1,1,28,33,0.179808,"\text{Not used}","int(x^2*(A + B*x^2)*(a + b*x^2),x)","\frac{B\,b\,x^7}{7}+\left(\frac{A\,b}{5}+\frac{B\,a}{5}\right)\,x^5+\frac{A\,a\,x^3}{3}","Not used",1,"x^5*((A*b)/5 + (B*a)/5) + (A*a*x^3)/3 + (B*b*x^7)/7","B"
2,1,28,33,0.038075,"\text{Not used}","int(x*(A + B*x^2)*(a + b*x^2),x)","\frac{B\,b\,x^6}{6}+\left(\frac{A\,b}{4}+\frac{B\,a}{4}\right)\,x^4+\frac{A\,a\,x^2}{2}","Not used",1,"x^4*((A*b)/4 + (B*a)/4) + (A*a*x^2)/2 + (B*b*x^6)/6","B"
3,1,25,28,0.039599,"\text{Not used}","int((A + B*x^2)*(a + b*x^2),x)","\frac{B\,b\,x^5}{5}+\left(\frac{A\,b}{3}+\frac{B\,a}{3}\right)\,x^3+A\,a\,x","Not used",1,"x^3*((A*b)/3 + (B*a)/3) + A*a*x + (B*b*x^5)/5","B"
4,1,26,29,0.062842,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2))/x,x)","x^2\,\left(\frac{A\,b}{2}+\frac{B\,a}{2}\right)+\frac{B\,b\,x^4}{4}+A\,a\,\ln\left(x\right)","Not used",1,"x^2*((A*b)/2 + (B*a)/2) + (B*b*x^4)/4 + A*a*log(x)","B"
5,1,24,26,0.077454,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2))/x^2,x)","x\,\left(A\,b+B\,a\right)-\frac{A\,a}{x}+\frac{B\,b\,x^3}{3}","Not used",1,"x*(A*b + B*a) - (A*a)/x + (B*b*x^3)/3","B"
6,1,25,29,0.058709,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2))/x^3,x)","\ln\left(x\right)\,\left(A\,b+B\,a\right)-\frac{A\,a}{2\,x^2}+\frac{B\,b\,x^2}{2}","Not used",1,"log(x)*(A*b + B*a) - (A*a)/(2*x^2) + (B*b*x^2)/2","B"
7,1,26,26,0.032603,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2))/x^4,x)","B\,b\,x-\frac{\left(A\,b+B\,a\right)\,x^2+\frac{A\,a}{3}}{x^3}","Not used",1,"B*b*x - ((A*a)/3 + x^2*(A*b + B*a))/x^3","B"
8,1,29,29,0.071466,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2))/x^5,x)","B\,b\,\ln\left(x\right)-\frac{\left(\frac{A\,b}{2}+\frac{B\,a}{2}\right)\,x^2+\frac{A\,a}{4}}{x^4}","Not used",1,"B*b*log(x) - ((A*a)/4 + x^2*((A*b)/2 + (B*a)/2))/x^4","B"
9,1,29,31,0.035578,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2))/x^6,x)","-\frac{B\,b\,x^4+\left(\frac{A\,b}{3}+\frac{B\,a}{3}\right)\,x^2+\frac{A\,a}{5}}{x^5}","Not used",1,"-((A*a)/5 + x^2*((A*b)/3 + (B*a)/3) + B*b*x^4)/x^5","B"
10,1,30,33,0.035574,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2))/x^7,x)","-\frac{\frac{B\,b\,x^4}{2}+\left(\frac{A\,b}{4}+\frac{B\,a}{4}\right)\,x^2+\frac{A\,a}{6}}{x^6}","Not used",1,"-((A*a)/6 + x^2*((A*b)/4 + (B*a)/4) + (B*b*x^4)/2)/x^6","B"
11,1,51,55,0.076179,"\text{Not used}","int(x^2*(A + B*x^2)*(a + b*x^2)^2,x)","x^5\,\left(\frac{B\,a^2}{5}+\frac{2\,A\,b\,a}{5}\right)+x^7\,\left(\frac{A\,b^2}{7}+\frac{2\,B\,a\,b}{7}\right)+\frac{A\,a^2\,x^3}{3}+\frac{B\,b^2\,x^9}{9}","Not used",1,"x^5*((B*a^2)/5 + (2*A*a*b)/5) + x^7*((A*b^2)/7 + (2*B*a*b)/7) + (A*a^2*x^3)/3 + (B*b^2*x^9)/9","B"
12,1,51,42,0.043862,"\text{Not used}","int(x*(A + B*x^2)*(a + b*x^2)^2,x)","x^4\,\left(\frac{B\,a^2}{4}+\frac{A\,b\,a}{2}\right)+x^6\,\left(\frac{A\,b^2}{6}+\frac{B\,a\,b}{3}\right)+\frac{A\,a^2\,x^2}{2}+\frac{B\,b^2\,x^8}{8}","Not used",1,"x^4*((B*a^2)/4 + (A*a*b)/2) + x^6*((A*b^2)/6 + (B*a*b)/3) + (A*a^2*x^2)/2 + (B*b^2*x^8)/8","B"
13,1,48,50,0.042611,"\text{Not used}","int((A + B*x^2)*(a + b*x^2)^2,x)","x^3\,\left(\frac{B\,a^2}{3}+\frac{2\,A\,b\,a}{3}\right)+x^5\,\left(\frac{A\,b^2}{5}+\frac{2\,B\,a\,b}{5}\right)+\frac{B\,b^2\,x^7}{7}+A\,a^2\,x","Not used",1,"x^3*((B*a^2)/3 + (2*A*a*b)/3) + x^5*((A*b^2)/5 + (2*B*a*b)/5) + (B*b^2*x^7)/7 + A*a^2*x","B"
14,1,48,43,0.038480,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^2)/x,x)","x^2\,\left(\frac{B\,a^2}{2}+A\,b\,a\right)+x^4\,\left(\frac{A\,b^2}{4}+\frac{B\,a\,b}{2}\right)+\frac{B\,b^2\,x^6}{6}+A\,a^2\,\ln\left(x\right)","Not used",1,"x^2*((B*a^2)/2 + A*a*b) + x^4*((A*b^2)/4 + (B*a*b)/2) + (B*b^2*x^6)/6 + A*a^2*log(x)","B"
15,1,48,48,0.045682,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^2)/x^2,x)","x^3\,\left(\frac{A\,b^2}{3}+\frac{2\,B\,a\,b}{3}\right)+x\,\left(B\,a^2+2\,A\,b\,a\right)-\frac{A\,a^2}{x}+\frac{B\,b^2\,x^5}{5}","Not used",1,"x^3*((A*b^2)/3 + (2*B*a*b)/3) + x*(B*a^2 + 2*A*a*b) - (A*a^2)/x + (B*b^2*x^5)/5","B"
16,1,48,51,0.042159,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^2)/x^3,x)","x^2\,\left(\frac{A\,b^2}{2}+B\,a\,b\right)+\ln\left(x\right)\,\left(B\,a^2+2\,A\,b\,a\right)-\frac{A\,a^2}{2\,x^2}+\frac{B\,b^2\,x^4}{4}","Not used",1,"x^2*((A*b^2)/2 + B*a*b) + log(x)*(B*a^2 + 2*A*a*b) - (A*a^2)/(2*x^2) + (B*b^2*x^4)/4","B"
17,1,50,48,0.065526,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^2)/x^4,x)","x\,\left(A\,b^2+2\,B\,a\,b\right)-\frac{x^2\,\left(B\,a^2+2\,A\,b\,a\right)+\frac{A\,a^2}{3}}{x^3}+\frac{B\,b^2\,x^3}{3}","Not used",1,"x*(A*b^2 + 2*B*a*b) - (x^2*(B*a^2 + 2*A*a*b) + (A*a^2)/3)/x^3 + (B*b^2*x^3)/3","B"
18,1,51,51,0.081127,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^2)/x^5,x)","\ln\left(x\right)\,\left(A\,b^2+2\,B\,a\,b\right)-\frac{x^2\,\left(\frac{B\,a^2}{2}+A\,b\,a\right)+\frac{A\,a^2}{4}}{x^4}+\frac{B\,b^2\,x^2}{2}","Not used",1,"log(x)*(A*b^2 + 2*B*a*b) - (x^2*((B*a^2)/2 + A*a*b) + (A*a^2)/4)/x^4 + (B*b^2*x^2)/2","B"
19,1,50,48,0.043761,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^2)/x^6,x)","B\,b^2\,x-\frac{x^2\,\left(\frac{B\,a^2}{3}+\frac{2\,A\,b\,a}{3}\right)+x^4\,\left(A\,b^2+2\,B\,a\,b\right)+\frac{A\,a^2}{5}}{x^5}","Not used",1,"B*b^2*x - (x^2*((B*a^2)/3 + (2*A*a*b)/3) + x^4*(A*b^2 + 2*B*a*b) + (A*a^2)/5)/x^5","B"
20,1,51,51,0.085325,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^2)/x^7,x)","B\,b^2\,\ln\left(x\right)-\frac{x^2\,\left(\frac{B\,a^2}{4}+\frac{A\,b\,a}{2}\right)+x^4\,\left(\frac{A\,b^2}{2}+B\,a\,b\right)+\frac{A\,a^2}{6}}{x^6}","Not used",1,"B*b^2*log(x) - (x^2*((B*a^2)/4 + (A*a*b)/2) + x^4*((A*b^2)/2 + B*a*b) + (A*a^2)/6)/x^6","B"
21,1,52,53,0.034302,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^2)/x^8,x)","-\frac{x^2\,\left(\frac{B\,a^2}{5}+\frac{2\,A\,b\,a}{5}\right)+x^4\,\left(\frac{A\,b^2}{3}+\frac{2\,B\,a\,b}{3}\right)+\frac{A\,a^2}{7}+B\,b^2\,x^6}{x^7}","Not used",1,"-(x^2*((B*a^2)/5 + (2*A*a*b)/5) + x^4*((A*b^2)/3 + (2*B*a*b)/3) + (A*a^2)/7 + B*b^2*x^6)/x^7","B"
22,1,53,48,0.054650,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^2)/x^9,x)","-\frac{x^2\,\left(\frac{B\,a^2}{6}+\frac{A\,b\,a}{3}\right)+x^4\,\left(\frac{A\,b^2}{4}+\frac{B\,a\,b}{2}\right)+\frac{A\,a^2}{8}+\frac{B\,b^2\,x^6}{2}}{x^8}","Not used",1,"-(x^2*((B*a^2)/6 + (A*a*b)/3) + x^4*((A*b^2)/4 + (B*a*b)/2) + (A*a^2)/8 + (B*b^2*x^6)/2)/x^8","B"
23,1,107,117,0.200946,"\text{Not used}","int(x^9*(A + B*x^2)*(a + b*x^2)^5,x)","x^{12}\,\left(\frac{B\,a^5}{12}+\frac{5\,A\,b\,a^4}{12}\right)+x^{20}\,\left(\frac{A\,b^5}{20}+\frac{B\,a\,b^4}{4}\right)+\frac{A\,a^5\,x^{10}}{10}+\frac{B\,b^5\,x^{22}}{22}+\frac{5\,a^2\,b^2\,x^{16}\,\left(A\,b+B\,a\right)}{8}+\frac{5\,a^3\,b\,x^{14}\,\left(2\,A\,b+B\,a\right)}{14}+\frac{5\,a\,b^3\,x^{18}\,\left(A\,b+2\,B\,a\right)}{18}","Not used",1,"x^12*((B*a^5)/12 + (5*A*a^4*b)/12) + x^20*((A*b^5)/20 + (B*a*b^4)/4) + (A*a^5*x^10)/10 + (B*b^5*x^22)/22 + (5*a^2*b^2*x^16*(A*b + B*a))/8 + (5*a^3*b*x^14*(2*A*b + B*a))/14 + (5*a*b^3*x^18*(A*b + 2*B*a))/18","B"
24,1,107,117,0.041004,"\text{Not used}","int(x^8*(A + B*x^2)*(a + b*x^2)^5,x)","x^{11}\,\left(\frac{B\,a^5}{11}+\frac{5\,A\,b\,a^4}{11}\right)+x^{19}\,\left(\frac{A\,b^5}{19}+\frac{5\,B\,a\,b^4}{19}\right)+\frac{A\,a^5\,x^9}{9}+\frac{B\,b^5\,x^{21}}{21}+\frac{2\,a^2\,b^2\,x^{15}\,\left(A\,b+B\,a\right)}{3}+\frac{5\,a^3\,b\,x^{13}\,\left(2\,A\,b+B\,a\right)}{13}+\frac{5\,a\,b^3\,x^{17}\,\left(A\,b+2\,B\,a\right)}{17}","Not used",1,"x^11*((B*a^5)/11 + (5*A*a^4*b)/11) + x^19*((A*b^5)/19 + (5*B*a*b^4)/19) + (A*a^5*x^9)/9 + (B*b^5*x^21)/21 + (2*a^2*b^2*x^15*(A*b + B*a))/3 + (5*a^3*b*x^13*(2*A*b + B*a))/13 + (5*a*b^3*x^17*(A*b + 2*B*a))/17","B"
25,1,107,122,0.039110,"\text{Not used}","int(x^7*(A + B*x^2)*(a + b*x^2)^5,x)","x^{10}\,\left(\frac{B\,a^5}{10}+\frac{A\,b\,a^4}{2}\right)+x^{18}\,\left(\frac{A\,b^5}{18}+\frac{5\,B\,a\,b^4}{18}\right)+\frac{A\,a^5\,x^8}{8}+\frac{B\,b^5\,x^{20}}{20}+\frac{5\,a^2\,b^2\,x^{14}\,\left(A\,b+B\,a\right)}{7}+\frac{5\,a^3\,b\,x^{12}\,\left(2\,A\,b+B\,a\right)}{12}+\frac{5\,a\,b^3\,x^{16}\,\left(A\,b+2\,B\,a\right)}{16}","Not used",1,"x^10*((B*a^5)/10 + (A*a^4*b)/2) + x^18*((A*b^5)/18 + (5*B*a*b^4)/18) + (A*a^5*x^8)/8 + (B*b^5*x^20)/20 + (5*a^2*b^2*x^14*(A*b + B*a))/7 + (5*a^3*b*x^12*(2*A*b + B*a))/12 + (5*a*b^3*x^16*(A*b + 2*B*a))/16","B"
26,1,107,117,0.039552,"\text{Not used}","int(x^6*(A + B*x^2)*(a + b*x^2)^5,x)","x^9\,\left(\frac{B\,a^5}{9}+\frac{5\,A\,b\,a^4}{9}\right)+x^{17}\,\left(\frac{A\,b^5}{17}+\frac{5\,B\,a\,b^4}{17}\right)+\frac{A\,a^5\,x^7}{7}+\frac{B\,b^5\,x^{19}}{19}+\frac{10\,a^2\,b^2\,x^{13}\,\left(A\,b+B\,a\right)}{13}+\frac{5\,a^3\,b\,x^{11}\,\left(2\,A\,b+B\,a\right)}{11}+\frac{a\,b^3\,x^{15}\,\left(A\,b+2\,B\,a\right)}{3}","Not used",1,"x^9*((B*a^5)/9 + (5*A*a^4*b)/9) + x^17*((A*b^5)/17 + (5*B*a*b^4)/17) + (A*a^5*x^7)/7 + (B*b^5*x^19)/19 + (10*a^2*b^2*x^13*(A*b + B*a))/13 + (5*a^3*b*x^11*(2*A*b + B*a))/11 + (a*b^3*x^15*(A*b + 2*B*a))/3","B"
27,1,107,95,0.038800,"\text{Not used}","int(x^5*(A + B*x^2)*(a + b*x^2)^5,x)","x^8\,\left(\frac{B\,a^5}{8}+\frac{5\,A\,b\,a^4}{8}\right)+x^{16}\,\left(\frac{A\,b^5}{16}+\frac{5\,B\,a\,b^4}{16}\right)+\frac{A\,a^5\,x^6}{6}+\frac{B\,b^5\,x^{18}}{18}+\frac{5\,a^2\,b^2\,x^{12}\,\left(A\,b+B\,a\right)}{6}+\frac{a^3\,b\,x^{10}\,\left(2\,A\,b+B\,a\right)}{2}+\frac{5\,a\,b^3\,x^{14}\,\left(A\,b+2\,B\,a\right)}{14}","Not used",1,"x^8*((B*a^5)/8 + (5*A*a^4*b)/8) + x^16*((A*b^5)/16 + (5*B*a*b^4)/16) + (A*a^5*x^6)/6 + (B*b^5*x^18)/18 + (5*a^2*b^2*x^12*(A*b + B*a))/6 + (a^3*b*x^10*(2*A*b + B*a))/2 + (5*a*b^3*x^14*(A*b + 2*B*a))/14","B"
28,1,107,117,0.038927,"\text{Not used}","int(x^4*(A + B*x^2)*(a + b*x^2)^5,x)","x^7\,\left(\frac{B\,a^5}{7}+\frac{5\,A\,b\,a^4}{7}\right)+x^{15}\,\left(\frac{A\,b^5}{15}+\frac{B\,a\,b^4}{3}\right)+\frac{A\,a^5\,x^5}{5}+\frac{B\,b^5\,x^{17}}{17}+\frac{10\,a^2\,b^2\,x^{11}\,\left(A\,b+B\,a\right)}{11}+\frac{5\,a^3\,b\,x^9\,\left(2\,A\,b+B\,a\right)}{9}+\frac{5\,a\,b^3\,x^{13}\,\left(A\,b+2\,B\,a\right)}{13}","Not used",1,"x^7*((B*a^5)/7 + (5*A*a^4*b)/7) + x^15*((A*b^5)/15 + (B*a*b^4)/3) + (A*a^5*x^5)/5 + (B*b^5*x^17)/17 + (10*a^2*b^2*x^11*(A*b + B*a))/11 + (5*a^3*b*x^9*(2*A*b + B*a))/9 + (5*a*b^3*x^13*(A*b + 2*B*a))/13","B"
29,1,106,67,0.040391,"\text{Not used}","int(x^3*(A + B*x^2)*(a + b*x^2)^5,x)","x^6\,\left(\frac{B\,a^5}{6}+\frac{5\,A\,b\,a^4}{6}\right)+x^{14}\,\left(\frac{A\,b^5}{14}+\frac{5\,B\,a\,b^4}{14}\right)+\frac{A\,a^5\,x^4}{4}+\frac{B\,b^5\,x^{16}}{16}+a^2\,b^2\,x^{10}\,\left(A\,b+B\,a\right)+\frac{5\,a^3\,b\,x^8\,\left(2\,A\,b+B\,a\right)}{8}+\frac{5\,a\,b^3\,x^{12}\,\left(A\,b+2\,B\,a\right)}{12}","Not used",1,"x^6*((B*a^5)/6 + (5*A*a^4*b)/6) + x^14*((A*b^5)/14 + (5*B*a*b^4)/14) + (A*a^5*x^4)/4 + (B*b^5*x^16)/16 + a^2*b^2*x^10*(A*b + B*a) + (5*a^3*b*x^8*(2*A*b + B*a))/8 + (5*a*b^3*x^12*(A*b + 2*B*a))/12","B"
30,1,106,117,0.039930,"\text{Not used}","int(x^2*(A + B*x^2)*(a + b*x^2)^5,x)","x^5\,\left(\frac{B\,a^5}{5}+A\,b\,a^4\right)+x^{13}\,\left(\frac{A\,b^5}{13}+\frac{5\,B\,a\,b^4}{13}\right)+\frac{A\,a^5\,x^3}{3}+\frac{B\,b^5\,x^{15}}{15}+\frac{10\,a^2\,b^2\,x^9\,\left(A\,b+B\,a\right)}{9}+\frac{5\,a^3\,b\,x^7\,\left(2\,A\,b+B\,a\right)}{7}+\frac{5\,a\,b^3\,x^{11}\,\left(A\,b+2\,B\,a\right)}{11}","Not used",1,"x^5*((B*a^5)/5 + A*a^4*b) + x^13*((A*b^5)/13 + (5*B*a*b^4)/13) + (A*a^5*x^3)/3 + (B*b^5*x^15)/15 + (10*a^2*b^2*x^9*(A*b + B*a))/9 + (5*a^3*b*x^7*(2*A*b + B*a))/7 + (5*a*b^3*x^11*(A*b + 2*B*a))/11","B"
31,1,107,42,0.039223,"\text{Not used}","int(x*(A + B*x^2)*(a + b*x^2)^5,x)","x^4\,\left(\frac{B\,a^5}{4}+\frac{5\,A\,b\,a^4}{4}\right)+x^{12}\,\left(\frac{A\,b^5}{12}+\frac{5\,B\,a\,b^4}{12}\right)+\frac{A\,a^5\,x^2}{2}+\frac{B\,b^5\,x^{14}}{14}+\frac{5\,a^2\,b^2\,x^8\,\left(A\,b+B\,a\right)}{4}+\frac{5\,a^3\,b\,x^6\,\left(2\,A\,b+B\,a\right)}{6}+\frac{a\,b^3\,x^{10}\,\left(A\,b+2\,B\,a\right)}{2}","Not used",1,"x^4*((B*a^5)/4 + (5*A*a^4*b)/4) + x^12*((A*b^5)/12 + (5*B*a*b^4)/12) + (A*a^5*x^2)/2 + (B*b^5*x^14)/14 + (5*a^2*b^2*x^8*(A*b + B*a))/4 + (5*a^3*b*x^6*(2*A*b + B*a))/6 + (a*b^3*x^10*(A*b + 2*B*a))/2","B"
32,1,103,109,0.039748,"\text{Not used}","int((A + B*x^2)*(a + b*x^2)^5,x)","x^3\,\left(\frac{B\,a^5}{3}+\frac{5\,A\,b\,a^4}{3}\right)+x^{11}\,\left(\frac{A\,b^5}{11}+\frac{5\,B\,a\,b^4}{11}\right)+\frac{B\,b^5\,x^{13}}{13}+A\,a^5\,x+\frac{10\,a^2\,b^2\,x^7\,\left(A\,b+B\,a\right)}{7}+a^3\,b\,x^5\,\left(2\,A\,b+B\,a\right)+\frac{5\,a\,b^3\,x^9\,\left(A\,b+2\,B\,a\right)}{9}","Not used",1,"x^3*((B*a^5)/3 + (5*A*a^4*b)/3) + x^11*((A*b^5)/11 + (5*B*a*b^4)/11) + (B*b^5*x^13)/13 + A*a^5*x + (10*a^2*b^2*x^7*(A*b + B*a))/7 + a^3*b*x^5*(2*A*b + B*a) + (5*a*b^3*x^9*(A*b + 2*B*a))/9","B"
33,1,105,88,0.043461,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^5)/x,x)","x^2\,\left(\frac{B\,a^5}{2}+\frac{5\,A\,b\,a^4}{2}\right)+x^{10}\,\left(\frac{A\,b^5}{10}+\frac{B\,a\,b^4}{2}\right)+\frac{B\,b^5\,x^{12}}{12}+A\,a^5\,\ln\left(x\right)+\frac{5\,a^2\,b^2\,x^6\,\left(A\,b+B\,a\right)}{3}+\frac{5\,a^3\,b\,x^4\,\left(2\,A\,b+B\,a\right)}{4}+\frac{5\,a\,b^3\,x^8\,\left(A\,b+2\,B\,a\right)}{8}","Not used",1,"x^2*((B*a^5)/2 + (5*A*a^4*b)/2) + x^10*((A*b^5)/10 + (B*a*b^4)/2) + (B*b^5*x^12)/12 + A*a^5*log(x) + (5*a^2*b^2*x^6*(A*b + B*a))/3 + (5*a^3*b*x^4*(2*A*b + B*a))/4 + (5*a*b^3*x^8*(A*b + 2*B*a))/8","B"
34,1,104,108,0.042297,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^5)/x^2,x)","x\,\left(B\,a^5+5\,A\,b\,a^4\right)+x^9\,\left(\frac{A\,b^5}{9}+\frac{5\,B\,a\,b^4}{9}\right)-\frac{A\,a^5}{x}+\frac{B\,b^5\,x^{11}}{11}+2\,a^2\,b^2\,x^5\,\left(A\,b+B\,a\right)+\frac{5\,a^3\,b\,x^3\,\left(2\,A\,b+B\,a\right)}{3}+\frac{5\,a\,b^3\,x^7\,\left(A\,b+2\,B\,a\right)}{7}","Not used",1,"x*(B*a^5 + 5*A*a^4*b) + x^9*((A*b^5)/9 + (5*B*a*b^4)/9) - (A*a^5)/x + (B*b^5*x^11)/11 + 2*a^2*b^2*x^5*(A*b + B*a) + (5*a^3*b*x^3*(2*A*b + B*a))/3 + (5*a*b^3*x^7*(A*b + 2*B*a))/7","B"
35,1,105,113,0.075563,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^5)/x^3,x)","x^8\,\left(\frac{A\,b^5}{8}+\frac{5\,B\,a\,b^4}{8}\right)+\ln\left(x\right)\,\left(B\,a^5+5\,A\,b\,a^4\right)-\frac{A\,a^5}{2\,x^2}+\frac{B\,b^5\,x^{10}}{10}+\frac{5\,a^2\,b^2\,x^4\,\left(A\,b+B\,a\right)}{2}+\frac{5\,a^3\,b\,x^2\,\left(2\,A\,b+B\,a\right)}{2}+\frac{5\,a\,b^3\,x^6\,\left(A\,b+2\,B\,a\right)}{6}","Not used",1,"x^8*((A*b^5)/8 + (5*B*a*b^4)/8) + log(x)*(B*a^5 + 5*A*a^4*b) - (A*a^5)/(2*x^2) + (B*b^5*x^10)/10 + (5*a^2*b^2*x^4*(A*b + B*a))/2 + (5*a^3*b*x^2*(2*A*b + B*a))/2 + (5*a*b^3*x^6*(A*b + 2*B*a))/6","B"
36,1,106,108,0.042783,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^5)/x^4,x)","x^7\,\left(\frac{A\,b^5}{7}+\frac{5\,B\,a\,b^4}{7}\right)-\frac{\frac{A\,a^5}{3}+x^2\,\left(B\,a^5+5\,A\,b\,a^4\right)}{x^3}+\frac{B\,b^5\,x^9}{9}+\frac{10\,a^2\,b^2\,x^3\,\left(A\,b+B\,a\right)}{3}+5\,a^3\,b\,x\,\left(2\,A\,b+B\,a\right)+a\,b^3\,x^5\,\left(A\,b+2\,B\,a\right)","Not used",1,"x^7*((A*b^5)/7 + (5*B*a*b^4)/7) - ((A*a^5)/3 + x^2*(B*a^5 + 5*A*a^4*b))/x^3 + (B*b^5*x^9)/9 + (10*a^2*b^2*x^3*(A*b + B*a))/3 + 5*a^3*b*x*(2*A*b + B*a) + a*b^3*x^5*(A*b + 2*B*a)","B"
37,1,113,112,0.047755,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^5)/x^5,x)","\ln\left(x\right)\,\left(5\,B\,a^4\,b+10\,A\,a^3\,b^2\right)-\frac{\frac{A\,a^5}{4}+x^2\,\left(\frac{B\,a^5}{2}+\frac{5\,A\,b\,a^4}{2}\right)}{x^4}+x^6\,\left(\frac{A\,b^5}{6}+\frac{5\,B\,a\,b^4}{6}\right)+\frac{B\,b^5\,x^8}{8}+5\,a^2\,b^2\,x^2\,\left(A\,b+B\,a\right)+\frac{5\,a\,b^3\,x^4\,\left(A\,b+2\,B\,a\right)}{4}","Not used",1,"log(x)*(10*A*a^3*b^2 + 5*B*a^4*b) - ((A*a^5)/4 + x^2*((B*a^5)/2 + (5*A*a^4*b)/2))/x^4 + x^6*((A*b^5)/6 + (5*B*a*b^4)/6) + (B*b^5*x^8)/8 + 5*a^2*b^2*x^2*(A*b + B*a) + (5*a*b^3*x^4*(A*b + 2*B*a))/4","B"
38,1,111,111,0.071698,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^5)/x^6,x)","x^5\,\left(\frac{A\,b^5}{5}+B\,a\,b^4\right)-\frac{\frac{A\,a^5}{5}+x^4\,\left(5\,B\,a^4\,b+10\,A\,a^3\,b^2\right)+x^2\,\left(\frac{B\,a^5}{3}+\frac{5\,A\,b\,a^4}{3}\right)}{x^5}+\frac{B\,b^5\,x^7}{7}+10\,a^2\,b^2\,x\,\left(A\,b+B\,a\right)+\frac{5\,a\,b^3\,x^3\,\left(A\,b+2\,B\,a\right)}{3}","Not used",1,"x^5*((A*b^5)/5 + B*a*b^4) - ((A*a^5)/5 + x^4*(10*A*a^3*b^2 + 5*B*a^4*b) + x^2*((B*a^5)/3 + (5*A*a^4*b)/3))/x^5 + (B*b^5*x^7)/7 + 10*a^2*b^2*x*(A*b + B*a) + (5*a*b^3*x^3*(A*b + 2*B*a))/3","B"
39,1,118,114,0.080336,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^5)/x^7,x)","x^4\,\left(\frac{A\,b^5}{4}+\frac{5\,B\,a\,b^4}{4}\right)-\frac{\frac{A\,a^5}{6}+x^4\,\left(\frac{5\,B\,a^4\,b}{2}+5\,A\,a^3\,b^2\right)+x^2\,\left(\frac{B\,a^5}{4}+\frac{5\,A\,b\,a^4}{4}\right)}{x^6}+\ln\left(x\right)\,\left(10\,B\,a^3\,b^2+10\,A\,a^2\,b^3\right)+\frac{B\,b^5\,x^6}{6}+\frac{5\,a\,b^3\,x^2\,\left(A\,b+2\,B\,a\right)}{2}","Not used",1,"x^4*((A*b^5)/4 + (5*B*a*b^4)/4) - ((A*a^5)/6 + x^4*(5*A*a^3*b^2 + (5*B*a^4*b)/2) + x^2*((B*a^5)/4 + (5*A*a^4*b)/4))/x^6 + log(x)*(10*A*a^2*b^3 + 10*B*a^3*b^2) + (B*b^5*x^6)/6 + (5*a*b^3*x^2*(A*b + 2*B*a))/2","B"
40,1,116,111,0.100911,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^5)/x^8,x)","x^3\,\left(\frac{A\,b^5}{3}+\frac{5\,B\,a\,b^4}{3}\right)-\frac{\frac{A\,a^5}{7}+x^4\,\left(\frac{5\,B\,a^4\,b}{3}+\frac{10\,A\,a^3\,b^2}{3}\right)+x^2\,\left(\frac{B\,a^5}{5}+A\,b\,a^4\right)+x^6\,\left(10\,B\,a^3\,b^2+10\,A\,a^2\,b^3\right)}{x^7}+\frac{B\,b^5\,x^5}{5}+5\,a\,b^3\,x\,\left(A\,b+2\,B\,a\right)","Not used",1,"x^3*((A*b^5)/3 + (5*B*a*b^4)/3) - ((A*a^5)/7 + x^4*((10*A*a^3*b^2)/3 + (5*B*a^4*b)/3) + x^2*((B*a^5)/5 + A*a^4*b) + x^6*(10*A*a^2*b^3 + 10*B*a^3*b^2))/x^7 + (B*b^5*x^5)/5 + 5*a*b^3*x*(A*b + 2*B*a)","B"
41,1,122,112,0.062419,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^5)/x^9,x)","\ln\left(x\right)\,\left(10\,B\,a^2\,b^3+5\,A\,a\,b^4\right)-\frac{\frac{A\,a^5}{8}+x^4\,\left(\frac{5\,B\,a^4\,b}{4}+\frac{5\,A\,a^3\,b^2}{2}\right)+x^2\,\left(\frac{B\,a^5}{6}+\frac{5\,A\,b\,a^4}{6}\right)+x^6\,\left(5\,B\,a^3\,b^2+5\,A\,a^2\,b^3\right)}{x^8}+x^2\,\left(\frac{A\,b^5}{2}+\frac{5\,B\,a\,b^4}{2}\right)+\frac{B\,b^5\,x^4}{4}","Not used",1,"log(x)*(10*B*a^2*b^3 + 5*A*a*b^4) - ((A*a^5)/8 + x^4*((5*A*a^3*b^2)/2 + (5*B*a^4*b)/4) + x^2*((B*a^5)/6 + (5*A*a^4*b)/6) + x^6*(5*A*a^2*b^3 + 5*B*a^3*b^2))/x^8 + x^2*((A*b^5)/2 + (5*B*a*b^4)/2) + (B*b^5*x^4)/4","B"
42,1,119,108,0.073392,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^5)/x^10,x)","x\,\left(A\,b^5+5\,B\,a\,b^4\right)-\frac{\frac{A\,a^5}{9}+x^4\,\left(B\,a^4\,b+2\,A\,a^3\,b^2\right)+x^8\,\left(10\,B\,a^2\,b^3+5\,A\,a\,b^4\right)+x^2\,\left(\frac{B\,a^5}{7}+\frac{5\,A\,b\,a^4}{7}\right)+x^6\,\left(\frac{10\,B\,a^3\,b^2}{3}+\frac{10\,A\,a^2\,b^3}{3}\right)}{x^9}+\frac{B\,b^5\,x^3}{3}","Not used",1,"x*(A*b^5 + 5*B*a*b^4) - ((A*a^5)/9 + x^4*(2*A*a^3*b^2 + B*a^4*b) + x^8*(10*B*a^2*b^3 + 5*A*a*b^4) + x^2*((B*a^5)/7 + (5*A*a^4*b)/7) + x^6*((10*A*a^2*b^3)/3 + (10*B*a^3*b^2)/3))/x^9 + (B*b^5*x^3)/3","B"
43,1,121,113,0.108855,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^5)/x^11,x)","\ln\left(x\right)\,\left(A\,b^5+5\,B\,a\,b^4\right)-\frac{\frac{A\,a^5}{10}+x^8\,\left(5\,B\,a^2\,b^3+\frac{5\,A\,a\,b^4}{2}\right)+x^4\,\left(\frac{5\,B\,a^4\,b}{6}+\frac{5\,A\,a^3\,b^2}{3}\right)+x^2\,\left(\frac{B\,a^5}{8}+\frac{5\,A\,b\,a^4}{8}\right)+x^6\,\left(\frac{5\,B\,a^3\,b^2}{2}+\frac{5\,A\,a^2\,b^3}{2}\right)}{x^{10}}+\frac{B\,b^5\,x^2}{2}","Not used",1,"log(x)*(A*b^5 + 5*B*a*b^4) - ((A*a^5)/10 + x^8*(5*B*a^2*b^3 + (5*A*a*b^4)/2) + x^4*((5*A*a^3*b^2)/3 + (5*B*a^4*b)/6) + x^2*((B*a^5)/8 + (5*A*a^4*b)/8) + x^6*((5*A*a^2*b^3)/2 + (5*B*a^3*b^2)/2))/x^10 + (B*b^5*x^2)/2","B"
44,1,119,108,0.074837,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^5)/x^12,x)","B\,b^5\,x-\frac{\frac{A\,a^5}{11}+x^8\,\left(\frac{10\,B\,a^2\,b^3}{3}+\frac{5\,A\,a\,b^4}{3}\right)+x^4\,\left(\frac{5\,B\,a^4\,b}{7}+\frac{10\,A\,a^3\,b^2}{7}\right)+x^2\,\left(\frac{B\,a^5}{9}+\frac{5\,A\,b\,a^4}{9}\right)+x^{10}\,\left(A\,b^5+5\,B\,a\,b^4\right)+x^6\,\left(2\,B\,a^3\,b^2+2\,A\,a^2\,b^3\right)}{x^{11}}","Not used",1,"B*b^5*x - ((A*a^5)/11 + x^8*((10*B*a^2*b^3)/3 + (5*A*a*b^4)/3) + x^4*((10*A*a^3*b^2)/7 + (5*B*a^4*b)/7) + x^2*((B*a^5)/9 + (5*A*a^4*b)/9) + x^10*(A*b^5 + 5*B*a*b^4) + x^6*(2*A*a^2*b^3 + 2*B*a^3*b^2))/x^11","B"
45,1,121,91,0.120043,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^5)/x^13,x)","B\,b^5\,\ln\left(x\right)-\frac{\frac{A\,a^5}{12}+x^8\,\left(\frac{5\,B\,a^2\,b^3}{2}+\frac{5\,A\,a\,b^4}{4}\right)+x^4\,\left(\frac{5\,B\,a^4\,b}{8}+\frac{5\,A\,a^3\,b^2}{4}\right)+x^2\,\left(\frac{B\,a^5}{10}+\frac{A\,b\,a^4}{2}\right)+x^{10}\,\left(\frac{A\,b^5}{2}+\frac{5\,B\,a\,b^4}{2}\right)+x^6\,\left(\frac{5\,B\,a^3\,b^2}{3}+\frac{5\,A\,a^2\,b^3}{3}\right)}{x^{12}}","Not used",1,"B*b^5*log(x) - ((A*a^5)/12 + x^8*((5*B*a^2*b^3)/2 + (5*A*a*b^4)/4) + x^4*((5*A*a^3*b^2)/4 + (5*B*a^4*b)/8) + x^2*((B*a^5)/10 + (A*a^4*b)/2) + x^10*((A*b^5)/2 + (5*B*a*b^4)/2) + x^6*((5*A*a^2*b^3)/3 + (5*B*a^3*b^2)/3))/x^12","B"
46,1,120,113,0.091783,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^5)/x^14,x)","-\frac{\frac{A\,a^5}{13}+x^8\,\left(2\,B\,a^2\,b^3+A\,a\,b^4\right)+x^4\,\left(\frac{5\,B\,a^4\,b}{9}+\frac{10\,A\,a^3\,b^2}{9}\right)+x^2\,\left(\frac{B\,a^5}{11}+\frac{5\,A\,b\,a^4}{11}\right)+x^{10}\,\left(\frac{A\,b^5}{3}+\frac{5\,B\,a\,b^4}{3}\right)+x^6\,\left(\frac{10\,B\,a^3\,b^2}{7}+\frac{10\,A\,a^2\,b^3}{7}\right)+B\,b^5\,x^{12}}{x^{13}}","Not used",1,"-((A*a^5)/13 + x^8*(2*B*a^2*b^3 + A*a*b^4) + x^4*((10*A*a^3*b^2)/9 + (5*B*a^4*b)/9) + x^2*((B*a^5)/11 + (5*A*a^4*b)/11) + x^10*((A*b^5)/3 + (5*B*a*b^4)/3) + x^6*((10*A*a^2*b^3)/7 + (10*B*a^3*b^2)/7) + B*b^5*x^12)/x^13","B"
47,1,121,48,0.062009,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^5)/x^15,x)","-\frac{\frac{A\,a^5}{14}+x^4\,\left(\frac{B\,a^4\,b}{2}+A\,a^3\,b^2\right)+x^8\,\left(\frac{5\,B\,a^2\,b^3}{3}+\frac{5\,A\,a\,b^4}{6}\right)+x^2\,\left(\frac{B\,a^5}{12}+\frac{5\,A\,b\,a^4}{12}\right)+x^{10}\,\left(\frac{A\,b^5}{4}+\frac{5\,B\,a\,b^4}{4}\right)+x^6\,\left(\frac{5\,B\,a^3\,b^2}{4}+\frac{5\,A\,a^2\,b^3}{4}\right)+\frac{B\,b^5\,x^{12}}{2}}{x^{14}}","Not used",1,"-((A*a^5)/14 + x^4*(A*a^3*b^2 + (B*a^4*b)/2) + x^8*((5*B*a^2*b^3)/3 + (5*A*a*b^4)/6) + x^2*((B*a^5)/12 + (5*A*a^4*b)/12) + x^10*((A*b^5)/4 + (5*B*a*b^4)/4) + x^6*((5*A*a^2*b^3)/4 + (5*B*a^3*b^2)/4) + (B*b^5*x^12)/2)/x^14","B"
48,1,121,117,0.064760,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^5)/x^16,x)","-\frac{\frac{A\,a^5}{15}+x^8\,\left(\frac{10\,B\,a^2\,b^3}{7}+\frac{5\,A\,a\,b^4}{7}\right)+x^4\,\left(\frac{5\,B\,a^4\,b}{11}+\frac{10\,A\,a^3\,b^2}{11}\right)+x^2\,\left(\frac{B\,a^5}{13}+\frac{5\,A\,b\,a^4}{13}\right)+x^{10}\,\left(\frac{A\,b^5}{5}+B\,a\,b^4\right)+x^6\,\left(\frac{10\,B\,a^3\,b^2}{9}+\frac{10\,A\,a^2\,b^3}{9}\right)+\frac{B\,b^5\,x^{12}}{3}}{x^{15}}","Not used",1,"-((A*a^5)/15 + x^8*((10*B*a^2*b^3)/7 + (5*A*a*b^4)/7) + x^4*((10*A*a^3*b^2)/11 + (5*B*a^4*b)/11) + x^2*((B*a^5)/13 + (5*A*a^4*b)/13) + x^10*((A*b^5)/5 + B*a*b^4) + x^6*((10*A*a^2*b^3)/9 + (10*B*a^3*b^2)/9) + (B*b^5*x^12)/3)/x^15","B"
49,1,120,76,0.092438,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^5)/x^17,x)","-\frac{\frac{A\,a^5}{16}+x^8\,\left(\frac{5\,B\,a^2\,b^3}{4}+\frac{5\,A\,a\,b^4}{8}\right)+x^4\,\left(\frac{5\,B\,a^4\,b}{12}+\frac{5\,A\,a^3\,b^2}{6}\right)+x^2\,\left(\frac{B\,a^5}{14}+\frac{5\,A\,b\,a^4}{14}\right)+x^{10}\,\left(\frac{A\,b^5}{6}+\frac{5\,B\,a\,b^4}{6}\right)+x^6\,\left(B\,a^3\,b^2+A\,a^2\,b^3\right)+\frac{B\,b^5\,x^{12}}{4}}{x^{16}}","Not used",1,"-((A*a^5)/16 + x^8*((5*B*a^2*b^3)/4 + (5*A*a*b^4)/8) + x^4*((5*A*a^3*b^2)/6 + (5*B*a^4*b)/12) + x^2*((B*a^5)/14 + (5*A*a^4*b)/14) + x^10*((A*b^5)/6 + (5*B*a*b^4)/6) + x^6*(A*a^2*b^3 + B*a^3*b^2) + (B*b^5*x^12)/4)/x^16","B"
50,1,122,117,0.093902,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^5)/x^18,x)","-\frac{\frac{A\,a^5}{17}+x^8\,\left(\frac{10\,B\,a^2\,b^3}{9}+\frac{5\,A\,a\,b^4}{9}\right)+x^4\,\left(\frac{5\,B\,a^4\,b}{13}+\frac{10\,A\,a^3\,b^2}{13}\right)+x^2\,\left(\frac{B\,a^5}{15}+\frac{A\,b\,a^4}{3}\right)+x^{10}\,\left(\frac{A\,b^5}{7}+\frac{5\,B\,a\,b^4}{7}\right)+x^6\,\left(\frac{10\,B\,a^3\,b^2}{11}+\frac{10\,A\,a^2\,b^3}{11}\right)+\frac{B\,b^5\,x^{12}}{5}}{x^{17}}","Not used",1,"-((A*a^5)/17 + x^8*((10*B*a^2*b^3)/9 + (5*A*a*b^4)/9) + x^4*((10*A*a^3*b^2)/13 + (5*B*a^4*b)/13) + x^2*((B*a^5)/15 + (A*a^4*b)/3) + x^10*((A*b^5)/7 + (5*B*a*b^4)/7) + x^6*((10*A*a^2*b^3)/11 + (10*B*a^3*b^2)/11) + (B*b^5*x^12)/5)/x^17","B"
51,1,121,117,0.062646,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^5)/x^19,x)","-\frac{\frac{A\,a^5}{18}+x^8\,\left(B\,a^2\,b^3+\frac{A\,a\,b^4}{2}\right)+x^4\,\left(\frac{5\,B\,a^4\,b}{14}+\frac{5\,A\,a^3\,b^2}{7}\right)+x^2\,\left(\frac{B\,a^5}{16}+\frac{5\,A\,b\,a^4}{16}\right)+x^{10}\,\left(\frac{A\,b^5}{8}+\frac{5\,B\,a\,b^4}{8}\right)+x^6\,\left(\frac{5\,B\,a^3\,b^2}{6}+\frac{5\,A\,a^2\,b^3}{6}\right)+\frac{B\,b^5\,x^{12}}{6}}{x^{18}}","Not used",1,"-((A*a^5)/18 + x^8*(B*a^2*b^3 + (A*a*b^4)/2) + x^4*((5*A*a^3*b^2)/7 + (5*B*a^4*b)/14) + x^2*((B*a^5)/16 + (5*A*a^4*b)/16) + x^10*((A*b^5)/8 + (5*B*a*b^4)/8) + x^6*((5*A*a^2*b^3)/6 + (5*B*a^3*b^2)/6) + (B*b^5*x^12)/6)/x^18","B"
52,1,122,117,0.093798,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^5)/x^20,x)","-\frac{\frac{A\,a^5}{19}+x^4\,\left(\frac{B\,a^4\,b}{3}+\frac{2\,A\,a^3\,b^2}{3}\right)+x^8\,\left(\frac{10\,B\,a^2\,b^3}{11}+\frac{5\,A\,a\,b^4}{11}\right)+x^2\,\left(\frac{B\,a^5}{17}+\frac{5\,A\,b\,a^4}{17}\right)+x^{10}\,\left(\frac{A\,b^5}{9}+\frac{5\,B\,a\,b^4}{9}\right)+x^6\,\left(\frac{10\,B\,a^3\,b^2}{13}+\frac{10\,A\,a^2\,b^3}{13}\right)+\frac{B\,b^5\,x^{12}}{7}}{x^{19}}","Not used",1,"-((A*a^5)/19 + x^4*((2*A*a^3*b^2)/3 + (B*a^4*b)/3) + x^8*((10*B*a^2*b^3)/11 + (5*A*a*b^4)/11) + x^2*((B*a^5)/17 + (5*A*a^4*b)/17) + x^10*((A*b^5)/9 + (5*B*a*b^4)/9) + x^6*((10*A*a^2*b^3)/13 + (10*B*a^3*b^2)/13) + (B*b^5*x^12)/7)/x^19","B"
53,1,122,117,0.091403,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^5)/x^21,x)","-\frac{\frac{A\,a^5}{20}+x^8\,\left(\frac{5\,B\,a^2\,b^3}{6}+\frac{5\,A\,a\,b^4}{12}\right)+x^4\,\left(\frac{5\,B\,a^4\,b}{16}+\frac{5\,A\,a^3\,b^2}{8}\right)+x^2\,\left(\frac{B\,a^5}{18}+\frac{5\,A\,b\,a^4}{18}\right)+x^{10}\,\left(\frac{A\,b^5}{10}+\frac{B\,a\,b^4}{2}\right)+x^6\,\left(\frac{5\,B\,a^3\,b^2}{7}+\frac{5\,A\,a^2\,b^3}{7}\right)+\frac{B\,b^5\,x^{12}}{8}}{x^{20}}","Not used",1,"-((A*a^5)/20 + x^8*((5*B*a^2*b^3)/6 + (5*A*a*b^4)/12) + x^4*((5*A*a^3*b^2)/8 + (5*B*a^4*b)/16) + x^2*((B*a^5)/18 + (5*A*a^4*b)/18) + x^10*((A*b^5)/10 + (B*a*b^4)/2) + x^6*((5*A*a^2*b^3)/7 + (5*B*a^3*b^2)/7) + (B*b^5*x^12)/8)/x^20","B"
54,1,122,117,0.093860,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^5)/x^22,x)","-\frac{\frac{A\,a^5}{21}+x^8\,\left(\frac{10\,B\,a^2\,b^3}{13}+\frac{5\,A\,a\,b^4}{13}\right)+x^4\,\left(\frac{5\,B\,a^4\,b}{17}+\frac{10\,A\,a^3\,b^2}{17}\right)+x^2\,\left(\frac{B\,a^5}{19}+\frac{5\,A\,b\,a^4}{19}\right)+x^{10}\,\left(\frac{A\,b^5}{11}+\frac{5\,B\,a\,b^4}{11}\right)+x^6\,\left(\frac{2\,B\,a^3\,b^2}{3}+\frac{2\,A\,a^2\,b^3}{3}\right)+\frac{B\,b^5\,x^{12}}{9}}{x^{21}}","Not used",1,"-((A*a^5)/21 + x^8*((10*B*a^2*b^3)/13 + (5*A*a*b^4)/13) + x^4*((10*A*a^3*b^2)/17 + (5*B*a^4*b)/17) + x^2*((B*a^5)/19 + (5*A*a^4*b)/19) + x^10*((A*b^5)/11 + (5*B*a*b^4)/11) + x^6*((2*A*a^2*b^3)/3 + (2*B*a^3*b^2)/3) + (B*b^5*x^12)/9)/x^21","B"
55,1,122,117,0.063751,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^5)/x^23,x)","-\frac{\frac{A\,a^5}{22}+x^8\,\left(\frac{5\,B\,a^2\,b^3}{7}+\frac{5\,A\,a\,b^4}{14}\right)+x^4\,\left(\frac{5\,B\,a^4\,b}{18}+\frac{5\,A\,a^3\,b^2}{9}\right)+x^2\,\left(\frac{B\,a^5}{20}+\frac{A\,b\,a^4}{4}\right)+x^{10}\,\left(\frac{A\,b^5}{12}+\frac{5\,B\,a\,b^4}{12}\right)+x^6\,\left(\frac{5\,B\,a^3\,b^2}{8}+\frac{5\,A\,a^2\,b^3}{8}\right)+\frac{B\,b^5\,x^{12}}{10}}{x^{22}}","Not used",1,"-((A*a^5)/22 + x^8*((5*B*a^2*b^3)/7 + (5*A*a*b^4)/14) + x^4*((5*A*a^3*b^2)/9 + (5*B*a^4*b)/18) + x^2*((B*a^5)/20 + (A*a^4*b)/4) + x^10*((A*b^5)/12 + (5*B*a*b^4)/12) + x^6*((5*A*a^2*b^3)/8 + (5*B*a^3*b^2)/8) + (B*b^5*x^12)/10)/x^22","B"
56,1,118,98,0.048750,"\text{Not used}","int((x^6*(A + B*x^2))/(a + b*x^2),x)","x^5\,\left(\frac{A}{5\,b}-\frac{B\,a}{5\,b^2}\right)+\frac{B\,x^7}{7\,b}+\frac{a^{5/2}\,\mathrm{atan}\left(\frac{a^{5/2}\,\sqrt{b}\,x\,\left(A\,b-B\,a\right)}{B\,a^4-A\,a^3\,b}\right)\,\left(A\,b-B\,a\right)}{b^{9/2}}-\frac{a\,x^3\,\left(\frac{A}{b}-\frac{B\,a}{b^2}\right)}{3\,b}+\frac{a^2\,x\,\left(\frac{A}{b}-\frac{B\,a}{b^2}\right)}{b^2}","Not used",1,"x^5*(A/(5*b) - (B*a)/(5*b^2)) + (B*x^7)/(7*b) + (a^(5/2)*atan((a^(5/2)*b^(1/2)*x*(A*b - B*a))/(B*a^4 - A*a^3*b))*(A*b - B*a))/b^(9/2) - (a*x^3*(A/b - (B*a)/b^2))/(3*b) + (a^2*x*(A/b - (B*a)/b^2))/b^2","B"
57,1,76,75,0.056622,"\text{Not used}","int((x^5*(A + B*x^2))/(a + b*x^2),x)","x^4\,\left(\frac{A}{4\,b}-\frac{B\,a}{4\,b^2}\right)+\frac{B\,x^6}{6\,b}-\frac{\ln\left(b\,x^2+a\right)\,\left(B\,a^3-A\,a^2\,b\right)}{2\,b^4}-\frac{a\,x^2\,\left(\frac{A}{b}-\frac{B\,a}{b^2}\right)}{2\,b}","Not used",1,"x^4*(A/(4*b) - (B*a)/(4*b^2)) + (B*x^6)/(6*b) - (log(a + b*x^2)*(B*a^3 - A*a^2*b))/(2*b^4) - (a*x^2*(A/b - (B*a)/b^2))/(2*b)","B"
58,1,96,77,0.089295,"\text{Not used}","int((x^4*(A + B*x^2))/(a + b*x^2),x)","x^3\,\left(\frac{A}{3\,b}-\frac{B\,a}{3\,b^2}\right)+\frac{B\,x^5}{5\,b}-\frac{a^{3/2}\,\mathrm{atan}\left(\frac{a^{3/2}\,\sqrt{b}\,x\,\left(A\,b-B\,a\right)}{B\,a^3-A\,a^2\,b}\right)\,\left(A\,b-B\,a\right)}{b^{7/2}}-\frac{a\,x\,\left(\frac{A}{b}-\frac{B\,a}{b^2}\right)}{b}","Not used",1,"x^3*(A/(3*b) - (B*a)/(3*b^2)) + (B*x^5)/(5*b) - (a^(3/2)*atan((a^(3/2)*b^(1/2)*x*(A*b - B*a))/(B*a^3 - A*a^2*b))*(A*b - B*a))/b^(7/2) - (a*x*(A/b - (B*a)/b^2))/b","B"
59,1,52,54,0.097988,"\text{Not used}","int((x^3*(A + B*x^2))/(a + b*x^2),x)","x^2\,\left(\frac{A}{2\,b}-\frac{B\,a}{2\,b^2}\right)+\frac{\ln\left(b\,x^2+a\right)\,\left(B\,a^2-A\,a\,b\right)}{2\,b^3}+\frac{B\,x^4}{4\,b}","Not used",1,"x^2*(A/(2*b) - (B*a)/(2*b^2)) + (log(a + b*x^2)*(B*a^2 - A*a*b))/(2*b^3) + (B*x^4)/(4*b)","B"
60,1,70,58,0.100463,"\text{Not used}","int((x^2*(A + B*x^2))/(a + b*x^2),x)","x\,\left(\frac{A}{b}-\frac{B\,a}{b^2}\right)+\frac{B\,x^3}{3\,b}+\frac{\sqrt{a}\,\mathrm{atan}\left(\frac{\sqrt{a}\,\sqrt{b}\,x\,\left(A\,b-B\,a\right)}{B\,a^2-A\,a\,b}\right)\,\left(A\,b-B\,a\right)}{b^{5/2}}","Not used",1,"x*(A/b - (B*a)/b^2) + (B*x^3)/(3*b) + (a^(1/2)*atan((a^(1/2)*b^(1/2)*x*(A*b - B*a))/(B*a^2 - A*a*b))*(A*b - B*a))/b^(5/2)","B"
61,1,31,35,0.053473,"\text{Not used}","int((x*(A + B*x^2))/(a + b*x^2),x)","\frac{B\,x^2}{2\,b}+\frac{\ln\left(b\,x^2+a\right)\,\left(A\,b-B\,a\right)}{2\,b^2}","Not used",1,"(B*x^2)/(2*b) + (log(a + b*x^2)*(A*b - B*a))/(2*b^2)","B"
62,1,31,39,0.051671,"\text{Not used}","int((A + B*x^2)/(a + b*x^2),x)","\frac{B\,x}{b}+\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)\,\left(A\,b-B\,a\right)}{\sqrt{a}\,b^{3/2}}","Not used",1,"(B*x)/b + (atan((b^(1/2)*x)/a^(1/2))*(A*b - B*a))/(a^(1/2)*b^(3/2))","B"
63,1,32,34,0.134923,"\text{Not used}","int((A + B*x^2)/(x*(a + b*x^2)),x)","\frac{A\,\ln\left(x\right)}{a}-\frac{\ln\left(b\,x^2+a\right)\,\left(A\,b-B\,a\right)}{2\,a\,b}","Not used",1,"(A*log(x))/a - (log(a + b*x^2)*(A*b - B*a))/(2*a*b)","B"
64,1,35,43,0.057030,"\text{Not used}","int((A + B*x^2)/(x^2*(a + b*x^2)),x)","-\frac{A}{a\,x}-\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)\,\left(A\,b-B\,a\right)}{a^{3/2}\,\sqrt{b}}","Not used",1,"- A/(a*x) - (atan((b^(1/2)*x)/a^(1/2))*(A*b - B*a))/(a^(3/2)*b^(1/2))","B"
65,1,46,50,0.131711,"\text{Not used}","int((A + B*x^2)/(x^3*(a + b*x^2)),x)","\frac{\ln\left(b\,x^2+a\right)\,\left(A\,b-B\,a\right)}{2\,a^2}-\frac{A}{2\,a\,x^2}-\frac{\ln\left(x\right)\,\left(A\,b-B\,a\right)}{a^2}","Not used",1,"(log(a + b*x^2)*(A*b - B*a))/(2*a^2) - A/(2*a*x^2) - (log(x)*(A*b - B*a))/a^2","B"
66,1,53,59,0.103503,"\text{Not used}","int((A + B*x^2)/(x^4*(a + b*x^2)),x)","\frac{\sqrt{b}\,\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)\,\left(A\,b-B\,a\right)}{a^{5/2}}-\frac{\frac{A}{3\,a}-\frac{x^2\,\left(A\,b-B\,a\right)}{a^2}}{x^3}","Not used",1,"(b^(1/2)*atan((b^(1/2)*x)/a^(1/2))*(A*b - B*a))/a^(5/2) - (A/(3*a) - (x^2*(A*b - B*a))/a^2)/x^3","B"
67,1,70,69,0.133910,"\text{Not used}","int((A + B*x^2)/(x^5*(a + b*x^2)),x)","\frac{\ln\left(x\right)\,\left(A\,b^2-B\,a\,b\right)}{a^3}-\frac{\ln\left(b\,x^2+a\right)\,\left(A\,b^2-B\,a\,b\right)}{2\,a^3}-\frac{\frac{A}{4\,a}-\frac{x^2\,\left(A\,b-B\,a\right)}{2\,a^2}}{x^4}","Not used",1,"(log(x)*(A*b^2 - B*a*b))/a^3 - (log(a + b*x^2)*(A*b^2 - B*a*b))/(2*a^3) - (A/(4*a) - (x^2*(A*b - B*a))/(2*a^2))/x^4","B"
68,1,70,80,0.097215,"\text{Not used}","int((A + B*x^2)/(x^6*(a + b*x^2)),x)","-\frac{\frac{A}{5\,a}-\frac{x^2\,\left(A\,b-B\,a\right)}{3\,a^2}+\frac{b\,x^4\,\left(A\,b-B\,a\right)}{a^3}}{x^5}-\frac{b^{3/2}\,\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)\,\left(A\,b-B\,a\right)}{a^{7/2}}","Not used",1,"- (A/(5*a) - (x^2*(A*b - B*a))/(3*a^2) + (b*x^4*(A*b - B*a))/a^3)/x^5 - (b^(3/2)*atan((b^(1/2)*x)/a^(1/2))*(A*b - B*a))/a^(7/2)","B"
69,1,92,93,0.136093,"\text{Not used}","int((A + B*x^2)/(x^7*(a + b*x^2)),x)","\frac{\ln\left(b\,x^2+a\right)\,\left(A\,b^3-B\,a\,b^2\right)}{2\,a^4}-\frac{\frac{A}{6\,a}-\frac{x^2\,\left(A\,b-B\,a\right)}{4\,a^2}+\frac{b\,x^4\,\left(A\,b-B\,a\right)}{2\,a^3}}{x^6}-\frac{\ln\left(x\right)\,\left(A\,b^3-B\,a\,b^2\right)}{a^4}","Not used",1,"(log(a + b*x^2)*(A*b^3 - B*a*b^2))/(2*a^4) - (A/(6*a) - (x^2*(A*b - B*a))/(4*a^2) + (b*x^4*(A*b - B*a))/(2*a^3))/x^6 - (log(x)*(A*b^3 - B*a*b^2))/a^4","B"
70,1,89,99,0.120584,"\text{Not used}","int((A + B*x^2)/(x^8*(a + b*x^2)),x)","\frac{b^{5/2}\,\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)\,\left(A\,b-B\,a\right)}{a^{9/2}}-\frac{\frac{A}{7\,a}-\frac{x^2\,\left(A\,b-B\,a\right)}{5\,a^2}-\frac{b^2\,x^6\,\left(A\,b-B\,a\right)}{a^4}+\frac{b\,x^4\,\left(A\,b-B\,a\right)}{3\,a^3}}{x^7}","Not used",1,"(b^(5/2)*atan((b^(1/2)*x)/a^(1/2))*(A*b - B*a))/a^(9/2) - (A/(7*a) - (x^2*(A*b - B*a))/(5*a^2) - (b^2*x^6*(A*b - B*a))/a^4 + (b*x^4*(A*b - B*a))/(3*a^3))/x^7","B"
71,1,181,126,0.101352,"\text{Not used}","int((x^9*(A + B*x^2))/(a + b*x^2)^2,x)","x^2\,\left(\frac{a\,\left(\frac{2\,a\,\left(\frac{A}{b^2}-\frac{2\,B\,a}{b^3}\right)}{b}+\frac{B\,a^2}{b^4}\right)}{b}-\frac{a^2\,\left(\frac{A}{b^2}-\frac{2\,B\,a}{b^3}\right)}{2\,b^2}\right)+x^6\,\left(\frac{A}{6\,b^2}-\frac{B\,a}{3\,b^3}\right)-x^4\,\left(\frac{a\,\left(\frac{A}{b^2}-\frac{2\,B\,a}{b^3}\right)}{2\,b}+\frac{B\,a^2}{4\,b^4}\right)+\frac{B\,x^8}{8\,b^2}+\frac{\ln\left(b\,x^2+a\right)\,\left(5\,B\,a^4-4\,A\,a^3\,b\right)}{2\,b^6}+\frac{B\,a^5-A\,a^4\,b}{2\,b\,\left(b^6\,x^2+a\,b^5\right)}","Not used",1,"x^2*((a*((2*a*(A/b^2 - (2*B*a)/b^3))/b + (B*a^2)/b^4))/b - (a^2*(A/b^2 - (2*B*a)/b^3))/(2*b^2)) + x^6*(A/(6*b^2) - (B*a)/(3*b^3)) - x^4*((a*(A/b^2 - (2*B*a)/b^3))/(2*b) + (B*a^2)/(4*b^4)) + (B*x^8)/(8*b^2) + (log(a + b*x^2)*(5*B*a^4 - 4*A*a^3*b))/(2*b^6) + (B*a^5 - A*a^4*b)/(2*b*(a*b^5 + b^6*x^2))","B"
72,1,203,131,0.052585,"\text{Not used}","int((x^8*(A + B*x^2))/(a + b*x^2)^2,x)","x\,\left(\frac{2\,a\,\left(\frac{2\,a\,\left(\frac{A}{b^2}-\frac{2\,B\,a}{b^3}\right)}{b}+\frac{B\,a^2}{b^4}\right)}{b}-\frac{a^2\,\left(\frac{A}{b^2}-\frac{2\,B\,a}{b^3}\right)}{b^2}\right)+x^5\,\left(\frac{A}{5\,b^2}-\frac{2\,B\,a}{5\,b^3}\right)-x^3\,\left(\frac{2\,a\,\left(\frac{A}{b^2}-\frac{2\,B\,a}{b^3}\right)}{3\,b}+\frac{B\,a^2}{3\,b^4}\right)+\frac{B\,x^7}{7\,b^2}-\frac{x\,\left(\frac{B\,a^4}{2}-\frac{A\,a^3\,b}{2}\right)}{b^6\,x^2+a\,b^5}+\frac{a^{5/2}\,\mathrm{atan}\left(\frac{a^{5/2}\,\sqrt{b}\,x\,\left(7\,A\,b-9\,B\,a\right)}{9\,B\,a^4-7\,A\,a^3\,b}\right)\,\left(7\,A\,b-9\,B\,a\right)}{2\,b^{11/2}}","Not used",1,"x*((2*a*((2*a*(A/b^2 - (2*B*a)/b^3))/b + (B*a^2)/b^4))/b - (a^2*(A/b^2 - (2*B*a)/b^3))/b^2) + x^5*(A/(5*b^2) - (2*B*a)/(5*b^3)) - x^3*((2*a*(A/b^2 - (2*B*a)/b^3))/(3*b) + (B*a^2)/(3*b^4)) + (B*x^7)/(7*b^2) - (x*((B*a^4)/2 - (A*a^3*b)/2))/(a*b^5 + b^6*x^2) + (a^(5/2)*atan((a^(5/2)*b^(1/2)*x*(7*A*b - 9*B*a))/(9*B*a^4 - 7*A*a^3*b))*(7*A*b - 9*B*a))/(2*b^(11/2))","B"
73,1,121,104,0.093929,"\text{Not used}","int((x^7*(A + B*x^2))/(a + b*x^2)^2,x)","x^4\,\left(\frac{A}{4\,b^2}-\frac{B\,a}{2\,b^3}\right)-x^2\,\left(\frac{a\,\left(\frac{A}{b^2}-\frac{2\,B\,a}{b^3}\right)}{b}+\frac{B\,a^2}{2\,b^4}\right)+\frac{B\,x^6}{6\,b^2}-\frac{\ln\left(b\,x^2+a\right)\,\left(4\,B\,a^3-3\,A\,a^2\,b\right)}{2\,b^5}-\frac{B\,a^4-A\,a^3\,b}{2\,b\,\left(b^5\,x^2+a\,b^4\right)}","Not used",1,"x^4*(A/(4*b^2) - (B*a)/(2*b^3)) - x^2*((a*(A/b^2 - (2*B*a)/b^3))/b + (B*a^2)/(2*b^4)) + (B*x^6)/(6*b^2) - (log(a + b*x^2)*(4*B*a^3 - 3*A*a^2*b))/(2*b^5) - (B*a^4 - A*a^3*b)/(2*b*(a*b^4 + b^5*x^2))","B"
74,1,141,110,0.048213,"\text{Not used}","int((x^6*(A + B*x^2))/(a + b*x^2)^2,x)","x^3\,\left(\frac{A}{3\,b^2}-\frac{2\,B\,a}{3\,b^3}\right)-x\,\left(\frac{2\,a\,\left(\frac{A}{b^2}-\frac{2\,B\,a}{b^3}\right)}{b}+\frac{B\,a^2}{b^4}\right)+\frac{B\,x^5}{5\,b^2}+\frac{x\,\left(\frac{B\,a^3}{2}-\frac{A\,a^2\,b}{2}\right)}{b^5\,x^2+a\,b^4}-\frac{a^{3/2}\,\mathrm{atan}\left(\frac{a^{3/2}\,\sqrt{b}\,x\,\left(5\,A\,b-7\,B\,a\right)}{7\,B\,a^3-5\,A\,a^2\,b}\right)\,\left(5\,A\,b-7\,B\,a\right)}{2\,b^{9/2}}","Not used",1,"x^3*(A/(3*b^2) - (2*B*a)/(3*b^3)) - x*((2*a*(A/b^2 - (2*B*a)/b^3))/b + (B*a^2)/b^4) + (B*x^5)/(5*b^2) + (x*((B*a^3)/2 - (A*a^2*b)/2))/(a*b^4 + b^5*x^2) - (a^(3/2)*atan((a^(3/2)*b^(1/2)*x*(5*A*b - 7*B*a))/(7*B*a^3 - 5*A*a^2*b))*(5*A*b - 7*B*a))/(2*b^(9/2))","B"
75,1,86,82,0.066477,"\text{Not used}","int((x^5*(A + B*x^2))/(a + b*x^2)^2,x)","x^2\,\left(\frac{A}{2\,b^2}-\frac{B\,a}{b^3}\right)+\frac{\ln\left(b\,x^2+a\right)\,\left(3\,B\,a^2-2\,A\,a\,b\right)}{2\,b^4}+\frac{B\,x^4}{4\,b^2}+\frac{B\,a^3-A\,a^2\,b}{2\,b\,\left(b^4\,x^2+a\,b^3\right)}","Not used",1,"x^2*(A/(2*b^2) - (B*a)/b^3) + (log(a + b*x^2)*(3*B*a^2 - 2*A*a*b))/(2*b^4) + (B*x^4)/(4*b^2) + (B*a^3 - A*a^2*b)/(2*b*(a*b^3 + b^4*x^2))","B"
76,1,104,87,0.069147,"\text{Not used}","int((x^4*(A + B*x^2))/(a + b*x^2)^2,x)","x\,\left(\frac{A}{b^2}-\frac{2\,B\,a}{b^3}\right)-\frac{x\,\left(\frac{B\,a^2}{2}-\frac{A\,a\,b}{2}\right)}{b^4\,x^2+a\,b^3}+\frac{B\,x^3}{3\,b^2}+\frac{\sqrt{a}\,\mathrm{atan}\left(\frac{\sqrt{a}\,\sqrt{b}\,x\,\left(3\,A\,b-5\,B\,a\right)}{5\,B\,a^2-3\,A\,a\,b}\right)\,\left(3\,A\,b-5\,B\,a\right)}{2\,b^{7/2}}","Not used",1,"x*(A/b^2 - (2*B*a)/b^3) - (x*((B*a^2)/2 - (A*a*b)/2))/(a*b^3 + b^4*x^2) + (B*x^3)/(3*b^2) + (a^(1/2)*atan((a^(1/2)*b^(1/2)*x*(3*A*b - 5*B*a))/(5*B*a^2 - 3*A*a*b))*(3*A*b - 5*B*a))/(2*b^(7/2))","B"
77,1,62,60,0.070414,"\text{Not used}","int((x^3*(A + B*x^2))/(a + b*x^2)^2,x)","\frac{B\,x^2}{2\,b^2}+\frac{\ln\left(b\,x^2+a\right)\,\left(A\,b-2\,B\,a\right)}{2\,b^3}-\frac{B\,a^2-A\,a\,b}{2\,b\,\left(b^3\,x^2+a\,b^2\right)}","Not used",1,"(B*x^2)/(2*b^2) + (log(a + b*x^2)*(A*b - 2*B*a))/(2*b^3) - (B*a^2 - A*a*b)/(2*b*(a*b^2 + b^3*x^2))","B"
78,1,59,67,0.121227,"\text{Not used}","int((x^2*(A + B*x^2))/(a + b*x^2)^2,x)","\frac{B\,x}{b^2}-\frac{x\,\left(\frac{A\,b}{2}-\frac{B\,a}{2}\right)}{b^3\,x^2+a\,b^2}+\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)\,\left(A\,b-3\,B\,a\right)}{2\,\sqrt{a}\,b^{5/2}}","Not used",1,"(B*x)/b^2 - (x*((A*b)/2 - (B*a)/2))/(a*b^2 + b^3*x^2) + (atan((b^(1/2)*x)/a^(1/2))*(A*b - 3*B*a))/(2*a^(1/2)*b^(5/2))","B"
79,1,37,41,0.084832,"\text{Not used}","int((x*(A + B*x^2))/(a + b*x^2)^2,x)","\frac{B\,\ln\left(b\,x^2+a\right)}{2\,b^2}-\frac{A\,b-B\,a}{2\,b^2\,\left(b\,x^2+a\right)}","Not used",1,"(B*log(a + b*x^2))/(2*b^2) - (A*b - B*a)/(2*b^2*(a + b*x^2))","B"
80,1,51,63,0.115698,"\text{Not used}","int((A + B*x^2)/(a + b*x^2)^2,x)","\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)\,\left(A\,b+B\,a\right)}{2\,a^{3/2}\,b^{3/2}}+\frac{x\,\left(A\,b-B\,a\right)}{2\,a\,b\,\left(b\,x^2+a\right)}","Not used",1,"(atan((b^(1/2)*x)/a^(1/2))*(A*b + B*a))/(2*a^(3/2)*b^(3/2)) + (x*(A*b - B*a))/(2*a*b*(a + b*x^2))","B"
81,1,47,51,0.154274,"\text{Not used}","int((A + B*x^2)/(x*(a + b*x^2)^2),x)","\frac{A\,\ln\left(x\right)}{a^2}-\frac{A\,\ln\left(b\,x^2+a\right)}{2\,a^2}+\frac{A\,b-B\,a}{2\,a\,b\,\left(b\,x^2+a\right)}","Not used",1,"(A*log(x))/a^2 - (A*log(a + b*x^2))/(2*a^2) + (A*b - B*a)/(2*a*b*(a + b*x^2))","B"
82,1,63,71,0.124540,"\text{Not used}","int((A + B*x^2)/(x^2*(a + b*x^2)^2),x)","-\frac{\frac{A}{a}+\frac{x^2\,\left(3\,A\,b-B\,a\right)}{2\,a^2}}{b\,x^3+a\,x}-\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)\,\left(3\,A\,b-B\,a\right)}{2\,a^{5/2}\,\sqrt{b}}","Not used",1,"- (A/a + (x^2*(3*A*b - B*a))/(2*a^2))/(a*x + b*x^3) - (atan((b^(1/2)*x)/a^(1/2))*(3*A*b - B*a))/(2*a^(5/2)*b^(1/2))","B"
83,1,78,76,0.138502,"\text{Not used}","int((A + B*x^2)/(x^3*(a + b*x^2)^2),x)","\frac{\ln\left(b\,x^2+a\right)\,\left(2\,A\,b-B\,a\right)}{2\,a^3}-\frac{\frac{A}{2\,a}+\frac{x^2\,\left(2\,A\,b-B\,a\right)}{2\,a^2}}{b\,x^4+a\,x^2}-\frac{\ln\left(x\right)\,\left(2\,A\,b-B\,a\right)}{a^3}","Not used",1,"(log(a + b*x^2)*(2*A*b - B*a))/(2*a^3) - (A/(2*a) + (x^2*(2*A*b - B*a))/(2*a^2))/(a*x^2 + b*x^4) - (log(x)*(2*A*b - B*a))/a^3","B"
84,1,83,90,0.138970,"\text{Not used}","int((A + B*x^2)/(x^4*(a + b*x^2)^2),x)","\frac{\frac{x^2\,\left(5\,A\,b-3\,B\,a\right)}{3\,a^2}-\frac{A}{3\,a}+\frac{b\,x^4\,\left(5\,A\,b-3\,B\,a\right)}{2\,a^3}}{b\,x^5+a\,x^3}+\frac{\sqrt{b}\,\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)\,\left(5\,A\,b-3\,B\,a\right)}{2\,a^{7/2}}","Not used",1,"((x^2*(5*A*b - 3*B*a))/(3*a^2) - A/(3*a) + (b*x^4*(5*A*b - 3*B*a))/(2*a^3))/(a*x^3 + b*x^5) + (b^(1/2)*atan((b^(1/2)*x)/a^(1/2))*(5*A*b - 3*B*a))/(2*a^(7/2))","B"
85,1,100,97,0.137326,"\text{Not used}","int((A + B*x^2)/(x^5*(a + b*x^2)^2),x)","\frac{\frac{x^2\,\left(3\,A\,b-2\,B\,a\right)}{4\,a^2}-\frac{A}{4\,a}+\frac{b\,x^4\,\left(3\,A\,b-2\,B\,a\right)}{2\,a^3}}{b\,x^6+a\,x^4}-\frac{\ln\left(b\,x^2+a\right)\,\left(3\,A\,b^2-2\,B\,a\,b\right)}{2\,a^4}+\frac{\ln\left(x\right)\,\left(3\,A\,b^2-2\,B\,a\,b\right)}{a^4}","Not used",1,"((x^2*(3*A*b - 2*B*a))/(4*a^2) - A/(4*a) + (b*x^4*(3*A*b - 2*B*a))/(2*a^3))/(a*x^4 + b*x^6) - (log(a + b*x^2)*(3*A*b^2 - 2*B*a*b))/(2*a^4) + (log(x)*(3*A*b^2 - 2*B*a*b))/a^4","B"
86,1,104,113,0.152099,"\text{Not used}","int((A + B*x^2)/(x^6*(a + b*x^2)^2),x)","-\frac{\frac{A}{5\,a}-\frac{x^2\,\left(7\,A\,b-5\,B\,a\right)}{15\,a^2}+\frac{b^2\,x^6\,\left(7\,A\,b-5\,B\,a\right)}{2\,a^4}+\frac{b\,x^4\,\left(7\,A\,b-5\,B\,a\right)}{3\,a^3}}{b\,x^7+a\,x^5}-\frac{b^{3/2}\,\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)\,\left(7\,A\,b-5\,B\,a\right)}{2\,a^{9/2}}","Not used",1,"- (A/(5*a) - (x^2*(7*A*b - 5*B*a))/(15*a^2) + (b^2*x^6*(7*A*b - 5*B*a))/(2*a^4) + (b*x^4*(7*A*b - 5*B*a))/(3*a^3))/(a*x^5 + b*x^7) - (b^(3/2)*atan((b^(1/2)*x)/a^(1/2))*(7*A*b - 5*B*a))/(2*a^(9/2))","B"
87,1,126,124,0.160625,"\text{Not used}","int((A + B*x^2)/(x^7*(a + b*x^2)^2),x)","\frac{\ln\left(b\,x^2+a\right)\,\left(4\,A\,b^3-3\,B\,a\,b^2\right)}{2\,a^5}-\frac{\frac{A}{6\,a}-\frac{x^2\,\left(4\,A\,b-3\,B\,a\right)}{12\,a^2}+\frac{b^2\,x^6\,\left(4\,A\,b-3\,B\,a\right)}{2\,a^4}+\frac{b\,x^4\,\left(4\,A\,b-3\,B\,a\right)}{4\,a^3}}{b\,x^8+a\,x^6}-\frac{\ln\left(x\right)\,\left(4\,A\,b^3-3\,B\,a\,b^2\right)}{a^5}","Not used",1,"(log(a + b*x^2)*(4*A*b^3 - 3*B*a*b^2))/(2*a^5) - (A/(6*a) - (x^2*(4*A*b - 3*B*a))/(12*a^2) + (b^2*x^6*(4*A*b - 3*B*a))/(2*a^4) + (b*x^4*(4*A*b - 3*B*a))/(4*a^3))/(a*x^6 + b*x^8) - (log(x)*(4*A*b^3 - 3*B*a*b^2))/a^5","B"
88,1,225,150,0.120215,"\text{Not used}","int((x^11*(A + B*x^2))/(a + b*x^2)^3,x)","\frac{\frac{11\,B\,a^6-9\,A\,a^5\,b}{4\,b}+x^2\,\left(3\,B\,a^5-\frac{5\,A\,a^4\,b}{2}\right)}{a^2\,b^6+2\,a\,b^7\,x^2+b^8\,x^4}-x^2\,\left(\frac{B\,a^3}{2\,b^6}-\frac{3\,a\,\left(\frac{3\,a\,\left(\frac{A}{b^3}-\frac{3\,B\,a}{b^4}\right)}{b}+\frac{3\,B\,a^2}{b^5}\right)}{2\,b}+\frac{3\,a^2\,\left(\frac{A}{b^3}-\frac{3\,B\,a}{b^4}\right)}{2\,b^2}\right)+x^6\,\left(\frac{A}{6\,b^3}-\frac{B\,a}{2\,b^4}\right)-x^4\,\left(\frac{3\,a\,\left(\frac{A}{b^3}-\frac{3\,B\,a}{b^4}\right)}{4\,b}+\frac{3\,B\,a^2}{4\,b^5}\right)+\frac{B\,x^8}{8\,b^3}+\frac{\ln\left(b\,x^2+a\right)\,\left(15\,B\,a^4-10\,A\,a^3\,b\right)}{2\,b^7}","Not used",1,"((11*B*a^6 - 9*A*a^5*b)/(4*b) + x^2*(3*B*a^5 - (5*A*a^4*b)/2))/(a^2*b^6 + b^8*x^4 + 2*a*b^7*x^2) - x^2*((B*a^3)/(2*b^6) - (3*a*((3*a*(A/b^3 - (3*B*a)/b^4))/b + (3*B*a^2)/b^5))/(2*b) + (3*a^2*(A/b^3 - (3*B*a)/b^4))/(2*b^2)) + x^6*(A/(6*b^3) - (B*a)/(2*b^4)) - x^4*((3*a*(A/b^3 - (3*B*a)/b^4))/(4*b) + (3*B*a^2)/(4*b^5)) + (B*x^8)/(8*b^3) + (log(a + b*x^2)*(15*B*a^4 - 10*A*a^3*b))/(2*b^7)","B"
89,1,155,128,0.072961,"\text{Not used}","int((x^9*(A + B*x^2))/(a + b*x^2)^3,x)","x^4\,\left(\frac{A}{4\,b^3}-\frac{3\,B\,a}{4\,b^4}\right)-\frac{\frac{9\,B\,a^5-7\,A\,a^4\,b}{4\,b}+x^2\,\left(\frac{5\,B\,a^4}{2}-2\,A\,a^3\,b\right)}{a^2\,b^5+2\,a\,b^6\,x^2+b^7\,x^4}-x^2\,\left(\frac{3\,a\,\left(\frac{A}{b^3}-\frac{3\,B\,a}{b^4}\right)}{2\,b}+\frac{3\,B\,a^2}{2\,b^5}\right)+\frac{B\,x^6}{6\,b^3}-\frac{\ln\left(b\,x^2+a\right)\,\left(5\,B\,a^3-3\,A\,a^2\,b\right)}{b^6}","Not used",1,"x^4*(A/(4*b^3) - (3*B*a)/(4*b^4)) - ((9*B*a^5 - 7*A*a^4*b)/(4*b) + x^2*((5*B*a^4)/2 - 2*A*a^3*b))/(a^2*b^5 + b^7*x^4 + 2*a*b^6*x^2) - x^2*((3*a*(A/b^3 - (3*B*a)/b^4))/(2*b) + (3*B*a^2)/(2*b^5)) + (B*x^6)/(6*b^3) - (log(a + b*x^2)*(5*B*a^3 - 3*A*a^2*b))/b^6","B"
90,1,118,109,0.078184,"\text{Not used}","int((x^7*(A + B*x^2))/(a + b*x^2)^3,x)","\frac{\frac{7\,B\,a^4-5\,A\,a^3\,b}{4\,b}+x^2\,\left(2\,B\,a^3-\frac{3\,A\,a^2\,b}{2}\right)}{a^2\,b^4+2\,a\,b^5\,x^2+b^6\,x^4}+x^2\,\left(\frac{A}{2\,b^3}-\frac{3\,B\,a}{2\,b^4}\right)+\frac{\ln\left(b\,x^2+a\right)\,\left(6\,B\,a^2-3\,A\,a\,b\right)}{2\,b^5}+\frac{B\,x^4}{4\,b^3}","Not used",1,"((7*B*a^4 - 5*A*a^3*b)/(4*b) + x^2*(2*B*a^3 - (3*A*a^2*b)/2))/(a^2*b^4 + b^6*x^4 + 2*a*b^5*x^2) + x^2*(A/(2*b^3) - (3*B*a)/(2*b^4)) + (log(a + b*x^2)*(6*B*a^2 - 3*A*a*b))/(2*b^5) + (B*x^4)/(4*b^3)","B"
91,1,95,88,0.129029,"\text{Not used}","int((x^5*(A + B*x^2))/(a + b*x^2)^3,x)","\frac{B\,x^2}{2\,b^3}-\frac{x^2\,\left(\frac{3\,B\,a^2}{2}-A\,a\,b\right)+\frac{5\,B\,a^3-3\,A\,a^2\,b}{4\,b}}{a^2\,b^3+2\,a\,b^4\,x^2+b^5\,x^4}+\frac{\ln\left(b\,x^2+a\right)\,\left(A\,b-3\,B\,a\right)}{2\,b^4}","Not used",1,"(B*x^2)/(2*b^3) - (x^2*((3*B*a^2)/2 - A*a*b) + (5*B*a^3 - 3*A*a^2*b)/(4*b))/(a^2*b^3 + b^5*x^4 + 2*a*b^4*x^2) + (log(a + b*x^2)*(A*b - 3*B*a))/(2*b^4)","B"
92,1,70,66,0.107783,"\text{Not used}","int((x^3*(A + B*x^2))/(a + b*x^2)^3,x)","\frac{\frac{3\,B\,a^2-A\,a\,b}{4\,b^3}-\frac{x^2\,\left(A\,b-2\,B\,a\right)}{2\,b^2}}{a^2+2\,a\,b\,x^2+b^2\,x^4}+\frac{B\,\ln\left(b\,x^2+a\right)}{2\,b^3}","Not used",1,"((3*B*a^2 - A*a*b)/(4*b^3) - (x^2*(A*b - 2*B*a))/(2*b^2))/(a^2 + b^2*x^4 + 2*a*b*x^2) + (B*log(a + b*x^2))/(2*b^3)","B"
93,1,44,32,0.069669,"\text{Not used}","int((x*(A + B*x^2))/(a + b*x^2)^3,x)","-\frac{\frac{A\,b+B\,a}{4\,b^2}+\frac{B\,x^2}{2\,b}}{a^2+2\,a\,b\,x^2+b^2\,x^4}","Not used",1,"-((A*b + B*a)/(4*b^2) + (B*x^2)/(2*b))/(a^2 + b^2*x^4 + 2*a*b*x^2)","B"
94,1,71,68,0.177714,"\text{Not used}","int((A + B*x^2)/(x*(a + b*x^2)^3),x)","\frac{\frac{3\,A\,b-B\,a}{4\,a\,b}+\frac{A\,b\,x^2}{2\,a^2}}{a^2+2\,a\,b\,x^2+b^2\,x^4}-\frac{A\,\ln\left(b\,x^2+a\right)}{2\,a^3}+\frac{A\,\ln\left(x\right)}{a^3}","Not used",1,"((3*A*b - B*a)/(4*a*b) + (A*b*x^2)/(2*a^2))/(a^2 + b^2*x^4 + 2*a*b*x^2) - (A*log(a + b*x^2))/(2*a^3) + (A*log(x))/a^3","B"
95,1,107,101,0.104809,"\text{Not used}","int((A + B*x^2)/(x^3*(a + b*x^2)^3),x)","\frac{\ln\left(b\,x^2+a\right)\,\left(3\,A\,b-B\,a\right)}{2\,a^4}-\frac{\frac{A}{2\,a}+\frac{3\,x^2\,\left(3\,A\,b-B\,a\right)}{4\,a^2}+\frac{b\,x^4\,\left(3\,A\,b-B\,a\right)}{2\,a^3}}{a^2\,x^2+2\,a\,b\,x^4+b^2\,x^6}-\frac{\ln\left(x\right)\,\left(3\,A\,b-B\,a\right)}{a^4}","Not used",1,"(log(a + b*x^2)*(3*A*b - B*a))/(2*a^4) - (A/(2*a) + (3*x^2*(3*A*b - B*a))/(4*a^2) + (b*x^4*(3*A*b - B*a))/(2*a^3))/(a^2*x^2 + b^2*x^6 + 2*a*b*x^4) - (log(x)*(3*A*b - B*a))/a^4","B"
96,1,131,124,0.155589,"\text{Not used}","int((A + B*x^2)/(x^5*(a + b*x^2)^3),x)","\frac{\frac{x^2\,\left(2\,A\,b-B\,a\right)}{2\,a^2}-\frac{A}{4\,a}+\frac{3\,b^2\,x^6\,\left(2\,A\,b-B\,a\right)}{2\,a^4}+\frac{9\,b\,x^4\,\left(2\,A\,b-B\,a\right)}{4\,a^3}}{a^2\,x^4+2\,a\,b\,x^6+b^2\,x^8}-\frac{\ln\left(b\,x^2+a\right)\,\left(6\,A\,b^2-3\,B\,a\,b\right)}{2\,a^5}+\frac{\ln\left(x\right)\,\left(6\,A\,b^2-3\,B\,a\,b\right)}{a^5}","Not used",1,"((x^2*(2*A*b - B*a))/(2*a^2) - A/(4*a) + (3*b^2*x^6*(2*A*b - B*a))/(2*a^4) + (9*b*x^4*(2*A*b - B*a))/(4*a^3))/(a^2*x^4 + b^2*x^8 + 2*a*b*x^6) - (log(a + b*x^2)*(6*A*b^2 - 3*B*a*b))/(2*a^5) + (log(x)*(6*A*b^2 - 3*B*a*b))/a^5","B"
97,1,155,149,0.181120,"\text{Not used}","int((A + B*x^2)/(x^7*(a + b*x^2)^3),x)","\frac{\ln\left(b\,x^2+a\right)\,\left(5\,A\,b^3-3\,B\,a\,b^2\right)}{a^6}-\frac{\frac{A}{6\,a}-\frac{x^2\,\left(5\,A\,b-3\,B\,a\right)}{12\,a^2}+\frac{3\,b^2\,x^6\,\left(5\,A\,b-3\,B\,a\right)}{2\,a^4}+\frac{b^3\,x^8\,\left(5\,A\,b-3\,B\,a\right)}{a^5}+\frac{b\,x^4\,\left(5\,A\,b-3\,B\,a\right)}{3\,a^3}}{a^2\,x^6+2\,a\,b\,x^8+b^2\,x^{10}}-\frac{\ln\left(x\right)\,\left(10\,A\,b^3-6\,B\,a\,b^2\right)}{a^6}","Not used",1,"(log(a + b*x^2)*(5*A*b^3 - 3*B*a*b^2))/a^6 - (A/(6*a) - (x^2*(5*A*b - 3*B*a))/(12*a^2) + (3*b^2*x^6*(5*A*b - 3*B*a))/(2*a^4) + (b^3*x^8*(5*A*b - 3*B*a))/a^5 + (b*x^4*(5*A*b - 3*B*a))/(3*a^3))/(a^2*x^6 + b^2*x^10 + 2*a*b*x^8) - (log(x)*(10*A*b^3 - 6*B*a*b^2))/a^6","B"
98,1,246,158,0.114728,"\text{Not used}","int((x^10*(A + B*x^2))/(a + b*x^2)^3,x)","x^5\,\left(\frac{A}{5\,b^3}-\frac{3\,B\,a}{5\,b^4}\right)-\frac{x\,\left(\frac{19\,B\,a^5}{8}-\frac{15\,A\,a^4\,b}{8}\right)-x^3\,\left(\frac{17\,A\,a^3\,b^2}{8}-\frac{21\,B\,a^4\,b}{8}\right)}{a^2\,b^6+2\,a\,b^7\,x^2+b^8\,x^4}-x^3\,\left(\frac{a\,\left(\frac{A}{b^3}-\frac{3\,B\,a}{b^4}\right)}{b}+\frac{B\,a^2}{b^5}\right)-x\,\left(\frac{B\,a^3}{b^6}-\frac{3\,a\,\left(\frac{3\,a\,\left(\frac{A}{b^3}-\frac{3\,B\,a}{b^4}\right)}{b}+\frac{3\,B\,a^2}{b^5}\right)}{b}+\frac{3\,a^2\,\left(\frac{A}{b^3}-\frac{3\,B\,a}{b^4}\right)}{b^2}\right)+\frac{B\,x^7}{7\,b^3}+\frac{9\,a^{5/2}\,\mathrm{atan}\left(\frac{a^{5/2}\,\sqrt{b}\,x\,\left(7\,A\,b-11\,B\,a\right)}{11\,B\,a^4-7\,A\,a^3\,b}\right)\,\left(7\,A\,b-11\,B\,a\right)}{8\,b^{13/2}}","Not used",1,"x^5*(A/(5*b^3) - (3*B*a)/(5*b^4)) - (x*((19*B*a^5)/8 - (15*A*a^4*b)/8) - x^3*((17*A*a^3*b^2)/8 - (21*B*a^4*b)/8))/(a^2*b^6 + b^8*x^4 + 2*a*b^7*x^2) - x^3*((a*(A/b^3 - (3*B*a)/b^4))/b + (B*a^2)/b^5) - x*((B*a^3)/b^6 - (3*a*((3*a*(A/b^3 - (3*B*a)/b^4))/b + (3*B*a^2)/b^5))/b + (3*a^2*(A/b^3 - (3*B*a)/b^4))/b^2) + (B*x^7)/(7*b^3) + (9*a^(5/2)*atan((a^(5/2)*b^(1/2)*x*(7*A*b - 11*B*a))/(11*B*a^4 - 7*A*a^3*b))*(7*A*b - 11*B*a))/(8*b^(13/2))","B"
99,1,177,138,0.100540,"\text{Not used}","int((x^8*(A + B*x^2))/(a + b*x^2)^3,x)","\frac{x\,\left(\frac{15\,B\,a^4}{8}-\frac{11\,A\,a^3\,b}{8}\right)-x^3\,\left(\frac{13\,A\,a^2\,b^2}{8}-\frac{17\,B\,a^3\,b}{8}\right)}{a^2\,b^5+2\,a\,b^6\,x^2+b^7\,x^4}-x\,\left(\frac{3\,a\,\left(\frac{A}{b^3}-\frac{3\,B\,a}{b^4}\right)}{b}+\frac{3\,B\,a^2}{b^5}\right)+x^3\,\left(\frac{A}{3\,b^3}-\frac{B\,a}{b^4}\right)+\frac{B\,x^5}{5\,b^3}-\frac{7\,a^{3/2}\,\mathrm{atan}\left(\frac{a^{3/2}\,\sqrt{b}\,x\,\left(5\,A\,b-9\,B\,a\right)}{9\,B\,a^3-5\,A\,a^2\,b}\right)\,\left(5\,A\,b-9\,B\,a\right)}{8\,b^{11/2}}","Not used",1,"(x*((15*B*a^4)/8 - (11*A*a^3*b)/8) - x^3*((13*A*a^2*b^2)/8 - (17*B*a^3*b)/8))/(a^2*b^5 + b^7*x^4 + 2*a*b^6*x^2) - x*((3*a*(A/b^3 - (3*B*a)/b^4))/b + (3*B*a^2)/b^5) + x^3*(A/(3*b^3) - (B*a)/b^4) + (B*x^5)/(5*b^3) - (7*a^(3/2)*atan((a^(3/2)*b^(1/2)*x*(5*A*b - 9*B*a))/(9*B*a^3 - 5*A*a^2*b))*(5*A*b - 9*B*a))/(8*b^(11/2))","B"
100,1,138,116,0.111181,"\text{Not used}","int((x^6*(A + B*x^2))/(a + b*x^2)^3,x)","\frac{x^3\,\left(\frac{9\,A\,a\,b^2}{8}-\frac{13\,B\,a^2\,b}{8}\right)-x\,\left(\frac{11\,B\,a^3}{8}-\frac{7\,A\,a^2\,b}{8}\right)}{a^2\,b^4+2\,a\,b^5\,x^2+b^6\,x^4}+x\,\left(\frac{A}{b^3}-\frac{3\,B\,a}{b^4}\right)+\frac{B\,x^3}{3\,b^3}+\frac{5\,\sqrt{a}\,\mathrm{atan}\left(\frac{\sqrt{a}\,\sqrt{b}\,x\,\left(3\,A\,b-7\,B\,a\right)}{7\,B\,a^2-3\,A\,a\,b}\right)\,\left(3\,A\,b-7\,B\,a\right)}{8\,b^{9/2}}","Not used",1,"(x^3*((9*A*a*b^2)/8 - (13*B*a^2*b)/8) - x*((11*B*a^3)/8 - (7*A*a^2*b)/8))/(a^2*b^4 + b^6*x^4 + 2*a*b^5*x^2) + x*(A/b^3 - (3*B*a)/b^4) + (B*x^3)/(3*b^3) + (5*a^(1/2)*atan((a^(1/2)*b^(1/2)*x*(3*A*b - 7*B*a))/(7*B*a^2 - 3*A*a*b))*(3*A*b - 7*B*a))/(8*b^(9/2))","B"
101,1,92,94,0.252682,"\text{Not used}","int((x^4*(A + B*x^2))/(a + b*x^2)^3,x)","\frac{B\,x}{b^3}-\frac{x^3\,\left(\frac{5\,A\,b^2}{8}-\frac{9\,B\,a\,b}{8}\right)-x\,\left(\frac{7\,B\,a^2}{8}-\frac{3\,A\,a\,b}{8}\right)}{a^2\,b^3+2\,a\,b^4\,x^2+b^5\,x^4}+\frac{3\,\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)\,\left(A\,b-5\,B\,a\right)}{8\,\sqrt{a}\,b^{7/2}}","Not used",1,"(B*x)/b^3 - (x^3*((5*A*b^2)/8 - (9*B*a*b)/8) - x*((7*B*a^2)/8 - (3*A*a*b)/8))/(a^2*b^3 + b^5*x^4 + 2*a*b^4*x^2) + (3*atan((b^(1/2)*x)/a^(1/2))*(A*b - 5*B*a))/(8*a^(1/2)*b^(7/2))","B"
102,1,82,89,0.239505,"\text{Not used}","int((x^2*(A + B*x^2))/(a + b*x^2)^3,x)","\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)\,\left(A\,b+3\,B\,a\right)}{8\,a^{3/2}\,b^{5/2}}-\frac{\frac{x\,\left(A\,b+3\,B\,a\right)}{8\,b^2}-\frac{x^3\,\left(A\,b-5\,B\,a\right)}{8\,a\,b}}{a^2+2\,a\,b\,x^2+b^2\,x^4}","Not used",1,"(atan((b^(1/2)*x)/a^(1/2))*(A*b + 3*B*a))/(8*a^(3/2)*b^(5/2)) - ((x*(A*b + 3*B*a))/(8*b^2) - (x^3*(A*b - 5*B*a))/(8*a*b))/(a^2 + b^2*x^4 + 2*a*b*x^2)","B"
103,1,82,92,0.190696,"\text{Not used}","int((A + B*x^2)/(a + b*x^2)^3,x)","\frac{\frac{x^3\,\left(3\,A\,b+B\,a\right)}{8\,a^2}+\frac{x\,\left(5\,A\,b-B\,a\right)}{8\,a\,b}}{a^2+2\,a\,b\,x^2+b^2\,x^4}+\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)\,\left(3\,A\,b+B\,a\right)}{8\,a^{5/2}\,b^{3/2}}","Not used",1,"((x^3*(3*A*b + B*a))/(8*a^2) + (x*(5*A*b - B*a))/(8*a*b))/(a^2 + b^2*x^4 + 2*a*b*x^2) + (atan((b^(1/2)*x)/a^(1/2))*(3*A*b + B*a))/(8*a^(5/2)*b^(3/2))","B"
104,1,113,97,0.190844,"\text{Not used}","int((A + B*x^2)/(x^2*(a + b*x^2)^3),x)","-\frac{\frac{A}{a}+\frac{5\,x^2\,\left(5\,A\,b-B\,a\right)}{8\,a^2}+\frac{3\,b\,x^4\,\left(5\,A\,b-B\,a\right)}{8\,a^3}}{a^2\,x+2\,a\,b\,x^3+b^2\,x^5}-\frac{3\,\mathrm{atan}\left(\frac{3\,\sqrt{b}\,x\,\left(5\,A\,b-B\,a\right)}{\sqrt{a}\,\left(15\,A\,b-3\,B\,a\right)}\right)\,\left(5\,A\,b-B\,a\right)}{8\,a^{7/2}\,\sqrt{b}}","Not used",1,"- (A/a + (5*x^2*(5*A*b - B*a))/(8*a^2) + (3*b*x^4*(5*A*b - B*a))/(8*a^3))/(a^2*x + b^2*x^5 + 2*a*b*x^3) - (3*atan((3*b^(1/2)*x*(5*A*b - B*a))/(a^(1/2)*(15*A*b - 3*B*a)))*(5*A*b - B*a))/(8*a^(7/2)*b^(1/2))","B"
105,1,114,117,0.197187,"\text{Not used}","int((A + B*x^2)/(x^4*(a + b*x^2)^3),x)","\frac{\frac{x^2\,\left(7\,A\,b-3\,B\,a\right)}{3\,a^2}-\frac{A}{3\,a}+\frac{5\,b^2\,x^6\,\left(7\,A\,b-3\,B\,a\right)}{8\,a^4}+\frac{25\,b\,x^4\,\left(7\,A\,b-3\,B\,a\right)}{24\,a^3}}{a^2\,x^3+2\,a\,b\,x^5+b^2\,x^7}+\frac{5\,\sqrt{b}\,\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)\,\left(7\,A\,b-3\,B\,a\right)}{8\,a^{9/2}}","Not used",1,"((x^2*(7*A*b - 3*B*a))/(3*a^2) - A/(3*a) + (5*b^2*x^6*(7*A*b - 3*B*a))/(8*a^4) + (25*b*x^4*(7*A*b - 3*B*a))/(24*a^3))/(a^2*x^3 + b^2*x^7 + 2*a*b*x^5) + (5*b^(1/2)*atan((b^(1/2)*x)/a^(1/2))*(7*A*b - 3*B*a))/(8*a^(9/2))","B"
106,1,135,142,0.195397,"\text{Not used}","int((A + B*x^2)/(x^6*(a + b*x^2)^3),x)","-\frac{\frac{A}{5\,a}-\frac{x^2\,\left(9\,A\,b-5\,B\,a\right)}{15\,a^2}+\frac{35\,b^2\,x^6\,\left(9\,A\,b-5\,B\,a\right)}{24\,a^4}+\frac{7\,b^3\,x^8\,\left(9\,A\,b-5\,B\,a\right)}{8\,a^5}+\frac{7\,b\,x^4\,\left(9\,A\,b-5\,B\,a\right)}{15\,a^3}}{a^2\,x^5+2\,a\,b\,x^7+b^2\,x^9}-\frac{7\,b^{3/2}\,\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)\,\left(9\,A\,b-5\,B\,a\right)}{8\,a^{11/2}}","Not used",1,"- (A/(5*a) - (x^2*(9*A*b - 5*B*a))/(15*a^2) + (35*b^2*x^6*(9*A*b - 5*B*a))/(24*a^4) + (7*b^3*x^8*(9*A*b - 5*B*a))/(8*a^5) + (7*b*x^4*(9*A*b - 5*B*a))/(15*a^3))/(a^2*x^5 + b^2*x^9 + 2*a*b*x^7) - (7*b^(3/2)*atan((b^(1/2)*x)/a^(1/2))*(9*A*b - 5*B*a))/(8*a^(11/2))","B"
107,1,12,12,0.075059,"\text{Not used}","int((a + b*x^2)/(x^2 + 1),x)","b\,x+\mathrm{atan}\left(x\right)\,\left(a-b\right)","Not used",1,"b*x + atan(x)*(a - b)","B"
108,1,11,11,0.111070,"\text{Not used}","int(-(a + b*x^2)/(x^2 - 1),x)","\mathrm{atanh}\left(x\right)\,\left(a+b\right)-b\,x","Not used",1,"atanh(x)*(a + b) - b*x","B"
109,1,10,11,0.077414,"\text{Not used}","int((x^2 + 1)/(x^2 - 1)^2,x)","-\frac{x}{x^2-1}","Not used",1,"-x/(x^2 - 1)","B"
110,1,9,9,0.081892,"\text{Not used}","int(-(x^2 - 1)/(x^2 + 1)^2,x)","\frac{x}{x^2+1}","Not used",1,"x/(x^2 + 1)","B"
111,1,16,19,0.071591,"\text{Not used}","int((2*x^2 + 3)/(x^2 + 1)^2,x)","\frac{5\,\mathrm{atan}\left(x\right)}{2}+\frac{x}{2\,\left(x^2+1\right)}","Not used",1,"(5*atan(x))/2 + x/(2*(x^2 + 1))","B"
112,1,17,19,0.070006,"\text{Not used}","int((x^2 - 2)/(x^2 + 1)^2,x)","-\frac{\mathrm{atan}\left(x\right)}{2}-\frac{3\,x}{2\,\left(x^2+1\right)}","Not used",1,"- atan(x)/2 - (3*x)/(2*(x^2 + 1))","B"
113,1,14,14,0.024259,"\text{Not used}","int((x^2 + 3)/(x^2 + 1)^2,x)","2\,\mathrm{atan}\left(x\right)+\frac{x}{x^2+1}","Not used",1,"2*atan(x) + x/(x^2 + 1)","B"
114,1,12,12,0.043521,"\text{Not used}","int((a + b*x^2)/(a - b*x^2)^2,x)","\frac{x}{a-b\,x^2}","Not used",1,"x/(a - b*x^2)","B"
115,1,12,12,0.002218,"\text{Not used}","int((a + b*x^2)/(a - b*x^2)^2,x)","\frac{x}{a-b\,x^2}","Not used",1,"x/(a - b*x^2)","B"
116,1,31,39,0.140141,"\text{Not used}","int((A + B*x^2)/(a - b*x^2),x)","\frac{\mathrm{atanh}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)\,\left(A\,b+B\,a\right)}{\sqrt{a}\,b^{3/2}}-\frac{B\,x}{b}","Not used",1,"(atanh((b^(1/2)*x)/a^(1/2))*(A*b + B*a))/(a^(1/2)*b^(3/2)) - (B*x)/b","B"
117,1,30,35,0.079851,"\text{Not used}","int((x^2 + 1)/(x^2 + 16)^3,x)","\frac{19\,\mathrm{atan}\left(\frac{x}{4}\right)}{8192}-\frac{\frac{11\,x}{128}-\frac{19\,x^3}{2048}}{x^4+32\,x^2+256}","Not used",1,"(19*atan(x/4))/8192 - ((11*x)/128 - (19*x^3)/2048)/(32*x^2 + x^4 + 256)","B"
118,1,20,14,0.036331,"\text{Not used}","int((2*x^2 + 1)/(x^5*(x^2 + 1)^3),x)","-\frac{1}{4\,x^8+8\,x^6+4\,x^4}","Not used",1,"-1/(4*x^4 + 8*x^6 + 4*x^8)","B"
119,1,1,1,0.002045,"\text{Not used}","int(1,x)","x","Not used",1,"x","B"
120,1,6,8,0.023473,"\text{Not used}","int((x^3*(a*c + b*c*x^2))/(a + b*x^2),x)","\frac{c\,x^4}{4}","Not used",1,"(c*x^4)/4","B"
121,1,6,8,0.011435,"\text{Not used}","int((x^2*(a*c + b*c*x^2))/(a + b*x^2),x)","\frac{c\,x^3}{3}","Not used",1,"(c*x^3)/3","B"
122,1,6,8,0.013225,"\text{Not used}","int((x*(a*c + b*c*x^2))/(a + b*x^2),x)","\frac{c\,x^2}{2}","Not used",1,"(c*x^2)/2","B"
123,1,3,3,0.005640,"\text{Not used}","int((a*c + b*c*x^2)/(a + b*x^2),x)","c\,x","Not used",1,"c*x","B"
124,1,4,4,0.013892,"\text{Not used}","int((a*c + b*c*x^2)/(x*(a + b*x^2)),x)","c\,\ln\left(x\right)","Not used",1,"c*log(x)","B"
125,1,6,6,0.013332,"\text{Not used}","int((a*c + b*c*x^2)/(x^2*(a + b*x^2)),x)","-\frac{c}{x}","Not used",1,"-c/x","B"
126,1,6,8,0.017388,"\text{Not used}","int((a*c + b*c*x^2)/(x^3*(a + b*x^2)),x)","-\frac{c}{2\,x^2}","Not used",1,"-c/(2*x^2)","B"
127,1,23,29,0.040421,"\text{Not used}","int((x^3*(a*c + b*c*x^2))/(a + b*x^2)^2,x)","-\frac{c\,\left(a\,\ln\left(b\,x^2+a\right)-b\,x^2\right)}{2\,b^2}","Not used",1,"-(c*(a*log(a + b*x^2) - b*x^2))/(2*b^2)","B"
128,1,25,33,0.039955,"\text{Not used}","int((x^2*(a*c + b*c*x^2))/(a + b*x^2)^2,x)","\frac{c\,x}{b}-\frac{\sqrt{a}\,c\,\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)}{b^{3/2}}","Not used",1,"(c*x)/b - (a^(1/2)*c*atan((b^(1/2)*x)/a^(1/2)))/b^(3/2)","B"
129,1,14,16,0.031040,"\text{Not used}","int((x*(a*c + b*c*x^2))/(a + b*x^2)^2,x)","\frac{c\,\ln\left(b\,x^2+a\right)}{2\,b}","Not used",1,"(c*log(a + b*x^2))/(2*b)","B"
130,1,17,25,0.045989,"\text{Not used}","int((a*c + b*c*x^2)/(a + b*x^2)^2,x)","\frac{c\,\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)}{\sqrt{a}\,\sqrt{b}}","Not used",1,"(c*atan((b^(1/2)*x)/a^(1/2)))/(a^(1/2)*b^(1/2))","B"
131,1,19,24,0.099824,"\text{Not used}","int((a*c + b*c*x^2)/(x*(a + b*x^2)^2),x)","-\frac{c\,\left(\ln\left(b\,x^2+a\right)-2\,\ln\left(x\right)\right)}{2\,a}","Not used",1,"-(c*(log(a + b*x^2) - 2*log(x)))/(2*a)","B"
132,1,28,36,0.100140,"\text{Not used}","int((a*c + b*c*x^2)/(x^2*(a + b*x^2)^2),x)","-\frac{c}{a\,x}-\frac{\sqrt{b}\,c\,\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)}{a^{3/2}}","Not used",1,"- c/(a*x) - (b^(1/2)*c*atan((b^(1/2)*x)/a^(1/2)))/a^(3/2)","B"
133,1,34,38,0.108512,"\text{Not used}","int((a*c + b*c*x^2)/(x^3*(a + b*x^2)^2),x)","\frac{b\,c\,\ln\left(b\,x^2+a\right)}{2\,a^2}-\frac{c}{2\,a\,x^2}-\frac{b\,c\,\ln\left(x\right)}{a^2}","Not used",1,"(b*c*log(a + b*x^2))/(2*a^2) - c/(2*a*x^2) - (b*c*log(x))/a^2","B"
134,1,31,35,0.093503,"\text{Not used}","int((x^3*(a*c + b*c*x^2))/(a + b*x^2)^3,x)","\frac{c\,\ln\left(b\,x^2+a\right)}{2\,b^2}+\frac{a\,c}{2\,b^2\,\left(b\,x^2+a\right)}","Not used",1,"(c*log(a + b*x^2))/(2*b^2) + (a*c)/(2*b^2*(a + b*x^2))","B"
135,1,35,47,0.043533,"\text{Not used}","int((x^2*(a*c + b*c*x^2))/(a + b*x^2)^3,x)","\frac{c\,\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)}{2\,\sqrt{a}\,b^{3/2}}-\frac{c\,x}{2\,b\,\left(b\,x^2+a\right)}","Not used",1,"(c*atan((b^(1/2)*x)/a^(1/2)))/(2*a^(1/2)*b^(3/2)) - (c*x)/(2*b*(a + b*x^2))","B"
136,1,15,17,0.027325,"\text{Not used}","int((x*(a*c + b*c*x^2))/(a + b*x^2)^3,x)","-\frac{c}{2\,b\,\left(b\,x^2+a\right)}","Not used",1,"-c/(2*b*(a + b*x^2))","B"
137,1,35,47,0.043748,"\text{Not used}","int((a*c + b*c*x^2)/(a + b*x^2)^3,x)","\frac{c\,x}{2\,a\,\left(b\,x^2+a\right)}+\frac{c\,\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)}{2\,a^{3/2}\,\sqrt{b}}","Not used",1,"(c*x)/(2*a*(a + b*x^2)) + (c*atan((b^(1/2)*x)/a^(1/2)))/(2*a^(3/2)*b^(1/2))","B"
138,1,37,41,0.097207,"\text{Not used}","int((a*c + b*c*x^2)/(x*(a + b*x^2)^3),x)","\frac{c}{2\,a\,\left(b\,x^2+a\right)}-\frac{c\,\ln\left(b\,x^2+a\right)}{2\,a^2}+\frac{c\,\ln\left(x\right)}{a^2}","Not used",1,"c/(2*a*(a + b*x^2)) - (c*log(a + b*x^2))/(2*a^2) + (c*log(x))/a^2","B"
139,1,48,60,0.068611,"\text{Not used}","int((a*c + b*c*x^2)/(x^2*(a + b*x^2)^3),x)","-\frac{\frac{c}{a}+\frac{3\,b\,c\,x^2}{2\,a^2}}{b\,x^3+a\,x}-\frac{3\,\sqrt{b}\,c\,\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)}{2\,a^{5/2}}","Not used",1,"- (c/a + (3*b*c*x^2)/(2*a^2))/(a*x + b*x^3) - (3*b^(1/2)*c*atan((b^(1/2)*x)/a^(1/2)))/(2*a^(5/2))","B"
140,1,55,53,0.104137,"\text{Not used}","int((a*c + b*c*x^2)/(x^3*(a + b*x^2)^3),x)","\frac{b\,c\,\ln\left(b\,x^2+a\right)}{a^3}-\frac{\frac{c}{2\,a}+\frac{b\,c\,x^2}{a^2}}{b\,x^4+a\,x^2}-\frac{2\,b\,c\,\ln\left(x\right)}{a^3}","Not used",1,"(b*c*log(a + b*x^2))/a^3 - (c/(2*a) + (b*c*x^2)/a^2)/(a*x^2 + b*x^4) - (2*b*c*log(x))/a^3","B"
141,1,51,55,0.094120,"\text{Not used}","int(x^4*(a + b*x^2)^2*(c + d*x^2),x)","x^7\,\left(\frac{d\,a^2}{7}+\frac{2\,b\,c\,a}{7}\right)+x^9\,\left(\frac{c\,b^2}{9}+\frac{2\,a\,d\,b}{9}\right)+\frac{a^2\,c\,x^5}{5}+\frac{b^2\,d\,x^{11}}{11}","Not used",1,"x^7*((a^2*d)/7 + (2*a*b*c)/7) + x^9*((b^2*c)/9 + (2*a*b*d)/9) + (a^2*c*x^5)/5 + (b^2*d*x^11)/11","B"
142,1,51,55,0.045093,"\text{Not used}","int(x^3*(a + b*x^2)^2*(c + d*x^2),x)","x^6\,\left(\frac{d\,a^2}{6}+\frac{b\,c\,a}{3}\right)+x^8\,\left(\frac{c\,b^2}{8}+\frac{a\,d\,b}{4}\right)+\frac{a^2\,c\,x^4}{4}+\frac{b^2\,d\,x^{10}}{10}","Not used",1,"x^6*((a^2*d)/6 + (a*b*c)/3) + x^8*((b^2*c)/8 + (a*b*d)/4) + (a^2*c*x^4)/4 + (b^2*d*x^10)/10","B"
143,1,51,55,0.092869,"\text{Not used}","int(x^2*(a + b*x^2)^2*(c + d*x^2),x)","x^5\,\left(\frac{d\,a^2}{5}+\frac{2\,b\,c\,a}{5}\right)+x^7\,\left(\frac{c\,b^2}{7}+\frac{2\,a\,d\,b}{7}\right)+\frac{a^2\,c\,x^3}{3}+\frac{b^2\,d\,x^9}{9}","Not used",1,"x^5*((a^2*d)/5 + (2*a*b*c)/5) + x^7*((b^2*c)/7 + (2*a*b*d)/7) + (a^2*c*x^3)/3 + (b^2*d*x^9)/9","B"
144,1,51,42,0.043644,"\text{Not used}","int(x*(a + b*x^2)^2*(c + d*x^2),x)","x^4\,\left(\frac{d\,a^2}{4}+\frac{b\,c\,a}{2}\right)+x^6\,\left(\frac{c\,b^2}{6}+\frac{a\,d\,b}{3}\right)+\frac{a^2\,c\,x^2}{2}+\frac{b^2\,d\,x^8}{8}","Not used",1,"x^4*((a^2*d)/4 + (a*b*c)/2) + x^6*((b^2*c)/6 + (a*b*d)/3) + (a^2*c*x^2)/2 + (b^2*d*x^8)/8","B"
145,1,48,50,0.042300,"\text{Not used}","int((a + b*x^2)^2*(c + d*x^2),x)","x^3\,\left(\frac{d\,a^2}{3}+\frac{2\,b\,c\,a}{3}\right)+x^5\,\left(\frac{c\,b^2}{5}+\frac{2\,a\,d\,b}{5}\right)+\frac{b^2\,d\,x^7}{7}+a^2\,c\,x","Not used",1,"x^3*((a^2*d)/3 + (2*a*b*c)/3) + x^5*((b^2*c)/5 + (2*a*b*d)/5) + (b^2*d*x^7)/7 + a^2*c*x","B"
146,1,48,43,0.038319,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2))/x,x)","x^2\,\left(\frac{d\,a^2}{2}+b\,c\,a\right)+x^4\,\left(\frac{c\,b^2}{4}+\frac{a\,d\,b}{2}\right)+\frac{b^2\,d\,x^6}{6}+a^2\,c\,\ln\left(x\right)","Not used",1,"x^2*((a^2*d)/2 + a*b*c) + x^4*((b^2*c)/4 + (a*b*d)/2) + (b^2*d*x^6)/6 + a^2*c*log(x)","B"
147,1,48,48,0.049643,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2))/x^2,x)","x\,\left(d\,a^2+2\,b\,c\,a\right)+x^3\,\left(\frac{c\,b^2}{3}+\frac{2\,a\,d\,b}{3}\right)-\frac{a^2\,c}{x}+\frac{b^2\,d\,x^5}{5}","Not used",1,"x*(a^2*d + 2*a*b*c) + x^3*((b^2*c)/3 + (2*a*b*d)/3) - (a^2*c)/x + (b^2*d*x^5)/5","B"
148,1,48,51,0.090476,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2))/x^3,x)","x^2\,\left(\frac{c\,b^2}{2}+a\,d\,b\right)+\ln\left(x\right)\,\left(d\,a^2+2\,b\,c\,a\right)-\frac{a^2\,c}{2\,x^2}+\frac{b^2\,d\,x^4}{4}","Not used",1,"x^2*((b^2*c)/2 + a*b*d) + log(x)*(a^2*d + 2*a*b*c) - (a^2*c)/(2*x^2) + (b^2*d*x^4)/4","B"
149,1,50,48,0.045501,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2))/x^4,x)","x\,\left(c\,b^2+2\,a\,d\,b\right)-\frac{\frac{a^2\,c}{3}+x^2\,\left(d\,a^2+2\,b\,c\,a\right)}{x^3}+\frac{b^2\,d\,x^3}{3}","Not used",1,"x*(b^2*c + 2*a*b*d) - ((a^2*c)/3 + x^2*(a^2*d + 2*a*b*c))/x^3 + (b^2*d*x^3)/3","B"
150,1,78,87,0.049996,"\text{Not used}","int(x^4*(a + b*x^2)^2*(c + d*x^2)^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)+\frac{a^2\,c^2\,x^5}{5}+\frac{b^2\,d^2\,x^{13}}{13}+\frac{2\,a\,c\,x^7\,\left(a\,d+b\,c\right)}{7}+\frac{2\,b\,d\,x^{11}\,\left(a\,d+b\,c\right)}{11}","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^5)/5 + (b^2*d^2*x^13)/13 + (2*a*c*x^7*(a*d + b*c))/7 + (2*b*d*x^11*(a*d + b*c))/11","B"
151,1,78,87,0.027654,"\text{Not used}","int(x^3*(a + b*x^2)^2*(c + d*x^2)^2,x)","x^8\,\left(\frac{a^2\,d^2}{8}+\frac{a\,b\,c\,d}{2}+\frac{b^2\,c^2}{8}\right)+\frac{a^2\,c^2\,x^4}{4}+\frac{b^2\,d^2\,x^{12}}{12}+\frac{a\,c\,x^6\,\left(a\,d+b\,c\right)}{3}+\frac{b\,d\,x^{10}\,\left(a\,d+b\,c\right)}{5}","Not used",1,"x^8*((a^2*d^2)/8 + (b^2*c^2)/8 + (a*b*c*d)/2) + (a^2*c^2*x^4)/4 + (b^2*d^2*x^12)/12 + (a*c*x^6*(a*d + b*c))/3 + (b*d*x^10*(a*d + b*c))/5","B"
152,1,78,87,0.029119,"\text{Not used}","int(x^2*(a + b*x^2)^2*(c + d*x^2)^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)+\frac{a^2\,c^2\,x^3}{3}+\frac{b^2\,d^2\,x^{11}}{11}+\frac{2\,a\,c\,x^5\,\left(a\,d+b\,c\right)}{5}+\frac{2\,b\,d\,x^9\,\left(a\,d+b\,c\right)}{9}","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^3)/3 + (b^2*d^2*x^11)/11 + (2*a*c*x^5*(a*d + b*c))/5 + (2*b*d*x^9*(a*d + b*c))/9","B"
153,1,78,71,0.028472,"\text{Not used}","int(x*(a + b*x^2)^2*(c + d*x^2)^2,x)","x^6\,\left(\frac{a^2\,d^2}{6}+\frac{2\,a\,b\,c\,d}{3}+\frac{b^2\,c^2}{6}\right)+\frac{a^2\,c^2\,x^2}{2}+\frac{b^2\,d^2\,x^{10}}{10}+\frac{a\,c\,x^4\,\left(a\,d+b\,c\right)}{2}+\frac{b\,d\,x^8\,\left(a\,d+b\,c\right)}{4}","Not used",1,"x^6*((a^2*d^2)/6 + (b^2*c^2)/6 + (2*a*b*c*d)/3) + (a^2*c^2*x^2)/2 + (b^2*d^2*x^10)/10 + (a*c*x^4*(a*d + b*c))/2 + (b*d*x^8*(a*d + b*c))/4","B"
154,1,75,82,0.029475,"\text{Not used}","int((a + b*x^2)^2*(c + d*x^2)^2,x)","x^5\,\left(\frac{a^2\,d^2}{5}+\frac{4\,a\,b\,c\,d}{5}+\frac{b^2\,c^2}{5}\right)+a^2\,c^2\,x+\frac{b^2\,d^2\,x^9}{9}+\frac{2\,a\,c\,x^3\,\left(a\,d+b\,c\right)}{3}+\frac{2\,b\,d\,x^7\,\left(a\,d+b\,c\right)}{7}","Not used",1,"x^5*((a^2*d^2)/5 + (b^2*c^2)/5 + (4*a*b*c*d)/5) + a^2*c^2*x + (b^2*d^2*x^9)/9 + (2*a*c*x^3*(a*d + b*c))/3 + (2*b*d*x^7*(a*d + b*c))/7","B"
155,1,74,80,0.033272,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^2)/x,x)","x^4\,\left(\frac{a^2\,d^2}{4}+a\,b\,c\,d+\frac{b^2\,c^2}{4}\right)+\frac{b^2\,d^2\,x^8}{8}+a^2\,c^2\,\ln\left(x\right)+a\,c\,x^2\,\left(a\,d+b\,c\right)+\frac{b\,d\,x^6\,\left(a\,d+b\,c\right)}{3}","Not used",1,"x^4*((a^2*d^2)/4 + (b^2*c^2)/4 + a*b*c*d) + (b^2*d^2*x^8)/8 + a^2*c^2*log(x) + a*c*x^2*(a*d + b*c) + (b*d*x^6*(a*d + b*c))/3","B"
156,1,76,81,0.031410,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^2)/x^2,x)","x^3\,\left(\frac{a^2\,d^2}{3}+\frac{4\,a\,b\,c\,d}{3}+\frac{b^2\,c^2}{3}\right)-\frac{a^2\,c^2}{x}+\frac{b^2\,d^2\,x^7}{7}+2\,a\,c\,x\,\left(a\,d+b\,c\right)+\frac{2\,b\,d\,x^5\,\left(a\,d+b\,c\right)}{5}","Not used",1,"x^3*((a^2*d^2)/3 + (b^2*c^2)/3 + (4*a*b*c*d)/3) - (a^2*c^2)/x + (b^2*d^2*x^7)/7 + 2*a*c*x*(a*d + b*c) + (2*b*d*x^5*(a*d + b*c))/5","B"
157,1,82,84,0.037545,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^2)/x^3,x)","x^2\,\left(\frac{a^2\,d^2}{2}+2\,a\,b\,c\,d+\frac{b^2\,c^2}{2}\right)+\ln\left(x\right)\,\left(2\,d\,a^2\,c+2\,b\,a\,c^2\right)-\frac{a^2\,c^2}{2\,x^2}+\frac{b^2\,d^2\,x^6}{6}+\frac{b\,d\,x^4\,\left(a\,d+b\,c\right)}{2}","Not used",1,"x^2*((a^2*d^2)/2 + (b^2*c^2)/2 + 2*a*b*c*d) + log(x)*(2*a*b*c^2 + 2*a^2*c*d) - (a^2*c^2)/(2*x^2) + (b^2*d^2*x^6)/6 + (b*d*x^4*(a*d + b*c))/2","B"
158,1,82,80,0.053072,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^2)/x^4,x)","x\,\left(a^2\,d^2+4\,a\,b\,c\,d+b^2\,c^2\right)-\frac{x^2\,\left(2\,d\,a^2\,c+2\,b\,a\,c^2\right)+\frac{a^2\,c^2}{3}}{x^3}+\frac{b^2\,d^2\,x^5}{5}+\frac{2\,b\,d\,x^3\,\left(a\,d+b\,c\right)}{3}","Not used",1,"x*(a^2*d^2 + b^2*c^2 + 4*a*b*c*d) - (x^2*(2*a*b*c^2 + 2*a^2*c*d) + (a^2*c^2)/3)/x^3 + (b^2*d^2*x^5)/5 + (2*b*d*x^3*(a*d + b*c))/3","B"
159,1,119,127,0.095825,"\text{Not used}","int(x^4*(a + b*x^2)^2*(c + d*x^2)^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^{11}\,\left(\frac{a^2\,d^3}{11}+\frac{6\,a\,b\,c\,d^2}{11}+\frac{3\,b^2\,c^2\,d}{11}\right)+\frac{a^2\,c^3\,x^5}{5}+\frac{b^2\,d^3\,x^{15}}{15}+\frac{a\,c^2\,x^7\,\left(3\,a\,d+2\,b\,c\right)}{7}+\frac{b\,d^2\,x^{13}\,\left(2\,a\,d+3\,b\,c\right)}{13}","Not used",1,"x^9*((b^2*c^3)/9 + (a^2*c*d^2)/3 + (2*a*b*c^2*d)/3) + x^11*((a^2*d^3)/11 + (3*b^2*c^2*d)/11 + (6*a*b*c*d^2)/11) + (a^2*c^3*x^5)/5 + (b^2*d^3*x^15)/15 + (a*c^2*x^7*(3*a*d + 2*b*c))/7 + (b*d^2*x^13*(2*a*d + 3*b*c))/13","B"
160,1,119,106,0.036859,"\text{Not used}","int(x^3*(a + b*x^2)^2*(c + d*x^2)^3,x)","x^8\,\left(\frac{3\,a^2\,c\,d^2}{8}+\frac{3\,a\,b\,c^2\,d}{4}+\frac{b^2\,c^3}{8}\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)+\frac{a^2\,c^3\,x^4}{4}+\frac{b^2\,d^3\,x^{14}}{14}+\frac{a\,c^2\,x^6\,\left(3\,a\,d+2\,b\,c\right)}{6}+\frac{b\,d^2\,x^{12}\,\left(2\,a\,d+3\,b\,c\right)}{12}","Not used",1,"x^8*((b^2*c^3)/8 + (3*a^2*c*d^2)/8 + (3*a*b*c^2*d)/4) + 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^4)/4 + (b^2*d^3*x^14)/14 + (a*c^2*x^6*(3*a*d + 2*b*c))/6 + (b*d^2*x^12*(2*a*d + 3*b*c))/12","B"
161,1,119,127,0.037072,"\text{Not used}","int(x^2*(a + b*x^2)^2*(c + d*x^2)^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^9\,\left(\frac{a^2\,d^3}{9}+\frac{2\,a\,b\,c\,d^2}{3}+\frac{b^2\,c^2\,d}{3}\right)+\frac{a^2\,c^3\,x^3}{3}+\frac{b^2\,d^3\,x^{13}}{13}+\frac{a\,c^2\,x^5\,\left(3\,a\,d+2\,b\,c\right)}{5}+\frac{b\,d^2\,x^{11}\,\left(2\,a\,d+3\,b\,c\right)}{11}","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^9*((a^2*d^3)/9 + (b^2*c^2*d)/3 + (2*a*b*c*d^2)/3) + (a^2*c^3*x^3)/3 + (b^2*d^3*x^13)/13 + (a*c^2*x^5*(3*a*d + 2*b*c))/5 + (b*d^2*x^11*(2*a*d + 3*b*c))/11","B"
162,1,118,71,0.036593,"\text{Not used}","int(x*(a + b*x^2)^2*(c + d*x^2)^3,x)","x^6\,\left(\frac{a^2\,c\,d^2}{2}+a\,b\,c^2\,d+\frac{b^2\,c^3}{6}\right)+x^8\,\left(\frac{a^2\,d^3}{8}+\frac{3\,a\,b\,c\,d^2}{4}+\frac{3\,b^2\,c^2\,d}{8}\right)+\frac{a^2\,c^3\,x^2}{2}+\frac{b^2\,d^3\,x^{12}}{12}+\frac{a\,c^2\,x^4\,\left(3\,a\,d+2\,b\,c\right)}{4}+\frac{b\,d^2\,x^{10}\,\left(2\,a\,d+3\,b\,c\right)}{10}","Not used",1,"x^6*((b^2*c^3)/6 + (a^2*c*d^2)/2 + a*b*c^2*d) + x^8*((a^2*d^3)/8 + (3*b^2*c^2*d)/8 + (3*a*b*c*d^2)/4) + (a^2*c^3*x^2)/2 + (b^2*d^3*x^12)/12 + (a*c^2*x^4*(3*a*d + 2*b*c))/4 + (b*d^2*x^10*(2*a*d + 3*b*c))/10","B"
163,1,116,122,0.038786,"\text{Not used}","int((a + b*x^2)^2*(c + d*x^2)^3,x)","x^5\,\left(\frac{3\,a^2\,c\,d^2}{5}+\frac{6\,a\,b\,c^2\,d}{5}+\frac{b^2\,c^3}{5}\right)+x^7\,\left(\frac{a^2\,d^3}{7}+\frac{6\,a\,b\,c\,d^2}{7}+\frac{3\,b^2\,c^2\,d}{7}\right)+a^2\,c^3\,x+\frac{b^2\,d^3\,x^{11}}{11}+\frac{a\,c^2\,x^3\,\left(3\,a\,d+2\,b\,c\right)}{3}+\frac{b\,d^2\,x^9\,\left(2\,a\,d+3\,b\,c\right)}{9}","Not used",1,"x^5*((b^2*c^3)/5 + (3*a^2*c*d^2)/5 + (6*a*b*c^2*d)/5) + x^7*((a^2*d^3)/7 + (3*b^2*c^2*d)/7 + (6*a*b*c*d^2)/7) + a^2*c^3*x + (b^2*d^3*x^11)/11 + (a*c^2*x^3*(3*a*d + 2*b*c))/3 + (b*d^2*x^9*(2*a*d + 3*b*c))/9","B"
164,1,116,123,0.043332,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^3)/x,x)","x^4\,\left(\frac{3\,a^2\,c\,d^2}{4}+\frac{3\,a\,b\,c^2\,d}{2}+\frac{b^2\,c^3}{4}\right)+x^6\,\left(\frac{a^2\,d^3}{6}+a\,b\,c\,d^2+\frac{b^2\,c^2\,d}{2}\right)+\frac{b^2\,d^3\,x^{10}}{10}+a^2\,c^3\,\ln\left(x\right)+\frac{a\,c^2\,x^2\,\left(3\,a\,d+2\,b\,c\right)}{2}+\frac{b\,d^2\,x^8\,\left(2\,a\,d+3\,b\,c\right)}{8}","Not used",1,"x^4*((b^2*c^3)/4 + (3*a^2*c*d^2)/4 + (3*a*b*c^2*d)/2) + x^6*((a^2*d^3)/6 + (b^2*c^2*d)/2 + a*b*c*d^2) + (b^2*d^3*x^10)/10 + a^2*c^3*log(x) + (a*c^2*x^2*(3*a*d + 2*b*c))/2 + (b*d^2*x^8*(2*a*d + 3*b*c))/8","B"
165,1,115,120,0.086979,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^3)/x^2,x)","x^3\,\left(a^2\,c\,d^2+2\,a\,b\,c^2\,d+\frac{b^2\,c^3}{3}\right)+x^5\,\left(\frac{a^2\,d^3}{5}+\frac{6\,a\,b\,c\,d^2}{5}+\frac{3\,b^2\,c^2\,d}{5}\right)-\frac{a^2\,c^3}{x}+\frac{b^2\,d^3\,x^9}{9}+\frac{b\,d^2\,x^7\,\left(2\,a\,d+3\,b\,c\right)}{7}+a\,c^2\,x\,\left(3\,a\,d+2\,b\,c\right)","Not used",1,"x^3*((b^2*c^3)/3 + a^2*c*d^2 + 2*a*b*c^2*d) + x^5*((a^2*d^3)/5 + (3*b^2*c^2*d)/5 + (6*a*b*c*d^2)/5) - (a^2*c^3)/x + (b^2*d^3*x^9)/9 + (b*d^2*x^7*(2*a*d + 3*b*c))/7 + a*c^2*x*(3*a*d + 2*b*c)","B"
166,1,121,123,0.090442,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^3)/x^3,x)","x^2\,\left(\frac{3\,a^2\,c\,d^2}{2}+3\,a\,b\,c^2\,d+\frac{b^2\,c^3}{2}\right)+x^4\,\left(\frac{a^2\,d^3}{4}+\frac{3\,a\,b\,c\,d^2}{2}+\frac{3\,b^2\,c^2\,d}{4}\right)+\ln\left(x\right)\,\left(3\,d\,a^2\,c^2+2\,b\,a\,c^3\right)-\frac{a^2\,c^3}{2\,x^2}+\frac{b^2\,d^3\,x^8}{8}+\frac{b\,d^2\,x^6\,\left(2\,a\,d+3\,b\,c\right)}{6}","Not used",1,"x^2*((b^2*c^3)/2 + (3*a^2*c*d^2)/2 + 3*a*b*c^2*d) + x^4*((a^2*d^3)/4 + (3*b^2*c^2*d)/4 + (3*a*b*c*d^2)/2) + log(x)*(3*a^2*c^2*d + 2*a*b*c^3) - (a^2*c^3)/(2*x^2) + (b^2*d^3*x^8)/8 + (b*d^2*x^6*(2*a*d + 3*b*c))/6","B"
167,1,121,120,0.040914,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^3)/x^4,x)","x^3\,\left(\frac{a^2\,d^3}{3}+2\,a\,b\,c\,d^2+b^2\,c^2\,d\right)-\frac{x^2\,\left(3\,d\,a^2\,c^2+2\,b\,a\,c^3\right)+\frac{a^2\,c^3}{3}}{x^3}+x\,\left(3\,a^2\,c\,d^2+6\,a\,b\,c^2\,d+b^2\,c^3\right)+\frac{b^2\,d^3\,x^7}{7}+\frac{b\,d^2\,x^5\,\left(2\,a\,d+3\,b\,c\right)}{5}","Not used",1,"x^3*((a^2*d^3)/3 + b^2*c^2*d + 2*a*b*c*d^2) - (x^2*(3*a^2*c^2*d + 2*a*b*c^3) + (a^2*c^3)/3)/x^3 + x*(b^2*c^3 + 3*a^2*c*d^2 + 6*a*b*c^2*d) + (b^2*d^3*x^7)/7 + (b*d^2*x^5*(2*a*d + 3*b*c))/5","B"
168,1,169,104,0.057231,"\text{Not used}","int((x^4*(a + b*x^2)^2)/(c + d*x^2),x)","x^3\,\left(\frac{a^2}{3\,d}+\frac{c\,\left(\frac{b^2\,c}{d^2}-\frac{2\,a\,b}{d}\right)}{3\,d}\right)-x^5\,\left(\frac{b^2\,c}{5\,d^2}-\frac{2\,a\,b}{5\,d}\right)+\frac{b^2\,x^7}{7\,d}+\frac{c^{3/2}\,\mathrm{atan}\left(\frac{c^{3/2}\,\sqrt{d}\,x\,{\left(a\,d-b\,c\right)}^2}{a^2\,c^2\,d^2-2\,a\,b\,c^3\,d+b^2\,c^4}\right)\,{\left(a\,d-b\,c\right)}^2}{d^{9/2}}-\frac{c\,x\,\left(\frac{a^2}{d}+\frac{c\,\left(\frac{b^2\,c}{d^2}-\frac{2\,a\,b}{d}\right)}{d}\right)}{d}","Not used",1,"x^3*(a^2/(3*d) + (c*((b^2*c)/d^2 - (2*a*b)/d))/(3*d)) - x^5*((b^2*c)/(5*d^2) - (2*a*b)/(5*d)) + (b^2*x^7)/(7*d) + (c^(3/2)*atan((c^(3/2)*d^(1/2)*x*(a*d - b*c)^2)/(b^2*c^4 + a^2*c^2*d^2 - 2*a*b*c^3*d))*(a*d - b*c)^2)/d^(9/2) - (c*x*(a^2/d + (c*((b^2*c)/d^2 - (2*a*b)/d))/d))/d","B"
169,1,106,79,0.062426,"\text{Not used}","int((x^3*(a + b*x^2)^2)/(c + d*x^2),x)","x^2\,\left(\frac{a^2}{2\,d}+\frac{c\,\left(\frac{b^2\,c}{d^2}-\frac{2\,a\,b}{d}\right)}{2\,d}\right)-x^4\,\left(\frac{b^2\,c}{4\,d^2}-\frac{a\,b}{2\,d}\right)+\frac{b^2\,x^6}{6\,d}-\frac{\ln\left(d\,x^2+c\right)\,\left(a^2\,c\,d^2-2\,a\,b\,c^2\,d+b^2\,c^3\right)}{2\,d^4}","Not used",1,"x^2*(a^2/(2*d) + (c*((b^2*c)/d^2 - (2*a*b)/d))/(2*d)) - x^4*((b^2*c)/(4*d^2) - (a*b)/(2*d)) + (b^2*x^6)/(6*d) - (log(c + d*x^2)*(b^2*c^3 + a^2*c*d^2 - 2*a*b*c^2*d))/(2*d^4)","B"
170,1,128,83,0.061916,"\text{Not used}","int((x^2*(a + b*x^2)^2)/(c + d*x^2),x)","x\,\left(\frac{a^2}{d}+\frac{c\,\left(\frac{b^2\,c}{d^2}-\frac{2\,a\,b}{d}\right)}{d}\right)-x^3\,\left(\frac{b^2\,c}{3\,d^2}-\frac{2\,a\,b}{3\,d}\right)+\frac{b^2\,x^5}{5\,d}-\frac{\sqrt{c}\,\mathrm{atan}\left(\frac{\sqrt{c}\,\sqrt{d}\,x\,{\left(a\,d-b\,c\right)}^2}{a^2\,c\,d^2-2\,a\,b\,c^2\,d+b^2\,c^3}\right)\,{\left(a\,d-b\,c\right)}^2}{d^{7/2}}","Not used",1,"x*(a^2/d + (c*((b^2*c)/d^2 - (2*a*b)/d))/d) - x^3*((b^2*c)/(3*d^2) - (2*a*b)/(3*d)) + (b^2*x^5)/(5*d) - (c^(1/2)*atan((c^(1/2)*d^(1/2)*x*(a*d - b*c)^2)/(b^2*c^3 + a^2*c*d^2 - 2*a*b*c^2*d))*(a*d - b*c)^2)/d^(7/2)","B"
171,1,68,61,0.115956,"\text{Not used}","int((x*(a + b*x^2)^2)/(c + d*x^2),x)","\frac{b^2\,x^4}{4\,d}-x^2\,\left(\frac{b^2\,c}{2\,d^2}-\frac{a\,b}{d}\right)+\frac{\ln\left(d\,x^2+c\right)\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}{2\,d^3}","Not used",1,"(b^2*x^4)/(4*d) - x^2*((b^2*c)/(2*d^2) - (a*b)/d) + (log(c + d*x^2)*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/(2*d^3)","B"
172,1,90,63,0.073913,"\text{Not used}","int((a + b*x^2)^2/(c + d*x^2),x)","\frac{b^2\,x^3}{3\,d}-x\,\left(\frac{b^2\,c}{d^2}-\frac{2\,a\,b}{d}\right)+\frac{\mathrm{atan}\left(\frac{\sqrt{d}\,x\,{\left(a\,d-b\,c\right)}^2}{\sqrt{c}\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}\right)\,{\left(a\,d-b\,c\right)}^2}{\sqrt{c}\,d^{5/2}}","Not used",1,"(b^2*x^3)/(3*d) - x*((b^2*c)/d^2 - (2*a*b)/d) + (atan((d^(1/2)*x*(a*d - b*c)^2)/(c^(1/2)*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)))*(a*d - b*c)^2)/(c^(1/2)*d^(5/2))","B"
173,1,58,51,0.158967,"\text{Not used}","int((a + b*x^2)^2/(x*(c + d*x^2)),x)","\frac{b^2\,x^2}{2\,d}+\frac{a^2\,\ln\left(x\right)}{c}-\frac{\ln\left(d\,x^2+c\right)\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}{2\,c\,d^2}","Not used",1,"(b^2*x^2)/(2*d) + (a^2*log(x))/c - (log(c + d*x^2)*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/(2*c*d^2)","B"
174,1,80,55,0.124289,"\text{Not used}","int((a + b*x^2)^2/(x^2*(c + d*x^2)),x)","\frac{b^2\,x}{d}-\frac{a^2}{c\,x}-\frac{\mathrm{atan}\left(\frac{\sqrt{d}\,x\,{\left(a\,d-b\,c\right)}^2}{\sqrt{c}\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}\right)\,{\left(a\,d-b\,c\right)}^2}{c^{3/2}\,d^{3/2}}","Not used",1,"(b^2*x)/d - a^2/(c*x) - (atan((d^(1/2)*x*(a*d - b*c)^2)/(c^(1/2)*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)))*(a*d - b*c)^2)/(c^(3/2)*d^(3/2))","B"
175,1,67,58,0.172936,"\text{Not used}","int((a + b*x^2)^2/(x^3*(c + d*x^2)),x)","\frac{\ln\left(d\,x^2+c\right)\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}{2\,c^2\,d}-\frac{a^2}{2\,c\,x^2}-\frac{\ln\left(x\right)\,\left(a^2\,d-2\,a\,b\,c\right)}{c^2}","Not used",1,"(log(c + d*x^2)*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/(2*c^2*d) - a^2/(2*c*x^2) - (log(x)*(a^2*d - 2*a*b*c))/c^2","B"
176,1,90,66,0.131439,"\text{Not used}","int((a + b*x^2)^2/(x^4*(c + d*x^2)),x)","\frac{a^2\,d}{c^2\,x}-\frac{a^2}{3\,c\,x^3}+\frac{a^2\,d^{3/2}\,\mathrm{atan}\left(\frac{\sqrt{d}\,x}{\sqrt{c}}\right)}{c^{5/2}}+\frac{b^2\,\mathrm{atan}\left(\frac{\sqrt{d}\,x}{\sqrt{c}}\right)}{\sqrt{c}\,\sqrt{d}}-\frac{2\,a\,b}{c\,x}-\frac{2\,a\,b\,\sqrt{d}\,\mathrm{atan}\left(\frac{\sqrt{d}\,x}{\sqrt{c}}\right)}{c^{3/2}}","Not used",1,"(a^2*d)/(c^2*x) - a^2/(3*c*x^3) + (a^2*d^(3/2)*atan((d^(1/2)*x)/c^(1/2)))/c^(5/2) + (b^2*atan((d^(1/2)*x)/c^(1/2)))/(c^(1/2)*d^(1/2)) - (2*a*b)/(c*x) - (2*a*b*d^(1/2)*atan((d^(1/2)*x)/c^(1/2)))/c^(3/2)","B"
177,1,93,75,0.160129,"\text{Not used}","int((a + b*x^2)^2/(x^5*(c + d*x^2)),x)","\frac{\ln\left(x\right)\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}{c^3}-\frac{\frac{a^2}{4\,c}-\frac{a\,x^2\,\left(a\,d-2\,b\,c\right)}{2\,c^2}}{x^4}-\frac{\ln\left(d\,x^2+c\right)\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}{2\,c^3}","Not used",1,"(log(x)*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/c^3 - (a^2/(4*c) - (a*x^2*(a*d - 2*b*c))/(2*c^2))/x^4 - (log(c + d*x^2)*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/(2*c^3)","B"
178,1,129,87,0.089090,"\text{Not used}","int((a + b*x^2)^2/(x^6*(c + d*x^2)),x)","\frac{a^2\,d}{3\,c^2\,x^3}-\frac{b^2}{c\,x}-\frac{a^2}{5\,c\,x^5}-\frac{a^2\,d^{5/2}\,\mathrm{atan}\left(\frac{\sqrt{d}\,x}{\sqrt{c}}\right)}{c^{7/2}}-\frac{b^2\,\sqrt{d}\,\mathrm{atan}\left(\frac{\sqrt{d}\,x}{\sqrt{c}}\right)}{c^{3/2}}-\frac{a^2\,d^2}{c^3\,x}-\frac{2\,a\,b}{3\,c\,x^3}+\frac{2\,a\,b\,d}{c^2\,x}+\frac{2\,a\,b\,d^{3/2}\,\mathrm{atan}\left(\frac{\sqrt{d}\,x}{\sqrt{c}}\right)}{c^{5/2}}","Not used",1,"(a^2*d)/(3*c^2*x^3) - b^2/(c*x) - a^2/(5*c*x^5) - (a^2*d^(5/2)*atan((d^(1/2)*x)/c^(1/2)))/c^(7/2) - (b^2*d^(1/2)*atan((d^(1/2)*x)/c^(1/2)))/c^(3/2) - (a^2*d^2)/(c^3*x) - (2*a*b)/(3*c*x^3) + (2*a*b*d)/(c^2*x) + (2*a*b*d^(3/2)*atan((d^(1/2)*x)/c^(1/2)))/c^(5/2)","B"
179,1,129,98,0.124596,"\text{Not used}","int((a + b*x^2)^2/(x^7*(c + d*x^2)),x)","\frac{\ln\left(d\,x^2+c\right)\,\left(a^2\,d^3-2\,a\,b\,c\,d^2+b^2\,c^2\,d\right)}{2\,c^4}-\frac{\frac{a^2}{6\,c}+\frac{x^4\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}{2\,c^3}-\frac{a\,x^2\,\left(a\,d-2\,b\,c\right)}{4\,c^2}}{x^6}-\frac{\ln\left(x\right)\,\left(a^2\,d^3-2\,a\,b\,c\,d^2+b^2\,c^2\,d\right)}{c^4}","Not used",1,"(log(c + d*x^2)*(a^2*d^3 + b^2*c^2*d - 2*a*b*c*d^2))/(2*c^4) - (a^2/(6*c) + (x^4*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/(2*c^3) - (a*x^2*(a*d - 2*b*c))/(4*c^2))/x^6 - (log(x)*(a^2*d^3 + b^2*c^2*d - 2*a*b*c*d^2))/c^4","B"
180,1,200,145,0.136706,"\text{Not used}","int((x^4*(a + b*x^2)^2)/(c + d*x^2)^2,x)","x\,\left(\frac{a^2}{d^2}+\frac{2\,c\,\left(\frac{2\,b^2\,c}{d^3}-\frac{2\,a\,b}{d^2}\right)}{d}-\frac{b^2\,c^2}{d^4}\right)-x^3\,\left(\frac{2\,b^2\,c}{3\,d^3}-\frac{2\,a\,b}{3\,d^2}\right)+\frac{b^2\,x^5}{5\,d^2}+\frac{x\,\left(\frac{a^2\,c\,d^2}{2}-a\,b\,c^2\,d+\frac{b^2\,c^3}{2}\right)}{d^5\,x^2+c\,d^4}-\frac{\sqrt{c}\,\mathrm{atan}\left(\frac{\sqrt{c}\,\sqrt{d}\,x\,\left(a\,d-b\,c\right)\,\left(3\,a\,d-7\,b\,c\right)}{3\,a^2\,c\,d^2-10\,a\,b\,c^2\,d+7\,b^2\,c^3}\right)\,\left(a\,d-b\,c\right)\,\left(3\,a\,d-7\,b\,c\right)}{2\,d^{9/2}}","Not used",1,"x*(a^2/d^2 + (2*c*((2*b^2*c)/d^3 - (2*a*b)/d^2))/d - (b^2*c^2)/d^4) - x^3*((2*b^2*c)/(3*d^3) - (2*a*b)/(3*d^2)) + (b^2*x^5)/(5*d^2) + (x*((b^2*c^3)/2 + (a^2*c*d^2)/2 - a*b*c^2*d))/(c*d^4 + d^5*x^2) - (c^(1/2)*atan((c^(1/2)*d^(1/2)*x*(a*d - b*c)*(3*a*d - 7*b*c))/(7*b^2*c^3 + 3*a^2*c*d^2 - 10*a*b*c^2*d))*(a*d - b*c)*(3*a*d - 7*b*c))/(2*d^(9/2))","B"
181,1,112,90,0.121941,"\text{Not used}","int((x^3*(a + b*x^2)^2)/(c + d*x^2)^2,x)","\frac{a^2\,c\,d^2-2\,a\,b\,c^2\,d+b^2\,c^3}{2\,d\,\left(d^4\,x^2+c\,d^3\right)}-x^2\,\left(\frac{b^2\,c}{d^3}-\frac{a\,b}{d^2}\right)+\frac{b^2\,x^4}{4\,d^2}+\frac{\ln\left(d\,x^2+c\right)\,\left(a^2\,d^2-4\,a\,b\,c\,d+3\,b^2\,c^2\right)}{2\,d^4}","Not used",1,"(b^2*c^3 + a^2*c*d^2 - 2*a*b*c^2*d)/(2*d*(c*d^3 + d^4*x^2)) - x^2*((b^2*c)/d^3 - (a*b)/d^2) + (b^2*x^4)/(4*d^2) + (log(c + d*x^2)*(a^2*d^2 + 3*b^2*c^2 - 4*a*b*c*d))/(2*d^4)","B"
182,1,146,118,0.078999,"\text{Not used}","int((x^2*(a + b*x^2)^2)/(c + d*x^2)^2,x)","\frac{b^2\,x^3}{3\,d^2}-\frac{x\,\left(\frac{a^2\,d^2}{2}-a\,b\,c\,d+\frac{b^2\,c^2}{2}\right)}{d^4\,x^2+c\,d^3}-x\,\left(\frac{2\,b^2\,c}{d^3}-\frac{2\,a\,b}{d^2}\right)+\frac{\mathrm{atan}\left(\frac{\sqrt{d}\,x\,\left(a\,d-b\,c\right)\,\left(a\,d-5\,b\,c\right)}{\sqrt{c}\,\left(a^2\,d^2-6\,a\,b\,c\,d+5\,b^2\,c^2\right)}\right)\,\left(a\,d-b\,c\right)\,\left(a\,d-5\,b\,c\right)}{2\,\sqrt{c}\,d^{7/2}}","Not used",1,"(b^2*x^3)/(3*d^2) - (x*((a^2*d^2)/2 + (b^2*c^2)/2 - a*b*c*d))/(c*d^3 + d^4*x^2) - x*((2*b^2*c)/d^3 - (2*a*b)/d^2) + (atan((d^(1/2)*x*(a*d - b*c)*(a*d - 5*b*c))/(c^(1/2)*(a^2*d^2 + 5*b^2*c^2 - 6*a*b*c*d)))*(a*d - b*c)*(a*d - 5*b*c))/(2*c^(1/2)*d^(7/2))","B"
183,1,77,62,0.082762,"\text{Not used}","int((x*(a + b*x^2)^2)/(c + d*x^2)^2,x)","\frac{b^2\,x^2}{2\,d^2}-\frac{a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2}{2\,d\,\left(d^3\,x^2+c\,d^2\right)}-\frac{\ln\left(d\,x^2+c\right)\,\left(b^2\,c-a\,b\,d\right)}{d^3}","Not used",1,"(b^2*x^2)/(2*d^2) - (a^2*d^2 + b^2*c^2 - 2*a*b*c*d)/(2*d*(c*d^2 + d^3*x^2)) - (log(c + d*x^2)*(b^2*c - a*b*d))/d^3","B"
184,1,124,82,0.158386,"\text{Not used}","int((a + b*x^2)^2/(c + d*x^2)^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)}{2\,c\,\left(d^3\,x^2+c\,d^2\right)}+\frac{\mathrm{atan}\left(\frac{\sqrt{d}\,x\,\left(a\,d-b\,c\right)\,\left(a\,d+3\,b\,c\right)}{\sqrt{c}\,\left(a^2\,d^2+2\,a\,b\,c\,d-3\,b^2\,c^2\right)}\right)\,\left(a\,d-b\,c\right)\,\left(a\,d+3\,b\,c\right)}{2\,c^{3/2}\,d^{5/2}}","Not used",1,"(b^2*x)/d^2 + (x*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/(2*c*(c*d^2 + d^3*x^2)) + (atan((d^(1/2)*x*(a*d - b*c)*(a*d + 3*b*c))/(c^(1/2)*(a^2*d^2 - 3*b^2*c^2 + 2*a*b*c*d)))*(a*d - b*c)*(a*d + 3*b*c))/(2*c^(3/2)*d^(5/2))","B"
185,1,80,67,0.124310,"\text{Not used}","int((a + b*x^2)^2/(x*(c + d*x^2)^2),x)","\frac{a^2\,\ln\left(x\right)}{c^2}+\frac{a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2}{2\,c\,d^2\,\left(d\,x^2+c\right)}-\frac{\ln\left(d\,x^2+c\right)\,\left(a^2\,d^2-b^2\,c^2\right)}{2\,c^2\,d^2}","Not used",1,"(a^2*log(x))/c^2 + (a^2*d^2 + b^2*c^2 - 2*a*b*c*d)/(2*c*d^2*(c + d*x^2)) - (log(c + d*x^2)*(a^2*d^2 - b^2*c^2))/(2*c^2*d^2)","B"
186,1,128,106,0.190242,"\text{Not used}","int((a + b*x^2)^2/(x^2*(c + d*x^2)^2),x)","\frac{\mathrm{atan}\left(\frac{\sqrt{d}\,x\,\left(a\,d-b\,c\right)\,\left(3\,a\,d+b\,c\right)}{\sqrt{c}\,\left(-3\,a^2\,d^2+2\,a\,b\,c\,d+b^2\,c^2\right)}\right)\,\left(a\,d-b\,c\right)\,\left(3\,a\,d+b\,c\right)}{2\,c^{5/2}\,d^{3/2}}-\frac{\frac{a^2}{c}+\frac{x^2\,\left(3\,a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}{2\,c^2\,d}}{d\,x^3+c\,x}","Not used",1,"(atan((d^(1/2)*x*(a*d - b*c)*(3*a*d + b*c))/(c^(1/2)*(b^2*c^2 - 3*a^2*d^2 + 2*a*b*c*d)))*(a*d - b*c)*(3*a*d + b*c))/(2*c^(5/2)*d^(3/2)) - (a^2/c + (x^2*(3*a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/(2*c^2*d))/(c*x + d*x^3)","B"
187,1,100,81,0.092158,"\text{Not used}","int((a + b*x^2)^2/(x^3*(c + d*x^2)^2),x)","\frac{\ln\left(d\,x^2+c\right)\,\left(a^2\,d-a\,b\,c\right)}{c^3}-\frac{\frac{a^2}{2\,c}+\frac{x^2\,\left(2\,a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}{2\,c^2\,d}}{d\,x^4+c\,x^2}-\frac{\ln\left(x\right)\,\left(2\,a^2\,d-2\,a\,b\,c\right)}{c^3}","Not used",1,"(log(c + d*x^2)*(a^2*d - a*b*c))/c^3 - (a^2/(2*c) + (x^2*(2*a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/(2*c^2*d))/(c*x^2 + d*x^4) - (log(x)*(2*a^2*d - 2*a*b*c))/c^3","B"
188,1,147,126,0.191708,"\text{Not used}","int((a + b*x^2)^2/(x^4*(c + d*x^2)^2),x)","\frac{\frac{x^4\,\left(5\,a^2\,d^2-6\,a\,b\,c\,d+b^2\,c^2\right)}{2\,c^3}-\frac{a^2}{3\,c}+\frac{a\,x^2\,\left(5\,a\,d-6\,b\,c\right)}{3\,c^2}}{d\,x^5+c\,x^3}+\frac{\mathrm{atan}\left(\frac{\sqrt{d}\,x\,\left(a\,d-b\,c\right)\,\left(5\,a\,d-b\,c\right)}{\sqrt{c}\,\left(5\,a^2\,d^2-6\,a\,b\,c\,d+b^2\,c^2\right)}\right)\,\left(a\,d-b\,c\right)\,\left(5\,a\,d-b\,c\right)}{2\,c^{7/2}\,\sqrt{d}}","Not used",1,"((x^4*(5*a^2*d^2 + b^2*c^2 - 6*a*b*c*d))/(2*c^3) - a^2/(3*c) + (a*x^2*(5*a*d - 6*b*c))/(3*c^2))/(c*x^3 + d*x^5) + (atan((d^(1/2)*x*(a*d - b*c)*(5*a*d - b*c))/(c^(1/2)*(5*a^2*d^2 + b^2*c^2 - 6*a*b*c*d)))*(a*d - b*c)*(5*a*d - b*c))/(2*c^(7/2)*d^(1/2))","B"
189,1,159,163,0.159684,"\text{Not used}","int((x^4*(a + b*x^2)^2)/(c + d*x^2)^3,x)","\frac{b^2\,x^3}{3\,d^3}-\frac{\left(\frac{5\,a^2\,d^3}{8}-\frac{9\,a\,b\,c\,d^2}{4}+\frac{13\,b^2\,c^2\,d}{8}\right)\,x^3+\left(\frac{3\,a^2\,c\,d^2}{8}-\frac{7\,a\,b\,c^2\,d}{4}+\frac{11\,b^2\,c^3}{8}\right)\,x}{c^2\,d^4+2\,c\,d^5\,x^2+d^6\,x^4}-x\,\left(\frac{3\,b^2\,c}{d^4}-\frac{2\,a\,b}{d^3}\right)+\frac{\mathrm{atan}\left(\frac{\sqrt{d}\,x}{\sqrt{c}}\right)\,\left(3\,a^2\,d^2-30\,a\,b\,c\,d+35\,b^2\,c^2\right)}{8\,\sqrt{c}\,d^{9/2}}","Not used",1,"(b^2*x^3)/(3*d^3) - (x^3*((5*a^2*d^3)/8 + (13*b^2*c^2*d)/8 - (9*a*b*c*d^2)/4) + x*((11*b^2*c^3)/8 + (3*a^2*c*d^2)/8 - (7*a*b*c^2*d)/4))/(c^2*d^4 + d^6*x^4 + 2*c*d^5*x^2) - x*((3*b^2*c)/d^4 - (2*a*b)/d^3) + (atan((d^(1/2)*x)/c^(1/2))*(3*a^2*d^2 + 35*b^2*c^2 - 30*a*b*c*d))/(8*c^(1/2)*d^(9/2))","B"
190,1,123,99,0.146980,"\text{Not used}","int((x^3*(a + b*x^2)^2)/(c + d*x^2)^3,x)","\frac{b^2\,x^2}{2\,d^3}-\frac{\ln\left(d\,x^2+c\right)\,\left(3\,b^2\,c-2\,a\,b\,d\right)}{2\,d^4}-\frac{x^2\,\left(\frac{a^2\,d^2}{2}-2\,a\,b\,c\,d+\frac{3\,b^2\,c^2}{2}\right)+\frac{a^2\,c\,d^2-6\,a\,b\,c^2\,d+5\,b^2\,c^3}{4\,d}}{c^2\,d^3+2\,c\,d^4\,x^2+d^5\,x^4}","Not used",1,"(b^2*x^2)/(2*d^3) - (log(c + d*x^2)*(3*b^2*c - 2*a*b*d))/(2*d^4) - (x^2*((a^2*d^2)/2 + (3*b^2*c^2)/2 - 2*a*b*c*d) + (5*b^2*c^3 + a^2*c*d^2 - 6*a*b*c^2*d)/(4*d))/(c^2*d^3 + d^5*x^4 + 2*c*d^4*x^2)","B"
191,1,135,127,0.174298,"\text{Not used}","int((x^2*(a + b*x^2)^2)/(c + d*x^2)^3,x)","\frac{b^2\,x}{d^3}-\frac{x\,\left(\frac{a^2\,d^2}{8}+\frac{3\,a\,b\,c\,d}{4}-\frac{7\,b^2\,c^2}{8}\right)-\frac{x^3\,\left(a^2\,d^3-10\,a\,b\,c\,d^2+9\,b^2\,c^2\,d\right)}{8\,c}}{c^2\,d^3+2\,c\,d^4\,x^2+d^5\,x^4}+\frac{\mathrm{atan}\left(\frac{\sqrt{d}\,x}{\sqrt{c}}\right)\,\left(a^2\,d^2+6\,a\,b\,c\,d-15\,b^2\,c^2\right)}{8\,c^{3/2}\,d^{7/2}}","Not used",1,"(b^2*x)/d^3 - (x*((a^2*d^2)/8 - (7*b^2*c^2)/8 + (3*a*b*c*d)/4) - (x^3*(a^2*d^3 + 9*b^2*c^2*d - 10*a*b*c*d^2))/(8*c))/(c^2*d^3 + d^5*x^4 + 2*c*d^4*x^2) + (atan((d^(1/2)*x)/c^(1/2))*(a^2*d^2 - 15*b^2*c^2 + 6*a*b*c*d))/(8*c^(3/2)*d^(7/2))","B"
192,1,83,67,0.071269,"\text{Not used}","int((x*(a + b*x^2)^2)/(c + d*x^2)^3,x)","\frac{b^2\,\ln\left(d\,x^2+c\right)}{2\,d^3}-\frac{\frac{a^2\,d^2+2\,a\,b\,c\,d-3\,b^2\,c^2}{4\,d^3}+\frac{b\,x^2\,\left(a\,d-b\,c\right)}{d^2}}{c^2+2\,c\,d\,x^2+d^2\,x^4}","Not used",1,"(b^2*log(c + d*x^2))/(2*d^3) - ((a^2*d^2 - 3*b^2*c^2 + 2*a*b*c*d)/(4*d^3) + (b*x^2*(a*d - b*c))/d^2)/(c^2 + d^2*x^4 + 2*c*d*x^2)","B"
193,1,130,116,0.199137,"\text{Not used}","int((a + b*x^2)^2/(c + d*x^2)^3,x)","\frac{\mathrm{atan}\left(\frac{\sqrt{d}\,x}{\sqrt{c}}\right)\,\left(3\,a^2\,d^2+2\,a\,b\,c\,d+3\,b^2\,c^2\right)}{8\,c^{5/2}\,d^{5/2}}-\frac{\frac{x\,\left(-5\,a^2\,d^2+2\,a\,b\,c\,d+3\,b^2\,c^2\right)}{8\,c\,d^2}-\frac{x^3\,\left(3\,a^2\,d^2+2\,a\,b\,c\,d-5\,b^2\,c^2\right)}{8\,c^2\,d}}{c^2+2\,c\,d\,x^2+d^2\,x^4}","Not used",1,"(atan((d^(1/2)*x)/c^(1/2))*(3*a^2*d^2 + 3*b^2*c^2 + 2*a*b*c*d))/(8*c^(5/2)*d^(5/2)) - ((x*(3*b^2*c^2 - 5*a^2*d^2 + 2*a*b*c*d))/(8*c*d^2) - (x^3*(3*a^2*d^2 - 5*b^2*c^2 + 2*a*b*c*d))/(8*c^2*d))/(c^2 + d^2*x^4 + 2*c*d*x^2)","B"
194,1,106,86,0.126436,"\text{Not used}","int((a + b*x^2)^2/(x*(c + d*x^2)^3),x)","\frac{a^2\,\ln\left(x\right)}{c^3}-\frac{a^2\,\ln\left(d\,x^2+c\right)}{2\,c^3}-\frac{\frac{-3\,a^2\,d^2+2\,a\,b\,c\,d+b^2\,c^2}{4\,c\,d^2}-\frac{x^2\,\left(a^2\,d^2-b^2\,c^2\right)}{2\,c^2\,d}}{c^2+2\,c\,d\,x^2+d^2\,x^4}","Not used",1,"(a^2*log(x))/c^3 - (a^2*log(c + d*x^2))/(2*c^3) - ((b^2*c^2 - 3*a^2*d^2 + 2*a*b*c*d)/(4*c*d^2) - (x^2*(a^2*d^2 - b^2*c^2))/(2*c^2*d))/(c^2 + d^2*x^4 + 2*c*d*x^2)","B"
195,1,135,152,0.182109,"\text{Not used}","int((a + b*x^2)^2/(x^2*(c + d*x^2)^3),x)","\frac{\mathrm{atan}\left(\frac{\sqrt{d}\,x}{\sqrt{c}}\right)\,\left(-15\,a^2\,d^2+6\,a\,b\,c\,d+b^2\,c^2\right)}{8\,c^{7/2}\,d^{3/2}}-\frac{\frac{a^2}{c}-\frac{x^4\,\left(-15\,a^2\,d^2+6\,a\,b\,c\,d+b^2\,c^2\right)}{8\,c^3}+\frac{x^2\,\left(25\,a^2\,d^2-10\,a\,b\,c\,d+b^2\,c^2\right)}{8\,c^2\,d}}{c^2\,x+2\,c\,d\,x^3+d^2\,x^5}","Not used",1,"(atan((d^(1/2)*x)/c^(1/2))*(b^2*c^2 - 15*a^2*d^2 + 6*a*b*c*d))/(8*c^(7/2)*d^(3/2)) - (a^2/c - (x^4*(b^2*c^2 - 15*a^2*d^2 + 6*a*b*c*d))/(8*c^3) + (x^2*(25*a^2*d^2 + b^2*c^2 - 10*a*b*c*d))/(8*c^2*d))/(c^2*x + d^2*x^5 + 2*c*d*x^3)","B"
196,1,132,106,0.113399,"\text{Not used}","int((a + b*x^2)^2/(x^3*(c + d*x^2)^3),x)","\frac{\ln\left(d\,x^2+c\right)\,\left(3\,a^2\,d-2\,a\,b\,c\right)}{2\,c^4}-\frac{\frac{a^2}{2\,c}+\frac{x^2\,\left(9\,a^2\,d^2-6\,a\,b\,c\,d+b^2\,c^2\right)}{4\,c^2\,d}+\frac{a\,d\,x^4\,\left(3\,a\,d-2\,b\,c\right)}{2\,c^3}}{c^2\,x^2+2\,c\,d\,x^4+d^2\,x^6}-\frac{\ln\left(x\right)\,\left(3\,a^2\,d-2\,a\,b\,c\right)}{c^4}","Not used",1,"(log(c + d*x^2)*(3*a^2*d - 2*a*b*c))/(2*c^4) - (a^2/(2*c) + (x^2*(9*a^2*d^2 + b^2*c^2 - 6*a*b*c*d))/(4*c^2*d) + (a*d*x^4*(3*a*d - 2*b*c))/(2*c^3))/(c^2*x^2 + d^2*x^6 + 2*c*d*x^4) - (log(x)*(3*a^2*d - 2*a*b*c))/c^4","B"
197,1,156,161,0.194934,"\text{Not used}","int((a + b*x^2)^2/(x^4*(c + d*x^2)^3),x)","\frac{\frac{5\,x^4\,\left(35\,a^2\,d^2-30\,a\,b\,c\,d+3\,b^2\,c^2\right)}{24\,c^3}-\frac{a^2}{3\,c}+\frac{a\,x^2\,\left(7\,a\,d-6\,b\,c\right)}{3\,c^2}+\frac{d\,x^6\,\left(35\,a^2\,d^2-30\,a\,b\,c\,d+3\,b^2\,c^2\right)}{8\,c^4}}{c^2\,x^3+2\,c\,d\,x^5+d^2\,x^7}+\frac{\mathrm{atan}\left(\frac{\sqrt{d}\,x}{\sqrt{c}}\right)\,\left(35\,a^2\,d^2-30\,a\,b\,c\,d+3\,b^2\,c^2\right)}{8\,c^{9/2}\,\sqrt{d}}","Not used",1,"((5*x^4*(35*a^2*d^2 + 3*b^2*c^2 - 30*a*b*c*d))/(24*c^3) - a^2/(3*c) + (a*x^2*(7*a*d - 6*b*c))/(3*c^2) + (d*x^6*(35*a^2*d^2 + 3*b^2*c^2 - 30*a*b*c*d))/(8*c^4))/(c^2*x^3 + d^2*x^7 + 2*c*d*x^5) + (atan((d^(1/2)*x)/c^(1/2))*(35*a^2*d^2 + 3*b^2*c^2 - 30*a*b*c*d))/(8*c^(9/2)*d^(1/2))","B"
198,1,76,75,0.116199,"\text{Not used}","int((x^5*(c + d*x^2))/(a + b*x^2),x)","x^4\,\left(\frac{c}{4\,b}-\frac{a\,d}{4\,b^2}\right)+\frac{d\,x^6}{6\,b}-\frac{\ln\left(b\,x^2+a\right)\,\left(a^3\,d-a^2\,b\,c\right)}{2\,b^4}-\frac{a\,x^2\,\left(\frac{c}{b}-\frac{a\,d}{b^2}\right)}{2\,b}","Not used",1,"x^4*(c/(4*b) - (a*d)/(4*b^2)) + (d*x^6)/(6*b) - (log(a + b*x^2)*(a^3*d - a^2*b*c))/(2*b^4) - (a*x^2*(c/b - (a*d)/b^2))/(2*b)","B"
199,1,96,77,0.116676,"\text{Not used}","int((x^4*(c + d*x^2))/(a + b*x^2),x)","x^3\,\left(\frac{c}{3\,b}-\frac{a\,d}{3\,b^2}\right)+\frac{d\,x^5}{5\,b}-\frac{a^{3/2}\,\mathrm{atan}\left(\frac{a^{3/2}\,\sqrt{b}\,x\,\left(a\,d-b\,c\right)}{a^3\,d-a^2\,b\,c}\right)\,\left(a\,d-b\,c\right)}{b^{7/2}}-\frac{a\,x\,\left(\frac{c}{b}-\frac{a\,d}{b^2}\right)}{b}","Not used",1,"x^3*(c/(3*b) - (a*d)/(3*b^2)) + (d*x^5)/(5*b) - (a^(3/2)*atan((a^(3/2)*b^(1/2)*x*(a*d - b*c))/(a^3*d - a^2*b*c))*(a*d - b*c))/b^(7/2) - (a*x*(c/b - (a*d)/b^2))/b","B"
200,1,52,54,0.063744,"\text{Not used}","int((x^3*(c + d*x^2))/(a + b*x^2),x)","x^2\,\left(\frac{c}{2\,b}-\frac{a\,d}{2\,b^2}\right)+\frac{\ln\left(b\,x^2+a\right)\,\left(a^2\,d-a\,b\,c\right)}{2\,b^3}+\frac{d\,x^4}{4\,b}","Not used",1,"x^2*(c/(2*b) - (a*d)/(2*b^2)) + (log(a + b*x^2)*(a^2*d - a*b*c))/(2*b^3) + (d*x^4)/(4*b)","B"
201,1,70,58,0.070047,"\text{Not used}","int((x^2*(c + d*x^2))/(a + b*x^2),x)","x\,\left(\frac{c}{b}-\frac{a\,d}{b^2}\right)+\frac{d\,x^3}{3\,b}+\frac{\sqrt{a}\,\mathrm{atan}\left(\frac{\sqrt{a}\,\sqrt{b}\,x\,\left(a\,d-b\,c\right)}{a^2\,d-a\,b\,c}\right)\,\left(a\,d-b\,c\right)}{b^{5/2}}","Not used",1,"x*(c/b - (a*d)/b^2) + (d*x^3)/(3*b) + (a^(1/2)*atan((a^(1/2)*b^(1/2)*x*(a*d - b*c))/(a^2*d - a*b*c))*(a*d - b*c))/b^(5/2)","B"
202,1,31,35,0.105043,"\text{Not used}","int((x*(c + d*x^2))/(a + b*x^2),x)","\frac{d\,x^2}{2\,b}-\frac{\ln\left(b\,x^2+a\right)\,\left(a\,d-b\,c\right)}{2\,b^2}","Not used",1,"(d*x^2)/(2*b) - (log(a + b*x^2)*(a*d - b*c))/(2*b^2)","B"
203,1,32,39,0.050736,"\text{Not used}","int((c + d*x^2)/(a + b*x^2),x)","\frac{d\,x}{b}-\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)\,\left(a\,d-b\,c\right)}{\sqrt{a}\,b^{3/2}}","Not used",1,"(d*x)/b - (atan((b^(1/2)*x)/a^(1/2))*(a*d - b*c))/(a^(1/2)*b^(3/2))","B"
204,1,32,34,0.075904,"\text{Not used}","int((c + d*x^2)/(x*(a + b*x^2)),x)","\frac{c\,\ln\left(x\right)}{a}+\frac{\ln\left(b\,x^2+a\right)\,\left(a\,d-b\,c\right)}{2\,a\,b}","Not used",1,"(c*log(x))/a + (log(a + b*x^2)*(a*d - b*c))/(2*a*b)","B"
205,1,34,43,0.111694,"\text{Not used}","int((c + d*x^2)/(x^2*(a + b*x^2)),x)","\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)\,\left(a\,d-b\,c\right)}{a^{3/2}\,\sqrt{b}}-\frac{c}{a\,x}","Not used",1,"(atan((b^(1/2)*x)/a^(1/2))*(a*d - b*c))/(a^(3/2)*b^(1/2)) - c/(a*x)","B"
206,1,45,50,0.145169,"\text{Not used}","int((c + d*x^2)/(x^3*(a + b*x^2)),x)","\frac{\ln\left(x\right)\,\left(a\,d-b\,c\right)}{a^2}-\frac{\ln\left(b\,x^2+a\right)\,\left(a\,d-b\,c\right)}{2\,a^2}-\frac{c}{2\,a\,x^2}","Not used",1,"(log(x)*(a*d - b*c))/a^2 - (log(a + b*x^2)*(a*d - b*c))/(2*a^2) - c/(2*a*x^2)","B"
207,1,53,59,0.120220,"\text{Not used}","int((c + d*x^2)/(x^4*(a + b*x^2)),x)","-\frac{\frac{c}{3\,a}+\frac{x^2\,\left(a\,d-b\,c\right)}{a^2}}{x^3}-\frac{\sqrt{b}\,\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)\,\left(a\,d-b\,c\right)}{a^{5/2}}","Not used",1,"- (c/(3*a) + (x^2*(a*d - b*c))/a^2)/x^3 - (b^(1/2)*atan((b^(1/2)*x)/a^(1/2))*(a*d - b*c))/a^(5/2)","B"
208,1,146,103,0.110368,"\text{Not used}","int((x^5*(c + d*x^2)^2)/(a + b*x^2),x)","x^4\,\left(\frac{c^2}{4\,b}+\frac{a\,\left(\frac{a\,d^2}{b^2}-\frac{2\,c\,d}{b}\right)}{4\,b}\right)-x^6\,\left(\frac{a\,d^2}{6\,b^2}-\frac{c\,d}{3\,b}\right)+\frac{\ln\left(b\,x^2+a\right)\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}{2\,b^5}+\frac{d^2\,x^8}{8\,b}-\frac{a\,x^2\,\left(\frac{c^2}{b}+\frac{a\,\left(\frac{a\,d^2}{b^2}-\frac{2\,c\,d}{b}\right)}{b}\right)}{2\,b}","Not used",1,"x^4*(c^2/(4*b) + (a*((a*d^2)/b^2 - (2*c*d)/b))/(4*b)) - x^6*((a*d^2)/(6*b^2) - (c*d)/(3*b)) + (log(a + b*x^2)*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d))/(2*b^5) + (d^2*x^8)/(8*b) - (a*x^2*(c^2/b + (a*((a*d^2)/b^2 - (2*c*d)/b))/b))/(2*b)","B"
209,1,169,105,0.096321,"\text{Not used}","int((x^4*(c + d*x^2)^2)/(a + b*x^2),x)","x^3\,\left(\frac{c^2}{3\,b}+\frac{a\,\left(\frac{a\,d^2}{b^2}-\frac{2\,c\,d}{b}\right)}{3\,b}\right)-x^5\,\left(\frac{a\,d^2}{5\,b^2}-\frac{2\,c\,d}{5\,b}\right)+\frac{d^2\,x^7}{7\,b}+\frac{a^{3/2}\,\mathrm{atan}\left(\frac{a^{3/2}\,\sqrt{b}\,x\,{\left(a\,d-b\,c\right)}^2}{a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2}\right)\,{\left(a\,d-b\,c\right)}^2}{b^{9/2}}-\frac{a\,x\,\left(\frac{c^2}{b}+\frac{a\,\left(\frac{a\,d^2}{b^2}-\frac{2\,c\,d}{b}\right)}{b}\right)}{b}","Not used",1,"x^3*(c^2/(3*b) + (a*((a*d^2)/b^2 - (2*c*d)/b))/(3*b)) - x^5*((a*d^2)/(5*b^2) - (2*c*d)/(5*b)) + (d^2*x^7)/(7*b) + (a^(3/2)*atan((a^(3/2)*b^(1/2)*x*(a*d - b*c)^2)/(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d))*(a*d - b*c)^2)/b^(9/2) - (a*x*(c^2/b + (a*((a*d^2)/b^2 - (2*c*d)/b))/b))/b","B"
210,1,106,80,0.113112,"\text{Not used}","int((x^3*(c + d*x^2)^2)/(a + b*x^2),x)","x^2\,\left(\frac{c^2}{2\,b}+\frac{a\,\left(\frac{a\,d^2}{b^2}-\frac{2\,c\,d}{b}\right)}{2\,b}\right)-x^4\,\left(\frac{a\,d^2}{4\,b^2}-\frac{c\,d}{2\,b}\right)-\frac{\ln\left(b\,x^2+a\right)\,\left(a^3\,d^2-2\,a^2\,b\,c\,d+a\,b^2\,c^2\right)}{2\,b^4}+\frac{d^2\,x^6}{6\,b}","Not used",1,"x^2*(c^2/(2*b) + (a*((a*d^2)/b^2 - (2*c*d)/b))/(2*b)) - x^4*((a*d^2)/(4*b^2) - (c*d)/(2*b)) - (log(a + b*x^2)*(a^3*d^2 + a*b^2*c^2 - 2*a^2*b*c*d))/(2*b^4) + (d^2*x^6)/(6*b)","B"
211,1,128,84,0.120359,"\text{Not used}","int((x^2*(c + d*x^2)^2)/(a + b*x^2),x)","x\,\left(\frac{c^2}{b}+\frac{a\,\left(\frac{a\,d^2}{b^2}-\frac{2\,c\,d}{b}\right)}{b}\right)-x^3\,\left(\frac{a\,d^2}{3\,b^2}-\frac{2\,c\,d}{3\,b}\right)+\frac{d^2\,x^5}{5\,b}-\frac{\sqrt{a}\,\mathrm{atan}\left(\frac{\sqrt{a}\,\sqrt{b}\,x\,{\left(a\,d-b\,c\right)}^2}{a^3\,d^2-2\,a^2\,b\,c\,d+a\,b^2\,c^2}\right)\,{\left(a\,d-b\,c\right)}^2}{b^{7/2}}","Not used",1,"x*(c^2/b + (a*((a*d^2)/b^2 - (2*c*d)/b))/b) - x^3*((a*d^2)/(3*b^2) - (2*c*d)/(3*b)) + (d^2*x^5)/(5*b) - (a^(1/2)*atan((a^(1/2)*b^(1/2)*x*(a*d - b*c)^2)/(a^3*d^2 + a*b^2*c^2 - 2*a^2*b*c*d))*(a*d - b*c)^2)/b^(7/2)","B"
212,1,68,61,0.064665,"\text{Not used}","int((x*(c + d*x^2)^2)/(a + b*x^2),x)","\frac{d^2\,x^4}{4\,b}-x^2\,\left(\frac{a\,d^2}{2\,b^2}-\frac{c\,d}{b}\right)+\frac{\ln\left(b\,x^2+a\right)\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}{2\,b^3}","Not used",1,"(d^2*x^4)/(4*b) - x^2*((a*d^2)/(2*b^2) - (c*d)/b) + (log(a + b*x^2)*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/(2*b^3)","B"
213,1,90,63,0.073673,"\text{Not used}","int((c + d*x^2)^2/(a + b*x^2),x)","\frac{d^2\,x^3}{3\,b}-x\,\left(\frac{a\,d^2}{b^2}-\frac{2\,c\,d}{b}\right)+\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x\,{\left(a\,d-b\,c\right)}^2}{\sqrt{a}\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}\right)\,{\left(a\,d-b\,c\right)}^2}{\sqrt{a}\,b^{5/2}}","Not used",1,"(d^2*x^3)/(3*b) - x*((a*d^2)/b^2 - (2*c*d)/b) + (atan((b^(1/2)*x*(a*d - b*c)^2)/(a^(1/2)*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)))*(a*d - b*c)^2)/(a^(1/2)*b^(5/2))","B"
214,1,58,51,0.166203,"\text{Not used}","int((c + d*x^2)^2/(x*(a + b*x^2)),x)","\frac{d^2\,x^2}{2\,b}+\frac{c^2\,\ln\left(x\right)}{a}-\frac{\ln\left(b\,x^2+a\right)\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}{2\,a\,b^2}","Not used",1,"(d^2*x^2)/(2*b) + (c^2*log(x))/a - (log(a + b*x^2)*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/(2*a*b^2)","B"
215,1,80,55,0.073786,"\text{Not used}","int((c + d*x^2)^2/(x^2*(a + b*x^2)),x)","\frac{d^2\,x}{b}-\frac{c^2}{a\,x}-\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x\,{\left(a\,d-b\,c\right)}^2}{\sqrt{a}\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}\right)\,{\left(a\,d-b\,c\right)}^2}{a^{3/2}\,b^{3/2}}","Not used",1,"(d^2*x)/b - c^2/(a*x) - (atan((b^(1/2)*x*(a*d - b*c)^2)/(a^(1/2)*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)))*(a*d - b*c)^2)/(a^(3/2)*b^(3/2))","B"
216,1,67,58,0.182678,"\text{Not used}","int((c + d*x^2)^2/(x^3*(a + b*x^2)),x)","\frac{\ln\left(b\,x^2+a\right)\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}{2\,a^2\,b}-\frac{c^2}{2\,a\,x^2}-\frac{\ln\left(x\right)\,\left(b\,c^2-2\,a\,c\,d\right)}{a^2}","Not used",1,"(log(a + b*x^2)*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/(2*a^2*b) - c^2/(2*a*x^2) - (log(x)*(b*c^2 - 2*a*c*d))/a^2","B"
217,1,90,64,0.133667,"\text{Not used}","int((c + d*x^2)^2/(x^4*(a + b*x^2)),x)","\frac{b\,c^2}{a^2\,x}-\frac{c^2}{3\,a\,x^3}+\frac{b^{3/2}\,c^2\,\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)}{a^{5/2}}+\frac{d^2\,\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)}{\sqrt{a}\,\sqrt{b}}-\frac{2\,c\,d}{a\,x}-\frac{2\,\sqrt{b}\,c\,d\,\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)}{a^{3/2}}","Not used",1,"(b*c^2)/(a^2*x) - c^2/(3*a*x^3) + (b^(3/2)*c^2*atan((b^(1/2)*x)/a^(1/2)))/a^(5/2) + (d^2*atan((b^(1/2)*x)/a^(1/2)))/(a^(1/2)*b^(1/2)) - (2*c*d)/(a*x) - (2*b^(1/2)*c*d*atan((b^(1/2)*x)/a^(1/2)))/a^(3/2)","B"
218,1,236,138,0.119581,"\text{Not used}","int((x^5*(c + d*x^2)^3)/(a + b*x^2),x)","x^4\,\left(\frac{c^3}{4\,b}-\frac{a\,\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)}{4\,b}\right)-x^8\,\left(\frac{a\,d^3}{8\,b^2}-\frac{3\,c\,d^2}{8\,b}\right)+x^6\,\left(\frac{c^2\,d}{2\,b}+\frac{a\,\left(\frac{a\,d^3}{b^2}-\frac{3\,c\,d^2}{b}\right)}{6\,b}\right)-\frac{\ln\left(b\,x^2+a\right)\,\left(a^5\,d^3-3\,a^4\,b\,c\,d^2+3\,a^3\,b^2\,c^2\,d-a^2\,b^3\,c^3\right)}{2\,b^6}+\frac{d^3\,x^{10}}{10\,b}-\frac{a\,x^2\,\left(\frac{c^3}{b}-\frac{a\,\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)}{b}\right)}{2\,b}","Not used",1,"x^4*(c^3/(4*b) - (a*((3*c^2*d)/b + (a*((a*d^3)/b^2 - (3*c*d^2)/b))/b))/(4*b)) - x^8*((a*d^3)/(8*b^2) - (3*c*d^2)/(8*b)) + x^6*((c^2*d)/(2*b) + (a*((a*d^3)/b^2 - (3*c*d^2)/b))/(6*b)) - (log(a + b*x^2)*(a^5*d^3 - a^2*b^3*c^3 + 3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2))/(2*b^6) + (d^3*x^10)/(10*b) - (a*x^2*(c^3/b - (a*((3*c^2*d)/b + (a*((a*d^3)/b^2 - (3*c*d^2)/b))/b))/b))/(2*b)","B"
219,1,260,140,0.114877,"\text{Not used}","int((x^4*(c + d*x^2)^3)/(a + b*x^2),x)","x^3\,\left(\frac{c^3}{3\,b}-\frac{a\,\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)}{3\,b}\right)-x^7\,\left(\frac{a\,d^3}{7\,b^2}-\frac{3\,c\,d^2}{7\,b}\right)+x^5\,\left(\frac{3\,c^2\,d}{5\,b}+\frac{a\,\left(\frac{a\,d^3}{b^2}-\frac{3\,c\,d^2}{b}\right)}{5\,b}\right)+\frac{d^3\,x^9}{9\,b}-\frac{a^{3/2}\,\mathrm{atan}\left(\frac{a^{3/2}\,\sqrt{b}\,x\,{\left(a\,d-b\,c\right)}^3}{a^5\,d^3-3\,a^4\,b\,c\,d^2+3\,a^3\,b^2\,c^2\,d-a^2\,b^3\,c^3}\right)\,{\left(a\,d-b\,c\right)}^3}{b^{11/2}}-\frac{a\,x\,\left(\frac{c^3}{b}-\frac{a\,\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)}{b}\right)}{b}","Not used",1,"x^3*(c^3/(3*b) - (a*((3*c^2*d)/b + (a*((a*d^3)/b^2 - (3*c*d^2)/b))/b))/(3*b)) - x^7*((a*d^3)/(7*b^2) - (3*c*d^2)/(7*b)) + x^5*((3*c^2*d)/(5*b) + (a*((a*d^3)/b^2 - (3*c*d^2)/b))/(5*b)) + (d^3*x^9)/(9*b) - (a^(3/2)*atan((a^(3/2)*b^(1/2)*x*(a*d - b*c)^3)/(a^5*d^3 - a^2*b^3*c^3 + 3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2))*(a*d - b*c)^3)/b^(11/2) - (a*x*(c^3/b - (a*((3*c^2*d)/b + (a*((a*d^3)/b^2 - (3*c*d^2)/b))/b))/b))/b","B"
220,1,178,115,0.053997,"\text{Not used}","int((x^3*(c + d*x^2)^3)/(a + b*x^2),x)","x^2\,\left(\frac{c^3}{2\,b}-\frac{a\,\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)}{2\,b}\right)-x^6\,\left(\frac{a\,d^3}{6\,b^2}-\frac{c\,d^2}{2\,b}\right)+x^4\,\left(\frac{3\,c^2\,d}{4\,b}+\frac{a\,\left(\frac{a\,d^3}{b^2}-\frac{3\,c\,d^2}{b}\right)}{4\,b}\right)+\frac{\ln\left(b\,x^2+a\right)\,\left(a^4\,d^3-3\,a^3\,b\,c\,d^2+3\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3\right)}{2\,b^5}+\frac{d^3\,x^8}{8\,b}","Not used",1,"x^2*(c^3/(2*b) - (a*((3*c^2*d)/b + (a*((a*d^3)/b^2 - (3*c*d^2)/b))/b))/(2*b)) - x^6*((a*d^3)/(6*b^2) - (c*d^2)/(2*b)) + x^4*((3*c^2*d)/(4*b) + (a*((a*d^3)/b^2 - (3*c*d^2)/b))/(4*b)) + (log(a + b*x^2)*(a^4*d^3 - a*b^3*c^3 + 3*a^2*b^2*c^2*d - 3*a^3*b*c*d^2))/(2*b^5) + (d^3*x^8)/(8*b)","B"
221,1,199,119,0.102063,"\text{Not used}","int((x^2*(c + d*x^2)^3)/(a + b*x^2),x)","x^3\,\left(\frac{c^2\,d}{b}+\frac{a\,\left(\frac{a\,d^3}{b^2}-\frac{3\,c\,d^2}{b}\right)}{3\,b}\right)-x^5\,\left(\frac{a\,d^3}{5\,b^2}-\frac{3\,c\,d^2}{5\,b}\right)+x\,\left(\frac{c^3}{b}-\frac{a\,\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)}{b}\right)+\frac{d^3\,x^7}{7\,b}+\frac{\sqrt{a}\,\mathrm{atan}\left(\frac{\sqrt{a}\,\sqrt{b}\,x\,{\left(a\,d-b\,c\right)}^3}{a^4\,d^3-3\,a^3\,b\,c\,d^2+3\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3}\right)\,{\left(a\,d-b\,c\right)}^3}{b^{9/2}}","Not used",1,"x^3*((c^2*d)/b + (a*((a*d^3)/b^2 - (3*c*d^2)/b))/(3*b)) - x^5*((a*d^3)/(5*b^2) - (3*c*d^2)/(5*b)) + x*(c^3/b - (a*((3*c^2*d)/b + (a*((a*d^3)/b^2 - (3*c*d^2)/b))/b))/b) + (d^3*x^7)/(7*b) + (a^(1/2)*atan((a^(1/2)*b^(1/2)*x*(a*d - b*c)^3)/(a^4*d^3 - a*b^3*c^3 + 3*a^2*b^2*c^2*d - 3*a^3*b*c*d^2))*(a*d - b*c)^3)/b^(9/2)","B"
222,1,123,87,0.059993,"\text{Not used}","int((x*(c + d*x^2)^3)/(a + b*x^2),x)","x^2\,\left(\frac{3\,c^2\,d}{2\,b}+\frac{a\,\left(\frac{a\,d^3}{b^2}-\frac{3\,c\,d^2}{b}\right)}{2\,b}\right)-x^4\,\left(\frac{a\,d^3}{4\,b^2}-\frac{3\,c\,d^2}{4\,b}\right)-\frac{\ln\left(b\,x^2+a\right)\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)}{2\,b^4}+\frac{d^3\,x^6}{6\,b}","Not used",1,"x^2*((3*c^2*d)/(2*b) + (a*((a*d^3)/b^2 - (3*c*d^2)/b))/(2*b)) - x^4*((a*d^3)/(4*b^2) - (3*c*d^2)/(4*b)) - (log(a + b*x^2)*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))/(2*b^4) + (d^3*x^6)/(6*b)","B"
223,1,146,98,0.123851,"\text{Not used}","int((c + d*x^2)^3/(a + b*x^2),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^3\,\left(\frac{a\,d^3}{3\,b^2}-\frac{c\,d^2}{b}\right)+\frac{d^3\,x^5}{5\,b}-\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x\,{\left(a\,d-b\,c\right)}^3}{\sqrt{a}\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)}\right)\,{\left(a\,d-b\,c\right)}^3}{\sqrt{a}\,b^{7/2}}","Not used",1,"x*((3*c^2*d)/b + (a*((a*d^3)/b^2 - (3*c*d^2)/b))/b) - x^3*((a*d^3)/(3*b^2) - (c*d^2)/b) + (d^3*x^5)/(5*b) - (atan((b^(1/2)*x*(a*d - b*c)^3)/(a^(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*d - b*c)^3)/(a^(1/2)*b^(7/2))","B"
224,1,97,73,0.148570,"\text{Not used}","int((c + d*x^2)^3/(x*(a + b*x^2)),x)","\frac{d^3\,x^4}{4\,b}-x^2\,\left(\frac{a\,d^3}{2\,b^2}-\frac{3\,c\,d^2}{2\,b}\right)+\frac{c^3\,\ln\left(x\right)}{a}+\frac{\ln\left(b\,x^2+a\right)\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)}{2\,a\,b^3}","Not used",1,"(d^3*x^4)/(4*b) - x^2*((a*d^3)/(2*b^2) - (3*c*d^2)/(2*b)) + (c^3*log(x))/a + (log(a + b*x^2)*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))/(2*a*b^3)","B"
225,1,118,77,0.074966,"\text{Not used}","int((c + d*x^2)^3/(x^2*(a + b*x^2)),x)","\frac{d^3\,x^3}{3\,b}-\frac{c^3}{a\,x}-x\,\left(\frac{a\,d^3}{b^2}-\frac{3\,c\,d^2}{b}\right)+\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x\,{\left(a\,d-b\,c\right)}^3}{\sqrt{a}\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)}\right)\,{\left(a\,d-b\,c\right)}^3}{a^{3/2}\,b^{5/2}}","Not used",1,"(d^3*x^3)/(3*b) - c^3/(a*x) - x*((a*d^3)/b^2 - (3*c*d^2)/b) + (atan((b^(1/2)*x*(a*d - b*c)^3)/(a^(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*d - b*c)^3)/(a^(3/2)*b^(5/2))","B"
226,1,95,73,0.168333,"\text{Not used}","int((c + d*x^2)^3/(x^3*(a + b*x^2)),x)","\frac{d^3\,x^2}{2\,b}-\frac{c^3}{2\,a\,x^2}-\frac{\ln\left(x\right)\,\left(b\,c^3-3\,a\,c^2\,d\right)}{a^2}-\frac{\ln\left(b\,x^2+a\right)\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)}{2\,a^2\,b^2}","Not used",1,"(d^3*x^2)/(2*b) - c^3/(2*a*x^2) - (log(x)*(b*c^3 - 3*a*c^2*d))/a^2 - (log(a + b*x^2)*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))/(2*a^2*b^2)","B"
227,1,122,74,0.144767,"\text{Not used}","int((c + d*x^2)^3/(x^4*(a + b*x^2)),x)","\frac{d^3\,x}{b}-\frac{\frac{b\,c^3}{3\,a}+\frac{b\,c^2\,x^2\,\left(3\,a\,d-b\,c\right)}{a^2}}{b\,x^3}-\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x\,{\left(a\,d-b\,c\right)}^3}{\sqrt{a}\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)}\right)\,{\left(a\,d-b\,c\right)}^3}{a^{5/2}\,b^{3/2}}","Not used",1,"(d^3*x)/b - ((b*c^3)/(3*a) + (b*c^2*x^2*(3*a*d - b*c))/a^2)/(b*x^3) - (atan((b^(1/2)*x*(a*d - b*c)^3)/(a^(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*d - b*c)^3)/(a^(5/2)*b^(3/2))","B"
228,1,68,70,0.323390,"\text{Not used}","int(x^5/((a + b*x^2)*(c + d*x^2)),x)","\frac{a^2\,\ln\left(b\,x^2+a\right)}{2\,b^3\,c-2\,a\,b^2\,d}+\frac{c^2\,\ln\left(d\,x^2+c\right)}{2\,a\,d^3-2\,b\,c\,d^2}+\frac{x^2}{2\,b\,d}","Not used",1,"(a^2*log(a + b*x^2))/(2*b^3*c - 2*a*b^2*d) + (c^2*log(c + d*x^2))/(2*a*d^3 - 2*b*c*d^2) + x^2/(2*b*d)","B"
229,1,343,78,0.612193,"\text{Not used}","int(x^4/((a + b*x^2)*(c + d*x^2)),x)","\frac{\ln\left(a^5\,b^4\,d^3-a^2\,b^7\,c^3+d^3\,x\,{\left(-a^3\,b^3\right)}^{3/2}+b^6\,c^3\,x\,\sqrt{-a^3\,b^3}\right)\,\sqrt{-a^3\,b^3}}{2\,b^4\,c-2\,a\,b^3\,d}-\frac{\ln\left(a^2\,b^7\,c^3-a^5\,b^4\,d^3+d^3\,x\,{\left(-a^3\,b^3\right)}^{3/2}+b^6\,c^3\,x\,\sqrt{-a^3\,b^3}\right)\,\sqrt{-a^3\,b^3}}{2\,\left(b^4\,c-a\,b^3\,d\right)}+\frac{x}{b\,d}-\frac{\ln\left(a^3\,c^2\,d^7-b^3\,c^5\,d^4+b^3\,x\,{\left(-c^3\,d^3\right)}^{3/2}+a^3\,d^6\,x\,\sqrt{-c^3\,d^3}\right)\,\sqrt{-c^3\,d^3}}{2\,\left(a\,d^4-b\,c\,d^3\right)}+\frac{\ln\left(b^3\,c^5\,d^4-a^3\,c^2\,d^7+b^3\,x\,{\left(-c^3\,d^3\right)}^{3/2}+a^3\,d^6\,x\,\sqrt{-c^3\,d^3}\right)\,\sqrt{-c^3\,d^3}}{2\,a\,d^4-2\,b\,c\,d^3}","Not used",1,"(log(a^5*b^4*d^3 - a^2*b^7*c^3 + d^3*x*(-a^3*b^3)^(3/2) + b^6*c^3*x*(-a^3*b^3)^(1/2))*(-a^3*b^3)^(1/2))/(2*b^4*c - 2*a*b^3*d) - (log(a^2*b^7*c^3 - a^5*b^4*d^3 + d^3*x*(-a^3*b^3)^(3/2) + b^6*c^3*x*(-a^3*b^3)^(1/2))*(-a^3*b^3)^(1/2))/(2*(b^4*c - a*b^3*d)) + x/(b*d) - (log(a^3*c^2*d^7 - b^3*c^5*d^4 + b^3*x*(-c^3*d^3)^(3/2) + a^3*d^6*x*(-c^3*d^3)^(1/2))*(-c^3*d^3)^(1/2))/(2*(a*d^4 - b*c*d^3)) + (log(b^3*c^5*d^4 - a^3*c^2*d^7 + b^3*x*(-c^3*d^3)^(3/2) + a^3*d^6*x*(-c^3*d^3)^(1/2))*(-c^3*d^3)^(1/2))/(2*a*d^4 - 2*b*c*d^3)","B"
230,1,51,53,0.271338,"\text{Not used}","int(x^3/((a + b*x^2)*(c + d*x^2)),x)","-\frac{a\,\ln\left(b\,x^2+a\right)}{2\,b^2\,c-2\,a\,b\,d}-\frac{c\,\ln\left(d\,x^2+c\right)}{2\,a\,d^2-2\,b\,c\,d}","Not used",1,"- (a*log(a + b*x^2))/(2*b^2*c - 2*a*b*d) - (c*log(c + d*x^2))/(2*a*d^2 - 2*b*c*d)","B"
231,1,133,70,0.343618,"\text{Not used}","int(x^2/((a + b*x^2)*(c + d*x^2)),x)","\frac{\ln\left(a+x\,\sqrt{-a\,b}\right)\,\sqrt{-a\,b}}{2\,b^2\,c-2\,a\,b\,d}-\frac{\ln\left(a-x\,\sqrt{-a\,b}\right)\,\sqrt{-a\,b}}{2\,\left(b^2\,c-a\,b\,d\right)}-\frac{\ln\left(c-x\,\sqrt{-c\,d}\right)\,\sqrt{-c\,d}}{2\,\left(a\,d^2-b\,c\,d\right)}+\frac{\ln\left(c+x\,\sqrt{-c\,d}\right)\,\sqrt{-c\,d}}{2\,a\,d^2-2\,b\,c\,d}","Not used",1,"(log(a + x*(-a*b)^(1/2))*(-a*b)^(1/2))/(2*b^2*c - 2*a*b*d) - (log(a - x*(-a*b)^(1/2))*(-a*b)^(1/2))/(2*(b^2*c - a*b*d)) - (log(c - x*(-c*d)^(1/2))*(-c*d)^(1/2))/(2*(a*d^2 - b*c*d)) + (log(c + x*(-c*d)^(1/2))*(-c*d)^(1/2))/(2*a*d^2 - 2*b*c*d)","B"
232,1,148,45,0.197845,"\text{Not used}","int(x/((a + b*x^2)*(c + d*x^2)),x)","\frac{2\,\mathrm{atanh}\left(\frac{8\,b^2\,d^2\,x^2}{\left(2\,a\,d-2\,b\,c\right)\,\left(\frac{32\,a\,b^2\,c\,d^2}{4\,a^2\,d^2-8\,a\,b\,c\,d+4\,b^2\,c^2}+\frac{16\,a\,b^2\,d^3\,x^2}{4\,a^2\,d^2-8\,a\,b\,c\,d+4\,b^2\,c^2}+\frac{16\,b^3\,c\,d^2\,x^2}{4\,a^2\,d^2-8\,a\,b\,c\,d+4\,b^2\,c^2}\right)}\right)}{2\,a\,d-2\,b\,c}","Not used",1,"(2*atanh((8*b^2*d^2*x^2)/((2*a*d - 2*b*c)*((32*a*b^2*c*d^2)/(4*a^2*d^2 + 4*b^2*c^2 - 8*a*b*c*d) + (16*a*b^2*d^3*x^2)/(4*a^2*d^2 + 4*b^2*c^2 - 8*a*b*c*d) + (16*b^3*c*d^2*x^2)/(4*a^2*d^2 + 4*b^2*c^2 - 8*a*b*c*d)))))/(2*a*d - 2*b*c)","B"
233,1,135,70,0.342966,"\text{Not used}","int(1/((a + b*x^2)*(c + d*x^2)),x)","\frac{\ln\left(b\,x-\sqrt{-a\,b}\right)\,\sqrt{-a\,b}}{2\,a^2\,d-2\,a\,b\,c}-\frac{\ln\left(d\,x+\sqrt{-c\,d}\right)\,\sqrt{-c\,d}}{2\,\left(b\,c^2-a\,c\,d\right)}-\frac{\ln\left(b\,x+\sqrt{-a\,b}\right)\,\sqrt{-a\,b}}{2\,\left(a^2\,d-a\,b\,c\right)}+\frac{\ln\left(d\,x-\sqrt{-c\,d}\right)\,\sqrt{-c\,d}}{2\,b\,c^2-2\,a\,c\,d}","Not used",1,"(log(b*x - (-a*b)^(1/2))*(-a*b)^(1/2))/(2*a^2*d - 2*a*b*c) - (log(d*x + (-c*d)^(1/2))*(-c*d)^(1/2))/(2*(b*c^2 - a*c*d)) - (log(b*x + (-a*b)^(1/2))*(-a*b)^(1/2))/(2*(a^2*d - a*b*c)) + (log(d*x - (-c*d)^(1/2))*(-c*d)^(1/2))/(2*b*c^2 - 2*a*c*d)","B"
234,1,58,62,0.303131,"\text{Not used}","int(1/(x*(a + b*x^2)*(c + d*x^2)),x)","\frac{b\,\ln\left(b\,x^2+a\right)}{2\,a^2\,d-2\,a\,b\,c}+\frac{d\,\ln\left(d\,x^2+c\right)}{2\,b\,c^2-2\,a\,c\,d}+\frac{\ln\left(x\right)}{a\,c}","Not used",1,"(b*log(a + b*x^2))/(2*a^2*d - 2*a*b*c) + (d*log(c + d*x^2))/(2*b*c^2 - 2*a*c*d) + log(x)/(a*c)","B"
235,1,338,81,0.627612,"\text{Not used}","int(1/(x^2*(a + b*x^2)*(c + d*x^2)),x)","\frac{\ln\left(a^3\,c^5\,d^4-b^3\,c^8\,d+a^3\,x\,{\left(-c^3\,d^3\right)}^{3/2}+b^3\,c^6\,x\,\sqrt{-c^3\,d^3}\right)\,\sqrt{-c^3\,d^3}}{2\,b\,c^4-2\,a\,c^3\,d}-\frac{\ln\left(b^3\,c^8\,d-a^3\,c^5\,d^4+a^3\,x\,{\left(-c^3\,d^3\right)}^{3/2}+b^3\,c^6\,x\,\sqrt{-c^3\,d^3}\right)\,\sqrt{-c^3\,d^3}}{2\,\left(b\,c^4-a\,c^3\,d\right)}-\frac{1}{a\,c\,x}-\frac{\ln\left(a^8\,b\,d^3-a^5\,b^4\,c^3+c^3\,x\,{\left(-a^3\,b^3\right)}^{3/2}+a^6\,d^3\,x\,\sqrt{-a^3\,b^3}\right)\,\sqrt{-a^3\,b^3}}{2\,\left(a^4\,d-a^3\,b\,c\right)}+\frac{\ln\left(a^5\,b^4\,c^3-a^8\,b\,d^3+c^3\,x\,{\left(-a^3\,b^3\right)}^{3/2}+a^6\,d^3\,x\,\sqrt{-a^3\,b^3}\right)\,\sqrt{-a^3\,b^3}}{2\,a^4\,d-2\,a^3\,b\,c}","Not used",1,"(log(a^3*c^5*d^4 - b^3*c^8*d + a^3*x*(-c^3*d^3)^(3/2) + b^3*c^6*x*(-c^3*d^3)^(1/2))*(-c^3*d^3)^(1/2))/(2*b*c^4 - 2*a*c^3*d) - (log(b^3*c^8*d - a^3*c^5*d^4 + a^3*x*(-c^3*d^3)^(3/2) + b^3*c^6*x*(-c^3*d^3)^(1/2))*(-c^3*d^3)^(1/2))/(2*(b*c^4 - a*c^3*d)) - 1/(a*c*x) - (log(a^8*b*d^3 - a^5*b^4*c^3 + c^3*x*(-a^3*b^3)^(3/2) + a^6*d^3*x*(-a^3*b^3)^(1/2))*(-a^3*b^3)^(1/2))/(2*(a^4*d - a^3*b*c)) + (log(a^5*b^4*c^3 - a^8*b*d^3 + c^3*x*(-a^3*b^3)^(3/2) + a^6*d^3*x*(-a^3*b^3)^(1/2))*(-a^3*b^3)^(1/2))/(2*a^4*d - 2*a^3*b*c)","B"
236,1,87,87,0.347863,"\text{Not used}","int(1/(x^3*(a + b*x^2)*(c + d*x^2)),x)","-\frac{b^2\,\ln\left(b\,x^2+a\right)}{2\,\left(a^3\,d-a^2\,b\,c\right)}-\frac{d^2\,\ln\left(d\,x^2+c\right)}{2\,\left(b\,c^3-a\,c^2\,d\right)}-\frac{1}{2\,a\,c\,x^2}-\frac{\ln\left(x\right)\,\left(a\,d+b\,c\right)}{a^2\,c^2}","Not used",1,"- (b^2*log(a + b*x^2))/(2*(a^3*d - a^2*b*c)) - (d^2*log(c + d*x^2))/(2*(b*c^3 - a*c^2*d)) - 1/(2*a*c*x^2) - (log(x)*(a*d + b*c))/(a^2*c^2)","B"
237,1,367,100,0.614947,"\text{Not used}","int(1/(x^4*(a + b*x^2)*(c + d*x^2)),x)","\frac{\ln\left(a^{13}\,b^2\,d^5-a^8\,b^7\,c^5+c^5\,x\,{\left(-a^5\,b^5\right)}^{3/2}+a^{10}\,d^5\,x\,\sqrt{-a^5\,b^5}\right)\,\sqrt{-a^5\,b^5}}{2\,a^6\,d-2\,a^5\,b\,c}-\frac{\ln\left(a^8\,b^7\,c^5-a^{13}\,b^2\,d^5+c^5\,x\,{\left(-a^5\,b^5\right)}^{3/2}+a^{10}\,d^5\,x\,\sqrt{-a^5\,b^5}\right)\,\sqrt{-a^5\,b^5}}{2\,\left(a^6\,d-a^5\,b\,c\right)}-\frac{\frac{1}{3\,a\,c}-\frac{x^2\,\left(a\,d+b\,c\right)}{a^2\,c^2}}{x^3}-\frac{\ln\left(a^5\,c^8\,d^7-b^5\,c^{13}\,d^2+a^5\,x\,{\left(-c^5\,d^5\right)}^{3/2}+b^5\,c^{10}\,x\,\sqrt{-c^5\,d^5}\right)\,\sqrt{-c^5\,d^5}}{2\,\left(b\,c^6-a\,c^5\,d\right)}+\frac{\ln\left(b^5\,c^{13}\,d^2-a^5\,c^8\,d^7+a^5\,x\,{\left(-c^5\,d^5\right)}^{3/2}+b^5\,c^{10}\,x\,\sqrt{-c^5\,d^5}\right)\,\sqrt{-c^5\,d^5}}{2\,b\,c^6-2\,a\,c^5\,d}","Not used",1,"(log(a^13*b^2*d^5 - a^8*b^7*c^5 + c^5*x*(-a^5*b^5)^(3/2) + a^10*d^5*x*(-a^5*b^5)^(1/2))*(-a^5*b^5)^(1/2))/(2*a^6*d - 2*a^5*b*c) - (log(a^8*b^7*c^5 - a^13*b^2*d^5 + c^5*x*(-a^5*b^5)^(3/2) + a^10*d^5*x*(-a^5*b^5)^(1/2))*(-a^5*b^5)^(1/2))/(2*(a^6*d - a^5*b*c)) - (1/(3*a*c) - (x^2*(a*d + b*c))/(a^2*c^2))/x^3 - (log(a^5*c^8*d^7 - b^5*c^13*d^2 + a^5*x*(-c^5*d^5)^(3/2) + b^5*c^10*x*(-c^5*d^5)^(1/2))*(-c^5*d^5)^(1/2))/(2*(b*c^6 - a*c^5*d)) + (log(b^5*c^13*d^2 - a^5*c^8*d^7 + a^5*x*(-c^5*d^5)^(3/2) + b^5*c^10*x*(-c^5*d^5)^(1/2))*(-c^5*d^5)^(1/2))/(2*b*c^6 - 2*a*c^5*d)","B"
238,1,118,119,0.431417,"\text{Not used}","int(1/(x^5*(a + b*x^2)*(c + d*x^2)),x)","\frac{b^3\,\ln\left(b\,x^2+a\right)}{2\,a^4\,d-2\,a^3\,b\,c}-\frac{\frac{1}{4\,a\,c}-\frac{x^2\,\left(a\,d+b\,c\right)}{2\,a^2\,c^2}}{x^4}+\frac{d^3\,\ln\left(d\,x^2+c\right)}{2\,b\,c^4-2\,a\,c^3\,d}+\frac{\ln\left(x\right)\,\left(a^2\,d^2+a\,b\,c\,d+b^2\,c^2\right)}{a^3\,c^3}","Not used",1,"(b^3*log(a + b*x^2))/(2*a^4*d - 2*a^3*b*c) - (1/(4*a*c) - (x^2*(a*d + b*c))/(2*a^2*c^2))/x^4 + (d^3*log(c + d*x^2))/(2*b*c^4 - 2*a*c^3*d) + (log(x)*(a^2*d^2 + b^2*c^2 + a*b*c*d))/(a^3*c^3)","B"
239,1,397,134,0.625227,"\text{Not used}","int(1/(x^6*(a + b*x^2)*(c + d*x^2)),x)","\frac{\ln\left(a^{11}\,b^{10}\,c^7-a^{18}\,b^3\,d^7+c^7\,x\,{\left(-a^7\,b^7\right)}^{3/2}+a^{14}\,d^7\,x\,\sqrt{-a^7\,b^7}\right)\,\sqrt{-a^7\,b^7}}{2\,a^8\,d-2\,a^7\,b\,c}-\frac{\ln\left(a^{18}\,b^3\,d^7-a^{11}\,b^{10}\,c^7+c^7\,x\,{\left(-a^7\,b^7\right)}^{3/2}+a^{14}\,d^7\,x\,\sqrt{-a^7\,b^7}\right)\,\sqrt{-a^7\,b^7}}{2\,\left(a^8\,d-a^7\,b\,c\right)}-\frac{\frac{1}{5\,a\,c}-\frac{x^2\,\left(a\,d+b\,c\right)}{3\,a^2\,c^2}+\frac{x^4\,\left(a^2\,d^2+a\,b\,c\,d+b^2\,c^2\right)}{a^3\,c^3}}{x^5}-\frac{\ln\left(b^7\,c^{18}\,d^3-a^7\,c^{11}\,d^{10}+a^7\,x\,{\left(-c^7\,d^7\right)}^{3/2}+b^7\,c^{14}\,x\,\sqrt{-c^7\,d^7}\right)\,\sqrt{-c^7\,d^7}}{2\,\left(b\,c^8-a\,c^7\,d\right)}+\frac{\ln\left(a^7\,c^{11}\,d^{10}-b^7\,c^{18}\,d^3+a^7\,x\,{\left(-c^7\,d^7\right)}^{3/2}+b^7\,c^{14}\,x\,\sqrt{-c^7\,d^7}\right)\,\sqrt{-c^7\,d^7}}{2\,b\,c^8-2\,a\,c^7\,d}","Not used",1,"(log(a^11*b^10*c^7 - a^18*b^3*d^7 + c^7*x*(-a^7*b^7)^(3/2) + a^14*d^7*x*(-a^7*b^7)^(1/2))*(-a^7*b^7)^(1/2))/(2*a^8*d - 2*a^7*b*c) - (log(a^18*b^3*d^7 - a^11*b^10*c^7 + c^7*x*(-a^7*b^7)^(3/2) + a^14*d^7*x*(-a^7*b^7)^(1/2))*(-a^7*b^7)^(1/2))/(2*(a^8*d - a^7*b*c)) - (1/(5*a*c) - (x^2*(a*d + b*c))/(3*a^2*c^2) + (x^4*(a^2*d^2 + b^2*c^2 + a*b*c*d))/(a^3*c^3))/x^5 - (log(b^7*c^18*d^3 - a^7*c^11*d^10 + a^7*x*(-c^7*d^7)^(3/2) + b^7*c^14*x*(-c^7*d^7)^(1/2))*(-c^7*d^7)^(1/2))/(2*(b*c^8 - a*c^7*d)) + (log(a^7*c^11*d^10 - b^7*c^18*d^3 + a^7*x*(-c^7*d^7)^(3/2) + b^7*c^14*x*(-c^7*d^7)^(1/2))*(-c^7*d^7)^(1/2))/(2*b*c^8 - 2*a*c^7*d)","B"
240,1,165,155,0.485897,"\text{Not used}","int(1/(x^7*(a + b*x^2)*(c + d*x^2)),x)","-\frac{\frac{1}{6\,a\,c}-\frac{x^2\,\left(a\,d+b\,c\right)}{4\,a^2\,c^2}+\frac{x^4\,\left(a^2\,d^2+a\,b\,c\,d+b^2\,c^2\right)}{2\,a^3\,c^3}}{x^6}-\frac{b^4\,\ln\left(b\,x^2+a\right)}{2\,\left(a^5\,d-a^4\,b\,c\right)}-\frac{d^4\,\ln\left(d\,x^2+c\right)}{2\,\left(b\,c^5-a\,c^4\,d\right)}-\frac{\ln\left(x\right)\,\left(a^3\,d^3+a^2\,b\,c\,d^2+a\,b^2\,c^2\,d+b^3\,c^3\right)}{a^4\,c^4}","Not used",1,"- (1/(6*a*c) - (x^2*(a*d + b*c))/(4*a^2*c^2) + (x^4*(a^2*d^2 + b^2*c^2 + a*b*c*d))/(2*a^3*c^3))/x^6 - (b^4*log(a + b*x^2))/(2*(a^5*d - a^4*b*c)) - (d^4*log(c + d*x^2))/(2*(b*c^5 - a*c^4*d)) - (log(x)*(a^3*d^3 + b^3*c^3 + a*b^2*c^2*d + a^2*b*c*d^2))/(a^4*c^4)","B"
241,1,169,93,0.454252,"\text{Not used}","int(x^5/((a + b*x^2)^2*(c + d*x^2)),x)","\frac{a^2}{2\,\left(d\,a^2\,b^2+d\,a\,b^3\,x^2-c\,a\,b^3-c\,b^4\,x^2\right)}+\frac{c^2\,\ln\left(d\,x^2+c\right)}{2\,a^2\,d^3-4\,a\,b\,c\,d^2+2\,b^2\,c^2\,d}+\frac{a^2\,d\,\ln\left(b\,x^2+a\right)}{2\,a^2\,b^2\,d^2-4\,a\,b^3\,c\,d+2\,b^4\,c^2}-\frac{2\,a\,b\,c\,\ln\left(b\,x^2+a\right)}{2\,a^2\,b^2\,d^2-4\,a\,b^3\,c\,d+2\,b^4\,c^2}","Not used",1,"a^2/(2*(a^2*b^2*d - b^4*c*x^2 - a*b^3*c + a*b^3*d*x^2)) + (c^2*log(c + d*x^2))/(2*a^2*d^3 + 2*b^2*c^2*d - 4*a*b*c*d^2) + (a^2*d*log(a + b*x^2))/(2*b^4*c^2 + 2*a^2*b^2*d^2 - 4*a*b^3*c*d) - (2*a*b*c*log(a + b*x^2))/(2*b^4*c^2 + 2*a^2*b^2*d^2 - 4*a*b^3*c*d)","B"
242,1,3572,108,0.944105,"\text{Not used}","int(x^4/((a + b*x^2)*(c + d*x^2)^2),x)","\frac{c\,x}{2\,d\,\left(d\,x^2+c\right)\,\left(a\,d-b\,c\right)}-\frac{\mathrm{atan}\left(-\frac{\frac{\left(\frac{\sqrt{-a^3\,b}\,\left(\frac{2\,a^5\,b^2\,c\,d^6-8\,a^4\,b^3\,c^2\,d^5+12\,a^3\,b^4\,c^3\,d^4-8\,a^2\,b^5\,c^4\,d^3+2\,a\,b^6\,c^5\,d^2}{2\,\left(a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d\right)}-\frac{x\,\sqrt{-a^3\,b}\,\left(16\,a^5\,b^2\,d^8-48\,a^4\,b^3\,c\,d^7+32\,a^3\,b^4\,c^2\,d^6+32\,a^2\,b^5\,c^3\,d^5-48\,a\,b^6\,c^4\,d^4+16\,b^7\,c^5\,d^3\right)}{8\,\left(a^2\,b\,d^2-2\,a\,b^2\,c\,d+b^3\,c^2\right)\,\left(a^2\,d^3-2\,a\,b\,c\,d^2+b^2\,c^2\,d\right)}\right)}{2\,\left(a^2\,b\,d^2-2\,a\,b^2\,c\,d+b^3\,c^2\right)}-\frac{x\,\left(4\,a^4\,b\,d^4+9\,a^2\,b^3\,c^2\,d^2-6\,a\,b^4\,c^3\,d+b^5\,c^4\right)}{4\,\left(a^2\,d^3-2\,a\,b\,c\,d^2+b^2\,c^2\,d\right)}\right)\,\sqrt{-a^3\,b}\,1{}\mathrm{i}}{a^2\,b\,d^2-2\,a\,b^2\,c\,d+b^3\,c^2}-\frac{\left(\frac{\sqrt{-a^3\,b}\,\left(\frac{2\,a^5\,b^2\,c\,d^6-8\,a^4\,b^3\,c^2\,d^5+12\,a^3\,b^4\,c^3\,d^4-8\,a^2\,b^5\,c^4\,d^3+2\,a\,b^6\,c^5\,d^2}{2\,\left(a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d\right)}+\frac{x\,\sqrt{-a^3\,b}\,\left(16\,a^5\,b^2\,d^8-48\,a^4\,b^3\,c\,d^7+32\,a^3\,b^4\,c^2\,d^6+32\,a^2\,b^5\,c^3\,d^5-48\,a\,b^6\,c^4\,d^4+16\,b^7\,c^5\,d^3\right)}{8\,\left(a^2\,b\,d^2-2\,a\,b^2\,c\,d+b^3\,c^2\right)\,\left(a^2\,d^3-2\,a\,b\,c\,d^2+b^2\,c^2\,d\right)}\right)}{2\,\left(a^2\,b\,d^2-2\,a\,b^2\,c\,d+b^3\,c^2\right)}+\frac{x\,\left(4\,a^4\,b\,d^4+9\,a^2\,b^3\,c^2\,d^2-6\,a\,b^4\,c^3\,d+b^5\,c^4\right)}{4\,\left(a^2\,d^3-2\,a\,b\,c\,d^2+b^2\,c^2\,d\right)}\right)\,\sqrt{-a^3\,b}\,1{}\mathrm{i}}{a^2\,b\,d^2-2\,a\,b^2\,c\,d+b^3\,c^2}}{\frac{3\,a^4\,b\,c\,d^2-\frac{5\,a^3\,b^2\,c^2\,d}{2}+\frac{a^2\,b^3\,c^3}{2}}{a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d}+\frac{\left(\frac{\sqrt{-a^3\,b}\,\left(\frac{2\,a^5\,b^2\,c\,d^6-8\,a^4\,b^3\,c^2\,d^5+12\,a^3\,b^4\,c^3\,d^4-8\,a^2\,b^5\,c^4\,d^3+2\,a\,b^6\,c^5\,d^2}{2\,\left(a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d\right)}-\frac{x\,\sqrt{-a^3\,b}\,\left(16\,a^5\,b^2\,d^8-48\,a^4\,b^3\,c\,d^7+32\,a^3\,b^4\,c^2\,d^6+32\,a^2\,b^5\,c^3\,d^5-48\,a\,b^6\,c^4\,d^4+16\,b^7\,c^5\,d^3\right)}{8\,\left(a^2\,b\,d^2-2\,a\,b^2\,c\,d+b^3\,c^2\right)\,\left(a^2\,d^3-2\,a\,b\,c\,d^2+b^2\,c^2\,d\right)}\right)}{2\,\left(a^2\,b\,d^2-2\,a\,b^2\,c\,d+b^3\,c^2\right)}-\frac{x\,\left(4\,a^4\,b\,d^4+9\,a^2\,b^3\,c^2\,d^2-6\,a\,b^4\,c^3\,d+b^5\,c^4\right)}{4\,\left(a^2\,d^3-2\,a\,b\,c\,d^2+b^2\,c^2\,d\right)}\right)\,\sqrt{-a^3\,b}}{a^2\,b\,d^2-2\,a\,b^2\,c\,d+b^3\,c^2}+\frac{\left(\frac{\sqrt{-a^3\,b}\,\left(\frac{2\,a^5\,b^2\,c\,d^6-8\,a^4\,b^3\,c^2\,d^5+12\,a^3\,b^4\,c^3\,d^4-8\,a^2\,b^5\,c^4\,d^3+2\,a\,b^6\,c^5\,d^2}{2\,\left(a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d\right)}+\frac{x\,\sqrt{-a^3\,b}\,\left(16\,a^5\,b^2\,d^8-48\,a^4\,b^3\,c\,d^7+32\,a^3\,b^4\,c^2\,d^6+32\,a^2\,b^5\,c^3\,d^5-48\,a\,b^6\,c^4\,d^4+16\,b^7\,c^5\,d^3\right)}{8\,\left(a^2\,b\,d^2-2\,a\,b^2\,c\,d+b^3\,c^2\right)\,\left(a^2\,d^3-2\,a\,b\,c\,d^2+b^2\,c^2\,d\right)}\right)}{2\,\left(a^2\,b\,d^2-2\,a\,b^2\,c\,d+b^3\,c^2\right)}+\frac{x\,\left(4\,a^4\,b\,d^4+9\,a^2\,b^3\,c^2\,d^2-6\,a\,b^4\,c^3\,d+b^5\,c^4\right)}{4\,\left(a^2\,d^3-2\,a\,b\,c\,d^2+b^2\,c^2\,d\right)}\right)\,\sqrt{-a^3\,b}}{a^2\,b\,d^2-2\,a\,b^2\,c\,d+b^3\,c^2}}\right)\,\sqrt{-a^3\,b}\,1{}\mathrm{i}}{a^2\,b\,d^2-2\,a\,b^2\,c\,d+b^3\,c^2}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{x\,\left(4\,a^4\,b\,d^4+9\,a^2\,b^3\,c^2\,d^2-6\,a\,b^4\,c^3\,d+b^5\,c^4\right)}{2\,\left(a^2\,d^3-2\,a\,b\,c\,d^2+b^2\,c^2\,d\right)}-\frac{\sqrt{-c\,d^3}\,\left(3\,a\,d-b\,c\right)\,\left(\frac{2\,a^5\,b^2\,c\,d^6-8\,a^4\,b^3\,c^2\,d^5+12\,a^3\,b^4\,c^3\,d^4-8\,a^2\,b^5\,c^4\,d^3+2\,a\,b^6\,c^5\,d^2}{a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d}-\frac{x\,\sqrt{-c\,d^3}\,\left(3\,a\,d-b\,c\right)\,\left(16\,a^5\,b^2\,d^8-48\,a^4\,b^3\,c\,d^7+32\,a^3\,b^4\,c^2\,d^6+32\,a^2\,b^5\,c^3\,d^5-48\,a\,b^6\,c^4\,d^4+16\,b^7\,c^5\,d^3\right)}{8\,\left(a^2\,d^5-2\,a\,b\,c\,d^4+b^2\,c^2\,d^3\right)\,\left(a^2\,d^3-2\,a\,b\,c\,d^2+b^2\,c^2\,d\right)}\right)}{4\,\left(a^2\,d^5-2\,a\,b\,c\,d^4+b^2\,c^2\,d^3\right)}\right)\,\sqrt{-c\,d^3}\,\left(3\,a\,d-b\,c\right)\,1{}\mathrm{i}}{4\,\left(a^2\,d^5-2\,a\,b\,c\,d^4+b^2\,c^2\,d^3\right)}+\frac{\left(\frac{x\,\left(4\,a^4\,b\,d^4+9\,a^2\,b^3\,c^2\,d^2-6\,a\,b^4\,c^3\,d+b^5\,c^4\right)}{2\,\left(a^2\,d^3-2\,a\,b\,c\,d^2+b^2\,c^2\,d\right)}+\frac{\sqrt{-c\,d^3}\,\left(3\,a\,d-b\,c\right)\,\left(\frac{2\,a^5\,b^2\,c\,d^6-8\,a^4\,b^3\,c^2\,d^5+12\,a^3\,b^4\,c^3\,d^4-8\,a^2\,b^5\,c^4\,d^3+2\,a\,b^6\,c^5\,d^2}{a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d}+\frac{x\,\sqrt{-c\,d^3}\,\left(3\,a\,d-b\,c\right)\,\left(16\,a^5\,b^2\,d^8-48\,a^4\,b^3\,c\,d^7+32\,a^3\,b^4\,c^2\,d^6+32\,a^2\,b^5\,c^3\,d^5-48\,a\,b^6\,c^4\,d^4+16\,b^7\,c^5\,d^3\right)}{8\,\left(a^2\,d^5-2\,a\,b\,c\,d^4+b^2\,c^2\,d^3\right)\,\left(a^2\,d^3-2\,a\,b\,c\,d^2+b^2\,c^2\,d\right)}\right)}{4\,\left(a^2\,d^5-2\,a\,b\,c\,d^4+b^2\,c^2\,d^3\right)}\right)\,\sqrt{-c\,d^3}\,\left(3\,a\,d-b\,c\right)\,1{}\mathrm{i}}{4\,\left(a^2\,d^5-2\,a\,b\,c\,d^4+b^2\,c^2\,d^3\right)}}{\frac{3\,a^4\,b\,c\,d^2-\frac{5\,a^3\,b^2\,c^2\,d}{2}+\frac{a^2\,b^3\,c^3}{2}}{a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d}-\frac{\left(\frac{x\,\left(4\,a^4\,b\,d^4+9\,a^2\,b^3\,c^2\,d^2-6\,a\,b^4\,c^3\,d+b^5\,c^4\right)}{2\,\left(a^2\,d^3-2\,a\,b\,c\,d^2+b^2\,c^2\,d\right)}-\frac{\sqrt{-c\,d^3}\,\left(3\,a\,d-b\,c\right)\,\left(\frac{2\,a^5\,b^2\,c\,d^6-8\,a^4\,b^3\,c^2\,d^5+12\,a^3\,b^4\,c^3\,d^4-8\,a^2\,b^5\,c^4\,d^3+2\,a\,b^6\,c^5\,d^2}{a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d}-\frac{x\,\sqrt{-c\,d^3}\,\left(3\,a\,d-b\,c\right)\,\left(16\,a^5\,b^2\,d^8-48\,a^4\,b^3\,c\,d^7+32\,a^3\,b^4\,c^2\,d^6+32\,a^2\,b^5\,c^3\,d^5-48\,a\,b^6\,c^4\,d^4+16\,b^7\,c^5\,d^3\right)}{8\,\left(a^2\,d^5-2\,a\,b\,c\,d^4+b^2\,c^2\,d^3\right)\,\left(a^2\,d^3-2\,a\,b\,c\,d^2+b^2\,c^2\,d\right)}\right)}{4\,\left(a^2\,d^5-2\,a\,b\,c\,d^4+b^2\,c^2\,d^3\right)}\right)\,\sqrt{-c\,d^3}\,\left(3\,a\,d-b\,c\right)}{4\,\left(a^2\,d^5-2\,a\,b\,c\,d^4+b^2\,c^2\,d^3\right)}+\frac{\left(\frac{x\,\left(4\,a^4\,b\,d^4+9\,a^2\,b^3\,c^2\,d^2-6\,a\,b^4\,c^3\,d+b^5\,c^4\right)}{2\,\left(a^2\,d^3-2\,a\,b\,c\,d^2+b^2\,c^2\,d\right)}+\frac{\sqrt{-c\,d^3}\,\left(3\,a\,d-b\,c\right)\,\left(\frac{2\,a^5\,b^2\,c\,d^6-8\,a^4\,b^3\,c^2\,d^5+12\,a^3\,b^4\,c^3\,d^4-8\,a^2\,b^5\,c^4\,d^3+2\,a\,b^6\,c^5\,d^2}{a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d}+\frac{x\,\sqrt{-c\,d^3}\,\left(3\,a\,d-b\,c\right)\,\left(16\,a^5\,b^2\,d^8-48\,a^4\,b^3\,c\,d^7+32\,a^3\,b^4\,c^2\,d^6+32\,a^2\,b^5\,c^3\,d^5-48\,a\,b^6\,c^4\,d^4+16\,b^7\,c^5\,d^3\right)}{8\,\left(a^2\,d^5-2\,a\,b\,c\,d^4+b^2\,c^2\,d^3\right)\,\left(a^2\,d^3-2\,a\,b\,c\,d^2+b^2\,c^2\,d\right)}\right)}{4\,\left(a^2\,d^5-2\,a\,b\,c\,d^4+b^2\,c^2\,d^3\right)}\right)\,\sqrt{-c\,d^3}\,\left(3\,a\,d-b\,c\right)}{4\,\left(a^2\,d^5-2\,a\,b\,c\,d^4+b^2\,c^2\,d^3\right)}}\right)\,\sqrt{-c\,d^3}\,\left(3\,a\,d-b\,c\right)\,1{}\mathrm{i}}{2\,\left(a^2\,d^5-2\,a\,b\,c\,d^4+b^2\,c^2\,d^3\right)}","Not used",1,"(c*x)/(2*d*(c + d*x^2)*(a*d - b*c)) - (atan(((((x*(b^5*c^4 + 4*a^4*b*d^4 + 9*a^2*b^3*c^2*d^2 - 6*a*b^4*c^3*d))/(2*(a^2*d^3 + b^2*c^2*d - 2*a*b*c*d^2)) - ((-c*d^3)^(1/2)*(3*a*d - b*c)*((2*a*b^6*c^5*d^2 + 2*a^5*b^2*c*d^6 - 8*a^2*b^5*c^4*d^3 + 12*a^3*b^4*c^3*d^4 - 8*a^4*b^3*c^2*d^5)/(a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3) - (x*(-c*d^3)^(1/2)*(3*a*d - b*c)*(16*a^5*b^2*d^8 + 16*b^7*c^5*d^3 - 48*a*b^6*c^4*d^4 - 48*a^4*b^3*c*d^7 + 32*a^2*b^5*c^3*d^5 + 32*a^3*b^4*c^2*d^6))/(8*(a^2*d^5 + b^2*c^2*d^3 - 2*a*b*c*d^4)*(a^2*d^3 + b^2*c^2*d - 2*a*b*c*d^2))))/(4*(a^2*d^5 + b^2*c^2*d^3 - 2*a*b*c*d^4)))*(-c*d^3)^(1/2)*(3*a*d - b*c)*1i)/(4*(a^2*d^5 + b^2*c^2*d^3 - 2*a*b*c*d^4)) + (((x*(b^5*c^4 + 4*a^4*b*d^4 + 9*a^2*b^3*c^2*d^2 - 6*a*b^4*c^3*d))/(2*(a^2*d^3 + b^2*c^2*d - 2*a*b*c*d^2)) + ((-c*d^3)^(1/2)*(3*a*d - b*c)*((2*a*b^6*c^5*d^2 + 2*a^5*b^2*c*d^6 - 8*a^2*b^5*c^4*d^3 + 12*a^3*b^4*c^3*d^4 - 8*a^4*b^3*c^2*d^5)/(a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3) + (x*(-c*d^3)^(1/2)*(3*a*d - b*c)*(16*a^5*b^2*d^8 + 16*b^7*c^5*d^3 - 48*a*b^6*c^4*d^4 - 48*a^4*b^3*c*d^7 + 32*a^2*b^5*c^3*d^5 + 32*a^3*b^4*c^2*d^6))/(8*(a^2*d^5 + b^2*c^2*d^3 - 2*a*b*c*d^4)*(a^2*d^3 + b^2*c^2*d - 2*a*b*c*d^2))))/(4*(a^2*d^5 + b^2*c^2*d^3 - 2*a*b*c*d^4)))*(-c*d^3)^(1/2)*(3*a*d - b*c)*1i)/(4*(a^2*d^5 + b^2*c^2*d^3 - 2*a*b*c*d^4)))/(((a^2*b^3*c^3)/2 - (5*a^3*b^2*c^2*d)/2 + 3*a^4*b*c*d^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) - (((x*(b^5*c^4 + 4*a^4*b*d^4 + 9*a^2*b^3*c^2*d^2 - 6*a*b^4*c^3*d))/(2*(a^2*d^3 + b^2*c^2*d - 2*a*b*c*d^2)) - ((-c*d^3)^(1/2)*(3*a*d - b*c)*((2*a*b^6*c^5*d^2 + 2*a^5*b^2*c*d^6 - 8*a^2*b^5*c^4*d^3 + 12*a^3*b^4*c^3*d^4 - 8*a^4*b^3*c^2*d^5)/(a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3) - (x*(-c*d^3)^(1/2)*(3*a*d - b*c)*(16*a^5*b^2*d^8 + 16*b^7*c^5*d^3 - 48*a*b^6*c^4*d^4 - 48*a^4*b^3*c*d^7 + 32*a^2*b^5*c^3*d^5 + 32*a^3*b^4*c^2*d^6))/(8*(a^2*d^5 + b^2*c^2*d^3 - 2*a*b*c*d^4)*(a^2*d^3 + b^2*c^2*d - 2*a*b*c*d^2))))/(4*(a^2*d^5 + b^2*c^2*d^3 - 2*a*b*c*d^4)))*(-c*d^3)^(1/2)*(3*a*d - b*c))/(4*(a^2*d^5 + b^2*c^2*d^3 - 2*a*b*c*d^4)) + (((x*(b^5*c^4 + 4*a^4*b*d^4 + 9*a^2*b^3*c^2*d^2 - 6*a*b^4*c^3*d))/(2*(a^2*d^3 + b^2*c^2*d - 2*a*b*c*d^2)) + ((-c*d^3)^(1/2)*(3*a*d - b*c)*((2*a*b^6*c^5*d^2 + 2*a^5*b^2*c*d^6 - 8*a^2*b^5*c^4*d^3 + 12*a^3*b^4*c^3*d^4 - 8*a^4*b^3*c^2*d^5)/(a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3) + (x*(-c*d^3)^(1/2)*(3*a*d - b*c)*(16*a^5*b^2*d^8 + 16*b^7*c^5*d^3 - 48*a*b^6*c^4*d^4 - 48*a^4*b^3*c*d^7 + 32*a^2*b^5*c^3*d^5 + 32*a^3*b^4*c^2*d^6))/(8*(a^2*d^5 + b^2*c^2*d^3 - 2*a*b*c*d^4)*(a^2*d^3 + b^2*c^2*d - 2*a*b*c*d^2))))/(4*(a^2*d^5 + b^2*c^2*d^3 - 2*a*b*c*d^4)))*(-c*d^3)^(1/2)*(3*a*d - b*c))/(4*(a^2*d^5 + b^2*c^2*d^3 - 2*a*b*c*d^4))))*(-c*d^3)^(1/2)*(3*a*d - b*c)*1i)/(2*(a^2*d^5 + b^2*c^2*d^3 - 2*a*b*c*d^4)) - (atan(-(((((-a^3*b)^(1/2)*((2*a*b^6*c^5*d^2 + 2*a^5*b^2*c*d^6 - 8*a^2*b^5*c^4*d^3 + 12*a^3*b^4*c^3*d^4 - 8*a^4*b^3*c^2*d^5)/(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)) - (x*(-a^3*b)^(1/2)*(16*a^5*b^2*d^8 + 16*b^7*c^5*d^3 - 48*a*b^6*c^4*d^4 - 48*a^4*b^3*c*d^7 + 32*a^2*b^5*c^3*d^5 + 32*a^3*b^4*c^2*d^6))/(8*(b^3*c^2 + a^2*b*d^2 - 2*a*b^2*c*d)*(a^2*d^3 + b^2*c^2*d - 2*a*b*c*d^2))))/(2*(b^3*c^2 + a^2*b*d^2 - 2*a*b^2*c*d)) - (x*(b^5*c^4 + 4*a^4*b*d^4 + 9*a^2*b^3*c^2*d^2 - 6*a*b^4*c^3*d))/(4*(a^2*d^3 + b^2*c^2*d - 2*a*b*c*d^2)))*(-a^3*b)^(1/2)*1i)/(b^3*c^2 + a^2*b*d^2 - 2*a*b^2*c*d) - ((((-a^3*b)^(1/2)*((2*a*b^6*c^5*d^2 + 2*a^5*b^2*c*d^6 - 8*a^2*b^5*c^4*d^3 + 12*a^3*b^4*c^3*d^4 - 8*a^4*b^3*c^2*d^5)/(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)) + (x*(-a^3*b)^(1/2)*(16*a^5*b^2*d^8 + 16*b^7*c^5*d^3 - 48*a*b^6*c^4*d^4 - 48*a^4*b^3*c*d^7 + 32*a^2*b^5*c^3*d^5 + 32*a^3*b^4*c^2*d^6))/(8*(b^3*c^2 + a^2*b*d^2 - 2*a*b^2*c*d)*(a^2*d^3 + b^2*c^2*d - 2*a*b*c*d^2))))/(2*(b^3*c^2 + a^2*b*d^2 - 2*a*b^2*c*d)) + (x*(b^5*c^4 + 4*a^4*b*d^4 + 9*a^2*b^3*c^2*d^2 - 6*a*b^4*c^3*d))/(4*(a^2*d^3 + b^2*c^2*d - 2*a*b*c*d^2)))*(-a^3*b)^(1/2)*1i)/(b^3*c^2 + a^2*b*d^2 - 2*a*b^2*c*d))/(((a^2*b^3*c^3)/2 - (5*a^3*b^2*c^2*d)/2 + 3*a^4*b*c*d^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) + ((((-a^3*b)^(1/2)*((2*a*b^6*c^5*d^2 + 2*a^5*b^2*c*d^6 - 8*a^2*b^5*c^4*d^3 + 12*a^3*b^4*c^3*d^4 - 8*a^4*b^3*c^2*d^5)/(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)) - (x*(-a^3*b)^(1/2)*(16*a^5*b^2*d^8 + 16*b^7*c^5*d^3 - 48*a*b^6*c^4*d^4 - 48*a^4*b^3*c*d^7 + 32*a^2*b^5*c^3*d^5 + 32*a^3*b^4*c^2*d^6))/(8*(b^3*c^2 + a^2*b*d^2 - 2*a*b^2*c*d)*(a^2*d^3 + b^2*c^2*d - 2*a*b*c*d^2))))/(2*(b^3*c^2 + a^2*b*d^2 - 2*a*b^2*c*d)) - (x*(b^5*c^4 + 4*a^4*b*d^4 + 9*a^2*b^3*c^2*d^2 - 6*a*b^4*c^3*d))/(4*(a^2*d^3 + b^2*c^2*d - 2*a*b*c*d^2)))*(-a^3*b)^(1/2))/(b^3*c^2 + a^2*b*d^2 - 2*a*b^2*c*d) + ((((-a^3*b)^(1/2)*((2*a*b^6*c^5*d^2 + 2*a^5*b^2*c*d^6 - 8*a^2*b^5*c^4*d^3 + 12*a^3*b^4*c^3*d^4 - 8*a^4*b^3*c^2*d^5)/(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)) + (x*(-a^3*b)^(1/2)*(16*a^5*b^2*d^8 + 16*b^7*c^5*d^3 - 48*a*b^6*c^4*d^4 - 48*a^4*b^3*c*d^7 + 32*a^2*b^5*c^3*d^5 + 32*a^3*b^4*c^2*d^6))/(8*(b^3*c^2 + a^2*b*d^2 - 2*a*b^2*c*d)*(a^2*d^3 + b^2*c^2*d - 2*a*b*c*d^2))))/(2*(b^3*c^2 + a^2*b*d^2 - 2*a*b^2*c*d)) + (x*(b^5*c^4 + 4*a^4*b*d^4 + 9*a^2*b^3*c^2*d^2 - 6*a*b^4*c^3*d))/(4*(a^2*d^3 + b^2*c^2*d - 2*a*b*c*d^2)))*(-a^3*b)^(1/2))/(b^3*c^2 + a^2*b*d^2 - 2*a*b^2*c*d)))*(-a^3*b)^(1/2)*1i)/(b^3*c^2 + a^2*b*d^2 - 2*a*b^2*c*d)","B"
243,1,173,74,0.266603,"\text{Not used}","int(x^3/((a + b*x^2)*(c + d*x^2)^2),x)","-\frac{b\,c^2-c\,\left(a\,d-a\,d\,\mathrm{atan}\left(\frac{a\,d\,x^2\,1{}\mathrm{i}-b\,c\,x^2\,1{}\mathrm{i}}{2\,a\,c+a\,d\,x^2+b\,c\,x^2}\right)\,2{}\mathrm{i}\right)+a\,d^2\,x^2\,\mathrm{atan}\left(\frac{a\,d\,x^2\,1{}\mathrm{i}-b\,c\,x^2\,1{}\mathrm{i}}{2\,a\,c+a\,d\,x^2+b\,c\,x^2}\right)\,2{}\mathrm{i}}{2\,a^2\,c\,d^3+2\,a^2\,d^4\,x^2-4\,a\,b\,c^2\,d^2-4\,a\,b\,c\,d^3\,x^2+2\,b^2\,c^3\,d+2\,b^2\,c^2\,d^2\,x^2}","Not used",1,"-(b*c^2 - c*(a*d - a*d*atan((a*d*x^2*1i - b*c*x^2*1i)/(2*a*c + a*d*x^2 + b*c*x^2))*2i) + a*d^2*x^2*atan((a*d*x^2*1i - b*c*x^2*1i)/(2*a*c + a*d*x^2 + b*c*x^2))*2i)/(2*a^2*c*d^3 + 2*b^2*c^3*d + 2*a^2*d^4*x^2 + 2*b^2*c^2*d^2*x^2 - 4*a*b*c^2*d^2 - 4*a*b*c*d^3*x^2)","B"
244,1,3154,104,0.784612,"\text{Not used}","int(x^2/((a + b*x^2)*(c + d*x^2)^2),x)","-\frac{x}{2\,\left(d\,x^2+c\right)\,\left(a\,d-b\,c\right)}+\frac{\mathrm{atan}\left(-\frac{\frac{\sqrt{-a\,b}\,\left(\frac{\sqrt{-a\,b}\,\left(\frac{2\,a^5\,b^2\,d^6-8\,a^4\,b^3\,c\,d^5+12\,a^3\,b^4\,c^2\,d^4-8\,a^2\,b^5\,c^3\,d^3+2\,a\,b^6\,c^4\,d^2}{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)}-\frac{x\,\sqrt{-a\,b}\,\left(16\,a^5\,b^2\,d^7-48\,a^4\,b^3\,c\,d^6+32\,a^3\,b^4\,c^2\,d^5+32\,a^2\,b^5\,c^3\,d^4-48\,a\,b^6\,c^4\,d^3+16\,b^7\,c^5\,d^2\right)}{8\,{\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}^2}\right)}{2\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}-\frac{x\,\left(5\,a^2\,b^3\,d^3+2\,a\,b^4\,c\,d^2+b^5\,c^2\,d\right)}{4\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}\right)\,1{}\mathrm{i}}{a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2}-\frac{\sqrt{-a\,b}\,\left(\frac{\sqrt{-a\,b}\,\left(\frac{2\,a^5\,b^2\,d^6-8\,a^4\,b^3\,c\,d^5+12\,a^3\,b^4\,c^2\,d^4-8\,a^2\,b^5\,c^3\,d^3+2\,a\,b^6\,c^4\,d^2}{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)}+\frac{x\,\sqrt{-a\,b}\,\left(16\,a^5\,b^2\,d^7-48\,a^4\,b^3\,c\,d^6+32\,a^3\,b^4\,c^2\,d^5+32\,a^2\,b^5\,c^3\,d^4-48\,a\,b^6\,c^4\,d^3+16\,b^7\,c^5\,d^2\right)}{8\,{\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}^2}\right)}{2\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}+\frac{x\,\left(5\,a^2\,b^3\,d^3+2\,a\,b^4\,c\,d^2+b^5\,c^2\,d\right)}{4\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}\right)\,1{}\mathrm{i}}{a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2}}{\frac{\frac{a^2\,b^3\,d^2}{2}+\frac{c\,a\,b^4\,d}{2}}{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}+\frac{\sqrt{-a\,b}\,\left(\frac{\sqrt{-a\,b}\,\left(\frac{2\,a^5\,b^2\,d^6-8\,a^4\,b^3\,c\,d^5+12\,a^3\,b^4\,c^2\,d^4-8\,a^2\,b^5\,c^3\,d^3+2\,a\,b^6\,c^4\,d^2}{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)}-\frac{x\,\sqrt{-a\,b}\,\left(16\,a^5\,b^2\,d^7-48\,a^4\,b^3\,c\,d^6+32\,a^3\,b^4\,c^2\,d^5+32\,a^2\,b^5\,c^3\,d^4-48\,a\,b^6\,c^4\,d^3+16\,b^7\,c^5\,d^2\right)}{8\,{\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}^2}\right)}{2\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}-\frac{x\,\left(5\,a^2\,b^3\,d^3+2\,a\,b^4\,c\,d^2+b^5\,c^2\,d\right)}{4\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}\right)}{a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2}+\frac{\sqrt{-a\,b}\,\left(\frac{\sqrt{-a\,b}\,\left(\frac{2\,a^5\,b^2\,d^6-8\,a^4\,b^3\,c\,d^5+12\,a^3\,b^4\,c^2\,d^4-8\,a^2\,b^5\,c^3\,d^3+2\,a\,b^6\,c^4\,d^2}{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)}+\frac{x\,\sqrt{-a\,b}\,\left(16\,a^5\,b^2\,d^7-48\,a^4\,b^3\,c\,d^6+32\,a^3\,b^4\,c^2\,d^5+32\,a^2\,b^5\,c^3\,d^4-48\,a\,b^6\,c^4\,d^3+16\,b^7\,c^5\,d^2\right)}{8\,{\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}^2}\right)}{2\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}+\frac{x\,\left(5\,a^2\,b^3\,d^3+2\,a\,b^4\,c\,d^2+b^5\,c^2\,d\right)}{4\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}\right)}{a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2}}\right)\,\sqrt{-a\,b}\,1{}\mathrm{i}}{a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-c\,d}\,\left(\frac{x\,\left(5\,a^2\,b^3\,d^3+2\,a\,b^4\,c\,d^2+b^5\,c^2\,d\right)}{2\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}-\frac{\sqrt{-c\,d}\,\left(\frac{2\,a^5\,b^2\,d^6-8\,a^4\,b^3\,c\,d^5+12\,a^3\,b^4\,c^2\,d^4-8\,a^2\,b^5\,c^3\,d^3+2\,a\,b^6\,c^4\,d^2}{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}-\frac{x\,\sqrt{-c\,d}\,\left(a\,d+b\,c\right)\,\left(16\,a^5\,b^2\,d^7-48\,a^4\,b^3\,c\,d^6+32\,a^3\,b^4\,c^2\,d^5+32\,a^2\,b^5\,c^3\,d^4-48\,a\,b^6\,c^4\,d^3+16\,b^7\,c^5\,d^2\right)}{8\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)\,\left(a^2\,c\,d^3-2\,a\,b\,c^2\,d^2+b^2\,c^3\,d\right)}\right)\,\left(a\,d+b\,c\right)}{4\,\left(a^2\,c\,d^3-2\,a\,b\,c^2\,d^2+b^2\,c^3\,d\right)}\right)\,\left(a\,d+b\,c\right)\,1{}\mathrm{i}}{4\,\left(a^2\,c\,d^3-2\,a\,b\,c^2\,d^2+b^2\,c^3\,d\right)}+\frac{\sqrt{-c\,d}\,\left(\frac{x\,\left(5\,a^2\,b^3\,d^3+2\,a\,b^4\,c\,d^2+b^5\,c^2\,d\right)}{2\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}+\frac{\sqrt{-c\,d}\,\left(\frac{2\,a^5\,b^2\,d^6-8\,a^4\,b^3\,c\,d^5+12\,a^3\,b^4\,c^2\,d^4-8\,a^2\,b^5\,c^3\,d^3+2\,a\,b^6\,c^4\,d^2}{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}+\frac{x\,\sqrt{-c\,d}\,\left(a\,d+b\,c\right)\,\left(16\,a^5\,b^2\,d^7-48\,a^4\,b^3\,c\,d^6+32\,a^3\,b^4\,c^2\,d^5+32\,a^2\,b^5\,c^3\,d^4-48\,a\,b^6\,c^4\,d^3+16\,b^7\,c^5\,d^2\right)}{8\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)\,\left(a^2\,c\,d^3-2\,a\,b\,c^2\,d^2+b^2\,c^3\,d\right)}\right)\,\left(a\,d+b\,c\right)}{4\,\left(a^2\,c\,d^3-2\,a\,b\,c^2\,d^2+b^2\,c^3\,d\right)}\right)\,\left(a\,d+b\,c\right)\,1{}\mathrm{i}}{4\,\left(a^2\,c\,d^3-2\,a\,b\,c^2\,d^2+b^2\,c^3\,d\right)}}{\frac{\frac{a^2\,b^3\,d^2}{2}+\frac{c\,a\,b^4\,d}{2}}{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}-\frac{\sqrt{-c\,d}\,\left(\frac{x\,\left(5\,a^2\,b^3\,d^3+2\,a\,b^4\,c\,d^2+b^5\,c^2\,d\right)}{2\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}-\frac{\sqrt{-c\,d}\,\left(\frac{2\,a^5\,b^2\,d^6-8\,a^4\,b^3\,c\,d^5+12\,a^3\,b^4\,c^2\,d^4-8\,a^2\,b^5\,c^3\,d^3+2\,a\,b^6\,c^4\,d^2}{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}-\frac{x\,\sqrt{-c\,d}\,\left(a\,d+b\,c\right)\,\left(16\,a^5\,b^2\,d^7-48\,a^4\,b^3\,c\,d^6+32\,a^3\,b^4\,c^2\,d^5+32\,a^2\,b^5\,c^3\,d^4-48\,a\,b^6\,c^4\,d^3+16\,b^7\,c^5\,d^2\right)}{8\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)\,\left(a^2\,c\,d^3-2\,a\,b\,c^2\,d^2+b^2\,c^3\,d\right)}\right)\,\left(a\,d+b\,c\right)}{4\,\left(a^2\,c\,d^3-2\,a\,b\,c^2\,d^2+b^2\,c^3\,d\right)}\right)\,\left(a\,d+b\,c\right)}{4\,\left(a^2\,c\,d^3-2\,a\,b\,c^2\,d^2+b^2\,c^3\,d\right)}+\frac{\sqrt{-c\,d}\,\left(\frac{x\,\left(5\,a^2\,b^3\,d^3+2\,a\,b^4\,c\,d^2+b^5\,c^2\,d\right)}{2\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}+\frac{\sqrt{-c\,d}\,\left(\frac{2\,a^5\,b^2\,d^6-8\,a^4\,b^3\,c\,d^5+12\,a^3\,b^4\,c^2\,d^4-8\,a^2\,b^5\,c^3\,d^3+2\,a\,b^6\,c^4\,d^2}{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}+\frac{x\,\sqrt{-c\,d}\,\left(a\,d+b\,c\right)\,\left(16\,a^5\,b^2\,d^7-48\,a^4\,b^3\,c\,d^6+32\,a^3\,b^4\,c^2\,d^5+32\,a^2\,b^5\,c^3\,d^4-48\,a\,b^6\,c^4\,d^3+16\,b^7\,c^5\,d^2\right)}{8\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)\,\left(a^2\,c\,d^3-2\,a\,b\,c^2\,d^2+b^2\,c^3\,d\right)}\right)\,\left(a\,d+b\,c\right)}{4\,\left(a^2\,c\,d^3-2\,a\,b\,c^2\,d^2+b^2\,c^3\,d\right)}\right)\,\left(a\,d+b\,c\right)}{4\,\left(a^2\,c\,d^3-2\,a\,b\,c^2\,d^2+b^2\,c^3\,d\right)}}\right)\,\sqrt{-c\,d}\,\left(a\,d+b\,c\right)\,1{}\mathrm{i}}{2\,\left(a^2\,c\,d^3-2\,a\,b\,c^2\,d^2+b^2\,c^3\,d\right)}","Not used",1,"(atan(-(((-a*b)^(1/2)*(((-a*b)^(1/2)*((2*a^5*b^2*d^6 + 2*a*b^6*c^4*d^2 - 8*a^4*b^3*c*d^5 - 8*a^2*b^5*c^3*d^3 + 12*a^3*b^4*c^2*d^4)/(2*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)) - (x*(-a*b)^(1/2)*(16*a^5*b^2*d^7 + 16*b^7*c^5*d^2 - 48*a*b^6*c^4*d^3 - 48*a^4*b^3*c*d^6 + 32*a^2*b^5*c^3*d^4 + 32*a^3*b^4*c^2*d^5))/(8*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)^2)))/(2*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) - (x*(b^5*c^2*d + 5*a^2*b^3*d^3 + 2*a*b^4*c*d^2))/(4*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)))*1i)/(a^2*d^2 + b^2*c^2 - 2*a*b*c*d) - ((-a*b)^(1/2)*(((-a*b)^(1/2)*((2*a^5*b^2*d^6 + 2*a*b^6*c^4*d^2 - 8*a^4*b^3*c*d^5 - 8*a^2*b^5*c^3*d^3 + 12*a^3*b^4*c^2*d^4)/(2*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)) + (x*(-a*b)^(1/2)*(16*a^5*b^2*d^7 + 16*b^7*c^5*d^2 - 48*a*b^6*c^4*d^3 - 48*a^4*b^3*c*d^6 + 32*a^2*b^5*c^3*d^4 + 32*a^3*b^4*c^2*d^5))/(8*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)^2)))/(2*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) + (x*(b^5*c^2*d + 5*a^2*b^3*d^3 + 2*a*b^4*c*d^2))/(4*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)))*1i)/(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/(((a^2*b^3*d^2)/2 + (a*b^4*c*d)/2)/(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2) + ((-a*b)^(1/2)*(((-a*b)^(1/2)*((2*a^5*b^2*d^6 + 2*a*b^6*c^4*d^2 - 8*a^4*b^3*c*d^5 - 8*a^2*b^5*c^3*d^3 + 12*a^3*b^4*c^2*d^4)/(2*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)) - (x*(-a*b)^(1/2)*(16*a^5*b^2*d^7 + 16*b^7*c^5*d^2 - 48*a*b^6*c^4*d^3 - 48*a^4*b^3*c*d^6 + 32*a^2*b^5*c^3*d^4 + 32*a^3*b^4*c^2*d^5))/(8*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)^2)))/(2*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) - (x*(b^5*c^2*d + 5*a^2*b^3*d^3 + 2*a*b^4*c*d^2))/(4*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))))/(a^2*d^2 + b^2*c^2 - 2*a*b*c*d) + ((-a*b)^(1/2)*(((-a*b)^(1/2)*((2*a^5*b^2*d^6 + 2*a*b^6*c^4*d^2 - 8*a^4*b^3*c*d^5 - 8*a^2*b^5*c^3*d^3 + 12*a^3*b^4*c^2*d^4)/(2*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)) + (x*(-a*b)^(1/2)*(16*a^5*b^2*d^7 + 16*b^7*c^5*d^2 - 48*a*b^6*c^4*d^3 - 48*a^4*b^3*c*d^6 + 32*a^2*b^5*c^3*d^4 + 32*a^3*b^4*c^2*d^5))/(8*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)^2)))/(2*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) + (x*(b^5*c^2*d + 5*a^2*b^3*d^3 + 2*a*b^4*c*d^2))/(4*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))))/(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)))*(-a*b)^(1/2)*1i)/(a^2*d^2 + b^2*c^2 - 2*a*b*c*d) - x/(2*(c + d*x^2)*(a*d - b*c)) + (atan((((-c*d)^(1/2)*((x*(b^5*c^2*d + 5*a^2*b^3*d^3 + 2*a*b^4*c*d^2))/(2*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) - ((-c*d)^(1/2)*((2*a^5*b^2*d^6 + 2*a*b^6*c^4*d^2 - 8*a^4*b^3*c*d^5 - 8*a^2*b^5*c^3*d^3 + 12*a^3*b^4*c^2*d^4)/(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2) - (x*(-c*d)^(1/2)*(a*d + b*c)*(16*a^5*b^2*d^7 + 16*b^7*c^5*d^2 - 48*a*b^6*c^4*d^3 - 48*a^4*b^3*c*d^6 + 32*a^2*b^5*c^3*d^4 + 32*a^3*b^4*c^2*d^5))/(8*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)*(a^2*c*d^3 + b^2*c^3*d - 2*a*b*c^2*d^2)))*(a*d + b*c))/(4*(a^2*c*d^3 + b^2*c^3*d - 2*a*b*c^2*d^2)))*(a*d + b*c)*1i)/(4*(a^2*c*d^3 + b^2*c^3*d - 2*a*b*c^2*d^2)) + ((-c*d)^(1/2)*((x*(b^5*c^2*d + 5*a^2*b^3*d^3 + 2*a*b^4*c*d^2))/(2*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) + ((-c*d)^(1/2)*((2*a^5*b^2*d^6 + 2*a*b^6*c^4*d^2 - 8*a^4*b^3*c*d^5 - 8*a^2*b^5*c^3*d^3 + 12*a^3*b^4*c^2*d^4)/(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2) + (x*(-c*d)^(1/2)*(a*d + b*c)*(16*a^5*b^2*d^7 + 16*b^7*c^5*d^2 - 48*a*b^6*c^4*d^3 - 48*a^4*b^3*c*d^6 + 32*a^2*b^5*c^3*d^4 + 32*a^3*b^4*c^2*d^5))/(8*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)*(a^2*c*d^3 + b^2*c^3*d - 2*a*b*c^2*d^2)))*(a*d + b*c))/(4*(a^2*c*d^3 + b^2*c^3*d - 2*a*b*c^2*d^2)))*(a*d + b*c)*1i)/(4*(a^2*c*d^3 + b^2*c^3*d - 2*a*b*c^2*d^2)))/(((a^2*b^3*d^2)/2 + (a*b^4*c*d)/2)/(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2) - ((-c*d)^(1/2)*((x*(b^5*c^2*d + 5*a^2*b^3*d^3 + 2*a*b^4*c*d^2))/(2*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) - ((-c*d)^(1/2)*((2*a^5*b^2*d^6 + 2*a*b^6*c^4*d^2 - 8*a^4*b^3*c*d^5 - 8*a^2*b^5*c^3*d^3 + 12*a^3*b^4*c^2*d^4)/(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2) - (x*(-c*d)^(1/2)*(a*d + b*c)*(16*a^5*b^2*d^7 + 16*b^7*c^5*d^2 - 48*a*b^6*c^4*d^3 - 48*a^4*b^3*c*d^6 + 32*a^2*b^5*c^3*d^4 + 32*a^3*b^4*c^2*d^5))/(8*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)*(a^2*c*d^3 + b^2*c^3*d - 2*a*b*c^2*d^2)))*(a*d + b*c))/(4*(a^2*c*d^3 + b^2*c^3*d - 2*a*b*c^2*d^2)))*(a*d + b*c))/(4*(a^2*c*d^3 + b^2*c^3*d - 2*a*b*c^2*d^2)) + ((-c*d)^(1/2)*((x*(b^5*c^2*d + 5*a^2*b^3*d^3 + 2*a*b^4*c*d^2))/(2*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) + ((-c*d)^(1/2)*((2*a^5*b^2*d^6 + 2*a*b^6*c^4*d^2 - 8*a^4*b^3*c*d^5 - 8*a^2*b^5*c^3*d^3 + 12*a^3*b^4*c^2*d^4)/(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2) + (x*(-c*d)^(1/2)*(a*d + b*c)*(16*a^5*b^2*d^7 + 16*b^7*c^5*d^2 - 48*a*b^6*c^4*d^3 - 48*a^4*b^3*c*d^6 + 32*a^2*b^5*c^3*d^4 + 32*a^3*b^4*c^2*d^5))/(8*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)*(a^2*c*d^3 + b^2*c^3*d - 2*a*b*c^2*d^2)))*(a*d + b*c))/(4*(a^2*c*d^3 + b^2*c^3*d - 2*a*b*c^2*d^2)))*(a*d + b*c))/(4*(a^2*c*d^3 + b^2*c^3*d - 2*a*b*c^2*d^2))))*(-c*d)^(1/2)*(a*d + b*c)*1i)/(2*(a^2*c*d^3 + b^2*c^3*d - 2*a*b*c^2*d^2))","B"
245,1,160,70,0.270619,"\text{Not used}","int(x/((a + b*x^2)*(c + d*x^2)^2),x)","\frac{-a\,d+c\,\left(b+b\,\mathrm{atan}\left(\frac{a\,d\,x^2\,1{}\mathrm{i}-b\,c\,x^2\,1{}\mathrm{i}}{2\,a\,c+a\,d\,x^2+b\,c\,x^2}\right)\,2{}\mathrm{i}\right)+b\,d\,x^2\,\mathrm{atan}\left(\frac{a\,d\,x^2\,1{}\mathrm{i}-b\,c\,x^2\,1{}\mathrm{i}}{2\,a\,c+a\,d\,x^2+b\,c\,x^2}\right)\,2{}\mathrm{i}}{2\,a^2\,c\,d^2+2\,a^2\,d^3\,x^2-4\,a\,b\,c^2\,d-4\,a\,b\,c\,d^2\,x^2+2\,b^2\,c^3+2\,b^2\,c^2\,d\,x^2}","Not used",1,"(c*(b + b*atan((a*d*x^2*1i - b*c*x^2*1i)/(2*a*c + a*d*x^2 + b*c*x^2))*2i) - a*d + b*d*x^2*atan((a*d*x^2*1i - b*c*x^2*1i)/(2*a*c + a*d*x^2 + b*c*x^2))*2i)/(2*b^2*c^3 + 2*a^2*c*d^2 + 2*a^2*d^3*x^2 + 2*b^2*c^2*d*x^2 - 4*a*b*c^2*d - 4*a*b*c*d^2*x^2)","B"
246,1,3637,109,0.978325,"\text{Not used}","int(1/((a + b*x^2)*(c + d*x^2)^2),x)","\frac{d\,x}{2\,c\,\left(d\,x^2+c\right)\,\left(a\,d-b\,c\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-a\,b^3}\,\left(\frac{\left(\frac{-2\,a^5\,b^2\,c\,d^7+12\,a^4\,b^3\,c^2\,d^6-28\,a^3\,b^4\,c^3\,d^5+32\,a^2\,b^5\,c^4\,d^4-18\,a\,b^6\,c^5\,d^3+4\,b^7\,c^6\,d^2}{2\,\left(-a^3\,c^2\,d^3+3\,a^2\,b\,c^3\,d^2-3\,a\,b^2\,c^4\,d+b^3\,c^5\right)}-\frac{x\,\sqrt{-a\,b^3}\,\left(16\,a^5\,b^2\,c^2\,d^7-48\,a^4\,b^3\,c^3\,d^6+32\,a^3\,b^4\,c^4\,d^5+32\,a^2\,b^5\,c^5\,d^4-48\,a\,b^6\,c^6\,d^3+16\,b^7\,c^7\,d^2\right)}{8\,\left(a^2\,c^2\,d^2-2\,a\,b\,c^3\,d+b^2\,c^4\right)\,\left(a^3\,d^2-2\,a^2\,b\,c\,d+a\,b^2\,c^2\right)}\right)\,\sqrt{-a\,b^3}}{2\,\left(a^3\,d^2-2\,a^2\,b\,c\,d+a\,b^2\,c^2\right)}-\frac{x\,\left(a^2\,b^3\,d^5-6\,a\,b^4\,c\,d^4+13\,b^5\,c^2\,d^3\right)}{4\,\left(a^2\,c^2\,d^2-2\,a\,b\,c^3\,d+b^2\,c^4\right)}\right)\,1{}\mathrm{i}}{a^3\,d^2-2\,a^2\,b\,c\,d+a\,b^2\,c^2}-\frac{\sqrt{-a\,b^3}\,\left(\frac{\left(\frac{-2\,a^5\,b^2\,c\,d^7+12\,a^4\,b^3\,c^2\,d^6-28\,a^3\,b^4\,c^3\,d^5+32\,a^2\,b^5\,c^4\,d^4-18\,a\,b^6\,c^5\,d^3+4\,b^7\,c^6\,d^2}{2\,\left(-a^3\,c^2\,d^3+3\,a^2\,b\,c^3\,d^2-3\,a\,b^2\,c^4\,d+b^3\,c^5\right)}+\frac{x\,\sqrt{-a\,b^3}\,\left(16\,a^5\,b^2\,c^2\,d^7-48\,a^4\,b^3\,c^3\,d^6+32\,a^3\,b^4\,c^4\,d^5+32\,a^2\,b^5\,c^5\,d^4-48\,a\,b^6\,c^6\,d^3+16\,b^7\,c^7\,d^2\right)}{8\,\left(a^2\,c^2\,d^2-2\,a\,b\,c^3\,d+b^2\,c^4\right)\,\left(a^3\,d^2-2\,a^2\,b\,c\,d+a\,b^2\,c^2\right)}\right)\,\sqrt{-a\,b^3}}{2\,\left(a^3\,d^2-2\,a^2\,b\,c\,d+a\,b^2\,c^2\right)}+\frac{x\,\left(a^2\,b^3\,d^5-6\,a\,b^4\,c\,d^4+13\,b^5\,c^2\,d^3\right)}{4\,\left(a^2\,c^2\,d^2-2\,a\,b\,c^3\,d+b^2\,c^4\right)}\right)\,1{}\mathrm{i}}{a^3\,d^2-2\,a^2\,b\,c\,d+a\,b^2\,c^2}}{\frac{\sqrt{-a\,b^3}\,\left(\frac{\left(\frac{-2\,a^5\,b^2\,c\,d^7+12\,a^4\,b^3\,c^2\,d^6-28\,a^3\,b^4\,c^3\,d^5+32\,a^2\,b^5\,c^4\,d^4-18\,a\,b^6\,c^5\,d^3+4\,b^7\,c^6\,d^2}{2\,\left(-a^3\,c^2\,d^3+3\,a^2\,b\,c^3\,d^2-3\,a\,b^2\,c^4\,d+b^3\,c^5\right)}-\frac{x\,\sqrt{-a\,b^3}\,\left(16\,a^5\,b^2\,c^2\,d^7-48\,a^4\,b^3\,c^3\,d^6+32\,a^3\,b^4\,c^4\,d^5+32\,a^2\,b^5\,c^5\,d^4-48\,a\,b^6\,c^6\,d^3+16\,b^7\,c^7\,d^2\right)}{8\,\left(a^2\,c^2\,d^2-2\,a\,b\,c^3\,d+b^2\,c^4\right)\,\left(a^3\,d^2-2\,a^2\,b\,c\,d+a\,b^2\,c^2\right)}\right)\,\sqrt{-a\,b^3}}{2\,\left(a^3\,d^2-2\,a^2\,b\,c\,d+a\,b^2\,c^2\right)}-\frac{x\,\left(a^2\,b^3\,d^5-6\,a\,b^4\,c\,d^4+13\,b^5\,c^2\,d^3\right)}{4\,\left(a^2\,c^2\,d^2-2\,a\,b\,c^3\,d+b^2\,c^4\right)}\right)}{a^3\,d^2-2\,a^2\,b\,c\,d+a\,b^2\,c^2}-\frac{\frac{a\,b^4\,d^4}{2}-\frac{3\,b^5\,c\,d^3}{2}}{-a^3\,c^2\,d^3+3\,a^2\,b\,c^3\,d^2-3\,a\,b^2\,c^4\,d+b^3\,c^5}+\frac{\sqrt{-a\,b^3}\,\left(\frac{\left(\frac{-2\,a^5\,b^2\,c\,d^7+12\,a^4\,b^3\,c^2\,d^6-28\,a^3\,b^4\,c^3\,d^5+32\,a^2\,b^5\,c^4\,d^4-18\,a\,b^6\,c^5\,d^3+4\,b^7\,c^6\,d^2}{2\,\left(-a^3\,c^2\,d^3+3\,a^2\,b\,c^3\,d^2-3\,a\,b^2\,c^4\,d+b^3\,c^5\right)}+\frac{x\,\sqrt{-a\,b^3}\,\left(16\,a^5\,b^2\,c^2\,d^7-48\,a^4\,b^3\,c^3\,d^6+32\,a^3\,b^4\,c^4\,d^5+32\,a^2\,b^5\,c^5\,d^4-48\,a\,b^6\,c^6\,d^3+16\,b^7\,c^7\,d^2\right)}{8\,\left(a^2\,c^2\,d^2-2\,a\,b\,c^3\,d+b^2\,c^4\right)\,\left(a^3\,d^2-2\,a^2\,b\,c\,d+a\,b^2\,c^2\right)}\right)\,\sqrt{-a\,b^3}}{2\,\left(a^3\,d^2-2\,a^2\,b\,c\,d+a\,b^2\,c^2\right)}+\frac{x\,\left(a^2\,b^3\,d^5-6\,a\,b^4\,c\,d^4+13\,b^5\,c^2\,d^3\right)}{4\,\left(a^2\,c^2\,d^2-2\,a\,b\,c^3\,d+b^2\,c^4\right)}\right)}{a^3\,d^2-2\,a^2\,b\,c\,d+a\,b^2\,c^2}}\right)\,\sqrt{-a\,b^3}\,1{}\mathrm{i}}{a^3\,d^2-2\,a^2\,b\,c\,d+a\,b^2\,c^2}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-c^3\,d}\,\left(a\,d-3\,b\,c\right)\,\left(\frac{x\,\left(a^2\,b^3\,d^5-6\,a\,b^4\,c\,d^4+13\,b^5\,c^2\,d^3\right)}{2\,\left(a^2\,c^2\,d^2-2\,a\,b\,c^3\,d+b^2\,c^4\right)}-\frac{\left(\frac{-2\,a^5\,b^2\,c\,d^7+12\,a^4\,b^3\,c^2\,d^6-28\,a^3\,b^4\,c^3\,d^5+32\,a^2\,b^5\,c^4\,d^4-18\,a\,b^6\,c^5\,d^3+4\,b^7\,c^6\,d^2}{-a^3\,c^2\,d^3+3\,a^2\,b\,c^3\,d^2-3\,a\,b^2\,c^4\,d+b^3\,c^5}-\frac{x\,\sqrt{-c^3\,d}\,\left(a\,d-3\,b\,c\right)\,\left(16\,a^5\,b^2\,c^2\,d^7-48\,a^4\,b^3\,c^3\,d^6+32\,a^3\,b^4\,c^4\,d^5+32\,a^2\,b^5\,c^5\,d^4-48\,a\,b^6\,c^6\,d^3+16\,b^7\,c^7\,d^2\right)}{8\,\left(a^2\,c^2\,d^2-2\,a\,b\,c^3\,d+b^2\,c^4\right)\,\left(a^2\,c^3\,d^2-2\,a\,b\,c^4\,d+b^2\,c^5\right)}\right)\,\sqrt{-c^3\,d}\,\left(a\,d-3\,b\,c\right)}{4\,\left(a^2\,c^3\,d^2-2\,a\,b\,c^4\,d+b^2\,c^5\right)}\right)\,1{}\mathrm{i}}{4\,\left(a^2\,c^3\,d^2-2\,a\,b\,c^4\,d+b^2\,c^5\right)}+\frac{\sqrt{-c^3\,d}\,\left(a\,d-3\,b\,c\right)\,\left(\frac{x\,\left(a^2\,b^3\,d^5-6\,a\,b^4\,c\,d^4+13\,b^5\,c^2\,d^3\right)}{2\,\left(a^2\,c^2\,d^2-2\,a\,b\,c^3\,d+b^2\,c^4\right)}+\frac{\left(\frac{-2\,a^5\,b^2\,c\,d^7+12\,a^4\,b^3\,c^2\,d^6-28\,a^3\,b^4\,c^3\,d^5+32\,a^2\,b^5\,c^4\,d^4-18\,a\,b^6\,c^5\,d^3+4\,b^7\,c^6\,d^2}{-a^3\,c^2\,d^3+3\,a^2\,b\,c^3\,d^2-3\,a\,b^2\,c^4\,d+b^3\,c^5}+\frac{x\,\sqrt{-c^3\,d}\,\left(a\,d-3\,b\,c\right)\,\left(16\,a^5\,b^2\,c^2\,d^7-48\,a^4\,b^3\,c^3\,d^6+32\,a^3\,b^4\,c^4\,d^5+32\,a^2\,b^5\,c^5\,d^4-48\,a\,b^6\,c^6\,d^3+16\,b^7\,c^7\,d^2\right)}{8\,\left(a^2\,c^2\,d^2-2\,a\,b\,c^3\,d+b^2\,c^4\right)\,\left(a^2\,c^3\,d^2-2\,a\,b\,c^4\,d+b^2\,c^5\right)}\right)\,\sqrt{-c^3\,d}\,\left(a\,d-3\,b\,c\right)}{4\,\left(a^2\,c^3\,d^2-2\,a\,b\,c^4\,d+b^2\,c^5\right)}\right)\,1{}\mathrm{i}}{4\,\left(a^2\,c^3\,d^2-2\,a\,b\,c^4\,d+b^2\,c^5\right)}}{\frac{\frac{a\,b^4\,d^4}{2}-\frac{3\,b^5\,c\,d^3}{2}}{-a^3\,c^2\,d^3+3\,a^2\,b\,c^3\,d^2-3\,a\,b^2\,c^4\,d+b^3\,c^5}+\frac{\sqrt{-c^3\,d}\,\left(a\,d-3\,b\,c\right)\,\left(\frac{x\,\left(a^2\,b^3\,d^5-6\,a\,b^4\,c\,d^4+13\,b^5\,c^2\,d^3\right)}{2\,\left(a^2\,c^2\,d^2-2\,a\,b\,c^3\,d+b^2\,c^4\right)}-\frac{\left(\frac{-2\,a^5\,b^2\,c\,d^7+12\,a^4\,b^3\,c^2\,d^6-28\,a^3\,b^4\,c^3\,d^5+32\,a^2\,b^5\,c^4\,d^4-18\,a\,b^6\,c^5\,d^3+4\,b^7\,c^6\,d^2}{-a^3\,c^2\,d^3+3\,a^2\,b\,c^3\,d^2-3\,a\,b^2\,c^4\,d+b^3\,c^5}-\frac{x\,\sqrt{-c^3\,d}\,\left(a\,d-3\,b\,c\right)\,\left(16\,a^5\,b^2\,c^2\,d^7-48\,a^4\,b^3\,c^3\,d^6+32\,a^3\,b^4\,c^4\,d^5+32\,a^2\,b^5\,c^5\,d^4-48\,a\,b^6\,c^6\,d^3+16\,b^7\,c^7\,d^2\right)}{8\,\left(a^2\,c^2\,d^2-2\,a\,b\,c^3\,d+b^2\,c^4\right)\,\left(a^2\,c^3\,d^2-2\,a\,b\,c^4\,d+b^2\,c^5\right)}\right)\,\sqrt{-c^3\,d}\,\left(a\,d-3\,b\,c\right)}{4\,\left(a^2\,c^3\,d^2-2\,a\,b\,c^4\,d+b^2\,c^5\right)}\right)}{4\,\left(a^2\,c^3\,d^2-2\,a\,b\,c^4\,d+b^2\,c^5\right)}-\frac{\sqrt{-c^3\,d}\,\left(a\,d-3\,b\,c\right)\,\left(\frac{x\,\left(a^2\,b^3\,d^5-6\,a\,b^4\,c\,d^4+13\,b^5\,c^2\,d^3\right)}{2\,\left(a^2\,c^2\,d^2-2\,a\,b\,c^3\,d+b^2\,c^4\right)}+\frac{\left(\frac{-2\,a^5\,b^2\,c\,d^7+12\,a^4\,b^3\,c^2\,d^6-28\,a^3\,b^4\,c^3\,d^5+32\,a^2\,b^5\,c^4\,d^4-18\,a\,b^6\,c^5\,d^3+4\,b^7\,c^6\,d^2}{-a^3\,c^2\,d^3+3\,a^2\,b\,c^3\,d^2-3\,a\,b^2\,c^4\,d+b^3\,c^5}+\frac{x\,\sqrt{-c^3\,d}\,\left(a\,d-3\,b\,c\right)\,\left(16\,a^5\,b^2\,c^2\,d^7-48\,a^4\,b^3\,c^3\,d^6+32\,a^3\,b^4\,c^4\,d^5+32\,a^2\,b^5\,c^5\,d^4-48\,a\,b^6\,c^6\,d^3+16\,b^7\,c^7\,d^2\right)}{8\,\left(a^2\,c^2\,d^2-2\,a\,b\,c^3\,d+b^2\,c^4\right)\,\left(a^2\,c^3\,d^2-2\,a\,b\,c^4\,d+b^2\,c^5\right)}\right)\,\sqrt{-c^3\,d}\,\left(a\,d-3\,b\,c\right)}{4\,\left(a^2\,c^3\,d^2-2\,a\,b\,c^4\,d+b^2\,c^5\right)}\right)}{4\,\left(a^2\,c^3\,d^2-2\,a\,b\,c^4\,d+b^2\,c^5\right)}}\right)\,\sqrt{-c^3\,d}\,\left(a\,d-3\,b\,c\right)\,1{}\mathrm{i}}{2\,\left(a^2\,c^3\,d^2-2\,a\,b\,c^4\,d+b^2\,c^5\right)}","Not used",1,"(d*x)/(2*c*(c + d*x^2)*(a*d - b*c)) - (atan((((-c^3*d)^(1/2)*(a*d - 3*b*c)*((x*(a^2*b^3*d^5 + 13*b^5*c^2*d^3 - 6*a*b^4*c*d^4))/(2*(b^2*c^4 + a^2*c^2*d^2 - 2*a*b*c^3*d)) - (((4*b^7*c^6*d^2 - 18*a*b^6*c^5*d^3 - 2*a^5*b^2*c*d^7 + 32*a^2*b^5*c^4*d^4 - 28*a^3*b^4*c^3*d^5 + 12*a^4*b^3*c^2*d^6)/(b^3*c^5 - a^3*c^2*d^3 + 3*a^2*b*c^3*d^2 - 3*a*b^2*c^4*d) - (x*(-c^3*d)^(1/2)*(a*d - 3*b*c)*(16*b^7*c^7*d^2 - 48*a*b^6*c^6*d^3 + 32*a^2*b^5*c^5*d^4 + 32*a^3*b^4*c^4*d^5 - 48*a^4*b^3*c^3*d^6 + 16*a^5*b^2*c^2*d^7))/(8*(b^2*c^4 + a^2*c^2*d^2 - 2*a*b*c^3*d)*(b^2*c^5 + a^2*c^3*d^2 - 2*a*b*c^4*d)))*(-c^3*d)^(1/2)*(a*d - 3*b*c))/(4*(b^2*c^5 + a^2*c^3*d^2 - 2*a*b*c^4*d)))*1i)/(4*(b^2*c^5 + a^2*c^3*d^2 - 2*a*b*c^4*d)) + ((-c^3*d)^(1/2)*(a*d - 3*b*c)*((x*(a^2*b^3*d^5 + 13*b^5*c^2*d^3 - 6*a*b^4*c*d^4))/(2*(b^2*c^4 + a^2*c^2*d^2 - 2*a*b*c^3*d)) + (((4*b^7*c^6*d^2 - 18*a*b^6*c^5*d^3 - 2*a^5*b^2*c*d^7 + 32*a^2*b^5*c^4*d^4 - 28*a^3*b^4*c^3*d^5 + 12*a^4*b^3*c^2*d^6)/(b^3*c^5 - a^3*c^2*d^3 + 3*a^2*b*c^3*d^2 - 3*a*b^2*c^4*d) + (x*(-c^3*d)^(1/2)*(a*d - 3*b*c)*(16*b^7*c^7*d^2 - 48*a*b^6*c^6*d^3 + 32*a^2*b^5*c^5*d^4 + 32*a^3*b^4*c^4*d^5 - 48*a^4*b^3*c^3*d^6 + 16*a^5*b^2*c^2*d^7))/(8*(b^2*c^4 + a^2*c^2*d^2 - 2*a*b*c^3*d)*(b^2*c^5 + a^2*c^3*d^2 - 2*a*b*c^4*d)))*(-c^3*d)^(1/2)*(a*d - 3*b*c))/(4*(b^2*c^5 + a^2*c^3*d^2 - 2*a*b*c^4*d)))*1i)/(4*(b^2*c^5 + a^2*c^3*d^2 - 2*a*b*c^4*d)))/(((a*b^4*d^4)/2 - (3*b^5*c*d^3)/2)/(b^3*c^5 - a^3*c^2*d^3 + 3*a^2*b*c^3*d^2 - 3*a*b^2*c^4*d) + ((-c^3*d)^(1/2)*(a*d - 3*b*c)*((x*(a^2*b^3*d^5 + 13*b^5*c^2*d^3 - 6*a*b^4*c*d^4))/(2*(b^2*c^4 + a^2*c^2*d^2 - 2*a*b*c^3*d)) - (((4*b^7*c^6*d^2 - 18*a*b^6*c^5*d^3 - 2*a^5*b^2*c*d^7 + 32*a^2*b^5*c^4*d^4 - 28*a^3*b^4*c^3*d^5 + 12*a^4*b^3*c^2*d^6)/(b^3*c^5 - a^3*c^2*d^3 + 3*a^2*b*c^3*d^2 - 3*a*b^2*c^4*d) - (x*(-c^3*d)^(1/2)*(a*d - 3*b*c)*(16*b^7*c^7*d^2 - 48*a*b^6*c^6*d^3 + 32*a^2*b^5*c^5*d^4 + 32*a^3*b^4*c^4*d^5 - 48*a^4*b^3*c^3*d^6 + 16*a^5*b^2*c^2*d^7))/(8*(b^2*c^4 + a^2*c^2*d^2 - 2*a*b*c^3*d)*(b^2*c^5 + a^2*c^3*d^2 - 2*a*b*c^4*d)))*(-c^3*d)^(1/2)*(a*d - 3*b*c))/(4*(b^2*c^5 + a^2*c^3*d^2 - 2*a*b*c^4*d))))/(4*(b^2*c^5 + a^2*c^3*d^2 - 2*a*b*c^4*d)) - ((-c^3*d)^(1/2)*(a*d - 3*b*c)*((x*(a^2*b^3*d^5 + 13*b^5*c^2*d^3 - 6*a*b^4*c*d^4))/(2*(b^2*c^4 + a^2*c^2*d^2 - 2*a*b*c^3*d)) + (((4*b^7*c^6*d^2 - 18*a*b^6*c^5*d^3 - 2*a^5*b^2*c*d^7 + 32*a^2*b^5*c^4*d^4 - 28*a^3*b^4*c^3*d^5 + 12*a^4*b^3*c^2*d^6)/(b^3*c^5 - a^3*c^2*d^3 + 3*a^2*b*c^3*d^2 - 3*a*b^2*c^4*d) + (x*(-c^3*d)^(1/2)*(a*d - 3*b*c)*(16*b^7*c^7*d^2 - 48*a*b^6*c^6*d^3 + 32*a^2*b^5*c^5*d^4 + 32*a^3*b^4*c^4*d^5 - 48*a^4*b^3*c^3*d^6 + 16*a^5*b^2*c^2*d^7))/(8*(b^2*c^4 + a^2*c^2*d^2 - 2*a*b*c^3*d)*(b^2*c^5 + a^2*c^3*d^2 - 2*a*b*c^4*d)))*(-c^3*d)^(1/2)*(a*d - 3*b*c))/(4*(b^2*c^5 + a^2*c^3*d^2 - 2*a*b*c^4*d))))/(4*(b^2*c^5 + a^2*c^3*d^2 - 2*a*b*c^4*d))))*(-c^3*d)^(1/2)*(a*d - 3*b*c)*1i)/(2*(b^2*c^5 + a^2*c^3*d^2 - 2*a*b*c^4*d)) - (atan((((-a*b^3)^(1/2)*((((4*b^7*c^6*d^2 - 18*a*b^6*c^5*d^3 - 2*a^5*b^2*c*d^7 + 32*a^2*b^5*c^4*d^4 - 28*a^3*b^4*c^3*d^5 + 12*a^4*b^3*c^2*d^6)/(2*(b^3*c^5 - a^3*c^2*d^3 + 3*a^2*b*c^3*d^2 - 3*a*b^2*c^4*d)) - (x*(-a*b^3)^(1/2)*(16*b^7*c^7*d^2 - 48*a*b^6*c^6*d^3 + 32*a^2*b^5*c^5*d^4 + 32*a^3*b^4*c^4*d^5 - 48*a^4*b^3*c^3*d^6 + 16*a^5*b^2*c^2*d^7))/(8*(b^2*c^4 + a^2*c^2*d^2 - 2*a*b*c^3*d)*(a^3*d^2 + a*b^2*c^2 - 2*a^2*b*c*d)))*(-a*b^3)^(1/2))/(2*(a^3*d^2 + a*b^2*c^2 - 2*a^2*b*c*d)) - (x*(a^2*b^3*d^5 + 13*b^5*c^2*d^3 - 6*a*b^4*c*d^4))/(4*(b^2*c^4 + a^2*c^2*d^2 - 2*a*b*c^3*d)))*1i)/(a^3*d^2 + a*b^2*c^2 - 2*a^2*b*c*d) - ((-a*b^3)^(1/2)*((((4*b^7*c^6*d^2 - 18*a*b^6*c^5*d^3 - 2*a^5*b^2*c*d^7 + 32*a^2*b^5*c^4*d^4 - 28*a^3*b^4*c^3*d^5 + 12*a^4*b^3*c^2*d^6)/(2*(b^3*c^5 - a^3*c^2*d^3 + 3*a^2*b*c^3*d^2 - 3*a*b^2*c^4*d)) + (x*(-a*b^3)^(1/2)*(16*b^7*c^7*d^2 - 48*a*b^6*c^6*d^3 + 32*a^2*b^5*c^5*d^4 + 32*a^3*b^4*c^4*d^5 - 48*a^4*b^3*c^3*d^6 + 16*a^5*b^2*c^2*d^7))/(8*(b^2*c^4 + a^2*c^2*d^2 - 2*a*b*c^3*d)*(a^3*d^2 + a*b^2*c^2 - 2*a^2*b*c*d)))*(-a*b^3)^(1/2))/(2*(a^3*d^2 + a*b^2*c^2 - 2*a^2*b*c*d)) + (x*(a^2*b^3*d^5 + 13*b^5*c^2*d^3 - 6*a*b^4*c*d^4))/(4*(b^2*c^4 + a^2*c^2*d^2 - 2*a*b*c^3*d)))*1i)/(a^3*d^2 + a*b^2*c^2 - 2*a^2*b*c*d))/(((-a*b^3)^(1/2)*((((4*b^7*c^6*d^2 - 18*a*b^6*c^5*d^3 - 2*a^5*b^2*c*d^7 + 32*a^2*b^5*c^4*d^4 - 28*a^3*b^4*c^3*d^5 + 12*a^4*b^3*c^2*d^6)/(2*(b^3*c^5 - a^3*c^2*d^3 + 3*a^2*b*c^3*d^2 - 3*a*b^2*c^4*d)) - (x*(-a*b^3)^(1/2)*(16*b^7*c^7*d^2 - 48*a*b^6*c^6*d^3 + 32*a^2*b^5*c^5*d^4 + 32*a^3*b^4*c^4*d^5 - 48*a^4*b^3*c^3*d^6 + 16*a^5*b^2*c^2*d^7))/(8*(b^2*c^4 + a^2*c^2*d^2 - 2*a*b*c^3*d)*(a^3*d^2 + a*b^2*c^2 - 2*a^2*b*c*d)))*(-a*b^3)^(1/2))/(2*(a^3*d^2 + a*b^2*c^2 - 2*a^2*b*c*d)) - (x*(a^2*b^3*d^5 + 13*b^5*c^2*d^3 - 6*a*b^4*c*d^4))/(4*(b^2*c^4 + a^2*c^2*d^2 - 2*a*b*c^3*d))))/(a^3*d^2 + a*b^2*c^2 - 2*a^2*b*c*d) - ((a*b^4*d^4)/2 - (3*b^5*c*d^3)/2)/(b^3*c^5 - a^3*c^2*d^3 + 3*a^2*b*c^3*d^2 - 3*a*b^2*c^4*d) + ((-a*b^3)^(1/2)*((((4*b^7*c^6*d^2 - 18*a*b^6*c^5*d^3 - 2*a^5*b^2*c*d^7 + 32*a^2*b^5*c^4*d^4 - 28*a^3*b^4*c^3*d^5 + 12*a^4*b^3*c^2*d^6)/(2*(b^3*c^5 - a^3*c^2*d^3 + 3*a^2*b*c^3*d^2 - 3*a*b^2*c^4*d)) + (x*(-a*b^3)^(1/2)*(16*b^7*c^7*d^2 - 48*a*b^6*c^6*d^3 + 32*a^2*b^5*c^5*d^4 + 32*a^3*b^4*c^4*d^5 - 48*a^4*b^3*c^3*d^6 + 16*a^5*b^2*c^2*d^7))/(8*(b^2*c^4 + a^2*c^2*d^2 - 2*a*b*c^3*d)*(a^3*d^2 + a*b^2*c^2 - 2*a^2*b*c*d)))*(-a*b^3)^(1/2))/(2*(a^3*d^2 + a*b^2*c^2 - 2*a^2*b*c*d)) + (x*(a^2*b^3*d^5 + 13*b^5*c^2*d^3 - 6*a*b^4*c*d^4))/(4*(b^2*c^4 + a^2*c^2*d^2 - 2*a*b*c^3*d))))/(a^3*d^2 + a*b^2*c^2 - 2*a^2*b*c*d)))*(-a*b^3)^(1/2)*1i)/(a^3*d^2 + a*b^2*c^2 - 2*a^2*b*c*d)","B"
247,1,127,100,0.708176,"\text{Not used}","int(1/(x*(a + b*x^2)*(c + d*x^2)^2),x)","\frac{\ln\left(x\right)}{a\,c^2}-\frac{\ln\left(d\,x^2+c\right)\,\left(a\,d^2-2\,b\,c\,d\right)}{2\,a^2\,c^2\,d^2-4\,a\,b\,c^3\,d+2\,b^2\,c^4}-\frac{b^2\,\ln\left(b\,x^2+a\right)}{2\,a^3\,d^2-4\,a^2\,b\,c\,d+2\,a\,b^2\,c^2}+\frac{d}{2\,c\,\left(d\,x^2+c\right)\,\left(a\,d-b\,c\right)}","Not used",1,"log(x)/(a*c^2) - (log(c + d*x^2)*(a*d^2 - 2*b*c*d))/(2*b^2*c^4 + 2*a^2*c^2*d^2 - 4*a*b*c^3*d) - (b^2*log(a + b*x^2))/(2*a^3*d^2 + 2*a*b^2*c^2 - 4*a^2*b*c*d) + d/(2*c*(c + d*x^2)*(a*d - b*c))","B"
248,1,432,144,0.828525,"\text{Not used}","int(1/(x^2*(a + b*x^2)*(c + d*x^2)^2),x)","-\frac{\frac{1}{a\,c}+\frac{x^2\,\left(3\,a\,d^2-2\,b\,c\,d\right)}{2\,a\,c^2\,\left(a\,d-b\,c\right)}}{d\,x^3+c\,x}+\frac{\mathrm{atan}\left(\frac{b\,c^5\,x\,{\left(-a^3\,b^5\right)}^{3/2}\,4{}\mathrm{i}+a^8\,b\,d^5\,x\,\sqrt{-a^3\,b^5}\,9{}\mathrm{i}+a^6\,b^3\,c^2\,d^3\,x\,\sqrt{-a^3\,b^5}\,25{}\mathrm{i}-a^7\,b^2\,c\,d^4\,x\,\sqrt{-a^3\,b^5}\,30{}\mathrm{i}}{-9\,a^{10}\,b^3\,d^5+30\,a^9\,b^4\,c\,d^4-25\,a^8\,b^5\,c^2\,d^3+4\,a^5\,b^8\,c^5}\right)\,\sqrt{-a^3\,b^5}\,1{}\mathrm{i}}{a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2}+\frac{\mathrm{atan}\left(\frac{a^5\,d^3\,x\,{\left(-c^5\,d^3\right)}^{3/2}\,9{}\mathrm{i}+b^5\,c^{10}\,d\,x\,\sqrt{-c^5\,d^3}\,4{}\mathrm{i}-a^4\,b\,c\,d^2\,x\,{\left(-c^5\,d^3\right)}^{3/2}\,30{}\mathrm{i}+a^3\,b^2\,c^2\,d\,x\,{\left(-c^5\,d^3\right)}^{3/2}\,25{}\mathrm{i}}{9\,a^5\,c^8\,d^7-30\,a^4\,b\,c^9\,d^6+25\,a^3\,b^2\,c^{10}\,d^5-4\,b^5\,c^{13}\,d^2}\right)\,\left(3\,a\,d-5\,b\,c\right)\,\sqrt{-c^5\,d^3}\,1{}\mathrm{i}}{2\,\left(a^2\,c^5\,d^2-2\,a\,b\,c^6\,d+b^2\,c^7\right)}","Not used",1,"(atan((b*c^5*x*(-a^3*b^5)^(3/2)*4i + a^8*b*d^5*x*(-a^3*b^5)^(1/2)*9i + a^6*b^3*c^2*d^3*x*(-a^3*b^5)^(1/2)*25i - a^7*b^2*c*d^4*x*(-a^3*b^5)^(1/2)*30i)/(4*a^5*b^8*c^5 - 9*a^10*b^3*d^5 + 30*a^9*b^4*c*d^4 - 25*a^8*b^5*c^2*d^3))*(-a^3*b^5)^(1/2)*1i)/(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d) - (1/(a*c) + (x^2*(3*a*d^2 - 2*b*c*d))/(2*a*c^2*(a*d - b*c)))/(c*x + d*x^3) + (atan((a^5*d^3*x*(-c^5*d^3)^(3/2)*9i + b^5*c^10*d*x*(-c^5*d^3)^(1/2)*4i - a^4*b*c*d^2*x*(-c^5*d^3)^(3/2)*30i + a^3*b^2*c^2*d*x*(-c^5*d^3)^(3/2)*25i)/(9*a^5*c^8*d^7 - 4*b^5*c^13*d^2 - 30*a^4*b*c^9*d^6 + 25*a^3*b^2*c^10*d^5))*(3*a*d - 5*b*c)*(-c^5*d^3)^(1/2)*1i)/(2*(b^2*c^7 + a^2*c^5*d^2 - 2*a*b*c^6*d))","B"
249,1,171,126,0.927657,"\text{Not used}","int(1/(x^3*(a + b*x^2)*(c + d*x^2)^2),x)","\frac{b^3\,\ln\left(b\,x^2+a\right)}{2\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}-\frac{\frac{1}{2\,a\,c}+\frac{x^2\,\left(2\,a\,d^2-b\,c\,d\right)}{2\,a\,c^2\,\left(a\,d-b\,c\right)}}{d\,x^4+c\,x^2}+\frac{\ln\left(d\,x^2+c\right)\,\left(2\,a\,d^3-3\,b\,c\,d^2\right)}{2\,a^2\,c^3\,d^2-4\,a\,b\,c^4\,d+2\,b^2\,c^5}-\frac{\ln\left(x\right)\,\left(2\,a\,d+b\,c\right)}{a^2\,c^3}","Not used",1,"(b^3*log(a + b*x^2))/(2*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)) - (1/(2*a*c) + (x^2*(2*a*d^2 - b*c*d))/(2*a*c^2*(a*d - b*c)))/(c*x^2 + d*x^4) + (log(c + d*x^2)*(2*a*d^3 - 3*b*c*d^2))/(2*b^2*c^5 + 2*a^2*c^3*d^2 - 4*a*b*c^4*d) - (log(x)*(2*a*d + b*c))/(a^2*c^3)","B"
250,1,469,189,0.938474,"\text{Not used}","int(1/(x^4*(a + b*x^2)*(c + d*x^2)^2),x)","-\frac{\frac{1}{3\,a\,c}-\frac{x^2\,\left(5\,a\,d+3\,b\,c\right)}{3\,a^2\,c^2}+\frac{x^4\,\left(-5\,a^2\,d^3+2\,a\,b\,c\,d^2+2\,b^2\,c^2\,d\right)}{2\,a^2\,c^3\,\left(a\,d-b\,c\right)}}{d\,x^5+c\,x^3}-\frac{\mathrm{atan}\left(\frac{b\,c^7\,x\,{\left(-a^5\,b^7\right)}^{3/2}\,4{}\mathrm{i}+a^{12}\,b\,d^7\,x\,\sqrt{-a^5\,b^7}\,25{}\mathrm{i}+a^{10}\,b^3\,c^2\,d^5\,x\,\sqrt{-a^5\,b^7}\,49{}\mathrm{i}-a^{11}\,b^2\,c\,d^6\,x\,\sqrt{-a^5\,b^7}\,70{}\mathrm{i}}{-25\,a^{15}\,b^4\,d^7+70\,a^{14}\,b^5\,c\,d^6-49\,a^{13}\,b^6\,c^2\,d^5+4\,a^8\,b^{11}\,c^7}\right)\,\sqrt{-a^5\,b^7}\,1{}\mathrm{i}}{a^7\,d^2-2\,a^6\,b\,c\,d+a^5\,b^2\,c^2}-\frac{\mathrm{atan}\left(\frac{a^7\,d^3\,x\,{\left(-c^7\,d^5\right)}^{3/2}\,25{}\mathrm{i}+b^7\,c^{14}\,d\,x\,\sqrt{-c^7\,d^5}\,4{}\mathrm{i}-a^6\,b\,c\,d^2\,x\,{\left(-c^7\,d^5\right)}^{3/2}\,70{}\mathrm{i}+a^5\,b^2\,c^2\,d\,x\,{\left(-c^7\,d^5\right)}^{3/2}\,49{}\mathrm{i}}{25\,a^7\,c^{11}\,d^{10}-70\,a^6\,b\,c^{12}\,d^9+49\,a^5\,b^2\,c^{13}\,d^8-4\,b^7\,c^{18}\,d^3}\right)\,\left(5\,a\,d-7\,b\,c\right)\,\sqrt{-c^7\,d^5}\,1{}\mathrm{i}}{2\,\left(a^2\,c^7\,d^2-2\,a\,b\,c^8\,d+b^2\,c^9\right)}","Not used",1,"- (1/(3*a*c) - (x^2*(5*a*d + 3*b*c))/(3*a^2*c^2) + (x^4*(2*b^2*c^2*d - 5*a^2*d^3 + 2*a*b*c*d^2))/(2*a^2*c^3*(a*d - b*c)))/(c*x^3 + d*x^5) - (atan((b*c^7*x*(-a^5*b^7)^(3/2)*4i + a^12*b*d^7*x*(-a^5*b^7)^(1/2)*25i + a^10*b^3*c^2*d^5*x*(-a^5*b^7)^(1/2)*49i - a^11*b^2*c*d^6*x*(-a^5*b^7)^(1/2)*70i)/(4*a^8*b^11*c^7 - 25*a^15*b^4*d^7 + 70*a^14*b^5*c*d^6 - 49*a^13*b^6*c^2*d^5))*(-a^5*b^7)^(1/2)*1i)/(a^7*d^2 + a^5*b^2*c^2 - 2*a^6*b*c*d) - (atan((a^7*d^3*x*(-c^7*d^5)^(3/2)*25i + b^7*c^14*d*x*(-c^7*d^5)^(1/2)*4i - a^6*b*c*d^2*x*(-c^7*d^5)^(3/2)*70i + a^5*b^2*c^2*d*x*(-c^7*d^5)^(3/2)*49i)/(25*a^7*c^11*d^10 - 4*b^7*c^18*d^3 - 70*a^6*b*c^12*d^9 + 49*a^5*b^2*c^13*d^8))*(5*a*d - 7*b*c)*(-c^7*d^5)^(1/2)*1i)/(2*(b^2*c^9 + a^2*c^7*d^2 - 2*a*b*c^8*d))","B"
251,1,370,116,0.524099,"\text{Not used}","int(x^5/((a + b*x^2)^3*(c + d*x^2)),x)","\frac{b^3\,\left(4\,a\,c^2\,x^2+a\,c^2\,x^2\,\mathrm{atan}\left(\frac{a\,d\,x^2\,1{}\mathrm{i}-b\,c\,x^2\,1{}\mathrm{i}}{2\,a\,c+a\,d\,x^2+b\,c\,x^2}\right)\,8{}\mathrm{i}\right)+b\,\left(2\,a^3\,d^2\,x^2-4\,a^3\,c\,d\right)+a^4\,d^2+b^2\,\left(3\,a^2\,c^2-6\,a^2\,c\,d\,x^2+a^2\,c^2\,\mathrm{atan}\left(\frac{a\,d\,x^2\,1{}\mathrm{i}-b\,c\,x^2\,1{}\mathrm{i}}{2\,a\,c+a\,d\,x^2+b\,c\,x^2}\right)\,4{}\mathrm{i}\right)+b^4\,c^2\,x^4\,\mathrm{atan}\left(\frac{a\,d\,x^2\,1{}\mathrm{i}-b\,c\,x^2\,1{}\mathrm{i}}{2\,a\,c+a\,d\,x^2+b\,c\,x^2}\right)\,4{}\mathrm{i}}{-4\,a^5\,b^2\,d^3+12\,a^4\,b^3\,c\,d^2-8\,a^4\,b^3\,d^3\,x^2-12\,a^3\,b^4\,c^2\,d+24\,a^3\,b^4\,c\,d^2\,x^2-4\,a^3\,b^4\,d^3\,x^4+4\,a^2\,b^5\,c^3-24\,a^2\,b^5\,c^2\,d\,x^2+12\,a^2\,b^5\,c\,d^2\,x^4+8\,a\,b^6\,c^3\,x^2-12\,a\,b^6\,c^2\,d\,x^4+4\,b^7\,c^3\,x^4}","Not used",1,"(b^3*(4*a*c^2*x^2 + a*c^2*x^2*atan((a*d*x^2*1i - b*c*x^2*1i)/(2*a*c + a*d*x^2 + b*c*x^2))*8i) + b*(2*a^3*d^2*x^2 - 4*a^3*c*d) + a^4*d^2 + b^2*(3*a^2*c^2 + a^2*c^2*atan((a*d*x^2*1i - b*c*x^2*1i)/(2*a*c + a*d*x^2 + b*c*x^2))*4i - 6*a^2*c*d*x^2) + b^4*c^2*x^4*atan((a*d*x^2*1i - b*c*x^2*1i)/(2*a*c + a*d*x^2 + b*c*x^2))*4i)/(4*a^2*b^5*c^3 - 4*a^5*b^2*d^3 + 4*b^7*c^3*x^4 - 12*a^3*b^4*c^2*d + 12*a^4*b^3*c*d^2 + 8*a*b^6*c^3*x^2 - 8*a^4*b^3*d^3*x^2 - 4*a^3*b^4*d^3*x^4 - 12*a*b^6*c^2*d*x^4 - 24*a^2*b^5*c^2*d*x^2 + 24*a^3*b^4*c*d^2*x^2 + 12*a^2*b^5*c*d^2*x^4)","B"
