^6*b*c^4*d^6 + 21*a^2*b^5*c^8*d^2 - 35*a^3*b^4*c^7*d^3 + 35*a^4*b^3*c^6*d^4 - 21*a^5*b^2*c^5*d^5 - 7*a*b^6*c^9*d)))/(4880*a^10*b^16*c^17*d^7 - 450*a^9*b^17*c^18*d^6 - 23428*a^11*b^15*c^16*d^8 + 65234*a^12*b^14*c^15*d^9 - 115136*a^13*b^13*c^14*d^10 + 129800*a^14*b^12*c^13*d^11 - 83040*a^15*b^11*c^12*d^12 + 5916*a^16*b^10*c^11*d^13 + 45702*a^17*b^9*c^10*d^14 - 51528*a^18*b^8*c^9*d^15 + 32500*a^19*b^7*c^8*d^16 - 13790*a^20*b^6*c^7*d^17 + 4012*a^21*b^5*c^6*d^18 - 736*a^22*b^4*c^5*d^19 + 64*a^23*b^3*c^4*d^20 + ((d^7*(a*d - b*c)^7)^(1/2)*((a + b/x)^(1/2)*(670*a^10*b^18*c^22*d^4 - 50*a^9*b^19*c^23*d^3 - 4082*a^11*b^17*c^21*d^5 + 14830*a^12*b^16*c^20*d^6 - 35210*a^13*b^15*c^19*d^7 + 55510*a^14*b^14*c^18*d^8 - 53852*a^15*b^13*c^17*d^9 + 19048*a^16*b^12*c^16*d^10 + 25730*a^17*b^11*c^15*d^11 - 39550*a^18*b^10*c^14*d^12 + 10670*a^19*b^9*c^13*d^13 + 29414*a^20*b^8*c^12*d^14 - 45430*a^21*b^7*c^11*d^15 + 34490*a^22*b^6*c^10*d^16 - 16240*a^23*b^5*c^9*d^17 + 4820*a^24*b^4*c^8*d^18 - 832*a^25*b^3*c^7*d^19 + 64*a^26*b^2*c^6*d^20) - ((d^7*(a*d - b*c)^7)^(1/2)*(4*a*d - 9*b*c)*(304*a^13*b^18*c^25*d^3 - 20*a^12*b^19*c^26*d^2 - 2144*a^14*b^17*c^24*d^4 + 9280*a^15*b^16*c^23*d^5 - 27476*a^16*b^15*c^22*d^6 + 58688*a^17*b^14*c^21*d^7 - 92840*a^18*b^13*c^20*d^8 + 109648*a^19*b^12*c^19*d^9 - 95700*a^20*b^11*c^18*d^10 + 59312*a^21*b^10*c^17*d^11 - 23056*a^22*b^9*c^16*d^12 + 2528*a^23*b^8*c^15*d^13 + 2996*a^24*b^7*c^14*d^14 - 2080*a^25*b^6*c^13*d^15 + 664*a^26*b^5*c^12*d^16 - 112*a^27*b^4*c^11*d^17 + 8*a^28*b^3*c^10*d^18 + ((d^7*(a*d - b*c)^7)^(1/2)*(a + b/x)^(1/2)*(4*a*d - 9*b*c)*(8*a^15*b^18*c^28*d^2 - 136*a^16*b^17*c^27*d^3 + 1080*a^17*b^16*c^26*d^4 - 5320*a^18*b^15*c^25*d^5 + 18200*a^19*b^14*c^24*d^6 - 45864*a^20*b^13*c^23*d^7 + 88088*a^21*b^12*c^22*d^8 - 131560*a^22*b^11*c^21*d^9 + 154440*a^23*b^10*c^20*d^10 - 143000*a^24*b^9*c^19*d^11 + 104104*a^25*b^8*c^18*d^12 - 58968*a^26*b^7*c^17*d^13 + 25480*a^27*b^6*c^16*d^14 - 8120*a^28*b^5*c^15*d^15 + 1800*a^29*b^4*c^14*d^16 - 248*a^30*b^3*c^13*d^17 + 16*a^31*b^2*c^12*d^18))/(2*(b^7*c^10 - a^7*c^3*d^7 + 7*a^6*b*c^4*d^6 + 21*a^2*b^5*c^8*d^2 - 35*a^3*b^4*c^7*d^3 + 35*a^4*b^3*c^6*d^4 - 21*a^5*b^2*c^5*d^5 - 7*a*b^6*c^9*d))))/(2*(b^7*c^10 - a^7*c^3*d^7 + 7*a^6*b*c^4*d^6 + 21*a^2*b^5*c^8*d^2 - 35*a^3*b^4*c^7*d^3 + 35*a^4*b^3*c^6*d^4 - 21*a^5*b^2*c^5*d^5 - 7*a*b^6*c^9*d)))*(4*a*d - 9*b*c))/(2*(b^7*c^10 - a^7*c^3*d^7 + 7*a^6*b*c^4*d^6 + 21*a^2*b^5*c^8*d^2 - 35*a^3*b^4*c^7*d^3 + 35*a^4*b^3*c^6*d^4 - 21*a^5*b^2*c^5*d^5 - 7*a*b^6*c^9*d)) - ((d^7*(a*d - b*c)^7)^(1/2)*((a + b/x)^(1/2)*(670*a^10*b^18*c^22*d^4 - 50*a^9*b^19*c^23*d^3 - 4082*a^11*b^17*c^21*d^5 + 14830*a^12*b^16*c^20*d^6 - 35210*a^13*b^15*c^19*d^7 + 55510*a^14*b^14*c^18*d^8 - 53852*a^15*b^13*c^17*d^9 + 19048*a^16*b^12*c^16*d^10 + 25730*a^17*b^11*c^15*d^11 - 39550*a^18*b^10*c^14*d^12 + 10670*a^19*b^9*c^13*d^13 + 29414*a^20*b^8*c^12*d^14 - 45430*a^21*b^7*c^11*d^15 + 34490*a^22*b^6*c^10*d^16 - 16240*a^23*b^5*c^9*d^17 + 4820*a^24*b^4*c^8*d^18 - 832*a^25*b^3*c^7*d^19 + 64*a^26*b^2*c^6*d^20) - ((d^7*(a*d - b*c)^7)^(1/2)*(4*a*d - 9*b*c)*(20*a^12*b^19*c^26*d^2 - 304*a^13*b^18*c^25*d^3 + 2144*a^14*b^17*c^24*d^4 - 9280*a^15*b^16*c^23*d^5 + 27476*a^16*b^15*c^22*d^6 - 58688*a^17*b^14*c^21*d^7 + 92840*a^18*b^13*c^20*d^8 - 109648*a^19*b^12*c^19*d^9 + 95700*a^20*b^11*c^18*d^10 - 59312*a^21*b^10*c^17*d^11 + 23056*a^22*b^9*c^16*d^12 - 2528*a^23*b^8*c^15*d^13 - 2996*a^24*b^7*c^14*d^14 + 2080*a^25*b^6*c^13*d^15 - 664*a^26*b^5*c^12*d^16 + 112*a^27*b^4*c^11*d^17 - 8*a^28*b^3*c^10*d^18 + ((d^7*(a*d - b*c)^7)^(1/2)*(a + b/x)^(1/2)*(4*a*d - 9*b*c)*(8*a^15*b^18*c^28*d^2 - 136*a^16*b^17*c^27*d^3 + 1080*a^17*b^16*c^26*d^4 - 5320*a^18*b^15*c^25*d^5 + 18200*a^19*b^14*c^24*d^6 - 45864*a^20*b^13*c^23*d^7 + 88088*a^21*b^12*c^22*d^8 - 131560*a^22*b^11*c^21*d^9 + 154440*a^23*b^10*c^20*d^10 - 143000*a^24*b^9*c^19*d^11 + 104104*a^25*b^8*c^18*d^12 - 58968*a^26*b^7*c^17*d^13 + 25480*a^27*b^6*c^16*d^14 - 8120*a^28*b^5*c^15*d^15 + 1800*a^29*b^4*c^14*d^16 - 248*a^30*b^3*c^13*d^17 + 16*a^31*b^2*c^12*d^18))/(2*(b^7*c^10 - a^7*c^3*d^7 + 7*a^6*b*c^4*d^6 + 21*a^2*b^5*c^8*d^2 - 35*a^3*b^4*c^7*d^3 + 35*a^4*b^3*c^6*d^4 - 21*a^5*b^2*c^5*d^5 - 7*a*b^6*c^9*d))))/(2*(b^7*c^10 - a^7*c^3*d^7 + 7*a^6*b*c^4*d^6 + 21*a^2*b^5*c^8*d^2 - 35*a^3*b^4*c^7*d^3 + 35*a^4*b^3*c^6*d^4 - 21*a^5*b^2*c^5*d^5 - 7*a*b^6*c^9*d)))*(4*a*d - 9*b*c))/(2*(b^7*c^10 - a^7*c^3*d^7 + 7*a^6*b*c^4*d^6 + 21*a^2*b^5*c^8*d^2 - 35*a^3*b^4*c^7*d^3 + 35*a^4*b^3*c^6*d^4 - 21*a^5*b^2*c^5*d^5 - 7*a*b^6*c^9*d))))*(d^7*(a*d - b*c)^7)^(1/2)*(4*a*d - 9*b*c)*1i)/(b^7*c^10 - a^7*c^3*d^7 + 7*a^6*b*c^4*d^6 + 21*a^2*b^5*c^8*d^2 - 35*a^3*b^4*c^7*d^3 + 35*a^4*b^3*c^6*d^4 - 21*a^5*b^2*c^5*d^5 - 7*a*b^6*c^9*d)","B"
265,1,4284,409,8.227308,"\text{Not used}","int(1/((a + b/x)^(5/2)*(c + d/x)^3),x)","\frac{\frac{2\,b^4}{3\,\left(a^2\,d-a\,b\,c\right)}+\frac{2\,b^4\,\left(a+\frac{b}{x}\right)\,\left(12\,a\,d-5\,b\,c\right)}{3\,{\left(a^2\,d-a\,b\,c\right)}^2}+\frac{b\,{\left(a+\frac{b}{x}\right)}^2\,\left(36\,a^5\,d^5-123\,a^4\,b\,c\,d^4+120\,a^3\,b^2\,c^2\,d^3-456\,a^2\,b^3\,c^3\,d^2+308\,a\,b^4\,c^4\,d-60\,b^5\,c^5\right)}{12\,a^2\,c^3\,\left(a^2\,d-a\,b\,c\right)\,{\left(a\,d-b\,c\right)}^2}+\frac{b\,{\left(a+\frac{b}{x}\right)}^4\,\left(12\,a^4\,d^6-35\,a^3\,b\,c\,d^5+24\,a^2\,b^2\,c^2\,d^4-56\,a\,b^3\,c^3\,d^3+20\,b^4\,c^4\,d^2\right)}{4\,a^2\,c^3\,\left(a^2\,d-a\,b\,c\right)\,{\left(a\,d-b\,c\right)}^3}-\frac{b\,{\left(a+\frac{b}{x}\right)}^3\,\left(72\,a^5\,d^6-264\,a^4\,b\,c\,d^5+303\,a^3\,b^2\,c^2\,d^4-592\,a^2\,b^3\,c^3\,d^3+496\,a\,b^4\,c^4\,d^2-120\,b^5\,c^5\,d\right)}{12\,a^2\,c^3\,\left(a^2\,d-a\,b\,c\right)\,{\left(a\,d-b\,c\right)}^3}}{{\left(a+\frac{b}{x}\right)}^{5/2}\,\left(3\,a^2\,d^2-4\,a\,b\,c\,d+b^2\,c^2\right)-{\left(a+\frac{b}{x}\right)}^{7/2}\,\left(3\,a\,d^2-2\,b\,c\,d\right)+d^2\,{\left(a+\frac{b}{x}\right)}^{9/2}-{\left(a+\frac{b}{x}\right)}^{3/2}\,\left(a^3\,d^2-2\,a^2\,b\,c\,d+a\,b^2\,c^2\right)}+\frac{\ln\left(400\,b^{25}\,c^{25}\,d^4-8240\,a\,b^{24}\,c^{24}\,d^5-1152\,a^{11}\,d^5\,{\left(d^7\,{\left(a\,d-b\,c\right)}^9\right)}^{3/2}\,\sqrt{a+\frac{b}{x}}+1152\,a^{20}\,d^{21}\,\sqrt{d^7\,{\left(a\,d-b\,c\right)}^9}\,\sqrt{a+\frac{b}{x}}+79696\,a^2\,b^{23}\,c^{23}\,d^6-478768\,a^3\,b^{22}\,c^{22}\,d^7+1987568\,a^4\,b^{21}\,c^{21}\,d^8-5978896\,a^5\,b^{20}\,c^{20}\,d^9+13176240\,a^6\,b^{19}\,c^{19}\,d^{10}-20525703\,a^7\,b^{18}\,c^{18}\,d^{11}+18765714\,a^8\,b^{17}\,c^{17}\,d^{12}+3763331\,a^9\,b^{16}\,c^{16}\,d^{13}-49787452\,a^{10}\,b^{15}\,c^{15}\,d^{14}+104120705\,a^{11}\,b^{14}\,c^{14}\,d^{15}-140185682\,a^{12}\,b^{13}\,c^{13}\,d^{16}+139985251\,a^{13}\,b^{12}\,c^{12}\,d^{17}-108046616\,a^{14}\,b^{11}\,c^{11}\,d^{18}+65184867\,a^{15}\,b^{10}\,c^{10}\,d^{19}-30607170\,a^{16}\,b^9\,c^9\,d^{20}+10996689\,a^{17}\,b^8\,c^8\,d^{21}-2926572\,a^{18}\,b^7\,c^7\,d^{22}+544467\,a^{19}\,b^6\,c^6\,d^{23}-63294\,a^{20}\,b^5\,c^5\,d^{24}+3465\,a^{21}\,b^4\,c^4\,d^{25}+400\,b^{20}\,c^{20}\,d\,\sqrt{d^7\,{\left(a\,d-b\,c\right)}^9}\,\sqrt{a+\frac{b}{x}}+9801\,a^6\,b^5\,c^5\,{\left(d^7\,{\left(a\,d-b\,c\right)}^9\right)}^{3/2}\,\sqrt{a+\frac{b}{x}}-37026\,a^7\,b^4\,c^4\,d\,{\left(d^7\,{\left(a\,d-b\,c\right)}^9\right)}^{3/2}\,\sqrt{a+\frac{b}{x}}-6240\,a\,b^{19}\,c^{19}\,d^2\,\sqrt{d^7\,{\left(a\,d-b\,c\right)}^9}\,\sqrt{a+\frac{b}{x}}+47344\,a^8\,b^3\,c^3\,d^2\,{\left(d^7\,{\left(a\,d-b\,c\right)}^9\right)}^{3/2}\,\sqrt{a+\frac{b}{x}}-29216\,a^9\,b^2\,c^2\,d^3\,{\left(d^7\,{\left(a\,d-b\,c\right)}^9\right)}^{3/2}\,\sqrt{a+\frac{b}{x}}+44496\,a^2\,b^{18}\,c^{18}\,d^3\,\sqrt{d^7\,{\left(a\,d-b\,c\right)}^9}\,\sqrt{a+\frac{b}{x}}-189888\,a^3\,b^{17}\,c^{17}\,d^4\,\sqrt{d^7\,{\left(a\,d-b\,c\right)}^9}\,\sqrt{a+\frac{b}{x}}+528768\,a^4\,b^{16}\,c^{16}\,d^5\,\sqrt{d^7\,{\left(a\,d-b\,c\right)}^9}\,\sqrt{a+\frac{b}{x}}-959616\,a^5\,b^{15}\,c^{15}\,d^6\,\sqrt{d^7\,{\left(a\,d-b\,c\right)}^9}\,\sqrt{a+\frac{b}{x}}+972681\,a^6\,b^{14}\,c^{14}\,d^7\,\sqrt{d^7\,{\left(a\,d-b\,c\right)}^9}\,\sqrt{a+\frac{b}{x}}+41238\,a^7\,b^{13}\,c^{13}\,d^8\,\sqrt{d^7\,{\left(a\,d-b\,c\right)}^9}\,\sqrt{a+\frac{b}{x}}-1727195\,a^8\,b^{12}\,c^{12}\,d^9\,\sqrt{d^7\,{\left(a\,d-b\,c\right)}^9}\,\sqrt{a+\frac{b}{x}}+2139672\,a^9\,b^{11}\,c^{11}\,d^{10}\,\sqrt{d^7\,{\left(a\,d-b\,c\right)}^9}\,\sqrt{a+\frac{b}{x}}+786834\,a^{10}\,b^{10}\,c^{10}\,d^{11}\,\sqrt{d^7\,{\left(a\,d-b\,c\right)}^9}\,\sqrt{a+\frac{b}{x}}-6551292\,a^{11}\,b^9\,c^9\,d^{12}\,\sqrt{d^7\,{\left(a\,d-b\,c\right)}^9}\,\sqrt{a+\frac{b}{x}}+11685186\,a^{12}\,b^8\,c^8\,d^{13}\,\sqrt{d^7\,{\left(a\,d-b\,c\right)}^9}\,\sqrt{a+\frac{b}{x}}-12876696\,a^{13}\,b^7\,c^7\,d^{14}\,\sqrt{d^7\,{\left(a\,d-b\,c\right)}^9}\,\sqrt{a+\frac{b}{x}}+10033077\,a^{14}\,b^6\,c^6\,d^{15}\,\sqrt{d^7\,{\left(a\,d-b\,c\right)}^9}\,\sqrt{a+\frac{b}{x}}-5737770\,a^{15}\,b^5\,c^5\,d^{16}\,\sqrt{d^7\,{\left(a\,d-b\,c\right)}^9}\,\sqrt{a+\frac{b}{x}}+2414601\,a^{16}\,b^4\,c^4\,d^{17}\,\sqrt{d^7\,{\left(a\,d-b\,c\right)}^9}\,\sqrt{a+\frac{b}{x}}-731920\,a^{17}\,b^3\,c^3\,d^{18}\,\sqrt{d^7\,{\left(a\,d-b\,c\right)}^9}\,\sqrt{a+\frac{b}{x}}+151904\,a^{18}\,b^2\,c^2\,d^{19}\,\sqrt{d^7\,{\left(a\,d-b\,c\right)}^9}\,\sqrt{a+\frac{b}{x}}+9024\,a^{10}\,b\,c\,d^4\,{\left(d^7\,{\left(a\,d-b\,c\right)}^9\right)}^{3/2}\,\sqrt{a+\frac{b}{x}}-19392\,a^{19}\,b\,c\,d^{20}\,\sqrt{d^7\,{\left(a\,d-b\,c\right)}^9}\,\sqrt{a+\frac{b}{x}}\right)\,\sqrt{d^7\,{\left(a\,d-b\,c\right)}^9}\,\left(3\,a^2\,d^2-11\,a\,b\,c\,d+\frac{99\,b^2\,c^2}{8}\right)}{-a^9\,c^4\,d^9+9\,a^8\,b\,c^5\,d^8-36\,a^7\,b^2\,c^6\,d^7+84\,a^6\,b^3\,c^7\,d^6-126\,a^5\,b^4\,c^8\,d^5+126\,a^4\,b^5\,c^9\,d^4-84\,a^3\,b^6\,c^{10}\,d^3+36\,a^2\,b^7\,c^{11}\,d^2-9\,a\,b^8\,c^{12}\,d+b^9\,c^{13}}-\frac{\ln\left(8240\,a\,b^{24}\,c^{24}\,d^5-400\,b^{25}\,c^{25}\,d^4-1152\,a^{11}\,d^5\,{\left(d^7\,{\left(a\,d-b\,c\right)}^9\right)}^{3/2}\,\sqrt{a+\frac{b}{x}}+1152\,a^{20}\,d^{21}\,\sqrt{d^7\,{\left(a\,d-b\,c\right)}^9}\,\sqrt{a+\frac{b}{x}}-79696\,a^2\,b^{23}\,c^{23}\,d^6+478768\,a^3\,b^{22}\,c^{22}\,d^7-1987568\,a^4\,b^{21}\,c^{21}\,d^8+5978896\,a^5\,b^{20}\,c^{20}\,d^9-13176240\,a^6\,b^{19}\,c^{19}\,d^{10}+20525703\,a^7\,b^{18}\,c^{18}\,d^{11}-18765714\,a^8\,b^{17}\,c^{17}\,d^{12}-3763331\,a^9\,b^{16}\,c^{16}\,d^{13}+49787452\,a^{10}\,b^{15}\,c^{15}\,d^{14}-104120705\,a^{11}\,b^{14}\,c^{14}\,d^{15}+140185682\,a^{12}\,b^{13}\,c^{13}\,d^{16}-139985251\,a^{13}\,b^{12}\,c^{12}\,d^{17}+108046616\,a^{14}\,b^{11}\,c^{11}\,d^{18}-65184867\,a^{15}\,b^{10}\,c^{10}\,d^{19}+30607170\,a^{16}\,b^9\,c^9\,d^{20}-10996689\,a^{17}\,b^8\,c^8\,d^{21}+2926572\,a^{18}\,b^7\,c^7\,d^{22}-544467\,a^{19}\,b^6\,c^6\,d^{23}+63294\,a^{20}\,b^5\,c^5\,d^{24}-3465\,a^{21}\,b^4\,c^4\,d^{25}+400\,b^{20}\,c^{20}\,d\,\sqrt{d^7\,{\left(a\,d-b\,c\right)}^9}\,\sqrt{a+\frac{b}{x}}+9801\,a^6\,b^5\,c^5\,{\left(d^7\,{\left(a\,d-b\,c\right)}^9\right)}^{3/2}\,\sqrt{a+\frac{b}{x}}-37026\,a^7\,b^4\,c^4\,d\,{\left(d^7\,{\left(a\,d-b\,c\right)}^9\right)}^{3/2}\,\sqrt{a+\frac{b}{x}}-6240\,a\,b^{19}\,c^{19}\,d^2\,\sqrt{d^7\,{\left(a\,d-b\,c\right)}^9}\,\sqrt{a+\frac{b}{x}}+47344\,a^8\,b^3\,c^3\,d^2\,{\left(d^7\,{\left(a\,d-b\,c\right)}^9\right)}^{3/2}\,\sqrt{a+\frac{b}{x}}-29216\,a^9\,b^2\,c^2\,d^3\,{\left(d^7\,{\left(a\,d-b\,c\right)}^9\right)}^{3/2}\,\sqrt{a+\frac{b}{x}}+44496\,a^2\,b^{18}\,c^{18}\,d^3\,\sqrt{d^7\,{\left(a\,d-b\,c\right)}^9}\,\sqrt{a+\frac{b}{x}}-189888\,a^3\,b^{17}\,c^{17}\,d^4\,\sqrt{d^7\,{\left(a\,d-b\,c\right)}^9}\,\sqrt{a+\frac{b}{x}}+528768\,a^4\,b^{16}\,c^{16}\,d^5\,\sqrt{d^7\,{\left(a\,d-b\,c\right)}^9}\,\sqrt{a+\frac{b}{x}}-959616\,a^5\,b^{15}\,c^{15}\,d^6\,\sqrt{d^7\,{\left(a\,d-b\,c\right)}^9}\,\sqrt{a+\frac{b}{x}}+972681\,a^6\,b^{14}\,c^{14}\,d^7\,\sqrt{d^7\,{\left(a\,d-b\,c\right)}^9}\,\sqrt{a+\frac{b}{x}}+41238\,a^7\,b^{13}\,c^{13}\,d^8\,\sqrt{d^7\,{\left(a\,d-b\,c\right)}^9}\,\sqrt{a+\frac{b}{x}}-1727195\,a^8\,b^{12}\,c^{12}\,d^9\,\sqrt{d^7\,{\left(a\,d-b\,c\right)}^9}\,\sqrt{a+\frac{b}{x}}+2139672\,a^9\,b^{11}\,c^{11}\,d^{10}\,\sqrt{d^7\,{\left(a\,d-b\,c\right)}^9}\,\sqrt{a+\frac{b}{x}}+786834\,a^{10}\,b^{10}\,c^{10}\,d^{11}\,\sqrt{d^7\,{\left(a\,d-b\,c\right)}^9}\,\sqrt{a+\frac{b}{x}}-6551292\,a^{11}\,b^9\,c^9\,d^{12}\,\sqrt{d^7\,{\left(a\,d-b\,c\right)}^9}\,\sqrt{a+\frac{b}{x}}+11685186\,a^{12}\,b^8\,c^8\,d^{13}\,\sqrt{d^7\,{\left(a\,d-b\,c\right)}^9}\,\sqrt{a+\frac{b}{x}}-12876696\,a^{13}\,b^7\,c^7\,d^{14}\,\sqrt{d^7\,{\left(a\,d-b\,c\right)}^9}\,\sqrt{a+\frac{b}{x}}+10033077\,a^{14}\,b^6\,c^6\,d^{15}\,\sqrt{d^7\,{\left(a\,d-b\,c\right)}^9}\,\sqrt{a+\frac{b}{x}}-5737770\,a^{15}\,b^5\,c^5\,d^{16}\,\sqrt{d^7\,{\left(a\,d-b\,c\right)}^9}\,\sqrt{a+\frac{b}{x}}+2414601\,a^{16}\,b^4\,c^4\,d^{17}\,\sqrt{d^7\,{\left(a\,d-b\,c\right)}^9}\,\sqrt{a+\frac{b}{x}}-731920\,a^{17}\,b^3\,c^3\,d^{18}\,\sqrt{d^7\,{\left(a\,d-b\,c\right)}^9}\,\sqrt{a+\frac{b}{x}}+151904\,a^{18}\,b^2\,c^2\,d^{19}\,\sqrt{d^7\,{\left(a\,d-b\,c\right)}^9}\,\sqrt{a+\frac{b}{x}}+9024\,a^{10}\,b\,c\,d^4\,{\left(d^7\,{\left(a\,d-b\,c\right)}^9\right)}^{3/2}\,\sqrt{a+\frac{b}{x}}-19392\,a^{19}\,b\,c\,d^{20}\,\sqrt{d^7\,{\left(a\,d-b\,c\right)}^9}\,\sqrt{a+\frac{b}{x}}\right)\,\sqrt{d^7\,{\left(a\,d-b\,c\right)}^9}\,\left(24\,a^2\,d^2-88\,a\,b\,c\,d+99\,b^2\,c^2\right)}{8\,\left(-a^9\,c^4\,d^9+9\,a^8\,b\,c^5\,d^8-36\,a^7\,b^2\,c^6\,d^7+84\,a^6\,b^3\,c^7\,d^6-126\,a^5\,b^4\,c^8\,d^5+126\,a^4\,b^5\,c^9\,d^4-84\,a^3\,b^6\,c^{10}\,d^3+36\,a^2\,b^7\,c^{11}\,d^2-9\,a\,b^8\,c^{12}\,d+b^9\,c^{13}\right)}+\frac{\mathrm{atan}\left(\frac{a^{15}\,b^{24}\,c^{24}\,\sqrt{a+\frac{b}{x}}\,2000{}\mathrm{i}+a^{17}\,b^{22}\,c^{22}\,d^2\,\sqrt{a+\frac{b}{x}}\,277440{}\mathrm{i}-a^{18}\,b^{21}\,c^{21}\,d^3\,\sqrt{a+\frac{b}{x}}\,1325984{}\mathrm{i}+a^{19}\,b^{20}\,c^{20}\,d^4\,\sqrt{a+\frac{b}{x}}\,4135824{}\mathrm{i}-a^{20}\,b^{19}\,c^{19}\,d^5\,\sqrt{a+\frac{b}{x}}\,8371440{}\mathrm{i}+a^{21}\,b^{18}\,c^{18}\,d^6\,\sqrt{a+\frac{b}{x}}\,9129120{}\mathrm{i}+a^{22}\,b^{17}\,c^{17}\,d^7\,\sqrt{a+\frac{b}{x}}\,3058605{}\mathrm{i}-a^{23}\,b^{16}\,c^{16}\,d^8\,\sqrt{a+\frac{b}{x}}\,32337558{}\mathrm{i}+a^{24}\,b^{15}\,c^{15}\,d^9\,\sqrt{a+\frac{b}{x}}\,63677218{}\mathrm{i}-a^{25}\,b^{14}\,c^{14}\,d^{10}\,\sqrt{a+\frac{b}{x}}\,66665280{}\mathrm{i}+a^{26}\,b^{13}\,c^{13}\,d^{11}\,\sqrt{a+\frac{b}{x}}\,24871035{}\mathrm{i}+a^{27}\,b^{12}\,c^{12}\,d^{12}\,\sqrt{a+\frac{b}{x}}\,40203170{}\mathrm{i}-a^{28}\,b^{11}\,c^{11}\,d^{13}\,\sqrt{a+\frac{b}{x}}\,85652532{}\mathrm{i}+a^{29}\,b^{10}\,c^{10}\,d^{14}\,\sqrt{a+\frac{b}{x}}\,88170192{}\mathrm{i}-a^{30}\,b^9\,c^9\,d^{15}\,\sqrt{a+\frac{b}{x}}\,60362445{}\mathrm{i}+a^{31}\,b^8\,c^8\,d^{16}\,\sqrt{a+\frac{b}{x}}\,29178270{}\mathrm{i}-a^{32}\,b^7\,c^7\,d^{17}\,\sqrt{a+\frac{b}{x}}\,9940590{}\mathrm{i}+a^{33}\,b^6\,c^6\,d^{18}\,\sqrt{a+\frac{b}{x}}\,2287824{}\mathrm{i}-a^{34}\,b^5\,c^5\,d^{19}\,\sqrt{a+\frac{b}{x}}\,320859{}\mathrm{i}+a^{35}\,b^4\,c^4\,d^{20}\,\sqrt{a+\frac{b}{x}}\,20790{}\mathrm{i}-a^{16}\,b^{23}\,c^{23}\,d\,\sqrt{a+\frac{b}{x}}\,34800{}\mathrm{i}}{a^7\,\sqrt{a^7}\,\left(a^7\,\left(a^7\,\left(a^7\,\left(20790\,a^4\,b^4\,c^4\,d^{20}-320859\,a^3\,b^5\,c^5\,d^{19}+2287824\,a^2\,b^6\,c^6\,d^{18}-9940590\,a\,b^7\,c^7\,d^{17}+29178270\,b^8\,c^8\,d^{16}\right)+63677218\,b^{15}\,c^{15}\,d^9-66665280\,a\,b^{14}\,c^{14}\,d^{10}+24871035\,a^2\,b^{13}\,c^{13}\,d^{11}+40203170\,a^3\,b^{12}\,c^{12}\,d^{12}-85652532\,a^4\,b^{11}\,c^{11}\,d^{13}+88170192\,a^5\,b^{10}\,c^{10}\,d^{14}-60362445\,a^6\,b^9\,c^9\,d^{15}\right)+277440\,b^{22}\,c^{22}\,d^2-1325984\,a\,b^{21}\,c^{21}\,d^3+4135824\,a^2\,b^{20}\,c^{20}\,d^4-8371440\,a^3\,b^{19}\,c^{19}\,d^5+9129120\,a^4\,b^{18}\,c^{18}\,d^6+3058605\,a^5\,b^{17}\,c^{17}\,d^7-32337558\,a^6\,b^{16}\,c^{16}\,d^8\right)+2000\,a^5\,b^{24}\,c^{24}-34800\,a^6\,b^{23}\,c^{23}\,d\right)}\right)\,\left(6\,a\,d+5\,b\,c\right)\,1{}\mathrm{i}}{c^4\,\sqrt{a^7}}","Not used",1,"((2*b^4)/(3*(a^2*d - a*b*c)) + (2*b^4*(a + b/x)*(12*a*d - 5*b*c))/(3*(a^2*d - a*b*c)^2) + (b*(a + b/x)^2*(36*a^5*d^5 - 60*b^5*c^5 - 456*a^2*b^3*c^3*d^2 + 120*a^3*b^2*c^2*d^3 + 308*a*b^4*c^4*d - 123*a^4*b*c*d^4))/(12*a^2*c^3*(a^2*d - a*b*c)*(a*d - b*c)^2) + (b*(a + b/x)^4*(12*a^4*d^6 + 20*b^4*c^4*d^2 - 56*a*b^3*c^3*d^3 + 24*a^2*b^2*c^2*d^4 - 35*a^3*b*c*d^5))/(4*a^2*c^3*(a^2*d - a*b*c)*(a*d - b*c)^3) - (b*(a + b/x)^3*(72*a^5*d^6 - 120*b^5*c^5*d + 496*a*b^4*c^4*d^2 - 592*a^2*b^3*c^3*d^3 + 303*a^3*b^2*c^2*d^4 - 264*a^4*b*c*d^5))/(12*a^2*c^3*(a^2*d - a*b*c)*(a*d - b*c)^3))/((a + b/x)^(5/2)*(3*a^2*d^2 + b^2*c^2 - 4*a*b*c*d) - (a + b/x)^(7/2)*(3*a*d^2 - 2*b*c*d) + d^2*(a + b/x)^(9/2) - (a + b/x)^(3/2)*(a^3*d^2 + a*b^2*c^2 - 2*a^2*b*c*d)) + (atan((a^15*b^24*c^24*(a + b/x)^(1/2)*2000i + a^17*b^22*c^22*d^2*(a + b/x)^(1/2)*277440i - a^18*b^21*c^21*d^3*(a + b/x)^(1/2)*1325984i + a^19*b^20*c^20*d^4*(a + b/x)^(1/2)*4135824i - a^20*b^19*c^19*d^5*(a + b/x)^(1/2)*8371440i + a^21*b^18*c^18*d^6*(a + b/x)^(1/2)*9129120i + a^22*b^17*c^17*d^7*(a + b/x)^(1/2)*3058605i - a^23*b^16*c^16*d^8*(a + b/x)^(1/2)*32337558i + a^24*b^15*c^15*d^9*(a + b/x)^(1/2)*63677218i - a^25*b^14*c^14*d^10*(a + b/x)^(1/2)*66665280i + a^26*b^13*c^13*d^11*(a + b/x)^(1/2)*24871035i + a^27*b^12*c^12*d^12*(a + b/x)^(1/2)*40203170i - a^28*b^11*c^11*d^13*(a + b/x)^(1/2)*85652532i + a^29*b^10*c^10*d^14*(a + b/x)^(1/2)*88170192i - a^30*b^9*c^9*d^15*(a + b/x)^(1/2)*60362445i + a^31*b^8*c^8*d^16*(a + b/x)^(1/2)*29178270i - a^32*b^7*c^7*d^17*(a + b/x)^(1/2)*9940590i + a^33*b^6*c^6*d^18*(a + b/x)^(1/2)*2287824i - a^34*b^5*c^5*d^19*(a + b/x)^(1/2)*320859i + a^35*b^4*c^4*d^20*(a + b/x)^(1/2)*20790i - a^16*b^23*c^23*d*(a + b/x)^(1/2)*34800i)/(a^7*(a^7)^(1/2)*(a^7*(a^7*(a^7*(29178270*b^8*c^8*d^16 - 9940590*a*b^7*c^7*d^17 + 2287824*a^2*b^6*c^6*d^18 - 320859*a^3*b^5*c^5*d^19 + 20790*a^4*b^4*c^4*d^20) + 63677218*b^15*c^15*d^9 - 66665280*a*b^14*c^14*d^10 + 24871035*a^2*b^13*c^13*d^11 + 40203170*a^3*b^12*c^12*d^12 - 85652532*a^4*b^11*c^11*d^13 + 88170192*a^5*b^10*c^10*d^14 - 60362445*a^6*b^9*c^9*d^15) + 277440*b^22*c^22*d^2 - 1325984*a*b^21*c^21*d^3 + 4135824*a^2*b^20*c^20*d^4 - 8371440*a^3*b^19*c^19*d^5 + 9129120*a^4*b^18*c^18*d^6 + 3058605*a^5*b^17*c^17*d^7 - 32337558*a^6*b^16*c^16*d^8) + 2000*a^5*b^24*c^24 - 34800*a^6*b^23*c^23*d)))*(6*a*d + 5*b*c)*1i)/(c^4*(a^7)^(1/2)) + (log(400*b^25*c^25*d^4 - 8240*a*b^24*c^24*d^5 - 1152*a^11*d^5*(d^7*(a*d - b*c)^9)^(3/2)*(a + b/x)^(1/2) + 1152*a^20*d^21*(d^7*(a*d - b*c)^9)^(1/2)*(a + b/x)^(1/2) + 79696*a^2*b^23*c^23*d^6 - 478768*a^3*b^22*c^22*d^7 + 1987568*a^4*b^21*c^21*d^8 - 5978896*a^5*b^20*c^20*d^9 + 13176240*a^6*b^19*c^19*d^10 - 20525703*a^7*b^18*c^18*d^11 + 18765714*a^8*b^17*c^17*d^12 + 3763331*a^9*b^16*c^16*d^13 - 49787452*a^10*b^15*c^15*d^14 + 104120705*a^11*b^14*c^14*d^15 - 140185682*a^12*b^13*c^13*d^16 + 139985251*a^13*b^12*c^12*d^17 - 108046616*a^14*b^11*c^11*d^18 + 65184867*a^15*b^10*c^10*d^19 - 30607170*a^16*b^9*c^9*d^20 + 10996689*a^17*b^8*c^8*d^21 - 2926572*a^18*b^7*c^7*d^22 + 544467*a^19*b^6*c^6*d^23 - 63294*a^20*b^5*c^5*d^24 + 3465*a^21*b^4*c^4*d^25 + 400*b^20*c^20*d*(d^7*(a*d - b*c)^9)^(1/2)*(a + b/x)^(1/2) + 9801*a^6*b^5*c^5*(d^7*(a*d - b*c)^9)^(3/2)*(a + b/x)^(1/2) - 37026*a^7*b^4*c^4*d*(d^7*(a*d - b*c)^9)^(3/2)*(a + b/x)^(1/2) - 6240*a*b^19*c^19*d^2*(d^7*(a*d - b*c)^9)^(1/2)*(a + b/x)^(1/2) + 47344*a^8*b^3*c^3*d^2*(d^7*(a*d - b*c)^9)^(3/2)*(a + b/x)^(1/2) - 29216*a^9*b^2*c^2*d^3*(d^7*(a*d - b*c)^9)^(3/2)*(a + b/x)^(1/2) + 44496*a^2*b^18*c^18*d^3*(d^7*(a*d - b*c)^9)^(1/2)*(a + b/x)^(1/2) - 189888*a^3*b^17*c^17*d^4*(d^7*(a*d - b*c)^9)^(1/2)*(a + b/x)^(1/2) + 528768*a^4*b^16*c^16*d^5*(d^7*(a*d - b*c)^9)^(1/2)*(a + b/x)^(1/2) - 959616*a^5*b^15*c^15*d^6*(d^7*(a*d - b*c)^9)^(1/2)*(a + b/x)^(1/2) + 972681*a^6*b^14*c^14*d^7*(d^7*(a*d - b*c)^9)^(1/2)*(a + b/x)^(1/2) + 41238*a^7*b^13*c^13*d^8*(d^7*(a*d - b*c)^9)^(1/2)*(a + b/x)^(1/2) - 1727195*a^8*b^12*c^12*d^9*(d^7*(a*d - b*c)^9)^(1/2)*(a + b/x)^(1/2) + 2139672*a^9*b^11*c^11*d^10*(d^7*(a*d - b*c)^9)^(1/2)*(a + b/x)^(1/2) + 786834*a^10*b^10*c^10*d^11*(d^7*(a*d - b*c)^9)^(1/2)*(a + b/x)^(1/2) - 6551292*a^11*b^9*c^9*d^12*(d^7*(a*d - b*c)^9)^(1/2)*(a + b/x)^(1/2) + 11685186*a^12*b^8*c^8*d^13*(d^7*(a*d - b*c)^9)^(1/2)*(a + b/x)^(1/2) - 12876696*a^13*b^7*c^7*d^14*(d^7*(a*d - b*c)^9)^(1/2)*(a + b/x)^(1/2) + 10033077*a^14*b^6*c^6*d^15*(d^7*(a*d - b*c)^9)^(1/2)*(a + b/x)^(1/2) - 5737770*a^15*b^5*c^5*d^16*(d^7*(a*d - b*c)^9)^(1/2)*(a + b/x)^(1/2) + 2414601*a^16*b^4*c^4*d^17*(d^7*(a*d - b*c)^9)^(1/2)*(a + b/x)^(1/2) - 731920*a^17*b^3*c^3*d^18*(d^7*(a*d - b*c)^9)^(1/2)*(a + b/x)^(1/2) + 151904*a^18*b^2*c^2*d^19*(d^7*(a*d - b*c)^9)^(1/2)*(a + b/x)^(1/2) + 9024*a^10*b*c*d^4*(d^7*(a*d - b*c)^9)^(3/2)*(a + b/x)^(1/2) - 19392*a^19*b*c*d^20*(d^7*(a*d - b*c)^9)^(1/2)*(a + b/x)^(1/2))*(d^7*(a*d - b*c)^9)^(1/2)*(3*a^2*d^2 + (99*b^2*c^2)/8 - 11*a*b*c*d))/(b^9*c^13 - a^9*c^4*d^9 + 9*a^8*b*c^5*d^8 + 36*a^2*b^7*c^11*d^2 - 84*a^3*b^6*c^10*d^3 + 126*a^4*b^5*c^9*d^4 - 126*a^5*b^4*c^8*d^5 + 84*a^6*b^3*c^7*d^6 - 36*a^7*b^2*c^6*d^7 - 9*a*b^8*c^12*d) - (log(8240*a*b^24*c^24*d^5 - 400*b^25*c^25*d^4 - 1152*a^11*d^5*(d^7*(a*d - b*c)^9)^(3/2)*(a + b/x)^(1/2) + 1152*a^20*d^21*(d^7*(a*d - b*c)^9)^(1/2)*(a + b/x)^(1/2) - 79696*a^2*b^23*c^23*d^6 + 478768*a^3*b^22*c^22*d^7 - 1987568*a^4*b^21*c^21*d^8 + 5978896*a^5*b^20*c^20*d^9 - 13176240*a^6*b^19*c^19*d^10 + 20525703*a^7*b^18*c^18*d^11 - 18765714*a^8*b^17*c^17*d^12 - 3763331*a^9*b^16*c^16*d^13 + 49787452*a^10*b^15*c^15*d^14 - 104120705*a^11*b^14*c^14*d^15 + 140185682*a^12*b^13*c^13*d^16 - 139985251*a^13*b^12*c^12*d^17 + 108046616*a^14*b^11*c^11*d^18 - 65184867*a^15*b^10*c^10*d^19 + 30607170*a^16*b^9*c^9*d^20 - 10996689*a^17*b^8*c^8*d^21 + 2926572*a^18*b^7*c^7*d^22 - 544467*a^19*b^6*c^6*d^23 + 63294*a^20*b^5*c^5*d^24 - 3465*a^21*b^4*c^4*d^25 + 400*b^20*c^20*d*(d^7*(a*d - b*c)^9)^(1/2)*(a + b/x)^(1/2) + 9801*a^6*b^5*c^5*(d^7*(a*d - b*c)^9)^(3/2)*(a + b/x)^(1/2) - 37026*a^7*b^4*c^4*d*(d^7*(a*d - b*c)^9)^(3/2)*(a + b/x)^(1/2) - 6240*a*b^19*c^19*d^2*(d^7*(a*d - b*c)^9)^(1/2)*(a + b/x)^(1/2) + 47344*a^8*b^3*c^3*d^2*(d^7*(a*d - b*c)^9)^(3/2)*(a + b/x)^(1/2) - 29216*a^9*b^2*c^2*d^3*(d^7*(a*d - b*c)^9)^(3/2)*(a + b/x)^(1/2) + 44496*a^2*b^18*c^18*d^3*(d^7*(a*d - b*c)^9)^(1/2)*(a + b/x)^(1/2) - 189888*a^3*b^17*c^17*d^4*(d^7*(a*d - b*c)^9)^(1/2)*(a + b/x)^(1/2) + 528768*a^4*b^16*c^16*d^5*(d^7*(a*d - b*c)^9)^(1/2)*(a + b/x)^(1/2) - 959616*a^5*b^15*c^15*d^6*(d^7*(a*d - b*c)^9)^(1/2)*(a + b/x)^(1/2) + 972681*a^6*b^14*c^14*d^7*(d^7*(a*d - b*c)^9)^(1/2)*(a + b/x)^(1/2) + 41238*a^7*b^13*c^13*d^8*(d^7*(a*d - b*c)^9)^(1/2)*(a + b/x)^(1/2) - 1727195*a^8*b^12*c^12*d^9*(d^7*(a*d - b*c)^9)^(1/2)*(a + b/x)^(1/2) + 2139672*a^9*b^11*c^11*d^10*(d^7*(a*d - b*c)^9)^(1/2)*(a + b/x)^(1/2) + 786834*a^10*b^10*c^10*d^11*(d^7*(a*d - b*c)^9)^(1/2)*(a + b/x)^(1/2) - 6551292*a^11*b^9*c^9*d^12*(d^7*(a*d - b*c)^9)^(1/2)*(a + b/x)^(1/2) + 11685186*a^12*b^8*c^8*d^13*(d^7*(a*d - b*c)^9)^(1/2)*(a + b/x)^(1/2) - 12876696*a^13*b^7*c^7*d^14*(d^7*(a*d - b*c)^9)^(1/2)*(a + b/x)^(1/2) + 10033077*a^14*b^6*c^6*d^15*(d^7*(a*d - b*c)^9)^(1/2)*(a + b/x)^(1/2) - 5737770*a^15*b^5*c^5*d^16*(d^7*(a*d - b*c)^9)^(1/2)*(a + b/x)^(1/2) + 2414601*a^16*b^4*c^4*d^17*(d^7*(a*d - b*c)^9)^(1/2)*(a + b/x)^(1/2) - 731920*a^17*b^3*c^3*d^18*(d^7*(a*d - b*c)^9)^(1/2)*(a + b/x)^(1/2) + 151904*a^18*b^2*c^2*d^19*(d^7*(a*d - b*c)^9)^(1/2)*(a + b/x)^(1/2) + 9024*a^10*b*c*d^4*(d^7*(a*d - b*c)^9)^(3/2)*(a + b/x)^(1/2) - 19392*a^19*b*c*d^20*(d^7*(a*d - b*c)^9)^(1/2)*(a + b/x)^(1/2))*(d^7*(a*d - b*c)^9)^(1/2)*(24*a^2*d^2 + 99*b^2*c^2 - 88*a*b*c*d))/(8*(b^9*c^13 - a^9*c^4*d^9 + 9*a^8*b*c^5*d^8 + 36*a^2*b^7*c^11*d^2 - 84*a^3*b^6*c^10*d^3 + 126*a^4*b^5*c^9*d^4 - 126*a^5*b^4*c^8*d^5 + 84*a^6*b^3*c^7*d^6 - 36*a^7*b^2*c^6*d^7 - 9*a*b^8*c^12*d))","B"
266,1,4674,123,22.224237,"\text{Not used}","int((a + b/x)^(1/2)*(c + d/x)^(1/2),x)","\frac{d\,\left(\sqrt{a+\frac{b}{x}}-\sqrt{a}\right)}{4\,\left(\sqrt{c+\frac{d}{x}}-\sqrt{c}\right)}-\frac{\frac{\left(\sqrt{a+\frac{b}{x}}-\sqrt{a}\right)\,\left(\frac{c\,b^2}{4}+\frac{a\,d\,b}{4}\right)}{\sqrt{a}\,\sqrt{c}\,d\,\left(\sqrt{c+\frac{d}{x}}-\sqrt{c}\right)}-\frac{b^2}{4\,d}+\frac{{\left(\sqrt{a+\frac{b}{x}}-\sqrt{a}\right)}^2\,\left(\frac{a^2\,d^2}{4}-\frac{3\,a\,b\,c\,d}{4}+\frac{b^2\,c^2}{4}\right)}{a\,c\,d\,{\left(\sqrt{c+\frac{d}{x}}-\sqrt{c}\right)}^2}}{\frac{{\left(\sqrt{a+\frac{b}{x}}-\sqrt{a}\right)}^3}{{\left(\sqrt{c+\frac{d}{x}}-\sqrt{c}\right)}^3}+\frac{b\,\left(\sqrt{a+\frac{b}{x}}-\sqrt{a}\right)}{d\,\left(\sqrt{c+\frac{d}{x}}-\sqrt{c}\right)}-\frac{{\left(\sqrt{a+\frac{b}{x}}-\sqrt{a}\right)}^2\,\left(a\,d+b\,c\right)}{\sqrt{a}\,\sqrt{c}\,d\,{\left(\sqrt{c+\frac{d}{x}}-\sqrt{c}\right)}^2}}+\frac{\ln\left(\frac{\sqrt{a+\frac{b}{x}}-\sqrt{a}}{\sqrt{c+\frac{d}{x}}-\sqrt{c}}\right)\,\left(a\,d+b\,c\right)}{2\,\sqrt{a}\,\sqrt{c}}-\frac{\ln\left(\frac{\left(\sqrt{c}\,\sqrt{a+\frac{b}{x}}-\sqrt{a}\,\sqrt{c+\frac{d}{x}}\right)\,\left(b\,\sqrt{c}-\frac{\sqrt{a}\,d\,\left(\sqrt{a+\frac{b}{x}}-\sqrt{a}\right)}{\sqrt{c+\frac{d}{x}}-\sqrt{c}}\right)}{\sqrt{c+\frac{d}{x}}-\sqrt{c}}\right)\,\left(\sqrt{a}\,b\,c^{3/2}+a^{3/2}\,\sqrt{c}\,d\right)}{2\,a\,c}+\mathrm{atan}\left(\frac{\sqrt{b\,d}\,\left(2\,\sqrt{b\,d}\,\left(2\,\sqrt{b\,d}\,\left(2\,\sqrt{b\,d}\,\left(\frac{2\,\left(4\,a^{9/2}\,b^9\,c^{19/2}-4\,a^{13/2}\,b^7\,c^{15/2}\,d^2-4\,a^{15/2}\,b^6\,c^{13/2}\,d^3+4\,a^{19/2}\,b^4\,c^{9/2}\,d^5\right)}{a^7\,c^7\,d^9}-\frac{\left(\sqrt{a+\frac{b}{x}}-\sqrt{a}\right)\,\left(32\,a^{10}\,b^3\,c^4\,d^6-120\,a^9\,b^4\,c^5\,d^5+288\,a^8\,b^5\,c^6\,d^4-400\,a^7\,b^6\,c^7\,d^3+288\,a^6\,b^7\,c^8\,d^2-120\,a^5\,b^8\,c^9\,d+32\,a^4\,b^9\,c^{10}\right)}{2\,a^7\,c^7\,d^9\,\left(\sqrt{c+\frac{d}{x}}-\sqrt{c}\right)}\right)-\frac{2\,\left(8\,a^9\,b^5\,c^5\,d^5+16\,a^8\,b^6\,c^6\,d^4-48\,a^7\,b^7\,c^7\,d^3+16\,a^6\,b^8\,c^8\,d^2+8\,a^5\,b^9\,c^9\,d\right)}{a^7\,c^7\,d^9}+\frac{\left(\sqrt{a+\frac{b}{x}}-\sqrt{a}\right)\,\left(16\,a^{7/2}\,b^{10}\,c^{21/2}-76\,a^{9/2}\,b^9\,c^{19/2}\,d+228\,a^{11/2}\,b^8\,c^{17/2}\,d^2-168\,a^{13/2}\,b^7\,c^{15/2}\,d^3-168\,a^{15/2}\,b^6\,c^{13/2}\,d^4+228\,a^{17/2}\,b^5\,c^{11/2}\,d^5-76\,a^{19/2}\,b^4\,c^{9/2}\,d^6+16\,a^{21/2}\,b^3\,c^{7/2}\,d^7\right)}{2\,a^7\,c^7\,d^9\,\left(\sqrt{c+\frac{d}{x}}-\sqrt{c}\right)}\right)-\frac{2\,\left(a^{7/2}\,b^{11}\,c^{21/2}+16\,a^{9/2}\,b^{10}\,c^{19/2}\,d-42\,a^{11/2}\,b^9\,c^{17/2}\,d^2+25\,a^{13/2}\,b^8\,c^{15/2}\,d^3+25\,a^{15/2}\,b^7\,c^{13/2}\,d^4-42\,a^{17/2}\,b^6\,c^{11/2}\,d^5+16\,a^{19/2}\,b^5\,c^{9/2}\,d^6+a^{21/2}\,b^4\,c^{7/2}\,d^7\right)}{a^7\,c^7\,d^9}+\frac{\left(\sqrt{a+\frac{b}{x}}-\sqrt{a}\right)\,\left(146\,a^{10}\,b^4\,c^4\,d^7-556\,a^9\,b^5\,c^5\,d^6+1006\,a^8\,b^6\,c^6\,d^5-1192\,a^7\,b^7\,c^7\,d^4+1006\,a^6\,b^8\,c^8\,d^3-556\,a^5\,b^9\,c^9\,d^2+146\,a^4\,b^{10}\,c^{10}\,d\right)}{2\,a^7\,c^7\,d^9\,\left(\sqrt{c+\frac{d}{x}}-\sqrt{c}\right)}\right)+\frac{2\,\left(2\,a^{10}\,b^5\,c^4\,d^7+8\,a^9\,b^6\,c^5\,d^6-2\,a^8\,b^7\,c^6\,d^5-16\,a^7\,b^8\,c^7\,d^4-2\,a^6\,b^9\,c^8\,d^3+8\,a^5\,b^{10}\,c^9\,d^2+2\,a^4\,b^{11}\,c^{10}\,d\right)}{a^7\,c^7\,d^9}-\frac{\left(\sqrt{a+\frac{b}{x}}-\sqrt{a}\right)\,\left(65\,a^{7/2}\,b^{11}\,c^{21/2}\,d-297\,a^{9/2}\,b^{10}\,c^{19/2}\,d^2+597\,a^{11/2}\,b^9\,c^{17/2}\,d^3-365\,a^{13/2}\,b^8\,c^{15/2}\,d^4-365\,a^{15/2}\,b^7\,c^{13/2}\,d^5+597\,a^{17/2}\,b^6\,c^{11/2}\,d^6-297\,a^{19/2}\,b^5\,c^{9/2}\,d^7+65\,a^{21/2}\,b^4\,c^{7/2}\,d^8\right)}{2\,a^7\,c^7\,d^9\,\left(\sqrt{c+\frac{d}{x}}-\sqrt{c}\right)}\right)\,1{}\mathrm{i}-\sqrt{b\,d}\,\left(2\,\sqrt{b\,d}\,\left(2\,\sqrt{b\,d}\,\left(2\,\sqrt{b\,d}\,\left(\frac{2\,\left(4\,a^{9/2}\,b^9\,c^{19/2}-4\,a^{13/2}\,b^7\,c^{15/2}\,d^2-4\,a^{15/2}\,b^6\,c^{13/2}\,d^3+4\,a^{19/2}\,b^4\,c^{9/2}\,d^5\right)}{a^7\,c^7\,d^9}-\frac{\left(\sqrt{a+\frac{b}{x}}-\sqrt{a}\right)\,\left(32\,a^{10}\,b^3\,c^4\,d^6-120\,a^9\,b^4\,c^5\,d^5+288\,a^8\,b^5\,c^6\,d^4-400\,a^7\,b^6\,c^7\,d^3+288\,a^6\,b^7\,c^8\,d^2-120\,a^5\,b^8\,c^9\,d+32\,a^4\,b^9\,c^{10}\right)}{2\,a^7\,c^7\,d^9\,\left(\sqrt{c+\frac{d}{x}}-\sqrt{c}\right)}\right)+\frac{2\,\left(8\,a^9\,b^5\,c^5\,d^5+16\,a^8\,b^6\,c^6\,d^4-48\,a^7\,b^7\,c^7\,d^3+16\,a^6\,b^8\,c^8\,d^2+8\,a^5\,b^9\,c^9\,d\right)}{a^7\,c^7\,d^9}-\frac{\left(\sqrt{a+\frac{b}{x}}-\sqrt{a}\right)\,\left(16\,a^{7/2}\,b^{10}\,c^{21/2}-76\,a^{9/2}\,b^9\,c^{19/2}\,d+228\,a^{11/2}\,b^8\,c^{17/2}\,d^2-168\,a^{13/2}\,b^7\,c^{15/2}\,d^3-168\,a^{15/2}\,b^6\,c^{13/2}\,d^4+228\,a^{17/2}\,b^5\,c^{11/2}\,d^5-76\,a^{19/2}\,b^4\,c^{9/2}\,d^6+16\,a^{21/2}\,b^3\,c^{7/2}\,d^7\right)}{2\,a^7\,c^7\,d^9\,\left(\sqrt{c+\frac{d}{x}}-\sqrt{c}\right)}\right)-\frac{2\,\left(a^{7/2}\,b^{11}\,c^{21/2}+16\,a^{9/2}\,b^{10}\,c^{19/2}\,d-42\,a^{11/2}\,b^9\,c^{17/2}\,d^2+25\,a^{13/2}\,b^8\,c^{15/2}\,d^3+25\,a^{15/2}\,b^7\,c^{13/2}\,d^4-42\,a^{17/2}\,b^6\,c^{11/2}\,d^5+16\,a^{19/2}\,b^5\,c^{9/2}\,d^6+a^{21/2}\,b^4\,c^{7/2}\,d^7\right)}{a^7\,c^7\,d^9}+\frac{\left(\sqrt{a+\frac{b}{x}}-\sqrt{a}\right)\,\left(146\,a^{10}\,b^4\,c^4\,d^7-556\,a^9\,b^5\,c^5\,d^6+1006\,a^8\,b^6\,c^6\,d^5-1192\,a^7\,b^7\,c^7\,d^4+1006\,a^6\,b^8\,c^8\,d^3-556\,a^5\,b^9\,c^9\,d^2+146\,a^4\,b^{10}\,c^{10}\,d\right)}{2\,a^7\,c^7\,d^9\,\left(\sqrt{c+\frac{d}{x}}-\sqrt{c}\right)}\right)-\frac{2\,\left(2\,a^{10}\,b^5\,c^4\,d^7+8\,a^9\,b^6\,c^5\,d^6-2\,a^8\,b^7\,c^6\,d^5-16\,a^7\,b^8\,c^7\,d^4-2\,a^6\,b^9\,c^8\,d^3+8\,a^5\,b^{10}\,c^9\,d^2+2\,a^4\,b^{11}\,c^{10}\,d\right)}{a^7\,c^7\,d^9}+\frac{\left(\sqrt{a+\frac{b}{x}}-\sqrt{a}\right)\,\left(65\,a^{7/2}\,b^{11}\,c^{21/2}\,d-297\,a^{9/2}\,b^{10}\,c^{19/2}\,d^2+597\,a^{11/2}\,b^9\,c^{17/2}\,d^3-365\,a^{13/2}\,b^8\,c^{15/2}\,d^4-365\,a^{15/2}\,b^7\,c^{13/2}\,d^5+597\,a^{17/2}\,b^6\,c^{11/2}\,d^6-297\,a^{19/2}\,b^5\,c^{9/2}\,d^7+65\,a^{21/2}\,b^4\,c^{7/2}\,d^8\right)}{2\,a^7\,c^7\,d^9\,\left(\sqrt{c+\frac{d}{x}}-\sqrt{c}\right)}\right)\,1{}\mathrm{i}}{\sqrt{b\,d}\,\left(2\,\sqrt{b\,d}\,\left(2\,\sqrt{b\,d}\,\left(2\,\sqrt{b\,d}\,\left(\frac{2\,\left(4\,a^{9/2}\,b^9\,c^{19/2}-4\,a^{13/2}\,b^7\,c^{15/2}\,d^2-4\,a^{15/2}\,b^6\,c^{13/2}\,d^3+4\,a^{19/2}\,b^4\,c^{9/2}\,d^5\right)}{a^7\,c^7\,d^9}-\frac{\left(\sqrt{a+\frac{b}{x}}-\sqrt{a}\right)\,\left(32\,a^{10}\,b^3\,c^4\,d^6-120\,a^9\,b^4\,c^5\,d^5+288\,a^8\,b^5\,c^6\,d^4-400\,a^7\,b^6\,c^7\,d^3+288\,a^6\,b^7\,c^8\,d^2-120\,a^5\,b^8\,c^9\,d+32\,a^4\,b^9\,c^{10}\right)}{2\,a^7\,c^7\,d^9\,\left(\sqrt{c+\frac{d}{x}}-\sqrt{c}\right)}\right)-\frac{2\,\left(8\,a^9\,b^5\,c^5\,d^5+16\,a^8\,b^6\,c^6\,d^4-48\,a^7\,b^7\,c^7\,d^3+16\,a^6\,b^8\,c^8\,d^2+8\,a^5\,b^9\,c^9\,d\right)}{a^7\,c^7\,d^9}+\frac{\left(\sqrt{a+\frac{b}{x}}-\sqrt{a}\right)\,\left(16\,a^{7/2}\,b^{10}\,c^{21/2}-76\,a^{9/2}\,b^9\,c^{19/2}\,d+228\,a^{11/2}\,b^8\,c^{17/2}\,d^2-168\,a^{13/2}\,b^7\,c^{15/2}\,d^3-168\,a^{15/2}\,b^6\,c^{13/2}\,d^4+228\,a^{17/2}\,b^5\,c^{11/2}\,d^5-76\,a^{19/2}\,b^4\,c^{9/2}\,d^6+16\,a^{21/2}\,b^3\,c^{7/2}\,d^7\right)}{2\,a^7\,c^7\,d^9\,\left(\sqrt{c+\frac{d}{x}}-\sqrt{c}\right)}\right)-\frac{2\,\left(a^{7/2}\,b^{11}\,c^{21/2}+16\,a^{9/2}\,b^{10}\,c^{19/2}\,d-42\,a^{11/2}\,b^9\,c^{17/2}\,d^2+25\,a^{13/2}\,b^8\,c^{15/2}\,d^3+25\,a^{15/2}\,b^7\,c^{13/2}\,d^4-42\,a^{17/2}\,b^6\,c^{11/2}\,d^5+16\,a^{19/2}\,b^5\,c^{9/2}\,d^6+a^{21/2}\,b^4\,c^{7/2}\,d^7\right)}{a^7\,c^7\,d^9}+\frac{\left(\sqrt{a+\frac{b}{x}}-\sqrt{a}\right)\,\left(146\,a^{10}\,b^4\,c^4\,d^7-556\,a^9\,b^5\,c^5\,d^6+1006\,a^8\,b^6\,c^6\,d^5-1192\,a^7\,b^7\,c^7\,d^4+1006\,a^6\,b^8\,c^8\,d^3-556\,a^5\,b^9\,c^9\,d^2+146\,a^4\,b^{10}\,c^{10}\,d\right)}{2\,a^7\,c^7\,d^9\,\left(\sqrt{c+\frac{d}{x}}-\sqrt{c}\right)}\right)+\frac{2\,\left(2\,a^{10}\,b^5\,c^4\,d^7+8\,a^9\,b^6\,c^5\,d^6-2\,a^8\,b^7\,c^6\,d^5-16\,a^7\,b^8\,c^7\,d^4-2\,a^6\,b^9\,c^8\,d^3+8\,a^5\,b^{10}\,c^9\,d^2+2\,a^4\,b^{11}\,c^{10}\,d\right)}{a^7\,c^7\,d^9}-\frac{\left(\sqrt{a+\frac{b}{x}}-\sqrt{a}\right)\,\left(65\,a^{7/2}\,b^{11}\,c^{21/2}\,d-297\,a^{9/2}\,b^{10}\,c^{19/2}\,d^2+597\,a^{11/2}\,b^9\,c^{17/2}\,d^3-365\,a^{13/2}\,b^8\,c^{15/2}\,d^4-365\,a^{15/2}\,b^7\,c^{13/2}\,d^5+597\,a^{17/2}\,b^6\,c^{11/2}\,d^6-297\,a^{19/2}\,b^5\,c^{9/2}\,d^7+65\,a^{21/2}\,b^4\,c^{7/2}\,d^8\right)}{2\,a^7\,c^7\,d^9\,\left(\sqrt{c+\frac{d}{x}}-\sqrt{c}\right)}\right)+\sqrt{b\,d}\,\left(2\,\sqrt{b\,d}\,\left(2\,\sqrt{b\,d}\,\left(2\,\sqrt{b\,d}\,\left(\frac{2\,\left(4\,a^{9/2}\,b^9\,c^{19/2}-4\,a^{13/2}\,b^7\,c^{15/2}\,d^2-4\,a^{15/2}\,b^6\,c^{13/2}\,d^3+4\,a^{19/2}\,b^4\,c^{9/2}\,d^5\right)}{a^7\,c^7\,d^9}-\frac{\left(\sqrt{a+\frac{b}{x}}-\sqrt{a}\right)\,\left(32\,a^{10}\,b^3\,c^4\,d^6-120\,a^9\,b^4\,c^5\,d^5+288\,a^8\,b^5\,c^6\,d^4-400\,a^7\,b^6\,c^7\,d^3+288\,a^6\,b^7\,c^8\,d^2-120\,a^5\,b^8\,c^9\,d+32\,a^4\,b^9\,c^{10}\right)}{2\,a^7\,c^7\,d^9\,\left(\sqrt{c+\frac{d}{x}}-\sqrt{c}\right)}\right)+\frac{2\,\left(8\,a^9\,b^5\,c^5\,d^5+16\,a^8\,b^6\,c^6\,d^4-48\,a^7\,b^7\,c^7\,d^3+16\,a^6\,b^8\,c^8\,d^2+8\,a^5\,b^9\,c^9\,d\right)}{a^7\,c^7\,d^9}-\frac{\left(\sqrt{a+\frac{b}{x}}-\sqrt{a}\right)\,\left(16\,a^{7/2}\,b^{10}\,c^{21/2}-76\,a^{9/2}\,b^9\,c^{19/2}\,d+228\,a^{11/2}\,b^8\,c^{17/2}\,d^2-168\,a^{13/2}\,b^7\,c^{15/2}\,d^3-168\,a^{15/2}\,b^6\,c^{13/2}\,d^4+228\,a^{17/2}\,b^5\,c^{11/2}\,d^5-76\,a^{19/2}\,b^4\,c^{9/2}\,d^6+16\,a^{21/2}\,b^3\,c^{7/2}\,d^7\right)}{2\,a^7\,c^7\,d^9\,\left(\sqrt{c+\frac{d}{x}}-\sqrt{c}\right)}\right)-\frac{2\,\left(a^{7/2}\,b^{11}\,c^{21/2}+16\,a^{9/2}\,b^{10}\,c^{19/2}\,d-42\,a^{11/2}\,b^9\,c^{17/2}\,d^2+25\,a^{13/2}\,b^8\,c^{15/2}\,d^3+25\,a^{15/2}\,b^7\,c^{13/2}\,d^4-42\,a^{17/2}\,b^6\,c^{11/2}\,d^5+16\,a^{19/2}\,b^5\,c^{9/2}\,d^6+a^{21/2}\,b^4\,c^{7/2}\,d^7\right)}{a^7\,c^7\,d^9}+\frac{\left(\sqrt{a+\frac{b}{x}}-\sqrt{a}\right)\,\left(146\,a^{10}\,b^4\,c^4\,d^7-556\,a^9\,b^5\,c^5\,d^6+1006\,a^8\,b^6\,c^6\,d^5-1192\,a^7\,b^7\,c^7\,d^4+1006\,a^6\,b^8\,c^8\,d^3-556\,a^5\,b^9\,c^9\,d^2+146\,a^4\,b^{10}\,c^{10}\,d\right)}{2\,a^7\,c^7\,d^9\,\left(\sqrt{c+\frac{d}{x}}-\sqrt{c}\right)}\right)-\frac{2\,\left(2\,a^{10}\,b^5\,c^4\,d^7+8\,a^9\,b^6\,c^5\,d^6-2\,a^8\,b^7\,c^6\,d^5-16\,a^7\,b^8\,c^7\,d^4-2\,a^6\,b^9\,c^8\,d^3+8\,a^5\,b^{10}\,c^9\,d^2+2\,a^4\,b^{11}\,c^{10}\,d\right)}{a^7\,c^7\,d^9}+\frac{\left(\sqrt{a+\frac{b}{x}}-\sqrt{a}\right)\,\left(65\,a^{7/2}\,b^{11}\,c^{21/2}\,d-297\,a^{9/2}\,b^{10}\,c^{19/2}\,d^2+597\,a^{11/2}\,b^9\,c^{17/2}\,d^3-365\,a^{13/2}\,b^8\,c^{15/2}\,d^4-365\,a^{15/2}\,b^7\,c^{13/2}\,d^5+597\,a^{17/2}\,b^6\,c^{11/2}\,d^6-297\,a^{19/2}\,b^5\,c^{9/2}\,d^7+65\,a^{21/2}\,b^4\,c^{7/2}\,d^8\right)}{2\,a^7\,c^7\,d^9\,\left(\sqrt{c+\frac{d}{x}}-\sqrt{c}\right)}\right)+\frac{7\,a^{7/2}\,b^{12}\,c^{21/2}\,d-7\,a^{9/2}\,b^{11}\,c^{19/2}\,d^2-21\,a^{11/2}\,b^{10}\,c^{17/2}\,d^3+21\,a^{13/2}\,b^9\,c^{15/2}\,d^4+21\,a^{15/2}\,b^8\,c^{13/2}\,d^5-21\,a^{17/2}\,b^7\,c^{11/2}\,d^6-7\,a^{19/2}\,b^6\,c^{9/2}\,d^7+7\,a^{21/2}\,b^5\,c^{7/2}\,d^8}{a^7\,c^7\,d^9}+\frac{\left(\sqrt{a+\frac{b}{x}}-\sqrt{a}\right)\,\left(-56\,a^{10}\,b^5\,c^4\,d^8+112\,a^9\,b^6\,c^5\,d^7+56\,a^8\,b^7\,c^6\,d^6-224\,a^7\,b^8\,c^7\,d^5+56\,a^6\,b^9\,c^8\,d^4+112\,a^5\,b^{10}\,c^9\,d^3-56\,a^4\,b^{11}\,c^{10}\,d^2\right)}{2\,a^7\,c^7\,d^9\,\left(\sqrt{c+\frac{d}{x}}-\sqrt{c}\right)}}\right)\,\sqrt{b\,d}\,4{}\mathrm{i}","Not used",1,"atan(((b*d)^(1/2)*(2*(b*d)^(1/2)*(2*(b*d)^(1/2)*(2*(b*d)^(1/2)*((2*(4*a^(9/2)*b^9*c^(19/2) - 4*a^(13/2)*b^7*c^(15/2)*d^2 - 4*a^(15/2)*b^6*c^(13/2)*d^3 + 4*a^(19/2)*b^4*c^(9/2)*d^5))/(a^7*c^7*d^9) - (((a + b/x)^(1/2) - a^(1/2))*(32*a^4*b^9*c^10 - 120*a^5*b^8*c^9*d + 288*a^6*b^7*c^8*d^2 - 400*a^7*b^6*c^7*d^3 + 288*a^8*b^5*c^6*d^4 - 120*a^9*b^4*c^5*d^5 + 32*a^10*b^3*c^4*d^6))/(2*a^7*c^7*d^9*((c + d/x)^(1/2) - c^(1/2)))) - (2*(8*a^5*b^9*c^9*d + 16*a^6*b^8*c^8*d^2 - 48*a^7*b^7*c^7*d^3 + 16*a^8*b^6*c^6*d^4 + 8*a^9*b^5*c^5*d^5))/(a^7*c^7*d^9) + (((a + b/x)^(1/2) - a^(1/2))*(16*a^(7/2)*b^10*c^(21/2) - 76*a^(9/2)*b^9*c^(19/2)*d + 228*a^(11/2)*b^8*c^(17/2)*d^2 - 168*a^(13/2)*b^7*c^(15/2)*d^3 - 168*a^(15/2)*b^6*c^(13/2)*d^4 + 228*a^(17/2)*b^5*c^(11/2)*d^5 - 76*a^(19/2)*b^4*c^(9/2)*d^6 + 16*a^(21/2)*b^3*c^(7/2)*d^7))/(2*a^7*c^7*d^9*((c + d/x)^(1/2) - c^(1/2)))) - (2*(a^(7/2)*b^11*c^(21/2) + 16*a^(9/2)*b^10*c^(19/2)*d - 42*a^(11/2)*b^9*c^(17/2)*d^2 + 25*a^(13/2)*b^8*c^(15/2)*d^3 + 25*a^(15/2)*b^7*c^(13/2)*d^4 - 42*a^(17/2)*b^6*c^(11/2)*d^5 + 16*a^(19/2)*b^5*c^(9/2)*d^6 + a^(21/2)*b^4*c^(7/2)*d^7))/(a^7*c^7*d^9) + (((a + b/x)^(1/2) - a^(1/2))*(146*a^4*b^10*c^10*d - 556*a^5*b^9*c^9*d^2 + 1006*a^6*b^8*c^8*d^3 - 1192*a^7*b^7*c^7*d^4 + 1006*a^8*b^6*c^6*d^5 - 556*a^9*b^5*c^5*d^6 + 146*a^10*b^4*c^4*d^7))/(2*a^7*c^7*d^9*((c + d/x)^(1/2) - c^(1/2)))) + (2*(2*a^4*b^11*c^10*d + 8*a^5*b^10*c^9*d^2 - 2*a^6*b^9*c^8*d^3 - 16*a^7*b^8*c^7*d^4 - 2*a^8*b^7*c^6*d^5 + 8*a^9*b^6*c^5*d^6 + 2*a^10*b^5*c^4*d^7))/(a^7*c^7*d^9) - (((a + b/x)^(1/2) - a^(1/2))*(65*a^(7/2)*b^11*c^(21/2)*d - 297*a^(9/2)*b^10*c^(19/2)*d^2 + 597*a^(11/2)*b^9*c^(17/2)*d^3 - 365*a^(13/2)*b^8*c^(15/2)*d^4 - 365*a^(15/2)*b^7*c^(13/2)*d^5 + 597*a^(17/2)*b^6*c^(11/2)*d^6 - 297*a^(19/2)*b^5*c^(9/2)*d^7 + 65*a^(21/2)*b^4*c^(7/2)*d^8))/(2*a^7*c^7*d^9*((c + d/x)^(1/2) - c^(1/2))))*1i - (b*d)^(1/2)*(2*(b*d)^(1/2)*(2*(b*d)^(1/2)*(2*(b*d)^(1/2)*((2*(4*a^(9/2)*b^9*c^(19/2) - 4*a^(13/2)*b^7*c^(15/2)*d^2 - 4*a^(15/2)*b^6*c^(13/2)*d^3 + 4*a^(19/2)*b^4*c^(9/2)*d^5))/(a^7*c^7*d^9) - (((a + b/x)^(1/2) - a^(1/2))*(32*a^4*b^9*c^10 - 120*a^5*b^8*c^9*d + 288*a^6*b^7*c^8*d^2 - 400*a^7*b^6*c^7*d^3 + 288*a^8*b^5*c^6*d^4 - 120*a^9*b^4*c^5*d^5 + 32*a^10*b^3*c^4*d^6))/(2*a^7*c^7*d^9*((c + d/x)^(1/2) - c^(1/2)))) + (2*(8*a^5*b^9*c^9*d + 16*a^6*b^8*c^8*d^2 - 48*a^7*b^7*c^7*d^3 + 16*a^8*b^6*c^6*d^4 + 8*a^9*b^5*c^5*d^5))/(a^7*c^7*d^9) - (((a + b/x)^(1/2) - a^(1/2))*(16*a^(7/2)*b^10*c^(21/2) - 76*a^(9/2)*b^9*c^(19/2)*d + 228*a^(11/2)*b^8*c^(17/2)*d^2 - 168*a^(13/2)*b^7*c^(15/2)*d^3 - 168*a^(15/2)*b^6*c^(13/2)*d^4 + 228*a^(17/2)*b^5*c^(11/2)*d^5 - 76*a^(19/2)*b^4*c^(9/2)*d^6 + 16*a^(21/2)*b^3*c^(7/2)*d^7))/(2*a^7*c^7*d^9*((c + d/x)^(1/2) - c^(1/2)))) - (2*(a^(7/2)*b^11*c^(21/2) + 16*a^(9/2)*b^10*c^(19/2)*d - 42*a^(11/2)*b^9*c^(17/2)*d^2 + 25*a^(13/2)*b^8*c^(15/2)*d^3 + 25*a^(15/2)*b^7*c^(13/2)*d^4 - 42*a^(17/2)*b^6*c^(11/2)*d^5 + 16*a^(19/2)*b^5*c^(9/2)*d^6 + a^(21/2)*b^4*c^(7/2)*d^7))/(a^7*c^7*d^9) + (((a + b/x)^(1/2) - a^(1/2))*(146*a^4*b^10*c^10*d - 556*a^5*b^9*c^9*d^2 + 1006*a^6*b^8*c^8*d^3 - 1192*a^7*b^7*c^7*d^4 + 1006*a^8*b^6*c^6*d^5 - 556*a^9*b^5*c^5*d^6 + 146*a^10*b^4*c^4*d^7))/(2*a^7*c^7*d^9*((c + d/x)^(1/2) - c^(1/2)))) - (2*(2*a^4*b^11*c^10*d + 8*a^5*b^10*c^9*d^2 - 2*a^6*b^9*c^8*d^3 - 16*a^7*b^8*c^7*d^4 - 2*a^8*b^7*c^6*d^5 + 8*a^9*b^6*c^5*d^6 + 2*a^10*b^5*c^4*d^7))/(a^7*c^7*d^9) + (((a + b/x)^(1/2) - a^(1/2))*(65*a^(7/2)*b^11*c^(21/2)*d - 297*a^(9/2)*b^10*c^(19/2)*d^2 + 597*a^(11/2)*b^9*c^(17/2)*d^3 - 365*a^(13/2)*b^8*c^(15/2)*d^4 - 365*a^(15/2)*b^7*c^(13/2)*d^5 + 597*a^(17/2)*b^6*c^(11/2)*d^6 - 297*a^(19/2)*b^5*c^(9/2)*d^7 + 65*a^(21/2)*b^4*c^(7/2)*d^8))/(2*a^7*c^7*d^9*((c + d/x)^(1/2) - c^(1/2))))*1i)/((b*d)^(1/2)*(2*(b*d)^(1/2)*(2*(b*d)^(1/2)*(2*(b*d)^(1/2)*((2*(4*a^(9/2)*b^9*c^(19/2) - 4*a^(13/2)*b^7*c^(15/2)*d^2 - 4*a^(15/2)*b^6*c^(13/2)*d^3 + 4*a^(19/2)*b^4*c^(9/2)*d^5))/(a^7*c^7*d^9) - (((a + b/x)^(1/2) - a^(1/2))*(32*a^4*b^9*c^10 - 120*a^5*b^8*c^9*d + 288*a^6*b^7*c^8*d^2 - 400*a^7*b^6*c^7*d^3 + 288*a^8*b^5*c^6*d^4 - 120*a^9*b^4*c^5*d^5 + 32*a^10*b^3*c^4*d^6))/(2*a^7*c^7*d^9*((c + d/x)^(1/2) - c^(1/2)))) - (2*(8*a^5*b^9*c^9*d + 16*a^6*b^8*c^8*d^2 - 48*a^7*b^7*c^7*d^3 + 16*a^8*b^6*c^6*d^4 + 8*a^9*b^5*c^5*d^5))/(a^7*c^7*d^9) + (((a + b/x)^(1/2) - a^(1/2))*(16*a^(7/2)*b^10*c^(21/2) - 76*a^(9/2)*b^9*c^(19/2)*d + 228*a^(11/2)*b^8*c^(17/2)*d^2 - 168*a^(13/2)*b^7*c^(15/2)*d^3 - 168*a^(15/2)*b^6*c^(13/2)*d^4 + 228*a^(17/2)*b^5*c^(11/2)*d^5 - 76*a^(19/2)*b^4*c^(9/2)*d^6 + 16*a^(21/2)*b^3*c^(7/2)*d^7))/(2*a^7*c^7*d^9*((c + d/x)^(1/2) - c^(1/2)))) - (2*(a^(7/2)*b^11*c^(21/2) + 16*a^(9/2)*b^10*c^(19/2)*d - 42*a^(11/2)*b^9*c^(17/2)*d^2 + 25*a^(13/2)*b^8*c^(15/2)*d^3 + 25*a^(15/2)*b^7*c^(13/2)*d^4 - 42*a^(17/2)*b^6*c^(11/2)*d^5 + 16*a^(19/2)*b^5*c^(9/2)*d^6 + a^(21/2)*b^4*c^(7/2)*d^7))/(a^7*c^7*d^9) + (((a + b/x)^(1/2) - a^(1/2))*(146*a^4*b^10*c^10*d - 556*a^5*b^9*c^9*d^2 + 1006*a^6*b^8*c^8*d^3 - 1192*a^7*b^7*c^7*d^4 + 1006*a^8*b^6*c^6*d^5 - 556*a^9*b^5*c^5*d^6 + 146*a^10*b^4*c^4*d^7))/(2*a^7*c^7*d^9*((c + d/x)^(1/2) - c^(1/2)))) + (2*(2*a^4*b^11*c^10*d + 8*a^5*b^10*c^9*d^2 - 2*a^6*b^9*c^8*d^3 - 16*a^7*b^8*c^7*d^4 - 2*a^8*b^7*c^6*d^5 + 8*a^9*b^6*c^5*d^6 + 2*a^10*b^5*c^4*d^7))/(a^7*c^7*d^9) - (((a + b/x)^(1/2) - a^(1/2))*(65*a^(7/2)*b^11*c^(21/2)*d - 297*a^(9/2)*b^10*c^(19/2)*d^2 + 597*a^(11/2)*b^9*c^(17/2)*d^3 - 365*a^(13/2)*b^8*c^(15/2)*d^4 - 365*a^(15/2)*b^7*c^(13/2)*d^5 + 597*a^(17/2)*b^6*c^(11/2)*d^6 - 297*a^(19/2)*b^5*c^(9/2)*d^7 + 65*a^(21/2)*b^4*c^(7/2)*d^8))/(2*a^7*c^7*d^9*((c + d/x)^(1/2) - c^(1/2)))) + (b*d)^(1/2)*(2*(b*d)^(1/2)*(2*(b*d)^(1/2)*(2*(b*d)^(1/2)*((2*(4*a^(9/2)*b^9*c^(19/2) - 4*a^(13/2)*b^7*c^(15/2)*d^2 - 4*a^(15/2)*b^6*c^(13/2)*d^3 + 4*a^(19/2)*b^4*c^(9/2)*d^5))/(a^7*c^7*d^9) - (((a + b/x)^(1/2) - a^(1/2))*(32*a^4*b^9*c^10 - 120*a^5*b^8*c^9*d + 288*a^6*b^7*c^8*d^2 - 400*a^7*b^6*c^7*d^3 + 288*a^8*b^5*c^6*d^4 - 120*a^9*b^4*c^5*d^5 + 32*a^10*b^3*c^4*d^6))/(2*a^7*c^7*d^9*((c + d/x)^(1/2) - c^(1/2)))) + (2*(8*a^5*b^9*c^9*d + 16*a^6*b^8*c^8*d^2 - 48*a^7*b^7*c^7*d^3 + 16*a^8*b^6*c^6*d^4 + 8*a^9*b^5*c^5*d^5))/(a^7*c^7*d^9) - (((a + b/x)^(1/2) - a^(1/2))*(16*a^(7/2)*b^10*c^(21/2) - 76*a^(9/2)*b^9*c^(19/2)*d + 228*a^(11/2)*b^8*c^(17/2)*d^2 - 168*a^(13/2)*b^7*c^(15/2)*d^3 - 168*a^(15/2)*b^6*c^(13/2)*d^4 + 228*a^(17/2)*b^5*c^(11/2)*d^5 - 76*a^(19/2)*b^4*c^(9/2)*d^6 + 16*a^(21/2)*b^3*c^(7/2)*d^7))/(2*a^7*c^7*d^9*((c + d/x)^(1/2) - c^(1/2)))) - (2*(a^(7/2)*b^11*c^(21/2) + 16*a^(9/2)*b^10*c^(19/2)*d - 42*a^(11/2)*b^9*c^(17/2)*d^2 + 25*a^(13/2)*b^8*c^(15/2)*d^3 + 25*a^(15/2)*b^7*c^(13/2)*d^4 - 42*a^(17/2)*b^6*c^(11/2)*d^5 + 16*a^(19/2)*b^5*c^(9/2)*d^6 + a^(21/2)*b^4*c^(7/2)*d^7))/(a^7*c^7*d^9) + (((a + b/x)^(1/2) - a^(1/2))*(146*a^4*b^10*c^10*d - 556*a^5*b^9*c^9*d^2 + 1006*a^6*b^8*c^8*d^3 - 1192*a^7*b^7*c^7*d^4 + 1006*a^8*b^6*c^6*d^5 - 556*a^9*b^5*c^5*d^6 + 146*a^10*b^4*c^4*d^7))/(2*a^7*c^7*d^9*((c + d/x)^(1/2) - c^(1/2)))) - (2*(2*a^4*b^11*c^10*d + 8*a^5*b^10*c^9*d^2 - 2*a^6*b^9*c^8*d^3 - 16*a^7*b^8*c^7*d^4 - 2*a^8*b^7*c^6*d^5 + 8*a^9*b^6*c^5*d^6 + 2*a^10*b^5*c^4*d^7))/(a^7*c^7*d^9) + (((a + b/x)^(1/2) - a^(1/2))*(65*a^(7/2)*b^11*c^(21/2)*d - 297*a^(9/2)*b^10*c^(19/2)*d^2 + 597*a^(11/2)*b^9*c^(17/2)*d^3 - 365*a^(13/2)*b^8*c^(15/2)*d^4 - 365*a^(15/2)*b^7*c^(13/2)*d^5 + 597*a^(17/2)*b^6*c^(11/2)*d^6 - 297*a^(19/2)*b^5*c^(9/2)*d^7 + 65*a^(21/2)*b^4*c^(7/2)*d^8))/(2*a^7*c^7*d^9*((c + d/x)^(1/2) - c^(1/2)))) + (7*a^(7/2)*b^12*c^(21/2)*d - 7*a^(9/2)*b^11*c^(19/2)*d^2 - 21*a^(11/2)*b^10*c^(17/2)*d^3 + 21*a^(13/2)*b^9*c^(15/2)*d^4 + 21*a^(15/2)*b^8*c^(13/2)*d^5 - 21*a^(17/2)*b^7*c^(11/2)*d^6 - 7*a^(19/2)*b^6*c^(9/2)*d^7 + 7*a^(21/2)*b^5*c^(7/2)*d^8)/(a^7*c^7*d^9) + (((a + b/x)^(1/2) - a^(1/2))*(112*a^5*b^10*c^9*d^3 - 56*a^4*b^11*c^10*d^2 + 56*a^6*b^9*c^8*d^4 - 224*a^7*b^8*c^7*d^5 + 56*a^8*b^7*c^6*d^6 + 112*a^9*b^6*c^5*d^7 - 56*a^10*b^5*c^4*d^8))/(2*a^7*c^7*d^9*((c + d/x)^(1/2) - c^(1/2)))))*(b*d)^(1/2)*4i - ((((a + b/x)^(1/2) - a^(1/2))*((b^2*c)/4 + (a*b*d)/4))/(a^(1/2)*c^(1/2)*d*((c + d/x)^(1/2) - c^(1/2))) - b^2/(4*d) + (((a + b/x)^(1/2) - a^(1/2))^2*((a^2*d^2)/4 + (b^2*c^2)/4 - (3*a*b*c*d)/4))/(a*c*d*((c + d/x)^(1/2) - c^(1/2))^2))/(((a + b/x)^(1/2) - a^(1/2))^3/((c + d/x)^(1/2) - c^(1/2))^3 + (b*((a + b/x)^(1/2) - a^(1/2)))/(d*((c + d/x)^(1/2) - c^(1/2))) - (((a + b/x)^(1/2) - a^(1/2))^2*(a*d + b*c))/(a^(1/2)*c^(1/2)*d*((c + d/x)^(1/2) - c^(1/2))^2)) + (d*((a + b/x)^(1/2) - a^(1/2)))/(4*((c + d/x)^(1/2) - c^(1/2))) + (log(((a + b/x)^(1/2) - a^(1/2))/((c + d/x)^(1/2) - c^(1/2)))*(a*d + b*c))/(2*a^(1/2)*c^(1/2)) - (log(((c^(1/2)*(a + b/x)^(1/2) - a^(1/2)*(c + d/x)^(1/2))*(b*c^(1/2) - (a^(1/2)*d*((a + b/x)^(1/2) - a^(1/2)))/((c + d/x)^(1/2) - c^(1/2))))/((c + d/x)^(1/2) - c^(1/2)))*(a^(1/2)*b*c^(3/2) + a^(3/2)*c^(1/2)*d))/(2*a*c)","B"
267,1,478,81,6.583007,"\text{Not used}","int((a + b/x)^(1/2)/(c + d/x)^(1/2),x)","\frac{d\,\left(\sqrt{a+\frac{b}{x}}-\sqrt{a}\right)}{4\,c\,\left(\sqrt{c+\frac{d}{x}}-\sqrt{c}\right)}-\frac{\frac{\left(\sqrt{a+\frac{b}{x}}-\sqrt{a}\right)\,\left(\frac{c\,b^2}{4}+\frac{a\,d\,b}{4}\right)}{\sqrt{a}\,c^{3/2}\,d\,\left(\sqrt{c+\frac{d}{x}}-\sqrt{c}\right)}-\frac{b^2}{4\,c\,d}+\frac{{\left(\sqrt{a+\frac{b}{x}}-\sqrt{a}\right)}^2\,\left(\frac{a^2\,d^2}{4}-\frac{3\,a\,b\,c\,d}{4}+\frac{b^2\,c^2}{4}\right)}{a\,c^2\,d\,{\left(\sqrt{c+\frac{d}{x}}-\sqrt{c}\right)}^2}}{\frac{{\left(\sqrt{a+\frac{b}{x}}-\sqrt{a}\right)}^3}{{\left(\sqrt{c+\frac{d}{x}}-\sqrt{c}\right)}^3}+\frac{b\,\left(\sqrt{a+\frac{b}{x}}-\sqrt{a}\right)}{d\,\left(\sqrt{c+\frac{d}{x}}-\sqrt{c}\right)}-\frac{{\left(\sqrt{a+\frac{b}{x}}-\sqrt{a}\right)}^2\,\left(a\,d+b\,c\right)}{\sqrt{a}\,\sqrt{c}\,d\,{\left(\sqrt{c+\frac{d}{x}}-\sqrt{c}\right)}^2}}+\frac{\ln\left(\frac{\sqrt{a+\frac{b}{x}}-\sqrt{a}}{\sqrt{c+\frac{d}{x}}-\sqrt{c}}\right)\,\left(\sqrt{a}\,b\,c^{3/2}-a^{3/2}\,\sqrt{c}\,d\right)}{2\,a\,c^2}-\frac{\ln\left(\frac{\left(\sqrt{c}\,\sqrt{a+\frac{b}{x}}-\sqrt{a}\,\sqrt{c+\frac{d}{x}}\right)\,\left(b\,\sqrt{c}-\frac{\sqrt{a}\,d\,\left(\sqrt{a+\frac{b}{x}}-\sqrt{a}\right)}{\sqrt{c+\frac{d}{x}}-\sqrt{c}}\right)}{\sqrt{c+\frac{d}{x}}-\sqrt{c}}\right)\,\left(\sqrt{a}\,b\,c^{3/2}-a^{3/2}\,\sqrt{c}\,d\right)}{2\,a\,c^2}","Not used",1,"(d*((a + b/x)^(1/2) - a^(1/2)))/(4*c*((c + d/x)^(1/2) - c^(1/2))) - ((((a + b/x)^(1/2) - a^(1/2))*((b^2*c)/4 + (a*b*d)/4))/(a^(1/2)*c^(3/2)*d*((c + d/x)^(1/2) - c^(1/2))) - b^2/(4*c*d) + (((a + b/x)^(1/2) - a^(1/2))^2*((a^2*d^2)/4 + (b^2*c^2)/4 - (3*a*b*c*d)/4))/(a*c^2*d*((c + d/x)^(1/2) - c^(1/2))^2))/(((a + b/x)^(1/2) - a^(1/2))^3/((c + d/x)^(1/2) - c^(1/2))^3 + (b*((a + b/x)^(1/2) - a^(1/2)))/(d*((c + d/x)^(1/2) - c^(1/2))) - (((a + b/x)^(1/2) - a^(1/2))^2*(a*d + b*c))/(a^(1/2)*c^(1/2)*d*((c + d/x)^(1/2) - c^(1/2))^2)) + (log(((a + b/x)^(1/2) - a^(1/2))/((c + d/x)^(1/2) - c^(1/2)))*(a^(1/2)*b*c^(3/2) - a^(3/2)*c^(1/2)*d))/(2*a*c^2) - (log(((c^(1/2)*(a + b/x)^(1/2) - a^(1/2)*(c + d/x)^(1/2))*(b*c^(1/2) - (a^(1/2)*d*((a + b/x)^(1/2) - a^(1/2)))/((c + d/x)^(1/2) - c^(1/2))))/((c + d/x)^(1/2) - c^(1/2)))*(a^(1/2)*b*c^(3/2) - a^(3/2)*c^(1/2)*d))/(2*a*c^2)","B"
268,0,-1,122,0.000000,"\text{Not used}","int((a + b/x)^(1/2)/(c + d/x)^(3/2),x)","\int \frac{\sqrt{a+\frac{b}{x}}}{{\left(c+\frac{d}{x}\right)}^{3/2}} \,d x","Not used",1,"int((a + b/x)^(1/2)/(c + d/x)^(3/2), x)","F"
269,0,-1,96,0.000000,"\text{Not used}","int((a + b/x)^p*(c + d/x)^q,x)","\int {\left(a+\frac{b}{x}\right)}^p\,{\left(c+\frac{d}{x}\right)}^q \,d x","Not used",1,"int((a + b/x)^p*(c + d/x)^q, x)","F"
270,1,32,39,0.068679,"\text{Not used}","int((a + b/x^2)/(c + d/x^2),x)","\frac{a\,x}{c}-\frac{\mathrm{atan}\left(\frac{\sqrt{c}\,x}{\sqrt{d}}\right)\,\left(a\,d-b\,c\right)}{c^{3/2}\,\sqrt{d}}","Not used",1,"(a*x)/c - (atan((c^(1/2)*x)/d^(1/2))*(a*d - b*c))/(c^(3/2)*d^(1/2))","B"
271,0,-1,233,0.000000,"\text{Not used}","int((a + b/x^2)^(1/2)*(c + d/x^2)^(1/2),x)","\int \sqrt{a+\frac{b}{x^2}}\,\sqrt{c+\frac{d}{x^2}} \,d x","Not used",1,"int((a + b/x^2)^(1/2)*(c + d/x^2)^(1/2), x)","F"
272,0,-1,232,0.000000,"\text{Not used}","int((a + b/x^2)^(1/2)/(c + d/x^2)^(1/2),x)","\int \frac{\sqrt{a+\frac{b}{x^2}}}{\sqrt{c+\frac{d}{x^2}}} \,d x","Not used",1,"int((a + b/x^2)^(1/2)/(c + d/x^2)^(1/2), x)","F"
273,0,-1,262,0.000000,"\text{Not used}","int((a + b/x^2)^(1/2)/(c + d/x^2)^(3/2),x)","\int \frac{\sqrt{a+\frac{b}{x^2}}}{{\left(c+\frac{d}{x^2}\right)}^{3/2}} \,d x","Not used",1,"int((a + b/x^2)^(1/2)/(c + d/x^2)^(3/2), x)","F"
274,0,-1,79,0.000000,"\text{Not used}","int((a + b/x^2)^p*(c + d/x^2)^q,x)","\int {\left(a+\frac{b}{x^2}\right)}^p\,{\left(c+\frac{d}{x^2}\right)}^q \,d x","Not used",1,"int((a + b/x^2)^p*(c + d/x^2)^q, x)","F"
275,1,123,145,0.274440,"\text{Not used}","int((a + b/x^3)/(c + d/x^3),x)","\frac{a\,x}{c}-\frac{\ln\left(c^{1/3}\,x+d^{1/3}\right)\,\left(a\,d-b\,c\right)}{3\,c^{4/3}\,d^{2/3}}+\frac{\ln\left(d^{1/3}-2\,c^{1/3}\,x+\sqrt{3}\,d^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(a\,d-b\,c\right)}{3\,c^{4/3}\,d^{2/3}}-\frac{\ln\left(2\,c^{1/3}\,x-d^{1/3}+\sqrt{3}\,d^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(a\,d-b\,c\right)}{3\,c^{4/3}\,d^{2/3}}","Not used",1,"(a*x)/c - (log(c^(1/3)*x + d^(1/3))*(a*d - b*c))/(3*c^(4/3)*d^(2/3)) + (log(3^(1/2)*d^(1/3)*1i - 2*c^(1/3)*x + d^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(a*d - b*c))/(3*c^(4/3)*d^(2/3)) - (log(3^(1/2)*d^(1/3)*1i + 2*c^(1/3)*x - d^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(a*d - b*c))/(3*c^(4/3)*d^(2/3))","B"
276,1,49,49,0.074253,"\text{Not used}","int((a + b*x^(1/2))/(c + d*x^(1/2)),x)","\sqrt{x}\,\left(\frac{2\,a}{d}-\frac{2\,b\,c}{d^2}\right)+\frac{\ln\left(c+d\,\sqrt{x}\right)\,\left(2\,b\,c^2-2\,a\,c\,d\right)}{d^3}+\frac{b\,x}{d}","Not used",1,"x^(1/2)*((2*a)/d - (2*b*c)/d^2) + (log(c + d*x^(1/2))*(2*b*c^2 - 2*a*c*d))/d^3 + (b*x)/d","B"
277,1,20,26,0.033597,"\text{Not used}","int((x^(1/3) - 1)/(x^(1/3) + 1),x)","x-6\,\ln\left(x^{1/3}+1\right)+6\,x^{1/3}-3\,x^{2/3}","Not used",1,"x - 6*log(x^(1/3) + 1) + 6*x^(1/3) - 3*x^(2/3)","B"
278,1,13,17,1.458045,"\text{Not used}","int((x^(2/3) + 1)/(x^(2/3) - 1),x)","x-6\,\mathrm{atanh}\left(x^{1/3}\right)+6\,x^{1/3}","Not used",1,"x - 6*atanh(x^(1/3)) + 6*x^(1/3)","B"
279,1,90,104,1.496680,"\text{Not used}","int((x^(3/4) - 16)/(x^(3/4) + 16),x)","x+\frac{256\,2^{1/3}\,\ln\left(12288\,2^{1/3}+6144\,x^{1/4}\right)}{3}-128\,x^{1/4}+\frac{128\,2^{1/3}\,\ln\left(6144\,x^{1/4}+6144\,2^{1/3}\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{3}-\frac{128\,2^{1/3}\,\ln\left(6144\,x^{1/4}-6144\,2^{1/3}\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{3}","Not used",1,"x + (256*2^(1/3)*log(12288*2^(1/3) + 6144*x^(1/4)))/3 - 128*x^(1/4) + (128*2^(1/3)*log(6144*x^(1/4) + 6144*2^(1/3)*(3^(1/2)*1i - 1))*(3^(1/2)*1i - 1))/3 - (128*2^(1/3)*log(6144*x^(1/4) - 6144*2^(1/3)*(3^(1/2)*1i + 1))*(3^(1/2)*1i + 1))/3","B"
280,1,22,30,0.041431,"\text{Not used}","int((1/x^(1/3) + 1)/(1/x^(1/3) - 1),x)","-x-6\,\ln\left(x^{1/3}-1\right)-6\,x^{1/3}-3\,x^{2/3}","Not used",1,"- x - 6*log(x^(1/3) - 1) - 6*x^(1/3) - 3*x^(2/3)","B"
281,0,-1,79,0.000000,"\text{Not used}","int((a + b*x^n)^(3/2)*(a - b*x^n)^(3/2),x)","\int {\left(a+b\,x^n\right)}^{3/2}\,{\left(a-b\,x^n\right)}^{3/2} \,d x","Not used",1,"int((a + b*x^n)^(3/2)*(a - b*x^n)^(3/2), x)","F"
282,0,-1,76,0.000000,"\text{Not used}","int((a + b*x^n)^(1/2)*(a - b*x^n)^(1/2),x)","\int \sqrt{a+b\,x^n}\,\sqrt{a-b\,x^n} \,d x","Not used",1,"int((a + b*x^n)^(1/2)*(a - b*x^n)^(1/2), x)","F"
283,0,-1,72,0.000000,"\text{Not used}","int((a + b*x^n)^p*(a - b*x^n)^p,x)","\int {\left(a+b\,x^n\right)}^p\,{\left(a-b\,x^n\right)}^p \,d x","Not used",1,"int((a + b*x^n)^p*(a - b*x^n)^p, x)","F"
284,1,131,132,1.637685,"\text{Not used}","int((a + b*x^n)*(c + d*x^n)^4,x)","a\,c^4\,x+\frac{x\,x^n\,\left(b\,c^4+4\,a\,d\,c^3\right)}{n+1}+\frac{x\,x^{4\,n}\,\left(a\,d^4+4\,b\,c\,d^3\right)}{4\,n+1}+\frac{b\,d^4\,x\,x^{5\,n}}{5\,n+1}+\frac{2\,c^2\,d\,x\,x^{2\,n}\,\left(3\,a\,d+2\,b\,c\right)}{2\,n+1}+\frac{2\,c\,d^2\,x\,x^{3\,n}\,\left(2\,a\,d+3\,b\,c\right)}{3\,n+1}","Not used",1,"a*c^4*x + (x*x^n*(b*c^4 + 4*a*c^3*d))/(n + 1) + (x*x^(4*n)*(a*d^4 + 4*b*c*d^3))/(4*n + 1) + (b*d^4*x*x^(5*n))/(5*n + 1) + (2*c^2*d*x*x^(2*n)*(3*a*d + 2*b*c))/(2*n + 1) + (2*c*d^2*x*x^(3*n)*(2*a*d + 3*b*c))/(3*n + 1)","B"
285,1,99,99,1.557311,"\text{Not used}","int((a + b*x^n)*(c + d*x^n)^3,x)","a\,c^3\,x+\frac{x\,x^n\,\left(b\,c^3+3\,a\,d\,c^2\right)}{n+1}+\frac{x\,x^{3\,n}\,\left(a\,d^3+3\,b\,c\,d^2\right)}{3\,n+1}+\frac{b\,d^3\,x\,x^{4\,n}}{4\,n+1}+\frac{3\,c\,d\,x\,x^{2\,n}\,\left(a\,d+b\,c\right)}{2\,n+1}","Not used",1,"a*c^3*x + (x*x^n*(b*c^3 + 3*a*c^2*d))/(n + 1) + (x*x^(3*n)*(a*d^3 + 3*b*c*d^2))/(3*n + 1) + (b*d^3*x*x^(4*n))/(4*n + 1) + (3*c*d*x*x^(2*n)*(a*d + b*c))/(2*n + 1)","B"
286,1,71,70,1.534607,"\text{Not used}","int((a + b*x^n)*(c + d*x^n)^2,x)","a\,c^2\,x+\frac{x\,x^{2\,n}\,\left(a\,d^2+2\,b\,c\,d\right)}{2\,n+1}+\frac{x\,x^n\,\left(b\,c^2+2\,a\,d\,c\right)}{n+1}+\frac{b\,d^2\,x\,x^{3\,n}}{3\,n+1}","Not used",1,"a*c^2*x + (x*x^(2*n)*(a*d^2 + 2*b*c*d))/(2*n + 1) + (x*x^n*(b*c^2 + 2*a*c*d))/(n + 1) + (b*d^2*x*x^(3*n))/(3*n + 1)","B"
287,1,38,40,1.482542,"\text{Not used}","int((a + b*x^n)*(c + d*x^n),x)","a\,c\,x+\frac{x\,x^n\,\left(a\,d+b\,c\right)}{n+1}+\frac{b\,d\,x\,x^{2\,n}}{2\,n+1}","Not used",1,"a*c*x + (x*x^n*(a*d + b*c))/(n + 1) + (b*d*x*x^(2*n))/(2*n + 1)","B"
288,0,-1,43,0.000000,"\text{Not used}","int((a + b*x^n)/(c + d*x^n),x)","\int \frac{a+b\,x^n}{c+d\,x^n} \,d x","Not used",1,"int((a + b*x^n)/(c + d*x^n), x)","F"
289,0,-1,73,0.000000,"\text{Not used}","int((a + b*x^n)/(c + d*x^n)^2,x)","\int \frac{a+b\,x^n}{{\left(c+d\,x^n\right)}^2} \,d x","Not used",1,"int((a + b*x^n)/(c + d*x^n)^2, x)","F"
290,0,-1,78,0.000000,"\text{Not used}","int((a + b*x^n)/(c + d*x^n)^3,x)","\int \frac{a+b\,x^n}{{\left(c+d\,x^n\right)}^3} \,d x","Not used",1,"int((a + b*x^n)/(c + d*x^n)^3, x)","F"
291,0,-1,78,0.000000,"\text{Not used}","int((a + b*x^n)/(c + d*x^n)^4,x)","\int \frac{a+b\,x^n}{{\left(c+d\,x^n\right)}^4} \,d x","Not used",1,"int((a + b*x^n)/(c + d*x^n)^4, x)","F"
292,1,157,158,1.705429,"\text{Not used}","int((a + b*x^n)^2*(d + e*x^n)^3,x)","a^2\,d^3\,x+\frac{x\,x^{2\,n}\,\left(3\,a^2\,d\,e^2+6\,a\,b\,d^2\,e+b^2\,d^3\right)}{2\,n+1}+\frac{x\,x^{3\,n}\,\left(a^2\,e^3+6\,a\,b\,d\,e^2+3\,b^2\,d^2\,e\right)}{3\,n+1}+\frac{b^2\,e^3\,x\,x^{5\,n}}{5\,n+1}+\frac{a\,d^2\,x\,x^n\,\left(3\,a\,e+2\,b\,d\right)}{n+1}+\frac{b\,e^2\,x\,x^{4\,n}\,\left(2\,a\,e+3\,b\,d\right)}{4\,n+1}","Not used",1,"a^2*d^3*x + (x*x^(2*n)*(b^2*d^3 + 3*a^2*d*e^2 + 6*a*b*d^2*e))/(2*n + 1) + (x*x^(3*n)*(a^2*e^3 + 3*b^2*d^2*e + 6*a*b*d*e^2))/(3*n + 1) + (b^2*e^3*x*x^(5*n))/(5*n + 1) + (a*d^2*x*x^n*(3*a*e + 2*b*d))/(n + 1) + (b*e^2*x*x^(4*n)*(2*a*e + 3*b*d))/(4*n + 1)","B"
293,1,108,112,1.566394,"\text{Not used}","int((a + b*x^n)^2*(d + e*x^n)^2,x)","a^2\,d^2\,x+\frac{x\,x^{2\,n}\,\left(a^2\,e^2+4\,a\,b\,d\,e+b^2\,d^2\right)}{2\,n+1}+\frac{b^2\,e^2\,x\,x^{4\,n}}{4\,n+1}+\frac{2\,b\,e\,x\,x^{3\,n}\,\left(a\,e+b\,d\right)}{3\,n+1}+\frac{2\,a\,d\,x\,x^n\,\left(a\,e+b\,d\right)}{n+1}","Not used",1,"a^2*d^2*x + (x*x^(2*n)*(a^2*e^2 + b^2*d^2 + 4*a*b*d*e))/(2*n + 1) + (b^2*e^2*x*x^(4*n))/(4*n + 1) + (2*b*e*x*x^(3*n)*(a*e + b*d))/(3*n + 1) + (2*a*d*x*x^n*(a*e + b*d))/(n + 1)","B"
294,1,71,70,1.530754,"\text{Not used}","int((a + b*x^n)^2*(c + d*x^n),x)","a^2\,c\,x+\frac{x\,x^{2\,n}\,\left(c\,b^2+2\,a\,d\,b\right)}{2\,n+1}+\frac{x\,x^n\,\left(d\,a^2+2\,b\,c\,a\right)}{n+1}+\frac{b^2\,d\,x\,x^{3\,n}}{3\,n+1}","Not used",1,"a^2*c*x + (x*x^(2*n)*(b^2*c + 2*a*b*d))/(2*n + 1) + (x*x^n*(a^2*d + 2*a*b*c))/(n + 1) + (b^2*d*x*x^(3*n))/(3*n + 1)","B"
295,0,-1,84,0.000000,"\text{Not used}","int((a + b*x^n)^2/(c + d*x^n),x)","\int \frac{{\left(a+b\,x^n\right)}^2}{c+d\,x^n} \,d x","Not used",1,"int((a + b*x^n)^2/(c + d*x^n), x)","F"
296,0,-1,115,0.000000,"\text{Not used}","int((a + b*x^n)^2/(c + d*x^n)^2,x)","\int \frac{{\left(a+b\,x^n\right)}^2}{{\left(c+d\,x^n\right)}^2} \,d x","Not used",1,"int((a + b*x^n)^2/(c + d*x^n)^2, x)","F"
297,0,-1,160,0.000000,"\text{Not used}","int((a + b*x^n)^2/(c + d*x^n)^3,x)","\int \frac{{\left(a+b\,x^n\right)}^2}{{\left(c+d\,x^n\right)}^3} \,d x","Not used",1,"int((a + b*x^n)^2/(c + d*x^n)^3, x)","F"
298,0,-1,310,0.000000,"\text{Not used}","int((c + d*x^n)^4/(a + b*x^n),x)","\int \frac{{\left(c+d\,x^n\right)}^4}{a+b\,x^n} \,d x","Not used",1,"int((c + d*x^n)^4/(a + b*x^n), x)","F"
299,0,-1,173,0.000000,"\text{Not used}","int((c + d*x^n)^3/(a + b*x^n),x)","\int \frac{{\left(c+d\,x^n\right)}^3}{a+b\,x^n} \,d x","Not used",1,"int((c + d*x^n)^3/(a + b*x^n), x)","F"
300,0,-1,84,0.000000,"\text{Not used}","int((c + d*x^n)^2/(a + b*x^n),x)","\int \frac{{\left(c+d\,x^n\right)}^2}{a+b\,x^n} \,d x","Not used",1,"int((c + d*x^n)^2/(a + b*x^n), x)","F"
301,0,-1,42,0.000000,"\text{Not used}","int((c + d*x^n)/(a + b*x^n),x)","\int \frac{c+d\,x^n}{a+b\,x^n} \,d x","Not used",1,"int((c + d*x^n)/(a + b*x^n), x)","F"
302,0,-1,72,0.000000,"\text{Not used}","int(1/((a + b*x^n)*(c + d*x^n)),x)","\int \frac{1}{\left(a+b\,x^n\right)\,\left(c+d\,x^n\right)} \,d x","Not used",1,"int(1/((a + b*x^n)*(c + d*x^n)), x)","F"
303,0,-1,123,0.000000,"\text{Not used}","int(1/((a + b*x^n)*(c + d*x^n)^2),x)","\int \frac{1}{\left(a+b\,x^n\right)\,{\left(c+d\,x^n\right)}^2} \,d x","Not used",1,"int(1/((a + b*x^n)*(c + d*x^n)^2), x)","F"
304,0,-1,210,0.000000,"\text{Not used}","int(1/((a + b*x^n)*(c + d*x^n)^3),x)","\int \frac{1}{\left(a+b\,x^n\right)\,{\left(c+d\,x^n\right)}^3} \,d x","Not used",1,"int(1/((a + b*x^n)*(c + d*x^n)^3), x)","F"
305,0,-1,341,0.000000,"\text{Not used}","int((c + d*x^n)^4/(a + b*x^n)^2,x)","\int \frac{{\left(c+d\,x^n\right)}^4}{{\left(a+b\,x^n\right)}^2} \,d x","Not used",1,"int((c + d*x^n)^4/(a + b*x^n)^2, x)","F"
306,0,-1,200,0.000000,"\text{Not used}","int((c + d*x^n)^3/(a + b*x^n)^2,x)","\int \frac{{\left(c+d\,x^n\right)}^3}{{\left(a+b\,x^n\right)}^2} \,d x","Not used",1,"int((c + d*x^n)^3/(a + b*x^n)^2, x)","F"
307,0,-1,115,0.000000,"\text{Not used}","int((c + d*x^n)^2/(a + b*x^n)^2,x)","\int \frac{{\left(c+d\,x^n\right)}^2}{{\left(a+b\,x^n\right)}^2} \,d x","Not used",1,"int((c + d*x^n)^2/(a + b*x^n)^2, x)","F"
308,0,-1,72,0.000000,"\text{Not used}","int((c + d*x^n)/(a + b*x^n)^2,x)","\int \frac{c+d\,x^n}{{\left(a+b\,x^n\right)}^2} \,d x","Not used",1,"int((c + d*x^n)/(a + b*x^n)^2, x)","F"
309,0,-1,122,0.000000,"\text{Not used}","int(1/((a + b*x^n)^2*(c + d*x^n)),x)","\int \frac{1}{{\left(a+b\,x^n\right)}^2\,\left(c+d\,x^n\right)} \,d x","Not used",1,"int(1/((a + b*x^n)^2*(c + d*x^n)), x)","F"
310,0,-1,193,0.000000,"\text{Not used}","int(1/((a + b*x^n)^2*(c + d*x^n)^2),x)","\int \frac{1}{{\left(a+b\,x^n\right)}^2\,{\left(c+d\,x^n\right)}^2} \,d x","Not used",1,"int(1/((a + b*x^n)^2*(c + d*x^n)^2), x)","F"
311,0,-1,299,0.000000,"\text{Not used}","int(1/((a + b*x^n)^2*(c + d*x^n)^3),x)","\int \frac{1}{{\left(a+b\,x^n\right)}^2\,{\left(c+d\,x^n\right)}^3} \,d x","Not used",1,"int(1/((a + b*x^n)^2*(c + d*x^n)^3), x)","F"
312,0,-1,81,0.000000,"\text{Not used}","int((a + b*x^n)^p*(c + d*x^n)^q,x)","\int {\left(a+b\,x^n\right)}^p\,{\left(c+d\,x^n\right)}^q \,d x","Not used",1,"int((a + b*x^n)^p*(c + d*x^n)^q, x)","F"
313,0,-1,402,0.000000,"\text{Not used}","int((a + b*x^n)^p*(c + d*x^n)^3,x)","\int {\left(a+b\,x^n\right)}^p\,{\left(c+d\,x^n\right)}^3 \,d x","Not used",1,"int((a + b*x^n)^p*(c + d*x^n)^3, x)","F"
314,0,-1,202,0.000000,"\text{Not used}","int((a + b*x^n)^p*(c + d*x^n)^2,x)","\int {\left(a+b\,x^n\right)}^p\,{\left(c+d\,x^n\right)}^2 \,d x","Not used",1,"int((a + b*x^n)^p*(c + d*x^n)^2, x)","F"
315,0,-1,98,0.000000,"\text{Not used}","int((a + b*x^n)^p*(c + d*x^n),x)","\int {\left(a+b\,x^n\right)}^p\,\left(c+d\,x^n\right) \,d x","Not used",1,"int((a + b*x^n)^p*(c + d*x^n), x)","F"
316,1,47,46,2.298566,"\text{Not used}","int((a + b*x^n)^p,x)","\frac{x\,{\left(a+b\,x^n\right)}^p\,{{}}_2{\mathrm{F}}_1\left(\frac{1}{n},-p;\ \frac{1}{n}+1;\ -\frac{b\,x^n}{a}\right)}{{\left(\frac{b\,x^n}{a}+1\right)}^p}","Not used",1,"(x*(a + b*x^n)^p*hypergeom([1/n, -p], 1/n + 1, -(b*x^n)/a))/((b*x^n)/a + 1)^p","B"
317,0,-1,59,0.000000,"\text{Not used}","int((a + b*x^n)^p/(c + d*x^n),x)","\int \frac{{\left(a+b\,x^n\right)}^p}{c+d\,x^n} \,d x","Not used",1,"int((a + b*x^n)^p/(c + d*x^n), x)","F"
318,0,-1,59,0.000000,"\text{Not used}","int((a + b*x^n)^p/(c + d*x^n)^2,x)","\int \frac{{\left(a+b\,x^n\right)}^p}{{\left(c+d\,x^n\right)}^2} \,d x","Not used",1,"int((a + b*x^n)^p/(c + d*x^n)^2, x)","F"
319,0,-1,59,0.000000,"\text{Not used}","int((a + b*x^n)^p/(c + d*x^n)^3,x)","\int \frac{{\left(a+b\,x^n\right)}^p}{{\left(c+d\,x^n\right)}^3} \,d x","Not used",1,"int((a + b*x^n)^p/(c + d*x^n)^3, x)","F"
320,0,-1,93,0.000000,"\text{Not used}","int((a + b*x^n)^p/(c + d*x^n)^(p + 1/n + 1),x)","\int \frac{{\left(a+b\,x^n\right)}^p}{{\left(c+d\,x^n\right)}^{p+\frac{1}{n}+1}} \,d x","Not used",1,"int((a + b*x^n)^p/(c + d*x^n)^(p + 1/n + 1), x)","F"
321,0,-1,178,0.000000,"\text{Not used}","int((a + b*x^n)^3/(c + d*x^n)^(1/n + 4),x)","\int \frac{{\left(a+b\,x^n\right)}^3}{{\left(c+d\,x^n\right)}^{\frac{1}{n}+4}} \,d x","Not used",1,"int((a + b*x^n)^3/(c + d*x^n)^(1/n + 4), x)","F"
322,0,-1,116,0.000000,"\text{Not used}","int((a + b*x^n)^2/(c + d*x^n)^(1/n + 3),x)","\int \frac{{\left(a+b\,x^n\right)}^2}{{\left(c+d\,x^n\right)}^{\frac{1}{n}+3}} \,d x","Not used",1,"int((a + b*x^n)^2/(c + d*x^n)^(1/n + 3), x)","F"
323,0,-1,58,0.000000,"\text{Not used}","int((a + b*x^n)/(c + d*x^n)^(1/n + 2),x)","\int \frac{a+b\,x^n}{{\left(c+d\,x^n\right)}^{\frac{1}{n}+2}} \,d x","Not used",1,"int((a + b*x^n)/(c + d*x^n)^(1/n + 2), x)","F"
324,1,75,18,1.755615,"\text{Not used}","int(1/(c + d*x^n)^(1/n + 1),x)","\frac{d\,x^{n+1}\,\left(\frac{c}{d\,x^n}-{\left(\frac{c}{d\,x^n}+1\right)}^{\frac{n+1}{n}}+1\right)}{c\,n\,\left(\frac{n+1}{n}-1\right)\,{\left(c+d\,x^n\right)}^{\frac{n+1}{n}}}","Not used",1,"(d*x^(n + 1)*(c/(d*x^n) - (c/(d*x^n) + 1)^((n + 1)/n) + 1))/(c*n*((n + 1)/n - 1)*(c + d*x^n)^((n + 1)/n))","B"
325,0,-1,53,0.000000,"\text{Not used}","int(1/((a + b*x^n)*(c + d*x^n)^(1/n)),x)","\int \frac{1}{\left(a+b\,x^n\right)\,{\left(c+d\,x^n\right)}^{1/n}} \,d x","Not used",1,"int(1/((a + b*x^n)*(c + d*x^n)^(1/n)), x)","F"
326,0,-1,54,0.000000,"\text{Not used}","int((c + d*x^n)^(1 - 1/n)/(a + b*x^n)^2,x)","\int \frac{{\left(c+d\,x^n\right)}^{1-\frac{1}{n}}}{{\left(a+b\,x^n\right)}^2} \,d x","Not used",1,"int((c + d*x^n)^(1 - 1/n)/(a + b*x^n)^2, x)","F"
327,0,-1,56,0.000000,"\text{Not used}","int((c + d*x^n)^(2 - 1/n)/(a + b*x^n)^3,x)","\int \frac{{\left(c+d\,x^n\right)}^{2-\frac{1}{n}}}{{\left(a+b\,x^n\right)}^3} \,d x","Not used",1,"int((c + d*x^n)^(2 - 1/n)/(a + b*x^n)^3, x)","F"
328,0,-1,193,0.000000,"\text{Not used}","int((a + b*x^n)^p/(c + d*x^n)^(p + 1/n + 2),x)","\int \frac{{\left(a+b\,x^n\right)}^p}{{\left(c+d\,x^n\right)}^{p+\frac{1}{n}+2}} \,d x","Not used",1,"int((a + b*x^n)^p/(c + d*x^n)^(p + 1/n + 2), x)","F"
329,0,-1,57,0.000000,"\text{Not used}","int(1/((a + b*x^n)^((a*d*n - b*c*(n + 1))/(n*(a*d - b*c)))*(c + d*x^n)^((a*d + a*d*n - b*c*n)/(a*d*n - b*c*n))),x)","\int \frac{1}{{\left(a+b\,x^n\right)}^{\frac{a\,d\,n-b\,c\,\left(n+1\right)}{n\,\left(a\,d-b\,c\right)}}\,{\left(c+d\,x^n\right)}^{\frac{a\,d+a\,d\,n-b\,c\,n}{a\,d\,n-b\,c\,n}}} \,d x","Not used",1,"int(1/((a + b*x^n)^((a*d*n - b*c*(n + 1))/(n*(a*d - b*c)))*(c + d*x^n)^((a*d + a*d*n - b*c*n)/(a*d*n - b*c*n))), x)","F"
330,0,-1,327,0.000000,"\text{Not used}","int((a + b*x^n)^2/(c + d*x^n)^(1/n + 4),x)","\int \frac{{\left(a+b\,x^n\right)}^2}{{\left(c+d\,x^n\right)}^{\frac{1}{n}+4}} \,d x","Not used",1,"int((a + b*x^n)^2/(c + d*x^n)^(1/n + 4), x)","F"
331,0,-1,127,0.000000,"\text{Not used}","int((a + b*x^n)/(c + d*x^n)^(1/n + 3),x)","\int \frac{a+b\,x^n}{{\left(c+d\,x^n\right)}^{\frac{1}{n}+3}} \,d x","Not used",1,"int((a + b*x^n)/(c + d*x^n)^(1/n + 3), x)","F"
332,1,64,50,1.763435,"\text{Not used}","int(1/(c + d*x^n)^(1/n + 2),x)","-\frac{x^{1-2\,n}\,{\left(\frac{c}{d\,x^n}+1\right)}^{1/n}\,{{}}_2{\mathrm{F}}_1\left(2,\frac{1}{n}+2;\ 3;\ -\frac{c}{d\,x^n}\right)}{2\,d^2\,n\,{\left(c+d\,x^n\right)}^{1/n}}","Not used",1,"-(x^(1 - 2*n)*(c/(d*x^n) + 1)^(1/n)*hypergeom([2, 1/n + 2], 3, -c/(d*x^n)))/(2*d^2*n*(c + d*x^n)^(1/n))","B"
333,0,-1,95,0.000000,"\text{Not used}","int(1/((a + b*x^n)*(c + d*x^n)^(1/n + 1)),x)","\int \frac{1}{\left(a+b\,x^n\right)\,{\left(c+d\,x^n\right)}^{\frac{1}{n}+1}} \,d x","Not used",1,"int(1/((a + b*x^n)*(c + d*x^n)^(1/n + 1)), x)","F"
334,0,-1,127,0.000000,"\text{Not used}","int(1/((a + b*x^n)^2*(c + d*x^n)^(1/n)),x)","\int \frac{1}{{\left(a+b\,x^n\right)}^2\,{\left(c+d\,x^n\right)}^{1/n}} \,d x","Not used",1,"int(1/((a + b*x^n)^2*(c + d*x^n)^(1/n)), x)","F"
335,0,-1,131,0.000000,"\text{Not used}","int((c + d*x^n)^(1 - 1/n)/(a + b*x^n)^3,x)","\int \frac{{\left(c+d\,x^n\right)}^{1-\frac{1}{n}}}{{\left(a+b\,x^n\right)}^3} \,d x","Not used",1,"int((c + d*x^n)^(1 - 1/n)/(a + b*x^n)^3, x)","F"
336,0,-1,133,0.000000,"\text{Not used}","int((c + d*x^n)^(2 - 1/n)/(a + b*x^n)^4,x)","\int \frac{{\left(c+d\,x^n\right)}^{2-\frac{1}{n}}}{{\left(a+b\,x^n\right)}^4} \,d x","Not used",1,"int((c + d*x^n)^(2 - 1/n)/(a + b*x^n)^4, x)","F"
337,1,152,152,1.761120,"\text{Not used}","int(x^5*(a + b*x^2)*(c + d*x)^(1/2)*(d*x - c)^(1/2),x)","-\sqrt{d\,x-c}\,\left(\frac{\left(16\,b\,c^8+24\,a\,c^6\,d^2\right)\,\sqrt{c+d\,x}}{315\,d^8}-\frac{b\,x^8\,\sqrt{c+d\,x}}{9}+\frac{x^4\,\left(6\,b\,c^4\,d^4+9\,a\,c^2\,d^6\right)\,\sqrt{c+d\,x}}{315\,d^8}+\frac{x^2\,\left(8\,b\,c^6\,d^2+12\,a\,c^4\,d^4\right)\,\sqrt{c+d\,x}}{315\,d^8}-\frac{x^6\,\left(45\,a\,d^8-5\,b\,c^2\,d^6\right)\,\sqrt{c+d\,x}}{315\,d^8}\right)","Not used",1,"-(d*x - c)^(1/2)*(((16*b*c^8 + 24*a*c^6*d^2)*(c + d*x)^(1/2))/(315*d^8) - (b*x^8*(c + d*x)^(1/2))/9 + (x^4*(9*a*c^2*d^6 + 6*b*c^4*d^4)*(c + d*x)^(1/2))/(315*d^8) + (x^2*(12*a*c^4*d^4 + 8*b*c^6*d^2)*(c + d*x)^(1/2))/(315*d^8) - (x^6*(45*a*d^8 - 5*b*c^2*d^6)*(c + d*x)^(1/2))/(315*d^8))","B"
338,1,118,109,1.735823,"\text{Not used}","int(x^3*(a + b*x^2)*(c + d*x)^(1/2)*(d*x - c)^(1/2),x)","-\sqrt{d\,x-c}\,\left(\frac{\left(8\,b\,c^6+14\,a\,c^4\,d^2\right)\,\sqrt{c+d\,x}}{105\,d^6}-\frac{b\,x^6\,\sqrt{c+d\,x}}{7}+\frac{x^2\,\left(4\,b\,c^4\,d^2+7\,a\,c^2\,d^4\right)\,\sqrt{c+d\,x}}{105\,d^6}-\frac{x^4\,\left(21\,a\,d^6-3\,b\,c^2\,d^4\right)\,\sqrt{c+d\,x}}{105\,d^6}\right)","Not used",1,"-(d*x - c)^(1/2)*(((8*b*c^6 + 14*a*c^4*d^2)*(c + d*x)^(1/2))/(105*d^6) - (b*x^6*(c + d*x)^(1/2))/7 + (x^2*(7*a*c^2*d^4 + 4*b*c^4*d^2)*(c + d*x)^(1/2))/(105*d^6) - (x^4*(21*a*d^6 - 3*b*c^2*d^4)*(c + d*x)^(1/2))/(105*d^6))","B"
339,1,83,67,1.640586,"\text{Not used}","int(x*(a + b*x^2)*(c + d*x)^(1/2)*(d*x - c)^(1/2),x)","\sqrt{d\,x-c}\,\left(\frac{b\,x^4\,\sqrt{c+d\,x}}{5}-\frac{\left(2\,b\,c^4+5\,a\,c^2\,d^2\right)\,\sqrt{c+d\,x}}{15\,d^4}+\frac{x^2\,\left(5\,a\,d^4-b\,c^2\,d^2\right)\,\sqrt{c+d\,x}}{15\,d^4}\right)","Not used",1,"(d*x - c)^(1/2)*((b*x^4*(c + d*x)^(1/2))/5 - ((2*b*c^4 + 5*a*c^2*d^2)*(c + d*x)^(1/2))/(15*d^4) + (x^2*(5*a*d^4 - b*c^2*d^2)*(c + d*x)^(1/2))/(15*d^4))","B"
340,1,248,80,3.597613,"\text{Not used}","int(((a + b*x^2)*(c + d*x)^(1/2)*(d*x - c)^(1/2))/x,x)","a\,\sqrt{-c}\,\sqrt{c}\,\ln\left(\frac{{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^2}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^2}+1\right)-a\,\sqrt{-c}\,\sqrt{c}\,\ln\left(\frac{\sqrt{c+d\,x}-\sqrt{c}}{\sqrt{-c}-\sqrt{d\,x-c}}\right)-\frac{b\,\left(c^2-d^2\,x^2\right)\,\sqrt{c+d\,x}\,\sqrt{d\,x-c}}{3\,d^2}-\frac{8\,a\,\sqrt{-c}\,\sqrt{c}\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^2}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^2\,\left(\frac{{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^4}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^4}-\frac{2\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^2}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^2}+1\right)}","Not used",1,"a*(-c)^(1/2)*c^(1/2)*log(((c + d*x)^(1/2) - c^(1/2))^2/((-c)^(1/2) - (d*x - c)^(1/2))^2 + 1) - a*(-c)^(1/2)*c^(1/2)*log(((c + d*x)^(1/2) - c^(1/2))/((-c)^(1/2) - (d*x - c)^(1/2))) - (b*(c^2 - d^2*x^2)*(c + d*x)^(1/2)*(d*x - c)^(1/2))/(3*d^2) - (8*a*(-c)^(1/2)*c^(1/2)*((c + d*x)^(1/2) - c^(1/2))^2)/(((-c)^(1/2) - (d*x - c)^(1/2))^2*(((c + d*x)^(1/2) - c^(1/2))^4/((-c)^(1/2) - (d*x - c)^(1/2))^4 - (2*((c + d*x)^(1/2) - c^(1/2))^2)/((-c)^(1/2) - (d*x - c)^(1/2))^2 + 1))","B"
341,1,584,96,6.889794,"\text{Not used}","int(((a + b*x^2)*(c + d*x)^(1/2)*(d*x - c)^(1/2))/x^3,x)","b\,\sqrt{-c}\,\sqrt{c}\,\ln\left(\frac{{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^2}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^2}+1\right)-\frac{\frac{a\,\sqrt{-c}\,d^2}{32\,c^{3/2}}+\frac{a\,\sqrt{-c}\,d^2\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^2}{16\,c^{3/2}\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^2}-\frac{15\,a\,\sqrt{-c}\,d^2\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^4}{32\,c^{3/2}\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^4}}{\frac{{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^2}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^2}+\frac{2\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^4}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^4}+\frac{{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^6}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^6}}-b\,\sqrt{-c}\,\sqrt{c}\,\ln\left(\frac{\sqrt{c+d\,x}-\sqrt{c}}{\sqrt{-c}-\sqrt{d\,x-c}}\right)+\frac{a\,\sqrt{-c}\,d^2\,\ln\left(\frac{\sqrt{c+d\,x}-\sqrt{c}}{\sqrt{-c}-\sqrt{d\,x-c}}\right)}{2\,c^{3/2}}-\frac{a\,\sqrt{-c}\,d^2\,\ln\left(\frac{{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^2}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^2}+1\right)}{2\,c^{3/2}}-\frac{a\,\sqrt{-c}\,d^2\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^2}{32\,c^{3/2}\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^2}-\frac{8\,b\,\sqrt{-c}\,\sqrt{c}\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^2}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^2\,\left(\frac{{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^4}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^4}-\frac{2\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^2}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^2}+1\right)}","Not used",1,"b*(-c)^(1/2)*c^(1/2)*log(((c + d*x)^(1/2) - c^(1/2))^2/((-c)^(1/2) - (d*x - c)^(1/2))^2 + 1) - ((a*(-c)^(1/2)*d^2)/(32*c^(3/2)) + (a*(-c)^(1/2)*d^2*((c + d*x)^(1/2) - c^(1/2))^2)/(16*c^(3/2)*((-c)^(1/2) - (d*x - c)^(1/2))^2) - (15*a*(-c)^(1/2)*d^2*((c + d*x)^(1/2) - c^(1/2))^4)/(32*c^(3/2)*((-c)^(1/2) - (d*x - c)^(1/2))^4))/(((c + d*x)^(1/2) - c^(1/2))^2/((-c)^(1/2) - (d*x - c)^(1/2))^2 + (2*((c + d*x)^(1/2) - c^(1/2))^4)/((-c)^(1/2) - (d*x - c)^(1/2))^4 + ((c + d*x)^(1/2) - c^(1/2))^6/((-c)^(1/2) - (d*x - c)^(1/2))^6) - b*(-c)^(1/2)*c^(1/2)*log(((c + d*x)^(1/2) - c^(1/2))/((-c)^(1/2) - (d*x - c)^(1/2))) + (a*(-c)^(1/2)*d^2*log(((c + d*x)^(1/2) - c^(1/2))/((-c)^(1/2) - (d*x - c)^(1/2))))/(2*c^(3/2)) - (a*(-c)^(1/2)*d^2*log(((c + d*x)^(1/2) - c^(1/2))^2/((-c)^(1/2) - (d*x - c)^(1/2))^2 + 1))/(2*c^(3/2)) - (a*(-c)^(1/2)*d^2*((c + d*x)^(1/2) - c^(1/2))^2)/(32*c^(3/2)*((-c)^(1/2) - (d*x - c)^(1/2))^2) - (8*b*(-c)^(1/2)*c^(1/2)*((c + d*x)^(1/2) - c^(1/2))^2)/(((-c)^(1/2) - (d*x - c)^(1/2))^2*(((c + d*x)^(1/2) - c^(1/2))^4/((-c)^(1/2) - (d*x - c)^(1/2))^4 - (2*((c + d*x)^(1/2) - c^(1/2))^2)/((-c)^(1/2) - (d*x - c)^(1/2))^2 + 1))","B"
342,1,1004,121,15.557428,"\text{Not used}","int(((a + b*x^2)*(c + d*x)^(1/2)*(d*x - c)^(1/2))/x^5,x)","\frac{\frac{a\,\sqrt{-c}\,d^4}{1024\,c^{7/2}}+\frac{a\,\sqrt{-c}\,d^4\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^2}{128\,c^{7/2}\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^2}+\frac{11\,a\,\sqrt{-c}\,d^4\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^4}{512\,c^{7/2}\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^4}+\frac{7\,a\,\sqrt{-c}\,d^4\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^6}{256\,c^{7/2}\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^6}-\frac{239\,a\,\sqrt{-c}\,d^4\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^8}{1024\,c^{7/2}\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^8}+\frac{a\,\sqrt{-c}\,d^4\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{10}}{256\,c^{7/2}\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{10}}}{\frac{{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^4}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^4}+\frac{4\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^6}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^6}+\frac{6\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^8}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^8}+\frac{4\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{10}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{10}}+\frac{{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{12}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{12}}}-\frac{\frac{b\,\sqrt{-c}\,d^2}{32\,c^{3/2}}+\frac{b\,\sqrt{-c}\,d^2\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^2}{16\,c^{3/2}\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^2}-\frac{15\,b\,\sqrt{-c}\,d^2\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^4}{32\,c^{3/2}\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^4}}{\frac{{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^2}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^2}+\frac{2\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^4}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^4}+\frac{{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^6}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^6}}+\frac{a\,\sqrt{-c}\,d^4\,\ln\left(\frac{\sqrt{c+d\,x}-\sqrt{c}}{\sqrt{-c}-\sqrt{d\,x-c}}\right)}{8\,c^{7/2}}+\frac{b\,\sqrt{-c}\,d^2\,\ln\left(\frac{\sqrt{c+d\,x}-\sqrt{c}}{\sqrt{-c}-\sqrt{d\,x-c}}\right)}{2\,c^{3/2}}-\frac{a\,\sqrt{-c}\,d^4\,\ln\left(\frac{{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^2}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^2}+1\right)}{8\,c^{7/2}}-\frac{b\,\sqrt{-c}\,d^2\,\ln\left(\frac{{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^2}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^2}+1\right)}{2\,c^{3/2}}+\frac{a\,\sqrt{-c}\,d^4\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^2}{256\,c^{7/2}\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^2}+\frac{a\,\sqrt{-c}\,d^4\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^4}{1024\,c^{7/2}\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^4}-\frac{b\,\sqrt{-c}\,d^2\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^2}{32\,c^{3/2}\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^2}","Not used",1,"((a*(-c)^(1/2)*d^4)/(1024*c^(7/2)) + (a*(-c)^(1/2)*d^4*((c + d*x)^(1/2) - c^(1/2))^2)/(128*c^(7/2)*((-c)^(1/2) - (d*x - c)^(1/2))^2) + (11*a*(-c)^(1/2)*d^4*((c + d*x)^(1/2) - c^(1/2))^4)/(512*c^(7/2)*((-c)^(1/2) - (d*x - c)^(1/2))^4) + (7*a*(-c)^(1/2)*d^4*((c + d*x)^(1/2) - c^(1/2))^6)/(256*c^(7/2)*((-c)^(1/2) - (d*x - c)^(1/2))^6) - (239*a*(-c)^(1/2)*d^4*((c + d*x)^(1/2) - c^(1/2))^8)/(1024*c^(7/2)*((-c)^(1/2) - (d*x - c)^(1/2))^8) + (a*(-c)^(1/2)*d^4*((c + d*x)^(1/2) - c^(1/2))^10)/(256*c^(7/2)*((-c)^(1/2) - (d*x - c)^(1/2))^10))/(((c + d*x)^(1/2) - c^(1/2))^4/((-c)^(1/2) - (d*x - c)^(1/2))^4 + (4*((c + d*x)^(1/2) - c^(1/2))^6)/((-c)^(1/2) - (d*x - c)^(1/2))^6 + (6*((c + d*x)^(1/2) - c^(1/2))^8)/((-c)^(1/2) - (d*x - c)^(1/2))^8 + (4*((c + d*x)^(1/2) - c^(1/2))^10)/((-c)^(1/2) - (d*x - c)^(1/2))^10 + ((c + d*x)^(1/2) - c^(1/2))^12/((-c)^(1/2) - (d*x - c)^(1/2))^12) - ((b*(-c)^(1/2)*d^2)/(32*c^(3/2)) + (b*(-c)^(1/2)*d^2*((c + d*x)^(1/2) - c^(1/2))^2)/(16*c^(3/2)*((-c)^(1/2) - (d*x - c)^(1/2))^2) - (15*b*(-c)^(1/2)*d^2*((c + d*x)^(1/2) - c^(1/2))^4)/(32*c^(3/2)*((-c)^(1/2) - (d*x - c)^(1/2))^4))/(((c + d*x)^(1/2) - c^(1/2))^2/((-c)^(1/2) - (d*x - c)^(1/2))^2 + (2*((c + d*x)^(1/2) - c^(1/2))^4)/((-c)^(1/2) - (d*x - c)^(1/2))^4 + ((c + d*x)^(1/2) - c^(1/2))^6/((-c)^(1/2) - (d*x - c)^(1/2))^6) + (a*(-c)^(1/2)*d^4*log(((c + d*x)^(1/2) - c^(1/2))/((-c)^(1/2) - (d*x - c)^(1/2))))/(8*c^(7/2)) + (b*(-c)^(1/2)*d^2*log(((c + d*x)^(1/2) - c^(1/2))/((-c)^(1/2) - (d*x - c)^(1/2))))/(2*c^(3/2)) - (a*(-c)^(1/2)*d^4*log(((c + d*x)^(1/2) - c^(1/2))^2/((-c)^(1/2) - (d*x - c)^(1/2))^2 + 1))/(8*c^(7/2)) - (b*(-c)^(1/2)*d^2*log(((c + d*x)^(1/2) - c^(1/2))^2/((-c)^(1/2) - (d*x - c)^(1/2))^2 + 1))/(2*c^(3/2)) + (a*(-c)^(1/2)*d^4*((c + d*x)^(1/2) - c^(1/2))^2)/(256*c^(7/2)*((-c)^(1/2) - (d*x - c)^(1/2))^2) + (a*(-c)^(1/2)*d^4*((c + d*x)^(1/2) - c^(1/2))^4)/(1024*c^(7/2)*((-c)^(1/2) - (d*x - c)^(1/2))^4) - (b*(-c)^(1/2)*d^2*((c + d*x)^(1/2) - c^(1/2))^2)/(32*c^(3/2)*((-c)^(1/2) - (d*x - c)^(1/2))^2)","B"
343,1,2314,208,39.151329,"\text{Not used}","int(x^4*(a + b*x^2)*(c + d*x)^(1/2)*(d*x - c)^(1/2),x)","\frac{\frac{35\,a\,c^6\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^3}{12\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^3}-\frac{a\,c^6\,\left(\sqrt{c+d\,x}-\sqrt{c}\right)}{4\,\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}+\frac{757\,a\,c^6\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^5}{4\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^5}+\frac{7339\,a\,c^6\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^7}{4\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^7}+\frac{41929\,a\,c^6\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^9}{6\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^9}+\frac{25661\,a\,c^6\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{11}}{2\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{11}}+\frac{25661\,a\,c^6\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{13}}{2\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{13}}+\frac{41929\,a\,c^6\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{15}}{6\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{15}}+\frac{7339\,a\,c^6\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{17}}{4\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{17}}+\frac{757\,a\,c^6\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{19}}{4\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{19}}+\frac{35\,a\,c^6\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{21}}{12\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{21}}-\frac{a\,c^6\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{23}}{4\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{23}}}{d^5-\frac{12\,d^5\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^2}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^2}+\frac{66\,d^5\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^4}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^4}-\frac{220\,d^5\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^6}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^6}+\frac{495\,d^5\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^8}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^8}-\frac{792\,d^5\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{10}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{10}}+\frac{924\,d^5\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{12}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{12}}-\frac{792\,d^5\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{14}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{14}}+\frac{495\,d^5\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{16}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{16}}-\frac{220\,d^5\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{18}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{18}}+\frac{66\,d^5\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{20}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{20}}-\frac{12\,d^5\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{22}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{22}}+\frac{d^5\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{24}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{24}}}-\frac{\frac{5\,b\,c^8\,\left(\sqrt{c+d\,x}-\sqrt{c}\right)}{32\,\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}-\frac{235\,b\,c^8\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^3}{96\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^3}+\frac{1723\,b\,c^8\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^5}{96\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^5}+\frac{72283\,b\,c^8\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^7}{32\