252,1,5754,157,1.983889,"\text{Not used}","int(x^4/((a + b*x^2)*(c + d*x^2)^3),x)","-\frac{\frac{x^3\,\left(5\,a\,d-b\,c\right)}{8\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}+\frac{c\,x\,\left(3\,a\,d+b\,c\right)}{8\,\left(a^2\,d^3-2\,a\,b\,c\,d^2+b^2\,c^2\,d\right)}}{c^2+2\,c\,d\,x^2+d^2\,x^4}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-a^3\,b}\,\left(\frac{\sqrt{-a^3\,b}\,\left(\frac{96\,a^8\,b^2\,d^9-544\,a^7\,b^3\,c\,d^8+1248\,a^6\,b^4\,c^2\,d^7-1440\,a^5\,b^5\,c^3\,d^6+800\,a^4\,b^6\,c^4\,d^5-96\,a^3\,b^7\,c^5\,d^4-96\,a^2\,b^8\,c^6\,d^3+32\,a\,b^9\,c^7\,d^2}{64\,\left(a^6\,d^7-6\,a^5\,b\,c\,d^6+15\,a^4\,b^2\,c^2\,d^5-20\,a^3\,b^3\,c^3\,d^4+15\,a^2\,b^4\,c^4\,d^3-6\,a\,b^5\,c^5\,d^2+b^6\,c^6\,d\right)}-\frac{x\,\sqrt{-a^3\,b}\,\left(256\,a^7\,b^2\,d^{10}-1280\,a^6\,b^3\,c\,d^9+2304\,a^5\,b^4\,c^2\,d^8-1280\,a^4\,b^5\,c^3\,d^7-1280\,a^3\,b^6\,c^4\,d^6+2304\,a^2\,b^7\,c^5\,d^5-1280\,a\,b^8\,c^6\,d^4+256\,b^9\,c^7\,d^3\right)}{64\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)\,\left(a^4\,d^5-4\,a^3\,b\,c\,d^4+6\,a^2\,b^2\,c^2\,d^3-4\,a\,b^3\,c^3\,d^2+b^4\,c^4\,d\right)}\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)}-\frac{x\,\left(73\,a^4\,b^3\,d^4+36\,a^3\,b^4\,c\,d^3+30\,a^2\,b^5\,c^2\,d^2-12\,a\,b^6\,c^3\,d+b^7\,c^4\right)}{32\,\left(a^4\,d^5-4\,a^3\,b\,c\,d^4+6\,a^2\,b^2\,c^2\,d^3-4\,a\,b^3\,c^3\,d^2+b^4\,c^4\,d\right)}\right)\,1{}\mathrm{i}}{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)}-\frac{\sqrt{-a^3\,b}\,\left(\frac{\sqrt{-a^3\,b}\,\left(\frac{96\,a^8\,b^2\,d^9-544\,a^7\,b^3\,c\,d^8+1248\,a^6\,b^4\,c^2\,d^7-1440\,a^5\,b^5\,c^3\,d^6+800\,a^4\,b^6\,c^4\,d^5-96\,a^3\,b^7\,c^5\,d^4-96\,a^2\,b^8\,c^6\,d^3+32\,a\,b^9\,c^7\,d^2}{64\,\left(a^6\,d^7-6\,a^5\,b\,c\,d^6+15\,a^4\,b^2\,c^2\,d^5-20\,a^3\,b^3\,c^3\,d^4+15\,a^2\,b^4\,c^4\,d^3-6\,a\,b^5\,c^5\,d^2+b^6\,c^6\,d\right)}+\frac{x\,\sqrt{-a^3\,b}\,\left(256\,a^7\,b^2\,d^{10}-1280\,a^6\,b^3\,c\,d^9+2304\,a^5\,b^4\,c^2\,d^8-1280\,a^4\,b^5\,c^3\,d^7-1280\,a^3\,b^6\,c^4\,d^6+2304\,a^2\,b^7\,c^5\,d^5-1280\,a\,b^8\,c^6\,d^4+256\,b^9\,c^7\,d^3\right)}{64\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)\,\left(a^4\,d^5-4\,a^3\,b\,c\,d^4+6\,a^2\,b^2\,c^2\,d^3-4\,a\,b^3\,c^3\,d^2+b^4\,c^4\,d\right)}\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)}+\frac{x\,\left(73\,a^4\,b^3\,d^4+36\,a^3\,b^4\,c\,d^3+30\,a^2\,b^5\,c^2\,d^2-12\,a\,b^6\,c^3\,d+b^7\,c^4\right)}{32\,\left(a^4\,d^5-4\,a^3\,b\,c\,d^4+6\,a^2\,b^2\,c^2\,d^3-4\,a\,b^3\,c^3\,d^2+b^4\,c^4\,d\right)}\right)\,1{}\mathrm{i}}{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)}}{\frac{15\,a^5\,b^3\,d^3+27\,a^4\,b^4\,c\,d^2-11\,a^3\,b^5\,c^2\,d+a^2\,b^6\,c^3}{32\,\left(a^6\,d^7-6\,a^5\,b\,c\,d^6+15\,a^4\,b^2\,c^2\,d^5-20\,a^3\,b^3\,c^3\,d^4+15\,a^2\,b^4\,c^4\,d^3-6\,a\,b^5\,c^5\,d^2+b^6\,c^6\,d\right)}+\frac{\sqrt{-a^3\,b}\,\left(\frac{\sqrt{-a^3\,b}\,\left(\frac{96\,a^8\,b^2\,d^9-544\,a^7\,b^3\,c\,d^8+1248\,a^6\,b^4\,c^2\,d^7-1440\,a^5\,b^5\,c^3\,d^6+800\,a^4\,b^6\,c^4\,d^5-96\,a^3\,b^7\,c^5\,d^4-96\,a^2\,b^8\,c^6\,d^3+32\,a\,b^9\,c^7\,d^2}{64\,\left(a^6\,d^7-6\,a^5\,b\,c\,d^6+15\,a^4\,b^2\,c^2\,d^5-20\,a^3\,b^3\,c^3\,d^4+15\,a^2\,b^4\,c^4\,d^3-6\,a\,b^5\,c^5\,d^2+b^6\,c^6\,d\right)}-\frac{x\,\sqrt{-a^3\,b}\,\left(256\,a^7\,b^2\,d^{10}-1280\,a^6\,b^3\,c\,d^9+2304\,a^5\,b^4\,c^2\,d^8-1280\,a^4\,b^5\,c^3\,d^7-1280\,a^3\,b^6\,c^4\,d^6+2304\,a^2\,b^7\,c^5\,d^5-1280\,a\,b^8\,c^6\,d^4+256\,b^9\,c^7\,d^3\right)}{64\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)\,\left(a^4\,d^5-4\,a^3\,b\,c\,d^4+6\,a^2\,b^2\,c^2\,d^3-4\,a\,b^3\,c^3\,d^2+b^4\,c^4\,d\right)}\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)}-\frac{x\,\left(73\,a^4\,b^3\,d^4+36\,a^3\,b^4\,c\,d^3+30\,a^2\,b^5\,c^2\,d^2-12\,a\,b^6\,c^3\,d+b^7\,c^4\right)}{32\,\left(a^4\,d^5-4\,a^3\,b\,c\,d^4+6\,a^2\,b^2\,c^2\,d^3-4\,a\,b^3\,c^3\,d^2+b^4\,c^4\,d\right)}\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)}+\frac{\sqrt{-a^3\,b}\,\left(\frac{\sqrt{-a^3\,b}\,\left(\frac{96\,a^8\,b^2\,d^9-544\,a^7\,b^3\,c\,d^8+1248\,a^6\,b^4\,c^2\,d^7-1440\,a^5\,b^5\,c^3\,d^6+800\,a^4\,b^6\,c^4\,d^5-96\,a^3\,b^7\,c^5\,d^4-96\,a^2\,b^8\,c^6\,d^3+32\,a\,b^9\,c^7\,d^2}{64\,\left(a^6\,d^7-6\,a^5\,b\,c\,d^6+15\,a^4\,b^2\,c^2\,d^5-20\,a^3\,b^3\,c^3\,d^4+15\,a^2\,b^4\,c^4\,d^3-6\,a\,b^5\,c^5\,d^2+b^6\,c^6\,d\right)}+\frac{x\,\sqrt{-a^3\,b}\,\left(256\,a^7\,b^2\,d^{10}-1280\,a^6\,b^3\,c\,d^9+2304\,a^5\,b^4\,c^2\,d^8-1280\,a^4\,b^5\,c^3\,d^7-1280\,a^3\,b^6\,c^4\,d^6+2304\,a^2\,b^7\,c^5\,d^5-1280\,a\,b^8\,c^6\,d^4+256\,b^9\,c^7\,d^3\right)}{64\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)\,\left(a^4\,d^5-4\,a^3\,b\,c\,d^4+6\,a^2\,b^2\,c^2\,d^3-4\,a\,b^3\,c^3\,d^2+b^4\,c^4\,d\right)}\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)}+\frac{x\,\left(73\,a^4\,b^3\,d^4+36\,a^3\,b^4\,c\,d^3+30\,a^2\,b^5\,c^2\,d^2-12\,a\,b^6\,c^3\,d+b^7\,c^4\right)}{32\,\left(a^4\,d^5-4\,a^3\,b\,c\,d^4+6\,a^2\,b^2\,c^2\,d^3-4\,a\,b^3\,c^3\,d^2+b^4\,c^4\,d\right)}\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)}}\right)\,\sqrt{-a^3\,b}\,1{}\mathrm{i}}{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-c\,d^3}\,\left(\frac{x\,\left(73\,a^4\,b^3\,d^4+36\,a^3\,b^4\,c\,d^3+30\,a^2\,b^5\,c^2\,d^2-12\,a\,b^6\,c^3\,d+b^7\,c^4\right)}{32\,\left(a^4\,d^5-4\,a^3\,b\,c\,d^4+6\,a^2\,b^2\,c^2\,d^3-4\,a\,b^3\,c^3\,d^2+b^4\,c^4\,d\right)}-\frac{\left(\frac{96\,a^8\,b^2\,d^9-544\,a^7\,b^3\,c\,d^8+1248\,a^6\,b^4\,c^2\,d^7-1440\,a^5\,b^5\,c^3\,d^6+800\,a^4\,b^6\,c^4\,d^5-96\,a^3\,b^7\,c^5\,d^4-96\,a^2\,b^8\,c^6\,d^3+32\,a\,b^9\,c^7\,d^2}{64\,\left(a^6\,d^7-6\,a^5\,b\,c\,d^6+15\,a^4\,b^2\,c^2\,d^5-20\,a^3\,b^3\,c^3\,d^4+15\,a^2\,b^4\,c^4\,d^3-6\,a\,b^5\,c^5\,d^2+b^6\,c^6\,d\right)}-\frac{x\,\sqrt{-c\,d^3}\,\left(3\,a^2\,d^2+6\,a\,b\,c\,d-b^2\,c^2\right)\,\left(256\,a^7\,b^2\,d^{10}-1280\,a^6\,b^3\,c\,d^9+2304\,a^5\,b^4\,c^2\,d^8-1280\,a^4\,b^5\,c^3\,d^7-1280\,a^3\,b^6\,c^4\,d^6+2304\,a^2\,b^7\,c^5\,d^5-1280\,a\,b^8\,c^6\,d^4+256\,b^9\,c^7\,d^3\right)}{512\,\left(a^3\,c\,d^6-3\,a^2\,b\,c^2\,d^5+3\,a\,b^2\,c^3\,d^4-b^3\,c^4\,d^3\right)\,\left(a^4\,d^5-4\,a^3\,b\,c\,d^4+6\,a^2\,b^2\,c^2\,d^3-4\,a\,b^3\,c^3\,d^2+b^4\,c^4\,d\right)}\right)\,\sqrt{-c\,d^3}\,\left(3\,a^2\,d^2+6\,a\,b\,c\,d-b^2\,c^2\right)}{16\,\left(a^3\,c\,d^6-3\,a^2\,b\,c^2\,d^5+3\,a\,b^2\,c^3\,d^4-b^3\,c^4\,d^3\right)}\right)\,\left(3\,a^2\,d^2+6\,a\,b\,c\,d-b^2\,c^2\right)\,1{}\mathrm{i}}{16\,\left(a^3\,c\,d^6-3\,a^2\,b\,c^2\,d^5+3\,a\,b^2\,c^3\,d^4-b^3\,c^4\,d^3\right)}+\frac{\sqrt{-c\,d^3}\,\left(\frac{x\,\left(73\,a^4\,b^3\,d^4+36\,a^3\,b^4\,c\,d^3+30\,a^2\,b^5\,c^2\,d^2-12\,a\,b^6\,c^3\,d+b^7\,c^4\right)}{32\,\left(a^4\,d^5-4\,a^3\,b\,c\,d^4+6\,a^2\,b^2\,c^2\,d^3-4\,a\,b^3\,c^3\,d^2+b^4\,c^4\,d\right)}+\frac{\left(\frac{96\,a^8\,b^2\,d^9-544\,a^7\,b^3\,c\,d^8+1248\,a^6\,b^4\,c^2\,d^7-1440\,a^5\,b^5\,c^3\,d^6+800\,a^4\,b^6\,c^4\,d^5-96\,a^3\,b^7\,c^5\,d^4-96\,a^2\,b^8\,c^6\,d^3+32\,a\,b^9\,c^7\,d^2}{64\,\left(a^6\,d^7-6\,a^5\,b\,c\,d^6+15\,a^4\,b^2\,c^2\,d^5-20\,a^3\,b^3\,c^3\,d^4+15\,a^2\,b^4\,c^4\,d^3-6\,a\,b^5\,c^5\,d^2+b^6\,c^6\,d\right)}+\frac{x\,\sqrt{-c\,d^3}\,\left(3\,a^2\,d^2+6\,a\,b\,c\,d-b^2\,c^2\right)\,\left(256\,a^7\,b^2\,d^{10}-1280\,a^6\,b^3\,c\,d^9+2304\,a^5\,b^4\,c^2\,d^8-1280\,a^4\,b^5\,c^3\,d^7-1280\,a^3\,b^6\,c^4\,d^6+2304\,a^2\,b^7\,c^5\,d^5-1280\,a\,b^8\,c^6\,d^4+256\,b^9\,c^7\,d^3\right)}{512\,\left(a^3\,c\,d^6-3\,a^2\,b\,c^2\,d^5+3\,a\,b^2\,c^3\,d^4-b^3\,c^4\,d^3\right)\,\left(a^4\,d^5-4\,a^3\,b\,c\,d^4+6\,a^2\,b^2\,c^2\,d^3-4\,a\,b^3\,c^3\,d^2+b^4\,c^4\,d\right)}\right)\,\sqrt{-c\,d^3}\,\left(3\,a^2\,d^2+6\,a\,b\,c\,d-b^2\,c^2\right)}{16\,\left(a^3\,c\,d^6-3\,a^2\,b\,c^2\,d^5+3\,a\,b^2\,c^3\,d^4-b^3\,c^4\,d^3\right)}\right)\,\left(3\,a^2\,d^2+6\,a\,b\,c\,d-b^2\,c^2\right)\,1{}\mathrm{i}}{16\,\left(a^3\,c\,d^6-3\,a^2\,b\,c^2\,d^5+3\,a\,b^2\,c^3\,d^4-b^3\,c^4\,d^3\right)}}{\frac{15\,a^5\,b^3\,d^3+27\,a^4\,b^4\,c\,d^2-11\,a^3\,b^5\,c^2\,d+a^2\,b^6\,c^3}{32\,\left(a^6\,d^7-6\,a^5\,b\,c\,d^6+15\,a^4\,b^2\,c^2\,d^5-20\,a^3\,b^3\,c^3\,d^4+15\,a^2\,b^4\,c^4\,d^3-6\,a\,b^5\,c^5\,d^2+b^6\,c^6\,d\right)}-\frac{\sqrt{-c\,d^3}\,\left(\frac{x\,\left(73\,a^4\,b^3\,d^4+36\,a^3\,b^4\,c\,d^3+30\,a^2\,b^5\,c^2\,d^2-12\,a\,b^6\,c^3\,d+b^7\,c^4\right)}{32\,\left(a^4\,d^5-4\,a^3\,b\,c\,d^4+6\,a^2\,b^2\,c^2\,d^3-4\,a\,b^3\,c^3\,d^2+b^4\,c^4\,d\right)}-\frac{\left(\frac{96\,a^8\,b^2\,d^9-544\,a^7\,b^3\,c\,d^8+1248\,a^6\,b^4\,c^2\,d^7-1440\,a^5\,b^5\,c^3\,d^6+800\,a^4\,b^6\,c^4\,d^5-96\,a^3\,b^7\,c^5\,d^4-96\,a^2\,b^8\,c^6\,d^3+32\,a\,b^9\,c^7\,d^2}{64\,\left(a^6\,d^7-6\,a^5\,b\,c\,d^6+15\,a^4\,b^2\,c^2\,d^5-20\,a^3\,b^3\,c^3\,d^4+15\,a^2\,b^4\,c^4\,d^3-6\,a\,b^5\,c^5\,d^2+b^6\,c^6\,d\right)}-\frac{x\,\sqrt{-c\,d^3}\,\left(3\,a^2\,d^2+6\,a\,b\,c\,d-b^2\,c^2\right)\,\left(256\,a^7\,b^2\,d^{10}-1280\,a^6\,b^3\,c\,d^9+2304\,a^5\,b^4\,c^2\,d^8-1280\,a^4\,b^5\,c^3\,d^7-1280\,a^3\,b^6\,c^4\,d^6+2304\,a^2\,b^7\,c^5\,d^5-1280\,a\,b^8\,c^6\,d^4+256\,b^9\,c^7\,d^3\right)}{512\,\left(a^3\,c\,d^6-3\,a^2\,b\,c^2\,d^5+3\,a\,b^2\,c^3\,d^4-b^3\,c^4\,d^3\right)\,\left(a^4\,d^5-4\,a^3\,b\,c\,d^4+6\,a^2\,b^2\,c^2\,d^3-4\,a\,b^3\,c^3\,d^2+b^4\,c^4\,d\right)}\right)\,\sqrt{-c\,d^3}\,\left(3\,a^2\,d^2+6\,a\,b\,c\,d-b^2\,c^2\right)}{16\,\left(a^3\,c\,d^6-3\,a^2\,b\,c^2\,d^5+3\,a\,b^2\,c^3\,d^4-b^3\,c^4\,d^3\right)}\right)\,\left(3\,a^2\,d^2+6\,a\,b\,c\,d-b^2\,c^2\right)}{16\,\left(a^3\,c\,d^6-3\,a^2\,b\,c^2\,d^5+3\,a\,b^2\,c^3\,d^4-b^3\,c^4\,d^3\right)}+\frac{\sqrt{-c\,d^3}\,\left(\frac{x\,\left(73\,a^4\,b^3\,d^4+36\,a^3\,b^4\,c\,d^3+30\,a^2\,b^5\,c^2\,d^2-12\,a\,b^6\,c^3\,d+b^7\,c^4\right)}{32\,\left(a^4\,d^5-4\,a^3\,b\,c\,d^4+6\,a^2\,b^2\,c^2\,d^3-4\,a\,b^3\,c^3\,d^2+b^4\,c^4\,d\right)}+\frac{\left(\frac{96\,a^8\,b^2\,d^9-544\,a^7\,b^3\,c\,d^8+1248\,a^6\,b^4\,c^2\,d^7-1440\,a^5\,b^5\,c^3\,d^6+800\,a^4\,b^6\,c^4\,d^5-96\,a^3\,b^7\,c^5\,d^4-96\,a^2\,b^8\,c^6\,d^3+32\,a\,b^9\,c^7\,d^2}{64\,\left(a^6\,d^7-6\,a^5\,b\,c\,d^6+15\,a^4\,b^2\,c^2\,d^5-20\,a^3\,b^3\,c^3\,d^4+15\,a^2\,b^4\,c^4\,d^3-6\,a\,b^5\,c^5\,d^2+b^6\,c^6\,d\right)}+\frac{x\,\sqrt{-c\,d^3}\,\left(3\,a^2\,d^2+6\,a\,b\,c\,d-b^2\,c^2\right)\,\left(256\,a^7\,b^2\,d^{10}-1280\,a^6\,b^3\,c\,d^9+2304\,a^5\,b^4\,c^2\,d^8-1280\,a^4\,b^5\,c^3\,d^7-1280\,a^3\,b^6\,c^4\,d^6+2304\,a^2\,b^7\,c^5\,d^5-1280\,a\,b^8\,c^6\,d^4+256\,b^9\,c^7\,d^3\right)}{512\,\left(a^3\,c\,d^6-3\,a^2\,b\,c^2\,d^5+3\,a\,b^2\,c^3\,d^4-b^3\,c^4\,d^3\right)\,\left(a^4\,d^5-4\,a^3\,b\,c\,d^4+6\,a^2\,b^2\,c^2\,d^3-4\,a\,b^3\,c^3\,d^2+b^4\,c^4\,d\right)}\right)\,\sqrt{-c\,d^3}\,\left(3\,a^2\,d^2+6\,a\,b\,c\,d-b^2\,c^2\right)}{16\,\left(a^3\,c\,d^6-3\,a^2\,b\,c^2\,d^5+3\,a\,b^2\,c^3\,d^4-b^3\,c^4\,d^3\right)}\right)\,\left(3\,a^2\,d^2+6\,a\,b\,c\,d-b^2\,c^2\right)}{16\,\left(a^3\,c\,d^6-3\,a^2\,b\,c^2\,d^5+3\,a\,b^2\,c^3\,d^4-b^3\,c^4\,d^3\right)}}\right)\,\sqrt{-c\,d^3}\,\left(3\,a^2\,d^2+6\,a\,b\,c\,d-b^2\,c^2\right)\,1{}\mathrm{i}}{8\,\left(a^3\,c\,d^6-3\,a^2\,b\,c^2\,d^5+3\,a\,b^2\,c^3\,d^4-b^3\,c^4\,d^3\right)}","Not used",1,"(atan((((-c*d^3)^(1/2)*((x*(b^7*c^4 + 73*a^4*b^3*d^4 + 36*a^3*b^4*c*d^3 + 30*a^2*b^5*c^2*d^2 - 12*a*b^6*c^3*d))/(32*(a^4*d^5 + b^4*c^4*d - 4*a*b^3*c^3*d^2 + 6*a^2*b^2*c^2*d^3 - 4*a^3*b*c*d^4)) - (((96*a^8*b^2*d^9 + 32*a*b^9*c^7*d^2 - 544*a^7*b^3*c*d^8 - 96*a^2*b^8*c^6*d^3 - 96*a^3*b^7*c^5*d^4 + 800*a^4*b^6*c^4*d^5 - 1440*a^5*b^5*c^3*d^6 + 1248*a^6*b^4*c^2*d^7)/(64*(a^6*d^7 + b^6*c^6*d - 6*a*b^5*c^5*d^2 + 15*a^2*b^4*c^4*d^3 - 20*a^3*b^3*c^3*d^4 + 15*a^4*b^2*c^2*d^5 - 6*a^5*b*c*d^6)) - (x*(-c*d^3)^(1/2)*(3*a^2*d^2 - b^2*c^2 + 6*a*b*c*d)*(256*a^7*b^2*d^10 + 256*b^9*c^7*d^3 - 1280*a*b^8*c^6*d^4 - 1280*a^6*b^3*c*d^9 + 2304*a^2*b^7*c^5*d^5 - 1280*a^3*b^6*c^4*d^6 - 1280*a^4*b^5*c^3*d^7 + 2304*a^5*b^4*c^2*d^8))/(512*(a^3*c*d^6 - b^3*c^4*d^3 + 3*a*b^2*c^3*d^4 - 3*a^2*b*c^2*d^5)*(a^4*d^5 + b^4*c^4*d - 4*a*b^3*c^3*d^2 + 6*a^2*b^2*c^2*d^3 - 4*a^3*b*c*d^4)))*(-c*d^3)^(1/2)*(3*a^2*d^2 - b^2*c^2 + 6*a*b*c*d))/(16*(a^3*c*d^6 - b^3*c^4*d^3 + 3*a*b^2*c^3*d^4 - 3*a^2*b*c^2*d^5)))*(3*a^2*d^2 - b^2*c^2 + 6*a*b*c*d)*1i)/(16*(a^3*c*d^6 - b^3*c^4*d^3 + 3*a*b^2*c^3*d^4 - 3*a^2*b*c^2*d^5)) + ((-c*d^3)^(1/2)*((x*(b^7*c^4 + 73*a^4*b^3*d^4 + 36*a^3*b^4*c*d^3 + 30*a^2*b^5*c^2*d^2 - 12*a*b^6*c^3*d))/(32*(a^4*d^5 + b^4*c^4*d - 4*a*b^3*c^3*d^2 + 6*a^2*b^2*c^2*d^3 - 4*a^3*b*c*d^4)) + (((96*a^8*b^2*d^9 + 32*a*b^9*c^7*d^2 - 544*a^7*b^3*c*d^8 - 96*a^2*b^8*c^6*d^3 - 96*a^3*b^7*c^5*d^4 + 800*a^4*b^6*c^4*d^5 - 1440*a^5*b^5*c^3*d^6 + 1248*a^6*b^4*c^2*d^7)/(64*(a^6*d^7 + b^6*c^6*d - 6*a*b^5*c^5*d^2 + 15*a^2*b^4*c^4*d^3 - 20*a^3*b^3*c^3*d^4 + 15*a^4*b^2*c^2*d^5 - 6*a^5*b*c*d^6)) + (x*(-c*d^3)^(1/2)*(3*a^2*d^2 - b^2*c^2 + 6*a*b*c*d)*(256*a^7*b^2*d^10 + 256*b^9*c^7*d^3 - 1280*a*b^8*c^6*d^4 - 1280*a^6*b^3*c*d^9 + 2304*a^2*b^7*c^5*d^5 - 1280*a^3*b^6*c^4*d^6 - 1280*a^4*b^5*c^3*d^7 + 2304*a^5*b^4*c^2*d^8))/(512*(a^3*c*d^6 - b^3*c^4*d^3 + 3*a*b^2*c^3*d^4 - 3*a^2*b*c^2*d^5)*(a^4*d^5 + b^4*c^4*d - 4*a*b^3*c^3*d^2 + 6*a^2*b^2*c^2*d^3 - 4*a^3*b*c*d^4)))*(-c*d^3)^(1/2)*(3*a^2*d^2 - b^2*c^2 + 6*a*b*c*d))/(16*(a^3*c*d^6 - b^3*c^4*d^3 + 3*a*b^2*c^3*d^4 - 3*a^2*b*c^2*d^5)))*(3*a^2*d^2 - b^2*c^2 + 6*a*b*c*d)*1i)/(16*(a^3*c*d^6 - b^3*c^4*d^3 + 3*a*b^2*c^3*d^4 - 3*a^2*b*c^2*d^5)))/((a^2*b^6*c^3 + 15*a^5*b^3*d^3 - 11*a^3*b^5*c^2*d + 27*a^4*b^4*c*d^2)/(32*(a^6*d^7 + b^6*c^6*d - 6*a*b^5*c^5*d^2 + 15*a^2*b^4*c^4*d^3 - 20*a^3*b^3*c^3*d^4 + 15*a^4*b^2*c^2*d^5 - 6*a^5*b*c*d^6)) - ((-c*d^3)^(1/2)*((x*(b^7*c^4 + 73*a^4*b^3*d^4 + 36*a^3*b^4*c*d^3 + 30*a^2*b^5*c^2*d^2 - 12*a*b^6*c^3*d))/(32*(a^4*d^5 + b^4*c^4*d - 4*a*b^3*c^3*d^2 + 6*a^2*b^2*c^2*d^3 - 4*a^3*b*c*d^4)) - (((96*a^8*b^2*d^9 + 32*a*b^9*c^7*d^2 - 544*a^7*b^3*c*d^8 - 96*a^2*b^8*c^6*d^3 - 96*a^3*b^7*c^5*d^4 + 800*a^4*b^6*c^4*d^5 - 1440*a^5*b^5*c^3*d^6 + 1248*a^6*b^4*c^2*d^7)/(64*(a^6*d^7 + b^6*c^6*d - 6*a*b^5*c^5*d^2 + 15*a^2*b^4*c^4*d^3 - 20*a^3*b^3*c^3*d^4 + 15*a^4*b^2*c^2*d^5 - 6*a^5*b*c*d^6)) - (x*(-c*d^3)^(1/2)*(3*a^2*d^2 - b^2*c^2 + 6*a*b*c*d)*(256*a^7*b^2*d^10 + 256*b^9*c^7*d^3 - 1280*a*b^8*c^6*d^4 - 1280*a^6*b^3*c*d^9 + 2304*a^2*b^7*c^5*d^5 - 1280*a^3*b^6*c^4*d^6 - 1280*a^4*b^5*c^3*d^7 + 2304*a^5*b^4*c^2*d^8))/(512*(a^3*c*d^6 - b^3*c^4*d^3 + 3*a*b^2*c^3*d^4 - 3*a^2*b*c^2*d^5)*(a^4*d^5 + b^4*c^4*d - 4*a*b^3*c^3*d^2 + 6*a^2*b^2*c^2*d^3 - 4*a^3*b*c*d^4)))*(-c*d^3)^(1/2)*(3*a^2*d^2 - b^2*c^2 + 6*a*b*c*d))/(16*(a^3*c*d^6 - b^3*c^4*d^3 + 3*a*b^2*c^3*d^4 - 3*a^2*b*c^2*d^5)))*(3*a^2*d^2 - b^2*c^2 + 6*a*b*c*d))/(16*(a^3*c*d^6 - b^3*c^4*d^3 + 3*a*b^2*c^3*d^4 - 3*a^2*b*c^2*d^5)) + ((-c*d^3)^(1/2)*((x*(b^7*c^4 + 73*a^4*b^3*d^4 + 36*a^3*b^4*c*d^3 + 30*a^2*b^5*c^2*d^2 - 12*a*b^6*c^3*d))/(32*(a^4*d^5 + b^4*c^4*d - 4*a*b^3*c^3*d^2 + 6*a^2*b^2*c^2*d^3 - 4*a^3*b*c*d^4)) + (((96*a^8*b^2*d^9 + 32*a*b^9*c^7*d^2 - 544*a^7*b^3*c*d^8 - 96*a^2*b^8*c^6*d^3 - 96*a^3*b^7*c^5*d^4 + 800*a^4*b^6*c^4*d^5 - 1440*a^5*b^5*c^3*d^6 + 1248*a^6*b^4*c^2*d^7)/(64*(a^6*d^7 + b^6*c^6*d - 6*a*b^5*c^5*d^2 + 15*a^2*b^4*c^4*d^3 - 20*a^3*b^3*c^3*d^4 + 15*a^4*b^2*c^2*d^5 - 6*a^5*b*c*d^6)) + (x*(-c*d^3)^(1/2)*(3*a^2*d^2 - b^2*c^2 + 6*a*b*c*d)*(256*a^7*b^2*d^10 + 256*b^9*c^7*d^3 - 1280*a*b^8*c^6*d^4 - 1280*a^6*b^3*c*d^9 + 2304*a^2*b^7*c^5*d^5 - 1280*a^3*b^6*c^4*d^6 - 1280*a^4*b^5*c^3*d^7 + 2304*a^5*b^4*c^2*d^8))/(512*(a^3*c*d^6 - b^3*c^4*d^3 + 3*a*b^2*c^3*d^4 - 3*a^2*b*c^2*d^5)*(a^4*d^5 + b^4*c^4*d - 4*a*b^3*c^3*d^2 + 6*a^2*b^2*c^2*d^3 - 4*a^3*b*c*d^4)))*(-c*d^3)^(1/2)*(3*a^2*d^2 - b^2*c^2 + 6*a*b*c*d))/(16*(a^3*c*d^6 - b^3*c^4*d^3 + 3*a*b^2*c^3*d^4 - 3*a^2*b*c^2*d^5)))*(3*a^2*d^2 - b^2*c^2 + 6*a*b*c*d))/(16*(a^3*c*d^6 - b^3*c^4*d^3 + 3*a*b^2*c^3*d^4 - 3*a^2*b*c^2*d^5))))*(-c*d^3)^(1/2)*(3*a^2*d^2 - b^2*c^2 + 6*a*b*c*d)*1i)/(8*(a^3*c*d^6 - b^3*c^4*d^3 + 3*a*b^2*c^3*d^4 - 3*a^2*b*c^2*d^5)) - (atan((((-a^3*b)^(1/2)*(((-a^3*b)^(1/2)*((96*a^8*b^2*d^9 + 32*a*b^9*c^7*d^2 - 544*a^7*b^3*c*d^8 - 96*a^2*b^8*c^6*d^3 - 96*a^3*b^7*c^5*d^4 + 800*a^4*b^6*c^4*d^5 - 1440*a^5*b^5*c^3*d^6 + 1248*a^6*b^4*c^2*d^7)/(64*(a^6*d^7 + b^6*c^6*d - 6*a*b^5*c^5*d^2 + 15*a^2*b^4*c^4*d^3 - 20*a^3*b^3*c^3*d^4 + 15*a^4*b^2*c^2*d^5 - 6*a^5*b*c*d^6)) - (x*(-a^3*b)^(1/2)*(256*a^7*b^2*d^10 + 256*b^9*c^7*d^3 - 1280*a*b^8*c^6*d^4 - 1280*a^6*b^3*c*d^9 + 2304*a^2*b^7*c^5*d^5 - 1280*a^3*b^6*c^4*d^6 - 1280*a^4*b^5*c^3*d^7 + 2304*a^5*b^4*c^2*d^8))/(64*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)*(a^4*d^5 + b^4*c^4*d - 4*a*b^3*c^3*d^2 + 6*a^2*b^2*c^2*d^3 - 4*a^3*b*c*d^4))))/(2*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)) - (x*(b^7*c^4 + 73*a^4*b^3*d^4 + 36*a^3*b^4*c*d^3 + 30*a^2*b^5*c^2*d^2 - 12*a*b^6*c^3*d))/(32*(a^4*d^5 + b^4*c^4*d - 4*a*b^3*c^3*d^2 + 6*a^2*b^2*c^2*d^3 - 4*a^3*b*c*d^4)))*1i)/(2*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)) - ((-a^3*b)^(1/2)*(((-a^3*b)^(1/2)*((96*a^8*b^2*d^9 + 32*a*b^9*c^7*d^2 - 544*a^7*b^3*c*d^8 - 96*a^2*b^8*c^6*d^3 - 96*a^3*b^7*c^5*d^4 + 800*a^4*b^6*c^4*d^5 - 1440*a^5*b^5*c^3*d^6 + 1248*a^6*b^4*c^2*d^7)/(64*(a^6*d^7 + b^6*c^6*d - 6*a*b^5*c^5*d^2 + 15*a^2*b^4*c^4*d^3 - 20*a^3*b^3*c^3*d^4 + 15*a^4*b^2*c^2*d^5 - 6*a^5*b*c*d^6)) + (x*(-a^3*b)^(1/2)*(256*a^7*b^2*d^10 + 256*b^9*c^7*d^3 - 1280*a*b^8*c^6*d^4 - 1280*a^6*b^3*c*d^9 + 2304*a^2*b^7*c^5*d^5 - 1280*a^3*b^6*c^4*d^6 - 1280*a^4*b^5*c^3*d^7 + 2304*a^5*b^4*c^2*d^8))/(64*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)*(a^4*d^5 + b^4*c^4*d - 4*a*b^3*c^3*d^2 + 6*a^2*b^2*c^2*d^3 - 4*a^3*b*c*d^4))))/(2*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)) + (x*(b^7*c^4 + 73*a^4*b^3*d^4 + 36*a^3*b^4*c*d^3 + 30*a^2*b^5*c^2*d^2 - 12*a*b^6*c^3*d))/(32*(a^4*d^5 + b^4*c^4*d - 4*a*b^3*c^3*d^2 + 6*a^2*b^2*c^2*d^3 - 4*a^3*b*c*d^4)))*1i)/(2*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)))/((a^2*b^6*c^3 + 15*a^5*b^3*d^3 - 11*a^3*b^5*c^2*d + 27*a^4*b^4*c*d^2)/(32*(a^6*d^7 + b^6*c^6*d - 6*a*b^5*c^5*d^2 + 15*a^2*b^4*c^4*d^3 - 20*a^3*b^3*c^3*d^4 + 15*a^4*b^2*c^2*d^5 - 6*a^5*b*c*d^6)) + ((-a^3*b)^(1/2)*(((-a^3*b)^(1/2)*((96*a^8*b^2*d^9 + 32*a*b^9*c^7*d^2 - 544*a^7*b^3*c*d^8 - 96*a^2*b^8*c^6*d^3 - 96*a^3*b^7*c^5*d^4 + 800*a^4*b^6*c^4*d^5 - 1440*a^5*b^5*c^3*d^6 + 1248*a^6*b^4*c^2*d^7)/(64*(a^6*d^7 + b^6*c^6*d - 6*a*b^5*c^5*d^2 + 15*a^2*b^4*c^4*d^3 - 20*a^3*b^3*c^3*d^4 + 15*a^4*b^2*c^2*d^5 - 6*a^5*b*c*d^6)) - (x*(-a^3*b)^(1/2)*(256*a^7*b^2*d^10 + 256*b^9*c^7*d^3 - 1280*a*b^8*c^6*d^4 - 1280*a^6*b^3*c*d^9 + 2304*a^2*b^7*c^5*d^5 - 1280*a^3*b^6*c^4*d^6 - 1280*a^4*b^5*c^3*d^7 + 2304*a^5*b^4*c^2*d^8))/(64*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)*(a^4*d^5 + b^4*c^4*d - 4*a*b^3*c^3*d^2 + 6*a^2*b^2*c^2*d^3 - 4*a^3*b*c*d^4))))/(2*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)) - (x*(b^7*c^4 + 73*a^4*b^3*d^4 + 36*a^3*b^4*c*d^3 + 30*a^2*b^5*c^2*d^2 - 12*a*b^6*c^3*d))/(32*(a^4*d^5 + b^4*c^4*d - 4*a*b^3*c^3*d^2 + 6*a^2*b^2*c^2*d^3 - 4*a^3*b*c*d^4))))/(2*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)) + ((-a^3*b)^(1/2)*(((-a^3*b)^(1/2)*((96*a^8*b^2*d^9 + 32*a*b^9*c^7*d^2 - 544*a^7*b^3*c*d^8 - 96*a^2*b^8*c^6*d^3 - 96*a^3*b^7*c^5*d^4 + 800*a^4*b^6*c^4*d^5 - 1440*a^5*b^5*c^3*d^6 + 1248*a^6*b^4*c^2*d^7)/(64*(a^6*d^7 + b^6*c^6*d - 6*a*b^5*c^5*d^2 + 15*a^2*b^4*c^4*d^3 - 20*a^3*b^3*c^3*d^4 + 15*a^4*b^2*c^2*d^5 - 6*a^5*b*c*d^6)) + (x*(-a^3*b)^(1/2)*(256*a^7*b^2*d^10 + 256*b^9*c^7*d^3 - 1280*a*b^8*c^6*d^4 - 1280*a^6*b^3*c*d^9 + 2304*a^2*b^7*c^5*d^5 - 1280*a^3*b^6*c^4*d^6 - 1280*a^4*b^5*c^3*d^7 + 2304*a^5*b^4*c^2*d^8))/(64*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)*(a^4*d^5 + b^4*c^4*d - 4*a*b^3*c^3*d^2 + 6*a^2*b^2*c^2*d^3 - 4*a^3*b*c*d^4))))/(2*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)) + (x*(b^7*c^4 + 73*a^4*b^3*d^4 + 36*a^3*b^4*c*d^3 + 30*a^2*b^5*c^2*d^2 - 12*a*b^6*c^3*d))/(32*(a^4*d^5 + b^4*c^4*d - 4*a*b^3*c^3*d^2 + 6*a^2*b^2*c^2*d^3 - 4*a^3*b*c*d^4))))/(2*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))))*(-a^3*b)^(1/2)*1i)/(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2) - ((x^3*(5*a*d - b*c))/(8*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) + (c*x*(3*a*d + b*c))/(8*(a^2*d^3 + b^2*c^2*d - 2*a*b*c*d^2)))/(c^2 + d^2*x^4 + 2*c*d*x^2)","B"
253,1,343,100,0.467335,"\text{Not used}","int(x^3/((a + b*x^2)*(c + d*x^2)^3),x)","-\frac{b^2\,c^3-a^2\,c\,d^2-2\,a^2\,d^3\,x^2+2\,a\,b\,c\,d^2\,x^2+a\,b\,c^2\,d\,\mathrm{atan}\left(\frac{a\,d\,x^2\,1{}\mathrm{i}-b\,c\,x^2\,1{}\mathrm{i}}{2\,a\,c+a\,d\,x^2+b\,c\,x^2}\right)\,4{}\mathrm{i}+a\,b\,d^3\,x^4\,\mathrm{atan}\left(\frac{a\,d\,x^2\,1{}\mathrm{i}-b\,c\,x^2\,1{}\mathrm{i}}{2\,a\,c+a\,d\,x^2+b\,c\,x^2}\right)\,4{}\mathrm{i}+a\,b\,c\,d^2\,x^2\,\mathrm{atan}\left(\frac{a\,d\,x^2\,1{}\mathrm{i}-b\,c\,x^2\,1{}\mathrm{i}}{2\,a\,c+a\,d\,x^2+b\,c\,x^2}\right)\,8{}\mathrm{i}}{-4\,a^3\,c^2\,d^4-8\,a^3\,c\,d^5\,x^2-4\,a^3\,d^6\,x^4+12\,a^2\,b\,c^3\,d^3+24\,a^2\,b\,c^2\,d^4\,x^2+12\,a^2\,b\,c\,d^5\,x^4-12\,a\,b^2\,c^4\,d^2-24\,a\,b^2\,c^3\,d^3\,x^2-12\,a\,b^2\,c^2\,d^4\,x^4+4\,b^3\,c^5\,d+8\,b^3\,c^4\,d^2\,x^2+4\,b^3\,c^3\,d^3\,x^4}","Not used",1,"-(b^2*c^3 - a^2*c*d^2 - 2*a^2*d^3*x^2 + 2*a*b*c*d^2*x^2 + a*b*c^2*d*atan((a*d*x^2*1i - b*c*x^2*1i)/(2*a*c + a*d*x^2 + b*c*x^2))*4i + a*b*d^3*x^4*atan((a*d*x^2*1i - b*c*x^2*1i)/(2*a*c + a*d*x^2 + b*c*x^2))*4i + a*b*c*d^2*x^2*atan((a*d*x^2*1i - b*c*x^2*1i)/(2*a*c + a*d*x^2 + b*c*x^2))*8i)/(4*b^3*c^5*d - 4*a^3*c^2*d^4 - 4*a^3*d^6*x^4 - 12*a*b^2*c^4*d^2 + 12*a^2*b*c^3*d^3 - 8*a^3*c*d^5*x^2 + 8*b^3*c^4*d^2*x^2 + 4*b^3*c^3*d^3*x^4 + 12*a^2*b*c*d^5*x^4 - 24*a*b^2*c^3*d^3*x^2 + 24*a^2*b*c^2*d^4*x^2 - 12*a*b^2*c^2*d^4*x^4)","B"
254,1,5898,155,1.984738,"\text{Not used}","int(x^2/((a + b*x^2)*(c + d*x^2)^3),x)","-\frac{\frac{x\,\left(a\,d-5\,b\,c\right)}{8\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}-\frac{x^3\,\left(a\,d^2+3\,b\,c\,d\right)}{8\,c\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}}{c^2+2\,c\,d\,x^2+d^2\,x^4}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-a\,b^3}\,\left(\frac{\left(\frac{-32\,a^8\,b^2\,c\,d^9+352\,a^7\,b^3\,c^2\,d^8-1440\,a^6\,b^4\,c^3\,d^7+3040\,a^5\,b^5\,c^4\,d^6-3680\,a^4\,b^6\,c^5\,d^5+2592\,a^3\,b^7\,c^6\,d^4-992\,a^2\,b^8\,c^7\,d^3+160\,a\,b^9\,c^8\,d^2}{64\,\left(a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8\right)}-\frac{x\,\sqrt{-a\,b^3}\,\left(256\,a^7\,b^2\,c^2\,d^9-1280\,a^6\,b^3\,c^3\,d^8+2304\,a^5\,b^4\,c^4\,d^7-1280\,a^4\,b^5\,c^5\,d^6-1280\,a^3\,b^6\,c^6\,d^5+2304\,a^2\,b^7\,c^7\,d^4-1280\,a\,b^8\,c^8\,d^3+256\,b^9\,c^9\,d^2\right)}{64\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)\,\left(a^4\,c^2\,d^4-4\,a^3\,b\,c^3\,d^3+6\,a^2\,b^2\,c^4\,d^2-4\,a\,b^3\,c^5\,d+b^4\,c^6\right)}\right)\,\sqrt{-a\,b^3}}{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)}-\frac{x\,\left(a^4\,b^3\,d^5-12\,a^3\,b^4\,c\,d^4+94\,a^2\,b^5\,c^2\,d^3+36\,a\,b^6\,c^3\,d^2+9\,b^7\,c^4\,d\right)}{32\,\left(a^4\,c^2\,d^4-4\,a^3\,b\,c^3\,d^3+6\,a^2\,b^2\,c^4\,d^2-4\,a\,b^3\,c^5\,d+b^4\,c^6\right)}\right)\,1{}\mathrm{i}}{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)}-\frac{\sqrt{-a\,b^3}\,\left(\frac{\left(\frac{-32\,a^8\,b^2\,c\,d^9+352\,a^7\,b^3\,c^2\,d^8-1440\,a^6\,b^4\,c^3\,d^7+3040\,a^5\,b^5\,c^4\,d^6-3680\,a^4\,b^6\,c^5\,d^5+2592\,a^3\,b^7\,c^6\,d^4-992\,a^2\,b^8\,c^7\,d^3+160\,a\,b^9\,c^8\,d^2}{64\,\left(a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8\right)}+\frac{x\,\sqrt{-a\,b^3}\,\left(256\,a^7\,b^2\,c^2\,d^9-1280\,a^6\,b^3\,c^3\,d^8+2304\,a^5\,b^4\,c^4\,d^7-1280\,a^4\,b^5\,c^5\,d^6-1280\,a^3\,b^6\,c^6\,d^5+2304\,a^2\,b^7\,c^7\,d^4-1280\,a\,b^8\,c^8\,d^3+256\,b^9\,c^9\,d^2\right)}{64\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)\,\left(a^4\,c^2\,d^4-4\,a^3\,b\,c^3\,d^3+6\,a^2\,b^2\,c^4\,d^2-4\,a\,b^3\,c^5\,d+b^4\,c^6\right)}\right)\,\sqrt{-a\,b^3}}{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)}+\frac{x\,\left(a^4\,b^3\,d^5-12\,a^3\,b^4\,c\,d^4+94\,a^2\,b^5\,c^2\,d^3+36\,a\,b^6\,c^3\,d^2+9\,b^7\,c^4\,d\right)}{32\,\left(a^4\,c^2\,d^4-4\,a^3\,b\,c^3\,d^3+6\,a^2\,b^2\,c^4\,d^2-4\,a\,b^3\,c^5\,d+b^4\,c^6\right)}\right)\,1{}\mathrm{i}}{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)}}{\frac{-a^4\,b^4\,d^4+3\,a^3\,b^5\,c\,d^3+21\,a^2\,b^6\,c^2\,d^2+9\,a\,b^7\,c^3\,d}{32\,\left(a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8\right)}+\frac{\sqrt{-a\,b^3}\,\left(\frac{\left(\frac{-32\,a^8\,b^2\,c\,d^9+352\,a^7\,b^3\,c^2\,d^8-1440\,a^6\,b^4\,c^3\,d^7+3040\,a^5\,b^5\,c^4\,d^6-3680\,a^4\,b^6\,c^5\,d^5+2592\,a^3\,b^7\,c^6\,d^4-992\,a^2\,b^8\,c^7\,d^3+160\,a\,b^9\,c^8\,d^2}{64\,\left(a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8\right)}-\frac{x\,\sqrt{-a\,b^3}\,\left(256\,a^7\,b^2\,c^2\,d^9-1280\,a^6\,b^3\,c^3\,d^8+2304\,a^5\,b^4\,c^4\,d^7-1280\,a^4\,b^5\,c^5\,d^6-1280\,a^3\,b^6\,c^6\,d^5+2304\,a^2\,b^7\,c^7\,d^4-1280\,a\,b^8\,c^8\,d^3+256\,b^9\,c^9\,d^2\right)}{64\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)\,\left(a^4\,c^2\,d^4-4\,a^3\,b\,c^3\,d^3+6\,a^2\,b^2\,c^4\,d^2-4\,a\,b^3\,c^5\,d+b^4\,c^6\right)}\right)\,\sqrt{-a\,b^3}}{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)}-\frac{x\,\left(a^4\,b^3\,d^5-12\,a^3\,b^4\,c\,d^4+94\,a^2\,b^5\,c^2\,d^3+36\,a\,b^6\,c^3\,d^2+9\,b^7\,c^4\,d\right)}{32\,\left(a^4\,c^2\,d^4-4\,a^3\,b\,c^3\,d^3+6\,a^2\,b^2\,c^4\,d^2-4\,a\,b^3\,c^5\,d+b^4\,c^6\right)}\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)}+\frac{\sqrt{-a\,b^3}\,\left(\frac{\left(\frac{-32\,a^8\,b^2\,c\,d^9+352\,a^7\,b^3\,c^2\,d^8-1440\,a^6\,b^4\,c^3\,d^7+3040\,a^5\,b^5\,c^4\,d^6-3680\,a^4\,b^6\,c^5\,d^5+2592\,a^3\,b^7\,c^6\,d^4-992\,a^2\,b^8\,c^7\,d^3+160\,a\,b^9\,c^8\,d^2}{64\,\left(a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8\right)}+\frac{x\,\sqrt{-a\,b^3}\,\left(256\,a^7\,b^2\,c^2\,d^9-1280\,a^6\,b^3\,c^3\,d^8+2304\,a^5\,b^4\,c^4\,d^7-1280\,a^4\,b^5\,c^5\,d^6-1280\,a^3\,b^6\,c^6\,d^5+2304\,a^2\,b^7\,c^7\,d^4-1280\,a\,b^8\,c^8\,d^3+256\,b^9\,c^9\,d^2\right)}{64\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)\,\left(a^4\,c^2\,d^4-4\,a^3\,b\,c^3\,d^3+6\,a^2\,b^2\,c^4\,d^2-4\,a\,b^3\,c^5\,d+b^4\,c^6\right)}\right)\,\sqrt{-a\,b^3}}{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)}+\frac{x\,\left(a^4\,b^3\,d^5-12\,a^3\,b^4\,c\,d^4+94\,a^2\,b^5\,c^2\,d^3+36\,a\,b^6\,c^3\,d^2+9\,b^7\,c^4\,d\right)}{32\,\left(a^4\,c^2\,d^4-4\,a^3\,b\,c^3\,d^3+6\,a^2\,b^2\,c^4\,d^2-4\,a\,b^3\,c^5\,d+b^4\,c^6\right)}\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)}}\right)\,\sqrt{-a\,b^3}\,1{}\mathrm{i}}{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-c^3\,d}\,\left(\frac{x\,\left(a^4\,b^3\,d^5-12\,a^3\,b^4\,c\,d^4+94\,a^2\,b^5\,c^2\,d^3+36\,a\,b^6\,c^3\,d^2+9\,b^7\,c^4\,d\right)}{32\,\left(a^4\,c^2\,d^4-4\,a^3\,b\,c^3\,d^3+6\,a^2\,b^2\,c^4\,d^2-4\,a\,b^3\,c^5\,d+b^4\,c^6\right)}-\frac{\left(\frac{-32\,a^8\,b^2\,c\,d^9+352\,a^7\,b^3\,c^2\,d^8-1440\,a^6\,b^4\,c^3\,d^7+3040\,a^5\,b^5\,c^4\,d^6-3680\,a^4\,b^6\,c^5\,d^5+2592\,a^3\,b^7\,c^6\,d^4-992\,a^2\,b^8\,c^7\,d^3+160\,a\,b^9\,c^8\,d^2}{64\,\left(a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8\right)}-\frac{x\,\sqrt{-c^3\,d}\,\left(-a^2\,d^2+6\,a\,b\,c\,d+3\,b^2\,c^2\right)\,\left(256\,a^7\,b^2\,c^2\,d^9-1280\,a^6\,b^3\,c^3\,d^8+2304\,a^5\,b^4\,c^4\,d^7-1280\,a^4\,b^5\,c^5\,d^6-1280\,a^3\,b^6\,c^6\,d^5+2304\,a^2\,b^7\,c^7\,d^4-1280\,a\,b^8\,c^8\,d^3+256\,b^9\,c^9\,d^2\right)}{512\,\left(-a^3\,c^3\,d^4+3\,a^2\,b\,c^4\,d^3-3\,a\,b^2\,c^5\,d^2+b^3\,c^6\,d\right)\,\left(a^4\,c^2\,d^4-4\,a^3\,b\,c^3\,d^3+6\,a^2\,b^2\,c^4\,d^2-4\,a\,b^3\,c^5\,d+b^4\,c^6\right)}\right)\,\sqrt{-c^3\,d}\,\left(-a^2\,d^2+6\,a\,b\,c\,d+3\,b^2\,c^2\right)}{16\,\left(-a^3\,c^3\,d^4+3\,a^2\,b\,c^4\,d^3-3\,a\,b^2\,c^5\,d^2+b^3\,c^6\,d\right)}\right)\,\left(-a^2\,d^2+6\,a\,b\,c\,d+3\,b^2\,c^2\right)\,1{}\mathrm{i}}{16\,\left(-a^3\,c^3\,d^4+3\,a^2\,b\,c^4\,d^3-3\,a\,b^2\,c^5\,d^2+b^3\,c^6\,d\right)}+\frac{\sqrt{-c^3\,d}\,\left(\frac{x\,\left(a^4\,b^3\,d^5-12\,a^3\,b^4\,c\,d^4+94\,a^2\,b^5\,c^2\,d^3+36\,a\,b^6\,c^3\,d^2+9\,b^7\,c^4\,d\right)}{32\,\left(a^4\,c^2\,d^4-4\,a^3\,b\,c^3\,d^3+6\,a^2\,b^2\,c^4\,d^2-4\,a\,b^3\,c^5\,d+b^4\,c^6\right)}+\frac{\left(\frac{-32\,a^8\,b^2\,c\,d^9+352\,a^7\,b^3\,c^2\,d^8-1440\,a^6\,b^4\,c^3\,d^7+3040\,a^5\,b^5\,c^4\,d^6-3680\,a^4\,b^6\,c^5\,d^5+2592\,a^3\,b^7\,c^6\,d^4-992\,a^2\,b^8\,c^7\,d^3+160\,a\,b^9\,c^8\,d^2}{64\,\left(a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8\right)}+\frac{x\,\sqrt{-c^3\,d}\,\left(-a^2\,d^2+6\,a\,b\,c\,d+3\,b^2\,c^2\right)\,\left(256\,a^7\,b^2\,c^2\,d^9-1280\,a^6\,b^3\,c^3\,d^8+2304\,a^5\,b^4\,c^4\,d^7-1280\,a^4\,b^5\,c^5\,d^6-1280\,a^3\,b^6\,c^6\,d^5+2304\,a^2\,b^7\,c^7\,d^4-1280\,a\,b^8\,c^8\,d^3+256\,b^9\,c^9\,d^2\right)}{512\,\left(-a^3\,c^3\,d^4+3\,a^2\,b\,c^4\,d^3-3\,a\,b^2\,c^5\,d^2+b^3\,c^6\,d\right)\,\left(a^4\,c^2\,d^4-4\,a^3\,b\,c^3\,d^3+6\,a^2\,b^2\,c^4\,d^2-4\,a\,b^3\,c^5\,d+b^4\,c^6\right)}\right)\,\sqrt{-c^3\,d}\,\left(-a^2\,d^2+6\,a\,b\,c\,d+3\,b^2\,c^2\right)}{16\,\left(-a^3\,c^3\,d^4+3\,a^2\,b\,c^4\,d^3-3\,a\,b^2\,c^5\,d^2+b^3\,c^6\,d\right)}\right)\,\left(-a^2\,d^2+6\,a\,b\,c\,d+3\,b^2\,c^2\right)\,1{}\mathrm{i}}{16\,\left(-a^3\,c^3\,d^4+3\,a^2\,b\,c^4\,d^3-3\,a\,b^2\,c^5\,d^2+b^3\,c^6\,d\right)}}{\frac{-a^4\,b^4\,d^4+3\,a^3\,b^5\,c\,d^3+21\,a^2\,b^6\,c^2\,d^2+9\,a\,b^7\,c^3\,d}{32\,\left(a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8\right)}-\frac{\sqrt{-c^3\,d}\,\left(\frac{x\,\left(a^4\,b^3\,d^5-12\,a^3\,b^4\,c\,d^4+94\,a^2\,b^5\,c^2\,d^3+36\,a\,b^6\,c^3\,d^2+9\,b^7\,c^4\,d\right)}{32\,\left(a^4\,c^2\,d^4-4\,a^3\,b\,c^3\,d^3+6\,a^2\,b^2\,c^4\,d^2-4\,a\,b^3\,c^5\,d+b^4\,c^6\right)}-\frac{\left(\frac{-32\,a^8\,b^2\,c\,d^9+352\,a^7\,b^3\,c^2\,d^8-1440\,a^6\,b^4\,c^3\,d^7+3040\,a^5\,b^5\,c^4\,d^6-3680\,a^4\,b^6\,c^5\,d^5+2592\,a^3\,b^7\,c^6\,d^4-992\,a^2\,b^8\,c^7\,d^3+160\,a\,b^9\,c^8\,d^2}{64\,\left(a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8\right)}-\frac{x\,\sqrt{-c^3\,d}\,\left(-a^2\,d^2+6\,a\,b\,c\,d+3\,b^2\,c^2\right)\,\left(256\,a^7\,b^2\,c^2\,d^9-1280\,a^6\,b^3\,c^3\,d^8+2304\,a^5\,b^4\,c^4\,d^7-1280\,a^4\,b^5\,c^5\,d^6-1280\,a^3\,b^6\,c^6\,d^5+2304\,a^2\,b^7\,c^7\,d^4-1280\,a\,b^8\,c^8\,d^3+256\,b^9\,c^9\,d^2\right)}{512\,\left(-a^3\,c^3\,d^4+3\,a^2\,b\,c^4\,d^3-3\,a\,b^2\,c^5\,d^2+b^3\,c^6\,d\right)\,\left(a^4\,c^2\,d^4-4\,a^3\,b\,c^3\,d^3+6\,a^2\,b^2\,c^4\,d^2-4\,a\,b^3\,c^5\,d+b^4\,c^6\right)}\right)\,\sqrt{-c^3\,d}\,\left(-a^2\,d^2+6\,a\,b\,c\,d+3\,b^2\,c^2\right)}{16\,\left(-a^3\,c^3\,d^4+3\,a^2\,b\,c^4\,d^3-3\,a\,b^2\,c^5\,d^2+b^3\,c^6\,d\right)}\right)\,\left(-a^2\,d^2+6\,a\,b\,c\,d+3\,b^2\,c^2\right)}{16\,\left(-a^3\,c^3\,d^4+3\,a^2\,b\,c^4\,d^3-3\,a\,b^2\,c^5\,d^2+b^3\,c^6\,d\right)}+\frac{\sqrt{-c^3\,d}\,\left(\frac{x\,\left(a^4\,b^3\,d^5-12\,a^3\,b^4\,c\,d^4+94\,a^2\,b^5\,c^2\,d^3+36\,a\,b^6\,c^3\,d^2+9\,b^7\,c^4\,d\right)}{32\,\left(a^4\,c^2\,d^4-4\,a^3\,b\,c^3\,d^3+6\,a^2\,b^2\,c^4\,d^2-4\,a\,b^3\,c^5\,d+b^4\,c^6\right)}+\frac{\left(\frac{-32\,a^8\,b^2\,c\,d^9+352\,a^7\,b^3\,c^2\,d^8-1440\,a^6\,b^4\,c^3\,d^7+3040\,a^5\,b^5\,c^4\,d^6-3680\,a^4\,b^6\,c^5\,d^5+2592\,a^3\,b^7\,c^6\,d^4-992\,a^2\,b^8\,c^7\,d^3+160\,a\,b^9\,c^8\,d^2}{64\,\left(a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8\right)}+\frac{x\,\sqrt{-c^3\,d}\,\left(-a^2\,d^2+6\,a\,b\,c\,d+3\,b^2\,c^2\right)\,\left(256\,a^7\,b^2\,c^2\,d^9-1280\,a^6\,b^3\,c^3\,d^8+2304\,a^5\,b^4\,c^4\,d^7-1280\,a^4\,b^5\,c^5\,d^6-1280\,a^3\,b^6\,c^6\,d^5+2304\,a^2\,b^7\,c^7\,d^4-1280\,a\,b^8\,c^8\,d^3+256\,b^9\,c^9\,d^2\right)}{512\,\left(-a^3\,c^3\,d^4+3\,a^2\,b\,c^4\,d^3-3\,a\,b^2\,c^5\,d^2+b^3\,c^6\,d\right)\,\left(a^4\,c^2\,d^4-4\,a^3\,b\,c^3\,d^3+6\,a^2\,b^2\,c^4\,d^2-4\,a\,b^3\,c^5\,d+b^4\,c^6\right)}\right)\,\sqrt{-c^3\,d}\,\left(-a^2\,d^2+6\,a\,b\,c\,d+3\,b^2\,c^2\right)}{16\,\left(-a^3\,c^3\,d^4+3\,a^2\,b\,c^4\,d^3-3\,a\,b^2\,c^5\,d^2+b^3\,c^6\,d\right)}\right)\,\left(-a^2\,d^2+6\,a\,b\,c\,d+3\,b^2\,c^2\right)}{16\,\left(-a^3\,c^3\,d^4+3\,a^2\,b\,c^4\,d^3-3\,a\,b^2\,c^5\,d^2+b^3\,c^6\,d\right)}}\right)\,\sqrt{-c^3\,d}\,\left(-a^2\,d^2+6\,a\,b\,c\,d+3\,b^2\,c^2\right)\,1{}\mathrm{i}}{8\,\left(-a^3\,c^3\,d^4+3\,a^2\,b\,c^4\,d^3-3\,a\,b^2\,c^5\,d^2+b^3\,c^6\,d\right)}","Not used",1,"(atan((((-a*b^3)^(1/2)*((((160*a*b^9*c^8*d^2 - 32*a^8*b^2*c*d^9 - 992*a^2*b^8*c^7*d^3 + 2592*a^3*b^7*c^6*d^4 - 3680*a^4*b^6*c^5*d^5 + 3040*a^5*b^5*c^4*d^6 - 1440*a^6*b^4*c^3*d^7 + 352*a^7*b^3*c^2*d^8)/(64*(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d)) - (x*(-a*b^3)^(1/2)*(256*b^9*c^9*d^2 - 1280*a*b^8*c^8*d^3 + 2304*a^2*b^7*c^7*d^4 - 1280*a^3*b^6*c^6*d^5 - 1280*a^4*b^5*c^5*d^6 + 2304*a^5*b^4*c^4*d^7 - 1280*a^6*b^3*c^3*d^8 + 256*a^7*b^2*c^2*d^9))/(64*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)*(b^4*c^6 + a^4*c^2*d^4 - 4*a^3*b*c^3*d^3 + 6*a^2*b^2*c^4*d^2 - 4*a*b^3*c^5*d)))*(-a*b^3)^(1/2))/(2*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)) - (x*(9*b^7*c^4*d + a^4*b^3*d^5 + 36*a*b^6*c^3*d^2 - 12*a^3*b^4*c*d^4 + 94*a^2*b^5*c^2*d^3))/(32*(b^4*c^6 + a^4*c^2*d^4 - 4*a^3*b*c^3*d^3 + 6*a^2*b^2*c^4*d^2 - 4*a*b^3*c^5*d)))*1i)/(2*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)) - ((-a*b^3)^(1/2)*((((160*a*b^9*c^8*d^2 - 32*a^8*b^2*c*d^9 - 992*a^2*b^8*c^7*d^3 + 2592*a^3*b^7*c^6*d^4 - 3680*a^4*b^6*c^5*d^5 + 3040*a^5*b^5*c^4*d^6 - 1440*a^6*b^4*c^3*d^7 + 352*a^7*b^3*c^2*d^8)/(64*(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d)) + (x*(-a*b^3)^(1/2)*(256*b^9*c^9*d^2 - 1280*a*b^8*c^8*d^3 + 2304*a^2*b^7*c^7*d^4 - 1280*a^3*b^6*c^6*d^5 - 1280*a^4*b^5*c^5*d^6 + 2304*a^5*b^4*c^4*d^7 - 1280*a^6*b^3*c^3*d^8 + 256*a^7*b^2*c^2*d^9))/(64*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)*(b^4*c^6 + a^4*c^2*d^4 - 4*a^3*b*c^3*d^3 + 6*a^2*b^2*c^4*d^2 - 4*a*b^3*c^5*d)))*(-a*b^3)^(1/2))/(2*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)) + (x*(9*b^7*c^4*d + a^4*b^3*d^5 + 36*a*b^6*c^3*d^2 - 12*a^3*b^4*c*d^4 + 94*a^2*b^5*c^2*d^3))/(32*(b^4*c^6 + a^4*c^2*d^4 - 4*a^3*b*c^3*d^3 + 6*a^2*b^2*c^4*d^2 - 4*a*b^3*c^5*d)))*1i)/(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^3*b^5*c*d^3 - a^4*b^4*d^4 + 21*a^2*b^6*c^2*d^2 + 9*a*b^7*c^3*d)/(32*(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d)) + ((-a*b^3)^(1/2)*((((160*a*b^9*c^8*d^2 - 32*a^8*b^2*c*d^9 - 992*a^2*b^8*c^7*d^3 + 2592*a^3*b^7*c^6*d^4 - 3680*a^4*b^6*c^5*d^5 + 3040*a^5*b^5*c^4*d^6 - 1440*a^6*b^4*c^3*d^7 + 352*a^7*b^3*c^2*d^8)/(64*(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d)) - (x*(-a*b^3)^(1/2)*(256*b^9*c^9*d^2 - 1280*a*b^8*c^8*d^3 + 2304*a^2*b^7*c^7*d^4 - 1280*a^3*b^6*c^6*d^5 - 1280*a^4*b^5*c^5*d^6 + 2304*a^5*b^4*c^4*d^7 - 1280*a^6*b^3*c^3*d^8 + 256*a^7*b^2*c^2*d^9))/(64*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)*(b^4*c^6 + a^4*c^2*d^4 - 4*a^3*b*c^3*d^3 + 6*a^2*b^2*c^4*d^2 - 4*a*b^3*c^5*d)))*(-a*b^3)^(1/2))/(2*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)) - (x*(9*b^7*c^4*d + a^4*b^3*d^5 + 36*a*b^6*c^3*d^2 - 12*a^3*b^4*c*d^4 + 94*a^2*b^5*c^2*d^3))/(32*(b^4*c^6 + a^4*c^2*d^4 - 4*a^3*b*c^3*d^3 + 6*a^2*b^2*c^4*d^2 - 4*a*b^3*c^5*d))))/(2*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)) + ((-a*b^3)^(1/2)*((((160*a*b^9*c^8*d^2 - 32*a^8*b^2*c*d^9 - 992*a^2*b^8*c^7*d^3 + 2592*a^3*b^7*c^6*d^4 - 3680*a^4*b^6*c^5*d^5 + 3040*a^5*b^5*c^4*d^6 - 1440*a^6*b^4*c^3*d^7 + 352*a^7*b^3*c^2*d^8)/(64*(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d)) + (x*(-a*b^3)^(1/2)*(256*b^9*c^9*d^2 - 1280*a*b^8*c^8*d^3 + 2304*a^2*b^7*c^7*d^4 - 1280*a^3*b^6*c^6*d^5 - 1280*a^4*b^5*c^5*d^6 + 2304*a^5*b^4*c^4*d^7 - 1280*a^6*b^3*c^3*d^8 + 256*a^7*b^2*c^2*d^9))/(64*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)*(b^4*c^6 + a^4*c^2*d^4 - 4*a^3*b*c^3*d^3 + 6*a^2*b^2*c^4*d^2 - 4*a*b^3*c^5*d)))*(-a*b^3)^(1/2))/(2*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)) + (x*(9*b^7*c^4*d + a^4*b^3*d^5 + 36*a*b^6*c^3*d^2 - 12*a^3*b^4*c*d^4 + 94*a^2*b^5*c^2*d^3))/(32*(b^4*c^6 + a^4*c^2*d^4 - 4*a^3*b*c^3*d^3 + 6*a^2*b^2*c^4*d^2 - 4*a*b^3*c^5*d))))/(2*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))))*(-a*b^3)^(1/2)*1i)/(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2) - ((x*(a*d - 5*b*c))/(8*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) - (x^3*(a*d^2 + 3*b*c*d))/(8*c*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)))/(c^2 + d^2*x^4 + 2*c*d*x^2) - (atan((((-c^3*d)^(1/2)*((x*(9*b^7*c^4*d + a^4*b^3*d^5 + 36*a*b^6*c^3*d^2 - 12*a^3*b^4*c*d^4 + 94*a^2*b^5*c^2*d^3))/(32*(b^4*c^6 + a^4*c^2*d^4 - 4*a^3*b*c^3*d^3 + 6*a^2*b^2*c^4*d^2 - 4*a*b^3*c^5*d)) - (((160*a*b^9*c^8*d^2 - 32*a^8*b^2*c*d^9 - 992*a^2*b^8*c^7*d^3 + 2592*a^3*b^7*c^6*d^4 - 3680*a^4*b^6*c^5*d^5 + 3040*a^5*b^5*c^4*d^6 - 1440*a^6*b^4*c^3*d^7 + 352*a^7*b^3*c^2*d^8)/(64*(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d)) - (x*(-c^3*d)^(1/2)*(3*b^2*c^2 - a^2*d^2 + 6*a*b*c*d)*(256*b^9*c^9*d^2 - 1280*a*b^8*c^8*d^3 + 2304*a^2*b^7*c^7*d^4 - 1280*a^3*b^6*c^6*d^5 - 1280*a^4*b^5*c^5*d^6 + 2304*a^5*b^4*c^4*d^7 - 1280*a^6*b^3*c^3*d^8 + 256*a^7*b^2*c^2*d^9))/(512*(b^3*c^6*d - a^3*c^3*d^4 - 3*a*b^2*c^5*d^2 + 3*a^2*b*c^4*d^3)*(b^4*c^6 + a^4*c^2*d^4 - 4*a^3*b*c^3*d^3 + 6*a^2*b^2*c^4*d^2 - 4*a*b^3*c^5*d)))*(-c^3*d)^(1/2)*(3*b^2*c^2 - a^2*d^2 + 6*a*b*c*d))/(16*(b^3*c^6*d - a^3*c^3*d^4 - 3*a*b^2*c^5*d^2 + 3*a^2*b*c^4*d^3)))*(3*b^2*c^2 - a^2*d^2 + 6*a*b*c*d)*1i)/(16*(b^3*c^6*d - a^3*c^3*d^4 - 3*a*b^2*c^5*d^2 + 3*a^2*b*c^4*d^3)) + ((-c^3*d)^(1/2)*((x*(9*b^7*c^4*d + a^4*b^3*d^5 + 36*a*b^6*c^3*d^2 - 12*a^3*b^4*c*d^4 + 94*a^2*b^5*c^2*d^3))/(32*(b^4*c^6 + a^4*c^2*d^4 - 4*a^3*b*c^3*d^3 + 6*a^2*b^2*c^4*d^2 - 4*a*b^3*c^5*d)) + (((160*a*b^9*c^8*d^2 - 32*a^8*b^2*c*d^9 - 992*a^2*b^8*c^7*d^3 + 2592*a^3*b^7*c^6*d^4 - 3680*a^4*b^6*c^5*d^5 + 3040*a^5*b^5*c^4*d^6 - 1440*a^6*b^4*c^3*d^7 + 352*a^7*b^3*c^2*d^8)/(64*(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d)) + (x*(-c^3*d)^(1/2)*(3*b^2*c^2 - a^2*d^2 + 6*a*b*c*d)*(256*b^9*c^9*d^2 - 1280*a*b^8*c^8*d^3 + 2304*a^2*b^7*c^7*d^4 - 1280*a^3*b^6*c^6*d^5 - 1280*a^4*b^5*c^5*d^6 + 2304*a^5*b^4*c^4*d^7 - 1280*a^6*b^3*c^3*d^8 + 256*a^7*b^2*c^2*d^9))/(512*(b^3*c^6*d - a^3*c^3*d^4 - 3*a*b^2*c^5*d^2 + 3*a^2*b*c^4*d^3)*(b^4*c^6 + a^4*c^2*d^4 - 4*a^3*b*c^3*d^3 + 6*a^2*b^2*c^4*d^2 - 4*a*b^3*c^5*d)))*(-c^3*d)^(1/2)*(3*b^2*c^2 - a^2*d^2 + 6*a*b*c*d))/(16*(b^3*c^6*d - a^3*c^3*d^4 - 3*a*b^2*c^5*d^2 + 3*a^2*b*c^4*d^3)))*(3*b^2*c^2 - a^2*d^2 + 6*a*b*c*d)*1i)/(16*(b^3*c^6*d - a^3*c^3*d^4 - 3*a*b^2*c^5*d^2 + 3*a^2*b*c^4*d^3)))/((3*a^3*b^5*c*d^3 - a^4*b^4*d^4 + 21*a^2*b^6*c^2*d^2 + 9*a*b^7*c^3*d)/(32*(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d)) - ((-c^3*d)^(1/2)*((x*(9*b^7*c^4*d + a^4*b^3*d^5 + 36*a*b^6*c^3*d^2 - 12*a^3*b^4*c*d^4 + 94*a^2*b^5*c^2*d^3))/(32*(b^4*c^6 + a^4*c^2*d^4 - 4*a^3*b*c^3*d^3 + 6*a^2*b^2*c^4*d^2 - 4*a*b^3*c^5*d)) - (((160*a*b^9*c^8*d^2 - 32*a^8*b^2*c*d^9 - 992*a^2*b^8*c^7*d^3 + 2592*a^3*b^7*c^6*d^4 - 3680*a^4*b^6*c^5*d^5 + 3040*a^5*b^5*c^4*d^6 - 1440*a^6*b^4*c^3*d^7 + 352*a^7*b^3*c^2*d^8)/(64*(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d)) - (x*(-c^3*d)^(1/2)*(3*b^2*c^2 - a^2*d^2 + 6*a*b*c*d)*(256*b^9*c^9*d^2 - 1280*a*b^8*c^8*d^3 + 2304*a^2*b^7*c^7*d^4 - 1280*a^3*b^6*c^6*d^5 - 1280*a^4*b^5*c^5*d^6 + 2304*a^5*b^4*c^4*d^7 - 1280*a^6*b^3*c^3*d^8 + 256*a^7*b^2*c^2*d^9))/(512*(b^3*c^6*d - a^3*c^3*d^4 - 3*a*b^2*c^5*d^2 + 3*a^2*b*c^4*d^3)*(b^4*c^6 + a^4*c^2*d^4 - 4*a^3*b*c^3*d^3 + 6*a^2*b^2*c^4*d^2 - 4*a*b^3*c^5*d)))*(-c^3*d)^(1/2)*(3*b^2*c^2 - a^2*d^2 + 6*a*b*c*d))/(16*(b^3*c^6*d - a^3*c^3*d^4 - 3*a*b^2*c^5*d^2 + 3*a^2*b*c^4*d^3)))*(3*b^2*c^2 - a^2*d^2 + 6*a*b*c*d))/(16*(b^3*c^6*d - a^3*c^3*d^4 - 3*a*b^2*c^5*d^2 + 3*a^2*b*c^4*d^3)) + ((-c^3*d)^(1/2)*((x*(9*b^7*c^4*d + a^4*b^3*d^5 + 36*a*b^6*c^3*d^2 - 12*a^3*b^4*c*d^4 + 94*a^2*b^5*c^2*d^3))/(32*(b^4*c^6 + a^4*c^2*d^4 - 4*a^3*b*c^3*d^3 + 6*a^2*b^2*c^4*d^2 - 4*a*b^3*c^5*d)) + (((160*a*b^9*c^8*d^2 - 32*a^8*b^2*c*d^9 - 992*a^2*b^8*c^7*d^3 + 2592*a^3*b^7*c^6*d^4 - 3680*a^4*b^6*c^5*d^5 + 3040*a^5*b^5*c^4*d^6 - 1440*a^6*b^4*c^3*d^7 + 352*a^7*b^3*c^2*d^8)/(64*(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d)) + (x*(-c^3*d)^(1/2)*(3*b^2*c^2 - a^2*d^2 + 6*a*b*c*d)*(256*b^9*c^9*d^2 - 1280*a*b^8*c^8*d^3 + 2304*a^2*b^7*c^7*d^4 - 1280*a^3*b^6*c^6*d^5 - 1280*a^4*b^5*c^5*d^6 + 2304*a^5*b^4*c^4*d^7 - 1280*a^6*b^3*c^3*d^8 + 256*a^7*b^2*c^2*d^9))/(512*(b^3*c^6*d - a^3*c^3*d^4 - 3*a*b^2*c^5*d^2 + 3*a^2*b*c^4*d^3)*(b^4*c^6 + a^4*c^2*d^4 - 4*a^3*b*c^3*d^3 + 6*a^2*b^2*c^4*d^2 - 4*a*b^3*c^5*d)))*(-c^3*d)^(1/2)*(3*b^2*c^2 - a^2*d^2 + 6*a*b*c*d))/(16*(b^3*c^6*d - a^3*c^3*d^4 - 3*a*b^2*c^5*d^2 + 3*a^2*b*c^4*d^3)))*(3*b^2*c^2 - a^2*d^2 + 6*a*b*c*d))/(16*(b^3*c^6*d - a^3*c^3*d^4 - 3*a*b^2*c^5*d^2 + 3*a^2*b*c^4*d^3))))*(-c^3*d)^(1/2)*(3*b^2*c^2 - a^2*d^2 + 6*a*b*c*d)*1i)/(8*(b^3*c^6*d - a^3*c^3*d^4 - 3*a*b^2*c^5*d^2 + 3*a^2*b*c^4*d^3))","B"
255,1,340,98,0.349409,"\text{Not used}","int(x/((a + b*x^2)*(c + d*x^2)^3),x)","\frac{a^2\,d^2+3\,b^2\,c^2+b^2\,c^2\,\mathrm{atan}\left(\frac{a\,d\,x^2\,1{}\mathrm{i}-b\,c\,x^2\,1{}\mathrm{i}}{2\,a\,c+a\,d\,x^2+b\,c\,x^2}\right)\,4{}\mathrm{i}+b^2\,d^2\,x^4\,\mathrm{atan}\left(\frac{a\,d\,x^2\,1{}\mathrm{i}-b\,c\,x^2\,1{}\mathrm{i}}{2\,a\,c+a\,d\,x^2+b\,c\,x^2}\right)\,4{}\mathrm{i}-2\,a\,b\,d^2\,x^2+2\,b^2\,c\,d\,x^2-4\,a\,b\,c\,d+b^2\,c\,d\,x^2\,\mathrm{atan}\left(\frac{a\,d\,x^2\,1{}\mathrm{i}-b\,c\,x^2\,1{}\mathrm{i}}{2\,a\,c+a\,d\,x^2+b\,c\,x^2}\right)\,8{}\mathrm{i}}{-4\,a^3\,c^2\,d^3-8\,a^3\,c\,d^4\,x^2-4\,a^3\,d^5\,x^4+12\,a^2\,b\,c^3\,d^2+24\,a^2\,b\,c^2\,d^3\,x^2+12\,a^2\,b\,c\,d^4\,x^4-12\,a\,b^2\,c^4\,d-24\,a\,b^2\,c^3\,d^2\,x^2-12\,a\,b^2\,c^2\,d^3\,x^4+4\,b^3\,c^5+8\,b^3\,c^4\,d\,x^2+4\,b^3\,c^3\,d^2\,x^4}","Not used",1,"(a^2*d^2 + 3*b^2*c^2 + b^2*c^2*atan((a*d*x^2*1i - b*c*x^2*1i)/(2*a*c + a*d*x^2 + b*c*x^2))*4i + b^2*d^2*x^4*atan((a*d*x^2*1i - b*c*x^2*1i)/(2*a*c + a*d*x^2 + b*c*x^2))*4i - 2*a*b*d^2*x^2 + 2*b^2*c*d*x^2 - 4*a*b*c*d + b^2*c*d*x^2*atan((a*d*x^2*1i - b*c*x^2*1i)/(2*a*c + a*d*x^2 + b*c*x^2))*8i)/(4*b^3*c^5 - 4*a^3*c^2*d^3 - 4*a^3*d^5*x^4 + 12*a^2*b*c^3*d^2 - 8*a^3*c*d^4*x^2 + 8*b^3*c^4*d*x^2 + 4*b^3*c^3*d^2*x^4 - 12*a*b^2*c^4*d + 12*a^2*b*c*d^4*x^4 - 24*a*b^2*c^3*d^2*x^2 + 24*a^2*b*c^2*d^3*x^2 - 12*a*b^2*c^2*d^3*x^4)","B"
256,1,6033,160,2.368379,"\text{Not used}","int(1/((a + b*x^2)*(c + d*x^2)^3),x)","\frac{\frac{x^3\,\left(3\,a\,d^3-7\,b\,c\,d^2\right)}{8\,c^2\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}+\frac{x\,\left(5\,a\,d^2-9\,b\,c\,d\right)}{8\,c\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}}{c^2+2\,c\,d\,x^2+d^2\,x^4}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-a\,b^5}\,\left(\frac{x\,\left(9\,a^4\,b^3\,d^7-60\,a^3\,b^4\,c\,d^6+190\,a^2\,b^5\,c^2\,d^5-300\,a\,b^6\,c^3\,d^4+289\,b^7\,c^4\,d^3\right)}{32\,\left(a^4\,c^4\,d^4-4\,a^3\,b\,c^5\,d^3+6\,a^2\,b^2\,c^6\,d^2-4\,a\,b^3\,c^7\,d+b^4\,c^8\right)}-\frac{\sqrt{-a\,b^5}\,\left(\frac{96\,a^8\,b^2\,c^2\,d^{10}-800\,a^7\,b^3\,c^3\,d^9+3040\,a^6\,b^4\,c^4\,d^8-6816\,a^5\,b^5\,c^5\,d^7+9760\,a^4\,b^6\,c^6\,d^6-9056\,a^3\,b^7\,c^7\,d^5+5280\,a^2\,b^8\,c^8\,d^4-1760\,a\,b^9\,c^9\,d^3+256\,b^{10}\,c^{10}\,d^2}{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)}-\frac{x\,\sqrt{-a\,b^5}\,\left(256\,a^7\,b^2\,c^4\,d^9-1280\,a^6\,b^3\,c^5\,d^8+2304\,a^5\,b^4\,c^6\,d^7-1280\,a^4\,b^5\,c^7\,d^6-1280\,a^3\,b^6\,c^8\,d^5+2304\,a^2\,b^7\,c^9\,d^4-1280\,a\,b^8\,c^{10}\,d^3+256\,b^9\,c^{11}\,d^2\right)}{64\,\left(a^4\,d^3-3\,a^3\,b\,c\,d^2+3\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3\right)\,\left(a^4\,c^4\,d^4-4\,a^3\,b\,c^5\,d^3+6\,a^2\,b^2\,c^6\,d^2-4\,a\,b^3\,c^7\,d+b^4\,c^8\right)}\right)}{2\,\left(a^4\,d^3-3\,a^3\,b\,c\,d^2+3\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3\right)}\right)\,1{}\mathrm{i}}{2\,\left(a^4\,d^3-3\,a^3\,b\,c\,d^2+3\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3\right)}+\frac{\sqrt{-a\,b^5}\,\left(\frac{x\,\left(9\,a^4\,b^3\,d^7-60\,a^3\,b^4\,c\,d^6+190\,a^2\,b^5\,c^2\,d^5-300\,a\,b^6\,c^3\,d^4+289\,b^7\,c^4\,d^3\right)}{32\,\left(a^4\,c^4\,d^4-4\,a^3\,b\,c^5\,d^3+6\,a^2\,b^2\,c^6\,d^2-4\,a\,b^3\,c^7\,d+b^4\,c^8\right)}+\frac{\sqrt{-a\,b^5}\,\left(\frac{96\,a^8\,b^2\,c^2\,d^{10}-800\,a^7\,b^3\,c^3\,d^9+3040\,a^6\,b^4\,c^4\,d^8-6816\,a^5\,b^5\,c^5\,d^7+9760\,a^4\,b^6\,c^6\,d^6-9056\,a^3\,b^7\,c^7\,d^5+5280\,a^2\,b^8\,c^8\,d^4-1760\,a\,b^9\,c^9\,d^3+256\,b^{10}\,c^{10}\,d^2}{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)}+\frac{x\,\sqrt{-a\,b^5}\,\left(256\,a^7\,b^2\,c^4\,d^9-1280\,a^6\,b^3\,c^5\,d^8+2304\,a^5\,b^4\,c^6\,d^7-1280\,a^4\,b^5\,c^7\,d^6-1280\,a^3\,b^6\,c^8\,d^5+2304\,a^2\,b^7\,c^9\,d^4-1280\,a\,b^8\,c^{10}\,d^3+256\,b^9\,c^{11}\,d^2\right)}{64\,\left(a^4\,d^3-3\,a^3\,b\,c\,d^2+3\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3\right)\,\left(a^4\,c^4\,d^4-4\,a^3\,b\,c^5\,d^3+6\,a^2\,b^2\,c^6\,d^2-4\,a\,b^3\,c^7\,d+b^4\,c^8\right)}\right)}{2\,\left(a^4\,d^3-3\,a^3\,b\,c\,d^2+3\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3\right)}\right)\,1{}\mathrm{i}}{2\,\left(a^4\,d^3-3\,a^3\,b\,c\,d^2+3\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3\right)}}{\frac{9\,a^3\,b^5\,d^6-51\,a^2\,b^6\,c\,d^5+115\,a\,b^7\,c^2\,d^4-105\,b^8\,c^3\,d^3}{32\,\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)}+\frac{\sqrt{-a\,b^5}\,\left(\frac{x\,\left(9\,a^4\,b^3\,d^7-60\,a^3\,b^4\,c\,d^6+190\,a^2\,b^5\,c^2\,d^5-300\,a\,b^6\,c^3\,d^4+289\,b^7\,c^4\,d^3\right)}{32\,\left(a^4\,c^4\,d^4-4\,a^3\,b\,c^5\,d^3+6\,a^2\,b^2\,c^6\,d^2-4\,a\,b^3\,c^7\,d+b^4\,c^8\right)}-\frac{\sqrt{-a\,b^5}\,\left(\frac{96\,a^8\,b^2\,c^2\,d^{10}-800\,a^7\,b^3\,c^3\,d^9+3040\,a^6\,b^4\,c^4\,d^8-6816\,a^5\,b^5\,c^5\,d^7+9760\,a^4\,b^6\,c^6\,d^6-9056\,a^3\,b^7\,c^7\,d^5+5280\,a^2\,b^8\,c^8\,d^4-1760\,a\,b^9\,c^9\,d^3+256\,b^{10}\,c^{10}\,d^2}{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)}-\frac{x\,\sqrt{-a\,b^5}\,\left(256\,a^7\,b^2\,c^4\,d^9-1280\,a^6\,b^3\,c^5\,d^8+2304\,a^5\,b^4\,c^6\,d^7-1280\,a^4\,b^5\,c^7\,d^6-1280\,a^3\,b^6\,c^8\,d^5+2304\,a^2\,b^7\,c^9\,d^4-1280\,a\,b^8\,c^{10}\,d^3+256\,b^9\,c^{11}\,d^2\right)}{64\,\left(a^4\,d^3-3\,a^3\,b\,c\,d^2+3\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3\right)\,\left(a^4\,c^4\,d^4-4\,a^3\,b\,c^5\,d^3+6\,a^2\,b^2\,c^6\,d^2-4\,a\,b^3\,c^7\,d+b^4\,c^8\right)}\right)}{2\,\left(a^4\,d^3-3\,a^3\,b\,c\,d^2+3\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3\right)}\right)}{2\,\left(a^4\,d^3-3\,a^3\,b\,c\,d^2+3\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3\right)}-\frac{\sqrt{-a\,b^5}\,\left(\frac{x\,\left(9\,a^4\,b^3\,d^7-60\,a^3\,b^4\,c\,d^6+190\,a^2\,b^5\,c^2\,d^5-300\,a\,b^6\,c^3\,d^4+289\,b^7\,c^4\,d^3\right)}{32\,\left(a^4\,c^4\,d^4-4\,a^3\,b\,c^5\,d^3+6\,a^2\,b^2\,c^6\,d^2-4\,a\,b^3\,c^7\,d+b^4\,c^8\right)}+\frac{\sqrt{-a\,b^5}\,\left(\frac{96\,a^8\,b^2\,c^2\,d^{10}-800\,a^7\,b^3\,c^3\,d^9+3040\,a^6\,b^4\,c^4\,d^8-6816\,a^5\,b^5\,c^5\,d^7+9760\,a^4\,b^6\,c^6\,d^6-9056\,a^3\,b^7\,c^7\,d^5+5280\,a^2\,b^8\,c^8\,d^4-1760\,a\,b^9\,c^9\,d^3+256\,b^{10}\,c^{10}\,d^2}{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)}+\frac{x\,\sqrt{-a\,b^5}\,\left(256\,a^7\,b^2\,c^4\,d^9-1280\,a^6\,b^3\,c^5\,d^8+2304\,a^5\,b^4\,c^6\,d^7-1280\,a^4\,b^5\,c^7\,d^6-1280\,a^3\,b^6\,c^8\,d^5+2304\,a^2\,b^7\,c^9\,d^4-1280\,a\,b^8\,c^{10}\,d^3+256\,b^9\,c^{11}\,d^2\right)}{64\,\left(a^4\,d^3-3\,a^3\,b\,c\,d^2+3\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3\right)\,\left(a^4\,c^4\,d^4-4\,a^3\,b\,c^5\,d^3+6\,a^2\,b^2\,c^6\,d^2-4\,a\,b^3\,c^7\,d+b^4\,c^8\right)}\right)}{2\,\left(a^4\,d^3-3\,a^3\,b\,c\,d^2+3\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3\right)}\right)}{2\,\left(a^4\,d^3-3\,a^3\,b\,c\,d^2+3\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3\right)}}\right)\,\sqrt{-a\,b^5}\,1{}\mathrm{i}}{a^4\,d^3-3\,a^3\,b\,c\,d^2+3\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{x\,\left(9\,a^4\,b^3\,d^7-60\,a^3\,b^4\,c\,d^6+190\,a^2\,b^5\,c^2\,d^5-300\,a\,b^6\,c^3\,d^4+289\,b^7\,c^4\,d^3\right)}{32\,\left(a^4\,c^4\,d^4-4\,a^3\,b\,c^5\,d^3+6\,a^2\,b^2\,c^6\,d^2-4\,a\,b^3\,c^7\,d+b^4\,c^8\right)}-\frac{\left(\frac{96\,a^8\,b^2\,c^2\,d^{10}-800\,a^7\,b^3\,c^3\,d^9+3040\,a^6\,b^4\,c^4\,d^8-6816\,a^5\,b^5\,c^5\,d^7+9760\,a^4\,b^6\,c^6\,d^6-9056\,a^3\,b^7\,c^7\,d^5+5280\,a^2\,b^8\,c^8\,d^4-1760\,a\,b^9\,c^9\,d^3+256\,b^{10}\,c^{10}\,d^2}{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)}-\frac{x\,\sqrt{-c^5\,d}\,\left(3\,a^2\,d^2-10\,a\,b\,c\,d+15\,b^2\,c^2\right)\,\left(256\,a^7\,b^2\,c^4\,d^9-1280\,a^6\,b^3\,c^5\,d^8+2304\,a^5\,b^4\,c^6\,d^7-1280\,a^4\,b^5\,c^7\,d^6-1280\,a^3\,b^6\,c^8\,d^5+2304\,a^2\,b^7\,c^9\,d^4-1280\,a\,b^8\,c^{10}\,d^3+256\,b^9\,c^{11}\,d^2\right)}{512\,\left(-a^3\,c^5\,d^3+3\,a^2\,b\,c^6\,d^2-3\,a\,b^2\,c^7\,d+b^3\,c^8\right)\,\left(a^4\,c^4\,d^4-4\,a^3\,b\,c^5\,d^3+6\,a^2\,b^2\,c^6\,d^2-4\,a\,b^3\,c^7\,d+b^4\,c^8\right)}\right)\,\sqrt{-c^5\,d}\,\left(3\,a^2\,d^2-10\,a\,b\,c\,d+15\,b^2\,c^2\right)}{16\,\left(-a^3\,c^5\,d^3+3\,a^2\,b\,c^6\,d^2-3\,a\,b^2\,c^7\,d+b^3\,c^8\right)}\right)\,\sqrt{-c^5\,d}\,\left(3\,a^2\,d^2-10\,a\,b\,c\,d+15\,b^2\,c^2\right)\,1{}\mathrm{i}}{16\,\left(-a^3\,c^5\,d^3+3\,a^2\,b\,c^6\,d^2-3\,a\,b^2\,c^7\,d+b^3\,c^8\right)}+\frac{\left(\frac{x\,\left(9\,a^4\,b^3\,d^7-60\,a^3\,b^4\,c\,d^6+190\,a^2\,b^5\,c^2\,d^5-300\,a\,b^6\,c^3\,d^4+289\,b^7\,c^4\,d^3\right)}{32\,\left(a^4\,c^4\,d^4-4\,a^3\,b\,c^5\,d^3+6\,a^2\,b^2\,c^6\,d^2-4\,a\,b^3\,c^7\,d+b^4\,c^8\right)}+\frac{\left(\frac{96\,a^8\,b^2\,c^2\,d^{10}-800\,a^7\,b^3\,c^3\,d^9+3040\,a^6\,b^4\,c^4\,d^8-6816\,a^5\,b^5\,c^5\,d^7+9760\,a^4\,b^6\,c^6\,d^6-9056\,a^3\,b^7\,c^7\,d^5+5280\,a^2\,b^8\,c^8\,d^4-1760\,a\,b^9\,c^9\,d^3+256\,b^{10}\,c^{10}\,d^2}{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)}+\frac{x\,\sqrt{-c^5\,d}\,\left(3\,a^2\,d^2-10\,a\,b\,c\,d+15\,b^2\,c^2\right)\,\left(256\,a^7\,b^2\,c^4\,d^9-1280\,a^6\,b^3\,c^5\,d^8+2304\,a^5\,b^4\,c^6\,d^7-1280\,a^4\,b^5\,c^7\,d^6-1280\,a^3\,b^6\,c^8\,d^5+2304\,a^2\,b^7\,c^9\,d^4-1280\,a\,b^8\,c^{10}\,d^3+256\,b^9\,c^{11}\,d^2\right)}{512\,\left(-a^3\,c^5\,d^3+3\,a^2\,b\,c^6\,d^2-3\,a\,b^2\,c^7\,d+b^3\,c^8\right)\,\left(a^4\,c^4\,d^4-4\,a^3\,b\,c^5\,d^3+6\,a^2\,b^2\,c^6\,d^2-4\,a\,b^3\,c^7\,d+b^4\,c^8\right)}\right)\,\sqrt{-c^5\,d}\,\left(3\,a^2\,d^2-10\,a\,b\,c\,d+15\,b^2\,c^2\right)}{16\,\left(-a^3\,c^5\,d^3+3\,a^2\,b\,c^6\,d^2-3\,a\,b^2\,c^7\,d+b^3\,c^8\right)}\right)\,\sqrt{-c^5\,d}\,\left(3\,a^2\,d^2-10\,a\,b\,c\,d+15\,b^2\,c^2\right)\,1{}\mathrm{i}}{16\,\left(-a^3\,c^5\,d^3+3\,a^2\,b\,c^6\,d^2-3\,a\,b^2\,c^7\,d+b^3\,c^8\right)}}{\frac{9\,a^3\,b^5\,d^6-51\,a^2\,b^6\,c\,d^5+115\,a\,b^7\,c^2\,d^4-105\,b^8\,c^3\,d^3}{32\,\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)}+\frac{\left(\frac{x\,\left(9\,a^4\,b^3\,d^7-60\,a^3\,b^4\,c\,d^6+190\,a^2\,b^5\,c^2\,d^5-300\,a\,b^6\,c^3\,d^4+289\,b^7\,c^4\,d^3\right)}{32\,\left(a^4\,c^4\,d^4-4\,a^3\,b\,c^5\,d^3+6\,a^2\,b^2\,c^6\,d^2-4\,a\,b^3\,c^7\,d+b^4\,c^8\right)}-\frac{\left(\frac{96\,a^8\,b^2\,c^2\,d^{10}-800\,a^7\,b^3\,c^3\,d^9+3040\,a^6\,b^4\,c^4\,d^8-6816\,a^5\,b^5\,c^5\,d^7+9760\,a^4\,b^6\,c^6\,d^6-9056\,a^3\,b^7\,c^7\,d^5+5280\,a^2\,b^8\,c^8\,d^4-1760\,a\,b^9\,c^9\,d^3+256\,b^{10}\,c^{10}\,d^2}{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)}-\frac{x\,\sqrt{-c^5\,d}\,\left(3\,a^2\,d^2-10\,a\,b\,c\,d+15\,b^2\,c^2\right)\,\left(256\,a^7\,b^2\,c^4\,d^9-1280\,a^6\,b^3\,c^5\,d^8+2304\,a^5\,b^4\,c^6\,d^7-1280\,a^4\,b^5\,c^7\,d^6-1280\,a^3\,b^6\,c^8\,d^5+2304\,a^2\,b^7\,c^9\,d^4-1280\,a\,b^8\,c^{10}\,d^3+256\,b^9\,c^{11}\,d^2\right)}{512\,\left(-a^3\,c^5\,d^3+3\,a^2\,b\,c^6\,d^2-3\,a\,b^2\,c^7\,d+b^3\,c^8\right)\,\left(a^4\,c^4\,d^4-4\,a^3\,b\,c^5\,d^3+6\,a^2\,b^2\,c^6\,d^2-4\,a\,b^3\,c^7\,d+b^4\,c^8\right)}\right)\,\sqrt{-c^5\,d}\,\left(3\,a^2\,d^2-10\,a\,b\,c\,d+15\,b^2\,c^2\right)}{16\,\left(-a^3\,c^5\,d^3+3\,a^2\,b\,c^6\,d^2-3\,a\,b^2\,c^7\,d+b^3\,c^8\right)}\right)\,\sqrt{-c^5\,d}\,\left(3\,a^2\,d^2-10\,a\,b\,c\,d+15\,b^2\,c^2\right)}{16\,\left(-a^3\,c^5\,d^3+3\,a^2\,b\,c^6\,d^2-3\,a\,b^2\,c^7\,d+b^3\,c^8\right)}-\frac{\left(\frac{x\,\left(9\,a^4\,b^3\,d^7-60\,a^3\,b^4\,c\,d^6+190\,a^2\,b^5\,c^2\,d^5-300\,a\,b^6\,c^3\,d^4+289\,b^7\,c^4\,d^3\right)}{32\,\left(a^4\,c^4\,d^4-4\,a^3\,b\,c^5\,d^3+6\,a^2\,b^2\,c^6\,d^2-4\,a\,b^3\,c^7\,d+b^4\,c^8\right)}+\frac{\left(\frac{96\,a^8\,b^2\,c^2\,d^{10}-800\,a^7\,b^3\,c^3\,d^9+3040\,a^6\,b^4\,c^4\,d^8-6816\,a^5\,b^5\,c^5\,d^7+9760\,a^4\,b^6\,c^6\,d^6-9056\,a^3\,b^7\,c^7\,d^5+5280\,a^2\,b^8\,c^8\,d^4-1760\,a\,b^9\,c^9\,d^3+256\,b^{10}\,c^{10}\,d^2}{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)}+\frac{x\,\sqrt{-c^5\,d}\,\left(3\,a^2\,d^2-10\,a\,b\,c\,d+15\,b^2\,c^2\right)\,\left(256\,a^7\,b^2\,c^4\,d^9-1280\,a^6\,b^3\,c^5\,d^8+2304\,a^5\,b^4\,c^6\,d^7-1280\,a^4\,b^5\,c^7\,d^6-1280\,a^3\,b^6\,c^8\,d^5+2304\,a^2\,b^7\,c^9\,d^4-1280\,a\,b^8\,c^{10}\,d^3+256\,b^9\,c^{11}\,d^2\right)}{512\,\left(-a^3\,c^5\,d^3+3\,a^2\,b\,c^6\,d^2-3\,a\,b^2\,c^7\,d+b^3\,c^8\right)\,\left(a^4\,c^4\,d^4-4\,a^3\,b\,c^5\,d^3+6\,a^2\,b^2\,c^6\,d^2-4\,a\,b^3\,c^7\,d+b^4\,c^8\right)}\right)\,\sqrt{-c^5\,d}\,\left(3\,a^2\,d^2-10\,a\,b\,c\,d+15\,b^2\,c^2\right)}{16\,\left(-a^3\,c^5\,d^3+3\,a^2\,b\,c^6\,d^2-3\,a\,b^2\,c^7\,d+b^3\,c^8\right)}\right)\,\sqrt{-c^5\,d}\,\left(3\,a^2\,d^2-10\,a\,b\,c\,d+15\,b^2\,c^2\right)}{16\,\left(-a^3\,c^5\,d^3+3\,a^2\,b\,c^6\,d^2-3\,a\,b^2\,c^7\,d+b^3\,c^8\right)}}\right)\,\sqrt{-c^5\,d}\,\left(3\,a^2\,d^2-10\,a\,b\,c\,d+15\,b^2\,c^2\right)\,1{}\mathrm{i}}{8\,\left(-a^3\,c^5\,d^3+3\,a^2\,b\,c^6\,d^2-3\,a\,b^2\,c^7\,d+b^3\,c^8\right)}","Not used",1,"((x^3*(3*a*d^3 - 7*b*c*d^2))/(8*c^2*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) + (x*(5*a*d^2 - 9*b*c*d))/(8*c*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)))/(c^2 + d^2*x^4 + 2*c*d*x^2) - (atan((((-a*b^5)^(1/2)*((x*(9*a^4*b^3*d^7 + 289*b^7*c^4*d^3 - 300*a*b^6*c^3*d^4 - 60*a^3*b^4*c*d^6 + 190*a^2*b^5*c^2*d^5))/(32*(b^4*c^8 + a^4*c^4*d^4 - 4*a^3*b*c^5*d^3 + 6*a^2*b^2*c^6*d^2 - 4*a*b^3*c^7*d)) - ((-a*b^5)^(1/2)*((256*b^10*c^10*d^2 - 1760*a*b^9*c^9*d^3 + 5280*a^2*b^8*c^8*d^4 - 9056*a^3*b^7*c^7*d^5 + 9760*a^4*b^6*c^6*d^6 - 6816*a^5*b^5*c^5*d^7 + 3040*a^6*b^4*c^4*d^8 - 800*a^7*b^3*c^3*d^9 + 96*a^8*b^2*c^2*d^10)/(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*(-a*b^5)^(1/2)*(256*b^9*c^11*d^2 - 1280*a*b^8*c^10*d^3 + 2304*a^2*b^7*c^9*d^4 - 1280*a^3*b^6*c^8*d^5 - 1280*a^4*b^5*c^7*d^6 + 2304*a^5*b^4*c^6*d^7 - 1280*a^6*b^3*c^5*d^8 + 256*a^7*b^2*c^4*d^9))/(64*(a^4*d^3 - a*b^3*c^3 + 3*a^2*b^2*c^2*d - 3*a^3*b*c*d^2)*(b^4*c^8 + a^4*c^4*d^4 - 4*a^3*b*c^5*d^3 + 6*a^2*b^2*c^6*d^2 - 4*a*b^3*c^7*d))))/(2*(a^4*d^3 - a*b^3*c^3 + 3*a^2*b^2*c^2*d - 3*a^3*b*c*d^2)))*1i)/(2*(a^4*d^3 - a*b^3*c^3 + 3*a^2*b^2*c^2*d - 3*a^3*b*c*d^2)) + ((-a*b^5)^(1/2)*((x*(9*a^4*b^3*d^7 + 289*b^7*c^4*d^3 - 300*a*b^6*c^3*d^4 - 60*a^3*b^4*c*d^6 + 190*a^2*b^5*c^2*d^5))/(32*(b^4*c^8 + a^4*c^4*d^4 - 4*a^3*b*c^5*d^3 + 6*a^2*b^2*c^6*d^2 - 4*a*b^3*c^7*d)) + ((-a*b^5)^(1/2)*((256*b^10*c^10*d^2 - 1760*a*b^9*c^9*d^3 + 5280*a^2*b^8*c^8*d^4 - 9056*a^3*b^7*c^7*d^5 + 9760*a^4*b^6*c^6*d^6 - 6816*a^5*b^5*c^5*d^7 + 3040*a^6*b^4*c^4*d^8 - 800*a^7*b^3*c^3*d^9 + 96*a^8*b^2*c^2*d^10)/(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*(-a*b^5)^(1/2)*(256*b^9*c^11*d^2 - 1280*a*b^8*c^10*d^3 + 2304*a^2*b^7*c^9*d^4 - 1280*a^3*b^6*c^8*d^5 - 1280*a^4*b^5*c^7*d^6 + 2304*a^5*b^4*c^6*d^7 - 1280*a^6*b^3*c^5*d^8 + 256*a^7*b^2*c^4*d^9))/(64*(a^4*d^3 - a*b^3*c^3 + 3*a^2*b^2*c^2*d - 3*a^3*b*c*d^2)*(b^4*c^8 + a^4*c^4*d^4 - 4*a^3*b*c^5*d^3 + 6*a^2*b^2*c^6*d^2 - 4*a*b^3*c^7*d))))/(2*(a^4*d^3 - a*b^3*c^3 + 3*a^2*b^2*c^2*d - 3*a^3*b*c*d^2)))*1i)/(2*(a^4*d^3 - a*b^3*c^3 + 3*a^2*b^2*c^2*d - 3*a^3*b*c*d^2)))/((9*a^3*b^5*d^6 - 105*b^8*c^3*d^3 + 115*a*b^7*c^2*d^4 - 51*a^2*b^6*c*d^5)/(32*(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)) + ((-a*b^5)^(1/2)*((x*(9*a^4*b^3*d^7 + 289*b^7*c^4*d^3 - 300*a*b^6*c^3*d^4 - 60*a^3*b^4*c*d^6 + 190*a^2*b^5*c^2*d^5))/(32*(b^4*c^8 + a^4*c^4*d^4 - 4*a^3*b*c^5*d^3 + 6*a^2*b^2*c^6*d^2 - 4*a*b^3*c^7*d)) - ((-a*b^5)^(1/2)*((256*b^10*c^10*d^2 - 1760*a*b^9*c^9*d^3 + 5280*a^2*b^8*c^8*d^4 - 9056*a^3*b^7*c^7*d^5 + 9760*a^4*b^6*c^6*d^6 - 6816*a^5*b^5*c^5*d^7 + 3040*a^6*b^4*c^4*d^8 - 800*a^7*b^3*c^3*d^9 + 96*a^8*b^2*c^2*d^10)/(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*(-a*b^5)^(1/2)*(256*b^9*c^11*d^2 - 1280*a*b^8*c^10*d^3 + 2304*a^2*b^7*c^9*d^4 - 1280*a^3*b^6*c^8*d^5 - 1280*a^4*b^5*c^7*d^6 + 2304*a^5*b^4*c^6*d^7 - 1280*a^6*b^3*c^5*d^8 + 256*a^7*b^2*c^4*d^9))/(64*(a^4*d^3 - a*b^3*c^3 + 3*a^2*b^2*c^2*d - 3*a^3*b*c*d^2)*(b^4*c^8 + a^4*c^4*d^4 - 4*a^3*b*c^5*d^3 + 6*a^2*b^2*c^6*d^2 - 4*a*b^3*c^7*d))))/(2*(a^4*d^3 - a*b^3*c^3 + 3*a^2*b^2*c^2*d - 3*a^3*b*c*d^2))))/(2*(a^4*d^3 - a*b^3*c^3 + 3*a^2*b^2*c^2*d - 3*a^3*b*c*d^2)) - ((-a*b^5)^(1/2)*((x*(9*a^4*b^3*d^7 + 289*b^7*c^4*d^3 - 300*a*b^6*c^3*d^4 - 60*a^3*b^4*c*d^6 + 190*a^2*b^5*c^2*d^5))/(32*(b^4*c^8 + a^4*c^4*d^4 - 4*a^3*b*c^5*d^3 + 6*a^2*b^2*c^6*d^2 - 4*a*b^3*c^7*d)) + ((-a*b^5)^(1/2)*((256*b^10*c^10*d^2 - 1760*a*b^9*c^9*d^3 + 5280*a^2*b^8*c^8*d^4 - 9056*a^3*b^7*c^7*d^5 + 9760*a^4*b^6*c^6*d^6 - 6816*a^5*b^5*c^5*d^7 + 3040*a^6*b^4*c^4*d^8 - 800*a^7*b^3*c^3*d^9 + 96*a^8*b^2*c^2*d^10)/(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*(-a*b^5)^(1/2)*(256*b^9*c^11*d^2 - 1280*a*b^8*c^10*d^3 + 2304*a^2*b^7*c^9*d^4 - 1280*a^3*b^6*c^8*d^5 - 1280*a^4*b^5*c^7*d^6 + 2304*a^5*b^4*c^6*d^7 - 1280*a^6*b^3*c^5*d^8 + 256*a^7*b^2*c^4*d^9))/(64*(a^4*d^3 - a*b^3*c^3 + 3*a^2*b^2*c^2*d - 3*a^3*b*c*d^2)*(b^4*c^8 + a^4*c^4*d^4 - 4*a^3*b*c^5*d^3 + 6*a^2*b^2*c^6*d^2 - 4*a*b^3*c^7*d))))/(2*(a^4*d^3 - a*b^3*c^3 + 3*a^2*b^2*c^2*d - 3*a^3*b*c*d^2))))/(2*(a^4*d^3 - a*b^3*c^3 + 3*a^2*b^2*c^2*d - 3*a^3*b*c*d^2))))*(-a*b^5)^(1/2)*1i)/(a^4*d^3 - a*b^3*c^3 + 3*a^2*b^2*c^2*d - 3*a^3*b*c*d^2) - (atan(((((x*(9*a^4*b^3*d^7 + 289*b^7*c^4*d^3 - 300*a*b^6*c^3*d^4 - 60*a^3*b^4*c*d^6 + 190*a^2*b^5*c^2*d^5))/(32*(b^4*c^8 + a^4*c^4*d^4 - 4*a^3*b*c^5*d^3 + 6*a^2*b^2*c^6*d^2 - 4*a*b^3*c^7*d)) - (((256*b^10*c^10*d^2 - 1760*a*b^9*c^9*d^3 + 5280*a^2*b^8*c^8*d^4 - 9056*a^3*b^7*c^7*d^5 + 9760*a^4*b^6*c^6*d^6 - 6816*a^5*b^5*c^5*d^7 + 3040*a^6*b^4*c^4*d^8 - 800*a^7*b^3*c^3*d^9 + 96*a^8*b^2*c^2*d^10)/(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*(-c^5*d)^(1/2)*(3*a^2*d^2 + 15*b^2*c^2 - 10*a*b*c*d)*(256*b^9*c^11*d^2 - 1280*a*b^8*c^10*d^3 + 2304*a^2*b^7*c^9*d^4 - 1280*a^3*b^6*c^8*d^5 - 1280*a^4*b^5*c^7*d^6 + 2304*a^5*b^4*c^6*d^7 - 1280*a^6*b^3*c^5*d^8 + 256*a^7*b^2*c^4*d^9))/(512*(b^3*c^8 - a^3*c^5*d^3 + 3*a^2*b*c^6*d^2 - 3*a*b^2*c^7*d)*(b^4*c^8 + a^4*c^4*d^4 - 4*a^3*b*c^5*d^3 + 6*a^2*b^2*c^6*d^2 - 4*a*b^3*c^7*d)))*(-c^5*d)^(1/2)*(3*a^2*d^2 + 15*b^2*c^2 - 10*a*b*c*d))/(16*(b^3*c^8 - a^3*c^5*d^3 + 3*a^2*b*c^6*d^2 - 3*a*b^2*c^7*d)))*(-c^5*d)^(1/2)*(3*a^2*d^2 + 15*b^2*c^2 - 10*a*b*c*d)*1i)/(16*(b^3*c^8 - a^3*c^5*d^3 + 3*a^2*b*c^6*d^2 - 3*a*b^2*c^7*d)) + (((x*(9*a^4*b^3*d^7 + 289*b^7*c^4*d^3 - 300*a*b^6*c^3*d^4 - 60*a^3*b^4*c*d^6 + 190*a^2*b^5*c^2*d^5))/(32*(b^4*c^8 + a^4*c^4*d^4 - 4*a^3*b*c^5*d^3 + 6*a^2*b^2*c^6*d^2 - 4*a*b^3*c^7*d)) + (((256*b^10*c^10*d^2 - 1760*a*b^9*c^9*d^3 + 5280*a^2*b^8*c^8*d^4 - 9056*a^3*b^7*c^7*d^5 + 9760*a^4*b^6*c^6*d^6 - 6816*a^5*b^5*c^5*d^7 + 3040*a^6*b^4*c^4*d^8 - 800*a^7*b^3*c^3*d^9 + 96*a^8*b^2*c^2*d^10)/(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*(-c^5*d)^(1/2)*(3*a^2*d^2 + 15*b^2*c^2 - 10*a*b*c*d)*(256*b^9*c^11*d^2 - 1280*a*b^8*c^10*d^3 + 2304*a^2*b^7*c^9*d^4 - 1280*a^3*b^6*c^8*d^5 - 1280*a^4*b^5*c^7*d^6 + 2304*a^5*b^4*c^6*d^7 - 1280*a^6*b^3*c^5*d^8 + 256*a^7*b^2*c^4*d^9))/(512*(b^3*c^8 - a^3*c^5*d^3 + 3*a^2*b*c^6*d^2 - 3*a*b^2*c^7*d)*(b^4*c^8 + a^4*c^4*d^4 - 4*a^3*b*c^5*d^3 + 6*a^2*b^2*c^6*d^2 - 4*a*b^3*c^7*d)))*(-c^5*d)^(1/2)*(3*a^2*d^2 + 15*b^2*c^2 - 10*a*b*c*d))/(16*(b^3*c^8 - a^3*c^5*d^3 + 3*a^2*b*c^6*d^2 - 3*a*b^2*c^7*d)))*(-c^5*d)^(1/2)*(3*a^2*d^2 + 15*b^2*c^2 - 10*a*b*c*d)*1i)/(16*(b^3*c^8 - a^3*c^5*d^3 + 3*a^2*b*c^6*d^2 - 3*a*b^2*c^7*d)))/((9*a^3*b^5*d^6 - 105*b^8*c^3*d^3 + 115*a*b^7*c^2*d^4 - 51*a^2*b^6*c*d^5)/(32*(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*(9*a^4*b^3*d^7 + 289*b^7*c^4*d^3 - 300*a*b^6*c^3*d^4 - 60*a^3*b^4*c*d^6 + 190*a^2*b^5*c^2*d^5))/(32*(b^4*c^8 + a^4*c^4*d^4 - 4*a^3*b*c^5*d^3 + 6*a^2*b^2*c^6*d^2 - 4*a*b^3*c^7*d)) - (((256*b^10*c^10*d^2 - 1760*a*b^9*c^9*d^3 + 5280*a^2*b^8*c^8*d^4 - 9056*a^3*b^7*c^7*d^5 + 9760*a^4*b^6*c^6*d^6 - 6816*a^5*b^5*c^5*d^7 + 3040*a^6*b^4*c^4*d^8 - 800*a^7*b^3*c^3*d^9 + 96*a^8*b^2*c^2*d^10)/(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*(-c^5*d)^(1/2)*(3*a^2*d^2 + 15*b^2*c^2 - 10*a*b*c*d)*(256*b^9*c^11*d^2 - 1280*a*b^8*c^10*d^3 + 2304*a^2*b^7*c^9*d^4 - 1280*a^3*b^6*c^8*d^5 - 1280*a^4*b^5*c^7*d^6 + 2304*a^5*b^4*c^6*d^7 - 1280*a^6*b^3*c^5*d^8 + 256*a^7*b^2*c^4*d^9))/(512*(b^3*c^8 - a^3*c^5*d^3 + 3*a^2*b*c^6*d^2 - 3*a*b^2*c^7*d)*(b^4*c^8 + a^4*c^4*d^4 - 4*a^3*b*c^5*d^3 + 6*a^2*b^2*c^6*d^2 - 4*a*b^3*c^7*d)))*(-c^5*d)^(1/2)*(3*a^2*d^2 + 15*b^2*c^2 - 10*a*b*c*d))/(16*(b^3*c^8 - a^3*c^5*d^3 + 3*a^2*b*c^6*d^2 - 3*a*b^2*c^7*d)))*(-c^5*d)^(1/2)*(3*a^2*d^2 + 15*b^2*c^2 - 10*a*b*c*d))/(16*(b^3*c^8 - a^3*c^5*d^3 + 3*a^2*b*c^6*d^2 - 3*a*b^2*c^7*d)) - (((x*(9*a^4*b^3*d^7 + 289*b^7*c^4*d^3 - 300*a*b^6*c^3*d^4 - 60*a^3*b^4*c*d^6 + 190*a^2*b^5*c^2*d^5))/(32*(b^4*c^8 + a^4*c^4*d^4 - 4*a^3*b*c^5*d^3 + 6*a^2*b^2*c^6*d^2 - 4*a*b^3*c^7*d)) + (((256*b^10*c^10*d^2 - 1760*a*b^9*c^9*d^3 + 5280*a^2*b^8*c^8*d^4 - 9056*a^3*b^7*c^7*d^5 + 9760*a^4*b^6*c^6*d^6 - 6816*a^5*b^5*c^5*d^7 + 3040*a^6*b^4*c^4*d^8 - 800*a^7*b^3*c^3*d^9 + 96*a^8*b^2*c^2*d^10)/(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*(-c^5*d)^(1/2)*(3*a^2*d^2 + 15*b^2*c^2 - 10*a*b*c*d)*(256*b^9*c^11*d^2 - 1280*a*b^8*c^10*d^3 + 2304*a^2*b^7*c^9*d^4 - 1280*a^3*b^6*c^8*d^5 - 1280*a^4*b^5*c^7*d^6 + 2304*a^5*b^4*c^6*d^7 - 1280*a^6*b^3*c^5*d^8 + 256*a^7*b^2*c^4*d^9))/(512*(b^3*c^8 - a^3*c^5*d^3 + 3*a^2*b*c^6*d^2 - 3*a*b^2*c^7*d)*(b^4*c^8 + a^4*c^4*d^4 - 4*a^3*b*c^5*d^3 + 6*a^2*b^2*c^6*d^2 - 4*a*b^3*c^7*d)))*(-c^5*d)^(1/2)*(3*a^2*d^2 + 15*b^2*c^2 - 10*a*b*c*d))/(16*(b^3*c^8 - a^3*c^5*d^3 + 3*a^2*b*c^6*d^2 - 3*a*b^2*c^7*d)))*(-c^5*d)^(1/2)*(3*a^2*d^2 + 15*b^2*c^2 - 10*a*b*c*d))/(16*(b^3*c^8 - a^3*c^5*d^3 + 3*a^2*b*c^6*d^2 - 3*a*b^2*c^7*d))))*(-c^5*d)^(1/2)*(3*a^2*d^2 + 15*b^2*c^2 - 10*a*b*c*d)*1i)/(8*(b^3*c^8 - a^3*c^5*d^3 + 3*a^2*b*c^6*d^2 - 3*a*b^2*c^7*d))","B"
257,1,246,149,1.401286,"\text{Not used}","int(1/(x*(a + b*x^2)*(c + d*x^2)^3),x)","\frac{\frac{3\,a\,d^2-5\,b\,c\,d}{4\,c\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}+\frac{d^2\,x^2\,\left(a\,d-2\,b\,c\right)}{2\,c^2\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}}{c^2+2\,c\,d\,x^2+d^2\,x^4}+\frac{b^3\,\ln\left(b\,x^2+a\right)}{2\,a^4\,d^3-6\,a^3\,b\,c\,d^2+6\,a^2\,b^2\,c^2\,d-2\,a\,b^3\,c^3}+\frac{\ln\left(x\right)}{a\,c^3}+\frac{\ln\left(d\,x^2+c\right)\,\left(a^2\,d^3-3\,a\,b\,c\,d^2+3\,b^2\,c^2\,d\right)}{-2\,a^3\,c^3\,d^3+6\,a^2\,b\,c^4\,d^2-6\,a\,b^2\,c^5\,d+2\,b^3\,c^6}","Not used",1,"((3*a*d^2 - 5*b*c*d)/(4*c*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) + (d^2*x^2*(a*d - 2*b*c))/(2*c^2*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)))/(c^2 + d^2*x^4 + 2*c*d*x^2) + (b^3*log(a + b*x^2))/(2*a^4*d^3 - 2*a*b^3*c^3 + 6*a^2*b^2*c^2*d - 6*a^3*b*c*d^2) + log(x)/(a*c^3) + (log(c + d*x^2)*(a^2*d^3 + 3*b^2*c^2*d - 3*a*b*c*d^2))/(2*b^3*c^6 - 2*a^3*c^3*d^3 + 6*a^2*b*c^4*d^2 - 6*a*b^2*c^5*d)","B"
258,1,738,211,1.304591,"\text{Not used}","int(1/(x^2*(a + b*x^2)*(c + d*x^2)^3),x)","-\frac{\frac{1}{a\,c}+\frac{x^4\,\left(15\,a^2\,d^4-27\,a\,b\,c\,d^3+8\,b^2\,c^2\,d^2\right)}{8\,a\,c^3\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}+\frac{x^2\,\left(25\,a^2\,d^3-45\,a\,b\,c\,d^2+16\,b^2\,c^2\,d\right)}{8\,a\,c^2\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}}{c^2\,x+2\,c\,d\,x^3+d^2\,x^5}-\frac{\mathrm{atan}\left(\frac{b\,c^7\,x\,{\left(-a^3\,b^7\right)}^{3/2}\,64{}\mathrm{i}+a^{10}\,b\,d^7\,x\,\sqrt{-a^3\,b^7}\,225{}\mathrm{i}+a^6\,b^5\,c^4\,d^3\,x\,\sqrt{-a^3\,b^7}\,1225{}\mathrm{i}-a^7\,b^4\,c^3\,d^4\,x\,\sqrt{-a^3\,b^7}\,2940{}\mathrm{i}+a^8\,b^3\,c^2\,d^5\,x\,\sqrt{-a^3\,b^7}\,2814{}\mathrm{i}-a^9\,b^2\,c\,d^6\,x\,\sqrt{-a^3\,b^7}\,1260{}\mathrm{i}}{a^3\,b^7\,\left(2940\,a^6\,c^3\,d^4-1225\,a^5\,b\,c^4\,d^3+64\,a^2\,b^4\,c^7\right)-225\,a^{12}\,b^4\,d^7+1260\,a^{11}\,b^5\,c\,d^6-2814\,a^{10}\,b^6\,c^2\,d^5}\right)\,\sqrt{-a^3\,b^7}\,1{}\mathrm{i}}{a^6\,d^3-3\,a^5\,b\,c\,d^2+3\,a^4\,b^2\,c^2\,d-a^3\,b^3\,c^3}-\frac{\mathrm{atan}\left(\frac{a^7\,d^5\,x\,{\left(-c^7\,d^3\right)}^{3/2}\,225{}\mathrm{i}+b^7\,c^{14}\,d\,x\,\sqrt{-c^7\,d^3}\,64{}\mathrm{i}-a^4\,b^3\,c^3\,d^2\,x\,{\left(-c^7\,d^3\right)}^{3/2}\,2940{}\mathrm{i}+a^5\,b^2\,c^2\,d^3\,x\,{\left(-c^7\,d^3\right)}^{3/2}\,2814{}\mathrm{i}-a^6\,b\,c\,d^4\,x\,{\left(-c^7\,d^3\right)}^{3/2}\,1260{}\mathrm{i}+a^3\,b^4\,c^4\,d\,x\,{\left(-c^7\,d^3\right)}^{3/2}\,1225{}\mathrm{i}}{225\,a^7\,c^{11}\,d^9-1260\,a^6\,b\,c^{12}\,d^8+2814\,a^5\,b^2\,c^{13}\,d^7-2940\,a^4\,b^3\,c^{14}\,d^6+1225\,a^3\,b^4\,c^{15}\,d^5-64\,b^7\,c^{18}\,d^2}\right)\,\sqrt{-c^7\,d^3}\,\left(15\,a^2\,d^2-42\,a\,b\,c\,d+35\,b^2\,c^2\right)\,1{}\mathrm{i}}{8\,\left(-a^3\,c^7\,d^3+3\,a^2\,b\,c^8\,d^2-3\,a\,b^2\,c^9\,d+b^3\,c^{10}\right)}","Not used",1,"- (1/(a*c) + (x^4*(15*a^2*d^4 + 8*b^2*c^2*d^2 - 27*a*b*c*d^3))/(8*a*c^3*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) + (x^2*(25*a^2*d^3 + 16*b^2*c^2*d - 45*a*b*c*d^2))/(8*a*c^2*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)))/(c^2*x + d^2*x^5 + 2*c*d*x^3) - (atan((b*c^7*x*(-a^3*b^7)^(3/2)*64i + a^10*b*d^7*x*(-a^3*b^7)^(1/2)*225i + a^6*b^5*c^4*d^3*x*(-a^3*b^7)^(1/2)*1225i - a^7*b^4*c^3*d^4*x*(-a^3*b^7)^(1/2)*2940i + a^8*b^3*c^2*d^5*x*(-a^3*b^7)^(1/2)*2814i - a^9*b^2*c*d^6*x*(-a^3*b^7)^(1/2)*1260i)/(a^3*b^7*(64*a^2*b^4*c^7 + 2940*a^6*c^3*d^4 - 1225*a^5*b*c^4*d^3) - 225*a^12*b^4*d^7 + 1260*a^11*b^5*c*d^6 - 2814*a^10*b^6*c^2*d^5))*(-a^3*b^7)^(1/2)*1i)/(a^6*d^3 - a^3*b^3*c^3 + 3*a^4*b^2*c^2*d - 3*a^5*b*c*d^2) - (atan((a^7*d^5*x*(-c^7*d^3)^(3/2)*225i + b^7*c^14*d*x*(-c^7*d^3)^(1/2)*64i - a^4*b^3*c^3*d^2*x*(-c^7*d^3)^(3/2)*2940i + a^5*b^2*c^2*d^3*x*(-c^7*d^3)^(3/2)*2814i - a^6*b*c*d^4*x*(-c^7*d^3)^(3/2)*1260i + a^3*b^4*c^4*d*x*(-c^7*d^3)^(3/2)*1225i)/(225*a^7*c^11*d^9 - 64*b^7*c^18*d^2 - 1260*a^6*b*c^12*d^8 + 1225*a^3*b^4*c^15*d^5 - 2940*a^4*b^3*c^14*d^6 + 2814*a^5*b^2*c^13*d^7))*(-c^7*d^3)^(1/2)*(15*a^2*d^2 + 35*b^2*c^2 - 42*a*b*c*d)*1i)/(8*(b^3*c^10 - a^3*c^7*d^3 + 3*a^2*b*c^8*d^2 - 3*a*b^2*c^9*d))","B"
259,1,314,178,1.503777,"\text{Not used}","int(1/(x^3*(a + b*x^2)*(c + d*x^2)^3),x)","-\frac{\frac{1}{2\,a\,c}+\frac{x^4\,\left(3\,a^2\,d^4-5\,a\,b\,c\,d^3+b^2\,c^2\,d^2\right)}{2\,a\,c^3\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}+\frac{x^2\,\left(9\,a^2\,d^3-15\,a\,b\,c\,d^2+4\,b^2\,c^2\,d\right)}{4\,a\,c^2\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}}{c^2\,x^2+2\,c\,d\,x^4+d^2\,x^6}-\frac{\ln\left(d\,x^2+c\right)\,\left(3\,a^2\,d^4-8\,a\,b\,c\,d^3+6\,b^2\,c^2\,d^2\right)}{-2\,a^3\,c^4\,d^3+6\,a^2\,b\,c^5\,d^2-6\,a\,b^2\,c^6\,d+2\,b^3\,c^7}-\frac{b^4\,\ln\left(b\,x^2+a\right)}{2\,\left(a^5\,d^3-3\,a^4\,b\,c\,d^2+3\,a^3\,b^2\,c^2\,d-a^2\,b^3\,c^3\right)}-\frac{\ln\left(x\right)\,\left(3\,a\,d+b\,c\right)}{a^2\,c^4}","Not used",1,"- (1/(2*a*c) + (x^4*(3*a^2*d^4 + b^2*c^2*d^2 - 5*a*b*c*d^3))/(2*a*c^3*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) + (x^2*(9*a^2*d^3 + 4*b^2*c^2*d - 15*a*b*c*d^2))/(4*a*c^2*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)))/(c^2*x^2 + d^2*x^6 + 2*c*d*x^4) - (log(c + d*x^2)*(3*a^2*d^4 + 6*b^2*c^2*d^2 - 8*a*b*c*d^3))/(2*b^3*c^7 - 2*a^3*c^4*d^3 + 6*a^2*b*c^5*d^2 - 6*a*b^2*c^6*d) - (b^4*log(a + b*x^2))/(2*(a^5*d^3 - a^2*b^3*c^3 + 3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2)) - (log(x)*(3*a*d + b*c))/(a^2*c^4)","B"
260,1,785,270,1.421714,"\text{Not used}","int(1/(x^4*(a + b*x^2)*(c + d*x^2)^3),x)","\frac{\frac{x^2\,\left(7\,a\,d+3\,b\,c\right)}{3\,a^2\,c^2}-\frac{1}{3\,a\,c}+\frac{x^4\,\left(175\,a^3\,d^4-275\,a^2\,b\,c\,d^3+40\,a\,b^2\,c^2\,d^2+48\,b^3\,c^3\,d\right)}{24\,a^2\,c^3\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}+\frac{x^6\,\left(35\,a^3\,d^5-55\,a^2\,b\,c\,d^4+8\,a\,b^2\,c^2\,d^3+8\,b^3\,c^3\,d^2\right)}{8\,a^2\,c^4\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}}{c^2\,x^3+2\,c\,d\,x^5+d^2\,x^7}+\frac{\mathrm{atan}\left(\frac{b\,c^9\,x\,{\left(-a^5\,b^9\right)}^{3/2}\,64{}\mathrm{i}+a^{14}\,b\,d^9\,x\,\sqrt{-a^5\,b^9}\,1225{}\mathrm{i}+a^{10}\,b^5\,c^4\,d^5\,x\,\sqrt{-a^5\,b^9}\,3969{}\mathrm{i}-a^{11}\,b^4\,c^3\,d^6\,x\,\sqrt{-a^5\,b^9}\,11340{}\mathrm{i}+a^{12}\,b^3\,c^2\,d^7\,x\,\sqrt{-a^5\,b^9}\,12510{}\mathrm{i}-a^{13}\,b^2\,c\,d^8\,x\,\sqrt{-a^5\,b^9}\,6300{}\mathrm{i}}{-1225\,a^{17}\,b^5\,d^9+6300\,a^{16}\,b^6\,c\,d^8-12510\,a^{15}\,b^7\,c^2\,d^7+11340\,a^{14}\,b^8\,c^3\,d^6-3969\,a^{13}\,b^9\,c^4\,d^5+64\,a^8\,b^{14}\,c^9}\right)\,\sqrt{-a^5\,b^9}\,1{}\mathrm{i}}{a^8\,d^3-3\,a^7\,b\,c\,d^2+3\,a^6\,b^2\,c^2\,d-a^5\,b^3\,c^3}+\frac{\mathrm{atan}\left(\frac{a^9\,d^5\,x\,{\left(-c^9\,d^5\right)}^{3/2}\,1225{}\mathrm{i}+b^9\,c^{18}\,d\,x\,\sqrt{-c^9\,d^5}\,64{}\mathrm{i}-a^6\,b^3\,c^3\,d^2\,x\,{\left(-c^9\,d^5\right)}^{3/2}\,11340{}\mathrm{i}+a^7\,b^2\,c^2\,d^3\,x\,{\left(-c^9\,d^5\right)}^{3/2}\,12510{}\mathrm{i}-a^8\,b\,c\,d^4\,x\,{\left(-c^9\,d^5\right)}^{3/2}\,6300{}\mathrm{i}+a^5\,b^4\,c^4\,d\,x\,{\left(-c^9\,d^5\right)}^{3/2}\,3969{}\mathrm{i}}{1225\,a^9\,c^{14}\,d^{12}-6300\,a^8\,b\,c^{15}\,d^{11}+12510\,a^7\,b^2\,c^{16}\,d^{10}-11340\,a^6\,b^3\,c^{17}\,d^9+3969\,a^5\,b^4\,c^{18}\,d^8-64\,b^9\,c^{23}\,d^3}\right)\,\sqrt{-c^9\,d^5}\,\left(35\,a^2\,d^2-90\,a\,b\,c\,d+63\,b^2\,c^2\right)\,1{}\mathrm{i}}{8\,\left(-a^3\,c^9\,d^3+3\,a^2\,b\,c^{10}\,d^2-3\,a\,b^2\,c^{11}\,d+b^3\,c^{12}\right)}","Not used",1,"((x^2*(7*a*d + 3*b*c))/(3*a^2*c^2) - 1/(3*a*c) + (x^4*(175*a^3*d^4 + 48*b^3*c^3*d + 40*a*b^2*c^2*d^2 - 275*a^2*b*c*d^3))/(24*a^2*c^3*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) + (x^6*(35*a^3*d^5 + 8*b^3*c^3*d^2 + 8*a*b^2*c^2*d^3 - 55*a^2*b*c*d^4))/(8*a^2*c^4*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)))/(c^2*x^3 + d^2*x^7 + 2*c*d*x^5) + (atan((b*c^9*x*(-a^5*b^9)^(3/2)*64i + a^14*b*d^9*x*(-a^5*b^9)^(1/2)*1225i + a^10*b^5*c^4*d^5*x*(-a^5*b^9)^(1/2)*3969i - a^11*b^4*c^3*d^6*x*(-a^5*b^9)^(1/2)*11340i + a^12*b^3*c^2*d^7*x*(-a^5*b^9)^(1/2)*12510i - a^13*b^2*c*d^8*x*(-a^5*b^9)^(1/2)*6300i)/(64*a^8*b^14*c^9 - 1225*a^17*b^5*d^9 + 6300*a^16*b^6*c*d^8 - 3969*a^13*b^9*c^4*d^5 + 11340*a^14*b^8*c^3*d^6 - 12510*a^15*b^7*c^2*d^7))*(-a^5*b^9)^(1/2)*1i)/(a^8*d^3 - a^5*b^3*c^3 + 3*a^6*b^2*c^2*d - 3*a^7*b*c*d^2) + (atan((a^9*d^5*x*(-c^9*d^5)^(3/2)*1225i + b^9*c^18*d*x*(-c^9*d^5)^(1/2)*64i - a^6*b^3*c^3*d^2*x*(-c^9*d^5)^(3/2)*11340i + a^7*b^2*c^2*d^3*x*(-c^9*d^5)^(3/2)*12510i - a^8*b*c*d^4*x*(-c^9*d^5)^(3/2)*6300i + a^5*b^4*c^4*d*x*(-c^9*d^5)^(3/2)*3969i)/(1225*a^9*c^14*d^12 - 64*b^9*c^23*d^3 - 6300*a^8*b*c^15*d^11 + 3969*a^5*b^4*c^18*d^8 - 11340*a^6*b^3*c^17*d^9 + 12510*a^7*b^2*c^16*d^10))*(-c^9*d^5)^(1/2)*(35*a^2*d^2 + 63*b^2*c^2 - 90*a*b*c*d)*1i)/(8*(b^3*c^12 - a^3*c^9*d^3 + 3*a^2*b*c^10*d^2 - 3*a*b^2*c^11*d))","B"
261,1,17,21,0.147920,"\text{Not used}","int(x/((x^2 + 1)*(x^2 + 4)),x)","\frac{\mathrm{atanh}\left(\frac{3\,x^2}{5\,x^2+8}\right)}{3}","Not used",1,"atanh((3*x^2)/(5*x^2 + 8))/3","B"
262,1,104,87,0.083966,"\text{Not used}","int((x^4*(c + d*x^2))/(a + b*x^2)^2,x)","x\,\left(\frac{c}{b^2}-\frac{2\,a\,d}{b^3}\right)+\frac{d\,x^3}{3\,b^2}-\frac{x\,\left(\frac{a^2\,d}{2}-\frac{a\,b\,c}{2}\right)}{b^4\,x^2+a\,b^3}+\frac{\sqrt{a}\,\mathrm{atan}\left(\frac{\sqrt{a}\,\sqrt{b}\,x\,\left(5\,a\,d-3\,b\,c\right)}{5\,a^2\,d-3\,a\,b\,c}\right)\,\left(5\,a\,d-3\,b\,c\right)}{2\,b^{7/2}}","Not used",1,"x*(c/b^2 - (2*a*d)/b^3) + (d*x^3)/(3*b^2) - (x*((a^2*d)/2 - (a*b*c)/2))/(a*b^3 + b^4*x^2) + (a^(1/2)*atan((a^(1/2)*b^(1/2)*x*(5*a*d - 3*b*c))/(5*a^2*d - 3*a*b*c))*(5*a*d - 3*b*c))/(2*b^(7/2))","B"
263,1,63,60,0.076352,"\text{Not used}","int((x^3*(c + d*x^2))/(a + b*x^2)^2,x)","\frac{d\,x^2}{2\,b^2}-\frac{\ln\left(b\,x^2+a\right)\,\left(2\,a\,d-b\,c\right)}{2\,b^3}-\frac{a^2\,d-a\,b\,c}{2\,b\,\left(b^3\,x^2+a\,b^2\right)}","Not used",1,"(d*x^2)/(2*b^2) - (log(a + b*x^2)*(2*a*d - b*c))/(2*b^3) - (a^2*d - a*b*c)/(2*b*(a*b^2 + b^3*x^2))","B"
264,1,59,67,0.180512,"\text{Not used}","int((x^2*(c + d*x^2))/(a + b*x^2)^2,x)","\frac{x\,\left(\frac{a\,d}{2}-\frac{b\,c}{2}\right)}{b^3\,x^2+a\,b^2}+\frac{d\,x}{b^2}-\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)\,\left(3\,a\,d-b\,c\right)}{2\,\sqrt{a}\,b^{5/2}}","Not used",1,"(x*((a*d)/2 - (b*c)/2))/(a*b^2 + b^3*x^2) + (d*x)/b^2 - (atan((b^(1/2)*x)/a^(1/2))*(3*a*d - b*c))/(2*a^(1/2)*b^(5/2))","B"
265,1,37,41,0.148275,"\text{Not used}","int((x*(c + d*x^2))/(a + b*x^2)^2,x)","\frac{d\,\ln\left(b\,x^2+a\right)}{2\,b^2}+\frac{a\,d-b\,c}{2\,b^2\,\left(b\,x^2+a\right)}","Not used",1,"(d*log(a + b*x^2))/(2*b^2) + (a*d - b*c)/(2*b^2*(a + b*x^2))","B"
266,1,51,63,0.180885,"\text{Not used}","int((c + d*x^2)/(a + b*x^2)^2,x)","\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)\,\left(a\,d+b\,c\right)}{2\,a^{3/2}\,b^{3/2}}-\frac{x\,\left(a\,d-b\,c\right)}{2\,a\,b\,\left(b\,x^2+a\right)}","Not used",1,"(atan((b^(1/2)*x)/a^(1/2))*(a*d + b*c))/(2*a^(3/2)*b^(3/2)) - (x*(a*d - b*c))/(2*a*b*(a + b*x^2))","B"
267,1,47,51,0.056176,"\text{Not used}","int((c + d*x^2)/(x*(a + b*x^2)^2),x)","\frac{c\,\ln\left(x\right)}{a^2}-\frac{c\,\ln\left(b\,x^2+a\right)}{2\,a^2}-\frac{a\,d-b\,c}{2\,a\,b\,\left(b\,x^2+a\right)}","Not used",1,"(c*log(x))/a^2 - (c*log(a + b*x^2))/(2*a^2) - (a*d - b*c)/(2*a*b*(a + b*x^2))","B"
268,1,61,71,0.188189,"\text{Not used}","int((c + d*x^2)/(x^2*(a + b*x^2)^2),x)","\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)\,\left(a\,d-3\,b\,c\right)}{2\,a^{5/2}\,\sqrt{b}}-\frac{\frac{c}{a}-\frac{x^2\,\left(a\,d-3\,b\,c\right)}{2\,a^2}}{b\,x^3+a\,x}","Not used",1,"(atan((b^(1/2)*x)/a^(1/2))*(a*d - 3*b*c))/(2*a^(5/2)*b^(1/2)) - (c/a - (x^2*(a*d - 3*b*c))/(2*a^2))/(a*x + b*x^3)","B"
269,1,74,76,0.109517,"\text{Not used}","int((c + d*x^2)/(x^3*(a + b*x^2)^2),x)","\frac{\ln\left(x\right)\,\left(a\,d-2\,b\,c\right)}{a^3}-\frac{\ln\left(b\,x^2+a\right)\,\left(a\,d-2\,b\,c\right)}{2\,a^3}-\frac{\frac{c}{2\,a}-\frac{x^2\,\left(a\,d-2\,b\,c\right)}{2\,a^2}}{b\,x^4+a\,x^2}","Not used",1,"(log(x)*(a*d - 2*b*c))/a^3 - (log(a + b*x^2)*(a*d - 2*b*c))/(2*a^3) - (c/(2*a) - (x^2*(a*d - 2*b*c))/(2*a^2))/(a*x^2 + b*x^4)","B"
270,1,84,90,0.198644,"\text{Not used}","int((c + d*x^2)/(x^4*(a + b*x^2)^2),x)","-\frac{\frac{c}{3\,a}+\frac{x^2\,\left(3\,a\,d-5\,b\,c\right)}{3\,a^2}+\frac{b\,x^4\,\left(3\,a\,d-5\,b\,c\right)}{2\,a^3}}{b\,x^5+a\,x^3}-\frac{\sqrt{b}\,\mathrm{atan}\left(\frac{\sqrt{b}\,x}{\sqrt{a}}\right)\,\left(3\,a\,d-5\,b\,c\right)}{2\,a^{7/2}}","Not used",1,"- (c/(3*a) + (x^2*(3*a*d - 5*b*c))/(3*a^2) + (b*x^4*(3*a*d - 5*b*c))/(2*a^3))/(a*x^3 + b*x^5) - (b^(1/2)*atan((b^(1/2)*x)/a^(1/2))*(3*a*d - 5*b*c))/(2*a^(7/2))","B"
271,1,200,145,0.172093,"\text{Not used}","int((x^4*(c + d*x^2)^2)/(a + b*x^2)^2,x)","x\,\left(\frac{c^2}{b^2}+\frac{2\,a\,\left(\frac{2\,a\,d^2}{b^3}-\frac{2\,c\,d}{b^2}\right)}{b}-\frac{a^2\,d^2}{b^4}\right)-x^3\,\left(\frac{2\,a\,d^2}{3\,b^3}-\frac{2\,c\,d}{3\,b^2}\right)+\frac{d^2\,x^5}{5\,b^2}+\frac{x\,\left(\frac{a^3\,d^2}{2}-a^2\,b\,c\,d+\frac{a\,b^2\,c^2}{2}\right)}{b^5\,x^2+a\,b^4}-\frac{\sqrt{a}\,\mathrm{atan}\left(\frac{\sqrt{a}\,\sqrt{b}\,x\,\left(a\,d-b\,c\right)\,\left(7\,a\,d-3\,b\,c\right)}{7\,a^3\,d^2-10\,a^2\,b\,c\,d+3\,a\,b^2\,c^2}\right)\,\left(a\,d-b\,c\right)\,\left(7\,a\,d-3\,b\,c\right)}{2\,b^{9/2}}","Not used",1,"x*(c^2/b^2 + (2*a*((2*a*d^2)/b^3 - (2*c*d)/b^2))/b - (a^2*d^2)/b^4) - x^3*((2*a*d^2)/(3*b^3) - (2*c*d)/(3*b^2)) + (d^2*x^5)/(5*b^2) + (x*((a^3*d^2)/2 + (a*b^2*c^2)/2 - a^2*b*c*d))/(a*b^4 + b^5*x^2) - (a^(1/2)*atan((a^(1/2)*b^(1/2)*x*(a*d - b*c)*(7*a*d - 3*b*c))/(7*a^3*d^2 + 3*a*b^2*c^2 - 10*a^2*b*c*d))*(a*d - b*c)*(7*a*d - 3*b*c))/(2*b^(9/2))","B"
272,1,112,88,0.071519,"\text{Not used}","int((x^3*(c + d*x^2)^2)/(a + b*x^2)^2,x)","\frac{a^3\,d^2-2\,a^2\,b\,c\,d+a\,b^2\,c^2}{2\,b\,\left(b^4\,x^2+a\,b^3\right)}-x^2\,\left(\frac{a\,d^2}{b^3}-\frac{c\,d}{b^2}\right)+\frac{d^2\,x^4}{4\,b^2}+\frac{\ln\left(b\,x^2+a\right)\,\left(3\,a^2\,d^2-4\,a\,b\,c\,d+b^2\,c^2\right)}{2\,b^4}","Not used",1,"(a^3*d^2 + a*b^2*c^2 - 2*a^2*b*c*d)/(2*b*(a*b^3 + b^4*x^2)) - x^2*((a*d^2)/b^3 - (c*d)/b^2) + (d^2*x^4)/(4*b^2) + (log(a + b*x^2)*(3*a^2*d^2 + b^2*c^2 - 4*a*b*c*d))/(2*b^4)","B"
273,1,148,116,0.176135,"\text{Not used}","int((x^2*(c + d*x^2)^2)/(a + b*x^2)^2,x)","\frac{d^2\,x^3}{3\,b^2}-\frac{x\,\left(\frac{a^2\,d^2}{2}-a\,b\,c\,d+\frac{b^2\,c^2}{2}\right)}{b^4\,x^2+a\,b^3}-x\,\left(\frac{2\,a\,d^2}{b^3}-\frac{2\,c\,d}{b^2}\right)+\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x\,\left(a\,d-b\,c\right)\,\left(5\,a\,d-b\,c\right)}{\sqrt{a}\,\left(5\,a^2\,d^2-6\,a\,b\,c\,d+b^2\,c^2\right)}\right)\,\left(a\,d-b\,c\right)\,\left(5\,a\,d-b\,c\right)}{2\,\sqrt{a}\,b^{7/2}}","Not used",1,"(d^2*x^3)/(3*b^2) - (x*((a^2*d^2)/2 + (b^2*c^2)/2 - a*b*c*d))/(a*b^3 + b^4*x^2) - x*((2*a*d^2)/b^3 - (2*c*d)/b^2) + (atan((b^(1/2)*x*(a*d - b*c)*(5*a*d - b*c))/(a^(1/2)*(5*a^2*d^2 + b^2*c^2 - 6*a*b*c*d)))*(a*d - b*c)*(5*a*d - b*c))/(2*a^(1/2)*b^(7/2))","B"
274,1,77,61,0.256505,"\text{Not used}","int((x*(c + d*x^2)^2)/(a + b*x^2)^2,x)","\frac{d^2\,x^2}{2\,b^2}-\frac{a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2}{2\,b\,\left(b^3\,x^2+a\,b^2\right)}-\frac{\ln\left(b\,x^2+a\right)\,\left(a\,d^2-b\,c\,d\right)}{b^3}","Not used",1,"(d^2*x^2)/(2*b^2) - (a^2*d^2 + b^2*c^2 - 2*a*b*c*d)/(2*b*(a*b^2 + b^3*x^2)) - (log(a + b*x^2)*(a*d^2 - b*c*d))/b^3","B"
275,1,124,82,0.283104,"\text{Not used}","int((c + d*x^2)^2/(a + b*x^2)^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)}{2\,a\,\left(b^3\,x^2+a\,b^2\right)}+\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x\,\left(a\,d-b\,c\right)\,\left(3\,a\,d+b\,c\right)}{\sqrt{a}\,\left(-3\,a^2\,d^2+2\,a\,b\,c\,d+b^2\,c^2\right)}\right)\,\left(a\,d-b\,c\right)\,\left(3\,a\,d+b\,c\right)}{2\,a^{3/2}\,b^{5/2}}","Not used",1,"(d^2*x)/b^2 + (x*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/(2*a*(a*b^2 + b^3*x^2)) + (atan((b^(1/2)*x*(a*d - b*c)*(3*a*d + b*c))/(a^(1/2)*(b^2*c^2 - 3*a^2*d^2 + 2*a*b*c*d)))*(a*d - b*c)*(3*a*d + b*c))/(2*a^(3/2)*b^(5/2))","B"
276,1,80,67,0.307973,"\text{Not used}","int((c + d*x^2)^2/(x*(a + b*x^2)^2),x)","\frac{c^2\,\ln\left(x\right)}{a^2}+\frac{a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2}{2\,a\,b^2\,\left(b\,x^2+a\right)}+\frac{\ln\left(b\,x^2+a\right)\,\left(a^2\,d^2-b^2\,c^2\right)}{2\,a^2\,b^2}","Not used",1,"(c^2*log(x))/a^2 + (a^2*d^2 + b^2*c^2 - 2*a*b*c*d)/(2*a*b^2*(a + b*x^2)) + (log(a + b*x^2)*(a^2*d^2 - b^2*c^2))/(2*a^2*b^2)","B"
277,1,128,103,0.138798,"\text{Not used}","int((c + d*x^2)^2/(x^2*(a + b*x^2)^2),x)","\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x\,\left(a\,d-b\,c\right)\,\left(a\,d+3\,b\,c\right)}{\sqrt{a}\,\left(a^2\,d^2+2\,a\,b\,c\,d-3\,b^2\,c^2\right)}\right)\,\left(a\,d-b\,c\right)\,\left(a\,d+3\,b\,c\right)}{2\,a^{5/2}\,b^{3/2}}-\frac{\frac{c^2}{a}+\frac{x^2\,\left(a^2\,d^2-2\,a\,b\,c\,d+3\,b^2\,c^2\right)}{2\,a^2\,b}}{b\,x^3+a\,x}","Not used",1,"(atan((b^(1/2)*x*(a*d - b*c)*(a*d + 3*b*c))/(a^(1/2)*(a^2*d^2 - 3*b^2*c^2 + 2*a*b*c*d)))*(a*d - b*c)*(a*d + 3*b*c))/(2*a^(5/2)*b^(3/2)) - (c^2/a + (x^2*(a^2*d^2 + 3*b^2*c^2 - 2*a*b*c*d))/(2*a^2*b))/(a*x + b*x^3)","B"
278,1,100,80,0.200387,"\text{Not used}","int((c + d*x^2)^2/(x^3*(a + b*x^2)^2),x)","\frac{\ln\left(b\,x^2+a\right)\,\left(b\,c^2-a\,c\,d\right)}{a^3}-\frac{\frac{c^2}{2\,a}+\frac{x^2\,\left(a^2\,d^2-2\,a\,b\,c\,d+2\,b^2\,c^2\right)}{2\,a^2\,b}}{b\,x^4+a\,x^2}-\frac{\ln\left(x\right)\,\left(2\,b\,c^2-2\,a\,c\,d\right)}{a^3}","Not used",1,"(log(a + b*x^2)*(b*c^2 - a*c*d))/a^3 - (c^2/(2*a) + (x^2*(a^2*d^2 + 2*b^2*c^2 - 2*a*b*c*d))/(2*a^2*b))/(a*x^2 + b*x^4) - (log(x)*(2*b*c^2 - 2*a*c*d))/a^3","B"
279,1,146,127,0.254388,"\text{Not used}","int((c + d*x^2)^2/(x^4*(a + b*x^2)^2),x)","\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x\,\left(a\,d-b\,c\right)\,\left(a\,d-5\,b\,c\right)}{\sqrt{a}\,\left(a^2\,d^2-6\,a\,b\,c\,d+5\,b^2\,c^2\right)}\right)\,\left(a\,d-b\,c\right)\,\left(a\,d-5\,b\,c\right)}{2\,a^{7/2}\,\sqrt{b}}-\frac{\frac{c^2}{3\,a}-\frac{x^4\,\left(a^2\,d^2-6\,a\,b\,c\,d+5\,b^2\,c^2\right)}{2\,a^3}+\frac{c\,x^2\,\left(6\,a\,d-5\,b\,c\right)}{3\,a^2}}{b\,x^5+a\,x^3}","Not used",1,"(atan((b^(1/2)*x*(a*d - b*c)*(a*d - 5*b*c))/(a^(1/2)*(a^2*d^2 + 5*b^2*c^2 - 6*a*b*c*d)))*(a*d - b*c)*(a*d - 5*b*c))/(2*a^(7/2)*b^(1/2)) - (c^2/(3*a) - (x^4*(a^2*d^2 + 5*b^2*c^2 - 6*a*b*c*d))/(2*a^3) + (c*x^2*(6*a*d - 5*b*c))/(3*a^2))/(a*x^3 + b*x^5)","B"
280,1,328,169,0.198963,"\text{Not used}","int((x^4*(c + d*x^2)^3)/(a + b*x^2)^2,x)","x\,\left(\frac{c^3}{b^2}-\frac{2\,a\,\left(\frac{3\,c^2\,d}{b^2}+\frac{2\,a\,\left(\frac{2\,a\,d^3}{b^3}-\frac{3\,c\,d^2}{b^2}\right)}{b}-\frac{a^2\,d^3}{b^4}\right)}{b}+\frac{a^2\,\left(\frac{2\,a\,d^3}{b^3}-\frac{3\,c\,d^2}{b^2}\right)}{b^2}\right)-x^5\,\left(\frac{2\,a\,d^3}{5\,b^3}-\frac{3\,c\,d^2}{5\,b^2}\right)+x^3\,\left(\frac{c^2\,d}{b^2}+\frac{2\,a\,\left(\frac{2\,a\,d^3}{b^3}-\frac{3\,c\,d^2}{b^2}\right)}{3\,b}-\frac{a^2\,d^3}{3\,b^4}\right)-\frac{x\,\left(\frac{a^4\,d^3}{2}-\frac{3\,a^3\,b\,c\,d^2}{2}+\frac{3\,a^2\,b^2\,c^2\,d}{2}-\frac{a\,b^3\,c^3}{2}\right)}{b^6\,x^2+a\,b^5}+\frac{d^3\,x^7}{7\,b^2}+\frac{3\,\sqrt{a}\,\mathrm{atan}\left(\frac{\sqrt{a}\,\sqrt{b}\,x\,{\left(a\,d-b\,c\right)}^2\,\left(3\,a\,d-b\,c\right)}{3\,a^4\,d^3-7\,a^3\,b\,c\,d^2+5\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(3\,a\,d-b\,c\right)}{2\,b^{11/2}}","Not used",1,"x*(c^3/b^2 - (2*a*((3*c^2*d)/b^2 + (2*a*((2*a*d^3)/b^3 - (3*c*d^2)/b^2))/b - (a^2*d^3)/b^4))/b + (a^2*((2*a*d^3)/b^3 - (3*c*d^2)/b^2))/b^2) - x^5*((2*a*d^3)/(5*b^3) - (3*c*d^2)/(5*b^2)) + x^3*((c^2*d)/b^2 + (2*a*((2*a*d^3)/b^3 - (3*c*d^2)/b^2))/(3*b) - (a^2*d^3)/(3*b^4)) - (x*((a^4*d^3)/2 - (a*b^3*c^3)/2 + (3*a^2*b^2*c^2*d)/2 - (3*a^3*b*c*d^2)/2))/(a*b^5 + b^6*x^2) + (d^3*x^7)/(7*b^2) + (3*a^(1/2)*atan((a^(1/2)*b^(1/2)*x*(a*d - b*c)^2*(3*a*d - b*c))/(3*a^4*d^3 - a*b^3*c^3 + 5*a^2*b^2*c^2*d - 7*a^3*b*c*d^2))*(a*d - b*c)^2*(3*a*d - b*c))/(2*b^(11/2))","B"
281,1,194,117,0.173982,"\text{Not used}","int((x^3*(c + d*x^2)^3)/(a + b*x^2)^2,x)","x^2\,\left(\frac{3\,c^2\,d}{2\,b^2}+\frac{a\,\left(\frac{2\,a\,d^3}{b^3}-\frac{3\,c\,d^2}{b^2}\right)}{b}-\frac{a^2\,d^3}{2\,b^4}\right)-x^4\,\left(\frac{a\,d^3}{2\,b^3}-\frac{3\,c\,d^2}{4\,b^2}\right)-\frac{\ln\left(b\,x^2+a\right)\,\left(4\,a^3\,d^3-9\,a^2\,b\,c\,d^2+6\,a\,b^2\,c^2\,d-b^3\,c^3\right)}{2\,b^5}-\frac{a^4\,d^3-3\,a^3\,b\,c\,d^2+3\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3}{2\,b\,\left(b^5\,x^2+a\,b^4\right)}+\frac{d^3\,x^6}{6\,b^2}","Not used",1,"x^2*((3*c^2*d)/(2*b^2) + (a*((2*a*d^3)/b^3 - (3*c*d^2)/b^2))/b - (a^2*d^3)/(2*b^4)) - x^4*((a*d^3)/(2*b^3) - (3*c*d^2)/(4*b^2)) - (log(a + b*x^2)*(4*a^3*d^3 - b^3*c^3 + 6*a*b^2*c^2*d - 9*a^2*b*c*d^2))/(2*b^5) - (a^4*d^3 - a*b^3*c^3 + 3*a^2*b^2*c^2*d - 3*a^3*b*c*d^2)/(2*b*(a*b^4 + b^5*x^2)) + (d^3*x^6)/(6*b^2)","B"
282,1,232,147,0.065495,"\text{Not used}","int((x^2*(c + d*x^2)^3)/(a + b*x^2)^2,x)","x\,\left(\frac{3\,c^2\,d}{b^2}+\frac{2\,a\,\left(\frac{2\,a\,d^3}{b^3}-\frac{3\,c\,d^2}{b^2}\right)}{b}-\frac{a^2\,d^3}{b^4}\right)-x^3\,\left(\frac{2\,a\,d^3}{3\,b^3}-\frac{c\,d^2}{b^2}\right)+\frac{x\,\left(\frac{a^3\,d^3}{2}-\frac{3\,a^2\,b\,c\,d^2}{2}+\frac{3\,a\,b^2\,c^2\,d}{2}-\frac{b^3\,c^3}{2}\right)}{b^5\,x^2+a\,b^4}+\frac{d^3\,x^5}{5\,b^2}-\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x\,{\left(a\,d-b\,c\right)}^2\,\left(7\,a\,d-b\,c\right)}{\sqrt{a}\,\left(7\,a^3\,d^3-15\,a^2\,b\,c\,d^2+9\,a\,b^2\,c^2\,d-b^3\,c^3\right)}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(7\,a\,d-b\,c\right)}{2\,\sqrt{a}\,b^{9/2}}","Not used",1,"x*((3*c^2*d)/b^2 + (2*a*((2*a*d^3)/b^3 - (3*c*d^2)/b^2))/b - (a^2*d^3)/b^4) - x^3*((2*a*d^3)/(3*b^3) - (c*d^2)/b^2) + (x*((a^3*d^3)/2 - (b^3*c^3)/2 + (3*a*b^2*c^2*d)/2 - (3*a^2*b*c*d^2)/2))/(a*b^4 + b^5*x^2) + (d^3*x^5)/(5*b^2) - (atan((b^(1/2)*x*(a*d - b*c)^2*(7*a*d - b*c))/(a^(1/2)*(7*a^3*d^3 - b^3*c^3 + 9*a*b^2*c^2*d - 15*a^2*b*c*d^2)))*(a*d - b*c)^2*(7*a*d - b*c))/(2*a^(1/2)*b^(9/2))","B"
283,1,130,88,0.179879,"\text{Not used}","int((x*(c + d*x^2)^3)/(a + b*x^2)^2,x)","\frac{\ln\left(b\,x^2+a\right)\,\left(3\,a^2\,d^3-6\,a\,b\,c\,d^2+3\,b^2\,c^2\,d\right)}{2\,b^4}-x^2\,\left(\frac{a\,d^3}{b^3}-\frac{3\,c\,d^2}{2\,b^2}\right)+\frac{d^3\,x^4}{4\,b^2}+\frac{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}{2\,b\,\left(b^4\,x^2+a\,b^3\right)}","Not used",1,"(log(a + b*x^2)*(3*a^2*d^3 + 3*b^2*c^2*d - 6*a*b*c*d^2))/(2*b^4) - x^2*((a*d^3)/b^3 - (3*c*d^2)/(2*b^2)) + (d^3*x^4)/(4*b^2) + (a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)/(2*b*(a*b^3 + b^4*x^2))","B"
284,1,182,106,0.192390,"\text{Not used}","int((c + d*x^2)^3/(a + b*x^2)^2,x)","\frac{d^3\,x^3}{3\,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)}{2\,a\,\left(b^4\,x^2+a\,b^3\right)}+\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x\,{\left(a\,d-b\,c\right)}^2\,\left(5\,a\,d+b\,c\right)}{\sqrt{a}\,\left(5\,a^3\,d^3-9\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d+b^3\,c^3\right)}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(5\,a\,d+b\,c\right)}{2\,a^{3/2}\,b^{7/2}}","Not used",1,"(d^3*x^3)/(3*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))/(2*a*(a*b^3 + b^4*x^2)) + (atan((b^(1/2)*x*(a*d - b*c)^2*(5*a*d + b*c))/(a^(1/2)*(5*a^3*d^3 + b^3*c^3 + 3*a*b^2*c^2*d - 9*a^2*b*c*d^2)))*(a*d - b*c)^2*(5*a*d + b*c))/(2*a^(3/2)*b^(7/2))","B"
285,1,122,88,0.116553,"\text{Not used}","int((c + d*x^2)^3/(x*(a + b*x^2)^2),x)","\frac{d^3\,x^2}{2\,b^2}+\frac{c^3\,\ln\left(x\right)}{a^2}-\frac{\ln\left(b\,x^2+a\right)\,\left(2\,a^3\,d^3-3\,a^2\,b\,c\,d^2+b^3\,c^3\right)}{2\,a^2\,b^3}-\frac{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}{2\,a\,b\,\left(b^3\,x^2+a\,b^2\right)}","Not used",1,"(d^3*x^2)/(2*b^2) + (c^3*log(x))/a^2 - (log(a + b*x^2)*(2*a^3*d^3 + b^3*c^3 - 3*a^2*b*c*d^2))/(2*a^2*b^3) - (a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)/(2*a*b*(a*b^2 + b^3*x^2))","B"
286,1,173,131,0.224428,"\text{Not used}","int((c + d*x^2)^3/(x^2*(a + b*x^2)^2),x)","\frac{\frac{x^2\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-3\,b^3\,c^3\right)}{2\,a^2}-\frac{b^2\,c^3}{a}}{b^3\,x^3+a\,b^2\,x}+\frac{d^3\,x}{b^2}-\frac{3\,\mathrm{atan}\left(\frac{3\,\sqrt{b}\,x\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^2}{\sqrt{a}\,\left(3\,a^3\,d^3-3\,a^2\,b\,c\,d^2-3\,a\,b^2\,c^2\,d+3\,b^3\,c^3\right)}\right)\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^2}{2\,a^{5/2}\,b^{5/2}}","Not used",1,"((x^2*(a^3*d^3 - 3*b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))/(2*a^2) - (b^2*c^3)/a)/(b^3*x^3 + a*b^2*x) + (d^3*x)/b^2 - (3*atan((3*b^(1/2)*x*(a*d + b*c)*(a*d - b*c)^2)/(a^(1/2)*(3*a^3*d^3 + 3*b^3*c^3 - 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)))*(a*d + b*c)*(a*d - b*c)^2)/(2*a^(5/2)*b^(5/2))","B"
287,1,135,98,0.270350,"\text{Not used}","int((c + d*x^2)^3/(x^3*(a + b*x^2)^2),x)","\frac{\ln\left(b\,x^2+a\right)\,\left(a^3\,d^3-3\,a\,b^2\,c^2\,d+2\,b^3\,c^3\right)}{2\,a^3\,b^2}-\frac{\ln\left(x\right)\,\left(2\,b\,c^3-3\,a\,c^2\,d\right)}{a^3}-\frac{\frac{c^3}{2\,a}-\frac{x^2\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-2\,b^3\,c^3\right)}{2\,a^2\,b^2}}{b\,x^4+a\,x^2}","Not used",1,"(log(a + b*x^2)*(a^3*d^3 + 2*b^3*c^3 - 3*a*b^2*c^2*d))/(2*a^3*b^2) - (log(x)*(2*b*c^3 - 3*a*c^2*d))/a^3 - (c^3/(2*a) - (x^2*(a^3*d^3 - 2*b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))/(2*a^2*b^2))/(a*x^2 + b*x^4)","B"
288,1,183,147,0.259250,"\text{Not used}","int((c + d*x^2)^3/(x^4*(a + b*x^2)^2),x)","\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,x\,{\left(a\,d-b\,c\right)}^2\,\left(a\,d+5\,b\,c\right)}{\sqrt{a}\,\left(a^3\,d^3+3\,a^2\,b\,c\,d^2-9\,a\,b^2\,c^2\,d+5\,b^3\,c^3\right)}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(a\,d+5\,b\,c\right)}{2\,a^{7/2}\,b^{3/2}}-\frac{\frac{c^3}{3\,a}+\frac{x^4\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+9\,a\,b^2\,c^2\,d-5\,b^3\,c^3\right)}{2\,a^3\,b}+\frac{c^2\,x^2\,\left(9\,a\,d-5\,b\,c\right)}{3\,a^2}}{b\,x^5+a\,x^3}","Not used",1,"(atan((b^(1/2)*x*(a*d - b*c)^2*(a*d + 5*b*c))/(a^(1/2)*(a^3*d^3 + 5*b^3*c^3 - 9*a*b^2*c^2*d + 3*a^2*b*c*d^2)))*(a*d - b*c)^2*(a*d + 5*b*c))/(2*a^(7/2)*b^(3/2)) - (c^3/(3*a) + (x^4*(a^3*d^3 - 5*b^3*c^3 + 9*a*b^2*c^2*d - 3*a^2*b*c*d^2))/(2*a^3*b) + (c^2*x^2*(9*a*d - 5*b*c))/(3*a^2))/(a*x^3 + b*x^5)","B"
289,1,3558,109,1.059314,"\text{Not used}","int(x^4/((a + b*x^2)^2*(c + d*x^2)),x)","-\frac{a\,x}{2\,b\,\left(b\,x^2+a\right)\,\left(a\,d-b\,c\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\sqrt{-c^3\,d}\,\left(\frac{2\,a^5\,b^2\,c\,d^6-8\,a^4\,b^3\,c^2\,d^5+12\,a^3\,b^4\,c^3\,d^4-8\,a^2\,b^5\,c^4\,d^3+2\,a\,b^6\,c^5\,d^2}{2\,\left(-a^3\,b\,d^3+3\,a^2\,b^2\,c\,d^2-3\,a\,b^3\,c^2\,d+b^4\,c^3\right)}-\frac{x\,\sqrt{-c^3\,d}\,\left(16\,a^5\,b^3\,d^7-48\,a^4\,b^4\,c\,d^6+32\,a^3\,b^5\,c^2\,d^5+32\,a^2\,b^6\,c^3\,d^4-48\,a\,b^7\,c^4\,d^3+16\,b^8\,c^5\,d^2\right)}{8\,\left(a^2\,b\,d^2-2\,a\,b^2\,c\,d+b^3\,c^2\right)\,\left(a^2\,d^3-2\,a\,b\,c\,d^2+b^2\,c^2\,d\right)}\right)}{2\,\left(a^2\,d^3-2\,a\,b\,c\,d^2+b^2\,c^2\,d\right)}-\frac{x\,\left(a^4\,d^5-6\,a^3\,b\,c\,d^4+9\,a^2\,b^2\,c^2\,d^3+4\,b^4\,c^4\,d\right)}{4\,\left(a^2\,b\,d^2-2\,a\,b^2\,c\,d+b^3\,c^2\right)}\right)\,\sqrt{-c^3\,d}\,1{}\mathrm{i}}{a^2\,d^3-2\,a\,b\,c\,d^2+b^2\,c^2\,d}-\frac{\left(\frac{\sqrt{-c^3\,d}\,\left(\frac{2\,a^5\,b^2\,c\,d^6-8\,a^4\,b^3\,c^2\,d^5+12\,a^3\,b^4\,c^3\,d^4-8\,a^2\,b^5\,c^4\,d^3+2\,a\,b^6\,c^5\,d^2}{2\,\left(-a^3\,b\,d^3+3\,a^2\,b^2\,c\,d^2-3\,a\,b^3\,c^2\,d+b^4\,c^3\right)}+\frac{x\,\sqrt{-c^3\,d}\,\left(16\,a^5\,b^3\,d^7-48\,a^4\,b^4\,c\,d^6+32\,a^3\,b^5\,c^2\,d^5+32\,a^2\,b^6\,c^3\,d^4-48\,a\,b^7\,c^4\,d^3+16\,b^8\,c^5\,d^2\right)}{8\,\left(a^2\,b\,d^2-2\,a\,b^2\,c\,d+b^3\,c^2\right)\,\left(a^2\,d^3-2\,a\,b\,c\,d^2+b^2\,c^2\,d\right)}\right)}{2\,\left(a^2\,d^3-2\,a\,b\,c\,d^2+b^2\,c^2\,d\right)}+\frac{x\,\left(a^4\,d^5-6\,a^3\,b\,c\,d^4+9\,a^2\,b^2\,c^2\,d^3+4\,b^4\,c^4\,d\right)}{4\,\left(a^2\,b\,d^2-2\,a\,b^2\,c\,d+b^3\,c^2\right)}\right)\,\sqrt{-c^3\,d}\,1{}\mathrm{i}}{a^2\,d^3-2\,a\,b\,c\,d^2+b^2\,c^2\,d}}{\frac{\frac{a^3\,c^2\,d^3}{2}-\frac{5\,a^2\,b\,c^3\,d^2}{2}+3\,a\,b^2\,c^4\,d}{-a^3\,b\,d^3+3\,a^2\,b^2\,c\,d^2-3\,a\,b^3\,c^2\,d+b^4\,c^3}+\frac{\left(\frac{\sqrt{-c^3\,d}\,\left(\frac{2\,a^5\,b^2\,c\,d^6-8\,a^4\,b^3\,c^2\,d^5+12\,a^3\,b^4\,c^3\,d^4-8\,a^2\,b^5\,c^4\,d^3+2\,a\,b^6\,c^5\,d^2}{2\,\left(-a^3\,b\,d^3+3\,a^2\,b^2\,c\,d^2-3\,a\,b^3\,c^2\,d+b^4\,c^3\right)}-\frac{x\,\sqrt{-c^3\,d}\,\left(16\,a^5\,b^3\,d^7-48\,a^4\,b^4\,c\,d^6+32\,a^3\,b^5\,c^2\,d^5+32\,a^2\,b^6\,c^3\,d^4-48\,a\,b^7\,c^4\,d^3+16\,b^8\,c^5\,d^2\right)}{8\,\left(a^2\,b\,d^2-2\,a\,b^2\,c\,d+b^3\,c^2\right)\,\left(a^2\,d^3-2\,a\,b\,c\,d^2+b^2\,c^2\,d\right)}\right)}{2\,\left(a^2\,d^3-2\,a\,b\,c\,d^2+b^2\,c^2\,d\right)}-\frac{x\,\left(a^4\,d^5-6\,a^3\,b\,c\,d^4+9\,a^2\,b^2\,c^2\,d^3+4\,b^4\,c^4\,d\right)}{4\,\left(a^2\,b\,d^2-2\,a\,b^2\,c\,d+b^3\,c^2\right)}\right)\,\sqrt{-c^3\,d}}{a^2\,d^3-2\,a\,b\,c\,d^2+b^2\,c^2\,d}+\frac{\left(\frac{\sqrt{-c^3\,d}\,\left(\frac{2\,a^5\,b^2\,c\,d^6-8\,a^4\,b^3\,c^2\,d^5+12\,a^3\,b^4\,c^3\,d^4-8\,a^2\,b^5\,c^4\,d^3+2\,a\,b^6\,c^5\,d^2}{2\,\left(-a^3\,b\,d^3+3\,a^2\,b^2\,c\,d^2-3\,a\,b^3\,c^2\,d+b^4\,c^3\right)}+\frac{x\,\sqrt{-c^3\,d}\,\left(16\,a^5\,b^3\,d^7-48\,a^4\,b^4\,c\,d^6+32\,a^3\,b^5\,c^2\,d^5+32\,a^2\,b^6\,c^3\,d^4-48\,a\,b^7\,c^4\,d^3+16\,b^8\,c^5\,d^2\right)}{8\,\left(a^2\,b\,d^2-2\,a\,b^2\,c\,d+b^3\,c^2\right)\,\left(a^2\,d^3-2\,a\,b\,c\,d^2+b^2\,c^2\,d\right)}\right)}{2\,\left(a^2\,d^3-2\,a\,b\,c\,d^2+b^2\,c^2\,d\right)}+\frac{x\,\left(a^4\,d^5-6\,a^3\,b\,c\,d^4+9\,a^2\,b^2\,c^2\,d^3+4\,b^4\,c^4\,d\right)}{4\,\left(a^2\,b\,d^2-2\,a\,b^2\,c\,d+b^3\,c^2\right)}\right)\,\sqrt{-c^3\,d}}{a^2\,d^3-2\,a\,b\,c\,d^2+b^2\,c^2\,d}}\right)\,\sqrt{-c^3\,d}\,1{}\mathrm{i}}{a^2\,d^3-2\,a\,b\,c\,d^2+b^2\,c^2\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{x\,\left(a^4\,d^5-6\,a^3\,b\,c\,d^4+9\,a^2\,b^2\,c^2\,d^3+4\,b^4\,c^4\,d\right)}{2\,\left(a^2\,b\,d^2-2\,a\,b^2\,c\,d+b^3\,c^2\right)}-\frac{\sqrt{-a\,b^3}\,\left(\frac{2\,a^5\,b^2\,c\,d^6-8\,a^4\,b^3\,c^2\,d^5+12\,a^3\,b^4\,c^3\,d^4-8\,a^2\,b^5\,c^4\,d^3+2\,a\,b^6\,c^5\,d^2}{-a^3\,b\,d^3+3\,a^2\,b^2\,c\,d^2-3\,a\,b^3\,c^2\,d+b^4\,c^3}-\frac{x\,\sqrt{-a\,b^3}\,\left(a\,d-3\,b\,c\right)\,\left(16\,a^5\,b^3\,d^7-48\,a^4\,b^4\,c\,d^6+32\,a^3\,b^5\,c^2\,d^5+32\,a^2\,b^6\,c^3\,d^4-48\,a\,b^7\,c^4\,d^3+16\,b^8\,c^5\,d^2\right)}{8\,\left(a^2\,b^3\,d^2-2\,a\,b^4\,c\,d+b^5\,c^2\right)\,\left(a^2\,b\,d^2-2\,a\,b^2\,c\,d+b^3\,c^2\right)}\right)\,\left(a\,d-3\,b\,c\right)}{4\,\left(a^2\,b^3\,d^2-2\,a\,b^4\,c\,d+b^5\,c^2\right)}\right)\,\sqrt{-a\,b^3}\,\left(a\,d-3\,b\,c\right)\,1{}\mathrm{i}}{4\,\left(a^2\,b^3\,d^2-2\,a\,b^4\,c\,d+b^5\,c^2\right)}+\frac{\left(\frac{x\,\left(a^4\,d^5-6\,a^3\,b\,c\,d^4+9\,a^2\,b^2\,c^2\,d^3+4\,b^4\,c^4\,d\right)}{2\,\left(a^2\,b\,d^2-2\,a\,b^2\,c\,d+b^3\,c^2\right)}+\frac{\sqrt{-a\,b^3}\,\left(\frac{2\,a^5\,b^2\,c\,d^6-8\,a^4\,b^3\,c^2\,d^5+12\,a^3\,b^4\,c^3\,d^4-8\,a^2\,b^5\,c^4\,d^3+2\,a\,b^6\,c^5\,d^2}{-a^3\,b\,d^3+3\,a^2\,b^2\,c\,d^2-3\,a\,b^3\,c^2\,d+b^4\,c^3}+\frac{x\,\sqrt{-a\,b^3}\,\left(a\,d-3\,b\,c\right)\,\left(16\,a^5\,b^3\,d^7-48\,a^4\,b^4\,c\,d^6+32\,a^3\,b^5\,c^2\,d^5+32\,a^2\,b^6\,c^3\,d^4-48\,a\,b^7\,c^4\,d^3+16\,b^8\,c^5\,d^2\right)}{8\,\left(a^2\,b^3\,d^2-2\,a\,b^4\,c\,d+b^5\,c^2\right)\,\left(a^2\,b\,d^2-2\,a\,b^2\,c\,d+b^3\,c^2\right)}\right)\,\left(a\,d-3\,b\,c\right)}{4\,\left(a^2\,b^3\,d^2-2\,a\,b^4\,c\,d+b^5\,c^2\right)}\right)\,\sqrt{-a\,b^3}\,\left(a\,d-3\,b\,c\right)\,1{}\mathrm{i}}{4\,\left(a^2\,b^3\,d^2-2\,a\,b^4\,c\,d+b^5\,c^2\right)}}{\frac{\frac{a^3\,c^2\,d^3}{2}-\frac{5\,a^2\,b\,c^3\,d^2}{2}+3\,a\,b^2\,c^4\,d}{-a^3\,b\,d^3+3\,a^2\,b^2\,c\,d^2-3\,a\,b^3\,c^2\,d+b^4\,c^3}-\frac{\left(\frac{x\,\left(a^4\,d^5-6\,a^3\,b\,c\,d^4+9\,a^2\,b^2\,c^2\,d^3+4\,b^4\,c^4\,d\right)}{2\,\left(a^2\,b\,d^2-2\,a\,b^2\,c\,d+b^3\,c^2\right)}-\frac{\sqrt{-a\,b^3}\,\left(\frac{2\,a^5\,b^2\,c\,d^6-8\,a^4\,b^3\,c^2\,d^5+12\,a^3\,b^4\,c^3\,d^4-8\,a^2\,b^5\,c^4\,d^3+2\,a\,b^6\,c^5\,d^2}{-a^3\,b\,d^3+3\,a^2\,b^2\,c\,d^2-3\,a\,b^3\,c^2\,d+b^4\,c^3}-\frac{x\,\sqrt{-a\,b^3}\,\left(a\,d-3\,b\,c\right)\,\left(16\,a^5\,b^3\,d^7-48\,a^4\,b^4\,c\,d^6+32\,a^3\,b^5\,c^2\,d^5+32\,a^2\,b^6\,c^3\,d^4-48\,a\,b^7\,c^4\,d^3+16\,b^8\,c^5\,d^2\right)}{8\,\left(a^2\,b^3\,d^2-2\,a\,b^4\,c\,d+b^5\,c^2\right)\,\left(a^2\,b\,d^2-2\,a\,b^2\,c\,d+b^3\,c^2\right)}\right)\,\left(a\,d-3\,b\,c\right)}{4\,\left(a^2\,b^3\,d^2-2\,a\,b^4\,c\,d+b^5\,c^2\right)}\right)\,\sqrt{-a\,b^3}\,\left(a\,d-3\,b\,c\right)}{4\,\left(a^2\,b^3\,d^2-2\,a\,b^4\,c\,d+b^5\,c^2\right)}+\frac{\left(\frac{x\,\left(a^4\,d^5-6\,a^3\,b\,c\,d^4+9\,a^2\,b^2\,c^2\,d^3+4\,b^4\,c^4\,d\right)}{2\,\left(a^2\,b\,d^2-2\,a\,b^2\,c\,d+b^3\,c^2\right)}+\frac{\sqrt{-a\,b^3}\,\left(\frac{2\,a^5\,b^2\,c\,d^6-8\,a^4\,b^3\,c^2\,d^5+12\,a^3\,b^4\,c^3\,d^4-8\,a^2\,b^5\,c^4\,d^3+2\,a\,b^6\,c^5\,d^2}{-a^3\,b\,d^3+3\,a^2\,b^2\,c\,d^2-3\,a\,b^3\,c^2\,d+b^4\,c^3}+\frac{x\,\sqrt{-a\,b^3}\,\left(a\,d-3\,b\,c\right)\,\left(16\,a^5\,b^3\,d^7-48\,a^4\,b^4\,c\,d^6+32\,a^3\,b^5\,c^2\,d^5+32\,a^2\,b^6\,c^3\,d^4-48\,a\,b^7\,c^4\,d^3+16\,b^8\,c^5\,d^2\right)}{8\,\left(a^2\,b^3\,d^2-2\,a\,b^4\,c\,d+b^5\,c^2\right)\,\left(a^2\,b\,d^2-2\,a\,b^2\,c\,d+b^3\,c^2\right)}\right)\,\left(a\,d-3\,b\,c\right)}{4\,\left(a^2\,b^3\,d^2-2\,a\,b^4\,c\,d+b^5\,c^2\right)}\right)\,\sqrt{-a\,b^3}\,\left(a\,d-3\,b\,c\right)}{4\,\left(a^2\,b^3\,d^2-2\,a\,b^4\,c\,d+b^5\,c^2\right)}}\right)\,\sqrt{-a\,b^3}\,\left(a\,d-3\,b\,c\right)\,1{}\mathrm{i}}{2\,\left(a^2\,b^3\,d^2-2\,a\,b^4\,c\,d+b^5\,c^2\right)}","Not used",1,"(atan((((((-c^3*d)^(1/2)*((2*a*b^6*c^5*d^2 + 2*a^5*b^2*c*d^6 - 8*a^2*b^5*c^4*d^3 + 12*a^3*b^4*c^3*d^4 - 8*a^4*b^3*c^2*d^5)/(2*(b^4*c^3 - a^3*b*d^3 + 3*a^2*b^2*c*d^2 - 3*a*b^3*c^2*d)) - (x*(-c^3*d)^(1/2)*(16*a^5*b^3*d^7 + 16*b^8*c^5*d^2 - 48*a*b^7*c^4*d^3 - 48*a^4*b^4*c*d^6 + 32*a^2*b^6*c^3*d^4 + 32*a^3*b^5*c^2*d^5))/(8*(b^3*c^2 + a^2*b*d^2 - 2*a*b^2*c*d)*(a^2*d^3 + b^2*c^2*d - 2*a*b*c*d^2))))/(2*(a^2*d^3 + b^2*c^2*d - 2*a*b*c*d^2)) - (x*(a^4*d^5 + 4*b^4*c^4*d + 9*a^2*b^2*c^2*d^3 - 6*a^3*b*c*d^4))/(4*(b^3*c^2 + a^2*b*d^2 - 2*a*b^2*c*d)))*(-c^3*d)^(1/2)*1i)/(a^2*d^3 + b^2*c^2*d - 2*a*b*c*d^2) - ((((-c^3*d)^(1/2)*((2*a*b^6*c^5*d^2 + 2*a^5*b^2*c*d^6 - 8*a^2*b^5*c^4*d^3 + 12*a^3*b^4*c^3*d^4 - 8*a^4*b^3*c^2*d^5)/(2*(b^4*c^3 - a^3*b*d^3 + 3*a^2*b^2*c*d^2 - 3*a*b^3*c^2*d)) + (x*(-c^3*d)^(1/2)*(16*a^5*b^3*d^7 + 16*b^8*c^5*d^2 - 48*a*b^7*c^4*d^3 - 48*a^4*b^4*c*d^6 + 32*a^2*b^6*c^3*d^4 + 32*a^3*b^5*c^2*d^5))/(8*(b^3*c^2 + a^2*b*d^2 - 2*a*b^2*c*d)*(a^2*d^3 + b^2*c^2*d - 2*a*b*c*d^2))))/(2*(a^2*d^3 + b^2*c^2*d - 2*a*b*c*d^2)) + (x*(a^4*d^5 + 4*b^4*c^4*d + 9*a^2*b^2*c^2*d^3 - 6*a^3*b*c*d^4))/(4*(b^3*c^2 + a^2*b*d^2 - 2*a*b^2*c*d)))*(-c^3*d)^(1/2)*1i)/(a^2*d^3 + b^2*c^2*d - 2*a*b*c*d^2))/(((a^3*c^2*d^3)/2 - (5*a^2*b*c^3*d^2)/2 + 3*a*b^2*c^4*d)/(b^4*c^3 - a^3*b*d^3 + 3*a^2*b^2*c*d^2 - 3*a*b^3*c^2*d) + ((((-c^3*d)^(1/2)*((2*a*b^6*c^5*d^2 + 2*a^5*b^2*c*d^6 - 8*a^2*b^5*c^4*d^3 + 12*a^3*b^4*c^3*d^4 - 8*a^4*b^3*c^2*d^5)/(2*(b^4*c^3 - a^3*b*d^3 + 3*a^2*b^2*c*d^2 - 3*a*b^3*c^2*d)) - (x*(-c^3*d)^(1/2)*(16*a^5*b^3*d^7 + 16*b^8*c^5*d^2 - 48*a*b^7*c^4*d^3 - 48*a^4*b^4*c*d^6 + 32*a^2*b^6*c^3*d^4 + 32*a^3*b^5*c^2*d^5))/(8*(b^3*c^2 + a^2*b*d^2 - 2*a*b^2*c*d)*(a^2*d^3 + b^2*c^2*d - 2*a*b*c*d^2))))/(2*(a^2*d^3 + b^2*c^2*d - 2*a*b*c*d^2)) - (x*(a^4*d^5 + 4*b^4*c^4*d + 9*a^2*b^2*c^2*d^3 - 6*a^3*b*c*d^4))/(4*(b^3*c^2 + a^2*b*d^2 - 2*a*b^2*c*d)))*(-c^3*d)^(1/2))/(a^2*d^3 + b^2*c^2*d - 2*a*b*c*d^2) + ((((-c^3*d)^(1/2)*((2*a*b^6*c^5*d^2 + 2*a^5*b^2*c*d^6 - 8*a^2*b^5*c^4*d^3 + 12*a^3*b^4*c^3*d^4 - 8*a^4*b^3*c^2*d^5)/(2*(b^4*c^3 - a^3*b*d^3 + 3*a^2*b^2*c*d^2 - 3*a*b^3*c^2*d)) + (x*(-c^3*d)^(1/2)*(16*a^5*b^3*d^7 + 16*b^8*c^5*d^2 - 48*a*b^7*c^4*d^3 - 48*a^4*b^4*c*d^6 + 32*a^2*b^6*c^3*d^4 + 32*a^3*b^5*c^2*d^5))/(8*(b^3*c^2 + a^2*b*d^2 - 2*a*b^2*c*d)*(a^2*d^3 + b^2*c^2*d - 2*a*b*c*d^2))))/(2*(a^2*d^3 + b^2*c^2*d - 2*a*b*c*d^2)) + (x*(a^4*d^5 + 4*b^4*c^4*d + 9*a^2*b^2*c^2*d^3 - 6*a^3*b*c*d^4))/(4*(b^3*c^2 + a^2*b*d^2 - 2*a*b^2*c*d)))*(-c^3*d)^(1/2))/(a^2*d^3 + b^2*c^2*d - 2*a*b*c*d^2)))*(-c^3*d)^(1/2)*1i)/(a^2*d^3 + b^2*c^2*d - 2*a*b*c*d^2) - (atan(((((x*(a^4*d^5 + 4*b^4*c^4*d + 9*a^2*b^2*c^2*d^3 - 6*a^3*b*c*d^4))/(2*(b^3*c^2 + a^2*b*d^2 - 2*a*b^2*c*d)) - ((-a*b^3)^(1/2)*((2*a*b^6*c^5*d^2 + 2*a^5*b^2*c*d^6 - 8*a^2*b^5*c^4*d^3 + 12*a^3*b^4*c^3*d^4 - 8*a^4*b^3*c^2*d^5)/(b^4*c^3 - a^3*b*d^3 + 3*a^2*b^2*c*d^2 - 3*a*b^3*c^2*d) - (x*(-a*b^3)^(1/2)*(a*d - 3*b*c)*(16*a^5*b^3*d^7 + 16*b^8*c^5*d^2 - 48*a*b^7*c^4*d^3 - 48*a^4*b^4*c*d^6 + 32*a^2*b^6*c^3*d^4 + 32*a^3*b^5*c^2*d^5))/(8*(b^5*c^2 + a^2*b^3*d^2 - 2*a*b^4*c*d)*(b^3*c^2 + a^2*b*d^2 - 2*a*b^2*c*d)))*(a*d - 3*b*c))/(4*(b^5*c^2 + a^2*b^3*d^2 - 2*a*b^4*c*d)))*(-a*b^3)^(1/2)*(a*d - 3*b*c)*1i)/(4*(b^5*c^2 + a^2*b^3*d^2 - 2*a*b^4*c*d)) + (((x*(a^4*d^5 + 4*b^4*c^4*d + 9*a^2*b^2*c^2*d^3 - 6*a^3*b*c*d^4))/(2*(b^3*c^2 + a^2*b*d^2 - 2*a*b^2*c*d)) + ((-a*b^3)^(1/2)*((2*a*b^6*c^5*d^2 + 2*a^5*b^2*c*d^6 - 8*a^2*b^5*c^4*d^3 + 12*a^3*b^4*c^3*d^4 - 8*a^4*b^3*c^2*d^5)/(b^4*c^3 - a^3*b*d^3 + 3*a^2*b^2*c*d^2 - 3*a*b^3*c^2*d) + (x*(-a*b^3)^(1/2)*(a*d - 3*b*c)*(16*a^5*b^3*d^7 + 16*b^8*c^5*d^2 - 48*a*b^7*c^4*d^3 - 48*a^4*b^4*c*d^6 + 32*a^2*b^6*c^3*d^4 + 32*a^3*b^5*c^2*d^5))/(8*(b^5*c^2 + a^2*b^3*d^2 - 2*a*b^4*c*d)*(b^3*c^2 + a^2*b*d^2 - 2*a*b^2*c*d)))*(a*d - 3*b*c))/(4*(b^5*c^2 + a^2*b^3*d^2 - 2*a*b^4*c*d)))*(-a*b^3)^(1/2)*(a*d - 3*b*c)*1i)/(4*(b^5*c^2 + a^2*b^3*d^2 - 2*a*b^4*c*d)))/(((a^3*c^2*d^3)/2 - (5*a^2*b*c^3*d^2)/2 + 3*a*b^2*c^4*d)/(b^4*c^3 - a^3*b*d^3 + 3*a^2*b^2*c*d^2 - 3*a*b^3*c^2*d) - (((x*(a^4*d^5 + 4*b^4*c^4*d + 9*a^2*b^2*c^2*d^3 - 6*a^3*b*c*d^4))/(2*(b^3*c^2 + a^2*b*d^2 - 2*a*b^2*c*d)) - ((-a*b^3)^(1/2)*((2*a*b^6*c^5*d^2 + 2*a^5*b^2*c*d^6 - 8*a^2*b^5*c^4*d^3 + 12*a^3*b^4*c^3*d^4 - 8*a^4*b^3*c^2*d^5)/(b^4*c^3 - a^3*b*d^3 + 3*a^2*b^2*c*d^2 - 3*a*b^3*c^2*d) - (x*(-a*b^3)^(1/2)*(a*d - 3*b*c)*(16*a^5*b^3*d^7 + 16*b^8*c^5*d^2 - 48*a*b^7*c^4*d^3 - 48*a^4*b^4*c*d^6 + 32*a^2*b^6*c^3*d^4 + 32*a^3*b^5*c^2*d^5))/(8*(b^5*c^2 + a^2*b^3*d^2 - 2*a*b^4*c*d)*(b^3*c^2 + a^2*b*d^2 - 2*a*b^2*c*d)))*(a*d - 3*b*c))/(4*(b^5*c^2 + a^2*b^3*d^2 - 2*a*b^4*c*d)))*(-a*b^3)^(1/2)*(a*d - 3*b*c))/(4*(b^5*c^2 + a^2*b^3*d^2 - 2*a*b^4*c*d)) + (((x*(a^4*d^5 + 4*b^4*c^4*d + 9*a^2*b^2*c^2*d^3 - 6*a^3*b*c*d^4))/(2*(b^3*c^2 + a^2*b*d^2 - 2*a*b^2*c*d)) + ((-a*b^3)^(1/2)*((2*a*b^6*c^5*d^2 + 2*a^5*b^2*c*d^6 - 8*a^2*b^5*c^4*d^3 + 12*a^3*b^4*c^3*d^4 - 8*a^4*b^3*c^2*d^5)/(b^4*c^3 - a^3*b*d^3 + 3*a^2*b^2*c*d^2 - 3*a*b^3*c^2*d) + (x*(-a*b^3)^(1/2)*(a*d - 3*b*c)*(16*a^5*b^3*d^7 + 16*b^8*c^5*d^2 - 48*a*b^7*c^4*d^3 - 48*a^4*b^4*c*d^6 + 32*a^2*b^6*c^3*d^4 + 32*a^3*b^5*c^2*d^5))/(8*(b^5*c^2 + a^2*b^3*d^2 - 2*a*b^4*c*d)*(b^3*c^2 + a^2*b*d^2 - 2*a*b^2*c*d)))*(a*d - 3*b*c))/(4*(b^5*c^2 + a^2*b^3*d^2 - 2*a*b^4*c*d)))*(-a*b^3)^(1/2)*(a*d - 3*b*c))/(4*(b^5*c^2 + a^2*b^3*d^2 - 2*a*b^4*c*d))))*(-a*b^3)^(1/2)*(a*d - 3*b*c)*1i)/(2*(b^5*c^2 + a^2*b^3*d^2 - 2*a*b^4*c*d)) - (a*x)/(2*b*(a + b*x^2)*(a*d - b*c))","B"
290,1,172,74,0.312678,"\text{Not used}","int(x^3/((a + b*x^2)^2*(c + d*x^2)),x)","\frac{a\,\left(b\,c+b\,c\,\mathrm{atan}\left(\frac{a\,d\,x^2\,1{}\mathrm{i}-b\,c\,x^2\,1{}\mathrm{i}}{2\,a\,c+a\,d\,x^2+b\,c\,x^2}\right)\,2{}\mathrm{i}\right)-a^2\,d+b^2\,c\,x^2\,\mathrm{atan}\left(\frac{a\,d\,x^2\,1{}\mathrm{i}-b\,c\,x^2\,1{}\mathrm{i}}{2\,a\,c+a\,d\,x^2+b\,c\,x^2}\right)\,2{}\mathrm{i}}{2\,a^3\,b\,d^2-4\,a^2\,b^2\,c\,d+2\,a^2\,b^2\,d^2\,x^2+2\,a\,b^3\,c^2-4\,a\,b^3\,c\,d\,x^2+2\,b^4\,c^2\,x^2}","Not used",1,"(a*(b*c + b*c*atan((a*d*x^2*1i - b*c*x^2*1i)/(2*a*c + a*d*x^2 + b*c*x^2))*2i) - a^2*d + b^2*c*x^2*atan((a*d*x^2*1i - b*c*x^2*1i)/(2*a*c + a*d*x^2 + b*c*x^2))*2i)/(2*a*b^3*c^2 + 2*a^3*b*d^2 + 2*b^4*c^2*x^2 + 2*a^2*b^2*d^2*x^2 - 4*a^2*b^2*c*d - 4*a*b^3*c*d*x^2)","B"
291,1,3153,104,0.892271,"\text{Not used}","int(x^2/((a + b*x^2)^2*(c + d*x^2)),x)","\frac{x}{2\,\left(b\,x^2+a\right)\,\left(a\,d-b\,c\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-c\,d}\,\left(\frac{\sqrt{-c\,d}\,\left(\frac{2\,a^4\,b^2\,c\,d^6-8\,a^3\,b^3\,c^2\,d^5+12\,a^2\,b^4\,c^3\,d^4-8\,a\,b^5\,c^4\,d^3+2\,b^6\,c^5\,d^2}{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)}-\frac{x\,\sqrt{-c\,d}\,\left(16\,a^5\,b^2\,d^7-48\,a^4\,b^3\,c\,d^6+32\,a^3\,b^4\,c^2\,d^5+32\,a^2\,b^5\,c^3\,d^4-48\,a\,b^6\,c^4\,d^3+16\,b^7\,c^5\,d^2\right)}{8\,{\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}^2}\right)}{2\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}-\frac{x\,\left(a^2\,b\,d^5+2\,a\,b^2\,c\,d^4+5\,b^3\,c^2\,d^3\right)}{4\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}\right)\,1{}\mathrm{i}}{a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2}-\frac{\sqrt{-c\,d}\,\left(\frac{\sqrt{-c\,d}\,\left(\frac{2\,a^4\,b^2\,c\,d^6-8\,a^3\,b^3\,c^2\,d^5+12\,a^2\,b^4\,c^3\,d^4-8\,a\,b^5\,c^4\,d^3+2\,b^6\,c^5\,d^2}{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)}+\frac{x\,\sqrt{-c\,d}\,\left(16\,a^5\,b^2\,d^7-48\,a^4\,b^3\,c\,d^6+32\,a^3\,b^4\,c^2\,d^5+32\,a^2\,b^5\,c^3\,d^4-48\,a\,b^6\,c^4\,d^3+16\,b^7\,c^5\,d^2\right)}{8\,{\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}^2}\right)}{2\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}+\frac{x\,\left(a^2\,b\,d^5+2\,a\,b^2\,c\,d^4+5\,b^3\,c^2\,d^3\right)}{4\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}\right)\,1{}\mathrm{i}}{a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2}}{\frac{\frac{b^2\,c^2\,d^3}{2}+\frac{a\,b\,c\,d^4}{2}}{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}+\frac{\sqrt{-c\,d}\,\left(\frac{\sqrt{-c\,d}\,\left(\frac{2\,a^4\,b^2\,c\,d^6-8\,a^3\,b^3\,c^2\,d^5+12\,a^2\,b^4\,c^3\,d^4-8\,a\,b^5\,c^4\,d^3+2\,b^6\,c^5\,d^2}{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)}-\frac{x\,\sqrt{-c\,d}\,\left(16\,a^5\,b^2\,d^7-48\,a^4\,b^3\,c\,d^6+32\,a^3\,b^4\,c^2\,d^5+32\,a^2\,b^5\,c^3\,d^4-48\,a\,b^6\,c^4\,d^3+16\,b^7\,c^5\,d^2\right)}{8\,{\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}^2}\right)}{2\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}-\frac{x\,\left(a^2\,b\,d^5+2\,a\,b^2\,c\,d^4+5\,b^3\,c^2\,d^3\right)}{4\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}\right)}{a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2}+\frac{\sqrt{-c\,d}\,\left(\frac{\sqrt{-c\,d}\,\left(\frac{2\,a^4\,b^2\,c\,d^6-8\,a^3\,b^3\,c^2\,d^5+12\,a^2\,b^4\,c^3\,d^4-8\,a\,b^5\,c^4\,d^3+2\,b^6\,c^5\,d^2}{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)}+\frac{x\,\sqrt{-c\,d}\,\left(16\,a^5\,b^2\,d^7-48\,a^4\,b^3\,c\,d^6+32\,a^3\,b^4\,c^2\,d^5+32\,a^2\,b^5\,c^3\,d^4-48\,a\,b^6\,c^4\,d^3+16\,b^7\,c^5\,d^2\right)}{8\,{\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}^2}\right)}{2\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}+\frac{x\,\left(a^2\,b\,d^5+2\,a\,b^2\,c\,d^4+5\,b^3\,c^2\,d^3\right)}{4\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}\right)}{a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2}}\right)\,\sqrt{-c\,d}\,1{}\mathrm{i}}{a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-a\,b}\,\left(\frac{x\,\left(a^2\,b\,d^5+2\,a\,b^2\,c\,d^4+5\,b^3\,c^2\,d^3\right)}{2\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}-\frac{\sqrt{-a\,b}\,\left(\frac{2\,a^4\,b^2\,c\,d^6-8\,a^3\,b^3\,c^2\,d^5+12\,a^2\,b^4\,c^3\,d^4-8\,a\,b^5\,c^4\,d^3+2\,b^6\,c^5\,d^2}{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}-\frac{x\,\sqrt{-a\,b}\,\left(a\,d+b\,c\right)\,\left(16\,a^5\,b^2\,d^7-48\,a^4\,b^3\,c\,d^6+32\,a^3\,b^4\,c^2\,d^5+32\,a^2\,b^5\,c^3\,d^4-48\,a\,b^6\,c^4\,d^3+16\,b^7\,c^5\,d^2\right)}{8\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)\,\left(a^3\,b\,d^2-2\,a^2\,b^2\,c\,d+a\,b^3\,c^2\right)}\right)\,\left(a\,d+b\,c\right)}{4\,\left(a^3\,b\,d^2-2\,a^2\,b^2\,c\,d+a\,b^3\,c^2\right)}\right)\,\left(a\,d+b\,c\right)\,1{}\mathrm{i}}{4\,\left(a^3\,b\,d^2-2\,a^2\,b^2\,c\,d+a\,b^3\,c^2\right)}+\frac{\sqrt{-a\,b}\,\left(\frac{x\,\left(a^2\,b\,d^5+2\,a\,b^2\,c\,d^4+5\,b^3\,c^2\,d^3\right)}{2\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}+\frac{\sqrt{-a\,b}\,\left(\frac{2\,a^4\,b^2\,c\,d^6-8\,a^3\,b^3\,c^2\,d^5+12\,a^2\,b^4\,c^3\,d^4-8\,a\,b^5\,c^4\,d^3+2\,b^6\,c^5\,d^2}{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}+\frac{x\,\sqrt{-a\,b}\,\left(a\,d+b\,c\right)\,\left(16\,a^5\,b^2\,d^7-48\,a^4\,b^3\,c\,d^6+32\,a^3\,b^4\,c^2\,d^5+32\,a^2\,b^5\,c^3\,d^4-48\,a\,b^6\,c^4\,d^3+16\,b^7\,c^5\,d^2\right)}{8\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)\,\left(a^3\,b\,d^2-2\,a^2\,b^2\,c\,d+a\,b^3\,c^2\right)}\right)\,\left(a\,d+b\,c\right)}{4\,\left(a^3\,b\,d^2-2\,a^2\,b^2\,c\,d+a\,b^3\,c^2\right)}\right)\,\left(a\,d+b\,c\right)\,1{}\mathrm{i}}{4\,\left(a^3\,b\,d^2-2\,a^2\,b^2\,c\,d+a\,b^3\,c^2\right)}}{\frac{\frac{b^2\,c^2\,d^3}{2}+\frac{a\,b\,c\,d^4}{2}}{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}-\frac{\sqrt{-a\,b}\,\left(\frac{x\,\left(a^2\,b\,d^5+2\,a\,b^2\,c\,d^4+5\,b^3\,c^2\,d^3\right)}{2\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}-\frac{\sqrt{-a\,b}\,\left(\frac{2\,a^4\,b^2\,c\,d^6-8\,a^3\,b^3\,c^2\,d^5+12\,a^2\,b^4\,c^3\,d^4-8\,a\,b^5\,c^4\,d^3+2\,b^6\,c^5\,d^2}{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}-\frac{x\,\sqrt{-a\,b}\,\left(a\,d+b\,c\right)\,\left(16\,a^5\,b^2\,d^7-48\,a^4\,b^3\,c\,d^6+32\,a^3\,b^4\,c^2\,d^5+32\,a^2\,b^5\,c^3\,d^4-48\,a\,b^6\,c^4\,d^3+16\,b^7\,c^5\,d^2\right)}{8\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)\,\left(a^3\,b\,d^2-2\,a^2\,b^2\,c\,d+a\,b^3\,c^2\right)}\right)\,\left(a\,d+b\,c\right)}{4\,\left(a^3\,b\,d^2-2\,a^2\,b^2\,c\,d+a\,b^3\,c^2\right)}\right)\,\left(a\,d+b\,c\right)}{4\,\left(a^3\,b\,d^2-2\,a^2\,b^2\,c\,d+a\,b^3\,c^2\right)}+\frac{\sqrt{-a\,b}\,\left(\frac{x\,\left(a^2\,b\,d^5+2\,a\,b^2\,c\,d^4+5\,b^3\,c^2\,d^3\right)}{2\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}+\frac{\sqrt{-a\,b}\,\left(\frac{2\,a^4\,b^2\,c\,d^6-8\,a^3\,b^3\,c^2\,d^5+12\,a^2\,b^4\,c^3\,d^4-8\,a\,b^5\,c^4\,d^3+2\,b^6\,c^5\,d^2}{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}+\frac{x\,\sqrt{-a\,b}\,\left(a\,d+b\,c\right)\,\left(16\,a^5\,b^2\,d^7-48\,a^4\,b^3\,c\,d^6+32\,a^3\,b^4\,c^2\,d^5+32\,a^2\,b^5\,c^3\,d^4-48\,a\,b^6\,c^4\,d^3+16\,b^7\,c^5\,d^2\right)}{8\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)\,\left(a^3\,b\,d^2-2\,a^2\,b^2\,c\,d+a\,b^3\,c^2\right)}\right)\,\left(a\,d+b\,c\right)}{4\,\left(a^3\,b\,d^2-2\,a^2\,b^2\,c\,d+a\,b^3\,c^2\right)}\right)\,\left(a\,d+b\,c\right)}{4\,\left(a^3\,b\,d^2-2\,a^2\,b^2\,c\,d+a\,b^3\,c^2\right)}}\right)\,\sqrt{-a\,b}\,\left(a\,d+b\,c\right)\,1{}\mathrm{i}}{2\,\left(a^3\,b\,d^2-2\,a^2\,b^2\,c\,d+a\,b^3\,c^2\right)}","Not used",1,"x/(2*(a + b*x^2)*(a*d - b*c)) + (atan((((-c*d)^(1/2)*(((-c*d)^(1/2)*((2*b^6*c^5*d^2 - 8*a*b^5*c^4*d^3 + 2*a^4*b^2*c*d^6 + 12*a^2*b^4*c^3*d^4 - 8*a^3*b^3*c^2*d^5)/(2*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)) - (x*(-c*d)^(1/2)*(16*a^5*b^2*d^7 + 16*b^7*c^5*d^2 - 48*a*b^6*c^4*d^3 - 48*a^4*b^3*c*d^6 + 32*a^2*b^5*c^3*d^4 + 32*a^3*b^4*c^2*d^5))/(8*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)^2)))/(2*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) - (x*(a^2*b*d^5 + 5*b^3*c^2*d^3 + 2*a*b^2*c*d^4))/(4*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)))*1i)/(a^2*d^2 + b^2*c^2 - 2*a*b*c*d) - ((-c*d)^(1/2)*(((-c*d)^(1/2)*((2*b^6*c^5*d^2 - 8*a*b^5*c^4*d^3 + 2*a^4*b^2*c*d^6 + 12*a^2*b^4*c^3*d^4 - 8*a^3*b^3*c^2*d^5)/(2*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)) + (x*(-c*d)^(1/2)*(16*a^5*b^2*d^7 + 16*b^7*c^5*d^2 - 48*a*b^6*c^4*d^3 - 48*a^4*b^3*c*d^6 + 32*a^2*b^5*c^3*d^4 + 32*a^3*b^4*c^2*d^5))/(8*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)^2)))/(2*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) + (x*(a^2*b*d^5 + 5*b^3*c^2*d^3 + 2*a*b^2*c*d^4))/(4*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)))*1i)/(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/(((b^2*c^2*d^3)/2 + (a*b*c*d^4)/2)/(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2) + ((-c*d)^(1/2)*(((-c*d)^(1/2)*((2*b^6*c^5*d^2 - 8*a*b^5*c^4*d^3 + 2*a^4*b^2*c*d^6 + 12*a^2*b^4*c^3*d^4 - 8*a^3*b^3*c^2*d^5)/(2*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)) - (x*(-c*d)^(1/2)*(16*a^5*b^2*d^7 + 16*b^7*c^5*d^2 - 48*a*b^6*c^4*d^3 - 48*a^4*b^3*c*d^6 + 32*a^2*b^5*c^3*d^4 + 32*a^3*b^4*c^2*d^5))/(8*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)^2)))/(2*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) - (x*(a^2*b*d^5 + 5*b^3*c^2*d^3 + 2*a*b^2*c*d^4))/(4*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))))/(a^2*d^2 + b^2*c^2 - 2*a*b*c*d) + ((-c*d)^(1/2)*(((-c*d)^(1/2)*((2*b^6*c^5*d^2 - 8*a*b^5*c^4*d^3 + 2*a^4*b^2*c*d^6 + 12*a^2*b^4*c^3*d^4 - 8*a^3*b^3*c^2*d^5)/(2*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)) + (x*(-c*d)^(1/2)*(16*a^5*b^2*d^7 + 16*b^7*c^5*d^2 - 48*a*b^6*c^4*d^3 - 48*a^4*b^3*c*d^6 + 32*a^2*b^5*c^3*d^4 + 32*a^3*b^4*c^2*d^5))/(8*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)^2)))/(2*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) + (x*(a^2*b*d^5 + 5*b^3*c^2*d^3 + 2*a*b^2*c*d^4))/(4*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))))/(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)))*(-c*d)^(1/2)*1i)/(a^2*d^2 + b^2*c^2 - 2*a*b*c*d) - (atan((((-a*b)^(1/2)*((x*(a^2*b*d^5 + 5*b^3*c^2*d^3 + 2*a*b^2*c*d^4))/(2*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) - ((-a*b)^(1/2)*((2*b^6*c^5*d^2 - 8*a*b^5*c^4*d^3 + 2*a^4*b^2*c*d^6 + 12*a^2*b^4*c^3*d^4 - 8*a^3*b^3*c^2*d^5)/(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2) - (x*(-a*b)^(1/2)*(a*d + b*c)*(16*a^5*b^2*d^7 + 16*b^7*c^5*d^2 - 48*a*b^6*c^4*d^3 - 48*a^4*b^3*c*d^6 + 32*a^2*b^5*c^3*d^4 + 32*a^3*b^4*c^2*d^5))/(8*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)*(a*b^3*c^2 + a^3*b*d^2 - 2*a^2*b^2*c*d)))*(a*d + b*c))/(4*(a*b^3*c^2 + a^3*b*d^2 - 2*a^2*b^2*c*d)))*(a*d + b*c)*1i)/(4*(a*b^3*c^2 + a^3*b*d^2 - 2*a^2*b^2*c*d)) + ((-a*b)^(1/2)*((x*(a^2*b*d^5 + 5*b^3*c^2*d^3 + 2*a*b^2*c*d^4))/(2*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) + ((-a*b)^(1/2)*((2*b^6*c^5*d^2 - 8*a*b^5*c^4*d^3 + 2*a^4*b^2*c*d^6 + 12*a^2*b^4*c^3*d^4 - 8*a^3*b^3*c^2*d^5)/(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2) + (x*(-a*b)^(1/2)*(a*d + b*c)*(16*a^5*b^2*d^7 + 16*b^7*c^5*d^2 - 48*a*b^6*c^4*d^3 - 48*a^4*b^3*c*d^6 + 32*a^2*b^5*c^3*d^4 + 32*a^3*b^4*c^2*d^5))/(8*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)*(a*b^3*c^2 + a^3*b*d^2 - 2*a^2*b^2*c*d)))*(a*d + b*c))/(4*(a*b^3*c^2 + a^3*b*d^2 - 2*a^2*b^2*c*d)))*(a*d + b*c)*1i)/(4*(a*b^3*c^2 + a^3*b*d^2 - 2*a^2*b^2*c*d)))/(((b^2*c^2*d^3)/2 + (a*b*c*d^4)/2)/(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2) - ((-a*b)^(1/2)*((x*(a^2*b*d^5 + 5*b^3*c^2*d^3 + 2*a*b^2*c*d^4))/(2*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) - ((-a*b)^(1/2)*((2*b^6*c^5*d^2 - 8*a*b^5*c^4*d^3 + 2*a^4*b^2*c*d^6 + 12*a^2*b^4*c^3*d^4 - 8*a^3*b^3*c^2*d^5)/(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2) - (x*(-a*b)^(1/2)*(a*d + b*c)*(16*a^5*b^2*d^7 + 16*b^7*c^5*d^2 - 48*a*b^6*c^4*d^3 - 48*a^4*b^3*c*d^6 + 32*a^2*b^5*c^3*d^4 + 32*a^3*b^4*c^2*d^5))/(8*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)*(a*b^3*c^2 + a^3*b*d^2 - 2*a^2*b^2*c*d)))*(a*d + b*c))/(4*(a*b^3*c^2 + a^3*b*d^2 - 2*a^2*b^2*c*d)))*(a*d + b*c))/(4*(a*b^3*c^2 + a^3*b*d^2 - 2*a^2*b^2*c*d)) + ((-a*b)^(1/2)*((x*(a^2*b*d^5 + 5*b^3*c^2*d^3 + 2*a*b^2*c*d^4))/(2*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) + ((-a*b)^(1/2)*((2*b^6*c^5*d^2 - 8*a*b^5*c^4*d^3 + 2*a^4*b^2*c*d^6 + 12*a^2*b^4*c^3*d^4 - 8*a^3*b^3*c^2*d^5)/(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2) + (x*(-a*b)^(1/2)*(a*d + b*c)*(16*a^5*b^2*d^7 + 16*b^7*c^5*d^2 - 48*a*b^6*c^4*d^3 - 48*a^4*b^3*c*d^6 + 32*a^2*b^5*c^3*d^4 + 32*a^3*b^4*c^2*d^5))/(8*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)*(a*b^3*c^2 + a^3*b*d^2 - 2*a^2*b^2*c*d)))*(a*d + b*c))/(4*(a*b^3*c^2 + a^3*b*d^2 - 2*a^2*b^2*c*d)))*(a*d + b*c))/(4*(a*b^3*c^2 + a^3*b*d^2 - 2*a^2*b^2*c*d))))*(-a*b)^(1/2)*(a*d + b*c)*1i)/(2*(a*b^3*c^2 + a^3*b*d^2 - 2*a^2*b^2*c*d))","B"
292,1,161,70,0.320246,"\text{Not used}","int(x/((a + b*x^2)^2*(c + d*x^2)),x)","-\frac{b\,c-a\,\left(d-d\,\mathrm{atan}\left(\frac{a\,d\,x^2\,1{}\mathrm{i}-b\,c\,x^2\,1{}\mathrm{i}}{2\,a\,c+a\,d\,x^2+b\,c\,x^2}\right)\,2{}\mathrm{i}\right)+b\,d\,x^2\,\mathrm{atan}\left(\frac{a\,d\,x^2\,1{}\mathrm{i}-b\,c\,x^2\,1{}\mathrm{i}}{2\,a\,c+a\,d\,x^2+b\,c\,x^2}\right)\,2{}\mathrm{i}}{2\,a^3\,d^2-4\,a^2\,b\,c\,d+2\,a^2\,b\,d^2\,x^2+2\,a\,b^2\,c^2-4\,a\,b^2\,c\,d\,x^2+2\,b^3\,c^2\,x^2}","Not used",1,"-(b*c - a*(d - d*atan((a*d*x^2*1i - b*c*x^2*1i)/(2*a*c + a*d*x^2 + b*c*x^2))*2i) + b*d*x^2*atan((a*d*x^2*1i - b*c*x^2*1i)/(2*a*c + a*d*x^2 + b*c*x^2))*2i)/(2*a^3*d^2 + 2*a*b^2*c^2 + 2*b^3*c^2*x^2 + 2*a^2*b*d^2*x^2 - 4*a^2*b*c*d - 4*a*b^2*c*d*x^2)","B"
293,1,3649,108,1.014723,"\text{Not used}","int(1/((a + b*x^2)^2*(c + d*x^2)),x)","-\frac{b\,x}{2\,a\,\left(b\,x^2+a\right)\,\left(a\,d-b\,c\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-c\,d^3}\,\left(\frac{\left(\frac{4\,a^6\,b^2\,d^7-18\,a^5\,b^3\,c\,d^6+32\,a^4\,b^4\,c^2\,d^5-28\,a^3\,b^5\,c^3\,d^4+12\,a^2\,b^6\,c^4\,d^3-2\,a\,b^7\,c^5\,d^2}{2\,\left(a^5\,d^3-3\,a^4\,b\,c\,d^2+3\,a^3\,b^2\,c^2\,d-a^2\,b^3\,c^3\right)}-\frac{x\,\sqrt{-c\,d^3}\,\left(16\,a^7\,b^2\,d^7-48\,a^6\,b^3\,c\,d^6+32\,a^5\,b^4\,c^2\,d^5+32\,a^4\,b^5\,c^3\,d^4-48\,a^3\,b^6\,c^4\,d^3+16\,a^2\,b^7\,c^5\,d^2\right)}{8\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)\,\left(a^2\,c\,d^2-2\,a\,b\,c^2\,d+b^2\,c^3\right)}\right)\,\sqrt{-c\,d^3}}{2\,\left(a^2\,c\,d^2-2\,a\,b\,c^2\,d+b^2\,c^3\right)}-\frac{x\,\left(13\,a^2\,b^3\,d^5-6\,a\,b^4\,c\,d^4+b^5\,c^2\,d^3\right)}{4\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}\right)\,1{}\mathrm{i}}{a^2\,c\,d^2-2\,a\,b\,c^2\,d+b^2\,c^3}-\frac{\sqrt{-c\,d^3}\,\left(\frac{\left(\frac{4\,a^6\,b^2\,d^7-18\,a^5\,b^3\,c\,d^6+32\,a^4\,b^4\,c^2\,d^5-28\,a^3\,b^5\,c^3\,d^4+12\,a^2\,b^6\,c^4\,d^3-2\,a\,b^7\,c^5\,d^2}{2\,\left(a^5\,d^3-3\,a^4\,b\,c\,d^2+3\,a^3\,b^2\,c^2\,d-a^2\,b^3\,c^3\right)}+\frac{x\,\sqrt{-c\,d^3}\,\left(16\,a^7\,b^2\,d^7-48\,a^6\,b^3\,c\,d^6+32\,a^5\,b^4\,c^2\,d^5+32\,a^4\,b^5\,c^3\,d^4-48\,a^3\,b^6\,c^4\,d^3+16\,a^2\,b^7\,c^5\,d^2\right)}{8\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)\,\left(a^2\,c\,d^2-2\,a\,b\,c^2\,d+b^2\,c^3\right)}\right)\,\sqrt{-c\,d^3}}{2\,\left(a^2\,c\,d^2-2\,a\,b\,c^2\,d+b^2\,c^3\right)}+\frac{x\,\left(13\,a^2\,b^3\,d^5-6\,a\,b^4\,c\,d^4+b^5\,c^2\,d^3\right)}{4\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}\right)\,1{}\mathrm{i}}{a^2\,c\,d^2-2\,a\,b\,c^2\,d+b^2\,c^3}}{\frac{\frac{3\,a\,b^3\,d^5}{2}-\frac{b^4\,c\,d^4}{2}}{a^5\,d^3-3\,a^4\,b\,c\,d^2+3\,a^3\,b^2\,c^2\,d-a^2\,b^3\,c^3}+\frac{\sqrt{-c\,d^3}\,\left(\frac{\left(\frac{4\,a^6\,b^2\,d^7-18\,a^5\,b^3\,c\,d^6+32\,a^4\,b^4\,c^2\,d^5-28\,a^3\,b^5\,c^3\,d^4+12\,a^2\,b^6\,c^4\,d^3-2\,a\,b^7\,c^5\,d^2}{2\,\left(a^5\,d^3-3\,a^4\,b\,c\,d^2+3\,a^3\,b^2\,c^2\,d-a^2\,b^3\,c^3\right)}-\frac{x\,\sqrt{-c\,d^3}\,\left(16\,a^7\,b^2\,d^7-48\,a^6\,b^3\,c\,d^6+32\,a^5\,b^4\,c^2\,d^5+32\,a^4\,b^5\,c^3\,d^4-48\,a^3\,b^6\,c^4\,d^3+16\,a^2\,b^7\,c^5\,d^2\right)}{8\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)\,\left(a^2\,c\,d^2-2\,a\,b\,c^2\,d+b^2\,c^3\right)}\right)\,\sqrt{-c\,d^3}}{2\,\left(a^2\,c\,d^2-2\,a\,b\,c^2\,d+b^2\,c^3\right)}-\frac{x\,\left(13\,a^2\,b^3\,d^5-6\,a\,b^4\,c\,d^4+b^5\,c^2\,d^3\right)}{4\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}\right)}{a^2\,c\,d^2-2\,a\,b\,c^2\,d+b^2\,c^3}+\frac{\sqrt{-c\,d^3}\,\left(\frac{\left(\frac{4\,a^6\,b^2\,d^7-18\,a^5\,b^3\,c\,d^6+32\,a^4\,b^4\,c^2\,d^5-28\,a^3\,b^5\,c^3\,d^4+12\,a^2\,b^6\,c^4\,d^3-2\,a\,b^7\,c^5\,d^2}{2\,\left(a^5\,d^3-3\,a^4\,b\,c\,d^2+3\,a^3\,b^2\,c^2\,d-a^2\,b^3\,c^3\right)}+\frac{x\,\sqrt{-c\,d^3}\,\left(16\,a^7\,b^2\,d^7-48\,a^6\,b^3\,c\,d^6+32\,a^5\,b^4\,c^2\,d^5+32\,a^4\,b^5\,c^3\,d^4-48\,a^3\,b^6\,c^4\,d^3+16\,a^2\,b^7\,c^5\,d^2\right)}{8\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)\,\left(a^2\,c\,d^2-2\,a\,b\,c^2\,d+b^2\,c^3\right)}\right)\,\sqrt{-c\,d^3}}{2\,\left(a^2\,c\,d^2-2\,a\,b\,c^2\,d+b^2\,c^3\right)}+\frac{x\,\left(13\,a^2\,b^3\,d^5-6\,a\,b^4\,c\,d^4+b^5\,c^2\,d^3\right)}{4\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}\right)}{a^2\,c\,d^2-2\,a\,b\,c^2\,d+b^2\,c^3}}\right)\,\sqrt{-c\,d^3}\,1{}\mathrm{i}}{a^2\,c\,d^2-2\,a\,b\,c^2\,d+b^2\,c^3}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-a^3\,b}\,\left(3\,a\,d-b\,c\right)\,\left(\frac{x\,\left(13\,a^2\,b^3\,d^5-6\,a\,b^4\,c\,d^4+b^5\,c^2\,d^3\right)}{2\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}-\frac{\left(\frac{4\,a^6\,b^2\,d^7-18\,a^5\,b^3\,c\,d^6+32\,a^4\,b^4\,c^2\,d^5-28\,a^3\,b^5\,c^3\,d^4+12\,a^2\,b^6\,c^4\,d^3-2\,a\,b^7\,c^5\,d^2}{a^5\,d^3-3\,a^4\,b\,c\,d^2+3\,a^3\,b^2\,c^2\,d-a^2\,b^3\,c^3}-\frac{x\,\sqrt{-a^3\,b}\,\left(3\,a\,d-b\,c\right)\,\left(16\,a^7\,b^2\,d^7-48\,a^6\,b^3\,c\,d^6+32\,a^5\,b^4\,c^2\,d^5+32\,a^4\,b^5\,c^3\,d^4-48\,a^3\,b^6\,c^4\,d^3+16\,a^2\,b^7\,c^5\,d^2\right)}{8\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)\,\left(a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2\right)}\right)\,\sqrt{-a^3\,b}\,\left(3\,a\,d-b\,c\right)}{4\,\left(a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2\right)}\right)\,1{}\mathrm{i}}{4\,\left(a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2\right)}+\frac{\sqrt{-a^3\,b}\,\left(3\,a\,d-b\,c\right)\,\left(\frac{x\,\left(13\,a^2\,b^3\,d^5-6\,a\,b^4\,c\,d^4+b^5\,c^2\,d^3\right)}{2\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}+\frac{\left(\frac{4\,a^6\,b^2\,d^7-18\,a^5\,b^3\,c\,d^6+32\,a^4\,b^4\,c^2\,d^5-28\,a^3\,b^5\,c^3\,d^4+12\,a^2\,b^6\,c^4\,d^3-2\,a\,b^7\,c^5\,d^2}{a^5\,d^3-3\,a^4\,b\,c\,d^2+3\,a^3\,b^2\,c^2\,d-a^2\,b^3\,c^3}+\frac{x\,\sqrt{-a^3\,b}\,\left(3\,a\,d-b\,c\right)\,\left(16\,a^7\,b^2\,d^7-48\,a^6\,b^3\,c\,d^6+32\,a^5\,b^4\,c^2\,d^5+32\,a^4\,b^5\,c^3\,d^4-48\,a^3\,b^6\,c^4\,d^3+16\,a^2\,b^7\,c^5\,d^2\right)}{8\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)\,\left(a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2\right)}\right)\,\sqrt{-a^3\,b}\,\left(3\,a\,d-b\,c\right)}{4\,\left(a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2\right)}\right)\,1{}\mathrm{i}}{4\,\left(a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2\right)}}{\frac{\frac{3\,a\,b^3\,d^5}{2}-\frac{b^4\,c\,d^4}{2}}{a^5\,d^3-3\,a^4\,b\,c\,d^2+3\,a^3\,b^2\,c^2\,d-a^2\,b^3\,c^3}-\frac{\sqrt{-a^3\,b}\,\left(3\,a\,d-b\,c\right)\,\left(\frac{x\,\left(13\,a^2\,b^3\,d^5-6\,a\,b^4\,c\,d^4+b^5\,c^2\,d^3\right)}{2\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}-\frac{\left(\frac{4\,a^6\,b^2\,d^7-18\,a^5\,b^3\,c\,d^6+32\,a^4\,b^4\,c^2\,d^5-28\,a^3\,b^5\,c^3\,d^4+12\,a^2\,b^6\,c^4\,d^3-2\,a\,b^7\,c^5\,d^2}{a^5\,d^3-3\,a^4\,b\,c\,d^2+3\,a^3\,b^2\,c^2\,d-a^2\,b^3\,c^3}-\frac{x\,\sqrt{-a^3\,b}\,\left(3\,a\,d-b\,c\right)\,\left(16\,a^7\,b^2\,d^7-48\,a^6\,b^3\,c\,d^6+32\,a^5\,b^4\,c^2\,d^5+32\,a^4\,b^5\,c^3\,d^4-48\,a^3\,b^6\,c^4\,d^3+16\,a^2\,b^7\,c^5\,d^2\right)}{8\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)\,\left(a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2\right)}\right)\,\sqrt{-a^3\,b}\,\left(3\,a\,d-b\,c\right)}{4\,\left(a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2\right)}\right)}{4\,\left(a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2\right)}+\frac{\sqrt{-a^3\,b}\,\left(3\,a\,d-b\,c\right)\,\left(\frac{x\,\left(13\,a^2\,b^3\,d^5-6\,a\,b^4\,c\,d^4+b^5\,c^2\,d^3\right)}{2\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}+\frac{\left(\frac{4\,a^6\,b^2\,d^7-18\,a^5\,b^3\,c\,d^6+32\,a^4\,b^4\,c^2\,d^5-28\,a^3\,b^5\,c^3\,d^4+12\,a^2\,b^6\,c^4\,d^3-2\,a\,b^7\,c^5\,d^2}{a^5\,d^3-3\,a^4\,b\,c\,d^2+3\,a^3\,b^2\,c^2\,d-a^2\,b^3\,c^3}+\frac{x\,\sqrt{-a^3\,b}\,\left(3\,a\,d-b\,c\right)\,\left(16\,a^7\,b^2\,d^7-48\,a^6\,b^3\,c\,d^6+32\,a^5\,b^4\,c^2\,d^5+32\,a^4\,b^5\,c^3\,d^4-48\,a^3\,b^6\,c^4\,d^3+16\,a^2\,b^7\,c^5\,d^2\right)}{8\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)\,\left(a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2\right)}\right)\,\sqrt{-a^3\,b}\,\left(3\,a\,d-b\,c\right)}{4\,\left(a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2\right)}\right)}{4\,\left(a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2\right)}}\right)\,\sqrt{-a^3\,b}\,\left(3\,a\,d-b\,c\right)\,1{}\mathrm{i}}{2\,\left(a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2\right)}","Not used",1,"(atan((((-a^3*b)^(1/2)*(3*a*d - b*c)*((x*(13*a^2*b^3*d^5 + b^5*c^2*d^3 - 6*a*b^4*c*d^4))/(2*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)) - (((4*a^6*b^2*d^7 - 2*a*b^7*c^5*d^2 - 18*a^5*b^3*c*d^6 + 12*a^2*b^6*c^4*d^3 - 28*a^3*b^5*c^3*d^4 + 32*a^4*b^4*c^2*d^5)/(a^5*d^3 - a^2*b^3*c^3 + 3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2) - (x*(-a^3*b)^(1/2)*(3*a*d - b*c)*(16*a^7*b^2*d^7 - 48*a^6*b^3*c*d^6 + 16*a^2*b^7*c^5*d^2 - 48*a^3*b^6*c^4*d^3 + 32*a^4*b^5*c^3*d^4 + 32*a^5*b^4*c^2*d^5))/(8*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)*(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d)))*(-a^3*b)^(1/2)*(3*a*d - b*c))/(4*(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d)))*1i)/(4*(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d)) + ((-a^3*b)^(1/2)*(3*a*d - b*c)*((x*(13*a^2*b^3*d^5 + b^5*c^2*d^3 - 6*a*b^4*c*d^4))/(2*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)) + (((4*a^6*b^2*d^7 - 2*a*b^7*c^5*d^2 - 18*a^5*b^3*c*d^6 + 12*a^2*b^6*c^4*d^3 - 28*a^3*b^5*c^3*d^4 + 32*a^4*b^4*c^2*d^5)/(a^5*d^3 - a^2*b^3*c^3 + 3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2) + (x*(-a^3*b)^(1/2)*(3*a*d - b*c)*(16*a^7*b^2*d^7 - 48*a^6*b^3*c*d^6 + 16*a^2*b^7*c^5*d^2 - 48*a^3*b^6*c^4*d^3 + 32*a^4*b^5*c^3*d^4 + 32*a^5*b^4*c^2*d^5))/(8*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)*(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d)))*(-a^3*b)^(1/2)*(3*a*d - b*c))/(4*(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d)))*1i)/(4*(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d)))/(((3*a*b^3*d^5)/2 - (b^4*c*d^4)/2)/(a^5*d^3 - a^2*b^3*c^3 + 3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2) - ((-a^3*b)^(1/2)*(3*a*d - b*c)*((x*(13*a^2*b^3*d^5 + b^5*c^2*d^3 - 6*a*b^4*c*d^4))/(2*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)) - (((4*a^6*b^2*d^7 - 2*a*b^7*c^5*d^2 - 18*a^5*b^3*c*d^6 + 12*a^2*b^6*c^4*d^3 - 28*a^3*b^5*c^3*d^4 + 32*a^4*b^4*c^2*d^5)/(a^5*d^3 - a^2*b^3*c^3 + 3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2) - (x*(-a^3*b)^(1/2)*(3*a*d - b*c)*(16*a^7*b^2*d^7 - 48*a^6*b^3*c*d^6 + 16*a^2*b^7*c^5*d^2 - 48*a^3*b^6*c^4*d^3 + 32*a^4*b^5*c^3*d^4 + 32*a^5*b^4*c^2*d^5))/(8*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)*(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d)))*(-a^3*b)^(1/2)*(3*a*d - b*c))/(4*(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d))))/(4*(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d)) + ((-a^3*b)^(1/2)*(3*a*d - b*c)*((x*(13*a^2*b^3*d^5 + b^5*c^2*d^3 - 6*a*b^4*c*d^4))/(2*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)) + (((4*a^6*b^2*d^7 - 2*a*b^7*c^5*d^2 - 18*a^5*b^3*c*d^6 + 12*a^2*b^6*c^4*d^3 - 28*a^3*b^5*c^3*d^4 + 32*a^4*b^4*c^2*d^5)/(a^5*d^3 - a^2*b^3*c^3 + 3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2) + (x*(-a^3*b)^(1/2)*(3*a*d - b*c)*(16*a^7*b^2*d^7 - 48*a^6*b^3*c*d^6 + 16*a^2*b^7*c^5*d^2 - 48*a^3*b^6*c^4*d^3 + 32*a^4*b^5*c^3*d^4 + 32*a^5*b^4*c^2*d^5))/(8*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)*(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d)))*(-a^3*b)^(1/2)*(3*a*d - b*c))/(4*(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d))))/(4*(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d))))*(-a^3*b)^(1/2)*(3*a*d - b*c)*1i)/(2*(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d)) - (atan((((-c*d^3)^(1/2)*((((4*a^6*b^2*d^7 - 2*a*b^7*c^5*d^2 - 18*a^5*b^3*c*d^6 + 12*a^2*b^6*c^4*d^3 - 28*a^3*b^5*c^3*d^4 + 32*a^4*b^4*c^2*d^5)/(2*(a^5*d^3 - a^2*b^3*c^3 + 3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2)) - (x*(-c*d^3)^(1/2)*(16*a^7*b^2*d^7 - 48*a^6*b^3*c*d^6 + 16*a^2*b^7*c^5*d^2 - 48*a^3*b^6*c^4*d^3 + 32*a^4*b^5*c^3*d^4 + 32*a^5*b^4*c^2*d^5))/(8*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)*(b^2*c^3 + a^2*c*d^2 - 2*a*b*c^2*d)))*(-c*d^3)^(1/2))/(2*(b^2*c^3 + a^2*c*d^2 - 2*a*b*c^2*d)) - (x*(13*a^2*b^3*d^5 + b^5*c^2*d^3 - 6*a*b^4*c*d^4))/(4*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)))*1i)/(b^2*c^3 + a^2*c*d^2 - 2*a*b*c^2*d) - ((-c*d^3)^(1/2)*((((4*a^6*b^2*d^7 - 2*a*b^7*c^5*d^2 - 18*a^5*b^3*c*d^6 + 12*a^2*b^6*c^4*d^3 - 28*a^3*b^5*c^3*d^4 + 32*a^4*b^4*c^2*d^5)/(2*(a^5*d^3 - a^2*b^3*c^3 + 3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2)) + (x*(-c*d^3)^(1/2)*(16*a^7*b^2*d^7 - 48*a^6*b^3*c*d^6 + 16*a^2*b^7*c^5*d^2 - 48*a^3*b^6*c^4*d^3 + 32*a^4*b^5*c^3*d^4 + 32*a^5*b^4*c^2*d^5))/(8*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)*(b^2*c^3 + a^2*c*d^2 - 2*a*b*c^2*d)))*(-c*d^3)^(1/2))/(2*(b^2*c^3 + a^2*c*d^2 - 2*a*b*c^2*d)) + (x*(13*a^2*b^3*d^5 + b^5*c^2*d^3 - 6*a*b^4*c*d^4))/(4*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)))*1i)/(b^2*c^3 + a^2*c*d^2 - 2*a*b*c^2*d))/(((3*a*b^3*d^5)/2 - (b^4*c*d^4)/2)/(a^5*d^3 - a^2*b^3*c^3 + 3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2) + ((-c*d^3)^(1/2)*((((4*a^6*b^2*d^7 - 2*a*b^7*c^5*d^2 - 18*a^5*b^3*c*d^6 + 12*a^2*b^6*c^4*d^3 - 28*a^3*b^5*c^3*d^4 + 32*a^4*b^4*c^2*d^5)/(2*(a^5*d^3 - a^2*b^3*c^3 + 3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2)) - (x*(-c*d^3)^(1/2)*(16*a^7*b^2*d^7 - 48*a^6*b^3*c*d^6 + 16*a^2*b^7*c^5*d^2 - 48*a^3*b^6*c^4*d^3 + 32*a^4*b^5*c^3*d^4 + 32*a^5*b^4*c^2*d^5))/(8*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)*(b^2*c^3 + a^2*c*d^2 - 2*a*b*c^2*d)))*(-c*d^3)^(1/2))/(2*(b^2*c^3 + a^2*c*d^2 - 2*a*b*c^2*d)) - (x*(13*a^2*b^3*d^5 + b^5*c^2*d^3 - 6*a*b^4*c*d^4))/(4*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d))))/(b^2*c^3 + a^2*c*d^2 - 2*a*b*c^2*d) + ((-c*d^3)^(1/2)*((((4*a^6*b^2*d^7 - 2*a*b^7*c^5*d^2 - 18*a^5*b^3*c*d^6 + 12*a^2*b^6*c^4*d^3 - 28*a^3*b^5*c^3*d^4 + 32*a^4*b^4*c^2*d^5)/(2*(a^5*d^3 - a^2*b^3*c^3 + 3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2)) + (x*(-c*d^3)^(1/2)*(16*a^7*b^2*d^7 - 48*a^6*b^3*c*d^6 + 16*a^2*b^7*c^5*d^2 - 48*a^3*b^6*c^4*d^3 + 32*a^4*b^5*c^3*d^4 + 32*a^5*b^4*c^2*d^5))/(8*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)*(b^2*c^3 + a^2*c*d^2 - 2*a*b*c^2*d)))*(-c*d^3)^(1/2))/(2*(b^2*c^3 + a^2*c*d^2 - 2*a*b*c^2*d)) + (x*(13*a^2*b^3*d^5 + b^5*c^2*d^3 - 6*a*b^4*c*d^4))/(4*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d))))/(b^2*c^3 + a^2*c*d^2 - 2*a*b*c^2*d)))*(-c*d^3)^(1/2)*1i)/(b^2*c^3 + a^2*c*d^2 - 2*a*b*c^2*d) - (b*x)/(2*a*(a + b*x^2)*(a*d - b*c))","B"
294,1,127,99,0.733758,"\text{Not used}","int(1/(x*(a + b*x^2)^2*(c + d*x^2)),x)","\frac{\ln\left(x\right)}{a^2\,c}-\frac{d^2\,\ln\left(d\,x^2+c\right)}{2\,a^2\,c\,d^2-4\,a\,b\,c^2\,d+2\,b^2\,c^3}-\frac{\ln\left(b\,x^2+a\right)\,\left(b^2\,c-2\,a\,b\,d\right)}{2\,a^4\,d^2-4\,a^3\,b\,c\,d+2\,a^2\,b^2\,c^2}-\frac{b}{2\,a\,\left(b\,x^2+a\right)\,\left(a\,d-b\,c\right)}","Not used",1,"log(x)/(a^2*c) - (d^2*log(c + d*x^2))/(2*b^2*c^3 + 2*a^2*c*d^2 - 4*a*b*c^2*d) - (log(a + b*x^2)*(b^2*c - 2*a*b*d))/(2*a^4*d^2 + 2*a^2*b^2*c^2 - 4*a^3*b*c*d) - b/(2*a*(a + b*x^2)*(a*d - b*c))","B"
295,1,2400,144,1.001012,"\text{Not used}","int(1/(x^2*(a + b*x^2)^2*(c + d*x^2)),x)","-\frac{\frac{1}{a\,c}-\frac{x^2\,\left(3\,b^2\,c-2\,a\,b\,d\right)}{2\,a^2\,c\,\left(a\,d-b\,c\right)}}{b\,x^3+a\,x}+\frac{\mathrm{atan}\left(\frac{a^5\,d\,x\,{\left(-c^3\,d^5\right)}^{3/2}\,4{}\mathrm{i}+b^5\,c^8\,d\,x\,\sqrt{-c^3\,d^5}\,9{}\mathrm{i}+a^2\,b^3\,c^6\,d^3\,x\,\sqrt{-c^3\,d^5}\,25{}\mathrm{i}-a\,b^4\,c^7\,d^2\,x\,\sqrt{-c^3\,d^5}\,30{}\mathrm{i}}{4\,a^5\,c^5\,d^8-25\,a^2\,b^3\,c^8\,d^5+30\,a\,b^4\,c^9\,d^4-9\,b^5\,c^{10}\,d^3}\right)\,\sqrt{-c^3\,d^5}\,1{}\mathrm{i}}{a^2\,c^3\,d^2-2\,a\,b\,c^4\,d+b^2\,c^5}-\frac{\mathrm{atan}\left(\frac{\frac{\left(x\,\left(-64\,a^{13}\,b^3\,c^3\,d^{10}+192\,a^{12}\,b^4\,c^4\,d^9-592\,a^{11}\,b^5\,c^5\,d^8+1744\,a^{10}\,b^6\,c^6\,d^7-2784\,a^9\,b^7\,c^7\,d^6+2272\,a^8\,b^8\,c^8\,d^5-912\,a^7\,b^9\,c^9\,d^4+144\,a^6\,b^{10}\,c^{10}\,d^3\right)+\frac{\left(5\,a\,d-3\,b\,c\right)\,\sqrt{-a^5\,b^3}\,\left(1280\,a^9\,b^9\,c^{11}\,d^3-192\,a^8\,b^{10}\,c^{12}\,d^2-3520\,a^{10}\,b^8\,c^{10}\,d^4+4992\,a^{11}\,b^7\,c^9\,d^5-3520\,a^{12}\,b^6\,c^8\,d^6+512\,a^{13}\,b^5\,c^7\,d^7+960\,a^{14}\,b^4\,c^6\,d^8-640\,a^{15}\,b^3\,c^5\,d^9+128\,a^{16}\,b^2\,c^4\,d^{10}+\frac{x\,\left(5\,a\,d-3\,b\,c\right)\,\sqrt{-a^5\,b^3}\,\left(-256\,a^{18}\,b^2\,c^5\,d^{10}+1536\,a^{17}\,b^3\,c^6\,d^9-3584\,a^{16}\,b^4\,c^7\,d^8+3584\,a^{15}\,b^5\,c^8\,d^7-3584\,a^{13}\,b^7\,c^{10}\,d^5+3584\,a^{12}\,b^8\,c^{11}\,d^4-1536\,a^{11}\,b^9\,c^{12}\,d^3+256\,a^{10}\,b^{10}\,c^{13}\,d^2\right)}{4\,\left(a^7\,d^2-2\,a^6\,b\,c\,d+a^5\,b^2\,c^2\right)}\right)}{4\,\left(a^7\,d^2-2\,a^6\,b\,c\,d+a^5\,b^2\,c^2\right)}\right)\,\left(5\,a\,d-3\,b\,c\right)\,\sqrt{-a^5\,b^3}\,1{}\mathrm{i}}{4\,\left(a^7\,d^2-2\,a^6\,b\,c\,d+a^5\,b^2\,c^2\right)}+\frac{\left(x\,\left(-64\,a^{13}\,b^3\,c^3\,d^{10}+192\,a^{12}\,b^4\,c^4\,d^9-592\,a^{11}\,b^5\,c^5\,d^8+1744\,a^{10}\,b^6\,c^6\,d^7-2784\,a^9\,b^7\,c^7\,d^6+2272\,a^8\,b^8\,c^8\,d^5-912\,a^7\,b^9\,c^9\,d^4+144\,a^6\,b^{10}\,c^{10}\,d^3\right)+\frac{\left(5\,a\,d-3\,b\,c\right)\,\sqrt{-a^5\,b^3}\,\left(192\,a^8\,b^{10}\,c^{12}\,d^2-1280\,a^9\,b^9\,c^{11}\,d^3+3520\,a^{10}\,b^8\,c^{10}\,d^4-4992\,a^{11}\,b^7\,c^9\,d^5+3520\,a^{12}\,b^6\,c^8\,d^6-512\,a^{13}\,b^5\,c^7\,d^7-960\,a^{14}\,b^4\,c^6\,d^8+640\,a^{15}\,b^3\,c^5\,d^9-128\,a^{16}\,b^2\,c^4\,d^{10}+\frac{x\,\left(5\,a\,d-3\,b\,c\right)\,\sqrt{-a^5\,b^3}\,\left(-256\,a^{18}\,b^2\,c^5\,d^{10}+1536\,a^{17}\,b^3\,c^6\,d^9-3584\,a^{16}\,b^4\,c^7\,d^8+3584\,a^{15}\,b^5\,c^8\,d^7-3584\,a^{13}\,b^7\,c^{10}\,d^5+3584\,a^{12}\,b^8\,c^{11}\,d^4-1536\,a^{11}\,b^9\,c^{12}\,d^3+256\,a^{10}\,b^{10}\,c^{13}\,d^2\right)}{4\,\left(a^7\,d^2-2\,a^6\,b\,c\,d+a^5\,b^2\,c^2\right)}\right)}{4\,\left(a^7\,d^2-2\,a^6\,b\,c\,d+a^5\,b^2\,c^2\right)}\right)\,\left(5\,a\,d-3\,b\,c\right)\,\sqrt{-a^5\,b^3}\,1{}\mathrm{i}}{4\,\left(a^7\,d^2-2\,a^6\,b\,c\,d+a^5\,b^2\,c^2\right)}}{\frac{\left(x\,\left(-64\,a^{13}\,b^3\,c^3\,d^{10}+192\,a^{12}\,b^4\,c^4\,d^9-592\,a^{11}\,b^5\,c^5\,d^8+1744\,a^{10}\,b^6\,c^6\,d^7-2784\,a^9\,b^7\,c^7\,d^6+2272\,a^8\,b^8\,c^8\,d^5-912\,a^7\,b^9\,c^9\,d^4+144\,a^6\,b^{10}\,c^{10}\,d^3\right)+\frac{\left(5\,a\,d-3\,b\,c\right)\,\sqrt{-a^5\,b^3}\,\left(192\,a^8\,b^{10}\,c^{12}\,d^2-1280\,a^9\,b^9\,c^{11}\,d^3+3520\,a^{10}\,b^8\,c^{10}\,d^4-4992\,a^{11}\,b^7\,c^9\,d^5+3520\,a^{12}\,b^6\,c^8\,d^6-512\,a^{13}\,b^5\,c^7\,d^7-960\,a^{14}\,b^4\,c^6\,d^8+640\,a^{15}\,b^3\,c^5\,d^9-128\,a^{16}\,b^2\,c^4\,d^{10}+\frac{x\,\left(5\,a\,d-3\,b\,c\right)\,\sqrt{-a^5\,b^3}\,\left(-256\,a^{18}\,b^2\,c^5\,d^{10}+1536\,a^{17}\,b^3\,c^6\,d^9-3584\,a^{16}\,b^4\,c^7\,d^8+3584\,a^{15}\,b^5\,c^8\,d^7-3584\,a^{13}\,b^7\,c^{10}\,d^5+3584\,a^{12}\,b^8\,c^{11}\,d^4-1536\,a^{11}\,b^9\,c^{12}\,d^3+256\,a^{10}\,b^{10}\,c^{13}\,d^2\right)}{4\,\left(a^7\,d^2-2\,a^6\,b\,c\,d+a^5\,b^2\,c^2\right)}\right)}{4\,\left(a^7\,d^2-2\,a^6\,b\,c\,d+a^5\,b^2\,c^2\right)}\right)\,\left(5\,a\,d-3\,b\,c\right)\,\sqrt{-a^5\,b^3}}{4\,\left(a^7\,d^2-2\,a^6\,b\,c\,d+a^5\,b^2\,c^2\right)}-\frac{\left(x\,\left(-64\,a^{13}\,b^3\,c^3\,d^{10}+192\,a^{12}\,b^4\,c^4\,d^9-592\,a^{11}\,b^5\,c^5\,d^8+1744\,a^{10}\,b^6\,c^6\,d^7-2784\,a^9\,b^7\,c^7\,d^6+2272\,a^8\,b^8\,c^8\,d^5-912\,a^7\,b^9\,c^9\,d^4+144\,a^6\,b^{10}\,c^{10}\,d^3\right)+\frac{\left(5\,a\,d-3\,b\,c\right)\,\sqrt{-a^5\,b^3}\,\left(1280\,a^9\,b^9\,c^{11}\,d^3-192\,a^8\,b^{10}\,c^{12}\,d^2-3520\,a^{10}\,b^8\,c^{10}\,d^4+4992\,a^{11}\,b^7\,c^9\,d^5-3520\,a^{12}\,b^6\,c^8\,d^6+512\,a^{13}\,b^5\,c^7\,d^7+960\,a^{14}\,b^4\,c^6\,d^8-640\,a^{15}\,b^3\,c^5\,d^9+128\,a^{16}\,b^2\,c^4\,d^{10}+\frac{x\,\left(5\,a\,d-3\,b\,c\right)\,\sqrt{-a^5\,b^3}\,\left(-256\,a^{18}\,b^2\,c^5\,d^{10}+1536\,a^{17}\,b^3\,c^6\,d^9-3584\,a^{16}\,b^4\,c^7\,d^8+3584\,a^{15}\,b^5\,c^8\,d^7-3584\,a^{13}\,b^7\,c^{10}\,d^5+3584\,a^{12}\,b^8\,c^{11}\,d^4-1536\,a^{11}\,b^9\,c^{12}\,d^3+256\,a^{10}\,b^{10}\,c^{13}\,d^2\right)}{4\,\left(a^7\,d^2-2\,a^6\,b\,c\,d+a^5\,b^2\,c^2\right)}\right)}{4\,\left(a^7\,d^2-2\,a^6\,b\,c\,d+a^5\,b^2\,c^2\right)}\right)\,\left(5\,a\,d-3\,b\,c\right)\,\sqrt{-a^5\,b^3}}{4\,\left(a^7\,d^2-2\,a^6\,b\,c\,d+a^5\,b^2\,c^2\right)}+144\,a^6\,b^8\,c^7\,d^5-624\,a^7\,b^7\,c^6\,d^6+976\,a^8\,b^6\,c^5\,d^7-656\,a^9\,b^5\,c^4\,d^8+160\,a^{10}\,b^4\,c^3\,d^9}\right)\,\left(5\,a\,d-3\,b\,c\right)\,\sqrt{-a^5\,b^3}\,1{}\mathrm{i}}{2\,\left(a^7\,d^2-2\,a^6\,b\,c\,d+a^5\,b^2\,c^2\right)}","Not used",1,"(atan((a^5*d*x*(-c^3*d^5)^(3/2)*4i + b^5*c^8*d*x*(-c^3*d^5)^(1/2)*9i + a^2*b^3*c^6*d^3*x*(-c^3*d^5)^(1/2)*25i - a*b^4*c^7*d^2*x*(-c^3*d^5)^(1/2)*30i)/(4*a^5*c^5*d^8 - 9*b^5*c^10*d^3 + 30*a*b^4*c^9*d^4 - 25*a^2*b^3*c^8*d^5))*(-c^3*d^5)^(1/2)*1i)/(b^2*c^5 + a^2*c^3*d^2 - 2*a*b*c^4*d) - (1/(a*c) - (x^2*(3*b^2*c - 2*a*b*d))/(2*a^2*c*(a*d - b*c)))/(a*x + b*x^3) - (atan((((x*(144*a^6*b^10*c^10*d^3 - 912*a^7*b^9*c^9*d^4 + 2272*a^8*b^8*c^8*d^5 - 2784*a^9*b^7*c^7*d^6 + 1744*a^10*b^6*c^6*d^7 - 592*a^11*b^5*c^5*d^8 + 192*a^12*b^4*c^4*d^9 - 64*a^13*b^3*c^3*d^10) + ((5*a*d - 3*b*c)*(-a^5*b^3)^(1/2)*(1280*a^9*b^9*c^11*d^3 - 192*a^8*b^10*c^12*d^2 - 3520*a^10*b^8*c^10*d^4 + 4992*a^11*b^7*c^9*d^5 - 3520*a^12*b^6*c^8*d^6 + 512*a^13*b^5*c^7*d^7 + 960*a^14*b^4*c^6*d^8 - 640*a^15*b^3*c^5*d^9 + 128*a^16*b^2*c^4*d^10 + (x*(5*a*d - 3*b*c)*(-a^5*b^3)^(1/2)*(256*a^10*b^10*c^13*d^2 - 1536*a^11*b^9*c^12*d^3 + 3584*a^12*b^8*c^11*d^4 - 3584*a^13*b^7*c^10*d^5 + 3584*a^15*b^5*c^8*d^7 - 3584*a^16*b^4*c^7*d^8 + 1536*a^17*b^3*c^6*d^9 - 256*a^18*b^2*c^5*d^10))/(4*(a^7*d^2 + a^5*b^2*c^2 - 2*a^6*b*c*d))))/(4*(a^7*d^2 + a^5*b^2*c^2 - 2*a^6*b*c*d)))*(5*a*d - 3*b*c)*(-a^5*b^3)^(1/2)*1i)/(4*(a^7*d^2 + a^5*b^2*c^2 - 2*a^6*b*c*d)) + ((x*(144*a^6*b^10*c^10*d^3 - 912*a^7*b^9*c^9*d^4 + 2272*a^8*b^8*c^8*d^5 - 2784*a^9*b^7*c^7*d^6 + 1744*a^10*b^6*c^6*d^7 - 592*a^11*b^5*c^5*d^8 + 192*a^12*b^4*c^4*d^9 - 64*a^13*b^3*c^3*d^10) + ((5*a*d - 3*b*c)*(-a^5*b^3)^(1/2)*(192*a^8*b^10*c^12*d^2 - 1280*a^9*b^9*c^11*d^3 + 3520*a^10*b^8*c^10*d^4 - 4992*a^11*b^7*c^9*d^5 + 3520*a^12*b^6*c^8*d^6 - 512*a^13*b^5*c^7*d^7 - 960*a^14*b^4*c^6*d^8 + 640*a^15*b^3*c^5*d^9 - 128*a^16*b^2*c^4*d^10 + (x*(5*a*d - 3*b*c)*(-a^5*b^3)^(1/2)*(256*a^10*b^10*c^13*d^2 - 1536*a^11*b^9*c^12*d^3 + 3584*a^12*b^8*c^11*d^4 - 3584*a^13*b^7*c^10*d^5 + 3584*a^15*b^5*c^8*d^7 - 3584*a^16*b^4*c^7*d^8 + 1536*a^17*b^3*c^6*d^9 - 256*a^18*b^2*c^5*d^10))/(4*(a^7*d^2 + a^5*b^2*c^2 - 2*a^6*b*c*d))))/(4*(a^7*d^2 + a^5*b^2*c^2 - 2*a^6*b*c*d)))*(5*a*d - 3*b*c)*(-a^5*b^3)^(1/2)*1i)/(4*(a^7*d^2 + a^5*b^2*c^2 - 2*a^6*b*c*d)))/(((x*(144*a^6*b^10*c^10*d^3 - 912*a^7*b^9*c^9*d^4 + 2272*a^8*b^8*c^8*d^5 - 2784*a^9*b^7*c^7*d^6 + 1744*a^10*b^6*c^6*d^7 - 592*a^11*b^5*c^5*d^8 + 192*a^12*b^4*c^4*d^9 - 64*a^13*b^3*c^3*d^10) + ((5*a*d - 3*b*c)*(-a^5*b^3)^(1/2)*(192*a^8*b^10*c^12*d^2 - 1280*a^9*b^9*c^11*d^3 + 3520*a^10*b^8*c^10*d^4 - 4992*a^11*b^7*c^9*d^5 + 3520*a^12*b^6*c^8*d^6 - 512*a^13*b^5*c^7*d^7 - 960*a^14*b^4*c^6*d^8 + 640*a^15*b^3*c^5*d^9 - 128*a^16*b^2*c^4*d^10 + (x*(5*a*d - 3*b*c)*(-a^5*b^3)^(1/2)*(256*a^10*b^10*c^13*d^2 - 1536*a^11*b^9*c^12*d^3 + 3584*a^12*b^8*c^11*d^4 - 3584*a^13*b^7*c^10*d^5 + 3584*a^15*b^5*c^8*d^7 - 3584*a^16*b^4*c^7*d^8 + 1536*a^17*b^3*c^6*d^9 - 256*a^18*b^2*c^5*d^10))/(4*(a^7*d^2 + a^5*b^2*c^2 - 2*a^6*b*c*d))))/(4*(a^7*d^2 + a^5*b^2*c^2 - 2*a^6*b*c*d)))*(5*a*d - 3*b*c)*(-a^5*b^3)^(1/2))/(4*(a^7*d^2 + a^5*b^2*c^2 - 2*a^6*b*c*d)) - ((x*(144*a^6*b^10*c^10*d^3 - 912*a^7*b^9*c^9*d^4 + 2272*a^8*b^8*c^8*d^5 - 2784*a^9*b^7*c^7*d^6 + 1744*a^10*b^6*c^6*d^7 - 592*a^11*b^5*c^5*d^8 + 192*a^12*b^4*c^4*d^9 - 64*a^13*b^3*c^3*d^10) + ((5*a*d - 3*b*c)*(-a^5*b^3)^(1/2)*(1280*a^9*b^9*c^11*d^3 - 192*a^8*b^10*c^12*d^2 - 3520*a^10*b^8*c^10*d^4 + 4992*a^11*b^7*c^9*d^5 - 3520*a^12*b^6*c^8*d^6 + 512*a^13*b^5*c^7*d^7 + 960*a^14*b^4*c^6*d^8 - 640*a^15*b^3*c^5*d^9 + 128*a^16*b^2*c^4*d^10 + (x*(5*a*d - 3*b*c)*(-a^5*b^3)^(1/2)*(256*a^10*b^10*c^13*d^2 - 1536*a^11*b^9*c^12*d^3 + 3584*a^12*b^8*c^11*d^4 - 3584*a^13*b^7*c^10*d^5 + 3584*a^15*b^5*c^8*d^7 - 3584*a^16*b^4*c^7*d^8 + 1536*a^17*b^3*c^6*d^9 - 256*a^18*b^2*c^5*d^10))/(4*(a^7*d^2 + a^5*b^2*c^2 - 2*a^6*b*c*d))))/(4*(a^7*d^2 + a^5*b^2*c^2 - 2*a^6*b*c*d)))*(5*a*d - 3*b*c)*(-a^5*b^3)^(1/2))/(4*(a^7*d^2 + a^5*b^2*c^2 - 2*a^6*b*c*d)) + 144*a^6*b^8*c^7*d^5 - 624*a^7*b^7*c^6*d^6 + 976*a^8*b^6*c^5*d^7 - 656*a^9*b^5*c^4*d^8 + 160*a^10*b^4*c^3*d^9))*(5*a*d - 3*b*c)*(-a^5*b^3)^(1/2)*1i)/(2*(a^7*d^2 + a^5*b^2*c^2 - 2*a^6*b*c*d))","B"
296,1,171,126,1.024111,"\text{Not used}","int(1/(x^3*(a + b*x^2)^2*(c + d*x^2)),x)","\frac{\ln\left(b\,x^2+a\right)\,\left(2\,b^3\,c-3\,a\,b^2\,d\right)}{2\,a^5\,d^2-4\,a^4\,b\,c\,d+2\,a^3\,b^2\,c^2}-\frac{\frac{1}{2\,a\,c}-\frac{x^2\,\left(2\,b^2\,c-a\,b\,d\right)}{2\,a^2\,c\,\left(a\,d-b\,c\right)}}{b\,x^4+a\,x^2}+\frac{d^3\,\ln\left(d\,x^2+c\right)}{2\,\left(a^2\,c^2\,d^2-2\,a\,b\,c^3\,d+b^2\,c^4\right)}-\frac{\ln\left(x\right)\,\left(a\,d+2\,b\,c\right)}{a^3\,c^2}","Not used",1,"(log(a + b*x^2)*(2*b^3*c - 3*a*b^2*d))/(2*a^5*d^2 + 2*a^3*b^2*c^2 - 4*a^4*b*c*d) - (1/(2*a*c) - (x^2*(2*b^2*c - a*b*d))/(2*a^2*c*(a*d - b*c)))/(a*x^2 + b*x^4) + (d^3*log(c + d*x^2))/(2*(b^2*c^4 + a^2*c^2*d^2 - 2*a*b*c^3*d)) - (log(x)*(a*d + 2*b*c))/(a^3*c^2)","B"
297,1,4654,189,1.231894,"\text{Not used}","int(1/(x^4*(a + b*x^2)^2*(c + d*x^2)),x)","\frac{\frac{x^2\,\left(3\,a\,d+5\,b\,c\right)}{3\,a^2\,c^2}-\frac{1}{3\,a\,c}+\frac{x^4\,\left(2\,a^2\,b\,d^2+2\,a\,b^2\,c\,d-5\,b^3\,c^2\right)}{2\,a^3\,c^2\,\left(a\,d-b\,c\right)}}{b\,x^5+a\,x^3}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{x\,\left(-64\,a^{18}\,b^3\,c^6\,d^{12}+192\,a^{17}\,b^4\,c^7\,d^{11}-192\,a^{16}\,b^5\,c^8\,d^{10}+64\,a^{15}\,b^6\,c^9\,d^9-784\,a^{14}\,b^7\,c^{10}\,d^8+3472\,a^{13}\,b^8\,c^{11}\,d^7-6112\,a^{12}\,b^9\,c^{12}\,d^6+5344\,a^{11}\,b^{10}\,c^{13}\,d^5-2320\,a^{10}\,b^{11}\,c^{14}\,d^4+400\,a^9\,b^{12}\,c^{15}\,d^3\right)}{2}+\frac{\sqrt{-c^5\,d^7}\,\left(\frac{x\,\sqrt{-c^5\,d^7}\,\left(-256\,a^{23}\,b^2\,c^{10}\,d^{10}+1536\,a^{22}\,b^3\,c^{11}\,d^9-3584\,a^{21}\,b^4\,c^{12}\,d^8+3584\,a^{20}\,b^5\,c^{13}\,d^7-3584\,a^{18}\,b^7\,c^{15}\,d^5+3584\,a^{17}\,b^8\,c^{16}\,d^4-1536\,a^{16}\,b^9\,c^{17}\,d^3+256\,a^{15}\,b^{10}\,c^{18}\,d^2\right)}{4\,\left(a^2\,c^5\,d^2-2\,a\,b\,c^6\,d+b^2\,c^7\right)}-160\,a^{12}\,b^{11}\,c^{17}\,d^2+1024\,a^{13}\,b^{10}\,c^{16}\,d^3-2720\,a^{14}\,b^9\,c^{15}\,d^4+3840\,a^{15}\,b^8\,c^{14}\,d^5-3104\,a^{16}\,b^7\,c^{13}\,d^6+1600\,a^{17}\,b^6\,c^{12}\,d^7-864\,a^{18}\,b^5\,c^{11}\,d^8+640\,a^{19}\,b^4\,c^{10}\,d^9-320\,a^{20}\,b^3\,c^9\,d^{10}+64\,a^{21}\,b^2\,c^8\,d^{11}\right)}{2\,\left(a^2\,c^5\,d^2-2\,a\,b\,c^6\,d+b^2\,c^7\right)}\right)\,\sqrt{-c^5\,d^7}\,1{}\mathrm{i}}{a^2\,c^5\,d^2-2\,a\,b\,c^6\,d+b^2\,c^7}+\frac{\left(\frac{x\,\left(-64\,a^{18}\,b^3\,c^6\,d^{12}+192\,a^{17}\,b^4\,c^7\,d^{11}-192\,a^{16}\,b^5\,c^8\,d^{10}+64\,a^{15}\,b^6\,c^9\,d^9-784\,a^{14}\,b^7\,c^{10}\,d^8+3472\,a^{13}\,b^8\,c^{11}\,d^7-6112\,a^{12}\,b^9\,c^{12}\,d^6+5344\,a^{11}\,b^{10}\,c^{13}\,d^5-2320\,a^{10}\,b^{11}\,c^{14}\,d^4+400\,a^9\,b^{12}\,c^{15}\,d^3\right)}{2}+\frac{\sqrt{-c^5\,d^7}\,\left(\frac{x\,\sqrt{-c^5\,d^7}\,\left(-256\,a^{23}\,b^2\,c^{10}\,d^{10}+1536\,a^{22}\,b^3\,c^{11}\,d^9-3584\,a^{21}\,b^4\,c^{12}\,d^8+3584\,a^{20}\,b^5\,c^{13}\,d^7-3584\,a^{18}\,b^7\,c^{15}\,d^5+3584\,a^{17}\,b^8\,c^{16}\,d^4-1536\,a^{16}\,b^9\,c^{17}\,d^3+256\,a^{15}\,b^{10}\,c^{18}\,d^2\right)}{4\,\left(a^2\,c^5\,d^2-2\,a\,b\,c^6\,d+b^2\,c^7\right)}+160\,a^{12}\,b^{11}\,c^{17}\,d^2-1024\,a^{13}\,b^{10}\,c^{16}\,d^3+2720\,a^{14}\,b^9\,c^{15}\,d^4-3840\,a^{15}\,b^8\,c^{14}\,d^5+3104\,a^{16}\,b^7\,c^{13}\,d^6-1600\,a^{17}\,b^6\,c^{12}\,d^7+864\,a^{18}\,b^5\,c^{11}\,d^8-640\,a^{19}\,b^4\,c^{10}\,d^9+320\,a^{20}\,b^3\,c^9\,d^{10}-64\,a^{21}\,b^2\,c^8\,d^{11}\right)}{2\,\left(a^2\,c^5\,d^2-2\,a\,b\,c^6\,d+b^2\,c^7\right)}\right)\,\sqrt{-c^5\,d^7}\,1{}\mathrm{i}}{a^2\,c^5\,d^2-2\,a\,b\,c^6\,d+b^2\,c^7}}{\frac{\left(\frac{x\,\left(-64\,a^{18}\,b^3\,c^6\,d^{12}+192\,a^{17}\,b^4\,c^7\,d^{11}-192\,a^{16}\,b^5\,c^8\,d^{10}+64\,a^{15}\,b^6\,c^9\,d^9-784\,a^{14}\,b^7\,c^{10}\,d^8+3472\,a^{13}\,b^8\,c^{11}\,d^7-6112\,a^{12}\,b^9\,c^{12}\,d^6+5344\,a^{11}\,b^{10}\,c^{13}\,d^5-2320\,a^{10}\,b^{11}\,c^{14}\,d^4+400\,a^9\,b^{12}\,c^{15}\,d^3\right)}{2}+\frac{\sqrt{-c^5\,d^7}\,\left(\frac{x\,\sqrt{-c^5\,d^7}\,\left(-256\,a^{23}\,b^2\,c^{10}\,d^{10}+1536\,a^{22}\,b^3\,c^{11}\,d^9-3584\,a^{21}\,b^4\,c^{12}\,d^8+3584\,a^{20}\,b^5\,c^{13}\,d^7-3584\,a^{18}\,b^7\,c^{15}\,d^5+3584\,a^{17}\,b^8\,c^{16}\,d^4-1536\,a^{16}\,b^9\,c^{17}\,d^3+256\,a^{15}\,b^{10}\,c^{18}\,d^2\right)}{4\,\left(a^2\,c^5\,d^2-2\,a\,b\,c^6\,d+b^2\,c^7\right)}-160\,a^{12}\,b^{11}\,c^{17}\,d^2+1024\,a^{13}\,b^{10}\,c^{16}\,d^3-2720\,a^{14}\,b^9\,c^{15}\,d^4+3840\,a^{15}\,b^8\,c^{14}\,d^5-3104\,a^{16}\,b^7\,c^{13}\,d^6+1600\,a^{17}\,b^6\,c^{12}\,d^7-864\,a^{18}\,b^5\,c^{11}\,d^8+640\,a^{19}\,b^4\,c^{10}\,d^9-320\,a^{20}\,b^3\,c^9\,d^{10}+64\,a^{21}\,b^2\,c^8\,d^{11}\right)}{2\,\left(a^2\,c^5\,d^2-2\,a\,b\,c^6\,d+b^2\,c^7\right)}\right)\,\sqrt{-c^5\,d^7}}{a^2\,c^5\,d^2-2\,a\,b\,c^6\,d+b^2\,c^7}-\frac{\left(\frac{x\,\left(-64\,a^{18}\,b^3\,c^6\,d^{12}+192\,a^{17}\,b^4\,c^7\,d^{11}-192\,a^{16}\,b^5\,c^8\,d^{10}+64\,a^{15}\,b^6\,c^9\,d^9-784\,a^{14}\,b^7\,c^{10}\,d^8+3472\,a^{13}\,b^8\,c^{11}\,d^7-6112\,a^{12}\,b^9\,c^{12}\,d^6+5344\,a^{11}\,b^{10}\,c^{13}\,d^5-2320\,a^{10}\,b^{11}\,c^{14}\,d^4+400\,a^9\,b^{12}\,c^{15}\,d^3\right)}{2}+\frac{\sqrt{-c^5\,d^7}\,\left(\frac{x\,\sqrt{-c^5\,d^7}\,\left(-256\,a^{23}\,b^2\,c^{10}\,d^{10}+1536\,a^{22}\,b^3\,c^{11}\,d^9-3584\,a^{21}\,b^4\,c^{12}\,d^8+3584\,a^{20}\,b^5\,c^{13}\,d^7-3584\,a^{18}\,b^7\,c^{15}\,d^5+3584\,a^{17}\,b^8\,c^{16}\,d^4-1536\,a^{16}\,b^9\,c^{17}\,d^3+256\,a^{15}\,b^{10}\,c^{18}\,d^2\right)}{4\,\left(a^2\,c^5\,d^2-2\,a\,b\,c^6\,d+b^2\,c^7\right)}+160\,a^{12}\,b^{11}\,c^{17}\,d^2-1024\,a^{13}\,b^{10}\,c^{16}\,d^3+2720\,a^{14}\,b^9\,c^{15}\,d^4-3840\,a^{15}\,b^8\,c^{14}\,d^5+3104\,a^{16}\,b^7\,c^{13}\,d^6-1600\,a^{17}\,b^6\,c^{12}\,d^7+864\,a^{18}\,b^5\,c^{11}\,d^8-640\,a^{19}\,b^4\,c^{10}\,d^9+320\,a^{20}\,b^3\,c^9\,d^{10}-64\,a^{21}\,b^2\,c^8\,d^{11}\right)}{2\,\left(a^2\,c^5\,d^2-2\,a\,b\,c^6\,d+b^2\,c^7\right)}\right)\,\sqrt{-c^5\,d^7}}{a^2\,c^5\,d^2-2\,a\,b\,c^6\,d+b^2\,c^7}-400\,a^9\,b^{10}\,c^{11}\,d^6+1520\,a^{10}\,b^9\,c^{10}\,d^7-1904\,a^{11}\,b^8\,c^9\,d^8+624\,a^{12}\,b^7\,c^8\,d^9+384\,a^{13}\,b^6\,c^7\,d^{10}-224\,a^{14}\,b^5\,c^6\,d^{11}}\right)\,\sqrt{-c^5\,d^7}\,1{}\mathrm{i}}{a^2\,c^5\,d^2-2\,a\,b\,c^6\,d+b^2\,c^7}+\frac{\mathrm{atan}\left(\frac{\frac{\left(7\,a\,d-5\,b\,c\right)\,\left(x\,\left(-64\,a^{18}\,b^3\,c^6\,d^{12}+192\,a^{17}\,b^4\,c^7\,d^{11}-192\,a^{16}\,b^5\,c^8\,d^{10}+64\,a^{15}\,b^6\,c^9\,d^9-784\,a^{14}\,b^7\,c^{10}\,d^8+3472\,a^{13}\,b^8\,c^{11}\,d^7-6112\,a^{12}\,b^9\,c^{12}\,d^6+5344\,a^{11}\,b^{10}\,c^{13}\,d^5-2320\,a^{10}\,b^{11}\,c^{14}\,d^4+400\,a^9\,b^{12}\,c^{15}\,d^3\right)+\frac{\left(7\,a\,d-5\,b\,c\right)\,\sqrt{-a^7\,b^5}\,\left(2048\,a^{13}\,b^{10}\,c^{16}\,d^3-320\,a^{12}\,b^{11}\,c^{17}\,d^2-5440\,a^{14}\,b^9\,c^{15}\,d^4+7680\,a^{15}\,b^8\,c^{14}\,d^5-6208\,a^{16}\,b^7\,c^{13}\,d^6+3200\,a^{17}\,b^6\,c^{12}\,d^7-1728\,a^{18}\,b^5\,c^{11}\,d^8+1280\,a^{19}\,b^4\,c^{10}\,d^9-640\,a^{20}\,b^3\,c^9\,d^{10}+128\,a^{21}\,b^2\,c^8\,d^{11}+\frac{x\,\left(7\,a\,d-5\,b\,c\right)\,\sqrt{-a^7\,b^5}\,\left(-256\,a^{23}\,b^2\,c^{10}\,d^{10}+1536\,a^{22}\,b^3\,c^{11}\,d^9-3584\,a^{21}\,b^4\,c^{12}\,d^8+3584\,a^{20}\,b^5\,c^{13}\,d^7-3584\,a^{18}\,b^7\,c^{15}\,d^5+3584\,a^{17}\,b^8\,c^{16}\,d^4-1536\,a^{16}\,b^9\,c^{17}\,d^3+256\,a^{15}\,b^{10}\,c^{18}\,d^2\right)}{4\,\left(a^9\,d^2-2\,a^8\,b\,c\,d+a^7\,b^2\,c^2\right)}\right)}{4\,\left(a^9\,d^2-2\,a^8\,b\,c\,d+a^7\,b^2\,c^2\right)}\right)\,\sqrt{-a^7\,b^5}\,1{}\mathrm{i}}{4\,\left(a^9\,d^2-2\,a^8\,b\,c\,d+a^7\,b^2\,c^2\right)}+\frac{\left(7\,a\,d-5\,b\,c\right)\,\left(x\,\left(-64\,a^{18}\,b^3\,c^6\,d^{12}+192\,a^{17}\,b^4\,c^7\,d^{11}-192\,a^{16}\,b^5\,c^8\,d^{10}+64\,a^{15}\,b^6\,c^9\,d^9-784\,a^{14}\,b^7\,c^{10}\,d^8+3472\,a^{13}\,b^8\,c^{11}\,d^7-6112\,a^{12}\,b^9\,c^{12}\,d^6+5344\,a^{11}\,b^{10}\,c^{13}\,d^5-2320\,a^{10}\,b^{11}\,c^{14}\,d^4+400\,a^9\,b^{12}\,c^{15}\,d^3\right)+\frac{\left(7\,a\,d-5\,b\,c\right)\,\sqrt{-a^7\,b^5}\,\left(320\,a^{12}\,b^{11}\,c^{17}\,d^2-2048\,a^{13}\,b^{10}\,c^{16}\,d^3+5440\,a^{14}\,b^9\,c^{15}\,d^4-7680\,a^{15}\,b^8\,c^{14}\,d^5+6208\,a^{16}\,b^7\,c^{13}\,d^6-3200\,a^{17}\,b^6\,c^{12}\,d^7+1728\,a^{18}\,b^5\,c^{11}\,d^8-1280\,a^{19}\,b^4\,c^{10}\,d^9+640\,a^{20}\,b^3\,c^9\,d^{10}-128\,a^{21}\,b^2\,c^8\,d^{11}+\frac{x\,\left(7\,a\,d-5\,b\,c\right)\,\sqrt{-a^7\,b^5}\,\left(-256\,a^{23}\,b^2\,c^{10}\,d^{10}+1536\,a^{22}\,b^3\,c^{11}\,d^9-3584\,a^{21}\,b^4\,c^{12}\,d^8+3584\,a^{20}\,b^5\,c^{13}\,d^7-3584\,a^{18}\,b^7\,c^{15}\,d^5+3584\,a^{17}\,b^8\,c^{16}\,d^4-1536\,a^{16}\,b^9\,c^{17}\,d^3+256\,a^{15}\,b^{10}\,c^{18}\,d^2\right)}{4\,\left(a^9\,d^2-2\,a^8\,b\,c\,d+a^7\,b^2\,c^2\right)}\right)}{4\,\left(a^9\,d^2-2\,a^8\,b\,c\,d+a^7\,b^2\,c^2\right)}\right)\,\sqrt{-a^7\,b^5}\,1{}\mathrm{i}}{4\,\left(a^9\,d^2-2\,a^8\,b\,c\,d+a^7\,b^2\,c^2\right)}}{400\,a^9\,b^{10}\,c^{11}\,d^6-1520\,a^{10}\,b^9\,c^{10}\,d^7+1904\,a^{11}\,b^8\,c^9\,d^8-624\,a^{12}\,b^7\,c^8\,d^9-384\,a^{13}\,b^6\,c^7\,d^{10}+224\,a^{14}\,b^5\,c^6\,d^{11}-\frac{\left(7\,a\,d-5\,b\,c\right)\,\left(x\,\left(-64\,a^{18}\,b^3\,c^6\,d^{12}+192\,a^{17}\,b^4\,c^7\,d^{11}-192\,a^{16}\,b^5\,c^8\,d^{10}+64\,a^{15}\,b^6\,c^9\,d^9-784\,a^{14}\,b^7\,c^{10}\,d^8+3472\,a^{13}\,b^8\,c^{11}\,d^7-6112\,a^{12}\,b^9\,c^{12}\,d^6+5344\,a^{11}\,b^{10}\,c^{13}\,d^5-2320\,a^{10}\,b^{11}\,c^{14}\,d^4+400\,a^9\,b^{12}\,c^{15}\,d^3\right)+\frac{\left(7\,a\,d-5\,b\,c\right)\,\sqrt{-a^7\,b^5}\,\left(2048\,a^{13}\,b^{10}\,c^{16}\,d^3-320\,a^{12}\,b^{11}\,c^{17}\,d^2-5440\,a^{14}\,b^9\,c^{15}\,d^4+7680\,a^{15}\,b^8\,c^{14}\,d^5-6208\,a^{16}\,b^7\,c^{13}\,d^6+3200\,a^{17}\,b^6\,c^{12}\,d^7-1728\,a^{18}\,b^5\,c^{11}\,d^8+1280\,a^{19}\,b^4\,c^{10}\,d^9-640\,a^{20}\,b^3\,c^9\,d^{10}+128\,a^{21}\,b^2\,c^8\,d^{11}+\frac{x\,\left(7\,a\,d-5\,b\,c\right)\,\sqrt{-a^7\,b^5}\,\left(-256\,a^{23}\,b^2\,c^{10}\,d^{10}+1536\,a^{22}\,b^3\,c^{11}\,d^9-3584\,a^{21}\,b^4\,c^{12}\,d^8+3584\,a^{20}\,b^5\,c^{13}\,d^7-3584\,a^{18}\,b^7\,c^{15}\,d^5+3584\,a^{17}\,b^8\,c^{16}\,d^4-1536\,a^{16}\,b^9\,c^{17}\,d^3+256\,a^{15}\,b^{10}\,c^{18}\,d^2\right)}{4\,\left(a^9\,d^2-2\,a^8\,b\,c\,d+a^7\,b^2\,c^2\right)}\right)}{4\,\left(a^9\,d^2-2\,a^8\,b\,c\,d+a^7\,b^2\,c^2\right)}\right)\,\sqrt{-a^7\,b^5}}{4\,\left(a^9\,d^2-2\,a^8\,b\,c\,d+a^7\,b^2\,c^2\right)}+\frac{\left(7\,a\,d-5\,b\,c\right)\,\left(x\,\left(-64\,a^{18}\,b^3\,c^6\,d^{12}+192\,a^{17}\,b^4\,c^7\,d^{11}-192\,a^{16}\,b^5\,c^8\,d^{10}+64\,a^{15}\,b^6\,c^9\,d^9-784\,a^{14}\,b^7\,c^{10}\,d^8+3472\,a^{13}\,b^8\,c^{11}\,d^7-6112\,a^{12}\,b^9\,c^{12}\,d^6+5344\,a^{11}\,b^{10}\,c^{13}\,d^5-2320\,a^{10}\,b^{11}\,c^{14}\,d^4+400\,a^9\,b^{12}\,c^{15}\,d^3\right)+\frac{\left(7\,a\,d-5\,b\,c\right)\,\sqrt{-a^7\,b^5}\,\left(320\,a^{12}\,b^{11}\,c^{17}\,d^2-2048\,a^{13}\,b^{10}\,c^{16}\,d^3+5440\,a^{14}\,b^9\,c^{15}\,d^4-7680\,a^{15}\,b^8\,c^{14}\,d^5+6208\,a^{16}\,b^7\,c^{13}\,d^6-3200\,a^{17}\,b^6\,c^{12}\,d^7+1728\,a^{18}\,b^5\,c^{11}\,d^8-1280\,a^{19}\,b^4\,c^{10}\,d^9+640\,a^{20}\,b^3\,c^9\,d^{10}-128\,a^{21}\,b^2\,c^8\,d^{11}+\frac{x\,\left(7\,a\,d-5\,b\,c\right)\,\sqrt{-a^7\,b^5}\,\left(-256\,a^{23}\,b^2\,c^{10}\,d^{10}+1536\,a^{22}\,b^3\,c^{11}\,d^9-3584\,a^{21}\,b^4\,c^{12}\,d^8+3584\,a^{20}\,b^5\,c^{13}\,d^7-3584\,a^{18}\,b^7\,c^{15}\,d^5+3584\,a^{17}\,b^8\,c^{16}\,d^4-1536\,a^{16}\,b^9\,c^{17}\,d^3+256\,a^{15}\,b^{10}\,c^{18}\,d^2\right)}{4\,\left(a^9\,d^2-2\,a^8\,b\,c\,d+a^7\,b^2\,c^2\right)}\right)}{4\,\left(a^9\,d^2-2\,a^8\,b\,c\,d+a^7\,b^2\,c^2\right)}\right)\,\sqrt{-a^7\,b^5}}{4\,\left(a^9\,d^2-2\,a^8\,b\,c\,d+a^7\,b^2\,c^2\right)}}\right)\,\left(7\,a\,d-5\,b\,c\right)\,\sqrt{-a^7\,b^5}\,1{}\mathrm{i}}{2\,\left(a^9\,d^2-2\,a^8\,b\,c\,d+a^7\,b^2\,c^2\right)}","Not used",1,"((x^2*(3*a*d + 5*b*c))/(3*a^2*c^2) - 1/(3*a*c) + (x^4*(2*a^2*b*d^2 - 5*b^3*c^2 + 2*a*b^2*c*d))/(2*a^3*c^2*(a*d - b*c)))/(a*x^3 + b*x^5) - (atan(((((x*(400*a^9*b^12*c^15*d^3 - 2320*a^10*b^11*c^14*d^4 + 5344*a^11*b^10*c^13*d^5 - 6112*a^12*b^9*c^12*d^6 + 3472*a^13*b^8*c^11*d^7 - 784*a^14*b^7*c^10*d^8 + 64*a^15*b^6*c^9*d^9 - 192*a^16*b^5*c^8*d^10 + 192*a^17*b^4*c^7*d^11 - 64*a^18*b^3*c^6*d^12))/2 + ((-c^5*d^7)^(1/2)*((x*(-c^5*d^7)^(1/2)*(256*a^15*b^10*c^18*d^2 - 1536*a^16*b^9*c^17*d^3 + 3584*a^17*b^8*c^16*d^4 - 3584*a^18*b^7*c^15*d^5 + 3584*a^20*b^5*c^13*d^7 - 3584*a^21*b^4*c^12*d^8 + 1536*a^22*b^3*c^11*d^9 - 256*a^23*b^2*c^10*d^10))/(4*(b^2*c^7 + a^2*c^5*d^2 - 2*a*b*c^6*d)) - 160*a^12*b^11*c^17*d^2 + 1024*a^13*b^10*c^16*d^3 - 2720*a^14*b^9*c^15*d^4 + 3840*a^15*b^8*c^14*d^5 - 3104*a^16*b^7*c^13*d^6 + 1600*a^17*b^6*c^12*d^7 - 864*a^18*b^5*c^11*d^8 + 640*a^19*b^4*c^10*d^9 - 320*a^20*b^3*c^9*d^10 + 64*a^21*b^2*c^8*d^11))/(2*(b^2*c^7 + a^2*c^5*d^2 - 2*a*b*c^6*d)))*(-c^5*d^7)^(1/2)*1i)/(b^2*c^7 + a^2*c^5*d^2 - 2*a*b*c^6*d) + (((x*(400*a^9*b^12*c^15*d^3 - 2320*a^10*b^11*c^14*d^4 + 5344*a^11*b^10*c^13*d^5 - 6112*a^12*b^9*c^12*d^6 + 3472*a^13*b^8*c^11*d^7 - 784*a^14*b^7*c^10*d^8 + 64*a^15*b^6*c^9*d^9 - 192*a^16*b^5*c^8*d^10 + 192*a^17*b^4*c^7*d^11 - 64*a^18*b^3*c^6*d^12))/2 + ((-c^5*d^7)^(1/2)*((x*(-c^5*d^7)^(1/2)*(256*a^15*b^10*c^18*d^2 - 1536*a^16*b^9*c^17*d^3 + 3584*a^17*b^8*c^16*d^4 - 3584*a^18*b^7*c^15*d^5 + 3584*a^20*b^5*c^13*d^7 - 3584*a^21*b^4*c^12*d^8 + 1536*a^22*b^3*c^11*d^9 - 256*a^23*b^2*c^10*d^10))/(4*(b^2*c^7 + a^2*c^5*d^2 - 2*a*b*c^6*d)) + 160*a^12*b^11*c^17*d^2 - 1024*a^13*b^10*c^16*d^3 + 2720*a^14*b^9*c^15*d^4 - 3840*a^15*b^8*c^14*d^5 + 3104*a^16*b^7*c^13*d^6 - 1600*a^17*b^6*c^12*d^7 + 864*a^18*b^5*c^11*d^8 - 640*a^19*b^4*c^10*d^9 + 320*a^20*b^3*c^9*d^10 - 64*a^21*b^2*c^8*d^11))/(2*(b^2*c^7 + a^2*c^5*d^2 - 2*a*b*c^6*d)))*(-c^5*d^7)^(1/2)*1i)/(b^2*c^7 + a^2*c^5*d^2 - 2*a*b*c^6*d))/((((x*(400*a^9*b^12*c^15*d^3 - 2320*a^10*b^11*c^14*d^4 + 5344*a^11*b^10*c^13*d^5 - 6112*a^12*b^9*c^12*d^6 + 3472*a^13*b^8*c^11*d^7 - 784*a^14*b^7*c^10*d^8 + 64*a^15*b^6*c^9*d^9 - 192*a^16*b^5*c^8*d^10 + 192*a^17*b^4*c^7*d^11 - 64*a^18*b^3*c^6*d^12))/2 + ((-c^5*d^7)^(1/2)*((x*(-c^5*d^7)^(1/2)*(256*a^15*b^10*c^18*d^2 - 1536*a^16*b^9*c^17*d^3 + 3584*a^17*b^8*c^16*d^4 - 3584*a^18*b^7*c^15*d^5 + 3584*a^20*b^5*c^13*d^7 - 3584*a^21*b^4*c^12*d^8 + 1536*a^22*b^3*c^11*d^9 - 256*a^23*b^2*c^10*d^10))/(4*(b^2*c^7 + a^2*c^5*d^2 - 2*a*b*c^6*d)) - 160*a^12*b^11*c^17*d^2 + 1024*a^13*b^10*c^16*d^3 - 2720*a^14*b^9*c^15*d^4 + 3840*a^15*b^8*c^14*d^5 - 3104*a^16*b^7*c^13*d^6 + 1600*a^17*b^6*c^12*d^7 - 864*a^18*b^5*c^11*d^8 + 640*a^19*b^4*c^10*d^9 - 320*a^20*b^3*c^9*d^10 + 64*a^21*b^2*c^8*d^11))/(2*(b^2*c^7 + a^2*c^5*d^2 - 2*a*b*c^6*d)))*(-c^5*d^7)^(1/2))/(b^2*c^7 + a^2*c^5*d^2 - 2*a*b*c^6*d) - (((x*(400*a^9*b^12*c^15*d^3 - 2320*a^10*b^11*c^14*d^4 + 5344*a^11*b^10*c^13*d^5 - 6112*a^12*b^9*c^12*d^6 + 3472*a^13*b^8*c^11*d^7 - 784*a^14*b^7*c^10*d^8 + 64*a^15*b^6*c^9*d^9 - 192*a^16*b^5*c^8*d^10 + 192*a^17*b^4*c^7*d^11 - 64*a^18*b^3*c^6*d^12))/2 + ((-c^5*d^7)^(1/2)*((x*(-c^5*d^7)^(1/2)*(256*a^15*b^10*c^18*d^2 - 1536*a^16*b^9*c^17*d^3 + 3584*a^17*b^8*c^16*d^4 - 3584*a^18*b^7*c^15*d^5 + 3584*a^20*b^5*c^13*d^7 - 3584*a^21*b^4*c^12*d^8 + 1536*a^22*b^3*c^11*d^9 - 256*a^23*b^2*c^10*d^10))/(4*(b^2*c^7 + a^2*c^5*d^2 - 2*a*b*c^6*d)) + 160*a^12*b^11*c^17*d^2 - 1024*a^13*b^10*c^16*d^3 + 2720*a^14*b^9*c^15*d^4 - 3840*a^15*b^8*c^14*d^5 + 3104*a^16*b^7*c^13*d^6 - 1600*a^17*b^6*c^12*d^7 + 864*a^18*b^5*c^11*d^8 - 640*a^19*b^4*c^10*d^9 + 320*a^20*b^3*c^9*d^10 - 64*a^21*b^2*c^8*d^11))/(2*(b^2*c^7 + a^2*c^5*d^2 - 2*a*b*c^6*d)))*(-c^5*d^7)^(1/2))/(b^2*c^7 + a^2*c^5*d^2 - 2*a*b*c^6*d) - 400*a^9*b^10*c^11*d^6 + 1520*a^10*b^9*c^10*d^7 - 1904*a^11*b^8*c^9*d^8 + 624*a^12*b^7*c^8*d^9 + 384*a^13*b^6*c^7*d^10 - 224*a^14*b^5*c^6*d^11))*(-c^5*d^7)^(1/2)*1i)/(b^2*c^7 + a^2*c^5*d^2 - 2*a*b*c^6*d) + (atan((((7*a*d - 5*b*c)*(x*(400*a^9*b^12*c^15*d^3 - 2320*a^10*b^11*c^14*d^4 + 5344*a^11*b^10*c^13*d^5 - 6112*a^12*b^9*c^12*d^6 + 3472*a^13*b^8*c^11*d^7 - 784*a^14*b^7*c^10*d^8 + 64*a^15*b^6*c^9*d^9 - 192*a^16*b^5*c^8*d^10 + 192*a^17*b^4*c^7*d^11 - 64*a^18*b^3*c^6*d^12) + ((7*a*d - 5*b*c)*(-a^7*b^5)^(1/2)*(2048*a^13*b^10*c^16*d^3 - 320*a^12*b^11*c^17*d^2 - 5440*a^14*b^9*c^15*d^4 + 7680*a^15*b^8*c^14*d^5 - 6208*a^16*b^7*c^13*d^6 + 3200*a^17*b^6*c^12*d^7 - 1728*a^18*b^5*c^11*d^8 + 1280*a^19*b^4*c^10*d^9 - 640*a^20*b^3*c^9*d^10 + 128*a^21*b^2*c^8*d^11 + (x*(7*a*d - 5*b*c)*(-a^7*b^5)^(1/2)*(256*a^15*b^10*c^18*d^2 - 1536*a^16*b^9*c^17*d^3 + 3584*a^17*b^8*c^16*d^4 - 3584*a^18*b^7*c^15*d^5 + 3584*a^20*b^5*c^13*d^7 - 3584*a^21*b^4*c^12*d^8 + 1536*a^22*b^3*c^11*d^9 - 256*a^23*b^2*c^10*d^10))/(4*(a^9*d^2 + a^7*b^2*c^2 - 2*a^8*b*c*d))))/(4*(a^9*d^2 + a^7*b^2*c^2 - 2*a^8*b*c*d)))*(-a^7*b^5)^(1/2)*1i)/(4*(a^9*d^2 + a^7*b^2*c^2 - 2*a^8*b*c*d)) + ((7*a*d - 5*b*c)*(x*(400*a^9*b^12*c^15*d^3 - 2320*a^10*b^11*c^14*d^4 + 5344*a^11*b^10*c^13*d^5 - 6112*a^12*b^9*c^12*d^6 + 3472*a^13*b^8*c^11*d^7 - 784*a^14*b^7*c^10*d^8 + 64*a^15*b^6*c^9*d^9 - 192*a^16*b^5*c^8*d^10 + 192*a^17*b^4*c^7*d^11 - 64*a^18*b^3*c^6*d^12) + ((7*a*d - 5*b*c)*(-a^7*b^5)^(1/2)*(320*a^12*b^11*c^17*d^2 - 2048*a^13*b^10*c^16*d^3 + 5440*a^14*b^9*c^15*d^4 - 7680*a^15*b^8*c^14*d^5 + 6208*a^16*b^7*c^13*d^6 - 3200*a^17*b^6*c^12*d^7 + 1728*a^18*b^5*c^11*d^8 - 1280*a^19*b^4*c^10*d^9 + 640*a^20*b^3*c^9*d^10 - 128*a^21*b^2*c^8*d^11 + (x*(7*a*d - 5*b*c)*(-a^7*b^5)^(1/2)*(256*a^15*b^10*c^18*d^2 - 1536*a^16*b^9*c^17*d^3 + 3584*a^17*b^8*c^16*d^4 - 3584*a^18*b^7*c^15*d^5 + 3584*a^20*b^5*c^13*d^7 - 3584*a^21*b^4*c^12*d^8 + 1536*a^22*b^3*c^11*d^9 - 256*a^23*b^2*c^10*d^10))/(4*(a^9*d^2 + a^7*b^2*c^2 - 2*a^8*b*c*d))))/(4*(a^9*d^2 + a^7*b^2*c^2 - 2*a^8*b*c*d)))*(-a^7*b^5)^(1/2)*1i)/(4*(a^9*d^2 + a^7*b^2*c^2 - 2*a^8*b*c*d)))/(400*a^9*b^10*c^11*d^6 - 1520*a^10*b^9*c^10*d^7 + 1904*a^11*b^8*c^9*d^8 - 624*a^12*b^7*c^8*d^9 - 384*a^13*b^6*c^7*d^10 + 224*a^14*b^5*c^6*d^11 - ((7*a*d - 5*b*c)*(x*(400*a^9*b^12*c^15*d^3 - 2320*a^10*b^11*c^14*d^4 + 5344*a^11*b^10*c^13*d^5 - 6112*a^12*b^9*c^12*d^6 + 3472*a^13*b^8*c^11*d^7 - 784*a^14*b^7*c^10*d^8 + 64*a^15*b^6*c^9*d^9 - 192*a^16*b^5*c^8*d^10 + 192*a^17*b^4*c^7*d^11 - 64*a^18*b^3*c^6*d^12) + ((7*a*d - 5*b*c)*(-a^7*b^5)^(1/2)*(2048*a^13*b^10*c^16*d^3 - 320*a^12*b^11*c^17*d^2 - 5440*a^14*b^9*c^15*d^4 + 7680*a^15*b^8*c^14*d^5 - 6208*a^16*b^7*c^13*d^6 + 3200*a^17*b^6*c^12*d^7 - 1728*a^18*b^5*c^11*d^8 + 1280*a^19*b^4*c^10*d^9 - 640*a^20*b^3*c^9*d^10 + 128*a^21*b^2*c^8*d^11 + (x*(7*a*d - 5*b*c)*(-a^7*b^5)^(1/2)*(256*a^15*b^10*c^18*d^2 - 1536*a^16*b^9*c^17*d^3 + 3584*a^17*b^8*c^16*d^4 - 3584*a^18*b^7*c^15*d^5 + 3584*a^20*b^5*c^13*d^7 - 3584*a^21*b^4*c^12*d^8 + 1536*a^22*b^3*c^11*d^9 - 256*a^23*b^2*c^10*d^10))/(4*(a^9*d^2 + a^7*b^2*c^2 - 2*a^8*b*c*d))))/(4*(a^9*d^2 + a^7*b^2*c^2 - 2*a^8*b*c*d)))*(-a^7*b^5)^(1/2))/(4*(a^9*d^2 + a^7*b^2*c^2 - 2*a^8*b*c*d)) + ((7*a*d - 5*b*c)*(x*(400*a^9*b^12*c^15*d^3 - 2320*a^10*b^11*c^14*d^4 + 5344*a^11*b^10*c^13*d^5 - 6112*a^12*b^9*c^12*d^6 + 3472*a^13*b^8*c^11*d^7 - 784*a^14*b^7*c^10*d^8 + 64*a^15*b^6*c^9*d^9 - 192*a^16*b^5*c^8*d^10 + 192*a^17*b^4*c^7*d^11 - 64*a^18*b^3*c^6*d^12) + ((7*a*d - 5*b*c)*(-a^7*b^5)^(1/2)*(320*a^12*b^11*c^17*d^2 - 2048*a^13*b^10*c^16*d^3 + 5440*a^14*b^9*c^15*d^4 - 7680*a^15*b^8*c^14*d^5 + 6208*a^16*b^7*c^13*d^6 - 3200*a^17*b^6*c^12*d^7 + 1728*a^18*b^5*c^11*d^8 - 1280*a^19*b^4*c^10*d^9 + 640*a^20*b^3*c^9*d^10 - 128*a^21*b^2*c^8*d^11 + (x*(7*a*d - 5*b*c)*(-a^7*b^5)^(1/2)*(256*a^15*b^10*c^18*d^2 - 1536*a^16*b^9*c^17*d^3 + 3584*a^17*b^8*c^16*d^4 - 3584*a^18*b^7*c^15*d^5 + 3584*a^20*b^5*c^13*d^7 - 3584*a^21*b^4*c^12*d^8 + 1536*a^22*b^3*c^11*d^9 - 256*a^23*b^2*c^10*d^10))/(4*(a^9*d^2 + a^7*b^2*c^2 - 2*a^8*b*c*d))))/(4*(a^9*d^2 + a^7*b^2*c^2 - 2*a^8*b*c*d)))*(-a^7*b^5)^(1/2))/(4*(a^9*d^2 + a^7*b^2*c^2 - 2*a^8*b*c*d))))*(7*a*d - 5*b*c)*(-a^7*b^5)^(1/2)*1i)/(2*(a^9*d^2 + a^7*b^2*c^2 - 2*a^8*b*c*d))","B"
298,1,217,160,1.106789,"\text{Not used}","int(1/(x^5*(a + b*x^2)^2*(c + d*x^2)),x)","\frac{\frac{x^2\,\left(2\,a\,d+3\,b\,c\right)}{4\,a^2\,c^2}-\frac{1}{4\,a\,c}+\frac{x^4\,\left(a^2\,b\,d^2+a\,b^2\,c\,d-3\,b^3\,c^2\right)}{2\,a^3\,c^2\,\left(a\,d-b\,c\right)}}{b\,x^6+a\,x^4}-\frac{\ln\left(b\,x^2+a\right)\,\left(3\,b^4\,c-4\,a\,b^3\,d\right)}{2\,a^6\,d^2-4\,a^5\,b\,c\,d+2\,a^4\,b^2\,c^2}-\frac{d^4\,\ln\left(d\,x^2+c\right)}{2\,\left(a^2\,c^3\,d^2-2\,a\,b\,c^4\,d+b^2\,c^5\right)}+\frac{\ln\left(x\right)\,\left(a^2\,d^2+2\,a\,b\,c\,d+3\,b^2\,c^2\right)}{a^4\,c^3}","Not used",1,"((x^2*(2*a*d + 3*b*c))/(4*a^2*c^2) - 1/(4*a*c) + (x^4*(a^2*b*d^2 - 3*b^3*c^2 + a*b^2*c*d))/(2*a^3*c^2*(a*d - b*c)))/(a*x^4 + b*x^6) - (log(a + b*x^2)*(3*b^4*c - 4*a*b^3*d))/(2*a^6*d^2 + 2*a^4*b^2*c^2 - 4*a^5*b*c*d) - (d^4*log(c + d*x^2))/(2*(b^2*c^5 + a^2*c^3*d^2 - 2*a*b*c^4*d)) + (log(x)*(a^2*d^2 + 3*b^2*c^2 + 2*a*b*c*d))/(a^4*c^3)","B"
299,1,2737,250,1.284794,"\text{Not used}","int(1/(x^6*(a + b*x^2)^2*(c + d*x^2)),x)","-\frac{\frac{1}{5\,a\,c}-\frac{x^2\,\left(5\,a\,d+7\,b\,c\right)}{15\,a^2\,c^2}+\frac{x^4\,\left(3\,a^2\,d^2+5\,a\,b\,c\,d+7\,b^2\,c^2\right)}{3\,a^3\,c^3}+\frac{x^6\,\left(2\,a^3\,b\,d^3+2\,a^2\,b^2\,c\,d^2+2\,a\,b^3\,c^2\,d-7\,b^4\,c^3\right)}{2\,a^4\,c^3\,\left(a\,d-b\,c\right)}}{b\,x^7+a\,x^5}+\frac{\mathrm{atan}\left(\frac{a^9\,d\,x\,{\left(-c^7\,d^9\right)}^{3/2}\,4{}\mathrm{i}+b^9\,c^{16}\,d\,x\,\sqrt{-c^7\,d^9}\,49{}\mathrm{i}+a^2\,b^7\,c^{14}\,d^3\,x\,\sqrt{-c^7\,d^9}\,81{}\mathrm{i}-a\,b^8\,c^{15}\,d^2\,x\,\sqrt{-c^7\,d^9}\,126{}\mathrm{i}}{4\,a^9\,c^{11}\,d^{14}-81\,a^2\,b^7\,c^{18}\,d^7+126\,a\,b^8\,c^{19}\,d^6-49\,b^9\,c^{20}\,d^5}\right)\,\sqrt{-c^7\,d^9}\,1{}\mathrm{i}}{a^2\,c^7\,d^2-2\,a\,b\,c^8\,d+b^2\,c^9}-\frac{\mathrm{atan}\left(\frac{\frac{\left(x\,\left(-64\,a^{23}\,b^3\,c^9\,d^{14}+192\,a^{22}\,b^4\,c^{10}\,d^{13}-192\,a^{21}\,b^5\,c^{11}\,d^{12}+64\,a^{20}\,b^6\,c^{12}\,d^{11}-1296\,a^{17}\,b^9\,c^{15}\,d^8+5904\,a^{16}\,b^{10}\,c^{16}\,d^7-10720\,a^{15}\,b^{11}\,c^{17}\,d^6+9696\,a^{14}\,b^{12}\,c^{18}\,d^5-4368\,a^{13}\,b^{13}\,c^{19}\,d^4+784\,a^{12}\,b^{14}\,c^{20}\,d^3\right)+\frac{\left(9\,a\,d-7\,b\,c\right)\,\sqrt{-a^9\,b^7}\,\left(2816\,a^{17}\,b^{11}\,c^{21}\,d^3-448\,a^{16}\,b^{12}\,c^{22}\,d^2-7360\,a^{18}\,b^{10}\,c^{20}\,d^4+10240\,a^{19}\,b^9\,c^{19}\,d^5-8000\,a^{20}\,b^8\,c^{18}\,d^6+3200\,a^{21}\,b^7\,c^{17}\,d^7+64\,a^{22}\,b^6\,c^{16}\,d^8-1280\,a^{23}\,b^5\,c^{15}\,d^9+1280\,a^{24}\,b^4\,c^{14}\,d^{10}-640\,a^{25}\,b^3\,c^{13}\,d^{11}+128\,a^{26}\,b^2\,c^{12}\,d^{12}+\frac{x\,\left(9\,a\,d-7\,b\,c\right)\,\sqrt{-a^9\,b^7}\,\left(-256\,a^{28}\,b^2\,c^{15}\,d^{10}+1536\,a^{27}\,b^3\,c^{16}\,d^9-3584\,a^{26}\,b^4\,c^{17}\,d^8+3584\,a^{25}\,b^5\,c^{18}\,d^7-3584\,a^{23}\,b^7\,c^{20}\,d^5+3584\,a^{22}\,b^8\,c^{21}\,d^4-1536\,a^{21}\,b^9\,c^{22}\,d^3+256\,a^{20}\,b^{10}\,c^{23}\,d^2\right)}{4\,\left(a^{11}\,d^2-2\,a^{10}\,b\,c\,d+a^9\,b^2\,c^2\right)}\right)}{4\,\left(a^{11}\,d^2-2\,a^{10}\,b\,c\,d+a^9\,b^2\,c^2\right)}\right)\,\left(9\,a\,d-7\,b\,c\right)\,\sqrt{-a^9\,b^7}\,1{}\mathrm{i}}{4\,\left(a^{11}\,d^2-2\,a^{10}\,b\,c\,d+a^9\,b^2\,c^2\right)}+\frac{\left(x\,\left(-64\,a^{23}\,b^3\,c^9\,d^{14}+192\,a^{22}\,b^4\,c^{10}\,d^{13}-192\,a^{21}\,b^5\,c^{11}\,d^{12}+64\,a^{20}\,b^6\,c^{12}\,d^{11}-1296\,a^{17}\,b^9\,c^{15}\,d^8+5904\,a^{16}\,b^{10}\,c^{16}\,d^7-10720\,a^{15}\,b^{11}\,c^{17}\,d^6+9696\,a^{14}\,b^{12}\,c^{18}\,d^5-4368\,a^{13}\,b^{13}\,c^{19}\,d^4+784\,a^{12}\,b^{14}\,c^{20}\,d^3\right)+\frac{\left(9\,a\,d-7\,b\,c\right)\,\sqrt{-a^9\,b^7}\,\left(448\,a^{16}\,b^{12}\,c^{22}\,d^2-2816\,a^{17}\,b^{11}\,c^{21}\,d^3+7360\,a^{18}\,b^{10}\,c^{20}\,d^4-10240\,a^{19}\,b^9\,c^{19}\,d^5+8000\,a^{20}\,b^8\,c^{18}\,d^6-3200\,a^{21}\,b^7\,c^{17}\,d^7-64\,a^{22}\,b^6\,c^{16}\,d^8+1280\,a^{23}\,b^5\,c^{15}\,d^9-1280\,a^{24}\,b^4\,c^{14}\,d^{10}+640\,a^{25}\,b^3\,c^{13}\,d^{11}-128\,a^{26}\,b^2\,c^{12}\,d^{12}+\frac{x\,\left(9\,a\,d-7\,b\,c\right)\,\sqrt{-a^9\,b^7}\,\left(-256\,a^{28}\,b^2\,c^{15}\,d^{10}+1536\,a^{27}\,b^3\,c^{16}\,d^9-3584\,a^{26}\,b^4\,c^{17}\,d^8+3584\,a^{25}\,b^5\,c^{18}\,d^7-3584\,a^{23}\,b^7\,c^{20}\,d^5+3584\,a^{22}\,b^8\,c^{21}\,d^4-1536\,a^{21}\,b^9\,c^{22}\,d^3+256\,a^{20}\,b^{10}\,c^{23}\,d^2\right)}{4\,\left(a^{11}\,d^2-2\,a^{10}\,b\,c\,d+a^9\,b^2\,c^2\right)}\right)}{4\,\left(a^{11}\,d^2-2\,a^{10}\,b\,c\,d+a^9\,b^2\,c^2\right)}\right)\,\left(9\,a\,d-7\,b\,c\right)\,\sqrt{-a^9\,b^7}\,1{}\mathrm{i}}{4\,\left(a^{11}\,d^2-2\,a^{10}\,b\,c\,d+a^9\,b^2\,c^2\right)}}{\frac{\left(x\,\left(-64\,a^{23}\,b^3\,c^9\,d^{14}+192\,a^{22}\,b^4\,c^{10}\,d^{13}-192\,a^{21}\,b^5\,c^{11}\,d^{12}+64\,a^{20}\,b^6\,c^{12}\,d^{11}-1296\,a^{17}\,b^9\,c^{15}\,d^8+5904\,a^{16}\,b^{10}\,c^{16}\,d^7-10720\,a^{15}\,b^{11}\,c^{17}\,d^6+9696\,a^{14}\,b^{12}\,c^{18}\,d^5-4368\,a^{13}\,b^{13}\,c^{19}\,d^4+784\,a^{12}\,b^{14}\,c^{20}\,d^3\right)+\frac{\left(9\,a\,d-7\,b\,c\right)\,\sqrt{-a^9\,b^7}\,\left(448\,a^{16}\,b^{12}\,c^{22}\,d^2-2816\,a^{17}\,b^{11}\,c^{21}\,d^3+7360\,a^{18}\,b^{10}\,c^{20}\,d^4-10240\,a^{19}\,b^9\,c^{19}\,d^5+8000\,a^{20}\,b^8\,c^{18}\,d^6-3200\,a^{21}\,b^7\,c^{17}\,d^7-64\,a^{22}\,b^6\,c^{16}\,d^8+1280\,a^{23}\,b^5\,c^{15}\,d^9-1280\,a^{24}\,b^4\,c^{14}\,d^{10}+640\,a^{25}\,b^3\,c^{13}\,d^{11}-128\,a^{26}\,b^2\,c^{12}\,d^{12}+\frac{x\,\left(9\,a\,d-7\,b\,c\right)\,\sqrt{-a^9\,b^7}\,\left(-256\,a^{28}\,b^2\,c^{15}\,d^{10}+1536\,a^{27}\,b^3\,c^{16}\,d^9-3584\,a^{26}\,b^4\,c^{17}\,d^8+3584\,a^{25}\,b^5\,c^{18}\,d^7-3584\,a^{23}\,b^7\,c^{20}\,d^5+3584\,a^{22}\,b^8\,c^{21}\,d^4-1536\,a^{21}\,b^9\,c^{22}\,d^3+256\,a^{20}\,b^{10}\,c^{23}\,d^2\right)}{4\,\left(a^{11}\,d^2-2\,a^{10}\,b\,c\,d+a^9\,b^2\,c^2\right)}\right)}{4\,\left(a^{11}\,d^2-2\,a^{10}\,b\,c\,d+a^9\,b^2\,c^2\right)}\right)\,\left(9\,a\,d-7\,b\,c\right)\,\sqrt{-a^9\,b^7}}{4\,\left(a^{11}\,d^2-2\,a^{10}\,b\,c\,d+a^9\,b^2\,c^2\right)}-\frac{\left(x\,\left(-64\,a^{23}\,b^3\,c^9\,d^{14}+192\,a^{22}\,b^4\,c^{10}\,d^{13}-192\,a^{21}\,b^5\,c^{11}\,d^{12}+64\,a^{20}\,b^6\,c^{12}\,d^{11}-1296\,a^{17}\,b^9\,c^{15}\,d^8+5904\,a^{16}\,b^{10}\,c^{16}\,d^7-10720\,a^{15}\,b^{11}\,c^{17}\,d^6+9696\,a^{14}\,b^{12}\,c^{18}\,d^5-4368\,a^{13}\,b^{13}\,c^{19}\,d^4+784\,a^{12}\,b^{14}\,c^{20}\,d^3\right)+\frac{\left(9\,a\,d-7\,b\,c\right)\,\sqrt{-a^9\,b^7}\,\left(2816\,a^{17}\,b^{11}\,c^{21}\,d^3-448\,a^{16}\,b^{12}\,c^{22}\,d^2-7360\,a^{18}\,b^{10}\,c^{20}\,d^4+10240\,a^{19}\,b^9\,c^{19}\,d^5-8000\,a^{20}\,b^8\,c^{18}\,d^6+3200\,a^{21}\,b^7\,c^{17}\,d^7+64\,a^{22}\,b^6\,c^{16}\,d^8-1280\,a^{23}\,b^5\,c^{15}\,d^9+1280\,a^{24}\,b^4\,c^{14}\,d^{10}-640\,a^{25}\,b^3\,c^{13}\,d^{11}+128\,a^{26}\,b^2\,c^{12}\,d^{12}+\frac{x\,\left(9\,a\,d-7\,b\,c\right)\,\sqrt{-a^9\,b^7}\,\left(-256\,a^{28}\,b^2\,c^{15}\,d^{10}+1536\,a^{27}\,b^3\,c^{16}\,d^9-3584\,a^{26}\,b^4\,c^{17}\,d^8+3584\,a^{25}\,b^5\,c^{18}\,d^7-3584\,a^{23}\,b^7\,c^{20}\,d^5+3584\,a^{22}\,b^8\,c^{21}\,d^4-1536\,a^{21}\,b^9\,c^{22}\,d^3+256\,a^{20}\,b^{10}\,c^{23}\,d^2\right)}{4\,\left(a^{11}\,d^2-2\,a^{10}\,b\,c\,d+a^9\,b^2\,c^2\right)}\right)}{4\,\left(a^{11}\,d^2-2\,a^{10}\,b\,c\,d+a^9\,b^2\,c^2\right)}\right)\,\left(9\,a\,d-7\,b\,c\right)\,\sqrt{-a^9\,b^7}}{4\,\left(a^{11}\,d^2-2\,a^{10}\,b\,c\,d+a^9\,b^2\,c^2\right)}+784\,a^{12}\,b^{12}\,c^{15}\,d^7-2800\,a^{13}\,b^{11}\,c^{14}\,d^8+3312\,a^{14}\,b^{10}\,c^{13}\,d^9-1296\,a^{15}\,b^9\,c^{12}\,d^{10}+224\,a^{16}\,b^8\,c^{11}\,d^{11}-512\,a^{17}\,b^7\,c^{10}\,d^{12}+288\,a^{18}\,b^6\,c^9\,d^{13}}\right)\,\left(9\,a\,d-7\,b\,c\right)\,\sqrt{-a^9\,b^7}\,1{}\mathrm{i}}{2\,\left(a^{11}\,d^2-2\,a^{10}\,b\,c\,d+a^9\,b^2\,c^2\right)}","Not used",1,"(atan((a^9*d*x*(-c^7*d^9)^(3/2)*4i + b^9*c^16*d*x*(-c^7*d^9)^(1/2)*49i + a^2*b^7*c^14*d^3*x*(-c^7*d^9)^(1/2)*81i - a*b^8*c^15*d^2*x*(-c^7*d^9)^(1/2)*126i)/(4*a^9*c^11*d^14 - 49*b^9*c^20*d^5 + 126*a*b^8*c^19*d^6 - 81*a^2*b^7*c^18*d^7))*(-c^7*d^9)^(1/2)*1i)/(b^2*c^9 + a^2*c^7*d^2 - 2*a*b*c^8*d) - (1/(5*a*c) - (x^2*(5*a*d + 7*b*c))/(15*a^2*c^2) + (x^4*(3*a^2*d^2 + 7*b^2*c^2 + 5*a*b*c*d))/(3*a^3*c^3) + (x^6*(2*a^3*b*d^3 - 7*b^4*c^3 + 2*a^2*b^2*c*d^2 + 2*a*b^3*c^2*d))/(2*a^4*c^3*(a*d - b*c)))/(a*x^5 + b*x^7) - (atan((((x*(784*a^12*b^14*c^20*d^3 - 4368*a^13*b^13*c^19*d^4 + 9696*a^14*b^12*c^18*d^5 - 10720*a^15*b^11*c^17*d^6 + 5904*a^16*b^10*c^16*d^7 - 1296*a^17*b^9*c^15*d^8 + 64*a^20*b^6*c^12*d^11 - 192*a^21*b^5*c^11*d^12 + 192*a^22*b^4*c^10*d^13 - 64*a^23*b^3*c^9*d^14) + ((9*a*d - 7*b*c)*(-a^9*b^7)^(1/2)*(2816*a^17*b^11*c^21*d^3 - 448*a^16*b^12*c^22*d^2 - 7360*a^18*b^10*c^20*d^4 + 10240*a^19*b^9*c^19*d^5 - 8000*a^20*b^8*c^18*d^6 + 3200*a^21*b^7*c^17*d^7 + 64*a^22*b^6*c^16*d^8 - 1280*a^23*b^5*c^15*d^9 + 1280*a^24*b^4*c^14*d^10 - 640*a^25*b^3*c^13*d^11 + 128*a^26*b^2*c^12*d^12 + (x*(9*a*d - 7*b*c)*(-a^9*b^7)^(1/2)*(256*a^20*b^10*c^23*d^2 - 1536*a^21*b^9*c^22*d^3 + 3584*a^22*b^8*c^21*d^4 - 3584*a^23*b^7*c^20*d^5 + 3584*a^25*b^5*c^18*d^7 - 3584*a^26*b^4*c^17*d^8 + 1536*a^27*b^3*c^16*d^9 - 256*a^28*b^2*c^15*d^10))/(4*(a^11*d^2 + a^9*b^2*c^2 - 2*a^10*b*c*d))))/(4*(a^11*d^2 + a^9*b^2*c^2 - 2*a^10*b*c*d)))*(9*a*d - 7*b*c)*(-a^9*b^7)^(1/2)*1i)/(4*(a^11*d^2 + a^9*b^2*c^2 - 2*a^10*b*c*d)) + ((x*(784*a^12*b^14*c^20*d^3 - 4368*a^13*b^13*c^19*d^4 + 9696*a^14*b^12*c^18*d^5 - 10720*a^15*b^11*c^17*d^6 + 5904*a^16*b^10*c^16*d^7 - 1296*a^17*b^9*c^15*d^8 + 64*a^20*b^6*c^12*d^11 - 192*a^21*b^5*c^11*d^12 + 192*a^22*b^4*c^10*d^13 - 64*a^23*b^3*c^9*d^14) + ((9*a*d - 7*b*c)*(-a^9*b^7)^(1/2)*(448*a^16*b^12*c^22*d^2 - 2816*a^17*b^11*c^21*d^3 + 7360*a^18*b^10*c^20*d^4 - 10240*a^19*b^9*c^19*d^5 + 8000*a^20*b^8*c^18*d^6 - 3200*a^21*b^7*c^17*d^7 - 64*a^22*b^6*c^16*d^8 + 1280*a^23*b^5*c^15*d^9 - 1280*a^24*b^4*c^14*d^10 + 640*a^25*b^3*c^13*d^11 - 128*a^26*b^2*c^12*d^12 + (x*(9*a*d - 7*b*c)*(-a^9*b^7)^(1/2)*(256*a^20*b^10*c^23*d^2 - 1536*a^21*b^9*c^22*d^3 + 3584*a^22*b^8*c^21*d^4 - 3584*a^23*b^7*c^20*d^5 + 3584*a^25*b^5*c^18*d^7 - 3584*a^26*b^4*c^17*d^8 + 1536*a^27*b^3*c^16*d^9 - 256*a^28*b^2*c^15*d^10))/(4*(a^11*d^2 + a^9*b^2*c^2 - 2*a^10*b*c*d))))/(4*(a^11*d^2 + a^9*b^2*c^2 - 2*a^10*b*c*d)))*(9*a*d - 7*b*c)*(-a^9*b^7)^(1/2)*1i)/(4*(a^11*d^2 + a^9*b^2*c^2 - 2*a^10*b*c*d)))/(((x*(784*a^12*b^14*c^20*d^3 - 4368*a^13*b^13*c^19*d^4 + 9696*a^14*b^12*c^18*d^5 - 10720*a^15*b^11*c^17*d^6 + 5904*a^16*b^10*c^16*d^7 - 1296*a^17*b^9*c^15*d^8 + 64*a^20*b^6*c^12*d^11 - 192*a^21*b^5*c^11*d^12 + 192*a^22*b^4*c^10*d^13 - 64*a^23*b^3*c^9*d^14) + ((9*a*d - 7*b*c)*(-a^9*b^7)^(1/2)*(448*a^16*b^12*c^22*d^2 - 2816*a^17*b^11*c^21*d^3 + 7360*a^18*b^10*c^20*d^4 - 10240*a^19*b^9*c^19*d^5 + 8000*a^20*b^8*c^18*d^6 - 3200*a^21*b^7*c^17*d^7 - 64*a^22*b^6*c^16*d^8 + 1280*a^23*b^5*c^15*d^9 - 1280*a^24*b^4*c^14*d^10 + 640*a^25*b^3*c^13*d^11 - 128*a^26*b^2*c^12*d^12 + (x*(9*a*d - 7*b*c)*(-a^9*b^7)^(1/2)*(256*a^20*b^10*c^23*d^2 - 1536*a^21*b^9*c^22*d^3 + 3584*a^22*b^8*c^21*d^4 - 3584*a^23*b^7*c^20*d^5 + 3584*a^25*b^5*c^18*d^7 - 3584*a^26*b^4*c^17*d^8 + 1536*a^27*b^3*c^16*d^9 - 256*a^28*b^2*c^15*d^10))/(4*(a^11*d^2 + a^9*b^2*c^2 - 2*a^10*b*c*d))))/(4*(a^11*d^2 + a^9*b^2*c^2 - 2*a^10*b*c*d)))*(9*a*d - 7*b*c)*(-a^9*b^7)^(1/2))/(4*(a^11*d^2 + a^9*b^2*c^2 - 2*a^10*b*c*d)) - ((x*(784*a^12*b^14*c^20*d^3 - 4368*a^13*b^13*c^19*d^4 + 9696*a^14*b^12*c^18*d^5 - 10720*a^15*b^11*c^17*d^6 + 5904*a^16*b^10*c^16*d^7 - 1296*a^17*b^9*c^15*d^8 + 64*a^20*b^6*c^12*d^11 - 192*a^21*b^5*c^11*d^12 + 192*a^22*b^4*c^10*d^13 - 64*a^23*b^3*c^9*d^14) + ((9*a*d - 7*b*c)*(-a^9*b^7)^(1/2)*(2816*a^17*b^11*c^21*d^3 - 448*a^16*b^12*c^22*d^2 - 7360*a^18*b^10*c^20*d^4 + 10240*a^19*b^9*c^19*d^5 - 8000*a^20*b^8*c^18*d^6 + 3200*a^21*b^7*c^17*d^7 + 64*a^22*b^6*c^16*d^8 - 1280*a^23*b^5*c^15*d^9 + 1280*a^24*b^4*c^14*d^10 - 640*a^25*b^3*c^13*d^11 + 128*a^26*b^2*c^12*d^12 + (x*(9*a*d - 7*b*c)*(-a^9*b^7)^(1/2)*(256*a^20*b^10*c^23*d^2 - 1536*a^21*b^9*c^22*d^3 + 3584*a^22*b^8*c^21*d^4 - 3584*a^23*b^7*c^20*d^5 + 3584*a^25*b^5*c^18*d^7 - 3584*a^26*b^4*c^17*d^8 + 1536*a^27*b^3*c^16*d^9 - 256*a^28*b^2*c^15*d^10))/(4*(a^11*d^2 + a^9*b^2*c^2 - 2*a^10*b*c*d))))/(4*(a^11*d^2 + a^9*b^2*c^2 - 2*a^10*b*c*d)))*(9*a*d - 7*b*c)*(-a^9*b^7)^(1/2))/(4*(a^11*d^2 + a^9*b^2*c^2 - 2*a^10*b*c*d)) + 784*a^12*b^12*c^15*d^7 - 2800*a^13*b^11*c^14*d^8 + 3312*a^14*b^10*c^13*d^9 - 1296*a^15*b^9*c^12*d^10 + 224*a^16*b^8*c^11*d^11 - 512*a^17*b^7*c^10*d^12 + 288*a^18*b^6*c^9*d^13))*(9*a*d - 7*b*c)*(-a^9*b^7)^(1/2)*1i)/(2*(a^11*d^2 + a^9*b^2*c^2 - 2*a^10*b*c*d))","B"
300,1,278,210,1.225985,"\text{Not used}","int(1/(x^7*(a + b*x^2)^2*(c + d*x^2)),x)","\frac{\ln\left(b\,x^2+a\right)\,\left(4\,b^5\,c-5\,a\,b^4\,d\right)}{2\,a^7\,d^2-4\,a^6\,b\,c\,d+2\,a^5\,b^2\,c^2}-\frac{\frac{1}{6\,a\,c}-\frac{x^2\,\left(3\,a\,d+4\,b\,c\right)}{12\,a^2\,c^2}+\frac{x^4\,\left(2\,a^2\,d^2+3\,a\,b\,c\,d+4\,b^2\,c^2\right)}{4\,a^3\,c^3}+\frac{x^6\,\left(a^3\,b\,d^3+a^2\,b^2\,c\,d^2+a\,b^3\,c^2\,d-4\,b^4\,c^3\right)}{2\,a^4\,c^3\,\left(a\,d-b\,c\right)}}{b\,x^8+a\,x^6}+\frac{d^5\,\ln\left(d\,x^2+c\right)}{2\,\left(a^2\,c^4\,d^2-2\,a\,b\,c^5\,d+b^2\,c^6\right)}-\frac{\ln\left(x\right)\,\left(a^3\,d^3+2\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d+4\,b^3\,c^3\right)}{a^5\,c^4}","Not used",1,"(log(a + b*x^2)*(4*b^5*c - 5*a*b^4*d))/(2*a^7*d^2 + 2*a^5*b^2*c^2 - 4*a^6*b*c*d) - (1/(6*a*c) - (x^2*(3*a*d + 4*b*c))/(12*a^2*c^2) + (x^4*(2*a^2*d^2 + 4*b^2*c^2 + 3*a*b*c*d))/(4*a^3*c^3) + (x^6*(a^3*b*d^3 - 4*b^4*c^3 + a^2*b^2*c*d^2 + a*b^3*c^2*d))/(2*a^4*c^3*(a*d - b*c)))/(a*x^6 + b*x^8) + (d^5*log(c + d*x^2))/(2*(b^2*c^6 + a^2*c^4*d^2 - 2*a*b*c^5*d)) - (log(x)*(a^3*d^3 + 4*b^3*c^3 + 3*a*b^2*c^2*d + 2*a^2*b*c*d^2))/(a^5*c^4)","B"
301,1,5395,162,1.843352,"\text{Not used}","int(x^4/((a + b*x^2)^2*(c + d*x^2)^2),x)","\frac{\frac{x^3\,\left(a\,d+b\,c\right)}{2\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}+\frac{a\,c\,x}{a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2}}{b\,d\,x^4+\left(a\,d+b\,c\right)\,x^2+a\,c}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-c\,d}\,\left(\frac{x\,\left(a^4\,b\,d^5+6\,a^3\,b^2\,c\,d^4+18\,a^2\,b^3\,c^2\,d^3+6\,a\,b^4\,c^3\,d^2+b^5\,c^4\,d\right)}{2\,\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)}-\frac{\sqrt{-c\,d}\,\left(\frac{4\,a^7\,b^2\,c\,d^8-24\,a^6\,b^3\,c^2\,d^7+60\,a^5\,b^4\,c^3\,d^6-80\,a^4\,b^5\,c^4\,d^5+60\,a^3\,b^6\,c^5\,d^4-24\,a^2\,b^7\,c^6\,d^3+4\,a\,b^8\,c^7\,d^2}{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}-\frac{x\,\sqrt{-c\,d}\,\left(3\,a\,d+b\,c\right)\,\left(16\,a^7\,b^2\,d^9-80\,a^6\,b^3\,c\,d^8+144\,a^5\,b^4\,c^2\,d^7-80\,a^4\,b^5\,c^3\,d^6-80\,a^3\,b^6\,c^4\,d^5+144\,a^2\,b^7\,c^5\,d^4-80\,a\,b^8\,c^6\,d^3+16\,b^9\,c^7\,d^2\right)}{8\,\left(a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d\right)\,\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)}\right)\,\left(3\,a\,d+b\,c\right)}{4\,\left(a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d\right)}\right)\,\left(3\,a\,d+b\,c\right)\,1{}\mathrm{i}}{4\,\left(a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d\right)}+\frac{\sqrt{-c\,d}\,\left(\frac{x\,\left(a^4\,b\,d^5+6\,a^3\,b^2\,c\,d^4+18\,a^2\,b^3\,c^2\,d^3+6\,a\,b^4\,c^3\,d^2+b^5\,c^4\,d\right)}{2\,\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)}+\frac{\sqrt{-c\,d}\,\left(\frac{4\,a^7\,b^2\,c\,d^8-24\,a^6\,b^3\,c^2\,d^7+60\,a^5\,b^4\,c^3\,d^6-80\,a^4\,b^5\,c^4\,d^5+60\,a^3\,b^6\,c^5\,d^4-24\,a^2\,b^7\,c^6\,d^3+4\,a\,b^8\,c^7\,d^2}{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}+\frac{x\,\sqrt{-c\,d}\,\left(3\,a\,d+b\,c\right)\,\left(16\,a^7\,b^2\,d^9-80\,a^6\,b^3\,c\,d^8+144\,a^5\,b^4\,c^2\,d^7-80\,a^4\,b^5\,c^3\,d^6-80\,a^3\,b^6\,c^4\,d^5+144\,a^2\,b^7\,c^5\,d^4-80\,a\,b^8\,c^6\,d^3+16\,b^9\,c^7\,d^2\right)}{8\,\left(a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d\right)\,\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)}\right)\,\left(3\,a\,d+b\,c\right)}{4\,\left(a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d\right)}\right)\,\left(3\,a\,d+b\,c\right)\,1{}\mathrm{i}}{4\,\left(a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d\right)}}{\frac{\frac{3\,a^4\,b\,c\,d^4}{4}+\frac{13\,a^3\,b^2\,c^2\,d^3}{4}+\frac{13\,a^2\,b^3\,c^3\,d^2}{4}+\frac{3\,a\,b^4\,c^4\,d}{4}}{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}-\frac{\sqrt{-c\,d}\,\left(\frac{x\,\left(a^4\,b\,d^5+6\,a^3\,b^2\,c\,d^4+18\,a^2\,b^3\,c^2\,d^3+6\,a\,b^4\,c^3\,d^2+b^5\,c^4\,d\right)}{2\,\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)}-\frac{\sqrt{-c\,d}\,\left(\frac{4\,a^7\,b^2\,c\,d^8-24\,a^6\,b^3\,c^2\,d^7+60\,a^5\,b^4\,c^3\,d^6-80\,a^4\,b^5\,c^4\,d^5+60\,a^3\,b^6\,c^5\,d^4-24\,a^2\,b^7\,c^6\,d^3+4\,a\,b^8\,c^7\,d^2}{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}-\frac{x\,\sqrt{-c\,d}\,\left(3\,a\,d+b\,c\right)\,\left(16\,a^7\,b^2\,d^9-80\,a^6\,b^3\,c\,d^8+144\,a^5\,b^4\,c^2\,d^7-80\,a^4\,b^5\,c^3\,d^6-80\,a^3\,b^6\,c^4\,d^5+144\,a^2\,b^7\,c^5\,d^4-80\,a\,b^8\,c^6\,d^3+16\,b^9\,c^7\,d^2\right)}{8\,\left(a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d\right)\,\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)}\right)\,\left(3\,a\,d+b\,c\right)}{4\,\left(a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d\right)}\right)\,\left(3\,a\,d+b\,c\right)}{4\,\left(a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d\right)}+\frac{\sqrt{-c\,d}\,\left(\frac{x\,\left(a^4\,b\,d^5+6\,a^3\,b^2\,c\,d^4+18\,a^2\,b^3\,c^2\,d^3+6\,a\,b^4\,c^3\,d^2+b^5\,c^4\,d\right)}{2\,\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)}+\frac{\sqrt{-c\,d}\,\left(\frac{4\,a^7\,b^2\,c\,d^8-24\,a^6\,b^3\,c^2\,d^7+60\,a^5\,b^4\,c^3\,d^6-80\,a^4\,b^5\,c^4\,d^5+60\,a^3\,b^6\,c^5\,d^4-24\,a^2\,b^7\,c^6\,d^3+4\,a\,b^8\,c^7\,d^2}{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}+\frac{x\,\sqrt{-c\,d}\,\left(3\,a\,d+b\,c\right)\,\left(16\,a^7\,b^2\,d^9-80\,a^6\,b^3\,c\,d^8+144\,a^5\,b^4\,c^2\,d^7-80\,a^4\,b^5\,c^3\,d^6-80\,a^3\,b^6\,c^4\,d^5+144\,a^2\,b^7\,c^5\,d^4-80\,a\,b^8\,c^6\,d^3+16\,b^9\,c^7\,d^2\right)}{8\,\left(a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d\right)\,\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)}\right)\,\left(3\,a\,d+b\,c\right)}{4\,\left(a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d\right)}\right)\,\left(3\,a\,d+b\,c\right)}{4\,\left(a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d\right)}}\right)\,\sqrt{-c\,d}\,\left(3\,a\,d+b\,c\right)\,1{}\mathrm{i}}{2\,\left(a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-a\,b}\,\left(\frac{x\,\left(a^4\,b\,d^5+6\,a^3\,b^2\,c\,d^4+18\,a^2\,b^3\,c^2\,d^3+6\,a\,b^4\,c^3\,d^2+b^5\,c^4\,d\right)}{2\,\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)}-\frac{\sqrt{-a\,b}\,\left(\frac{4\,a^7\,b^2\,c\,d^8-24\,a^6\,b^3\,c^2\,d^7+60\,a^5\,b^4\,c^3\,d^6-80\,a^4\,b^5\,c^4\,d^5+60\,a^3\,b^6\,c^5\,d^4-24\,a^2\,b^7\,c^6\,d^3+4\,a\,b^8\,c^7\,d^2}{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}-\frac{x\,\sqrt{-a\,b}\,\left(a\,d+3\,b\,c\right)\,\left(16\,a^7\,b^2\,d^9-80\,a^6\,b^3\,c\,d^8+144\,a^5\,b^4\,c^2\,d^7-80\,a^4\,b^5\,c^3\,d^6-80\,a^3\,b^6\,c^4\,d^5+144\,a^2\,b^7\,c^5\,d^4-80\,a\,b^8\,c^6\,d^3+16\,b^9\,c^7\,d^2\right)}{8\,\left(-a^3\,b\,d^3+3\,a^2\,b^2\,c\,d^2-3\,a\,b^3\,c^2\,d+b^4\,c^3\right)\,\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)}\right)\,\left(a\,d+3\,b\,c\right)}{4\,\left(-a^3\,b\,d^3+3\,a^2\,b^2\,c\,d^2-3\,a\,b^3\,c^2\,d+b^4\,c^3\right)}\right)\,\left(a\,d+3\,b\,c\right)\,1{}\mathrm{i}}{4\,\left(-a^3\,b\,d^3+3\,a^2\,b^2\,c\,d^2-3\,a\,b^3\,c^2\,d+b^4\,c^3\right)}+\frac{\sqrt{-a\,b}\,\left(\frac{x\,\left(a^4\,b\,d^5+6\,a^3\,b^2\,c\,d^4+18\,a^2\,b^3\,c^2\,d^3+6\,a\,b^4\,c^3\,d^2+b^5\,c^4\,d\right)}{2\,\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)}+\frac{\sqrt{-a\,b}\,\left(\frac{4\,a^7\,b^2\,c\,d^8-24\,a^6\,b^3\,c^2\,d^7+60\,a^5\,b^4\,c^3\,d^6-80\,a^4\,b^5\,c^4\,d^5+60\,a^3\,b^6\,c^5\,d^4-24\,a^2\,b^7\,c^6\,d^3+4\,a\,b^8\,c^7\,d^2}{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}+\frac{x\,\sqrt{-a\,b}\,\left(a\,d+3\,b\,c\right)\,\left(16\,a^7\,b^2\,d^9-80\,a^6\,b^3\,c\,d^8+144\,a^5\,b^4\,c^2\,d^7-80\,a^4\,b^5\,c^3\,d^6-80\,a^3\,b^6\,c^4\,d^5+144\,a^2\,b^7\,c^5\,d^4-80\,a\,b^8\,c^6\,d^3+16\,b^9\,c^7\,d^2\right)}{8\,\left(-a^3\,b\,d^3+3\,a^2\,b^2\,c\,d^2-3\,a\,b^3\,c^2\,d+b^4\,c^3\right)\,\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)}\right)\,\left(a\,d+3\,b\,c\right)}{4\,\left(-a^3\,b\,d^3+3\,a^2\,b^2\,c\,d^2-3\,a\,b^3\,c^2\,d+b^4\,c^3\right)}\right)\,\left(a\,d+3\,b\,c\right)\,1{}\mathrm{i}}{4\,\left(-a^3\,b\,d^3+3\,a^2\,b^2\,c\,d^2-3\,a\,b^3\,c^2\,d+b^4\,c^3\right)}}{\frac{\frac{3\,a^4\,b\,c\,d^4}{4}+\frac{13\,a^3\,b^2\,c^2\,d^3}{4}+\frac{13\,a^2\,b^3\,c^3\,d^2}{4}+\frac{3\,a\,b^4\,c^4\,d}{4}}{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}-\frac{\sqrt{-a\,b}\,\left(\frac{x\,\left(a^4\,b\,d^5+6\,a^3\,b^2\,c\,d^4+18\,a^2\,b^3\,c^2\,d^3+6\,a\,b^4\,c^3\,d^2+b^5\,c^4\,d\right)}{2\,\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)}-\frac{\sqrt{-a\,b}\,\left(\frac{4\,a^7\,b^2\,c\,d^8-24\,a^6\,b^3\,c^2\,d^7+60\,a^5\,b^4\,c^3\,d^6-80\,a^4\,b^5\,c^4\,d^5+60\,a^3\,b^6\,c^5\,d^4-24\,a^2\,b^7\,c^6\,d^3+4\,a\,b^8\,c^7\,d^2}{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}-\frac{x\,\sqrt{-a\,b}\,\left(a\,d+3\,b\,c\right)\,\left(16\,a^7\,b^2\,d^9-80\,a^6\,b^3\,c\,d^8+144\,a^5\,b^4\,c^2\,d^7-80\,a^4\,b^5\,c^3\,d^6-80\,a^3\,b^6\,c^4\,d^5+144\,a^2\,b^7\,c^5\,d^4-80\,a\,b^8\,c^6\,d^3+16\,b^9\,c^7\,d^2\right)}{8\,\left(-a^3\,b\,d^3+3\,a^2\,b^2\,c\,d^2-3\,a\,b^3\,c^2\,d+b^4\,c^3\right)\,\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)}\right)\,\left(a\,d+3\,b\,c\right)}{4\,\left(-a^3\,b\,d^3+3\,a^2\,b^2\,c\,d^2-3\,a\,b^3\,c^2\,d+b^4\,c^3\right)}\right)\,\left(a\,d+3\,b\,c\right)}{4\,\left(-a^3\,b\,d^3+3\,a^2\,b^2\,c\,d^2-3\,a\,b^3\,c^2\,d+b^4\,c^3\right)}+\frac{\sqrt{-a\,b}\,\left(\frac{x\,\left(a^4\,b\,d^5+6\,a^3\,b^2\,c\,d^4+18\,a^2\,b^3\,c^2\,d^3+6\,a\,b^4\,c^3\,d^2+b^5\,c^4\,d\right)}{2\,\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)}+\frac{\sqrt{-a\,b}\,\left(\frac{4\,a^7\,b^2\,c\,d^8-24\,a^6\,b^3\,c^2\,d^7+60\,a^5\,b^4\,c^3\,d^6-80\,a^4\,b^5\,c^4\,d^5+60\,a^3\,b^6\,c^5\,d^4-24\,a^2\,b^7\,c^6\,d^3+4\,a\,b^8\,c^7\,d^2}{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}+\frac{x\,\sqrt{-a\,b}\,\left(a\,d+3\,b\,c\right)\,\left(16\,a^7\,b^2\,d^9-80\,a^6\,b^3\,c\,d^8+144\,a^5\,b^4\,c^2\,d^7-80\,a^4\,b^5\,c^3\,d^6-80\,a^3\,b^6\,c^4\,d^5+144\,a^2\,b^7\,c^5\,d^4-80\,a\,b^8\,c^6\,d^3+16\,b^9\,c^7\,d^2\right)}{8\,\left(-a^3\,b\,d^3+3\,a^2\,b^2\,c\,d^2-3\,a\,b^3\,c^2\,d+b^4\,c^3\right)\,\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)}\right)\,\left(a\,d+3\,b\,c\right)}{4\,\left(-a^3\,b\,d^3+3\,a^2\,b^2\,c\,d^2-3\,a\,b^3\,c^2\,d+b^4\,c^3\right)}\right)\,\left(a\,d+3\,b\,c\right)}{4\,\left(-a^3\,b\,d^3+3\,a^2\,b^2\,c\,d^2-3\,a\,b^3\,c^2\,d+b^4\,c^3\right)}}\right)\,\sqrt{-a\,b}\,\left(a\,d+3\,b\,c\right)\,1{}\mathrm{i}}{2\,\left(-a^3\,b\,d^3+3\,a^2\,b^2\,c\,d^2-3\,a\,b^3\,c^2\,d+b^4\,c^3\right)}","Not used",1,"((x^3*(a*d + b*c))/(2*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) + (a*c*x)/(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/(a*c + x^2*(a*d + b*c) + b*d*x^4) - (atan((((-c*d)^(1/2)*((x*(a^4*b*d^5 + b^5*c^4*d + 6*a*b^4*c^3*d^2 + 6*a^3*b^2*c*d^4 + 18*a^2*b^3*c^2*d^3))/(2*(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)) - ((-c*d)^(1/2)*((4*a*b^8*c^7*d^2 + 4*a^7*b^2*c*d^8 - 24*a^2*b^7*c^6*d^3 + 60*a^3*b^6*c^5*d^4 - 80*a^4*b^5*c^4*d^5 + 60*a^5*b^4*c^3*d^6 - 24*a^6*b^3*c^2*d^7)/(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) - (x*(-c*d)^(1/2)*(3*a*d + b*c)*(16*a^7*b^2*d^9 + 16*b^9*c^7*d^2 - 80*a*b^8*c^6*d^3 - 80*a^6*b^3*c*d^8 + 144*a^2*b^7*c^5*d^4 - 80*a^3*b^6*c^4*d^5 - 80*a^4*b^5*c^3*d^6 + 144*a^5*b^4*c^2*d^7))/(8*(a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3)*(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*d + b*c))/(4*(a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3)))*(3*a*d + b*c)*1i)/(4*(a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3)) + ((-c*d)^(1/2)*((x*(a^4*b*d^5 + b^5*c^4*d + 6*a*b^4*c^3*d^2 + 6*a^3*b^2*c*d^4 + 18*a^2*b^3*c^2*d^3))/(2*(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)) + ((-c*d)^(1/2)*((4*a*b^8*c^7*d^2 + 4*a^7*b^2*c*d^8 - 24*a^2*b^7*c^6*d^3 + 60*a^3*b^6*c^5*d^4 - 80*a^4*b^5*c^4*d^5 + 60*a^5*b^4*c^3*d^6 - 24*a^6*b^3*c^2*d^7)/(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) + (x*(-c*d)^(1/2)*(3*a*d + b*c)*(16*a^7*b^2*d^9 + 16*b^9*c^7*d^2 - 80*a*b^8*c^6*d^3 - 80*a^6*b^3*c*d^8 + 144*a^2*b^7*c^5*d^4 - 80*a^3*b^6*c^4*d^5 - 80*a^4*b^5*c^3*d^6 + 144*a^5*b^4*c^2*d^7))/(8*(a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3)*(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*d + b*c))/(4*(a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3)))*(3*a*d + b*c)*1i)/(4*(a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3)))/(((13*a^2*b^3*c^3*d^2)/4 + (13*a^3*b^2*c^2*d^3)/4 + (3*a*b^4*c^4*d)/4 + (3*a^4*b*c*d^4)/4)/(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) - ((-c*d)^(1/2)*((x*(a^4*b*d^5 + b^5*c^4*d + 6*a*b^4*c^3*d^2 + 6*a^3*b^2*c*d^4 + 18*a^2*b^3*c^2*d^3))/(2*(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)) - ((-c*d)^(1/2)*((4*a*b^8*c^7*d^2 + 4*a^7*b^2*c*d^8 - 24*a^2*b^7*c^6*d^3 + 60*a^3*b^6*c^5*d^4 - 80*a^4*b^5*c^4*d^5 + 60*a^5*b^4*c^3*d^6 - 24*a^6*b^3*c^2*d^7)/(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) - (x*(-c*d)^(1/2)*(3*a*d + b*c)*(16*a^7*b^2*d^9 + 16*b^9*c^7*d^2 - 80*a*b^8*c^6*d^3 - 80*a^6*b^3*c*d^8 + 144*a^2*b^7*c^5*d^4 - 80*a^3*b^6*c^4*d^5 - 80*a^4*b^5*c^3*d^6 + 144*a^5*b^4*c^2*d^7))/(8*(a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3)*(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*d + b*c))/(4*(a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3)))*(3*a*d + b*c))/(4*(a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3)) + ((-c*d)^(1/2)*((x*(a^4*b*d^5 + b^5*c^4*d + 6*a*b^4*c^3*d^2 + 6*a^3*b^2*c*d^4 + 18*a^2*b^3*c^2*d^3))/(2*(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)) + ((-c*d)^(1/2)*((4*a*b^8*c^7*d^2 + 4*a^7*b^2*c*d^8 - 24*a^2*b^7*c^6*d^3 + 60*a^3*b^6*c^5*d^4 - 80*a^4*b^5*c^4*d^5 + 60*a^5*b^4*c^3*d^6 - 24*a^6*b^3*c^2*d^7)/(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) + (x*(-c*d)^(1/2)*(3*a*d + b*c)*(16*a^7*b^2*d^9 + 16*b^9*c^7*d^2 - 80*a*b^8*c^6*d^3 - 80*a^6*b^3*c*d^8 + 144*a^2*b^7*c^5*d^4 - 80*a^3*b^6*c^4*d^5 - 80*a^4*b^5*c^3*d^6 + 144*a^5*b^4*c^2*d^7))/(8*(a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3)*(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*d + b*c))/(4*(a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3)))*(3*a*d + b*c))/(4*(a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3))))*(-c*d)^(1/2)*(3*a*d + b*c)*1i)/(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)) - (atan((((-a*b)^(1/2)*((x*(a^4*b*d^5 + b^5*c^4*d + 6*a*b^4*c^3*d^2 + 6*a^3*b^2*c*d^4 + 18*a^2*b^3*c^2*d^3))/(2*(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)) - ((-a*b)^(1/2)*((4*a*b^8*c^7*d^2 + 4*a^7*b^2*c*d^8 - 24*a^2*b^7*c^6*d^3 + 60*a^3*b^6*c^5*d^4 - 80*a^4*b^5*c^4*d^5 + 60*a^5*b^4*c^3*d^6 - 24*a^6*b^3*c^2*d^7)/(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) - (x*(-a*b)^(1/2)*(a*d + 3*b*c)*(16*a^7*b^2*d^9 + 16*b^9*c^7*d^2 - 80*a*b^8*c^6*d^3 - 80*a^6*b^3*c*d^8 + 144*a^2*b^7*c^5*d^4 - 80*a^3*b^6*c^4*d^5 - 80*a^4*b^5*c^3*d^6 + 144*a^5*b^4*c^2*d^7))/(8*(b^4*c^3 - a^3*b*d^3 + 3*a^2*b^2*c*d^2 - 3*a*b^3*c^2*d)*(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)))*(a*d + 3*b*c))/(4*(b^4*c^3 - a^3*b*d^3 + 3*a^2*b^2*c*d^2 - 3*a*b^3*c^2*d)))*(a*d + 3*b*c)*1i)/(4*(b^4*c^3 - a^3*b*d^3 + 3*a^2*b^2*c*d^2 - 3*a*b^3*c^2*d)) + ((-a*b)^(1/2)*((x*(a^4*b*d^5 + b^5*c^4*d + 6*a*b^4*c^3*d^2 + 6*a^3*b^2*c*d^4 + 18*a^2*b^3*c^2*d^3))/(2*(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)) + ((-a*b)^(1/2)*((4*a*b^8*c^7*d^2 + 4*a^7*b^2*c*d^8 - 24*a^2*b^7*c^6*d^3 + 60*a^3*b^6*c^5*d^4 - 80*a^4*b^5*c^4*d^5 + 60*a^5*b^4*c^3*d^6 - 24*a^6*b^3*c^2*d^7)/(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) + (x*(-a*b)^(1/2)*(a*d + 3*b*c)*(16*a^7*b^2*d^9 + 16*b^9*c^7*d^2 - 80*a*b^8*c^6*d^3 - 80*a^6*b^3*c*d^8 + 144*a^2*b^7*c^5*d^4 - 80*a^3*b^6*c^4*d^5 - 80*a^4*b^5*c^3*d^6 + 144*a^5*b^4*c^2*d^7))/(8*(b^4*c^3 - a^3*b*d^3 + 3*a^2*b^2*c*d^2 - 3*a*b^3*c^2*d)*(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)))*(a*d + 3*b*c))/(4*(b^4*c^3 - a^3*b*d^3 + 3*a^2*b^2*c*d^2 - 3*a*b^3*c^2*d)))*(a*d + 3*b*c)*1i)/(4*(b^4*c^3 - a^3*b*d^3 + 3*a^2*b^2*c*d^2 - 3*a*b^3*c^2*d)))/(((13*a^2*b^3*c^3*d^2)/4 + (13*a^3*b^2*c^2*d^3)/4 + (3*a*b^4*c^4*d)/4 + (3*a^4*b*c*d^4)/4)/(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) - ((-a*b)^(1/2)*((x*(a^4*b*d^5 + b^5*c^4*d + 6*a*b^4*c^3*d^2 + 6*a^3*b^2*c*d^4 + 18*a^2*b^3*c^2*d^3))/(2*(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)) - ((-a*b)^(1/2)*((4*a*b^8*c^7*d^2 + 4*a^7*b^2*c*d^8 - 24*a^2*b^7*c^6*d^3 + 60*a^3*b^6*c^5*d^4 - 80*a^4*b^5*c^4*d^5 + 60*a^5*b^4*c^3*d^6 - 24*a^6*b^3*c^2*d^7)/(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) - (x*(-a*b)^(1/2)*(a*d + 3*b*c)*(16*a^7*b^2*d^9 + 16*b^9*c^7*d^2 - 80*a*b^8*c^6*d^3 - 80*a^6*b^3*c*d^8 + 144*a^2*b^7*c^5*d^4 - 80*a^3*b^6*c^4*d^5 - 80*a^4*b^5*c^3*d^6 + 144*a^5*b^4*c^2*d^7))/(8*(b^4*c^3 - a^3*b*d^3 + 3*a^2*b^2*c*d^2 - 3*a*b^3*c^2*d)*(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)))*(a*d + 3*b*c))/(4*(b^4*c^3 - a^3*b*d^3 + 3*a^2*b^2*c*d^2 - 3*a*b^3*c^2*d)))*(a*d + 3*b*c))/(4*(b^4*c^3 - a^3*b*d^3 + 3*a^2*b^2*c*d^2 - 3*a*b^3*c^2*d)) + ((-a*b)^(1/2)*((x*(a^4*b*d^5 + b^5*c^4*d + 6*a*b^4*c^3*d^2 + 6*a^3*b^2*c*d^4 + 18*a^2*b^3*c^2*d^3))/(2*(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)) + ((-a*b)^(1/2)*((4*a*b^8*c^7*d^2 + 4*a^7*b^2*c*d^8 - 24*a^2*b^7*c^6*d^3 + 60*a^3*b^6*c^5*d^4 - 80*a^4*b^5*c^4*d^5 + 60*a^5*b^4*c^3*d^6 - 24*a^6*b^3*c^2*d^7)/(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) + (x*(-a*b)^(1/2)*(a*d + 3*b*c)*(16*a^7*b^2*d^9 + 16*b^9*c^7*d^2 - 80*a*b^8*c^6*d^3 - 80*a^6*b^3*c*d^8 + 144*a^2*b^7*c^5*d^4 - 80*a^3*b^6*c^4*d^5 - 80*a^4*b^5*c^3*d^6 + 144*a^5*b^4*c^2*d^7))/(8*(b^4*c^3 - a^3*b*d^3 + 3*a^2*b^2*c*d^2 - 3*a*b^3*c^2*d)*(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)))*(a*d + 3*b*c))/(4*(b^4*c^3 - a^3*b*d^3 + 3*a^2*b^2*c*d^2 - 3*a*b^3*c^2*d)))*(a*d + 3*b*c))/(4*(b^4*c^3 - a^3*b*d^3 + 3*a^2*b^2*c*d^2 - 3*a*b^3*c^2*d))))*(-a*b)^(1/2)*(a*d + 3*b*c)*1i)/(2*(b^4*c^3 - a^3*b*d^3 + 3*a^2*b^2*c*d^2 - 3*a*b^3*c^2*d))","B"
302,1,522,107,0.529929,"\text{Not used}","int(x^3/((a + b*x^2)^2*(c + d*x^2)^2),x)","\frac{b^2\,c^2\,x^2-a^2\,d^2\,x^2+2\,a\,b\,c^2-2\,a^2\,c\,d+a^2\,d^2\,x^2\,\mathrm{atan}\left(\frac{a\,d\,x^2\,1{}\mathrm{i}-b\,c\,x^2\,1{}\mathrm{i}}{2\,a\,c+a\,d\,x^2+b\,c\,x^2}\right)\,2{}\mathrm{i}+b^2\,c^2\,x^2\,\mathrm{atan}\left(\frac{a\,d\,x^2\,1{}\mathrm{i}-b\,c\,x^2\,1{}\mathrm{i}}{2\,a\,c+a\,d\,x^2+b\,c\,x^2}\right)\,2{}\mathrm{i}+a\,b\,c^2\,\mathrm{atan}\left(\frac{a\,d\,x^2\,1{}\mathrm{i}-b\,c\,x^2\,1{}\mathrm{i}}{2\,a\,c+a\,d\,x^2+b\,c\,x^2}\right)\,2{}\mathrm{i}+a^2\,c\,d\,\mathrm{atan}\left(\frac{a\,d\,x^2\,1{}\mathrm{i}-b\,c\,x^2\,1{}\mathrm{i}}{2\,a\,c+a\,d\,x^2+b\,c\,x^2}\right)\,2{}\mathrm{i}+a\,b\,d^2\,x^4\,\mathrm{atan}\left(\frac{a\,d\,x^2\,1{}\mathrm{i}-b\,c\,x^2\,1{}\mathrm{i}}{2\,a\,c+a\,d\,x^2+b\,c\,x^2}\right)\,2{}\mathrm{i}+b^2\,c\,d\,x^4\,\mathrm{atan}\left(\frac{a\,d\,x^2\,1{}\mathrm{i}-b\,c\,x^2\,1{}\mathrm{i}}{2\,a\,c+a\,d\,x^2+b\,c\,x^2}\right)\,2{}\mathrm{i}+a\,b\,c\,d\,x^2\,\mathrm{atan}\left(\frac{a\,d\,x^2\,1{}\mathrm{i}-b\,c\,x^2\,1{}\mathrm{i}}{2\,a\,c+a\,d\,x^2+b\,c\,x^2}\right)\,4{}\mathrm{i}}{-2\,a^4\,c\,d^3-2\,a^4\,d^4\,x^2+6\,a^3\,b\,c^2\,d^2+4\,a^3\,b\,c\,d^3\,x^2-2\,a^3\,b\,d^4\,x^4-6\,a^2\,b^2\,c^3\,d+6\,a^2\,b^2\,c\,d^3\,x^4+2\,a\,b^3\,c^4-4\,a\,b^3\,c^3\,d\,x^2-6\,a\,b^3\,c^2\,d^2\,x^4+2\,b^4\,c^4\,x^2+2\,b^4\,c^3\,d\,x^4}","Not used",1,"(b^2*c^2*x^2 - a^2*d^2*x^2 + 2*a*b*c^2 - 2*a^2*c*d + a^2*d^2*x^2*atan((a*d*x^2*1i - b*c*x^2*1i)/(2*a*c + a*d*x^2 + b*c*x^2))*2i + b^2*c^2*x^2*atan((a*d*x^2*1i - b*c*x^2*1i)/(2*a*c + a*d*x^2 + b*c*x^2))*2i + a*b*c^2*atan((a*d*x^2*1i - b*c*x^2*1i)/(2*a*c + a*d*x^2 + b*c*x^2))*2i + a^2*c*d*atan((a*d*x^2*1i - b*c*x^2*1i)/(2*a*c + a*d*x^2 + b*c*x^2))*2i + a*b*d^2*x^4*atan((a*d*x^2*1i - b*c*x^2*1i)/(2*a*c + a*d*x^2 + b*c*x^2))*2i + b^2*c*d*x^4*atan((a*d*x^2*1i - b*c*x^2*1i)/(2*a*c + a*d*x^2 + b*c*x^2))*2i + a*b*c*d*x^2*atan((a*d*x^2*1i - b*c*x^2*1i)/(2*a*c + a*d*x^2 + b*c*x^2))*4i)/(2*a*b^3*c^4 - 2*a^4*c*d^3 - 2*a^4*d^4*x^2 + 2*b^4*c^4*x^2 - 6*a^2*b^2*c^3*d + 6*a^3*b*c^2*d^2 - 2*a^3*b*d^4*x^4 + 2*b^4*c^3*d*x^4 - 4*a*b^3*c^3*d*x^2 + 4*a^3*b*c*d^3*x^2 - 6*a*b^3*c^2*d^2*x^4 + 6*a^2*b^2*c*d^3*x^4)","B"
303,1,5236,147,1.669352,"\text{Not used}","int(x^2/((a + b*x^2)^2*(c + d*x^2)^2),x)","-\frac{\frac{x\,\left(a\,d+b\,c\right)}{2\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}+\frac{b\,d\,x^3}{a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2}}{b\,d\,x^4+\left(a\,d+b\,c\right)\,x^2+a\,c}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-a\,b}\,\left(\frac{x\,\left(5\,a^2\,b^3\,d^5+6\,a\,b^4\,c\,d^4+5\,b^5\,c^2\,d^3\right)}{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}-\frac{\sqrt{-a\,b}\,\left(\frac{2\,a^7\,b^2\,d^9-10\,a^6\,b^3\,c\,d^8+18\,a^5\,b^4\,c^2\,d^7-10\,a^4\,b^5\,c^3\,d^6-10\,a^3\,b^6\,c^4\,d^5+18\,a^2\,b^7\,c^5\,d^4-10\,a\,b^8\,c^6\,d^3+2\,b^9\,c^7\,d^2}{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}-\frac{x\,\sqrt{-a\,b}\,\left(3\,a\,d+b\,c\right)\,\left(8\,a^7\,b^2\,d^9-40\,a^6\,b^3\,c\,d^8+72\,a^5\,b^4\,c^2\,d^7-40\,a^4\,b^5\,c^3\,d^6-40\,a^3\,b^6\,c^4\,d^5+72\,a^2\,b^7\,c^5\,d^4-40\,a\,b^8\,c^6\,d^3+8\,b^9\,c^7\,d^2\right)}{4\,\left(a^4\,d^3-3\,a^3\,b\,c\,d^2+3\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3\right)\,\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)}\right)\,\left(3\,a\,d+b\,c\right)}{4\,\left(a^4\,d^3-3\,a^3\,b\,c\,d^2+3\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3\right)}\right)\,\left(3\,a\,d+b\,c\right)\,1{}\mathrm{i}}{4\,\left(a^4\,d^3-3\,a^3\,b\,c\,d^2+3\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3\right)}+\frac{\sqrt{-a\,b}\,\left(\frac{x\,\left(5\,a^2\,b^3\,d^5+6\,a\,b^4\,c\,d^4+5\,b^5\,c^2\,d^3\right)}{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}+\frac{\sqrt{-a\,b}\,\left(\frac{2\,a^7\,b^2\,d^9-10\,a^6\,b^3\,c\,d^8+18\,a^5\,b^4\,c^2\,d^7-10\,a^4\,b^5\,c^3\,d^6-10\,a^3\,b^6\,c^4\,d^5+18\,a^2\,b^7\,c^5\,d^4-10\,a\,b^8\,c^6\,d^3+2\,b^9\,c^7\,d^2}{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}+\frac{x\,\sqrt{-a\,b}\,\left(3\,a\,d+b\,c\right)\,\left(8\,a^7\,b^2\,d^9-40\,a^6\,b^3\,c\,d^8+72\,a^5\,b^4\,c^2\,d^7-40\,a^4\,b^5\,c^3\,d^6-40\,a^3\,b^6\,c^4\,d^5+72\,a^2\,b^7\,c^5\,d^4-40\,a\,b^8\,c^6\,d^3+8\,b^9\,c^7\,d^2\right)}{4\,\left(a^4\,d^3-3\,a^3\,b\,c\,d^2+3\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3\right)\,\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)}\right)\,\left(3\,a\,d+b\,c\right)}{4\,\left(a^4\,d^3-3\,a^3\,b\,c\,d^2+3\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3\right)}\right)\,\left(3\,a\,d+b\,c\right)\,1{}\mathrm{i}}{4\,\left(a^4\,d^3-3\,a^3\,b\,c\,d^2+3\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3\right)}}{\frac{\frac{3\,a^2\,b^3\,d^5}{2}+5\,a\,b^4\,c\,d^4+\frac{3\,b^5\,c^2\,d^3}{2}}{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}-\frac{\sqrt{-a\,b}\,\left(\frac{x\,\left(5\,a^2\,b^3\,d^5+6\,a\,b^4\,c\,d^4+5\,b^5\,c^2\,d^3\right)}{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}-\frac{\sqrt{-a\,b}\,\left(\frac{2\,a^7\,b^2\,d^9-10\,a^6\,b^3\,c\,d^8+18\,a^5\,b^4\,c^2\,d^7-10\,a^4\,b^5\,c^3\,d^6-10\,a^3\,b^6\,c^4\,d^5+18\,a^2\,b^7\,c^5\,d^4-10\,a\,b^8\,c^6\,d^3+2\,b^9\,c^7\,d^2}{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}-\frac{x\,\sqrt{-a\,b}\,\left(3\,a\,d+b\,c\right)\,\left(8\,a^7\,b^2\,d^9-40\,a^6\,b^3\,c\,d^8+72\,a^5\,b^4\,c^2\,d^7-40\,a^4\,b^5\,c^3\,d^6-40\,a^3\,b^6\,c^4\,d^5+72\,a^2\,b^7\,c^5\,d^4-40\,a\,b^8\,c^6\,d^3+8\,b^9\,c^7\,d^2\right)}{4\,\left(a^4\,d^3-3\,a^3\,b\,c\,d^2+3\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3\right)\,\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)}\right)\,\left(3\,a\,d+b\,c\right)}{4\,\left(a^4\,d^3-3\,a^3\,b\,c\,d^2+3\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3\right)}\right)\,\left(3\,a\,d+b\,c\right)}{4\,\left(a^4\,d^3-3\,a^3\,b\,c\,d^2+3\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3\right)}+\frac{\sqrt{-a\,b}\,\left(\frac{x\,\left(5\,a^2\,b^3\,d^5+6\,a\,b^4\,c\,d^4+5\,b^5\,c^2\,d^3\right)}{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}+\frac{\sqrt{-a\,b}\,\left(\frac{2\,a^7\,b^2\,d^9-10\,a^6\,b^3\,c\,d^8+18\,a^5\,b^4\,c^2\,d^7-10\,a^4\,b^5\,c^3\,d^6-10\,a^3\,b^6\,c^4\,d^5+18\,a^2\,b^7\,c^5\,d^4-10\,a\,b^8\,c^6\,d^3+2\,b^9\,c^7\,d^2}{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}+\frac{x\,\sqrt{-a\,b}\,\left(3\,a\,d+b\,c\right)\,\left(8\,a^7\,b^2\,d^9-40\,a^6\,b^3\,c\,d^8+72\,a^5\,b^4\,c^2\,d^7-40\,a^4\,b^5\,c^3\,d^6-40\,a^3\,b^6\,c^4\,d^5+72\,a^2\,b^7\,c^5\,d^4-40\,a\,b^8\,c^6\,d^3+8\,b^9\,c^7\,d^2\right)}{4\,\left(a^4\,d^3-3\,a^3\,b\,c\,d^2+3\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3\right)\,\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)}\right)\,\left(3\,a\,d+b\,c\right)}{4\,\left(a^4\,d^3-3\,a^3\,b\,c\,d^2+3\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3\right)}\right)\,\left(3\,a\,d+b\,c\right)}{4\,\left(a^4\,d^3-3\,a^3\,b\,c\,d^2+3\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3\right)}}\right)\,\sqrt{-a\,b}\,\left(3\,a\,d+b\,c\right)\,1{}\mathrm{i}}{2\,\left(a^4\,d^3-3\,a^3\,b\,c\,d^2+3\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-c\,d}\,\left(\frac{x\,\left(5\,a^2\,b^3\,d^5+6\,a\,b^4\,c\,d^4+5\,b^5\,c^2\,d^3\right)}{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}-\frac{\sqrt{-c\,d}\,\left(\frac{2\,a^7\,b^2\,d^9-10\,a^6\,b^3\,c\,d^8+18\,a^5\,b^4\,c^2\,d^7-10\,a^4\,b^5\,c^3\,d^6-10\,a^3\,b^6\,c^4\,d^5+18\,a^2\,b^7\,c^5\,d^4-10\,a\,b^8\,c^6\,d^3+2\,b^9\,c^7\,d^2}{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}-\frac{x\,\sqrt{-c\,d}\,\left(a\,d+3\,b\,c\right)\,\left(8\,a^7\,b^2\,d^9-40\,a^6\,b^3\,c\,d^8+72\,a^5\,b^4\,c^2\,d^7-40\,a^4\,b^5\,c^3\,d^6-40\,a^3\,b^6\,c^4\,d^5+72\,a^2\,b^7\,c^5\,d^4-40\,a\,b^8\,c^6\,d^3+8\,b^9\,c^7\,d^2\right)}{4\,\left(-a^3\,c\,d^3+3\,a^2\,b\,c^2\,d^2-3\,a\,b^2\,c^3\,d+b^3\,c^4\right)\,\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)}\right)\,\left(a\,d+3\,b\,c\right)}{4\,\left(-a^3\,c\,d^3+3\,a^2\,b\,c^2\,d^2-3\,a\,b^2\,c^3\,d+b^3\,c^4\right)}\right)\,\left(a\,d+3\,b\,c\right)\,1{}\mathrm{i}}{4\,\left(-a^3\,c\,d^3+3\,a^2\,b\,c^2\,d^2-3\,a\,b^2\,c^3\,d+b^3\,c^4\right)}+\frac{\sqrt{-c\,d}\,\left(\frac{x\,\left(5\,a^2\,b^3\,d^5+6\,a\,b^4\,c\,d^4+5\,b^5\,c^2\,d^3\right)}{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}+\frac{\sqrt{-c\,d}\,\left(\frac{2\,a^7\,b^2\,d^9-10\,a^6\,b^3\,c\,d^8+18\,a^5\,b^4\,c^2\,d^7-10\,a^4\,b^5\,c^3\,d^6-10\,a^3\,b^6\,c^4\,d^5+18\,a^2\,b^7\,c^5\,d^4-10\,a\,b^8\,c^6\,d^3+2\,b^9\,c^7\,d^2}{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}+\frac{x\,\sqrt{-c\,d}\,\left(a\,d+3\,b\,c\right)\,\left(8\,a^7\,b^2\,d^9-40\,a^6\,b^3\,c\,d^8+72\,a^5\,b^4\,c^2\,d^7-40\,a^4\,b^5\,c^3\,d^6-40\,a^3\,b^6\,c^4\,d^5+72\,a^2\,b^7\,c^5\,d^4-40\,a\,b^8\,c^6\,d^3+8\,b^9\,c^7\,d^2\right)}{4\,\left(-a^3\,c\,d^3+3\,a^2\,b\,c^2\,d^2-3\,a\,b^2\,c^3\,d+b^3\,c^4\right)\,\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)}\right)\,\left(a\,d+3\,b\,c\right)}{4\,\left(-a^3\,c\,d^3+3\,a^2\,b\,c^2\,d^2-3\,a\,b^2\,c^3\,d+b^3\,c^4\right)}\right)\,\left(a\,d+3\,b\,c\right)\,1{}\mathrm{i}}{4\,\left(-a^3\,c\,d^3+3\,a^2\,b\,c^2\,d^2-3\,a\,b^2\,c^3\,d+b^3\,c^4\right)}}{\frac{\frac{3\,a^2\,b^3\,d^5}{2}+5\,a\,b^4\,c\,d^4+\frac{3\,b^5\,c^2\,d^3}{2}}{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}-\frac{\sqrt{-c\,d}\,\left(\frac{x\,\left(5\,a^2\,b^3\,d^5+6\,a\,b^4\,c\,d^4+5\,b^5\,c^2\,d^3\right)}{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}-\frac{\sqrt{-c\,d}\,\left(\frac{2\,a^7\,b^2\,d^9-10\,a^6\,b^3\,c\,d^8+18\,a^5\,b^4\,c^2\,d^7-10\,a^4\,b^5\,c^3\,d^6-10\,a^3\,b^6\,c^4\,d^5+18\,a^2\,b^7\,c^5\,d^4-10\,a\,b^8\,c^6\,d^3+2\,b^9\,c^7\,d^2}{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}-\frac{x\,\sqrt{-c\,d}\,\left(a\,d+3\,b\,c\right)\,\left(8\,a^7\,b^2\,d^9-40\,a^6\,b^3\,c\,d^8+72\,a^5\,b^4\,c^2\,d^7-40\,a^4\,b^5\,c^3\,d^6-40\,a^3\,b^6\,c^4\,d^5+72\,a^2\,b^7\,c^5\,d^4-40\,a\,b^8\,c^6\,d^3+8\,b^9\,c^7\,d^2\right)}{4\,\left(-a^3\,c\,d^3+3\,a^2\,b\,c^2\,d^2-3\,a\,b^2\,c^3\,d+b^3\,c^4\right)\,\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)}\right)\,\left(a\,d+3\,b\,c\right)}{4\,\left(-a^3\,c\,d^3+3\,a^2\,b\,c^2\,d^2-3\,a\,b^2\,c^3\,d+b^3\,c^4\right)}\right)\,\left(a\,d+3\,b\,c\right)}{4\,\left(-a^3\,c\,d^3+3\,a^2\,b\,c^2\,d^2-3\,a\,b^2\,c^3\,d+b^3\,c^4\right)}+\frac{\sqrt{-c\,d}\,\left(\frac{x\,\left(5\,a^2\,b^3\,d^5+6\,a\,b^4\,c\,d^4+5\,b^5\,c^2\,d^3\right)}{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}+\frac{\sqrt{-c\,d}\,\left(\frac{2\,a^7\,b^2\,d^9-10\,a^6\,b^3\,c\,d^8+18\,a^5\,b^4\,c^2\,d^7-10\,a^4\,b^5\,c^3\,d^6-10\,a^3\,b^6\,c^4\,d^5+18\,a^2\,b^7\,c^5\,d^4-10\,a\,b^8\,c^6\,d^3+2\,b^9\,c^7\,d^2}{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}+\frac{x\,\sqrt{-c\,d}\,\left(a\,d+3\,b\,c\right)\,\left(8\,a^7\,b^2\,d^9-40\,a^6\,b^3\,c\,d^8+72\,a^5\,b^4\,c^2\,d^7-40\,a^4\,b^5\,c^3\,d^6-40\,a^3\,b^6\,c^4\,d^5+72\,a^2\,b^7\,c^5\,d^4-40\,a\,b^8\,c^6\,d^3+8\,b^9\,c^7\,d^2\right)}{4\,\left(-a^3\,c\,d^3+3\,a^2\,b\,c^2\,d^2-3\,a\,b^2\,c^3\,d+b^3\,c^4\right)\,\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)}\right)\,\left(a\,d+3\,b\,c\right)}{4\,\left(-a^3\,c\,d^3+3\,a^2\,b\,c^2\,d^2-3\,a\,b^2\,c^3\,d+b^3\,c^4\right)}\right)\,\left(a\,d+3\,b\,c\right)}{4\,\left(-a^3\,c\,d^3+3\,a^2\,b\,c^2\,d^2-3\,a\,b^2\,c^3\,d+b^3\,c^4\right)}}\right)\,\sqrt{-c\,d}\,\left(a\,d+3\,b\,c\right)\,1{}\mathrm{i}}{2\,\left(-a^3\,c\,d^3+3\,a^2\,b\,c^2\,d^2-3\,a\,b^2\,c^3\,d+b^3\,c^4\right)}","Not used",1,"(atan((((-a*b)^(1/2)*((x*(5*a^2*b^3*d^5 + 5*b^5*c^2*d^3 + 6*a*b^4*c*d^4))/(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) - ((-a*b)^(1/2)*((2*a^7*b^2*d^9 + 2*b^9*c^7*d^2 - 10*a*b^8*c^6*d^3 - 10*a^6*b^3*c*d^8 + 18*a^2*b^7*c^5*d^4 - 10*a^3*b^6*c^4*d^5 - 10*a^4*b^5*c^3*d^6 + 18*a^5*b^4*c^2*d^7)/(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) - (x*(-a*b)^(1/2)*(3*a*d + b*c)*(8*a^7*b^2*d^9 + 8*b^9*c^7*d^2 - 40*a*b^8*c^6*d^3 - 40*a^6*b^3*c*d^8 + 72*a^2*b^7*c^5*d^4 - 40*a^3*b^6*c^4*d^5 - 40*a^4*b^5*c^3*d^6 + 72*a^5*b^4*c^2*d^7))/(4*(a^4*d^3 - a*b^3*c^3 + 3*a^2*b^2*c^2*d - 3*a^3*b*c*d^2)*(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*d + b*c))/(4*(a^4*d^3 - a*b^3*c^3 + 3*a^2*b^2*c^2*d - 3*a^3*b*c*d^2)))*(3*a*d + b*c)*1i)/(4*(a^4*d^3 - a*b^3*c^3 + 3*a^2*b^2*c^2*d - 3*a^3*b*c*d^2)) + ((-a*b)^(1/2)*((x*(5*a^2*b^3*d^5 + 5*b^5*c^2*d^3 + 6*a*b^4*c*d^4))/(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) + ((-a*b)^(1/2)*((2*a^7*b^2*d^9 + 2*b^9*c^7*d^2 - 10*a*b^8*c^6*d^3 - 10*a^6*b^3*c*d^8 + 18*a^2*b^7*c^5*d^4 - 10*a^3*b^6*c^4*d^5 - 10*a^4*b^5*c^3*d^6 + 18*a^5*b^4*c^2*d^7)/(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) + (x*(-a*b)^(1/2)*(3*a*d + b*c)*(8*a^7*b^2*d^9 + 8*b^9*c^7*d^2 - 40*a*b^8*c^6*d^3 - 40*a^6*b^3*c*d^8 + 72*a^2*b^7*c^5*d^4 - 40*a^3*b^6*c^4*d^5 - 40*a^4*b^5*c^3*d^6 + 72*a^5*b^4*c^2*d^7))/(4*(a^4*d^3 - a*b^3*c^3 + 3*a^2*b^2*c^2*d - 3*a^3*b*c*d^2)*(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*d + b*c))/(4*(a^4*d^3 - a*b^3*c^3 + 3*a^2*b^2*c^2*d - 3*a^3*b*c*d^2)))*(3*a*d + b*c)*1i)/(4*(a^4*d^3 - a*b^3*c^3 + 3*a^2*b^2*c^2*d - 3*a^3*b*c*d^2)))/(((3*a^2*b^3*d^5)/2 + (3*b^5*c^2*d^3)/2 + 5*a*b^4*c*d^4)/(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) - ((-a*b)^(1/2)*((x*(5*a^2*b^3*d^5 + 5*b^5*c^2*d^3 + 6*a*b^4*c*d^4))/(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) - ((-a*b)^(1/2)*((2*a^7*b^2*d^9 + 2*b^9*c^7*d^2 - 10*a*b^8*c^6*d^3 - 10*a^6*b^3*c*d^8 + 18*a^2*b^7*c^5*d^4 - 10*a^3*b^6*c^4*d^5 - 10*a^4*b^5*c^3*d^6 + 18*a^5*b^4*c^2*d^7)/(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) - (x*(-a*b)^(1/2)*(3*a*d + b*c)*(8*a^7*b^2*d^9 + 8*b^9*c^7*d^2 - 40*a*b^8*c^6*d^3 - 40*a^6*b^3*c*d^8 + 72*a^2*b^7*c^5*d^4 - 40*a^3*b^6*c^4*d^5 - 40*a^4*b^5*c^3*d^6 + 72*a^5*b^4*c^2*d^7))/(4*(a^4*d^3 - a*b^3*c^3 + 3*a^2*b^2*c^2*d - 3*a^3*b*c*d^2)*(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*d + b*c))/(4*(a^4*d^3 - a*b^3*c^3 + 3*a^2*b^2*c^2*d - 3*a^3*b*c*d^2)))*(3*a*d + b*c))/(4*(a^4*d^3 - a*b^3*c^3 + 3*a^2*b^2*c^2*d - 3*a^3*b*c*d^2)) + ((-a*b)^(1/2)*((x*(5*a^2*b^3*d^5 + 5*b^5*c^2*d^3 + 6*a*b^4*c*d^4))/(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) + ((-a*b)^(1/2)*((2*a^7*b^2*d^9 + 2*b^9*c^7*d^2 - 10*a*b^8*c^6*d^3 - 10*a^6*b^3*c*d^8 + 18*a^2*b^7*c^5*d^4 - 10*a^3*b^6*c^4*d^5 - 10*a^4*b^5*c^3*d^6 + 18*a^5*b^4*c^2*d^7)/(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) + (x*(-a*b)^(1/2)*(3*a*d + b*c)*(8*a^7*b^2*d^9 + 8*b^9*c^7*d^2 - 40*a*b^8*c^6*d^3 - 40*a^6*b^3*c*d^8 + 72*a^2*b^7*c^5*d^4 - 40*a^3*b^6*c^4*d^5 - 40*a^4*b^5*c^3*d^6 + 72*a^5*b^4*c^2*d^7))/(4*(a^4*d^3 - a*b^3*c^3 + 3*a^2*b^2*c^2*d - 3*a^3*b*c*d^2)*(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*d + b*c))/(4*(a^4*d^3 - a*b^3*c^3 + 3*a^2*b^2*c^2*d - 3*a^3*b*c*d^2)))*(3*a*d + b*c))/(4*(a^4*d^3 - a*b^3*c^3 + 3*a^2*b^2*c^2*d - 3*a^3*b*c*d^2))))*(-a*b)^(1/2)*(3*a*d + b*c)*1i)/(2*(a^4*d^3 - a*b^3*c^3 + 3*a^2*b^2*c^2*d - 3*a^3*b*c*d^2)) - ((x*(a*d + b*c))/(2*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) + (b*d*x^3)/(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/(a*c + x^2*(a*d + b*c) + b*d*x^4) + (atan((((-c*d)^(1/2)*((x*(5*a^2*b^3*d^5 + 5*b^5*c^2*d^3 + 6*a*b^4*c*d^4))/(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) - ((-c*d)^(1/2)*((2*a^7*b^2*d^9 + 2*b^9*c^7*d^2 - 10*a*b^8*c^6*d^3 - 10*a^6*b^3*c*d^8 + 18*a^2*b^7*c^5*d^4 - 10*a^3*b^6*c^4*d^5 - 10*a^4*b^5*c^3*d^6 + 18*a^5*b^4*c^2*d^7)/(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) - (x*(-c*d)^(1/2)*(a*d + 3*b*c)*(8*a^7*b^2*d^9 + 8*b^9*c^7*d^2 - 40*a*b^8*c^6*d^3 - 40*a^6*b^3*c*d^8 + 72*a^2*b^7*c^5*d^4 - 40*a^3*b^6*c^4*d^5 - 40*a^4*b^5*c^3*d^6 + 72*a^5*b^4*c^2*d^7))/(4*(b^3*c^4 - a^3*c*d^3 + 3*a^2*b*c^2*d^2 - 3*a*b^2*c^3*d)*(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)))*(a*d + 3*b*c))/(4*(b^3*c^4 - a^3*c*d^3 + 3*a^2*b*c^2*d^2 - 3*a*b^2*c^3*d)))*(a*d + 3*b*c)*1i)/(4*(b^3*c^4 - a^3*c*d^3 + 3*a^2*b*c^2*d^2 - 3*a*b^2*c^3*d)) + ((-c*d)^(1/2)*((x*(5*a^2*b^3*d^5 + 5*b^5*c^2*d^3 + 6*a*b^4*c*d^4))/(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) + ((-c*d)^(1/2)*((2*a^7*b^2*d^9 + 2*b^9*c^7*d^2 - 10*a*b^8*c^6*d^3 - 10*a^6*b^3*c*d^8 + 18*a^2*b^7*c^5*d^4 - 10*a^3*b^6*c^4*d^5 - 10*a^4*b^5*c^3*d^6 + 18*a^5*b^4*c^2*d^7)/(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) + (x*(-c*d)^(1/2)*(a*d + 3*b*c)*(8*a^7*b^2*d^9 + 8*b^9*c^7*d^2 - 40*a*b^8*c^6*d^3 - 40*a^6*b^3*c*d^8 + 72*a^2*b^7*c^5*d^4 - 40*a^3*b^6*c^4*d^5 - 40*a^4*b^5*c^3*d^6 + 72*a^5*b^4*c^2*d^7))/(4*(b^3*c^4 - a^3*c*d^3 + 3*a^2*b*c^2*d^2 - 3*a*b^2*c^3*d)*(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)))*(a*d + 3*b*c))/(4*(b^3*c^4 - a^3*c*d^3 + 3*a^2*b*c^2*d^2 - 3*a*b^2*c^3*d)))*(a*d + 3*b*c)*1i)/(4*(b^3*c^4 - a^3*c*d^3 + 3*a^2*b*c^2*d^2 - 3*a*b^2*c^3*d)))/(((3*a^2*b^3*d^5)/2 + (3*b^5*c^2*d^3)/2 + 5*a*b^4*c*d^4)/(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) - ((-c*d)^(1/2)*((x*(5*a^2*b^3*d^5 + 5*b^5*c^2*d^3 + 6*a*b^4*c*d^4))/(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) - ((-c*d)^(1/2)*((2*a^7*b^2*d^9 + 2*b^9*c^7*d^2 - 10*a*b^8*c^6*d^3 - 10*a^6*b^3*c*d^8 + 18*a^2*b^7*c^5*d^4 - 10*a^3*b^6*c^4*d^5 - 10*a^4*b^5*c^3*d^6 + 18*a^5*b^4*c^2*d^7)/(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) - (x*(-c*d)^(1/2)*(a*d + 3*b*c)*(8*a^7*b^2*d^9 + 8*b^9*c^7*d^2 - 40*a*b^8*c^6*d^3 - 40*a^6*b^3*c*d^8 + 72*a^2*b^7*c^5*d^4 - 40*a^3*b^6*c^4*d^5 - 40*a^4*b^5*c^3*d^6 + 72*a^5*b^4*c^2*d^7))/(4*(b^3*c^4 - a^3*c*d^3 + 3*a^2*b*c^2*d^2 - 3*a*b^2*c^3*d)*(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)))*(a*d + 3*b*c))/(4*(b^3*c^4 - a^3*c*d^3 + 3*a^2*b*c^2*d^2 - 3*a*b^2*c^3*d)))*(a*d + 3*b*c))/(4*(b^3*c^4 - a^3*c*d^3 + 3*a^2*b*c^2*d^2 - 3*a*b^2*c^3*d)) + ((-c*d)^(1/2)*((x*(5*a^2*b^3*d^5 + 5*b^5*c^2*d^3 + 6*a*b^4*c*d^4))/(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) + ((-c*d)^(1/2)*((2*a^7*b^2*d^9 + 2*b^9*c^7*d^2 - 10*a*b^8*c^6*d^3 - 10*a^6*b^3*c*d^8 + 18*a^2*b^7*c^5*d^4 - 10*a^3*b^6*c^4*d^5 - 10*a^4*b^5*c^3*d^6 + 18*a^5*b^4*c^2*d^7)/(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) + (x*(-c*d)^(1/2)*(a*d + 3*b*c)*(8*a^7*b^2*d^9 + 8*b^9*c^7*d^2 - 40*a*b^8*c^6*d^3 - 40*a^6*b^3*c*d^8 + 72*a^2*b^7*c^5*d^4 - 40*a^3*b^6*c^4*d^5 - 40*a^4*b^5*c^3*d^6 + 72*a^5*b^4*c^2*d^7))/(4*(b^3*c^4 - a^3*c*d^3 + 3*a^2*b*c^2*d^2 - 3*a*b^2*c^3*d)*(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)))*(a*d + 3*b*c))/(4*(b^3*c^4 - a^3*c*d^3 + 3*a^2*b*c^2*d^2 - 3*a*b^2*c^3*d)))*(a*d + 3*b*c))/(4*(b^3*c^4 - a^3*c*d^3 + 3*a^2*b*c^2*d^2 - 3*a*b^2*c^3*d))))*(-c*d)^(1/2)*(a*d + 3*b*c)*1i)/(2*(b^3*c^4 - a^3*c*d^3 + 3*a^2*b*c^2*d^2 - 3*a*b^2*c^3*d))","B"
304,1,378,92,0.286734,"\text{Not used}","int(x/((a + b*x^2)^2*(c + d*x^2)^2),x)","-\frac{b^2\,c^2-a^2\,d^2+b^2\,d^2\,x^4\,\mathrm{atan}\left(\frac{a\,d\,x^2\,1{}\mathrm{i}-b\,c\,x^2\,1{}\mathrm{i}}{2\,a\,c+a\,d\,x^2+b\,c\,x^2}\right)\,4{}\mathrm{i}-2\,a\,b\,d^2\,x^2+2\,b^2\,c\,d\,x^2+a\,b\,d^2\,x^2\,\mathrm{atan}\left(\frac{a\,d\,x^2\,1{}\mathrm{i}-b\,c\,x^2\,1{}\mathrm{i}}{2\,a\,c+a\,d\,x^2+b\,c\,x^2}\right)\,4{}\mathrm{i}+b^2\,c\,d\,x^2\,\mathrm{atan}\left(\frac{a\,d\,x^2\,1{}\mathrm{i}-b\,c\,x^2\,1{}\mathrm{i}}{2\,a\,c+a\,d\,x^2+b\,c\,x^2}\right)\,4{}\mathrm{i}+a\,b\,c\,d\,\mathrm{atan}\left(\frac{a\,d\,x^2\,1{}\mathrm{i}-b\,c\,x^2\,1{}\mathrm{i}}{2\,a\,c+a\,d\,x^2+b\,c\,x^2}\right)\,4{}\mathrm{i}}{-2\,a^4\,c\,d^3-2\,a^4\,d^4\,x^2+6\,a^3\,b\,c^2\,d^2+4\,a^3\,b\,c\,d^3\,x^2-2\,a^3\,b\,d^4\,x^4-6\,a^2\,b^2\,c^3\,d+6\,a^2\,b^2\,c\,d^3\,x^4+2\,a\,b^3\,c^4-4\,a\,b^3\,c^3\,d\,x^2-6\,a\,b^3\,c^2\,d^2\,x^4+2\,b^4\,c^4\,x^2+2\,b^4\,c^3\,d\,x^4}","Not used",1,"-(b^2*c^2 - a^2*d^2 + b^2*d^2*x^4*atan((a*d*x^2*1i - b*c*x^2*1i)/(2*a*c + a*d*x^2 + b*c*x^2))*4i - 2*a*b*d^2*x^2 + 2*b^2*c*d*x^2 + a*b*d^2*x^2*atan((a*d*x^2*1i - b*c*x^2*1i)/(2*a*c + a*d*x^2 + b*c*x^2))*4i + b^2*c*d*x^2*atan((a*d*x^2*1i - b*c*x^2*1i)/(2*a*c + a*d*x^2 + b*c*x^2))*4i + a*b*c*d*atan((a*d*x^2*1i - b*c*x^2*1i)/(2*a*c + a*d*x^2 + b*c*x^2))*4i)/(2*a*b^3*c^4 - 2*a^4*c*d^3 - 2*a^4*d^4*x^2 + 2*b^4*c^4*x^2 - 6*a^2*b^2*c^3*d + 6*a^3*b*c^2*d^2 - 2*a^3*b*d^4*x^4 + 2*b^4*c^3*d*x^4 - 4*a*b^3*c^3*d*x^2 + 4*a^3*b*c*d^3*x^2 - 6*a*b^3*c^2*d^2*x^4 + 6*a^2*b^2*c*d^3*x^4)","B"
305,1,6183,167,2.066102,"\text{Not used}","int(1/((a + b*x^2)^2*(c + d*x^2)^2),x)","\frac{\frac{x\,\left(a^2\,d^2+b^2\,c^2\right)}{2\,a\,c\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}+\frac{b\,d\,x^3\,\left(a\,d+b\,c\right)}{2\,a\,c\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}}{b\,d\,x^4+\left(a\,d+b\,c\right)\,x^2+a\,c}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{x\,\left(a^4\,b^3\,d^7-10\,a^3\,b^4\,c\,d^6+50\,a^2\,b^5\,c^2\,d^5-10\,a\,b^6\,c^3\,d^4+b^7\,c^4\,d^3\right)}{2\,\left(a^6\,c^2\,d^4-4\,a^5\,b\,c^3\,d^3+6\,a^4\,b^2\,c^4\,d^2-4\,a^3\,b^3\,c^5\,d+a^2\,b^4\,c^6\right)}-\frac{\left(\frac{2\,a^9\,b^2\,c\,d^{10}-20\,a^8\,b^3\,c^2\,d^9+80\,a^7\,b^4\,c^3\,d^8-172\,a^6\,b^5\,c^4\,d^7+220\,a^5\,b^6\,c^5\,d^6-172\,a^4\,b^7\,c^6\,d^5+80\,a^3\,b^8\,c^7\,d^4-20\,a^2\,b^9\,c^8\,d^3+2\,a\,b^{10}\,c^9\,d^2}{a^8\,c^2\,d^6-6\,a^7\,b\,c^3\,d^5+15\,a^6\,b^2\,c^4\,d^4-20\,a^5\,b^3\,c^5\,d^3+15\,a^4\,b^4\,c^6\,d^2-6\,a^3\,b^5\,c^7\,d+a^2\,b^6\,c^8}-\frac{x\,\left(5\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^3}\,\left(16\,a^9\,b^2\,c^2\,d^9-80\,a^8\,b^3\,c^3\,d^8+144\,a^7\,b^4\,c^4\,d^7-80\,a^6\,b^5\,c^5\,d^6-80\,a^5\,b^6\,c^6\,d^5+144\,a^4\,b^7\,c^7\,d^4-80\,a^3\,b^8\,c^8\,d^3+16\,a^2\,b^9\,c^9\,d^2\right)}{8\,\left(a^6\,d^3-3\,a^5\,b\,c\,d^2+3\,a^4\,b^2\,c^2\,d-a^3\,b^3\,c^3\right)\,\left(a^6\,c^2\,d^4-4\,a^5\,b\,c^3\,d^3+6\,a^4\,b^2\,c^4\,d^2-4\,a^3\,b^3\,c^5\,d+a^2\,b^4\,c^6\right)}\right)\,\left(5\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^3}}{4\,\left(a^6\,d^3-3\,a^5\,b\,c\,d^2+3\,a^4\,b^2\,c^2\,d-a^3\,b^3\,c^3\right)}\right)\,\left(5\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^3}\,1{}\mathrm{i}}{4\,\left(a^6\,d^3-3\,a^5\,b\,c\,d^2+3\,a^4\,b^2\,c^2\,d-a^3\,b^3\,c^3\right)}+\frac{\left(\frac{x\,\left(a^4\,b^3\,d^7-10\,a^3\,b^4\,c\,d^6+50\,a^2\,b^5\,c^2\,d^5-10\,a\,b^6\,c^3\,d^4+b^7\,c^4\,d^3\right)}{2\,\left(a^6\,c^2\,d^4-4\,a^5\,b\,c^3\,d^3+6\,a^4\,b^2\,c^4\,d^2-4\,a^3\,b^3\,c^5\,d+a^2\,b^4\,c^6\right)}+\frac{\left(\frac{2\,a^9\,b^2\,c\,d^{10}-20\,a^8\,b^3\,c^2\,d^9+80\,a^7\,b^4\,c^3\,d^8-172\,a^6\,b^5\,c^4\,d^7+220\,a^5\,b^6\,c^5\,d^6-172\,a^4\,b^7\,c^6\,d^5+80\,a^3\,b^8\,c^7\,d^4-20\,a^2\,b^9\,c^8\,d^3+2\,a\,b^{10}\,c^9\,d^2}{a^8\,c^2\,d^6-6\,a^7\,b\,c^3\,d^5+15\,a^6\,b^2\,c^4\,d^4-20\,a^5\,b^3\,c^5\,d^3+15\,a^4\,b^4\,c^6\,d^2-6\,a^3\,b^5\,c^7\,d+a^2\,b^6\,c^8}+\frac{x\,\left(5\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^3}\,\left(16\,a^9\,b^2\,c^2\,d^9-80\,a^8\,b^3\,c^3\,d^8+144\,a^7\,b^4\,c^4\,d^7-80\,a^6\,b^5\,c^5\,d^6-80\,a^5\,b^6\,c^6\,d^5+144\,a^4\,b^7\,c^7\,d^4-80\,a^3\,b^8\,c^8\,d^3+16\,a^2\,b^9\,c^9\,d^2\right)}{8\,\left(a^6\,d^3-3\,a^5\,b\,c\,d^2+3\,a^4\,b^2\,c^2\,d-a^3\,b^3\,c^3\right)\,\left(a^6\,c^2\,d^4-4\,a^5\,b\,c^3\,d^3+6\,a^4\,b^2\,c^4\,d^2-4\,a^3\,b^3\,c^5\,d+a^2\,b^4\,c^6\right)}\right)\,\left(5\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^3}}{4\,\left(a^6\,d^3-3\,a^5\,b\,c\,d^2+3\,a^4\,b^2\,c^2\,d-a^3\,b^3\,c^3\right)}\right)\,\left(5\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^3}\,1{}\mathrm{i}}{4\,\left(a^6\,d^3-3\,a^5\,b\,c\,d^2+3\,a^4\,b^2\,c^2\,d-a^3\,b^3\,c^3\right)}}{\frac{\frac{5\,a^3\,b^4\,d^7}{4}-\frac{21\,a^2\,b^5\,c\,d^6}{4}-\frac{21\,a\,b^6\,c^2\,d^5}{4}+\frac{5\,b^7\,c^3\,d^4}{4}}{a^8\,c^2\,d^6-6\,a^7\,b\,c^3\,d^5+15\,a^6\,b^2\,c^4\,d^4-20\,a^5\,b^3\,c^5\,d^3+15\,a^4\,b^4\,c^6\,d^2-6\,a^3\,b^5\,c^7\,d+a^2\,b^6\,c^8}-\frac{\left(\frac{x\,\left(a^4\,b^3\,d^7-10\,a^3\,b^4\,c\,d^6+50\,a^2\,b^5\,c^2\,d^5-10\,a\,b^6\,c^3\,d^4+b^7\,c^4\,d^3\right)}{2\,\left(a^6\,c^2\,d^4-4\,a^5\,b\,c^3\,d^3+6\,a^4\,b^2\,c^4\,d^2-4\,a^3\,b^3\,c^5\,d+a^2\,b^4\,c^6\right)}-\frac{\left(\frac{2\,a^9\,b^2\,c\,d^{10}-20\,a^8\,b^3\,c^2\,d^9+80\,a^7\,b^4\,c^3\,d^8-172\,a^6\,b^5\,c^4\,d^7+220\,a^5\,b^6\,c^5\,d^6-172\,a^4\,b^7\,c^6\,d^5+80\,a^3\,b^8\,c^7\,d^4-20\,a^2\,b^9\,c^8\,d^3+2\,a\,b^{10}\,c^9\,d^2}{a^8\,c^2\,d^6-6\,a^7\,b\,c^3\,d^5+15\,a^6\,b^2\,c^4\,d^4-20\,a^5\,b^3\,c^5\,d^3+15\,a^4\,b^4\,c^6\,d^2-6\,a^3\,b^5\,c^7\,d+a^2\,b^6\,c^8}-\frac{x\,\left(5\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^3}\,\left(16\,a^9\,b^2\,c^2\,d^9-80\,a^8\,b^3\,c^3\,d^8+144\,a^7\,b^4\,c^4\,d^7-80\,a^6\,b^5\,c^5\,d^6-80\,a^5\,b^6\,c^6\,d^5+144\,a^4\,b^7\,c^7\,d^4-80\,a^3\,b^8\,c^8\,d^3+16\,a^2\,b^9\,c^9\,d^2\right)}{8\,\left(a^6\,d^3-3\,a^5\,b\,c\,d^2+3\,a^4\,b^2\,c^2\,d-a^3\,b^3\,c^3\right)\,\left(a^6\,c^2\,d^4-4\,a^5\,b\,c^3\,d^3+6\,a^4\,b^2\,c^4\,d^2-4\,a^3\,b^3\,c^5\,d+a^2\,b^4\,c^6\right)}\right)\,\left(5\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^3}}{4\,\left(a^6\,d^3-3\,a^5\,b\,c\,d^2+3\,a^4\,b^2\,c^2\,d-a^3\,b^3\,c^3\right)}\right)\,\left(5\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^3}}{4\,\left(a^6\,d^3-3\,a^5\,b\,c\,d^2+3\,a^4\,b^2\,c^2\,d-a^3\,b^3\,c^3\right)}+\frac{\left(\frac{x\,\left(a^4\,b^3\,d^7-10\,a^3\,b^4\,c\,d^6+50\,a^2\,b^5\,c^2\,d^5-10\,a\,b^6\,c^3\,d^4+b^7\,c^4\,d^3\right)}{2\,\left(a^6\,c^2\,d^4-4\,a^5\,b\,c^3\,d^3+6\,a^4\,b^2\,c^4\,d^2-4\,a^3\,b^3\,c^5\,d+a^2\,b^4\,c^6\right)}+\frac{\left(\frac{2\,a^9\,b^2\,c\,d^{10}-20\,a^8\,b^3\,c^2\,d^9+80\,a^7\,b^4\,c^3\,d^8-172\,a^6\,b^5\,c^4\,d^7+220\,a^5\,b^6\,c^5\,d^6-172\,a^4\,b^7\,c^6\,d^5+80\,a^3\,b^8\,c^7\,d^4-20\,a^2\,b^9\,c^8\,d^3+2\,a\,b^{10}\,c^9\,d^2}{a^8\,c^2\,d^6-6\,a^7\,b\,c^3\,d^5+15\,a^6\,b^2\,c^4\,d^4-20\,a^5\,b^3\,c^5\,d^3+15\,a^4\,b^4\,c^6\,d^2-6\,a^3\,b^5\,c^7\,d+a^2\,b^6\,c^8}+\frac{x\,\left(5\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^3}\,\left(16\,a^9\,b^2\,c^2\,d^9-80\,a^8\,b^3\,c^3\,d^8+144\,a^7\,b^4\,c^4\,d^7-80\,a^6\,b^5\,c^5\,d^6-80\,a^5\,b^6\,c^6\,d^5+144\,a^4\,b^7\,c^7\,d^4-80\,a^3\,b^8\,c^8\,d^3+16\,a^2\,b^9\,c^9\,d^2\right)}{8\,\left(a^6\,d^3-3\,a^5\,b\,c\,d^2+3\,a^4\,b^2\,c^2\,d-a^3\,b^3\,c^3\right)\,\left(a^6\,c^2\,d^4-4\,a^5\,b\,c^3\,d^3+6\,a^4\,b^2\,c^4\,d^2-4\,a^3\,b^3\,c^5\,d+a^2\,b^4\,c^6\right)}\right)\,\left(5\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^3}}{4\,\left(a^6\,d^3-3\,a^5\,b\,c\,d^2+3\,a^4\,b^2\,c^2\,d-a^3\,b^3\,c^3\right)}\right)\,\left(5\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^3}}{4\,\left(a^6\,d^3-3\,a^5\,b\,c\,d^2+3\,a^4\,b^2\,c^2\,d-a^3\,b^3\,c^3\right)}}\right)\,\left(5\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^3}\,1{}\mathrm{i}}{2\,\left(a^6\,d^3-3\,a^5\,b\,c\,d^2+3\,a^4\,b^2\,c^2\,d-a^3\,b^3\,c^3\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{x\,\left(a^4\,b^3\,d^7-10\,a^3\,b^4\,c\,d^6+50\,a^2\,b^5\,c^2\,d^5-10\,a\,b^6\,c^3\,d^4+b^7\,c^4\,d^3\right)}{2\,\left(a^6\,c^2\,d^4-4\,a^5\,b\,c^3\,d^3+6\,a^4\,b^2\,c^4\,d^2-4\,a^3\,b^3\,c^5\,d+a^2\,b^4\,c^6\right)}-\frac{\left(\frac{2\,a^9\,b^2\,c\,d^{10}-20\,a^8\,b^3\,c^2\,d^9+80\,a^7\,b^4\,c^3\,d^8-172\,a^6\,b^5\,c^4\,d^7+220\,a^5\,b^6\,c^5\,d^6-172\,a^4\,b^7\,c^6\,d^5+80\,a^3\,b^8\,c^7\,d^4-20\,a^2\,b^9\,c^8\,d^3+2\,a\,b^{10}\,c^9\,d^2}{a^8\,c^2\,d^6-6\,a^7\,b\,c^3\,d^5+15\,a^6\,b^2\,c^4\,d^4-20\,a^5\,b^3\,c^5\,d^3+15\,a^4\,b^4\,c^6\,d^2-6\,a^3\,b^5\,c^7\,d+a^2\,b^6\,c^8}-\frac{x\,\left(a\,d-5\,b\,c\right)\,\sqrt{-c^3\,d^3}\,\left(16\,a^9\,b^2\,c^2\,d^9-80\,a^8\,b^3\,c^3\,d^8+144\,a^7\,b^4\,c^4\,d^7-80\,a^6\,b^5\,c^5\,d^6-80\,a^5\,b^6\,c^6\,d^5+144\,a^4\,b^7\,c^7\,d^4-80\,a^3\,b^8\,c^8\,d^3+16\,a^2\,b^9\,c^9\,d^2\right)}{8\,\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)\,\left(a^6\,c^2\,d^4-4\,a^5\,b\,c^3\,d^3+6\,a^4\,b^2\,c^4\,d^2-4\,a^3\,b^3\,c^5\,d+a^2\,b^4\,c^6\right)}\right)\,\left(a\,d-5\,b\,c\right)\,\sqrt{-c^3\,d^3}}{4\,\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)\,\left(a\,d-5\,b\,c\right)\,\sqrt{-c^3\,d^3}\,1{}\mathrm{i}}{4\,\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{\left(\frac{x\,\left(a^4\,b^3\,d^7-10\,a^3\,b^4\,c\,d^6+50\,a^2\,b^5\,c^2\,d^5-10\,a\,b^6\,c^3\,d^4+b^7\,c^4\,d^3\right)}{2\,\left(a^6\,c^2\,d^4-4\,a^5\,b\,c^3\,d^3+6\,a^4\,b^2\,c^4\,d^2-4\,a^3\,b^3\,c^5\,d+a^2\,b^4\,c^6\right)}+\frac{\left(\frac{2\,a^9\,b^2\,c\,d^{10}-20\,a^8\,b^3\,c^2\,d^9+80\,a^7\,b^4\,c^3\,d^8-172\,a^6\,b^5\,c^4\,d^7+220\,a^5\,b^6\,c^5\,d^6-172\,a^4\,b^7\,c^6\,d^5+80\,a^3\,b^8\,c^7\,d^4-20\,a^2\,b^9\,c^8\,d^3+2\,a\,b^{10}\,c^9\,d^2}{a^8\,c^2\,d^6-6\,a^7\,b\,c^3\,d^5+15\,a^6\,b^2\,c^4\,d^4-20\,a^5\,b^3\,c^5\,d^3+15\,a^4\,b^4\,c^6\,d^2-6\,a^3\,b^5\,c^7\,d+a^2\,b^6\,c^8}+\frac{x\,\left(a\,d-5\,b\,c\right)\,\sqrt{-c^3\,d^3}\,\left(16\,a^9\,b^2\,c^2\,d^9-80\,a^8\,b^3\,c^3\,d^8+144\,a^7\,b^4\,c^4\,d^7-80\,a^6\,b^5\,c^5\,d^6-80\,a^5\,b^6\,c^6\,d^5+144\,a^4\,b^7\,c^7\,d^4-80\,a^3\,b^8\,c^8\,d^3+16\,a^2\,b^9\,c^9\,d^2\right)}{8\,\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)\,\left(a^6\,c^2\,d^4-4\,a^5\,b\,c^3\,d^3+6\,a^4\,b^2\,c^4\,d^2-4\,a^3\,b^3\,c^5\,d+a^2\,b^4\,c^6\right)}\right)\,\left(a\,d-5\,b\,c\right)\,\sqrt{-c^3\,d^3}}{4\,\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)\,\left(a\,d-5\,b\,c\right)\,\sqrt{-c^3\,d^3}\,1{}\mathrm{i}}{4\,\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{\frac{5\,a^3\,b^4\,d^7}{4}-\frac{21\,a^2\,b^5\,c\,d^6}{4}-\frac{21\,a\,b^6\,c^2\,d^5}{4}+\frac{5\,b^7\,c^3\,d^4}{4}}{a^8\,c^2\,d^6-6\,a^7\,b\,c^3\,d^5+15\,a^6\,b^2\,c^4\,d^4-20\,a^5\,b^3\,c^5\,d^3+15\,a^4\,b^4\,c^6\,d^2-6\,a^3\,b^5\,c^7\,d+a^2\,b^6\,c^8}-\frac{\left(\frac{x\,\left(a^4\,b^3\,d^7-10\,a^3\,b^4\,c\,d^6+50\,a^2\,b^5\,c^2\,d^5-10\,a\,b^6\,c^3\,d^4+b^7\,c^4\,d^3\right)}{2\,\left(a^6\,c^2\,d^4-4\,a^5\,b\,c^3\,d^3+6\,a^4\,b^2\,c^4\,d^2-4\,a^3\,b^3\,c^5\,d+a^2\,b^4\,c^6\right)}-\frac{\left(\frac{2\,a^9\,b^2\,c\,d^{10}-20\,a^8\,b^3\,c^2\,d^9+80\,a^7\,b^4\,c^3\,d^8-172\,a^6\,b^5\,c^4\,d^7+220\,a^5\,b^6\,c^5\,d^6-172\,a^4\,b^7\,c^6\,d^5+80\,a^3\,b^8\,c^7\,d^4-20\,a^2\,b^9\,c^8\,d^3+2\,a\,b^{10}\,c^9\,d^2}{a^8\,c^2\,d^6-6\,a^7\,b\,c^3\,d^5+15\,a^6\,b^2\,c^4\,d^4-20\,a^5\,b^3\,c^5\,d^3+15\,a^4\,b^4\,c^6\,d^2-6\,a^3\,b^5\,c^7\,d+a^2\,b^6\,c^8}-\frac{x\,\left(a\,d-5\,b\,c\right)\,\sqrt{-c^3\,d^3}\,\left(16\,a^9\,b^2\,c^2\,d^9-80\,a^8\,b^3\,c^3\,d^8+144\,a^7\,b^4\,c^4\,d^7-80\,a^6\,b^5\,c^5\,d^6-80\,a^5\,b^6\,c^6\,d^5+144\,a^4\,b^7\,c^7\,d^4-80\,a^3\,b^8\,c^8\,d^3+16\,a^2\,b^9\,c^9\,d^2\right)}{8\,\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)\,\left(a^6\,c^2\,d^4-4\,a^5\,b\,c^3\,d^3+6\,a^4\,b^2\,c^4\,d^2-4\,a^3\,b^3\,c^5\,d+a^2\,b^4\,c^6\right)}\right)\,\left(a\,d-5\,b\,c\right)\,\sqrt{-c^3\,d^3}}{4\,\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)\,\left(a\,d-5\,b\,c\right)\,\sqrt{-c^3\,d^3}}{4\,\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{\left(\frac{x\,\left(a^4\,b^3\,d^7-10\,a^3\,b^4\,c\,d^6+50\,a^2\,b^5\,c^2\,d^5-10\,a\,b^6\,c^3\,d^4+b^7\,c^4\,d^3\right)}{2\,\left(a^6\,c^2\,d^4-4\,a^5\,b\,c^3\,d^3+6\,a^4\,b^2\,c^4\,d^2-4\,a^3\,b^3\,c^5\,d+a^2\,b^4\,c^6\right)}+\frac{\left(\frac{2\,a^9\,b^2\,c\,d^{10}-20\,a^8\,b^3\,c^2\,d^9+80\,a^7\,b^4\,c^3\,d^8-172\,a^6\,b^5\,c^4\,d^7+220\,a^5\,b^6\,c^5\,d^6-172\,a^4\,b^7\,c^6\,d^5+80\,a^3\,b^8\,c^7\,d^4-20\,a^2\,b^9\,c^8\,d^3+2\,a\,b^{10}\,c^9\,d^2}{a^8\,c^2\,d^6-6\,a^7\,b\,c^3\,d^5+15\,a^6\,b^2\,c^4\,d^4-20\,a^5\,b^3\,c^5\,d^3+15\,a^4\,b^4\,c^6\,d^2-6\,a^3\,b^5\,c^7\,d+a^2\,b^6\,c^8}+\frac{x\,\left(a\,d-5\,b\,c\right)\,\sqrt{-c^3\,d^3}\,\left(16\,a^9\,b^2\,c^2\,d^9-80\,a^8\,b^3\,c^3\,d^8+144\,a^7\,b^4\,c^4\,d^7-80\,a^6\,b^5\,c^5\,d^6-80\,a^5\,b^6\,c^6\,d^5+144\,a^4\,b^7\,c^7\,d^4-80\,a^3\,b^8\,c^8\,d^3+16\,a^2\,b^9\,c^9\,d^2\right)}{8\,\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)\,\left(a^6\,c^2\,d^4-4\,a^5\,b\,c^3\,d^3+6\,a^4\,b^2\,c^4\,d^2-4\,a^3\,b^3\,c^5\,d+a^2\,b^4\,c^6\right)}\right)\,\left(a\,d-5\,b\,c\right)\,\sqrt{-c^3\,d^3}}{4\,\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)\,\left(a\,d-5\,b\,c\right)\,\sqrt{-c^3\,d^3}}{4\,\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)\,\left(a\,d-5\,b\,c\right)\,\sqrt{-c^3\,d^3}\,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)}","Not used",1,"((x*(a^2*d^2 + b^2*c^2))/(2*a*c*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) + (b*d*x^3*(a*d + b*c))/(2*a*c*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)))/(a*c + x^2*(a*d + b*c) + b*d*x^4) + (atan(((((x*(a^4*b^3*d^7 + b^7*c^4*d^3 - 10*a*b^6*c^3*d^4 - 10*a^3*b^4*c*d^6 + 50*a^2*b^5*c^2*d^5))/(2*(a^2*b^4*c^6 + a^6*c^2*d^4 - 4*a^3*b^3*c^5*d - 4*a^5*b*c^3*d^3 + 6*a^4*b^2*c^4*d^2)) - (((2*a*b^10*c^9*d^2 + 2*a^9*b^2*c*d^10 - 20*a^2*b^9*c^8*d^3 + 80*a^3*b^8*c^7*d^4 - 172*a^4*b^7*c^6*d^5 + 220*a^5*b^6*c^5*d^6 - 172*a^6*b^5*c^4*d^7 + 80*a^7*b^4*c^3*d^8 - 20*a^8*b^3*c^2*d^9)/(a^2*b^6*c^8 + a^8*c^2*d^6 - 6*a^3*b^5*c^7*d - 6*a^7*b*c^3*d^5 + 15*a^4*b^4*c^6*d^2 - 20*a^5*b^3*c^5*d^3 + 15*a^6*b^2*c^4*d^4) - (x*(5*a*d - b*c)*(-a^3*b^3)^(1/2)*(16*a^2*b^9*c^9*d^2 - 80*a^3*b^8*c^8*d^3 + 144*a^4*b^7*c^7*d^4 - 80*a^5*b^6*c^6*d^5 - 80*a^6*b^5*c^5*d^6 + 144*a^7*b^4*c^4*d^7 - 80*a^8*b^3*c^3*d^8 + 16*a^9*b^2*c^2*d^9))/(8*(a^6*d^3 - a^3*b^3*c^3 + 3*a^4*b^2*c^2*d - 3*a^5*b*c*d^2)*(a^2*b^4*c^6 + a^6*c^2*d^4 - 4*a^3*b^3*c^5*d - 4*a^5*b*c^3*d^3 + 6*a^4*b^2*c^4*d^2)))*(5*a*d - b*c)*(-a^3*b^3)^(1/2))/(4*(a^6*d^3 - a^3*b^3*c^3 + 3*a^4*b^2*c^2*d - 3*a^5*b*c*d^2)))*(5*a*d - b*c)*(-a^3*b^3)^(1/2)*1i)/(4*(a^6*d^3 - a^3*b^3*c^3 + 3*a^4*b^2*c^2*d - 3*a^5*b*c*d^2)) + (((x*(a^4*b^3*d^7 + b^7*c^4*d^3 - 10*a*b^6*c^3*d^4 - 10*a^3*b^4*c*d^6 + 50*a^2*b^5*c^2*d^5))/(2*(a^2*b^4*c^6 + a^6*c^2*d^4 - 4*a^3*b^3*c^5*d - 4*a^5*b*c^3*d^3 + 6*a^4*b^2*c^4*d^2)) + (((2*a*b^10*c^9*d^2 + 2*a^9*b^2*c*d^10 - 20*a^2*b^9*c^8*d^3 + 80*a^3*b^8*c^7*d^4 - 172*a^4*b^7*c^6*d^5 + 220*a^5*b^6*c^5*d^6 - 172*a^6*b^5*c^4*d^7 + 80*a^7*b^4*c^3*d^8 - 20*a^8*b^3*c^2*d^9)/(a^2*b^6*c^8 + a^8*c^2*d^6 - 6*a^3*b^5*c^7*d - 6*a^7*b*c^3*d^5 + 15*a^4*b^4*c^6*d^2 - 20*a^5*b^3*c^5*d^3 + 15*a^6*b^2*c^4*d^4) + (x*(5*a*d - b*c)*(-a^3*b^3)^(1/2)*(16*a^2*b^9*c^9*d^2 - 80*a^3*b^8*c^8*d^3 + 144*a^4*b^7*c^7*d^4 - 80*a^5*b^6*c^6*d^5 - 80*a^6*b^5*c^5*d^6 + 144*a^7*b^4*c^4*d^7 - 80*a^8*b^3*c^3*d^8 + 16*a^9*b^2*c^2*d^9))/(8*(a^6*d^3 - a^3*b^3*c^3 + 3*a^4*b^2*c^2*d - 3*a^5*b*c*d^2)*(a^2*b^4*c^6 + a^6*c^2*d^4 - 4*a^3*b^3*c^5*d - 4*a^5*b*c^3*d^3 + 6*a^4*b^2*c^4*d^2)))*(5*a*d - b*c)*(-a^3*b^3)^(1/2))/(4*(a^6*d^3 - a^3*b^3*c^3 + 3*a^4*b^2*c^2*d - 3*a^5*b*c*d^2)))*(5*a*d - b*c)*(-a^3*b^3)^(1/2)*1i)/(4*(a^6*d^3 - a^3*b^3*c^3 + 3*a^4*b^2*c^2*d - 3*a^5*b*c*d^2)))/(((5*a^3*b^4*d^7)/4 + (5*b^7*c^3*d^4)/4 - (21*a*b^6*c^2*d^5)/4 - (21*a^2*b^5*c*d^6)/4)/(a^2*b^6*c^8 + a^8*c^2*d^6 - 6*a^3*b^5*c^7*d - 6*a^7*b*c^3*d^5 + 15*a^4*b^4*c^6*d^2 - 20*a^5*b^3*c^5*d^3 + 15*a^6*b^2*c^4*d^4) - (((x*(a^4*b^3*d^7 + b^7*c^4*d^3 - 10*a*b^6*c^3*d^4 - 10*a^3*b^4*c*d^6 + 50*a^2*b^5*c^2*d^5))/(2*(a^2*b^4*c^6 + a^6*c^2*d^4 - 4*a^3*b^3*c^5*d - 4*a^5*b*c^3*d^3 + 6*a^4*b^2*c^4*d^2)) - (((2*a*b^10*c^9*d^2 + 2*a^9*b^2*c*d^10 - 20*a^2*b^9*c^8*d^3 + 80*a^3*b^8*c^7*d^4 - 172*a^4*b^7*c^6*d^5 + 220*a^5*b^6*c^5*d^6 - 172*a^6*b^5*c^4*d^7 + 80*a^7*b^4*c^3*d^8 - 20*a^8*b^3*c^2*d^9)/(a^2*b^6*c^8 + a^8*c^2*d^6 - 6*a^3*b^5*c^7*d - 6*a^7*b*c^3*d^5 + 15*a^4*b^4*c^6*d^2 - 20*a^5*b^3*c^5*d^3 + 15*a^6*b^2*c^4*d^4) - (x*(5*a*d - b*c)*(-a^3*b^3)^(1/2)*(16*a^2*b^9*c^9*d^2 - 80*a^3*b^8*c^8*d^3 + 144*a^4*b^7*c^7*d^4 - 80*a^5*b^6*c^6*d^5 - 80*a^6*b^5*c^5*d^6 + 144*a^7*b^4*c^4*d^7 - 80*a^8*b^3*c^3*d^8 + 16*a^9*b^2*c^2*d^9))/(8*(a^6*d^3 - a^3*b^3*c^3 + 3*a^4*b^2*c^2*d - 3*a^5*b*c*d^2)*(a^2*b^4*c^6 + a^6*c^2*d^4 - 4*a^3*b^3*c^5*d - 4*a^5*b*c^3*d^3 + 6*a^4*b^2*c^4*d^2)))*(5*a*d - b*c)*(-a^3*b^3)^(1/2))/(4*(a^6*d^3 - a^3*b^3*c^3 + 3*a^4*b^2*c^2*d - 3*a^5*b*c*d^2)))*(5*a*d - b*c)*(-a^3*b^3)^(1/2))/(4*(a^6*d^3 - a^3*b^3*c^3 + 3*a^4*b^2*c^2*d - 3*a^5*b*c*d^2)) + (((x*(a^4*b^3*d^7 + b^7*c^4*d^3 - 10*a*b^6*c^3*d^4 - 10*a^3*b^4*c*d^6 + 50*a^2*b^5*c^2*d^5))/(2*(a^2*b^4*c^6 + a^6*c^2*d^4 - 4*a^3*b^3*c^5*d - 4*a^5*b*c^3*d^3 + 6*a^4*b^2*c^4*d^2)) + (((2*a*b^10*c^9*d^2 + 2*a^9*b^2*c*d^10 - 20*a^2*b^9*c^8*d^3 + 80*a^3*b^8*c^7*d^4 - 172*a^4*b^7*c^6*d^5 + 220*a^5*b^6*c^5*d^6 - 172*a^6*b^5*c^4*d^7 + 80*a^7*b^4*c^3*d^8 - 20*a^8*b^3*c^2*d^9)/(a^2*b^6*c^8 + a^8*c^2*d^6 - 6*a^3*b^5*c^7*d - 6*a^7*b*c^3*d^5 + 15*a^4*b^4*c^6*d^2 - 20*a^5*b^3*c^5*d^3 + 15*a^6*b^2*c^4*d^4) + (x*(5*a*d - b*c)*(-a^3*b^3)^(1/2)*(16*a^2*b^9*c^9*d^2 - 80*a^3*b^8*c^8*d^3 + 144*a^4*b^7*c^7*d^4 - 80*a^5*b^6*c^6*d^5 - 80*a^6*b^5*c^5*d^6 + 144*a^7*b^4*c^4*d^7 - 80*a^8*b^3*c^3*d^8 + 16*a^9*b^2*c^2*d^9))/(8*(a^6*d^3 - a^3*b^3*c^3 + 3*a^4*b^2*c^2*d - 3*a^5*b*c*d^2)*(a^2*b^4*c^6 + a^6*c^2*d^4 - 4*a^3*b^3*c^5*d - 4*a^5*b*c^3*d^3 + 6*a^4*b^2*c^4*d^2)))*(5*a*d - b*c)*(-a^3*b^3)^(1/2))/(4*(a^6*d^3 - a^3*b^3*c^3 + 3*a^4*b^2*c^2*d - 3*a^5*b*c*d^2)))*(5*a*d - b*c)*(-a^3*b^3)^(1/2))/(4*(a^6*d^3 - a^3*b^3*c^3 + 3*a^4*b^2*c^2*d - 3*a^5*b*c*d^2))))*(5*a*d - b*c)*(-a^3*b^3)^(1/2)*1i)/(2*(a^6*d^3 - a^3*b^3*c^3 + 3*a^4*b^2*c^2*d - 3*a^5*b*c*d^2)) + (atan(((((x*(a^4*b^3*d^7 + b^7*c^4*d^3 - 10*a*b^6*c^3*d^4 - 10*a^3*b^4*c*d^6 + 50*a^2*b^5*c^2*d^5))/(2*(a^2*b^4*c^6 + a^6*c^2*d^4 - 4*a^3*b^3*c^5*d - 4*a^5*b*c^3*d^3 + 6*a^4*b^2*c^4*d^2)) - (((2*a*b^10*c^9*d^2 + 2*a^9*b^2*c*d^10 - 20*a^2*b^9*c^8*d^3 + 80*a^3*b^8*c^7*d^4 - 172*a^4*b^7*c^6*d^5 + 220*a^5*b^6*c^5*d^6 - 172*a^6*b^5*c^4*d^7 + 80*a^7*b^4*c^3*d^8 - 20*a^8*b^3*c^2*d^9)/(a^2*b^6*c^8 + a^8*c^2*d^6 - 6*a^3*b^5*c^7*d - 6*a^7*b*c^3*d^5 + 15*a^4*b^4*c^6*d^2 - 20*a^5*b^3*c^5*d^3 + 15*a^6*b^2*c^4*d^4) - (x*(a*d - 5*b*c)*(-c^3*d^3)^(1/2)*(16*a^2*b^9*c^9*d^2 - 80*a^3*b^8*c^8*d^3 + 144*a^4*b^7*c^7*d^4 - 80*a^5*b^6*c^6*d^5 - 80*a^6*b^5*c^5*d^6 + 144*a^7*b^4*c^4*d^7 - 80*a^8*b^3*c^3*d^8 + 16*a^9*b^2*c^2*d^9))/(8*(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)*(a^2*b^4*c^6 + a^6*c^2*d^4 - 4*a^3*b^3*c^5*d - 4*a^5*b*c^3*d^3 + 6*a^4*b^2*c^4*d^2)))*(a*d - 5*b*c)*(-c^3*d^3)^(1/2))/(4*(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)))*(a*d - 5*b*c)*(-c^3*d^3)^(1/2)*1i)/(4*(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)) + (((x*(a^4*b^3*d^7 + b^7*c^4*d^3 - 10*a*b^6*c^3*d^4 - 10*a^3*b^4*c*d^6 + 50*a^2*b^5*c^2*d^5))/(2*(a^2*b^4*c^6 + a^6*c^2*d^4 - 4*a^3*b^3*c^5*d - 4*a^5*b*c^3*d^3 + 6*a^4*b^2*c^4*d^2)) + (((2*a*b^10*c^9*d^2 + 2*a^9*b^2*c*d^10 - 20*a^2*b^9*c^8*d^3 + 80*a^3*b^8*c^7*d^4 - 172*a^4*b^7*c^6*d^5 + 220*a^5*b^6*c^5*d^6 - 172*a^6*b^5*c^4*d^7 + 80*a^7*b^4*c^3*d^8 - 20*a^8*b^3*c^2*d^9)/(a^2*b^6*c^8 + a^8*c^2*d^6 - 6*a^3*b^5*c^7*d - 6*a^7*b*c^3*d^5 + 15*a^4*b^4*c^6*d^2 - 20*a^5*b^3*c^5*d^3 + 15*a^6*b^2*c^4*d^4) + (x*(a*d - 5*b*c)*(-c^3*d^3)^(1/2)*(16*a^2*b^9*c^9*d^2 - 80*a^3*b^8*c^8*d^3 + 144*a^4*b^7*c^7*d^4 - 80*a^5*b^6*c^6*d^5 - 80*a^6*b^5*c^5*d^6 + 144*a^7*b^4*c^4*d^7 - 80*a^8*b^3*c^3*d^8 + 16*a^9*b^2*c^2*d^9))/(8*(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)*(a^2*b^4*c^6 + a^6*c^2*d^4 - 4*a^3*b^3*c^5*d - 4*a^5*b*c^3*d^3 + 6*a^4*b^2*c^4*d^2)))*(a*d - 5*b*c)*(-c^3*d^3)^(1/2))/(4*(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)))*(a*d - 5*b*c)*(-c^3*d^3)^(1/2)*1i)/(4*(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)))/(((5*a^3*b^4*d^7)/4 + (5*b^7*c^3*d^4)/4 - (21*a*b^6*c^2*d^5)/4 - (21*a^2*b^5*c*d^6)/4)/(a^2*b^6*c^8 + a^8*c^2*d^6 - 6*a^3*b^5*c^7*d - 6*a^7*b*c^3*d^5 + 15*a^4*b^4*c^6*d^2 - 20*a^5*b^3*c^5*d^3 + 15*a^6*b^2*c^4*d^4) - (((x*(a^4*b^3*d^7 + b^7*c^4*d^3 - 10*a*b^6*c^3*d^4 - 10*a^3*b^4*c*d^6 + 50*a^2*b^5*c^2*d^5))/(2*(a^2*b^4*c^6 + a^6*c^2*d^4 - 4*a^3*b^3*c^5*d - 4*a^5*b*c^3*d^3 + 6*a^4*b^2*c^4*d^2)) - (((2*a*b^10*c^9*d^2 + 2*a^9*b^2*c*d^10 - 20*a^2*b^9*c^8*d^3 + 80*a^3*b^8*c^7*d^4 - 172*a^4*b^7*c^6*d^5 + 220*a^5*b^6*c^5*d^6 - 172*a^6*b^5*c^4*d^7 + 80*a^7*b^4*c^3*d^8 - 20*a^8*b^3*c^2*d^9)/(a^2*b^6*c^8 + a^8*c^2*d^6 - 6*a^3*b^5*c^7*d - 6*a^7*b*c^3*d^5 + 15*a^4*b^4*c^6*d^2 - 20*a^5*b^3*c^5*d^3 + 15*a^6*b^2*c^4*d^4) - (x*(a*d - 5*b*c)*(-c^3*d^3)^(1/2)*(16*a^2*b^9*c^9*d^2 - 80*a^3*b^8*c^8*d^3 + 144*a^4*b^7*c^7*d^4 - 80*a^5*b^6*c^6*d^5 - 80*a^6*b^5*c^5*d^6 + 144*a^7*b^4*c^4*d^7 - 80*a^8*b^3*c^3*d^8 + 16*a^9*b^2*c^2*d^9))/(8*(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)*(a^2*b^4*c^6 + a^6*c^2*d^4 - 4*a^3*b^3*c^5*d - 4*a^5*b*c^3*d^3 + 6*a^4*b^2*c^4*d^2)))*(a*d - 5*b*c)*(-c^3*d^3)^(1/2))/(4*(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)))*(a*d - 5*b*c)*(-c^3*d^3)^(1/2))/(4*(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)) + (((x*(a^4*b^3*d^7 + b^7*c^4*d^3 - 10*a*b^6*c^3*d^4 - 10*a^3*b^4*c*d^6 + 50*a^2*b^5*c^2*d^5))/(2*(a^2*b^4*c^6 + a^6*c^2*d^4 - 4*a^3*b^3*c^5*d - 4*a^5*b*c^3*d^3 + 6*a^4*b^2*c^4*d^2)) + (((2*a*b^10*c^9*d^2 + 2*a^9*b^2*c*d^10 - 20*a^2*b^9*c^8*d^3 + 80*a^3*b^8*c^7*d^4 - 172*a^4*b^7*c^6*d^5 + 220*a^5*b^6*c^5*d^6 - 172*a^6*b^5*c^4*d^7 + 80*a^7*b^4*c^3*d^8 - 20*a^8*b^3*c^2*d^9)/(a^2*b^6*c^8 + a^8*c^2*d^6 - 6*a^3*b^5*c^7*d - 6*a^7*b*c^3*d^5 + 15*a^4*b^4*c^6*d^2 - 20*a^5*b^3*c^5*d^3 + 15*a^6*b^2*c^4*d^4) + (x*(a*d - 5*b*c)*(-c^3*d^3)^(1/2)*(16*a^2*b^9*c^9*d^2 - 80*a^3*b^8*c^8*d^3 + 144*a^4*b^7*c^7*d^4 - 80*a^5*b^6*c^6*d^5 - 80*a^6*b^5*c^5*d^6 + 144*a^7*b^4*c^4*d^7 - 80*a^8*b^3*c^3*d^8 + 16*a^9*b^2*c^2*d^9))/(8*(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)*(a^2*b^4*c^6 + a^6*c^2*d^4 - 4*a^3*b^3*c^5*d - 4*a^5*b*c^3*d^3 + 6*a^4*b^2*c^4*d^2)))*(a*d - 5*b*c)*(-c^3*d^3)^(1/2))/(4*(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)))*(a*d - 5*b*c)*(-c^3*d^3)^(1/2))/(4*(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))))*(a*d - 5*b*c)*(-c^3*d^3)^(1/2)*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))","B"
306,1,193,141,1.437392,"\text{Not used}","int(1/(x*(a + b*x^2)^2*(c + d*x^2)^2),x)","\frac{\frac{a^2\,d^2+b^2\,c^2}{2\,a\,c\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}+\frac{b\,d\,x^2\,\left(a\,d+b\,c\right)}{2\,a\,c\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}}{b\,d\,x^4+\left(a\,d+b\,c\right)\,x^2+a\,c}+\frac{\ln\left(x\right)}{a^2\,c^2}-\frac{b^2\,\ln\left(b\,x^2+a\right)\,\left(3\,a\,d-b\,c\right)}{2\,a^2\,{\left(a\,d-b\,c\right)}^3}-\frac{d^2\,\ln\left(d\,x^2+c\right)\,\left(a\,d-3\,b\,c\right)}{2\,c^2\,{\left(a\,d-b\,c\right)}^3}","Not used",1,"((a^2*d^2 + b^2*c^2)/(2*a*c*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) + (b*d*x^2*(a*d + b*c))/(2*a*c*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)))/(a*c + x^2*(a*d + b*c) + b*d*x^4) + log(x)/(a^2*c^2) - (b^2*log(a + b*x^2)*(3*a*d - b*c))/(2*a^2*(a*d - b*c)^3) - (d^2*log(c + d*x^2)*(a*d - 3*b*c))/(2*c^2*(a*d - b*c)^3)","B"
307,1,3747,218,1.690887,"\text{Not used}","int(1/(x^2*(a + b*x^2)^2*(c + d*x^2)^2),x)","-\frac{\frac{1}{a\,c}+\frac{x^2\,\left(3\,a^3\,d^3-2\,a^2\,b\,c\,d^2-2\,a\,b^2\,c^2\,d+3\,b^3\,c^3\right)}{2\,a^2\,c^2\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}+\frac{b\,d\,x^4\,\left(3\,a^2\,d^2-4\,a\,b\,c\,d+3\,b^2\,c^2\right)}{2\,a^2\,c^2\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}}{b\,d\,x^5+\left(a\,d+b\,c\right)\,x^3+a\,c\,x}-\frac{\mathrm{atan}\left(\frac{a^7\,d^3\,x\,{\left(-c^5\,d^5\right)}^{3/2}\,9{}\mathrm{i}+b^7\,c^{12}\,d\,x\,\sqrt{-c^5\,d^5}\,9{}\mathrm{i}+a^2\,b^5\,c^{10}\,d^3\,x\,\sqrt{-c^5\,d^5}\,49{}\mathrm{i}-a^6\,b\,c\,d^2\,x\,{\left(-c^5\,d^5\right)}^{3/2}\,42{}\mathrm{i}+a^5\,b^2\,c^2\,d\,x\,{\left(-c^5\,d^5\right)}^{3/2}\,49{}\mathrm{i}-a\,b^6\,c^{11}\,d^2\,x\,\sqrt{-c^5\,d^5}\,42{}\mathrm{i}}{9\,a^7\,c^8\,d^{10}-42\,a^6\,b\,c^9\,d^9+49\,a^5\,b^2\,c^{10}\,d^8-49\,a^2\,b^5\,c^{13}\,d^5+42\,a\,b^6\,c^{14}\,d^4-9\,b^7\,c^{15}\,d^3}\right)\,\left(3\,a\,d-7\,b\,c\right)\,\sqrt{-c^5\,d^5}\,1{}\mathrm{i}}{2\,\left(-a^3\,c^5\,d^3+3\,a^2\,b\,c^6\,d^2-3\,a\,b^2\,c^7\,d+b^3\,c^8\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(7\,a\,d-3\,b\,c\right)\,\left(x\,\left(144\,a^{18}\,b^3\,c^6\,d^{15}-1536\,a^{17}\,b^4\,c^7\,d^{14}+6976\,a^{16}\,b^5\,c^8\,d^{13}-17664\,a^{15}\,b^6\,c^9\,d^{12}+28144\,a^{14}\,b^7\,c^{10}\,d^{11}-32000\,a^{13}\,b^8\,c^{11}\,d^{10}+31872\,a^{12}\,b^9\,c^{12}\,d^9-32000\,a^{11}\,b^{10}\,c^{13}\,d^8+28144\,a^{10}\,b^{11}\,c^{14}\,d^7-17664\,a^9\,b^{12}\,c^{15}\,d^6+6976\,a^8\,b^{13}\,c^{16}\,d^5-1536\,a^7\,b^{14}\,c^{17}\,d^4+144\,a^6\,b^{15}\,c^{18}\,d^3\right)-\frac{\left(7\,a\,d-3\,b\,c\right)\,\sqrt{-a^5\,b^5}\,\left(192\,a^8\,b^{15}\,c^{21}\,d^2-2176\,a^9\,b^{14}\,c^{20}\,d^3+10944\,a^{10}\,b^{13}\,c^{19}\,d^4-31808\,a^{11}\,b^{12}\,c^{18}\,d^5+57600\,a^{12}\,b^{11}\,c^{17}\,d^6-62784\,a^{13}\,b^{10}\,c^{16}\,d^7+28032\,a^{14}\,b^9\,c^{15}\,d^8+28032\,a^{15}\,b^8\,c^{14}\,d^9-62784\,a^{16}\,b^7\,c^{13}\,d^{10}+57600\,a^{17}\,b^6\,c^{12}\,d^{11}-31808\,a^{18}\,b^5\,c^{11}\,d^{12}+10944\,a^{19}\,b^4\,c^{10}\,d^{13}-2176\,a^{20}\,b^3\,c^9\,d^{14}+192\,a^{21}\,b^2\,c^8\,d^{15}-\frac{x\,\left(7\,a\,d-3\,b\,c\right)\,\sqrt{-a^5\,b^5}\,\left(256\,a^{23}\,b^2\,c^{10}\,d^{15}-2816\,a^{22}\,b^3\,c^{11}\,d^{14}+13824\,a^{21}\,b^4\,c^{12}\,d^{13}-39424\,a^{20}\,b^5\,c^{13}\,d^{12}+70400\,a^{19}\,b^6\,c^{14}\,d^{11}-76032\,a^{18}\,b^7\,c^{15}\,d^{10}+33792\,a^{17}\,b^8\,c^{16}\,d^9+33792\,a^{16}\,b^9\,c^{17}\,d^8-76032\,a^{15}\,b^{10}\,c^{18}\,d^7+70400\,a^{14}\,b^{11}\,c^{19}\,d^6-39424\,a^{13}\,b^{12}\,c^{20}\,d^5+13824\,a^{12}\,b^{13}\,c^{21}\,d^4-2816\,a^{11}\,b^{14}\,c^{22}\,d^3+256\,a^{10}\,b^{15}\,c^{23}\,d^2\right)}{4\,\left(a^8\,d^3-3\,a^7\,b\,c\,d^2+3\,a^6\,b^2\,c^2\,d-a^5\,b^3\,c^3\right)}\right)}{4\,\left(a^8\,d^3-3\,a^7\,b\,c\,d^2+3\,a^6\,b^2\,c^2\,d-a^5\,b^3\,c^3\right)}\right)\,\sqrt{-a^5\,b^5}\,1{}\mathrm{i}}{4\,\left(a^8\,d^3-3\,a^7\,b\,c\,d^2+3\,a^6\,b^2\,c^2\,d-a^5\,b^3\,c^3\right)}+\frac{\left(7\,a\,d-3\,b\,c\right)\,\left(x\,\left(144\,a^{18}\,b^3\,c^6\,d^{15}-1536\,a^{17}\,b^4\,c^7\,d^{14}+6976\,a^{16}\,b^5\,c^8\,d^{13}-17664\,a^{15}\,b^6\,c^9\,d^{12}+28144\,a^{14}\,b^7\,c^{10}\,d^{11}-32000\,a^{13}\,b^8\,c^{11}\,d^{10}+31872\,a^{12}\,b^9\,c^{12}\,d^9-32000\,a^{11}\,b^{10}\,c^{13}\,d^8+28144\,a^{10}\,b^{11}\,c^{14}\,d^7-17664\,a^9\,b^{12}\,c^{15}\,d^6+6976\,a^8\,b^{13}\,c^{16}\,d^5-1536\,a^7\,b^{14}\,c^{17}\,d^4+144\,a^6\,b^{15}\,c^{18}\,d^3\right)+\frac{\left(7\,a\,d-3\,b\,c\right)\,\sqrt{-a^5\,b^5}\,\left(192\,a^8\,b^{15}\,c^{21}\,d^2-2176\,a^9\,b^{14}\,c^{20}\,d^3+10944\,a^{10}\,b^{13}\,c^{19}\,d^4-31808\,a^{11}\,b^{12}\,c^{18}\,d^5+57600\,a^{12}\,b^{11}\,c^{17}\,d^6-62784\,a^{13}\,b^{10}\,c^{16}\,d^7+28032\,a^{14}\,b^9\,c^{15}\,d^8+28032\,a^{15}\,b^8\,c^{14}\,d^9-62784\,a^{16}\,b^7\,c^{13}\,d^{10}+57600\,a^{17}\,b^6\,c^{12}\,d^{11}-31808\,a^{18}\,b^5\,c^{11}\,d^{12}+10944\,a^{19}\,b^4\,c^{10}\,d^{13}-2176\,a^{20}\,b^3\,c^9\,d^{14}+192\,a^{21}\,b^2\,c^8\,d^{15}+\frac{x\,\left(7\,a\,d-3\,b\,c\right)\,\sqrt{-a^5\,b^5}\,\left(256\,a^{23}\,b^2\,c^{10}\,d^{15}-2816\,a^{22}\,b^3\,c^{11}\,d^{14}+13824\,a^{21}\,b^4\,c^{12}\,d^{13}-39424\,a^{20}\,b^5\,c^{13}\,d^{12}+70400\,a^{19}\,b^6\,c^{14}\,d^{11}-76032\,a^{18}\,b^7\,c^{15}\,d^{10}+33792\,a^{17}\,b^8\,c^{16}\,d^9+33792\,a^{16}\,b^9\,c^{17}\,d^8-76032\,a^{15}\,b^{10}\,c^{18}\,d^7+70400\,a^{14}\,b^{11}\,c^{19}\,d^6-39424\,a^{13}\,b^{12}\,c^{20}\,d^5+13824\,a^{12}\,b^{13}\,c^{21}\,d^4-2816\,a^{11}\,b^{14}\,c^{22}\,d^3+256\,a^{10}\,b^{15}\,c^{23}\,d^2\right)}{4\,\left(a^8\,d^3-3\,a^7\,b\,c\,d^2+3\,a^6\,b^2\,c^2\,d-a^5\,b^3\,c^3\right)}\right)}{4\,\left(a^8\,d^3-3\,a^7\,b\,c\,d^2+3\,a^6\,b^2\,c^2\,d-a^5\,b^3\,c^3\right)}\right)\,\sqrt{-a^5\,b^5}\,1{}\mathrm{i}}{4\,\left(a^8\,d^3-3\,a^7\,b\,c\,d^2+3\,a^6\,b^2\,c^2\,d-a^5\,b^3\,c^3\right)}}{\frac{\left(7\,a\,d-3\,b\,c\right)\,\left(x\,\left(144\,a^{18}\,b^3\,c^6\,d^{15}-1536\,a^{17}\,b^4\,c^7\,d^{14}+6976\,a^{16}\,b^5\,c^8\,d^{13}-17664\,a^{15}\,b^6\,c^9\,d^{12}+28144\,a^{14}\,b^7\,c^{10}\,d^{11}-32000\,a^{13}\,b^8\,c^{11}\,d^{10}+31872\,a^{12}\,b^9\,c^{12}\,d^9-32000\,a^{11}\,b^{10}\,c^{13}\,d^8+28144\,a^{10}\,b^{11}\,c^{14}\,d^7-17664\,a^9\,b^{12}\,c^{15}\,d^6+6976\,a^8\,b^{13}\,c^{16}\,d^5-1536\,a^7\,b^{14}\,c^{17}\,d^4+144\,a^6\,b^{15}\,c^{18}\,d^3\right)+\frac{\left(7\,a\,d-3\,b\,c\right)\,\sqrt{-a^5\,b^5}\,\left(192\,a^8\,b^{15}\,c^{21}\,d^2-2176\,a^9\,b^{14}\,c^{20}\,d^3+10944\,a^{10}\,b^{13}\,c^{19}\,d^4-31808\,a^{11}\,b^{12}\,c^{18}\,d^5+57600\,a^{12}\,b^{11}\,c^{17}\,d^6-62784\,a^{13}\,b^{10}\,c^{16}\,d^7+28032\,a^{14}\,b^9\,c^{15}\,d^8+28032\,a^{15}\,b^8\,c^{14}\,d^9-62784\,a^{16}\,b^7\,c^{13}\,d^{10}+57600\,a^{17}\,b^6\,c^{12}\,d^{11}-31808\,a^{18}\,b^5\,c^{11}\,d^{12}+10944\,a^{19}\,b^4\,c^{10}\,d^{13}-2176\,a^{20}\,b^3\,c^9\,d^{14}+192\,a^{21}\,b^2\,c^8\,d^{15}+\frac{x\,\left(7\,a\,d-3\,b\,c\right)\,\sqrt{-a^5\,b^5}\,\left(256\,a^{23}\,b^2\,c^{10}\,d^{15}-2816\,a^{22}\,b^3\,c^{11}\,d^{14}+13824\,a^{21}\,b^4\,c^{12}\,d^{13}-39424\,a^{20}\,b^5\,c^{13}\,d^{12}+70400\,a^{19}\,b^6\,c^{14}\,d^{11}-76032\,a^{18}\,b^7\,c^{15}\,d^{10}+33792\,a^{17}\,b^8\,c^{16}\,d^9+33792\,a^{16}\,b^9\,c^{17}\,d^8-76032\,a^{15}\,b^{10}\,c^{18}\,d^7+70400\,a^{14}\,b^{11}\,c^{19}\,d^6-39424\,a^{13}\,b^{12}\,c^{20}\,d^5+13824\,a^{12}\,b^{13}\,c^{21}\,d^4-2816\,a^{11}\,b^{14}\,c^{22}\,d^3+256\,a^{10}\,b^{15}\,c^{23}\,d^2\right)}{4\,\left(a^8\,d^3-3\,a^7\,b\,c\,d^2+3\,a^6\,b^2\,c^2\,d-a^5\,b^3\,c^3\right)}\right)}{4\,\left(a^8\,d^3-3\,a^7\,b\,c\,d^2+3\,a^6\,b^2\,c^2\,d-a^5\,b^3\,c^3\right)}\right)\,\sqrt{-a^5\,b^5}}{4\,\left(a^8\,d^3-3\,a^7\,b\,c\,d^2+3\,a^6\,b^2\,c^2\,d-a^5\,b^3\,c^3\right)}-\frac{\left(7\,a\,d-3\,b\,c\right)\,\left(x\,\left(144\,a^{18}\,b^3\,c^6\,d^{15}-1536\,a^{17}\,b^4\,c^7\,d^{14}+6976\,a^{16}\,b^5\,c^8\,d^{13}-17664\,a^{15}\,b^6\,c^9\,d^{12}+28144\,a^{14}\,b^7\,c^{10}\,d^{11}-32000\,a^{13}\,b^8\,c^{11}\,d^{10}+31872\,a^{12}\,b^9\,c^{12}\,d^9-32000\,a^{11}\,b^{10}\,c^{13}\,d^8+28144\,a^{10}\,b^{11}\,c^{14}\,d^7-17664\,a^9\,b^{12}\,c^{15}\,d^6+6976\,a^8\,b^{13}\,c^{16}\,d^5-1536\,a^7\,b^{14}\,c^{17}\,d^4+144\,a^6\,b^{15}\,c^{18}\,d^3\right)-\frac{\left(7\,a\,d-3\,b\,c\right)\,\sqrt{-a^5\,b^5}\,\left(192\,a^8\,b^{15}\,c^{21}\,d^2-2176\,a^9\,b^{14}\,c^{20}\,d^3+10944\,a^{10}\,b^{13}\,c^{19}\,d^4-31808\,a^{11}\,b^{12}\,c^{18}\,d^5+57600\,a^{12}\,b^{11}\,c^{17}\,d^6-62784\,a^{13}\,b^{10}\,c^{16}\,d^7+28032\,a^{14}\,b^9\,c^{15}\,d^8+28032\,a^{15}\,b^8\,c^{14}\,d^9-62784\,a^{16}\,b^7\,c^{13}\,d^{10}+57600\,a^{17}\,b^6\,c^{12}\,d^{11}-31808\,a^{18}\,b^5\,c^{11}\,d^{12}+10944\,a^{19}\,b^4\,c^{10}\,d^{13}-2176\,a^{20}\,b^3\,c^9\,d^{14}+192\,a^{21}\,b^2\,c^8\,d^{15}-\frac{x\,\left(7\,a\,d-3\,b\,c\right)\,\sqrt{-a^5\,b^5}\,\left(256\,a^{23}\,b^2\,c^{10}\,d^{15}-2816\,a^{22}\,b^3\,c^{11}\,d^{14}+13824\,a^{21}\,b^4\,c^{12}\,d^{13}-39424\,a^{20}\,b^5\,c^{13}\,d^{12}+70400\,a^{19}\,b^6\,c^{14}\,d^{11}-76032\,a^{18}\,b^7\,c^{15}\,d^{10}+33792\,a^{17}\,b^8\,c^{16}\,d^9+33792\,a^{16}\,b^9\,c^{17}\,d^8-76032\,a^{15}\,b^{10}\,c^{18}\,d^7+70400\,a^{14}\,b^{11}\,c^{19}\,d^6-39424\,a^{13}\,b^{12}\,c^{20}\,d^5+13824\,a^{12}\,b^{13}\,c^{21}\,d^4-2816\,a^{11}\,b^{14}\,c^{22}\,d^3+256\,a^{10}\,b^{15}\,c^{23}\,d^2\right)}{4\,\left(a^8\,d^3-3\,a^7\,b\,c\,d^2+3\,a^6\,b^2\,c^2\,d-a^5\,b^3\,c^3\right)}\right)}{4\,\left(a^8\,d^3-3\,a^7\,b\,c\,d^2+3\,a^6\,b^2\,c^2\,d-a^5\,b^3\,c^3\right)}\right)\,\sqrt{-a^5\,b^5}}{4\,\left(a^8\,d^3-3\,a^7\,b\,c\,d^2+3\,a^6\,b^2\,c^2\,d-a^5\,b^3\,c^3\right)}+504\,a^6\,b^{13}\,c^{14}\,d^5-4080\,a^7\,b^{12}\,c^{13}\,d^6+14144\,a^8\,b^{11}\,c^{12}\,d^7-27920\,a^9\,b^{10}\,c^{11}\,d^8+34704\,a^{10}\,b^9\,c^{10}\,d^9-27920\,a^{11}\,b^8\,c^9\,d^{10}+14144\,a^{12}\,b^7\,c^8\,d^{11}-4080\,a^{13}\,b^6\,c^7\,d^{12}+504\,a^{14}\,b^5\,c^6\,d^{13}}\right)\,\left(7\,a\,d-3\,b\,c\right)\,\sqrt{-a^5\,b^5}\,1{}\mathrm{i}}{2\,\left(a^8\,d^3-3\,a^7\,b\,c\,d^2+3\,a^6\,b^2\,c^2\,d-a^5\,b^3\,c^3\right)}","Not used",1,"- (1/(a*c) + (x^2*(3*a^3*d^3 + 3*b^3*c^3 - 2*a*b^2*c^2*d - 2*a^2*b*c*d^2))/(2*a^2*c^2*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) + (b*d*x^4*(3*a^2*d^2 + 3*b^2*c^2 - 4*a*b*c*d))/(2*a^2*c^2*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)))/(x^3*(a*d + b*c) + a*c*x + b*d*x^5) - (atan((a^7*d^3*x*(-c^5*d^5)^(3/2)*9i + b^7*c^12*d*x*(-c^5*d^5)^(1/2)*9i + a^2*b^5*c^10*d^3*x*(-c^5*d^5)^(1/2)*49i - a^6*b*c*d^2*x*(-c^5*d^5)^(3/2)*42i + a^5*b^2*c^2*d*x*(-c^5*d^5)^(3/2)*49i - a*b^6*c^11*d^2*x*(-c^5*d^5)^(1/2)*42i)/(9*a^7*c^8*d^10 - 9*b^7*c^15*d^3 + 42*a*b^6*c^14*d^4 - 42*a^6*b*c^9*d^9 - 49*a^2*b^5*c^13*d^5 + 49*a^5*b^2*c^10*d^8))*(3*a*d - 7*b*c)*(-c^5*d^5)^(1/2)*1i)/(2*(b^3*c^8 - a^3*c^5*d^3 + 3*a^2*b*c^6*d^2 - 3*a*b^2*c^7*d)) - (atan((((7*a*d - 3*b*c)*(x*(144*a^6*b^15*c^18*d^3 - 1536*a^7*b^14*c^17*d^4 + 6976*a^8*b^13*c^16*d^5 - 17664*a^9*b^12*c^15*d^6 + 28144*a^10*b^11*c^14*d^7 - 32000*a^11*b^10*c^13*d^8 + 31872*a^12*b^9*c^12*d^9 - 32000*a^13*b^8*c^11*d^10 + 28144*a^14*b^7*c^10*d^11 - 17664*a^15*b^6*c^9*d^12 + 6976*a^16*b^5*c^8*d^13 - 1536*a^17*b^4*c^7*d^14 + 144*a^18*b^3*c^6*d^15) - ((7*a*d - 3*b*c)*(-a^5*b^5)^(1/2)*(192*a^8*b^15*c^21*d^2 - 2176*a^9*b^14*c^20*d^3 + 10944*a^10*b^13*c^19*d^4 - 31808*a^11*b^12*c^18*d^5 + 57600*a^12*b^11*c^17*d^6 - 62784*a^13*b^10*c^16*d^7 + 28032*a^14*b^9*c^15*d^8 + 28032*a^15*b^8*c^14*d^9 - 62784*a^16*b^7*c^13*d^10 + 57600*a^17*b^6*c^12*d^11 - 31808*a^18*b^5*c^11*d^12 + 10944*a^19*b^4*c^10*d^13 - 2176*a^20*b^3*c^9*d^14 + 192*a^21*b^2*c^8*d^15 - (x*(7*a*d - 3*b*c)*(-a^5*b^5)^(1/2)*(256*a^10*b^15*c^23*d^2 - 2816*a^11*b^14*c^22*d^3 + 13824*a^12*b^13*c^21*d^4 - 39424*a^13*b^12*c^20*d^5 + 70400*a^14*b^11*c^19*d^6 - 76032*a^15*b^10*c^18*d^7 + 33792*a^16*b^9*c^17*d^8 + 33792*a^17*b^8*c^16*d^9 - 76032*a^18*b^7*c^15*d^10 + 70400*a^19*b^6*c^14*d^11 - 39424*a^20*b^5*c^13*d^12 + 13824*a^21*b^4*c^12*d^13 - 2816*a^22*b^3*c^11*d^14 + 256*a^23*b^2*c^10*d^15))/(4*(a^8*d^3 - a^5*b^3*c^3 + 3*a^6*b^2*c^2*d - 3*a^7*b*c*d^2))))/(4*(a^8*d^3 - a^5*b^3*c^3 + 3*a^6*b^2*c^2*d - 3*a^7*b*c*d^2)))*(-a^5*b^5)^(1/2)*1i)/(4*(a^8*d^3 - a^5*b^3*c^3 + 3*a^6*b^2*c^2*d - 3*a^7*b*c*d^2)) + ((7*a*d - 3*b*c)*(x*(144*a^6*b^15*c^18*d^3 - 1536*a^7*b^14*c^17*d^4 + 6976*a^8*b^13*c^16*d^5 - 17664*a^9*b^12*c^15*d^6 + 28144*a^10*b^11*c^14*d^7 - 32000*a^11*b^10*c^13*d^8 + 31872*a^12*b^9*c^12*d^9 - 32000*a^13*b^8*c^11*d^10 + 28144*a^14*b^7*c^10*d^11 - 17664*a^15*b^6*c^9*d^12 + 6976*a^16*b^5*c^8*d^13 - 1536*a^17*b^4*c^7*d^14 + 144*a^18*b^3*c^6*d^15) + ((7*a*d - 3*b*c)*(-a^5*b^5)^(1/2)*(192*a^8*b^15*c^21*d^2 - 2176*a^9*b^14*c^20*d^3 + 10944*a^10*b^13*c^19*d^4 - 31808*a^11*b^12*c^18*d^5 + 57600*a^12*b^11*c^17*d^6 - 62784*a^13*b^10*c^16*d^7 + 28032*a^14*b^9*c^15*d^8 + 28032*a^15*b^8*c^14*d^9 - 62784*a^16*b^7*c^13*d^10 + 57600*a^17*b^6*c^12*d^11 - 31808*a^18*b^5*c^11*d^12 + 10944*a^19*b^4*c^10*d^13 - 2176*a^20*b^3*c^9*d^14 + 192*a^21*b^2*c^8*d^15 + (x*(7*a*d - 3*b*c)*(-a^5*b^5)^(1/2)*(256*a^10*b^15*c^23*d^2 - 2816*a^11*b^14*c^22*d^3 + 13824*a^12*b^13*c^21*d^4 - 39424*a^13*b^12*c^20*d^5 + 70400*a^14*b^11*c^19*d^6 - 76032*a^15*b^10*c^18*d^7 + 33792*a^16*b^9*c^17*d^8 + 33792*a^17*b^8*c^16*d^9 - 76032*a^18*b^7*c^15*d^10 + 70400*a^19*b^6*c^14*d^11 - 39424*a^20*b^5*c^13*d^12 + 13824*a^21*b^4*c^12*d^13 - 2816*a^22*b^3*c^11*d^14 + 256*a^23*b^2*c^10*d^15))/(4*(a^8*d^3 - a^5*b^3*c^3 + 3*a^6*b^2*c^2*d - 3*a^7*b*c*d^2))))/(4*(a^8*d^3 - a^5*b^3*c^3 + 3*a^6*b^2*c^2*d - 3*a^7*b*c*d^2)))*(-a^5*b^5)^(1/2)*1i)/(4*(a^8*d^3 - a^5*b^3*c^3 + 3*a^6*b^2*c^2*d - 3*a^7*b*c*d^2)))/(((7*a*d - 3*b*c)*(x*(144*a^6*b^15*c^18*d^3 - 1536*a^7*b^14*c^17*d^4 + 6976*a^8*b^13*c^16*d^5 - 17664*a^9*b^12*c^15*d^6 + 28144*a^10*b^11*c^14*d^7 - 32000*a^11*b^10*c^13*d^8 + 31872*a^12*b^9*c^12*d^9 - 32000*a^13*b^8*c^11*d^10 + 28144*a^14*b^7*c^10*d^11 - 17664*a^15*b^6*c^9*d^12 + 6976*a^16*b^5*c^8*d^13 - 1536*a^17*b^4*c^7*d^14 + 144*a^18*b^3*c^6*d^15) + ((7*a*d - 3*b*c)*(-a^5*b^5)^(1/2)*(192*a^8*b^15*c^21*d^2 - 2176*a^9*b^14*c^20*d^3 + 10944*a^10*b^13*c^19*d^4 - 31808*a^11*b^12*c^18*d^5 + 57600*a^12*b^11*c^17*d^6 - 62784*a^13*b^10*c^16*d^7 + 28032*a^14*b^9*c^15*d^8 + 28032*a^15*b^8*c^14*d^9 - 62784*a^16*b^7*c^13*d^10 + 57600*a^17*b^6*c^12*d^11 - 31808*a^18*b^5*c^11*d^12 + 10944*a^19*b^4*c^10*d^13 - 2176*a^20*b^3*c^9*d^14 + 192*a^21*b^2*c^8*d^15 + (x*(7*a*d - 3*b*c)*(-a^5*b^5)^(1/2)*(256*a^10*b^15*c^23*d^2 - 2816*a^11*b^14*c^22*d^3 + 13824*a^12*b^13*c^21*d^4 - 39424*a^13*b^12*c^20*d^5 + 70400*a^14*b^11*c^19*d^6 - 76032*a^15*b^10*c^18*d^7 + 33792*a^16*b^9*c^17*d^8 + 33792*a^17*b^8*c^16*d^9 - 76032*a^18*b^7*c^15*d^10 + 70400*a^19*b^6*c^14*d^11 - 39424*a^20*b^5*c^13*d^12 + 13824*a^21*b^4*c^12*d^13 - 2816*a^22*b^3*c^11*d^14 + 256*a^23*b^2*c^10*d^15))/(4*(a^8*d^3 - a^5*b^3*c^3 + 3*a^6*b^2*c^2*d - 3*a^7*b*c*d^2))))/(4*(a^8*d^3 - a^5*b^3*c^3 + 3*a^6*b^2*c^2*d - 3*a^7*b*c*d^2)))*(-a^5*b^5)^(1/2))/(4*(a^8*d^3 - a^5*b^3*c^3 + 3*a^6*b^2*c^2*d - 3*a^7*b*c*d^2)) - ((7*a*d - 3*b*c)*(x*(144*a^6*b^15*c^18*d^3 - 1536*a^7*b^14*c^17*d^4 + 6976*a^8*b^13*c^16*d^5 - 17664*a^9*b^12*c^15*d^6 + 28144*a^10*b^11*c^14*d^7 - 32000*a^11*b^10*c^13*d^8 + 31872*a^12*b^9*c^12*d^9 - 32000*a^13*b^8*c^11*d^10 + 28144*a^14*b^7*c^10*d^11 - 17664*a^15*b^6*c^9*d^12 + 6976*a^16*b^5*c^8*d^13 - 1536*a^17*b^4*c^7*d^14 + 144*a^18*b^3*c^6*d^15) - ((7*a*d - 3*b*c)*(-a^5*b^5)^(1/2)*(192*a^8*b^15*c^21*d^2 - 2176*a^9*b^14*c^20*d^3 + 10944*a^10*b^13*c^19*d^4 - 31808*a^11*b^12*c^18*d^5 + 57600*a^12*b^11*c^17*d^6 - 62784*a^13*b^10*c^16*d^7 + 28032*a^14*b^9*c^15*d^8 + 28032*a^15*b^8*c^14*d^9 - 62784*a^16*b^7*c^13*d^10 + 57600*a^17*b^6*c^12*d^11 - 31808*a^18*b^5*c^11*d^12 + 10944*a^19*b^4*c^10*d^13 - 2176*a^20*b^3*c^9*d^14 + 192*a^21*b^2*c^8*d^15 - (x*(7*a*d - 3*b*c)*(-a^5*b^5)^(1/2)*(256*a^10*b^15*c^23*d^2 - 2816*a^11*b^14*c^22*d^3 + 13824*a^12*b^13*c^21*d^4 - 39424*a^13*b^12*c^20*d^5 + 70400*a^14*b^11*c^19*d^6 - 76032*a^15*b^10*c^18*d^7 + 33792*a^16*b^9*c^17*d^8 + 33792*a^17*b^8*c^16*d^9 - 76032*a^18*b^7*c^15*d^10 + 70400*a^19*b^6*c^14*d^11 - 39424*a^20*b^5*c^13*d^12 + 13824*a^21*b^4*c^12*d^13 - 2816*a^22*b^3*c^11*d^14 + 256*a^23*b^2*c^10*d^15))/(4*(a^8*d^3 - a^5*b^3*c^3 + 3*a^6*b^2*c^2*d - 3*a^7*b*c*d^2))))/(4*(a^8*d^3 - a^5*b^3*c^3 + 3*a^6*b^2*c^2*d - 3*a^7*b*c*d^2)))*(-a^5*b^5)^(1/2))/(4*(a^8*d^3 - a^5*b^3*c^3 + 3*a^6*b^2*c^2*d - 3*a^7*b*c*d^2)) + 504*a^6*b^13*c^14*d^5 - 4080*a^7*b^12*c^13*d^6 + 14144*a^8*b^11*c^12*d^7 - 27920*a^9*b^10*c^11*d^8 + 34704*a^10*b^9*c^10*d^9 - 27920*a^11*b^8*c^9*d^10 + 14144*a^12*b^7*c^8*d^11 - 4080*a^13*b^6*c^7*d^12 + 504*a^14*b^5*c^6*d^13))*(7*a*d - 3*b*c)*(-a^5*b^5)^(1/2)*1i)/(2*(a^8*d^3 - a^5*b^3*c^3 + 3*a^6*b^2*c^2*d - 3*a^7*b*c*d^2))","B"
308,1,313,156,1.635021,"\text{Not used}","int(1/(x^3*(a + b*x^2)^2*(c + d*x^2)^2),x)","-\frac{\frac{1}{2\,a\,c}+\frac{x^4\,\left(a^2\,b\,d^3-a\,b^2\,c\,d^2+b^3\,c^2\,d\right)}{a^2\,c^2\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}+\frac{x^2\,\left(a\,d+b\,c\right)\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+2\,b^2\,c^2\right)}{2\,a^2\,c^2\,\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^4+a\,c\,x^2}-\frac{\ln\left(b\,x^2+a\right)\,\left(b^4\,c-2\,a\,b^3\,d\right)}{a^6\,d^3-3\,a^5\,b\,c\,d^2+3\,a^4\,b^2\,c^2\,d-a^3\,b^3\,c^3}-\frac{\ln\left(d\,x^2+c\right)\,\left(a\,d^4-2\,b\,c\,d^3\right)}{-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}-\frac{\ln\left(x\right)\,\left(2\,a\,d+2\,b\,c\right)}{a^3\,c^3}","Not used",1,"- (1/(2*a*c) + (x^4*(a^2*b*d^3 + b^3*c^2*d - a*b^2*c*d^2))/(a^2*c^2*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) + (x^2*(a*d + b*c)*(2*a^2*d^2 + 2*b^2*c^2 - 3*a*b*c*d))/(2*a^2*c^2*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)))/(x^4*(a*d + b*c) + a*c*x^2 + b*d*x^6) - (log(a + b*x^2)*(b^4*c - 2*a*b^3*d))/(a^6*d^3 - a^3*b^3*c^3 + 3*a^4*b^2*c^2*d - 3*a^5*b*c*d^2) - (log(c + d*x^2)*(a*d^4 - 2*b*c*d^3))/(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) - (log(x)*(2*a*d + 2*b*c))/(a^3*c^3)","B"
309,1,3978,271,1.884668,"\text{Not used}","int(1/(x^4*(a + b*x^2)^2*(c + d*x^2)^2),x)","-\frac{\frac{1}{3\,a\,c}-\frac{5\,x^2\,\left(a\,d+b\,c\right)}{3\,a^2\,c^2}+\frac{x^4\,\left(-15\,a^4\,d^4+2\,a^3\,b\,c\,d^3+20\,a^2\,b^2\,c^2\,d^2+2\,a\,b^3\,c^3\,d-15\,b^4\,c^4\right)}{6\,a^3\,c^3\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}-\frac{b\,d\,x^6\,\left(5\,a^3\,d^3-4\,a^2\,b\,c\,d^2-4\,a\,b^2\,c^2\,d+5\,b^3\,c^3\right)}{2\,a^3\,c^3\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}}{b\,d\,x^7+\left(a\,d+b\,c\right)\,x^5+a\,c\,x^3}+\frac{\mathrm{atan}\left(\frac{a^9\,d^3\,x\,{\left(-c^7\,d^7\right)}^{3/2}\,25{}\mathrm{i}+b^9\,c^{16}\,d\,x\,\sqrt{-c^7\,d^7}\,25{}\mathrm{i}+a^2\,b^7\,c^{14}\,d^3\,x\,\sqrt{-c^7\,d^7}\,81{}\mathrm{i}-a^8\,b\,c\,d^2\,x\,{\left(-c^7\,d^7\right)}^{3/2}\,90{}\mathrm{i}+a^7\,b^2\,c^2\,d\,x\,{\left(-c^7\,d^7\right)}^{3/2}\,81{}\mathrm{i}-a\,b^8\,c^{15}\,d^2\,x\,\sqrt{-c^7\,d^7}\,90{}\mathrm{i}}{25\,a^9\,c^{11}\,d^{13}-90\,a^8\,b\,c^{12}\,d^{12}+81\,a^7\,b^2\,c^{13}\,d^{11}-81\,a^2\,b^7\,c^{18}\,d^6+90\,a\,b^8\,c^{19}\,d^5-25\,b^9\,c^{20}\,d^4}\right)\,\left(5\,a\,d-9\,b\,c\right)\,\sqrt{-c^7\,d^7}\,1{}\mathrm{i}}{2\,\left(-a^3\,c^7\,d^3+3\,a^2\,b\,c^8\,d^2-3\,a\,b^2\,c^9\,d+b^3\,c^{10}\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(x\,\left(400\,a^{23}\,b^3\,c^9\,d^{17}-3840\,a^{22}\,b^4\,c^{10}\,d^{16}+15936\,a^{21}\,b^5\,c^{11}\,d^{15}-37376\,a^{20}\,b^6\,c^{12}\,d^{14}+54240\,a^{19}\,b^7\,c^{13}\,d^{13}-49920\,a^{18}\,b^8\,c^{14}\,d^{12}+29776\,a^{17}\,b^9\,c^{15}\,d^{11}-18432\,a^{16}\,b^{10}\,c^{16}\,d^{10}+29776\,a^{15}\,b^{11}\,c^{17}\,d^9-49920\,a^{14}\,b^{12}\,c^{18}\,d^8+54240\,a^{13}\,b^{13}\,c^{19}\,d^7-37376\,a^{12}\,b^{14}\,c^{20}\,d^6+15936\,a^{11}\,b^{15}\,c^{21}\,d^5-3840\,a^{10}\,b^{16}\,c^{22}\,d^4+400\,a^9\,b^{17}\,c^{23}\,d^3\right)-\frac{\left(9\,a\,d-5\,b\,c\right)\,\sqrt{-a^7\,b^7}\,\left(320\,a^{12}\,b^{16}\,c^{26}\,d^2-3456\,a^{13}\,b^{15}\,c^{25}\,d^3+16704\,a^{14}\,b^{14}\,c^{24}\,d^4-47616\,a^{15}\,b^{13}\,c^{23}\,d^5+89280\,a^{16}\,b^{12}\,c^{22}\,d^6-118400\,a^{17}\,b^{11}\,c^{21}\,d^7+123072\,a^{18}\,b^{10}\,c^{20}\,d^8-119808\,a^{19}\,b^9\,c^{19}\,d^9+123072\,a^{20}\,b^8\,c^{18}\,d^{10}-118400\,a^{21}\,b^7\,c^{17}\,d^{11}+89280\,a^{22}\,b^6\,c^{16}\,d^{12}-47616\,a^{23}\,b^5\,c^{15}\,d^{13}+16704\,a^{24}\,b^4\,c^{14}\,d^{14}-3456\,a^{25}\,b^3\,c^{13}\,d^{15}+320\,a^{26}\,b^2\,c^{12}\,d^{16}-\frac{x\,\left(9\,a\,d-5\,b\,c\right)\,\sqrt{-a^7\,b^7}\,\left(256\,a^{28}\,b^2\,c^{15}\,d^{15}-2816\,a^{27}\,b^3\,c^{16}\,d^{14}+13824\,a^{26}\,b^4\,c^{17}\,d^{13}-39424\,a^{25}\,b^5\,c^{18}\,d^{12}+70400\,a^{24}\,b^6\,c^{19}\,d^{11}-76032\,a^{23}\,b^7\,c^{20}\,d^{10}+33792\,a^{22}\,b^8\,c^{21}\,d^9+33792\,a^{21}\,b^9\,c^{22}\,d^8-76032\,a^{20}\,b^{10}\,c^{23}\,d^7+70400\,a^{19}\,b^{11}\,c^{24}\,d^6-39424\,a^{18}\,b^{12}\,c^{25}\,d^5+13824\,a^{17}\,b^{13}\,c^{26}\,d^4-2816\,a^{16}\,b^{14}\,c^{27}\,d^3+256\,a^{15}\,b^{15}\,c^{28}\,d^2\right)}{4\,\left(a^{10}\,d^3-3\,a^9\,b\,c\,d^2+3\,a^8\,b^2\,c^2\,d-a^7\,b^3\,c^3\right)}\right)}{4\,\left(a^{10}\,d^3-3\,a^9\,b\,c\,d^2+3\,a^8\,b^2\,c^2\,d-a^7\,b^3\,c^3\right)}\right)\,\left(9\,a\,d-5\,b\,c\right)\,\sqrt{-a^7\,b^7}\,1{}\mathrm{i}}{4\,\left(a^{10}\,d^3-3\,a^9\,b\,c\,d^2+3\,a^8\,b^2\,c^2\,d-a^7\,b^3\,c^3\right)}+\frac{\left(x\,\left(400\,a^{23}\,b^3\,c^9\,d^{17}-3840\,a^{22}\,b^4\,c^{10}\,d^{16}+15936\,a^{21}\,b^5\,c^{11}\,d^{15}-37376\,a^{20}\,b^6\,c^{12}\,d^{14}+54240\,a^{19}\,b^7\,c^{13}\,d^{13}-49920\,a^{18}\,b^8\,c^{14}\,d^{12}+29776\,a^{17}\,b^9\,c^{15}\,d^{11}-18432\,a^{16}\,b^{10}\,c^{16}\,d^{10}+29776\,a^{15}\,b^{11}\,c^{17}\,d^9-49920\,a^{14}\,b^{12}\,c^{18}\,d^8+54240\,a^{13}\,b^{13}\,c^{19}\,d^7-37376\,a^{12}\,b^{14}\,c^{20}\,d^6+15936\,a^{11}\,b^{15}\,c^{21}\,d^5-3840\,a^{10}\,b^{16}\,c^{22}\,d^4+400\,a^9\,b^{17}\,c^{23}\,d^3\right)+\frac{\left(9\,a\,d-5\,b\,c\right)\,\sqrt{-a^7\,b^7}\,\left(320\,a^{12}\,b^{16}\,c^{26}\,d^2-3456\,a^{13}\,b^{15}\,c^{25}\,d^3+16704\,a^{14}\,b^{14}\,c^{24}\,d^4-47616\,a^{15}\,b^{13}\,c^{23}\,d^5+89280\,a^{16}\,b^{12}\,c^{22}\,d^6-118400\,a^{17}\,b^{11}\,c^{21}\,d^7+123072\,a^{18}\,b^{10}\,c^{20}\,d^8-119808\,a^{19}\,b^9\,c^{19}\,d^9+123072\,a^{20}\,b^8\,c^{18}\,d^{10}-118400\,a^{21}\,b^7\,c^{17}\,d^{11}+89280\,a^{22}\,b^6\,c^{16}\,d^{12}-47616\,a^{23}\,b^5\,c^{15}\,d^{13}+16704\,a^{24}\,b^4\,c^{14}\,d^{14}-3456\,a^{25}\,b^3\,c^{13}\,d^{15}+320\,a^{26}\,b^2\,c^{12}\,d^{16}+\frac{x\,\left(9\,a\,d-5\,b\,c\right)\,\sqrt{-a^7\,b^7}\,\left(256\,a^{28}\,b^2\,c^{15}\,d^{15}-2816\,a^{27}\,b^3\,c^{16}\,d^{14}+13824\,a^{26}\,b^4\,c^{17}\,d^{13}-39424\,a^{25}\,b^5\,c^{18}\,d^{12}+70400\,a^{24}\,b^6\,c^{19}\,d^{11}-76032\,a^{23}\,b^7\,c^{20}\,d^{10}+33792\,a^{22}\,b^8\,c^{21}\,d^9+33792\,a^{21}\,b^9\,c^{22}\,d^8-76032\,a^{20}\,b^{10}\,c^{23}\,d^7+70400\,a^{19}\,b^{11}\,c^{24}\,d^6-39424\,a^{18}\,b^{12}\,c^{25}\,d^5+13824\,a^{17}\,b^{13}\,c^{26}\,d^4-2816\,a^{16}\,b^{14}\,c^{27}\,d^3+256\,a^{15}\,b^{15}\,c^{28}\,d^2\right)}{4\,\left(a^{10}\,d^3-3\,a^9\,b\,c\,d^2+3\,a^8\,b^2\,c^2\,d-a^7\,b^3\,c^3\right)}\right)}{4\,\left(a^{10}\,d^3-3\,a^9\,b\,c\,d^2+3\,a^8\,b^2\,c^2\,d-a^7\,b^3\,c^3\right)}\right)\,\left(9\,a\,d-5\,b\,c\right)\,\sqrt{-a^7\,b^7}\,1{}\mathrm{i}}{4\,\left(a^{10}\,d^3-3\,a^9\,b\,c\,d^2+3\,a^8\,b^2\,c^2\,d-a^7\,b^3\,c^3\right)}}{\frac{\left(x\,\left(400\,a^{23}\,b^3\,c^9\,d^{17}-3840\,a^{22}\,b^4\,c^{10}\,d^{16}+15936\,a^{21}\,b^5\,c^{11}\,d^{15}-37376\,a^{20}\,b^6\,c^{12}\,d^{14}+54240\,a^{19}\,b^7\,c^{13}\,d^{13}-49920\,a^{18}\,b^8\,c^{14}\,d^{12}+29776\,a^{17}\,b^9\,c^{15}\,d^{11}-18432\,a^{16}\,b^{10}\,c^{16}\,d^{10}+29776\,a^{15}\,b^{11}\,c^{17}\,d^9-49920\,a^{14}\,b^{12}\,c^{18}\,d^8+54240\,a^{13}\,b^{13}\,c^{19}\,d^7-37376\,a^{12}\,b^{14}\,c^{20}\,d^6+15936\,a^{11}\,b^{15}\,c^{21}\,d^5-3840\,a^{10}\,b^{16}\,c^{22}\,d^4+400\,a^9\,b^{17}\,c^{23}\,d^3\right)+\frac{\left(9\,a\,d-5\,b\,c\right)\,\sqrt{-a^7\,b^7}\,\left(320\,a^{12}\,b^{16}\,c^{26}\,d^2-3456\,a^{13}\,b^{15}\,c^{25}\,d^3+16704\,a^{14}\,b^{14}\,c^{24}\,d^4-47616\,a^{15}\,b^{13}\,c^{23}\,d^5+89280\,a^{16}\,b^{12}\,c^{22}\,d^6-118400\,a^{17}\,b^{11}\,c^{21}\,d^7+123072\,a^{18}\,b^{10}\,c^{20}\,d^8-119808\,a^{19}\,b^9\,c^{19}\,d^9+123072\,a^{20}\,b^8\,c^{18}\,d^{10}-118400\,a^{21}\,b^7\,c^{17}\,d^{11}+89280\,a^{22}\,b^6\,c^{16}\,d^{12}-47616\,a^{23}\,b^5\,c^{15}\,d^{13}+16704\,a^{24}\,b^4\,c^{14}\,d^{14}-3456\,a^{25}\,b^3\,c^{13}\,d^{15}+320\,a^{26}\,b^2\,c^{12}\,d^{16}+\frac{x\,\left(9\,a\,d-5\,b\,c\right)\,\sqrt{-a^7\,b^7}\,\left(256\,a^{28}\,b^2\,c^{15}\,d^{15}-2816\,a^{27}\,b^3\,c^{16}\,d^{14}+13824\,a^{26}\,b^4\,c^{17}\,d^{13}-39424\,a^{25}\,b^5\,c^{18}\,d^{12}+70400\,a^{24}\,b^6\,c^{19}\,d^{11}-76032\,a^{23}\,b^7\,c^{20}\,d^{10}+33792\,a^{22}\,b^8\,c^{21}\,d^9+33792\,a^{21}\,b^9\,c^{22}\,d^8-76032\,a^{20}\,b^{10}\,c^{23}\,d^7+70400\,a^{19}\,b^{11}\,c^{24}\,d^6-39424\,a^{18}\,b^{12}\,c^{25}\,d^5+13824\,a^{17}\,b^{13}\,c^{26}\,d^4-2816\,a^{16}\,b^{14}\,c^{27}\,d^3+256\,a^{15}\,b^{15}\,c^{28}\,d^2\right)}{4\,\left(a^{10}\,d^3-3\,a^9\,b\,c\,d^2+3\,a^8\,b^2\,c^2\,d-a^7\,b^3\,c^3\right)}\right)}{4\,\left(a^{10}\,d^3-3\,a^9\,b\,c\,d^2+3\,a^8\,b^2\,c^2\,d-a^7\,b^3\,c^3\right)}\right)\,\left(9\,a\,d-5\,b\,c\right)\,\sqrt{-a^7\,b^7}}{4\,\left(a^{10}\,d^3-3\,a^9\,b\,c\,d^2+3\,a^8\,b^2\,c^2\,d-a^7\,b^3\,c^3\right)}-\frac{\left(x\,\left(400\,a^{23}\,b^3\,c^9\,d^{17}-3840\,a^{22}\,b^4\,c^{10}\,d^{16}+15936\,a^{21}\,b^5\,c^{11}\,d^{15}-37376\,a^{20}\,b^6\,c^{12}\,d^{14}+54240\,a^{19}\,b^7\,c^{13}\,d^{13}-49920\,a^{18}\,b^8\,c^{14}\,d^{12}+29776\,a^{17}\,b^9\,c^{15}\,d^{11}-18432\,a^{16}\,b^{10}\,c^{16}\,d^{10}+29776\,a^{15}\,b^{11}\,c^{17}\,d^9-49920\,a^{14}\,b^{12}\,c^{18}\,d^8+54240\,a^{13}\,b^{13}\,c^{19}\,d^7-37376\,a^{12}\,b^{14}\,c^{20}\,d^6+15936\,a^{11}\,b^{15}\,c^{21}\,d^5-3840\,a^{10}\,b^{16}\,c^{22}\,d^4+400\,a^9\,b^{17}\,c^{23}\,d^3\right)-\frac{\left(9\,a\,d-5\,b\,c\right)\,\sqrt{-a^7\,b^7}\,\left(320\,a^{12}\,b^{16}\,c^{26}\,d^2-3456\,a^{13}\,b^{15}\,c^{25}\,d^3+16704\,a^{14}\,b^{14}\,c^{24}\,d^4-47616\,a^{15}\,b^{13}\,c^{23}\,d^5+89280\,a^{16}\,b^{12}\,c^{22}\,d^6-118400\,a^{17}\,b^{11}\,c^{21}\,d^7+123072\,a^{18}\,b^{10}\,c^{20}\,d^8-119808\,a^{19}\,b^9\,c^{19}\,d^9+123072\,a^{20}\,b^8\,c^{18}\,d^{10}-118400\,a^{21}\,b^7\,c^{17}\,d^{11}+89280\,a^{22}\,b^6\,c^{16}\,d^{12}-47616\,a^{23}\,b^5\,c^{15}\,d^{13}+16704\,a^{24}\,b^4\,c^{14}\,d^{14}-3456\,a^{25}\,b^3\,c^{13}\,d^{15}+320\,a^{26}\,b^2\,c^{12}\,d^{16}-\frac{x\,\left(9\,a\,d-5\,b\,c\right)\,\sqrt{-a^7\,b^7}\,\left(256\,a^{28}\,b^2\,c^{15}\,d^{15}-2816\,a^{27}\,b^3\,c^{16}\,d^{14}+13824\,a^{26}\,b^4\,c^{17}\,d^{13}-39424\,a^{25}\,b^5\,c^{18}\,d^{12}+70400\,a^{24}\,b^6\,c^{19}\,d^{11}-76032\,a^{23}\,b^7\,c^{20}\,d^{10}+33792\,a^{22}\,b^8\,c^{21}\,d^9+33792\,a^{21}\,b^9\,c^{22}\,d^8-76032\,a^{20}\,b^{10}\,c^{23}\,d^7+70400\,a^{19}\,b^{11}\,c^{24}\,d^6-39424\,a^{18}\,b^{12}\,c^{25}\,d^5+13824\,a^{17}\,b^{13}\,c^{26}\,d^4-2816\,a^{16}\,b^{14}\,c^{27}\,d^3+256\,a^{15}\,b^{15}\,c^{28}\,d^2\right)}{4\,\left(a^{10}\,d^3-3\,a^9\,b\,c\,d^2+3\,a^8\,b^2\,c^2\,d-a^7\,b^3\,c^3\right)}\right)}{4\,\left(a^{10}\,d^3-3\,a^9\,b\,c\,d^2+3\,a^8\,b^2\,c^2\,d-a^7\,b^3\,c^3\right)}\right)\,\left(9\,a\,d-5\,b\,c\right)\,\sqrt{-a^7\,b^7}}{4\,\left(a^{10}\,d^3-3\,a^9\,b\,c\,d^2+3\,a^8\,b^2\,c^2\,d-a^7\,b^3\,c^3\right)}+1800\,a^9\,b^{15}\,c^{18}\,d^6-12880\,a^{10}\,b^{14}\,c^{17}\,d^7+37272\,a^{11}\,b^{13}\,c^{16}\,d^8-52536\,a^{12}\,b^{12}\,c^{15}\,d^9+26344\,a^{13}\,b^{11}\,c^{14}\,d^{10}+26344\,a^{14}\,b^{10}\,c^{13}\,d^{11}-52536\,a^{15}\,b^9\,c^{12}\,d^{12}+37272\,a^{16}\,b^8\,c^{11}\,d^{13}-12880\,a^{17}\,b^7\,c^{10}\,d^{14}+1800\,a^{18}\,b^6\,c^9\,d^{15}}\right)\,\left(9\,a\,d-5\,b\,c\right)\,\sqrt{-a^7\,b^7}\,1{}\mathrm{i}}{2\,\left(a^{10}\,d^3-3\,a^9\,b\,c\,d^2+3\,a^8\,b^2\,c^2\,d-a^7\,b^3\,c^3\right)}","Not used",1,"(atan((a^9*d^3*x*(-c^7*d^7)^(3/2)*25i + b^9*c^16*d*x*(-c^7*d^7)^(1/2)*25i + a^2*b^7*c^14*d^3*x*(-c^7*d^7)^(1/2)*81i - a^8*b*c*d^2*x*(-c^7*d^7)^(3/2)*90i + a^7*b^2*c^2*d*x*(-c^7*d^7)^(3/2)*81i - a*b^8*c^15*d^2*x*(-c^7*d^7)^(1/2)*90i)/(25*a^9*c^11*d^13 - 25*b^9*c^20*d^4 + 90*a*b^8*c^19*d^5 - 90*a^8*b*c^12*d^12 - 81*a^2*b^7*c^18*d^6 + 81*a^7*b^2*c^13*d^11))*(5*a*d - 9*b*c)*(-c^7*d^7)^(1/2)*1i)/(2*(b^3*c^10 - a^3*c^7*d^3 + 3*a^2*b*c^8*d^2 - 3*a*b^2*c^9*d)) - (1/(3*a*c) - (5*x^2*(a*d + b*c))/(3*a^2*c^2) + (x^4*(20*a^2*b^2*c^2*d^2 - 15*b^4*c^4 - 15*a^4*d^4 + 2*a*b^3*c^3*d + 2*a^3*b*c*d^3))/(6*a^3*c^3*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) - (b*d*x^6*(5*a^3*d^3 + 5*b^3*c^3 - 4*a*b^2*c^2*d - 4*a^2*b*c*d^2))/(2*a^3*c^3*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)))/(x^5*(a*d + b*c) + a*c*x^3 + b*d*x^7) + (atan((((x*(400*a^9*b^17*c^23*d^3 - 3840*a^10*b^16*c^22*d^4 + 15936*a^11*b^15*c^21*d^5 - 37376*a^12*b^14*c^20*d^6 + 54240*a^13*b^13*c^19*d^7 - 49920*a^14*b^12*c^18*d^8 + 29776*a^15*b^11*c^17*d^9 - 18432*a^16*b^10*c^16*d^10 + 29776*a^17*b^9*c^15*d^11 - 49920*a^18*b^8*c^14*d^12 + 54240*a^19*b^7*c^13*d^13 - 37376*a^20*b^6*c^12*d^14 + 15936*a^21*b^5*c^11*d^15 - 3840*a^22*b^4*c^10*d^16 + 400*a^23*b^3*c^9*d^17) - ((9*a*d - 5*b*c)*(-a^7*b^7)^(1/2)*(320*a^12*b^16*c^26*d^2 - 3456*a^13*b^15*c^25*d^3 + 16704*a^14*b^14*c^24*d^4 - 47616*a^15*b^13*c^23*d^5 + 89280*a^16*b^12*c^22*d^6 - 118400*a^17*b^11*c^21*d^7 + 123072*a^18*b^10*c^20*d^8 - 119808*a^19*b^9*c^19*d^9 + 123072*a^20*b^8*c^18*d^10 - 118400*a^21*b^7*c^17*d^11 + 89280*a^22*b^6*c^16*d^12 - 47616*a^23*b^5*c^15*d^13 + 16704*a^24*b^4*c^14*d^14 - 3456*a^25*b^3*c^13*d^15 + 320*a^26*b^2*c^12*d^16 - (x*(9*a*d - 5*b*c)*(-a^7*b^7)^(1/2)*(256*a^15*b^15*c^28*d^2 - 2816*a^16*b^14*c^27*d^3 + 13824*a^17*b^13*c^26*d^4 - 39424*a^18*b^12*c^25*d^5 + 70400*a^19*b^11*c^24*d^6 - 76032*a^20*b^10*c^23*d^7 + 33792*a^21*b^9*c^22*d^8 + 33792*a^22*b^8*c^21*d^9 - 76032*a^23*b^7*c^20*d^10 + 70400*a^24*b^6*c^19*d^11 - 39424*a^25*b^5*c^18*d^12 + 13824*a^26*b^4*c^17*d^13 - 2816*a^27*b^3*c^16*d^14 + 256*a^28*b^2*c^15*d^15))/(4*(a^10*d^3 - a^7*b^3*c^3 + 3*a^8*b^2*c^2*d - 3*a^9*b*c*d^2))))/(4*(a^10*d^3 - a^7*b^3*c^3 + 3*a^8*b^2*c^2*d - 3*a^9*b*c*d^2)))*(9*a*d - 5*b*c)*(-a^7*b^7)^(1/2)*1i)/(4*(a^10*d^3 - a^7*b^3*c^3 + 3*a^8*b^2*c^2*d - 3*a^9*b*c*d^2)) + ((x*(400*a^9*b^17*c^23*d^3 - 3840*a^10*b^16*c^22*d^4 + 15936*a^11*b^15*c^21*d^5 - 37376*a^12*b^14*c^20*d^6 + 54240*a^13*b^13*c^19*d^7 - 49920*a^14*b^12*c^18*d^8 + 29776*a^15*b^11*c^17*d^9 - 18432*a^16*b^10*c^16*d^10 + 29776*a^17*b^9*c^15*d^11 - 49920*a^18*b^8*c^14*d^12 + 54240*a^19*b^7*c^13*d^13 - 37376*a^20*b^6*c^12*d^14 + 15936*a^21*b^5*c^11*d^15 - 3840*a^22*b^4*c^10*d^16 + 400*a^23*b^3*c^9*d^17) + ((9*a*d - 5*b*c)*(-a^7*b^7)^(1/2)*(320*a^12*b^16*c^26*d^2 - 3456*a^13*b^15*c^25*d^3 + 16704*a^14*b^14*c^24*d^4 - 47616*a^15*b^13*c^23*d^5 + 89280*a^16*b^12*c^22*d^6 - 118400*a^17*b^11*c^21*d^7 + 123072*a^18*b^10*c^20*d^8 - 119808*a^19*b^9*c^19*d^9 + 123072*a^20*b^8*c^18*d^10 - 118400*a^21*b^7*c^17*d^11 + 89280*a^22*b^6*c^16*d^12 - 47616*a^23*b^5*c^15*d^13 + 16704*a^24*b^4*c^14*d^14 - 3456*a^25*b^3*c^13*d^15 + 320*a^26*b^2*c^12*d^16 + (x*(9*a*d - 5*b*c)*(-a^7*b^7)^(1/2)*(256*a^15*b^15*c^28*d^2 - 2816*a^16*b^14*c^27*d^3 + 13824*a^17*b^13*c^26*d^4 - 39424*a^18*b^12*c^25*d^5 + 70400*a^19*b^11*c^24*d^6 - 76032*a^20*b^10*c^23*d^7 + 33792*a^21*b^9*c^22*d^8 + 33792*a^22*b^8*c^21*d^9 - 76032*a^23*b^7*c^20*d^10 + 70400*a^24*b^6*c^19*d^11 - 39424*a^25*b^5*c^18*d^12 + 13824*a^26*b^4*c^17*d^13 - 2816*a^27*b^3*c^16*d^14 + 256*a^28*b^2*c^15*d^15))/(4*(a^10*d^3 - a^7*b^3*c^3 + 3*a^8*b^2*c^2*d - 3*a^9*b*c*d^2))))/(4*(a^10*d^3 - a^7*b^3*c^3 + 3*a^8*b^2*c^2*d - 3*a^9*b*c*d^2)))*(9*a*d - 5*b*c)*(-a^7*b^7)^(1/2)*1i)/(4*(a^10*d^3 - a^7*b^3*c^3 + 3*a^8*b^2*c^2*d - 3*a^9*b*c*d^2)))/(((x*(400*a^9*b^17*c^23*d^3 - 3840*a^10*b^16*c^22*d^4 + 15936*a^11*b^15*c^21*d^5 - 37376*a^12*b^14*c^20*d^6 + 54240*a^13*b^13*c^19*d^7 - 49920*a^14*b^12*c^18*d^8 + 29776*a^15*b^11*c^17*d^9 - 18432*a^16*b^10*c^16*d^10 + 29776*a^17*b^9*c^15*d^11 - 49920*a^18*b^8*c^14*d^12 + 54240*a^19*b^7*c^13*d^13 - 37376*a^20*b^6*c^12*d^14 + 15936*a^21*b^5*c^11*d^15 - 3840*a^22*b^4*c^10*d^16 + 400*a^23*b^3*c^9*d^17) + ((9*a*d - 5*b*c)*(-a^7*b^7)^(1/2)*(320*a^12*b^16*c^26*d^2 - 3456*a^13*b^15*c^25*d^3 + 16704*a^14*b^14*c^24*d^4 - 47616*a^15*b^13*c^23*d^5 + 89280*a^16*b^12*c^22*d^6 - 118400*a^17*b^11*c^21*d^7 + 123072*a^18*b^10*c^20*d^8 - 119808*a^19*b^9*c^19*d^9 + 123072*a^20*b^8*c^18*d^10 - 118400*a^21*b^7*c^17*d^11 + 89280*a^22*b^6*c^16*d^12 - 47616*a^23*b^5*c^15*d^13 + 16704*a^24*b^4*c^14*d^14 - 3456*a^25*b^3*c^13*d^15 + 320*a^26*b^2*c^12*d^16 + (x*(9*a*d - 5*b*c)*(-a^7*b^7)^(1/2)*(256*a^15*b^15*c^28*d^2 - 2816*a^16*b^14*c^27*d^3 + 13824*a^17*b^13*c^26*d^4 - 39424*a^18*b^12*c^25*d^5 + 70400*a^19*b^11*c^24*d^6 - 76032*a^20*b^10*c^23*d^7 + 33792*a^21*b^9*c^22*d^8 + 33792*a^22*b^8*c^21*d^9 - 76032*a^23*b^7*c^20*d^10 + 70400*a^24*b^6*c^19*d^11 - 39424*a^25*b^5*c^18*d^12 + 13824*a^26*b^4*c^17*d^13 - 2816*a^27*b^3*c^16*d^14 + 256*a^28*b^2*c^15*d^15))/(4*(a^10*d^3 - a^7*b^3*c^3 + 3*a^8*b^2*c^2*d - 3*a^9*b*c*d^2))))/(4*(a^10*d^3 - a^7*b^3*c^3 + 3*a^8*b^2*c^2*d - 3*a^9*b*c*d^2)))*(9*a*d - 5*b*c)*(-a^7*b^7)^(1/2))/(4*(a^10*d^3 - a^7*b^3*c^3 + 3*a^8*b^2*c^2*d - 3*a^9*b*c*d^2)) - ((x*(400*a^9*b^17*c^23*d^3 - 3840*a^10*b^16*c^22*d^4 + 15936*a^11*b^15*c^21*d^5 - 37376*a^12*b^14*c^20*d^6 + 54240*a^13*b^13*c^19*d^7 - 49920*a^14*b^12*c^18*d^8 + 29776*a^15*b^11*c^17*d^9 - 18432*a^16*b^10*c^16*d^10 + 29776*a^17*b^9*c^15*d^11 - 49920*a^18*b^8*c^14*d^12 + 54240*a^19*b^7*c^13*d^13 - 37376*a^20*b^6*c^12*d^14 + 15936*a^21*b^5*c^11*d^15 - 3840*a^22*b^4*c^10*d^16 + 400*a^23*b^3*c^9*d^17) - ((9*a*d - 5*b*c)*(-a^7*b^7)^(1/2)*(320*a^12*b^16*c^26*d^2 - 3456*a^13*b^15*c^25*d^3 + 16704*a^14*b^14*c^24*d^4 - 47616*a^15*b^13*c^23*d^5 + 89280*a^16*b^12*c^22*d^6 - 118400*a^17*b^11*c^21*d^7 + 123072*a^18*b^10*c^20*d^8 - 119808*a^19*b^9*c^19*d^9 + 123072*a^20*b^8*c^18*d^10 - 118400*a^21*b^7*c^17*d^11 + 89280*a^22*b^6*c^16*d^12 - 47616*a^23*b^5*c^15*d^13 + 16704*a^24*b^4*c^14*d^14 - 3456*a^25*b^3*c^13*d^15 + 320*a^26*b^2*c^12*d^16 - (x*(9*a*d - 5*b*c)*(-a^7*b^7)^(1/2)*(256*a^15*b^15*c^28*d^2 - 2816*a^16*b^14*c^27*d^3 + 13824*a^17*b^13*c^26*d^4 - 39424*a^18*b^12*c^25*d^5 + 70400*a^19*b^11*c^24*d^6 - 76032*a^20*b^10*c^23*d^7 + 33792*a^21*b^9*c^22*d^8 + 33792*a^22*b^8*c^21*d^9 - 76032*a^23*b^7*c^20*d^10 + 70400*a^24*b^6*c^19*d^11 - 39424*a^25*b^5*c^18*d^12 + 13824*a^26*b^4*c^17*d^13 - 2816*a^27*b^3*c^16*d^14 + 256*a^28*b^2*c^15*d^15))/(4*(a^10*d^3 - a^7*b^3*c^3 + 3*a^8*b^2*c^2*d - 3*a^9*b*c*d^2))))/(4*(a^10*d^3 - a^7*b^3*c^3 + 3*a^8*b^2*c^2*d - 3*a^9*b*c*d^2)))*(9*a*d - 5*b*c)*(-a^7*b^7)^(1/2))/(4*(a^10*d^3 - a^7*b^3*c^3 + 3*a^8*b^2*c^2*d - 3*a^9*b*c*d^2)) + 1800*a^9*b^15*c^18*d^6 - 12880*a^10*b^14*c^17*d^7 + 37272*a^11*b^13*c^16*d^8 - 52536*a^12*b^12*c^15*d^9 + 26344*a^13*b^11*c^14*d^10 + 26344*a^14*b^10*c^13*d^11 - 52536*a^15*b^9*c^12*d^12 + 37272*a^16*b^8*c^11*d^13 - 12880*a^17*b^7*c^10*d^14 + 1800*a^18*b^6*c^9*d^15))*(9*a*d - 5*b*c)*(-a^7*b^7)^(1/2)*1i)/(2*(a^10*d^3 - a^7*b^3*c^3 + 3*a^8*b^2*c^2*d - 3*a^9*b*c*d^2))","B"
310,1,7515,207,2.925526,"\text{Not used}","int(x^4/((a + b*x^2)^2*(c + d*x^2)^3),x)","-\frac{\frac{3\,x^5\,\left(c\,b^2\,d+3\,a\,b\,d^2\right)}{8\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)}+\frac{3\,x\,\left(d\,a^2\,c+3\,b\,a\,c^2\right)}{8\,\left(a\,d-b\,c\right)\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}+\frac{x^3\,\left(5\,a^2\,d^2+14\,a\,b\,c\,d+5\,b^2\,c^2\right)}{8\,\left(a\,d-b\,c\right)\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}}{a\,c^2+x^2\,\left(b\,c^2+2\,a\,d\,c\right)+x^4\,\left(a\,d^2+2\,b\,c\,d\right)+b\,d^2\,x^6}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{x\,\left(153\,a^4\,b^3\,d^5+396\,a^3\,b^4\,c\,d^4+486\,a^2\,b^5\,c^2\,d^3+108\,a\,b^6\,c^3\,d^2+9\,b^7\,c^4\,d\right)}{32\,\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)}-\frac{3\,\sqrt{-a\,b}\,\left(\frac{\frac{3\,a^{10}\,b^2\,d^{11}}{2}-\frac{15\,a^9\,b^3\,c\,d^{10}}{2}+6\,a^8\,b^4\,c^2\,d^9+42\,a^7\,b^5\,c^3\,d^8-147\,a^6\,b^6\,c^4\,d^7+231\,a^5\,b^7\,c^5\,d^6-210\,a^4\,b^8\,c^6\,d^5+114\,a^3\,b^9\,c^7\,d^4-\frac{69\,a^2\,b^{10}\,c^8\,d^3}{2}+\frac{9\,a\,b^{11}\,c^9\,d^2}{2}}{a^9\,d^9-9\,a^8\,b\,c\,d^8+36\,a^7\,b^2\,c^2\,d^7-84\,a^6\,b^3\,c^3\,d^6+126\,a^5\,b^4\,c^4\,d^5-126\,a^4\,b^5\,c^5\,d^4+84\,a^3\,b^6\,c^6\,d^3-36\,a^2\,b^7\,c^7\,d^2+9\,a\,b^8\,c^8\,d-b^9\,c^9}-\frac{3\,x\,\sqrt{-a\,b}\,\left(a\,d+b\,c\right)\,\left(256\,a^9\,b^2\,d^{11}-1792\,a^8\,b^3\,c\,d^{10}+5120\,a^7\,b^4\,c^2\,d^9-7168\,a^6\,b^5\,c^3\,d^8+3584\,a^5\,b^6\,c^4\,d^7+3584\,a^4\,b^7\,c^5\,d^6-7168\,a^3\,b^8\,c^6\,d^5+5120\,a^2\,b^9\,c^7\,d^4-1792\,a\,b^{10}\,c^8\,d^3+256\,b^{11}\,c^9\,d^2\right)}{128\,\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)\,\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)}\right)\,\left(a\,d+b\,c\right)}{4\,\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)}\right)\,\sqrt{-a\,b}\,\left(a\,d+b\,c\right)\,3{}\mathrm{i}}{4\,\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)}+\frac{\left(\frac{x\,\left(153\,a^4\,b^3\,d^5+396\,a^3\,b^4\,c\,d^4+486\,a^2\,b^5\,c^2\,d^3+108\,a\,b^6\,c^3\,d^2+9\,b^7\,c^4\,d\right)}{32\,\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)}+\frac{3\,\sqrt{-a\,b}\,\left(\frac{\frac{3\,a^{10}\,b^2\,d^{11}}{2}-\frac{15\,a^9\,b^3\,c\,d^{10}}{2}+6\,a^8\,b^4\,c^2\,d^9+42\,a^7\,b^5\,c^3\,d^8-147\,a^6\,b^6\,c^4\,d^7+231\,a^5\,b^7\,c^5\,d^6-210\,a^4\,b^8\,c^6\,d^5+114\,a^3\,b^9\,c^7\,d^4-\frac{69\,a^2\,b^{10}\,c^8\,d^3}{2}+\frac{9\,a\,b^{11}\,c^9\,d^2}{2}}{a^9\,d^9-9\,a^8\,b\,c\,d^8+36\,a^7\,b^2\,c^2\,d^7-84\,a^6\,b^3\,c^3\,d^6+126\,a^5\,b^4\,c^4\,d^5-126\,a^4\,b^5\,c^5\,d^4+84\,a^3\,b^6\,c^6\,d^3-36\,a^2\,b^7\,c^7\,d^2+9\,a\,b^8\,c^8\,d-b^9\,c^9}+\frac{3\,x\,\sqrt{-a\,b}\,\left(a\,d+b\,c\right)\,\left(256\,a^9\,b^2\,d^{11}-1792\,a^8\,b^3\,c\,d^{10}+5120\,a^7\,b^4\,c^2\,d^9-7168\,a^6\,b^5\,c^3\,d^8+3584\,a^5\,b^6\,c^4\,d^7+3584\,a^4\,b^7\,c^5\,d^6-7168\,a^3\,b^8\,c^6\,d^5+5120\,a^2\,b^9\,c^7\,d^4-1792\,a\,b^{10}\,c^8\,d^3+256\,b^{11}\,c^9\,d^2\right)}{128\,\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)\,\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)}\right)\,\left(a\,d+b\,c\right)}{4\,\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)}\right)\,\sqrt{-a\,b}\,\left(a\,d+b\,c\right)\,3{}\mathrm{i}}{4\,\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)}}{\frac{\frac{81\,a^5\,b^3\,d^5}{64}+\frac{297\,a^4\,b^4\,c\,d^4}{32}+\frac{189\,a^3\,b^5\,c^2\,d^3}{16}+\frac{135\,a^2\,b^6\,c^3\,d^2}{32}+\frac{27\,a\,b^7\,c^4\,d}{64}}{a^9\,d^9-9\,a^8\,b\,c\,d^8+36\,a^7\,b^2\,c^2\,d^7-84\,a^6\,b^3\,c^3\,d^6+126\,a^5\,b^4\,c^4\,d^5-126\,a^4\,b^5\,c^5\,d^4+84\,a^3\,b^6\,c^6\,d^3-36\,a^2\,b^7\,c^7\,d^2+9\,a\,b^8\,c^8\,d-b^9\,c^9}-\frac{3\,\left(\frac{x\,\left(153\,a^4\,b^3\,d^5+396\,a^3\,b^4\,c\,d^4+486\,a^2\,b^5\,c^2\,d^3+108\,a\,b^6\,c^3\,d^2+9\,b^7\,c^4\,d\right)}{32\,\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)}-\frac{3\,\sqrt{-a\,b}\,\left(\frac{\frac{3\,a^{10}\,b^2\,d^{11}}{2}-\frac{15\,a^9\,b^3\,c\,d^{10}}{2}+6\,a^8\,b^4\,c^2\,d^9+42\,a^7\,b^5\,c^3\,d^8-147\,a^6\,b^6\,c^4\,d^7+231\,a^5\,b^7\,c^5\,d^6-210\,a^4\,b^8\,c^6\,d^5+114\,a^3\,b^9\,c^7\,d^4-\frac{69\,a^2\,b^{10}\,c^8\,d^3}{2}+\frac{9\,a\,b^{11}\,c^9\,d^2}{2}}{a^9\,d^9-9\,a^8\,b\,c\,d^8+36\,a^7\,b^2\,c^2\,d^7-84\,a^6\,b^3\,c^3\,d^6+126\,a^5\,b^4\,c^4\,d^5-126\,a^4\,b^5\,c^5\,d^4+84\,a^3\,b^6\,c^6\,d^3-36\,a^2\,b^7\,c^7\,d^2+9\,a\,b^8\,c^8\,d-b^9\,c^9}-\frac{3\,x\,\sqrt{-a\,b}\,\left(a\,d+b\,c\right)\,\left(256\,a^9\,b^2\,d^{11}-1792\,a^8\,b^3\,c\,d^{10}+5120\,a^7\,b^4\,c^2\,d^9-7168\,a^6\,b^5\,c^3\,d^8+3584\,a^5\,b^6\,c^4\,d^7+3584\,a^4\,b^7\,c^5\,d^6-7168\,a^3\,b^8\,c^6\,d^5+5120\,a^2\,b^9\,c^7\,d^4-1792\,a\,b^{10}\,c^8\,d^3+256\,b^{11}\,c^9\,d^2\right)}{128\,\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)\,\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)}\right)\,\left(a\,d+b\,c\right)}{4\,\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)}\right)\,\sqrt{-a\,b}\,\left(a\,d+b\,c\right)}{4\,\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)}+\frac{3\,\left(\frac{x\,\left(153\,a^4\,b^3\,d^5+396\,a^3\,b^4\,c\,d^4+486\,a^2\,b^5\,c^2\,d^3+108\,a\,b^6\,c^3\,d^2+9\,b^7\,c^4\,d\right)}{32\,\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)}+\frac{3\,\sqrt{-a\,b}\,\left(\frac{\frac{3\,a^{10}\,b^2\,d^{11}}{2}-\frac{15\,a^9\,b^3\,c\,d^{10}}{2}+6\,a^8\,b^4\,c^2\,d^9+42\,a^7\,b^5\,c^3\,d^8-147\,a^6\,b^6\,c^4\,d^7+231\,a^5\,b^7\,c^5\,d^6-210\,a^4\,b^8\,c^6\,d^5+114\,a^3\,b^9\,c^7\,d^4-\frac{69\,a^2\,b^{10}\,c^8\,d^3}{2}+\frac{9\,a\,b^{11}\,c^9\,d^2}{2}}{a^9\,d^9-9\,a^8\,b\,c\,d^8+36\,a^7\,b^2\,c^2\,d^7-84\,a^6\,b^3\,c^3\,d^6+126\,a^5\,b^4\,c^4\,d^5-126\,a^4\,b^5\,c^5\,d^4+84\,a^3\,b^6\,c^6\,d^3-36\,a^2\,b^7\,c^7\,d^2+9\,a\,b^8\,c^8\,d-b^9\,c^9}+\frac{3\,x\,\sqrt{-a\,b}\,\left(a\,d+b\,c\right)\,\left(256\,a^9\,b^2\,d^{11}-1792\,a^8\,b^3\,c\,d^{10}+5120\,a^7\,b^4\,c^2\,d^9-7168\,a^6\,b^5\,c^3\,d^8+3584\,a^5\,b^6\,c^4\,d^7+3584\,a^4\,b^7\,c^5\,d^6-7168\,a^3\,b^8\,c^6\,d^5+5120\,a^2\,b^9\,c^7\,d^4-1792\,a\,b^{10}\,c^8\,d^3+256\,b^{11}\,c^9\,d^2\right)}{128\,\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)\,\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)}\right)\,\left(a\,d+b\,c\right)}{4\,\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)}\right)\,\sqrt{-a\,b}\,\left(a\,d+b\,c\right)}{4\,\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)}}\right)\,\sqrt{-a\,b}\,\left(a\,d+b\,c\right)\,3{}\mathrm{i}}{2\,\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)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{x\,\left(153\,a^4\,b^3\,d^5+396\,a^3\,b^4\,c\,d^4+486\,a^2\,b^5\,c^2\,d^3+108\,a\,b^6\,c^3\,d^2+9\,b^7\,c^4\,d\right)}{32\,\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)}-\frac{3\,\sqrt{-c\,d}\,\left(\frac{\frac{3\,a^{10}\,b^2\,d^{11}}{2}-\frac{15\,a^9\,b^3\,c\,d^{10}}{2}+6\,a^8\,b^4\,c^2\,d^9+42\,a^7\,b^5\,c^3\,d^8-147\,a^6\,b^6\,c^4\,d^7+231\,a^5\,b^7\,c^5\,d^6-210\,a^4\,b^8\,c^6\,d^5+114\,a^3\,b^9\,c^7\,d^4-\frac{69\,a^2\,b^{10}\,c^8\,d^3}{2}+\frac{9\,a\,b^{11}\,c^9\,d^2}{2}}{a^9\,d^9-9\,a^8\,b\,c\,d^8+36\,a^7\,b^2\,c^2\,d^7-84\,a^6\,b^3\,c^3\,d^6+126\,a^5\,b^4\,c^4\,d^5-126\,a^4\,b^5\,c^5\,d^4+84\,a^3\,b^6\,c^6\,d^3-36\,a^2\,b^7\,c^7\,d^2+9\,a\,b^8\,c^8\,d-b^9\,c^9}-\frac{3\,x\,\sqrt{-c\,d}\,\left(a^2\,d^2+6\,a\,b\,c\,d+b^2\,c^2\right)\,\left(256\,a^9\,b^2\,d^{11}-1792\,a^8\,b^3\,c\,d^{10}+5120\,a^7\,b^4\,c^2\,d^9-7168\,a^6\,b^5\,c^3\,d^8+3584\,a^5\,b^6\,c^4\,d^7+3584\,a^4\,b^7\,c^5\,d^6-7168\,a^3\,b^8\,c^6\,d^5+5120\,a^2\,b^9\,c^7\,d^4-1792\,a\,b^{10}\,c^8\,d^3+256\,b^{11}\,c^9\,d^2\right)}{512\,\left(a^4\,c\,d^5-4\,a^3\,b\,c^2\,d^4+6\,a^2\,b^2\,c^3\,d^3-4\,a\,b^3\,c^4\,d^2+b^4\,c^5\,d\right)\,\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)}\right)\,\left(a^2\,d^2+6\,a\,b\,c\,d+b^2\,c^2\right)}{16\,\left(a^4\,c\,d^5-4\,a^3\,b\,c^2\,d^4+6\,a^2\,b^2\,c^3\,d^3-4\,a\,b^3\,c^4\,d^2+b^4\,c^5\,d\right)}\right)\,\sqrt{-c\,d}\,\left(a^2\,d^2+6\,a\,b\,c\,d+b^2\,c^2\right)\,3{}\mathrm{i}}{16\,\left(a^4\,c\,d^5-4\,a^3\,b\,c^2\,d^4+6\,a^2\,b^2\,c^3\,d^3-4\,a\,b^3\,c^4\,d^2+b^4\,c^5\,d\right)}+\frac{\left(\frac{x\,\left(153\,a^4\,b^3\,d^5+396\,a^3\,b^4\,c\,d^4+486\,a^2\,b^5\,c^2\,d^3+108\,a\,b^6\,c^3\,d^2+9\,b^7\,c^4\,d\right)}{32\,\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)}+\frac{3\,\sqrt{-c\,d}\,\left(\frac{\frac{3\,a^{10}\,b^2\,d^{11}}{2}-\frac{15\,a^9\,b^3\,c\,d^{10}}{2}+6\,a^8\,b^4\,c^2\,d^9+42\,a^7\,b^5\,c^3\,d^8-147\,a^6\,b^6\,c^4\,d^7+231\,a^5\,b^7\,c^5\,d^6-210\,a^4\,b^8\,c^6\,d^5+114\,a^3\,b^9\,c^7\,d^4-\frac{69\,a^2\,b^{10}\,c^8\,d^3}{2}+\frac{9\,a\,b^{11}\,c^9\,d^2}{2}}{a^9\,d^9-9\,a^8\,b\,c\,d^8+36\,a^7\,b^2\,c^2\,d^7-84\,a^6\,b^3\,c^3\,d^6+126\,a^5\,b^4\,c^4\,d^5-126\,a^4\,b^5\,c^5\,d^4+84\,a^3\,b^6\,c^6\,d^3-36\,a^2\,b^7\,c^7\,d^2+9\,a\,b^8\,c^8\,d-b^9\,c^9}+\frac{3\,x\,\sqrt{-c\,d}\,\left(a^2\,d^2+6\,a\,b\,c\,d+b^2\,c^2\right)\,\left(256\,a^9\,b^2\,d^{11}-1792\,a^8\,b^3\,c\,d^{10}+5120\,a^7\,b^4\,c^2\,d^9-7168\,a^6\,b^5\,c^3\,d^8+3584\,a^5\,b^6\,c^4\,d^7+3584\,a^4\,b^7\,c^5\,d^6-7168\,a^3\,b^8\,c^6\,d^5+5120\,a^2\,b^9\,c^7\,d^4-1792\,a\,b^{10}\,c^8\,d^3+256\,b^{11}\,c^9\,d^2\right)}{512\,\left(a^4\,c\,d^5-4\,a^3\,b\,c^2\,d^4+6\,a^2\,b^2\,c^3\,d^3-4\,a\,b^3\,c^4\,d^2+b^4\,c^5\,d\right)\,\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)}\right)\,\left(a^2\,d^2+6\,a\,b\,c\,d+b^2\,c^2\right)}{16\,\left(a^4\,c\,d^5-4\,a^3\,b\,c^2\,d^4+6\,a^2\,b^2\,c^3\,d^3-4\,a\,b^3\,c^4\,d^2+b^4\,c^5\,d\right)}\right)\,\sqrt{-c\,d}\,\left(a^2\,d^2+6\,a\,b\,c\,d+b^2\,c^2\right)\,3{}\mathrm{i}}{16\,\left(a^4\,c\,d^5-4\,a^3\,b\,c^2\,d^4+6\,a^2\,b^2\,c^3\,d^3-4\,a\,b^3\,c^4\,d^2+b^4\,c^5\,d\right)}}{\frac{\frac{81\,a^5\,b^3\,d^5}{64}+\frac{297\,a^4\,b^4\,c\,d^4}{32}+\frac{189\,a^3\,b^5\,c^2\,d^3}{16}+\frac{135\,a^2\,b^6\,c^3\,d^2}{32}+\frac{27\,a\,b^7\,c^4\,d}{64}}{a^9\,d^9-9\,a^8\,b\,c\,d^8+36\,a^7\,b^2\,c^2\,d^7-84\,a^6\,b^3\,c^3\,d^6+126\,a^5\,b^4\,c^4\,d^5-126\,a^4\,b^5\,c^5\,d^4+84\,a^3\,b^6\,c^6\,d^3-36\,a^2\,b^7\,c^7\,d^2+9\,a\,b^8\,c^8\,d-b^9\,c^9}-\frac{3\,\left(\frac{x\,\left(153\,a^4\,b^3\,d^5+396\,a^3\,b^4\,c\,d^4+486\,a^2\,b^5\,c^2\,d^3+108\,a\,b^6\,c^3\,d^2+9\,b^7\,c^4\,d\right)}{32\,\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)}-\frac{3\,\sqrt{-c\,d}\,\left(\frac{\frac{3\,a^{10}\,b^2\,d^{11}}{2}-\frac{15\,a^9\,b^3\,c\,d^{10}}{2}+6\,a^8\,b^4\,c^2\,d^9+42\,a^7\,b^5\,c^3\,d^8-147\,a^6\,b^6\,c^4\,d^7+231\,a^5\,b^7\,c^5\,d^6-210\,a^4\,b^8\,c^6\,d^5+114\,a^3\,b^9\,c^7\,d^4-\frac{69\,a^2\,b^{10}\,c^8\,d^3}{2}+\frac{9\,a\,b^{11}\,c^9\,d^2}{2}}{a^9\,d^9-9\,a^8\,b\,c\,d^8+36\,a^7\,b^2\,c^2\,d^7-84\,a^6\,b^3\,c^3\,d^6+126\,a^5\,b^4\,c^4\,d^5-126\,a^4\,b^5\,c^5\,d^4+84\,a^3\,b^6\,c^6\,d^3-36\,a^2\,b^7\,c^7\,d^2+9\,a\,b^8\,c^8\,d-b^9\,c^9}-\frac{3\,x\,\sqrt{-c\,d}\,\left(a^2\,d^2+6\,a\,b\,c\,d+b^2\,c^2\right)\,\left(256\,a^9\,b^2\,d^{11}-1792\,a^8\,b^3\,c\,d^{10}+5120\,a^7\,b^4\,c^2\,d^9-7168\,a^6\,b^5\,c^3\,d^8+3584\,a^5\,b^6\,c^4\,d^7+3584\,a^4\,b^7\,c^5\,d^6-7168\,a^3\,b^8\,c^6\,d^5+5120\,a^2\,b^9\,c^7\,d^4-1792\,a\,b^{10}\,c^8\,d^3+256\,b^{11}\,c^9\,d^2\right)}{512\,\left(a^4\,c\,d^5-4\,a^3\,b\,c^2\,d^4+6\,a^2\,b^2\,c^3\,d^3-4\,a\,b^3\,c^4\,d^2+b^4\,c^5\,d\right)\,\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)}\right)\,\left(a^2\,d^2+6\,a\,b\,c\,d+b^2\,c^2\right)}{16\,\left(a^4\,c\,d^5-4\,a^3\,b\,c^2\,d^4+6\,a^2\,b^2\,c^3\,d^3-4\,a\,b^3\,c^4\,d^2+b^4\,c^5\,d\right)}\right)\,\sqrt{-c\,d}\,\left(a^2\,d^2+6\,a\,b\,c\,d+b^2\,c^2\right)}{16\,\left(a^4\,c\,d^5-4\,a^3\,b\,c^2\,d^4+6\,a^2\,b^2\,c^3\,d^3-4\,a\,b^3\,c^4\,d^2+b^4\,c^5\,d\right)}+\frac{3\,\left(\frac{x\,\left(153\,a^4\,b^3\,d^5+396\,a^3\,b^4\,c\,d^4+486\,a^2\,b^5\,c^2\,d^3+108\,a\,b^6\,c^3\,d^2+9\,b^7\,c^4\,d\right)}{32\,\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)}+\frac{3\,\sqrt{-c\,d}\,\left(\frac{\frac{3\,a^{10}\,b^2\,d^{11}}{2}-\frac{15\,a^9\,b^3\,c\,d^{10}}{2}+6\,a^8\,b^4\,c^2\,d^9+42\,a^7\,b^5\,c^3\,d^8-147\,a^6\,b^6\,c^4\,d^7+231\,a^5\,b^7\,c^5\,d^6-210\,a^4\,b^8\,c^6\,d^5+114\,a^3\,b^9\,c^7\,d^4-\frac{69\,a^2\,b^{10}\,c^8\,d^3}{2}+\frac{9\,a\,b^{11}\,c^9\,d^2}{2}}{a^9\,d^9-9\,a^8\,b\,c\,d^8+36\,a^7\,b^2\,c^2\,d^7-84\,a^6\,b^3\,c^3\,d^6+126\,a^5\,b^4\,c^4\,d^5-126\,a^4\,b^5\,c^5\,d^4+84\,a^3\,b^6\,c^6\,d^3-36\,a^2\,b^7\,c^7\,d^2+9\,a\,b^8\,c^8\,d-b^9\,c^9}+\frac{3\,x\,\sqrt{-c\,d}\,\left(a^2\,d^2+6\,a\,b\,c\,d+b^2\,c^2\right)\,\left(256\,a^9\,b^2\,d^{11}-1792\,a^8\,b^3\,c\,d^{10}+5120\,a^7\,b^4\,c^2\,d^9-7168\,a^6\,b^5\,c^3\,d^8+3584\,a^5\,b^6\,c^4\,d^7+3584\,a^4\,b^7\,c^5\,d^6-7168\,a^3\,b^8\,c^6\,d^5+5120\,a^2\,b^9\,c^7\,d^4-1792\,a\,b^{10}\,c^8\,d^3+256\,b^{11}\,c^9\,d^2\right)}{512\,\left(a^4\,c\,d^5-4\,a^3\,b\,c^2\,d^4+6\,a^2\,b^2\,c^3\,d^3-4\,a\,b^3\,c^4\,d^2+b^4\,c^5\,d\right)\,\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)}\right)\,\left(a^2\,d^2+6\,a\,b\,c\,d+b^2\,c^2\right)}{16\,\left(a^4\,c\,d^5-4\,a^3\,b\,c^2\,d^4+6\,a^2\,b^2\,c^3\,d^3-4\,a\,b^3\,c^4\,d^2+b^4\,c^5\,d\right)}\right)\,\sqrt{-c\,d}\,\left(a^2\,d^2+6\,a\,b\,c\,d+b^2\,c^2\right)}{16\,\left(a^4\,c\,d^5-4\,a^3\,b\,c^2\,d^4+6\,a^2\,b^2\,c^3\,d^3-4\,a\,b^3\,c^4\,d^2+b^4\,c^5\,d\right)}}\right)\,\sqrt{-c\,d}\,\left(a^2\,d^2+6\,a\,b\,c\,d+b^2\,c^2\right)\,3{}\mathrm{i}}{8\,\left(a^4\,c\,d^5-4\,a^3\,b\,c^2\,d^4+6\,a^2\,b^2\,c^3\,d^3-4\,a\,b^3\,c^4\,d^2+b^4\,c^5\,d\right)}","Not used",1,"(atan(((((x*(9*b^7*c^4*d + 153*a^4*b^3*d^5 + 108*a*b^6*c^3*d^2 + 396*a^3*b^4*c*d^4 + 486*a^2*b^5*c^2*d^3))/(32*(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)) - (3*(-a*b)^(1/2)*(((3*a^10*b^2*d^11)/2 + (9*a*b^11*c^9*d^2)/2 - (15*a^9*b^3*c*d^10)/2 - (69*a^2*b^10*c^8*d^3)/2 + 114*a^3*b^9*c^7*d^4 - 210*a^4*b^8*c^6*d^5 + 231*a^5*b^7*c^5*d^6 - 147*a^6*b^6*c^4*d^7 + 42*a^7*b^5*c^3*d^8 + 6*a^8*b^4*c^2*d^9)/(a^9*d^9 - b^9*c^9 - 36*a^2*b^7*c^7*d^2 + 84*a^3*b^6*c^6*d^3 - 126*a^4*b^5*c^5*d^4 + 126*a^5*b^4*c^4*d^5 - 84*a^6*b^3*c^3*d^6 + 36*a^7*b^2*c^2*d^7 + 9*a*b^8*c^8*d - 9*a^8*b*c*d^8) - (3*x*(-a*b)^(1/2)*(a*d + b*c)*(256*a^9*b^2*d^11 + 256*b^11*c^9*d^2 - 1792*a*b^10*c^8*d^3 - 1792*a^8*b^3*c*d^10 + 5120*a^2*b^9*c^7*d^4 - 7168*a^3*b^8*c^6*d^5 + 3584*a^4*b^7*c^5*d^6 + 3584*a^5*b^6*c^4*d^7 - 7168*a^6*b^5*c^3*d^8 + 5120*a^7*b^4*c^2*d^9))/(128*(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)*(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)))*(a*d + b*c))/(4*(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)))*(-a*b)^(1/2)*(a*d + b*c)*3i)/(4*(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)) + (((x*(9*b^7*c^4*d + 153*a^4*b^3*d^5 + 108*a*b^6*c^3*d^2 + 396*a^3*b^4*c*d^4 + 486*a^2*b^5*c^2*d^3))/(32*(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)) + (3*(-a*b)^(1/2)*(((3*a^10*b^2*d^11)/2 + (9*a*b^11*c^9*d^2)/2 - (15*a^9*b^3*c*d^10)/2 - (69*a^2*b^10*c^8*d^3)/2 + 114*a^3*b^9*c^7*d^4 - 210*a^4*b^8*c^6*d^5 + 231*a^5*b^7*c^5*d^6 - 147*a^6*b^6*c^4*d^7 + 42*a^7*b^5*c^3*d^8 + 6*a^8*b^4*c^2*d^9)/(a^9*d^9 - b^9*c^9 - 36*a^2*b^7*c^7*d^2 + 84*a^3*b^6*c^6*d^3 - 126*a^4*b^5*c^5*d^4 + 126*a^5*b^4*c^4*d^5 - 84*a^6*b^3*c^3*d^6 + 36*a^7*b^2*c^2*d^7 + 9*a*b^8*c^8*d - 9*a^8*b*c*d^8) + (3*x*(-a*b)^(1/2)*(a*d + b*c)*(256*a^9*b^2*d^11 + 256*b^11*c^9*d^2 - 1792*a*b^10*c^8*d^3 - 1792*a^8*b^3*c*d^10 + 5120*a^2*b^9*c^7*d^4 - 7168*a^3*b^8*c^6*d^5 + 3584*a^4*b^7*c^5*d^6 + 3584*a^5*b^6*c^4*d^7 - 7168*a^6*b^5*c^3*d^8 + 5120*a^7*b^4*c^2*d^9))/(128*(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)*(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)))*(a*d + b*c))/(4*(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)))*(-a*b)^(1/2)*(a*d + b*c)*3i)/(4*(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)))/(((81*a^5*b^3*d^5)/64 + (297*a^4*b^4*c*d^4)/32 + (135*a^2*b^6*c^3*d^2)/32 + (189*a^3*b^5*c^2*d^3)/16 + (27*a*b^7*c^4*d)/64)/(a^9*d^9 - b^9*c^9 - 36*a^2*b^7*c^7*d^2 + 84*a^3*b^6*c^6*d^3 - 126*a^4*b^5*c^5*d^4 + 126*a^5*b^4*c^4*d^5 - 84*a^6*b^3*c^3*d^6 + 36*a^7*b^2*c^2*d^7 + 9*a*b^8*c^8*d - 9*a^8*b*c*d^8) - (3*((x*(9*b^7*c^4*d + 153*a^4*b^3*d^5 + 108*a*b^6*c^3*d^2 + 396*a^3*b^4*c*d^4 + 486*a^2*b^5*c^2*d^3))/(32*(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)) - (3*(-a*b)^(1/2)*(((3*a^10*b^2*d^11)/2 + (9*a*b^11*c^9*d^2)/2 - (15*a^9*b^3*c*d^10)/2 - (69*a^2*b^10*c^8*d^3)/2 + 114*a^3*b^9*c^7*d^4 - 210*a^4*b^8*c^6*d^5 + 231*a^5*b^7*c^5*d^6 - 147*a^6*b^6*c^4*d^7 + 42*a^7*b^5*c^3*d^8 + 6*a^8*b^4*c^2*d^9)/(a^9*d^9 - b^9*c^9 - 36*a^2*b^7*c^7*d^2 + 84*a^3*b^6*c^6*d^3 - 126*a^4*b^5*c^5*d^4 + 126*a^5*b^4*c^4*d^5 - 84*a^6*b^3*c^3*d^6 + 36*a^7*b^2*c^2*d^7 + 9*a*b^8*c^8*d - 9*a^8*b*c*d^8) - (3*x*(-a*b)^(1/2)*(a*d + b*c)*(256*a^9*b^2*d^11 + 256*b^11*c^9*d^2 - 1792*a*b^10*c^8*d^3 - 1792*a^8*b^3*c*d^10 + 5120*a^2*b^9*c^7*d^4 - 7168*a^3*b^8*c^6*d^5 + 3584*a^4*b^7*c^5*d^6 + 3584*a^5*b^6*c^4*d^7 - 7168*a^6*b^5*c^3*d^8 + 5120*a^7*b^4*c^2*d^9))/(128*(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)*(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)))*(a*d + b*c))/(4*(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)))*(-a*b)^(1/2)*(a*d + b*c))/(4*(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*((x*(9*b^7*c^4*d + 153*a^4*b^3*d^5 + 108*a*b^6*c^3*d^2 + 396*a^3*b^4*c*d^4 + 486*a^2*b^5*c^2*d^3))/(32*(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)) + (3*(-a*b)^(1/2)*(((3*a^10*b^2*d^11)/2 + (9*a*b^11*c^9*d^2)/2 - (15*a^9*b^3*c*d^10)/2 - (69*a^2*b^10*c^8*d^3)/2 + 114*a^3*b^9*c^7*d^4 - 210*a^4*b^8*c^6*d^5 + 231*a^5*b^7*c^5*d^6 - 147*a^6*b^6*c^4*d^7 + 42*a^7*b^5*c^3*d^8 + 6*a^8*b^4*c^2*d^9)/(a^9*d^9 - b^9*c^9 - 36*a^2*b^7*c^7*d^2 + 84*a^3*b^6*c^6*d^3 - 126*a^4*b^5*c^5*d^4 + 126*a^5*b^4*c^4*d^5 - 84*a^6*b^3*c^3*d^6 + 36*a^7*b^2*c^2*d^7 + 9*a*b^8*c^8*d - 9*a^8*b*c*d^8) + (3*x*(-a*b)^(1/2)*(a*d + b*c)*(256*a^9*b^2*d^11 + 256*b^11*c^9*d^2 - 1792*a*b^10*c^8*d^3 - 1792*a^8*b^3*c*d^10 + 5120*a^2*b^9*c^7*d^4 - 7168*a^3*b^8*c^6*d^5 + 3584*a^4*b^7*c^5*d^6 + 3584*a^5*b^6*c^4*d^7 - 7168*a^6*b^5*c^3*d^8 + 5120*a^7*b^4*c^2*d^9))/(128*(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)*(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)))*(a*d + b*c))/(4*(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)))*(-a*b)^(1/2)*(a*d + b*c))/(4*(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))))*(-a*b)^(1/2)*(a*d + b*c)*3i)/(2*(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*x^5*(3*a*b*d^2 + b^2*c*d))/(8*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)) + (3*x*(3*a*b*c^2 + a^2*c*d))/(8*(a*d - b*c)*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) + (x^3*(5*a^2*d^2 + 5*b^2*c^2 + 14*a*b*c*d))/(8*(a*d - b*c)*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)))/(a*c^2 + x^2*(b*c^2 + 2*a*c*d) + x^4*(a*d^2 + 2*b*c*d) + b*d^2*x^6) + (atan(((((x*(9*b^7*c^4*d + 153*a^4*b^3*d^5 + 108*a*b^6*c^3*d^2 + 396*a^3*b^4*c*d^4 + 486*a^2*b^5*c^2*d^3))/(32*(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)) - (3*(-c*d)^(1/2)*(((3*a^10*b^2*d^11)/2 + (9*a*b^11*c^9*d^2)/2 - (15*a^9*b^3*c*d^10)/2 - (69*a^2*b^10*c^8*d^3)/2 + 114*a^3*b^9*c^7*d^4 - 210*a^4*b^8*c^6*d^5 + 231*a^5*b^7*c^5*d^6 - 147*a^6*b^6*c^4*d^7 + 42*a^7*b^5*c^3*d^8 + 6*a^8*b^4*c^2*d^9)/(a^9*d^9 - b^9*c^9 - 36*a^2*b^7*c^7*d^2 + 84*a^3*b^6*c^6*d^3 - 126*a^4*b^5*c^5*d^4 + 126*a^5*b^4*c^4*d^5 - 84*a^6*b^3*c^3*d^6 + 36*a^7*b^2*c^2*d^7 + 9*a*b^8*c^8*d - 9*a^8*b*c*d^8) - (3*x*(-c*d)^(1/2)*(a^2*d^2 + b^2*c^2 + 6*a*b*c*d)*(256*a^9*b^2*d^11 + 256*b^11*c^9*d^2 - 1792*a*b^10*c^8*d^3 - 1792*a^8*b^3*c*d^10 + 5120*a^2*b^9*c^7*d^4 - 7168*a^3*b^8*c^6*d^5 + 3584*a^4*b^7*c^5*d^6 + 3584*a^5*b^6*c^4*d^7 - 7168*a^6*b^5*c^3*d^8 + 5120*a^7*b^4*c^2*d^9))/(512*(a^4*c*d^5 + b^4*c^5*d - 4*a*b^3*c^4*d^2 - 4*a^3*b*c^2*d^4 + 6*a^2*b^2*c^3*d^3)*(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)))*(a^2*d^2 + b^2*c^2 + 6*a*b*c*d))/(16*(a^4*c*d^5 + b^4*c^5*d - 4*a*b^3*c^4*d^2 - 4*a^3*b*c^2*d^4 + 6*a^2*b^2*c^3*d^3)))*(-c*d)^(1/2)*(a^2*d^2 + b^2*c^2 + 6*a*b*c*d)*3i)/(16*(a^4*c*d^5 + b^4*c^5*d - 4*a*b^3*c^4*d^2 - 4*a^3*b*c^2*d^4 + 6*a^2*b^2*c^3*d^3)) + (((x*(9*b^7*c^4*d + 153*a^4*b^3*d^5 + 108*a*b^6*c^3*d^2 + 396*a^3*b^4*c*d^4 + 486*a^2*b^5*c^2*d^3))/(32*(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)) + (3*(-c*d)^(1/2)*(((3*a^10*b^2*d^11)/2 + (9*a*b^11*c^9*d^2)/2 - (15*a^9*b^3*c*d^10)/2 - (69*a^2*b^10*c^8*d^3)/2 + 114*a^3*b^9*c^7*d^4 - 210*a^4*b^8*c^6*d^5 + 231*a^5*b^7*c^5*d^6 - 147*a^6*b^6*c^4*d^7 + 42*a^7*b^5*c^3*d^8 + 6*a^8*b^4*c^2*d^9)/(a^9*d^9 - b^9*c^9 - 36*a^2*b^7*c^7*d^2 + 84*a^3*b^6*c^6*d^3 - 126*a^4*b^5*c^5*d^4 + 126*a^5*b^4*c^4*d^5 - 84*a^6*b^3*c^3*d^6 + 36*a^7*b^2*c^2*d^7 + 9*a*b^8*c^8*d - 9*a^8*b*c*d^8) + (3*x*(-c*d)^(1/2)*(a^2*d^2 + b^2*c^2 + 6*a*b*c*d)*(256*a^9*b^2*d^11 + 256*b^11*c^9*d^2 - 1792*a*b^10*c^8*d^3 - 1792*a^8*b^3*c*d^10 + 5120*a^2*b^9*c^7*d^4 - 7168*a^3*b^8*c^6*d^5 + 3584*a^4*b^7*c^5*d^6 + 3584*a^5*b^6*c^4*d^7 - 7168*a^6*b^5*c^3*d^8 + 5120*a^7*b^4*c^2*d^9))/(512*(a^4*c*d^5 + b^4*c^5*d - 4*a*b^3*c^4*d^2 - 4*a^3*b*c^2*d^4 + 6*a^2*b^2*c^3*d^3)*(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)))*(a^2*d^2 + b^2*c^2 + 6*a*b*c*d))/(16*(a^4*c*d^5 + b^4*c^5*d - 4*a*b^3*c^4*d^2 - 4*a^3*b*c^2*d^4 + 6*a^2*b^2*c^3*d^3)))*(-c*d)^(1/2)*(a^2*d^2 + b^2*c^2 + 6*a*b*c*d)*3i)/(16*(a^4*c*d^5 + b^4*c^5*d - 4*a*b^3*c^4*d^2 - 4*a^3*b*c^2*d^4 + 6*a^2*b^2*c^3*d^3)))/(((81*a^5*b^3*d^5)/64 + (297*a^4*b^4*c*d^4)/32 + (135*a^2*b^6*c^3*d^2)/32 + (189*a^3*b^5*c^2*d^3)/16 + (27*a*b^7*c^4*d)/64)/(a^9*d^9 - b^9*c^9 - 36*a^2*b^7*c^7*d^2 + 84*a^3*b^6*c^6*d^3 - 126*a^4*b^5*c^5*d^4 + 126*a^5*b^4*c^4*d^5 - 84*a^6*b^3*c^3*d^6 + 36*a^7*b^2*c^2*d^7 + 9*a*b^8*c^8*d - 9*a^8*b*c*d^8) - (3*((x*(9*b^7*c^4*d + 153*a^4*b^3*d^5 + 108*a*b^6*c^3*d^2 + 396*a^3*b^4*c*d^4 + 486*a^2*b^5*c^2*d^3))/(32*(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)) - (3*(-c*d)^(1/2)*(((3*a^10*b^2*d^11)/2 + (9*a*b^11*c^9*d^2)/2 - (15*a^9*b^3*c*d^10)/2 - (69*a^2*b^10*c^8*d^3)/2 + 114*a^3*b^9*c^7*d^4 - 210*a^4*b^8*c^6*d^5 + 231*a^5*b^7*c^5*d^6 - 147*a^6*b^6*c^4*d^7 + 42*a^7*b^5*c^3*d^8 + 6*a^8*b^4*c^2*d^9)/(a^9*d^9 - b^9*c^9 - 36*a^2*b^7*c^7*d^2 + 84*a^3*b^6*c^6*d^3 - 126*a^4*b^5*c^5*d^4 + 126*a^5*b^4*c^4*d^5 - 84*a^6*b^3*c^3*d^6 + 36*a^7*b^2*c^2*d^7 + 9*a*b^8*c^8*d - 9*a^8*b*c*d^8) - (3*x*(-c*d)^(1/2)*(a^2*d^2 + b^2*c^2 + 6*a*b*c*d)*(256*a^9*b^2*d^11 + 256*b^11*c^9*d^2 - 1792*a*b^10*c^8*d^3 - 1792*a^8*b^3*c*d^10 + 5120*a^2*b^9*c^7*d^4 - 7168*a^3*b^8*c^6*d^5 + 3584*a^4*b^7*c^5*d^6 + 3584*a^5*b^6*c^4*d^7 - 7168*a^6*b^5*c^3*d^8 + 5120*a^7*b^4*c^2*d^9))/(512*(a^4*c*d^5 + b^4*c^5*d - 4*a*b^3*c^4*d^2 - 4*a^3*b*c^2*d^4 + 6*a^2*b^2*c^3*d^3)*(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)))*(a^2*d^2 + b^2*c^2 + 6*a*b*c*d))/(16*(a^4*c*d^5 + b^4*c^5*d - 4*a*b^3*c^4*d^2 - 4*a^3*b*c^2*d^4 + 6*a^2*b^2*c^3*d^3)))*(-c*d)^(1/2)*(a^2*d^2 + b^2*c^2 + 6*a*b*c*d))/(16*(a^4*c*d^5 + b^4*c^5*d - 4*a*b^3*c^4*d^2 - 4*a^3*b*c^2*d^4 + 6*a^2*b^2*c^3*d^3)) + (3*((x*(9*b^7*c^4*d + 153*a^4*b^3*d^5 + 108*a*b^6*c^3*d^2 + 396*a^3*b^4*c*d^4 + 486*a^2*b^5*c^2*d^3))/(32*(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)) + (3*(-c*d)^(1/2)*(((3*a^10*b^2*d^11)/2 + (9*a*b^11*c^9*d^2)/2 - (15*a^9*b^3*c*d^10)/2 - (69*a^2*b^10*c^8*d^3)/2 + 114*a^3*b^9*c^7*d^4 - 210*a^4*b^8*c^6*d^5 + 231*a^5*b^7*c^5*d^6 - 147*a^6*b^6*c^4*d^7 + 42*a^7*b^5*c^3*d^8 + 6*a^8*b^4*c^2*d^9)/(a^9*d^9 - b^9*c^9 - 36*a^2*b^7*c^7*d^2 + 84*a^3*b^6*c^6*d^3 - 126*a^4*b^5*c^5*d^4 + 126*a^5*b^4*c^4*d^5 - 84*a^6*b^3*c^3*d^6 + 36*a^7*b^2*c^2*d^7 + 9*a*b^8*c^8*d - 9*a^8*b*c*d^8) + (3*x*(-c*d)^(1/2)*(a^2*d^2 + b^2*c^2 + 6*a*b*c*d)*(256*a^9*b^2*d^11 + 256*b^11*c^9*d^2 - 1792*a*b^10*c^8*d^3 - 1792*a^8*b^3*c*d^10 + 5120*a^2*b^9*c^7*d^4 - 7168*a^3*b^8*c^6*d^5 + 3584*a^4*b^7*c^5*d^6 + 3584*a^5*b^6*c^4*d^7 - 7168*a^6*b^5*c^3*d^8 + 5120*a^7*b^4*c^2*d^9))/(512*(a^4*c*d^5 + b^4*c^5*d - 4*a*b^3*c^4*d^2 - 4*a^3*b*c^2*d^4 + 6*a^2*b^2*c^3*d^3)*(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)))*(a^2*d^2 + b^2*c^2 + 6*a*b*c*d))/(16*(a^4*c*d^5 + b^4*c^5*d - 4*a*b^3*c^4*d^2 - 4*a^3*b*c^2*d^4 + 6*a^2*b^2*c^3*d^3)))*(-c*d)^(1/2)*(a^2*d^2 + b^2*c^2 + 6*a*b*c*d))/(16*(a^4*c*d^5 + b^4*c^5*d - 4*a*b^3*c^4*d^2 - 4*a^3*b*c^2*d^4 + 6*a^2*b^2*c^3*d^3))))*(-c*d)^(1/2)*(a^2*d^2 + b^2*c^2 + 6*a*b*c*d)*3i)/(8*(a^4*c*d^5 + b^4*c^5*d - 4*a*b^3*c^4*d^2 - 4*a^3*b*c^2*d^4 + 6*a^2*b^2*c^3*d^3))","B"
311,1,926,142,0.703882,"\text{Not used}","int(x^3/((a + b*x^2)^2*(c + d*x^2)^3),x)","\frac{5\,a\,b^2\,c^3-a^3\,c\,d^2-2\,a^3\,d^3\,x^2+3\,b^3\,c^3\,x^2-4\,a^2\,b\,d^3\,x^4+2\,b^3\,c^2\,d\,x^4+a\,b^2\,c^3\,\mathrm{atan}\left(\frac{a\,d\,x^2\,1{}\mathrm{i}-b\,c\,x^2\,1{}\mathrm{i}}{2\,a\,c+a\,d\,x^2+b\,c\,x^2}\right)\,4{}\mathrm{i}-4\,a^2\,b\,c^2\,d+b^3\,c^3\,x^2\,\mathrm{atan}\left(\frac{a\,d\,x^2\,1{}\mathrm{i}-b\,c\,x^2\,1{}\mathrm{i}}{2\,a\,c+a\,d\,x^2+b\,c\,x^2}\right)\,4{}\mathrm{i}+a^2\,b\,d^3\,x^4\,\mathrm{atan}\left(\frac{a\,d\,x^2\,1{}\mathrm{i}-b\,c\,x^2\,1{}\mathrm{i}}{2\,a\,c+a\,d\,x^2+b\,c\,x^2}\right)\,8{}\mathrm{i}+a\,b^2\,d^3\,x^6\,\mathrm{atan}\left(\frac{a\,d\,x^2\,1{}\mathrm{i}-b\,c\,x^2\,1{}\mathrm{i}}{2\,a\,c+a\,d\,x^2+b\,c\,x^2}\right)\,8{}\mathrm{i}+b^3\,c^2\,d\,x^4\,\mathrm{atan}\left(\frac{a\,d\,x^2\,1{}\mathrm{i}-b\,c\,x^2\,1{}\mathrm{i}}{2\,a\,c+a\,d\,x^2+b\,c\,x^2}\right)\,8{}\mathrm{i}+b^3\,c\,d^2\,x^6\,\mathrm{atan}\left(\frac{a\,d\,x^2\,1{}\mathrm{i}-b\,c\,x^2\,1{}\mathrm{i}}{2\,a\,c+a\,d\,x^2+b\,c\,x^2}\right)\,4{}\mathrm{i}+4\,a\,b^2\,c^2\,d\,x^2-5\,a^2\,b\,c\,d^2\,x^2+2\,a\,b^2\,c\,d^2\,x^4+a^2\,b\,c^2\,d\,\mathrm{atan}\left(\frac{a\,d\,x^2\,1{}\mathrm{i}-b\,c\,x^2\,1{}\mathrm{i}}{2\,a\,c+a\,d\,x^2+b\,c\,x^2}\right)\,8{}\mathrm{i}+a\,b^2\,c^2\,d\,x^2\,\mathrm{atan}\left(\frac{a\,d\,x^2\,1{}\mathrm{i}-b\,c\,x^2\,1{}\mathrm{i}}{2\,a\,c+a\,d\,x^2+b\,c\,x^2}\right)\,16{}\mathrm{i}+a^2\,b\,c\,d^2\,x^2\,\mathrm{atan}\left(\frac{a\,d\,x^2\,1{}\mathrm{i}-b\,c\,x^2\,1{}\mathrm{i}}{2\,a\,c+a\,d\,x^2+b\,c\,x^2}\right)\,16{}\mathrm{i}+a\,b^2\,c\,d^2\,x^4\,\mathrm{atan}\left(\frac{a\,d\,x^2\,1{}\mathrm{i}-b\,c\,x^2\,1{}\mathrm{i}}{2\,a\,c+a\,d\,x^2+b\,c\,x^2}\right)\,20{}\mathrm{i}}{4\,a^5\,c^2\,d^4+8\,a^5\,c\,d^5\,x^2+4\,a^5\,d^6\,x^4-16\,a^4\,b\,c^3\,d^3-28\,a^4\,b\,c^2\,d^4\,x^2-8\,a^4\,b\,c\,d^5\,x^4+4\,a^4\,b\,d^6\,x^6+24\,a^3\,b^2\,c^4\,d^2+32\,a^3\,b^2\,c^3\,d^3\,x^2-8\,a^3\,b^2\,c^2\,d^4\,x^4-16\,a^3\,b^2\,c\,d^5\,x^6-16\,a^2\,b^3\,c^5\,d-8\,a^2\,b^3\,c^4\,d^2\,x^2+32\,a^2\,b^3\,c^3\,d^3\,x^4+24\,a^2\,b^3\,c^2\,d^4\,x^6+4\,a\,b^4\,c^6-8\,a\,b^4\,c^5\,d\,x^2-28\,a\,b^4\,c^4\,d^2\,x^4-16\,a\,b^4\,c^3\,d^3\,x^6+4\,b^5\,c^6\,x^2+8\,b^5\,c^5\,d\,x^4+4\,b^5\,c^4\,d^2\,x^6}","Not used",1,"(5*a*b^2*c^3 - a^3*c*d^2 - 2*a^3*d^3*x^2 + 3*b^3*c^3*x^2 - 4*a^2*b*d^3*x^4 + 2*b^3*c^2*d*x^4 + a*b^2*c^3*atan((a*d*x^2*1i - b*c*x^2*1i)/(2*a*c + a*d*x^2 + b*c*x^2))*4i - 4*a^2*b*c^2*d + b^3*c^3*x^2*atan((a*d*x^2*1i - b*c*x^2*1i)/(2*a*c + a*d*x^2 + b*c*x^2))*4i + a^2*b*d^3*x^4*atan((a*d*x^2*1i - b*c*x^2*1i)/(2*a*c + a*d*x^2 + b*c*x^2))*8i + a*b^2*d^3*x^6*atan((a*d*x^2*1i - b*c*x^2*1i)/(2*a*c + a*d*x^2 + b*c*x^2))*8i + b^3*c^2*d*x^4*atan((a*d*x^2*1i - b*c*x^2*1i)/(2*a*c + a*d*x^2 + b*c*x^2))*8i + b^3*c*d^2*x^6*atan((a*d*x^2*1i - b*c*x^2*1i)/(2*a*c + a*d*x^2 + b*c*x^2))*4i + 4*a*b^2*c^2*d*x^2 - 5*a^2*b*c*d^2*x^2 + 2*a*b^2*c*d^2*x^4 + a^2*b*c^2*d*atan((a*d*x^2*1i - b*c*x^2*1i)/(2*a*c + a*d*x^2 + b*c*x^2))*8i + a*b^2*c^2*d*x^2*atan((a*d*x^2*1i - b*c*x^2*1i)/(2*a*c + a*d*x^2 + b*c*x^2))*16i + a^2*b*c*d^2*x^2*atan((a*d*x^2*1i - b*c*x^2*1i)/(2*a*c + a*d*x^2 + b*c*x^2))*16i + a*b^2*c*d^2*x^4*atan((a*d*x^2*1i - b*c*x^2*1i)/(2*a*c + a*d*x^2 + b*c*x^2))*20i)/(4*a*b^4*c^6 + 4*a^5*c^2*d^4 + 4*b^5*c^6*x^2 + 4*a^5*d^6*x^4 - 16*a^2*b^3*c^5*d - 16*a^4*b*c^3*d^3 + 4*a^4*b*d^6*x^6 + 8*a^5*c*d^5*x^2 + 8*b^5*c^5*d*x^4 + 24*a^3*b^2*c^4*d^2 + 4*b^5*c^4*d^2*x^6 - 8*a^2*b^3*c^4*d^2*x^2 + 32*a^3*b^2*c^3*d^3*x^2 + 32*a^2*b^3*c^3*d^3*x^4 - 8*a^3*b^2*c^2*d^4*x^4 + 24*a^2*b^3*c^2*d^4*x^6 - 8*a*b^4*c^5*d*x^2 - 8*a^4*b*c*d^5*x^4 - 28*a^4*b*c^2*d^4*x^2 - 28*a*b^4*c^4*d^2*x^4 - 16*a*b^4*c^3*d^3*x^6 - 16*a^3*b^2*c*d^5*x^6)","B"
312,1,7929,200,2.766743,"\text{Not used}","int(x^2/((a + b*x^2)^2*(c + d*x^2)^3),x)","\frac{\frac{x^5\,\left(11\,c\,b^2\,d^2+a\,b\,d^3\right)}{8\,c\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)}+\frac{x\,\left(-a^2\,d^2+9\,a\,b\,c\,d+4\,b^2\,c^2\right)}{8\,\left(a\,d-b\,c\right)\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}+\frac{d\,x^3\,\left(a^2\,d^2+6\,a\,b\,c\,d+17\,b^2\,c^2\right)}{8\,c\,\left(a\,d-b\,c\right)\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}}{a\,c^2+x^2\,\left(b\,c^2+2\,a\,d\,c\right)+x^4\,\left(a\,d^2+2\,b\,c\,d\right)+b\,d^2\,x^6}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-a\,b^3}\,\left(5\,a\,d+b\,c\right)\,\left(\frac{x\,\left(a^4\,b^3\,d^7-20\,a^3\,b^4\,c\,d^6+470\,a^2\,b^5\,c^2\,d^5+460\,a\,b^6\,c^3\,d^4+241\,b^7\,c^4\,d^3\right)}{32\,\left(a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8\right)}-\frac{\left(\frac{-\frac{a^{10}\,b^2\,c\,d^{12}}{2}+\frac{17\,a^9\,b^3\,c^2\,d^{11}}{2}-48\,a^8\,b^4\,c^3\,d^{10}+138\,a^7\,b^5\,c^4\,d^9-231\,a^6\,b^6\,c^5\,d^8+231\,a^5\,b^7\,c^6\,d^7-126\,a^4\,b^8\,c^7\,d^6+18\,a^3\,b^9\,c^8\,d^5+\frac{39\,a^2\,b^{10}\,c^9\,d^4}{2}-\frac{23\,a\,b^{11}\,c^{10}\,d^3}{2}+2\,b^{12}\,c^{11}\,d^2}{-a^9\,c^2\,d^9+9\,a^8\,b\,c^3\,d^8-36\,a^7\,b^2\,c^4\,d^7+84\,a^6\,b^3\,c^5\,d^6-126\,a^5\,b^4\,c^6\,d^5+126\,a^4\,b^5\,c^7\,d^4-84\,a^3\,b^6\,c^8\,d^3+36\,a^2\,b^7\,c^9\,d^2-9\,a\,b^8\,c^{10}\,d+b^9\,c^{11}}-\frac{x\,\sqrt{-a\,b^3}\,\left(5\,a\,d+b\,c\right)\,\left(256\,a^9\,b^2\,c^2\,d^{11}-1792\,a^8\,b^3\,c^3\,d^{10}+5120\,a^7\,b^4\,c^4\,d^9-7168\,a^6\,b^5\,c^5\,d^8+3584\,a^5\,b^6\,c^6\,d^7+3584\,a^4\,b^7\,c^7\,d^6-7168\,a^3\,b^8\,c^8\,d^5+5120\,a^2\,b^9\,c^9\,d^4-1792\,a\,b^{10}\,c^{10}\,d^3+256\,b^{11}\,c^{11}\,d^2\right)}{128\,\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^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8\right)}\right)\,\sqrt{-a\,b^3}\,\left(5\,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)}\right)\,1{}\mathrm{i}}{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)}+\frac{\sqrt{-a\,b^3}\,\left(5\,a\,d+b\,c\right)\,\left(\frac{x\,\left(a^4\,b^3\,d^7-20\,a^3\,b^4\,c\,d^6+470\,a^2\,b^5\,c^2\,d^5+460\,a\,b^6\,c^3\,d^4+241\,b^7\,c^4\,d^3\right)}{32\,\left(a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8\right)}+\frac{\left(\frac{-\frac{a^{10}\,b^2\,c\,d^{12}}{2}+\frac{17\,a^9\,b^3\,c^2\,d^{11}}{2}-48\,a^8\,b^4\,c^3\,d^{10}+138\,a^7\,b^5\,c^4\,d^9-231\,a^6\,b^6\,c^5\,d^8+231\,a^5\,b^7\,c^6\,d^7-126\,a^4\,b^8\,c^7\,d^6+18\,a^3\,b^9\,c^8\,d^5+\frac{39\,a^2\,b^{10}\,c^9\,d^4}{2}-\frac{23\,a\,b^{11}\,c^{10}\,d^3}{2}+2\,b^{12}\,c^{11}\,d^2}{-a^9\,c^2\,d^9+9\,a^8\,b\,c^3\,d^8-36\,a^7\,b^2\,c^4\,d^7+84\,a^6\,b^3\,c^5\,d^6-126\,a^5\,b^4\,c^6\,d^5+126\,a^4\,b^5\,c^7\,d^4-84\,a^3\,b^6\,c^8\,d^3+36\,a^2\,b^7\,c^9\,d^2-9\,a\,b^8\,c^{10}\,d+b^9\,c^{11}}+\frac{x\,\sqrt{-a\,b^3}\,\left(5\,a\,d+b\,c\right)\,\left(256\,a^9\,b^2\,c^2\,d^{11}-1792\,a^8\,b^3\,c^3\,d^{10}+5120\,a^7\,b^4\,c^4\,d^9-7168\,a^6\,b^5\,c^5\,d^8+3584\,a^5\,b^6\,c^6\,d^7+3584\,a^4\,b^7\,c^7\,d^6-7168\,a^3\,b^8\,c^8\,d^5+5120\,a^2\,b^9\,c^9\,d^4-1792\,a\,b^{10}\,c^{10}\,d^3+256\,b^{11}\,c^{11}\,d^2\right)}{128\,\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^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8\right)}\right)\,\sqrt{-a\,b^3}\,\left(5\,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)}\right)\,1{}\mathrm{i}}{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)}}{\frac{-\frac{5\,a^4\,b^4\,d^7}{64}-\frac{3\,a^3\,b^5\,c\,d^6}{32}+\frac{39\,a^2\,b^6\,c^2\,d^5}{4}+\frac{475\,a\,b^7\,c^3\,d^4}{32}+\frac{165\,b^8\,c^4\,d^3}{64}}{-a^9\,c^2\,d^9+9\,a^8\,b\,c^3\,d^8-36\,a^7\,b^2\,c^4\,d^7+84\,a^6\,b^3\,c^5\,d^6-126\,a^5\,b^4\,c^6\,d^5+126\,a^4\,b^5\,c^7\,d^4-84\,a^3\,b^6\,c^8\,d^3+36\,a^2\,b^7\,c^9\,d^2-9\,a\,b^8\,c^{10}\,d+b^9\,c^{11}}-\frac{\sqrt{-a\,b^3}\,\left(5\,a\,d+b\,c\right)\,\left(\frac{x\,\left(a^4\,b^3\,d^7-20\,a^3\,b^4\,c\,d^6+470\,a^2\,b^5\,c^2\,d^5+460\,a\,b^6\,c^3\,d^4+241\,b^7\,c^4\,d^3\right)}{32\,\left(a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8\right)}-\frac{\left(\frac{-\frac{a^{10}\,b^2\,c\,d^{12}}{2}+\frac{17\,a^9\,b^3\,c^2\,d^{11}}{2}-48\,a^8\,b^4\,c^3\,d^{10}+138\,a^7\,b^5\,c^4\,d^9-231\,a^6\,b^6\,c^5\,d^8+231\,a^5\,b^7\,c^6\,d^7-126\,a^4\,b^8\,c^7\,d^6+18\,a^3\,b^9\,c^8\,d^5+\frac{39\,a^2\,b^{10}\,c^9\,d^4}{2}-\frac{23\,a\,b^{11}\,c^{10}\,d^3}{2}+2\,b^{12}\,c^{11}\,d^2}{-a^9\,c^2\,d^9+9\,a^8\,b\,c^3\,d^8-36\,a^7\,b^2\,c^4\,d^7+84\,a^6\,b^3\,c^5\,d^6-126\,a^5\,b^4\,c^6\,d^5+126\,a^4\,b^5\,c^7\,d^4-84\,a^3\,b^6\,c^8\,d^3+36\,a^2\,b^7\,c^9\,d^2-9\,a\,b^8\,c^{10}\,d+b^9\,c^{11}}-\frac{x\,\sqrt{-a\,b^3}\,\left(5\,a\,d+b\,c\right)\,\left(256\,a^9\,b^2\,c^2\,d^{11}-1792\,a^8\,b^3\,c^3\,d^{10}+5120\,a^7\,b^4\,c^4\,d^9-7168\,a^6\,b^5\,c^5\,d^8+3584\,a^5\,b^6\,c^6\,d^7+3584\,a^4\,b^7\,c^7\,d^6-7168\,a^3\,b^8\,c^8\,d^5+5120\,a^2\,b^9\,c^9\,d^4-1792\,a\,b^{10}\,c^{10}\,d^3+256\,b^{11}\,c^{11}\,d^2\right)}{128\,\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^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8\right)}\right)\,\sqrt{-a\,b^3}\,\left(5\,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)}\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)}+\frac{\sqrt{-a\,b^3}\,\left(5\,a\,d+b\,c\right)\,\left(\frac{x\,\left(a^4\,b^3\,d^7-20\,a^3\,b^4\,c\,d^6+470\,a^2\,b^5\,c^2\,d^5+460\,a\,b^6\,c^3\,d^4+241\,b^7\,c^4\,d^3\right)}{32\,\left(a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8\right)}+\frac{\left(\frac{-\frac{a^{10}\,b^2\,c\,d^{12}}{2}+\frac{17\,a^9\,b^3\,c^2\,d^{11}}{2}-48\,a^8\,b^4\,c^3\,d^{10}+138\,a^7\,b^5\,c^4\,d^9-231\,a^6\,b^6\,c^5\,d^8+231\,a^5\,b^7\,c^6\,d^7-126\,a^4\,b^8\,c^7\,d^6+18\,a^3\,b^9\,c^8\,d^5+\frac{39\,a^2\,b^{10}\,c^9\,d^4}{2}-\frac{23\,a\,b^{11}\,c^{10}\,d^3}{2}+2\,b^{12}\,c^{11}\,d^2}{-a^9\,c^2\,d^9+9\,a^8\,b\,c^3\,d^8-36\,a^7\,b^2\,c^4\,d^7+84\,a^6\,b^3\,c^5\,d^6-126\,a^5\,b^4\,c^6\,d^5+126\,a^4\,b^5\,c^7\,d^4-84\,a^3\,b^6\,c^8\,d^3+36\,a^2\,b^7\,c^9\,d^2-9\,a\,b^8\,c^{10}\,d+b^9\,c^{11}}+\frac{x\,\sqrt{-a\,b^3}\,\left(5\,a\,d+b\,c\right)\,\left(256\,a^9\,b^2\,c^2\,d^{11}-1792\,a^8\,b^3\,c^3\,d^{10}+5120\,a^7\,b^4\,c^4\,d^9-7168\,a^6\,b^5\,c^5\,d^8+3584\,a^5\,b^6\,c^6\,d^7+3584\,a^4\,b^7\,c^7\,d^6-7168\,a^3\,b^8\,c^8\,d^5+5120\,a^2\,b^9\,c^9\,d^4-1792\,a\,b^{10}\,c^{10}\,d^3+256\,b^{11}\,c^{11}\,d^2\right)}{128\,\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^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8\right)}\right)\,\sqrt{-a\,b^3}\,\left(5\,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)}\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)}}\right)\,\sqrt{-a\,b^3}\,\left(5\,a\,d+b\,c\right)\,1{}\mathrm{i}}{2\,\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)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{x\,\left(a^4\,b^3\,d^7-20\,a^3\,b^4\,c\,d^6+470\,a^2\,b^5\,c^2\,d^5+460\,a\,b^6\,c^3\,d^4+241\,b^7\,c^4\,d^3\right)}{32\,\left(a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8\right)}-\frac{\left(\frac{-\frac{a^{10}\,b^2\,c\,d^{12}}{2}+\frac{17\,a^9\,b^3\,c^2\,d^{11}}{2}-48\,a^8\,b^4\,c^3\,d^{10}+138\,a^7\,b^5\,c^4\,d^9-231\,a^6\,b^6\,c^5\,d^8+231\,a^5\,b^7\,c^6\,d^7-126\,a^4\,b^8\,c^7\,d^6+18\,a^3\,b^9\,c^8\,d^5+\frac{39\,a^2\,b^{10}\,c^9\,d^4}{2}-\frac{23\,a\,b^{11}\,c^{10}\,d^3}{2}+2\,b^{12}\,c^{11}\,d^2}{-a^9\,c^2\,d^9+9\,a^8\,b\,c^3\,d^8-36\,a^7\,b^2\,c^4\,d^7+84\,a^6\,b^3\,c^5\,d^6-126\,a^5\,b^4\,c^6\,d^5+126\,a^4\,b^5\,c^7\,d^4-84\,a^3\,b^6\,c^8\,d^3+36\,a^2\,b^7\,c^9\,d^2-9\,a\,b^8\,c^{10}\,d+b^9\,c^{11}}-\frac{x\,\sqrt{-c^3\,d}\,\left(-a^2\,d^2+10\,a\,b\,c\,d+15\,b^2\,c^2\right)\,\left(256\,a^9\,b^2\,c^2\,d^{11}-1792\,a^8\,b^3\,c^3\,d^{10}+5120\,a^7\,b^4\,c^4\,d^9-7168\,a^6\,b^5\,c^5\,d^8+3584\,a^5\,b^6\,c^6\,d^7+3584\,a^4\,b^7\,c^7\,d^6-7168\,a^3\,b^8\,c^8\,d^5+5120\,a^2\,b^9\,c^9\,d^4-1792\,a\,b^{10}\,c^{10}\,d^3+256\,b^{11}\,c^{11}\,d^2\right)}{512\,\left(a^4\,c^3\,d^4-4\,a^3\,b\,c^4\,d^3+6\,a^2\,b^2\,c^5\,d^2-4\,a\,b^3\,c^6\,d+b^4\,c^7\right)\,\left(a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8\right)}\right)\,\sqrt{-c^3\,d}\,\left(-a^2\,d^2+10\,a\,b\,c\,d+15\,b^2\,c^2\right)}{16\,\left(a^4\,c^3\,d^4-4\,a^3\,b\,c^4\,d^3+6\,a^2\,b^2\,c^5\,d^2-4\,a\,b^3\,c^6\,d+b^4\,c^7\right)}\right)\,\sqrt{-c^3\,d}\,\left(-a^2\,d^2+10\,a\,b\,c\,d+15\,b^2\,c^2\right)\,1{}\mathrm{i}}{16\,\left(a^4\,c^3\,d^4-4\,a^3\,b\,c^4\,d^3+6\,a^2\,b^2\,c^5\,d^2-4\,a\,b^3\,c^6\,d+b^4\,c^7\right)}+\frac{\left(\frac{x\,\left(a^4\,b^3\,d^7-20\,a^3\,b^4\,c\,d^6+470\,a^2\,b^5\,c^2\,d^5+460\,a\,b^6\,c^3\,d^4+241\,b^7\,c^4\,d^3\right)}{32\,\left(a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8\right)}+\frac{\left(\frac{-\frac{a^{10}\,b^2\,c\,d^{12}}{2}+\frac{17\,a^9\,b^3\,c^2\,d^{11}}{2}-48\,a^8\,b^4\,c^3\,d^{10}+138\,a^7\,b^5\,c^4\,d^9-231\,a^6\,b^6\,c^5\,d^8+231\,a^5\,b^7\,c^6\,d^7-126\,a^4\,b^8\,c^7\,d^6+18\,a^3\,b^9\,c^8\,d^5+\frac{39\,a^2\,b^{10}\,c^9\,d^4}{2}-\frac{23\,a\,b^{11}\,c^{10}\,d^3}{2}+2\,b^{12}\,c^{11}\,d^2}{-a^9\,c^2\,d^9+9\,a^8\,b\,c^3\,d^8-36\,a^7\,b^2\,c^4\,d^7+84\,a^6\,b^3\,c^5\,d^6-126\,a^5\,b^4\,c^6\,d^5+126\,a^4\,b^5\,c^7\,d^4-84\,a^3\,b^6\,c^8\,d^3+36\,a^2\,b^7\,c^9\,d^2-9\,a\,b^8\,c^{10}\,d+b^9\,c^{11}}+\frac{x\,\sqrt{-c^3\,d}\,\left(-a^2\,d^2+10\,a\,b\,c\,d+15\,b^2\,c^2\right)\,\left(256\,a^9\,b^2\,c^2\,d^{11}-1792\,a^8\,b^3\,c^3\,d^{10}+5120\,a^7\,b^4\,c^4\,d^9-7168\,a^6\,b^5\,c^5\,d^8+3584\,a^5\,b^6\,c^6\,d^7+3584\,a^4\,b^7\,c^7\,d^6-7168\,a^3\,b^8\,c^8\,d^5+5120\,a^2\,b^9\,c^9\,d^4-1792\,a\,b^{10}\,c^{10}\,d^3+256\,b^{11}\,c^{11}\,d^2\right)}{512\,\left(a^4\,c^3\,d^4-4\,a^3\,b\,c^4\,d^3+6\,a^2\,b^2\,c^5\,d^2-4\,a\,b^3\,c^6\,d+b^4\,c^7\right)\,\left(a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8\right)}\right)\,\sqrt{-c^3\,d}\,\left(-a^2\,d^2+10\,a\,b\,c\,d+15\,b^2\,c^2\right)}{16\,\left(a^4\,c^3\,d^4-4\,a^3\,b\,c^4\,d^3+6\,a^2\,b^2\,c^5\,d^2-4\,a\,b^3\,c^6\,d+b^4\,c^7\right)}\right)\,\sqrt{-c^3\,d}\,\left(-a^2\,d^2+10\,a\,b\,c\,d+15\,b^2\,c^2\right)\,1{}\mathrm{i}}{16\,\left(a^4\,c^3\,d^4-4\,a^3\,b\,c^4\,d^3+6\,a^2\,b^2\,c^5\,d^2-4\,a\,b^3\,c^6\,d+b^4\,c^7\right)}}{\frac{-\frac{5\,a^4\,b^4\,d^7}{64}-\frac{3\,a^3\,b^5\,c\,d^6}{32}+\frac{39\,a^2\,b^6\,c^2\,d^5}{4}+\frac{475\,a\,b^7\,c^3\,d^4}{32}+\frac{165\,b^8\,c^4\,d^3}{64}}{-a^9\,c^2\,d^9+9\,a^8\,b\,c^3\,d^8-36\,a^7\,b^2\,c^4\,d^7+84\,a^6\,b^3\,c^5\,d^6-126\,a^5\,b^4\,c^6\,d^5+126\,a^4\,b^5\,c^7\,d^4-84\,a^3\,b^6\,c^8\,d^3+36\,a^2\,b^7\,c^9\,d^2-9\,a\,b^8\,c^{10}\,d+b^9\,c^{11}}-\frac{\left(\frac{x\,\left(a^4\,b^3\,d^7-20\,a^3\,b^4\,c\,d^6+470\,a^2\,b^5\,c^2\,d^5+460\,a\,b^6\,c^3\,d^4+241\,b^7\,c^4\,d^3\right)}{32\,\left(a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8\right)}-\frac{\left(\frac{-\frac{a^{10}\,b^2\,c\,d^{12}}{2}+\frac{17\,a^9\,b^3\,c^2\,d^{11}}{2}-48\,a^8\,b^4\,c^3\,d^{10}+138\,a^7\,b^5\,c^4\,d^9-231\,a^6\,b^6\,c^5\,d^8+231\,a^5\,b^7\,c^6\,d^7-126\,a^4\,b^8\,c^7\,d^6+18\,a^3\,b^9\,c^8\,d^5+\frac{39\,a^2\,b^{10}\,c^9\,d^4}{2}-\frac{23\,a\,b^{11}\,c^{10}\,d^3}{2}+2\,b^{12}\,c^{11}\,d^2}{-a^9\,c^2\,d^9+9\,a^8\,b\,c^3\,d^8-36\,a^7\,b^2\,c^4\,d^7+84\,a^6\,b^3\,c^5\,d^6-126\,a^5\,b^4\,c^6\,d^5+126\,a^4\,b^5\,c^7\,d^4-84\,a^3\,b^6\,c^8\,d^3+36\,a^2\,b^7\,c^9\,d^2-9\,a\,b^8\,c^{10}\,d+b^9\,c^{11}}-\frac{x\,\sqrt{-c^3\,d}\,\left(-a^2\,d^2+10\,a\,b\,c\,d+15\,b^2\,c^2\right)\,\left(256\,a^9\,b^2\,c^2\,d^{11}-1792\,a^8\,b^3\,c^3\,d^{10}+5120\,a^7\,b^4\,c^4\,d^9-7168\,a^6\,b^5\,c^5\,d^8+3584\,a^5\,b^6\,c^6\,d^7+3584\,a^4\,b^7\,c^7\,d^6-7168\,a^3\,b^8\,c^8\,d^5+5120\,a^2\,b^9\,c^9\,d^4-1792\,a\,b^{10}\,c^{10}\,d^3+256\,b^{11}\,c^{11}\,d^2\right)}{512\,\left(a^4\,c^3\,d^4-4\,a^3\,b\,c^4\,d^3+6\,a^2\,b^2\,c^5\,d^2-4\,a\,b^3\,c^6\,d+b^4\,c^7\right)\,\left(a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8\right)}\right)\,\sqrt{-c^3\,d}\,\left(-a^2\,d^2+10\,a\,b\,c\,d+15\,b^2\,c^2\right)}{16\,\left(a^4\,c^3\,d^4-4\,a^3\,b\,c^4\,d^3+6\,a^2\,b^2\,c^5\,d^2-4\,a\,b^3\,c^6\,d+b^4\,c^7\right)}\right)\,\sqrt{-c^3\,d}\,\left(-a^2\,d^2+10\,a\,b\,c\,d+15\,b^2\,c^2\right)}{16\,\left(a^4\,c^3\,d^4-4\,a^3\,b\,c^4\,d^3+6\,a^2\,b^2\,c^5\,d^2-4\,a\,b^3\,c^6\,d+b^4\,c^7\right)}+\frac{\left(\frac{x\,\left(a^4\,b^3\,d^7-20\,a^3\,b^4\,c\,d^6+470\,a^2\,b^5\,c^2\,d^5+460\,a\,b^6\,c^3\,d^4+241\,b^7\,c^4\,d^3\right)}{32\,\left(a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8\right)}+\frac{\left(\frac{-\frac{a^{10}\,b^2\,c\,d^{12}}{2}+\frac{17\,a^9\,b^3\,c^2\,d^{11}}{2}-48\,a^8\,b^4\,c^3\,d^{10}+138\,a^7\,b^5\,c^4\,d^9-231\,a^6\,b^6\,c^5\,d^8+231\,a^5\,b^7\,c^6\,d^7-126\,a^4\,b^8\,c^7\,d^6+18\,a^3\,b^9\,c^8\,d^5+\frac{39\,a^2\,b^{10}\,c^9\,d^4}{2}-\frac{23\,a\,b^{11}\,c^{10}\,d^3}{2}+2\,b^{12}\,c^{11}\,d^2}{-a^9\,c^2\,d^9+9\,a^8\,b\,c^3\,d^8-36\,a^7\,b^2\,c^4\,d^7+84\,a^6\,b^3\,c^5\,d^6-126\,a^5\,b^4\,c^6\,d^5+126\,a^4\,b^5\,c^7\,d^4-84\,a^3\,b^6\,c^8\,d^3+36\,a^2\,b^7\,c^9\,d^2-9\,a\,b^8\,c^{10}\,d+b^9\,c^{11}}+\frac{x\,\sqrt{-c^3\,d}\,\left(-a^2\,d^2+10\,a\,b\,c\,d+15\,b^2\,c^2\right)\,\left(256\,a^9\,b^2\,c^2\,d^{11}-1792\,a^8\,b^3\,c^3\,d^{10}+5120\,a^7\,b^4\,c^4\,d^9-7168\,a^6\,b^5\,c^5\,d^8+3584\,a^5\,b^6\,c^6\,d^7+3584\,a^4\,b^7\,c^7\,d^6-7168\,a^3\,b^8\,c^8\,d^5+5120\,a^2\,b^9\,c^9\,d^4-1792\,a\,b^{10}\,c^{10}\,d^3+256\,b^{11}\,c^{11}\,d^2\right)}{512\,\left(a^4\,c^3\,d^4-4\,a^3\,b\,c^4\,d^3+6\,a^2\,b^2\,c^5\,d^2-4\,a\,b^3\,c^6\,d+b^4\,c^7\right)\,\left(a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8\right)}\right)\,\sqrt{-c^3\,d}\,\left(-a^2\,d^2+10\,a\,b\,c\,d+15\,b^2\,c^2\right)}{16\,\left(a^4\,c^3\,d^4-4\,a^3\,b\,c^4\,d^3+6\,a^2\,b^2\,c^5\,d^2-4\,a\,b^3\,c^6\,d+b^4\,c^7\right)}\right)\,\sqrt{-c^3\,d}\,\left(-a^2\,d^2+10\,a\,b\,c\,d+15\,b^2\,c^2\right)}{16\,\left(a^4\,c^3\,d^4-4\,a^3\,b\,c^4\,d^3+6\,a^2\,b^2\,c^5\,d^2-4\,a\,b^3\,c^6\,d+b^4\,c^7\right)}}\right)\,\sqrt{-c^3\,d}\,\left(-a^2\,d^2+10\,a\,b\,c\,d+15\,b^2\,c^2\right)\,1{}\mathrm{i}}{8\,\left(a^4\,c^3\,d^4-4\,a^3\,b\,c^4\,d^3+6\,a^2\,b^2\,c^5\,d^2-4\,a\,b^3\,c^6\,d+b^4\,c^7\right)}","Not used",1,"((x^5*(11*b^2*c*d^2 + a*b*d^3))/(8*c*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)) + (x*(4*b^2*c^2 - a^2*d^2 + 9*a*b*c*d))/(8*(a*d - b*c)*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) + (d*x^3*(a^2*d^2 + 17*b^2*c^2 + 6*a*b*c*d))/(8*c*(a*d - b*c)*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)))/(a*c^2 + x^2*(b*c^2 + 2*a*c*d) + x^4*(a*d^2 + 2*b*c*d) + b*d^2*x^6) + (atan((((-a*b^3)^(1/2)*(5*a*d + b*c)*((x*(a^4*b^3*d^7 + 241*b^7*c^4*d^3 + 460*a*b^6*c^3*d^4 - 20*a^3*b^4*c*d^6 + 470*a^2*b^5*c^2*d^5))/(32*(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d)) - (((2*b^12*c^11*d^2 - (23*a*b^11*c^10*d^3)/2 - (a^10*b^2*c*d^12)/2 + (39*a^2*b^10*c^9*d^4)/2 + 18*a^3*b^9*c^8*d^5 - 126*a^4*b^8*c^7*d^6 + 231*a^5*b^7*c^6*d^7 - 231*a^6*b^6*c^5*d^8 + 138*a^7*b^5*c^4*d^9 - 48*a^8*b^4*c^3*d^10 + (17*a^9*b^3*c^2*d^11)/2)/(b^9*c^11 - a^9*c^2*d^9 + 9*a^8*b*c^3*d^8 + 36*a^2*b^7*c^9*d^2 - 84*a^3*b^6*c^8*d^3 + 126*a^4*b^5*c^7*d^4 - 126*a^5*b^4*c^6*d^5 + 84*a^6*b^3*c^5*d^6 - 36*a^7*b^2*c^4*d^7 - 9*a*b^8*c^10*d) - (x*(-a*b^3)^(1/2)*(5*a*d + b*c)*(256*b^11*c^11*d^2 - 1792*a*b^10*c^10*d^3 + 5120*a^2*b^9*c^9*d^4 - 7168*a^3*b^8*c^8*d^5 + 3584*a^4*b^7*c^7*d^6 + 3584*a^5*b^6*c^6*d^7 - 7168*a^6*b^5*c^5*d^8 + 5120*a^7*b^4*c^4*d^9 - 1792*a^8*b^3*c^3*d^10 + 256*a^9*b^2*c^2*d^11))/(128*(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)*(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d)))*(-a*b^3)^(1/2)*(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)))*1i)/(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*b^3)^(1/2)*(5*a*d + b*c)*((x*(a^4*b^3*d^7 + 241*b^7*c^4*d^3 + 460*a*b^6*c^3*d^4 - 20*a^3*b^4*c*d^6 + 470*a^2*b^5*c^2*d^5))/(32*(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d)) + (((2*b^12*c^11*d^2 - (23*a*b^11*c^10*d^3)/2 - (a^10*b^2*c*d^12)/2 + (39*a^2*b^10*c^9*d^4)/2 + 18*a^3*b^9*c^8*d^5 - 126*a^4*b^8*c^7*d^6 + 231*a^5*b^7*c^6*d^7 - 231*a^6*b^6*c^5*d^8 + 138*a^7*b^5*c^4*d^9 - 48*a^8*b^4*c^3*d^10 + (17*a^9*b^3*c^2*d^11)/2)/(b^9*c^11 - a^9*c^2*d^9 + 9*a^8*b*c^3*d^8 + 36*a^2*b^7*c^9*d^2 - 84*a^3*b^6*c^8*d^3 + 126*a^4*b^5*c^7*d^4 - 126*a^5*b^4*c^6*d^5 + 84*a^6*b^3*c^5*d^6 - 36*a^7*b^2*c^4*d^7 - 9*a*b^8*c^10*d) + (x*(-a*b^3)^(1/2)*(5*a*d + b*c)*(256*b^11*c^11*d^2 - 1792*a*b^10*c^10*d^3 + 5120*a^2*b^9*c^9*d^4 - 7168*a^3*b^8*c^8*d^5 + 3584*a^4*b^7*c^7*d^6 + 3584*a^5*b^6*c^6*d^7 - 7168*a^6*b^5*c^5*d^8 + 5120*a^7*b^4*c^4*d^9 - 1792*a^8*b^3*c^3*d^10 + 256*a^9*b^2*c^2*d^11))/(128*(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)*(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d)))*(-a*b^3)^(1/2)*(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)))*1i)/(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)))/(((165*b^8*c^4*d^3)/64 - (5*a^4*b^4*d^7)/64 + (475*a*b^7*c^3*d^4)/32 - (3*a^3*b^5*c*d^6)/32 + (39*a^2*b^6*c^2*d^5)/4)/(b^9*c^11 - a^9*c^2*d^9 + 9*a^8*b*c^3*d^8 + 36*a^2*b^7*c^9*d^2 - 84*a^3*b^6*c^8*d^3 + 126*a^4*b^5*c^7*d^4 - 126*a^5*b^4*c^6*d^5 + 84*a^6*b^3*c^5*d^6 - 36*a^7*b^2*c^4*d^7 - 9*a*b^8*c^10*d) - ((-a*b^3)^(1/2)*(5*a*d + b*c)*((x*(a^4*b^3*d^7 + 241*b^7*c^4*d^3 + 460*a*b^6*c^3*d^4 - 20*a^3*b^4*c*d^6 + 470*a^2*b^5*c^2*d^5))/(32*(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d)) - (((2*b^12*c^11*d^2 - (23*a*b^11*c^10*d^3)/2 - (a^10*b^2*c*d^12)/2 + (39*a^2*b^10*c^9*d^4)/2 + 18*a^3*b^9*c^8*d^5 - 126*a^4*b^8*c^7*d^6 + 231*a^5*b^7*c^6*d^7 - 231*a^6*b^6*c^5*d^8 + 138*a^7*b^5*c^4*d^9 - 48*a^8*b^4*c^3*d^10 + (17*a^9*b^3*c^2*d^11)/2)/(b^9*c^11 - a^9*c^2*d^9 + 9*a^8*b*c^3*d^8 + 36*a^2*b^7*c^9*d^2 - 84*a^3*b^6*c^8*d^3 + 126*a^4*b^5*c^7*d^4 - 126*a^5*b^4*c^6*d^5 + 84*a^6*b^3*c^5*d^6 - 36*a^7*b^2*c^4*d^7 - 9*a*b^8*c^10*d) - (x*(-a*b^3)^(1/2)*(5*a*d + b*c)*(256*b^11*c^11*d^2 - 1792*a*b^10*c^10*d^3 + 5120*a^2*b^9*c^9*d^4 - 7168*a^3*b^8*c^8*d^5 + 3584*a^4*b^7*c^7*d^6 + 3584*a^5*b^6*c^6*d^7 - 7168*a^6*b^5*c^5*d^8 + 5120*a^7*b^4*c^4*d^9 - 1792*a^8*b^3*c^3*d^10 + 256*a^9*b^2*c^2*d^11))/(128*(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)*(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d)))*(-a*b^3)^(1/2)*(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))))/(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*b^3)^(1/2)*(5*a*d + b*c)*((x*(a^4*b^3*d^7 + 241*b^7*c^4*d^3 + 460*a*b^6*c^3*d^4 - 20*a^3*b^4*c*d^6 + 470*a^2*b^5*c^2*d^5))/(32*(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d)) + (((2*b^12*c^11*d^2 - (23*a*b^11*c^10*d^3)/2 - (a^10*b^2*c*d^12)/2 + (39*a^2*b^10*c^9*d^4)/2 + 18*a^3*b^9*c^8*d^5 - 126*a^4*b^8*c^7*d^6 + 231*a^5*b^7*c^6*d^7 - 231*a^6*b^6*c^5*d^8 + 138*a^7*b^5*c^4*d^9 - 48*a^8*b^4*c^3*d^10 + (17*a^9*b^3*c^2*d^11)/2)/(b^9*c^11 - a^9*c^2*d^9 + 9*a^8*b*c^3*d^8 + 36*a^2*b^7*c^9*d^2 - 84*a^3*b^6*c^8*d^3 + 126*a^4*b^5*c^7*d^4 - 126*a^5*b^4*c^6*d^5 + 84*a^6*b^3*c^5*d^6 - 36*a^7*b^2*c^4*d^7 - 9*a*b^8*c^10*d) + (x*(-a*b^3)^(1/2)*(5*a*d + b*c)*(256*b^11*c^11*d^2 - 1792*a*b^10*c^10*d^3 + 5120*a^2*b^9*c^9*d^4 - 7168*a^3*b^8*c^8*d^5 + 3584*a^4*b^7*c^7*d^6 + 3584*a^5*b^6*c^6*d^7 - 7168*a^6*b^5*c^5*d^8 + 5120*a^7*b^4*c^4*d^9 - 1792*a^8*b^3*c^3*d^10 + 256*a^9*b^2*c^2*d^11))/(128*(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)*(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d)))*(-a*b^3)^(1/2)*(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))))/(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*b^3)^(1/2)*(5*a*d + b*c)*1i)/(2*(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)) + (atan(((((x*(a^4*b^3*d^7 + 241*b^7*c^4*d^3 + 460*a*b^6*c^3*d^4 - 20*a^3*b^4*c*d^6 + 470*a^2*b^5*c^2*d^5))/(32*(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d)) - (((2*b^12*c^11*d^2 - (23*a*b^11*c^10*d^3)/2 - (a^10*b^2*c*d^12)/2 + (39*a^2*b^10*c^9*d^4)/2 + 18*a^3*b^9*c^8*d^5 - 126*a^4*b^8*c^7*d^6 + 231*a^5*b^7*c^6*d^7 - 231*a^6*b^6*c^5*d^8 + 138*a^7*b^5*c^4*d^9 - 48*a^8*b^4*c^3*d^10 + (17*a^9*b^3*c^2*d^11)/2)/(b^9*c^11 - a^9*c^2*d^9 + 9*a^8*b*c^3*d^8 + 36*a^2*b^7*c^9*d^2 - 84*a^3*b^6*c^8*d^3 + 126*a^4*b^5*c^7*d^4 - 126*a^5*b^4*c^6*d^5 + 84*a^6*b^3*c^5*d^6 - 36*a^7*b^2*c^4*d^7 - 9*a*b^8*c^10*d) - (x*(-c^3*d)^(1/2)*(15*b^2*c^2 - a^2*d^2 + 10*a*b*c*d)*(256*b^11*c^11*d^2 - 1792*a*b^10*c^10*d^3 + 5120*a^2*b^9*c^9*d^4 - 7168*a^3*b^8*c^8*d^5 + 3584*a^4*b^7*c^7*d^6 + 3584*a^5*b^6*c^6*d^7 - 7168*a^6*b^5*c^5*d^8 + 5120*a^7*b^4*c^4*d^9 - 1792*a^8*b^3*c^3*d^10 + 256*a^9*b^2*c^2*d^11))/(512*(b^4*c^7 + a^4*c^3*d^4 - 4*a^3*b*c^4*d^3 + 6*a^2*b^2*c^5*d^2 - 4*a*b^3*c^6*d)*(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d)))*(-c^3*d)^(1/2)*(15*b^2*c^2 - a^2*d^2 + 10*a*b*c*d))/(16*(b^4*c^7 + a^4*c^3*d^4 - 4*a^3*b*c^4*d^3 + 6*a^2*b^2*c^5*d^2 - 4*a*b^3*c^6*d)))*(-c^3*d)^(1/2)*(15*b^2*c^2 - a^2*d^2 + 10*a*b*c*d)*1i)/(16*(b^4*c^7 + a^4*c^3*d^4 - 4*a^3*b*c^4*d^3 + 6*a^2*b^2*c^5*d^2 - 4*a*b^3*c^6*d)) + (((x*(a^4*b^3*d^7 + 241*b^7*c^4*d^3 + 460*a*b^6*c^3*d^4 - 20*a^3*b^4*c*d^6 + 470*a^2*b^5*c^2*d^5))/(32*(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d)) + (((2*b^12*c^11*d^2 - (23*a*b^11*c^10*d^3)/2 - (a^10*b^2*c*d^12)/2 + (39*a^2*b^10*c^9*d^4)/2 + 18*a^3*b^9*c^8*d^5 - 126*a^4*b^8*c^7*d^6 + 231*a^5*b^7*c^6*d^7 - 231*a^6*b^6*c^5*d^8 + 138*a^7*b^5*c^4*d^9 - 48*a^8*b^4*c^3*d^10 + (17*a^9*b^3*c^2*d^11)/2)/(b^9*c^11 - a^9*c^2*d^9 + 9*a^8*b*c^3*d^8 + 36*a^2*b^7*c^9*d^2 - 84*a^3*b^6*c^8*d^3 + 126*a^4*b^5*c^7*d^4 - 126*a^5*b^4*c^6*d^5 + 84*a^6*b^3*c^5*d^6 - 36*a^7*b^2*c^4*d^7 - 9*a*b^8*c^10*d) + (x*(-c^3*d)^(1/2)*(15*b^2*c^2 - a^2*d^2 + 10*a*b*c*d)*(256*b^11*c^11*d^2 - 1792*a*b^10*c^10*d^3 + 5120*a^2*b^9*c^9*d^4 - 7168*a^3*b^8*c^8*d^5 + 3584*a^4*b^7*c^7*d^6 + 3584*a^5*b^6*c^6*d^7 - 7168*a^6*b^5*c^5*d^8 + 5120*a^7*b^4*c^4*d^9 - 1792*a^8*b^3*c^3*d^10 + 256*a^9*b^2*c^2*d^11))/(512*(b^4*c^7 + a^4*c^3*d^4 - 4*a^3*b*c^4*d^3 + 6*a^2*b^2*c^5*d^2 - 4*a*b^3*c^6*d)*(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d)))*(-c^3*d)^(1/2)*(15*b^2*c^2 - a^2*d^2 + 10*a*b*c*d))/(16*(b^4*c^7 + a^4*c^3*d^4 - 4*a^3*b*c^4*d^3 + 6*a^2*b^2*c^5*d^2 - 4*a*b^3*c^6*d)))*(-c^3*d)^(1/2)*(15*b^2*c^2 - a^2*d^2 + 10*a*b*c*d)*1i)/(16*(b^4*c^7 + a^4*c^3*d^4 - 4*a^3*b*c^4*d^3 + 6*a^2*b^2*c^5*d^2 - 4*a*b^3*c^6*d)))/(((165*b^8*c^4*d^3)/64 - (5*a^4*b^4*d^7)/64 + (475*a*b^7*c^3*d^4)/32 - (3*a^3*b^5*c*d^6)/32 + (39*a^2*b^6*c^2*d^5)/4)/(b^9*c^11 - a^9*c^2*d^9 + 9*a^8*b*c^3*d^8 + 36*a^2*b^7*c^9*d^2 - 84*a^3*b^6*c^8*d^3 + 126*a^4*b^5*c^7*d^4 - 126*a^5*b^4*c^6*d^5 + 84*a^6*b^3*c^5*d^6 - 36*a^7*b^2*c^4*d^7 - 9*a*b^8*c^10*d) - (((x*(a^4*b^3*d^7 + 241*b^7*c^4*d^3 + 460*a*b^6*c^3*d^4 - 20*a^3*b^4*c*d^6 + 470*a^2*b^5*c^2*d^5))/(32*(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d)) - (((2*b^12*c^11*d^2 - (23*a*b^11*c^10*d^3)/2 - (a^10*b^2*c*d^12)/2 + (39*a^2*b^10*c^9*d^4)/2 + 18*a^3*b^9*c^8*d^5 - 126*a^4*b^8*c^7*d^6 + 231*a^5*b^7*c^6*d^7 - 231*a^6*b^6*c^5*d^8 + 138*a^7*b^5*c^4*d^9 - 48*a^8*b^4*c^3*d^10 + (17*a^9*b^3*c^2*d^11)/2)/(b^9*c^11 - a^9*c^2*d^9 + 9*a^8*b*c^3*d^8 + 36*a^2*b^7*c^9*d^2 - 84*a^3*b^6*c^8*d^3 + 126*a^4*b^5*c^7*d^4 - 126*a^5*b^4*c^6*d^5 + 84*a^6*b^3*c^5*d^6 - 36*a^7*b^2*c^4*d^7 - 9*a*b^8*c^10*d) - (x*(-c^3*d)^(1/2)*(15*b^2*c^2 - a^2*d^2 + 10*a*b*c*d)*(256*b^11*c^11*d^2 - 1792*a*b^10*c^10*d^3 + 5120*a^2*b^9*c^9*d^4 - 7168*a^3*b^8*c^8*d^5 + 3584*a^4*b^7*c^7*d^6 + 3584*a^5*b^6*c^6*d^7 - 7168*a^6*b^5*c^5*d^8 + 5120*a^7*b^4*c^4*d^9 - 1792*a^8*b^3*c^3*d^10 + 256*a^9*b^2*c^2*d^11))/(512*(b^4*c^7 + a^4*c^3*d^4 - 4*a^3*b*c^4*d^3 + 6*a^2*b^2*c^5*d^2 - 4*a*b^3*c^6*d)*(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d)))*(-c^3*d)^(1/2)*(15*b^2*c^2 - a^2*d^2 + 10*a*b*c*d))/(16*(b^4*c^7 + a^4*c^3*d^4 - 4*a^3*b*c^4*d^3 + 6*a^2*b^2*c^5*d^2 - 4*a*b^3*c^6*d)))*(-c^3*d)^(1/2)*(15*b^2*c^2 - a^2*d^2 + 10*a*b*c*d))/(16*(b^4*c^7 + a^4*c^3*d^4 - 4*a^3*b*c^4*d^3 + 6*a^2*b^2*c^5*d^2 - 4*a*b^3*c^6*d)) + (((x*(a^4*b^3*d^7 + 241*b^7*c^4*d^3 + 460*a*b^6*c^3*d^4 - 20*a^3*b^4*c*d^6 + 470*a^2*b^5*c^2*d^5))/(32*(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d)) + (((2*b^12*c^11*d^2 - (23*a*b^11*c^10*d^3)/2 - (a^10*b^2*c*d^12)/2 + (39*a^2*b^10*c^9*d^4)/2 + 18*a^3*b^9*c^8*d^5 - 126*a^4*b^8*c^7*d^6 + 231*a^5*b^7*c^6*d^7 - 231*a^6*b^6*c^5*d^8 + 138*a^7*b^5*c^4*d^9 - 48*a^8*b^4*c^3*d^10 + (17*a^9*b^3*c^2*d^11)/2)/(b^9*c^11 - a^9*c^2*d^9 + 9*a^8*b*c^3*d^8 + 36*a^2*b^7*c^9*d^2 - 84*a^3*b^6*c^8*d^3 + 126*a^4*b^5*c^7*d^4 - 126*a^5*b^4*c^6*d^5 + 84*a^6*b^3*c^5*d^6 - 36*a^7*b^2*c^4*d^7 - 9*a*b^8*c^10*d) + (x*(-c^3*d)^(1/2)*(15*b^2*c^2 - a^2*d^2 + 10*a*b*c*d)*(256*b^11*c^11*d^2 - 1792*a*b^10*c^10*d^3 + 5120*a^2*b^9*c^9*d^4 - 7168*a^3*b^8*c^8*d^5 + 3584*a^4*b^7*c^7*d^6 + 3584*a^5*b^6*c^6*d^7 - 7168*a^6*b^5*c^5*d^8 + 5120*a^7*b^4*c^4*d^9 - 1792*a^8*b^3*c^3*d^10 + 256*a^9*b^2*c^2*d^11))/(512*(b^4*c^7 + a^4*c^3*d^4 - 4*a^3*b*c^4*d^3 + 6*a^2*b^2*c^5*d^2 - 4*a*b^3*c^6*d)*(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d)))*(-c^3*d)^(1/2)*(15*b^2*c^2 - a^2*d^2 + 10*a*b*c*d))/(16*(b^4*c^7 + a^4*c^3*d^4 - 4*a^3*b*c^4*d^3 + 6*a^2*b^2*c^5*d^2 - 4*a*b^3*c^6*d)))*(-c^3*d)^(1/2)*(15*b^2*c^2 - a^2*d^2 + 10*a*b*c*d))/(16*(b^4*c^7 + a^4*c^3*d^4 - 4*a^3*b*c^4*d^3 + 6*a^2*b^2*c^5*d^2 - 4*a*b^3*c^6*d))))*(-c^3*d)^(1/2)*(15*b^2*c^2 - a^2*d^2 + 10*a*b*c*d)*1i)/(8*(b^4*c^7 + a^4*c^3*d^4 - 4*a^3*b*c^4*d^3 + 6*a^2*b^2*c^5*d^2 - 4*a*b^3*c^6*d))","B"
313,1,707,126,0.586319,"\text{Not used}","int(x/((a + b*x^2)^2*(c + d*x^2)^3),x)","-\frac{a^3\,d^3+2\,b^3\,c^3-3\,a^2\,b\,d^3\,x^2-6\,a\,b^2\,d^3\,x^4+9\,b^3\,c^2\,d\,x^2+6\,b^3\,c\,d^2\,x^4+3\,a\,b^2\,c^2\,d-6\,a^2\,b\,c\,d^2+b^3\,d^3\,x^6\,\mathrm{atan}\left(\frac{a\,d\,x^2\,1{}\mathrm{i}-b\,c\,x^2\,1{}\mathrm{i}}{2\,a\,c+a\,d\,x^2+b\,c\,x^2}\right)\,12{}\mathrm{i}+a\,b^2\,d^3\,x^4\,\mathrm{atan}\left(\frac{a\,d\,x^2\,1{}\mathrm{i}-b\,c\,x^2\,1{}\mathrm{i}}{2\,a\,c+a\,d\,x^2+b\,c\,x^2}\right)\,12{}\mathrm{i}+b^3\,c^2\,d\,x^2\,\mathrm{atan}\left(\frac{a\,d\,x^2\,1{}\mathrm{i}-b\,c\,x^2\,1{}\mathrm{i}}{2\,a\,c+a\,d\,x^2+b\,c\,x^2}\right)\,12{}\mathrm{i}+b^3\,c\,d^2\,x^4\,\mathrm{atan}\left(\frac{a\,d\,x^2\,1{}\mathrm{i}-b\,c\,x^2\,1{}\mathrm{i}}{2\,a\,c+a\,d\,x^2+b\,c\,x^2}\right)\,24{}\mathrm{i}-6\,a\,b^2\,c\,d^2\,x^2+a\,b^2\,c^2\,d\,\mathrm{atan}\left(\frac{a\,d\,x^2\,1{}\mathrm{i}-b\,c\,x^2\,1{}\mathrm{i}}{2\,a\,c+a\,d\,x^2+b\,c\,x^2}\right)\,12{}\mathrm{i}+a\,b^2\,c\,d^2\,x^2\,\mathrm{atan}\left(\frac{a\,d\,x^2\,1{}\mathrm{i}-b\,c\,x^2\,1{}\mathrm{i}}{2\,a\,c+a\,d\,x^2+b\,c\,x^2}\right)\,24{}\mathrm{i}}{4\,a^5\,c^2\,d^4+8\,a^5\,c\,d^5\,x^2+4\,a^5\,d^6\,x^4-16\,a^4\,b\,c^3\,d^3-28\,a^4\,b\,c^2\,d^4\,x^2-8\,a^4\,b\,c\,d^5\,x^4+4\,a^4\,b\,d^6\,x^6+24\,a^3\,b^2\,c^4\,d^2+32\,a^3\,b^2\,c^3\,d^3\,x^2-8\,a^3\,b^2\,c^2\,d^4\,x^4-16\,a^3\,b^2\,c\,d^5\,x^6-16\,a^2\,b^3\,c^5\,d-8\,a^2\,b^3\,c^4\,d^2\,x^2+32\,a^2\,b^3\,c^3\,d^3\,x^4+24\,a^2\,b^3\,c^2\,d^4\,x^6+4\,a\,b^4\,c^6-8\,a\,b^4\,c^5\,d\,x^2-28\,a\,b^4\,c^4\,d^2\,x^4-16\,a\,b^4\,c^3\,d^3\,x^6+4\,b^5\,c^6\,x^2+8\,b^5\,c^5\,d\,x^4+4\,b^5\,c^4\,d^2\,x^6}","Not used",1,"-(a^3*d^3 + 2*b^3*c^3 - 3*a^2*b*d^3*x^2 - 6*a*b^2*d^3*x^4 + 9*b^3*c^2*d*x^2 + 6*b^3*c*d^2*x^4 + 3*a*b^2*c^2*d - 6*a^2*b*c*d^2 + b^3*d^3*x^6*atan((a*d*x^2*1i - b*c*x^2*1i)/(2*a*c + a*d*x^2 + b*c*x^2))*12i + a*b^2*d^3*x^4*atan((a*d*x^2*1i - b*c*x^2*1i)/(2*a*c + a*d*x^2 + b*c*x^2))*12i + b^3*c^2*d*x^2*atan((a*d*x^2*1i - b*c*x^2*1i)/(2*a*c + a*d*x^2 + b*c*x^2))*12i + b^3*c*d^2*x^4*atan((a*d*x^2*1i - b*c*x^2*1i)/(2*a*c + a*d*x^2 + b*c*x^2))*24i - 6*a*b^2*c*d^2*x^2 + a*b^2*c^2*d*atan((a*d*x^2*1i - b*c*x^2*1i)/(2*a*c + a*d*x^2 + b*c*x^2))*12i + a*b^2*c*d^2*x^2*atan((a*d*x^2*1i - b*c*x^2*1i)/(2*a*c + a*d*x^2 + b*c*x^2))*24i)/(4*a*b^4*c^6 + 4*a^5*c^2*d^4 + 4*b^5*c^6*x^2 + 4*a^5*d^6*x^4 - 16*a^2*b^3*c^5*d - 16*a^4*b*c^3*d^3 + 4*a^4*b*d^6*x^6 + 8*a^5*c*d^5*x^2 + 8*b^5*c^5*d*x^4 + 24*a^3*b^2*c^4*d^2 + 4*b^5*c^4*d^2*x^6 - 8*a^2*b^3*c^4*d^2*x^2 + 32*a^3*b^2*c^3*d^3*x^2 + 32*a^2*b^3*c^3*d^3*x^4 - 8*a^3*b^2*c^2*d^4*x^4 + 24*a^2*b^3*c^2*d^4*x^6 - 8*a*b^4*c^5*d*x^2 - 8*a^4*b*c*d^5*x^4 - 28*a^4*b*c^2*d^4*x^2 - 28*a*b^4*c^4*d^2*x^4 - 16*a*b^4*c^3*d^3*x^6 - 16*a^3*b^2*c*d^5*x^6)","B"
314,1,8649,230,3.000617,"\text{Not used}","int(1/((a + b*x^2)^2*(c + d*x^2)^3),x)","-\frac{\frac{x^5\,\left(-3\,a^2\,b\,d^4+11\,a\,b^2\,c\,d^3+4\,b^3\,c^2\,d^2\right)}{8\,a\,c^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)}+\frac{x\,\left(-5\,a^3\,d^3+13\,a^2\,b\,c\,d^2+4\,b^3\,c^3\right)}{8\,a\,c\,\left(a\,d-b\,c\right)\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}+\frac{d\,x^3\,\left(-3\,a^3\,d^3+6\,a^2\,b\,c\,d^2+13\,a\,b^2\,c^2\,d+8\,b^3\,c^3\right)}{8\,a\,c^2\,\left(a\,d-b\,c\right)\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}}{a\,c^2+x^2\,\left(b\,c^2+2\,a\,d\,c\right)+x^4\,\left(a\,d^2+2\,b\,c\,d\right)+b\,d^2\,x^6}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{x\,\left(9\,a^6\,b^3\,d^9-84\,a^5\,b^4\,c\,d^8+406\,a^4\,b^5\,c^2\,d^7-980\,a^3\,b^6\,c^3\,d^6+2009\,a^2\,b^7\,c^4\,d^5-224\,a\,b^8\,c^5\,d^4+16\,b^9\,c^6\,d^3\right)}{32\,\left(a^8\,c^4\,d^6-6\,a^7\,b\,c^5\,d^5+15\,a^6\,b^2\,c^6\,d^4-20\,a^5\,b^3\,c^7\,d^3+15\,a^4\,b^4\,c^8\,d^2-6\,a^3\,b^5\,c^9\,d+a^2\,b^6\,c^{10}\right)}-\frac{\left(\frac{-\frac{3\,a^{12}\,b^2\,c^2\,d^{13}}{2}+\frac{35\,a^{11}\,b^3\,c^3\,d^{12}}{2}-98\,a^{10}\,b^4\,c^4\,d^{11}+336\,a^9\,b^5\,c^5\,d^{10}-765\,a^8\,b^6\,c^6\,d^9+1197\,a^7\,b^7\,c^7\,d^8-1302\,a^6\,b^8\,c^8\,d^7+978\,a^5\,b^9\,c^9\,d^6-\frac{987\,a^4\,b^{10}\,c^{10}\,d^5}{2}+\frac{315\,a^3\,b^{11}\,c^{11}\,d^4}{2}-28\,a^2\,b^{12}\,c^{12}\,d^3+2\,a\,b^{13}\,c^{13}\,d^2}{-a^{11}\,c^4\,d^9+9\,a^{10}\,b\,c^5\,d^8-36\,a^9\,b^2\,c^6\,d^7+84\,a^8\,b^3\,c^7\,d^6-126\,a^7\,b^4\,c^8\,d^5+126\,a^6\,b^5\,c^9\,d^4-84\,a^5\,b^6\,c^{10}\,d^3+36\,a^4\,b^7\,c^{11}\,d^2-9\,a^3\,b^8\,c^{12}\,d+a^2\,b^9\,c^{13}}-\frac{x\,\sqrt{-c^5\,d^3}\,\left(3\,a^2\,d^2-14\,a\,b\,c\,d+35\,b^2\,c^2\right)\,\left(256\,a^{11}\,b^2\,c^4\,d^{11}-1792\,a^{10}\,b^3\,c^5\,d^{10}+5120\,a^9\,b^4\,c^6\,d^9-7168\,a^8\,b^5\,c^7\,d^8+3584\,a^7\,b^6\,c^8\,d^7+3584\,a^6\,b^7\,c^9\,d^6-7168\,a^5\,b^8\,c^{10}\,d^5+5120\,a^4\,b^9\,c^{11}\,d^4-1792\,a^3\,b^{10}\,c^{12}\,d^3+256\,a^2\,b^{11}\,c^{13}\,d^2\right)}{512\,\left(a^4\,c^5\,d^4-4\,a^3\,b\,c^6\,d^3+6\,a^2\,b^2\,c^7\,d^2-4\,a\,b^3\,c^8\,d+b^4\,c^9\right)\,\left(a^8\,c^4\,d^6-6\,a^7\,b\,c^5\,d^5+15\,a^6\,b^2\,c^6\,d^4-20\,a^5\,b^3\,c^7\,d^3+15\,a^4\,b^4\,c^8\,d^2-6\,a^3\,b^5\,c^9\,d+a^2\,b^6\,c^{10}\right)}\right)\,\sqrt{-c^5\,d^3}\,\left(3\,a^2\,d^2-14\,a\,b\,c\,d+35\,b^2\,c^2\right)}{16\,\left(a^4\,c^5\,d^4-4\,a^3\,b\,c^6\,d^3+6\,a^2\,b^2\,c^7\,d^2-4\,a\,b^3\,c^8\,d+b^4\,c^9\right)}\right)\,\sqrt{-c^5\,d^3}\,\left(3\,a^2\,d^2-14\,a\,b\,c\,d+35\,b^2\,c^2\right)\,1{}\mathrm{i}}{16\,\left(a^4\,c^5\,d^4-4\,a^3\,b\,c^6\,d^3+6\,a^2\,b^2\,c^7\,d^2-4\,a\,b^3\,c^8\,d+b^4\,c^9\right)}+\frac{\left(\frac{x\,\left(9\,a^6\,b^3\,d^9-84\,a^5\,b^4\,c\,d^8+406\,a^4\,b^5\,c^2\,d^7-980\,a^3\,b^6\,c^3\,d^6+2009\,a^2\,b^7\,c^4\,d^5-224\,a\,b^8\,c^5\,d^4+16\,b^9\,c^6\,d^3\right)}{32\,\left(a^8\,c^4\,d^6-6\,a^7\,b\,c^5\,d^5+15\,a^6\,b^2\,c^6\,d^4-20\,a^5\,b^3\,c^7\,d^3+15\,a^4\,b^4\,c^8\,d^2-6\,a^3\,b^5\,c^9\,d+a^2\,b^6\,c^{10}\right)}+\frac{\left(\frac{-\frac{3\,a^{12}\,b^2\,c^2\,d^{13}}{2}+\frac{35\,a^{11}\,b^3\,c^3\,d^{12}}{2}-98\,a^{10}\,b^4\,c^4\,d^{11}+336\,a^9\,b^5\,c^5\,d^{10}-765\,a^8\,b^6\,c^6\,d^9+1197\,a^7\,b^7\,c^7\,d^8-1302\,a^6\,b^8\,c^8\,d^7+978\,a^5\,b^9\,c^9\,d^6-\frac{987\,a^4\,b^{10}\,c^{10}\,d^5}{2}+\frac{315\,a^3\,b^{11}\,c^{11}\,d^4}{2}-28\,a^2\,b^{12}\,c^{12}\,d^3+2\,a\,b^{13}\,c^{13}\,d^2}{-a^{11}\,c^4\,d^9+9\,a^{10}\,b\,c^5\,d^8-36\,a^9\,b^2\,c^6\,d^7+84\,a^8\,b^3\,c^7\,d^6-126\,a^7\,b^4\,c^8\,d^5+126\,a^6\,b^5\,c^9\,d^4-84\,a^5\,b^6\,c^{10}\,d^3+36\,a^4\,b^7\,c^{11}\,d^2-9\,a^3\,b^8\,c^{12}\,d+a^2\,b^9\,c^{13}}+\frac{x\,\sqrt{-c^5\,d^3}\,\left(3\,a^2\,d^2-14\,a\,b\,c\,d+35\,b^2\,c^2\right)\,\left(256\,a^{11}\,b^2\,c^4\,d^{11}-1792\,a^{10}\,b^3\,c^5\,d^{10}+5120\,a^9\,b^4\,c^6\,d^9-7168\,a^8\,b^5\,c^7\,d^8+3584\,a^7\,b^6\,c^8\,d^7+3584\,a^6\,b^7\,c^9\,d^6-7168\,a^5\,b^8\,c^{10}\,d^5+5120\,a^4\,b^9\,c^{11}\,d^4-1792\,a^3\,b^{10}\,c^{12}\,d^3+256\,a^2\,b^{11}\,c^{13}\,d^2\right)}{512\,\left(a^4\,c^5\,d^4-4\,a^3\,b\,c^6\,d^3+6\,a^2\,b^2\,c^7\,d^2-4\,a\,b^3\,c^8\,d+b^4\,c^9\right)\,\left(a^8\,c^4\,d^6-6\,a^7\,b\,c^5\,d^5+15\,a^6\,b^2\,c^6\,d^4-20\,a^5\,b^3\,c^7\,d^3+15\,a^4\,b^4\,c^8\,d^2-6\,a^3\,b^5\,c^9\,d+a^2\,b^6\,c^{10}\right)}\right)\,\sqrt{-c^5\,d^3}\,\left(3\,a^2\,d^2-14\,a\,b\,c\,d+35\,b^2\,c^2\right)}{16\,\left(a^4\,c^5\,d^4-4\,a^3\,b\,c^6\,d^3+6\,a^2\,b^2\,c^7\,d^2-4\,a\,b^3\,c^8\,d+b^4\,c^9\right)}\right)\,\sqrt{-c^5\,d^3}\,\left(3\,a^2\,d^2-14\,a\,b\,c\,d+35\,b^2\,c^2\right)\,1{}\mathrm{i}}{16\,\left(a^4\,c^5\,d^4-4\,a^3\,b\,c^6\,d^3+6\,a^2\,b^2\,c^7\,d^2-4\,a\,b^3\,c^8\,d+b^4\,c^9\right)}}{\frac{\frac{63\,a^5\,b^5\,d^9}{64}-\frac{267\,a^4\,b^6\,c\,d^8}{32}+\frac{451\,a^3\,b^7\,c^2\,d^7}{16}-\frac{1275\,a^2\,b^8\,c^3\,d^6}{32}-\frac{651\,a\,b^9\,c^4\,d^5}{64}+\frac{35\,b^{10}\,c^5\,d^4}{16}}{-a^{11}\,c^4\,d^9+9\,a^{10}\,b\,c^5\,d^8-36\,a^9\,b^2\,c^6\,d^7+84\,a^8\,b^3\,c^7\,d^6-126\,a^7\,b^4\,c^8\,d^5+126\,a^6\,b^5\,c^9\,d^4-84\,a^5\,b^6\,c^{10}\,d^3+36\,a^4\,b^7\,c^{11}\,d^2-9\,a^3\,b^8\,c^{12}\,d+a^2\,b^9\,c^{13}}-\frac{\left(\frac{x\,\left(9\,a^6\,b^3\,d^9-84\,a^5\,b^4\,c\,d^8+406\,a^4\,b^5\,c^2\,d^7-980\,a^3\,b^6\,c^3\,d^6+2009\,a^2\,b^7\,c^4\,d^5-224\,a\,b^8\,c^5\,d^4+16\,b^9\,c^6\,d^3\right)}{32\,\left(a^8\,c^4\,d^6-6\,a^7\,b\,c^5\,d^5+15\,a^6\,b^2\,c^6\,d^4-20\,a^5\,b^3\,c^7\,d^3+15\,a^4\,b^4\,c^8\,d^2-6\,a^3\,b^5\,c^9\,d+a^2\,b^6\,c^{10}\right)}-\frac{\left(\frac{-\frac{3\,a^{12}\,b^2\,c^2\,d^{13}}{2}+\frac{35\,a^{11}\,b^3\,c^3\,d^{12}}{2}-98\,a^{10}\,b^4\,c^4\,d^{11}+336\,a^9\,b^5\,c^5\,d^{10}-765\,a^8\,b^6\,c^6\,d^9+1197\,a^7\,b^7\,c^7\,d^8-1302\,a^6\,b^8\,c^8\,d^7+978\,a^5\,b^9\,c^9\,d^6-\frac{987\,a^4\,b^{10}\,c^{10}\,d^5}{2}+\frac{315\,a^3\,b^{11}\,c^{11}\,d^4}{2}-28\,a^2\,b^{12}\,c^{12}\,d^3+2\,a\,b^{13}\,c^{13}\,d^2}{-a^{11}\,c^4\,d^9+9\,a^{10}\,b\,c^5\,d^8-36\,a^9\,b^2\,c^6\,d^7+84\,a^8\,b^3\,c^7\,d^6-126\,a^7\,b^4\,c^8\,d^5+126\,a^6\,b^5\,c^9\,d^4-84\,a^5\,b^6\,c^{10}\,d^3+36\,a^4\,b^7\,c^{11}\,d^2-9\,a^3\,b^8\,c^{12}\,d+a^2\,b^9\,c^{13}}-\frac{x\,\sqrt{-c^5\,d^3}\,\left(3\,a^2\,d^2-14\,a\,b\,c\,d+35\,b^2\,c^2\right)\,\left(256\,a^{11}\,b^2\,c^4\,d^{11}-1792\,a^{10}\,b^3\,c^5\,d^{10}+5120\,a^9\,b^4\,c^6\,d^9-7168\,a^8\,b^5\,c^7\,d^8+3584\,a^7\,b^6\,c^8\,d^7+3584\,a^6\,b^7\,c^9\,d^6-7168\,a^5\,b^8\,c^{10}\,d^5+5120\,a^4\,b^9\,c^{11}\,d^4-1792\,a^3\,b^{10}\,c^{12}\,d^3+256\,a^2\,b^{11}\,c^{13}\,d^2\right)}{512\,\left(a^4\,c^5\,d^4-4\,a^3\,b\,c^6\,d^3+6\,a^2\,b^2\,c^7\,d^2-4\,a\,b^3\,c^8\,d+b^4\,c^9\right)\,\left(a^8\,c^4\,d^6-6\,a^7\,b\,c^5\,d^5+15\,a^6\,b^2\,c^6\,d^4-20\,a^5\,b^3\,c^7\,d^3+15\,a^4\,b^4\,c^8\,d^2-6\,a^3\,b^5\,c^9\,d+a^2\,b^6\,c^{10}\right)}\right)\,\sqrt{-c^5\,d^3}\,\left(3\,a^2\,d^2-14\,a\,b\,c\,d+35\,b^2\,c^2\right)}{16\,\left(a^4\,c^5\,d^4-4\,a^3\,b\,c^6\,d^3+6\,a^2\,b^2\,c^7\,d^2-4\,a\,b^3\,c^8\,d+b^4\,c^9\right)}\right)\,\sqrt{-c^5\,d^3}\,\left(3\,a^2\,d^2-14\,a\,b\,c\,d+35\,b^2\,c^2\right)}{16\,\left(a^4\,c^5\,d^4-4\,a^3\,b\,c^6\,d^3+6\,a^2\,b^2\,c^7\,d^2-4\,a\,b^3\,c^8\,d+b^4\,c^9\right)}+\frac{\left(\frac{x\,\left(9\,a^6\,b^3\,d^9-84\,a^5\,b^4\,c\,d^8+406\,a^4\,b^5\,c^2\,d^7-980\,a^3\,b^6\,c^3\,d^6+2009\,a^2\,b^7\,c^4\,d^5-224\,a\,b^8\,c^5\,d^4+16\,b^9\,c^6\,d^3\right)}{32\,\left(a^8\,c^4\,d^6-6\,a^7\,b\,c^5\,d^5+15\,a^6\,b^2\,c^6\,d^4-20\,a^5\,b^3\,c^7\,d^3+15\,a^4\,b^4\,c^8\,d^2-6\,a^3\,b^5\,c^9\,d+a^2\,b^6\,c^{10}\right)}+\frac{\left(\frac{-\frac{3\,a^{12}\,b^2\,c^2\,d^{13}}{2}+\frac{35\,a^{11}\,b^3\,c^3\,d^{12}}{2}-98\,a^{10}\,b^4\,c^4\,d^{11}+336\,a^9\,b^5\,c^5\,d^{10}-765\,a^8\,b^6\,c^6\,d^9+1197\,a^7\,b^7\,c^7\,d^8-1302\,a^6\,b^8\,c^8\,d^7+978\,a^5\,b^9\,c^9\,d^6-\frac{987\,a^4\,b^{10}\,c^{10}\,d^5}{2}+\frac{315\,a^3\,b^{11}\,c^{11}\,d^4}{2}-28\,a^2\,b^{12}\,c^{12}\,d^3+2\,a\,b^{13}\,c^{13}\,d^2}{-a^{11}\,c^4\,d^9+9\,a^{10}\,b\,c^5\,d^8-36\,a^9\,b^2\,c^6\,d^7+84\,a^8\,b^3\,c^7\,d^6-126\,a^7\,b^4\,c^8\,d^5+126\,a^6\,b^5\,c^9\,d^4-84\,a^5\,b^6\,c^{10}\,d^3+36\,a^4\,b^7\,c^{11}\,d^2-9\,a^3\,b^8\,c^{12}\,d+a^2\,b^9\,c^{13}}+\frac{x\,\sqrt{-c^5\,d^3}\,\left(3\,a^2\,d^2-14\,a\,b\,c\,d+35\,b^2\,c^2\right)\,\left(256\,a^{11}\,b^2\,c^4\,d^{11}-1792\,a^{10}\,b^3\,c^5\,d^{10}+5120\,a^9\,b^4\,c^6\,d^9-7168\,a^8\,b^5\,c^7\,d^8+3584\,a^7\,b^6\,c^8\,d^7+3584\,a^6\,b^7\,c^9\,d^6-7168\,a^5\,b^8\,c^{10}\,d^5+5120\,a^4\,b^9\,c^{11}\,d^4-1792\,a^3\,b^{10}\,c^{12}\,d^3+256\,a^2\,b^{11}\,c^{13}\,d^2\right)}{512\,\left(a^4\,c^5\,d^4-4\,a^3\,b\,c^6\,d^3+6\,a^2\,b^2\,c^7\,d^2-4\,a\,b^3\,c^8\,d+b^4\,c^9\right)\,\left(a^8\,c^4\,d^6-6\,a^7\,b\,c^5\,d^5+15\,a^6\,b^2\,c^6\,d^4-20\,a^5\,b^3\,c^7\,d^3+15\,a^4\,b^4\,c^8\,d^2-6\,a^3\,b^5\,c^9\,d+a^2\,b^6\,c^{10}\right)}\right)\,\sqrt{-c^5\,d^3}\,\left(3\,a^2\,d^2-14\,a\,b\,c\,d+35\,b^2\,c^2\right)}{16\,\left(a^4\,c^5\,d^4-4\,a^3\,b\,c^6\,d^3+6\,a^2\,b^2\,c^7\,d^2-4\,a\,b^3\,c^8\,d+b^4\,c^9\right)}\right)\,\sqrt{-c^5\,d^3}\,\left(3\,a^2\,d^2-14\,a\,b\,c\,d+35\,b^2\,c^2\right)}{16\,\left(a^4\,c^5\,d^4-4\,a^3\,b\,c^6\,d^3+6\,a^2\,b^2\,c^7\,d^2-4\,a\,b^3\,c^8\,d+b^4\,c^9\right)}}\right)\,\sqrt{-c^5\,d^3}\,\left(3\,a^2\,d^2-14\,a\,b\,c\,d+35\,b^2\,c^2\right)\,1{}\mathrm{i}}{8\,\left(a^4\,c^5\,d^4-4\,a^3\,b\,c^6\,d^3+6\,a^2\,b^2\,c^7\,d^2-4\,a\,b^3\,c^8\,d+b^4\,c^9\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{x\,\left(9\,a^6\,b^3\,d^9-84\,a^5\,b^4\,c\,d^8+406\,a^4\,b^5\,c^2\,d^7-980\,a^3\,b^6\,c^3\,d^6+2009\,a^2\,b^7\,c^4\,d^5-224\,a\,b^8\,c^5\,d^4+16\,b^9\,c^6\,d^3\right)}{32\,\left(a^8\,c^4\,d^6-6\,a^7\,b\,c^5\,d^5+15\,a^6\,b^2\,c^6\,d^4-20\,a^5\,b^3\,c^7\,d^3+15\,a^4\,b^4\,c^8\,d^2-6\,a^3\,b^5\,c^9\,d+a^2\,b^6\,c^{10}\right)}-\frac{\left(7\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^5}\,\left(\frac{-\frac{3\,a^{12}\,b^2\,c^2\,d^{13}}{2}+\frac{35\,a^{11}\,b^3\,c^3\,d^{12}}{2}-98\,a^{10}\,b^4\,c^4\,d^{11}+336\,a^9\,b^5\,c^5\,d^{10}-765\,a^8\,b^6\,c^6\,d^9+1197\,a^7\,b^7\,c^7\,d^8-1302\,a^6\,b^8\,c^8\,d^7+978\,a^5\,b^9\,c^9\,d^6-\frac{987\,a^4\,b^{10}\,c^{10}\,d^5}{2}+\frac{315\,a^3\,b^{11}\,c^{11}\,d^4}{2}-28\,a^2\,b^{12}\,c^{12}\,d^3+2\,a\,b^{13}\,c^{13}\,d^2}{-a^{11}\,c^4\,d^9+9\,a^{10}\,b\,c^5\,d^8-36\,a^9\,b^2\,c^6\,d^7+84\,a^8\,b^3\,c^7\,d^6-126\,a^7\,b^4\,c^8\,d^5+126\,a^6\,b^5\,c^9\,d^4-84\,a^5\,b^6\,c^{10}\,d^3+36\,a^4\,b^7\,c^{11}\,d^2-9\,a^3\,b^8\,c^{12}\,d+a^2\,b^9\,c^{13}}-\frac{x\,\left(7\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^5}\,\left(256\,a^{11}\,b^2\,c^4\,d^{11}-1792\,a^{10}\,b^3\,c^5\,d^{10}+5120\,a^9\,b^4\,c^6\,d^9-7168\,a^8\,b^5\,c^7\,d^8+3584\,a^7\,b^6\,c^8\,d^7+3584\,a^6\,b^7\,c^9\,d^6-7168\,a^5\,b^8\,c^{10}\,d^5+5120\,a^4\,b^9\,c^{11}\,d^4-1792\,a^3\,b^{10}\,c^{12}\,d^3+256\,a^2\,b^{11}\,c^{13}\,d^2\right)}{128\,\left(a^7\,d^4-4\,a^6\,b\,c\,d^3+6\,a^5\,b^2\,c^2\,d^2-4\,a^4\,b^3\,c^3\,d+a^3\,b^4\,c^4\right)\,\left(a^8\,c^4\,d^6-6\,a^7\,b\,c^5\,d^5+15\,a^6\,b^2\,c^6\,d^4-20\,a^5\,b^3\,c^7\,d^3+15\,a^4\,b^4\,c^8\,d^2-6\,a^3\,b^5\,c^9\,d+a^2\,b^6\,c^{10}\right)}\right)}{4\,\left(a^7\,d^4-4\,a^6\,b\,c\,d^3+6\,a^5\,b^2\,c^2\,d^2-4\,a^4\,b^3\,c^3\,d+a^3\,b^4\,c^4\right)}\right)\,\left(7\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^5}\,1{}\mathrm{i}}{4\,\left(a^7\,d^4-4\,a^6\,b\,c\,d^3+6\,a^5\,b^2\,c^2\,d^2-4\,a^4\,b^3\,c^3\,d+a^3\,b^4\,c^4\right)}+\frac{\left(\frac{x\,\left(9\,a^6\,b^3\,d^9-84\,a^5\,b^4\,c\,d^8+406\,a^4\,b^5\,c^2\,d^7-980\,a^3\,b^6\,c^3\,d^6+2009\,a^2\,b^7\,c^4\,d^5-224\,a\,b^8\,c^5\,d^4+16\,b^9\,c^6\,d^3\right)}{32\,\left(a^8\,c^4\,d^6-6\,a^7\,b\,c^5\,d^5+15\,a^6\,b^2\,c^6\,d^4-20\,a^5\,b^3\,c^7\,d^3+15\,a^4\,b^4\,c^8\,d^2-6\,a^3\,b^5\,c^9\,d+a^2\,b^6\,c^{10}\right)}+\frac{\left(7\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^5}\,\left(\frac{-\frac{3\,a^{12}\,b^2\,c^2\,d^{13}}{2}+\frac{35\,a^{11}\,b^3\,c^3\,d^{12}}{2}-98\,a^{10}\,b^4\,c^4\,d^{11}+336\,a^9\,b^5\,c^5\,d^{10}-765\,a^8\,b^6\,c^6\,d^9+1197\,a^7\,b^7\,c^7\,d^8-1302\,a^6\,b^8\,c^8\,d^7+978\,a^5\,b^9\,c^9\,d^6-\frac{987\,a^4\,b^{10}\,c^{10}\,d^5}{2}+\frac{315\,a^3\,b^{11}\,c^{11}\,d^4}{2}-28\,a^2\,b^{12}\,c^{12}\,d^3+2\,a\,b^{13}\,c^{13}\,d^2}{-a^{11}\,c^4\,d^9+9\,a^{10}\,b\,c^5\,d^8-36\,a^9\,b^2\,c^6\,d^7+84\,a^8\,b^3\,c^7\,d^6-126\,a^7\,b^4\,c^8\,d^5+126\,a^6\,b^5\,c^9\,d^4-84\,a^5\,b^6\,c^{10}\,d^3+36\,a^4\,b^7\,c^{11}\,d^2-9\,a^3\,b^8\,c^{12}\,d+a^2\,b^9\,c^{13}}+\frac{x\,\left(7\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^5}\,\left(256\,a^{11}\,b^2\,c^4\,d^{11}-1792\,a^{10}\,b^3\,c^5\,d^{10}+5120\,a^9\,b^4\,c^6\,d^9-7168\,a^8\,b^5\,c^7\,d^8+3584\,a^7\,b^6\,c^8\,d^7+3584\,a^6\,b^7\,c^9\,d^6-7168\,a^5\,b^8\,c^{10}\,d^5+5120\,a^4\,b^9\,c^{11}\,d^4-1792\,a^3\,b^{10}\,c^{12}\,d^3+256\,a^2\,b^{11}\,c^{13}\,d^2\right)}{128\,\left(a^7\,d^4-4\,a^6\,b\,c\,d^3+6\,a^5\,b^2\,c^2\,d^2-4\,a^4\,b^3\,c^3\,d+a^3\,b^4\,c^4\right)\,\left(a^8\,c^4\,d^6-6\,a^7\,b\,c^5\,d^5+15\,a^6\,b^2\,c^6\,d^4-20\,a^5\,b^3\,c^7\,d^3+15\,a^4\,b^4\,c^8\,d^2-6\,a^3\,b^5\,c^9\,d+a^2\,b^6\,c^{10}\right)}\right)}{4\,\left(a^7\,d^4-4\,a^6\,b\,c\,d^3+6\,a^5\,b^2\,c^2\,d^2-4\,a^4\,b^3\,c^3\,d+a^3\,b^4\,c^4\right)}\right)\,\left(7\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^5}\,1{}\mathrm{i}}{4\,\left(a^7\,d^4-4\,a^6\,b\,c\,d^3+6\,a^5\,b^2\,c^2\,d^2-4\,a^4\,b^3\,c^3\,d+a^3\,b^4\,c^4\right)}}{\frac{\frac{63\,a^5\,b^5\,d^9}{64}-\frac{267\,a^4\,b^6\,c\,d^8}{32}+\frac{451\,a^3\,b^7\,c^2\,d^7}{16}-\frac{1275\,a^2\,b^8\,c^3\,d^6}{32}-\frac{651\,a\,b^9\,c^4\,d^5}{64}+\frac{35\,b^{10}\,c^5\,d^4}{16}}{-a^{11}\,c^4\,d^9+9\,a^{10}\,b\,c^5\,d^8-36\,a^9\,b^2\,c^6\,d^7+84\,a^8\,b^3\,c^7\,d^6-126\,a^7\,b^4\,c^8\,d^5+126\,a^6\,b^5\,c^9\,d^4-84\,a^5\,b^6\,c^{10}\,d^3+36\,a^4\,b^7\,c^{11}\,d^2-9\,a^3\,b^8\,c^{12}\,d+a^2\,b^9\,c^{13}}-\frac{\left(\frac{x\,\left(9\,a^6\,b^3\,d^9-84\,a^5\,b^4\,c\,d^8+406\,a^4\,b^5\,c^2\,d^7-980\,a^3\,b^6\,c^3\,d^6+2009\,a^2\,b^7\,c^4\,d^5-224\,a\,b^8\,c^5\,d^4+16\,b^9\,c^6\,d^3\right)}{32\,\left(a^8\,c^4\,d^6-6\,a^7\,b\,c^5\,d^5+15\,a^6\,b^2\,c^6\,d^4-20\,a^5\,b^3\,c^7\,d^3+15\,a^4\,b^4\,c^8\,d^2-6\,a^3\,b^5\,c^9\,d+a^2\,b^6\,c^{10}\right)}-\frac{\left(7\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^5}\,\left(\frac{-\frac{3\,a^{12}\,b^2\,c^2\,d^{13}}{2}+\frac{35\,a^{11}\,b^3\,c^3\,d^{12}}{2}-98\,a^{10}\,b^4\,c^4\,d^{11}+336\,a^9\,b^5\,c^5\,d^{10}-765\,a^8\,b^6\,c^6\,d^9+1197\,a^7\,b^7\,c^7\,d^8-1302\,a^6\,b^8\,c^8\,d^7+978\,a^5\,b^9\,c^9\,d^6-\frac{987\,a^4\,b^{10}\,c^{10}\,d^5}{2}+\frac{315\,a^3\,b^{11}\,c^{11}\,d^4}{2}-28\,a^2\,b^{12}\,c^{12}\,d^3+2\,a\,b^{13}\,c^{13}\,d^2}{-a^{11}\,c^4\,d^9+9\,a^{10}\,b\,c^5\,d^8-36\,a^9\,b^2\,c^6\,d^7+84\,a^8\,b^3\,c^7\,d^6-126\,a^7\,b^4\,c^8\,d^5+126\,a^6\,b^5\,c^9\,d^4-84\,a^5\,b^6\,c^{10}\,d^3+36\,a^4\,b^7\,c^{11}\,d^2-9\,a^3\,b^8\,c^{12}\,d+a^2\,b^9\,c^{13}}-\frac{x\,\left(7\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^5}\,\left(256\,a^{11}\,b^2\,c^4\,d^{11}-1792\,a^{10}\,b^3\,c^5\,d^{10}+5120\,a^9\,b^4\,c^6\,d^9-7168\,a^8\,b^5\,c^7\,d^8+3584\,a^7\,b^6\,c^8\,d^7+3584\,a^6\,b^7\,c^9\,d^6-7168\,a^5\,b^8\,c^{10}\,d^5+5120\,a^4\,b^9\,c^{11}\,d^4-1792\,a^3\,b^{10}\,c^{12}\,d^3+256\,a^2\,b^{11}\,c^{13}\,d^2\right)}{128\,\left(a^7\,d^4-4\,a^6\,b\,c\,d^3+6\,a^5\,b^2\,c^2\,d^2-4\,a^4\,b^3\,c^3\,d+a^3\,b^4\,c^4\right)\,\left(a^8\,c^4\,d^6-6\,a^7\,b\,c^5\,d^5+15\,a^6\,b^2\,c^6\,d^4-20\,a^5\,b^3\,c^7\,d^3+15\,a^4\,b^4\,c^8\,d^2-6\,a^3\,b^5\,c^9\,d+a^2\,b^6\,c^{10}\right)}\right)}{4\,\left(a^7\,d^4-4\,a^6\,b\,c\,d^3+6\,a^5\,b^2\,c^2\,d^2-4\,a^4\,b^3\,c^3\,d+a^3\,b^4\,c^4\right)}\right)\,\left(7\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^5}}{4\,\left(a^7\,d^4-4\,a^6\,b\,c\,d^3+6\,a^5\,b^2\,c^2\,d^2-4\,a^4\,b^3\,c^3\,d+a^3\,b^4\,c^4\right)}+\frac{\left(\frac{x\,\left(9\,a^6\,b^3\,d^9-84\,a^5\,b^4\,c\,d^8+406\,a^4\,b^5\,c^2\,d^7-980\,a^3\,b^6\,c^3\,d^6+2009\,a^2\,b^7\,c^4\,d^5-224\,a\,b^8\,c^5\,d^4+16\,b^9\,c^6\,d^3\right)}{32\,\left(a^8\,c^4\,d^6-6\,a^7\,b\,c^5\,d^5+15\,a^6\,b^2\,c^6\,d^4-20\,a^5\,b^3\,c^7\,d^3+15\,a^4\,b^4\,c^8\,d^2-6\,a^3\,b^5\,c^9\,d+a^2\,b^6\,c^{10}\right)}+\frac{\left(7\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^5}\,\left(\frac{-\frac{3\,a^{12}\,b^2\,c^2\,d^{13}}{2}+\frac{35\,a^{11}\,b^3\,c^3\,d^{12}}{2}-98\,a^{10}\,b^4\,c^4\,d^{11}+336\,a^9\,b^5\,c^5\,d^{10}-765\,a^8\,b^6\,c^6\,d^9+1197\,a^7\,b^7\,c^7\,d^8-1302\,a^6\,b^8\,c^8\,d^7+978\,a^5\,b^9\,c^9\,d^6-\frac{987\,a^4\,b^{10}\,c^{10}\,d^5}{2}+\frac{315\,a^3\,b^{11}\,c^{11}\,d^4}{2}-28\,a^2\,b^{12}\,c^{12}\,d^3+2\,a\,b^{13}\,c^{13}\,d^2}{-a^{11}\,c^4\,d^9+9\,a^{10}\,b\,c^5\,d^8-36\,a^9\,b^2\,c^6\,d^7+84\,a^8\,b^3\,c^7\,d^6-126\,a^7\,b^4\,c^8\,d^5+126\,a^6\,b^5\,c^9\,d^4-84\,a^5\,b^6\,c^{10}\,d^3+36\,a^4\,b^7\,c^{11}\,d^2-9\,a^3\,b^8\,c^{12}\,d+a^2\,b^9\,c^{13}}+\frac{x\,\left(7\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^5}\,\left(256\,a^{11}\,b^2\,c^4\,d^{11}-1792\,a^{10}\,b^3\,c^5\,d^{10}+5120\,a^9\,b^4\,c^6\,d^9-7168\,a^8\,b^5\,c^7\,d^8+3584\,a^7\,b^6\,c^8\,d^7+3584\,a^6\,b^7\,c^9\,d^6-7168\,a^5\,b^8\,c^{10}\,d^5+5120\,a^4\,b^9\,c^{11}\,d^4-1792\,a^3\,b^{10}\,c^{12}\,d^3+256\,a^2\,b^{11}\,c^{13}\,d^2\right)}{128\,\left(a^7\,d^4-4\,a^6\,b\,c\,d^3+6\,a^5\,b^2\,c^2\,d^2-4\,a^4\,b^3\,c^3\,d+a^3\,b^4\,c^4\right)\,\left(a^8\,c^4\,d^6-6\,a^7\,b\,c^5\,d^5+15\,a^6\,b^2\,c^6\,d^4-20\,a^5\,b^3\,c^7\,d^3+15\,a^4\,b^4\,c^8\,d^2-6\,a^3\,b^5\,c^9\,d+a^2\,b^6\,c^{10}\right)}\right)}{4\,\left(a^7\,d^4-4\,a^6\,b\,c\,d^3+6\,a^5\,b^2\,c^2\,d^2-4\,a^4\,b^3\,c^3\,d+a^3\,b^4\,c^4\right)}\right)\,\left(7\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^5}}{4\,\left(a^7\,d^4-4\,a^6\,b\,c\,d^3+6\,a^5\,b^2\,c^2\,d^2-4\,a^4\,b^3\,c^3\,d+a^3\,b^4\,c^4\right)}}\right)\,\left(7\,a\,d-b\,c\right)\,\sqrt{-a^3\,b^5}\,1{}\mathrm{i}}{2\,\left(a^7\,d^4-4\,a^6\,b\,c\,d^3+6\,a^5\,b^2\,c^2\,d^2-4\,a^4\,b^3\,c^3\,d+a^3\,b^4\,c^4\right)}","Not used",1,"(atan(((((x*(9*a^6*b^3*d^9 + 16*b^9*c^6*d^3 - 224*a*b^8*c^5*d^4 - 84*a^5*b^4*c*d^8 + 2009*a^2*b^7*c^4*d^5 - 980*a^3*b^6*c^3*d^6 + 406*a^4*b^5*c^2*d^7))/(32*(a^2*b^6*c^10 + a^8*c^4*d^6 - 6*a^3*b^5*c^9*d - 6*a^7*b*c^5*d^5 + 15*a^4*b^4*c^8*d^2 - 20*a^5*b^3*c^7*d^3 + 15*a^6*b^2*c^6*d^4)) - (((2*a*b^13*c^13*d^2 - 28*a^2*b^12*c^12*d^3 + (315*a^3*b^11*c^11*d^4)/2 - (987*a^4*b^10*c^10*d^5)/2 + 978*a^5*b^9*c^9*d^6 - 1302*a^6*b^8*c^8*d^7 + 1197*a^7*b^7*c^7*d^8 - 765*a^8*b^6*c^6*d^9 + 336*a^9*b^5*c^5*d^10 - 98*a^10*b^4*c^4*d^11 + (35*a^11*b^3*c^3*d^12)/2 - (3*a^12*b^2*c^2*d^13)/2)/(a^2*b^9*c^13 - a^11*c^4*d^9 - 9*a^3*b^8*c^12*d + 9*a^10*b*c^5*d^8 + 36*a^4*b^7*c^11*d^2 - 84*a^5*b^6*c^10*d^3 + 126*a^6*b^5*c^9*d^4 - 126*a^7*b^4*c^8*d^5 + 84*a^8*b^3*c^7*d^6 - 36*a^9*b^2*c^6*d^7) - (x*(-c^5*d^3)^(1/2)*(3*a^2*d^2 + 35*b^2*c^2 - 14*a*b*c*d)*(256*a^2*b^11*c^13*d^2 - 1792*a^3*b^10*c^12*d^3 + 5120*a^4*b^9*c^11*d^4 - 7168*a^5*b^8*c^10*d^5 + 3584*a^6*b^7*c^9*d^6 + 3584*a^7*b^6*c^8*d^7 - 7168*a^8*b^5*c^7*d^8 + 5120*a^9*b^4*c^6*d^9 - 1792*a^10*b^3*c^5*d^10 + 256*a^11*b^2*c^4*d^11))/(512*(b^4*c^9 + a^4*c^5*d^4 - 4*a^3*b*c^6*d^3 + 6*a^2*b^2*c^7*d^2 - 4*a*b^3*c^8*d)*(a^2*b^6*c^10 + a^8*c^4*d^6 - 6*a^3*b^5*c^9*d - 6*a^7*b*c^5*d^5 + 15*a^4*b^4*c^8*d^2 - 20*a^5*b^3*c^7*d^3 + 15*a^6*b^2*c^6*d^4)))*(-c^5*d^3)^(1/2)*(3*a^2*d^2 + 35*b^2*c^2 - 14*a*b*c*d))/(16*(b^4*c^9 + a^4*c^5*d^4 - 4*a^3*b*c^6*d^3 + 6*a^2*b^2*c^7*d^2 - 4*a*b^3*c^8*d)))*(-c^5*d^3)^(1/2)*(3*a^2*d^2 + 35*b^2*c^2 - 14*a*b*c*d)*1i)/(16*(b^4*c^9 + a^4*c^5*d^4 - 4*a^3*b*c^6*d^3 + 6*a^2*b^2*c^7*d^2 - 4*a*b^3*c^8*d)) + (((x*(9*a^6*b^3*d^9 + 16*b^9*c^6*d^3 - 224*a*b^8*c^5*d^4 - 84*a^5*b^4*c*d^8 + 2009*a^2*b^7*c^4*d^5 - 980*a^3*b^6*c^3*d^6 + 406*a^4*b^5*c^2*d^7))/(32*(a^2*b^6*c^10 + a^8*c^4*d^6 - 6*a^3*b^5*c^9*d - 6*a^7*b*c^5*d^5 + 15*a^4*b^4*c^8*d^2 - 20*a^5*b^3*c^7*d^3 + 15*a^6*b^2*c^6*d^4)) + (((2*a*b^13*c^13*d^2 - 28*a^2*b^12*c^12*d^3 + (315*a^3*b^11*c^11*d^4)/2 - (987*a^4*b^10*c^10*d^5)/2 + 978*a^5*b^9*c^9*d^6 - 1302*a^6*b^8*c^8*d^7 + 1197*a^7*b^7*c^7*d^8 - 765*a^8*b^6*c^6*d^9 + 336*a^9*b^5*c^5*d^10 - 98*a^10*b^4*c^4*d^11 + (35*a^11*b^3*c^3*d^12)/2 - (3*a^12*b^2*c^2*d^13)/2)/(a^2*b^9*c^13 - a^11*c^4*d^9 - 9*a^3*b^8*c^12*d + 9*a^10*b*c^5*d^8 + 36*a^4*b^7*c^11*d^2 - 84*a^5*b^6*c^10*d^3 + 126*a^6*b^5*c^9*d^4 - 126*a^7*b^4*c^8*d^5 + 84*a^8*b^3*c^7*d^6 - 36*a^9*b^2*c^6*d^7) + (x*(-c^5*d^3)^(1/2)*(3*a^2*d^2 + 35*b^2*c^2 - 14*a*b*c*d)*(256*a^2*b^11*c^13*d^2 - 1792*a^3*b^10*c^12*d^3 + 5120*a^4*b^9*c^11*d^4 - 7168*a^5*b^8*c^10*d^5 + 3584*a^6*b^7*c^9*d^6 + 3584*a^7*b^6*c^8*d^7 - 7168*a^8*b^5*c^7*d^8 + 5120*a^9*b^4*c^6*d^9 - 1792*a^10*b^3*c^5*d^10 + 256*a^11*b^2*c^4*d^11))/(512*(b^4*c^9 + a^4*c^5*d^4 - 4*a^3*b*c^6*d^3 + 6*a^2*b^2*c^7*d^2 - 4*a*b^3*c^8*d)*(a^2*b^6*c^10 + a^8*c^4*d^6 - 6*a^3*b^5*c^9*d - 6*a^7*b*c^5*d^5 + 15*a^4*b^4*c^8*d^2 - 20*a^5*b^3*c^7*d^3 + 15*a^6*b^2*c^6*d^4)))*(-c^5*d^3)^(1/2)*(3*a^2*d^2 + 35*b^2*c^2 - 14*a*b*c*d))/(16*(b^4*c^9 + a^4*c^5*d^4 - 4*a^3*b*c^6*d^3 + 6*a^2*b^2*c^7*d^2 - 4*a*b^3*c^8*d)))*(-c^5*d^3)^(1/2)*(3*a^2*d^2 + 35*b^2*c^2 - 14*a*b*c*d)*1i)/(16*(b^4*c^9 + a^4*c^5*d^4 - 4*a^3*b*c^6*d^3 + 6*a^2*b^2*c^7*d^2 - 4*a*b^3*c^8*d)))/(((63*a^5*b^5*d^9)/64 + (35*b^10*c^5*d^4)/16 - (651*a*b^9*c^4*d^5)/64 - (267*a^4*b^6*c*d^8)/32 - (1275*a^2*b^8*c^3*d^6)/32 + (451*a^3*b^7*c^2*d^7)/16)/(a^2*b^9*c^13 - a^11*c^4*d^9 - 9*a^3*b^8*c^12*d + 9*a^10*b*c^5*d^8 + 36*a^4*b^7*c^11*d^2 - 84*a^5*b^6*c^10*d^3 + 126*a^6*b^5*c^9*d^4 - 126*a^7*b^4*c^8*d^5 + 84*a^8*b^3*c^7*d^6 - 36*a^9*b^2*c^6*d^7) - (((x*(9*a^6*b^3*d^9 + 16*b^9*c^6*d^3 - 224*a*b^8*c^5*d^4 - 84*a^5*b^4*c*d^8 + 2009*a^2*b^7*c^4*d^5 - 980*a^3*b^6*c^3*d^6 + 406*a^4*b^5*c^2*d^7))/(32*(a^2*b^6*c^10 + a^8*c^4*d^6 - 6*a^3*b^5*c^9*d - 6*a^7*b*c^5*d^5 + 15*a^4*b^4*c^8*d^2 - 20*a^5*b^3*c^7*d^3 + 15*a^6*b^2*c^6*d^4)) - (((2*a*b^13*c^13*d^2 - 28*a^2*b^12*c^12*d^3 + (315*a^3*b^11*c^11*d^4)/2 - (987*a^4*b^10*c^10*d^5)/2 + 978*a^5*b^9*c^9*d^6 - 1302*a^6*b^8*c^8*d^7 + 1197*a^7*b^7*c^7*d^8 - 765*a^8*b^6*c^6*d^9 + 336*a^9*b^5*c^5*d^10 - 98*a^10*b^4*c^4*d^11 + (35*a^11*b^3*c^3*d^12)/2 - (3*a^12*b^2*c^2*d^13)/2)/(a^2*b^9*c^13 - a^11*c^4*d^9 - 9*a^3*b^8*c^12*d + 9*a^10*b*c^5*d^8 + 36*a^4*b^7*c^11*d^2 - 84*a^5*b^6*c^10*d^3 + 126*a^6*b^5*c^9*d^4 - 126*a^7*b^4*c^8*d^5 + 84*a^8*b^3*c^7*d^6 - 36*a^9*b^2*c^6*d^7) - (x*(-c^5*d^3)^(1/2)*(3*a^2*d^2 + 35*b^2*c^2 - 14*a*b*c*d)*(256*a^2*b^11*c^13*d^2 - 1792*a^3*b^10*c^12*d^3 + 5120*a^4*b^9*c^11*d^4 - 7168*a^5*b^8*c^10*d^5 + 3584*a^6*b^7*c^9*d^6 + 3584*a^7*b^6*c^8*d^7 - 7168*a^8*b^5*c^7*d^8 + 5120*a^9*b^4*c^6*d^9 - 1792*a^10*b^3*c^5*d^10 + 256*a^11*b^2*c^4*d^11))/(512*(b^4*c^9 + a^4*c^5*d^4 - 4*a^3*b*c^6*d^3 + 6*a^2*b^2*c^7*d^2 - 4*a*b^3*c^8*d)*(a^2*b^6*c^10 + a^8*c^4*d^6 - 6*a^3*b^5*c^9*d - 6*a^7*b*c^5*d^5 + 15*a^4*b^4*c^8*d^2 - 20*a^5*b^3*c^7*d^3 + 15*a^6*b^2*c^6*d^4)))*(-c^5*d^3)^(1/2)*(3*a^2*d^2 + 35*b^2*c^2 - 14*a*b*c*d))/(16*(b^4*c^9 + a^4*c^5*d^4 - 4*a^3*b*c^6*d^3 + 6*a^2*b^2*c^7*d^2 - 4*a*b^3*c^8*d)))*(-c^5*d^3)^(1/2)*(3*a^2*d^2 + 35*b^2*c^2 - 14*a*b*c*d))/(16*(b^4*c^9 + a^4*c^5*d^4 - 4*a^3*b*c^6*d^3 + 6*a^2*b^2*c^7*d^2 - 4*a*b^3*c^8*d)) + (((x*(9*a^6*b^3*d^9 + 16*b^9*c^6*d^3 - 224*a*b^8*c^5*d^4 - 84*a^5*b^4*c*d^8 + 2009*a^2*b^7*c^4*d^5 - 980*a^3*b^6*c^3*d^6 + 406*a^4*b^5*c^2*d^7))/(32*(a^2*b^6*c^10 + a^8*c^4*d^6 - 6*a^3*b^5*c^9*d - 6*a^7*b*c^5*d^5 + 15*a^4*b^4*c^8*d^2 - 20*a^5*b^3*c^7*d^3 + 15*a^6*b^2*c^6*d^4)) + (((2*a*b^13*c^13*d^2 - 28*a^2*b^12*c^12*d^3 + (315*a^3*b^11*c^11*d^4)/2 - (987*a^4*b^10*c^10*d^5)/2 + 978*a^5*b^9*c^9*d^6 - 1302*a^6*b^8*c^8*d^7 + 1197*a^7*b^7*c^7*d^8 - 765*a^8*b^6*c^6*d^9 + 336*a^9*b^5*c^5*d^10 - 98*a^10*b^4*c^4*d^11 + (35*a^11*b^3*c^3*d^12)/2 - (3*a^12*b^2*c^2*d^13)/2)/(a^2*b^9*c^13 - a^11*c^4*d^9 - 9*a^3*b^8*c^12*d + 9*a^10*b*c^5*d^8 + 36*a^4*b^7*c^11*d^2 - 84*a^5*b^6*c^10*d^3 + 126*a^6*b^5*c^9*d^4 - 126*a^7*b^4*c^8*d^5 + 84*a^8*b^3*c^7*d^6 - 36*a^9*b^2*c^6*d^7) + (x*(-c^5*d^3)^(1/2)*(3*a^2*d^2 + 35*b^2*c^2 - 14*a*b*c*d)*(256*a^2*b^11*c^13*d^2 - 1792*a^3*b^10*c^12*d^3 + 5120*a^4*b^9*c^11*d^4 - 7168*a^5*b^8*c^10*d^5 + 3584*a^6*b^7*c^9*d^6 + 3584*a^7*b^6*c^8*d^7 - 7168*a^8*b^5*c^7*d^8 + 5120*a^9*b^4*c^6*d^9 - 1792*a^10*b^3*c^5*d^10 + 256*a^11*b^2*c^4*d^11))/(512*(b^4*c^9 + a^4*c^5*d^4 - 4*a^3*b*c^6*d^3 + 6*a^2*b^2*c^7*d^2 - 4*a*b^3*c^8*d)*(a^2*b^6*c^10 + a^8*c^4*d^6 - 6*a^3*b^5*c^9*d - 6*a^7*b*c^5*d^5 + 15*a^4*b^4*c^8*d^2 - 20*a^5*b^3*c^7*d^3 + 15*a^6*b^2*c^6*d^4)))*(-c^5*d^3)^(1/2)*(3*a^2*d^2 + 35*b^2*c^2 - 14*a*b*c*d))/(16*(b^4*c^9 + a^4*c^5*d^4 - 4*a^3*b*c^6*d^3 + 6*a^2*b^2*c^7*d^2 - 4*a*b^3*c^8*d)))*(-c^5*d^3)^(1/2)*(3*a^2*d^2 + 35*b^2*c^2 - 14*a*b*c*d))/(16*(b^4*c^9 + a^4*c^5*d^4 - 4*a^3*b*c^6*d^3 + 6*a^2*b^2*c^7*d^2 - 4*a*b^3*c^8*d))))*(-c^5*d^3)^(1/2)*(3*a^2*d^2 + 35*b^2*c^2 - 14*a*b*c*d)*1i)/(8*(b^4*c^9 + a^4*c^5*d^4 - 4*a^3*b*c^6*d^3 + 6*a^2*b^2*c^7*d^2 - 4*a*b^3*c^8*d)) - ((x^5*(4*b^3*c^2*d^2 - 3*a^2*b*d^4 + 11*a*b^2*c*d^3))/(8*a*c^2*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)) + (x*(4*b^3*c^3 - 5*a^3*d^3 + 13*a^2*b*c*d^2))/(8*a*c*(a*d - b*c)*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) + (d*x^3*(8*b^3*c^3 - 3*a^3*d^3 + 13*a*b^2*c^2*d + 6*a^2*b*c*d^2))/(8*a*c^2*(a*d - b*c)*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)))/(a*c^2 + x^2*(b*c^2 + 2*a*c*d) + x^4*(a*d^2 + 2*b*c*d) + b*d^2*x^6) + (atan(((((x*(9*a^6*b^3*d^9 + 16*b^9*c^6*d^3 - 224*a*b^8*c^5*d^4 - 84*a^5*b^4*c*d^8 + 2009*a^2*b^7*c^4*d^5 - 980*a^3*b^6*c^3*d^6 + 406*a^4*b^5*c^2*d^7))/(32*(a^2*b^6*c^10 + a^8*c^4*d^6 - 6*a^3*b^5*c^9*d - 6*a^7*b*c^5*d^5 + 15*a^4*b^4*c^8*d^2 - 20*a^5*b^3*c^7*d^3 + 15*a^6*b^2*c^6*d^4)) - ((7*a*d - b*c)*(-a^3*b^5)^(1/2)*((2*a*b^13*c^13*d^2 - 28*a^2*b^12*c^12*d^3 + (315*a^3*b^11*c^11*d^4)/2 - (987*a^4*b^10*c^10*d^5)/2 + 978*a^5*b^9*c^9*d^6 - 1302*a^6*b^8*c^8*d^7 + 1197*a^7*b^7*c^7*d^8 - 765*a^8*b^6*c^6*d^9 + 336*a^9*b^5*c^5*d^10 - 98*a^10*b^4*c^4*d^11 + (35*a^11*b^3*c^3*d^12)/2 - (3*a^12*b^2*c^2*d^13)/2)/(a^2*b^9*c^13 - a^11*c^4*d^9 - 9*a^3*b^8*c^12*d + 9*a^10*b*c^5*d^8 + 36*a^4*b^7*c^11*d^2 - 84*a^5*b^6*c^10*d^3 + 126*a^6*b^5*c^9*d^4 - 126*a^7*b^4*c^8*d^5 + 84*a^8*b^3*c^7*d^6 - 36*a^9*b^2*c^6*d^7) - (x*(7*a*d - b*c)*(-a^3*b^5)^(1/2)*(256*a^2*b^11*c^13*d^2 - 1792*a^3*b^10*c^12*d^3 + 5120*a^4*b^9*c^11*d^4 - 7168*a^5*b^8*c^10*d^5 + 3584*a^6*b^7*c^9*d^6 + 3584*a^7*b^6*c^8*d^7 - 7168*a^8*b^5*c^7*d^8 + 5120*a^9*b^4*c^6*d^9 - 1792*a^10*b^3*c^5*d^10 + 256*a^11*b^2*c^4*d^11))/(128*(a^7*d^4 + a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3)*(a^2*b^6*c^10 + a^8*c^4*d^6 - 6*a^3*b^5*c^9*d - 6*a^7*b*c^5*d^5 + 15*a^4*b^4*c^8*d^2 - 20*a^5*b^3*c^7*d^3 + 15*a^6*b^2*c^6*d^4))))/(4*(a^7*d^4 + a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3)))*(7*a*d - b*c)*(-a^3*b^5)^(1/2)*1i)/(4*(a^7*d^4 + a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3)) + (((x*(9*a^6*b^3*d^9 + 16*b^9*c^6*d^3 - 224*a*b^8*c^5*d^4 - 84*a^5*b^4*c*d^8 + 2009*a^2*b^7*c^4*d^5 - 980*a^3*b^6*c^3*d^6 + 406*a^4*b^5*c^2*d^7))/(32*(a^2*b^6*c^10 + a^8*c^4*d^6 - 6*a^3*b^5*c^9*d - 6*a^7*b*c^5*d^5 + 15*a^4*b^4*c^8*d^2 - 20*a^5*b^3*c^7*d^3 + 15*a^6*b^2*c^6*d^4)) + ((7*a*d - b*c)*(-a^3*b^5)^(1/2)*((2*a*b^13*c^13*d^2 - 28*a^2*b^12*c^12*d^3 + (315*a^3*b^11*c^11*d^4)/2 - (987*a^4*b^10*c^10*d^5)/2 + 978*a^5*b^9*c^9*d^6 - 1302*a^6*b^8*c^8*d^7 + 1197*a^7*b^7*c^7*d^8 - 765*a^8*b^6*c^6*d^9 + 336*a^9*b^5*c^5*d^10 - 98*a^10*b^4*c^4*d^11 + (35*a^11*b^3*c^3*d^12)/2 - (3*a^12*b^2*c^2*d^13)/2)/(a^2*b^9*c^13 - a^11*c^4*d^9 - 9*a^3*b^8*c^12*d + 9*a^10*b*c^5*d^8 + 36*a^4*b^7*c^11*d^2 - 84*a^5*b^6*c^10*d^3 + 126*a^6*b^5*c^9*d^4 - 126*a^7*b^4*c^8*d^5 + 84*a^8*b^3*c^7*d^6 - 36*a^9*b^2*c^6*d^7) + (x*(7*a*d - b*c)*(-a^3*b^5)^(1/2)*(256*a^2*b^11*c^13*d^2 - 1792*a^3*b^10*c^12*d^3 + 5120*a^4*b^9*c^11*d^4 - 7168*a^5*b^8*c^10*d^5 + 3584*a^6*b^7*c^9*d^6 + 3584*a^7*b^6*c^8*d^7 - 7168*a^8*b^5*c^7*d^8 + 5120*a^9*b^4*c^6*d^9 - 1792*a^10*b^3*c^5*d^10 + 256*a^11*b^2*c^4*d^11))/(128*(a^7*d^4 + a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3)*(a^2*b^6*c^10 + a^8*c^4*d^6 - 6*a^3*b^5*c^9*d - 6*a^7*b*c^5*d^5 + 15*a^4*b^4*c^8*d^2 - 20*a^5*b^3*c^7*d^3 + 15*a^6*b^2*c^6*d^4))))/(4*(a^7*d^4 + a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3)))*(7*a*d - b*c)*(-a^3*b^5)^(1/2)*1i)/(4*(a^7*d^4 + a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3)))/(((63*a^5*b^5*d^9)/64 + (35*b^10*c^5*d^4)/16 - (651*a*b^9*c^4*d^5)/64 - (267*a^4*b^6*c*d^8)/32 - (1275*a^2*b^8*c^3*d^6)/32 + (451*a^3*b^7*c^2*d^7)/16)/(a^2*b^9*c^13 - a^11*c^4*d^9 - 9*a^3*b^8*c^12*d + 9*a^10*b*c^5*d^8 + 36*a^4*b^7*c^11*d^2 - 84*a^5*b^6*c^10*d^3 + 126*a^6*b^5*c^9*d^4 - 126*a^7*b^4*c^8*d^5 + 84*a^8*b^3*c^7*d^6 - 36*a^9*b^2*c^6*d^7) - (((x*(9*a^6*b^3*d^9 + 16*b^9*c^6*d^3 - 224*a*b^8*c^5*d^4 - 84*a^5*b^4*c*d^8 + 2009*a^2*b^7*c^4*d^5 - 980*a^3*b^6*c^3*d^6 + 406*a^4*b^5*c^2*d^7))/(32*(a^2*b^6*c^10 + a^8*c^4*d^6 - 6*a^3*b^5*c^9*d - 6*a^7*b*c^5*d^5 + 15*a^4*b^4*c^8*d^2 - 20*a^5*b^3*c^7*d^3 + 15*a^6*b^2*c^6*d^4)) - ((7*a*d - b*c)*(-a^3*b^5)^(1/2)*((2*a*b^13*c^13*d^2 - 28*a^2*b^12*c^12*d^3 + (315*a^3*b^11*c^11*d^4)/2 - (987*a^4*b^10*c^10*d^5)/2 + 978*a^5*b^9*c^9*d^6 - 1302*a^6*b^8*c^8*d^7 + 1197*a^7*b^7*c^7*d^8 - 765*a^8*b^6*c^6*d^9 + 336*a^9*b^5*c^5*d^10 - 98*a^10*b^4*c^4*d^11 + (35*a^11*b^3*c^3*d^12)/2 - (3*a^12*b^2*c^2*d^13)/2)/(a^2*b^9*c^13 - a^11*c^4*d^9 - 9*a^3*b^8*c^12*d + 9*a^10*b*c^5*d^8 + 36*a^4*b^7*c^11*d^2 - 84*a^5*b^6*c^10*d^3 + 126*a^6*b^5*c^9*d^4 - 126*a^7*b^4*c^8*d^5 + 84*a^8*b^3*c^7*d^6 - 36*a^9*b^2*c^6*d^7) - (x*(7*a*d - b*c)*(-a^3*b^5)^(1/2)*(256*a^2*b^11*c^13*d^2 - 1792*a^3*b^10*c^12*d^3 + 5120*a^4*b^9*c^11*d^4 - 7168*a^5*b^8*c^10*d^5 + 3584*a^6*b^7*c^9*d^6 + 3584*a^7*b^6*c^8*d^7 - 7168*a^8*b^5*c^7*d^8 + 5120*a^9*b^4*c^6*d^9 - 1792*a^10*b^3*c^5*d^10 + 256*a^11*b^2*c^4*d^11))/(128*(a^7*d^4 + a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3)*(a^2*b^6*c^10 + a^8*c^4*d^6 - 6*a^3*b^5*c^9*d - 6*a^7*b*c^5*d^5 + 15*a^4*b^4*c^8*d^2 - 20*a^5*b^3*c^7*d^3 + 15*a^6*b^2*c^6*d^4))))/(4*(a^7*d^4 + a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3)))*(7*a*d - b*c)*(-a^3*b^5)^(1/2))/(4*(a^7*d^4 + a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3)) + (((x*(9*a^6*b^3*d^9 + 16*b^9*c^6*d^3 - 224*a*b^8*c^5*d^4 - 84*a^5*b^4*c*d^8 + 2009*a^2*b^7*c^4*d^5 - 980*a^3*b^6*c^3*d^6 + 406*a^4*b^5*c^2*d^7))/(32*(a^2*b^6*c^10 + a^8*c^4*d^6 - 6*a^3*b^5*c^9*d - 6*a^7*b*c^5*d^5 + 15*a^4*b^4*c^8*d^2 - 20*a^5*b^3*c^7*d^3 + 15*a^6*b^2*c^6*d^4)) + ((7*a*d - b*c)*(-a^3*b^5)^(1/2)*((2*a*b^13*c^13*d^2 - 28*a^2*b^12*c^12*d^3 + (315*a^3*b^11*c^11*d^4)/2 - (987*a^4*b^10*c^10*d^5)/2 + 978*a^5*b^9*c^9*d^6 - 1302*a^6*b^8*c^8*d^7 + 1197*a^7*b^7*c^7*d^8 - 765*a^8*b^6*c^6*d^9 + 336*a^9*b^5*c^5*d^10 - 98*a^10*b^4*c^4*d^11 + (35*a^11*b^3*c^3*d^12)/2 - (3*a^12*b^2*c^2*d^13)/2)/(a^2*b^9*c^13 - a^11*c^4*d^9 - 9*a^3*b^8*c^12*d + 9*a^10*b*c^5*d^8 + 36*a^4*b^7*c^11*d^2 - 84*a^5*b^6*c^10*d^3 + 126*a^6*b^5*c^9*d^4 - 126*a^7*b^4*c^8*d^5 + 84*a^8*b^3*c^7*d^6 - 36*a^9*b^2*c^6*d^7) + (x*(7*a*d - b*c)*(-a^3*b^5)^(1/2)*(256*a^2*b^11*c^13*d^2 - 1792*a^3*b^10*c^12*d^3 + 5120*a^4*b^9*c^11*d^4 - 7168*a^5*b^8*c^10*d^5 + 3584*a^6*b^7*c^9*d^6 + 3584*a^7*b^6*c^8*d^7 - 7168*a^8*b^5*c^7*d^8 + 5120*a^9*b^4*c^6*d^9 - 1792*a^10*b^3*c^5*d^10 + 256*a^11*b^2*c^4*d^11))/(128*(a^7*d^4 + a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3)*(a^2*b^6*c^10 + a^8*c^4*d^6 - 6*a^3*b^5*c^9*d - 6*a^7*b*c^5*d^5 + 15*a^4*b^4*c^8*d^2 - 20*a^5*b^3*c^7*d^3 + 15*a^6*b^2*c^6*d^4))))/(4*(a^7*d^4 + a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3)))*(7*a*d - b*c)*(-a^3*b^5)^(1/2))/(4*(a^7*d^4 + a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3))))*(7*a*d - b*c)*(-a^3*b^5)^(1/2)*1i)/(2*(a^7*d^4 + a^3*b^4*c^4 - 4*a^4*b^3*c^3*d + 6*a^5*b^2*c^2*d^2 - 4*a^6*b*c*d^3))","B"
315,1,472,192,2.069841,"\text{Not used}","int(1/(x*(a + b*x^2)^2*(c + d*x^2)^3),x)","\frac{\ln\left(x\right)}{a^2\,c^3}-\frac{\ln\left(b\,x^2+a\right)\,\left(b^4\,c-4\,a\,b^3\,d\right)}{2\,a^6\,d^4-8\,a^5\,b\,c\,d^3+12\,a^4\,b^2\,c^2\,d^2-8\,a^3\,b^3\,c^3\,d+2\,a^2\,b^4\,c^4}-\frac{\ln\left(d\,x^2+c\right)\,\left(a^2\,d^4-4\,a\,b\,c\,d^3+6\,b^2\,c^2\,d^2\right)}{2\,a^4\,c^3\,d^4-8\,a^3\,b\,c^4\,d^3+12\,a^2\,b^2\,c^5\,d^2-8\,a\,b^3\,c^6\,d+2\,b^4\,c^7}-\frac{\frac{-3\,a^3\,d^3+7\,a^2\,b\,c\,d^2+2\,b^3\,c^3}{4\,a\,c\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)}+\frac{x^2\,\left(-2\,a^3\,d^4+3\,a^2\,b\,c\,d^3+7\,a\,b^2\,c^2\,d^2+4\,b^3\,c^3\,d\right)}{4\,a\,c^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)}+\frac{b\,d^2\,x^4\,\left(-a^2\,d^2+3\,a\,b\,c\,d+b^2\,c^2\right)}{2\,a\,c^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^2+x^2\,\left(b\,c^2+2\,a\,d\,c\right)+x^4\,\left(a\,d^2+2\,b\,c\,d\right)+b\,d^2\,x^6}","Not used",1,"log(x)/(a^2*c^3) - (log(a + b*x^2)*(b^4*c - 4*a*b^3*d))/(2*a^6*d^4 + 2*a^2*b^4*c^4 - 8*a^3*b^3*c^3*d + 12*a^4*b^2*c^2*d^2 - 8*a^5*b*c*d^3) - (log(c + d*x^2)*(a^2*d^4 + 6*b^2*c^2*d^2 - 4*a*b*c*d^3))/(2*b^4*c^7 + 2*a^4*c^3*d^4 - 8*a^3*b*c^4*d^3 + 12*a^2*b^2*c^5*d^2 - 8*a*b^3*c^6*d) - ((2*b^3*c^3 - 3*a^3*d^3 + 7*a^2*b*c*d^2)/(4*a*c*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)) + (x^2*(4*b^3*c^3*d - 2*a^3*d^4 + 7*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3))/(4*a*c^2*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)) + (b*d^2*x^4*(b^2*c^2 - a^2*d^2 + 3*a*b*c*d))/(2*a*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^2 + x^2*(b*c^2 + 2*a*c*d) + x^4*(a*d^2 + 2*b*c*d) + b*d^2*x^6)","B"