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^7}+\frac{848801\,b\,c^8\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^9}{32\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^9}+\frac{4181067\,b\,c^8\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{11}}{32\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{11}}+\frac{10994181\,b\,c^8\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{13}}{32\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{13}}+\frac{17457599\,b\,c^8\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{15}}{32\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{15}}+\frac{17457599\,b\,c^8\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{17}}{32\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{17}}+\frac{10994181\,b\,c^8\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{19}}{32\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{19}}+\frac{4181067\,b\,c^8\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{21}}{32\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{21}}+\frac{848801\,b\,c^8\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{23}}{32\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{23}}+\frac{72283\,b\,c^8\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{25}}{32\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{25}}+\frac{1723\,b\,c^8\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{27}}{96\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{27}}-\frac{235\,b\,c^8\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{29}}{96\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{29}}+\frac{5\,b\,c^8\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{31}}{32\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{31}}}{d^7-\frac{16\,d^7\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^2}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^2}+\frac{120\,d^7\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^4}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^4}-\frac{560\,d^7\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^6}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^6}+\frac{1820\,d^7\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^8}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^8}-\frac{4368\,d^7\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{10}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{10}}+\frac{8008\,d^7\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{12}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{12}}-\frac{11440\,d^7\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{14}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{14}}+\frac{12870\,d^7\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{16}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{16}}-\frac{11440\,d^7\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{18}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{18}}+\frac{8008\,d^7\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{20}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{20}}-\frac{4368\,d^7\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{22}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{22}}+\frac{1820\,d^7\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{24}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{24}}-\frac{560\,d^7\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{26}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{26}}+\frac{120\,d^7\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{28}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{28}}-\frac{16\,d^7\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{30}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{30}}+\frac{d^7\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{32}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{32}}}+\frac{a\,c^6\,\mathrm{atanh}\left(\frac{\sqrt{c+d\,x}-\sqrt{c}}{\sqrt{-c}-\sqrt{d\,x-c}}\right)}{4\,d^5}+\frac{5\,b\,c^8\,\mathrm{atanh}\left(\frac{\sqrt{c+d\,x}-\sqrt{c}}{\sqrt{-c}-\sqrt{d\,x-c}}\right)}{32\,d^7}","Not used",1,"((35*a*c^6*((c + d*x)^(1/2) - c^(1/2))^3)/(12*((-c)^(1/2) - (d*x - c)^(1/2))^3) - (a*c^6*((c + d*x)^(1/2) - c^(1/2)))/(4*((-c)^(1/2) - (d*x - c)^(1/2))) + (757*a*c^6*((c + d*x)^(1/2) - c^(1/2))^5)/(4*((-c)^(1/2) - (d*x - c)^(1/2))^5) + (7339*a*c^6*((c + d*x)^(1/2) - c^(1/2))^7)/(4*((-c)^(1/2) - (d*x - c)^(1/2))^7) + (41929*a*c^6*((c + d*x)^(1/2) - c^(1/2))^9)/(6*((-c)^(1/2) - (d*x - c)^(1/2))^9) + (25661*a*c^6*((c + d*x)^(1/2) - c^(1/2))^11)/(2*((-c)^(1/2) - (d*x - c)^(1/2))^11) + (25661*a*c^6*((c + d*x)^(1/2) - c^(1/2))^13)/(2*((-c)^(1/2) - (d*x - c)^(1/2))^13) + (41929*a*c^6*((c + d*x)^(1/2) - c^(1/2))^15)/(6*((-c)^(1/2) - (d*x - c)^(1/2))^15) + (7339*a*c^6*((c + d*x)^(1/2) - c^(1/2))^17)/(4*((-c)^(1/2) - (d*x - c)^(1/2))^17) + (757*a*c^6*((c + d*x)^(1/2) - c^(1/2))^19)/(4*((-c)^(1/2) - (d*x - c)^(1/2))^19) + (35*a*c^6*((c + d*x)^(1/2) - c^(1/2))^21)/(12*((-c)^(1/2) - (d*x - c)^(1/2))^21) - (a*c^6*((c + d*x)^(1/2) - c^(1/2))^23)/(4*((-c)^(1/2) - (d*x - c)^(1/2))^23))/(d^5 - (12*d^5*((c + d*x)^(1/2) - c^(1/2))^2)/((-c)^(1/2) - (d*x - c)^(1/2))^2 + (66*d^5*((c + d*x)^(1/2) - c^(1/2))^4)/((-c)^(1/2) - (d*x - c)^(1/2))^4 - (220*d^5*((c + d*x)^(1/2) - c^(1/2))^6)/((-c)^(1/2) - (d*x - c)^(1/2))^6 + (495*d^5*((c + d*x)^(1/2) - c^(1/2))^8)/((-c)^(1/2) - (d*x - c)^(1/2))^8 - (792*d^5*((c + d*x)^(1/2) - c^(1/2))^10)/((-c)^(1/2) - (d*x - c)^(1/2))^10 + (924*d^5*((c + d*x)^(1/2) - c^(1/2))^12)/((-c)^(1/2) - (d*x - c)^(1/2))^12 - (792*d^5*((c + d*x)^(1/2) - c^(1/2))^14)/((-c)^(1/2) - (d*x - c)^(1/2))^14 + (495*d^5*((c + d*x)^(1/2) - c^(1/2))^16)/((-c)^(1/2) - (d*x - c)^(1/2))^16 - (220*d^5*((c + d*x)^(1/2) - c^(1/2))^18)/((-c)^(1/2) - (d*x - c)^(1/2))^18 + (66*d^5*((c + d*x)^(1/2) - c^(1/2))^20)/((-c)^(1/2) - (d*x - c)^(1/2))^20 - (12*d^5*((c + d*x)^(1/2) - c^(1/2))^22)/((-c)^(1/2) - (d*x - c)^(1/2))^22 + (d^5*((c + d*x)^(1/2) - c^(1/2))^24)/((-c)^(1/2) - (d*x - c)^(1/2))^24) - ((5*b*c^8*((c + d*x)^(1/2) - c^(1/2)))/(32*((-c)^(1/2) - (d*x - c)^(1/2))) - (235*b*c^8*((c + d*x)^(1/2) - c^(1/2))^3)/(96*((-c)^(1/2) - (d*x - c)^(1/2))^3) + (1723*b*c^8*((c + d*x)^(1/2) - c^(1/2))^5)/(96*((-c)^(1/2) - (d*x - c)^(1/2))^5) + (72283*b*c^8*((c + d*x)^(1/2) - c^(1/2))^7)/(32*((-c)^(1/2) - (d*x - c)^(1/2))^7) + (848801*b*c^8*((c + d*x)^(1/2) - c^(1/2))^9)/(32*((-c)^(1/2) - (d*x - c)^(1/2))^9) + (4181067*b*c^8*((c + d*x)^(1/2) - c^(1/2))^11)/(32*((-c)^(1/2) - (d*x - c)^(1/2))^11) + (10994181*b*c^8*((c + d*x)^(1/2) - c^(1/2))^13)/(32*((-c)^(1/2) - (d*x - c)^(1/2))^13) + (17457599*b*c^8*((c + d*x)^(1/2) - c^(1/2))^15)/(32*((-c)^(1/2) - (d*x - c)^(1/2))^15) + (17457599*b*c^8*((c + d*x)^(1/2) - c^(1/2))^17)/(32*((-c)^(1/2) - (d*x - c)^(1/2))^17) + (10994181*b*c^8*((c + d*x)^(1/2) - c^(1/2))^19)/(32*((-c)^(1/2) - (d*x - c)^(1/2))^19) + (4181067*b*c^8*((c + d*x)^(1/2) - c^(1/2))^21)/(32*((-c)^(1/2) - (d*x - c)^(1/2))^21) + (848801*b*c^8*((c + d*x)^(1/2) - c^(1/2))^23)/(32*((-c)^(1/2) - (d*x - c)^(1/2))^23) + (72283*b*c^8*((c + d*x)^(1/2) - c^(1/2))^25)/(32*((-c)^(1/2) - (d*x - c)^(1/2))^25) + (1723*b*c^8*((c + d*x)^(1/2) - c^(1/2))^27)/(96*((-c)^(1/2) - (d*x - c)^(1/2))^27) - (235*b*c^8*((c + d*x)^(1/2) - c^(1/2))^29)/(96*((-c)^(1/2) - (d*x - c)^(1/2))^29) + (5*b*c^8*((c + d*x)^(1/2) - c^(1/2))^31)/(32*((-c)^(1/2) - (d*x - c)^(1/2))^31))/(d^7 - (16*d^7*((c + d*x)^(1/2) - c^(1/2))^2)/((-c)^(1/2) - (d*x - c)^(1/2))^2 + (120*d^7*((c + d*x)^(1/2) - c^(1/2))^4)/((-c)^(1/2) - (d*x - c)^(1/2))^4 - (560*d^7*((c + d*x)^(1/2) - c^(1/2))^6)/((-c)^(1/2) - (d*x - c)^(1/2))^6 + (1820*d^7*((c + d*x)^(1/2) - c^(1/2))^8)/((-c)^(1/2) - (d*x - c)^(1/2))^8 - (4368*d^7*((c + d*x)^(1/2) - c^(1/2))^10)/((-c)^(1/2) - (d*x - c)^(1/2))^10 + (8008*d^7*((c + d*x)^(1/2) - c^(1/2))^12)/((-c)^(1/2) - (d*x - c)^(1/2))^12 - (11440*d^7*((c + d*x)^(1/2) - c^(1/2))^14)/((-c)^(1/2) - (d*x - c)^(1/2))^14 + (12870*d^7*((c + d*x)^(1/2) - c^(1/2))^16)/((-c)^(1/2) - (d*x - c)^(1/2))^16 - (11440*d^7*((c + d*x)^(1/2) - c^(1/2))^18)/((-c)^(1/2) - (d*x - c)^(1/2))^18 + (8008*d^7*((c + d*x)^(1/2) - c^(1/2))^20)/((-c)^(1/2) - (d*x - c)^(1/2))^20 - (4368*d^7*((c + d*x)^(1/2) - c^(1/2))^22)/((-c)^(1/2) - (d*x - c)^(1/2))^22 + (1820*d^7*((c + d*x)^(1/2) - c^(1/2))^24)/((-c)^(1/2) - (d*x - c)^(1/2))^24 - (560*d^7*((c + d*x)^(1/2) - c^(1/2))^26)/((-c)^(1/2) - (d*x - c)^(1/2))^26 + (120*d^7*((c + d*x)^(1/2) - c^(1/2))^28)/((-c)^(1/2) - (d*x - c)^(1/2))^28 - (16*d^7*((c + d*x)^(1/2) - c^(1/2))^30)/((-c)^(1/2) - (d*x - c)^(1/2))^30 + (d^7*((c + d*x)^(1/2) - c^(1/2))^32)/((-c)^(1/2) - (d*x - c)^(1/2))^32) + (a*c^6*atanh(((c + d*x)^(1/2) - c^(1/2))/((-c)^(1/2) - (d*x - c)^(1/2))))/(4*d^5) + (5*b*c^8*atanh(((c + d*x)^(1/2) - c^(1/2))/((-c)^(1/2) - (d*x - c)^(1/2))))/(32*d^7)","B"
344,1,1681,159,42.568185,"\text{Not used}","int(x^2*(a + b*x^2)*(c + d*x)^(1/2)*(d*x - c)^(1/2),x)","\frac{\frac{35\,b\,c^6\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^3}{12\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^3}-\frac{b\,c^6\,\left(\sqrt{c+d\,x}-\sqrt{c}\right)}{4\,\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}+\frac{757\,b\,c^6\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^5}{4\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^5}+\frac{7339\,b\,c^6\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^7}{4\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^7}+\frac{41929\,b\,c^6\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^9}{6\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^9}+\frac{25661\,b\,c^6\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{11}}{2\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{11}}+\frac{25661\,b\,c^6\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{13}}{2\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{13}}+\frac{41929\,b\,c^6\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{15}}{6\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{15}}+\frac{7339\,b\,c^6\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{17}}{4\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{17}}+\frac{757\,b\,c^6\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{19}}{4\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{19}}+\frac{35\,b\,c^6\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{21}}{12\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{21}}-\frac{b\,c^6\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{23}}{4\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{23}}}{d^5-\frac{12\,d^5\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^2}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^2}+\frac{66\,d^5\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^4}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^4}-\frac{220\,d^5\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^6}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^6}+\frac{495\,d^5\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^8}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^8}-\frac{792\,d^5\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{10}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{10}}+\frac{924\,d^5\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{12}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{12}}-\frac{792\,d^5\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{14}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{14}}+\frac{495\,d^5\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{16}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{16}}-\frac{220\,d^5\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{18}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{18}}+\frac{66\,d^5\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{20}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{20}}-\frac{12\,d^5\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{22}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{22}}+\frac{d^5\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{24}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{24}}}-\frac{\frac{a\,c^4\,\left(\sqrt{c+d\,x}-\sqrt{c}\right)}{2\,\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}+\frac{35\,a\,c^4\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^3}{2\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^3}+\frac{273\,a\,c^4\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^5}{2\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^5}+\frac{715\,a\,c^4\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^7}{2\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^7}+\frac{715\,a\,c^4\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^9}{2\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^9}+\frac{273\,a\,c^4\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{11}}{2\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{11}}+\frac{35\,a\,c^4\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{13}}{2\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{13}}+\frac{a\,c^4\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{15}}{2\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{15}}}{d^3-\frac{8\,d^3\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^2}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^2}+\frac{28\,d^3\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^4}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^4}-\frac{56\,d^3\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^6}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^6}+\frac{70\,d^3\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^8}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^8}-\frac{56\,d^3\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{10}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{10}}+\frac{28\,d^3\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{12}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{12}}-\frac{8\,d^3\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{14}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{14}}+\frac{d^3\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{16}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{16}}}+\frac{a\,c^4\,\mathrm{atanh}\left(\frac{\sqrt{c+d\,x}-\sqrt{c}}{\sqrt{-c}-\sqrt{d\,x-c}}\right)}{2\,d^3}+\frac{b\,c^6\,\mathrm{atanh}\left(\frac{\sqrt{c+d\,x}-\sqrt{c}}{\sqrt{-c}-\sqrt{d\,x-c}}\right)}{4\,d^5}","Not used",1,"((35*b*c^6*((c + d*x)^(1/2) - c^(1/2))^3)/(12*((-c)^(1/2) - (d*x - c)^(1/2))^3) - (b*c^6*((c + d*x)^(1/2) - c^(1/2)))/(4*((-c)^(1/2) - (d*x - c)^(1/2))) + (757*b*c^6*((c + d*x)^(1/2) - c^(1/2))^5)/(4*((-c)^(1/2) - (d*x - c)^(1/2))^5) + (7339*b*c^6*((c + d*x)^(1/2) - c^(1/2))^7)/(4*((-c)^(1/2) - (d*x - c)^(1/2))^7) + (41929*b*c^6*((c + d*x)^(1/2) - c^(1/2))^9)/(6*((-c)^(1/2) - (d*x - c)^(1/2))^9) + (25661*b*c^6*((c + d*x)^(1/2) - c^(1/2))^11)/(2*((-c)^(1/2) - (d*x - c)^(1/2))^11) + (25661*b*c^6*((c + d*x)^(1/2) - c^(1/2))^13)/(2*((-c)^(1/2) - (d*x - c)^(1/2))^13) + (41929*b*c^6*((c + d*x)^(1/2) - c^(1/2))^15)/(6*((-c)^(1/2) - (d*x - c)^(1/2))^15) + (7339*b*c^6*((c + d*x)^(1/2) - c^(1/2))^17)/(4*((-c)^(1/2) - (d*x - c)^(1/2))^17) + (757*b*c^6*((c + d*x)^(1/2) - c^(1/2))^19)/(4*((-c)^(1/2) - (d*x - c)^(1/2))^19) + (35*b*c^6*((c + d*x)^(1/2) - c^(1/2))^21)/(12*((-c)^(1/2) - (d*x - c)^(1/2))^21) - (b*c^6*((c + d*x)^(1/2) - c^(1/2))^23)/(4*((-c)^(1/2) - (d*x - c)^(1/2))^23))/(d^5 - (12*d^5*((c + d*x)^(1/2) - c^(1/2))^2)/((-c)^(1/2) - (d*x - c)^(1/2))^2 + (66*d^5*((c + d*x)^(1/2) - c^(1/2))^4)/((-c)^(1/2) - (d*x - c)^(1/2))^4 - (220*d^5*((c + d*x)^(1/2) - c^(1/2))^6)/((-c)^(1/2) - (d*x - c)^(1/2))^6 + (495*d^5*((c + d*x)^(1/2) - c^(1/2))^8)/((-c)^(1/2) - (d*x - c)^(1/2))^8 - (792*d^5*((c + d*x)^(1/2) - c^(1/2))^10)/((-c)^(1/2) - (d*x - c)^(1/2))^10 + (924*d^5*((c + d*x)^(1/2) - c^(1/2))^12)/((-c)^(1/2) - (d*x - c)^(1/2))^12 - (792*d^5*((c + d*x)^(1/2) - c^(1/2))^14)/((-c)^(1/2) - (d*x - c)^(1/2))^14 + (495*d^5*((c + d*x)^(1/2) - c^(1/2))^16)/((-c)^(1/2) - (d*x - c)^(1/2))^16 - (220*d^5*((c + d*x)^(1/2) - c^(1/2))^18)/((-c)^(1/2) - (d*x - c)^(1/2))^18 + (66*d^5*((c + d*x)^(1/2) - c^(1/2))^20)/((-c)^(1/2) - (d*x - c)^(1/2))^20 - (12*d^5*((c + d*x)^(1/2) - c^(1/2))^22)/((-c)^(1/2) - (d*x - c)^(1/2))^22 + (d^5*((c + d*x)^(1/2) - c^(1/2))^24)/((-c)^(1/2) - (d*x - c)^(1/2))^24) - ((a*c^4*((c + d*x)^(1/2) - c^(1/2)))/(2*((-c)^(1/2) - (d*x - c)^(1/2))) + (35*a*c^4*((c + d*x)^(1/2) - c^(1/2))^3)/(2*((-c)^(1/2) - (d*x - c)^(1/2))^3) + (273*a*c^4*((c + d*x)^(1/2) - c^(1/2))^5)/(2*((-c)^(1/2) - (d*x - c)^(1/2))^5) + (715*a*c^4*((c + d*x)^(1/2) - c^(1/2))^7)/(2*((-c)^(1/2) - (d*x - c)^(1/2))^7) + (715*a*c^4*((c + d*x)^(1/2) - c^(1/2))^9)/(2*((-c)^(1/2) - (d*x - c)^(1/2))^9) + (273*a*c^4*((c + d*x)^(1/2) - c^(1/2))^11)/(2*((-c)^(1/2) - (d*x - c)^(1/2))^11) + (35*a*c^4*((c + d*x)^(1/2) - c^(1/2))^13)/(2*((-c)^(1/2) - (d*x - c)^(1/2))^13) + (a*c^4*((c + d*x)^(1/2) - c^(1/2))^15)/(2*((-c)^(1/2) - (d*x - c)^(1/2))^15))/(d^3 - (8*d^3*((c + d*x)^(1/2) - c^(1/2))^2)/((-c)^(1/2) - (d*x - c)^(1/2))^2 + (28*d^3*((c + d*x)^(1/2) - c^(1/2))^4)/((-c)^(1/2) - (d*x - c)^(1/2))^4 - (56*d^3*((c + d*x)^(1/2) - c^(1/2))^6)/((-c)^(1/2) - (d*x - c)^(1/2))^6 + (70*d^3*((c + d*x)^(1/2) - c^(1/2))^8)/((-c)^(1/2) - (d*x - c)^(1/2))^8 - (56*d^3*((c + d*x)^(1/2) - c^(1/2))^10)/((-c)^(1/2) - (d*x - c)^(1/2))^10 + (28*d^3*((c + d*x)^(1/2) - c^(1/2))^12)/((-c)^(1/2) - (d*x - c)^(1/2))^12 - (8*d^3*((c + d*x)^(1/2) - c^(1/2))^14)/((-c)^(1/2) - (d*x - c)^(1/2))^14 + (d^3*((c + d*x)^(1/2) - c^(1/2))^16)/((-c)^(1/2) - (d*x - c)^(1/2))^16) + (a*c^4*atanh(((c + d*x)^(1/2) - c^(1/2))/((-c)^(1/2) - (d*x - c)^(1/2))))/(2*d^3) + (b*c^6*atanh(((c + d*x)^(1/2) - c^(1/2))/((-c)^(1/2) - (d*x - c)^(1/2))))/(4*d^5)","B"
345,1,734,114,17.425293,"\text{Not used}","int((a + b*x^2)*(c + d*x)^(1/2)*(d*x - c)^(1/2),x)","\frac{a\,x\,\sqrt{c+d\,x}\,\sqrt{d\,x-c}}{2}-\frac{\frac{b\,c^4\,\left(\sqrt{c+d\,x}-\sqrt{c}\right)}{2\,\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}+\frac{35\,b\,c^4\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^3}{2\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^3}+\frac{273\,b\,c^4\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^5}{2\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^5}+\frac{715\,b\,c^4\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^7}{2\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^7}+\frac{715\,b\,c^4\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^9}{2\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^9}+\frac{273\,b\,c^4\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{11}}{2\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{11}}+\frac{35\,b\,c^4\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{13}}{2\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{13}}+\frac{b\,c^4\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{15}}{2\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{15}}}{d^3-\frac{8\,d^3\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^2}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^2}+\frac{28\,d^3\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^4}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^4}-\frac{56\,d^3\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^6}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^6}+\frac{70\,d^3\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^8}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^8}-\frac{56\,d^3\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{10}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{10}}+\frac{28\,d^3\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{12}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{12}}-\frac{8\,d^3\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{14}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{14}}+\frac{d^3\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{16}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{16}}}-\frac{a\,c^2\,\ln\left(d\,x+\sqrt{c+d\,x}\,\sqrt{d\,x-c}\right)}{2\,d}+\frac{b\,c^4\,\mathrm{atanh}\left(\frac{\sqrt{c+d\,x}-\sqrt{c}}{\sqrt{-c}-\sqrt{d\,x-c}}\right)}{2\,d^3}","Not used",1,"(a*x*(c + d*x)^(1/2)*(d*x - c)^(1/2))/2 - ((b*c^4*((c + d*x)^(1/2) - c^(1/2)))/(2*((-c)^(1/2) - (d*x - c)^(1/2))) + (35*b*c^4*((c + d*x)^(1/2) - c^(1/2))^3)/(2*((-c)^(1/2) - (d*x - c)^(1/2))^3) + (273*b*c^4*((c + d*x)^(1/2) - c^(1/2))^5)/(2*((-c)^(1/2) - (d*x - c)^(1/2))^5) + (715*b*c^4*((c + d*x)^(1/2) - c^(1/2))^7)/(2*((-c)^(1/2) - (d*x - c)^(1/2))^7) + (715*b*c^4*((c + d*x)^(1/2) - c^(1/2))^9)/(2*((-c)^(1/2) - (d*x - c)^(1/2))^9) + (273*b*c^4*((c + d*x)^(1/2) - c^(1/2))^11)/(2*((-c)^(1/2) - (d*x - c)^(1/2))^11) + (35*b*c^4*((c + d*x)^(1/2) - c^(1/2))^13)/(2*((-c)^(1/2) - (d*x - c)^(1/2))^13) + (b*c^4*((c + d*x)^(1/2) - c^(1/2))^15)/(2*((-c)^(1/2) - (d*x - c)^(1/2))^15))/(d^3 - (8*d^3*((c + d*x)^(1/2) - c^(1/2))^2)/((-c)^(1/2) - (d*x - c)^(1/2))^2 + (28*d^3*((c + d*x)^(1/2) - c^(1/2))^4)/((-c)^(1/2) - (d*x - c)^(1/2))^4 - (56*d^3*((c + d*x)^(1/2) - c^(1/2))^6)/((-c)^(1/2) - (d*x - c)^(1/2))^6 + (70*d^3*((c + d*x)^(1/2) - c^(1/2))^8)/((-c)^(1/2) - (d*x - c)^(1/2))^8 - (56*d^3*((c + d*x)^(1/2) - c^(1/2))^10)/((-c)^(1/2) - (d*x - c)^(1/2))^10 + (28*d^3*((c + d*x)^(1/2) - c^(1/2))^12)/((-c)^(1/2) - (d*x - c)^(1/2))^12 - (8*d^3*((c + d*x)^(1/2) - c^(1/2))^14)/((-c)^(1/2) - (d*x - c)^(1/2))^14 + (d^3*((c + d*x)^(1/2) - c^(1/2))^16)/((-c)^(1/2) - (d*x - c)^(1/2))^16) - (a*c^2*log(d*x + (c + d*x)^(1/2)*(d*x - c)^(1/2)))/(2*d) + (b*c^4*atanh(((c + d*x)^(1/2) - c^(1/2))/((-c)^(1/2) - (d*x - c)^(1/2))))/(2*d^3)","B"