316,1,5060,297,2.804124,"\text{Not used}","int(1/(x^2*(a + b*x^2)^2*(c + d*x^2)^3),x)","-\frac{\frac{1}{a\,c}+\frac{3\,x^6\,\left(5\,a^3\,b\,d^5-13\,a^2\,b^2\,c\,d^4+8\,a\,b^3\,c^2\,d^3-4\,b^4\,c^3\,d^2\right)}{8\,a^2\,c^3\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)}+\frac{x^2\,\left(25\,a^4\,d^4-57\,a^3\,b\,c\,d^3+24\,a^2\,b^2\,c^2\,d^2+8\,a\,b^3\,c^3\,d-12\,b^4\,c^4\right)}{8\,a^2\,c^2\,\left(a\,d-b\,c\right)\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}-\frac{d\,x^4\,\left(-15\,a^4\,d^4+14\,a^3\,b\,c\,d^3+41\,a^2\,b^2\,c^2\,d^2-40\,a\,b^3\,c^3\,d+24\,b^4\,c^4\right)}{8\,a^2\,c^3\,\left(a\,d-b\,c\right)\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}}{x^3\,\left(b\,c^2+2\,a\,d\,c\right)+x^5\,\left(a\,d^2+2\,b\,c\,d\right)+b\,d^2\,x^7+a\,c^2\,x}-\frac{\mathrm{atan}\left(\frac{\frac{\left(x\,\left(-230400\,a^{23}\,b^3\,c^9\,d^{20}+3732480\,a^{22}\,b^4\,c^{10}\,d^{19}-28145664\,a^{21}\,b^5\,c^{11}\,d^{18}+130332672\,a^{20}\,b^6\,c^{12}\,d^{17}-412314624\,a^{19}\,b^7\,c^{13}\,d^{16}+938843136\,a^{18}\,b^8\,c^{14}\,d^{15}-1581355008\,a^{17}\,b^9\,c^{15}\,d^{14}+1999835136\,a^{16}\,b^{10}\,c^{16}\,d^{13}-1921047552\,a^{15}\,b^{11}\,c^{17}\,d^{12}+1434332160\,a^{14}\,b^{12}\,c^{18}\,d^{11}-885012480\,a^{13}\,b^{13}\,c^{19}\,d^{10}+505018368\,a^{12}\,b^{14}\,c^{20}\,d^9-285078528\,a^{11}\,b^{15}\,c^{21}\,d^8+144737280\,a^{10}\,b^{16}\,c^{22}\,d^7-56180736\,a^9\,b^{17}\,c^{23}\,d^6+14598144\,a^8\,b^{18}\,c^{24}\,d^5-2211840\,a^7\,b^{19}\,c^{25}\,d^4+147456\,a^6\,b^{20}\,c^{26}\,d^3\right)+\frac{3\,\left(3\,a\,d-b\,c\right)\,\sqrt{-a^5\,b^7}\,\left(3145728\,a^9\,b^{19}\,c^{29}\,d^3-196608\,a^8\,b^{20}\,c^{30}\,d^2-23003136\,a^{10}\,b^{18}\,c^{28}\,d^4+101203968\,a^{11}\,b^{17}\,c^{27}\,d^5-294961152\,a^{12}\,b^{16}\,c^{26}\,d^6+582500352\,a^{13}\,b^{15}\,c^{25}\,d^7-729071616\,a^{14}\,b^{14}\,c^{24}\,d^8+339296256\,a^{15}\,b^{13}\,c^{23}\,d^9+766132224\,a^{16}\,b^{12}\,c^{22}\,d^{10}-2185936896\,a^{17}\,b^{11}\,c^{21}\,d^{11}+3127787520\,a^{18}\,b^{10}\,c^{20}\,d^{12}-3084337152\,a^{19}\,b^9\,c^{19}\,d^{13}+2249834496\,a^{20}\,b^8\,c^{18}\,d^{14}-1236221952\,a^{21}\,b^7\,c^{17}\,d^{15}+508674048\,a^{22}\,b^6\,c^{16}\,d^{16}-152715264\,a^{23}\,b^5\,c^{15}\,d^{17}+31703040\,a^{24}\,b^4\,c^{14}\,d^{18}-4079616\,a^{25}\,b^3\,c^{13}\,d^{19}+245760\,a^{26}\,b^2\,c^{12}\,d^{20}+\frac{3\,x\,\left(3\,a\,d-b\,c\right)\,\sqrt{-a^5\,b^7}\,\left(-262144\,a^{28}\,b^2\,c^{15}\,d^{20}+4194304\,a^{27}\,b^3\,c^{16}\,d^{19}-31195136\,a^{26}\,b^4\,c^{17}\,d^{18}+142606336\,a^{25}\,b^5\,c^{18}\,d^{17}-445644800\,a^{24}\,b^6\,c^{19}\,d^{16}+998244352\,a^{23}\,b^7\,c^{20}\,d^{15}-1622147072\,a^{22}\,b^8\,c^{21}\,d^{14}+1853882368\,a^{21}\,b^9\,c^{22}\,d^{13}-1274544128\,a^{20}\,b^{10}\,c^{23}\,d^{12}+1274544128\,a^{18}\,b^{12}\,c^{25}\,d^{10}-1853882368\,a^{17}\,b^{13}\,c^{26}\,d^9+1622147072\,a^{16}\,b^{14}\,c^{27}\,d^8-998244352\,a^{15}\,b^{15}\,c^{28}\,d^7+445644800\,a^{14}\,b^{16}\,c^{29}\,d^6-142606336\,a^{13}\,b^{17}\,c^{30}\,d^5+31195136\,a^{12}\,b^{18}\,c^{31}\,d^4-4194304\,a^{11}\,b^{19}\,c^{32}\,d^3+262144\,a^{10}\,b^{20}\,c^{33}\,d^2\right)}{4\,\left(a^9\,d^4-4\,a^8\,b\,c\,d^3+6\,a^7\,b^2\,c^2\,d^2-4\,a^6\,b^3\,c^3\,d+a^5\,b^4\,c^4\right)}\right)}{4\,\left(a^9\,d^4-4\,a^8\,b\,c\,d^3+6\,a^7\,b^2\,c^2\,d^2-4\,a^6\,b^3\,c^3\,d+a^5\,b^4\,c^4\right)}\right)\,\left(3\,a\,d-b\,c\right)\,\sqrt{-a^5\,b^7}\,3{}\mathrm{i}}{4\,\left(a^9\,d^4-4\,a^8\,b\,c\,d^3+6\,a^7\,b^2\,c^2\,d^2-4\,a^6\,b^3\,c^3\,d+a^5\,b^4\,c^4\right)}+\frac{\left(x\,\left(-230400\,a^{23}\,b^3\,c^9\,d^{20}+3732480\,a^{22}\,b^4\,c^{10}\,d^{19}-28145664\,a^{21}\,b^5\,c^{11}\,d^{18}+130332672\,a^{20}\,b^6\,c^{12}\,d^{17}-412314624\,a^{19}\,b^7\,c^{13}\,d^{16}+938843136\,a^{18}\,b^8\,c^{14}\,d^{15}-1581355008\,a^{17}\,b^9\,c^{15}\,d^{14}+1999835136\,a^{16}\,b^{10}\,c^{16}\,d^{13}-1921047552\,a^{15}\,b^{11}\,c^{17}\,d^{12}+1434332160\,a^{14}\,b^{12}\,c^{18}\,d^{11}-885012480\,a^{13}\,b^{13}\,c^{19}\,d^{10}+505018368\,a^{12}\,b^{14}\,c^{20}\,d^9-285078528\,a^{11}\,b^{15}\,c^{21}\,d^8+144737280\,a^{10}\,b^{16}\,c^{22}\,d^7-56180736\,a^9\,b^{17}\,c^{23}\,d^6+14598144\,a^8\,b^{18}\,c^{24}\,d^5-2211840\,a^7\,b^{19}\,c^{25}\,d^4+147456\,a^6\,b^{20}\,c^{26}\,d^3\right)+\frac{3\,\left(3\,a\,d-b\,c\right)\,\sqrt{-a^5\,b^7}\,\left(196608\,a^8\,b^{20}\,c^{30}\,d^2-3145728\,a^9\,b^{19}\,c^{29}\,d^3+23003136\,a^{10}\,b^{18}\,c^{28}\,d^4-101203968\,a^{11}\,b^{17}\,c^{27}\,d^5+294961152\,a^{12}\,b^{16}\,c^{26}\,d^6-582500352\,a^{13}\,b^{15}\,c^{25}\,d^7+729071616\,a^{14}\,b^{14}\,c^{24}\,d^8-339296256\,a^{15}\,b^{13}\,c^{23}\,d^9-766132224\,a^{16}\,b^{12}\,c^{22}\,d^{10}+2185936896\,a^{17}\,b^{11}\,c^{21}\,d^{11}-3127787520\,a^{18}\,b^{10}\,c^{20}\,d^{12}+3084337152\,a^{19}\,b^9\,c^{19}\,d^{13}-2249834496\,a^{20}\,b^8\,c^{18}\,d^{14}+1236221952\,a^{21}\,b^7\,c^{17}\,d^{15}-508674048\,a^{22}\,b^6\,c^{16}\,d^{16}+152715264\,a^{23}\,b^5\,c^{15}\,d^{17}-31703040\,a^{24}\,b^4\,c^{14}\,d^{18}+4079616\,a^{25}\,b^3\,c^{13}\,d^{19}-245760\,a^{26}\,b^2\,c^{12}\,d^{20}+\frac{3\,x\,\left(3\,a\,d-b\,c\right)\,\sqrt{-a^5\,b^7}\,\left(-262144\,a^{28}\,b^2\,c^{15}\,d^{20}+4194304\,a^{27}\,b^3\,c^{16}\,d^{19}-31195136\,a^{26}\,b^4\,c^{17}\,d^{18}+142606336\,a^{25}\,b^5\,c^{18}\,d^{17}-445644800\,a^{24}\,b^6\,c^{19}\,d^{16}+998244352\,a^{23}\,b^7\,c^{20}\,d^{15}-1622147072\,a^{22}\,b^8\,c^{21}\,d^{14}+1853882368\,a^{21}\,b^9\,c^{22}\,d^{13}-1274544128\,a^{20}\,b^{10}\,c^{23}\,d^{12}+1274544128\,a^{18}\,b^{12}\,c^{25}\,d^{10}-1853882368\,a^{17}\,b^{13}\,c^{26}\,d^9+1622147072\,a^{16}\,b^{14}\,c^{27}\,d^8-998244352\,a^{15}\,b^{15}\,c^{28}\,d^7+445644800\,a^{14}\,b^{16}\,c^{29}\,d^6-142606336\,a^{13}\,b^{17}\,c^{30}\,d^5+31195136\,a^{12}\,b^{18}\,c^{31}\,d^4-4194304\,a^{11}\,b^{19}\,c^{32}\,d^3+262144\,a^{10}\,b^{20}\,c^{33}\,d^2\right)}{4\,\left(a^9\,d^4-4\,a^8\,b\,c\,d^3+6\,a^7\,b^2\,c^2\,d^2-4\,a^6\,b^3\,c^3\,d+a^5\,b^4\,c^4\right)}\right)}{4\,\left(a^9\,d^4-4\,a^8\,b\,c\,d^3+6\,a^7\,b^2\,c^2\,d^2-4\,a^6\,b^3\,c^3\,d+a^5\,b^4\,c^4\right)}\right)\,\left(3\,a\,d-b\,c\right)\,\sqrt{-a^5\,b^7}\,3{}\mathrm{i}}{4\,\left(a^9\,d^4-4\,a^8\,b\,c\,d^3+6\,a^7\,b^2\,c^2\,d^2-4\,a^6\,b^3\,c^3\,d+a^5\,b^4\,c^4\right)}}{1161216\,a^6\,b^{18}\,c^{21}\,d^5-13768704\,a^7\,b^{17}\,c^{20}\,d^6+74221056\,a^8\,b^{16}\,c^{19}\,d^7-244574208\,a^9\,b^{15}\,c^{18}\,d^8+551397888\,a^{10}\,b^{14}\,c^{17}\,d^9-893251584\,a^{11}\,b^{13}\,c^{16}\,d^{10}+1058724864\,a^{12}\,b^{12}\,c^{15}\,d^{11}-918245376\,a^{13}\,b^{11}\,c^{14}\,d^{12}+575106048\,a^{14}\,b^{10}\,c^{13}\,d^{13}-252868608\,a^{15}\,b^9\,c^{12}\,d^{14}+74055168\,a^{16}\,b^8\,c^{11}\,d^{15}-12994560\,a^{17}\,b^7\,c^{10}\,d^{16}+1036800\,a^{18}\,b^6\,c^9\,d^{17}-\frac{3\,\left(x\,\left(-230400\,a^{23}\,b^3\,c^9\,d^{20}+3732480\,a^{22}\,b^4\,c^{10}\,d^{19}-28145664\,a^{21}\,b^5\,c^{11}\,d^{18}+130332672\,a^{20}\,b^6\,c^{12}\,d^{17}-412314624\,a^{19}\,b^7\,c^{13}\,d^{16}+938843136\,a^{18}\,b^8\,c^{14}\,d^{15}-1581355008\,a^{17}\,b^9\,c^{15}\,d^{14}+1999835136\,a^{16}\,b^{10}\,c^{16}\,d^{13}-1921047552\,a^{15}\,b^{11}\,c^{17}\,d^{12}+1434332160\,a^{14}\,b^{12}\,c^{18}\,d^{11}-885012480\,a^{13}\,b^{13}\,c^{19}\,d^{10}+505018368\,a^{12}\,b^{14}\,c^{20}\,d^9-285078528\,a^{11}\,b^{15}\,c^{21}\,d^8+144737280\,a^{10}\,b^{16}\,c^{22}\,d^7-56180736\,a^9\,b^{17}\,c^{23}\,d^6+14598144\,a^8\,b^{18}\,c^{24}\,d^5-2211840\,a^7\,b^{19}\,c^{25}\,d^4+147456\,a^6\,b^{20}\,c^{26}\,d^3\right)+\frac{3\,\left(3\,a\,d-b\,c\right)\,\sqrt{-a^5\,b^7}\,\left(3145728\,a^9\,b^{19}\,c^{29}\,d^3-196608\,a^8\,b^{20}\,c^{30}\,d^2-23003136\,a^{10}\,b^{18}\,c^{28}\,d^4+101203968\,a^{11}\,b^{17}\,c^{27}\,d^5-294961152\,a^{12}\,b^{16}\,c^{26}\,d^6+582500352\,a^{13}\,b^{15}\,c^{25}\,d^7-729071616\,a^{14}\,b^{14}\,c^{24}\,d^8+339296256\,a^{15}\,b^{13}\,c^{23}\,d^9+766132224\,a^{16}\,b^{12}\,c^{22}\,d^{10}-2185936896\,a^{17}\,b^{11}\,c^{21}\,d^{11}+3127787520\,a^{18}\,b^{10}\,c^{20}\,d^{12}-3084337152\,a^{19}\,b^9\,c^{19}\,d^{13}+2249834496\,a^{20}\,b^8\,c^{18}\,d^{14}-1236221952\,a^{21}\,b^7\,c^{17}\,d^{15}+508674048\,a^{22}\,b^6\,c^{16}\,d^{16}-152715264\,a^{23}\,b^5\,c^{15}\,d^{17}+31703040\,a^{24}\,b^4\,c^{14}\,d^{18}-4079616\,a^{25}\,b^3\,c^{13}\,d^{19}+245760\,a^{26}\,b^2\,c^{12}\,d^{20}+\frac{3\,x\,\left(3\,a\,d-b\,c\right)\,\sqrt{-a^5\,b^7}\,\left(-262144\,a^{28}\,b^2\,c^{15}\,d^{20}+4194304\,a^{27}\,b^3\,c^{16}\,d^{19}-31195136\,a^{26}\,b^4\,c^{17}\,d^{18}+142606336\,a^{25}\,b^5\,c^{18}\,d^{17}-445644800\,a^{24}\,b^6\,c^{19}\,d^{16}+998244352\,a^{23}\,b^7\,c^{20}\,d^{15}-1622147072\,a^{22}\,b^8\,c^{21}\,d^{14}+1853882368\,a^{21}\,b^9\,c^{22}\,d^{13}-1274544128\,a^{20}\,b^{10}\,c^{23}\,d^{12}+1274544128\,a^{18}\,b^{12}\,c^{25}\,d^{10}-1853882368\,a^{17}\,b^{13}\,c^{26}\,d^9+1622147072\,a^{16}\,b^{14}\,c^{27}\,d^8-998244352\,a^{15}\,b^{15}\,c^{28}\,d^7+445644800\,a^{14}\,b^{16}\,c^{29}\,d^6-142606336\,a^{13}\,b^{17}\,c^{30}\,d^5+31195136\,a^{12}\,b^{18}\,c^{31}\,d^4-4194304\,a^{11}\,b^{19}\,c^{32}\,d^3+262144\,a^{10}\,b^{20}\,c^{33}\,d^2\right)}{4\,\left(a^9\,d^4-4\,a^8\,b\,c\,d^3+6\,a^7\,b^2\,c^2\,d^2-4\,a^6\,b^3\,c^3\,d+a^5\,b^4\,c^4\right)}\right)}{4\,\left(a^9\,d^4-4\,a^8\,b\,c\,d^3+6\,a^7\,b^2\,c^2\,d^2-4\,a^6\,b^3\,c^3\,d+a^5\,b^4\,c^4\right)}\right)\,\left(3\,a\,d-b\,c\right)\,\sqrt{-a^5\,b^7}}{4\,\left(a^9\,d^4-4\,a^8\,b\,c\,d^3+6\,a^7\,b^2\,c^2\,d^2-4\,a^6\,b^3\,c^3\,d+a^5\,b^4\,c^4\right)}+\frac{3\,\left(x\,\left(-230400\,a^{23}\,b^3\,c^9\,d^{20}+3732480\,a^{22}\,b^4\,c^{10}\,d^{19}-28145664\,a^{21}\,b^5\,c^{11}\,d^{18}+130332672\,a^{20}\,b^6\,c^{12}\,d^{17}-412314624\,a^{19}\,b^7\,c^{13}\,d^{16}+938843136\,a^{18}\,b^8\,c^{14}\,d^{15}-1581355008\,a^{17}\,b^9\,c^{15}\,d^{14}+1999835136\,a^{16}\,b^{10}\,c^{16}\,d^{13}-1921047552\,a^{15}\,b^{11}\,c^{17}\,d^{12}+1434332160\,a^{14}\,b^{12}\,c^{18}\,d^{11}-885012480\,a^{13}\,b^{13}\,c^{19}\,d^{10}+505018368\,a^{12}\,b^{14}\,c^{20}\,d^9-285078528\,a^{11}\,b^{15}\,c^{21}\,d^8+144737280\,a^{10}\,b^{16}\,c^{22}\,d^7-56180736\,a^9\,b^{17}\,c^{23}\,d^6+14598144\,a^8\,b^{18}\,c^{24}\,d^5-2211840\,a^7\,b^{19}\,c^{25}\,d^4+147456\,a^6\,b^{20}\,c^{26}\,d^3\right)+\frac{3\,\left(3\,a\,d-b\,c\right)\,\sqrt{-a^5\,b^7}\,\left(196608\,a^8\,b^{20}\,c^{30}\,d^2-3145728\,a^9\,b^{19}\,c^{29}\,d^3+23003136\,a^{10}\,b^{18}\,c^{28}\,d^4-101203968\,a^{11}\,b^{17}\,c^{27}\,d^5+294961152\,a^{12}\,b^{16}\,c^{26}\,d^6-582500352\,a^{13}\,b^{15}\,c^{25}\,d^7+729071616\,a^{14}\,b^{14}\,c^{24}\,d^8-339296256\,a^{15}\,b^{13}\,c^{23}\,d^9-766132224\,a^{16}\,b^{12}\,c^{22}\,d^{10}+2185936896\,a^{17}\,b^{11}\,c^{21}\,d^{11}-3127787520\,a^{18}\,b^{10}\,c^{20}\,d^{12}+3084337152\,a^{19}\,b^9\,c^{19}\,d^{13}-2249834496\,a^{20}\,b^8\,c^{18}\,d^{14}+1236221952\,a^{21}\,b^7\,c^{17}\,d^{15}-508674048\,a^{22}\,b^6\,c^{16}\,d^{16}+152715264\,a^{23}\,b^5\,c^{15}\,d^{17}-31703040\,a^{24}\,b^4\,c^{14}\,d^{18}+4079616\,a^{25}\,b^3\,c^{13}\,d^{19}-245760\,a^{26}\,b^2\,c^{12}\,d^{20}+\frac{3\,x\,\left(3\,a\,d-b\,c\right)\,\sqrt{-a^5\,b^7}\,\left(-262144\,a^{28}\,b^2\,c^{15}\,d^{20}+4194304\,a^{27}\,b^3\,c^{16}\,d^{19}-31195136\,a^{26}\,b^4\,c^{17}\,d^{18}+142606336\,a^{25}\,b^5\,c^{18}\,d^{17}-445644800\,a^{24}\,b^6\,c^{19}\,d^{16}+998244352\,a^{23}\,b^7\,c^{20}\,d^{15}-1622147072\,a^{22}\,b^8\,c^{21}\,d^{14}+1853882368\,a^{21}\,b^9\,c^{22}\,d^{13}-1274544128\,a^{20}\,b^{10}\,c^{23}\,d^{12}+1274544128\,a^{18}\,b^{12}\,c^{25}\,d^{10}-1853882368\,a^{17}\,b^{13}\,c^{26}\,d^9+1622147072\,a^{16}\,b^{14}\,c^{27}\,d^8-998244352\,a^{15}\,b^{15}\,c^{28}\,d^7+445644800\,a^{14}\,b^{16}\,c^{29}\,d^6-142606336\,a^{13}\,b^{17}\,c^{30}\,d^5+31195136\,a^{12}\,b^{18}\,c^{31}\,d^4-4194304\,a^{11}\,b^{19}\,c^{32}\,d^3+262144\,a^{10}\,b^{20}\,c^{33}\,d^2\right)}{4\,\left(a^9\,d^4-4\,a^8\,b\,c\,d^3+6\,a^7\,b^2\,c^2\,d^2-4\,a^6\,b^3\,c^3\,d+a^5\,b^4\,c^4\right)}\right)}{4\,\left(a^9\,d^4-4\,a^8\,b\,c\,d^3+6\,a^7\,b^2\,c^2\,d^2-4\,a^6\,b^3\,c^3\,d+a^5\,b^4\,c^4\right)}\right)\,\left(3\,a\,d-b\,c\right)\,\sqrt{-a^5\,b^7}}{4\,\left(a^9\,d^4-4\,a^8\,b\,c\,d^3+6\,a^7\,b^2\,c^2\,d^2-4\,a^6\,b^3\,c^3\,d+a^5\,b^4\,c^4\right)}}\right)\,\left(3\,a\,d-b\,c\right)\,\sqrt{-a^5\,b^7}\,3{}\mathrm{i}}{2\,\left(a^9\,d^4-4\,a^8\,b\,c\,d^3+6\,a^7\,b^2\,c^2\,d^2-4\,a^6\,b^3\,c^3\,d+a^5\,b^4\,c^4\right)}+\frac{\mathrm{atan}\left(\frac{a^9\,d^5\,x\,{\left(-c^7\,d^5\right)}^{3/2}\,25{}\mathrm{i}+b^9\,c^{16}\,d\,x\,\sqrt{-c^7\,d^5}\,16{}\mathrm{i}-a^6\,b^3\,c^3\,d^2\,x\,{\left(-c^7\,d^5\right)}^{3/2}\,756{}\mathrm{i}+a^7\,b^2\,c^2\,d^3\,x\,{\left(-c^7\,d^5\right)}^{3/2}\,534{}\mathrm{i}+a^2\,b^7\,c^{14}\,d^3\,x\,\sqrt{-c^7\,d^5}\,144{}\mathrm{i}-a^8\,b\,c\,d^4\,x\,{\left(-c^7\,d^5\right)}^{3/2}\,180{}\mathrm{i}+a^5\,b^4\,c^4\,d\,x\,{\left(-c^7\,d^5\right)}^{3/2}\,441{}\mathrm{i}-a\,b^8\,c^{15}\,d^2\,x\,\sqrt{-c^7\,d^5}\,96{}\mathrm{i}}{25\,a^9\,c^{11}\,d^{12}-180\,a^8\,b\,c^{12}\,d^{11}+534\,a^7\,b^2\,c^{13}\,d^{10}-756\,a^6\,b^3\,c^{14}\,d^9+441\,a^5\,b^4\,c^{15}\,d^8-144\,a^2\,b^7\,c^{18}\,d^5+96\,a\,b^8\,c^{19}\,d^4-16\,b^9\,c^{20}\,d^3}\right)\,\sqrt{-c^7\,d^5}\,\left(5\,a^2\,d^2-18\,a\,b\,c\,d+21\,b^2\,c^2\right)\,3{}\mathrm{i}}{8\,\left(a^4\,c^7\,d^4-4\,a^3\,b\,c^8\,d^3+6\,a^2\,b^2\,c^9\,d^2-4\,a\,b^3\,c^{10}\,d+b^4\,c^{11}\right)}","Not used",1,"(atan((a^9*d^5*x*(-c^7*d^5)^(3/2)*25i + b^9*c^16*d*x*(-c^7*d^5)^(1/2)*16i - a^6*b^3*c^3*d^2*x*(-c^7*d^5)^(3/2)*756i + a^7*b^2*c^2*d^3*x*(-c^7*d^5)^(3/2)*534i + a^2*b^7*c^14*d^3*x*(-c^7*d^5)^(1/2)*144i - a^8*b*c*d^4*x*(-c^7*d^5)^(3/2)*180i + a^5*b^4*c^4*d*x*(-c^7*d^5)^(3/2)*441i - a*b^8*c^15*d^2*x*(-c^7*d^5)^(1/2)*96i)/(25*a^9*c^11*d^12 - 16*b^9*c^20*d^3 + 96*a*b^8*c^19*d^4 - 180*a^8*b*c^12*d^11 - 144*a^2*b^7*c^18*d^5 + 441*a^5*b^4*c^15*d^8 - 756*a^6*b^3*c^14*d^9 + 534*a^7*b^2*c^13*d^10))*(-c^7*d^5)^(1/2)*(5*a^2*d^2 + 21*b^2*c^2 - 18*a*b*c*d)*3i)/(8*(b^4*c^11 + a^4*c^7*d^4 - 4*a^3*b*c^8*d^3 + 6*a^2*b^2*c^9*d^2 - 4*a*b^3*c^10*d)) - (atan((((x*(147456*a^6*b^20*c^26*d^3 - 2211840*a^7*b^19*c^25*d^4 + 14598144*a^8*b^18*c^24*d^5 - 56180736*a^9*b^17*c^23*d^6 + 144737280*a^10*b^16*c^22*d^7 - 285078528*a^11*b^15*c^21*d^8 + 505018368*a^12*b^14*c^20*d^9 - 885012480*a^13*b^13*c^19*d^10 + 1434332160*a^14*b^12*c^18*d^11 - 1921047552*a^15*b^11*c^17*d^12 + 1999835136*a^16*b^10*c^16*d^13 - 1581355008*a^17*b^9*c^15*d^14 + 938843136*a^18*b^8*c^14*d^15 - 412314624*a^19*b^7*c^13*d^16 + 130332672*a^20*b^6*c^12*d^17 - 28145664*a^21*b^5*c^11*d^18 + 3732480*a^22*b^4*c^10*d^19 - 230400*a^23*b^3*c^9*d^20) + (3*(3*a*d - b*c)*(-a^5*b^7)^(1/2)*(3145728*a^9*b^19*c^29*d^3 - 196608*a^8*b^20*c^30*d^2 - 23003136*a^10*b^18*c^28*d^4 + 101203968*a^11*b^17*c^27*d^5 - 294961152*a^12*b^16*c^26*d^6 + 582500352*a^13*b^15*c^25*d^7 - 729071616*a^14*b^14*c^24*d^8 + 339296256*a^15*b^13*c^23*d^9 + 766132224*a^16*b^12*c^22*d^10 - 2185936896*a^17*b^11*c^21*d^11 + 3127787520*a^18*b^10*c^20*d^12 - 3084337152*a^19*b^9*c^19*d^13 + 2249834496*a^20*b^8*c^18*d^14 - 1236221952*a^21*b^7*c^17*d^15 + 508674048*a^22*b^6*c^16*d^16 - 152715264*a^23*b^5*c^15*d^17 + 31703040*a^24*b^4*c^14*d^18 - 4079616*a^25*b^3*c^13*d^19 + 245760*a^26*b^2*c^12*d^20 + (3*x*(3*a*d - b*c)*(-a^5*b^7)^(1/2)*(262144*a^10*b^20*c^33*d^2 - 4194304*a^11*b^19*c^32*d^3 + 31195136*a^12*b^18*c^31*d^4 - 142606336*a^13*b^17*c^30*d^5 + 445644800*a^14*b^16*c^29*d^6 - 998244352*a^15*b^15*c^28*d^7 + 1622147072*a^16*b^14*c^27*d^8 - 1853882368*a^17*b^13*c^26*d^9 + 1274544128*a^18*b^12*c^25*d^10 - 1274544128*a^20*b^10*c^23*d^12 + 1853882368*a^21*b^9*c^22*d^13 - 1622147072*a^22*b^8*c^21*d^14 + 998244352*a^23*b^7*c^20*d^15 - 445644800*a^24*b^6*c^19*d^16 + 142606336*a^25*b^5*c^18*d^17 - 31195136*a^26*b^4*c^17*d^18 + 4194304*a^27*b^3*c^16*d^19 - 262144*a^28*b^2*c^15*d^20))/(4*(a^9*d^4 + a^5*b^4*c^4 - 4*a^6*b^3*c^3*d + 6*a^7*b^2*c^2*d^2 - 4*a^8*b*c*d^3))))/(4*(a^9*d^4 + a^5*b^4*c^4 - 4*a^6*b^3*c^3*d + 6*a^7*b^2*c^2*d^2 - 4*a^8*b*c*d^3)))*(3*a*d - b*c)*(-a^5*b^7)^(1/2)*3i)/(4*(a^9*d^4 + a^5*b^4*c^4 - 4*a^6*b^3*c^3*d + 6*a^7*b^2*c^2*d^2 - 4*a^8*b*c*d^3)) + ((x*(147456*a^6*b^20*c^26*d^3 - 2211840*a^7*b^19*c^25*d^4 + 14598144*a^8*b^18*c^24*d^5 - 56180736*a^9*b^17*c^23*d^6 + 144737280*a^10*b^16*c^22*d^7 - 285078528*a^11*b^15*c^21*d^8 + 505018368*a^12*b^14*c^20*d^9 - 885012480*a^13*b^13*c^19*d^10 + 1434332160*a^14*b^12*c^18*d^11 - 1921047552*a^15*b^11*c^17*d^12 + 1999835136*a^16*b^10*c^16*d^13 - 1581355008*a^17*b^9*c^15*d^14 + 938843136*a^18*b^8*c^14*d^15 - 412314624*a^19*b^7*c^13*d^16 + 130332672*a^20*b^6*c^12*d^17 - 28145664*a^21*b^5*c^11*d^18 + 3732480*a^22*b^4*c^10*d^19 - 230400*a^23*b^3*c^9*d^20) + (3*(3*a*d - b*c)*(-a^5*b^7)^(1/2)*(196608*a^8*b^20*c^30*d^2 - 3145728*a^9*b^19*c^29*d^3 + 23003136*a^10*b^18*c^28*d^4 - 101203968*a^11*b^17*c^27*d^5 + 294961152*a^12*b^16*c^26*d^6 - 582500352*a^13*b^15*c^25*d^7 + 729071616*a^14*b^14*c^24*d^8 - 339296256*a^15*b^13*c^23*d^9 - 766132224*a^16*b^12*c^22*d^10 + 2185936896*a^17*b^11*c^21*d^11 - 3127787520*a^18*b^10*c^20*d^12 + 3084337152*a^19*b^9*c^19*d^13 - 2249834496*a^20*b^8*c^18*d^14 + 1236221952*a^21*b^7*c^17*d^15 - 508674048*a^22*b^6*c^16*d^16 + 152715264*a^23*b^5*c^15*d^17 - 31703040*a^24*b^4*c^14*d^18 + 4079616*a^25*b^3*c^13*d^19 - 245760*a^26*b^2*c^12*d^20 + (3*x*(3*a*d - b*c)*(-a^5*b^7)^(1/2)*(262144*a^10*b^20*c^33*d^2 - 4194304*a^11*b^19*c^32*d^3 + 31195136*a^12*b^18*c^31*d^4 - 142606336*a^13*b^17*c^30*d^5 + 445644800*a^14*b^16*c^29*d^6 - 998244352*a^15*b^15*c^28*d^7 + 1622147072*a^16*b^14*c^27*d^8 - 1853882368*a^17*b^13*c^26*d^9 + 1274544128*a^18*b^12*c^25*d^10 - 1274544128*a^20*b^10*c^23*d^12 + 1853882368*a^21*b^9*c^22*d^13 - 1622147072*a^22*b^8*c^21*d^14 + 998244352*a^23*b^7*c^20*d^15 - 445644800*a^24*b^6*c^19*d^16 + 142606336*a^25*b^5*c^18*d^17 - 31195136*a^26*b^4*c^17*d^18 + 4194304*a^27*b^3*c^16*d^19 - 262144*a^28*b^2*c^15*d^20))/(4*(a^9*d^4 + a^5*b^4*c^4 - 4*a^6*b^3*c^3*d + 6*a^7*b^2*c^2*d^2 - 4*a^8*b*c*d^3))))/(4*(a^9*d^4 + a^5*b^4*c^4 - 4*a^6*b^3*c^3*d + 6*a^7*b^2*c^2*d^2 - 4*a^8*b*c*d^3)))*(3*a*d - b*c)*(-a^5*b^7)^(1/2)*3i)/(4*(a^9*d^4 + a^5*b^4*c^4 - 4*a^6*b^3*c^3*d + 6*a^7*b^2*c^2*d^2 - 4*a^8*b*c*d^3)))/(1161216*a^6*b^18*c^21*d^5 - 13768704*a^7*b^17*c^20*d^6 + 74221056*a^8*b^16*c^19*d^7 - 244574208*a^9*b^15*c^18*d^8 + 551397888*a^10*b^14*c^17*d^9 - 893251584*a^11*b^13*c^16*d^10 + 1058724864*a^12*b^12*c^15*d^11 - 918245376*a^13*b^11*c^14*d^12 + 575106048*a^14*b^10*c^13*d^13 - 252868608*a^15*b^9*c^12*d^14 + 74055168*a^16*b^8*c^11*d^15 - 12994560*a^17*b^7*c^10*d^16 + 1036800*a^18*b^6*c^9*d^17 - (3*(x*(147456*a^6*b^20*c^26*d^3 - 2211840*a^7*b^19*c^25*d^4 + 14598144*a^8*b^18*c^24*d^5 - 56180736*a^9*b^17*c^23*d^6 + 144737280*a^10*b^16*c^22*d^7 - 285078528*a^11*b^15*c^21*d^8 + 505018368*a^12*b^14*c^20*d^9 - 885012480*a^13*b^13*c^19*d^10 + 1434332160*a^14*b^12*c^18*d^11 - 1921047552*a^15*b^11*c^17*d^12 + 1999835136*a^16*b^10*c^16*d^13 - 1581355008*a^17*b^9*c^15*d^14 + 938843136*a^18*b^8*c^14*d^15 - 412314624*a^19*b^7*c^13*d^16 + 130332672*a^20*b^6*c^12*d^17 - 28145664*a^21*b^5*c^11*d^18 + 3732480*a^22*b^4*c^10*d^19 - 230400*a^23*b^3*c^9*d^20) + (3*(3*a*d - b*c)*(-a^5*b^7)^(1/2)*(3145728*a^9*b^19*c^29*d^3 - 196608*a^8*b^20*c^30*d^2 - 23003136*a^10*b^18*c^28*d^4 + 101203968*a^11*b^17*c^27*d^5 - 294961152*a^12*b^16*c^26*d^6 + 582500352*a^13*b^15*c^25*d^7 - 729071616*a^14*b^14*c^24*d^8 + 339296256*a^15*b^13*c^23*d^9 + 766132224*a^16*b^12*c^22*d^10 - 2185936896*a^17*b^11*c^21*d^11 + 3127787520*a^18*b^10*c^20*d^12 - 3084337152*a^19*b^9*c^19*d^13 + 2249834496*a^20*b^8*c^18*d^14 - 1236221952*a^21*b^7*c^17*d^15 + 508674048*a^22*b^6*c^16*d^16 - 152715264*a^23*b^5*c^15*d^17 + 31703040*a^24*b^4*c^14*d^18 - 4079616*a^25*b^3*c^13*d^19 + 245760*a^26*b^2*c^12*d^20 + (3*x*(3*a*d - b*c)*(-a^5*b^7)^(1/2)*(262144*a^10*b^20*c^33*d^2 - 4194304*a^11*b^19*c^32*d^3 + 31195136*a^12*b^18*c^31*d^4 - 142606336*a^13*b^17*c^30*d^5 + 445644800*a^14*b^16*c^29*d^6 - 998244352*a^15*b^15*c^28*d^7 + 1622147072*a^16*b^14*c^27*d^8 - 1853882368*a^17*b^13*c^26*d^9 + 1274544128*a^18*b^12*c^25*d^10 - 1274544128*a^20*b^10*c^23*d^12 + 1853882368*a^21*b^9*c^22*d^13 - 1622147072*a^22*b^8*c^21*d^14 + 998244352*a^23*b^7*c^20*d^15 - 445644800*a^24*b^6*c^19*d^16 + 142606336*a^25*b^5*c^18*d^17 - 31195136*a^26*b^4*c^17*d^18 + 4194304*a^27*b^3*c^16*d^19 - 262144*a^28*b^2*c^15*d^20))/(4*(a^9*d^4 + a^5*b^4*c^4 - 4*a^6*b^3*c^3*d + 6*a^7*b^2*c^2*d^2 - 4*a^8*b*c*d^3))))/(4*(a^9*d^4 + a^5*b^4*c^4 - 4*a^6*b^3*c^3*d + 6*a^7*b^2*c^2*d^2 - 4*a^8*b*c*d^3)))*(3*a*d - b*c)*(-a^5*b^7)^(1/2))/(4*(a^9*d^4 + a^5*b^4*c^4 - 4*a^6*b^3*c^3*d + 6*a^7*b^2*c^2*d^2 - 4*a^8*b*c*d^3)) + (3*(x*(147456*a^6*b^20*c^26*d^3 - 2211840*a^7*b^19*c^25*d^4 + 14598144*a^8*b^18*c^24*d^5 - 56180736*a^9*b^17*c^23*d^6 + 144737280*a^10*b^16*c^22*d^7 - 285078528*a^11*b^15*c^21*d^8 + 505018368*a^12*b^14*c^20*d^9 - 885012480*a^13*b^13*c^19*d^10 + 1434332160*a^14*b^12*c^18*d^11 - 1921047552*a^15*b^11*c^17*d^12 + 1999835136*a^16*b^10*c^16*d^13 - 1581355008*a^17*b^9*c^15*d^14 + 938843136*a^18*b^8*c^14*d^15 - 412314624*a^19*b^7*c^13*d^16 + 130332672*a^20*b^6*c^12*d^17 - 28145664*a^21*b^5*c^11*d^18 + 3732480*a^22*b^4*c^10*d^19 - 230400*a^23*b^3*c^9*d^20) + (3*(3*a*d - b*c)*(-a^5*b^7)^(1/2)*(196608*a^8*b^20*c^30*d^2 - 3145728*a^9*b^19*c^29*d^3 + 23003136*a^10*b^18*c^28*d^4 - 101203968*a^11*b^17*c^27*d^5 + 294961152*a^12*b^16*c^26*d^6 - 582500352*a^13*b^15*c^25*d^7 + 729071616*a^14*b^14*c^24*d^8 - 339296256*a^15*b^13*c^23*d^9 - 766132224*a^16*b^12*c^22*d^10 + 2185936896*a^17*b^11*c^21*d^11 - 3127787520*a^18*b^10*c^20*d^12 + 3084337152*a^19*b^9*c^19*d^13 - 2249834496*a^20*b^8*c^18*d^14 + 1236221952*a^21*b^7*c^17*d^15 - 508674048*a^22*b^6*c^16*d^16 + 152715264*a^23*b^5*c^15*d^17 - 31703040*a^24*b^4*c^14*d^18 + 4079616*a^25*b^3*c^13*d^19 - 245760*a^26*b^2*c^12*d^20 + (3*x*(3*a*d - b*c)*(-a^5*b^7)^(1/2)*(262144*a^10*b^20*c^33*d^2 - 4194304*a^11*b^19*c^32*d^3 + 31195136*a^12*b^18*c^31*d^4 - 142606336*a^13*b^17*c^30*d^5 + 445644800*a^14*b^16*c^29*d^6 - 998244352*a^15*b^15*c^28*d^7 + 1622147072*a^16*b^14*c^27*d^8 - 1853882368*a^17*b^13*c^26*d^9 + 1274544128*a^18*b^12*c^25*d^10 - 1274544128*a^20*b^10*c^23*d^12 + 1853882368*a^21*b^9*c^22*d^13 - 1622147072*a^22*b^8*c^21*d^14 + 998244352*a^23*b^7*c^20*d^15 - 445644800*a^24*b^6*c^19*d^16 + 142606336*a^25*b^5*c^18*d^17 - 31195136*a^26*b^4*c^17*d^18 + 4194304*a^27*b^3*c^16*d^19 - 262144*a^28*b^2*c^15*d^20))/(4*(a^9*d^4 + a^5*b^4*c^4 - 4*a^6*b^3*c^3*d + 6*a^7*b^2*c^2*d^2 - 4*a^8*b*c*d^3))))/(4*(a^9*d^4 + a^5*b^4*c^4 - 4*a^6*b^3*c^3*d + 6*a^7*b^2*c^2*d^2 - 4*a^8*b*c*d^3)))*(3*a*d - b*c)*(-a^5*b^7)^(1/2))/(4*(a^9*d^4 + a^5*b^4*c^4 - 4*a^6*b^3*c^3*d + 6*a^7*b^2*c^2*d^2 - 4*a^8*b*c*d^3))))*(3*a*d - b*c)*(-a^5*b^7)^(1/2)*3i)/(2*(a^9*d^4 + a^5*b^4*c^4 - 4*a^6*b^3*c^3*d + 6*a^7*b^2*c^2*d^2 - 4*a^8*b*c*d^3)) - (1/(a*c) + (3*x^6*(5*a^3*b*d^5 - 4*b^4*c^3*d^2 + 8*a*b^3*c^2*d^3 - 13*a^2*b^2*c*d^4))/(8*a^2*c^3*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)) + (x^2*(25*a^4*d^4 - 12*b^4*c^4 + 24*a^2*b^2*c^2*d^2 + 8*a*b^3*c^3*d - 57*a^3*b*c*d^3))/(8*a^2*c^2*(a*d - b*c)*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) - (d*x^4*(24*b^4*c^4 - 15*a^4*d^4 + 41*a^2*b^2*c^2*d^2 - 40*a*b^3*c^3*d + 14*a^3*b*c*d^3))/(8*a^2*c^3*(a*d - b*c)*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)))/(x^3*(b*c^2 + 2*a*c*d) + x^5*(a*d^2 + 2*b*c*d) + b*d^2*x^7 + a*c^2*x)","B"
317,1,549,215,2.419665,"\text{Not used}","int(1/(x^3*(a + b*x^2)^2*(c + d*x^2)^3),x)","\frac{\ln\left(b\,x^2+a\right)\,\left(2\,b^5\,c-5\,a\,b^4\,d\right)}{2\,a^7\,d^4-8\,a^6\,b\,c\,d^3+12\,a^5\,b^2\,c^2\,d^2-8\,a^4\,b^3\,c^3\,d+2\,a^3\,b^4\,c^4}-\frac{\frac{1}{2\,a\,c}-\frac{x^4\,\left(-6\,a^4\,d^5+5\,a^3\,b\,c\,d^4+15\,a^2\,b^2\,c^2\,d^3-10\,a\,b^3\,c^3\,d^2+8\,b^4\,c^4\,d\right)}{4\,a^2\,c^3\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)}+\frac{x^2\,\left(9\,a^4\,d^4-19\,a^3\,b\,c\,d^3+6\,a^2\,b^2\,c^2\,d^2+2\,a\,b^3\,c^3\,d-4\,b^4\,c^4\right)}{4\,a^2\,c^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)}+\frac{b\,d^2\,x^6\,\left(3\,a^3\,d^3-7\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-2\,b^3\,c^3\right)}{2\,a^2\,c^3\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)}}{x^4\,\left(b\,c^2+2\,a\,d\,c\right)+x^6\,\left(a\,d^2+2\,b\,c\,d\right)+a\,c^2\,x^2+b\,d^2\,x^8}+\frac{\ln\left(d\,x^2+c\right)\,\left(3\,a^2\,d^5-10\,a\,b\,c\,d^4+10\,b^2\,c^2\,d^3\right)}{2\,a^4\,c^4\,d^4-8\,a^3\,b\,c^5\,d^3+12\,a^2\,b^2\,c^6\,d^2-8\,a\,b^3\,c^7\,d+2\,b^4\,c^8}-\frac{\ln\left(x\right)\,\left(3\,a\,d+2\,b\,c\right)}{a^3\,c^4}","Not used",1,"(log(a + b*x^2)*(2*b^5*c - 5*a*b^4*d))/(2*a^7*d^4 + 2*a^3*b^4*c^4 - 8*a^4*b^3*c^3*d + 12*a^5*b^2*c^2*d^2 - 8*a^6*b*c*d^3) - (1/(2*a*c) - (x^4*(8*b^4*c^4*d - 6*a^4*d^5 - 10*a*b^3*c^3*d^2 + 15*a^2*b^2*c^2*d^3 + 5*a^3*b*c*d^4))/(4*a^2*c^3*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)) + (x^2*(9*a^4*d^4 - 4*b^4*c^4 + 6*a^2*b^2*c^2*d^2 + 2*a*b^3*c^3*d - 19*a^3*b*c*d^3))/(4*a^2*c^2*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)) + (b*d^2*x^6*(3*a^3*d^3 - 2*b^3*c^3 + 3*a*b^2*c^2*d - 7*a^2*b*c*d^2))/(2*a^2*c^3*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)))/(x^4*(b*c^2 + 2*a*c*d) + x^6*(a*d^2 + 2*b*c*d) + a*c^2*x^2 + b*d^2*x^8) + (log(c + d*x^2)*(3*a^2*d^5 + 10*b^2*c^2*d^3 - 10*a*b*c*d^4))/(2*b^4*c^8 + 2*a^4*c^4*d^4 - 8*a^3*b*c^5*d^3 + 12*a^2*b^2*c^6*d^2 - 8*a*b^3*c^7*d) - (log(x)*(3*a*d + 2*b*c))/(a^3*c^4)","B"
318,1,1161,377,2.290076,"\text{Not used}","int(1/(x^4*(a + b*x^2)^2*(c + d*x^2)^3),x)","\frac{\frac{x^2\,\left(7\,a\,d+5\,b\,c\right)}{3\,a^2\,c^2}-\frac{1}{3\,a\,c}+\frac{x^8\,\left(35\,a^4\,b\,d^6-75\,a^3\,b^2\,c\,d^5+24\,a^2\,b^3\,c^2\,d^4+24\,a\,b^4\,c^3\,d^3-20\,b^5\,c^4\,d^2\right)}{8\,a^3\,c^4\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)}-\frac{x^4\,\left(-175\,a^5\,d^5+319\,a^4\,b\,c\,d^4-176\,a^2\,b^3\,c^3\,d^2+8\,a\,b^4\,c^4\,d+60\,b^5\,c^5\right)}{24\,a^3\,c^3\,\left(a\,d-b\,c\right)\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}+\frac{d\,x^6\,\left(105\,a^5\,d^5-50\,a^4\,b\,c\,d^4-303\,a^3\,b^2\,c^2\,d^3+192\,a^2\,b^3\,c^3\,d^2+104\,a\,b^4\,c^4\,d-120\,b^5\,c^5\right)}{24\,a^3\,c^4\,\left(a\,d-b\,c\right)\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}}{x^5\,\left(b\,c^2+2\,a\,d\,c\right)+x^7\,\left(a\,d^2+2\,b\,c\,d\right)+a\,c^2\,x^3+b\,d^2\,x^9}+\frac{\mathrm{atan}\left(\frac{b^3\,c^{11}\,x\,{\left(-a^7\,b^9\right)}^{3/2}\,400{}\mathrm{i}+a^{18}\,b\,d^{11}\,x\,\sqrt{-a^7\,b^9}\,1225{}\mathrm{i}+a^{14}\,b^5\,c^4\,d^7\,x\,\sqrt{-a^7\,b^9}\,9801{}\mathrm{i}-a^{15}\,b^4\,c^3\,d^8\,x\,\sqrt{-a^7\,b^9}\,21780{}\mathrm{i}+a^{16}\,b^3\,c^2\,d^9\,x\,\sqrt{-a^7\,b^9}\,19030{}\mathrm{i}-a\,b^2\,c^{10}\,d\,x\,{\left(-a^7\,b^9\right)}^{3/2}\,1760{}\mathrm{i}+a^2\,b\,c^9\,d^2\,x\,{\left(-a^7\,b^9\right)}^{3/2}\,1936{}\mathrm{i}-a^{17}\,b^2\,c\,d^{10}\,x\,\sqrt{-a^7\,b^9}\,7700{}\mathrm{i}}{-1225\,a^{22}\,b^5\,d^{11}+7700\,a^{21}\,b^6\,c\,d^{10}-19030\,a^{20}\,b^7\,c^2\,d^9+21780\,a^{19}\,b^8\,c^3\,d^8-9801\,a^{18}\,b^9\,c^4\,d^7+1936\,a^{13}\,b^{14}\,c^9\,d^2-1760\,a^{12}\,b^{15}\,c^{10}\,d+400\,a^{11}\,b^{16}\,c^{11}}\right)\,\left(11\,a\,d-5\,b\,c\right)\,\sqrt{-a^7\,b^9}\,1{}\mathrm{i}}{2\,\left(a^{11}\,d^4-4\,a^{10}\,b\,c\,d^3+6\,a^9\,b^2\,c^2\,d^2-4\,a^8\,b^3\,c^3\,d+a^7\,b^4\,c^4\right)}-\frac{\mathrm{atan}\left(\frac{a^{11}\,d^5\,x\,{\left(-c^9\,d^7\right)}^{3/2}\,1225{}\mathrm{i}+b^{11}\,c^{20}\,d\,x\,\sqrt{-c^9\,d^7}\,400{}\mathrm{i}-a^8\,b^3\,c^3\,d^2\,x\,{\left(-c^9\,d^7\right)}^{3/2}\,21780{}\mathrm{i}+a^9\,b^2\,c^2\,d^3\,x\,{\left(-c^9\,d^7\right)}^{3/2}\,19030{}\mathrm{i}+a^2\,b^9\,c^{18}\,d^3\,x\,\sqrt{-c^9\,d^7}\,1936{}\mathrm{i}-a^{10}\,b\,c\,d^4\,x\,{\left(-c^9\,d^7\right)}^{3/2}\,7700{}\mathrm{i}+a^7\,b^4\,c^4\,d\,x\,{\left(-c^9\,d^7\right)}^{3/2}\,9801{}\mathrm{i}-a\,b^{10}\,c^{19}\,d^2\,x\,\sqrt{-c^9\,d^7}\,1760{}\mathrm{i}}{1225\,a^{11}\,c^{14}\,d^{15}-7700\,a^{10}\,b\,c^{15}\,d^{14}+19030\,a^9\,b^2\,c^{16}\,d^{13}-21780\,a^8\,b^3\,c^{17}\,d^{12}+9801\,a^7\,b^4\,c^{18}\,d^{11}-1936\,a^2\,b^9\,c^{23}\,d^6+1760\,a\,b^{10}\,c^{24}\,d^5-400\,b^{11}\,c^{25}\,d^4}\right)\,\sqrt{-c^9\,d^7}\,\left(35\,a^2\,d^2-110\,a\,b\,c\,d+99\,b^2\,c^2\right)\,1{}\mathrm{i}}{8\,\left(a^4\,c^9\,d^4-4\,a^3\,b\,c^{10}\,d^3+6\,a^2\,b^2\,c^{11}\,d^2-4\,a\,b^3\,c^{12}\,d+b^4\,c^{13}\right)}","Not used",1,"((x^2*(7*a*d + 5*b*c))/(3*a^2*c^2) - 1/(3*a*c) + (x^8*(35*a^4*b*d^6 - 20*b^5*c^4*d^2 + 24*a*b^4*c^3*d^3 - 75*a^3*b^2*c*d^5 + 24*a^2*b^3*c^2*d^4))/(8*a^3*c^4*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)) - (x^4*(60*b^5*c^5 - 175*a^5*d^5 - 176*a^2*b^3*c^3*d^2 + 8*a*b^4*c^4*d + 319*a^4*b*c*d^4))/(24*a^3*c^3*(a*d - b*c)*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) + (d*x^6*(105*a^5*d^5 - 120*b^5*c^5 + 192*a^2*b^3*c^3*d^2 - 303*a^3*b^2*c^2*d^3 + 104*a*b^4*c^4*d - 50*a^4*b*c*d^4))/(24*a^3*c^4*(a*d - b*c)*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)))/(x^5*(b*c^2 + 2*a*c*d) + x^7*(a*d^2 + 2*b*c*d) + a*c^2*x^3 + b*d^2*x^9) + (atan((b^3*c^11*x*(-a^7*b^9)^(3/2)*400i + a^18*b*d^11*x*(-a^7*b^9)^(1/2)*1225i + a^14*b^5*c^4*d^7*x*(-a^7*b^9)^(1/2)*9801i - a^15*b^4*c^3*d^8*x*(-a^7*b^9)^(1/2)*21780i + a^16*b^3*c^2*d^9*x*(-a^7*b^9)^(1/2)*19030i - a*b^2*c^10*d*x*(-a^7*b^9)^(3/2)*1760i + a^2*b*c^9*d^2*x*(-a^7*b^9)^(3/2)*1936i - a^17*b^2*c*d^10*x*(-a^7*b^9)^(1/2)*7700i)/(400*a^11*b^16*c^11 - 1225*a^22*b^5*d^11 - 1760*a^12*b^15*c^10*d + 7700*a^21*b^6*c*d^10 + 1936*a^13*b^14*c^9*d^2 - 9801*a^18*b^9*c^4*d^7 + 21780*a^19*b^8*c^3*d^8 - 19030*a^20*b^7*c^2*d^9))*(11*a*d - 5*b*c)*(-a^7*b^9)^(1/2)*1i)/(2*(a^11*d^4 + a^7*b^4*c^4 - 4*a^8*b^3*c^3*d + 6*a^9*b^2*c^2*d^2 - 4*a^10*b*c*d^3)) - (atan((a^11*d^5*x*(-c^9*d^7)^(3/2)*1225i + b^11*c^20*d*x*(-c^9*d^7)^(1/2)*400i - a^8*b^3*c^3*d^2*x*(-c^9*d^7)^(3/2)*21780i + a^9*b^2*c^2*d^3*x*(-c^9*d^7)^(3/2)*19030i + a^2*b^9*c^18*d^3*x*(-c^9*d^7)^(1/2)*1936i - a^10*b*c*d^4*x*(-c^9*d^7)^(3/2)*7700i + a^7*b^4*c^4*d*x*(-c^9*d^7)^(3/2)*9801i - a*b^10*c^19*d^2*x*(-c^9*d^7)^(1/2)*1760i)/(1225*a^11*c^14*d^15 - 400*b^11*c^25*d^4 + 1760*a*b^10*c^24*d^5 - 7700*a^10*b*c^15*d^14 - 1936*a^2*b^9*c^23*d^6 + 9801*a^7*b^4*c^18*d^11 - 21780*a^8*b^3*c^17*d^12 + 19030*a^9*b^2*c^16*d^13))*(-c^9*d^7)^(1/2)*(35*a^2*d^2 + 99*b^2*c^2 - 110*a*b*c*d)*1i)/(8*(b^4*c^13 + a^4*c^9*d^4 - 4*a^3*b*c^10*d^3 + 6*a^2*b^2*c^11*d^2 - 4*a*b^3*c^12*d))","B"
319,1,289,96,0.495497,"\text{Not used}","int(x^m*(A + B*x^2)*(a + b*x^2)^3,x)","\frac{A\,a^3\,x\,x^m\,\left(m^4+24\,m^3+206\,m^2+744\,m+945\right)}{m^5+25\,m^4+230\,m^3+950\,m^2+1689\,m+945}+\frac{B\,b^3\,x^m\,x^9\,\left(m^4+16\,m^3+86\,m^2+176\,m+105\right)}{m^5+25\,m^4+230\,m^3+950\,m^2+1689\,m+945}+\frac{a^2\,x^m\,x^3\,\left(3\,A\,b+B\,a\right)\,\left(m^4+22\,m^3+164\,m^2+458\,m+315\right)}{m^5+25\,m^4+230\,m^3+950\,m^2+1689\,m+945}+\frac{b^2\,x^m\,x^7\,\left(A\,b+3\,B\,a\right)\,\left(m^4+18\,m^3+104\,m^2+222\,m+135\right)}{m^5+25\,m^4+230\,m^3+950\,m^2+1689\,m+945}+\frac{3\,a\,b\,x^m\,x^5\,\left(A\,b+B\,a\right)\,\left(m^4+20\,m^3+130\,m^2+300\,m+189\right)}{m^5+25\,m^4+230\,m^3+950\,m^2+1689\,m+945}","Not used",1,"(A*a^3*x*x^m*(744*m + 206*m^2 + 24*m^3 + m^4 + 945))/(1689*m + 950*m^2 + 230*m^3 + 25*m^4 + m^5 + 945) + (B*b^3*x^m*x^9*(176*m + 86*m^2 + 16*m^3 + m^4 + 105))/(1689*m + 950*m^2 + 230*m^3 + 25*m^4 + m^5 + 945) + (a^2*x^m*x^3*(3*A*b + B*a)*(458*m + 164*m^2 + 22*m^3 + m^4 + 315))/(1689*m + 950*m^2 + 230*m^3 + 25*m^4 + m^5 + 945) + (b^2*x^m*x^7*(A*b + 3*B*a)*(222*m + 104*m^2 + 18*m^3 + m^4 + 135))/(1689*m + 950*m^2 + 230*m^3 + 25*m^4 + m^5 + 945) + (3*a*b*x^m*x^5*(A*b + B*a)*(300*m + 130*m^2 + 20*m^3 + m^4 + 189))/(1689*m + 950*m^2 + 230*m^3 + 25*m^4 + m^5 + 945)","B"
320,1,177,71,0.343185,"\text{Not used}","int(x^m*(A + B*x^2)*(a + b*x^2)^2,x)","x^m\,\left(\frac{B\,b^2\,x^7\,\left(m^3+9\,m^2+23\,m+15\right)}{m^4+16\,m^3+86\,m^2+176\,m+105}+\frac{A\,a^2\,x\,\left(m^3+15\,m^2+71\,m+105\right)}{m^4+16\,m^3+86\,m^2+176\,m+105}+\frac{a\,x^3\,\left(2\,A\,b+B\,a\right)\,\left(m^3+13\,m^2+47\,m+35\right)}{m^4+16\,m^3+86\,m^2+176\,m+105}+\frac{b\,x^5\,\left(A\,b+2\,B\,a\right)\,\left(m^3+11\,m^2+31\,m+21\right)}{m^4+16\,m^3+86\,m^2+176\,m+105}\right)","Not used",1,"x^m*((B*b^2*x^7*(23*m + 9*m^2 + m^3 + 15))/(176*m + 86*m^2 + 16*m^3 + m^4 + 105) + (A*a^2*x*(71*m + 15*m^2 + m^3 + 105))/(176*m + 86*m^2 + 16*m^3 + m^4 + 105) + (a*x^3*(2*A*b + B*a)*(47*m + 13*m^2 + m^3 + 35))/(176*m + 86*m^2 + 16*m^3 + m^4 + 105) + (b*x^5*(A*b + 2*B*a)*(31*m + 11*m^2 + m^3 + 21))/(176*m + 86*m^2 + 16*m^3 + m^4 + 105))","B"
321,1,95,45,0.300015,"\text{Not used}","int(x^m*(A + B*x^2)*(a + b*x^2),x)","x^m\,\left(\frac{x^3\,\left(A\,b+B\,a\right)\,\left(m^2+6\,m+5\right)}{m^3+9\,m^2+23\,m+15}+\frac{B\,b\,x^5\,\left(m^2+4\,m+3\right)}{m^3+9\,m^2+23\,m+15}+\frac{A\,a\,x\,\left(m^2+8\,m+15\right)}{m^3+9\,m^2+23\,m+15}\right)","Not used",1,"x^m*((x^3*(A*b + B*a)*(6*m + m^2 + 5))/(23*m + 9*m^2 + m^3 + 15) + (B*b*x^5*(4*m + m^2 + 3))/(23*m + 9*m^2 + m^3 + 15) + (A*a*x*(8*m + m^2 + 15))/(23*m + 9*m^2 + m^3 + 15))","B"
322,0,-1,66,0.000000,"\text{Not used}","int((x^m*(A + B*x^2))/(a + b*x^2),x)","\int \frac{x^m\,\left(B\,x^2+A\right)}{b\,x^2+a} \,d x","Not used",1,"int((x^m*(A + B*x^2))/(a + b*x^2), x)","F"
323,0,-1,93,0.000000,"\text{Not used}","int((x^m*(A + B*x^2))/(a + b*x^2)^2,x)","\int \frac{x^m\,\left(B\,x^2+A\right)}{{\left(b\,x^2+a\right)}^2} \,d x","Not used",1,"int((x^m*(A + B*x^2))/(a + b*x^2)^2, x)","F"
324,0,-1,93,0.000000,"\text{Not used}","int((x^m*(A + B*x^2))/(a + b*x^2)^3,x)","\int \frac{x^m\,\left(B\,x^2+A\right)}{{\left(b\,x^2+a\right)}^3} \,d x","Not used",1,"int((x^m*(A + B*x^2))/(a + b*x^2)^3, x)","F"
325,1,443,151,0.658272,"\text{Not used}","int(x^m*(a + b*x^2)^2*(c + d*x^2)^3,x)","\frac{a^2\,c^3\,x\,x^m\,\left(m^5+35\,m^4+470\,m^3+3010\,m^2+9129\,m+10395\right)}{m^6+36\,m^5+505\,m^4+3480\,m^3+12139\,m^2+19524\,m+10395}+\frac{c\,x^m\,x^5\,\left(3\,a^2\,d^2+6\,a\,b\,c\,d+b^2\,c^2\right)\,\left(m^5+31\,m^4+350\,m^3+1730\,m^2+3489\,m+2079\right)}{m^6+36\,m^5+505\,m^4+3480\,m^3+12139\,m^2+19524\,m+10395}+\frac{d\,x^m\,x^7\,\left(a^2\,d^2+6\,a\,b\,c\,d+3\,b^2\,c^2\right)\,\left(m^5+29\,m^4+302\,m^3+1366\,m^2+2577\,m+1485\right)}{m^6+36\,m^5+505\,m^4+3480\,m^3+12139\,m^2+19524\,m+10395}+\frac{b^2\,d^3\,x^m\,x^{11}\,\left(m^5+25\,m^4+230\,m^3+950\,m^2+1689\,m+945\right)}{m^6+36\,m^5+505\,m^4+3480\,m^3+12139\,m^2+19524\,m+10395}+\frac{a\,c^2\,x^m\,x^3\,\left(3\,a\,d+2\,b\,c\right)\,\left(m^5+33\,m^4+406\,m^3+2262\,m^2+5353\,m+3465\right)}{m^6+36\,m^5+505\,m^4+3480\,m^3+12139\,m^2+19524\,m+10395}+\frac{b\,d^2\,x^m\,x^9\,\left(2\,a\,d+3\,b\,c\right)\,\left(m^5+27\,m^4+262\,m^3+1122\,m^2+2041\,m+1155\right)}{m^6+36\,m^5+505\,m^4+3480\,m^3+12139\,m^2+19524\,m+10395}","Not used",1,"(a^2*c^3*x*x^m*(9129*m + 3010*m^2 + 470*m^3 + 35*m^4 + m^5 + 10395))/(19524*m + 12139*m^2 + 3480*m^3 + 505*m^4 + 36*m^5 + m^6 + 10395) + (c*x^m*x^5*(3*a^2*d^2 + b^2*c^2 + 6*a*b*c*d)*(3489*m + 1730*m^2 + 350*m^3 + 31*m^4 + m^5 + 2079))/(19524*m + 12139*m^2 + 3480*m^3 + 505*m^4 + 36*m^5 + m^6 + 10395) + (d*x^m*x^7*(a^2*d^2 + 3*b^2*c^2 + 6*a*b*c*d)*(2577*m + 1366*m^2 + 302*m^3 + 29*m^4 + m^5 + 1485))/(19524*m + 12139*m^2 + 3480*m^3 + 505*m^4 + 36*m^5 + m^6 + 10395) + (b^2*d^3*x^m*x^11*(1689*m + 950*m^2 + 230*m^3 + 25*m^4 + m^5 + 945))/(19524*m + 12139*m^2 + 3480*m^3 + 505*m^4 + 36*m^5 + m^6 + 10395) + (a*c^2*x^m*x^3*(3*a*d + 2*b*c)*(5353*m + 2262*m^2 + 406*m^3 + 33*m^4 + m^5 + 3465))/(19524*m + 12139*m^2 + 3480*m^3 + 505*m^4 + 36*m^5 + m^6 + 10395) + (b*d^2*x^m*x^9*(2*a*d + 3*b*c)*(2041*m + 1122*m^2 + 262*m^3 + 27*m^4 + m^5 + 1155))/(19524*m + 12139*m^2 + 3480*m^3 + 505*m^4 + 36*m^5 + m^6 + 10395)","B"
326,1,302,109,0.469452,"\text{Not used}","int(x^m*(a + b*x^2)^2*(c + d*x^2)^2,x)","\frac{x^m\,x^5\,\left(a^2\,d^2+4\,a\,b\,c\,d+b^2\,c^2\right)\,\left(m^4+20\,m^3+130\,m^2+300\,m+189\right)}{m^5+25\,m^4+230\,m^3+950\,m^2+1689\,m+945}+\frac{b^2\,d^2\,x^m\,x^9\,\left(m^4+16\,m^3+86\,m^2+176\,m+105\right)}{m^5+25\,m^4+230\,m^3+950\,m^2+1689\,m+945}+\frac{a^2\,c^2\,x\,x^m\,\left(m^4+24\,m^3+206\,m^2+744\,m+945\right)}{m^5+25\,m^4+230\,m^3+950\,m^2+1689\,m+945}+\frac{2\,a\,c\,x^m\,x^3\,\left(a\,d+b\,c\right)\,\left(m^4+22\,m^3+164\,m^2+458\,m+315\right)}{m^5+25\,m^4+230\,m^3+950\,m^2+1689\,m+945}+\frac{2\,b\,d\,x^m\,x^7\,\left(a\,d+b\,c\right)\,\left(m^4+18\,m^3+104\,m^2+222\,m+135\right)}{m^5+25\,m^4+230\,m^3+950\,m^2+1689\,m+945}","Not used",1,"(x^m*x^5*(a^2*d^2 + b^2*c^2 + 4*a*b*c*d)*(300*m + 130*m^2 + 20*m^3 + m^4 + 189))/(1689*m + 950*m^2 + 230*m^3 + 25*m^4 + m^5 + 945) + (b^2*d^2*x^m*x^9*(176*m + 86*m^2 + 16*m^3 + m^4 + 105))/(1689*m + 950*m^2 + 230*m^3 + 25*m^4 + m^5 + 945) + (a^2*c^2*x*x^m*(744*m + 206*m^2 + 24*m^3 + m^4 + 945))/(1689*m + 950*m^2 + 230*m^3 + 25*m^4 + m^5 + 945) + (2*a*c*x^m*x^3*(a*d + b*c)*(458*m + 164*m^2 + 22*m^3 + m^4 + 315))/(1689*m + 950*m^2 + 230*m^3 + 25*m^4 + m^5 + 945) + (2*b*d*x^m*x^7*(a*d + b*c)*(222*m + 104*m^2 + 18*m^3 + m^4 + 135))/(1689*m + 950*m^2 + 230*m^3 + 25*m^4 + m^5 + 945)","B"
327,1,177,71,0.355030,"\text{Not used}","int(x^m*(a + b*x^2)^2*(c + d*x^2),x)","x^m\,\left(\frac{a\,x^3\,\left(a\,d+2\,b\,c\right)\,\left(m^3+13\,m^2+47\,m+35\right)}{m^4+16\,m^3+86\,m^2+176\,m+105}+\frac{b\,x^5\,\left(2\,a\,d+b\,c\right)\,\left(m^3+11\,m^2+31\,m+21\right)}{m^4+16\,m^3+86\,m^2+176\,m+105}+\frac{b^2\,d\,x^7\,\left(m^3+9\,m^2+23\,m+15\right)}{m^4+16\,m^3+86\,m^2+176\,m+105}+\frac{a^2\,c\,x\,\left(m^3+15\,m^2+71\,m+105\right)}{m^4+16\,m^3+86\,m^2+176\,m+105}\right)","Not used",1,"x^m*((a*x^3*(a*d + 2*b*c)*(47*m + 13*m^2 + m^3 + 35))/(176*m + 86*m^2 + 16*m^3 + m^4 + 105) + (b*x^5*(2*a*d + b*c)*(31*m + 11*m^2 + m^3 + 21))/(176*m + 86*m^2 + 16*m^3 + m^4 + 105) + (b^2*d*x^7*(23*m + 9*m^2 + m^3 + 15))/(176*m + 86*m^2 + 16*m^3 + m^4 + 105) + (a^2*c*x*(71*m + 15*m^2 + m^3 + 105))/(176*m + 86*m^2 + 16*m^3 + m^4 + 105))","B"
328,0,-1,94,0.000000,"\text{Not used}","int((x^m*(a + b*x^2)^2)/(c + d*x^2),x)","\int \frac{x^m\,{\left(b\,x^2+a\right)}^2}{d\,x^2+c} \,d x","Not used",1,"int((x^m*(a + b*x^2)^2)/(c + d*x^2), x)","F"
329,0,-1,120,0.000000,"\text{Not used}","int((x^m*(a + b*x^2)^2)/(c + d*x^2)^2,x)","\int \frac{x^m\,{\left(b\,x^2+a\right)}^2}{{\left(d\,x^2+c\right)}^2} \,d x","Not used",1,"int((x^m*(a + b*x^2)^2)/(c + d*x^2)^2, x)","F"
330,0,-1,171,0.000000,"\text{Not used}","int((x^m*(a + b*x^2)^2)/(c + d*x^2)^3,x)","\int \frac{x^m\,{\left(b\,x^2+a\right)}^2}{{\left(d\,x^2+c\right)}^3} \,d x","Not used",1,"int((x^m*(a + b*x^2)^2)/(c + d*x^2)^3, x)","F"
331,0,-1,133,0.000000,"\text{Not used}","int((x^m*(c + d*x^2)^3)/(a + b*x^2),x)","\int \frac{x^m\,{\left(d\,x^2+c\right)}^3}{b\,x^2+a} \,d x","Not used",1,"int((x^m*(c + d*x^2)^3)/(a + b*x^2), x)","F"
332,0,-1,94,0.000000,"\text{Not used}","int((x^m*(c + d*x^2)^2)/(a + b*x^2),x)","\int \frac{x^m\,{\left(d\,x^2+c\right)}^2}{b\,x^2+a} \,d x","Not used",1,"int((x^m*(c + d*x^2)^2)/(a + b*x^2), x)","F"
333,0,-1,66,0.000000,"\text{Not used}","int((x^m*(c + d*x^2))/(a + b*x^2),x)","\int \frac{x^m\,\left(d\,x^2+c\right)}{b\,x^2+a} \,d x","Not used",1,"int((x^m*(c + d*x^2))/(a + b*x^2), x)","F"
334,0,-1,102,0.000000,"\text{Not used}","int(x^m/((a + b*x^2)*(c + d*x^2)),x)","\int \frac{x^m}{\left(b\,x^2+a\right)\,\left(d\,x^2+c\right)} \,d x","Not used",1,"int(x^m/((a + b*x^2)*(c + d*x^2)), x)","F"
335,0,-1,156,0.000000,"\text{Not used}","int(x^m/((a + b*x^2)^2*(c + d*x^2)),x)","\int \frac{x^m}{{\left(b\,x^2+a\right)}^2\,\left(d\,x^2+c\right)} \,d x","Not used",1,"int(x^m/((a + b*x^2)^2*(c + d*x^2)), x)","F"
336,0,-1,234,0.000000,"\text{Not used}","int(x^m/((a + b*x^2)^3*(c + d*x^2)),x)","\int \frac{x^m}{{\left(b\,x^2+a\right)}^3\,\left(d\,x^2+c\right)} \,d x","Not used",1,"int(x^m/((a + b*x^2)^3*(c + d*x^2)), x)","F"
337,0,-1,201,0.000000,"\text{Not used}","int((x^m*(c + d*x^2)^3)/(a + b*x^2)^2,x)","\int \frac{x^m\,{\left(d\,x^2+c\right)}^3}{{\left(b\,x^2+a\right)}^2} \,d x","Not used",1,"int((x^m*(c + d*x^2)^3)/(a + b*x^2)^2, x)","F"
338,0,-1,120,0.000000,"\text{Not used}","int((x^m*(c + d*x^2)^2)/(a + b*x^2)^2,x)","\int \frac{x^m\,{\left(d\,x^2+c\right)}^2}{{\left(b\,x^2+a\right)}^2} \,d x","Not used",1,"int((x^m*(c + d*x^2)^2)/(a + b*x^2)^2, x)","F"
339,0,-1,93,0.000000,"\text{Not used}","int((x^m*(c + d*x^2))/(a + b*x^2)^2,x)","\int \frac{x^m\,\left(d\,x^2+c\right)}{{\left(b\,x^2+a\right)}^2} \,d x","Not used",1,"int((x^m*(c + d*x^2))/(a + b*x^2)^2, x)","F"
340,0,-1,156,0.000000,"\text{Not used}","int(x^m/((a + b*x^2)^2*(c + d*x^2)),x)","\int \frac{x^m}{{\left(b\,x^2+a\right)}^2\,\left(d\,x^2+c\right)} \,d x","Not used",1,"int(x^m/((a + b*x^2)^2*(c + d*x^2)), x)","F"
341,0,-1,230,0.000000,"\text{Not used}","int(x^m/((a + b*x^2)^2*(c + d*x^2)^2),x)","\int \frac{x^m}{{\left(b\,x^2+a\right)}^2\,{\left(d\,x^2+c\right)}^2} \,d x","Not used",1,"int(x^m/((a + b*x^2)^2*(c + d*x^2)^2), x)","F"
342,0,-1,325,0.000000,"\text{Not used}","int(x^m/((a + b*x^2)^2*(c + d*x^2)^3),x)","\int \frac{x^m}{{\left(b\,x^2+a\right)}^2\,{\left(d\,x^2+c\right)}^3} \,d x","Not used",1,"int(x^m/((a + b*x^2)^2*(c + d*x^2)^3), x)","F"
343,1,31,39,0.199452,"\text{Not used}","int(x^(7/2)*(A + B*x^2)*(a + b*x^2),x)","\frac{2\,x^{9/2}\,\left(221\,A\,a+153\,A\,b\,x^2+153\,B\,a\,x^2+117\,B\,b\,x^4\right)}{1989}","Not used",1,"(2*x^(9/2)*(221*A*a + 153*A*b*x^2 + 153*B*a*x^2 + 117*B*b*x^4))/1989","B"
344,1,31,39,0.193057,"\text{Not used}","int(x^(5/2)*(A + B*x^2)*(a + b*x^2),x)","\frac{2\,x^{7/2}\,\left(165\,A\,a+105\,A\,b\,x^2+105\,B\,a\,x^2+77\,B\,b\,x^4\right)}{1155}","Not used",1,"(2*x^(7/2)*(165*A*a + 105*A*b*x^2 + 105*B*a*x^2 + 77*B*b*x^4))/1155","B"
345,1,31,39,0.042709,"\text{Not used}","int(x^(3/2)*(A + B*x^2)*(a + b*x^2),x)","\frac{2\,x^{5/2}\,\left(117\,A\,a+65\,A\,b\,x^2+65\,B\,a\,x^2+45\,B\,b\,x^4\right)}{585}","Not used",1,"(2*x^(5/2)*(117*A*a + 65*A*b*x^2 + 65*B*a*x^2 + 45*B*b*x^4))/585","B"
346,1,31,39,0.040585,"\text{Not used}","int(x^(1/2)*(A + B*x^2)*(a + b*x^2),x)","\frac{2\,x^{3/2}\,\left(77\,A\,a+33\,A\,b\,x^2+33\,B\,a\,x^2+21\,B\,b\,x^4\right)}{231}","Not used",1,"(2*x^(3/2)*(77*A*a + 33*A*b*x^2 + 33*B*a*x^2 + 21*B*b*x^4))/231","B"
347,1,31,37,0.190653,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2))/x^(1/2),x)","\frac{2\,\sqrt{x}\,\left(45\,A\,a+9\,A\,b\,x^2+9\,B\,a\,x^2+5\,B\,b\,x^4\right)}{45}","Not used",1,"(2*x^(1/2)*(45*A*a + 9*A*b*x^2 + 9*B*a*x^2 + 5*B*b*x^4))/45","B"
348,1,31,37,0.192158,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2))/x^(3/2),x)","\frac{14\,A\,b\,x^2-42\,A\,a+14\,B\,a\,x^2+6\,B\,b\,x^4}{21\,\sqrt{x}}","Not used",1,"(14*A*b*x^2 - 42*A*a + 14*B*a*x^2 + 6*B*b*x^4)/(21*x^(1/2))","B"
349,1,31,37,0.039917,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2))/x^(5/2),x)","\frac{30\,A\,b\,x^2-10\,A\,a+30\,B\,a\,x^2+6\,B\,b\,x^4}{15\,x^{3/2}}","Not used",1,"(30*A*b*x^2 - 10*A*a + 30*B*a*x^2 + 6*B*b*x^4)/(15*x^(3/2))","B"
350,1,31,37,0.037764,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2))/x^(7/2),x)","-\frac{6\,A\,a+30\,A\,b\,x^2+30\,B\,a\,x^2-10\,B\,b\,x^4}{15\,x^{5/2}}","Not used",1,"-(6*A*a + 30*A*b*x^2 + 30*B*a*x^2 - 10*B*b*x^4)/(15*x^(5/2))","B"
351,1,51,63,0.214846,"\text{Not used}","int(x^(7/2)*(A + B*x^2)*(a + b*x^2)^2,x)","x^{13/2}\,\left(\frac{2\,B\,a^2}{13}+\frac{4\,A\,b\,a}{13}\right)+x^{17/2}\,\left(\frac{2\,A\,b^2}{17}+\frac{4\,B\,a\,b}{17}\right)+\frac{2\,A\,a^2\,x^{9/2}}{9}+\frac{2\,B\,b^2\,x^{21/2}}{21}","Not used",1,"x^(13/2)*((2*B*a^2)/13 + (4*A*a*b)/13) + x^(17/2)*((2*A*b^2)/17 + (4*B*a*b)/17) + (2*A*a^2*x^(9/2))/9 + (2*B*b^2*x^(21/2))/21","B"
352,1,51,63,0.052200,"\text{Not used}","int(x^(5/2)*(A + B*x^2)*(a + b*x^2)^2,x)","x^{11/2}\,\left(\frac{2\,B\,a^2}{11}+\frac{4\,A\,b\,a}{11}\right)+x^{15/2}\,\left(\frac{2\,A\,b^2}{15}+\frac{4\,B\,a\,b}{15}\right)+\frac{2\,A\,a^2\,x^{7/2}}{7}+\frac{2\,B\,b^2\,x^{19/2}}{19}","Not used",1,"x^(11/2)*((2*B*a^2)/11 + (4*A*a*b)/11) + x^(15/2)*((2*A*b^2)/15 + (4*B*a*b)/15) + (2*A*a^2*x^(7/2))/7 + (2*B*b^2*x^(19/2))/19","B"
353,1,51,63,0.053424,"\text{Not used}","int(x^(3/2)*(A + B*x^2)*(a + b*x^2)^2,x)","x^{9/2}\,\left(\frac{2\,B\,a^2}{9}+\frac{4\,A\,b\,a}{9}\right)+x^{13/2}\,\left(\frac{2\,A\,b^2}{13}+\frac{4\,B\,a\,b}{13}\right)+\frac{2\,A\,a^2\,x^{5/2}}{5}+\frac{2\,B\,b^2\,x^{17/2}}{17}","Not used",1,"x^(9/2)*((2*B*a^2)/9 + (4*A*a*b)/9) + x^(13/2)*((2*A*b^2)/13 + (4*B*a*b)/13) + (2*A*a^2*x^(5/2))/5 + (2*B*b^2*x^(17/2))/17","B"
354,1,51,63,0.052031,"\text{Not used}","int(x^(1/2)*(A + B*x^2)*(a + b*x^2)^2,x)","x^{7/2}\,\left(\frac{2\,B\,a^2}{7}+\frac{4\,A\,b\,a}{7}\right)+x^{11/2}\,\left(\frac{2\,A\,b^2}{11}+\frac{4\,B\,a\,b}{11}\right)+\frac{2\,A\,a^2\,x^{3/2}}{3}+\frac{2\,B\,b^2\,x^{15/2}}{15}","Not used",1,"x^(7/2)*((2*B*a^2)/7 + (4*A*a*b)/7) + x^(11/2)*((2*A*b^2)/11 + (4*B*a*b)/11) + (2*A*a^2*x^(3/2))/3 + (2*B*b^2*x^(15/2))/15","B"
355,1,51,61,0.047879,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^2)/x^(1/2),x)","x^{5/2}\,\left(\frac{2\,B\,a^2}{5}+\frac{4\,A\,b\,a}{5}\right)+x^{9/2}\,\left(\frac{2\,A\,b^2}{9}+\frac{4\,B\,a\,b}{9}\right)+2\,A\,a^2\,\sqrt{x}+\frac{2\,B\,b^2\,x^{13/2}}{13}","Not used",1,"x^(5/2)*((2*B*a^2)/5 + (4*A*a*b)/5) + x^(9/2)*((2*A*b^2)/9 + (4*B*a*b)/9) + 2*A*a^2*x^(1/2) + (2*B*b^2*x^(13/2))/13","B"
356,1,51,61,0.050621,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^2)/x^(3/2),x)","x^{3/2}\,\left(\frac{2\,B\,a^2}{3}+\frac{4\,A\,b\,a}{3}\right)+x^{7/2}\,\left(\frac{2\,A\,b^2}{7}+\frac{4\,B\,a\,b}{7}\right)-\frac{2\,A\,a^2}{\sqrt{x}}+\frac{2\,B\,b^2\,x^{11/2}}{11}","Not used",1,"x^(3/2)*((2*B*a^2)/3 + (4*A*a*b)/3) + x^(7/2)*((2*A*b^2)/7 + (4*B*a*b)/7) - (2*A*a^2)/x^(1/2) + (2*B*b^2*x^(11/2))/11","B"
357,1,51,61,0.052253,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^2)/x^(5/2),x)","\sqrt{x}\,\left(2\,B\,a^2+4\,A\,b\,a\right)+x^{5/2}\,\left(\frac{2\,A\,b^2}{5}+\frac{4\,B\,a\,b}{5}\right)-\frac{2\,A\,a^2}{3\,x^{3/2}}+\frac{2\,B\,b^2\,x^{9/2}}{9}","Not used",1,"x^(1/2)*(2*B*a^2 + 4*A*a*b) + x^(5/2)*((2*A*b^2)/5 + (4*B*a*b)/5) - (2*A*a^2)/(3*x^(3/2)) + (2*B*b^2*x^(9/2))/9","B"
358,1,55,61,0.248446,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^2)/x^(7/2),x)","-\frac{210\,B\,a^2\,x^2+42\,A\,a^2-140\,B\,a\,b\,x^4+420\,A\,a\,b\,x^2-30\,B\,b^2\,x^6-70\,A\,b^2\,x^4}{105\,x^{5/2}}","Not used",1,"-(42*A*a^2 + 210*B*a^2*x^2 - 70*A*b^2*x^4 - 30*B*b^2*x^6 + 420*A*a*b*x^2 - 140*B*a*b*x^4)/(105*x^(5/2))","B"
359,1,69,85,0.043381,"\text{Not used}","int(x^(7/2)*(A + B*x^2)*(a + b*x^2)^3,x)","x^{13/2}\,\left(\frac{2\,B\,a^3}{13}+\frac{6\,A\,b\,a^2}{13}\right)+x^{21/2}\,\left(\frac{2\,A\,b^3}{21}+\frac{2\,B\,a\,b^2}{7}\right)+\frac{2\,A\,a^3\,x^{9/2}}{9}+\frac{2\,B\,b^3\,x^{25/2}}{25}+\frac{6\,a\,b\,x^{17/2}\,\left(A\,b+B\,a\right)}{17}","Not used",1,"x^(13/2)*((2*B*a^3)/13 + (6*A*a^2*b)/13) + x^(21/2)*((2*A*b^3)/21 + (2*B*a*b^2)/7) + (2*A*a^3*x^(9/2))/9 + (2*B*b^3*x^(25/2))/25 + (6*a*b*x^(17/2)*(A*b + B*a))/17","B"
360,1,69,85,0.033768,"\text{Not used}","int(x^(5/2)*(A + B*x^2)*(a + b*x^2)^3,x)","x^{11/2}\,\left(\frac{2\,B\,a^3}{11}+\frac{6\,A\,b\,a^2}{11}\right)+x^{19/2}\,\left(\frac{2\,A\,b^3}{19}+\frac{6\,B\,a\,b^2}{19}\right)+\frac{2\,A\,a^3\,x^{7/2}}{7}+\frac{2\,B\,b^3\,x^{23/2}}{23}+\frac{2\,a\,b\,x^{15/2}\,\left(A\,b+B\,a\right)}{5}","Not used",1,"x^(11/2)*((2*B*a^3)/11 + (6*A*a^2*b)/11) + x^(19/2)*((2*A*b^3)/19 + (6*B*a*b^2)/19) + (2*A*a^3*x^(7/2))/7 + (2*B*b^3*x^(23/2))/23 + (2*a*b*x^(15/2)*(A*b + B*a))/5","B"
361,1,69,85,0.048895,"\text{Not used}","int(x^(3/2)*(A + B*x^2)*(a + b*x^2)^3,x)","x^{9/2}\,\left(\frac{2\,B\,a^3}{9}+\frac{2\,A\,b\,a^2}{3}\right)+x^{17/2}\,\left(\frac{2\,A\,b^3}{17}+\frac{6\,B\,a\,b^2}{17}\right)+\frac{2\,A\,a^3\,x^{5/2}}{5}+\frac{2\,B\,b^3\,x^{21/2}}{21}+\frac{6\,a\,b\,x^{13/2}\,\left(A\,b+B\,a\right)}{13}","Not used",1,"x^(9/2)*((2*B*a^3)/9 + (2*A*a^2*b)/3) + x^(17/2)*((2*A*b^3)/17 + (6*B*a*b^2)/17) + (2*A*a^3*x^(5/2))/5 + (2*B*b^3*x^(21/2))/21 + (6*a*b*x^(13/2)*(A*b + B*a))/13","B"
362,1,69,85,0.030347,"\text{Not used}","int(x^(1/2)*(A + B*x^2)*(a + b*x^2)^3,x)","x^{7/2}\,\left(\frac{2\,B\,a^3}{7}+\frac{6\,A\,b\,a^2}{7}\right)+x^{15/2}\,\left(\frac{2\,A\,b^3}{15}+\frac{2\,B\,a\,b^2}{5}\right)+\frac{2\,A\,a^3\,x^{3/2}}{3}+\frac{2\,B\,b^3\,x^{19/2}}{19}+\frac{6\,a\,b\,x^{11/2}\,\left(A\,b+B\,a\right)}{11}","Not used",1,"x^(7/2)*((2*B*a^3)/7 + (6*A*a^2*b)/7) + x^(15/2)*((2*A*b^3)/15 + (2*B*a*b^2)/5) + (2*A*a^3*x^(3/2))/3 + (2*B*b^3*x^(19/2))/19 + (6*a*b*x^(11/2)*(A*b + B*a))/11","B"
363,1,69,83,0.034241,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^3)/x^(1/2),x)","x^{5/2}\,\left(\frac{2\,B\,a^3}{5}+\frac{6\,A\,b\,a^2}{5}\right)+x^{13/2}\,\left(\frac{2\,A\,b^3}{13}+\frac{6\,B\,a\,b^2}{13}\right)+2\,A\,a^3\,\sqrt{x}+\frac{2\,B\,b^3\,x^{17/2}}{17}+\frac{2\,a\,b\,x^{9/2}\,\left(A\,b+B\,a\right)}{3}","Not used",1,"x^(5/2)*((2*B*a^3)/5 + (6*A*a^2*b)/5) + x^(13/2)*((2*A*b^3)/13 + (6*B*a*b^2)/13) + 2*A*a^3*x^(1/2) + (2*B*b^3*x^(17/2))/17 + (2*a*b*x^(9/2)*(A*b + B*a))/3","B"
364,1,69,83,0.033410,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^3)/x^(3/2),x)","x^{3/2}\,\left(\frac{2\,B\,a^3}{3}+2\,A\,b\,a^2\right)+x^{11/2}\,\left(\frac{2\,A\,b^3}{11}+\frac{6\,B\,a\,b^2}{11}\right)-\frac{2\,A\,a^3}{\sqrt{x}}+\frac{2\,B\,b^3\,x^{15/2}}{15}+\frac{6\,a\,b\,x^{7/2}\,\left(A\,b+B\,a\right)}{7}","Not used",1,"x^(3/2)*((2*B*a^3)/3 + 2*A*a^2*b) + x^(11/2)*((2*A*b^3)/11 + (6*B*a*b^2)/11) - (2*A*a^3)/x^(1/2) + (2*B*b^3*x^(15/2))/15 + (6*a*b*x^(7/2)*(A*b + B*a))/7","B"
365,1,69,83,0.032769,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^3)/x^(5/2),x)","\sqrt{x}\,\left(2\,B\,a^3+6\,A\,b\,a^2\right)+x^{9/2}\,\left(\frac{2\,A\,b^3}{9}+\frac{2\,B\,a\,b^2}{3}\right)-\frac{2\,A\,a^3}{3\,x^{3/2}}+\frac{2\,B\,b^3\,x^{13/2}}{13}+\frac{6\,a\,b\,x^{5/2}\,\left(A\,b+B\,a\right)}{5}","Not used",1,"x^(1/2)*(2*B*a^3 + 6*A*a^2*b) + x^(9/2)*((2*A*b^3)/9 + (2*B*a*b^2)/3) - (2*A*a^3)/(3*x^(3/2)) + (2*B*b^3*x^(13/2))/13 + (6*a*b*x^(5/2)*(A*b + B*a))/5","B"
366,1,72,81,0.058909,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^3)/x^(7/2),x)","x^{7/2}\,\left(\frac{2\,A\,b^3}{7}+\frac{6\,B\,a\,b^2}{7}\right)-\frac{\frac{2\,A\,a^3}{5}+x^2\,\left(2\,B\,a^3+6\,A\,b\,a^2\right)}{x^{5/2}}+\frac{2\,B\,b^3\,x^{11/2}}{11}+2\,a\,b\,x^{3/2}\,\left(A\,b+B\,a\right)","Not used",1,"x^(7/2)*((2*A*b^3)/7 + (6*B*a*b^2)/7) - ((2*A*a^3)/5 + x^2*(2*B*a^3 + 6*A*a^2*b))/x^(5/2) + (2*B*b^3*x^(11/2))/11 + 2*a*b*x^(3/2)*(A*b + B*a)","B"
367,1,788,276,0.378376,"\text{Not used}","int((x^(7/2)*(A + B*x^2))/(a + b*x^2),x)","x^{5/2}\,\left(\frac{2\,A}{5\,b}-\frac{2\,B\,a}{5\,b^2}\right)+\frac{2\,B\,x^{9/2}}{9\,b}-\frac{{\left(-a\right)}^{5/4}\,\mathrm{atan}\left(\frac{\frac{{\left(-a\right)}^{5/4}\,\left(\frac{16\,\sqrt{x}\,\left(A^2\,a^4\,b^2-2\,A\,B\,a^5\,b+B^2\,a^6\right)}{b^3}-\frac{{\left(-a\right)}^{5/4}\,\left(A\,b-B\,a\right)\,\left(32\,B\,a^4-32\,A\,a^3\,b\right)\,1{}\mathrm{i}}{2\,b^{13/4}}\right)\,\left(A\,b-B\,a\right)}{2\,b^{13/4}}+\frac{{\left(-a\right)}^{5/4}\,\left(\frac{16\,\sqrt{x}\,\left(A^2\,a^4\,b^2-2\,A\,B\,a^5\,b+B^2\,a^6\right)}{b^3}+\frac{{\left(-a\right)}^{5/4}\,\left(A\,b-B\,a\right)\,\left(32\,B\,a^4-32\,A\,a^3\,b\right)\,1{}\mathrm{i}}{2\,b^{13/4}}\right)\,\left(A\,b-B\,a\right)}{2\,b^{13/4}}}{\frac{{\left(-a\right)}^{5/4}\,\left(\frac{16\,\sqrt{x}\,\left(A^2\,a^4\,b^2-2\,A\,B\,a^5\,b+B^2\,a^6\right)}{b^3}-\frac{{\left(-a\right)}^{5/4}\,\left(A\,b-B\,a\right)\,\left(32\,B\,a^4-32\,A\,a^3\,b\right)\,1{}\mathrm{i}}{2\,b^{13/4}}\right)\,\left(A\,b-B\,a\right)\,1{}\mathrm{i}}{2\,b^{13/4}}-\frac{{\left(-a\right)}^{5/4}\,\left(\frac{16\,\sqrt{x}\,\left(A^2\,a^4\,b^2-2\,A\,B\,a^5\,b+B^2\,a^6\right)}{b^3}+\frac{{\left(-a\right)}^{5/4}\,\left(A\,b-B\,a\right)\,\left(32\,B\,a^4-32\,A\,a^3\,b\right)\,1{}\mathrm{i}}{2\,b^{13/4}}\right)\,\left(A\,b-B\,a\right)\,1{}\mathrm{i}}{2\,b^{13/4}}}\right)\,\left(A\,b-B\,a\right)}{b^{13/4}}-\frac{a\,\sqrt{x}\,\left(\frac{2\,A}{b}-\frac{2\,B\,a}{b^2}\right)}{b}-\frac{{\left(-a\right)}^{5/4}\,\mathrm{atan}\left(\frac{\frac{{\left(-a\right)}^{5/4}\,\left(\frac{16\,\sqrt{x}\,\left(A^2\,a^4\,b^2-2\,A\,B\,a^5\,b+B^2\,a^6\right)}{b^3}-\frac{{\left(-a\right)}^{5/4}\,\left(A\,b-B\,a\right)\,\left(32\,B\,a^4-32\,A\,a^3\,b\right)}{2\,b^{13/4}}\right)\,\left(A\,b-B\,a\right)\,1{}\mathrm{i}}{2\,b^{13/4}}+\frac{{\left(-a\right)}^{5/4}\,\left(\frac{16\,\sqrt{x}\,\left(A^2\,a^4\,b^2-2\,A\,B\,a^5\,b+B^2\,a^6\right)}{b^3}+\frac{{\left(-a\right)}^{5/4}\,\left(A\,b-B\,a\right)\,\left(32\,B\,a^4-32\,A\,a^3\,b\right)}{2\,b^{13/4}}\right)\,\left(A\,b-B\,a\right)\,1{}\mathrm{i}}{2\,b^{13/4}}}{\frac{{\left(-a\right)}^{5/4}\,\left(\frac{16\,\sqrt{x}\,\left(A^2\,a^4\,b^2-2\,A\,B\,a^5\,b+B^2\,a^6\right)}{b^3}-\frac{{\left(-a\right)}^{5/4}\,\left(A\,b-B\,a\right)\,\left(32\,B\,a^4-32\,A\,a^3\,b\right)}{2\,b^{13/4}}\right)\,\left(A\,b-B\,a\right)}{2\,b^{13/4}}-\frac{{\left(-a\right)}^{5/4}\,\left(\frac{16\,\sqrt{x}\,\left(A^2\,a^4\,b^2-2\,A\,B\,a^5\,b+B^2\,a^6\right)}{b^3}+\frac{{\left(-a\right)}^{5/4}\,\left(A\,b-B\,a\right)\,\left(32\,B\,a^4-32\,A\,a^3\,b\right)}{2\,b^{13/4}}\right)\,\left(A\,b-B\,a\right)}{2\,b^{13/4}}}\right)\,\left(A\,b-B\,a\right)\,1{}\mathrm{i}}{b^{13/4}}","Not used",1,"x^(5/2)*((2*A)/(5*b) - (2*B*a)/(5*b^2)) + (2*B*x^(9/2))/(9*b) - ((-a)^(5/4)*atan((((-a)^(5/4)*((16*x^(1/2)*(B^2*a^6 + A^2*a^4*b^2 - 2*A*B*a^5*b))/b^3 - ((-a)^(5/4)*(A*b - B*a)*(32*B*a^4 - 32*A*a^3*b))/(2*b^(13/4)))*(A*b - B*a)*1i)/(2*b^(13/4)) + ((-a)^(5/4)*((16*x^(1/2)*(B^2*a^6 + A^2*a^4*b^2 - 2*A*B*a^5*b))/b^3 + ((-a)^(5/4)*(A*b - B*a)*(32*B*a^4 - 32*A*a^3*b))/(2*b^(13/4)))*(A*b - B*a)*1i)/(2*b^(13/4)))/(((-a)^(5/4)*((16*x^(1/2)*(B^2*a^6 + A^2*a^4*b^2 - 2*A*B*a^5*b))/b^3 - ((-a)^(5/4)*(A*b - B*a)*(32*B*a^4 - 32*A*a^3*b))/(2*b^(13/4)))*(A*b - B*a))/(2*b^(13/4)) - ((-a)^(5/4)*((16*x^(1/2)*(B^2*a^6 + A^2*a^4*b^2 - 2*A*B*a^5*b))/b^3 + ((-a)^(5/4)*(A*b - B*a)*(32*B*a^4 - 32*A*a^3*b))/(2*b^(13/4)))*(A*b - B*a))/(2*b^(13/4))))*(A*b - B*a)*1i)/b^(13/4) - ((-a)^(5/4)*atan((((-a)^(5/4)*((16*x^(1/2)*(B^2*a^6 + A^2*a^4*b^2 - 2*A*B*a^5*b))/b^3 - ((-a)^(5/4)*(A*b - B*a)*(32*B*a^4 - 32*A*a^3*b)*1i)/(2*b^(13/4)))*(A*b - B*a))/(2*b^(13/4)) + ((-a)^(5/4)*((16*x^(1/2)*(B^2*a^6 + A^2*a^4*b^2 - 2*A*B*a^5*b))/b^3 + ((-a)^(5/4)*(A*b - B*a)*(32*B*a^4 - 32*A*a^3*b)*1i)/(2*b^(13/4)))*(A*b - B*a))/(2*b^(13/4)))/(((-a)^(5/4)*((16*x^(1/2)*(B^2*a^6 + A^2*a^4*b^2 - 2*A*B*a^5*b))/b^3 - ((-a)^(5/4)*(A*b - B*a)*(32*B*a^4 - 32*A*a^3*b)*1i)/(2*b^(13/4)))*(A*b - B*a)*1i)/(2*b^(13/4)) - ((-a)^(5/4)*((16*x^(1/2)*(B^2*a^6 + A^2*a^4*b^2 - 2*A*B*a^5*b))/b^3 + ((-a)^(5/4)*(A*b - B*a)*(32*B*a^4 - 32*A*a^3*b)*1i)/(2*b^(13/4)))*(A*b - B*a)*1i)/(2*b^(13/4))))*(A*b - B*a))/b^(13/4) - (a*x^(1/2)*((2*A)/b - (2*B*a)/b^2))/b","B"
368,1,92,257,0.178897,"\text{Not used}","int((x^(5/2)*(A + B*x^2))/(a + b*x^2),x)","x^{3/2}\,\left(\frac{2\,A}{3\,b}-\frac{2\,B\,a}{3\,b^2}\right)+\frac{2\,B\,x^{7/2}}{7\,b}+\frac{{\left(-a\right)}^{3/4}\,\mathrm{atan}\left(\frac{b^{1/4}\,\sqrt{x}}{{\left(-a\right)}^{1/4}}\right)\,\left(A\,b-B\,a\right)}{b^{11/4}}+\frac{{\left(-a\right)}^{3/4}\,\mathrm{atan}\left(\frac{b^{1/4}\,\sqrt{x}\,1{}\mathrm{i}}{{\left(-a\right)}^{1/4}}\right)\,\left(A\,b-B\,a\right)\,1{}\mathrm{i}}{b^{11/4}}","Not used",1,"x^(3/2)*((2*A)/(3*b) - (2*B*a)/(3*b^2)) + (2*B*x^(7/2))/(7*b) + ((-a)^(3/4)*atan((b^(1/4)*x^(1/2))/(-a)^(1/4))*(A*b - B*a))/b^(11/4) + ((-a)^(3/4)*atan((b^(1/4)*x^(1/2)*1i)/(-a)^(1/4))*(A*b - B*a)*1i)/b^(11/4)","B"
369,1,789,255,0.380022,"\text{Not used}","int((x^(3/2)*(A + B*x^2))/(a + b*x^2),x)","\sqrt{x}\,\left(\frac{2\,A}{b}-\frac{2\,B\,a}{b^2}\right)+\frac{2\,B\,x^{5/2}}{5\,b}-\frac{{\left(-a\right)}^{1/4}\,\mathrm{atan}\left(\frac{\frac{{\left(-a\right)}^{1/4}\,\left(A\,b-B\,a\right)\,\left(\frac{16\,\sqrt{x}\,\left(A^2\,a^2\,b^2-2\,A\,B\,a^3\,b+B^2\,a^4\right)}{b}-\frac{{\left(-a\right)}^{1/4}\,\left(32\,A\,a^2\,b^2-32\,B\,a^3\,b\right)\,\left(A\,b-B\,a\right)}{2\,b^{9/4}}\right)\,1{}\mathrm{i}}{2\,b^{9/4}}+\frac{{\left(-a\right)}^{1/4}\,\left(A\,b-B\,a\right)\,\left(\frac{16\,\sqrt{x}\,\left(A^2\,a^2\,b^2-2\,A\,B\,a^3\,b+B^2\,a^4\right)}{b}+\frac{{\left(-a\right)}^{1/4}\,\left(32\,A\,a^2\,b^2-32\,B\,a^3\,b\right)\,\left(A\,b-B\,a\right)}{2\,b^{9/4}}\right)\,1{}\mathrm{i}}{2\,b^{9/4}}}{\frac{{\left(-a\right)}^{1/4}\,\left(A\,b-B\,a\right)\,\left(\frac{16\,\sqrt{x}\,\left(A^2\,a^2\,b^2-2\,A\,B\,a^3\,b+B^2\,a^4\right)}{b}-\frac{{\left(-a\right)}^{1/4}\,\left(32\,A\,a^2\,b^2-32\,B\,a^3\,b\right)\,\left(A\,b-B\,a\right)}{2\,b^{9/4}}\right)}{2\,b^{9/4}}-\frac{{\left(-a\right)}^{1/4}\,\left(A\,b-B\,a\right)\,\left(\frac{16\,\sqrt{x}\,\left(A^2\,a^2\,b^2-2\,A\,B\,a^3\,b+B^2\,a^4\right)}{b}+\frac{{\left(-a\right)}^{1/4}\,\left(32\,A\,a^2\,b^2-32\,B\,a^3\,b\right)\,\left(A\,b-B\,a\right)}{2\,b^{9/4}}\right)}{2\,b^{9/4}}}\right)\,\left(A\,b-B\,a\right)\,1{}\mathrm{i}}{b^{9/4}}-\frac{{\left(-a\right)}^{1/4}\,\mathrm{atan}\left(\frac{\frac{{\left(-a\right)}^{1/4}\,\left(A\,b-B\,a\right)\,\left(\frac{16\,\sqrt{x}\,\left(A^2\,a^2\,b^2-2\,A\,B\,a^3\,b+B^2\,a^4\right)}{b}-\frac{{\left(-a\right)}^{1/4}\,\left(32\,A\,a^2\,b^2-32\,B\,a^3\,b\right)\,\left(A\,b-B\,a\right)\,1{}\mathrm{i}}{2\,b^{9/4}}\right)}{2\,b^{9/4}}+\frac{{\left(-a\right)}^{1/4}\,\left(A\,b-B\,a\right)\,\left(\frac{16\,\sqrt{x}\,\left(A^2\,a^2\,b^2-2\,A\,B\,a^3\,b+B^2\,a^4\right)}{b}+\frac{{\left(-a\right)}^{1/4}\,\left(32\,A\,a^2\,b^2-32\,B\,a^3\,b\right)\,\left(A\,b-B\,a\right)\,1{}\mathrm{i}}{2\,b^{9/4}}\right)}{2\,b^{9/4}}}{\frac{{\left(-a\right)}^{1/4}\,\left(A\,b-B\,a\right)\,\left(\frac{16\,\sqrt{x}\,\left(A^2\,a^2\,b^2-2\,A\,B\,a^3\,b+B^2\,a^4\right)}{b}-\frac{{\left(-a\right)}^{1/4}\,\left(32\,A\,a^2\,b^2-32\,B\,a^3\,b\right)\,\left(A\,b-B\,a\right)\,1{}\mathrm{i}}{2\,b^{9/4}}\right)\,1{}\mathrm{i}}{2\,b^{9/4}}-\frac{{\left(-a\right)}^{1/4}\,\left(A\,b-B\,a\right)\,\left(\frac{16\,\sqrt{x}\,\left(A^2\,a^2\,b^2-2\,A\,B\,a^3\,b+B^2\,a^4\right)}{b}+\frac{{\left(-a\right)}^{1/4}\,\left(32\,A\,a^2\,b^2-32\,B\,a^3\,b\right)\,\left(A\,b-B\,a\right)\,1{}\mathrm{i}}{2\,b^{9/4}}\right)\,1{}\mathrm{i}}{2\,b^{9/4}}}\right)\,\left(A\,b-B\,a\right)}{b^{9/4}}","Not used",1,"x^(1/2)*((2*A)/b - (2*B*a)/b^2) + (2*B*x^(5/2))/(5*b) - ((-a)^(1/4)*atan((((-a)^(1/4)*(A*b - B*a)*((16*x^(1/2)*(B^2*a^4 + A^2*a^2*b^2 - 2*A*B*a^3*b))/b - ((-a)^(1/4)*(32*A*a^2*b^2 - 32*B*a^3*b)*(A*b - B*a))/(2*b^(9/4)))*1i)/(2*b^(9/4)) + ((-a)^(1/4)*(A*b - B*a)*((16*x^(1/2)*(B^2*a^4 + A^2*a^2*b^2 - 2*A*B*a^3*b))/b + ((-a)^(1/4)*(32*A*a^2*b^2 - 32*B*a^3*b)*(A*b - B*a))/(2*b^(9/4)))*1i)/(2*b^(9/4)))/(((-a)^(1/4)*(A*b - B*a)*((16*x^(1/2)*(B^2*a^4 + A^2*a^2*b^2 - 2*A*B*a^3*b))/b - ((-a)^(1/4)*(32*A*a^2*b^2 - 32*B*a^3*b)*(A*b - B*a))/(2*b^(9/4))))/(2*b^(9/4)) - ((-a)^(1/4)*(A*b - B*a)*((16*x^(1/2)*(B^2*a^4 + A^2*a^2*b^2 - 2*A*B*a^3*b))/b + ((-a)^(1/4)*(32*A*a^2*b^2 - 32*B*a^3*b)*(A*b - B*a))/(2*b^(9/4))))/(2*b^(9/4))))*(A*b - B*a)*1i)/b^(9/4) - ((-a)^(1/4)*atan((((-a)^(1/4)*(A*b - B*a)*((16*x^(1/2)*(B^2*a^4 + A^2*a^2*b^2 - 2*A*B*a^3*b))/b - ((-a)^(1/4)*(32*A*a^2*b^2 - 32*B*a^3*b)*(A*b - B*a)*1i)/(2*b^(9/4))))/(2*b^(9/4)) + ((-a)^(1/4)*(A*b - B*a)*((16*x^(1/2)*(B^2*a^4 + A^2*a^2*b^2 - 2*A*B*a^3*b))/b + ((-a)^(1/4)*(32*A*a^2*b^2 - 32*B*a^3*b)*(A*b - B*a)*1i)/(2*b^(9/4))))/(2*b^(9/4)))/(((-a)^(1/4)*(A*b - B*a)*((16*x^(1/2)*(B^2*a^4 + A^2*a^2*b^2 - 2*A*B*a^3*b))/b - ((-a)^(1/4)*(32*A*a^2*b^2 - 32*B*a^3*b)*(A*b - B*a)*1i)/(2*b^(9/4)))*1i)/(2*b^(9/4)) - ((-a)^(1/4)*(A*b - B*a)*((16*x^(1/2)*(B^2*a^4 + A^2*a^2*b^2 - 2*A*B*a^3*b))/b + ((-a)^(1/4)*(32*A*a^2*b^2 - 32*B*a^3*b)*(A*b - B*a)*1i)/(2*b^(9/4)))*1i)/(2*b^(9/4))))*(A*b - B*a))/b^(9/4)","B"
370,1,71,237,0.154296,"\text{Not used}","int((x^(1/2)*(A + B*x^2))/(a + b*x^2),x)","\frac{2\,B\,x^{3/2}}{3\,b}+\frac{\mathrm{atan}\left(\frac{b^{1/4}\,\sqrt{x}}{{\left(-a\right)}^{1/4}}\right)\,\left(A\,b-B\,a\right)}{{\left(-a\right)}^{1/4}\,b^{7/4}}-\frac{\mathrm{atanh}\left(\frac{b^{1/4}\,\sqrt{x}}{{\left(-a\right)}^{1/4}}\right)\,\left(A\,b-B\,a\right)}{{\left(-a\right)}^{1/4}\,b^{7/4}}","Not used",1,"(2*B*x^(3/2))/(3*b) + (atan((b^(1/4)*x^(1/2))/(-a)^(1/4))*(A*b - B*a))/((-a)^(1/4)*b^(7/4)) - (atanh((b^(1/4)*x^(1/2))/(-a)^(1/4))*(A*b - B*a))/((-a)^(1/4)*b^(7/4))","B"
371,1,739,235,0.238761,"\text{Not used}","int((A + B*x^2)/(x^(1/2)*(a + b*x^2)),x)","\frac{2\,B\,\sqrt{x}}{b}-\frac{\mathrm{atan}\left(\frac{\frac{\left(A\,b-B\,a\right)\,\left(\sqrt{x}\,\left(16\,A^2\,b^3-32\,A\,B\,a\,b^2+16\,B^2\,a^2\,b\right)-\frac{\left(32\,B\,a^2\,b^2-32\,A\,a\,b^3\right)\,\left(A\,b-B\,a\right)}{2\,{\left(-a\right)}^{3/4}\,b^{5/4}}\right)\,1{}\mathrm{i}}{2\,{\left(-a\right)}^{3/4}\,b^{5/4}}+\frac{\left(A\,b-B\,a\right)\,\left(\sqrt{x}\,\left(16\,A^2\,b^3-32\,A\,B\,a\,b^2+16\,B^2\,a^2\,b\right)+\frac{\left(32\,B\,a^2\,b^2-32\,A\,a\,b^3\right)\,\left(A\,b-B\,a\right)}{2\,{\left(-a\right)}^{3/4}\,b^{5/4}}\right)\,1{}\mathrm{i}}{2\,{\left(-a\right)}^{3/4}\,b^{5/4}}}{\frac{\left(A\,b-B\,a\right)\,\left(\sqrt{x}\,\left(16\,A^2\,b^3-32\,A\,B\,a\,b^2+16\,B^2\,a^2\,b\right)-\frac{\left(32\,B\,a^2\,b^2-32\,A\,a\,b^3\right)\,\left(A\,b-B\,a\right)}{2\,{\left(-a\right)}^{3/4}\,b^{5/4}}\right)}{2\,{\left(-a\right)}^{3/4}\,b^{5/4}}-\frac{\left(A\,b-B\,a\right)\,\left(\sqrt{x}\,\left(16\,A^2\,b^3-32\,A\,B\,a\,b^2+16\,B^2\,a^2\,b\right)+\frac{\left(32\,B\,a^2\,b^2-32\,A\,a\,b^3\right)\,\left(A\,b-B\,a\right)}{2\,{\left(-a\right)}^{3/4}\,b^{5/4}}\right)}{2\,{\left(-a\right)}^{3/4}\,b^{5/4}}}\right)\,\left(A\,b-B\,a\right)\,1{}\mathrm{i}}{{\left(-a\right)}^{3/4}\,b^{5/4}}-\frac{\mathrm{atan}\left(\frac{\frac{\left(A\,b-B\,a\right)\,\left(\sqrt{x}\,\left(16\,A^2\,b^3-32\,A\,B\,a\,b^2+16\,B^2\,a^2\,b\right)-\frac{\left(32\,B\,a^2\,b^2-32\,A\,a\,b^3\right)\,\left(A\,b-B\,a\right)\,1{}\mathrm{i}}{2\,{\left(-a\right)}^{3/4}\,b^{5/4}}\right)}{2\,{\left(-a\right)}^{3/4}\,b^{5/4}}+\frac{\left(A\,b-B\,a\right)\,\left(\sqrt{x}\,\left(16\,A^2\,b^3-32\,A\,B\,a\,b^2+16\,B^2\,a^2\,b\right)+\frac{\left(32\,B\,a^2\,b^2-32\,A\,a\,b^3\right)\,\left(A\,b-B\,a\right)\,1{}\mathrm{i}}{2\,{\left(-a\right)}^{3/4}\,b^{5/4}}\right)}{2\,{\left(-a\right)}^{3/4}\,b^{5/4}}}{\frac{\left(A\,b-B\,a\right)\,\left(\sqrt{x}\,\left(16\,A^2\,b^3-32\,A\,B\,a\,b^2+16\,B^2\,a^2\,b\right)-\frac{\left(32\,B\,a^2\,b^2-32\,A\,a\,b^3\right)\,\left(A\,b-B\,a\right)\,1{}\mathrm{i}}{2\,{\left(-a\right)}^{3/4}\,b^{5/4}}\right)\,1{}\mathrm{i}}{2\,{\left(-a\right)}^{3/4}\,b^{5/4}}-\frac{\left(A\,b-B\,a\right)\,\left(\sqrt{x}\,\left(16\,A^2\,b^3-32\,A\,B\,a\,b^2+16\,B^2\,a^2\,b\right)+\frac{\left(32\,B\,a^2\,b^2-32\,A\,a\,b^3\right)\,\left(A\,b-B\,a\right)\,1{}\mathrm{i}}{2\,{\left(-a\right)}^{3/4}\,b^{5/4}}\right)\,1{}\mathrm{i}}{2\,{\left(-a\right)}^{3/4}\,b^{5/4}}}\right)\,\left(A\,b-B\,a\right)}{{\left(-a\right)}^{3/4}\,b^{5/4}}","Not used",1,"(2*B*x^(1/2))/b - (atan((((A*b - B*a)*(x^(1/2)*(16*A^2*b^3 + 16*B^2*a^2*b - 32*A*B*a*b^2) - ((32*B*a^2*b^2 - 32*A*a*b^3)*(A*b - B*a))/(2*(-a)^(3/4)*b^(5/4)))*1i)/(2*(-a)^(3/4)*b^(5/4)) + ((A*b - B*a)*(x^(1/2)*(16*A^2*b^3 + 16*B^2*a^2*b - 32*A*B*a*b^2) + ((32*B*a^2*b^2 - 32*A*a*b^3)*(A*b - B*a))/(2*(-a)^(3/4)*b^(5/4)))*1i)/(2*(-a)^(3/4)*b^(5/4)))/(((A*b - B*a)*(x^(1/2)*(16*A^2*b^3 + 16*B^2*a^2*b - 32*A*B*a*b^2) - ((32*B*a^2*b^2 - 32*A*a*b^3)*(A*b - B*a))/(2*(-a)^(3/4)*b^(5/4))))/(2*(-a)^(3/4)*b^(5/4)) - ((A*b - B*a)*(x^(1/2)*(16*A^2*b^3 + 16*B^2*a^2*b - 32*A*B*a*b^2) + ((32*B*a^2*b^2 - 32*A*a*b^3)*(A*b - B*a))/(2*(-a)^(3/4)*b^(5/4))))/(2*(-a)^(3/4)*b^(5/4))))*(A*b - B*a)*1i)/((-a)^(3/4)*b^(5/4)) - (atan((((A*b - B*a)*(x^(1/2)*(16*A^2*b^3 + 16*B^2*a^2*b - 32*A*B*a*b^2) - ((32*B*a^2*b^2 - 32*A*a*b^3)*(A*b - B*a)*1i)/(2*(-a)^(3/4)*b^(5/4))))/(2*(-a)^(3/4)*b^(5/4)) + ((A*b - B*a)*(x^(1/2)*(16*A^2*b^3 + 16*B^2*a^2*b - 32*A*B*a*b^2) + ((32*B*a^2*b^2 - 32*A*a*b^3)*(A*b - B*a)*1i)/(2*(-a)^(3/4)*b^(5/4))))/(2*(-a)^(3/4)*b^(5/4)))/(((A*b - B*a)*(x^(1/2)*(16*A^2*b^3 + 16*B^2*a^2*b - 32*A*B*a*b^2) - ((32*B*a^2*b^2 - 32*A*a*b^3)*(A*b - B*a)*1i)/(2*(-a)^(3/4)*b^(5/4)))*1i)/(2*(-a)^(3/4)*b^(5/4)) - ((A*b - B*a)*(x^(1/2)*(16*A^2*b^3 + 16*B^2*a^2*b - 32*A*B*a*b^2) + ((32*B*a^2*b^2 - 32*A*a*b^3)*(A*b - B*a)*1i)/(2*(-a)^(3/4)*b^(5/4)))*1i)/(2*(-a)^(3/4)*b^(5/4))))*(A*b - B*a))/((-a)^(3/4)*b^(5/4))","B"
372,1,71,235,0.156563,"\text{Not used}","int((A + B*x^2)/(x^(3/2)*(a + b*x^2)),x)","\frac{\mathrm{atan}\left(\frac{b^{1/4}\,\sqrt{x}}{{\left(-a\right)}^{1/4}}\right)\,\left(A\,b-B\,a\right)}{{\left(-a\right)}^{5/4}\,b^{3/4}}-\frac{2\,A}{a\,\sqrt{x}}-\frac{\mathrm{atanh}\left(\frac{b^{1/4}\,\sqrt{x}}{{\left(-a\right)}^{1/4}}\right)\,\left(A\,b-B\,a\right)}{{\left(-a\right)}^{5/4}\,b^{3/4}}","Not used",1,"(atan((b^(1/4)*x^(1/2))/(-a)^(1/4))*(A*b - B*a))/((-a)^(5/4)*b^(3/4)) - (2*A)/(a*x^(1/2)) - (atanh((b^(1/4)*x^(1/2))/(-a)^(1/4))*(A*b - B*a))/((-a)^(5/4)*b^(3/4))","B"
373,1,811,237,0.384077,"\text{Not used}","int((A + B*x^2)/(x^(5/2)*(a + b*x^2)),x)","-\frac{2\,A}{3\,a\,x^{3/2}}-\frac{\mathrm{atan}\left(\frac{\frac{\left(A\,b-B\,a\right)\,\left(\sqrt{x}\,\left(16\,A^2\,a^3\,b^5-32\,A\,B\,a^4\,b^4+16\,B^2\,a^5\,b^3\right)-\frac{\left(A\,b-B\,a\right)\,\left(32\,A\,a^5\,b^4-32\,B\,a^6\,b^3\right)}{2\,{\left(-a\right)}^{7/4}\,b^{1/4}}\right)\,1{}\mathrm{i}}{2\,{\left(-a\right)}^{7/4}\,b^{1/4}}+\frac{\left(A\,b-B\,a\right)\,\left(\sqrt{x}\,\left(16\,A^2\,a^3\,b^5-32\,A\,B\,a^4\,b^4+16\,B^2\,a^5\,b^3\right)+\frac{\left(A\,b-B\,a\right)\,\left(32\,A\,a^5\,b^4-32\,B\,a^6\,b^3\right)}{2\,{\left(-a\right)}^{7/4}\,b^{1/4}}\right)\,1{}\mathrm{i}}{2\,{\left(-a\right)}^{7/4}\,b^{1/4}}}{\frac{\left(A\,b-B\,a\right)\,\left(\sqrt{x}\,\left(16\,A^2\,a^3\,b^5-32\,A\,B\,a^4\,b^4+16\,B^2\,a^5\,b^3\right)-\frac{\left(A\,b-B\,a\right)\,\left(32\,A\,a^5\,b^4-32\,B\,a^6\,b^3\right)}{2\,{\left(-a\right)}^{7/4}\,b^{1/4}}\right)}{2\,{\left(-a\right)}^{7/4}\,b^{1/4}}-\frac{\left(A\,b-B\,a\right)\,\left(\sqrt{x}\,\left(16\,A^2\,a^3\,b^5-32\,A\,B\,a^4\,b^4+16\,B^2\,a^5\,b^3\right)+\frac{\left(A\,b-B\,a\right)\,\left(32\,A\,a^5\,b^4-32\,B\,a^6\,b^3\right)}{2\,{\left(-a\right)}^{7/4}\,b^{1/4}}\right)}{2\,{\left(-a\right)}^{7/4}\,b^{1/4}}}\right)\,\left(A\,b-B\,a\right)\,1{}\mathrm{i}}{{\left(-a\right)}^{7/4}\,b^{1/4}}-\frac{\mathrm{atan}\left(\frac{\frac{\left(A\,b-B\,a\right)\,\left(\sqrt{x}\,\left(16\,A^2\,a^3\,b^5-32\,A\,B\,a^4\,b^4+16\,B^2\,a^5\,b^3\right)-\frac{\left(A\,b-B\,a\right)\,\left(32\,A\,a^5\,b^4-32\,B\,a^6\,b^3\right)\,1{}\mathrm{i}}{2\,{\left(-a\right)}^{7/4}\,b^{1/4}}\right)}{2\,{\left(-a\right)}^{7/4}\,b^{1/4}}+\frac{\left(A\,b-B\,a\right)\,\left(\sqrt{x}\,\left(16\,A^2\,a^3\,b^5-32\,A\,B\,a^4\,b^4+16\,B^2\,a^5\,b^3\right)+\frac{\left(A\,b-B\,a\right)\,\left(32\,A\,a^5\,b^4-32\,B\,a^6\,b^3\right)\,1{}\mathrm{i}}{2\,{\left(-a\right)}^{7/4}\,b^{1/4}}\right)}{2\,{\left(-a\right)}^{7/4}\,b^{1/4}}}{\frac{\left(A\,b-B\,a\right)\,\left(\sqrt{x}\,\left(16\,A^2\,a^3\,b^5-32\,A\,B\,a^4\,b^4+16\,B^2\,a^5\,b^3\right)-\frac{\left(A\,b-B\,a\right)\,\left(32\,A\,a^5\,b^4-32\,B\,a^6\,b^3\right)\,1{}\mathrm{i}}{2\,{\left(-a\right)}^{7/4}\,b^{1/4}}\right)\,1{}\mathrm{i}}{2\,{\left(-a\right)}^{7/4}\,b^{1/4}}-\frac{\left(A\,b-B\,a\right)\,\left(\sqrt{x}\,\left(16\,A^2\,a^3\,b^5-32\,A\,B\,a^4\,b^4+16\,B^2\,a^5\,b^3\right)+\frac{\left(A\,b-B\,a\right)\,\left(32\,A\,a^5\,b^4-32\,B\,a^6\,b^3\right)\,1{}\mathrm{i}}{2\,{\left(-a\right)}^{7/4}\,b^{1/4}}\right)\,1{}\mathrm{i}}{2\,{\left(-a\right)}^{7/4}\,b^{1/4}}}\right)\,\left(A\,b-B\,a\right)}{{\left(-a\right)}^{7/4}\,b^{1/4}}","Not used",1,"- (2*A)/(3*a*x^(3/2)) - (atan((((A*b - B*a)*(x^(1/2)*(16*A^2*a^3*b^5 + 16*B^2*a^5*b^3 - 32*A*B*a^4*b^4) - ((A*b - B*a)*(32*A*a^5*b^4 - 32*B*a^6*b^3))/(2*(-a)^(7/4)*b^(1/4)))*1i)/(2*(-a)^(7/4)*b^(1/4)) + ((A*b - B*a)*(x^(1/2)*(16*A^2*a^3*b^5 + 16*B^2*a^5*b^3 - 32*A*B*a^4*b^4) + ((A*b - B*a)*(32*A*a^5*b^4 - 32*B*a^6*b^3))/(2*(-a)^(7/4)*b^(1/4)))*1i)/(2*(-a)^(7/4)*b^(1/4)))/(((A*b - B*a)*(x^(1/2)*(16*A^2*a^3*b^5 + 16*B^2*a^5*b^3 - 32*A*B*a^4*b^4) - ((A*b - B*a)*(32*A*a^5*b^4 - 32*B*a^6*b^3))/(2*(-a)^(7/4)*b^(1/4))))/(2*(-a)^(7/4)*b^(1/4)) - ((A*b - B*a)*(x^(1/2)*(16*A^2*a^3*b^5 + 16*B^2*a^5*b^3 - 32*A*B*a^4*b^4) + ((A*b - B*a)*(32*A*a^5*b^4 - 32*B*a^6*b^3))/(2*(-a)^(7/4)*b^(1/4))))/(2*(-a)^(7/4)*b^(1/4))))*(A*b - B*a)*1i)/((-a)^(7/4)*b^(1/4)) - (atan((((A*b - B*a)*(x^(1/2)*(16*A^2*a^3*b^5 + 16*B^2*a^5*b^3 - 32*A*B*a^4*b^4) - ((A*b - B*a)*(32*A*a^5*b^4 - 32*B*a^6*b^3)*1i)/(2*(-a)^(7/4)*b^(1/4))))/(2*(-a)^(7/4)*b^(1/4)) + ((A*b - B*a)*(x^(1/2)*(16*A^2*a^3*b^5 + 16*B^2*a^5*b^3 - 32*A*B*a^4*b^4) + ((A*b - B*a)*(32*A*a^5*b^4 - 32*B*a^6*b^3)*1i)/(2*(-a)^(7/4)*b^(1/4))))/(2*(-a)^(7/4)*b^(1/4)))/(((A*b - B*a)*(x^(1/2)*(16*A^2*a^3*b^5 + 16*B^2*a^5*b^3 - 32*A*B*a^4*b^4) - ((A*b - B*a)*(32*A*a^5*b^4 - 32*B*a^6*b^3)*1i)/(2*(-a)^(7/4)*b^(1/4)))*1i)/(2*(-a)^(7/4)*b^(1/4)) - ((A*b - B*a)*(x^(1/2)*(16*A^2*a^3*b^5 + 16*B^2*a^5*b^3 - 32*A*B*a^4*b^4) + ((A*b - B*a)*(32*A*a^5*b^4 - 32*B*a^6*b^3)*1i)/(2*(-a)^(7/4)*b^(1/4)))*1i)/(2*(-a)^(7/4)*b^(1/4))))*(A*b - B*a))/((-a)^(7/4)*b^(1/4))","B"
374,1,90,255,0.307646,"\text{Not used}","int((A + B*x^2)/(x^(7/2)*(a + b*x^2)),x)","\frac{{\left(-b\right)}^{1/4}\,\mathrm{atan}\left(\frac{{\left(-b\right)}^{1/4}\,\sqrt{x}}{a^{1/4}}\right)\,\left(A\,b-B\,a\right)}{a^{9/4}}-\frac{\frac{2\,A}{5\,a}-\frac{2\,x^2\,\left(A\,b-B\,a\right)}{a^2}}{x^{5/2}}-\frac{{\left(-b\right)}^{1/4}\,\mathrm{atanh}\left(\frac{{\left(-b\right)}^{1/4}\,\sqrt{x}}{a^{1/4}}\right)\,\left(A\,b-B\,a\right)}{a^{9/4}}","Not used",1,"((-b)^(1/4)*atan(((-b)^(1/4)*x^(1/2))/a^(1/4))*(A*b - B*a))/a^(9/4) - ((2*A)/(5*a) - (2*x^2*(A*b - B*a))/a^2)/x^(5/2) - ((-b)^(1/4)*atanh(((-b)^(1/4)*x^(1/2))/a^(1/4))*(A*b - B*a))/a^(9/4)","B"
375,1,823,310,0.365053,"\text{Not used}","int((x^(7/2)*(A + B*x^2))/(a + b*x^2)^2,x)","\sqrt{x}\,\left(\frac{2\,A}{b^2}-\frac{4\,B\,a}{b^3}\right)+\frac{2\,B\,x^{5/2}}{5\,b^2}-\frac{\sqrt{x}\,\left(\frac{B\,a^2}{2}-\frac{A\,a\,b}{2}\right)}{b^4\,x^2+a\,b^3}+\frac{{\left(-a\right)}^{1/4}\,\mathrm{atan}\left(\frac{\frac{{\left(-a\right)}^{1/4}\,\left(\frac{\sqrt{x}\,\left(25\,A^2\,a^2\,b^2-90\,A\,B\,a^3\,b+81\,B^2\,a^4\right)}{b^3}-\frac{{\left(-a\right)}^{1/4}\,\left(5\,A\,b-9\,B\,a\right)\,\left(72\,B\,a^3-40\,A\,a^2\,b\right)}{8\,b^{13/4}}\right)\,\left(5\,A\,b-9\,B\,a\right)\,1{}\mathrm{i}}{8\,b^{13/4}}+\frac{{\left(-a\right)}^{1/4}\,\left(\frac{\sqrt{x}\,\left(25\,A^2\,a^2\,b^2-90\,A\,B\,a^3\,b+81\,B^2\,a^4\right)}{b^3}+\frac{{\left(-a\right)}^{1/4}\,\left(5\,A\,b-9\,B\,a\right)\,\left(72\,B\,a^3-40\,A\,a^2\,b\right)}{8\,b^{13/4}}\right)\,\left(5\,A\,b-9\,B\,a\right)\,1{}\mathrm{i}}{8\,b^{13/4}}}{\frac{{\left(-a\right)}^{1/4}\,\left(\frac{\sqrt{x}\,\left(25\,A^2\,a^2\,b^2-90\,A\,B\,a^3\,b+81\,B^2\,a^4\right)}{b^3}-\frac{{\left(-a\right)}^{1/4}\,\left(5\,A\,b-9\,B\,a\right)\,\left(72\,B\,a^3-40\,A\,a^2\,b\right)}{8\,b^{13/4}}\right)\,\left(5\,A\,b-9\,B\,a\right)}{8\,b^{13/4}}-\frac{{\left(-a\right)}^{1/4}\,\left(\frac{\sqrt{x}\,\left(25\,A^2\,a^2\,b^2-90\,A\,B\,a^3\,b+81\,B^2\,a^4\right)}{b^3}+\frac{{\left(-a\right)}^{1/4}\,\left(5\,A\,b-9\,B\,a\right)\,\left(72\,B\,a^3-40\,A\,a^2\,b\right)}{8\,b^{13/4}}\right)\,\left(5\,A\,b-9\,B\,a\right)}{8\,b^{13/4}}}\right)\,\left(5\,A\,b-9\,B\,a\right)\,1{}\mathrm{i}}{4\,b^{13/4}}+\frac{{\left(-a\right)}^{1/4}\,\mathrm{atan}\left(\frac{\frac{{\left(-a\right)}^{1/4}\,\left(\frac{\sqrt{x}\,\left(25\,A^2\,a^2\,b^2-90\,A\,B\,a^3\,b+81\,B^2\,a^4\right)}{b^3}-\frac{{\left(-a\right)}^{1/4}\,\left(5\,A\,b-9\,B\,a\right)\,\left(72\,B\,a^3-40\,A\,a^2\,b\right)\,1{}\mathrm{i}}{8\,b^{13/4}}\right)\,\left(5\,A\,b-9\,B\,a\right)}{8\,b^{13/4}}+\frac{{\left(-a\right)}^{1/4}\,\left(\frac{\sqrt{x}\,\left(25\,A^2\,a^2\,b^2-90\,A\,B\,a^3\,b+81\,B^2\,a^4\right)}{b^3}+\frac{{\left(-a\right)}^{1/4}\,\left(5\,A\,b-9\,B\,a\right)\,\left(72\,B\,a^3-40\,A\,a^2\,b\right)\,1{}\mathrm{i}}{8\,b^{13/4}}\right)\,\left(5\,A\,b-9\,B\,a\right)}{8\,b^{13/4}}}{\frac{{\left(-a\right)}^{1/4}\,\left(\frac{\sqrt{x}\,\left(25\,A^2\,a^2\,b^2-90\,A\,B\,a^3\,b+81\,B^2\,a^4\right)}{b^3}-\frac{{\left(-a\right)}^{1/4}\,\left(5\,A\,b-9\,B\,a\right)\,\left(72\,B\,a^3-40\,A\,a^2\,b\right)\,1{}\mathrm{i}}{8\,b^{13/4}}\right)\,\left(5\,A\,b-9\,B\,a\right)\,1{}\mathrm{i}}{8\,b^{13/4}}-\frac{{\left(-a\right)}^{1/4}\,\left(\frac{\sqrt{x}\,\left(25\,A^2\,a^2\,b^2-90\,A\,B\,a^3\,b+81\,B^2\,a^4\right)}{b^3}+\frac{{\left(-a\right)}^{1/4}\,\left(5\,A\,b-9\,B\,a\right)\,\left(72\,B\,a^3-40\,A\,a^2\,b\right)\,1{}\mathrm{i}}{8\,b^{13/4}}\right)\,\left(5\,A\,b-9\,B\,a\right)\,1{}\mathrm{i}}{8\,b^{13/4}}}\right)\,\left(5\,A\,b-9\,B\,a\right)}{4\,b^{13/4}}","Not used",1,"x^(1/2)*((2*A)/b^2 - (4*B*a)/b^3) + (2*B*x^(5/2))/(5*b^2) - (x^(1/2)*((B*a^2)/2 - (A*a*b)/2))/(a*b^3 + b^4*x^2) + ((-a)^(1/4)*atan((((-a)^(1/4)*((x^(1/2)*(81*B^2*a^4 + 25*A^2*a^2*b^2 - 90*A*B*a^3*b))/b^3 - ((-a)^(1/4)*(5*A*b - 9*B*a)*(72*B*a^3 - 40*A*a^2*b))/(8*b^(13/4)))*(5*A*b - 9*B*a)*1i)/(8*b^(13/4)) + ((-a)^(1/4)*((x^(1/2)*(81*B^2*a^4 + 25*A^2*a^2*b^2 - 90*A*B*a^3*b))/b^3 + ((-a)^(1/4)*(5*A*b - 9*B*a)*(72*B*a^3 - 40*A*a^2*b))/(8*b^(13/4)))*(5*A*b - 9*B*a)*1i)/(8*b^(13/4)))/(((-a)^(1/4)*((x^(1/2)*(81*B^2*a^4 + 25*A^2*a^2*b^2 - 90*A*B*a^3*b))/b^3 - ((-a)^(1/4)*(5*A*b - 9*B*a)*(72*B*a^3 - 40*A*a^2*b))/(8*b^(13/4)))*(5*A*b - 9*B*a))/(8*b^(13/4)) - ((-a)^(1/4)*((x^(1/2)*(81*B^2*a^4 + 25*A^2*a^2*b^2 - 90*A*B*a^3*b))/b^3 + ((-a)^(1/4)*(5*A*b - 9*B*a)*(72*B*a^3 - 40*A*a^2*b))/(8*b^(13/4)))*(5*A*b - 9*B*a))/(8*b^(13/4))))*(5*A*b - 9*B*a)*1i)/(4*b^(13/4)) + ((-a)^(1/4)*atan((((-a)^(1/4)*((x^(1/2)*(81*B^2*a^4 + 25*A^2*a^2*b^2 - 90*A*B*a^3*b))/b^3 - ((-a)^(1/4)*(5*A*b - 9*B*a)*(72*B*a^3 - 40*A*a^2*b)*1i)/(8*b^(13/4)))*(5*A*b - 9*B*a))/(8*b^(13/4)) + ((-a)^(1/4)*((x^(1/2)*(81*B^2*a^4 + 25*A^2*a^2*b^2 - 90*A*B*a^3*b))/b^3 + ((-a)^(1/4)*(5*A*b - 9*B*a)*(72*B*a^3 - 40*A*a^2*b)*1i)/(8*b^(13/4)))*(5*A*b - 9*B*a))/(8*b^(13/4)))/(((-a)^(1/4)*((x^(1/2)*(81*B^2*a^4 + 25*A^2*a^2*b^2 - 90*A*B*a^3*b))/b^3 - ((-a)^(1/4)*(5*A*b - 9*B*a)*(72*B*a^3 - 40*A*a^2*b)*1i)/(8*b^(13/4)))*(5*A*b - 9*B*a)*1i)/(8*b^(13/4)) - ((-a)^(1/4)*((x^(1/2)*(81*B^2*a^4 + 25*A^2*a^2*b^2 - 90*A*B*a^3*b))/b^3 + ((-a)^(1/4)*(5*A*b - 9*B*a)*(72*B*a^3 - 40*A*a^2*b)*1i)/(8*b^(13/4)))*(5*A*b - 9*B*a)*1i)/(8*b^(13/4))))*(5*A*b - 9*B*a))/(4*b^(13/4))","B"
376,1,106,289,0.196660,"\text{Not used}","int((x^(5/2)*(A + B*x^2))/(a + b*x^2)^2,x)","\frac{2\,B\,x^{3/2}}{3\,b^2}-\frac{x^{3/2}\,\left(\frac{A\,b}{2}-\frac{B\,a}{2}\right)}{b^3\,x^2+a\,b^2}+\frac{\mathrm{atan}\left(\frac{b^{1/4}\,\sqrt{x}}{{\left(-a\right)}^{1/4}}\right)\,\left(3\,A\,b-7\,B\,a\right)}{4\,{\left(-a\right)}^{1/4}\,b^{11/4}}+\frac{\mathrm{atan}\left(\frac{b^{1/4}\,\sqrt{x}\,1{}\mathrm{i}}{{\left(-a\right)}^{1/4}}\right)\,\left(3\,A\,b-7\,B\,a\right)\,1{}\mathrm{i}}{4\,{\left(-a\right)}^{1/4}\,b^{11/4}}","Not used",1,"(2*B*x^(3/2))/(3*b^2) - (x^(3/2)*((A*b)/2 - (B*a)/2))/(a*b^2 + b^3*x^2) + (atan((b^(1/4)*x^(1/2))/(-a)^(1/4))*(3*A*b - 7*B*a))/(4*(-a)^(1/4)*b^(11/4)) + (atan((b^(1/4)*x^(1/2)*1i)/(-a)^(1/4))*(3*A*b - 7*B*a)*1i)/(4*(-a)^(1/4)*b^(11/4))","B"
377,1,744,284,0.371552,"\text{Not used}","int((x^(3/2)*(A + B*x^2))/(a + b*x^2)^2,x)","\frac{2\,B\,\sqrt{x}}{b^2}-\frac{\sqrt{x}\,\left(\frac{A\,b}{2}-\frac{B\,a}{2}\right)}{b^3\,x^2+a\,b^2}+\frac{\mathrm{atan}\left(\frac{\frac{\left(A\,b-5\,B\,a\right)\,\left(\frac{\sqrt{x}\,\left(A^2\,b^2-10\,A\,B\,a\,b+25\,B^2\,a^2\right)}{b}-\frac{\left(A\,b-5\,B\,a\right)\,\left(8\,A\,a\,b^2-40\,B\,a^2\,b\right)}{8\,{\left(-a\right)}^{3/4}\,b^{9/4}}\right)\,1{}\mathrm{i}}{8\,{\left(-a\right)}^{3/4}\,b^{9/4}}+\frac{\left(A\,b-5\,B\,a\right)\,\left(\frac{\sqrt{x}\,\left(A^2\,b^2-10\,A\,B\,a\,b+25\,B^2\,a^2\right)}{b}+\frac{\left(A\,b-5\,B\,a\right)\,\left(8\,A\,a\,b^2-40\,B\,a^2\,b\right)}{8\,{\left(-a\right)}^{3/4}\,b^{9/4}}\right)\,1{}\mathrm{i}}{8\,{\left(-a\right)}^{3/4}\,b^{9/4}}}{\frac{\left(A\,b-5\,B\,a\right)\,\left(\frac{\sqrt{x}\,\left(A^2\,b^2-10\,A\,B\,a\,b+25\,B^2\,a^2\right)}{b}-\frac{\left(A\,b-5\,B\,a\right)\,\left(8\,A\,a\,b^2-40\,B\,a^2\,b\right)}{8\,{\left(-a\right)}^{3/4}\,b^{9/4}}\right)}{8\,{\left(-a\right)}^{3/4}\,b^{9/4}}-\frac{\left(A\,b-5\,B\,a\right)\,\left(\frac{\sqrt{x}\,\left(A^2\,b^2-10\,A\,B\,a\,b+25\,B^2\,a^2\right)}{b}+\frac{\left(A\,b-5\,B\,a\right)\,\left(8\,A\,a\,b^2-40\,B\,a^2\,b\right)}{8\,{\left(-a\right)}^{3/4}\,b^{9/4}}\right)}{8\,{\left(-a\right)}^{3/4}\,b^{9/4}}}\right)\,\left(A\,b-5\,B\,a\right)\,1{}\mathrm{i}}{4\,{\left(-a\right)}^{3/4}\,b^{9/4}}+\frac{\mathrm{atan}\left(\frac{\frac{\left(A\,b-5\,B\,a\right)\,\left(\frac{\sqrt{x}\,\left(A^2\,b^2-10\,A\,B\,a\,b+25\,B^2\,a^2\right)}{b}-\frac{\left(A\,b-5\,B\,a\right)\,\left(8\,A\,a\,b^2-40\,B\,a^2\,b\right)\,1{}\mathrm{i}}{8\,{\left(-a\right)}^{3/4}\,b^{9/4}}\right)}{8\,{\left(-a\right)}^{3/4}\,b^{9/4}}+\frac{\left(A\,b-5\,B\,a\right)\,\left(\frac{\sqrt{x}\,\left(A^2\,b^2-10\,A\,B\,a\,b+25\,B^2\,a^2\right)}{b}+\frac{\left(A\,b-5\,B\,a\right)\,\left(8\,A\,a\,b^2-40\,B\,a^2\,b\right)\,1{}\mathrm{i}}{8\,{\left(-a\right)}^{3/4}\,b^{9/4}}\right)}{8\,{\left(-a\right)}^{3/4}\,b^{9/4}}}{\frac{\left(A\,b-5\,B\,a\right)\,\left(\frac{\sqrt{x}\,\left(A^2\,b^2-10\,A\,B\,a\,b+25\,B^2\,a^2\right)}{b}-\frac{\left(A\,b-5\,B\,a\right)\,\left(8\,A\,a\,b^2-40\,B\,a^2\,b\right)\,1{}\mathrm{i}}{8\,{\left(-a\right)}^{3/4}\,b^{9/4}}\right)\,1{}\mathrm{i}}{8\,{\left(-a\right)}^{3/4}\,b^{9/4}}-\frac{\left(A\,b-5\,B\,a\right)\,\left(\frac{\sqrt{x}\,\left(A^2\,b^2-10\,A\,B\,a\,b+25\,B^2\,a^2\right)}{b}+\frac{\left(A\,b-5\,B\,a\right)\,\left(8\,A\,a\,b^2-40\,B\,a^2\,b\right)\,1{}\mathrm{i}}{8\,{\left(-a\right)}^{3/4}\,b^{9/4}}\right)\,1{}\mathrm{i}}{8\,{\left(-a\right)}^{3/4}\,b^{9/4}}}\right)\,\left(A\,b-5\,B\,a\right)}{4\,{\left(-a\right)}^{3/4}\,b^{9/4}}","Not used",1,"(2*B*x^(1/2))/b^2 - (x^(1/2)*((A*b)/2 - (B*a)/2))/(a*b^2 + b^3*x^2) + (atan((((A*b - 5*B*a)*((x^(1/2)*(A^2*b^2 + 25*B^2*a^2 - 10*A*B*a*b))/b - ((A*b - 5*B*a)*(8*A*a*b^2 - 40*B*a^2*b))/(8*(-a)^(3/4)*b^(9/4)))*1i)/(8*(-a)^(3/4)*b^(9/4)) + ((A*b - 5*B*a)*((x^(1/2)*(A^2*b^2 + 25*B^2*a^2 - 10*A*B*a*b))/b + ((A*b - 5*B*a)*(8*A*a*b^2 - 40*B*a^2*b))/(8*(-a)^(3/4)*b^(9/4)))*1i)/(8*(-a)^(3/4)*b^(9/4)))/(((A*b - 5*B*a)*((x^(1/2)*(A^2*b^2 + 25*B^2*a^2 - 10*A*B*a*b))/b - ((A*b - 5*B*a)*(8*A*a*b^2 - 40*B*a^2*b))/(8*(-a)^(3/4)*b^(9/4))))/(8*(-a)^(3/4)*b^(9/4)) - ((A*b - 5*B*a)*((x^(1/2)*(A^2*b^2 + 25*B^2*a^2 - 10*A*B*a*b))/b + ((A*b - 5*B*a)*(8*A*a*b^2 - 40*B*a^2*b))/(8*(-a)^(3/4)*b^(9/4))))/(8*(-a)^(3/4)*b^(9/4))))*(A*b - 5*B*a)*1i)/(4*(-a)^(3/4)*b^(9/4)) + (atan((((A*b - 5*B*a)*((x^(1/2)*(A^2*b^2 + 25*B^2*a^2 - 10*A*B*a*b))/b - ((A*b - 5*B*a)*(8*A*a*b^2 - 40*B*a^2*b)*1i)/(8*(-a)^(3/4)*b^(9/4))))/(8*(-a)^(3/4)*b^(9/4)) + ((A*b - 5*B*a)*((x^(1/2)*(A^2*b^2 + 25*B^2*a^2 - 10*A*B*a*b))/b + ((A*b - 5*B*a)*(8*A*a*b^2 - 40*B*a^2*b)*1i)/(8*(-a)^(3/4)*b^(9/4))))/(8*(-a)^(3/4)*b^(9/4)))/(((A*b - 5*B*a)*((x^(1/2)*(A^2*b^2 + 25*B^2*a^2 - 10*A*B*a*b))/b - ((A*b - 5*B*a)*(8*A*a*b^2 - 40*B*a^2*b)*1i)/(8*(-a)^(3/4)*b^(9/4)))*1i)/(8*(-a)^(3/4)*b^(9/4)) - ((A*b - 5*B*a)*((x^(1/2)*(A^2*b^2 + 25*B^2*a^2 - 10*A*B*a*b))/b + ((A*b - 5*B*a)*(8*A*a*b^2 - 40*B*a^2*b)*1i)/(8*(-a)^(3/4)*b^(9/4)))*1i)/(8*(-a)^(3/4)*b^(9/4))))*(A*b - 5*B*a))/(4*(-a)^(3/4)*b^(9/4))","B"
378,1,91,261,0.312632,"\text{Not used}","int((x^(1/2)*(A + B*x^2))/(a + b*x^2)^2,x)","\frac{\mathrm{atanh}\left(\frac{b^{1/4}\,\sqrt{x}}{{\left(-a\right)}^{1/4}}\right)\,\left(A\,b+3\,B\,a\right)}{4\,{\left(-a\right)}^{5/4}\,b^{7/4}}-\frac{\mathrm{atan}\left(\frac{b^{1/4}\,\sqrt{x}}{{\left(-a\right)}^{1/4}}\right)\,\left(A\,b+3\,B\,a\right)}{4\,{\left(-a\right)}^{5/4}\,b^{7/4}}+\frac{x^{3/2}\,\left(A\,b-B\,a\right)}{2\,a\,b\,\left(b\,x^2+a\right)}","Not used",1,"(atanh((b^(1/4)*x^(1/2))/(-a)^(1/4))*(A*b + 3*B*a))/(4*(-a)^(5/4)*b^(7/4)) - (atan((b^(1/4)*x^(1/2))/(-a)^(1/4))*(A*b + 3*B*a))/(4*(-a)^(5/4)*b^(7/4)) + (x^(3/2)*(A*b - B*a))/(2*a*b*(a + b*x^2))","B"
379,1,750,261,0.428744,"\text{Not used}","int((A + B*x^2)/(x^(1/2)*(a + b*x^2)^2),x)","\frac{\mathrm{atan}\left(\frac{\frac{\left(3\,A\,b+B\,a\right)\,\left(\frac{\sqrt{x}\,\left(9\,A^2\,b^3+6\,A\,B\,a\,b^2+B^2\,a^2\,b\right)}{a^2}-\frac{\left(3\,A\,b+B\,a\right)\,\left(24\,A\,b^3+8\,B\,a\,b^2\right)\,1{}\mathrm{i}}{8\,{\left(-a\right)}^{7/4}\,b^{5/4}}\right)}{8\,{\left(-a\right)}^{7/4}\,b^{5/4}}+\frac{\left(3\,A\,b+B\,a\right)\,\left(\frac{\sqrt{x}\,\left(9\,A^2\,b^3+6\,A\,B\,a\,b^2+B^2\,a^2\,b\right)}{a^2}+\frac{\left(3\,A\,b+B\,a\right)\,\left(24\,A\,b^3+8\,B\,a\,b^2\right)\,1{}\mathrm{i}}{8\,{\left(-a\right)}^{7/4}\,b^{5/4}}\right)}{8\,{\left(-a\right)}^{7/4}\,b^{5/4}}}{\frac{\left(3\,A\,b+B\,a\right)\,\left(\frac{\sqrt{x}\,\left(9\,A^2\,b^3+6\,A\,B\,a\,b^2+B^2\,a^2\,b\right)}{a^2}-\frac{\left(3\,A\,b+B\,a\right)\,\left(24\,A\,b^3+8\,B\,a\,b^2\right)\,1{}\mathrm{i}}{8\,{\left(-a\right)}^{7/4}\,b^{5/4}}\right)\,1{}\mathrm{i}}{8\,{\left(-a\right)}^{7/4}\,b^{5/4}}-\frac{\left(3\,A\,b+B\,a\right)\,\left(\frac{\sqrt{x}\,\left(9\,A^2\,b^3+6\,A\,B\,a\,b^2+B^2\,a^2\,b\right)}{a^2}+\frac{\left(3\,A\,b+B\,a\right)\,\left(24\,A\,b^3+8\,B\,a\,b^2\right)\,1{}\mathrm{i}}{8\,{\left(-a\right)}^{7/4}\,b^{5/4}}\right)\,1{}\mathrm{i}}{8\,{\left(-a\right)}^{7/4}\,b^{5/4}}}\right)\,\left(3\,A\,b+B\,a\right)}{4\,{\left(-a\right)}^{7/4}\,b^{5/4}}+\frac{\sqrt{x}\,\left(A\,b-B\,a\right)}{2\,a\,b\,\left(b\,x^2+a\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(3\,A\,b+B\,a\right)\,\left(\frac{\sqrt{x}\,\left(9\,A^2\,b^3+6\,A\,B\,a\,b^2+B^2\,a^2\,b\right)}{a^2}-\frac{\left(3\,A\,b+B\,a\right)\,\left(24\,A\,b^3+8\,B\,a\,b^2\right)}{8\,{\left(-a\right)}^{7/4}\,b^{5/4}}\right)\,1{}\mathrm{i}}{8\,{\left(-a\right)}^{7/4}\,b^{5/4}}+\frac{\left(3\,A\,b+B\,a\right)\,\left(\frac{\sqrt{x}\,\left(9\,A^2\,b^3+6\,A\,B\,a\,b^2+B^2\,a^2\,b\right)}{a^2}+\frac{\left(3\,A\,b+B\,a\right)\,\left(24\,A\,b^3+8\,B\,a\,b^2\right)}{8\,{\left(-a\right)}^{7/4}\,b^{5/4}}\right)\,1{}\mathrm{i}}{8\,{\left(-a\right)}^{7/4}\,b^{5/4}}}{\frac{\left(3\,A\,b+B\,a\right)\,\left(\frac{\sqrt{x}\,\left(9\,A^2\,b^3+6\,A\,B\,a\,b^2+B^2\,a^2\,b\right)}{a^2}-\frac{\left(3\,A\,b+B\,a\right)\,\left(24\,A\,b^3+8\,B\,a\,b^2\right)}{8\,{\left(-a\right)}^{7/4}\,b^{5/4}}\right)}{8\,{\left(-a\right)}^{7/4}\,b^{5/4}}-\frac{\left(3\,A\,b+B\,a\right)\,\left(\frac{\sqrt{x}\,\left(9\,A^2\,b^3+6\,A\,B\,a\,b^2+B^2\,a^2\,b\right)}{a^2}+\frac{\left(3\,A\,b+B\,a\right)\,\left(24\,A\,b^3+8\,B\,a\,b^2\right)}{8\,{\left(-a\right)}^{7/4}\,b^{5/4}}\right)}{8\,{\left(-a\right)}^{7/4}\,b^{5/4}}}\right)\,\left(3\,A\,b+B\,a\right)\,1{}\mathrm{i}}{4\,{\left(-a\right)}^{7/4}\,b^{5/4}}","Not used",1,"(atan((((3*A*b + B*a)*((x^(1/2)*(9*A^2*b^3 + B^2*a^2*b + 6*A*B*a*b^2))/a^2 - ((3*A*b + B*a)*(24*A*b^3 + 8*B*a*b^2))/(8*(-a)^(7/4)*b^(5/4)))*1i)/(8*(-a)^(7/4)*b^(5/4)) + ((3*A*b + B*a)*((x^(1/2)*(9*A^2*b^3 + B^2*a^2*b + 6*A*B*a*b^2))/a^2 + ((3*A*b + B*a)*(24*A*b^3 + 8*B*a*b^2))/(8*(-a)^(7/4)*b^(5/4)))*1i)/(8*(-a)^(7/4)*b^(5/4)))/(((3*A*b + B*a)*((x^(1/2)*(9*A^2*b^3 + B^2*a^2*b + 6*A*B*a*b^2))/a^2 - ((3*A*b + B*a)*(24*A*b^3 + 8*B*a*b^2))/(8*(-a)^(7/4)*b^(5/4))))/(8*(-a)^(7/4)*b^(5/4)) - ((3*A*b + B*a)*((x^(1/2)*(9*A^2*b^3 + B^2*a^2*b + 6*A*B*a*b^2))/a^2 + ((3*A*b + B*a)*(24*A*b^3 + 8*B*a*b^2))/(8*(-a)^(7/4)*b^(5/4))))/(8*(-a)^(7/4)*b^(5/4))))*(3*A*b + B*a)*1i)/(4*(-a)^(7/4)*b^(5/4)) + (atan((((3*A*b + B*a)*((x^(1/2)*(9*A^2*b^3 + B^2*a^2*b + 6*A*B*a*b^2))/a^2 - ((3*A*b + B*a)*(24*A*b^3 + 8*B*a*b^2)*1i)/(8*(-a)^(7/4)*b^(5/4))))/(8*(-a)^(7/4)*b^(5/4)) + ((3*A*b + B*a)*((x^(1/2)*(9*A^2*b^3 + B^2*a^2*b + 6*A*B*a*b^2))/a^2 + ((3*A*b + B*a)*(24*A*b^3 + 8*B*a*b^2)*1i)/(8*(-a)^(7/4)*b^(5/4))))/(8*(-a)^(7/4)*b^(5/4)))/(((3*A*b + B*a)*((x^(1/2)*(9*A^2*b^3 + B^2*a^2*b + 6*A*B*a*b^2))/a^2 - ((3*A*b + B*a)*(24*A*b^3 + 8*B*a*b^2)*1i)/(8*(-a)^(7/4)*b^(5/4)))*1i)/(8*(-a)^(7/4)*b^(5/4)) - ((3*A*b + B*a)*((x^(1/2)*(9*A^2*b^3 + B^2*a^2*b + 6*A*B*a*b^2))/a^2 + ((3*A*b + B*a)*(24*A*b^3 + 8*B*a*b^2)*1i)/(8*(-a)^(7/4)*b^(5/4)))*1i)/(8*(-a)^(7/4)*b^(5/4))))*(3*A*b + B*a))/(4*(-a)^(7/4)*b^(5/4)) + (x^(1/2)*(A*b - B*a))/(2*a*b*(a + b*x^2))","B"
380,1,104,289,0.320135,"\text{Not used}","int((A + B*x^2)/(x^(3/2)*(a + b*x^2)^2),x)","\frac{\mathrm{atanh}\left(\frac{b^{1/4}\,\sqrt{x}}{{\left(-a\right)}^{1/4}}\right)\,\left(5\,A\,b-B\,a\right)}{4\,{\left(-a\right)}^{9/4}\,b^{3/4}}-\frac{\mathrm{atan}\left(\frac{b^{1/4}\,\sqrt{x}}{{\left(-a\right)}^{1/4}}\right)\,\left(5\,A\,b-B\,a\right)}{4\,{\left(-a\right)}^{9/4}\,b^{3/4}}-\frac{\frac{2\,A}{a}+\frac{x^2\,\left(5\,A\,b-B\,a\right)}{2\,a^2}}{a\,\sqrt{x}+b\,x^{5/2}}","Not used",1,"(atanh((b^(1/4)*x^(1/2))/(-a)^(1/4))*(5*A*b - B*a))/(4*(-a)^(9/4)*b^(3/4)) - (atan((b^(1/4)*x^(1/2))/(-a)^(1/4))*(5*A*b - B*a))/(4*(-a)^(9/4)*b^(3/4)) - ((2*A)/a + (x^2*(5*A*b - B*a))/(2*a^2))/(a*x^(1/2) + b*x^(5/2))","B"
381,1,859,289,0.468973,"\text{Not used}","int((A + B*x^2)/(x^(5/2)*(a + b*x^2)^2),x)","-\frac{\frac{2\,A}{3\,a}+\frac{x^2\,\left(7\,A\,b-3\,B\,a\right)}{6\,a^2}}{a\,x^{3/2}+b\,x^{7/2}}-\frac{\mathrm{atan}\left(\frac{\frac{\left(7\,A\,b-3\,B\,a\right)\,\left(\sqrt{x}\,\left(1568\,A^2\,a^6\,b^5-1344\,A\,B\,a^7\,b^4+288\,B^2\,a^8\,b^3\right)-\frac{\left(7\,A\,b-3\,B\,a\right)\,\left(1792\,A\,a^9\,b^4-768\,B\,a^{10}\,b^3\right)}{8\,{\left(-a\right)}^{11/4}\,b^{1/4}}\right)\,1{}\mathrm{i}}{8\,{\left(-a\right)}^{11/4}\,b^{1/4}}+\frac{\left(7\,A\,b-3\,B\,a\right)\,\left(\sqrt{x}\,\left(1568\,A^2\,a^6\,b^5-1344\,A\,B\,a^7\,b^4+288\,B^2\,a^8\,b^3\right)+\frac{\left(7\,A\,b-3\,B\,a\right)\,\left(1792\,A\,a^9\,b^4-768\,B\,a^{10}\,b^3\right)}{8\,{\left(-a\right)}^{11/4}\,b^{1/4}}\right)\,1{}\mathrm{i}}{8\,{\left(-a\right)}^{11/4}\,b^{1/4}}}{\frac{\left(7\,A\,b-3\,B\,a\right)\,\left(\sqrt{x}\,\left(1568\,A^2\,a^6\,b^5-1344\,A\,B\,a^7\,b^4+288\,B^2\,a^8\,b^3\right)-\frac{\left(7\,A\,b-3\,B\,a\right)\,\left(1792\,A\,a^9\,b^4-768\,B\,a^{10}\,b^3\right)}{8\,{\left(-a\right)}^{11/4}\,b^{1/4}}\right)}{8\,{\left(-a\right)}^{11/4}\,b^{1/4}}-\frac{\left(7\,A\,b-3\,B\,a\right)\,\left(\sqrt{x}\,\left(1568\,A^2\,a^6\,b^5-1344\,A\,B\,a^7\,b^4+288\,B^2\,a^8\,b^3\right)+\frac{\left(7\,A\,b-3\,B\,a\right)\,\left(1792\,A\,a^9\,b^4-768\,B\,a^{10}\,b^3\right)}{8\,{\left(-a\right)}^{11/4}\,b^{1/4}}\right)}{8\,{\left(-a\right)}^{11/4}\,b^{1/4}}}\right)\,\left(7\,A\,b-3\,B\,a\right)\,1{}\mathrm{i}}{4\,{\left(-a\right)}^{11/4}\,b^{1/4}}-\frac{\mathrm{atan}\left(\frac{\frac{\left(7\,A\,b-3\,B\,a\right)\,\left(\sqrt{x}\,\left(1568\,A^2\,a^6\,b^5-1344\,A\,B\,a^7\,b^4+288\,B^2\,a^8\,b^3\right)-\frac{\left(7\,A\,b-3\,B\,a\right)\,\left(1792\,A\,a^9\,b^4-768\,B\,a^{10}\,b^3\right)\,1{}\mathrm{i}}{8\,{\left(-a\right)}^{11/4}\,b^{1/4}}\right)}{8\,{\left(-a\right)}^{11/4}\,b^{1/4}}+\frac{\left(7\,A\,b-3\,B\,a\right)\,\left(\sqrt{x}\,\left(1568\,A^2\,a^6\,b^5-1344\,A\,B\,a^7\,b^4+288\,B^2\,a^8\,b^3\right)+\frac{\left(7\,A\,b-3\,B\,a\right)\,\left(1792\,A\,a^9\,b^4-768\,B\,a^{10}\,b^3\right)\,1{}\mathrm{i}}{8\,{\left(-a\right)}^{11/4}\,b^{1/4}}\right)}{8\,{\left(-a\right)}^{11/4}\,b^{1/4}}}{\frac{\left(7\,A\,b-3\,B\,a\right)\,\left(\sqrt{x}\,\left(1568\,A^2\,a^6\,b^5-1344\,A\,B\,a^7\,b^4+288\,B^2\,a^8\,b^3\right)-\frac{\left(7\,A\,b-3\,B\,a\right)\,\left(1792\,A\,a^9\,b^4-768\,B\,a^{10}\,b^3\right)\,1{}\mathrm{i}}{8\,{\left(-a\right)}^{11/4}\,b^{1/4}}\right)\,1{}\mathrm{i}}{8\,{\left(-a\right)}^{11/4}\,b^{1/4}}-\frac{\left(7\,A\,b-3\,B\,a\right)\,\left(\sqrt{x}\,\left(1568\,A^2\,a^6\,b^5-1344\,A\,B\,a^7\,b^4+288\,B^2\,a^8\,b^3\right)+\frac{\left(7\,A\,b-3\,B\,a\right)\,\left(1792\,A\,a^9\,b^4-768\,B\,a^{10}\,b^3\right)\,1{}\mathrm{i}}{8\,{\left(-a\right)}^{11/4}\,b^{1/4}}\right)\,1{}\mathrm{i}}{8\,{\left(-a\right)}^{11/4}\,b^{1/4}}}\right)\,\left(7\,A\,b-3\,B\,a\right)}{4\,{\left(-a\right)}^{11/4}\,b^{1/4}}","Not used",1,"- ((2*A)/(3*a) + (x^2*(7*A*b - 3*B*a))/(6*a^2))/(a*x^(3/2) + b*x^(7/2)) - (atan((((7*A*b - 3*B*a)*(x^(1/2)*(1568*A^2*a^6*b^5 + 288*B^2*a^8*b^3 - 1344*A*B*a^7*b^4) - ((7*A*b - 3*B*a)*(1792*A*a^9*b^4 - 768*B*a^10*b^3))/(8*(-a)^(11/4)*b^(1/4)))*1i)/(8*(-a)^(11/4)*b^(1/4)) + ((7*A*b - 3*B*a)*(x^(1/2)*(1568*A^2*a^6*b^5 + 288*B^2*a^8*b^3 - 1344*A*B*a^7*b^4) + ((7*A*b - 3*B*a)*(1792*A*a^9*b^4 - 768*B*a^10*b^3))/(8*(-a)^(11/4)*b^(1/4)))*1i)/(8*(-a)^(11/4)*b^(1/4)))/(((7*A*b - 3*B*a)*(x^(1/2)*(1568*A^2*a^6*b^5 + 288*B^2*a^8*b^3 - 1344*A*B*a^7*b^4) - ((7*A*b - 3*B*a)*(1792*A*a^9*b^4 - 768*B*a^10*b^3))/(8*(-a)^(11/4)*b^(1/4))))/(8*(-a)^(11/4)*b^(1/4)) - ((7*A*b - 3*B*a)*(x^(1/2)*(1568*A^2*a^6*b^5 + 288*B^2*a^8*b^3 - 1344*A*B*a^7*b^4) + ((7*A*b - 3*B*a)*(1792*A*a^9*b^4 - 768*B*a^10*b^3))/(8*(-a)^(11/4)*b^(1/4))))/(8*(-a)^(11/4)*b^(1/4))))*(7*A*b - 3*B*a)*1i)/(4*(-a)^(11/4)*b^(1/4)) - (atan((((7*A*b - 3*B*a)*(x^(1/2)*(1568*A^2*a^6*b^5 + 288*B^2*a^8*b^3 - 1344*A*B*a^7*b^4) - ((7*A*b - 3*B*a)*(1792*A*a^9*b^4 - 768*B*a^10*b^3)*1i)/(8*(-a)^(11/4)*b^(1/4))))/(8*(-a)^(11/4)*b^(1/4)) + ((7*A*b - 3*B*a)*(x^(1/2)*(1568*A^2*a^6*b^5 + 288*B^2*a^8*b^3 - 1344*A*B*a^7*b^4) + ((7*A*b - 3*B*a)*(1792*A*a^9*b^4 - 768*B*a^10*b^3)*1i)/(8*(-a)^(11/4)*b^(1/4))))/(8*(-a)^(11/4)*b^(1/4)))/(((7*A*b - 3*B*a)*(x^(1/2)*(1568*A^2*a^6*b^5 + 288*B^2*a^8*b^3 - 1344*A*B*a^7*b^4) - ((7*A*b - 3*B*a)*(1792*A*a^9*b^4 - 768*B*a^10*b^3)*1i)/(8*(-a)^(11/4)*b^(1/4)))*1i)/(8*(-a)^(11/4)*b^(1/4)) - ((7*A*b - 3*B*a)*(x^(1/2)*(1568*A^2*a^6*b^5 + 288*B^2*a^8*b^3 - 1344*A*B*a^7*b^4) + ((7*A*b - 3*B*a)*(1792*A*a^9*b^4 - 768*B*a^10*b^3)*1i)/(8*(-a)^(11/4)*b^(1/4)))*1i)/(8*(-a)^(11/4)*b^(1/4))))*(7*A*b - 3*B*a))/(4*(-a)^(11/4)*b^(1/4))","B"
382,1,121,310,0.175850,"\text{Not used}","int((A + B*x^2)/(x^(7/2)*(a + b*x^2)^2),x)","\frac{\frac{2\,x^2\,\left(9\,A\,b-5\,B\,a\right)}{5\,a^2}-\frac{2\,A}{5\,a}+\frac{b\,x^4\,\left(9\,A\,b-5\,B\,a\right)}{2\,a^3}}{a\,x^{5/2}+b\,x^{9/2}}+\frac{{\left(-b\right)}^{1/4}\,\mathrm{atan}\left(\frac{{\left(-b\right)}^{1/4}\,\sqrt{x}}{a^{1/4}}\right)\,\left(9\,A\,b-5\,B\,a\right)}{4\,a^{13/4}}-\frac{{\left(-b\right)}^{1/4}\,\mathrm{atanh}\left(\frac{{\left(-b\right)}^{1/4}\,\sqrt{x}}{a^{1/4}}\right)\,\left(9\,A\,b-5\,B\,a\right)}{4\,a^{13/4}}","Not used",1,"((2*x^2*(9*A*b - 5*B*a))/(5*a^2) - (2*A)/(5*a) + (b*x^4*(9*A*b - 5*B*a))/(2*a^3))/(a*x^(5/2) + b*x^(9/2)) + ((-b)^(1/4)*atan(((-b)^(1/4)*x^(1/2))/a^(1/4))*(9*A*b - 5*B*a))/(4*a^(13/4)) - ((-b)^(1/4)*atanh(((-b)^(1/4)*x^(1/2))/a^(1/4))*(9*A*b - 5*B*a))/(4*a^(13/4))","B"
383,1,760,316,0.397549,"\text{Not used}","int((x^(7/2)*(A + B*x^2))/(a + b*x^2)^3,x)","\frac{\sqrt{x}\,\left(\frac{13\,B\,a^2}{16}-\frac{5\,A\,a\,b}{16}\right)-x^{5/2}\,\left(\frac{9\,A\,b^2}{16}-\frac{17\,B\,a\,b}{16}\right)}{a^2\,b^3+2\,a\,b^4\,x^2+b^5\,x^4}+\frac{2\,B\,\sqrt{x}}{b^3}-\frac{\mathrm{atan}\left(\frac{\frac{\left(A\,b-9\,B\,a\right)\,\left(\frac{25\,\sqrt{x}\,\left(A^2\,b^2-18\,A\,B\,a\,b+81\,B^2\,a^2\right)}{64\,b^3}-\frac{5\,\left(45\,B\,a^2-5\,A\,a\,b\right)\,\left(A\,b-9\,B\,a\right)}{64\,{\left(-a\right)}^{3/4}\,b^{13/4}}\right)\,5{}\mathrm{i}}{64\,{\left(-a\right)}^{3/4}\,b^{13/4}}+\frac{\left(A\,b-9\,B\,a\right)\,\left(\frac{25\,\sqrt{x}\,\left(A^2\,b^2-18\,A\,B\,a\,b+81\,B^2\,a^2\right)}{64\,b^3}+\frac{5\,\left(45\,B\,a^2-5\,A\,a\,b\right)\,\left(A\,b-9\,B\,a\right)}{64\,{\left(-a\right)}^{3/4}\,b^{13/4}}\right)\,5{}\mathrm{i}}{64\,{\left(-a\right)}^{3/4}\,b^{13/4}}}{\frac{5\,\left(A\,b-9\,B\,a\right)\,\left(\frac{25\,\sqrt{x}\,\left(A^2\,b^2-18\,A\,B\,a\,b+81\,B^2\,a^2\right)}{64\,b^3}-\frac{5\,\left(45\,B\,a^2-5\,A\,a\,b\right)\,\left(A\,b-9\,B\,a\right)}{64\,{\left(-a\right)}^{3/4}\,b^{13/4}}\right)}{64\,{\left(-a\right)}^{3/4}\,b^{13/4}}-\frac{5\,\left(A\,b-9\,B\,a\right)\,\left(\frac{25\,\sqrt{x}\,\left(A^2\,b^2-18\,A\,B\,a\,b+81\,B^2\,a^2\right)}{64\,b^3}+\frac{5\,\left(45\,B\,a^2-5\,A\,a\,b\right)\,\left(A\,b-9\,B\,a\right)}{64\,{\left(-a\right)}^{3/4}\,b^{13/4}}\right)}{64\,{\left(-a\right)}^{3/4}\,b^{13/4}}}\right)\,\left(A\,b-9\,B\,a\right)\,5{}\mathrm{i}}{32\,{\left(-a\right)}^{3/4}\,b^{13/4}}-\frac{5\,\mathrm{atan}\left(\frac{\frac{5\,\left(A\,b-9\,B\,a\right)\,\left(\frac{25\,\sqrt{x}\,\left(A^2\,b^2-18\,A\,B\,a\,b+81\,B^2\,a^2\right)}{64\,b^3}-\frac{\left(45\,B\,a^2-5\,A\,a\,b\right)\,\left(A\,b-9\,B\,a\right)\,5{}\mathrm{i}}{64\,{\left(-a\right)}^{3/4}\,b^{13/4}}\right)}{64\,{\left(-a\right)}^{3/4}\,b^{13/4}}+\frac{5\,\left(A\,b-9\,B\,a\right)\,\left(\frac{25\,\sqrt{x}\,\left(A^2\,b^2-18\,A\,B\,a\,b+81\,B^2\,a^2\right)}{64\,b^3}+\frac{\left(45\,B\,a^2-5\,A\,a\,b\right)\,\left(A\,b-9\,B\,a\right)\,5{}\mathrm{i}}{64\,{\left(-a\right)}^{3/4}\,b^{13/4}}\right)}{64\,{\left(-a\right)}^{3/4}\,b^{13/4}}}{\frac{\left(A\,b-9\,B\,a\right)\,\left(\frac{25\,\sqrt{x}\,\left(A^2\,b^2-18\,A\,B\,a\,b+81\,B^2\,a^2\right)}{64\,b^3}-\frac{\left(45\,B\,a^2-5\,A\,a\,b\right)\,\left(A\,b-9\,B\,a\right)\,5{}\mathrm{i}}{64\,{\left(-a\right)}^{3/4}\,b^{13/4}}\right)\,5{}\mathrm{i}}{64\,{\left(-a\right)}^{3/4}\,b^{13/4}}-\frac{\left(A\,b-9\,B\,a\right)\,\left(\frac{25\,\sqrt{x}\,\left(A^2\,b^2-18\,A\,B\,a\,b+81\,B^2\,a^2\right)}{64\,b^3}+\frac{\left(45\,B\,a^2-5\,A\,a\,b\right)\,\left(A\,b-9\,B\,a\right)\,5{}\mathrm{i}}{64\,{\left(-a\right)}^{3/4}\,b^{13/4}}\right)\,5{}\mathrm{i}}{64\,{\left(-a\right)}^{3/4}\,b^{13/4}}}\right)\,\left(A\,b-9\,B\,a\right)}{32\,{\left(-a\right)}^{3/4}\,b^{13/4}}","Not used",1,"(x^(1/2)*((13*B*a^2)/16 - (5*A*a*b)/16) - x^(5/2)*((9*A*b^2)/16 - (17*B*a*b)/16))/(a^2*b^3 + b^5*x^4 + 2*a*b^4*x^2) + (2*B*x^(1/2))/b^3 - (atan((((A*b - 9*B*a)*((25*x^(1/2)*(A^2*b^2 + 81*B^2*a^2 - 18*A*B*a*b))/(64*b^3) - (5*(45*B*a^2 - 5*A*a*b)*(A*b - 9*B*a))/(64*(-a)^(3/4)*b^(13/4)))*5i)/(64*(-a)^(3/4)*b^(13/4)) + ((A*b - 9*B*a)*((25*x^(1/2)*(A^2*b^2 + 81*B^2*a^2 - 18*A*B*a*b))/(64*b^3) + (5*(45*B*a^2 - 5*A*a*b)*(A*b - 9*B*a))/(64*(-a)^(3/4)*b^(13/4)))*5i)/(64*(-a)^(3/4)*b^(13/4)))/((5*(A*b - 9*B*a)*((25*x^(1/2)*(A^2*b^2 + 81*B^2*a^2 - 18*A*B*a*b))/(64*b^3) - (5*(45*B*a^2 - 5*A*a*b)*(A*b - 9*B*a))/(64*(-a)^(3/4)*b^(13/4))))/(64*(-a)^(3/4)*b^(13/4)) - (5*(A*b - 9*B*a)*((25*x^(1/2)*(A^2*b^2 + 81*B^2*a^2 - 18*A*B*a*b))/(64*b^3) + (5*(45*B*a^2 - 5*A*a*b)*(A*b - 9*B*a))/(64*(-a)^(3/4)*b^(13/4))))/(64*(-a)^(3/4)*b^(13/4))))*(A*b - 9*B*a)*5i)/(32*(-a)^(3/4)*b^(13/4)) - (5*atan(((5*(A*b - 9*B*a)*((25*x^(1/2)*(A^2*b^2 + 81*B^2*a^2 - 18*A*B*a*b))/(64*b^3) - ((45*B*a^2 - 5*A*a*b)*(A*b - 9*B*a)*5i)/(64*(-a)^(3/4)*b^(13/4))))/(64*(-a)^(3/4)*b^(13/4)) + (5*(A*b - 9*B*a)*((25*x^(1/2)*(A^2*b^2 + 81*B^2*a^2 - 18*A*B*a*b))/(64*b^3) + ((45*B*a^2 - 5*A*a*b)*(A*b - 9*B*a)*5i)/(64*(-a)^(3/4)*b^(13/4))))/(64*(-a)^(3/4)*b^(13/4)))/(((A*b - 9*B*a)*((25*x^(1/2)*(A^2*b^2 + 81*B^2*a^2 - 18*A*B*a*b))/(64*b^3) - ((45*B*a^2 - 5*A*a*b)*(A*b - 9*B*a)*5i)/(64*(-a)^(3/4)*b^(13/4)))*5i)/(64*(-a)^(3/4)*b^(13/4)) - ((A*b - 9*B*a)*((25*x^(1/2)*(A^2*b^2 + 81*B^2*a^2 - 18*A*B*a*b))/(64*b^3) + ((45*B*a^2 - 5*A*a*b)*(A*b - 9*B*a)*5i)/(64*(-a)^(3/4)*b^(13/4)))*5i)/(64*(-a)^(3/4)*b^(13/4))))*(A*b - 9*B*a))/(32*(-a)^(3/4)*b^(13/4))","B"
384,1,122,293,0.185415,"\text{Not used}","int((x^(5/2)*(A + B*x^2))/(a + b*x^2)^3,x)","\frac{3\,\mathrm{atanh}\left(\frac{b^{1/4}\,\sqrt{x}}{{\left(-a\right)}^{1/4}}\right)\,\left(A\,b+7\,B\,a\right)}{32\,{\left(-a\right)}^{5/4}\,b^{11/4}}-\frac{3\,\mathrm{atan}\left(\frac{b^{1/4}\,\sqrt{x}}{{\left(-a\right)}^{1/4}}\right)\,\left(A\,b+7\,B\,a\right)}{32\,{\left(-a\right)}^{5/4}\,b^{11/4}}-\frac{\frac{x^{3/2}\,\left(A\,b+7\,B\,a\right)}{16\,b^2}-\frac{x^{7/2}\,\left(3\,A\,b-11\,B\,a\right)}{16\,a\,b}}{a^2+2\,a\,b\,x^2+b^2\,x^4}","Not used",1,"(3*atanh((b^(1/4)*x^(1/2))/(-a)^(1/4))*(A*b + 7*B*a))/(32*(-a)^(5/4)*b^(11/4)) - (3*atan((b^(1/4)*x^(1/2))/(-a)^(1/4))*(A*b + 7*B*a))/(32*(-a)^(5/4)*b^(11/4)) - ((x^(3/2)*(A*b + 7*B*a))/(16*b^2) - (x^(7/2)*(3*A*b - 11*B*a))/(16*a*b))/(a^2 + b^2*x^4 + 2*a*b*x^2)","B"
385,1,799,298,0.470518,"\text{Not used}","int((x^(3/2)*(A + B*x^2))/(a + b*x^2)^3,x)","-\frac{\frac{\sqrt{x}\,\left(3\,A\,b+5\,B\,a\right)}{16\,b^2}-\frac{x^{5/2}\,\left(A\,b-9\,B\,a\right)}{16\,a\,b}}{a^2+2\,a\,b\,x^2+b^2\,x^4}+\frac{\mathrm{atan}\left(\frac{\frac{\left(3\,A\,b+5\,B\,a\right)\,\left(\frac{\sqrt{x}\,\left(9\,A^2\,b^2+30\,A\,B\,a\,b+25\,B^2\,a^2\right)}{64\,a^2\,b}-\frac{\left(3\,A\,b^2+5\,B\,a\,b\right)\,\left(3\,A\,b+5\,B\,a\right)}{64\,{\left(-a\right)}^{7/4}\,b^{9/4}}\right)\,1{}\mathrm{i}}{64\,{\left(-a\right)}^{7/4}\,b^{9/4}}+\frac{\left(3\,A\,b+5\,B\,a\right)\,\left(\frac{\sqrt{x}\,\left(9\,A^2\,b^2+30\,A\,B\,a\,b+25\,B^2\,a^2\right)}{64\,a^2\,b}+\frac{\left(3\,A\,b^2+5\,B\,a\,b\right)\,\left(3\,A\,b+5\,B\,a\right)}{64\,{\left(-a\right)}^{7/4}\,b^{9/4}}\right)\,1{}\mathrm{i}}{64\,{\left(-a\right)}^{7/4}\,b^{9/4}}}{\frac{\left(3\,A\,b+5\,B\,a\right)\,\left(\frac{\sqrt{x}\,\left(9\,A^2\,b^2+30\,A\,B\,a\,b+25\,B^2\,a^2\right)}{64\,a^2\,b}-\frac{\left(3\,A\,b^2+5\,B\,a\,b\right)\,\left(3\,A\,b+5\,B\,a\right)}{64\,{\left(-a\right)}^{7/4}\,b^{9/4}}\right)}{64\,{\left(-a\right)}^{7/4}\,b^{9/4}}-\frac{\left(3\,A\,b+5\,B\,a\right)\,\left(\frac{\sqrt{x}\,\left(9\,A^2\,b^2+30\,A\,B\,a\,b+25\,B^2\,a^2\right)}{64\,a^2\,b}+\frac{\left(3\,A\,b^2+5\,B\,a\,b\right)\,\left(3\,A\,b+5\,B\,a\right)}{64\,{\left(-a\right)}^{7/4}\,b^{9/4}}\right)}{64\,{\left(-a\right)}^{7/4}\,b^{9/4}}}\right)\,\left(3\,A\,b+5\,B\,a\right)\,1{}\mathrm{i}}{32\,{\left(-a\right)}^{7/4}\,b^{9/4}}+\frac{\mathrm{atan}\left(\frac{\frac{\left(3\,A\,b+5\,B\,a\right)\,\left(\frac{\sqrt{x}\,\left(9\,A^2\,b^2+30\,A\,B\,a\,b+25\,B^2\,a^2\right)}{64\,a^2\,b}-\frac{\left(3\,A\,b^2+5\,B\,a\,b\right)\,\left(3\,A\,b+5\,B\,a\right)\,1{}\mathrm{i}}{64\,{\left(-a\right)}^{7/4}\,b^{9/4}}\right)}{64\,{\left(-a\right)}^{7/4}\,b^{9/4}}+\frac{\left(3\,A\,b+5\,B\,a\right)\,\left(\frac{\sqrt{x}\,\left(9\,A^2\,b^2+30\,A\,B\,a\,b+25\,B^2\,a^2\right)}{64\,a^2\,b}+\frac{\left(3\,A\,b^2+5\,B\,a\,b\right)\,\left(3\,A\,b+5\,B\,a\right)\,1{}\mathrm{i}}{64\,{\left(-a\right)}^{7/4}\,b^{9/4}}\right)}{64\,{\left(-a\right)}^{7/4}\,b^{9/4}}}{\frac{\left(3\,A\,b+5\,B\,a\right)\,\left(\frac{\sqrt{x}\,\left(9\,A^2\,b^2+30\,A\,B\,a\,b+25\,B^2\,a^2\right)}{64\,a^2\,b}-\frac{\left(3\,A\,b^2+5\,B\,a\,b\right)\,\left(3\,A\,b+5\,B\,a\right)\,1{}\mathrm{i}}{64\,{\left(-a\right)}^{7/4}\,b^{9/4}}\right)\,1{}\mathrm{i}}{64\,{\left(-a\right)}^{7/4}\,b^{9/4}}-\frac{\left(3\,A\,b+5\,B\,a\right)\,\left(\frac{\sqrt{x}\,\left(9\,A^2\,b^2+30\,A\,B\,a\,b+25\,B^2\,a^2\right)}{64\,a^2\,b}+\frac{\left(3\,A\,b^2+5\,B\,a\,b\right)\,\left(3\,A\,b+5\,B\,a\right)\,1{}\mathrm{i}}{64\,{\left(-a\right)}^{7/4}\,b^{9/4}}\right)\,1{}\mathrm{i}}{64\,{\left(-a\right)}^{7/4}\,b^{9/4}}}\right)\,\left(3\,A\,b+5\,B\,a\right)}{32\,{\left(-a\right)}^{7/4}\,b^{9/4}}","Not used",1,"(atan((((3*A*b + 5*B*a)*((x^(1/2)*(9*A^2*b^2 + 25*B^2*a^2 + 30*A*B*a*b))/(64*a^2*b) - ((3*A*b^2 + 5*B*a*b)*(3*A*b + 5*B*a))/(64*(-a)^(7/4)*b^(9/4)))*1i)/(64*(-a)^(7/4)*b^(9/4)) + ((3*A*b + 5*B*a)*((x^(1/2)*(9*A^2*b^2 + 25*B^2*a^2 + 30*A*B*a*b))/(64*a^2*b) + ((3*A*b^2 + 5*B*a*b)*(3*A*b + 5*B*a))/(64*(-a)^(7/4)*b^(9/4)))*1i)/(64*(-a)^(7/4)*b^(9/4)))/(((3*A*b + 5*B*a)*((x^(1/2)*(9*A^2*b^2 + 25*B^2*a^2 + 30*A*B*a*b))/(64*a^2*b) - ((3*A*b^2 + 5*B*a*b)*(3*A*b + 5*B*a))/(64*(-a)^(7/4)*b^(9/4))))/(64*(-a)^(7/4)*b^(9/4)) - ((3*A*b + 5*B*a)*((x^(1/2)*(9*A^2*b^2 + 25*B^2*a^2 + 30*A*B*a*b))/(64*a^2*b) + ((3*A*b^2 + 5*B*a*b)*(3*A*b + 5*B*a))/(64*(-a)^(7/4)*b^(9/4))))/(64*(-a)^(7/4)*b^(9/4))))*(3*A*b + 5*B*a)*1i)/(32*(-a)^(7/4)*b^(9/4)) - ((x^(1/2)*(3*A*b + 5*B*a))/(16*b^2) - (x^(5/2)*(A*b - 9*B*a))/(16*a*b))/(a^2 + b^2*x^4 + 2*a*b*x^2) + (atan((((3*A*b + 5*B*a)*((x^(1/2)*(9*A^2*b^2 + 25*B^2*a^2 + 30*A*B*a*b))/(64*a^2*b) - ((3*A*b^2 + 5*B*a*b)*(3*A*b + 5*B*a)*1i)/(64*(-a)^(7/4)*b^(9/4))))/(64*(-a)^(7/4)*b^(9/4)) + ((3*A*b + 5*B*a)*((x^(1/2)*(9*A^2*b^2 + 25*B^2*a^2 + 30*A*B*a*b))/(64*a^2*b) + ((3*A*b^2 + 5*B*a*b)*(3*A*b + 5*B*a)*1i)/(64*(-a)^(7/4)*b^(9/4))))/(64*(-a)^(7/4)*b^(9/4)))/(((3*A*b + 5*B*a)*((x^(1/2)*(9*A^2*b^2 + 25*B^2*a^2 + 30*A*B*a*b))/(64*a^2*b) - ((3*A*b^2 + 5*B*a*b)*(3*A*b + 5*B*a)*1i)/(64*(-a)^(7/4)*b^(9/4)))*1i)/(64*(-a)^(7/4)*b^(9/4)) - ((3*A*b + 5*B*a)*((x^(1/2)*(9*A^2*b^2 + 25*B^2*a^2 + 30*A*B*a*b))/(64*a^2*b) + ((3*A*b^2 + 5*B*a*b)*(3*A*b + 5*B*a)*1i)/(64*(-a)^(7/4)*b^(9/4)))*1i)/(64*(-a)^(7/4)*b^(9/4))))*(3*A*b + 5*B*a))/(32*(-a)^(7/4)*b^(9/4))","B"
386,1,124,298,0.322149,"\text{Not used}","int((x^(1/2)*(A + B*x^2))/(a + b*x^2)^3,x)","\frac{\frac{x^{7/2}\,\left(5\,A\,b+3\,B\,a\right)}{16\,a^2}+\frac{x^{3/2}\,\left(9\,A\,b-B\,a\right)}{16\,a\,b}}{a^2+2\,a\,b\,x^2+b^2\,x^4}+\frac{\mathrm{atan}\left(\frac{b^{1/4}\,\sqrt{x}}{{\left(-a\right)}^{1/4}}\right)\,\left(5\,A\,b+3\,B\,a\right)}{32\,{\left(-a\right)}^{9/4}\,b^{7/4}}-\frac{\mathrm{atanh}\left(\frac{b^{1/4}\,\sqrt{x}}{{\left(-a\right)}^{1/4}}\right)\,\left(5\,A\,b+3\,B\,a\right)}{32\,{\left(-a\right)}^{9/4}\,b^{7/4}}","Not used",1,"((x^(7/2)*(5*A*b + 3*B*a))/(16*a^2) + (x^(3/2)*(9*A*b - B*a))/(16*a*b))/(a^2 + b^2*x^4 + 2*a*b*x^2) + (atan((b^(1/4)*x^(1/2))/(-a)^(1/4))*(5*A*b + 3*B*a))/(32*(-a)^(9/4)*b^(7/4)) - (atanh((b^(1/4)*x^(1/2))/(-a)^(1/4))*(5*A*b + 3*B*a))/(32*(-a)^(9/4)*b^(7/4))","B"
387,1,780,293,0.479213,"\text{Not used}","int((A + B*x^2)/(x^(1/2)*(a + b*x^2)^3),x)","\frac{\frac{x^{5/2}\,\left(7\,A\,b+B\,a\right)}{16\,a^2}+\frac{\sqrt{x}\,\left(11\,A\,b-3\,B\,a\right)}{16\,a\,b}}{a^2+2\,a\,b\,x^2+b^2\,x^4}-\frac{\mathrm{atan}\left(\frac{\frac{\left(7\,A\,b+B\,a\right)\,\left(\frac{9\,\sqrt{x}\,\left(49\,A^2\,b^3+14\,A\,B\,a\,b^2+B^2\,a^2\,b\right)}{64\,a^4}-\frac{9\,\left(7\,A\,b+B\,a\right)\,\left(7\,A\,b^3+B\,a\,b^2\right)}{64\,{\left(-a\right)}^{15/4}\,b^{5/4}}\right)\,3{}\mathrm{i}}{64\,{\left(-a\right)}^{11/4}\,b^{5/4}}+\frac{\left(7\,A\,b+B\,a\right)\,\left(\frac{9\,\sqrt{x}\,\left(49\,A^2\,b^3+14\,A\,B\,a\,b^2+B^2\,a^2\,b\right)}{64\,a^4}+\frac{9\,\left(7\,A\,b+B\,a\right)\,\left(7\,A\,b^3+B\,a\,b^2\right)}{64\,{\left(-a\right)}^{15/4}\,b^{5/4}}\right)\,3{}\mathrm{i}}{64\,{\left(-a\right)}^{11/4}\,b^{5/4}}}{\frac{3\,\left(7\,A\,b+B\,a\right)\,\left(\frac{9\,\sqrt{x}\,\left(49\,A^2\,b^3+14\,A\,B\,a\,b^2+B^2\,a^2\,b\right)}{64\,a^4}-\frac{9\,\left(7\,A\,b+B\,a\right)\,\left(7\,A\,b^3+B\,a\,b^2\right)}{64\,{\left(-a\right)}^{15/4}\,b^{5/4}}\right)}{64\,{\left(-a\right)}^{11/4}\,b^{5/4}}-\frac{3\,\left(7\,A\,b+B\,a\right)\,\left(\frac{9\,\sqrt{x}\,\left(49\,A^2\,b^3+14\,A\,B\,a\,b^2+B^2\,a^2\,b\right)}{64\,a^4}+\frac{9\,\left(7\,A\,b+B\,a\right)\,\left(7\,A\,b^3+B\,a\,b^2\right)}{64\,{\left(-a\right)}^{15/4}\,b^{5/4}}\right)}{64\,{\left(-a\right)}^{11/4}\,b^{5/4}}}\right)\,\left(7\,A\,b+B\,a\right)\,3{}\mathrm{i}}{32\,{\left(-a\right)}^{11/4}\,b^{5/4}}-\frac{3\,\mathrm{atan}\left(\frac{\frac{3\,\left(7\,A\,b+B\,a\right)\,\left(\frac{9\,\sqrt{x}\,\left(49\,A^2\,b^3+14\,A\,B\,a\,b^2+B^2\,a^2\,b\right)}{64\,a^4}-\frac{\left(7\,A\,b+B\,a\right)\,\left(7\,A\,b^3+B\,a\,b^2\right)\,9{}\mathrm{i}}{64\,{\left(-a\right)}^{15/4}\,b^{5/4}}\right)}{64\,{\left(-a\right)}^{11/4}\,b^{5/4}}+\frac{3\,\left(7\,A\,b+B\,a\right)\,\left(\frac{9\,\sqrt{x}\,\left(49\,A^2\,b^3+14\,A\,B\,a\,b^2+B^2\,a^2\,b\right)}{64\,a^4}+\frac{\left(7\,A\,b+B\,a\right)\,\left(7\,A\,b^3+B\,a\,b^2\right)\,9{}\mathrm{i}}{64\,{\left(-a\right)}^{15/4}\,b^{5/4}}\right)}{64\,{\left(-a\right)}^{11/4}\,b^{5/4}}}{\frac{\left(7\,A\,b+B\,a\right)\,\left(\frac{9\,\sqrt{x}\,\left(49\,A^2\,b^3+14\,A\,B\,a\,b^2+B^2\,a^2\,b\right)}{64\,a^4}-\frac{\left(7\,A\,b+B\,a\right)\,\left(7\,A\,b^3+B\,a\,b^2\right)\,9{}\mathrm{i}}{64\,{\left(-a\right)}^{15/4}\,b^{5/4}}\right)\,3{}\mathrm{i}}{64\,{\left(-a\right)}^{11/4}\,b^{5/4}}-\frac{\left(7\,A\,b+B\,a\right)\,\left(\frac{9\,\sqrt{x}\,\left(49\,A^2\,b^3+14\,A\,B\,a\,b^2+B^2\,a^2\,b\right)}{64\,a^4}+\frac{\left(7\,A\,b+B\,a\right)\,\left(7\,A\,b^3+B\,a\,b^2\right)\,9{}\mathrm{i}}{64\,{\left(-a\right)}^{15/4}\,b^{5/4}}\right)\,3{}\mathrm{i}}{64\,{\left(-a\right)}^{11/4}\,b^{5/4}}}\right)\,\left(7\,A\,b+B\,a\right)}{32\,{\left(-a\right)}^{11/4}\,b^{5/4}}","Not used",1,"((x^(5/2)*(7*A*b + B*a))/(16*a^2) + (x^(1/2)*(11*A*b - 3*B*a))/(16*a*b))/(a^2 + b^2*x^4 + 2*a*b*x^2) - (atan((((7*A*b + B*a)*((9*x^(1/2)*(49*A^2*b^3 + B^2*a^2*b + 14*A*B*a*b^2))/(64*a^4) - (9*(7*A*b + B*a)*(7*A*b^3 + B*a*b^2))/(64*(-a)^(15/4)*b^(5/4)))*3i)/(64*(-a)^(11/4)*b^(5/4)) + ((7*A*b + B*a)*((9*x^(1/2)*(49*A^2*b^3 + B^2*a^2*b + 14*A*B*a*b^2))/(64*a^4) + (9*(7*A*b + B*a)*(7*A*b^3 + B*a*b^2))/(64*(-a)^(15/4)*b^(5/4)))*3i)/(64*(-a)^(11/4)*b^(5/4)))/((3*(7*A*b + B*a)*((9*x^(1/2)*(49*A^2*b^3 + B^2*a^2*b + 14*A*B*a*b^2))/(64*a^4) - (9*(7*A*b + B*a)*(7*A*b^3 + B*a*b^2))/(64*(-a)^(15/4)*b^(5/4))))/(64*(-a)^(11/4)*b^(5/4)) - (3*(7*A*b + B*a)*((9*x^(1/2)*(49*A^2*b^3 + B^2*a^2*b + 14*A*B*a*b^2))/(64*a^4) + (9*(7*A*b + B*a)*(7*A*b^3 + B*a*b^2))/(64*(-a)^(15/4)*b^(5/4))))/(64*(-a)^(11/4)*b^(5/4))))*(7*A*b + B*a)*3i)/(32*(-a)^(11/4)*b^(5/4)) - (3*atan(((3*(7*A*b + B*a)*((9*x^(1/2)*(49*A^2*b^3 + B^2*a^2*b + 14*A*B*a*b^2))/(64*a^4) - ((7*A*b + B*a)*(7*A*b^3 + B*a*b^2)*9i)/(64*(-a)^(15/4)*b^(5/4))))/(64*(-a)^(11/4)*b^(5/4)) + (3*(7*A*b + B*a)*((9*x^(1/2)*(49*A^2*b^3 + B^2*a^2*b + 14*A*B*a*b^2))/(64*a^4) + ((7*A*b + B*a)*(7*A*b^3 + B*a*b^2)*9i)/(64*(-a)^(15/4)*b^(5/4))))/(64*(-a)^(11/4)*b^(5/4)))/(((7*A*b + B*a)*((9*x^(1/2)*(49*A^2*b^3 + B^2*a^2*b + 14*A*B*a*b^2))/(64*a^4) - ((7*A*b + B*a)*(7*A*b^3 + B*a*b^2)*9i)/(64*(-a)^(15/4)*b^(5/4)))*3i)/(64*(-a)^(11/4)*b^(5/4)) - ((7*A*b + B*a)*((9*x^(1/2)*(49*A^2*b^3 + B^2*a^2*b + 14*A*B*a*b^2))/(64*a^4) + ((7*A*b + B*a)*(7*A*b^3 + B*a*b^2)*9i)/(64*(-a)^(15/4)*b^(5/4)))*3i)/(64*(-a)^(11/4)*b^(5/4))))*(7*A*b + B*a))/(32*(-a)^(11/4)*b^(5/4))","B"
388,1,133,322,0.187188,"\text{Not used}","int((A + B*x^2)/(x^(3/2)*(a + b*x^2)^3),x)","\frac{5\,\mathrm{atan}\left(\frac{b^{1/4}\,\sqrt{x}}{{\left(-a\right)}^{1/4}}\right)\,\left(9\,A\,b-B\,a\right)}{32\,{\left(-a\right)}^{13/4}\,b^{3/4}}-\frac{\frac{2\,A}{a}+\frac{9\,x^2\,\left(9\,A\,b-B\,a\right)}{16\,a^2}+\frac{5\,b\,x^4\,\left(9\,A\,b-B\,a\right)}{16\,a^3}}{a^2\,\sqrt{x}+b^2\,x^{9/2}+2\,a\,b\,x^{5/2}}-\frac{5\,\mathrm{atanh}\left(\frac{b^{1/4}\,\sqrt{x}}{{\left(-a\right)}^{1/4}}\right)\,\left(9\,A\,b-B\,a\right)}{32\,{\left(-a\right)}^{13/4}\,b^{3/4}}","Not used",1,"(5*atan((b^(1/4)*x^(1/2))/(-a)^(1/4))*(9*A*b - B*a))/(32*(-a)^(13/4)*b^(3/4)) - ((2*A)/a + (9*x^2*(9*A*b - B*a))/(16*a^2) + (5*b*x^4*(9*A*b - B*a))/(16*a^3))/(a^2*x^(1/2) + b^2*x^(9/2) + 2*a*b*x^(5/2)) - (5*atanh((b^(1/4)*x^(1/2))/(-a)^(1/4))*(9*A*b - B*a))/(32*(-a)^(13/4)*b^(3/4))","B"
389,1,888,322,0.534204,"\text{Not used}","int((A + B*x^2)/(x^(5/2)*(a + b*x^2)^3),x)","-\frac{\frac{2\,A}{3\,a}+\frac{11\,x^2\,\left(11\,A\,b-3\,B\,a\right)}{48\,a^2}+\frac{7\,b\,x^4\,\left(11\,A\,b-3\,B\,a\right)}{48\,a^3}}{a^2\,x^{3/2}+b^2\,x^{11/2}+2\,a\,b\,x^{7/2}}-\frac{\mathrm{atan}\left(\frac{\frac{\left(11\,A\,b-3\,B\,a\right)\,\left(\sqrt{x}\,\left(97140736\,A^2\,a^9\,b^5-52985856\,A\,B\,a^{10}\,b^4+7225344\,B^2\,a^{11}\,b^3\right)-\frac{7\,\left(11\,A\,b-3\,B\,a\right)\,\left(80740352\,A\,a^{13}\,b^4-22020096\,B\,a^{14}\,b^3\right)}{64\,{\left(-a\right)}^{15/4}\,b^{1/4}}\right)\,7{}\mathrm{i}}{64\,{\left(-a\right)}^{15/4}\,b^{1/4}}+\frac{\left(11\,A\,b-3\,B\,a\right)\,\left(\sqrt{x}\,\left(97140736\,A^2\,a^9\,b^5-52985856\,A\,B\,a^{10}\,b^4+7225344\,B^2\,a^{11}\,b^3\right)+\frac{7\,\left(11\,A\,b-3\,B\,a\right)\,\left(80740352\,A\,a^{13}\,b^4-22020096\,B\,a^{14}\,b^3\right)}{64\,{\left(-a\right)}^{15/4}\,b^{1/4}}\right)\,7{}\mathrm{i}}{64\,{\left(-a\right)}^{15/4}\,b^{1/4}}}{\frac{7\,\left(11\,A\,b-3\,B\,a\right)\,\left(\sqrt{x}\,\left(97140736\,A^2\,a^9\,b^5-52985856\,A\,B\,a^{10}\,b^4+7225344\,B^2\,a^{11}\,b^3\right)-\frac{7\,\left(11\,A\,b-3\,B\,a\right)\,\left(80740352\,A\,a^{13}\,b^4-22020096\,B\,a^{14}\,b^3\right)}{64\,{\left(-a\right)}^{15/4}\,b^{1/4}}\right)}{64\,{\left(-a\right)}^{15/4}\,b^{1/4}}-\frac{7\,\left(11\,A\,b-3\,B\,a\right)\,\left(\sqrt{x}\,\left(97140736\,A^2\,a^9\,b^5-52985856\,A\,B\,a^{10}\,b^4+7225344\,B^2\,a^{11}\,b^3\right)+\frac{7\,\left(11\,A\,b-3\,B\,a\right)\,\left(80740352\,A\,a^{13}\,b^4-22020096\,B\,a^{14}\,b^3\right)}{64\,{\left(-a\right)}^{15/4}\,b^{1/4}}\right)}{64\,{\left(-a\right)}^{15/4}\,b^{1/4}}}\right)\,\left(11\,A\,b-3\,B\,a\right)\,7{}\mathrm{i}}{32\,{\left(-a\right)}^{15/4}\,b^{1/4}}-\frac{7\,\mathrm{atan}\left(\frac{\frac{7\,\left(11\,A\,b-3\,B\,a\right)\,\left(\sqrt{x}\,\left(97140736\,A^2\,a^9\,b^5-52985856\,A\,B\,a^{10}\,b^4+7225344\,B^2\,a^{11}\,b^3\right)-\frac{\left(11\,A\,b-3\,B\,a\right)\,\left(80740352\,A\,a^{13}\,b^4-22020096\,B\,a^{14}\,b^3\right)\,7{}\mathrm{i}}{64\,{\left(-a\right)}^{15/4}\,b^{1/4}}\right)}{64\,{\left(-a\right)}^{15/4}\,b^{1/4}}+\frac{7\,\left(11\,A\,b-3\,B\,a\right)\,\left(\sqrt{x}\,\left(97140736\,A^2\,a^9\,b^5-52985856\,A\,B\,a^{10}\,b^4+7225344\,B^2\,a^{11}\,b^3\right)+\frac{\left(11\,A\,b-3\,B\,a\right)\,\left(80740352\,A\,a^{13}\,b^4-22020096\,B\,a^{14}\,b^3\right)\,7{}\mathrm{i}}{64\,{\left(-a\right)}^{15/4}\,b^{1/4}}\right)}{64\,{\left(-a\right)}^{15/4}\,b^{1/4}}}{\frac{\left(11\,A\,b-3\,B\,a\right)\,\left(\sqrt{x}\,\left(97140736\,A^2\,a^9\,b^5-52985856\,A\,B\,a^{10}\,b^4+7225344\,B^2\,a^{11}\,b^3\right)-\frac{\left(11\,A\,b-3\,B\,a\right)\,\left(80740352\,A\,a^{13}\,b^4-22020096\,B\,a^{14}\,b^3\right)\,7{}\mathrm{i}}{64\,{\left(-a\right)}^{15/4}\,b^{1/4}}\right)\,7{}\mathrm{i}}{64\,{\left(-a\right)}^{15/4}\,b^{1/4}}-\frac{\left(11\,A\,b-3\,B\,a\right)\,\left(\sqrt{x}\,\left(97140736\,A^2\,a^9\,b^5-52985856\,A\,B\,a^{10}\,b^4+7225344\,B^2\,a^{11}\,b^3\right)+\frac{\left(11\,A\,b-3\,B\,a\right)\,\left(80740352\,A\,a^{13}\,b^4-22020096\,B\,a^{14}\,b^3\right)\,7{}\mathrm{i}}{64\,{\left(-a\right)}^{15/4}\,b^{1/4}}\right)\,7{}\mathrm{i}}{64\,{\left(-a\right)}^{15/4}\,b^{1/4}}}\right)\,\left(11\,A\,b-3\,B\,a\right)}{32\,{\left(-a\right)}^{15/4}\,b^{1/4}}","Not used",1,"- ((2*A)/(3*a) + (11*x^2*(11*A*b - 3*B*a))/(48*a^2) + (7*b*x^4*(11*A*b - 3*B*a))/(48*a^3))/(a^2*x^(3/2) + b^2*x^(11/2) + 2*a*b*x^(7/2)) - (atan((((11*A*b - 3*B*a)*(x^(1/2)*(97140736*A^2*a^9*b^5 + 7225344*B^2*a^11*b^3 - 52985856*A*B*a^10*b^4) - (7*(11*A*b - 3*B*a)*(80740352*A*a^13*b^4 - 22020096*B*a^14*b^3))/(64*(-a)^(15/4)*b^(1/4)))*7i)/(64*(-a)^(15/4)*b^(1/4)) + ((11*A*b - 3*B*a)*(x^(1/2)*(97140736*A^2*a^9*b^5 + 7225344*B^2*a^11*b^3 - 52985856*A*B*a^10*b^4) + (7*(11*A*b - 3*B*a)*(80740352*A*a^13*b^4 - 22020096*B*a^14*b^3))/(64*(-a)^(15/4)*b^(1/4)))*7i)/(64*(-a)^(15/4)*b^(1/4)))/((7*(11*A*b - 3*B*a)*(x^(1/2)*(97140736*A^2*a^9*b^5 + 7225344*B^2*a^11*b^3 - 52985856*A*B*a^10*b^4) - (7*(11*A*b - 3*B*a)*(80740352*A*a^13*b^4 - 22020096*B*a^14*b^3))/(64*(-a)^(15/4)*b^(1/4))))/(64*(-a)^(15/4)*b^(1/4)) - (7*(11*A*b - 3*B*a)*(x^(1/2)*(97140736*A^2*a^9*b^5 + 7225344*B^2*a^11*b^3 - 52985856*A*B*a^10*b^4) + (7*(11*A*b - 3*B*a)*(80740352*A*a^13*b^4 - 22020096*B*a^14*b^3))/(64*(-a)^(15/4)*b^(1/4))))/(64*(-a)^(15/4)*b^(1/4))))*(11*A*b - 3*B*a)*7i)/(32*(-a)^(15/4)*b^(1/4)) - (7*atan(((7*(11*A*b - 3*B*a)*(x^(1/2)*(97140736*A^2*a^9*b^5 + 7225344*B^2*a^11*b^3 - 52985856*A*B*a^10*b^4) - ((11*A*b - 3*B*a)*(80740352*A*a^13*b^4 - 22020096*B*a^14*b^3)*7i)/(64*(-a)^(15/4)*b^(1/4))))/(64*(-a)^(15/4)*b^(1/4)) + (7*(11*A*b - 3*B*a)*(x^(1/2)*(97140736*A^2*a^9*b^5 + 7225344*B^2*a^11*b^3 - 52985856*A*B*a^10*b^4) + ((11*A*b - 3*B*a)*(80740352*A*a^13*b^4 - 22020096*B*a^14*b^3)*7i)/(64*(-a)^(15/4)*b^(1/4))))/(64*(-a)^(15/4)*b^(1/4)))/(((11*A*b - 3*B*a)*(x^(1/2)*(97140736*A^2*a^9*b^5 + 7225344*B^2*a^11*b^3 - 52985856*A*B*a^10*b^4) - ((11*A*b - 3*B*a)*(80740352*A*a^13*b^4 - 22020096*B*a^14*b^3)*7i)/(64*(-a)^(15/4)*b^(1/4)))*7i)/(64*(-a)^(15/4)*b^(1/4)) - ((11*A*b - 3*B*a)*(x^(1/2)*(97140736*A^2*a^9*b^5 + 7225344*B^2*a^11*b^3 - 52985856*A*B*a^10*b^4) + ((11*A*b - 3*B*a)*(80740352*A*a^13*b^4 - 22020096*B*a^14*b^3)*7i)/(64*(-a)^(15/4)*b^(1/4)))*7i)/(64*(-a)^(15/4)*b^(1/4))))*(11*A*b - 3*B*a))/(32*(-a)^(15/4)*b^(1/4))","B"
390,1,152,343,0.353036,"\text{Not used}","int((A + B*x^2)/(x^(7/2)*(a + b*x^2)^3),x)","\frac{\frac{2\,x^2\,\left(13\,A\,b-5\,B\,a\right)}{5\,a^2}-\frac{2\,A}{5\,a}+\frac{9\,b^2\,x^6\,\left(13\,A\,b-5\,B\,a\right)}{16\,a^4}+\frac{81\,b\,x^4\,\left(13\,A\,b-5\,B\,a\right)}{80\,a^3}}{a^2\,x^{5/2}+b^2\,x^{13/2}+2\,a\,b\,x^{9/2}}+\frac{9\,{\left(-b\right)}^{1/4}\,\mathrm{atan}\left(\frac{{\left(-b\right)}^{1/4}\,\sqrt{x}}{a^{1/4}}\right)\,\left(13\,A\,b-5\,B\,a\right)}{32\,a^{17/4}}-\frac{9\,{\left(-b\right)}^{1/4}\,\mathrm{atanh}\left(\frac{{\left(-b\right)}^{1/4}\,\sqrt{x}}{a^{1/4}}\right)\,\left(13\,A\,b-5\,B\,a\right)}{32\,a^{17/4}}","Not used",1,"((2*x^2*(13*A*b - 5*B*a))/(5*a^2) - (2*A)/(5*a) + (9*b^2*x^6*(13*A*b - 5*B*a))/(16*a^4) + (81*b*x^4*(13*A*b - 5*B*a))/(80*a^3))/(a^2*x^(5/2) + b^2*x^(13/2) + 2*a*b*x^(9/2)) + (9*(-b)^(1/4)*atan(((-b)^(1/4)*x^(1/2))/a^(1/4))*(13*A*b - 5*B*a))/(32*a^(17/4)) - (9*(-b)^(1/4)*atanh(((-b)^(1/4)*x^(1/2))/a^(1/4))*(13*A*b - 5*B*a))/(32*a^(17/4))","B"
391,1,51,63,0.060981,"\text{Not used}","int(x^(7/2)*(a + b*x^2)^2*(c + d*x^2),x)","x^{13/2}\,\left(\frac{2\,d\,a^2}{13}+\frac{4\,b\,c\,a}{13}\right)+x^{17/2}\,\left(\frac{2\,c\,b^2}{17}+\frac{4\,a\,d\,b}{17}\right)+\frac{2\,a^2\,c\,x^{9/2}}{9}+\frac{2\,b^2\,d\,x^{21/2}}{21}","Not used",1,"x^(13/2)*((2*a^2*d)/13 + (4*a*b*c)/13) + x^(17/2)*((2*b^2*c)/17 + (4*a*b*d)/17) + (2*a^2*c*x^(9/2))/9 + (2*b^2*d*x^(21/2))/21","B"
392,1,51,63,0.047641,"\text{Not used}","int(x^(5/2)*(a + b*x^2)^2*(c + d*x^2),x)","x^{11/2}\,\left(\frac{2\,d\,a^2}{11}+\frac{4\,b\,c\,a}{11}\right)+x^{15/2}\,\left(\frac{2\,c\,b^2}{15}+\frac{4\,a\,d\,b}{15}\right)+\frac{2\,a^2\,c\,x^{7/2}}{7}+\frac{2\,b^2\,d\,x^{19/2}}{19}","Not used",1,"x^(11/2)*((2*a^2*d)/11 + (4*a*b*c)/11) + x^(15/2)*((2*b^2*c)/15 + (4*a*b*d)/15) + (2*a^2*c*x^(7/2))/7 + (2*b^2*d*x^(19/2))/19","B"
393,1,51,63,0.047509,"\text{Not used}","int(x^(3/2)*(a + b*x^2)^2*(c + d*x^2),x)","x^{9/2}\,\left(\frac{2\,d\,a^2}{9}+\frac{4\,b\,c\,a}{9}\right)+x^{13/2}\,\left(\frac{2\,c\,b^2}{13}+\frac{4\,a\,d\,b}{13}\right)+\frac{2\,a^2\,c\,x^{5/2}}{5}+\frac{2\,b^2\,d\,x^{17/2}}{17}","Not used",1,"x^(9/2)*((2*a^2*d)/9 + (4*a*b*c)/9) + x^(13/2)*((2*b^2*c)/13 + (4*a*b*d)/13) + (2*a^2*c*x^(5/2))/5 + (2*b^2*d*x^(17/2))/17","B"
394,1,51,63,0.051769,"\text{Not used}","int(x^(1/2)*(a + b*x^2)^2*(c + d*x^2),x)","x^{7/2}\,\left(\frac{2\,d\,a^2}{7}+\frac{4\,b\,c\,a}{7}\right)+x^{11/2}\,\left(\frac{2\,c\,b^2}{11}+\frac{4\,a\,d\,b}{11}\right)+\frac{2\,a^2\,c\,x^{3/2}}{3}+\frac{2\,b^2\,d\,x^{15/2}}{15}","Not used",1,"x^(7/2)*((2*a^2*d)/7 + (4*a*b*c)/7) + x^(11/2)*((2*b^2*c)/11 + (4*a*b*d)/11) + (2*a^2*c*x^(3/2))/3 + (2*b^2*d*x^(15/2))/15","B"
395,1,51,61,0.045894,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2))/x^(1/2),x)","x^{5/2}\,\left(\frac{2\,d\,a^2}{5}+\frac{4\,b\,c\,a}{5}\right)+x^{9/2}\,\left(\frac{2\,c\,b^2}{9}+\frac{4\,a\,d\,b}{9}\right)+2\,a^2\,c\,\sqrt{x}+\frac{2\,b^2\,d\,x^{13/2}}{13}","Not used",1,"x^(5/2)*((2*a^2*d)/5 + (4*a*b*c)/5) + x^(9/2)*((2*b^2*c)/9 + (4*a*b*d)/9) + 2*a^2*c*x^(1/2) + (2*b^2*d*x^(13/2))/13","B"
396,1,51,61,0.050725,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2))/x^(3/2),x)","x^{3/2}\,\left(\frac{2\,d\,a^2}{3}+\frac{4\,b\,c\,a}{3}\right)+x^{7/2}\,\left(\frac{2\,c\,b^2}{7}+\frac{4\,a\,d\,b}{7}\right)-\frac{2\,a^2\,c}{\sqrt{x}}+\frac{2\,b^2\,d\,x^{11/2}}{11}","Not used",1,"x^(3/2)*((2*a^2*d)/3 + (4*a*b*c)/3) + x^(7/2)*((2*b^2*c)/7 + (4*a*b*d)/7) - (2*a^2*c)/x^(1/2) + (2*b^2*d*x^(11/2))/11","B"
397,1,51,61,0.052398,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2))/x^(5/2),x)","\sqrt{x}\,\left(2\,d\,a^2+4\,b\,c\,a\right)+x^{5/2}\,\left(\frac{2\,c\,b^2}{5}+\frac{4\,a\,d\,b}{5}\right)-\frac{2\,a^2\,c}{3\,x^{3/2}}+\frac{2\,b^2\,d\,x^{9/2}}{9}","Not used",1,"x^(1/2)*(2*a^2*d + 4*a*b*c) + x^(5/2)*((2*b^2*c)/5 + (4*a*b*d)/5) - (2*a^2*c)/(3*x^(3/2)) + (2*b^2*d*x^(9/2))/9","B"
398,1,55,61,0.052825,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2))/x^(7/2),x)","-\frac{210\,d\,a^2\,x^2+42\,c\,a^2-140\,d\,a\,b\,x^4+420\,c\,a\,b\,x^2-30\,d\,b^2\,x^6-70\,c\,b^2\,x^4}{105\,x^{5/2}}","Not used",1,"-(42*a^2*c + 210*a^2*d*x^2 - 70*b^2*c*x^4 - 30*b^2*d*x^6 + 420*a*b*c*x^2 - 140*a*b*d*x^4)/(105*x^(5/2))","B"
399,1,78,97,0.051162,"\text{Not used}","int(x^(7/2)*(a + b*x^2)^2*(c + d*x^2)^2,x)","x^{17/2}\,\left(\frac{2\,a^2\,d^2}{17}+\frac{8\,a\,b\,c\,d}{17}+\frac{2\,b^2\,c^2}{17}\right)+\frac{2\,a^2\,c^2\,x^{9/2}}{9}+\frac{2\,b^2\,d^2\,x^{25/2}}{25}+\frac{4\,a\,c\,x^{13/2}\,\left(a\,d+b\,c\right)}{13}+\frac{4\,b\,d\,x^{21/2}\,\left(a\,d+b\,c\right)}{21}","Not used",1,"x^(17/2)*((2*a^2*d^2)/17 + (2*b^2*c^2)/17 + (8*a*b*c*d)/17) + (2*a^2*c^2*x^(9/2))/9 + (2*b^2*d^2*x^(25/2))/25 + (4*a*c*x^(13/2)*(a*d + b*c))/13 + (4*b*d*x^(21/2)*(a*d + b*c))/21","B"
400,1,78,97,0.033432,"\text{Not used}","int(x^(5/2)*(a + b*x^2)^2*(c + d*x^2)^2,x)","x^{15/2}\,\left(\frac{2\,a^2\,d^2}{15}+\frac{8\,a\,b\,c\,d}{15}+\frac{2\,b^2\,c^2}{15}\right)+\frac{2\,a^2\,c^2\,x^{7/2}}{7}+\frac{2\,b^2\,d^2\,x^{23/2}}{23}+\frac{4\,a\,c\,x^{11/2}\,\left(a\,d+b\,c\right)}{11}+\frac{4\,b\,d\,x^{19/2}\,\left(a\,d+b\,c\right)}{19}","Not used",1,"x^(15/2)*((2*a^2*d^2)/15 + (2*b^2*c^2)/15 + (8*a*b*c*d)/15) + (2*a^2*c^2*x^(7/2))/7 + (2*b^2*d^2*x^(23/2))/23 + (4*a*c*x^(11/2)*(a*d + b*c))/11 + (4*b*d*x^(19/2)*(a*d + b*c))/19","B"
401,1,78,97,0.031868,"\text{Not used}","int(x^(3/2)*(a + b*x^2)^2*(c + d*x^2)^2,x)","x^{13/2}\,\left(\frac{2\,a^2\,d^2}{13}+\frac{8\,a\,b\,c\,d}{13}+\frac{2\,b^2\,c^2}{13}\right)+\frac{2\,a^2\,c^2\,x^{5/2}}{5}+\frac{2\,b^2\,d^2\,x^{21/2}}{21}+\frac{4\,a\,c\,x^{9/2}\,\left(a\,d+b\,c\right)}{9}+\frac{4\,b\,d\,x^{17/2}\,\left(a\,d+b\,c\right)}{17}","Not used",1,"x^(13/2)*((2*a^2*d^2)/13 + (2*b^2*c^2)/13 + (8*a*b*c*d)/13) + (2*a^2*c^2*x^(5/2))/5 + (2*b^2*d^2*x^(21/2))/21 + (4*a*c*x^(9/2)*(a*d + b*c))/9 + (4*b*d*x^(17/2)*(a*d + b*c))/17","B"
402,1,78,97,0.032483,"\text{Not used}","int(x^(1/2)*(a + b*x^2)^2*(c + d*x^2)^2,x)","x^{11/2}\,\left(\frac{2\,a^2\,d^2}{11}+\frac{8\,a\,b\,c\,d}{11}+\frac{2\,b^2\,c^2}{11}\right)+\frac{2\,a^2\,c^2\,x^{3/2}}{3}+\frac{2\,b^2\,d^2\,x^{19/2}}{19}+\frac{4\,a\,c\,x^{7/2}\,\left(a\,d+b\,c\right)}{7}+\frac{4\,b\,d\,x^{15/2}\,\left(a\,d+b\,c\right)}{15}","Not used",1,"x^(11/2)*((2*a^2*d^2)/11 + (2*b^2*c^2)/11 + (8*a*b*c*d)/11) + (2*a^2*c^2*x^(3/2))/3 + (2*b^2*d^2*x^(19/2))/19 + (4*a*c*x^(7/2)*(a*d + b*c))/7 + (4*b*d*x^(15/2)*(a*d + b*c))/15","B"
403,1,78,95,0.031550,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^2)/x^(1/2),x)","x^{9/2}\,\left(\frac{2\,a^2\,d^2}{9}+\frac{8\,a\,b\,c\,d}{9}+\frac{2\,b^2\,c^2}{9}\right)+2\,a^2\,c^2\,\sqrt{x}+\frac{2\,b^2\,d^2\,x^{17/2}}{17}+\frac{4\,a\,c\,x^{5/2}\,\left(a\,d+b\,c\right)}{5}+\frac{4\,b\,d\,x^{13/2}\,\left(a\,d+b\,c\right)}{13}","Not used",1,"x^(9/2)*((2*a^2*d^2)/9 + (2*b^2*c^2)/9 + (8*a*b*c*d)/9) + 2*a^2*c^2*x^(1/2) + (2*b^2*d^2*x^(17/2))/17 + (4*a*c*x^(5/2)*(a*d + b*c))/5 + (4*b*d*x^(13/2)*(a*d + b*c))/13","B"
404,1,78,95,0.033919,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^2)/x^(3/2),x)","x^{7/2}\,\left(\frac{2\,a^2\,d^2}{7}+\frac{8\,a\,b\,c\,d}{7}+\frac{2\,b^2\,c^2}{7}\right)-\frac{2\,a^2\,c^2}{\sqrt{x}}+\frac{2\,b^2\,d^2\,x^{15/2}}{15}+\frac{4\,a\,c\,x^{3/2}\,\left(a\,d+b\,c\right)}{3}+\frac{4\,b\,d\,x^{11/2}\,\left(a\,d+b\,c\right)}{11}","Not used",1,"x^(7/2)*((2*a^2*d^2)/7 + (2*b^2*c^2)/7 + (8*a*b*c*d)/7) - (2*a^2*c^2)/x^(1/2) + (2*b^2*d^2*x^(15/2))/15 + (4*a*c*x^(3/2)*(a*d + b*c))/3 + (4*b*d*x^(11/2)*(a*d + b*c))/11","B"
405,1,78,95,0.032965,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^2)/x^(5/2),x)","x^{5/2}\,\left(\frac{2\,a^2\,d^2}{5}+\frac{8\,a\,b\,c\,d}{5}+\frac{2\,b^2\,c^2}{5}\right)-\frac{2\,a^2\,c^2}{3\,x^{3/2}}+\frac{2\,b^2\,d^2\,x^{13/2}}{13}+4\,a\,c\,\sqrt{x}\,\left(a\,d+b\,c\right)+\frac{4\,b\,d\,x^{9/2}\,\left(a\,d+b\,c\right)}{9}","Not used",1,"x^(5/2)*((2*a^2*d^2)/5 + (2*b^2*c^2)/5 + (8*a*b*c*d)/5) - (2*a^2*c^2)/(3*x^(3/2)) + (2*b^2*d^2*x^(13/2))/13 + 4*a*c*x^(1/2)*(a*d + b*c) + (4*b*d*x^(9/2)*(a*d + b*c))/9","B"
406,1,86,95,0.060891,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^2)/x^(7/2),x)","x^{3/2}\,\left(\frac{2\,a^2\,d^2}{3}+\frac{8\,a\,b\,c\,d}{3}+\frac{2\,b^2\,c^2}{3}\right)-\frac{x^2\,\left(4\,d\,a^2\,c+4\,b\,a\,c^2\right)+\frac{2\,a^2\,c^2}{5}}{x^{5/2}}+\frac{2\,b^2\,d^2\,x^{11/2}}{11}+\frac{4\,b\,d\,x^{7/2}\,\left(a\,d+b\,c\right)}{7}","Not used",1,"x^(3/2)*((2*a^2*d^2)/3 + (2*b^2*c^2)/3 + (8*a*b*c*d)/3) - (x^2*(4*a*b*c^2 + 4*a^2*c*d) + (2*a^2*c^2)/5)/x^(5/2) + (2*b^2*d^2*x^(11/2))/11 + (4*b*d*x^(7/2)*(a*d + b*c))/7","B"
407,1,119,139,0.214111,"\text{Not used}","int(x^(7/2)*(a + b*x^2)^2*(c + d*x^2)^3,x)","x^{17/2}\,\left(\frac{6\,a^2\,c\,d^2}{17}+\frac{12\,a\,b\,c^2\,d}{17}+\frac{2\,b^2\,c^3}{17}\right)+x^{21/2}\,\left(\frac{2\,a^2\,d^3}{21}+\frac{4\,a\,b\,c\,d^2}{7}+\frac{2\,b^2\,c^2\,d}{7}\right)+\frac{2\,a^2\,c^3\,x^{9/2}}{9}+\frac{2\,b^2\,d^3\,x^{29/2}}{29}+\frac{2\,a\,c^2\,x^{13/2}\,\left(3\,a\,d+2\,b\,c\right)}{13}+\frac{2\,b\,d^2\,x^{25/2}\,\left(2\,a\,d+3\,b\,c\right)}{25}","Not used",1,"x^(17/2)*((2*b^2*c^3)/17 + (6*a^2*c*d^2)/17 + (12*a*b*c^2*d)/17) + x^(21/2)*((2*a^2*d^3)/21 + (2*b^2*c^2*d)/7 + (4*a*b*c*d^2)/7) + (2*a^2*c^3*x^(9/2))/9 + (2*b^2*d^3*x^(29/2))/29 + (2*a*c^2*x^(13/2)*(3*a*d + 2*b*c))/13 + (2*b*d^2*x^(25/2)*(2*a*d + 3*b*c))/25","B"
408,1,119,139,0.039358,"\text{Not used}","int(x^(5/2)*(a + b*x^2)^2*(c + d*x^2)^3,x)","x^{15/2}\,\left(\frac{2\,a^2\,c\,d^2}{5}+\frac{4\,a\,b\,c^2\,d}{5}+\frac{2\,b^2\,c^3}{15}\right)+x^{19/2}\,\left(\frac{2\,a^2\,d^3}{19}+\frac{12\,a\,b\,c\,d^2}{19}+\frac{6\,b^2\,c^2\,d}{19}\right)+\frac{2\,a^2\,c^3\,x^{7/2}}{7}+\frac{2\,b^2\,d^3\,x^{27/2}}{27}+\frac{2\,a\,c^2\,x^{11/2}\,\left(3\,a\,d+2\,b\,c\right)}{11}+\frac{2\,b\,d^2\,x^{23/2}\,\left(2\,a\,d+3\,b\,c\right)}{23}","Not used",1,"x^(15/2)*((2*b^2*c^3)/15 + (2*a^2*c*d^2)/5 + (4*a*b*c^2*d)/5) + x^(19/2)*((2*a^2*d^3)/19 + (6*b^2*c^2*d)/19 + (12*a*b*c*d^2)/19) + (2*a^2*c^3*x^(7/2))/7 + (2*b^2*d^3*x^(27/2))/27 + (2*a*c^2*x^(11/2)*(3*a*d + 2*b*c))/11 + (2*b*d^2*x^(23/2)*(2*a*d + 3*b*c))/23","B"
409,1,119,139,0.039770,"\text{Not used}","int(x^(3/2)*(a + b*x^2)^2*(c + d*x^2)^3,x)","x^{13/2}\,\left(\frac{6\,a^2\,c\,d^2}{13}+\frac{12\,a\,b\,c^2\,d}{13}+\frac{2\,b^2\,c^3}{13}\right)+x^{17/2}\,\left(\frac{2\,a^2\,d^3}{17}+\frac{12\,a\,b\,c\,d^2}{17}+\frac{6\,b^2\,c^2\,d}{17}\right)+\frac{2\,a^2\,c^3\,x^{5/2}}{5}+\frac{2\,b^2\,d^3\,x^{25/2}}{25}+\frac{2\,a\,c^2\,x^{9/2}\,\left(3\,a\,d+2\,b\,c\right)}{9}+\frac{2\,b\,d^2\,x^{21/2}\,\left(2\,a\,d+3\,b\,c\right)}{21}","Not used",1,"x^(13/2)*((2*b^2*c^3)/13 + (6*a^2*c*d^2)/13 + (12*a*b*c^2*d)/13) + x^(17/2)*((2*a^2*d^3)/17 + (6*b^2*c^2*d)/17 + (12*a*b*c*d^2)/17) + (2*a^2*c^3*x^(5/2))/5 + (2*b^2*d^3*x^(25/2))/25 + (2*a*c^2*x^(9/2)*(3*a*d + 2*b*c))/9 + (2*b*d^2*x^(21/2)*(2*a*d + 3*b*c))/21","B"
410,1,119,139,0.042157,"\text{Not used}","int(x^(1/2)*(a + b*x^2)^2*(c + d*x^2)^3,x)","x^{11/2}\,\left(\frac{6\,a^2\,c\,d^2}{11}+\frac{12\,a\,b\,c^2\,d}{11}+\frac{2\,b^2\,c^3}{11}\right)+x^{15/2}\,\left(\frac{2\,a^2\,d^3}{15}+\frac{4\,a\,b\,c\,d^2}{5}+\frac{2\,b^2\,c^2\,d}{5}\right)+\frac{2\,a^2\,c^3\,x^{3/2}}{3}+\frac{2\,b^2\,d^3\,x^{23/2}}{23}+\frac{2\,a\,c^2\,x^{7/2}\,\left(3\,a\,d+2\,b\,c\right)}{7}+\frac{2\,b\,d^2\,x^{19/2}\,\left(2\,a\,d+3\,b\,c\right)}{19}","Not used",1,"x^(11/2)*((2*b^2*c^3)/11 + (6*a^2*c*d^2)/11 + (12*a*b*c^2*d)/11) + x^(15/2)*((2*a^2*d^3)/15 + (2*b^2*c^2*d)/5 + (4*a*b*c*d^2)/5) + (2*a^2*c^3*x^(3/2))/3 + (2*b^2*d^3*x^(23/2))/23 + (2*a*c^2*x^(7/2)*(3*a*d + 2*b*c))/7 + (2*b*d^2*x^(19/2)*(2*a*d + 3*b*c))/19","B"
411,1,119,137,0.039393,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^3)/x^(1/2),x)","x^{9/2}\,\left(\frac{2\,a^2\,c\,d^2}{3}+\frac{4\,a\,b\,c^2\,d}{3}+\frac{2\,b^2\,c^3}{9}\right)+x^{13/2}\,\left(\frac{2\,a^2\,d^3}{13}+\frac{12\,a\,b\,c\,d^2}{13}+\frac{6\,b^2\,c^2\,d}{13}\right)+2\,a^2\,c^3\,\sqrt{x}+\frac{2\,b^2\,d^3\,x^{21/2}}{21}+\frac{2\,a\,c^2\,x^{5/2}\,\left(3\,a\,d+2\,b\,c\right)}{5}+\frac{2\,b\,d^2\,x^{17/2}\,\left(2\,a\,d+3\,b\,c\right)}{17}","Not used",1,"x^(9/2)*((2*b^2*c^3)/9 + (2*a^2*c*d^2)/3 + (4*a*b*c^2*d)/3) + x^(13/2)*((2*a^2*d^3)/13 + (6*b^2*c^2*d)/13 + (12*a*b*c*d^2)/13) + 2*a^2*c^3*x^(1/2) + (2*b^2*d^3*x^(21/2))/21 + (2*a*c^2*x^(5/2)*(3*a*d + 2*b*c))/5 + (2*b*d^2*x^(17/2)*(2*a*d + 3*b*c))/17","B"
412,1,119,137,0.043574,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^3)/x^(3/2),x)","x^{7/2}\,\left(\frac{6\,a^2\,c\,d^2}{7}+\frac{12\,a\,b\,c^2\,d}{7}+\frac{2\,b^2\,c^3}{7}\right)+x^{11/2}\,\left(\frac{2\,a^2\,d^3}{11}+\frac{12\,a\,b\,c\,d^2}{11}+\frac{6\,b^2\,c^2\,d}{11}\right)-\frac{2\,a^2\,c^3}{\sqrt{x}}+\frac{2\,b^2\,d^3\,x^{19/2}}{19}+\frac{2\,a\,c^2\,x^{3/2}\,\left(3\,a\,d+2\,b\,c\right)}{3}+\frac{2\,b\,d^2\,x^{15/2}\,\left(2\,a\,d+3\,b\,c\right)}{15}","Not used",1,"x^(7/2)*((2*b^2*c^3)/7 + (6*a^2*c*d^2)/7 + (12*a*b*c^2*d)/7) + x^(11/2)*((2*a^2*d^3)/11 + (6*b^2*c^2*d)/11 + (12*a*b*c*d^2)/11) - (2*a^2*c^3)/x^(1/2) + (2*b^2*d^3*x^(19/2))/19 + (2*a*c^2*x^(3/2)*(3*a*d + 2*b*c))/3 + (2*b*d^2*x^(15/2)*(2*a*d + 3*b*c))/15","B"
413,1,119,137,0.042398,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^3)/x^(5/2),x)","x^{5/2}\,\left(\frac{6\,a^2\,c\,d^2}{5}+\frac{12\,a\,b\,c^2\,d}{5}+\frac{2\,b^2\,c^3}{5}\right)+x^{9/2}\,\left(\frac{2\,a^2\,d^3}{9}+\frac{4\,a\,b\,c\,d^2}{3}+\frac{2\,b^2\,c^2\,d}{3}\right)-\frac{2\,a^2\,c^3}{3\,x^{3/2}}+\frac{2\,b^2\,d^3\,x^{17/2}}{17}+2\,a\,c^2\,\sqrt{x}\,\left(3\,a\,d+2\,b\,c\right)+\frac{2\,b\,d^2\,x^{13/2}\,\left(2\,a\,d+3\,b\,c\right)}{13}","Not used",1,"x^(5/2)*((2*b^2*c^3)/5 + (6*a^2*c*d^2)/5 + (12*a*b*c^2*d)/5) + x^(9/2)*((2*a^2*d^3)/9 + (2*b^2*c^2*d)/3 + (4*a*b*c*d^2)/3) - (2*a^2*c^3)/(3*x^(3/2)) + (2*b^2*d^3*x^(17/2))/17 + 2*a*c^2*x^(1/2)*(3*a*d + 2*b*c) + (2*b*d^2*x^(13/2)*(2*a*d + 3*b*c))/13","B"
414,1,125,137,0.043026,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^3)/x^(7/2),x)","x^{3/2}\,\left(2\,a^2\,c\,d^2+4\,a\,b\,c^2\,d+\frac{2\,b^2\,c^3}{3}\right)+x^{7/2}\,\left(\frac{2\,a^2\,d^3}{7}+\frac{12\,a\,b\,c\,d^2}{7}+\frac{6\,b^2\,c^2\,d}{7}\right)-\frac{x^2\,\left(6\,d\,a^2\,c^2+4\,b\,a\,c^3\right)+\frac{2\,a^2\,c^3}{5}}{x^{5/2}}+\frac{2\,b^2\,d^3\,x^{15/2}}{15}+\frac{2\,b\,d^2\,x^{11/2}\,\left(2\,a\,d+3\,b\,c\right)}{11}","Not used",1,"x^(3/2)*((2*b^2*c^3)/3 + 2*a^2*c*d^2 + 4*a*b*c^2*d) + x^(7/2)*((2*a^2*d^3)/7 + (6*b^2*c^2*d)/7 + (12*a*b*c*d^2)/7) - (x^2*(6*a^2*c^2*d + 4*a*b*c^3) + (2*a^2*c^3)/5)/x^(5/2) + (2*b^2*d^3*x^(15/2))/15 + (2*b*d^2*x^(11/2)*(2*a*d + 3*b*c))/11","B"
415,1,1202,311,0.381961,"\text{Not used}","int((x^(7/2)*(a + b*x^2)^2)/(c + d*x^2),x)","x^{5/2}\,\left(\frac{2\,a^2}{5\,d}+\frac{c\,\left(\frac{2\,b^2\,c}{d^2}-\frac{4\,a\,b}{d}\right)}{5\,d}\right)-x^{9/2}\,\left(\frac{2\,b^2\,c}{9\,d^2}-\frac{4\,a\,b}{9\,d}\right)+\frac{2\,b^2\,x^{13/2}}{13\,d}-\frac{c\,\sqrt{x}\,\left(\frac{2\,a^2}{d}+\frac{c\,\left(\frac{2\,b^2\,c}{d^2}-\frac{4\,a\,b}{d}\right)}{d}\right)}{d}+\frac{{\left(-c\right)}^{5/4}\,\mathrm{atan}\left(\frac{\frac{{\left(-c\right)}^{5/4}\,{\left(a\,d-b\,c\right)}^2\,\left(\frac{16\,\sqrt{x}\,\left(a^4\,c^4\,d^4-4\,a^3\,b\,c^5\,d^3+6\,a^2\,b^2\,c^6\,d^2-4\,a\,b^3\,c^7\,d+b^4\,c^8\right)}{d^5}-\frac{16\,{\left(-c\right)}^{5/4}\,{\left(a\,d-b\,c\right)}^2\,\left(a^2\,c^3\,d^2-2\,a\,b\,c^4\,d+b^2\,c^5\right)}{d^{21/4}}\right)\,1{}\mathrm{i}}{2\,d^{17/4}}+\frac{{\left(-c\right)}^{5/4}\,{\left(a\,d-b\,c\right)}^2\,\left(\frac{16\,\sqrt{x}\,\left(a^4\,c^4\,d^4-4\,a^3\,b\,c^5\,d^3+6\,a^2\,b^2\,c^6\,d^2-4\,a\,b^3\,c^7\,d+b^4\,c^8\right)}{d^5}+\frac{16\,{\left(-c\right)}^{5/4}\,{\left(a\,d-b\,c\right)}^2\,\left(a^2\,c^3\,d^2-2\,a\,b\,c^4\,d+b^2\,c^5\right)}{d^{21/4}}\right)\,1{}\mathrm{i}}{2\,d^{17/4}}}{\frac{{\left(-c\right)}^{5/4}\,{\left(a\,d-b\,c\right)}^2\,\left(\frac{16\,\sqrt{x}\,\left(a^4\,c^4\,d^4-4\,a^3\,b\,c^5\,d^3+6\,a^2\,b^2\,c^6\,d^2-4\,a\,b^3\,c^7\,d+b^4\,c^8\right)}{d^5}-\frac{16\,{\left(-c\right)}^{5/4}\,{\left(a\,d-b\,c\right)}^2\,\left(a^2\,c^3\,d^2-2\,a\,b\,c^4\,d+b^2\,c^5\right)}{d^{21/4}}\right)}{2\,d^{17/4}}-\frac{{\left(-c\right)}^{5/4}\,{\left(a\,d-b\,c\right)}^2\,\left(\frac{16\,\sqrt{x}\,\left(a^4\,c^4\,d^4-4\,a^3\,b\,c^5\,d^3+6\,a^2\,b^2\,c^6\,d^2-4\,a\,b^3\,c^7\,d+b^4\,c^8\right)}{d^5}+\frac{16\,{\left(-c\right)}^{5/4}\,{\left(a\,d-b\,c\right)}^2\,\left(a^2\,c^3\,d^2-2\,a\,b\,c^4\,d+b^2\,c^5\right)}{d^{21/4}}\right)}{2\,d^{17/4}}}\right)\,{\left(a\,d-b\,c\right)}^2\,1{}\mathrm{i}}{d^{17/4}}+\frac{{\left(-c\right)}^{5/4}\,\mathrm{atan}\left(\frac{\frac{{\left(-c\right)}^{5/4}\,{\left(a\,d-b\,c\right)}^2\,\left(\frac{16\,\sqrt{x}\,\left(a^4\,c^4\,d^4-4\,a^3\,b\,c^5\,d^3+6\,a^2\,b^2\,c^6\,d^2-4\,a\,b^3\,c^7\,d+b^4\,c^8\right)}{d^5}-\frac{{\left(-c\right)}^{5/4}\,{\left(a\,d-b\,c\right)}^2\,\left(a^2\,c^3\,d^2-2\,a\,b\,c^4\,d+b^2\,c^5\right)\,16{}\mathrm{i}}{d^{21/4}}\right)}{2\,d^{17/4}}+\frac{{\left(-c\right)}^{5/4}\,{\left(a\,d-b\,c\right)}^2\,\left(\frac{16\,\sqrt{x}\,\left(a^4\,c^4\,d^4-4\,a^3\,b\,c^5\,d^3+6\,a^2\,b^2\,c^6\,d^2-4\,a\,b^3\,c^7\,d+b^4\,c^8\right)}{d^5}+\frac{{\left(-c\right)}^{5/4}\,{\left(a\,d-b\,c\right)}^2\,\left(a^2\,c^3\,d^2-2\,a\,b\,c^4\,d+b^2\,c^5\right)\,16{}\mathrm{i}}{d^{21/4}}\right)}{2\,d^{17/4}}}{\frac{{\left(-c\right)}^{5/4}\,{\left(a\,d-b\,c\right)}^2\,\left(\frac{16\,\sqrt{x}\,\left(a^4\,c^4\,d^4-4\,a^3\,b\,c^5\,d^3+6\,a^2\,b^2\,c^6\,d^2-4\,a\,b^3\,c^7\,d+b^4\,c^8\right)}{d^5}-\frac{{\left(-c\right)}^{5/4}\,{\left(a\,d-b\,c\right)}^2\,\left(a^2\,c^3\,d^2-2\,a\,b\,c^4\,d+b^2\,c^5\right)\,16{}\mathrm{i}}{d^{21/4}}\right)\,1{}\mathrm{i}}{2\,d^{17/4}}-\frac{{\left(-c\right)}^{5/4}\,{\left(a\,d-b\,c\right)}^2\,\left(\frac{16\,\sqrt{x}\,\left(a^4\,c^4\,d^4-4\,a^3\,b\,c^5\,d^3+6\,a^2\,b^2\,c^6\,d^2-4\,a\,b^3\,c^7\,d+b^4\,c^8\right)}{d^5}+\frac{{\left(-c\right)}^{5/4}\,{\left(a\,d-b\,c\right)}^2\,\left(a^2\,c^3\,d^2-2\,a\,b\,c^4\,d+b^2\,c^5\right)\,16{}\mathrm{i}}{d^{21/4}}\right)\,1{}\mathrm{i}}{2\,d^{17/4}}}\right)\,{\left(a\,d-b\,c\right)}^2}{d^{17/4}}","Not used",1,"x^(5/2)*((2*a^2)/(5*d) + (c*((2*b^2*c)/d^2 - (4*a*b)/d))/(5*d)) - x^(9/2)*((2*b^2*c)/(9*d^2) - (4*a*b)/(9*d)) + (2*b^2*x^(13/2))/(13*d) - (c*x^(1/2)*((2*a^2)/d + (c*((2*b^2*c)/d^2 - (4*a*b)/d))/d))/d + ((-c)^(5/4)*atan((((-c)^(5/4)*(a*d - b*c)^2*((16*x^(1/2)*(b^4*c^8 + a^4*c^4*d^4 - 4*a^3*b*c^5*d^3 + 6*a^2*b^2*c^6*d^2 - 4*a*b^3*c^7*d))/d^5 - (16*(-c)^(5/4)*(a*d - b*c)^2*(b^2*c^5 + a^2*c^3*d^2 - 2*a*b*c^4*d))/d^(21/4))*1i)/(2*d^(17/4)) + ((-c)^(5/4)*(a*d - b*c)^2*((16*x^(1/2)*(b^4*c^8 + a^4*c^4*d^4 - 4*a^3*b*c^5*d^3 + 6*a^2*b^2*c^6*d^2 - 4*a*b^3*c^7*d))/d^5 + (16*(-c)^(5/4)*(a*d - b*c)^2*(b^2*c^5 + a^2*c^3*d^2 - 2*a*b*c^4*d))/d^(21/4))*1i)/(2*d^(17/4)))/(((-c)^(5/4)*(a*d - b*c)^2*((16*x^(1/2)*(b^4*c^8 + a^4*c^4*d^4 - 4*a^3*b*c^5*d^3 + 6*a^2*b^2*c^6*d^2 - 4*a*b^3*c^7*d))/d^5 - (16*(-c)^(5/4)*(a*d - b*c)^2*(b^2*c^5 + a^2*c^3*d^2 - 2*a*b*c^4*d))/d^(21/4)))/(2*d^(17/4)) - ((-c)^(5/4)*(a*d - b*c)^2*((16*x^(1/2)*(b^4*c^8 + a^4*c^4*d^4 - 4*a^3*b*c^5*d^3 + 6*a^2*b^2*c^6*d^2 - 4*a*b^3*c^7*d))/d^5 + (16*(-c)^(5/4)*(a*d - b*c)^2*(b^2*c^5 + a^2*c^3*d^2 - 2*a*b*c^4*d))/d^(21/4)))/(2*d^(17/4))))*(a*d - b*c)^2*1i)/d^(17/4) + ((-c)^(5/4)*atan((((-c)^(5/4)*(a*d - b*c)^2*((16*x^(1/2)*(b^4*c^8 + a^4*c^4*d^4 - 4*a^3*b*c^5*d^3 + 6*a^2*b^2*c^6*d^2 - 4*a*b^3*c^7*d))/d^5 - ((-c)^(5/4)*(a*d - b*c)^2*(b^2*c^5 + a^2*c^3*d^2 - 2*a*b*c^4*d)*16i)/d^(21/4)))/(2*d^(17/4)) + ((-c)^(5/4)*(a*d - b*c)^2*((16*x^(1/2)*(b^4*c^8 + a^4*c^4*d^4 - 4*a^3*b*c^5*d^3 + 6*a^2*b^2*c^6*d^2 - 4*a*b^3*c^7*d))/d^5 + ((-c)^(5/4)*(a*d - b*c)^2*(b^2*c^5 + a^2*c^3*d^2 - 2*a*b*c^4*d)*16i)/d^(21/4)))/(2*d^(17/4)))/(((-c)^(5/4)*(a*d - b*c)^2*((16*x^(1/2)*(b^4*c^8 + a^4*c^4*d^4 - 4*a^3*b*c^5*d^3 + 6*a^2*b^2*c^6*d^2 - 4*a*b^3*c^7*d))/d^5 - ((-c)^(5/4)*(a*d - b*c)^2*(b^2*c^5 + a^2*c^3*d^2 - 2*a*b*c^4*d)*16i)/d^(21/4))*1i)/(2*d^(17/4)) - ((-c)^(5/4)*(a*d - b*c)^2*((16*x^(1/2)*(b^4*c^8 + a^4*c^4*d^4 - 4*a^3*b*c^5*d^3 + 6*a^2*b^2*c^6*d^2 - 4*a*b^3*c^7*d))/d^5 + ((-c)^(5/4)*(a*d - b*c)^2*(b^2*c^5 + a^2*c^3*d^2 - 2*a*b*c^4*d)*16i)/d^(21/4))*1i)/(2*d^(17/4))))*(a*d - b*c)^2)/d^(17/4)","B"
416,1,435,290,0.310736,"\text{Not used}","int((x^(5/2)*(a + b*x^2)^2)/(c + d*x^2),x)","x^{3/2}\,\left(\frac{2\,a^2}{3\,d}+\frac{c\,\left(\frac{2\,b^2\,c}{d^2}-\frac{4\,a\,b}{d}\right)}{3\,d}\right)-x^{7/2}\,\left(\frac{2\,b^2\,c}{7\,d^2}-\frac{4\,a\,b}{7\,d}\right)+\frac{2\,b^2\,x^{11/2}}{11\,d}-\frac{{\left(-c\right)}^{3/4}\,\mathrm{atan}\left(\frac{{\left(-c\right)}^{3/4}\,d^{1/4}\,\sqrt{x}\,{\left(a\,d-b\,c\right)}^2\,\left(a^4\,c^3\,d^4-4\,a^3\,b\,c^4\,d^3+6\,a^2\,b^2\,c^5\,d^2-4\,a\,b^3\,c^6\,d+b^4\,c^7\right)}{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)\,{\left(a\,d-b\,c\right)}^2}{d^{15/4}}-\frac{{\left(-c\right)}^{3/4}\,\mathrm{atan}\left(\frac{{\left(-c\right)}^{3/4}\,d^{1/4}\,\sqrt{x}\,{\left(a\,d-b\,c\right)}^2\,\left(a^4\,c^3\,d^4-4\,a^3\,b\,c^4\,d^3+6\,a^2\,b^2\,c^5\,d^2-4\,a\,b^3\,c^6\,d+b^4\,c^7\right)\,1{}\mathrm{i}}{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)\,{\left(a\,d-b\,c\right)}^2\,1{}\mathrm{i}}{d^{15/4}}","Not used",1,"x^(3/2)*((2*a^2)/(3*d) + (c*((2*b^2*c)/d^2 - (4*a*b)/d))/(3*d)) - x^(7/2)*((2*b^2*c)/(7*d^2) - (4*a*b)/(7*d)) + (2*b^2*x^(11/2))/(11*d) - ((-c)^(3/4)*atan(((-c)^(3/4)*d^(1/4)*x^(1/2)*(a*d - b*c)^2*(b^4*c^7 + a^4*c^3*d^4 - 4*a^3*b*c^4*d^3 + 6*a^2*b^2*c^5*d^2 - 4*a*b^3*c^6*d))/(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))*(a*d - b*c)^2)/d^(15/4) - ((-c)^(3/4)*atan(((-c)^(3/4)*d^(1/4)*x^(1/2)*(a*d - b*c)^2*(b^4*c^7 + a^4*c^3*d^4 - 4*a^3*b*c^4*d^3 + 6*a^2*b^2*c^5*d^2 - 4*a*b^3*c^6*d)*1i)/(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))*(a*d - b*c)^2*1i)/d^(15/4)","B"
417,1,1175,288,0.350632,"\text{Not used}","int((x^(3/2)*(a + b*x^2)^2)/(c + d*x^2),x)","\sqrt{x}\,\left(\frac{2\,a^2}{d}+\frac{c\,\left(\frac{2\,b^2\,c}{d^2}-\frac{4\,a\,b}{d}\right)}{d}\right)-x^{5/2}\,\left(\frac{2\,b^2\,c}{5\,d^2}-\frac{4\,a\,b}{5\,d}\right)+\frac{2\,b^2\,x^{9/2}}{9\,d}-\frac{{\left(-c\right)}^{1/4}\,\mathrm{atan}\left(\frac{\frac{{\left(-c\right)}^{1/4}\,{\left(a\,d-b\,c\right)}^2\,\left(\frac{8\,\sqrt{x}\,\left(a^4\,c^2\,d^4-4\,a^3\,b\,c^3\,d^3+6\,a^2\,b^2\,c^4\,d^2-4\,a\,b^3\,c^5\,d+b^4\,c^6\right)}{d^3}-\frac{{\left(-c\right)}^{1/4}\,{\left(a\,d-b\,c\right)}^2\,\left(16\,a^2\,c^2\,d^2-32\,a\,b\,c^3\,d+16\,b^2\,c^4\right)}{2\,d^{13/4}}\right)\,1{}\mathrm{i}}{d^{13/4}}+\frac{{\left(-c\right)}^{1/4}\,{\left(a\,d-b\,c\right)}^2\,\left(\frac{8\,\sqrt{x}\,\left(a^4\,c^2\,d^4-4\,a^3\,b\,c^3\,d^3+6\,a^2\,b^2\,c^4\,d^2-4\,a\,b^3\,c^5\,d+b^4\,c^6\right)}{d^3}+\frac{{\left(-c\right)}^{1/4}\,{\left(a\,d-b\,c\right)}^2\,\left(16\,a^2\,c^2\,d^2-32\,a\,b\,c^3\,d+16\,b^2\,c^4\right)}{2\,d^{13/4}}\right)\,1{}\mathrm{i}}{d^{13/4}}}{\frac{{\left(-c\right)}^{1/4}\,{\left(a\,d-b\,c\right)}^2\,\left(\frac{8\,\sqrt{x}\,\left(a^4\,c^2\,d^4-4\,a^3\,b\,c^3\,d^3+6\,a^2\,b^2\,c^4\,d^2-4\,a\,b^3\,c^5\,d+b^4\,c^6\right)}{d^3}-\frac{{\left(-c\right)}^{1/4}\,{\left(a\,d-b\,c\right)}^2\,\left(16\,a^2\,c^2\,d^2-32\,a\,b\,c^3\,d+16\,b^2\,c^4\right)}{2\,d^{13/4}}\right)}{d^{13/4}}-\frac{{\left(-c\right)}^{1/4}\,{\left(a\,d-b\,c\right)}^2\,\left(\frac{8\,\sqrt{x}\,\left(a^4\,c^2\,d^4-4\,a^3\,b\,c^3\,d^3+6\,a^2\,b^2\,c^4\,d^2-4\,a\,b^3\,c^5\,d+b^4\,c^6\right)}{d^3}+\frac{{\left(-c\right)}^{1/4}\,{\left(a\,d-b\,c\right)}^2\,\left(16\,a^2\,c^2\,d^2-32\,a\,b\,c^3\,d+16\,b^2\,c^4\right)}{2\,d^{13/4}}\right)}{d^{13/4}}}\right)\,{\left(a\,d-b\,c\right)}^2\,1{}\mathrm{i}}{d^{13/4}}-\frac{{\left(-c\right)}^{1/4}\,\mathrm{atan}\left(\frac{\frac{{\left(-c\right)}^{1/4}\,{\left(a\,d-b\,c\right)}^2\,\left(\frac{8\,\sqrt{x}\,\left(a^4\,c^2\,d^4-4\,a^3\,b\,c^3\,d^3+6\,a^2\,b^2\,c^4\,d^2-4\,a\,b^3\,c^5\,d+b^4\,c^6\right)}{d^3}-\frac{{\left(-c\right)}^{1/4}\,{\left(a\,d-b\,c\right)}^2\,\left(16\,a^2\,c^2\,d^2-32\,a\,b\,c^3\,d+16\,b^2\,c^4\right)\,1{}\mathrm{i}}{2\,d^{13/4}}\right)}{d^{13/4}}+\frac{{\left(-c\right)}^{1/4}\,{\left(a\,d-b\,c\right)}^2\,\left(\frac{8\,\sqrt{x}\,\left(a^4\,c^2\,d^4-4\,a^3\,b\,c^3\,d^3+6\,a^2\,b^2\,c^4\,d^2-4\,a\,b^3\,c^5\,d+b^4\,c^6\right)}{d^3}+\frac{{\left(-c\right)}^{1/4}\,{\left(a\,d-b\,c\right)}^2\,\left(16\,a^2\,c^2\,d^2-32\,a\,b\,c^3\,d+16\,b^2\,c^4\right)\,1{}\mathrm{i}}{2\,d^{13/4}}\right)}{d^{13/4}}}{\frac{{\left(-c\right)}^{1/4}\,{\left(a\,d-b\,c\right)}^2\,\left(\frac{8\,\sqrt{x}\,\left(a^4\,c^2\,d^4-4\,a^3\,b\,c^3\,d^3+6\,a^2\,b^2\,c^4\,d^2-4\,a\,b^3\,c^5\,d+b^4\,c^6\right)}{d^3}-\frac{{\left(-c\right)}^{1/4}\,{\left(a\,d-b\,c\right)}^2\,\left(16\,a^2\,c^2\,d^2-32\,a\,b\,c^3\,d+16\,b^2\,c^4\right)\,1{}\mathrm{i}}{2\,d^{13/4}}\right)\,1{}\mathrm{i}}{d^{13/4}}-\frac{{\left(-c\right)}^{1/4}\,{\left(a\,d-b\,c\right)}^2\,\left(\frac{8\,\sqrt{x}\,\left(a^4\,c^2\,d^4-4\,a^3\,b\,c^3\,d^3+6\,a^2\,b^2\,c^4\,d^2-4\,a\,b^3\,c^5\,d+b^4\,c^6\right)}{d^3}+\frac{{\left(-c\right)}^{1/4}\,{\left(a\,d-b\,c\right)}^2\,\left(16\,a^2\,c^2\,d^2-32\,a\,b\,c^3\,d+16\,b^2\,c^4\right)\,1{}\mathrm{i}}{2\,d^{13/4}}\right)\,1{}\mathrm{i}}{d^{13/4}}}\right)\,{\left(a\,d-b\,c\right)}^2}{d^{13/4}}","Not used",1,"x^(1/2)*((2*a^2)/d + (c*((2*b^2*c)/d^2 - (4*a*b)/d))/d) - x^(5/2)*((2*b^2*c)/(5*d^2) - (4*a*b)/(5*d)) + (2*b^2*x^(9/2))/(9*d) - ((-c)^(1/4)*atan((((-c)^(1/4)*(a*d - b*c)^2*((8*x^(1/2)*(b^4*c^6 + a^4*c^2*d^4 - 4*a^3*b*c^3*d^3 + 6*a^2*b^2*c^4*d^2 - 4*a*b^3*c^5*d))/d^3 - ((-c)^(1/4)*(a*d - b*c)^2*(16*b^2*c^4 + 16*a^2*c^2*d^2 - 32*a*b*c^3*d))/(2*d^(13/4)))*1i)/d^(13/4) + ((-c)^(1/4)*(a*d - b*c)^2*((8*x^(1/2)*(b^4*c^6 + a^4*c^2*d^4 - 4*a^3*b*c^3*d^3 + 6*a^2*b^2*c^4*d^2 - 4*a*b^3*c^5*d))/d^3 + ((-c)^(1/4)*(a*d - b*c)^2*(16*b^2*c^4 + 16*a^2*c^2*d^2 - 32*a*b*c^3*d))/(2*d^(13/4)))*1i)/d^(13/4))/(((-c)^(1/4)*(a*d - b*c)^2*((8*x^(1/2)*(b^4*c^6 + a^4*c^2*d^4 - 4*a^3*b*c^3*d^3 + 6*a^2*b^2*c^4*d^2 - 4*a*b^3*c^5*d))/d^3 - ((-c)^(1/4)*(a*d - b*c)^2*(16*b^2*c^4 + 16*a^2*c^2*d^2 - 32*a*b*c^3*d))/(2*d^(13/4))))/d^(13/4) - ((-c)^(1/4)*(a*d - b*c)^2*((8*x^(1/2)*(b^4*c^6 + a^4*c^2*d^4 - 4*a^3*b*c^3*d^3 + 6*a^2*b^2*c^4*d^2 - 4*a*b^3*c^5*d))/d^3 + ((-c)^(1/4)*(a*d - b*c)^2*(16*b^2*c^4 + 16*a^2*c^2*d^2 - 32*a*b*c^3*d))/(2*d^(13/4))))/d^(13/4)))*(a*d - b*c)^2*1i)/d^(13/4) - ((-c)^(1/4)*atan((((-c)^(1/4)*(a*d - b*c)^2*((8*x^(1/2)*(b^4*c^6 + a^4*c^2*d^4 - 4*a^3*b*c^3*d^3 + 6*a^2*b^2*c^4*d^2 - 4*a*b^3*c^5*d))/d^3 - ((-c)^(1/4)*(a*d - b*c)^2*(16*b^2*c^4 + 16*a^2*c^2*d^2 - 32*a*b*c^3*d)*1i)/(2*d^(13/4))))/d^(13/4) + ((-c)^(1/4)*(a*d - b*c)^2*((8*x^(1/2)*(b^4*c^6 + a^4*c^2*d^4 - 4*a^3*b*c^3*d^3 + 6*a^2*b^2*c^4*d^2 - 4*a*b^3*c^5*d))/d^3 + ((-c)^(1/4)*(a*d - b*c)^2*(16*b^2*c^4 + 16*a^2*c^2*d^2 - 32*a*b*c^3*d)*1i)/(2*d^(13/4))))/d^(13/4))/(((-c)^(1/4)*(a*d - b*c)^2*((8*x^(1/2)*(b^4*c^6 + a^4*c^2*d^4 - 4*a^3*b*c^3*d^3 + 6*a^2*b^2*c^4*d^2 - 4*a*b^3*c^5*d))/d^3 - ((-c)^(1/4)*(a*d - b*c)^2*(16*b^2*c^4 + 16*a^2*c^2*d^2 - 32*a*b*c^3*d)*1i)/(2*d^(13/4)))*1i)/d^(13/4) - ((-c)^(1/4)*(a*d - b*c)^2*((8*x^(1/2)*(b^4*c^6 + a^4*c^2*d^4 - 4*a^3*b*c^3*d^3 + 6*a^2*b^2*c^4*d^2 - 4*a*b^3*c^5*d))/d^3 + ((-c)^(1/4)*(a*d - b*c)^2*(16*b^2*c^4 + 16*a^2*c^2*d^2 - 32*a*b*c^3*d)*1i)/(2*d^(13/4)))*1i)/d^(13/4)))*(a*d - b*c)^2)/d^(13/4)","B"
418,1,390,268,0.175705,"\text{Not used}","int((x^(1/2)*(a + b*x^2)^2)/(c + d*x^2),x)","\frac{2\,b^2\,x^{7/2}}{7\,d}-x^{3/2}\,\left(\frac{2\,b^2\,c}{3\,d^2}-\frac{4\,a\,b}{3\,d}\right)+\frac{\mathrm{atan}\left(\frac{d^{1/4}\,\sqrt{x}\,{\left(a\,d-b\,c\right)}^2\,\left(a^4\,c\,d^4-4\,a^3\,b\,c^2\,d^3+6\,a^2\,b^2\,c^3\,d^2-4\,a\,b^3\,c^4\,d+b^4\,c^5\right)}{{\left(-c\right)}^{1/4}\,\left(a^6\,c\,d^6-6\,a^5\,b\,c^2\,d^5+15\,a^4\,b^2\,c^3\,d^4-20\,a^3\,b^3\,c^4\,d^3+15\,a^2\,b^4\,c^5\,d^2-6\,a\,b^5\,c^6\,d+b^6\,c^7\right)}\right)\,{\left(a\,d-b\,c\right)}^2}{{\left(-c\right)}^{1/4}\,d^{11/4}}+\frac{\mathrm{atan}\left(\frac{d^{1/4}\,\sqrt{x}\,{\left(a\,d-b\,c\right)}^2\,\left(a^4\,c\,d^4-4\,a^3\,b\,c^2\,d^3+6\,a^2\,b^2\,c^3\,d^2-4\,a\,b^3\,c^4\,d+b^4\,c^5\right)\,1{}\mathrm{i}}{{\left(-c\right)}^{1/4}\,\left(a^6\,c\,d^6-6\,a^5\,b\,c^2\,d^5+15\,a^4\,b^2\,c^3\,d^4-20\,a^3\,b^3\,c^4\,d^3+15\,a^2\,b^4\,c^5\,d^2-6\,a\,b^5\,c^6\,d+b^6\,c^7\right)}\right)\,{\left(a\,d-b\,c\right)}^2\,1{}\mathrm{i}}{{\left(-c\right)}^{1/4}\,d^{11/4}}","Not used",1,"(2*b^2*x^(7/2))/(7*d) - x^(3/2)*((2*b^2*c)/(3*d^2) - (4*a*b)/(3*d)) + (atan((d^(1/4)*x^(1/2)*(a*d - b*c)^2*(b^4*c^5 + a^4*c*d^4 - 4*a^3*b*c^2*d^3 + 6*a^2*b^2*c^3*d^2 - 4*a*b^3*c^4*d))/((-c)^(1/4)*(b^6*c^7 + a^6*c*d^6 - 6*a^5*b*c^2*d^5 + 15*a^2*b^4*c^5*d^2 - 20*a^3*b^3*c^4*d^3 + 15*a^4*b^2*c^3*d^4 - 6*a*b^5*c^6*d)))*(a*d - b*c)^2)/((-c)^(1/4)*d^(11/4)) + (atan((d^(1/4)*x^(1/2)*(a*d - b*c)^2*(b^4*c^5 + a^4*c*d^4 - 4*a^3*b*c^2*d^3 + 6*a^2*b^2*c^3*d^2 - 4*a*b^3*c^4*d)*1i)/((-c)^(1/4)*(b^6*c^7 + a^6*c*d^6 - 6*a^5*b*c^2*d^5 + 15*a^2*b^4*c^5*d^2 - 20*a^3*b^3*c^4*d^3 + 15*a^4*b^2*c^3*d^4 - 6*a*b^5*c^6*d)))*(a*d - b*c)^2*1i)/((-c)^(1/4)*d^(11/4))","B"
419,1,1107,266,0.371383,"\text{Not used}","int((a + b*x^2)^2/(x^(1/2)*(c + d*x^2)),x)","\frac{2\,b^2\,x^{5/2}}{5\,d}-\sqrt{x}\,\left(\frac{2\,b^2\,c}{d^2}-\frac{4\,a\,b}{d}\right)+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\sqrt{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(16\,a^2\,c\,d^3-32\,a\,b\,c^2\,d^2+16\,b^2\,c^3\,d\right)}{2\,{\left(-c\right)}^{3/4}\,d^{9/4}}\right)\,{\left(a\,d-b\,c\right)}^2\,1{}\mathrm{i}}{{\left(-c\right)}^{3/4}\,d^{9/4}}+\frac{\left(\frac{8\,\sqrt{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(16\,a^2\,c\,d^3-32\,a\,b\,c^2\,d^2+16\,b^2\,c^3\,d\right)}{2\,{\left(-c\right)}^{3/4}\,d^{9/4}}\right)\,{\left(a\,d-b\,c\right)}^2\,1{}\mathrm{i}}{{\left(-c\right)}^{3/4}\,d^{9/4}}}{\frac{\left(\frac{8\,\sqrt{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(16\,a^2\,c\,d^3-32\,a\,b\,c^2\,d^2+16\,b^2\,c^3\,d\right)}{2\,{\left(-c\right)}^{3/4}\,d^{9/4}}\right)\,{\left(a\,d-b\,c\right)}^2}{{\left(-c\right)}^{3/4}\,d^{9/4}}-\frac{\left(\frac{8\,\sqrt{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(16\,a^2\,c\,d^3-32\,a\,b\,c^2\,d^2+16\,b^2\,c^3\,d\right)}{2\,{\left(-c\right)}^{3/4}\,d^{9/4}}\right)\,{\left(a\,d-b\,c\right)}^2}{{\left(-c\right)}^{3/4}\,d^{9/4}}}\right)\,{\left(a\,d-b\,c\right)}^2\,1{}\mathrm{i}}{{\left(-c\right)}^{3/4}\,d^{9/4}}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\sqrt{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(16\,a^2\,c\,d^3-32\,a\,b\,c^2\,d^2+16\,b^2\,c^3\,d\right)\,1{}\mathrm{i}}{2\,{\left(-c\right)}^{3/4}\,d^{9/4}}\right)\,{\left(a\,d-b\,c\right)}^2}{{\left(-c\right)}^{3/4}\,d^{9/4}}+\frac{\left(\frac{8\,\sqrt{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(16\,a^2\,c\,d^3-32\,a\,b\,c^2\,d^2+16\,b^2\,c^3\,d\right)\,1{}\mathrm{i}}{2\,{\left(-c\right)}^{3/4}\,d^{9/4}}\right)\,{\left(a\,d-b\,c\right)}^2}{{\left(-c\right)}^{3/4}\,d^{9/4}}}{\frac{\left(\frac{8\,\sqrt{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(16\,a^2\,c\,d^3-32\,a\,b\,c^2\,d^2+16\,b^2\,c^3\,d\right)\,1{}\mathrm{i}}{2\,{\left(-c\right)}^{3/4}\,d^{9/4}}\right)\,{\left(a\,d-b\,c\right)}^2\,1{}\mathrm{i}}{{\left(-c\right)}^{3/4}\,d^{9/4}}-\frac{\left(\frac{8\,\sqrt{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(16\,a^2\,c\,d^3-32\,a\,b\,c^2\,d^2+16\,b^2\,c^3\,d\right)\,1{}\mathrm{i}}{2\,{\left(-c\right)}^{3/4}\,d^{9/4}}\right)\,{\left(a\,d-b\,c\right)}^2\,1{}\mathrm{i}}{{\left(-c\right)}^{3/4}\,d^{9/4}}}\right)\,{\left(a\,d-b\,c\right)}^2}{{\left(-c\right)}^{3/4}\,d^{9/4}}","Not used",1,"(2*b^2*x^(5/2))/(5*d) - x^(1/2)*((2*b^2*c)/d^2 - (4*a*b)/d) + (atan(((((8*x^(1/2)*(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*(16*a^2*c*d^3 + 16*b^2*c^3*d - 32*a*b*c^2*d^2))/(2*(-c)^(3/4)*d^(9/4)))*(a*d - b*c)^2*1i)/((-c)^(3/4)*d^(9/4)) + (((8*x^(1/2)*(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*(16*a^2*c*d^3 + 16*b^2*c^3*d - 32*a*b*c^2*d^2))/(2*(-c)^(3/4)*d^(9/4)))*(a*d - b*c)^2*1i)/((-c)^(3/4)*d^(9/4)))/((((8*x^(1/2)*(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*(16*a^2*c*d^3 + 16*b^2*c^3*d - 32*a*b*c^2*d^2))/(2*(-c)^(3/4)*d^(9/4)))*(a*d - b*c)^2)/((-c)^(3/4)*d^(9/4)) - (((8*x^(1/2)*(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*(16*a^2*c*d^3 + 16*b^2*c^3*d - 32*a*b*c^2*d^2))/(2*(-c)^(3/4)*d^(9/4)))*(a*d - b*c)^2)/((-c)^(3/4)*d^(9/4))))*(a*d - b*c)^2*1i)/((-c)^(3/4)*d^(9/4)) + (atan(((((8*x^(1/2)*(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*(16*a^2*c*d^3 + 16*b^2*c^3*d - 32*a*b*c^2*d^2)*1i)/(2*(-c)^(3/4)*d^(9/4)))*(a*d - b*c)^2)/((-c)^(3/4)*d^(9/4)) + (((8*x^(1/2)*(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*(16*a^2*c*d^3 + 16*b^2*c^3*d - 32*a*b*c^2*d^2)*1i)/(2*(-c)^(3/4)*d^(9/4)))*(a*d - b*c)^2)/((-c)^(3/4)*d^(9/4)))/((((8*x^(1/2)*(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*(16*a^2*c*d^3 + 16*b^2*c^3*d - 32*a*b*c^2*d^2)*1i)/(2*(-c)^(3/4)*d^(9/4)))*(a*d - b*c)^2*1i)/((-c)^(3/4)*d^(9/4)) - (((8*x^(1/2)*(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*(16*a^2*c*d^3 + 16*b^2*c^3*d - 32*a*b*c^2*d^2)*1i)/(2*(-c)^(3/4)*d^(9/4)))*(a*d - b*c)^2*1i)/((-c)^(3/4)*d^(9/4))))*(a*d - b*c)^2)/((-c)^(3/4)*d^(9/4))","B"
420,1,416,260,0.342923,"\text{Not used}","int((a + b*x^2)^2/(x^(3/2)*(c + d*x^2)),x)","\frac{2\,b^2\,x^{3/2}}{3\,d}-\frac{2\,a^2}{c\,\sqrt{x}}-\frac{\mathrm{atan}\left(\frac{\sqrt{x}\,{\left(a\,d-b\,c\right)}^2\,\left(16\,a^4\,c^4\,d^9-64\,a^3\,b\,c^5\,d^8+96\,a^2\,b^2\,c^6\,d^7-64\,a\,b^3\,c^7\,d^6+16\,b^4\,c^8\,d^5\right)}{{\left(-c\right)}^{5/4}\,d^{7/4}\,\left(16\,a^6\,c^3\,d^9-96\,a^5\,b\,c^4\,d^8+240\,a^4\,b^2\,c^5\,d^7-320\,a^3\,b^3\,c^6\,d^6+240\,a^2\,b^4\,c^7\,d^5-96\,a\,b^5\,c^8\,d^4+16\,b^6\,c^9\,d^3\right)}\right)\,{\left(a\,d-b\,c\right)}^2}{{\left(-c\right)}^{5/4}\,d^{7/4}}-\frac{\mathrm{atan}\left(\frac{\sqrt{x}\,{\left(a\,d-b\,c\right)}^2\,\left(16\,a^4\,c^4\,d^9-64\,a^3\,b\,c^5\,d^8+96\,a^2\,b^2\,c^6\,d^7-64\,a\,b^3\,c^7\,d^6+16\,b^4\,c^8\,d^5\right)\,1{}\mathrm{i}}{{\left(-c\right)}^{5/4}\,d^{7/4}\,\left(16\,a^6\,c^3\,d^9-96\,a^5\,b\,c^4\,d^8+240\,a^4\,b^2\,c^5\,d^7-320\,a^3\,b^3\,c^6\,d^6+240\,a^2\,b^4\,c^7\,d^5-96\,a\,b^5\,c^8\,d^4+16\,b^6\,c^9\,d^3\right)}\right)\,{\left(a\,d-b\,c\right)}^2\,1{}\mathrm{i}}{{\left(-c\right)}^{5/4}\,d^{7/4}}","Not used",1,"(2*b^2*x^(3/2))/(3*d) - (2*a^2)/(c*x^(1/2)) - (atan((x^(1/2)*(a*d - b*c)^2*(16*a^4*c^4*d^9 + 16*b^4*c^8*d^5 - 64*a*b^3*c^7*d^6 - 64*a^3*b*c^5*d^8 + 96*a^2*b^2*c^6*d^7))/((-c)^(5/4)*d^(7/4)*(16*a^6*c^3*d^9 + 16*b^6*c^9*d^3 - 96*a*b^5*c^8*d^4 - 96*a^5*b*c^4*d^8 + 240*a^2*b^4*c^7*d^5 - 320*a^3*b^3*c^6*d^6 + 240*a^4*b^2*c^5*d^7)))*(a*d - b*c)^2)/((-c)^(5/4)*d^(7/4)) - (atan((x^(1/2)*(a*d - b*c)^2*(16*a^4*c^4*d^9 + 16*b^4*c^8*d^5 - 64*a*b^3*c^7*d^6 - 64*a^3*b*c^5*d^8 + 96*a^2*b^2*c^6*d^7)*1i)/((-c)^(5/4)*d^(7/4)*(16*a^6*c^3*d^9 + 16*b^6*c^9*d^3 - 96*a*b^5*c^8*d^4 - 96*a^5*b*c^4*d^8 + 240*a^2*b^4*c^7*d^5 - 320*a^3*b^3*c^6*d^6 + 240*a^4*b^2*c^5*d^7)))*(a*d - b*c)^2*1i)/((-c)^(5/4)*d^(7/4))","B"
421,1,1201,260,0.380634,"\text{Not used}","int((a + b*x^2)^2/(x^(5/2)*(c + d*x^2)),x)","\frac{2\,b^2\,\sqrt{x}}{d}-\frac{2\,a^2}{3\,c\,x^{3/2}}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\sqrt{x}\,\left(16\,a^4\,c^3\,d^{10}-64\,a^3\,b\,c^4\,d^9+96\,a^2\,b^2\,c^5\,d^8-64\,a\,b^3\,c^6\,d^7+16\,b^4\,c^7\,d^6\right)}{2}-\frac{{\left(a\,d-b\,c\right)}^2\,\left(16\,a^2\,c^5\,d^9-32\,a\,b\,c^6\,d^8+16\,b^2\,c^7\,d^7\right)}{2\,{\left(-c\right)}^{7/4}\,d^{5/4}}\right)\,{\left(a\,d-b\,c\right)}^2\,1{}\mathrm{i}}{{\left(-c\right)}^{7/4}\,d^{5/4}}+\frac{\left(\frac{\sqrt{x}\,\left(16\,a^4\,c^3\,d^{10}-64\,a^3\,b\,c^4\,d^9+96\,a^2\,b^2\,c^5\,d^8-64\,a\,b^3\,c^6\,d^7+16\,b^4\,c^7\,d^6\right)}{2}+\frac{{\left(a\,d-b\,c\right)}^2\,\left(16\,a^2\,c^5\,d^9-32\,a\,b\,c^6\,d^8+16\,b^2\,c^7\,d^7\right)}{2\,{\left(-c\right)}^{7/4}\,d^{5/4}}\right)\,{\left(a\,d-b\,c\right)}^2\,1{}\mathrm{i}}{{\left(-c\right)}^{7/4}\,d^{5/4}}}{\frac{\left(\frac{\sqrt{x}\,\left(16\,a^4\,c^3\,d^{10}-64\,a^3\,b\,c^4\,d^9+96\,a^2\,b^2\,c^5\,d^8-64\,a\,b^3\,c^6\,d^7+16\,b^4\,c^7\,d^6\right)}{2}-\frac{{\left(a\,d-b\,c\right)}^2\,\left(16\,a^2\,c^5\,d^9-32\,a\,b\,c^6\,d^8+16\,b^2\,c^7\,d^7\right)}{2\,{\left(-c\right)}^{7/4}\,d^{5/4}}\right)\,{\left(a\,d-b\,c\right)}^2}{{\left(-c\right)}^{7/4}\,d^{5/4}}-\frac{\left(\frac{\sqrt{x}\,\left(16\,a^4\,c^3\,d^{10}-64\,a^3\,b\,c^4\,d^9+96\,a^2\,b^2\,c^5\,d^8-64\,a\,b^3\,c^6\,d^7+16\,b^4\,c^7\,d^6\right)}{2}+\frac{{\left(a\,d-b\,c\right)}^2\,\left(16\,a^2\,c^5\,d^9-32\,a\,b\,c^6\,d^8+16\,b^2\,c^7\,d^7\right)}{2\,{\left(-c\right)}^{7/4}\,d^{5/4}}\right)\,{\left(a\,d-b\,c\right)}^2}{{\left(-c\right)}^{7/4}\,d^{5/4}}}\right)\,{\left(a\,d-b\,c\right)}^2\,1{}\mathrm{i}}{{\left(-c\right)}^{7/4}\,d^{5/4}}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\sqrt{x}\,\left(16\,a^4\,c^3\,d^{10}-64\,a^3\,b\,c^4\,d^9+96\,a^2\,b^2\,c^5\,d^8-64\,a\,b^3\,c^6\,d^7+16\,b^4\,c^7\,d^6\right)}{2}-\frac{{\left(a\,d-b\,c\right)}^2\,\left(16\,a^2\,c^5\,d^9-32\,a\,b\,c^6\,d^8+16\,b^2\,c^7\,d^7\right)\,1{}\mathrm{i}}{2\,{\left(-c\right)}^{7/4}\,d^{5/4}}\right)\,{\left(a\,d-b\,c\right)}^2}{{\left(-c\right)}^{7/4}\,d^{5/4}}+\frac{\left(\frac{\sqrt{x}\,\left(16\,a^4\,c^3\,d^{10}-64\,a^3\,b\,c^4\,d^9+96\,a^2\,b^2\,c^5\,d^8-64\,a\,b^3\,c^6\,d^7+16\,b^4\,c^7\,d^6\right)}{2}+\frac{{\left(a\,d-b\,c\right)}^2\,\left(16\,a^2\,c^5\,d^9-32\,a\,b\,c^6\,d^8+16\,b^2\,c^7\,d^7\right)\,1{}\mathrm{i}}{2\,{\left(-c\right)}^{7/4}\,d^{5/4}}\right)\,{\left(a\,d-b\,c\right)}^2}{{\left(-c\right)}^{7/4}\,d^{5/4}}}{\frac{\left(\frac{\sqrt{x}\,\left(16\,a^4\,c^3\,d^{10}-64\,a^3\,b\,c^4\,d^9+96\,a^2\,b^2\,c^5\,d^8-64\,a\,b^3\,c^6\,d^7+16\,b^4\,c^7\,d^6\right)}{2}-\frac{{\left(a\,d-b\,c\right)}^2\,\left(16\,a^2\,c^5\,d^9-32\,a\,b\,c^6\,d^8+16\,b^2\,c^7\,d^7\right)\,1{}\mathrm{i}}{2\,{\left(-c\right)}^{7/4}\,d^{5/4}}\right)\,{\left(a\,d-b\,c\right)}^2\,1{}\mathrm{i}}{{\left(-c\right)}^{7/4}\,d^{5/4}}-\frac{\left(\frac{\sqrt{x}\,\left(16\,a^4\,c^3\,d^{10}-64\,a^3\,b\,c^4\,d^9+96\,a^2\,b^2\,c^5\,d^8-64\,a\,b^3\,c^6\,d^7+16\,b^4\,c^7\,d^6\right)}{2}+\frac{{\left(a\,d-b\,c\right)}^2\,\left(16\,a^2\,c^5\,d^9-32\,a\,b\,c^6\,d^8+16\,b^2\,c^7\,d^7\right)\,1{}\mathrm{i}}{2\,{\left(-c\right)}^{7/4}\,d^{5/4}}\right)\,{\left(a\,d-b\,c\right)}^2\,1{}\mathrm{i}}{{\left(-c\right)}^{7/4}\,d^{5/4}}}\right)\,{\left(a\,d-b\,c\right)}^2}{{\left(-c\right)}^{7/4}\,d^{5/4}}","Not used",1,"(2*b^2*x^(1/2))/d - (2*a^2)/(3*c*x^(3/2)) - (atan(((((x^(1/2)*(16*a^4*c^3*d^10 + 16*b^4*c^7*d^6 - 64*a*b^3*c^6*d^7 - 64*a^3*b*c^4*d^9 + 96*a^2*b^2*c^5*d^8))/2 - ((a*d - b*c)^2*(16*a^2*c^5*d^9 + 16*b^2*c^7*d^7 - 32*a*b*c^6*d^8))/(2*(-c)^(7/4)*d^(5/4)))*(a*d - b*c)^2*1i)/((-c)^(7/4)*d^(5/4)) + (((x^(1/2)*(16*a^4*c^3*d^10 + 16*b^4*c^7*d^6 - 64*a*b^3*c^6*d^7 - 64*a^3*b*c^4*d^9 + 96*a^2*b^2*c^5*d^8))/2 + ((a*d - b*c)^2*(16*a^2*c^5*d^9 + 16*b^2*c^7*d^7 - 32*a*b*c^6*d^8))/(2*(-c)^(7/4)*d^(5/4)))*(a*d - b*c)^2*1i)/((-c)^(7/4)*d^(5/4)))/((((x^(1/2)*(16*a^4*c^3*d^10 + 16*b^4*c^7*d^6 - 64*a*b^3*c^6*d^7 - 64*a^3*b*c^4*d^9 + 96*a^2*b^2*c^5*d^8))/2 - ((a*d - b*c)^2*(16*a^2*c^5*d^9 + 16*b^2*c^7*d^7 - 32*a*b*c^6*d^8))/(2*(-c)^(7/4)*d^(5/4)))*(a*d - b*c)^2)/((-c)^(7/4)*d^(5/4)) - (((x^(1/2)*(16*a^4*c^3*d^10 + 16*b^4*c^7*d^6 - 64*a*b^3*c^6*d^7 - 64*a^3*b*c^4*d^9 + 96*a^2*b^2*c^5*d^8))/2 + ((a*d - b*c)^2*(16*a^2*c^5*d^9 + 16*b^2*c^7*d^7 - 32*a*b*c^6*d^8))/(2*(-c)^(7/4)*d^(5/4)))*(a*d - b*c)^2)/((-c)^(7/4)*d^(5/4))))*(a*d - b*c)^2*1i)/((-c)^(7/4)*d^(5/4)) - (atan(((((x^(1/2)*(16*a^4*c^3*d^10 + 16*b^4*c^7*d^6 - 64*a*b^3*c^6*d^7 - 64*a^3*b*c^4*d^9 + 96*a^2*b^2*c^5*d^8))/2 - ((a*d - b*c)^2*(16*a^2*c^5*d^9 + 16*b^2*c^7*d^7 - 32*a*b*c^6*d^8)*1i)/(2*(-c)^(7/4)*d^(5/4)))*(a*d - b*c)^2)/((-c)^(7/4)*d^(5/4)) + (((x^(1/2)*(16*a^4*c^3*d^10 + 16*b^4*c^7*d^6 - 64*a*b^3*c^6*d^7 - 64*a^3*b*c^4*d^9 + 96*a^2*b^2*c^5*d^8))/2 + ((a*d - b*c)^2*(16*a^2*c^5*d^9 + 16*b^2*c^7*d^7 - 32*a*b*c^6*d^8)*1i)/(2*(-c)^(7/4)*d^(5/4)))*(a*d - b*c)^2)/((-c)^(7/4)*d^(5/4)))/((((x^(1/2)*(16*a^4*c^3*d^10 + 16*b^4*c^7*d^6 - 64*a*b^3*c^6*d^7 - 64*a^3*b*c^4*d^9 + 96*a^2*b^2*c^5*d^8))/2 - ((a*d - b*c)^2*(16*a^2*c^5*d^9 + 16*b^2*c^7*d^7 - 32*a*b*c^6*d^8)*1i)/(2*(-c)^(7/4)*d^(5/4)))*(a*d - b*c)^2*1i)/((-c)^(7/4)*d^(5/4)) - (((x^(1/2)*(16*a^4*c^3*d^10 + 16*b^4*c^7*d^6 - 64*a*b^3*c^6*d^7 - 64*a^3*b*c^4*d^9 + 96*a^2*b^2*c^5*d^8))/2 + ((a*d - b*c)^2*(16*a^2*c^5*d^9 + 16*b^2*c^7*d^7 - 32*a*b*c^6*d^8)*1i)/(2*(-c)^(7/4)*d^(5/4)))*(a*d - b*c)^2*1i)/((-c)^(7/4)*d^(5/4))))*(a*d - b*c)^2)/((-c)^(7/4)*d^(5/4))","B"
422,1,417,267,0.335222,"\text{Not used}","int((a + b*x^2)^2/(x^(7/2)*(c + d*x^2)),x)","\frac{\mathrm{atan}\left(\frac{\sqrt{x}\,{\left(a\,d-b\,c\right)}^2\,\left(16\,a^4\,c^7\,d^6-64\,a^3\,b\,c^8\,d^5+96\,a^2\,b^2\,c^9\,d^4-64\,a\,b^3\,c^{10}\,d^3+16\,b^4\,c^{11}\,d^2\right)}{{\left(-c\right)}^{9/4}\,d^{3/4}\,\left(16\,a^6\,c^5\,d^7-96\,a^5\,b\,c^6\,d^6+240\,a^4\,b^2\,c^7\,d^5-320\,a^3\,b^3\,c^8\,d^4+240\,a^2\,b^4\,c^9\,d^3-96\,a\,b^5\,c^{10}\,d^2+16\,b^6\,c^{11}\,d\right)}\right)\,{\left(a\,d-b\,c\right)}^2}{{\left(-c\right)}^{9/4}\,d^{3/4}}-\frac{\frac{2\,a^2}{5\,c}-\frac{2\,a\,x^2\,\left(a\,d-2\,b\,c\right)}{c^2}}{x^{5/2}}-\frac{\mathrm{atanh}\left(\frac{\sqrt{x}\,{\left(a\,d-b\,c\right)}^2\,\left(16\,a^4\,c^7\,d^6-64\,a^3\,b\,c^8\,d^5+96\,a^2\,b^2\,c^9\,d^4-64\,a\,b^3\,c^{10}\,d^3+16\,b^4\,c^{11}\,d^2\right)}{{\left(-c\right)}^{9/4}\,d^{3/4}\,\left(16\,a^6\,c^5\,d^7-96\,a^5\,b\,c^6\,d^6+240\,a^4\,b^2\,c^7\,d^5-320\,a^3\,b^3\,c^8\,d^4+240\,a^2\,b^4\,c^9\,d^3-96\,a\,b^5\,c^{10}\,d^2+16\,b^6\,c^{11}\,d\right)}\right)\,{\left(a\,d-b\,c\right)}^2}{{\left(-c\right)}^{9/4}\,d^{3/4}}","Not used",1,"(atan((x^(1/2)*(a*d - b*c)^2*(16*a^4*c^7*d^6 + 16*b^4*c^11*d^2 - 64*a*b^3*c^10*d^3 - 64*a^3*b*c^8*d^5 + 96*a^2*b^2*c^9*d^4))/((-c)^(9/4)*d^(3/4)*(16*b^6*c^11*d + 16*a^6*c^5*d^7 - 96*a*b^5*c^10*d^2 - 96*a^5*b*c^6*d^6 + 240*a^2*b^4*c^9*d^3 - 320*a^3*b^3*c^8*d^4 + 240*a^4*b^2*c^7*d^5)))*(a*d - b*c)^2)/((-c)^(9/4)*d^(3/4)) - ((2*a^2)/(5*c) - (2*a*x^2*(a*d - 2*b*c))/c^2)/x^(5/2) - (atanh((x^(1/2)*(a*d - b*c)^2*(16*a^4*c^7*d^6 + 16*b^4*c^11*d^2 - 64*a*b^3*c^10*d^3 - 64*a^3*b*c^8*d^5 + 96*a^2*b^2*c^9*d^4))/((-c)^(9/4)*d^(3/4)*(16*b^6*c^11*d + 16*a^6*c^5*d^7 - 96*a*b^5*c^10*d^2 - 96*a^5*b*c^6*d^6 + 240*a^2*b^4*c^9*d^3 - 320*a^3*b^3*c^8*d^4 + 240*a^4*b^2*c^7*d^5)))*(a*d - b*c)^2)/((-c)^(9/4)*d^(3/4))","B"
423,1,1209,269,0.440947,"\text{Not used}","int((a + b*x^2)^2/(x^(9/2)*(c + d*x^2)),x)","-\frac{\frac{2\,a^2}{7\,c}-\frac{2\,a\,x^2\,\left(a\,d-2\,b\,c\right)}{3\,c^2}}{x^{7/2}}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\sqrt{x}\,\left(16\,a^4\,c^6\,d^7-64\,a^3\,b\,c^7\,d^6+96\,a^2\,b^2\,c^8\,d^5-64\,a\,b^3\,c^9\,d^4+16\,b^4\,c^{10}\,d^3\right)}{2}-\frac{{\left(a\,d-b\,c\right)}^2\,\left(16\,a^2\,c^9\,d^5-32\,a\,b\,c^{10}\,d^4+16\,b^2\,c^{11}\,d^3\right)}{2\,{\left(-c\right)}^{11/4}\,d^{1/4}}\right)\,{\left(a\,d-b\,c\right)}^2\,1{}\mathrm{i}}{{\left(-c\right)}^{11/4}\,d^{1/4}}+\frac{\left(\frac{\sqrt{x}\,\left(16\,a^4\,c^6\,d^7-64\,a^3\,b\,c^7\,d^6+96\,a^2\,b^2\,c^8\,d^5-64\,a\,b^3\,c^9\,d^4+16\,b^4\,c^{10}\,d^3\right)}{2}+\frac{{\left(a\,d-b\,c\right)}^2\,\left(16\,a^2\,c^9\,d^5-32\,a\,b\,c^{10}\,d^4+16\,b^2\,c^{11}\,d^3\right)}{2\,{\left(-c\right)}^{11/4}\,d^{1/4}}\right)\,{\left(a\,d-b\,c\right)}^2\,1{}\mathrm{i}}{{\left(-c\right)}^{11/4}\,d^{1/4}}}{\frac{\left(\frac{\sqrt{x}\,\left(16\,a^4\,c^6\,d^7-64\,a^3\,b\,c^7\,d^6+96\,a^2\,b^2\,c^8\,d^5-64\,a\,b^3\,c^9\,d^4+16\,b^4\,c^{10}\,d^3\right)}{2}-\frac{{\left(a\,d-b\,c\right)}^2\,\left(16\,a^2\,c^9\,d^5-32\,a\,b\,c^{10}\,d^4+16\,b^2\,c^{11}\,d^3\right)}{2\,{\left(-c\right)}^{11/4}\,d^{1/4}}\right)\,{\left(a\,d-b\,c\right)}^2}{{\left(-c\right)}^{11/4}\,d^{1/4}}-\frac{\left(\frac{\sqrt{x}\,\left(16\,a^4\,c^6\,d^7-64\,a^3\,b\,c^7\,d^6+96\,a^2\,b^2\,c^8\,d^5-64\,a\,b^3\,c^9\,d^4+16\,b^4\,c^{10}\,d^3\right)}{2}+\frac{{\left(a\,d-b\,c\right)}^2\,\left(16\,a^2\,c^9\,d^5-32\,a\,b\,c^{10}\,d^4+16\,b^2\,c^{11}\,d^3\right)}{2\,{\left(-c\right)}^{11/4}\,d^{1/4}}\right)\,{\left(a\,d-b\,c\right)}^2}{{\left(-c\right)}^{11/4}\,d^{1/4}}}\right)\,{\left(a\,d-b\,c\right)}^2\,1{}\mathrm{i}}{{\left(-c\right)}^{11/4}\,d^{1/4}}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\sqrt{x}\,\left(16\,a^4\,c^6\,d^7-64\,a^3\,b\,c^7\,d^6+96\,a^2\,b^2\,c^8\,d^5-64\,a\,b^3\,c^9\,d^4+16\,b^4\,c^{10}\,d^3\right)}{2}-\frac{{\left(a\,d-b\,c\right)}^2\,\left(16\,a^2\,c^9\,d^5-32\,a\,b\,c^{10}\,d^4+16\,b^2\,c^{11}\,d^3\right)\,1{}\mathrm{i}}{2\,{\left(-c\right)}^{11/4}\,d^{1/4}}\right)\,{\left(a\,d-b\,c\right)}^2}{{\left(-c\right)}^{11/4}\,d^{1/4}}+\frac{\left(\frac{\sqrt{x}\,\left(16\,a^4\,c^6\,d^7-64\,a^3\,b\,c^7\,d^6+96\,a^2\,b^2\,c^8\,d^5-64\,a\,b^3\,c^9\,d^4+16\,b^4\,c^{10}\,d^3\right)}{2}+\frac{{\left(a\,d-b\,c\right)}^2\,\left(16\,a^2\,c^9\,d^5-32\,a\,b\,c^{10}\,d^4+16\,b^2\,c^{11}\,d^3\right)\,1{}\mathrm{i}}{2\,{\left(-c\right)}^{11/4}\,d^{1/4}}\right)\,{\left(a\,d-b\,c\right)}^2}{{\left(-c\right)}^{11/4}\,d^{1/4}}}{\frac{\left(\frac{\sqrt{x}\,\left(16\,a^4\,c^6\,d^7-64\,a^3\,b\,c^7\,d^6+96\,a^2\,b^2\,c^8\,d^5-64\,a\,b^3\,c^9\,d^4+16\,b^4\,c^{10}\,d^3\right)}{2}-\frac{{\left(a\,d-b\,c\right)}^2\,\left(16\,a^2\,c^9\,d^5-32\,a\,b\,c^{10}\,d^4+16\,b^2\,c^{11}\,d^3\right)\,1{}\mathrm{i}}{2\,{\left(-c\right)}^{11/4}\,d^{1/4}}\right)\,{\left(a\,d-b\,c\right)}^2\,1{}\mathrm{i}}{{\left(-c\right)}^{11/4}\,d^{1/4}}-\frac{\left(\frac{\sqrt{x}\,\left(16\,a^4\,c^6\,d^7-64\,a^3\,b\,c^7\,d^6+96\,a^2\,b^2\,c^8\,d^5-64\,a\,b^3\,c^9\,d^4+16\,b^4\,c^{10}\,d^3\right)}{2}+\frac{{\left(a\,d-b\,c\right)}^2\,\left(16\,a^2\,c^9\,d^5-32\,a\,b\,c^{10}\,d^4+16\,b^2\,c^{11}\,d^3\right)\,1{}\mathrm{i}}{2\,{\left(-c\right)}^{11/4}\,d^{1/4}}\right)\,{\left(a\,d-b\,c\right)}^2\,1{}\mathrm{i}}{{\left(-c\right)}^{11/4}\,d^{1/4}}}\right)\,{\left(a\,d-b\,c\right)}^2}{{\left(-c\right)}^{11/4}\,d^{1/4}}","Not used",1,"(atan(((((x^(1/2)*(16*a^4*c^6*d^7 + 16*b^4*c^10*d^3 - 64*a*b^3*c^9*d^4 - 64*a^3*b*c^7*d^6 + 96*a^2*b^2*c^8*d^5))/2 - ((a*d - b*c)^2*(16*a^2*c^9*d^5 + 16*b^2*c^11*d^3 - 32*a*b*c^10*d^4))/(2*(-c)^(11/4)*d^(1/4)))*(a*d - b*c)^2*1i)/((-c)^(11/4)*d^(1/4)) + (((x^(1/2)*(16*a^4*c^6*d^7 + 16*b^4*c^10*d^3 - 64*a*b^3*c^9*d^4 - 64*a^3*b*c^7*d^6 + 96*a^2*b^2*c^8*d^5))/2 + ((a*d - b*c)^2*(16*a^2*c^9*d^5 + 16*b^2*c^11*d^3 - 32*a*b*c^10*d^4))/(2*(-c)^(11/4)*d^(1/4)))*(a*d - b*c)^2*1i)/((-c)^(11/4)*d^(1/4)))/((((x^(1/2)*(16*a^4*c^6*d^7 + 16*b^4*c^10*d^3 - 64*a*b^3*c^9*d^4 - 64*a^3*b*c^7*d^6 + 96*a^2*b^2*c^8*d^5))/2 - ((a*d - b*c)^2*(16*a^2*c^9*d^5 + 16*b^2*c^11*d^3 - 32*a*b*c^10*d^4))/(2*(-c)^(11/4)*d^(1/4)))*(a*d - b*c)^2)/((-c)^(11/4)*d^(1/4)) - (((x^(1/2)*(16*a^4*c^6*d^7 + 16*b^4*c^10*d^3 - 64*a*b^3*c^9*d^4 - 64*a^3*b*c^7*d^6 + 96*a^2*b^2*c^8*d^5))/2 + ((a*d - b*c)^2*(16*a^2*c^9*d^5 + 16*b^2*c^11*d^3 - 32*a*b*c^10*d^4))/(2*(-c)^(11/4)*d^(1/4)))*(a*d - b*c)^2)/((-c)^(11/4)*d^(1/4))))*(a*d - b*c)^2*1i)/((-c)^(11/4)*d^(1/4)) - ((2*a^2)/(7*c) - (2*a*x^2*(a*d - 2*b*c))/(3*c^2))/x^(7/2) + (atan(((((x^(1/2)*(16*a^4*c^6*d^7 + 16*b^4*c^10*d^3 - 64*a*b^3*c^9*d^4 - 64*a^3*b*c^7*d^6 + 96*a^2*b^2*c^8*d^5))/2 - ((a*d - b*c)^2*(16*a^2*c^9*d^5 + 16*b^2*c^11*d^3 - 32*a*b*c^10*d^4)*1i)/(2*(-c)^(11/4)*d^(1/4)))*(a*d - b*c)^2)/((-c)^(11/4)*d^(1/4)) + (((x^(1/2)*(16*a^4*c^6*d^7 + 16*b^4*c^10*d^3 - 64*a*b^3*c^9*d^4 - 64*a^3*b*c^7*d^6 + 96*a^2*b^2*c^8*d^5))/2 + ((a*d - b*c)^2*(16*a^2*c^9*d^5 + 16*b^2*c^11*d^3 - 32*a*b*c^10*d^4)*1i)/(2*(-c)^(11/4)*d^(1/4)))*(a*d - b*c)^2)/((-c)^(11/4)*d^(1/4)))/((((x^(1/2)*(16*a^4*c^6*d^7 + 16*b^4*c^10*d^3 - 64*a*b^3*c^9*d^4 - 64*a^3*b*c^7*d^6 + 96*a^2*b^2*c^8*d^5))/2 - ((a*d - b*c)^2*(16*a^2*c^9*d^5 + 16*b^2*c^11*d^3 - 32*a*b*c^10*d^4)*1i)/(2*(-c)^(11/4)*d^(1/4)))*(a*d - b*c)^2*1i)/((-c)^(11/4)*d^(1/4)) - (((x^(1/2)*(16*a^4*c^6*d^7 + 16*b^4*c^10*d^3 - 64*a*b^3*c^9*d^4 - 64*a^3*b*c^7*d^6 + 96*a^2*b^2*c^8*d^5))/2 + ((a*d - b*c)^2*(16*a^2*c^9*d^5 + 16*b^2*c^11*d^3 - 32*a*b*c^10*d^4)*1i)/(2*(-c)^(11/4)*d^(1/4)))*(a*d - b*c)^2*1i)/((-c)^(11/4)*d^(1/4))))*(a*d - b*c)^2)/((-c)^(11/4)*d^(1/4))","B"
424,1,451,288,0.350809,"\text{Not used}","int((c + d*x^2)^2/(x^(11/2)*(a + b*x^2)),x)","\frac{{\left(-b\right)}^{1/4}\,\mathrm{atanh}\left(\frac{{\left(-b\right)}^{1/4}\,\sqrt{x}\,{\left(a\,d-b\,c\right)}^2\,\left(16\,a^{14}\,b^4\,d^4-64\,a^{13}\,b^5\,c\,d^3+96\,a^{12}\,b^6\,c^2\,d^2-64\,a^{11}\,b^7\,c^3\,d+16\,a^{10}\,b^8\,c^4\right)}{a^{13/4}\,\left(16\,a^{13}\,b^4\,d^6-96\,a^{12}\,b^5\,c\,d^5+240\,a^{11}\,b^6\,c^2\,d^4-320\,a^{10}\,b^7\,c^3\,d^3+240\,a^9\,b^8\,c^4\,d^2-96\,a^8\,b^9\,c^5\,d+16\,a^7\,b^{10}\,c^6\right)}\right)\,{\left(a\,d-b\,c\right)}^2}{a^{13/4}}-\frac{{\left(-b\right)}^{1/4}\,\mathrm{atan}\left(\frac{{\left(-b\right)}^{1/4}\,\sqrt{x}\,{\left(a\,d-b\,c\right)}^2\,\left(16\,a^{14}\,b^4\,d^4-64\,a^{13}\,b^5\,c\,d^3+96\,a^{12}\,b^6\,c^2\,d^2-64\,a^{11}\,b^7\,c^3\,d+16\,a^{10}\,b^8\,c^4\right)}{a^{13/4}\,\left(16\,a^{13}\,b^4\,d^6-96\,a^{12}\,b^5\,c\,d^5+240\,a^{11}\,b^6\,c^2\,d^4-320\,a^{10}\,b^7\,c^3\,d^3+240\,a^9\,b^8\,c^4\,d^2-96\,a^8\,b^9\,c^5\,d+16\,a^7\,b^{10}\,c^6\right)}\right)\,{\left(a\,d-b\,c\right)}^2}{a^{13/4}}-\frac{\frac{2\,c^2}{9\,a}+\frac{2\,x^4\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}{a^3}+\frac{2\,c\,x^2\,\left(2\,a\,d-b\,c\right)}{5\,a^2}}{x^{9/2}}","Not used",1,"((-b)^(1/4)*atanh(((-b)^(1/4)*x^(1/2)*(a*d - b*c)^2*(16*a^10*b^8*c^4 + 16*a^14*b^4*d^4 - 64*a^11*b^7*c^3*d - 64*a^13*b^5*c*d^3 + 96*a^12*b^6*c^2*d^2))/(a^(13/4)*(16*a^7*b^10*c^6 + 16*a^13*b^4*d^6 - 96*a^8*b^9*c^5*d - 96*a^12*b^5*c*d^5 + 240*a^9*b^8*c^4*d^2 - 320*a^10*b^7*c^3*d^3 + 240*a^11*b^6*c^2*d^4)))*(a*d - b*c)^2)/a^(13/4) - ((-b)^(1/4)*atan(((-b)^(1/4)*x^(1/2)*(a*d - b*c)^2*(16*a^10*b^8*c^4 + 16*a^14*b^4*d^4 - 64*a^11*b^7*c^3*d - 64*a^13*b^5*c*d^3 + 96*a^12*b^6*c^2*d^2))/(a^(13/4)*(16*a^7*b^10*c^6 + 16*a^13*b^4*d^6 - 96*a^8*b^9*c^5*d - 96*a^12*b^5*c*d^5 + 240*a^9*b^8*c^4*d^2 - 320*a^10*b^7*c^3*d^3 + 240*a^11*b^6*c^2*d^4)))*(a*d - b*c)^2)/a^(13/4) - ((2*c^2)/(9*a) + (2*x^4*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/a^3 + (2*c*x^2*(2*a*d - b*c))/(5*a^2))/x^(9/2)","B"
425,1,1367,375,0.444066,"\text{Not used}","int((x^(7/2)*(a + b*x^2)^2)/(c + d*x^2)^2,x)","\sqrt{x}\,\left(\frac{2\,a^2}{d^2}+\frac{2\,c\,\left(\frac{4\,b^2\,c}{d^3}-\frac{4\,a\,b}{d^2}\right)}{d}-\frac{2\,b^2\,c^2}{d^4}\right)-x^{5/2}\,\left(\frac{4\,b^2\,c}{5\,d^3}-\frac{4\,a\,b}{5\,d^2}\right)+\frac{\sqrt{x}\,\left(\frac{a^2\,c\,d^2}{2}-a\,b\,c^2\,d+\frac{b^2\,c^3}{2}\right)}{d^5\,x^2+c\,d^4}+\frac{2\,b^2\,x^{9/2}}{9\,d^2}+\frac{{\left(-c\right)}^{1/4}\,\mathrm{atan}\left(\frac{\frac{{\left(-c\right)}^{1/4}\,\left(\frac{\sqrt{x}\,\left(25\,a^4\,c^2\,d^4-180\,a^3\,b\,c^3\,d^3+454\,a^2\,b^2\,c^4\,d^2-468\,a\,b^3\,c^5\,d+169\,b^4\,c^6\right)}{d^5}+\frac{{\left(-c\right)}^{1/4}\,\left(a\,d-b\,c\right)\,\left(5\,a\,d-13\,b\,c\right)\,\left(5\,a^2\,c^2\,d^2-18\,a\,b\,c^3\,d+13\,b^2\,c^4\right)}{d^{21/4}}\right)\,\left(a\,d-b\,c\right)\,\left(5\,a\,d-13\,b\,c\right)\,1{}\mathrm{i}}{8\,d^{17/4}}+\frac{{\left(-c\right)}^{1/4}\,\left(\frac{\sqrt{x}\,\left(25\,a^4\,c^2\,d^4-180\,a^3\,b\,c^3\,d^3+454\,a^2\,b^2\,c^4\,d^2-468\,a\,b^3\,c^5\,d+169\,b^4\,c^6\right)}{d^5}-\frac{{\left(-c\right)}^{1/4}\,\left(a\,d-b\,c\right)\,\left(5\,a\,d-13\,b\,c\right)\,\left(5\,a^2\,c^2\,d^2-18\,a\,b\,c^3\,d+13\,b^2\,c^4\right)}{d^{21/4}}\right)\,\left(a\,d-b\,c\right)\,\left(5\,a\,d-13\,b\,c\right)\,1{}\mathrm{i}}{8\,d^{17/4}}}{\frac{{\left(-c\right)}^{1/4}\,\left(\frac{\sqrt{x}\,\left(25\,a^4\,c^2\,d^4-180\,a^3\,b\,c^3\,d^3+454\,a^2\,b^2\,c^4\,d^2-468\,a\,b^3\,c^5\,d+169\,b^4\,c^6\right)}{d^5}+\frac{{\left(-c\right)}^{1/4}\,\left(a\,d-b\,c\right)\,\left(5\,a\,d-13\,b\,c\right)\,\left(5\,a^2\,c^2\,d^2-18\,a\,b\,c^3\,d+13\,b^2\,c^4\right)}{d^{21/4}}\right)\,\left(a\,d-b\,c\right)\,\left(5\,a\,d-13\,b\,c\right)}{8\,d^{17/4}}-\frac{{\left(-c\right)}^{1/4}\,\left(\frac{\sqrt{x}\,\left(25\,a^4\,c^2\,d^4-180\,a^3\,b\,c^3\,d^3+454\,a^2\,b^2\,c^4\,d^2-468\,a\,b^3\,c^5\,d+169\,b^4\,c^6\right)}{d^5}-\frac{{\left(-c\right)}^{1/4}\,\left(a\,d-b\,c\right)\,\left(5\,a\,d-13\,b\,c\right)\,\left(5\,a^2\,c^2\,d^2-18\,a\,b\,c^3\,d+13\,b^2\,c^4\right)}{d^{21/4}}\right)\,\left(a\,d-b\,c\right)\,\left(5\,a\,d-13\,b\,c\right)}{8\,d^{17/4}}}\right)\,\left(a\,d-b\,c\right)\,\left(5\,a\,d-13\,b\,c\right)\,1{}\mathrm{i}}{4\,d^{17/4}}-\frac{{\left(-c\right)}^{1/4}\,\mathrm{atan}\left(\frac{\frac{{\left(-c\right)}^{1/4}\,\left(\frac{\sqrt{x}\,\left(25\,a^4\,c^2\,d^4-180\,a^3\,b\,c^3\,d^3+454\,a^2\,b^2\,c^4\,d^2-468\,a\,b^3\,c^5\,d+169\,b^4\,c^6\right)}{d^5}-\frac{{\left(-c\right)}^{1/4}\,\left(a\,d-b\,c\right)\,\left(5\,a\,d-13\,b\,c\right)\,\left(5\,a^2\,c^2\,d^2-18\,a\,b\,c^3\,d+13\,b^2\,c^4\right)\,1{}\mathrm{i}}{d^{21/4}}\right)\,\left(a\,d-b\,c\right)\,\left(5\,a\,d-13\,b\,c\right)}{8\,d^{17/4}}+\frac{{\left(-c\right)}^{1/4}\,\left(\frac{\sqrt{x}\,\left(25\,a^4\,c^2\,d^4-180\,a^3\,b\,c^3\,d^3+454\,a^2\,b^2\,c^4\,d^2-468\,a\,b^3\,c^5\,d+169\,b^4\,c^6\right)}{d^5}+\frac{{\left(-c\right)}^{1/4}\,\left(a\,d-b\,c\right)\,\left(5\,a\,d-13\,b\,c\right)\,\left(5\,a^2\,c^2\,d^2-18\,a\,b\,c^3\,d+13\,b^2\,c^4\right)\,1{}\mathrm{i}}{d^{21/4}}\right)\,\left(a\,d-b\,c\right)\,\left(5\,a\,d-13\,b\,c\right)}{8\,d^{17/4}}}{\frac{{\left(-c\right)}^{1/4}\,\left(\frac{\sqrt{x}\,\left(25\,a^4\,c^2\,d^4-180\,a^3\,b\,c^3\,d^3+454\,a^2\,b^2\,c^4\,d^2-468\,a\,b^3\,c^5\,d+169\,b^4\,c^6\right)}{d^5}-\frac{{\left(-c\right)}^{1/4}\,\left(a\,d-b\,c\right)\,\left(5\,a\,d-13\,b\,c\right)\,\left(5\,a^2\,c^2\,d^2-18\,a\,b\,c^3\,d+13\,b^2\,c^4\right)\,1{}\mathrm{i}}{d^{21/4}}\right)\,\left(a\,d-b\,c\right)\,\left(5\,a\,d-13\,b\,c\right)\,1{}\mathrm{i}}{8\,d^{17/4}}-\frac{{\left(-c\right)}^{1/4}\,\left(\frac{\sqrt{x}\,\left(25\,a^4\,c^2\,d^4-180\,a^3\,b\,c^3\,d^3+454\,a^2\,b^2\,c^4\,d^2-468\,a\,b^3\,c^5\,d+169\,b^4\,c^6\right)}{d^5}+\frac{{\left(-c\right)}^{1/4}\,\left(a\,d-b\,c\right)\,\left(5\,a\,d-13\,b\,c\right)\,\left(5\,a^2\,c^2\,d^2-18\,a\,b\,c^3\,d+13\,b^2\,c^4\right)\,1{}\mathrm{i}}{d^{21/4}}\right)\,\left(a\,d-b\,c\right)\,\left(5\,a\,d-13\,b\,c\right)\,1{}\mathrm{i}}{8\,d^{17/4}}}\right)\,\left(a\,d-b\,c\right)\,\left(5\,a\,d-13\,b\,c\right)}{4\,d^{17/4}}","Not used",1,"x^(1/2)*((2*a^2)/d^2 + (2*c*((4*b^2*c)/d^3 - (4*a*b)/d^2))/d - (2*b^2*c^2)/d^4) - x^(5/2)*((4*b^2*c)/(5*d^3) - (4*a*b)/(5*d^2)) + (x^(1/2)*((b^2*c^3)/2 + (a^2*c*d^2)/2 - a*b*c^2*d))/(c*d^4 + d^5*x^2) + (2*b^2*x^(9/2))/(9*d^2) + ((-c)^(1/4)*atan((((-c)^(1/4)*((x^(1/2)*(169*b^4*c^6 + 25*a^4*c^2*d^4 - 180*a^3*b*c^3*d^3 + 454*a^2*b^2*c^4*d^2 - 468*a*b^3*c^5*d))/d^5 + ((-c)^(1/4)*(a*d - b*c)*(5*a*d - 13*b*c)*(13*b^2*c^4 + 5*a^2*c^2*d^2 - 18*a*b*c^3*d))/d^(21/4))*(a*d - b*c)*(5*a*d - 13*b*c)*1i)/(8*d^(17/4)) + ((-c)^(1/4)*((x^(1/2)*(169*b^4*c^6 + 25*a^4*c^2*d^4 - 180*a^3*b*c^3*d^3 + 454*a^2*b^2*c^4*d^2 - 468*a*b^3*c^5*d))/d^5 - ((-c)^(1/4)*(a*d - b*c)*(5*a*d - 13*b*c)*(13*b^2*c^4 + 5*a^2*c^2*d^2 - 18*a*b*c^3*d))/d^(21/4))*(a*d - b*c)*(5*a*d - 13*b*c)*1i)/(8*d^(17/4)))/(((-c)^(1/4)*((x^(1/2)*(169*b^4*c^6 + 25*a^4*c^2*d^4 - 180*a^3*b*c^3*d^3 + 454*a^2*b^2*c^4*d^2 - 468*a*b^3*c^5*d))/d^5 + ((-c)^(1/4)*(a*d - b*c)*(5*a*d - 13*b*c)*(13*b^2*c^4 + 5*a^2*c^2*d^2 - 18*a*b*c^3*d))/d^(21/4))*(a*d - b*c)*(5*a*d - 13*b*c))/(8*d^(17/4)) - ((-c)^(1/4)*((x^(1/2)*(169*b^4*c^6 + 25*a^4*c^2*d^4 - 180*a^3*b*c^3*d^3 + 454*a^2*b^2*c^4*d^2 - 468*a*b^3*c^5*d))/d^5 - ((-c)^(1/4)*(a*d - b*c)*(5*a*d - 13*b*c)*(13*b^2*c^4 + 5*a^2*c^2*d^2 - 18*a*b*c^3*d))/d^(21/4))*(a*d - b*c)*(5*a*d - 13*b*c))/(8*d^(17/4))))*(a*d - b*c)*(5*a*d - 13*b*c)*1i)/(4*d^(17/4)) - ((-c)^(1/4)*atan((((-c)^(1/4)*((x^(1/2)*(169*b^4*c^6 + 25*a^4*c^2*d^4 - 180*a^3*b*c^3*d^3 + 454*a^2*b^2*c^4*d^2 - 468*a*b^3*c^5*d))/d^5 - ((-c)^(1/4)*(a*d - b*c)*(5*a*d - 13*b*c)*(13*b^2*c^4 + 5*a^2*c^2*d^2 - 18*a*b*c^3*d)*1i)/d^(21/4))*(a*d - b*c)*(5*a*d - 13*b*c))/(8*d^(17/4)) + ((-c)^(1/4)*((x^(1/2)*(169*b^4*c^6 + 25*a^4*c^2*d^4 - 180*a^3*b*c^3*d^3 + 454*a^2*b^2*c^4*d^2 - 468*a*b^3*c^5*d))/d^5 + ((-c)^(1/4)*(a*d - b*c)*(5*a*d - 13*b*c)*(13*b^2*c^4 + 5*a^2*c^2*d^2 - 18*a*b*c^3*d)*1i)/d^(21/4))*(a*d - b*c)*(5*a*d - 13*b*c))/(8*d^(17/4)))/(((-c)^(1/4)*((x^(1/2)*(169*b^4*c^6 + 25*a^4*c^2*d^4 - 180*a^3*b*c^3*d^3 + 454*a^2*b^2*c^4*d^2 - 468*a*b^3*c^5*d))/d^5 - ((-c)^(1/4)*(a*d - b*c)*(5*a*d - 13*b*c)*(13*b^2*c^4 + 5*a^2*c^2*d^2 - 18*a*b*c^3*d)*1i)/d^(21/4))*(a*d - b*c)*(5*a*d - 13*b*c)*1i)/(8*d^(17/4)) - ((-c)^(1/4)*((x^(1/2)*(169*b^4*c^6 + 25*a^4*c^2*d^4 - 180*a^3*b*c^3*d^3 + 454*a^2*b^2*c^4*d^2 - 468*a*b^3*c^5*d))/d^5 + ((-c)^(1/4)*(a*d - b*c)*(5*a*d - 13*b*c)*(13*b^2*c^4 + 5*a^2*c^2*d^2 - 18*a*b*c^3*d)*1i)/d^(21/4))*(a*d - b*c)*(5*a*d - 13*b*c)*1i)/(8*d^(17/4))))*(a*d - b*c)*(5*a*d - 13*b*c))/(4*d^(17/4))","B"
426,1,160,346,0.216416,"\text{Not used}","int((x^(5/2)*(a + b*x^2)^2)/(c + d*x^2)^2,x)","\frac{2\,b^2\,x^{7/2}}{7\,d^2}-\frac{x^{3/2}\,\left(\frac{a^2\,d^2}{2}-a\,b\,c\,d+\frac{b^2\,c^2}{2}\right)}{d^4\,x^2+c\,d^3}-x^{3/2}\,\left(\frac{4\,b^2\,c}{3\,d^3}-\frac{4\,a\,b}{3\,d^2}\right)+\frac{\mathrm{atan}\left(\frac{d^{1/4}\,\sqrt{x}}{{\left(-c\right)}^{1/4}}\right)\,\left(a\,d-b\,c\right)\,\left(3\,a\,d-11\,b\,c\right)}{4\,{\left(-c\right)}^{1/4}\,d^{15/4}}+\frac{\mathrm{atan}\left(\frac{d^{1/4}\,\sqrt{x}\,1{}\mathrm{i}}{{\left(-c\right)}^{1/4}}\right)\,\left(a\,d-b\,c\right)\,\left(3\,a\,d-11\,b\,c\right)\,1{}\mathrm{i}}{4\,{\left(-c\right)}^{1/4}\,d^{15/4}}","Not used",1,"(2*b^2*x^(7/2))/(7*d^2) - (x^(3/2)*((a^2*d^2)/2 + (b^2*c^2)/2 - a*b*c*d))/(c*d^3 + d^4*x^2) - x^(3/2)*((4*b^2*c)/(3*d^3) - (4*a*b)/(3*d^2)) + (atan((d^(1/4)*x^(1/2))/(-c)^(1/4))*(a*d - b*c)*(3*a*d - 11*b*c))/(4*(-c)^(1/4)*d^(15/4)) + (atan((d^(1/4)*x^(1/2)*1i)/(-c)^(1/4))*(a*d - b*c)*(3*a*d - 11*b*c)*1i)/(4*(-c)^(1/4)*d^(15/4))","B"
427,1,1238,346,0.263237,"\text{Not used}","int((x^(3/2)*(a + b*x^2)^2)/(c + d*x^2)^2,x)","\frac{2\,b^2\,x^{5/2}}{5\,d^2}-\frac{\sqrt{x}\,\left(\frac{a^2\,d^2}{2}-a\,b\,c\,d+\frac{b^2\,c^2}{2}\right)}{d^4\,x^2+c\,d^3}-\sqrt{x}\,\left(\frac{4\,b^2\,c}{d^3}-\frac{4\,a\,b}{d^2}\right)+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\sqrt{x}\,\left(a^4\,d^4-20\,a^3\,b\,c\,d^3+118\,a^2\,b^2\,c^2\,d^2-180\,a\,b^3\,c^3\,d+81\,b^4\,c^4\right)}{d^3}-\frac{\left(a\,d-b\,c\right)\,\left(a\,d-9\,b\,c\right)\,\left(8\,a^2\,c\,d^2-80\,a\,b\,c^2\,d+72\,b^2\,c^3\right)}{8\,{\left(-c\right)}^{3/4}\,d^{13/4}}\right)\,\left(a\,d-b\,c\right)\,\left(a\,d-9\,b\,c\right)\,1{}\mathrm{i}}{8\,{\left(-c\right)}^{3/4}\,d^{13/4}}+\frac{\left(\frac{\sqrt{x}\,\left(a^4\,d^4-20\,a^3\,b\,c\,d^3+118\,a^2\,b^2\,c^2\,d^2-180\,a\,b^3\,c^3\,d+81\,b^4\,c^4\right)}{d^3}+\frac{\left(a\,d-b\,c\right)\,\left(a\,d-9\,b\,c\right)\,\left(8\,a^2\,c\,d^2-80\,a\,b\,c^2\,d+72\,b^2\,c^3\right)}{8\,{\left(-c\right)}^{3/4}\,d^{13/4}}\right)\,\left(a\,d-b\,c\right)\,\left(a\,d-9\,b\,c\right)\,1{}\mathrm{i}}{8\,{\left(-c\right)}^{3/4}\,d^{13/4}}}{\frac{\left(\frac{\sqrt{x}\,\left(a^4\,d^4-20\,a^3\,b\,c\,d^3+118\,a^2\,b^2\,c^2\,d^2-180\,a\,b^3\,c^3\,d+81\,b^4\,c^4\right)}{d^3}-\frac{\left(a\,d-b\,c\right)\,\left(a\,d-9\,b\,c\right)\,\left(8\,a^2\,c\,d^2-80\,a\,b\,c^2\,d+72\,b^2\,c^3\right)}{8\,{\left(-c\right)}^{3/4}\,d^{13/4}}\right)\,\left(a\,d-b\,c\right)\,\left(a\,d-9\,b\,c\right)}{8\,{\left(-c\right)}^{3/4}\,d^{13/4}}-\frac{\left(\frac{\sqrt{x}\,\left(a^4\,d^4-20\,a^3\,b\,c\,d^3+118\,a^2\,b^2\,c^2\,d^2-180\,a\,b^3\,c^3\,d+81\,b^4\,c^4\right)}{d^3}+\frac{\left(a\,d-b\,c\right)\,\left(a\,d-9\,b\,c\right)\,\left(8\,a^2\,c\,d^2-80\,a\,b\,c^2\,d+72\,b^2\,c^3\right)}{8\,{\left(-c\right)}^{3/4}\,d^{13/4}}\right)\,\left(a\,d-b\,c\right)\,\left(a\,d-9\,b\,c\right)}{8\,{\left(-c\right)}^{3/4}\,d^{13/4}}}\right)\,\left(a\,d-b\,c\right)\,\left(a\,d-9\,b\,c\right)\,1{}\mathrm{i}}{4\,{\left(-c\right)}^{3/4}\,d^{13/4}}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\sqrt{x}\,\left(a^4\,d^4-20\,a^3\,b\,c\,d^3+118\,a^2\,b^2\,c^2\,d^2-180\,a\,b^3\,c^3\,d+81\,b^4\,c^4\right)}{d^3}-\frac{\left(a\,d-b\,c\right)\,\left(a\,d-9\,b\,c\right)\,\left(8\,a^2\,c\,d^2-80\,a\,b\,c^2\,d+72\,b^2\,c^3\right)\,1{}\mathrm{i}}{8\,{\left(-c\right)}^{3/4}\,d^{13/4}}\right)\,\left(a\,d-b\,c\right)\,\left(a\,d-9\,b\,c\right)}{8\,{\left(-c\right)}^{3/4}\,d^{13/4}}+\frac{\left(\frac{\sqrt{x}\,\left(a^4\,d^4-20\,a^3\,b\,c\,d^3+118\,a^2\,b^2\,c^2\,d^2-180\,a\,b^3\,c^3\,d+81\,b^4\,c^4\right)}{d^3}+\frac{\left(a\,d-b\,c\right)\,\left(a\,d-9\,b\,c\right)\,\left(8\,a^2\,c\,d^2-80\,a\,b\,c^2\,d+72\,b^2\,c^3\right)\,1{}\mathrm{i}}{8\,{\left(-c\right)}^{3/4}\,d^{13/4}}\right)\,\left(a\,d-b\,c\right)\,\left(a\,d-9\,b\,c\right)}{8\,{\left(-c\right)}^{3/4}\,d^{13/4}}}{\frac{\left(\frac{\sqrt{x}\,\left(a^4\,d^4-20\,a^3\,b\,c\,d^3+118\,a^2\,b^2\,c^2\,d^2-180\,a\,b^3\,c^3\,d+81\,b^4\,c^4\right)}{d^3}-\frac{\left(a\,d-b\,c\right)\,\left(a\,d-9\,b\,c\right)\,\left(8\,a^2\,c\,d^2-80\,a\,b\,c^2\,d+72\,b^2\,c^3\right)\,1{}\mathrm{i}}{8\,{\left(-c\right)}^{3/4}\,d^{13/4}}\right)\,\left(a\,d-b\,c\right)\,\left(a\,d-9\,b\,c\right)\,1{}\mathrm{i}}{8\,{\left(-c\right)}^{3/4}\,d^{13/4}}-\frac{\left(\frac{\sqrt{x}\,\left(a^4\,d^4-20\,a^3\,b\,c\,d^3+118\,a^2\,b^2\,c^2\,d^2-180\,a\,b^3\,c^3\,d+81\,b^4\,c^4\right)}{d^3}+\frac{\left(a\,d-b\,c\right)\,\left(a\,d-9\,b\,c\right)\,\left(8\,a^2\,c\,d^2-80\,a\,b\,c^2\,d+72\,b^2\,c^3\right)\,1{}\mathrm{i}}{8\,{\left(-c\right)}^{3/4}\,d^{13/4}}\right)\,\left(a\,d-b\,c\right)\,\left(a\,d-9\,b\,c\right)\,1{}\mathrm{i}}{8\,{\left(-c\right)}^{3/4}\,d^{13/4}}}\right)\,\left(a\,d-b\,c\right)\,\left(a\,d-9\,b\,c\right)}{4\,{\left(-c\right)}^{3/4}\,d^{13/4}}","Not used",1,"(2*b^2*x^(5/2))/(5*d^2) - (x^(1/2)*((a^2*d^2)/2 + (b^2*c^2)/2 - a*b*c*d))/(c*d^3 + d^4*x^2) - x^(1/2)*((4*b^2*c)/d^3 - (4*a*b)/d^2) + (atan(((((x^(1/2)*(a^4*d^4 + 81*b^4*c^4 + 118*a^2*b^2*c^2*d^2 - 180*a*b^3*c^3*d - 20*a^3*b*c*d^3))/d^3 - ((a*d - b*c)*(a*d - 9*b*c)*(72*b^2*c^3 + 8*a^2*c*d^2 - 80*a*b*c^2*d))/(8*(-c)^(3/4)*d^(13/4)))*(a*d - b*c)*(a*d - 9*b*c)*1i)/(8*(-c)^(3/4)*d^(13/4)) + (((x^(1/2)*(a^4*d^4 + 81*b^4*c^4 + 118*a^2*b^2*c^2*d^2 - 180*a*b^3*c^3*d - 20*a^3*b*c*d^3))/d^3 + ((a*d - b*c)*(a*d - 9*b*c)*(72*b^2*c^3 + 8*a^2*c*d^2 - 80*a*b*c^2*d))/(8*(-c)^(3/4)*d^(13/4)))*(a*d - b*c)*(a*d - 9*b*c)*1i)/(8*(-c)^(3/4)*d^(13/4)))/((((x^(1/2)*(a^4*d^4 + 81*b^4*c^4 + 118*a^2*b^2*c^2*d^2 - 180*a*b^3*c^3*d - 20*a^3*b*c*d^3))/d^3 - ((a*d - b*c)*(a*d - 9*b*c)*(72*b^2*c^3 + 8*a^2*c*d^2 - 80*a*b*c^2*d))/(8*(-c)^(3/4)*d^(13/4)))*(a*d - b*c)*(a*d - 9*b*c))/(8*(-c)^(3/4)*d^(13/4)) - (((x^(1/2)*(a^4*d^4 + 81*b^4*c^4 + 118*a^2*b^2*c^2*d^2 - 180*a*b^3*c^3*d - 20*a^3*b*c*d^3))/d^3 + ((a*d - b*c)*(a*d - 9*b*c)*(72*b^2*c^3 + 8*a^2*c*d^2 - 80*a*b*c^2*d))/(8*(-c)^(3/4)*d^(13/4)))*(a*d - b*c)*(a*d - 9*b*c))/(8*(-c)^(3/4)*d^(13/4))))*(a*d - b*c)*(a*d - 9*b*c)*1i)/(4*(-c)^(3/4)*d^(13/4)) + (atan(((((x^(1/2)*(a^4*d^4 + 81*b^4*c^4 + 118*a^2*b^2*c^2*d^2 - 180*a*b^3*c^3*d - 20*a^3*b*c*d^3))/d^3 - ((a*d - b*c)*(a*d - 9*b*c)*(72*b^2*c^3 + 8*a^2*c*d^2 - 80*a*b*c^2*d)*1i)/(8*(-c)^(3/4)*d^(13/4)))*(a*d - b*c)*(a*d - 9*b*c))/(8*(-c)^(3/4)*d^(13/4)) + (((x^(1/2)*(a^4*d^4 + 81*b^4*c^4 + 118*a^2*b^2*c^2*d^2 - 180*a*b^3*c^3*d - 20*a^3*b*c*d^3))/d^3 + ((a*d - b*c)*(a*d - 9*b*c)*(72*b^2*c^3 + 8*a^2*c*d^2 - 80*a*b*c^2*d)*1i)/(8*(-c)^(3/4)*d^(13/4)))*(a*d - b*c)*(a*d - 9*b*c))/(8*(-c)^(3/4)*d^(13/4)))/((((x^(1/2)*(a^4*d^4 + 81*b^4*c^4 + 118*a^2*b^2*c^2*d^2 - 180*a*b^3*c^3*d - 20*a^3*b*c*d^3))/d^3 - ((a*d - b*c)*(a*d - 9*b*c)*(72*b^2*c^3 + 8*a^2*c*d^2 - 80*a*b*c^2*d)*1i)/(8*(-c)^(3/4)*d^(13/4)))*(a*d - b*c)*(a*d - 9*b*c)*1i)/(8*(-c)^(3/4)*d^(13/4)) - (((x^(1/2)*(a^4*d^4 + 81*b^4*c^4 + 118*a^2*b^2*c^2*d^2 - 180*a*b^3*c^3*d - 20*a^3*b*c*d^3))/d^3 + ((a*d - b*c)*(a*d - 9*b*c)*(72*b^2*c^3 + 8*a^2*c*d^2 - 80*a*b*c^2*d)*1i)/(8*(-c)^(3/4)*d^(13/4)))*(a*d - b*c)*(a*d - 9*b*c)*1i)/(8*(-c)^(3/4)*d^(13/4))))*(a*d - b*c)*(a*d - 9*b*c))/(4*(-c)^(3/4)*d^(13/4))","B"
428,1,137,310,0.401482,"\text{Not used}","int((x^(1/2)*(a + b*x^2)^2)/(c + d*x^2)^2,x)","\frac{2\,b^2\,x^{3/2}}{3\,d^2}+\frac{x^{3/2}\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}{2\,c\,\left(d^3\,x^2+c\,d^2\right)}-\frac{\mathrm{atan}\left(\frac{d^{1/4}\,\sqrt{x}}{{\left(-c\right)}^{1/4}}\right)\,\left(a\,d-b\,c\right)\,\left(a\,d+7\,b\,c\right)}{4\,{\left(-c\right)}^{5/4}\,d^{11/4}}-\frac{\mathrm{atan}\left(\frac{d^{1/4}\,\sqrt{x}\,1{}\mathrm{i}}{{\left(-c\right)}^{1/4}}\right)\,\left(a\,d-b\,c\right)\,\left(a\,d+7\,b\,c\right)\,1{}\mathrm{i}}{4\,{\left(-c\right)}^{5/4}\,d^{11/4}}","Not used",1,"(2*b^2*x^(3/2))/(3*d^2) + (x^(3/2)*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/(2*c*(c*d^2 + d^3*x^2)) - (atan((d^(1/4)*x^(1/2))/(-c)^(1/4))*(a*d - b*c)*(a*d + 7*b*c))/(4*(-c)^(5/4)*d^(11/4)) - (atan((d^(1/4)*x^(1/2)*1i)/(-c)^(1/4))*(a*d - b*c)*(a*d + 7*b*c)*1i)/(4*(-c)^(5/4)*d^(11/4))","B"
429,1,1267,312,0.458034,"\text{Not used}","int((a + b*x^2)^2/(x^(1/2)*(c + d*x^2)^2),x)","\frac{2\,b^2\,\sqrt{x}}{d^2}+\frac{\sqrt{x}\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}{2\,c\,\left(d^3\,x^2+c\,d^2\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\sqrt{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)}{c^2\,d}-\frac{\left(a\,d-b\,c\right)\,\left(3\,a\,d+5\,b\,c\right)\,\left(24\,a^2\,d^3+16\,a\,b\,c\,d^2-40\,b^2\,c^2\,d\right)}{8\,{\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{\left(\frac{\sqrt{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)}{c^2\,d}+\frac{\left(a\,d-b\,c\right)\,\left(3\,a\,d+5\,b\,c\right)\,\left(24\,a^2\,d^3+16\,a\,b\,c\,d^2-40\,b^2\,c^2\,d\right)}{8\,{\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{\left(\frac{\sqrt{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)}{c^2\,d}-\frac{\left(a\,d-b\,c\right)\,\left(3\,a\,d+5\,b\,c\right)\,\left(24\,a^2\,d^3+16\,a\,b\,c\,d^2-40\,b^2\,c^2\,d\right)}{8\,{\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}}-\frac{\left(\frac{\sqrt{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)}{c^2\,d}+\frac{\left(a\,d-b\,c\right)\,\left(3\,a\,d+5\,b\,c\right)\,\left(24\,a^2\,d^3+16\,a\,b\,c\,d^2-40\,b^2\,c^2\,d\right)}{8\,{\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}}}\right)\,\left(a\,d-b\,c\right)\,\left(3\,a\,d+5\,b\,c\right)\,1{}\mathrm{i}}{4\,{\left(-c\right)}^{7/4}\,d^{9/4}}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\sqrt{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)}{c^2\,d}-\frac{\left(a\,d-b\,c\right)\,\left(3\,a\,d+5\,b\,c\right)\,\left(24\,a^2\,d^3+16\,a\,b\,c\,d^2-40\,b^2\,c^2\,d\right)\,1{}\mathrm{i}}{8\,{\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}}+\frac{\left(\frac{\sqrt{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)}{c^2\,d}+\frac{\left(a\,d-b\,c\right)\,\left(3\,a\,d+5\,b\,c\right)\,\left(24\,a^2\,d^3+16\,a\,b\,c\,d^2-40\,b^2\,c^2\,d\right)\,1{}\mathrm{i}}{8\,{\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}}}{\frac{\left(\frac{\sqrt{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)}{c^2\,d}-\frac{\left(a\,d-b\,c\right)\,\left(3\,a\,d+5\,b\,c\right)\,\left(24\,a^2\,d^3+16\,a\,b\,c\,d^2-40\,b^2\,c^2\,d\right)\,1{}\mathrm{i}}{8\,{\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{\left(\frac{\sqrt{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)}{c^2\,d}+\frac{\left(a\,d-b\,c\right)\,\left(3\,a\,d+5\,b\,c\right)\,\left(24\,a^2\,d^3+16\,a\,b\,c\,d^2-40\,b^2\,c^2\,d\right)\,1{}\mathrm{i}}{8\,{\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}}}\right)\,\left(a\,d-b\,c\right)\,\left(3\,a\,d+5\,b\,c\right)}{4\,{\left(-c\right)}^{7/4}\,d^{9/4}}","Not used",1,"(2*b^2*x^(1/2))/d^2 + (x^(1/2)*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/(2*c*(c*d^2 + d^3*x^2)) + (atan(((((x^(1/2)*(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))/(c^2*d) - ((a*d - b*c)*(3*a*d + 5*b*c)*(24*a^2*d^3 - 40*b^2*c^2*d + 16*a*b*c*d^2))/(8*(-c)^(7/4)*d^(9/4)))*(a*d - b*c)*(3*a*d + 5*b*c)*1i)/(8*(-c)^(7/4)*d^(9/4)) + (((x^(1/2)*(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))/(c^2*d) + ((a*d - b*c)*(3*a*d + 5*b*c)*(24*a^2*d^3 - 40*b^2*c^2*d + 16*a*b*c*d^2))/(8*(-c)^(7/4)*d^(9/4)))*(a*d - b*c)*(3*a*d + 5*b*c)*1i)/(8*(-c)^(7/4)*d^(9/4)))/((((x^(1/2)*(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))/(c^2*d) - ((a*d - b*c)*(3*a*d + 5*b*c)*(24*a^2*d^3 - 40*b^2*c^2*d + 16*a*b*c*d^2))/(8*(-c)^(7/4)*d^(9/4)))*(a*d - b*c)*(3*a*d + 5*b*c))/(8*(-c)^(7/4)*d^(9/4)) - (((x^(1/2)*(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))/(c^2*d) + ((a*d - b*c)*(3*a*d + 5*b*c)*(24*a^2*d^3 - 40*b^2*c^2*d + 16*a*b*c*d^2))/(8*(-c)^(7/4)*d^(9/4)))*(a*d - b*c)*(3*a*d + 5*b*c))/(8*(-c)^(7/4)*d^(9/4))))*(a*d - b*c)*(3*a*d + 5*b*c)*1i)/(4*(-c)^(7/4)*d^(9/4)) + (atan(((((x^(1/2)*(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))/(c^2*d) - ((a*d - b*c)*(3*a*d + 5*b*c)*(24*a^2*d^3 - 40*b^2*c^2*d + 16*a*b*c*d^2)*1i)/(8*(-c)^(7/4)*d^(9/4)))*(a*d - b*c)*(3*a*d + 5*b*c))/(8*(-c)^(7/4)*d^(9/4)) + (((x^(1/2)*(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))/(c^2*d) + ((a*d - b*c)*(3*a*d + 5*b*c)*(24*a^2*d^3 - 40*b^2*c^2*d + 16*a*b*c*d^2)*1i)/(8*(-c)^(7/4)*d^(9/4)))*(a*d - b*c)*(3*a*d + 5*b*c))/(8*(-c)^(7/4)*d^(9/4)))/((((x^(1/2)*(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))/(c^2*d) - ((a*d - b*c)*(3*a*d + 5*b*c)*(24*a^2*d^3 - 40*b^2*c^2*d + 16*a*b*c*d^2)*1i)/(8*(-c)^(7/4)*d^(9/4)))*(a*d - b*c)*(3*a*d + 5*b*c)*1i)/(8*(-c)^(7/4)*d^(9/4)) - (((x^(1/2)*(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))/(c^2*d) + ((a*d - b*c)*(3*a*d + 5*b*c)*(24*a^2*d^3 - 40*b^2*c^2*d + 16*a*b*c*d^2)*1i)/(8*(-c)^(7/4)*d^(9/4)))*(a*d - b*c)*(3*a*d + 5*b*c)*1i)/(8*(-c)^(7/4)*d^(9/4))))*(a*d - b*c)*(3*a*d + 5*b*c))/(4*(-c)^(7/4)*d^(9/4))","B"
430,1,138,333,0.394256,"\text{Not used}","int((a + b*x^2)^2/(x^(3/2)*(c + d*x^2)^2),x)","\frac{\mathrm{atanh}\left(\frac{d^{1/4}\,\sqrt{x}}{{\left(-c\right)}^{1/4}}\right)\,\left(a\,d-b\,c\right)\,\left(5\,a\,d+3\,b\,c\right)}{4\,{\left(-c\right)}^{9/4}\,d^{7/4}}-\frac{\mathrm{atan}\left(\frac{d^{1/4}\,\sqrt{x}}{{\left(-c\right)}^{1/4}}\right)\,\left(a\,d-b\,c\right)\,\left(5\,a\,d+3\,b\,c\right)}{4\,{\left(-c\right)}^{9/4}\,d^{7/4}}-\frac{\frac{2\,a^2}{c}+\frac{x^2\,\left(5\,a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}{2\,c^2\,d}}{c\,\sqrt{x}+d\,x^{5/2}}","Not used",1,"(atanh((d^(1/4)*x^(1/2))/(-c)^(1/4))*(a*d - b*c)*(5*a*d + 3*b*c))/(4*(-c)^(9/4)*d^(7/4)) - (atan((d^(1/4)*x^(1/2))/(-c)^(1/4))*(a*d - b*c)*(5*a*d + 3*b*c))/(4*(-c)^(9/4)*d^(7/4)) - ((2*a^2)/c + (x^2*(5*a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/(2*c^2*d))/(c*x^(1/2) + d*x^(5/2))","B"
431,1,1340,332,0.560502,"\text{Not used}","int((a + b*x^2)^2/(x^(5/2)*(c + d*x^2)^2),x)","-\frac{\frac{2\,a^2}{3\,c}+\frac{x^2\,\left(7\,a^2\,d^2-6\,a\,b\,c\,d+3\,b^2\,c^2\right)}{6\,c^2\,d}}{c\,x^{3/2}+d\,x^{7/2}}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\sqrt{x}\,\left(1568\,a^4\,c^6\,d^{10}-2688\,a^3\,b\,c^7\,d^9+704\,a^2\,b^2\,c^8\,d^8+384\,a\,b^3\,c^9\,d^7+32\,b^4\,c^{10}\,d^6\right)-\frac{\left(a\,d-b\,c\right)\,\left(7\,a\,d+b\,c\right)\,\left(-1792\,a^2\,c^9\,d^9+1536\,a\,b\,c^{10}\,d^8+256\,b^2\,c^{11}\,d^7\right)}{8\,{\left(-c\right)}^{11/4}\,d^{5/4}}\right)\,\left(a\,d-b\,c\right)\,\left(7\,a\,d+b\,c\right)\,1{}\mathrm{i}}{8\,{\left(-c\right)}^{11/4}\,d^{5/4}}+\frac{\left(\sqrt{x}\,\left(1568\,a^4\,c^6\,d^{10}-2688\,a^3\,b\,c^7\,d^9+704\,a^2\,b^2\,c^8\,d^8+384\,a\,b^3\,c^9\,d^7+32\,b^4\,c^{10}\,d^6\right)+\frac{\left(a\,d-b\,c\right)\,\left(7\,a\,d+b\,c\right)\,\left(-1792\,a^2\,c^9\,d^9+1536\,a\,b\,c^{10}\,d^8+256\,b^2\,c^{11}\,d^7\right)}{8\,{\left(-c\right)}^{11/4}\,d^{5/4}}\right)\,\left(a\,d-b\,c\right)\,\left(7\,a\,d+b\,c\right)\,1{}\mathrm{i}}{8\,{\left(-c\right)}^{11/4}\,d^{5/4}}}{\frac{\left(\sqrt{x}\,\left(1568\,a^4\,c^6\,d^{10}-2688\,a^3\,b\,c^7\,d^9+704\,a^2\,b^2\,c^8\,d^8+384\,a\,b^3\,c^9\,d^7+32\,b^4\,c^{10}\,d^6\right)-\frac{\left(a\,d-b\,c\right)\,\left(7\,a\,d+b\,c\right)\,\left(-1792\,a^2\,c^9\,d^9+1536\,a\,b\,c^{10}\,d^8+256\,b^2\,c^{11}\,d^7\right)}{8\,{\left(-c\right)}^{11/4}\,d^{5/4}}\right)\,\left(a\,d-b\,c\right)\,\left(7\,a\,d+b\,c\right)}{8\,{\left(-c\right)}^{11/4}\,d^{5/4}}-\frac{\left(\sqrt{x}\,\left(1568\,a^4\,c^6\,d^{10}-2688\,a^3\,b\,c^7\,d^9+704\,a^2\,b^2\,c^8\,d^8+384\,a\,b^3\,c^9\,d^7+32\,b^4\,c^{10}\,d^6\right)+\frac{\left(a\,d-b\,c\right)\,\left(7\,a\,d+b\,c\right)\,\left(-1792\,a^2\,c^9\,d^9+1536\,a\,b\,c^{10}\,d^8+256\,b^2\,c^{11}\,d^7\right)}{8\,{\left(-c\right)}^{11/4}\,d^{5/4}}\right)\,\left(a\,d-b\,c\right)\,\left(7\,a\,d+b\,c\right)}{8\,{\left(-c\right)}^{11/4}\,d^{5/4}}}\right)\,\left(a\,d-b\,c\right)\,\left(7\,a\,d+b\,c\right)\,1{}\mathrm{i}}{4\,{\left(-c\right)}^{11/4}\,d^{5/4}}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\sqrt{x}\,\left(1568\,a^4\,c^6\,d^{10}-2688\,a^3\,b\,c^7\,d^9+704\,a^2\,b^2\,c^8\,d^8+384\,a\,b^3\,c^9\,d^7+32\,b^4\,c^{10}\,d^6\right)-\frac{\left(a\,d-b\,c\right)\,\left(7\,a\,d+b\,c\right)\,\left(-1792\,a^2\,c^9\,d^9+1536\,a\,b\,c^{10}\,d^8+256\,b^2\,c^{11}\,d^7\right)\,1{}\mathrm{i}}{8\,{\left(-c\right)}^{11/4}\,d^{5/4}}\right)\,\left(a\,d-b\,c\right)\,\left(7\,a\,d+b\,c\right)}{8\,{\left(-c\right)}^{11/4}\,d^{5/4}}+\frac{\left(\sqrt{x}\,\left(1568\,a^4\,c^6\,d^{10}-2688\,a^3\,b\,c^7\,d^9+704\,a^2\,b^2\,c^8\,d^8+384\,a\,b^3\,c^9\,d^7+32\,b^4\,c^{10}\,d^6\right)+\frac{\left(a\,d-b\,c\right)\,\left(7\,a\,d+b\,c\right)\,\left(-1792\,a^2\,c^9\,d^9+1536\,a\,b\,c^{10}\,d^8+256\,b^2\,c^{11}\,d^7\right)\,1{}\mathrm{i}}{8\,{\left(-c\right)}^{11/4}\,d^{5/4}}\right)\,\left(a\,d-b\,c\right)\,\left(7\,a\,d+b\,c\right)}{8\,{\left(-c\right)}^{11/4}\,d^{5/4}}}{\frac{\left(\sqrt{x}\,\left(1568\,a^4\,c^6\,d^{10}-2688\,a^3\,b\,c^7\,d^9+704\,a^2\,b^2\,c^8\,d^8+384\,a\,b^3\,c^9\,d^7+32\,b^4\,c^{10}\,d^6\right)-\frac{\left(a\,d-b\,c\right)\,\left(7\,a\,d+b\,c\right)\,\left(-1792\,a^2\,c^9\,d^9+1536\,a\,b\,c^{10}\,d^8+256\,b^2\,c^{11}\,d^7\right)\,1{}\mathrm{i}}{8\,{\left(-c\right)}^{11/4}\,d^{5/4}}\right)\,\left(a\,d-b\,c\right)\,\left(7\,a\,d+b\,c\right)\,1{}\mathrm{i}}{8\,{\left(-c\right)}^{11/4}\,d^{5/4}}-\frac{\left(\sqrt{x}\,\left(1568\,a^4\,c^6\,d^{10}-2688\,a^3\,b\,c^7\,d^9+704\,a^2\,b^2\,c^8\,d^8+384\,a\,b^3\,c^9\,d^7+32\,b^4\,c^{10}\,d^6\right)+\frac{\left(a\,d-b\,c\right)\,\left(7\,a\,d+b\,c\right)\,\left(-1792\,a^2\,c^9\,d^9+1536\,a\,b\,c^{10}\,d^8+256\,b^2\,c^{11}\,d^7\right)\,1{}\mathrm{i}}{8\,{\left(-c\right)}^{11/4}\,d^{5/4}}\right)\,\left(a\,d-b\,c\right)\,\left(7\,a\,d+b\,c\right)\,1{}\mathrm{i}}{8\,{\left(-c\right)}^{11/4}\,d^{5/4}}}\right)\,\left(a\,d-b\,c\right)\,\left(7\,a\,d+b\,c\right)}{4\,{\left(-c\right)}^{11/4}\,d^{5/4}}","Not used",1,"(atan((((x^(1/2)*(1568*a^4*c^6*d^10 + 32*b^4*c^10*d^6 + 384*a*b^3*c^9*d^7 - 2688*a^3*b*c^7*d^9 + 704*a^2*b^2*c^8*d^8) - ((a*d - b*c)*(7*a*d + b*c)*(256*b^2*c^11*d^7 - 1792*a^2*c^9*d^9 + 1536*a*b*c^10*d^8))/(8*(-c)^(11/4)*d^(5/4)))*(a*d - b*c)*(7*a*d + b*c)*1i)/(8*(-c)^(11/4)*d^(5/4)) + ((x^(1/2)*(1568*a^4*c^6*d^10 + 32*b^4*c^10*d^6 + 384*a*b^3*c^9*d^7 - 2688*a^3*b*c^7*d^9 + 704*a^2*b^2*c^8*d^8) + ((a*d - b*c)*(7*a*d + b*c)*(256*b^2*c^11*d^7 - 1792*a^2*c^9*d^9 + 1536*a*b*c^10*d^8))/(8*(-c)^(11/4)*d^(5/4)))*(a*d - b*c)*(7*a*d + b*c)*1i)/(8*(-c)^(11/4)*d^(5/4)))/(((x^(1/2)*(1568*a^4*c^6*d^10 + 32*b^4*c^10*d^6 + 384*a*b^3*c^9*d^7 - 2688*a^3*b*c^7*d^9 + 704*a^2*b^2*c^8*d^8) - ((a*d - b*c)*(7*a*d + b*c)*(256*b^2*c^11*d^7 - 1792*a^2*c^9*d^9 + 1536*a*b*c^10*d^8))/(8*(-c)^(11/4)*d^(5/4)))*(a*d - b*c)*(7*a*d + b*c))/(8*(-c)^(11/4)*d^(5/4)) - ((x^(1/2)*(1568*a^4*c^6*d^10 + 32*b^4*c^10*d^6 + 384*a*b^3*c^9*d^7 - 2688*a^3*b*c^7*d^9 + 704*a^2*b^2*c^8*d^8) + ((a*d - b*c)*(7*a*d + b*c)*(256*b^2*c^11*d^7 - 1792*a^2*c^9*d^9 + 1536*a*b*c^10*d^8))/(8*(-c)^(11/4)*d^(5/4)))*(a*d - b*c)*(7*a*d + b*c))/(8*(-c)^(11/4)*d^(5/4))))*(a*d - b*c)*(7*a*d + b*c)*1i)/(4*(-c)^(11/4)*d^(5/4)) - ((2*a^2)/(3*c) + (x^2*(7*a^2*d^2 + 3*b^2*c^2 - 6*a*b*c*d))/(6*c^2*d))/(c*x^(3/2) + d*x^(7/2)) + (atan((((x^(1/2)*(1568*a^4*c^6*d^10 + 32*b^4*c^10*d^6 + 384*a*b^3*c^9*d^7 - 2688*a^3*b*c^7*d^9 + 704*a^2*b^2*c^8*d^8) - ((a*d - b*c)*(7*a*d + b*c)*(256*b^2*c^11*d^7 - 1792*a^2*c^9*d^9 + 1536*a*b*c^10*d^8)*1i)/(8*(-c)^(11/4)*d^(5/4)))*(a*d - b*c)*(7*a*d + b*c))/(8*(-c)^(11/4)*d^(5/4)) + ((x^(1/2)*(1568*a^4*c^6*d^10 + 32*b^4*c^10*d^6 + 384*a*b^3*c^9*d^7 - 2688*a^3*b*c^7*d^9 + 704*a^2*b^2*c^8*d^8) + ((a*d - b*c)*(7*a*d + b*c)*(256*b^2*c^11*d^7 - 1792*a^2*c^9*d^9 + 1536*a*b*c^10*d^8)*1i)/(8*(-c)^(11/4)*d^(5/4)))*(a*d - b*c)*(7*a*d + b*c))/(8*(-c)^(11/4)*d^(5/4)))/(((x^(1/2)*(1568*a^4*c^6*d^10 + 32*b^4*c^10*d^6 + 384*a*b^3*c^9*d^7 - 2688*a^3*b*c^7*d^9 + 704*a^2*b^2*c^8*d^8) - ((a*d - b*c)*(7*a*d + b*c)*(256*b^2*c^11*d^7 - 1792*a^2*c^9*d^9 + 1536*a*b*c^10*d^8)*1i)/(8*(-c)^(11/4)*d^(5/4)))*(a*d - b*c)*(7*a*d + b*c)*1i)/(8*(-c)^(11/4)*d^(5/4)) - ((x^(1/2)*(1568*a^4*c^6*d^10 + 32*b^4*c^10*d^6 + 384*a*b^3*c^9*d^7 - 2688*a^3*b*c^7*d^9 + 704*a^2*b^2*c^8*d^8) + ((a*d - b*c)*(7*a*d + b*c)*(256*b^2*c^11*d^7 - 1792*a^2*c^9*d^9 + 1536*a*b*c^10*d^8)*1i)/(8*(-c)^(11/4)*d^(5/4)))*(a*d - b*c)*(7*a*d + b*c)*1i)/(8*(-c)^(11/4)*d^(5/4))))*(a*d - b*c)*(7*a*d + b*c))/(4*(-c)^(11/4)*d^(5/4))","B"
432,1,152,363,0.232742,"\text{Not used}","int((a + b*x^2)^2/(x^(7/2)*(c + d*x^2)^2),x)","\frac{\frac{x^4\,\left(9\,a^2\,d^2-10\,a\,b\,c\,d+b^2\,c^2\right)}{2\,c^3}-\frac{2\,a^2}{5\,c}+\frac{2\,a\,x^2\,\left(9\,a\,d-10\,b\,c\right)}{5\,c^2}}{c\,x^{5/2}+d\,x^{9/2}}-\frac{\mathrm{atan}\left(\frac{d^{1/4}\,\sqrt{x}}{{\left(-c\right)}^{1/4}}\right)\,\left(a\,d-b\,c\right)\,\left(9\,a\,d-b\,c\right)}{4\,{\left(-c\right)}^{13/4}\,d^{3/4}}+\frac{\mathrm{atanh}\left(\frac{d^{1/4}\,\sqrt{x}}{{\left(-c\right)}^{1/4}}\right)\,\left(a\,d-b\,c\right)\,\left(9\,a\,d-b\,c\right)}{4\,{\left(-c\right)}^{13/4}\,d^{3/4}}","Not used",1,"((x^4*(9*a^2*d^2 + b^2*c^2 - 10*a*b*c*d))/(2*c^3) - (2*a^2)/(5*c) + (2*a*x^2*(9*a*d - 10*b*c))/(5*c^2))/(c*x^(5/2) + d*x^(9/2)) - (atan((d^(1/4)*x^(1/2))/(-c)^(1/4))*(a*d - b*c)*(9*a*d - b*c))/(4*(-c)^(13/4)*d^(3/4)) + (atanh((d^(1/4)*x^(1/2))/(-c)^(1/4))*(a*d - b*c)*(9*a*d - b*c))/(4*(-c)^(13/4)*d^(3/4))","B"
433,1,1426,440,0.479581,"\text{Not used}","int((x^(7/2)*(a + b*x^2)^2)/(c + d*x^2)^3,x)","\frac{2\,b^2\,x^{5/2}}{5\,d^3}-\frac{\sqrt{x}\,\left(\frac{5\,a^2\,c\,d^2}{16}-\frac{13\,a\,b\,c^2\,d}{8}+\frac{21\,b^2\,c^3}{16}\right)+x^{5/2}\,\left(\frac{9\,a^2\,d^3}{16}-\frac{17\,a\,b\,c\,d^2}{8}+\frac{25\,b^2\,c^2\,d}{16}\right)}{c^2\,d^4+2\,c\,d^5\,x^2+d^6\,x^4}-\sqrt{x}\,\left(\frac{6\,b^2\,c}{d^4}-\frac{4\,a\,b}{d^3}\right)+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\sqrt{x}\,\left(25\,a^4\,d^4-900\,a^3\,b\,c\,d^3+9270\,a^2\,b^2\,c^2\,d^2-21060\,a\,b^3\,c^3\,d+13689\,b^4\,c^4\right)}{64\,d^5}-\frac{\left(5\,a^2\,d^2-90\,a\,b\,c\,d+117\,b^2\,c^2\right)\,\left(5\,a^2\,c\,d^2-90\,a\,b\,c^2\,d+117\,b^2\,c^3\right)}{64\,{\left(-c\right)}^{3/4}\,d^{21/4}}\right)\,\left(5\,a^2\,d^2-90\,a\,b\,c\,d+117\,b^2\,c^2\right)\,1{}\mathrm{i}}{64\,{\left(-c\right)}^{3/4}\,d^{17/4}}+\frac{\left(\frac{\sqrt{x}\,\left(25\,a^4\,d^4-900\,a^3\,b\,c\,d^3+9270\,a^2\,b^2\,c^2\,d^2-21060\,a\,b^3\,c^3\,d+13689\,b^4\,c^4\right)}{64\,d^5}+\frac{\left(5\,a^2\,d^2-90\,a\,b\,c\,d+117\,b^2\,c^2\right)\,\left(5\,a^2\,c\,d^2-90\,a\,b\,c^2\,d+117\,b^2\,c^3\right)}{64\,{\left(-c\right)}^{3/4}\,d^{21/4}}\right)\,\left(5\,a^2\,d^2-90\,a\,b\,c\,d+117\,b^2\,c^2\right)\,1{}\mathrm{i}}{64\,{\left(-c\right)}^{3/4}\,d^{17/4}}}{\frac{\left(\frac{\sqrt{x}\,\left(25\,a^4\,d^4-900\,a^3\,b\,c\,d^3+9270\,a^2\,b^2\,c^2\,d^2-21060\,a\,b^3\,c^3\,d+13689\,b^4\,c^4\right)}{64\,d^5}-\frac{\left(5\,a^2\,d^2-90\,a\,b\,c\,d+117\,b^2\,c^2\right)\,\left(5\,a^2\,c\,d^2-90\,a\,b\,c^2\,d+117\,b^2\,c^3\right)}{64\,{\left(-c\right)}^{3/4}\,d^{21/4}}\right)\,\left(5\,a^2\,d^2-90\,a\,b\,c\,d+117\,b^2\,c^2\right)}{64\,{\left(-c\right)}^{3/4}\,d^{17/4}}-\frac{\left(\frac{\sqrt{x}\,\left(25\,a^4\,d^4-900\,a^3\,b\,c\,d^3+9270\,a^2\,b^2\,c^2\,d^2-21060\,a\,b^3\,c^3\,d+13689\,b^4\,c^4\right)}{64\,d^5}+\frac{\left(5\,a^2\,d^2-90\,a\,b\,c\,d+117\,b^2\,c^2\right)\,\left(5\,a^2\,c\,d^2-90\,a\,b\,c^2\,d+117\,b^2\,c^3\right)}{64\,{\left(-c\right)}^{3/4}\,d^{21/4}}\right)\,\left(5\,a^2\,d^2-90\,a\,b\,c\,d+117\,b^2\,c^2\right)}{64\,{\left(-c\right)}^{3/4}\,d^{17/4}}}\right)\,\left(5\,a^2\,d^2-90\,a\,b\,c\,d+117\,b^2\,c^2\right)\,1{}\mathrm{i}}{32\,{\left(-c\right)}^{3/4}\,d^{17/4}}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\sqrt{x}\,\left(25\,a^4\,d^4-900\,a^3\,b\,c\,d^3+9270\,a^2\,b^2\,c^2\,d^2-21060\,a\,b^3\,c^3\,d+13689\,b^4\,c^4\right)}{64\,d^5}-\frac{\left(5\,a^2\,d^2-90\,a\,b\,c\,d+117\,b^2\,c^2\right)\,\left(5\,a^2\,c\,d^2-90\,a\,b\,c^2\,d+117\,b^2\,c^3\right)\,1{}\mathrm{i}}{64\,{\left(-c\right)}^{3/4}\,d^{21/4}}\right)\,\left(5\,a^2\,d^2-90\,a\,b\,c\,d+117\,b^2\,c^2\right)}{64\,{\left(-c\right)}^{3/4}\,d^{17/4}}+\frac{\left(\frac{\sqrt{x}\,\left(25\,a^4\,d^4-900\,a^3\,b\,c\,d^3+9270\,a^2\,b^2\,c^2\,d^2-21060\,a\,b^3\,c^3\,d+13689\,b^4\,c^4\right)}{64\,d^5}+\frac{\left(5\,a^2\,d^2-90\,a\,b\,c\,d+117\,b^2\,c^2\right)\,\left(5\,a^2\,c\,d^2-90\,a\,b\,c^2\,d+117\,b^2\,c^3\right)\,1{}\mathrm{i}}{64\,{\left(-c\right)}^{3/4}\,d^{21/4}}\right)\,\left(5\,a^2\,d^2-90\,a\,b\,c\,d+117\,b^2\,c^2\right)}{64\,{\left(-c\right)}^{3/4}\,d^{17/4}}}{\frac{\left(\frac{\sqrt{x}\,\left(25\,a^4\,d^4-900\,a^3\,b\,c\,d^3+9270\,a^2\,b^2\,c^2\,d^2-21060\,a\,b^3\,c^3\,d+13689\,b^4\,c^4\right)}{64\,d^5}-\frac{\left(5\,a^2\,d^2-90\,a\,b\,c\,d+117\,b^2\,c^2\right)\,\left(5\,a^2\,c\,d^2-90\,a\,b\,c^2\,d+117\,b^2\,c^3\right)\,1{}\mathrm{i}}{64\,{\left(-c\right)}^{3/4}\,d^{21/4}}\right)\,\left(5\,a^2\,d^2-90\,a\,b\,c\,d+117\,b^2\,c^2\right)\,1{}\mathrm{i}}{64\,{\left(-c\right)}^{3/4}\,d^{17/4}}-\frac{\left(\frac{\sqrt{x}\,\left(25\,a^4\,d^4-900\,a^3\,b\,c\,d^3+9270\,a^2\,b^2\,c^2\,d^2-21060\,a\,b^3\,c^3\,d+13689\,b^4\,c^4\right)}{64\,d^5}+\frac{\left(5\,a^2\,d^2-90\,a\,b\,c\,d+117\,b^2\,c^2\right)\,\left(5\,a^2\,c\,d^2-90\,a\,b\,c^2\,d+117\,b^2\,c^3\right)\,1{}\mathrm{i}}{64\,{\left(-c\right)}^{3/4}\,d^{21/4}}\right)\,\left(5\,a^2\,d^2-90\,a\,b\,c\,d+117\,b^2\,c^2\right)\,1{}\mathrm{i}}{64\,{\left(-c\right)}^{3/4}\,d^{17/4}}}\right)\,\left(5\,a^2\,d^2-90\,a\,b\,c\,d+117\,b^2\,c^2\right)}{32\,{\left(-c\right)}^{3/4}\,d^{17/4}}","Not used",1,"(2*b^2*x^(5/2))/(5*d^3) - (x^(1/2)*((21*b^2*c^3)/16 + (5*a^2*c*d^2)/16 - (13*a*b*c^2*d)/8) + x^(5/2)*((9*a^2*d^3)/16 + (25*b^2*c^2*d)/16 - (17*a*b*c*d^2)/8))/(c^2*d^4 + d^6*x^4 + 2*c*d^5*x^2) - x^(1/2)*((6*b^2*c)/d^4 - (4*a*b)/d^3) + (atan(((((x^(1/2)*(25*a^4*d^4 + 13689*b^4*c^4 + 9270*a^2*b^2*c^2*d^2 - 21060*a*b^3*c^3*d - 900*a^3*b*c*d^3))/(64*d^5) - ((5*a^2*d^2 + 117*b^2*c^2 - 90*a*b*c*d)*(117*b^2*c^3 + 5*a^2*c*d^2 - 90*a*b*c^2*d))/(64*(-c)^(3/4)*d^(21/4)))*(5*a^2*d^2 + 117*b^2*c^2 - 90*a*b*c*d)*1i)/(64*(-c)^(3/4)*d^(17/4)) + (((x^(1/2)*(25*a^4*d^4 + 13689*b^4*c^4 + 9270*a^2*b^2*c^2*d^2 - 21060*a*b^3*c^3*d - 900*a^3*b*c*d^3))/(64*d^5) + ((5*a^2*d^2 + 117*b^2*c^2 - 90*a*b*c*d)*(117*b^2*c^3 + 5*a^2*c*d^2 - 90*a*b*c^2*d))/(64*(-c)^(3/4)*d^(21/4)))*(5*a^2*d^2 + 117*b^2*c^2 - 90*a*b*c*d)*1i)/(64*(-c)^(3/4)*d^(17/4)))/((((x^(1/2)*(25*a^4*d^4 + 13689*b^4*c^4 + 9270*a^2*b^2*c^2*d^2 - 21060*a*b^3*c^3*d - 900*a^3*b*c*d^3))/(64*d^5) - ((5*a^2*d^2 + 117*b^2*c^2 - 90*a*b*c*d)*(117*b^2*c^3 + 5*a^2*c*d^2 - 90*a*b*c^2*d))/(64*(-c)^(3/4)*d^(21/4)))*(5*a^2*d^2 + 117*b^2*c^2 - 90*a*b*c*d))/(64*(-c)^(3/4)*d^(17/4)) - (((x^(1/2)*(25*a^4*d^4 + 13689*b^4*c^4 + 9270*a^2*b^2*c^2*d^2 - 21060*a*b^3*c^3*d - 900*a^3*b*c*d^3))/(64*d^5) + ((5*a^2*d^2 + 117*b^2*c^2 - 90*a*b*c*d)*(117*b^2*c^3 + 5*a^2*c*d^2 - 90*a*b*c^2*d))/(64*(-c)^(3/4)*d^(21/4)))*(5*a^2*d^2 + 117*b^2*c^2 - 90*a*b*c*d))/(64*(-c)^(3/4)*d^(17/4))))*(5*a^2*d^2 + 117*b^2*c^2 - 90*a*b*c*d)*1i)/(32*(-c)^(3/4)*d^(17/4)) + (atan(((((x^(1/2)*(25*a^4*d^4 + 13689*b^4*c^4 + 9270*a^2*b^2*c^2*d^2 - 21060*a*b^3*c^3*d - 900*a^3*b*c*d^3))/(64*d^5) - ((5*a^2*d^2 + 117*b^2*c^2 - 90*a*b*c*d)*(117*b^2*c^3 + 5*a^2*c*d^2 - 90*a*b*c^2*d)*1i)/(64*(-c)^(3/4)*d^(21/4)))*(5*a^2*d^2 + 117*b^2*c^2 - 90*a*b*c*d))/(64*(-c)^(3/4)*d^(17/4)) + (((x^(1/2)*(25*a^4*d^4 + 13689*b^4*c^4 + 9270*a^2*b^2*c^2*d^2 - 21060*a*b^3*c^3*d - 900*a^3*b*c*d^3))/(64*d^5) + ((5*a^2*d^2 + 117*b^2*c^2 - 90*a*b*c*d)*(117*b^2*c^3 + 5*a^2*c*d^2 - 90*a*b*c^2*d)*1i)/(64*(-c)^(3/4)*d^(21/4)))*(5*a^2*d^2 + 117*b^2*c^2 - 90*a*b*c*d))/(64*(-c)^(3/4)*d^(17/4)))/((((x^(1/2)*(25*a^4*d^4 + 13689*b^4*c^4 + 9270*a^2*b^2*c^2*d^2 - 21060*a*b^3*c^3*d - 900*a^3*b*c*d^3))/(64*d^5) - ((5*a^2*d^2 + 117*b^2*c^2 - 90*a*b*c*d)*(117*b^2*c^3 + 5*a^2*c*d^2 - 90*a*b*c^2*d)*1i)/(64*(-c)^(3/4)*d^(21/4)))*(5*a^2*d^2 + 117*b^2*c^2 - 90*a*b*c*d)*1i)/(64*(-c)^(3/4)*d^(17/4)) - (((x^(1/2)*(25*a^4*d^4 + 13689*b^4*c^4 + 9270*a^2*b^2*c^2*d^2 - 21060*a*b^3*c^3*d - 900*a^3*b*c*d^3))/(64*d^5) + ((5*a^2*d^2 + 117*b^2*c^2 - 90*a*b*c*d)*(117*b^2*c^3 + 5*a^2*c*d^2 - 90*a*b*c^2*d)*1i)/(64*(-c)^(3/4)*d^(21/4)))*(5*a^2*d^2 + 117*b^2*c^2 - 90*a*b*c*d)*1i)/(64*(-c)^(3/4)*d^(17/4))))*(5*a^2*d^2 + 117*b^2*c^2 - 90*a*b*c*d))/(32*(-c)^(3/4)*d^(17/4))","B"
434,1,197,401,0.419456,"\text{Not used}","int((x^(5/2)*(a + b*x^2)^2)/(c + d*x^2)^3,x)","\frac{2\,b^2\,x^{3/2}}{3\,d^3}-\frac{x^{3/2}\,\left(\frac{a^2\,d^2}{16}+\frac{7\,a\,b\,c\,d}{8}-\frac{15\,b^2\,c^2}{16}\right)-\frac{x^{7/2}\,\left(3\,a^2\,d^3-22\,a\,b\,c\,d^2+19\,b^2\,c^2\,d\right)}{16\,c}}{c^2\,d^3+2\,c\,d^4\,x^2+d^5\,x^4}-\frac{\mathrm{atan}\left(\frac{d^{1/4}\,\sqrt{x}}{{\left(-c\right)}^{1/4}}\right)\,\left(3\,a^2\,d^2+42\,a\,b\,c\,d-77\,b^2\,c^2\right)}{32\,{\left(-c\right)}^{5/4}\,d^{15/4}}-\frac{\mathrm{atan}\left(\frac{d^{1/4}\,\sqrt{x}\,1{}\mathrm{i}}{{\left(-c\right)}^{1/4}}\right)\,\left(3\,a^2\,d^2+42\,a\,b\,c\,d-77\,b^2\,c^2\right)\,1{}\mathrm{i}}{32\,{\left(-c\right)}^{5/4}\,d^{15/4}}","Not used",1,"(2*b^2*x^(3/2))/(3*d^3) - (x^(3/2)*((a^2*d^2)/16 - (15*b^2*c^2)/16 + (7*a*b*c*d)/8) - (x^(7/2)*(3*a^2*d^3 + 19*b^2*c^2*d - 22*a*b*c*d^2))/(16*c))/(c^2*d^3 + d^5*x^4 + 2*c*d^4*x^2) - (atan((d^(1/4)*x^(1/2))/(-c)^(1/4))*(3*a^2*d^2 - 77*b^2*c^2 + 42*a*b*c*d))/(32*(-c)^(5/4)*d^(15/4)) - (atan((d^(1/4)*x^(1/2)*1i)/(-c)^(1/4))*(3*a^2*d^2 - 77*b^2*c^2 + 42*a*b*c*d)*1i)/(32*(-c)^(5/4)*d^(15/4))","B"
435,1,1236,402,0.440998,"\text{Not used}","int((x^(3/2)*(a + b*x^2)^2)/(c + d*x^2)^3,x)","\frac{2\,b^2\,\sqrt{x}}{d^3}-\frac{\sqrt{x}\,\left(\frac{3\,a^2\,d^2}{16}+\frac{5\,a\,b\,c\,d}{8}-\frac{13\,b^2\,c^2}{16}\right)-\frac{x^{5/2}\,\left(a^2\,d^3-18\,a\,b\,c\,d^2+17\,b^2\,c^2\,d\right)}{16\,c}}{c^2\,d^3+2\,c\,d^4\,x^2+d^5\,x^4}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{{\left(3\,a^2\,d^2+10\,a\,b\,c\,d-45\,b^2\,c^2\right)}^2}{64\,{\left(-c\right)}^{7/4}\,d^{13/4}}-\frac{\sqrt{x}\,\left(9\,a^4\,d^4+60\,a^3\,b\,c\,d^3-170\,a^2\,b^2\,c^2\,d^2-900\,a\,b^3\,c^3\,d+2025\,b^4\,c^4\right)}{64\,c^2\,d^3}\right)\,\left(3\,a^2\,d^2+10\,a\,b\,c\,d-45\,b^2\,c^2\right)\,1{}\mathrm{i}}{64\,{\left(-c\right)}^{7/4}\,d^{13/4}}-\frac{\left(\frac{{\left(3\,a^2\,d^2+10\,a\,b\,c\,d-45\,b^2\,c^2\right)}^2}{64\,{\left(-c\right)}^{7/4}\,d^{13/4}}+\frac{\sqrt{x}\,\left(9\,a^4\,d^4+60\,a^3\,b\,c\,d^3-170\,a^2\,b^2\,c^2\,d^2-900\,a\,b^3\,c^3\,d+2025\,b^4\,c^4\right)}{64\,c^2\,d^3}\right)\,\left(3\,a^2\,d^2+10\,a\,b\,c\,d-45\,b^2\,c^2\right)\,1{}\mathrm{i}}{64\,{\left(-c\right)}^{7/4}\,d^{13/4}}}{\frac{\left(\frac{{\left(3\,a^2\,d^2+10\,a\,b\,c\,d-45\,b^2\,c^2\right)}^2}{64\,{\left(-c\right)}^{7/4}\,d^{13/4}}-\frac{\sqrt{x}\,\left(9\,a^4\,d^4+60\,a^3\,b\,c\,d^3-170\,a^2\,b^2\,c^2\,d^2-900\,a\,b^3\,c^3\,d+2025\,b^4\,c^4\right)}{64\,c^2\,d^3}\right)\,\left(3\,a^2\,d^2+10\,a\,b\,c\,d-45\,b^2\,c^2\right)}{64\,{\left(-c\right)}^{7/4}\,d^{13/4}}+\frac{\left(\frac{{\left(3\,a^2\,d^2+10\,a\,b\,c\,d-45\,b^2\,c^2\right)}^2}{64\,{\left(-c\right)}^{7/4}\,d^{13/4}}+\frac{\sqrt{x}\,\left(9\,a^4\,d^4+60\,a^3\,b\,c\,d^3-170\,a^2\,b^2\,c^2\,d^2-900\,a\,b^3\,c^3\,d+2025\,b^4\,c^4\right)}{64\,c^2\,d^3}\right)\,\left(3\,a^2\,d^2+10\,a\,b\,c\,d-45\,b^2\,c^2\right)}{64\,{\left(-c\right)}^{7/4}\,d^{13/4}}}\right)\,\left(3\,a^2\,d^2+10\,a\,b\,c\,d-45\,b^2\,c^2\right)\,1{}\mathrm{i}}{32\,{\left(-c\right)}^{7/4}\,d^{13/4}}+\frac{\mathrm{atan}\left(\frac{\frac{\left(-\frac{\sqrt{x}\,\left(9\,a^4\,d^4+60\,a^3\,b\,c\,d^3-170\,a^2\,b^2\,c^2\,d^2-900\,a\,b^3\,c^3\,d+2025\,b^4\,c^4\right)}{64\,c^2\,d^3}+\frac{{\left(3\,a^2\,d^2+10\,a\,b\,c\,d-45\,b^2\,c^2\right)}^2\,1{}\mathrm{i}}{64\,{\left(-c\right)}^{7/4}\,d^{13/4}}\right)\,\left(3\,a^2\,d^2+10\,a\,b\,c\,d-45\,b^2\,c^2\right)}{64\,{\left(-c\right)}^{7/4}\,d^{13/4}}-\frac{\left(\frac{\sqrt{x}\,\left(9\,a^4\,d^4+60\,a^3\,b\,c\,d^3-170\,a^2\,b^2\,c^2\,d^2-900\,a\,b^3\,c^3\,d+2025\,b^4\,c^4\right)}{64\,c^2\,d^3}+\frac{{\left(3\,a^2\,d^2+10\,a\,b\,c\,d-45\,b^2\,c^2\right)}^2\,1{}\mathrm{i}}{64\,{\left(-c\right)}^{7/4}\,d^{13/4}}\right)\,\left(3\,a^2\,d^2+10\,a\,b\,c\,d-45\,b^2\,c^2\right)}{64\,{\left(-c\right)}^{7/4}\,d^{13/4}}}{\frac{\left(-\frac{\sqrt{x}\,\left(9\,a^4\,d^4+60\,a^3\,b\,c\,d^3-170\,a^2\,b^2\,c^2\,d^2-900\,a\,b^3\,c^3\,d+2025\,b^4\,c^4\right)}{64\,c^2\,d^3}+\frac{{\left(3\,a^2\,d^2+10\,a\,b\,c\,d-45\,b^2\,c^2\right)}^2\,1{}\mathrm{i}}{64\,{\left(-c\right)}^{7/4}\,d^{13/4}}\right)\,\left(3\,a^2\,d^2+10\,a\,b\,c\,d-45\,b^2\,c^2\right)\,1{}\mathrm{i}}{64\,{\left(-c\right)}^{7/4}\,d^{13/4}}+\frac{\left(\frac{\sqrt{x}\,\left(9\,a^4\,d^4+60\,a^3\,b\,c\,d^3-170\,a^2\,b^2\,c^2\,d^2-900\,a\,b^3\,c^3\,d+2025\,b^4\,c^4\right)}{64\,c^2\,d^3}+\frac{{\left(3\,a^2\,d^2+10\,a\,b\,c\,d-45\,b^2\,c^2\right)}^2\,1{}\mathrm{i}}{64\,{\left(-c\right)}^{7/4}\,d^{13/4}}\right)\,\left(3\,a^2\,d^2+10\,a\,b\,c\,d-45\,b^2\,c^2\right)\,1{}\mathrm{i}}{64\,{\left(-c\right)}^{7/4}\,d^{13/4}}}\right)\,\left(3\,a^2\,d^2+10\,a\,b\,c\,d-45\,b^2\,c^2\right)}{32\,{\left(-c\right)}^{7/4}\,d^{13/4}}","Not used",1,"(2*b^2*x^(1/2))/d^3 - (x^(1/2)*((3*a^2*d^2)/16 - (13*b^2*c^2)/16 + (5*a*b*c*d)/8) - (x^(5/2)*(a^2*d^3 + 17*b^2*c^2*d - 18*a*b*c*d^2))/(16*c))/(c^2*d^3 + d^5*x^4 + 2*c*d^4*x^2) + (atan(((((3*a^2*d^2 - 45*b^2*c^2 + 10*a*b*c*d)^2/(64*(-c)^(7/4)*d^(13/4)) - (x^(1/2)*(9*a^4*d^4 + 2025*b^4*c^4 - 170*a^2*b^2*c^2*d^2 - 900*a*b^3*c^3*d + 60*a^3*b*c*d^3))/(64*c^2*d^3))*(3*a^2*d^2 - 45*b^2*c^2 + 10*a*b*c*d)*1i)/(64*(-c)^(7/4)*d^(13/4)) - (((3*a^2*d^2 - 45*b^2*c^2 + 10*a*b*c*d)^2/(64*(-c)^(7/4)*d^(13/4)) + (x^(1/2)*(9*a^4*d^4 + 2025*b^4*c^4 - 170*a^2*b^2*c^2*d^2 - 900*a*b^3*c^3*d + 60*a^3*b*c*d^3))/(64*c^2*d^3))*(3*a^2*d^2 - 45*b^2*c^2 + 10*a*b*c*d)*1i)/(64*(-c)^(7/4)*d^(13/4)))/((((3*a^2*d^2 - 45*b^2*c^2 + 10*a*b*c*d)^2/(64*(-c)^(7/4)*d^(13/4)) - (x^(1/2)*(9*a^4*d^4 + 2025*b^4*c^4 - 170*a^2*b^2*c^2*d^2 - 900*a*b^3*c^3*d + 60*a^3*b*c*d^3))/(64*c^2*d^3))*(3*a^2*d^2 - 45*b^2*c^2 + 10*a*b*c*d))/(64*(-c)^(7/4)*d^(13/4)) + (((3*a^2*d^2 - 45*b^2*c^2 + 10*a*b*c*d)^2/(64*(-c)^(7/4)*d^(13/4)) + (x^(1/2)*(9*a^4*d^4 + 2025*b^4*c^4 - 170*a^2*b^2*c^2*d^2 - 900*a*b^3*c^3*d + 60*a^3*b*c*d^3))/(64*c^2*d^3))*(3*a^2*d^2 - 45*b^2*c^2 + 10*a*b*c*d))/(64*(-c)^(7/4)*d^(13/4))))*(3*a^2*d^2 - 45*b^2*c^2 + 10*a*b*c*d)*1i)/(32*(-c)^(7/4)*d^(13/4)) + (atan((((((3*a^2*d^2 - 45*b^2*c^2 + 10*a*b*c*d)^2*1i)/(64*(-c)^(7/4)*d^(13/4)) - (x^(1/2)*(9*a^4*d^4 + 2025*b^4*c^4 - 170*a^2*b^2*c^2*d^2 - 900*a*b^3*c^3*d + 60*a^3*b*c*d^3))/(64*c^2*d^3))*(3*a^2*d^2 - 45*b^2*c^2 + 10*a*b*c*d))/(64*(-c)^(7/4)*d^(13/4)) - ((((3*a^2*d^2 - 45*b^2*c^2 + 10*a*b*c*d)^2*1i)/(64*(-c)^(7/4)*d^(13/4)) + (x^(1/2)*(9*a^4*d^4 + 2025*b^4*c^4 - 170*a^2*b^2*c^2*d^2 - 900*a*b^3*c^3*d + 60*a^3*b*c*d^3))/(64*c^2*d^3))*(3*a^2*d^2 - 45*b^2*c^2 + 10*a*b*c*d))/(64*(-c)^(7/4)*d^(13/4)))/(((((3*a^2*d^2 - 45*b^2*c^2 + 10*a*b*c*d)^2*1i)/(64*(-c)^(7/4)*d^(13/4)) - (x^(1/2)*(9*a^4*d^4 + 2025*b^4*c^4 - 170*a^2*b^2*c^2*d^2 - 900*a*b^3*c^3*d + 60*a^3*b*c*d^3))/(64*c^2*d^3))*(3*a^2*d^2 - 45*b^2*c^2 + 10*a*b*c*d)*1i)/(64*(-c)^(7/4)*d^(13/4)) + ((((3*a^2*d^2 - 45*b^2*c^2 + 10*a*b*c*d)^2*1i)/(64*(-c)^(7/4)*d^(13/4)) + (x^(1/2)*(9*a^4*d^4 + 2025*b^4*c^4 - 170*a^2*b^2*c^2*d^2 - 900*a*b^3*c^3*d + 60*a^3*b*c*d^3))/(64*c^2*d^3))*(3*a^2*d^2 - 45*b^2*c^2 + 10*a*b*c*d)*1i)/(64*(-c)^(7/4)*d^(13/4))))*(3*a^2*d^2 - 45*b^2*c^2 + 10*a*b*c*d))/(32*(-c)^(7/4)*d^(13/4))","B"
436,1,184,364,0.395172,"\text{Not used}","int((x^(1/2)*(a + b*x^2)^2)/(c + d*x^2)^3,x)","\frac{\mathrm{atan}\left(\frac{d^{1/4}\,\sqrt{x}}{{\left(-c\right)}^{1/4}}\right)\,\left(5\,a^2\,d^2+6\,a\,b\,c\,d+21\,b^2\,c^2\right)}{32\,{\left(-c\right)}^{9/4}\,d^{11/4}}-\frac{\frac{x^{3/2}\,\left(-9\,a^2\,d^2+2\,a\,b\,c\,d+7\,b^2\,c^2\right)}{16\,c\,d^2}-\frac{x^{7/2}\,\left(5\,a^2\,d^2+6\,a\,b\,c\,d-11\,b^2\,c^2\right)}{16\,c^2\,d}}{c^2+2\,c\,d\,x^2+d^2\,x^4}-\frac{\mathrm{atanh}\left(\frac{d^{1/4}\,\sqrt{x}}{{\left(-c\right)}^{1/4}}\right)\,\left(5\,a^2\,d^2+6\,a\,b\,c\,d+21\,b^2\,c^2\right)}{32\,{\left(-c\right)}^{9/4}\,d^{11/4}}","Not used",1,"(atan((d^(1/4)*x^(1/2))/(-c)^(1/4))*(5*a^2*d^2 + 21*b^2*c^2 + 6*a*b*c*d))/(32*(-c)^(9/4)*d^(11/4)) - ((x^(3/2)*(7*b^2*c^2 - 9*a^2*d^2 + 2*a*b*c*d))/(16*c*d^2) - (x^(7/2)*(5*a^2*d^2 - 11*b^2*c^2 + 6*a*b*c*d))/(16*c^2*d))/(c^2 + d^2*x^4 + 2*c*d*x^2) - (atanh((d^(1/4)*x^(1/2))/(-c)^(1/4))*(5*a^2*d^2 + 21*b^2*c^2 + 6*a*b*c*d))/(32*(-c)^(9/4)*d^(11/4))","B"
437,1,1419,364,0.605509,"\text{Not used}","int((a + b*x^2)^2/(x^(1/2)*(c + d*x^2)^3),x)","-\frac{\frac{\sqrt{x}\,\left(-11\,a^2\,d^2+6\,a\,b\,c\,d+5\,b^2\,c^2\right)}{16\,c\,d^2}-\frac{x^{5/2}\,\left(7\,a^2\,d^2+2\,a\,b\,c\,d-9\,b^2\,c^2\right)}{16\,c^2\,d}}{c^2+2\,c\,d\,x^2+d^2\,x^4}-\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)}{64\,{\left(-c\right)}^{15/4}\,d^{9/4}}-\frac{\sqrt{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)}{64\,c^4\,d}\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{\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)}{64\,{\left(-c\right)}^{15/4}\,d^{9/4}}+\frac{\sqrt{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)}{64\,c^4\,d}\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{\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)}{64\,{\left(-c\right)}^{15/4}\,d^{9/4}}-\frac{\sqrt{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)}{64\,c^4\,d}\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}}+\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)}{64\,{\left(-c\right)}^{15/4}\,d^{9/4}}+\frac{\sqrt{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)}{64\,c^4\,d}\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}}}\right)\,\left(21\,a^2\,d^2+6\,a\,b\,c\,d+5\,b^2\,c^2\right)\,1{}\mathrm{i}}{32\,{\left(-c\right)}^{11/4}\,d^{9/4}}-\frac{\mathrm{atan}\left(\frac{\frac{\left(-\frac{\sqrt{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)}{64\,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}}{64\,{\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)}{64\,{\left(-c\right)}^{11/4}\,d^{9/4}}-\frac{\left(\frac{\sqrt{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)}{64\,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}}{64\,{\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)}{64\,{\left(-c\right)}^{11/4}\,d^{9/4}}}{\frac{\left(-\frac{\sqrt{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)}{64\,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}}{64\,{\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}}{64\,{\left(-c\right)}^{11/4}\,d^{9/4}}+\frac{\left(\frac{\sqrt{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)}{64\,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}}{64\,{\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}}{64\,{\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)}{32\,{\left(-c\right)}^{11/4}\,d^{9/4}}","Not used",1,"- ((x^(1/2)*(5*b^2*c^2 - 11*a^2*d^2 + 6*a*b*c*d))/(16*c*d^2) - (x^(5/2)*(7*a^2*d^2 - 9*b^2*c^2 + 2*a*b*c*d))/(16*c^2*d))/(c^2 + d^2*x^4 + 2*c*d*x^2) - (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))/(64*(-c)^(15/4)*d^(9/4)) - (x^(1/2)*(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))/(64*c^4*d))*(21*a^2*d^2 + 5*b^2*c^2 + 6*a*b*c*d)*1i)/(64*(-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))/(64*(-c)^(15/4)*d^(9/4)) + (x^(1/2)*(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))/(64*c^4*d))*(21*a^2*d^2 + 5*b^2*c^2 + 6*a*b*c*d)*1i)/(64*(-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))/(64*(-c)^(15/4)*d^(9/4)) - (x^(1/2)*(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))/(64*c^4*d))*(21*a^2*d^2 + 5*b^2*c^2 + 6*a*b*c*d))/(64*(-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))/(64*(-c)^(15/4)*d^(9/4)) + (x^(1/2)*(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))/(64*c^4*d))*(21*a^2*d^2 + 5*b^2*c^2 + 6*a*b*c*d))/(64*(-c)^(11/4)*d^(9/4))))*(21*a^2*d^2 + 5*b^2*c^2 + 6*a*b*c*d)*1i)/(32*(-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)/(64*(-c)^(15/4)*d^(9/4)) - (x^(1/2)*(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))/(64*c^4*d))*(21*a^2*d^2 + 5*b^2*c^2 + 6*a*b*c*d))/(64*(-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)/(64*(-c)^(15/4)*d^(9/4)) + (x^(1/2)*(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))/(64*c^4*d))*(21*a^2*d^2 + 5*b^2*c^2 + 6*a*b*c*d))/(64*(-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)/(64*(-c)^(15/4)*d^(9/4)) - (x^(1/2)*(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))/(64*c^4*d))*(21*a^2*d^2 + 5*b^2*c^2 + 6*a*b*c*d)*1i)/(64*(-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)/(64*(-c)^(15/4)*d^(9/4)) + (x^(1/2)*(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))/(64*c^4*d))*(21*a^2*d^2 + 5*b^2*c^2 + 6*a*b*c*d)*1i)/(64*(-c)^(11/4)*d^(9/4))))*(21*a^2*d^2 + 5*b^2*c^2 + 6*a*b*c*d))/(32*(-c)^(11/4)*d^(9/4))","B"
438,1,192,399,0.398593,"\text{Not used}","int((a + b*x^2)^2/(x^(3/2)*(c + d*x^2)^3),x)","\frac{\mathrm{atanh}\left(\frac{d^{1/4}\,\sqrt{x}}{{\left(-c\right)}^{1/4}}\right)\,\left(-45\,a^2\,d^2+10\,a\,b\,c\,d+3\,b^2\,c^2\right)}{32\,{\left(-c\right)}^{13/4}\,d^{7/4}}-\frac{\mathrm{atan}\left(\frac{d^{1/4}\,\sqrt{x}}{{\left(-c\right)}^{1/4}}\right)\,\left(-45\,a^2\,d^2+10\,a\,b\,c\,d+3\,b^2\,c^2\right)}{32\,{\left(-c\right)}^{13/4}\,d^{7/4}}-\frac{\frac{2\,a^2}{c}-\frac{x^4\,\left(-45\,a^2\,d^2+10\,a\,b\,c\,d+3\,b^2\,c^2\right)}{16\,c^3}+\frac{x^2\,\left(81\,a^2\,d^2-18\,a\,b\,c\,d+b^2\,c^2\right)}{16\,c^2\,d}}{c^2\,\sqrt{x}+d^2\,x^{9/2}+2\,c\,d\,x^{5/2}}","Not used",1,"(atanh((d^(1/4)*x^(1/2))/(-c)^(1/4))*(3*b^2*c^2 - 45*a^2*d^2 + 10*a*b*c*d))/(32*(-c)^(13/4)*d^(7/4)) - (atan((d^(1/4)*x^(1/2))/(-c)^(1/4))*(3*b^2*c^2 - 45*a^2*d^2 + 10*a*b*c*d))/(32*(-c)^(13/4)*d^(7/4)) - ((2*a^2)/c - (x^4*(3*b^2*c^2 - 45*a^2*d^2 + 10*a*b*c*d))/(16*c^3) + (x^2*(81*a^2*d^2 + b^2*c^2 - 18*a*b*c*d))/(16*c^2*d))/(c^2*x^(1/2) + d^2*x^(9/2) + 2*c*d*x^(5/2))","B"
439,1,1508,402,0.635165,"\text{Not used}","int((a + b*x^2)^2/(x^(5/2)*(c + d*x^2)^3),x)","-\frac{\frac{2\,a^2}{3\,c}-\frac{x^4\,\left(-77\,a^2\,d^2+42\,a\,b\,c\,d+3\,b^2\,c^2\right)}{48\,c^3}+\frac{x^2\,\left(121\,a^2\,d^2-66\,a\,b\,c\,d+9\,b^2\,c^2\right)}{48\,c^2\,d}}{c^2\,x^{3/2}+d^2\,x^{11/2}+2\,c\,d\,x^{7/2}}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\sqrt{x}\,\left(97140736\,a^4\,c^9\,d^{10}-105971712\,a^3\,b\,c^{10}\,d^9+21331968\,a^2\,b^2\,c^{11}\,d^8+4128768\,a\,b^3\,c^{12}\,d^7+147456\,b^4\,c^{13}\,d^6\right)-\frac{\left(-77\,a^2\,d^2+42\,a\,b\,c\,d+3\,b^2\,c^2\right)\,\left(-80740352\,a^2\,c^{13}\,d^9+44040192\,a\,b\,c^{14}\,d^8+3145728\,b^2\,c^{15}\,d^7\right)}{64\,{\left(-c\right)}^{15/4}\,d^{5/4}}\right)\,\left(-77\,a^2\,d^2+42\,a\,b\,c\,d+3\,b^2\,c^2\right)\,1{}\mathrm{i}}{64\,{\left(-c\right)}^{15/4}\,d^{5/4}}+\frac{\left(\sqrt{x}\,\left(97140736\,a^4\,c^9\,d^{10}-105971712\,a^3\,b\,c^{10}\,d^9+21331968\,a^2\,b^2\,c^{11}\,d^8+4128768\,a\,b^3\,c^{12}\,d^7+147456\,b^4\,c^{13}\,d^6\right)+\frac{\left(-77\,a^2\,d^2+42\,a\,b\,c\,d+3\,b^2\,c^2\right)\,\left(-80740352\,a^2\,c^{13}\,d^9+44040192\,a\,b\,c^{14}\,d^8+3145728\,b^2\,c^{15}\,d^7\right)}{64\,{\left(-c\right)}^{15/4}\,d^{5/4}}\right)\,\left(-77\,a^2\,d^2+42\,a\,b\,c\,d+3\,b^2\,c^2\right)\,1{}\mathrm{i}}{64\,{\left(-c\right)}^{15/4}\,d^{5/4}}}{\frac{\left(\sqrt{x}\,\left(97140736\,a^4\,c^9\,d^{10}-105971712\,a^3\,b\,c^{10}\,d^9+21331968\,a^2\,b^2\,c^{11}\,d^8+4128768\,a\,b^3\,c^{12}\,d^7+147456\,b^4\,c^{13}\,d^6\right)-\frac{\left(-77\,a^2\,d^2+42\,a\,b\,c\,d+3\,b^2\,c^2\right)\,\left(-80740352\,a^2\,c^{13}\,d^9+44040192\,a\,b\,c^{14}\,d^8+3145728\,b^2\,c^{15}\,d^7\right)}{64\,{\left(-c\right)}^{15/4}\,d^{5/4}}\right)\,\left(-77\,a^2\,d^2+42\,a\,b\,c\,d+3\,b^2\,c^2\right)}{64\,{\left(-c\right)}^{15/4}\,d^{5/4}}-\frac{\left(\sqrt{x}\,\left(97140736\,a^4\,c^9\,d^{10}-105971712\,a^3\,b\,c^{10}\,d^9+21331968\,a^2\,b^2\,c^{11}\,d^8+4128768\,a\,b^3\,c^{12}\,d^7+147456\,b^4\,c^{13}\,d^6\right)+\frac{\left(-77\,a^2\,d^2+42\,a\,b\,c\,d+3\,b^2\,c^2\right)\,\left(-80740352\,a^2\,c^{13}\,d^9+44040192\,a\,b\,c^{14}\,d^8+3145728\,b^2\,c^{15}\,d^7\right)}{64\,{\left(-c\right)}^{15/4}\,d^{5/4}}\right)\,\left(-77\,a^2\,d^2+42\,a\,b\,c\,d+3\,b^2\,c^2\right)}{64\,{\left(-c\right)}^{15/4}\,d^{5/4}}}\right)\,\left(-77\,a^2\,d^2+42\,a\,b\,c\,d+3\,b^2\,c^2\right)\,1{}\mathrm{i}}{32\,{\left(-c\right)}^{15/4}\,d^{5/4}}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\sqrt{x}\,\left(97140736\,a^4\,c^9\,d^{10}-105971712\,a^3\,b\,c^{10}\,d^9+21331968\,a^2\,b^2\,c^{11}\,d^8+4128768\,a\,b^3\,c^{12}\,d^7+147456\,b^4\,c^{13}\,d^6\right)-\frac{\left(-77\,a^2\,d^2+42\,a\,b\,c\,d+3\,b^2\,c^2\right)\,\left(-80740352\,a^2\,c^{13}\,d^9+44040192\,a\,b\,c^{14}\,d^8+3145728\,b^2\,c^{15}\,d^7\right)\,1{}\mathrm{i}}{64\,{\left(-c\right)}^{15/4}\,d^{5/4}}\right)\,\left(-77\,a^2\,d^2+42\,a\,b\,c\,d+3\,b^2\,c^2\right)}{64\,{\left(-c\right)}^{15/4}\,d^{5/4}}+\frac{\left(\sqrt{x}\,\left(97140736\,a^4\,c^9\,d^{10}-105971712\,a^3\,b\,c^{10}\,d^9+21331968\,a^2\,b^2\,c^{11}\,d^8+4128768\,a\,b^3\,c^{12}\,d^7+147456\,b^4\,c^{13}\,d^6\right)+\frac{\left(-77\,a^2\,d^2+42\,a\,b\,c\,d+3\,b^2\,c^2\right)\,\left(-80740352\,a^2\,c^{13}\,d^9+44040192\,a\,b\,c^{14}\,d^8+3145728\,b^2\,c^{15}\,d^7\right)\,1{}\mathrm{i}}{64\,{\left(-c\right)}^{15/4}\,d^{5/4}}\right)\,\left(-77\,a^2\,d^2+42\,a\,b\,c\,d+3\,b^2\,c^2\right)}{64\,{\left(-c\right)}^{15/4}\,d^{5/4}}}{\frac{\left(\sqrt{x}\,\left(97140736\,a^4\,c^9\,d^{10}-105971712\,a^3\,b\,c^{10}\,d^9+21331968\,a^2\,b^2\,c^{11}\,d^8+4128768\,a\,b^3\,c^{12}\,d^7+147456\,b^4\,c^{13}\,d^6\right)-\frac{\left(-77\,a^2\,d^2+42\,a\,b\,c\,d+3\,b^2\,c^2\right)\,\left(-80740352\,a^2\,c^{13}\,d^9+44040192\,a\,b\,c^{14}\,d^8+3145728\,b^2\,c^{15}\,d^7\right)\,1{}\mathrm{i}}{64\,{\left(-c\right)}^{15/4}\,d^{5/4}}\right)\,\left(-77\,a^2\,d^2+42\,a\,b\,c\,d+3\,b^2\,c^2\right)\,1{}\mathrm{i}}{64\,{\left(-c\right)}^{15/4}\,d^{5/4}}-\frac{\left(\sqrt{x}\,\left(97140736\,a^4\,c^9\,d^{10}-105971712\,a^3\,b\,c^{10}\,d^9+21331968\,a^2\,b^2\,c^{11}\,d^8+4128768\,a\,b^3\,c^{12}\,d^7+147456\,b^4\,c^{13}\,d^6\right)+\frac{\left(-77\,a^2\,d^2+42\,a\,b\,c\,d+3\,b^2\,c^2\right)\,\left(-80740352\,a^2\,c^{13}\,d^9+44040192\,a\,b\,c^{14}\,d^8+3145728\,b^2\,c^{15}\,d^7\right)\,1{}\mathrm{i}}{64\,{\left(-c\right)}^{15/4}\,d^{5/4}}\right)\,\left(-77\,a^2\,d^2+42\,a\,b\,c\,d+3\,b^2\,c^2\right)\,1{}\mathrm{i}}{64\,{\left(-c\right)}^{15/4}\,d^{5/4}}}\right)\,\left(-77\,a^2\,d^2+42\,a\,b\,c\,d+3\,b^2\,c^2\right)}{32\,{\left(-c\right)}^{15/4}\,d^{5/4}}","Not used",1,"(atan((((x^(1/2)*(97140736*a^4*c^9*d^10 + 147456*b^4*c^13*d^6 + 4128768*a*b^3*c^12*d^7 - 105971712*a^3*b*c^10*d^9 + 21331968*a^2*b^2*c^11*d^8) - ((3*b^2*c^2 - 77*a^2*d^2 + 42*a*b*c*d)*(3145728*b^2*c^15*d^7 - 80740352*a^2*c^13*d^9 + 44040192*a*b*c^14*d^8))/(64*(-c)^(15/4)*d^(5/4)))*(3*b^2*c^2 - 77*a^2*d^2 + 42*a*b*c*d)*1i)/(64*(-c)^(15/4)*d^(5/4)) + ((x^(1/2)*(97140736*a^4*c^9*d^10 + 147456*b^4*c^13*d^6 + 4128768*a*b^3*c^12*d^7 - 105971712*a^3*b*c^10*d^9 + 21331968*a^2*b^2*c^11*d^8) + ((3*b^2*c^2 - 77*a^2*d^2 + 42*a*b*c*d)*(3145728*b^2*c^15*d^7 - 80740352*a^2*c^13*d^9 + 44040192*a*b*c^14*d^8))/(64*(-c)^(15/4)*d^(5/4)))*(3*b^2*c^2 - 77*a^2*d^2 + 42*a*b*c*d)*1i)/(64*(-c)^(15/4)*d^(5/4)))/(((x^(1/2)*(97140736*a^4*c^9*d^10 + 147456*b^4*c^13*d^6 + 4128768*a*b^3*c^12*d^7 - 105971712*a^3*b*c^10*d^9 + 21331968*a^2*b^2*c^11*d^8) - ((3*b^2*c^2 - 77*a^2*d^2 + 42*a*b*c*d)*(3145728*b^2*c^15*d^7 - 80740352*a^2*c^13*d^9 + 44040192*a*b*c^14*d^8))/(64*(-c)^(15/4)*d^(5/4)))*(3*b^2*c^2 - 77*a^2*d^2 + 42*a*b*c*d))/(64*(-c)^(15/4)*d^(5/4)) - ((x^(1/2)*(97140736*a^4*c^9*d^10 + 147456*b^4*c^13*d^6 + 4128768*a*b^3*c^12*d^7 - 105971712*a^3*b*c^10*d^9 + 21331968*a^2*b^2*c^11*d^8) + ((3*b^2*c^2 - 77*a^2*d^2 + 42*a*b*c*d)*(3145728*b^2*c^15*d^7 - 80740352*a^2*c^13*d^9 + 44040192*a*b*c^14*d^8))/(64*(-c)^(15/4)*d^(5/4)))*(3*b^2*c^2 - 77*a^2*d^2 + 42*a*b*c*d))/(64*(-c)^(15/4)*d^(5/4))))*(3*b^2*c^2 - 77*a^2*d^2 + 42*a*b*c*d)*1i)/(32*(-c)^(15/4)*d^(5/4)) - ((2*a^2)/(3*c) - (x^4*(3*b^2*c^2 - 77*a^2*d^2 + 42*a*b*c*d))/(48*c^3) + (x^2*(121*a^2*d^2 + 9*b^2*c^2 - 66*a*b*c*d))/(48*c^2*d))/(c^2*x^(3/2) + d^2*x^(11/2) + 2*c*d*x^(7/2)) + (atan((((x^(1/2)*(97140736*a^4*c^9*d^10 + 147456*b^4*c^13*d^6 + 4128768*a*b^3*c^12*d^7 - 105971712*a^3*b*c^10*d^9 + 21331968*a^2*b^2*c^11*d^8) - ((3*b^2*c^2 - 77*a^2*d^2 + 42*a*b*c*d)*(3145728*b^2*c^15*d^7 - 80740352*a^2*c^13*d^9 + 44040192*a*b*c^14*d^8)*1i)/(64*(-c)^(15/4)*d^(5/4)))*(3*b^2*c^2 - 77*a^2*d^2 + 42*a*b*c*d))/(64*(-c)^(15/4)*d^(5/4)) + ((x^(1/2)*(97140736*a^4*c^9*d^10 + 147456*b^4*c^13*d^6 + 4128768*a*b^3*c^12*d^7 - 105971712*a^3*b*c^10*d^9 + 21331968*a^2*b^2*c^11*d^8) + ((3*b^2*c^2 - 77*a^2*d^2 + 42*a*b*c*d)*(3145728*b^2*c^15*d^7 - 80740352*a^2*c^13*d^9 + 44040192*a*b*c^14*d^8)*1i)/(64*(-c)^(15/4)*d^(5/4)))*(3*b^2*c^2 - 77*a^2*d^2 + 42*a*b*c*d))/(64*(-c)^(15/4)*d^(5/4)))/(((x^(1/2)*(97140736*a^4*c^9*d^10 + 147456*b^4*c^13*d^6 + 4128768*a*b^3*c^12*d^7 - 105971712*a^3*b*c^10*d^9 + 21331968*a^2*b^2*c^11*d^8) - ((3*b^2*c^2 - 77*a^2*d^2 + 42*a*b*c*d)*(3145728*b^2*c^15*d^7 - 80740352*a^2*c^13*d^9 + 44040192*a*b*c^14*d^8)*1i)/(64*(-c)^(15/4)*d^(5/4)))*(3*b^2*c^2 - 77*a^2*d^2 + 42*a*b*c*d)*1i)/(64*(-c)^(15/4)*d^(5/4)) - ((x^(1/2)*(97140736*a^4*c^9*d^10 + 147456*b^4*c^13*d^6 + 4128768*a*b^3*c^12*d^7 - 105971712*a^3*b*c^10*d^9 + 21331968*a^2*b^2*c^11*d^8) + ((3*b^2*c^2 - 77*a^2*d^2 + 42*a*b*c*d)*(3145728*b^2*c^15*d^7 - 80740352*a^2*c^13*d^9 + 44040192*a*b*c^14*d^8)*1i)/(64*(-c)^(15/4)*d^(5/4)))*(3*b^2*c^2 - 77*a^2*d^2 + 42*a*b*c*d)*1i)/(64*(-c)^(15/4)*d^(5/4))))*(3*b^2*c^2 - 77*a^2*d^2 + 42*a*b*c*d))/(32*(-c)^(15/4)*d^(5/4))","B"
440,1,208,439,0.236607,"\text{Not used}","int((a + b*x^2)^2/(x^(7/2)*(c + d*x^2)^3),x)","\frac{\frac{9\,x^4\,\left(117\,a^2\,d^2-90\,a\,b\,c\,d+5\,b^2\,c^2\right)}{80\,c^3}-\frac{2\,a^2}{5\,c}+\frac{2\,a\,x^2\,\left(13\,a\,d-10\,b\,c\right)}{5\,c^2}+\frac{d\,x^6\,\left(117\,a^2\,d^2-90\,a\,b\,c\,d+5\,b^2\,c^2\right)}{16\,c^4}}{c^2\,x^{5/2}+d^2\,x^{13/2}+2\,c\,d\,x^{9/2}}+\frac{\mathrm{atan}\left(\frac{d^{1/4}\,\sqrt{x}}{{\left(-c\right)}^{1/4}}\right)\,\left(117\,a^2\,d^2-90\,a\,b\,c\,d+5\,b^2\,c^2\right)}{32\,{\left(-c\right)}^{17/4}\,d^{3/4}}-\frac{\mathrm{atanh}\left(\frac{d^{1/4}\,\sqrt{x}}{{\left(-c\right)}^{1/4}}\right)\,\left(117\,a^2\,d^2-90\,a\,b\,c\,d+5\,b^2\,c^2\right)}{32\,{\left(-c\right)}^{17/4}\,d^{3/4}}","Not used",1,"((9*x^4*(117*a^2*d^2 + 5*b^2*c^2 - 90*a*b*c*d))/(80*c^3) - (2*a^2)/(5*c) + (2*a*x^2*(13*a*d - 10*b*c))/(5*c^2) + (d*x^6*(117*a^2*d^2 + 5*b^2*c^2 - 90*a*b*c*d))/(16*c^4))/(c^2*x^(5/2) + d^2*x^(13/2) + 2*c*d*x^(9/2)) + (atan((d^(1/4)*x^(1/2))/(-c)^(1/4))*(117*a^2*d^2 + 5*b^2*c^2 - 90*a*b*c*d))/(32*(-c)^(17/4)*d^(3/4)) - (atanh((d^(1/4)*x^(1/2))/(-c)^(1/4))*(117*a^2*d^2 + 5*b^2*c^2 - 90*a*b*c*d))/(32*(-c)^(17/4)*d^(3/4))","B"
441,1,634,328,0.370566,"\text{Not used}","int((x^(5/2)*(c + d*x^2)^3)/(a + b*x^2),x)","x^{3/2}\,\left(\frac{2\,c^3}{3\,b}-\frac{a\,\left(\frac{6\,c^2\,d}{b}+\frac{a\,\left(\frac{2\,a\,d^3}{b^2}-\frac{6\,c\,d^2}{b}\right)}{b}\right)}{3\,b}\right)-x^{11/2}\,\left(\frac{2\,a\,d^3}{11\,b^2}-\frac{6\,c\,d^2}{11\,b}\right)+x^{7/2}\,\left(\frac{6\,c^2\,d}{7\,b}+\frac{a\,\left(\frac{2\,a\,d^3}{b^2}-\frac{6\,c\,d^2}{b}\right)}{7\,b}\right)+\frac{2\,d^3\,x^{15/2}}{15\,b}+\frac{{\left(-a\right)}^{3/4}\,\mathrm{atan}\left(\frac{{\left(-a\right)}^{3/4}\,b^{1/4}\,\sqrt{x}\,{\left(a\,d-b\,c\right)}^3\,\left(a^9\,d^6-6\,a^8\,b\,c\,d^5+15\,a^7\,b^2\,c^2\,d^4-20\,a^6\,b^3\,c^3\,d^3+15\,a^5\,b^4\,c^4\,d^2-6\,a^4\,b^5\,c^5\,d+a^3\,b^6\,c^6\right)}{a^{13}\,d^9-9\,a^{12}\,b\,c\,d^8+36\,a^{11}\,b^2\,c^2\,d^7-84\,a^{10}\,b^3\,c^3\,d^6+126\,a^9\,b^4\,c^4\,d^5-126\,a^8\,b^5\,c^5\,d^4+84\,a^7\,b^6\,c^6\,d^3-36\,a^6\,b^7\,c^7\,d^2+9\,a^5\,b^8\,c^8\,d-a^4\,b^9\,c^9}\right)\,{\left(a\,d-b\,c\right)}^3}{b^{19/4}}+\frac{{\left(-a\right)}^{3/4}\,\mathrm{atan}\left(\frac{{\left(-a\right)}^{3/4}\,b^{1/4}\,\sqrt{x}\,{\left(a\,d-b\,c\right)}^3\,\left(a^9\,d^6-6\,a^8\,b\,c\,d^5+15\,a^7\,b^2\,c^2\,d^4-20\,a^6\,b^3\,c^3\,d^3+15\,a^5\,b^4\,c^4\,d^2-6\,a^4\,b^5\,c^5\,d+a^3\,b^6\,c^6\right)\,1{}\mathrm{i}}{a^{13}\,d^9-9\,a^{12}\,b\,c\,d^8+36\,a^{11}\,b^2\,c^2\,d^7-84\,a^{10}\,b^3\,c^3\,d^6+126\,a^9\,b^4\,c^4\,d^5-126\,a^8\,b^5\,c^5\,d^4+84\,a^7\,b^6\,c^6\,d^3-36\,a^6\,b^7\,c^7\,d^2+9\,a^5\,b^8\,c^8\,d-a^4\,b^9\,c^9}\right)\,{\left(a\,d-b\,c\right)}^3\,1{}\mathrm{i}}{b^{19/4}}","Not used",1,"x^(3/2)*((2*c^3)/(3*b) - (a*((6*c^2*d)/b + (a*((2*a*d^3)/b^2 - (6*c*d^2)/b))/b))/(3*b)) - x^(11/2)*((2*a*d^3)/(11*b^2) - (6*c*d^2)/(11*b)) + x^(7/2)*((6*c^2*d)/(7*b) + (a*((2*a*d^3)/b^2 - (6*c*d^2)/b))/(7*b)) + (2*d^3*x^(15/2))/(15*b) + ((-a)^(3/4)*atan(((-a)^(3/4)*b^(1/4)*x^(1/2)*(a*d - b*c)^3*(a^9*d^6 + a^3*b^6*c^6 - 6*a^4*b^5*c^5*d + 15*a^5*b^4*c^4*d^2 - 20*a^6*b^3*c^3*d^3 + 15*a^7*b^2*c^2*d^4 - 6*a^8*b*c*d^5))/(a^13*d^9 - a^4*b^9*c^9 + 9*a^5*b^8*c^8*d - 36*a^6*b^7*c^7*d^2 + 84*a^7*b^6*c^6*d^3 - 126*a^8*b^5*c^5*d^4 + 126*a^9*b^4*c^4*d^5 - 84*a^10*b^3*c^3*d^6 + 36*a^11*b^2*c^2*d^7 - 9*a^12*b*c*d^8))*(a*d - b*c)^3)/b^(19/4) + ((-a)^(3/4)*atan(((-a)^(3/4)*b^(1/4)*x^(1/2)*(a*d - b*c)^3*(a^9*d^6 + a^3*b^6*c^6 - 6*a^4*b^5*c^5*d + 15*a^5*b^4*c^4*d^2 - 20*a^6*b^3*c^3*d^3 + 15*a^7*b^2*c^2*d^4 - 6*a^8*b*c*d^5)*1i)/(a^13*d^9 - a^4*b^9*c^9 + 9*a^5*b^8*c^8*d - 36*a^6*b^7*c^7*d^2 + 84*a^7*b^6*c^6*d^3 - 126*a^8*b^5*c^5*d^4 + 126*a^9*b^4*c^4*d^5 - 84*a^10*b^3*c^3*d^6 + 36*a^11*b^2*c^2*d^7 - 9*a^12*b*c*d^8))*(a*d - b*c)^3*1i)/b^(19/4)","B"
442,1,1564,326,0.390811,"\text{Not used}","int((x^(3/2)*(c + d*x^2)^3)/(a + b*x^2),x)","\sqrt{x}\,\left(\frac{2\,c^3}{b}-\frac{a\,\left(\frac{6\,c^2\,d}{b}+\frac{a\,\left(\frac{2\,a\,d^3}{b^2}-\frac{6\,c\,d^2}{b}\right)}{b}\right)}{b}\right)-x^{9/2}\,\left(\frac{2\,a\,d^3}{9\,b^2}-\frac{2\,c\,d^2}{3\,b}\right)+x^{5/2}\,\left(\frac{6\,c^2\,d}{5\,b}+\frac{a\,\left(\frac{2\,a\,d^3}{b^2}-\frac{6\,c\,d^2}{b}\right)}{5\,b}\right)+\frac{2\,d^3\,x^{13/2}}{13\,b}+\frac{{\left(-a\right)}^{1/4}\,\mathrm{atan}\left(\frac{\frac{{\left(-a\right)}^{1/4}\,\left(\frac{16\,\sqrt{x}\,\left(a^8\,d^6-6\,a^7\,b\,c\,d^5+15\,a^6\,b^2\,c^2\,d^4-20\,a^5\,b^3\,c^3\,d^3+15\,a^4\,b^4\,c^4\,d^2-6\,a^3\,b^5\,c^5\,d+a^2\,b^6\,c^6\right)}{b^5}-\frac{16\,{\left(-a\right)}^{1/4}\,{\left(a\,d-b\,c\right)}^3\,\left(a^5\,d^3-3\,a^4\,b\,c\,d^2+3\,a^3\,b^2\,c^2\,d-a^2\,b^3\,c^3\right)}{b^{21/4}}\right)\,{\left(a\,d-b\,c\right)}^3\,1{}\mathrm{i}}{2\,b^{17/4}}+\frac{{\left(-a\right)}^{1/4}\,\left(\frac{16\,\sqrt{x}\,\left(a^8\,d^6-6\,a^7\,b\,c\,d^5+15\,a^6\,b^2\,c^2\,d^4-20\,a^5\,b^3\,c^3\,d^3+15\,a^4\,b^4\,c^4\,d^2-6\,a^3\,b^5\,c^5\,d+a^2\,b^6\,c^6\right)}{b^5}+\frac{16\,{\left(-a\right)}^{1/4}\,{\left(a\,d-b\,c\right)}^3\,\left(a^5\,d^3-3\,a^4\,b\,c\,d^2+3\,a^3\,b^2\,c^2\,d-a^2\,b^3\,c^3\right)}{b^{21/4}}\right)\,{\left(a\,d-b\,c\right)}^3\,1{}\mathrm{i}}{2\,b^{17/4}}}{\frac{{\left(-a\right)}^{1/4}\,\left(\frac{16\,\sqrt{x}\,\left(a^8\,d^6-6\,a^7\,b\,c\,d^5+15\,a^6\,b^2\,c^2\,d^4-20\,a^5\,b^3\,c^3\,d^3+15\,a^4\,b^4\,c^4\,d^2-6\,a^3\,b^5\,c^5\,d+a^2\,b^6\,c^6\right)}{b^5}-\frac{16\,{\left(-a\right)}^{1/4}\,{\left(a\,d-b\,c\right)}^3\,\left(a^5\,d^3-3\,a^4\,b\,c\,d^2+3\,a^3\,b^2\,c^2\,d-a^2\,b^3\,c^3\right)}{b^{21/4}}\right)\,{\left(a\,d-b\,c\right)}^3}{2\,b^{17/4}}-\frac{{\left(-a\right)}^{1/4}\,\left(\frac{16\,\sqrt{x}\,\left(a^8\,d^6-6\,a^7\,b\,c\,d^5+15\,a^6\,b^2\,c^2\,d^4-20\,a^5\,b^3\,c^3\,d^3+15\,a^4\,b^4\,c^4\,d^2-6\,a^3\,b^5\,c^5\,d+a^2\,b^6\,c^6\right)}{b^5}+\frac{16\,{\left(-a\right)}^{1/4}\,{\left(a\,d-b\,c\right)}^3\,\left(a^5\,d^3-3\,a^4\,b\,c\,d^2+3\,a^3\,b^2\,c^2\,d-a^2\,b^3\,c^3\right)}{b^{21/4}}\right)\,{\left(a\,d-b\,c\right)}^3}{2\,b^{17/4}}}\right)\,{\left(a\,d-b\,c\right)}^3\,1{}\mathrm{i}}{b^{17/4}}+\frac{{\left(-a\right)}^{1/4}\,\mathrm{atan}\left(\frac{\frac{{\left(-a\right)}^{1/4}\,\left(\frac{16\,\sqrt{x}\,\left(a^8\,d^6-6\,a^7\,b\,c\,d^5+15\,a^6\,b^2\,c^2\,d^4-20\,a^5\,b^3\,c^3\,d^3+15\,a^4\,b^4\,c^4\,d^2-6\,a^3\,b^5\,c^5\,d+a^2\,b^6\,c^6\right)}{b^5}-\frac{{\left(-a\right)}^{1/4}\,{\left(a\,d-b\,c\right)}^3\,\left(a^5\,d^3-3\,a^4\,b\,c\,d^2+3\,a^3\,b^2\,c^2\,d-a^2\,b^3\,c^3\right)\,16{}\mathrm{i}}{b^{21/4}}\right)\,{\left(a\,d-b\,c\right)}^3}{2\,b^{17/4}}+\frac{{\left(-a\right)}^{1/4}\,\left(\frac{16\,\sqrt{x}\,\left(a^8\,d^6-6\,a^7\,b\,c\,d^5+15\,a^6\,b^2\,c^2\,d^4-20\,a^5\,b^3\,c^3\,d^3+15\,a^4\,b^4\,c^4\,d^2-6\,a^3\,b^5\,c^5\,d+a^2\,b^6\,c^6\right)}{b^5}+\frac{{\left(-a\right)}^{1/4}\,{\left(a\,d-b\,c\right)}^3\,\left(a^5\,d^3-3\,a^4\,b\,c\,d^2+3\,a^3\,b^2\,c^2\,d-a^2\,b^3\,c^3\right)\,16{}\mathrm{i}}{b^{21/4}}\right)\,{\left(a\,d-b\,c\right)}^3}{2\,b^{17/4}}}{\frac{{\left(-a\right)}^{1/4}\,\left(\frac{16\,\sqrt{x}\,\left(a^8\,d^6-6\,a^7\,b\,c\,d^5+15\,a^6\,b^2\,c^2\,d^4-20\,a^5\,b^3\,c^3\,d^3+15\,a^4\,b^4\,c^4\,d^2-6\,a^3\,b^5\,c^5\,d+a^2\,b^6\,c^6\right)}{b^5}-\frac{{\left(-a\right)}^{1/4}\,{\left(a\,d-b\,c\right)}^3\,\left(a^5\,d^3-3\,a^4\,b\,c\,d^2+3\,a^3\,b^2\,c^2\,d-a^2\,b^3\,c^3\right)\,16{}\mathrm{i}}{b^{21/4}}\right)\,{\left(a\,d-b\,c\right)}^3\,1{}\mathrm{i}}{2\,b^{17/4}}-\frac{{\left(-a\right)}^{1/4}\,\left(\frac{16\,\sqrt{x}\,\left(a^8\,d^6-6\,a^7\,b\,c\,d^5+15\,a^6\,b^2\,c^2\,d^4-20\,a^5\,b^3\,c^3\,d^3+15\,a^4\,b^4\,c^4\,d^2-6\,a^3\,b^5\,c^5\,d+a^2\,b^6\,c^6\right)}{b^5}+\frac{{\left(-a\right)}^{1/4}\,{\left(a\,d-b\,c\right)}^3\,\left(a^5\,d^3-3\,a^4\,b\,c\,d^2+3\,a^3\,b^2\,c^2\,d-a^2\,b^3\,c^3\right)\,16{}\mathrm{i}}{b^{21/4}}\right)\,{\left(a\,d-b\,c\right)}^3\,1{}\mathrm{i}}{2\,b^{17/4}}}\right)\,{\left(a\,d-b\,c\right)}^3}{b^{17/4}}","Not used",1,"x^(1/2)*((2*c^3)/b - (a*((6*c^2*d)/b + (a*((2*a*d^3)/b^2 - (6*c*d^2)/b))/b))/b) - x^(9/2)*((2*a*d^3)/(9*b^2) - (2*c*d^2)/(3*b)) + x^(5/2)*((6*c^2*d)/(5*b) + (a*((2*a*d^3)/b^2 - (6*c*d^2)/b))/(5*b)) + (2*d^3*x^(13/2))/(13*b) + ((-a)^(1/4)*atan((((-a)^(1/4)*((16*x^(1/2)*(a^8*d^6 + a^2*b^6*c^6 - 6*a^3*b^5*c^5*d + 15*a^4*b^4*c^4*d^2 - 20*a^5*b^3*c^3*d^3 + 15*a^6*b^2*c^2*d^4 - 6*a^7*b*c*d^5))/b^5 - (16*(-a)^(1/4)*(a*d - b*c)^3*(a^5*d^3 - a^2*b^3*c^3 + 3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2))/b^(21/4))*(a*d - b*c)^3*1i)/(2*b^(17/4)) + ((-a)^(1/4)*((16*x^(1/2)*(a^8*d^6 + a^2*b^6*c^6 - 6*a^3*b^5*c^5*d + 15*a^4*b^4*c^4*d^2 - 20*a^5*b^3*c^3*d^3 + 15*a^6*b^2*c^2*d^4 - 6*a^7*b*c*d^5))/b^5 + (16*(-a)^(1/4)*(a*d - b*c)^3*(a^5*d^3 - a^2*b^3*c^3 + 3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2))/b^(21/4))*(a*d - b*c)^3*1i)/(2*b^(17/4)))/(((-a)^(1/4)*((16*x^(1/2)*(a^8*d^6 + a^2*b^6*c^6 - 6*a^3*b^5*c^5*d + 15*a^4*b^4*c^4*d^2 - 20*a^5*b^3*c^3*d^3 + 15*a^6*b^2*c^2*d^4 - 6*a^7*b*c*d^5))/b^5 - (16*(-a)^(1/4)*(a*d - b*c)^3*(a^5*d^3 - a^2*b^3*c^3 + 3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2))/b^(21/4))*(a*d - b*c)^3)/(2*b^(17/4)) - ((-a)^(1/4)*((16*x^(1/2)*(a^8*d^6 + a^2*b^6*c^6 - 6*a^3*b^5*c^5*d + 15*a^4*b^4*c^4*d^2 - 20*a^5*b^3*c^3*d^3 + 15*a^6*b^2*c^2*d^4 - 6*a^7*b*c*d^5))/b^5 + (16*(-a)^(1/4)*(a*d - b*c)^3*(a^5*d^3 - a^2*b^3*c^3 + 3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2))/b^(21/4))*(a*d - b*c)^3)/(2*b^(17/4))))*(a*d - b*c)^3*1i)/b^(17/4) + ((-a)^(1/4)*atan((((-a)^(1/4)*((16*x^(1/2)*(a^8*d^6 + a^2*b^6*c^6 - 6*a^3*b^5*c^5*d + 15*a^4*b^4*c^4*d^2 - 20*a^5*b^3*c^3*d^3 + 15*a^6*b^2*c^2*d^4 - 6*a^7*b*c*d^5))/b^5 - ((-a)^(1/4)*(a*d - b*c)^3*(a^5*d^3 - a^2*b^3*c^3 + 3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2)*16i)/b^(21/4))*(a*d - b*c)^3)/(2*b^(17/4)) + ((-a)^(1/4)*((16*x^(1/2)*(a^8*d^6 + a^2*b^6*c^6 - 6*a^3*b^5*c^5*d + 15*a^4*b^4*c^4*d^2 - 20*a^5*b^3*c^3*d^3 + 15*a^6*b^2*c^2*d^4 - 6*a^7*b*c*d^5))/b^5 + ((-a)^(1/4)*(a*d - b*c)^3*(a^5*d^3 - a^2*b^3*c^3 + 3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2)*16i)/b^(21/4))*(a*d - b*c)^3)/(2*b^(17/4)))/(((-a)^(1/4)*((16*x^(1/2)*(a^8*d^6 + a^2*b^6*c^6 - 6*a^3*b^5*c^5*d + 15*a^4*b^4*c^4*d^2 - 20*a^5*b^3*c^3*d^3 + 15*a^6*b^2*c^2*d^4 - 6*a^7*b*c*d^5))/b^5 - ((-a)^(1/4)*(a*d - b*c)^3*(a^5*d^3 - a^2*b^3*c^3 + 3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2)*16i)/b^(21/4))*(a*d - b*c)^3*1i)/(2*b^(17/4)) - ((-a)^(1/4)*((16*x^(1/2)*(a^8*d^6 + a^2*b^6*c^6 - 6*a^3*b^5*c^5*d + 15*a^4*b^4*c^4*d^2 - 20*a^5*b^3*c^3*d^3 + 15*a^6*b^2*c^2*d^4 - 6*a^7*b*c*d^5))/b^5 + ((-a)^(1/4)*(a*d - b*c)^3*(a^5*d^3 - a^2*b^3*c^3 + 3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2)*16i)/b^(21/4))*(a*d - b*c)^3*1i)/(2*b^(17/4))))*(a*d - b*c)^3)/b^(17/4)","B"
443,1,574,306,0.156658,"\text{Not used}","int((x^(1/2)*(c + d*x^2)^3)/(a + b*x^2),x)","x^{3/2}\,\left(\frac{2\,c^2\,d}{b}+\frac{a\,\left(\frac{2\,a\,d^3}{b^2}-\frac{6\,c\,d^2}{b}\right)}{3\,b}\right)-x^{7/2}\,\left(\frac{2\,a\,d^3}{7\,b^2}-\frac{6\,c\,d^2}{7\,b}\right)+\frac{2\,d^3\,x^{11/2}}{11\,b}-\frac{\mathrm{atan}\left(\frac{b^{1/4}\,\sqrt{x}\,{\left(a\,d-b\,c\right)}^3\,\left(a^7\,d^6-6\,a^6\,b\,c\,d^5+15\,a^5\,b^2\,c^2\,d^4-20\,a^4\,b^3\,c^3\,d^3+15\,a^3\,b^4\,c^4\,d^2-6\,a^2\,b^5\,c^5\,d+a\,b^6\,c^6\right)}{{\left(-a\right)}^{1/4}\,\left(a^{10}\,d^9-9\,a^9\,b\,c\,d^8+36\,a^8\,b^2\,c^2\,d^7-84\,a^7\,b^3\,c^3\,d^6+126\,a^6\,b^4\,c^4\,d^5-126\,a^5\,b^5\,c^5\,d^4+84\,a^4\,b^6\,c^6\,d^3-36\,a^3\,b^7\,c^7\,d^2+9\,a^2\,b^8\,c^8\,d-a\,b^9\,c^9\right)}\right)\,{\left(a\,d-b\,c\right)}^3}{{\left(-a\right)}^{1/4}\,b^{15/4}}-\frac{\mathrm{atan}\left(\frac{b^{1/4}\,\sqrt{x}\,{\left(a\,d-b\,c\right)}^3\,\left(a^7\,d^6-6\,a^6\,b\,c\,d^5+15\,a^5\,b^2\,c^2\,d^4-20\,a^4\,b^3\,c^3\,d^3+15\,a^3\,b^4\,c^4\,d^2-6\,a^2\,b^5\,c^5\,d+a\,b^6\,c^6\right)\,1{}\mathrm{i}}{{\left(-a\right)}^{1/4}\,\left(a^{10}\,d^9-9\,a^9\,b\,c\,d^8+36\,a^8\,b^2\,c^2\,d^7-84\,a^7\,b^3\,c^3\,d^6+126\,a^6\,b^4\,c^4\,d^5-126\,a^5\,b^5\,c^5\,d^4+84\,a^4\,b^6\,c^6\,d^3-36\,a^3\,b^7\,c^7\,d^2+9\,a^2\,b^8\,c^8\,d-a\,b^9\,c^9\right)}\right)\,{\left(a\,d-b\,c\right)}^3\,1{}\mathrm{i}}{{\left(-a\right)}^{1/4}\,b^{15/4}}","Not used",1,"x^(3/2)*((2*c^2*d)/b + (a*((2*a*d^3)/b^2 - (6*c*d^2)/b))/(3*b)) - x^(7/2)*((2*a*d^3)/(7*b^2) - (6*c*d^2)/(7*b)) + (2*d^3*x^(11/2))/(11*b) - (atan((b^(1/4)*x^(1/2)*(a*d - b*c)^3*(a^7*d^6 + a*b^6*c^6 - 6*a^2*b^5*c^5*d + 15*a^3*b^4*c^4*d^2 - 20*a^4*b^3*c^3*d^3 + 15*a^5*b^2*c^2*d^4 - 6*a^6*b*c*d^5))/((-a)^(1/4)*(a^10*d^9 - a*b^9*c^9 + 9*a^2*b^8*c^8*d - 36*a^3*b^7*c^7*d^2 + 84*a^4*b^6*c^6*d^3 - 126*a^5*b^5*c^5*d^4 + 126*a^6*b^4*c^4*d^5 - 84*a^7*b^3*c^3*d^6 + 36*a^8*b^2*c^2*d^7 - 9*a^9*b*c*d^8)))*(a*d - b*c)^3)/((-a)^(1/4)*b^(15/4)) - (atan((b^(1/4)*x^(1/2)*(a*d - b*c)^3*(a^7*d^6 + a*b^6*c^6 - 6*a^2*b^5*c^5*d + 15*a^3*b^4*c^4*d^2 - 20*a^4*b^3*c^3*d^3 + 15*a^5*b^2*c^2*d^4 - 6*a^6*b*c*d^5)*1i)/((-a)^(1/4)*(a^10*d^9 - a*b^9*c^9 + 9*a^2*b^8*c^8*d - 36*a^3*b^7*c^7*d^2 + 84*a^4*b^6*c^6*d^3 - 126*a^5*b^5*c^5*d^4 + 126*a^6*b^4*c^4*d^5 - 84*a^7*b^3*c^3*d^6 + 36*a^8*b^2*c^2*d^7 - 9*a^9*b*c*d^8)))*(a*d - b*c)^3*1i)/((-a)^(1/4)*b^(15/4))","B"
444,1,1460,304,0.377183,"\text{Not used}","int((c + d*x^2)^3/(x^(1/2)*(a + b*x^2)),x)","\sqrt{x}\,\left(\frac{6\,c^2\,d}{b}+\frac{a\,\left(\frac{2\,a\,d^3}{b^2}-\frac{6\,c\,d^2}{b}\right)}{b}\right)-x^{5/2}\,\left(\frac{2\,a\,d^3}{5\,b^2}-\frac{6\,c\,d^2}{5\,b}\right)+\frac{2\,d^3\,x^{9/2}}{9\,b}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\sqrt{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(16\,a^4\,d^3-48\,a^3\,b\,c\,d^2+48\,a^2\,b^2\,c^2\,d-16\,a\,b^3\,c^3\right)}{2\,{\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{8\,\sqrt{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(16\,a^4\,d^3-48\,a^3\,b\,c\,d^2+48\,a^2\,b^2\,c^2\,d-16\,a\,b^3\,c^3\right)}{2\,{\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{8\,\sqrt{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(16\,a^4\,d^3-48\,a^3\,b\,c\,d^2+48\,a^2\,b^2\,c^2\,d-16\,a\,b^3\,c^3\right)}{2\,{\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{8\,\sqrt{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(16\,a^4\,d^3-48\,a^3\,b\,c\,d^2+48\,a^2\,b^2\,c^2\,d-16\,a\,b^3\,c^3\right)}{2\,{\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}}{{\left(-a\right)}^{3/4}\,b^{13/4}}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{8\,\sqrt{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(16\,a^4\,d^3-48\,a^3\,b\,c\,d^2+48\,a^2\,b^2\,c^2\,d-16\,a\,b^3\,c^3\right)\,1{}\mathrm{i}}{2\,{\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{8\,\sqrt{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(16\,a^4\,d^3-48\,a^3\,b\,c\,d^2+48\,a^2\,b^2\,c^2\,d-16\,a\,b^3\,c^3\right)\,1{}\mathrm{i}}{2\,{\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{8\,\sqrt{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(16\,a^4\,d^3-48\,a^3\,b\,c\,d^2+48\,a^2\,b^2\,c^2\,d-16\,a\,b^3\,c^3\right)\,1{}\mathrm{i}}{2\,{\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{8\,\sqrt{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(16\,a^4\,d^3-48\,a^3\,b\,c\,d^2+48\,a^2\,b^2\,c^2\,d-16\,a\,b^3\,c^3\right)\,1{}\mathrm{i}}{2\,{\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}{{\left(-a\right)}^{3/4}\,b^{13/4}}","Not used",1,"x^(1/2)*((6*c^2*d)/b + (a*((2*a*d^3)/b^2 - (6*c*d^2)/b))/b) - x^(5/2)*((2*a*d^3)/(5*b^2) - (6*c*d^2)/(5*b)) + (2*d^3*x^(9/2))/(9*b) - (atan(((((8*x^(1/2)*(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*(16*a^4*d^3 - 16*a*b^3*c^3 + 48*a^2*b^2*c^2*d - 48*a^3*b*c*d^2))/(2*(-a)^(3/4)*b^(13/4)))*(a*d - b*c)^3*1i)/((-a)^(3/4)*b^(13/4)) + (((8*x^(1/2)*(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*(16*a^4*d^3 - 16*a*b^3*c^3 + 48*a^2*b^2*c^2*d - 48*a^3*b*c*d^2))/(2*(-a)^(3/4)*b^(13/4)))*(a*d - b*c)^3*1i)/((-a)^(3/4)*b^(13/4)))/((((8*x^(1/2)*(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*(16*a^4*d^3 - 16*a*b^3*c^3 + 48*a^2*b^2*c^2*d - 48*a^3*b*c*d^2))/(2*(-a)^(3/4)*b^(13/4)))*(a*d - b*c)^3)/((-a)^(3/4)*b^(13/4)) - (((8*x^(1/2)*(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*(16*a^4*d^3 - 16*a*b^3*c^3 + 48*a^2*b^2*c^2*d - 48*a^3*b*c*d^2))/(2*(-a)^(3/4)*b^(13/4)))*(a*d - b*c)^3)/((-a)^(3/4)*b^(13/4))))*(a*d - b*c)^3*1i)/((-a)^(3/4)*b^(13/4)) - (atan(((((8*x^(1/2)*(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*(16*a^4*d^3 - 16*a*b^3*c^3 + 48*a^2*b^2*c^2*d - 48*a^3*b*c*d^2)*1i)/(2*(-a)^(3/4)*b^(13/4)))*(a*d - b*c)^3)/((-a)^(3/4)*b^(13/4)) + (((8*x^(1/2)*(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*(16*a^4*d^3 - 16*a*b^3*c^3 + 48*a^2*b^2*c^2*d - 48*a^3*b*c*d^2)*1i)/(2*(-a)^(3/4)*b^(13/4)))*(a*d - b*c)^3)/((-a)^(3/4)*b^(13/4)))/((((8*x^(1/2)*(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*(16*a^4*d^3 - 16*a*b^3*c^3 + 48*a^2*b^2*c^2*d - 48*a^3*b*c*d^2)*1i)/(2*(-a)^(3/4)*b^(13/4)))*(a*d - b*c)^3*1i)/((-a)^(3/4)*b^(13/4)) - (((8*x^(1/2)*(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*(16*a^4*d^3 - 16*a*b^3*c^3 + 48*a^2*b^2*c^2*d - 48*a^3*b*c*d^2)*1i)/(2*(-a)^(3/4)*b^(13/4)))*(a*d - b*c)^3*1i)/((-a)^(3/4)*b^(13/4))))*(a*d - b*c)^3)/((-a)^(3/4)*b^(13/4))","B"
445,1,580,284,0.173169,"\text{Not used}","int((c + d*x^2)^3/(x^(3/2)*(a + b*x^2)),x)","\frac{2\,d^3\,x^{7/2}}{7\,b}-\frac{2\,c^3}{a\,\sqrt{x}}-x^{3/2}\,\left(\frac{2\,a\,d^3}{3\,b^2}-\frac{2\,c\,d^2}{b}\right)-\frac{\mathrm{atan}\left(\frac{\sqrt{x}\,{\left(a\,d-b\,c\right)}^3\,\left(16\,a^{10}\,b^8\,d^6-96\,a^9\,b^9\,c\,d^5+240\,a^8\,b^{10}\,c^2\,d^4-320\,a^7\,b^{11}\,c^3\,d^3+240\,a^6\,b^{12}\,c^4\,d^2-96\,a^5\,b^{13}\,c^5\,d+16\,a^4\,b^{14}\,c^6\right)}{{\left(-a\right)}^{5/4}\,b^{11/4}\,\left(-16\,a^{12}\,b^5\,d^9+144\,a^{11}\,b^6\,c\,d^8-576\,a^{10}\,b^7\,c^2\,d^7+1344\,a^9\,b^8\,c^3\,d^6-2016\,a^8\,b^9\,c^4\,d^5+2016\,a^7\,b^{10}\,c^5\,d^4-1344\,a^6\,b^{11}\,c^6\,d^3+576\,a^5\,b^{12}\,c^7\,d^2-144\,a^4\,b^{13}\,c^8\,d+16\,a^3\,b^{14}\,c^9\right)}\right)\,{\left(a\,d-b\,c\right)}^3}{{\left(-a\right)}^{5/4}\,b^{11/4}}-\frac{\mathrm{atan}\left(\frac{\sqrt{x}\,{\left(a\,d-b\,c\right)}^3\,\left(16\,a^{10}\,b^8\,d^6-96\,a^9\,b^9\,c\,d^5+240\,a^8\,b^{10}\,c^2\,d^4-320\,a^7\,b^{11}\,c^3\,d^3+240\,a^6\,b^{12}\,c^4\,d^2-96\,a^5\,b^{13}\,c^5\,d+16\,a^4\,b^{14}\,c^6\right)\,1{}\mathrm{i}}{{\left(-a\right)}^{5/4}\,b^{11/4}\,\left(-16\,a^{12}\,b^5\,d^9+144\,a^{11}\,b^6\,c\,d^8-576\,a^{10}\,b^7\,c^2\,d^7+1344\,a^9\,b^8\,c^3\,d^6-2016\,a^8\,b^9\,c^4\,d^5+2016\,a^7\,b^{10}\,c^5\,d^4-1344\,a^6\,b^{11}\,c^6\,d^3+576\,a^5\,b^{12}\,c^7\,d^2-144\,a^4\,b^{13}\,c^8\,d+16\,a^3\,b^{14}\,c^9\right)}\right)\,{\left(a\,d-b\,c\right)}^3\,1{}\mathrm{i}}{{\left(-a\right)}^{5/4}\,b^{11/4}}","Not used",1,"(2*d^3*x^(7/2))/(7*b) - (2*c^3)/(a*x^(1/2)) - x^(3/2)*((2*a*d^3)/(3*b^2) - (2*c*d^2)/b) - (atan((x^(1/2)*(a*d - b*c)^3*(16*a^4*b^14*c^6 + 16*a^10*b^8*d^6 - 96*a^5*b^13*c^5*d - 96*a^9*b^9*c*d^5 + 240*a^6*b^12*c^4*d^2 - 320*a^7*b^11*c^3*d^3 + 240*a^8*b^10*c^2*d^4))/((-a)^(5/4)*b^(11/4)*(16*a^3*b^14*c^9 - 16*a^12*b^5*d^9 - 144*a^4*b^13*c^8*d + 144*a^11*b^6*c*d^8 + 576*a^5*b^12*c^7*d^2 - 1344*a^6*b^11*c^6*d^3 + 2016*a^7*b^10*c^5*d^4 - 2016*a^8*b^9*c^4*d^5 + 1344*a^9*b^8*c^3*d^6 - 576*a^10*b^7*c^2*d^7)))*(a*d - b*c)^3)/((-a)^(5/4)*b^(11/4)) - (atan((x^(1/2)*(a*d - b*c)^3*(16*a^4*b^14*c^6 + 16*a^10*b^8*d^6 - 96*a^5*b^13*c^5*d - 96*a^9*b^9*c*d^5 + 240*a^6*b^12*c^4*d^2 - 320*a^7*b^11*c^3*d^3 + 240*a^8*b^10*c^2*d^4)*1i)/((-a)^(5/4)*b^(11/4)*(16*a^3*b^14*c^9 - 16*a^12*b^5*d^9 - 144*a^4*b^13*c^8*d + 144*a^11*b^6*c*d^8 + 576*a^5*b^12*c^7*d^2 - 1344*a^6*b^11*c^6*d^3 + 2016*a^7*b^10*c^5*d^4 - 2016*a^8*b^9*c^4*d^5 + 1344*a^9*b^8*c^3*d^6 - 576*a^10*b^7*c^2*d^7)))*(a*d - b*c)^3*1i)/((-a)^(5/4)*b^(11/4))","B"
446,1,1561,284,0.223012,"\text{Not used}","int((c + d*x^2)^3/(x^(5/2)*(a + b*x^2)),x)","\frac{2\,d^3\,x^{5/2}}{5\,b}-\frac{2\,c^3}{3\,a\,x^{3/2}}-\sqrt{x}\,\left(\frac{2\,a\,d^3}{b^2}-\frac{6\,c\,d^2}{b}\right)-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\sqrt{x}\,\left(16\,a^9\,b^9\,d^6-96\,a^8\,b^{10}\,c\,d^5+240\,a^7\,b^{11}\,c^2\,d^4-320\,a^6\,b^{12}\,c^3\,d^3+240\,a^5\,b^{13}\,c^4\,d^2-96\,a^4\,b^{14}\,c^5\,d+16\,a^3\,b^{15}\,c^6\right)}{2}-\frac{{\left(a\,d-b\,c\right)}^3\,\left(-16\,a^8\,b^{11}\,d^3+48\,a^7\,b^{12}\,c\,d^2-48\,a^6\,b^{13}\,c^2\,d+16\,a^5\,b^{14}\,c^3\right)}{2\,{\left(-a\right)}^{7/4}\,b^{9/4}}\right)\,{\left(a\,d-b\,c\right)}^3\,1{}\mathrm{i}}{{\left(-a\right)}^{7/4}\,b^{9/4}}+\frac{\left(\frac{\sqrt{x}\,\left(16\,a^9\,b^9\,d^6-96\,a^8\,b^{10}\,c\,d^5+240\,a^7\,b^{11}\,c^2\,d^4-320\,a^6\,b^{12}\,c^3\,d^3+240\,a^5\,b^{13}\,c^4\,d^2-96\,a^4\,b^{14}\,c^5\,d+16\,a^3\,b^{15}\,c^6\right)}{2}+\frac{{\left(a\,d-b\,c\right)}^3\,\left(-16\,a^8\,b^{11}\,d^3+48\,a^7\,b^{12}\,c\,d^2-48\,a^6\,b^{13}\,c^2\,d+16\,a^5\,b^{14}\,c^3\right)}{2\,{\left(-a\right)}^{7/4}\,b^{9/4}}\right)\,{\left(a\,d-b\,c\right)}^3\,1{}\mathrm{i}}{{\left(-a\right)}^{7/4}\,b^{9/4}}}{\frac{\left(\frac{\sqrt{x}\,\left(16\,a^9\,b^9\,d^6-96\,a^8\,b^{10}\,c\,d^5+240\,a^7\,b^{11}\,c^2\,d^4-320\,a^6\,b^{12}\,c^3\,d^3+240\,a^5\,b^{13}\,c^4\,d^2-96\,a^4\,b^{14}\,c^5\,d+16\,a^3\,b^{15}\,c^6\right)}{2}-\frac{{\left(a\,d-b\,c\right)}^3\,\left(-16\,a^8\,b^{11}\,d^3+48\,a^7\,b^{12}\,c\,d^2-48\,a^6\,b^{13}\,c^2\,d+16\,a^5\,b^{14}\,c^3\right)}{2\,{\left(-a\right)}^{7/4}\,b^{9/4}}\right)\,{\left(a\,d-b\,c\right)}^3}{{\left(-a\right)}^{7/4}\,b^{9/4}}-\frac{\left(\frac{\sqrt{x}\,\left(16\,a^9\,b^9\,d^6-96\,a^8\,b^{10}\,c\,d^5+240\,a^7\,b^{11}\,c^2\,d^4-320\,a^6\,b^{12}\,c^3\,d^3+240\,a^5\,b^{13}\,c^4\,d^2-96\,a^4\,b^{14}\,c^5\,d+16\,a^3\,b^{15}\,c^6\right)}{2}+\frac{{\left(a\,d-b\,c\right)}^3\,\left(-16\,a^8\,b^{11}\,d^3+48\,a^7\,b^{12}\,c\,d^2-48\,a^6\,b^{13}\,c^2\,d+16\,a^5\,b^{14}\,c^3\right)}{2\,{\left(-a\right)}^{7/4}\,b^{9/4}}\right)\,{\left(a\,d-b\,c\right)}^3}{{\left(-a\right)}^{7/4}\,b^{9/4}}}\right)\,{\left(a\,d-b\,c\right)}^3\,1{}\mathrm{i}}{{\left(-a\right)}^{7/4}\,b^{9/4}}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\sqrt{x}\,\left(16\,a^9\,b^9\,d^6-96\,a^8\,b^{10}\,c\,d^5+240\,a^7\,b^{11}\,c^2\,d^4-320\,a^6\,b^{12}\,c^3\,d^3+240\,a^5\,b^{13}\,c^4\,d^2-96\,a^4\,b^{14}\,c^5\,d+16\,a^3\,b^{15}\,c^6\right)}{2}-\frac{{\left(a\,d-b\,c\right)}^3\,\left(-16\,a^8\,b^{11}\,d^3+48\,a^7\,b^{12}\,c\,d^2-48\,a^6\,b^{13}\,c^2\,d+16\,a^5\,b^{14}\,c^3\right)\,1{}\mathrm{i}}{2\,{\left(-a\right)}^{7/4}\,b^{9/4}}\right)\,{\left(a\,d-b\,c\right)}^3}{{\left(-a\right)}^{7/4}\,b^{9/4}}+\frac{\left(\frac{\sqrt{x}\,\left(16\,a^9\,b^9\,d^6-96\,a^8\,b^{10}\,c\,d^5+240\,a^7\,b^{11}\,c^2\,d^4-320\,a^6\,b^{12}\,c^3\,d^3+240\,a^5\,b^{13}\,c^4\,d^2-96\,a^4\,b^{14}\,c^5\,d+16\,a^3\,b^{15}\,c^6\right)}{2}+\frac{{\left(a\,d-b\,c\right)}^3\,\left(-16\,a^8\,b^{11}\,d^3+48\,a^7\,b^{12}\,c\,d^2-48\,a^6\,b^{13}\,c^2\,d+16\,a^5\,b^{14}\,c^3\right)\,1{}\mathrm{i}}{2\,{\left(-a\right)}^{7/4}\,b^{9/4}}\right)\,{\left(a\,d-b\,c\right)}^3}{{\left(-a\right)}^{7/4}\,b^{9/4}}}{\frac{\left(\frac{\sqrt{x}\,\left(16\,a^9\,b^9\,d^6-96\,a^8\,b^{10}\,c\,d^5+240\,a^7\,b^{11}\,c^2\,d^4-320\,a^6\,b^{12}\,c^3\,d^3+240\,a^5\,b^{13}\,c^4\,d^2-96\,a^4\,b^{14}\,c^5\,d+16\,a^3\,b^{15}\,c^6\right)}{2}-\frac{{\left(a\,d-b\,c\right)}^3\,\left(-16\,a^8\,b^{11}\,d^3+48\,a^7\,b^{12}\,c\,d^2-48\,a^6\,b^{13}\,c^2\,d+16\,a^5\,b^{14}\,c^3\right)\,1{}\mathrm{i}}{2\,{\left(-a\right)}^{7/4}\,b^{9/4}}\right)\,{\left(a\,d-b\,c\right)}^3\,1{}\mathrm{i}}{{\left(-a\right)}^{7/4}\,b^{9/4}}-\frac{\left(\frac{\sqrt{x}\,\left(16\,a^9\,b^9\,d^6-96\,a^8\,b^{10}\,c\,d^5+240\,a^7\,b^{11}\,c^2\,d^4-320\,a^6\,b^{12}\,c^3\,d^3+240\,a^5\,b^{13}\,c^4\,d^2-96\,a^4\,b^{14}\,c^5\,d+16\,a^3\,b^{15}\,c^6\right)}{2}+\frac{{\left(a\,d-b\,c\right)}^3\,\left(-16\,a^8\,b^{11}\,d^3+48\,a^7\,b^{12}\,c\,d^2-48\,a^6\,b^{13}\,c^2\,d+16\,a^5\,b^{14}\,c^3\right)\,1{}\mathrm{i}}{2\,{\left(-a\right)}^{7/4}\,b^{9/4}}\right)\,{\left(a\,d-b\,c\right)}^3\,1{}\mathrm{i}}{{\left(-a\right)}^{7/4}\,b^{9/4}}}\right)\,{\left(a\,d-b\,c\right)}^3}{{\left(-a\right)}^{7/4}\,b^{9/4}}","Not used",1,"(2*d^3*x^(5/2))/(5*b) - (2*c^3)/(3*a*x^(3/2)) - x^(1/2)*((2*a*d^3)/b^2 - (6*c*d^2)/b) - (atan(((((x^(1/2)*(16*a^3*b^15*c^6 + 16*a^9*b^9*d^6 - 96*a^4*b^14*c^5*d - 96*a^8*b^10*c*d^5 + 240*a^5*b^13*c^4*d^2 - 320*a^6*b^12*c^3*d^3 + 240*a^7*b^11*c^2*d^4))/2 - ((a*d - b*c)^3*(16*a^5*b^14*c^3 - 16*a^8*b^11*d^3 - 48*a^6*b^13*c^2*d + 48*a^7*b^12*c*d^2))/(2*(-a)^(7/4)*b^(9/4)))*(a*d - b*c)^3*1i)/((-a)^(7/4)*b^(9/4)) + (((x^(1/2)*(16*a^3*b^15*c^6 + 16*a^9*b^9*d^6 - 96*a^4*b^14*c^5*d - 96*a^8*b^10*c*d^5 + 240*a^5*b^13*c^4*d^2 - 320*a^6*b^12*c^3*d^3 + 240*a^7*b^11*c^2*d^4))/2 + ((a*d - b*c)^3*(16*a^5*b^14*c^3 - 16*a^8*b^11*d^3 - 48*a^6*b^13*c^2*d + 48*a^7*b^12*c*d^2))/(2*(-a)^(7/4)*b^(9/4)))*(a*d - b*c)^3*1i)/((-a)^(7/4)*b^(9/4)))/((((x^(1/2)*(16*a^3*b^15*c^6 + 16*a^9*b^9*d^6 - 96*a^4*b^14*c^5*d - 96*a^8*b^10*c*d^5 + 240*a^5*b^13*c^4*d^2 - 320*a^6*b^12*c^3*d^3 + 240*a^7*b^11*c^2*d^4))/2 - ((a*d - b*c)^3*(16*a^5*b^14*c^3 - 16*a^8*b^11*d^3 - 48*a^6*b^13*c^2*d + 48*a^7*b^12*c*d^2))/(2*(-a)^(7/4)*b^(9/4)))*(a*d - b*c)^3)/((-a)^(7/4)*b^(9/4)) - (((x^(1/2)*(16*a^3*b^15*c^6 + 16*a^9*b^9*d^6 - 96*a^4*b^14*c^5*d - 96*a^8*b^10*c*d^5 + 240*a^5*b^13*c^4*d^2 - 320*a^6*b^12*c^3*d^3 + 240*a^7*b^11*c^2*d^4))/2 + ((a*d - b*c)^3*(16*a^5*b^14*c^3 - 16*a^8*b^11*d^3 - 48*a^6*b^13*c^2*d + 48*a^7*b^12*c*d^2))/(2*(-a)^(7/4)*b^(9/4)))*(a*d - b*c)^3)/((-a)^(7/4)*b^(9/4))))*(a*d - b*c)^3*1i)/((-a)^(7/4)*b^(9/4)) - (atan(((((x^(1/2)*(16*a^3*b^15*c^6 + 16*a^9*b^9*d^6 - 96*a^4*b^14*c^5*d - 96*a^8*b^10*c*d^5 + 240*a^5*b^13*c^4*d^2 - 320*a^6*b^12*c^3*d^3 + 240*a^7*b^11*c^2*d^4))/2 - ((a*d - b*c)^3*(16*a^5*b^14*c^3 - 16*a^8*b^11*d^3 - 48*a^6*b^13*c^2*d + 48*a^7*b^12*c*d^2)*1i)/(2*(-a)^(7/4)*b^(9/4)))*(a*d - b*c)^3)/((-a)^(7/4)*b^(9/4)) + (((x^(1/2)*(16*a^3*b^15*c^6 + 16*a^9*b^9*d^6 - 96*a^4*b^14*c^5*d - 96*a^8*b^10*c*d^5 + 240*a^5*b^13*c^4*d^2 - 320*a^6*b^12*c^3*d^3 + 240*a^7*b^11*c^2*d^4))/2 + ((a*d - b*c)^3*(16*a^5*b^14*c^3 - 16*a^8*b^11*d^3 - 48*a^6*b^13*c^2*d + 48*a^7*b^12*c*d^2)*1i)/(2*(-a)^(7/4)*b^(9/4)))*(a*d - b*c)^3)/((-a)^(7/4)*b^(9/4)))/((((x^(1/2)*(16*a^3*b^15*c^6 + 16*a^9*b^9*d^6 - 96*a^4*b^14*c^5*d - 96*a^8*b^10*c*d^5 + 240*a^5*b^13*c^4*d^2 - 320*a^6*b^12*c^3*d^3 + 240*a^7*b^11*c^2*d^4))/2 - ((a*d - b*c)^3*(16*a^5*b^14*c^3 - 16*a^8*b^11*d^3 - 48*a^6*b^13*c^2*d + 48*a^7*b^12*c*d^2)*1i)/(2*(-a)^(7/4)*b^(9/4)))*(a*d - b*c)^3*1i)/((-a)^(7/4)*b^(9/4)) - (((x^(1/2)*(16*a^3*b^15*c^6 + 16*a^9*b^9*d^6 - 96*a^4*b^14*c^5*d - 96*a^8*b^10*c*d^5 + 240*a^5*b^13*c^4*d^2 - 320*a^6*b^12*c^3*d^3 + 240*a^7*b^11*c^2*d^4))/2 + ((a*d - b*c)^3*(16*a^5*b^14*c^3 - 16*a^8*b^11*d^3 - 48*a^6*b^13*c^2*d + 48*a^7*b^12*c*d^2)*1i)/(2*(-a)^(7/4)*b^(9/4)))*(a*d - b*c)^3*1i)/((-a)^(7/4)*b^(9/4))))*(a*d - b*c)^3)/((-a)^(7/4)*b^(9/4))","B"
447,1,583,283,0.366780,"\text{Not used}","int((c + d*x^2)^3/(x^(7/2)*(a + b*x^2)),x)","\frac{2\,d^3\,x^{3/2}}{3\,b}-\frac{\frac{2\,b\,c^3}{5\,a}+\frac{2\,b\,c^2\,x^2\,\left(3\,a\,d-b\,c\right)}{a^2}}{b\,x^{5/2}}+\frac{\mathrm{atan}\left(\frac{\sqrt{x}\,{\left(a\,d-b\,c\right)}^3\,\left(16\,a^{13}\,b^5\,d^6-96\,a^{12}\,b^6\,c\,d^5+240\,a^{11}\,b^7\,c^2\,d^4-320\,a^{10}\,b^8\,c^3\,d^3+240\,a^9\,b^9\,c^4\,d^2-96\,a^8\,b^{10}\,c^5\,d+16\,a^7\,b^{11}\,c^6\right)}{{\left(-a\right)}^{9/4}\,b^{7/4}\,\left(-16\,a^{14}\,b^3\,d^9+144\,a^{13}\,b^4\,c\,d^8-576\,a^{12}\,b^5\,c^2\,d^7+1344\,a^{11}\,b^6\,c^3\,d^6-2016\,a^{10}\,b^7\,c^4\,d^5+2016\,a^9\,b^8\,c^5\,d^4-1344\,a^8\,b^9\,c^6\,d^3+576\,a^7\,b^{10}\,c^7\,d^2-144\,a^6\,b^{11}\,c^8\,d+16\,a^5\,b^{12}\,c^9\right)}\right)\,{\left(a\,d-b\,c\right)}^3}{{\left(-a\right)}^{9/4}\,b^{7/4}}+\frac{\mathrm{atan}\left(\frac{\sqrt{x}\,{\left(a\,d-b\,c\right)}^3\,\left(16\,a^{13}\,b^5\,d^6-96\,a^{12}\,b^6\,c\,d^5+240\,a^{11}\,b^7\,c^2\,d^4-320\,a^{10}\,b^8\,c^3\,d^3+240\,a^9\,b^9\,c^4\,d^2-96\,a^8\,b^{10}\,c^5\,d+16\,a^7\,b^{11}\,c^6\right)\,1{}\mathrm{i}}{{\left(-a\right)}^{9/4}\,b^{7/4}\,\left(-16\,a^{14}\,b^3\,d^9+144\,a^{13}\,b^4\,c\,d^8-576\,a^{12}\,b^5\,c^2\,d^7+1344\,a^{11}\,b^6\,c^3\,d^6-2016\,a^{10}\,b^7\,c^4\,d^5+2016\,a^9\,b^8\,c^5\,d^4-1344\,a^8\,b^9\,c^6\,d^3+576\,a^7\,b^{10}\,c^7\,d^2-144\,a^6\,b^{11}\,c^8\,d+16\,a^5\,b^{12}\,c^9\right)}\right)\,{\left(a\,d-b\,c\right)}^3\,1{}\mathrm{i}}{{\left(-a\right)}^{9/4}\,b^{7/4}}","Not used",1,"(2*d^3*x^(3/2))/(3*b) - ((2*b*c^3)/(5*a) + (2*b*c^2*x^2*(3*a*d - b*c))/a^2)/(b*x^(5/2)) + (atan((x^(1/2)*(a*d - b*c)^3*(16*a^7*b^11*c^6 + 16*a^13*b^5*d^6 - 96*a^8*b^10*c^5*d - 96*a^12*b^6*c*d^5 + 240*a^9*b^9*c^4*d^2 - 320*a^10*b^8*c^3*d^3 + 240*a^11*b^7*c^2*d^4))/((-a)^(9/4)*b^(7/4)*(16*a^5*b^12*c^9 - 16*a^14*b^3*d^9 - 144*a^6*b^11*c^8*d + 144*a^13*b^4*c*d^8 + 576*a^7*b^10*c^7*d^2 - 1344*a^8*b^9*c^6*d^3 + 2016*a^9*b^8*c^5*d^4 - 2016*a^10*b^7*c^4*d^5 + 1344*a^11*b^6*c^3*d^6 - 576*a^12*b^5*c^2*d^7)))*(a*d - b*c)^3)/((-a)^(9/4)*b^(7/4)) + (atan((x^(1/2)*(a*d - b*c)^3*(16*a^7*b^11*c^6 + 16*a^13*b^5*d^6 - 96*a^8*b^10*c^5*d - 96*a^12*b^6*c*d^5 + 240*a^9*b^9*c^4*d^2 - 320*a^10*b^8*c^3*d^3 + 240*a^11*b^7*c^2*d^4)*1i)/((-a)^(9/4)*b^(7/4)*(16*a^5*b^12*c^9 - 16*a^14*b^3*d^9 - 144*a^6*b^11*c^8*d + 144*a^13*b^4*c*d^8 + 576*a^7*b^10*c^7*d^2 - 1344*a^8*b^9*c^6*d^3 + 2016*a^9*b^8*c^5*d^4 - 2016*a^10*b^7*c^4*d^5 + 1344*a^11*b^6*c^3*d^6 - 576*a^12*b^5*c^2*d^7)))*(a*d - b*c)^3*1i)/((-a)^(9/4)*b^(7/4))","B"
448,1,1564,283,0.253984,"\text{Not used}","int((c + d*x^2)^3/(x^(9/2)*(a + b*x^2)),x)","\frac{2\,d^3\,\sqrt{x}}{b}-\frac{\frac{2\,b\,c^3}{7\,a}+\frac{2\,b\,c^2\,x^2\,\left(3\,a\,d-b\,c\right)}{3\,a^2}}{b\,x^{7/2}}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\sqrt{x}\,\left(16\,a^{12}\,b^6\,d^6-96\,a^{11}\,b^7\,c\,d^5+240\,a^{10}\,b^8\,c^2\,d^4-320\,a^9\,b^9\,c^3\,d^3+240\,a^8\,b^{10}\,c^4\,d^2-96\,a^7\,b^{11}\,c^5\,d+16\,a^6\,b^{12}\,c^6\right)}{2}-\frac{{\left(a\,d-b\,c\right)}^3\,\left(-16\,a^{12}\,b^7\,d^3+48\,a^{11}\,b^8\,c\,d^2-48\,a^{10}\,b^9\,c^2\,d+16\,a^9\,b^{10}\,c^3\right)}{2\,{\left(-a\right)}^{11/4}\,b^{5/4}}\right)\,{\left(a\,d-b\,c\right)}^3\,1{}\mathrm{i}}{{\left(-a\right)}^{11/4}\,b^{5/4}}+\frac{\left(\frac{\sqrt{x}\,\left(16\,a^{12}\,b^6\,d^6-96\,a^{11}\,b^7\,c\,d^5+240\,a^{10}\,b^8\,c^2\,d^4-320\,a^9\,b^9\,c^3\,d^3+240\,a^8\,b^{10}\,c^4\,d^2-96\,a^7\,b^{11}\,c^5\,d+16\,a^6\,b^{12}\,c^6\right)}{2}+\frac{{\left(a\,d-b\,c\right)}^3\,\left(-16\,a^{12}\,b^7\,d^3+48\,a^{11}\,b^8\,c\,d^2-48\,a^{10}\,b^9\,c^2\,d+16\,a^9\,b^{10}\,c^3\right)}{2\,{\left(-a\right)}^{11/4}\,b^{5/4}}\right)\,{\left(a\,d-b\,c\right)}^3\,1{}\mathrm{i}}{{\left(-a\right)}^{11/4}\,b^{5/4}}}{\frac{\left(\frac{\sqrt{x}\,\left(16\,a^{12}\,b^6\,d^6-96\,a^{11}\,b^7\,c\,d^5+240\,a^{10}\,b^8\,c^2\,d^4-320\,a^9\,b^9\,c^3\,d^3+240\,a^8\,b^{10}\,c^4\,d^2-96\,a^7\,b^{11}\,c^5\,d+16\,a^6\,b^{12}\,c^6\right)}{2}-\frac{{\left(a\,d-b\,c\right)}^3\,\left(-16\,a^{12}\,b^7\,d^3+48\,a^{11}\,b^8\,c\,d^2-48\,a^{10}\,b^9\,c^2\,d+16\,a^9\,b^{10}\,c^3\right)}{2\,{\left(-a\right)}^{11/4}\,b^{5/4}}\right)\,{\left(a\,d-b\,c\right)}^3}{{\left(-a\right)}^{11/4}\,b^{5/4}}-\frac{\left(\frac{\sqrt{x}\,\left(16\,a^{12}\,b^6\,d^6-96\,a^{11}\,b^7\,c\,d^5+240\,a^{10}\,b^8\,c^2\,d^4-320\,a^9\,b^9\,c^3\,d^3+240\,a^8\,b^{10}\,c^4\,d^2-96\,a^7\,b^{11}\,c^5\,d+16\,a^6\,b^{12}\,c^6\right)}{2}+\frac{{\left(a\,d-b\,c\right)}^3\,\left(-16\,a^{12}\,b^7\,d^3+48\,a^{11}\,b^8\,c\,d^2-48\,a^{10}\,b^9\,c^2\,d+16\,a^9\,b^{10}\,c^3\right)}{2\,{\left(-a\right)}^{11/4}\,b^{5/4}}\right)\,{\left(a\,d-b\,c\right)}^3}{{\left(-a\right)}^{11/4}\,b^{5/4}}}\right)\,{\left(a\,d-b\,c\right)}^3\,1{}\mathrm{i}}{{\left(-a\right)}^{11/4}\,b^{5/4}}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\sqrt{x}\,\left(16\,a^{12}\,b^6\,d^6-96\,a^{11}\,b^7\,c\,d^5+240\,a^{10}\,b^8\,c^2\,d^4-320\,a^9\,b^9\,c^3\,d^3+240\,a^8\,b^{10}\,c^4\,d^2-96\,a^7\,b^{11}\,c^5\,d+16\,a^6\,b^{12}\,c^6\right)}{2}-\frac{{\left(a\,d-b\,c\right)}^3\,\left(-16\,a^{12}\,b^7\,d^3+48\,a^{11}\,b^8\,c\,d^2-48\,a^{10}\,b^9\,c^2\,d+16\,a^9\,b^{10}\,c^3\right)\,1{}\mathrm{i}}{2\,{\left(-a\right)}^{11/4}\,b^{5/4}}\right)\,{\left(a\,d-b\,c\right)}^3}{{\left(-a\right)}^{11/4}\,b^{5/4}}+\frac{\left(\frac{\sqrt{x}\,\left(16\,a^{12}\,b^6\,d^6-96\,a^{11}\,b^7\,c\,d^5+240\,a^{10}\,b^8\,c^2\,d^4-320\,a^9\,b^9\,c^3\,d^3+240\,a^8\,b^{10}\,c^4\,d^2-96\,a^7\,b^{11}\,c^5\,d+16\,a^6\,b^{12}\,c^6\right)}{2}+\frac{{\left(a\,d-b\,c\right)}^3\,\left(-16\,a^{12}\,b^7\,d^3+48\,a^{11}\,b^8\,c\,d^2-48\,a^{10}\,b^9\,c^2\,d+16\,a^9\,b^{10}\,c^3\right)\,1{}\mathrm{i}}{2\,{\left(-a\right)}^{11/4}\,b^{5/4}}\right)\,{\left(a\,d-b\,c\right)}^3}{{\left(-a\right)}^{11/4}\,b^{5/4}}}{\frac{\left(\frac{\sqrt{x}\,\left(16\,a^{12}\,b^6\,d^6-96\,a^{11}\,b^7\,c\,d^5+240\,a^{10}\,b^8\,c^2\,d^4-320\,a^9\,b^9\,c^3\,d^3+240\,a^8\,b^{10}\,c^4\,d^2-96\,a^7\,b^{11}\,c^5\,d+16\,a^6\,b^{12}\,c^6\right)}{2}-\frac{{\left(a\,d-b\,c\right)}^3\,\left(-16\,a^{12}\,b^7\,d^3+48\,a^{11}\,b^8\,c\,d^2-48\,a^{10}\,b^9\,c^2\,d+16\,a^9\,b^{10}\,c^3\right)\,1{}\mathrm{i}}{2\,{\left(-a\right)}^{11/4}\,b^{5/4}}\right)\,{\left(a\,d-b\,c\right)}^3\,1{}\mathrm{i}}{{\left(-a\right)}^{11/4}\,b^{5/4}}-\frac{\left(\frac{\sqrt{x}\,\left(16\,a^{12}\,b^6\,d^6-96\,a^{11}\,b^7\,c\,d^5+240\,a^{10}\,b^8\,c^2\,d^4-320\,a^9\,b^9\,c^3\,d^3+240\,a^8\,b^{10}\,c^4\,d^2-96\,a^7\,b^{11}\,c^5\,d+16\,a^6\,b^{12}\,c^6\right)}{2}+\frac{{\left(a\,d-b\,c\right)}^3\,\left(-16\,a^{12}\,b^7\,d^3+48\,a^{11}\,b^8\,c\,d^2-48\,a^{10}\,b^9\,c^2\,d+16\,a^9\,b^{10}\,c^3\right)\,1{}\mathrm{i}}{2\,{\left(-a\right)}^{11/4}\,b^{5/4}}\right)\,{\left(a\,d-b\,c\right)}^3\,1{}\mathrm{i}}{{\left(-a\right)}^{11/4}\,b^{5/4}}}\right)\,{\left(a\,d-b\,c\right)}^3}{{\left(-a\right)}^{11/4}\,b^{5/4}}","Not used",1,"(2*d^3*x^(1/2))/b - ((2*b*c^3)/(7*a) + (2*b*c^2*x^2*(3*a*d - b*c))/(3*a^2))/(b*x^(7/2)) + (atan(((((x^(1/2)*(16*a^6*b^12*c^6 + 16*a^12*b^6*d^6 - 96*a^7*b^11*c^5*d - 96*a^11*b^7*c*d^5 + 240*a^8*b^10*c^4*d^2 - 320*a^9*b^9*c^3*d^3 + 240*a^10*b^8*c^2*d^4))/2 - ((a*d - b*c)^3*(16*a^9*b^10*c^3 - 16*a^12*b^7*d^3 - 48*a^10*b^9*c^2*d + 48*a^11*b^8*c*d^2))/(2*(-a)^(11/4)*b^(5/4)))*(a*d - b*c)^3*1i)/((-a)^(11/4)*b^(5/4)) + (((x^(1/2)*(16*a^6*b^12*c^6 + 16*a^12*b^6*d^6 - 96*a^7*b^11*c^5*d - 96*a^11*b^7*c*d^5 + 240*a^8*b^10*c^4*d^2 - 320*a^9*b^9*c^3*d^3 + 240*a^10*b^8*c^2*d^4))/2 + ((a*d - b*c)^3*(16*a^9*b^10*c^3 - 16*a^12*b^7*d^3 - 48*a^10*b^9*c^2*d + 48*a^11*b^8*c*d^2))/(2*(-a)^(11/4)*b^(5/4)))*(a*d - b*c)^3*1i)/((-a)^(11/4)*b^(5/4)))/((((x^(1/2)*(16*a^6*b^12*c^6 + 16*a^12*b^6*d^6 - 96*a^7*b^11*c^5*d - 96*a^11*b^7*c*d^5 + 240*a^8*b^10*c^4*d^2 - 320*a^9*b^9*c^3*d^3 + 240*a^10*b^8*c^2*d^4))/2 - ((a*d - b*c)^3*(16*a^9*b^10*c^3 - 16*a^12*b^7*d^3 - 48*a^10*b^9*c^2*d + 48*a^11*b^8*c*d^2))/(2*(-a)^(11/4)*b^(5/4)))*(a*d - b*c)^3)/((-a)^(11/4)*b^(5/4)) - (((x^(1/2)*(16*a^6*b^12*c^6 + 16*a^12*b^6*d^6 - 96*a^7*b^11*c^5*d - 96*a^11*b^7*c*d^5 + 240*a^8*b^10*c^4*d^2 - 320*a^9*b^9*c^3*d^3 + 240*a^10*b^8*c^2*d^4))/2 + ((a*d - b*c)^3*(16*a^9*b^10*c^3 - 16*a^12*b^7*d^3 - 48*a^10*b^9*c^2*d + 48*a^11*b^8*c*d^2))/(2*(-a)^(11/4)*b^(5/4)))*(a*d - b*c)^3)/((-a)^(11/4)*b^(5/4))))*(a*d - b*c)^3*1i)/((-a)^(11/4)*b^(5/4)) + (atan(((((x^(1/2)*(16*a^6*b^12*c^6 + 16*a^12*b^6*d^6 - 96*a^7*b^11*c^5*d - 96*a^11*b^7*c*d^5 + 240*a^8*b^10*c^4*d^2 - 320*a^9*b^9*c^3*d^3 + 240*a^10*b^8*c^2*d^4))/2 - ((a*d - b*c)^3*(16*a^9*b^10*c^3 - 16*a^12*b^7*d^3 - 48*a^10*b^9*c^2*d + 48*a^11*b^8*c*d^2)*1i)/(2*(-a)^(11/4)*b^(5/4)))*(a*d - b*c)^3)/((-a)^(11/4)*b^(5/4)) + (((x^(1/2)*(16*a^6*b^12*c^6 + 16*a^12*b^6*d^6 - 96*a^7*b^11*c^5*d - 96*a^11*b^7*c*d^5 + 240*a^8*b^10*c^4*d^2 - 320*a^9*b^9*c^3*d^3 + 240*a^10*b^8*c^2*d^4))/2 + ((a*d - b*c)^3*(16*a^9*b^10*c^3 - 16*a^12*b^7*d^3 - 48*a^10*b^9*c^2*d + 48*a^11*b^8*c*d^2)*1i)/(2*(-a)^(11/4)*b^(5/4)))*(a*d - b*c)^3)/((-a)^(11/4)*b^(5/4)))/((((x^(1/2)*(16*a^6*b^12*c^6 + 16*a^12*b^6*d^6 - 96*a^7*b^11*c^5*d - 96*a^11*b^7*c*d^5 + 240*a^8*b^10*c^4*d^2 - 320*a^9*b^9*c^3*d^3 + 240*a^10*b^8*c^2*d^4))/2 - ((a*d - b*c)^3*(16*a^9*b^10*c^3 - 16*a^12*b^7*d^3 - 48*a^10*b^9*c^2*d + 48*a^11*b^8*c*d^2)*1i)/(2*(-a)^(11/4)*b^(5/4)))*(a*d - b*c)^3*1i)/((-a)^(11/4)*b^(5/4)) - (((x^(1/2)*(16*a^6*b^12*c^6 + 16*a^12*b^6*d^6 - 96*a^7*b^11*c^5*d - 96*a^11*b^7*c*d^5 + 240*a^8*b^10*c^4*d^2 - 320*a^9*b^9*c^3*d^3 + 240*a^10*b^8*c^2*d^4))/2 + ((a*d - b*c)^3*(16*a^9*b^10*c^3 - 16*a^12*b^7*d^3 - 48*a^10*b^9*c^2*d + 48*a^11*b^8*c*d^2)*1i)/(2*(-a)^(11/4)*b^(5/4)))*(a*d - b*c)^3*1i)/((-a)^(11/4)*b^(5/4))))*(a*d - b*c)^3)/((-a)^(11/4)*b^(5/4))","B"
449,1,591,303,0.364834,"\text{Not used}","int((c + d*x^2)^3/(x^(11/2)*(a + b*x^2)),x)","\frac{\mathrm{atan}\left(\frac{\sqrt{x}\,{\left(a\,d-b\,c\right)}^3\,\left(16\,a^{16}\,b^2\,d^6-96\,a^{15}\,b^3\,c\,d^5+240\,a^{14}\,b^4\,c^2\,d^4-320\,a^{13}\,b^5\,c^3\,d^3+240\,a^{12}\,b^6\,c^4\,d^2-96\,a^{11}\,b^7\,c^5\,d+16\,a^{10}\,b^8\,c^6\right)}{{\left(-a\right)}^{13/4}\,b^{3/4}\,\left(16\,a^{16}\,b\,d^9-144\,a^{15}\,b^2\,c\,d^8+576\,a^{14}\,b^3\,c^2\,d^7-1344\,a^{13}\,b^4\,c^3\,d^6+2016\,a^{12}\,b^5\,c^4\,d^5-2016\,a^{11}\,b^6\,c^5\,d^4+1344\,a^{10}\,b^7\,c^6\,d^3-576\,a^9\,b^8\,c^7\,d^2+144\,a^8\,b^9\,c^8\,d-16\,a^7\,b^{10}\,c^9\right)}\right)\,{\left(a\,d-b\,c\right)}^3}{{\left(-a\right)}^{13/4}\,b^{3/4}}-\frac{\frac{2\,c^3}{9\,a}+\frac{2\,c^2\,x^2\,\left(3\,a\,d-b\,c\right)}{5\,a^2}+\frac{2\,c\,x^4\,\left(3\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)}{a^3}}{x^{9/2}}-\frac{\mathrm{atanh}\left(\frac{\sqrt{x}\,{\left(a\,d-b\,c\right)}^3\,\left(16\,a^{16}\,b^2\,d^6-96\,a^{15}\,b^3\,c\,d^5+240\,a^{14}\,b^4\,c^2\,d^4-320\,a^{13}\,b^5\,c^3\,d^3+240\,a^{12}\,b^6\,c^4\,d^2-96\,a^{11}\,b^7\,c^5\,d+16\,a^{10}\,b^8\,c^6\right)}{{\left(-a\right)}^{13/4}\,b^{3/4}\,\left(16\,a^{16}\,b\,d^9-144\,a^{15}\,b^2\,c\,d^8+576\,a^{14}\,b^3\,c^2\,d^7-1344\,a^{13}\,b^4\,c^3\,d^6+2016\,a^{12}\,b^5\,c^4\,d^5-2016\,a^{11}\,b^6\,c^5\,d^4+1344\,a^{10}\,b^7\,c^6\,d^3-576\,a^9\,b^8\,c^7\,d^2+144\,a^8\,b^9\,c^8\,d-16\,a^7\,b^{10}\,c^9\right)}\right)\,{\left(a\,d-b\,c\right)}^3}{{\left(-a\right)}^{13/4}\,b^{3/4}}","Not used",1,"(atan((x^(1/2)*(a*d - b*c)^3*(16*a^10*b^8*c^6 + 16*a^16*b^2*d^6 - 96*a^11*b^7*c^5*d - 96*a^15*b^3*c*d^5 + 240*a^12*b^6*c^4*d^2 - 320*a^13*b^5*c^3*d^3 + 240*a^14*b^4*c^2*d^4))/((-a)^(13/4)*b^(3/4)*(16*a^16*b*d^9 - 16*a^7*b^10*c^9 + 144*a^8*b^9*c^8*d - 144*a^15*b^2*c*d^8 - 576*a^9*b^8*c^7*d^2 + 1344*a^10*b^7*c^6*d^3 - 2016*a^11*b^6*c^5*d^4 + 2016*a^12*b^5*c^4*d^5 - 1344*a^13*b^4*c^3*d^6 + 576*a^14*b^3*c^2*d^7)))*(a*d - b*c)^3)/((-a)^(13/4)*b^(3/4)) - ((2*c^3)/(9*a) + (2*c^2*x^2*(3*a*d - b*c))/(5*a^2) + (2*c*x^4*(3*a^2*d^2 + b^2*c^2 - 3*a*b*c*d))/a^3)/x^(9/2) - (atanh((x^(1/2)*(a*d - b*c)^3*(16*a^10*b^8*c^6 + 16*a^16*b^2*d^6 - 96*a^11*b^7*c^5*d - 96*a^15*b^3*c*d^5 + 240*a^12*b^6*c^4*d^2 - 320*a^13*b^5*c^3*d^3 + 240*a^14*b^4*c^2*d^4))/((-a)^(13/4)*b^(3/4)*(16*a^16*b*d^9 - 16*a^7*b^10*c^9 + 144*a^8*b^9*c^8*d - 144*a^15*b^2*c*d^8 - 576*a^9*b^8*c^7*d^2 + 1344*a^10*b^7*c^6*d^3 - 2016*a^11*b^6*c^5*d^4 + 2016*a^12*b^5*c^4*d^5 - 1344*a^13*b^4*c^3*d^6 + 576*a^14*b^3*c^2*d^7)))*(a*d - b*c)^3)/((-a)^(13/4)*b^(3/4))","B"
450,1,1580,305,0.507285,"\text{Not used}","int((c + d*x^2)^3/(x^(13/2)*(a + b*x^2)),x)","-\frac{\frac{2\,c^3}{11\,a}+\frac{2\,c^2\,x^2\,\left(3\,a\,d-b\,c\right)}{7\,a^2}+\frac{2\,c\,x^4\,\left(3\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)}{3\,a^3}}{x^{11/2}}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\sqrt{x}\,\left(16\,a^{15}\,b^3\,d^6-96\,a^{14}\,b^4\,c\,d^5+240\,a^{13}\,b^5\,c^2\,d^4-320\,a^{12}\,b^6\,c^3\,d^3+240\,a^{11}\,b^7\,c^4\,d^2-96\,a^{10}\,b^8\,c^5\,d+16\,a^9\,b^9\,c^6\right)}{2}-\frac{{\left(a\,d-b\,c\right)}^3\,\left(-16\,a^{16}\,b^3\,d^3+48\,a^{15}\,b^4\,c\,d^2-48\,a^{14}\,b^5\,c^2\,d+16\,a^{13}\,b^6\,c^3\right)}{2\,{\left(-a\right)}^{15/4}\,b^{1/4}}\right)\,{\left(a\,d-b\,c\right)}^3\,1{}\mathrm{i}}{{\left(-a\right)}^{15/4}\,b^{1/4}}+\frac{\left(\frac{\sqrt{x}\,\left(16\,a^{15}\,b^3\,d^6-96\,a^{14}\,b^4\,c\,d^5+240\,a^{13}\,b^5\,c^2\,d^4-320\,a^{12}\,b^6\,c^3\,d^3+240\,a^{11}\,b^7\,c^4\,d^2-96\,a^{10}\,b^8\,c^5\,d+16\,a^9\,b^9\,c^6\right)}{2}+\frac{{\left(a\,d-b\,c\right)}^3\,\left(-16\,a^{16}\,b^3\,d^3+48\,a^{15}\,b^4\,c\,d^2-48\,a^{14}\,b^5\,c^2\,d+16\,a^{13}\,b^6\,c^3\right)}{2\,{\left(-a\right)}^{15/4}\,b^{1/4}}\right)\,{\left(a\,d-b\,c\right)}^3\,1{}\mathrm{i}}{{\left(-a\right)}^{15/4}\,b^{1/4}}}{\frac{\left(\frac{\sqrt{x}\,\left(16\,a^{15}\,b^3\,d^6-96\,a^{14}\,b^4\,c\,d^5+240\,a^{13}\,b^5\,c^2\,d^4-320\,a^{12}\,b^6\,c^3\,d^3+240\,a^{11}\,b^7\,c^4\,d^2-96\,a^{10}\,b^8\,c^5\,d+16\,a^9\,b^9\,c^6\right)}{2}-\frac{{\left(a\,d-b\,c\right)}^3\,\left(-16\,a^{16}\,b^3\,d^3+48\,a^{15}\,b^4\,c\,d^2-48\,a^{14}\,b^5\,c^2\,d+16\,a^{13}\,b^6\,c^3\right)}{2\,{\left(-a\right)}^{15/4}\,b^{1/4}}\right)\,{\left(a\,d-b\,c\right)}^3}{{\left(-a\right)}^{15/4}\,b^{1/4}}-\frac{\left(\frac{\sqrt{x}\,\left(16\,a^{15}\,b^3\,d^6-96\,a^{14}\,b^4\,c\,d^5+240\,a^{13}\,b^5\,c^2\,d^4-320\,a^{12}\,b^6\,c^3\,d^3+240\,a^{11}\,b^7\,c^4\,d^2-96\,a^{10}\,b^8\,c^5\,d+16\,a^9\,b^9\,c^6\right)}{2}+\frac{{\left(a\,d-b\,c\right)}^3\,\left(-16\,a^{16}\,b^3\,d^3+48\,a^{15}\,b^4\,c\,d^2-48\,a^{14}\,b^5\,c^2\,d+16\,a^{13}\,b^6\,c^3\right)}{2\,{\left(-a\right)}^{15/4}\,b^{1/4}}\right)\,{\left(a\,d-b\,c\right)}^3}{{\left(-a\right)}^{15/4}\,b^{1/4}}}\right)\,{\left(a\,d-b\,c\right)}^3\,1{}\mathrm{i}}{{\left(-a\right)}^{15/4}\,b^{1/4}}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\sqrt{x}\,\left(16\,a^{15}\,b^3\,d^6-96\,a^{14}\,b^4\,c\,d^5+240\,a^{13}\,b^5\,c^2\,d^4-320\,a^{12}\,b^6\,c^3\,d^3+240\,a^{11}\,b^7\,c^4\,d^2-96\,a^{10}\,b^8\,c^5\,d+16\,a^9\,b^9\,c^6\right)}{2}-\frac{{\left(a\,d-b\,c\right)}^3\,\left(-16\,a^{16}\,b^3\,d^3+48\,a^{15}\,b^4\,c\,d^2-48\,a^{14}\,b^5\,c^2\,d+16\,a^{13}\,b^6\,c^3\right)\,1{}\mathrm{i}}{2\,{\left(-a\right)}^{15/4}\,b^{1/4}}\right)\,{\left(a\,d-b\,c\right)}^3}{{\left(-a\right)}^{15/4}\,b^{1/4}}+\frac{\left(\frac{\sqrt{x}\,\left(16\,a^{15}\,b^3\,d^6-96\,a^{14}\,b^4\,c\,d^5+240\,a^{13}\,b^5\,c^2\,d^4-320\,a^{12}\,b^6\,c^3\,d^3+240\,a^{11}\,b^7\,c^4\,d^2-96\,a^{10}\,b^8\,c^5\,d+16\,a^9\,b^9\,c^6\right)}{2}+\frac{{\left(a\,d-b\,c\right)}^3\,\left(-16\,a^{16}\,b^3\,d^3+48\,a^{15}\,b^4\,c\,d^2-48\,a^{14}\,b^5\,c^2\,d+16\,a^{13}\,b^6\,c^3\right)\,1{}\mathrm{i}}{2\,{\left(-a\right)}^{15/4}\,b^{1/4}}\right)\,{\left(a\,d-b\,c\right)}^3}{{\left(-a\right)}^{15/4}\,b^{1/4}}}{\frac{\left(\frac{\sqrt{x}\,\left(16\,a^{15}\,b^3\,d^6-96\,a^{14}\,b^4\,c\,d^5+240\,a^{13}\,b^5\,c^2\,d^4-320\,a^{12}\,b^6\,c^3\,d^3+240\,a^{11}\,b^7\,c^4\,d^2-96\,a^{10}\,b^8\,c^5\,d+16\,a^9\,b^9\,c^6\right)}{2}-\frac{{\left(a\,d-b\,c\right)}^3\,\left(-16\,a^{16}\,b^3\,d^3+48\,a^{15}\,b^4\,c\,d^2-48\,a^{14}\,b^5\,c^2\,d+16\,a^{13}\,b^6\,c^3\right)\,1{}\mathrm{i}}{2\,{\left(-a\right)}^{15/4}\,b^{1/4}}\right)\,{\left(a\,d-b\,c\right)}^3\,1{}\mathrm{i}}{{\left(-a\right)}^{15/4}\,b^{1/4}}-\frac{\left(\frac{\sqrt{x}\,\left(16\,a^{15}\,b^3\,d^6-96\,a^{14}\,b^4\,c\,d^5+240\,a^{13}\,b^5\,c^2\,d^4-320\,a^{12}\,b^6\,c^3\,d^3+240\,a^{11}\,b^7\,c^4\,d^2-96\,a^{10}\,b^8\,c^5\,d+16\,a^9\,b^9\,c^6\right)}{2}+\frac{{\left(a\,d-b\,c\right)}^3\,\left(-16\,a^{16}\,b^3\,d^3+48\,a^{15}\,b^4\,c\,d^2-48\,a^{14}\,b^5\,c^2\,d+16\,a^{13}\,b^6\,c^3\right)\,1{}\mathrm{i}}{2\,{\left(-a\right)}^{15/4}\,b^{1/4}}\right)\,{\left(a\,d-b\,c\right)}^3\,1{}\mathrm{i}}{{\left(-a\right)}^{15/4}\,b^{1/4}}}\right)\,{\left(a\,d-b\,c\right)}^3}{{\left(-a\right)}^{15/4}\,b^{1/4}}","Not used",1,"- ((2*c^3)/(11*a) + (2*c^2*x^2*(3*a*d - b*c))/(7*a^2) + (2*c*x^4*(3*a^2*d^2 + b^2*c^2 - 3*a*b*c*d))/(3*a^3))/x^(11/2) - (atan(((((x^(1/2)*(16*a^9*b^9*c^6 + 16*a^15*b^3*d^6 - 96*a^10*b^8*c^5*d - 96*a^14*b^4*c*d^5 + 240*a^11*b^7*c^4*d^2 - 320*a^12*b^6*c^3*d^3 + 240*a^13*b^5*c^2*d^4))/2 - ((a*d - b*c)^3*(16*a^13*b^6*c^3 - 16*a^16*b^3*d^3 - 48*a^14*b^5*c^2*d + 48*a^15*b^4*c*d^2))/(2*(-a)^(15/4)*b^(1/4)))*(a*d - b*c)^3*1i)/((-a)^(15/4)*b^(1/4)) + (((x^(1/2)*(16*a^9*b^9*c^6 + 16*a^15*b^3*d^6 - 96*a^10*b^8*c^5*d - 96*a^14*b^4*c*d^5 + 240*a^11*b^7*c^4*d^2 - 320*a^12*b^6*c^3*d^3 + 240*a^13*b^5*c^2*d^4))/2 + ((a*d - b*c)^3*(16*a^13*b^6*c^3 - 16*a^16*b^3*d^3 - 48*a^14*b^5*c^2*d + 48*a^15*b^4*c*d^2))/(2*(-a)^(15/4)*b^(1/4)))*(a*d - b*c)^3*1i)/((-a)^(15/4)*b^(1/4)))/((((x^(1/2)*(16*a^9*b^9*c^6 + 16*a^15*b^3*d^6 - 96*a^10*b^8*c^5*d - 96*a^14*b^4*c*d^5 + 240*a^11*b^7*c^4*d^2 - 320*a^12*b^6*c^3*d^3 + 240*a^13*b^5*c^2*d^4))/2 - ((a*d - b*c)^3*(16*a^13*b^6*c^3 - 16*a^16*b^3*d^3 - 48*a^14*b^5*c^2*d + 48*a^15*b^4*c*d^2))/(2*(-a)^(15/4)*b^(1/4)))*(a*d - b*c)^3)/((-a)^(15/4)*b^(1/4)) - (((x^(1/2)*(16*a^9*b^9*c^6 + 16*a^15*b^3*d^6 - 96*a^10*b^8*c^5*d - 96*a^14*b^4*c*d^5 + 240*a^11*b^7*c^4*d^2 - 320*a^12*b^6*c^3*d^3 + 240*a^13*b^5*c^2*d^4))/2 + ((a*d - b*c)^3*(16*a^13*b^6*c^3 - 16*a^16*b^3*d^3 - 48*a^14*b^5*c^2*d + 48*a^15*b^4*c*d^2))/(2*(-a)^(15/4)*b^(1/4)))*(a*d - b*c)^3)/((-a)^(15/4)*b^(1/4))))*(a*d - b*c)^3*1i)/((-a)^(15/4)*b^(1/4)) - (atan(((((x^(1/2)*(16*a^9*b^9*c^6 + 16*a^15*b^3*d^6 - 96*a^10*b^8*c^5*d - 96*a^14*b^4*c*d^5 + 240*a^11*b^7*c^4*d^2 - 320*a^12*b^6*c^3*d^3 + 240*a^13*b^5*c^2*d^4))/2 - ((a*d - b*c)^3*(16*a^13*b^6*c^3 - 16*a^16*b^3*d^3 - 48*a^14*b^5*c^2*d + 48*a^15*b^4*c*d^2)*1i)/(2*(-a)^(15/4)*b^(1/4)))*(a*d - b*c)^3)/((-a)^(15/4)*b^(1/4)) + (((x^(1/2)*(16*a^9*b^9*c^6 + 16*a^15*b^3*d^6 - 96*a^10*b^8*c^5*d - 96*a^14*b^4*c*d^5 + 240*a^11*b^7*c^4*d^2 - 320*a^12*b^6*c^3*d^3 + 240*a^13*b^5*c^2*d^4))/2 + ((a*d - b*c)^3*(16*a^13*b^6*c^3 - 16*a^16*b^3*d^3 - 48*a^14*b^5*c^2*d + 48*a^15*b^4*c*d^2)*1i)/(2*(-a)^(15/4)*b^(1/4)))*(a*d - b*c)^3)/((-a)^(15/4)*b^(1/4)))/((((x^(1/2)*(16*a^9*b^9*c^6 + 16*a^15*b^3*d^6 - 96*a^10*b^8*c^5*d - 96*a^14*b^4*c*d^5 + 240*a^11*b^7*c^4*d^2 - 320*a^12*b^6*c^3*d^3 + 240*a^13*b^5*c^2*d^4))/2 - ((a*d - b*c)^3*(16*a^13*b^6*c^3 - 16*a^16*b^3*d^3 - 48*a^14*b^5*c^2*d + 48*a^15*b^4*c*d^2)*1i)/(2*(-a)^(15/4)*b^(1/4)))*(a*d - b*c)^3*1i)/((-a)^(15/4)*b^(1/4)) - (((x^(1/2)*(16*a^9*b^9*c^6 + 16*a^15*b^3*d^6 - 96*a^10*b^8*c^5*d - 96*a^14*b^4*c*d^5 + 240*a^11*b^7*c^4*d^2 - 320*a^12*b^6*c^3*d^3 + 240*a^13*b^5*c^2*d^4))/2 + ((a*d - b*c)^3*(16*a^13*b^6*c^3 - 16*a^16*b^3*d^3 - 48*a^14*b^5*c^2*d + 48*a^15*b^4*c*d^2)*1i)/(2*(-a)^(15/4)*b^(1/4)))*(a*d - b*c)^3*1i)/((-a)^(15/4)*b^(1/4))))*(a*d - b*c)^3)/((-a)^(15/4)*b^(1/4))","B"
451,1,639,325,0.385618,"\text{Not used}","int((c + d*x^2)^3/(x^(15/2)*(a + b*x^2)),x)","\frac{{\left(-b\right)}^{1/4}\,\mathrm{atan}\left(\frac{{\left(-b\right)}^{1/4}\,\sqrt{x}\,{\left(a\,d-b\,c\right)}^3\,\left(16\,a^{19}\,b^4\,d^6-96\,a^{18}\,b^5\,c\,d^5+240\,a^{17}\,b^6\,c^2\,d^4-320\,a^{16}\,b^7\,c^3\,d^3+240\,a^{15}\,b^8\,c^4\,d^2-96\,a^{14}\,b^9\,c^5\,d+16\,a^{13}\,b^{10}\,c^6\right)}{a^{17/4}\,\left(-16\,a^{18}\,b^4\,d^9+144\,a^{17}\,b^5\,c\,d^8-576\,a^{16}\,b^6\,c^2\,d^7+1344\,a^{15}\,b^7\,c^3\,d^6-2016\,a^{14}\,b^8\,c^4\,d^5+2016\,a^{13}\,b^9\,c^5\,d^4-1344\,a^{12}\,b^{10}\,c^6\,d^3+576\,a^{11}\,b^{11}\,c^7\,d^2-144\,a^{10}\,b^{12}\,c^8\,d+16\,a^9\,b^{13}\,c^9\right)}\right)\,{\left(a\,d-b\,c\right)}^3}{a^{17/4}}-\frac{\frac{2\,c^3}{13\,a}+\frac{2\,x^6\,\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^4}+\frac{2\,c^2\,x^2\,\left(3\,a\,d-b\,c\right)}{9\,a^2}+\frac{2\,c\,x^4\,\left(3\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)}{5\,a^3}}{x^{13/2}}-\frac{{\left(-b\right)}^{1/4}\,\mathrm{atanh}\left(\frac{{\left(-b\right)}^{1/4}\,\sqrt{x}\,{\left(a\,d-b\,c\right)}^3\,\left(16\,a^{19}\,b^4\,d^6-96\,a^{18}\,b^5\,c\,d^5+240\,a^{17}\,b^6\,c^2\,d^4-320\,a^{16}\,b^7\,c^3\,d^3+240\,a^{15}\,b^8\,c^4\,d^2-96\,a^{14}\,b^9\,c^5\,d+16\,a^{13}\,b^{10}\,c^6\right)}{a^{17/4}\,\left(-16\,a^{18}\,b^4\,d^9+144\,a^{17}\,b^5\,c\,d^8-576\,a^{16}\,b^6\,c^2\,d^7+1344\,a^{15}\,b^7\,c^3\,d^6-2016\,a^{14}\,b^8\,c^4\,d^5+2016\,a^{13}\,b^9\,c^5\,d^4-1344\,a^{12}\,b^{10}\,c^6\,d^3+576\,a^{11}\,b^{11}\,c^7\,d^2-144\,a^{10}\,b^{12}\,c^8\,d+16\,a^9\,b^{13}\,c^9\right)}\right)\,{\left(a\,d-b\,c\right)}^3}{a^{17/4}}","Not used",1,"((-b)^(1/4)*atan(((-b)^(1/4)*x^(1/2)*(a*d - b*c)^3*(16*a^13*b^10*c^6 + 16*a^19*b^4*d^6 - 96*a^14*b^9*c^5*d - 96*a^18*b^5*c*d^5 + 240*a^15*b^8*c^4*d^2 - 320*a^16*b^7*c^3*d^3 + 240*a^17*b^6*c^2*d^4))/(a^(17/4)*(16*a^9*b^13*c^9 - 16*a^18*b^4*d^9 - 144*a^10*b^12*c^8*d + 144*a^17*b^5*c*d^8 + 576*a^11*b^11*c^7*d^2 - 1344*a^12*b^10*c^6*d^3 + 2016*a^13*b^9*c^5*d^4 - 2016*a^14*b^8*c^4*d^5 + 1344*a^15*b^7*c^3*d^6 - 576*a^16*b^6*c^2*d^7)))*(a*d - b*c)^3)/a^(17/4) - ((2*c^3)/(13*a) + (2*x^6*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))/a^4 + (2*c^2*x^2*(3*a*d - b*c))/(9*a^2) + (2*c*x^4*(3*a^2*d^2 + b^2*c^2 - 3*a*b*c*d))/(5*a^3))/x^(13/2) - ((-b)^(1/4)*atanh(((-b)^(1/4)*x^(1/2)*(a*d - b*c)^3*(16*a^13*b^10*c^6 + 16*a^19*b^4*d^6 - 96*a^14*b^9*c^5*d - 96*a^18*b^5*c*d^5 + 240*a^15*b^8*c^4*d^2 - 320*a^16*b^7*c^3*d^3 + 240*a^17*b^6*c^2*d^4))/(a^(17/4)*(16*a^9*b^13*c^9 - 16*a^18*b^4*d^9 - 144*a^10*b^12*c^8*d + 144*a^17*b^5*c*d^8 + 576*a^11*b^11*c^7*d^2 - 1344*a^12*b^10*c^6*d^3 + 2016*a^13*b^9*c^5*d^4 - 2016*a^14*b^8*c^4*d^5 + 1344*a^15*b^7*c^3*d^6 - 576*a^16*b^6*c^2*d^7)))*(a*d - b*c)^3)/a^(17/4)","B"
452,1,1850,409,0.303896,"\text{Not used}","int((x^(7/2)*(c + d*x^2)^3)/(a + b*x^2)^2,x)","\sqrt{x}\,\left(\frac{2\,c^3}{b^2}-\frac{2\,a\,\left(\frac{6\,c^2\,d}{b^2}+\frac{2\,a\,\left(\frac{4\,a\,d^3}{b^3}-\frac{6\,c\,d^2}{b^2}\right)}{b}-\frac{2\,a^2\,d^3}{b^4}\right)}{b}+\frac{a^2\,\left(\frac{4\,a\,d^3}{b^3}-\frac{6\,c\,d^2}{b^2}\right)}{b^2}\right)-x^{9/2}\,\left(\frac{4\,a\,d^3}{9\,b^3}-\frac{2\,c\,d^2}{3\,b^2}\right)+x^{5/2}\,\left(\frac{6\,c^2\,d}{5\,b^2}+\frac{2\,a\,\left(\frac{4\,a\,d^3}{b^3}-\frac{6\,c\,d^2}{b^2}\right)}{5\,b}-\frac{2\,a^2\,d^3}{5\,b^4}\right)-\frac{\sqrt{x}\,\left(\frac{a^4\,d^3}{2}-\frac{3\,a^3\,b\,c\,d^2}{2}+\frac{3\,a^2\,b^2\,c^2\,d}{2}-\frac{a\,b^3\,c^3}{2}\right)}{b^6\,x^2+a\,b^5}+\frac{2\,d^3\,x^{13/2}}{13\,b^2}-\frac{{\left(-a\right)}^{1/4}\,\mathrm{atan}\left(\frac{\frac{{\left(-a\right)}^{1/4}\,{\left(a\,d-b\,c\right)}^2\,\left(17\,a\,d-5\,b\,c\right)\,\left(\frac{\sqrt{x}\,\left(289\,a^8\,d^6-1326\,a^7\,b\,c\,d^5+2439\,a^6\,b^2\,c^2\,d^4-2276\,a^5\,b^3\,c^3\,d^3+1119\,a^4\,b^4\,c^4\,d^2-270\,a^3\,b^5\,c^5\,d+25\,a^2\,b^6\,c^6\right)}{b^7}+\frac{{\left(-a\right)}^{1/4}\,{\left(a\,d-b\,c\right)}^2\,\left(17\,a\,d-5\,b\,c\right)\,\left(17\,a^5\,d^3-39\,a^4\,b\,c\,d^2+27\,a^3\,b^2\,c^2\,d-5\,a^2\,b^3\,c^3\right)}{b^{29/4}}\right)\,1{}\mathrm{i}}{8\,b^{21/4}}+\frac{{\left(-a\right)}^{1/4}\,{\left(a\,d-b\,c\right)}^2\,\left(17\,a\,d-5\,b\,c\right)\,\left(\frac{\sqrt{x}\,\left(289\,a^8\,d^6-1326\,a^7\,b\,c\,d^5+2439\,a^6\,b^2\,c^2\,d^4-2276\,a^5\,b^3\,c^3\,d^3+1119\,a^4\,b^4\,c^4\,d^2-270\,a^3\,b^5\,c^5\,d+25\,a^2\,b^6\,c^6\right)}{b^7}-\frac{{\left(-a\right)}^{1/4}\,{\left(a\,d-b\,c\right)}^2\,\left(17\,a\,d-5\,b\,c\right)\,\left(17\,a^5\,d^3-39\,a^4\,b\,c\,d^2+27\,a^3\,b^2\,c^2\,d-5\,a^2\,b^3\,c^3\right)}{b^{29/4}}\right)\,1{}\mathrm{i}}{8\,b^{21/4}}}{\frac{{\left(-a\right)}^{1/4}\,{\left(a\,d-b\,c\right)}^2\,\left(17\,a\,d-5\,b\,c\right)\,\left(\frac{\sqrt{x}\,\left(289\,a^8\,d^6-1326\,a^7\,b\,c\,d^5+2439\,a^6\,b^2\,c^2\,d^4-2276\,a^5\,b^3\,c^3\,d^3+1119\,a^4\,b^4\,c^4\,d^2-270\,a^3\,b^5\,c^5\,d+25\,a^2\,b^6\,c^6\right)}{b^7}+\frac{{\left(-a\right)}^{1/4}\,{\left(a\,d-b\,c\right)}^2\,\left(17\,a\,d-5\,b\,c\right)\,\left(17\,a^5\,d^3-39\,a^4\,b\,c\,d^2+27\,a^3\,b^2\,c^2\,d-5\,a^2\,b^3\,c^3\right)}{b^{29/4}}\right)}{8\,b^{21/4}}-\frac{{\left(-a\right)}^{1/4}\,{\left(a\,d-b\,c\right)}^2\,\left(17\,a\,d-5\,b\,c\right)\,\left(\frac{\sqrt{x}\,\left(289\,a^8\,d^6-1326\,a^7\,b\,c\,d^5+2439\,a^6\,b^2\,c^2\,d^4-2276\,a^5\,b^3\,c^3\,d^3+1119\,a^4\,b^4\,c^4\,d^2-270\,a^3\,b^5\,c^5\,d+25\,a^2\,b^6\,c^6\right)}{b^7}-\frac{{\left(-a\right)}^{1/4}\,{\left(a\,d-b\,c\right)}^2\,\left(17\,a\,d-5\,b\,c\right)\,\left(17\,a^5\,d^3-39\,a^4\,b\,c\,d^2+27\,a^3\,b^2\,c^2\,d-5\,a^2\,b^3\,c^3\right)}{b^{29/4}}\right)}{8\,b^{21/4}}}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(17\,a\,d-5\,b\,c\right)\,1{}\mathrm{i}}{4\,b^{21/4}}+\frac{{\left(-a\right)}^{1/4}\,\mathrm{atan}\left(\frac{\frac{{\left(-a\right)}^{1/4}\,{\left(a\,d-b\,c\right)}^2\,\left(17\,a\,d-5\,b\,c\right)\,\left(\frac{\sqrt{x}\,\left(289\,a^8\,d^6-1326\,a^7\,b\,c\,d^5+2439\,a^6\,b^2\,c^2\,d^4-2276\,a^5\,b^3\,c^3\,d^3+1119\,a^4\,b^4\,c^4\,d^2-270\,a^3\,b^5\,c^5\,d+25\,a^2\,b^6\,c^6\right)}{b^7}-\frac{{\left(-a\right)}^{1/4}\,{\left(a\,d-b\,c\right)}^2\,\left(17\,a\,d-5\,b\,c\right)\,\left(17\,a^5\,d^3-39\,a^4\,b\,c\,d^2+27\,a^3\,b^2\,c^2\,d-5\,a^2\,b^3\,c^3\right)\,1{}\mathrm{i}}{b^{29/4}}\right)}{8\,b^{21/4}}+\frac{{\left(-a\right)}^{1/4}\,{\left(a\,d-b\,c\right)}^2\,\left(17\,a\,d-5\,b\,c\right)\,\left(\frac{\sqrt{x}\,\left(289\,a^8\,d^6-1326\,a^7\,b\,c\,d^5+2439\,a^6\,b^2\,c^2\,d^4-2276\,a^5\,b^3\,c^3\,d^3+1119\,a^4\,b^4\,c^4\,d^2-270\,a^3\,b^5\,c^5\,d+25\,a^2\,b^6\,c^6\right)}{b^7}+\frac{{\left(-a\right)}^{1/4}\,{\left(a\,d-b\,c\right)}^2\,\left(17\,a\,d-5\,b\,c\right)\,\left(17\,a^5\,d^3-39\,a^4\,b\,c\,d^2+27\,a^3\,b^2\,c^2\,d-5\,a^2\,b^3\,c^3\right)\,1{}\mathrm{i}}{b^{29/4}}\right)}{8\,b^{21/4}}}{\frac{{\left(-a\right)}^{1/4}\,{\left(a\,d-b\,c\right)}^2\,\left(17\,a\,d-5\,b\,c\right)\,\left(\frac{\sqrt{x}\,\left(289\,a^8\,d^6-1326\,a^7\,b\,c\,d^5+2439\,a^6\,b^2\,c^2\,d^4-2276\,a^5\,b^3\,c^3\,d^3+1119\,a^4\,b^4\,c^4\,d^2-270\,a^3\,b^5\,c^5\,d+25\,a^2\,b^6\,c^6\right)}{b^7}-\frac{{\left(-a\right)}^{1/4}\,{\left(a\,d-b\,c\right)}^2\,\left(17\,a\,d-5\,b\,c\right)\,\left(17\,a^5\,d^3-39\,a^4\,b\,c\,d^2+27\,a^3\,b^2\,c^2\,d-5\,a^2\,b^3\,c^3\right)\,1{}\mathrm{i}}{b^{29/4}}\right)\,1{}\mathrm{i}}{8\,b^{21/4}}-\frac{{\left(-a\right)}^{1/4}\,{\left(a\,d-b\,c\right)}^2\,\left(17\,a\,d-5\,b\,c\right)\,\left(\frac{\sqrt{x}\,\left(289\,a^8\,d^6-1326\,a^7\,b\,c\,d^5+2439\,a^6\,b^2\,c^2\,d^4-2276\,a^5\,b^3\,c^3\,d^3+1119\,a^4\,b^4\,c^4\,d^2-270\,a^3\,b^5\,c^5\,d+25\,a^2\,b^6\,c^6\right)}{b^7}+\frac{{\left(-a\right)}^{1/4}\,{\left(a\,d-b\,c\right)}^2\,\left(17\,a\,d-5\,b\,c\right)\,\left(17\,a^5\,d^3-39\,a^4\,b\,c\,d^2+27\,a^3\,b^2\,c^2\,d-5\,a^2\,b^3\,c^3\right)\,1{}\mathrm{i}}{b^{29/4}}\right)\,1{}\mathrm{i}}{8\,b^{21/4}}}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(17\,a\,d-5\,b\,c\right)}{4\,b^{21/4}}","Not used",1,"x^(1/2)*((2*c^3)/b^2 - (2*a*((6*c^2*d)/b^2 + (2*a*((4*a*d^3)/b^3 - (6*c*d^2)/b^2))/b - (2*a^2*d^3)/b^4))/b + (a^2*((4*a*d^3)/b^3 - (6*c*d^2)/b^2))/b^2) - x^(9/2)*((4*a*d^3)/(9*b^3) - (2*c*d^2)/(3*b^2)) + x^(5/2)*((6*c^2*d)/(5*b^2) + (2*a*((4*a*d^3)/b^3 - (6*c*d^2)/b^2))/(5*b) - (2*a^2*d^3)/(5*b^4)) - (x^(1/2)*((a^4*d^3)/2 - (a*b^3*c^3)/2 + (3*a^2*b^2*c^2*d)/2 - (3*a^3*b*c*d^2)/2))/(a*b^5 + b^6*x^2) + (2*d^3*x^(13/2))/(13*b^2) - ((-a)^(1/4)*atan((((-a)^(1/4)*(a*d - b*c)^2*(17*a*d - 5*b*c)*((x^(1/2)*(289*a^8*d^6 + 25*a^2*b^6*c^6 - 270*a^3*b^5*c^5*d + 1119*a^4*b^4*c^4*d^2 - 2276*a^5*b^3*c^3*d^3 + 2439*a^6*b^2*c^2*d^4 - 1326*a^7*b*c*d^5))/b^7 + ((-a)^(1/4)*(a*d - b*c)^2*(17*a*d - 5*b*c)*(17*a^5*d^3 - 5*a^2*b^3*c^3 + 27*a^3*b^2*c^2*d - 39*a^4*b*c*d^2))/b^(29/4))*1i)/(8*b^(21/4)) + ((-a)^(1/4)*(a*d - b*c)^2*(17*a*d - 5*b*c)*((x^(1/2)*(289*a^8*d^6 + 25*a^2*b^6*c^6 - 270*a^3*b^5*c^5*d + 1119*a^4*b^4*c^4*d^2 - 2276*a^5*b^3*c^3*d^3 + 2439*a^6*b^2*c^2*d^4 - 1326*a^7*b*c*d^5))/b^7 - ((-a)^(1/4)*(a*d - b*c)^2*(17*a*d - 5*b*c)*(17*a^5*d^3 - 5*a^2*b^3*c^3 + 27*a^3*b^2*c^2*d - 39*a^4*b*c*d^2))/b^(29/4))*1i)/(8*b^(21/4)))/(((-a)^(1/4)*(a*d - b*c)^2*(17*a*d - 5*b*c)*((x^(1/2)*(289*a^8*d^6 + 25*a^2*b^6*c^6 - 270*a^3*b^5*c^5*d + 1119*a^4*b^4*c^4*d^2 - 2276*a^5*b^3*c^3*d^3 + 2439*a^6*b^2*c^2*d^4 - 1326*a^7*b*c*d^5))/b^7 + ((-a)^(1/4)*(a*d - b*c)^2*(17*a*d - 5*b*c)*(17*a^5*d^3 - 5*a^2*b^3*c^3 + 27*a^3*b^2*c^2*d - 39*a^4*b*c*d^2))/b^(29/4)))/(8*b^(21/4)) - ((-a)^(1/4)*(a*d - b*c)^2*(17*a*d - 5*b*c)*((x^(1/2)*(289*a^8*d^6 + 25*a^2*b^6*c^6 - 270*a^3*b^5*c^5*d + 1119*a^4*b^4*c^4*d^2 - 2276*a^5*b^3*c^3*d^3 + 2439*a^6*b^2*c^2*d^4 - 1326*a^7*b*c*d^5))/b^7 - ((-a)^(1/4)*(a*d - b*c)^2*(17*a*d - 5*b*c)*(17*a^5*d^3 - 5*a^2*b^3*c^3 + 27*a^3*b^2*c^2*d - 39*a^4*b*c*d^2))/b^(29/4)))/(8*b^(21/4))))*(a*d - b*c)^2*(17*a*d - 5*b*c)*1i)/(4*b^(21/4)) + ((-a)^(1/4)*atan((((-a)^(1/4)*(a*d - b*c)^2*(17*a*d - 5*b*c)*((x^(1/2)*(289*a^8*d^6 + 25*a^2*b^6*c^6 - 270*a^3*b^5*c^5*d + 1119*a^4*b^4*c^4*d^2 - 2276*a^5*b^3*c^3*d^3 + 2439*a^6*b^2*c^2*d^4 - 1326*a^7*b*c*d^5))/b^7 - ((-a)^(1/4)*(a*d - b*c)^2*(17*a*d - 5*b*c)*(17*a^5*d^3 - 5*a^2*b^3*c^3 + 27*a^3*b^2*c^2*d - 39*a^4*b*c*d^2)*1i)/b^(29/4)))/(8*b^(21/4)) + ((-a)^(1/4)*(a*d - b*c)^2*(17*a*d - 5*b*c)*((x^(1/2)*(289*a^8*d^6 + 25*a^2*b^6*c^6 - 270*a^3*b^5*c^5*d + 1119*a^4*b^4*c^4*d^2 - 2276*a^5*b^3*c^3*d^3 + 2439*a^6*b^2*c^2*d^4 - 1326*a^7*b*c*d^5))/b^7 + ((-a)^(1/4)*(a*d - b*c)^2*(17*a*d - 5*b*c)*(17*a^5*d^3 - 5*a^2*b^3*c^3 + 27*a^3*b^2*c^2*d - 39*a^4*b*c*d^2)*1i)/b^(29/4)))/(8*b^(21/4)))/(((-a)^(1/4)*(a*d - b*c)^2*(17*a*d - 5*b*c)*((x^(1/2)*(289*a^8*d^6 + 25*a^2*b^6*c^6 - 270*a^3*b^5*c^5*d + 1119*a^4*b^4*c^4*d^2 - 2276*a^5*b^3*c^3*d^3 + 2439*a^6*b^2*c^2*d^4 - 1326*a^7*b*c*d^5))/b^7 - ((-a)^(1/4)*(a*d - b*c)^2*(17*a*d - 5*b*c)*(17*a^5*d^3 - 5*a^2*b^3*c^3 + 27*a^3*b^2*c^2*d - 39*a^4*b*c*d^2)*1i)/b^(29/4))*1i)/(8*b^(21/4)) - ((-a)^(1/4)*(a*d - b*c)^2*(17*a*d - 5*b*c)*((x^(1/2)*(289*a^8*d^6 + 25*a^2*b^6*c^6 - 270*a^3*b^5*c^5*d + 1119*a^4*b^4*c^4*d^2 - 2276*a^5*b^3*c^3*d^3 + 2439*a^6*b^2*c^2*d^4 - 1326*a^7*b*c*d^5))/b^7 + ((-a)^(1/4)*(a*d - b*c)^2*(17*a*d - 5*b*c)*(17*a^5*d^3 - 5*a^2*b^3*c^3 + 27*a^3*b^2*c^2*d - 39*a^4*b*c*d^2)*1i)/b^(29/4))*1i)/(8*b^(21/4))))*(a*d - b*c)^2*(17*a*d - 5*b*c))/(4*b^(21/4))","B"
453,1,681,374,0.453713,"\text{Not used}","int((x^(5/2)*(c + d*x^2)^3)/(a + b*x^2)^2,x)","x^{3/2}\,\left(\frac{2\,c^2\,d}{b^2}+\frac{2\,a\,\left(\frac{4\,a\,d^3}{b^3}-\frac{6\,c\,d^2}{b^2}\right)}{3\,b}-\frac{2\,a^2\,d^3}{3\,b^4}\right)-x^{7/2}\,\left(\frac{4\,a\,d^3}{7\,b^3}-\frac{6\,c\,d^2}{7\,b^2}\right)+\frac{2\,d^3\,x^{11/2}}{11\,b^2}+\frac{x^{3/2}\,\left(\frac{a^3\,d^3}{2}-\frac{3\,a^2\,b\,c\,d^2}{2}+\frac{3\,a\,b^2\,c^2\,d}{2}-\frac{b^3\,c^3}{2}\right)}{b^5\,x^2+a\,b^4}-\frac{3\,\mathrm{atan}\left(\frac{b^{1/4}\,\sqrt{x}\,{\left(a\,d-b\,c\right)}^2\,\left(5\,a\,d-b\,c\right)\,\left(25\,a^7\,d^6-110\,a^6\,b\,c\,d^5+191\,a^5\,b^2\,c^2\,d^4-164\,a^4\,b^3\,c^3\,d^3+71\,a^3\,b^4\,c^4\,d^2-14\,a^2\,b^5\,c^5\,d+a\,b^6\,c^6\right)}{{\left(-a\right)}^{1/4}\,\left(125\,a^{10}\,d^9-825\,a^9\,b\,c\,d^8+2340\,a^8\,b^2\,c^2\,d^7-3716\,a^7\,b^3\,c^3\,d^6+3606\,a^6\,b^4\,c^4\,d^5-2190\,a^5\,b^5\,c^5\,d^4+820\,a^4\,b^6\,c^6\,d^3-180\,a^3\,b^7\,c^7\,d^2+21\,a^2\,b^8\,c^8\,d-a\,b^9\,c^9\right)}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(5\,a\,d-b\,c\right)}{4\,{\left(-a\right)}^{1/4}\,b^{19/4}}-\frac{\mathrm{atan}\left(\frac{b^{1/4}\,\sqrt{x}\,{\left(a\,d-b\,c\right)}^2\,\left(5\,a\,d-b\,c\right)\,\left(25\,a^7\,d^6-110\,a^6\,b\,c\,d^5+191\,a^5\,b^2\,c^2\,d^4-164\,a^4\,b^3\,c^3\,d^3+71\,a^3\,b^4\,c^4\,d^2-14\,a^2\,b^5\,c^5\,d+a\,b^6\,c^6\right)\,1{}\mathrm{i}}{{\left(-a\right)}^{1/4}\,\left(125\,a^{10}\,d^9-825\,a^9\,b\,c\,d^8+2340\,a^8\,b^2\,c^2\,d^7-3716\,a^7\,b^3\,c^3\,d^6+3606\,a^6\,b^4\,c^4\,d^5-2190\,a^5\,b^5\,c^5\,d^4+820\,a^4\,b^6\,c^6\,d^3-180\,a^3\,b^7\,c^7\,d^2+21\,a^2\,b^8\,c^8\,d-a\,b^9\,c^9\right)}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(5\,a\,d-b\,c\right)\,3{}\mathrm{i}}{4\,{\left(-a\right)}^{1/4}\,b^{19/4}}","Not used",1,"x^(3/2)*((2*c^2*d)/b^2 + (2*a*((4*a*d^3)/b^3 - (6*c*d^2)/b^2))/(3*b) - (2*a^2*d^3)/(3*b^4)) - x^(7/2)*((4*a*d^3)/(7*b^3) - (6*c*d^2)/(7*b^2)) + (2*d^3*x^(11/2))/(11*b^2) + (x^(3/2)*((a^3*d^3)/2 - (b^3*c^3)/2 + (3*a*b^2*c^2*d)/2 - (3*a^2*b*c*d^2)/2))/(a*b^4 + b^5*x^2) - (3*atan((b^(1/4)*x^(1/2)*(a*d - b*c)^2*(5*a*d - b*c)*(25*a^7*d^6 + a*b^6*c^6 - 14*a^2*b^5*c^5*d + 71*a^3*b^4*c^4*d^2 - 164*a^4*b^3*c^3*d^3 + 191*a^5*b^2*c^2*d^4 - 110*a^6*b*c*d^5))/((-a)^(1/4)*(125*a^10*d^9 - a*b^9*c^9 + 21*a^2*b^8*c^8*d - 180*a^3*b^7*c^7*d^2 + 820*a^4*b^6*c^6*d^3 - 2190*a^5*b^5*c^5*d^4 + 3606*a^6*b^4*c^4*d^5 - 3716*a^7*b^3*c^3*d^6 + 2340*a^8*b^2*c^2*d^7 - 825*a^9*b*c*d^8)))*(a*d - b*c)^2*(5*a*d - b*c))/(4*(-a)^(1/4)*b^(19/4)) - (atan((b^(1/4)*x^(1/2)*(a*d - b*c)^2*(5*a*d - b*c)*(25*a^7*d^6 + a*b^6*c^6 - 14*a^2*b^5*c^5*d + 71*a^3*b^4*c^4*d^2 - 164*a^4*b^3*c^3*d^3 + 191*a^5*b^2*c^2*d^4 - 110*a^6*b*c*d^5)*1i)/((-a)^(1/4)*(125*a^10*d^9 - a*b^9*c^9 + 21*a^2*b^8*c^8*d - 180*a^3*b^7*c^7*d^2 + 820*a^4*b^6*c^6*d^3 - 2190*a^5*b^5*c^5*d^4 + 3606*a^6*b^4*c^4*d^5 - 3716*a^7*b^3*c^3*d^6 + 2340*a^8*b^2*c^2*d^7 - 825*a^9*b*c*d^8)))*(a*d - b*c)^2*(5*a*d - b*c)*3i)/(4*(-a)^(1/4)*b^(19/4))","B"
454,1,1691,386,0.446401,"\text{Not used}","int((x^(3/2)*(c + d*x^2)^3)/(a + b*x^2)^2,x)","\sqrt{x}\,\left(\frac{6\,c^2\,d}{b^2}+\frac{2\,a\,\left(\frac{4\,a\,d^3}{b^3}-\frac{6\,c\,d^2}{b^2}\right)}{b}-\frac{2\,a^2\,d^3}{b^4}\right)-x^{5/2}\,\left(\frac{4\,a\,d^3}{5\,b^3}-\frac{6\,c\,d^2}{5\,b^2}\right)+\frac{2\,d^3\,x^{9/2}}{9\,b^2}+\frac{\sqrt{x}\,\left(\frac{a^3\,d^3}{2}-\frac{3\,a^2\,b\,c\,d^2}{2}+\frac{3\,a\,b^2\,c^2\,d}{2}-\frac{b^3\,c^3}{2}\right)}{b^5\,x^2+a\,b^4}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\sqrt{x}\,\left(169\,a^6\,d^6-702\,a^5\,b\,c\,d^5+1119\,a^4\,b^2\,c^2\,d^4-836\,a^3\,b^3\,c^3\,d^3+279\,a^2\,b^4\,c^4\,d^2-30\,a\,b^5\,c^5\,d+b^6\,c^6\right)}{b^5}+\frac{{\left(a\,d-b\,c\right)}^2\,\left(13\,a\,d-b\,c\right)\,\left(13\,a^4\,d^3-27\,a^3\,b\,c\,d^2+15\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3\right)}{{\left(-a\right)}^{3/4}\,b^{21/4}}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(13\,a\,d-b\,c\right)\,1{}\mathrm{i}}{8\,{\left(-a\right)}^{3/4}\,b^{17/4}}+\frac{\left(\frac{\sqrt{x}\,\left(169\,a^6\,d^6-702\,a^5\,b\,c\,d^5+1119\,a^4\,b^2\,c^2\,d^4-836\,a^3\,b^3\,c^3\,d^3+279\,a^2\,b^4\,c^4\,d^2-30\,a\,b^5\,c^5\,d+b^6\,c^6\right)}{b^5}-\frac{{\left(a\,d-b\,c\right)}^2\,\left(13\,a\,d-b\,c\right)\,\left(13\,a^4\,d^3-27\,a^3\,b\,c\,d^2+15\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3\right)}{{\left(-a\right)}^{3/4}\,b^{21/4}}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(13\,a\,d-b\,c\right)\,1{}\mathrm{i}}{8\,{\left(-a\right)}^{3/4}\,b^{17/4}}}{\frac{\left(\frac{\sqrt{x}\,\left(169\,a^6\,d^6-702\,a^5\,b\,c\,d^5+1119\,a^4\,b^2\,c^2\,d^4-836\,a^3\,b^3\,c^3\,d^3+279\,a^2\,b^4\,c^4\,d^2-30\,a\,b^5\,c^5\,d+b^6\,c^6\right)}{b^5}+\frac{{\left(a\,d-b\,c\right)}^2\,\left(13\,a\,d-b\,c\right)\,\left(13\,a^4\,d^3-27\,a^3\,b\,c\,d^2+15\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3\right)}{{\left(-a\right)}^{3/4}\,b^{21/4}}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(13\,a\,d-b\,c\right)}{8\,{\left(-a\right)}^{3/4}\,b^{17/4}}-\frac{\left(\frac{\sqrt{x}\,\left(169\,a^6\,d^6-702\,a^5\,b\,c\,d^5+1119\,a^4\,b^2\,c^2\,d^4-836\,a^3\,b^3\,c^3\,d^3+279\,a^2\,b^4\,c^4\,d^2-30\,a\,b^5\,c^5\,d+b^6\,c^6\right)}{b^5}-\frac{{\left(a\,d-b\,c\right)}^2\,\left(13\,a\,d-b\,c\right)\,\left(13\,a^4\,d^3-27\,a^3\,b\,c\,d^2+15\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3\right)}{{\left(-a\right)}^{3/4}\,b^{21/4}}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(13\,a\,d-b\,c\right)}{8\,{\left(-a\right)}^{3/4}\,b^{17/4}}}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(13\,a\,d-b\,c\right)\,1{}\mathrm{i}}{4\,{\left(-a\right)}^{3/4}\,b^{17/4}}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\sqrt{x}\,\left(169\,a^6\,d^6-702\,a^5\,b\,c\,d^5+1119\,a^4\,b^2\,c^2\,d^4-836\,a^3\,b^3\,c^3\,d^3+279\,a^2\,b^4\,c^4\,d^2-30\,a\,b^5\,c^5\,d+b^6\,c^6\right)}{b^5}-\frac{{\left(a\,d-b\,c\right)}^2\,\left(13\,a\,d-b\,c\right)\,\left(13\,a^4\,d^3-27\,a^3\,b\,c\,d^2+15\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3\right)\,1{}\mathrm{i}}{{\left(-a\right)}^{3/4}\,b^{21/4}}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(13\,a\,d-b\,c\right)}{8\,{\left(-a\right)}^{3/4}\,b^{17/4}}+\frac{\left(\frac{\sqrt{x}\,\left(169\,a^6\,d^6-702\,a^5\,b\,c\,d^5+1119\,a^4\,b^2\,c^2\,d^4-836\,a^3\,b^3\,c^3\,d^3+279\,a^2\,b^4\,c^4\,d^2-30\,a\,b^5\,c^5\,d+b^6\,c^6\right)}{b^5}+\frac{{\left(a\,d-b\,c\right)}^2\,\left(13\,a\,d-b\,c\right)\,\left(13\,a^4\,d^3-27\,a^3\,b\,c\,d^2+15\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3\right)\,1{}\mathrm{i}}{{\left(-a\right)}^{3/4}\,b^{21/4}}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(13\,a\,d-b\,c\right)}{8\,{\left(-a\right)}^{3/4}\,b^{17/4}}}{\frac{\left(\frac{\sqrt{x}\,\left(169\,a^6\,d^6-702\,a^5\,b\,c\,d^5+1119\,a^4\,b^2\,c^2\,d^4-836\,a^3\,b^3\,c^3\,d^3+279\,a^2\,b^4\,c^4\,d^2-30\,a\,b^5\,c^5\,d+b^6\,c^6\right)}{b^5}-\frac{{\left(a\,d-b\,c\right)}^2\,\left(13\,a\,d-b\,c\right)\,\left(13\,a^4\,d^3-27\,a^3\,b\,c\,d^2+15\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3\right)\,1{}\mathrm{i}}{{\left(-a\right)}^{3/4}\,b^{21/4}}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(13\,a\,d-b\,c\right)\,1{}\mathrm{i}}{8\,{\left(-a\right)}^{3/4}\,b^{17/4}}-\frac{\left(\frac{\sqrt{x}\,\left(169\,a^6\,d^6-702\,a^5\,b\,c\,d^5+1119\,a^4\,b^2\,c^2\,d^4-836\,a^3\,b^3\,c^3\,d^3+279\,a^2\,b^4\,c^4\,d^2-30\,a\,b^5\,c^5\,d+b^6\,c^6\right)}{b^5}+\frac{{\left(a\,d-b\,c\right)}^2\,\left(13\,a\,d-b\,c\right)\,\left(13\,a^4\,d^3-27\,a^3\,b\,c\,d^2+15\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3\right)\,1{}\mathrm{i}}{{\left(-a\right)}^{3/4}\,b^{21/4}}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(13\,a\,d-b\,c\right)\,1{}\mathrm{i}}{8\,{\left(-a\right)}^{3/4}\,b^{17/4}}}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(13\,a\,d-b\,c\right)}{4\,{\left(-a\right)}^{3/4}\,b^{17/4}}","Not used",1,"x^(1/2)*((6*c^2*d)/b^2 + (2*a*((4*a*d^3)/b^3 - (6*c*d^2)/b^2))/b - (2*a^2*d^3)/b^4) - x^(5/2)*((4*a*d^3)/(5*b^3) - (6*c*d^2)/(5*b^2)) + (2*d^3*x^(9/2))/(9*b^2) + (x^(1/2)*((a^3*d^3)/2 - (b^3*c^3)/2 + (3*a*b^2*c^2*d)/2 - (3*a^2*b*c*d^2)/2))/(a*b^4 + b^5*x^2) + (atan(((((x^(1/2)*(169*a^6*d^6 + b^6*c^6 + 279*a^2*b^4*c^4*d^2 - 836*a^3*b^3*c^3*d^3 + 1119*a^4*b^2*c^2*d^4 - 30*a*b^5*c^5*d - 702*a^5*b*c*d^5))/b^5 + ((a*d - b*c)^2*(13*a*d - b*c)*(13*a^4*d^3 - a*b^3*c^3 + 15*a^2*b^2*c^2*d - 27*a^3*b*c*d^2))/((-a)^(3/4)*b^(21/4)))*(a*d - b*c)^2*(13*a*d - b*c)*1i)/(8*(-a)^(3/4)*b^(17/4)) + (((x^(1/2)*(169*a^6*d^6 + b^6*c^6 + 279*a^2*b^4*c^4*d^2 - 836*a^3*b^3*c^3*d^3 + 1119*a^4*b^2*c^2*d^4 - 30*a*b^5*c^5*d - 702*a^5*b*c*d^5))/b^5 - ((a*d - b*c)^2*(13*a*d - b*c)*(13*a^4*d^3 - a*b^3*c^3 + 15*a^2*b^2*c^2*d - 27*a^3*b*c*d^2))/((-a)^(3/4)*b^(21/4)))*(a*d - b*c)^2*(13*a*d - b*c)*1i)/(8*(-a)^(3/4)*b^(17/4)))/((((x^(1/2)*(169*a^6*d^6 + b^6*c^6 + 279*a^2*b^4*c^4*d^2 - 836*a^3*b^3*c^3*d^3 + 1119*a^4*b^2*c^2*d^4 - 30*a*b^5*c^5*d - 702*a^5*b*c*d^5))/b^5 + ((a*d - b*c)^2*(13*a*d - b*c)*(13*a^4*d^3 - a*b^3*c^3 + 15*a^2*b^2*c^2*d - 27*a^3*b*c*d^2))/((-a)^(3/4)*b^(21/4)))*(a*d - b*c)^2*(13*a*d - b*c))/(8*(-a)^(3/4)*b^(17/4)) - (((x^(1/2)*(169*a^6*d^6 + b^6*c^6 + 279*a^2*b^4*c^4*d^2 - 836*a^3*b^3*c^3*d^3 + 1119*a^4*b^2*c^2*d^4 - 30*a*b^5*c^5*d - 702*a^5*b*c*d^5))/b^5 - ((a*d - b*c)^2*(13*a*d - b*c)*(13*a^4*d^3 - a*b^3*c^3 + 15*a^2*b^2*c^2*d - 27*a^3*b*c*d^2))/((-a)^(3/4)*b^(21/4)))*(a*d - b*c)^2*(13*a*d - b*c))/(8*(-a)^(3/4)*b^(17/4))))*(a*d - b*c)^2*(13*a*d - b*c)*1i)/(4*(-a)^(3/4)*b^(17/4)) - (atan(((((x^(1/2)*(169*a^6*d^6 + b^6*c^6 + 279*a^2*b^4*c^4*d^2 - 836*a^3*b^3*c^3*d^3 + 1119*a^4*b^2*c^2*d^4 - 30*a*b^5*c^5*d - 702*a^5*b*c*d^5))/b^5 - ((a*d - b*c)^2*(13*a*d - b*c)*(13*a^4*d^3 - a*b^3*c^3 + 15*a^2*b^2*c^2*d - 27*a^3*b*c*d^2)*1i)/((-a)^(3/4)*b^(21/4)))*(a*d - b*c)^2*(13*a*d - b*c))/(8*(-a)^(3/4)*b^(17/4)) + (((x^(1/2)*(169*a^6*d^6 + b^6*c^6 + 279*a^2*b^4*c^4*d^2 - 836*a^3*b^3*c^3*d^3 + 1119*a^4*b^2*c^2*d^4 - 30*a*b^5*c^5*d - 702*a^5*b*c*d^5))/b^5 + ((a*d - b*c)^2*(13*a*d - b*c)*(13*a^4*d^3 - a*b^3*c^3 + 15*a^2*b^2*c^2*d - 27*a^3*b*c*d^2)*1i)/((-a)^(3/4)*b^(21/4)))*(a*d - b*c)^2*(13*a*d - b*c))/(8*(-a)^(3/4)*b^(17/4)))/((((x^(1/2)*(169*a^6*d^6 + b^6*c^6 + 279*a^2*b^4*c^4*d^2 - 836*a^3*b^3*c^3*d^3 + 1119*a^4*b^2*c^2*d^4 - 30*a*b^5*c^5*d - 702*a^5*b*c*d^5))/b^5 - ((a*d - b*c)^2*(13*a*d - b*c)*(13*a^4*d^3 - a*b^3*c^3 + 15*a^2*b^2*c^2*d - 27*a^3*b*c*d^2)*1i)/((-a)^(3/4)*b^(21/4)))*(a*d - b*c)^2*(13*a*d - b*c)*1i)/(8*(-a)^(3/4)*b^(17/4)) - (((x^(1/2)*(169*a^6*d^6 + b^6*c^6 + 279*a^2*b^4*c^4*d^2 - 836*a^3*b^3*c^3*d^3 + 1119*a^4*b^2*c^2*d^4 - 30*a*b^5*c^5*d - 702*a^5*b*c*d^5))/b^5 + ((a*d - b*c)^2*(13*a*d - b*c)*(13*a^4*d^3 - a*b^3*c^3 + 15*a^2*b^2*c^2*d - 27*a^3*b*c*d^2)*1i)/((-a)^(3/4)*b^(21/4)))*(a*d - b*c)^2*(13*a*d - b*c)*1i)/(8*(-a)^(3/4)*b^(17/4))))*(a*d - b*c)^2*(13*a*d - b*c))/(4*(-a)^(3/4)*b^(17/4))","B"
455,1,616,376,0.231341,"\text{Not used}","int((x^(1/2)*(c + d*x^2)^3)/(a + b*x^2)^2,x)","\frac{2\,d^3\,x^{7/2}}{7\,b^2}-x^{3/2}\,\left(\frac{4\,a\,d^3}{3\,b^3}-\frac{2\,c\,d^2}{b^2}\right)-\frac{x^{3/2}\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)}{2\,a\,\left(b^4\,x^2+a\,b^3\right)}-\frac{\mathrm{atan}\left(\frac{b^{1/4}\,\sqrt{x}\,{\left(a\,d-b\,c\right)}^2\,\left(11\,a\,d+b\,c\right)\,\left(121\,a^6\,d^6-462\,a^5\,b\,c\,d^5+639\,a^4\,b^2\,c^2\,d^4-356\,a^3\,b^3\,c^3\,d^3+39\,a^2\,b^4\,c^4\,d^2+18\,a\,b^5\,c^5\,d+b^6\,c^6\right)}{{\left(-a\right)}^{1/4}\,\left(1331\,a^9\,d^9-7623\,a^8\,b\,c\,d^8+17820\,a^7\,b^2\,c^2\,d^7-21372\,a^6\,b^3\,c^3\,d^6+13194\,a^5\,b^4\,c^4\,d^5-3186\,a^4\,b^5\,c^5\,d^4-372\,a^3\,b^6\,c^6\,d^3+180\,a^2\,b^7\,c^7\,d^2+27\,a\,b^8\,c^8\,d+b^9\,c^9\right)}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(11\,a\,d+b\,c\right)}{4\,{\left(-a\right)}^{5/4}\,b^{15/4}}-\frac{\mathrm{atan}\left(\frac{b^{1/4}\,\sqrt{x}\,{\left(a\,d-b\,c\right)}^2\,\left(11\,a\,d+b\,c\right)\,\left(121\,a^6\,d^6-462\,a^5\,b\,c\,d^5+639\,a^4\,b^2\,c^2\,d^4-356\,a^3\,b^3\,c^3\,d^3+39\,a^2\,b^4\,c^4\,d^2+18\,a\,b^5\,c^5\,d+b^6\,c^6\right)\,1{}\mathrm{i}}{{\left(-a\right)}^{1/4}\,\left(1331\,a^9\,d^9-7623\,a^8\,b\,c\,d^8+17820\,a^7\,b^2\,c^2\,d^7-21372\,a^6\,b^3\,c^3\,d^6+13194\,a^5\,b^4\,c^4\,d^5-3186\,a^4\,b^5\,c^5\,d^4-372\,a^3\,b^6\,c^6\,d^3+180\,a^2\,b^7\,c^7\,d^2+27\,a\,b^8\,c^8\,d+b^9\,c^9\right)}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(11\,a\,d+b\,c\right)\,1{}\mathrm{i}}{4\,{\left(-a\right)}^{5/4}\,b^{15/4}}","Not used",1,"(2*d^3*x^(7/2))/(7*b^2) - x^(3/2)*((4*a*d^3)/(3*b^3) - (2*c*d^2)/b^2) - (x^(3/2)*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))/(2*a*(a*b^3 + b^4*x^2)) - (atan((b^(1/4)*x^(1/2)*(a*d - b*c)^2*(11*a*d + b*c)*(121*a^6*d^6 + b^6*c^6 + 39*a^2*b^4*c^4*d^2 - 356*a^3*b^3*c^3*d^3 + 639*a^4*b^2*c^2*d^4 + 18*a*b^5*c^5*d - 462*a^5*b*c*d^5))/((-a)^(1/4)*(1331*a^9*d^9 + b^9*c^9 + 180*a^2*b^7*c^7*d^2 - 372*a^3*b^6*c^6*d^3 - 3186*a^4*b^5*c^5*d^4 + 13194*a^5*b^4*c^4*d^5 - 21372*a^6*b^3*c^3*d^6 + 17820*a^7*b^2*c^2*d^7 + 27*a*b^8*c^8*d - 7623*a^8*b*c*d^8)))*(a*d - b*c)^2*(11*a*d + b*c))/(4*(-a)^(5/4)*b^(15/4)) - (atan((b^(1/4)*x^(1/2)*(a*d - b*c)^2*(11*a*d + b*c)*(121*a^6*d^6 + b^6*c^6 + 39*a^2*b^4*c^4*d^2 - 356*a^3*b^3*c^3*d^3 + 639*a^4*b^2*c^2*d^4 + 18*a*b^5*c^5*d - 462*a^5*b*c*d^5)*1i)/((-a)^(1/4)*(1331*a^9*d^9 + b^9*c^9 + 180*a^2*b^7*c^7*d^2 - 372*a^3*b^6*c^6*d^3 - 3186*a^4*b^5*c^5*d^4 + 13194*a^5*b^4*c^4*d^5 - 21372*a^6*b^3*c^3*d^6 + 17820*a^7*b^2*c^2*d^7 + 27*a*b^8*c^8*d - 7623*a^8*b*c*d^8)))*(a*d - b*c)^2*(11*a*d + b*c)*1i)/(4*(-a)^(5/4)*b^(15/4))","B"
456,1,1636,340,0.251373,"\text{Not used}","int((c + d*x^2)^3/(x^(1/2)*(a + b*x^2)^2),x)","\frac{2\,d^3\,x^{5/2}}{5\,b^2}-\sqrt{x}\,\left(\frac{4\,a\,d^3}{b^3}-\frac{6\,c\,d^2}{b^2}\right)-\frac{\sqrt{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)}{2\,a\,\left(b^4\,x^2+a\,b^3\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{9\,\sqrt{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)}{a^2\,b^3}-\frac{3\,{\left(a\,d-b\,c\right)}^2\,\left(3\,a\,d+b\,c\right)\,\left(72\,a^3\,d^3-120\,a^2\,b\,c\,d^2+24\,a\,b^2\,c^2\,d+24\,b^3\,c^3\right)}{8\,{\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{\left(\frac{9\,\sqrt{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)}{a^2\,b^3}+\frac{3\,{\left(a\,d-b\,c\right)}^2\,\left(3\,a\,d+b\,c\right)\,\left(72\,a^3\,d^3-120\,a^2\,b\,c\,d^2+24\,a\,b^2\,c^2\,d+24\,b^3\,c^3\right)}{8\,{\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\,\left(\frac{9\,\sqrt{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)}{a^2\,b^3}-\frac{3\,{\left(a\,d-b\,c\right)}^2\,\left(3\,a\,d+b\,c\right)\,\left(72\,a^3\,d^3-120\,a^2\,b\,c\,d^2+24\,a\,b^2\,c^2\,d+24\,b^3\,c^3\right)}{8\,{\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}}-\frac{3\,\left(\frac{9\,\sqrt{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)}{a^2\,b^3}+\frac{3\,{\left(a\,d-b\,c\right)}^2\,\left(3\,a\,d+b\,c\right)\,\left(72\,a^3\,d^3-120\,a^2\,b\,c\,d^2+24\,a\,b^2\,c^2\,d+24\,b^3\,c^3\right)}{8\,{\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}}}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(3\,a\,d+b\,c\right)\,3{}\mathrm{i}}{4\,{\left(-a\right)}^{7/4}\,b^{13/4}}+\frac{3\,\mathrm{atan}\left(\frac{\frac{3\,\left(\frac{9\,\sqrt{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)}{a^2\,b^3}-\frac{{\left(a\,d-b\,c\right)}^2\,\left(3\,a\,d+b\,c\right)\,\left(72\,a^3\,d^3-120\,a^2\,b\,c\,d^2+24\,a\,b^2\,c^2\,d+24\,b^3\,c^3\right)\,3{}\mathrm{i}}{8\,{\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}}+\frac{3\,\left(\frac{9\,\sqrt{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)}{a^2\,b^3}+\frac{{\left(a\,d-b\,c\right)}^2\,\left(3\,a\,d+b\,c\right)\,\left(72\,a^3\,d^3-120\,a^2\,b\,c\,d^2+24\,a\,b^2\,c^2\,d+24\,b^3\,c^3\right)\,3{}\mathrm{i}}{8\,{\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}}}{\frac{\left(\frac{9\,\sqrt{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)}{a^2\,b^3}-\frac{{\left(a\,d-b\,c\right)}^2\,\left(3\,a\,d+b\,c\right)\,\left(72\,a^3\,d^3-120\,a^2\,b\,c\,d^2+24\,a\,b^2\,c^2\,d+24\,b^3\,c^3\right)\,3{}\mathrm{i}}{8\,{\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{\left(\frac{9\,\sqrt{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)}{a^2\,b^3}+\frac{{\left(a\,d-b\,c\right)}^2\,\left(3\,a\,d+b\,c\right)\,\left(72\,a^3\,d^3-120\,a^2\,b\,c\,d^2+24\,a\,b^2\,c^2\,d+24\,b^3\,c^3\right)\,3{}\mathrm{i}}{8\,{\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}}}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(3\,a\,d+b\,c\right)}{4\,{\left(-a\right)}^{7/4}\,b^{13/4}}","Not used",1,"(2*d^3*x^(5/2))/(5*b^2) - x^(1/2)*((4*a*d^3)/b^3 - (6*c*d^2)/b^2) - (x^(1/2)*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))/(2*a*(a*b^3 + b^4*x^2)) + (atan(((((9*x^(1/2)*(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))/(a^2*b^3) - (3*(a*d - b*c)^2*(3*a*d + b*c)*(72*a^3*d^3 + 24*b^3*c^3 + 24*a*b^2*c^2*d - 120*a^2*b*c*d^2))/(8*(-a)^(7/4)*b^(13/4)))*(a*d - b*c)^2*(3*a*d + b*c)*3i)/(8*(-a)^(7/4)*b^(13/4)) + (((9*x^(1/2)*(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))/(a^2*b^3) + (3*(a*d - b*c)^2*(3*a*d + b*c)*(72*a^3*d^3 + 24*b^3*c^3 + 24*a*b^2*c^2*d - 120*a^2*b*c*d^2))/(8*(-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*((9*x^(1/2)*(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))/(a^2*b^3) - (3*(a*d - b*c)^2*(3*a*d + b*c)*(72*a^3*d^3 + 24*b^3*c^3 + 24*a*b^2*c^2*d - 120*a^2*b*c*d^2))/(8*(-a)^(7/4)*b^(13/4)))*(a*d - b*c)^2*(3*a*d + b*c))/(8*(-a)^(7/4)*b^(13/4)) - (3*((9*x^(1/2)*(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))/(a^2*b^3) + (3*(a*d - b*c)^2*(3*a*d + b*c)*(72*a^3*d^3 + 24*b^3*c^3 + 24*a*b^2*c^2*d - 120*a^2*b*c*d^2))/(8*(-a)^(7/4)*b^(13/4)))*(a*d - b*c)^2*(3*a*d + b*c))/(8*(-a)^(7/4)*b^(13/4))))*(a*d - b*c)^2*(3*a*d + b*c)*3i)/(4*(-a)^(7/4)*b^(13/4)) + (3*atan(((3*((9*x^(1/2)*(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))/(a^2*b^3) - ((a*d - b*c)^2*(3*a*d + b*c)*(72*a^3*d^3 + 24*b^3*c^3 + 24*a*b^2*c^2*d - 120*a^2*b*c*d^2)*3i)/(8*(-a)^(7/4)*b^(13/4)))*(a*d - b*c)^2*(3*a*d + b*c))/(8*(-a)^(7/4)*b^(13/4)) + (3*((9*x^(1/2)*(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))/(a^2*b^3) + ((a*d - b*c)^2*(3*a*d + b*c)*(72*a^3*d^3 + 24*b^3*c^3 + 24*a*b^2*c^2*d - 120*a^2*b*c*d^2)*3i)/(8*(-a)^(7/4)*b^(13/4)))*(a*d - b*c)^2*(3*a*d + b*c))/(8*(-a)^(7/4)*b^(13/4)))/((((9*x^(1/2)*(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))/(a^2*b^3) - ((a*d - b*c)^2*(3*a*d + b*c)*(72*a^3*d^3 + 24*b^3*c^3 + 24*a*b^2*c^2*d - 120*a^2*b*c*d^2)*3i)/(8*(-a)^(7/4)*b^(13/4)))*(a*d - b*c)^2*(3*a*d + b*c)*3i)/(8*(-a)^(7/4)*b^(13/4)) - (((9*x^(1/2)*(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))/(a^2*b^3) + ((a*d - b*c)^2*(3*a*d + b*c)*(72*a^3*d^3 + 24*b^3*c^3 + 24*a*b^2*c^2*d - 120*a^2*b*c*d^2)*3i)/(8*(-a)^(7/4)*b^(13/4)))*(a*d - b*c)^2*(3*a*d + b*c)*3i)/(8*(-a)^(7/4)*b^(13/4))))*(a*d - b*c)^2*(3*a*d + b*c))/(4*(-a)^(7/4)*b^(13/4))","B"
457,1,657,368,0.411596,"\text{Not used}","int((c + d*x^2)^3/(x^(3/2)*(a + b*x^2)^2),x)","\frac{\frac{x^2\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-5\,b^3\,c^3\right)}{2\,a^2}-\frac{2\,b^2\,c^3}{a}}{b^3\,x^{5/2}+a\,b^2\,\sqrt{x}}+\frac{2\,d^3\,x^{3/2}}{3\,b^2}-\frac{\mathrm{atan}\left(\frac{\sqrt{x}\,{\left(a\,d-b\,c\right)}^2\,\left(7\,a\,d+5\,b\,c\right)\,\left(1568\,a^{13}\,b^8\,d^6-4032\,a^{12}\,b^9\,c\,d^5+1248\,a^{11}\,b^{10}\,c^2\,d^4+3968\,a^{10}\,b^{11}\,c^3\,d^3-2592\,a^9\,b^{12}\,c^4\,d^2-960\,a^8\,b^{13}\,c^5\,d+800\,a^7\,b^{14}\,c^6\right)}{4\,{\left(-a\right)}^{9/4}\,b^{11/4}\,\left(2744\,a^{14}\,b^5\,d^9-10584\,a^{13}\,b^6\,c\,d^8+10080\,a^{12}\,b^7\,c^2\,d^7+9120\,a^{11}\,b^8\,c^3\,d^6-19440\,a^{10}\,b^9\,c^4\,d^5+2736\,a^9\,b^{10}\,c^5\,d^4+10464\,a^8\,b^{11}\,c^6\,d^3-4320\,a^7\,b^{12}\,c^7\,d^2-1800\,a^6\,b^{13}\,c^8\,d+1000\,a^5\,b^{14}\,c^9\right)}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(7\,a\,d+5\,b\,c\right)}{4\,{\left(-a\right)}^{9/4}\,b^{11/4}}-\frac{\mathrm{atan}\left(\frac{\sqrt{x}\,{\left(a\,d-b\,c\right)}^2\,\left(7\,a\,d+5\,b\,c\right)\,\left(1568\,a^{13}\,b^8\,d^6-4032\,a^{12}\,b^9\,c\,d^5+1248\,a^{11}\,b^{10}\,c^2\,d^4+3968\,a^{10}\,b^{11}\,c^3\,d^3-2592\,a^9\,b^{12}\,c^4\,d^2-960\,a^8\,b^{13}\,c^5\,d+800\,a^7\,b^{14}\,c^6\right)\,1{}\mathrm{i}}{4\,{\left(-a\right)}^{9/4}\,b^{11/4}\,\left(2744\,a^{14}\,b^5\,d^9-10584\,a^{13}\,b^6\,c\,d^8+10080\,a^{12}\,b^7\,c^2\,d^7+9120\,a^{11}\,b^8\,c^3\,d^6-19440\,a^{10}\,b^9\,c^4\,d^5+2736\,a^9\,b^{10}\,c^5\,d^4+10464\,a^8\,b^{11}\,c^6\,d^3-4320\,a^7\,b^{12}\,c^7\,d^2-1800\,a^6\,b^{13}\,c^8\,d+1000\,a^5\,b^{14}\,c^9\right)}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(7\,a\,d+5\,b\,c\right)\,1{}\mathrm{i}}{4\,{\left(-a\right)}^{9/4}\,b^{11/4}}","Not used",1,"((x^2*(a^3*d^3 - 5*b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))/(2*a^2) - (2*b^2*c^3)/a)/(b^3*x^(5/2) + a*b^2*x^(1/2)) + (2*d^3*x^(3/2))/(3*b^2) - (atan((x^(1/2)*(a*d - b*c)^2*(7*a*d + 5*b*c)*(800*a^7*b^14*c^6 + 1568*a^13*b^8*d^6 - 960*a^8*b^13*c^5*d - 4032*a^12*b^9*c*d^5 - 2592*a^9*b^12*c^4*d^2 + 3968*a^10*b^11*c^3*d^3 + 1248*a^11*b^10*c^2*d^4))/(4*(-a)^(9/4)*b^(11/4)*(1000*a^5*b^14*c^9 + 2744*a^14*b^5*d^9 - 1800*a^6*b^13*c^8*d - 10584*a^13*b^6*c*d^8 - 4320*a^7*b^12*c^7*d^2 + 10464*a^8*b^11*c^6*d^3 + 2736*a^9*b^10*c^5*d^4 - 19440*a^10*b^9*c^4*d^5 + 9120*a^11*b^8*c^3*d^6 + 10080*a^12*b^7*c^2*d^7)))*(a*d - b*c)^2*(7*a*d + 5*b*c))/(4*(-a)^(9/4)*b^(11/4)) - (atan((x^(1/2)*(a*d - b*c)^2*(7*a*d + 5*b*c)*(800*a^7*b^14*c^6 + 1568*a^13*b^8*d^6 - 960*a^8*b^13*c^5*d - 4032*a^12*b^9*c*d^5 - 2592*a^9*b^12*c^4*d^2 + 3968*a^10*b^11*c^3*d^3 + 1248*a^11*b^10*c^2*d^4)*1i)/(4*(-a)^(9/4)*b^(11/4)*(1000*a^5*b^14*c^9 + 2744*a^14*b^5*d^9 - 1800*a^6*b^13*c^8*d - 10584*a^13*b^6*c*d^8 - 4320*a^7*b^12*c^7*d^2 + 10464*a^8*b^11*c^6*d^3 + 2736*a^9*b^10*c^5*d^4 - 19440*a^10*b^9*c^4*d^5 + 9120*a^11*b^8*c^3*d^6 + 10080*a^12*b^7*c^2*d^7)))*(a*d - b*c)^2*(7*a*d + 5*b*c)*1i)/(4*(-a)^(9/4)*b^(11/4))","B"
458,1,1759,367,0.473225,"\text{Not used}","int((c + d*x^2)^3/(x^(5/2)*(a + b*x^2)^2),x)","\frac{\frac{x^2\,\left(3\,a^3\,d^3-9\,a^2\,b\,c\,d^2+9\,a\,b^2\,c^2\,d-7\,b^3\,c^3\right)}{6\,a^2}-\frac{2\,b^2\,c^3}{3\,a}}{b^3\,x^{7/2}+a\,b^2\,x^{3/2}}+\frac{2\,d^3\,\sqrt{x}}{b^2}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\sqrt{x}\,\left(800\,a^{12}\,b^9\,d^6-960\,a^{11}\,b^{10}\,c\,d^5-2592\,a^{10}\,b^{11}\,c^2\,d^4+3968\,a^9\,b^{12}\,c^3\,d^3+1248\,a^8\,b^{13}\,c^4\,d^2-4032\,a^7\,b^{14}\,c^5\,d+1568\,a^6\,b^{15}\,c^6\right)-\frac{{\left(a\,d-b\,c\right)}^2\,\left(5\,a\,d+7\,b\,c\right)\,\left(1280\,a^{12}\,b^{11}\,d^3-768\,a^{11}\,b^{12}\,c\,d^2-2304\,a^{10}\,b^{13}\,c^2\,d+1792\,a^9\,b^{14}\,c^3\right)}{8\,{\left(-a\right)}^{11/4}\,b^{9/4}}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(5\,a\,d+7\,b\,c\right)\,1{}\mathrm{i}}{8\,{\left(-a\right)}^{11/4}\,b^{9/4}}+\frac{\left(\sqrt{x}\,\left(800\,a^{12}\,b^9\,d^6-960\,a^{11}\,b^{10}\,c\,d^5-2592\,a^{10}\,b^{11}\,c^2\,d^4+3968\,a^9\,b^{12}\,c^3\,d^3+1248\,a^8\,b^{13}\,c^4\,d^2-4032\,a^7\,b^{14}\,c^5\,d+1568\,a^6\,b^{15}\,c^6\right)+\frac{{\left(a\,d-b\,c\right)}^2\,\left(5\,a\,d+7\,b\,c\right)\,\left(1280\,a^{12}\,b^{11}\,d^3-768\,a^{11}\,b^{12}\,c\,d^2-2304\,a^{10}\,b^{13}\,c^2\,d+1792\,a^9\,b^{14}\,c^3\right)}{8\,{\left(-a\right)}^{11/4}\,b^{9/4}}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(5\,a\,d+7\,b\,c\right)\,1{}\mathrm{i}}{8\,{\left(-a\right)}^{11/4}\,b^{9/4}}}{\frac{\left(\sqrt{x}\,\left(800\,a^{12}\,b^9\,d^6-960\,a^{11}\,b^{10}\,c\,d^5-2592\,a^{10}\,b^{11}\,c^2\,d^4+3968\,a^9\,b^{12}\,c^3\,d^3+1248\,a^8\,b^{13}\,c^4\,d^2-4032\,a^7\,b^{14}\,c^5\,d+1568\,a^6\,b^{15}\,c^6\right)-\frac{{\left(a\,d-b\,c\right)}^2\,\left(5\,a\,d+7\,b\,c\right)\,\left(1280\,a^{12}\,b^{11}\,d^3-768\,a^{11}\,b^{12}\,c\,d^2-2304\,a^{10}\,b^{13}\,c^2\,d+1792\,a^9\,b^{14}\,c^3\right)}{8\,{\left(-a\right)}^{11/4}\,b^{9/4}}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(5\,a\,d+7\,b\,c\right)}{8\,{\left(-a\right)}^{11/4}\,b^{9/4}}-\frac{\left(\sqrt{x}\,\left(800\,a^{12}\,b^9\,d^6-960\,a^{11}\,b^{10}\,c\,d^5-2592\,a^{10}\,b^{11}\,c^2\,d^4+3968\,a^9\,b^{12}\,c^3\,d^3+1248\,a^8\,b^{13}\,c^4\,d^2-4032\,a^7\,b^{14}\,c^5\,d+1568\,a^6\,b^{15}\,c^6\right)+\frac{{\left(a\,d-b\,c\right)}^2\,\left(5\,a\,d+7\,b\,c\right)\,\left(1280\,a^{12}\,b^{11}\,d^3-768\,a^{11}\,b^{12}\,c\,d^2-2304\,a^{10}\,b^{13}\,c^2\,d+1792\,a^9\,b^{14}\,c^3\right)}{8\,{\left(-a\right)}^{11/4}\,b^{9/4}}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(5\,a\,d+7\,b\,c\right)}{8\,{\left(-a\right)}^{11/4}\,b^{9/4}}}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(5\,a\,d+7\,b\,c\right)\,1{}\mathrm{i}}{4\,{\left(-a\right)}^{11/4}\,b^{9/4}}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\sqrt{x}\,\left(800\,a^{12}\,b^9\,d^6-960\,a^{11}\,b^{10}\,c\,d^5-2592\,a^{10}\,b^{11}\,c^2\,d^4+3968\,a^9\,b^{12}\,c^3\,d^3+1248\,a^8\,b^{13}\,c^4\,d^2-4032\,a^7\,b^{14}\,c^5\,d+1568\,a^6\,b^{15}\,c^6\right)-\frac{{\left(a\,d-b\,c\right)}^2\,\left(5\,a\,d+7\,b\,c\right)\,\left(1280\,a^{12}\,b^{11}\,d^3-768\,a^{11}\,b^{12}\,c\,d^2-2304\,a^{10}\,b^{13}\,c^2\,d+1792\,a^9\,b^{14}\,c^3\right)\,1{}\mathrm{i}}{8\,{\left(-a\right)}^{11/4}\,b^{9/4}}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(5\,a\,d+7\,b\,c\right)}{8\,{\left(-a\right)}^{11/4}\,b^{9/4}}+\frac{\left(\sqrt{x}\,\left(800\,a^{12}\,b^9\,d^6-960\,a^{11}\,b^{10}\,c\,d^5-2592\,a^{10}\,b^{11}\,c^2\,d^4+3968\,a^9\,b^{12}\,c^3\,d^3+1248\,a^8\,b^{13}\,c^4\,d^2-4032\,a^7\,b^{14}\,c^5\,d+1568\,a^6\,b^{15}\,c^6\right)+\frac{{\left(a\,d-b\,c\right)}^2\,\left(5\,a\,d+7\,b\,c\right)\,\left(1280\,a^{12}\,b^{11}\,d^3-768\,a^{11}\,b^{12}\,c\,d^2-2304\,a^{10}\,b^{13}\,c^2\,d+1792\,a^9\,b^{14}\,c^3\right)\,1{}\mathrm{i}}{8\,{\left(-a\right)}^{11/4}\,b^{9/4}}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(5\,a\,d+7\,b\,c\right)}{8\,{\left(-a\right)}^{11/4}\,b^{9/4}}}{\frac{\left(\sqrt{x}\,\left(800\,a^{12}\,b^9\,d^6-960\,a^{11}\,b^{10}\,c\,d^5-2592\,a^{10}\,b^{11}\,c^2\,d^4+3968\,a^9\,b^{12}\,c^3\,d^3+1248\,a^8\,b^{13}\,c^4\,d^2-4032\,a^7\,b^{14}\,c^5\,d+1568\,a^6\,b^{15}\,c^6\right)-\frac{{\left(a\,d-b\,c\right)}^2\,\left(5\,a\,d+7\,b\,c\right)\,\left(1280\,a^{12}\,b^{11}\,d^3-768\,a^{11}\,b^{12}\,c\,d^2-2304\,a^{10}\,b^{13}\,c^2\,d+1792\,a^9\,b^{14}\,c^3\right)\,1{}\mathrm{i}}{8\,{\left(-a\right)}^{11/4}\,b^{9/4}}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(5\,a\,d+7\,b\,c\right)\,1{}\mathrm{i}}{8\,{\left(-a\right)}^{11/4}\,b^{9/4}}-\frac{\left(\sqrt{x}\,\left(800\,a^{12}\,b^9\,d^6-960\,a^{11}\,b^{10}\,c\,d^5-2592\,a^{10}\,b^{11}\,c^2\,d^4+3968\,a^9\,b^{12}\,c^3\,d^3+1248\,a^8\,b^{13}\,c^4\,d^2-4032\,a^7\,b^{14}\,c^5\,d+1568\,a^6\,b^{15}\,c^6\right)+\frac{{\left(a\,d-b\,c\right)}^2\,\left(5\,a\,d+7\,b\,c\right)\,\left(1280\,a^{12}\,b^{11}\,d^3-768\,a^{11}\,b^{12}\,c\,d^2-2304\,a^{10}\,b^{13}\,c^2\,d+1792\,a^9\,b^{14}\,c^3\right)\,1{}\mathrm{i}}{8\,{\left(-a\right)}^{11/4}\,b^{9/4}}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(5\,a\,d+7\,b\,c\right)\,1{}\mathrm{i}}{8\,{\left(-a\right)}^{11/4}\,b^{9/4}}}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(5\,a\,d+7\,b\,c\right)}{4\,{\left(-a\right)}^{11/4}\,b^{9/4}}","Not used",1,"((x^2*(3*a^3*d^3 - 7*b^3*c^3 + 9*a*b^2*c^2*d - 9*a^2*b*c*d^2))/(6*a^2) - (2*b^2*c^3)/(3*a))/(b^3*x^(7/2) + a*b^2*x^(3/2)) + (2*d^3*x^(1/2))/b^2 - (atan((((x^(1/2)*(1568*a^6*b^15*c^6 + 800*a^12*b^9*d^6 - 4032*a^7*b^14*c^5*d - 960*a^11*b^10*c*d^5 + 1248*a^8*b^13*c^4*d^2 + 3968*a^9*b^12*c^3*d^3 - 2592*a^10*b^11*c^2*d^4) - ((a*d - b*c)^2*(5*a*d + 7*b*c)*(1792*a^9*b^14*c^3 + 1280*a^12*b^11*d^3 - 2304*a^10*b^13*c^2*d - 768*a^11*b^12*c*d^2))/(8*(-a)^(11/4)*b^(9/4)))*(a*d - b*c)^2*(5*a*d + 7*b*c)*1i)/(8*(-a)^(11/4)*b^(9/4)) + ((x^(1/2)*(1568*a^6*b^15*c^6 + 800*a^12*b^9*d^6 - 4032*a^7*b^14*c^5*d - 960*a^11*b^10*c*d^5 + 1248*a^8*b^13*c^4*d^2 + 3968*a^9*b^12*c^3*d^3 - 2592*a^10*b^11*c^2*d^4) + ((a*d - b*c)^2*(5*a*d + 7*b*c)*(1792*a^9*b^14*c^3 + 1280*a^12*b^11*d^3 - 2304*a^10*b^13*c^2*d - 768*a^11*b^12*c*d^2))/(8*(-a)^(11/4)*b^(9/4)))*(a*d - b*c)^2*(5*a*d + 7*b*c)*1i)/(8*(-a)^(11/4)*b^(9/4)))/(((x^(1/2)*(1568*a^6*b^15*c^6 + 800*a^12*b^9*d^6 - 4032*a^7*b^14*c^5*d - 960*a^11*b^10*c*d^5 + 1248*a^8*b^13*c^4*d^2 + 3968*a^9*b^12*c^3*d^3 - 2592*a^10*b^11*c^2*d^4) - ((a*d - b*c)^2*(5*a*d + 7*b*c)*(1792*a^9*b^14*c^3 + 1280*a^12*b^11*d^3 - 2304*a^10*b^13*c^2*d - 768*a^11*b^12*c*d^2))/(8*(-a)^(11/4)*b^(9/4)))*(a*d - b*c)^2*(5*a*d + 7*b*c))/(8*(-a)^(11/4)*b^(9/4)) - ((x^(1/2)*(1568*a^6*b^15*c^6 + 800*a^12*b^9*d^6 - 4032*a^7*b^14*c^5*d - 960*a^11*b^10*c*d^5 + 1248*a^8*b^13*c^4*d^2 + 3968*a^9*b^12*c^3*d^3 - 2592*a^10*b^11*c^2*d^4) + ((a*d - b*c)^2*(5*a*d + 7*b*c)*(1792*a^9*b^14*c^3 + 1280*a^12*b^11*d^3 - 2304*a^10*b^13*c^2*d - 768*a^11*b^12*c*d^2))/(8*(-a)^(11/4)*b^(9/4)))*(a*d - b*c)^2*(5*a*d + 7*b*c))/(8*(-a)^(11/4)*b^(9/4))))*(a*d - b*c)^2*(5*a*d + 7*b*c)*1i)/(4*(-a)^(11/4)*b^(9/4)) - (atan((((x^(1/2)*(1568*a^6*b^15*c^6 + 800*a^12*b^9*d^6 - 4032*a^7*b^14*c^5*d - 960*a^11*b^10*c*d^5 + 1248*a^8*b^13*c^4*d^2 + 3968*a^9*b^12*c^3*d^3 - 2592*a^10*b^11*c^2*d^4) - ((a*d - b*c)^2*(5*a*d + 7*b*c)*(1792*a^9*b^14*c^3 + 1280*a^12*b^11*d^3 - 2304*a^10*b^13*c^2*d - 768*a^11*b^12*c*d^2)*1i)/(8*(-a)^(11/4)*b^(9/4)))*(a*d - b*c)^2*(5*a*d + 7*b*c))/(8*(-a)^(11/4)*b^(9/4)) + ((x^(1/2)*(1568*a^6*b^15*c^6 + 800*a^12*b^9*d^6 - 4032*a^7*b^14*c^5*d - 960*a^11*b^10*c*d^5 + 1248*a^8*b^13*c^4*d^2 + 3968*a^9*b^12*c^3*d^3 - 2592*a^10*b^11*c^2*d^4) + ((a*d - b*c)^2*(5*a*d + 7*b*c)*(1792*a^9*b^14*c^3 + 1280*a^12*b^11*d^3 - 2304*a^10*b^13*c^2*d - 768*a^11*b^12*c*d^2)*1i)/(8*(-a)^(11/4)*b^(9/4)))*(a*d - b*c)^2*(5*a*d + 7*b*c))/(8*(-a)^(11/4)*b^(9/4)))/(((x^(1/2)*(1568*a^6*b^15*c^6 + 800*a^12*b^9*d^6 - 4032*a^7*b^14*c^5*d - 960*a^11*b^10*c*d^5 + 1248*a^8*b^13*c^4*d^2 + 3968*a^9*b^12*c^3*d^3 - 2592*a^10*b^11*c^2*d^4) - ((a*d - b*c)^2*(5*a*d + 7*b*c)*(1792*a^9*b^14*c^3 + 1280*a^12*b^11*d^3 - 2304*a^10*b^13*c^2*d - 768*a^11*b^12*c*d^2)*1i)/(8*(-a)^(11/4)*b^(9/4)))*(a*d - b*c)^2*(5*a*d + 7*b*c)*1i)/(8*(-a)^(11/4)*b^(9/4)) - ((x^(1/2)*(1568*a^6*b^15*c^6 + 800*a^12*b^9*d^6 - 4032*a^7*b^14*c^5*d - 960*a^11*b^10*c*d^5 + 1248*a^8*b^13*c^4*d^2 + 3968*a^9*b^12*c^3*d^3 - 2592*a^10*b^11*c^2*d^4) + ((a*d - b*c)^2*(5*a*d + 7*b*c)*(1792*a^9*b^14*c^3 + 1280*a^12*b^11*d^3 - 2304*a^10*b^13*c^2*d - 768*a^11*b^12*c*d^2)*1i)/(8*(-a)^(11/4)*b^(9/4)))*(a*d - b*c)^2*(5*a*d + 7*b*c)*1i)/(8*(-a)^(11/4)*b^(9/4))))*(a*d - b*c)^2*(5*a*d + 7*b*c))/(4*(-a)^(11/4)*b^(9/4))","B"
459,1,656,376,0.251394,"\text{Not used}","int((c + d*x^2)^3/(x^(7/2)*(a + b*x^2)^2),x)","\frac{3\,\mathrm{atan}\left(\frac{3\,\sqrt{x}\,{\left(a\,d-b\,c\right)}^2\,\left(a\,d+3\,b\,c\right)\,\left(288\,a^{16}\,b^5\,d^6+576\,a^{15}\,b^6\,c\,d^5-2592\,a^{14}\,b^7\,c^2\,d^4-1152\,a^{13}\,b^8\,c^3\,d^3+8928\,a^{12}\,b^9\,c^4\,d^2-8640\,a^{11}\,b^{10}\,c^5\,d+2592\,a^{10}\,b^{11}\,c^6\right)}{4\,{\left(-a\right)}^{13/4}\,b^{7/4}\,\left(216\,a^{16}\,b^3\,d^9+648\,a^{15}\,b^4\,c\,d^8-2592\,a^{14}\,b^5\,c^2\,d^7-4320\,a^{13}\,b^6\,c^3\,d^6+16848\,a^{12}\,b^7\,c^4\,d^5-1296\,a^{11}\,b^8\,c^5\,d^4-40608\,a^{10}\,b^9\,c^6\,d^3+54432\,a^9\,b^{10}\,c^7\,d^2-29160\,a^8\,b^{11}\,c^8\,d+5832\,a^7\,b^{12}\,c^9\right)}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(a\,d+3\,b\,c\right)}{4\,{\left(-a\right)}^{13/4}\,b^{7/4}}-\frac{\frac{2\,c^3}{5\,a}+\frac{x^4\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+15\,a\,b^2\,c^2\,d-9\,b^3\,c^3\right)}{2\,a^3\,b}+\frac{6\,c^2\,x^2\,\left(5\,a\,d-3\,b\,c\right)}{5\,a^2}}{a\,x^{5/2}+b\,x^{9/2}}-\frac{3\,\mathrm{atanh}\left(\frac{3\,\sqrt{x}\,{\left(a\,d-b\,c\right)}^2\,\left(a\,d+3\,b\,c\right)\,\left(288\,a^{16}\,b^5\,d^6+576\,a^{15}\,b^6\,c\,d^5-2592\,a^{14}\,b^7\,c^2\,d^4-1152\,a^{13}\,b^8\,c^3\,d^3+8928\,a^{12}\,b^9\,c^4\,d^2-8640\,a^{11}\,b^{10}\,c^5\,d+2592\,a^{10}\,b^{11}\,c^6\right)}{4\,{\left(-a\right)}^{13/4}\,b^{7/4}\,\left(216\,a^{16}\,b^3\,d^9+648\,a^{15}\,b^4\,c\,d^8-2592\,a^{14}\,b^5\,c^2\,d^7-4320\,a^{13}\,b^6\,c^3\,d^6+16848\,a^{12}\,b^7\,c^4\,d^5-1296\,a^{11}\,b^8\,c^5\,d^4-40608\,a^{10}\,b^9\,c^6\,d^3+54432\,a^9\,b^{10}\,c^7\,d^2-29160\,a^8\,b^{11}\,c^8\,d+5832\,a^7\,b^{12}\,c^9\right)}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(a\,d+3\,b\,c\right)}{4\,{\left(-a\right)}^{13/4}\,b^{7/4}}","Not used",1,"(3*atan((3*x^(1/2)*(a*d - b*c)^2*(a*d + 3*b*c)*(2592*a^10*b^11*c^6 + 288*a^16*b^5*d^6 - 8640*a^11*b^10*c^5*d + 576*a^15*b^6*c*d^5 + 8928*a^12*b^9*c^4*d^2 - 1152*a^13*b^8*c^3*d^3 - 2592*a^14*b^7*c^2*d^4))/(4*(-a)^(13/4)*b^(7/4)*(5832*a^7*b^12*c^9 + 216*a^16*b^3*d^9 - 29160*a^8*b^11*c^8*d + 648*a^15*b^4*c*d^8 + 54432*a^9*b^10*c^7*d^2 - 40608*a^10*b^9*c^6*d^3 - 1296*a^11*b^8*c^5*d^4 + 16848*a^12*b^7*c^4*d^5 - 4320*a^13*b^6*c^3*d^6 - 2592*a^14*b^5*c^2*d^7)))*(a*d - b*c)^2*(a*d + 3*b*c))/(4*(-a)^(13/4)*b^(7/4)) - ((2*c^3)/(5*a) + (x^4*(a^3*d^3 - 9*b^3*c^3 + 15*a*b^2*c^2*d - 3*a^2*b*c*d^2))/(2*a^3*b) + (6*c^2*x^2*(5*a*d - 3*b*c))/(5*a^2))/(a*x^(5/2) + b*x^(9/2)) - (3*atanh((3*x^(1/2)*(a*d - b*c)^2*(a*d + 3*b*c)*(2592*a^10*b^11*c^6 + 288*a^16*b^5*d^6 - 8640*a^11*b^10*c^5*d + 576*a^15*b^6*c*d^5 + 8928*a^12*b^9*c^4*d^2 - 1152*a^13*b^8*c^3*d^3 - 2592*a^14*b^7*c^2*d^4))/(4*(-a)^(13/4)*b^(7/4)*(5832*a^7*b^12*c^9 + 216*a^16*b^3*d^9 - 29160*a^8*b^11*c^8*d + 648*a^15*b^4*c*d^8 + 54432*a^9*b^10*c^7*d^2 - 40608*a^10*b^9*c^6*d^3 - 1296*a^11*b^8*c^5*d^4 + 16848*a^12*b^7*c^4*d^5 - 4320*a^13*b^6*c^3*d^6 - 2592*a^14*b^5*c^2*d^7)))*(a*d - b*c)^2*(a*d + 3*b*c))/(4*(-a)^(13/4)*b^(7/4))","B"
460,1,1746,376,0.606416,"\text{Not used}","int((c + d*x^2)^3/(x^(9/2)*(a + b*x^2)^2),x)","-\frac{\frac{2\,c^3}{7\,a}+\frac{x^4\,\left(3\,a^3\,d^3-9\,a^2\,b\,c\,d^2+21\,a\,b^2\,c^2\,d-11\,b^3\,c^3\right)}{6\,a^3\,b}+\frac{2\,c^2\,x^2\,\left(21\,a\,d-11\,b\,c\right)}{21\,a^2}}{a\,x^{7/2}+b\,x^{11/2}}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\sqrt{x}\,\left(32\,a^{15}\,b^6\,d^6+576\,a^{14}\,b^7\,c\,d^5+1248\,a^{13}\,b^8\,c^2\,d^4-11392\,a^{12}\,b^9\,c^3\,d^3+20448\,a^{11}\,b^{10}\,c^4\,d^2-14784\,a^{10}\,b^{11}\,c^5\,d+3872\,a^9\,b^{12}\,c^6\right)-\frac{{\left(a\,d-b\,c\right)}^2\,\left(a\,d+11\,b\,c\right)\,\left(256\,a^{16}\,b^7\,d^3+2304\,a^{15}\,b^8\,c\,d^2-5376\,a^{14}\,b^9\,c^2\,d+2816\,a^{13}\,b^{10}\,c^3\right)}{8\,{\left(-a\right)}^{15/4}\,b^{5/4}}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(a\,d+11\,b\,c\right)\,1{}\mathrm{i}}{8\,{\left(-a\right)}^{15/4}\,b^{5/4}}+\frac{\left(\sqrt{x}\,\left(32\,a^{15}\,b^6\,d^6+576\,a^{14}\,b^7\,c\,d^5+1248\,a^{13}\,b^8\,c^2\,d^4-11392\,a^{12}\,b^9\,c^3\,d^3+20448\,a^{11}\,b^{10}\,c^4\,d^2-14784\,a^{10}\,b^{11}\,c^5\,d+3872\,a^9\,b^{12}\,c^6\right)+\frac{{\left(a\,d-b\,c\right)}^2\,\left(a\,d+11\,b\,c\right)\,\left(256\,a^{16}\,b^7\,d^3+2304\,a^{15}\,b^8\,c\,d^2-5376\,a^{14}\,b^9\,c^2\,d+2816\,a^{13}\,b^{10}\,c^3\right)}{8\,{\left(-a\right)}^{15/4}\,b^{5/4}}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(a\,d+11\,b\,c\right)\,1{}\mathrm{i}}{8\,{\left(-a\right)}^{15/4}\,b^{5/4}}}{\frac{\left(\sqrt{x}\,\left(32\,a^{15}\,b^6\,d^6+576\,a^{14}\,b^7\,c\,d^5+1248\,a^{13}\,b^8\,c^2\,d^4-11392\,a^{12}\,b^9\,c^3\,d^3+20448\,a^{11}\,b^{10}\,c^4\,d^2-14784\,a^{10}\,b^{11}\,c^5\,d+3872\,a^9\,b^{12}\,c^6\right)-\frac{{\left(a\,d-b\,c\right)}^2\,\left(a\,d+11\,b\,c\right)\,\left(256\,a^{16}\,b^7\,d^3+2304\,a^{15}\,b^8\,c\,d^2-5376\,a^{14}\,b^9\,c^2\,d+2816\,a^{13}\,b^{10}\,c^3\right)}{8\,{\left(-a\right)}^{15/4}\,b^{5/4}}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(a\,d+11\,b\,c\right)}{8\,{\left(-a\right)}^{15/4}\,b^{5/4}}-\frac{\left(\sqrt{x}\,\left(32\,a^{15}\,b^6\,d^6+576\,a^{14}\,b^7\,c\,d^5+1248\,a^{13}\,b^8\,c^2\,d^4-11392\,a^{12}\,b^9\,c^3\,d^3+20448\,a^{11}\,b^{10}\,c^4\,d^2-14784\,a^{10}\,b^{11}\,c^5\,d+3872\,a^9\,b^{12}\,c^6\right)+\frac{{\left(a\,d-b\,c\right)}^2\,\left(a\,d+11\,b\,c\right)\,\left(256\,a^{16}\,b^7\,d^3+2304\,a^{15}\,b^8\,c\,d^2-5376\,a^{14}\,b^9\,c^2\,d+2816\,a^{13}\,b^{10}\,c^3\right)}{8\,{\left(-a\right)}^{15/4}\,b^{5/4}}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(a\,d+11\,b\,c\right)}{8\,{\left(-a\right)}^{15/4}\,b^{5/4}}}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(a\,d+11\,b\,c\right)\,1{}\mathrm{i}}{4\,{\left(-a\right)}^{15/4}\,b^{5/4}}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\sqrt{x}\,\left(32\,a^{15}\,b^6\,d^6+576\,a^{14}\,b^7\,c\,d^5+1248\,a^{13}\,b^8\,c^2\,d^4-11392\,a^{12}\,b^9\,c^3\,d^3+20448\,a^{11}\,b^{10}\,c^4\,d^2-14784\,a^{10}\,b^{11}\,c^5\,d+3872\,a^9\,b^{12}\,c^6\right)-\frac{{\left(a\,d-b\,c\right)}^2\,\left(a\,d+11\,b\,c\right)\,\left(256\,a^{16}\,b^7\,d^3+2304\,a^{15}\,b^8\,c\,d^2-5376\,a^{14}\,b^9\,c^2\,d+2816\,a^{13}\,b^{10}\,c^3\right)\,1{}\mathrm{i}}{8\,{\left(-a\right)}^{15/4}\,b^{5/4}}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(a\,d+11\,b\,c\right)}{8\,{\left(-a\right)}^{15/4}\,b^{5/4}}+\frac{\left(\sqrt{x}\,\left(32\,a^{15}\,b^6\,d^6+576\,a^{14}\,b^7\,c\,d^5+1248\,a^{13}\,b^8\,c^2\,d^4-11392\,a^{12}\,b^9\,c^3\,d^3+20448\,a^{11}\,b^{10}\,c^4\,d^2-14784\,a^{10}\,b^{11}\,c^5\,d+3872\,a^9\,b^{12}\,c^6\right)+\frac{{\left(a\,d-b\,c\right)}^2\,\left(a\,d+11\,b\,c\right)\,\left(256\,a^{16}\,b^7\,d^3+2304\,a^{15}\,b^8\,c\,d^2-5376\,a^{14}\,b^9\,c^2\,d+2816\,a^{13}\,b^{10}\,c^3\right)\,1{}\mathrm{i}}{8\,{\left(-a\right)}^{15/4}\,b^{5/4}}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(a\,d+11\,b\,c\right)}{8\,{\left(-a\right)}^{15/4}\,b^{5/4}}}{\frac{\left(\sqrt{x}\,\left(32\,a^{15}\,b^6\,d^6+576\,a^{14}\,b^7\,c\,d^5+1248\,a^{13}\,b^8\,c^2\,d^4-11392\,a^{12}\,b^9\,c^3\,d^3+20448\,a^{11}\,b^{10}\,c^4\,d^2-14784\,a^{10}\,b^{11}\,c^5\,d+3872\,a^9\,b^{12}\,c^6\right)-\frac{{\left(a\,d-b\,c\right)}^2\,\left(a\,d+11\,b\,c\right)\,\left(256\,a^{16}\,b^7\,d^3+2304\,a^{15}\,b^8\,c\,d^2-5376\,a^{14}\,b^9\,c^2\,d+2816\,a^{13}\,b^{10}\,c^3\right)\,1{}\mathrm{i}}{8\,{\left(-a\right)}^{15/4}\,b^{5/4}}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(a\,d+11\,b\,c\right)\,1{}\mathrm{i}}{8\,{\left(-a\right)}^{15/4}\,b^{5/4}}-\frac{\left(\sqrt{x}\,\left(32\,a^{15}\,b^6\,d^6+576\,a^{14}\,b^7\,c\,d^5+1248\,a^{13}\,b^8\,c^2\,d^4-11392\,a^{12}\,b^9\,c^3\,d^3+20448\,a^{11}\,b^{10}\,c^4\,d^2-14784\,a^{10}\,b^{11}\,c^5\,d+3872\,a^9\,b^{12}\,c^6\right)+\frac{{\left(a\,d-b\,c\right)}^2\,\left(a\,d+11\,b\,c\right)\,\left(256\,a^{16}\,b^7\,d^3+2304\,a^{15}\,b^8\,c\,d^2-5376\,a^{14}\,b^9\,c^2\,d+2816\,a^{13}\,b^{10}\,c^3\right)\,1{}\mathrm{i}}{8\,{\left(-a\right)}^{15/4}\,b^{5/4}}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(a\,d+11\,b\,c\right)\,1{}\mathrm{i}}{8\,{\left(-a\right)}^{15/4}\,b^{5/4}}}\right)\,{\left(a\,d-b\,c\right)}^2\,\left(a\,d+11\,b\,c\right)}{4\,{\left(-a\right)}^{15/4}\,b^{5/4}}","Not used",1,"(atan((((x^(1/2)*(3872*a^9*b^12*c^6 + 32*a^15*b^6*d^6 - 14784*a^10*b^11*c^5*d + 576*a^14*b^7*c*d^5 + 20448*a^11*b^10*c^4*d^2 - 11392*a^12*b^9*c^3*d^3 + 1248*a^13*b^8*c^2*d^4) - ((a*d - b*c)^2*(a*d + 11*b*c)*(2816*a^13*b^10*c^3 + 256*a^16*b^7*d^3 - 5376*a^14*b^9*c^2*d + 2304*a^15*b^8*c*d^2))/(8*(-a)^(15/4)*b^(5/4)))*(a*d - b*c)^2*(a*d + 11*b*c)*1i)/(8*(-a)^(15/4)*b^(5/4)) + ((x^(1/2)*(3872*a^9*b^12*c^6 + 32*a^15*b^6*d^6 - 14784*a^10*b^11*c^5*d + 576*a^14*b^7*c*d^5 + 20448*a^11*b^10*c^4*d^2 - 11392*a^12*b^9*c^3*d^3 + 1248*a^13*b^8*c^2*d^4) + ((a*d - b*c)^2*(a*d + 11*b*c)*(2816*a^13*b^10*c^3 + 256*a^16*b^7*d^3 - 5376*a^14*b^9*c^2*d + 2304*a^15*b^8*c*d^2))/(8*(-a)^(15/4)*b^(5/4)))*(a*d - b*c)^2*(a*d + 11*b*c)*1i)/(8*(-a)^(15/4)*b^(5/4)))/(((x^(1/2)*(3872*a^9*b^12*c^6 + 32*a^15*b^6*d^6 - 14784*a^10*b^11*c^5*d + 576*a^14*b^7*c*d^5 + 20448*a^11*b^10*c^4*d^2 - 11392*a^12*b^9*c^3*d^3 + 1248*a^13*b^8*c^2*d^4) - ((a*d - b*c)^2*(a*d + 11*b*c)*(2816*a^13*b^10*c^3 + 256*a^16*b^7*d^3 - 5376*a^14*b^9*c^2*d + 2304*a^15*b^8*c*d^2))/(8*(-a)^(15/4)*b^(5/4)))*(a*d - b*c)^2*(a*d + 11*b*c))/(8*(-a)^(15/4)*b^(5/4)) - ((x^(1/2)*(3872*a^9*b^12*c^6 + 32*a^15*b^6*d^6 - 14784*a^10*b^11*c^5*d + 576*a^14*b^7*c*d^5 + 20448*a^11*b^10*c^4*d^2 - 11392*a^12*b^9*c^3*d^3 + 1248*a^13*b^8*c^2*d^4) + ((a*d - b*c)^2*(a*d + 11*b*c)*(2816*a^13*b^10*c^3 + 256*a^16*b^7*d^3 - 5376*a^14*b^9*c^2*d + 2304*a^15*b^8*c*d^2))/(8*(-a)^(15/4)*b^(5/4)))*(a*d - b*c)^2*(a*d + 11*b*c))/(8*(-a)^(15/4)*b^(5/4))))*(a*d - b*c)^2*(a*d + 11*b*c)*1i)/(4*(-a)^(15/4)*b^(5/4)) - ((2*c^3)/(7*a) + (x^4*(3*a^3*d^3 - 11*b^3*c^3 + 21*a*b^2*c^2*d - 9*a^2*b*c*d^2))/(6*a^3*b) + (2*c^2*x^2*(21*a*d - 11*b*c))/(21*a^2))/(a*x^(7/2) + b*x^(11/2)) + (atan((((x^(1/2)*(3872*a^9*b^12*c^6 + 32*a^15*b^6*d^6 - 14784*a^10*b^11*c^5*d + 576*a^14*b^7*c*d^5 + 20448*a^11*b^10*c^4*d^2 - 11392*a^12*b^9*c^3*d^3 + 1248*a^13*b^8*c^2*d^4) - ((a*d - b*c)^2*(a*d + 11*b*c)*(2816*a^13*b^10*c^3 + 256*a^16*b^7*d^3 - 5376*a^14*b^9*c^2*d + 2304*a^15*b^8*c*d^2)*1i)/(8*(-a)^(15/4)*b^(5/4)))*(a*d - b*c)^2*(a*d + 11*b*c))/(8*(-a)^(15/4)*b^(5/4)) + ((x^(1/2)*(3872*a^9*b^12*c^6 + 32*a^15*b^6*d^6 - 14784*a^10*b^11*c^5*d + 576*a^14*b^7*c*d^5 + 20448*a^11*b^10*c^4*d^2 - 11392*a^12*b^9*c^3*d^3 + 1248*a^13*b^8*c^2*d^4) + ((a*d - b*c)^2*(a*d + 11*b*c)*(2816*a^13*b^10*c^3 + 256*a^16*b^7*d^3 - 5376*a^14*b^9*c^2*d + 2304*a^15*b^8*c*d^2)*1i)/(8*(-a)^(15/4)*b^(5/4)))*(a*d - b*c)^2*(a*d + 11*b*c))/(8*(-a)^(15/4)*b^(5/4)))/(((x^(1/2)*(3872*a^9*b^12*c^6 + 32*a^15*b^6*d^6 - 14784*a^10*b^11*c^5*d + 576*a^14*b^7*c*d^5 + 20448*a^11*b^10*c^4*d^2 - 11392*a^12*b^9*c^3*d^3 + 1248*a^13*b^8*c^2*d^4) - ((a*d - b*c)^2*(a*d + 11*b*c)*(2816*a^13*b^10*c^3 + 256*a^16*b^7*d^3 - 5376*a^14*b^9*c^2*d + 2304*a^15*b^8*c*d^2)*1i)/(8*(-a)^(15/4)*b^(5/4)))*(a*d - b*c)^2*(a*d + 11*b*c)*1i)/(8*(-a)^(15/4)*b^(5/4)) - ((x^(1/2)*(3872*a^9*b^12*c^6 + 32*a^15*b^6*d^6 - 14784*a^10*b^11*c^5*d + 576*a^14*b^7*c*d^5 + 20448*a^11*b^10*c^4*d^2 - 11392*a^12*b^9*c^3*d^3 + 1248*a^13*b^8*c^2*d^4) + ((a*d - b*c)^2*(a*d + 11*b*c)*(2816*a^13*b^10*c^3 + 256*a^16*b^7*d^3 - 5376*a^14*b^9*c^2*d + 2304*a^15*b^8*c*d^2)*1i)/(8*(-a)^(15/4)*b^(5/4)))*(a*d - b*c)^2*(a*d + 11*b*c)*1i)/(8*(-a)^(15/4)*b^(5/4))))*(a*d - b*c)^2*(a*d + 11*b*c))/(4*(-a)^(15/4)*b^(5/4))","B"
461,1,7892,478,1.934300,"\text{Not used}","int(x^(9/2)/((a + b*x^2)*(c + d*x^2)),x)","2\,\mathrm{atan}\left(\frac{{\left(-\frac{c^7}{16\,a^4\,d^{11}-64\,a^3\,b\,c\,d^{10}+96\,a^2\,b^2\,c^2\,d^9-64\,a\,b^3\,c^3\,d^8+16\,b^4\,c^4\,d^7}\right)}^{1/4}\,\left(\frac{256\,\sqrt{x}\,\left(a^{10}\,c^5\,d^5+a^5\,b^5\,c^{10}\right)}{b^3\,d^3}+{\left(-\frac{c^7}{16\,a^4\,d^{11}-64\,a^3\,b\,c\,d^{10}+96\,a^2\,b^2\,c^2\,d^9-64\,a\,b^3\,c^3\,d^8+16\,b^4\,c^4\,d^7}\right)}^{3/4}\,\left(\frac{128\,\left(16\,a^{10}\,b^3\,c^3\,d^{10}-48\,a^9\,b^4\,c^4\,d^9+48\,a^8\,b^5\,c^5\,d^8-16\,a^7\,b^6\,c^6\,d^7-16\,a^6\,b^7\,c^7\,d^6+48\,a^5\,b^8\,c^8\,d^5-48\,a^4\,b^9\,c^9\,d^4+16\,a^3\,b^{10}\,c^{10}\,d^3\right)}{b^3\,d^3}-\frac{\sqrt{x}\,{\left(-\frac{c^7}{16\,a^4\,d^{11}-64\,a^3\,b\,c\,d^{10}+96\,a^2\,b^2\,c^2\,d^9-64\,a\,b^3\,c^3\,d^8+16\,b^4\,c^4\,d^7}\right)}^{1/4}\,\left(16\,a^9\,b^5\,c^3\,d^{11}-64\,a^8\,b^6\,c^4\,d^{10}+112\,a^7\,b^7\,c^5\,d^9-128\,a^6\,b^8\,c^6\,d^8+112\,a^5\,b^9\,c^7\,d^7-64\,a^4\,b^{10}\,c^8\,d^6+16\,a^3\,b^{11}\,c^9\,d^5\right)\,256{}\mathrm{i}}{b^3\,d^3}\right)\,1{}\mathrm{i}\right)-{\left(-\frac{c^7}{16\,a^4\,d^{11}-64\,a^3\,b\,c\,d^{10}+96\,a^2\,b^2\,c^2\,d^9-64\,a\,b^3\,c^3\,d^8+16\,b^4\,c^4\,d^7}\right)}^{1/4}\,\left(-\frac{256\,\sqrt{x}\,\left(a^{10}\,c^5\,d^5+a^5\,b^5\,c^{10}\right)}{b^3\,d^3}+{\left(-\frac{c^7}{16\,a^4\,d^{11}-64\,a^3\,b\,c\,d^{10}+96\,a^2\,b^2\,c^2\,d^9-64\,a\,b^3\,c^3\,d^8+16\,b^4\,c^4\,d^7}\right)}^{3/4}\,\left(\frac{128\,\left(16\,a^{10}\,b^3\,c^3\,d^{10}-48\,a^9\,b^4\,c^4\,d^9+48\,a^8\,b^5\,c^5\,d^8-16\,a^7\,b^6\,c^6\,d^7-16\,a^6\,b^7\,c^7\,d^6+48\,a^5\,b^8\,c^8\,d^5-48\,a^4\,b^9\,c^9\,d^4+16\,a^3\,b^{10}\,c^{10}\,d^3\right)}{b^3\,d^3}+\frac{\sqrt{x}\,{\left(-\frac{c^7}{16\,a^4\,d^{11}-64\,a^3\,b\,c\,d^{10}+96\,a^2\,b^2\,c^2\,d^9-64\,a\,b^3\,c^3\,d^8+16\,b^4\,c^4\,d^7}\right)}^{1/4}\,\left(16\,a^9\,b^5\,c^3\,d^{11}-64\,a^8\,b^6\,c^4\,d^{10}+112\,a^7\,b^7\,c^5\,d^9-128\,a^6\,b^8\,c^6\,d^8+112\,a^5\,b^9\,c^7\,d^7-64\,a^4\,b^{10}\,c^8\,d^6+16\,a^3\,b^{11}\,c^9\,d^5\right)\,256{}\mathrm{i}}{b^3\,d^3}\right)\,1{}\mathrm{i}\right)}{\frac{256\,\left(a^9\,c^7\,d^2+a^8\,b\,c^8\,d+a^7\,b^2\,c^9\right)}{b^3\,d^3}+{\left(-\frac{c^7}{16\,a^4\,d^{11}-64\,a^3\,b\,c\,d^{10}+96\,a^2\,b^2\,c^2\,d^9-64\,a\,b^3\,c^3\,d^8+16\,b^4\,c^4\,d^7}\right)}^{1/4}\,\left(\frac{256\,\sqrt{x}\,\left(a^{10}\,c^5\,d^5+a^5\,b^5\,c^{10}\right)}{b^3\,d^3}+{\left(-\frac{c^7}{16\,a^4\,d^{11}-64\,a^3\,b\,c\,d^{10}+96\,a^2\,b^2\,c^2\,d^9-64\,a\,b^3\,c^3\,d^8+16\,b^4\,c^4\,d^7}\right)}^{3/4}\,\left(\frac{128\,\left(16\,a^{10}\,b^3\,c^3\,d^{10}-48\,a^9\,b^4\,c^4\,d^9+48\,a^8\,b^5\,c^5\,d^8-16\,a^7\,b^6\,c^6\,d^7-16\,a^6\,b^7\,c^7\,d^6+48\,a^5\,b^8\,c^8\,d^5-48\,a^4\,b^9\,c^9\,d^4+16\,a^3\,b^{10}\,c^{10}\,d^3\right)}{b^3\,d^3}-\frac{\sqrt{x}\,{\left(-\frac{c^7}{16\,a^4\,d^{11}-64\,a^3\,b\,c\,d^{10}+96\,a^2\,b^2\,c^2\,d^9-64\,a\,b^3\,c^3\,d^8+16\,b^4\,c^4\,d^7}\right)}^{1/4}\,\left(16\,a^9\,b^5\,c^3\,d^{11}-64\,a^8\,b^6\,c^4\,d^{10}+112\,a^7\,b^7\,c^5\,d^9-128\,a^6\,b^8\,c^6\,d^8+112\,a^5\,b^9\,c^7\,d^7-64\,a^4\,b^{10}\,c^8\,d^6+16\,a^3\,b^{11}\,c^9\,d^5\right)\,256{}\mathrm{i}}{b^3\,d^3}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}+{\left(-\frac{c^7}{16\,a^4\,d^{11}-64\,a^3\,b\,c\,d^{10}+96\,a^2\,b^2\,c^2\,d^9-64\,a\,b^3\,c^3\,d^8+16\,b^4\,c^4\,d^7}\right)}^{1/4}\,\left(-\frac{256\,\sqrt{x}\,\left(a^{10}\,c^5\,d^5+a^5\,b^5\,c^{10}\right)}{b^3\,d^3}+{\left(-\frac{c^7}{16\,a^4\,d^{11}-64\,a^3\,b\,c\,d^{10}+96\,a^2\,b^2\,c^2\,d^9-64\,a\,b^3\,c^3\,d^8+16\,b^4\,c^4\,d^7}\right)}^{3/4}\,\left(\frac{128\,\left(16\,a^{10}\,b^3\,c^3\,d^{10}-48\,a^9\,b^4\,c^4\,d^9+48\,a^8\,b^5\,c^5\,d^8-16\,a^7\,b^6\,c^6\,d^7-16\,a^6\,b^7\,c^7\,d^6+48\,a^5\,b^8\,c^8\,d^5-48\,a^4\,b^9\,c^9\,d^4+16\,a^3\,b^{10}\,c^{10}\,d^3\right)}{b^3\,d^3}+\frac{\sqrt{x}\,{\left(-\frac{c^7}{16\,a^4\,d^{11}-64\,a^3\,b\,c\,d^{10}+96\,a^2\,b^2\,c^2\,d^9-64\,a\,b^3\,c^3\,d^8+16\,b^4\,c^4\,d^7}\right)}^{1/4}\,\left(16\,a^9\,b^5\,c^3\,d^{11}-64\,a^8\,b^6\,c^4\,d^{10}+112\,a^7\,b^7\,c^5\,d^9-128\,a^6\,b^8\,c^6\,d^8+112\,a^5\,b^9\,c^7\,d^7-64\,a^4\,b^{10}\,c^8\,d^6+16\,a^3\,b^{11}\,c^9\,d^5\right)\,256{}\mathrm{i}}{b^3\,d^3}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}\right)\,{\left(-\frac{c^7}{16\,a^4\,d^{11}-64\,a^3\,b\,c\,d^{10}+96\,a^2\,b^2\,c^2\,d^9-64\,a\,b^3\,c^3\,d^8+16\,b^4\,c^4\,d^7}\right)}^{1/4}+2\,\mathrm{atan}\left(\frac{{\left(-\frac{a^7}{16\,a^4\,b^7\,d^4-64\,a^3\,b^8\,c\,d^3+96\,a^2\,b^9\,c^2\,d^2-64\,a\,b^{10}\,c^3\,d+16\,b^{11}\,c^4}\right)}^{1/4}\,\left(\frac{256\,\sqrt{x}\,\left(a^{10}\,c^5\,d^5+a^5\,b^5\,c^{10}\right)}{b^3\,d^3}+{\left(-\frac{a^7}{16\,a^4\,b^7\,d^4-64\,a^3\,b^8\,c\,d^3+96\,a^2\,b^9\,c^2\,d^2-64\,a\,b^{10}\,c^3\,d+16\,b^{11}\,c^4}\right)}^{3/4}\,\left(\frac{128\,\left(16\,a^{10}\,b^3\,c^3\,d^{10}-48\,a^9\,b^4\,c^4\,d^9+48\,a^8\,b^5\,c^5\,d^8-16\,a^7\,b^6\,c^6\,d^7-16\,a^6\,b^7\,c^7\,d^6+48\,a^5\,b^8\,c^8\,d^5-48\,a^4\,b^9\,c^9\,d^4+16\,a^3\,b^{10}\,c^{10}\,d^3\right)}{b^3\,d^3}-\frac{\sqrt{x}\,{\left(-\frac{a^7}{16\,a^4\,b^7\,d^4-64\,a^3\,b^8\,c\,d^3+96\,a^2\,b^9\,c^2\,d^2-64\,a\,b^{10}\,c^3\,d+16\,b^{11}\,c^4}\right)}^{1/4}\,\left(16\,a^9\,b^5\,c^3\,d^{11}-64\,a^8\,b^6\,c^4\,d^{10}+112\,a^7\,b^7\,c^5\,d^9-128\,a^6\,b^8\,c^6\,d^8+112\,a^5\,b^9\,c^7\,d^7-64\,a^4\,b^{10}\,c^8\,d^6+16\,a^3\,b^{11}\,c^9\,d^5\right)\,256{}\mathrm{i}}{b^3\,d^3}\right)\,1{}\mathrm{i}\right)-{\left(-\frac{a^7}{16\,a^4\,b^7\,d^4-64\,a^3\,b^8\,c\,d^3+96\,a^2\,b^9\,c^2\,d^2-64\,a\,b^{10}\,c^3\,d+16\,b^{11}\,c^4}\right)}^{1/4}\,\left(-\frac{256\,\sqrt{x}\,\left(a^{10}\,c^5\,d^5+a^5\,b^5\,c^{10}\right)}{b^3\,d^3}+{\left(-\frac{a^7}{16\,a^4\,b^7\,d^4-64\,a^3\,b^8\,c\,d^3+96\,a^2\,b^9\,c^2\,d^2-64\,a\,b^{10}\,c^3\,d+16\,b^{11}\,c^4}\right)}^{3/4}\,\left(\frac{128\,\left(16\,a^{10}\,b^3\,c^3\,d^{10}-48\,a^9\,b^4\,c^4\,d^9+48\,a^8\,b^5\,c^5\,d^8-16\,a^7\,b^6\,c^6\,d^7-16\,a^6\,b^7\,c^7\,d^6+48\,a^5\,b^8\,c^8\,d^5-48\,a^4\,b^9\,c^9\,d^4+16\,a^3\,b^{10}\,c^{10}\,d^3\right)}{b^3\,d^3}+\frac{\sqrt{x}\,{\left(-\frac{a^7}{16\,a^4\,b^7\,d^4-64\,a^3\,b^8\,c\,d^3+96\,a^2\,b^9\,c^2\,d^2-64\,a\,b^{10}\,c^3\,d+16\,b^{11}\,c^4}\right)}^{1/4}\,\left(16\,a^9\,b^5\,c^3\,d^{11}-64\,a^8\,b^6\,c^4\,d^{10}+112\,a^7\,b^7\,c^5\,d^9-128\,a^6\,b^8\,c^6\,d^8+112\,a^5\,b^9\,c^7\,d^7-64\,a^4\,b^{10}\,c^8\,d^6+16\,a^3\,b^{11}\,c^9\,d^5\right)\,256{}\mathrm{i}}{b^3\,d^3}\right)\,1{}\mathrm{i}\right)}{\frac{256\,\left(a^9\,c^7\,d^2+a^8\,b\,c^8\,d+a^7\,b^2\,c^9\right)}{b^3\,d^3}+{\left(-\frac{a^7}{16\,a^4\,b^7\,d^4-64\,a^3\,b^8\,c\,d^3+96\,a^2\,b^9\,c^2\,d^2-64\,a\,b^{10}\,c^3\,d+16\,b^{11}\,c^4}\right)}^{1/4}\,\left(\frac{256\,\sqrt{x}\,\left(a^{10}\,c^5\,d^5+a^5\,b^5\,c^{10}\right)}{b^3\,d^3}+{\left(-\frac{a^7}{16\,a^4\,b^7\,d^4-64\,a^3\,b^8\,c\,d^3+96\,a^2\,b^9\,c^2\,d^2-64\,a\,b^{10}\,c^3\,d+16\,b^{11}\,c^4}\right)}^{3/4}\,\left(\frac{128\,\left(16\,a^{10}\,b^3\,c^3\,d^{10}-48\,a^9\,b^4\,c^4\,d^9+48\,a^8\,b^5\,c^5\,d^8-16\,a^7\,b^6\,c^6\,d^7-16\,a^6\,b^7\,c^7\,d^6+48\,a^5\,b^8\,c^8\,d^5-48\,a^4\,b^9\,c^9\,d^4+16\,a^3\,b^{10}\,c^{10}\,d^3\right)}{b^3\,d^3}-\frac{\sqrt{x}\,{\left(-\frac{a^7}{16\,a^4\,b^7\,d^4-64\,a^3\,b^8\,c\,d^3+96\,a^2\,b^9\,c^2\,d^2-64\,a\,b^{10}\,c^3\,d+16\,b^{11}\,c^4}\right)}^{1/4}\,\left(16\,a^9\,b^5\,c^3\,d^{11}-64\,a^8\,b^6\,c^4\,d^{10}+112\,a^7\,b^7\,c^5\,d^9-128\,a^6\,b^8\,c^6\,d^8+112\,a^5\,b^9\,c^7\,d^7-64\,a^4\,b^{10}\,c^8\,d^6+16\,a^3\,b^{11}\,c^9\,d^5\right)\,256{}\mathrm{i}}{b^3\,d^3}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}+{\left(-\frac{a^7}{16\,a^4\,b^7\,d^4-64\,a^3\,b^8\,c\,d^3+96\,a^2\,b^9\,c^2\,d^2-64\,a\,b^{10}\,c^3\,d+16\,b^{11}\,c^4}\right)}^{1/4}\,\left(-\frac{256\,\sqrt{x}\,\left(a^{10}\,c^5\,d^5+a^5\,b^5\,c^{10}\right)}{b^3\,d^3}+{\left(-\frac{a^7}{16\,a^4\,b^7\,d^4-64\,a^3\,b^8\,c\,d^3+96\,a^2\,b^9\,c^2\,d^2-64\,a\,b^{10}\,c^3\,d+16\,b^{11}\,c^4}\right)}^{3/4}\,\left(\frac{128\,\left(16\,a^{10}\,b^3\,c^3\,d^{10}-48\,a^9\,b^4\,c^4\,d^9+48\,a^8\,b^5\,c^5\,d^8-16\,a^7\,b^6\,c^6\,d^7-16\,a^6\,b^7\,c^7\,d^6+48\,a^5\,b^8\,c^8\,d^5-48\,a^4\,b^9\,c^9\,d^4+16\,a^3\,b^{10}\,c^{10}\,d^3\right)}{b^3\,d^3}+\frac{\sqrt{x}\,{\left(-\frac{a^7}{16\,a^4\,b^7\,d^4-64\,a^3\,b^8\,c\,d^3+96\,a^2\,b^9\,c^2\,d^2-64\,a\,b^{10}\,c^3\,d+16\,b^{11}\,c^4}\right)}^{1/4}\,\left(16\,a^9\,b^5\,c^3\,d^{11}-64\,a^8\,b^6\,c^4\,d^{10}+112\,a^7\,b^7\,c^5\,d^9-128\,a^6\,b^8\,c^6\,d^8+112\,a^5\,b^9\,c^7\,d^7-64\,a^4\,b^{10}\,c^8\,d^6+16\,a^3\,b^{11}\,c^9\,d^5\right)\,256{}\mathrm{i}}{b^3\,d^3}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}\right)\,{\left(-\frac{a^7}{16\,a^4\,b^7\,d^4-64\,a^3\,b^8\,c\,d^3+96\,a^2\,b^9\,c^2\,d^2-64\,a\,b^{10}\,c^3\,d+16\,b^{11}\,c^4}\right)}^{1/4}+\frac{2\,x^{3/2}}{3\,b\,d}+\mathrm{atan}\left(\frac{{\left(-\frac{c^7}{16\,a^4\,d^{11}-64\,a^3\,b\,c\,d^{10}+96\,a^2\,b^2\,c^2\,d^9-64\,a\,b^3\,c^3\,d^8+16\,b^4\,c^4\,d^7}\right)}^{1/4}\,\left({\left(-\frac{c^7}{16\,a^4\,d^{11}-64\,a^3\,b\,c\,d^{10}+96\,a^2\,b^2\,c^2\,d^9-64\,a\,b^3\,c^3\,d^8+16\,b^4\,c^4\,d^7}\right)}^{3/4}\,\left(\frac{128\,\left(16\,a^{10}\,b^3\,c^3\,d^{10}-48\,a^9\,b^4\,c^4\,d^9+48\,a^8\,b^5\,c^5\,d^8-16\,a^7\,b^6\,c^6\,d^7-16\,a^6\,b^7\,c^7\,d^6+48\,a^5\,b^8\,c^8\,d^5-48\,a^4\,b^9\,c^9\,d^4+16\,a^3\,b^{10}\,c^{10}\,d^3\right)}{b^3\,d^3}-\frac{256\,\sqrt{x}\,{\left(-\frac{c^7}{16\,a^4\,d^{11}-64\,a^3\,b\,c\,d^{10}+96\,a^2\,b^2\,c^2\,d^9-64\,a\,b^3\,c^3\,d^8+16\,b^4\,c^4\,d^7}\right)}^{1/4}\,\left(16\,a^9\,b^5\,c^3\,d^{11}-64\,a^8\,b^6\,c^4\,d^{10}+112\,a^7\,b^7\,c^5\,d^9-128\,a^6\,b^8\,c^6\,d^8+112\,a^5\,b^9\,c^7\,d^7-64\,a^4\,b^{10}\,c^8\,d^6+16\,a^3\,b^{11}\,c^9\,d^5\right)}{b^3\,d^3}\right)-\frac{256\,\sqrt{x}\,\left(a^{10}\,c^5\,d^5+a^5\,b^5\,c^{10}\right)}{b^3\,d^3}\right)\,1{}\mathrm{i}-{\left(-\frac{c^7}{16\,a^4\,d^{11}-64\,a^3\,b\,c\,d^{10}+96\,a^2\,b^2\,c^2\,d^9-64\,a\,b^3\,c^3\,d^8+16\,b^4\,c^4\,d^7}\right)}^{1/4}\,\left({\left(-\frac{c^7}{16\,a^4\,d^{11}-64\,a^3\,b\,c\,d^{10}+96\,a^2\,b^2\,c^2\,d^9-64\,a\,b^3\,c^3\,d^8+16\,b^4\,c^4\,d^7}\right)}^{3/4}\,\left(\frac{128\,\left(16\,a^{10}\,b^3\,c^3\,d^{10}-48\,a^9\,b^4\,c^4\,d^9+48\,a^8\,b^5\,c^5\,d^8-16\,a^7\,b^6\,c^6\,d^7-16\,a^6\,b^7\,c^7\,d^6+48\,a^5\,b^8\,c^8\,d^5-48\,a^4\,b^9\,c^9\,d^4+16\,a^3\,b^{10}\,c^{10}\,d^3\right)}{b^3\,d^3}+\frac{256\,\sqrt{x}\,{\left(-\frac{c^7}{16\,a^4\,d^{11}-64\,a^3\,b\,c\,d^{10}+96\,a^2\,b^2\,c^2\,d^9-64\,a\,b^3\,c^3\,d^8+16\,b^4\,c^4\,d^7}\right)}^{1/4}\,\left(16\,a^9\,b^5\,c^3\,d^{11}-64\,a^8\,b^6\,c^4\,d^{10}+112\,a^7\,b^7\,c^5\,d^9-128\,a^6\,b^8\,c^6\,d^8+112\,a^5\,b^9\,c^7\,d^7-64\,a^4\,b^{10}\,c^8\,d^6+16\,a^3\,b^{11}\,c^9\,d^5\right)}{b^3\,d^3}\right)+\frac{256\,\sqrt{x}\,\left(a^{10}\,c^5\,d^5+a^5\,b^5\,c^{10}\right)}{b^3\,d^3}\right)\,1{}\mathrm{i}}{{\left(-\frac{c^7}{16\,a^4\,d^{11}-64\,a^3\,b\,c\,d^{10}+96\,a^2\,b^2\,c^2\,d^9-64\,a\,b^3\,c^3\,d^8+16\,b^4\,c^4\,d^7}\right)}^{1/4}\,\left({\left(-\frac{c^7}{16\,a^4\,d^{11}-64\,a^3\,b\,c\,d^{10}+96\,a^2\,b^2\,c^2\,d^9-64\,a\,b^3\,c^3\,d^8+16\,b^4\,c^4\,d^7}\right)}^{3/4}\,\left(\frac{128\,\left(16\,a^{10}\,b^3\,c^3\,d^{10}-48\,a^9\,b^4\,c^4\,d^9+48\,a^8\,b^5\,c^5\,d^8-16\,a^7\,b^6\,c^6\,d^7-16\,a^6\,b^7\,c^7\,d^6+48\,a^5\,b^8\,c^8\,d^5-48\,a^4\,b^9\,c^9\,d^4+16\,a^3\,b^{10}\,c^{10}\,d^3\right)}{b^3\,d^3}-\frac{256\,\sqrt{x}\,{\left(-\frac{c^7}{16\,a^4\,d^{11}-64\,a^3\,b\,c\,d^{10}+96\,a^2\,b^2\,c^2\,d^9-64\,a\,b^3\,c^3\,d^8+16\,b^4\,c^4\,d^7}\right)}^{1/4}\,\left(16\,a^9\,b^5\,c^3\,d^{11}-64\,a^8\,b^6\,c^4\,d^{10}+112\,a^7\,b^7\,c^5\,d^9-128\,a^6\,b^8\,c^6\,d^8+112\,a^5\,b^9\,c^7\,d^7-64\,a^4\,b^{10}\,c^8\,d^6+16\,a^3\,b^{11}\,c^9\,d^5\right)}{b^3\,d^3}\right)-\frac{256\,\sqrt{x}\,\left(a^{10}\,c^5\,d^5+a^5\,b^5\,c^{10}\right)}{b^3\,d^3}\right)+{\left(-\frac{c^7}{16\,a^4\,d^{11}-64\,a^3\,b\,c\,d^{10}+96\,a^2\,b^2\,c^2\,d^9-64\,a\,b^3\,c^3\,d^8+16\,b^4\,c^4\,d^7}\right)}^{1/4}\,\left({\left(-\frac{c^7}{16\,a^4\,d^{11}-64\,a^3\,b\,c\,d^{10}+96\,a^2\,b^2\,c^2\,d^9-64\,a\,b^3\,c^3\,d^8+16\,b^4\,c^4\,d^7}\right)}^{3/4}\,\left(\frac{128\,\left(16\,a^{10}\,b^3\,c^3\,d^{10}-48\,a^9\,b^4\,c^4\,d^9+48\,a^8\,b^5\,c^5\,d^8-16\,a^7\,b^6\,c^6\,d^7-16\,a^6\,b^7\,c^7\,d^6+48\,a^5\,b^8\,c^8\,d^5-48\,a^4\,b^9\,c^9\,d^4+16\,a^3\,b^{10}\,c^{10}\,d^3\right)}{b^3\,d^3}+\frac{256\,\sqrt{x}\,{\left(-\frac{c^7}{16\,a^4\,d^{11}-64\,a^3\,b\,c\,d^{10}+96\,a^2\,b^2\,c^2\,d^9-64\,a\,b^3\,c^3\,d^8+16\,b^4\,c^4\,d^7}\right)}^{1/4}\,\left(16\,a^9\,b^5\,c^3\,d^{11}-64\,a^8\,b^6\,c^4\,d^{10}+112\,a^7\,b^7\,c^5\,d^9-128\,a^6\,b^8\,c^6\,d^8+112\,a^5\,b^9\,c^7\,d^7-64\,a^4\,b^{10}\,c^8\,d^6+16\,a^3\,b^{11}\,c^9\,d^5\right)}{b^3\,d^3}\right)+\frac{256\,\sqrt{x}\,\left(a^{10}\,c^5\,d^5+a^5\,b^5\,c^{10}\right)}{b^3\,d^3}\right)-\frac{256\,\left(a^9\,c^7\,d^2+a^8\,b\,c^8\,d+a^7\,b^2\,c^9\right)}{b^3\,d^3}}\right)\,{\left(-\frac{c^7}{16\,a^4\,d^{11}-64\,a^3\,b\,c\,d^{10}+96\,a^2\,b^2\,c^2\,d^9-64\,a\,b^3\,c^3\,d^8+16\,b^4\,c^4\,d^7}\right)}^{1/4}\,2{}\mathrm{i}+\mathrm{atan}\left(\frac{{\left(-\frac{a^7}{16\,a^4\,b^7\,d^4-64\,a^3\,b^8\,c\,d^3+96\,a^2\,b^9\,c^2\,d^2-64\,a\,b^{10}\,c^3\,d+16\,b^{11}\,c^4}\right)}^{1/4}\,\left({\left(-\frac{a^7}{16\,a^4\,b^7\,d^4-64\,a^3\,b^8\,c\,d^3+96\,a^2\,b^9\,c^2\,d^2-64\,a\,b^{10}\,c^3\,d+16\,b^{11}\,c^4}\right)}^{3/4}\,\left(\frac{128\,\left(16\,a^{10}\,b^3\,c^3\,d^{10}-48\,a^9\,b^4\,c^4\,d^9+48\,a^8\,b^5\,c^5\,d^8-16\,a^7\,b^6\,c^6\,d^7-16\,a^6\,b^7\,c^7\,d^6+48\,a^5\,b^8\,c^8\,d^5-48\,a^4\,b^9\,c^9\,d^4+16\,a^3\,b^{10}\,c^{10}\,d^3\right)}{b^3\,d^3}-\frac{256\,\sqrt{x}\,{\left(-\frac{a^7}{16\,a^4\,b^7\,d^4-64\,a^3\,b^8\,c\,d^3+96\,a^2\,b^9\,c^2\,d^2-64\,a\,b^{10}\,c^3\,d+16\,b^{11}\,c^4}\right)}^{1/4}\,\left(16\,a^9\,b^5\,c^3\,d^{11}-64\,a^8\,b^6\,c^4\,d^{10}+112\,a^7\,b^7\,c^5\,d^9-128\,a^6\,b^8\,c^6\,d^8+112\,a^5\,b^9\,c^7\,d^7-64\,a^4\,b^{10}\,c^8\,d^6+16\,a^3\,b^{11}\,c^9\,d^5\right)}{b^3\,d^3}\right)-\frac{256\,\sqrt{x}\,\left(a^{10}\,c^5\,d^5+a^5\,b^5\,c^{10}\right)}{b^3\,d^3}\right)\,1{}\mathrm{i}-{\left(-\frac{a^7}{16\,a^4\,b^7\,d^4-64\,a^3\,b^8\,c\,d^3+96\,a^2\,b^9\,c^2\,d^2-64\,a\,b^{10}\,c^3\,d+16\,b^{11}\,c^4}\right)}^{1/4}\,\left({\left(-\frac{a^7}{16\,a^4\,b^7\,d^4-64\,a^3\,b^8\,c\,d^3+96\,a^2\,b^9\,c^2\,d^2-64\,a\,b^{10}\,c^3\,d+16\,b^{11}\,c^4}\right)}^{3/4}\,\left(\frac{128\,\left(16\,a^{10}\,b^3\,c^3\,d^{10}-48\,a^9\,b^4\,c^4\,d^9+48\,a^8\,b^5\,c^5\,d^8-16\,a^7\,b^6\,c^6\,d^7-16\,a^6\,b^7\,c^7\,d^6+48\,a^5\,b^8\,c^8\,d^5-48\,a^4\,b^9\,c^9\,d^4+16\,a^3\,b^{10}\,c^{10}\,d^3\right)}{b^3\,d^3}+\frac{256\,\sqrt{x}\,{\left(-\frac{a^7}{16\,a^4\,b^7\,d^4-64\,a^3\,b^8\,c\,d^3+96\,a^2\,b^9\,c^2\,d^2-64\,a\,b^{10}\,c^3\,d+16\,b^{11}\,c^4}\right)}^{1/4}\,\left(16\,a^9\,b^5\,c^3\,d^{11}-64\,a^8\,b^6\,c^4\,d^{10}+112\,a^7\,b^7\,c^5\,d^9-128\,a^6\,b^8\,c^6\,d^8+112\,a^5\,b^9\,c^7\,d^7-64\,a^4\,b^{10}\,c^8\,d^6+16\,a^3\,b^{11}\,c^9\,d^5\right)}{b^3\,d^3}\right)+\frac{256\,\sqrt{x}\,\left(a^{10}\,c^5\,d^5+a^5\,b^5\,c^{10}\right)}{b^3\,d^3}\right)\,1{}\mathrm{i}}{{\left(-\frac{a^7}{16\,a^4\,b^7\,d^4-64\,a^3\,b^8\,c\,d^3+96\,a^2\,b^9\,c^2\,d^2-64\,a\,b^{10}\,c^3\,d+16\,b^{11}\,c^4}\right)}^{1/4}\,\left({\left(-\frac{a^7}{16\,a^4\,b^7\,d^4-64\,a^3\,b^8\,c\,d^3+96\,a^2\,b^9\,c^2\,d^2-64\,a\,b^{10}\,c^3\,d+16\,b^{11}\,c^4}\right)}^{3/4}\,\left(\frac{128\,\left(16\,a^{10}\,b^3\,c^3\,d^{10}-48\,a^9\,b^4\,c^4\,d^9+48\,a^8\,b^5\,c^5\,d^8-16\,a^7\,b^6\,c^6\,d^7-16\,a^6\,b^7\,c^7\,d^6+48\,a^5\,b^8\,c^8\,d^5-48\,a^4\,b^9\,c^9\,d^4+16\,a^3\,b^{10}\,c^{10}\,d^3\right)}{b^3\,d^3}-\frac{256\,\sqrt{x}\,{\left(-\frac{a^7}{16\,a^4\,b^7\,d^4-64\,a^3\,b^8\,c\,d^3+96\,a^2\,b^9\,c^2\,d^2-64\,a\,b^{10}\,c^3\,d+16\,b^{11}\,c^4}\right)}^{1/4}\,\left(16\,a^9\,b^5\,c^3\,d^{11}-64\,a^8\,b^6\,c^4\,d^{10}+112\,a^7\,b^7\,c^5\,d^9-128\,a^6\,b^8\,c^6\,d^8+112\,a^5\,b^9\,c^7\,d^7-64\,a^4\,b^{10}\,c^8\,d^6+16\,a^3\,b^{11}\,c^9\,d^5\right)}{b^3\,d^3}\right)-\frac{256\,\sqrt{x}\,\left(a^{10}\,c^5\,d^5+a^5\,b^5\,c^{10}\right)}{b^3\,d^3}\right)+{\left(-\frac{a^7}{16\,a^4\,b^7\,d^4-64\,a^3\,b^8\,c\,d^3+96\,a^2\,b^9\,c^2\,d^2-64\,a\,b^{10}\,c^3\,d+16\,b^{11}\,c^4}\right)}^{1/4}\,\left({\left(-\frac{a^7}{16\,a^4\,b^7\,d^4-64\,a^3\,b^8\,c\,d^3+96\,a^2\,b^9\,c^2\,d^2-64\,a\,b^{10}\,c^3\,d+16\,b^{11}\,c^4}\right)}^{3/4}\,\left(\frac{128\,\left(16\,a^{10}\,b^3\,c^3\,d^{10}-48\,a^9\,b^4\,c^4\,d^9+48\,a^8\,b^5\,c^5\,d^8-16\,a^7\,b^6\,c^6\,d^7-16\,a^6\,b^7\,c^7\,d^6+48\,a^5\,b^8\,c^8\,d^5-48\,a^4\,b^9\,c^9\,d^4+16\,a^3\,b^{10}\,c^{10}\,d^3\right)}{b^3\,d^3}+\frac{256\,\sqrt{x}\,{\left(-\frac{a^7}{16\,a^4\,b^7\,d^4-64\,a^3\,b^8\,c\,d^3+96\,a^2\,b^9\,c^2\,d^2-64\,a\,b^{10}\,c^3\,d+16\,b^{11}\,c^4}\right)}^{1/4}\,\left(16\,a^9\,b^5\,c^3\,d^{11}-64\,a^8\,b^6\,c^4\,d^{10}+112\,a^7\,b^7\,c^5\,d^9-128\,a^6\,b^8\,c^6\,d^8+112\,a^5\,b^9\,c^7\,d^7-64\,a^4\,b^{10}\,c^8\,d^6+16\,a^3\,b^{11}\,c^9\,d^5\right)}{b^3\,d^3}\right)+\frac{256\,\sqrt{x}\,\left(a^{10}\,c^5\,d^5+a^5\,b^5\,c^{10}\right)}{b^3\,d^3}\right)-\frac{256\,\left(a^9\,c^7\,d^2+a^8\,b\,c^8\,d+a^7\,b^2\,c^9\right)}{b^3\,d^3}}\right)\,{\left(-\frac{a^7}{16\,a^4\,b^7\,d^4-64\,a^3\,b^8\,c\,d^3+96\,a^2\,b^9\,c^2\,d^2-64\,a\,b^{10}\,c^3\,d+16\,b^{11}\,c^4}\right)}^{1/4}\,2{}\mathrm{i}","Not used",1,"atan(((-c^7/(16*a^4*d^11 + 16*b^4*c^4*d^7 - 64*a*b^3*c^3*d^8 + 96*a^2*b^2*c^2*d^9 - 64*a^3*b*c*d^10))^(1/4)*((-c^7/(16*a^4*d^11 + 16*b^4*c^4*d^7 - 64*a*b^3*c^3*d^8 + 96*a^2*b^2*c^2*d^9 - 64*a^3*b*c*d^10))^(3/4)*((128*(16*a^3*b^10*c^10*d^3 - 48*a^4*b^9*c^9*d^4 + 48*a^5*b^8*c^8*d^5 - 16*a^6*b^7*c^7*d^6 - 16*a^7*b^6*c^6*d^7 + 48*a^8*b^5*c^5*d^8 - 48*a^9*b^4*c^4*d^9 + 16*a^10*b^3*c^3*d^10))/(b^3*d^3) - (256*x^(1/2)*(-c^7/(16*a^4*d^11 + 16*b^4*c^4*d^7 - 64*a*b^3*c^3*d^8 + 96*a^2*b^2*c^2*d^9 - 64*a^3*b*c*d^10))^(1/4)*(16*a^3*b^11*c^9*d^5 - 64*a^4*b^10*c^8*d^6 + 112*a^5*b^9*c^7*d^7 - 128*a^6*b^8*c^6*d^8 + 112*a^7*b^7*c^5*d^9 - 64*a^8*b^6*c^4*d^10 + 16*a^9*b^5*c^3*d^11))/(b^3*d^3)) - (256*x^(1/2)*(a^5*b^5*c^10 + a^10*c^5*d^5))/(b^3*d^3))*1i - (-c^7/(16*a^4*d^11 + 16*b^4*c^4*d^7 - 64*a*b^3*c^3*d^8 + 96*a^2*b^2*c^2*d^9 - 64*a^3*b*c*d^10))^(1/4)*((-c^7/(16*a^4*d^11 + 16*b^4*c^4*d^7 - 64*a*b^3*c^3*d^8 + 96*a^2*b^2*c^2*d^9 - 64*a^3*b*c*d^10))^(3/4)*((128*(16*a^3*b^10*c^10*d^3 - 48*a^4*b^9*c^9*d^4 + 48*a^5*b^8*c^8*d^5 - 16*a^6*b^7*c^7*d^6 - 16*a^7*b^6*c^6*d^7 + 48*a^8*b^5*c^5*d^8 - 48*a^9*b^4*c^4*d^9 + 16*a^10*b^3*c^3*d^10))/(b^3*d^3) + (256*x^(1/2)*(-c^7/(16*a^4*d^11 + 16*b^4*c^4*d^7 - 64*a*b^3*c^3*d^8 + 96*a^2*b^2*c^2*d^9 - 64*a^3*b*c*d^10))^(1/4)*(16*a^3*b^11*c^9*d^5 - 64*a^4*b^10*c^8*d^6 + 112*a^5*b^9*c^7*d^7 - 128*a^6*b^8*c^6*d^8 + 112*a^7*b^7*c^5*d^9 - 64*a^8*b^6*c^4*d^10 + 16*a^9*b^5*c^3*d^11))/(b^3*d^3)) + (256*x^(1/2)*(a^5*b^5*c^10 + a^10*c^5*d^5))/(b^3*d^3))*1i)/((-c^7/(16*a^4*d^11 + 16*b^4*c^4*d^7 - 64*a*b^3*c^3*d^8 + 96*a^2*b^2*c^2*d^9 - 64*a^3*b*c*d^10))^(1/4)*((-c^7/(16*a^4*d^11 + 16*b^4*c^4*d^7 - 64*a*b^3*c^3*d^8 + 96*a^2*b^2*c^2*d^9 - 64*a^3*b*c*d^10))^(3/4)*((128*(16*a^3*b^10*c^10*d^3 - 48*a^4*b^9*c^9*d^4 + 48*a^5*b^8*c^8*d^5 - 16*a^6*b^7*c^7*d^6 - 16*a^7*b^6*c^6*d^7 + 48*a^8*b^5*c^5*d^8 - 48*a^9*b^4*c^4*d^9 + 16*a^10*b^3*c^3*d^10))/(b^3*d^3) - (256*x^(1/2)*(-c^7/(16*a^4*d^11 + 16*b^4*c^4*d^7 - 64*a*b^3*c^3*d^8 + 96*a^2*b^2*c^2*d^9 - 64*a^3*b*c*d^10))^(1/4)*(16*a^3*b^11*c^9*d^5 - 64*a^4*b^10*c^8*d^6 + 112*a^5*b^9*c^7*d^7 - 128*a^6*b^8*c^6*d^8 + 112*a^7*b^7*c^5*d^9 - 64*a^8*b^6*c^4*d^10 + 16*a^9*b^5*c^3*d^11))/(b^3*d^3)) - (256*x^(1/2)*(a^5*b^5*c^10 + a^10*c^5*d^5))/(b^3*d^3)) + (-c^7/(16*a^4*d^11 + 16*b^4*c^4*d^7 - 64*a*b^3*c^3*d^8 + 96*a^2*b^2*c^2*d^9 - 64*a^3*b*c*d^10))^(1/4)*((-c^7/(16*a^4*d^11 + 16*b^4*c^4*d^7 - 64*a*b^3*c^3*d^8 + 96*a^2*b^2*c^2*d^9 - 64*a^3*b*c*d^10))^(3/4)*((128*(16*a^3*b^10*c^10*d^3 - 48*a^4*b^9*c^9*d^4 + 48*a^5*b^8*c^8*d^5 - 16*a^6*b^7*c^7*d^6 - 16*a^7*b^6*c^6*d^7 + 48*a^8*b^5*c^5*d^8 - 48*a^9*b^4*c^4*d^9 + 16*a^10*b^3*c^3*d^10))/(b^3*d^3) + (256*x^(1/2)*(-c^7/(16*a^4*d^11 + 16*b^4*c^4*d^7 - 64*a*b^3*c^3*d^8 + 96*a^2*b^2*c^2*d^9 - 64*a^3*b*c*d^10))^(1/4)*(16*a^3*b^11*c^9*d^5 - 64*a^4*b^10*c^8*d^6 + 112*a^5*b^9*c^7*d^7 - 128*a^6*b^8*c^6*d^8 + 112*a^7*b^7*c^5*d^9 - 64*a^8*b^6*c^4*d^10 + 16*a^9*b^5*c^3*d^11))/(b^3*d^3)) + (256*x^(1/2)*(a^5*b^5*c^10 + a^10*c^5*d^5))/(b^3*d^3)) - (256*(a^7*b^2*c^9 + a^9*c^7*d^2 + a^8*b*c^8*d))/(b^3*d^3)))*(-c^7/(16*a^4*d^11 + 16*b^4*c^4*d^7 - 64*a*b^3*c^3*d^8 + 96*a^2*b^2*c^2*d^9 - 64*a^3*b*c*d^10))^(1/4)*2i + 2*atan(((-c^7/(16*a^4*d^11 + 16*b^4*c^4*d^7 - 64*a*b^3*c^3*d^8 + 96*a^2*b^2*c^2*d^9 - 64*a^3*b*c*d^10))^(1/4)*((-c^7/(16*a^4*d^11 + 16*b^4*c^4*d^7 - 64*a*b^3*c^3*d^8 + 96*a^2*b^2*c^2*d^9 - 64*a^3*b*c*d^10))^(3/4)*((128*(16*a^3*b^10*c^10*d^3 - 48*a^4*b^9*c^9*d^4 + 48*a^5*b^8*c^8*d^5 - 16*a^6*b^7*c^7*d^6 - 16*a^7*b^6*c^6*d^7 + 48*a^8*b^5*c^5*d^8 - 48*a^9*b^4*c^4*d^9 + 16*a^10*b^3*c^3*d^10))/(b^3*d^3) - (x^(1/2)*(-c^7/(16*a^4*d^11 + 16*b^4*c^4*d^7 - 64*a*b^3*c^3*d^8 + 96*a^2*b^2*c^2*d^9 - 64*a^3*b*c*d^10))^(1/4)*(16*a^3*b^11*c^9*d^5 - 64*a^4*b^10*c^8*d^6 + 112*a^5*b^9*c^7*d^7 - 128*a^6*b^8*c^6*d^8 + 112*a^7*b^7*c^5*d^9 - 64*a^8*b^6*c^4*d^10 + 16*a^9*b^5*c^3*d^11)*256i)/(b^3*d^3))*1i + (256*x^(1/2)*(a^5*b^5*c^10 + a^10*c^5*d^5))/(b^3*d^3)) - (-c^7/(16*a^4*d^11 + 16*b^4*c^4*d^7 - 64*a*b^3*c^3*d^8 + 96*a^2*b^2*c^2*d^9 - 64*a^3*b*c*d^10))^(1/4)*((-c^7/(16*a^4*d^11 + 16*b^4*c^4*d^7 - 64*a*b^3*c^3*d^8 + 96*a^2*b^2*c^2*d^9 - 64*a^3*b*c*d^10))^(3/4)*((128*(16*a^3*b^10*c^10*d^3 - 48*a^4*b^9*c^9*d^4 + 48*a^5*b^8*c^8*d^5 - 16*a^6*b^7*c^7*d^6 - 16*a^7*b^6*c^6*d^7 + 48*a^8*b^5*c^5*d^8 - 48*a^9*b^4*c^4*d^9 + 16*a^10*b^3*c^3*d^10))/(b^3*d^3) + (x^(1/2)*(-c^7/(16*a^4*d^11 + 16*b^4*c^4*d^7 - 64*a*b^3*c^3*d^8 + 96*a^2*b^2*c^2*d^9 - 64*a^3*b*c*d^10))^(1/4)*(16*a^3*b^11*c^9*d^5 - 64*a^4*b^10*c^8*d^6 + 112*a^5*b^9*c^7*d^7 - 128*a^6*b^8*c^6*d^8 + 112*a^7*b^7*c^5*d^9 - 64*a^8*b^6*c^4*d^10 + 16*a^9*b^5*c^3*d^11)*256i)/(b^3*d^3))*1i - (256*x^(1/2)*(a^5*b^5*c^10 + a^10*c^5*d^5))/(b^3*d^3)))/((-c^7/(16*a^4*d^11 + 16*b^4*c^4*d^7 - 64*a*b^3*c^3*d^8 + 96*a^2*b^2*c^2*d^9 - 64*a^3*b*c*d^10))^(1/4)*((-c^7/(16*a^4*d^11 + 16*b^4*c^4*d^7 - 64*a*b^3*c^3*d^8 + 96*a^2*b^2*c^2*d^9 - 64*a^3*b*c*d^10))^(3/4)*((128*(16*a^3*b^10*c^10*d^3 - 48*a^4*b^9*c^9*d^4 + 48*a^5*b^8*c^8*d^5 - 16*a^6*b^7*c^7*d^6 - 16*a^7*b^6*c^6*d^7 + 48*a^8*b^5*c^5*d^8 - 48*a^9*b^4*c^4*d^9 + 16*a^10*b^3*c^3*d^10))/(b^3*d^3) - (x^(1/2)*(-c^7/(16*a^4*d^11 + 16*b^4*c^4*d^7 - 64*a*b^3*c^3*d^8 + 96*a^2*b^2*c^2*d^9 - 64*a^3*b*c*d^10))^(1/4)*(16*a^3*b^11*c^9*d^5 - 64*a^4*b^10*c^8*d^6 + 112*a^5*b^9*c^7*d^7 - 128*a^6*b^8*c^6*d^8 + 112*a^7*b^7*c^5*d^9 - 64*a^8*b^6*c^4*d^10 + 16*a^9*b^5*c^3*d^11)*256i)/(b^3*d^3))*1i + (256*x^(1/2)*(a^5*b^5*c^10 + a^10*c^5*d^5))/(b^3*d^3))*1i + (-c^7/(16*a^4*d^11 + 16*b^4*c^4*d^7 - 64*a*b^3*c^3*d^8 + 96*a^2*b^2*c^2*d^9 - 64*a^3*b*c*d^10))^(1/4)*((-c^7/(16*a^4*d^11 + 16*b^4*c^4*d^7 - 64*a*b^3*c^3*d^8 + 96*a^2*b^2*c^2*d^9 - 64*a^3*b*c*d^10))^(3/4)*((128*(16*a^3*b^10*c^10*d^3 - 48*a^4*b^9*c^9*d^4 + 48*a^5*b^8*c^8*d^5 - 16*a^6*b^7*c^7*d^6 - 16*a^7*b^6*c^6*d^7 + 48*a^8*b^5*c^5*d^8 - 48*a^9*b^4*c^4*d^9 + 16*a^10*b^3*c^3*d^10))/(b^3*d^3) + (x^(1/2)*(-c^7/(16*a^4*d^11 + 16*b^4*c^4*d^7 - 64*a*b^3*c^3*d^8 + 96*a^2*b^2*c^2*d^9 - 64*a^3*b*c*d^10))^(1/4)*(16*a^3*b^11*c^9*d^5 - 64*a^4*b^10*c^8*d^6 + 112*a^5*b^9*c^7*d^7 - 128*a^6*b^8*c^6*d^8 + 112*a^7*b^7*c^5*d^9 - 64*a^8*b^6*c^4*d^10 + 16*a^9*b^5*c^3*d^11)*256i)/(b^3*d^3))*1i - (256*x^(1/2)*(a^5*b^5*c^10 + a^10*c^5*d^5))/(b^3*d^3))*1i + (256*(a^7*b^2*c^9 + a^9*c^7*d^2 + a^8*b*c^8*d))/(b^3*d^3)))*(-c^7/(16*a^4*d^11 + 16*b^4*c^4*d^7 - 64*a*b^3*c^3*d^8 + 96*a^2*b^2*c^2*d^9 - 64*a^3*b*c*d^10))^(1/4) + atan(((-a^7/(16*b^11*c^4 + 16*a^4*b^7*d^4 - 64*a^3*b^8*c*d^3 + 96*a^2*b^9*c^2*d^2 - 64*a*b^10*c^3*d))^(1/4)*((-a^7/(16*b^11*c^4 + 16*a^4*b^7*d^4 - 64*a^3*b^8*c*d^3 + 96*a^2*b^9*c^2*d^2 - 64*a*b^10*c^3*d))^(3/4)*((128*(16*a^3*b^10*c^10*d^3 - 48*a^4*b^9*c^9*d^4 + 48*a^5*b^8*c^8*d^5 - 16*a^6*b^7*c^7*d^6 - 16*a^7*b^6*c^6*d^7 + 48*a^8*b^5*c^5*d^8 - 48*a^9*b^4*c^4*d^9 + 16*a^10*b^3*c^3*d^10))/(b^3*d^3) - (256*x^(1/2)*(-a^7/(16*b^11*c^4 + 16*a^4*b^7*d^4 - 64*a^3*b^8*c*d^3 + 96*a^2*b^9*c^2*d^2 - 64*a*b^10*c^3*d))^(1/4)*(16*a^3*b^11*c^9*d^5 - 64*a^4*b^10*c^8*d^6 + 112*a^5*b^9*c^7*d^7 - 128*a^6*b^8*c^6*d^8 + 112*a^7*b^7*c^5*d^9 - 64*a^8*b^6*c^4*d^10 + 16*a^9*b^5*c^3*d^11))/(b^3*d^3)) - (256*x^(1/2)*(a^5*b^5*c^10 + a^10*c^5*d^5))/(b^3*d^3))*1i - (-a^7/(16*b^11*c^4 + 16*a^4*b^7*d^4 - 64*a^3*b^8*c*d^3 + 96*a^2*b^9*c^2*d^2 - 64*a*b^10*c^3*d))^(1/4)*((-a^7/(16*b^11*c^4 + 16*a^4*b^7*d^4 - 64*a^3*b^8*c*d^3 + 96*a^2*b^9*c^2*d^2 - 64*a*b^10*c^3*d))^(3/4)*((128*(16*a^3*b^10*c^10*d^3 - 48*a^4*b^9*c^9*d^4 + 48*a^5*b^8*c^8*d^5 - 16*a^6*b^7*c^7*d^6 - 16*a^7*b^6*c^6*d^7 + 48*a^8*b^5*c^5*d^8 - 48*a^9*b^4*c^4*d^9 + 16*a^10*b^3*c^3*d^10))/(b^3*d^3) + (256*x^(1/2)*(-a^7/(16*b^11*c^4 + 16*a^4*b^7*d^4 - 64*a^3*b^8*c*d^3 + 96*a^2*b^9*c^2*d^2 - 64*a*b^10*c^3*d))^(1/4)*(16*a^3*b^11*c^9*d^5 - 64*a^4*b^10*c^8*d^6 + 112*a^5*b^9*c^7*d^7 - 128*a^6*b^8*c^6*d^8 + 112*a^7*b^7*c^5*d^9 - 64*a^8*b^6*c^4*d^10 + 16*a^9*b^5*c^3*d^11))/(b^3*d^3)) + (256*x^(1/2)*(a^5*b^5*c^10 + a^10*c^5*d^5))/(b^3*d^3))*1i)/((-a^7/(16*b^11*c^4 + 16*a^4*b^7*d^4 - 64*a^3*b^8*c*d^3 + 96*a^2*b^9*c^2*d^2 - 64*a*b^10*c^3*d))^(1/4)*((-a^7/(16*b^11*c^4 + 16*a^4*b^7*d^4 - 64*a^3*b^8*c*d^3 + 96*a^2*b^9*c^2*d^2 - 64*a*b^10*c^3*d))^(3/4)*((128*(16*a^3*b^10*c^10*d^3 - 48*a^4*b^9*c^9*d^4 + 48*a^5*b^8*c^8*d^5 - 16*a^6*b^7*c^7*d^6 - 16*a^7*b^6*c^6*d^7 + 48*a^8*b^5*c^5*d^8 - 48*a^9*b^4*c^4*d^9 + 16*a^10*b^3*c^3*d^10))/(b^3*d^3) - (256*x^(1/2)*(-a^7/(16*b^11*c^4 + 16*a^4*b^7*d^4 - 64*a^3*b^8*c*d^3 + 96*a^2*b^9*c^2*d^2 - 64*a*b^10*c^3*d))^(1/4)*(16*a^3*b^11*c^9*d^5 - 64*a^4*b^10*c^8*d^6 + 112*a^5*b^9*c^7*d^7 - 128*a^6*b^8*c^6*d^8 + 112*a^7*b^7*c^5*d^9 - 64*a^8*b^6*c^4*d^10 + 16*a^9*b^5*c^3*d^11))/(b^3*d^3)) - (256*x^(1/2)*(a^5*b^5*c^10 + a^10*c^5*d^5))/(b^3*d^3)) + (-a^7/(16*b^11*c^4 + 16*a^4*b^7*d^4 - 64*a^3*b^8*c*d^3 + 96*a^2*b^9*c^2*d^2 - 64*a*b^10*c^3*d))^(1/4)*((-a^7/(16*b^11*c^4 + 16*a^4*b^7*d^4 - 64*a^3*b^8*c*d^3 + 96*a^2*b^9*c^2*d^2 - 64*a*b^10*c^3*d))^(3/4)*((128*(16*a^3*b^10*c^10*d^3 - 48*a^4*b^9*c^9*d^4 + 48*a^5*b^8*c^8*d^5 - 16*a^6*b^7*c^7*d^6 - 16*a^7*b^6*c^6*d^7 + 48*a^8*b^5*c^5*d^8 - 48*a^9*b^4*c^4*d^9 + 16*a^10*b^3*c^3*d^10))/(b^3*d^3) + (256*x^(1/2)*(-a^7/(16*b^11*c^4 + 16*a^4*b^7*d^4 - 64*a^3*b^8*c*d^3 + 96*a^2*b^9*c^2*d^2 - 64*a*b^10*c^3*d))^(1/4)*(16*a^3*b^11*c^9*d^5 - 64*a^4*b^10*c^8*d^6 + 112*a^5*b^9*c^7*d^7 - 128*a^6*b^8*c^6*d^8 + 112*a^7*b^7*c^5*d^9 - 64*a^8*b^6*c^4*d^10 + 16*a^9*b^5*c^3*d^11))/(b^3*d^3)) + (256*x^(1/2)*(a^5*b^5*c^10 + a^10*c^5*d^5))/(b^3*d^3)) - (256*(a^7*b^2*c^9 + a^9*c^7*d^2 + a^8*b*c^8*d))/(b^3*d^3)))*(-a^7/(16*b^11*c^4 + 16*a^4*b^7*d^4 - 64*a^3*b^8*c*d^3 + 96*a^2*b^9*c^2*d^2 - 64*a*b^10*c^3*d))^(1/4)*2i + 2*atan(((-a^7/(16*b^11*c^4 + 16*a^4*b^7*d^4 - 64*a^3*b^8*c*d^3 + 96*a^2*b^9*c^2*d^2 - 64*a*b^10*c^3*d))^(1/4)*((-a^7/(16*b^11*c^4 + 16*a^4*b^7*d^4 - 64*a^3*b^8*c*d^3 + 96*a^2*b^9*c^2*d^2 - 64*a*b^10*c^3*d))^(3/4)*((128*(16*a^3*b^10*c^10*d^3 - 48*a^4*b^9*c^9*d^4 + 48*a^5*b^8*c^8*d^5 - 16*a^6*b^7*c^7*d^6 - 16*a^7*b^6*c^6*d^7 + 48*a^8*b^5*c^5*d^8 - 48*a^9*b^4*c^4*d^9 + 16*a^10*b^3*c^3*d^10))/(b^3*d^3) - (x^(1/2)*(-a^7/(16*b^11*c^4 + 16*a^4*b^7*d^4 - 64*a^3*b^8*c*d^3 + 96*a^2*b^9*c^2*d^2 - 64*a*b^10*c^3*d))^(1/4)*(16*a^3*b^11*c^9*d^5 - 64*a^4*b^10*c^8*d^6 + 112*a^5*b^9*c^7*d^7 - 128*a^6*b^8*c^6*d^8 + 112*a^7*b^7*c^5*d^9 - 64*a^8*b^6*c^4*d^10 + 16*a^9*b^5*c^3*d^11)*256i)/(b^3*d^3))*1i + (256*x^(1/2)*(a^5*b^5*c^10 + a^10*c^5*d^5))/(b^3*d^3)) - (-a^7/(16*b^11*c^4 + 16*a^4*b^7*d^4 - 64*a^3*b^8*c*d^3 + 96*a^2*b^9*c^2*d^2 - 64*a*b^10*c^3*d))^(1/4)*((-a^7/(16*b^11*c^4 + 16*a^4*b^7*d^4 - 64*a^3*b^8*c*d^3 + 96*a^2*b^9*c^2*d^2 - 64*a*b^10*c^3*d))^(3/4)*((128*(16*a^3*b^10*c^10*d^3 - 48*a^4*b^9*c^9*d^4 + 48*a^5*b^8*c^8*d^5 - 16*a^6*b^7*c^7*d^6 - 16*a^7*b^6*c^6*d^7 + 48*a^8*b^5*c^5*d^8 - 48*a^9*b^4*c^4*d^9 + 16*a^10*b^3*c^3*d^10))/(b^3*d^3) + (x^(1/2)*(-a^7/(16*b^11*c^4 + 16*a^4*b^7*d^4 - 64*a^3*b^8*c*d^3 + 96*a^2*b^9*c^2*d^2 - 64*a*b^10*c^3*d))^(1/4)*(16*a^3*b^11*c^9*d^5 - 64*a^4*b^10*c^8*d^6 + 112*a^5*b^9*c^7*d^7 - 128*a^6*b^8*c^6*d^8 + 112*a^7*b^7*c^5*d^9 - 64*a^8*b^6*c^4*d^10 + 16*a^9*b^5*c^3*d^11)*256i)/(b^3*d^3))*1i - (256*x^(1/2)*(a^5*b^5*c^10 + a^10*c^5*d^5))/(b^3*d^3)))/((-a^7/(16*b^11*c^4 + 16*a^4*b^7*d^4 - 64*a^3*b^8*c*d^3 + 96*a^2*b^9*c^2*d^2 - 64*a*b^10*c^3*d))^(1/4)*((-a^7/(16*b^11*c^4 + 16*a^4*b^7*d^4 - 64*a^3*b^8*c*d^3 + 96*a^2*b^9*c^2*d^2 - 64*a*b^10*c^3*d))^(3/4)*((128*(16*a^3*b^10*c^10*d^3 - 48*a^4*b^9*c^9*d^4 + 48*a^5*b^8*c^8*d^5 - 16*a^6*b^7*c^7*d^6 - 16*a^7*b^6*c^6*d^7 + 48*a^8*b^5*c^5*d^8 - 48*a^9*b^4*c^4*d^9 + 16*a^10*b^3*c^3*d^10))/(b^3*d^3) - (x^(1/2)*(-a^7/(16*b^11*c^4 + 16*a^4*b^7*d^4 - 64*a^3*b^8*c*d^3 + 96*a^2*b^9*c^2*d^2 - 64*a*b^10*c^3*d))^(1/4)*(16*a^3*b^11*c^9*d^5 - 64*a^4*b^10*c^8*d^6 + 112*a^5*b^9*c^7*d^7 - 128*a^6*b^8*c^6*d^8 + 112*a^7*b^7*c^5*d^9 - 64*a^8*b^6*c^4*d^10 + 16*a^9*b^5*c^3*d^11)*256i)/(b^3*d^3))*1i + (256*x^(1/2)*(a^5*b^5*c^10 + a^10*c^5*d^5))/(b^3*d^3))*1i + (-a^7/(16*b^11*c^4 + 16*a^4*b^7*d^4 - 64*a^3*b^8*c*d^3 + 96*a^2*b^9*c^2*d^2 - 64*a*b^10*c^3*d))^(1/4)*((-a^7/(16*b^11*c^4 + 16*a^4*b^7*d^4 - 64*a^3*b^8*c*d^3 + 96*a^2*b^9*c^2*d^2 - 64*a*b^10*c^3*d))^(3/4)*((128*(16*a^3*b^10*c^10*d^3 - 48*a^4*b^9*c^9*d^4 + 48*a^5*b^8*c^8*d^5 - 16*a^6*b^7*c^7*d^6 - 16*a^7*b^6*c^6*d^7 + 48*a^8*b^5*c^5*d^8 - 48*a^9*b^4*c^4*d^9 + 16*a^10*b^3*c^3*d^10))/(b^3*d^3) + (x^(1/2)*(-a^7/(16*b^11*c^4 + 16*a^4*b^7*d^4 - 64*a^3*b^8*c*d^3 + 96*a^2*b^9*c^2*d^2 - 64*a*b^10*c^3*d))^(1/4)*(16*a^3*b^11*c^9*d^5 - 64*a^4*b^10*c^8*d^6 + 112*a^5*b^9*c^7*d^7 - 128*a^6*b^8*c^6*d^8 + 112*a^7*b^7*c^5*d^9 - 64*a^8*b^6*c^4*d^10 + 16*a^9*b^5*c^3*d^11)*256i)/(b^3*d^3))*1i - (256*x^(1/2)*(a^5*b^5*c^10 + a^10*c^5*d^5))/(b^3*d^3))*1i + (256*(a^7*b^2*c^9 + a^9*c^7*d^2 + a^8*b*c^8*d))/(b^3*d^3)))*(-a^7/(16*b^11*c^4 + 16*a^4*b^7*d^4 - 64*a^3*b^8*c*d^3 + 96*a^2*b^9*c^2*d^2 - 64*a*b^10*c^3*d))^(1/4) + (2*x^(3/2))/(3*b*d)","B"