346,1,243,104,3.485988,"\text{Not used}","int(((a + b*x^2)*(c + d*x)^(1/2)*(d*x - c)^(1/2))/x^2,x)","\frac{a\,d+\frac{5\,a\,d\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^2}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^2}}{\frac{4\,\left(\sqrt{c+d\,x}-\sqrt{c}\right)}{\sqrt{-c}-\sqrt{d\,x-c}}+\frac{4\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^3}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^3}}-4\,a\,d\,\mathrm{atanh}\left(\frac{\sqrt{c+d\,x}-\sqrt{c}}{\sqrt{-c}-\sqrt{d\,x-c}}\right)+\frac{b\,x\,\sqrt{c+d\,x}\,\sqrt{d\,x-c}}{2}-\frac{b\,c^2\,\ln\left(d\,x+\sqrt{c+d\,x}\,\sqrt{d\,x-c}\right)}{2\,d}+\frac{a\,d\,\left(\sqrt{c+d\,x}-\sqrt{c}\right)}{4\,\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}","Not used",1,"(a*d + (5*a*d*((c + d*x)^(1/2) - c^(1/2))^2)/((-c)^(1/2) - (d*x - c)^(1/2))^2)/((4*((c + d*x)^(1/2) - c^(1/2)))/((-c)^(1/2) - (d*x - c)^(1/2)) + (4*((c + d*x)^(1/2) - c^(1/2))^3)/((-c)^(1/2) - (d*x - c)^(1/2))^3) - 4*a*d*atanh(((c + d*x)^(1/2) - c^(1/2))/((-c)^(1/2) - (d*x - c)^(1/2))) + (b*x*(c + d*x)^(1/2)*(d*x - c)^(1/2))/2 - (b*c^2*log(d*x + (c + d*x)^(1/2)*(d*x - c)^(1/2)))/(2*d) + (a*d*((c + d*x)^(1/2) - c^(1/2)))/(4*((-c)^(1/2) - (d*x - c)^(1/2)))","B"
347,1,236,84,3.438197,"\text{Not used}","int(((a + b*x^2)*(c + d*x)^(1/2)*(d*x - c)^(1/2))/x^4,x)","\frac{b\,d+\frac{5\,b\,d\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^2}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^2}}{\frac{4\,\left(\sqrt{c+d\,x}-\sqrt{c}\right)}{\sqrt{-c}-\sqrt{d\,x-c}}+\frac{4\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^3}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^3}}-4\,b\,d\,\mathrm{atanh}\left(\frac{\sqrt{c+d\,x}-\sqrt{c}}{\sqrt{-c}-\sqrt{d\,x-c}}\right)-\frac{\left(\frac{a\,\sqrt{c+d\,x}}{3}-\frac{a\,d^2\,x^2\,\sqrt{c+d\,x}}{3\,c^2}\right)\,\sqrt{d\,x-c}}{x^3}+\frac{b\,d\,\left(\sqrt{c+d\,x}-\sqrt{c}\right)}{4\,\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}","Not used",1,"(b*d + (5*b*d*((c + d*x)^(1/2) - c^(1/2))^2)/((-c)^(1/2) - (d*x - c)^(1/2))^2)/((4*((c + d*x)^(1/2) - c^(1/2)))/((-c)^(1/2) - (d*x - c)^(1/2)) + (4*((c + d*x)^(1/2) - c^(1/2))^3)/((-c)^(1/2) - (d*x - c)^(1/2))^3) - 4*b*d*atanh(((c + d*x)^(1/2) - c^(1/2))/((-c)^(1/2) - (d*x - c)^(1/2))) - (((a*(c + d*x)^(1/2))/3 - (a*d^2*x^2*(c + d*x)^(1/2))/(3*c^2))*(d*x - c)^(1/2))/x^3 + (b*d*((c + d*x)^(1/2) - c^(1/2)))/(4*((-c)^(1/2) - (d*x - c)^(1/2)))","B"
348,1,1154,125,32.625028,"\text{Not used}","int((x^4*(a + b*x^2))/((c*x - 1)^(1/2)*(c*x + 1)^(1/2)),x)","-\frac{-\frac{175\,b\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^3}{12\,{\left(\sqrt{c\,x+1}-1\right)}^3}+\frac{311\,b\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^5}{4\,{\left(\sqrt{c\,x+1}-1\right)}^5}+\frac{8361\,b\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^7}{4\,{\left(\sqrt{c\,x+1}-1\right)}^7}+\frac{42259\,b\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^9}{6\,{\left(\sqrt{c\,x+1}-1\right)}^9}+\frac{25295\,b\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^{11}}{2\,{\left(\sqrt{c\,x+1}-1\right)}^{11}}+\frac{25295\,b\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^{13}}{2\,{\left(\sqrt{c\,x+1}-1\right)}^{13}}+\frac{42259\,b\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^{15}}{6\,{\left(\sqrt{c\,x+1}-1\right)}^{15}}+\frac{8361\,b\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^{17}}{4\,{\left(\sqrt{c\,x+1}-1\right)}^{17}}+\frac{311\,b\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^{19}}{4\,{\left(\sqrt{c\,x+1}-1\right)}^{19}}-\frac{175\,b\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^{21}}{12\,{\left(\sqrt{c\,x+1}-1\right)}^{21}}+\frac{5\,b\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^{23}}{4\,{\left(\sqrt{c\,x+1}-1\right)}^{23}}+\frac{5\,b\,\left(\sqrt{c\,x-1}-\mathrm{i}\right)}{4\,\left(\sqrt{c\,x+1}-1\right)}}{c^7-\frac{12\,c^7\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{c\,x+1}-1\right)}^2}+\frac{66\,c^7\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^4}{{\left(\sqrt{c\,x+1}-1\right)}^4}-\frac{220\,c^7\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^6}{{\left(\sqrt{c\,x+1}-1\right)}^6}+\frac{495\,c^7\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^8}{{\left(\sqrt{c\,x+1}-1\right)}^8}-\frac{792\,c^7\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^{10}}{{\left(\sqrt{c\,x+1}-1\right)}^{10}}+\frac{924\,c^7\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^{12}}{{\left(\sqrt{c\,x+1}-1\right)}^{12}}-\frac{792\,c^7\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^{14}}{{\left(\sqrt{c\,x+1}-1\right)}^{14}}+\frac{495\,c^7\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^{16}}{{\left(\sqrt{c\,x+1}-1\right)}^{16}}-\frac{220\,c^7\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^{18}}{{\left(\sqrt{c\,x+1}-1\right)}^{18}}+\frac{66\,c^7\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^{20}}{{\left(\sqrt{c\,x+1}-1\right)}^{20}}-\frac{12\,c^7\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^{22}}{{\left(\sqrt{c\,x+1}-1\right)}^{22}}+\frac{c^7\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^{24}}{{\left(\sqrt{c\,x+1}-1\right)}^{24}}}+\frac{\frac{23\,a\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^3}{2\,{\left(\sqrt{c\,x+1}-1\right)}^3}+\frac{333\,a\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^5}{2\,{\left(\sqrt{c\,x+1}-1\right)}^5}+\frac{671\,a\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^7}{2\,{\left(\sqrt{c\,x+1}-1\right)}^7}+\frac{671\,a\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^9}{2\,{\left(\sqrt{c\,x+1}-1\right)}^9}+\frac{333\,a\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^{11}}{2\,{\left(\sqrt{c\,x+1}-1\right)}^{11}}+\frac{23\,a\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^{13}}{2\,{\left(\sqrt{c\,x+1}-1\right)}^{13}}-\frac{3\,a\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^{15}}{2\,{\left(\sqrt{c\,x+1}-1\right)}^{15}}-\frac{3\,a\,\left(\sqrt{c\,x-1}-\mathrm{i}\right)}{2\,\left(\sqrt{c\,x+1}-1\right)}}{c^5-\frac{8\,c^5\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{c\,x+1}-1\right)}^2}+\frac{28\,c^5\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^4}{{\left(\sqrt{c\,x+1}-1\right)}^4}-\frac{56\,c^5\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^6}{{\left(\sqrt{c\,x+1}-1\right)}^6}+\frac{70\,c^5\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^8}{{\left(\sqrt{c\,x+1}-1\right)}^8}-\frac{56\,c^5\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^{10}}{{\left(\sqrt{c\,x+1}-1\right)}^{10}}+\frac{28\,c^5\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^{12}}{{\left(\sqrt{c\,x+1}-1\right)}^{12}}-\frac{8\,c^5\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^{14}}{{\left(\sqrt{c\,x+1}-1\right)}^{14}}+\frac{c^5\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^{16}}{{\left(\sqrt{c\,x+1}-1\right)}^{16}}}+\frac{3\,a\,\mathrm{atanh}\left(\frac{\sqrt{c\,x-1}-\mathrm{i}}{\sqrt{c\,x+1}-1}\right)}{2\,c^5}+\frac{5\,b\,\mathrm{atanh}\left(\frac{\sqrt{c\,x-1}-\mathrm{i}}{\sqrt{c\,x+1}-1}\right)}{4\,c^7}","Not used",1,"((23*a*((c*x - 1)^(1/2) - 1i)^3)/(2*((c*x + 1)^(1/2) - 1)^3) + (333*a*((c*x - 1)^(1/2) - 1i)^5)/(2*((c*x + 1)^(1/2) - 1)^5) + (671*a*((c*x - 1)^(1/2) - 1i)^7)/(2*((c*x + 1)^(1/2) - 1)^7) + (671*a*((c*x - 1)^(1/2) - 1i)^9)/(2*((c*x + 1)^(1/2) - 1)^9) + (333*a*((c*x - 1)^(1/2) - 1i)^11)/(2*((c*x + 1)^(1/2) - 1)^11) + (23*a*((c*x - 1)^(1/2) - 1i)^13)/(2*((c*x + 1)^(1/2) - 1)^13) - (3*a*((c*x - 1)^(1/2) - 1i)^15)/(2*((c*x + 1)^(1/2) - 1)^15) - (3*a*((c*x - 1)^(1/2) - 1i))/(2*((c*x + 1)^(1/2) - 1)))/(c^5 - (8*c^5*((c*x - 1)^(1/2) - 1i)^2)/((c*x + 1)^(1/2) - 1)^2 + (28*c^5*((c*x - 1)^(1/2) - 1i)^4)/((c*x + 1)^(1/2) - 1)^4 - (56*c^5*((c*x - 1)^(1/2) - 1i)^6)/((c*x + 1)^(1/2) - 1)^6 + (70*c^5*((c*x - 1)^(1/2) - 1i)^8)/((c*x + 1)^(1/2) - 1)^8 - (56*c^5*((c*x - 1)^(1/2) - 1i)^10)/((c*x + 1)^(1/2) - 1)^10 + (28*c^5*((c*x - 1)^(1/2) - 1i)^12)/((c*x + 1)^(1/2) - 1)^12 - (8*c^5*((c*x - 1)^(1/2) - 1i)^14)/((c*x + 1)^(1/2) - 1)^14 + (c^5*((c*x - 1)^(1/2) - 1i)^16)/((c*x + 1)^(1/2) - 1)^16) - ((311*b*((c*x - 1)^(1/2) - 1i)^5)/(4*((c*x + 1)^(1/2) - 1)^5) - (175*b*((c*x - 1)^(1/2) - 1i)^3)/(12*((c*x + 1)^(1/2) - 1)^3) + (8361*b*((c*x - 1)^(1/2) - 1i)^7)/(4*((c*x + 1)^(1/2) - 1)^7) + (42259*b*((c*x - 1)^(1/2) - 1i)^9)/(6*((c*x + 1)^(1/2) - 1)^9) + (25295*b*((c*x - 1)^(1/2) - 1i)^11)/(2*((c*x + 1)^(1/2) - 1)^11) + (25295*b*((c*x - 1)^(1/2) - 1i)^13)/(2*((c*x + 1)^(1/2) - 1)^13) + (42259*b*((c*x - 1)^(1/2) - 1i)^15)/(6*((c*x + 1)^(1/2) - 1)^15) + (8361*b*((c*x - 1)^(1/2) - 1i)^17)/(4*((c*x + 1)^(1/2) - 1)^17) + (311*b*((c*x - 1)^(1/2) - 1i)^19)/(4*((c*x + 1)^(1/2) - 1)^19) - (175*b*((c*x - 1)^(1/2) - 1i)^21)/(12*((c*x + 1)^(1/2) - 1)^21) + (5*b*((c*x - 1)^(1/2) - 1i)^23)/(4*((c*x + 1)^(1/2) - 1)^23) + (5*b*((c*x - 1)^(1/2) - 1i))/(4*((c*x + 1)^(1/2) - 1)))/(c^7 - (12*c^7*((c*x - 1)^(1/2) - 1i)^2)/((c*x + 1)^(1/2) - 1)^2 + (66*c^7*((c*x - 1)^(1/2) - 1i)^4)/((c*x + 1)^(1/2) - 1)^4 - (220*c^7*((c*x - 1)^(1/2) - 1i)^6)/((c*x + 1)^(1/2) - 1)^6 + (495*c^7*((c*x - 1)^(1/2) - 1i)^8)/((c*x + 1)^(1/2) - 1)^8 - (792*c^7*((c*x - 1)^(1/2) - 1i)^10)/((c*x + 1)^(1/2) - 1)^10 + (924*c^7*((c*x - 1)^(1/2) - 1i)^12)/((c*x + 1)^(1/2) - 1)^12 - (792*c^7*((c*x - 1)^(1/2) - 1i)^14)/((c*x + 1)^(1/2) - 1)^14 + (495*c^7*((c*x - 1)^(1/2) - 1i)^16)/((c*x + 1)^(1/2) - 1)^16 - (220*c^7*((c*x - 1)^(1/2) - 1i)^18)/((c*x + 1)^(1/2) - 1)^18 + (66*c^7*((c*x - 1)^(1/2) - 1i)^20)/((c*x + 1)^(1/2) - 1)^20 - (12*c^7*((c*x - 1)^(1/2) - 1i)^22)/((c*x + 1)^(1/2) - 1)^22 + (c^7*((c*x - 1)^(1/2) - 1i)^24)/((c*x + 1)^(1/2) - 1)^24) + (3*a*atanh(((c*x - 1)^(1/2) - 1i)/((c*x + 1)^(1/2) - 1)))/(2*c^5) + (5*b*atanh(((c*x - 1)^(1/2) - 1i)/((c*x + 1)^(1/2) - 1)))/(4*c^7)","B"
349,1,108,103,2.440270,"\text{Not used}","int((x^3*(a + b*x^2))/((c*x - 1)^(1/2)*(c*x + 1)^(1/2)),x)","\frac{\sqrt{c\,x-1}\,\left(\frac{10\,a\,c^2+8\,b}{15\,c^6}+\frac{b\,x^5}{5\,c}+\frac{b\,x^4}{5\,c^2}+\frac{x^2\,\left(5\,a\,c^4+4\,b\,c^2\right)}{15\,c^6}+\frac{x^3\,\left(5\,a\,c^5+4\,b\,c^3\right)}{15\,c^6}+\frac{x\,\left(10\,a\,c^3+8\,b\,c\right)}{15\,c^6}\right)}{\sqrt{c\,x+1}}","Not used",1,"((c*x - 1)^(1/2)*((8*b + 10*a*c^2)/(15*c^6) + (b*x^5)/(5*c) + (b*x^4)/(5*c^2) + (x^2*(5*a*c^4 + 4*b*c^2))/(15*c^6) + (x^3*(5*a*c^5 + 4*b*c^3))/(15*c^6) + (x*(8*b*c + 10*a*c^3))/(15*c^6)))/(c*x + 1)^(1/2)","B"
350,1,720,87,22.496161,"\text{Not used}","int((x^2*(a + b*x^2))/((c*x - 1)^(1/2)*(c*x + 1)^(1/2)),x)","\frac{\frac{23\,b\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^3}{2\,{\left(\sqrt{c\,x+1}-1\right)}^3}+\frac{333\,b\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^5}{2\,{\left(\sqrt{c\,x+1}-1\right)}^5}+\frac{671\,b\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^7}{2\,{\left(\sqrt{c\,x+1}-1\right)}^7}+\frac{671\,b\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^9}{2\,{\left(\sqrt{c\,x+1}-1\right)}^9}+\frac{333\,b\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^{11}}{2\,{\left(\sqrt{c\,x+1}-1\right)}^{11}}+\frac{23\,b\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^{13}}{2\,{\left(\sqrt{c\,x+1}-1\right)}^{13}}-\frac{3\,b\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^{15}}{2\,{\left(\sqrt{c\,x+1}-1\right)}^{15}}-\frac{3\,b\,\left(\sqrt{c\,x-1}-\mathrm{i}\right)}{2\,\left(\sqrt{c\,x+1}-1\right)}}{c^5-\frac{8\,c^5\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{c\,x+1}-1\right)}^2}+\frac{28\,c^5\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^4}{{\left(\sqrt{c\,x+1}-1\right)}^4}-\frac{56\,c^5\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^6}{{\left(\sqrt{c\,x+1}-1\right)}^6}+\frac{70\,c^5\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^8}{{\left(\sqrt{c\,x+1}-1\right)}^8}-\frac{56\,c^5\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^{10}}{{\left(\sqrt{c\,x+1}-1\right)}^{10}}+\frac{28\,c^5\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^{12}}{{\left(\sqrt{c\,x+1}-1\right)}^{12}}-\frac{8\,c^5\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^{14}}{{\left(\sqrt{c\,x+1}-1\right)}^{14}}+\frac{c^5\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^{16}}{{\left(\sqrt{c\,x+1}-1\right)}^{16}}}-\frac{\frac{14\,a\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^3}{{\left(\sqrt{c\,x+1}-1\right)}^3}+\frac{14\,a\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^5}{{\left(\sqrt{c\,x+1}-1\right)}^5}+\frac{2\,a\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^7}{{\left(\sqrt{c\,x+1}-1\right)}^7}+\frac{2\,a\,\left(\sqrt{c\,x-1}-\mathrm{i}\right)}{\sqrt{c\,x+1}-1}}{c^3-\frac{4\,c^3\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{c\,x+1}-1\right)}^2}+\frac{6\,c^3\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^4}{{\left(\sqrt{c\,x+1}-1\right)}^4}-\frac{4\,c^3\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^6}{{\left(\sqrt{c\,x+1}-1\right)}^6}+\frac{c^3\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^8}{{\left(\sqrt{c\,x+1}-1\right)}^8}}+\frac{2\,a\,\mathrm{atanh}\left(\frac{\sqrt{c\,x-1}-\mathrm{i}}{\sqrt{c\,x+1}-1}\right)}{c^3}+\frac{3\,b\,\mathrm{atanh}\left(\frac{\sqrt{c\,x-1}-\mathrm{i}}{\sqrt{c\,x+1}-1}\right)}{2\,c^5}","Not used",1,"((23*b*((c*x - 1)^(1/2) - 1i)^3)/(2*((c*x + 1)^(1/2) - 1)^3) + (333*b*((c*x - 1)^(1/2) - 1i)^5)/(2*((c*x + 1)^(1/2) - 1)^5) + (671*b*((c*x - 1)^(1/2) - 1i)^7)/(2*((c*x + 1)^(1/2) - 1)^7) + (671*b*((c*x - 1)^(1/2) - 1i)^9)/(2*((c*x + 1)^(1/2) - 1)^9) + (333*b*((c*x - 1)^(1/2) - 1i)^11)/(2*((c*x + 1)^(1/2) - 1)^11) + (23*b*((c*x - 1)^(1/2) - 1i)^13)/(2*((c*x + 1)^(1/2) - 1)^13) - (3*b*((c*x - 1)^(1/2) - 1i)^15)/(2*((c*x + 1)^(1/2) - 1)^15) - (3*b*((c*x - 1)^(1/2) - 1i))/(2*((c*x + 1)^(1/2) - 1)))/(c^5 - (8*c^5*((c*x - 1)^(1/2) - 1i)^2)/((c*x + 1)^(1/2) - 1)^2 + (28*c^5*((c*x - 1)^(1/2) - 1i)^4)/((c*x + 1)^(1/2) - 1)^4 - (56*c^5*((c*x - 1)^(1/2) - 1i)^6)/((c*x + 1)^(1/2) - 1)^6 + (70*c^5*((c*x - 1)^(1/2) - 1i)^8)/((c*x + 1)^(1/2) - 1)^8 - (56*c^5*((c*x - 1)^(1/2) - 1i)^10)/((c*x + 1)^(1/2) - 1)^10 + (28*c^5*((c*x - 1)^(1/2) - 1i)^12)/((c*x + 1)^(1/2) - 1)^12 - (8*c^5*((c*x - 1)^(1/2) - 1i)^14)/((c*x + 1)^(1/2) - 1)^14 + (c^5*((c*x - 1)^(1/2) - 1i)^16)/((c*x + 1)^(1/2) - 1)^16) - ((14*a*((c*x - 1)^(1/2) - 1i)^3)/((c*x + 1)^(1/2) - 1)^3 + (14*a*((c*x - 1)^(1/2) - 1i)^5)/((c*x + 1)^(1/2) - 1)^5 + (2*a*((c*x - 1)^(1/2) - 1i)^7)/((c*x + 1)^(1/2) - 1)^7 + (2*a*((c*x - 1)^(1/2) - 1i))/((c*x + 1)^(1/2) - 1))/(c^3 - (4*c^3*((c*x - 1)^(1/2) - 1i)^2)/((c*x + 1)^(1/2) - 1)^2 + (6*c^3*((c*x - 1)^(1/2) - 1i)^4)/((c*x + 1)^(1/2) - 1)^4 - (4*c^3*((c*x - 1)^(1/2) - 1i)^6)/((c*x + 1)^(1/2) - 1)^6 + (c^3*((c*x - 1)^(1/2) - 1i)^8)/((c*x + 1)^(1/2) - 1)^8) + (2*a*atanh(((c*x - 1)^(1/2) - 1i)/((c*x + 1)^(1/2) - 1)))/c^3 + (3*b*atanh(((c*x - 1)^(1/2) - 1i)/((c*x + 1)^(1/2) - 1)))/(2*c^5)","B"
351,1,66,65,2.358758,"\text{Not used}","int((x*(a + b*x^2))/((c*x - 1)^(1/2)*(c*x + 1)^(1/2)),x)","\frac{\sqrt{c\,x-1}\,\left(\frac{3\,a\,c^2+2\,b}{3\,c^4}+\frac{b\,x^3}{3\,c}+\frac{b\,x^2}{3\,c^2}+\frac{x\,\left(3\,a\,c^3+2\,b\,c\right)}{3\,c^4}\right)}{\sqrt{c\,x+1}}","Not used",1,"((c*x - 1)^(1/2)*((2*b + 3*a*c^2)/(3*c^4) + (b*x^3)/(3*c) + (b*x^2)/(3*c^2) + (x*(2*b*c + 3*a*c^3))/(3*c^4)))/(c*x + 1)^(1/2)","B"
352,1,293,47,12.685471,"\text{Not used}","int((a + b*x^2)/((c*x - 1)^(1/2)*(c*x + 1)^(1/2)),x)","-\frac{\frac{14\,b\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^3}{{\left(\sqrt{c\,x+1}-1\right)}^3}+\frac{14\,b\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^5}{{\left(\sqrt{c\,x+1}-1\right)}^5}+\frac{2\,b\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^7}{{\left(\sqrt{c\,x+1}-1\right)}^7}+\frac{2\,b\,\left(\sqrt{c\,x-1}-\mathrm{i}\right)}{\sqrt{c\,x+1}-1}}{c^3-\frac{4\,c^3\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{c\,x+1}-1\right)}^2}+\frac{6\,c^3\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^4}{{\left(\sqrt{c\,x+1}-1\right)}^4}-\frac{4\,c^3\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^6}{{\left(\sqrt{c\,x+1}-1\right)}^6}+\frac{c^3\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^8}{{\left(\sqrt{c\,x+1}-1\right)}^8}}+\frac{2\,b\,\mathrm{atanh}\left(\frac{\sqrt{c\,x-1}-\mathrm{i}}{\sqrt{c\,x+1}-1}\right)}{c^3}-\frac{4\,a\,\mathrm{atan}\left(\frac{c\,\left(\sqrt{c\,x-1}-\mathrm{i}\right)}{\left(\sqrt{c\,x+1}-1\right)\,\sqrt{-c^2}}\right)}{\sqrt{-c^2}}","Not used",1,"(2*b*atanh(((c*x - 1)^(1/2) - 1i)/((c*x + 1)^(1/2) - 1)))/c^3 - ((14*b*((c*x - 1)^(1/2) - 1i)^3)/((c*x + 1)^(1/2) - 1)^3 + (14*b*((c*x - 1)^(1/2) - 1i)^5)/((c*x + 1)^(1/2) - 1)^5 + (2*b*((c*x - 1)^(1/2) - 1i)^7)/((c*x + 1)^(1/2) - 1)^7 + (2*b*((c*x - 1)^(1/2) - 1i))/((c*x + 1)^(1/2) - 1))/(c^3 - (4*c^3*((c*x - 1)^(1/2) - 1i)^2)/((c*x + 1)^(1/2) - 1)^2 + (6*c^3*((c*x - 1)^(1/2) - 1i)^4)/((c*x + 1)^(1/2) - 1)^4 - (4*c^3*((c*x - 1)^(1/2) - 1i)^6)/((c*x + 1)^(1/2) - 1)^6 + (c^3*((c*x - 1)^(1/2) - 1i)^8)/((c*x + 1)^(1/2) - 1)^8) - (4*a*atan((c*((c*x - 1)^(1/2) - 1i))/(((c*x + 1)^(1/2) - 1)*(-c^2)^(1/2))))/(-c^2)^(1/2)","B"
353,1,77,46,3.864993,"\text{Not used}","int((a + b*x^2)/(x*(c*x - 1)^(1/2)*(c*x + 1)^(1/2)),x)","\frac{b\,\sqrt{c\,x-1}\,\sqrt{c\,x+1}}{c^2}-a\,\left(\ln\left(\frac{{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{c\,x+1}-1\right)}^2}+1\right)-\ln\left(\frac{\sqrt{c\,x-1}-\mathrm{i}}{\sqrt{c\,x+1}-1}\right)\right)\,1{}\mathrm{i}","Not used",1,"(b*(c*x - 1)^(1/2)*(c*x + 1)^(1/2))/c^2 - a*(log(((c*x - 1)^(1/2) - 1i)^2/((c*x + 1)^(1/2) - 1)^2 + 1) - log(((c*x - 1)^(1/2) - 1i)/((c*x + 1)^(1/2) - 1)))*1i","B"
354,1,61,33,2.592972,"\text{Not used}","int((a + b*x^2)/(x^2*(c*x - 1)^(1/2)*(c*x + 1)^(1/2)),x)","\frac{a\,\sqrt{c\,x-1}\,\sqrt{c\,x+1}}{x}-\frac{4\,b\,\mathrm{atan}\left(\frac{c\,\left(\sqrt{c\,x-1}-\mathrm{i}\right)}{\left(\sqrt{c\,x+1}-1\right)\,\sqrt{-c^2}}\right)}{\sqrt{-c^2}}","Not used",1,"(a*(c*x - 1)^(1/2)*(c*x + 1)^(1/2))/x - (4*b*atan((c*((c*x - 1)^(1/2) - 1i))/(((c*x + 1)^(1/2) - 1)*(-c^2)^(1/2))))/(-c^2)^(1/2)","B"