462,1,6428,476,1.601629,"\text{Not used}","int(x^(7/2)/((a + b*x^2)*(c + d*x^2)),x)","\frac{2\,\sqrt{x}}{b\,d}-2\,\mathrm{atan}\left(\frac{\left(\frac{256\,\sqrt{x}\,\left(a^8\,c^4\,d^4+a^4\,b^4\,c^8\right)}{b\,d}+\left(\frac{512\,\left(a^9\,c^3\,d^6-a^8\,b\,c^4\,d^5-a^4\,b^5\,c^8\,d+a^3\,b^6\,c^9\right)}{b\,d}-\frac{\sqrt{x}\,{\left(-\frac{c^5}{16\,a^4\,d^9-64\,a^3\,b\,c\,d^8+96\,a^2\,b^2\,c^2\,d^7-64\,a\,b^3\,c^3\,d^6+16\,b^4\,c^4\,d^5}\right)}^{3/4}\,\left(16\,a^8\,b^4\,c^3\,d^9-48\,a^7\,b^5\,c^4\,d^8+32\,a^6\,b^6\,c^5\,d^7+32\,a^5\,b^7\,c^6\,d^6-48\,a^4\,b^8\,c^7\,d^5+16\,a^3\,b^9\,c^8\,d^4\right)\,256{}\mathrm{i}}{b\,d}\right)\,{\left(-\frac{c^5}{16\,a^4\,d^9-64\,a^3\,b\,c\,d^8+96\,a^2\,b^2\,c^2\,d^7-64\,a\,b^3\,c^3\,d^6+16\,b^4\,c^4\,d^5}\right)}^{1/4}\,1{}\mathrm{i}\right)\,{\left(-\frac{c^5}{16\,a^4\,d^9-64\,a^3\,b\,c\,d^8+96\,a^2\,b^2\,c^2\,d^7-64\,a\,b^3\,c^3\,d^6+16\,b^4\,c^4\,d^5}\right)}^{1/4}-\left(-\frac{256\,\sqrt{x}\,\left(a^8\,c^4\,d^4+a^4\,b^4\,c^8\right)}{b\,d}+\left(\frac{512\,\left(a^9\,c^3\,d^6-a^8\,b\,c^4\,d^5-a^4\,b^5\,c^8\,d+a^3\,b^6\,c^9\right)}{b\,d}+\frac{\sqrt{x}\,{\left(-\frac{c^5}{16\,a^4\,d^9-64\,a^3\,b\,c\,d^8+96\,a^2\,b^2\,c^2\,d^7-64\,a\,b^3\,c^3\,d^6+16\,b^4\,c^4\,d^5}\right)}^{3/4}\,\left(16\,a^8\,b^4\,c^3\,d^9-48\,a^7\,b^5\,c^4\,d^8+32\,a^6\,b^6\,c^5\,d^7+32\,a^5\,b^7\,c^6\,d^6-48\,a^4\,b^8\,c^7\,d^5+16\,a^3\,b^9\,c^8\,d^4\right)\,256{}\mathrm{i}}{b\,d}\right)\,{\left(-\frac{c^5}{16\,a^4\,d^9-64\,a^3\,b\,c\,d^8+96\,a^2\,b^2\,c^2\,d^7-64\,a\,b^3\,c^3\,d^6+16\,b^4\,c^4\,d^5}\right)}^{1/4}\,1{}\mathrm{i}\right)\,{\left(-\frac{c^5}{16\,a^4\,d^9-64\,a^3\,b\,c\,d^8+96\,a^2\,b^2\,c^2\,d^7-64\,a\,b^3\,c^3\,d^6+16\,b^4\,c^4\,d^5}\right)}^{1/4}}{\left(\frac{256\,\sqrt{x}\,\left(a^8\,c^4\,d^4+a^4\,b^4\,c^8\right)}{b\,d}+\left(\frac{512\,\left(a^9\,c^3\,d^6-a^8\,b\,c^4\,d^5-a^4\,b^5\,c^8\,d+a^3\,b^6\,c^9\right)}{b\,d}-\frac{\sqrt{x}\,{\left(-\frac{c^5}{16\,a^4\,d^9-64\,a^3\,b\,c\,d^8+96\,a^2\,b^2\,c^2\,d^7-64\,a\,b^3\,c^3\,d^6+16\,b^4\,c^4\,d^5}\right)}^{3/4}\,\left(16\,a^8\,b^4\,c^3\,d^9-48\,a^7\,b^5\,c^4\,d^8+32\,a^6\,b^6\,c^5\,d^7+32\,a^5\,b^7\,c^6\,d^6-48\,a^4\,b^8\,c^7\,d^5+16\,a^3\,b^9\,c^8\,d^4\right)\,256{}\mathrm{i}}{b\,d}\right)\,{\left(-\frac{c^5}{16\,a^4\,d^9-64\,a^3\,b\,c\,d^8+96\,a^2\,b^2\,c^2\,d^7-64\,a\,b^3\,c^3\,d^6+16\,b^4\,c^4\,d^5}\right)}^{1/4}\,1{}\mathrm{i}\right)\,{\left(-\frac{c^5}{16\,a^4\,d^9-64\,a^3\,b\,c\,d^8+96\,a^2\,b^2\,c^2\,d^7-64\,a\,b^3\,c^3\,d^6+16\,b^4\,c^4\,d^5}\right)}^{1/4}\,1{}\mathrm{i}+\left(-\frac{256\,\sqrt{x}\,\left(a^8\,c^4\,d^4+a^4\,b^4\,c^8\right)}{b\,d}+\left(\frac{512\,\left(a^9\,c^3\,d^6-a^8\,b\,c^4\,d^5-a^4\,b^5\,c^8\,d+a^3\,b^6\,c^9\right)}{b\,d}+\frac{\sqrt{x}\,{\left(-\frac{c^5}{16\,a^4\,d^9-64\,a^3\,b\,c\,d^8+96\,a^2\,b^2\,c^2\,d^7-64\,a\,b^3\,c^3\,d^6+16\,b^4\,c^4\,d^5}\right)}^{3/4}\,\left(16\,a^8\,b^4\,c^3\,d^9-48\,a^7\,b^5\,c^4\,d^8+32\,a^6\,b^6\,c^5\,d^7+32\,a^5\,b^7\,c^6\,d^6-48\,a^4\,b^8\,c^7\,d^5+16\,a^3\,b^9\,c^8\,d^4\right)\,256{}\mathrm{i}}{b\,d}\right)\,{\left(-\frac{c^5}{16\,a^4\,d^9-64\,a^3\,b\,c\,d^8+96\,a^2\,b^2\,c^2\,d^7-64\,a\,b^3\,c^3\,d^6+16\,b^4\,c^4\,d^5}\right)}^{1/4}\,1{}\mathrm{i}\right)\,{\left(-\frac{c^5}{16\,a^4\,d^9-64\,a^3\,b\,c\,d^8+96\,a^2\,b^2\,c^2\,d^7-64\,a\,b^3\,c^3\,d^6+16\,b^4\,c^4\,d^5}\right)}^{1/4}\,1{}\mathrm{i}}\right)\,{\left(-\frac{c^5}{16\,a^4\,d^9-64\,a^3\,b\,c\,d^8+96\,a^2\,b^2\,c^2\,d^7-64\,a\,b^3\,c^3\,d^6+16\,b^4\,c^4\,d^5}\right)}^{1/4}-2\,\mathrm{atan}\left(\frac{\left(\frac{256\,\sqrt{x}\,\left(a^8\,c^4\,d^4+a^4\,b^4\,c^8\right)}{b\,d}+\left(\frac{512\,\left(a^9\,c^3\,d^6-a^8\,b\,c^4\,d^5-a^4\,b^5\,c^8\,d+a^3\,b^6\,c^9\right)}{b\,d}-\frac{\sqrt{x}\,{\left(-\frac{a^5}{16\,a^4\,b^5\,d^4-64\,a^3\,b^6\,c\,d^3+96\,a^2\,b^7\,c^2\,d^2-64\,a\,b^8\,c^3\,d+16\,b^9\,c^4}\right)}^{3/4}\,\left(16\,a^8\,b^4\,c^3\,d^9-48\,a^7\,b^5\,c^4\,d^8+32\,a^6\,b^6\,c^5\,d^7+32\,a^5\,b^7\,c^6\,d^6-48\,a^4\,b^8\,c^7\,d^5+16\,a^3\,b^9\,c^8\,d^4\right)\,256{}\mathrm{i}}{b\,d}\right)\,{\left(-\frac{a^5}{16\,a^4\,b^5\,d^4-64\,a^3\,b^6\,c\,d^3+96\,a^2\,b^7\,c^2\,d^2-64\,a\,b^8\,c^3\,d+16\,b^9\,c^4}\right)}^{1/4}\,1{}\mathrm{i}\right)\,{\left(-\frac{a^5}{16\,a^4\,b^5\,d^4-64\,a^3\,b^6\,c\,d^3+96\,a^2\,b^7\,c^2\,d^2-64\,a\,b^8\,c^3\,d+16\,b^9\,c^4}\right)}^{1/4}-\left(-\frac{256\,\sqrt{x}\,\left(a^8\,c^4\,d^4+a^4\,b^4\,c^8\right)}{b\,d}+\left(\frac{512\,\left(a^9\,c^3\,d^6-a^8\,b\,c^4\,d^5-a^4\,b^5\,c^8\,d+a^3\,b^6\,c^9\right)}{b\,d}+\frac{\sqrt{x}\,{\left(-\frac{a^5}{16\,a^4\,b^5\,d^4-64\,a^3\,b^6\,c\,d^3+96\,a^2\,b^7\,c^2\,d^2-64\,a\,b^8\,c^3\,d+16\,b^9\,c^4}\right)}^{3/4}\,\left(16\,a^8\,b^4\,c^3\,d^9-48\,a^7\,b^5\,c^4\,d^8+32\,a^6\,b^6\,c^5\,d^7+32\,a^5\,b^7\,c^6\,d^6-48\,a^4\,b^8\,c^7\,d^5+16\,a^3\,b^9\,c^8\,d^4\right)\,256{}\mathrm{i}}{b\,d}\right)\,{\left(-\frac{a^5}{16\,a^4\,b^5\,d^4-64\,a^3\,b^6\,c\,d^3+96\,a^2\,b^7\,c^2\,d^2-64\,a\,b^8\,c^3\,d+16\,b^9\,c^4}\right)}^{1/4}\,1{}\mathrm{i}\right)\,{\left(-\frac{a^5}{16\,a^4\,b^5\,d^4-64\,a^3\,b^6\,c\,d^3+96\,a^2\,b^7\,c^2\,d^2-64\,a\,b^8\,c^3\,d+16\,b^9\,c^4}\right)}^{1/4}}{\left(\frac{256\,\sqrt{x}\,\left(a^8\,c^4\,d^4+a^4\,b^4\,c^8\right)}{b\,d}+\left(\frac{512\,\left(a^9\,c^3\,d^6-a^8\,b\,c^4\,d^5-a^4\,b^5\,c^8\,d+a^3\,b^6\,c^9\right)}{b\,d}-\frac{\sqrt{x}\,{\left(-\frac{a^5}{16\,a^4\,b^5\,d^4-64\,a^3\,b^6\,c\,d^3+96\,a^2\,b^7\,c^2\,d^2-64\,a\,b^8\,c^3\,d+16\,b^9\,c^4}\right)}^{3/4}\,\left(16\,a^8\,b^4\,c^3\,d^9-48\,a^7\,b^5\,c^4\,d^8+32\,a^6\,b^6\,c^5\,d^7+32\,a^5\,b^7\,c^6\,d^6-48\,a^4\,b^8\,c^7\,d^5+16\,a^3\,b^9\,c^8\,d^4\right)\,256{}\mathrm{i}}{b\,d}\right)\,{\left(-\frac{a^5}{16\,a^4\,b^5\,d^4-64\,a^3\,b^6\,c\,d^3+96\,a^2\,b^7\,c^2\,d^2-64\,a\,b^8\,c^3\,d+16\,b^9\,c^4}\right)}^{1/4}\,1{}\mathrm{i}\right)\,{\left(-\frac{a^5}{16\,a^4\,b^5\,d^4-64\,a^3\,b^6\,c\,d^3+96\,a^2\,b^7\,c^2\,d^2-64\,a\,b^8\,c^3\,d+16\,b^9\,c^4}\right)}^{1/4}\,1{}\mathrm{i}+\left(-\frac{256\,\sqrt{x}\,\left(a^8\,c^4\,d^4+a^4\,b^4\,c^8\right)}{b\,d}+\left(\frac{512\,\left(a^9\,c^3\,d^6-a^8\,b\,c^4\,d^5-a^4\,b^5\,c^8\,d+a^3\,b^6\,c^9\right)}{b\,d}+\frac{\sqrt{x}\,{\left(-\frac{a^5}{16\,a^4\,b^5\,d^4-64\,a^3\,b^6\,c\,d^3+96\,a^2\,b^7\,c^2\,d^2-64\,a\,b^8\,c^3\,d+16\,b^9\,c^4}\right)}^{3/4}\,\left(16\,a^8\,b^4\,c^3\,d^9-48\,a^7\,b^5\,c^4\,d^8+32\,a^6\,b^6\,c^5\,d^7+32\,a^5\,b^7\,c^6\,d^6-48\,a^4\,b^8\,c^7\,d^5+16\,a^3\,b^9\,c^8\,d^4\right)\,256{}\mathrm{i}}{b\,d}\right)\,{\left(-\frac{a^5}{16\,a^4\,b^5\,d^4-64\,a^3\,b^6\,c\,d^3+96\,a^2\,b^7\,c^2\,d^2-64\,a\,b^8\,c^3\,d+16\,b^9\,c^4}\right)}^{1/4}\,1{}\mathrm{i}\right)\,{\left(-\frac{a^5}{16\,a^4\,b^5\,d^4-64\,a^3\,b^6\,c\,d^3+96\,a^2\,b^7\,c^2\,d^2-64\,a\,b^8\,c^3\,d+16\,b^9\,c^4}\right)}^{1/4}\,1{}\mathrm{i}}\right)\,{\left(-\frac{a^5}{16\,a^4\,b^5\,d^4-64\,a^3\,b^6\,c\,d^3+96\,a^2\,b^7\,c^2\,d^2-64\,a\,b^8\,c^3\,d+16\,b^9\,c^4}\right)}^{1/4}+\mathrm{atan}\left(\frac{\left(\left(\frac{512\,\left(a^9\,c^3\,d^6-a^8\,b\,c^4\,d^5-a^4\,b^5\,c^8\,d+a^3\,b^6\,c^9\right)}{b\,d}-\frac{256\,\sqrt{x}\,{\left(-\frac{a^5}{16\,a^4\,b^5\,d^4-64\,a^3\,b^6\,c\,d^3+96\,a^2\,b^7\,c^2\,d^2-64\,a\,b^8\,c^3\,d+16\,b^9\,c^4}\right)}^{3/4}\,\left(16\,a^8\,b^4\,c^3\,d^9-48\,a^7\,b^5\,c^4\,d^8+32\,a^6\,b^6\,c^5\,d^7+32\,a^5\,b^7\,c^6\,d^6-48\,a^4\,b^8\,c^7\,d^5+16\,a^3\,b^9\,c^8\,d^4\right)}{b\,d}\right)\,{\left(-\frac{a^5}{16\,a^4\,b^5\,d^4-64\,a^3\,b^6\,c\,d^3+96\,a^2\,b^7\,c^2\,d^2-64\,a\,b^8\,c^3\,d+16\,b^9\,c^4}\right)}^{1/4}-\frac{256\,\sqrt{x}\,\left(a^8\,c^4\,d^4+a^4\,b^4\,c^8\right)}{b\,d}\right)\,{\left(-\frac{a^5}{16\,a^4\,b^5\,d^4-64\,a^3\,b^6\,c\,d^3+96\,a^2\,b^7\,c^2\,d^2-64\,a\,b^8\,c^3\,d+16\,b^9\,c^4}\right)}^{1/4}\,1{}\mathrm{i}-\left(\left(\frac{512\,\left(a^9\,c^3\,d^6-a^8\,b\,c^4\,d^5-a^4\,b^5\,c^8\,d+a^3\,b^6\,c^9\right)}{b\,d}+\frac{256\,\sqrt{x}\,{\left(-\frac{a^5}{16\,a^4\,b^5\,d^4-64\,a^3\,b^6\,c\,d^3+96\,a^2\,b^7\,c^2\,d^2-64\,a\,b^8\,c^3\,d+16\,b^9\,c^4}\right)}^{3/4}\,\left(16\,a^8\,b^4\,c^3\,d^9-48\,a^7\,b^5\,c^4\,d^8+32\,a^6\,b^6\,c^5\,d^7+32\,a^5\,b^7\,c^6\,d^6-48\,a^4\,b^8\,c^7\,d^5+16\,a^3\,b^9\,c^8\,d^4\right)}{b\,d}\right)\,{\left(-\frac{a^5}{16\,a^4\,b^5\,d^4-64\,a^3\,b^6\,c\,d^3+96\,a^2\,b^7\,c^2\,d^2-64\,a\,b^8\,c^3\,d+16\,b^9\,c^4}\right)}^{1/4}+\frac{256\,\sqrt{x}\,\left(a^8\,c^4\,d^4+a^4\,b^4\,c^8\right)}{b\,d}\right)\,{\left(-\frac{a^5}{16\,a^4\,b^5\,d^4-64\,a^3\,b^6\,c\,d^3+96\,a^2\,b^7\,c^2\,d^2-64\,a\,b^8\,c^3\,d+16\,b^9\,c^4}\right)}^{1/4}\,1{}\mathrm{i}}{\left(\left(\frac{512\,\left(a^9\,c^3\,d^6-a^8\,b\,c^4\,d^5-a^4\,b^5\,c^8\,d+a^3\,b^6\,c^9\right)}{b\,d}-\frac{256\,\sqrt{x}\,{\left(-\frac{a^5}{16\,a^4\,b^5\,d^4-64\,a^3\,b^6\,c\,d^3+96\,a^2\,b^7\,c^2\,d^2-64\,a\,b^8\,c^3\,d+16\,b^9\,c^4}\right)}^{3/4}\,\left(16\,a^8\,b^4\,c^3\,d^9-48\,a^7\,b^5\,c^4\,d^8+32\,a^6\,b^6\,c^5\,d^7+32\,a^5\,b^7\,c^6\,d^6-48\,a^4\,b^8\,c^7\,d^5+16\,a^3\,b^9\,c^8\,d^4\right)}{b\,d}\right)\,{\left(-\frac{a^5}{16\,a^4\,b^5\,d^4-64\,a^3\,b^6\,c\,d^3+96\,a^2\,b^7\,c^2\,d^2-64\,a\,b^8\,c^3\,d+16\,b^9\,c^4}\right)}^{1/4}-\frac{256\,\sqrt{x}\,\left(a^8\,c^4\,d^4+a^4\,b^4\,c^8\right)}{b\,d}\right)\,{\left(-\frac{a^5}{16\,a^4\,b^5\,d^4-64\,a^3\,b^6\,c\,d^3+96\,a^2\,b^7\,c^2\,d^2-64\,a\,b^8\,c^3\,d+16\,b^9\,c^4}\right)}^{1/4}+\left(\left(\frac{512\,\left(a^9\,c^3\,d^6-a^8\,b\,c^4\,d^5-a^4\,b^5\,c^8\,d+a^3\,b^6\,c^9\right)}{b\,d}+\frac{256\,\sqrt{x}\,{\left(-\frac{a^5}{16\,a^4\,b^5\,d^4-64\,a^3\,b^6\,c\,d^3+96\,a^2\,b^7\,c^2\,d^2-64\,a\,b^8\,c^3\,d+16\,b^9\,c^4}\right)}^{3/4}\,\left(16\,a^8\,b^4\,c^3\,d^9-48\,a^7\,b^5\,c^4\,d^8+32\,a^6\,b^6\,c^5\,d^7+32\,a^5\,b^7\,c^6\,d^6-48\,a^4\,b^8\,c^7\,d^5+16\,a^3\,b^9\,c^8\,d^4\right)}{b\,d}\right)\,{\left(-\frac{a^5}{16\,a^4\,b^5\,d^4-64\,a^3\,b^6\,c\,d^3+96\,a^2\,b^7\,c^2\,d^2-64\,a\,b^8\,c^3\,d+16\,b^9\,c^4}\right)}^{1/4}+\frac{256\,\sqrt{x}\,\left(a^8\,c^4\,d^4+a^4\,b^4\,c^8\right)}{b\,d}\right)\,{\left(-\frac{a^5}{16\,a^4\,b^5\,d^4-64\,a^3\,b^6\,c\,d^3+96\,a^2\,b^7\,c^2\,d^2-64\,a\,b^8\,c^3\,d+16\,b^9\,c^4}\right)}^{1/4}}\right)\,{\left(-\frac{a^5}{16\,a^4\,b^5\,d^4-64\,a^3\,b^6\,c\,d^3+96\,a^2\,b^7\,c^2\,d^2-64\,a\,b^8\,c^3\,d+16\,b^9\,c^4}\right)}^{1/4}\,2{}\mathrm{i}+\mathrm{atan}\left(\frac{\left(\left(\frac{512\,\left(a^9\,c^3\,d^6-a^8\,b\,c^4\,d^5-a^4\,b^5\,c^8\,d+a^3\,b^6\,c^9\right)}{b\,d}-\frac{256\,\sqrt{x}\,{\left(-\frac{c^5}{16\,a^4\,d^9-64\,a^3\,b\,c\,d^8+96\,a^2\,b^2\,c^2\,d^7-64\,a\,b^3\,c^3\,d^6+16\,b^4\,c^4\,d^5}\right)}^{3/4}\,\left(16\,a^8\,b^4\,c^3\,d^9-48\,a^7\,b^5\,c^4\,d^8+32\,a^6\,b^6\,c^5\,d^7+32\,a^5\,b^7\,c^6\,d^6-48\,a^4\,b^8\,c^7\,d^5+16\,a^3\,b^9\,c^8\,d^4\right)}{b\,d}\right)\,{\left(-\frac{c^5}{16\,a^4\,d^9-64\,a^3\,b\,c\,d^8+96\,a^2\,b^2\,c^2\,d^7-64\,a\,b^3\,c^3\,d^6+16\,b^4\,c^4\,d^5}\right)}^{1/4}-\frac{256\,\sqrt{x}\,\left(a^8\,c^4\,d^4+a^4\,b^4\,c^8\right)}{b\,d}\right)\,{\left(-\frac{c^5}{16\,a^4\,d^9-64\,a^3\,b\,c\,d^8+96\,a^2\,b^2\,c^2\,d^7-64\,a\,b^3\,c^3\,d^6+16\,b^4\,c^4\,d^5}\right)}^{1/4}\,1{}\mathrm{i}-\left(\left(\frac{512\,\left(a^9\,c^3\,d^6-a^8\,b\,c^4\,d^5-a^4\,b^5\,c^8\,d+a^3\,b^6\,c^9\right)}{b\,d}+\frac{256\,\sqrt{x}\,{\left(-\frac{c^5}{16\,a^4\,d^9-64\,a^3\,b\,c\,d^8+96\,a^2\,b^2\,c^2\,d^7-64\,a\,b^3\,c^3\,d^6+16\,b^4\,c^4\,d^5}\right)}^{3/4}\,\left(16\,a^8\,b^4\,c^3\,d^9-48\,a^7\,b^5\,c^4\,d^8+32\,a^6\,b^6\,c^5\,d^7+32\,a^5\,b^7\,c^6\,d^6-48\,a^4\,b^8\,c^7\,d^5+16\,a^3\,b^9\,c^8\,d^4\right)}{b\,d}\right)\,{\left(-\frac{c^5}{16\,a^4\,d^9-64\,a^3\,b\,c\,d^8+96\,a^2\,b^2\,c^2\,d^7-64\,a\,b^3\,c^3\,d^6+16\,b^4\,c^4\,d^5}\right)}^{1/4}+\frac{256\,\sqrt{x}\,\left(a^8\,c^4\,d^4+a^4\,b^4\,c^8\right)}{b\,d}\right)\,{\left(-\frac{c^5}{16\,a^4\,d^9-64\,a^3\,b\,c\,d^8+96\,a^2\,b^2\,c^2\,d^7-64\,a\,b^3\,c^3\,d^6+16\,b^4\,c^4\,d^5}\right)}^{1/4}\,1{}\mathrm{i}}{\left(\left(\frac{512\,\left(a^9\,c^3\,d^6-a^8\,b\,c^4\,d^5-a^4\,b^5\,c^8\,d+a^3\,b^6\,c^9\right)}{b\,d}-\frac{256\,\sqrt{x}\,{\left(-\frac{c^5}{16\,a^4\,d^9-64\,a^3\,b\,c\,d^8+96\,a^2\,b^2\,c^2\,d^7-64\,a\,b^3\,c^3\,d^6+16\,b^4\,c^4\,d^5}\right)}^{3/4}\,\left(16\,a^8\,b^4\,c^3\,d^9-48\,a^7\,b^5\,c^4\,d^8+32\,a^6\,b^6\,c^5\,d^7+32\,a^5\,b^7\,c^6\,d^6-48\,a^4\,b^8\,c^7\,d^5+16\,a^3\,b^9\,c^8\,d^4\right)}{b\,d}\right)\,{\left(-\frac{c^5}{16\,a^4\,d^9-64\,a^3\,b\,c\,d^8+96\,a^2\,b^2\,c^2\,d^7-64\,a\,b^3\,c^3\,d^6+16\,b^4\,c^4\,d^5}\right)}^{1/4}-\frac{256\,\sqrt{x}\,\left(a^8\,c^4\,d^4+a^4\,b^4\,c^8\right)}{b\,d}\right)\,{\left(-\frac{c^5}{16\,a^4\,d^9-64\,a^3\,b\,c\,d^8+96\,a^2\,b^2\,c^2\,d^7-64\,a\,b^3\,c^3\,d^6+16\,b^4\,c^4\,d^5}\right)}^{1/4}+\left(\left(\frac{512\,\left(a^9\,c^3\,d^6-a^8\,b\,c^4\,d^5-a^4\,b^5\,c^8\,d+a^3\,b^6\,c^9\right)}{b\,d}+\frac{256\,\sqrt{x}\,{\left(-\frac{c^5}{16\,a^4\,d^9-64\,a^3\,b\,c\,d^8+96\,a^2\,b^2\,c^2\,d^7-64\,a\,b^3\,c^3\,d^6+16\,b^4\,c^4\,d^5}\right)}^{3/4}\,\left(16\,a^8\,b^4\,c^3\,d^9-48\,a^7\,b^5\,c^4\,d^8+32\,a^6\,b^6\,c^5\,d^7+32\,a^5\,b^7\,c^6\,d^6-48\,a^4\,b^8\,c^7\,d^5+16\,a^3\,b^9\,c^8\,d^4\right)}{b\,d}\right)\,{\left(-\frac{c^5}{16\,a^4\,d^9-64\,a^3\,b\,c\,d^8+96\,a^2\,b^2\,c^2\,d^7-64\,a\,b^3\,c^3\,d^6+16\,b^4\,c^4\,d^5}\right)}^{1/4}+\frac{256\,\sqrt{x}\,\left(a^8\,c^4\,d^4+a^4\,b^4\,c^8\right)}{b\,d}\right)\,{\left(-\frac{c^5}{16\,a^4\,d^9-64\,a^3\,b\,c\,d^8+96\,a^2\,b^2\,c^2\,d^7-64\,a\,b^3\,c^3\,d^6+16\,b^4\,c^4\,d^5}\right)}^{1/4}}\right)\,{\left(-\frac{c^5}{16\,a^4\,d^9-64\,a^3\,b\,c\,d^8+96\,a^2\,b^2\,c^2\,d^7-64\,a\,b^3\,c^3\,d^6+16\,b^4\,c^4\,d^5}\right)}^{1/4}\,2{}\mathrm{i}","Not used",1,"atan(((((512*(a^3*b^6*c^9 + a^9*c^3*d^6 - a^4*b^5*c^8*d - a^8*b*c^4*d^5))/(b*d) - (256*x^(1/2)*(-a^5/(16*b^9*c^4 + 16*a^4*b^5*d^4 - 64*a^3*b^6*c*d^3 + 96*a^2*b^7*c^2*d^2 - 64*a*b^8*c^3*d))^(3/4)*(16*a^3*b^9*c^8*d^4 - 48*a^4*b^8*c^7*d^5 + 32*a^5*b^7*c^6*d^6 + 32*a^6*b^6*c^5*d^7 - 48*a^7*b^5*c^4*d^8 + 16*a^8*b^4*c^3*d^9))/(b*d))*(-a^5/(16*b^9*c^4 + 16*a^4*b^5*d^4 - 64*a^3*b^6*c*d^3 + 96*a^2*b^7*c^2*d^2 - 64*a*b^8*c^3*d))^(1/4) - (256*x^(1/2)*(a^4*b^4*c^8 + a^8*c^4*d^4))/(b*d))*(-a^5/(16*b^9*c^4 + 16*a^4*b^5*d^4 - 64*a^3*b^6*c*d^3 + 96*a^2*b^7*c^2*d^2 - 64*a*b^8*c^3*d))^(1/4)*1i - (((512*(a^3*b^6*c^9 + a^9*c^3*d^6 - a^4*b^5*c^8*d - a^8*b*c^4*d^5))/(b*d) + (256*x^(1/2)*(-a^5/(16*b^9*c^4 + 16*a^4*b^5*d^4 - 64*a^3*b^6*c*d^3 + 96*a^2*b^7*c^2*d^2 - 64*a*b^8*c^3*d))^(3/4)*(16*a^3*b^9*c^8*d^4 - 48*a^4*b^8*c^7*d^5 + 32*a^5*b^7*c^6*d^6 + 32*a^6*b^6*c^5*d^7 - 48*a^7*b^5*c^4*d^8 + 16*a^8*b^4*c^3*d^9))/(b*d))*(-a^5/(16*b^9*c^4 + 16*a^4*b^5*d^4 - 64*a^3*b^6*c*d^3 + 96*a^2*b^7*c^2*d^2 - 64*a*b^8*c^3*d))^(1/4) + (256*x^(1/2)*(a^4*b^4*c^8 + a^8*c^4*d^4))/(b*d))*(-a^5/(16*b^9*c^4 + 16*a^4*b^5*d^4 - 64*a^3*b^6*c*d^3 + 96*a^2*b^7*c^2*d^2 - 64*a*b^8*c^3*d))^(1/4)*1i)/((((512*(a^3*b^6*c^9 + a^9*c^3*d^6 - a^4*b^5*c^8*d - a^8*b*c^4*d^5))/(b*d) - (256*x^(1/2)*(-a^5/(16*b^9*c^4 + 16*a^4*b^5*d^4 - 64*a^3*b^6*c*d^3 + 96*a^2*b^7*c^2*d^2 - 64*a*b^8*c^3*d))^(3/4)*(16*a^3*b^9*c^8*d^4 - 48*a^4*b^8*c^7*d^5 + 32*a^5*b^7*c^6*d^6 + 32*a^6*b^6*c^5*d^7 - 48*a^7*b^5*c^4*d^8 + 16*a^8*b^4*c^3*d^9))/(b*d))*(-a^5/(16*b^9*c^4 + 16*a^4*b^5*d^4 - 64*a^3*b^6*c*d^3 + 96*a^2*b^7*c^2*d^2 - 64*a*b^8*c^3*d))^(1/4) - (256*x^(1/2)*(a^4*b^4*c^8 + a^8*c^4*d^4))/(b*d))*(-a^5/(16*b^9*c^4 + 16*a^4*b^5*d^4 - 64*a^3*b^6*c*d^3 + 96*a^2*b^7*c^2*d^2 - 64*a*b^8*c^3*d))^(1/4) + (((512*(a^3*b^6*c^9 + a^9*c^3*d^6 - a^4*b^5*c^8*d - a^8*b*c^4*d^5))/(b*d) + (256*x^(1/2)*(-a^5/(16*b^9*c^4 + 16*a^4*b^5*d^4 - 64*a^3*b^6*c*d^3 + 96*a^2*b^7*c^2*d^2 - 64*a*b^8*c^3*d))^(3/4)*(16*a^3*b^9*c^8*d^4 - 48*a^4*b^8*c^7*d^5 + 32*a^5*b^7*c^6*d^6 + 32*a^6*b^6*c^5*d^7 - 48*a^7*b^5*c^4*d^8 + 16*a^8*b^4*c^3*d^9))/(b*d))*(-a^5/(16*b^9*c^4 + 16*a^4*b^5*d^4 - 64*a^3*b^6*c*d^3 + 96*a^2*b^7*c^2*d^2 - 64*a*b^8*c^3*d))^(1/4) + (256*x^(1/2)*(a^4*b^4*c^8 + a^8*c^4*d^4))/(b*d))*(-a^5/(16*b^9*c^4 + 16*a^4*b^5*d^4 - 64*a^3*b^6*c*d^3 + 96*a^2*b^7*c^2*d^2 - 64*a*b^8*c^3*d))^(1/4)))*(-a^5/(16*b^9*c^4 + 16*a^4*b^5*d^4 - 64*a^3*b^6*c*d^3 + 96*a^2*b^7*c^2*d^2 - 64*a*b^8*c^3*d))^(1/4)*2i - 2*atan(((((512*(a^3*b^6*c^9 + a^9*c^3*d^6 - a^4*b^5*c^8*d - a^8*b*c^4*d^5))/(b*d) - (x^(1/2)*(-a^5/(16*b^9*c^4 + 16*a^4*b^5*d^4 - 64*a^3*b^6*c*d^3 + 96*a^2*b^7*c^2*d^2 - 64*a*b^8*c^3*d))^(3/4)*(16*a^3*b^9*c^8*d^4 - 48*a^4*b^8*c^7*d^5 + 32*a^5*b^7*c^6*d^6 + 32*a^6*b^6*c^5*d^7 - 48*a^7*b^5*c^4*d^8 + 16*a^8*b^4*c^3*d^9)*256i)/(b*d))*(-a^5/(16*b^9*c^4 + 16*a^4*b^5*d^4 - 64*a^3*b^6*c*d^3 + 96*a^2*b^7*c^2*d^2 - 64*a*b^8*c^3*d))^(1/4)*1i + (256*x^(1/2)*(a^4*b^4*c^8 + a^8*c^4*d^4))/(b*d))*(-a^5/(16*b^9*c^4 + 16*a^4*b^5*d^4 - 64*a^3*b^6*c*d^3 + 96*a^2*b^7*c^2*d^2 - 64*a*b^8*c^3*d))^(1/4) - (((512*(a^3*b^6*c^9 + a^9*c^3*d^6 - a^4*b^5*c^8*d - a^8*b*c^4*d^5))/(b*d) + (x^(1/2)*(-a^5/(16*b^9*c^4 + 16*a^4*b^5*d^4 - 64*a^3*b^6*c*d^3 + 96*a^2*b^7*c^2*d^2 - 64*a*b^8*c^3*d))^(3/4)*(16*a^3*b^9*c^8*d^4 - 48*a^4*b^8*c^7*d^5 + 32*a^5*b^7*c^6*d^6 + 32*a^6*b^6*c^5*d^7 - 48*a^7*b^5*c^4*d^8 + 16*a^8*b^4*c^3*d^9)*256i)/(b*d))*(-a^5/(16*b^9*c^4 + 16*a^4*b^5*d^4 - 64*a^3*b^6*c*d^3 + 96*a^2*b^7*c^2*d^2 - 64*a*b^8*c^3*d))^(1/4)*1i - (256*x^(1/2)*(a^4*b^4*c^8 + a^8*c^4*d^4))/(b*d))*(-a^5/(16*b^9*c^4 + 16*a^4*b^5*d^4 - 64*a^3*b^6*c*d^3 + 96*a^2*b^7*c^2*d^2 - 64*a*b^8*c^3*d))^(1/4))/((((512*(a^3*b^6*c^9 + a^9*c^3*d^6 - a^4*b^5*c^8*d - a^8*b*c^4*d^5))/(b*d) - (x^(1/2)*(-a^5/(16*b^9*c^4 + 16*a^4*b^5*d^4 - 64*a^3*b^6*c*d^3 + 96*a^2*b^7*c^2*d^2 - 64*a*b^8*c^3*d))^(3/4)*(16*a^3*b^9*c^8*d^4 - 48*a^4*b^8*c^7*d^5 + 32*a^5*b^7*c^6*d^6 + 32*a^6*b^6*c^5*d^7 - 48*a^7*b^5*c^4*d^8 + 16*a^8*b^4*c^3*d^9)*256i)/(b*d))*(-a^5/(16*b^9*c^4 + 16*a^4*b^5*d^4 - 64*a^3*b^6*c*d^3 + 96*a^2*b^7*c^2*d^2 - 64*a*b^8*c^3*d))^(1/4)*1i + (256*x^(1/2)*(a^4*b^4*c^8 + a^8*c^4*d^4))/(b*d))*(-a^5/(16*b^9*c^4 + 16*a^4*b^5*d^4 - 64*a^3*b^6*c*d^3 + 96*a^2*b^7*c^2*d^2 - 64*a*b^8*c^3*d))^(1/4)*1i + (((512*(a^3*b^6*c^9 + a^9*c^3*d^6 - a^4*b^5*c^8*d - a^8*b*c^4*d^5))/(b*d) + (x^(1/2)*(-a^5/(16*b^9*c^4 + 16*a^4*b^5*d^4 - 64*a^3*b^6*c*d^3 + 96*a^2*b^7*c^2*d^2 - 64*a*b^8*c^3*d))^(3/4)*(16*a^3*b^9*c^8*d^4 - 48*a^4*b^8*c^7*d^5 + 32*a^5*b^7*c^6*d^6 + 32*a^6*b^6*c^5*d^7 - 48*a^7*b^5*c^4*d^8 + 16*a^8*b^4*c^3*d^9)*256i)/(b*d))*(-a^5/(16*b^9*c^4 + 16*a^4*b^5*d^4 - 64*a^3*b^6*c*d^3 + 96*a^2*b^7*c^2*d^2 - 64*a*b^8*c^3*d))^(1/4)*1i - (256*x^(1/2)*(a^4*b^4*c^8 + a^8*c^4*d^4))/(b*d))*(-a^5/(16*b^9*c^4 + 16*a^4*b^5*d^4 - 64*a^3*b^6*c*d^3 + 96*a^2*b^7*c^2*d^2 - 64*a*b^8*c^3*d))^(1/4)*1i))*(-a^5/(16*b^9*c^4 + 16*a^4*b^5*d^4 - 64*a^3*b^6*c*d^3 + 96*a^2*b^7*c^2*d^2 - 64*a*b^8*c^3*d))^(1/4) + atan(((((512*(a^3*b^6*c^9 + a^9*c^3*d^6 - a^4*b^5*c^8*d - a^8*b*c^4*d^5))/(b*d) - (256*x^(1/2)*(-c^5/(16*a^4*d^9 + 16*b^4*c^4*d^5 - 64*a*b^3*c^3*d^6 + 96*a^2*b^2*c^2*d^7 - 64*a^3*b*c*d^8))^(3/4)*(16*a^3*b^9*c^8*d^4 - 48*a^4*b^8*c^7*d^5 + 32*a^5*b^7*c^6*d^6 + 32*a^6*b^6*c^5*d^7 - 48*a^7*b^5*c^4*d^8 + 16*a^8*b^4*c^3*d^9))/(b*d))*(-c^5/(16*a^4*d^9 + 16*b^4*c^4*d^5 - 64*a*b^3*c^3*d^6 + 96*a^2*b^2*c^2*d^7 - 64*a^3*b*c*d^8))^(1/4) - (256*x^(1/2)*(a^4*b^4*c^8 + a^8*c^4*d^4))/(b*d))*(-c^5/(16*a^4*d^9 + 16*b^4*c^4*d^5 - 64*a*b^3*c^3*d^6 + 96*a^2*b^2*c^2*d^7 - 64*a^3*b*c*d^8))^(1/4)*1i - (((512*(a^3*b^6*c^9 + a^9*c^3*d^6 - a^4*b^5*c^8*d - a^8*b*c^4*d^5))/(b*d) + (256*x^(1/2)*(-c^5/(16*a^4*d^9 + 16*b^4*c^4*d^5 - 64*a*b^3*c^3*d^6 + 96*a^2*b^2*c^2*d^7 - 64*a^3*b*c*d^8))^(3/4)*(16*a^3*b^9*c^8*d^4 - 48*a^4*b^8*c^7*d^5 + 32*a^5*b^7*c^6*d^6 + 32*a^6*b^6*c^5*d^7 - 48*a^7*b^5*c^4*d^8 + 16*a^8*b^4*c^3*d^9))/(b*d))*(-c^5/(16*a^4*d^9 + 16*b^4*c^4*d^5 - 64*a*b^3*c^3*d^6 + 96*a^2*b^2*c^2*d^7 - 64*a^3*b*c*d^8))^(1/4) + (256*x^(1/2)*(a^4*b^4*c^8 + a^8*c^4*d^4))/(b*d))*(-c^5/(16*a^4*d^9 + 16*b^4*c^4*d^5 - 64*a*b^3*c^3*d^6 + 96*a^2*b^2*c^2*d^7 - 64*a^3*b*c*d^8))^(1/4)*1i)/((((512*(a^3*b^6*c^9 + a^9*c^3*d^6 - a^4*b^5*c^8*d - a^8*b*c^4*d^5))/(b*d) - (256*x^(1/2)*(-c^5/(16*a^4*d^9 + 16*b^4*c^4*d^5 - 64*a*b^3*c^3*d^6 + 96*a^2*b^2*c^2*d^7 - 64*a^3*b*c*d^8))^(3/4)*(16*a^3*b^9*c^8*d^4 - 48*a^4*b^8*c^7*d^5 + 32*a^5*b^7*c^6*d^6 + 32*a^6*b^6*c^5*d^7 - 48*a^7*b^5*c^4*d^8 + 16*a^8*b^4*c^3*d^9))/(b*d))*(-c^5/(16*a^4*d^9 + 16*b^4*c^4*d^5 - 64*a*b^3*c^3*d^6 + 96*a^2*b^2*c^2*d^7 - 64*a^3*b*c*d^8))^(1/4) - (256*x^(1/2)*(a^4*b^4*c^8 + a^8*c^4*d^4))/(b*d))*(-c^5/(16*a^4*d^9 + 16*b^4*c^4*d^5 - 64*a*b^3*c^3*d^6 + 96*a^2*b^2*c^2*d^7 - 64*a^3*b*c*d^8))^(1/4) + (((512*(a^3*b^6*c^9 + a^9*c^3*d^6 - a^4*b^5*c^8*d - a^8*b*c^4*d^5))/(b*d) + (256*x^(1/2)*(-c^5/(16*a^4*d^9 + 16*b^4*c^4*d^5 - 64*a*b^3*c^3*d^6 + 96*a^2*b^2*c^2*d^7 - 64*a^3*b*c*d^8))^(3/4)*(16*a^3*b^9*c^8*d^4 - 48*a^4*b^8*c^7*d^5 + 32*a^5*b^7*c^6*d^6 + 32*a^6*b^6*c^5*d^7 - 48*a^7*b^5*c^4*d^8 + 16*a^8*b^4*c^3*d^9))/(b*d))*(-c^5/(16*a^4*d^9 + 16*b^4*c^4*d^5 - 64*a*b^3*c^3*d^6 + 96*a^2*b^2*c^2*d^7 - 64*a^3*b*c*d^8))^(1/4) + (256*x^(1/2)*(a^4*b^4*c^8 + a^8*c^4*d^4))/(b*d))*(-c^5/(16*a^4*d^9 + 16*b^4*c^4*d^5 - 64*a*b^3*c^3*d^6 + 96*a^2*b^2*c^2*d^7 - 64*a^3*b*c*d^8))^(1/4)))*(-c^5/(16*a^4*d^9 + 16*b^4*c^4*d^5 - 64*a*b^3*c^3*d^6 + 96*a^2*b^2*c^2*d^7 - 64*a^3*b*c*d^8))^(1/4)*2i - 2*atan(((((512*(a^3*b^6*c^9 + a^9*c^3*d^6 - a^4*b^5*c^8*d - a^8*b*c^4*d^5))/(b*d) - (x^(1/2)*(-c^5/(16*a^4*d^9 + 16*b^4*c^4*d^5 - 64*a*b^3*c^3*d^6 + 96*a^2*b^2*c^2*d^7 - 64*a^3*b*c*d^8))^(3/4)*(16*a^3*b^9*c^8*d^4 - 48*a^4*b^8*c^7*d^5 + 32*a^5*b^7*c^6*d^6 + 32*a^6*b^6*c^5*d^7 - 48*a^7*b^5*c^4*d^8 + 16*a^8*b^4*c^3*d^9)*256i)/(b*d))*(-c^5/(16*a^4*d^9 + 16*b^4*c^4*d^5 - 64*a*b^3*c^3*d^6 + 96*a^2*b^2*c^2*d^7 - 64*a^3*b*c*d^8))^(1/4)*1i + (256*x^(1/2)*(a^4*b^4*c^8 + a^8*c^4*d^4))/(b*d))*(-c^5/(16*a^4*d^9 + 16*b^4*c^4*d^5 - 64*a*b^3*c^3*d^6 + 96*a^2*b^2*c^2*d^7 - 64*a^3*b*c*d^8))^(1/4) - (((512*(a^3*b^6*c^9 + a^9*c^3*d^6 - a^4*b^5*c^8*d - a^8*b*c^4*d^5))/(b*d) + (x^(1/2)*(-c^5/(16*a^4*d^9 + 16*b^4*c^4*d^5 - 64*a*b^3*c^3*d^6 + 96*a^2*b^2*c^2*d^7 - 64*a^3*b*c*d^8))^(3/4)*(16*a^3*b^9*c^8*d^4 - 48*a^4*b^8*c^7*d^5 + 32*a^5*b^7*c^6*d^6 + 32*a^6*b^6*c^5*d^7 - 48*a^7*b^5*c^4*d^8 + 16*a^8*b^4*c^3*d^9)*256i)/(b*d))*(-c^5/(16*a^4*d^9 + 16*b^4*c^4*d^5 - 64*a*b^3*c^3*d^6 + 96*a^2*b^2*c^2*d^7 - 64*a^3*b*c*d^8))^(1/4)*1i - (256*x^(1/2)*(a^4*b^4*c^8 + a^8*c^4*d^4))/(b*d))*(-c^5/(16*a^4*d^9 + 16*b^4*c^4*d^5 - 64*a*b^3*c^3*d^6 + 96*a^2*b^2*c^2*d^7 - 64*a^3*b*c*d^8))^(1/4))/((((512*(a^3*b^6*c^9 + a^9*c^3*d^6 - a^4*b^5*c^8*d - a^8*b*c^4*d^5))/(b*d) - (x^(1/2)*(-c^5/(16*a^4*d^9 + 16*b^4*c^4*d^5 - 64*a*b^3*c^3*d^6 + 96*a^2*b^2*c^2*d^7 - 64*a^3*b*c*d^8))^(3/4)*(16*a^3*b^9*c^8*d^4 - 48*a^4*b^8*c^7*d^5 + 32*a^5*b^7*c^6*d^6 + 32*a^6*b^6*c^5*d^7 - 48*a^7*b^5*c^4*d^8 + 16*a^8*b^4*c^3*d^9)*256i)/(b*d))*(-c^5/(16*a^4*d^9 + 16*b^4*c^4*d^5 - 64*a*b^3*c^3*d^6 + 96*a^2*b^2*c^2*d^7 - 64*a^3*b*c*d^8))^(1/4)*1i + (256*x^(1/2)*(a^4*b^4*c^8 + a^8*c^4*d^4))/(b*d))*(-c^5/(16*a^4*d^9 + 16*b^4*c^4*d^5 - 64*a*b^3*c^3*d^6 + 96*a^2*b^2*c^2*d^7 - 64*a^3*b*c*d^8))^(1/4)*1i + (((512*(a^3*b^6*c^9 + a^9*c^3*d^6 - a^4*b^5*c^8*d - a^8*b*c^4*d^5))/(b*d) + (x^(1/2)*(-c^5/(16*a^4*d^9 + 16*b^4*c^4*d^5 - 64*a*b^3*c^3*d^6 + 96*a^2*b^2*c^2*d^7 - 64*a^3*b*c*d^8))^(3/4)*(16*a^3*b^9*c^8*d^4 - 48*a^4*b^8*c^7*d^5 + 32*a^5*b^7*c^6*d^6 + 32*a^6*b^6*c^5*d^7 - 48*a^7*b^5*c^4*d^8 + 16*a^8*b^4*c^3*d^9)*256i)/(b*d))*(-c^5/(16*a^4*d^9 + 16*b^4*c^4*d^5 - 64*a*b^3*c^3*d^6 + 96*a^2*b^2*c^2*d^7 - 64*a^3*b*c*d^8))^(1/4)*1i - (256*x^(1/2)*(a^4*b^4*c^8 + a^8*c^4*d^4))/(b*d))*(-c^5/(16*a^4*d^9 + 16*b^4*c^4*d^5 - 64*a*b^3*c^3*d^6 + 96*a^2*b^2*c^2*d^7 - 64*a^3*b*c*d^8))^(1/4)*1i))*(-c^5/(16*a^4*d^9 + 16*b^4*c^4*d^5 - 64*a*b^3*c^3*d^6 + 96*a^2*b^2*c^2*d^7 - 64*a^3*b*c*d^8))^(1/4) + (2*x^(1/2))/(b*d)","B"
463,1,2609,463,1.268466,"\text{Not used}","int(x^(5/2)/((a + b*x^2)*(c + d*x^2)),x)","-2\,\mathrm{atan}\left(\frac{2\,b^4\,c^3\,\sqrt{x}\,{\left(-\frac{a^3}{16\,a^4\,b^3\,d^4-64\,a^3\,b^4\,c\,d^3+96\,a^2\,b^5\,c^2\,d^2-64\,a\,b^6\,c^3\,d+16\,b^7\,c^4}\right)}^{1/4}+64\,a^4\,b^4\,d^7\,\sqrt{x}\,{\left(-\frac{a^3}{16\,a^4\,b^3\,d^4-64\,a^3\,b^4\,c\,d^3+96\,a^2\,b^5\,c^2\,d^2-64\,a\,b^6\,c^3\,d+16\,b^7\,c^4}\right)}^{5/4}+64\,b^8\,c^4\,d^3\,\sqrt{x}\,{\left(-\frac{a^3}{16\,a^4\,b^3\,d^4-64\,a^3\,b^4\,c\,d^3+96\,a^2\,b^5\,c^2\,d^2-64\,a\,b^6\,c^3\,d+16\,b^7\,c^4}\right)}^{5/4}+2\,a^3\,b\,d^3\,\sqrt{x}\,{\left(-\frac{a^3}{16\,a^4\,b^3\,d^4-64\,a^3\,b^4\,c\,d^3+96\,a^2\,b^5\,c^2\,d^2-64\,a\,b^6\,c^3\,d+16\,b^7\,c^4}\right)}^{1/4}+384\,a^2\,b^6\,c^2\,d^5\,\sqrt{x}\,{\left(-\frac{a^3}{16\,a^4\,b^3\,d^4-64\,a^3\,b^4\,c\,d^3+96\,a^2\,b^5\,c^2\,d^2-64\,a\,b^6\,c^3\,d+16\,b^7\,c^4}\right)}^{5/4}-256\,a\,b^7\,c^3\,d^4\,\sqrt{x}\,{\left(-\frac{a^3}{16\,a^4\,b^3\,d^4-64\,a^3\,b^4\,c\,d^3+96\,a^2\,b^5\,c^2\,d^2-64\,a\,b^6\,c^3\,d+16\,b^7\,c^4}\right)}^{5/4}-256\,a^3\,b^5\,c\,d^6\,\sqrt{x}\,{\left(-\frac{a^3}{16\,a^4\,b^3\,d^4-64\,a^3\,b^4\,c\,d^3+96\,a^2\,b^5\,c^2\,d^2-64\,a\,b^6\,c^3\,d+16\,b^7\,c^4}\right)}^{5/4}}{a^3\,d^2+a^2\,b\,c\,d+a\,b^2\,c^2}\right)\,{\left(-\frac{a^3}{16\,a^4\,b^3\,d^4-64\,a^3\,b^4\,c\,d^3+96\,a^2\,b^5\,c^2\,d^2-64\,a\,b^6\,c^3\,d+16\,b^7\,c^4}\right)}^{1/4}-\mathrm{atan}\left(\frac{b^4\,c^3\,\sqrt{x}\,{\left(-\frac{a^3}{16\,a^4\,b^3\,d^4-64\,a^3\,b^4\,c\,d^3+96\,a^2\,b^5\,c^2\,d^2-64\,a\,b^6\,c^3\,d+16\,b^7\,c^4}\right)}^{1/4}\,2{}\mathrm{i}+a^4\,b^4\,d^7\,\sqrt{x}\,{\left(-\frac{a^3}{16\,a^4\,b^3\,d^4-64\,a^3\,b^4\,c\,d^3+96\,a^2\,b^5\,c^2\,d^2-64\,a\,b^6\,c^3\,d+16\,b^7\,c^4}\right)}^{5/4}\,64{}\mathrm{i}+b^8\,c^4\,d^3\,\sqrt{x}\,{\left(-\frac{a^3}{16\,a^4\,b^3\,d^4-64\,a^3\,b^4\,c\,d^3+96\,a^2\,b^5\,c^2\,d^2-64\,a\,b^6\,c^3\,d+16\,b^7\,c^4}\right)}^{5/4}\,64{}\mathrm{i}+a^3\,b\,d^3\,\sqrt{x}\,{\left(-\frac{a^3}{16\,a^4\,b^3\,d^4-64\,a^3\,b^4\,c\,d^3+96\,a^2\,b^5\,c^2\,d^2-64\,a\,b^6\,c^3\,d+16\,b^7\,c^4}\right)}^{1/4}\,2{}\mathrm{i}+a^2\,b^6\,c^2\,d^5\,\sqrt{x}\,{\left(-\frac{a^3}{16\,a^4\,b^3\,d^4-64\,a^3\,b^4\,c\,d^3+96\,a^2\,b^5\,c^2\,d^2-64\,a\,b^6\,c^3\,d+16\,b^7\,c^4}\right)}^{5/4}\,384{}\mathrm{i}-a\,b^7\,c^3\,d^4\,\sqrt{x}\,{\left(-\frac{a^3}{16\,a^4\,b^3\,d^4-64\,a^3\,b^4\,c\,d^3+96\,a^2\,b^5\,c^2\,d^2-64\,a\,b^6\,c^3\,d+16\,b^7\,c^4}\right)}^{5/4}\,256{}\mathrm{i}-a^3\,b^5\,c\,d^6\,\sqrt{x}\,{\left(-\frac{a^3}{16\,a^4\,b^3\,d^4-64\,a^3\,b^4\,c\,d^3+96\,a^2\,b^5\,c^2\,d^2-64\,a\,b^6\,c^3\,d+16\,b^7\,c^4}\right)}^{5/4}\,256{}\mathrm{i}}{a^3\,d^2+a^2\,b\,c\,d+a\,b^2\,c^2}\right)\,{\left(-\frac{a^3}{16\,a^4\,b^3\,d^4-64\,a^3\,b^4\,c\,d^3+96\,a^2\,b^5\,c^2\,d^2-64\,a\,b^6\,c^3\,d+16\,b^7\,c^4}\right)}^{1/4}\,2{}\mathrm{i}-2\,\mathrm{atan}\left(\frac{2\,a^3\,d^4\,\sqrt{x}\,{\left(-\frac{c^3}{16\,a^4\,d^7-64\,a^3\,b\,c\,d^6+96\,a^2\,b^2\,c^2\,d^5-64\,a\,b^3\,c^3\,d^4+16\,b^4\,c^4\,d^3}\right)}^{1/4}+2\,b^3\,c^3\,d\,\sqrt{x}\,{\left(-\frac{c^3}{16\,a^4\,d^7-64\,a^3\,b\,c\,d^6+96\,a^2\,b^2\,c^2\,d^5-64\,a\,b^3\,c^3\,d^4+16\,b^4\,c^4\,d^3}\right)}^{1/4}+64\,a^4\,b^3\,d^8\,\sqrt{x}\,{\left(-\frac{c^3}{16\,a^4\,d^7-64\,a^3\,b\,c\,d^6+96\,a^2\,b^2\,c^2\,d^5-64\,a\,b^3\,c^3\,d^4+16\,b^4\,c^4\,d^3}\right)}^{5/4}+64\,b^7\,c^4\,d^4\,\sqrt{x}\,{\left(-\frac{c^3}{16\,a^4\,d^7-64\,a^3\,b\,c\,d^6+96\,a^2\,b^2\,c^2\,d^5-64\,a\,b^3\,c^3\,d^4+16\,b^4\,c^4\,d^3}\right)}^{5/4}+384\,a^2\,b^5\,c^2\,d^6\,\sqrt{x}\,{\left(-\frac{c^3}{16\,a^4\,d^7-64\,a^3\,b\,c\,d^6+96\,a^2\,b^2\,c^2\,d^5-64\,a\,b^3\,c^3\,d^4+16\,b^4\,c^4\,d^3}\right)}^{5/4}-256\,a\,b^6\,c^3\,d^5\,\sqrt{x}\,{\left(-\frac{c^3}{16\,a^4\,d^7-64\,a^3\,b\,c\,d^6+96\,a^2\,b^2\,c^2\,d^5-64\,a\,b^3\,c^3\,d^4+16\,b^4\,c^4\,d^3}\right)}^{5/4}-256\,a^3\,b^4\,c\,d^7\,\sqrt{x}\,{\left(-\frac{c^3}{16\,a^4\,d^7-64\,a^3\,b\,c\,d^6+96\,a^2\,b^2\,c^2\,d^5-64\,a\,b^3\,c^3\,d^4+16\,b^4\,c^4\,d^3}\right)}^{5/4}}{a^2\,c\,d^2+a\,b\,c^2\,d+b^2\,c^3}\right)\,{\left(-\frac{c^3}{16\,a^4\,d^7-64\,a^3\,b\,c\,d^6+96\,a^2\,b^2\,c^2\,d^5-64\,a\,b^3\,c^3\,d^4+16\,b^4\,c^4\,d^3}\right)}^{1/4}-\mathrm{atan}\left(\frac{a^3\,d^4\,\sqrt{x}\,{\left(-\frac{c^3}{16\,a^4\,d^7-64\,a^3\,b\,c\,d^6+96\,a^2\,b^2\,c^2\,d^5-64\,a\,b^3\,c^3\,d^4+16\,b^4\,c^4\,d^3}\right)}^{1/4}\,2{}\mathrm{i}+b^3\,c^3\,d\,\sqrt{x}\,{\left(-\frac{c^3}{16\,a^4\,d^7-64\,a^3\,b\,c\,d^6+96\,a^2\,b^2\,c^2\,d^5-64\,a\,b^3\,c^3\,d^4+16\,b^4\,c^4\,d^3}\right)}^{1/4}\,2{}\mathrm{i}+a^4\,b^3\,d^8\,\sqrt{x}\,{\left(-\frac{c^3}{16\,a^4\,d^7-64\,a^3\,b\,c\,d^6+96\,a^2\,b^2\,c^2\,d^5-64\,a\,b^3\,c^3\,d^4+16\,b^4\,c^4\,d^3}\right)}^{5/4}\,64{}\mathrm{i}+b^7\,c^4\,d^4\,\sqrt{x}\,{\left(-\frac{c^3}{16\,a^4\,d^7-64\,a^3\,b\,c\,d^6+96\,a^2\,b^2\,c^2\,d^5-64\,a\,b^3\,c^3\,d^4+16\,b^4\,c^4\,d^3}\right)}^{5/4}\,64{}\mathrm{i}+a^2\,b^5\,c^2\,d^6\,\sqrt{x}\,{\left(-\frac{c^3}{16\,a^4\,d^7-64\,a^3\,b\,c\,d^6+96\,a^2\,b^2\,c^2\,d^5-64\,a\,b^3\,c^3\,d^4+16\,b^4\,c^4\,d^3}\right)}^{5/4}\,384{}\mathrm{i}-a\,b^6\,c^3\,d^5\,\sqrt{x}\,{\left(-\frac{c^3}{16\,a^4\,d^7-64\,a^3\,b\,c\,d^6+96\,a^2\,b^2\,c^2\,d^5-64\,a\,b^3\,c^3\,d^4+16\,b^4\,c^4\,d^3}\right)}^{5/4}\,256{}\mathrm{i}-a^3\,b^4\,c\,d^7\,\sqrt{x}\,{\left(-\frac{c^3}{16\,a^4\,d^7-64\,a^3\,b\,c\,d^6+96\,a^2\,b^2\,c^2\,d^5-64\,a\,b^3\,c^3\,d^4+16\,b^4\,c^4\,d^3}\right)}^{5/4}\,256{}\mathrm{i}}{a^2\,c\,d^2+a\,b\,c^2\,d+b^2\,c^3}\right)\,{\left(-\frac{c^3}{16\,a^4\,d^7-64\,a^3\,b\,c\,d^6+96\,a^2\,b^2\,c^2\,d^5-64\,a\,b^3\,c^3\,d^4+16\,b^4\,c^4\,d^3}\right)}^{1/4}\,2{}\mathrm{i}","Not used",1,"- 2*atan((2*b^4*c^3*x^(1/2)*(-a^3/(16*b^7*c^4 + 16*a^4*b^3*d^4 - 64*a^3*b^4*c*d^3 + 96*a^2*b^5*c^2*d^2 - 64*a*b^6*c^3*d))^(1/4) + 64*a^4*b^4*d^7*x^(1/2)*(-a^3/(16*b^7*c^4 + 16*a^4*b^3*d^4 - 64*a^3*b^4*c*d^3 + 96*a^2*b^5*c^2*d^2 - 64*a*b^6*c^3*d))^(5/4) + 64*b^8*c^4*d^3*x^(1/2)*(-a^3/(16*b^7*c^4 + 16*a^4*b^3*d^4 - 64*a^3*b^4*c*d^3 + 96*a^2*b^5*c^2*d^2 - 64*a*b^6*c^3*d))^(5/4) + 2*a^3*b*d^3*x^(1/2)*(-a^3/(16*b^7*c^4 + 16*a^4*b^3*d^4 - 64*a^3*b^4*c*d^3 + 96*a^2*b^5*c^2*d^2 - 64*a*b^6*c^3*d))^(1/4) + 384*a^2*b^6*c^2*d^5*x^(1/2)*(-a^3/(16*b^7*c^4 + 16*a^4*b^3*d^4 - 64*a^3*b^4*c*d^3 + 96*a^2*b^5*c^2*d^2 - 64*a*b^6*c^3*d))^(5/4) - 256*a*b^7*c^3*d^4*x^(1/2)*(-a^3/(16*b^7*c^4 + 16*a^4*b^3*d^4 - 64*a^3*b^4*c*d^3 + 96*a^2*b^5*c^2*d^2 - 64*a*b^6*c^3*d))^(5/4) - 256*a^3*b^5*c*d^6*x^(1/2)*(-a^3/(16*b^7*c^4 + 16*a^4*b^3*d^4 - 64*a^3*b^4*c*d^3 + 96*a^2*b^5*c^2*d^2 - 64*a*b^6*c^3*d))^(5/4))/(a^3*d^2 + a*b^2*c^2 + a^2*b*c*d))*(-a^3/(16*b^7*c^4 + 16*a^4*b^3*d^4 - 64*a^3*b^4*c*d^3 + 96*a^2*b^5*c^2*d^2 - 64*a*b^6*c^3*d))^(1/4) - atan((b^4*c^3*x^(1/2)*(-a^3/(16*b^7*c^4 + 16*a^4*b^3*d^4 - 64*a^3*b^4*c*d^3 + 96*a^2*b^5*c^2*d^2 - 64*a*b^6*c^3*d))^(1/4)*2i + a^4*b^4*d^7*x^(1/2)*(-a^3/(16*b^7*c^4 + 16*a^4*b^3*d^4 - 64*a^3*b^4*c*d^3 + 96*a^2*b^5*c^2*d^2 - 64*a*b^6*c^3*d))^(5/4)*64i + b^8*c^4*d^3*x^(1/2)*(-a^3/(16*b^7*c^4 + 16*a^4*b^3*d^4 - 64*a^3*b^4*c*d^3 + 96*a^2*b^5*c^2*d^2 - 64*a*b^6*c^3*d))^(5/4)*64i + a^3*b*d^3*x^(1/2)*(-a^3/(16*b^7*c^4 + 16*a^4*b^3*d^4 - 64*a^3*b^4*c*d^3 + 96*a^2*b^5*c^2*d^2 - 64*a*b^6*c^3*d))^(1/4)*2i + a^2*b^6*c^2*d^5*x^(1/2)*(-a^3/(16*b^7*c^4 + 16*a^4*b^3*d^4 - 64*a^3*b^4*c*d^3 + 96*a^2*b^5*c^2*d^2 - 64*a*b^6*c^3*d))^(5/4)*384i - a*b^7*c^3*d^4*x^(1/2)*(-a^3/(16*b^7*c^4 + 16*a^4*b^3*d^4 - 64*a^3*b^4*c*d^3 + 96*a^2*b^5*c^2*d^2 - 64*a*b^6*c^3*d))^(5/4)*256i - a^3*b^5*c*d^6*x^(1/2)*(-a^3/(16*b^7*c^4 + 16*a^4*b^3*d^4 - 64*a^3*b^4*c*d^3 + 96*a^2*b^5*c^2*d^2 - 64*a*b^6*c^3*d))^(5/4)*256i)/(a^3*d^2 + a*b^2*c^2 + a^2*b*c*d))*(-a^3/(16*b^7*c^4 + 16*a^4*b^3*d^4 - 64*a^3*b^4*c*d^3 + 96*a^2*b^5*c^2*d^2 - 64*a*b^6*c^3*d))^(1/4)*2i - 2*atan((2*a^3*d^4*x^(1/2)*(-c^3/(16*a^4*d^7 + 16*b^4*c^4*d^3 - 64*a*b^3*c^3*d^4 + 96*a^2*b^2*c^2*d^5 - 64*a^3*b*c*d^6))^(1/4) + 2*b^3*c^3*d*x^(1/2)*(-c^3/(16*a^4*d^7 + 16*b^4*c^4*d^3 - 64*a*b^3*c^3*d^4 + 96*a^2*b^2*c^2*d^5 - 64*a^3*b*c*d^6))^(1/4) + 64*a^4*b^3*d^8*x^(1/2)*(-c^3/(16*a^4*d^7 + 16*b^4*c^4*d^3 - 64*a*b^3*c^3*d^4 + 96*a^2*b^2*c^2*d^5 - 64*a^3*b*c*d^6))^(5/4) + 64*b^7*c^4*d^4*x^(1/2)*(-c^3/(16*a^4*d^7 + 16*b^4*c^4*d^3 - 64*a*b^3*c^3*d^4 + 96*a^2*b^2*c^2*d^5 - 64*a^3*b*c*d^6))^(5/4) + 384*a^2*b^5*c^2*d^6*x^(1/2)*(-c^3/(16*a^4*d^7 + 16*b^4*c^4*d^3 - 64*a*b^3*c^3*d^4 + 96*a^2*b^2*c^2*d^5 - 64*a^3*b*c*d^6))^(5/4) - 256*a*b^6*c^3*d^5*x^(1/2)*(-c^3/(16*a^4*d^7 + 16*b^4*c^4*d^3 - 64*a*b^3*c^3*d^4 + 96*a^2*b^2*c^2*d^5 - 64*a^3*b*c*d^6))^(5/4) - 256*a^3*b^4*c*d^7*x^(1/2)*(-c^3/(16*a^4*d^7 + 16*b^4*c^4*d^3 - 64*a*b^3*c^3*d^4 + 96*a^2*b^2*c^2*d^5 - 64*a^3*b*c*d^6))^(5/4))/(b^2*c^3 + a^2*c*d^2 + a*b*c^2*d))*(-c^3/(16*a^4*d^7 + 16*b^4*c^4*d^3 - 64*a*b^3*c^3*d^4 + 96*a^2*b^2*c^2*d^5 - 64*a^3*b*c*d^6))^(1/4) - atan((a^3*d^4*x^(1/2)*(-c^3/(16*a^4*d^7 + 16*b^4*c^4*d^3 - 64*a*b^3*c^3*d^4 + 96*a^2*b^2*c^2*d^5 - 64*a^3*b*c*d^6))^(1/4)*2i + b^3*c^3*d*x^(1/2)*(-c^3/(16*a^4*d^7 + 16*b^4*c^4*d^3 - 64*a*b^3*c^3*d^4 + 96*a^2*b^2*c^2*d^5 - 64*a^3*b*c*d^6))^(1/4)*2i + a^4*b^3*d^8*x^(1/2)*(-c^3/(16*a^4*d^7 + 16*b^4*c^4*d^3 - 64*a*b^3*c^3*d^4 + 96*a^2*b^2*c^2*d^5 - 64*a^3*b*c*d^6))^(5/4)*64i + b^7*c^4*d^4*x^(1/2)*(-c^3/(16*a^4*d^7 + 16*b^4*c^4*d^3 - 64*a*b^3*c^3*d^4 + 96*a^2*b^2*c^2*d^5 - 64*a^3*b*c*d^6))^(5/4)*64i + a^2*b^5*c^2*d^6*x^(1/2)*(-c^3/(16*a^4*d^7 + 16*b^4*c^4*d^3 - 64*a*b^3*c^3*d^4 + 96*a^2*b^2*c^2*d^5 - 64*a^3*b*c*d^6))^(5/4)*384i - a*b^6*c^3*d^5*x^(1/2)*(-c^3/(16*a^4*d^7 + 16*b^4*c^4*d^3 - 64*a*b^3*c^3*d^4 + 96*a^2*b^2*c^2*d^5 - 64*a^3*b*c*d^6))^(5/4)*256i - a^3*b^4*c*d^7*x^(1/2)*(-c^3/(16*a^4*d^7 + 16*b^4*c^4*d^3 - 64*a*b^3*c^3*d^4 + 96*a^2*b^2*c^2*d^5 - 64*a^3*b*c*d^6))^(5/4)*256i)/(b^2*c^3 + a^2*c*d^2 + a*b*c^2*d))*(-c^3/(16*a^4*d^7 + 16*b^4*c^4*d^3 - 64*a*b^3*c^3*d^4 + 96*a^2*b^2*c^2*d^5 - 64*a^3*b*c*d^6))^(1/4)*2i","B"
464,1,5963,463,1.418791,"\text{Not used}","int(x^(3/2)/((a + b*x^2)*(c + d*x^2)),x)","-\mathrm{atan}\left(\frac{a^2\,d^2\,\sqrt{x}\,1{}\mathrm{i}+b^2\,c^2\,\sqrt{x}\,1{}\mathrm{i}-\frac{a^6\,b\,d^6\,\sqrt{x}\,16{}\mathrm{i}}{16\,a^4\,b\,d^4-64\,a^3\,b^2\,c\,d^3+96\,a^2\,b^3\,c^2\,d^2-64\,a\,b^4\,c^3\,d+16\,b^5\,c^4}+\frac{a^2\,b^5\,c^4\,d^2\,\sqrt{x}\,48{}\mathrm{i}}{16\,a^4\,b\,d^4-64\,a^3\,b^2\,c\,d^3+96\,a^2\,b^3\,c^2\,d^2-64\,a\,b^4\,c^3\,d+16\,b^5\,c^4}-\frac{a^3\,b^4\,c^3\,d^3\,\sqrt{x}\,32{}\mathrm{i}}{16\,a^4\,b\,d^4-64\,a^3\,b^2\,c\,d^3+96\,a^2\,b^3\,c^2\,d^2-64\,a\,b^4\,c^3\,d+16\,b^5\,c^4}-\frac{a^4\,b^3\,c^2\,d^4\,\sqrt{x}\,32{}\mathrm{i}}{16\,a^4\,b\,d^4-64\,a^3\,b^2\,c\,d^3+96\,a^2\,b^3\,c^2\,d^2-64\,a\,b^4\,c^3\,d+16\,b^5\,c^4}-\frac{a\,b^6\,c^5\,d\,\sqrt{x}\,16{}\mathrm{i}}{16\,a^4\,b\,d^4-64\,a^3\,b^2\,c\,d^3+96\,a^2\,b^3\,c^2\,d^2-64\,a\,b^4\,c^3\,d+16\,b^5\,c^4}+\frac{a^5\,b^2\,c\,d^5\,\sqrt{x}\,48{}\mathrm{i}}{16\,a^4\,b\,d^4-64\,a^3\,b^2\,c\,d^3+96\,a^2\,b^3\,c^2\,d^2-64\,a\,b^4\,c^3\,d+16\,b^5\,c^4}}{{\left(-\frac{a}{16\,a^4\,b\,d^4-64\,a^3\,b^2\,c\,d^3+96\,a^2\,b^3\,c^2\,d^2-64\,a\,b^4\,c^3\,d+16\,b^5\,c^4}\right)}^{1/4}\,\left(\frac{a\,\left(32\,a^6\,b\,d^7-192\,a^5\,b^2\,c\,d^6+480\,a^4\,b^3\,c^2\,d^5-640\,a^3\,b^4\,c^3\,d^4+480\,a^2\,b^5\,c^4\,d^3-192\,a\,b^6\,c^5\,d^2+32\,b^7\,c^6\,d\right)}{16\,a^4\,b\,d^4-64\,a^3\,b^2\,c\,d^3+96\,a^2\,b^3\,c^2\,d^2-64\,a\,b^4\,c^3\,d+16\,b^5\,c^4}-2\,b^3\,c^3-2\,a^3\,d^3+2\,a\,b^2\,c^2\,d+2\,a^2\,b\,c\,d^2\right)}\right)\,{\left(-\frac{a}{16\,a^4\,b\,d^4-64\,a^3\,b^2\,c\,d^3+96\,a^2\,b^3\,c^2\,d^2-64\,a\,b^4\,c^3\,d+16\,b^5\,c^4}\right)}^{1/4}\,2{}\mathrm{i}-\mathrm{atan}\left(\frac{a^2\,d^2\,\sqrt{x}\,1{}\mathrm{i}+b^2\,c^2\,\sqrt{x}\,1{}\mathrm{i}-\frac{b^6\,c^6\,d\,\sqrt{x}\,16{}\mathrm{i}}{16\,a^4\,d^5-64\,a^3\,b\,c\,d^4+96\,a^2\,b^2\,c^2\,d^3-64\,a\,b^3\,c^3\,d^2+16\,b^4\,c^4\,d}-\frac{a^2\,b^4\,c^4\,d^3\,\sqrt{x}\,32{}\mathrm{i}}{16\,a^4\,d^5-64\,a^3\,b\,c\,d^4+96\,a^2\,b^2\,c^2\,d^3-64\,a\,b^3\,c^3\,d^2+16\,b^4\,c^4\,d}-\frac{a^3\,b^3\,c^3\,d^4\,\sqrt{x}\,32{}\mathrm{i}}{16\,a^4\,d^5-64\,a^3\,b\,c\,d^4+96\,a^2\,b^2\,c^2\,d^3-64\,a\,b^3\,c^3\,d^2+16\,b^4\,c^4\,d}+\frac{a^4\,b^2\,c^2\,d^5\,\sqrt{x}\,48{}\mathrm{i}}{16\,a^4\,d^5-64\,a^3\,b\,c\,d^4+96\,a^2\,b^2\,c^2\,d^3-64\,a\,b^3\,c^3\,d^2+16\,b^4\,c^4\,d}-\frac{a^5\,b\,c\,d^6\,\sqrt{x}\,16{}\mathrm{i}}{16\,a^4\,d^5-64\,a^3\,b\,c\,d^4+96\,a^2\,b^2\,c^2\,d^3-64\,a\,b^3\,c^3\,d^2+16\,b^4\,c^4\,d}+\frac{a\,b^5\,c^5\,d^2\,\sqrt{x}\,48{}\mathrm{i}}{16\,a^4\,d^5-64\,a^3\,b\,c\,d^4+96\,a^2\,b^2\,c^2\,d^3-64\,a\,b^3\,c^3\,d^2+16\,b^4\,c^4\,d}}{{\left(-\frac{c}{16\,a^4\,d^5-64\,a^3\,b\,c\,d^4+96\,a^2\,b^2\,c^2\,d^3-64\,a\,b^3\,c^3\,d^2+16\,b^4\,c^4\,d}\right)}^{1/4}\,\left(\frac{c\,\left(32\,a^6\,b\,d^7-192\,a^5\,b^2\,c\,d^6+480\,a^4\,b^3\,c^2\,d^5-640\,a^3\,b^4\,c^3\,d^4+480\,a^2\,b^5\,c^4\,d^3-192\,a\,b^6\,c^5\,d^2+32\,b^7\,c^6\,d\right)}{16\,a^4\,d^5-64\,a^3\,b\,c\,d^4+96\,a^2\,b^2\,c^2\,d^3-64\,a\,b^3\,c^3\,d^2+16\,b^4\,c^4\,d}-2\,b^3\,c^3-2\,a^3\,d^3+2\,a\,b^2\,c^2\,d+2\,a^2\,b\,c\,d^2\right)}\right)\,{\left(-\frac{c}{16\,a^4\,d^5-64\,a^3\,b\,c\,d^4+96\,a^2\,b^2\,c^2\,d^3-64\,a\,b^3\,c^3\,d^2+16\,b^4\,c^4\,d}\right)}^{1/4}\,2{}\mathrm{i}+2\,\mathrm{atan}\left(-\frac{{\left(-\frac{a}{16\,a^4\,b\,d^4-64\,a^3\,b^2\,c\,d^3+96\,a^2\,b^3\,c^2\,d^2-64\,a\,b^4\,c^3\,d+16\,b^5\,c^4}\right)}^{1/4}\,\left(-\sqrt{x}\,\left(256\,a^4\,b^3\,c^2\,d^5+256\,a^2\,b^5\,c^4\,d^3\right)+{\left(-\frac{a}{16\,a^4\,b\,d^4-64\,a^3\,b^2\,c\,d^3+96\,a^2\,b^3\,c^2\,d^2-64\,a\,b^4\,c^3\,d+16\,b^5\,c^4}\right)}^{1/4}\,\left(512\,a^2\,b^6\,c^5\,d^3-512\,a^3\,b^5\,c^4\,d^4-512\,a^4\,b^4\,c^3\,d^5+512\,a^5\,b^3\,c^2\,d^6+\left(\sqrt{x}\,\left(4096\,a^7\,b^4\,c^2\,d^9-12288\,a^6\,b^5\,c^3\,d^8+8192\,a^5\,b^6\,c^4\,d^7+8192\,a^4\,b^7\,c^5\,d^6-12288\,a^3\,b^8\,c^6\,d^5+4096\,a^2\,b^9\,c^7\,d^4\right)-{\left(-\frac{a}{16\,a^4\,b\,d^4-64\,a^3\,b^2\,c\,d^3+96\,a^2\,b^3\,c^2\,d^2-64\,a\,b^4\,c^3\,d+16\,b^5\,c^4}\right)}^{1/4}\,\left(8192\,a^8\,b^4\,c^2\,d^{10}-49152\,a^7\,b^5\,c^3\,d^9+122880\,a^6\,b^6\,c^4\,d^8-163840\,a^5\,b^7\,c^5\,d^7+122880\,a^4\,b^8\,c^6\,d^6-49152\,a^3\,b^9\,c^7\,d^5+8192\,a^2\,b^{10}\,c^8\,d^4\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{a}{16\,a^4\,b\,d^4-64\,a^3\,b^2\,c\,d^3+96\,a^2\,b^3\,c^2\,d^2-64\,a\,b^4\,c^3\,d+16\,b^5\,c^4}\right)}^{3/4}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)+{\left(-\frac{a}{16\,a^4\,b\,d^4-64\,a^3\,b^2\,c\,d^3+96\,a^2\,b^3\,c^2\,d^2-64\,a\,b^4\,c^3\,d+16\,b^5\,c^4}\right)}^{1/4}\,\left(-\sqrt{x}\,\left(256\,a^4\,b^3\,c^2\,d^5+256\,a^2\,b^5\,c^4\,d^3\right)+{\left(-\frac{a}{16\,a^4\,b\,d^4-64\,a^3\,b^2\,c\,d^3+96\,a^2\,b^3\,c^2\,d^2-64\,a\,b^4\,c^3\,d+16\,b^5\,c^4}\right)}^{1/4}\,\left(512\,a^3\,b^5\,c^4\,d^4-512\,a^2\,b^6\,c^5\,d^3+512\,a^4\,b^4\,c^3\,d^5-512\,a^5\,b^3\,c^2\,d^6+\left(\sqrt{x}\,\left(4096\,a^7\,b^4\,c^2\,d^9-12288\,a^6\,b^5\,c^3\,d^8+8192\,a^5\,b^6\,c^4\,d^7+8192\,a^4\,b^7\,c^5\,d^6-12288\,a^3\,b^8\,c^6\,d^5+4096\,a^2\,b^9\,c^7\,d^4\right)+{\left(-\frac{a}{16\,a^4\,b\,d^4-64\,a^3\,b^2\,c\,d^3+96\,a^2\,b^3\,c^2\,d^2-64\,a\,b^4\,c^3\,d+16\,b^5\,c^4}\right)}^{1/4}\,\left(8192\,a^8\,b^4\,c^2\,d^{10}-49152\,a^7\,b^5\,c^3\,d^9+122880\,a^6\,b^6\,c^4\,d^8-163840\,a^5\,b^7\,c^5\,d^7+122880\,a^4\,b^8\,c^6\,d^6-49152\,a^3\,b^9\,c^7\,d^5+8192\,a^2\,b^{10}\,c^8\,d^4\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{a}{16\,a^4\,b\,d^4-64\,a^3\,b^2\,c\,d^3+96\,a^2\,b^3\,c^2\,d^2-64\,a\,b^4\,c^3\,d+16\,b^5\,c^4}\right)}^{3/4}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)}{{\left(-\frac{a}{16\,a^4\,b\,d^4-64\,a^3\,b^2\,c\,d^3+96\,a^2\,b^3\,c^2\,d^2-64\,a\,b^4\,c^3\,d+16\,b^5\,c^4}\right)}^{1/4}\,\left(-\sqrt{x}\,\left(256\,a^4\,b^3\,c^2\,d^5+256\,a^2\,b^5\,c^4\,d^3\right)+{\left(-\frac{a}{16\,a^4\,b\,d^4-64\,a^3\,b^2\,c\,d^3+96\,a^2\,b^3\,c^2\,d^2-64\,a\,b^4\,c^3\,d+16\,b^5\,c^4}\right)}^{1/4}\,\left(512\,a^2\,b^6\,c^5\,d^3-512\,a^3\,b^5\,c^4\,d^4-512\,a^4\,b^4\,c^3\,d^5+512\,a^5\,b^3\,c^2\,d^6+\left(\sqrt{x}\,\left(4096\,a^7\,b^4\,c^2\,d^9-12288\,a^6\,b^5\,c^3\,d^8+8192\,a^5\,b^6\,c^4\,d^7+8192\,a^4\,b^7\,c^5\,d^6-12288\,a^3\,b^8\,c^6\,d^5+4096\,a^2\,b^9\,c^7\,d^4\right)-{\left(-\frac{a}{16\,a^4\,b\,d^4-64\,a^3\,b^2\,c\,d^3+96\,a^2\,b^3\,c^2\,d^2-64\,a\,b^4\,c^3\,d+16\,b^5\,c^4}\right)}^{1/4}\,\left(8192\,a^8\,b^4\,c^2\,d^{10}-49152\,a^7\,b^5\,c^3\,d^9+122880\,a^6\,b^6\,c^4\,d^8-163840\,a^5\,b^7\,c^5\,d^7+122880\,a^4\,b^8\,c^6\,d^6-49152\,a^3\,b^9\,c^7\,d^5+8192\,a^2\,b^{10}\,c^8\,d^4\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{a}{16\,a^4\,b\,d^4-64\,a^3\,b^2\,c\,d^3+96\,a^2\,b^3\,c^2\,d^2-64\,a\,b^4\,c^3\,d+16\,b^5\,c^4}\right)}^{3/4}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}-{\left(-\frac{a}{16\,a^4\,b\,d^4-64\,a^3\,b^2\,c\,d^3+96\,a^2\,b^3\,c^2\,d^2-64\,a\,b^4\,c^3\,d+16\,b^5\,c^4}\right)}^{1/4}\,\left(-\sqrt{x}\,\left(256\,a^4\,b^3\,c^2\,d^5+256\,a^2\,b^5\,c^4\,d^3\right)+{\left(-\frac{a}{16\,a^4\,b\,d^4-64\,a^3\,b^2\,c\,d^3+96\,a^2\,b^3\,c^2\,d^2-64\,a\,b^4\,c^3\,d+16\,b^5\,c^4}\right)}^{1/4}\,\left(512\,a^3\,b^5\,c^4\,d^4-512\,a^2\,b^6\,c^5\,d^3+512\,a^4\,b^4\,c^3\,d^5-512\,a^5\,b^3\,c^2\,d^6+\left(\sqrt{x}\,\left(4096\,a^7\,b^4\,c^2\,d^9-12288\,a^6\,b^5\,c^3\,d^8+8192\,a^5\,b^6\,c^4\,d^7+8192\,a^4\,b^7\,c^5\,d^6-12288\,a^3\,b^8\,c^6\,d^5+4096\,a^2\,b^9\,c^7\,d^4\right)+{\left(-\frac{a}{16\,a^4\,b\,d^4-64\,a^3\,b^2\,c\,d^3+96\,a^2\,b^3\,c^2\,d^2-64\,a\,b^4\,c^3\,d+16\,b^5\,c^4}\right)}^{1/4}\,\left(8192\,a^8\,b^4\,c^2\,d^{10}-49152\,a^7\,b^5\,c^3\,d^9+122880\,a^6\,b^6\,c^4\,d^8-163840\,a^5\,b^7\,c^5\,d^7+122880\,a^4\,b^8\,c^6\,d^6-49152\,a^3\,b^9\,c^7\,d^5+8192\,a^2\,b^{10}\,c^8\,d^4\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{a}{16\,a^4\,b\,d^4-64\,a^3\,b^2\,c\,d^3+96\,a^2\,b^3\,c^2\,d^2-64\,a\,b^4\,c^3\,d+16\,b^5\,c^4}\right)}^{3/4}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}\right)\,{\left(-\frac{a}{16\,a^4\,b\,d^4-64\,a^3\,b^2\,c\,d^3+96\,a^2\,b^3\,c^2\,d^2-64\,a\,b^4\,c^3\,d+16\,b^5\,c^4}\right)}^{1/4}+2\,\mathrm{atan}\left(-\frac{{\left(-\frac{c}{16\,a^4\,d^5-64\,a^3\,b\,c\,d^4+96\,a^2\,b^2\,c^2\,d^3-64\,a\,b^3\,c^3\,d^2+16\,b^4\,c^4\,d}\right)}^{1/4}\,\left(-\sqrt{x}\,\left(256\,a^4\,b^3\,c^2\,d^5+256\,a^2\,b^5\,c^4\,d^3\right)+{\left(-\frac{c}{16\,a^4\,d^5-64\,a^3\,b\,c\,d^4+96\,a^2\,b^2\,c^2\,d^3-64\,a\,b^3\,c^3\,d^2+16\,b^4\,c^4\,d}\right)}^{1/4}\,\left(512\,a^2\,b^6\,c^5\,d^3-512\,a^3\,b^5\,c^4\,d^4-512\,a^4\,b^4\,c^3\,d^5+512\,a^5\,b^3\,c^2\,d^6+\left(\sqrt{x}\,\left(4096\,a^7\,b^4\,c^2\,d^9-12288\,a^6\,b^5\,c^3\,d^8+8192\,a^5\,b^6\,c^4\,d^7+8192\,a^4\,b^7\,c^5\,d^6-12288\,a^3\,b^8\,c^6\,d^5+4096\,a^2\,b^9\,c^7\,d^4\right)-{\left(-\frac{c}{16\,a^4\,d^5-64\,a^3\,b\,c\,d^4+96\,a^2\,b^2\,c^2\,d^3-64\,a\,b^3\,c^3\,d^2+16\,b^4\,c^4\,d}\right)}^{1/4}\,\left(8192\,a^8\,b^4\,c^2\,d^{10}-49152\,a^7\,b^5\,c^3\,d^9+122880\,a^6\,b^6\,c^4\,d^8-163840\,a^5\,b^7\,c^5\,d^7+122880\,a^4\,b^8\,c^6\,d^6-49152\,a^3\,b^9\,c^7\,d^5+8192\,a^2\,b^{10}\,c^8\,d^4\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{c}{16\,a^4\,d^5-64\,a^3\,b\,c\,d^4+96\,a^2\,b^2\,c^2\,d^3-64\,a\,b^3\,c^3\,d^2+16\,b^4\,c^4\,d}\right)}^{3/4}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)+{\left(-\frac{c}{16\,a^4\,d^5-64\,a^3\,b\,c\,d^4+96\,a^2\,b^2\,c^2\,d^3-64\,a\,b^3\,c^3\,d^2+16\,b^4\,c^4\,d}\right)}^{1/4}\,\left(-\sqrt{x}\,\left(256\,a^4\,b^3\,c^2\,d^5+256\,a^2\,b^5\,c^4\,d^3\right)+{\left(-\frac{c}{16\,a^4\,d^5-64\,a^3\,b\,c\,d^4+96\,a^2\,b^2\,c^2\,d^3-64\,a\,b^3\,c^3\,d^2+16\,b^4\,c^4\,d}\right)}^{1/4}\,\left(512\,a^3\,b^5\,c^4\,d^4-512\,a^2\,b^6\,c^5\,d^3+512\,a^4\,b^4\,c^3\,d^5-512\,a^5\,b^3\,c^2\,d^6+\left(\sqrt{x}\,\left(4096\,a^7\,b^4\,c^2\,d^9-12288\,a^6\,b^5\,c^3\,d^8+8192\,a^5\,b^6\,c^4\,d^7+8192\,a^4\,b^7\,c^5\,d^6-12288\,a^3\,b^8\,c^6\,d^5+4096\,a^2\,b^9\,c^7\,d^4\right)+{\left(-\frac{c}{16\,a^4\,d^5-64\,a^3\,b\,c\,d^4+96\,a^2\,b^2\,c^2\,d^3-64\,a\,b^3\,c^3\,d^2+16\,b^4\,c^4\,d}\right)}^{1/4}\,\left(8192\,a^8\,b^4\,c^2\,d^{10}-49152\,a^7\,b^5\,c^3\,d^9+122880\,a^6\,b^6\,c^4\,d^8-163840\,a^5\,b^7\,c^5\,d^7+122880\,a^4\,b^8\,c^6\,d^6-49152\,a^3\,b^9\,c^7\,d^5+8192\,a^2\,b^{10}\,c^8\,d^4\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{c}{16\,a^4\,d^5-64\,a^3\,b\,c\,d^4+96\,a^2\,b^2\,c^2\,d^3-64\,a\,b^3\,c^3\,d^2+16\,b^4\,c^4\,d}\right)}^{3/4}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)}{{\left(-\frac{c}{16\,a^4\,d^5-64\,a^3\,b\,c\,d^4+96\,a^2\,b^2\,c^2\,d^3-64\,a\,b^3\,c^3\,d^2+16\,b^4\,c^4\,d}\right)}^{1/4}\,\left(-\sqrt{x}\,\left(256\,a^4\,b^3\,c^2\,d^5+256\,a^2\,b^5\,c^4\,d^3\right)+{\left(-\frac{c}{16\,a^4\,d^5-64\,a^3\,b\,c\,d^4+96\,a^2\,b^2\,c^2\,d^3-64\,a\,b^3\,c^3\,d^2+16\,b^4\,c^4\,d}\right)}^{1/4}\,\left(512\,a^2\,b^6\,c^5\,d^3-512\,a^3\,b^5\,c^4\,d^4-512\,a^4\,b^4\,c^3\,d^5+512\,a^5\,b^3\,c^2\,d^6+\left(\sqrt{x}\,\left(4096\,a^7\,b^4\,c^2\,d^9-12288\,a^6\,b^5\,c^3\,d^8+8192\,a^5\,b^6\,c^4\,d^7+8192\,a^4\,b^7\,c^5\,d^6-12288\,a^3\,b^8\,c^6\,d^5+4096\,a^2\,b^9\,c^7\,d^4\right)-{\left(-\frac{c}{16\,a^4\,d^5-64\,a^3\,b\,c\,d^4+96\,a^2\,b^2\,c^2\,d^3-64\,a\,b^3\,c^3\,d^2+16\,b^4\,c^4\,d}\right)}^{1/4}\,\left(8192\,a^8\,b^4\,c^2\,d^{10}-49152\,a^7\,b^5\,c^3\,d^9+122880\,a^6\,b^6\,c^4\,d^8-163840\,a^5\,b^7\,c^5\,d^7+122880\,a^4\,b^8\,c^6\,d^6-49152\,a^3\,b^9\,c^7\,d^5+8192\,a^2\,b^{10}\,c^8\,d^4\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{c}{16\,a^4\,d^5-64\,a^3\,b\,c\,d^4+96\,a^2\,b^2\,c^2\,d^3-64\,a\,b^3\,c^3\,d^2+16\,b^4\,c^4\,d}\right)}^{3/4}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}-{\left(-\frac{c}{16\,a^4\,d^5-64\,a^3\,b\,c\,d^4+96\,a^2\,b^2\,c^2\,d^3-64\,a\,b^3\,c^3\,d^2+16\,b^4\,c^4\,d}\right)}^{1/4}\,\left(-\sqrt{x}\,\left(256\,a^4\,b^3\,c^2\,d^5+256\,a^2\,b^5\,c^4\,d^3\right)+{\left(-\frac{c}{16\,a^4\,d^5-64\,a^3\,b\,c\,d^4+96\,a^2\,b^2\,c^2\,d^3-64\,a\,b^3\,c^3\,d^2+16\,b^4\,c^4\,d}\right)}^{1/4}\,\left(512\,a^3\,b^5\,c^4\,d^4-512\,a^2\,b^6\,c^5\,d^3+512\,a^4\,b^4\,c^3\,d^5-512\,a^5\,b^3\,c^2\,d^6+\left(\sqrt{x}\,\left(4096\,a^7\,b^4\,c^2\,d^9-12288\,a^6\,b^5\,c^3\,d^8+8192\,a^5\,b^6\,c^4\,d^7+8192\,a^4\,b^7\,c^5\,d^6-12288\,a^3\,b^8\,c^6\,d^5+4096\,a^2\,b^9\,c^7\,d^4\right)+{\left(-\frac{c}{16\,a^4\,d^5-64\,a^3\,b\,c\,d^4+96\,a^2\,b^2\,c^2\,d^3-64\,a\,b^3\,c^3\,d^2+16\,b^4\,c^4\,d}\right)}^{1/4}\,\left(8192\,a^8\,b^4\,c^2\,d^{10}-49152\,a^7\,b^5\,c^3\,d^9+122880\,a^6\,b^6\,c^4\,d^8-163840\,a^5\,b^7\,c^5\,d^7+122880\,a^4\,b^8\,c^6\,d^6-49152\,a^3\,b^9\,c^7\,d^5+8192\,a^2\,b^{10}\,c^8\,d^4\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{c}{16\,a^4\,d^5-64\,a^3\,b\,c\,d^4+96\,a^2\,b^2\,c^2\,d^3-64\,a\,b^3\,c^3\,d^2+16\,b^4\,c^4\,d}\right)}^{3/4}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}\right)\,{\left(-\frac{c}{16\,a^4\,d^5-64\,a^3\,b\,c\,d^4+96\,a^2\,b^2\,c^2\,d^3-64\,a\,b^3\,c^3\,d^2+16\,b^4\,c^4\,d}\right)}^{1/4}","Not used",1,"2*atan(-((-a/(16*b^5*c^4 + 16*a^4*b*d^4 - 64*a^3*b^2*c*d^3 + 96*a^2*b^3*c^2*d^2 - 64*a*b^4*c^3*d))^(1/4)*((-a/(16*b^5*c^4 + 16*a^4*b*d^4 - 64*a^3*b^2*c*d^3 + 96*a^2*b^3*c^2*d^2 - 64*a*b^4*c^3*d))^(1/4)*((x^(1/2)*(4096*a^2*b^9*c^7*d^4 - 12288*a^3*b^8*c^6*d^5 + 8192*a^4*b^7*c^5*d^6 + 8192*a^5*b^6*c^4*d^7 - 12288*a^6*b^5*c^3*d^8 + 4096*a^7*b^4*c^2*d^9) - (-a/(16*b^5*c^4 + 16*a^4*b*d^4 - 64*a^3*b^2*c*d^3 + 96*a^2*b^3*c^2*d^2 - 64*a*b^4*c^3*d))^(1/4)*(8192*a^2*b^10*c^8*d^4 - 49152*a^3*b^9*c^7*d^5 + 122880*a^4*b^8*c^6*d^6 - 163840*a^5*b^7*c^5*d^7 + 122880*a^6*b^6*c^4*d^8 - 49152*a^7*b^5*c^3*d^9 + 8192*a^8*b^4*c^2*d^10)*1i)*(-a/(16*b^5*c^4 + 16*a^4*b*d^4 - 64*a^3*b^2*c*d^3 + 96*a^2*b^3*c^2*d^2 - 64*a*b^4*c^3*d))^(3/4)*1i + 512*a^2*b^6*c^5*d^3 - 512*a^3*b^5*c^4*d^4 - 512*a^4*b^4*c^3*d^5 + 512*a^5*b^3*c^2*d^6)*1i - x^(1/2)*(256*a^2*b^5*c^4*d^3 + 256*a^4*b^3*c^2*d^5)) + (-a/(16*b^5*c^4 + 16*a^4*b*d^4 - 64*a^3*b^2*c*d^3 + 96*a^2*b^3*c^2*d^2 - 64*a*b^4*c^3*d))^(1/4)*((-a/(16*b^5*c^4 + 16*a^4*b*d^4 - 64*a^3*b^2*c*d^3 + 96*a^2*b^3*c^2*d^2 - 64*a*b^4*c^3*d))^(1/4)*((x^(1/2)*(4096*a^2*b^9*c^7*d^4 - 12288*a^3*b^8*c^6*d^5 + 8192*a^4*b^7*c^5*d^6 + 8192*a^5*b^6*c^4*d^7 - 12288*a^6*b^5*c^3*d^8 + 4096*a^7*b^4*c^2*d^9) + (-a/(16*b^5*c^4 + 16*a^4*b*d^4 - 64*a^3*b^2*c*d^3 + 96*a^2*b^3*c^2*d^2 - 64*a*b^4*c^3*d))^(1/4)*(8192*a^2*b^10*c^8*d^4 - 49152*a^3*b^9*c^7*d^5 + 122880*a^4*b^8*c^6*d^6 - 163840*a^5*b^7*c^5*d^7 + 122880*a^6*b^6*c^4*d^8 - 49152*a^7*b^5*c^3*d^9 + 8192*a^8*b^4*c^2*d^10)*1i)*(-a/(16*b^5*c^4 + 16*a^4*b*d^4 - 64*a^3*b^2*c*d^3 + 96*a^2*b^3*c^2*d^2 - 64*a*b^4*c^3*d))^(3/4)*1i - 512*a^2*b^6*c^5*d^3 + 512*a^3*b^5*c^4*d^4 + 512*a^4*b^4*c^3*d^5 - 512*a^5*b^3*c^2*d^6)*1i - x^(1/2)*(256*a^2*b^5*c^4*d^3 + 256*a^4*b^3*c^2*d^5)))/((-a/(16*b^5*c^4 + 16*a^4*b*d^4 - 64*a^3*b^2*c*d^3 + 96*a^2*b^3*c^2*d^2 - 64*a*b^4*c^3*d))^(1/4)*((-a/(16*b^5*c^4 + 16*a^4*b*d^4 - 64*a^3*b^2*c*d^3 + 96*a^2*b^3*c^2*d^2 - 64*a*b^4*c^3*d))^(1/4)*((x^(1/2)*(4096*a^2*b^9*c^7*d^4 - 12288*a^3*b^8*c^6*d^5 + 8192*a^4*b^7*c^5*d^6 + 8192*a^5*b^6*c^4*d^7 - 12288*a^6*b^5*c^3*d^8 + 4096*a^7*b^4*c^2*d^9) - (-a/(16*b^5*c^4 + 16*a^4*b*d^4 - 64*a^3*b^2*c*d^3 + 96*a^2*b^3*c^2*d^2 - 64*a*b^4*c^3*d))^(1/4)*(8192*a^2*b^10*c^8*d^4 - 49152*a^3*b^9*c^7*d^5 + 122880*a^4*b^8*c^6*d^6 - 163840*a^5*b^7*c^5*d^7 + 122880*a^6*b^6*c^4*d^8 - 49152*a^7*b^5*c^3*d^9 + 8192*a^8*b^4*c^2*d^10)*1i)*(-a/(16*b^5*c^4 + 16*a^4*b*d^4 - 64*a^3*b^2*c*d^3 + 96*a^2*b^3*c^2*d^2 - 64*a*b^4*c^3*d))^(3/4)*1i + 512*a^2*b^6*c^5*d^3 - 512*a^3*b^5*c^4*d^4 - 512*a^4*b^4*c^3*d^5 + 512*a^5*b^3*c^2*d^6)*1i - x^(1/2)*(256*a^2*b^5*c^4*d^3 + 256*a^4*b^3*c^2*d^5))*1i - (-a/(16*b^5*c^4 + 16*a^4*b*d^4 - 64*a^3*b^2*c*d^3 + 96*a^2*b^3*c^2*d^2 - 64*a*b^4*c^3*d))^(1/4)*((-a/(16*b^5*c^4 + 16*a^4*b*d^4 - 64*a^3*b^2*c*d^3 + 96*a^2*b^3*c^2*d^2 - 64*a*b^4*c^3*d))^(1/4)*((x^(1/2)*(4096*a^2*b^9*c^7*d^4 - 12288*a^3*b^8*c^6*d^5 + 8192*a^4*b^7*c^5*d^6 + 8192*a^5*b^6*c^4*d^7 - 12288*a^6*b^5*c^3*d^8 + 4096*a^7*b^4*c^2*d^9) + (-a/(16*b^5*c^4 + 16*a^4*b*d^4 - 64*a^3*b^2*c*d^3 + 96*a^2*b^3*c^2*d^2 - 64*a*b^4*c^3*d))^(1/4)*(8192*a^2*b^10*c^8*d^4 - 49152*a^3*b^9*c^7*d^5 + 122880*a^4*b^8*c^6*d^6 - 163840*a^5*b^7*c^5*d^7 + 122880*a^6*b^6*c^4*d^8 - 49152*a^7*b^5*c^3*d^9 + 8192*a^8*b^4*c^2*d^10)*1i)*(-a/(16*b^5*c^4 + 16*a^4*b*d^4 - 64*a^3*b^2*c*d^3 + 96*a^2*b^3*c^2*d^2 - 64*a*b^4*c^3*d))^(3/4)*1i - 512*a^2*b^6*c^5*d^3 + 512*a^3*b^5*c^4*d^4 + 512*a^4*b^4*c^3*d^5 - 512*a^5*b^3*c^2*d^6)*1i - x^(1/2)*(256*a^2*b^5*c^4*d^3 + 256*a^4*b^3*c^2*d^5))*1i))*(-a/(16*b^5*c^4 + 16*a^4*b*d^4 - 64*a^3*b^2*c*d^3 + 96*a^2*b^3*c^2*d^2 - 64*a*b^4*c^3*d))^(1/4) - atan((a^2*d^2*x^(1/2)*1i + b^2*c^2*x^(1/2)*1i - (b^6*c^6*d*x^(1/2)*16i)/(16*a^4*d^5 + 16*b^4*c^4*d - 64*a*b^3*c^3*d^2 + 96*a^2*b^2*c^2*d^3 - 64*a^3*b*c*d^4) - (a^2*b^4*c^4*d^3*x^(1/2)*32i)/(16*a^4*d^5 + 16*b^4*c^4*d - 64*a*b^3*c^3*d^2 + 96*a^2*b^2*c^2*d^3 - 64*a^3*b*c*d^4) - (a^3*b^3*c^3*d^4*x^(1/2)*32i)/(16*a^4*d^5 + 16*b^4*c^4*d - 64*a*b^3*c^3*d^2 + 96*a^2*b^2*c^2*d^3 - 64*a^3*b*c*d^4) + (a^4*b^2*c^2*d^5*x^(1/2)*48i)/(16*a^4*d^5 + 16*b^4*c^4*d - 64*a*b^3*c^3*d^2 + 96*a^2*b^2*c^2*d^3 - 64*a^3*b*c*d^4) - (a^5*b*c*d^6*x^(1/2)*16i)/(16*a^4*d^5 + 16*b^4*c^4*d - 64*a*b^3*c^3*d^2 + 96*a^2*b^2*c^2*d^3 - 64*a^3*b*c*d^4) + (a*b^5*c^5*d^2*x^(1/2)*48i)/(16*a^4*d^5 + 16*b^4*c^4*d - 64*a*b^3*c^3*d^2 + 96*a^2*b^2*c^2*d^3 - 64*a^3*b*c*d^4))/((-c/(16*a^4*d^5 + 16*b^4*c^4*d - 64*a*b^3*c^3*d^2 + 96*a^2*b^2*c^2*d^3 - 64*a^3*b*c*d^4))^(1/4)*((c*(32*a^6*b*d^7 + 32*b^7*c^6*d - 192*a*b^6*c^5*d^2 - 192*a^5*b^2*c*d^6 + 480*a^2*b^5*c^4*d^3 - 640*a^3*b^4*c^3*d^4 + 480*a^4*b^3*c^2*d^5))/(16*a^4*d^5 + 16*b^4*c^4*d - 64*a*b^3*c^3*d^2 + 96*a^2*b^2*c^2*d^3 - 64*a^3*b*c*d^4) - 2*b^3*c^3 - 2*a^3*d^3 + 2*a*b^2*c^2*d + 2*a^2*b*c*d^2)))*(-c/(16*a^4*d^5 + 16*b^4*c^4*d - 64*a*b^3*c^3*d^2 + 96*a^2*b^2*c^2*d^3 - 64*a^3*b*c*d^4))^(1/4)*2i - atan((a^2*d^2*x^(1/2)*1i + b^2*c^2*x^(1/2)*1i - (a^6*b*d^6*x^(1/2)*16i)/(16*b^5*c^4 + 16*a^4*b*d^4 - 64*a^3*b^2*c*d^3 + 96*a^2*b^3*c^2*d^2 - 64*a*b^4*c^3*d) + (a^2*b^5*c^4*d^2*x^(1/2)*48i)/(16*b^5*c^4 + 16*a^4*b*d^4 - 64*a^3*b^2*c*d^3 + 96*a^2*b^3*c^2*d^2 - 64*a*b^4*c^3*d) - (a^3*b^4*c^3*d^3*x^(1/2)*32i)/(16*b^5*c^4 + 16*a^4*b*d^4 - 64*a^3*b^2*c*d^3 + 96*a^2*b^3*c^2*d^2 - 64*a*b^4*c^3*d) - (a^4*b^3*c^2*d^4*x^(1/2)*32i)/(16*b^5*c^4 + 16*a^4*b*d^4 - 64*a^3*b^2*c*d^3 + 96*a^2*b^3*c^2*d^2 - 64*a*b^4*c^3*d) - (a*b^6*c^5*d*x^(1/2)*16i)/(16*b^5*c^4 + 16*a^4*b*d^4 - 64*a^3*b^2*c*d^3 + 96*a^2*b^3*c^2*d^2 - 64*a*b^4*c^3*d) + (a^5*b^2*c*d^5*x^(1/2)*48i)/(16*b^5*c^4 + 16*a^4*b*d^4 - 64*a^3*b^2*c*d^3 + 96*a^2*b^3*c^2*d^2 - 64*a*b^4*c^3*d))/((-a/(16*b^5*c^4 + 16*a^4*b*d^4 - 64*a^3*b^2*c*d^3 + 96*a^2*b^3*c^2*d^2 - 64*a*b^4*c^3*d))^(1/4)*((a*(32*a^6*b*d^7 + 32*b^7*c^6*d - 192*a*b^6*c^5*d^2 - 192*a^5*b^2*c*d^6 + 480*a^2*b^5*c^4*d^3 - 640*a^3*b^4*c^3*d^4 + 480*a^4*b^3*c^2*d^5))/(16*b^5*c^4 + 16*a^4*b*d^4 - 64*a^3*b^2*c*d^3 + 96*a^2*b^3*c^2*d^2 - 64*a*b^4*c^3*d) - 2*b^3*c^3 - 2*a^3*d^3 + 2*a*b^2*c^2*d + 2*a^2*b*c*d^2)))*(-a/(16*b^5*c^4 + 16*a^4*b*d^4 - 64*a^3*b^2*c*d^3 + 96*a^2*b^3*c^2*d^2 - 64*a*b^4*c^3*d))^(1/4)*2i + 2*atan(-((-c/(16*a^4*d^5 + 16*b^4*c^4*d - 64*a*b^3*c^3*d^2 + 96*a^2*b^2*c^2*d^3 - 64*a^3*b*c*d^4))^(1/4)*((-c/(16*a^4*d^5 + 16*b^4*c^4*d - 64*a*b^3*c^3*d^2 + 96*a^2*b^2*c^2*d^3 - 64*a^3*b*c*d^4))^(1/4)*((x^(1/2)*(4096*a^2*b^9*c^7*d^4 - 12288*a^3*b^8*c^6*d^5 + 8192*a^4*b^7*c^5*d^6 + 8192*a^5*b^6*c^4*d^7 - 12288*a^6*b^5*c^3*d^8 + 4096*a^7*b^4*c^2*d^9) - (-c/(16*a^4*d^5 + 16*b^4*c^4*d - 64*a*b^3*c^3*d^2 + 96*a^2*b^2*c^2*d^3 - 64*a^3*b*c*d^4))^(1/4)*(8192*a^2*b^10*c^8*d^4 - 49152*a^3*b^9*c^7*d^5 + 122880*a^4*b^8*c^6*d^6 - 163840*a^5*b^7*c^5*d^7 + 122880*a^6*b^6*c^4*d^8 - 49152*a^7*b^5*c^3*d^9 + 8192*a^8*b^4*c^2*d^10)*1i)*(-c/(16*a^4*d^5 + 16*b^4*c^4*d - 64*a*b^3*c^3*d^2 + 96*a^2*b^2*c^2*d^3 - 64*a^3*b*c*d^4))^(3/4)*1i + 512*a^2*b^6*c^5*d^3 - 512*a^3*b^5*c^4*d^4 - 512*a^4*b^4*c^3*d^5 + 512*a^5*b^3*c^2*d^6)*1i - x^(1/2)*(256*a^2*b^5*c^4*d^3 + 256*a^4*b^3*c^2*d^5)) + (-c/(16*a^4*d^5 + 16*b^4*c^4*d - 64*a*b^3*c^3*d^2 + 96*a^2*b^2*c^2*d^3 - 64*a^3*b*c*d^4))^(1/4)*((-c/(16*a^4*d^5 + 16*b^4*c^4*d - 64*a*b^3*c^3*d^2 + 96*a^2*b^2*c^2*d^3 - 64*a^3*b*c*d^4))^(1/4)*((x^(1/2)*(4096*a^2*b^9*c^7*d^4 - 12288*a^3*b^8*c^6*d^5 + 8192*a^4*b^7*c^5*d^6 + 8192*a^5*b^6*c^4*d^7 - 12288*a^6*b^5*c^3*d^8 + 4096*a^7*b^4*c^2*d^9) + (-c/(16*a^4*d^5 + 16*b^4*c^4*d - 64*a*b^3*c^3*d^2 + 96*a^2*b^2*c^2*d^3 - 64*a^3*b*c*d^4))^(1/4)*(8192*a^2*b^10*c^8*d^4 - 49152*a^3*b^9*c^7*d^5 + 122880*a^4*b^8*c^6*d^6 - 163840*a^5*b^7*c^5*d^7 + 122880*a^6*b^6*c^4*d^8 - 49152*a^7*b^5*c^3*d^9 + 8192*a^8*b^4*c^2*d^10)*1i)*(-c/(16*a^4*d^5 + 16*b^4*c^4*d - 64*a*b^3*c^3*d^2 + 96*a^2*b^2*c^2*d^3 - 64*a^3*b*c*d^4))^(3/4)*1i - 512*a^2*b^6*c^5*d^3 + 512*a^3*b^5*c^4*d^4 + 512*a^4*b^4*c^3*d^5 - 512*a^5*b^3*c^2*d^6)*1i - x^(1/2)*(256*a^2*b^5*c^4*d^3 + 256*a^4*b^3*c^2*d^5)))/((-c/(16*a^4*d^5 + 16*b^4*c^4*d - 64*a*b^3*c^3*d^2 + 96*a^2*b^2*c^2*d^3 - 64*a^3*b*c*d^4))^(1/4)*((-c/(16*a^4*d^5 + 16*b^4*c^4*d - 64*a*b^3*c^3*d^2 + 96*a^2*b^2*c^2*d^3 - 64*a^3*b*c*d^4))^(1/4)*((x^(1/2)*(4096*a^2*b^9*c^7*d^4 - 12288*a^3*b^8*c^6*d^5 + 8192*a^4*b^7*c^5*d^6 + 8192*a^5*b^6*c^4*d^7 - 12288*a^6*b^5*c^3*d^8 + 4096*a^7*b^4*c^2*d^9) - (-c/(16*a^4*d^5 + 16*b^4*c^4*d - 64*a*b^3*c^3*d^2 + 96*a^2*b^2*c^2*d^3 - 64*a^3*b*c*d^4))^(1/4)*(8192*a^2*b^10*c^8*d^4 - 49152*a^3*b^9*c^7*d^5 + 122880*a^4*b^8*c^6*d^6 - 163840*a^5*b^7*c^5*d^7 + 122880*a^6*b^6*c^4*d^8 - 49152*a^7*b^5*c^3*d^9 + 8192*a^8*b^4*c^2*d^10)*1i)*(-c/(16*a^4*d^5 + 16*b^4*c^4*d - 64*a*b^3*c^3*d^2 + 96*a^2*b^2*c^2*d^3 - 64*a^3*b*c*d^4))^(3/4)*1i + 512*a^2*b^6*c^5*d^3 - 512*a^3*b^5*c^4*d^4 - 512*a^4*b^4*c^3*d^5 + 512*a^5*b^3*c^2*d^6)*1i - x^(1/2)*(256*a^2*b^5*c^4*d^3 + 256*a^4*b^3*c^2*d^5))*1i - (-c/(16*a^4*d^5 + 16*b^4*c^4*d - 64*a*b^3*c^3*d^2 + 96*a^2*b^2*c^2*d^3 - 64*a^3*b*c*d^4))^(1/4)*((-c/(16*a^4*d^5 + 16*b^4*c^4*d - 64*a*b^3*c^3*d^2 + 96*a^2*b^2*c^2*d^3 - 64*a^3*b*c*d^4))^(1/4)*((x^(1/2)*(4096*a^2*b^9*c^7*d^4 - 12288*a^3*b^8*c^6*d^5 + 8192*a^4*b^7*c^5*d^6 + 8192*a^5*b^6*c^4*d^7 - 12288*a^6*b^5*c^3*d^8 + 4096*a^7*b^4*c^2*d^9) + (-c/(16*a^4*d^5 + 16*b^4*c^4*d - 64*a*b^3*c^3*d^2 + 96*a^2*b^2*c^2*d^3 - 64*a^3*b*c*d^4))^(1/4)*(8192*a^2*b^10*c^8*d^4 - 49152*a^3*b^9*c^7*d^5 + 122880*a^4*b^8*c^6*d^6 - 163840*a^5*b^7*c^5*d^7 + 122880*a^6*b^6*c^4*d^8 - 49152*a^7*b^5*c^3*d^9 + 8192*a^8*b^4*c^2*d^10)*1i)*(-c/(16*a^4*d^5 + 16*b^4*c^4*d - 64*a*b^3*c^3*d^2 + 96*a^2*b^2*c^2*d^3 - 64*a^3*b*c*d^4))^(3/4)*1i - 512*a^2*b^6*c^5*d^3 + 512*a^3*b^5*c^4*d^4 + 512*a^4*b^4*c^3*d^5 - 512*a^5*b^3*c^2*d^6)*1i - x^(1/2)*(256*a^2*b^5*c^4*d^3 + 256*a^4*b^3*c^2*d^5))*1i))*(-c/(16*a^4*d^5 + 16*b^4*c^4*d - 64*a*b^3*c^3*d^2 + 96*a^2*b^2*c^2*d^3 - 64*a^3*b*c*d^4))^(1/4)","B"
465,1,6701,463,1.154071,"\text{Not used}","int(x^(1/2)/((a + b*x^2)*(c + d*x^2)),x)","\mathrm{atan}\left(\frac{\left({\left(-\frac{b}{16\,a^5\,d^4-64\,a^4\,b\,c\,d^3+96\,a^3\,b^2\,c^2\,d^2-64\,a^2\,b^3\,c^3\,d+16\,a\,b^4\,c^4}\right)}^{3/4}\,\left(\sqrt{x}\,{\left(-\frac{b}{16\,a^5\,d^4-64\,a^4\,b\,c\,d^3+96\,a^3\,b^2\,c^2\,d^2-64\,a^2\,b^3\,c^3\,d+16\,a\,b^4\,c^4}\right)}^{1/4}\,\left(4096\,a^7\,b^4\,c\,d^{10}-16384\,a^6\,b^5\,c^2\,d^9+28672\,a^5\,b^6\,c^3\,d^8-32768\,a^4\,b^7\,c^4\,d^7+28672\,a^3\,b^8\,c^5\,d^6-16384\,a^2\,b^9\,c^6\,d^5+4096\,a\,b^{10}\,c^7\,d^4\right)+2048\,a\,b^9\,c^6\,d^4+2048\,a^6\,b^4\,c\,d^9-6144\,a^2\,b^8\,c^5\,d^5+4096\,a^3\,b^7\,c^4\,d^6+4096\,a^4\,b^6\,c^3\,d^7-6144\,a^5\,b^5\,c^2\,d^8\right)+\sqrt{x}\,\left(256\,a^2\,b^5\,c\,d^6+256\,a\,b^6\,c^2\,d^5\right)\right)\,{\left(-\frac{b}{16\,a^5\,d^4-64\,a^4\,b\,c\,d^3+96\,a^3\,b^2\,c^2\,d^2-64\,a^2\,b^3\,c^3\,d+16\,a\,b^4\,c^4}\right)}^{1/4}\,1{}\mathrm{i}-\left({\left(-\frac{b}{16\,a^5\,d^4-64\,a^4\,b\,c\,d^3+96\,a^3\,b^2\,c^2\,d^2-64\,a^2\,b^3\,c^3\,d+16\,a\,b^4\,c^4}\right)}^{3/4}\,\left(2048\,a\,b^9\,c^6\,d^4-\sqrt{x}\,{\left(-\frac{b}{16\,a^5\,d^4-64\,a^4\,b\,c\,d^3+96\,a^3\,b^2\,c^2\,d^2-64\,a^2\,b^3\,c^3\,d+16\,a\,b^4\,c^4}\right)}^{1/4}\,\left(4096\,a^7\,b^4\,c\,d^{10}-16384\,a^6\,b^5\,c^2\,d^9+28672\,a^5\,b^6\,c^3\,d^8-32768\,a^4\,b^7\,c^4\,d^7+28672\,a^3\,b^8\,c^5\,d^6-16384\,a^2\,b^9\,c^6\,d^5+4096\,a\,b^{10}\,c^7\,d^4\right)+2048\,a^6\,b^4\,c\,d^9-6144\,a^2\,b^8\,c^5\,d^5+4096\,a^3\,b^7\,c^4\,d^6+4096\,a^4\,b^6\,c^3\,d^7-6144\,a^5\,b^5\,c^2\,d^8\right)-\sqrt{x}\,\left(256\,a^2\,b^5\,c\,d^6+256\,a\,b^6\,c^2\,d^5\right)\right)\,{\left(-\frac{b}{16\,a^5\,d^4-64\,a^4\,b\,c\,d^3+96\,a^3\,b^2\,c^2\,d^2-64\,a^2\,b^3\,c^3\,d+16\,a\,b^4\,c^4}\right)}^{1/4}\,1{}\mathrm{i}}{\left({\left(-\frac{b}{16\,a^5\,d^4-64\,a^4\,b\,c\,d^3+96\,a^3\,b^2\,c^2\,d^2-64\,a^2\,b^3\,c^3\,d+16\,a\,b^4\,c^4}\right)}^{3/4}\,\left(\sqrt{x}\,{\left(-\frac{b}{16\,a^5\,d^4-64\,a^4\,b\,c\,d^3+96\,a^3\,b^2\,c^2\,d^2-64\,a^2\,b^3\,c^3\,d+16\,a\,b^4\,c^4}\right)}^{1/4}\,\left(4096\,a^7\,b^4\,c\,d^{10}-16384\,a^6\,b^5\,c^2\,d^9+28672\,a^5\,b^6\,c^3\,d^8-32768\,a^4\,b^7\,c^4\,d^7+28672\,a^3\,b^8\,c^5\,d^6-16384\,a^2\,b^9\,c^6\,d^5+4096\,a\,b^{10}\,c^7\,d^4\right)+2048\,a\,b^9\,c^6\,d^4+2048\,a^6\,b^4\,c\,d^9-6144\,a^2\,b^8\,c^5\,d^5+4096\,a^3\,b^7\,c^4\,d^6+4096\,a^4\,b^6\,c^3\,d^7-6144\,a^5\,b^5\,c^2\,d^8\right)+\sqrt{x}\,\left(256\,a^2\,b^5\,c\,d^6+256\,a\,b^6\,c^2\,d^5\right)\right)\,{\left(-\frac{b}{16\,a^5\,d^4-64\,a^4\,b\,c\,d^3+96\,a^3\,b^2\,c^2\,d^2-64\,a^2\,b^3\,c^3\,d+16\,a\,b^4\,c^4}\right)}^{1/4}+\left({\left(-\frac{b}{16\,a^5\,d^4-64\,a^4\,b\,c\,d^3+96\,a^3\,b^2\,c^2\,d^2-64\,a^2\,b^3\,c^3\,d+16\,a\,b^4\,c^4}\right)}^{3/4}\,\left(2048\,a\,b^9\,c^6\,d^4-\sqrt{x}\,{\left(-\frac{b}{16\,a^5\,d^4-64\,a^4\,b\,c\,d^3+96\,a^3\,b^2\,c^2\,d^2-64\,a^2\,b^3\,c^3\,d+16\,a\,b^4\,c^4}\right)}^{1/4}\,\left(4096\,a^7\,b^4\,c\,d^{10}-16384\,a^6\,b^5\,c^2\,d^9+28672\,a^5\,b^6\,c^3\,d^8-32768\,a^4\,b^7\,c^4\,d^7+28672\,a^3\,b^8\,c^5\,d^6-16384\,a^2\,b^9\,c^6\,d^5+4096\,a\,b^{10}\,c^7\,d^4\right)+2048\,a^6\,b^4\,c\,d^9-6144\,a^2\,b^8\,c^5\,d^5+4096\,a^3\,b^7\,c^4\,d^6+4096\,a^4\,b^6\,c^3\,d^7-6144\,a^5\,b^5\,c^2\,d^8\right)-\sqrt{x}\,\left(256\,a^2\,b^5\,c\,d^6+256\,a\,b^6\,c^2\,d^5\right)\right)\,{\left(-\frac{b}{16\,a^5\,d^4-64\,a^4\,b\,c\,d^3+96\,a^3\,b^2\,c^2\,d^2-64\,a^2\,b^3\,c^3\,d+16\,a\,b^4\,c^4}\right)}^{1/4}+256\,a\,b^5\,c\,d^5}\right)\,{\left(-\frac{b}{16\,a^5\,d^4-64\,a^4\,b\,c\,d^3+96\,a^3\,b^2\,c^2\,d^2-64\,a^2\,b^3\,c^3\,d+16\,a\,b^4\,c^4}\right)}^{1/4}\,2{}\mathrm{i}-2\,\mathrm{atan}\left(\frac{\left(\sqrt{x}\,\left(256\,a^2\,b^5\,c\,d^6+256\,a\,b^6\,c^2\,d^5\right)+{\left(-\frac{b}{16\,a^5\,d^4-64\,a^4\,b\,c\,d^3+96\,a^3\,b^2\,c^2\,d^2-64\,a^2\,b^3\,c^3\,d+16\,a\,b^4\,c^4}\right)}^{3/4}\,\left(2048\,a\,b^9\,c^6\,d^4+2048\,a^6\,b^4\,c\,d^9-6144\,a^2\,b^8\,c^5\,d^5+4096\,a^3\,b^7\,c^4\,d^6+4096\,a^4\,b^6\,c^3\,d^7-6144\,a^5\,b^5\,c^2\,d^8-\sqrt{x}\,{\left(-\frac{b}{16\,a^5\,d^4-64\,a^4\,b\,c\,d^3+96\,a^3\,b^2\,c^2\,d^2-64\,a^2\,b^3\,c^3\,d+16\,a\,b^4\,c^4}\right)}^{1/4}\,\left(4096\,a^7\,b^4\,c\,d^{10}-16384\,a^6\,b^5\,c^2\,d^9+28672\,a^5\,b^6\,c^3\,d^8-32768\,a^4\,b^7\,c^4\,d^7+28672\,a^3\,b^8\,c^5\,d^6-16384\,a^2\,b^9\,c^6\,d^5+4096\,a\,b^{10}\,c^7\,d^4\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{b}{16\,a^5\,d^4-64\,a^4\,b\,c\,d^3+96\,a^3\,b^2\,c^2\,d^2-64\,a^2\,b^3\,c^3\,d+16\,a\,b^4\,c^4}\right)}^{1/4}-\left(-\sqrt{x}\,\left(256\,a^2\,b^5\,c\,d^6+256\,a\,b^6\,c^2\,d^5\right)+{\left(-\frac{b}{16\,a^5\,d^4-64\,a^4\,b\,c\,d^3+96\,a^3\,b^2\,c^2\,d^2-64\,a^2\,b^3\,c^3\,d+16\,a\,b^4\,c^4}\right)}^{3/4}\,\left(2048\,a\,b^9\,c^6\,d^4+2048\,a^6\,b^4\,c\,d^9-6144\,a^2\,b^8\,c^5\,d^5+4096\,a^3\,b^7\,c^4\,d^6+4096\,a^4\,b^6\,c^3\,d^7-6144\,a^5\,b^5\,c^2\,d^8+\sqrt{x}\,{\left(-\frac{b}{16\,a^5\,d^4-64\,a^4\,b\,c\,d^3+96\,a^3\,b^2\,c^2\,d^2-64\,a^2\,b^3\,c^3\,d+16\,a\,b^4\,c^4}\right)}^{1/4}\,\left(4096\,a^7\,b^4\,c\,d^{10}-16384\,a^6\,b^5\,c^2\,d^9+28672\,a^5\,b^6\,c^3\,d^8-32768\,a^4\,b^7\,c^4\,d^7+28672\,a^3\,b^8\,c^5\,d^6-16384\,a^2\,b^9\,c^6\,d^5+4096\,a\,b^{10}\,c^7\,d^4\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{b}{16\,a^5\,d^4-64\,a^4\,b\,c\,d^3+96\,a^3\,b^2\,c^2\,d^2-64\,a^2\,b^3\,c^3\,d+16\,a\,b^4\,c^4}\right)}^{1/4}}{-256\,a\,b^5\,c\,d^5+\left(\sqrt{x}\,\left(256\,a^2\,b^5\,c\,d^6+256\,a\,b^6\,c^2\,d^5\right)+{\left(-\frac{b}{16\,a^5\,d^4-64\,a^4\,b\,c\,d^3+96\,a^3\,b^2\,c^2\,d^2-64\,a^2\,b^3\,c^3\,d+16\,a\,b^4\,c^4}\right)}^{3/4}\,\left(2048\,a\,b^9\,c^6\,d^4+2048\,a^6\,b^4\,c\,d^9-6144\,a^2\,b^8\,c^5\,d^5+4096\,a^3\,b^7\,c^4\,d^6+4096\,a^4\,b^6\,c^3\,d^7-6144\,a^5\,b^5\,c^2\,d^8-\sqrt{x}\,{\left(-\frac{b}{16\,a^5\,d^4-64\,a^4\,b\,c\,d^3+96\,a^3\,b^2\,c^2\,d^2-64\,a^2\,b^3\,c^3\,d+16\,a\,b^4\,c^4}\right)}^{1/4}\,\left(4096\,a^7\,b^4\,c\,d^{10}-16384\,a^6\,b^5\,c^2\,d^9+28672\,a^5\,b^6\,c^3\,d^8-32768\,a^4\,b^7\,c^4\,d^7+28672\,a^3\,b^8\,c^5\,d^6-16384\,a^2\,b^9\,c^6\,d^5+4096\,a\,b^{10}\,c^7\,d^4\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{b}{16\,a^5\,d^4-64\,a^4\,b\,c\,d^3+96\,a^3\,b^2\,c^2\,d^2-64\,a^2\,b^3\,c^3\,d+16\,a\,b^4\,c^4}\right)}^{1/4}\,1{}\mathrm{i}+\left(-\sqrt{x}\,\left(256\,a^2\,b^5\,c\,d^6+256\,a\,b^6\,c^2\,d^5\right)+{\left(-\frac{b}{16\,a^5\,d^4-64\,a^4\,b\,c\,d^3+96\,a^3\,b^2\,c^2\,d^2-64\,a^2\,b^3\,c^3\,d+16\,a\,b^4\,c^4}\right)}^{3/4}\,\left(2048\,a\,b^9\,c^6\,d^4+2048\,a^6\,b^4\,c\,d^9-6144\,a^2\,b^8\,c^5\,d^5+4096\,a^3\,b^7\,c^4\,d^6+4096\,a^4\,b^6\,c^3\,d^7-6144\,a^5\,b^5\,c^2\,d^8+\sqrt{x}\,{\left(-\frac{b}{16\,a^5\,d^4-64\,a^4\,b\,c\,d^3+96\,a^3\,b^2\,c^2\,d^2-64\,a^2\,b^3\,c^3\,d+16\,a\,b^4\,c^4}\right)}^{1/4}\,\left(4096\,a^7\,b^4\,c\,d^{10}-16384\,a^6\,b^5\,c^2\,d^9+28672\,a^5\,b^6\,c^3\,d^8-32768\,a^4\,b^7\,c^4\,d^7+28672\,a^3\,b^8\,c^5\,d^6-16384\,a^2\,b^9\,c^6\,d^5+4096\,a\,b^{10}\,c^7\,d^4\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{b}{16\,a^5\,d^4-64\,a^4\,b\,c\,d^3+96\,a^3\,b^2\,c^2\,d^2-64\,a^2\,b^3\,c^3\,d+16\,a\,b^4\,c^4}\right)}^{1/4}\,1{}\mathrm{i}}\right)\,{\left(-\frac{b}{16\,a^5\,d^4-64\,a^4\,b\,c\,d^3+96\,a^3\,b^2\,c^2\,d^2-64\,a^2\,b^3\,c^3\,d+16\,a\,b^4\,c^4}\right)}^{1/4}+\mathrm{atan}\left(\frac{\left({\left(-\frac{d}{16\,a^4\,c\,d^4-64\,a^3\,b\,c^2\,d^3+96\,a^2\,b^2\,c^3\,d^2-64\,a\,b^3\,c^4\,d+16\,b^4\,c^5}\right)}^{3/4}\,\left(\sqrt{x}\,{\left(-\frac{d}{16\,a^4\,c\,d^4-64\,a^3\,b\,c^2\,d^3+96\,a^2\,b^2\,c^3\,d^2-64\,a\,b^3\,c^4\,d+16\,b^4\,c^5}\right)}^{1/4}\,\left(4096\,a^7\,b^4\,c\,d^{10}-16384\,a^6\,b^5\,c^2\,d^9+28672\,a^5\,b^6\,c^3\,d^8-32768\,a^4\,b^7\,c^4\,d^7+28672\,a^3\,b^8\,c^5\,d^6-16384\,a^2\,b^9\,c^6\,d^5+4096\,a\,b^{10}\,c^7\,d^4\right)+2048\,a\,b^9\,c^6\,d^4+2048\,a^6\,b^4\,c\,d^9-6144\,a^2\,b^8\,c^5\,d^5+4096\,a^3\,b^7\,c^4\,d^6+4096\,a^4\,b^6\,c^3\,d^7-6144\,a^5\,b^5\,c^2\,d^8\right)+\sqrt{x}\,\left(256\,a^2\,b^5\,c\,d^6+256\,a\,b^6\,c^2\,d^5\right)\right)\,{\left(-\frac{d}{16\,a^4\,c\,d^4-64\,a^3\,b\,c^2\,d^3+96\,a^2\,b^2\,c^3\,d^2-64\,a\,b^3\,c^4\,d+16\,b^4\,c^5}\right)}^{1/4}\,1{}\mathrm{i}-\left({\left(-\frac{d}{16\,a^4\,c\,d^4-64\,a^3\,b\,c^2\,d^3+96\,a^2\,b^2\,c^3\,d^2-64\,a\,b^3\,c^4\,d+16\,b^4\,c^5}\right)}^{3/4}\,\left(2048\,a\,b^9\,c^6\,d^4-\sqrt{x}\,{\left(-\frac{d}{16\,a^4\,c\,d^4-64\,a^3\,b\,c^2\,d^3+96\,a^2\,b^2\,c^3\,d^2-64\,a\,b^3\,c^4\,d+16\,b^4\,c^5}\right)}^{1/4}\,\left(4096\,a^7\,b^4\,c\,d^{10}-16384\,a^6\,b^5\,c^2\,d^9+28672\,a^5\,b^6\,c^3\,d^8-32768\,a^4\,b^7\,c^4\,d^7+28672\,a^3\,b^8\,c^5\,d^6-16384\,a^2\,b^9\,c^6\,d^5+4096\,a\,b^{10}\,c^7\,d^4\right)+2048\,a^6\,b^4\,c\,d^9-6144\,a^2\,b^8\,c^5\,d^5+4096\,a^3\,b^7\,c^4\,d^6+4096\,a^4\,b^6\,c^3\,d^7-6144\,a^5\,b^5\,c^2\,d^8\right)-\sqrt{x}\,\left(256\,a^2\,b^5\,c\,d^6+256\,a\,b^6\,c^2\,d^5\right)\right)\,{\left(-\frac{d}{16\,a^4\,c\,d^4-64\,a^3\,b\,c^2\,d^3+96\,a^2\,b^2\,c^3\,d^2-64\,a\,b^3\,c^4\,d+16\,b^4\,c^5}\right)}^{1/4}\,1{}\mathrm{i}}{\left({\left(-\frac{d}{16\,a^4\,c\,d^4-64\,a^3\,b\,c^2\,d^3+96\,a^2\,b^2\,c^3\,d^2-64\,a\,b^3\,c^4\,d+16\,b^4\,c^5}\right)}^{3/4}\,\left(\sqrt{x}\,{\left(-\frac{d}{16\,a^4\,c\,d^4-64\,a^3\,b\,c^2\,d^3+96\,a^2\,b^2\,c^3\,d^2-64\,a\,b^3\,c^4\,d+16\,b^4\,c^5}\right)}^{1/4}\,\left(4096\,a^7\,b^4\,c\,d^{10}-16384\,a^6\,b^5\,c^2\,d^9+28672\,a^5\,b^6\,c^3\,d^8-32768\,a^4\,b^7\,c^4\,d^7+28672\,a^3\,b^8\,c^5\,d^6-16384\,a^2\,b^9\,c^6\,d^5+4096\,a\,b^{10}\,c^7\,d^4\right)+2048\,a\,b^9\,c^6\,d^4+2048\,a^6\,b^4\,c\,d^9-6144\,a^2\,b^8\,c^5\,d^5+4096\,a^3\,b^7\,c^4\,d^6+4096\,a^4\,b^6\,c^3\,d^7-6144\,a^5\,b^5\,c^2\,d^8\right)+\sqrt{x}\,\left(256\,a^2\,b^5\,c\,d^6+256\,a\,b^6\,c^2\,d^5\right)\right)\,{\left(-\frac{d}{16\,a^4\,c\,d^4-64\,a^3\,b\,c^2\,d^3+96\,a^2\,b^2\,c^3\,d^2-64\,a\,b^3\,c^4\,d+16\,b^4\,c^5}\right)}^{1/4}+\left({\left(-\frac{d}{16\,a^4\,c\,d^4-64\,a^3\,b\,c^2\,d^3+96\,a^2\,b^2\,c^3\,d^2-64\,a\,b^3\,c^4\,d+16\,b^4\,c^5}\right)}^{3/4}\,\left(2048\,a\,b^9\,c^6\,d^4-\sqrt{x}\,{\left(-\frac{d}{16\,a^4\,c\,d^4-64\,a^3\,b\,c^2\,d^3+96\,a^2\,b^2\,c^3\,d^2-64\,a\,b^3\,c^4\,d+16\,b^4\,c^5}\right)}^{1/4}\,\left(4096\,a^7\,b^4\,c\,d^{10}-16384\,a^6\,b^5\,c^2\,d^9+28672\,a^5\,b^6\,c^3\,d^8-32768\,a^4\,b^7\,c^4\,d^7+28672\,a^3\,b^8\,c^5\,d^6-16384\,a^2\,b^9\,c^6\,d^5+4096\,a\,b^{10}\,c^7\,d^4\right)+2048\,a^6\,b^4\,c\,d^9-6144\,a^2\,b^8\,c^5\,d^5+4096\,a^3\,b^7\,c^4\,d^6+4096\,a^4\,b^6\,c^3\,d^7-6144\,a^5\,b^5\,c^2\,d^8\right)-\sqrt{x}\,\left(256\,a^2\,b^5\,c\,d^6+256\,a\,b^6\,c^2\,d^5\right)\right)\,{\left(-\frac{d}{16\,a^4\,c\,d^4-64\,a^3\,b\,c^2\,d^3+96\,a^2\,b^2\,c^3\,d^2-64\,a\,b^3\,c^4\,d+16\,b^4\,c^5}\right)}^{1/4}+256\,a\,b^5\,c\,d^5}\right)\,{\left(-\frac{d}{16\,a^4\,c\,d^4-64\,a^3\,b\,c^2\,d^3+96\,a^2\,b^2\,c^3\,d^2-64\,a\,b^3\,c^4\,d+16\,b^4\,c^5}\right)}^{1/4}\,2{}\mathrm{i}-2\,\mathrm{atan}\left(\frac{\left(\sqrt{x}\,\left(256\,a^2\,b^5\,c\,d^6+256\,a\,b^6\,c^2\,d^5\right)+{\left(-\frac{d}{16\,a^4\,c\,d^4-64\,a^3\,b\,c^2\,d^3+96\,a^2\,b^2\,c^3\,d^2-64\,a\,b^3\,c^4\,d+16\,b^4\,c^5}\right)}^{3/4}\,\left(2048\,a\,b^9\,c^6\,d^4+2048\,a^6\,b^4\,c\,d^9-6144\,a^2\,b^8\,c^5\,d^5+4096\,a^3\,b^7\,c^4\,d^6+4096\,a^4\,b^6\,c^3\,d^7-6144\,a^5\,b^5\,c^2\,d^8-\sqrt{x}\,{\left(-\frac{d}{16\,a^4\,c\,d^4-64\,a^3\,b\,c^2\,d^3+96\,a^2\,b^2\,c^3\,d^2-64\,a\,b^3\,c^4\,d+16\,b^4\,c^5}\right)}^{1/4}\,\left(4096\,a^7\,b^4\,c\,d^{10}-16384\,a^6\,b^5\,c^2\,d^9+28672\,a^5\,b^6\,c^3\,d^8-32768\,a^4\,b^7\,c^4\,d^7+28672\,a^3\,b^8\,c^5\,d^6-16384\,a^2\,b^9\,c^6\,d^5+4096\,a\,b^{10}\,c^7\,d^4\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{d}{16\,a^4\,c\,d^4-64\,a^3\,b\,c^2\,d^3+96\,a^2\,b^2\,c^3\,d^2-64\,a\,b^3\,c^4\,d+16\,b^4\,c^5}\right)}^{1/4}-\left(-\sqrt{x}\,\left(256\,a^2\,b^5\,c\,d^6+256\,a\,b^6\,c^2\,d^5\right)+{\left(-\frac{d}{16\,a^4\,c\,d^4-64\,a^3\,b\,c^2\,d^3+96\,a^2\,b^2\,c^3\,d^2-64\,a\,b^3\,c^4\,d+16\,b^4\,c^5}\right)}^{3/4}\,\left(2048\,a\,b^9\,c^6\,d^4+2048\,a^6\,b^4\,c\,d^9-6144\,a^2\,b^8\,c^5\,d^5+4096\,a^3\,b^7\,c^4\,d^6+4096\,a^4\,b^6\,c^3\,d^7-6144\,a^5\,b^5\,c^2\,d^8+\sqrt{x}\,{\left(-\frac{d}{16\,a^4\,c\,d^4-64\,a^3\,b\,c^2\,d^3+96\,a^2\,b^2\,c^3\,d^2-64\,a\,b^3\,c^4\,d+16\,b^4\,c^5}\right)}^{1/4}\,\left(4096\,a^7\,b^4\,c\,d^{10}-16384\,a^6\,b^5\,c^2\,d^9+28672\,a^5\,b^6\,c^3\,d^8-32768\,a^4\,b^7\,c^4\,d^7+28672\,a^3\,b^8\,c^5\,d^6-16384\,a^2\,b^9\,c^6\,d^5+4096\,a\,b^{10}\,c^7\,d^4\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{d}{16\,a^4\,c\,d^4-64\,a^3\,b\,c^2\,d^3+96\,a^2\,b^2\,c^3\,d^2-64\,a\,b^3\,c^4\,d+16\,b^4\,c^5}\right)}^{1/4}}{-256\,a\,b^5\,c\,d^5+\left(\sqrt{x}\,\left(256\,a^2\,b^5\,c\,d^6+256\,a\,b^6\,c^2\,d^5\right)+{\left(-\frac{d}{16\,a^4\,c\,d^4-64\,a^3\,b\,c^2\,d^3+96\,a^2\,b^2\,c^3\,d^2-64\,a\,b^3\,c^4\,d+16\,b^4\,c^5}\right)}^{3/4}\,\left(2048\,a\,b^9\,c^6\,d^4+2048\,a^6\,b^4\,c\,d^9-6144\,a^2\,b^8\,c^5\,d^5+4096\,a^3\,b^7\,c^4\,d^6+4096\,a^4\,b^6\,c^3\,d^7-6144\,a^5\,b^5\,c^2\,d^8-\sqrt{x}\,{\left(-\frac{d}{16\,a^4\,c\,d^4-64\,a^3\,b\,c^2\,d^3+96\,a^2\,b^2\,c^3\,d^2-64\,a\,b^3\,c^4\,d+16\,b^4\,c^5}\right)}^{1/4}\,\left(4096\,a^7\,b^4\,c\,d^{10}-16384\,a^6\,b^5\,c^2\,d^9+28672\,a^5\,b^6\,c^3\,d^8-32768\,a^4\,b^7\,c^4\,d^7+28672\,a^3\,b^8\,c^5\,d^6-16384\,a^2\,b^9\,c^6\,d^5+4096\,a\,b^{10}\,c^7\,d^4\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{d}{16\,a^4\,c\,d^4-64\,a^3\,b\,c^2\,d^3+96\,a^2\,b^2\,c^3\,d^2-64\,a\,b^3\,c^4\,d+16\,b^4\,c^5}\right)}^{1/4}\,1{}\mathrm{i}+\left(-\sqrt{x}\,\left(256\,a^2\,b^5\,c\,d^6+256\,a\,b^6\,c^2\,d^5\right)+{\left(-\frac{d}{16\,a^4\,c\,d^4-64\,a^3\,b\,c^2\,d^3+96\,a^2\,b^2\,c^3\,d^2-64\,a\,b^3\,c^4\,d+16\,b^4\,c^5}\right)}^{3/4}\,\left(2048\,a\,b^9\,c^6\,d^4+2048\,a^6\,b^4\,c\,d^9-6144\,a^2\,b^8\,c^5\,d^5+4096\,a^3\,b^7\,c^4\,d^6+4096\,a^4\,b^6\,c^3\,d^7-6144\,a^5\,b^5\,c^2\,d^8+\sqrt{x}\,{\left(-\frac{d}{16\,a^4\,c\,d^4-64\,a^3\,b\,c^2\,d^3+96\,a^2\,b^2\,c^3\,d^2-64\,a\,b^3\,c^4\,d+16\,b^4\,c^5}\right)}^{1/4}\,\left(4096\,a^7\,b^4\,c\,d^{10}-16384\,a^6\,b^5\,c^2\,d^9+28672\,a^5\,b^6\,c^3\,d^8-32768\,a^4\,b^7\,c^4\,d^7+28672\,a^3\,b^8\,c^5\,d^6-16384\,a^2\,b^9\,c^6\,d^5+4096\,a\,b^{10}\,c^7\,d^4\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{d}{16\,a^4\,c\,d^4-64\,a^3\,b\,c^2\,d^3+96\,a^2\,b^2\,c^3\,d^2-64\,a\,b^3\,c^4\,d+16\,b^4\,c^5}\right)}^{1/4}\,1{}\mathrm{i}}\right)\,{\left(-\frac{d}{16\,a^4\,c\,d^4-64\,a^3\,b\,c^2\,d^3+96\,a^2\,b^2\,c^3\,d^2-64\,a\,b^3\,c^4\,d+16\,b^4\,c^5}\right)}^{1/4}","Not used",1,"atan((((-b/(16*a^5*d^4 + 16*a*b^4*c^4 - 64*a^2*b^3*c^3*d + 96*a^3*b^2*c^2*d^2 - 64*a^4*b*c*d^3))^(3/4)*(x^(1/2)*(-b/(16*a^5*d^4 + 16*a*b^4*c^4 - 64*a^2*b^3*c^3*d + 96*a^3*b^2*c^2*d^2 - 64*a^4*b*c*d^3))^(1/4)*(4096*a*b^10*c^7*d^4 + 4096*a^7*b^4*c*d^10 - 16384*a^2*b^9*c^6*d^5 + 28672*a^3*b^8*c^5*d^6 - 32768*a^4*b^7*c^4*d^7 + 28672*a^5*b^6*c^3*d^8 - 16384*a^6*b^5*c^2*d^9) + 2048*a*b^9*c^6*d^4 + 2048*a^6*b^4*c*d^9 - 6144*a^2*b^8*c^5*d^5 + 4096*a^3*b^7*c^4*d^6 + 4096*a^4*b^6*c^3*d^7 - 6144*a^5*b^5*c^2*d^8) + x^(1/2)*(256*a*b^6*c^2*d^5 + 256*a^2*b^5*c*d^6))*(-b/(16*a^5*d^4 + 16*a*b^4*c^4 - 64*a^2*b^3*c^3*d + 96*a^3*b^2*c^2*d^2 - 64*a^4*b*c*d^3))^(1/4)*1i - ((-b/(16*a^5*d^4 + 16*a*b^4*c^4 - 64*a^2*b^3*c^3*d + 96*a^3*b^2*c^2*d^2 - 64*a^4*b*c*d^3))^(3/4)*(2048*a*b^9*c^6*d^4 - x^(1/2)*(-b/(16*a^5*d^4 + 16*a*b^4*c^4 - 64*a^2*b^3*c^3*d + 96*a^3*b^2*c^2*d^2 - 64*a^4*b*c*d^3))^(1/4)*(4096*a*b^10*c^7*d^4 + 4096*a^7*b^4*c*d^10 - 16384*a^2*b^9*c^6*d^5 + 28672*a^3*b^8*c^5*d^6 - 32768*a^4*b^7*c^4*d^7 + 28672*a^5*b^6*c^3*d^8 - 16384*a^6*b^5*c^2*d^9) + 2048*a^6*b^4*c*d^9 - 6144*a^2*b^8*c^5*d^5 + 4096*a^3*b^7*c^4*d^6 + 4096*a^4*b^6*c^3*d^7 - 6144*a^5*b^5*c^2*d^8) - x^(1/2)*(256*a*b^6*c^2*d^5 + 256*a^2*b^5*c*d^6))*(-b/(16*a^5*d^4 + 16*a*b^4*c^4 - 64*a^2*b^3*c^3*d + 96*a^3*b^2*c^2*d^2 - 64*a^4*b*c*d^3))^(1/4)*1i)/(((-b/(16*a^5*d^4 + 16*a*b^4*c^4 - 64*a^2*b^3*c^3*d + 96*a^3*b^2*c^2*d^2 - 64*a^4*b*c*d^3))^(3/4)*(x^(1/2)*(-b/(16*a^5*d^4 + 16*a*b^4*c^4 - 64*a^2*b^3*c^3*d + 96*a^3*b^2*c^2*d^2 - 64*a^4*b*c*d^3))^(1/4)*(4096*a*b^10*c^7*d^4 + 4096*a^7*b^4*c*d^10 - 16384*a^2*b^9*c^6*d^5 + 28672*a^3*b^8*c^5*d^6 - 32768*a^4*b^7*c^4*d^7 + 28672*a^5*b^6*c^3*d^8 - 16384*a^6*b^5*c^2*d^9) + 2048*a*b^9*c^6*d^4 + 2048*a^6*b^4*c*d^9 - 6144*a^2*b^8*c^5*d^5 + 4096*a^3*b^7*c^4*d^6 + 4096*a^4*b^6*c^3*d^7 - 6144*a^5*b^5*c^2*d^8) + x^(1/2)*(256*a*b^6*c^2*d^5 + 256*a^2*b^5*c*d^6))*(-b/(16*a^5*d^4 + 16*a*b^4*c^4 - 64*a^2*b^3*c^3*d + 96*a^3*b^2*c^2*d^2 - 64*a^4*b*c*d^3))^(1/4) + ((-b/(16*a^5*d^4 + 16*a*b^4*c^4 - 64*a^2*b^3*c^3*d + 96*a^3*b^2*c^2*d^2 - 64*a^4*b*c*d^3))^(3/4)*(2048*a*b^9*c^6*d^4 - x^(1/2)*(-b/(16*a^5*d^4 + 16*a*b^4*c^4 - 64*a^2*b^3*c^3*d + 96*a^3*b^2*c^2*d^2 - 64*a^4*b*c*d^3))^(1/4)*(4096*a*b^10*c^7*d^4 + 4096*a^7*b^4*c*d^10 - 16384*a^2*b^9*c^6*d^5 + 28672*a^3*b^8*c^5*d^6 - 32768*a^4*b^7*c^4*d^7 + 28672*a^5*b^6*c^3*d^8 - 16384*a^6*b^5*c^2*d^9) + 2048*a^6*b^4*c*d^9 - 6144*a^2*b^8*c^5*d^5 + 4096*a^3*b^7*c^4*d^6 + 4096*a^4*b^6*c^3*d^7 - 6144*a^5*b^5*c^2*d^8) - x^(1/2)*(256*a*b^6*c^2*d^5 + 256*a^2*b^5*c*d^6))*(-b/(16*a^5*d^4 + 16*a*b^4*c^4 - 64*a^2*b^3*c^3*d + 96*a^3*b^2*c^2*d^2 - 64*a^4*b*c*d^3))^(1/4) + 256*a*b^5*c*d^5))*(-b/(16*a^5*d^4 + 16*a*b^4*c^4 - 64*a^2*b^3*c^3*d + 96*a^3*b^2*c^2*d^2 - 64*a^4*b*c*d^3))^(1/4)*2i - 2*atan((((-b/(16*a^5*d^4 + 16*a*b^4*c^4 - 64*a^2*b^3*c^3*d + 96*a^3*b^2*c^2*d^2 - 64*a^4*b*c*d^3))^(3/4)*(2048*a*b^9*c^6*d^4 - x^(1/2)*(-b/(16*a^5*d^4 + 16*a*b^4*c^4 - 64*a^2*b^3*c^3*d + 96*a^3*b^2*c^2*d^2 - 64*a^4*b*c*d^3))^(1/4)*(4096*a*b^10*c^7*d^4 + 4096*a^7*b^4*c*d^10 - 16384*a^2*b^9*c^6*d^5 + 28672*a^3*b^8*c^5*d^6 - 32768*a^4*b^7*c^4*d^7 + 28672*a^5*b^6*c^3*d^8 - 16384*a^6*b^5*c^2*d^9)*1i + 2048*a^6*b^4*c*d^9 - 6144*a^2*b^8*c^5*d^5 + 4096*a^3*b^7*c^4*d^6 + 4096*a^4*b^6*c^3*d^7 - 6144*a^5*b^5*c^2*d^8)*1i + x^(1/2)*(256*a*b^6*c^2*d^5 + 256*a^2*b^5*c*d^6))*(-b/(16*a^5*d^4 + 16*a*b^4*c^4 - 64*a^2*b^3*c^3*d + 96*a^3*b^2*c^2*d^2 - 64*a^4*b*c*d^3))^(1/4) - ((-b/(16*a^5*d^4 + 16*a*b^4*c^4 - 64*a^2*b^3*c^3*d + 96*a^3*b^2*c^2*d^2 - 64*a^4*b*c*d^3))^(3/4)*(x^(1/2)*(-b/(16*a^5*d^4 + 16*a*b^4*c^4 - 64*a^2*b^3*c^3*d + 96*a^3*b^2*c^2*d^2 - 64*a^4*b*c*d^3))^(1/4)*(4096*a*b^10*c^7*d^4 + 4096*a^7*b^4*c*d^10 - 16384*a^2*b^9*c^6*d^5 + 28672*a^3*b^8*c^5*d^6 - 32768*a^4*b^7*c^4*d^7 + 28672*a^5*b^6*c^3*d^8 - 16384*a^6*b^5*c^2*d^9)*1i + 2048*a*b^9*c^6*d^4 + 2048*a^6*b^4*c*d^9 - 6144*a^2*b^8*c^5*d^5 + 4096*a^3*b^7*c^4*d^6 + 4096*a^4*b^6*c^3*d^7 - 6144*a^5*b^5*c^2*d^8)*1i - x^(1/2)*(256*a*b^6*c^2*d^5 + 256*a^2*b^5*c*d^6))*(-b/(16*a^5*d^4 + 16*a*b^4*c^4 - 64*a^2*b^3*c^3*d + 96*a^3*b^2*c^2*d^2 - 64*a^4*b*c*d^3))^(1/4))/(((-b/(16*a^5*d^4 + 16*a*b^4*c^4 - 64*a^2*b^3*c^3*d + 96*a^3*b^2*c^2*d^2 - 64*a^4*b*c*d^3))^(3/4)*(2048*a*b^9*c^6*d^4 - x^(1/2)*(-b/(16*a^5*d^4 + 16*a*b^4*c^4 - 64*a^2*b^3*c^3*d + 96*a^3*b^2*c^2*d^2 - 64*a^4*b*c*d^3))^(1/4)*(4096*a*b^10*c^7*d^4 + 4096*a^7*b^4*c*d^10 - 16384*a^2*b^9*c^6*d^5 + 28672*a^3*b^8*c^5*d^6 - 32768*a^4*b^7*c^4*d^7 + 28672*a^5*b^6*c^3*d^8 - 16384*a^6*b^5*c^2*d^9)*1i + 2048*a^6*b^4*c*d^9 - 6144*a^2*b^8*c^5*d^5 + 4096*a^3*b^7*c^4*d^6 + 4096*a^4*b^6*c^3*d^7 - 6144*a^5*b^5*c^2*d^8)*1i + x^(1/2)*(256*a*b^6*c^2*d^5 + 256*a^2*b^5*c*d^6))*(-b/(16*a^5*d^4 + 16*a*b^4*c^4 - 64*a^2*b^3*c^3*d + 96*a^3*b^2*c^2*d^2 - 64*a^4*b*c*d^3))^(1/4)*1i + ((-b/(16*a^5*d^4 + 16*a*b^4*c^4 - 64*a^2*b^3*c^3*d + 96*a^3*b^2*c^2*d^2 - 64*a^4*b*c*d^3))^(3/4)*(x^(1/2)*(-b/(16*a^5*d^4 + 16*a*b^4*c^4 - 64*a^2*b^3*c^3*d + 96*a^3*b^2*c^2*d^2 - 64*a^4*b*c*d^3))^(1/4)*(4096*a*b^10*c^7*d^4 + 4096*a^7*b^4*c*d^10 - 16384*a^2*b^9*c^6*d^5 + 28672*a^3*b^8*c^5*d^6 - 32768*a^4*b^7*c^4*d^7 + 28672*a^5*b^6*c^3*d^8 - 16384*a^6*b^5*c^2*d^9)*1i + 2048*a*b^9*c^6*d^4 + 2048*a^6*b^4*c*d^9 - 6144*a^2*b^8*c^5*d^5 + 4096*a^3*b^7*c^4*d^6 + 4096*a^4*b^6*c^3*d^7 - 6144*a^5*b^5*c^2*d^8)*1i - x^(1/2)*(256*a*b^6*c^2*d^5 + 256*a^2*b^5*c*d^6))*(-b/(16*a^5*d^4 + 16*a*b^4*c^4 - 64*a^2*b^3*c^3*d + 96*a^3*b^2*c^2*d^2 - 64*a^4*b*c*d^3))^(1/4)*1i - 256*a*b^5*c*d^5))*(-b/(16*a^5*d^4 + 16*a*b^4*c^4 - 64*a^2*b^3*c^3*d + 96*a^3*b^2*c^2*d^2 - 64*a^4*b*c*d^3))^(1/4) + atan((((-d/(16*b^4*c^5 + 16*a^4*c*d^4 - 64*a^3*b*c^2*d^3 + 96*a^2*b^2*c^3*d^2 - 64*a*b^3*c^4*d))^(3/4)*(x^(1/2)*(-d/(16*b^4*c^5 + 16*a^4*c*d^4 - 64*a^3*b*c^2*d^3 + 96*a^2*b^2*c^3*d^2 - 64*a*b^3*c^4*d))^(1/4)*(4096*a*b^10*c^7*d^4 + 4096*a^7*b^4*c*d^10 - 16384*a^2*b^9*c^6*d^5 + 28672*a^3*b^8*c^5*d^6 - 32768*a^4*b^7*c^4*d^7 + 28672*a^5*b^6*c^3*d^8 - 16384*a^6*b^5*c^2*d^9) + 2048*a*b^9*c^6*d^4 + 2048*a^6*b^4*c*d^9 - 6144*a^2*b^8*c^5*d^5 + 4096*a^3*b^7*c^4*d^6 + 4096*a^4*b^6*c^3*d^7 - 6144*a^5*b^5*c^2*d^8) + x^(1/2)*(256*a*b^6*c^2*d^5 + 256*a^2*b^5*c*d^6))*(-d/(16*b^4*c^5 + 16*a^4*c*d^4 - 64*a^3*b*c^2*d^3 + 96*a^2*b^2*c^3*d^2 - 64*a*b^3*c^4*d))^(1/4)*1i - ((-d/(16*b^4*c^5 + 16*a^4*c*d^4 - 64*a^3*b*c^2*d^3 + 96*a^2*b^2*c^3*d^2 - 64*a*b^3*c^4*d))^(3/4)*(2048*a*b^9*c^6*d^4 - x^(1/2)*(-d/(16*b^4*c^5 + 16*a^4*c*d^4 - 64*a^3*b*c^2*d^3 + 96*a^2*b^2*c^3*d^2 - 64*a*b^3*c^4*d))^(1/4)*(4096*a*b^10*c^7*d^4 + 4096*a^7*b^4*c*d^10 - 16384*a^2*b^9*c^6*d^5 + 28672*a^3*b^8*c^5*d^6 - 32768*a^4*b^7*c^4*d^7 + 28672*a^5*b^6*c^3*d^8 - 16384*a^6*b^5*c^2*d^9) + 2048*a^6*b^4*c*d^9 - 6144*a^2*b^8*c^5*d^5 + 4096*a^3*b^7*c^4*d^6 + 4096*a^4*b^6*c^3*d^7 - 6144*a^5*b^5*c^2*d^8) - x^(1/2)*(256*a*b^6*c^2*d^5 + 256*a^2*b^5*c*d^6))*(-d/(16*b^4*c^5 + 16*a^4*c*d^4 - 64*a^3*b*c^2*d^3 + 96*a^2*b^2*c^3*d^2 - 64*a*b^3*c^4*d))^(1/4)*1i)/(((-d/(16*b^4*c^5 + 16*a^4*c*d^4 - 64*a^3*b*c^2*d^3 + 96*a^2*b^2*c^3*d^2 - 64*a*b^3*c^4*d))^(3/4)*(x^(1/2)*(-d/(16*b^4*c^5 + 16*a^4*c*d^4 - 64*a^3*b*c^2*d^3 + 96*a^2*b^2*c^3*d^2 - 64*a*b^3*c^4*d))^(1/4)*(4096*a*b^10*c^7*d^4 + 4096*a^7*b^4*c*d^10 - 16384*a^2*b^9*c^6*d^5 + 28672*a^3*b^8*c^5*d^6 - 32768*a^4*b^7*c^4*d^7 + 28672*a^5*b^6*c^3*d^8 - 16384*a^6*b^5*c^2*d^9) + 2048*a*b^9*c^6*d^4 + 2048*a^6*b^4*c*d^9 - 6144*a^2*b^8*c^5*d^5 + 4096*a^3*b^7*c^4*d^6 + 4096*a^4*b^6*c^3*d^7 - 6144*a^5*b^5*c^2*d^8) + x^(1/2)*(256*a*b^6*c^2*d^5 + 256*a^2*b^5*c*d^6))*(-d/(16*b^4*c^5 + 16*a^4*c*d^4 - 64*a^3*b*c^2*d^3 + 96*a^2*b^2*c^3*d^2 - 64*a*b^3*c^4*d))^(1/4) + ((-d/(16*b^4*c^5 + 16*a^4*c*d^4 - 64*a^3*b*c^2*d^3 + 96*a^2*b^2*c^3*d^2 - 64*a*b^3*c^4*d))^(3/4)*(2048*a*b^9*c^6*d^4 - x^(1/2)*(-d/(16*b^4*c^5 + 16*a^4*c*d^4 - 64*a^3*b*c^2*d^3 + 96*a^2*b^2*c^3*d^2 - 64*a*b^3*c^4*d))^(1/4)*(4096*a*b^10*c^7*d^4 + 4096*a^7*b^4*c*d^10 - 16384*a^2*b^9*c^6*d^5 + 28672*a^3*b^8*c^5*d^6 - 32768*a^4*b^7*c^4*d^7 + 28672*a^5*b^6*c^3*d^8 - 16384*a^6*b^5*c^2*d^9) + 2048*a^6*b^4*c*d^9 - 6144*a^2*b^8*c^5*d^5 + 4096*a^3*b^7*c^4*d^6 + 4096*a^4*b^6*c^3*d^7 - 6144*a^5*b^5*c^2*d^8) - x^(1/2)*(256*a*b^6*c^2*d^5 + 256*a^2*b^5*c*d^6))*(-d/(16*b^4*c^5 + 16*a^4*c*d^4 - 64*a^3*b*c^2*d^3 + 96*a^2*b^2*c^3*d^2 - 64*a*b^3*c^4*d))^(1/4) + 256*a*b^5*c*d^5))*(-d/(16*b^4*c^5 + 16*a^4*c*d^4 - 64*a^3*b*c^2*d^3 + 96*a^2*b^2*c^3*d^2 - 64*a*b^3*c^4*d))^(1/4)*2i - 2*atan((((-d/(16*b^4*c^5 + 16*a^4*c*d^4 - 64*a^3*b*c^2*d^3 + 96*a^2*b^2*c^3*d^2 - 64*a*b^3*c^4*d))^(3/4)*(2048*a*b^9*c^6*d^4 - x^(1/2)*(-d/(16*b^4*c^5 + 16*a^4*c*d^4 - 64*a^3*b*c^2*d^3 + 96*a^2*b^2*c^3*d^2 - 64*a*b^3*c^4*d))^(1/4)*(4096*a*b^10*c^7*d^4 + 4096*a^7*b^4*c*d^10 - 16384*a^2*b^9*c^6*d^5 + 28672*a^3*b^8*c^5*d^6 - 32768*a^4*b^7*c^4*d^7 + 28672*a^5*b^6*c^3*d^8 - 16384*a^6*b^5*c^2*d^9)*1i + 2048*a^6*b^4*c*d^9 - 6144*a^2*b^8*c^5*d^5 + 4096*a^3*b^7*c^4*d^6 + 4096*a^4*b^6*c^3*d^7 - 6144*a^5*b^5*c^2*d^8)*1i + x^(1/2)*(256*a*b^6*c^2*d^5 + 256*a^2*b^5*c*d^6))*(-d/(16*b^4*c^5 + 16*a^4*c*d^4 - 64*a^3*b*c^2*d^3 + 96*a^2*b^2*c^3*d^2 - 64*a*b^3*c^4*d))^(1/4) - ((-d/(16*b^4*c^5 + 16*a^4*c*d^4 - 64*a^3*b*c^2*d^3 + 96*a^2*b^2*c^3*d^2 - 64*a*b^3*c^4*d))^(3/4)*(x^(1/2)*(-d/(16*b^4*c^5 + 16*a^4*c*d^4 - 64*a^3*b*c^2*d^3 + 96*a^2*b^2*c^3*d^2 - 64*a*b^3*c^4*d))^(1/4)*(4096*a*b^10*c^7*d^4 + 4096*a^7*b^4*c*d^10 - 16384*a^2*b^9*c^6*d^5 + 28672*a^3*b^8*c^5*d^6 - 32768*a^4*b^7*c^4*d^7 + 28672*a^5*b^6*c^3*d^8 - 16384*a^6*b^5*c^2*d^9)*1i + 2048*a*b^9*c^6*d^4 + 2048*a^6*b^4*c*d^9 - 6144*a^2*b^8*c^5*d^5 + 4096*a^3*b^7*c^4*d^6 + 4096*a^4*b^6*c^3*d^7 - 6144*a^5*b^5*c^2*d^8)*1i - x^(1/2)*(256*a*b^6*c^2*d^5 + 256*a^2*b^5*c*d^6))*(-d/(16*b^4*c^5 + 16*a^4*c*d^4 - 64*a^3*b*c^2*d^3 + 96*a^2*b^2*c^3*d^2 - 64*a*b^3*c^4*d))^(1/4))/(((-d/(16*b^4*c^5 + 16*a^4*c*d^4 - 64*a^3*b*c^2*d^3 + 96*a^2*b^2*c^3*d^2 - 64*a*b^3*c^4*d))^(3/4)*(2048*a*b^9*c^6*d^4 - x^(1/2)*(-d/(16*b^4*c^5 + 16*a^4*c*d^4 - 64*a^3*b*c^2*d^3 + 96*a^2*b^2*c^3*d^2 - 64*a*b^3*c^4*d))^(1/4)*(4096*a*b^10*c^7*d^4 + 4096*a^7*b^4*c*d^10 - 16384*a^2*b^9*c^6*d^5 + 28672*a^3*b^8*c^5*d^6 - 32768*a^4*b^7*c^4*d^7 + 28672*a^5*b^6*c^3*d^8 - 16384*a^6*b^5*c^2*d^9)*1i + 2048*a^6*b^4*c*d^9 - 6144*a^2*b^8*c^5*d^5 + 4096*a^3*b^7*c^4*d^6 + 4096*a^4*b^6*c^3*d^7 - 6144*a^5*b^5*c^2*d^8)*1i + x^(1/2)*(256*a*b^6*c^2*d^5 + 256*a^2*b^5*c*d^6))*(-d/(16*b^4*c^5 + 16*a^4*c*d^4 - 64*a^3*b*c^2*d^3 + 96*a^2*b^2*c^3*d^2 - 64*a*b^3*c^4*d))^(1/4)*1i + ((-d/(16*b^4*c^5 + 16*a^4*c*d^4 - 64*a^3*b*c^2*d^3 + 96*a^2*b^2*c^3*d^2 - 64*a*b^3*c^4*d))^(3/4)*(x^(1/2)*(-d/(16*b^4*c^5 + 16*a^4*c*d^4 - 64*a^3*b*c^2*d^3 + 96*a^2*b^2*c^3*d^2 - 64*a*b^3*c^4*d))^(1/4)*(4096*a*b^10*c^7*d^4 + 4096*a^7*b^4*c*d^10 - 16384*a^2*b^9*c^6*d^5 + 28672*a^3*b^8*c^5*d^6 - 32768*a^4*b^7*c^4*d^7 + 28672*a^5*b^6*c^3*d^8 - 16384*a^6*b^5*c^2*d^9)*1i + 2048*a*b^9*c^6*d^4 + 2048*a^6*b^4*c*d^9 - 6144*a^2*b^8*c^5*d^5 + 4096*a^3*b^7*c^4*d^6 + 4096*a^4*b^6*c^3*d^7 - 6144*a^5*b^5*c^2*d^8)*1i - x^(1/2)*(256*a*b^6*c^2*d^5 + 256*a^2*b^5*c*d^6))*(-d/(16*b^4*c^5 + 16*a^4*c*d^4 - 64*a^3*b*c^2*d^3 + 96*a^2*b^2*c^3*d^2 - 64*a*b^3*c^4*d))^(1/4)*1i - 256*a*b^5*c*d^5))*(-d/(16*b^4*c^5 + 16*a^4*c*d^4 - 64*a^3*b*c^2*d^3 + 96*a^2*b^2*c^3*d^2 - 64*a*b^3*c^4*d))^(1/4)","B"
466,1,8785,463,1.674613,"\text{Not used}","int(1/(x^(1/2)*(a + b*x^2)*(c + d*x^2)),x)","-\mathrm{atan}\left(\frac{{\left(-\frac{d^3}{16\,a^4\,c^3\,d^4-64\,a^3\,b\,c^4\,d^3+96\,a^2\,b^2\,c^5\,d^2-64\,a\,b^3\,c^6\,d+16\,b^4\,c^7}\right)}^{1/4}\,\left({\left(-\frac{d^3}{16\,a^4\,c^3\,d^4-64\,a^3\,b\,c^4\,d^3+96\,a^2\,b^2\,c^5\,d^2-64\,a\,b^3\,c^6\,d+16\,b^4\,c^7}\right)}^{1/4}\,\left(\left({\left(-\frac{d^3}{16\,a^4\,c^3\,d^4-64\,a^3\,b\,c^4\,d^3+96\,a^2\,b^2\,c^5\,d^2-64\,a\,b^3\,c^6\,d+16\,b^4\,c^7}\right)}^{1/4}\,\left(8192\,a^8\,b^4\,c\,d^{11}-40960\,a^7\,b^5\,c^2\,d^{10}+73728\,a^6\,b^6\,c^3\,d^9-40960\,a^5\,b^7\,c^4\,d^8-40960\,a^4\,b^8\,c^5\,d^7+73728\,a^3\,b^9\,c^6\,d^6-40960\,a^2\,b^{10}\,c^7\,d^5+8192\,a\,b^{11}\,c^8\,d^4\right)+\sqrt{x}\,\left(4096\,a^7\,b^4\,d^{11}-16384\,a^6\,b^5\,c\,d^{10}+24576\,a^5\,b^6\,c^2\,d^9-12288\,a^4\,b^7\,c^3\,d^8-12288\,a^3\,b^8\,c^4\,d^7+24576\,a^2\,b^9\,c^5\,d^6-16384\,a\,b^{10}\,c^6\,d^5+4096\,b^{11}\,c^7\,d^4\right)\right)\,{\left(-\frac{d^3}{16\,a^4\,c^3\,d^4-64\,a^3\,b\,c^4\,d^3+96\,a^2\,b^2\,c^5\,d^2-64\,a\,b^3\,c^6\,d+16\,b^4\,c^7}\right)}^{3/4}-512\,a^2\,b^6\,d^8-512\,b^8\,c^2\,d^6+1024\,a\,b^7\,c\,d^7\right)+512\,b^7\,d^7\,\sqrt{x}\right)\,1{}\mathrm{i}-{\left(-\frac{d^3}{16\,a^4\,c^3\,d^4-64\,a^3\,b\,c^4\,d^3+96\,a^2\,b^2\,c^5\,d^2-64\,a\,b^3\,c^6\,d+16\,b^4\,c^7}\right)}^{1/4}\,\left({\left(-\frac{d^3}{16\,a^4\,c^3\,d^4-64\,a^3\,b\,c^4\,d^3+96\,a^2\,b^2\,c^5\,d^2-64\,a\,b^3\,c^6\,d+16\,b^4\,c^7}\right)}^{1/4}\,\left(\left({\left(-\frac{d^3}{16\,a^4\,c^3\,d^4-64\,a^3\,b\,c^4\,d^3+96\,a^2\,b^2\,c^5\,d^2-64\,a\,b^3\,c^6\,d+16\,b^4\,c^7}\right)}^{1/4}\,\left(8192\,a^8\,b^4\,c\,d^{11}-40960\,a^7\,b^5\,c^2\,d^{10}+73728\,a^6\,b^6\,c^3\,d^9-40960\,a^5\,b^7\,c^4\,d^8-40960\,a^4\,b^8\,c^5\,d^7+73728\,a^3\,b^9\,c^6\,d^6-40960\,a^2\,b^{10}\,c^7\,d^5+8192\,a\,b^{11}\,c^8\,d^4\right)-\sqrt{x}\,\left(4096\,a^7\,b^4\,d^{11}-16384\,a^6\,b^5\,c\,d^{10}+24576\,a^5\,b^6\,c^2\,d^9-12288\,a^4\,b^7\,c^3\,d^8-12288\,a^3\,b^8\,c^4\,d^7+24576\,a^2\,b^9\,c^5\,d^6-16384\,a\,b^{10}\,c^6\,d^5+4096\,b^{11}\,c^7\,d^4\right)\right)\,{\left(-\frac{d^3}{16\,a^4\,c^3\,d^4-64\,a^3\,b\,c^4\,d^3+96\,a^2\,b^2\,c^5\,d^2-64\,a\,b^3\,c^6\,d+16\,b^4\,c^7}\right)}^{3/4}-512\,a^2\,b^6\,d^8-512\,b^8\,c^2\,d^6+1024\,a\,b^7\,c\,d^7\right)-512\,b^7\,d^7\,\sqrt{x}\right)\,1{}\mathrm{i}}{{\left(-\frac{d^3}{16\,a^4\,c^3\,d^4-64\,a^3\,b\,c^4\,d^3+96\,a^2\,b^2\,c^5\,d^2-64\,a\,b^3\,c^6\,d+16\,b^4\,c^7}\right)}^{1/4}\,\left({\left(-\frac{d^3}{16\,a^4\,c^3\,d^4-64\,a^3\,b\,c^4\,d^3+96\,a^2\,b^2\,c^5\,d^2-64\,a\,b^3\,c^6\,d+16\,b^4\,c^7}\right)}^{1/4}\,\left(\left({\left(-\frac{d^3}{16\,a^4\,c^3\,d^4-64\,a^3\,b\,c^4\,d^3+96\,a^2\,b^2\,c^5\,d^2-64\,a\,b^3\,c^6\,d+16\,b^4\,c^7}\right)}^{1/4}\,\left(8192\,a^8\,b^4\,c\,d^{11}-40960\,a^7\,b^5\,c^2\,d^{10}+73728\,a^6\,b^6\,c^3\,d^9-40960\,a^5\,b^7\,c^4\,d^8-40960\,a^4\,b^8\,c^5\,d^7+73728\,a^3\,b^9\,c^6\,d^6-40960\,a^2\,b^{10}\,c^7\,d^5+8192\,a\,b^{11}\,c^8\,d^4\right)+\sqrt{x}\,\left(4096\,a^7\,b^4\,d^{11}-16384\,a^6\,b^5\,c\,d^{10}+24576\,a^5\,b^6\,c^2\,d^9-12288\,a^4\,b^7\,c^3\,d^8-12288\,a^3\,b^8\,c^4\,d^7+24576\,a^2\,b^9\,c^5\,d^6-16384\,a\,b^{10}\,c^6\,d^5+4096\,b^{11}\,c^7\,d^4\right)\right)\,{\left(-\frac{d^3}{16\,a^4\,c^3\,d^4-64\,a^3\,b\,c^4\,d^3+96\,a^2\,b^2\,c^5\,d^2-64\,a\,b^3\,c^6\,d+16\,b^4\,c^7}\right)}^{3/4}-512\,a^2\,b^6\,d^8-512\,b^8\,c^2\,d^6+1024\,a\,b^7\,c\,d^7\right)+512\,b^7\,d^7\,\sqrt{x}\right)+{\left(-\frac{d^3}{16\,a^4\,c^3\,d^4-64\,a^3\,b\,c^4\,d^3+96\,a^2\,b^2\,c^5\,d^2-64\,a\,b^3\,c^6\,d+16\,b^4\,c^7}\right)}^{1/4}\,\left({\left(-\frac{d^3}{16\,a^4\,c^3\,d^4-64\,a^3\,b\,c^4\,d^3+96\,a^2\,b^2\,c^5\,d^2-64\,a\,b^3\,c^6\,d+16\,b^4\,c^7}\right)}^{1/4}\,\left(\left({\left(-\frac{d^3}{16\,a^4\,c^3\,d^4-64\,a^3\,b\,c^4\,d^3+96\,a^2\,b^2\,c^5\,d^2-64\,a\,b^3\,c^6\,d+16\,b^4\,c^7}\right)}^{1/4}\,\left(8192\,a^8\,b^4\,c\,d^{11}-40960\,a^7\,b^5\,c^2\,d^{10}+73728\,a^6\,b^6\,c^3\,d^9-40960\,a^5\,b^7\,c^4\,d^8-40960\,a^4\,b^8\,c^5\,d^7+73728\,a^3\,b^9\,c^6\,d^6-40960\,a^2\,b^{10}\,c^7\,d^5+8192\,a\,b^{11}\,c^8\,d^4\right)-\sqrt{x}\,\left(4096\,a^7\,b^4\,d^{11}-16384\,a^6\,b^5\,c\,d^{10}+24576\,a^5\,b^6\,c^2\,d^9-12288\,a^4\,b^7\,c^3\,d^8-12288\,a^3\,b^8\,c^4\,d^7+24576\,a^2\,b^9\,c^5\,d^6-16384\,a\,b^{10}\,c^6\,d^5+4096\,b^{11}\,c^7\,d^4\right)\right)\,{\left(-\frac{d^3}{16\,a^4\,c^3\,d^4-64\,a^3\,b\,c^4\,d^3+96\,a^2\,b^2\,c^5\,d^2-64\,a\,b^3\,c^6\,d+16\,b^4\,c^7}\right)}^{3/4}-512\,a^2\,b^6\,d^8-512\,b^8\,c^2\,d^6+1024\,a\,b^7\,c\,d^7\right)-512\,b^7\,d^7\,\sqrt{x}\right)}\right)\,{\left(-\frac{d^3}{16\,a^4\,c^3\,d^4-64\,a^3\,b\,c^4\,d^3+96\,a^2\,b^2\,c^5\,d^2-64\,a\,b^3\,c^6\,d+16\,b^4\,c^7}\right)}^{1/4}\,2{}\mathrm{i}-2\,\mathrm{atan}\left(\frac{{\left(-\frac{d^3}{16\,a^4\,c^3\,d^4-64\,a^3\,b\,c^4\,d^3+96\,a^2\,b^2\,c^5\,d^2-64\,a\,b^3\,c^6\,d+16\,b^4\,c^7}\right)}^{1/4}\,\left(-512\,b^7\,d^7\,\sqrt{x}+{\left(-\frac{d^3}{16\,a^4\,c^3\,d^4-64\,a^3\,b\,c^4\,d^3+96\,a^2\,b^2\,c^5\,d^2-64\,a\,b^3\,c^6\,d+16\,b^4\,c^7}\right)}^{1/4}\,\left(512\,a^2\,b^6\,d^8+512\,b^8\,c^2\,d^6-1024\,a\,b^7\,c\,d^7+\left(\sqrt{x}\,\left(4096\,a^7\,b^4\,d^{11}-16384\,a^6\,b^5\,c\,d^{10}+24576\,a^5\,b^6\,c^2\,d^9-12288\,a^4\,b^7\,c^3\,d^8-12288\,a^3\,b^8\,c^4\,d^7+24576\,a^2\,b^9\,c^5\,d^6-16384\,a\,b^{10}\,c^6\,d^5+4096\,b^{11}\,c^7\,d^4\right)+{\left(-\frac{d^3}{16\,a^4\,c^3\,d^4-64\,a^3\,b\,c^4\,d^3+96\,a^2\,b^2\,c^5\,d^2-64\,a\,b^3\,c^6\,d+16\,b^4\,c^7}\right)}^{1/4}\,\left(8192\,a^8\,b^4\,c\,d^{11}-40960\,a^7\,b^5\,c^2\,d^{10}+73728\,a^6\,b^6\,c^3\,d^9-40960\,a^5\,b^7\,c^4\,d^8-40960\,a^4\,b^8\,c^5\,d^7+73728\,a^3\,b^9\,c^6\,d^6-40960\,a^2\,b^{10}\,c^7\,d^5+8192\,a\,b^{11}\,c^8\,d^4\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{d^3}{16\,a^4\,c^3\,d^4-64\,a^3\,b\,c^4\,d^3+96\,a^2\,b^2\,c^5\,d^2-64\,a\,b^3\,c^6\,d+16\,b^4\,c^7}\right)}^{3/4}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)-{\left(-\frac{d^3}{16\,a^4\,c^3\,d^4-64\,a^3\,b\,c^4\,d^3+96\,a^2\,b^2\,c^5\,d^2-64\,a\,b^3\,c^6\,d+16\,b^4\,c^7}\right)}^{1/4}\,\left(512\,b^7\,d^7\,\sqrt{x}+{\left(-\frac{d^3}{16\,a^4\,c^3\,d^4-64\,a^3\,b\,c^4\,d^3+96\,a^2\,b^2\,c^5\,d^2-64\,a\,b^3\,c^6\,d+16\,b^4\,c^7}\right)}^{1/4}\,\left(512\,a^2\,b^6\,d^8+512\,b^8\,c^2\,d^6-1024\,a\,b^7\,c\,d^7+\left(-\sqrt{x}\,\left(4096\,a^7\,b^4\,d^{11}-16384\,a^6\,b^5\,c\,d^{10}+24576\,a^5\,b^6\,c^2\,d^9-12288\,a^4\,b^7\,c^3\,d^8-12288\,a^3\,b^8\,c^4\,d^7+24576\,a^2\,b^9\,c^5\,d^6-16384\,a\,b^{10}\,c^6\,d^5+4096\,b^{11}\,c^7\,d^4\right)+{\left(-\frac{d^3}{16\,a^4\,c^3\,d^4-64\,a^3\,b\,c^4\,d^3+96\,a^2\,b^2\,c^5\,d^2-64\,a\,b^3\,c^6\,d+16\,b^4\,c^7}\right)}^{1/4}\,\left(8192\,a^8\,b^4\,c\,d^{11}-40960\,a^7\,b^5\,c^2\,d^{10}+73728\,a^6\,b^6\,c^3\,d^9-40960\,a^5\,b^7\,c^4\,d^8-40960\,a^4\,b^8\,c^5\,d^7+73728\,a^3\,b^9\,c^6\,d^6-40960\,a^2\,b^{10}\,c^7\,d^5+8192\,a\,b^{11}\,c^8\,d^4\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{d^3}{16\,a^4\,c^3\,d^4-64\,a^3\,b\,c^4\,d^3+96\,a^2\,b^2\,c^5\,d^2-64\,a\,b^3\,c^6\,d+16\,b^4\,c^7}\right)}^{3/4}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)}{{\left(-\frac{d^3}{16\,a^4\,c^3\,d^4-64\,a^3\,b\,c^4\,d^3+96\,a^2\,b^2\,c^5\,d^2-64\,a\,b^3\,c^6\,d+16\,b^4\,c^7}\right)}^{1/4}\,\left(-512\,b^7\,d^7\,\sqrt{x}+{\left(-\frac{d^3}{16\,a^4\,c^3\,d^4-64\,a^3\,b\,c^4\,d^3+96\,a^2\,b^2\,c^5\,d^2-64\,a\,b^3\,c^6\,d+16\,b^4\,c^7}\right)}^{1/4}\,\left(512\,a^2\,b^6\,d^8+512\,b^8\,c^2\,d^6-1024\,a\,b^7\,c\,d^7+\left(\sqrt{x}\,\left(4096\,a^7\,b^4\,d^{11}-16384\,a^6\,b^5\,c\,d^{10}+24576\,a^5\,b^6\,c^2\,d^9-12288\,a^4\,b^7\,c^3\,d^8-12288\,a^3\,b^8\,c^4\,d^7+24576\,a^2\,b^9\,c^5\,d^6-16384\,a\,b^{10}\,c^6\,d^5+4096\,b^{11}\,c^7\,d^4\right)+{\left(-\frac{d^3}{16\,a^4\,c^3\,d^4-64\,a^3\,b\,c^4\,d^3+96\,a^2\,b^2\,c^5\,d^2-64\,a\,b^3\,c^6\,d+16\,b^4\,c^7}\right)}^{1/4}\,\left(8192\,a^8\,b^4\,c\,d^{11}-40960\,a^7\,b^5\,c^2\,d^{10}+73728\,a^6\,b^6\,c^3\,d^9-40960\,a^5\,b^7\,c^4\,d^8-40960\,a^4\,b^8\,c^5\,d^7+73728\,a^3\,b^9\,c^6\,d^6-40960\,a^2\,b^{10}\,c^7\,d^5+8192\,a\,b^{11}\,c^8\,d^4\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{d^3}{16\,a^4\,c^3\,d^4-64\,a^3\,b\,c^4\,d^3+96\,a^2\,b^2\,c^5\,d^2-64\,a\,b^3\,c^6\,d+16\,b^4\,c^7}\right)}^{3/4}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}+{\left(-\frac{d^3}{16\,a^4\,c^3\,d^4-64\,a^3\,b\,c^4\,d^3+96\,a^2\,b^2\,c^5\,d^2-64\,a\,b^3\,c^6\,d+16\,b^4\,c^7}\right)}^{1/4}\,\left(512\,b^7\,d^7\,\sqrt{x}+{\left(-\frac{d^3}{16\,a^4\,c^3\,d^4-64\,a^3\,b\,c^4\,d^3+96\,a^2\,b^2\,c^5\,d^2-64\,a\,b^3\,c^6\,d+16\,b^4\,c^7}\right)}^{1/4}\,\left(512\,a^2\,b^6\,d^8+512\,b^8\,c^2\,d^6-1024\,a\,b^7\,c\,d^7+\left(-\sqrt{x}\,\left(4096\,a^7\,b^4\,d^{11}-16384\,a^6\,b^5\,c\,d^{10}+24576\,a^5\,b^6\,c^2\,d^9-12288\,a^4\,b^7\,c^3\,d^8-12288\,a^3\,b^8\,c^4\,d^7+24576\,a^2\,b^9\,c^5\,d^6-16384\,a\,b^{10}\,c^6\,d^5+4096\,b^{11}\,c^7\,d^4\right)+{\left(-\frac{d^3}{16\,a^4\,c^3\,d^4-64\,a^3\,b\,c^4\,d^3+96\,a^2\,b^2\,c^5\,d^2-64\,a\,b^3\,c^6\,d+16\,b^4\,c^7}\right)}^{1/4}\,\left(8192\,a^8\,b^4\,c\,d^{11}-40960\,a^7\,b^5\,c^2\,d^{10}+73728\,a^6\,b^6\,c^3\,d^9-40960\,a^5\,b^7\,c^4\,d^8-40960\,a^4\,b^8\,c^5\,d^7+73728\,a^3\,b^9\,c^6\,d^6-40960\,a^2\,b^{10}\,c^7\,d^5+8192\,a\,b^{11}\,c^8\,d^4\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{d^3}{16\,a^4\,c^3\,d^4-64\,a^3\,b\,c^4\,d^3+96\,a^2\,b^2\,c^5\,d^2-64\,a\,b^3\,c^6\,d+16\,b^4\,c^7}\right)}^{3/4}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}\right)\,{\left(-\frac{d^3}{16\,a^4\,c^3\,d^4-64\,a^3\,b\,c^4\,d^3+96\,a^2\,b^2\,c^5\,d^2-64\,a\,b^3\,c^6\,d+16\,b^4\,c^7}\right)}^{1/4}-\mathrm{atan}\left(\frac{{\left(-\frac{b^3}{16\,a^7\,d^4-64\,a^6\,b\,c\,d^3+96\,a^5\,b^2\,c^2\,d^2-64\,a^4\,b^3\,c^3\,d+16\,a^3\,b^4\,c^4}\right)}^{1/4}\,\left({\left(-\frac{b^3}{16\,a^7\,d^4-64\,a^6\,b\,c\,d^3+96\,a^5\,b^2\,c^2\,d^2-64\,a^4\,b^3\,c^3\,d+16\,a^3\,b^4\,c^4}\right)}^{1/4}\,\left(\left({\left(-\frac{b^3}{16\,a^7\,d^4-64\,a^6\,b\,c\,d^3+96\,a^5\,b^2\,c^2\,d^2-64\,a^4\,b^3\,c^3\,d+16\,a^3\,b^4\,c^4}\right)}^{1/4}\,\left(8192\,a^8\,b^4\,c\,d^{11}-40960\,a^7\,b^5\,c^2\,d^{10}+73728\,a^6\,b^6\,c^3\,d^9-40960\,a^5\,b^7\,c^4\,d^8-40960\,a^4\,b^8\,c^5\,d^7+73728\,a^3\,b^9\,c^6\,d^6-40960\,a^2\,b^{10}\,c^7\,d^5+8192\,a\,b^{11}\,c^8\,d^4\right)+\sqrt{x}\,\left(4096\,a^7\,b^4\,d^{11}-16384\,a^6\,b^5\,c\,d^{10}+24576\,a^5\,b^6\,c^2\,d^9-12288\,a^4\,b^7\,c^3\,d^8-12288\,a^3\,b^8\,c^4\,d^7+24576\,a^2\,b^9\,c^5\,d^6-16384\,a\,b^{10}\,c^6\,d^5+4096\,b^{11}\,c^7\,d^4\right)\right)\,{\left(-\frac{b^3}{16\,a^7\,d^4-64\,a^6\,b\,c\,d^3+96\,a^5\,b^2\,c^2\,d^2-64\,a^4\,b^3\,c^3\,d+16\,a^3\,b^4\,c^4}\right)}^{3/4}-512\,a^2\,b^6\,d^8-512\,b^8\,c^2\,d^6+1024\,a\,b^7\,c\,d^7\right)+512\,b^7\,d^7\,\sqrt{x}\right)\,1{}\mathrm{i}-{\left(-\frac{b^3}{16\,a^7\,d^4-64\,a^6\,b\,c\,d^3+96\,a^5\,b^2\,c^2\,d^2-64\,a^4\,b^3\,c^3\,d+16\,a^3\,b^4\,c^4}\right)}^{1/4}\,\left({\left(-\frac{b^3}{16\,a^7\,d^4-64\,a^6\,b\,c\,d^3+96\,a^5\,b^2\,c^2\,d^2-64\,a^4\,b^3\,c^3\,d+16\,a^3\,b^4\,c^4}\right)}^{1/4}\,\left(\left({\left(-\frac{b^3}{16\,a^7\,d^4-64\,a^6\,b\,c\,d^3+96\,a^5\,b^2\,c^2\,d^2-64\,a^4\,b^3\,c^3\,d+16\,a^3\,b^4\,c^4}\right)}^{1/4}\,\left(8192\,a^8\,b^4\,c\,d^{11}-40960\,a^7\,b^5\,c^2\,d^{10}+73728\,a^6\,b^6\,c^3\,d^9-40960\,a^5\,b^7\,c^4\,d^8-40960\,a^4\,b^8\,c^5\,d^7+73728\,a^3\,b^9\,c^6\,d^6-40960\,a^2\,b^{10}\,c^7\,d^5+8192\,a\,b^{11}\,c^8\,d^4\right)-\sqrt{x}\,\left(4096\,a^7\,b^4\,d^{11}-16384\,a^6\,b^5\,c\,d^{10}+24576\,a^5\,b^6\,c^2\,d^9-12288\,a^4\,b^7\,c^3\,d^8-12288\,a^3\,b^8\,c^4\,d^7+24576\,a^2\,b^9\,c^5\,d^6-16384\,a\,b^{10}\,c^6\,d^5+4096\,b^{11}\,c^7\,d^4\right)\right)\,{\left(-\frac{b^3}{16\,a^7\,d^4-64\,a^6\,b\,c\,d^3+96\,a^5\,b^2\,c^2\,d^2-64\,a^4\,b^3\,c^3\,d+16\,a^3\,b^4\,c^4}\right)}^{3/4}-512\,a^2\,b^6\,d^8-512\,b^8\,c^2\,d^6+1024\,a\,b^7\,c\,d^7\right)-512\,b^7\,d^7\,\sqrt{x}\right)\,1{}\mathrm{i}}{{\left(-\frac{b^3}{16\,a^7\,d^4-64\,a^6\,b\,c\,d^3+96\,a^5\,b^2\,c^2\,d^2-64\,a^4\,b^3\,c^3\,d+16\,a^3\,b^4\,c^4}\right)}^{1/4}\,\left({\left(-\frac{b^3}{16\,a^7\,d^4-64\,a^6\,b\,c\,d^3+96\,a^5\,b^2\,c^2\,d^2-64\,a^4\,b^3\,c^3\,d+16\,a^3\,b^4\,c^4}\right)}^{1/4}\,\left(\left({\left(-\frac{b^3}{16\,a^7\,d^4-64\,a^6\,b\,c\,d^3+96\,a^5\,b^2\,c^2\,d^2-64\,a^4\,b^3\,c^3\,d+16\,a^3\,b^4\,c^4}\right)}^{1/4}\,\left(8192\,a^8\,b^4\,c\,d^{11}-40960\,a^7\,b^5\,c^2\,d^{10}+73728\,a^6\,b^6\,c^3\,d^9-40960\,a^5\,b^7\,c^4\,d^8-40960\,a^4\,b^8\,c^5\,d^7+73728\,a^3\,b^9\,c^6\,d^6-40960\,a^2\,b^{10}\,c^7\,d^5+8192\,a\,b^{11}\,c^8\,d^4\right)+\sqrt{x}\,\left(4096\,a^7\,b^4\,d^{11}-16384\,a^6\,b^5\,c\,d^{10}+24576\,a^5\,b^6\,c^2\,d^9-12288\,a^4\,b^7\,c^3\,d^8-12288\,a^3\,b^8\,c^4\,d^7+24576\,a^2\,b^9\,c^5\,d^6-16384\,a\,b^{10}\,c^6\,d^5+4096\,b^{11}\,c^7\,d^4\right)\right)\,{\left(-\frac{b^3}{16\,a^7\,d^4-64\,a^6\,b\,c\,d^3+96\,a^5\,b^2\,c^2\,d^2-64\,a^4\,b^3\,c^3\,d+16\,a^3\,b^4\,c^4}\right)}^{3/4}-512\,a^2\,b^6\,d^8-512\,b^8\,c^2\,d^6+1024\,a\,b^7\,c\,d^7\right)+512\,b^7\,d^7\,\sqrt{x}\right)+{\left(-\frac{b^3}{16\,a^7\,d^4-64\,a^6\,b\,c\,d^3+96\,a^5\,b^2\,c^2\,d^2-64\,a^4\,b^3\,c^3\,d+16\,a^3\,b^4\,c^4}\right)}^{1/4}\,\left({\left(-\frac{b^3}{16\,a^7\,d^4-64\,a^6\,b\,c\,d^3+96\,a^5\,b^2\,c^2\,d^2-64\,a^4\,b^3\,c^3\,d+16\,a^3\,b^4\,c^4}\right)}^{1/4}\,\left(\left({\left(-\frac{b^3}{16\,a^7\,d^4-64\,a^6\,b\,c\,d^3+96\,a^5\,b^2\,c^2\,d^2-64\,a^4\,b^3\,c^3\,d+16\,a^3\,b^4\,c^4}\right)}^{1/4}\,\left(8192\,a^8\,b^4\,c\,d^{11}-40960\,a^7\,b^5\,c^2\,d^{10}+73728\,a^6\,b^6\,c^3\,d^9-40960\,a^5\,b^7\,c^4\,d^8-40960\,a^4\,b^8\,c^5\,d^7+73728\,a^3\,b^9\,c^6\,d^6-40960\,a^2\,b^{10}\,c^7\,d^5+8192\,a\,b^{11}\,c^8\,d^4\right)-\sqrt{x}\,\left(4096\,a^7\,b^4\,d^{11}-16384\,a^6\,b^5\,c\,d^{10}+24576\,a^5\,b^6\,c^2\,d^9-12288\,a^4\,b^7\,c^3\,d^8-12288\,a^3\,b^8\,c^4\,d^7+24576\,a^2\,b^9\,c^5\,d^6-16384\,a\,b^{10}\,c^6\,d^5+4096\,b^{11}\,c^7\,d^4\right)\right)\,{\left(-\frac{b^3}{16\,a^7\,d^4-64\,a^6\,b\,c\,d^3+96\,a^5\,b^2\,c^2\,d^2-64\,a^4\,b^3\,c^3\,d+16\,a^3\,b^4\,c^4}\right)}^{3/4}-512\,a^2\,b^6\,d^8-512\,b^8\,c^2\,d^6+1024\,a\,b^7\,c\,d^7\right)-512\,b^7\,d^7\,\sqrt{x}\right)}\right)\,{\left(-\frac{b^3}{16\,a^7\,d^4-64\,a^6\,b\,c\,d^3+96\,a^5\,b^2\,c^2\,d^2-64\,a^4\,b^3\,c^3\,d+16\,a^3\,b^4\,c^4}\right)}^{1/4}\,2{}\mathrm{i}-2\,\mathrm{atan}\left(\frac{{\left(-\frac{b^3}{16\,a^7\,d^4-64\,a^6\,b\,c\,d^3+96\,a^5\,b^2\,c^2\,d^2-64\,a^4\,b^3\,c^3\,d+16\,a^3\,b^4\,c^4}\right)}^{1/4}\,\left(-512\,b^7\,d^7\,\sqrt{x}+{\left(-\frac{b^3}{16\,a^7\,d^4-64\,a^6\,b\,c\,d^3+96\,a^5\,b^2\,c^2\,d^2-64\,a^4\,b^3\,c^3\,d+16\,a^3\,b^4\,c^4}\right)}^{1/4}\,\left(512\,a^2\,b^6\,d^8+512\,b^8\,c^2\,d^6-1024\,a\,b^7\,c\,d^7+\left(\sqrt{x}\,\left(4096\,a^7\,b^4\,d^{11}-16384\,a^6\,b^5\,c\,d^{10}+24576\,a^5\,b^6\,c^2\,d^9-12288\,a^4\,b^7\,c^3\,d^8-12288\,a^3\,b^8\,c^4\,d^7+24576\,a^2\,b^9\,c^5\,d^6-16384\,a\,b^{10}\,c^6\,d^5+4096\,b^{11}\,c^7\,d^4\right)+{\left(-\frac{b^3}{16\,a^7\,d^4-64\,a^6\,b\,c\,d^3+96\,a^5\,b^2\,c^2\,d^2-64\,a^4\,b^3\,c^3\,d+16\,a^3\,b^4\,c^4}\right)}^{1/4}\,\left(8192\,a^8\,b^4\,c\,d^{11}-40960\,a^7\,b^5\,c^2\,d^{10}+73728\,a^6\,b^6\,c^3\,d^9-40960\,a^5\,b^7\,c^4\,d^8-40960\,a^4\,b^8\,c^5\,d^7+73728\,a^3\,b^9\,c^6\,d^6-40960\,a^2\,b^{10}\,c^7\,d^5+8192\,a\,b^{11}\,c^8\,d^4\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{b^3}{16\,a^7\,d^4-64\,a^6\,b\,c\,d^3+96\,a^5\,b^2\,c^2\,d^2-64\,a^4\,b^3\,c^3\,d+16\,a^3\,b^4\,c^4}\right)}^{3/4}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)-{\left(-\frac{b^3}{16\,a^7\,d^4-64\,a^6\,b\,c\,d^3+96\,a^5\,b^2\,c^2\,d^2-64\,a^4\,b^3\,c^3\,d+16\,a^3\,b^4\,c^4}\right)}^{1/4}\,\left(512\,b^7\,d^7\,\sqrt{x}+{\left(-\frac{b^3}{16\,a^7\,d^4-64\,a^6\,b\,c\,d^3+96\,a^5\,b^2\,c^2\,d^2-64\,a^4\,b^3\,c^3\,d+16\,a^3\,b^4\,c^4}\right)}^{1/4}\,\left(512\,a^2\,b^6\,d^8+512\,b^8\,c^2\,d^6-1024\,a\,b^7\,c\,d^7+\left(-\sqrt{x}\,\left(4096\,a^7\,b^4\,d^{11}-16384\,a^6\,b^5\,c\,d^{10}+24576\,a^5\,b^6\,c^2\,d^9-12288\,a^4\,b^7\,c^3\,d^8-12288\,a^3\,b^8\,c^4\,d^7+24576\,a^2\,b^9\,c^5\,d^6-16384\,a\,b^{10}\,c^6\,d^5+4096\,b^{11}\,c^7\,d^4\right)+{\left(-\frac{b^3}{16\,a^7\,d^4-64\,a^6\,b\,c\,d^3+96\,a^5\,b^2\,c^2\,d^2-64\,a^4\,b^3\,c^3\,d+16\,a^3\,b^4\,c^4}\right)}^{1/4}\,\left(8192\,a^8\,b^4\,c\,d^{11}-40960\,a^7\,b^5\,c^2\,d^{10}+73728\,a^6\,b^6\,c^3\,d^9-40960\,a^5\,b^7\,c^4\,d^8-40960\,a^4\,b^8\,c^5\,d^7+73728\,a^3\,b^9\,c^6\,d^6-40960\,a^2\,b^{10}\,c^7\,d^5+8192\,a\,b^{11}\,c^8\,d^4\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{b^3}{16\,a^7\,d^4-64\,a^6\,b\,c\,d^3+96\,a^5\,b^2\,c^2\,d^2-64\,a^4\,b^3\,c^3\,d+16\,a^3\,b^4\,c^4}\right)}^{3/4}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)}{{\left(-\frac{b^3}{16\,a^7\,d^4-64\,a^6\,b\,c\,d^3+96\,a^5\,b^2\,c^2\,d^2-64\,a^4\,b^3\,c^3\,d+16\,a^3\,b^4\,c^4}\right)}^{1/4}\,\left(-512\,b^7\,d^7\,\sqrt{x}+{\left(-\frac{b^3}{16\,a^7\,d^4-64\,a^6\,b\,c\,d^3+96\,a^5\,b^2\,c^2\,d^2-64\,a^4\,b^3\,c^3\,d+16\,a^3\,b^4\,c^4}\right)}^{1/4}\,\left(512\,a^2\,b^6\,d^8+512\,b^8\,c^2\,d^6-1024\,a\,b^7\,c\,d^7+\left(\sqrt{x}\,\left(4096\,a^7\,b^4\,d^{11}-16384\,a^6\,b^5\,c\,d^{10}+24576\,a^5\,b^6\,c^2\,d^9-12288\,a^4\,b^7\,c^3\,d^8-12288\,a^3\,b^8\,c^4\,d^7+24576\,a^2\,b^9\,c^5\,d^6-16384\,a\,b^{10}\,c^6\,d^5+4096\,b^{11}\,c^7\,d^4\right)+{\left(-\frac{b^3}{16\,a^7\,d^4-64\,a^6\,b\,c\,d^3+96\,a^5\,b^2\,c^2\,d^2-64\,a^4\,b^3\,c^3\,d+16\,a^3\,b^4\,c^4}\right)}^{1/4}\,\left(8192\,a^8\,b^4\,c\,d^{11}-40960\,a^7\,b^5\,c^2\,d^{10}+73728\,a^6\,b^6\,c^3\,d^9-40960\,a^5\,b^7\,c^4\,d^8-40960\,a^4\,b^8\,c^5\,d^7+73728\,a^3\,b^9\,c^6\,d^6-40960\,a^2\,b^{10}\,c^7\,d^5+8192\,a\,b^{11}\,c^8\,d^4\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{b^3}{16\,a^7\,d^4-64\,a^6\,b\,c\,d^3+96\,a^5\,b^2\,c^2\,d^2-64\,a^4\,b^3\,c^3\,d+16\,a^3\,b^4\,c^4}\right)}^{3/4}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}+{\left(-\frac{b^3}{16\,a^7\,d^4-64\,a^6\,b\,c\,d^3+96\,a^5\,b^2\,c^2\,d^2-64\,a^4\,b^3\,c^3\,d+16\,a^3\,b^4\,c^4}\right)}^{1/4}\,\left(512\,b^7\,d^7\,\sqrt{x}+{\left(-\frac{b^3}{16\,a^7\,d^4-64\,a^6\,b\,c\,d^3+96\,a^5\,b^2\,c^2\,d^2-64\,a^4\,b^3\,c^3\,d+16\,a^3\,b^4\,c^4}\right)}^{1/4}\,\left(512\,a^2\,b^6\,d^8+512\,b^8\,c^2\,d^6-1024\,a\,b^7\,c\,d^7+\left(-\sqrt{x}\,\left(4096\,a^7\,b^4\,d^{11}-16384\,a^6\,b^5\,c\,d^{10}+24576\,a^5\,b^6\,c^2\,d^9-12288\,a^4\,b^7\,c^3\,d^8-12288\,a^3\,b^8\,c^4\,d^7+24576\,a^2\,b^9\,c^5\,d^6-16384\,a\,b^{10}\,c^6\,d^5+4096\,b^{11}\,c^7\,d^4\right)+{\left(-\frac{b^3}{16\,a^7\,d^4-64\,a^6\,b\,c\,d^3+96\,a^5\,b^2\,c^2\,d^2-64\,a^4\,b^3\,c^3\,d+16\,a^3\,b^4\,c^4}\right)}^{1/4}\,\left(8192\,a^8\,b^4\,c\,d^{11}-40960\,a^7\,b^5\,c^2\,d^{10}+73728\,a^6\,b^6\,c^3\,d^9-40960\,a^5\,b^7\,c^4\,d^8-40960\,a^4\,b^8\,c^5\,d^7+73728\,a^3\,b^9\,c^6\,d^6-40960\,a^2\,b^{10}\,c^7\,d^5+8192\,a\,b^{11}\,c^8\,d^4\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{b^3}{16\,a^7\,d^4-64\,a^6\,b\,c\,d^3+96\,a^5\,b^2\,c^2\,d^2-64\,a^4\,b^3\,c^3\,d+16\,a^3\,b^4\,c^4}\right)}^{3/4}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}\right)\,{\left(-\frac{b^3}{16\,a^7\,d^4-64\,a^6\,b\,c\,d^3+96\,a^5\,b^2\,c^2\,d^2-64\,a^4\,b^3\,c^3\,d+16\,a^3\,b^4\,c^4}\right)}^{1/4}","Not used",1,"- atan(((-d^3/(16*b^4*c^7 + 16*a^4*c^3*d^4 - 64*a^3*b*c^4*d^3 + 96*a^2*b^2*c^5*d^2 - 64*a*b^3*c^6*d))^(1/4)*((-d^3/(16*b^4*c^7 + 16*a^4*c^3*d^4 - 64*a^3*b*c^4*d^3 + 96*a^2*b^2*c^5*d^2 - 64*a*b^3*c^6*d))^(1/4)*(((-d^3/(16*b^4*c^7 + 16*a^4*c^3*d^4 - 64*a^3*b*c^4*d^3 + 96*a^2*b^2*c^5*d^2 - 64*a*b^3*c^6*d))^(1/4)*(8192*a*b^11*c^8*d^4 + 8192*a^8*b^4*c*d^11 - 40960*a^2*b^10*c^7*d^5 + 73728*a^3*b^9*c^6*d^6 - 40960*a^4*b^8*c^5*d^7 - 40960*a^5*b^7*c^4*d^8 + 73728*a^6*b^6*c^3*d^9 - 40960*a^7*b^5*c^2*d^10) + x^(1/2)*(4096*a^7*b^4*d^11 + 4096*b^11*c^7*d^4 - 16384*a*b^10*c^6*d^5 - 16384*a^6*b^5*c*d^10 + 24576*a^2*b^9*c^5*d^6 - 12288*a^3*b^8*c^4*d^7 - 12288*a^4*b^7*c^3*d^8 + 24576*a^5*b^6*c^2*d^9))*(-d^3/(16*b^4*c^7 + 16*a^4*c^3*d^4 - 64*a^3*b*c^4*d^3 + 96*a^2*b^2*c^5*d^2 - 64*a*b^3*c^6*d))^(3/4) - 512*a^2*b^6*d^8 - 512*b^8*c^2*d^6 + 1024*a*b^7*c*d^7) + 512*b^7*d^7*x^(1/2))*1i - (-d^3/(16*b^4*c^7 + 16*a^4*c^3*d^4 - 64*a^3*b*c^4*d^3 + 96*a^2*b^2*c^5*d^2 - 64*a*b^3*c^6*d))^(1/4)*((-d^3/(16*b^4*c^7 + 16*a^4*c^3*d^4 - 64*a^3*b*c^4*d^3 + 96*a^2*b^2*c^5*d^2 - 64*a*b^3*c^6*d))^(1/4)*(((-d^3/(16*b^4*c^7 + 16*a^4*c^3*d^4 - 64*a^3*b*c^4*d^3 + 96*a^2*b^2*c^5*d^2 - 64*a*b^3*c^6*d))^(1/4)*(8192*a*b^11*c^8*d^4 + 8192*a^8*b^4*c*d^11 - 40960*a^2*b^10*c^7*d^5 + 73728*a^3*b^9*c^6*d^6 - 40960*a^4*b^8*c^5*d^7 - 40960*a^5*b^7*c^4*d^8 + 73728*a^6*b^6*c^3*d^9 - 40960*a^7*b^5*c^2*d^10) - x^(1/2)*(4096*a^7*b^4*d^11 + 4096*b^11*c^7*d^4 - 16384*a*b^10*c^6*d^5 - 16384*a^6*b^5*c*d^10 + 24576*a^2*b^9*c^5*d^6 - 12288*a^3*b^8*c^4*d^7 - 12288*a^4*b^7*c^3*d^8 + 24576*a^5*b^6*c^2*d^9))*(-d^3/(16*b^4*c^7 + 16*a^4*c^3*d^4 - 64*a^3*b*c^4*d^3 + 96*a^2*b^2*c^5*d^2 - 64*a*b^3*c^6*d))^(3/4) - 512*a^2*b^6*d^8 - 512*b^8*c^2*d^6 + 1024*a*b^7*c*d^7) - 512*b^7*d^7*x^(1/2))*1i)/((-d^3/(16*b^4*c^7 + 16*a^4*c^3*d^4 - 64*a^3*b*c^4*d^3 + 96*a^2*b^2*c^5*d^2 - 64*a*b^3*c^6*d))^(1/4)*((-d^3/(16*b^4*c^7 + 16*a^4*c^3*d^4 - 64*a^3*b*c^4*d^3 + 96*a^2*b^2*c^5*d^2 - 64*a*b^3*c^6*d))^(1/4)*(((-d^3/(16*b^4*c^7 + 16*a^4*c^3*d^4 - 64*a^3*b*c^4*d^3 + 96*a^2*b^2*c^5*d^2 - 64*a*b^3*c^6*d))^(1/4)*(8192*a*b^11*c^8*d^4 + 8192*a^8*b^4*c*d^11 - 40960*a^2*b^10*c^7*d^5 + 73728*a^3*b^9*c^6*d^6 - 40960*a^4*b^8*c^5*d^7 - 40960*a^5*b^7*c^4*d^8 + 73728*a^6*b^6*c^3*d^9 - 40960*a^7*b^5*c^2*d^10) + x^(1/2)*(4096*a^7*b^4*d^11 + 4096*b^11*c^7*d^4 - 16384*a*b^10*c^6*d^5 - 16384*a^6*b^5*c*d^10 + 24576*a^2*b^9*c^5*d^6 - 12288*a^3*b^8*c^4*d^7 - 12288*a^4*b^7*c^3*d^8 + 24576*a^5*b^6*c^2*d^9))*(-d^3/(16*b^4*c^7 + 16*a^4*c^3*d^4 - 64*a^3*b*c^4*d^3 + 96*a^2*b^2*c^5*d^2 - 64*a*b^3*c^6*d))^(3/4) - 512*a^2*b^6*d^8 - 512*b^8*c^2*d^6 + 1024*a*b^7*c*d^7) + 512*b^7*d^7*x^(1/2)) + (-d^3/(16*b^4*c^7 + 16*a^4*c^3*d^4 - 64*a^3*b*c^4*d^3 + 96*a^2*b^2*c^5*d^2 - 64*a*b^3*c^6*d))^(1/4)*((-d^3/(16*b^4*c^7 + 16*a^4*c^3*d^4 - 64*a^3*b*c^4*d^3 + 96*a^2*b^2*c^5*d^2 - 64*a*b^3*c^6*d))^(1/4)*(((-d^3/(16*b^4*c^7 + 16*a^4*c^3*d^4 - 64*a^3*b*c^4*d^3 + 96*a^2*b^2*c^5*d^2 - 64*a*b^3*c^6*d))^(1/4)*(8192*a*b^11*c^8*d^4 + 8192*a^8*b^4*c*d^11 - 40960*a^2*b^10*c^7*d^5 + 73728*a^3*b^9*c^6*d^6 - 40960*a^4*b^8*c^5*d^7 - 40960*a^5*b^7*c^4*d^8 + 73728*a^6*b^6*c^3*d^9 - 40960*a^7*b^5*c^2*d^10) - x^(1/2)*(4096*a^7*b^4*d^11 + 4096*b^11*c^7*d^4 - 16384*a*b^10*c^6*d^5 - 16384*a^6*b^5*c*d^10 + 24576*a^2*b^9*c^5*d^6 - 12288*a^3*b^8*c^4*d^7 - 12288*a^4*b^7*c^3*d^8 + 24576*a^5*b^6*c^2*d^9))*(-d^3/(16*b^4*c^7 + 16*a^4*c^3*d^4 - 64*a^3*b*c^4*d^3 + 96*a^2*b^2*c^5*d^2 - 64*a*b^3*c^6*d))^(3/4) - 512*a^2*b^6*d^8 - 512*b^8*c^2*d^6 + 1024*a*b^7*c*d^7) - 512*b^7*d^7*x^(1/2))))*(-d^3/(16*b^4*c^7 + 16*a^4*c^3*d^4 - 64*a^3*b*c^4*d^3 + 96*a^2*b^2*c^5*d^2 - 64*a*b^3*c^6*d))^(1/4)*2i - 2*atan(((-d^3/(16*b^4*c^7 + 16*a^4*c^3*d^4 - 64*a^3*b*c^4*d^3 + 96*a^2*b^2*c^5*d^2 - 64*a*b^3*c^6*d))^(1/4)*((-d^3/(16*b^4*c^7 + 16*a^4*c^3*d^4 - 64*a^3*b*c^4*d^3 + 96*a^2*b^2*c^5*d^2 - 64*a*b^3*c^6*d))^(1/4)*(((-d^3/(16*b^4*c^7 + 16*a^4*c^3*d^4 - 64*a^3*b*c^4*d^3 + 96*a^2*b^2*c^5*d^2 - 64*a*b^3*c^6*d))^(1/4)*(8192*a*b^11*c^8*d^4 + 8192*a^8*b^4*c*d^11 - 40960*a^2*b^10*c^7*d^5 + 73728*a^3*b^9*c^6*d^6 - 40960*a^4*b^8*c^5*d^7 - 40960*a^5*b^7*c^4*d^8 + 73728*a^6*b^6*c^3*d^9 - 40960*a^7*b^5*c^2*d^10)*1i + x^(1/2)*(4096*a^7*b^4*d^11 + 4096*b^11*c^7*d^4 - 16384*a*b^10*c^6*d^5 - 16384*a^6*b^5*c*d^10 + 24576*a^2*b^9*c^5*d^6 - 12288*a^3*b^8*c^4*d^7 - 12288*a^4*b^7*c^3*d^8 + 24576*a^5*b^6*c^2*d^9))*(-d^3/(16*b^4*c^7 + 16*a^4*c^3*d^4 - 64*a^3*b*c^4*d^3 + 96*a^2*b^2*c^5*d^2 - 64*a*b^3*c^6*d))^(3/4)*1i + 512*a^2*b^6*d^8 + 512*b^8*c^2*d^6 - 1024*a*b^7*c*d^7)*1i - 512*b^7*d^7*x^(1/2)) - (-d^3/(16*b^4*c^7 + 16*a^4*c^3*d^4 - 64*a^3*b*c^4*d^3 + 96*a^2*b^2*c^5*d^2 - 64*a*b^3*c^6*d))^(1/4)*((-d^3/(16*b^4*c^7 + 16*a^4*c^3*d^4 - 64*a^3*b*c^4*d^3 + 96*a^2*b^2*c^5*d^2 - 64*a*b^3*c^6*d))^(1/4)*(((-d^3/(16*b^4*c^7 + 16*a^4*c^3*d^4 - 64*a^3*b*c^4*d^3 + 96*a^2*b^2*c^5*d^2 - 64*a*b^3*c^6*d))^(1/4)*(8192*a*b^11*c^8*d^4 + 8192*a^8*b^4*c*d^11 - 40960*a^2*b^10*c^7*d^5 + 73728*a^3*b^9*c^6*d^6 - 40960*a^4*b^8*c^5*d^7 - 40960*a^5*b^7*c^4*d^8 + 73728*a^6*b^6*c^3*d^9 - 40960*a^7*b^5*c^2*d^10)*1i - x^(1/2)*(4096*a^7*b^4*d^11 + 4096*b^11*c^7*d^4 - 16384*a*b^10*c^6*d^5 - 16384*a^6*b^5*c*d^10 + 24576*a^2*b^9*c^5*d^6 - 12288*a^3*b^8*c^4*d^7 - 12288*a^4*b^7*c^3*d^8 + 24576*a^5*b^6*c^2*d^9))*(-d^3/(16*b^4*c^7 + 16*a^4*c^3*d^4 - 64*a^3*b*c^4*d^3 + 96*a^2*b^2*c^5*d^2 - 64*a*b^3*c^6*d))^(3/4)*1i + 512*a^2*b^6*d^8 + 512*b^8*c^2*d^6 - 1024*a*b^7*c*d^7)*1i + 512*b^7*d^7*x^(1/2)))/((-d^3/(16*b^4*c^7 + 16*a^4*c^3*d^4 - 64*a^3*b*c^4*d^3 + 96*a^2*b^2*c^5*d^2 - 64*a*b^3*c^6*d))^(1/4)*((-d^3/(16*b^4*c^7 + 16*a^4*c^3*d^4 - 64*a^3*b*c^4*d^3 + 96*a^2*b^2*c^5*d^2 - 64*a*b^3*c^6*d))^(1/4)*(((-d^3/(16*b^4*c^7 + 16*a^4*c^3*d^4 - 64*a^3*b*c^4*d^3 + 96*a^2*b^2*c^5*d^2 - 64*a*b^3*c^6*d))^(1/4)*(8192*a*b^11*c^8*d^4 + 8192*a^8*b^4*c*d^11 - 40960*a^2*b^10*c^7*d^5 + 73728*a^3*b^9*c^6*d^6 - 40960*a^4*b^8*c^5*d^7 - 40960*a^5*b^7*c^4*d^8 + 73728*a^6*b^6*c^3*d^9 - 40960*a^7*b^5*c^2*d^10)*1i + x^(1/2)*(4096*a^7*b^4*d^11 + 4096*b^11*c^7*d^4 - 16384*a*b^10*c^6*d^5 - 16384*a^6*b^5*c*d^10 + 24576*a^2*b^9*c^5*d^6 - 12288*a^3*b^8*c^4*d^7 - 12288*a^4*b^7*c^3*d^8 + 24576*a^5*b^6*c^2*d^9))*(-d^3/(16*b^4*c^7 + 16*a^4*c^3*d^4 - 64*a^3*b*c^4*d^3 + 96*a^2*b^2*c^5*d^2 - 64*a*b^3*c^6*d))^(3/4)*1i + 512*a^2*b^6*d^8 + 512*b^8*c^2*d^6 - 1024*a*b^7*c*d^7)*1i - 512*b^7*d^7*x^(1/2))*1i + (-d^3/(16*b^4*c^7 + 16*a^4*c^3*d^4 - 64*a^3*b*c^4*d^3 + 96*a^2*b^2*c^5*d^2 - 64*a*b^3*c^6*d))^(1/4)*((-d^3/(16*b^4*c^7 + 16*a^4*c^3*d^4 - 64*a^3*b*c^4*d^3 + 96*a^2*b^2*c^5*d^2 - 64*a*b^3*c^6*d))^(1/4)*(((-d^3/(16*b^4*c^7 + 16*a^4*c^3*d^4 - 64*a^3*b*c^4*d^3 + 96*a^2*b^2*c^5*d^2 - 64*a*b^3*c^6*d))^(1/4)*(8192*a*b^11*c^8*d^4 + 8192*a^8*b^4*c*d^11 - 40960*a^2*b^10*c^7*d^5 + 73728*a^3*b^9*c^6*d^6 - 40960*a^4*b^8*c^5*d^7 - 40960*a^5*b^7*c^4*d^8 + 73728*a^6*b^6*c^3*d^9 - 40960*a^7*b^5*c^2*d^10)*1i - x^(1/2)*(4096*a^7*b^4*d^11 + 4096*b^11*c^7*d^4 - 16384*a*b^10*c^6*d^5 - 16384*a^6*b^5*c*d^10 + 24576*a^2*b^9*c^5*d^6 - 12288*a^3*b^8*c^4*d^7 - 12288*a^4*b^7*c^3*d^8 + 24576*a^5*b^6*c^2*d^9))*(-d^3/(16*b^4*c^7 + 16*a^4*c^3*d^4 - 64*a^3*b*c^4*d^3 + 96*a^2*b^2*c^5*d^2 - 64*a*b^3*c^6*d))^(3/4)*1i + 512*a^2*b^6*d^8 + 512*b^8*c^2*d^6 - 1024*a*b^7*c*d^7)*1i + 512*b^7*d^7*x^(1/2))*1i))*(-d^3/(16*b^4*c^7 + 16*a^4*c^3*d^4 - 64*a^3*b*c^4*d^3 + 96*a^2*b^2*c^5*d^2 - 64*a*b^3*c^6*d))^(1/4) - atan(((-b^3/(16*a^7*d^4 + 16*a^3*b^4*c^4 - 64*a^4*b^3*c^3*d + 96*a^5*b^2*c^2*d^2 - 64*a^6*b*c*d^3))^(1/4)*((-b^3/(16*a^7*d^4 + 16*a^3*b^4*c^4 - 64*a^4*b^3*c^3*d + 96*a^5*b^2*c^2*d^2 - 64*a^6*b*c*d^3))^(1/4)*(((-b^3/(16*a^7*d^4 + 16*a^3*b^4*c^4 - 64*a^4*b^3*c^3*d + 96*a^5*b^2*c^2*d^2 - 64*a^6*b*c*d^3))^(1/4)*(8192*a*b^11*c^8*d^4 + 8192*a^8*b^4*c*d^11 - 40960*a^2*b^10*c^7*d^5 + 73728*a^3*b^9*c^6*d^6 - 40960*a^4*b^8*c^5*d^7 - 40960*a^5*b^7*c^4*d^8 + 73728*a^6*b^6*c^3*d^9 - 40960*a^7*b^5*c^2*d^10) + x^(1/2)*(4096*a^7*b^4*d^11 + 4096*b^11*c^7*d^4 - 16384*a*b^10*c^6*d^5 - 16384*a^6*b^5*c*d^10 + 24576*a^2*b^9*c^5*d^6 - 12288*a^3*b^8*c^4*d^7 - 12288*a^4*b^7*c^3*d^8 + 24576*a^5*b^6*c^2*d^9))*(-b^3/(16*a^7*d^4 + 16*a^3*b^4*c^4 - 64*a^4*b^3*c^3*d + 96*a^5*b^2*c^2*d^2 - 64*a^6*b*c*d^3))^(3/4) - 512*a^2*b^6*d^8 - 512*b^8*c^2*d^6 + 1024*a*b^7*c*d^7) + 512*b^7*d^7*x^(1/2))*1i - (-b^3/(16*a^7*d^4 + 16*a^3*b^4*c^4 - 64*a^4*b^3*c^3*d + 96*a^5*b^2*c^2*d^2 - 64*a^6*b*c*d^3))^(1/4)*((-b^3/(16*a^7*d^4 + 16*a^3*b^4*c^4 - 64*a^4*b^3*c^3*d + 96*a^5*b^2*c^2*d^2 - 64*a^6*b*c*d^3))^(1/4)*(((-b^3/(16*a^7*d^4 + 16*a^3*b^4*c^4 - 64*a^4*b^3*c^3*d + 96*a^5*b^2*c^2*d^2 - 64*a^6*b*c*d^3))^(1/4)*(8192*a*b^11*c^8*d^4 + 8192*a^8*b^4*c*d^11 - 40960*a^2*b^10*c^7*d^5 + 73728*a^3*b^9*c^6*d^6 - 40960*a^4*b^8*c^5*d^7 - 40960*a^5*b^7*c^4*d^8 + 73728*a^6*b^6*c^3*d^9 - 40960*a^7*b^5*c^2*d^10) - x^(1/2)*(4096*a^7*b^4*d^11 + 4096*b^11*c^7*d^4 - 16384*a*b^10*c^6*d^5 - 16384*a^6*b^5*c*d^10 + 24576*a^2*b^9*c^5*d^6 - 12288*a^3*b^8*c^4*d^7 - 12288*a^4*b^7*c^3*d^8 + 24576*a^5*b^6*c^2*d^9))*(-b^3/(16*a^7*d^4 + 16*a^3*b^4*c^4 - 64*a^4*b^3*c^3*d + 96*a^5*b^2*c^2*d^2 - 64*a^6*b*c*d^3))^(3/4) - 512*a^2*b^6*d^8 - 512*b^8*c^2*d^6 + 1024*a*b^7*c*d^7) - 512*b^7*d^7*x^(1/2))*1i)/((-b^3/(16*a^7*d^4 + 16*a^3*b^4*c^4 - 64*a^4*b^3*c^3*d + 96*a^5*b^2*c^2*d^2 - 64*a^6*b*c*d^3))^(1/4)*((-b^3/(16*a^7*d^4 + 16*a^3*b^4*c^4 - 64*a^4*b^3*c^3*d + 96*a^5*b^2*c^2*d^2 - 64*a^6*b*c*d^3))^(1/4)*(((-b^3/(16*a^7*d^4 + 16*a^3*b^4*c^4 - 64*a^4*b^3*c^3*d + 96*a^5*b^2*c^2*d^2 - 64*a^6*b*c*d^3))^(1/4)*(8192*a*b^11*c^8*d^4 + 8192*a^8*b^4*c*d^11 - 40960*a^2*b^10*c^7*d^5 + 73728*a^3*b^9*c^6*d^6 - 40960*a^4*b^8*c^5*d^7 - 40960*a^5*b^7*c^4*d^8 + 73728*a^6*b^6*c^3*d^9 - 40960*a^7*b^5*c^2*d^10) + x^(1/2)*(4096*a^7*b^4*d^11 + 4096*b^11*c^7*d^4 - 16384*a*b^10*c^6*d^5 - 16384*a^6*b^5*c*d^10 + 24576*a^2*b^9*c^5*d^6 - 12288*a^3*b^8*c^4*d^7 - 12288*a^4*b^7*c^3*d^8 + 24576*a^5*b^6*c^2*d^9))*(-b^3/(16*a^7*d^4 + 16*a^3*b^4*c^4 - 64*a^4*b^3*c^3*d + 96*a^5*b^2*c^2*d^2 - 64*a^6*b*c*d^3))^(3/4) - 512*a^2*b^6*d^8 - 512*b^8*c^2*d^6 + 1024*a*b^7*c*d^7) + 512*b^7*d^7*x^(1/2)) + (-b^3/(16*a^7*d^4 + 16*a^3*b^4*c^4 - 64*a^4*b^3*c^3*d + 96*a^5*b^2*c^2*d^2 - 64*a^6*b*c*d^3))^(1/4)*((-b^3/(16*a^7*d^4 + 16*a^3*b^4*c^4 - 64*a^4*b^3*c^3*d + 96*a^5*b^2*c^2*d^2 - 64*a^6*b*c*d^3))^(1/4)*(((-b^3/(16*a^7*d^4 + 16*a^3*b^4*c^4 - 64*a^4*b^3*c^3*d + 96*a^5*b^2*c^2*d^2 - 64*a^6*b*c*d^3))^(1/4)*(8192*a*b^11*c^8*d^4 + 8192*a^8*b^4*c*d^11 - 40960*a^2*b^10*c^7*d^5 + 73728*a^3*b^9*c^6*d^6 - 40960*a^4*b^8*c^5*d^7 - 40960*a^5*b^7*c^4*d^8 + 73728*a^6*b^6*c^3*d^9 - 40960*a^7*b^5*c^2*d^10) - x^(1/2)*(4096*a^7*b^4*d^11 + 4096*b^11*c^7*d^4 - 16384*a*b^10*c^6*d^5 - 16384*a^6*b^5*c*d^10 + 24576*a^2*b^9*c^5*d^6 - 12288*a^3*b^8*c^4*d^7 - 12288*a^4*b^7*c^3*d^8 + 24576*a^5*b^6*c^2*d^9))*(-b^3/(16*a^7*d^4 + 16*a^3*b^4*c^4 - 64*a^4*b^3*c^3*d + 96*a^5*b^2*c^2*d^2 - 64*a^6*b*c*d^3))^(3/4) - 512*a^2*b^6*d^8 - 512*b^8*c^2*d^6 + 1024*a*b^7*c*d^7) - 512*b^7*d^7*x^(1/2))))*(-b^3/(16*a^7*d^4 + 16*a^3*b^4*c^4 - 64*a^4*b^3*c^3*d + 96*a^5*b^2*c^2*d^2 - 64*a^6*b*c*d^3))^(1/4)*2i - 2*atan(((-b^3/(16*a^7*d^4 + 16*a^3*b^4*c^4 - 64*a^4*b^3*c^3*d + 96*a^5*b^2*c^2*d^2 - 64*a^6*b*c*d^3))^(1/4)*((-b^3/(16*a^7*d^4 + 16*a^3*b^4*c^4 - 64*a^4*b^3*c^3*d + 96*a^5*b^2*c^2*d^2 - 64*a^6*b*c*d^3))^(1/4)*(((-b^3/(16*a^7*d^4 + 16*a^3*b^4*c^4 - 64*a^4*b^3*c^3*d + 96*a^5*b^2*c^2*d^2 - 64*a^6*b*c*d^3))^(1/4)*(8192*a*b^11*c^8*d^4 + 8192*a^8*b^4*c*d^11 - 40960*a^2*b^10*c^7*d^5 + 73728*a^3*b^9*c^6*d^6 - 40960*a^4*b^8*c^5*d^7 - 40960*a^5*b^7*c^4*d^8 + 73728*a^6*b^6*c^3*d^9 - 40960*a^7*b^5*c^2*d^10)*1i + x^(1/2)*(4096*a^7*b^4*d^11 + 4096*b^11*c^7*d^4 - 16384*a*b^10*c^6*d^5 - 16384*a^6*b^5*c*d^10 + 24576*a^2*b^9*c^5*d^6 - 12288*a^3*b^8*c^4*d^7 - 12288*a^4*b^7*c^3*d^8 + 24576*a^5*b^6*c^2*d^9))*(-b^3/(16*a^7*d^4 + 16*a^3*b^4*c^4 - 64*a^4*b^3*c^3*d + 96*a^5*b^2*c^2*d^2 - 64*a^6*b*c*d^3))^(3/4)*1i + 512*a^2*b^6*d^8 + 512*b^8*c^2*d^6 - 1024*a*b^7*c*d^7)*1i - 512*b^7*d^7*x^(1/2)) - (-b^3/(16*a^7*d^4 + 16*a^3*b^4*c^4 - 64*a^4*b^3*c^3*d + 96*a^5*b^2*c^2*d^2 - 64*a^6*b*c*d^3))^(1/4)*((-b^3/(16*a^7*d^4 + 16*a^3*b^4*c^4 - 64*a^4*b^3*c^3*d + 96*a^5*b^2*c^2*d^2 - 64*a^6*b*c*d^3))^(1/4)*(((-b^3/(16*a^7*d^4 + 16*a^3*b^4*c^4 - 64*a^4*b^3*c^3*d + 96*a^5*b^2*c^2*d^2 - 64*a^6*b*c*d^3))^(1/4)*(8192*a*b^11*c^8*d^4 + 8192*a^8*b^4*c*d^11 - 40960*a^2*b^10*c^7*d^5 + 73728*a^3*b^9*c^6*d^6 - 40960*a^4*b^8*c^5*d^7 - 40960*a^5*b^7*c^4*d^8 + 73728*a^6*b^6*c^3*d^9 - 40960*a^7*b^5*c^2*d^10)*1i - x^(1/2)*(4096*a^7*b^4*d^11 + 4096*b^11*c^7*d^4 - 16384*a*b^10*c^6*d^5 - 16384*a^6*b^5*c*d^10 + 24576*a^2*b^9*c^5*d^6 - 12288*a^3*b^8*c^4*d^7 - 12288*a^4*b^7*c^3*d^8 + 24576*a^5*b^6*c^2*d^9))*(-b^3/(16*a^7*d^4 + 16*a^3*b^4*c^4 - 64*a^4*b^3*c^3*d + 96*a^5*b^2*c^2*d^2 - 64*a^6*b*c*d^3))^(3/4)*1i + 512*a^2*b^6*d^8 + 512*b^8*c^2*d^6 - 1024*a*b^7*c*d^7)*1i + 512*b^7*d^7*x^(1/2)))/((-b^3/(16*a^7*d^4 + 16*a^3*b^4*c^4 - 64*a^4*b^3*c^3*d + 96*a^5*b^2*c^2*d^2 - 64*a^6*b*c*d^3))^(1/4)*((-b^3/(16*a^7*d^4 + 16*a^3*b^4*c^4 - 64*a^4*b^3*c^3*d + 96*a^5*b^2*c^2*d^2 - 64*a^6*b*c*d^3))^(1/4)*(((-b^3/(16*a^7*d^4 + 16*a^3*b^4*c^4 - 64*a^4*b^3*c^3*d + 96*a^5*b^2*c^2*d^2 - 64*a^6*b*c*d^3))^(1/4)*(8192*a*b^11*c^8*d^4 + 8192*a^8*b^4*c*d^11 - 40960*a^2*b^10*c^7*d^5 + 73728*a^3*b^9*c^6*d^6 - 40960*a^4*b^8*c^5*d^7 - 40960*a^5*b^7*c^4*d^8 + 73728*a^6*b^6*c^3*d^9 - 40960*a^7*b^5*c^2*d^10)*1i + x^(1/2)*(4096*a^7*b^4*d^11 + 4096*b^11*c^7*d^4 - 16384*a*b^10*c^6*d^5 - 16384*a^6*b^5*c*d^10 + 24576*a^2*b^9*c^5*d^6 - 12288*a^3*b^8*c^4*d^7 - 12288*a^4*b^7*c^3*d^8 + 24576*a^5*b^6*c^2*d^9))*(-b^3/(16*a^7*d^4 + 16*a^3*b^4*c^4 - 64*a^4*b^3*c^3*d + 96*a^5*b^2*c^2*d^2 - 64*a^6*b*c*d^3))^(3/4)*1i + 512*a^2*b^6*d^8 + 512*b^8*c^2*d^6 - 1024*a*b^7*c*d^7)*1i - 512*b^7*d^7*x^(1/2))*1i + (-b^3/(16*a^7*d^4 + 16*a^3*b^4*c^4 - 64*a^4*b^3*c^3*d + 96*a^5*b^2*c^2*d^2 - 64*a^6*b*c*d^3))^(1/4)*((-b^3/(16*a^7*d^4 + 16*a^3*b^4*c^4 - 64*a^4*b^3*c^3*d + 96*a^5*b^2*c^2*d^2 - 64*a^6*b*c*d^3))^(1/4)*(((-b^3/(16*a^7*d^4 + 16*a^3*b^4*c^4 - 64*a^4*b^3*c^3*d + 96*a^5*b^2*c^2*d^2 - 64*a^6*b*c*d^3))^(1/4)*(8192*a*b^11*c^8*d^4 + 8192*a^8*b^4*c*d^11 - 40960*a^2*b^10*c^7*d^5 + 73728*a^3*b^9*c^6*d^6 - 40960*a^4*b^8*c^5*d^7 - 40960*a^5*b^7*c^4*d^8 + 73728*a^6*b^6*c^3*d^9 - 40960*a^7*b^5*c^2*d^10)*1i - x^(1/2)*(4096*a^7*b^4*d^11 + 4096*b^11*c^7*d^4 - 16384*a*b^10*c^6*d^5 - 16384*a^6*b^5*c*d^10 + 24576*a^2*b^9*c^5*d^6 - 12288*a^3*b^8*c^4*d^7 - 12288*a^4*b^7*c^3*d^8 + 24576*a^5*b^6*c^2*d^9))*(-b^3/(16*a^7*d^4 + 16*a^3*b^4*c^4 - 64*a^4*b^3*c^3*d + 96*a^5*b^2*c^2*d^2 - 64*a^6*b*c*d^3))^(3/4)*1i + 512*a^2*b^6*d^8 + 512*b^8*c^2*d^6 - 1024*a*b^7*c*d^7)*1i + 512*b^7*d^7*x^(1/2))*1i))*(-b^3/(16*a^7*d^4 + 16*a^3*b^4*c^4 - 64*a^4*b^3*c^3*d + 96*a^5*b^2*c^2*d^2 - 64*a^6*b*c*d^3))^(1/4)","B"
467,1,6038,476,1.642749,"\text{Not used}","int(1/(x^(3/2)*(a + b*x^2)*(c + d*x^2)),x)","2\,\mathrm{atan}\left(\frac{{\left(-\frac{b^5}{16\,a^9\,d^4-64\,a^8\,b\,c\,d^3+96\,a^7\,b^2\,c^2\,d^2-64\,a^6\,b^3\,c^3\,d+16\,a^5\,b^4\,c^4}\right)}^{1/4}\,\left(\sqrt{x}\,\left(256\,a^{12}\,b^8\,c^{11}\,d^9+256\,a^{11}\,b^9\,c^{12}\,d^8\right)-{\left(-\frac{b^5}{16\,a^9\,d^4-64\,a^8\,b\,c\,d^3+96\,a^7\,b^2\,c^2\,d^2-64\,a^6\,b^3\,c^3\,d+16\,a^5\,b^4\,c^4}\right)}^{3/4}\,\left(6144\,a^{12}\,b^{11}\,c^{18}\,d^5-2048\,a^{11}\,b^{12}\,c^{19}\,d^4-6144\,a^{13}\,b^{10}\,c^{17}\,d^6+2048\,a^{14}\,b^9\,c^{16}\,d^7+2048\,a^{16}\,b^7\,c^{14}\,d^9-6144\,a^{17}\,b^6\,c^{13}\,d^{10}+6144\,a^{18}\,b^5\,c^{12}\,d^{11}-2048\,a^{19}\,b^4\,c^{11}\,d^{12}+\sqrt{x}\,{\left(-\frac{b^5}{16\,a^9\,d^4-64\,a^8\,b\,c\,d^3+96\,a^7\,b^2\,c^2\,d^2-64\,a^6\,b^3\,c^3\,d+16\,a^5\,b^4\,c^4}\right)}^{1/4}\,\left(4096\,a^{20}\,b^4\,c^{12}\,d^{12}-16384\,a^{19}\,b^5\,c^{13}\,d^{11}+24576\,a^{18}\,b^6\,c^{14}\,d^{10}-16384\,a^{17}\,b^7\,c^{15}\,d^9+8192\,a^{16}\,b^8\,c^{16}\,d^8-16384\,a^{15}\,b^9\,c^{17}\,d^7+24576\,a^{14}\,b^{10}\,c^{18}\,d^6-16384\,a^{13}\,b^{11}\,c^{19}\,d^5+4096\,a^{12}\,b^{12}\,c^{20}\,d^4\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)+{\left(-\frac{b^5}{16\,a^9\,d^4-64\,a^8\,b\,c\,d^3+96\,a^7\,b^2\,c^2\,d^2-64\,a^6\,b^3\,c^3\,d+16\,a^5\,b^4\,c^4}\right)}^{1/4}\,\left(\sqrt{x}\,\left(256\,a^{12}\,b^8\,c^{11}\,d^9+256\,a^{11}\,b^9\,c^{12}\,d^8\right)-{\left(-\frac{b^5}{16\,a^9\,d^4-64\,a^8\,b\,c\,d^3+96\,a^7\,b^2\,c^2\,d^2-64\,a^6\,b^3\,c^3\,d+16\,a^5\,b^4\,c^4}\right)}^{3/4}\,\left(2048\,a^{11}\,b^{12}\,c^{19}\,d^4-6144\,a^{12}\,b^{11}\,c^{18}\,d^5+6144\,a^{13}\,b^{10}\,c^{17}\,d^6-2048\,a^{14}\,b^9\,c^{16}\,d^7-2048\,a^{16}\,b^7\,c^{14}\,d^9+6144\,a^{17}\,b^6\,c^{13}\,d^{10}-6144\,a^{18}\,b^5\,c^{12}\,d^{11}+2048\,a^{19}\,b^4\,c^{11}\,d^{12}+\sqrt{x}\,{\left(-\frac{b^5}{16\,a^9\,d^4-64\,a^8\,b\,c\,d^3+96\,a^7\,b^2\,c^2\,d^2-64\,a^6\,b^3\,c^3\,d+16\,a^5\,b^4\,c^4}\right)}^{1/4}\,\left(4096\,a^{20}\,b^4\,c^{12}\,d^{12}-16384\,a^{19}\,b^5\,c^{13}\,d^{11}+24576\,a^{18}\,b^6\,c^{14}\,d^{10}-16384\,a^{17}\,b^7\,c^{15}\,d^9+8192\,a^{16}\,b^8\,c^{16}\,d^8-16384\,a^{15}\,b^9\,c^{17}\,d^7+24576\,a^{14}\,b^{10}\,c^{18}\,d^6-16384\,a^{13}\,b^{11}\,c^{19}\,d^5+4096\,a^{12}\,b^{12}\,c^{20}\,d^4\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)}{{\left(-\frac{b^5}{16\,a^9\,d^4-64\,a^8\,b\,c\,d^3+96\,a^7\,b^2\,c^2\,d^2-64\,a^6\,b^3\,c^3\,d+16\,a^5\,b^4\,c^4}\right)}^{1/4}\,\left(\sqrt{x}\,\left(256\,a^{12}\,b^8\,c^{11}\,d^9+256\,a^{11}\,b^9\,c^{12}\,d^8\right)-{\left(-\frac{b^5}{16\,a^9\,d^4-64\,a^8\,b\,c\,d^3+96\,a^7\,b^2\,c^2\,d^2-64\,a^6\,b^3\,c^3\,d+16\,a^5\,b^4\,c^4}\right)}^{3/4}\,\left(6144\,a^{12}\,b^{11}\,c^{18}\,d^5-2048\,a^{11}\,b^{12}\,c^{19}\,d^4-6144\,a^{13}\,b^{10}\,c^{17}\,d^6+2048\,a^{14}\,b^9\,c^{16}\,d^7+2048\,a^{16}\,b^7\,c^{14}\,d^9-6144\,a^{17}\,b^6\,c^{13}\,d^{10}+6144\,a^{18}\,b^5\,c^{12}\,d^{11}-2048\,a^{19}\,b^4\,c^{11}\,d^{12}+\sqrt{x}\,{\left(-\frac{b^5}{16\,a^9\,d^4-64\,a^8\,b\,c\,d^3+96\,a^7\,b^2\,c^2\,d^2-64\,a^6\,b^3\,c^3\,d+16\,a^5\,b^4\,c^4}\right)}^{1/4}\,\left(4096\,a^{20}\,b^4\,c^{12}\,d^{12}-16384\,a^{19}\,b^5\,c^{13}\,d^{11}+24576\,a^{18}\,b^6\,c^{14}\,d^{10}-16384\,a^{17}\,b^7\,c^{15}\,d^9+8192\,a^{16}\,b^8\,c^{16}\,d^8-16384\,a^{15}\,b^9\,c^{17}\,d^7+24576\,a^{14}\,b^{10}\,c^{18}\,d^6-16384\,a^{13}\,b^{11}\,c^{19}\,d^5+4096\,a^{12}\,b^{12}\,c^{20}\,d^4\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}-{\left(-\frac{b^5}{16\,a^9\,d^4-64\,a^8\,b\,c\,d^3+96\,a^7\,b^2\,c^2\,d^2-64\,a^6\,b^3\,c^3\,d+16\,a^5\,b^4\,c^4}\right)}^{1/4}\,\left(\sqrt{x}\,\left(256\,a^{12}\,b^8\,c^{11}\,d^9+256\,a^{11}\,b^9\,c^{12}\,d^8\right)-{\left(-\frac{b^5}{16\,a^9\,d^4-64\,a^8\,b\,c\,d^3+96\,a^7\,b^2\,c^2\,d^2-64\,a^6\,b^3\,c^3\,d+16\,a^5\,b^4\,c^4}\right)}^{3/4}\,\left(2048\,a^{11}\,b^{12}\,c^{19}\,d^4-6144\,a^{12}\,b^{11}\,c^{18}\,d^5+6144\,a^{13}\,b^{10}\,c^{17}\,d^6-2048\,a^{14}\,b^9\,c^{16}\,d^7-2048\,a^{16}\,b^7\,c^{14}\,d^9+6144\,a^{17}\,b^6\,c^{13}\,d^{10}-6144\,a^{18}\,b^5\,c^{12}\,d^{11}+2048\,a^{19}\,b^4\,c^{11}\,d^{12}+\sqrt{x}\,{\left(-\frac{b^5}{16\,a^9\,d^4-64\,a^8\,b\,c\,d^3+96\,a^7\,b^2\,c^2\,d^2-64\,a^6\,b^3\,c^3\,d+16\,a^5\,b^4\,c^4}\right)}^{1/4}\,\left(4096\,a^{20}\,b^4\,c^{12}\,d^{12}-16384\,a^{19}\,b^5\,c^{13}\,d^{11}+24576\,a^{18}\,b^6\,c^{14}\,d^{10}-16384\,a^{17}\,b^7\,c^{15}\,d^9+8192\,a^{16}\,b^8\,c^{16}\,d^8-16384\,a^{15}\,b^9\,c^{17}\,d^7+24576\,a^{14}\,b^{10}\,c^{18}\,d^6-16384\,a^{13}\,b^{11}\,c^{19}\,d^5+4096\,a^{12}\,b^{12}\,c^{20}\,d^4\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}\right)\,{\left(-\frac{b^5}{16\,a^9\,d^4-64\,a^8\,b\,c\,d^3+96\,a^7\,b^2\,c^2\,d^2-64\,a^6\,b^3\,c^3\,d+16\,a^5\,b^4\,c^4}\right)}^{1/4}+2\,\mathrm{atan}\left(\frac{{\left(-\frac{d^5}{16\,a^4\,c^5\,d^4-64\,a^3\,b\,c^6\,d^3+96\,a^2\,b^2\,c^7\,d^2-64\,a\,b^3\,c^8\,d+16\,b^4\,c^9}\right)}^{1/4}\,\left(\sqrt{x}\,\left(256\,a^{12}\,b^8\,c^{11}\,d^9+256\,a^{11}\,b^9\,c^{12}\,d^8\right)-{\left(-\frac{d^5}{16\,a^4\,c^5\,d^4-64\,a^3\,b\,c^6\,d^3+96\,a^2\,b^2\,c^7\,d^2-64\,a\,b^3\,c^8\,d+16\,b^4\,c^9}\right)}^{3/4}\,\left(6144\,a^{12}\,b^{11}\,c^{18}\,d^5-2048\,a^{11}\,b^{12}\,c^{19}\,d^4-6144\,a^{13}\,b^{10}\,c^{17}\,d^6+2048\,a^{14}\,b^9\,c^{16}\,d^7+2048\,a^{16}\,b^7\,c^{14}\,d^9-6144\,a^{17}\,b^6\,c^{13}\,d^{10}+6144\,a^{18}\,b^5\,c^{12}\,d^{11}-2048\,a^{19}\,b^4\,c^{11}\,d^{12}+\sqrt{x}\,{\left(-\frac{d^5}{16\,a^4\,c^5\,d^4-64\,a^3\,b\,c^6\,d^3+96\,a^2\,b^2\,c^7\,d^2-64\,a\,b^3\,c^8\,d+16\,b^4\,c^9}\right)}^{1/4}\,\left(4096\,a^{20}\,b^4\,c^{12}\,d^{12}-16384\,a^{19}\,b^5\,c^{13}\,d^{11}+24576\,a^{18}\,b^6\,c^{14}\,d^{10}-16384\,a^{17}\,b^7\,c^{15}\,d^9+8192\,a^{16}\,b^8\,c^{16}\,d^8-16384\,a^{15}\,b^9\,c^{17}\,d^7+24576\,a^{14}\,b^{10}\,c^{18}\,d^6-16384\,a^{13}\,b^{11}\,c^{19}\,d^5+4096\,a^{12}\,b^{12}\,c^{20}\,d^4\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)+{\left(-\frac{d^5}{16\,a^4\,c^5\,d^4-64\,a^3\,b\,c^6\,d^3+96\,a^2\,b^2\,c^7\,d^2-64\,a\,b^3\,c^8\,d+16\,b^4\,c^9}\right)}^{1/4}\,\left(\sqrt{x}\,\left(256\,a^{12}\,b^8\,c^{11}\,d^9+256\,a^{11}\,b^9\,c^{12}\,d^8\right)-{\left(-\frac{d^5}{16\,a^4\,c^5\,d^4-64\,a^3\,b\,c^6\,d^3+96\,a^2\,b^2\,c^7\,d^2-64\,a\,b^3\,c^8\,d+16\,b^4\,c^9}\right)}^{3/4}\,\left(2048\,a^{11}\,b^{12}\,c^{19}\,d^4-6144\,a^{12}\,b^{11}\,c^{18}\,d^5+6144\,a^{13}\,b^{10}\,c^{17}\,d^6-2048\,a^{14}\,b^9\,c^{16}\,d^7-2048\,a^{16}\,b^7\,c^{14}\,d^9+6144\,a^{17}\,b^6\,c^{13}\,d^{10}-6144\,a^{18}\,b^5\,c^{12}\,d^{11}+2048\,a^{19}\,b^4\,c^{11}\,d^{12}+\sqrt{x}\,{\left(-\frac{d^5}{16\,a^4\,c^5\,d^4-64\,a^3\,b\,c^6\,d^3+96\,a^2\,b^2\,c^7\,d^2-64\,a\,b^3\,c^8\,d+16\,b^4\,c^9}\right)}^{1/4}\,\left(4096\,a^{20}\,b^4\,c^{12}\,d^{12}-16384\,a^{19}\,b^5\,c^{13}\,d^{11}+24576\,a^{18}\,b^6\,c^{14}\,d^{10}-16384\,a^{17}\,b^7\,c^{15}\,d^9+8192\,a^{16}\,b^8\,c^{16}\,d^8-16384\,a^{15}\,b^9\,c^{17}\,d^7+24576\,a^{14}\,b^{10}\,c^{18}\,d^6-16384\,a^{13}\,b^{11}\,c^{19}\,d^5+4096\,a^{12}\,b^{12}\,c^{20}\,d^4\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)}{{\left(-\frac{d^5}{16\,a^4\,c^5\,d^4-64\,a^3\,b\,c^6\,d^3+96\,a^2\,b^2\,c^7\,d^2-64\,a\,b^3\,c^8\,d+16\,b^4\,c^9}\right)}^{1/4}\,\left(\sqrt{x}\,\left(256\,a^{12}\,b^8\,c^{11}\,d^9+256\,a^{11}\,b^9\,c^{12}\,d^8\right)-{\left(-\frac{d^5}{16\,a^4\,c^5\,d^4-64\,a^3\,b\,c^6\,d^3+96\,a^2\,b^2\,c^7\,d^2-64\,a\,b^3\,c^8\,d+16\,b^4\,c^9}\right)}^{3/4}\,\left(6144\,a^{12}\,b^{11}\,c^{18}\,d^5-2048\,a^{11}\,b^{12}\,c^{19}\,d^4-6144\,a^{13}\,b^{10}\,c^{17}\,d^6+2048\,a^{14}\,b^9\,c^{16}\,d^7+2048\,a^{16}\,b^7\,c^{14}\,d^9-6144\,a^{17}\,b^6\,c^{13}\,d^{10}+6144\,a^{18}\,b^5\,c^{12}\,d^{11}-2048\,a^{19}\,b^4\,c^{11}\,d^{12}+\sqrt{x}\,{\left(-\frac{d^5}{16\,a^4\,c^5\,d^4-64\,a^3\,b\,c^6\,d^3+96\,a^2\,b^2\,c^7\,d^2-64\,a\,b^3\,c^8\,d+16\,b^4\,c^9}\right)}^{1/4}\,\left(4096\,a^{20}\,b^4\,c^{12}\,d^{12}-16384\,a^{19}\,b^5\,c^{13}\,d^{11}+24576\,a^{18}\,b^6\,c^{14}\,d^{10}-16384\,a^{17}\,b^7\,c^{15}\,d^9+8192\,a^{16}\,b^8\,c^{16}\,d^8-16384\,a^{15}\,b^9\,c^{17}\,d^7+24576\,a^{14}\,b^{10}\,c^{18}\,d^6-16384\,a^{13}\,b^{11}\,c^{19}\,d^5+4096\,a^{12}\,b^{12}\,c^{20}\,d^4\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}-{\left(-\frac{d^5}{16\,a^4\,c^5\,d^4-64\,a^3\,b\,c^6\,d^3+96\,a^2\,b^2\,c^7\,d^2-64\,a\,b^3\,c^8\,d+16\,b^4\,c^9}\right)}^{1/4}\,\left(\sqrt{x}\,\left(256\,a^{12}\,b^8\,c^{11}\,d^9+256\,a^{11}\,b^9\,c^{12}\,d^8\right)-{\left(-\frac{d^5}{16\,a^4\,c^5\,d^4-64\,a^3\,b\,c^6\,d^3+96\,a^2\,b^2\,c^7\,d^2-64\,a\,b^3\,c^8\,d+16\,b^4\,c^9}\right)}^{3/4}\,\left(2048\,a^{11}\,b^{12}\,c^{19}\,d^4-6144\,a^{12}\,b^{11}\,c^{18}\,d^5+6144\,a^{13}\,b^{10}\,c^{17}\,d^6-2048\,a^{14}\,b^9\,c^{16}\,d^7-2048\,a^{16}\,b^7\,c^{14}\,d^9+6144\,a^{17}\,b^6\,c^{13}\,d^{10}-6144\,a^{18}\,b^5\,c^{12}\,d^{11}+2048\,a^{19}\,b^4\,c^{11}\,d^{12}+\sqrt{x}\,{\left(-\frac{d^5}{16\,a^4\,c^5\,d^4-64\,a^3\,b\,c^6\,d^3+96\,a^2\,b^2\,c^7\,d^2-64\,a\,b^3\,c^8\,d+16\,b^4\,c^9}\right)}^{1/4}\,\left(4096\,a^{20}\,b^4\,c^{12}\,d^{12}-16384\,a^{19}\,b^5\,c^{13}\,d^{11}+24576\,a^{18}\,b^6\,c^{14}\,d^{10}-16384\,a^{17}\,b^7\,c^{15}\,d^9+8192\,a^{16}\,b^8\,c^{16}\,d^8-16384\,a^{15}\,b^9\,c^{17}\,d^7+24576\,a^{14}\,b^{10}\,c^{18}\,d^6-16384\,a^{13}\,b^{11}\,c^{19}\,d^5+4096\,a^{12}\,b^{12}\,c^{20}\,d^4\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}\right)\,{\left(-\frac{d^5}{16\,a^4\,c^5\,d^4-64\,a^3\,b\,c^6\,d^3+96\,a^2\,b^2\,c^7\,d^2-64\,a\,b^3\,c^8\,d+16\,b^4\,c^9}\right)}^{1/4}-\frac{2}{a\,c\,\sqrt{x}}+\mathrm{atan}\left(\frac{a^6\,b^8\,c^9\,\sqrt{x}\,{\left(-\frac{b^5}{16\,a^9\,d^4-64\,a^8\,b\,c\,d^3+96\,a^7\,b^2\,c^2\,d^2-64\,a^6\,b^3\,c^3\,d+16\,a^5\,b^4\,c^4}\right)}^{5/4}\,32{}\mathrm{i}+a^6\,b^4\,d^5\,\sqrt{x}\,{\left(-\frac{b^5}{16\,a^9\,d^4-64\,a^8\,b\,c\,d^3+96\,a^7\,b^2\,c^2\,d^2-64\,a^6\,b^3\,c^3\,d+16\,a^5\,b^4\,c^4}\right)}^{1/4}\,2{}\mathrm{i}+a^{14}\,c\,d^8\,\sqrt{x}\,{\left(-\frac{b^5}{16\,a^9\,d^4-64\,a^8\,b\,c\,d^3+96\,a^7\,b^2\,c^2\,d^2-64\,a^6\,b^3\,c^3\,d+16\,a^5\,b^4\,c^4}\right)}^{5/4}\,32{}\mathrm{i}+a^8\,b^6\,c^7\,d^2\,\sqrt{x}\,{\left(-\frac{b^5}{16\,a^9\,d^4-64\,a^8\,b\,c\,d^3+96\,a^7\,b^2\,c^2\,d^2-64\,a^6\,b^3\,c^3\,d+16\,a^5\,b^4\,c^4}\right)}^{5/4}\,192{}\mathrm{i}-a^9\,b^5\,c^6\,d^3\,\sqrt{x}\,{\left(-\frac{b^5}{16\,a^9\,d^4-64\,a^8\,b\,c\,d^3+96\,a^7\,b^2\,c^2\,d^2-64\,a^6\,b^3\,c^3\,d+16\,a^5\,b^4\,c^4}\right)}^{5/4}\,128{}\mathrm{i}+a^{10}\,b^4\,c^5\,d^4\,\sqrt{x}\,{\left(-\frac{b^5}{16\,a^9\,d^4-64\,a^8\,b\,c\,d^3+96\,a^7\,b^2\,c^2\,d^2-64\,a^6\,b^3\,c^3\,d+16\,a^5\,b^4\,c^4}\right)}^{5/4}\,64{}\mathrm{i}-a^{11}\,b^3\,c^4\,d^5\,\sqrt{x}\,{\left(-\frac{b^5}{16\,a^9\,d^4-64\,a^8\,b\,c\,d^3+96\,a^7\,b^2\,c^2\,d^2-64\,a^6\,b^3\,c^3\,d+16\,a^5\,b^4\,c^4}\right)}^{5/4}\,128{}\mathrm{i}+a^{12}\,b^2\,c^3\,d^6\,\sqrt{x}\,{\left(-\frac{b^5}{16\,a^9\,d^4-64\,a^8\,b\,c\,d^3+96\,a^7\,b^2\,c^2\,d^2-64\,a^6\,b^3\,c^3\,d+16\,a^5\,b^4\,c^4}\right)}^{5/4}\,192{}\mathrm{i}+a^5\,b^5\,c\,d^4\,\sqrt{x}\,{\left(-\frac{b^5}{16\,a^9\,d^4-64\,a^8\,b\,c\,d^3+96\,a^7\,b^2\,c^2\,d^2-64\,a^6\,b^3\,c^3\,d+16\,a^5\,b^4\,c^4}\right)}^{1/4}\,2{}\mathrm{i}-a^7\,b^7\,c^8\,d\,\sqrt{x}\,{\left(-\frac{b^5}{16\,a^9\,d^4-64\,a^8\,b\,c\,d^3+96\,a^7\,b^2\,c^2\,d^2-64\,a^6\,b^3\,c^3\,d+16\,a^5\,b^4\,c^4}\right)}^{5/4}\,128{}\mathrm{i}-a^{13}\,b\,c^2\,d^7\,\sqrt{x}\,{\left(-\frac{b^5}{16\,a^9\,d^4-64\,a^8\,b\,c\,d^3+96\,a^7\,b^2\,c^2\,d^2-64\,a^6\,b^3\,c^3\,d+16\,a^5\,b^4\,c^4}\right)}^{5/4}\,128{}\mathrm{i}}{a^4\,b^5\,d^4+a^3\,b^6\,c\,d^3+a^2\,b^7\,c^2\,d^2+a\,b^8\,c^3\,d+b^9\,c^4}\right)\,{\left(-\frac{b^5}{16\,a^9\,d^4-64\,a^8\,b\,c\,d^3+96\,a^7\,b^2\,c^2\,d^2-64\,a^6\,b^3\,c^3\,d+16\,a^5\,b^4\,c^4}\right)}^{1/4}\,2{}\mathrm{i}+\mathrm{atan}\left(\frac{a^9\,c^6\,d^8\,\sqrt{x}\,{\left(-\frac{d^5}{16\,a^4\,c^5\,d^4-64\,a^3\,b\,c^6\,d^3+96\,a^2\,b^2\,c^7\,d^2-64\,a\,b^3\,c^8\,d+16\,b^4\,c^9}\right)}^{5/4}\,32{}\mathrm{i}+b^5\,c^6\,d^4\,\sqrt{x}\,{\left(-\frac{d^5}{16\,a^4\,c^5\,d^4-64\,a^3\,b\,c^6\,d^3+96\,a^2\,b^2\,c^7\,d^2-64\,a\,b^3\,c^8\,d+16\,b^4\,c^9}\right)}^{1/4}\,2{}\mathrm{i}+a\,b^8\,c^{14}\,\sqrt{x}\,{\left(-\frac{d^5}{16\,a^4\,c^5\,d^4-64\,a^3\,b\,c^6\,d^3+96\,a^2\,b^2\,c^7\,d^2-64\,a\,b^3\,c^8\,d+16\,b^4\,c^9}\right)}^{5/4}\,32{}\mathrm{i}+a^3\,b^6\,c^{12}\,d^2\,\sqrt{x}\,{\left(-\frac{d^5}{16\,a^4\,c^5\,d^4-64\,a^3\,b\,c^6\,d^3+96\,a^2\,b^2\,c^7\,d^2-64\,a\,b^3\,c^8\,d+16\,b^4\,c^9}\right)}^{5/4}\,192{}\mathrm{i}-a^4\,b^5\,c^{11}\,d^3\,\sqrt{x}\,{\left(-\frac{d^5}{16\,a^4\,c^5\,d^4-64\,a^3\,b\,c^6\,d^3+96\,a^2\,b^2\,c^7\,d^2-64\,a\,b^3\,c^8\,d+16\,b^4\,c^9}\right)}^{5/4}\,128{}\mathrm{i}+a^5\,b^4\,c^{10}\,d^4\,\sqrt{x}\,{\left(-\frac{d^5}{16\,a^4\,c^5\,d^4-64\,a^3\,b\,c^6\,d^3+96\,a^2\,b^2\,c^7\,d^2-64\,a\,b^3\,c^8\,d+16\,b^4\,c^9}\right)}^{5/4}\,64{}\mathrm{i}-a^6\,b^3\,c^9\,d^5\,\sqrt{x}\,{\left(-\frac{d^5}{16\,a^4\,c^5\,d^4-64\,a^3\,b\,c^6\,d^3+96\,a^2\,b^2\,c^7\,d^2-64\,a\,b^3\,c^8\,d+16\,b^4\,c^9}\right)}^{5/4}\,128{}\mathrm{i}+a^7\,b^2\,c^8\,d^6\,\sqrt{x}\,{\left(-\frac{d^5}{16\,a^4\,c^5\,d^4-64\,a^3\,b\,c^6\,d^3+96\,a^2\,b^2\,c^7\,d^2-64\,a\,b^3\,c^8\,d+16\,b^4\,c^9}\right)}^{5/4}\,192{}\mathrm{i}+a\,b^4\,c^5\,d^5\,\sqrt{x}\,{\left(-\frac{d^5}{16\,a^4\,c^5\,d^4-64\,a^3\,b\,c^6\,d^3+96\,a^2\,b^2\,c^7\,d^2-64\,a\,b^3\,c^8\,d+16\,b^4\,c^9}\right)}^{1/4}\,2{}\mathrm{i}-a^2\,b^7\,c^{13}\,d\,\sqrt{x}\,{\left(-\frac{d^5}{16\,a^4\,c^5\,d^4-64\,a^3\,b\,c^6\,d^3+96\,a^2\,b^2\,c^7\,d^2-64\,a\,b^3\,c^8\,d+16\,b^4\,c^9}\right)}^{5/4}\,128{}\mathrm{i}-a^8\,b\,c^7\,d^7\,\sqrt{x}\,{\left(-\frac{d^5}{16\,a^4\,c^5\,d^4-64\,a^3\,b\,c^6\,d^3+96\,a^2\,b^2\,c^7\,d^2-64\,a\,b^3\,c^8\,d+16\,b^4\,c^9}\right)}^{5/4}\,128{}\mathrm{i}}{a^4\,d^9+a^3\,b\,c\,d^8+a^2\,b^2\,c^2\,d^7+a\,b^3\,c^3\,d^6+b^4\,c^4\,d^5}\right)\,{\left(-\frac{d^5}{16\,a^4\,c^5\,d^4-64\,a^3\,b\,c^6\,d^3+96\,a^2\,b^2\,c^7\,d^2-64\,a\,b^3\,c^8\,d+16\,b^4\,c^9}\right)}^{1/4}\,2{}\mathrm{i}","Not used",1,"atan((a^6*b^8*c^9*x^(1/2)*(-b^5/(16*a^9*d^4 + 16*a^5*b^4*c^4 - 64*a^6*b^3*c^3*d + 96*a^7*b^2*c^2*d^2 - 64*a^8*b*c*d^3))^(5/4)*32i + a^6*b^4*d^5*x^(1/2)*(-b^5/(16*a^9*d^4 + 16*a^5*b^4*c^4 - 64*a^6*b^3*c^3*d + 96*a^7*b^2*c^2*d^2 - 64*a^8*b*c*d^3))^(1/4)*2i + a^14*c*d^8*x^(1/2)*(-b^5/(16*a^9*d^4 + 16*a^5*b^4*c^4 - 64*a^6*b^3*c^3*d + 96*a^7*b^2*c^2*d^2 - 64*a^8*b*c*d^3))^(5/4)*32i + a^8*b^6*c^7*d^2*x^(1/2)*(-b^5/(16*a^9*d^4 + 16*a^5*b^4*c^4 - 64*a^6*b^3*c^3*d + 96*a^7*b^2*c^2*d^2 - 64*a^8*b*c*d^3))^(5/4)*192i - a^9*b^5*c^6*d^3*x^(1/2)*(-b^5/(16*a^9*d^4 + 16*a^5*b^4*c^4 - 64*a^6*b^3*c^3*d + 96*a^7*b^2*c^2*d^2 - 64*a^8*b*c*d^3))^(5/4)*128i + a^10*b^4*c^5*d^4*x^(1/2)*(-b^5/(16*a^9*d^4 + 16*a^5*b^4*c^4 - 64*a^6*b^3*c^3*d + 96*a^7*b^2*c^2*d^2 - 64*a^8*b*c*d^3))^(5/4)*64i - a^11*b^3*c^4*d^5*x^(1/2)*(-b^5/(16*a^9*d^4 + 16*a^5*b^4*c^4 - 64*a^6*b^3*c^3*d + 96*a^7*b^2*c^2*d^2 - 64*a^8*b*c*d^3))^(5/4)*128i + a^12*b^2*c^3*d^6*x^(1/2)*(-b^5/(16*a^9*d^4 + 16*a^5*b^4*c^4 - 64*a^6*b^3*c^3*d + 96*a^7*b^2*c^2*d^2 - 64*a^8*b*c*d^3))^(5/4)*192i + a^5*b^5*c*d^4*x^(1/2)*(-b^5/(16*a^9*d^4 + 16*a^5*b^4*c^4 - 64*a^6*b^3*c^3*d + 96*a^7*b^2*c^2*d^2 - 64*a^8*b*c*d^3))^(1/4)*2i - a^7*b^7*c^8*d*x^(1/2)*(-b^5/(16*a^9*d^4 + 16*a^5*b^4*c^4 - 64*a^6*b^3*c^3*d + 96*a^7*b^2*c^2*d^2 - 64*a^8*b*c*d^3))^(5/4)*128i - a^13*b*c^2*d^7*x^(1/2)*(-b^5/(16*a^9*d^4 + 16*a^5*b^4*c^4 - 64*a^6*b^3*c^3*d + 96*a^7*b^2*c^2*d^2 - 64*a^8*b*c*d^3))^(5/4)*128i)/(b^9*c^4 + a^4*b^5*d^4 + a^3*b^6*c*d^3 + a^2*b^7*c^2*d^2 + a*b^8*c^3*d))*(-b^5/(16*a^9*d^4 + 16*a^5*b^4*c^4 - 64*a^6*b^3*c^3*d + 96*a^7*b^2*c^2*d^2 - 64*a^8*b*c*d^3))^(1/4)*2i + atan((a^9*c^6*d^8*x^(1/2)*(-d^5/(16*b^4*c^9 + 16*a^4*c^5*d^4 - 64*a^3*b*c^6*d^3 + 96*a^2*b^2*c^7*d^2 - 64*a*b^3*c^8*d))^(5/4)*32i + b^5*c^6*d^4*x^(1/2)*(-d^5/(16*b^4*c^9 + 16*a^4*c^5*d^4 - 64*a^3*b*c^6*d^3 + 96*a^2*b^2*c^7*d^2 - 64*a*b^3*c^8*d))^(1/4)*2i + a*b^8*c^14*x^(1/2)*(-d^5/(16*b^4*c^9 + 16*a^4*c^5*d^4 - 64*a^3*b*c^6*d^3 + 96*a^2*b^2*c^7*d^2 - 64*a*b^3*c^8*d))^(5/4)*32i + a^3*b^6*c^12*d^2*x^(1/2)*(-d^5/(16*b^4*c^9 + 16*a^4*c^5*d^4 - 64*a^3*b*c^6*d^3 + 96*a^2*b^2*c^7*d^2 - 64*a*b^3*c^8*d))^(5/4)*192i - a^4*b^5*c^11*d^3*x^(1/2)*(-d^5/(16*b^4*c^9 + 16*a^4*c^5*d^4 - 64*a^3*b*c^6*d^3 + 96*a^2*b^2*c^7*d^2 - 64*a*b^3*c^8*d))^(5/4)*128i + a^5*b^4*c^10*d^4*x^(1/2)*(-d^5/(16*b^4*c^9 + 16*a^4*c^5*d^4 - 64*a^3*b*c^6*d^3 + 96*a^2*b^2*c^7*d^2 - 64*a*b^3*c^8*d))^(5/4)*64i - a^6*b^3*c^9*d^5*x^(1/2)*(-d^5/(16*b^4*c^9 + 16*a^4*c^5*d^4 - 64*a^3*b*c^6*d^3 + 96*a^2*b^2*c^7*d^2 - 64*a*b^3*c^8*d))^(5/4)*128i + a^7*b^2*c^8*d^6*x^(1/2)*(-d^5/(16*b^4*c^9 + 16*a^4*c^5*d^4 - 64*a^3*b*c^6*d^3 + 96*a^2*b^2*c^7*d^2 - 64*a*b^3*c^8*d))^(5/4)*192i + a*b^4*c^5*d^5*x^(1/2)*(-d^5/(16*b^4*c^9 + 16*a^4*c^5*d^4 - 64*a^3*b*c^6*d^3 + 96*a^2*b^2*c^7*d^2 - 64*a*b^3*c^8*d))^(1/4)*2i - a^2*b^7*c^13*d*x^(1/2)*(-d^5/(16*b^4*c^9 + 16*a^4*c^5*d^4 - 64*a^3*b*c^6*d^3 + 96*a^2*b^2*c^7*d^2 - 64*a*b^3*c^8*d))^(5/4)*128i - a^8*b*c^7*d^7*x^(1/2)*(-d^5/(16*b^4*c^9 + 16*a^4*c^5*d^4 - 64*a^3*b*c^6*d^3 + 96*a^2*b^2*c^7*d^2 - 64*a*b^3*c^8*d))^(5/4)*128i)/(a^4*d^9 + b^4*c^4*d^5 + a*b^3*c^3*d^6 + a^2*b^2*c^2*d^7 + a^3*b*c*d^8))*(-d^5/(16*b^4*c^9 + 16*a^4*c^5*d^4 - 64*a^3*b*c^6*d^3 + 96*a^2*b^2*c^7*d^2 - 64*a*b^3*c^8*d))^(1/4)*2i + 2*atan(((-b^5/(16*a^9*d^4 + 16*a^5*b^4*c^4 - 64*a^6*b^3*c^3*d + 96*a^7*b^2*c^2*d^2 - 64*a^8*b*c*d^3))^(1/4)*(x^(1/2)*(256*a^11*b^9*c^12*d^8 + 256*a^12*b^8*c^11*d^9) - (-b^5/(16*a^9*d^4 + 16*a^5*b^4*c^4 - 64*a^6*b^3*c^3*d + 96*a^7*b^2*c^2*d^2 - 64*a^8*b*c*d^3))^(3/4)*(x^(1/2)*(-b^5/(16*a^9*d^4 + 16*a^5*b^4*c^4 - 64*a^6*b^3*c^3*d + 96*a^7*b^2*c^2*d^2 - 64*a^8*b*c*d^3))^(1/4)*(4096*a^12*b^12*c^20*d^4 - 16384*a^13*b^11*c^19*d^5 + 24576*a^14*b^10*c^18*d^6 - 16384*a^15*b^9*c^17*d^7 + 8192*a^16*b^8*c^16*d^8 - 16384*a^17*b^7*c^15*d^9 + 24576*a^18*b^6*c^14*d^10 - 16384*a^19*b^5*c^13*d^11 + 4096*a^20*b^4*c^12*d^12)*1i - 2048*a^11*b^12*c^19*d^4 + 6144*a^12*b^11*c^18*d^5 - 6144*a^13*b^10*c^17*d^6 + 2048*a^14*b^9*c^16*d^7 + 2048*a^16*b^7*c^14*d^9 - 6144*a^17*b^6*c^13*d^10 + 6144*a^18*b^5*c^12*d^11 - 2048*a^19*b^4*c^11*d^12)*1i) + (-b^5/(16*a^9*d^4 + 16*a^5*b^4*c^4 - 64*a^6*b^3*c^3*d + 96*a^7*b^2*c^2*d^2 - 64*a^8*b*c*d^3))^(1/4)*(x^(1/2)*(256*a^11*b^9*c^12*d^8 + 256*a^12*b^8*c^11*d^9) - (-b^5/(16*a^9*d^4 + 16*a^5*b^4*c^4 - 64*a^6*b^3*c^3*d + 96*a^7*b^2*c^2*d^2 - 64*a^8*b*c*d^3))^(3/4)*(x^(1/2)*(-b^5/(16*a^9*d^4 + 16*a^5*b^4*c^4 - 64*a^6*b^3*c^3*d + 96*a^7*b^2*c^2*d^2 - 64*a^8*b*c*d^3))^(1/4)*(4096*a^12*b^12*c^20*d^4 - 16384*a^13*b^11*c^19*d^5 + 24576*a^14*b^10*c^18*d^6 - 16384*a^15*b^9*c^17*d^7 + 8192*a^16*b^8*c^16*d^8 - 16384*a^17*b^7*c^15*d^9 + 24576*a^18*b^6*c^14*d^10 - 16384*a^19*b^5*c^13*d^11 + 4096*a^20*b^4*c^12*d^12)*1i + 2048*a^11*b^12*c^19*d^4 - 6144*a^12*b^11*c^18*d^5 + 6144*a^13*b^10*c^17*d^6 - 2048*a^14*b^9*c^16*d^7 - 2048*a^16*b^7*c^14*d^9 + 6144*a^17*b^6*c^13*d^10 - 6144*a^18*b^5*c^12*d^11 + 2048*a^19*b^4*c^11*d^12)*1i))/((-b^5/(16*a^9*d^4 + 16*a^5*b^4*c^4 - 64*a^6*b^3*c^3*d + 96*a^7*b^2*c^2*d^2 - 64*a^8*b*c*d^3))^(1/4)*(x^(1/2)*(256*a^11*b^9*c^12*d^8 + 256*a^12*b^8*c^11*d^9) - (-b^5/(16*a^9*d^4 + 16*a^5*b^4*c^4 - 64*a^6*b^3*c^3*d + 96*a^7*b^2*c^2*d^2 - 64*a^8*b*c*d^3))^(3/4)*(x^(1/2)*(-b^5/(16*a^9*d^4 + 16*a^5*b^4*c^4 - 64*a^6*b^3*c^3*d + 96*a^7*b^2*c^2*d^2 - 64*a^8*b*c*d^3))^(1/4)*(4096*a^12*b^12*c^20*d^4 - 16384*a^13*b^11*c^19*d^5 + 24576*a^14*b^10*c^18*d^6 - 16384*a^15*b^9*c^17*d^7 + 8192*a^16*b^8*c^16*d^8 - 16384*a^17*b^7*c^15*d^9 + 24576*a^18*b^6*c^14*d^10 - 16384*a^19*b^5*c^13*d^11 + 4096*a^20*b^4*c^12*d^12)*1i - 2048*a^11*b^12*c^19*d^4 + 6144*a^12*b^11*c^18*d^5 - 6144*a^13*b^10*c^17*d^6 + 2048*a^14*b^9*c^16*d^7 + 2048*a^16*b^7*c^14*d^9 - 6144*a^17*b^6*c^13*d^10 + 6144*a^18*b^5*c^12*d^11 - 2048*a^19*b^4*c^11*d^12)*1i)*1i - (-b^5/(16*a^9*d^4 + 16*a^5*b^4*c^4 - 64*a^6*b^3*c^3*d + 96*a^7*b^2*c^2*d^2 - 64*a^8*b*c*d^3))^(1/4)*(x^(1/2)*(256*a^11*b^9*c^12*d^8 + 256*a^12*b^8*c^11*d^9) - (-b^5/(16*a^9*d^4 + 16*a^5*b^4*c^4 - 64*a^6*b^3*c^3*d + 96*a^7*b^2*c^2*d^2 - 64*a^8*b*c*d^3))^(3/4)*(x^(1/2)*(-b^5/(16*a^9*d^4 + 16*a^5*b^4*c^4 - 64*a^6*b^3*c^3*d + 96*a^7*b^2*c^2*d^2 - 64*a^8*b*c*d^3))^(1/4)*(4096*a^12*b^12*c^20*d^4 - 16384*a^13*b^11*c^19*d^5 + 24576*a^14*b^10*c^18*d^6 - 16384*a^15*b^9*c^17*d^7 + 8192*a^16*b^8*c^16*d^8 - 16384*a^17*b^7*c^15*d^9 + 24576*a^18*b^6*c^14*d^10 - 16384*a^19*b^5*c^13*d^11 + 4096*a^20*b^4*c^12*d^12)*1i + 2048*a^11*b^12*c^19*d^4 - 6144*a^12*b^11*c^18*d^5 + 6144*a^13*b^10*c^17*d^6 - 2048*a^14*b^9*c^16*d^7 - 2048*a^16*b^7*c^14*d^9 + 6144*a^17*b^6*c^13*d^10 - 6144*a^18*b^5*c^12*d^11 + 2048*a^19*b^4*c^11*d^12)*1i)*1i))*(-b^5/(16*a^9*d^4 + 16*a^5*b^4*c^4 - 64*a^6*b^3*c^3*d + 96*a^7*b^2*c^2*d^2 - 64*a^8*b*c*d^3))^(1/4) + 2*atan(((-d^5/(16*b^4*c^9 + 16*a^4*c^5*d^4 - 64*a^3*b*c^6*d^3 + 96*a^2*b^2*c^7*d^2 - 64*a*b^3*c^8*d))^(1/4)*(x^(1/2)*(256*a^11*b^9*c^12*d^8 + 256*a^12*b^8*c^11*d^9) - (-d^5/(16*b^4*c^9 + 16*a^4*c^5*d^4 - 64*a^3*b*c^6*d^3 + 96*a^2*b^2*c^7*d^2 - 64*a*b^3*c^8*d))^(3/4)*(x^(1/2)*(-d^5/(16*b^4*c^9 + 16*a^4*c^5*d^4 - 64*a^3*b*c^6*d^3 + 96*a^2*b^2*c^7*d^2 - 64*a*b^3*c^8*d))^(1/4)*(4096*a^12*b^12*c^20*d^4 - 16384*a^13*b^11*c^19*d^5 + 24576*a^14*b^10*c^18*d^6 - 16384*a^15*b^9*c^17*d^7 + 8192*a^16*b^8*c^16*d^8 - 16384*a^17*b^7*c^15*d^9 + 24576*a^18*b^6*c^14*d^10 - 16384*a^19*b^5*c^13*d^11 + 4096*a^20*b^4*c^12*d^12)*1i - 2048*a^11*b^12*c^19*d^4 + 6144*a^12*b^11*c^18*d^5 - 6144*a^13*b^10*c^17*d^6 + 2048*a^14*b^9*c^16*d^7 + 2048*a^16*b^7*c^14*d^9 - 6144*a^17*b^6*c^13*d^10 + 6144*a^18*b^5*c^12*d^11 - 2048*a^19*b^4*c^11*d^12)*1i) + (-d^5/(16*b^4*c^9 + 16*a^4*c^5*d^4 - 64*a^3*b*c^6*d^3 + 96*a^2*b^2*c^7*d^2 - 64*a*b^3*c^8*d))^(1/4)*(x^(1/2)*(256*a^11*b^9*c^12*d^8 + 256*a^12*b^8*c^11*d^9) - (-d^5/(16*b^4*c^9 + 16*a^4*c^5*d^4 - 64*a^3*b*c^6*d^3 + 96*a^2*b^2*c^7*d^2 - 64*a*b^3*c^8*d))^(3/4)*(x^(1/2)*(-d^5/(16*b^4*c^9 + 16*a^4*c^5*d^4 - 64*a^3*b*c^6*d^3 + 96*a^2*b^2*c^7*d^2 - 64*a*b^3*c^8*d))^(1/4)*(4096*a^12*b^12*c^20*d^4 - 16384*a^13*b^11*c^19*d^5 + 24576*a^14*b^10*c^18*d^6 - 16384*a^15*b^9*c^17*d^7 + 8192*a^16*b^8*c^16*d^8 - 16384*a^17*b^7*c^15*d^9 + 24576*a^18*b^6*c^14*d^10 - 16384*a^19*b^5*c^13*d^11 + 4096*a^20*b^4*c^12*d^12)*1i + 2048*a^11*b^12*c^19*d^4 - 6144*a^12*b^11*c^18*d^5 + 6144*a^13*b^10*c^17*d^6 - 2048*a^14*b^9*c^16*d^7 - 2048*a^16*b^7*c^14*d^9 + 6144*a^17*b^6*c^13*d^10 - 6144*a^18*b^5*c^12*d^11 + 2048*a^19*b^4*c^11*d^12)*1i))/((-d^5/(16*b^4*c^9 + 16*a^4*c^5*d^4 - 64*a^3*b*c^6*d^3 + 96*a^2*b^2*c^7*d^2 - 64*a*b^3*c^8*d))^(1/4)*(x^(1/2)*(256*a^11*b^9*c^12*d^8 + 256*a^12*b^8*c^11*d^9) - (-d^5/(16*b^4*c^9 + 16*a^4*c^5*d^4 - 64*a^3*b*c^6*d^3 + 96*a^2*b^2*c^7*d^2 - 64*a*b^3*c^8*d))^(3/4)*(x^(1/2)*(-d^5/(16*b^4*c^9 + 16*a^4*c^5*d^4 - 64*a^3*b*c^6*d^3 + 96*a^2*b^2*c^7*d^2 - 64*a*b^3*c^8*d))^(1/4)*(4096*a^12*b^12*c^20*d^4 - 16384*a^13*b^11*c^19*d^5 + 24576*a^14*b^10*c^18*d^6 - 16384*a^15*b^9*c^17*d^7 + 8192*a^16*b^8*c^16*d^8 - 16384*a^17*b^7*c^15*d^9 + 24576*a^18*b^6*c^14*d^10 - 16384*a^19*b^5*c^13*d^11 + 4096*a^20*b^4*c^12*d^12)*1i - 2048*a^11*b^12*c^19*d^4 + 6144*a^12*b^11*c^18*d^5 - 6144*a^13*b^10*c^17*d^6 + 2048*a^14*b^9*c^16*d^7 + 2048*a^16*b^7*c^14*d^9 - 6144*a^17*b^6*c^13*d^10 + 6144*a^18*b^5*c^12*d^11 - 2048*a^19*b^4*c^11*d^12)*1i)*1i - (-d^5/(16*b^4*c^9 + 16*a^4*c^5*d^4 - 64*a^3*b*c^6*d^3 + 96*a^2*b^2*c^7*d^2 - 64*a*b^3*c^8*d))^(1/4)*(x^(1/2)*(256*a^11*b^9*c^12*d^8 + 256*a^12*b^8*c^11*d^9) - (-d^5/(16*b^4*c^9 + 16*a^4*c^5*d^4 - 64*a^3*b*c^6*d^3 + 96*a^2*b^2*c^7*d^2 - 64*a*b^3*c^8*d))^(3/4)*(x^(1/2)*(-d^5/(16*b^4*c^9 + 16*a^4*c^5*d^4 - 64*a^3*b*c^6*d^3 + 96*a^2*b^2*c^7*d^2 - 64*a*b^3*c^8*d))^(1/4)*(4096*a^12*b^12*c^20*d^4 - 16384*a^13*b^11*c^19*d^5 + 24576*a^14*b^10*c^18*d^6 - 16384*a^15*b^9*c^17*d^7 + 8192*a^16*b^8*c^16*d^8 - 16384*a^17*b^7*c^15*d^9 + 24576*a^18*b^6*c^14*d^10 - 16384*a^19*b^5*c^13*d^11 + 4096*a^20*b^4*c^12*d^12)*1i + 2048*a^11*b^12*c^19*d^4 - 6144*a^12*b^11*c^18*d^5 + 6144*a^13*b^10*c^17*d^6 - 2048*a^14*b^9*c^16*d^7 - 2048*a^16*b^7*c^14*d^9 + 6144*a^17*b^6*c^13*d^10 - 6144*a^18*b^5*c^12*d^11 + 2048*a^19*b^4*c^11*d^12)*1i)*1i))*(-d^5/(16*b^4*c^9 + 16*a^4*c^5*d^4 - 64*a^3*b*c^6*d^3 + 96*a^2*b^2*c^7*d^2 - 64*a*b^3*c^8*d))^(1/4) - 2/(a*c*x^(1/2))","B"
468,1,7540,478,2.395033,"\text{Not used}","int(1/(x^(5/2)*(a + b*x^2)*(c + d*x^2)),x)","2\,\mathrm{atan}\left(\frac{\left(\sqrt{x}\,\left(256\,a^{11}\,b^9\,c^9\,d^{11}+256\,a^9\,b^{11}\,c^{11}\,d^9\right)-{\left(-\frac{d^7}{16\,a^4\,c^7\,d^4-64\,a^3\,b\,c^8\,d^3+96\,a^2\,b^2\,c^9\,d^2-64\,a\,b^3\,c^{10}\,d+16\,b^4\,c^{11}}\right)}^{1/4}\,\left(512\,a^9\,b^{12}\,c^{14}\,d^7-512\,a^{10}\,b^{11}\,c^{13}\,d^8-512\,a^{13}\,b^8\,c^{10}\,d^{11}+512\,a^{14}\,b^7\,c^9\,d^{12}+\left(\sqrt{x}\,\left(4096\,a^{20}\,b^4\,c^{11}\,d^{13}-16384\,a^{19}\,b^5\,c^{12}\,d^{12}+24576\,a^{18}\,b^6\,c^{13}\,d^{11}-16384\,a^{17}\,b^7\,c^{14}\,d^{10}+4096\,a^{16}\,b^8\,c^{15}\,d^9+4096\,a^{15}\,b^9\,c^{16}\,d^8-16384\,a^{14}\,b^{10}\,c^{17}\,d^7+24576\,a^{13}\,b^{11}\,c^{18}\,d^6-16384\,a^{12}\,b^{12}\,c^{19}\,d^5+4096\,a^{11}\,b^{13}\,c^{20}\,d^4\right)+{\left(-\frac{d^7}{16\,a^4\,c^7\,d^4-64\,a^3\,b\,c^8\,d^3+96\,a^2\,b^2\,c^9\,d^2-64\,a\,b^3\,c^{10}\,d+16\,b^4\,c^{11}}\right)}^{1/4}\,\left(8192\,a^{21}\,b^4\,c^{13}\,d^{12}-40960\,a^{20}\,b^5\,c^{14}\,d^{11}+81920\,a^{19}\,b^6\,c^{15}\,d^{10}-90112\,a^{18}\,b^7\,c^{16}\,d^9+81920\,a^{17}\,b^8\,c^{17}\,d^8-90112\,a^{16}\,b^9\,c^{18}\,d^7+81920\,a^{15}\,b^{10}\,c^{19}\,d^6-40960\,a^{14}\,b^{11}\,c^{20}\,d^5+8192\,a^{13}\,b^{12}\,c^{21}\,d^4\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{d^7}{16\,a^4\,c^7\,d^4-64\,a^3\,b\,c^8\,d^3+96\,a^2\,b^2\,c^9\,d^2-64\,a\,b^3\,c^{10}\,d+16\,b^4\,c^{11}}\right)}^{3/4}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{d^7}{16\,a^4\,c^7\,d^4-64\,a^3\,b\,c^8\,d^3+96\,a^2\,b^2\,c^9\,d^2-64\,a\,b^3\,c^{10}\,d+16\,b^4\,c^{11}}\right)}^{1/4}+\left(\sqrt{x}\,\left(256\,a^{11}\,b^9\,c^9\,d^{11}+256\,a^9\,b^{11}\,c^{11}\,d^9\right)+{\left(-\frac{d^7}{16\,a^4\,c^7\,d^4-64\,a^3\,b\,c^8\,d^3+96\,a^2\,b^2\,c^9\,d^2-64\,a\,b^3\,c^{10}\,d+16\,b^4\,c^{11}}\right)}^{1/4}\,\left(512\,a^9\,b^{12}\,c^{14}\,d^7-512\,a^{10}\,b^{11}\,c^{13}\,d^8-512\,a^{13}\,b^8\,c^{10}\,d^{11}+512\,a^{14}\,b^7\,c^9\,d^{12}+\left(-\sqrt{x}\,\left(4096\,a^{20}\,b^4\,c^{11}\,d^{13}-16384\,a^{19}\,b^5\,c^{12}\,d^{12}+24576\,a^{18}\,b^6\,c^{13}\,d^{11}-16384\,a^{17}\,b^7\,c^{14}\,d^{10}+4096\,a^{16}\,b^8\,c^{15}\,d^9+4096\,a^{15}\,b^9\,c^{16}\,d^8-16384\,a^{14}\,b^{10}\,c^{17}\,d^7+24576\,a^{13}\,b^{11}\,c^{18}\,d^6-16384\,a^{12}\,b^{12}\,c^{19}\,d^5+4096\,a^{11}\,b^{13}\,c^{20}\,d^4\right)+{\left(-\frac{d^7}{16\,a^4\,c^7\,d^4-64\,a^3\,b\,c^8\,d^3+96\,a^2\,b^2\,c^9\,d^2-64\,a\,b^3\,c^{10}\,d+16\,b^4\,c^{11}}\right)}^{1/4}\,\left(8192\,a^{21}\,b^4\,c^{13}\,d^{12}-40960\,a^{20}\,b^5\,c^{14}\,d^{11}+81920\,a^{19}\,b^6\,c^{15}\,d^{10}-90112\,a^{18}\,b^7\,c^{16}\,d^9+81920\,a^{17}\,b^8\,c^{17}\,d^8-90112\,a^{16}\,b^9\,c^{18}\,d^7+81920\,a^{15}\,b^{10}\,c^{19}\,d^6-40960\,a^{14}\,b^{11}\,c^{20}\,d^5+8192\,a^{13}\,b^{12}\,c^{21}\,d^4\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{d^7}{16\,a^4\,c^7\,d^4-64\,a^3\,b\,c^8\,d^3+96\,a^2\,b^2\,c^9\,d^2-64\,a\,b^3\,c^{10}\,d+16\,b^4\,c^{11}}\right)}^{3/4}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{d^7}{16\,a^4\,c^7\,d^4-64\,a^3\,b\,c^8\,d^3+96\,a^2\,b^2\,c^9\,d^2-64\,a\,b^3\,c^{10}\,d+16\,b^4\,c^{11}}\right)}^{1/4}}{\left(\sqrt{x}\,\left(256\,a^{11}\,b^9\,c^9\,d^{11}+256\,a^9\,b^{11}\,c^{11}\,d^9\right)-{\left(-\frac{d^7}{16\,a^4\,c^7\,d^4-64\,a^3\,b\,c^8\,d^3+96\,a^2\,b^2\,c^9\,d^2-64\,a\,b^3\,c^{10}\,d+16\,b^4\,c^{11}}\right)}^{1/4}\,\left(512\,a^9\,b^{12}\,c^{14}\,d^7-512\,a^{10}\,b^{11}\,c^{13}\,d^8-512\,a^{13}\,b^8\,c^{10}\,d^{11}+512\,a^{14}\,b^7\,c^9\,d^{12}+\left(\sqrt{x}\,\left(4096\,a^{20}\,b^4\,c^{11}\,d^{13}-16384\,a^{19}\,b^5\,c^{12}\,d^{12}+24576\,a^{18}\,b^6\,c^{13}\,d^{11}-16384\,a^{17}\,b^7\,c^{14}\,d^{10}+4096\,a^{16}\,b^8\,c^{15}\,d^9+4096\,a^{15}\,b^9\,c^{16}\,d^8-16384\,a^{14}\,b^{10}\,c^{17}\,d^7+24576\,a^{13}\,b^{11}\,c^{18}\,d^6-16384\,a^{12}\,b^{12}\,c^{19}\,d^5+4096\,a^{11}\,b^{13}\,c^{20}\,d^4\right)+{\left(-\frac{d^7}{16\,a^4\,c^7\,d^4-64\,a^3\,b\,c^8\,d^3+96\,a^2\,b^2\,c^9\,d^2-64\,a\,b^3\,c^{10}\,d+16\,b^4\,c^{11}}\right)}^{1/4}\,\left(8192\,a^{21}\,b^4\,c^{13}\,d^{12}-40960\,a^{20}\,b^5\,c^{14}\,d^{11}+81920\,a^{19}\,b^6\,c^{15}\,d^{10}-90112\,a^{18}\,b^7\,c^{16}\,d^9+81920\,a^{17}\,b^8\,c^{17}\,d^8-90112\,a^{16}\,b^9\,c^{18}\,d^7+81920\,a^{15}\,b^{10}\,c^{19}\,d^6-40960\,a^{14}\,b^{11}\,c^{20}\,d^5+8192\,a^{13}\,b^{12}\,c^{21}\,d^4\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{d^7}{16\,a^4\,c^7\,d^4-64\,a^3\,b\,c^8\,d^3+96\,a^2\,b^2\,c^9\,d^2-64\,a\,b^3\,c^{10}\,d+16\,b^4\,c^{11}}\right)}^{3/4}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{d^7}{16\,a^4\,c^7\,d^4-64\,a^3\,b\,c^8\,d^3+96\,a^2\,b^2\,c^9\,d^2-64\,a\,b^3\,c^{10}\,d+16\,b^4\,c^{11}}\right)}^{1/4}\,1{}\mathrm{i}-\left(\sqrt{x}\,\left(256\,a^{11}\,b^9\,c^9\,d^{11}+256\,a^9\,b^{11}\,c^{11}\,d^9\right)+{\left(-\frac{d^7}{16\,a^4\,c^7\,d^4-64\,a^3\,b\,c^8\,d^3+96\,a^2\,b^2\,c^9\,d^2-64\,a\,b^3\,c^{10}\,d+16\,b^4\,c^{11}}\right)}^{1/4}\,\left(512\,a^9\,b^{12}\,c^{14}\,d^7-512\,a^{10}\,b^{11}\,c^{13}\,d^8-512\,a^{13}\,b^8\,c^{10}\,d^{11}+512\,a^{14}\,b^7\,c^9\,d^{12}+\left(-\sqrt{x}\,\left(4096\,a^{20}\,b^4\,c^{11}\,d^{13}-16384\,a^{19}\,b^5\,c^{12}\,d^{12}+24576\,a^{18}\,b^6\,c^{13}\,d^{11}-16384\,a^{17}\,b^7\,c^{14}\,d^{10}+4096\,a^{16}\,b^8\,c^{15}\,d^9+4096\,a^{15}\,b^9\,c^{16}\,d^8-16384\,a^{14}\,b^{10}\,c^{17}\,d^7+24576\,a^{13}\,b^{11}\,c^{18}\,d^6-16384\,a^{12}\,b^{12}\,c^{19}\,d^5+4096\,a^{11}\,b^{13}\,c^{20}\,d^4\right)+{\left(-\frac{d^7}{16\,a^4\,c^7\,d^4-64\,a^3\,b\,c^8\,d^3+96\,a^2\,b^2\,c^9\,d^2-64\,a\,b^3\,c^{10}\,d+16\,b^4\,c^{11}}\right)}^{1/4}\,\left(8192\,a^{21}\,b^4\,c^{13}\,d^{12}-40960\,a^{20}\,b^5\,c^{14}\,d^{11}+81920\,a^{19}\,b^6\,c^{15}\,d^{10}-90112\,a^{18}\,b^7\,c^{16}\,d^9+81920\,a^{17}\,b^8\,c^{17}\,d^8-90112\,a^{16}\,b^9\,c^{18}\,d^7+81920\,a^{15}\,b^{10}\,c^{19}\,d^6-40960\,a^{14}\,b^{11}\,c^{20}\,d^5+8192\,a^{13}\,b^{12}\,c^{21}\,d^4\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{d^7}{16\,a^4\,c^7\,d^4-64\,a^3\,b\,c^8\,d^3+96\,a^2\,b^2\,c^9\,d^2-64\,a\,b^3\,c^{10}\,d+16\,b^4\,c^{11}}\right)}^{3/4}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{d^7}{16\,a^4\,c^7\,d^4-64\,a^3\,b\,c^8\,d^3+96\,a^2\,b^2\,c^9\,d^2-64\,a\,b^3\,c^{10}\,d+16\,b^4\,c^{11}}\right)}^{1/4}\,1{}\mathrm{i}}\right)\,{\left(-\frac{d^7}{16\,a^4\,c^7\,d^4-64\,a^3\,b\,c^8\,d^3+96\,a^2\,b^2\,c^9\,d^2-64\,a\,b^3\,c^{10}\,d+16\,b^4\,c^{11}}\right)}^{1/4}+2\,\mathrm{atan}\left(\frac{\left(\sqrt{x}\,\left(256\,a^{11}\,b^9\,c^9\,d^{11}+256\,a^9\,b^{11}\,c^{11}\,d^9\right)-{\left(-\frac{b^7}{16\,a^{11}\,d^4-64\,a^{10}\,b\,c\,d^3+96\,a^9\,b^2\,c^2\,d^2-64\,a^8\,b^3\,c^3\,d+16\,a^7\,b^4\,c^4}\right)}^{1/4}\,\left(512\,a^9\,b^{12}\,c^{14}\,d^7-512\,a^{10}\,b^{11}\,c^{13}\,d^8-512\,a^{13}\,b^8\,c^{10}\,d^{11}+512\,a^{14}\,b^7\,c^9\,d^{12}+\left(\sqrt{x}\,\left(4096\,a^{20}\,b^4\,c^{11}\,d^{13}-16384\,a^{19}\,b^5\,c^{12}\,d^{12}+24576\,a^{18}\,b^6\,c^{13}\,d^{11}-16384\,a^{17}\,b^7\,c^{14}\,d^{10}+4096\,a^{16}\,b^8\,c^{15}\,d^9+4096\,a^{15}\,b^9\,c^{16}\,d^8-16384\,a^{14}\,b^{10}\,c^{17}\,d^7+24576\,a^{13}\,b^{11}\,c^{18}\,d^6-16384\,a^{12}\,b^{12}\,c^{19}\,d^5+4096\,a^{11}\,b^{13}\,c^{20}\,d^4\right)+{\left(-\frac{b^7}{16\,a^{11}\,d^4-64\,a^{10}\,b\,c\,d^3+96\,a^9\,b^2\,c^2\,d^2-64\,a^8\,b^3\,c^3\,d+16\,a^7\,b^4\,c^4}\right)}^{1/4}\,\left(8192\,a^{21}\,b^4\,c^{13}\,d^{12}-40960\,a^{20}\,b^5\,c^{14}\,d^{11}+81920\,a^{19}\,b^6\,c^{15}\,d^{10}-90112\,a^{18}\,b^7\,c^{16}\,d^9+81920\,a^{17}\,b^8\,c^{17}\,d^8-90112\,a^{16}\,b^9\,c^{18}\,d^7+81920\,a^{15}\,b^{10}\,c^{19}\,d^6-40960\,a^{14}\,b^{11}\,c^{20}\,d^5+8192\,a^{13}\,b^{12}\,c^{21}\,d^4\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{b^7}{16\,a^{11}\,d^4-64\,a^{10}\,b\,c\,d^3+96\,a^9\,b^2\,c^2\,d^2-64\,a^8\,b^3\,c^3\,d+16\,a^7\,b^4\,c^4}\right)}^{3/4}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{b^7}{16\,a^{11}\,d^4-64\,a^{10}\,b\,c\,d^3+96\,a^9\,b^2\,c^2\,d^2-64\,a^8\,b^3\,c^3\,d+16\,a^7\,b^4\,c^4}\right)}^{1/4}+\left(\sqrt{x}\,\left(256\,a^{11}\,b^9\,c^9\,d^{11}+256\,a^9\,b^{11}\,c^{11}\,d^9\right)+{\left(-\frac{b^7}{16\,a^{11}\,d^4-64\,a^{10}\,b\,c\,d^3+96\,a^9\,b^2\,c^2\,d^2-64\,a^8\,b^3\,c^3\,d+16\,a^7\,b^4\,c^4}\right)}^{1/4}\,\left(512\,a^9\,b^{12}\,c^{14}\,d^7-512\,a^{10}\,b^{11}\,c^{13}\,d^8-512\,a^{13}\,b^8\,c^{10}\,d^{11}+512\,a^{14}\,b^7\,c^9\,d^{12}+\left(-\sqrt{x}\,\left(4096\,a^{20}\,b^4\,c^{11}\,d^{13}-16384\,a^{19}\,b^5\,c^{12}\,d^{12}+24576\,a^{18}\,b^6\,c^{13}\,d^{11}-16384\,a^{17}\,b^7\,c^{14}\,d^{10}+4096\,a^{16}\,b^8\,c^{15}\,d^9+4096\,a^{15}\,b^9\,c^{16}\,d^8-16384\,a^{14}\,b^{10}\,c^{17}\,d^7+24576\,a^{13}\,b^{11}\,c^{18}\,d^6-16384\,a^{12}\,b^{12}\,c^{19}\,d^5+4096\,a^{11}\,b^{13}\,c^{20}\,d^4\right)+{\left(-\frac{b^7}{16\,a^{11}\,d^4-64\,a^{10}\,b\,c\,d^3+96\,a^9\,b^2\,c^2\,d^2-64\,a^8\,b^3\,c^3\,d+16\,a^7\,b^4\,c^4}\right)}^{1/4}\,\left(8192\,a^{21}\,b^4\,c^{13}\,d^{12}-40960\,a^{20}\,b^5\,c^{14}\,d^{11}+81920\,a^{19}\,b^6\,c^{15}\,d^{10}-90112\,a^{18}\,b^7\,c^{16}\,d^9+81920\,a^{17}\,b^8\,c^{17}\,d^8-90112\,a^{16}\,b^9\,c^{18}\,d^7+81920\,a^{15}\,b^{10}\,c^{19}\,d^6-40960\,a^{14}\,b^{11}\,c^{20}\,d^5+8192\,a^{13}\,b^{12}\,c^{21}\,d^4\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{b^7}{16\,a^{11}\,d^4-64\,a^{10}\,b\,c\,d^3+96\,a^9\,b^2\,c^2\,d^2-64\,a^8\,b^3\,c^3\,d+16\,a^7\,b^4\,c^4}\right)}^{3/4}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{b^7}{16\,a^{11}\,d^4-64\,a^{10}\,b\,c\,d^3+96\,a^9\,b^2\,c^2\,d^2-64\,a^8\,b^3\,c^3\,d+16\,a^7\,b^4\,c^4}\right)}^{1/4}}{\left(\sqrt{x}\,\left(256\,a^{11}\,b^9\,c^9\,d^{11}+256\,a^9\,b^{11}\,c^{11}\,d^9\right)-{\left(-\frac{b^7}{16\,a^{11}\,d^4-64\,a^{10}\,b\,c\,d^3+96\,a^9\,b^2\,c^2\,d^2-64\,a^8\,b^3\,c^3\,d+16\,a^7\,b^4\,c^4}\right)}^{1/4}\,\left(512\,a^9\,b^{12}\,c^{14}\,d^7-512\,a^{10}\,b^{11}\,c^{13}\,d^8-512\,a^{13}\,b^8\,c^{10}\,d^{11}+512\,a^{14}\,b^7\,c^9\,d^{12}+\left(\sqrt{x}\,\left(4096\,a^{20}\,b^4\,c^{11}\,d^{13}-16384\,a^{19}\,b^5\,c^{12}\,d^{12}+24576\,a^{18}\,b^6\,c^{13}\,d^{11}-16384\,a^{17}\,b^7\,c^{14}\,d^{10}+4096\,a^{16}\,b^8\,c^{15}\,d^9+4096\,a^{15}\,b^9\,c^{16}\,d^8-16384\,a^{14}\,b^{10}\,c^{17}\,d^7+24576\,a^{13}\,b^{11}\,c^{18}\,d^6-16384\,a^{12}\,b^{12}\,c^{19}\,d^5+4096\,a^{11}\,b^{13}\,c^{20}\,d^4\right)+{\left(-\frac{b^7}{16\,a^{11}\,d^4-64\,a^{10}\,b\,c\,d^3+96\,a^9\,b^2\,c^2\,d^2-64\,a^8\,b^3\,c^3\,d+16\,a^7\,b^4\,c^4}\right)}^{1/4}\,\left(8192\,a^{21}\,b^4\,c^{13}\,d^{12}-40960\,a^{20}\,b^5\,c^{14}\,d^{11}+81920\,a^{19}\,b^6\,c^{15}\,d^{10}-90112\,a^{18}\,b^7\,c^{16}\,d^9+81920\,a^{17}\,b^8\,c^{17}\,d^8-90112\,a^{16}\,b^9\,c^{18}\,d^7+81920\,a^{15}\,b^{10}\,c^{19}\,d^6-40960\,a^{14}\,b^{11}\,c^{20}\,d^5+8192\,a^{13}\,b^{12}\,c^{21}\,d^4\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{b^7}{16\,a^{11}\,d^4-64\,a^{10}\,b\,c\,d^3+96\,a^9\,b^2\,c^2\,d^2-64\,a^8\,b^3\,c^3\,d+16\,a^7\,b^4\,c^4}\right)}^{3/4}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{b^7}{16\,a^{11}\,d^4-64\,a^{10}\,b\,c\,d^3+96\,a^9\,b^2\,c^2\,d^2-64\,a^8\,b^3\,c^3\,d+16\,a^7\,b^4\,c^4}\right)}^{1/4}\,1{}\mathrm{i}-\left(\sqrt{x}\,\left(256\,a^{11}\,b^9\,c^9\,d^{11}+256\,a^9\,b^{11}\,c^{11}\,d^9\right)+{\left(-\frac{b^7}{16\,a^{11}\,d^4-64\,a^{10}\,b\,c\,d^3+96\,a^9\,b^2\,c^2\,d^2-64\,a^8\,b^3\,c^3\,d+16\,a^7\,b^4\,c^4}\right)}^{1/4}\,\left(512\,a^9\,b^{12}\,c^{14}\,d^7-512\,a^{10}\,b^{11}\,c^{13}\,d^8-512\,a^{13}\,b^8\,c^{10}\,d^{11}+512\,a^{14}\,b^7\,c^9\,d^{12}+\left(-\sqrt{x}\,\left(4096\,a^{20}\,b^4\,c^{11}\,d^{13}-16384\,a^{19}\,b^5\,c^{12}\,d^{12}+24576\,a^{18}\,b^6\,c^{13}\,d^{11}-16384\,a^{17}\,b^7\,c^{14}\,d^{10}+4096\,a^{16}\,b^8\,c^{15}\,d^9+4096\,a^{15}\,b^9\,c^{16}\,d^8-16384\,a^{14}\,b^{10}\,c^{17}\,d^7+24576\,a^{13}\,b^{11}\,c^{18}\,d^6-16384\,a^{12}\,b^{12}\,c^{19}\,d^5+4096\,a^{11}\,b^{13}\,c^{20}\,d^4\right)+{\left(-\frac{b^7}{16\,a^{11}\,d^4-64\,a^{10}\,b\,c\,d^3+96\,a^9\,b^2\,c^2\,d^2-64\,a^8\,b^3\,c^3\,d+16\,a^7\,b^4\,c^4}\right)}^{1/4}\,\left(8192\,a^{21}\,b^4\,c^{13}\,d^{12}-40960\,a^{20}\,b^5\,c^{14}\,d^{11}+81920\,a^{19}\,b^6\,c^{15}\,d^{10}-90112\,a^{18}\,b^7\,c^{16}\,d^9+81920\,a^{17}\,b^8\,c^{17}\,d^8-90112\,a^{16}\,b^9\,c^{18}\,d^7+81920\,a^{15}\,b^{10}\,c^{19}\,d^6-40960\,a^{14}\,b^{11}\,c^{20}\,d^5+8192\,a^{13}\,b^{12}\,c^{21}\,d^4\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{b^7}{16\,a^{11}\,d^4-64\,a^{10}\,b\,c\,d^3+96\,a^9\,b^2\,c^2\,d^2-64\,a^8\,b^3\,c^3\,d+16\,a^7\,b^4\,c^4}\right)}^{3/4}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{b^7}{16\,a^{11}\,d^4-64\,a^{10}\,b\,c\,d^3+96\,a^9\,b^2\,c^2\,d^2-64\,a^8\,b^3\,c^3\,d+16\,a^7\,b^4\,c^4}\right)}^{1/4}\,1{}\mathrm{i}}\right)\,{\left(-\frac{b^7}{16\,a^{11}\,d^4-64\,a^{10}\,b\,c\,d^3+96\,a^9\,b^2\,c^2\,d^2-64\,a^8\,b^3\,c^3\,d+16\,a^7\,b^4\,c^4}\right)}^{1/4}-\frac{2}{3\,a\,c\,x^{3/2}}-\mathrm{atan}\left(\frac{a^2\,b^5\,d^7\,\sqrt{x}\,1{}\mathrm{i}+b^7\,c^2\,d^5\,\sqrt{x}\,1{}\mathrm{i}-\frac{a^2\,b^{16}\,c^{11}\,\sqrt{x}\,16{}\mathrm{i}}{16\,a^{11}\,d^4-64\,a^{10}\,b\,c\,d^3+96\,a^9\,b^2\,c^2\,d^2-64\,a^8\,b^3\,c^3\,d+16\,a^7\,b^4\,c^4}+\frac{a^3\,b^{15}\,c^{10}\,d\,\sqrt{x}\,64{}\mathrm{i}}{16\,a^{11}\,d^4-64\,a^{10}\,b\,c\,d^3+96\,a^9\,b^2\,c^2\,d^2-64\,a^8\,b^3\,c^3\,d+16\,a^7\,b^4\,c^4}-\frac{a^4\,b^{14}\,c^9\,d^2\,\sqrt{x}\,96{}\mathrm{i}}{16\,a^{11}\,d^4-64\,a^{10}\,b\,c\,d^3+96\,a^9\,b^2\,c^2\,d^2-64\,a^8\,b^3\,c^3\,d+16\,a^7\,b^4\,c^4}+\frac{a^5\,b^{13}\,c^8\,d^3\,\sqrt{x}\,64{}\mathrm{i}}{16\,a^{11}\,d^4-64\,a^{10}\,b\,c\,d^3+96\,a^9\,b^2\,c^2\,d^2-64\,a^8\,b^3\,c^3\,d+16\,a^7\,b^4\,c^4}-\frac{a^6\,b^{12}\,c^7\,d^4\,\sqrt{x}\,16{}\mathrm{i}}{16\,a^{11}\,d^4-64\,a^{10}\,b\,c\,d^3+96\,a^9\,b^2\,c^2\,d^2-64\,a^8\,b^3\,c^3\,d+16\,a^7\,b^4\,c^4}-\frac{a^7\,b^{11}\,c^6\,d^5\,\sqrt{x}\,16{}\mathrm{i}}{16\,a^{11}\,d^4-64\,a^{10}\,b\,c\,d^3+96\,a^9\,b^2\,c^2\,d^2-64\,a^8\,b^3\,c^3\,d+16\,a^7\,b^4\,c^4}+\frac{a^8\,b^{10}\,c^5\,d^6\,\sqrt{x}\,64{}\mathrm{i}}{16\,a^{11}\,d^4-64\,a^{10}\,b\,c\,d^3+96\,a^9\,b^2\,c^2\,d^2-64\,a^8\,b^3\,c^3\,d+16\,a^7\,b^4\,c^4}-\frac{a^9\,b^9\,c^4\,d^7\,\sqrt{x}\,96{}\mathrm{i}}{16\,a^{11}\,d^4-64\,a^{10}\,b\,c\,d^3+96\,a^9\,b^2\,c^2\,d^2-64\,a^8\,b^3\,c^3\,d+16\,a^7\,b^4\,c^4}+\frac{a^{10}\,b^8\,c^3\,d^8\,\sqrt{x}\,64{}\mathrm{i}}{16\,a^{11}\,d^4-64\,a^{10}\,b\,c\,d^3+96\,a^9\,b^2\,c^2\,d^2-64\,a^8\,b^3\,c^3\,d+16\,a^7\,b^4\,c^4}-\frac{a^{11}\,b^7\,c^2\,d^9\,\sqrt{x}\,16{}\mathrm{i}}{16\,a^{11}\,d^4-64\,a^{10}\,b\,c\,d^3+96\,a^9\,b^2\,c^2\,d^2-64\,a^8\,b^3\,c^3\,d+16\,a^7\,b^4\,c^4}}{{\left(-\frac{b^7}{16\,a^{11}\,d^4-64\,a^{10}\,b\,c\,d^3+96\,a^9\,b^2\,c^2\,d^2-64\,a^8\,b^3\,c^3\,d+16\,a^7\,b^4\,c^4}\right)}^{1/4}\,\left(\frac{b^7\,\left(32\,a^{12}\,c^4\,d^8-160\,a^{11}\,b\,c^5\,d^7+320\,a^{10}\,b^2\,c^6\,d^6-352\,a^9\,b^3\,c^7\,d^5+320\,a^8\,b^4\,c^8\,d^4-352\,a^7\,b^5\,c^9\,d^3+320\,a^6\,b^6\,c^{10}\,d^2-160\,a^5\,b^7\,c^{11}\,d+32\,a^4\,b^8\,c^{12}\right)}{16\,a^{11}\,d^4-64\,a^{10}\,b\,c\,d^3+96\,a^9\,b^2\,c^2\,d^2-64\,a^8\,b^3\,c^3\,d+16\,a^7\,b^4\,c^4}+2\,a^5\,b^3\,d^8+2\,b^8\,c^5\,d^3-2\,a\,b^7\,c^4\,d^4-2\,a^4\,b^4\,c\,d^7\right)}\right)\,{\left(-\frac{b^7}{16\,a^{11}\,d^4-64\,a^{10}\,b\,c\,d^3+96\,a^9\,b^2\,c^2\,d^2-64\,a^8\,b^3\,c^3\,d+16\,a^7\,b^4\,c^4}\right)}^{1/4}\,2{}\mathrm{i}-\mathrm{atan}\left(\frac{a^2\,b^5\,d^7\,\sqrt{x}\,1{}\mathrm{i}+b^7\,c^2\,d^5\,\sqrt{x}\,1{}\mathrm{i}-\frac{a^{11}\,c^2\,d^{16}\,\sqrt{x}\,16{}\mathrm{i}}{16\,a^4\,c^7\,d^4-64\,a^3\,b\,c^8\,d^3+96\,a^2\,b^2\,c^9\,d^2-64\,a\,b^3\,c^{10}\,d+16\,b^4\,c^{11}}+\frac{a^{10}\,b\,c^3\,d^{15}\,\sqrt{x}\,64{}\mathrm{i}}{16\,a^4\,c^7\,d^4-64\,a^3\,b\,c^8\,d^3+96\,a^2\,b^2\,c^9\,d^2-64\,a\,b^3\,c^{10}\,d+16\,b^4\,c^{11}}-\frac{a^2\,b^9\,c^{11}\,d^7\,\sqrt{x}\,16{}\mathrm{i}}{16\,a^4\,c^7\,d^4-64\,a^3\,b\,c^8\,d^3+96\,a^2\,b^2\,c^9\,d^2-64\,a\,b^3\,c^{10}\,d+16\,b^4\,c^{11}}+\frac{a^3\,b^8\,c^{10}\,d^8\,\sqrt{x}\,64{}\mathrm{i}}{16\,a^4\,c^7\,d^4-64\,a^3\,b\,c^8\,d^3+96\,a^2\,b^2\,c^9\,d^2-64\,a\,b^3\,c^{10}\,d+16\,b^4\,c^{11}}-\frac{a^4\,b^7\,c^9\,d^9\,\sqrt{x}\,96{}\mathrm{i}}{16\,a^4\,c^7\,d^4-64\,a^3\,b\,c^8\,d^3+96\,a^2\,b^2\,c^9\,d^2-64\,a\,b^3\,c^{10}\,d+16\,b^4\,c^{11}}+\frac{a^5\,b^6\,c^8\,d^{10}\,\sqrt{x}\,64{}\mathrm{i}}{16\,a^4\,c^7\,d^4-64\,a^3\,b\,c^8\,d^3+96\,a^2\,b^2\,c^9\,d^2-64\,a\,b^3\,c^{10}\,d+16\,b^4\,c^{11}}-\frac{a^6\,b^5\,c^7\,d^{11}\,\sqrt{x}\,16{}\mathrm{i}}{16\,a^4\,c^7\,d^4-64\,a^3\,b\,c^8\,d^3+96\,a^2\,b^2\,c^9\,d^2-64\,a\,b^3\,c^{10}\,d+16\,b^4\,c^{11}}-\frac{a^7\,b^4\,c^6\,d^{12}\,\sqrt{x}\,16{}\mathrm{i}}{16\,a^4\,c^7\,d^4-64\,a^3\,b\,c^8\,d^3+96\,a^2\,b^2\,c^9\,d^2-64\,a\,b^3\,c^{10}\,d+16\,b^4\,c^{11}}+\frac{a^8\,b^3\,c^5\,d^{13}\,\sqrt{x}\,64{}\mathrm{i}}{16\,a^4\,c^7\,d^4-64\,a^3\,b\,c^8\,d^3+96\,a^2\,b^2\,c^9\,d^2-64\,a\,b^3\,c^{10}\,d+16\,b^4\,c^{11}}-\frac{a^9\,b^2\,c^4\,d^{14}\,\sqrt{x}\,96{}\mathrm{i}}{16\,a^4\,c^7\,d^4-64\,a^3\,b\,c^8\,d^3+96\,a^2\,b^2\,c^9\,d^2-64\,a\,b^3\,c^{10}\,d+16\,b^4\,c^{11}}}{{\left(-\frac{d^7}{16\,a^4\,c^7\,d^4-64\,a^3\,b\,c^8\,d^3+96\,a^2\,b^2\,c^9\,d^2-64\,a\,b^3\,c^{10}\,d+16\,b^4\,c^{11}}\right)}^{1/4}\,\left(\frac{d^7\,\left(32\,a^{12}\,c^4\,d^8-160\,a^{11}\,b\,c^5\,d^7+320\,a^{10}\,b^2\,c^6\,d^6-352\,a^9\,b^3\,c^7\,d^5+320\,a^8\,b^4\,c^8\,d^4-352\,a^7\,b^5\,c^9\,d^3+320\,a^6\,b^6\,c^{10}\,d^2-160\,a^5\,b^7\,c^{11}\,d+32\,a^4\,b^8\,c^{12}\right)}{16\,a^4\,c^7\,d^4-64\,a^3\,b\,c^8\,d^3+96\,a^2\,b^2\,c^9\,d^2-64\,a\,b^3\,c^{10}\,d+16\,b^4\,c^{11}}+2\,a^5\,b^3\,d^8+2\,b^8\,c^5\,d^3-2\,a\,b^7\,c^4\,d^4-2\,a^4\,b^4\,c\,d^7\right)}\right)\,{\left(-\frac{d^7}{16\,a^4\,c^7\,d^4-64\,a^3\,b\,c^8\,d^3+96\,a^2\,b^2\,c^9\,d^2-64\,a\,b^3\,c^{10}\,d+16\,b^4\,c^{11}}\right)}^{1/4}\,2{}\mathrm{i}","Not used",1,"2*atan(((x^(1/2)*(256*a^9*b^11*c^11*d^9 + 256*a^11*b^9*c^9*d^11) - (-d^7/(16*b^4*c^11 + 16*a^4*c^7*d^4 - 64*a^3*b*c^8*d^3 + 96*a^2*b^2*c^9*d^2 - 64*a*b^3*c^10*d))^(1/4)*(((-d^7/(16*b^4*c^11 + 16*a^4*c^7*d^4 - 64*a^3*b*c^8*d^3 + 96*a^2*b^2*c^9*d^2 - 64*a*b^3*c^10*d))^(1/4)*(8192*a^13*b^12*c^21*d^4 - 40960*a^14*b^11*c^20*d^5 + 81920*a^15*b^10*c^19*d^6 - 90112*a^16*b^9*c^18*d^7 + 81920*a^17*b^8*c^17*d^8 - 90112*a^18*b^7*c^16*d^9 + 81920*a^19*b^6*c^15*d^10 - 40960*a^20*b^5*c^14*d^11 + 8192*a^21*b^4*c^13*d^12)*1i + x^(1/2)*(4096*a^11*b^13*c^20*d^4 - 16384*a^12*b^12*c^19*d^5 + 24576*a^13*b^11*c^18*d^6 - 16384*a^14*b^10*c^17*d^7 + 4096*a^15*b^9*c^16*d^8 + 4096*a^16*b^8*c^15*d^9 - 16384*a^17*b^7*c^14*d^10 + 24576*a^18*b^6*c^13*d^11 - 16384*a^19*b^5*c^12*d^12 + 4096*a^20*b^4*c^11*d^13))*(-d^7/(16*b^4*c^11 + 16*a^4*c^7*d^4 - 64*a^3*b*c^8*d^3 + 96*a^2*b^2*c^9*d^2 - 64*a*b^3*c^10*d))^(3/4)*1i + 512*a^9*b^12*c^14*d^7 - 512*a^10*b^11*c^13*d^8 - 512*a^13*b^8*c^10*d^11 + 512*a^14*b^7*c^9*d^12)*1i)*(-d^7/(16*b^4*c^11 + 16*a^4*c^7*d^4 - 64*a^3*b*c^8*d^3 + 96*a^2*b^2*c^9*d^2 - 64*a*b^3*c^10*d))^(1/4) + (x^(1/2)*(256*a^9*b^11*c^11*d^9 + 256*a^11*b^9*c^9*d^11) + (-d^7/(16*b^4*c^11 + 16*a^4*c^7*d^4 - 64*a^3*b*c^8*d^3 + 96*a^2*b^2*c^9*d^2 - 64*a*b^3*c^10*d))^(1/4)*(((-d^7/(16*b^4*c^11 + 16*a^4*c^7*d^4 - 64*a^3*b*c^8*d^3 + 96*a^2*b^2*c^9*d^2 - 64*a*b^3*c^10*d))^(1/4)*(8192*a^13*b^12*c^21*d^4 - 40960*a^14*b^11*c^20*d^5 + 81920*a^15*b^10*c^19*d^6 - 90112*a^16*b^9*c^18*d^7 + 81920*a^17*b^8*c^17*d^8 - 90112*a^18*b^7*c^16*d^9 + 81920*a^19*b^6*c^15*d^10 - 40960*a^20*b^5*c^14*d^11 + 8192*a^21*b^4*c^13*d^12)*1i - x^(1/2)*(4096*a^11*b^13*c^20*d^4 - 16384*a^12*b^12*c^19*d^5 + 24576*a^13*b^11*c^18*d^6 - 16384*a^14*b^10*c^17*d^7 + 4096*a^15*b^9*c^16*d^8 + 4096*a^16*b^8*c^15*d^9 - 16384*a^17*b^7*c^14*d^10 + 24576*a^18*b^6*c^13*d^11 - 16384*a^19*b^5*c^12*d^12 + 4096*a^20*b^4*c^11*d^13))*(-d^7/(16*b^4*c^11 + 16*a^4*c^7*d^4 - 64*a^3*b*c^8*d^3 + 96*a^2*b^2*c^9*d^2 - 64*a*b^3*c^10*d))^(3/4)*1i + 512*a^9*b^12*c^14*d^7 - 512*a^10*b^11*c^13*d^8 - 512*a^13*b^8*c^10*d^11 + 512*a^14*b^7*c^9*d^12)*1i)*(-d^7/(16*b^4*c^11 + 16*a^4*c^7*d^4 - 64*a^3*b*c^8*d^3 + 96*a^2*b^2*c^9*d^2 - 64*a*b^3*c^10*d))^(1/4))/((x^(1/2)*(256*a^9*b^11*c^11*d^9 + 256*a^11*b^9*c^9*d^11) - (-d^7/(16*b^4*c^11 + 16*a^4*c^7*d^4 - 64*a^3*b*c^8*d^3 + 96*a^2*b^2*c^9*d^2 - 64*a*b^3*c^10*d))^(1/4)*(((-d^7/(16*b^4*c^11 + 16*a^4*c^7*d^4 - 64*a^3*b*c^8*d^3 + 96*a^2*b^2*c^9*d^2 - 64*a*b^3*c^10*d))^(1/4)*(8192*a^13*b^12*c^21*d^4 - 40960*a^14*b^11*c^20*d^5 + 81920*a^15*b^10*c^19*d^6 - 90112*a^16*b^9*c^18*d^7 + 81920*a^17*b^8*c^17*d^8 - 90112*a^18*b^7*c^16*d^9 + 81920*a^19*b^6*c^15*d^10 - 40960*a^20*b^5*c^14*d^11 + 8192*a^21*b^4*c^13*d^12)*1i + x^(1/2)*(4096*a^11*b^13*c^20*d^4 - 16384*a^12*b^12*c^19*d^5 + 24576*a^13*b^11*c^18*d^6 - 16384*a^14*b^10*c^17*d^7 + 4096*a^15*b^9*c^16*d^8 + 4096*a^16*b^8*c^15*d^9 - 16384*a^17*b^7*c^14*d^10 + 24576*a^18*b^6*c^13*d^11 - 16384*a^19*b^5*c^12*d^12 + 4096*a^20*b^4*c^11*d^13))*(-d^7/(16*b^4*c^11 + 16*a^4*c^7*d^4 - 64*a^3*b*c^8*d^3 + 96*a^2*b^2*c^9*d^2 - 64*a*b^3*c^10*d))^(3/4)*1i + 512*a^9*b^12*c^14*d^7 - 512*a^10*b^11*c^13*d^8 - 512*a^13*b^8*c^10*d^11 + 512*a^14*b^7*c^9*d^12)*1i)*(-d^7/(16*b^4*c^11 + 16*a^4*c^7*d^4 - 64*a^3*b*c^8*d^3 + 96*a^2*b^2*c^9*d^2 - 64*a*b^3*c^10*d))^(1/4)*1i - (x^(1/2)*(256*a^9*b^11*c^11*d^9 + 256*a^11*b^9*c^9*d^11) + (-d^7/(16*b^4*c^11 + 16*a^4*c^7*d^4 - 64*a^3*b*c^8*d^3 + 96*a^2*b^2*c^9*d^2 - 64*a*b^3*c^10*d))^(1/4)*(((-d^7/(16*b^4*c^11 + 16*a^4*c^7*d^4 - 64*a^3*b*c^8*d^3 + 96*a^2*b^2*c^9*d^2 - 64*a*b^3*c^10*d))^(1/4)*(8192*a^13*b^12*c^21*d^4 - 40960*a^14*b^11*c^20*d^5 + 81920*a^15*b^10*c^19*d^6 - 90112*a^16*b^9*c^18*d^7 + 81920*a^17*b^8*c^17*d^8 - 90112*a^18*b^7*c^16*d^9 + 81920*a^19*b^6*c^15*d^10 - 40960*a^20*b^5*c^14*d^11 + 8192*a^21*b^4*c^13*d^12)*1i - x^(1/2)*(4096*a^11*b^13*c^20*d^4 - 16384*a^12*b^12*c^19*d^5 + 24576*a^13*b^11*c^18*d^6 - 16384*a^14*b^10*c^17*d^7 + 4096*a^15*b^9*c^16*d^8 + 4096*a^16*b^8*c^15*d^9 - 16384*a^17*b^7*c^14*d^10 + 24576*a^18*b^6*c^13*d^11 - 16384*a^19*b^5*c^12*d^12 + 4096*a^20*b^4*c^11*d^13))*(-d^7/(16*b^4*c^11 + 16*a^4*c^7*d^4 - 64*a^3*b*c^8*d^3 + 96*a^2*b^2*c^9*d^2 - 64*a*b^3*c^10*d))^(3/4)*1i + 512*a^9*b^12*c^14*d^7 - 512*a^10*b^11*c^13*d^8 - 512*a^13*b^8*c^10*d^11 + 512*a^14*b^7*c^9*d^12)*1i)*(-d^7/(16*b^4*c^11 + 16*a^4*c^7*d^4 - 64*a^3*b*c^8*d^3 + 96*a^2*b^2*c^9*d^2 - 64*a*b^3*c^10*d))^(1/4)*1i))*(-d^7/(16*b^4*c^11 + 16*a^4*c^7*d^4 - 64*a^3*b*c^8*d^3 + 96*a^2*b^2*c^9*d^2 - 64*a*b^3*c^10*d))^(1/4) - atan((a^2*b^5*d^7*x^(1/2)*1i + b^7*c^2*d^5*x^(1/2)*1i - (a^2*b^16*c^11*x^(1/2)*16i)/(16*a^11*d^4 + 16*a^7*b^4*c^4 - 64*a^8*b^3*c^3*d + 96*a^9*b^2*c^2*d^2 - 64*a^10*b*c*d^3) + (a^3*b^15*c^10*d*x^(1/2)*64i)/(16*a^11*d^4 + 16*a^7*b^4*c^4 - 64*a^8*b^3*c^3*d + 96*a^9*b^2*c^2*d^2 - 64*a^10*b*c*d^3) - (a^4*b^14*c^9*d^2*x^(1/2)*96i)/(16*a^11*d^4 + 16*a^7*b^4*c^4 - 64*a^8*b^3*c^3*d + 96*a^9*b^2*c^2*d^2 - 64*a^10*b*c*d^3) + (a^5*b^13*c^8*d^3*x^(1/2)*64i)/(16*a^11*d^4 + 16*a^7*b^4*c^4 - 64*a^8*b^3*c^3*d + 96*a^9*b^2*c^2*d^2 - 64*a^10*b*c*d^3) - (a^6*b^12*c^7*d^4*x^(1/2)*16i)/(16*a^11*d^4 + 16*a^7*b^4*c^4 - 64*a^8*b^3*c^3*d + 96*a^9*b^2*c^2*d^2 - 64*a^10*b*c*d^3) - (a^7*b^11*c^6*d^5*x^(1/2)*16i)/(16*a^11*d^4 + 16*a^7*b^4*c^4 - 64*a^8*b^3*c^3*d + 96*a^9*b^2*c^2*d^2 - 64*a^10*b*c*d^3) + (a^8*b^10*c^5*d^6*x^(1/2)*64i)/(16*a^11*d^4 + 16*a^7*b^4*c^4 - 64*a^8*b^3*c^3*d + 96*a^9*b^2*c^2*d^2 - 64*a^10*b*c*d^3) - (a^9*b^9*c^4*d^7*x^(1/2)*96i)/(16*a^11*d^4 + 16*a^7*b^4*c^4 - 64*a^8*b^3*c^3*d + 96*a^9*b^2*c^2*d^2 - 64*a^10*b*c*d^3) + (a^10*b^8*c^3*d^8*x^(1/2)*64i)/(16*a^11*d^4 + 16*a^7*b^4*c^4 - 64*a^8*b^3*c^3*d + 96*a^9*b^2*c^2*d^2 - 64*a^10*b*c*d^3) - (a^11*b^7*c^2*d^9*x^(1/2)*16i)/(16*a^11*d^4 + 16*a^7*b^4*c^4 - 64*a^8*b^3*c^3*d + 96*a^9*b^2*c^2*d^2 - 64*a^10*b*c*d^3))/((-b^7/(16*a^11*d^4 + 16*a^7*b^4*c^4 - 64*a^8*b^3*c^3*d + 96*a^9*b^2*c^2*d^2 - 64*a^10*b*c*d^3))^(1/4)*((b^7*(32*a^4*b^8*c^12 + 32*a^12*c^4*d^8 - 160*a^5*b^7*c^11*d - 160*a^11*b*c^5*d^7 + 320*a^6*b^6*c^10*d^2 - 352*a^7*b^5*c^9*d^3 + 320*a^8*b^4*c^8*d^4 - 352*a^9*b^3*c^7*d^5 + 320*a^10*b^2*c^6*d^6))/(16*a^11*d^4 + 16*a^7*b^4*c^4 - 64*a^8*b^3*c^3*d + 96*a^9*b^2*c^2*d^2 - 64*a^10*b*c*d^3) + 2*a^5*b^3*d^8 + 2*b^8*c^5*d^3 - 2*a*b^7*c^4*d^4 - 2*a^4*b^4*c*d^7)))*(-b^7/(16*a^11*d^4 + 16*a^7*b^4*c^4 - 64*a^8*b^3*c^3*d + 96*a^9*b^2*c^2*d^2 - 64*a^10*b*c*d^3))^(1/4)*2i - atan((a^2*b^5*d^7*x^(1/2)*1i + b^7*c^2*d^5*x^(1/2)*1i - (a^11*c^2*d^16*x^(1/2)*16i)/(16*b^4*c^11 + 16*a^4*c^7*d^4 - 64*a^3*b*c^8*d^3 + 96*a^2*b^2*c^9*d^2 - 64*a*b^3*c^10*d) + (a^10*b*c^3*d^15*x^(1/2)*64i)/(16*b^4*c^11 + 16*a^4*c^7*d^4 - 64*a^3*b*c^8*d^3 + 96*a^2*b^2*c^9*d^2 - 64*a*b^3*c^10*d) - (a^2*b^9*c^11*d^7*x^(1/2)*16i)/(16*b^4*c^11 + 16*a^4*c^7*d^4 - 64*a^3*b*c^8*d^3 + 96*a^2*b^2*c^9*d^2 - 64*a*b^3*c^10*d) + (a^3*b^8*c^10*d^8*x^(1/2)*64i)/(16*b^4*c^11 + 16*a^4*c^7*d^4 - 64*a^3*b*c^8*d^3 + 96*a^2*b^2*c^9*d^2 - 64*a*b^3*c^10*d) - (a^4*b^7*c^9*d^9*x^(1/2)*96i)/(16*b^4*c^11 + 16*a^4*c^7*d^4 - 64*a^3*b*c^8*d^3 + 96*a^2*b^2*c^9*d^2 - 64*a*b^3*c^10*d) + (a^5*b^6*c^8*d^10*x^(1/2)*64i)/(16*b^4*c^11 + 16*a^4*c^7*d^4 - 64*a^3*b*c^8*d^3 + 96*a^2*b^2*c^9*d^2 - 64*a*b^3*c^10*d) - (a^6*b^5*c^7*d^11*x^(1/2)*16i)/(16*b^4*c^11 + 16*a^4*c^7*d^4 - 64*a^3*b*c^8*d^3 + 96*a^2*b^2*c^9*d^2 - 64*a*b^3*c^10*d) - (a^7*b^4*c^6*d^12*x^(1/2)*16i)/(16*b^4*c^11 + 16*a^4*c^7*d^4 - 64*a^3*b*c^8*d^3 + 96*a^2*b^2*c^9*d^2 - 64*a*b^3*c^10*d) + (a^8*b^3*c^5*d^13*x^(1/2)*64i)/(16*b^4*c^11 + 16*a^4*c^7*d^4 - 64*a^3*b*c^8*d^3 + 96*a^2*b^2*c^9*d^2 - 64*a*b^3*c^10*d) - (a^9*b^2*c^4*d^14*x^(1/2)*96i)/(16*b^4*c^11 + 16*a^4*c^7*d^4 - 64*a^3*b*c^8*d^3 + 96*a^2*b^2*c^9*d^2 - 64*a*b^3*c^10*d))/((-d^7/(16*b^4*c^11 + 16*a^4*c^7*d^4 - 64*a^3*b*c^8*d^3 + 96*a^2*b^2*c^9*d^2 - 64*a*b^3*c^10*d))^(1/4)*((d^7*(32*a^4*b^8*c^12 + 32*a^12*c^4*d^8 - 160*a^5*b^7*c^11*d - 160*a^11*b*c^5*d^7 + 320*a^6*b^6*c^10*d^2 - 352*a^7*b^5*c^9*d^3 + 320*a^8*b^4*c^8*d^4 - 352*a^9*b^3*c^7*d^5 + 320*a^10*b^2*c^6*d^6))/(16*b^4*c^11 + 16*a^4*c^7*d^4 - 64*a^3*b*c^8*d^3 + 96*a^2*b^2*c^9*d^2 - 64*a*b^3*c^10*d) + 2*a^5*b^3*d^8 + 2*b^8*c^5*d^3 - 2*a*b^7*c^4*d^4 - 2*a^4*b^4*c*d^7)))*(-d^7/(16*b^4*c^11 + 16*a^4*c^7*d^4 - 64*a^3*b*c^8*d^3 + 96*a^2*b^2*c^9*d^2 - 64*a*b^3*c^10*d))^(1/4)*2i + 2*atan(((x^(1/2)*(256*a^9*b^11*c^11*d^9 + 256*a^11*b^9*c^9*d^11) - (-b^7/(16*a^11*d^4 + 16*a^7*b^4*c^4 - 64*a^8*b^3*c^3*d + 96*a^9*b^2*c^2*d^2 - 64*a^10*b*c*d^3))^(1/4)*(((-b^7/(16*a^11*d^4 + 16*a^7*b^4*c^4 - 64*a^8*b^3*c^3*d + 96*a^9*b^2*c^2*d^2 - 64*a^10*b*c*d^3))^(1/4)*(8192*a^13*b^12*c^21*d^4 - 40960*a^14*b^11*c^20*d^5 + 81920*a^15*b^10*c^19*d^6 - 90112*a^16*b^9*c^18*d^7 + 81920*a^17*b^8*c^17*d^8 - 90112*a^18*b^7*c^16*d^9 + 81920*a^19*b^6*c^15*d^10 - 40960*a^20*b^5*c^14*d^11 + 8192*a^21*b^4*c^13*d^12)*1i + x^(1/2)*(4096*a^11*b^13*c^20*d^4 - 16384*a^12*b^12*c^19*d^5 + 24576*a^13*b^11*c^18*d^6 - 16384*a^14*b^10*c^17*d^7 + 4096*a^15*b^9*c^16*d^8 + 4096*a^16*b^8*c^15*d^9 - 16384*a^17*b^7*c^14*d^10 + 24576*a^18*b^6*c^13*d^11 - 16384*a^19*b^5*c^12*d^12 + 4096*a^20*b^4*c^11*d^13))*(-b^7/(16*a^11*d^4 + 16*a^7*b^4*c^4 - 64*a^8*b^3*c^3*d + 96*a^9*b^2*c^2*d^2 - 64*a^10*b*c*d^3))^(3/4)*1i + 512*a^9*b^12*c^14*d^7 - 512*a^10*b^11*c^13*d^8 - 512*a^13*b^8*c^10*d^11 + 512*a^14*b^7*c^9*d^12)*1i)*(-b^7/(16*a^11*d^4 + 16*a^7*b^4*c^4 - 64*a^8*b^3*c^3*d + 96*a^9*b^2*c^2*d^2 - 64*a^10*b*c*d^3))^(1/4) + (x^(1/2)*(256*a^9*b^11*c^11*d^9 + 256*a^11*b^9*c^9*d^11) + (-b^7/(16*a^11*d^4 + 16*a^7*b^4*c^4 - 64*a^8*b^3*c^3*d + 96*a^9*b^2*c^2*d^2 - 64*a^10*b*c*d^3))^(1/4)*(((-b^7/(16*a^11*d^4 + 16*a^7*b^4*c^4 - 64*a^8*b^3*c^3*d + 96*a^9*b^2*c^2*d^2 - 64*a^10*b*c*d^3))^(1/4)*(8192*a^13*b^12*c^21*d^4 - 40960*a^14*b^11*c^20*d^5 + 81920*a^15*b^10*c^19*d^6 - 90112*a^16*b^9*c^18*d^7 + 81920*a^17*b^8*c^17*d^8 - 90112*a^18*b^7*c^16*d^9 + 81920*a^19*b^6*c^15*d^10 - 40960*a^20*b^5*c^14*d^11 + 8192*a^21*b^4*c^13*d^12)*1i - x^(1/2)*(4096*a^11*b^13*c^20*d^4 - 16384*a^12*b^12*c^19*d^5 + 24576*a^13*b^11*c^18*d^6 - 16384*a^14*b^10*c^17*d^7 + 4096*a^15*b^9*c^16*d^8 + 4096*a^16*b^8*c^15*d^9 - 16384*a^17*b^7*c^14*d^10 + 24576*a^18*b^6*c^13*d^11 - 16384*a^19*b^5*c^12*d^12 + 4096*a^20*b^4*c^11*d^13))*(-b^7/(16*a^11*d^4 + 16*a^7*b^4*c^4 - 64*a^8*b^3*c^3*d + 96*a^9*b^2*c^2*d^2 - 64*a^10*b*c*d^3))^(3/4)*1i + 512*a^9*b^12*c^14*d^7 - 512*a^10*b^11*c^13*d^8 - 512*a^13*b^8*c^10*d^11 + 512*a^14*b^7*c^9*d^12)*1i)*(-b^7/(16*a^11*d^4 + 16*a^7*b^4*c^4 - 64*a^8*b^3*c^3*d + 96*a^9*b^2*c^2*d^2 - 64*a^10*b*c*d^3))^(1/4))/((x^(1/2)*(256*a^9*b^11*c^11*d^9 + 256*a^11*b^9*c^9*d^11) - (-b^7/(16*a^11*d^4 + 16*a^7*b^4*c^4 - 64*a^8*b^3*c^3*d + 96*a^9*b^2*c^2*d^2 - 64*a^10*b*c*d^3))^(1/4)*(((-b^7/(16*a^11*d^4 + 16*a^7*b^4*c^4 - 64*a^8*b^3*c^3*d + 96*a^9*b^2*c^2*d^2 - 64*a^10*b*c*d^3))^(1/4)*(8192*a^13*b^12*c^21*d^4 - 40960*a^14*b^11*c^20*d^5 + 81920*a^15*b^10*c^19*d^6 - 90112*a^16*b^9*c^18*d^7 + 81920*a^17*b^8*c^17*d^8 - 90112*a^18*b^7*c^16*d^9 + 81920*a^19*b^6*c^15*d^10 - 40960*a^20*b^5*c^14*d^11 + 8192*a^21*b^4*c^13*d^12)*1i + x^(1/2)*(4096*a^11*b^13*c^20*d^4 - 16384*a^12*b^12*c^19*d^5 + 24576*a^13*b^11*c^18*d^6 - 16384*a^14*b^10*c^17*d^7 + 4096*a^15*b^9*c^16*d^8 + 4096*a^16*b^8*c^15*d^9 - 16384*a^17*b^7*c^14*d^10 + 24576*a^18*b^6*c^13*d^11 - 16384*a^19*b^5*c^12*d^12 + 4096*a^20*b^4*c^11*d^13))*(-b^7/(16*a^11*d^4 + 16*a^7*b^4*c^4 - 64*a^8*b^3*c^3*d + 96*a^9*b^2*c^2*d^2 - 64*a^10*b*c*d^3))^(3/4)*1i + 512*a^9*b^12*c^14*d^7 - 512*a^10*b^11*c^13*d^8 - 512*a^13*b^8*c^10*d^11 + 512*a^14*b^7*c^9*d^12)*1i)*(-b^7/(16*a^11*d^4 + 16*a^7*b^4*c^4 - 64*a^8*b^3*c^3*d + 96*a^9*b^2*c^2*d^2 - 64*a^10*b*c*d^3))^(1/4)*1i - (x^(1/2)*(256*a^9*b^11*c^11*d^9 + 256*a^11*b^9*c^9*d^11) + (-b^7/(16*a^11*d^4 + 16*a^7*b^4*c^4 - 64*a^8*b^3*c^3*d + 96*a^9*b^2*c^2*d^2 - 64*a^10*b*c*d^3))^(1/4)*(((-b^7/(16*a^11*d^4 + 16*a^7*b^4*c^4 - 64*a^8*b^3*c^3*d + 96*a^9*b^2*c^2*d^2 - 64*a^10*b*c*d^3))^(1/4)*(8192*a^13*b^12*c^21*d^4 - 40960*a^14*b^11*c^20*d^5 + 81920*a^15*b^10*c^19*d^6 - 90112*a^16*b^9*c^18*d^7 + 81920*a^17*b^8*c^17*d^8 - 90112*a^18*b^7*c^16*d^9 + 81920*a^19*b^6*c^15*d^10 - 40960*a^20*b^5*c^14*d^11 + 8192*a^21*b^4*c^13*d^12)*1i - x^(1/2)*(4096*a^11*b^13*c^20*d^4 - 16384*a^12*b^12*c^19*d^5 + 24576*a^13*b^11*c^18*d^6 - 16384*a^14*b^10*c^17*d^7 + 4096*a^15*b^9*c^16*d^8 + 4096*a^16*b^8*c^15*d^9 - 16384*a^17*b^7*c^14*d^10 + 24576*a^18*b^6*c^13*d^11 - 16384*a^19*b^5*c^12*d^12 + 4096*a^20*b^4*c^11*d^13))*(-b^7/(16*a^11*d^4 + 16*a^7*b^4*c^4 - 64*a^8*b^3*c^3*d + 96*a^9*b^2*c^2*d^2 - 64*a^10*b*c*d^3))^(3/4)*1i + 512*a^9*b^12*c^14*d^7 - 512*a^10*b^11*c^13*d^8 - 512*a^13*b^8*c^10*d^11 + 512*a^14*b^7*c^9*d^12)*1i)*(-b^7/(16*a^11*d^4 + 16*a^7*b^4*c^4 - 64*a^8*b^3*c^3*d + 96*a^9*b^2*c^2*d^2 - 64*a^10*b*c*d^3))^(1/4)*1i))*(-b^7/(16*a^11*d^4 + 16*a^7*b^4*c^4 - 64*a^8*b^3*c^3*d + 96*a^9*b^2*c^2*d^2 - 64*a^10*b*c*d^3))^(1/4) - 2/(3*a*c*x^(3/2))","B"
469,1,4643,498,2.732400,"\text{Not used}","int(1/(x^(7/2)*(a + b*x^2)*(c + d*x^2)),x)","-2\,\mathrm{atan}\left(\frac{32\,a^{11}\,b^{10}\,c^{13}\,\sqrt{x}\,{\left(-\frac{b^9}{16\,a^{13}\,d^4-64\,a^{12}\,b\,c\,d^3+96\,a^{11}\,b^2\,c^2\,d^2-64\,a^{10}\,b^3\,c^3\,d+16\,a^9\,b^4\,c^4}\right)}^{5/4}+2\,a^{11}\,b^6\,d^9\,\sqrt{x}\,{\left(-\frac{b^9}{16\,a^{13}\,d^4-64\,a^{12}\,b\,c\,d^3+96\,a^{11}\,b^2\,c^2\,d^2-64\,a^{10}\,b^3\,c^3\,d+16\,a^9\,b^4\,c^4}\right)}^{1/4}+32\,a^{21}\,c^3\,d^{10}\,\sqrt{x}\,{\left(-\frac{b^9}{16\,a^{13}\,d^4-64\,a^{12}\,b\,c\,d^3+96\,a^{11}\,b^2\,c^2\,d^2-64\,a^{10}\,b^3\,c^3\,d+16\,a^9\,b^4\,c^4}\right)}^{5/4}+2\,a^8\,b^9\,c^3\,d^6\,\sqrt{x}\,{\left(-\frac{b^9}{16\,a^{13}\,d^4-64\,a^{12}\,b\,c\,d^3+96\,a^{11}\,b^2\,c^2\,d^2-64\,a^{10}\,b^3\,c^3\,d+16\,a^9\,b^4\,c^4}\right)}^{1/4}+192\,a^{13}\,b^8\,c^{11}\,d^2\,\sqrt{x}\,{\left(-\frac{b^9}{16\,a^{13}\,d^4-64\,a^{12}\,b\,c\,d^3+96\,a^{11}\,b^2\,c^2\,d^2-64\,a^{10}\,b^3\,c^3\,d+16\,a^9\,b^4\,c^4}\right)}^{5/4}-128\,a^{14}\,b^7\,c^{10}\,d^3\,\sqrt{x}\,{\left(-\frac{b^9}{16\,a^{13}\,d^4-64\,a^{12}\,b\,c\,d^3+96\,a^{11}\,b^2\,c^2\,d^2-64\,a^{10}\,b^3\,c^3\,d+16\,a^9\,b^4\,c^4}\right)}^{5/4}+32\,a^{15}\,b^6\,c^9\,d^4\,\sqrt{x}\,{\left(-\frac{b^9}{16\,a^{13}\,d^4-64\,a^{12}\,b\,c\,d^3+96\,a^{11}\,b^2\,c^2\,d^2-64\,a^{10}\,b^3\,c^3\,d+16\,a^9\,b^4\,c^4}\right)}^{5/4}+32\,a^{17}\,b^4\,c^7\,d^6\,\sqrt{x}\,{\left(-\frac{b^9}{16\,a^{13}\,d^4-64\,a^{12}\,b\,c\,d^3+96\,a^{11}\,b^2\,c^2\,d^2-64\,a^{10}\,b^3\,c^3\,d+16\,a^9\,b^4\,c^4}\right)}^{5/4}-128\,a^{18}\,b^3\,c^6\,d^7\,\sqrt{x}\,{\left(-\frac{b^9}{16\,a^{13}\,d^4-64\,a^{12}\,b\,c\,d^3+96\,a^{11}\,b^2\,c^2\,d^2-64\,a^{10}\,b^3\,c^3\,d+16\,a^9\,b^4\,c^4}\right)}^{5/4}+192\,a^{19}\,b^2\,c^5\,d^8\,\sqrt{x}\,{\left(-\frac{b^9}{16\,a^{13}\,d^4-64\,a^{12}\,b\,c\,d^3+96\,a^{11}\,b^2\,c^2\,d^2-64\,a^{10}\,b^3\,c^3\,d+16\,a^9\,b^4\,c^4}\right)}^{5/4}-128\,a^{12}\,b^9\,c^{12}\,d\,\sqrt{x}\,{\left(-\frac{b^9}{16\,a^{13}\,d^4-64\,a^{12}\,b\,c\,d^3+96\,a^{11}\,b^2\,c^2\,d^2-64\,a^{10}\,b^3\,c^3\,d+16\,a^9\,b^4\,c^4}\right)}^{5/4}-128\,a^{20}\,b\,c^4\,d^9\,\sqrt{x}\,{\left(-\frac{b^9}{16\,a^{13}\,d^4-64\,a^{12}\,b\,c\,d^3+96\,a^{11}\,b^2\,c^2\,d^2-64\,a^{10}\,b^3\,c^3\,d+16\,a^9\,b^4\,c^4}\right)}^{5/4}}{a^8\,b^8\,d^8+a^7\,b^9\,c\,d^7+a^6\,b^{10}\,c^2\,d^6+a^5\,b^{11}\,c^3\,d^5+a^4\,b^{12}\,c^4\,d^4+a^3\,b^{13}\,c^5\,d^3+a^2\,b^{14}\,c^6\,d^2+a\,b^{15}\,c^7\,d+b^{16}\,c^8}\right)\,{\left(-\frac{b^9}{16\,a^{13}\,d^4-64\,a^{12}\,b\,c\,d^3+96\,a^{11}\,b^2\,c^2\,d^2-64\,a^{10}\,b^3\,c^3\,d+16\,a^9\,b^4\,c^4}\right)}^{1/4}-\mathrm{atan}\left(\frac{a^{11}\,b^{10}\,c^{13}\,\sqrt{x}\,{\left(-\frac{b^9}{16\,a^{13}\,d^4-64\,a^{12}\,b\,c\,d^3+96\,a^{11}\,b^2\,c^2\,d^2-64\,a^{10}\,b^3\,c^3\,d+16\,a^9\,b^4\,c^4}\right)}^{5/4}\,32{}\mathrm{i}+a^{11}\,b^6\,d^9\,\sqrt{x}\,{\left(-\frac{b^9}{16\,a^{13}\,d^4-64\,a^{12}\,b\,c\,d^3+96\,a^{11}\,b^2\,c^2\,d^2-64\,a^{10}\,b^3\,c^3\,d+16\,a^9\,b^4\,c^4}\right)}^{1/4}\,2{}\mathrm{i}+a^{21}\,c^3\,d^{10}\,\sqrt{x}\,{\left(-\frac{b^9}{16\,a^{13}\,d^4-64\,a^{12}\,b\,c\,d^3+96\,a^{11}\,b^2\,c^2\,d^2-64\,a^{10}\,b^3\,c^3\,d+16\,a^9\,b^4\,c^4}\right)}^{5/4}\,32{}\mathrm{i}+a^8\,b^9\,c^3\,d^6\,\sqrt{x}\,{\left(-\frac{b^9}{16\,a^{13}\,d^4-64\,a^{12}\,b\,c\,d^3+96\,a^{11}\,b^2\,c^2\,d^2-64\,a^{10}\,b^3\,c^3\,d+16\,a^9\,b^4\,c^4}\right)}^{1/4}\,2{}\mathrm{i}+a^{13}\,b^8\,c^{11}\,d^2\,\sqrt{x}\,{\left(-\frac{b^9}{16\,a^{13}\,d^4-64\,a^{12}\,b\,c\,d^3+96\,a^{11}\,b^2\,c^2\,d^2-64\,a^{10}\,b^3\,c^3\,d+16\,a^9\,b^4\,c^4}\right)}^{5/4}\,192{}\mathrm{i}-a^{14}\,b^7\,c^{10}\,d^3\,\sqrt{x}\,{\left(-\frac{b^9}{16\,a^{13}\,d^4-64\,a^{12}\,b\,c\,d^3+96\,a^{11}\,b^2\,c^2\,d^2-64\,a^{10}\,b^3\,c^3\,d+16\,a^9\,b^4\,c^4}\right)}^{5/4}\,128{}\mathrm{i}+a^{15}\,b^6\,c^9\,d^4\,\sqrt{x}\,{\left(-\frac{b^9}{16\,a^{13}\,d^4-64\,a^{12}\,b\,c\,d^3+96\,a^{11}\,b^2\,c^2\,d^2-64\,a^{10}\,b^3\,c^3\,d+16\,a^9\,b^4\,c^4}\right)}^{5/4}\,32{}\mathrm{i}+a^{17}\,b^4\,c^7\,d^6\,\sqrt{x}\,{\left(-\frac{b^9}{16\,a^{13}\,d^4-64\,a^{12}\,b\,c\,d^3+96\,a^{11}\,b^2\,c^2\,d^2-64\,a^{10}\,b^3\,c^3\,d+16\,a^9\,b^4\,c^4}\right)}^{5/4}\,32{}\mathrm{i}-a^{18}\,b^3\,c^6\,d^7\,\sqrt{x}\,{\left(-\frac{b^9}{16\,a^{13}\,d^4-64\,a^{12}\,b\,c\,d^3+96\,a^{11}\,b^2\,c^2\,d^2-64\,a^{10}\,b^3\,c^3\,d+16\,a^9\,b^4\,c^4}\right)}^{5/4}\,128{}\mathrm{i}+a^{19}\,b^2\,c^5\,d^8\,\sqrt{x}\,{\left(-\frac{b^9}{16\,a^{13}\,d^4-64\,a^{12}\,b\,c\,d^3+96\,a^{11}\,b^2\,c^2\,d^2-64\,a^{10}\,b^3\,c^3\,d+16\,a^9\,b^4\,c^4}\right)}^{5/4}\,192{}\mathrm{i}-a^{12}\,b^9\,c^{12}\,d\,\sqrt{x}\,{\left(-\frac{b^9}{16\,a^{13}\,d^4-64\,a^{12}\,b\,c\,d^3+96\,a^{11}\,b^2\,c^2\,d^2-64\,a^{10}\,b^3\,c^3\,d+16\,a^9\,b^4\,c^4}\right)}^{5/4}\,128{}\mathrm{i}-a^{20}\,b\,c^4\,d^9\,\sqrt{x}\,{\left(-\frac{b^9}{16\,a^{13}\,d^4-64\,a^{12}\,b\,c\,d^3+96\,a^{11}\,b^2\,c^2\,d^2-64\,a^{10}\,b^3\,c^3\,d+16\,a^9\,b^4\,c^4}\right)}^{5/4}\,128{}\mathrm{i}}{a^8\,b^8\,d^8+a^7\,b^9\,c\,d^7+a^6\,b^{10}\,c^2\,d^6+a^5\,b^{11}\,c^3\,d^5+a^4\,b^{12}\,c^4\,d^4+a^3\,b^{13}\,c^5\,d^3+a^2\,b^{14}\,c^6\,d^2+a\,b^{15}\,c^7\,d+b^{16}\,c^8}\right)\,{\left(-\frac{b^9}{16\,a^{13}\,d^4-64\,a^{12}\,b\,c\,d^3+96\,a^{11}\,b^2\,c^2\,d^2-64\,a^{10}\,b^3\,c^3\,d+16\,a^9\,b^4\,c^4}\right)}^{1/4}\,2{}\mathrm{i}-\frac{\frac{2}{5\,a\,c}-\frac{2\,x^2\,\left(a\,d+b\,c\right)}{a^2\,c^2}}{x^{5/2}}-2\,\mathrm{atan}\left(\frac{32\,a^3\,b^{10}\,c^{21}\,\sqrt{x}\,{\left(-\frac{d^9}{16\,a^4\,c^9\,d^4-64\,a^3\,b\,c^{10}\,d^3+96\,a^2\,b^2\,c^{11}\,d^2-64\,a\,b^3\,c^{12}\,d+16\,b^4\,c^{13}}\right)}^{5/4}+32\,a^{13}\,c^{11}\,d^{10}\,\sqrt{x}\,{\left(-\frac{d^9}{16\,a^4\,c^9\,d^4-64\,a^3\,b\,c^{10}\,d^3+96\,a^2\,b^2\,c^{11}\,d^2-64\,a\,b^3\,c^{12}\,d+16\,b^4\,c^{13}}\right)}^{5/4}+2\,b^9\,c^{11}\,d^6\,\sqrt{x}\,{\left(-\frac{d^9}{16\,a^4\,c^9\,d^4-64\,a^3\,b\,c^{10}\,d^3+96\,a^2\,b^2\,c^{11}\,d^2-64\,a\,b^3\,c^{12}\,d+16\,b^4\,c^{13}}\right)}^{1/4}+2\,a^3\,b^6\,c^8\,d^9\,\sqrt{x}\,{\left(-\frac{d^9}{16\,a^4\,c^9\,d^4-64\,a^3\,b\,c^{10}\,d^3+96\,a^2\,b^2\,c^{11}\,d^2-64\,a\,b^3\,c^{12}\,d+16\,b^4\,c^{13}}\right)}^{1/4}+192\,a^5\,b^8\,c^{19}\,d^2\,\sqrt{x}\,{\left(-\frac{d^9}{16\,a^4\,c^9\,d^4-64\,a^3\,b\,c^{10}\,d^3+96\,a^2\,b^2\,c^{11}\,d^2-64\,a\,b^3\,c^{12}\,d+16\,b^4\,c^{13}}\right)}^{5/4}-128\,a^6\,b^7\,c^{18}\,d^3\,\sqrt{x}\,{\left(-\frac{d^9}{16\,a^4\,c^9\,d^4-64\,a^3\,b\,c^{10}\,d^3+96\,a^2\,b^2\,c^{11}\,d^2-64\,a\,b^3\,c^{12}\,d+16\,b^4\,c^{13}}\right)}^{5/4}+32\,a^7\,b^6\,c^{17}\,d^4\,\sqrt{x}\,{\left(-\frac{d^9}{16\,a^4\,c^9\,d^4-64\,a^3\,b\,c^{10}\,d^3+96\,a^2\,b^2\,c^{11}\,d^2-64\,a\,b^3\,c^{12}\,d+16\,b^4\,c^{13}}\right)}^{5/4}+32\,a^9\,b^4\,c^{15}\,d^6\,\sqrt{x}\,{\left(-\frac{d^9}{16\,a^4\,c^9\,d^4-64\,a^3\,b\,c^{10}\,d^3+96\,a^2\,b^2\,c^{11}\,d^2-64\,a\,b^3\,c^{12}\,d+16\,b^4\,c^{13}}\right)}^{5/4}-128\,a^{10}\,b^3\,c^{14}\,d^7\,\sqrt{x}\,{\left(-\frac{d^9}{16\,a^4\,c^9\,d^4-64\,a^3\,b\,c^{10}\,d^3+96\,a^2\,b^2\,c^{11}\,d^2-64\,a\,b^3\,c^{12}\,d+16\,b^4\,c^{13}}\right)}^{5/4}+192\,a^{11}\,b^2\,c^{13}\,d^8\,\sqrt{x}\,{\left(-\frac{d^9}{16\,a^4\,c^9\,d^4-64\,a^3\,b\,c^{10}\,d^3+96\,a^2\,b^2\,c^{11}\,d^2-64\,a\,b^3\,c^{12}\,d+16\,b^4\,c^{13}}\right)}^{5/4}-128\,a^4\,b^9\,c^{20}\,d\,\sqrt{x}\,{\left(-\frac{d^9}{16\,a^4\,c^9\,d^4-64\,a^3\,b\,c^{10}\,d^3+96\,a^2\,b^2\,c^{11}\,d^2-64\,a\,b^3\,c^{12}\,d+16\,b^4\,c^{13}}\right)}^{5/4}-128\,a^{12}\,b\,c^{12}\,d^9\,\sqrt{x}\,{\left(-\frac{d^9}{16\,a^4\,c^9\,d^4-64\,a^3\,b\,c^{10}\,d^3+96\,a^2\,b^2\,c^{11}\,d^2-64\,a\,b^3\,c^{12}\,d+16\,b^4\,c^{13}}\right)}^{5/4}}{a^8\,d^{16}+a^7\,b\,c\,d^{15}+a^6\,b^2\,c^2\,d^{14}+a^5\,b^3\,c^3\,d^{13}+a^4\,b^4\,c^4\,d^{12}+a^3\,b^5\,c^5\,d^{11}+a^2\,b^6\,c^6\,d^{10}+a\,b^7\,c^7\,d^9+b^8\,c^8\,d^8}\right)\,{\left(-\frac{d^9}{16\,a^4\,c^9\,d^4-64\,a^3\,b\,c^{10}\,d^3+96\,a^2\,b^2\,c^{11}\,d^2-64\,a\,b^3\,c^{12}\,d+16\,b^4\,c^{13}}\right)}^{1/4}-\mathrm{atan}\left(\frac{a^3\,b^{10}\,c^{21}\,\sqrt{x}\,{\left(-\frac{d^9}{16\,a^4\,c^9\,d^4-64\,a^3\,b\,c^{10}\,d^3+96\,a^2\,b^2\,c^{11}\,d^2-64\,a\,b^3\,c^{12}\,d+16\,b^4\,c^{13}}\right)}^{5/4}\,32{}\mathrm{i}+a^{13}\,c^{11}\,d^{10}\,\sqrt{x}\,{\left(-\frac{d^9}{16\,a^4\,c^9\,d^4-64\,a^3\,b\,c^{10}\,d^3+96\,a^2\,b^2\,c^{11}\,d^2-64\,a\,b^3\,c^{12}\,d+16\,b^4\,c^{13}}\right)}^{5/4}\,32{}\mathrm{i}+b^9\,c^{11}\,d^6\,\sqrt{x}\,{\left(-\frac{d^9}{16\,a^4\,c^9\,d^4-64\,a^3\,b\,c^{10}\,d^3+96\,a^2\,b^2\,c^{11}\,d^2-64\,a\,b^3\,c^{12}\,d+16\,b^4\,c^{13}}\right)}^{1/4}\,2{}\mathrm{i}+a^3\,b^6\,c^8\,d^9\,\sqrt{x}\,{\left(-\frac{d^9}{16\,a^4\,c^9\,d^4-64\,a^3\,b\,c^{10}\,d^3+96\,a^2\,b^2\,c^{11}\,d^2-64\,a\,b^3\,c^{12}\,d+16\,b^4\,c^{13}}\right)}^{1/4}\,2{}\mathrm{i}+a^5\,b^8\,c^{19}\,d^2\,\sqrt{x}\,{\left(-\frac{d^9}{16\,a^4\,c^9\,d^4-64\,a^3\,b\,c^{10}\,d^3+96\,a^2\,b^2\,c^{11}\,d^2-64\,a\,b^3\,c^{12}\,d+16\,b^4\,c^{13}}\right)}^{5/4}\,192{}\mathrm{i}-a^6\,b^7\,c^{18}\,d^3\,\sqrt{x}\,{\left(-\frac{d^9}{16\,a^4\,c^9\,d^4-64\,a^3\,b\,c^{10}\,d^3+96\,a^2\,b^2\,c^{11}\,d^2-64\,a\,b^3\,c^{12}\,d+16\,b^4\,c^{13}}\right)}^{5/4}\,128{}\mathrm{i}+a^7\,b^6\,c^{17}\,d^4\,\sqrt{x}\,{\left(-\frac{d^9}{16\,a^4\,c^9\,d^4-64\,a^3\,b\,c^{10}\,d^3+96\,a^2\,b^2\,c^{11}\,d^2-64\,a\,b^3\,c^{12}\,d+16\,b^4\,c^{13}}\right)}^{5/4}\,32{}\mathrm{i}+a^9\,b^4\,c^{15}\,d^6\,\sqrt{x}\,{\left(-\frac{d^9}{16\,a^4\,c^9\,d^4-64\,a^3\,b\,c^{10}\,d^3+96\,a^2\,b^2\,c^{11}\,d^2-64\,a\,b^3\,c^{12}\,d+16\,b^4\,c^{13}}\right)}^{5/4}\,32{}\mathrm{i}-a^{10}\,b^3\,c^{14}\,d^7\,\sqrt{x}\,{\left(-\frac{d^9}{16\,a^4\,c^9\,d^4-64\,a^3\,b\,c^{10}\,d^3+96\,a^2\,b^2\,c^{11}\,d^2-64\,a\,b^3\,c^{12}\,d+16\,b^4\,c^{13}}\right)}^{5/4}\,128{}\mathrm{i}+a^{11}\,b^2\,c^{13}\,d^8\,\sqrt{x}\,{\left(-\frac{d^9}{16\,a^4\,c^9\,d^4-64\,a^3\,b\,c^{10}\,d^3+96\,a^2\,b^2\,c^{11}\,d^2-64\,a\,b^3\,c^{12}\,d+16\,b^4\,c^{13}}\right)}^{5/4}\,192{}\mathrm{i}-a^4\,b^9\,c^{20}\,d\,\sqrt{x}\,{\left(-\frac{d^9}{16\,a^4\,c^9\,d^4-64\,a^3\,b\,c^{10}\,d^3+96\,a^2\,b^2\,c^{11}\,d^2-64\,a\,b^3\,c^{12}\,d+16\,b^4\,c^{13}}\right)}^{5/4}\,128{}\mathrm{i}-a^{12}\,b\,c^{12}\,d^9\,\sqrt{x}\,{\left(-\frac{d^9}{16\,a^4\,c^9\,d^4-64\,a^3\,b\,c^{10}\,d^3+96\,a^2\,b^2\,c^{11}\,d^2-64\,a\,b^3\,c^{12}\,d+16\,b^4\,c^{13}}\right)}^{5/4}\,128{}\mathrm{i}}{a^8\,d^{16}+a^7\,b\,c\,d^{15}+a^6\,b^2\,c^2\,d^{14}+a^5\,b^3\,c^3\,d^{13}+a^4\,b^4\,c^4\,d^{12}+a^3\,b^5\,c^5\,d^{11}+a^2\,b^6\,c^6\,d^{10}+a\,b^7\,c^7\,d^9+b^8\,c^8\,d^8}\right)\,{\left(-\frac{d^9}{16\,a^4\,c^9\,d^4-64\,a^3\,b\,c^{10}\,d^3+96\,a^2\,b^2\,c^{11}\,d^2-64\,a\,b^3\,c^{12}\,d+16\,b^4\,c^{13}}\right)}^{1/4}\,2{}\mathrm{i}","Not used",1,"- 2*atan((32*a^11*b^10*c^13*x^(1/2)*(-b^9/(16*a^13*d^4 + 16*a^9*b^4*c^4 - 64*a^10*b^3*c^3*d + 96*a^11*b^2*c^2*d^2 - 64*a^12*b*c*d^3))^(5/4) + 2*a^11*b^6*d^9*x^(1/2)*(-b^9/(16*a^13*d^4 + 16*a^9*b^4*c^4 - 64*a^10*b^3*c^3*d + 96*a^11*b^2*c^2*d^2 - 64*a^12*b*c*d^3))^(1/4) + 32*a^21*c^3*d^10*x^(1/2)*(-b^9/(16*a^13*d^4 + 16*a^9*b^4*c^4 - 64*a^10*b^3*c^3*d + 96*a^11*b^2*c^2*d^2 - 64*a^12*b*c*d^3))^(5/4) + 2*a^8*b^9*c^3*d^6*x^(1/2)*(-b^9/(16*a^13*d^4 + 16*a^9*b^4*c^4 - 64*a^10*b^3*c^3*d + 96*a^11*b^2*c^2*d^2 - 64*a^12*b*c*d^3))^(1/4) + 192*a^13*b^8*c^11*d^2*x^(1/2)*(-b^9/(16*a^13*d^4 + 16*a^9*b^4*c^4 - 64*a^10*b^3*c^3*d + 96*a^11*b^2*c^2*d^2 - 64*a^12*b*c*d^3))^(5/4) - 128*a^14*b^7*c^10*d^3*x^(1/2)*(-b^9/(16*a^13*d^4 + 16*a^9*b^4*c^4 - 64*a^10*b^3*c^3*d + 96*a^11*b^2*c^2*d^2 - 64*a^12*b*c*d^3))^(5/4) + 32*a^15*b^6*c^9*d^4*x^(1/2)*(-b^9/(16*a^13*d^4 + 16*a^9*b^4*c^4 - 64*a^10*b^3*c^3*d + 96*a^11*b^2*c^2*d^2 - 64*a^12*b*c*d^3))^(5/4) + 32*a^17*b^4*c^7*d^6*x^(1/2)*(-b^9/(16*a^13*d^4 + 16*a^9*b^4*c^4 - 64*a^10*b^3*c^3*d + 96*a^11*b^2*c^2*d^2 - 64*a^12*b*c*d^3))^(5/4) - 128*a^18*b^3*c^6*d^7*x^(1/2)*(-b^9/(16*a^13*d^4 + 16*a^9*b^4*c^4 - 64*a^10*b^3*c^3*d + 96*a^11*b^2*c^2*d^2 - 64*a^12*b*c*d^3))^(5/4) + 192*a^19*b^2*c^5*d^8*x^(1/2)*(-b^9/(16*a^13*d^4 + 16*a^9*b^4*c^4 - 64*a^10*b^3*c^3*d + 96*a^11*b^2*c^2*d^2 - 64*a^12*b*c*d^3))^(5/4) - 128*a^12*b^9*c^12*d*x^(1/2)*(-b^9/(16*a^13*d^4 + 16*a^9*b^4*c^4 - 64*a^10*b^3*c^3*d + 96*a^11*b^2*c^2*d^2 - 64*a^12*b*c*d^3))^(5/4) - 128*a^20*b*c^4*d^9*x^(1/2)*(-b^9/(16*a^13*d^4 + 16*a^9*b^4*c^4 - 64*a^10*b^3*c^3*d + 96*a^11*b^2*c^2*d^2 - 64*a^12*b*c*d^3))^(5/4))/(b^16*c^8 + a^8*b^8*d^8 + a^7*b^9*c*d^7 + a^2*b^14*c^6*d^2 + a^3*b^13*c^5*d^3 + a^4*b^12*c^4*d^4 + a^5*b^11*c^3*d^5 + a^6*b^10*c^2*d^6 + a*b^15*c^7*d))*(-b^9/(16*a^13*d^4 + 16*a^9*b^4*c^4 - 64*a^10*b^3*c^3*d + 96*a^11*b^2*c^2*d^2 - 64*a^12*b*c*d^3))^(1/4) - atan((a^11*b^10*c^13*x^(1/2)*(-b^9/(16*a^13*d^4 + 16*a^9*b^4*c^4 - 64*a^10*b^3*c^3*d + 96*a^11*b^2*c^2*d^2 - 64*a^12*b*c*d^3))^(5/4)*32i + a^11*b^6*d^9*x^(1/2)*(-b^9/(16*a^13*d^4 + 16*a^9*b^4*c^4 - 64*a^10*b^3*c^3*d + 96*a^11*b^2*c^2*d^2 - 64*a^12*b*c*d^3))^(1/4)*2i + a^21*c^3*d^10*x^(1/2)*(-b^9/(16*a^13*d^4 + 16*a^9*b^4*c^4 - 64*a^10*b^3*c^3*d + 96*a^11*b^2*c^2*d^2 - 64*a^12*b*c*d^3))^(5/4)*32i + a^8*b^9*c^3*d^6*x^(1/2)*(-b^9/(16*a^13*d^4 + 16*a^9*b^4*c^4 - 64*a^10*b^3*c^3*d + 96*a^11*b^2*c^2*d^2 - 64*a^12*b*c*d^3))^(1/4)*2i + a^13*b^8*c^11*d^2*x^(1/2)*(-b^9/(16*a^13*d^4 + 16*a^9*b^4*c^4 - 64*a^10*b^3*c^3*d + 96*a^11*b^2*c^2*d^2 - 64*a^12*b*c*d^3))^(5/4)*192i - a^14*b^7*c^10*d^3*x^(1/2)*(-b^9/(16*a^13*d^4 + 16*a^9*b^4*c^4 - 64*a^10*b^3*c^3*d + 96*a^11*b^2*c^2*d^2 - 64*a^12*b*c*d^3))^(5/4)*128i + a^15*b^6*c^9*d^4*x^(1/2)*(-b^9/(16*a^13*d^4 + 16*a^9*b^4*c^4 - 64*a^10*b^3*c^3*d + 96*a^11*b^2*c^2*d^2 - 64*a^12*b*c*d^3))^(5/4)*32i + a^17*b^4*c^7*d^6*x^(1/2)*(-b^9/(16*a^13*d^4 + 16*a^9*b^4*c^4 - 64*a^10*b^3*c^3*d + 96*a^11*b^2*c^2*d^2 - 64*a^12*b*c*d^3))^(5/4)*32i - a^18*b^3*c^6*d^7*x^(1/2)*(-b^9/(16*a^13*d^4 + 16*a^9*b^4*c^4 - 64*a^10*b^3*c^3*d + 96*a^11*b^2*c^2*d^2 - 64*a^12*b*c*d^3))^(5/4)*128i + a^19*b^2*c^5*d^8*x^(1/2)*(-b^9/(16*a^13*d^4 + 16*a^9*b^4*c^4 - 64*a^10*b^3*c^3*d + 96*a^11*b^2*c^2*d^2 - 64*a^12*b*c*d^3))^(5/4)*192i - a^12*b^9*c^12*d*x^(1/2)*(-b^9/(16*a^13*d^4 + 16*a^9*b^4*c^4 - 64*a^10*b^3*c^3*d + 96*a^11*b^2*c^2*d^2 - 64*a^12*b*c*d^3))^(5/4)*128i - a^20*b*c^4*d^9*x^(1/2)*(-b^9/(16*a^13*d^4 + 16*a^9*b^4*c^4 - 64*a^10*b^3*c^3*d + 96*a^11*b^2*c^2*d^2 - 64*a^12*b*c*d^3))^(5/4)*128i)/(b^16*c^8 + a^8*b^8*d^8 + a^7*b^9*c*d^7 + a^2*b^14*c^6*d^2 + a^3*b^13*c^5*d^3 + a^4*b^12*c^4*d^4 + a^5*b^11*c^3*d^5 + a^6*b^10*c^2*d^6 + a*b^15*c^7*d))*(-b^9/(16*a^13*d^4 + 16*a^9*b^4*c^4 - 64*a^10*b^3*c^3*d + 96*a^11*b^2*c^2*d^2 - 64*a^12*b*c*d^3))^(1/4)*2i - (2/(5*a*c) - (2*x^2*(a*d + b*c))/(a^2*c^2))/x^(5/2) - 2*atan((32*a^3*b^10*c^21*x^(1/2)*(-d^9/(16*b^4*c^13 + 16*a^4*c^9*d^4 - 64*a^3*b*c^10*d^3 + 96*a^2*b^2*c^11*d^2 - 64*a*b^3*c^12*d))^(5/4) + 32*a^13*c^11*d^10*x^(1/2)*(-d^9/(16*b^4*c^13 + 16*a^4*c^9*d^4 - 64*a^3*b*c^10*d^3 + 96*a^2*b^2*c^11*d^2 - 64*a*b^3*c^12*d))^(5/4) + 2*b^9*c^11*d^6*x^(1/2)*(-d^9/(16*b^4*c^13 + 16*a^4*c^9*d^4 - 64*a^3*b*c^10*d^3 + 96*a^2*b^2*c^11*d^2 - 64*a*b^3*c^12*d))^(1/4) + 2*a^3*b^6*c^8*d^9*x^(1/2)*(-d^9/(16*b^4*c^13 + 16*a^4*c^9*d^4 - 64*a^3*b*c^10*d^3 + 96*a^2*b^2*c^11*d^2 - 64*a*b^3*c^12*d))^(1/4) + 192*a^5*b^8*c^19*d^2*x^(1/2)*(-d^9/(16*b^4*c^13 + 16*a^4*c^9*d^4 - 64*a^3*b*c^10*d^3 + 96*a^2*b^2*c^11*d^2 - 64*a*b^3*c^12*d))^(5/4) - 128*a^6*b^7*c^18*d^3*x^(1/2)*(-d^9/(16*b^4*c^13 + 16*a^4*c^9*d^4 - 64*a^3*b*c^10*d^3 + 96*a^2*b^2*c^11*d^2 - 64*a*b^3*c^12*d))^(5/4) + 32*a^7*b^6*c^17*d^4*x^(1/2)*(-d^9/(16*b^4*c^13 + 16*a^4*c^9*d^4 - 64*a^3*b*c^10*d^3 + 96*a^2*b^2*c^11*d^2 - 64*a*b^3*c^12*d))^(5/4) + 32*a^9*b^4*c^15*d^6*x^(1/2)*(-d^9/(16*b^4*c^13 + 16*a^4*c^9*d^4 - 64*a^3*b*c^10*d^3 + 96*a^2*b^2*c^11*d^2 - 64*a*b^3*c^12*d))^(5/4) - 128*a^10*b^3*c^14*d^7*x^(1/2)*(-d^9/(16*b^4*c^13 + 16*a^4*c^9*d^4 - 64*a^3*b*c^10*d^3 + 96*a^2*b^2*c^11*d^2 - 64*a*b^3*c^12*d))^(5/4) + 192*a^11*b^2*c^13*d^8*x^(1/2)*(-d^9/(16*b^4*c^13 + 16*a^4*c^9*d^4 - 64*a^3*b*c^10*d^3 + 96*a^2*b^2*c^11*d^2 - 64*a*b^3*c^12*d))^(5/4) - 128*a^4*b^9*c^20*d*x^(1/2)*(-d^9/(16*b^4*c^13 + 16*a^4*c^9*d^4 - 64*a^3*b*c^10*d^3 + 96*a^2*b^2*c^11*d^2 - 64*a*b^3*c^12*d))^(5/4) - 128*a^12*b*c^12*d^9*x^(1/2)*(-d^9/(16*b^4*c^13 + 16*a^4*c^9*d^4 - 64*a^3*b*c^10*d^3 + 96*a^2*b^2*c^11*d^2 - 64*a*b^3*c^12*d))^(5/4))/(a^8*d^16 + b^8*c^8*d^8 + a*b^7*c^7*d^9 + a^2*b^6*c^6*d^10 + a^3*b^5*c^5*d^11 + a^4*b^4*c^4*d^12 + a^5*b^3*c^3*d^13 + a^6*b^2*c^2*d^14 + a^7*b*c*d^15))*(-d^9/(16*b^4*c^13 + 16*a^4*c^9*d^4 - 64*a^3*b*c^10*d^3 + 96*a^2*b^2*c^11*d^2 - 64*a*b^3*c^12*d))^(1/4) - atan((a^3*b^10*c^21*x^(1/2)*(-d^9/(16*b^4*c^13 + 16*a^4*c^9*d^4 - 64*a^3*b*c^10*d^3 + 96*a^2*b^2*c^11*d^2 - 64*a*b^3*c^12*d))^(5/4)*32i + a^13*c^11*d^10*x^(1/2)*(-d^9/(16*b^4*c^13 + 16*a^4*c^9*d^4 - 64*a^3*b*c^10*d^3 + 96*a^2*b^2*c^11*d^2 - 64*a*b^3*c^12*d))^(5/4)*32i + b^9*c^11*d^6*x^(1/2)*(-d^9/(16*b^4*c^13 + 16*a^4*c^9*d^4 - 64*a^3*b*c^10*d^3 + 96*a^2*b^2*c^11*d^2 - 64*a*b^3*c^12*d))^(1/4)*2i + a^3*b^6*c^8*d^9*x^(1/2)*(-d^9/(16*b^4*c^13 + 16*a^4*c^9*d^4 - 64*a^3*b*c^10*d^3 + 96*a^2*b^2*c^11*d^2 - 64*a*b^3*c^12*d))^(1/4)*2i + a^5*b^8*c^19*d^2*x^(1/2)*(-d^9/(16*b^4*c^13 + 16*a^4*c^9*d^4 - 64*a^3*b*c^10*d^3 + 96*a^2*b^2*c^11*d^2 - 64*a*b^3*c^12*d))^(5/4)*192i - a^6*b^7*c^18*d^3*x^(1/2)*(-d^9/(16*b^4*c^13 + 16*a^4*c^9*d^4 - 64*a^3*b*c^10*d^3 + 96*a^2*b^2*c^11*d^2 - 64*a*b^3*c^12*d))^(5/4)*128i + a^7*b^6*c^17*d^4*x^(1/2)*(-d^9/(16*b^4*c^13 + 16*a^4*c^9*d^4 - 64*a^3*b*c^10*d^3 + 96*a^2*b^2*c^11*d^2 - 64*a*b^3*c^12*d))^(5/4)*32i + a^9*b^4*c^15*d^6*x^(1/2)*(-d^9/(16*b^4*c^13 + 16*a^4*c^9*d^4 - 64*a^3*b*c^10*d^3 + 96*a^2*b^2*c^11*d^2 - 64*a*b^3*c^12*d))^(5/4)*32i - a^10*b^3*c^14*d^7*x^(1/2)*(-d^9/(16*b^4*c^13 + 16*a^4*c^9*d^4 - 64*a^3*b*c^10*d^3 + 96*a^2*b^2*c^11*d^2 - 64*a*b^3*c^12*d))^(5/4)*128i + a^11*b^2*c^13*d^8*x^(1/2)*(-d^9/(16*b^4*c^13 + 16*a^4*c^9*d^4 - 64*a^3*b*c^10*d^3 + 96*a^2*b^2*c^11*d^2 - 64*a*b^3*c^12*d))^(5/4)*192i - a^4*b^9*c^20*d*x^(1/2)*(-d^9/(16*b^4*c^13 + 16*a^4*c^9*d^4 - 64*a^3*b*c^10*d^3 + 96*a^2*b^2*c^11*d^2 - 64*a*b^3*c^12*d))^(5/4)*128i - a^12*b*c^12*d^9*x^(1/2)*(-d^9/(16*b^4*c^13 + 16*a^4*c^9*d^4 - 64*a^3*b*c^10*d^3 + 96*a^2*b^2*c^11*d^2 - 64*a*b^3*c^12*d))^(5/4)*128i)/(a^8*d^16 + b^8*c^8*d^8 + a*b^7*c^7*d^9 + a^2*b^6*c^6*d^10 + a^3*b^5*c^5*d^11 + a^4*b^4*c^4*d^12 + a^5*b^3*c^3*d^13 + a^6*b^2*c^2*d^14 + a^7*b*c*d^15))*(-d^9/(16*b^4*c^13 + 16*a^4*c^9*d^4 - 64*a^3*b*c^10*d^3 + 96*a^2*b^2*c^11*d^2 - 64*a*b^3*c^12*d))^(1/4)*2i","B"
470,1,22978,570,3.254487,"\text{Not used}","int(x^(11/2)/((a + b*x^2)*(c + d*x^2)^2),x)","2\,\mathrm{atan}\left(\frac{\left(-\frac{\sqrt{x}\,\left(1296\,a^{14}\,c^4\,d^8-1440\,a^{13}\,b\,c^5\,d^7+400\,a^{12}\,b^2\,c^6\,d^6+6561\,a^{10}\,b^4\,c^8\,d^4-14580\,a^9\,b^5\,c^9\,d^3+12150\,a^8\,b^6\,c^{10}\,d^2-4500\,a^7\,b^7\,c^{11}\,d+625\,a^6\,b^8\,c^{12}\right)}{a^6\,b\,d^{11}-6\,a^5\,b^2\,c\,d^{10}+15\,a^4\,b^3\,c^2\,d^9-20\,a^3\,b^4\,c^3\,d^8+15\,a^2\,b^5\,c^4\,d^7-6\,a\,b^6\,c^5\,d^6+b^7\,c^6\,d^5}+{\left(-\frac{a^9}{16\,a^8\,b^5\,d^8-128\,a^7\,b^6\,c\,d^7+448\,a^6\,b^7\,c^2\,d^6-896\,a^5\,b^8\,c^3\,d^5+1120\,a^4\,b^9\,c^4\,d^4-896\,a^3\,b^{10}\,c^5\,d^3+448\,a^2\,b^{11}\,c^6\,d^2-128\,a\,b^{12}\,c^7\,d+16\,b^{13}\,c^8}\right)}^{1/4}\,\left(\frac{2\,\left(576\,a^{12}\,c^3\,d^8+256\,a^{11}\,b\,c^4\,d^7+256\,a^{10}\,b^2\,c^5\,d^6+256\,a^9\,b^3\,c^6\,d^5+256\,a^8\,b^4\,c^7\,d^4-6305\,a^7\,b^5\,c^8\,d^3+8275\,a^6\,b^6\,c^9\,d^2-3875\,a^5\,b^7\,c^{10}\,d+625\,a^4\,b^8\,c^{11}\right)}{a^3\,b\,d^8-3\,a^2\,b^2\,c\,d^7+3\,a\,b^3\,c^2\,d^6-b^4\,c^3\,d^5}+{\left(-\frac{a^9}{16\,a^8\,b^5\,d^8-128\,a^7\,b^6\,c\,d^7+448\,a^6\,b^7\,c^2\,d^6-896\,a^5\,b^8\,c^3\,d^5+1120\,a^4\,b^9\,c^4\,d^4-896\,a^3\,b^{10}\,c^5\,d^3+448\,a^2\,b^{11}\,c^6\,d^2-128\,a\,b^{12}\,c^7\,d+16\,b^{13}\,c^8}\right)}^{3/4}\,\left(\frac{\sqrt{x}\,\left(4096\,a^{14}\,b^4\,c^3\,d^{17}-12032\,a^{13}\,b^5\,c^4\,d^{16}-74240\,a^{12}\,b^6\,c^5\,d^{15}+541952\,a^{11}\,b^7\,c^6\,d^{14}-1570816\,a^{10}\,b^8\,c^7\,d^{13}+2691584\,a^9\,b^9\,c^8\,d^{12}-3017728\,a^8\,b^{10}\,c^9\,d^{11}+2286080\,a^7\,b^{11}\,c^{10}\,d^{10}-1165312\,a^6\,b^{12}\,c^{11}\,d^9+384256\,a^5\,b^{13}\,c^{12}\,d^8-74240\,a^4\,b^{14}\,c^{13}\,d^7+6400\,a^3\,b^{15}\,c^{14}\,d^6\right)}{a^6\,b\,d^{11}-6\,a^5\,b^2\,c\,d^{10}+15\,a^4\,b^3\,c^2\,d^9-20\,a^3\,b^4\,c^3\,d^8+15\,a^2\,b^5\,c^4\,d^7-6\,a\,b^6\,c^5\,d^6+b^7\,c^6\,d^5}-\frac{{\left(-\frac{a^9}{16\,a^8\,b^5\,d^8-128\,a^7\,b^6\,c\,d^7+448\,a^6\,b^7\,c^2\,d^6-896\,a^5\,b^8\,c^3\,d^5+1120\,a^4\,b^9\,c^4\,d^4-896\,a^3\,b^{10}\,c^5\,d^3+448\,a^2\,b^{11}\,c^6\,d^2-128\,a\,b^{12}\,c^7\,d+16\,b^{13}\,c^8}\right)}^{1/4}\,\left(5120\,a^{11}\,b^5\,c^3\,d^{16}-40960\,a^{10}\,b^6\,c^4\,d^{15}+143360\,a^9\,b^7\,c^5\,d^{14}-286720\,a^8\,b^8\,c^6\,d^{13}+358400\,a^7\,b^9\,c^7\,d^{12}-286720\,a^6\,b^{10}\,c^8\,d^{11}+143360\,a^5\,b^{11}\,c^9\,d^{10}-40960\,a^4\,b^{12}\,c^{10}\,d^9+5120\,a^3\,b^{13}\,c^{11}\,d^8\right)\,2{}\mathrm{i}}{a^3\,b\,d^8-3\,a^2\,b^2\,c\,d^7+3\,a\,b^3\,c^2\,d^6-b^4\,c^3\,d^5}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{a^9}{16\,a^8\,b^5\,d^8-128\,a^7\,b^6\,c\,d^7+448\,a^6\,b^7\,c^2\,d^6-896\,a^5\,b^8\,c^3\,d^5+1120\,a^4\,b^9\,c^4\,d^4-896\,a^3\,b^{10}\,c^5\,d^3+448\,a^2\,b^{11}\,c^6\,d^2-128\,a\,b^{12}\,c^7\,d+16\,b^{13}\,c^8}\right)}^{1/4}+\left(-\frac{\sqrt{x}\,\left(1296\,a^{14}\,c^4\,d^8-1440\,a^{13}\,b\,c^5\,d^7+400\,a^{12}\,b^2\,c^6\,d^6+6561\,a^{10}\,b^4\,c^8\,d^4-14580\,a^9\,b^5\,c^9\,d^3+12150\,a^8\,b^6\,c^{10}\,d^2-4500\,a^7\,b^7\,c^{11}\,d+625\,a^6\,b^8\,c^{12}\right)}{a^6\,b\,d^{11}-6\,a^5\,b^2\,c\,d^{10}+15\,a^4\,b^3\,c^2\,d^9-20\,a^3\,b^4\,c^3\,d^8+15\,a^2\,b^5\,c^4\,d^7-6\,a\,b^6\,c^5\,d^6+b^7\,c^6\,d^5}+{\left(-\frac{a^9}{16\,a^8\,b^5\,d^8-128\,a^7\,b^6\,c\,d^7+448\,a^6\,b^7\,c^2\,d^6-896\,a^5\,b^8\,c^3\,d^5+1120\,a^4\,b^9\,c^4\,d^4-896\,a^3\,b^{10}\,c^5\,d^3+448\,a^2\,b^{11}\,c^6\,d^2-128\,a\,b^{12}\,c^7\,d+16\,b^{13}\,c^8}\right)}^{1/4}\,\left(-\frac{2\,\left(576\,a^{12}\,c^3\,d^8+256\,a^{11}\,b\,c^4\,d^7+256\,a^{10}\,b^2\,c^5\,d^6+256\,a^9\,b^3\,c^6\,d^5+256\,a^8\,b^4\,c^7\,d^4-6305\,a^7\,b^5\,c^8\,d^3+8275\,a^6\,b^6\,c^9\,d^2-3875\,a^5\,b^7\,c^{10}\,d+625\,a^4\,b^8\,c^{11}\right)}{a^3\,b\,d^8-3\,a^2\,b^2\,c\,d^7+3\,a\,b^3\,c^2\,d^6-b^4\,c^3\,d^5}+{\left(-\frac{a^9}{16\,a^8\,b^5\,d^8-128\,a^7\,b^6\,c\,d^7+448\,a^6\,b^7\,c^2\,d^6-896\,a^5\,b^8\,c^3\,d^5+1120\,a^4\,b^9\,c^4\,d^4-896\,a^3\,b^{10}\,c^5\,d^3+448\,a^2\,b^{11}\,c^6\,d^2-128\,a\,b^{12}\,c^7\,d+16\,b^{13}\,c^8}\right)}^{3/4}\,\left(\frac{\sqrt{x}\,\left(4096\,a^{14}\,b^4\,c^3\,d^{17}-12032\,a^{13}\,b^5\,c^4\,d^{16}-74240\,a^{12}\,b^6\,c^5\,d^{15}+541952\,a^{11}\,b^7\,c^6\,d^{14}-1570816\,a^{10}\,b^8\,c^7\,d^{13}+2691584\,a^9\,b^9\,c^8\,d^{12}-3017728\,a^8\,b^{10}\,c^9\,d^{11}+2286080\,a^7\,b^{11}\,c^{10}\,d^{10}-1165312\,a^6\,b^{12}\,c^{11}\,d^9+384256\,a^5\,b^{13}\,c^{12}\,d^8-74240\,a^4\,b^{14}\,c^{13}\,d^7+6400\,a^3\,b^{15}\,c^{14}\,d^6\right)}{a^6\,b\,d^{11}-6\,a^5\,b^2\,c\,d^{10}+15\,a^4\,b^3\,c^2\,d^9-20\,a^3\,b^4\,c^3\,d^8+15\,a^2\,b^5\,c^4\,d^7-6\,a\,b^6\,c^5\,d^6+b^7\,c^6\,d^5}+\frac{{\left(-\frac{a^9}{16\,a^8\,b^5\,d^8-128\,a^7\,b^6\,c\,d^7+448\,a^6\,b^7\,c^2\,d^6-896\,a^5\,b^8\,c^3\,d^5+1120\,a^4\,b^9\,c^4\,d^4-896\,a^3\,b^{10}\,c^5\,d^3+448\,a^2\,b^{11}\,c^6\,d^2-128\,a\,b^{12}\,c^7\,d+16\,b^{13}\,c^8}\right)}^{1/4}\,\left(5120\,a^{11}\,b^5\,c^3\,d^{16}-40960\,a^{10}\,b^6\,c^4\,d^{15}+143360\,a^9\,b^7\,c^5\,d^{14}-286720\,a^8\,b^8\,c^6\,d^{13}+358400\,a^7\,b^9\,c^7\,d^{12}-286720\,a^6\,b^{10}\,c^8\,d^{11}+143360\,a^5\,b^{11}\,c^9\,d^{10}-40960\,a^4\,b^{12}\,c^{10}\,d^9+5120\,a^3\,b^{13}\,c^{11}\,d^8\right)\,2{}\mathrm{i}}{a^3\,b\,d^8-3\,a^2\,b^2\,c\,d^7+3\,a\,b^3\,c^2\,d^6-b^4\,c^3\,d^5}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{a^9}{16\,a^8\,b^5\,d^8-128\,a^7\,b^6\,c\,d^7+448\,a^6\,b^7\,c^2\,d^6-896\,a^5\,b^8\,c^3\,d^5+1120\,a^4\,b^9\,c^4\,d^4-896\,a^3\,b^{10}\,c^5\,d^3+448\,a^2\,b^{11}\,c^6\,d^2-128\,a\,b^{12}\,c^7\,d+16\,b^{13}\,c^8}\right)}^{1/4}}{\left(-\frac{\sqrt{x}\,\left(1296\,a^{14}\,c^4\,d^8-1440\,a^{13}\,b\,c^5\,d^7+400\,a^{12}\,b^2\,c^6\,d^6+6561\,a^{10}\,b^4\,c^8\,d^4-14580\,a^9\,b^5\,c^9\,d^3+12150\,a^8\,b^6\,c^{10}\,d^2-4500\,a^7\,b^7\,c^{11}\,d+625\,a^6\,b^8\,c^{12}\right)}{a^6\,b\,d^{11}-6\,a^5\,b^2\,c\,d^{10}+15\,a^4\,b^3\,c^2\,d^9-20\,a^3\,b^4\,c^3\,d^8+15\,a^2\,b^5\,c^4\,d^7-6\,a\,b^6\,c^5\,d^6+b^7\,c^6\,d^5}+{\left(-\frac{a^9}{16\,a^8\,b^5\,d^8-128\,a^7\,b^6\,c\,d^7+448\,a^6\,b^7\,c^2\,d^6-896\,a^5\,b^8\,c^3\,d^5+1120\,a^4\,b^9\,c^4\,d^4-896\,a^3\,b^{10}\,c^5\,d^3+448\,a^2\,b^{11}\,c^6\,d^2-128\,a\,b^{12}\,c^7\,d+16\,b^{13}\,c^8}\right)}^{1/4}\,\left(\frac{2\,\left(576\,a^{12}\,c^3\,d^8+256\,a^{11}\,b\,c^4\,d^7+256\,a^{10}\,b^2\,c^5\,d^6+256\,a^9\,b^3\,c^6\,d^5+256\,a^8\,b^4\,c^7\,d^4-6305\,a^7\,b^5\,c^8\,d^3+8275\,a^6\,b^6\,c^9\,d^2-3875\,a^5\,b^7\,c^{10}\,d+625\,a^4\,b^8\,c^{11}\right)}{a^3\,b\,d^8-3\,a^2\,b^2\,c\,d^7+3\,a\,b^3\,c^2\,d^6-b^4\,c^3\,d^5}+{\left(-\frac{a^9}{16\,a^8\,b^5\,d^8-128\,a^7\,b^6\,c\,d^7+448\,a^6\,b^7\,c^2\,d^6-896\,a^5\,b^8\,c^3\,d^5+1120\,a^4\,b^9\,c^4\,d^4-896\,a^3\,b^{10}\,c^5\,d^3+448\,a^2\,b^{11}\,c^6\,d^2-128\,a\,b^{12}\,c^7\,d+16\,b^{13}\,c^8}\right)}^{3/4}\,\left(\frac{\sqrt{x}\,\left(4096\,a^{14}\,b^4\,c^3\,d^{17}-12032\,a^{13}\,b^5\,c^4\,d^{16}-74240\,a^{12}\,b^6\,c^5\,d^{15}+541952\,a^{11}\,b^7\,c^6\,d^{14}-1570816\,a^{10}\,b^8\,c^7\,d^{13}+2691584\,a^9\,b^9\,c^8\,d^{12}-3017728\,a^8\,b^{10}\,c^9\,d^{11}+2286080\,a^7\,b^{11}\,c^{10}\,d^{10}-1165312\,a^6\,b^{12}\,c^{11}\,d^9+384256\,a^5\,b^{13}\,c^{12}\,d^8-74240\,a^4\,b^{14}\,c^{13}\,d^7+6400\,a^3\,b^{15}\,c^{14}\,d^6\right)}{a^6\,b\,d^{11}-6\,a^5\,b^2\,c\,d^{10}+15\,a^4\,b^3\,c^2\,d^9-20\,a^3\,b^4\,c^3\,d^8+15\,a^2\,b^5\,c^4\,d^7-6\,a\,b^6\,c^5\,d^6+b^7\,c^6\,d^5}-\frac{{\left(-\frac{a^9}{16\,a^8\,b^5\,d^8-128\,a^7\,b^6\,c\,d^7+448\,a^6\,b^7\,c^2\,d^6-896\,a^5\,b^8\,c^3\,d^5+1120\,a^4\,b^9\,c^4\,d^4-896\,a^3\,b^{10}\,c^5\,d^3+448\,a^2\,b^{11}\,c^6\,d^2-128\,a\,b^{12}\,c^7\,d+16\,b^{13}\,c^8}\right)}^{1/4}\,\left(5120\,a^{11}\,b^5\,c^3\,d^{16}-40960\,a^{10}\,b^6\,c^4\,d^{15}+143360\,a^9\,b^7\,c^5\,d^{14}-286720\,a^8\,b^8\,c^6\,d^{13}+358400\,a^7\,b^9\,c^7\,d^{12}-286720\,a^6\,b^{10}\,c^8\,d^{11}+143360\,a^5\,b^{11}\,c^9\,d^{10}-40960\,a^4\,b^{12}\,c^{10}\,d^9+5120\,a^3\,b^{13}\,c^{11}\,d^8\right)\,2{}\mathrm{i}}{a^3\,b\,d^8-3\,a^2\,b^2\,c\,d^7+3\,a\,b^3\,c^2\,d^6-b^4\,c^3\,d^5}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{a^9}{16\,a^8\,b^5\,d^8-128\,a^7\,b^6\,c\,d^7+448\,a^6\,b^7\,c^2\,d^6-896\,a^5\,b^8\,c^3\,d^5+1120\,a^4\,b^9\,c^4\,d^4-896\,a^3\,b^{10}\,c^5\,d^3+448\,a^2\,b^{11}\,c^6\,d^2-128\,a\,b^{12}\,c^7\,d+16\,b^{13}\,c^8}\right)}^{1/4}\,1{}\mathrm{i}-\left(-\frac{\sqrt{x}\,\left(1296\,a^{14}\,c^4\,d^8-1440\,a^{13}\,b\,c^5\,d^7+400\,a^{12}\,b^2\,c^6\,d^6+6561\,a^{10}\,b^4\,c^8\,d^4-14580\,a^9\,b^5\,c^9\,d^3+12150\,a^8\,b^6\,c^{10}\,d^2-4500\,a^7\,b^7\,c^{11}\,d+625\,a^6\,b^8\,c^{12}\right)}{a^6\,b\,d^{11}-6\,a^5\,b^2\,c\,d^{10}+15\,a^4\,b^3\,c^2\,d^9-20\,a^3\,b^4\,c^3\,d^8+15\,a^2\,b^5\,c^4\,d^7-6\,a\,b^6\,c^5\,d^6+b^7\,c^6\,d^5}+{\left(-\frac{a^9}{16\,a^8\,b^5\,d^8-128\,a^7\,b^6\,c\,d^7+448\,a^6\,b^7\,c^2\,d^6-896\,a^5\,b^8\,c^3\,d^5+1120\,a^4\,b^9\,c^4\,d^4-896\,a^3\,b^{10}\,c^5\,d^3+448\,a^2\,b^{11}\,c^6\,d^2-128\,a\,b^{12}\,c^7\,d+16\,b^{13}\,c^8}\right)}^{1/4}\,\left(-\frac{2\,\left(576\,a^{12}\,c^3\,d^8+256\,a^{11}\,b\,c^4\,d^7+256\,a^{10}\,b^2\,c^5\,d^6+256\,a^9\,b^3\,c^6\,d^5+256\,a^8\,b^4\,c^7\,d^4-6305\,a^7\,b^5\,c^8\,d^3+8275\,a^6\,b^6\,c^9\,d^2-3875\,a^5\,b^7\,c^{10}\,d+625\,a^4\,b^8\,c^{11}\right)}{a^3\,b\,d^8-3\,a^2\,b^2\,c\,d^7+3\,a\,b^3\,c^2\,d^6-b^4\,c^3\,d^5}+{\left(-\frac{a^9}{16\,a^8\,b^5\,d^8-128\,a^7\,b^6\,c\,d^7+448\,a^6\,b^7\,c^2\,d^6-896\,a^5\,b^8\,c^3\,d^5+1120\,a^4\,b^9\,c^4\,d^4-896\,a^3\,b^{10}\,c^5\,d^3+448\,a^2\,b^{11}\,c^6\,d^2-128\,a\,b^{12}\,c^7\,d+16\,b^{13}\,c^8}\right)}^{3/4}\,\left(\frac{\sqrt{x}\,\left(4096\,a^{14}\,b^4\,c^3\,d^{17}-12032\,a^{13}\,b^5\,c^4\,d^{16}-74240\,a^{12}\,b^6\,c^5\,d^{15}+541952\,a^{11}\,b^7\,c^6\,d^{14}-1570816\,a^{10}\,b^8\,c^7\,d^{13}+2691584\,a^9\,b^9\,c^8\,d^{12}-3017728\,a^8\,b^{10}\,c^9\,d^{11}+2286080\,a^7\,b^{11}\,c^{10}\,d^{10}-1165312\,a^6\,b^{12}\,c^{11}\,d^9+384256\,a^5\,b^{13}\,c^{12}\,d^8-74240\,a^4\,b^{14}\,c^{13}\,d^7+6400\,a^3\,b^{15}\,c^{14}\,d^6\right)}{a^6\,b\,d^{11}-6\,a^5\,b^2\,c\,d^{10}+15\,a^4\,b^3\,c^2\,d^9-20\,a^3\,b^4\,c^3\,d^8+15\,a^2\,b^5\,c^4\,d^7-6\,a\,b^6\,c^5\,d^6+b^7\,c^6\,d^5}+\frac{{\left(-\frac{a^9}{16\,a^8\,b^5\,d^8-128\,a^7\,b^6\,c\,d^7+448\,a^6\,b^7\,c^2\,d^6-896\,a^5\,b^8\,c^3\,d^5+1120\,a^4\,b^9\,c^4\,d^4-896\,a^3\,b^{10}\,c^5\,d^3+448\,a^2\,b^{11}\,c^6\,d^2-128\,a\,b^{12}\,c^7\,d+16\,b^{13}\,c^8}\right)}^{1/4}\,\left(5120\,a^{11}\,b^5\,c^3\,d^{16}-40960\,a^{10}\,b^6\,c^4\,d^{15}+143360\,a^9\,b^7\,c^5\,d^{14}-286720\,a^8\,b^8\,c^6\,d^{13}+358400\,a^7\,b^9\,c^7\,d^{12}-286720\,a^6\,b^{10}\,c^8\,d^{11}+143360\,a^5\,b^{11}\,c^9\,d^{10}-40960\,a^4\,b^{12}\,c^{10}\,d^9+5120\,a^3\,b^{13}\,c^{11}\,d^8\right)\,2{}\mathrm{i}}{a^3\,b\,d^8-3\,a^2\,b^2\,c\,d^7+3\,a\,b^3\,c^2\,d^6-b^4\,c^3\,d^5}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{a^9}{16\,a^8\,b^5\,d^8-128\,a^7\,b^6\,c\,d^7+448\,a^6\,b^7\,c^2\,d^6-896\,a^5\,b^8\,c^3\,d^5+1120\,a^4\,b^9\,c^4\,d^4-896\,a^3\,b^{10}\,c^5\,d^3+448\,a^2\,b^{11}\,c^6\,d^2-128\,a\,b^{12}\,c^7\,d+16\,b^{13}\,c^8}\right)}^{1/4}\,1{}\mathrm{i}}\right)\,{\left(-\frac{a^9}{16\,a^8\,b^5\,d^8-128\,a^7\,b^6\,c\,d^7+448\,a^6\,b^7\,c^2\,d^6-896\,a^5\,b^8\,c^3\,d^5+1120\,a^4\,b^9\,c^4\,d^4-896\,a^3\,b^{10}\,c^5\,d^3+448\,a^2\,b^{11}\,c^6\,d^2-128\,a\,b^{12}\,c^7\,d+16\,b^{13}\,c^8}\right)}^{1/4}+2\,\mathrm{atan}\left(\frac{{\left(-\frac{6561\,a^4\,c^5\,d^4-14580\,a^3\,b\,c^6\,d^3+12150\,a^2\,b^2\,c^7\,d^2-4500\,a\,b^3\,c^8\,d+625\,b^4\,c^9}{4096\,a^8\,d^{17}-32768\,a^7\,b\,c\,d^{16}+114688\,a^6\,b^2\,c^2\,d^{15}-229376\,a^5\,b^3\,c^3\,d^{14}+286720\,a^4\,b^4\,c^4\,d^{13}-229376\,a^3\,b^5\,c^5\,d^{12}+114688\,a^2\,b^6\,c^6\,d^{11}-32768\,a\,b^7\,c^7\,d^{10}+4096\,b^8\,c^8\,d^9}\right)}^{1/4}\,\left(-\frac{\sqrt{x}\,\left(1296\,a^{14}\,c^4\,d^8-1440\,a^{13}\,b\,c^5\,d^7+400\,a^{12}\,b^2\,c^6\,d^6+6561\,a^{10}\,b^4\,c^8\,d^4-14580\,a^9\,b^5\,c^9\,d^3+12150\,a^8\,b^6\,c^{10}\,d^2-4500\,a^7\,b^7\,c^{11}\,d+625\,a^6\,b^8\,c^{12}\right)}{a^6\,b\,d^{11}-6\,a^5\,b^2\,c\,d^{10}+15\,a^4\,b^3\,c^2\,d^9-20\,a^3\,b^4\,c^3\,d^8+15\,a^2\,b^5\,c^4\,d^7-6\,a\,b^6\,c^5\,d^6+b^7\,c^6\,d^5}+{\left(-\frac{6561\,a^4\,c^5\,d^4-14580\,a^3\,b\,c^6\,d^3+12150\,a^2\,b^2\,c^7\,d^2-4500\,a\,b^3\,c^8\,d+625\,b^4\,c^9}{4096\,a^8\,d^{17}-32768\,a^7\,b\,c\,d^{16}+114688\,a^6\,b^2\,c^2\,d^{15}-229376\,a^5\,b^3\,c^3\,d^{14}+286720\,a^4\,b^4\,c^4\,d^{13}-229376\,a^3\,b^5\,c^5\,d^{12}+114688\,a^2\,b^6\,c^6\,d^{11}-32768\,a\,b^7\,c^7\,d^{10}+4096\,b^8\,c^8\,d^9}\right)}^{1/4}\,\left(\frac{2\,\left(576\,a^{12}\,c^3\,d^8+256\,a^{11}\,b\,c^4\,d^7+256\,a^{10}\,b^2\,c^5\,d^6+256\,a^9\,b^3\,c^6\,d^5+256\,a^8\,b^4\,c^7\,d^4-6305\,a^7\,b^5\,c^8\,d^3+8275\,a^6\,b^6\,c^9\,d^2-3875\,a^5\,b^7\,c^{10}\,d+625\,a^4\,b^8\,c^{11}\right)}{a^3\,b\,d^8-3\,a^2\,b^2\,c\,d^7+3\,a\,b^3\,c^2\,d^6-b^4\,c^3\,d^5}+{\left(-\frac{6561\,a^4\,c^5\,d^4-14580\,a^3\,b\,c^6\,d^3+12150\,a^2\,b^2\,c^7\,d^2-4500\,a\,b^3\,c^8\,d+625\,b^4\,c^9}{4096\,a^8\,d^{17}-32768\,a^7\,b\,c\,d^{16}+114688\,a^6\,b^2\,c^2\,d^{15}-229376\,a^5\,b^3\,c^3\,d^{14}+286720\,a^4\,b^4\,c^4\,d^{13}-229376\,a^3\,b^5\,c^5\,d^{12}+114688\,a^2\,b^6\,c^6\,d^{11}-32768\,a\,b^7\,c^7\,d^{10}+4096\,b^8\,c^8\,d^9}\right)}^{3/4}\,\left(\frac{\sqrt{x}\,\left(4096\,a^{14}\,b^4\,c^3\,d^{17}-12032\,a^{13}\,b^5\,c^4\,d^{16}-74240\,a^{12}\,b^6\,c^5\,d^{15}+541952\,a^{11}\,b^7\,c^6\,d^{14}-1570816\,a^{10}\,b^8\,c^7\,d^{13}+2691584\,a^9\,b^9\,c^8\,d^{12}-3017728\,a^8\,b^{10}\,c^9\,d^{11}+2286080\,a^7\,b^{11}\,c^{10}\,d^{10}-1165312\,a^6\,b^{12}\,c^{11}\,d^9+384256\,a^5\,b^{13}\,c^{12}\,d^8-74240\,a^4\,b^{14}\,c^{13}\,d^7+6400\,a^3\,b^{15}\,c^{14}\,d^6\right)}{a^6\,b\,d^{11}-6\,a^5\,b^2\,c\,d^{10}+15\,a^4\,b^3\,c^2\,d^9-20\,a^3\,b^4\,c^3\,d^8+15\,a^2\,b^5\,c^4\,d^7-6\,a\,b^6\,c^5\,d^6+b^7\,c^6\,d^5}-\frac{{\left(-\frac{6561\,a^4\,c^5\,d^4-14580\,a^3\,b\,c^6\,d^3+12150\,a^2\,b^2\,c^7\,d^2-4500\,a\,b^3\,c^8\,d+625\,b^4\,c^9}{4096\,a^8\,d^{17}-32768\,a^7\,b\,c\,d^{16}+114688\,a^6\,b^2\,c^2\,d^{15}-229376\,a^5\,b^3\,c^3\,d^{14}+286720\,a^4\,b^4\,c^4\,d^{13}-229376\,a^3\,b^5\,c^5\,d^{12}+114688\,a^2\,b^6\,c^6\,d^{11}-32768\,a\,b^7\,c^7\,d^{10}+4096\,b^8\,c^8\,d^9}\right)}^{1/4}\,\left(5120\,a^{11}\,b^5\,c^3\,d^{16}-40960\,a^{10}\,b^6\,c^4\,d^{15}+143360\,a^9\,b^7\,c^5\,d^{14}-286720\,a^8\,b^8\,c^6\,d^{13}+358400\,a^7\,b^9\,c^7\,d^{12}-286720\,a^6\,b^{10}\,c^8\,d^{11}+143360\,a^5\,b^{11}\,c^9\,d^{10}-40960\,a^4\,b^{12}\,c^{10}\,d^9+5120\,a^3\,b^{13}\,c^{11}\,d^8\right)\,2{}\mathrm{i}}{a^3\,b\,d^8-3\,a^2\,b^2\,c\,d^7+3\,a\,b^3\,c^2\,d^6-b^4\,c^3\,d^5}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)+{\left(-\frac{6561\,a^4\,c^5\,d^4-14580\,a^3\,b\,c^6\,d^3+12150\,a^2\,b^2\,c^7\,d^2-4500\,a\,b^3\,c^8\,d+625\,b^4\,c^9}{4096\,a^8\,d^{17}-32768\,a^7\,b\,c\,d^{16}+114688\,a^6\,b^2\,c^2\,d^{15}-229376\,a^5\,b^3\,c^3\,d^{14}+286720\,a^4\,b^4\,c^4\,d^{13}-229376\,a^3\,b^5\,c^5\,d^{12}+114688\,a^2\,b^6\,c^6\,d^{11}-32768\,a\,b^7\,c^7\,d^{10}+4096\,b^8\,c^8\,d^9}\right)}^{1/4}\,\left(-\frac{\sqrt{x}\,\left(1296\,a^{14}\,c^4\,d^8-1440\,a^{13}\,b\,c^5\,d^7+400\,a^{12}\,b^2\,c^6\,d^6+6561\,a^{10}\,b^4\,c^8\,d^4-14580\,a^9\,b^5\,c^9\,d^3+12150\,a^8\,b^6\,c^{10}\,d^2-4500\,a^7\,b^7\,c^{11}\,d+625\,a^6\,b^8\,c^{12}\right)}{a^6\,b\,d^{11}-6\,a^5\,b^2\,c\,d^{10}+15\,a^4\,b^3\,c^2\,d^9-20\,a^3\,b^4\,c^3\,d^8+15\,a^2\,b^5\,c^4\,d^7-6\,a\,b^6\,c^5\,d^6+b^7\,c^6\,d^5}+{\left(-\frac{6561\,a^4\,c^5\,d^4-14580\,a^3\,b\,c^6\,d^3+12150\,a^2\,b^2\,c^7\,d^2-4500\,a\,b^3\,c^8\,d+625\,b^4\,c^9}{4096\,a^8\,d^{17}-32768\,a^7\,b\,c\,d^{16}+114688\,a^6\,b^2\,c^2\,d^{15}-229376\,a^5\,b^3\,c^3\,d^{14}+286720\,a^4\,b^4\,c^4\,d^{13}-229376\,a^3\,b^5\,c^5\,d^{12}+114688\,a^2\,b^6\,c^6\,d^{11}-32768\,a\,b^7\,c^7\,d^{10}+4096\,b^8\,c^8\,d^9}\right)}^{1/4}\,\left(-\frac{2\,\left(576\,a^{12}\,c^3\,d^8+256\,a^{11}\,b\,c^4\,d^7+256\,a^{10}\,b^2\,c^5\,d^6+256\,a^9\,b^3\,c^6\,d^5+256\,a^8\,b^4\,c^7\,d^4-6305\,a^7\,b^5\,c^8\,d^3+8275\,a^6\,b^6\,c^9\,d^2-3875\,a^5\,b^7\,c^{10}\,d+625\,a^4\,b^8\,c^{11}\right)}{a^3\,b\,d^8-3\,a^2\,b^2\,c\,d^7+3\,a\,b^3\,c^2\,d^6-b^4\,c^3\,d^5}+{\left(-\frac{6561\,a^4\,c^5\,d^4-14580\,a^3\,b\,c^6\,d^3+12150\,a^2\,b^2\,c^7\,d^2-4500\,a\,b^3\,c^8\,d+625\,b^4\,c^9}{4096\,a^8\,d^{17}-32768\,a^7\,b\,c\,d^{16}+114688\,a^6\,b^2\,c^2\,d^{15}-229376\,a^5\,b^3\,c^3\,d^{14}+286720\,a^4\,b^4\,c^4\,d^{13}-229376\,a^3\,b^5\,c^5\,d^{12}+114688\,a^2\,b^6\,c^6\,d^{11}-32768\,a\,b^7\,c^7\,d^{10}+4096\,b^8\,c^8\,d^9}\right)}^{3/4}\,\left(\frac{\sqrt{x}\,\left(4096\,a^{14}\,b^4\,c^3\,d^{17}-12032\,a^{13}\,b^5\,c^4\,d^{16}-74240\,a^{12}\,b^6\,c^5\,d^{15}+541952\,a^{11}\,b^7\,c^6\,d^{14}-1570816\,a^{10}\,b^8\,c^7\,d^{13}+2691584\,a^9\,b^9\,c^8\,d^{12}-3017728\,a^8\,b^{10}\,c^9\,d^{11}+2286080\,a^7\,b^{11}\,c^{10}\,d^{10}-1165312\,a^6\,b^{12}\,c^{11}\,d^9+384256\,a^5\,b^{13}\,c^{12}\,d^8-74240\,a^4\,b^{14}\,c^{13}\,d^7+6400\,a^3\,b^{15}\,c^{14}\,d^6\right)}{a^6\,b\,d^{11}-6\,a^5\,b^2\,c\,d^{10}+15\,a^4\,b^3\,c^2\,d^9-20\,a^3\,b^4\,c^3\,d^8+15\,a^2\,b^5\,c^4\,d^7-6\,a\,b^6\,c^5\,d^6+b^7\,c^6\,d^5}+\frac{{\left(-\frac{6561\,a^4\,c^5\,d^4-14580\,a^3\,b\,c^6\,d^3+12150\,a^2\,b^2\,c^7\,d^2-4500\,a\,b^3\,c^8\,d+625\,b^4\,c^9}{4096\,a^8\,d^{17}-32768\,a^7\,b\,c\,d^{16}+114688\,a^6\,b^2\,c^2\,d^{15}-229376\,a^5\,b^3\,c^3\,d^{14}+286720\,a^4\,b^4\,c^4\,d^{13}-229376\,a^3\,b^5\,c^5\,d^{12}+114688\,a^2\,b^6\,c^6\,d^{11}-32768\,a\,b^7\,c^7\,d^{10}+4096\,b^8\,c^8\,d^9}\right)}^{1/4}\,\left(5120\,a^{11}\,b^5\,c^3\,d^{16}-40960\,a^{10}\,b^6\,c^4\,d^{15}+143360\,a^9\,b^7\,c^5\,d^{14}-286720\,a^8\,b^8\,c^6\,d^{13}+358400\,a^7\,b^9\,c^7\,d^{12}-286720\,a^6\,b^{10}\,c^8\,d^{11}+143360\,a^5\,b^{11}\,c^9\,d^{10}-40960\,a^4\,b^{12}\,c^{10}\,d^9+5120\,a^3\,b^{13}\,c^{11}\,d^8\right)\,2{}\mathrm{i}}{a^3\,b\,d^8-3\,a^2\,b^2\,c\,d^7+3\,a\,b^3\,c^2\,d^6-b^4\,c^3\,d^5}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)}{{\left(-\frac{6561\,a^4\,c^5\,d^4-14580\,a^3\,b\,c^6\,d^3+12150\,a^2\,b^2\,c^7\,d^2-4500\,a\,b^3\,c^8\,d+625\,b^4\,c^9}{4096\,a^8\,d^{17}-32768\,a^7\,b\,c\,d^{16}+114688\,a^6\,b^2\,c^2\,d^{15}-229376\,a^5\,b^3\,c^3\,d^{14}+286720\,a^4\,b^4\,c^4\,d^{13}-229376\,a^3\,b^5\,c^5\,d^{12}+114688\,a^2\,b^6\,c^6\,d^{11}-32768\,a\,b^7\,c^7\,d^{10}+4096\,b^8\,c^8\,d^9}\right)}^{1/4}\,\left(-\frac{\sqrt{x}\,\left(1296\,a^{14}\,c^4\,d^8-1440\,a^{13}\,b\,c^5\,d^7+400\,a^{12}\,b^2\,c^6\,d^6+6561\,a^{10}\,b^4\,c^8\,d^4-14580\,a^9\,b^5\,c^9\,d^3+12150\,a^8\,b^6\,c^{10}\,d^2-4500\,a^7\,b^7\,c^{11}\,d+625\,a^6\,b^8\,c^{12}\right)}{a^6\,b\,d^{11}-6\,a^5\,b^2\,c\,d^{10}+15\,a^4\,b^3\,c^2\,d^9-20\,a^3\,b^4\,c^3\,d^8+15\,a^2\,b^5\,c^4\,d^7-6\,a\,b^6\,c^5\,d^6+b^7\,c^6\,d^5}+{\left(-\frac{6561\,a^4\,c^5\,d^4-14580\,a^3\,b\,c^6\,d^3+12150\,a^2\,b^2\,c^7\,d^2-4500\,a\,b^3\,c^8\,d+625\,b^4\,c^9}{4096\,a^8\,d^{17}-32768\,a^7\,b\,c\,d^{16}+114688\,a^6\,b^2\,c^2\,d^{15}-229376\,a^5\,b^3\,c^3\,d^{14}+286720\,a^4\,b^4\,c^4\,d^{13}-229376\,a^3\,b^5\,c^5\,d^{12}+114688\,a^2\,b^6\,c^6\,d^{11}-32768\,a\,b^7\,c^7\,d^{10}+4096\,b^8\,c^8\,d^9}\right)}^{1/4}\,\left(\frac{2\,\left(576\,a^{12}\,c^3\,d^8+256\,a^{11}\,b\,c^4\,d^7+256\,a^{10}\,b^2\,c^5\,d^6+256\,a^9\,b^3\,c^6\,d^5+256\,a^8\,b^4\,c^7\,d^4-6305\,a^7\,b^5\,c^8\,d^3+8275\,a^6\,b^6\,c^9\,d^2-3875\,a^5\,b^7\,c^{10}\,d+625\,a^4\,b^8\,c^{11}\right)}{a^3\,b\,d^8-3\,a^2\,b^2\,c\,d^7+3\,a\,b^3\,c^2\,d^6-b^4\,c^3\,d^5}+{\left(-\frac{6561\,a^4\,c^5\,d^4-14580\,a^3\,b\,c^6\,d^3+12150\,a^2\,b^2\,c^7\,d^2-4500\,a\,b^3\,c^8\,d+625\,b^4\,c^9}{4096\,a^8\,d^{17}-32768\,a^7\,b\,c\,d^{16}+114688\,a^6\,b^2\,c^2\,d^{15}-229376\,a^5\,b^3\,c^3\,d^{14}+286720\,a^4\,b^4\,c^4\,d^{13}-229376\,a^3\,b^5\,c^5\,d^{12}+114688\,a^2\,b^6\,c^6\,d^{11}-32768\,a\,b^7\,c^7\,d^{10}+4096\,b^8\,c^8\,d^9}\right)}^{3/4}\,\left(\frac{\sqrt{x}\,\left(4096\,a^{14}\,b^4\,c^3\,d^{17}-12032\,a^{13}\,b^5\,c^4\,d^{16}-74240\,a^{12}\,b^6\,c^5\,d^{15}+541952\,a^{11}\,b^7\,c^6\,d^{14}-1570816\,a^{10}\,b^8\,c^7\,d^{13}+2691584\,a^9\,b^9\,c^8\,d^{12}-3017728\,a^8\,b^{10}\,c^9\,d^{11}+2286080\,a^7\,b^{11}\,c^{10}\,d^{10}-1165312\,a^6\,b^{12}\,c^{11}\,d^9+384256\,a^5\,b^{13}\,c^{12}\,d^8-74240\,a^4\,b^{14}\,c^{13}\,d^7+6400\,a^3\,b^{15}\,c^{14}\,d^6\right)}{a^6\,b\,d^{11}-6\,a^5\,b^2\,c\,d^{10}+15\,a^4\,b^3\,c^2\,d^9-20\,a^3\,b^4\,c^3\,d^8+15\,a^2\,b^5\,c^4\,d^7-6\,a\,b^6\,c^5\,d^6+b^7\,c^6\,d^5}-\frac{{\left(-\frac{6561\,a^4\,c^5\,d^4-14580\,a^3\,b\,c^6\,d^3+12150\,a^2\,b^2\,c^7\,d^2-4500\,a\,b^3\,c^8\,d+625\,b^4\,c^9}{4096\,a^8\,d^{17}-32768\,a^7\,b\,c\,d^{16}+114688\,a^6\,b^2\,c^2\,d^{15}-229376\,a^5\,b^3\,c^3\,d^{14}+286720\,a^4\,b^4\,c^4\,d^{13}-229376\,a^3\,b^5\,c^5\,d^{12}+114688\,a^2\,b^6\,c^6\,d^{11}-32768\,a\,b^7\,c^7\,d^{10}+4096\,b^8\,c^8\,d^9}\right)}^{1/4}\,\left(5120\,a^{11}\,b^5\,c^3\,d^{16}-40960\,a^{10}\,b^6\,c^4\,d^{15}+143360\,a^9\,b^7\,c^5\,d^{14}-286720\,a^8\,b^8\,c^6\,d^{13}+358400\,a^7\,b^9\,c^7\,d^{12}-286720\,a^6\,b^{10}\,c^8\,d^{11}+143360\,a^5\,b^{11}\,c^9\,d^{10}-40960\,a^4\,b^{12}\,c^{10}\,d^9+5120\,a^3\,b^{13}\,c^{11}\,d^8\right)\,2{}\mathrm{i}}{a^3\,b\,d^8-3\,a^2\,b^2\,c\,d^7+3\,a\,b^3\,c^2\,d^6-b^4\,c^3\,d^5}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}-{\left(-\frac{6561\,a^4\,c^5\,d^4-14580\,a^3\,b\,c^6\,d^3+12150\,a^2\,b^2\,c^7\,d^2-4500\,a\,b^3\,c^8\,d+625\,b^4\,c^9}{4096\,a^8\,d^{17}-32768\,a^7\,b\,c\,d^{16}+114688\,a^6\,b^2\,c^2\,d^{15}-229376\,a^5\,b^3\,c^3\,d^{14}+286720\,a^4\,b^4\,c^4\,d^{13}-229376\,a^3\,b^5\,c^5\,d^{12}+114688\,a^2\,b^6\,c^6\,d^{11}-32768\,a\,b^7\,c^7\,d^{10}+4096\,b^8\,c^8\,d^9}\right)}^{1/4}\,\left(-\frac{\sqrt{x}\,\left(1296\,a^{14}\,c^4\,d^8-1440\,a^{13}\,b\,c^5\,d^7+400\,a^{12}\,b^2\,c^6\,d^6+6561\,a^{10}\,b^4\,c^8\,d^4-14580\,a^9\,b^5\,c^9\,d^3+12150\,a^8\,b^6\,c^{10}\,d^2-4500\,a^7\,b^7\,c^{11}\,d+625\,a^6\,b^8\,c^{12}\right)}{a^6\,b\,d^{11}-6\,a^5\,b^2\,c\,d^{10}+15\,a^4\,b^3\,c^2\,d^9-20\,a^3\,b^4\,c^3\,d^8+15\,a^2\,b^5\,c^4\,d^7-6\,a\,b^6\,c^5\,d^6+b^7\,c^6\,d^5}+{\left(-\frac{6561\,a^4\,c^5\,d^4-14580\,a^3\,b\,c^6\,d^3+12150\,a^2\,b^2\,c^7\,d^2-4500\,a\,b^3\,c^8\,d+625\,b^4\,c^9}{4096\,a^8\,d^{17}-32768\,a^7\,b\,c\,d^{16}+114688\,a^6\,b^2\,c^2\,d^{15}-229376\,a^5\,b^3\,c^3\,d^{14}+286720\,a^4\,b^4\,c^4\,d^{13}-229376\,a^3\,b^5\,c^5\,d^{12}+114688\,a^2\,b^6\,c^6\,d^{11}-32768\,a\,b^7\,c^7\,d^{10}+4096\,b^8\,c^8\,d^9}\right)}^{1/4}\,\left(-\frac{2\,\left(576\,a^{12}\,c^3\,d^8+256\,a^{11}\,b\,c^4\,d^7+256\,a^{10}\,b^2\,c^5\,d^6+256\,a^9\,b^3\,c^6\,d^5+256\,a^8\,b^4\,c^7\,d^4-6305\,a^7\,b^5\,c^8\,d^3+8275\,a^6\,b^6\,c^9\,d^2-3875\,a^5\,b^7\,c^{10}\,d+625\,a^4\,b^8\,c^{11}\right)}{a^3\,b\,d^8-3\,a^2\,b^2\,c\,d^7+3\,a\,b^3\,c^2\,d^6-b^4\,c^3\,d^5}+{\left(-\frac{6561\,a^4\,c^5\,d^4-14580\,a^3\,b\,c^6\,d^3+12150\,a^2\,b^2\,c^7\,d^2-4500\,a\,b^3\,c^8\,d+625\,b^4\,c^9}{4096\,a^8\,d^{17}-32768\,a^7\,b\,c\,d^{16}+114688\,a^6\,b^2\,c^2\,d^{15}-229376\,a^5\,b^3\,c^3\,d^{14}+286720\,a^4\,b^4\,c^4\,d^{13}-229376\,a^3\,b^5\,c^5\,d^{12}+114688\,a^2\,b^6\,c^6\,d^{11}-32768\,a\,b^7\,c^7\,d^{10}+4096\,b^8\,c^8\,d^9}\right)}^{3/4}\,\left(\frac{\sqrt{x}\,\left(4096\,a^{14}\,b^4\,c^3\,d^{17}-12032\,a^{13}\,b^5\,c^4\,d^{16}-74240\,a^{12}\,b^6\,c^5\,d^{15}+541952\,a^{11}\,b^7\,c^6\,d^{14}-1570816\,a^{10}\,b^8\,c^7\,d^{13}+2691584\,a^9\,b^9\,c^8\,d^{12}-3017728\,a^8\,b^{10}\,c^9\,d^{11}+2286080\,a^7\,b^{11}\,c^{10}\,d^{10}-1165312\,a^6\,b^{12}\,c^{11}\,d^9+384256\,a^5\,b^{13}\,c^{12}\,d^8-74240\,a^4\,b^{14}\,c^{13}\,d^7+6400\,a^3\,b^{15}\,c^{14}\,d^6\right)}{a^6\,b\,d^{11}-6\,a^5\,b^2\,c\,d^{10}+15\,a^4\,b^3\,c^2\,d^9-20\,a^3\,b^4\,c^3\,d^8+15\,a^2\,b^5\,c^4\,d^7-6\,a\,b^6\,c^5\,d^6+b^7\,c^6\,d^5}+\frac{{\left(-\frac{6561\,a^4\,c^5\,d^4-14580\,a^3\,b\,c^6\,d^3+12150\,a^2\,b^2\,c^7\,d^2-4500\,a\,b^3\,c^8\,d+625\,b^4\,c^9}{4096\,a^8\,d^{17}-32768\,a^7\,b\,c\,d^{16}+114688\,a^6\,b^2\,c^2\,d^{15}-229376\,a^5\,b^3\,c^3\,d^{14}+286720\,a^4\,b^4\,c^4\,d^{13}-229376\,a^3\,b^5\,c^5\,d^{12}+114688\,a^2\,b^6\,c^6\,d^{11}-32768\,a\,b^7\,c^7\,d^{10}+4096\,b^8\,c^8\,d^9}\right)}^{1/4}\,\left(5120\,a^{11}\,b^5\,c^3\,d^{16}-40960\,a^{10}\,b^6\,c^4\,d^{15}+143360\,a^9\,b^7\,c^5\,d^{14}-286720\,a^8\,b^8\,c^6\,d^{13}+358400\,a^7\,b^9\,c^7\,d^{12}-286720\,a^6\,b^{10}\,c^8\,d^{11}+143360\,a^5\,b^{11}\,c^9\,d^{10}-40960\,a^4\,b^{12}\,c^{10}\,d^9+5120\,a^3\,b^{13}\,c^{11}\,d^8\right)\,2{}\mathrm{i}}{a^3\,b\,d^8-3\,a^2\,b^2\,c\,d^7+3\,a\,b^3\,c^2\,d^6-b^4\,c^3\,d^5}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}\right)\,{\left(-\frac{6561\,a^4\,c^5\,d^4-14580\,a^3\,b\,c^6\,d^3+12150\,a^2\,b^2\,c^7\,d^2-4500\,a\,b^3\,c^8\,d+625\,b^4\,c^9}{4096\,a^8\,d^{17}-32768\,a^7\,b\,c\,d^{16}+114688\,a^6\,b^2\,c^2\,d^{15}-229376\,a^5\,b^3\,c^3\,d^{14}+286720\,a^4\,b^4\,c^4\,d^{13}-229376\,a^3\,b^5\,c^5\,d^{12}+114688\,a^2\,b^6\,c^6\,d^{11}-32768\,a\,b^7\,c^7\,d^{10}+4096\,b^8\,c^8\,d^9}\right)}^{1/4}+\frac{2\,\sqrt{x}}{b\,d^2}-\frac{b\,c^2\,\sqrt{x}}{2\,\left(b\,d^3\,x^2+b\,c\,d^2\right)\,\left(a\,d-b\,c\right)}+\mathrm{atan}\left(\frac{\left({\left(-\frac{a^9}{16\,a^8\,b^5\,d^8-128\,a^7\,b^6\,c\,d^7+448\,a^6\,b^7\,c^2\,d^6-896\,a^5\,b^8\,c^3\,d^5+1120\,a^4\,b^9\,c^4\,d^4-896\,a^3\,b^{10}\,c^5\,d^3+448\,a^2\,b^{11}\,c^6\,d^2-128\,a\,b^{12}\,c^7\,d+16\,b^{13}\,c^8}\right)}^{1/4}\,\left({\left(-\frac{a^9}{16\,a^8\,b^5\,d^8-128\,a^7\,b^6\,c\,d^7+448\,a^6\,b^7\,c^2\,d^6-896\,a^5\,b^8\,c^3\,d^5+1120\,a^4\,b^9\,c^4\,d^4-896\,a^3\,b^{10}\,c^5\,d^3+448\,a^2\,b^{11}\,c^6\,d^2-128\,a\,b^{12}\,c^7\,d+16\,b^{13}\,c^8}\right)}^{3/4}\,\left(\frac{\sqrt{x}\,\left(4096\,a^{14}\,b^4\,c^3\,d^{17}-12032\,a^{13}\,b^5\,c^4\,d^{16}-74240\,a^{12}\,b^6\,c^5\,d^{15}+541952\,a^{11}\,b^7\,c^6\,d^{14}-1570816\,a^{10}\,b^8\,c^7\,d^{13}+2691584\,a^9\,b^9\,c^8\,d^{12}-3017728\,a^8\,b^{10}\,c^9\,d^{11}+2286080\,a^7\,b^{11}\,c^{10}\,d^{10}-1165312\,a^6\,b^{12}\,c^{11}\,d^9+384256\,a^5\,b^{13}\,c^{12}\,d^8-74240\,a^4\,b^{14}\,c^{13}\,d^7+6400\,a^3\,b^{15}\,c^{14}\,d^6\right)}{a^6\,b\,d^{11}-6\,a^5\,b^2\,c\,d^{10}+15\,a^4\,b^3\,c^2\,d^9-20\,a^3\,b^4\,c^3\,d^8+15\,a^2\,b^5\,c^4\,d^7-6\,a\,b^6\,c^5\,d^6+b^7\,c^6\,d^5}-\frac{2\,{\left(-\frac{a^9}{16\,a^8\,b^5\,d^8-128\,a^7\,b^6\,c\,d^7+448\,a^6\,b^7\,c^2\,d^6-896\,a^5\,b^8\,c^3\,d^5+1120\,a^4\,b^9\,c^4\,d^4-896\,a^3\,b^{10}\,c^5\,d^3+448\,a^2\,b^{11}\,c^6\,d^2-128\,a\,b^{12}\,c^7\,d+16\,b^{13}\,c^8}\right)}^{1/4}\,\left(5120\,a^{11}\,b^5\,c^3\,d^{16}-40960\,a^{10}\,b^6\,c^4\,d^{15}+143360\,a^9\,b^7\,c^5\,d^{14}-286720\,a^8\,b^8\,c^6\,d^{13}+358400\,a^7\,b^9\,c^7\,d^{12}-286720\,a^6\,b^{10}\,c^8\,d^{11}+143360\,a^5\,b^{11}\,c^9\,d^{10}-40960\,a^4\,b^{12}\,c^{10}\,d^9+5120\,a^3\,b^{13}\,c^{11}\,d^8\right)}{a^3\,b\,d^8-3\,a^2\,b^2\,c\,d^7+3\,a\,b^3\,c^2\,d^6-b^4\,c^3\,d^5}\right)-\frac{2\,\left(576\,a^{12}\,c^3\,d^8+256\,a^{11}\,b\,c^4\,d^7+256\,a^{10}\,b^2\,c^5\,d^6+256\,a^9\,b^3\,c^6\,d^5+256\,a^8\,b^4\,c^7\,d^4-6305\,a^7\,b^5\,c^8\,d^3+8275\,a^6\,b^6\,c^9\,d^2-3875\,a^5\,b^7\,c^{10}\,d+625\,a^4\,b^8\,c^{11}\right)}{a^3\,b\,d^8-3\,a^2\,b^2\,c\,d^7+3\,a\,b^3\,c^2\,d^6-b^4\,c^3\,d^5}\right)+\frac{\sqrt{x}\,\left(1296\,a^{14}\,c^4\,d^8-1440\,a^{13}\,b\,c^5\,d^7+400\,a^{12}\,b^2\,c^6\,d^6+6561\,a^{10}\,b^4\,c^8\,d^4-14580\,a^9\,b^5\,c^9\,d^3+12150\,a^8\,b^6\,c^{10}\,d^2-4500\,a^7\,b^7\,c^{11}\,d+625\,a^6\,b^8\,c^{12}\right)}{a^6\,b\,d^{11}-6\,a^5\,b^2\,c\,d^{10}+15\,a^4\,b^3\,c^2\,d^9-20\,a^3\,b^4\,c^3\,d^8+15\,a^2\,b^5\,c^4\,d^7-6\,a\,b^6\,c^5\,d^6+b^7\,c^6\,d^5}\right)\,{\left(-\frac{a^9}{16\,a^8\,b^5\,d^8-128\,a^7\,b^6\,c\,d^7+448\,a^6\,b^7\,c^2\,d^6-896\,a^5\,b^8\,c^3\,d^5+1120\,a^4\,b^9\,c^4\,d^4-896\,a^3\,b^{10}\,c^5\,d^3+448\,a^2\,b^{11}\,c^6\,d^2-128\,a\,b^{12}\,c^7\,d+16\,b^{13}\,c^8}\right)}^{1/4}\,1{}\mathrm{i}+\left({\left(-\frac{a^9}{16\,a^8\,b^5\,d^8-128\,a^7\,b^6\,c\,d^7+448\,a^6\,b^7\,c^2\,d^6-896\,a^5\,b^8\,c^3\,d^5+1120\,a^4\,b^9\,c^4\,d^4-896\,a^3\,b^{10}\,c^5\,d^3+448\,a^2\,b^{11}\,c^6\,d^2-128\,a\,b^{12}\,c^7\,d+16\,b^{13}\,c^8}\right)}^{1/4}\,\left({\left(-\frac{a^9}{16\,a^8\,b^5\,d^8-128\,a^7\,b^6\,c\,d^7+448\,a^6\,b^7\,c^2\,d^6-896\,a^5\,b^8\,c^3\,d^5+1120\,a^4\,b^9\,c^4\,d^4-896\,a^3\,b^{10}\,c^5\,d^3+448\,a^2\,b^{11}\,c^6\,d^2-128\,a\,b^{12}\,c^7\,d+16\,b^{13}\,c^8}\right)}^{3/4}\,\left(\frac{\sqrt{x}\,\left(4096\,a^{14}\,b^4\,c^3\,d^{17}-12032\,a^{13}\,b^5\,c^4\,d^{16}-74240\,a^{12}\,b^6\,c^5\,d^{15}+541952\,a^{11}\,b^7\,c^6\,d^{14}-1570816\,a^{10}\,b^8\,c^7\,d^{13}+2691584\,a^9\,b^9\,c^8\,d^{12}-3017728\,a^8\,b^{10}\,c^9\,d^{11}+2286080\,a^7\,b^{11}\,c^{10}\,d^{10}-1165312\,a^6\,b^{12}\,c^{11}\,d^9+384256\,a^5\,b^{13}\,c^{12}\,d^8-74240\,a^4\,b^{14}\,c^{13}\,d^7+6400\,a^3\,b^{15}\,c^{14}\,d^6\right)}{a^6\,b\,d^{11}-6\,a^5\,b^2\,c\,d^{10}+15\,a^4\,b^3\,c^2\,d^9-20\,a^3\,b^4\,c^3\,d^8+15\,a^2\,b^5\,c^4\,d^7-6\,a\,b^6\,c^5\,d^6+b^7\,c^6\,d^5}+\frac{2\,{\left(-\frac{a^9}{16\,a^8\,b^5\,d^8-128\,a^7\,b^6\,c\,d^7+448\,a^6\,b^7\,c^2\,d^6-896\,a^5\,b^8\,c^3\,d^5+1120\,a^4\,b^9\,c^4\,d^4-896\,a^3\,b^{10}\,c^5\,d^3+448\,a^2\,b^{11}\,c^6\,d^2-128\,a\,b^{12}\,c^7\,d+16\,b^{13}\,c^8}\right)}^{1/4}\,\left(5120\,a^{11}\,b^5\,c^3\,d^{16}-40960\,a^{10}\,b^6\,c^4\,d^{15}+143360\,a^9\,b^7\,c^5\,d^{14}-286720\,a^8\,b^8\,c^6\,d^{13}+358400\,a^7\,b^9\,c^7\,d^{12}-286720\,a^6\,b^{10}\,c^8\,d^{11}+143360\,a^5\,b^{11}\,c^9\,d^{10}-40960\,a^4\,b^{12}\,c^{10}\,d^9+5120\,a^3\,b^{13}\,c^{11}\,d^8\right)}{a^3\,b\,d^8-3\,a^2\,b^2\,c\,d^7+3\,a\,b^3\,c^2\,d^6-b^4\,c^3\,d^5}\right)+\frac{2\,\left(576\,a^{12}\,c^3\,d^8+256\,a^{11}\,b\,c^4\,d^7+256\,a^{10}\,b^2\,c^5\,d^6+256\,a^9\,b^3\,c^6\,d^5+256\,a^8\,b^4\,c^7\,d^4-6305\,a^7\,b^5\,c^8\,d^3+8275\,a^6\,b^6\,c^9\,d^2-3875\,a^5\,b^7\,c^{10}\,d+625\,a^4\,b^8\,c^{11}\right)}{a^3\,b\,d^8-3\,a^2\,b^2\,c\,d^7+3\,a\,b^3\,c^2\,d^6-b^4\,c^3\,d^5}\right)+\frac{\sqrt{x}\,\left(1296\,a^{14}\,c^4\,d^8-1440\,a^{13}\,b\,c^5\,d^7+400\,a^{12}\,b^2\,c^6\,d^6+6561\,a^{10}\,b^4\,c^8\,d^4-14580\,a^9\,b^5\,c^9\,d^3+12150\,a^8\,b^6\,c^{10}\,d^2-4500\,a^7\,b^7\,c^{11}\,d+625\,a^6\,b^8\,c^{12}\right)}{a^6\,b\,d^{11}-6\,a^5\,b^2\,c\,d^{10}+15\,a^4\,b^3\,c^2\,d^9-20\,a^3\,b^4\,c^3\,d^8+15\,a^2\,b^5\,c^4\,d^7-6\,a\,b^6\,c^5\,d^6+b^7\,c^6\,d^5}\right)\,{\left(-\frac{a^9}{16\,a^8\,b^5\,d^8-128\,a^7\,b^6\,c\,d^7+448\,a^6\,b^7\,c^2\,d^6-896\,a^5\,b^8\,c^3\,d^5+1120\,a^4\,b^9\,c^4\,d^4-896\,a^3\,b^{10}\,c^5\,d^3+448\,a^2\,b^{11}\,c^6\,d^2-128\,a\,b^{12}\,c^7\,d+16\,b^{13}\,c^8}\right)}^{1/4}\,1{}\mathrm{i}}{\left({\left(-\frac{a^9}{16\,a^8\,b^5\,d^8-128\,a^7\,b^6\,c\,d^7+448\,a^6\,b^7\,c^2\,d^6-896\,a^5\,b^8\,c^3\,d^5+1120\,a^4\,b^9\,c^4\,d^4-896\,a^3\,b^{10}\,c^5\,d^3+448\,a^2\,b^{11}\,c^6\,d^2-128\,a\,b^{12}\,c^7\,d+16\,b^{13}\,c^8}\right)}^{1/4}\,\left({\left(-\frac{a^9}{16\,a^8\,b^5\,d^8-128\,a^7\,b^6\,c\,d^7+448\,a^6\,b^7\,c^2\,d^6-896\,a^5\,b^8\,c^3\,d^5+1120\,a^4\,b^9\,c^4\,d^4-896\,a^3\,b^{10}\,c^5\,d^3+448\,a^2\,b^{11}\,c^6\,d^2-128\,a\,b^{12}\,c^7\,d+16\,b^{13}\,c^8}\right)}^{3/4}\,\left(\frac{\sqrt{x}\,\left(4096\,a^{14}\,b^4\,c^3\,d^{17}-12032\,a^{13}\,b^5\,c^4\,d^{16}-74240\,a^{12}\,b^6\,c^5\,d^{15}+541952\,a^{11}\,b^7\,c^6\,d^{14}-1570816\,a^{10}\,b^8\,c^7\,d^{13}+2691584\,a^9\,b^9\,c^8\,d^{12}-3017728\,a^8\,b^{10}\,c^9\,d^{11}+2286080\,a^7\,b^{11}\,c^{10}\,d^{10}-1165312\,a^6\,b^{12}\,c^{11}\,d^9+384256\,a^5\,b^{13}\,c^{12}\,d^8-74240\,a^4\,b^{14}\,c^{13}\,d^7+6400\,a^3\,b^{15}\,c^{14}\,d^6\right)}{a^6\,b\,d^{11}-6\,a^5\,b^2\,c\,d^{10}+15\,a^4\,b^3\,c^2\,d^9-20\,a^3\,b^4\,c^3\,d^8+15\,a^2\,b^5\,c^4\,d^7-6\,a\,b^6\,c^5\,d^6+b^7\,c^6\,d^5}-\frac{2\,{\left(-\frac{a^9}{16\,a^8\,b^5\,d^8-128\,a^7\,b^6\,c\,d^7+448\,a^6\,b^7\,c^2\,d^6-896\,a^5\,b^8\,c^3\,d^5+1120\,a^4\,b^9\,c^4\,d^4-896\,a^3\,b^{10}\,c^5\,d^3+448\,a^2\,b^{11}\,c^6\,d^2-128\,a\,b^{12}\,c^7\,d+16\,b^{13}\,c^8}\right)}^{1/4}\,\left(5120\,a^{11}\,b^5\,c^3\,d^{16}-40960\,a^{10}\,b^6\,c^4\,d^{15}+143360\,a^9\,b^7\,c^5\,d^{14}-286720\,a^8\,b^8\,c^6\,d^{13}+358400\,a^7\,b^9\,c^7\,d^{12}-286720\,a^6\,b^{10}\,c^8\,d^{11}+143360\,a^5\,b^{11}\,c^9\,d^{10}-40960\,a^4\,b^{12}\,c^{10}\,d^9+5120\,a^3\,b^{13}\,c^{11}\,d^8\right)}{a^3\,b\,d^8-3\,a^2\,b^2\,c\,d^7+3\,a\,b^3\,c^2\,d^6-b^4\,c^3\,d^5}\right)-\frac{2\,\left(576\,a^{12}\,c^3\,d^8+256\,a^{11}\,b\,c^4\,d^7+256\,a^{10}\,b^2\,c^5\,d^6+256\,a^9\,b^3\,c^6\,d^5+256\,a^8\,b^4\,c^7\,d^4-6305\,a^7\,b^5\,c^8\,d^3+8275\,a^6\,b^6\,c^9\,d^2-3875\,a^5\,b^7\,c^{10}\,d+625\,a^4\,b^8\,c^{11}\right)}{a^3\,b\,d^8-3\,a^2\,b^2\,c\,d^7+3\,a\,b^3\,c^2\,d^6-b^4\,c^3\,d^5}\right)+\frac{\sqrt{x}\,\left(1296\,a^{14}\,c^4\,d^8-1440\,a^{13}\,b\,c^5\,d^7+400\,a^{12}\,b^2\,c^6\,d^6+6561\,a^{10}\,b^4\,c^8\,d^4-14580\,a^9\,b^5\,c^9\,d^3+12150\,a^8\,b^6\,c^{10}\,d^2-4500\,a^7\,b^7\,c^{11}\,d+625\,a^6\,b^8\,c^{12}\right)}{a^6\,b\,d^{11}-6\,a^5\,b^2\,c\,d^{10}+15\,a^4\,b^3\,c^2\,d^9-20\,a^3\,b^4\,c^3\,d^8+15\,a^2\,b^5\,c^4\,d^7-6\,a\,b^6\,c^5\,d^6+b^7\,c^6\,d^5}\right)\,{\left(-\frac{a^9}{16\,a^8\,b^5\,d^8-128\,a^7\,b^6\,c\,d^7+448\,a^6\,b^7\,c^2\,d^6-896\,a^5\,b^8\,c^3\,d^5+1120\,a^4\,b^9\,c^4\,d^4-896\,a^3\,b^{10}\,c^5\,d^3+448\,a^2\,b^{11}\,c^6\,d^2-128\,a\,b^{12}\,c^7\,d+16\,b^{13}\,c^8}\right)}^{1/4}-\left({\left(-\frac{a^9}{16\,a^8\,b^5\,d^8-128\,a^7\,b^6\,c\,d^7+448\,a^6\,b^7\,c^2\,d^6-896\,a^5\,b^8\,c^3\,d^5+1120\,a^4\,b^9\,c^4\,d^4-896\,a^3\,b^{10}\,c^5\,d^3+448\,a^2\,b^{11}\,c^6\,d^2-128\,a\,b^{12}\,c^7\,d+16\,b^{13}\,c^8}\right)}^{1/4}\,\left({\left(-\frac{a^9}{16\,a^8\,b^5\,d^8-128\,a^7\,b^6\,c\,d^7+448\,a^6\,b^7\,c^2\,d^6-896\,a^5\,b^8\,c^3\,d^5+1120\,a^4\,b^9\,c^4\,d^4-896\,a^3\,b^{10}\,c^5\,d^3+448\,a^2\,b^{11}\,c^6\,d^2-128\,a\,b^{12}\,c^7\,d+16\,b^{13}\,c^8}\right)}^{3/4}\,\left(\frac{\sqrt{x}\,\left(4096\,a^{14}\,b^4\,c^3\,d^{17}-12032\,a^{13}\,b^5\,c^4\,d^{16}-74240\,a^{12}\,b^6\,c^5\,d^{15}+541952\,a^{11}\,b^7\,c^6\,d^{14}-1570816\,a^{10}\,b^8\,c^7\,d^{13}+2691584\,a^9\,b^9\,c^8\,d^{12}-3017728\,a^8\,b^{10}\,c^9\,d^{11}+2286080\,a^7\,b^{11}\,c^{10}\,d^{10}-1165312\,a^6\,b^{12}\,c^{11}\,d^9+384256\,a^5\,b^{13}\,c^{12}\,d^8-74240\,a^4\,b^{14}\,c^{13}\,d^7+6400\,a^3\,b^{15}\,c^{14}\,d^6\right)}{a^6\,b\,d^{11}-6\,a^5\,b^2\,c\,d^{10}+15\,a^4\,b^3\,c^2\,d^9-20\,a^3\,b^4\,c^3\,d^8+15\,a^2\,b^5\,c^4\,d^7-6\,a\,b^6\,c^5\,d^6+b^7\,c^6\,d^5}+\frac{2\,{\left(-\frac{a^9}{16\,a^8\,b^5\,d^8-128\,a^7\,b^6\,c\,d^7+448\,a^6\,b^7\,c^2\,d^6-896\,a^5\,b^8\,c^3\,d^5+1120\,a^4\,b^9\,c^4\,d^4-896\,a^3\,b^{10}\,c^5\,d^3+448\,a^2\,b^{11}\,c^6\,d^2-128\,a\,b^{12}\,c^7\,d+16\,b^{13}\,c^8}\right)}^{1/4}\,\left(5120\,a^{11}\,b^5\,c^3\,d^{16}-40960\,a^{10}\,b^6\,c^4\,d^{15}+143360\,a^9\,b^7\,c^5\,d^{14}-286720\,a^8\,b^8\,c^6\,d^{13}+358400\,a^7\,b^9\,c^7\,d^{12}-286720\,a^6\,b^{10}\,c^8\,d^{11}+143360\,a^5\,b^{11}\,c^9\,d^{10}-40960\,a^4\,b^{12}\,c^{10}\,d^9+5120\,a^3\,b^{13}\,c^{11}\,d^8\right)}{a^3\,b\,d^8-3\,a^2\,b^2\,c\,d^7+3\,a\,b^3\,c^2\,d^6-b^4\,c^3\,d^5}\right)+\frac{2\,\left(576\,a^{12}\,c^3\,d^8+256\,a^{11}\,b\,c^4\,d^7+256\,a^{10}\,b^2\,c^5\,d^6+256\,a^9\,b^3\,c^6\,d^5+256\,a^8\,b^4\,c^7\,d^4-6305\,a^7\,b^5\,c^8\,d^3+8275\,a^6\,b^6\,c^9\,d^2-3875\,a^5\,b^7\,c^{10}\,d+625\,a^4\,b^8\,c^{11}\right)}{a^3\,b\,d^8-3\,a^2\,b^2\,c\,d^7+3\,a\,b^3\,c^2\,d^6-b^4\,c^3\,d^5}\right)+\frac{\sqrt{x}\,\left(1296\,a^{14}\,c^4\,d^8-1440\,a^{13}\,b\,c^5\,d^7+400\,a^{12}\,b^2\,c^6\,d^6+6561\,a^{10}\,b^4\,c^8\,d^4-14580\,a^9\,b^5\,c^9\,d^3+12150\,a^8\,b^6\,c^{10}\,d^2-4500\,a^7\,b^7\,c^{11}\,d+625\,a^6\,b^8\,c^{12}\right)}{a^6\,b\,d^{11}-6\,a^5\,b^2\,c\,d^{10}+15\,a^4\,b^3\,c^2\,d^9-20\,a^3\,b^4\,c^3\,d^8+15\,a^2\,b^5\,c^4\,d^7-6\,a\,b^6\,c^5\,d^6+b^7\,c^6\,d^5}\right)\,{\left(-\frac{a^9}{16\,a^8\,b^5\,d^8-128\,a^7\,b^6\,c\,d^7+448\,a^6\,b^7\,c^2\,d^6-896\,a^5\,b^8\,c^3\,d^5+1120\,a^4\,b^9\,c^4\,d^4-896\,a^3\,b^{10}\,c^5\,d^3+448\,a^2\,b^{11}\,c^6\,d^2-128\,a\,b^{12}\,c^7\,d+16\,b^{13}\,c^8}\right)}^{1/4}}\right)\,{\left(-\frac{a^9}{16\,a^8\,b^5\,d^8-128\,a^7\,b^6\,c\,d^7+448\,a^6\,b^7\,c^2\,d^6-896\,a^5\,b^8\,c^3\,d^5+1120\,a^4\,b^9\,c^4\,d^4-896\,a^3\,b^{10}\,c^5\,d^3+448\,a^2\,b^{11}\,c^6\,d^2-128\,a\,b^{12}\,c^7\,d+16\,b^{13}\,c^8}\right)}^{1/4}\,2{}\mathrm{i}+\mathrm{atan}\left(\frac{{\left(-\frac{6561\,a^4\,c^5\,d^4-14580\,a^3\,b\,c^6\,d^3+12150\,a^2\,b^2\,c^7\,d^2-4500\,a\,b^3\,c^8\,d+625\,b^4\,c^9}{4096\,a^8\,d^{17}-32768\,a^7\,b\,c\,d^{16}+114688\,a^6\,b^2\,c^2\,d^{15}-229376\,a^5\,b^3\,c^3\,d^{14}+286720\,a^4\,b^4\,c^4\,d^{13}-229376\,a^3\,b^5\,c^5\,d^{12}+114688\,a^2\,b^6\,c^6\,d^{11}-32768\,a\,b^7\,c^7\,d^{10}+4096\,b^8\,c^8\,d^9}\right)}^{1/4}\,\left({\left(-\frac{6561\,a^4\,c^5\,d^4-14580\,a^3\,b\,c^6\,d^3+12150\,a^2\,b^2\,c^7\,d^2-4500\,a\,b^3\,c^8\,d+625\,b^4\,c^9}{4096\,a^8\,d^{17}-32768\,a^7\,b\,c\,d^{16}+114688\,a^6\,b^2\,c^2\,d^{15}-229376\,a^5\,b^3\,c^3\,d^{14}+286720\,a^4\,b^4\,c^4\,d^{13}-229376\,a^3\,b^5\,c^5\,d^{12}+114688\,a^2\,b^6\,c^6\,d^{11}-32768\,a\,b^7\,c^7\,d^{10}+4096\,b^8\,c^8\,d^9}\right)}^{1/4}\,\left({\left(-\frac{6561\,a^4\,c^5\,d^4-14580\,a^3\,b\,c^6\,d^3+12150\,a^2\,b^2\,c^7\,d^2-4500\,a\,b^3\,c^8\,d+625\,b^4\,c^9}{4096\,a^8\,d^{17}-32768\,a^7\,b\,c\,d^{16}+114688\,a^6\,b^2\,c^2\,d^{15}-229376\,a^5\,b^3\,c^3\,d^{14}+286720\,a^4\,b^4\,c^4\,d^{13}-229376\,a^3\,b^5\,c^5\,d^{12}+114688\,a^2\,b^6\,c^6\,d^{11}-32768\,a\,b^7\,c^7\,d^{10}+4096\,b^8\,c^8\,d^9}\right)}^{3/4}\,\left(\frac{\sqrt{x}\,\left(4096\,a^{14}\,b^4\,c^3\,d^{17}-12032\,a^{13}\,b^5\,c^4\,d^{16}-74240\,a^{12}\,b^6\,c^5\,d^{15}+541952\,a^{11}\,b^7\,c^6\,d^{14}-1570816\,a^{10}\,b^8\,c^7\,d^{13}+2691584\,a^9\,b^9\,c^8\,d^{12}-3017728\,a^8\,b^{10}\,c^9\,d^{11}+2286080\,a^7\,b^{11}\,c^{10}\,d^{10}-1165312\,a^6\,b^{12}\,c^{11}\,d^9+384256\,a^5\,b^{13}\,c^{12}\,d^8-74240\,a^4\,b^{14}\,c^{13}\,d^7+6400\,a^3\,b^{15}\,c^{14}\,d^6\right)}{a^6\,b\,d^{11}-6\,a^5\,b^2\,c\,d^{10}+15\,a^4\,b^3\,c^2\,d^9-20\,a^3\,b^4\,c^3\,d^8+15\,a^2\,b^5\,c^4\,d^7-6\,a\,b^6\,c^5\,d^6+b^7\,c^6\,d^5}-\frac{2\,{\left(-\frac{6561\,a^4\,c^5\,d^4-14580\,a^3\,b\,c^6\,d^3+12150\,a^2\,b^2\,c^7\,d^2-4500\,a\,b^3\,c^8\,d+625\,b^4\,c^9}{4096\,a^8\,d^{17}-32768\,a^7\,b\,c\,d^{16}+114688\,a^6\,b^2\,c^2\,d^{15}-229376\,a^5\,b^3\,c^3\,d^{14}+286720\,a^4\,b^4\,c^4\,d^{13}-229376\,a^3\,b^5\,c^5\,d^{12}+114688\,a^2\,b^6\,c^6\,d^{11}-32768\,a\,b^7\,c^7\,d^{10}+4096\,b^8\,c^8\,d^9}\right)}^{1/4}\,\left(5120\,a^{11}\,b^5\,c^3\,d^{16}-40960\,a^{10}\,b^6\,c^4\,d^{15}+143360\,a^9\,b^7\,c^5\,d^{14}-286720\,a^8\,b^8\,c^6\,d^{13}+358400\,a^7\,b^9\,c^7\,d^{12}-286720\,a^6\,b^{10}\,c^8\,d^{11}+143360\,a^5\,b^{11}\,c^9\,d^{10}-40960\,a^4\,b^{12}\,c^{10}\,d^9+5120\,a^3\,b^{13}\,c^{11}\,d^8\right)}{a^3\,b\,d^8-3\,a^2\,b^2\,c\,d^7+3\,a\,b^3\,c^2\,d^6-b^4\,c^3\,d^5}\right)-\frac{2\,\left(576\,a^{12}\,c^3\,d^8+256\,a^{11}\,b\,c^4\,d^7+256\,a^{10}\,b^2\,c^5\,d^6+256\,a^9\,b^3\,c^6\,d^5+256\,a^8\,b^4\,c^7\,d^4-6305\,a^7\,b^5\,c^8\,d^3+8275\,a^6\,b^6\,c^9\,d^2-3875\,a^5\,b^7\,c^{10}\,d+625\,a^4\,b^8\,c^{11}\right)}{a^3\,b\,d^8-3\,a^2\,b^2\,c\,d^7+3\,a\,b^3\,c^2\,d^6-b^4\,c^3\,d^5}\right)+\frac{\sqrt{x}\,\left(1296\,a^{14}\,c^4\,d^8-1440\,a^{13}\,b\,c^5\,d^7+400\,a^{12}\,b^2\,c^6\,d^6+6561\,a^{10}\,b^4\,c^8\,d^4-14580\,a^9\,b^5\,c^9\,d^3+12150\,a^8\,b^6\,c^{10}\,d^2-4500\,a^7\,b^7\,c^{11}\,d+625\,a^6\,b^8\,c^{12}\right)}{a^6\,b\,d^{11}-6\,a^5\,b^2\,c\,d^{10}+15\,a^4\,b^3\,c^2\,d^9-20\,a^3\,b^4\,c^3\,d^8+15\,a^2\,b^5\,c^4\,d^7-6\,a\,b^6\,c^5\,d^6+b^7\,c^6\,d^5}\right)\,1{}\mathrm{i}+{\left(-\frac{6561\,a^4\,c^5\,d^4-14580\,a^3\,b\,c^6\,d^3+12150\,a^2\,b^2\,c^7\,d^2-4500\,a\,b^3\,c^8\,d+625\,b^4\,c^9}{4096\,a^8\,d^{17}-32768\,a^7\,b\,c\,d^{16}+114688\,a^6\,b^2\,c^2\,d^{15}-229376\,a^5\,b^3\,c^3\,d^{14}+286720\,a^4\,b^4\,c^4\,d^{13}-229376\,a^3\,b^5\,c^5\,d^{12}+114688\,a^2\,b^6\,c^6\,d^{11}-32768\,a\,b^7\,c^7\,d^{10}+4096\,b^8\,c^8\,d^9}\right)}^{1/4}\,\left({\left(-\frac{6561\,a^4\,c^5\,d^4-14580\,a^3\,b\,c^6\,d^3+12150\,a^2\,b^2\,c^7\,d^2-4500\,a\,b^3\,c^8\,d+625\,b^4\,c^9}{4096\,a^8\,d^{17}-32768\,a^7\,b\,c\,d^{16}+114688\,a^6\,b^2\,c^2\,d^{15}-229376\,a^5\,b^3\,c^3\,d^{14}+286720\,a^4\,b^4\,c^4\,d^{13}-229376\,a^3\,b^5\,c^5\,d^{12}+114688\,a^2\,b^6\,c^6\,d^{11}-32768\,a\,b^7\,c^7\,d^{10}+4096\,b^8\,c^8\,d^9}\right)}^{1/4}\,\left({\left(-\frac{6561\,a^4\,c^5\,d^4-14580\,a^3\,b\,c^6\,d^3+12150\,a^2\,b^2\,c^7\,d^2-4500\,a\,b^3\,c^8\,d+625\,b^4\,c^9}{4096\,a^8\,d^{17}-32768\,a^7\,b\,c\,d^{16}+114688\,a^6\,b^2\,c^2\,d^{15}-229376\,a^5\,b^3\,c^3\,d^{14}+286720\,a^4\,b^4\,c^4\,d^{13}-229376\,a^3\,b^5\,c^5\,d^{12}+114688\,a^2\,b^6\,c^6\,d^{11}-32768\,a\,b^7\,c^7\,d^{10}+4096\,b^8\,c^8\,d^9}\right)}^{3/4}\,\left(\frac{\sqrt{x}\,\left(4096\,a^{14}\,b^4\,c^3\,d^{17}-12032\,a^{13}\,b^5\,c^4\,d^{16}-74240\,a^{12}\,b^6\,c^5\,d^{15}+541952\,a^{11}\,b^7\,c^6\,d^{14}-1570816\,a^{10}\,b^8\,c^7\,d^{13}+2691584\,a^9\,b^9\,c^8\,d^{12}-3017728\,a^8\,b^{10}\,c^9\,d^{11}+2286080\,a^7\,b^{11}\,c^{10}\,d^{10}-1165312\,a^6\,b^{12}\,c^{11}\,d^9+384256\,a^5\,b^{13}\,c^{12}\,d^8-74240\,a^4\,b^{14}\,c^{13}\,d^7+6400\,a^3\,b^{15}\,c^{14}\,d^6\right)}{a^6\,b\,d^{11}-6\,a^5\,b^2\,c\,d^{10}+15\,a^4\,b^3\,c^2\,d^9-20\,a^3\,b^4\,c^3\,d^8+15\,a^2\,b^5\,c^4\,d^7-6\,a\,b^6\,c^5\,d^6+b^7\,c^6\,d^5}+\frac{2\,{\left(-\frac{6561\,a^4\,c^5\,d^4-14580\,a^3\,b\,c^6\,d^3+12150\,a^2\,b^2\,c^7\,d^2-4500\,a\,b^3\,c^8\,d+625\,b^4\,c^9}{4096\,a^8\,d^{17}-32768\,a^7\,b\,c\,d^{16}+114688\,a^6\,b^2\,c^2\,d^{15}-229376\,a^5\,b^3\,c^3\,d^{14}+286720\,a^4\,b^4\,c^4\,d^{13}-229376\,a^3\,b^5\,c^5\,d^{12}+114688\,a^2\,b^6\,c^6\,d^{11}-32768\,a\,b^7\,c^7\,d^{10}+4096\,b^8\,c^8\,d^9}\right)}^{1/4}\,\left(5120\,a^{11}\,b^5\,c^3\,d^{16}-40960\,a^{10}\,b^6\,c^4\,d^{15}+143360\,a^9\,b^7\,c^5\,d^{14}-286720\,a^8\,b^8\,c^6\,d^{13}+358400\,a^7\,b^9\,c^7\,d^{12}-286720\,a^6\,b^{10}\,c^8\,d^{11}+143360\,a^5\,b^{11}\,c^9\,d^{10}-40960\,a^4\,b^{12}\,c^{10}\,d^9+5120\,a^3\,b^{13}\,c^{11}\,d^8\right)}{a^3\,b\,d^8-3\,a^2\,b^2\,c\,d^7+3\,a\,b^3\,c^2\,d^6-b^4\,c^3\,d^5}\right)+\frac{2\,\left(576\,a^{12}\,c^3\,d^8+256\,a^{11}\,b\,c^4\,d^7+256\,a^{10}\,b^2\,c^5\,d^6+256\,a^9\,b^3\,c^6\,d^5+256\,a^8\,b^4\,c^7\,d^4-6305\,a^7\,b^5\,c^8\,d^3+8275\,a^6\,b^6\,c^9\,d^2-3875\,a^5\,b^7\,c^{10}\,d+625\,a^4\,b^8\,c^{11}\right)}{a^3\,b\,d^8-3\,a^2\,b^2\,c\,d^7+3\,a\,b^3\,c^2\,d^6-b^4\,c^3\,d^5}\right)+\frac{\sqrt{x}\,\left(1296\,a^{14}\,c^4\,d^8-1440\,a^{13}\,b\,c^5\,d^7+400\,a^{12}\,b^2\,c^6\,d^6+6561\,a^{10}\,b^4\,c^8\,d^4-14580\,a^9\,b^5\,c^9\,d^3+12150\,a^8\,b^6\,c^{10}\,d^2-4500\,a^7\,b^7\,c^{11}\,d+625\,a^6\,b^8\,c^{12}\right)}{a^6\,b\,d^{11}-6\,a^5\,b^2\,c\,d^{10}+15\,a^4\,b^3\,c^2\,d^9-20\,a^3\,b^4\,c^3\,d^8+15\,a^2\,b^5\,c^4\,d^7-6\,a\,b^6\,c^5\,d^6+b^7\,c^6\,d^5}\right)\,1{}\mathrm{i}}{{\left(-\frac{6561\,a^4\,c^5\,d^4-14580\,a^3\,b\,c^6\,d^3+12150\,a^2\,b^2\,c^7\,d^2-4500\,a\,b^3\,c^8\,d+625\,b^4\,c^9}{4096\,a^8\,d^{17}-32768\,a^7\,b\,c\,d^{16}+114688\,a^6\,b^2\,c^2\,d^{15}-229376\,a^5\,b^3\,c^3\,d^{14}+286720\,a^4\,b^4\,c^4\,d^{13}-229376\,a^3\,b^5\,c^5\,d^{12}+114688\,a^2\,b^6\,c^6\,d^{11}-32768\,a\,b^7\,c^7\,d^{10}+4096\,b^8\,c^8\,d^9}\right)}^{1/4}\,\left({\left(-\frac{6561\,a^4\,c^5\,d^4-14580\,a^3\,b\,c^6\,d^3+12150\,a^2\,b^2\,c^7\,d^2-4500\,a\,b^3\,c^8\,d+625\,b^4\,c^9}{4096\,a^8\,d^{17}-32768\,a^7\,b\,c\,d^{16}+114688\,a^6\,b^2\,c^2\,d^{15}-229376\,a^5\,b^3\,c^3\,d^{14}+286720\,a^4\,b^4\,c^4\,d^{13}-229376\,a^3\,b^5\,c^5\,d^{12}+114688\,a^2\,b^6\,c^6\,d^{11}-32768\,a\,b^7\,c^7\,d^{10}+4096\,b^8\,c^8\,d^9}\right)}^{1/4}\,\left({\left(-\frac{6561\,a^4\,c^5\,d^4-14580\,a^3\,b\,c^6\,d^3+12150\,a^2\,b^2\,c^7\,d^2-4500\,a\,b^3\,c^8\,d+625\,b^4\,c^9}{4096\,a^8\,d^{17}-32768\,a^7\,b\,c\,d^{16}+114688\,a^6\,b^2\,c^2\,d^{15}-229376\,a^5\,b^3\,c^3\,d^{14}+286720\,a^4\,b^4\,c^4\,d^{13}-229376\,a^3\,b^5\,c^5\,d^{12}+114688\,a^2\,b^6\,c^6\,d^{11}-32768\,a\,b^7\,c^7\,d^{10}+4096\,b^8\,c^8\,d^9}\right)}^{3/4}\,\left(\frac{\sqrt{x}\,\left(4096\,a^{14}\,b^4\,c^3\,d^{17}-12032\,a^{13}\,b^5\,c^4\,d^{16}-74240\,a^{12}\,b^6\,c^5\,d^{15}+541952\,a^{11}\,b^7\,c^6\,d^{14}-1570816\,a^{10}\,b^8\,c^7\,d^{13}+2691584\,a^9\,b^9\,c^8\,d^{12}-3017728\,a^8\,b^{10}\,c^9\,d^{11}+2286080\,a^7\,b^{11}\,c^{10}\,d^{10}-1165312\,a^6\,b^{12}\,c^{11}\,d^9+384256\,a^5\,b^{13}\,c^{12}\,d^8-74240\,a^4\,b^{14}\,c^{13}\,d^7+6400\,a^3\,b^{15}\,c^{14}\,d^6\right)}{a^6\,b\,d^{11}-6\,a^5\,b^2\,c\,d^{10}+15\,a^4\,b^3\,c^2\,d^9-20\,a^3\,b^4\,c^3\,d^8+15\,a^2\,b^5\,c^4\,d^7-6\,a\,b^6\,c^5\,d^6+b^7\,c^6\,d^5}-\frac{2\,{\left(-\frac{6561\,a^4\,c^5\,d^4-14580\,a^3\,b\,c^6\,d^3+12150\,a^2\,b^2\,c^7\,d^2-4500\,a\,b^3\,c^8\,d+625\,b^4\,c^9}{4096\,a^8\,d^{17}-32768\,a^7\,b\,c\,d^{16}+114688\,a^6\,b^2\,c^2\,d^{15}-229376\,a^5\,b^3\,c^3\,d^{14}+286720\,a^4\,b^4\,c^4\,d^{13}-229376\,a^3\,b^5\,c^5\,d^{12}+114688\,a^2\,b^6\,c^6\,d^{11}-32768\,a\,b^7\,c^7\,d^{10}+4096\,b^8\,c^8\,d^9}\right)}^{1/4}\,\left(5120\,a^{11}\,b^5\,c^3\,d^{16}-40960\,a^{10}\,b^6\,c^4\,d^{15}+143360\,a^9\,b^7\,c^5\,d^{14}-286720\,a^8\,b^8\,c^6\,d^{13}+358400\,a^7\,b^9\,c^7\,d^{12}-286720\,a^6\,b^{10}\,c^8\,d^{11}+143360\,a^5\,b^{11}\,c^9\,d^{10}-40960\,a^4\,b^{12}\,c^{10}\,d^9+5120\,a^3\,b^{13}\,c^{11}\,d^8\right)}{a^3\,b\,d^8-3\,a^2\,b^2\,c\,d^7+3\,a\,b^3\,c^2\,d^6-b^4\,c^3\,d^5}\right)-\frac{2\,\left(576\,a^{12}\,c^3\,d^8+256\,a^{11}\,b\,c^4\,d^7+256\,a^{10}\,b^2\,c^5\,d^6+256\,a^9\,b^3\,c^6\,d^5+256\,a^8\,b^4\,c^7\,d^4-6305\,a^7\,b^5\,c^8\,d^3+8275\,a^6\,b^6\,c^9\,d^2-3875\,a^5\,b^7\,c^{10}\,d+625\,a^4\,b^8\,c^{11}\right)}{a^3\,b\,d^8-3\,a^2\,b^2\,c\,d^7+3\,a\,b^3\,c^2\,d^6-b^4\,c^3\,d^5}\right)+\frac{\sqrt{x}\,\left(1296\,a^{14}\,c^4\,d^8-1440\,a^{13}\,b\,c^5\,d^7+400\,a^{12}\,b^2\,c^6\,d^6+6561\,a^{10}\,b^4\,c^8\,d^4-14580\,a^9\,b^5\,c^9\,d^3+12150\,a^8\,b^6\,c^{10}\,d^2-4500\,a^7\,b^7\,c^{11}\,d+625\,a^6\,b^8\,c^{12}\right)}{a^6\,b\,d^{11}-6\,a^5\,b^2\,c\,d^{10}+15\,a^4\,b^3\,c^2\,d^9-20\,a^3\,b^4\,c^3\,d^8+15\,a^2\,b^5\,c^4\,d^7-6\,a\,b^6\,c^5\,d^6+b^7\,c^6\,d^5}\right)-{\left(-\frac{6561\,a^4\,c^5\,d^4-14580\,a^3\,b\,c^6\,d^3+12150\,a^2\,b^2\,c^7\,d^2-4500\,a\,b^3\,c^8\,d+625\,b^4\,c^9}{4096\,a^8\,d^{17}-32768\,a^7\,b\,c\,d^{16}+114688\,a^6\,b^2\,c^2\,d^{15}-229376\,a^5\,b^3\,c^3\,d^{14}+286720\,a^4\,b^4\,c^4\,d^{13}-229376\,a^3\,b^5\,c^5\,d^{12}+114688\,a^2\,b^6\,c^6\,d^{11}-32768\,a\,b^7\,c^7\,d^{10}+4096\,b^8\,c^8\,d^9}\right)}^{1/4}\,\left({\left(-\frac{6561\,a^4\,c^5\,d^4-14580\,a^3\,b\,c^6\,d^3+12150\,a^2\,b^2\,c^7\,d^2-4500\,a\,b^3\,c^8\,d+625\,b^4\,c^9}{4096\,a^8\,d^{17}-32768\,a^7\,b\,c\,d^{16}+114688\,a^6\,b^2\,c^2\,d^{15}-229376\,a^5\,b^3\,c^3\,d^{14}+286720\,a^4\,b^4\,c^4\,d^{13}-229376\,a^3\,b^5\,c^5\,d^{12}+114688\,a^2\,b^6\,c^6\,d^{11}-32768\,a\,b^7\,c^7\,d^{10}+4096\,b^8\,c^8\,d^9}\right)}^{1/4}\,\left({\left(-\frac{6561\,a^4\,c^5\,d^4-14580\,a^3\,b\,c^6\,d^3+12150\,a^2\,b^2\,c^7\,d^2-4500\,a\,b^3\,c^8\,d+625\,b^4\,c^9}{4096\,a^8\,d^{17}-32768\,a^7\,b\,c\,d^{16}+114688\,a^6\,b^2\,c^2\,d^{15}-229376\,a^5\,b^3\,c^3\,d^{14}+286720\,a^4\,b^4\,c^4\,d^{13}-229376\,a^3\,b^5\,c^5\,d^{12}+114688\,a^2\,b^6\,c^6\,d^{11}-32768\,a\,b^7\,c^7\,d^{10}+4096\,b^8\,c^8\,d^9}\right)}^{3/4}\,\left(\frac{\sqrt{x}\,\left(4096\,a^{14}\,b^4\,c^3\,d^{17}-12032\,a^{13}\,b^5\,c^4\,d^{16}-74240\,a^{12}\,b^6\,c^5\,d^{15}+541952\,a^{11}\,b^7\,c^6\,d^{14}-1570816\,a^{10}\,b^8\,c^7\,d^{13}+2691584\,a^9\,b^9\,c^8\,d^{12}-3017728\,a^8\,b^{10}\,c^9\,d^{11}+2286080\,a^7\,b^{11}\,c^{10}\,d^{10}-1165312\,a^6\,b^{12}\,c^{11}\,d^9+384256\,a^5\,b^{13}\,c^{12}\,d^8-74240\,a^4\,b^{14}\,c^{13}\,d^7+6400\,a^3\,b^{15}\,c^{14}\,d^6\right)}{a^6\,b\,d^{11}-6\,a^5\,b^2\,c\,d^{10}+15\,a^4\,b^3\,c^2\,d^9-20\,a^3\,b^4\,c^3\,d^8+15\,a^2\,b^5\,c^4\,d^7-6\,a\,b^6\,c^5\,d^6+b^7\,c^6\,d^5}+\frac{2\,{\left(-\frac{6561\,a^4\,c^5\,d^4-14580\,a^3\,b\,c^6\,d^3+12150\,a^2\,b^2\,c^7\,d^2-4500\,a\,b^3\,c^8\,d+625\,b^4\,c^9}{4096\,a^8\,d^{17}-32768\,a^7\,b\,c\,d^{16}+114688\,a^6\,b^2\,c^2\,d^{15}-229376\,a^5\,b^3\,c^3\,d^{14}+286720\,a^4\,b^4\,c^4\,d^{13}-229376\,a^3\,b^5\,c^5\,d^{12}+114688\,a^2\,b^6\,c^6\,d^{11}-32768\,a\,b^7\,c^7\,d^{10}+4096\,b^8\,c^8\,d^9}\right)}^{1/4}\,\left(5120\,a^{11}\,b^5\,c^3\,d^{16}-40960\,a^{10}\,b^6\,c^4\,d^{15}+143360\,a^9\,b^7\,c^5\,d^{14}-286720\,a^8\,b^8\,c^6\,d^{13}+358400\,a^7\,b^9\,c^7\,d^{12}-286720\,a^6\,b^{10}\,c^8\,d^{11}+143360\,a^5\,b^{11}\,c^9\,d^{10}-40960\,a^4\,b^{12}\,c^{10}\,d^9+5120\,a^3\,b^{13}\,c^{11}\,d^8\right)}{a^3\,b\,d^8-3\,a^2\,b^2\,c\,d^7+3\,a\,b^3\,c^2\,d^6-b^4\,c^3\,d^5}\right)+\frac{2\,\left(576\,a^{12}\,c^3\,d^8+256\,a^{11}\,b\,c^4\,d^7+256\,a^{10}\,b^2\,c^5\,d^6+256\,a^9\,b^3\,c^6\,d^5+256\,a^8\,b^4\,c^7\,d^4-6305\,a^7\,b^5\,c^8\,d^3+8275\,a^6\,b^6\,c^9\,d^2-3875\,a^5\,b^7\,c^{10}\,d+625\,a^4\,b^8\,c^{11}\right)}{a^3\,b\,d^8-3\,a^2\,b^2\,c\,d^7+3\,a\,b^3\,c^2\,d^6-b^4\,c^3\,d^5}\right)+\frac{\sqrt{x}\,\left(1296\,a^{14}\,c^4\,d^8-1440\,a^{13}\,b\,c^5\,d^7+400\,a^{12}\,b^2\,c^6\,d^6+6561\,a^{10}\,b^4\,c^8\,d^4-14580\,a^9\,b^5\,c^9\,d^3+12150\,a^8\,b^6\,c^{10}\,d^2-4500\,a^7\,b^7\,c^{11}\,d+625\,a^6\,b^8\,c^{12}\right)}{a^6\,b\,d^{11}-6\,a^5\,b^2\,c\,d^{10}+15\,a^4\,b^3\,c^2\,d^9-20\,a^3\,b^4\,c^3\,d^8+15\,a^2\,b^5\,c^4\,d^7-6\,a\,b^6\,c^5\,d^6+b^7\,c^6\,d^5}\right)}\right)\,{\left(-\frac{6561\,a^4\,c^5\,d^4-14580\,a^3\,b\,c^6\,d^3+12150\,a^2\,b^2\,c^7\,d^2-4500\,a\,b^3\,c^8\,d+625\,b^4\,c^9}{4096\,a^8\,d^{17}-32768\,a^7\,b\,c\,d^{16}+114688\,a^6\,b^2\,c^2\,d^{15}-229376\,a^5\,b^3\,c^3\,d^{14}+286720\,a^4\,b^4\,c^4\,d^{13}-229376\,a^3\,b^5\,c^5\,d^{12}+114688\,a^2\,b^6\,c^6\,d^{11}-32768\,a\,b^7\,c^7\,d^{10}+4096\,b^8\,c^8\,d^9}\right)}^{1/4}\,2{}\mathrm{i}","Not used",1,"atan((((-a^9/(16*b^13*c^8 + 16*a^8*b^5*d^8 - 128*a^7*b^6*c*d^7 + 448*a^2*b^11*c^6*d^2 - 896*a^3*b^10*c^5*d^3 + 1120*a^4*b^9*c^4*d^4 - 896*a^5*b^8*c^3*d^5 + 448*a^6*b^7*c^2*d^6 - 128*a*b^12*c^7*d))^(1/4)*((-a^9/(16*b^13*c^8 + 16*a^8*b^5*d^8 - 128*a^7*b^6*c*d^7 + 448*a^2*b^11*c^6*d^2 - 896*a^3*b^10*c^5*d^3 + 1120*a^4*b^9*c^4*d^4 - 896*a^5*b^8*c^3*d^5 + 448*a^6*b^7*c^2*d^6 - 128*a*b^12*c^7*d))^(3/4)*((x^(1/2)*(6400*a^3*b^15*c^14*d^6 - 74240*a^4*b^14*c^13*d^7 + 384256*a^5*b^13*c^12*d^8 - 1165312*a^6*b^12*c^11*d^9 + 2286080*a^7*b^11*c^10*d^10 - 3017728*a^8*b^10*c^9*d^11 + 2691584*a^9*b^9*c^8*d^12 - 1570816*a^10*b^8*c^7*d^13 + 541952*a^11*b^7*c^6*d^14 - 74240*a^12*b^6*c^5*d^15 - 12032*a^13*b^5*c^4*d^16 + 4096*a^14*b^4*c^3*d^17))/(a^6*b*d^11 + b^7*c^6*d^5 - 6*a*b^6*c^5*d^6 - 6*a^5*b^2*c*d^10 + 15*a^2*b^5*c^4*d^7 - 20*a^3*b^4*c^3*d^8 + 15*a^4*b^3*c^2*d^9) - (2*(-a^9/(16*b^13*c^8 + 16*a^8*b^5*d^8 - 128*a^7*b^6*c*d^7 + 448*a^2*b^11*c^6*d^2 - 896*a^3*b^10*c^5*d^3 + 1120*a^4*b^9*c^4*d^4 - 896*a^5*b^8*c^3*d^5 + 448*a^6*b^7*c^2*d^6 - 128*a*b^12*c^7*d))^(1/4)*(5120*a^3*b^13*c^11*d^8 - 40960*a^4*b^12*c^10*d^9 + 143360*a^5*b^11*c^9*d^10 - 286720*a^6*b^10*c^8*d^11 + 358400*a^7*b^9*c^7*d^12 - 286720*a^8*b^8*c^6*d^13 + 143360*a^9*b^7*c^5*d^14 - 40960*a^10*b^6*c^4*d^15 + 5120*a^11*b^5*c^3*d^16))/(a^3*b*d^8 - b^4*c^3*d^5 + 3*a*b^3*c^2*d^6 - 3*a^2*b^2*c*d^7)) - (2*(625*a^4*b^8*c^11 + 576*a^12*c^3*d^8 - 3875*a^5*b^7*c^10*d + 256*a^11*b*c^4*d^7 + 8275*a^6*b^6*c^9*d^2 - 6305*a^7*b^5*c^8*d^3 + 256*a^8*b^4*c^7*d^4 + 256*a^9*b^3*c^6*d^5 + 256*a^10*b^2*c^5*d^6))/(a^3*b*d^8 - b^4*c^3*d^5 + 3*a*b^3*c^2*d^6 - 3*a^2*b^2*c*d^7)) + (x^(1/2)*(625*a^6*b^8*c^12 + 1296*a^14*c^4*d^8 - 4500*a^7*b^7*c^11*d - 1440*a^13*b*c^5*d^7 + 12150*a^8*b^6*c^10*d^2 - 14580*a^9*b^5*c^9*d^3 + 6561*a^10*b^4*c^8*d^4 + 400*a^12*b^2*c^6*d^6))/(a^6*b*d^11 + b^7*c^6*d^5 - 6*a*b^6*c^5*d^6 - 6*a^5*b^2*c*d^10 + 15*a^2*b^5*c^4*d^7 - 20*a^3*b^4*c^3*d^8 + 15*a^4*b^3*c^2*d^9))*(-a^9/(16*b^13*c^8 + 16*a^8*b^5*d^8 - 128*a^7*b^6*c*d^7 + 448*a^2*b^11*c^6*d^2 - 896*a^3*b^10*c^5*d^3 + 1120*a^4*b^9*c^4*d^4 - 896*a^5*b^8*c^3*d^5 + 448*a^6*b^7*c^2*d^6 - 128*a*b^12*c^7*d))^(1/4)*1i + ((-a^9/(16*b^13*c^8 + 16*a^8*b^5*d^8 - 128*a^7*b^6*c*d^7 + 448*a^2*b^11*c^6*d^2 - 896*a^3*b^10*c^5*d^3 + 1120*a^4*b^9*c^4*d^4 - 896*a^5*b^8*c^3*d^5 + 448*a^6*b^7*c^2*d^6 - 128*a*b^12*c^7*d))^(1/4)*((-a^9/(16*b^13*c^8 + 16*a^8*b^5*d^8 - 128*a^7*b^6*c*d^7 + 448*a^2*b^11*c^6*d^2 - 896*a^3*b^10*c^5*d^3 + 1120*a^4*b^9*c^4*d^4 - 896*a^5*b^8*c^3*d^5 + 448*a^6*b^7*c^2*d^6 - 128*a*b^12*c^7*d))^(3/4)*((x^(1/2)*(6400*a^3*b^15*c^14*d^6 - 74240*a^4*b^14*c^13*d^7 + 384256*a^5*b^13*c^12*d^8 - 1165312*a^6*b^12*c^11*d^9 + 2286080*a^7*b^11*c^10*d^10 - 3017728*a^8*b^10*c^9*d^11 + 2691584*a^9*b^9*c^8*d^12 - 1570816*a^10*b^8*c^7*d^13 + 541952*a^11*b^7*c^6*d^14 - 74240*a^12*b^6*c^5*d^15 - 12032*a^13*b^5*c^4*d^16 + 4096*a^14*b^4*c^3*d^17))/(a^6*b*d^11 + b^7*c^6*d^5 - 6*a*b^6*c^5*d^6 - 6*a^5*b^2*c*d^10 + 15*a^2*b^5*c^4*d^7 - 20*a^3*b^4*c^3*d^8 + 15*a^4*b^3*c^2*d^9) + (2*(-a^9/(16*b^13*c^8 + 16*a^8*b^5*d^8 - 128*a^7*b^6*c*d^7 + 448*a^2*b^11*c^6*d^2 - 896*a^3*b^10*c^5*d^3 + 1120*a^4*b^9*c^4*d^4 - 896*a^5*b^8*c^3*d^5 + 448*a^6*b^7*c^2*d^6 - 128*a*b^12*c^7*d))^(1/4)*(5120*a^3*b^13*c^11*d^8 - 40960*a^4*b^12*c^10*d^9 + 143360*a^5*b^11*c^9*d^10 - 286720*a^6*b^10*c^8*d^11 + 358400*a^7*b^9*c^7*d^12 - 286720*a^8*b^8*c^6*d^13 + 143360*a^9*b^7*c^5*d^14 - 40960*a^10*b^6*c^4*d^15 + 5120*a^11*b^5*c^3*d^16))/(a^3*b*d^8 - b^4*c^3*d^5 + 3*a*b^3*c^2*d^6 - 3*a^2*b^2*c*d^7)) + (2*(625*a^4*b^8*c^11 + 576*a^12*c^3*d^8 - 3875*a^5*b^7*c^10*d + 256*a^11*b*c^4*d^7 + 8275*a^6*b^6*c^9*d^2 - 6305*a^7*b^5*c^8*d^3 + 256*a^8*b^4*c^7*d^4 + 256*a^9*b^3*c^6*d^5 + 256*a^10*b^2*c^5*d^6))/(a^3*b*d^8 - b^4*c^3*d^5 + 3*a*b^3*c^2*d^6 - 3*a^2*b^2*c*d^7)) + (x^(1/2)*(625*a^6*b^8*c^12 + 1296*a^14*c^4*d^8 - 4500*a^7*b^7*c^11*d - 1440*a^13*b*c^5*d^7 + 12150*a^8*b^6*c^10*d^2 - 14580*a^9*b^5*c^9*d^3 + 6561*a^10*b^4*c^8*d^4 + 400*a^12*b^2*c^6*d^6))/(a^6*b*d^11 + b^7*c^6*d^5 - 6*a*b^6*c^5*d^6 - 6*a^5*b^2*c*d^10 + 15*a^2*b^5*c^4*d^7 - 20*a^3*b^4*c^3*d^8 + 15*a^4*b^3*c^2*d^9))*(-a^9/(16*b^13*c^8 + 16*a^8*b^5*d^8 - 128*a^7*b^6*c*d^7 + 448*a^2*b^11*c^6*d^2 - 896*a^3*b^10*c^5*d^3 + 1120*a^4*b^9*c^4*d^4 - 896*a^5*b^8*c^3*d^5 + 448*a^6*b^7*c^2*d^6 - 128*a*b^12*c^7*d))^(1/4)*1i)/(((-a^9/(16*b^13*c^8 + 16*a^8*b^5*d^8 - 128*a^7*b^6*c*d^7 + 448*a^2*b^11*c^6*d^2 - 896*a^3*b^10*c^5*d^3 + 1120*a^4*b^9*c^4*d^4 - 896*a^5*b^8*c^3*d^5 + 448*a^6*b^7*c^2*d^6 - 128*a*b^12*c^7*d))^(1/4)*((-a^9/(16*b^13*c^8 + 16*a^8*b^5*d^8 - 128*a^7*b^6*c*d^7 + 448*a^2*b^11*c^6*d^2 - 896*a^3*b^10*c^5*d^3 + 1120*a^4*b^9*c^4*d^4 - 896*a^5*b^8*c^3*d^5 + 448*a^6*b^7*c^2*d^6 - 128*a*b^12*c^7*d))^(3/4)*((x^(1/2)*(6400*a^3*b^15*c^14*d^6 - 74240*a^4*b^14*c^13*d^7 + 384256*a^5*b^13*c^12*d^8 - 1165312*a^6*b^12*c^11*d^9 + 2286080*a^7*b^11*c^10*d^10 - 3017728*a^8*b^10*c^9*d^11 + 2691584*a^9*b^9*c^8*d^12 - 1570816*a^10*b^8*c^7*d^13 + 541952*a^11*b^7*c^6*d^14 - 74240*a^12*b^6*c^5*d^15 - 12032*a^13*b^5*c^4*d^16 + 4096*a^14*b^4*c^3*d^17))/(a^6*b*d^11 + b^7*c^6*d^5 - 6*a*b^6*c^5*d^6 - 6*a^5*b^2*c*d^10 + 15*a^2*b^5*c^4*d^7 - 20*a^3*b^4*c^3*d^8 + 15*a^4*b^3*c^2*d^9) - (2*(-a^9/(16*b^13*c^8 + 16*a^8*b^5*d^8 - 128*a^7*b^6*c*d^7 + 448*a^2*b^11*c^6*d^2 - 896*a^3*b^10*c^5*d^3 + 1120*a^4*b^9*c^4*d^4 - 896*a^5*b^8*c^3*d^5 + 448*a^6*b^7*c^2*d^6 - 128*a*b^12*c^7*d))^(1/4)*(5120*a^3*b^13*c^11*d^8 - 40960*a^4*b^12*c^10*d^9 + 143360*a^5*b^11*c^9*d^10 - 286720*a^6*b^10*c^8*d^11 + 358400*a^7*b^9*c^7*d^12 - 286720*a^8*b^8*c^6*d^13 + 143360*a^9*b^7*c^5*d^14 - 40960*a^10*b^6*c^4*d^15 + 5120*a^11*b^5*c^3*d^16))/(a^3*b*d^8 - b^4*c^3*d^5 + 3*a*b^3*c^2*d^6 - 3*a^2*b^2*c*d^7)) - (2*(625*a^4*b^8*c^11 + 576*a^12*c^3*d^8 - 3875*a^5*b^7*c^10*d + 256*a^11*b*c^4*d^7 + 8275*a^6*b^6*c^9*d^2 - 6305*a^7*b^5*c^8*d^3 + 256*a^8*b^4*c^7*d^4 + 256*a^9*b^3*c^6*d^5 + 256*a^10*b^2*c^5*d^6))/(a^3*b*d^8 - b^4*c^3*d^5 + 3*a*b^3*c^2*d^6 - 3*a^2*b^2*c*d^7)) + (x^(1/2)*(625*a^6*b^8*c^12 + 1296*a^14*c^4*d^8 - 4500*a^7*b^7*c^11*d - 1440*a^13*b*c^5*d^7 + 12150*a^8*b^6*c^10*d^2 - 14580*a^9*b^5*c^9*d^3 + 6561*a^10*b^4*c^8*d^4 + 400*a^12*b^2*c^6*d^6))/(a^6*b*d^11 + b^7*c^6*d^5 - 6*a*b^6*c^5*d^6 - 6*a^5*b^2*c*d^10 + 15*a^2*b^5*c^4*d^7 - 20*a^3*b^4*c^3*d^8 + 15*a^4*b^3*c^2*d^9))*(-a^9/(16*b^13*c^8 + 16*a^8*b^5*d^8 - 128*a^7*b^6*c*d^7 + 448*a^2*b^11*c^6*d^2 - 896*a^3*b^10*c^5*d^3 + 1120*a^4*b^9*c^4*d^4 - 896*a^5*b^8*c^3*d^5 + 448*a^6*b^7*c^2*d^6 - 128*a*b^12*c^7*d))^(1/4) - ((-a^9/(16*b^13*c^8 + 16*a^8*b^5*d^8 - 128*a^7*b^6*c*d^7 + 448*a^2*b^11*c^6*d^2 - 896*a^3*b^10*c^5*d^3 + 1120*a^4*b^9*c^4*d^4 - 896*a^5*b^8*c^3*d^5 + 448*a^6*b^7*c^2*d^6 - 128*a*b^12*c^7*d))^(1/4)*((-a^9/(16*b^13*c^8 + 16*a^8*b^5*d^8 - 128*a^7*b^6*c*d^7 + 448*a^2*b^11*c^6*d^2 - 896*a^3*b^10*c^5*d^3 + 1120*a^4*b^9*c^4*d^4 - 896*a^5*b^8*c^3*d^5 + 448*a^6*b^7*c^2*d^6 - 128*a*b^12*c^7*d))^(3/4)*((x^(1/2)*(6400*a^3*b^15*c^14*d^6 - 74240*a^4*b^14*c^13*d^7 + 384256*a^5*b^13*c^12*d^8 - 1165312*a^6*b^12*c^11*d^9 + 2286080*a^7*b^11*c^10*d^10 - 3017728*a^8*b^10*c^9*d^11 + 2691584*a^9*b^9*c^8*d^12 - 1570816*a^10*b^8*c^7*d^13 + 541952*a^11*b^7*c^6*d^14 - 74240*a^12*b^6*c^5*d^15 - 12032*a^13*b^5*c^4*d^16 + 4096*a^14*b^4*c^3*d^17))/(a^6*b*d^11 + b^7*c^6*d^5 - 6*a*b^6*c^5*d^6 - 6*a^5*b^2*c*d^10 + 15*a^2*b^5*c^4*d^7 - 20*a^3*b^4*c^3*d^8 + 15*a^4*b^3*c^2*d^9) + (2*(-a^9/(16*b^13*c^8 + 16*a^8*b^5*d^8 - 128*a^7*b^6*c*d^7 + 448*a^2*b^11*c^6*d^2 - 896*a^3*b^10*c^5*d^3 + 1120*a^4*b^9*c^4*d^4 - 896*a^5*b^8*c^3*d^5 + 448*a^6*b^7*c^2*d^6 - 128*a*b^12*c^7*d))^(1/4)*(5120*a^3*b^13*c^11*d^8 - 40960*a^4*b^12*c^10*d^9 + 143360*a^5*b^11*c^9*d^10 - 286720*a^6*b^10*c^8*d^11 + 358400*a^7*b^9*c^7*d^12 - 286720*a^8*b^8*c^6*d^13 + 143360*a^9*b^7*c^5*d^14 - 40960*a^10*b^6*c^4*d^15 + 5120*a^11*b^5*c^3*d^16))/(a^3*b*d^8 - b^4*c^3*d^5 + 3*a*b^3*c^2*d^6 - 3*a^2*b^2*c*d^7)) + (2*(625*a^4*b^8*c^11 + 576*a^12*c^3*d^8 - 3875*a^5*b^7*c^10*d + 256*a^11*b*c^4*d^7 + 8275*a^6*b^6*c^9*d^2 - 6305*a^7*b^5*c^8*d^3 + 256*a^8*b^4*c^7*d^4 + 256*a^9*b^3*c^6*d^5 + 256*a^10*b^2*c^5*d^6))/(a^3*b*d^8 - b^4*c^3*d^5 + 3*a*b^3*c^2*d^6 - 3*a^2*b^2*c*d^7)) + (x^(1/2)*(625*a^6*b^8*c^12 + 1296*a^14*c^4*d^8 - 4500*a^7*b^7*c^11*d - 1440*a^13*b*c^5*d^7 + 12150*a^8*b^6*c^10*d^2 - 14580*a^9*b^5*c^9*d^3 + 6561*a^10*b^4*c^8*d^4 + 400*a^12*b^2*c^6*d^6))/(a^6*b*d^11 + b^7*c^6*d^5 - 6*a*b^6*c^5*d^6 - 6*a^5*b^2*c*d^10 + 15*a^2*b^5*c^4*d^7 - 20*a^3*b^4*c^3*d^8 + 15*a^4*b^3*c^2*d^9))*(-a^9/(16*b^13*c^8 + 16*a^8*b^5*d^8 - 128*a^7*b^6*c*d^7 + 448*a^2*b^11*c^6*d^2 - 896*a^3*b^10*c^5*d^3 + 1120*a^4*b^9*c^4*d^4 - 896*a^5*b^8*c^3*d^5 + 448*a^6*b^7*c^2*d^6 - 128*a*b^12*c^7*d))^(1/4)))*(-a^9/(16*b^13*c^8 + 16*a^8*b^5*d^8 - 128*a^7*b^6*c*d^7 + 448*a^2*b^11*c^6*d^2 - 896*a^3*b^10*c^5*d^3 + 1120*a^4*b^9*c^4*d^4 - 896*a^5*b^8*c^3*d^5 + 448*a^6*b^7*c^2*d^6 - 128*a*b^12*c^7*d))^(1/4)*2i + 2*atan((((-a^9/(16*b^13*c^8 + 16*a^8*b^5*d^8 - 128*a^7*b^6*c*d^7 + 448*a^2*b^11*c^6*d^2 - 896*a^3*b^10*c^5*d^3 + 1120*a^4*b^9*c^4*d^4 - 896*a^5*b^8*c^3*d^5 + 448*a^6*b^7*c^2*d^6 - 128*a*b^12*c^7*d))^(1/4)*((-a^9/(16*b^13*c^8 + 16*a^8*b^5*d^8 - 128*a^7*b^6*c*d^7 + 448*a^2*b^11*c^6*d^2 - 896*a^3*b^10*c^5*d^3 + 1120*a^4*b^9*c^4*d^4 - 896*a^5*b^8*c^3*d^5 + 448*a^6*b^7*c^2*d^6 - 128*a*b^12*c^7*d))^(3/4)*((x^(1/2)*(6400*a^3*b^15*c^14*d^6 - 74240*a^4*b^14*c^13*d^7 + 384256*a^5*b^13*c^12*d^8 - 1165312*a^6*b^12*c^11*d^9 + 2286080*a^7*b^11*c^10*d^10 - 3017728*a^8*b^10*c^9*d^11 + 2691584*a^9*b^9*c^8*d^12 - 1570816*a^10*b^8*c^7*d^13 + 541952*a^11*b^7*c^6*d^14 - 74240*a^12*b^6*c^5*d^15 - 12032*a^13*b^5*c^4*d^16 + 4096*a^14*b^4*c^3*d^17))/(a^6*b*d^11 + b^7*c^6*d^5 - 6*a*b^6*c^5*d^6 - 6*a^5*b^2*c*d^10 + 15*a^2*b^5*c^4*d^7 - 20*a^3*b^4*c^3*d^8 + 15*a^4*b^3*c^2*d^9) - ((-a^9/(16*b^13*c^8 + 16*a^8*b^5*d^8 - 128*a^7*b^6*c*d^7 + 448*a^2*b^11*c^6*d^2 - 896*a^3*b^10*c^5*d^3 + 1120*a^4*b^9*c^4*d^4 - 896*a^5*b^8*c^3*d^5 + 448*a^6*b^7*c^2*d^6 - 128*a*b^12*c^7*d))^(1/4)*(5120*a^3*b^13*c^11*d^8 - 40960*a^4*b^12*c^10*d^9 + 143360*a^5*b^11*c^9*d^10 - 286720*a^6*b^10*c^8*d^11 + 358400*a^7*b^9*c^7*d^12 - 286720*a^8*b^8*c^6*d^13 + 143360*a^9*b^7*c^5*d^14 - 40960*a^10*b^6*c^4*d^15 + 5120*a^11*b^5*c^3*d^16)*2i)/(a^3*b*d^8 - b^4*c^3*d^5 + 3*a*b^3*c^2*d^6 - 3*a^2*b^2*c*d^7))*1i + (2*(625*a^4*b^8*c^11 + 576*a^12*c^3*d^8 - 3875*a^5*b^7*c^10*d + 256*a^11*b*c^4*d^7 + 8275*a^6*b^6*c^9*d^2 - 6305*a^7*b^5*c^8*d^3 + 256*a^8*b^4*c^7*d^4 + 256*a^9*b^3*c^6*d^5 + 256*a^10*b^2*c^5*d^6))/(a^3*b*d^8 - b^4*c^3*d^5 + 3*a*b^3*c^2*d^6 - 3*a^2*b^2*c*d^7))*1i - (x^(1/2)*(625*a^6*b^8*c^12 + 1296*a^14*c^4*d^8 - 4500*a^7*b^7*c^11*d - 1440*a^13*b*c^5*d^7 + 12150*a^8*b^6*c^10*d^2 - 14580*a^9*b^5*c^9*d^3 + 6561*a^10*b^4*c^8*d^4 + 400*a^12*b^2*c^6*d^6))/(a^6*b*d^11 + b^7*c^6*d^5 - 6*a*b^6*c^5*d^6 - 6*a^5*b^2*c*d^10 + 15*a^2*b^5*c^4*d^7 - 20*a^3*b^4*c^3*d^8 + 15*a^4*b^3*c^2*d^9))*(-a^9/(16*b^13*c^8 + 16*a^8*b^5*d^8 - 128*a^7*b^6*c*d^7 + 448*a^2*b^11*c^6*d^2 - 896*a^3*b^10*c^5*d^3 + 1120*a^4*b^9*c^4*d^4 - 896*a^5*b^8*c^3*d^5 + 448*a^6*b^7*c^2*d^6 - 128*a*b^12*c^7*d))^(1/4) + ((-a^9/(16*b^13*c^8 + 16*a^8*b^5*d^8 - 128*a^7*b^6*c*d^7 + 448*a^2*b^11*c^6*d^2 - 896*a^3*b^10*c^5*d^3 + 1120*a^4*b^9*c^4*d^4 - 896*a^5*b^8*c^3*d^5 + 448*a^6*b^7*c^2*d^6 - 128*a*b^12*c^7*d))^(1/4)*((-a^9/(16*b^13*c^8 + 16*a^8*b^5*d^8 - 128*a^7*b^6*c*d^7 + 448*a^2*b^11*c^6*d^2 - 896*a^3*b^10*c^5*d^3 + 1120*a^4*b^9*c^4*d^4 - 896*a^5*b^8*c^3*d^5 + 448*a^6*b^7*c^2*d^6 - 128*a*b^12*c^7*d))^(3/4)*((x^(1/2)*(6400*a^3*b^15*c^14*d^6 - 74240*a^4*b^14*c^13*d^7 + 384256*a^5*b^13*c^12*d^8 - 1165312*a^6*b^12*c^11*d^9 + 2286080*a^7*b^11*c^10*d^10 - 3017728*a^8*b^10*c^9*d^11 + 2691584*a^9*b^9*c^8*d^12 - 1570816*a^10*b^8*c^7*d^13 + 541952*a^11*b^7*c^6*d^14 - 74240*a^12*b^6*c^5*d^15 - 12032*a^13*b^5*c^4*d^16 + 4096*a^14*b^4*c^3*d^17))/(a^6*b*d^11 + b^7*c^6*d^5 - 6*a*b^6*c^5*d^6 - 6*a^5*b^2*c*d^10 + 15*a^2*b^5*c^4*d^7 - 20*a^3*b^4*c^3*d^8 + 15*a^4*b^3*c^2*d^9) + ((-a^9/(16*b^13*c^8 + 16*a^8*b^5*d^8 - 128*a^7*b^6*c*d^7 + 448*a^2*b^11*c^6*d^2 - 896*a^3*b^10*c^5*d^3 + 1120*a^4*b^9*c^4*d^4 - 896*a^5*b^8*c^3*d^5 + 448*a^6*b^7*c^2*d^6 - 128*a*b^12*c^7*d))^(1/4)*(5120*a^3*b^13*c^11*d^8 - 40960*a^4*b^12*c^10*d^9 + 143360*a^5*b^11*c^9*d^10 - 286720*a^6*b^10*c^8*d^11 + 358400*a^7*b^9*c^7*d^12 - 286720*a^8*b^8*c^6*d^13 + 143360*a^9*b^7*c^5*d^14 - 40960*a^10*b^6*c^4*d^15 + 5120*a^11*b^5*c^3*d^16)*2i)/(a^3*b*d^8 - b^4*c^3*d^5 + 3*a*b^3*c^2*d^6 - 3*a^2*b^2*c*d^7))*1i - (2*(625*a^4*b^8*c^11 + 576*a^12*c^3*d^8 - 3875*a^5*b^7*c^10*d + 256*a^11*b*c^4*d^7 + 8275*a^6*b^6*c^9*d^2 - 6305*a^7*b^5*c^8*d^3 + 256*a^8*b^4*c^7*d^4 + 256*a^9*b^3*c^6*d^5 + 256*a^10*b^2*c^5*d^6))/(a^3*b*d^8 - b^4*c^3*d^5 + 3*a*b^3*c^2*d^6 - 3*a^2*b^2*c*d^7))*1i - (x^(1/2)*(625*a^6*b^8*c^12 + 1296*a^14*c^4*d^8 - 4500*a^7*b^7*c^11*d - 1440*a^13*b*c^5*d^7 + 12150*a^8*b^6*c^10*d^2 - 14580*a^9*b^5*c^9*d^3 + 6561*a^10*b^4*c^8*d^4 + 400*a^12*b^2*c^6*d^6))/(a^6*b*d^11 + b^7*c^6*d^5 - 6*a*b^6*c^5*d^6 - 6*a^5*b^2*c*d^10 + 15*a^2*b^5*c^4*d^7 - 20*a^3*b^4*c^3*d^8 + 15*a^4*b^3*c^2*d^9))*(-a^9/(16*b^13*c^8 + 16*a^8*b^5*d^8 - 128*a^7*b^6*c*d^7 + 448*a^2*b^11*c^6*d^2 - 896*a^3*b^10*c^5*d^3 + 1120*a^4*b^9*c^4*d^4 - 896*a^5*b^8*c^3*d^5 + 448*a^6*b^7*c^2*d^6 - 128*a*b^12*c^7*d))^(1/4))/(((-a^9/(16*b^13*c^8 + 16*a^8*b^5*d^8 - 128*a^7*b^6*c*d^7 + 448*a^2*b^11*c^6*d^2 - 896*a^3*b^10*c^5*d^3 + 1120*a^4*b^9*c^4*d^4 - 896*a^5*b^8*c^3*d^5 + 448*a^6*b^7*c^2*d^6 - 128*a*b^12*c^7*d))^(1/4)*((-a^9/(16*b^13*c^8 + 16*a^8*b^5*d^8 - 128*a^7*b^6*c*d^7 + 448*a^2*b^11*c^6*d^2 - 896*a^3*b^10*c^5*d^3 + 1120*a^4*b^9*c^4*d^4 - 896*a^5*b^8*c^3*d^5 + 448*a^6*b^7*c^2*d^6 - 128*a*b^12*c^7*d))^(3/4)*((x^(1/2)*(6400*a^3*b^15*c^14*d^6 - 74240*a^4*b^14*c^13*d^7 + 384256*a^5*b^13*c^12*d^8 - 1165312*a^6*b^12*c^11*d^9 + 2286080*a^7*b^11*c^10*d^10 - 3017728*a^8*b^10*c^9*d^11 + 2691584*a^9*b^9*c^8*d^12 - 1570816*a^10*b^8*c^7*d^13 + 541952*a^11*b^7*c^6*d^14 - 74240*a^12*b^6*c^5*d^15 - 12032*a^13*b^5*c^4*d^16 + 4096*a^14*b^4*c^3*d^17))/(a^6*b*d^11 + b^7*c^6*d^5 - 6*a*b^6*c^5*d^6 - 6*a^5*b^2*c*d^10 + 15*a^2*b^5*c^4*d^7 - 20*a^3*b^4*c^3*d^8 + 15*a^4*b^3*c^2*d^9) - ((-a^9/(16*b^13*c^8 + 16*a^8*b^5*d^8 - 128*a^7*b^6*c*d^7 + 448*a^2*b^11*c^6*d^2 - 896*a^3*b^10*c^5*d^3 + 1120*a^4*b^9*c^4*d^4 - 896*a^5*b^8*c^3*d^5 + 448*a^6*b^7*c^2*d^6 - 128*a*b^12*c^7*d))^(1/4)*(5120*a^3*b^13*c^11*d^8 - 40960*a^4*b^12*c^10*d^9 + 143360*a^5*b^11*c^9*d^10 - 286720*a^6*b^10*c^8*d^11 + 358400*a^7*b^9*c^7*d^12 - 286720*a^8*b^8*c^6*d^13 + 143360*a^9*b^7*c^5*d^14 - 40960*a^10*b^6*c^4*d^15 + 5120*a^11*b^5*c^3*d^16)*2i)/(a^3*b*d^8 - b^4*c^3*d^5 + 3*a*b^3*c^2*d^6 - 3*a^2*b^2*c*d^7))*1i + (2*(625*a^4*b^8*c^11 + 576*a^12*c^3*d^8 - 3875*a^5*b^7*c^10*d + 256*a^11*b*c^4*d^7 + 8275*a^6*b^6*c^9*d^2 - 6305*a^7*b^5*c^8*d^3 + 256*a^8*b^4*c^7*d^4 + 256*a^9*b^3*c^6*d^5 + 256*a^10*b^2*c^5*d^6))/(a^3*b*d^8 - b^4*c^3*d^5 + 3*a*b^3*c^2*d^6 - 3*a^2*b^2*c*d^7))*1i - (x^(1/2)*(625*a^6*b^8*c^12 + 1296*a^14*c^4*d^8 - 4500*a^7*b^7*c^11*d - 1440*a^13*b*c^5*d^7 + 12150*a^8*b^6*c^10*d^2 - 14580*a^9*b^5*c^9*d^3 + 6561*a^10*b^4*c^8*d^4 + 400*a^12*b^2*c^6*d^6))/(a^6*b*d^11 + b^7*c^6*d^5 - 6*a*b^6*c^5*d^6 - 6*a^5*b^2*c*d^10 + 15*a^2*b^5*c^4*d^7 - 20*a^3*b^4*c^3*d^8 + 15*a^4*b^3*c^2*d^9))*(-a^9/(16*b^13*c^8 + 16*a^8*b^5*d^8 - 128*a^7*b^6*c*d^7 + 448*a^2*b^11*c^6*d^2 - 896*a^3*b^10*c^5*d^3 + 1120*a^4*b^9*c^4*d^4 - 896*a^5*b^8*c^3*d^5 + 448*a^6*b^7*c^2*d^6 - 128*a*b^12*c^7*d))^(1/4)*1i - ((-a^9/(16*b^13*c^8 + 16*a^8*b^5*d^8 - 128*a^7*b^6*c*d^7 + 448*a^2*b^11*c^6*d^2 - 896*a^3*b^10*c^5*d^3 + 1120*a^4*b^9*c^4*d^4 - 896*a^5*b^8*c^3*d^5 + 448*a^6*b^7*c^2*d^6 - 128*a*b^12*c^7*d))^(1/4)*((-a^9/(16*b^13*c^8 + 16*a^8*b^5*d^8 - 128*a^7*b^6*c*d^7 + 448*a^2*b^11*c^6*d^2 - 896*a^3*b^10*c^5*d^3 + 1120*a^4*b^9*c^4*d^4 - 896*a^5*b^8*c^3*d^5 + 448*a^6*b^7*c^2*d^6 - 128*a*b^12*c^7*d))^(3/4)*((x^(1/2)*(6400*a^3*b^15*c^14*d^6 - 74240*a^4*b^14*c^13*d^7 + 384256*a^5*b^13*c^12*d^8 - 1165312*a^6*b^12*c^11*d^9 + 2286080*a^7*b^11*c^10*d^10 - 3017728*a^8*b^10*c^9*d^11 + 2691584*a^9*b^9*c^8*d^12 - 1570816*a^10*b^8*c^7*d^13 + 541952*a^11*b^7*c^6*d^14 - 74240*a^12*b^6*c^5*d^15 - 12032*a^13*b^5*c^4*d^16 + 4096*a^14*b^4*c^3*d^17))/(a^6*b*d^11 + b^7*c^6*d^5 - 6*a*b^6*c^5*d^6 - 6*a^5*b^2*c*d^10 + 15*a^2*b^5*c^4*d^7 - 20*a^3*b^4*c^3*d^8 + 15*a^4*b^3*c^2*d^9) + ((-a^9/(16*b^13*c^8 + 16*a^8*b^5*d^8 - 128*a^7*b^6*c*d^7 + 448*a^2*b^11*c^6*d^2 - 896*a^3*b^10*c^5*d^3 + 1120*a^4*b^9*c^4*d^4 - 896*a^5*b^8*c^3*d^5 + 448*a^6*b^7*c^2*d^6 - 128*a*b^12*c^7*d))^(1/4)*(5120*a^3*b^13*c^11*d^8 - 40960*a^4*b^12*c^10*d^9 + 143360*a^5*b^11*c^9*d^10 - 286720*a^6*b^10*c^8*d^11 + 358400*a^7*b^9*c^7*d^12 - 286720*a^8*b^8*c^6*d^13 + 143360*a^9*b^7*c^5*d^14 - 40960*a^10*b^6*c^4*d^15 + 5120*a^11*b^5*c^3*d^16)*2i)/(a^3*b*d^8 - b^4*c^3*d^5 + 3*a*b^3*c^2*d^6 - 3*a^2*b^2*c*d^7))*1i - (2*(625*a^4*b^8*c^11 + 576*a^12*c^3*d^8 - 3875*a^5*b^7*c^10*d + 256*a^11*b*c^4*d^7 + 8275*a^6*b^6*c^9*d^2 - 6305*a^7*b^5*c^8*d^3 + 256*a^8*b^4*c^7*d^4 + 256*a^9*b^3*c^6*d^5 + 256*a^10*b^2*c^5*d^6))/(a^3*b*d^8 - b^4*c^3*d^5 + 3*a*b^3*c^2*d^6 - 3*a^2*b^2*c*d^7))*1i - (x^(1/2)*(625*a^6*b^8*c^12 + 1296*a^14*c^4*d^8 - 4500*a^7*b^7*c^11*d - 1440*a^13*b*c^5*d^7 + 12150*a^8*b^6*c^10*d^2 - 14580*a^9*b^5*c^9*d^3 + 6561*a^10*b^4*c^8*d^4 + 400*a^12*b^2*c^6*d^6))/(a^6*b*d^11 + b^7*c^6*d^5 - 6*a*b^6*c^5*d^6 - 6*a^5*b^2*c*d^10 + 15*a^2*b^5*c^4*d^7 - 20*a^3*b^4*c^3*d^8 + 15*a^4*b^3*c^2*d^9))*(-a^9/(16*b^13*c^8 + 16*a^8*b^5*d^8 - 128*a^7*b^6*c*d^7 + 448*a^2*b^11*c^6*d^2 - 896*a^3*b^10*c^5*d^3 + 1120*a^4*b^9*c^4*d^4 - 896*a^5*b^8*c^3*d^5 + 448*a^6*b^7*c^2*d^6 - 128*a*b^12*c^7*d))^(1/4)*1i))*(-a^9/(16*b^13*c^8 + 16*a^8*b^5*d^8 - 128*a^7*b^6*c*d^7 + 448*a^2*b^11*c^6*d^2 - 896*a^3*b^10*c^5*d^3 + 1120*a^4*b^9*c^4*d^4 - 896*a^5*b^8*c^3*d^5 + 448*a^6*b^7*c^2*d^6 - 128*a*b^12*c^7*d))^(1/4) + atan(((-(625*b^4*c^9 + 6561*a^4*c^5*d^4 - 14580*a^3*b*c^6*d^3 + 12150*a^2*b^2*c^7*d^2 - 4500*a*b^3*c^8*d)/(4096*a^8*d^17 + 4096*b^8*c^8*d^9 - 32768*a*b^7*c^7*d^10 + 114688*a^2*b^6*c^6*d^11 - 229376*a^3*b^5*c^5*d^12 + 286720*a^4*b^4*c^4*d^13 - 229376*a^5*b^3*c^3*d^14 + 114688*a^6*b^2*c^2*d^15 - 32768*a^7*b*c*d^16))^(1/4)*((-(625*b^4*c^9 + 6561*a^4*c^5*d^4 - 14580*a^3*b*c^6*d^3 + 12150*a^2*b^2*c^7*d^2 - 4500*a*b^3*c^8*d)/(4096*a^8*d^17 + 4096*b^8*c^8*d^9 - 32768*a*b^7*c^7*d^10 + 114688*a^2*b^6*c^6*d^11 - 229376*a^3*b^5*c^5*d^12 + 286720*a^4*b^4*c^4*d^13 - 229376*a^5*b^3*c^3*d^14 + 114688*a^6*b^2*c^2*d^15 - 32768*a^7*b*c*d^16))^(1/4)*((-(625*b^4*c^9 + 6561*a^4*c^5*d^4 - 14580*a^3*b*c^6*d^3 + 12150*a^2*b^2*c^7*d^2 - 4500*a*b^3*c^8*d)/(4096*a^8*d^17 + 4096*b^8*c^8*d^9 - 32768*a*b^7*c^7*d^10 + 114688*a^2*b^6*c^6*d^11 - 229376*a^3*b^5*c^5*d^12 + 286720*a^4*b^4*c^4*d^13 - 229376*a^5*b^3*c^3*d^14 + 114688*a^6*b^2*c^2*d^15 - 32768*a^7*b*c*d^16))^(3/4)*((x^(1/2)*(6400*a^3*b^15*c^14*d^6 - 74240*a^4*b^14*c^13*d^7 + 384256*a^5*b^13*c^12*d^8 - 1165312*a^6*b^12*c^11*d^9 + 2286080*a^7*b^11*c^10*d^10 - 3017728*a^8*b^10*c^9*d^11 + 2691584*a^9*b^9*c^8*d^12 - 1570816*a^10*b^8*c^7*d^13 + 541952*a^11*b^7*c^6*d^14 - 74240*a^12*b^6*c^5*d^15 - 12032*a^13*b^5*c^4*d^16 + 4096*a^14*b^4*c^3*d^17))/(a^6*b*d^11 + b^7*c^6*d^5 - 6*a*b^6*c^5*d^6 - 6*a^5*b^2*c*d^10 + 15*a^2*b^5*c^4*d^7 - 20*a^3*b^4*c^3*d^8 + 15*a^4*b^3*c^2*d^9) - (2*(-(625*b^4*c^9 + 6561*a^4*c^5*d^4 - 14580*a^3*b*c^6*d^3 + 12150*a^2*b^2*c^7*d^2 - 4500*a*b^3*c^8*d)/(4096*a^8*d^17 + 4096*b^8*c^8*d^9 - 32768*a*b^7*c^7*d^10 + 114688*a^2*b^6*c^6*d^11 - 229376*a^3*b^5*c^5*d^12 + 286720*a^4*b^4*c^4*d^13 - 229376*a^5*b^3*c^3*d^14 + 114688*a^6*b^2*c^2*d^15 - 32768*a^7*b*c*d^16))^(1/4)*(5120*a^3*b^13*c^11*d^8 - 40960*a^4*b^12*c^10*d^9 + 143360*a^5*b^11*c^9*d^10 - 286720*a^6*b^10*c^8*d^11 + 358400*a^7*b^9*c^7*d^12 - 286720*a^8*b^8*c^6*d^13 + 143360*a^9*b^7*c^5*d^14 - 40960*a^10*b^6*c^4*d^15 + 5120*a^11*b^5*c^3*d^16))/(a^3*b*d^8 - b^4*c^3*d^5 + 3*a*b^3*c^2*d^6 - 3*a^2*b^2*c*d^7)) - (2*(625*a^4*b^8*c^11 + 576*a^12*c^3*d^8 - 3875*a^5*b^7*c^10*d + 256*a^11*b*c^4*d^7 + 8275*a^6*b^6*c^9*d^2 - 6305*a^7*b^5*c^8*d^3 + 256*a^8*b^4*c^7*d^4 + 256*a^9*b^3*c^6*d^5 + 256*a^10*b^2*c^5*d^6))/(a^3*b*d^8 - b^4*c^3*d^5 + 3*a*b^3*c^2*d^6 - 3*a^2*b^2*c*d^7)) + (x^(1/2)*(625*a^6*b^8*c^12 + 1296*a^14*c^4*d^8 - 4500*a^7*b^7*c^11*d - 1440*a^13*b*c^5*d^7 + 12150*a^8*b^6*c^10*d^2 - 14580*a^9*b^5*c^9*d^3 + 6561*a^10*b^4*c^8*d^4 + 400*a^12*b^2*c^6*d^6))/(a^6*b*d^11 + b^7*c^6*d^5 - 6*a*b^6*c^5*d^6 - 6*a^5*b^2*c*d^10 + 15*a^2*b^5*c^4*d^7 - 20*a^3*b^4*c^3*d^8 + 15*a^4*b^3*c^2*d^9))*1i + (-(625*b^4*c^9 + 6561*a^4*c^5*d^4 - 14580*a^3*b*c^6*d^3 + 12150*a^2*b^2*c^7*d^2 - 4500*a*b^3*c^8*d)/(4096*a^8*d^17 + 4096*b^8*c^8*d^9 - 32768*a*b^7*c^7*d^10 + 114688*a^2*b^6*c^6*d^11 - 229376*a^3*b^5*c^5*d^12 + 286720*a^4*b^4*c^4*d^13 - 229376*a^5*b^3*c^3*d^14 + 114688*a^6*b^2*c^2*d^15 - 32768*a^7*b*c*d^16))^(1/4)*((-(625*b^4*c^9 + 6561*a^4*c^5*d^4 - 14580*a^3*b*c^6*d^3 + 12150*a^2*b^2*c^7*d^2 - 4500*a*b^3*c^8*d)/(4096*a^8*d^17 + 4096*b^8*c^8*d^9 - 32768*a*b^7*c^7*d^10 + 114688*a^2*b^6*c^6*d^11 - 229376*a^3*b^5*c^5*d^12 + 286720*a^4*b^4*c^4*d^13 - 229376*a^5*b^3*c^3*d^14 + 114688*a^6*b^2*c^2*d^15 - 32768*a^7*b*c*d^16))^(1/4)*((-(625*b^4*c^9 + 6561*a^4*c^5*d^4 - 14580*a^3*b*c^6*d^3 + 12150*a^2*b^2*c^7*d^2 - 4500*a*b^3*c^8*d)/(4096*a^8*d^17 + 4096*b^8*c^8*d^9 - 32768*a*b^7*c^7*d^10 + 114688*a^2*b^6*c^6*d^11 - 229376*a^3*b^5*c^5*d^12 + 286720*a^4*b^4*c^4*d^13 - 229376*a^5*b^3*c^3*d^14 + 114688*a^6*b^2*c^2*d^15 - 32768*a^7*b*c*d^16))^(3/4)*((x^(1/2)*(6400*a^3*b^15*c^14*d^6 - 74240*a^4*b^14*c^13*d^7 + 384256*a^5*b^13*c^12*d^8 - 1165312*a^6*b^12*c^11*d^9 + 2286080*a^7*b^11*c^10*d^10 - 3017728*a^8*b^10*c^9*d^11 + 2691584*a^9*b^9*c^8*d^12 - 1570816*a^10*b^8*c^7*d^13 + 541952*a^11*b^7*c^6*d^14 - 74240*a^12*b^6*c^5*d^15 - 12032*a^13*b^5*c^4*d^16 + 4096*a^14*b^4*c^3*d^17))/(a^6*b*d^11 + b^7*c^6*d^5 - 6*a*b^6*c^5*d^6 - 6*a^5*b^2*c*d^10 + 15*a^2*b^5*c^4*d^7 - 20*a^3*b^4*c^3*d^8 + 15*a^4*b^3*c^2*d^9) + (2*(-(625*b^4*c^9 + 6561*a^4*c^5*d^4 - 14580*a^3*b*c^6*d^3 + 12150*a^2*b^2*c^7*d^2 - 4500*a*b^3*c^8*d)/(4096*a^8*d^17 + 4096*b^8*c^8*d^9 - 32768*a*b^7*c^7*d^10 + 114688*a^2*b^6*c^6*d^11 - 229376*a^3*b^5*c^5*d^12 + 286720*a^4*b^4*c^4*d^13 - 229376*a^5*b^3*c^3*d^14 + 114688*a^6*b^2*c^2*d^15 - 32768*a^7*b*c*d^16))^(1/4)*(5120*a^3*b^13*c^11*d^8 - 40960*a^4*b^12*c^10*d^9 + 143360*a^5*b^11*c^9*d^10 - 286720*a^6*b^10*c^8*d^11 + 358400*a^7*b^9*c^7*d^12 - 286720*a^8*b^8*c^6*d^13 + 143360*a^9*b^7*c^5*d^14 - 40960*a^10*b^6*c^4*d^15 + 5120*a^11*b^5*c^3*d^16))/(a^3*b*d^8 - b^4*c^3*d^5 + 3*a*b^3*c^2*d^6 - 3*a^2*b^2*c*d^7)) + (2*(625*a^4*b^8*c^11 + 576*a^12*c^3*d^8 - 3875*a^5*b^7*c^10*d + 256*a^11*b*c^4*d^7 + 8275*a^6*b^6*c^9*d^2 - 6305*a^7*b^5*c^8*d^3 + 256*a^8*b^4*c^7*d^4 + 256*a^9*b^3*c^6*d^5 + 256*a^10*b^2*c^5*d^6))/(a^3*b*d^8 - b^4*c^3*d^5 + 3*a*b^3*c^2*d^6 - 3*a^2*b^2*c*d^7)) + (x^(1/2)*(625*a^6*b^8*c^12 + 1296*a^14*c^4*d^8 - 4500*a^7*b^7*c^11*d - 1440*a^13*b*c^5*d^7 + 12150*a^8*b^6*c^10*d^2 - 14580*a^9*b^5*c^9*d^3 + 6561*a^10*b^4*c^8*d^4 + 400*a^12*b^2*c^6*d^6))/(a^6*b*d^11 + b^7*c^6*d^5 - 6*a*b^6*c^5*d^6 - 6*a^5*b^2*c*d^10 + 15*a^2*b^5*c^4*d^7 - 20*a^3*b^4*c^3*d^8 + 15*a^4*b^3*c^2*d^9))*1i)/((-(625*b^4*c^9 + 6561*a^4*c^5*d^4 - 14580*a^3*b*c^6*d^3 + 12150*a^2*b^2*c^7*d^2 - 4500*a*b^3*c^8*d)/(4096*a^8*d^17 + 4096*b^8*c^8*d^9 - 32768*a*b^7*c^7*d^10 + 114688*a^2*b^6*c^6*d^11 - 229376*a^3*b^5*c^5*d^12 + 286720*a^4*b^4*c^4*d^13 - 229376*a^5*b^3*c^3*d^14 + 114688*a^6*b^2*c^2*d^15 - 32768*a^7*b*c*d^16))^(1/4)*((-(625*b^4*c^9 + 6561*a^4*c^5*d^4 - 14580*a^3*b*c^6*d^3 + 12150*a^2*b^2*c^7*d^2 - 4500*a*b^3*c^8*d)/(4096*a^8*d^17 + 4096*b^8*c^8*d^9 - 32768*a*b^7*c^7*d^10 + 114688*a^2*b^6*c^6*d^11 - 229376*a^3*b^5*c^5*d^12 + 286720*a^4*b^4*c^4*d^13 - 229376*a^5*b^3*c^3*d^14 + 114688*a^6*b^2*c^2*d^15 - 32768*a^7*b*c*d^16))^(1/4)*((-(625*b^4*c^9 + 6561*a^4*c^5*d^4 - 14580*a^3*b*c^6*d^3 + 12150*a^2*b^2*c^7*d^2 - 4500*a*b^3*c^8*d)/(4096*a^8*d^17 + 4096*b^8*c^8*d^9 - 32768*a*b^7*c^7*d^10 + 114688*a^2*b^6*c^6*d^11 - 229376*a^3*b^5*c^5*d^12 + 286720*a^4*b^4*c^4*d^13 - 229376*a^5*b^3*c^3*d^14 + 114688*a^6*b^2*c^2*d^15 - 32768*a^7*b*c*d^16))^(3/4)*((x^(1/2)*(6400*a^3*b^15*c^14*d^6 - 74240*a^4*b^14*c^13*d^7 + 384256*a^5*b^13*c^12*d^8 - 1165312*a^6*b^12*c^11*d^9 + 2286080*a^7*b^11*c^10*d^10 - 3017728*a^8*b^10*c^9*d^11 + 2691584*a^9*b^9*c^8*d^12 - 1570816*a^10*b^8*c^7*d^13 + 541952*a^11*b^7*c^6*d^14 - 74240*a^12*b^6*c^5*d^15 - 12032*a^13*b^5*c^4*d^16 + 4096*a^14*b^4*c^3*d^17))/(a^6*b*d^11 + b^7*c^6*d^5 - 6*a*b^6*c^5*d^6 - 6*a^5*b^2*c*d^10 + 15*a^2*b^5*c^4*d^7 - 20*a^3*b^4*c^3*d^8 + 15*a^4*b^3*c^2*d^9) - (2*(-(625*b^4*c^9 + 6561*a^4*c^5*d^4 - 14580*a^3*b*c^6*d^3 + 12150*a^2*b^2*c^7*d^2 - 4500*a*b^3*c^8*d)/(4096*a^8*d^17 + 4096*b^8*c^8*d^9 - 32768*a*b^7*c^7*d^10 + 114688*a^2*b^6*c^6*d^11 - 229376*a^3*b^5*c^5*d^12 + 286720*a^4*b^4*c^4*d^13 - 229376*a^5*b^3*c^3*d^14 + 114688*a^6*b^2*c^2*d^15 - 32768*a^7*b*c*d^16))^(1/4)*(5120*a^3*b^13*c^11*d^8 - 40960*a^4*b^12*c^10*d^9 + 143360*a^5*b^11*c^9*d^10 - 286720*a^6*b^10*c^8*d^11 + 358400*a^7*b^9*c^7*d^12 - 286720*a^8*b^8*c^6*d^13 + 143360*a^9*b^7*c^5*d^14 - 40960*a^10*b^6*c^4*d^15 + 5120*a^11*b^5*c^3*d^16))/(a^3*b*d^8 - b^4*c^3*d^5 + 3*a*b^3*c^2*d^6 - 3*a^2*b^2*c*d^7)) - (2*(625*a^4*b^8*c^11 + 576*a^12*c^3*d^8 - 3875*a^5*b^7*c^10*d + 256*a^11*b*c^4*d^7 + 8275*a^6*b^6*c^9*d^2 - 6305*a^7*b^5*c^8*d^3 + 256*a^8*b^4*c^7*d^4 + 256*a^9*b^3*c^6*d^5 + 256*a^10*b^2*c^5*d^6))/(a^3*b*d^8 - b^4*c^3*d^5 + 3*a*b^3*c^2*d^6 - 3*a^2*b^2*c*d^7)) + (x^(1/2)*(625*a^6*b^8*c^12 + 1296*a^14*c^4*d^8 - 4500*a^7*b^7*c^11*d - 1440*a^13*b*c^5*d^7 + 12150*a^8*b^6*c^10*d^2 - 14580*a^9*b^5*c^9*d^3 + 6561*a^10*b^4*c^8*d^4 + 400*a^12*b^2*c^6*d^6))/(a^6*b*d^11 + b^7*c^6*d^5 - 6*a*b^6*c^5*d^6 - 6*a^5*b^2*c*d^10 + 15*a^2*b^5*c^4*d^7 - 20*a^3*b^4*c^3*d^8 + 15*a^4*b^3*c^2*d^9)) - (-(625*b^4*c^9 + 6561*a^4*c^5*d^4 - 14580*a^3*b*c^6*d^3 + 12150*a^2*b^2*c^7*d^2 - 4500*a*b^3*c^8*d)/(4096*a^8*d^17 + 4096*b^8*c^8*d^9 - 32768*a*b^7*c^7*d^10 + 114688*a^2*b^6*c^6*d^11 - 229376*a^3*b^5*c^5*d^12 + 286720*a^4*b^4*c^4*d^13 - 229376*a^5*b^3*c^3*d^14 + 114688*a^6*b^2*c^2*d^15 - 32768*a^7*b*c*d^16))^(1/4)*((-(625*b^4*c^9 + 6561*a^4*c^5*d^4 - 14580*a^3*b*c^6*d^3 + 12150*a^2*b^2*c^7*d^2 - 4500*a*b^3*c^8*d)/(4096*a^8*d^17 + 4096*b^8*c^8*d^9 - 32768*a*b^7*c^7*d^10 + 114688*a^2*b^6*c^6*d^11 - 229376*a^3*b^5*c^5*d^12 + 286720*a^4*b^4*c^4*d^13 - 229376*a^5*b^3*c^3*d^14 + 114688*a^6*b^2*c^2*d^15 - 32768*a^7*b*c*d^16))^(1/4)*((-(625*b^4*c^9 + 6561*a^4*c^5*d^4 - 14580*a^3*b*c^6*d^3 + 12150*a^2*b^2*c^7*d^2 - 4500*a*b^3*c^8*d)/(4096*a^8*d^17 + 4096*b^8*c^8*d^9 - 32768*a*b^7*c^7*d^10 + 114688*a^2*b^6*c^6*d^11 - 229376*a^3*b^5*c^5*d^12 + 286720*a^4*b^4*c^4*d^13 - 229376*a^5*b^3*c^3*d^14 + 114688*a^6*b^2*c^2*d^15 - 32768*a^7*b*c*d^16))^(3/4)*((x^(1/2)*(6400*a^3*b^15*c^14*d^6 - 74240*a^4*b^14*c^13*d^7 + 384256*a^5*b^13*c^12*d^8 - 1165312*a^6*b^12*c^11*d^9 + 2286080*a^7*b^11*c^10*d^10 - 3017728*a^8*b^10*c^9*d^11 + 2691584*a^9*b^9*c^8*d^12 - 1570816*a^10*b^8*c^7*d^13 + 541952*a^11*b^7*c^6*d^14 - 74240*a^12*b^6*c^5*d^15 - 12032*a^13*b^5*c^4*d^16 + 4096*a^14*b^4*c^3*d^17))/(a^6*b*d^11 + b^7*c^6*d^5 - 6*a*b^6*c^5*d^6 - 6*a^5*b^2*c*d^10 + 15*a^2*b^5*c^4*d^7 - 20*a^3*b^4*c^3*d^8 + 15*a^4*b^3*c^2*d^9) + (2*(-(625*b^4*c^9 + 6561*a^4*c^5*d^4 - 14580*a^3*b*c^6*d^3 + 12150*a^2*b^2*c^7*d^2 - 4500*a*b^3*c^8*d)/(4096*a^8*d^17 + 4096*b^8*c^8*d^9 - 32768*a*b^7*c^7*d^10 + 114688*a^2*b^6*c^6*d^11 - 229376*a^3*b^5*c^5*d^12 + 286720*a^4*b^4*c^4*d^13 - 229376*a^5*b^3*c^3*d^14 + 114688*a^6*b^2*c^2*d^15 - 32768*a^7*b*c*d^16))^(1/4)*(5120*a^3*b^13*c^11*d^8 - 40960*a^4*b^12*c^10*d^9 + 143360*a^5*b^11*c^9*d^10 - 286720*a^6*b^10*c^8*d^11 + 358400*a^7*b^9*c^7*d^12 - 286720*a^8*b^8*c^6*d^13 + 143360*a^9*b^7*c^5*d^14 - 40960*a^10*b^6*c^4*d^15 + 5120*a^11*b^5*c^3*d^16))/(a^3*b*d^8 - b^4*c^3*d^5 + 3*a*b^3*c^2*d^6 - 3*a^2*b^2*c*d^7)) + (2*(625*a^4*b^8*c^11 + 576*a^12*c^3*d^8 - 3875*a^5*b^7*c^10*d + 256*a^11*b*c^4*d^7 + 8275*a^6*b^6*c^9*d^2 - 6305*a^7*b^5*c^8*d^3 + 256*a^8*b^4*c^7*d^4 + 256*a^9*b^3*c^6*d^5 + 256*a^10*b^2*c^5*d^6))/(a^3*b*d^8 - b^4*c^3*d^5 + 3*a*b^3*c^2*d^6 - 3*a^2*b^2*c*d^7)) + (x^(1/2)*(625*a^6*b^8*c^12 + 1296*a^14*c^4*d^8 - 4500*a^7*b^7*c^11*d - 1440*a^13*b*c^5*d^7 + 12150*a^8*b^6*c^10*d^2 - 14580*a^9*b^5*c^9*d^3 + 6561*a^10*b^4*c^8*d^4 + 400*a^12*b^2*c^6*d^6))/(a^6*b*d^11 + b^7*c^6*d^5 - 6*a*b^6*c^5*d^6 - 6*a^5*b^2*c*d^10 + 15*a^2*b^5*c^4*d^7 - 20*a^3*b^4*c^3*d^8 + 15*a^4*b^3*c^2*d^9))))*(-(625*b^4*c^9 + 6561*a^4*c^5*d^4 - 14580*a^3*b*c^6*d^3 + 12150*a^2*b^2*c^7*d^2 - 4500*a*b^3*c^8*d)/(4096*a^8*d^17 + 4096*b^8*c^8*d^9 - 32768*a*b^7*c^7*d^10 + 114688*a^2*b^6*c^6*d^11 - 229376*a^3*b^5*c^5*d^12 + 286720*a^4*b^4*c^4*d^13 - 229376*a^5*b^3*c^3*d^14 + 114688*a^6*b^2*c^2*d^15 - 32768*a^7*b*c*d^16))^(1/4)*2i + 2*atan(((-(625*b^4*c^9 + 6561*a^4*c^5*d^4 - 14580*a^3*b*c^6*d^3 + 12150*a^2*b^2*c^7*d^2 - 4500*a*b^3*c^8*d)/(4096*a^8*d^17 + 4096*b^8*c^8*d^9 - 32768*a*b^7*c^7*d^10 + 114688*a^2*b^6*c^6*d^11 - 229376*a^3*b^5*c^5*d^12 + 286720*a^4*b^4*c^4*d^13 - 229376*a^5*b^3*c^3*d^14 + 114688*a^6*b^2*c^2*d^15 - 32768*a^7*b*c*d^16))^(1/4)*((-(625*b^4*c^9 + 6561*a^4*c^5*d^4 - 14580*a^3*b*c^6*d^3 + 12150*a^2*b^2*c^7*d^2 - 4500*a*b^3*c^8*d)/(4096*a^8*d^17 + 4096*b^8*c^8*d^9 - 32768*a*b^7*c^7*d^10 + 114688*a^2*b^6*c^6*d^11 - 229376*a^3*b^5*c^5*d^12 + 286720*a^4*b^4*c^4*d^13 - 229376*a^5*b^3*c^3*d^14 + 114688*a^6*b^2*c^2*d^15 - 32768*a^7*b*c*d^16))^(1/4)*((-(625*b^4*c^9 + 6561*a^4*c^5*d^4 - 14580*a^3*b*c^6*d^3 + 12150*a^2*b^2*c^7*d^2 - 4500*a*b^3*c^8*d)/(4096*a^8*d^17 + 4096*b^8*c^8*d^9 - 32768*a*b^7*c^7*d^10 + 114688*a^2*b^6*c^6*d^11 - 229376*a^3*b^5*c^5*d^12 + 286720*a^4*b^4*c^4*d^13 - 229376*a^5*b^3*c^3*d^14 + 114688*a^6*b^2*c^2*d^15 - 32768*a^7*b*c*d^16))^(3/4)*((x^(1/2)*(6400*a^3*b^15*c^14*d^6 - 74240*a^4*b^14*c^13*d^7 + 384256*a^5*b^13*c^12*d^8 - 1165312*a^6*b^12*c^11*d^9 + 2286080*a^7*b^11*c^10*d^10 - 3017728*a^8*b^10*c^9*d^11 + 2691584*a^9*b^9*c^8*d^12 - 1570816*a^10*b^8*c^7*d^13 + 541952*a^11*b^7*c^6*d^14 - 74240*a^12*b^6*c^5*d^15 - 12032*a^13*b^5*c^4*d^16 + 4096*a^14*b^4*c^3*d^17))/(a^6*b*d^11 + b^7*c^6*d^5 - 6*a*b^6*c^5*d^6 - 6*a^5*b^2*c*d^10 + 15*a^2*b^5*c^4*d^7 - 20*a^3*b^4*c^3*d^8 + 15*a^4*b^3*c^2*d^9) - ((-(625*b^4*c^9 + 6561*a^4*c^5*d^4 - 14580*a^3*b*c^6*d^3 + 12150*a^2*b^2*c^7*d^2 - 4500*a*b^3*c^8*d)/(4096*a^8*d^17 + 4096*b^8*c^8*d^9 - 32768*a*b^7*c^7*d^10 + 114688*a^2*b^6*c^6*d^11 - 229376*a^3*b^5*c^5*d^12 + 286720*a^4*b^4*c^4*d^13 - 229376*a^5*b^3*c^3*d^14 + 114688*a^6*b^2*c^2*d^15 - 32768*a^7*b*c*d^16))^(1/4)*(5120*a^3*b^13*c^11*d^8 - 40960*a^4*b^12*c^10*d^9 + 143360*a^5*b^11*c^9*d^10 - 286720*a^6*b^10*c^8*d^11 + 358400*a^7*b^9*c^7*d^12 - 286720*a^8*b^8*c^6*d^13 + 143360*a^9*b^7*c^5*d^14 - 40960*a^10*b^6*c^4*d^15 + 5120*a^11*b^5*c^3*d^16)*2i)/(a^3*b*d^8 - b^4*c^3*d^5 + 3*a*b^3*c^2*d^6 - 3*a^2*b^2*c*d^7))*1i + (2*(625*a^4*b^8*c^11 + 576*a^12*c^3*d^8 - 3875*a^5*b^7*c^10*d + 256*a^11*b*c^4*d^7 + 8275*a^6*b^6*c^9*d^2 - 6305*a^7*b^5*c^8*d^3 + 256*a^8*b^4*c^7*d^4 + 256*a^9*b^3*c^6*d^5 + 256*a^10*b^2*c^5*d^6))/(a^3*b*d^8 - b^4*c^3*d^5 + 3*a*b^3*c^2*d^6 - 3*a^2*b^2*c*d^7))*1i - (x^(1/2)*(625*a^6*b^8*c^12 + 1296*a^14*c^4*d^8 - 4500*a^7*b^7*c^11*d - 1440*a^13*b*c^5*d^7 + 12150*a^8*b^6*c^10*d^2 - 14580*a^9*b^5*c^9*d^3 + 6561*a^10*b^4*c^8*d^4 + 400*a^12*b^2*c^6*d^6))/(a^6*b*d^11 + b^7*c^6*d^5 - 6*a*b^6*c^5*d^6 - 6*a^5*b^2*c*d^10 + 15*a^2*b^5*c^4*d^7 - 20*a^3*b^4*c^3*d^8 + 15*a^4*b^3*c^2*d^9)) + (-(625*b^4*c^9 + 6561*a^4*c^5*d^4 - 14580*a^3*b*c^6*d^3 + 12150*a^2*b^2*c^7*d^2 - 4500*a*b^3*c^8*d)/(4096*a^8*d^17 + 4096*b^8*c^8*d^9 - 32768*a*b^7*c^7*d^10 + 114688*a^2*b^6*c^6*d^11 - 229376*a^3*b^5*c^5*d^12 + 286720*a^4*b^4*c^4*d^13 - 229376*a^5*b^3*c^3*d^14 + 114688*a^6*b^2*c^2*d^15 - 32768*a^7*b*c*d^16))^(1/4)*((-(625*b^4*c^9 + 6561*a^4*c^5*d^4 - 14580*a^3*b*c^6*d^3 + 12150*a^2*b^2*c^7*d^2 - 4500*a*b^3*c^8*d)/(4096*a^8*d^17 + 4096*b^8*c^8*d^9 - 32768*a*b^7*c^7*d^10 + 114688*a^2*b^6*c^6*d^11 - 229376*a^3*b^5*c^5*d^12 + 286720*a^4*b^4*c^4*d^13 - 229376*a^5*b^3*c^3*d^14 + 114688*a^6*b^2*c^2*d^15 - 32768*a^7*b*c*d^16))^(1/4)*((-(625*b^4*c^9 + 6561*a^4*c^5*d^4 - 14580*a^3*b*c^6*d^3 + 12150*a^2*b^2*c^7*d^2 - 4500*a*b^3*c^8*d)/(4096*a^8*d^17 + 4096*b^8*c^8*d^9 - 32768*a*b^7*c^7*d^10 + 114688*a^2*b^6*c^6*d^11 - 229376*a^3*b^5*c^5*d^12 + 286720*a^4*b^4*c^4*d^13 - 229376*a^5*b^3*c^3*d^14 + 114688*a^6*b^2*c^2*d^15 - 32768*a^7*b*c*d^16))^(3/4)*((x^(1/2)*(6400*a^3*b^15*c^14*d^6 - 74240*a^4*b^14*c^13*d^7 + 384256*a^5*b^13*c^12*d^8 - 1165312*a^6*b^12*c^11*d^9 + 2286080*a^7*b^11*c^10*d^10 - 3017728*a^8*b^10*c^9*d^11 + 2691584*a^9*b^9*c^8*d^12 - 1570816*a^10*b^8*c^7*d^13 + 541952*a^11*b^7*c^6*d^14 - 74240*a^12*b^6*c^5*d^15 - 12032*a^13*b^5*c^4*d^16 + 4096*a^14*b^4*c^3*d^17))/(a^6*b*d^11 + b^7*c^6*d^5 - 6*a*b^6*c^5*d^6 - 6*a^5*b^2*c*d^10 + 15*a^2*b^5*c^4*d^7 - 20*a^3*b^4*c^3*d^8 + 15*a^4*b^3*c^2*d^9) + ((-(625*b^4*c^9 + 6561*a^4*c^5*d^4 - 14580*a^3*b*c^6*d^3 + 12150*a^2*b^2*c^7*d^2 - 4500*a*b^3*c^8*d)/(4096*a^8*d^17 + 4096*b^8*c^8*d^9 - 32768*a*b^7*c^7*d^10 + 114688*a^2*b^6*c^6*d^11 - 229376*a^3*b^5*c^5*d^12 + 286720*a^4*b^4*c^4*d^13 - 229376*a^5*b^3*c^3*d^14 + 114688*a^6*b^2*c^2*d^15 - 32768*a^7*b*c*d^16))^(1/4)*(5120*a^3*b^13*c^11*d^8 - 40960*a^4*b^12*c^10*d^9 + 143360*a^5*b^11*c^9*d^10 - 286720*a^6*b^10*c^8*d^11 + 358400*a^7*b^9*c^7*d^12 - 286720*a^8*b^8*c^6*d^13 + 143360*a^9*b^7*c^5*d^14 - 40960*a^10*b^6*c^4*d^15 + 5120*a^11*b^5*c^3*d^16)*2i)/(a^3*b*d^8 - b^4*c^3*d^5 + 3*a*b^3*c^2*d^6 - 3*a^2*b^2*c*d^7))*1i - (2*(625*a^4*b^8*c^11 + 576*a^12*c^3*d^8 - 3875*a^5*b^7*c^10*d + 256*a^11*b*c^4*d^7 + 8275*a^6*b^6*c^9*d^2 - 6305*a^7*b^5*c^8*d^3 + 256*a^8*b^4*c^7*d^4 + 256*a^9*b^3*c^6*d^5 + 256*a^10*b^2*c^5*d^6))/(a^3*b*d^8 - b^4*c^3*d^5 + 3*a*b^3*c^2*d^6 - 3*a^2*b^2*c*d^7))*1i - (x^(1/2)*(625*a^6*b^8*c^12 + 1296*a^14*c^4*d^8 - 4500*a^7*b^7*c^11*d - 1440*a^13*b*c^5*d^7 + 12150*a^8*b^6*c^10*d^2 - 14580*a^9*b^5*c^9*d^3 + 6561*a^10*b^4*c^8*d^4 + 400*a^12*b^2*c^6*d^6))/(a^6*b*d^11 + b^7*c^6*d^5 - 6*a*b^6*c^5*d^6 - 6*a^5*b^2*c*d^10 + 15*a^2*b^5*c^4*d^7 - 20*a^3*b^4*c^3*d^8 + 15*a^4*b^3*c^2*d^9)))/((-(625*b^4*c^9 + 6561*a^4*c^5*d^4 - 14580*a^3*b*c^6*d^3 + 12150*a^2*b^2*c^7*d^2 - 4500*a*b^3*c^8*d)/(4096*a^8*d^17 + 4096*b^8*c^8*d^9 - 32768*a*b^7*c^7*d^10 + 114688*a^2*b^6*c^6*d^11 - 229376*a^3*b^5*c^5*d^12 + 286720*a^4*b^4*c^4*d^13 - 229376*a^5*b^3*c^3*d^14 + 114688*a^6*b^2*c^2*d^15 - 32768*a^7*b*c*d^16))^(1/4)*((-(625*b^4*c^9 + 6561*a^4*c^5*d^4 - 14580*a^3*b*c^6*d^3 + 12150*a^2*b^2*c^7*d^2 - 4500*a*b^3*c^8*d)/(4096*a^8*d^17 + 4096*b^8*c^8*d^9 - 32768*a*b^7*c^7*d^10 + 114688*a^2*b^6*c^6*d^11 - 229376*a^3*b^5*c^5*d^12 + 286720*a^4*b^4*c^4*d^13 - 229376*a^5*b^3*c^3*d^14 + 114688*a^6*b^2*c^2*d^15 - 32768*a^7*b*c*d^16))^(1/4)*((-(625*b^4*c^9 + 6561*a^4*c^5*d^4 - 14580*a^3*b*c^6*d^3 + 12150*a^2*b^2*c^7*d^2 - 4500*a*b^3*c^8*d)/(4096*a^8*d^17 + 4096*b^8*c^8*d^9 - 32768*a*b^7*c^7*d^10 + 114688*a^2*b^6*c^6*d^11 - 229376*a^3*b^5*c^5*d^12 + 286720*a^4*b^4*c^4*d^13 - 229376*a^5*b^3*c^3*d^14 + 114688*a^6*b^2*c^2*d^15 - 32768*a^7*b*c*d^16))^(3/4)*((x^(1/2)*(6400*a^3*b^15*c^14*d^6 - 74240*a^4*b^14*c^13*d^7 + 384256*a^5*b^13*c^12*d^8 - 1165312*a^6*b^12*c^11*d^9 + 2286080*a^7*b^11*c^10*d^10 - 3017728*a^8*b^10*c^9*d^11 + 2691584*a^9*b^9*c^8*d^12 - 1570816*a^10*b^8*c^7*d^13 + 541952*a^11*b^7*c^6*d^14 - 74240*a^12*b^6*c^5*d^15 - 12032*a^13*b^5*c^4*d^16 + 4096*a^14*b^4*c^3*d^17))/(a^6*b*d^11 + b^7*c^6*d^5 - 6*a*b^6*c^5*d^6 - 6*a^5*b^2*c*d^10 + 15*a^2*b^5*c^4*d^7 - 20*a^3*b^4*c^3*d^8 + 15*a^4*b^3*c^2*d^9) - ((-(625*b^4*c^9 + 6561*a^4*c^5*d^4 - 14580*a^3*b*c^6*d^3 + 12150*a^2*b^2*c^7*d^2 - 4500*a*b^3*c^8*d)/(4096*a^8*d^17 + 4096*b^8*c^8*d^9 - 32768*a*b^7*c^7*d^10 + 114688*a^2*b^6*c^6*d^11 - 229376*a^3*b^5*c^5*d^12 + 286720*a^4*b^4*c^4*d^13 - 229376*a^5*b^3*c^3*d^14 + 114688*a^6*b^2*c^2*d^15 - 32768*a^7*b*c*d^16))^(1/4)*(5120*a^3*b^13*c^11*d^8 - 40960*a^4*b^12*c^10*d^9 + 143360*a^5*b^11*c^9*d^10 - 286720*a^6*b^10*c^8*d^11 + 358400*a^7*b^9*c^7*d^12 - 286720*a^8*b^8*c^6*d^13 + 143360*a^9*b^7*c^5*d^14 - 40960*a^10*b^6*c^4*d^15 + 5120*a^11*b^5*c^3*d^16)*2i)/(a^3*b*d^8 - b^4*c^3*d^5 + 3*a*b^3*c^2*d^6 - 3*a^2*b^2*c*d^7))*1i + (2*(625*a^4*b^8*c^11 + 576*a^12*c^3*d^8 - 3875*a^5*b^7*c^10*d + 256*a^11*b*c^4*d^7 + 8275*a^6*b^6*c^9*d^2 - 6305*a^7*b^5*c^8*d^3 + 256*a^8*b^4*c^7*d^4 + 256*a^9*b^3*c^6*d^5 + 256*a^10*b^2*c^5*d^6))/(a^3*b*d^8 - b^4*c^3*d^5 + 3*a*b^3*c^2*d^6 - 3*a^2*b^2*c*d^7))*1i - (x^(1/2)*(625*a^6*b^8*c^12 + 1296*a^14*c^4*d^8 - 4500*a^7*b^7*c^11*d - 1440*a^13*b*c^5*d^7 + 12150*a^8*b^6*c^10*d^2 - 14580*a^9*b^5*c^9*d^3 + 6561*a^10*b^4*c^8*d^4 + 400*a^12*b^2*c^6*d^6))/(a^6*b*d^11 + b^7*c^6*d^5 - 6*a*b^6*c^5*d^6 - 6*a^5*b^2*c*d^10 + 15*a^2*b^5*c^4*d^7 - 20*a^3*b^4*c^3*d^8 + 15*a^4*b^3*c^2*d^9))*1i - (-(625*b^4*c^9 + 6561*a^4*c^5*d^4 - 14580*a^3*b*c^6*d^3 + 12150*a^2*b^2*c^7*d^2 - 4500*a*b^3*c^8*d)/(4096*a^8*d^17 + 4096*b^8*c^8*d^9 - 32768*a*b^7*c^7*d^10 + 114688*a^2*b^6*c^6*d^11 - 229376*a^3*b^5*c^5*d^12 + 286720*a^4*b^4*c^4*d^13 - 229376*a^5*b^3*c^3*d^14 + 114688*a^6*b^2*c^2*d^15 - 32768*a^7*b*c*d^16))^(1/4)*((-(625*b^4*c^9 + 6561*a^4*c^5*d^4 - 14580*a^3*b*c^6*d^3 + 12150*a^2*b^2*c^7*d^2 - 4500*a*b^3*c^8*d)/(4096*a^8*d^17 + 4096*b^8*c^8*d^9 - 32768*a*b^7*c^7*d^10 + 114688*a^2*b^6*c^6*d^11 - 229376*a^3*b^5*c^5*d^12 + 286720*a^4*b^4*c^4*d^13 - 229376*a^5*b^3*c^3*d^14 + 114688*a^6*b^2*c^2*d^15 - 32768*a^7*b*c*d^16))^(1/4)*((-(625*b^4*c^9 + 6561*a^4*c^5*d^4 - 14580*a^3*b*c^6*d^3 + 12150*a^2*b^2*c^7*d^2 - 4500*a*b^3*c^8*d)/(4096*a^8*d^17 + 4096*b^8*c^8*d^9 - 32768*a*b^7*c^7*d^10 + 114688*a^2*b^6*c^6*d^11 - 229376*a^3*b^5*c^5*d^12 + 286720*a^4*b^4*c^4*d^13 - 229376*a^5*b^3*c^3*d^14 + 114688*a^6*b^2*c^2*d^15 - 32768*a^7*b*c*d^16))^(3/4)*((x^(1/2)*(6400*a^3*b^15*c^14*d^6 - 74240*a^4*b^14*c^13*d^7 + 384256*a^5*b^13*c^12*d^8 - 1165312*a^6*b^12*c^11*d^9 + 2286080*a^7*b^11*c^10*d^10 - 3017728*a^8*b^10*c^9*d^11 + 2691584*a^9*b^9*c^8*d^12 - 1570816*a^10*b^8*c^7*d^13 + 541952*a^11*b^7*c^6*d^14 - 74240*a^12*b^6*c^5*d^15 - 12032*a^13*b^5*c^4*d^16 + 4096*a^14*b^4*c^3*d^17))/(a^6*b*d^11 + b^7*c^6*d^5 - 6*a*b^6*c^5*d^6 - 6*a^5*b^2*c*d^10 + 15*a^2*b^5*c^4*d^7 - 20*a^3*b^4*c^3*d^8 + 15*a^4*b^3*c^2*d^9) + ((-(625*b^4*c^9 + 6561*a^4*c^5*d^4 - 14580*a^3*b*c^6*d^3 + 12150*a^2*b^2*c^7*d^2 - 4500*a*b^3*c^8*d)/(4096*a^8*d^17 + 4096*b^8*c^8*d^9 - 32768*a*b^7*c^7*d^10 + 114688*a^2*b^6*c^6*d^11 - 229376*a^3*b^5*c^5*d^12 + 286720*a^4*b^4*c^4*d^13 - 229376*a^5*b^3*c^3*d^14 + 114688*a^6*b^2*c^2*d^15 - 32768*a^7*b*c*d^16))^(1/4)*(5120*a^3*b^13*c^11*d^8 - 40960*a^4*b^12*c^10*d^9 + 143360*a^5*b^11*c^9*d^10 - 286720*a^6*b^10*c^8*d^11 + 358400*a^7*b^9*c^7*d^12 - 286720*a^8*b^8*c^6*d^13 + 143360*a^9*b^7*c^5*d^14 - 40960*a^10*b^6*c^4*d^15 + 5120*a^11*b^5*c^3*d^16)*2i)/(a^3*b*d^8 - b^4*c^3*d^5 + 3*a*b^3*c^2*d^6 - 3*a^2*b^2*c*d^7))*1i - (2*(625*a^4*b^8*c^11 + 576*a^12*c^3*d^8 - 3875*a^5*b^7*c^10*d + 256*a^11*b*c^4*d^7 + 8275*a^6*b^6*c^9*d^2 - 6305*a^7*b^5*c^8*d^3 + 256*a^8*b^4*c^7*d^4 + 256*a^9*b^3*c^6*d^5 + 256*a^10*b^2*c^5*d^6))/(a^3*b*d^8 - b^4*c^3*d^5 + 3*a*b^3*c^2*d^6 - 3*a^2*b^2*c*d^7))*1i - (x^(1/2)*(625*a^6*b^8*c^12 + 1296*a^14*c^4*d^8 - 4500*a^7*b^7*c^11*d - 1440*a^13*b*c^5*d^7 + 12150*a^8*b^6*c^10*d^2 - 14580*a^9*b^5*c^9*d^3 + 6561*a^10*b^4*c^8*d^4 + 400*a^12*b^2*c^6*d^6))/(a^6*b*d^11 + b^7*c^6*d^5 - 6*a*b^6*c^5*d^6 - 6*a^5*b^2*c*d^10 + 15*a^2*b^5*c^4*d^7 - 20*a^3*b^4*c^3*d^8 + 15*a^4*b^3*c^2*d^9))*1i))*(-(625*b^4*c^9 + 6561*a^4*c^5*d^4 - 14580*a^3*b*c^6*d^3 + 12150*a^2*b^2*c^7*d^2 - 4500*a*b^3*c^8*d)/(4096*a^8*d^17 + 4096*b^8*c^8*d^9 - 32768*a*b^7*c^7*d^10 + 114688*a^2*b^6*c^6*d^11 - 229376*a^3*b^5*c^5*d^12 + 286720*a^4*b^4*c^4*d^13 - 229376*a^5*b^3*c^3*d^14 + 114688*a^6*b^2*c^2*d^15 - 32768*a^7*b*c*d^16))^(1/4) + (2*x^(1/2))/(b*d^2) - (b*c^2*x^(1/2))/(2*(b*d^3*x^2 + b*c*d^2)*(a*d - b*c))","B"
471,1,19871,536,2.527456,"\text{Not used}","int(x^(9/2)/((a + b*x^2)*(c + d*x^2)^2),x)","2\,\mathrm{atan}\left(\frac{{\left(-\frac{a^7}{16\,a^8\,b^3\,d^8-128\,a^7\,b^4\,c\,d^7+448\,a^6\,b^5\,c^2\,d^6-896\,a^5\,b^6\,c^3\,d^5+1120\,a^4\,b^7\,c^4\,d^4-896\,a^3\,b^8\,c^5\,d^3+448\,a^2\,b^9\,c^6\,d^2-128\,a\,b^{10}\,c^7\,d+16\,b^{11}\,c^8}\right)}^{1/4}\,\left({\left(-\frac{a^7}{16\,a^8\,b^3\,d^8-128\,a^7\,b^4\,c\,d^7+448\,a^6\,b^5\,c^2\,d^6-896\,a^5\,b^6\,c^3\,d^5+1120\,a^4\,b^7\,c^4\,d^4-896\,a^3\,b^8\,c^5\,d^3+448\,a^2\,b^9\,c^6\,d^2-128\,a\,b^{10}\,c^7\,d+16\,b^{11}\,c^8}\right)}^{3/4}\,\left(\frac{\sqrt{x}\,{\left(-\frac{a^7}{16\,a^8\,b^3\,d^8-128\,a^7\,b^4\,c\,d^7+448\,a^6\,b^5\,c^2\,d^6-896\,a^5\,b^6\,c^3\,d^5+1120\,a^4\,b^7\,c^4\,d^4-896\,a^3\,b^8\,c^5\,d^3+448\,a^2\,b^9\,c^6\,d^2-128\,a\,b^{10}\,c^7\,d+16\,b^{11}\,c^8}\right)}^{1/4}\,\left(16640\,a^{13}\,b^4\,c^3\,d^{15}-143872\,a^{12}\,b^5\,c^4\,d^{14}+554240\,a^{11}\,b^6\,c^5\,d^{13}-1251328\,a^{10}\,b^7\,c^6\,d^{12}+1831424\,a^9\,b^8\,c^7\,d^{11}-1813504\,a^8\,b^9\,c^8\,d^{10}+1229312\,a^7\,b^{10}\,c^9\,d^9-563200\,a^6\,b^{11}\,c^{10}\,d^8+167168\,a^5\,b^{12}\,c^{11}\,d^7-29184\,a^4\,b^{13}\,c^{12}\,d^6+2304\,a^3\,b^{14}\,c^{13}\,d^5\right)}{a^6\,d^9-6\,a^5\,b\,c\,d^8+15\,a^4\,b^2\,c^2\,d^7-20\,a^3\,b^3\,c^3\,d^6+15\,a^2\,b^4\,c^4\,d^5-6\,a\,b^5\,c^5\,d^4+b^6\,c^6\,d^3}+\frac{\left(-2048\,a^{14}\,b^3\,c^3\,d^{14}+25312\,a^{13}\,b^4\,c^4\,d^{13}-133952\,a^{12}\,b^5\,c^5\,d^{12}+407008\,a^{11}\,b^6\,c^6\,d^{11}-795392\,a^{10}\,b^7\,c^7\,d^{10}+1054144\,a^9\,b^8\,c^8\,d^9-968576\,a^8\,b^9\,c^9\,d^8+617152\,a^7\,b^{10}\,c^{10}\,d^7-267008\,a^6\,b^{11}\,c^{11}\,d^6+74592\,a^5\,b^{12}\,c^{12}\,d^5-12096\,a^4\,b^{13}\,c^{13}\,d^4+864\,a^3\,b^{14}\,c^{14}\,d^3\right)\,1{}\mathrm{i}}{a^7\,d^{10}-7\,a^6\,b\,c\,d^9+21\,a^5\,b^2\,c^2\,d^8-35\,a^4\,b^3\,c^3\,d^7+35\,a^3\,b^4\,c^4\,d^6-21\,a^2\,b^5\,c^5\,d^5+7\,a\,b^6\,c^6\,d^4-b^7\,c^7\,d^3}\right)+\frac{\sqrt{x}\,\left(784\,a^{12}\,b\,c^3\,d^7-672\,a^{11}\,b^2\,c^4\,d^6+144\,a^{10}\,b^3\,c^5\,d^5+2401\,a^9\,b^4\,c^6\,d^4-4116\,a^8\,b^5\,c^7\,d^3+2646\,a^7\,b^6\,c^8\,d^2-756\,a^6\,b^7\,c^9\,d+81\,a^5\,b^8\,c^{10}\right)}{a^6\,d^9-6\,a^5\,b\,c\,d^8+15\,a^4\,b^2\,c^2\,d^7-20\,a^3\,b^3\,c^3\,d^6+15\,a^2\,b^4\,c^4\,d^5-6\,a\,b^5\,c^5\,d^4+b^6\,c^6\,d^3}\right)-{\left(-\frac{a^7}{16\,a^8\,b^3\,d^8-128\,a^7\,b^4\,c\,d^7+448\,a^6\,b^5\,c^2\,d^6-896\,a^5\,b^6\,c^3\,d^5+1120\,a^4\,b^7\,c^4\,d^4-896\,a^3\,b^8\,c^5\,d^3+448\,a^2\,b^9\,c^6\,d^2-128\,a\,b^{10}\,c^7\,d+16\,b^{11}\,c^8}\right)}^{1/4}\,\left({\left(-\frac{a^7}{16\,a^8\,b^3\,d^8-128\,a^7\,b^4\,c\,d^7+448\,a^6\,b^5\,c^2\,d^6-896\,a^5\,b^6\,c^3\,d^5+1120\,a^4\,b^7\,c^4\,d^4-896\,a^3\,b^8\,c^5\,d^3+448\,a^2\,b^9\,c^6\,d^2-128\,a\,b^{10}\,c^7\,d+16\,b^{11}\,c^8}\right)}^{3/4}\,\left(-\frac{\sqrt{x}\,{\left(-\frac{a^7}{16\,a^8\,b^3\,d^8-128\,a^7\,b^4\,c\,d^7+448\,a^6\,b^5\,c^2\,d^6-896\,a^5\,b^6\,c^3\,d^5+1120\,a^4\,b^7\,c^4\,d^4-896\,a^3\,b^8\,c^5\,d^3+448\,a^2\,b^9\,c^6\,d^2-128\,a\,b^{10}\,c^7\,d+16\,b^{11}\,c^8}\right)}^{1/4}\,\left(16640\,a^{13}\,b^4\,c^3\,d^{15}-143872\,a^{12}\,b^5\,c^4\,d^{14}+554240\,a^{11}\,b^6\,c^5\,d^{13}-1251328\,a^{10}\,b^7\,c^6\,d^{12}+1831424\,a^9\,b^8\,c^7\,d^{11}-1813504\,a^8\,b^9\,c^8\,d^{10}+1229312\,a^7\,b^{10}\,c^9\,d^9-563200\,a^6\,b^{11}\,c^{10}\,d^8+167168\,a^5\,b^{12}\,c^{11}\,d^7-29184\,a^4\,b^{13}\,c^{12}\,d^6+2304\,a^3\,b^{14}\,c^{13}\,d^5\right)}{a^6\,d^9-6\,a^5\,b\,c\,d^8+15\,a^4\,b^2\,c^2\,d^7-20\,a^3\,b^3\,c^3\,d^6+15\,a^2\,b^4\,c^4\,d^5-6\,a\,b^5\,c^5\,d^4+b^6\,c^6\,d^3}+\frac{\left(-2048\,a^{14}\,b^3\,c^3\,d^{14}+25312\,a^{13}\,b^4\,c^4\,d^{13}-133952\,a^{12}\,b^5\,c^5\,d^{12}+407008\,a^{11}\,b^6\,c^6\,d^{11}-795392\,a^{10}\,b^7\,c^7\,d^{10}+1054144\,a^9\,b^8\,c^8\,d^9-968576\,a^8\,b^9\,c^9\,d^8+617152\,a^7\,b^{10}\,c^{10}\,d^7-267008\,a^6\,b^{11}\,c^{11}\,d^6+74592\,a^5\,b^{12}\,c^{12}\,d^5-12096\,a^4\,b^{13}\,c^{13}\,d^4+864\,a^3\,b^{14}\,c^{14}\,d^3\right)\,1{}\mathrm{i}}{a^7\,d^{10}-7\,a^6\,b\,c\,d^9+21\,a^5\,b^2\,c^2\,d^8-35\,a^4\,b^3\,c^3\,d^7+35\,a^3\,b^4\,c^4\,d^6-21\,a^2\,b^5\,c^5\,d^5+7\,a\,b^6\,c^6\,d^4-b^7\,c^7\,d^3}\right)-\frac{\sqrt{x}\,\left(784\,a^{12}\,b\,c^3\,d^7-672\,a^{11}\,b^2\,c^4\,d^6+144\,a^{10}\,b^3\,c^5\,d^5+2401\,a^9\,b^4\,c^6\,d^4-4116\,a^8\,b^5\,c^7\,d^3+2646\,a^7\,b^6\,c^8\,d^2-756\,a^6\,b^7\,c^9\,d+81\,a^5\,b^8\,c^{10}\right)}{a^6\,d^9-6\,a^5\,b\,c\,d^8+15\,a^4\,b^2\,c^2\,d^7-20\,a^3\,b^3\,c^3\,d^6+15\,a^2\,b^4\,c^4\,d^5-6\,a\,b^5\,c^5\,d^4+b^6\,c^6\,d^3}\right)}{-\frac{1372\,a^{12}\,b\,c^4\,d^5-392\,a^{11}\,b^2\,c^5\,d^4-2037\,a^{10}\,b^3\,c^6\,d^3+1971\,a^9\,b^4\,c^7\,d^2-675\,a^8\,b^5\,c^8\,d+81\,a^7\,b^6\,c^9}{a^7\,d^{10}-7\,a^6\,b\,c\,d^9+21\,a^5\,b^2\,c^2\,d^8-35\,a^4\,b^3\,c^3\,d^7+35\,a^3\,b^4\,c^4\,d^6-21\,a^2\,b^5\,c^5\,d^5+7\,a\,b^6\,c^6\,d^4-b^7\,c^7\,d^3}+{\left(-\frac{a^7}{16\,a^8\,b^3\,d^8-128\,a^7\,b^4\,c\,d^7+448\,a^6\,b^5\,c^2\,d^6-896\,a^5\,b^6\,c^3\,d^5+1120\,a^4\,b^7\,c^4\,d^4-896\,a^3\,b^8\,c^5\,d^3+448\,a^2\,b^9\,c^6\,d^2-128\,a\,b^{10}\,c^7\,d+16\,b^{11}\,c^8}\right)}^{1/4}\,\left({\left(-\frac{a^7}{16\,a^8\,b^3\,d^8-128\,a^7\,b^4\,c\,d^7+448\,a^6\,b^5\,c^2\,d^6-896\,a^5\,b^6\,c^3\,d^5+1120\,a^4\,b^7\,c^4\,d^4-896\,a^3\,b^8\,c^5\,d^3+448\,a^2\,b^9\,c^6\,d^2-128\,a\,b^{10}\,c^7\,d+16\,b^{11}\,c^8}\right)}^{3/4}\,\left(\frac{\sqrt{x}\,{\left(-\frac{a^7}{16\,a^8\,b^3\,d^8-128\,a^7\,b^4\,c\,d^7+448\,a^6\,b^5\,c^2\,d^6-896\,a^5\,b^6\,c^3\,d^5+1120\,a^4\,b^7\,c^4\,d^4-896\,a^3\,b^8\,c^5\,d^3+448\,a^2\,b^9\,c^6\,d^2-128\,a\,b^{10}\,c^7\,d+16\,b^{11}\,c^8}\right)}^{1/4}\,\left(16640\,a^{13}\,b^4\,c^3\,d^{15}-143872\,a^{12}\,b^5\,c^4\,d^{14}+554240\,a^{11}\,b^6\,c^5\,d^{13}-1251328\,a^{10}\,b^7\,c^6\,d^{12}+1831424\,a^9\,b^8\,c^7\,d^{11}-1813504\,a^8\,b^9\,c^8\,d^{10}+1229312\,a^7\,b^{10}\,c^9\,d^9-563200\,a^6\,b^{11}\,c^{10}\,d^8+167168\,a^5\,b^{12}\,c^{11}\,d^7-29184\,a^4\,b^{13}\,c^{12}\,d^6+2304\,a^3\,b^{14}\,c^{13}\,d^5\right)}{a^6\,d^9-6\,a^5\,b\,c\,d^8+15\,a^4\,b^2\,c^2\,d^7-20\,a^3\,b^3\,c^3\,d^6+15\,a^2\,b^4\,c^4\,d^5-6\,a\,b^5\,c^5\,d^4+b^6\,c^6\,d^3}+\frac{\left(-2048\,a^{14}\,b^3\,c^3\,d^{14}+25312\,a^{13}\,b^4\,c^4\,d^{13}-133952\,a^{12}\,b^5\,c^5\,d^{12}+407008\,a^{11}\,b^6\,c^6\,d^{11}-795392\,a^{10}\,b^7\,c^7\,d^{10}+1054144\,a^9\,b^8\,c^8\,d^9-968576\,a^8\,b^9\,c^9\,d^8+617152\,a^7\,b^{10}\,c^{10}\,d^7-267008\,a^6\,b^{11}\,c^{11}\,d^6+74592\,a^5\,b^{12}\,c^{12}\,d^5-12096\,a^4\,b^{13}\,c^{13}\,d^4+864\,a^3\,b^{14}\,c^{14}\,d^3\right)\,1{}\mathrm{i}}{a^7\,d^{10}-7\,a^6\,b\,c\,d^9+21\,a^5\,b^2\,c^2\,d^8-35\,a^4\,b^3\,c^3\,d^7+35\,a^3\,b^4\,c^4\,d^6-21\,a^2\,b^5\,c^5\,d^5+7\,a\,b^6\,c^6\,d^4-b^7\,c^7\,d^3}\right)\,1{}\mathrm{i}+\frac{\sqrt{x}\,\left(784\,a^{12}\,b\,c^3\,d^7-672\,a^{11}\,b^2\,c^4\,d^6+144\,a^{10}\,b^3\,c^5\,d^5+2401\,a^9\,b^4\,c^6\,d^4-4116\,a^8\,b^5\,c^7\,d^3+2646\,a^7\,b^6\,c^8\,d^2-756\,a^6\,b^7\,c^9\,d+81\,a^5\,b^8\,c^{10}\right)\,1{}\mathrm{i}}{a^6\,d^9-6\,a^5\,b\,c\,d^8+15\,a^4\,b^2\,c^2\,d^7-20\,a^3\,b^3\,c^3\,d^6+15\,a^2\,b^4\,c^4\,d^5-6\,a\,b^5\,c^5\,d^4+b^6\,c^6\,d^3}\right)+{\left(-\frac{a^7}{16\,a^8\,b^3\,d^8-128\,a^7\,b^4\,c\,d^7+448\,a^6\,b^5\,c^2\,d^6-896\,a^5\,b^6\,c^3\,d^5+1120\,a^4\,b^7\,c^4\,d^4-896\,a^3\,b^8\,c^5\,d^3+448\,a^2\,b^9\,c^6\,d^2-128\,a\,b^{10}\,c^7\,d+16\,b^{11}\,c^8}\right)}^{1/4}\,\left({\left(-\frac{a^7}{16\,a^8\,b^3\,d^8-128\,a^7\,b^4\,c\,d^7+448\,a^6\,b^5\,c^2\,d^6-896\,a^5\,b^6\,c^3\,d^5+1120\,a^4\,b^7\,c^4\,d^4-896\,a^3\,b^8\,c^5\,d^3+448\,a^2\,b^9\,c^6\,d^2-128\,a\,b^{10}\,c^7\,d+16\,b^{11}\,c^8}\right)}^{3/4}\,\left(-\frac{\sqrt{x}\,{\left(-\frac{a^7}{16\,a^8\,b^3\,d^8-128\,a^7\,b^4\,c\,d^7+448\,a^6\,b^5\,c^2\,d^6-896\,a^5\,b^6\,c^3\,d^5+1120\,a^4\,b^7\,c^4\,d^4-896\,a^3\,b^8\,c^5\,d^3+448\,a^2\,b^9\,c^6\,d^2-128\,a\,b^{10}\,c^7\,d+16\,b^{11}\,c^8}\right)}^{1/4}\,\left(16640\,a^{13}\,b^4\,c^3\,d^{15}-143872\,a^{12}\,b^5\,c^4\,d^{14}+554240\,a^{11}\,b^6\,c^5\,d^{13}-1251328\,a^{10}\,b^7\,c^6\,d^{12}+1831424\,a^9\,b^8\,c^7\,d^{11}-1813504\,a^8\,b^9\,c^8\,d^{10}+1229312\,a^7\,b^{10}\,c^9\,d^9-563200\,a^6\,b^{11}\,c^{10}\,d^8+167168\,a^5\,b^{12}\,c^{11}\,d^7-29184\,a^4\,b^{13}\,c^{12}\,d^6+2304\,a^3\,b^{14}\,c^{13}\,d^5\right)}{a^6\,d^9-6\,a^5\,b\,c\,d^8+15\,a^4\,b^2\,c^2\,d^7-20\,a^3\,b^3\,c^3\,d^6+15\,a^2\,b^4\,c^4\,d^5-6\,a\,b^5\,c^5\,d^4+b^6\,c^6\,d^3}+\frac{\left(-2048\,a^{14}\,b^3\,c^3\,d^{14}+25312\,a^{13}\,b^4\,c^4\,d^{13}-133952\,a^{12}\,b^5\,c^5\,d^{12}+407008\,a^{11}\,b^6\,c^6\,d^{11}-795392\,a^{10}\,b^7\,c^7\,d^{10}+1054144\,a^9\,b^8\,c^8\,d^9-968576\,a^8\,b^9\,c^9\,d^8+617152\,a^7\,b^{10}\,c^{10}\,d^7-267008\,a^6\,b^{11}\,c^{11}\,d^6+74592\,a^5\,b^{12}\,c^{12}\,d^5-12096\,a^4\,b^{13}\,c^{13}\,d^4+864\,a^3\,b^{14}\,c^{14}\,d^3\right)\,1{}\mathrm{i}}{a^7\,d^{10}-7\,a^6\,b\,c\,d^9+21\,a^5\,b^2\,c^2\,d^8-35\,a^4\,b^3\,c^3\,d^7+35\,a^3\,b^4\,c^4\,d^6-21\,a^2\,b^5\,c^5\,d^5+7\,a\,b^6\,c^6\,d^4-b^7\,c^7\,d^3}\right)\,1{}\mathrm{i}-\frac{\sqrt{x}\,\left(784\,a^{12}\,b\,c^3\,d^7-672\,a^{11}\,b^2\,c^4\,d^6+144\,a^{10}\,b^3\,c^5\,d^5+2401\,a^9\,b^4\,c^6\,d^4-4116\,a^8\,b^5\,c^7\,d^3+2646\,a^7\,b^6\,c^8\,d^2-756\,a^6\,b^7\,c^9\,d+81\,a^5\,b^8\,c^{10}\right)\,1{}\mathrm{i}}{a^6\,d^9-6\,a^5\,b\,c\,d^8+15\,a^4\,b^2\,c^2\,d^7-20\,a^3\,b^3\,c^3\,d^6+15\,a^2\,b^4\,c^4\,d^5-6\,a\,b^5\,c^5\,d^4+b^6\,c^6\,d^3}\right)}\right)\,{\left(-\frac{a^7}{16\,a^8\,b^3\,d^8-128\,a^7\,b^4\,c\,d^7+448\,a^6\,b^5\,c^2\,d^6-896\,a^5\,b^6\,c^3\,d^5+1120\,a^4\,b^7\,c^4\,d^4-896\,a^3\,b^8\,c^5\,d^3+448\,a^2\,b^9\,c^6\,d^2-128\,a\,b^{10}\,c^7\,d+16\,b^{11}\,c^8}\right)}^{1/4}+2\,\mathrm{atan}\left(\frac{{\left(-\frac{2401\,a^4\,c^3\,d^4-4116\,a^3\,b\,c^4\,d^3+2646\,a^2\,b^2\,c^5\,d^2-756\,a\,b^3\,c^6\,d+81\,b^4\,c^7}{4096\,a^8\,d^{15}-32768\,a^7\,b\,c\,d^{14}+114688\,a^6\,b^2\,c^2\,d^{13}-229376\,a^5\,b^3\,c^3\,d^{12}+286720\,a^4\,b^4\,c^4\,d^{11}-229376\,a^3\,b^5\,c^5\,d^{10}+114688\,a^2\,b^6\,c^6\,d^9-32768\,a\,b^7\,c^7\,d^8+4096\,b^8\,c^8\,d^7}\right)}^{1/4}\,\left({\left(-\frac{2401\,a^4\,c^3\,d^4-4116\,a^3\,b\,c^4\,d^3+2646\,a^2\,b^2\,c^5\,d^2-756\,a\,b^3\,c^6\,d+81\,b^4\,c^7}{4096\,a^8\,d^{15}-32768\,a^7\,b\,c\,d^{14}+114688\,a^6\,b^2\,c^2\,d^{13}-229376\,a^5\,b^3\,c^3\,d^{12}+286720\,a^4\,b^4\,c^4\,d^{11}-229376\,a^3\,b^5\,c^5\,d^{10}+114688\,a^2\,b^6\,c^6\,d^9-32768\,a\,b^7\,c^7\,d^8+4096\,b^8\,c^8\,d^7}\right)}^{3/4}\,\left(\frac{\sqrt{x}\,{\left(-\frac{2401\,a^4\,c^3\,d^4-4116\,a^3\,b\,c^4\,d^3+2646\,a^2\,b^2\,c^5\,d^2-756\,a\,b^3\,c^6\,d+81\,b^4\,c^7}{4096\,a^8\,d^{15}-32768\,a^7\,b\,c\,d^{14}+114688\,a^6\,b^2\,c^2\,d^{13}-229376\,a^5\,b^3\,c^3\,d^{12}+286720\,a^4\,b^4\,c^4\,d^{11}-229376\,a^3\,b^5\,c^5\,d^{10}+114688\,a^2\,b^6\,c^6\,d^9-32768\,a\,b^7\,c^7\,d^8+4096\,b^8\,c^8\,d^7}\right)}^{1/4}\,\left(16640\,a^{13}\,b^4\,c^3\,d^{15}-143872\,a^{12}\,b^5\,c^4\,d^{14}+554240\,a^{11}\,b^6\,c^5\,d^{13}-1251328\,a^{10}\,b^7\,c^6\,d^{12}+1831424\,a^9\,b^8\,c^7\,d^{11}-1813504\,a^8\,b^9\,c^8\,d^{10}+1229312\,a^7\,b^{10}\,c^9\,d^9-563200\,a^6\,b^{11}\,c^{10}\,d^8+167168\,a^5\,b^{12}\,c^{11}\,d^7-29184\,a^4\,b^{13}\,c^{12}\,d^6+2304\,a^3\,b^{14}\,c^{13}\,d^5\right)}{a^6\,d^9-6\,a^5\,b\,c\,d^8+15\,a^4\,b^2\,c^2\,d^7-20\,a^3\,b^3\,c^3\,d^6+15\,a^2\,b^4\,c^4\,d^5-6\,a\,b^5\,c^5\,d^4+b^6\,c^6\,d^3}+\frac{\left(-2048\,a^{14}\,b^3\,c^3\,d^{14}+25312\,a^{13}\,b^4\,c^4\,d^{13}-133952\,a^{12}\,b^5\,c^5\,d^{12}+407008\,a^{11}\,b^6\,c^6\,d^{11}-795392\,a^{10}\,b^7\,c^7\,d^{10}+1054144\,a^9\,b^8\,c^8\,d^9-968576\,a^8\,b^9\,c^9\,d^8+617152\,a^7\,b^{10}\,c^{10}\,d^7-267008\,a^6\,b^{11}\,c^{11}\,d^6+74592\,a^5\,b^{12}\,c^{12}\,d^5-12096\,a^4\,b^{13}\,c^{13}\,d^4+864\,a^3\,b^{14}\,c^{14}\,d^3\right)\,1{}\mathrm{i}}{a^7\,d^{10}-7\,a^6\,b\,c\,d^9+21\,a^5\,b^2\,c^2\,d^8-35\,a^4\,b^3\,c^3\,d^7+35\,a^3\,b^4\,c^4\,d^6-21\,a^2\,b^5\,c^5\,d^5+7\,a\,b^6\,c^6\,d^4-b^7\,c^7\,d^3}\right)+\frac{\sqrt{x}\,\left(784\,a^{12}\,b\,c^3\,d^7-672\,a^{11}\,b^2\,c^4\,d^6+144\,a^{10}\,b^3\,c^5\,d^5+2401\,a^9\,b^4\,c^6\,d^4-4116\,a^8\,b^5\,c^7\,d^3+2646\,a^7\,b^6\,c^8\,d^2-756\,a^6\,b^7\,c^9\,d+81\,a^5\,b^8\,c^{10}\right)}{a^6\,d^9-6\,a^5\,b\,c\,d^8+15\,a^4\,b^2\,c^2\,d^7-20\,a^3\,b^3\,c^3\,d^6+15\,a^2\,b^4\,c^4\,d^5-6\,a\,b^5\,c^5\,d^4+b^6\,c^6\,d^3}\right)-{\left(-\frac{2401\,a^4\,c^3\,d^4-4116\,a^3\,b\,c^4\,d^3+2646\,a^2\,b^2\,c^5\,d^2-756\,a\,b^3\,c^6\,d+81\,b^4\,c^7}{4096\,a^8\,d^{15}-32768\,a^7\,b\,c\,d^{14}+114688\,a^6\,b^2\,c^2\,d^{13}-229376\,a^5\,b^3\,c^3\,d^{12}+286720\,a^4\,b^4\,c^4\,d^{11}-229376\,a^3\,b^5\,c^5\,d^{10}+114688\,a^2\,b^6\,c^6\,d^9-32768\,a\,b^7\,c^7\,d^8+4096\,b^8\,c^8\,d^7}\right)}^{1/4}\,\left({\left(-\frac{2401\,a^4\,c^3\,d^4-4116\,a^3\,b\,c^4\,d^3+2646\,a^2\,b^2\,c^5\,d^2-756\,a\,b^3\,c^6\,d+81\,b^4\,c^7}{4096\,a^8\,d^{15}-32768\,a^7\,b\,c\,d^{14}+114688\,a^6\,b^2\,c^2\,d^{13}-229376\,a^5\,b^3\,c^3\,d^{12}+286720\,a^4\,b^4\,c^4\,d^{11}-229376\,a^3\,b^5\,c^5\,d^{10}+114688\,a^2\,b^6\,c^6\,d^9-32768\,a\,b^7\,c^7\,d^8+4096\,b^8\,c^8\,d^7}\right)}^{3/4}\,\left(-\frac{\sqrt{x}\,{\left(-\frac{2401\,a^4\,c^3\,d^4-4116\,a^3\,b\,c^4\,d^3+2646\,a^2\,b^2\,c^5\,d^2-756\,a\,b^3\,c^6\,d+81\,b^4\,c^7}{4096\,a^8\,d^{15}-32768\,a^7\,b\,c\,d^{14}+114688\,a^6\,b^2\,c^2\,d^{13}-229376\,a^5\,b^3\,c^3\,d^{12}+286720\,a^4\,b^4\,c^4\,d^{11}-229376\,a^3\,b^5\,c^5\,d^{10}+114688\,a^2\,b^6\,c^6\,d^9-32768\,a\,b^7\,c^7\,d^8+4096\,b^8\,c^8\,d^7}\right)}^{1/4}\,\left(16640\,a^{13}\,b^4\,c^3\,d^{15}-143872\,a^{12}\,b^5\,c^4\,d^{14}+554240\,a^{11}\,b^6\,c^5\,d^{13}-1251328\,a^{10}\,b^7\,c^6\,d^{12}+1831424\,a^9\,b^8\,c^7\,d^{11}-1813504\,a^8\,b^9\,c^8\,d^{10}+1229312\,a^7\,b^{10}\,c^9\,d^9-563200\,a^6\,b^{11}\,c^{10}\,d^8+167168\,a^5\,b^{12}\,c^{11}\,d^7-29184\,a^4\,b^{13}\,c^{12}\,d^6+2304\,a^3\,b^{14}\,c^{13}\,d^5\right)}{a^6\,d^9-6\,a^5\,b\,c\,d^8+15\,a^4\,b^2\,c^2\,d^7-20\,a^3\,b^3\,c^3\,d^6+15\,a^2\,b^4\,c^4\,d^5-6\,a\,b^5\,c^5\,d^4+b^6\,c^6\,d^3}+\frac{\left(-2048\,a^{14}\,b^3\,c^3\,d^{14}+25312\,a^{13}\,b^4\,c^4\,d^{13}-133952\,a^{12}\,b^5\,c^5\,d^{12}+407008\,a^{11}\,b^6\,c^6\,d^{11}-795392\,a^{10}\,b^7\,c^7\,d^{10}+1054144\,a^9\,b^8\,c^8\,d^9-968576\,a^8\,b^9\,c^9\,d^8+617152\,a^7\,b^{10}\,c^{10}\,d^7-267008\,a^6\,b^{11}\,c^{11}\,d^6+74592\,a^5\,b^{12}\,c^{12}\,d^5-12096\,a^4\,b^{13}\,c^{13}\,d^4+864\,a^3\,b^{14}\,c^{14}\,d^3\right)\,1{}\mathrm{i}}{a^7\,d^{10}-7\,a^6\,b\,c\,d^9+21\,a^5\,b^2\,c^2\,d^8-35\,a^4\,b^3\,c^3\,d^7+35\,a^3\,b^4\,c^4\,d^6-21\,a^2\,b^5\,c^5\,d^5+7\,a\,b^6\,c^6\,d^4-b^7\,c^7\,d^3}\right)-\frac{\sqrt{x}\,\left(784\,a^{12}\,b\,c^3\,d^7-672\,a^{11}\,b^2\,c^4\,d^6+144\,a^{10}\,b^3\,c^5\,d^5+2401\,a^9\,b^4\,c^6\,d^4-4116\,a^8\,b^5\,c^7\,d^3+2646\,a^7\,b^6\,c^8\,d^2-756\,a^6\,b^7\,c^9\,d+81\,a^5\,b^8\,c^{10}\right)}{a^6\,d^9-6\,a^5\,b\,c\,d^8+15\,a^4\,b^2\,c^2\,d^7-20\,a^3\,b^3\,c^3\,d^6+15\,a^2\,b^4\,c^4\,d^5-6\,a\,b^5\,c^5\,d^4+b^6\,c^6\,d^3}\right)}{-\frac{1372\,a^{12}\,b\,c^4\,d^5-392\,a^{11}\,b^2\,c^5\,d^4-2037\,a^{10}\,b^3\,c^6\,d^3+1971\,a^9\,b^4\,c^7\,d^2-675\,a^8\,b^5\,c^8\,d+81\,a^7\,b^6\,c^9}{a^7\,d^{10}-7\,a^6\,b\,c\,d^9+21\,a^5\,b^2\,c^2\,d^8-35\,a^4\,b^3\,c^3\,d^7+35\,a^3\,b^4\,c^4\,d^6-21\,a^2\,b^5\,c^5\,d^5+7\,a\,b^6\,c^6\,d^4-b^7\,c^7\,d^3}+{\left(-\frac{2401\,a^4\,c^3\,d^4-4116\,a^3\,b\,c^4\,d^3+2646\,a^2\,b^2\,c^5\,d^2-756\,a\,b^3\,c^6\,d+81\,b^4\,c^7}{4096\,a^8\,d^{15}-32768\,a^7\,b\,c\,d^{14}+114688\,a^6\,b^2\,c^2\,d^{13}-229376\,a^5\,b^3\,c^3\,d^{12}+286720\,a^4\,b^4\,c^4\,d^{11}-229376\,a^3\,b^5\,c^5\,d^{10}+114688\,a^2\,b^6\,c^6\,d^9-32768\,a\,b^7\,c^7\,d^8+4096\,b^8\,c^8\,d^7}\right)}^{1/4}\,\left({\left(-\frac{2401\,a^4\,c^3\,d^4-4116\,a^3\,b\,c^4\,d^3+2646\,a^2\,b^2\,c^5\,d^2-756\,a\,b^3\,c^6\,d+81\,b^4\,c^7}{4096\,a^8\,d^{15}-32768\,a^7\,b\,c\,d^{14}+114688\,a^6\,b^2\,c^2\,d^{13}-229376\,a^5\,b^3\,c^3\,d^{12}+286720\,a^4\,b^4\,c^4\,d^{11}-229376\,a^3\,b^5\,c^5\,d^{10}+114688\,a^2\,b^6\,c^6\,d^9-32768\,a\,b^7\,c^7\,d^8+4096\,b^8\,c^8\,d^7}\right)}^{3/4}\,\left(\frac{\sqrt{x}\,{\left(-\frac{2401\,a^4\,c^3\,d^4-4116\,a^3\,b\,c^4\,d^3+2646\,a^2\,b^2\,c^5\,d^2-756\,a\,b^3\,c^6\,d+81\,b^4\,c^7}{4096\,a^8\,d^{15}-32768\,a^7\,b\,c\,d^{14}+114688\,a^6\,b^2\,c^2\,d^{13}-229376\,a^5\,b^3\,c^3\,d^{12}+286720\,a^4\,b^4\,c^4\,d^{11}-229376\,a^3\,b^5\,c^5\,d^{10}+114688\,a^2\,b^6\,c^6\,d^9-32768\,a\,b^7\,c^7\,d^8+4096\,b^8\,c^8\,d^7}\right)}^{1/4}\,\left(16640\,a^{13}\,b^4\,c^3\,d^{15}-143872\,a^{12}\,b^5\,c^4\,d^{14}+554240\,a^{11}\,b^6\,c^5\,d^{13}-1251328\,a^{10}\,b^7\,c^6\,d^{12}+1831424\,a^9\,b^8\,c^7\,d^{11}-1813504\,a^8\,b^9\,c^8\,d^{10}+1229312\,a^7\,b^{10}\,c^9\,d^9-563200\,a^6\,b^{11}\,c^{10}\,d^8+167168\,a^5\,b^{12}\,c^{11}\,d^7-29184\,a^4\,b^{13}\,c^{12}\,d^6+2304\,a^3\,b^{14}\,c^{13}\,d^5\right)}{a^6\,d^9-6\,a^5\,b\,c\,d^8+15\,a^4\,b^2\,c^2\,d^7-20\,a^3\,b^3\,c^3\,d^6+15\,a^2\,b^4\,c^4\,d^5-6\,a\,b^5\,c^5\,d^4+b^6\,c^6\,d^3}+\frac{\left(-2048\,a^{14}\,b^3\,c^3\,d^{14}+25312\,a^{13}\,b^4\,c^4\,d^{13}-133952\,a^{12}\,b^5\,c^5\,d^{12}+407008\,a^{11}\,b^6\,c^6\,d^{11}-795392\,a^{10}\,b^7\,c^7\,d^{10}+1054144\,a^9\,b^8\,c^8\,d^9-968576\,a^8\,b^9\,c^9\,d^8+617152\,a^7\,b^{10}\,c^{10}\,d^7-267008\,a^6\,b^{11}\,c^{11}\,d^6+74592\,a^5\,b^{12}\,c^{12}\,d^5-12096\,a^4\,b^{13}\,c^{13}\,d^4+864\,a^3\,b^{14}\,c^{14}\,d^3\right)\,1{}\mathrm{i}}{a^7\,d^{10}-7\,a^6\,b\,c\,d^9+21\,a^5\,b^2\,c^2\,d^8-35\,a^4\,b^3\,c^3\,d^7+35\,a^3\,b^4\,c^4\,d^6-21\,a^2\,b^5\,c^5\,d^5+7\,a\,b^6\,c^6\,d^4-b^7\,c^7\,d^3}\right)\,1{}\mathrm{i}+\frac{\sqrt{x}\,\left(784\,a^{12}\,b\,c^3\,d^7-672\,a^{11}\,b^2\,c^4\,d^6+144\,a^{10}\,b^3\,c^5\,d^5+2401\,a^9\,b^4\,c^6\,d^4-4116\,a^8\,b^5\,c^7\,d^3+2646\,a^7\,b^6\,c^8\,d^2-756\,a^6\,b^7\,c^9\,d+81\,a^5\,b^8\,c^{10}\right)\,1{}\mathrm{i}}{a^6\,d^9-6\,a^5\,b\,c\,d^8+15\,a^4\,b^2\,c^2\,d^7-20\,a^3\,b^3\,c^3\,d^6+15\,a^2\,b^4\,c^4\,d^5-6\,a\,b^5\,c^5\,d^4+b^6\,c^6\,d^3}\right)+{\left(-\frac{2401\,a^4\,c^3\,d^4-4116\,a^3\,b\,c^4\,d^3+2646\,a^2\,b^2\,c^5\,d^2-756\,a\,b^3\,c^6\,d+81\,b^4\,c^7}{4096\,a^8\,d^{15}-32768\,a^7\,b\,c\,d^{14}+114688\,a^6\,b^2\,c^2\,d^{13}-229376\,a^5\,b^3\,c^3\,d^{12}+286720\,a^4\,b^4\,c^4\,d^{11}-229376\,a^3\,b^5\,c^5\,d^{10}+114688\,a^2\,b^6\,c^6\,d^9-32768\,a\,b^7\,c^7\,d^8+4096\,b^8\,c^8\,d^7}\right)}^{1/4}\,\left({\left(-\frac{2401\,a^4\,c^3\,d^4-4116\,a^3\,b\,c^4\,d^3+2646\,a^2\,b^2\,c^5\,d^2-756\,a\,b^3\,c^6\,d+81\,b^4\,c^7}{4096\,a^8\,d^{15}-32768\,a^7\,b\,c\,d^{14}+114688\,a^6\,b^2\,c^2\,d^{13}-229376\,a^5\,b^3\,c^3\,d^{12}+286720\,a^4\,b^4\,c^4\,d^{11}-229376\,a^3\,b^5\,c^5\,d^{10}+114688\,a^2\,b^6\,c^6\,d^9-32768\,a\,b^7\,c^7\,d^8+4096\,b^8\,c^8\,d^7}\right)}^{3/4}\,\left(-\frac{\sqrt{x}\,{\left(-\frac{2401\,a^4\,c^3\,d^4-4116\,a^3\,b\,c^4\,d^3+2646\,a^2\,b^2\,c^5\,d^2-756\,a\,b^3\,c^6\,d+81\,b^4\,c^7}{4096\,a^8\,d^{15}-32768\,a^7\,b\,c\,d^{14}+114688\,a^6\,b^2\,c^2\,d^{13}-229376\,a^5\,b^3\,c^3\,d^{12}+286720\,a^4\,b^4\,c^4\,d^{11}-229376\,a^3\,b^5\,c^5\,d^{10}+114688\,a^2\,b^6\,c^6\,d^9-32768\,a\,b^7\,c^7\,d^8+4096\,b^8\,c^8\,d^7}\right)}^{1/4}\,\left(16640\,a^{13}\,b^4\,c^3\,d^{15}-143872\,a^{12}\,b^5\,c^4\,d^{14}+554240\,a^{11}\,b^6\,c^5\,d^{13}-1251328\,a^{10}\,b^7\,c^6\,d^{12}+1831424\,a^9\,b^8\,c^7\,d^{11}-1813504\,a^8\,b^9\,c^8\,d^{10}+1229312\,a^7\,b^{10}\,c^9\,d^9-563200\,a^6\,b^{11}\,c^{10}\,d^8+167168\,a^5\,b^{12}\,c^{11}\,d^7-29184\,a^4\,b^{13}\,c^{12}\,d^6+2304\,a^3\,b^{14}\,c^{13}\,d^5\right)}{a^6\,d^9-6\,a^5\,b\,c\,d^8+15\,a^4\,b^2\,c^2\,d^7-20\,a^3\,b^3\,c^3\,d^6+15\,a^2\,b^4\,c^4\,d^5-6\,a\,b^5\,c^5\,d^4+b^6\,c^6\,d^3}+\frac{\left(-2048\,a^{14}\,b^3\,c^3\,d^{14}+25312\,a^{13}\,b^4\,c^4\,d^{13}-133952\,a^{12}\,b^5\,c^5\,d^{12}+407008\,a^{11}\,b^6\,c^6\,d^{11}-795392\,a^{10}\,b^7\,c^7\,d^{10}+1054144\,a^9\,b^8\,c^8\,d^9-968576\,a^8\,b^9\,c^9\,d^8+617152\,a^7\,b^{10}\,c^{10}\,d^7-267008\,a^6\,b^{11}\,c^{11}\,d^6+74592\,a^5\,b^{12}\,c^{12}\,d^5-12096\,a^4\,b^{13}\,c^{13}\,d^4+864\,a^3\,b^{14}\,c^{14}\,d^3\right)\,1{}\mathrm{i}}{a^7\,d^{10}-7\,a^6\,b\,c\,d^9+21\,a^5\,b^2\,c^2\,d^8-35\,a^4\,b^3\,c^3\,d^7+35\,a^3\,b^4\,c^4\,d^6-21\,a^2\,b^5\,c^5\,d^5+7\,a\,b^6\,c^6\,d^4-b^7\,c^7\,d^3}\right)\,1{}\mathrm{i}-\frac{\sqrt{x}\,\left(784\,a^{12}\,b\,c^3\,d^7-672\,a^{11}\,b^2\,c^4\,d^6+144\,a^{10}\,b^3\,c^5\,d^5+2401\,a^9\,b^4\,c^6\,d^4-4116\,a^8\,b^5\,c^7\,d^3+2646\,a^7\,b^6\,c^8\,d^2-756\,a^6\,b^7\,c^9\,d+81\,a^5\,b^8\,c^{10}\right)\,1{}\mathrm{i}}{a^6\,d^9-6\,a^5\,b\,c\,d^8+15\,a^4\,b^2\,c^2\,d^7-20\,a^3\,b^3\,c^3\,d^6+15\,a^2\,b^4\,c^4\,d^5-6\,a\,b^5\,c^5\,d^4+b^6\,c^6\,d^3}\right)}\right)\,{\left(-\frac{2401\,a^4\,c^3\,d^4-4116\,a^3\,b\,c^4\,d^3+2646\,a^2\,b^2\,c^5\,d^2-756\,a\,b^3\,c^6\,d+81\,b^4\,c^7}{4096\,a^8\,d^{15}-32768\,a^7\,b\,c\,d^{14}+114688\,a^6\,b^2\,c^2\,d^{13}-229376\,a^5\,b^3\,c^3\,d^{12}+286720\,a^4\,b^4\,c^4\,d^{11}-229376\,a^3\,b^5\,c^5\,d^{10}+114688\,a^2\,b^6\,c^6\,d^9-32768\,a\,b^7\,c^7\,d^8+4096\,b^8\,c^8\,d^7}\right)}^{1/4}+\frac{c\,x^{3/2}}{2\,d\,\left(d\,x^2+c\right)\,\left(a\,d-b\,c\right)}-\mathrm{atan}\left(\frac{{\left(-\frac{a^7}{16\,a^8\,b^3\,d^8-128\,a^7\,b^4\,c\,d^7+448\,a^6\,b^5\,c^2\,d^6-896\,a^5\,b^6\,c^3\,d^5+1120\,a^4\,b^7\,c^4\,d^4-896\,a^3\,b^8\,c^5\,d^3+448\,a^2\,b^9\,c^6\,d^2-128\,a\,b^{10}\,c^7\,d+16\,b^{11}\,c^8}\right)}^{1/4}\,\left({\left(-\frac{a^7}{16\,a^8\,b^3\,d^8-128\,a^7\,b^4\,c\,d^7+448\,a^6\,b^5\,c^2\,d^6-896\,a^5\,b^6\,c^3\,d^5+1120\,a^4\,b^7\,c^4\,d^4-896\,a^3\,b^8\,c^5\,d^3+448\,a^2\,b^9\,c^6\,d^2-128\,a\,b^{10}\,c^7\,d+16\,b^{11}\,c^8}\right)}^{3/4}\,\left(\frac{-2048\,a^{14}\,b^3\,c^3\,d^{14}+25312\,a^{13}\,b^4\,c^4\,d^{13}-133952\,a^{12}\,b^5\,c^5\,d^{12}+407008\,a^{11}\,b^6\,c^6\,d^{11}-795392\,a^{10}\,b^7\,c^7\,d^{10}+1054144\,a^9\,b^8\,c^8\,d^9-968576\,a^8\,b^9\,c^9\,d^8+617152\,a^7\,b^{10}\,c^{10}\,d^7-267008\,a^6\,b^{11}\,c^{11}\,d^6+74592\,a^5\,b^{12}\,c^{12}\,d^5-12096\,a^4\,b^{13}\,c^{13}\,d^4+864\,a^3\,b^{14}\,c^{14}\,d^3}{a^7\,d^{10}-7\,a^6\,b\,c\,d^9+21\,a^5\,b^2\,c^2\,d^8-35\,a^4\,b^3\,c^3\,d^7+35\,a^3\,b^4\,c^4\,d^6-21\,a^2\,b^5\,c^5\,d^5+7\,a\,b^6\,c^6\,d^4-b^7\,c^7\,d^3}+\frac{\sqrt{x}\,{\left(-\frac{a^7}{16\,a^8\,b^3\,d^8-128\,a^7\,b^4\,c\,d^7+448\,a^6\,b^5\,c^2\,d^6-896\,a^5\,b^6\,c^3\,d^5+1120\,a^4\,b^7\,c^4\,d^4-896\,a^3\,b^8\,c^5\,d^3+448\,a^2\,b^9\,c^6\,d^2-128\,a\,b^{10}\,c^7\,d+16\,b^{11}\,c^8}\right)}^{1/4}\,\left(16640\,a^{13}\,b^4\,c^3\,d^{15}-143872\,a^{12}\,b^5\,c^4\,d^{14}+554240\,a^{11}\,b^6\,c^5\,d^{13}-1251328\,a^{10}\,b^7\,c^6\,d^{12}+1831424\,a^9\,b^8\,c^7\,d^{11}-1813504\,a^8\,b^9\,c^8\,d^{10}+1229312\,a^7\,b^{10}\,c^9\,d^9-563200\,a^6\,b^{11}\,c^{10}\,d^8+167168\,a^5\,b^{12}\,c^{11}\,d^7-29184\,a^4\,b^{13}\,c^{12}\,d^6+2304\,a^3\,b^{14}\,c^{13}\,d^5\right)}{a^6\,d^9-6\,a^5\,b\,c\,d^8+15\,a^4\,b^2\,c^2\,d^7-20\,a^3\,b^3\,c^3\,d^6+15\,a^2\,b^4\,c^4\,d^5-6\,a\,b^5\,c^5\,d^4+b^6\,c^6\,d^3}\right)\,1{}\mathrm{i}+\frac{\sqrt{x}\,\left(784\,a^{12}\,b\,c^3\,d^7-672\,a^{11}\,b^2\,c^4\,d^6+144\,a^{10}\,b^3\,c^5\,d^5+2401\,a^9\,b^4\,c^6\,d^4-4116\,a^8\,b^5\,c^7\,d^3+2646\,a^7\,b^6\,c^8\,d^2-756\,a^6\,b^7\,c^9\,d+81\,a^5\,b^8\,c^{10}\right)\,1{}\mathrm{i}}{a^6\,d^9-6\,a^5\,b\,c\,d^8+15\,a^4\,b^2\,c^2\,d^7-20\,a^3\,b^3\,c^3\,d^6+15\,a^2\,b^4\,c^4\,d^5-6\,a\,b^5\,c^5\,d^4+b^6\,c^6\,d^3}\right)-{\left(-\frac{a^7}{16\,a^8\,b^3\,d^8-128\,a^7\,b^4\,c\,d^7+448\,a^6\,b^5\,c^2\,d^6-896\,a^5\,b^6\,c^3\,d^5+1120\,a^4\,b^7\,c^4\,d^4-896\,a^3\,b^8\,c^5\,d^3+448\,a^2\,b^9\,c^6\,d^2-128\,a\,b^{10}\,c^7\,d+16\,b^{11}\,c^8}\right)}^{1/4}\,\left({\left(-\frac{a^7}{16\,a^8\,b^3\,d^8-128\,a^7\,b^4\,c\,d^7+448\,a^6\,b^5\,c^2\,d^6-896\,a^5\,b^6\,c^3\,d^5+1120\,a^4\,b^7\,c^4\,d^4-896\,a^3\,b^8\,c^5\,d^3+448\,a^2\,b^9\,c^6\,d^2-128\,a\,b^{10}\,c^7\,d+16\,b^{11}\,c^8}\right)}^{3/4}\,\left(\frac{-2048\,a^{14}\,b^3\,c^3\,d^{14}+25312\,a^{13}\,b^4\,c^4\,d^{13}-133952\,a^{12}\,b^5\,c^5\,d^{12}+407008\,a^{11}\,b^6\,c^6\,d^{11}-795392\,a^{10}\,b^7\,c^7\,d^{10}+1054144\,a^9\,b^8\,c^8\,d^9-968576\,a^8\,b^9\,c^9\,d^8+617152\,a^7\,b^{10}\,c^{10}\,d^7-267008\,a^6\,b^{11}\,c^{11}\,d^6+74592\,a^5\,b^{12}\,c^{12}\,d^5-12096\,a^4\,b^{13}\,c^{13}\,d^4+864\,a^3\,b^{14}\,c^{14}\,d^3}{a^7\,d^{10}-7\,a^6\,b\,c\,d^9+21\,a^5\,b^2\,c^2\,d^8-35\,a^4\,b^3\,c^3\,d^7+35\,a^3\,b^4\,c^4\,d^6-21\,a^2\,b^5\,c^5\,d^5+7\,a\,b^6\,c^6\,d^4-b^7\,c^7\,d^3}-\frac{\sqrt{x}\,{\left(-\frac{a^7}{16\,a^8\,b^3\,d^8-128\,a^7\,b^4\,c\,d^7+448\,a^6\,b^5\,c^2\,d^6-896\,a^5\,b^6\,c^3\,d^5+1120\,a^4\,b^7\,c^4\,d^4-896\,a^3\,b^8\,c^5\,d^3+448\,a^2\,b^9\,c^6\,d^2-128\,a\,b^{10}\,c^7\,d+16\,b^{11}\,c^8}\right)}^{1/4}\,\left(16640\,a^{13}\,b^4\,c^3\,d^{15}-143872\,a^{12}\,b^5\,c^4\,d^{14}+554240\,a^{11}\,b^6\,c^5\,d^{13}-1251328\,a^{10}\,b^7\,c^6\,d^{12}+1831424\,a^9\,b^8\,c^7\,d^{11}-1813504\,a^8\,b^9\,c^8\,d^{10}+1229312\,a^7\,b^{10}\,c^9\,d^9-563200\,a^6\,b^{11}\,c^{10}\,d^8+167168\,a^5\,b^{12}\,c^{11}\,d^7-29184\,a^4\,b^{13}\,c^{12}\,d^6+2304\,a^3\,b^{14}\,c^{13}\,d^5\right)}{a^6\,d^9-6\,a^5\,b\,c\,d^8+15\,a^4\,b^2\,c^2\,d^7-20\,a^3\,b^3\,c^3\,d^6+15\,a^2\,b^4\,c^4\,d^5-6\,a\,b^5\,c^5\,d^4+b^6\,c^6\,d^3}\right)\,1{}\mathrm{i}-\frac{\sqrt{x}\,\left(784\,a^{12}\,b\,c^3\,d^7-672\,a^{11}\,b^2\,c^4\,d^6+144\,a^{10}\,b^3\,c^5\,d^5+2401\,a^9\,b^4\,c^6\,d^4-4116\,a^8\,b^5\,c^7\,d^3+2646\,a^7\,b^6\,c^8\,d^2-756\,a^6\,b^7\,c^9\,d+81\,a^5\,b^8\,c^{10}\right)\,1{}\mathrm{i}}{a^6\,d^9-6\,a^5\,b\,c\,d^8+15\,a^4\,b^2\,c^2\,d^7-20\,a^3\,b^3\,c^3\,d^6+15\,a^2\,b^4\,c^4\,d^5-6\,a\,b^5\,c^5\,d^4+b^6\,c^6\,d^3}\right)}{\frac{1372\,a^{12}\,b\,c^4\,d^5-392\,a^{11}\,b^2\,c^5\,d^4-2037\,a^{10}\,b^3\,c^6\,d^3+1971\,a^9\,b^4\,c^7\,d^2-675\,a^8\,b^5\,c^8\,d+81\,a^7\,b^6\,c^9}{a^7\,d^{10}-7\,a^6\,b\,c\,d^9+21\,a^5\,b^2\,c^2\,d^8-35\,a^4\,b^3\,c^3\,d^7+35\,a^3\,b^4\,c^4\,d^6-21\,a^2\,b^5\,c^5\,d^5+7\,a\,b^6\,c^6\,d^4-b^7\,c^7\,d^3}+{\left(-\frac{a^7}{16\,a^8\,b^3\,d^8-128\,a^7\,b^4\,c\,d^7+448\,a^6\,b^5\,c^2\,d^6-896\,a^5\,b^6\,c^3\,d^5+1120\,a^4\,b^7\,c^4\,d^4-896\,a^3\,b^8\,c^5\,d^3+448\,a^2\,b^9\,c^6\,d^2-128\,a\,b^{10}\,c^7\,d+16\,b^{11}\,c^8}\right)}^{1/4}\,\left({\left(-\frac{a^7}{16\,a^8\,b^3\,d^8-128\,a^7\,b^4\,c\,d^7+448\,a^6\,b^5\,c^2\,d^6-896\,a^5\,b^6\,c^3\,d^5+1120\,a^4\,b^7\,c^4\,d^4-896\,a^3\,b^8\,c^5\,d^3+448\,a^2\,b^9\,c^6\,d^2-128\,a\,b^{10}\,c^7\,d+16\,b^{11}\,c^8}\right)}^{3/4}\,\left(\frac{-2048\,a^{14}\,b^3\,c^3\,d^{14}+25312\,a^{13}\,b^4\,c^4\,d^{13}-133952\,a^{12}\,b^5\,c^5\,d^{12}+407008\,a^{11}\,b^6\,c^6\,d^{11}-795392\,a^{10}\,b^7\,c^7\,d^{10}+1054144\,a^9\,b^8\,c^8\,d^9-968576\,a^8\,b^9\,c^9\,d^8+617152\,a^7\,b^{10}\,c^{10}\,d^7-267008\,a^6\,b^{11}\,c^{11}\,d^6+74592\,a^5\,b^{12}\,c^{12}\,d^5-12096\,a^4\,b^{13}\,c^{13}\,d^4+864\,a^3\,b^{14}\,c^{14}\,d^3}{a^7\,d^{10}-7\,a^6\,b\,c\,d^9+21\,a^5\,b^2\,c^2\,d^8-35\,a^4\,b^3\,c^3\,d^7+35\,a^3\,b^4\,c^4\,d^6-21\,a^2\,b^5\,c^5\,d^5+7\,a\,b^6\,c^6\,d^4-b^7\,c^7\,d^3}+\frac{\sqrt{x}\,{\left(-\frac{a^7}{16\,a^8\,b^3\,d^8-128\,a^7\,b^4\,c\,d^7+448\,a^6\,b^5\,c^2\,d^6-896\,a^5\,b^6\,c^3\,d^5+1120\,a^4\,b^7\,c^4\,d^4-896\,a^3\,b^8\,c^5\,d^3+448\,a^2\,b^9\,c^6\,d^2-128\,a\,b^{10}\,c^7\,d+16\,b^{11}\,c^8}\right)}^{1/4}\,\left(16640\,a^{13}\,b^4\,c^3\,d^{15}-143872\,a^{12}\,b^5\,c^4\,d^{14}+554240\,a^{11}\,b^6\,c^5\,d^{13}-1251328\,a^{10}\,b^7\,c^6\,d^{12}+1831424\,a^9\,b^8\,c^7\,d^{11}-1813504\,a^8\,b^9\,c^8\,d^{10}+1229312\,a^7\,b^{10}\,c^9\,d^9-563200\,a^6\,b^{11}\,c^{10}\,d^8+167168\,a^5\,b^{12}\,c^{11}\,d^7-29184\,a^4\,b^{13}\,c^{12}\,d^6+2304\,a^3\,b^{14}\,c^{13}\,d^5\right)}{a^6\,d^9-6\,a^5\,b\,c\,d^8+15\,a^4\,b^2\,c^2\,d^7-20\,a^3\,b^3\,c^3\,d^6+15\,a^2\,b^4\,c^4\,d^5-6\,a\,b^5\,c^5\,d^4+b^6\,c^6\,d^3}\right)+\frac{\sqrt{x}\,\left(784\,a^{12}\,b\,c^3\,d^7-672\,a^{11}\,b^2\,c^4\,d^6+144\,a^{10}\,b^3\,c^5\,d^5+2401\,a^9\,b^4\,c^6\,d^4-4116\,a^8\,b^5\,c^7\,d^3+2646\,a^7\,b^6\,c^8\,d^2-756\,a^6\,b^7\,c^9\,d+81\,a^5\,b^8\,c^{10}\right)}{a^6\,d^9-6\,a^5\,b\,c\,d^8+15\,a^4\,b^2\,c^2\,d^7-20\,a^3\,b^3\,c^3\,d^6+15\,a^2\,b^4\,c^4\,d^5-6\,a\,b^5\,c^5\,d^4+b^6\,c^6\,d^3}\right)+{\left(-\frac{a^7}{16\,a^8\,b^3\,d^8-128\,a^7\,b^4\,c\,d^7+448\,a^6\,b^5\,c^2\,d^6-896\,a^5\,b^6\,c^3\,d^5+1120\,a^4\,b^7\,c^4\,d^4-896\,a^3\,b^8\,c^5\,d^3+448\,a^2\,b^9\,c^6\,d^2-128\,a\,b^{10}\,c^7\,d+16\,b^{11}\,c^8}\right)}^{1/4}\,\left({\left(-\frac{a^7}{16\,a^8\,b^3\,d^8-128\,a^7\,b^4\,c\,d^7+448\,a^6\,b^5\,c^2\,d^6-896\,a^5\,b^6\,c^3\,d^5+1120\,a^4\,b^7\,c^4\,d^4-896\,a^3\,b^8\,c^5\,d^3+448\,a^2\,b^9\,c^6\,d^2-128\,a\,b^{10}\,c^7\,d+16\,b^{11}\,c^8}\right)}^{3/4}\,\left(\frac{-2048\,a^{14}\,b^3\,c^3\,d^{14}+25312\,a^{13}\,b^4\,c^4\,d^{13}-133952\,a^{12}\,b^5\,c^5\,d^{12}+407008\,a^{11}\,b^6\,c^6\,d^{11}-795392\,a^{10}\,b^7\,c^7\,d^{10}+1054144\,a^9\,b^8\,c^8\,d^9-968576\,a^8\,b^9\,c^9\,d^8+617152\,a^7\,b^{10}\,c^{10}\,d^7-267008\,a^6\,b^{11}\,c^{11}\,d^6+74592\,a^5\,b^{12}\,c^{12}\,d^5-12096\,a^4\,b^{13}\,c^{13}\,d^4+864\,a^3\,b^{14}\,c^{14}\,d^3}{a^7\,d^{10}-7\,a^6\,b\,c\,d^9+21\,a^5\,b^2\,c^2\,d^8-35\,a^4\,b^3\,c^3\,d^7+35\,a^3\,b^4\,c^4\,d^6-21\,a^2\,b^5\,c^5\,d^5+7\,a\,b^6\,c^6\,d^4-b^7\,c^7\,d^3}-\frac{\sqrt{x}\,{\left(-\frac{a^7}{16\,a^8\,b^3\,d^8-128\,a^7\,b^4\,c\,d^7+448\,a^6\,b^5\,c^2\,d^6-896\,a^5\,b^6\,c^3\,d^5+1120\,a^4\,b^7\,c^4\,d^4-896\,a^3\,b^8\,c^5\,d^3+448\,a^2\,b^9\,c^6\,d^2-128\,a\,b^{10}\,c^7\,d+16\,b^{11}\,c^8}\right)}^{1/4}\,\left(16640\,a^{13}\,b^4\,c^3\,d^{15}-143872\,a^{12}\,b^5\,c^4\,d^{14}+554240\,a^{11}\,b^6\,c^5\,d^{13}-1251328\,a^{10}\,b^7\,c^6\,d^{12}+1831424\,a^9\,b^8\,c^7\,d^{11}-1813504\,a^8\,b^9\,c^8\,d^{10}+1229312\,a^7\,b^{10}\,c^9\,d^9-563200\,a^6\,b^{11}\,c^{10}\,d^8+167168\,a^5\,b^{12}\,c^{11}\,d^7-29184\,a^4\,b^{13}\,c^{12}\,d^6+2304\,a^3\,b^{14}\,c^{13}\,d^5\right)}{a^6\,d^9-6\,a^5\,b\,c\,d^8+15\,a^4\,b^2\,c^2\,d^7-20\,a^3\,b^3\,c^3\,d^6+15\,a^2\,b^4\,c^4\,d^5-6\,a\,b^5\,c^5\,d^4+b^6\,c^6\,d^3}\right)-\frac{\sqrt{x}\,\left(784\,a^{12}\,b\,c^3\,d^7-672\,a^{11}\,b^2\,c^4\,d^6+144\,a^{10}\,b^3\,c^5\,d^5+2401\,a^9\,b^4\,c^6\,d^4-4116\,a^8\,b^5\,c^7\,d^3+2646\,a^7\,b^6\,c^8\,d^2-756\,a^6\,b^7\,c^9\,d+81\,a^5\,b^8\,c^{10}\right)}{a^6\,d^9-6\,a^5\,b\,c\,d^8+15\,a^4\,b^2\,c^2\,d^7-20\,a^3\,b^3\,c^3\,d^6+15\,a^2\,b^4\,c^4\,d^5-6\,a\,b^5\,c^5\,d^4+b^6\,c^6\,d^3}\right)}\right)\,{\left(-\frac{a^7}{16\,a^8\,b^3\,d^8-128\,a^7\,b^4\,c\,d^7+448\,a^6\,b^5\,c^2\,d^6-896\,a^5\,b^6\,c^3\,d^5+1120\,a^4\,b^7\,c^4\,d^4-896\,a^3\,b^8\,c^5\,d^3+448\,a^2\,b^9\,c^6\,d^2-128\,a\,b^{10}\,c^7\,d+16\,b^{11}\,c^8}\right)}^{1/4}\,2{}\mathrm{i}-\mathrm{atan}\left(\frac{{\left(-\frac{2401\,a^4\,c^3\,d^4-4116\,a^3\,b\,c^4\,d^3+2646\,a^2\,b^2\,c^5\,d^2-756\,a\,b^3\,c^6\,d+81\,b^4\,c^7}{4096\,a^8\,d^{15}-32768\,a^7\,b\,c\,d^{14}+114688\,a^6\,b^2\,c^2\,d^{13}-229376\,a^5\,b^3\,c^3\,d^{12}+286720\,a^4\,b^4\,c^4\,d^{11}-229376\,a^3\,b^5\,c^5\,d^{10}+114688\,a^2\,b^6\,c^6\,d^9-32768\,a\,b^7\,c^7\,d^8+4096\,b^8\,c^8\,d^7}\right)}^{1/4}\,\left({\left(-\frac{2401\,a^4\,c^3\,d^4-4116\,a^3\,b\,c^4\,d^3+2646\,a^2\,b^2\,c^5\,d^2-756\,a\,b^3\,c^6\,d+81\,b^4\,c^7}{4096\,a^8\,d^{15}-32768\,a^7\,b\,c\,d^{14}+114688\,a^6\,b^2\,c^2\,d^{13}-229376\,a^5\,b^3\,c^3\,d^{12}+286720\,a^4\,b^4\,c^4\,d^{11}-229376\,a^3\,b^5\,c^5\,d^{10}+114688\,a^2\,b^6\,c^6\,d^9-32768\,a\,b^7\,c^7\,d^8+4096\,b^8\,c^8\,d^7}\right)}^{3/4}\,\left(\frac{-2048\,a^{14}\,b^3\,c^3\,d^{14}+25312\,a^{13}\,b^4\,c^4\,d^{13}-133952\,a^{12}\,b^5\,c^5\,d^{12}+407008\,a^{11}\,b^6\,c^6\,d^{11}-795392\,a^{10}\,b^7\,c^7\,d^{10}+1054144\,a^9\,b^8\,c^8\,d^9-968576\,a^8\,b^9\,c^9\,d^8+617152\,a^7\,b^{10}\,c^{10}\,d^7-267008\,a^6\,b^{11}\,c^{11}\,d^6+74592\,a^5\,b^{12}\,c^{12}\,d^5-12096\,a^4\,b^{13}\,c^{13}\,d^4+864\,a^3\,b^{14}\,c^{14}\,d^3}{a^7\,d^{10}-7\,a^6\,b\,c\,d^9+21\,a^5\,b^2\,c^2\,d^8-35\,a^4\,b^3\,c^3\,d^7+35\,a^3\,b^4\,c^4\,d^6-21\,a^2\,b^5\,c^5\,d^5+7\,a\,b^6\,c^6\,d^4-b^7\,c^7\,d^3}+\frac{\sqrt{x}\,{\left(-\frac{2401\,a^4\,c^3\,d^4-4116\,a^3\,b\,c^4\,d^3+2646\,a^2\,b^2\,c^5\,d^2-756\,a\,b^3\,c^6\,d+81\,b^4\,c^7}{4096\,a^8\,d^{15}-32768\,a^7\,b\,c\,d^{14}+114688\,a^6\,b^2\,c^2\,d^{13}-229376\,a^5\,b^3\,c^3\,d^{12}+286720\,a^4\,b^4\,c^4\,d^{11}-229376\,a^3\,b^5\,c^5\,d^{10}+114688\,a^2\,b^6\,c^6\,d^9-32768\,a\,b^7\,c^7\,d^8+4096\,b^8\,c^8\,d^7}\right)}^{1/4}\,\left(16640\,a^{13}\,b^4\,c^3\,d^{15}-143872\,a^{12}\,b^5\,c^4\,d^{14}+554240\,a^{11}\,b^6\,c^5\,d^{13}-1251328\,a^{10}\,b^7\,c^6\,d^{12}+1831424\,a^9\,b^8\,c^7\,d^{11}-1813504\,a^8\,b^9\,c^8\,d^{10}+1229312\,a^7\,b^{10}\,c^9\,d^9-563200\,a^6\,b^{11}\,c^{10}\,d^8+167168\,a^5\,b^{12}\,c^{11}\,d^7-29184\,a^4\,b^{13}\,c^{12}\,d^6+2304\,a^3\,b^{14}\,c^{13}\,d^5\right)}{a^6\,d^9-6\,a^5\,b\,c\,d^8+15\,a^4\,b^2\,c^2\,d^7-20\,a^3\,b^3\,c^3\,d^6+15\,a^2\,b^4\,c^4\,d^5-6\,a\,b^5\,c^5\,d^4+b^6\,c^6\,d^3}\right)\,1{}\mathrm{i}+\frac{\sqrt{x}\,\left(784\,a^{12}\,b\,c^3\,d^7-672\,a^{11}\,b^2\,c^4\,d^6+144\,a^{10}\,b^3\,c^5\,d^5+2401\,a^9\,b^4\,c^6\,d^4-4116\,a^8\,b^5\,c^7\,d^3+2646\,a^7\,b^6\,c^8\,d^2-756\,a^6\,b^7\,c^9\,d+81\,a^5\,b^8\,c^{10}\right)\,1{}\mathrm{i}}{a^6\,d^9-6\,a^5\,b\,c\,d^8+15\,a^4\,b^2\,c^2\,d^7-20\,a^3\,b^3\,c^3\,d^6+15\,a^2\,b^4\,c^4\,d^5-6\,a\,b^5\,c^5\,d^4+b^6\,c^6\,d^3}\right)-{\left(-\frac{2401\,a^4\,c^3\,d^4-4116\,a^3\,b\,c^4\,d^3+2646\,a^2\,b^2\,c^5\,d^2-756\,a\,b^3\,c^6\,d+81\,b^4\,c^7}{4096\,a^8\,d^{15}-32768\,a^7\,b\,c\,d^{14}+114688\,a^6\,b^2\,c^2\,d^{13}-229376\,a^5\,b^3\,c^3\,d^{12}+286720\,a^4\,b^4\,c^4\,d^{11}-229376\,a^3\,b^5\,c^5\,d^{10}+114688\,a^2\,b^6\,c^6\,d^9-32768\,a\,b^7\,c^7\,d^8+4096\,b^8\,c^8\,d^7}\right)}^{1/4}\,\left({\left(-\frac{2401\,a^4\,c^3\,d^4-4116\,a^3\,b\,c^4\,d^3+2646\,a^2\,b^2\,c^5\,d^2-756\,a\,b^3\,c^6\,d+81\,b^4\,c^7}{4096\,a^8\,d^{15}-32768\,a^7\,b\,c\,d^{14}+114688\,a^6\,b^2\,c^2\,d^{13}-229376\,a^5\,b^3\,c^3\,d^{12}+286720\,a^4\,b^4\,c^4\,d^{11}-229376\,a^3\,b^5\,c^5\,d^{10}+114688\,a^2\,b^6\,c^6\,d^9-32768\,a\,b^7\,c^7\,d^8+4096\,b^8\,c^8\,d^7}\right)}^{3/4}\,\left(\frac{-2048\,a^{14}\,b^3\,c^3\,d^{14}+25312\,a^{13}\,b^4\,c^4\,d^{13}-133952\,a^{12}\,b^5\,c^5\,d^{12}+407008\,a^{11}\,b^6\,c^6\,d^{11}-795392\,a^{10}\,b^7\,c^7\,d^{10}+1054144\,a^9\,b^8\,c^8\,d^9-968576\,a^8\,b^9\,c^9\,d^8+617152\,a^7\,b^{10}\,c^{10}\,d^7-267008\,a^6\,b^{11}\,c^{11}\,d^6+74592\,a^5\,b^{12}\,c^{12}\,d^5-12096\,a^4\,b^{13}\,c^{13}\,d^4+864\,a^3\,b^{14}\,c^{14}\,d^3}{a^7\,d^{10}-7\,a^6\,b\,c\,d^9+21\,a^5\,b^2\,c^2\,d^8-35\,a^4\,b^3\,c^3\,d^7+35\,a^3\,b^4\,c^4\,d^6-21\,a^2\,b^5\,c^5\,d^5+7\,a\,b^6\,c^6\,d^4-b^7\,c^7\,d^3}-\frac{\sqrt{x}\,{\left(-\frac{2401\,a^4\,c^3\,d^4-4116\,a^3\,b\,c^4\,d^3+2646\,a^2\,b^2\,c^5\,d^2-756\,a\,b^3\,c^6\,d+81\,b^4\,c^7}{4096\,a^8\,d^{15}-32768\,a^7\,b\,c\,d^{14}+114688\,a^6\,b^2\,c^2\,d^{13}-229376\,a^5\,b^3\,c^3\,d^{12}+286720\,a^4\,b^4\,c^4\,d^{11}-229376\,a^3\,b^5\,c^5\,d^{10}+114688\,a^2\,b^6\,c^6\,d^9-32768\,a\,b^7\,c^7\,d^8+4096\,b^8\,c^8\,d^7}\right)}^{1/4}\,\left(16640\,a^{13}\,b^4\,c^3\,d^{15}-143872\,a^{12}\,b^5\,c^4\,d^{14}+554240\,a^{11}\,b^6\,c^5\,d^{13}-1251328\,a^{10}\,b^7\,c^6\,d^{12}+1831424\,a^9\,b^8\,c^7\,d^{11}-1813504\,a^8\,b^9\,c^8\,d^{10}+1229312\,a^7\,b^{10}\,c^9\,d^9-563200\,a^6\,b^{11}\,c^{10}\,d^8+167168\,a^5\,b^{12}\,c^{11}\,d^7-29184\,a^4\,b^{13}\,c^{12}\,d^6+2304\,a^3\,b^{14}\,c^{13}\,d^5\right)}{a^6\,d^9-6\,a^5\,b\,c\,d^8+15\,a^4\,b^2\,c^2\,d^7-20\,a^3\,b^3\,c^3\,d^6+15\,a^2\,b^4\,c^4\,d^5-6\,a\,b^5\,c^5\,d^4+b^6\,c^6\,d^3}\right)\,1{}\mathrm{i}-\frac{\sqrt{x}\,\left(784\,a^{12}\,b\,c^3\,d^7-672\,a^{11}\,b^2\,c^4\,d^6+144\,a^{10}\,b^3\,c^5\,d^5+2401\,a^9\,b^4\,c^6\,d^4-4116\,a^8\,b^5\,c^7\,d^3+2646\,a^7\,b^6\,c^8\,d^2-756\,a^6\,b^7\,c^9\,d+81\,a^5\,b^8\,c^{10}\right)\,1{}\mathrm{i}}{a^6\,d^9-6\,a^5\,b\,c\,d^8+15\,a^4\,b^2\,c^2\,d^7-20\,a^3\,b^3\,c^3\,d^6+15\,a^2\,b^4\,c^4\,d^5-6\,a\,b^5\,c^5\,d^4+b^6\,c^6\,d^3}\right)}{\frac{1372\,a^{12}\,b\,c^4\,d^5-392\,a^{11}\,b^2\,c^5\,d^4-2037\,a^{10}\,b^3\,c^6\,d^3+1971\,a^9\,b^4\,c^7\,d^2-675\,a^8\,b^5\,c^8\,d+81\,a^7\,b^6\,c^9}{a^7\,d^{10}-7\,a^6\,b\,c\,d^9+21\,a^5\,b^2\,c^2\,d^8-35\,a^4\,b^3\,c^3\,d^7+35\,a^3\,b^4\,c^4\,d^6-21\,a^2\,b^5\,c^5\,d^5+7\,a\,b^6\,c^6\,d^4-b^7\,c^7\,d^3}+{\left(-\frac{2401\,a^4\,c^3\,d^4-4116\,a^3\,b\,c^4\,d^3+2646\,a^2\,b^2\,c^5\,d^2-756\,a\,b^3\,c^6\,d+81\,b^4\,c^7}{4096\,a^8\,d^{15}-32768\,a^7\,b\,c\,d^{14}+114688\,a^6\,b^2\,c^2\,d^{13}-229376\,a^5\,b^3\,c^3\,d^{12}+286720\,a^4\,b^4\,c^4\,d^{11}-229376\,a^3\,b^5\,c^5\,d^{10}+114688\,a^2\,b^6\,c^6\,d^9-32768\,a\,b^7\,c^7\,d^8+4096\,b^8\,c^8\,d^7}\right)}^{1/4}\,\left({\left(-\frac{2401\,a^4\,c^3\,d^4-4116\,a^3\,b\,c^4\,d^3+2646\,a^2\,b^2\,c^5\,d^2-756\,a\,b^3\,c^6\,d+81\,b^4\,c^7}{4096\,a^8\,d^{15}-32768\,a^7\,b\,c\,d^{14}+114688\,a^6\,b^2\,c^2\,d^{13}-229376\,a^5\,b^3\,c^3\,d^{12}+286720\,a^4\,b^4\,c^4\,d^{11}-229376\,a^3\,b^5\,c^5\,d^{10}+114688\,a^2\,b^6\,c^6\,d^9-32768\,a\,b^7\,c^7\,d^8+4096\,b^8\,c^8\,d^7}\right)}^{3/4}\,\left(\frac{-2048\,a^{14}\,b^3\,c^3\,d^{14}+25312\,a^{13}\,b^4\,c^4\,d^{13}-133952\,a^{12}\,b^5\,c^5\,d^{12}+407008\,a^{11}\,b^6\,c^6\,d^{11}-795392\,a^{10}\,b^7\,c^7\,d^{10}+1054144\,a^9\,b^8\,c^8\,d^9-968576\,a^8\,b^9\,c^9\,d^8+617152\,a^7\,b^{10}\,c^{10}\,d^7-267008\,a^6\,b^{11}\,c^{11}\,d^6+74592\,a^5\,b^{12}\,c^{12}\,d^5-12096\,a^4\,b^{13}\,c^{13}\,d^4+864\,a^3\,b^{14}\,c^{14}\,d^3}{a^7\,d^{10}-7\,a^6\,b\,c\,d^9+21\,a^5\,b^2\,c^2\,d^8-35\,a^4\,b^3\,c^3\,d^7+35\,a^3\,b^4\,c^4\,d^6-21\,a^2\,b^5\,c^5\,d^5+7\,a\,b^6\,c^6\,d^4-b^7\,c^7\,d^3}+\frac{\sqrt{x}\,{\left(-\frac{2401\,a^4\,c^3\,d^4-4116\,a^3\,b\,c^4\,d^3+2646\,a^2\,b^2\,c^5\,d^2-756\,a\,b^3\,c^6\,d+81\,b^4\,c^7}{4096\,a^8\,d^{15}-32768\,a^7\,b\,c\,d^{14}+114688\,a^6\,b^2\,c^2\,d^{13}-229376\,a^5\,b^3\,c^3\,d^{12}+286720\,a^4\,b^4\,c^4\,d^{11}-229376\,a^3\,b^5\,c^5\,d^{10}+114688\,a^2\,b^6\,c^6\,d^9-32768\,a\,b^7\,c^7\,d^8+4096\,b^8\,c^8\,d^7}\right)}^{1/4}\,\left(16640\,a^{13}\,b^4\,c^3\,d^{15}-143872\,a^{12}\,b^5\,c^4\,d^{14}+554240\,a^{11}\,b^6\,c^5\,d^{13}-1251328\,a^{10}\,b^7\,c^6\,d^{12}+1831424\,a^9\,b^8\,c^7\,d^{11}-1813504\,a^8\,b^9\,c^8\,d^{10}+1229312\,a^7\,b^{10}\,c^9\,d^9-563200\,a^6\,b^{11}\,c^{10}\,d^8+167168\,a^5\,b^{12}\,c^{11}\,d^7-29184\,a^4\,b^{13}\,c^{12}\,d^6+2304\,a^3\,b^{14}\,c^{13}\,d^5\right)}{a^6\,d^9-6\,a^5\,b\,c\,d^8+15\,a^4\,b^2\,c^2\,d^7-20\,a^3\,b^3\,c^3\,d^6+15\,a^2\,b^4\,c^4\,d^5-6\,a\,b^5\,c^5\,d^4+b^6\,c^6\,d^3}\right)+\frac{\sqrt{x}\,\left(784\,a^{12}\,b\,c^3\,d^7-672\,a^{11}\,b^2\,c^4\,d^6+144\,a^{10}\,b^3\,c^5\,d^5+2401\,a^9\,b^4\,c^6\,d^4-4116\,a^8\,b^5\,c^7\,d^3+2646\,a^7\,b^6\,c^8\,d^2-756\,a^6\,b^7\,c^9\,d+81\,a^5\,b^8\,c^{10}\right)}{a^6\,d^9-6\,a^5\,b\,c\,d^8+15\,a^4\,b^2\,c^2\,d^7-20\,a^3\,b^3\,c^3\,d^6+15\,a^2\,b^4\,c^4\,d^5-6\,a\,b^5\,c^5\,d^4+b^6\,c^6\,d^3}\right)+{\left(-\frac{2401\,a^4\,c^3\,d^4-4116\,a^3\,b\,c^4\,d^3+2646\,a^2\,b^2\,c^5\,d^2-756\,a\,b^3\,c^6\,d+81\,b^4\,c^7}{4096\,a^8\,d^{15}-32768\,a^7\,b\,c\,d^{14}+114688\,a^6\,b^2\,c^2\,d^{13}-229376\,a^5\,b^3\,c^3\,d^{12}+286720\,a^4\,b^4\,c^4\,d^{11}-229376\,a^3\,b^5\,c^5\,d^{10}+114688\,a^2\,b^6\,c^6\,d^9-32768\,a\,b^7\,c^7\,d^8+4096\,b^8\,c^8\,d^7}\right)}^{1/4}\,\left({\left(-\frac{2401\,a^4\,c^3\,d^4-4116\,a^3\,b\,c^4\,d^3+2646\,a^2\,b^2\,c^5\,d^2-756\,a\,b^3\,c^6\,d+81\,b^4\,c^7}{4096\,a^8\,d^{15}-32768\,a^7\,b\,c\,d^{14}+114688\,a^6\,b^2\,c^2\,d^{13}-229376\,a^5\,b^3\,c^3\,d^{12}+286720\,a^4\,b^4\,c^4\,d^{11}-229376\,a^3\,b^5\,c^5\,d^{10}+114688\,a^2\,b^6\,c^6\,d^9-32768\,a\,b^7\,c^7\,d^8+4096\,b^8\,c^8\,d^7}\right)}^{3/4}\,\left(\frac{-2048\,a^{14}\,b^3\,c^3\,d^{14}+25312\,a^{13}\,b^4\,c^4\,d^{13}-133952\,a^{12}\,b^5\,c^5\,d^{12}+407008\,a^{11}\,b^6\,c^6\,d^{11}-795392\,a^{10}\,b^7\,c^7\,d^{10}+1054144\,a^9\,b^8\,c^8\,d^9-968576\,a^8\,b^9\,c^9\,d^8+617152\,a^7\,b^{10}\,c^{10}\,d^7-267008\,a^6\,b^{11}\,c^{11}\,d^6+74592\,a^5\,b^{12}\,c^{12}\,d^5-12096\,a^4\,b^{13}\,c^{13}\,d^4+864\,a^3\,b^{14}\,c^{14}\,d^3}{a^7\,d^{10}-7\,a^6\,b\,c\,d^9+21\,a^5\,b^2\,c^2\,d^8-35\,a^4\,b^3\,c^3\,d^7+35\,a^3\,b^4\,c^4\,d^6-21\,a^2\,b^5\,c^5\,d^5+7\,a\,b^6\,c^6\,d^4-b^7\,c^7\,d^3}-\frac{\sqrt{x}\,{\left(-\frac{2401\,a^4\,c^3\,d^4-4116\,a^3\,b\,c^4\,d^3+2646\,a^2\,b^2\,c^5\,d^2-756\,a\,b^3\,c^6\,d+81\,b^4\,c^7}{4096\,a^8\,d^{15}-32768\,a^7\,b\,c\,d^{14}+114688\,a^6\,b^2\,c^2\,d^{13}-229376\,a^5\,b^3\,c^3\,d^{12}+286720\,a^4\,b^4\,c^4\,d^{11}-229376\,a^3\,b^5\,c^5\,d^{10}+114688\,a^2\,b^6\,c^6\,d^9-32768\,a\,b^7\,c^7\,d^8+4096\,b^8\,c^8\,d^7}\right)}^{1/4}\,\left(16640\,a^{13}\,b^4\,c^3\,d^{15}-143872\,a^{12}\,b^5\,c^4\,d^{14}+554240\,a^{11}\,b^6\,c^5\,d^{13}-1251328\,a^{10}\,b^7\,c^6\,d^{12}+1831424\,a^9\,b^8\,c^7\,d^{11}-1813504\,a^8\,b^9\,c^8\,d^{10}+1229312\,a^7\,b^{10}\,c^9\,d^9-563200\,a^6\,b^{11}\,c^{10}\,d^8+167168\,a^5\,b^{12}\,c^{11}\,d^7-29184\,a^4\,b^{13}\,c^{12}\,d^6+2304\,a^3\,b^{14}\,c^{13}\,d^5\right)}{a^6\,d^9-6\,a^5\,b\,c\,d^8+15\,a^4\,b^2\,c^2\,d^7-20\,a^3\,b^3\,c^3\,d^6+15\,a^2\,b^4\,c^4\,d^5-6\,a\,b^5\,c^5\,d^4+b^6\,c^6\,d^3}\right)-\frac{\sqrt{x}\,\left(784\,a^{12}\,b\,c^3\,d^7-672\,a^{11}\,b^2\,c^4\,d^6+144\,a^{10}\,b^3\,c^5\,d^5+2401\,a^9\,b^4\,c^6\,d^4-4116\,a^8\,b^5\,c^7\,d^3+2646\,a^7\,b^6\,c^8\,d^2-756\,a^6\,b^7\,c^9\,d+81\,a^5\,b^8\,c^{10}\right)}{a^6\,d^9-6\,a^5\,b\,c\,d^8+15\,a^4\,b^2\,c^2\,d^7-20\,a^3\,b^3\,c^3\,d^6+15\,a^2\,b^4\,c^4\,d^5-6\,a\,b^5\,c^5\,d^4+b^6\,c^6\,d^3}\right)}\right)\,{\left(-\frac{2401\,a^4\,c^3\,d^4-4116\,a^3\,b\,c^4\,d^3+2646\,a^2\,b^2\,c^5\,d^2-756\,a\,b^3\,c^6\,d+81\,b^4\,c^7}{4096\,a^8\,d^{15}-32768\,a^7\,b\,c\,d^{14}+114688\,a^6\,b^2\,c^2\,d^{13}-229376\,a^5\,b^3\,c^3\,d^{12}+286720\,a^4\,b^4\,c^4\,d^{11}-229376\,a^3\,b^5\,c^5\,d^{10}+114688\,a^2\,b^6\,c^6\,d^9-32768\,a\,b^7\,c^7\,d^8+4096\,b^8\,c^8\,d^7}\right)}^{1/4}\,2{}\mathrm{i}","Not used",1,"2*atan(((-a^7/(16*b^11*c^8 + 16*a^8*b^3*d^8 - 128*a^7*b^4*c*d^7 + 448*a^2*b^9*c^6*d^2 - 896*a^3*b^8*c^5*d^3 + 1120*a^4*b^7*c^4*d^4 - 896*a^5*b^6*c^3*d^5 + 448*a^6*b^5*c^2*d^6 - 128*a*b^10*c^7*d))^(1/4)*((-a^7/(16*b^11*c^8 + 16*a^8*b^3*d^8 - 128*a^7*b^4*c*d^7 + 448*a^2*b^9*c^6*d^2 - 896*a^3*b^8*c^5*d^3 + 1120*a^4*b^7*c^4*d^4 - 896*a^5*b^6*c^3*d^5 + 448*a^6*b^5*c^2*d^6 - 128*a*b^10*c^7*d))^(3/4)*(((864*a^3*b^14*c^14*d^3 - 12096*a^4*b^13*c^13*d^4 + 74592*a^5*b^12*c^12*d^5 - 267008*a^6*b^11*c^11*d^6 + 617152*a^7*b^10*c^10*d^7 - 968576*a^8*b^9*c^9*d^8 + 1054144*a^9*b^8*c^8*d^9 - 795392*a^10*b^7*c^7*d^10 + 407008*a^11*b^6*c^6*d^11 - 133952*a^12*b^5*c^5*d^12 + 25312*a^13*b^4*c^4*d^13 - 2048*a^14*b^3*c^3*d^14)*1i)/(a^7*d^10 - b^7*c^7*d^3 + 7*a*b^6*c^6*d^4 - 21*a^2*b^5*c^5*d^5 + 35*a^3*b^4*c^4*d^6 - 35*a^4*b^3*c^3*d^7 + 21*a^5*b^2*c^2*d^8 - 7*a^6*b*c*d^9) + (x^(1/2)*(-a^7/(16*b^11*c^8 + 16*a^8*b^3*d^8 - 128*a^7*b^4*c*d^7 + 448*a^2*b^9*c^6*d^2 - 896*a^3*b^8*c^5*d^3 + 1120*a^4*b^7*c^4*d^4 - 896*a^5*b^6*c^3*d^5 + 448*a^6*b^5*c^2*d^6 - 128*a*b^10*c^7*d))^(1/4)*(2304*a^3*b^14*c^13*d^5 - 29184*a^4*b^13*c^12*d^6 + 167168*a^5*b^12*c^11*d^7 - 563200*a^6*b^11*c^10*d^8 + 1229312*a^7*b^10*c^9*d^9 - 1813504*a^8*b^9*c^8*d^10 + 1831424*a^9*b^8*c^7*d^11 - 1251328*a^10*b^7*c^6*d^12 + 554240*a^11*b^6*c^5*d^13 - 143872*a^12*b^5*c^4*d^14 + 16640*a^13*b^4*c^3*d^15))/(a^6*d^9 + b^6*c^6*d^3 - 6*a*b^5*c^5*d^4 + 15*a^2*b^4*c^4*d^5 - 20*a^3*b^3*c^3*d^6 + 15*a^4*b^2*c^2*d^7 - 6*a^5*b*c*d^8)) + (x^(1/2)*(81*a^5*b^8*c^10 - 756*a^6*b^7*c^9*d + 784*a^12*b*c^3*d^7 + 2646*a^7*b^6*c^8*d^2 - 4116*a^8*b^5*c^7*d^3 + 2401*a^9*b^4*c^6*d^4 + 144*a^10*b^3*c^5*d^5 - 672*a^11*b^2*c^4*d^6))/(a^6*d^9 + b^6*c^6*d^3 - 6*a*b^5*c^5*d^4 + 15*a^2*b^4*c^4*d^5 - 20*a^3*b^3*c^3*d^6 + 15*a^4*b^2*c^2*d^7 - 6*a^5*b*c*d^8)) - (-a^7/(16*b^11*c^8 + 16*a^8*b^3*d^8 - 128*a^7*b^4*c*d^7 + 448*a^2*b^9*c^6*d^2 - 896*a^3*b^8*c^5*d^3 + 1120*a^4*b^7*c^4*d^4 - 896*a^5*b^6*c^3*d^5 + 448*a^6*b^5*c^2*d^6 - 128*a*b^10*c^7*d))^(1/4)*((-a^7/(16*b^11*c^8 + 16*a^8*b^3*d^8 - 128*a^7*b^4*c*d^7 + 448*a^2*b^9*c^6*d^2 - 896*a^3*b^8*c^5*d^3 + 1120*a^4*b^7*c^4*d^4 - 896*a^5*b^6*c^3*d^5 + 448*a^6*b^5*c^2*d^6 - 128*a*b^10*c^7*d))^(3/4)*(((864*a^3*b^14*c^14*d^3 - 12096*a^4*b^13*c^13*d^4 + 74592*a^5*b^12*c^12*d^5 - 267008*a^6*b^11*c^11*d^6 + 617152*a^7*b^10*c^10*d^7 - 968576*a^8*b^9*c^9*d^8 + 1054144*a^9*b^8*c^8*d^9 - 795392*a^10*b^7*c^7*d^10 + 407008*a^11*b^6*c^6*d^11 - 133952*a^12*b^5*c^5*d^12 + 25312*a^13*b^4*c^4*d^13 - 2048*a^14*b^3*c^3*d^14)*1i)/(a^7*d^10 - b^7*c^7*d^3 + 7*a*b^6*c^6*d^4 - 21*a^2*b^5*c^5*d^5 + 35*a^3*b^4*c^4*d^6 - 35*a^4*b^3*c^3*d^7 + 21*a^5*b^2*c^2*d^8 - 7*a^6*b*c*d^9) - (x^(1/2)*(-a^7/(16*b^11*c^8 + 16*a^8*b^3*d^8 - 128*a^7*b^4*c*d^7 + 448*a^2*b^9*c^6*d^2 - 896*a^3*b^8*c^5*d^3 + 1120*a^4*b^7*c^4*d^4 - 896*a^5*b^6*c^3*d^5 + 448*a^6*b^5*c^2*d^6 - 128*a*b^10*c^7*d))^(1/4)*(2304*a^3*b^14*c^13*d^5 - 29184*a^4*b^13*c^12*d^6 + 167168*a^5*b^12*c^11*d^7 - 563200*a^6*b^11*c^10*d^8 + 1229312*a^7*b^10*c^9*d^9 - 1813504*a^8*b^9*c^8*d^10 + 1831424*a^9*b^8*c^7*d^11 - 1251328*a^10*b^7*c^6*d^12 + 554240*a^11*b^6*c^5*d^13 - 143872*a^12*b^5*c^4*d^14 + 16640*a^13*b^4*c^3*d^15))/(a^6*d^9 + b^6*c^6*d^3 - 6*a*b^5*c^5*d^4 + 15*a^2*b^4*c^4*d^5 - 20*a^3*b^3*c^3*d^6 + 15*a^4*b^2*c^2*d^7 - 6*a^5*b*c*d^8)) - (x^(1/2)*(81*a^5*b^8*c^10 - 756*a^6*b^7*c^9*d + 784*a^12*b*c^3*d^7 + 2646*a^7*b^6*c^8*d^2 - 4116*a^8*b^5*c^7*d^3 + 2401*a^9*b^4*c^6*d^4 + 144*a^10*b^3*c^5*d^5 - 672*a^11*b^2*c^4*d^6))/(a^6*d^9 + b^6*c^6*d^3 - 6*a*b^5*c^5*d^4 + 15*a^2*b^4*c^4*d^5 - 20*a^3*b^3*c^3*d^6 + 15*a^4*b^2*c^2*d^7 - 6*a^5*b*c*d^8)))/((-a^7/(16*b^11*c^8 + 16*a^8*b^3*d^8 - 128*a^7*b^4*c*d^7 + 448*a^2*b^9*c^6*d^2 - 896*a^3*b^8*c^5*d^3 + 1120*a^4*b^7*c^4*d^4 - 896*a^5*b^6*c^3*d^5 + 448*a^6*b^5*c^2*d^6 - 128*a*b^10*c^7*d))^(1/4)*((-a^7/(16*b^11*c^8 + 16*a^8*b^3*d^8 - 128*a^7*b^4*c*d^7 + 448*a^2*b^9*c^6*d^2 - 896*a^3*b^8*c^5*d^3 + 1120*a^4*b^7*c^4*d^4 - 896*a^5*b^6*c^3*d^5 + 448*a^6*b^5*c^2*d^6 - 128*a*b^10*c^7*d))^(3/4)*(((864*a^3*b^14*c^14*d^3 - 12096*a^4*b^13*c^13*d^4 + 74592*a^5*b^12*c^12*d^5 - 267008*a^6*b^11*c^11*d^6 + 617152*a^7*b^10*c^10*d^7 - 968576*a^8*b^9*c^9*d^8 + 1054144*a^9*b^8*c^8*d^9 - 795392*a^10*b^7*c^7*d^10 + 407008*a^11*b^6*c^6*d^11 - 133952*a^12*b^5*c^5*d^12 + 25312*a^13*b^4*c^4*d^13 - 2048*a^14*b^3*c^3*d^14)*1i)/(a^7*d^10 - b^7*c^7*d^3 + 7*a*b^6*c^6*d^4 - 21*a^2*b^5*c^5*d^5 + 35*a^3*b^4*c^4*d^6 - 35*a^4*b^3*c^3*d^7 + 21*a^5*b^2*c^2*d^8 - 7*a^6*b*c*d^9) + (x^(1/2)*(-a^7/(16*b^11*c^8 + 16*a^8*b^3*d^8 - 128*a^7*b^4*c*d^7 + 448*a^2*b^9*c^6*d^2 - 896*a^3*b^8*c^5*d^3 + 1120*a^4*b^7*c^4*d^4 - 896*a^5*b^6*c^3*d^5 + 448*a^6*b^5*c^2*d^6 - 128*a*b^10*c^7*d))^(1/4)*(2304*a^3*b^14*c^13*d^5 - 29184*a^4*b^13*c^12*d^6 + 167168*a^5*b^12*c^11*d^7 - 563200*a^6*b^11*c^10*d^8 + 1229312*a^7*b^10*c^9*d^9 - 1813504*a^8*b^9*c^8*d^10 + 1831424*a^9*b^8*c^7*d^11 - 1251328*a^10*b^7*c^6*d^12 + 554240*a^11*b^6*c^5*d^13 - 143872*a^12*b^5*c^4*d^14 + 16640*a^13*b^4*c^3*d^15))/(a^6*d^9 + b^6*c^6*d^3 - 6*a*b^5*c^5*d^4 + 15*a^2*b^4*c^4*d^5 - 20*a^3*b^3*c^3*d^6 + 15*a^4*b^2*c^2*d^7 - 6*a^5*b*c*d^8))*1i + (x^(1/2)*(81*a^5*b^8*c^10 - 756*a^6*b^7*c^9*d + 784*a^12*b*c^3*d^7 + 2646*a^7*b^6*c^8*d^2 - 4116*a^8*b^5*c^7*d^3 + 2401*a^9*b^4*c^6*d^4 + 144*a^10*b^3*c^5*d^5 - 672*a^11*b^2*c^4*d^6)*1i)/(a^6*d^9 + b^6*c^6*d^3 - 6*a*b^5*c^5*d^4 + 15*a^2*b^4*c^4*d^5 - 20*a^3*b^3*c^3*d^6 + 15*a^4*b^2*c^2*d^7 - 6*a^5*b*c*d^8)) - (81*a^7*b^6*c^9 - 675*a^8*b^5*c^8*d + 1372*a^12*b*c^4*d^5 + 1971*a^9*b^4*c^7*d^2 - 2037*a^10*b^3*c^6*d^3 - 392*a^11*b^2*c^5*d^4)/(a^7*d^10 - b^7*c^7*d^3 + 7*a*b^6*c^6*d^4 - 21*a^2*b^5*c^5*d^5 + 35*a^3*b^4*c^4*d^6 - 35*a^4*b^3*c^3*d^7 + 21*a^5*b^2*c^2*d^8 - 7*a^6*b*c*d^9) + (-a^7/(16*b^11*c^8 + 16*a^8*b^3*d^8 - 128*a^7*b^4*c*d^7 + 448*a^2*b^9*c^6*d^2 - 896*a^3*b^8*c^5*d^3 + 1120*a^4*b^7*c^4*d^4 - 896*a^5*b^6*c^3*d^5 + 448*a^6*b^5*c^2*d^6 - 128*a*b^10*c^7*d))^(1/4)*((-a^7/(16*b^11*c^8 + 16*a^8*b^3*d^8 - 128*a^7*b^4*c*d^7 + 448*a^2*b^9*c^6*d^2 - 896*a^3*b^8*c^5*d^3 + 1120*a^4*b^7*c^4*d^4 - 896*a^5*b^6*c^3*d^5 + 448*a^6*b^5*c^2*d^6 - 128*a*b^10*c^7*d))^(3/4)*(((864*a^3*b^14*c^14*d^3 - 12096*a^4*b^13*c^13*d^4 + 74592*a^5*b^12*c^12*d^5 - 267008*a^6*b^11*c^11*d^6 + 617152*a^7*b^10*c^10*d^7 - 968576*a^8*b^9*c^9*d^8 + 1054144*a^9*b^8*c^8*d^9 - 795392*a^10*b^7*c^7*d^10 + 407008*a^11*b^6*c^6*d^11 - 133952*a^12*b^5*c^5*d^12 + 25312*a^13*b^4*c^4*d^13 - 2048*a^14*b^3*c^3*d^14)*1i)/(a^7*d^10 - b^7*c^7*d^3 + 7*a*b^6*c^6*d^4 - 21*a^2*b^5*c^5*d^5 + 35*a^3*b^4*c^4*d^6 - 35*a^4*b^3*c^3*d^7 + 21*a^5*b^2*c^2*d^8 - 7*a^6*b*c*d^9) - (x^(1/2)*(-a^7/(16*b^11*c^8 + 16*a^8*b^3*d^8 - 128*a^7*b^4*c*d^7 + 448*a^2*b^9*c^6*d^2 - 896*a^3*b^8*c^5*d^3 + 1120*a^4*b^7*c^4*d^4 - 896*a^5*b^6*c^3*d^5 + 448*a^6*b^5*c^2*d^6 - 128*a*b^10*c^7*d))^(1/4)*(2304*a^3*b^14*c^13*d^5 - 29184*a^4*b^13*c^12*d^6 + 167168*a^5*b^12*c^11*d^7 - 563200*a^6*b^11*c^10*d^8 + 1229312*a^7*b^10*c^9*d^9 - 1813504*a^8*b^9*c^8*d^10 + 1831424*a^9*b^8*c^7*d^11 - 1251328*a^10*b^7*c^6*d^12 + 554240*a^11*b^6*c^5*d^13 - 143872*a^12*b^5*c^4*d^14 + 16640*a^13*b^4*c^3*d^15))/(a^6*d^9 + b^6*c^6*d^3 - 6*a*b^5*c^5*d^4 + 15*a^2*b^4*c^4*d^5 - 20*a^3*b^3*c^3*d^6 + 15*a^4*b^2*c^2*d^7 - 6*a^5*b*c*d^8))*1i - (x^(1/2)*(81*a^5*b^8*c^10 - 756*a^6*b^7*c^9*d + 784*a^12*b*c^3*d^7 + 2646*a^7*b^6*c^8*d^2 - 4116*a^8*b^5*c^7*d^3 + 2401*a^9*b^4*c^6*d^4 + 144*a^10*b^3*c^5*d^5 - 672*a^11*b^2*c^4*d^6)*1i)/(a^6*d^9 + b^6*c^6*d^3 - 6*a*b^5*c^5*d^4 + 15*a^2*b^4*c^4*d^5 - 20*a^3*b^3*c^3*d^6 + 15*a^4*b^2*c^2*d^7 - 6*a^5*b*c*d^8))))*(-a^7/(16*b^11*c^8 + 16*a^8*b^3*d^8 - 128*a^7*b^4*c*d^7 + 448*a^2*b^9*c^6*d^2 - 896*a^3*b^8*c^5*d^3 + 1120*a^4*b^7*c^4*d^4 - 896*a^5*b^6*c^3*d^5 + 448*a^6*b^5*c^2*d^6 - 128*a*b^10*c^7*d))^(1/4) - atan(((-a^7/(16*b^11*c^8 + 16*a^8*b^3*d^8 - 128*a^7*b^4*c*d^7 + 448*a^2*b^9*c^6*d^2 - 896*a^3*b^8*c^5*d^3 + 1120*a^4*b^7*c^4*d^4 - 896*a^5*b^6*c^3*d^5 + 448*a^6*b^5*c^2*d^6 - 128*a*b^10*c^7*d))^(1/4)*((-a^7/(16*b^11*c^8 + 16*a^8*b^3*d^8 - 128*a^7*b^4*c*d^7 + 448*a^2*b^9*c^6*d^2 - 896*a^3*b^8*c^5*d^3 + 1120*a^4*b^7*c^4*d^4 - 896*a^5*b^6*c^3*d^5 + 448*a^6*b^5*c^2*d^6 - 128*a*b^10*c^7*d))^(3/4)*((864*a^3*b^14*c^14*d^3 - 12096*a^4*b^13*c^13*d^4 + 74592*a^5*b^12*c^12*d^5 - 267008*a^6*b^11*c^11*d^6 + 617152*a^7*b^10*c^10*d^7 - 968576*a^8*b^9*c^9*d^8 + 1054144*a^9*b^8*c^8*d^9 - 795392*a^10*b^7*c^7*d^10 + 407008*a^11*b^6*c^6*d^11 - 133952*a^12*b^5*c^5*d^12 + 25312*a^13*b^4*c^4*d^13 - 2048*a^14*b^3*c^3*d^14)/(a^7*d^10 - b^7*c^7*d^3 + 7*a*b^6*c^6*d^4 - 21*a^2*b^5*c^5*d^5 + 35*a^3*b^4*c^4*d^6 - 35*a^4*b^3*c^3*d^7 + 21*a^5*b^2*c^2*d^8 - 7*a^6*b*c*d^9) + (x^(1/2)*(-a^7/(16*b^11*c^8 + 16*a^8*b^3*d^8 - 128*a^7*b^4*c*d^7 + 448*a^2*b^9*c^6*d^2 - 896*a^3*b^8*c^5*d^3 + 1120*a^4*b^7*c^4*d^4 - 896*a^5*b^6*c^3*d^5 + 448*a^6*b^5*c^2*d^6 - 128*a*b^10*c^7*d))^(1/4)*(2304*a^3*b^14*c^13*d^5 - 29184*a^4*b^13*c^12*d^6 + 167168*a^5*b^12*c^11*d^7 - 563200*a^6*b^11*c^10*d^8 + 1229312*a^7*b^10*c^9*d^9 - 1813504*a^8*b^9*c^8*d^10 + 1831424*a^9*b^8*c^7*d^11 - 1251328*a^10*b^7*c^6*d^12 + 554240*a^11*b^6*c^5*d^13 - 143872*a^12*b^5*c^4*d^14 + 16640*a^13*b^4*c^3*d^15))/(a^6*d^9 + b^6*c^6*d^3 - 6*a*b^5*c^5*d^4 + 15*a^2*b^4*c^4*d^5 - 20*a^3*b^3*c^3*d^6 + 15*a^4*b^2*c^2*d^7 - 6*a^5*b*c*d^8))*1i + (x^(1/2)*(81*a^5*b^8*c^10 - 756*a^6*b^7*c^9*d + 784*a^12*b*c^3*d^7 + 2646*a^7*b^6*c^8*d^2 - 4116*a^8*b^5*c^7*d^3 + 2401*a^9*b^4*c^6*d^4 + 144*a^10*b^3*c^5*d^5 - 672*a^11*b^2*c^4*d^6)*1i)/(a^6*d^9 + b^6*c^6*d^3 - 6*a*b^5*c^5*d^4 + 15*a^2*b^4*c^4*d^5 - 20*a^3*b^3*c^3*d^6 + 15*a^4*b^2*c^2*d^7 - 6*a^5*b*c*d^8)) - (-a^7/(16*b^11*c^8 + 16*a^8*b^3*d^8 - 128*a^7*b^4*c*d^7 + 448*a^2*b^9*c^6*d^2 - 896*a^3*b^8*c^5*d^3 + 1120*a^4*b^7*c^4*d^4 - 896*a^5*b^6*c^3*d^5 + 448*a^6*b^5*c^2*d^6 - 128*a*b^10*c^7*d))^(1/4)*((-a^7/(16*b^11*c^8 + 16*a^8*b^3*d^8 - 128*a^7*b^4*c*d^7 + 448*a^2*b^9*c^6*d^2 - 896*a^3*b^8*c^5*d^3 + 1120*a^4*b^7*c^4*d^4 - 896*a^5*b^6*c^3*d^5 + 448*a^6*b^5*c^2*d^6 - 128*a*b^10*c^7*d))^(3/4)*((864*a^3*b^14*c^14*d^3 - 12096*a^4*b^13*c^13*d^4 + 74592*a^5*b^12*c^12*d^5 - 267008*a^6*b^11*c^11*d^6 + 617152*a^7*b^10*c^10*d^7 - 968576*a^8*b^9*c^9*d^8 + 1054144*a^9*b^8*c^8*d^9 - 795392*a^10*b^7*c^7*d^10 + 407008*a^11*b^6*c^6*d^11 - 133952*a^12*b^5*c^5*d^12 + 25312*a^13*b^4*c^4*d^13 - 2048*a^14*b^3*c^3*d^14)/(a^7*d^10 - b^7*c^7*d^3 + 7*a*b^6*c^6*d^4 - 21*a^2*b^5*c^5*d^5 + 35*a^3*b^4*c^4*d^6 - 35*a^4*b^3*c^3*d^7 + 21*a^5*b^2*c^2*d^8 - 7*a^6*b*c*d^9) - (x^(1/2)*(-a^7/(16*b^11*c^8 + 16*a^8*b^3*d^8 - 128*a^7*b^4*c*d^7 + 448*a^2*b^9*c^6*d^2 - 896*a^3*b^8*c^5*d^3 + 1120*a^4*b^7*c^4*d^4 - 896*a^5*b^6*c^3*d^5 + 448*a^6*b^5*c^2*d^6 - 128*a*b^10*c^7*d))^(1/4)*(2304*a^3*b^14*c^13*d^5 - 29184*a^4*b^13*c^12*d^6 + 167168*a^5*b^12*c^11*d^7 - 563200*a^6*b^11*c^10*d^8 + 1229312*a^7*b^10*c^9*d^9 - 1813504*a^8*b^9*c^8*d^10 + 1831424*a^9*b^8*c^7*d^11 - 1251328*a^10*b^7*c^6*d^12 + 554240*a^11*b^6*c^5*d^13 - 143872*a^12*b^5*c^4*d^14 + 16640*a^13*b^4*c^3*d^15))/(a^6*d^9 + b^6*c^6*d^3 - 6*a*b^5*c^5*d^4 + 15*a^2*b^4*c^4*d^5 - 20*a^3*b^3*c^3*d^6 + 15*a^4*b^2*c^2*d^7 - 6*a^5*b*c*d^8))*1i - (x^(1/2)*(81*a^5*b^8*c^10 - 756*a^6*b^7*c^9*d + 784*a^12*b*c^3*d^7 + 2646*a^7*b^6*c^8*d^2 - 4116*a^8*b^5*c^7*d^3 + 2401*a^9*b^4*c^6*d^4 + 144*a^10*b^3*c^5*d^5 - 672*a^11*b^2*c^4*d^6)*1i)/(a^6*d^9 + b^6*c^6*d^3 - 6*a*b^5*c^5*d^4 + 15*a^2*b^4*c^4*d^5 - 20*a^3*b^3*c^3*d^6 + 15*a^4*b^2*c^2*d^7 - 6*a^5*b*c*d^8)))/((81*a^7*b^6*c^9 - 675*a^8*b^5*c^8*d + 1372*a^12*b*c^4*d^5 + 1971*a^9*b^4*c^7*d^2 - 2037*a^10*b^3*c^6*d^3 - 392*a^11*b^2*c^5*d^4)/(a^7*d^10 - b^7*c^7*d^3 + 7*a*b^6*c^6*d^4 - 21*a^2*b^5*c^5*d^5 + 35*a^3*b^4*c^4*d^6 - 35*a^4*b^3*c^3*d^7 + 21*a^5*b^2*c^2*d^8 - 7*a^6*b*c*d^9) + (-a^7/(16*b^11*c^8 + 16*a^8*b^3*d^8 - 128*a^7*b^4*c*d^7 + 448*a^2*b^9*c^6*d^2 - 896*a^3*b^8*c^5*d^3 + 1120*a^4*b^7*c^4*d^4 - 896*a^5*b^6*c^3*d^5 + 448*a^6*b^5*c^2*d^6 - 128*a*b^10*c^7*d))^(1/4)*((-a^7/(16*b^11*c^8 + 16*a^8*b^3*d^8 - 128*a^7*b^4*c*d^7 + 448*a^2*b^9*c^6*d^2 - 896*a^3*b^8*c^5*d^3 + 1120*a^4*b^7*c^4*d^4 - 896*a^5*b^6*c^3*d^5 + 448*a^6*b^5*c^2*d^6 - 128*a*b^10*c^7*d))^(3/4)*((864*a^3*b^14*c^14*d^3 - 12096*a^4*b^13*c^13*d^4 + 74592*a^5*b^12*c^12*d^5 - 267008*a^6*b^11*c^11*d^6 + 617152*a^7*b^10*c^10*d^7 - 968576*a^8*b^9*c^9*d^8 + 1054144*a^9*b^8*c^8*d^9 - 795392*a^10*b^7*c^7*d^10 + 407008*a^11*b^6*c^6*d^11 - 133952*a^12*b^5*c^5*d^12 + 25312*a^13*b^4*c^4*d^13 - 2048*a^14*b^3*c^3*d^14)/(a^7*d^10 - b^7*c^7*d^3 + 7*a*b^6*c^6*d^4 - 21*a^2*b^5*c^5*d^5 + 35*a^3*b^4*c^4*d^6 - 35*a^4*b^3*c^3*d^7 + 21*a^5*b^2*c^2*d^8 - 7*a^6*b*c*d^9) + (x^(1/2)*(-a^7/(16*b^11*c^8 + 16*a^8*b^3*d^8 - 128*a^7*b^4*c*d^7 + 448*a^2*b^9*c^6*d^2 - 896*a^3*b^8*c^5*d^3 + 1120*a^4*b^7*c^4*d^4 - 896*a^5*b^6*c^3*d^5 + 448*a^6*b^5*c^2*d^6 - 128*a*b^10*c^7*d))^(1/4)*(2304*a^3*b^14*c^13*d^5 - 29184*a^4*b^13*c^12*d^6 + 167168*a^5*b^12*c^11*d^7 - 563200*a^6*b^11*c^10*d^8 + 1229312*a^7*b^10*c^9*d^9 - 1813504*a^8*b^9*c^8*d^10 + 1831424*a^9*b^8*c^7*d^11 - 1251328*a^10*b^7*c^6*d^12 + 554240*a^11*b^6*c^5*d^13 - 143872*a^12*b^5*c^4*d^14 + 16640*a^13*b^4*c^3*d^15))/(a^6*d^9 + b^6*c^6*d^3 - 6*a*b^5*c^5*d^4 + 15*a^2*b^4*c^4*d^5 - 20*a^3*b^3*c^3*d^6 + 15*a^4*b^2*c^2*d^7 - 6*a^5*b*c*d^8)) + (x^(1/2)*(81*a^5*b^8*c^10 - 756*a^6*b^7*c^9*d + 784*a^12*b*c^3*d^7 + 2646*a^7*b^6*c^8*d^2 - 4116*a^8*b^5*c^7*d^3 + 2401*a^9*b^4*c^6*d^4 + 144*a^10*b^3*c^5*d^5 - 672*a^11*b^2*c^4*d^6))/(a^6*d^9 + b^6*c^6*d^3 - 6*a*b^5*c^5*d^4 + 15*a^2*b^4*c^4*d^5 - 20*a^3*b^3*c^3*d^6 + 15*a^4*b^2*c^2*d^7 - 6*a^5*b*c*d^8)) + (-a^7/(16*b^11*c^8 + 16*a^8*b^3*d^8 - 128*a^7*b^4*c*d^7 + 448*a^2*b^9*c^6*d^2 - 896*a^3*b^8*c^5*d^3 + 1120*a^4*b^7*c^4*d^4 - 896*a^5*b^6*c^3*d^5 + 448*a^6*b^5*c^2*d^6 - 128*a*b^10*c^7*d))^(1/4)*((-a^7/(16*b^11*c^8 + 16*a^8*b^3*d^8 - 128*a^7*b^4*c*d^7 + 448*a^2*b^9*c^6*d^2 - 896*a^3*b^8*c^5*d^3 + 1120*a^4*b^7*c^4*d^4 - 896*a^5*b^6*c^3*d^5 + 448*a^6*b^5*c^2*d^6 - 128*a*b^10*c^7*d))^(3/4)*((864*a^3*b^14*c^14*d^3 - 12096*a^4*b^13*c^13*d^4 + 74592*a^5*b^12*c^12*d^5 - 267008*a^6*b^11*c^11*d^6 + 617152*a^7*b^10*c^10*d^7 - 968576*a^8*b^9*c^9*d^8 + 1054144*a^9*b^8*c^8*d^9 - 795392*a^10*b^7*c^7*d^10 + 407008*a^11*b^6*c^6*d^11 - 133952*a^12*b^5*c^5*d^12 + 25312*a^13*b^4*c^4*d^13 - 2048*a^14*b^3*c^3*d^14)/(a^7*d^10 - b^7*c^7*d^3 + 7*a*b^6*c^6*d^4 - 21*a^2*b^5*c^5*d^5 + 35*a^3*b^4*c^4*d^6 - 35*a^4*b^3*c^3*d^7 + 21*a^5*b^2*c^2*d^8 - 7*a^6*b*c*d^9) - (x^(1/2)*(-a^7/(16*b^11*c^8 + 16*a^8*b^3*d^8 - 128*a^7*b^4*c*d^7 + 448*a^2*b^9*c^6*d^2 - 896*a^3*b^8*c^5*d^3 + 1120*a^4*b^7*c^4*d^4 - 896*a^5*b^6*c^3*d^5 + 448*a^6*b^5*c^2*d^6 - 128*a*b^10*c^7*d))^(1/4)*(2304*a^3*b^14*c^13*d^5 - 29184*a^4*b^13*c^12*d^6 + 167168*a^5*b^12*c^11*d^7 - 563200*a^6*b^11*c^10*d^8 + 1229312*a^7*b^10*c^9*d^9 - 1813504*a^8*b^9*c^8*d^10 + 1831424*a^9*b^8*c^7*d^11 - 1251328*a^10*b^7*c^6*d^12 + 554240*a^11*b^6*c^5*d^13 - 143872*a^12*b^5*c^4*d^14 + 16640*a^13*b^4*c^3*d^15))/(a^6*d^9 + b^6*c^6*d^3 - 6*a*b^5*c^5*d^4 + 15*a^2*b^4*c^4*d^5 - 20*a^3*b^3*c^3*d^6 + 15*a^4*b^2*c^2*d^7 - 6*a^5*b*c*d^8)) - (x^(1/2)*(81*a^5*b^8*c^10 - 756*a^6*b^7*c^9*d + 784*a^12*b*c^3*d^7 + 2646*a^7*b^6*c^8*d^2 - 4116*a^8*b^5*c^7*d^3 + 2401*a^9*b^4*c^6*d^4 + 144*a^10*b^3*c^5*d^5 - 672*a^11*b^2*c^4*d^6))/(a^6*d^9 + b^6*c^6*d^3 - 6*a*b^5*c^5*d^4 + 15*a^2*b^4*c^4*d^5 - 20*a^3*b^3*c^3*d^6 + 15*a^4*b^2*c^2*d^7 - 6*a^5*b*c*d^8))))*(-a^7/(16*b^11*c^8 + 16*a^8*b^3*d^8 - 128*a^7*b^4*c*d^7 + 448*a^2*b^9*c^6*d^2 - 896*a^3*b^8*c^5*d^3 + 1120*a^4*b^7*c^4*d^4 - 896*a^5*b^6*c^3*d^5 + 448*a^6*b^5*c^2*d^6 - 128*a*b^10*c^7*d))^(1/4)*2i - atan(((-(81*b^4*c^7 + 2401*a^4*c^3*d^4 - 4116*a^3*b*c^4*d^3 + 2646*a^2*b^2*c^5*d^2 - 756*a*b^3*c^6*d)/(4096*a^8*d^15 + 4096*b^8*c^8*d^7 - 32768*a*b^7*c^7*d^8 + 114688*a^2*b^6*c^6*d^9 - 229376*a^3*b^5*c^5*d^10 + 286720*a^4*b^4*c^4*d^11 - 229376*a^5*b^3*c^3*d^12 + 114688*a^6*b^2*c^2*d^13 - 32768*a^7*b*c*d^14))^(1/4)*((-(81*b^4*c^7 + 2401*a^4*c^3*d^4 - 4116*a^3*b*c^4*d^3 + 2646*a^2*b^2*c^5*d^2 - 756*a*b^3*c^6*d)/(4096*a^8*d^15 + 4096*b^8*c^8*d^7 - 32768*a*b^7*c^7*d^8 + 114688*a^2*b^6*c^6*d^9 - 229376*a^3*b^5*c^5*d^10 + 286720*a^4*b^4*c^4*d^11 - 229376*a^5*b^3*c^3*d^12 + 114688*a^6*b^2*c^2*d^13 - 32768*a^7*b*c*d^14))^(3/4)*((864*a^3*b^14*c^14*d^3 - 12096*a^4*b^13*c^13*d^4 + 74592*a^5*b^12*c^12*d^5 - 267008*a^6*b^11*c^11*d^6 + 617152*a^7*b^10*c^10*d^7 - 968576*a^8*b^9*c^9*d^8 + 1054144*a^9*b^8*c^8*d^9 - 795392*a^10*b^7*c^7*d^10 + 407008*a^11*b^6*c^6*d^11 - 133952*a^12*b^5*c^5*d^12 + 25312*a^13*b^4*c^4*d^13 - 2048*a^14*b^3*c^3*d^14)/(a^7*d^10 - b^7*c^7*d^3 + 7*a*b^6*c^6*d^4 - 21*a^2*b^5*c^5*d^5 + 35*a^3*b^4*c^4*d^6 - 35*a^4*b^3*c^3*d^7 + 21*a^5*b^2*c^2*d^8 - 7*a^6*b*c*d^9) + (x^(1/2)*(-(81*b^4*c^7 + 2401*a^4*c^3*d^4 - 4116*a^3*b*c^4*d^3 + 2646*a^2*b^2*c^5*d^2 - 756*a*b^3*c^6*d)/(4096*a^8*d^15 + 4096*b^8*c^8*d^7 - 32768*a*b^7*c^7*d^8 + 114688*a^2*b^6*c^6*d^9 - 229376*a^3*b^5*c^5*d^10 + 286720*a^4*b^4*c^4*d^11 - 229376*a^5*b^3*c^3*d^12 + 114688*a^6*b^2*c^2*d^13 - 32768*a^7*b*c*d^14))^(1/4)*(2304*a^3*b^14*c^13*d^5 - 29184*a^4*b^13*c^12*d^6 + 167168*a^5*b^12*c^11*d^7 - 563200*a^6*b^11*c^10*d^8 + 1229312*a^7*b^10*c^9*d^9 - 1813504*a^8*b^9*c^8*d^10 + 1831424*a^9*b^8*c^7*d^11 - 1251328*a^10*b^7*c^6*d^12 + 554240*a^11*b^6*c^5*d^13 - 143872*a^12*b^5*c^4*d^14 + 16640*a^13*b^4*c^3*d^15))/(a^6*d^9 + b^6*c^6*d^3 - 6*a*b^5*c^5*d^4 + 15*a^2*b^4*c^4*d^5 - 20*a^3*b^3*c^3*d^6 + 15*a^4*b^2*c^2*d^7 - 6*a^5*b*c*d^8))*1i + (x^(1/2)*(81*a^5*b^8*c^10 - 756*a^6*b^7*c^9*d + 784*a^12*b*c^3*d^7 + 2646*a^7*b^6*c^8*d^2 - 4116*a^8*b^5*c^7*d^3 + 2401*a^9*b^4*c^6*d^4 + 144*a^10*b^3*c^5*d^5 - 672*a^11*b^2*c^4*d^6)*1i)/(a^6*d^9 + b^6*c^6*d^3 - 6*a*b^5*c^5*d^4 + 15*a^2*b^4*c^4*d^5 - 20*a^3*b^3*c^3*d^6 + 15*a^4*b^2*c^2*d^7 - 6*a^5*b*c*d^8)) - (-(81*b^4*c^7 + 2401*a^4*c^3*d^4 - 4116*a^3*b*c^4*d^3 + 2646*a^2*b^2*c^5*d^2 - 756*a*b^3*c^6*d)/(4096*a^8*d^15 + 4096*b^8*c^8*d^7 - 32768*a*b^7*c^7*d^8 + 114688*a^2*b^6*c^6*d^9 - 229376*a^3*b^5*c^5*d^10 + 286720*a^4*b^4*c^4*d^11 - 229376*a^5*b^3*c^3*d^12 + 114688*a^6*b^2*c^2*d^13 - 32768*a^7*b*c*d^14))^(1/4)*((-(81*b^4*c^7 + 2401*a^4*c^3*d^4 - 4116*a^3*b*c^4*d^3 + 2646*a^2*b^2*c^5*d^2 - 756*a*b^3*c^6*d)/(4096*a^8*d^15 + 4096*b^8*c^8*d^7 - 32768*a*b^7*c^7*d^8 + 114688*a^2*b^6*c^6*d^9 - 229376*a^3*b^5*c^5*d^10 + 286720*a^4*b^4*c^4*d^11 - 229376*a^5*b^3*c^3*d^12 + 114688*a^6*b^2*c^2*d^13 - 32768*a^7*b*c*d^14))^(3/4)*((864*a^3*b^14*c^14*d^3 - 12096*a^4*b^13*c^13*d^4 + 74592*a^5*b^12*c^12*d^5 - 267008*a^6*b^11*c^11*d^6 + 617152*a^7*b^10*c^10*d^7 - 968576*a^8*b^9*c^9*d^8 + 1054144*a^9*b^8*c^8*d^9 - 795392*a^10*b^7*c^7*d^10 + 407008*a^11*b^6*c^6*d^11 - 133952*a^12*b^5*c^5*d^12 + 25312*a^13*b^4*c^4*d^13 - 2048*a^14*b^3*c^3*d^14)/(a^7*d^10 - b^7*c^7*d^3 + 7*a*b^6*c^6*d^4 - 21*a^2*b^5*c^5*d^5 + 35*a^3*b^4*c^4*d^6 - 35*a^4*b^3*c^3*d^7 + 21*a^5*b^2*c^2*d^8 - 7*a^6*b*c*d^9) - (x^(1/2)*(-(81*b^4*c^7 + 2401*a^4*c^3*d^4 - 4116*a^3*b*c^4*d^3 + 2646*a^2*b^2*c^5*d^2 - 756*a*b^3*c^6*d)/(4096*a^8*d^15 + 4096*b^8*c^8*d^7 - 32768*a*b^7*c^7*d^8 + 114688*a^2*b^6*c^6*d^9 - 229376*a^3*b^5*c^5*d^10 + 286720*a^4*b^4*c^4*d^11 - 229376*a^5*b^3*c^3*d^12 + 114688*a^6*b^2*c^2*d^13 - 32768*a^7*b*c*d^14))^(1/4)*(2304*a^3*b^14*c^13*d^5 - 29184*a^4*b^13*c^12*d^6 + 167168*a^5*b^12*c^11*d^7 - 563200*a^6*b^11*c^10*d^8 + 1229312*a^7*b^10*c^9*d^9 - 1813504*a^8*b^9*c^8*d^10 + 1831424*a^9*b^8*c^7*d^11 - 1251328*a^10*b^7*c^6*d^12 + 554240*a^11*b^6*c^5*d^13 - 143872*a^12*b^5*c^4*d^14 + 16640*a^13*b^4*c^3*d^15))/(a^6*d^9 + b^6*c^6*d^3 - 6*a*b^5*c^5*d^4 + 15*a^2*b^4*c^4*d^5 - 20*a^3*b^3*c^3*d^6 + 15*a^4*b^2*c^2*d^7 - 6*a^5*b*c*d^8))*1i - (x^(1/2)*(81*a^5*b^8*c^10 - 756*a^6*b^7*c^9*d + 784*a^12*b*c^3*d^7 + 2646*a^7*b^6*c^8*d^2 - 4116*a^8*b^5*c^7*d^3 + 2401*a^9*b^4*c^6*d^4 + 144*a^10*b^3*c^5*d^5 - 672*a^11*b^2*c^4*d^6)*1i)/(a^6*d^9 + b^6*c^6*d^3 - 6*a*b^5*c^5*d^4 + 15*a^2*b^4*c^4*d^5 - 20*a^3*b^3*c^3*d^6 + 15*a^4*b^2*c^2*d^7 - 6*a^5*b*c*d^8)))/((81*a^7*b^6*c^9 - 675*a^8*b^5*c^8*d + 1372*a^12*b*c^4*d^5 + 1971*a^9*b^4*c^7*d^2 - 2037*a^10*b^3*c^6*d^3 - 392*a^11*b^2*c^5*d^4)/(a^7*d^10 - b^7*c^7*d^3 + 7*a*b^6*c^6*d^4 - 21*a^2*b^5*c^5*d^5 + 35*a^3*b^4*c^4*d^6 - 35*a^4*b^3*c^3*d^7 + 21*a^5*b^2*c^2*d^8 - 7*a^6*b*c*d^9) + (-(81*b^4*c^7 + 2401*a^4*c^3*d^4 - 4116*a^3*b*c^4*d^3 + 2646*a^2*b^2*c^5*d^2 - 756*a*b^3*c^6*d)/(4096*a^8*d^15 + 4096*b^8*c^8*d^7 - 32768*a*b^7*c^7*d^8 + 114688*a^2*b^6*c^6*d^9 - 229376*a^3*b^5*c^5*d^10 + 286720*a^4*b^4*c^4*d^11 - 229376*a^5*b^3*c^3*d^12 + 114688*a^6*b^2*c^2*d^13 - 32768*a^7*b*c*d^14))^(1/4)*((-(81*b^4*c^7 + 2401*a^4*c^3*d^4 - 4116*a^3*b*c^4*d^3 + 2646*a^2*b^2*c^5*d^2 - 756*a*b^3*c^6*d)/(4096*a^8*d^15 + 4096*b^8*c^8*d^7 - 32768*a*b^7*c^7*d^8 + 114688*a^2*b^6*c^6*d^9 - 229376*a^3*b^5*c^5*d^10 + 286720*a^4*b^4*c^4*d^11 - 229376*a^5*b^3*c^3*d^12 + 114688*a^6*b^2*c^2*d^13 - 32768*a^7*b*c*d^14))^(3/4)*((864*a^3*b^14*c^14*d^3 - 12096*a^4*b^13*c^13*d^4 + 74592*a^5*b^12*c^12*d^5 - 267008*a^6*b^11*c^11*d^6 + 617152*a^7*b^10*c^10*d^7 - 968576*a^8*b^9*c^9*d^8 + 1054144*a^9*b^8*c^8*d^9 - 795392*a^10*b^7*c^7*d^10 + 407008*a^11*b^6*c^6*d^11 - 133952*a^12*b^5*c^5*d^12 + 25312*a^13*b^4*c^4*d^13 - 2048*a^14*b^3*c^3*d^14)/(a^7*d^10 - b^7*c^7*d^3 + 7*a*b^6*c^6*d^4 - 21*a^2*b^5*c^5*d^5 + 35*a^3*b^4*c^4*d^6 - 35*a^4*b^3*c^3*d^7 + 21*a^5*b^2*c^2*d^8 - 7*a^6*b*c*d^9) + (x^(1/2)*(-(81*b^4*c^7 + 2401*a^4*c^3*d^4 - 4116*a^3*b*c^4*d^3 + 2646*a^2*b^2*c^5*d^2 - 756*a*b^3*c^6*d)/(4096*a^8*d^15 + 4096*b^8*c^8*d^7 - 32768*a*b^7*c^7*d^8 + 114688*a^2*b^6*c^6*d^9 - 229376*a^3*b^5*c^5*d^10 + 286720*a^4*b^4*c^4*d^11 - 229376*a^5*b^3*c^3*d^12 + 114688*a^6*b^2*c^2*d^13 - 32768*a^7*b*c*d^14))^(1/4)*(2304*a^3*b^14*c^13*d^5 - 29184*a^4*b^13*c^12*d^6 + 167168*a^5*b^12*c^11*d^7 - 563200*a^6*b^11*c^10*d^8 + 1229312*a^7*b^10*c^9*d^9 - 1813504*a^8*b^9*c^8*d^10 + 1831424*a^9*b^8*c^7*d^11 - 1251328*a^10*b^7*c^6*d^12 + 554240*a^11*b^6*c^5*d^13 - 143872*a^12*b^5*c^4*d^14 + 16640*a^13*b^4*c^3*d^15))/(a^6*d^9 + b^6*c^6*d^3 - 6*a*b^5*c^5*d^4 + 15*a^2*b^4*c^4*d^5 - 20*a^3*b^3*c^3*d^6 + 15*a^4*b^2*c^2*d^7 - 6*a^5*b*c*d^8)) + (x^(1/2)*(81*a^5*b^8*c^10 - 756*a^6*b^7*c^9*d + 784*a^12*b*c^3*d^7 + 2646*a^7*b^6*c^8*d^2 - 4116*a^8*b^5*c^7*d^3 + 2401*a^9*b^4*c^6*d^4 + 144*a^10*b^3*c^5*d^5 - 672*a^11*b^2*c^4*d^6))/(a^6*d^9 + b^6*c^6*d^3 - 6*a*b^5*c^5*d^4 + 15*a^2*b^4*c^4*d^5 - 20*a^3*b^3*c^3*d^6 + 15*a^4*b^2*c^2*d^7 - 6*a^5*b*c*d^8)) + (-(81*b^4*c^7 + 2401*a^4*c^3*d^4 - 4116*a^3*b*c^4*d^3 + 2646*a^2*b^2*c^5*d^2 - 756*a*b^3*c^6*d)/(4096*a^8*d^15 + 4096*b^8*c^8*d^7 - 32768*a*b^7*c^7*d^8 + 114688*a^2*b^6*c^6*d^9 - 229376*a^3*b^5*c^5*d^10 + 286720*a^4*b^4*c^4*d^11 - 229376*a^5*b^3*c^3*d^12 + 114688*a^6*b^2*c^2*d^13 - 32768*a^7*b*c*d^14))^(1/4)*((-(81*b^4*c^7 + 2401*a^4*c^3*d^4 - 4116*a^3*b*c^4*d^3 + 2646*a^2*b^2*c^5*d^2 - 756*a*b^3*c^6*d)/(4096*a^8*d^15 + 4096*b^8*c^8*d^7 - 32768*a*b^7*c^7*d^8 + 114688*a^2*b^6*c^6*d^9 - 229376*a^3*b^5*c^5*d^10 + 286720*a^4*b^4*c^4*d^11 - 229376*a^5*b^3*c^3*d^12 + 114688*a^6*b^2*c^2*d^13 - 32768*a^7*b*c*d^14))^(3/4)*((864*a^3*b^14*c^14*d^3 - 12096*a^4*b^13*c^13*d^4 + 74592*a^5*b^12*c^12*d^5 - 267008*a^6*b^11*c^11*d^6 + 617152*a^7*b^10*c^10*d^7 - 968576*a^8*b^9*c^9*d^8 + 1054144*a^9*b^8*c^8*d^9 - 795392*a^10*b^7*c^7*d^10 + 407008*a^11*b^6*c^6*d^11 - 133952*a^12*b^5*c^5*d^12 + 25312*a^13*b^4*c^4*d^13 - 2048*a^14*b^3*c^3*d^14)/(a^7*d^10 - b^7*c^7*d^3 + 7*a*b^6*c^6*d^4 - 21*a^2*b^5*c^5*d^5 + 35*a^3*b^4*c^4*d^6 - 35*a^4*b^3*c^3*d^7 + 21*a^5*b^2*c^2*d^8 - 7*a^6*b*c*d^9) - (x^(1/2)*(-(81*b^4*c^7 + 2401*a^4*c^3*d^4 - 4116*a^3*b*c^4*d^3 + 2646*a^2*b^2*c^5*d^2 - 756*a*b^3*c^6*d)/(4096*a^8*d^15 + 4096*b^8*c^8*d^7 - 32768*a*b^7*c^7*d^8 + 114688*a^2*b^6*c^6*d^9 - 229376*a^3*b^5*c^5*d^10 + 286720*a^4*b^4*c^4*d^11 - 229376*a^5*b^3*c^3*d^12 + 114688*a^6*b^2*c^2*d^13 - 32768*a^7*b*c*d^14))^(1/4)*(2304*a^3*b^14*c^13*d^5 - 29184*a^4*b^13*c^12*d^6 + 167168*a^5*b^12*c^11*d^7 - 563200*a^6*b^11*c^10*d^8 + 1229312*a^7*b^10*c^9*d^9 - 1813504*a^8*b^9*c^8*d^10 + 1831424*a^9*b^8*c^7*d^11 - 1251328*a^10*b^7*c^6*d^12 + 554240*a^11*b^6*c^5*d^13 - 143872*a^12*b^5*c^4*d^14 + 16640*a^13*b^4*c^3*d^15))/(a^6*d^9 + b^6*c^6*d^3 - 6*a*b^5*c^5*d^4 + 15*a^2*b^4*c^4*d^5 - 20*a^3*b^3*c^3*d^6 + 15*a^4*b^2*c^2*d^7 - 6*a^5*b*c*d^8)) - (x^(1/2)*(81*a^5*b^8*c^10 - 756*a^6*b^7*c^9*d + 784*a^12*b*c^3*d^7 + 2646*a^7*b^6*c^8*d^2 - 4116*a^8*b^5*c^7*d^3 + 2401*a^9*b^4*c^6*d^4 + 144*a^10*b^3*c^5*d^5 - 672*a^11*b^2*c^4*d^6))/(a^6*d^9 + b^6*c^6*d^3 - 6*a*b^5*c^5*d^4 + 15*a^2*b^4*c^4*d^5 - 20*a^3*b^3*c^3*d^6 + 15*a^4*b^2*c^2*d^7 - 6*a^5*b*c*d^8))))*(-(81*b^4*c^7 + 2401*a^4*c^3*d^4 - 4116*a^3*b*c^4*d^3 + 2646*a^2*b^2*c^5*d^2 - 756*a*b^3*c^6*d)/(4096*a^8*d^15 + 4096*b^8*c^8*d^7 - 32768*a*b^7*c^7*d^8 + 114688*a^2*b^6*c^6*d^9 - 229376*a^3*b^5*c^5*d^10 + 286720*a^4*b^4*c^4*d^11 - 229376*a^5*b^3*c^3*d^12 + 114688*a^6*b^2*c^2*d^13 - 32768*a^7*b*c*d^14))^(1/4)*2i + 2*atan(((-(81*b^4*c^7 + 2401*a^4*c^3*d^4 - 4116*a^3*b*c^4*d^3 + 2646*a^2*b^2*c^5*d^2 - 756*a*b^3*c^6*d)/(4096*a^8*d^15 + 4096*b^8*c^8*d^7 - 32768*a*b^7*c^7*d^8 + 114688*a^2*b^6*c^6*d^9 - 229376*a^3*b^5*c^5*d^10 + 286720*a^4*b^4*c^4*d^11 - 229376*a^5*b^3*c^3*d^12 + 114688*a^6*b^2*c^2*d^13 - 32768*a^7*b*c*d^14))^(1/4)*((-(81*b^4*c^7 + 2401*a^4*c^3*d^4 - 4116*a^3*b*c^4*d^3 + 2646*a^2*b^2*c^5*d^2 - 756*a*b^3*c^6*d)/(4096*a^8*d^15 + 4096*b^8*c^8*d^7 - 32768*a*b^7*c^7*d^8 + 114688*a^2*b^6*c^6*d^9 - 229376*a^3*b^5*c^5*d^10 + 286720*a^4*b^4*c^4*d^11 - 229376*a^5*b^3*c^3*d^12 + 114688*a^6*b^2*c^2*d^13 - 32768*a^7*b*c*d^14))^(3/4)*(((864*a^3*b^14*c^14*d^3 - 12096*a^4*b^13*c^13*d^4 + 74592*a^5*b^12*c^12*d^5 - 267008*a^6*b^11*c^11*d^6 + 617152*a^7*b^10*c^10*d^7 - 968576*a^8*b^9*c^9*d^8 + 1054144*a^9*b^8*c^8*d^9 - 795392*a^10*b^7*c^7*d^10 + 407008*a^11*b^6*c^6*d^11 - 133952*a^12*b^5*c^5*d^12 + 25312*a^13*b^4*c^4*d^13 - 2048*a^14*b^3*c^3*d^14)*1i)/(a^7*d^10 - b^7*c^7*d^3 + 7*a*b^6*c^6*d^4 - 21*a^2*b^5*c^5*d^5 + 35*a^3*b^4*c^4*d^6 - 35*a^4*b^3*c^3*d^7 + 21*a^5*b^2*c^2*d^8 - 7*a^6*b*c*d^9) + (x^(1/2)*(-(81*b^4*c^7 + 2401*a^4*c^3*d^4 - 4116*a^3*b*c^4*d^3 + 2646*a^2*b^2*c^5*d^2 - 756*a*b^3*c^6*d)/(4096*a^8*d^15 + 4096*b^8*c^8*d^7 - 32768*a*b^7*c^7*d^8 + 114688*a^2*b^6*c^6*d^9 - 229376*a^3*b^5*c^5*d^10 + 286720*a^4*b^4*c^4*d^11 - 229376*a^5*b^3*c^3*d^12 + 114688*a^6*b^2*c^2*d^13 - 32768*a^7*b*c*d^14))^(1/4)*(2304*a^3*b^14*c^13*d^5 - 29184*a^4*b^13*c^12*d^6 + 167168*a^5*b^12*c^11*d^7 - 563200*a^6*b^11*c^10*d^8 + 1229312*a^7*b^10*c^9*d^9 - 1813504*a^8*b^9*c^8*d^10 + 1831424*a^9*b^8*c^7*d^11 - 1251328*a^10*b^7*c^6*d^12 + 554240*a^11*b^6*c^5*d^13 - 143872*a^12*b^5*c^4*d^14 + 16640*a^13*b^4*c^3*d^15))/(a^6*d^9 + b^6*c^6*d^3 - 6*a*b^5*c^5*d^4 + 15*a^2*b^4*c^4*d^5 - 20*a^3*b^3*c^3*d^6 + 15*a^4*b^2*c^2*d^7 - 6*a^5*b*c*d^8)) + (x^(1/2)*(81*a^5*b^8*c^10 - 756*a^6*b^7*c^9*d + 784*a^12*b*c^3*d^7 + 2646*a^7*b^6*c^8*d^2 - 4116*a^8*b^5*c^7*d^3 + 2401*a^9*b^4*c^6*d^4 + 144*a^10*b^3*c^5*d^5 - 672*a^11*b^2*c^4*d^6))/(a^6*d^9 + b^6*c^6*d^3 - 6*a*b^5*c^5*d^4 + 15*a^2*b^4*c^4*d^5 - 20*a^3*b^3*c^3*d^6 + 15*a^4*b^2*c^2*d^7 - 6*a^5*b*c*d^8)) - (-(81*b^4*c^7 + 2401*a^4*c^3*d^4 - 4116*a^3*b*c^4*d^3 + 2646*a^2*b^2*c^5*d^2 - 756*a*b^3*c^6*d)/(4096*a^8*d^15 + 4096*b^8*c^8*d^7 - 32768*a*b^7*c^7*d^8 + 114688*a^2*b^6*c^6*d^9 - 229376*a^3*b^5*c^5*d^10 + 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2646*a^2*b^2*c^5*d^2 - 756*a*b^3*c^6*d)/(4096*a^8*d^15 + 4096*b^8*c^8*d^7 - 32768*a*b^7*c^7*d^8 + 114688*a^2*b^6*c^6*d^9 - 229376*a^3*b^5*c^5*d^10 + 286720*a^4*b^4*c^4*d^11 - 229376*a^5*b^3*c^3*d^12 + 114688*a^6*b^2*c^2*d^13 - 32768*a^7*b*c*d^14))^(1/4)*((-(81*b^4*c^7 + 2401*a^4*c^3*d^4 - 4116*a^3*b*c^4*d^3 + 2646*a^2*b^2*c^5*d^2 - 756*a*b^3*c^6*d)/(4096*a^8*d^15 + 4096*b^8*c^8*d^7 - 32768*a*b^7*c^7*d^8 + 114688*a^2*b^6*c^6*d^9 - 229376*a^3*b^5*c^5*d^10 + 286720*a^4*b^4*c^4*d^11 - 229376*a^5*b^3*c^3*d^12 + 114688*a^6*b^2*c^2*d^13 - 32768*a^7*b*c*d^14))^(3/4)*(((864*a^3*b^14*c^14*d^3 - 12096*a^4*b^13*c^13*d^4 + 74592*a^5*b^12*c^12*d^5 - 267008*a^6*b^11*c^11*d^6 + 617152*a^7*b^10*c^10*d^7 - 968576*a^8*b^9*c^9*d^8 + 1054144*a^9*b^8*c^8*d^9 - 795392*a^10*b^7*c^7*d^10 + 407008*a^11*b^6*c^6*d^11 - 133952*a^12*b^5*c^5*d^12 + 25312*a^13*b^4*c^4*d^13 - 2048*a^14*b^3*c^3*d^14)*1i)/(a^7*d^10 - b^7*c^7*d^3 + 7*a*b^6*c^6*d^4 - 21*a^2*b^5*c^5*d^5 + 35*a^3*b^4*c^4*d^6 - 35*a^4*b^3*c^3*d^7 + 21*a^5*b^2*c^2*d^8 - 7*a^6*b*c*d^9) + (x^(1/2)*(-(81*b^4*c^7 + 2401*a^4*c^3*d^4 - 4116*a^3*b*c^4*d^3 + 2646*a^2*b^2*c^5*d^2 - 756*a*b^3*c^6*d)/(4096*a^8*d^15 + 4096*b^8*c^8*d^7 - 32768*a*b^7*c^7*d^8 + 114688*a^2*b^6*c^6*d^9 - 229376*a^3*b^5*c^5*d^10 + 286720*a^4*b^4*c^4*d^11 - 229376*a^5*b^3*c^3*d^12 + 114688*a^6*b^2*c^2*d^13 - 32768*a^7*b*c*d^14))^(1/4)*(2304*a^3*b^14*c^13*d^5 - 29184*a^4*b^13*c^12*d^6 + 167168*a^5*b^12*c^11*d^7 - 563200*a^6*b^11*c^10*d^8 + 1229312*a^7*b^10*c^9*d^9 - 1813504*a^8*b^9*c^8*d^10 + 1831424*a^9*b^8*c^7*d^11 - 1251328*a^10*b^7*c^6*d^12 + 554240*a^11*b^6*c^5*d^13 - 143872*a^12*b^5*c^4*d^14 + 16640*a^13*b^4*c^3*d^15))/(a^6*d^9 + b^6*c^6*d^3 - 6*a*b^5*c^5*d^4 + 15*a^2*b^4*c^4*d^5 - 20*a^3*b^3*c^3*d^6 + 15*a^4*b^2*c^2*d^7 - 6*a^5*b*c*d^8))*1i + (x^(1/2)*(81*a^5*b^8*c^10 - 756*a^6*b^7*c^9*d + 784*a^12*b*c^3*d^7 + 2646*a^7*b^6*c^8*d^2 - 4116*a^8*b^5*c^7*d^3 + 2401*a^9*b^4*c^6*d^4 + 144*a^10*b^3*c^5*d^5 - 672*a^11*b^2*c^4*d^6)*1i)/(a^6*d^9 + b^6*c^6*d^3 - 6*a*b^5*c^5*d^4 + 15*a^2*b^4*c^4*d^5 - 20*a^3*b^3*c^3*d^6 + 15*a^4*b^2*c^2*d^7 - 6*a^5*b*c*d^8)) - (81*a^7*b^6*c^9 - 675*a^8*b^5*c^8*d + 1372*a^12*b*c^4*d^5 + 1971*a^9*b^4*c^7*d^2 - 2037*a^10*b^3*c^6*d^3 - 392*a^11*b^2*c^5*d^4)/(a^7*d^10 - b^7*c^7*d^3 + 7*a*b^6*c^6*d^4 - 21*a^2*b^5*c^5*d^5 + 35*a^3*b^4*c^4*d^6 - 35*a^4*b^3*c^3*d^7 + 21*a^5*b^2*c^2*d^8 - 7*a^6*b*c*d^9) + (-(81*b^4*c^7 + 2401*a^4*c^3*d^4 - 4116*a^3*b*c^4*d^3 + 2646*a^2*b^2*c^5*d^2 - 756*a*b^3*c^6*d)/(4096*a^8*d^15 + 4096*b^8*c^8*d^7 - 32768*a*b^7*c^7*d^8 + 114688*a^2*b^6*c^6*d^9 - 229376*a^3*b^5*c^5*d^10 + 286720*a^4*b^4*c^4*d^11 - 229376*a^5*b^3*c^3*d^12 + 114688*a^6*b^2*c^2*d^13 - 32768*a^7*b*c*d^14))^(1/4)*((-(81*b^4*c^7 + 2401*a^4*c^3*d^4 - 4116*a^3*b*c^4*d^3 + 2646*a^2*b^2*c^5*d^2 - 756*a*b^3*c^6*d)/(4096*a^8*d^15 + 4096*b^8*c^8*d^7 - 32768*a*b^7*c^7*d^8 + 114688*a^2*b^6*c^6*d^9 - 229376*a^3*b^5*c^5*d^10 + 286720*a^4*b^4*c^4*d^11 - 229376*a^5*b^3*c^3*d^12 + 114688*a^6*b^2*c^2*d^13 - 32768*a^7*b*c*d^14))^(3/4)*(((864*a^3*b^14*c^14*d^3 - 12096*a^4*b^13*c^13*d^4 + 74592*a^5*b^12*c^12*d^5 - 267008*a^6*b^11*c^11*d^6 + 617152*a^7*b^10*c^10*d^7 - 968576*a^8*b^9*c^9*d^8 + 1054144*a^9*b^8*c^8*d^9 - 795392*a^10*b^7*c^7*d^10 + 407008*a^11*b^6*c^6*d^11 - 133952*a^12*b^5*c^5*d^12 + 25312*a^13*b^4*c^4*d^13 - 2048*a^14*b^3*c^3*d^14)*1i)/(a^7*d^10 - b^7*c^7*d^3 + 7*a*b^6*c^6*d^4 - 21*a^2*b^5*c^5*d^5 + 35*a^3*b^4*c^4*d^6 - 35*a^4*b^3*c^3*d^7 + 21*a^5*b^2*c^2*d^8 - 7*a^6*b*c*d^9) - (x^(1/2)*(-(81*b^4*c^7 + 2401*a^4*c^3*d^4 - 4116*a^3*b*c^4*d^3 + 2646*a^2*b^2*c^5*d^2 - 756*a*b^3*c^6*d)/(4096*a^8*d^15 + 4096*b^8*c^8*d^7 - 32768*a*b^7*c^7*d^8 + 114688*a^2*b^6*c^6*d^9 - 229376*a^3*b^5*c^5*d^10 + 286720*a^4*b^4*c^4*d^11 - 229376*a^5*b^3*c^3*d^12 + 114688*a^6*b^2*c^2*d^13 - 32768*a^7*b*c*d^14))^(1/4)*(2304*a^3*b^14*c^13*d^5 - 29184*a^4*b^13*c^12*d^6 + 167168*a^5*b^12*c^11*d^7 - 563200*a^6*b^11*c^10*d^8 + 1229312*a^7*b^10*c^9*d^9 - 1813504*a^8*b^9*c^8*d^10 + 1831424*a^9*b^8*c^7*d^11 - 1251328*a^10*b^7*c^6*d^12 + 554240*a^11*b^6*c^5*d^13 - 143872*a^12*b^5*c^4*d^14 + 16640*a^13*b^4*c^3*d^15))/(a^6*d^9 + b^6*c^6*d^3 - 6*a*b^5*c^5*d^4 + 15*a^2*b^4*c^4*d^5 - 20*a^3*b^3*c^3*d^6 + 15*a^4*b^2*c^2*d^7 - 6*a^5*b*c*d^8))*1i - (x^(1/2)*(81*a^5*b^8*c^10 - 756*a^6*b^7*c^9*d + 784*a^12*b*c^3*d^7 + 2646*a^7*b^6*c^8*d^2 - 4116*a^8*b^5*c^7*d^3 + 2401*a^9*b^4*c^6*d^4 + 144*a^10*b^3*c^5*d^5 - 672*a^11*b^2*c^4*d^6)*1i)/(a^6*d^9 + b^6*c^6*d^3 - 6*a*b^5*c^5*d^4 + 15*a^2*b^4*c^4*d^5 - 20*a^3*b^3*c^3*d^6 + 15*a^4*b^2*c^2*d^7 - 6*a^5*b*c*d^8))))*(-(81*b^4*c^7 + 2401*a^4*c^3*d^4 - 4116*a^3*b*c^4*d^3 + 2646*a^2*b^2*c^5*d^2 - 756*a*b^3*c^6*d)/(4096*a^8*d^15 + 4096*b^8*c^8*d^7 - 32768*a*b^7*c^7*d^8 + 114688*a^2*b^6*c^6*d^9 - 229376*a^3*b^5*c^5*d^10 + 286720*a^4*b^4*c^4*d^11 - 229376*a^5*b^3*c^3*d^12 + 114688*a^6*b^2*c^2*d^13 - 32768*a^7*b*c*d^14))^(1/4) + (c*x^(3/2))/(2*d*(c + d*x^2)*(a*d - b*c))","B"