355,1,297,60,8.667853,"\text{Not used}","int((a + b*x^2)/(x^3*(c*x - 1)^(1/2)*(c*x + 1)^(1/2)),x)","\frac{\frac{a\,c^2\,1{}\mathrm{i}}{32}+\frac{a\,c^2\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^2\,1{}\mathrm{i}}{16\,{\left(\sqrt{c\,x+1}-1\right)}^2}-\frac{a\,c^2\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^4\,15{}\mathrm{i}}{32\,{\left(\sqrt{c\,x+1}-1\right)}^4}}{\frac{{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{c\,x+1}-1\right)}^2}+\frac{2\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^4}{{\left(\sqrt{c\,x+1}-1\right)}^4}+\frac{{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^6}{{\left(\sqrt{c\,x+1}-1\right)}^6}}-b\,\left(\ln\left(\frac{{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{c\,x+1}-1\right)}^2}+1\right)-\ln\left(\frac{\sqrt{c\,x-1}-\mathrm{i}}{\sqrt{c\,x+1}-1}\right)\right)\,1{}\mathrm{i}-\frac{a\,c^2\,\ln\left(\frac{{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{c\,x+1}-1\right)}^2}+1\right)\,1{}\mathrm{i}}{2}+\frac{a\,c^2\,\ln\left(\frac{\sqrt{c\,x-1}-\mathrm{i}}{\sqrt{c\,x+1}-1}\right)\,1{}\mathrm{i}}{2}+\frac{a\,c^2\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^2\,1{}\mathrm{i}}{32\,{\left(\sqrt{c\,x+1}-1\right)}^2}","Not used",1,"((a*c^2*1i)/32 + (a*c^2*((c*x - 1)^(1/2) - 1i)^2*1i)/(16*((c*x + 1)^(1/2) - 1)^2) - (a*c^2*((c*x - 1)^(1/2) - 1i)^4*15i)/(32*((c*x + 1)^(1/2) - 1)^4))/(((c*x - 1)^(1/2) - 1i)^2/((c*x + 1)^(1/2) - 1)^2 + (2*((c*x - 1)^(1/2) - 1i)^4)/((c*x + 1)^(1/2) - 1)^4 + ((c*x - 1)^(1/2) - 1i)^6/((c*x + 1)^(1/2) - 1)^6) - b*(log(((c*x - 1)^(1/2) - 1i)^2/((c*x + 1)^(1/2) - 1)^2 + 1) - log(((c*x - 1)^(1/2) - 1i)/((c*x + 1)^(1/2) - 1)))*1i - (a*c^2*log(((c*x - 1)^(1/2) - 1i)^2/((c*x + 1)^(1/2) - 1)^2 + 1)*1i)/2 + (a*c^2*log(((c*x - 1)^(1/2) - 1i)/((c*x + 1)^(1/2) - 1))*1i)/2 + (a*c^2*((c*x - 1)^(1/2) - 1i)^2*1i)/(32*((c*x + 1)^(1/2) - 1)^2)","B"
356,1,53,62,2.439611,"\text{Not used}","int((a + b*x^2)/(x^4*(c*x - 1)^(1/2)*(c*x + 1)^(1/2)),x)","\frac{\sqrt{c\,x-1}\,\left(\left(\frac{2\,a\,c^3}{3}+b\,c\right)\,x^3+\left(\frac{2\,a\,c^2}{3}+b\right)\,x^2+\frac{a\,c\,x}{3}+\frac{a}{3}\right)}{x^3\,\sqrt{c\,x+1}}","Not used",1,"((c*x - 1)^(1/2)*(a/3 + x^3*(b*c + (2*a*c^3)/3) + x^2*(b + (2*a*c^2)/3) + (a*c*x)/3))/(x^3*(c*x + 1)^(1/2))","B"
357,1,650,99,21.454789,"\text{Not used}","int((a + b*x^2)/(x^5*(c*x - 1)^(1/2)*(c*x + 1)^(1/2)),x)","\frac{\frac{b\,c^2\,1{}\mathrm{i}}{32}+\frac{b\,c^2\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^2\,1{}\mathrm{i}}{16\,{\left(\sqrt{c\,x+1}-1\right)}^2}-\frac{b\,c^2\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^4\,15{}\mathrm{i}}{32\,{\left(\sqrt{c\,x+1}-1\right)}^4}}{\frac{{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{c\,x+1}-1\right)}^2}+\frac{2\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^4}{{\left(\sqrt{c\,x+1}-1\right)}^4}+\frac{{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^6}{{\left(\sqrt{c\,x+1}-1\right)}^6}}-\frac{\frac{a\,c^4\,1{}\mathrm{i}}{1024}-\frac{a\,c^4\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^2\,3{}\mathrm{i}}{128\,{\left(\sqrt{c\,x+1}-1\right)}^2}-\frac{a\,c^4\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^4\,53{}\mathrm{i}}{512\,{\left(\sqrt{c\,x+1}-1\right)}^4}+\frac{a\,c^4\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^6\,87{}\mathrm{i}}{256\,{\left(\sqrt{c\,x+1}-1\right)}^6}+\frac{a\,c^4\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^8\,657{}\mathrm{i}}{1024\,{\left(\sqrt{c\,x+1}-1\right)}^8}+\frac{a\,c^4\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^{10}\,121{}\mathrm{i}}{256\,{\left(\sqrt{c\,x+1}-1\right)}^{10}}}{\frac{{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^4}{{\left(\sqrt{c\,x+1}-1\right)}^4}+\frac{4\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^6}{{\left(\sqrt{c\,x+1}-1\right)}^6}+\frac{6\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^8}{{\left(\sqrt{c\,x+1}-1\right)}^8}+\frac{4\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^{10}}{{\left(\sqrt{c\,x+1}-1\right)}^{10}}+\frac{{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^{12}}{{\left(\sqrt{c\,x+1}-1\right)}^{12}}}-\frac{a\,c^4\,\ln\left(\frac{{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{c\,x+1}-1\right)}^2}+1\right)\,3{}\mathrm{i}}{8}-\frac{b\,c^2\,\ln\left(\frac{{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{c\,x+1}-1\right)}^2}+1\right)\,1{}\mathrm{i}}{2}+\frac{a\,c^4\,\ln\left(\frac{\sqrt{c\,x-1}-\mathrm{i}}{\sqrt{c\,x+1}-1}\right)\,3{}\mathrm{i}}{8}+\frac{b\,c^2\,\ln\left(\frac{\sqrt{c\,x-1}-\mathrm{i}}{\sqrt{c\,x+1}-1}\right)\,1{}\mathrm{i}}{2}+\frac{a\,c^4\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^2\,7{}\mathrm{i}}{256\,{\left(\sqrt{c\,x+1}-1\right)}^2}-\frac{a\,c^4\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^4\,1{}\mathrm{i}}{1024\,{\left(\sqrt{c\,x+1}-1\right)}^4}+\frac{b\,c^2\,{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^2\,1{}\mathrm{i}}{32\,{\left(\sqrt{c\,x+1}-1\right)}^2}","Not used",1,"((b*c^2*1i)/32 + (b*c^2*((c*x - 1)^(1/2) - 1i)^2*1i)/(16*((c*x + 1)^(1/2) - 1)^2) - (b*c^2*((c*x - 1)^(1/2) - 1i)^4*15i)/(32*((c*x + 1)^(1/2) - 1)^4))/(((c*x - 1)^(1/2) - 1i)^2/((c*x + 1)^(1/2) - 1)^2 + (2*((c*x - 1)^(1/2) - 1i)^4)/((c*x + 1)^(1/2) - 1)^4 + ((c*x - 1)^(1/2) - 1i)^6/((c*x + 1)^(1/2) - 1)^6) - ((a*c^4*1i)/1024 - (a*c^4*((c*x - 1)^(1/2) - 1i)^2*3i)/(128*((c*x + 1)^(1/2) - 1)^2) - (a*c^4*((c*x - 1)^(1/2) - 1i)^4*53i)/(512*((c*x + 1)^(1/2) - 1)^4) + (a*c^4*((c*x - 1)^(1/2) - 1i)^6*87i)/(256*((c*x + 1)^(1/2) - 1)^6) + (a*c^4*((c*x - 1)^(1/2) - 1i)^8*657i)/(1024*((c*x + 1)^(1/2) - 1)^8) + (a*c^4*((c*x - 1)^(1/2) - 1i)^10*121i)/(256*((c*x + 1)^(1/2) - 1)^10))/(((c*x - 1)^(1/2) - 1i)^4/((c*x + 1)^(1/2) - 1)^4 + (4*((c*x - 1)^(1/2) - 1i)^6)/((c*x + 1)^(1/2) - 1)^6 + (6*((c*x - 1)^(1/2) - 1i)^8)/((c*x + 1)^(1/2) - 1)^8 + (4*((c*x - 1)^(1/2) - 1i)^10)/((c*x + 1)^(1/2) - 1)^10 + ((c*x - 1)^(1/2) - 1i)^12/((c*x + 1)^(1/2) - 1)^12) - (a*c^4*log(((c*x - 1)^(1/2) - 1i)^2/((c*x + 1)^(1/2) - 1)^2 + 1)*3i)/8 - (b*c^2*log(((c*x - 1)^(1/2) - 1i)^2/((c*x + 1)^(1/2) - 1)^2 + 1)*1i)/2 + (a*c^4*log(((c*x - 1)^(1/2) - 1i)/((c*x + 1)^(1/2) - 1))*3i)/8 + (b*c^2*log(((c*x - 1)^(1/2) - 1i)/((c*x + 1)^(1/2) - 1))*1i)/2 + (a*c^4*((c*x - 1)^(1/2) - 1i)^2*7i)/(256*((c*x + 1)^(1/2) - 1)^2) - (a*c^4*((c*x - 1)^(1/2) - 1i)^4*1i)/(1024*((c*x + 1)^(1/2) - 1)^4) + (b*c^2*((c*x - 1)^(1/2) - 1i)^2*1i)/(32*((c*x + 1)^(1/2) - 1)^2)","B"
358,1,1682,164,42.655853,"\text{Not used}","int((x^4*(a + b*x^2))/((c + d*x)^(1/2)*(d*x - c)^(1/2)),x)","\frac{\frac{5\,b\,c^6\,\left(\sqrt{c+d\,x}-\sqrt{c}\right)}{4\,\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}-\frac{175\,b\,c^6\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^3}{12\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^3}+\frac{311\,b\,c^6\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^5}{4\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^5}+\frac{8361\,b\,c^6\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^7}{4\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^7}+\frac{42259\,b\,c^6\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^9}{6\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^9}+\frac{25295\,b\,c^6\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{11}}{2\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{11}}+\frac{25295\,b\,c^6\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{13}}{2\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{13}}+\frac{42259\,b\,c^6\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{15}}{6\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{15}}+\frac{8361\,b\,c^6\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{17}}{4\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{17}}+\frac{311\,b\,c^6\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{19}}{4\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{19}}-\frac{175\,b\,c^6\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{21}}{12\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{21}}+\frac{5\,b\,c^6\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{23}}{4\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{23}}}{d^7-\frac{12\,d^7\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^2}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^2}+\frac{66\,d^7\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^4}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^4}-\frac{220\,d^7\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^6}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^6}+\frac{495\,d^7\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^8}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^8}-\frac{792\,d^7\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{10}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{10}}+\frac{924\,d^7\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{12}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{12}}-\frac{792\,d^7\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{14}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{14}}+\frac{495\,d^7\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{16}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{16}}-\frac{220\,d^7\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{18}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{18}}+\frac{66\,d^7\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{20}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{20}}-\frac{12\,d^7\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{22}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{22}}+\frac{d^7\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{24}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{24}}}-\frac{\frac{23\,a\,c^4\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^3}{2\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^3}-\frac{3\,a\,c^4\,\left(\sqrt{c+d\,x}-\sqrt{c}\right)}{2\,\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}+\frac{333\,a\,c^4\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^5}{2\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^5}+\frac{671\,a\,c^4\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^7}{2\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^7}+\frac{671\,a\,c^4\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^9}{2\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^9}+\frac{333\,a\,c^4\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{11}}{2\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{11}}+\frac{23\,a\,c^4\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{13}}{2\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{13}}-\frac{3\,a\,c^4\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{15}}{2\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{15}}}{d^5-\frac{8\,d^5\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^2}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^2}+\frac{28\,d^5\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^4}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^4}-\frac{56\,d^5\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^6}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^6}+\frac{70\,d^5\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^8}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^8}-\frac{56\,d^5\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{10}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{10}}+\frac{28\,d^5\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{12}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{12}}-\frac{8\,d^5\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{14}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{14}}+\frac{d^5\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{16}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{16}}}-\frac{3\,a\,c^4\,\mathrm{atanh}\left(\frac{\sqrt{c+d\,x}-\sqrt{c}}{\sqrt{-c}-\sqrt{d\,x-c}}\right)}{2\,d^5}-\frac{5\,b\,c^6\,\mathrm{atanh}\left(\frac{\sqrt{c+d\,x}-\sqrt{c}}{\sqrt{-c}-\sqrt{d\,x-c}}\right)}{4\,d^7}","Not used",1,"((5*b*c^6*((c + d*x)^(1/2) - c^(1/2)))/(4*((-c)^(1/2) - (d*x - c)^(1/2))) - (175*b*c^6*((c + d*x)^(1/2) - c^(1/2))^3)/(12*((-c)^(1/2) - (d*x - c)^(1/2))^3) + (311*b*c^6*((c + d*x)^(1/2) - c^(1/2))^5)/(4*((-c)^(1/2) - (d*x - c)^(1/2))^5) + (8361*b*c^6*((c + d*x)^(1/2) - c^(1/2))^7)/(4*((-c)^(1/2) - (d*x - c)^(1/2))^7) + (42259*b*c^6*((c + d*x)^(1/2) - c^(1/2))^9)/(6*((-c)^(1/2) - (d*x - c)^(1/2))^9) + (25295*b*c^6*((c + d*x)^(1/2) - c^(1/2))^11)/(2*((-c)^(1/2) - (d*x - c)^(1/2))^11) + (25295*b*c^6*((c + d*x)^(1/2) - c^(1/2))^13)/(2*((-c)^(1/2) - (d*x - c)^(1/2))^13) + (42259*b*c^6*((c + d*x)^(1/2) - c^(1/2))^15)/(6*((-c)^(1/2) - (d*x - c)^(1/2))^15) + (8361*b*c^6*((c + d*x)^(1/2) - c^(1/2))^17)/(4*((-c)^(1/2) - (d*x - c)^(1/2))^17) + (311*b*c^6*((c + d*x)^(1/2) - c^(1/2))^19)/(4*((-c)^(1/2) - (d*x - c)^(1/2))^19) - (175*b*c^6*((c + d*x)^(1/2) - c^(1/2))^21)/(12*((-c)^(1/2) - (d*x - c)^(1/2))^21) + (5*b*c^6*((c + d*x)^(1/2) - c^(1/2))^23)/(4*((-c)^(1/2) - (d*x - c)^(1/2))^23))/(d^7 - (12*d^7*((c + d*x)^(1/2) - c^(1/2))^2)/((-c)^(1/2) - (d*x - c)^(1/2))^2 + (66*d^7*((c + d*x)^(1/2) - c^(1/2))^4)/((-c)^(1/2) - (d*x - c)^(1/2))^4 - (220*d^7*((c + d*x)^(1/2) - c^(1/2))^6)/((-c)^(1/2) - (d*x - c)^(1/2))^6 + (495*d^7*((c + d*x)^(1/2) - c^(1/2))^8)/((-c)^(1/2) - (d*x - c)^(1/2))^8 - (792*d^7*((c + d*x)^(1/2) - c^(1/2))^10)/((-c)^(1/2) - (d*x - c)^(1/2))^10 + (924*d^7*((c + d*x)^(1/2) - c^(1/2))^12)/((-c)^(1/2) - (d*x - c)^(1/2))^12 - (792*d^7*((c + d*x)^(1/2) - c^(1/2))^14)/((-c)^(1/2) - (d*x - c)^(1/2))^14 + (495*d^7*((c + d*x)^(1/2) - c^(1/2))^16)/((-c)^(1/2) - (d*x - c)^(1/2))^16 - (220*d^7*((c + d*x)^(1/2) - c^(1/2))^18)/((-c)^(1/2) - (d*x - c)^(1/2))^18 + (66*d^7*((c + d*x)^(1/2) - c^(1/2))^20)/((-c)^(1/2) - (d*x - c)^(1/2))^20 - (12*d^7*((c + d*x)^(1/2) - c^(1/2))^22)/((-c)^(1/2) - (d*x - c)^(1/2))^22 + (d^7*((c + d*x)^(1/2) - c^(1/2))^24)/((-c)^(1/2) - (d*x - c)^(1/2))^24) - ((23*a*c^4*((c + d*x)^(1/2) - c^(1/2))^3)/(2*((-c)^(1/2) - (d*x - c)^(1/2))^3) - (3*a*c^4*((c + d*x)^(1/2) - c^(1/2)))/(2*((-c)^(1/2) - (d*x - c)^(1/2))) + (333*a*c^4*((c + d*x)^(1/2) - c^(1/2))^5)/(2*((-c)^(1/2) - (d*x - c)^(1/2))^5) + (671*a*c^4*((c + d*x)^(1/2) - c^(1/2))^7)/(2*((-c)^(1/2) - (d*x - c)^(1/2))^7) + (671*a*c^4*((c + d*x)^(1/2) - c^(1/2))^9)/(2*((-c)^(1/2) - (d*x - c)^(1/2))^9) + (333*a*c^4*((c + d*x)^(1/2) - c^(1/2))^11)/(2*((-c)^(1/2) - (d*x - c)^(1/2))^11) + (23*a*c^4*((c + d*x)^(1/2) - c^(1/2))^13)/(2*((-c)^(1/2) - (d*x - c)^(1/2))^13) - (3*a*c^4*((c + d*x)^(1/2) - c^(1/2))^15)/(2*((-c)^(1/2) - (d*x - c)^(1/2))^15))/(d^5 - (8*d^5*((c + d*x)^(1/2) - c^(1/2))^2)/((-c)^(1/2) - (d*x - c)^(1/2))^2 + (28*d^5*((c + d*x)^(1/2) - c^(1/2))^4)/((-c)^(1/2) - (d*x - c)^(1/2))^4 - (56*d^5*((c + d*x)^(1/2) - c^(1/2))^6)/((-c)^(1/2) - (d*x - c)^(1/2))^6 + (70*d^5*((c + d*x)^(1/2) - c^(1/2))^8)/((-c)^(1/2) - (d*x - c)^(1/2))^8 - (56*d^5*((c + d*x)^(1/2) - c^(1/2))^10)/((-c)^(1/2) - (d*x - c)^(1/2))^10 + (28*d^5*((c + d*x)^(1/2) - c^(1/2))^12)/((-c)^(1/2) - (d*x - c)^(1/2))^12 - (8*d^5*((c + d*x)^(1/2) - c^(1/2))^14)/((-c)^(1/2) - (d*x - c)^(1/2))^14 + (d^5*((c + d*x)^(1/2) - c^(1/2))^16)/((-c)^(1/2) - (d*x - c)^(1/2))^16) - (3*a*c^4*atanh(((c + d*x)^(1/2) - c^(1/2))/((-c)^(1/2) - (d*x - c)^(1/2))))/(2*d^5) - (5*b*c^6*atanh(((c + d*x)^(1/2) - c^(1/2))/((-c)^(1/2) - (d*x - c)^(1/2))))/(4*d^7)","B"
359,1,130,118,2.700203,"\text{Not used}","int((x^3*(a + b*x^2))/((c + d*x)^(1/2)*(d*x - c)^(1/2)),x)","\frac{\sqrt{d\,x-c}\,\left(\frac{8\,b\,c^5+10\,a\,c^3\,d^2}{15\,d^6}+\frac{x^3\,\left(4\,b\,c^2\,d^3+5\,a\,d^5\right)}{15\,d^6}+\frac{x\,\left(8\,b\,c^4\,d+10\,a\,c^2\,d^3\right)}{15\,d^6}+\frac{b\,x^5}{5\,d}+\frac{x^2\,\left(4\,b\,c^3\,d^2+5\,a\,c\,d^4\right)}{15\,d^6}+\frac{b\,c\,x^4}{5\,d^2}\right)}{\sqrt{c+d\,x}}","Not used",1,"((d*x - c)^(1/2)*((8*b*c^5 + 10*a*c^3*d^2)/(15*d^6) + (x^3*(5*a*d^5 + 4*b*c^2*d^3))/(15*d^6) + (x*(10*a*c^2*d^3 + 8*b*c^4*d))/(15*d^6) + (b*x^5)/(5*d) + (x^2*(4*b*c^3*d^2 + 5*a*c*d^4))/(15*d^6) + (b*c*x^4)/(5*d^2)))/(c + d*x)^(1/2)","B"
360,1,1048,118,25.512832,"\text{Not used}","int((x^2*(a + b*x^2))/((c + d*x)^(1/2)*(d*x - c)^(1/2)),x)","\frac{\frac{2\,a\,c^2\,\left(\sqrt{c+d\,x}-\sqrt{c}\right)}{\sqrt{-c}-\sqrt{d\,x-c}}+\frac{14\,a\,c^2\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^3}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^3}+\frac{14\,a\,c^2\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^5}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^5}+\frac{2\,a\,c^2\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^7}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^7}}{d^3-\frac{4\,d^3\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^2}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^2}+\frac{6\,d^3\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^4}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^4}-\frac{4\,d^3\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^6}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^6}+\frac{d^3\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^8}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^8}}-\frac{\frac{23\,b\,c^4\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^3}{2\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^3}-\frac{3\,b\,c^4\,\left(\sqrt{c+d\,x}-\sqrt{c}\right)}{2\,\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}+\frac{333\,b\,c^4\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^5}{2\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^5}+\frac{671\,b\,c^4\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^7}{2\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^7}+\frac{671\,b\,c^4\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^9}{2\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^9}+\frac{333\,b\,c^4\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{11}}{2\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{11}}+\frac{23\,b\,c^4\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{13}}{2\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{13}}-\frac{3\,b\,c^4\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{15}}{2\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{15}}}{d^5-\frac{8\,d^5\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^2}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^2}+\frac{28\,d^5\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^4}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^4}-\frac{56\,d^5\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^6}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^6}+\frac{70\,d^5\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^8}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^8}-\frac{56\,d^5\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{10}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{10}}+\frac{28\,d^5\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{12}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{12}}-\frac{8\,d^5\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{14}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{14}}+\frac{d^5\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{16}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{16}}}-\frac{2\,a\,c^2\,\mathrm{atanh}\left(\frac{\sqrt{c+d\,x}-\sqrt{c}}{\sqrt{-c}-\sqrt{d\,x-c}}\right)}{d^3}-\frac{3\,b\,c^4\,\mathrm{atanh}\left(\frac{\sqrt{c+d\,x}-\sqrt{c}}{\sqrt{-c}-\sqrt{d\,x-c}}\right)}{2\,d^5}","Not used",1,"((2*a*c^2*((c + d*x)^(1/2) - c^(1/2)))/((-c)^(1/2) - (d*x - c)^(1/2)) + (14*a*c^2*((c + d*x)^(1/2) - c^(1/2))^3)/((-c)^(1/2) - (d*x - c)^(1/2))^3 + (14*a*c^2*((c + d*x)^(1/2) - c^(1/2))^5)/((-c)^(1/2) - (d*x - c)^(1/2))^5 + (2*a*c^2*((c + d*x)^(1/2) - c^(1/2))^7)/((-c)^(1/2) - (d*x - c)^(1/2))^7)/(d^3 - (4*d^3*((c + d*x)^(1/2) - c^(1/2))^2)/((-c)^(1/2) - (d*x - c)^(1/2))^2 + (6*d^3*((c + d*x)^(1/2) - c^(1/2))^4)/((-c)^(1/2) - (d*x - c)^(1/2))^4 - (4*d^3*((c + d*x)^(1/2) - c^(1/2))^6)/((-c)^(1/2) - (d*x - c)^(1/2))^6 + (d^3*((c + d*x)^(1/2) - c^(1/2))^8)/((-c)^(1/2) - (d*x - c)^(1/2))^8) - ((23*b*c^4*((c + d*x)^(1/2) - c^(1/2))^3)/(2*((-c)^(1/2) - (d*x - c)^(1/2))^3) - (3*b*c^4*((c + d*x)^(1/2) - c^(1/2)))/(2*((-c)^(1/2) - (d*x - c)^(1/2))) + (333*b*c^4*((c + d*x)^(1/2) - c^(1/2))^5)/(2*((-c)^(1/2) - (d*x - c)^(1/2))^5) + (671*b*c^4*((c + d*x)^(1/2) - c^(1/2))^7)/(2*((-c)^(1/2) - (d*x - c)^(1/2))^7) + (671*b*c^4*((c + d*x)^(1/2) - c^(1/2))^9)/(2*((-c)^(1/2) - (d*x - c)^(1/2))^9) + (333*b*c^4*((c + d*x)^(1/2) - c^(1/2))^11)/(2*((-c)^(1/2) - (d*x - c)^(1/2))^11) + (23*b*c^4*((c + d*x)^(1/2) - c^(1/2))^13)/(2*((-c)^(1/2) - (d*x - c)^(1/2))^13) - (3*b*c^4*((c + d*x)^(1/2) - c^(1/2))^15)/(2*((-c)^(1/2) - (d*x - c)^(1/2))^15))/(d^5 - (8*d^5*((c + d*x)^(1/2) - c^(1/2))^2)/((-c)^(1/2) - (d*x - c)^(1/2))^2 + (28*d^5*((c + d*x)^(1/2) - c^(1/2))^4)/((-c)^(1/2) - (d*x - c)^(1/2))^4 - (56*d^5*((c + d*x)^(1/2) - c^(1/2))^6)/((-c)^(1/2) - (d*x - c)^(1/2))^6 + (70*d^5*((c + d*x)^(1/2) - c^(1/2))^8)/((-c)^(1/2) - (d*x - c)^(1/2))^8 - (56*d^5*((c + d*x)^(1/2) - c^(1/2))^10)/((-c)^(1/2) - (d*x - c)^(1/2))^10 + (28*d^5*((c + d*x)^(1/2) - c^(1/2))^12)/((-c)^(1/2) - (d*x - c)^(1/2))^12 - (8*d^5*((c + d*x)^(1/2) - c^(1/2))^14)/((-c)^(1/2) - (d*x - c)^(1/2))^14 + (d^5*((c + d*x)^(1/2) - c^(1/2))^16)/((-c)^(1/2) - (d*x - c)^(1/2))^16) - (2*a*c^2*atanh(((c + d*x)^(1/2) - c^(1/2))/((-c)^(1/2) - (d*x - c)^(1/2))))/d^3 - (3*b*c^4*atanh(((c + d*x)^(1/2) - c^(1/2))/((-c)^(1/2) - (d*x - c)^(1/2))))/(2*d^5)","B"
361,1,76,72,2.663202,"\text{Not used}","int((x*(a + b*x^2))/((c + d*x)^(1/2)*(d*x - c)^(1/2)),x)","\frac{\sqrt{d\,x-c}\,\left(\frac{2\,b\,c^3+3\,a\,c\,d^2}{3\,d^4}+\frac{b\,x^3}{3\,d}+\frac{x\,\left(2\,b\,c^2\,d+3\,a\,d^3\right)}{3\,d^4}+\frac{b\,c\,x^2}{3\,d^2}\right)}{\sqrt{c+d\,x}}","Not used",1,"((d*x - c)^(1/2)*((2*b*c^3 + 3*a*c*d^2)/(3*d^4) + (b*x^3)/(3*d) + (x*(3*a*d^3 + 2*b*c^2*d))/(3*d^4) + (b*c*x^2)/(3*d^2)))/(c + d*x)^(1/2)","B"
362,1,417,68,10.799842,"\text{Not used}","int((a + b*x^2)/((c + d*x)^(1/2)*(d*x - c)^(1/2)),x)","\frac{\frac{2\,b\,c^2\,\left(\sqrt{c+d\,x}-\sqrt{c}\right)}{\sqrt{-c}-\sqrt{d\,x-c}}+\frac{14\,b\,c^2\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^3}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^3}+\frac{14\,b\,c^2\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^5}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^5}+\frac{2\,b\,c^2\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^7}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^7}}{d^3-\frac{4\,d^3\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^2}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^2}+\frac{6\,d^3\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^4}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^4}-\frac{4\,d^3\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^6}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^6}+\frac{d^3\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^8}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^8}}+\frac{4\,a\,\mathrm{atan}\left(\frac{d\,\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}{\sqrt{-d^2}\,\left(\sqrt{c+d\,x}-\sqrt{c}\right)}\right)}{\sqrt{-d^2}}-\frac{2\,b\,c^2\,\mathrm{atanh}\left(\frac{\sqrt{c+d\,x}-\sqrt{c}}{\sqrt{-c}-\sqrt{d\,x-c}}\right)}{d^3}","Not used",1,"((2*b*c^2*((c + d*x)^(1/2) - c^(1/2)))/((-c)^(1/2) - (d*x - c)^(1/2)) + (14*b*c^2*((c + d*x)^(1/2) - c^(1/2))^3)/((-c)^(1/2) - (d*x - c)^(1/2))^3 + (14*b*c^2*((c + d*x)^(1/2) - c^(1/2))^5)/((-c)^(1/2) - (d*x - c)^(1/2))^5 + (2*b*c^2*((c + d*x)^(1/2) - c^(1/2))^7)/((-c)^(1/2) - (d*x - c)^(1/2))^7)/(d^3 - (4*d^3*((c + d*x)^(1/2) - c^(1/2))^2)/((-c)^(1/2) - (d*x - c)^(1/2))^2 + (6*d^3*((c + d*x)^(1/2) - c^(1/2))^4)/((-c)^(1/2) - (d*x - c)^(1/2))^4 - (4*d^3*((c + d*x)^(1/2) - c^(1/2))^6)/((-c)^(1/2) - (d*x - c)^(1/2))^6 + (d^3*((c + d*x)^(1/2) - c^(1/2))^8)/((-c)^(1/2) - (d*x - c)^(1/2))^8) + (4*a*atan((d*((-c)^(1/2) - (d*x - c)^(1/2)))/((-d^2)^(1/2)*((c + d*x)^(1/2) - c^(1/2)))))/(-d^2)^(1/2) - (2*b*c^2*atanh(((c + d*x)^(1/2) - c^(1/2))/((-c)^(1/2) - (d*x - c)^(1/2))))/d^3","B"
363,1,108,56,3.966546,"\text{Not used}","int((a + b*x^2)/(x*(c + d*x)^(1/2)*(d*x - c)^(1/2)),x)","\frac{b\,\sqrt{c+d\,x}\,\sqrt{d\,x-c}}{d^2}-\frac{a\,\sqrt{-c}\,\left(\ln\left(\frac{{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^2}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^2}+1\right)-\ln\left(\frac{\sqrt{c+d\,x}-\sqrt{c}}{\sqrt{-c}-\sqrt{d\,x-c}}\right)\right)}{c^{3/2}}","Not used",1,"(b*(c + d*x)^(1/2)*(d*x - c)^(1/2))/d^2 - (a*(-c)^(1/2)*(log(((c + d*x)^(1/2) - c^(1/2))^2/((-c)^(1/2) - (d*x - c)^(1/2))^2 + 1) - log(((c + d*x)^(1/2) - c^(1/2))/((-c)^(1/2) - (d*x - c)^(1/2)))))/c^(3/2)","B"
364,1,77,57,2.944952,"\text{Not used}","int((a + b*x^2)/(x^2*(c + d*x)^(1/2)*(d*x - c)^(1/2)),x)","\frac{4\,b\,\mathrm{atan}\left(\frac{d\,\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}{\sqrt{-d^2}\,\left(\sqrt{c+d\,x}-\sqrt{c}\right)}\right)}{\sqrt{-d^2}}+\frac{a\,\sqrt{c+d\,x}\,\sqrt{d\,x-c}}{c^2\,x}","Not used",1,"(4*b*atan((d*((-c)^(1/2) - (d*x - c)^(1/2)))/((-d^2)^(1/2)*((c + d*x)^(1/2) - c^(1/2)))))/(-d^2)^(1/2) + (a*(c + d*x)^(1/2)*(d*x - c)^(1/2))/(c^2*x)","B"
365,1,457,76,7.499833,"\text{Not used}","int((a + b*x^2)/(x^3*(c + d*x)^(1/2)*(d*x - c)^(1/2)),x)","\frac{a\,{\left(-c\right)}^{3/2}\,d^2\,\ln\left(\frac{{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^2}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^2}+1\right)}{2\,c^{9/2}}-\frac{b\,\sqrt{-c}\,\left(\ln\left(\frac{{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^2}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^2}+1\right)-\ln\left(\frac{\sqrt{c+d\,x}-\sqrt{c}}{\sqrt{-c}-\sqrt{d\,x-c}}\right)\right)}{c^{3/2}}-\frac{a\,{\left(-c\right)}^{3/2}\,d^2\,\ln\left(\frac{\sqrt{c+d\,x}-\sqrt{c}}{\sqrt{-c}-\sqrt{d\,x-c}}\right)}{2\,c^{9/2}}-\frac{\frac{a\,{\left(-c\right)}^{3/2}\,d^2}{32\,c^{9/2}}+\frac{a\,{\left(-c\right)}^{3/2}\,d^2\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^2}{16\,c^{9/2}\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^2}-\frac{15\,a\,{\left(-c\right)}^{3/2}\,d^2\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^4}{32\,c^{9/2}\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^4}}{\frac{{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^2}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^2}+\frac{2\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^4}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^4}+\frac{{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^6}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^6}}+\frac{a\,d^2\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^2}{32\,{\left(-c\right)}^{3/2}\,c^{3/2}\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^2}","Not used",1,"(a*(-c)^(3/2)*d^2*log(((c + d*x)^(1/2) - c^(1/2))^2/((-c)^(1/2) - (d*x - c)^(1/2))^2 + 1))/(2*c^(9/2)) - (b*(-c)^(1/2)*(log(((c + d*x)^(1/2) - c^(1/2))^2/((-c)^(1/2) - (d*x - c)^(1/2))^2 + 1) - log(((c + d*x)^(1/2) - c^(1/2))/((-c)^(1/2) - (d*x - c)^(1/2)))))/c^(3/2) - (a*(-c)^(3/2)*d^2*log(((c + d*x)^(1/2) - c^(1/2))/((-c)^(1/2) - (d*x - c)^(1/2))))/(2*c^(9/2)) - ((a*(-c)^(3/2)*d^2)/(32*c^(9/2)) + (a*(-c)^(3/2)*d^2*((c + d*x)^(1/2) - c^(1/2))^2)/(16*c^(9/2)*((-c)^(1/2) - (d*x - c)^(1/2))^2) - (15*a*(-c)^(3/2)*d^2*((c + d*x)^(1/2) - c^(1/2))^4)/(32*c^(9/2)*((-c)^(1/2) - (d*x - c)^(1/2))^4))/(((c + d*x)^(1/2) - c^(1/2))^2/((-c)^(1/2) - (d*x - c)^(1/2))^2 + (2*((c + d*x)^(1/2) - c^(1/2))^4)/((-c)^(1/2) - (d*x - c)^(1/2))^4 + ((c + d*x)^(1/2) - c^(1/2))^6/((-c)^(1/2) - (d*x - c)^(1/2))^6) + (a*d^2*((c + d*x)^(1/2) - c^(1/2))^2)/(32*(-c)^(3/2)*c^(3/2)*((-c)^(1/2) - (d*x - c)^(1/2))^2)","B"
366,1,79,75,2.765452,"\text{Not used}","int((a + b*x^2)/(x^4*(c + d*x)^(1/2)*(d*x - c)^(1/2)),x)","\frac{\sqrt{d\,x-c}\,\left(\frac{a}{3\,c}+\frac{x^2\,\left(3\,b\,c^3+2\,a\,c\,d^2\right)}{3\,c^4}+\frac{x^3\,\left(3\,b\,c^2\,d+2\,a\,d^3\right)}{3\,c^4}+\frac{a\,d\,x}{3\,c^2}\right)}{x^3\,\sqrt{c+d\,x}}","Not used",1,"((d*x - c)^(1/2)*(a/(3*c) + (x^2*(3*b*c^3 + 2*a*c*d^2))/(3*c^4) + (x^3*(2*a*d^3 + 3*b*c^2*d))/(3*c^4) + (a*d*x)/(3*c^2)))/(x^3*(c + d*x)^(1/2))","B"
367,1,1005,123,19.134772,"\text{Not used}","int((a + b*x^2)/(x^5*(c + d*x)^(1/2)*(d*x - c)^(1/2)),x)","\frac{3\,a\,\sqrt{-c}\,d^4\,\ln\left(\frac{\sqrt{c+d\,x}-\sqrt{c}}{\sqrt{-c}-\sqrt{d\,x-c}}\right)}{8\,c^{11/2}}-\frac{\frac{b\,{\left(-c\right)}^{3/2}\,d^2}{32\,c^{9/2}}+\frac{b\,{\left(-c\right)}^{3/2}\,d^2\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^2}{16\,c^{9/2}\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^2}-\frac{15\,b\,{\left(-c\right)}^{3/2}\,d^2\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^4}{32\,c^{9/2}\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^4}}{\frac{{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^2}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^2}+\frac{2\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^4}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^4}+\frac{{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^6}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^6}}-\frac{\frac{a\,\sqrt{-c}\,d^4}{1024\,c^{11/2}}-\frac{3\,a\,\sqrt{-c}\,d^4\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^2}{128\,c^{11/2}\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^2}-\frac{53\,a\,\sqrt{-c}\,d^4\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^4}{512\,c^{11/2}\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^4}+\frac{87\,a\,\sqrt{-c}\,d^4\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^6}{256\,c^{11/2}\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^6}+\frac{657\,a\,\sqrt{-c}\,d^4\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^8}{1024\,c^{11/2}\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^8}+\frac{121\,a\,\sqrt{-c}\,d^4\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{10}}{256\,c^{11/2}\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{10}}}{\frac{{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^4}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^4}+\frac{4\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^6}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^6}+\frac{6\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^8}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^8}+\frac{4\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{10}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{10}}+\frac{{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^{12}}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^{12}}}-\frac{b\,{\left(-c\right)}^{3/2}\,d^2\,\ln\left(\frac{\sqrt{c+d\,x}-\sqrt{c}}{\sqrt{-c}-\sqrt{d\,x-c}}\right)}{2\,c^{9/2}}-\frac{3\,a\,\sqrt{-c}\,d^4\,\ln\left(\frac{{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^2}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^2}+1\right)}{8\,c^{11/2}}+\frac{b\,{\left(-c\right)}^{3/2}\,d^2\,\ln\left(\frac{{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^2}{{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^2}+1\right)}{2\,c^{9/2}}-\frac{7\,a\,d^4\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^2}{256\,\sqrt{-c}\,c^{9/2}\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^2}+\frac{a\,d^4\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^4}{1024\,\sqrt{-c}\,c^{9/2}\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^4}+\frac{b\,d^2\,{\left(\sqrt{c+d\,x}-\sqrt{c}\right)}^2}{32\,{\left(-c\right)}^{3/2}\,c^{3/2}\,{\left(\sqrt{-c}-\sqrt{d\,x-c}\right)}^2}","Not used",1,"(3*a*(-c)^(1/2)*d^4*log(((c + d*x)^(1/2) - c^(1/2))/((-c)^(1/2) - (d*x - c)^(1/2))))/(8*c^(11/2)) - ((b*(-c)^(3/2)*d^2)/(32*c^(9/2)) + (b*(-c)^(3/2)*d^2*((c + d*x)^(1/2) - c^(1/2))^2)/(16*c^(9/2)*((-c)^(1/2) - (d*x - c)^(1/2))^2) - (15*b*(-c)^(3/2)*d^2*((c + d*x)^(1/2) - c^(1/2))^4)/(32*c^(9/2)*((-c)^(1/2) - (d*x - c)^(1/2))^4))/(((c + d*x)^(1/2) - c^(1/2))^2/((-c)^(1/2) - (d*x - c)^(1/2))^2 + (2*((c + d*x)^(1/2) - c^(1/2))^4)/((-c)^(1/2) - (d*x - c)^(1/2))^4 + ((c + d*x)^(1/2) - c^(1/2))^6/((-c)^(1/2) - (d*x - c)^(1/2))^6) - ((a*(-c)^(1/2)*d^4)/(1024*c^(11/2)) - (3*a*(-c)^(1/2)*d^4*((c + d*x)^(1/2) - c^(1/2))^2)/(128*c^(11/2)*((-c)^(1/2) - (d*x - c)^(1/2))^2) - (53*a*(-c)^(1/2)*d^4*((c + d*x)^(1/2) - c^(1/2))^4)/(512*c^(11/2)*((-c)^(1/2) - (d*x - c)^(1/2))^4) + (87*a*(-c)^(1/2)*d^4*((c + d*x)^(1/2) - c^(1/2))^6)/(256*c^(11/2)*((-c)^(1/2) - (d*x - c)^(1/2))^6) + (657*a*(-c)^(1/2)*d^4*((c + d*x)^(1/2) - c^(1/2))^8)/(1024*c^(11/2)*((-c)^(1/2) - (d*x - c)^(1/2))^8) + (121*a*(-c)^(1/2)*d^4*((c + d*x)^(1/2) - c^(1/2))^10)/(256*c^(11/2)*((-c)^(1/2) - (d*x - c)^(1/2))^10))/(((c + d*x)^(1/2) - c^(1/2))^4/((-c)^(1/2) - (d*x - c)^(1/2))^4 + (4*((c + d*x)^(1/2) - c^(1/2))^6)/((-c)^(1/2) - (d*x - c)^(1/2))^6 + (6*((c + d*x)^(1/2) - c^(1/2))^8)/((-c)^(1/2) - (d*x - c)^(1/2))^8 + (4*((c + d*x)^(1/2) - c^(1/2))^10)/((-c)^(1/2) - (d*x - c)^(1/2))^10 + ((c + d*x)^(1/2) - c^(1/2))^12/((-c)^(1/2) - (d*x - c)^(1/2))^12) - (b*(-c)^(3/2)*d^2*log(((c + d*x)^(1/2) - c^(1/2))/((-c)^(1/2) - (d*x - c)^(1/2))))/(2*c^(9/2)) - (3*a*(-c)^(1/2)*d^4*log(((c + d*x)^(1/2) - c^(1/2))^2/((-c)^(1/2) - (d*x - c)^(1/2))^2 + 1))/(8*c^(11/2)) + (b*(-c)^(3/2)*d^2*log(((c + d*x)^(1/2) - c^(1/2))^2/((-c)^(1/2) - (d*x - c)^(1/2))^2 + 1))/(2*c^(9/2)) - (7*a*d^4*((c + d*x)^(1/2) - c^(1/2))^2)/(256*(-c)^(1/2)*c^(9/2)*((-c)^(1/2) - (d*x - c)^(1/2))^2) + (a*d^4*((c + d*x)^(1/2) - c^(1/2))^4)/(1024*(-c)^(1/2)*c^(9/2)*((-c)^(1/2) - (d*x - c)^(1/2))^4) + (b*d^2*((c + d*x)^(1/2) - c^(1/2))^2)/(32*(-c)^(3/2)*c^(3/2)*((-c)^(1/2) - (d*x - c)^(1/2))^2)","B"
368,0,-1,161,0.000000,"\text{Not used}","int((x^4*(a + b*x^2))/((c + d*x)^(3/2)*(d*x - c)^(3/2)),x)","\int \frac{x^4\,\left(b\,x^2+a\right)}{{\left(c+d\,x\right)}^{3/2}\,{\left(d\,x-c\right)}^{3/2}} \,d x","Not used",1,"int((x^4*(a + b*x^2))/((c + d*x)^(3/2)*(d*x - c)^(3/2)), x)","F"
369,1,90,115,2.800530,"\text{Not used}","int((x^3*(a + b*x^2))/((c + d*x)^(3/2)*(d*x - c)^(3/2)),x)","\frac{\sqrt{d\,x-c}\,\left(\frac{x^2\,\left(4\,b\,c^2\,d^2+3\,a\,d^4\right)}{3\,d^7}-\frac{8\,b\,c^4+6\,a\,c^2\,d^2}{3\,d^7}+\frac{b\,x^4}{3\,d^3}\right)}{x\,\sqrt{c+d\,x}-\frac{c\,\sqrt{c+d\,x}}{d}}","Not used",1,"((d*x - c)^(1/2)*((x^2*(3*a*d^4 + 4*b*c^2*d^2))/(3*d^7) - (8*b*c^4 + 6*a*c^2*d^2)/(3*d^7) + (b*x^4)/(3*d^3)))/(x*(c + d*x)^(1/2) - (c*(c + d*x)^(1/2))/d)","B"
370,0,-1,152,0.000000,"\text{Not used}","int((x^2*(a + b*x^2))/((c + d*x)^(3/2)*(d*x - c)^(3/2)),x)","\int \frac{x^2\,\left(b\,x^2+a\right)}{{\left(c+d\,x\right)}^{3/2}\,{\left(d\,x-c\right)}^{3/2}} \,d x","Not used",1,"int((x^2*(a + b*x^2))/((c + d*x)^(3/2)*(d*x - c)^(3/2)), x)","F"
371,1,67,76,2.746828,"\text{Not used}","int((x*(a + b*x^2))/((c + d*x)^(3/2)*(d*x - c)^(3/2)),x)","\frac{a\,d^2\,\sqrt{d\,x-c}+2\,b\,c^2\,\sqrt{d\,x-c}-b\,d^2\,x^2\,\sqrt{d\,x-c}}{d^4\,\sqrt{c+d\,x}\,\left(c-d\,x\right)}","Not used",1,"(a*d^2*(d*x - c)^(1/2) + 2*b*c^2*(d*x - c)^(1/2) - b*d^2*x^2*(d*x - c)^(1/2))/(d^4*(c + d*x)^(1/2)*(c - d*x))","B"
372,0,-1,63,0.000000,"\text{Not used}","int((a + b*x^2)/((c + d*x)^(3/2)*(d*x - c)^(3/2)),x)","\int \frac{b\,x^2+a}{{\left(c+d\,x\right)}^{3/2}\,{\left(d\,x-c\right)}^{3/2}} \,d x","Not used",1,"int((a + b*x^2)/((c + d*x)^(3/2)*(d*x - c)^(3/2)), x)","F"
373,0,-1,65,0.000000,"\text{Not used}","int((a + b*x^2)/(x*(c + d*x)^(3/2)*(d*x - c)^(3/2)),x)","\int \frac{b\,x^2+a}{x\,{\left(c+d\,x\right)}^{3/2}\,{\left(d\,x-c\right)}^{3/2}} \,d x","Not used",1,"int((a + b*x^2)/(x*(c + d*x)^(3/2)*(d*x - c)^(3/2)), x)","F"
374,1,73,67,2.866105,"\text{Not used}","int((a + b*x^2)/(x^2*(c + d*x)^(3/2)*(d*x - c)^(3/2)),x)","\frac{2\,a\,d^2\,x^2\,\sqrt{d\,x-c}-a\,c^2\,\sqrt{d\,x-c}+b\,c^2\,x^2\,\sqrt{d\,x-c}}{c^4\,x\,\sqrt{c+d\,x}\,\left(c-d\,x\right)}","Not used",1,"(2*a*d^2*x^2*(d*x - c)^(1/2) - a*c^2*(d*x - c)^(1/2) + b*c^2*x^2*(d*x - c)^(1/2))/(c^4*x*(c + d*x)^(1/2)*(c - d*x))","B"
375,0,-1,117,0.000000,"\text{Not used}","int((a + b*x^2)/(x^3*(c + d*x)^(3/2)*(d*x - c)^(3/2)),x)","\int \frac{b\,x^2+a}{x^3\,{\left(c+d\,x\right)}^{3/2}\,{\left(d\,x-c\right)}^{3/2}} \,d x","Not used",1,"int((a + b*x^2)/(x^3*(c + d*x)^(3/2)*(d*x - c)^(3/2)), x)","F"
376,1,104,119,2.896534,"\text{Not used}","int((a + b*x^2)/(x^4*(c + d*x)^(3/2)*(d*x - c)^(3/2)),x)","\frac{\sqrt{d\,x-c}\,\left(\frac{a}{3\,c^2\,d}+\frac{x^2\,\left(3\,b\,c^4+4\,a\,c^2\,d^2\right)}{3\,c^6\,d}-\frac{x^4\,\left(6\,b\,c^2\,d^2+8\,a\,d^4\right)}{3\,c^6\,d}\right)}{x^4\,\sqrt{c+d\,x}-\frac{c\,x^3\,\sqrt{c+d\,x}}{d}}","Not used",1,"((d*x - c)^(1/2)*(a/(3*c^2*d) + (x^2*(3*b*c^4 + 4*a*c^2*d^2))/(3*c^6*d) - (x^4*(8*a*d^4 + 6*b*c^2*d^2))/(3*c^6*d)))/(x^4*(c + d*x)^(1/2) - (c*x^3*(c + d*x)^(1/2))/d)","B"
377,0,-1,166,0.000000,"\text{Not used}","int((a + b*x^2)/(x^5*(c + d*x)^(3/2)*(d*x - c)^(3/2)),x)","\int \frac{b\,x^2+a}{x^5\,{\left(c+d\,x\right)}^{3/2}\,{\left(d\,x-c\right)}^{3/2}} \,d x","Not used",1,"int((a + b*x^2)/(x^5*(c + d*x)^(3/2)*(d*x - c)^(3/2)), x)","F"
378,1,72,40,3.652467,"\text{Not used}","int((c^2*x^2 + 1)/(x*(c*x - 1)^(1/2)*(c*x + 1)^(1/2)),x)","\sqrt{c\,x-1}\,\sqrt{c\,x+1}-\ln\left(\frac{{\left(\sqrt{c\,x-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{c\,x+1}-1\right)}^2}+1\right)\,1{}\mathrm{i}+\ln\left(\frac{\sqrt{c\,x-1}-\mathrm{i}}{\sqrt{c\,x+1}-1}\right)\,1{}\mathrm{i}","Not used",1,"log(((c*x - 1)^(1/2) - 1i)/((c*x + 1)^(1/2) - 1))*1i - log(((c*x - 1)^(1/2) - 1i)^2/((c*x + 1)^(1/2) - 1)^2 + 1)*1i + (c*x - 1)^(1/2)*(c*x + 1)^(1/2)","B"
379,1,96,53,3.274291,"\text{Not used}","int((c + d*x^2)/(x^((a^2*d + 2*b^2*c)/(a^2*d + b^2*c))*(a + b*x)^(1/2)*(b*x - a)^(1/2)),x)","-\frac{\frac{x\,\left(d\,a^4+c\,a^2\,b^2\right)}{a^2\,b^2}-\frac{x^3\,\left(d\,a^2\,b^2+c\,b^4\right)}{a^2\,b^2}}{x^{\frac{d\,a^2+2\,c\,b^2}{d\,a^2+c\,b^2}}\,\sqrt{a+b\,x}\,\sqrt{b\,x-a}}","Not used",1,"-((x*(a^4*d + a^2*b^2*c))/(a^2*b^2) - (x^3*(b^4*c + a^2*b^2*d))/(a^2*b^2))/(x^((a^2*d + 2*b^2*c)/(a^2*d + b^2*c))*(a + b*x)^(1/2)*(b*x - a)^(1/2))","B"
380,0,-1,36,0.000000,"\text{Not used}","int(1/((x^(1/2) - 1)^(1/2)*(- x^(1/2) - 1)^(1/2)*(x + 1)^(1/2)),x)","\int \frac{1}{\sqrt{\sqrt{x}-1}\,\sqrt{-\sqrt{x}-1}\,\sqrt{x+1}} \,d x","Not used",1,"int(1/((x^(1/2) - 1)^(1/2)*(- x^(1/2) - 1)^(1/2)*(x + 1)^(1/2)), x)","F"
381,0,-1,75,0.000000,"\text{Not used}","int(1/((a + b*x^(1/2))^(1/2)*(a - b*x^(1/2))^(1/2)*(b^2*x + a^2)^(1/2)),x)","\int \frac{1}{\sqrt{a+b\,\sqrt{x}}\,\sqrt{a-b\,\sqrt{x}}\,\sqrt{a^2+x\,b^2}} \,d x","Not used",1,"int(1/((a + b*x^(1/2))^(1/2)*(a - b*x^(1/2))^(1/2)*(b^2*x + a^2)^(1/2)), x)","F"
382,0,-1,113,0.000000,"\text{Not used}","int((c + d*x^(2*n))^q*(a + b*x^n)^p*(a - b*x^n)^p,x)","\int {\left(c+d\,x^{2\,n}\right)}^q\,{\left(a+b\,x^n\right)}^p\,{\left(a-b\,x^n\right)}^p \,d x","Not used",1,"int((c + d*x^(2*n))^q*(a + b*x^n)^p*(a - b*x^n)^p, x)","F"
383,0,-1,87,0.000000,"\text{Not used}","int((a + b*x^n)^p*(a - b*x^n)^p*(a^2 + b^2*x^(2*n))^p,x)","\int {\left(a+b\,x^n\right)}^p\,{\left(a-b\,x^n\right)}^p\,{\left(a^2+b^2\,x^{2\,n}\right)}^p \,d x","Not used",1,"int((a + b*x^n)^p*(a - b*x^n)^p*(a^2 + b^2*x^(2*n))^p, x)","F"
384,0,-1,76,0.000000,"\text{Not used}","int((c + d*x^(2*n))^p/((a + b*x^n)*(a - b*x^n)),x)","-\int -\frac{{\left(c+d\,x^{2\,n}\right)}^p}{a^2-b^2\,x^{2\,n}} \,d x","Not used",1,"-int(-(c + d*x^(2*n))^p/(a^2 - b^2*x^(2*n)), x)","F"
385,0,-1,96,0.000000,"\text{Not used}","int(((a + b*x^(n/2))^p*(a - b*x^(n/2))^p)/(d*x^n - (a^2*d*(p + 1))/(b^2*((2*n + n*p + 1)/n - 1)))^((2*n + n*p + 1)/n),x)","\int \frac{{\left(a+b\,x^{n/2}\right)}^p\,{\left(a-b\,x^{n/2}\right)}^p}{{\left(d\,x^n-\frac{a^2\,d\,\left(p+1\right)}{b^2\,\left(\frac{2\,n+n\,p+1}{n}-1\right)}\right)}^{\frac{2\,n+n\,p+1}{n}}} \,d x","Not used",1,"int(((a + b*x^(n/2))^p*(a - b*x^(n/2))^p)/(d*x^n - (a^2*d*(p + 1))/(b^2*((2*n + n*p + 1)/n - 1)))^((2*n + n*p + 1)/n), x)","F"