472,1,21485,532,2.484384,"\text{Not used}","int(x^(7/2)/((a + b*x^2)*(c + d*x^2)^2),x)","2\,\mathrm{atan}\left(\frac{\left(\frac{\sqrt{x}\,\left(400\,a^{10}\,b^3\,c^2\,d^6-160\,a^9\,b^4\,c^3\,d^5+641\,a^8\,b^5\,c^4\,d^4-500\,a^7\,b^6\,c^5\,d^3+150\,a^6\,b^7\,c^6\,d^2-20\,a^5\,b^8\,c^7\,d+a^4\,b^9\,c^8\right)}{a^6\,d^7-6\,a^5\,b\,c\,d^6+15\,a^4\,b^2\,c^2\,d^5-20\,a^3\,b^3\,c^3\,d^4+15\,a^2\,b^4\,c^4\,d^3-6\,a\,b^5\,c^5\,d^2+b^6\,c^6\,d}+{\left(-\frac{a^5}{16\,a^8\,b\,d^8-128\,a^7\,b^2\,c\,d^7+448\,a^6\,b^3\,c^2\,d^6-896\,a^5\,b^4\,c^3\,d^5+1120\,a^4\,b^5\,c^4\,d^4-896\,a^3\,b^6\,c^5\,d^3+448\,a^2\,b^7\,c^6\,d^2-128\,a\,b^8\,c^7\,d+16\,b^9\,c^8}\right)}^{1/4}\,\left(\frac{2\,\left(320\,a^8\,b^3\,c^2\,d^5+256\,a^7\,b^4\,c^3\,d^4-369\,a^6\,b^5\,c^4\,d^3+131\,a^5\,b^6\,c^5\,d^2-19\,a^4\,b^7\,c^6\,d+a^3\,b^8\,c^7\right)}{a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d}-\left(\frac{\sqrt{x}\,\left(6400\,a^{13}\,b^4\,c^2\,d^{14}-49664\,a^{12}\,b^5\,c^3\,d^{13}+167168\,a^{11}\,b^6\,c^4\,d^{12}-317440\,a^{10}\,b^7\,c^5\,d^{11}+369152\,a^9\,b^8\,c^6\,d^{10}-265216\,a^8\,b^9\,c^7\,d^9+111104\,a^7\,b^{10}\,c^8\,d^8-22528\,a^6\,b^{11}\,c^9\,d^7+1280\,a^5\,b^{12}\,c^{10}\,d^6-512\,a^4\,b^{13}\,c^{11}\,d^5+256\,a^3\,b^{14}\,c^{12}\,d^4\right)}{a^6\,d^7-6\,a^5\,b\,c\,d^6+15\,a^4\,b^2\,c^2\,d^5-20\,a^3\,b^3\,c^3\,d^4+15\,a^2\,b^4\,c^4\,d^3-6\,a\,b^5\,c^5\,d^2+b^6\,c^6\,d}+\frac{{\left(-\frac{a^5}{16\,a^8\,b\,d^8-128\,a^7\,b^2\,c\,d^7+448\,a^6\,b^3\,c^2\,d^6-896\,a^5\,b^4\,c^3\,d^5+1120\,a^4\,b^5\,c^4\,d^4-896\,a^3\,b^6\,c^5\,d^3+448\,a^2\,b^7\,c^6\,d^2-128\,a\,b^8\,c^7\,d+16\,b^9\,c^8}\right)}^{1/4}\,\left(5120\,a^{11}\,b^4\,c^2\,d^{13}-40960\,a^{10}\,b^5\,c^3\,d^{12}+143360\,a^9\,b^6\,c^4\,d^{11}-286720\,a^8\,b^7\,c^5\,d^{10}+358400\,a^7\,b^8\,c^6\,d^9-286720\,a^6\,b^9\,c^7\,d^8+143360\,a^5\,b^{10}\,c^8\,d^7-40960\,a^4\,b^{11}\,c^9\,d^6+5120\,a^3\,b^{12}\,c^{10}\,d^5\right)\,2{}\mathrm{i}}{a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d}\right)\,{\left(-\frac{a^5}{16\,a^8\,b\,d^8-128\,a^7\,b^2\,c\,d^7+448\,a^6\,b^3\,c^2\,d^6-896\,a^5\,b^4\,c^3\,d^5+1120\,a^4\,b^5\,c^4\,d^4-896\,a^3\,b^6\,c^5\,d^3+448\,a^2\,b^7\,c^6\,d^2-128\,a\,b^8\,c^7\,d+16\,b^9\,c^8}\right)}^{3/4}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{a^5}{16\,a^8\,b\,d^8-128\,a^7\,b^2\,c\,d^7+448\,a^6\,b^3\,c^2\,d^6-896\,a^5\,b^4\,c^3\,d^5+1120\,a^4\,b^5\,c^4\,d^4-896\,a^3\,b^6\,c^5\,d^3+448\,a^2\,b^7\,c^6\,d^2-128\,a\,b^8\,c^7\,d+16\,b^9\,c^8}\right)}^{1/4}-\left(-\frac{\sqrt{x}\,\left(400\,a^{10}\,b^3\,c^2\,d^6-160\,a^9\,b^4\,c^3\,d^5+641\,a^8\,b^5\,c^4\,d^4-500\,a^7\,b^6\,c^5\,d^3+150\,a^6\,b^7\,c^6\,d^2-20\,a^5\,b^8\,c^7\,d+a^4\,b^9\,c^8\right)}{a^6\,d^7-6\,a^5\,b\,c\,d^6+15\,a^4\,b^2\,c^2\,d^5-20\,a^3\,b^3\,c^3\,d^4+15\,a^2\,b^4\,c^4\,d^3-6\,a\,b^5\,c^5\,d^2+b^6\,c^6\,d}+{\left(-\frac{a^5}{16\,a^8\,b\,d^8-128\,a^7\,b^2\,c\,d^7+448\,a^6\,b^3\,c^2\,d^6-896\,a^5\,b^4\,c^3\,d^5+1120\,a^4\,b^5\,c^4\,d^4-896\,a^3\,b^6\,c^5\,d^3+448\,a^2\,b^7\,c^6\,d^2-128\,a\,b^8\,c^7\,d+16\,b^9\,c^8}\right)}^{1/4}\,\left(\frac{2\,\left(320\,a^8\,b^3\,c^2\,d^5+256\,a^7\,b^4\,c^3\,d^4-369\,a^6\,b^5\,c^4\,d^3+131\,a^5\,b^6\,c^5\,d^2-19\,a^4\,b^7\,c^6\,d+a^3\,b^8\,c^7\right)}{a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d}-\left(-\frac{\sqrt{x}\,\left(6400\,a^{13}\,b^4\,c^2\,d^{14}-49664\,a^{12}\,b^5\,c^3\,d^{13}+167168\,a^{11}\,b^6\,c^4\,d^{12}-317440\,a^{10}\,b^7\,c^5\,d^{11}+369152\,a^9\,b^8\,c^6\,d^{10}-265216\,a^8\,b^9\,c^7\,d^9+111104\,a^7\,b^{10}\,c^8\,d^8-22528\,a^6\,b^{11}\,c^9\,d^7+1280\,a^5\,b^{12}\,c^{10}\,d^6-512\,a^4\,b^{13}\,c^{11}\,d^5+256\,a^3\,b^{14}\,c^{12}\,d^4\right)}{a^6\,d^7-6\,a^5\,b\,c\,d^6+15\,a^4\,b^2\,c^2\,d^5-20\,a^3\,b^3\,c^3\,d^4+15\,a^2\,b^4\,c^4\,d^3-6\,a\,b^5\,c^5\,d^2+b^6\,c^6\,d}+\frac{{\left(-\frac{a^5}{16\,a^8\,b\,d^8-128\,a^7\,b^2\,c\,d^7+448\,a^6\,b^3\,c^2\,d^6-896\,a^5\,b^4\,c^3\,d^5+1120\,a^4\,b^5\,c^4\,d^4-896\,a^3\,b^6\,c^5\,d^3+448\,a^2\,b^7\,c^6\,d^2-128\,a\,b^8\,c^7\,d+16\,b^9\,c^8}\right)}^{1/4}\,\left(5120\,a^{11}\,b^4\,c^2\,d^{13}-40960\,a^{10}\,b^5\,c^3\,d^{12}+143360\,a^9\,b^6\,c^4\,d^{11}-286720\,a^8\,b^7\,c^5\,d^{10}+358400\,a^7\,b^8\,c^6\,d^9-286720\,a^6\,b^9\,c^7\,d^8+143360\,a^5\,b^{10}\,c^8\,d^7-40960\,a^4\,b^{11}\,c^9\,d^6+5120\,a^3\,b^{12}\,c^{10}\,d^5\right)\,2{}\mathrm{i}}{a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d}\right)\,{\left(-\frac{a^5}{16\,a^8\,b\,d^8-128\,a^7\,b^2\,c\,d^7+448\,a^6\,b^3\,c^2\,d^6-896\,a^5\,b^4\,c^3\,d^5+1120\,a^4\,b^5\,c^4\,d^4-896\,a^3\,b^6\,c^5\,d^3+448\,a^2\,b^7\,c^6\,d^2-128\,a\,b^8\,c^7\,d+16\,b^9\,c^8}\right)}^{3/4}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{a^5}{16\,a^8\,b\,d^8-128\,a^7\,b^2\,c\,d^7+448\,a^6\,b^3\,c^2\,d^6-896\,a^5\,b^4\,c^3\,d^5+1120\,a^4\,b^5\,c^4\,d^4-896\,a^3\,b^6\,c^5\,d^3+448\,a^2\,b^7\,c^6\,d^2-128\,a\,b^8\,c^7\,d+16\,b^9\,c^8}\right)}^{1/4}}{\left(\frac{\sqrt{x}\,\left(400\,a^{10}\,b^3\,c^2\,d^6-160\,a^9\,b^4\,c^3\,d^5+641\,a^8\,b^5\,c^4\,d^4-500\,a^7\,b^6\,c^5\,d^3+150\,a^6\,b^7\,c^6\,d^2-20\,a^5\,b^8\,c^7\,d+a^4\,b^9\,c^8\right)}{a^6\,d^7-6\,a^5\,b\,c\,d^6+15\,a^4\,b^2\,c^2\,d^5-20\,a^3\,b^3\,c^3\,d^4+15\,a^2\,b^4\,c^4\,d^3-6\,a\,b^5\,c^5\,d^2+b^6\,c^6\,d}+{\left(-\frac{a^5}{16\,a^8\,b\,d^8-128\,a^7\,b^2\,c\,d^7+448\,a^6\,b^3\,c^2\,d^6-896\,a^5\,b^4\,c^3\,d^5+1120\,a^4\,b^5\,c^4\,d^4-896\,a^3\,b^6\,c^5\,d^3+448\,a^2\,b^7\,c^6\,d^2-128\,a\,b^8\,c^7\,d+16\,b^9\,c^8}\right)}^{1/4}\,\left(\frac{2\,\left(320\,a^8\,b^3\,c^2\,d^5+256\,a^7\,b^4\,c^3\,d^4-369\,a^6\,b^5\,c^4\,d^3+131\,a^5\,b^6\,c^5\,d^2-19\,a^4\,b^7\,c^6\,d+a^3\,b^8\,c^7\right)}{a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d}-\left(\frac{\sqrt{x}\,\left(6400\,a^{13}\,b^4\,c^2\,d^{14}-49664\,a^{12}\,b^5\,c^3\,d^{13}+167168\,a^{11}\,b^6\,c^4\,d^{12}-317440\,a^{10}\,b^7\,c^5\,d^{11}+369152\,a^9\,b^8\,c^6\,d^{10}-265216\,a^8\,b^9\,c^7\,d^9+111104\,a^7\,b^{10}\,c^8\,d^8-22528\,a^6\,b^{11}\,c^9\,d^7+1280\,a^5\,b^{12}\,c^{10}\,d^6-512\,a^4\,b^{13}\,c^{11}\,d^5+256\,a^3\,b^{14}\,c^{12}\,d^4\right)}{a^6\,d^7-6\,a^5\,b\,c\,d^6+15\,a^4\,b^2\,c^2\,d^5-20\,a^3\,b^3\,c^3\,d^4+15\,a^2\,b^4\,c^4\,d^3-6\,a\,b^5\,c^5\,d^2+b^6\,c^6\,d}+\frac{{\left(-\frac{a^5}{16\,a^8\,b\,d^8-128\,a^7\,b^2\,c\,d^7+448\,a^6\,b^3\,c^2\,d^6-896\,a^5\,b^4\,c^3\,d^5+1120\,a^4\,b^5\,c^4\,d^4-896\,a^3\,b^6\,c^5\,d^3+448\,a^2\,b^7\,c^6\,d^2-128\,a\,b^8\,c^7\,d+16\,b^9\,c^8}\right)}^{1/4}\,\left(5120\,a^{11}\,b^4\,c^2\,d^{13}-40960\,a^{10}\,b^5\,c^3\,d^{12}+143360\,a^9\,b^6\,c^4\,d^{11}-286720\,a^8\,b^7\,c^5\,d^{10}+358400\,a^7\,b^8\,c^6\,d^9-286720\,a^6\,b^9\,c^7\,d^8+143360\,a^5\,b^{10}\,c^8\,d^7-40960\,a^4\,b^{11}\,c^9\,d^6+5120\,a^3\,b^{12}\,c^{10}\,d^5\right)\,2{}\mathrm{i}}{a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d}\right)\,{\left(-\frac{a^5}{16\,a^8\,b\,d^8-128\,a^7\,b^2\,c\,d^7+448\,a^6\,b^3\,c^2\,d^6-896\,a^5\,b^4\,c^3\,d^5+1120\,a^4\,b^5\,c^4\,d^4-896\,a^3\,b^6\,c^5\,d^3+448\,a^2\,b^7\,c^6\,d^2-128\,a\,b^8\,c^7\,d+16\,b^9\,c^8}\right)}^{3/4}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{a^5}{16\,a^8\,b\,d^8-128\,a^7\,b^2\,c\,d^7+448\,a^6\,b^3\,c^2\,d^6-896\,a^5\,b^4\,c^3\,d^5+1120\,a^4\,b^5\,c^4\,d^4-896\,a^3\,b^6\,c^5\,d^3+448\,a^2\,b^7\,c^6\,d^2-128\,a\,b^8\,c^7\,d+16\,b^9\,c^8}\right)}^{1/4}\,1{}\mathrm{i}+\left(-\frac{\sqrt{x}\,\left(400\,a^{10}\,b^3\,c^2\,d^6-160\,a^9\,b^4\,c^3\,d^5+641\,a^8\,b^5\,c^4\,d^4-500\,a^7\,b^6\,c^5\,d^3+150\,a^6\,b^7\,c^6\,d^2-20\,a^5\,b^8\,c^7\,d+a^4\,b^9\,c^8\right)}{a^6\,d^7-6\,a^5\,b\,c\,d^6+15\,a^4\,b^2\,c^2\,d^5-20\,a^3\,b^3\,c^3\,d^4+15\,a^2\,b^4\,c^4\,d^3-6\,a\,b^5\,c^5\,d^2+b^6\,c^6\,d}+{\left(-\frac{a^5}{16\,a^8\,b\,d^8-128\,a^7\,b^2\,c\,d^7+448\,a^6\,b^3\,c^2\,d^6-896\,a^5\,b^4\,c^3\,d^5+1120\,a^4\,b^5\,c^4\,d^4-896\,a^3\,b^6\,c^5\,d^3+448\,a^2\,b^7\,c^6\,d^2-128\,a\,b^8\,c^7\,d+16\,b^9\,c^8}\right)}^{1/4}\,\left(\frac{2\,\left(320\,a^8\,b^3\,c^2\,d^5+256\,a^7\,b^4\,c^3\,d^4-369\,a^6\,b^5\,c^4\,d^3+131\,a^5\,b^6\,c^5\,d^2-19\,a^4\,b^7\,c^6\,d+a^3\,b^8\,c^7\right)}{a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d}-\left(-\frac{\sqrt{x}\,\left(6400\,a^{13}\,b^4\,c^2\,d^{14}-49664\,a^{12}\,b^5\,c^3\,d^{13}+167168\,a^{11}\,b^6\,c^4\,d^{12}-317440\,a^{10}\,b^7\,c^5\,d^{11}+369152\,a^9\,b^8\,c^6\,d^{10}-265216\,a^8\,b^9\,c^7\,d^9+111104\,a^7\,b^{10}\,c^8\,d^8-22528\,a^6\,b^{11}\,c^9\,d^7+1280\,a^5\,b^{12}\,c^{10}\,d^6-512\,a^4\,b^{13}\,c^{11}\,d^5+256\,a^3\,b^{14}\,c^{12}\,d^4\right)}{a^6\,d^7-6\,a^5\,b\,c\,d^6+15\,a^4\,b^2\,c^2\,d^5-20\,a^3\,b^3\,c^3\,d^4+15\,a^2\,b^4\,c^4\,d^3-6\,a\,b^5\,c^5\,d^2+b^6\,c^6\,d}+\frac{{\left(-\frac{a^5}{16\,a^8\,b\,d^8-128\,a^7\,b^2\,c\,d^7+448\,a^6\,b^3\,c^2\,d^6-896\,a^5\,b^4\,c^3\,d^5+1120\,a^4\,b^5\,c^4\,d^4-896\,a^3\,b^6\,c^5\,d^3+448\,a^2\,b^7\,c^6\,d^2-128\,a\,b^8\,c^7\,d+16\,b^9\,c^8}\right)}^{1/4}\,\left(5120\,a^{11}\,b^4\,c^2\,d^{13}-40960\,a^{10}\,b^5\,c^3\,d^{12}+143360\,a^9\,b^6\,c^4\,d^{11}-286720\,a^8\,b^7\,c^5\,d^{10}+358400\,a^7\,b^8\,c^6\,d^9-286720\,a^6\,b^9\,c^7\,d^8+143360\,a^5\,b^{10}\,c^8\,d^7-40960\,a^4\,b^{11}\,c^9\,d^6+5120\,a^3\,b^{12}\,c^{10}\,d^5\right)\,2{}\mathrm{i}}{a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d}\right)\,{\left(-\frac{a^5}{16\,a^8\,b\,d^8-128\,a^7\,b^2\,c\,d^7+448\,a^6\,b^3\,c^2\,d^6-896\,a^5\,b^4\,c^3\,d^5+1120\,a^4\,b^5\,c^4\,d^4-896\,a^3\,b^6\,c^5\,d^3+448\,a^2\,b^7\,c^6\,d^2-128\,a\,b^8\,c^7\,d+16\,b^9\,c^8}\right)}^{3/4}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{a^5}{16\,a^8\,b\,d^8-128\,a^7\,b^2\,c\,d^7+448\,a^6\,b^3\,c^2\,d^6-896\,a^5\,b^4\,c^3\,d^5+1120\,a^4\,b^5\,c^4\,d^4-896\,a^3\,b^6\,c^5\,d^3+448\,a^2\,b^7\,c^6\,d^2-128\,a\,b^8\,c^7\,d+16\,b^9\,c^8}\right)}^{1/4}\,1{}\mathrm{i}}\right)\,{\left(-\frac{a^5}{16\,a^8\,b\,d^8-128\,a^7\,b^2\,c\,d^7+448\,a^6\,b^3\,c^2\,d^6-896\,a^5\,b^4\,c^3\,d^5+1120\,a^4\,b^5\,c^4\,d^4-896\,a^3\,b^6\,c^5\,d^3+448\,a^2\,b^7\,c^6\,d^2-128\,a\,b^8\,c^7\,d+16\,b^9\,c^8}\right)}^{1/4}+2\,\mathrm{atan}\left(\frac{\left(-\frac{\sqrt{x}\,\left(400\,a^{10}\,b^3\,c^2\,d^6-160\,a^9\,b^4\,c^3\,d^5+641\,a^8\,b^5\,c^4\,d^4-500\,a^7\,b^6\,c^5\,d^3+150\,a^6\,b^7\,c^6\,d^2-20\,a^5\,b^8\,c^7\,d+a^4\,b^9\,c^8\right)}{a^6\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d^{10}+286720\,a^4\,b^4\,c^4\,d^9-229376\,a^3\,b^5\,c^5\,d^8+114688\,a^2\,b^6\,c^6\,d^7-32768\,a\,b^7\,c^7\,d^6+4096\,b^8\,c^8\,d^5}\right)}^{1/4}\,1{}\mathrm{i}\right)\,{\left(-\frac{625\,a^4\,c\,d^4-500\,a^3\,b\,c^2\,d^3+150\,a^2\,b^2\,c^3\,d^2-20\,a\,b^3\,c^4\,d+b^4\,c^5}{4096\,a^8\,d^{13}-32768\,a^7\,b\,c\,d^{12}+114688\,a^6\,b^2\,c^2\,d^{11}-229376\,a^5\,b^3\,c^3\,d^{10}+286720\,a^4\,b^4\,c^4\,d^9-229376\,a^3\,b^5\,c^5\,d^8+114688\,a^2\,b^6\,c^6\,d^7-32768\,a\,b^7\,c^7\,d^6+4096\,b^8\,c^8\,d^5}\right)}^{1/4}}{\left(-\frac{\sqrt{x}\,\left(400\,a^{10}\,b^3\,c^2\,d^6-160\,a^9\,b^4\,c^3\,d^5+641\,a^8\,b^5\,c^4\,d^4-500\,a^7\,b^6\,c^5\,d^3+150\,a^6\,b^7\,c^6\,d^2-20\,a^5\,b^8\,c^7\,d+a^4\,b^9\,c^8\right)}{a^6\,d^7-6\,a^5\,b\,c\,d^6+15\,a^4\,b^2\,c^2\,d^5-20\,a^3\,b^3\,c^3\,d^4+15\,a^2\,b^4\,c^4\,d^3-6\,a\,b^5\,c^5\,d^2+b^6\,c^6\,d}+\left(-\frac{2\,\left(320\,a^8\,b^3\,c^2\,d^5+256\,a^7\,b^4\,c^3\,d^4-369\,a^6\,b^5\,c^4\,d^3+131\,a^5\,b^6\,c^5\,d^2-19\,a^4\,b^7\,c^6\,d+a^3\,b^8\,c^7\right)}{a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d}+\left(\frac{\sqrt{x}\,\left(6400\,a^{13}\,b^4\,c^2\,d^{14}-49664\,a^{12}\,b^5\,c^3\,d^{13}+167168\,a^{11}\,b^6\,c^4\,d^{12}-317440\,a^{10}\,b^7\,c^5\,d^{11}+369152\,a^9\,b^8\,c^6\,d^{10}-265216\,a^8\,b^9\,c^7\,d^9+111104\,a^7\,b^{10}\,c^8\,d^8-22528\,a^6\,b^{11}\,c^9\,d^7+1280\,a^5\,b^{12}\,c^{10}\,d^6-512\,a^4\,b^{13}\,c^{11}\,d^5+256\,a^3\,b^{14}\,c^{12}\,d^4\right)}{a^6\,d^7-6\,a^5\,b\,c\,d^6+15\,a^4\,b^2\,c^2\,d^5-20\,a^3\,b^3\,c^3\,d^4+15\,a^2\,b^4\,c^4\,d^3-6\,a\,b^5\,c^5\,d^2+b^6\,c^6\,d}+\frac{{\left(-\frac{625\,a^4\,c\,d^4-500\,a^3\,b\,c^2\,d^3+150\,a^2\,b^2\,c^3\,d^2-20\,a\,b^3\,c^4\,d+b^4\,c^5}{4096\,a^8\,d^{13}-32768\,a^7\,b\,c\,d^{12}+114688\,a^6\,b^2\,c^2\,d^{11}-229376\,a^5\,b^3\,c^3\,d^{10}+286720\,a^4\,b^4\,c^4\,d^9-229376\,a^3\,b^5\,c^5\,d^8+114688\,a^2\,b^6\,c^6\,d^7-32768\,a\,b^7\,c^7\,d^6+4096\,b^8\,c^8\,d^5}\right)}^{1/4}\,\left(5120\,a^{11}\,b^4\,c^2\,d^{13}-40960\,a^{10}\,b^5\,c^3\,d^{12}+143360\,a^9\,b^6\,c^4\,d^{11}-286720\,a^8\,b^7\,c^5\,d^{10}+358400\,a^7\,b^8\,c^6\,d^9-286720\,a^6\,b^9\,c^7\,d^8+143360\,a^5\,b^{10}\,c^8\,d^7-40960\,a^4\,b^{11}\,c^9\,d^6+5120\,a^3\,b^{12}\,c^{10}\,d^5\right)\,2{}\mathrm{i}}{a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d}\right)\,{\left(-\frac{625\,a^4\,c\,d^4-500\,a^3\,b\,c^2\,d^3+150\,a^2\,b^2\,c^3\,d^2-20\,a\,b^3\,c^4\,d+b^4\,c^5}{4096\,a^8\,d^{13}-32768\,a^7\,b\,c\,d^{12}+114688\,a^6\,b^2\,c^2\,d^{11}-229376\,a^5\,b^3\,c^3\,d^{10}+286720\,a^4\,b^4\,c^4\,d^9-229376\,a^3\,b^5\,c^5\,d^8+114688\,a^2\,b^6\,c^6\,d^7-32768\,a\,b^7\,c^7\,d^6+4096\,b^8\,c^8\,d^5}\right)}^{3/4}\,1{}\mathrm{i}\right)\,{\left(-\frac{625\,a^4\,c\,d^4-500\,a^3\,b\,c^2\,d^3+150\,a^2\,b^2\,c^3\,d^2-20\,a\,b^3\,c^4\,d+b^4\,c^5}{4096\,a^8\,d^{13}-32768\,a^7\,b\,c\,d^{12}+114688\,a^6\,b^2\,c^2\,d^{11}-229376\,a^5\,b^3\,c^3\,d^{10}+286720\,a^4\,b^4\,c^4\,d^9-229376\,a^3\,b^5\,c^5\,d^8+114688\,a^2\,b^6\,c^6\,d^7-32768\,a\,b^7\,c^7\,d^6+4096\,b^8\,c^8\,d^5}\right)}^{1/4}\,1{}\mathrm{i}\right)\,{\left(-\frac{625\,a^4\,c\,d^4-500\,a^3\,b\,c^2\,d^3+150\,a^2\,b^2\,c^3\,d^2-20\,a\,b^3\,c^4\,d+b^4\,c^5}{4096\,a^8\,d^{13}-32768\,a^7\,b\,c\,d^{12}+114688\,a^6\,b^2\,c^2\,d^{11}-229376\,a^5\,b^3\,c^3\,d^{10}+286720\,a^4\,b^4\,c^4\,d^9-229376\,a^3\,b^5\,c^5\,d^8+114688\,a^2\,b^6\,c^6\,d^7-32768\,a\,b^7\,c^7\,d^6+4096\,b^8\,c^8\,d^5}\right)}^{1/4}\,1{}\mathrm{i}+\left(\frac{\sqrt{x}\,\left(400\,a^{10}\,b^3\,c^2\,d^6-160\,a^9\,b^4\,c^3\,d^5+641\,a^8\,b^5\,c^4\,d^4-500\,a^7\,b^6\,c^5\,d^3+150\,a^6\,b^7\,c^6\,d^2-20\,a^5\,b^8\,c^7\,d+a^4\,b^9\,c^8\right)}{a^6\,d^7-6\,a^5\,b\,c\,d^6+15\,a^4\,b^2\,c^2\,d^5-20\,a^3\,b^3\,c^3\,d^4+15\,a^2\,b^4\,c^4\,d^3-6\,a\,b^5\,c^5\,d^2+b^6\,c^6\,d}+\left(-\frac{2\,\left(320\,a^8\,b^3\,c^2\,d^5+256\,a^7\,b^4\,c^3\,d^4-369\,a^6\,b^5\,c^4\,d^3+131\,a^5\,b^6\,c^5\,d^2-19\,a^4\,b^7\,c^6\,d+a^3\,b^8\,c^7\right)}{a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d}+\left(-\frac{\sqrt{x}\,\left(6400\,a^{13}\,b^4\,c^2\,d^{14}-49664\,a^{12}\,b^5\,c^3\,d^{13}+167168\,a^{11}\,b^6\,c^4\,d^{12}-317440\,a^{10}\,b^7\,c^5\,d^{11}+369152\,a^9\,b^8\,c^6\,d^{10}-265216\,a^8\,b^9\,c^7\,d^9+111104\,a^7\,b^{10}\,c^8\,d^8-22528\,a^6\,b^{11}\,c^9\,d^7+1280\,a^5\,b^{12}\,c^{10}\,d^6-512\,a^4\,b^{13}\,c^{11}\,d^5+256\,a^3\,b^{14}\,c^{12}\,d^4\right)}{a^6\,d^7-6\,a^5\,b\,c\,d^6+15\,a^4\,b^2\,c^2\,d^5-20\,a^3\,b^3\,c^3\,d^4+15\,a^2\,b^4\,c^4\,d^3-6\,a\,b^5\,c^5\,d^2+b^6\,c^6\,d}+\frac{{\left(-\frac{625\,a^4\,c\,d^4-500\,a^3\,b\,c^2\,d^3+150\,a^2\,b^2\,c^3\,d^2-20\,a\,b^3\,c^4\,d+b^4\,c^5}{4096\,a^8\,d^{13}-32768\,a^7\,b\,c\,d^{12}+114688\,a^6\,b^2\,c^2\,d^{11}-229376\,a^5\,b^3\,c^3\,d^{10}+286720\,a^4\,b^4\,c^4\,d^9-229376\,a^3\,b^5\,c^5\,d^8+114688\,a^2\,b^6\,c^6\,d^7-32768\,a\,b^7\,c^7\,d^6+4096\,b^8\,c^8\,d^5}\right)}^{1/4}\,\left(5120\,a^{11}\,b^4\,c^2\,d^{13}-40960\,a^{10}\,b^5\,c^3\,d^{12}+143360\,a^9\,b^6\,c^4\,d^{11}-286720\,a^8\,b^7\,c^5\,d^{10}+358400\,a^7\,b^8\,c^6\,d^9-286720\,a^6\,b^9\,c^7\,d^8+143360\,a^5\,b^{10}\,c^8\,d^7-40960\,a^4\,b^{11}\,c^9\,d^6+5120\,a^3\,b^{12}\,c^{10}\,d^5\right)\,2{}\mathrm{i}}{a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d}\right)\,{\left(-\frac{625\,a^4\,c\,d^4-500\,a^3\,b\,c^2\,d^3+150\,a^2\,b^2\,c^3\,d^2-20\,a\,b^3\,c^4\,d+b^4\,c^5}{4096\,a^8\,d^{13}-32768\,a^7\,b\,c\,d^{12}+114688\,a^6\,b^2\,c^2\,d^{11}-229376\,a^5\,b^3\,c^3\,d^{10}+286720\,a^4\,b^4\,c^4\,d^9-229376\,a^3\,b^5\,c^5\,d^8+114688\,a^2\,b^6\,c^6\,d^7-32768\,a\,b^7\,c^7\,d^6+4096\,b^8\,c^8\,d^5}\right)}^{3/4}\,1{}\mathrm{i}\right)\,{\left(-\frac{625\,a^4\,c\,d^4-500\,a^3\,b\,c^2\,d^3+150\,a^2\,b^2\,c^3\,d^2-20\,a\,b^3\,c^4\,d+b^4\,c^5}{4096\,a^8\,d^{13}-32768\,a^7\,b\,c\,d^{12}+114688\,a^6\,b^2\,c^2\,d^{11}-229376\,a^5\,b^3\,c^3\,d^{10}+286720\,a^4\,b^4\,c^4\,d^9-229376\,a^3\,b^5\,c^5\,d^8+114688\,a^2\,b^6\,c^6\,d^7-32768\,a\,b^7\,c^7\,d^6+4096\,b^8\,c^8\,d^5}\right)}^{1/4}\,1{}\mathrm{i}\right)\,{\left(-\frac{625\,a^4\,c\,d^4-500\,a^3\,b\,c^2\,d^3+150\,a^2\,b^2\,c^3\,d^2-20\,a\,b^3\,c^4\,d+b^4\,c^5}{4096\,a^8\,d^{13}-32768\,a^7\,b\,c\,d^{12}+114688\,a^6\,b^2\,c^2\,d^{11}-229376\,a^5\,b^3\,c^3\,d^{10}+286720\,a^4\,b^4\,c^4\,d^9-229376\,a^3\,b^5\,c^5\,d^8+114688\,a^2\,b^6\,c^6\,d^7-32768\,a\,b^7\,c^7\,d^6+4096\,b^8\,c^8\,d^5}\right)}^{1/4}\,1{}\mathrm{i}}\right)\,{\left(-\frac{625\,a^4\,c\,d^4-500\,a^3\,b\,c^2\,d^3+150\,a^2\,b^2\,c^3\,d^2-20\,a\,b^3\,c^4\,d+b^4\,c^5}{4096\,a^8\,d^{13}-32768\,a^7\,b\,c\,d^{12}+114688\,a^6\,b^2\,c^2\,d^{11}-229376\,a^5\,b^3\,c^3\,d^{10}+286720\,a^4\,b^4\,c^4\,d^9-229376\,a^3\,b^5\,c^5\,d^8+114688\,a^2\,b^6\,c^6\,d^7-32768\,a\,b^7\,c^7\,d^6+4096\,b^8\,c^8\,d^5}\right)}^{1/4}+\frac{c\,\sqrt{x}}{2\,d\,\left(d\,x^2+c\right)\,\left(a\,d-b\,c\right)}+\mathrm{atan}\left(\frac{\left({\left(-\frac{a^5}{16\,a^8\,b\,d^8-128\,a^7\,b^2\,c\,d^7+448\,a^6\,b^3\,c^2\,d^6-896\,a^5\,b^4\,c^3\,d^5+1120\,a^4\,b^5\,c^4\,d^4-896\,a^3\,b^6\,c^5\,d^3+448\,a^2\,b^7\,c^6\,d^2-128\,a\,b^8\,c^7\,d+16\,b^9\,c^8}\right)}^{1/4}\,\left(\frac{2\,\left(320\,a^8\,b^3\,c^2\,d^5+256\,a^7\,b^4\,c^3\,d^4-369\,a^6\,b^5\,c^4\,d^3+131\,a^5\,b^6\,c^5\,d^2-19\,a^4\,b^7\,c^6\,d+a^3\,b^8\,c^7\right)}{a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d}+\left(\frac{2\,{\left(-\frac{a^5}{16\,a^8\,b\,d^8-128\,a^7\,b^2\,c\,d^7+448\,a^6\,b^3\,c^2\,d^6-896\,a^5\,b^4\,c^3\,d^5+1120\,a^4\,b^5\,c^4\,d^4-896\,a^3\,b^6\,c^5\,d^3+448\,a^2\,b^7\,c^6\,d^2-128\,a\,b^8\,c^7\,d+16\,b^9\,c^8}\right)}^{1/4}\,\left(5120\,a^{11}\,b^4\,c^2\,d^{13}-40960\,a^{10}\,b^5\,c^3\,d^{12}+143360\,a^9\,b^6\,c^4\,d^{11}-286720\,a^8\,b^7\,c^5\,d^{10}+358400\,a^7\,b^8\,c^6\,d^9-286720\,a^6\,b^9\,c^7\,d^8+143360\,a^5\,b^{10}\,c^8\,d^7-40960\,a^4\,b^{11}\,c^9\,d^6+5120\,a^3\,b^{12}\,c^{10}\,d^5\right)}{a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d}+\frac{\sqrt{x}\,\left(6400\,a^{13}\,b^4\,c^2\,d^{14}-49664\,a^{12}\,b^5\,c^3\,d^{13}+167168\,a^{11}\,b^6\,c^4\,d^{12}-317440\,a^{10}\,b^7\,c^5\,d^{11}+369152\,a^9\,b^8\,c^6\,d^{10}-265216\,a^8\,b^9\,c^7\,d^9+111104\,a^7\,b^{10}\,c^8\,d^8-22528\,a^6\,b^{11}\,c^9\,d^7+1280\,a^5\,b^{12}\,c^{10}\,d^6-512\,a^4\,b^{13}\,c^{11}\,d^5+256\,a^3\,b^{14}\,c^{12}\,d^4\right)}{a^6\,d^7-6\,a^5\,b\,c\,d^6+15\,a^4\,b^2\,c^2\,d^5-20\,a^3\,b^3\,c^3\,d^4+15\,a^2\,b^4\,c^4\,d^3-6\,a\,b^5\,c^5\,d^2+b^6\,c^6\,d}\right)\,{\left(-\frac{a^5}{16\,a^8\,b\,d^8-128\,a^7\,b^2\,c\,d^7+448\,a^6\,b^3\,c^2\,d^6-896\,a^5\,b^4\,c^3\,d^5+1120\,a^4\,b^5\,c^4\,d^4-896\,a^3\,b^6\,c^5\,d^3+448\,a^2\,b^7\,c^6\,d^2-128\,a\,b^8\,c^7\,d+16\,b^9\,c^8}\right)}^{3/4}\right)+\frac{\sqrt{x}\,\left(400\,a^{10}\,b^3\,c^2\,d^6-160\,a^9\,b^4\,c^3\,d^5+641\,a^8\,b^5\,c^4\,d^4-500\,a^7\,b^6\,c^5\,d^3+150\,a^6\,b^7\,c^6\,d^2-20\,a^5\,b^8\,c^7\,d+a^4\,b^9\,c^8\right)}{a^6\,d^7-6\,a^5\,b\,c\,d^6+15\,a^4\,b^2\,c^2\,d^5-20\,a^3\,b^3\,c^3\,d^4+15\,a^2\,b^4\,c^4\,d^3-6\,a\,b^5\,c^5\,d^2+b^6\,c^6\,d}\right)\,{\left(-\frac{a^5}{16\,a^8\,b\,d^8-128\,a^7\,b^2\,c\,d^7+448\,a^6\,b^3\,c^2\,d^6-896\,a^5\,b^4\,c^3\,d^5+1120\,a^4\,b^5\,c^4\,d^4-896\,a^3\,b^6\,c^5\,d^3+448\,a^2\,b^7\,c^6\,d^2-128\,a\,b^8\,c^7\,d+16\,b^9\,c^8}\right)}^{1/4}\,1{}\mathrm{i}-\left({\left(-\frac{a^5}{16\,a^8\,b\,d^8-128\,a^7\,b^2\,c\,d^7+448\,a^6\,b^3\,c^2\,d^6-896\,a^5\,b^4\,c^3\,d^5+1120\,a^4\,b^5\,c^4\,d^4-896\,a^3\,b^6\,c^5\,d^3+448\,a^2\,b^7\,c^6\,d^2-128\,a\,b^8\,c^7\,d+16\,b^9\,c^8}\right)}^{1/4}\,\left(\frac{2\,\left(320\,a^8\,b^3\,c^2\,d^5+256\,a^7\,b^4\,c^3\,d^4-369\,a^6\,b^5\,c^4\,d^3+131\,a^5\,b^6\,c^5\,d^2-19\,a^4\,b^7\,c^6\,d+a^3\,b^8\,c^7\right)}{a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d}+\left(\frac{2\,{\left(-\frac{a^5}{16\,a^8\,b\,d^8-128\,a^7\,b^2\,c\,d^7+448\,a^6\,b^3\,c^2\,d^6-896\,a^5\,b^4\,c^3\,d^5+1120\,a^4\,b^5\,c^4\,d^4-896\,a^3\,b^6\,c^5\,d^3+448\,a^2\,b^7\,c^6\,d^2-128\,a\,b^8\,c^7\,d+16\,b^9\,c^8}\right)}^{1/4}\,\left(5120\,a^{11}\,b^4\,c^2\,d^{13}-40960\,a^{10}\,b^5\,c^3\,d^{12}+143360\,a^9\,b^6\,c^4\,d^{11}-286720\,a^8\,b^7\,c^5\,d^{10}+358400\,a^7\,b^8\,c^6\,d^9-286720\,a^6\,b^9\,c^7\,d^8+143360\,a^5\,b^{10}\,c^8\,d^7-40960\,a^4\,b^{11}\,c^9\,d^6+5120\,a^3\,b^{12}\,c^{10}\,d^5\right)}{a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d}-\frac{\sqrt{x}\,\left(6400\,a^{13}\,b^4\,c^2\,d^{14}-49664\,a^{12}\,b^5\,c^3\,d^{13}+167168\,a^{11}\,b^6\,c^4\,d^{12}-317440\,a^{10}\,b^7\,c^5\,d^{11}+369152\,a^9\,b^8\,c^6\,d^{10}-265216\,a^8\,b^9\,c^7\,d^9+111104\,a^7\,b^{10}\,c^8\,d^8-22528\,a^6\,b^{11}\,c^9\,d^7+1280\,a^5\,b^{12}\,c^{10}\,d^6-512\,a^4\,b^{13}\,c^{11}\,d^5+256\,a^3\,b^{14}\,c^{12}\,d^4\right)}{a^6\,d^7-6\,a^5\,b\,c\,d^6+15\,a^4\,b^2\,c^2\,d^5-20\,a^3\,b^3\,c^3\,d^4+15\,a^2\,b^4\,c^4\,d^3-6\,a\,b^5\,c^5\,d^2+b^6\,c^6\,d}\right)\,{\left(-\frac{a^5}{16\,a^8\,b\,d^8-128\,a^7\,b^2\,c\,d^7+448\,a^6\,b^3\,c^2\,d^6-896\,a^5\,b^4\,c^3\,d^5+1120\,a^4\,b^5\,c^4\,d^4-896\,a^3\,b^6\,c^5\,d^3+448\,a^2\,b^7\,c^6\,d^2-128\,a\,b^8\,c^7\,d+16\,b^9\,c^8}\right)}^{3/4}\right)-\frac{\sqrt{x}\,\left(400\,a^{10}\,b^3\,c^2\,d^6-160\,a^9\,b^4\,c^3\,d^5+641\,a^8\,b^5\,c^4\,d^4-500\,a^7\,b^6\,c^5\,d^3+150\,a^6\,b^7\,c^6\,d^2-20\,a^5\,b^8\,c^7\,d+a^4\,b^9\,c^8\right)}{a^6\,d^7-6\,a^5\,b\,c\,d^6+15\,a^4\,b^2\,c^2\,d^5-20\,a^3\,b^3\,c^3\,d^4+15\,a^2\,b^4\,c^4\,d^3-6\,a\,b^5\,c^5\,d^2+b^6\,c^6\,d}\right)\,{\left(-\frac{a^5}{16\,a^8\,b\,d^8-128\,a^7\,b^2\,c\,d^7+448\,a^6\,b^3\,c^2\,d^6-896\,a^5\,b^4\,c^3\,d^5+1120\,a^4\,b^5\,c^4\,d^4-896\,a^3\,b^6\,c^5\,d^3+448\,a^2\,b^7\,c^6\,d^2-128\,a\,b^8\,c^7\,d+16\,b^9\,c^8}\right)}^{1/4}\,1{}\mathrm{i}}{\left({\left(-\frac{a^5}{16\,a^8\,b\,d^8-128\,a^7\,b^2\,c\,d^7+448\,a^6\,b^3\,c^2\,d^6-896\,a^5\,b^4\,c^3\,d^5+1120\,a^4\,b^5\,c^4\,d^4-896\,a^3\,b^6\,c^5\,d^3+448\,a^2\,b^7\,c^6\,d^2-128\,a\,b^8\,c^7\,d+16\,b^9\,c^8}\right)}^{1/4}\,\left(\frac{2\,\left(320\,a^8\,b^3\,c^2\,d^5+256\,a^7\,b^4\,c^3\,d^4-369\,a^6\,b^5\,c^4\,d^3+131\,a^5\,b^6\,c^5\,d^2-19\,a^4\,b^7\,c^6\,d+a^3\,b^8\,c^7\right)}{a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d}+\left(\frac{2\,{\left(-\frac{a^5}{16\,a^8\,b\,d^8-128\,a^7\,b^2\,c\,d^7+448\,a^6\,b^3\,c^2\,d^6-896\,a^5\,b^4\,c^3\,d^5+1120\,a^4\,b^5\,c^4\,d^4-896\,a^3\,b^6\,c^5\,d^3+448\,a^2\,b^7\,c^6\,d^2-128\,a\,b^8\,c^7\,d+16\,b^9\,c^8}\right)}^{1/4}\,\left(5120\,a^{11}\,b^4\,c^2\,d^{13}-40960\,a^{10}\,b^5\,c^3\,d^{12}+143360\,a^9\,b^6\,c^4\,d^{11}-286720\,a^8\,b^7\,c^5\,d^{10}+358400\,a^7\,b^8\,c^6\,d^9-286720\,a^6\,b^9\,c^7\,d^8+143360\,a^5\,b^{10}\,c^8\,d^7-40960\,a^4\,b^{11}\,c^9\,d^6+5120\,a^3\,b^{12}\,c^{10}\,d^5\right)}{a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d}+\frac{\sqrt{x}\,\left(6400\,a^{13}\,b^4\,c^2\,d^{14}-49664\,a^{12}\,b^5\,c^3\,d^{13}+167168\,a^{11}\,b^6\,c^4\,d^{12}-317440\,a^{10}\,b^7\,c^5\,d^{11}+369152\,a^9\,b^8\,c^6\,d^{10}-265216\,a^8\,b^9\,c^7\,d^9+111104\,a^7\,b^{10}\,c^8\,d^8-22528\,a^6\,b^{11}\,c^9\,d^7+1280\,a^5\,b^{12}\,c^{10}\,d^6-512\,a^4\,b^{13}\,c^{11}\,d^5+256\,a^3\,b^{14}\,c^{12}\,d^4\right)}{a^6\,d^7-6\,a^5\,b\,c\,d^6+15\,a^4\,b^2\,c^2\,d^5-20\,a^3\,b^3\,c^3\,d^4+15\,a^2\,b^4\,c^4\,d^3-6\,a\,b^5\,c^5\,d^2+b^6\,c^6\,d}\right)\,{\left(-\frac{a^5}{16\,a^8\,b\,d^8-128\,a^7\,b^2\,c\,d^7+448\,a^6\,b^3\,c^2\,d^6-896\,a^5\,b^4\,c^3\,d^5+1120\,a^4\,b^5\,c^4\,d^4-896\,a^3\,b^6\,c^5\,d^3+448\,a^2\,b^7\,c^6\,d^2-128\,a\,b^8\,c^7\,d+16\,b^9\,c^8}\right)}^{3/4}\right)+\frac{\sqrt{x}\,\left(400\,a^{10}\,b^3\,c^2\,d^6-160\,a^9\,b^4\,c^3\,d^5+641\,a^8\,b^5\,c^4\,d^4-500\,a^7\,b^6\,c^5\,d^3+150\,a^6\,b^7\,c^6\,d^2-20\,a^5\,b^8\,c^7\,d+a^4\,b^9\,c^8\right)}{a^6\,d^7-6\,a^5\,b\,c\,d^6+15\,a^4\,b^2\,c^2\,d^5-20\,a^3\,b^3\,c^3\,d^4+15\,a^2\,b^4\,c^4\,d^3-6\,a\,b^5\,c^5\,d^2+b^6\,c^6\,d}\right)\,{\left(-\frac{a^5}{16\,a^8\,b\,d^8-128\,a^7\,b^2\,c\,d^7+448\,a^6\,b^3\,c^2\,d^6-896\,a^5\,b^4\,c^3\,d^5+1120\,a^4\,b^5\,c^4\,d^4-896\,a^3\,b^6\,c^5\,d^3+448\,a^2\,b^7\,c^6\,d^2-128\,a\,b^8\,c^7\,d+16\,b^9\,c^8}\right)}^{1/4}+\left({\left(-\frac{a^5}{16\,a^8\,b\,d^8-128\,a^7\,b^2\,c\,d^7+448\,a^6\,b^3\,c^2\,d^6-896\,a^5\,b^4\,c^3\,d^5+1120\,a^4\,b^5\,c^4\,d^4-896\,a^3\,b^6\,c^5\,d^3+448\,a^2\,b^7\,c^6\,d^2-128\,a\,b^8\,c^7\,d+16\,b^9\,c^8}\right)}^{1/4}\,\left(\frac{2\,\left(320\,a^8\,b^3\,c^2\,d^5+256\,a^7\,b^4\,c^3\,d^4-369\,a^6\,b^5\,c^4\,d^3+131\,a^5\,b^6\,c^5\,d^2-19\,a^4\,b^7\,c^6\,d+a^3\,b^8\,c^7\right)}{a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d}+\left(\frac{2\,{\left(-\frac{a^5}{16\,a^8\,b\,d^8-128\,a^7\,b^2\,c\,d^7+448\,a^6\,b^3\,c^2\,d^6-896\,a^5\,b^4\,c^3\,d^5+1120\,a^4\,b^5\,c^4\,d^4-896\,a^3\,b^6\,c^5\,d^3+448\,a^2\,b^7\,c^6\,d^2-128\,a\,b^8\,c^7\,d+16\,b^9\,c^8}\right)}^{1/4}\,\left(5120\,a^{11}\,b^4\,c^2\,d^{13}-40960\,a^{10}\,b^5\,c^3\,d^{12}+143360\,a^9\,b^6\,c^4\,d^{11}-286720\,a^8\,b^7\,c^5\,d^{10}+358400\,a^7\,b^8\,c^6\,d^9-286720\,a^6\,b^9\,c^7\,d^8+143360\,a^5\,b^{10}\,c^8\,d^7-40960\,a^4\,b^{11}\,c^9\,d^6+5120\,a^3\,b^{12}\,c^{10}\,d^5\right)}{a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d}-\frac{\sqrt{x}\,\left(6400\,a^{13}\,b^4\,c^2\,d^{14}-49664\,a^{12}\,b^5\,c^3\,d^{13}+167168\,a^{11}\,b^6\,c^4\,d^{12}-317440\,a^{10}\,b^7\,c^5\,d^{11}+369152\,a^9\,b^8\,c^6\,d^{10}-265216\,a^8\,b^9\,c^7\,d^9+111104\,a^7\,b^{10}\,c^8\,d^8-22528\,a^6\,b^{11}\,c^9\,d^7+1280\,a^5\,b^{12}\,c^{10}\,d^6-512\,a^4\,b^{13}\,c^{11}\,d^5+256\,a^3\,b^{14}\,c^{12}\,d^4\right)}{a^6\,d^7-6\,a^5\,b\,c\,d^6+15\,a^4\,b^2\,c^2\,d^5-20\,a^3\,b^3\,c^3\,d^4+15\,a^2\,b^4\,c^4\,d^3-6\,a\,b^5\,c^5\,d^2+b^6\,c^6\,d}\right)\,{\left(-\frac{a^5}{16\,a^8\,b\,d^8-128\,a^7\,b^2\,c\,d^7+448\,a^6\,b^3\,c^2\,d^6-896\,a^5\,b^4\,c^3\,d^5+1120\,a^4\,b^5\,c^4\,d^4-896\,a^3\,b^6\,c^5\,d^3+448\,a^2\,b^7\,c^6\,d^2-128\,a\,b^8\,c^7\,d+16\,b^9\,c^8}\right)}^{3/4}\right)-\frac{\sqrt{x}\,\left(400\,a^{10}\,b^3\,c^2\,d^6-160\,a^9\,b^4\,c^3\,d^5+641\,a^8\,b^5\,c^4\,d^4-500\,a^7\,b^6\,c^5\,d^3+150\,a^6\,b^7\,c^6\,d^2-20\,a^5\,b^8\,c^7\,d+a^4\,b^9\,c^8\right)}{a^6\,d^7-6\,a^5\,b\,c\,d^6+15\,a^4\,b^2\,c^2\,d^5-20\,a^3\,b^3\,c^3\,d^4+15\,a^2\,b^4\,c^4\,d^3-6\,a\,b^5\,c^5\,d^2+b^6\,c^6\,d}\right)\,{\left(-\frac{a^5}{16\,a^8\,b\,d^8-128\,a^7\,b^2\,c\,d^7+448\,a^6\,b^3\,c^2\,d^6-896\,a^5\,b^4\,c^3\,d^5+1120\,a^4\,b^5\,c^4\,d^4-896\,a^3\,b^6\,c^5\,d^3+448\,a^2\,b^7\,c^6\,d^2-128\,a\,b^8\,c^7\,d+16\,b^9\,c^8}\right)}^{1/4}}\right)\,{\left(-\frac{a^5}{16\,a^8\,b\,d^8-128\,a^7\,b^2\,c\,d^7+448\,a^6\,b^3\,c^2\,d^6-896\,a^5\,b^4\,c^3\,d^5+1120\,a^4\,b^5\,c^4\,d^4-896\,a^3\,b^6\,c^5\,d^3+448\,a^2\,b^7\,c^6\,d^2-128\,a\,b^8\,c^7\,d+16\,b^9\,c^8}\right)}^{1/4}\,2{}\mathrm{i}+\mathrm{atan}\left(\frac{\left(\left(\left(\frac{2\,{\left(-\frac{625\,a^4\,c\,d^4-500\,a^3\,b\,c^2\,d^3+150\,a^2\,b^2\,c^3\,d^2-20\,a\,b^3\,c^4\,d+b^4\,c^5}{4096\,a^8\,d^{13}-32768\,a^7\,b\,c\,d^{12}+114688\,a^6\,b^2\,c^2\,d^{11}-229376\,a^5\,b^3\,c^3\,d^{10}+286720\,a^4\,b^4\,c^4\,d^9-229376\,a^3\,b^5\,c^5\,d^8+114688\,a^2\,b^6\,c^6\,d^7-32768\,a\,b^7\,c^7\,d^6+4096\,b^8\,c^8\,d^5}\right)}^{1/4}\,\left(5120\,a^{11}\,b^4\,c^2\,d^{13}-40960\,a^{10}\,b^5\,c^3\,d^{12}+143360\,a^9\,b^6\,c^4\,d^{11}-286720\,a^8\,b^7\,c^5\,d^{10}+358400\,a^7\,b^8\,c^6\,d^9-286720\,a^6\,b^9\,c^7\,d^8+143360\,a^5\,b^{10}\,c^8\,d^7-40960\,a^4\,b^{11}\,c^9\,d^6+5120\,a^3\,b^{12}\,c^{10}\,d^5\right)}{a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d}+\frac{\sqrt{x}\,\left(6400\,a^{13}\,b^4\,c^2\,d^{14}-49664\,a^{12}\,b^5\,c^3\,d^{13}+167168\,a^{11}\,b^6\,c^4\,d^{12}-317440\,a^{10}\,b^7\,c^5\,d^{11}+369152\,a^9\,b^8\,c^6\,d^{10}-265216\,a^8\,b^9\,c^7\,d^9+111104\,a^7\,b^{10}\,c^8\,d^8-22528\,a^6\,b^{11}\,c^9\,d^7+1280\,a^5\,b^{12}\,c^{10}\,d^6-512\,a^4\,b^{13}\,c^{11}\,d^5+256\,a^3\,b^{14}\,c^{12}\,d^4\right)}{a^6\,d^7-6\,a^5\,b\,c\,d^6+15\,a^4\,b^2\,c^2\,d^5-20\,a^3\,b^3\,c^3\,d^4+15\,a^2\,b^4\,c^4\,d^3-6\,a\,b^5\,c^5\,d^2+b^6\,c^6\,d}\right)\,{\left(-\frac{625\,a^4\,c\,d^4-500\,a^3\,b\,c^2\,d^3+150\,a^2\,b^2\,c^3\,d^2-20\,a\,b^3\,c^4\,d+b^4\,c^5}{4096\,a^8\,d^{13}-32768\,a^7\,b\,c\,d^{12}+114688\,a^6\,b^2\,c^2\,d^{11}-229376\,a^5\,b^3\,c^3\,d^{10}+286720\,a^4\,b^4\,c^4\,d^9-229376\,a^3\,b^5\,c^5\,d^8+114688\,a^2\,b^6\,c^6\,d^7-32768\,a\,b^7\,c^7\,d^6+4096\,b^8\,c^8\,d^5}\right)}^{3/4}+\frac{2\,\left(320\,a^8\,b^3\,c^2\,d^5+256\,a^7\,b^4\,c^3\,d^4-369\,a^6\,b^5\,c^4\,d^3+131\,a^5\,b^6\,c^5\,d^2-19\,a^4\,b^7\,c^6\,d+a^3\,b^8\,c^7\right)}{a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d}\right)\,{\left(-\frac{625\,a^4\,c\,d^4-500\,a^3\,b\,c^2\,d^3+150\,a^2\,b^2\,c^3\,d^2-20\,a\,b^3\,c^4\,d+b^4\,c^5}{4096\,a^8\,d^{13}-32768\,a^7\,b\,c\,d^{12}+114688\,a^6\,b^2\,c^2\,d^{11}-229376\,a^5\,b^3\,c^3\,d^{10}+286720\,a^4\,b^4\,c^4\,d^9-229376\,a^3\,b^5\,c^5\,d^8+114688\,a^2\,b^6\,c^6\,d^7-32768\,a\,b^7\,c^7\,d^6+4096\,b^8\,c^8\,d^5}\right)}^{1/4}+\frac{\sqrt{x}\,\left(400\,a^{10}\,b^3\,c^2\,d^6-160\,a^9\,b^4\,c^3\,d^5+641\,a^8\,b^5\,c^4\,d^4-500\,a^7\,b^6\,c^5\,d^3+150\,a^6\,b^7\,c^6\,d^2-20\,a^5\,b^8\,c^7\,d+a^4\,b^9\,c^8\right)}{a^6\,d^7-6\,a^5\,b\,c\,d^6+15\,a^4\,b^2\,c^2\,d^5-20\,a^3\,b^3\,c^3\,d^4+15\,a^2\,b^4\,c^4\,d^3-6\,a\,b^5\,c^5\,d^2+b^6\,c^6\,d}\right)\,{\left(-\frac{625\,a^4\,c\,d^4-500\,a^3\,b\,c^2\,d^3+150\,a^2\,b^2\,c^3\,d^2-20\,a\,b^3\,c^4\,d+b^4\,c^5}{4096\,a^8\,d^{13}-32768\,a^7\,b\,c\,d^{12}+114688\,a^6\,b^2\,c^2\,d^{11}-229376\,a^5\,b^3\,c^3\,d^{10}+286720\,a^4\,b^4\,c^4\,d^9-229376\,a^3\,b^5\,c^5\,d^8+114688\,a^2\,b^6\,c^6\,d^7-32768\,a\,b^7\,c^7\,d^6+4096\,b^8\,c^8\,d^5}\right)}^{1/4}\,1{}\mathrm{i}-\left(\left(\left(\frac{2\,{\left(-\frac{625\,a^4\,c\,d^4-500\,a^3\,b\,c^2\,d^3+150\,a^2\,b^2\,c^3\,d^2-20\,a\,b^3\,c^4\,d+b^4\,c^5}{4096\,a^8\,d^{13}-32768\,a^7\,b\,c\,d^{12}+114688\,a^6\,b^2\,c^2\,d^{11}-229376\,a^5\,b^3\,c^3\,d^{10}+286720\,a^4\,b^4\,c^4\,d^9-229376\,a^3\,b^5\,c^5\,d^8+114688\,a^2\,b^6\,c^6\,d^7-32768\,a\,b^7\,c^7\,d^6+4096\,b^8\,c^8\,d^5}\right)}^{1/4}\,\left(5120\,a^{11}\,b^4\,c^2\,d^{13}-40960\,a^{10}\,b^5\,c^3\,d^{12}+143360\,a^9\,b^6\,c^4\,d^{11}-286720\,a^8\,b^7\,c^5\,d^{10}+358400\,a^7\,b^8\,c^6\,d^9-286720\,a^6\,b^9\,c^7\,d^8+143360\,a^5\,b^{10}\,c^8\,d^7-40960\,a^4\,b^{11}\,c^9\,d^6+5120\,a^3\,b^{12}\,c^{10}\,d^5\right)}{a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d}-\frac{\sqrt{x}\,\left(6400\,a^{13}\,b^4\,c^2\,d^{14}-49664\,a^{12}\,b^5\,c^3\,d^{13}+167168\,a^{11}\,b^6\,c^4\,d^{12}-317440\,a^{10}\,b^7\,c^5\,d^{11}+369152\,a^9\,b^8\,c^6\,d^{10}-265216\,a^8\,b^9\,c^7\,d^9+111104\,a^7\,b^{10}\,c^8\,d^8-22528\,a^6\,b^{11}\,c^9\,d^7+1280\,a^5\,b^{12}\,c^{10}\,d^6-512\,a^4\,b^{13}\,c^{11}\,d^5+256\,a^3\,b^{14}\,c^{12}\,d^4\right)}{a^6\,d^7-6\,a^5\,b\,c\,d^6+15\,a^4\,b^2\,c^2\,d^5-20\,a^3\,b^3\,c^3\,d^4+15\,a^2\,b^4\,c^4\,d^3-6\,a\,b^5\,c^5\,d^2+b^6\,c^6\,d}\right)\,{\left(-\frac{625\,a^4\,c\,d^4-500\,a^3\,b\,c^2\,d^3+150\,a^2\,b^2\,c^3\,d^2-20\,a\,b^3\,c^4\,d+b^4\,c^5}{4096\,a^8\,d^{13}-32768\,a^7\,b\,c\,d^{12}+114688\,a^6\,b^2\,c^2\,d^{11}-229376\,a^5\,b^3\,c^3\,d^{10}+286720\,a^4\,b^4\,c^4\,d^9-229376\,a^3\,b^5\,c^5\,d^8+114688\,a^2\,b^6\,c^6\,d^7-32768\,a\,b^7\,c^7\,d^6+4096\,b^8\,c^8\,d^5}\right)}^{3/4}+\frac{2\,\left(320\,a^8\,b^3\,c^2\,d^5+256\,a^7\,b^4\,c^3\,d^4-369\,a^6\,b^5\,c^4\,d^3+131\,a^5\,b^6\,c^5\,d^2-19\,a^4\,b^7\,c^6\,d+a^3\,b^8\,c^7\right)}{a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d}\right)\,{\left(-\frac{625\,a^4\,c\,d^4-500\,a^3\,b\,c^2\,d^3+150\,a^2\,b^2\,c^3\,d^2-20\,a\,b^3\,c^4\,d+b^4\,c^5}{4096\,a^8\,d^{13}-32768\,a^7\,b\,c\,d^{12}+114688\,a^6\,b^2\,c^2\,d^{11}-229376\,a^5\,b^3\,c^3\,d^{10}+286720\,a^4\,b^4\,c^4\,d^9-229376\,a^3\,b^5\,c^5\,d^8+114688\,a^2\,b^6\,c^6\,d^7-32768\,a\,b^7\,c^7\,d^6+4096\,b^8\,c^8\,d^5}\right)}^{1/4}-\frac{\sqrt{x}\,\left(400\,a^{10}\,b^3\,c^2\,d^6-160\,a^9\,b^4\,c^3\,d^5+641\,a^8\,b^5\,c^4\,d^4-500\,a^7\,b^6\,c^5\,d^3+150\,a^6\,b^7\,c^6\,d^2-20\,a^5\,b^8\,c^7\,d+a^4\,b^9\,c^8\right)}{a^6\,d^7-6\,a^5\,b\,c\,d^6+15\,a^4\,b^2\,c^2\,d^5-20\,a^3\,b^3\,c^3\,d^4+15\,a^2\,b^4\,c^4\,d^3-6\,a\,b^5\,c^5\,d^2+b^6\,c^6\,d}\right)\,{\left(-\frac{625\,a^4\,c\,d^4-500\,a^3\,b\,c^2\,d^3+150\,a^2\,b^2\,c^3\,d^2-20\,a\,b^3\,c^4\,d+b^4\,c^5}{4096\,a^8\,d^{13}-32768\,a^7\,b\,c\,d^{12}+114688\,a^6\,b^2\,c^2\,d^{11}-229376\,a^5\,b^3\,c^3\,d^{10}+286720\,a^4\,b^4\,c^4\,d^9-229376\,a^3\,b^5\,c^5\,d^8+114688\,a^2\,b^6\,c^6\,d^7-32768\,a\,b^7\,c^7\,d^6+4096\,b^8\,c^8\,d^5}\right)}^{1/4}\,1{}\mathrm{i}}{\left(\left(\left(\frac{2\,{\left(-\frac{625\,a^4\,c\,d^4-500\,a^3\,b\,c^2\,d^3+150\,a^2\,b^2\,c^3\,d^2-20\,a\,b^3\,c^4\,d+b^4\,c^5}{4096\,a^8\,d^{13}-32768\,a^7\,b\,c\,d^{12}+114688\,a^6\,b^2\,c^2\,d^{11}-229376\,a^5\,b^3\,c^3\,d^{10}+286720\,a^4\,b^4\,c^4\,d^9-229376\,a^3\,b^5\,c^5\,d^8+114688\,a^2\,b^6\,c^6\,d^7-32768\,a\,b^7\,c^7\,d^6+4096\,b^8\,c^8\,d^5}\right)}^{1/4}\,\left(5120\,a^{11}\,b^4\,c^2\,d^{13}-40960\,a^{10}\,b^5\,c^3\,d^{12}+143360\,a^9\,b^6\,c^4\,d^{11}-286720\,a^8\,b^7\,c^5\,d^{10}+358400\,a^7\,b^8\,c^6\,d^9-286720\,a^6\,b^9\,c^7\,d^8+143360\,a^5\,b^{10}\,c^8\,d^7-40960\,a^4\,b^{11}\,c^9\,d^6+5120\,a^3\,b^{12}\,c^{10}\,d^5\right)}{a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d}+\frac{\sqrt{x}\,\left(6400\,a^{13}\,b^4\,c^2\,d^{14}-49664\,a^{12}\,b^5\,c^3\,d^{13}+167168\,a^{11}\,b^6\,c^4\,d^{12}-317440\,a^{10}\,b^7\,c^5\,d^{11}+369152\,a^9\,b^8\,c^6\,d^{10}-265216\,a^8\,b^9\,c^7\,d^9+111104\,a^7\,b^{10}\,c^8\,d^8-22528\,a^6\,b^{11}\,c^9\,d^7+1280\,a^5\,b^{12}\,c^{10}\,d^6-512\,a^4\,b^{13}\,c^{11}\,d^5+256\,a^3\,b^{14}\,c^{12}\,d^4\right)}{a^6\,d^7-6\,a^5\,b\,c\,d^6+15\,a^4\,b^2\,c^2\,d^5-20\,a^3\,b^3\,c^3\,d^4+15\,a^2\,b^4\,c^4\,d^3-6\,a\,b^5\,c^5\,d^2+b^6\,c^6\,d}\right)\,{\left(-\frac{625\,a^4\,c\,d^4-500\,a^3\,b\,c^2\,d^3+150\,a^2\,b^2\,c^3\,d^2-20\,a\,b^3\,c^4\,d+b^4\,c^5}{4096\,a^8\,d^{13}-32768\,a^7\,b\,c\,d^{12}+114688\,a^6\,b^2\,c^2\,d^{11}-229376\,a^5\,b^3\,c^3\,d^{10}+286720\,a^4\,b^4\,c^4\,d^9-229376\,a^3\,b^5\,c^5\,d^8+114688\,a^2\,b^6\,c^6\,d^7-32768\,a\,b^7\,c^7\,d^6+4096\,b^8\,c^8\,d^5}\right)}^{3/4}+\frac{2\,\left(320\,a^8\,b^3\,c^2\,d^5+256\,a^7\,b^4\,c^3\,d^4-369\,a^6\,b^5\,c^4\,d^3+131\,a^5\,b^6\,c^5\,d^2-19\,a^4\,b^7\,c^6\,d+a^3\,b^8\,c^7\right)}{a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d}\right)\,{\left(-\frac{625\,a^4\,c\,d^4-500\,a^3\,b\,c^2\,d^3+150\,a^2\,b^2\,c^3\,d^2-20\,a\,b^3\,c^4\,d+b^4\,c^5}{4096\,a^8\,d^{13}-32768\,a^7\,b\,c\,d^{12}+114688\,a^6\,b^2\,c^2\,d^{11}-229376\,a^5\,b^3\,c^3\,d^{10}+286720\,a^4\,b^4\,c^4\,d^9-229376\,a^3\,b^5\,c^5\,d^8+114688\,a^2\,b^6\,c^6\,d^7-32768\,a\,b^7\,c^7\,d^6+4096\,b^8\,c^8\,d^5}\right)}^{1/4}+\frac{\sqrt{x}\,\left(400\,a^{10}\,b^3\,c^2\,d^6-160\,a^9\,b^4\,c^3\,d^5+641\,a^8\,b^5\,c^4\,d^4-500\,a^7\,b^6\,c^5\,d^3+150\,a^6\,b^7\,c^6\,d^2-20\,a^5\,b^8\,c^7\,d+a^4\,b^9\,c^8\right)}{a^6\,d^7-6\,a^5\,b\,c\,d^6+15\,a^4\,b^2\,c^2\,d^5-20\,a^3\,b^3\,c^3\,d^4+15\,a^2\,b^4\,c^4\,d^3-6\,a\,b^5\,c^5\,d^2+b^6\,c^6\,d}\right)\,{\left(-\frac{625\,a^4\,c\,d^4-500\,a^3\,b\,c^2\,d^3+150\,a^2\,b^2\,c^3\,d^2-20\,a\,b^3\,c^4\,d+b^4\,c^5}{4096\,a^8\,d^{13}-32768\,a^7\,b\,c\,d^{12}+114688\,a^6\,b^2\,c^2\,d^{11}-229376\,a^5\,b^3\,c^3\,d^{10}+286720\,a^4\,b^4\,c^4\,d^9-229376\,a^3\,b^5\,c^5\,d^8+114688\,a^2\,b^6\,c^6\,d^7-32768\,a\,b^7\,c^7\,d^6+4096\,b^8\,c^8\,d^5}\right)}^{1/4}+\left(\left(\left(\frac{2\,{\left(-\frac{625\,a^4\,c\,d^4-500\,a^3\,b\,c^2\,d^3+150\,a^2\,b^2\,c^3\,d^2-20\,a\,b^3\,c^4\,d+b^4\,c^5}{4096\,a^8\,d^{13}-32768\,a^7\,b\,c\,d^{12}+114688\,a^6\,b^2\,c^2\,d^{11}-229376\,a^5\,b^3\,c^3\,d^{10}+286720\,a^4\,b^4\,c^4\,d^9-229376\,a^3\,b^5\,c^5\,d^8+114688\,a^2\,b^6\,c^6\,d^7-32768\,a\,b^7\,c^7\,d^6+4096\,b^8\,c^8\,d^5}\right)}^{1/4}\,\left(5120\,a^{11}\,b^4\,c^2\,d^{13}-40960\,a^{10}\,b^5\,c^3\,d^{12}+143360\,a^9\,b^6\,c^4\,d^{11}-286720\,a^8\,b^7\,c^5\,d^{10}+358400\,a^7\,b^8\,c^6\,d^9-286720\,a^6\,b^9\,c^7\,d^8+143360\,a^5\,b^{10}\,c^8\,d^7-40960\,a^4\,b^{11}\,c^9\,d^6+5120\,a^3\,b^{12}\,c^{10}\,d^5\right)}{a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d}-\frac{\sqrt{x}\,\left(6400\,a^{13}\,b^4\,c^2\,d^{14}-49664\,a^{12}\,b^5\,c^3\,d^{13}+167168\,a^{11}\,b^6\,c^4\,d^{12}-317440\,a^{10}\,b^7\,c^5\,d^{11}+369152\,a^9\,b^8\,c^6\,d^{10}-265216\,a^8\,b^9\,c^7\,d^9+111104\,a^7\,b^{10}\,c^8\,d^8-22528\,a^6\,b^{11}\,c^9\,d^7+1280\,a^5\,b^{12}\,c^{10}\,d^6-512\,a^4\,b^{13}\,c^{11}\,d^5+256\,a^3\,b^{14}\,c^{12}\,d^4\right)}{a^6\,d^7-6\,a^5\,b\,c\,d^6+15\,a^4\,b^2\,c^2\,d^5-20\,a^3\,b^3\,c^3\,d^4+15\,a^2\,b^4\,c^4\,d^3-6\,a\,b^5\,c^5\,d^2+b^6\,c^6\,d}\right)\,{\left(-\frac{625\,a^4\,c\,d^4-500\,a^3\,b\,c^2\,d^3+150\,a^2\,b^2\,c^3\,d^2-20\,a\,b^3\,c^4\,d+b^4\,c^5}{4096\,a^8\,d^{13}-32768\,a^7\,b\,c\,d^{12}+114688\,a^6\,b^2\,c^2\,d^{11}-229376\,a^5\,b^3\,c^3\,d^{10}+286720\,a^4\,b^4\,c^4\,d^9-229376\,a^3\,b^5\,c^5\,d^8+114688\,a^2\,b^6\,c^6\,d^7-32768\,a\,b^7\,c^7\,d^6+4096\,b^8\,c^8\,d^5}\right)}^{3/4}+\frac{2\,\left(320\,a^8\,b^3\,c^2\,d^5+256\,a^7\,b^4\,c^3\,d^4-369\,a^6\,b^5\,c^4\,d^3+131\,a^5\,b^6\,c^5\,d^2-19\,a^4\,b^7\,c^6\,d+a^3\,b^8\,c^7\right)}{a^3\,d^4-3\,a^2\,b\,c\,d^3+3\,a\,b^2\,c^2\,d^2-b^3\,c^3\,d}\right)\,{\left(-\frac{625\,a^4\,c\,d^4-500\,a^3\,b\,c^2\,d^3+150\,a^2\,b^2\,c^3\,d^2-20\,a\,b^3\,c^4\,d+b^4\,c^5}{4096\,a^8\,d^{13}-32768\,a^7\,b\,c\,d^{12}+114688\,a^6\,b^2\,c^2\,d^{11}-229376\,a^5\,b^3\,c^3\,d^{10}+286720\,a^4\,b^4\,c^4\,d^9-229376\,a^3\,b^5\,c^5\,d^8+114688\,a^2\,b^6\,c^6\,d^7-32768\,a\,b^7\,c^7\,d^6+4096\,b^8\,c^8\,d^5}\right)}^{1/4}-\frac{\sqrt{x}\,\left(400\,a^{10}\,b^3\,c^2\,d^6-160\,a^9\,b^4\,c^3\,d^5+641\,a^8\,b^5\,c^4\,d^4-500\,a^7\,b^6\,c^5\,d^3+150\,a^6\,b^7\,c^6\,d^2-20\,a^5\,b^8\,c^7\,d+a^4\,b^9\,c^8\right)}{a^6\,d^7-6\,a^5\,b\,c\,d^6+15\,a^4\,b^2\,c^2\,d^5-20\,a^3\,b^3\,c^3\,d^4+15\,a^2\,b^4\,c^4\,d^3-6\,a\,b^5\,c^5\,d^2+b^6\,c^6\,d}\right)\,{\left(-\frac{625\,a^4\,c\,d^4-500\,a^3\,b\,c^2\,d^3+150\,a^2\,b^2\,c^3\,d^2-20\,a\,b^3\,c^4\,d+b^4\,c^5}{4096\,a^8\,d^{13}-32768\,a^7\,b\,c\,d^{12}+114688\,a^6\,b^2\,c^2\,d^{11}-229376\,a^5\,b^3\,c^3\,d^{10}+286720\,a^4\,b^4\,c^4\,d^9-229376\,a^3\,b^5\,c^5\,d^8+114688\,a^2\,b^6\,c^6\,d^7-32768\,a\,b^7\,c^7\,d^6+4096\,b^8\,c^8\,d^5}\right)}^{1/4}}\right)\,{\left(-\frac{625\,a^4\,c\,d^4-500\,a^3\,b\,c^2\,d^3+150\,a^2\,b^2\,c^3\,d^2-20\,a\,b^3\,c^4\,d+b^4\,c^5}{4096\,a^8\,d^{13}-32768\,a^7\,b\,c\,d^{12}+114688\,a^6\,b^2\,c^2\,d^{11}-229376\,a^5\,b^3\,c^3\,d^{10}+286720\,a^4\,b^4\,c^4\,d^9-229376\,a^3\,b^5\,c^5\,d^8+114688\,a^2\,b^6\,c^6\,d^7-32768\,a\,b^7\,c^7\,d^6+4096\,b^8\,c^8\,d^5}\right)}^{1/4}\,2{}\mathrm{i}","Not used",1,"atan((((-a^5/(16*b^9*c^8 + 16*a^8*b*d^8 - 128*a^7*b^2*c*d^7 + 448*a^2*b^7*c^6*d^2 - 896*a^3*b^6*c^5*d^3 + 1120*a^4*b^5*c^4*d^4 - 896*a^5*b^4*c^3*d^5 + 448*a^6*b^3*c^2*d^6 - 128*a*b^8*c^7*d))^(1/4)*((2*(a^3*b^8*c^7 - 19*a^4*b^7*c^6*d + 131*a^5*b^6*c^5*d^2 - 369*a^6*b^5*c^4*d^3 + 256*a^7*b^4*c^3*d^4 + 320*a^8*b^3*c^2*d^5))/(a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3) + ((2*(-a^5/(16*b^9*c^8 + 16*a^8*b*d^8 - 128*a^7*b^2*c*d^7 + 448*a^2*b^7*c^6*d^2 - 896*a^3*b^6*c^5*d^3 + 1120*a^4*b^5*c^4*d^4 - 896*a^5*b^4*c^3*d^5 + 448*a^6*b^3*c^2*d^6 - 128*a*b^8*c^7*d))^(1/4)*(5120*a^3*b^12*c^10*d^5 - 40960*a^4*b^11*c^9*d^6 + 143360*a^5*b^10*c^8*d^7 - 286720*a^6*b^9*c^7*d^8 + 358400*a^7*b^8*c^6*d^9 - 286720*a^8*b^7*c^5*d^10 + 143360*a^9*b^6*c^4*d^11 - 40960*a^10*b^5*c^3*d^12 + 5120*a^11*b^4*c^2*d^13))/(a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3) + (x^(1/2)*(256*a^3*b^14*c^12*d^4 - 512*a^4*b^13*c^11*d^5 + 1280*a^5*b^12*c^10*d^6 - 22528*a^6*b^11*c^9*d^7 + 111104*a^7*b^10*c^8*d^8 - 265216*a^8*b^9*c^7*d^9 + 369152*a^9*b^8*c^6*d^10 - 317440*a^10*b^7*c^5*d^11 + 167168*a^11*b^6*c^4*d^12 - 49664*a^12*b^5*c^3*d^13 + 6400*a^13*b^4*c^2*d^14))/(a^6*d^7 + b^6*c^6*d - 6*a*b^5*c^5*d^2 + 15*a^2*b^4*c^4*d^3 - 20*a^3*b^3*c^3*d^4 + 15*a^4*b^2*c^2*d^5 - 6*a^5*b*c*d^6))*(-a^5/(16*b^9*c^8 + 16*a^8*b*d^8 - 128*a^7*b^2*c*d^7 + 448*a^2*b^7*c^6*d^2 - 896*a^3*b^6*c^5*d^3 + 1120*a^4*b^5*c^4*d^4 - 896*a^5*b^4*c^3*d^5 + 448*a^6*b^3*c^2*d^6 - 128*a*b^8*c^7*d))^(3/4)) + (x^(1/2)*(a^4*b^9*c^8 - 20*a^5*b^8*c^7*d + 150*a^6*b^7*c^6*d^2 - 500*a^7*b^6*c^5*d^3 + 641*a^8*b^5*c^4*d^4 - 160*a^9*b^4*c^3*d^5 + 400*a^10*b^3*c^2*d^6))/(a^6*d^7 + b^6*c^6*d - 6*a*b^5*c^5*d^2 + 15*a^2*b^4*c^4*d^3 - 20*a^3*b^3*c^3*d^4 + 15*a^4*b^2*c^2*d^5 - 6*a^5*b*c*d^6))*(-a^5/(16*b^9*c^8 + 16*a^8*b*d^8 - 128*a^7*b^2*c*d^7 + 448*a^2*b^7*c^6*d^2 - 896*a^3*b^6*c^5*d^3 + 1120*a^4*b^5*c^4*d^4 - 896*a^5*b^4*c^3*d^5 + 448*a^6*b^3*c^2*d^6 - 128*a*b^8*c^7*d))^(1/4)*1i - ((-a^5/(16*b^9*c^8 + 16*a^8*b*d^8 - 128*a^7*b^2*c*d^7 + 448*a^2*b^7*c^6*d^2 - 896*a^3*b^6*c^5*d^3 + 1120*a^4*b^5*c^4*d^4 - 896*a^5*b^4*c^3*d^5 + 448*a^6*b^3*c^2*d^6 - 128*a*b^8*c^7*d))^(1/4)*((2*(a^3*b^8*c^7 - 19*a^4*b^7*c^6*d + 131*a^5*b^6*c^5*d^2 - 369*a^6*b^5*c^4*d^3 + 256*a^7*b^4*c^3*d^4 + 320*a^8*b^3*c^2*d^5))/(a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3) + ((2*(-a^5/(16*b^9*c^8 + 16*a^8*b*d^8 - 128*a^7*b^2*c*d^7 + 448*a^2*b^7*c^6*d^2 - 896*a^3*b^6*c^5*d^3 + 1120*a^4*b^5*c^4*d^4 - 896*a^5*b^4*c^3*d^5 + 448*a^6*b^3*c^2*d^6 - 128*a*b^8*c^7*d))^(1/4)*(5120*a^3*b^12*c^10*d^5 - 40960*a^4*b^11*c^9*d^6 + 143360*a^5*b^10*c^8*d^7 - 286720*a^6*b^9*c^7*d^8 + 358400*a^7*b^8*c^6*d^9 - 286720*a^8*b^7*c^5*d^10 + 143360*a^9*b^6*c^4*d^11 - 40960*a^10*b^5*c^3*d^12 + 5120*a^11*b^4*c^2*d^13))/(a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3) - (x^(1/2)*(256*a^3*b^14*c^12*d^4 - 512*a^4*b^13*c^11*d^5 + 1280*a^5*b^12*c^10*d^6 - 22528*a^6*b^11*c^9*d^7 + 111104*a^7*b^10*c^8*d^8 - 265216*a^8*b^9*c^7*d^9 + 369152*a^9*b^8*c^6*d^10 - 317440*a^10*b^7*c^5*d^11 + 167168*a^11*b^6*c^4*d^12 - 49664*a^12*b^5*c^3*d^13 + 6400*a^13*b^4*c^2*d^14))/(a^6*d^7 + b^6*c^6*d - 6*a*b^5*c^5*d^2 + 15*a^2*b^4*c^4*d^3 - 20*a^3*b^3*c^3*d^4 + 15*a^4*b^2*c^2*d^5 - 6*a^5*b*c*d^6))*(-a^5/(16*b^9*c^8 + 16*a^8*b*d^8 - 128*a^7*b^2*c*d^7 + 448*a^2*b^7*c^6*d^2 - 896*a^3*b^6*c^5*d^3 + 1120*a^4*b^5*c^4*d^4 - 896*a^5*b^4*c^3*d^5 + 448*a^6*b^3*c^2*d^6 - 128*a*b^8*c^7*d))^(3/4)) - (x^(1/2)*(a^4*b^9*c^8 - 20*a^5*b^8*c^7*d + 150*a^6*b^7*c^6*d^2 - 500*a^7*b^6*c^5*d^3 + 641*a^8*b^5*c^4*d^4 - 160*a^9*b^4*c^3*d^5 + 400*a^10*b^3*c^2*d^6))/(a^6*d^7 + b^6*c^6*d - 6*a*b^5*c^5*d^2 + 15*a^2*b^4*c^4*d^3 - 20*a^3*b^3*c^3*d^4 + 15*a^4*b^2*c^2*d^5 - 6*a^5*b*c*d^6))*(-a^5/(16*b^9*c^8 + 16*a^8*b*d^8 - 128*a^7*b^2*c*d^7 + 448*a^2*b^7*c^6*d^2 - 896*a^3*b^6*c^5*d^3 + 1120*a^4*b^5*c^4*d^4 - 896*a^5*b^4*c^3*d^5 + 448*a^6*b^3*c^2*d^6 - 128*a*b^8*c^7*d))^(1/4)*1i)/(((-a^5/(16*b^9*c^8 + 16*a^8*b*d^8 - 128*a^7*b^2*c*d^7 + 448*a^2*b^7*c^6*d^2 - 896*a^3*b^6*c^5*d^3 + 1120*a^4*b^5*c^4*d^4 - 896*a^5*b^4*c^3*d^5 + 448*a^6*b^3*c^2*d^6 - 128*a*b^8*c^7*d))^(1/4)*((2*(a^3*b^8*c^7 - 19*a^4*b^7*c^6*d + 131*a^5*b^6*c^5*d^2 - 369*a^6*b^5*c^4*d^3 + 256*a^7*b^4*c^3*d^4 + 320*a^8*b^3*c^2*d^5))/(a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3) + ((2*(-a^5/(16*b^9*c^8 + 16*a^8*b*d^8 - 128*a^7*b^2*c*d^7 + 448*a^2*b^7*c^6*d^2 - 896*a^3*b^6*c^5*d^3 + 1120*a^4*b^5*c^4*d^4 - 896*a^5*b^4*c^3*d^5 + 448*a^6*b^3*c^2*d^6 - 128*a*b^8*c^7*d))^(1/4)*(5120*a^3*b^12*c^10*d^5 - 40960*a^4*b^11*c^9*d^6 + 143360*a^5*b^10*c^8*d^7 - 286720*a^6*b^9*c^7*d^8 + 358400*a^7*b^8*c^6*d^9 - 286720*a^8*b^7*c^5*d^10 + 143360*a^9*b^6*c^4*d^11 - 40960*a^10*b^5*c^3*d^12 + 5120*a^11*b^4*c^2*d^13))/(a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3) + (x^(1/2)*(256*a^3*b^14*c^12*d^4 - 512*a^4*b^13*c^11*d^5 + 1280*a^5*b^12*c^10*d^6 - 22528*a^6*b^11*c^9*d^7 + 111104*a^7*b^10*c^8*d^8 - 265216*a^8*b^9*c^7*d^9 + 369152*a^9*b^8*c^6*d^10 - 317440*a^10*b^7*c^5*d^11 + 167168*a^11*b^6*c^4*d^12 - 49664*a^12*b^5*c^3*d^13 + 6400*a^13*b^4*c^2*d^14))/(a^6*d^7 + b^6*c^6*d - 6*a*b^5*c^5*d^2 + 15*a^2*b^4*c^4*d^3 - 20*a^3*b^3*c^3*d^4 + 15*a^4*b^2*c^2*d^5 - 6*a^5*b*c*d^6))*(-a^5/(16*b^9*c^8 + 16*a^8*b*d^8 - 128*a^7*b^2*c*d^7 + 448*a^2*b^7*c^6*d^2 - 896*a^3*b^6*c^5*d^3 + 1120*a^4*b^5*c^4*d^4 - 896*a^5*b^4*c^3*d^5 + 448*a^6*b^3*c^2*d^6 - 128*a*b^8*c^7*d))^(3/4)) + (x^(1/2)*(a^4*b^9*c^8 - 20*a^5*b^8*c^7*d + 150*a^6*b^7*c^6*d^2 - 500*a^7*b^6*c^5*d^3 + 641*a^8*b^5*c^4*d^4 - 160*a^9*b^4*c^3*d^5 + 400*a^10*b^3*c^2*d^6))/(a^6*d^7 + b^6*c^6*d - 6*a*b^5*c^5*d^2 + 15*a^2*b^4*c^4*d^3 - 20*a^3*b^3*c^3*d^4 + 15*a^4*b^2*c^2*d^5 - 6*a^5*b*c*d^6))*(-a^5/(16*b^9*c^8 + 16*a^8*b*d^8 - 128*a^7*b^2*c*d^7 + 448*a^2*b^7*c^6*d^2 - 896*a^3*b^6*c^5*d^3 + 1120*a^4*b^5*c^4*d^4 - 896*a^5*b^4*c^3*d^5 + 448*a^6*b^3*c^2*d^6 - 128*a*b^8*c^7*d))^(1/4) + ((-a^5/(16*b^9*c^8 + 16*a^8*b*d^8 - 128*a^7*b^2*c*d^7 + 448*a^2*b^7*c^6*d^2 - 896*a^3*b^6*c^5*d^3 + 1120*a^4*b^5*c^4*d^4 - 896*a^5*b^4*c^3*d^5 + 448*a^6*b^3*c^2*d^6 - 128*a*b^8*c^7*d))^(1/4)*((2*(a^3*b^8*c^7 - 19*a^4*b^7*c^6*d + 131*a^5*b^6*c^5*d^2 - 369*a^6*b^5*c^4*d^3 + 256*a^7*b^4*c^3*d^4 + 320*a^8*b^3*c^2*d^5))/(a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3) + ((2*(-a^5/(16*b^9*c^8 + 16*a^8*b*d^8 - 128*a^7*b^2*c*d^7 + 448*a^2*b^7*c^6*d^2 - 896*a^3*b^6*c^5*d^3 + 1120*a^4*b^5*c^4*d^4 - 896*a^5*b^4*c^3*d^5 + 448*a^6*b^3*c^2*d^6 - 128*a*b^8*c^7*d))^(1/4)*(5120*a^3*b^12*c^10*d^5 - 40960*a^4*b^11*c^9*d^6 + 143360*a^5*b^10*c^8*d^7 - 286720*a^6*b^9*c^7*d^8 + 358400*a^7*b^8*c^6*d^9 - 286720*a^8*b^7*c^5*d^10 + 143360*a^9*b^6*c^4*d^11 - 40960*a^10*b^5*c^3*d^12 + 5120*a^11*b^4*c^2*d^13))/(a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3) - (x^(1/2)*(256*a^3*b^14*c^12*d^4 - 512*a^4*b^13*c^11*d^5 + 1280*a^5*b^12*c^10*d^6 - 22528*a^6*b^11*c^9*d^7 + 111104*a^7*b^10*c^8*d^8 - 265216*a^8*b^9*c^7*d^9 + 369152*a^9*b^8*c^6*d^10 - 317440*a^10*b^7*c^5*d^11 + 167168*a^11*b^6*c^4*d^12 - 49664*a^12*b^5*c^3*d^13 + 6400*a^13*b^4*c^2*d^14))/(a^6*d^7 + b^6*c^6*d - 6*a*b^5*c^5*d^2 + 15*a^2*b^4*c^4*d^3 - 20*a^3*b^3*c^3*d^4 + 15*a^4*b^2*c^2*d^5 - 6*a^5*b*c*d^6))*(-a^5/(16*b^9*c^8 + 16*a^8*b*d^8 - 128*a^7*b^2*c*d^7 + 448*a^2*b^7*c^6*d^2 - 896*a^3*b^6*c^5*d^3 + 1120*a^4*b^5*c^4*d^4 - 896*a^5*b^4*c^3*d^5 + 448*a^6*b^3*c^2*d^6 - 128*a*b^8*c^7*d))^(3/4)) - (x^(1/2)*(a^4*b^9*c^8 - 20*a^5*b^8*c^7*d + 150*a^6*b^7*c^6*d^2 - 500*a^7*b^6*c^5*d^3 + 641*a^8*b^5*c^4*d^4 - 160*a^9*b^4*c^3*d^5 + 400*a^10*b^3*c^2*d^6))/(a^6*d^7 + b^6*c^6*d - 6*a*b^5*c^5*d^2 + 15*a^2*b^4*c^4*d^3 - 20*a^3*b^3*c^3*d^4 + 15*a^4*b^2*c^2*d^5 - 6*a^5*b*c*d^6))*(-a^5/(16*b^9*c^8 + 16*a^8*b*d^8 - 128*a^7*b^2*c*d^7 + 448*a^2*b^7*c^6*d^2 - 896*a^3*b^6*c^5*d^3 + 1120*a^4*b^5*c^4*d^4 - 896*a^5*b^4*c^3*d^5 + 448*a^6*b^3*c^2*d^6 - 128*a*b^8*c^7*d))^(1/4)))*(-a^5/(16*b^9*c^8 + 16*a^8*b*d^8 - 128*a^7*b^2*c*d^7 + 448*a^2*b^7*c^6*d^2 - 896*a^3*b^6*c^5*d^3 + 1120*a^4*b^5*c^4*d^4 - 896*a^5*b^4*c^3*d^5 + 448*a^6*b^3*c^2*d^6 - 128*a*b^8*c^7*d))^(1/4)*2i + 2*atan((((-a^5/(16*b^9*c^8 + 16*a^8*b*d^8 - 128*a^7*b^2*c*d^7 + 448*a^2*b^7*c^6*d^2 - 896*a^3*b^6*c^5*d^3 + 1120*a^4*b^5*c^4*d^4 - 896*a^5*b^4*c^3*d^5 + 448*a^6*b^3*c^2*d^6 - 128*a*b^8*c^7*d))^(1/4)*((2*(a^3*b^8*c^7 - 19*a^4*b^7*c^6*d + 131*a^5*b^6*c^5*d^2 - 369*a^6*b^5*c^4*d^3 + 256*a^7*b^4*c^3*d^4 + 320*a^8*b^3*c^2*d^5))/(a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3) - (((-a^5/(16*b^9*c^8 + 16*a^8*b*d^8 - 128*a^7*b^2*c*d^7 + 448*a^2*b^7*c^6*d^2 - 896*a^3*b^6*c^5*d^3 + 1120*a^4*b^5*c^4*d^4 - 896*a^5*b^4*c^3*d^5 + 448*a^6*b^3*c^2*d^6 - 128*a*b^8*c^7*d))^(1/4)*(5120*a^3*b^12*c^10*d^5 - 40960*a^4*b^11*c^9*d^6 + 143360*a^5*b^10*c^8*d^7 - 286720*a^6*b^9*c^7*d^8 + 358400*a^7*b^8*c^6*d^9 - 286720*a^8*b^7*c^5*d^10 + 143360*a^9*b^6*c^4*d^11 - 40960*a^10*b^5*c^3*d^12 + 5120*a^11*b^4*c^2*d^13)*2i)/(a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3) + (x^(1/2)*(256*a^3*b^14*c^12*d^4 - 512*a^4*b^13*c^11*d^5 + 1280*a^5*b^12*c^10*d^6 - 22528*a^6*b^11*c^9*d^7 + 111104*a^7*b^10*c^8*d^8 - 265216*a^8*b^9*c^7*d^9 + 369152*a^9*b^8*c^6*d^10 - 317440*a^10*b^7*c^5*d^11 + 167168*a^11*b^6*c^4*d^12 - 49664*a^12*b^5*c^3*d^13 + 6400*a^13*b^4*c^2*d^14))/(a^6*d^7 + b^6*c^6*d - 6*a*b^5*c^5*d^2 + 15*a^2*b^4*c^4*d^3 - 20*a^3*b^3*c^3*d^4 + 15*a^4*b^2*c^2*d^5 - 6*a^5*b*c*d^6))*(-a^5/(16*b^9*c^8 + 16*a^8*b*d^8 - 128*a^7*b^2*c*d^7 + 448*a^2*b^7*c^6*d^2 - 896*a^3*b^6*c^5*d^3 + 1120*a^4*b^5*c^4*d^4 - 896*a^5*b^4*c^3*d^5 + 448*a^6*b^3*c^2*d^6 - 128*a*b^8*c^7*d))^(3/4)*1i)*1i + (x^(1/2)*(a^4*b^9*c^8 - 20*a^5*b^8*c^7*d + 150*a^6*b^7*c^6*d^2 - 500*a^7*b^6*c^5*d^3 + 641*a^8*b^5*c^4*d^4 - 160*a^9*b^4*c^3*d^5 + 400*a^10*b^3*c^2*d^6))/(a^6*d^7 + b^6*c^6*d - 6*a*b^5*c^5*d^2 + 15*a^2*b^4*c^4*d^3 - 20*a^3*b^3*c^3*d^4 + 15*a^4*b^2*c^2*d^5 - 6*a^5*b*c*d^6))*(-a^5/(16*b^9*c^8 + 16*a^8*b*d^8 - 128*a^7*b^2*c*d^7 + 448*a^2*b^7*c^6*d^2 - 896*a^3*b^6*c^5*d^3 + 1120*a^4*b^5*c^4*d^4 - 896*a^5*b^4*c^3*d^5 + 448*a^6*b^3*c^2*d^6 - 128*a*b^8*c^7*d))^(1/4) - ((-a^5/(16*b^9*c^8 + 16*a^8*b*d^8 - 128*a^7*b^2*c*d^7 + 448*a^2*b^7*c^6*d^2 - 896*a^3*b^6*c^5*d^3 + 1120*a^4*b^5*c^4*d^4 - 896*a^5*b^4*c^3*d^5 + 448*a^6*b^3*c^2*d^6 - 128*a*b^8*c^7*d))^(1/4)*((2*(a^3*b^8*c^7 - 19*a^4*b^7*c^6*d + 131*a^5*b^6*c^5*d^2 - 369*a^6*b^5*c^4*d^3 + 256*a^7*b^4*c^3*d^4 + 320*a^8*b^3*c^2*d^5))/(a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3) - (((-a^5/(16*b^9*c^8 + 16*a^8*b*d^8 - 128*a^7*b^2*c*d^7 + 448*a^2*b^7*c^6*d^2 - 896*a^3*b^6*c^5*d^3 + 1120*a^4*b^5*c^4*d^4 - 896*a^5*b^4*c^3*d^5 + 448*a^6*b^3*c^2*d^6 - 128*a*b^8*c^7*d))^(1/4)*(5120*a^3*b^12*c^10*d^5 - 40960*a^4*b^11*c^9*d^6 + 143360*a^5*b^10*c^8*d^7 - 286720*a^6*b^9*c^7*d^8 + 358400*a^7*b^8*c^6*d^9 - 286720*a^8*b^7*c^5*d^10 + 143360*a^9*b^6*c^4*d^11 - 40960*a^10*b^5*c^3*d^12 + 5120*a^11*b^4*c^2*d^13)*2i)/(a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3) - (x^(1/2)*(256*a^3*b^14*c^12*d^4 - 512*a^4*b^13*c^11*d^5 + 1280*a^5*b^12*c^10*d^6 - 22528*a^6*b^11*c^9*d^7 + 111104*a^7*b^10*c^8*d^8 - 265216*a^8*b^9*c^7*d^9 + 369152*a^9*b^8*c^6*d^10 - 317440*a^10*b^7*c^5*d^11 + 167168*a^11*b^6*c^4*d^12 - 49664*a^12*b^5*c^3*d^13 + 6400*a^13*b^4*c^2*d^14))/(a^6*d^7 + b^6*c^6*d - 6*a*b^5*c^5*d^2 + 15*a^2*b^4*c^4*d^3 - 20*a^3*b^3*c^3*d^4 + 15*a^4*b^2*c^2*d^5 - 6*a^5*b*c*d^6))*(-a^5/(16*b^9*c^8 + 16*a^8*b*d^8 - 128*a^7*b^2*c*d^7 + 448*a^2*b^7*c^6*d^2 - 896*a^3*b^6*c^5*d^3 + 1120*a^4*b^5*c^4*d^4 - 896*a^5*b^4*c^3*d^5 + 448*a^6*b^3*c^2*d^6 - 128*a*b^8*c^7*d))^(3/4)*1i)*1i - (x^(1/2)*(a^4*b^9*c^8 - 20*a^5*b^8*c^7*d + 150*a^6*b^7*c^6*d^2 - 500*a^7*b^6*c^5*d^3 + 641*a^8*b^5*c^4*d^4 - 160*a^9*b^4*c^3*d^5 + 400*a^10*b^3*c^2*d^6))/(a^6*d^7 + b^6*c^6*d - 6*a*b^5*c^5*d^2 + 15*a^2*b^4*c^4*d^3 - 20*a^3*b^3*c^3*d^4 + 15*a^4*b^2*c^2*d^5 - 6*a^5*b*c*d^6))*(-a^5/(16*b^9*c^8 + 16*a^8*b*d^8 - 128*a^7*b^2*c*d^7 + 448*a^2*b^7*c^6*d^2 - 896*a^3*b^6*c^5*d^3 + 1120*a^4*b^5*c^4*d^4 - 896*a^5*b^4*c^3*d^5 + 448*a^6*b^3*c^2*d^6 - 128*a*b^8*c^7*d))^(1/4))/(((-a^5/(16*b^9*c^8 + 16*a^8*b*d^8 - 128*a^7*b^2*c*d^7 + 448*a^2*b^7*c^6*d^2 - 896*a^3*b^6*c^5*d^3 + 1120*a^4*b^5*c^4*d^4 - 896*a^5*b^4*c^3*d^5 + 448*a^6*b^3*c^2*d^6 - 128*a*b^8*c^7*d))^(1/4)*((2*(a^3*b^8*c^7 - 19*a^4*b^7*c^6*d + 131*a^5*b^6*c^5*d^2 - 369*a^6*b^5*c^4*d^3 + 256*a^7*b^4*c^3*d^4 + 320*a^8*b^3*c^2*d^5))/(a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3) - (((-a^5/(16*b^9*c^8 + 16*a^8*b*d^8 - 128*a^7*b^2*c*d^7 + 448*a^2*b^7*c^6*d^2 - 896*a^3*b^6*c^5*d^3 + 1120*a^4*b^5*c^4*d^4 - 896*a^5*b^4*c^3*d^5 + 448*a^6*b^3*c^2*d^6 - 128*a*b^8*c^7*d))^(1/4)*(5120*a^3*b^12*c^10*d^5 - 40960*a^4*b^11*c^9*d^6 + 143360*a^5*b^10*c^8*d^7 - 286720*a^6*b^9*c^7*d^8 + 358400*a^7*b^8*c^6*d^9 - 286720*a^8*b^7*c^5*d^10 + 143360*a^9*b^6*c^4*d^11 - 40960*a^10*b^5*c^3*d^12 + 5120*a^11*b^4*c^2*d^13)*2i)/(a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3) + (x^(1/2)*(256*a^3*b^14*c^12*d^4 - 512*a^4*b^13*c^11*d^5 + 1280*a^5*b^12*c^10*d^6 - 22528*a^6*b^11*c^9*d^7 + 111104*a^7*b^10*c^8*d^8 - 265216*a^8*b^9*c^7*d^9 + 369152*a^9*b^8*c^6*d^10 - 317440*a^10*b^7*c^5*d^11 + 167168*a^11*b^6*c^4*d^12 - 49664*a^12*b^5*c^3*d^13 + 6400*a^13*b^4*c^2*d^14))/(a^6*d^7 + b^6*c^6*d - 6*a*b^5*c^5*d^2 + 15*a^2*b^4*c^4*d^3 - 20*a^3*b^3*c^3*d^4 + 15*a^4*b^2*c^2*d^5 - 6*a^5*b*c*d^6))*(-a^5/(16*b^9*c^8 + 16*a^8*b*d^8 - 128*a^7*b^2*c*d^7 + 448*a^2*b^7*c^6*d^2 - 896*a^3*b^6*c^5*d^3 + 1120*a^4*b^5*c^4*d^4 - 896*a^5*b^4*c^3*d^5 + 448*a^6*b^3*c^2*d^6 - 128*a*b^8*c^7*d))^(3/4)*1i)*1i + (x^(1/2)*(a^4*b^9*c^8 - 20*a^5*b^8*c^7*d + 150*a^6*b^7*c^6*d^2 - 500*a^7*b^6*c^5*d^3 + 641*a^8*b^5*c^4*d^4 - 160*a^9*b^4*c^3*d^5 + 400*a^10*b^3*c^2*d^6))/(a^6*d^7 + b^6*c^6*d - 6*a*b^5*c^5*d^2 + 15*a^2*b^4*c^4*d^3 - 20*a^3*b^3*c^3*d^4 + 15*a^4*b^2*c^2*d^5 - 6*a^5*b*c*d^6))*(-a^5/(16*b^9*c^8 + 16*a^8*b*d^8 - 128*a^7*b^2*c*d^7 + 448*a^2*b^7*c^6*d^2 - 896*a^3*b^6*c^5*d^3 + 1120*a^4*b^5*c^4*d^4 - 896*a^5*b^4*c^3*d^5 + 448*a^6*b^3*c^2*d^6 - 128*a*b^8*c^7*d))^(1/4)*1i + ((-a^5/(16*b^9*c^8 + 16*a^8*b*d^8 - 128*a^7*b^2*c*d^7 + 448*a^2*b^7*c^6*d^2 - 896*a^3*b^6*c^5*d^3 + 1120*a^4*b^5*c^4*d^4 - 896*a^5*b^4*c^3*d^5 + 448*a^6*b^3*c^2*d^6 - 128*a*b^8*c^7*d))^(1/4)*((2*(a^3*b^8*c^7 - 19*a^4*b^7*c^6*d + 131*a^5*b^6*c^5*d^2 - 369*a^6*b^5*c^4*d^3 + 256*a^7*b^4*c^3*d^4 + 320*a^8*b^3*c^2*d^5))/(a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3) - (((-a^5/(16*b^9*c^8 + 16*a^8*b*d^8 - 128*a^7*b^2*c*d^7 + 448*a^2*b^7*c^6*d^2 - 896*a^3*b^6*c^5*d^3 + 1120*a^4*b^5*c^4*d^4 - 896*a^5*b^4*c^3*d^5 + 448*a^6*b^3*c^2*d^6 - 128*a*b^8*c^7*d))^(1/4)*(5120*a^3*b^12*c^10*d^5 - 40960*a^4*b^11*c^9*d^6 + 143360*a^5*b^10*c^8*d^7 - 286720*a^6*b^9*c^7*d^8 + 358400*a^7*b^8*c^6*d^9 - 286720*a^8*b^7*c^5*d^10 + 143360*a^9*b^6*c^4*d^11 - 40960*a^10*b^5*c^3*d^12 + 5120*a^11*b^4*c^2*d^13)*2i)/(a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3) - (x^(1/2)*(256*a^3*b^14*c^12*d^4 - 512*a^4*b^13*c^11*d^5 + 1280*a^5*b^12*c^10*d^6 - 22528*a^6*b^11*c^9*d^7 + 111104*a^7*b^10*c^8*d^8 - 265216*a^8*b^9*c^7*d^9 + 369152*a^9*b^8*c^6*d^10 - 317440*a^10*b^7*c^5*d^11 + 167168*a^11*b^6*c^4*d^12 - 49664*a^12*b^5*c^3*d^13 + 6400*a^13*b^4*c^2*d^14))/(a^6*d^7 + b^6*c^6*d - 6*a*b^5*c^5*d^2 + 15*a^2*b^4*c^4*d^3 - 20*a^3*b^3*c^3*d^4 + 15*a^4*b^2*c^2*d^5 - 6*a^5*b*c*d^6))*(-a^5/(16*b^9*c^8 + 16*a^8*b*d^8 - 128*a^7*b^2*c*d^7 + 448*a^2*b^7*c^6*d^2 - 896*a^3*b^6*c^5*d^3 + 1120*a^4*b^5*c^4*d^4 - 896*a^5*b^4*c^3*d^5 + 448*a^6*b^3*c^2*d^6 - 128*a*b^8*c^7*d))^(3/4)*1i)*1i - (x^(1/2)*(a^4*b^9*c^8 - 20*a^5*b^8*c^7*d + 150*a^6*b^7*c^6*d^2 - 500*a^7*b^6*c^5*d^3 + 641*a^8*b^5*c^4*d^4 - 160*a^9*b^4*c^3*d^5 + 400*a^10*b^3*c^2*d^6))/(a^6*d^7 + b^6*c^6*d - 6*a*b^5*c^5*d^2 + 15*a^2*b^4*c^4*d^3 - 20*a^3*b^3*c^3*d^4 + 15*a^4*b^2*c^2*d^5 - 6*a^5*b*c*d^6))*(-a^5/(16*b^9*c^8 + 16*a^8*b*d^8 - 128*a^7*b^2*c*d^7 + 448*a^2*b^7*c^6*d^2 - 896*a^3*b^6*c^5*d^3 + 1120*a^4*b^5*c^4*d^4 - 896*a^5*b^4*c^3*d^5 + 448*a^6*b^3*c^2*d^6 - 128*a*b^8*c^7*d))^(1/4)*1i))*(-a^5/(16*b^9*c^8 + 16*a^8*b*d^8 - 128*a^7*b^2*c*d^7 + 448*a^2*b^7*c^6*d^2 - 896*a^3*b^6*c^5*d^3 + 1120*a^4*b^5*c^4*d^4 - 896*a^5*b^4*c^3*d^5 + 448*a^6*b^3*c^2*d^6 - 128*a*b^8*c^7*d))^(1/4) + atan((((((2*(-(b^4*c^5 + 625*a^4*c*d^4 - 500*a^3*b*c^2*d^3 + 150*a^2*b^2*c^3*d^2 - 20*a*b^3*c^4*d)/(4096*a^8*d^13 + 4096*b^8*c^8*d^5 - 32768*a*b^7*c^7*d^6 + 114688*a^2*b^6*c^6*d^7 - 229376*a^3*b^5*c^5*d^8 + 286720*a^4*b^4*c^4*d^9 - 229376*a^5*b^3*c^3*d^10 + 114688*a^6*b^2*c^2*d^11 - 32768*a^7*b*c*d^12))^(1/4)*(5120*a^3*b^12*c^10*d^5 - 40960*a^4*b^11*c^9*d^6 + 143360*a^5*b^10*c^8*d^7 - 286720*a^6*b^9*c^7*d^8 + 358400*a^7*b^8*c^6*d^9 - 286720*a^8*b^7*c^5*d^10 + 143360*a^9*b^6*c^4*d^11 - 40960*a^10*b^5*c^3*d^12 + 5120*a^11*b^4*c^2*d^13))/(a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3) + (x^(1/2)*(256*a^3*b^14*c^12*d^4 - 512*a^4*b^13*c^11*d^5 + 1280*a^5*b^12*c^10*d^6 - 22528*a^6*b^11*c^9*d^7 + 111104*a^7*b^10*c^8*d^8 - 265216*a^8*b^9*c^7*d^9 + 369152*a^9*b^8*c^6*d^10 - 317440*a^10*b^7*c^5*d^11 + 167168*a^11*b^6*c^4*d^12 - 49664*a^12*b^5*c^3*d^13 + 6400*a^13*b^4*c^2*d^14))/(a^6*d^7 + b^6*c^6*d - 6*a*b^5*c^5*d^2 + 15*a^2*b^4*c^4*d^3 - 20*a^3*b^3*c^3*d^4 + 15*a^4*b^2*c^2*d^5 - 6*a^5*b*c*d^6))*(-(b^4*c^5 + 625*a^4*c*d^4 - 500*a^3*b*c^2*d^3 + 150*a^2*b^2*c^3*d^2 - 20*a*b^3*c^4*d)/(4096*a^8*d^13 + 4096*b^8*c^8*d^5 - 32768*a*b^7*c^7*d^6 + 114688*a^2*b^6*c^6*d^7 - 229376*a^3*b^5*c^5*d^8 + 286720*a^4*b^4*c^4*d^9 - 229376*a^5*b^3*c^3*d^10 + 114688*a^6*b^2*c^2*d^11 - 32768*a^7*b*c*d^12))^(3/4) + (2*(a^3*b^8*c^7 - 19*a^4*b^7*c^6*d + 131*a^5*b^6*c^5*d^2 - 369*a^6*b^5*c^4*d^3 + 256*a^7*b^4*c^3*d^4 + 320*a^8*b^3*c^2*d^5))/(a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3))*(-(b^4*c^5 + 625*a^4*c*d^4 - 500*a^3*b*c^2*d^3 + 150*a^2*b^2*c^3*d^2 - 20*a*b^3*c^4*d)/(4096*a^8*d^13 + 4096*b^8*c^8*d^5 - 32768*a*b^7*c^7*d^6 + 114688*a^2*b^6*c^6*d^7 - 229376*a^3*b^5*c^5*d^8 + 286720*a^4*b^4*c^4*d^9 - 229376*a^5*b^3*c^3*d^10 + 114688*a^6*b^2*c^2*d^11 - 32768*a^7*b*c*d^12))^(1/4) + (x^(1/2)*(a^4*b^9*c^8 - 20*a^5*b^8*c^7*d + 150*a^6*b^7*c^6*d^2 - 500*a^7*b^6*c^5*d^3 + 641*a^8*b^5*c^4*d^4 - 160*a^9*b^4*c^3*d^5 + 400*a^10*b^3*c^2*d^6))/(a^6*d^7 + b^6*c^6*d - 6*a*b^5*c^5*d^2 + 15*a^2*b^4*c^4*d^3 - 20*a^3*b^3*c^3*d^4 + 15*a^4*b^2*c^2*d^5 - 6*a^5*b*c*d^6))*(-(b^4*c^5 + 625*a^4*c*d^4 - 500*a^3*b*c^2*d^3 + 150*a^2*b^2*c^3*d^2 - 20*a*b^3*c^4*d)/(4096*a^8*d^13 + 4096*b^8*c^8*d^5 - 32768*a*b^7*c^7*d^6 + 114688*a^2*b^6*c^6*d^7 - 229376*a^3*b^5*c^5*d^8 + 286720*a^4*b^4*c^4*d^9 - 229376*a^5*b^3*c^3*d^10 + 114688*a^6*b^2*c^2*d^11 - 32768*a^7*b*c*d^12))^(1/4)*1i - ((((2*(-(b^4*c^5 + 625*a^4*c*d^4 - 500*a^3*b*c^2*d^3 + 150*a^2*b^2*c^3*d^2 - 20*a*b^3*c^4*d)/(4096*a^8*d^13 + 4096*b^8*c^8*d^5 - 32768*a*b^7*c^7*d^6 + 114688*a^2*b^6*c^6*d^7 - 229376*a^3*b^5*c^5*d^8 + 286720*a^4*b^4*c^4*d^9 - 229376*a^5*b^3*c^3*d^10 + 114688*a^6*b^2*c^2*d^11 - 32768*a^7*b*c*d^12))^(1/4)*(5120*a^3*b^12*c^10*d^5 - 40960*a^4*b^11*c^9*d^6 + 143360*a^5*b^10*c^8*d^7 - 286720*a^6*b^9*c^7*d^8 + 358400*a^7*b^8*c^6*d^9 - 286720*a^8*b^7*c^5*d^10 + 143360*a^9*b^6*c^4*d^11 - 40960*a^10*b^5*c^3*d^12 + 5120*a^11*b^4*c^2*d^13))/(a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3) - (x^(1/2)*(256*a^3*b^14*c^12*d^4 - 512*a^4*b^13*c^11*d^5 + 1280*a^5*b^12*c^10*d^6 - 22528*a^6*b^11*c^9*d^7 + 111104*a^7*b^10*c^8*d^8 - 265216*a^8*b^9*c^7*d^9 + 369152*a^9*b^8*c^6*d^10 - 317440*a^10*b^7*c^5*d^11 + 167168*a^11*b^6*c^4*d^12 - 49664*a^12*b^5*c^3*d^13 + 6400*a^13*b^4*c^2*d^14))/(a^6*d^7 + b^6*c^6*d - 6*a*b^5*c^5*d^2 + 15*a^2*b^4*c^4*d^3 - 20*a^3*b^3*c^3*d^4 + 15*a^4*b^2*c^2*d^5 - 6*a^5*b*c*d^6))*(-(b^4*c^5 + 625*a^4*c*d^4 - 500*a^3*b*c^2*d^3 + 150*a^2*b^2*c^3*d^2 - 20*a*b^3*c^4*d)/(4096*a^8*d^13 + 4096*b^8*c^8*d^5 - 32768*a*b^7*c^7*d^6 + 114688*a^2*b^6*c^6*d^7 - 229376*a^3*b^5*c^5*d^8 + 286720*a^4*b^4*c^4*d^9 - 229376*a^5*b^3*c^3*d^10 + 114688*a^6*b^2*c^2*d^11 - 32768*a^7*b*c*d^12))^(3/4) + (2*(a^3*b^8*c^7 - 19*a^4*b^7*c^6*d + 131*a^5*b^6*c^5*d^2 - 369*a^6*b^5*c^4*d^3 + 256*a^7*b^4*c^3*d^4 + 320*a^8*b^3*c^2*d^5))/(a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3))*(-(b^4*c^5 + 625*a^4*c*d^4 - 500*a^3*b*c^2*d^3 + 150*a^2*b^2*c^3*d^2 - 20*a*b^3*c^4*d)/(4096*a^8*d^13 + 4096*b^8*c^8*d^5 - 32768*a*b^7*c^7*d^6 + 114688*a^2*b^6*c^6*d^7 - 229376*a^3*b^5*c^5*d^8 + 286720*a^4*b^4*c^4*d^9 - 229376*a^5*b^3*c^3*d^10 + 114688*a^6*b^2*c^2*d^11 - 32768*a^7*b*c*d^12))^(1/4) - (x^(1/2)*(a^4*b^9*c^8 - 20*a^5*b^8*c^7*d + 150*a^6*b^7*c^6*d^2 - 500*a^7*b^6*c^5*d^3 + 641*a^8*b^5*c^4*d^4 - 160*a^9*b^4*c^3*d^5 + 400*a^10*b^3*c^2*d^6))/(a^6*d^7 + b^6*c^6*d - 6*a*b^5*c^5*d^2 + 15*a^2*b^4*c^4*d^3 - 20*a^3*b^3*c^3*d^4 + 15*a^4*b^2*c^2*d^5 - 6*a^5*b*c*d^6))*(-(b^4*c^5 + 625*a^4*c*d^4 - 500*a^3*b*c^2*d^3 + 150*a^2*b^2*c^3*d^2 - 20*a*b^3*c^4*d)/(4096*a^8*d^13 + 4096*b^8*c^8*d^5 - 32768*a*b^7*c^7*d^6 + 114688*a^2*b^6*c^6*d^7 - 229376*a^3*b^5*c^5*d^8 + 286720*a^4*b^4*c^4*d^9 - 229376*a^5*b^3*c^3*d^10 + 114688*a^6*b^2*c^2*d^11 - 32768*a^7*b*c*d^12))^(1/4)*1i)/(((((2*(-(b^4*c^5 + 625*a^4*c*d^4 - 500*a^3*b*c^2*d^3 + 150*a^2*b^2*c^3*d^2 - 20*a*b^3*c^4*d)/(4096*a^8*d^13 + 4096*b^8*c^8*d^5 - 32768*a*b^7*c^7*d^6 + 114688*a^2*b^6*c^6*d^7 - 229376*a^3*b^5*c^5*d^8 + 286720*a^4*b^4*c^4*d^9 - 229376*a^5*b^3*c^3*d^10 + 114688*a^6*b^2*c^2*d^11 - 32768*a^7*b*c*d^12))^(1/4)*(5120*a^3*b^12*c^10*d^5 - 40960*a^4*b^11*c^9*d^6 + 143360*a^5*b^10*c^8*d^7 - 286720*a^6*b^9*c^7*d^8 + 358400*a^7*b^8*c^6*d^9 - 286720*a^8*b^7*c^5*d^10 + 143360*a^9*b^6*c^4*d^11 - 40960*a^10*b^5*c^3*d^12 + 5120*a^11*b^4*c^2*d^13))/(a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3) + (x^(1/2)*(256*a^3*b^14*c^12*d^4 - 512*a^4*b^13*c^11*d^5 + 1280*a^5*b^12*c^10*d^6 - 22528*a^6*b^11*c^9*d^7 + 111104*a^7*b^10*c^8*d^8 - 265216*a^8*b^9*c^7*d^9 + 369152*a^9*b^8*c^6*d^10 - 317440*a^10*b^7*c^5*d^11 + 167168*a^11*b^6*c^4*d^12 - 49664*a^12*b^5*c^3*d^13 + 6400*a^13*b^4*c^2*d^14))/(a^6*d^7 + b^6*c^6*d - 6*a*b^5*c^5*d^2 + 15*a^2*b^4*c^4*d^3 - 20*a^3*b^3*c^3*d^4 + 15*a^4*b^2*c^2*d^5 - 6*a^5*b*c*d^6))*(-(b^4*c^5 + 625*a^4*c*d^4 - 500*a^3*b*c^2*d^3 + 150*a^2*b^2*c^3*d^2 - 20*a*b^3*c^4*d)/(4096*a^8*d^13 + 4096*b^8*c^8*d^5 - 32768*a*b^7*c^7*d^6 + 114688*a^2*b^6*c^6*d^7 - 229376*a^3*b^5*c^5*d^8 + 286720*a^4*b^4*c^4*d^9 - 229376*a^5*b^3*c^3*d^10 + 114688*a^6*b^2*c^2*d^11 - 32768*a^7*b*c*d^12))^(3/4) + (2*(a^3*b^8*c^7 - 19*a^4*b^7*c^6*d + 131*a^5*b^6*c^5*d^2 - 369*a^6*b^5*c^4*d^3 + 256*a^7*b^4*c^3*d^4 + 320*a^8*b^3*c^2*d^5))/(a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3))*(-(b^4*c^5 + 625*a^4*c*d^4 - 500*a^3*b*c^2*d^3 + 150*a^2*b^2*c^3*d^2 - 20*a*b^3*c^4*d)/(4096*a^8*d^13 + 4096*b^8*c^8*d^5 - 32768*a*b^7*c^7*d^6 + 114688*a^2*b^6*c^6*d^7 - 229376*a^3*b^5*c^5*d^8 + 286720*a^4*b^4*c^4*d^9 - 229376*a^5*b^3*c^3*d^10 + 114688*a^6*b^2*c^2*d^11 - 32768*a^7*b*c*d^12))^(1/4) + (x^(1/2)*(a^4*b^9*c^8 - 20*a^5*b^8*c^7*d + 150*a^6*b^7*c^6*d^2 - 500*a^7*b^6*c^5*d^3 + 641*a^8*b^5*c^4*d^4 - 160*a^9*b^4*c^3*d^5 + 400*a^10*b^3*c^2*d^6))/(a^6*d^7 + b^6*c^6*d - 6*a*b^5*c^5*d^2 + 15*a^2*b^4*c^4*d^3 - 20*a^3*b^3*c^3*d^4 + 15*a^4*b^2*c^2*d^5 - 6*a^5*b*c*d^6))*(-(b^4*c^5 + 625*a^4*c*d^4 - 500*a^3*b*c^2*d^3 + 150*a^2*b^2*c^3*d^2 - 20*a*b^3*c^4*d)/(4096*a^8*d^13 + 4096*b^8*c^8*d^5 - 32768*a*b^7*c^7*d^6 + 114688*a^2*b^6*c^6*d^7 - 229376*a^3*b^5*c^5*d^8 + 286720*a^4*b^4*c^4*d^9 - 229376*a^5*b^3*c^3*d^10 + 114688*a^6*b^2*c^2*d^11 - 32768*a^7*b*c*d^12))^(1/4) + ((((2*(-(b^4*c^5 + 625*a^4*c*d^4 - 500*a^3*b*c^2*d^3 + 150*a^2*b^2*c^3*d^2 - 20*a*b^3*c^4*d)/(4096*a^8*d^13 + 4096*b^8*c^8*d^5 - 32768*a*b^7*c^7*d^6 + 114688*a^2*b^6*c^6*d^7 - 229376*a^3*b^5*c^5*d^8 + 286720*a^4*b^4*c^4*d^9 - 229376*a^5*b^3*c^3*d^10 + 114688*a^6*b^2*c^2*d^11 - 32768*a^7*b*c*d^12))^(1/4)*(5120*a^3*b^12*c^10*d^5 - 40960*a^4*b^11*c^9*d^6 + 143360*a^5*b^10*c^8*d^7 - 286720*a^6*b^9*c^7*d^8 + 358400*a^7*b^8*c^6*d^9 - 286720*a^8*b^7*c^5*d^10 + 143360*a^9*b^6*c^4*d^11 - 40960*a^10*b^5*c^3*d^12 + 5120*a^11*b^4*c^2*d^13))/(a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3) - (x^(1/2)*(256*a^3*b^14*c^12*d^4 - 512*a^4*b^13*c^11*d^5 + 1280*a^5*b^12*c^10*d^6 - 22528*a^6*b^11*c^9*d^7 + 111104*a^7*b^10*c^8*d^8 - 265216*a^8*b^9*c^7*d^9 + 369152*a^9*b^8*c^6*d^10 - 317440*a^10*b^7*c^5*d^11 + 167168*a^11*b^6*c^4*d^12 - 49664*a^12*b^5*c^3*d^13 + 6400*a^13*b^4*c^2*d^14))/(a^6*d^7 + b^6*c^6*d - 6*a*b^5*c^5*d^2 + 15*a^2*b^4*c^4*d^3 - 20*a^3*b^3*c^3*d^4 + 15*a^4*b^2*c^2*d^5 - 6*a^5*b*c*d^6))*(-(b^4*c^5 + 625*a^4*c*d^4 - 500*a^3*b*c^2*d^3 + 150*a^2*b^2*c^3*d^2 - 20*a*b^3*c^4*d)/(4096*a^8*d^13 + 4096*b^8*c^8*d^5 - 32768*a*b^7*c^7*d^6 + 114688*a^2*b^6*c^6*d^7 - 229376*a^3*b^5*c^5*d^8 + 286720*a^4*b^4*c^4*d^9 - 229376*a^5*b^3*c^3*d^10 + 114688*a^6*b^2*c^2*d^11 - 32768*a^7*b*c*d^12))^(3/4) + (2*(a^3*b^8*c^7 - 19*a^4*b^7*c^6*d + 131*a^5*b^6*c^5*d^2 - 369*a^6*b^5*c^4*d^3 + 256*a^7*b^4*c^3*d^4 + 320*a^8*b^3*c^2*d^5))/(a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3))*(-(b^4*c^5 + 625*a^4*c*d^4 - 500*a^3*b*c^2*d^3 + 150*a^2*b^2*c^3*d^2 - 20*a*b^3*c^4*d)/(4096*a^8*d^13 + 4096*b^8*c^8*d^5 - 32768*a*b^7*c^7*d^6 + 114688*a^2*b^6*c^6*d^7 - 229376*a^3*b^5*c^5*d^8 + 286720*a^4*b^4*c^4*d^9 - 229376*a^5*b^3*c^3*d^10 + 114688*a^6*b^2*c^2*d^11 - 32768*a^7*b*c*d^12))^(1/4) - (x^(1/2)*(a^4*b^9*c^8 - 20*a^5*b^8*c^7*d + 150*a^6*b^7*c^6*d^2 - 500*a^7*b^6*c^5*d^3 + 641*a^8*b^5*c^4*d^4 - 160*a^9*b^4*c^3*d^5 + 400*a^10*b^3*c^2*d^6))/(a^6*d^7 + b^6*c^6*d - 6*a*b^5*c^5*d^2 + 15*a^2*b^4*c^4*d^3 - 20*a^3*b^3*c^3*d^4 + 15*a^4*b^2*c^2*d^5 - 6*a^5*b*c*d^6))*(-(b^4*c^5 + 625*a^4*c*d^4 - 500*a^3*b*c^2*d^3 + 150*a^2*b^2*c^3*d^2 - 20*a*b^3*c^4*d)/(4096*a^8*d^13 + 4096*b^8*c^8*d^5 - 32768*a*b^7*c^7*d^6 + 114688*a^2*b^6*c^6*d^7 - 229376*a^3*b^5*c^5*d^8 + 286720*a^4*b^4*c^4*d^9 - 229376*a^5*b^3*c^3*d^10 + 114688*a^6*b^2*c^2*d^11 - 32768*a^7*b*c*d^12))^(1/4)))*(-(b^4*c^5 + 625*a^4*c*d^4 - 500*a^3*b*c^2*d^3 + 150*a^2*b^2*c^3*d^2 - 20*a*b^3*c^4*d)/(4096*a^8*d^13 + 4096*b^8*c^8*d^5 - 32768*a*b^7*c^7*d^6 + 114688*a^2*b^6*c^6*d^7 - 229376*a^3*b^5*c^5*d^8 + 286720*a^4*b^4*c^4*d^9 - 229376*a^5*b^3*c^3*d^10 + 114688*a^6*b^2*c^2*d^11 - 32768*a^7*b*c*d^12))^(1/4)*2i + 2*atan(((((((-(b^4*c^5 + 625*a^4*c*d^4 - 500*a^3*b*c^2*d^3 + 150*a^2*b^2*c^3*d^2 - 20*a*b^3*c^4*d)/(4096*a^8*d^13 + 4096*b^8*c^8*d^5 - 32768*a*b^7*c^7*d^6 + 114688*a^2*b^6*c^6*d^7 - 229376*a^3*b^5*c^5*d^8 + 286720*a^4*b^4*c^4*d^9 - 229376*a^5*b^3*c^3*d^10 + 114688*a^6*b^2*c^2*d^11 - 32768*a^7*b*c*d^12))^(1/4)*(5120*a^3*b^12*c^10*d^5 - 40960*a^4*b^11*c^9*d^6 + 143360*a^5*b^10*c^8*d^7 - 286720*a^6*b^9*c^7*d^8 + 358400*a^7*b^8*c^6*d^9 - 286720*a^8*b^7*c^5*d^10 + 143360*a^9*b^6*c^4*d^11 - 40960*a^10*b^5*c^3*d^12 + 5120*a^11*b^4*c^2*d^13)*2i)/(a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3) + (x^(1/2)*(256*a^3*b^14*c^12*d^4 - 512*a^4*b^13*c^11*d^5 + 1280*a^5*b^12*c^10*d^6 - 22528*a^6*b^11*c^9*d^7 + 111104*a^7*b^10*c^8*d^8 - 265216*a^8*b^9*c^7*d^9 + 369152*a^9*b^8*c^6*d^10 - 317440*a^10*b^7*c^5*d^11 + 167168*a^11*b^6*c^4*d^12 - 49664*a^12*b^5*c^3*d^13 + 6400*a^13*b^4*c^2*d^14))/(a^6*d^7 + b^6*c^6*d - 6*a*b^5*c^5*d^2 + 15*a^2*b^4*c^4*d^3 - 20*a^3*b^3*c^3*d^4 + 15*a^4*b^2*c^2*d^5 - 6*a^5*b*c*d^6))*(-(b^4*c^5 + 625*a^4*c*d^4 - 500*a^3*b*c^2*d^3 + 150*a^2*b^2*c^3*d^2 - 20*a*b^3*c^4*d)/(4096*a^8*d^13 + 4096*b^8*c^8*d^5 - 32768*a*b^7*c^7*d^6 + 114688*a^2*b^6*c^6*d^7 - 229376*a^3*b^5*c^5*d^8 + 286720*a^4*b^4*c^4*d^9 - 229376*a^5*b^3*c^3*d^10 + 114688*a^6*b^2*c^2*d^11 - 32768*a^7*b*c*d^12))^(3/4)*1i - (2*(a^3*b^8*c^7 - 19*a^4*b^7*c^6*d + 131*a^5*b^6*c^5*d^2 - 369*a^6*b^5*c^4*d^3 + 256*a^7*b^4*c^3*d^4 + 320*a^8*b^3*c^2*d^5))/(a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3))*(-(b^4*c^5 + 625*a^4*c*d^4 - 500*a^3*b*c^2*d^3 + 150*a^2*b^2*c^3*d^2 - 20*a*b^3*c^4*d)/(4096*a^8*d^13 + 4096*b^8*c^8*d^5 - 32768*a*b^7*c^7*d^6 + 114688*a^2*b^6*c^6*d^7 - 229376*a^3*b^5*c^5*d^8 + 286720*a^4*b^4*c^4*d^9 - 229376*a^5*b^3*c^3*d^10 + 114688*a^6*b^2*c^2*d^11 - 32768*a^7*b*c*d^12))^(1/4)*1i - (x^(1/2)*(a^4*b^9*c^8 - 20*a^5*b^8*c^7*d + 150*a^6*b^7*c^6*d^2 - 500*a^7*b^6*c^5*d^3 + 641*a^8*b^5*c^4*d^4 - 160*a^9*b^4*c^3*d^5 + 400*a^10*b^3*c^2*d^6))/(a^6*d^7 + b^6*c^6*d - 6*a*b^5*c^5*d^2 + 15*a^2*b^4*c^4*d^3 - 20*a^3*b^3*c^3*d^4 + 15*a^4*b^2*c^2*d^5 - 6*a^5*b*c*d^6))*(-(b^4*c^5 + 625*a^4*c*d^4 - 500*a^3*b*c^2*d^3 + 150*a^2*b^2*c^3*d^2 - 20*a*b^3*c^4*d)/(4096*a^8*d^13 + 4096*b^8*c^8*d^5 - 32768*a*b^7*c^7*d^6 + 114688*a^2*b^6*c^6*d^7 - 229376*a^3*b^5*c^5*d^8 + 286720*a^4*b^4*c^4*d^9 - 229376*a^5*b^3*c^3*d^10 + 114688*a^6*b^2*c^2*d^11 - 32768*a^7*b*c*d^12))^(1/4) - (((((-(b^4*c^5 + 625*a^4*c*d^4 - 500*a^3*b*c^2*d^3 + 150*a^2*b^2*c^3*d^2 - 20*a*b^3*c^4*d)/(4096*a^8*d^13 + 4096*b^8*c^8*d^5 - 32768*a*b^7*c^7*d^6 + 114688*a^2*b^6*c^6*d^7 - 229376*a^3*b^5*c^5*d^8 + 286720*a^4*b^4*c^4*d^9 - 229376*a^5*b^3*c^3*d^10 + 114688*a^6*b^2*c^2*d^11 - 32768*a^7*b*c*d^12))^(1/4)*(5120*a^3*b^12*c^10*d^5 - 40960*a^4*b^11*c^9*d^6 + 143360*a^5*b^10*c^8*d^7 - 286720*a^6*b^9*c^7*d^8 + 358400*a^7*b^8*c^6*d^9 - 286720*a^8*b^7*c^5*d^10 + 143360*a^9*b^6*c^4*d^11 - 40960*a^10*b^5*c^3*d^12 + 5120*a^11*b^4*c^2*d^13)*2i)/(a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3) - (x^(1/2)*(256*a^3*b^14*c^12*d^4 - 512*a^4*b^13*c^11*d^5 + 1280*a^5*b^12*c^10*d^6 - 22528*a^6*b^11*c^9*d^7 + 111104*a^7*b^10*c^8*d^8 - 265216*a^8*b^9*c^7*d^9 + 369152*a^9*b^8*c^6*d^10 - 317440*a^10*b^7*c^5*d^11 + 167168*a^11*b^6*c^4*d^12 - 49664*a^12*b^5*c^3*d^13 + 6400*a^13*b^4*c^2*d^14))/(a^6*d^7 + b^6*c^6*d - 6*a*b^5*c^5*d^2 + 15*a^2*b^4*c^4*d^3 - 20*a^3*b^3*c^3*d^4 + 15*a^4*b^2*c^2*d^5 - 6*a^5*b*c*d^6))*(-(b^4*c^5 + 625*a^4*c*d^4 - 500*a^3*b*c^2*d^3 + 150*a^2*b^2*c^3*d^2 - 20*a*b^3*c^4*d)/(4096*a^8*d^13 + 4096*b^8*c^8*d^5 - 32768*a*b^7*c^7*d^6 + 114688*a^2*b^6*c^6*d^7 - 229376*a^3*b^5*c^5*d^8 + 286720*a^4*b^4*c^4*d^9 - 229376*a^5*b^3*c^3*d^10 + 114688*a^6*b^2*c^2*d^11 - 32768*a^7*b*c*d^12))^(3/4)*1i - (2*(a^3*b^8*c^7 - 19*a^4*b^7*c^6*d + 131*a^5*b^6*c^5*d^2 - 369*a^6*b^5*c^4*d^3 + 256*a^7*b^4*c^3*d^4 + 320*a^8*b^3*c^2*d^5))/(a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3))*(-(b^4*c^5 + 625*a^4*c*d^4 - 500*a^3*b*c^2*d^3 + 150*a^2*b^2*c^3*d^2 - 20*a*b^3*c^4*d)/(4096*a^8*d^13 + 4096*b^8*c^8*d^5 - 32768*a*b^7*c^7*d^6 + 114688*a^2*b^6*c^6*d^7 - 229376*a^3*b^5*c^5*d^8 + 286720*a^4*b^4*c^4*d^9 - 229376*a^5*b^3*c^3*d^10 + 114688*a^6*b^2*c^2*d^11 - 32768*a^7*b*c*d^12))^(1/4)*1i + (x^(1/2)*(a^4*b^9*c^8 - 20*a^5*b^8*c^7*d + 150*a^6*b^7*c^6*d^2 - 500*a^7*b^6*c^5*d^3 + 641*a^8*b^5*c^4*d^4 - 160*a^9*b^4*c^3*d^5 + 400*a^10*b^3*c^2*d^6))/(a^6*d^7 + b^6*c^6*d - 6*a*b^5*c^5*d^2 + 15*a^2*b^4*c^4*d^3 - 20*a^3*b^3*c^3*d^4 + 15*a^4*b^2*c^2*d^5 - 6*a^5*b*c*d^6))*(-(b^4*c^5 + 625*a^4*c*d^4 - 500*a^3*b*c^2*d^3 + 150*a^2*b^2*c^3*d^2 - 20*a*b^3*c^4*d)/(4096*a^8*d^13 + 4096*b^8*c^8*d^5 - 32768*a*b^7*c^7*d^6 + 114688*a^2*b^6*c^6*d^7 - 229376*a^3*b^5*c^5*d^8 + 286720*a^4*b^4*c^4*d^9 - 229376*a^5*b^3*c^3*d^10 + 114688*a^6*b^2*c^2*d^11 - 32768*a^7*b*c*d^12))^(1/4))/((((((-(b^4*c^5 + 625*a^4*c*d^4 - 500*a^3*b*c^2*d^3 + 150*a^2*b^2*c^3*d^2 - 20*a*b^3*c^4*d)/(4096*a^8*d^13 + 4096*b^8*c^8*d^5 - 32768*a*b^7*c^7*d^6 + 114688*a^2*b^6*c^6*d^7 - 229376*a^3*b^5*c^5*d^8 + 286720*a^4*b^4*c^4*d^9 - 229376*a^5*b^3*c^3*d^10 + 114688*a^6*b^2*c^2*d^11 - 32768*a^7*b*c*d^12))^(1/4)*(5120*a^3*b^12*c^10*d^5 - 40960*a^4*b^11*c^9*d^6 + 143360*a^5*b^10*c^8*d^7 - 286720*a^6*b^9*c^7*d^8 + 358400*a^7*b^8*c^6*d^9 - 286720*a^8*b^7*c^5*d^10 + 143360*a^9*b^6*c^4*d^11 - 40960*a^10*b^5*c^3*d^12 + 5120*a^11*b^4*c^2*d^13)*2i)/(a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3) + (x^(1/2)*(256*a^3*b^14*c^12*d^4 - 512*a^4*b^13*c^11*d^5 + 1280*a^5*b^12*c^10*d^6 - 22528*a^6*b^11*c^9*d^7 + 111104*a^7*b^10*c^8*d^8 - 265216*a^8*b^9*c^7*d^9 + 369152*a^9*b^8*c^6*d^10 - 317440*a^10*b^7*c^5*d^11 + 167168*a^11*b^6*c^4*d^12 - 49664*a^12*b^5*c^3*d^13 + 6400*a^13*b^4*c^2*d^14))/(a^6*d^7 + b^6*c^6*d - 6*a*b^5*c^5*d^2 + 15*a^2*b^4*c^4*d^3 - 20*a^3*b^3*c^3*d^4 + 15*a^4*b^2*c^2*d^5 - 6*a^5*b*c*d^6))*(-(b^4*c^5 + 625*a^4*c*d^4 - 500*a^3*b*c^2*d^3 + 150*a^2*b^2*c^3*d^2 - 20*a*b^3*c^4*d)/(4096*a^8*d^13 + 4096*b^8*c^8*d^5 - 32768*a*b^7*c^7*d^6 + 114688*a^2*b^6*c^6*d^7 - 229376*a^3*b^5*c^5*d^8 + 286720*a^4*b^4*c^4*d^9 - 229376*a^5*b^3*c^3*d^10 + 114688*a^6*b^2*c^2*d^11 - 32768*a^7*b*c*d^12))^(3/4)*1i - (2*(a^3*b^8*c^7 - 19*a^4*b^7*c^6*d + 131*a^5*b^6*c^5*d^2 - 369*a^6*b^5*c^4*d^3 + 256*a^7*b^4*c^3*d^4 + 320*a^8*b^3*c^2*d^5))/(a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3))*(-(b^4*c^5 + 625*a^4*c*d^4 - 500*a^3*b*c^2*d^3 + 150*a^2*b^2*c^3*d^2 - 20*a*b^3*c^4*d)/(4096*a^8*d^13 + 4096*b^8*c^8*d^5 - 32768*a*b^7*c^7*d^6 + 114688*a^2*b^6*c^6*d^7 - 229376*a^3*b^5*c^5*d^8 + 286720*a^4*b^4*c^4*d^9 - 229376*a^5*b^3*c^3*d^10 + 114688*a^6*b^2*c^2*d^11 - 32768*a^7*b*c*d^12))^(1/4)*1i - (x^(1/2)*(a^4*b^9*c^8 - 20*a^5*b^8*c^7*d + 150*a^6*b^7*c^6*d^2 - 500*a^7*b^6*c^5*d^3 + 641*a^8*b^5*c^4*d^4 - 160*a^9*b^4*c^3*d^5 + 400*a^10*b^3*c^2*d^6))/(a^6*d^7 + b^6*c^6*d - 6*a*b^5*c^5*d^2 + 15*a^2*b^4*c^4*d^3 - 20*a^3*b^3*c^3*d^4 + 15*a^4*b^2*c^2*d^5 - 6*a^5*b*c*d^6))*(-(b^4*c^5 + 625*a^4*c*d^4 - 500*a^3*b*c^2*d^3 + 150*a^2*b^2*c^3*d^2 - 20*a*b^3*c^4*d)/(4096*a^8*d^13 + 4096*b^8*c^8*d^5 - 32768*a*b^7*c^7*d^6 + 114688*a^2*b^6*c^6*d^7 - 229376*a^3*b^5*c^5*d^8 + 286720*a^4*b^4*c^4*d^9 - 229376*a^5*b^3*c^3*d^10 + 114688*a^6*b^2*c^2*d^11 - 32768*a^7*b*c*d^12))^(1/4)*1i + (((((-(b^4*c^5 + 625*a^4*c*d^4 - 500*a^3*b*c^2*d^3 + 150*a^2*b^2*c^3*d^2 - 20*a*b^3*c^4*d)/(4096*a^8*d^13 + 4096*b^8*c^8*d^5 - 32768*a*b^7*c^7*d^6 + 114688*a^2*b^6*c^6*d^7 - 229376*a^3*b^5*c^5*d^8 + 286720*a^4*b^4*c^4*d^9 - 229376*a^5*b^3*c^3*d^10 + 114688*a^6*b^2*c^2*d^11 - 32768*a^7*b*c*d^12))^(1/4)*(5120*a^3*b^12*c^10*d^5 - 40960*a^4*b^11*c^9*d^6 + 143360*a^5*b^10*c^8*d^7 - 286720*a^6*b^9*c^7*d^8 + 358400*a^7*b^8*c^6*d^9 - 286720*a^8*b^7*c^5*d^10 + 143360*a^9*b^6*c^4*d^11 - 40960*a^10*b^5*c^3*d^12 + 5120*a^11*b^4*c^2*d^13)*2i)/(a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3) - (x^(1/2)*(256*a^3*b^14*c^12*d^4 - 512*a^4*b^13*c^11*d^5 + 1280*a^5*b^12*c^10*d^6 - 22528*a^6*b^11*c^9*d^7 + 111104*a^7*b^10*c^8*d^8 - 265216*a^8*b^9*c^7*d^9 + 369152*a^9*b^8*c^6*d^10 - 317440*a^10*b^7*c^5*d^11 + 167168*a^11*b^6*c^4*d^12 - 49664*a^12*b^5*c^3*d^13 + 6400*a^13*b^4*c^2*d^14))/(a^6*d^7 + b^6*c^6*d - 6*a*b^5*c^5*d^2 + 15*a^2*b^4*c^4*d^3 - 20*a^3*b^3*c^3*d^4 + 15*a^4*b^2*c^2*d^5 - 6*a^5*b*c*d^6))*(-(b^4*c^5 + 625*a^4*c*d^4 - 500*a^3*b*c^2*d^3 + 150*a^2*b^2*c^3*d^2 - 20*a*b^3*c^4*d)/(4096*a^8*d^13 + 4096*b^8*c^8*d^5 - 32768*a*b^7*c^7*d^6 + 114688*a^2*b^6*c^6*d^7 - 229376*a^3*b^5*c^5*d^8 + 286720*a^4*b^4*c^4*d^9 - 229376*a^5*b^3*c^3*d^10 + 114688*a^6*b^2*c^2*d^11 - 32768*a^7*b*c*d^12))^(3/4)*1i - (2*(a^3*b^8*c^7 - 19*a^4*b^7*c^6*d + 131*a^5*b^6*c^5*d^2 - 369*a^6*b^5*c^4*d^3 + 256*a^7*b^4*c^3*d^4 + 320*a^8*b^3*c^2*d^5))/(a^3*d^4 - b^3*c^3*d + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3))*(-(b^4*c^5 + 625*a^4*c*d^4 - 500*a^3*b*c^2*d^3 + 150*a^2*b^2*c^3*d^2 - 20*a*b^3*c^4*d)/(4096*a^8*d^13 + 4096*b^8*c^8*d^5 - 32768*a*b^7*c^7*d^6 + 114688*a^2*b^6*c^6*d^7 - 229376*a^3*b^5*c^5*d^8 + 286720*a^4*b^4*c^4*d^9 - 229376*a^5*b^3*c^3*d^10 + 114688*a^6*b^2*c^2*d^11 - 32768*a^7*b*c*d^12))^(1/4)*1i + (x^(1/2)*(a^4*b^9*c^8 - 20*a^5*b^8*c^7*d + 150*a^6*b^7*c^6*d^2 - 500*a^7*b^6*c^5*d^3 + 641*a^8*b^5*c^4*d^4 - 160*a^9*b^4*c^3*d^5 + 400*a^10*b^3*c^2*d^6))/(a^6*d^7 + b^6*c^6*d - 6*a*b^5*c^5*d^2 + 15*a^2*b^4*c^4*d^3 - 20*a^3*b^3*c^3*d^4 + 15*a^4*b^2*c^2*d^5 - 6*a^5*b*c*d^6))*(-(b^4*c^5 + 625*a^4*c*d^4 - 500*a^3*b*c^2*d^3 + 150*a^2*b^2*c^3*d^2 - 20*a*b^3*c^4*d)/(4096*a^8*d^13 + 4096*b^8*c^8*d^5 - 32768*a*b^7*c^7*d^6 + 114688*a^2*b^6*c^6*d^7 - 229376*a^3*b^5*c^5*d^8 + 286720*a^4*b^4*c^4*d^9 - 229376*a^5*b^3*c^3*d^10 + 114688*a^6*b^2*c^2*d^11 - 32768*a^7*b*c*d^12))^(1/4)*1i))*(-(b^4*c^5 + 625*a^4*c*d^4 - 500*a^3*b*c^2*d^3 + 150*a^2*b^2*c^3*d^2 - 20*a*b^3*c^4*d)/(4096*a^8*d^13 + 4096*b^8*c^8*d^5 - 32768*a*b^7*c^7*d^6 + 114688*a^2*b^6*c^6*d^7 - 229376*a^3*b^5*c^5*d^8 + 286720*a^4*b^4*c^4*d^9 - 229376*a^5*b^3*c^3*d^10 + 114688*a^6*b^2*c^2*d^11 - 32768*a^7*b*c*d^12))^(1/4) + (c*x^(1/2))/(2*d*(c + d*x^2)*(a*d - b*c))","B"
473,1,18673,528,2.479880,"\text{Not used}","int(x^(5/2)/((a + b*x^2)*(c + d*x^2)^2),x)","-2\,\mathrm{atan}\left(\frac{\left(\left(\frac{\sqrt{x}\,{\left(-\frac{a^3\,b}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{1/4}\,\left(2304\,a^{13}\,b^4\,c\,d^{14}-16896\,a^{12}\,b^5\,c^2\,d^{13}+56576\,a^{11}\,b^6\,c^3\,d^{12}-120832\,a^{10}\,b^7\,c^4\,d^{11}+197120\,a^9\,b^8\,c^5\,d^{10}-265216\,a^8\,b^9\,c^6\,d^9+283136\,a^7\,b^{10}\,c^7\,d^8-219136\,a^6\,b^{11}\,c^8\,d^7+111872\,a^5\,b^{12}\,c^9\,d^6-33280\,a^4\,b^{13}\,c^{10}\,d^5+4352\,a^3\,b^{14}\,c^{11}\,d^4\right)}{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}+\frac{\left(864\,a^{13}\,b^4\,c\,d^{13}-5184\,a^{12}\,b^5\,c^2\,d^{12}+10336\,a^{11}\,b^6\,c^3\,d^{11}+256\,a^{10}\,b^7\,c^4\,d^{10}-37184\,a^9\,b^8\,c^5\,d^9+74368\,a^8\,b^9\,c^6\,d^8-74816\,a^7\,b^{10}\,c^7\,d^7+43264\,a^6\,b^{11}\,c^8\,d^6-13856\,a^5\,b^{12}\,c^9\,d^5+1984\,a^4\,b^{13}\,c^{10}\,d^4-32\,a^3\,b^{14}\,c^{11}\,d^3\right)\,1{}\mathrm{i}}{a^7\,d^7-7\,a^6\,b\,c\,d^6+21\,a^5\,b^2\,c^2\,d^5-35\,a^4\,b^3\,c^3\,d^4+35\,a^3\,b^4\,c^4\,d^3-21\,a^2\,b^5\,c^5\,d^2+7\,a\,b^6\,c^6\,d-b^7\,c^7}\right)\,{\left(-\frac{a^3\,b}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{3/4}+\frac{\sqrt{x}\,\left(144\,a^8\,b^5\,c\,d^6+177\,a^7\,b^6\,c^2\,d^5+124\,a^6\,b^7\,c^3\,d^4+54\,a^5\,b^8\,c^4\,d^3+12\,a^4\,b^9\,c^5\,d^2+a^3\,b^{10}\,c^6\,d\right)}{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)\,{\left(-\frac{a^3\,b}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{1/4}-\left(\left(-\frac{\sqrt{x}\,{\left(-\frac{a^3\,b}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{1/4}\,\left(2304\,a^{13}\,b^4\,c\,d^{14}-16896\,a^{12}\,b^5\,c^2\,d^{13}+56576\,a^{11}\,b^6\,c^3\,d^{12}-120832\,a^{10}\,b^7\,c^4\,d^{11}+197120\,a^9\,b^8\,c^5\,d^{10}-265216\,a^8\,b^9\,c^6\,d^9+283136\,a^7\,b^{10}\,c^7\,d^8-219136\,a^6\,b^{11}\,c^8\,d^7+111872\,a^5\,b^{12}\,c^9\,d^6-33280\,a^4\,b^{13}\,c^{10}\,d^5+4352\,a^3\,b^{14}\,c^{11}\,d^4\right)}{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}+\frac{\left(864\,a^{13}\,b^4\,c\,d^{13}-5184\,a^{12}\,b^5\,c^2\,d^{12}+10336\,a^{11}\,b^6\,c^3\,d^{11}+256\,a^{10}\,b^7\,c^4\,d^{10}-37184\,a^9\,b^8\,c^5\,d^9+74368\,a^8\,b^9\,c^6\,d^8-74816\,a^7\,b^{10}\,c^7\,d^7+43264\,a^6\,b^{11}\,c^8\,d^6-13856\,a^5\,b^{12}\,c^9\,d^5+1984\,a^4\,b^{13}\,c^{10}\,d^4-32\,a^3\,b^{14}\,c^{11}\,d^3\right)\,1{}\mathrm{i}}{a^7\,d^7-7\,a^6\,b\,c\,d^6+21\,a^5\,b^2\,c^2\,d^5-35\,a^4\,b^3\,c^3\,d^4+35\,a^3\,b^4\,c^4\,d^3-21\,a^2\,b^5\,c^5\,d^2+7\,a\,b^6\,c^6\,d-b^7\,c^7}\right)\,{\left(-\frac{a^3\,b}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{3/4}-\frac{\sqrt{x}\,\left(144\,a^8\,b^5\,c\,d^6+177\,a^7\,b^6\,c^2\,d^5+124\,a^6\,b^7\,c^3\,d^4+54\,a^5\,b^8\,c^4\,d^3+12\,a^4\,b^9\,c^5\,d^2+a^3\,b^{10}\,c^6\,d\right)}{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)\,{\left(-\frac{a^3\,b}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{1/4}}{-\frac{108\,a^8\,b^5\,c\,d^5+135\,a^7\,b^6\,c^2\,d^4+63\,a^6\,b^7\,c^3\,d^3+13\,a^5\,b^8\,c^4\,d^2+a^4\,b^9\,c^5\,d}{a^7\,d^7-7\,a^6\,b\,c\,d^6+21\,a^5\,b^2\,c^2\,d^5-35\,a^4\,b^3\,c^3\,d^4+35\,a^3\,b^4\,c^4\,d^3-21\,a^2\,b^5\,c^5\,d^2+7\,a\,b^6\,c^6\,d-b^7\,c^7}+\left(\left(\frac{\sqrt{x}\,{\left(-\frac{a^3\,b}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{1/4}\,\left(2304\,a^{13}\,b^4\,c\,d^{14}-16896\,a^{12}\,b^5\,c^2\,d^{13}+56576\,a^{11}\,b^6\,c^3\,d^{12}-120832\,a^{10}\,b^7\,c^4\,d^{11}+197120\,a^9\,b^8\,c^5\,d^{10}-265216\,a^8\,b^9\,c^6\,d^9+283136\,a^7\,b^{10}\,c^7\,d^8-219136\,a^6\,b^{11}\,c^8\,d^7+111872\,a^5\,b^{12}\,c^9\,d^6-33280\,a^4\,b^{13}\,c^{10}\,d^5+4352\,a^3\,b^{14}\,c^{11}\,d^4\right)}{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}+\frac{\left(864\,a^{13}\,b^4\,c\,d^{13}-5184\,a^{12}\,b^5\,c^2\,d^{12}+10336\,a^{11}\,b^6\,c^3\,d^{11}+256\,a^{10}\,b^7\,c^4\,d^{10}-37184\,a^9\,b^8\,c^5\,d^9+74368\,a^8\,b^9\,c^6\,d^8-74816\,a^7\,b^{10}\,c^7\,d^7+43264\,a^6\,b^{11}\,c^8\,d^6-13856\,a^5\,b^{12}\,c^9\,d^5+1984\,a^4\,b^{13}\,c^{10}\,d^4-32\,a^3\,b^{14}\,c^{11}\,d^3\right)\,1{}\mathrm{i}}{a^7\,d^7-7\,a^6\,b\,c\,d^6+21\,a^5\,b^2\,c^2\,d^5-35\,a^4\,b^3\,c^3\,d^4+35\,a^3\,b^4\,c^4\,d^3-21\,a^2\,b^5\,c^5\,d^2+7\,a\,b^6\,c^6\,d-b^7\,c^7}\right)\,{\left(-\frac{a^3\,b}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{3/4}\,1{}\mathrm{i}+\frac{\sqrt{x}\,\left(144\,a^8\,b^5\,c\,d^6+177\,a^7\,b^6\,c^2\,d^5+124\,a^6\,b^7\,c^3\,d^4+54\,a^5\,b^8\,c^4\,d^3+12\,a^4\,b^9\,c^5\,d^2+a^3\,b^{10}\,c^6\,d\right)\,1{}\mathrm{i}}{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)\,{\left(-\frac{a^3\,b}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{1/4}+\left(\left(-\frac{\sqrt{x}\,{\left(-\frac{a^3\,b}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{1/4}\,\left(2304\,a^{13}\,b^4\,c\,d^{14}-16896\,a^{12}\,b^5\,c^2\,d^{13}+56576\,a^{11}\,b^6\,c^3\,d^{12}-120832\,a^{10}\,b^7\,c^4\,d^{11}+197120\,a^9\,b^8\,c^5\,d^{10}-265216\,a^8\,b^9\,c^6\,d^9+283136\,a^7\,b^{10}\,c^7\,d^8-219136\,a^6\,b^{11}\,c^8\,d^7+111872\,a^5\,b^{12}\,c^9\,d^6-33280\,a^4\,b^{13}\,c^{10}\,d^5+4352\,a^3\,b^{14}\,c^{11}\,d^4\right)}{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}+\frac{\left(864\,a^{13}\,b^4\,c\,d^{13}-5184\,a^{12}\,b^5\,c^2\,d^{12}+10336\,a^{11}\,b^6\,c^3\,d^{11}+256\,a^{10}\,b^7\,c^4\,d^{10}-37184\,a^9\,b^8\,c^5\,d^9+74368\,a^8\,b^9\,c^6\,d^8-74816\,a^7\,b^{10}\,c^7\,d^7+43264\,a^6\,b^{11}\,c^8\,d^6-13856\,a^5\,b^{12}\,c^9\,d^5+1984\,a^4\,b^{13}\,c^{10}\,d^4-32\,a^3\,b^{14}\,c^{11}\,d^3\right)\,1{}\mathrm{i}}{a^7\,d^7-7\,a^6\,b\,c\,d^6+21\,a^5\,b^2\,c^2\,d^5-35\,a^4\,b^3\,c^3\,d^4+35\,a^3\,b^4\,c^4\,d^3-21\,a^2\,b^5\,c^5\,d^2+7\,a\,b^6\,c^6\,d-b^7\,c^7}\right)\,{\left(-\frac{a^3\,b}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{3/4}\,1{}\mathrm{i}-\frac{\sqrt{x}\,\left(144\,a^8\,b^5\,c\,d^6+177\,a^7\,b^6\,c^2\,d^5+124\,a^6\,b^7\,c^3\,d^4+54\,a^5\,b^8\,c^4\,d^3+12\,a^4\,b^9\,c^5\,d^2+a^3\,b^{10}\,c^6\,d\right)\,1{}\mathrm{i}}{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)\,{\left(-\frac{a^3\,b}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{1/4}}\right)\,{\left(-\frac{a^3\,b}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{1/4}-2\,\mathrm{atan}\left(\frac{\left(\left(\frac{\sqrt{x}\,{\left(-\frac{81\,a^4\,d^4+108\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+12\,a\,b^3\,c^3\,d+b^4\,c^4}{4096\,a^8\,c\,d^{11}-32768\,a^7\,b\,c^2\,d^{10}+114688\,a^6\,b^2\,c^3\,d^9-229376\,a^5\,b^3\,c^4\,d^8+286720\,a^4\,b^4\,c^5\,d^7-229376\,a^3\,b^5\,c^6\,d^6+114688\,a^2\,b^6\,c^7\,d^5-32768\,a\,b^7\,c^8\,d^4+4096\,b^8\,c^9\,d^3}\right)}^{1/4}\,\left(2304\,a^{13}\,b^4\,c\,d^{14}-16896\,a^{12}\,b^5\,c^2\,d^{13}+56576\,a^{11}\,b^6\,c^3\,d^{12}-120832\,a^{10}\,b^7\,c^4\,d^{11}+197120\,a^9\,b^8\,c^5\,d^{10}-265216\,a^8\,b^9\,c^6\,d^9+283136\,a^7\,b^{10}\,c^7\,d^8-219136\,a^6\,b^{11}\,c^8\,d^7+111872\,a^5\,b^{12}\,c^9\,d^6-33280\,a^4\,b^{13}\,c^{10}\,d^5+4352\,a^3\,b^{14}\,c^{11}\,d^4\right)}{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}+\frac{\left(864\,a^{13}\,b^4\,c\,d^{13}-5184\,a^{12}\,b^5\,c^2\,d^{12}+10336\,a^{11}\,b^6\,c^3\,d^{11}+256\,a^{10}\,b^7\,c^4\,d^{10}-37184\,a^9\,b^8\,c^5\,d^9+74368\,a^8\,b^9\,c^6\,d^8-74816\,a^7\,b^{10}\,c^7\,d^7+43264\,a^6\,b^{11}\,c^8\,d^6-13856\,a^5\,b^{12}\,c^9\,d^5+1984\,a^4\,b^{13}\,c^{10}\,d^4-32\,a^3\,b^{14}\,c^{11}\,d^3\right)\,1{}\mathrm{i}}{a^7\,d^7-7\,a^6\,b\,c\,d^6+21\,a^5\,b^2\,c^2\,d^5-35\,a^4\,b^3\,c^3\,d^4+35\,a^3\,b^4\,c^4\,d^3-21\,a^2\,b^5\,c^5\,d^2+7\,a\,b^6\,c^6\,d-b^7\,c^7}\right)\,{\left(-\frac{81\,a^4\,d^4+108\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+12\,a\,b^3\,c^3\,d+b^4\,c^4}{4096\,a^8\,c\,d^{11}-32768\,a^7\,b\,c^2\,d^{10}+114688\,a^6\,b^2\,c^3\,d^9-229376\,a^5\,b^3\,c^4\,d^8+286720\,a^4\,b^4\,c^5\,d^7-229376\,a^3\,b^5\,c^6\,d^6+114688\,a^2\,b^6\,c^7\,d^5-32768\,a\,b^7\,c^8\,d^4+4096\,b^8\,c^9\,d^3}\right)}^{3/4}+\frac{\sqrt{x}\,\left(144\,a^8\,b^5\,c\,d^6+177\,a^7\,b^6\,c^2\,d^5+124\,a^6\,b^7\,c^3\,d^4+54\,a^5\,b^8\,c^4\,d^3+12\,a^4\,b^9\,c^5\,d^2+a^3\,b^{10}\,c^6\,d\right)}{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)\,{\left(-\frac{81\,a^4\,d^4+108\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+12\,a\,b^3\,c^3\,d+b^4\,c^4}{4096\,a^8\,c\,d^{11}-32768\,a^7\,b\,c^2\,d^{10}+114688\,a^6\,b^2\,c^3\,d^9-229376\,a^5\,b^3\,c^4\,d^8+286720\,a^4\,b^4\,c^5\,d^7-229376\,a^3\,b^5\,c^6\,d^6+114688\,a^2\,b^6\,c^7\,d^5-32768\,a\,b^7\,c^8\,d^4+4096\,b^8\,c^9\,d^3}\right)}^{1/4}-\left(\left(-\frac{\sqrt{x}\,{\left(-\frac{81\,a^4\,d^4+108\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+12\,a\,b^3\,c^3\,d+b^4\,c^4}{4096\,a^8\,c\,d^{11}-32768\,a^7\,b\,c^2\,d^{10}+114688\,a^6\,b^2\,c^3\,d^9-229376\,a^5\,b^3\,c^4\,d^8+286720\,a^4\,b^4\,c^5\,d^7-229376\,a^3\,b^5\,c^6\,d^6+114688\,a^2\,b^6\,c^7\,d^5-32768\,a\,b^7\,c^8\,d^4+4096\,b^8\,c^9\,d^3}\right)}^{1/4}\,\left(2304\,a^{13}\,b^4\,c\,d^{14}-16896\,a^{12}\,b^5\,c^2\,d^{13}+56576\,a^{11}\,b^6\,c^3\,d^{12}-120832\,a^{10}\,b^7\,c^4\,d^{11}+197120\,a^9\,b^8\,c^5\,d^{10}-265216\,a^8\,b^9\,c^6\,d^9+283136\,a^7\,b^{10}\,c^7\,d^8-219136\,a^6\,b^{11}\,c^8\,d^7+111872\,a^5\,b^{12}\,c^9\,d^6-33280\,a^4\,b^{13}\,c^{10}\,d^5+4352\,a^3\,b^{14}\,c^{11}\,d^4\right)}{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}+\frac{\left(864\,a^{13}\,b^4\,c\,d^{13}-5184\,a^{12}\,b^5\,c^2\,d^{12}+10336\,a^{11}\,b^6\,c^3\,d^{11}+256\,a^{10}\,b^7\,c^4\,d^{10}-37184\,a^9\,b^8\,c^5\,d^9+74368\,a^8\,b^9\,c^6\,d^8-74816\,a^7\,b^{10}\,c^7\,d^7+43264\,a^6\,b^{11}\,c^8\,d^6-13856\,a^5\,b^{12}\,c^9\,d^5+1984\,a^4\,b^{13}\,c^{10}\,d^4-32\,a^3\,b^{14}\,c^{11}\,d^3\right)\,1{}\mathrm{i}}{a^7\,d^7-7\,a^6\,b\,c\,d^6+21\,a^5\,b^2\,c^2\,d^5-35\,a^4\,b^3\,c^3\,d^4+35\,a^3\,b^4\,c^4\,d^3-21\,a^2\,b^5\,c^5\,d^2+7\,a\,b^6\,c^6\,d-b^7\,c^7}\right)\,{\left(-\frac{81\,a^4\,d^4+108\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+12\,a\,b^3\,c^3\,d+b^4\,c^4}{4096\,a^8\,c\,d^{11}-32768\,a^7\,b\,c^2\,d^{10}+114688\,a^6\,b^2\,c^3\,d^9-229376\,a^5\,b^3\,c^4\,d^8+286720\,a^4\,b^4\,c^5\,d^7-229376\,a^3\,b^5\,c^6\,d^6+114688\,a^2\,b^6\,c^7\,d^5-32768\,a\,b^7\,c^8\,d^4+4096\,b^8\,c^9\,d^3}\right)}^{3/4}-\frac{\sqrt{x}\,\left(144\,a^8\,b^5\,c\,d^6+177\,a^7\,b^6\,c^2\,d^5+124\,a^6\,b^7\,c^3\,d^4+54\,a^5\,b^8\,c^4\,d^3+12\,a^4\,b^9\,c^5\,d^2+a^3\,b^{10}\,c^6\,d\right)}{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)\,{\left(-\frac{81\,a^4\,d^4+108\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+12\,a\,b^3\,c^3\,d+b^4\,c^4}{4096\,a^8\,c\,d^{11}-32768\,a^7\,b\,c^2\,d^{10}+114688\,a^6\,b^2\,c^3\,d^9-229376\,a^5\,b^3\,c^4\,d^8+286720\,a^4\,b^4\,c^5\,d^7-229376\,a^3\,b^5\,c^6\,d^6+114688\,a^2\,b^6\,c^7\,d^5-32768\,a\,b^7\,c^8\,d^4+4096\,b^8\,c^9\,d^3}\right)}^{1/4}}{-\frac{108\,a^8\,b^5\,c\,d^5+135\,a^7\,b^6\,c^2\,d^4+63\,a^6\,b^7\,c^3\,d^3+13\,a^5\,b^8\,c^4\,d^2+a^4\,b^9\,c^5\,d}{a^7\,d^7-7\,a^6\,b\,c\,d^6+21\,a^5\,b^2\,c^2\,d^5-35\,a^4\,b^3\,c^3\,d^4+35\,a^3\,b^4\,c^4\,d^3-21\,a^2\,b^5\,c^5\,d^2+7\,a\,b^6\,c^6\,d-b^7\,c^7}+\left(\left(\frac{\sqrt{x}\,{\left(-\frac{81\,a^4\,d^4+108\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+12\,a\,b^3\,c^3\,d+b^4\,c^4}{4096\,a^8\,c\,d^{11}-32768\,a^7\,b\,c^2\,d^{10}+114688\,a^6\,b^2\,c^3\,d^9-229376\,a^5\,b^3\,c^4\,d^8+286720\,a^4\,b^4\,c^5\,d^7-229376\,a^3\,b^5\,c^6\,d^6+114688\,a^2\,b^6\,c^7\,d^5-32768\,a\,b^7\,c^8\,d^4+4096\,b^8\,c^9\,d^3}\right)}^{1/4}\,\left(2304\,a^{13}\,b^4\,c\,d^{14}-16896\,a^{12}\,b^5\,c^2\,d^{13}+56576\,a^{11}\,b^6\,c^3\,d^{12}-120832\,a^{10}\,b^7\,c^4\,d^{11}+197120\,a^9\,b^8\,c^5\,d^{10}-265216\,a^8\,b^9\,c^6\,d^9+283136\,a^7\,b^{10}\,c^7\,d^8-219136\,a^6\,b^{11}\,c^8\,d^7+111872\,a^5\,b^{12}\,c^9\,d^6-33280\,a^4\,b^{13}\,c^{10}\,d^5+4352\,a^3\,b^{14}\,c^{11}\,d^4\right)}{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}+\frac{\left(864\,a^{13}\,b^4\,c\,d^{13}-5184\,a^{12}\,b^5\,c^2\,d^{12}+10336\,a^{11}\,b^6\,c^3\,d^{11}+256\,a^{10}\,b^7\,c^4\,d^{10}-37184\,a^9\,b^8\,c^5\,d^9+74368\,a^8\,b^9\,c^6\,d^8-74816\,a^7\,b^{10}\,c^7\,d^7+43264\,a^6\,b^{11}\,c^8\,d^6-13856\,a^5\,b^{12}\,c^9\,d^5+1984\,a^4\,b^{13}\,c^{10}\,d^4-32\,a^3\,b^{14}\,c^{11}\,d^3\right)\,1{}\mathrm{i}}{a^7\,d^7-7\,a^6\,b\,c\,d^6+21\,a^5\,b^2\,c^2\,d^5-35\,a^4\,b^3\,c^3\,d^4+35\,a^3\,b^4\,c^4\,d^3-21\,a^2\,b^5\,c^5\,d^2+7\,a\,b^6\,c^6\,d-b^7\,c^7}\right)\,{\left(-\frac{81\,a^4\,d^4+108\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+12\,a\,b^3\,c^3\,d+b^4\,c^4}{4096\,a^8\,c\,d^{11}-32768\,a^7\,b\,c^2\,d^{10}+114688\,a^6\,b^2\,c^3\,d^9-229376\,a^5\,b^3\,c^4\,d^8+286720\,a^4\,b^4\,c^5\,d^7-229376\,a^3\,b^5\,c^6\,d^6+114688\,a^2\,b^6\,c^7\,d^5-32768\,a\,b^7\,c^8\,d^4+4096\,b^8\,c^9\,d^3}\right)}^{3/4}\,1{}\mathrm{i}+\frac{\sqrt{x}\,\left(144\,a^8\,b^5\,c\,d^6+177\,a^7\,b^6\,c^2\,d^5+124\,a^6\,b^7\,c^3\,d^4+54\,a^5\,b^8\,c^4\,d^3+12\,a^4\,b^9\,c^5\,d^2+a^3\,b^{10}\,c^6\,d\right)\,1{}\mathrm{i}}{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)\,{\left(-\frac{81\,a^4\,d^4+108\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+12\,a\,b^3\,c^3\,d+b^4\,c^4}{4096\,a^8\,c\,d^{11}-32768\,a^7\,b\,c^2\,d^{10}+114688\,a^6\,b^2\,c^3\,d^9-229376\,a^5\,b^3\,c^4\,d^8+286720\,a^4\,b^4\,c^5\,d^7-229376\,a^3\,b^5\,c^6\,d^6+114688\,a^2\,b^6\,c^7\,d^5-32768\,a\,b^7\,c^8\,d^4+4096\,b^8\,c^9\,d^3}\right)}^{1/4}+\left(\left(-\frac{\sqrt{x}\,{\left(-\frac{81\,a^4\,d^4+108\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+12\,a\,b^3\,c^3\,d+b^4\,c^4}{4096\,a^8\,c\,d^{11}-32768\,a^7\,b\,c^2\,d^{10}+114688\,a^6\,b^2\,c^3\,d^9-229376\,a^5\,b^3\,c^4\,d^8+286720\,a^4\,b^4\,c^5\,d^7-229376\,a^3\,b^5\,c^6\,d^6+114688\,a^2\,b^6\,c^7\,d^5-32768\,a\,b^7\,c^8\,d^4+4096\,b^8\,c^9\,d^3}\right)}^{1/4}\,\left(2304\,a^{13}\,b^4\,c\,d^{14}-16896\,a^{12}\,b^5\,c^2\,d^{13}+56576\,a^{11}\,b^6\,c^3\,d^{12}-120832\,a^{10}\,b^7\,c^4\,d^{11}+197120\,a^9\,b^8\,c^5\,d^{10}-265216\,a^8\,b^9\,c^6\,d^9+283136\,a^7\,b^{10}\,c^7\,d^8-219136\,a^6\,b^{11}\,c^8\,d^7+111872\,a^5\,b^{12}\,c^9\,d^6-33280\,a^4\,b^{13}\,c^{10}\,d^5+4352\,a^3\,b^{14}\,c^{11}\,d^4\right)}{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}+\frac{\left(864\,a^{13}\,b^4\,c\,d^{13}-5184\,a^{12}\,b^5\,c^2\,d^{12}+10336\,a^{11}\,b^6\,c^3\,d^{11}+256\,a^{10}\,b^7\,c^4\,d^{10}-37184\,a^9\,b^8\,c^5\,d^9+74368\,a^8\,b^9\,c^6\,d^8-74816\,a^7\,b^{10}\,c^7\,d^7+43264\,a^6\,b^{11}\,c^8\,d^6-13856\,a^5\,b^{12}\,c^9\,d^5+1984\,a^4\,b^{13}\,c^{10}\,d^4-32\,a^3\,b^{14}\,c^{11}\,d^3\right)\,1{}\mathrm{i}}{a^7\,d^7-7\,a^6\,b\,c\,d^6+21\,a^5\,b^2\,c^2\,d^5-35\,a^4\,b^3\,c^3\,d^4+35\,a^3\,b^4\,c^4\,d^3-21\,a^2\,b^5\,c^5\,d^2+7\,a\,b^6\,c^6\,d-b^7\,c^7}\right)\,{\left(-\frac{81\,a^4\,d^4+108\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+12\,a\,b^3\,c^3\,d+b^4\,c^4}{4096\,a^8\,c\,d^{11}-32768\,a^7\,b\,c^2\,d^{10}+114688\,a^6\,b^2\,c^3\,d^9-229376\,a^5\,b^3\,c^4\,d^8+286720\,a^4\,b^4\,c^5\,d^7-229376\,a^3\,b^5\,c^6\,d^6+114688\,a^2\,b^6\,c^7\,d^5-32768\,a\,b^7\,c^8\,d^4+4096\,b^8\,c^9\,d^3}\right)}^{3/4}\,1{}\mathrm{i}-\frac{\sqrt{x}\,\left(144\,a^8\,b^5\,c\,d^6+177\,a^7\,b^6\,c^2\,d^5+124\,a^6\,b^7\,c^3\,d^4+54\,a^5\,b^8\,c^4\,d^3+12\,a^4\,b^9\,c^5\,d^2+a^3\,b^{10}\,c^6\,d\right)\,1{}\mathrm{i}}{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)\,{\left(-\frac{81\,a^4\,d^4+108\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+12\,a\,b^3\,c^3\,d+b^4\,c^4}{4096\,a^8\,c\,d^{11}-32768\,a^7\,b\,c^2\,d^{10}+114688\,a^6\,b^2\,c^3\,d^9-229376\,a^5\,b^3\,c^4\,d^8+286720\,a^4\,b^4\,c^5\,d^7-229376\,a^3\,b^5\,c^6\,d^6+114688\,a^2\,b^6\,c^7\,d^5-32768\,a\,b^7\,c^8\,d^4+4096\,b^8\,c^9\,d^3}\right)}^{1/4}}\right)\,{\left(-\frac{81\,a^4\,d^4+108\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+12\,a\,b^3\,c^3\,d+b^4\,c^4}{4096\,a^8\,c\,d^{11}-32768\,a^7\,b\,c^2\,d^{10}+114688\,a^6\,b^2\,c^3\,d^9-229376\,a^5\,b^3\,c^4\,d^8+286720\,a^4\,b^4\,c^5\,d^7-229376\,a^3\,b^5\,c^6\,d^6+114688\,a^2\,b^6\,c^7\,d^5-32768\,a\,b^7\,c^8\,d^4+4096\,b^8\,c^9\,d^3}\right)}^{1/4}-\frac{x^{3/2}}{2\,\left(d\,x^2+c\right)\,\left(a\,d-b\,c\right)}+\mathrm{atan}\left(\frac{\left(\left(\frac{864\,a^{13}\,b^4\,c\,d^{13}-5184\,a^{12}\,b^5\,c^2\,d^{12}+10336\,a^{11}\,b^6\,c^3\,d^{11}+256\,a^{10}\,b^7\,c^4\,d^{10}-37184\,a^9\,b^8\,c^5\,d^9+74368\,a^8\,b^9\,c^6\,d^8-74816\,a^7\,b^{10}\,c^7\,d^7+43264\,a^6\,b^{11}\,c^8\,d^6-13856\,a^5\,b^{12}\,c^9\,d^5+1984\,a^4\,b^{13}\,c^{10}\,d^4-32\,a^3\,b^{14}\,c^{11}\,d^3}{a^7\,d^7-7\,a^6\,b\,c\,d^6+21\,a^5\,b^2\,c^2\,d^5-35\,a^4\,b^3\,c^3\,d^4+35\,a^3\,b^4\,c^4\,d^3-21\,a^2\,b^5\,c^5\,d^2+7\,a\,b^6\,c^6\,d-b^7\,c^7}+\frac{\sqrt{x}\,{\left(-\frac{a^3\,b}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{1/4}\,\left(2304\,a^{13}\,b^4\,c\,d^{14}-16896\,a^{12}\,b^5\,c^2\,d^{13}+56576\,a^{11}\,b^6\,c^3\,d^{12}-120832\,a^{10}\,b^7\,c^4\,d^{11}+197120\,a^9\,b^8\,c^5\,d^{10}-265216\,a^8\,b^9\,c^6\,d^9+283136\,a^7\,b^{10}\,c^7\,d^8-219136\,a^6\,b^{11}\,c^8\,d^7+111872\,a^5\,b^{12}\,c^9\,d^6-33280\,a^4\,b^{13}\,c^{10}\,d^5+4352\,a^3\,b^{14}\,c^{11}\,d^4\right)}{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)\,{\left(-\frac{a^3\,b}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{3/4}\,1{}\mathrm{i}+\frac{\sqrt{x}\,\left(144\,a^8\,b^5\,c\,d^6+177\,a^7\,b^6\,c^2\,d^5+124\,a^6\,b^7\,c^3\,d^4+54\,a^5\,b^8\,c^4\,d^3+12\,a^4\,b^9\,c^5\,d^2+a^3\,b^{10}\,c^6\,d\right)\,1{}\mathrm{i}}{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)\,{\left(-\frac{a^3\,b}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{1/4}-\left(\left(\frac{864\,a^{13}\,b^4\,c\,d^{13}-5184\,a^{12}\,b^5\,c^2\,d^{12}+10336\,a^{11}\,b^6\,c^3\,d^{11}+256\,a^{10}\,b^7\,c^4\,d^{10}-37184\,a^9\,b^8\,c^5\,d^9+74368\,a^8\,b^9\,c^6\,d^8-74816\,a^7\,b^{10}\,c^7\,d^7+43264\,a^6\,b^{11}\,c^8\,d^6-13856\,a^5\,b^{12}\,c^9\,d^5+1984\,a^4\,b^{13}\,c^{10}\,d^4-32\,a^3\,b^{14}\,c^{11}\,d^3}{a^7\,d^7-7\,a^6\,b\,c\,d^6+21\,a^5\,b^2\,c^2\,d^5-35\,a^4\,b^3\,c^3\,d^4+35\,a^3\,b^4\,c^4\,d^3-21\,a^2\,b^5\,c^5\,d^2+7\,a\,b^6\,c^6\,d-b^7\,c^7}-\frac{\sqrt{x}\,{\left(-\frac{a^3\,b}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{1/4}\,\left(2304\,a^{13}\,b^4\,c\,d^{14}-16896\,a^{12}\,b^5\,c^2\,d^{13}+56576\,a^{11}\,b^6\,c^3\,d^{12}-120832\,a^{10}\,b^7\,c^4\,d^{11}+197120\,a^9\,b^8\,c^5\,d^{10}-265216\,a^8\,b^9\,c^6\,d^9+283136\,a^7\,b^{10}\,c^7\,d^8-219136\,a^6\,b^{11}\,c^8\,d^7+111872\,a^5\,b^{12}\,c^9\,d^6-33280\,a^4\,b^{13}\,c^{10}\,d^5+4352\,a^3\,b^{14}\,c^{11}\,d^4\right)}{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)\,{\left(-\frac{a^3\,b}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{3/4}\,1{}\mathrm{i}-\frac{\sqrt{x}\,\left(144\,a^8\,b^5\,c\,d^6+177\,a^7\,b^6\,c^2\,d^5+124\,a^6\,b^7\,c^3\,d^4+54\,a^5\,b^8\,c^4\,d^3+12\,a^4\,b^9\,c^5\,d^2+a^3\,b^{10}\,c^6\,d\right)\,1{}\mathrm{i}}{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)\,{\left(-\frac{a^3\,b}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{1/4}}{\frac{108\,a^8\,b^5\,c\,d^5+135\,a^7\,b^6\,c^2\,d^4+63\,a^6\,b^7\,c^3\,d^3+13\,a^5\,b^8\,c^4\,d^2+a^4\,b^9\,c^5\,d}{a^7\,d^7-7\,a^6\,b\,c\,d^6+21\,a^5\,b^2\,c^2\,d^5-35\,a^4\,b^3\,c^3\,d^4+35\,a^3\,b^4\,c^4\,d^3-21\,a^2\,b^5\,c^5\,d^2+7\,a\,b^6\,c^6\,d-b^7\,c^7}+\left(\left(\frac{864\,a^{13}\,b^4\,c\,d^{13}-5184\,a^{12}\,b^5\,c^2\,d^{12}+10336\,a^{11}\,b^6\,c^3\,d^{11}+256\,a^{10}\,b^7\,c^4\,d^{10}-37184\,a^9\,b^8\,c^5\,d^9+74368\,a^8\,b^9\,c^6\,d^8-74816\,a^7\,b^{10}\,c^7\,d^7+43264\,a^6\,b^{11}\,c^8\,d^6-13856\,a^5\,b^{12}\,c^9\,d^5+1984\,a^4\,b^{13}\,c^{10}\,d^4-32\,a^3\,b^{14}\,c^{11}\,d^3}{a^7\,d^7-7\,a^6\,b\,c\,d^6+21\,a^5\,b^2\,c^2\,d^5-35\,a^4\,b^3\,c^3\,d^4+35\,a^3\,b^4\,c^4\,d^3-21\,a^2\,b^5\,c^5\,d^2+7\,a\,b^6\,c^6\,d-b^7\,c^7}+\frac{\sqrt{x}\,{\left(-\frac{a^3\,b}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{1/4}\,\left(2304\,a^{13}\,b^4\,c\,d^{14}-16896\,a^{12}\,b^5\,c^2\,d^{13}+56576\,a^{11}\,b^6\,c^3\,d^{12}-120832\,a^{10}\,b^7\,c^4\,d^{11}+197120\,a^9\,b^8\,c^5\,d^{10}-265216\,a^8\,b^9\,c^6\,d^9+283136\,a^7\,b^{10}\,c^7\,d^8-219136\,a^6\,b^{11}\,c^8\,d^7+111872\,a^5\,b^{12}\,c^9\,d^6-33280\,a^4\,b^{13}\,c^{10}\,d^5+4352\,a^3\,b^{14}\,c^{11}\,d^4\right)}{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)\,{\left(-\frac{a^3\,b}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{3/4}+\frac{\sqrt{x}\,\left(144\,a^8\,b^5\,c\,d^6+177\,a^7\,b^6\,c^2\,d^5+124\,a^6\,b^7\,c^3\,d^4+54\,a^5\,b^8\,c^4\,d^3+12\,a^4\,b^9\,c^5\,d^2+a^3\,b^{10}\,c^6\,d\right)}{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)\,{\left(-\frac{a^3\,b}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{1/4}+\left(\left(\frac{864\,a^{13}\,b^4\,c\,d^{13}-5184\,a^{12}\,b^5\,c^2\,d^{12}+10336\,a^{11}\,b^6\,c^3\,d^{11}+256\,a^{10}\,b^7\,c^4\,d^{10}-37184\,a^9\,b^8\,c^5\,d^9+74368\,a^8\,b^9\,c^6\,d^8-74816\,a^7\,b^{10}\,c^7\,d^7+43264\,a^6\,b^{11}\,c^8\,d^6-13856\,a^5\,b^{12}\,c^9\,d^5+1984\,a^4\,b^{13}\,c^{10}\,d^4-32\,a^3\,b^{14}\,c^{11}\,d^3}{a^7\,d^7-7\,a^6\,b\,c\,d^6+21\,a^5\,b^2\,c^2\,d^5-35\,a^4\,b^3\,c^3\,d^4+35\,a^3\,b^4\,c^4\,d^3-21\,a^2\,b^5\,c^5\,d^2+7\,a\,b^6\,c^6\,d-b^7\,c^7}-\frac{\sqrt{x}\,{\left(-\frac{a^3\,b}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{1/4}\,\left(2304\,a^{13}\,b^4\,c\,d^{14}-16896\,a^{12}\,b^5\,c^2\,d^{13}+56576\,a^{11}\,b^6\,c^3\,d^{12}-120832\,a^{10}\,b^7\,c^4\,d^{11}+197120\,a^9\,b^8\,c^5\,d^{10}-265216\,a^8\,b^9\,c^6\,d^9+283136\,a^7\,b^{10}\,c^7\,d^8-219136\,a^6\,b^{11}\,c^8\,d^7+111872\,a^5\,b^{12}\,c^9\,d^6-33280\,a^4\,b^{13}\,c^{10}\,d^5+4352\,a^3\,b^{14}\,c^{11}\,d^4\right)}{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)\,{\left(-\frac{a^3\,b}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{3/4}-\frac{\sqrt{x}\,\left(144\,a^8\,b^5\,c\,d^6+177\,a^7\,b^6\,c^2\,d^5+124\,a^6\,b^7\,c^3\,d^4+54\,a^5\,b^8\,c^4\,d^3+12\,a^4\,b^9\,c^5\,d^2+a^3\,b^{10}\,c^6\,d\right)}{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)\,{\left(-\frac{a^3\,b}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{1/4}}\right)\,{\left(-\frac{a^3\,b}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{1/4}\,2{}\mathrm{i}+\mathrm{atan}\left(\frac{\left(\left(\frac{864\,a^{13}\,b^4\,c\,d^{13}-5184\,a^{12}\,b^5\,c^2\,d^{12}+10336\,a^{11}\,b^6\,c^3\,d^{11}+256\,a^{10}\,b^7\,c^4\,d^{10}-37184\,a^9\,b^8\,c^5\,d^9+74368\,a^8\,b^9\,c^6\,d^8-74816\,a^7\,b^{10}\,c^7\,d^7+43264\,a^6\,b^{11}\,c^8\,d^6-13856\,a^5\,b^{12}\,c^9\,d^5+1984\,a^4\,b^{13}\,c^{10}\,d^4-32\,a^3\,b^{14}\,c^{11}\,d^3}{a^7\,d^7-7\,a^6\,b\,c\,d^6+21\,a^5\,b^2\,c^2\,d^5-35\,a^4\,b^3\,c^3\,d^4+35\,a^3\,b^4\,c^4\,d^3-21\,a^2\,b^5\,c^5\,d^2+7\,a\,b^6\,c^6\,d-b^7\,c^7}+\frac{\sqrt{x}\,{\left(-\frac{81\,a^4\,d^4+108\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+12\,a\,b^3\,c^3\,d+b^4\,c^4}{4096\,a^8\,c\,d^{11}-32768\,a^7\,b\,c^2\,d^{10}+114688\,a^6\,b^2\,c^3\,d^9-229376\,a^5\,b^3\,c^4\,d^8+286720\,a^4\,b^4\,c^5\,d^7-229376\,a^3\,b^5\,c^6\,d^6+114688\,a^2\,b^6\,c^7\,d^5-32768\,a\,b^7\,c^8\,d^4+4096\,b^8\,c^9\,d^3}\right)}^{1/4}\,\left(2304\,a^{13}\,b^4\,c\,d^{14}-16896\,a^{12}\,b^5\,c^2\,d^{13}+56576\,a^{11}\,b^6\,c^3\,d^{12}-120832\,a^{10}\,b^7\,c^4\,d^{11}+197120\,a^9\,b^8\,c^5\,d^{10}-265216\,a^8\,b^9\,c^6\,d^9+283136\,a^7\,b^{10}\,c^7\,d^8-219136\,a^6\,b^{11}\,c^8\,d^7+111872\,a^5\,b^{12}\,c^9\,d^6-33280\,a^4\,b^{13}\,c^{10}\,d^5+4352\,a^3\,b^{14}\,c^{11}\,d^4\right)}{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)\,{\left(-\frac{81\,a^4\,d^4+108\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+12\,a\,b^3\,c^3\,d+b^4\,c^4}{4096\,a^8\,c\,d^{11}-32768\,a^7\,b\,c^2\,d^{10}+114688\,a^6\,b^2\,c^3\,d^9-229376\,a^5\,b^3\,c^4\,d^8+286720\,a^4\,b^4\,c^5\,d^7-229376\,a^3\,b^5\,c^6\,d^6+114688\,a^2\,b^6\,c^7\,d^5-32768\,a\,b^7\,c^8\,d^4+4096\,b^8\,c^9\,d^3}\right)}^{3/4}\,1{}\mathrm{i}+\frac{\sqrt{x}\,\left(144\,a^8\,b^5\,c\,d^6+177\,a^7\,b^6\,c^2\,d^5+124\,a^6\,b^7\,c^3\,d^4+54\,a^5\,b^8\,c^4\,d^3+12\,a^4\,b^9\,c^5\,d^2+a^3\,b^{10}\,c^6\,d\right)\,1{}\mathrm{i}}{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)\,{\left(-\frac{81\,a^4\,d^4+108\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+12\,a\,b^3\,c^3\,d+b^4\,c^4}{4096\,a^8\,c\,d^{11}-32768\,a^7\,b\,c^2\,d^{10}+114688\,a^6\,b^2\,c^3\,d^9-229376\,a^5\,b^3\,c^4\,d^8+286720\,a^4\,b^4\,c^5\,d^7-229376\,a^3\,b^5\,c^6\,d^6+114688\,a^2\,b^6\,c^7\,d^5-32768\,a\,b^7\,c^8\,d^4+4096\,b^8\,c^9\,d^3}\right)}^{1/4}-\left(\left(\frac{864\,a^{13}\,b^4\,c\,d^{13}-5184\,a^{12}\,b^5\,c^2\,d^{12}+10336\,a^{11}\,b^6\,c^3\,d^{11}+256\,a^{10}\,b^7\,c^4\,d^{10}-37184\,a^9\,b^8\,c^5\,d^9+74368\,a^8\,b^9\,c^6\,d^8-74816\,a^7\,b^{10}\,c^7\,d^7+43264\,a^6\,b^{11}\,c^8\,d^6-13856\,a^5\,b^{12}\,c^9\,d^5+1984\,a^4\,b^{13}\,c^{10}\,d^4-32\,a^3\,b^{14}\,c^{11}\,d^3}{a^7\,d^7-7\,a^6\,b\,c\,d^6+21\,a^5\,b^2\,c^2\,d^5-35\,a^4\,b^3\,c^3\,d^4+35\,a^3\,b^4\,c^4\,d^3-21\,a^2\,b^5\,c^5\,d^2+7\,a\,b^6\,c^6\,d-b^7\,c^7}-\frac{\sqrt{x}\,{\left(-\frac{81\,a^4\,d^4+108\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+12\,a\,b^3\,c^3\,d+b^4\,c^4}{4096\,a^8\,c\,d^{11}-32768\,a^7\,b\,c^2\,d^{10}+114688\,a^6\,b^2\,c^3\,d^9-229376\,a^5\,b^3\,c^4\,d^8+286720\,a^4\,b^4\,c^5\,d^7-229376\,a^3\,b^5\,c^6\,d^6+114688\,a^2\,b^6\,c^7\,d^5-32768\,a\,b^7\,c^8\,d^4+4096\,b^8\,c^9\,d^3}\right)}^{1/4}\,\left(2304\,a^{13}\,b^4\,c\,d^{14}-16896\,a^{12}\,b^5\,c^2\,d^{13}+56576\,a^{11}\,b^6\,c^3\,d^{12}-120832\,a^{10}\,b^7\,c^4\,d^{11}+197120\,a^9\,b^8\,c^5\,d^{10}-265216\,a^8\,b^9\,c^6\,d^9+283136\,a^7\,b^{10}\,c^7\,d^8-219136\,a^6\,b^{11}\,c^8\,d^7+111872\,a^5\,b^{12}\,c^9\,d^6-33280\,a^4\,b^{13}\,c^{10}\,d^5+4352\,a^3\,b^{14}\,c^{11}\,d^4\right)}{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)\,{\left(-\frac{81\,a^4\,d^4+108\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+12\,a\,b^3\,c^3\,d+b^4\,c^4}{4096\,a^8\,c\,d^{11}-32768\,a^7\,b\,c^2\,d^{10}+114688\,a^6\,b^2\,c^3\,d^9-229376\,a^5\,b^3\,c^4\,d^8+286720\,a^4\,b^4\,c^5\,d^7-229376\,a^3\,b^5\,c^6\,d^6+114688\,a^2\,b^6\,c^7\,d^5-32768\,a\,b^7\,c^8\,d^4+4096\,b^8\,c^9\,d^3}\right)}^{3/4}\,1{}\mathrm{i}-\frac{\sqrt{x}\,\left(144\,a^8\,b^5\,c\,d^6+177\,a^7\,b^6\,c^2\,d^5+124\,a^6\,b^7\,c^3\,d^4+54\,a^5\,b^8\,c^4\,d^3+12\,a^4\,b^9\,c^5\,d^2+a^3\,b^{10}\,c^6\,d\right)\,1{}\mathrm{i}}{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)\,{\left(-\frac{81\,a^4\,d^4+108\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+12\,a\,b^3\,c^3\,d+b^4\,c^4}{4096\,a^8\,c\,d^{11}-32768\,a^7\,b\,c^2\,d^{10}+114688\,a^6\,b^2\,c^3\,d^9-229376\,a^5\,b^3\,c^4\,d^8+286720\,a^4\,b^4\,c^5\,d^7-229376\,a^3\,b^5\,c^6\,d^6+114688\,a^2\,b^6\,c^7\,d^5-32768\,a\,b^7\,c^8\,d^4+4096\,b^8\,c^9\,d^3}\right)}^{1/4}}{\frac{108\,a^8\,b^5\,c\,d^5+135\,a^7\,b^6\,c^2\,d^4+63\,a^6\,b^7\,c^3\,d^3+13\,a^5\,b^8\,c^4\,d^2+a^4\,b^9\,c^5\,d}{a^7\,d^7-7\,a^6\,b\,c\,d^6+21\,a^5\,b^2\,c^2\,d^5-35\,a^4\,b^3\,c^3\,d^4+35\,a^3\,b^4\,c^4\,d^3-21\,a^2\,b^5\,c^5\,d^2+7\,a\,b^6\,c^6\,d-b^7\,c^7}+\left(\left(\frac{864\,a^{13}\,b^4\,c\,d^{13}-5184\,a^{12}\,b^5\,c^2\,d^{12}+10336\,a^{11}\,b^6\,c^3\,d^{11}+256\,a^{10}\,b^7\,c^4\,d^{10}-37184\,a^9\,b^8\,c^5\,d^9+74368\,a^8\,b^9\,c^6\,d^8-74816\,a^7\,b^{10}\,c^7\,d^7+43264\,a^6\,b^{11}\,c^8\,d^6-13856\,a^5\,b^{12}\,c^9\,d^5+1984\,a^4\,b^{13}\,c^{10}\,d^4-32\,a^3\,b^{14}\,c^{11}\,d^3}{a^7\,d^7-7\,a^6\,b\,c\,d^6+21\,a^5\,b^2\,c^2\,d^5-35\,a^4\,b^3\,c^3\,d^4+35\,a^3\,b^4\,c^4\,d^3-21\,a^2\,b^5\,c^5\,d^2+7\,a\,b^6\,c^6\,d-b^7\,c^7}+\frac{\sqrt{x}\,{\left(-\frac{81\,a^4\,d^4+108\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+12\,a\,b^3\,c^3\,d+b^4\,c^4}{4096\,a^8\,c\,d^{11}-32768\,a^7\,b\,c^2\,d^{10}+114688\,a^6\,b^2\,c^3\,d^9-229376\,a^5\,b^3\,c^4\,d^8+286720\,a^4\,b^4\,c^5\,d^7-229376\,a^3\,b^5\,c^6\,d^6+114688\,a^2\,b^6\,c^7\,d^5-32768\,a\,b^7\,c^8\,d^4+4096\,b^8\,c^9\,d^3}\right)}^{1/4}\,\left(2304\,a^{13}\,b^4\,c\,d^{14}-16896\,a^{12}\,b^5\,c^2\,d^{13}+56576\,a^{11}\,b^6\,c^3\,d^{12}-120832\,a^{10}\,b^7\,c^4\,d^{11}+197120\,a^9\,b^8\,c^5\,d^{10}-265216\,a^8\,b^9\,c^6\,d^9+283136\,a^7\,b^{10}\,c^7\,d^8-219136\,a^6\,b^{11}\,c^8\,d^7+111872\,a^5\,b^{12}\,c^9\,d^6-33280\,a^4\,b^{13}\,c^{10}\,d^5+4352\,a^3\,b^{14}\,c^{11}\,d^4\right)}{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)\,{\left(-\frac{81\,a^4\,d^4+108\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+12\,a\,b^3\,c^3\,d+b^4\,c^4}{4096\,a^8\,c\,d^{11}-32768\,a^7\,b\,c^2\,d^{10}+114688\,a^6\,b^2\,c^3\,d^9-229376\,a^5\,b^3\,c^4\,d^8+286720\,a^4\,b^4\,c^5\,d^7-229376\,a^3\,b^5\,c^6\,d^6+114688\,a^2\,b^6\,c^7\,d^5-32768\,a\,b^7\,c^8\,d^4+4096\,b^8\,c^9\,d^3}\right)}^{3/4}+\frac{\sqrt{x}\,\left(144\,a^8\,b^5\,c\,d^6+177\,a^7\,b^6\,c^2\,d^5+124\,a^6\,b^7\,c^3\,d^4+54\,a^5\,b^8\,c^4\,d^3+12\,a^4\,b^9\,c^5\,d^2+a^3\,b^{10}\,c^6\,d\right)}{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)\,{\left(-\frac{81\,a^4\,d^4+108\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+12\,a\,b^3\,c^3\,d+b^4\,c^4}{4096\,a^8\,c\,d^{11}-32768\,a^7\,b\,c^2\,d^{10}+114688\,a^6\,b^2\,c^3\,d^9-229376\,a^5\,b^3\,c^4\,d^8+286720\,a^4\,b^4\,c^5\,d^7-229376\,a^3\,b^5\,c^6\,d^6+114688\,a^2\,b^6\,c^7\,d^5-32768\,a\,b^7\,c^8\,d^4+4096\,b^8\,c^9\,d^3}\right)}^{1/4}+\left(\left(\frac{864\,a^{13}\,b^4\,c\,d^{13}-5184\,a^{12}\,b^5\,c^2\,d^{12}+10336\,a^{11}\,b^6\,c^3\,d^{11}+256\,a^{10}\,b^7\,c^4\,d^{10}-37184\,a^9\,b^8\,c^5\,d^9+74368\,a^8\,b^9\,c^6\,d^8-74816\,a^7\,b^{10}\,c^7\,d^7+43264\,a^6\,b^{11}\,c^8\,d^6-13856\,a^5\,b^{12}\,c^9\,d^5+1984\,a^4\,b^{13}\,c^{10}\,d^4-32\,a^3\,b^{14}\,c^{11}\,d^3}{a^7\,d^7-7\,a^6\,b\,c\,d^6+21\,a^5\,b^2\,c^2\,d^5-35\,a^4\,b^3\,c^3\,d^4+35\,a^3\,b^4\,c^4\,d^3-21\,a^2\,b^5\,c^5\,d^2+7\,a\,b^6\,c^6\,d-b^7\,c^7}-\frac{\sqrt{x}\,{\left(-\frac{81\,a^4\,d^4+108\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+12\,a\,b^3\,c^3\,d+b^4\,c^4}{4096\,a^8\,c\,d^{11}-32768\,a^7\,b\,c^2\,d^{10}+114688\,a^6\,b^2\,c^3\,d^9-229376\,a^5\,b^3\,c^4\,d^8+286720\,a^4\,b^4\,c^5\,d^7-229376\,a^3\,b^5\,c^6\,d^6+114688\,a^2\,b^6\,c^7\,d^5-32768\,a\,b^7\,c^8\,d^4+4096\,b^8\,c^9\,d^3}\right)}^{1/4}\,\left(2304\,a^{13}\,b^4\,c\,d^{14}-16896\,a^{12}\,b^5\,c^2\,d^{13}+56576\,a^{11}\,b^6\,c^3\,d^{12}-120832\,a^{10}\,b^7\,c^4\,d^{11}+197120\,a^9\,b^8\,c^5\,d^{10}-265216\,a^8\,b^9\,c^6\,d^9+283136\,a^7\,b^{10}\,c^7\,d^8-219136\,a^6\,b^{11}\,c^8\,d^7+111872\,a^5\,b^{12}\,c^9\,d^6-33280\,a^4\,b^{13}\,c^{10}\,d^5+4352\,a^3\,b^{14}\,c^{11}\,d^4\right)}{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)\,{\left(-\frac{81\,a^4\,d^4+108\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+12\,a\,b^3\,c^3\,d+b^4\,c^4}{4096\,a^8\,c\,d^{11}-32768\,a^7\,b\,c^2\,d^{10}+114688\,a^6\,b^2\,c^3\,d^9-229376\,a^5\,b^3\,c^4\,d^8+286720\,a^4\,b^4\,c^5\,d^7-229376\,a^3\,b^5\,c^6\,d^6+114688\,a^2\,b^6\,c^7\,d^5-32768\,a\,b^7\,c^8\,d^4+4096\,b^8\,c^9\,d^3}\right)}^{3/4}-\frac{\sqrt{x}\,\left(144\,a^8\,b^5\,c\,d^6+177\,a^7\,b^6\,c^2\,d^5+124\,a^6\,b^7\,c^3\,d^4+54\,a^5\,b^8\,c^4\,d^3+12\,a^4\,b^9\,c^5\,d^2+a^3\,b^{10}\,c^6\,d\right)}{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)\,{\left(-\frac{81\,a^4\,d^4+108\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+12\,a\,b^3\,c^3\,d+b^4\,c^4}{4096\,a^8\,c\,d^{11}-32768\,a^7\,b\,c^2\,d^{10}+114688\,a^6\,b^2\,c^3\,d^9-229376\,a^5\,b^3\,c^4\,d^8+286720\,a^4\,b^4\,c^5\,d^7-229376\,a^3\,b^5\,c^6\,d^6+114688\,a^2\,b^6\,c^7\,d^5-32768\,a\,b^7\,c^8\,d^4+4096\,b^8\,c^9\,d^3}\right)}^{1/4}}\right)\,{\left(-\frac{81\,a^4\,d^4+108\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+12\,a\,b^3\,c^3\,d+b^4\,c^4}{4096\,a^8\,c\,d^{11}-32768\,a^7\,b\,c^2\,d^{10}+114688\,a^6\,b^2\,c^3\,d^9-229376\,a^5\,b^3\,c^4\,d^8+286720\,a^4\,b^4\,c^5\,d^7-229376\,a^3\,b^5\,c^6\,d^6+114688\,a^2\,b^6\,c^7\,d^5-32768\,a\,b^7\,c^8\,d^4+4096\,b^8\,c^9\,d^3}\right)}^{1/4}\,2{}\mathrm{i}","Not used",1,"atan(((((864*a^13*b^4*c*d^13 - 32*a^3*b^14*c^11*d^3 + 1984*a^4*b^13*c^10*d^4 - 13856*a^5*b^12*c^9*d^5 + 43264*a^6*b^11*c^8*d^6 - 74816*a^7*b^10*c^7*d^7 + 74368*a^8*b^9*c^6*d^8 - 37184*a^9*b^8*c^5*d^9 + 256*a^10*b^7*c^4*d^10 + 10336*a^11*b^6*c^3*d^11 - 5184*a^12*b^5*c^2*d^12)/(a^7*d^7 - b^7*c^7 - 21*a^2*b^5*c^5*d^2 + 35*a^3*b^4*c^4*d^3 - 35*a^4*b^3*c^3*d^4 + 21*a^5*b^2*c^2*d^5 + 7*a*b^6*c^6*d - 7*a^6*b*c*d^6) + (x^(1/2)*(-(a^3*b)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(1/4)*(2304*a^13*b^4*c*d^14 + 4352*a^3*b^14*c^11*d^4 - 33280*a^4*b^13*c^10*d^5 + 111872*a^5*b^12*c^9*d^6 - 219136*a^6*b^11*c^8*d^7 + 283136*a^7*b^10*c^7*d^8 - 265216*a^8*b^9*c^6*d^9 + 197120*a^9*b^8*c^5*d^10 - 120832*a^10*b^7*c^4*d^11 + 56576*a^11*b^6*c^3*d^12 - 16896*a^12*b^5*c^2*d^13))/(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))*(-(a^3*b)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(3/4)*1i + (x^(1/2)*(a^3*b^10*c^6*d + 144*a^8*b^5*c*d^6 + 12*a^4*b^9*c^5*d^2 + 54*a^5*b^8*c^4*d^3 + 124*a^6*b^7*c^3*d^4 + 177*a^7*b^6*c^2*d^5)*1i)/(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))*(-(a^3*b)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(1/4) - (((864*a^13*b^4*c*d^13 - 32*a^3*b^14*c^11*d^3 + 1984*a^4*b^13*c^10*d^4 - 13856*a^5*b^12*c^9*d^5 + 43264*a^6*b^11*c^8*d^6 - 74816*a^7*b^10*c^7*d^7 + 74368*a^8*b^9*c^6*d^8 - 37184*a^9*b^8*c^5*d^9 + 256*a^10*b^7*c^4*d^10 + 10336*a^11*b^6*c^3*d^11 - 5184*a^12*b^5*c^2*d^12)/(a^7*d^7 - b^7*c^7 - 21*a^2*b^5*c^5*d^2 + 35*a^3*b^4*c^4*d^3 - 35*a^4*b^3*c^3*d^4 + 21*a^5*b^2*c^2*d^5 + 7*a*b^6*c^6*d - 7*a^6*b*c*d^6) - (x^(1/2)*(-(a^3*b)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(1/4)*(2304*a^13*b^4*c*d^14 + 4352*a^3*b^14*c^11*d^4 - 33280*a^4*b^13*c^10*d^5 + 111872*a^5*b^12*c^9*d^6 - 219136*a^6*b^11*c^8*d^7 + 283136*a^7*b^10*c^7*d^8 - 265216*a^8*b^9*c^6*d^9 + 197120*a^9*b^8*c^5*d^10 - 120832*a^10*b^7*c^4*d^11 + 56576*a^11*b^6*c^3*d^12 - 16896*a^12*b^5*c^2*d^13))/(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))*(-(a^3*b)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(3/4)*1i - (x^(1/2)*(a^3*b^10*c^6*d + 144*a^8*b^5*c*d^6 + 12*a^4*b^9*c^5*d^2 + 54*a^5*b^8*c^4*d^3 + 124*a^6*b^7*c^3*d^4 + 177*a^7*b^6*c^2*d^5)*1i)/(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))*(-(a^3*b)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(1/4))/((a^4*b^9*c^5*d + 108*a^8*b^5*c*d^5 + 13*a^5*b^8*c^4*d^2 + 63*a^6*b^7*c^3*d^3 + 135*a^7*b^6*c^2*d^4)/(a^7*d^7 - b^7*c^7 - 21*a^2*b^5*c^5*d^2 + 35*a^3*b^4*c^4*d^3 - 35*a^4*b^3*c^3*d^4 + 21*a^5*b^2*c^2*d^5 + 7*a*b^6*c^6*d - 7*a^6*b*c*d^6) + (((864*a^13*b^4*c*d^13 - 32*a^3*b^14*c^11*d^3 + 1984*a^4*b^13*c^10*d^4 - 13856*a^5*b^12*c^9*d^5 + 43264*a^6*b^11*c^8*d^6 - 74816*a^7*b^10*c^7*d^7 + 74368*a^8*b^9*c^6*d^8 - 37184*a^9*b^8*c^5*d^9 + 256*a^10*b^7*c^4*d^10 + 10336*a^11*b^6*c^3*d^11 - 5184*a^12*b^5*c^2*d^12)/(a^7*d^7 - b^7*c^7 - 21*a^2*b^5*c^5*d^2 + 35*a^3*b^4*c^4*d^3 - 35*a^4*b^3*c^3*d^4 + 21*a^5*b^2*c^2*d^5 + 7*a*b^6*c^6*d - 7*a^6*b*c*d^6) + (x^(1/2)*(-(a^3*b)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(1/4)*(2304*a^13*b^4*c*d^14 + 4352*a^3*b^14*c^11*d^4 - 33280*a^4*b^13*c^10*d^5 + 111872*a^5*b^12*c^9*d^6 - 219136*a^6*b^11*c^8*d^7 + 283136*a^7*b^10*c^7*d^8 - 265216*a^8*b^9*c^6*d^9 + 197120*a^9*b^8*c^5*d^10 - 120832*a^10*b^7*c^4*d^11 + 56576*a^11*b^6*c^3*d^12 - 16896*a^12*b^5*c^2*d^13))/(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))*(-(a^3*b)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(3/4) + (x^(1/2)*(a^3*b^10*c^6*d + 144*a^8*b^5*c*d^6 + 12*a^4*b^9*c^5*d^2 + 54*a^5*b^8*c^4*d^3 + 124*a^6*b^7*c^3*d^4 + 177*a^7*b^6*c^2*d^5))/(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))*(-(a^3*b)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(1/4) + (((864*a^13*b^4*c*d^13 - 32*a^3*b^14*c^11*d^3 + 1984*a^4*b^13*c^10*d^4 - 13856*a^5*b^12*c^9*d^5 + 43264*a^6*b^11*c^8*d^6 - 74816*a^7*b^10*c^7*d^7 + 74368*a^8*b^9*c^6*d^8 - 37184*a^9*b^8*c^5*d^9 + 256*a^10*b^7*c^4*d^10 + 10336*a^11*b^6*c^3*d^11 - 5184*a^12*b^5*c^2*d^12)/(a^7*d^7 - b^7*c^7 - 21*a^2*b^5*c^5*d^2 + 35*a^3*b^4*c^4*d^3 - 35*a^4*b^3*c^3*d^4 + 21*a^5*b^2*c^2*d^5 + 7*a*b^6*c^6*d - 7*a^6*b*c*d^6) - (x^(1/2)*(-(a^3*b)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(1/4)*(2304*a^13*b^4*c*d^14 + 4352*a^3*b^14*c^11*d^4 - 33280*a^4*b^13*c^10*d^5 + 111872*a^5*b^12*c^9*d^6 - 219136*a^6*b^11*c^8*d^7 + 283136*a^7*b^10*c^7*d^8 - 265216*a^8*b^9*c^6*d^9 + 197120*a^9*b^8*c^5*d^10 - 120832*a^10*b^7*c^4*d^11 + 56576*a^11*b^6*c^3*d^12 - 16896*a^12*b^5*c^2*d^13))/(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))*(-(a^3*b)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(3/4) - (x^(1/2)*(a^3*b^10*c^6*d + 144*a^8*b^5*c*d^6 + 12*a^4*b^9*c^5*d^2 + 54*a^5*b^8*c^4*d^3 + 124*a^6*b^7*c^3*d^4 + 177*a^7*b^6*c^2*d^5))/(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))*(-(a^3*b)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(1/4)))*(-(a^3*b)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(1/4)*2i - 2*atan((((((864*a^13*b^4*c*d^13 - 32*a^3*b^14*c^11*d^3 + 1984*a^4*b^13*c^10*d^4 - 13856*a^5*b^12*c^9*d^5 + 43264*a^6*b^11*c^8*d^6 - 74816*a^7*b^10*c^7*d^7 + 74368*a^8*b^9*c^6*d^8 - 37184*a^9*b^8*c^5*d^9 + 256*a^10*b^7*c^4*d^10 + 10336*a^11*b^6*c^3*d^11 - 5184*a^12*b^5*c^2*d^12)*1i)/(a^7*d^7 - b^7*c^7 - 21*a^2*b^5*c^5*d^2 + 35*a^3*b^4*c^4*d^3 - 35*a^4*b^3*c^3*d^4 + 21*a^5*b^2*c^2*d^5 + 7*a*b^6*c^6*d - 7*a^6*b*c*d^6) + (x^(1/2)*(-(a^3*b)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(1/4)*(2304*a^13*b^4*c*d^14 + 4352*a^3*b^14*c^11*d^4 - 33280*a^4*b^13*c^10*d^5 + 111872*a^5*b^12*c^9*d^6 - 219136*a^6*b^11*c^8*d^7 + 283136*a^7*b^10*c^7*d^8 - 265216*a^8*b^9*c^6*d^9 + 197120*a^9*b^8*c^5*d^10 - 120832*a^10*b^7*c^4*d^11 + 56576*a^11*b^6*c^3*d^12 - 16896*a^12*b^5*c^2*d^13))/(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))*(-(a^3*b)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(3/4) + (x^(1/2)*(a^3*b^10*c^6*d + 144*a^8*b^5*c*d^6 + 12*a^4*b^9*c^5*d^2 + 54*a^5*b^8*c^4*d^3 + 124*a^6*b^7*c^3*d^4 + 177*a^7*b^6*c^2*d^5))/(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))*(-(a^3*b)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(1/4) - ((((864*a^13*b^4*c*d^13 - 32*a^3*b^14*c^11*d^3 + 1984*a^4*b^13*c^10*d^4 - 13856*a^5*b^12*c^9*d^5 + 43264*a^6*b^11*c^8*d^6 - 74816*a^7*b^10*c^7*d^7 + 74368*a^8*b^9*c^6*d^8 - 37184*a^9*b^8*c^5*d^9 + 256*a^10*b^7*c^4*d^10 + 10336*a^11*b^6*c^3*d^11 - 5184*a^12*b^5*c^2*d^12)*1i)/(a^7*d^7 - b^7*c^7 - 21*a^2*b^5*c^5*d^2 + 35*a^3*b^4*c^4*d^3 - 35*a^4*b^3*c^3*d^4 + 21*a^5*b^2*c^2*d^5 + 7*a*b^6*c^6*d - 7*a^6*b*c*d^6) - (x^(1/2)*(-(a^3*b)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(1/4)*(2304*a^13*b^4*c*d^14 + 4352*a^3*b^14*c^11*d^4 - 33280*a^4*b^13*c^10*d^5 + 111872*a^5*b^12*c^9*d^6 - 219136*a^6*b^11*c^8*d^7 + 283136*a^7*b^10*c^7*d^8 - 265216*a^8*b^9*c^6*d^9 + 197120*a^9*b^8*c^5*d^10 - 120832*a^10*b^7*c^4*d^11 + 56576*a^11*b^6*c^3*d^12 - 16896*a^12*b^5*c^2*d^13))/(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))*(-(a^3*b)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(3/4) - (x^(1/2)*(a^3*b^10*c^6*d + 144*a^8*b^5*c*d^6 + 12*a^4*b^9*c^5*d^2 + 54*a^5*b^8*c^4*d^3 + 124*a^6*b^7*c^3*d^4 + 177*a^7*b^6*c^2*d^5))/(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))*(-(a^3*b)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(1/4))/(((((864*a^13*b^4*c*d^13 - 32*a^3*b^14*c^11*d^3 + 1984*a^4*b^13*c^10*d^4 - 13856*a^5*b^12*c^9*d^5 + 43264*a^6*b^11*c^8*d^6 - 74816*a^7*b^10*c^7*d^7 + 74368*a^8*b^9*c^6*d^8 - 37184*a^9*b^8*c^5*d^9 + 256*a^10*b^7*c^4*d^10 + 10336*a^11*b^6*c^3*d^11 - 5184*a^12*b^5*c^2*d^12)*1i)/(a^7*d^7 - b^7*c^7 - 21*a^2*b^5*c^5*d^2 + 35*a^3*b^4*c^4*d^3 - 35*a^4*b^3*c^3*d^4 + 21*a^5*b^2*c^2*d^5 + 7*a*b^6*c^6*d - 7*a^6*b*c*d^6) + (x^(1/2)*(-(a^3*b)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(1/4)*(2304*a^13*b^4*c*d^14 + 4352*a^3*b^14*c^11*d^4 - 33280*a^4*b^13*c^10*d^5 + 111872*a^5*b^12*c^9*d^6 - 219136*a^6*b^11*c^8*d^7 + 283136*a^7*b^10*c^7*d^8 - 265216*a^8*b^9*c^6*d^9 + 197120*a^9*b^8*c^5*d^10 - 120832*a^10*b^7*c^4*d^11 + 56576*a^11*b^6*c^3*d^12 - 16896*a^12*b^5*c^2*d^13))/(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))*(-(a^3*b)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(3/4)*1i + (x^(1/2)*(a^3*b^10*c^6*d + 144*a^8*b^5*c*d^6 + 12*a^4*b^9*c^5*d^2 + 54*a^5*b^8*c^4*d^3 + 124*a^6*b^7*c^3*d^4 + 177*a^7*b^6*c^2*d^5)*1i)/(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))*(-(a^3*b)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(1/4) - (a^4*b^9*c^5*d + 108*a^8*b^5*c*d^5 + 13*a^5*b^8*c^4*d^2 + 63*a^6*b^7*c^3*d^3 + 135*a^7*b^6*c^2*d^4)/(a^7*d^7 - b^7*c^7 - 21*a^2*b^5*c^5*d^2 + 35*a^3*b^4*c^4*d^3 - 35*a^4*b^3*c^3*d^4 + 21*a^5*b^2*c^2*d^5 + 7*a*b^6*c^6*d - 7*a^6*b*c*d^6) + ((((864*a^13*b^4*c*d^13 - 32*a^3*b^14*c^11*d^3 + 1984*a^4*b^13*c^10*d^4 - 13856*a^5*b^12*c^9*d^5 + 43264*a^6*b^11*c^8*d^6 - 74816*a^7*b^10*c^7*d^7 + 74368*a^8*b^9*c^6*d^8 - 37184*a^9*b^8*c^5*d^9 + 256*a^10*b^7*c^4*d^10 + 10336*a^11*b^6*c^3*d^11 - 5184*a^12*b^5*c^2*d^12)*1i)/(a^7*d^7 - b^7*c^7 - 21*a^2*b^5*c^5*d^2 + 35*a^3*b^4*c^4*d^3 - 35*a^4*b^3*c^3*d^4 + 21*a^5*b^2*c^2*d^5 + 7*a*b^6*c^6*d - 7*a^6*b*c*d^6) - (x^(1/2)*(-(a^3*b)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(1/4)*(2304*a^13*b^4*c*d^14 + 4352*a^3*b^14*c^11*d^4 - 33280*a^4*b^13*c^10*d^5 + 111872*a^5*b^12*c^9*d^6 - 219136*a^6*b^11*c^8*d^7 + 283136*a^7*b^10*c^7*d^8 - 265216*a^8*b^9*c^6*d^9 + 197120*a^9*b^8*c^5*d^10 - 120832*a^10*b^7*c^4*d^11 + 56576*a^11*b^6*c^3*d^12 - 16896*a^12*b^5*c^2*d^13))/(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))*(-(a^3*b)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(3/4)*1i - (x^(1/2)*(a^3*b^10*c^6*d + 144*a^8*b^5*c*d^6 + 12*a^4*b^9*c^5*d^2 + 54*a^5*b^8*c^4*d^3 + 124*a^6*b^7*c^3*d^4 + 177*a^7*b^6*c^2*d^5)*1i)/(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))*(-(a^3*b)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(1/4)))*(-(a^3*b)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(1/4) + atan(((((864*a^13*b^4*c*d^13 - 32*a^3*b^14*c^11*d^3 + 1984*a^4*b^13*c^10*d^4 - 13856*a^5*b^12*c^9*d^5 + 43264*a^6*b^11*c^8*d^6 - 74816*a^7*b^10*c^7*d^7 + 74368*a^8*b^9*c^6*d^8 - 37184*a^9*b^8*c^5*d^9 + 256*a^10*b^7*c^4*d^10 + 10336*a^11*b^6*c^3*d^11 - 5184*a^12*b^5*c^2*d^12)/(a^7*d^7 - b^7*c^7 - 21*a^2*b^5*c^5*d^2 + 35*a^3*b^4*c^4*d^3 - 35*a^4*b^3*c^3*d^4 + 21*a^5*b^2*c^2*d^5 + 7*a*b^6*c^6*d - 7*a^6*b*c*d^6) + (x^(1/2)*(-(81*a^4*d^4 + b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 12*a*b^3*c^3*d + 108*a^3*b*c*d^3)/(4096*a^8*c*d^11 + 4096*b^8*c^9*d^3 - 32768*a*b^7*c^8*d^4 - 32768*a^7*b*c^2*d^10 + 114688*a^2*b^6*c^7*d^5 - 229376*a^3*b^5*c^6*d^6 + 286720*a^4*b^4*c^5*d^7 - 229376*a^5*b^3*c^4*d^8 + 114688*a^6*b^2*c^3*d^9))^(1/4)*(2304*a^13*b^4*c*d^14 + 4352*a^3*b^14*c^11*d^4 - 33280*a^4*b^13*c^10*d^5 + 111872*a^5*b^12*c^9*d^6 - 219136*a^6*b^11*c^8*d^7 + 283136*a^7*b^10*c^7*d^8 - 265216*a^8*b^9*c^6*d^9 + 197120*a^9*b^8*c^5*d^10 - 120832*a^10*b^7*c^4*d^11 + 56576*a^11*b^6*c^3*d^12 - 16896*a^12*b^5*c^2*d^13))/(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))*(-(81*a^4*d^4 + b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 12*a*b^3*c^3*d + 108*a^3*b*c*d^3)/(4096*a^8*c*d^11 + 4096*b^8*c^9*d^3 - 32768*a*b^7*c^8*d^4 - 32768*a^7*b*c^2*d^10 + 114688*a^2*b^6*c^7*d^5 - 229376*a^3*b^5*c^6*d^6 + 286720*a^4*b^4*c^5*d^7 - 229376*a^5*b^3*c^4*d^8 + 114688*a^6*b^2*c^3*d^9))^(3/4)*1i + (x^(1/2)*(a^3*b^10*c^6*d + 144*a^8*b^5*c*d^6 + 12*a^4*b^9*c^5*d^2 + 54*a^5*b^8*c^4*d^3 + 124*a^6*b^7*c^3*d^4 + 177*a^7*b^6*c^2*d^5)*1i)/(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))*(-(81*a^4*d^4 + b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 12*a*b^3*c^3*d + 108*a^3*b*c*d^3)/(4096*a^8*c*d^11 + 4096*b^8*c^9*d^3 - 32768*a*b^7*c^8*d^4 - 32768*a^7*b*c^2*d^10 + 114688*a^2*b^6*c^7*d^5 - 229376*a^3*b^5*c^6*d^6 + 286720*a^4*b^4*c^5*d^7 - 229376*a^5*b^3*c^4*d^8 + 114688*a^6*b^2*c^3*d^9))^(1/4) - (((864*a^13*b^4*c*d^13 - 32*a^3*b^14*c^11*d^3 + 1984*a^4*b^13*c^10*d^4 - 13856*a^5*b^12*c^9*d^5 + 43264*a^6*b^11*c^8*d^6 - 74816*a^7*b^10*c^7*d^7 + 74368*a^8*b^9*c^6*d^8 - 37184*a^9*b^8*c^5*d^9 + 256*a^10*b^7*c^4*d^10 + 10336*a^11*b^6*c^3*d^11 - 5184*a^12*b^5*c^2*d^12)/(a^7*d^7 - b^7*c^7 - 21*a^2*b^5*c^5*d^2 + 35*a^3*b^4*c^4*d^3 - 35*a^4*b^3*c^3*d^4 + 21*a^5*b^2*c^2*d^5 + 7*a*b^6*c^6*d - 7*a^6*b*c*d^6) - (x^(1/2)*(-(81*a^4*d^4 + b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 12*a*b^3*c^3*d + 108*a^3*b*c*d^3)/(4096*a^8*c*d^11 + 4096*b^8*c^9*d^3 - 32768*a*b^7*c^8*d^4 - 32768*a^7*b*c^2*d^10 + 114688*a^2*b^6*c^7*d^5 - 229376*a^3*b^5*c^6*d^6 + 286720*a^4*b^4*c^5*d^7 - 229376*a^5*b^3*c^4*d^8 + 114688*a^6*b^2*c^3*d^9))^(1/4)*(2304*a^13*b^4*c*d^14 + 4352*a^3*b^14*c^11*d^4 - 33280*a^4*b^13*c^10*d^5 + 111872*a^5*b^12*c^9*d^6 - 219136*a^6*b^11*c^8*d^7 + 283136*a^7*b^10*c^7*d^8 - 265216*a^8*b^9*c^6*d^9 + 197120*a^9*b^8*c^5*d^10 - 120832*a^10*b^7*c^4*d^11 + 56576*a^11*b^6*c^3*d^12 - 16896*a^12*b^5*c^2*d^13))/(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))*(-(81*a^4*d^4 + b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 12*a*b^3*c^3*d + 108*a^3*b*c*d^3)/(4096*a^8*c*d^11 + 4096*b^8*c^9*d^3 - 32768*a*b^7*c^8*d^4 - 32768*a^7*b*c^2*d^10 + 114688*a^2*b^6*c^7*d^5 - 229376*a^3*b^5*c^6*d^6 + 286720*a^4*b^4*c^5*d^7 - 229376*a^5*b^3*c^4*d^8 + 114688*a^6*b^2*c^3*d^9))^(3/4)*1i - (x^(1/2)*(a^3*b^10*c^6*d + 144*a^8*b^5*c*d^6 + 12*a^4*b^9*c^5*d^2 + 54*a^5*b^8*c^4*d^3 + 124*a^6*b^7*c^3*d^4 + 177*a^7*b^6*c^2*d^5)*1i)/(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))*(-(81*a^4*d^4 + b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 12*a*b^3*c^3*d + 108*a^3*b*c*d^3)/(4096*a^8*c*d^11 + 4096*b^8*c^9*d^3 - 32768*a*b^7*c^8*d^4 - 32768*a^7*b*c^2*d^10 + 114688*a^2*b^6*c^7*d^5 - 229376*a^3*b^5*c^6*d^6 + 286720*a^4*b^4*c^5*d^7 - 229376*a^5*b^3*c^4*d^8 + 114688*a^6*b^2*c^3*d^9))^(1/4))/((a^4*b^9*c^5*d + 108*a^8*b^5*c*d^5 + 13*a^5*b^8*c^4*d^2 + 63*a^6*b^7*c^3*d^3 + 135*a^7*b^6*c^2*d^4)/(a^7*d^7 - b^7*c^7 - 21*a^2*b^5*c^5*d^2 + 35*a^3*b^4*c^4*d^3 - 35*a^4*b^3*c^3*d^4 + 21*a^5*b^2*c^2*d^5 + 7*a*b^6*c^6*d - 7*a^6*b*c*d^6) + (((864*a^13*b^4*c*d^13 - 32*a^3*b^14*c^11*d^3 + 1984*a^4*b^13*c^10*d^4 - 13856*a^5*b^12*c^9*d^5 + 43264*a^6*b^11*c^8*d^6 - 74816*a^7*b^10*c^7*d^7 + 74368*a^8*b^9*c^6*d^8 - 37184*a^9*b^8*c^5*d^9 + 256*a^10*b^7*c^4*d^10 + 10336*a^11*b^6*c^3*d^11 - 5184*a^12*b^5*c^2*d^12)/(a^7*d^7 - b^7*c^7 - 21*a^2*b^5*c^5*d^2 + 35*a^3*b^4*c^4*d^3 - 35*a^4*b^3*c^3*d^4 + 21*a^5*b^2*c^2*d^5 + 7*a*b^6*c^6*d - 7*a^6*b*c*d^6) + (x^(1/2)*(-(81*a^4*d^4 + b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 12*a*b^3*c^3*d + 108*a^3*b*c*d^3)/(4096*a^8*c*d^11 + 4096*b^8*c^9*d^3 - 32768*a*b^7*c^8*d^4 - 32768*a^7*b*c^2*d^10 + 114688*a^2*b^6*c^7*d^5 - 229376*a^3*b^5*c^6*d^6 + 286720*a^4*b^4*c^5*d^7 - 229376*a^5*b^3*c^4*d^8 + 114688*a^6*b^2*c^3*d^9))^(1/4)*(2304*a^13*b^4*c*d^14 + 4352*a^3*b^14*c^11*d^4 - 33280*a^4*b^13*c^10*d^5 + 111872*a^5*b^12*c^9*d^6 - 219136*a^6*b^11*c^8*d^7 + 283136*a^7*b^10*c^7*d^8 - 265216*a^8*b^9*c^6*d^9 + 197120*a^9*b^8*c^5*d^10 - 120832*a^10*b^7*c^4*d^11 + 56576*a^11*b^6*c^3*d^12 - 16896*a^12*b^5*c^2*d^13))/(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))*(-(81*a^4*d^4 + b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 12*a*b^3*c^3*d + 108*a^3*b*c*d^3)/(4096*a^8*c*d^11 + 4096*b^8*c^9*d^3 - 32768*a*b^7*c^8*d^4 - 32768*a^7*b*c^2*d^10 + 114688*a^2*b^6*c^7*d^5 - 229376*a^3*b^5*c^6*d^6 + 286720*a^4*b^4*c^5*d^7 - 229376*a^5*b^3*c^4*d^8 + 114688*a^6*b^2*c^3*d^9))^(3/4) + (x^(1/2)*(a^3*b^10*c^6*d + 144*a^8*b^5*c*d^6 + 12*a^4*b^9*c^5*d^2 + 54*a^5*b^8*c^4*d^3 + 124*a^6*b^7*c^3*d^4 + 177*a^7*b^6*c^2*d^5))/(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))*(-(81*a^4*d^4 + b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 12*a*b^3*c^3*d + 108*a^3*b*c*d^3)/(4096*a^8*c*d^11 + 4096*b^8*c^9*d^3 - 32768*a*b^7*c^8*d^4 - 32768*a^7*b*c^2*d^10 + 114688*a^2*b^6*c^7*d^5 - 229376*a^3*b^5*c^6*d^6 + 286720*a^4*b^4*c^5*d^7 - 229376*a^5*b^3*c^4*d^8 + 114688*a^6*b^2*c^3*d^9))^(1/4) + (((864*a^13*b^4*c*d^13 - 32*a^3*b^14*c^11*d^3 + 1984*a^4*b^13*c^10*d^4 - 13856*a^5*b^12*c^9*d^5 + 43264*a^6*b^11*c^8*d^6 - 74816*a^7*b^10*c^7*d^7 + 74368*a^8*b^9*c^6*d^8 - 37184*a^9*b^8*c^5*d^9 + 256*a^10*b^7*c^4*d^10 + 10336*a^11*b^6*c^3*d^11 - 5184*a^12*b^5*c^2*d^12)/(a^7*d^7 - b^7*c^7 - 21*a^2*b^5*c^5*d^2 + 35*a^3*b^4*c^4*d^3 - 35*a^4*b^3*c^3*d^4 + 21*a^5*b^2*c^2*d^5 + 7*a*b^6*c^6*d - 7*a^6*b*c*d^6) - (x^(1/2)*(-(81*a^4*d^4 + b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 12*a*b^3*c^3*d + 108*a^3*b*c*d^3)/(4096*a^8*c*d^11 + 4096*b^8*c^9*d^3 - 32768*a*b^7*c^8*d^4 - 32768*a^7*b*c^2*d^10 + 114688*a^2*b^6*c^7*d^5 - 229376*a^3*b^5*c^6*d^6 + 286720*a^4*b^4*c^5*d^7 - 229376*a^5*b^3*c^4*d^8 + 114688*a^6*b^2*c^3*d^9))^(1/4)*(2304*a^13*b^4*c*d^14 + 4352*a^3*b^14*c^11*d^4 - 33280*a^4*b^13*c^10*d^5 + 111872*a^5*b^12*c^9*d^6 - 219136*a^6*b^11*c^8*d^7 + 283136*a^7*b^10*c^7*d^8 - 265216*a^8*b^9*c^6*d^9 + 197120*a^9*b^8*c^5*d^10 - 120832*a^10*b^7*c^4*d^11 + 56576*a^11*b^6*c^3*d^12 - 16896*a^12*b^5*c^2*d^13))/(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))*(-(81*a^4*d^4 + b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 12*a*b^3*c^3*d + 108*a^3*b*c*d^3)/(4096*a^8*c*d^11 + 4096*b^8*c^9*d^3 - 32768*a*b^7*c^8*d^4 - 32768*a^7*b*c^2*d^10 + 114688*a^2*b^6*c^7*d^5 - 229376*a^3*b^5*c^6*d^6 + 286720*a^4*b^4*c^5*d^7 - 229376*a^5*b^3*c^4*d^8 + 114688*a^6*b^2*c^3*d^9))^(3/4) - (x^(1/2)*(a^3*b^10*c^6*d + 144*a^8*b^5*c*d^6 + 12*a^4*b^9*c^5*d^2 + 54*a^5*b^8*c^4*d^3 + 124*a^6*b^7*c^3*d^4 + 177*a^7*b^6*c^2*d^5))/(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))*(-(81*a^4*d^4 + b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 12*a*b^3*c^3*d + 108*a^3*b*c*d^3)/(4096*a^8*c*d^11 + 4096*b^8*c^9*d^3 - 32768*a*b^7*c^8*d^4 - 32768*a^7*b*c^2*d^10 + 114688*a^2*b^6*c^7*d^5 - 229376*a^3*b^5*c^6*d^6 + 286720*a^4*b^4*c^5*d^7 - 229376*a^5*b^3*c^4*d^8 + 114688*a^6*b^2*c^3*d^9))^(1/4)))*(-(81*a^4*d^4 + b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 12*a*b^3*c^3*d + 108*a^3*b*c*d^3)/(4096*a^8*c*d^11 + 4096*b^8*c^9*d^3 - 32768*a*b^7*c^8*d^4 - 32768*a^7*b*c^2*d^10 + 114688*a^2*b^6*c^7*d^5 - 229376*a^3*b^5*c^6*d^6 + 286720*a^4*b^4*c^5*d^7 - 229376*a^5*b^3*c^4*d^8 + 114688*a^6*b^2*c^3*d^9))^(1/4)*2i - 2*atan((((((864*a^13*b^4*c*d^13 - 32*a^3*b^14*c^11*d^3 + 1984*a^4*b^13*c^10*d^4 - 13856*a^5*b^12*c^9*d^5 + 43264*a^6*b^11*c^8*d^6 - 74816*a^7*b^10*c^7*d^7 + 74368*a^8*b^9*c^6*d^8 - 37184*a^9*b^8*c^5*d^9 + 256*a^10*b^7*c^4*d^10 + 10336*a^11*b^6*c^3*d^11 - 5184*a^12*b^5*c^2*d^12)*1i)/(a^7*d^7 - b^7*c^7 - 21*a^2*b^5*c^5*d^2 + 35*a^3*b^4*c^4*d^3 - 35*a^4*b^3*c^3*d^4 + 21*a^5*b^2*c^2*d^5 + 7*a*b^6*c^6*d - 7*a^6*b*c*d^6) + (x^(1/2)*(-(81*a^4*d^4 + b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 12*a*b^3*c^3*d + 108*a^3*b*c*d^3)/(4096*a^8*c*d^11 + 4096*b^8*c^9*d^3 - 32768*a*b^7*c^8*d^4 - 32768*a^7*b*c^2*d^10 + 114688*a^2*b^6*c^7*d^5 - 229376*a^3*b^5*c^6*d^6 + 286720*a^4*b^4*c^5*d^7 - 229376*a^5*b^3*c^4*d^8 + 114688*a^6*b^2*c^3*d^9))^(1/4)*(2304*a^13*b^4*c*d^14 + 4352*a^3*b^14*c^11*d^4 - 33280*a^4*b^13*c^10*d^5 + 111872*a^5*b^12*c^9*d^6 - 219136*a^6*b^11*c^8*d^7 + 283136*a^7*b^10*c^7*d^8 - 265216*a^8*b^9*c^6*d^9 + 197120*a^9*b^8*c^5*d^10 - 120832*a^10*b^7*c^4*d^11 + 56576*a^11*b^6*c^3*d^12 - 16896*a^12*b^5*c^2*d^13))/(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))*(-(81*a^4*d^4 + b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 12*a*b^3*c^3*d + 108*a^3*b*c*d^3)/(4096*a^8*c*d^11 + 4096*b^8*c^9*d^3 - 32768*a*b^7*c^8*d^4 - 32768*a^7*b*c^2*d^10 + 114688*a^2*b^6*c^7*d^5 - 229376*a^3*b^5*c^6*d^6 + 286720*a^4*b^4*c^5*d^7 - 229376*a^5*b^3*c^4*d^8 + 114688*a^6*b^2*c^3*d^9))^(3/4) + (x^(1/2)*(a^3*b^10*c^6*d + 144*a^8*b^5*c*d^6 + 12*a^4*b^9*c^5*d^2 + 54*a^5*b^8*c^4*d^3 + 124*a^6*b^7*c^3*d^4 + 177*a^7*b^6*c^2*d^5))/(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))*(-(81*a^4*d^4 + b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 12*a*b^3*c^3*d + 108*a^3*b*c*d^3)/(4096*a^8*c*d^11 + 4096*b^8*c^9*d^3 - 32768*a*b^7*c^8*d^4 - 32768*a^7*b*c^2*d^10 + 114688*a^2*b^6*c^7*d^5 - 229376*a^3*b^5*c^6*d^6 + 286720*a^4*b^4*c^5*d^7 - 229376*a^5*b^3*c^4*d^8 + 114688*a^6*b^2*c^3*d^9))^(1/4) - ((((864*a^13*b^4*c*d^13 - 32*a^3*b^14*c^11*d^3 + 1984*a^4*b^13*c^10*d^4 - 13856*a^5*b^12*c^9*d^5 + 43264*a^6*b^11*c^8*d^6 - 74816*a^7*b^10*c^7*d^7 + 74368*a^8*b^9*c^6*d^8 - 37184*a^9*b^8*c^5*d^9 + 256*a^10*b^7*c^4*d^10 + 10336*a^11*b^6*c^3*d^11 - 5184*a^12*b^5*c^2*d^12)*1i)/(a^7*d^7 - b^7*c^7 - 21*a^2*b^5*c^5*d^2 + 35*a^3*b^4*c^4*d^3 - 35*a^4*b^3*c^3*d^4 + 21*a^5*b^2*c^2*d^5 + 7*a*b^6*c^6*d - 7*a^6*b*c*d^6) - (x^(1/2)*(-(81*a^4*d^4 + b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 12*a*b^3*c^3*d + 108*a^3*b*c*d^3)/(4096*a^8*c*d^11 + 4096*b^8*c^9*d^3 - 32768*a*b^7*c^8*d^4 - 32768*a^7*b*c^2*d^10 + 114688*a^2*b^6*c^7*d^5 - 229376*a^3*b^5*c^6*d^6 + 286720*a^4*b^4*c^5*d^7 - 229376*a^5*b^3*c^4*d^8 + 114688*a^6*b^2*c^3*d^9))^(1/4)*(2304*a^13*b^4*c*d^14 + 4352*a^3*b^14*c^11*d^4 - 33280*a^4*b^13*c^10*d^5 + 111872*a^5*b^12*c^9*d^6 - 219136*a^6*b^11*c^8*d^7 + 283136*a^7*b^10*c^7*d^8 - 265216*a^8*b^9*c^6*d^9 + 197120*a^9*b^8*c^5*d^10 - 120832*a^10*b^7*c^4*d^11 + 56576*a^11*b^6*c^3*d^12 - 16896*a^12*b^5*c^2*d^13))/(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))*(-(81*a^4*d^4 + b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 12*a*b^3*c^3*d + 108*a^3*b*c*d^3)/(4096*a^8*c*d^11 + 4096*b^8*c^9*d^3 - 32768*a*b^7*c^8*d^4 - 32768*a^7*b*c^2*d^10 + 114688*a^2*b^6*c^7*d^5 - 229376*a^3*b^5*c^6*d^6 + 286720*a^4*b^4*c^5*d^7 - 229376*a^5*b^3*c^4*d^8 + 114688*a^6*b^2*c^3*d^9))^(3/4) - (x^(1/2)*(a^3*b^10*c^6*d + 144*a^8*b^5*c*d^6 + 12*a^4*b^9*c^5*d^2 + 54*a^5*b^8*c^4*d^3 + 124*a^6*b^7*c^3*d^4 + 177*a^7*b^6*c^2*d^5))/(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))*(-(81*a^4*d^4 + b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 12*a*b^3*c^3*d + 108*a^3*b*c*d^3)/(4096*a^8*c*d^11 + 4096*b^8*c^9*d^3 - 32768*a*b^7*c^8*d^4 - 32768*a^7*b*c^2*d^10 + 114688*a^2*b^6*c^7*d^5 - 229376*a^3*b^5*c^6*d^6 + 286720*a^4*b^4*c^5*d^7 - 229376*a^5*b^3*c^4*d^8 + 114688*a^6*b^2*c^3*d^9))^(1/4))/(((((864*a^13*b^4*c*d^13 - 32*a^3*b^14*c^11*d^3 + 1984*a^4*b^13*c^10*d^4 - 13856*a^5*b^12*c^9*d^5 + 43264*a^6*b^11*c^8*d^6 - 74816*a^7*b^10*c^7*d^7 + 74368*a^8*b^9*c^6*d^8 - 37184*a^9*b^8*c^5*d^9 + 256*a^10*b^7*c^4*d^10 + 10336*a^11*b^6*c^3*d^11 - 5184*a^12*b^5*c^2*d^12)*1i)/(a^7*d^7 - b^7*c^7 - 21*a^2*b^5*c^5*d^2 + 35*a^3*b^4*c^4*d^3 - 35*a^4*b^3*c^3*d^4 + 21*a^5*b^2*c^2*d^5 + 7*a*b^6*c^6*d - 7*a^6*b*c*d^6) + (x^(1/2)*(-(81*a^4*d^4 + b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 12*a*b^3*c^3*d + 108*a^3*b*c*d^3)/(4096*a^8*c*d^11 + 4096*b^8*c^9*d^3 - 32768*a*b^7*c^8*d^4 - 32768*a^7*b*c^2*d^10 + 114688*a^2*b^6*c^7*d^5 - 229376*a^3*b^5*c^6*d^6 + 286720*a^4*b^4*c^5*d^7 - 229376*a^5*b^3*c^4*d^8 + 114688*a^6*b^2*c^3*d^9))^(1/4)*(2304*a^13*b^4*c*d^14 + 4352*a^3*b^14*c^11*d^4 - 33280*a^4*b^13*c^10*d^5 + 111872*a^5*b^12*c^9*d^6 - 219136*a^6*b^11*c^8*d^7 + 283136*a^7*b^10*c^7*d^8 - 265216*a^8*b^9*c^6*d^9 + 197120*a^9*b^8*c^5*d^10 - 120832*a^10*b^7*c^4*d^11 + 56576*a^11*b^6*c^3*d^12 - 16896*a^12*b^5*c^2*d^13))/(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))*(-(81*a^4*d^4 + b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 12*a*b^3*c^3*d + 108*a^3*b*c*d^3)/(4096*a^8*c*d^11 + 4096*b^8*c^9*d^3 - 32768*a*b^7*c^8*d^4 - 32768*a^7*b*c^2*d^10 + 114688*a^2*b^6*c^7*d^5 - 229376*a^3*b^5*c^6*d^6 + 286720*a^4*b^4*c^5*d^7 - 229376*a^5*b^3*c^4*d^8 + 114688*a^6*b^2*c^3*d^9))^(3/4)*1i + (x^(1/2)*(a^3*b^10*c^6*d + 144*a^8*b^5*c*d^6 + 12*a^4*b^9*c^5*d^2 + 54*a^5*b^8*c^4*d^3 + 124*a^6*b^7*c^3*d^4 + 177*a^7*b^6*c^2*d^5)*1i)/(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))*(-(81*a^4*d^4 + b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 12*a*b^3*c^3*d + 108*a^3*b*c*d^3)/(4096*a^8*c*d^11 + 4096*b^8*c^9*d^3 - 32768*a*b^7*c^8*d^4 - 32768*a^7*b*c^2*d^10 + 114688*a^2*b^6*c^7*d^5 - 229376*a^3*b^5*c^6*d^6 + 286720*a^4*b^4*c^5*d^7 - 229376*a^5*b^3*c^4*d^8 + 114688*a^6*b^2*c^3*d^9))^(1/4) - (a^4*b^9*c^5*d + 108*a^8*b^5*c*d^5 + 13*a^5*b^8*c^4*d^2 + 63*a^6*b^7*c^3*d^3 + 135*a^7*b^6*c^2*d^4)/(a^7*d^7 - b^7*c^7 - 21*a^2*b^5*c^5*d^2 + 35*a^3*b^4*c^4*d^3 - 35*a^4*b^3*c^3*d^4 + 21*a^5*b^2*c^2*d^5 + 7*a*b^6*c^6*d - 7*a^6*b*c*d^6) + ((((864*a^13*b^4*c*d^13 - 32*a^3*b^14*c^11*d^3 + 1984*a^4*b^13*c^10*d^4 - 13856*a^5*b^12*c^9*d^5 + 43264*a^6*b^11*c^8*d^6 - 74816*a^7*b^10*c^7*d^7 + 74368*a^8*b^9*c^6*d^8 - 37184*a^9*b^8*c^5*d^9 + 256*a^10*b^7*c^4*d^10 + 10336*a^11*b^6*c^3*d^11 - 5184*a^12*b^5*c^2*d^12)*1i)/(a^7*d^7 - b^7*c^7 - 21*a^2*b^5*c^5*d^2 + 35*a^3*b^4*c^4*d^3 - 35*a^4*b^3*c^3*d^4 + 21*a^5*b^2*c^2*d^5 + 7*a*b^6*c^6*d - 7*a^6*b*c*d^6) - (x^(1/2)*(-(81*a^4*d^4 + b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 12*a*b^3*c^3*d + 108*a^3*b*c*d^3)/(4096*a^8*c*d^11 + 4096*b^8*c^9*d^3 - 32768*a*b^7*c^8*d^4 - 32768*a^7*b*c^2*d^10 + 114688*a^2*b^6*c^7*d^5 - 229376*a^3*b^5*c^6*d^6 + 286720*a^4*b^4*c^5*d^7 - 229376*a^5*b^3*c^4*d^8 + 114688*a^6*b^2*c^3*d^9))^(1/4)*(2304*a^13*b^4*c*d^14 + 4352*a^3*b^14*c^11*d^4 - 33280*a^4*b^13*c^10*d^5 + 111872*a^5*b^12*c^9*d^6 - 219136*a^6*b^11*c^8*d^7 + 283136*a^7*b^10*c^7*d^8 - 265216*a^8*b^9*c^6*d^9 + 197120*a^9*b^8*c^5*d^10 - 120832*a^10*b^7*c^4*d^11 + 56576*a^11*b^6*c^3*d^12 - 16896*a^12*b^5*c^2*d^13))/(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))*(-(81*a^4*d^4 + b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 12*a*b^3*c^3*d + 108*a^3*b*c*d^3)/(4096*a^8*c*d^11 + 4096*b^8*c^9*d^3 - 32768*a*b^7*c^8*d^4 - 32768*a^7*b*c^2*d^10 + 114688*a^2*b^6*c^7*d^5 - 229376*a^3*b^5*c^6*d^6 + 286720*a^4*b^4*c^5*d^7 - 229376*a^5*b^3*c^4*d^8 + 114688*a^6*b^2*c^3*d^9))^(3/4)*1i - (x^(1/2)*(a^3*b^10*c^6*d + 144*a^8*b^5*c*d^6 + 12*a^4*b^9*c^5*d^2 + 54*a^5*b^8*c^4*d^3 + 124*a^6*b^7*c^3*d^4 + 177*a^7*b^6*c^2*d^5)*1i)/(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))*(-(81*a^4*d^4 + b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 12*a*b^3*c^3*d + 108*a^3*b*c*d^3)/(4096*a^8*c*d^11 + 4096*b^8*c^9*d^3 - 32768*a*b^7*c^8*d^4 - 32768*a^7*b*c^2*d^10 + 114688*a^2*b^6*c^7*d^5 - 229376*a^3*b^5*c^6*d^6 + 286720*a^4*b^4*c^5*d^7 - 229376*a^5*b^3*c^4*d^8 + 114688*a^6*b^2*c^3*d^9))^(1/4)))*(-(81*a^4*d^4 + b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 12*a*b^3*c^3*d + 108*a^3*b*c*d^3)/(4096*a^8*c*d^11 + 4096*b^8*c^9*d^3 - 32768*a*b^7*c^8*d^4 - 32768*a^7*b*c^2*d^10 + 114688*a^2*b^6*c^7*d^5 - 229376*a^3*b^5*c^6*d^6 + 286720*a^4*b^4*c^5*d^7 - 229376*a^5*b^3*c^4*d^8 + 114688*a^6*b^2*c^3*d^9))^(1/4) - x^(3/2)/(2*(c + d*x^2)*(a*d - b*c))","B"
474,1,20689,528,2.358819,"\text{Not used}","int(x^(3/2)/((a + b*x^2)*(c + d*x^2)^2),x)","-2\,\mathrm{atan}\left(\frac{\left(\frac{\sqrt{x}\,\left(17\,a^6\,b^7\,d^7+108\,a^5\,b^8\,c\,d^6+198\,a^4\,b^9\,c^2\,d^5+108\,a^3\,b^{10}\,c^3\,d^4+81\,a^2\,b^{11}\,c^4\,d^3\right)}{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}+\left(\frac{2\,\left(-a^5\,b^6\,d^6+51\,a^4\,b^7\,c\,d^5+189\,a^3\,b^8\,c^2\,d^4+81\,a^2\,b^9\,c^3\,d^3\right)}{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}-\left(\frac{\sqrt{x}\,\left(256\,a^{13}\,b^4\,d^{15}-512\,a^{12}\,b^5\,c\,d^{14}-2816\,a^{11}\,b^6\,c^2\,d^{13}+14336\,a^{10}\,b^7\,c^3\,d^{12}-36352\,a^9\,b^8\,c^4\,d^{11}+78848\,a^8\,b^9\,c^5\,d^{10}-146944\,a^7\,b^{10}\,c^6\,d^9+198656\,a^6\,b^{11}\,c^7\,d^8-176896\,a^5\,b^{12}\,c^8\,d^7+97792\,a^4\,b^{13}\,c^9\,d^6-30464\,a^3\,b^{14}\,c^{10}\,d^5+4096\,a^2\,b^{15}\,c^{11}\,d^4\right)}{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}+\frac{{\left(-\frac{a\,b^3}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{1/4}\,\left(1024\,a^{11}\,b^4\,c\,d^{13}-4096\,a^{10}\,b^5\,c^2\,d^{12}-4096\,a^9\,b^6\,c^3\,d^{11}+57344\,a^8\,b^7\,c^4\,d^{10}-157696\,a^7\,b^8\,c^5\,d^9+229376\,a^6\,b^9\,c^6\,d^8-200704\,a^5\,b^{10}\,c^7\,d^7+106496\,a^4\,b^{11}\,c^8\,d^6-31744\,a^3\,b^{12}\,c^9\,d^5+4096\,a^2\,b^{13}\,c^{10}\,d^4\right)\,2{}\mathrm{i}}{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}\right)\,{\left(-\frac{a\,b^3}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{3/4}\,1{}\mathrm{i}\right)\,{\left(-\frac{a\,b^3}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{1/4}\,1{}\mathrm{i}\right)\,{\left(-\frac{a\,b^3}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{1/4}-\left(-\frac{\sqrt{x}\,\left(17\,a^6\,b^7\,d^7+108\,a^5\,b^8\,c\,d^6+198\,a^4\,b^9\,c^2\,d^5+108\,a^3\,b^{10}\,c^3\,d^4+81\,a^2\,b^{11}\,c^4\,d^3\right)}{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}+\left(\frac{2\,\left(-a^5\,b^6\,d^6+51\,a^4\,b^7\,c\,d^5+189\,a^3\,b^8\,c^2\,d^4+81\,a^2\,b^9\,c^3\,d^3\right)}{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}+\left(\frac{\sqrt{x}\,\left(256\,a^{13}\,b^4\,d^{15}-512\,a^{12}\,b^5\,c\,d^{14}-2816\,a^{11}\,b^6\,c^2\,d^{13}+14336\,a^{10}\,b^7\,c^3\,d^{12}-36352\,a^9\,b^8\,c^4\,d^{11}+78848\,a^8\,b^9\,c^5\,d^{10}-146944\,a^7\,b^{10}\,c^6\,d^9+198656\,a^6\,b^{11}\,c^7\,d^8-176896\,a^5\,b^{12}\,c^8\,d^7+97792\,a^4\,b^{13}\,c^9\,d^6-30464\,a^3\,b^{14}\,c^{10}\,d^5+4096\,a^2\,b^{15}\,c^{11}\,d^4\right)}{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}-\frac{{\left(-\frac{a\,b^3}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{1/4}\,\left(1024\,a^{11}\,b^4\,c\,d^{13}-4096\,a^{10}\,b^5\,c^2\,d^{12}-4096\,a^9\,b^6\,c^3\,d^{11}+57344\,a^8\,b^7\,c^4\,d^{10}-157696\,a^7\,b^8\,c^5\,d^9+229376\,a^6\,b^9\,c^6\,d^8-200704\,a^5\,b^{10}\,c^7\,d^7+106496\,a^4\,b^{11}\,c^8\,d^6-31744\,a^3\,b^{12}\,c^9\,d^5+4096\,a^2\,b^{13}\,c^{10}\,d^4\right)\,2{}\mathrm{i}}{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}\right)\,{\left(-\frac{a\,b^3}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{3/4}\,1{}\mathrm{i}\right)\,{\left(-\frac{a\,b^3}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{1/4}\,1{}\mathrm{i}\right)\,{\left(-\frac{a\,b^3}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{1/4}}{\left(\frac{\sqrt{x}\,\left(17\,a^6\,b^7\,d^7+108\,a^5\,b^8\,c\,d^6+198\,a^4\,b^9\,c^2\,d^5+108\,a^3\,b^{10}\,c^3\,d^4+81\,a^2\,b^{11}\,c^4\,d^3\right)}{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}+\left(\frac{2\,\left(-a^5\,b^6\,d^6+51\,a^4\,b^7\,c\,d^5+189\,a^3\,b^8\,c^2\,d^4+81\,a^2\,b^9\,c^3\,d^3\right)}{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}-\left(\frac{\sqrt{x}\,\left(256\,a^{13}\,b^4\,d^{15}-512\,a^{12}\,b^5\,c\,d^{14}-2816\,a^{11}\,b^6\,c^2\,d^{13}+14336\,a^{10}\,b^7\,c^3\,d^{12}-36352\,a^9\,b^8\,c^4\,d^{11}+78848\,a^8\,b^9\,c^5\,d^{10}-146944\,a^7\,b^{10}\,c^6\,d^9+198656\,a^6\,b^{11}\,c^7\,d^8-176896\,a^5\,b^{12}\,c^8\,d^7+97792\,a^4\,b^{13}\,c^9\,d^6-30464\,a^3\,b^{14}\,c^{10}\,d^5+4096\,a^2\,b^{15}\,c^{11}\,d^4\right)}{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}+\frac{{\left(-\frac{a\,b^3}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{1/4}\,\left(1024\,a^{11}\,b^4\,c\,d^{13}-4096\,a^{10}\,b^5\,c^2\,d^{12}-4096\,a^9\,b^6\,c^3\,d^{11}+57344\,a^8\,b^7\,c^4\,d^{10}-157696\,a^7\,b^8\,c^5\,d^9+229376\,a^6\,b^9\,c^6\,d^8-200704\,a^5\,b^{10}\,c^7\,d^7+106496\,a^4\,b^{11}\,c^8\,d^6-31744\,a^3\,b^{12}\,c^9\,d^5+4096\,a^2\,b^{13}\,c^{10}\,d^4\right)\,2{}\mathrm{i}}{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}\right)\,{\left(-\frac{a\,b^3}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{3/4}\,1{}\mathrm{i}\right)\,{\left(-\frac{a\,b^3}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{1/4}\,1{}\mathrm{i}\right)\,{\left(-\frac{a\,b^3}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{1/4}\,1{}\mathrm{i}+\left(-\frac{\sqrt{x}\,\left(17\,a^6\,b^7\,d^7+108\,a^5\,b^8\,c\,d^6+198\,a^4\,b^9\,c^2\,d^5+108\,a^3\,b^{10}\,c^3\,d^4+81\,a^2\,b^{11}\,c^4\,d^3\right)}{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}+\left(\frac{2\,\left(-a^5\,b^6\,d^6+51\,a^4\,b^7\,c\,d^5+189\,a^3\,b^8\,c^2\,d^4+81\,a^2\,b^9\,c^3\,d^3\right)}{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}+\left(\frac{\sqrt{x}\,\left(256\,a^{13}\,b^4\,d^{15}-512\,a^{12}\,b^5\,c\,d^{14}-2816\,a^{11}\,b^6\,c^2\,d^{13}+14336\,a^{10}\,b^7\,c^3\,d^{12}-36352\,a^9\,b^8\,c^4\,d^{11}+78848\,a^8\,b^9\,c^5\,d^{10}-146944\,a^7\,b^{10}\,c^6\,d^9+198656\,a^6\,b^{11}\,c^7\,d^8-176896\,a^5\,b^{12}\,c^8\,d^7+97792\,a^4\,b^{13}\,c^9\,d^6-30464\,a^3\,b^{14}\,c^{10}\,d^5+4096\,a^2\,b^{15}\,c^{11}\,d^4\right)}{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}-\frac{{\left(-\frac{a\,b^3}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{1/4}\,\left(1024\,a^{11}\,b^4\,c\,d^{13}-4096\,a^{10}\,b^5\,c^2\,d^{12}-4096\,a^9\,b^6\,c^3\,d^{11}+57344\,a^8\,b^7\,c^4\,d^{10}-157696\,a^7\,b^8\,c^5\,d^9+229376\,a^6\,b^9\,c^6\,d^8-200704\,a^5\,b^{10}\,c^7\,d^7+106496\,a^4\,b^{11}\,c^8\,d^6-31744\,a^3\,b^{12}\,c^9\,d^5+4096\,a^2\,b^{13}\,c^{10}\,d^4\right)\,2{}\mathrm{i}}{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}\right)\,{\left(-\frac{a\,b^3}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{3/4}\,1{}\mathrm{i}\right)\,{\left(-\frac{a\,b^3}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{1/4}\,1{}\mathrm{i}\right)\,{\left(-\frac{a\,b^3}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{1/4}\,1{}\mathrm{i}}\right)\,{\left(-\frac{a\,b^3}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{1/4}-2\,\mathrm{atan}\left(-\frac{\left(-\frac{\sqrt{x}\,\left(17\,a^6\,b^7\,d^7+108\,a^5\,b^8\,c\,d^6+198\,a^4\,b^9\,c^2\,d^5+108\,a^3\,b^{10}\,c^3\,d^4+81\,a^2\,b^{11}\,c^4\,d^3\right)}{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}+\left(\frac{2\,\left(-a^5\,b^6\,d^6+51\,a^4\,b^7\,c\,d^5+189\,a^3\,b^8\,c^2\,d^4+81\,a^2\,b^9\,c^3\,d^3\right)}{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}+\left(\frac{\sqrt{x}\,\left(256\,a^{13}\,b^4\,d^{15}-512\,a^{12}\,b^5\,c\,d^{14}-2816\,a^{11}\,b^6\,c^2\,d^{13}+14336\,a^{10}\,b^7\,c^3\,d^{12}-36352\,a^9\,b^8\,c^4\,d^{11}+78848\,a^8\,b^9\,c^5\,d^{10}-146944\,a^7\,b^{10}\,c^6\,d^9+198656\,a^6\,b^{11}\,c^7\,d^8-176896\,a^5\,b^{12}\,c^8\,d^7+97792\,a^4\,b^{13}\,c^9\,d^6-30464\,a^3\,b^{14}\,c^{10}\,d^5+4096\,a^2\,b^{15}\,c^{11}\,d^4\right)}{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}-\frac{{\left(-\frac{a^4\,d^4+12\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+108\,a\,b^3\,c^3\,d+81\,b^4\,c^4}{4096\,a^8\,c^3\,d^9-32768\,a^7\,b\,c^4\,d^8+114688\,a^6\,b^2\,c^5\,d^7-229376\,a^5\,b^3\,c^6\,d^6+286720\,a^4\,b^4\,c^7\,d^5-229376\,a^3\,b^5\,c^8\,d^4+114688\,a^2\,b^6\,c^9\,d^3-32768\,a\,b^7\,c^{10}\,d^2+4096\,b^8\,c^{11}\,d}\right)}^{1/4}\,\left(1024\,a^{11}\,b^4\,c\,d^{13}-4096\,a^{10}\,b^5\,c^2\,d^{12}-4096\,a^9\,b^6\,c^3\,d^{11}+57344\,a^8\,b^7\,c^4\,d^{10}-157696\,a^7\,b^8\,c^5\,d^9+229376\,a^6\,b^9\,c^6\,d^8-200704\,a^5\,b^{10}\,c^7\,d^7+106496\,a^4\,b^{11}\,c^8\,d^6-31744\,a^3\,b^{12}\,c^9\,d^5+4096\,a^2\,b^{13}\,c^{10}\,d^4\right)\,2{}\mathrm{i}}{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}\right)\,{\left(-\frac{a^4\,d^4+12\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+108\,a\,b^3\,c^3\,d+81\,b^4\,c^4}{4096\,a^8\,c^3\,d^9-32768\,a^7\,b\,c^4\,d^8+114688\,a^6\,b^2\,c^5\,d^7-229376\,a^5\,b^3\,c^6\,d^6+286720\,a^4\,b^4\,c^7\,d^5-229376\,a^3\,b^5\,c^8\,d^4+114688\,a^2\,b^6\,c^9\,d^3-32768\,a\,b^7\,c^{10}\,d^2+4096\,b^8\,c^{11}\,d}\right)}^{3/4}\,1{}\mathrm{i}\right)\,{\left(-\frac{a^4\,d^4+12\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+108\,a\,b^3\,c^3\,d+81\,b^4\,c^4}{4096\,a^8\,c^3\,d^9-32768\,a^7\,b\,c^4\,d^8+114688\,a^6\,b^2\,c^5\,d^7-229376\,a^5\,b^3\,c^6\,d^6+286720\,a^4\,b^4\,c^7\,d^5-229376\,a^3\,b^5\,c^8\,d^4+114688\,a^2\,b^6\,c^9\,d^3-32768\,a\,b^7\,c^{10}\,d^2+4096\,b^8\,c^{11}\,d}\right)}^{1/4}\,1{}\mathrm{i}\right)\,{\left(-\frac{a^4\,d^4+12\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+108\,a\,b^3\,c^3\,d+81\,b^4\,c^4}{4096\,a^8\,c^3\,d^9-32768\,a^7\,b\,c^4\,d^8+114688\,a^6\,b^2\,c^5\,d^7-229376\,a^5\,b^3\,c^6\,d^6+286720\,a^4\,b^4\,c^7\,d^5-229376\,a^3\,b^5\,c^8\,d^4+114688\,a^2\,b^6\,c^9\,d^3-32768\,a\,b^7\,c^{10}\,d^2+4096\,b^8\,c^{11}\,d}\right)}^{1/4}+\left(-\frac{\sqrt{x}\,\left(17\,a^6\,b^7\,d^7+108\,a^5\,b^8\,c\,d^6+198\,a^4\,b^9\,c^2\,d^5+108\,a^3\,b^{10}\,c^3\,d^4+81\,a^2\,b^{11}\,c^4\,d^3\right)}{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}+\left(-\frac{2\,\left(-a^5\,b^6\,d^6+51\,a^4\,b^7\,c\,d^5+189\,a^3\,b^8\,c^2\,d^4+81\,a^2\,b^9\,c^3\,d^3\right)}{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}+\left(\frac{\sqrt{x}\,\left(256\,a^{13}\,b^4\,d^{15}-512\,a^{12}\,b^5\,c\,d^{14}-2816\,a^{11}\,b^6\,c^2\,d^{13}+14336\,a^{10}\,b^7\,c^3\,d^{12}-36352\,a^9\,b^8\,c^4\,d^{11}+78848\,a^8\,b^9\,c^5\,d^{10}-146944\,a^7\,b^{10}\,c^6\,d^9+198656\,a^6\,b^{11}\,c^7\,d^8-176896\,a^5\,b^{12}\,c^8\,d^7+97792\,a^4\,b^{13}\,c^9\,d^6-30464\,a^3\,b^{14}\,c^{10}\,d^5+4096\,a^2\,b^{15}\,c^{11}\,d^4\right)}{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}+\frac{{\left(-\frac{a^4\,d^4+12\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+108\,a\,b^3\,c^3\,d+81\,b^4\,c^4}{4096\,a^8\,c^3\,d^9-32768\,a^7\,b\,c^4\,d^8+114688\,a^6\,b^2\,c^5\,d^7-229376\,a^5\,b^3\,c^6\,d^6+286720\,a^4\,b^4\,c^7\,d^5-229376\,a^3\,b^5\,c^8\,d^4+114688\,a^2\,b^6\,c^9\,d^3-32768\,a\,b^7\,c^{10}\,d^2+4096\,b^8\,c^{11}\,d}\right)}^{1/4}\,\left(1024\,a^{11}\,b^4\,c\,d^{13}-4096\,a^{10}\,b^5\,c^2\,d^{12}-4096\,a^9\,b^6\,c^3\,d^{11}+57344\,a^8\,b^7\,c^4\,d^{10}-157696\,a^7\,b^8\,c^5\,d^9+229376\,a^6\,b^9\,c^6\,d^8-200704\,a^5\,b^{10}\,c^7\,d^7+106496\,a^4\,b^{11}\,c^8\,d^6-31744\,a^3\,b^{12}\,c^9\,d^5+4096\,a^2\,b^{13}\,c^{10}\,d^4\right)\,2{}\mathrm{i}}{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}\right)\,{\left(-\frac{a^4\,d^4+12\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+108\,a\,b^3\,c^3\,d+81\,b^4\,c^4}{4096\,a^8\,c^3\,d^9-32768\,a^7\,b\,c^4\,d^8+114688\,a^6\,b^2\,c^5\,d^7-229376\,a^5\,b^3\,c^6\,d^6+286720\,a^4\,b^4\,c^7\,d^5-229376\,a^3\,b^5\,c^8\,d^4+114688\,a^2\,b^6\,c^9\,d^3-32768\,a\,b^7\,c^{10}\,d^2+4096\,b^8\,c^{11}\,d}\right)}^{3/4}\,1{}\mathrm{i}\right)\,{\left(-\frac{a^4\,d^4+12\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+108\,a\,b^3\,c^3\,d+81\,b^4\,c^4}{4096\,a^8\,c^3\,d^9-32768\,a^7\,b\,c^4\,d^8+114688\,a^6\,b^2\,c^5\,d^7-229376\,a^5\,b^3\,c^6\,d^6+286720\,a^4\,b^4\,c^7\,d^5-229376\,a^3\,b^5\,c^8\,d^4+114688\,a^2\,b^6\,c^9\,d^3-32768\,a\,b^7\,c^{10}\,d^2+4096\,b^8\,c^{11}\,d}\right)}^{1/4}\,1{}\mathrm{i}\right)\,{\left(-\frac{a^4\,d^4+12\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+108\,a\,b^3\,c^3\,d+81\,b^4\,c^4}{4096\,a^8\,c^3\,d^9-32768\,a^7\,b\,c^4\,d^8+114688\,a^6\,b^2\,c^5\,d^7-229376\,a^5\,b^3\,c^6\,d^6+286720\,a^4\,b^4\,c^7\,d^5-229376\,a^3\,b^5\,c^8\,d^4+114688\,a^2\,b^6\,c^9\,d^3-32768\,a\,b^7\,c^{10}\,d^2+4096\,b^8\,c^{11}\,d}\right)}^{1/4}}{\left(-\frac{\sqrt{x}\,\left(17\,a^6\,b^7\,d^7+108\,a^5\,b^8\,c\,d^6+198\,a^4\,b^9\,c^2\,d^5+108\,a^3\,b^{10}\,c^3\,d^4+81\,a^2\,b^{11}\,c^4\,d^3\right)}{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}+\left(\frac{2\,\left(-a^5\,b^6\,d^6+51\,a^4\,b^7\,c\,d^5+189\,a^3\,b^8\,c^2\,d^4+81\,a^2\,b^9\,c^3\,d^3\right)}{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}+\left(\frac{\sqrt{x}\,\left(256\,a^{13}\,b^4\,d^{15}-512\,a^{12}\,b^5\,c\,d^{14}-2816\,a^{11}\,b^6\,c^2\,d^{13}+14336\,a^{10}\,b^7\,c^3\,d^{12}-36352\,a^9\,b^8\,c^4\,d^{11}+78848\,a^8\,b^9\,c^5\,d^{10}-146944\,a^7\,b^{10}\,c^6\,d^9+198656\,a^6\,b^{11}\,c^7\,d^8-176896\,a^5\,b^{12}\,c^8\,d^7+97792\,a^4\,b^{13}\,c^9\,d^6-30464\,a^3\,b^{14}\,c^{10}\,d^5+4096\,a^2\,b^{15}\,c^{11}\,d^4\right)}{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}-\frac{{\left(-\frac{a^4\,d^4+12\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+108\,a\,b^3\,c^3\,d+81\,b^4\,c^4}{4096\,a^8\,c^3\,d^9-32768\,a^7\,b\,c^4\,d^8+114688\,a^6\,b^2\,c^5\,d^7-229376\,a^5\,b^3\,c^6\,d^6+286720\,a^4\,b^4\,c^7\,d^5-229376\,a^3\,b^5\,c^8\,d^4+114688\,a^2\,b^6\,c^9\,d^3-32768\,a\,b^7\,c^{10}\,d^2+4096\,b^8\,c^{11}\,d}\right)}^{1/4}\,\left(1024\,a^{11}\,b^4\,c\,d^{13}-4096\,a^{10}\,b^5\,c^2\,d^{12}-4096\,a^9\,b^6\,c^3\,d^{11}+57344\,a^8\,b^7\,c^4\,d^{10}-157696\,a^7\,b^8\,c^5\,d^9+229376\,a^6\,b^9\,c^6\,d^8-200704\,a^5\,b^{10}\,c^7\,d^7+106496\,a^4\,b^{11}\,c^8\,d^6-31744\,a^3\,b^{12}\,c^9\,d^5+4096\,a^2\,b^{13}\,c^{10}\,d^4\right)\,2{}\mathrm{i}}{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}\right)\,{\left(-\frac{a^4\,d^4+12\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+108\,a\,b^3\,c^3\,d+81\,b^4\,c^4}{4096\,a^8\,c^3\,d^9-32768\,a^7\,b\,c^4\,d^8+114688\,a^6\,b^2\,c^5\,d^7-229376\,a^5\,b^3\,c^6\,d^6+286720\,a^4\,b^4\,c^7\,d^5-229376\,a^3\,b^5\,c^8\,d^4+114688\,a^2\,b^6\,c^9\,d^3-32768\,a\,b^7\,c^{10}\,d^2+4096\,b^8\,c^{11}\,d}\right)}^{3/4}\,1{}\mathrm{i}\right)\,{\left(-\frac{a^4\,d^4+12\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+108\,a\,b^3\,c^3\,d+81\,b^4\,c^4}{4096\,a^8\,c^3\,d^9-32768\,a^7\,b\,c^4\,d^8+114688\,a^6\,b^2\,c^5\,d^7-229376\,a^5\,b^3\,c^6\,d^6+286720\,a^4\,b^4\,c^7\,d^5-229376\,a^3\,b^5\,c^8\,d^4+114688\,a^2\,b^6\,c^9\,d^3-32768\,a\,b^7\,c^{10}\,d^2+4096\,b^8\,c^{11}\,d}\right)}^{1/4}\,1{}\mathrm{i}\right)\,{\left(-\frac{a^4\,d^4+12\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+108\,a\,b^3\,c^3\,d+81\,b^4\,c^4}{4096\,a^8\,c^3\,d^9-32768\,a^7\,b\,c^4\,d^8+114688\,a^6\,b^2\,c^5\,d^7-229376\,a^5\,b^3\,c^6\,d^6+286720\,a^4\,b^4\,c^7\,d^5-229376\,a^3\,b^5\,c^8\,d^4+114688\,a^2\,b^6\,c^9\,d^3-32768\,a\,b^7\,c^{10}\,d^2+4096\,b^8\,c^{11}\,d}\right)}^{1/4}\,1{}\mathrm{i}-\left(-\frac{\sqrt{x}\,\left(17\,a^6\,b^7\,d^7+108\,a^5\,b^8\,c\,d^6+198\,a^4\,b^9\,c^2\,d^5+108\,a^3\,b^{10}\,c^3\,d^4+81\,a^2\,b^{11}\,c^4\,d^3\right)}{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}+\left(-\frac{2\,\left(-a^5\,b^6\,d^6+51\,a^4\,b^7\,c\,d^5+189\,a^3\,b^8\,c^2\,d^4+81\,a^2\,b^9\,c^3\,d^3\right)}{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}+\left(\frac{\sqrt{x}\,\left(256\,a^{13}\,b^4\,d^{15}-512\,a^{12}\,b^5\,c\,d^{14}-2816\,a^{11}\,b^6\,c^2\,d^{13}+14336\,a^{10}\,b^7\,c^3\,d^{12}-36352\,a^9\,b^8\,c^4\,d^{11}+78848\,a^8\,b^9\,c^5\,d^{10}-146944\,a^7\,b^{10}\,c^6\,d^9+198656\,a^6\,b^{11}\,c^7\,d^8-176896\,a^5\,b^{12}\,c^8\,d^7+97792\,a^4\,b^{13}\,c^9\,d^6-30464\,a^3\,b^{14}\,c^{10}\,d^5+4096\,a^2\,b^{15}\,c^{11}\,d^4\right)}{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}+\frac{{\left(-\frac{a^4\,d^4+12\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+108\,a\,b^3\,c^3\,d+81\,b^4\,c^4}{4096\,a^8\,c^3\,d^9-32768\,a^7\,b\,c^4\,d^8+114688\,a^6\,b^2\,c^5\,d^7-229376\,a^5\,b^3\,c^6\,d^6+286720\,a^4\,b^4\,c^7\,d^5-229376\,a^3\,b^5\,c^8\,d^4+114688\,a^2\,b^6\,c^9\,d^3-32768\,a\,b^7\,c^{10}\,d^2+4096\,b^8\,c^{11}\,d}\right)}^{1/4}\,\left(1024\,a^{11}\,b^4\,c\,d^{13}-4096\,a^{10}\,b^5\,c^2\,d^{12}-4096\,a^9\,b^6\,c^3\,d^{11}+57344\,a^8\,b^7\,c^4\,d^{10}-157696\,a^7\,b^8\,c^5\,d^9+229376\,a^6\,b^9\,c^6\,d^8-200704\,a^5\,b^{10}\,c^7\,d^7+106496\,a^4\,b^{11}\,c^8\,d^6-31744\,a^3\,b^{12}\,c^9\,d^5+4096\,a^2\,b^{13}\,c^{10}\,d^4\right)\,2{}\mathrm{i}}{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}\right)\,{\left(-\frac{a^4\,d^4+12\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+108\,a\,b^3\,c^3\,d+81\,b^4\,c^4}{4096\,a^8\,c^3\,d^9-32768\,a^7\,b\,c^4\,d^8+114688\,a^6\,b^2\,c^5\,d^7-229376\,a^5\,b^3\,c^6\,d^6+286720\,a^4\,b^4\,c^7\,d^5-229376\,a^3\,b^5\,c^8\,d^4+114688\,a^2\,b^6\,c^9\,d^3-32768\,a\,b^7\,c^{10}\,d^2+4096\,b^8\,c^{11}\,d}\right)}^{3/4}\,1{}\mathrm{i}\right)\,{\left(-\frac{a^4\,d^4+12\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+108\,a\,b^3\,c^3\,d+81\,b^4\,c^4}{4096\,a^8\,c^3\,d^9-32768\,a^7\,b\,c^4\,d^8+114688\,a^6\,b^2\,c^5\,d^7-229376\,a^5\,b^3\,c^6\,d^6+286720\,a^4\,b^4\,c^7\,d^5-229376\,a^3\,b^5\,c^8\,d^4+114688\,a^2\,b^6\,c^9\,d^3-32768\,a\,b^7\,c^{10}\,d^2+4096\,b^8\,c^{11}\,d}\right)}^{1/4}\,1{}\mathrm{i}\right)\,{\left(-\frac{a^4\,d^4+12\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+108\,a\,b^3\,c^3\,d+81\,b^4\,c^4}{4096\,a^8\,c^3\,d^9-32768\,a^7\,b\,c^4\,d^8+114688\,a^6\,b^2\,c^5\,d^7-229376\,a^5\,b^3\,c^6\,d^6+286720\,a^4\,b^4\,c^7\,d^5-229376\,a^3\,b^5\,c^8\,d^4+114688\,a^2\,b^6\,c^9\,d^3-32768\,a\,b^7\,c^{10}\,d^2+4096\,b^8\,c^{11}\,d}\right)}^{1/4}\,1{}\mathrm{i}}\right)\,{\left(-\frac{a^4\,d^4+12\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+108\,a\,b^3\,c^3\,d+81\,b^4\,c^4}{4096\,a^8\,c^3\,d^9-32768\,a^7\,b\,c^4\,d^8+114688\,a^6\,b^2\,c^5\,d^7-229376\,a^5\,b^3\,c^6\,d^6+286720\,a^4\,b^4\,c^7\,d^5-229376\,a^3\,b^5\,c^8\,d^4+114688\,a^2\,b^6\,c^9\,d^3-32768\,a\,b^7\,c^{10}\,d^2+4096\,b^8\,c^{11}\,d}\right)}^{1/4}-\frac{\sqrt{x}}{2\,\left(d\,x^2+c\right)\,\left(a\,d-b\,c\right)}-\mathrm{atan}\left(\frac{\left(\left(\frac{2\,\left(-a^5\,b^6\,d^6+51\,a^4\,b^7\,c\,d^5+189\,a^3\,b^8\,c^2\,d^4+81\,a^2\,b^9\,c^3\,d^3\right)}{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}+\left(\frac{\sqrt{x}\,\left(256\,a^{13}\,b^4\,d^{15}-512\,a^{12}\,b^5\,c\,d^{14}-2816\,a^{11}\,b^6\,c^2\,d^{13}+14336\,a^{10}\,b^7\,c^3\,d^{12}-36352\,a^9\,b^8\,c^4\,d^{11}+78848\,a^8\,b^9\,c^5\,d^{10}-146944\,a^7\,b^{10}\,c^6\,d^9+198656\,a^6\,b^{11}\,c^7\,d^8-176896\,a^5\,b^{12}\,c^8\,d^7+97792\,a^4\,b^{13}\,c^9\,d^6-30464\,a^3\,b^{14}\,c^{10}\,d^5+4096\,a^2\,b^{15}\,c^{11}\,d^4\right)}{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}+\frac{2\,{\left(-\frac{a\,b^3}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{1/4}\,\left(1024\,a^{11}\,b^4\,c\,d^{13}-4096\,a^{10}\,b^5\,c^2\,d^{12}-4096\,a^9\,b^6\,c^3\,d^{11}+57344\,a^8\,b^7\,c^4\,d^{10}-157696\,a^7\,b^8\,c^5\,d^9+229376\,a^6\,b^9\,c^6\,d^8-200704\,a^5\,b^{10}\,c^7\,d^7+106496\,a^4\,b^{11}\,c^8\,d^6-31744\,a^3\,b^{12}\,c^9\,d^5+4096\,a^2\,b^{13}\,c^{10}\,d^4\right)}{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}\right)\,{\left(-\frac{a\,b^3}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{3/4}\right)\,{\left(-\frac{a\,b^3}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{1/4}+\frac{\sqrt{x}\,\left(17\,a^6\,b^7\,d^7+108\,a^5\,b^8\,c\,d^6+198\,a^4\,b^9\,c^2\,d^5+108\,a^3\,b^{10}\,c^3\,d^4+81\,a^2\,b^{11}\,c^4\,d^3\right)}{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)\,{\left(-\frac{a\,b^3}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{1/4}\,1{}\mathrm{i}-\left(\left(\frac{2\,\left(-a^5\,b^6\,d^6+51\,a^4\,b^7\,c\,d^5+189\,a^3\,b^8\,c^2\,d^4+81\,a^2\,b^9\,c^3\,d^3\right)}{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}-\left(\frac{\sqrt{x}\,\left(256\,a^{13}\,b^4\,d^{15}-512\,a^{12}\,b^5\,c\,d^{14}-2816\,a^{11}\,b^6\,c^2\,d^{13}+14336\,a^{10}\,b^7\,c^3\,d^{12}-36352\,a^9\,b^8\,c^4\,d^{11}+78848\,a^8\,b^9\,c^5\,d^{10}-146944\,a^7\,b^{10}\,c^6\,d^9+198656\,a^6\,b^{11}\,c^7\,d^8-176896\,a^5\,b^{12}\,c^8\,d^7+97792\,a^4\,b^{13}\,c^9\,d^6-30464\,a^3\,b^{14}\,c^{10}\,d^5+4096\,a^2\,b^{15}\,c^{11}\,d^4\right)}{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}-\frac{2\,{\left(-\frac{a\,b^3}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{1/4}\,\left(1024\,a^{11}\,b^4\,c\,d^{13}-4096\,a^{10}\,b^5\,c^2\,d^{12}-4096\,a^9\,b^6\,c^3\,d^{11}+57344\,a^8\,b^7\,c^4\,d^{10}-157696\,a^7\,b^8\,c^5\,d^9+229376\,a^6\,b^9\,c^6\,d^8-200704\,a^5\,b^{10}\,c^7\,d^7+106496\,a^4\,b^{11}\,c^8\,d^6-31744\,a^3\,b^{12}\,c^9\,d^5+4096\,a^2\,b^{13}\,c^{10}\,d^4\right)}{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}\right)\,{\left(-\frac{a\,b^3}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{3/4}\right)\,{\left(-\frac{a\,b^3}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{1/4}-\frac{\sqrt{x}\,\left(17\,a^6\,b^7\,d^7+108\,a^5\,b^8\,c\,d^6+198\,a^4\,b^9\,c^2\,d^5+108\,a^3\,b^{10}\,c^3\,d^4+81\,a^2\,b^{11}\,c^4\,d^3\right)}{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)\,{\left(-\frac{a\,b^3}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{1/4}\,1{}\mathrm{i}}{\left(\left(\frac{2\,\left(-a^5\,b^6\,d^6+51\,a^4\,b^7\,c\,d^5+189\,a^3\,b^8\,c^2\,d^4+81\,a^2\,b^9\,c^3\,d^3\right)}{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}+\left(\frac{\sqrt{x}\,\left(256\,a^{13}\,b^4\,d^{15}-512\,a^{12}\,b^5\,c\,d^{14}-2816\,a^{11}\,b^6\,c^2\,d^{13}+14336\,a^{10}\,b^7\,c^3\,d^{12}-36352\,a^9\,b^8\,c^4\,d^{11}+78848\,a^8\,b^9\,c^5\,d^{10}-146944\,a^7\,b^{10}\,c^6\,d^9+198656\,a^6\,b^{11}\,c^7\,d^8-176896\,a^5\,b^{12}\,c^8\,d^7+97792\,a^4\,b^{13}\,c^9\,d^6-30464\,a^3\,b^{14}\,c^{10}\,d^5+4096\,a^2\,b^{15}\,c^{11}\,d^4\right)}{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}+\frac{2\,{\left(-\frac{a\,b^3}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{1/4}\,\left(1024\,a^{11}\,b^4\,c\,d^{13}-4096\,a^{10}\,b^5\,c^2\,d^{12}-4096\,a^9\,b^6\,c^3\,d^{11}+57344\,a^8\,b^7\,c^4\,d^{10}-157696\,a^7\,b^8\,c^5\,d^9+229376\,a^6\,b^9\,c^6\,d^8-200704\,a^5\,b^{10}\,c^7\,d^7+106496\,a^4\,b^{11}\,c^8\,d^6-31744\,a^3\,b^{12}\,c^9\,d^5+4096\,a^2\,b^{13}\,c^{10}\,d^4\right)}{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}\right)\,{\left(-\frac{a\,b^3}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{3/4}\right)\,{\left(-\frac{a\,b^3}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{1/4}+\frac{\sqrt{x}\,\left(17\,a^6\,b^7\,d^7+108\,a^5\,b^8\,c\,d^6+198\,a^4\,b^9\,c^2\,d^5+108\,a^3\,b^{10}\,c^3\,d^4+81\,a^2\,b^{11}\,c^4\,d^3\right)}{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)\,{\left(-\frac{a\,b^3}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{1/4}+\left(\left(\frac{2\,\left(-a^5\,b^6\,d^6+51\,a^4\,b^7\,c\,d^5+189\,a^3\,b^8\,c^2\,d^4+81\,a^2\,b^9\,c^3\,d^3\right)}{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}-\left(\frac{\sqrt{x}\,\left(256\,a^{13}\,b^4\,d^{15}-512\,a^{12}\,b^5\,c\,d^{14}-2816\,a^{11}\,b^6\,c^2\,d^{13}+14336\,a^{10}\,b^7\,c^3\,d^{12}-36352\,a^9\,b^8\,c^4\,d^{11}+78848\,a^8\,b^9\,c^5\,d^{10}-146944\,a^7\,b^{10}\,c^6\,d^9+198656\,a^6\,b^{11}\,c^7\,d^8-176896\,a^5\,b^{12}\,c^8\,d^7+97792\,a^4\,b^{13}\,c^9\,d^6-30464\,a^3\,b^{14}\,c^{10}\,d^5+4096\,a^2\,b^{15}\,c^{11}\,d^4\right)}{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}-\frac{2\,{\left(-\frac{a\,b^3}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{1/4}\,\left(1024\,a^{11}\,b^4\,c\,d^{13}-4096\,a^{10}\,b^5\,c^2\,d^{12}-4096\,a^9\,b^6\,c^3\,d^{11}+57344\,a^8\,b^7\,c^4\,d^{10}-157696\,a^7\,b^8\,c^5\,d^9+229376\,a^6\,b^9\,c^6\,d^8-200704\,a^5\,b^{10}\,c^7\,d^7+106496\,a^4\,b^{11}\,c^8\,d^6-31744\,a^3\,b^{12}\,c^9\,d^5+4096\,a^2\,b^{13}\,c^{10}\,d^4\right)}{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}\right)\,{\left(-\frac{a\,b^3}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{3/4}\right)\,{\left(-\frac{a\,b^3}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{1/4}-\frac{\sqrt{x}\,\left(17\,a^6\,b^7\,d^7+108\,a^5\,b^8\,c\,d^6+198\,a^4\,b^9\,c^2\,d^5+108\,a^3\,b^{10}\,c^3\,d^4+81\,a^2\,b^{11}\,c^4\,d^3\right)}{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)\,{\left(-\frac{a\,b^3}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{1/4}}\right)\,{\left(-\frac{a\,b^3}{16\,a^8\,d^8-128\,a^7\,b\,c\,d^7+448\,a^6\,b^2\,c^2\,d^6-896\,a^5\,b^3\,c^3\,d^5+1120\,a^4\,b^4\,c^4\,d^4-896\,a^3\,b^5\,c^5\,d^3+448\,a^2\,b^6\,c^6\,d^2-128\,a\,b^7\,c^7\,d+16\,b^8\,c^8}\right)}^{1/4}\,2{}\mathrm{i}-\mathrm{atan}\left(-\frac{\left(\left(\left(\frac{\sqrt{x}\,\left(256\,a^{13}\,b^4\,d^{15}-512\,a^{12}\,b^5\,c\,d^{14}-2816\,a^{11}\,b^6\,c^2\,d^{13}+14336\,a^{10}\,b^7\,c^3\,d^{12}-36352\,a^9\,b^8\,c^4\,d^{11}+78848\,a^8\,b^9\,c^5\,d^{10}-146944\,a^7\,b^{10}\,c^6\,d^9+198656\,a^6\,b^{11}\,c^7\,d^8-176896\,a^5\,b^{12}\,c^8\,d^7+97792\,a^4\,b^{13}\,c^9\,d^6-30464\,a^3\,b^{14}\,c^{10}\,d^5+4096\,a^2\,b^{15}\,c^{11}\,d^4\right)}{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}-\frac{2\,{\left(-\frac{a^4\,d^4+12\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+108\,a\,b^3\,c^3\,d+81\,b^4\,c^4}{4096\,a^8\,c^3\,d^9-32768\,a^7\,b\,c^4\,d^8+114688\,a^6\,b^2\,c^5\,d^7-229376\,a^5\,b^3\,c^6\,d^6+286720\,a^4\,b^4\,c^7\,d^5-229376\,a^3\,b^5\,c^8\,d^4+114688\,a^2\,b^6\,c^9\,d^3-32768\,a\,b^7\,c^{10}\,d^2+4096\,b^8\,c^{11}\,d}\right)}^{1/4}\,\left(1024\,a^{11}\,b^4\,c\,d^{13}-4096\,a^{10}\,b^5\,c^2\,d^{12}-4096\,a^9\,b^6\,c^3\,d^{11}+57344\,a^8\,b^7\,c^4\,d^{10}-157696\,a^7\,b^8\,c^5\,d^9+229376\,a^6\,b^9\,c^6\,d^8-200704\,a^5\,b^{10}\,c^7\,d^7+106496\,a^4\,b^{11}\,c^8\,d^6-31744\,a^3\,b^{12}\,c^9\,d^5+4096\,a^2\,b^{13}\,c^{10}\,d^4\right)}{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}\right)\,{\left(-\frac{a^4\,d^4+12\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+108\,a\,b^3\,c^3\,d+81\,b^4\,c^4}{4096\,a^8\,c^3\,d^9-32768\,a^7\,b\,c^4\,d^8+114688\,a^6\,b^2\,c^5\,d^7-229376\,a^5\,b^3\,c^6\,d^6+286720\,a^4\,b^4\,c^7\,d^5-229376\,a^3\,b^5\,c^8\,d^4+114688\,a^2\,b^6\,c^9\,d^3-32768\,a\,b^7\,c^{10}\,d^2+4096\,b^8\,c^{11}\,d}\right)}^{3/4}-\frac{2\,\left(-a^5\,b^6\,d^6+51\,a^4\,b^7\,c\,d^5+189\,a^3\,b^8\,c^2\,d^4+81\,a^2\,b^9\,c^3\,d^3\right)}{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}\right)\,{\left(-\frac{a^4\,d^4+12\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+108\,a\,b^3\,c^3\,d+81\,b^4\,c^4}{4096\,a^8\,c^3\,d^9-32768\,a^7\,b\,c^4\,d^8+114688\,a^6\,b^2\,c^5\,d^7-229376\,a^5\,b^3\,c^6\,d^6+286720\,a^4\,b^4\,c^7\,d^5-229376\,a^3\,b^5\,c^8\,d^4+114688\,a^2\,b^6\,c^9\,d^3-32768\,a\,b^7\,c^{10}\,d^2+4096\,b^8\,c^{11}\,d}\right)}^{1/4}+\frac{\sqrt{x}\,\left(17\,a^6\,b^7\,d^7+108\,a^5\,b^8\,c\,d^6+198\,a^4\,b^9\,c^2\,d^5+108\,a^3\,b^{10}\,c^3\,d^4+81\,a^2\,b^{11}\,c^4\,d^3\right)}{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)\,{\left(-\frac{a^4\,d^4+12\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+108\,a\,b^3\,c^3\,d+81\,b^4\,c^4}{4096\,a^8\,c^3\,d^9-32768\,a^7\,b\,c^4\,d^8+114688\,a^6\,b^2\,c^5\,d^7-229376\,a^5\,b^3\,c^6\,d^6+286720\,a^4\,b^4\,c^7\,d^5-229376\,a^3\,b^5\,c^8\,d^4+114688\,a^2\,b^6\,c^9\,d^3-32768\,a\,b^7\,c^{10}\,d^2+4096\,b^8\,c^{11}\,d}\right)}^{1/4}\,1{}\mathrm{i}+\left(\left(\left(\frac{\sqrt{x}\,\left(256\,a^{13}\,b^4\,d^{15}-512\,a^{12}\,b^5\,c\,d^{14}-2816\,a^{11}\,b^6\,c^2\,d^{13}+14336\,a^{10}\,b^7\,c^3\,d^{12}-36352\,a^9\,b^8\,c^4\,d^{11}+78848\,a^8\,b^9\,c^5\,d^{10}-146944\,a^7\,b^{10}\,c^6\,d^9+198656\,a^6\,b^{11}\,c^7\,d^8-176896\,a^5\,b^{12}\,c^8\,d^7+97792\,a^4\,b^{13}\,c^9\,d^6-30464\,a^3\,b^{14}\,c^{10}\,d^5+4096\,a^2\,b^{15}\,c^{11}\,d^4\right)}{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}+\frac{2\,{\left(-\frac{a^4\,d^4+12\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+108\,a\,b^3\,c^3\,d+81\,b^4\,c^4}{4096\,a^8\,c^3\,d^9-32768\,a^7\,b\,c^4\,d^8+114688\,a^6\,b^2\,c^5\,d^7-229376\,a^5\,b^3\,c^6\,d^6+286720\,a^4\,b^4\,c^7\,d^5-229376\,a^3\,b^5\,c^8\,d^4+114688\,a^2\,b^6\,c^9\,d^3-32768\,a\,b^7\,c^{10}\,d^2+4096\,b^8\,c^{11}\,d}\right)}^{1/4}\,\left(1024\,a^{11}\,b^4\,c\,d^{13}-4096\,a^{10}\,b^5\,c^2\,d^{12}-4096\,a^9\,b^6\,c^3\,d^{11}+57344\,a^8\,b^7\,c^4\,d^{10}-157696\,a^7\,b^8\,c^5\,d^9+229376\,a^6\,b^9\,c^6\,d^8-200704\,a^5\,b^{10}\,c^7\,d^7+106496\,a^4\,b^{11}\,c^8\,d^6-31744\,a^3\,b^{12}\,c^9\,d^5+4096\,a^2\,b^{13}\,c^{10}\,d^4\right)}{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}\right)\,{\left(-\frac{a^4\,d^4+12\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+108\,a\,b^3\,c^3\,d+81\,b^4\,c^4}{4096\,a^8\,c^3\,d^9-32768\,a^7\,b\,c^4\,d^8+114688\,a^6\,b^2\,c^5\,d^7-229376\,a^5\,b^3\,c^6\,d^6+286720\,a^4\,b^4\,c^7\,d^5-229376\,a^3\,b^5\,c^8\,d^4+114688\,a^2\,b^6\,c^9\,d^3-32768\,a\,b^7\,c^{10}\,d^2+4096\,b^8\,c^{11}\,d}\right)}^{3/4}+\frac{2\,\left(-a^5\,b^6\,d^6+51\,a^4\,b^7\,c\,d^5+189\,a^3\,b^8\,c^2\,d^4+81\,a^2\,b^9\,c^3\,d^3\right)}{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}\right)\,{\left(-\frac{a^4\,d^4+12\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+108\,a\,b^3\,c^3\,d+81\,b^4\,c^4}{4096\,a^8\,c^3\,d^9-32768\,a^7\,b\,c^4\,d^8+114688\,a^6\,b^2\,c^5\,d^7-229376\,a^5\,b^3\,c^6\,d^6+286720\,a^4\,b^4\,c^7\,d^5-229376\,a^3\,b^5\,c^8\,d^4+114688\,a^2\,b^6\,c^9\,d^3-32768\,a\,b^7\,c^{10}\,d^2+4096\,b^8\,c^{11}\,d}\right)}^{1/4}+\frac{\sqrt{x}\,\left(17\,a^6\,b^7\,d^7+108\,a^5\,b^8\,c\,d^6+198\,a^4\,b^9\,c^2\,d^5+108\,a^3\,b^{10}\,c^3\,d^4+81\,a^2\,b^{11}\,c^4\,d^3\right)}{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)\,{\left(-\frac{a^4\,d^4+12\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+108\,a\,b^3\,c^3\,d+81\,b^4\,c^4}{4096\,a^8\,c^3\,d^9-32768\,a^7\,b\,c^4\,d^8+114688\,a^6\,b^2\,c^5\,d^7-229376\,a^5\,b^3\,c^6\,d^6+286720\,a^4\,b^4\,c^7\,d^5-229376\,a^3\,b^5\,c^8\,d^4+114688\,a^2\,b^6\,c^9\,d^3-32768\,a\,b^7\,c^{10}\,d^2+4096\,b^8\,c^{11}\,d}\right)}^{1/4}\,1{}\mathrm{i}}{\left(\left(\left(\frac{\sqrt{x}\,\left(256\,a^{13}\,b^4\,d^{15}-512\,a^{12}\,b^5\,c\,d^{14}-2816\,a^{11}\,b^6\,c^2\,d^{13}+14336\,a^{10}\,b^7\,c^3\,d^{12}-36352\,a^9\,b^8\,c^4\,d^{11}+78848\,a^8\,b^9\,c^5\,d^{10}-146944\,a^7\,b^{10}\,c^6\,d^9+198656\,a^6\,b^{11}\,c^7\,d^8-176896\,a^5\,b^{12}\,c^8\,d^7+97792\,a^4\,b^{13}\,c^9\,d^6-30464\,a^3\,b^{14}\,c^{10}\,d^5+4096\,a^2\,b^{15}\,c^{11}\,d^4\right)}{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}-\frac{2\,{\left(-\frac{a^4\,d^4+12\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+108\,a\,b^3\,c^3\,d+81\,b^4\,c^4}{4096\,a^8\,c^3\,d^9-32768\,a^7\,b\,c^4\,d^8+114688\,a^6\,b^2\,c^5\,d^7-229376\,a^5\,b^3\,c^6\,d^6+286720\,a^4\,b^4\,c^7\,d^5-229376\,a^3\,b^5\,c^8\,d^4+114688\,a^2\,b^6\,c^9\,d^3-32768\,a\,b^7\,c^{10}\,d^2+4096\,b^8\,c^{11}\,d}\right)}^{1/4}\,\left(1024\,a^{11}\,b^4\,c\,d^{13}-4096\,a^{10}\,b^5\,c^2\,d^{12}-4096\,a^9\,b^6\,c^3\,d^{11}+57344\,a^8\,b^7\,c^4\,d^{10}-157696\,a^7\,b^8\,c^5\,d^9+229376\,a^6\,b^9\,c^6\,d^8-200704\,a^5\,b^{10}\,c^7\,d^7+106496\,a^4\,b^{11}\,c^8\,d^6-31744\,a^3\,b^{12}\,c^9\,d^5+4096\,a^2\,b^{13}\,c^{10}\,d^4\right)}{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}\right)\,{\left(-\frac{a^4\,d^4+12\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+108\,a\,b^3\,c^3\,d+81\,b^4\,c^4}{4096\,a^8\,c^3\,d^9-32768\,a^7\,b\,c^4\,d^8+114688\,a^6\,b^2\,c^5\,d^7-229376\,a^5\,b^3\,c^6\,d^6+286720\,a^4\,b^4\,c^7\,d^5-229376\,a^3\,b^5\,c^8\,d^4+114688\,a^2\,b^6\,c^9\,d^3-32768\,a\,b^7\,c^{10}\,d^2+4096\,b^8\,c^{11}\,d}\right)}^{3/4}-\frac{2\,\left(-a^5\,b^6\,d^6+51\,a^4\,b^7\,c\,d^5+189\,a^3\,b^8\,c^2\,d^4+81\,a^2\,b^9\,c^3\,d^3\right)}{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}\right)\,{\left(-\frac{a^4\,d^4+12\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+108\,a\,b^3\,c^3\,d+81\,b^4\,c^4}{4096\,a^8\,c^3\,d^9-32768\,a^7\,b\,c^4\,d^8+114688\,a^6\,b^2\,c^5\,d^7-229376\,a^5\,b^3\,c^6\,d^6+286720\,a^4\,b^4\,c^7\,d^5-229376\,a^3\,b^5\,c^8\,d^4+114688\,a^2\,b^6\,c^9\,d^3-32768\,a\,b^7\,c^{10}\,d^2+4096\,b^8\,c^{11}\,d}\right)}^{1/4}+\frac{\sqrt{x}\,\left(17\,a^6\,b^7\,d^7+108\,a^5\,b^8\,c\,d^6+198\,a^4\,b^9\,c^2\,d^5+108\,a^3\,b^{10}\,c^3\,d^4+81\,a^2\,b^{11}\,c^4\,d^3\right)}{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)\,{\left(-\frac{a^4\,d^4+12\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+108\,a\,b^3\,c^3\,d+81\,b^4\,c^4}{4096\,a^8\,c^3\,d^9-32768\,a^7\,b\,c^4\,d^8+114688\,a^6\,b^2\,c^5\,d^7-229376\,a^5\,b^3\,c^6\,d^6+286720\,a^4\,b^4\,c^7\,d^5-229376\,a^3\,b^5\,c^8\,d^4+114688\,a^2\,b^6\,c^9\,d^3-32768\,a\,b^7\,c^{10}\,d^2+4096\,b^8\,c^{11}\,d}\right)}^{1/4}-\left(\left(\left(\frac{\sqrt{x}\,\left(256\,a^{13}\,b^4\,d^{15}-512\,a^{12}\,b^5\,c\,d^{14}-2816\,a^{11}\,b^6\,c^2\,d^{13}+14336\,a^{10}\,b^7\,c^3\,d^{12}-36352\,a^9\,b^8\,c^4\,d^{11}+78848\,a^8\,b^9\,c^5\,d^{10}-146944\,a^7\,b^{10}\,c^6\,d^9+198656\,a^6\,b^{11}\,c^7\,d^8-176896\,a^5\,b^{12}\,c^8\,d^7+97792\,a^4\,b^{13}\,c^9\,d^6-30464\,a^3\,b^{14}\,c^{10}\,d^5+4096\,a^2\,b^{15}\,c^{11}\,d^4\right)}{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}+\frac{2\,{\left(-\frac{a^4\,d^4+12\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+108\,a\,b^3\,c^3\,d+81\,b^4\,c^4}{4096\,a^8\,c^3\,d^9-32768\,a^7\,b\,c^4\,d^8+114688\,a^6\,b^2\,c^5\,d^7-229376\,a^5\,b^3\,c^6\,d^6+286720\,a^4\,b^4\,c^7\,d^5-229376\,a^3\,b^5\,c^8\,d^4+114688\,a^2\,b^6\,c^9\,d^3-32768\,a\,b^7\,c^{10}\,d^2+4096\,b^8\,c^{11}\,d}\right)}^{1/4}\,\left(1024\,a^{11}\,b^4\,c\,d^{13}-4096\,a^{10}\,b^5\,c^2\,d^{12}-4096\,a^9\,b^6\,c^3\,d^{11}+57344\,a^8\,b^7\,c^4\,d^{10}-157696\,a^7\,b^8\,c^5\,d^9+229376\,a^6\,b^9\,c^6\,d^8-200704\,a^5\,b^{10}\,c^7\,d^7+106496\,a^4\,b^{11}\,c^8\,d^6-31744\,a^3\,b^{12}\,c^9\,d^5+4096\,a^2\,b^{13}\,c^{10}\,d^4\right)}{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}\right)\,{\left(-\frac{a^4\,d^4+12\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+108\,a\,b^3\,c^3\,d+81\,b^4\,c^4}{4096\,a^8\,c^3\,d^9-32768\,a^7\,b\,c^4\,d^8+114688\,a^6\,b^2\,c^5\,d^7-229376\,a^5\,b^3\,c^6\,d^6+286720\,a^4\,b^4\,c^7\,d^5-229376\,a^3\,b^5\,c^8\,d^4+114688\,a^2\,b^6\,c^9\,d^3-32768\,a\,b^7\,c^{10}\,d^2+4096\,b^8\,c^{11}\,d}\right)}^{3/4}+\frac{2\,\left(-a^5\,b^6\,d^6+51\,a^4\,b^7\,c\,d^5+189\,a^3\,b^8\,c^2\,d^4+81\,a^2\,b^9\,c^3\,d^3\right)}{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}\right)\,{\left(-\frac{a^4\,d^4+12\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+108\,a\,b^3\,c^3\,d+81\,b^4\,c^4}{4096\,a^8\,c^3\,d^9-32768\,a^7\,b\,c^4\,d^8+114688\,a^6\,b^2\,c^5\,d^7-229376\,a^5\,b^3\,c^6\,d^6+286720\,a^4\,b^4\,c^7\,d^5-229376\,a^3\,b^5\,c^8\,d^4+114688\,a^2\,b^6\,c^9\,d^3-32768\,a\,b^7\,c^{10}\,d^2+4096\,b^8\,c^{11}\,d}\right)}^{1/4}+\frac{\sqrt{x}\,\left(17\,a^6\,b^7\,d^7+108\,a^5\,b^8\,c\,d^6+198\,a^4\,b^9\,c^2\,d^5+108\,a^3\,b^{10}\,c^3\,d^4+81\,a^2\,b^{11}\,c^4\,d^3\right)}{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)\,{\left(-\frac{a^4\,d^4+12\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+108\,a\,b^3\,c^3\,d+81\,b^4\,c^4}{4096\,a^8\,c^3\,d^9-32768\,a^7\,b\,c^4\,d^8+114688\,a^6\,b^2\,c^5\,d^7-229376\,a^5\,b^3\,c^6\,d^6+286720\,a^4\,b^4\,c^7\,d^5-229376\,a^3\,b^5\,c^8\,d^4+114688\,a^2\,b^6\,c^9\,d^3-32768\,a\,b^7\,c^{10}\,d^2+4096\,b^8\,c^{11}\,d}\right)}^{1/4}}\right)\,{\left(-\frac{a^4\,d^4+12\,a^3\,b\,c\,d^3+54\,a^2\,b^2\,c^2\,d^2+108\,a\,b^3\,c^3\,d+81\,b^4\,c^4}{4096\,a^8\,c^3\,d^9-32768\,a^7\,b\,c^4\,d^8+114688\,a^6\,b^2\,c^5\,d^7-229376\,a^5\,b^3\,c^6\,d^6+286720\,a^4\,b^4\,c^7\,d^5-229376\,a^3\,b^5\,c^8\,d^4+114688\,a^2\,b^6\,c^9\,d^3-32768\,a\,b^7\,c^{10}\,d^2+4096\,b^8\,c^{11}\,d}\right)}^{1/4}\,2{}\mathrm{i}","Not used",1,"- atan(((((2*(51*a^4*b^7*c*d^5 - a^5*b^6*d^6 + 81*a^2*b^9*c^3*d^3 + 189*a^3*b^8*c^2*d^4))/(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2) + ((x^(1/2)*(256*a^13*b^4*d^15 - 512*a^12*b^5*c*d^14 + 4096*a^2*b^15*c^11*d^4 - 30464*a^3*b^14*c^10*d^5 + 97792*a^4*b^13*c^9*d^6 - 176896*a^5*b^12*c^8*d^7 + 198656*a^6*b^11*c^7*d^8 - 146944*a^7*b^10*c^6*d^9 + 78848*a^8*b^9*c^5*d^10 - 36352*a^9*b^8*c^4*d^11 + 14336*a^10*b^7*c^3*d^12 - 2816*a^11*b^6*c^2*d^13))/(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) + (2*(-(a*b^3)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(1/4)*(1024*a^11*b^4*c*d^13 + 4096*a^2*b^13*c^10*d^4 - 31744*a^3*b^12*c^9*d^5 + 106496*a^4*b^11*c^8*d^6 - 200704*a^5*b^10*c^7*d^7 + 229376*a^6*b^9*c^6*d^8 - 157696*a^7*b^8*c^5*d^9 + 57344*a^8*b^7*c^4*d^10 - 4096*a^9*b^6*c^3*d^11 - 4096*a^10*b^5*c^2*d^12))/(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))*(-(a*b^3)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(3/4))*(-(a*b^3)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(1/4) + (x^(1/2)*(17*a^6*b^7*d^7 + 108*a^5*b^8*c*d^6 + 81*a^2*b^11*c^4*d^3 + 108*a^3*b^10*c^3*d^4 + 198*a^4*b^9*c^2*d^5))/(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))*(-(a*b^3)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(1/4)*1i - (((2*(51*a^4*b^7*c*d^5 - a^5*b^6*d^6 + 81*a^2*b^9*c^3*d^3 + 189*a^3*b^8*c^2*d^4))/(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2) - ((x^(1/2)*(256*a^13*b^4*d^15 - 512*a^12*b^5*c*d^14 + 4096*a^2*b^15*c^11*d^4 - 30464*a^3*b^14*c^10*d^5 + 97792*a^4*b^13*c^9*d^6 - 176896*a^5*b^12*c^8*d^7 + 198656*a^6*b^11*c^7*d^8 - 146944*a^7*b^10*c^6*d^9 + 78848*a^8*b^9*c^5*d^10 - 36352*a^9*b^8*c^4*d^11 + 14336*a^10*b^7*c^3*d^12 - 2816*a^11*b^6*c^2*d^13))/(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) - (2*(-(a*b^3)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(1/4)*(1024*a^11*b^4*c*d^13 + 4096*a^2*b^13*c^10*d^4 - 31744*a^3*b^12*c^9*d^5 + 106496*a^4*b^11*c^8*d^6 - 200704*a^5*b^10*c^7*d^7 + 229376*a^6*b^9*c^6*d^8 - 157696*a^7*b^8*c^5*d^9 + 57344*a^8*b^7*c^4*d^10 - 4096*a^9*b^6*c^3*d^11 - 4096*a^10*b^5*c^2*d^12))/(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))*(-(a*b^3)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(3/4))*(-(a*b^3)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(1/4) - (x^(1/2)*(17*a^6*b^7*d^7 + 108*a^5*b^8*c*d^6 + 81*a^2*b^11*c^4*d^3 + 108*a^3*b^10*c^3*d^4 + 198*a^4*b^9*c^2*d^5))/(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))*(-(a*b^3)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(1/4)*1i)/((((2*(51*a^4*b^7*c*d^5 - a^5*b^6*d^6 + 81*a^2*b^9*c^3*d^3 + 189*a^3*b^8*c^2*d^4))/(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2) + ((x^(1/2)*(256*a^13*b^4*d^15 - 512*a^12*b^5*c*d^14 + 4096*a^2*b^15*c^11*d^4 - 30464*a^3*b^14*c^10*d^5 + 97792*a^4*b^13*c^9*d^6 - 176896*a^5*b^12*c^8*d^7 + 198656*a^6*b^11*c^7*d^8 - 146944*a^7*b^10*c^6*d^9 + 78848*a^8*b^9*c^5*d^10 - 36352*a^9*b^8*c^4*d^11 + 14336*a^10*b^7*c^3*d^12 - 2816*a^11*b^6*c^2*d^13))/(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) + (2*(-(a*b^3)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(1/4)*(1024*a^11*b^4*c*d^13 + 4096*a^2*b^13*c^10*d^4 - 31744*a^3*b^12*c^9*d^5 + 106496*a^4*b^11*c^8*d^6 - 200704*a^5*b^10*c^7*d^7 + 229376*a^6*b^9*c^6*d^8 - 157696*a^7*b^8*c^5*d^9 + 57344*a^8*b^7*c^4*d^10 - 4096*a^9*b^6*c^3*d^11 - 4096*a^10*b^5*c^2*d^12))/(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))*(-(a*b^3)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(3/4))*(-(a*b^3)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(1/4) + (x^(1/2)*(17*a^6*b^7*d^7 + 108*a^5*b^8*c*d^6 + 81*a^2*b^11*c^4*d^3 + 108*a^3*b^10*c^3*d^4 + 198*a^4*b^9*c^2*d^5))/(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))*(-(a*b^3)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(1/4) + (((2*(51*a^4*b^7*c*d^5 - a^5*b^6*d^6 + 81*a^2*b^9*c^3*d^3 + 189*a^3*b^8*c^2*d^4))/(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2) - ((x^(1/2)*(256*a^13*b^4*d^15 - 512*a^12*b^5*c*d^14 + 4096*a^2*b^15*c^11*d^4 - 30464*a^3*b^14*c^10*d^5 + 97792*a^4*b^13*c^9*d^6 - 176896*a^5*b^12*c^8*d^7 + 198656*a^6*b^11*c^7*d^8 - 146944*a^7*b^10*c^6*d^9 + 78848*a^8*b^9*c^5*d^10 - 36352*a^9*b^8*c^4*d^11 + 14336*a^10*b^7*c^3*d^12 - 2816*a^11*b^6*c^2*d^13))/(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) - (2*(-(a*b^3)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(1/4)*(1024*a^11*b^4*c*d^13 + 4096*a^2*b^13*c^10*d^4 - 31744*a^3*b^12*c^9*d^5 + 106496*a^4*b^11*c^8*d^6 - 200704*a^5*b^10*c^7*d^7 + 229376*a^6*b^9*c^6*d^8 - 157696*a^7*b^8*c^5*d^9 + 57344*a^8*b^7*c^4*d^10 - 4096*a^9*b^6*c^3*d^11 - 4096*a^10*b^5*c^2*d^12))/(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))*(-(a*b^3)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(3/4))*(-(a*b^3)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(1/4) - (x^(1/2)*(17*a^6*b^7*d^7 + 108*a^5*b^8*c*d^6 + 81*a^2*b^11*c^4*d^3 + 108*a^3*b^10*c^3*d^4 + 198*a^4*b^9*c^2*d^5))/(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))*(-(a*b^3)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(1/4)))*(-(a*b^3)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(1/4)*2i - 2*atan(((((2*(51*a^4*b^7*c*d^5 - a^5*b^6*d^6 + 81*a^2*b^9*c^3*d^3 + 189*a^3*b^8*c^2*d^4))/(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2) - ((x^(1/2)*(256*a^13*b^4*d^15 - 512*a^12*b^5*c*d^14 + 4096*a^2*b^15*c^11*d^4 - 30464*a^3*b^14*c^10*d^5 + 97792*a^4*b^13*c^9*d^6 - 176896*a^5*b^12*c^8*d^7 + 198656*a^6*b^11*c^7*d^8 - 146944*a^7*b^10*c^6*d^9 + 78848*a^8*b^9*c^5*d^10 - 36352*a^9*b^8*c^4*d^11 + 14336*a^10*b^7*c^3*d^12 - 2816*a^11*b^6*c^2*d^13))/(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) + ((-(a*b^3)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(1/4)*(1024*a^11*b^4*c*d^13 + 4096*a^2*b^13*c^10*d^4 - 31744*a^3*b^12*c^9*d^5 + 106496*a^4*b^11*c^8*d^6 - 200704*a^5*b^10*c^7*d^7 + 229376*a^6*b^9*c^6*d^8 - 157696*a^7*b^8*c^5*d^9 + 57344*a^8*b^7*c^4*d^10 - 4096*a^9*b^6*c^3*d^11 - 4096*a^10*b^5*c^2*d^12)*2i)/(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))*(-(a*b^3)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(3/4)*1i)*(-(a*b^3)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(1/4)*1i + (x^(1/2)*(17*a^6*b^7*d^7 + 108*a^5*b^8*c*d^6 + 81*a^2*b^11*c^4*d^3 + 108*a^3*b^10*c^3*d^4 + 198*a^4*b^9*c^2*d^5))/(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))*(-(a*b^3)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(1/4) - (((2*(51*a^4*b^7*c*d^5 - a^5*b^6*d^6 + 81*a^2*b^9*c^3*d^3 + 189*a^3*b^8*c^2*d^4))/(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2) + ((x^(1/2)*(256*a^13*b^4*d^15 - 512*a^12*b^5*c*d^14 + 4096*a^2*b^15*c^11*d^4 - 30464*a^3*b^14*c^10*d^5 + 97792*a^4*b^13*c^9*d^6 - 176896*a^5*b^12*c^8*d^7 + 198656*a^6*b^11*c^7*d^8 - 146944*a^7*b^10*c^6*d^9 + 78848*a^8*b^9*c^5*d^10 - 36352*a^9*b^8*c^4*d^11 + 14336*a^10*b^7*c^3*d^12 - 2816*a^11*b^6*c^2*d^13))/(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) - ((-(a*b^3)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(1/4)*(1024*a^11*b^4*c*d^13 + 4096*a^2*b^13*c^10*d^4 - 31744*a^3*b^12*c^9*d^5 + 106496*a^4*b^11*c^8*d^6 - 200704*a^5*b^10*c^7*d^7 + 229376*a^6*b^9*c^6*d^8 - 157696*a^7*b^8*c^5*d^9 + 57344*a^8*b^7*c^4*d^10 - 4096*a^9*b^6*c^3*d^11 - 4096*a^10*b^5*c^2*d^12)*2i)/(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))*(-(a*b^3)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(3/4)*1i)*(-(a*b^3)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(1/4)*1i - (x^(1/2)*(17*a^6*b^7*d^7 + 108*a^5*b^8*c*d^6 + 81*a^2*b^11*c^4*d^3 + 108*a^3*b^10*c^3*d^4 + 198*a^4*b^9*c^2*d^5))/(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))*(-(a*b^3)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(1/4))/((((2*(51*a^4*b^7*c*d^5 - a^5*b^6*d^6 + 81*a^2*b^9*c^3*d^3 + 189*a^3*b^8*c^2*d^4))/(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2) - ((x^(1/2)*(256*a^13*b^4*d^15 - 512*a^12*b^5*c*d^14 + 4096*a^2*b^15*c^11*d^4 - 30464*a^3*b^14*c^10*d^5 + 97792*a^4*b^13*c^9*d^6 - 176896*a^5*b^12*c^8*d^7 + 198656*a^6*b^11*c^7*d^8 - 146944*a^7*b^10*c^6*d^9 + 78848*a^8*b^9*c^5*d^10 - 36352*a^9*b^8*c^4*d^11 + 14336*a^10*b^7*c^3*d^12 - 2816*a^11*b^6*c^2*d^13))/(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) + ((-(a*b^3)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(1/4)*(1024*a^11*b^4*c*d^13 + 4096*a^2*b^13*c^10*d^4 - 31744*a^3*b^12*c^9*d^5 + 106496*a^4*b^11*c^8*d^6 - 200704*a^5*b^10*c^7*d^7 + 229376*a^6*b^9*c^6*d^8 - 157696*a^7*b^8*c^5*d^9 + 57344*a^8*b^7*c^4*d^10 - 4096*a^9*b^6*c^3*d^11 - 4096*a^10*b^5*c^2*d^12)*2i)/(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))*(-(a*b^3)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(3/4)*1i)*(-(a*b^3)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(1/4)*1i + (x^(1/2)*(17*a^6*b^7*d^7 + 108*a^5*b^8*c*d^6 + 81*a^2*b^11*c^4*d^3 + 108*a^3*b^10*c^3*d^4 + 198*a^4*b^9*c^2*d^5))/(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))*(-(a*b^3)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(1/4)*1i + (((2*(51*a^4*b^7*c*d^5 - a^5*b^6*d^6 + 81*a^2*b^9*c^3*d^3 + 189*a^3*b^8*c^2*d^4))/(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2) + ((x^(1/2)*(256*a^13*b^4*d^15 - 512*a^12*b^5*c*d^14 + 4096*a^2*b^15*c^11*d^4 - 30464*a^3*b^14*c^10*d^5 + 97792*a^4*b^13*c^9*d^6 - 176896*a^5*b^12*c^8*d^7 + 198656*a^6*b^11*c^7*d^8 - 146944*a^7*b^10*c^6*d^9 + 78848*a^8*b^9*c^5*d^10 - 36352*a^9*b^8*c^4*d^11 + 14336*a^10*b^7*c^3*d^12 - 2816*a^11*b^6*c^2*d^13))/(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) - ((-(a*b^3)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(1/4)*(1024*a^11*b^4*c*d^13 + 4096*a^2*b^13*c^10*d^4 - 31744*a^3*b^12*c^9*d^5 + 106496*a^4*b^11*c^8*d^6 - 200704*a^5*b^10*c^7*d^7 + 229376*a^6*b^9*c^6*d^8 - 157696*a^7*b^8*c^5*d^9 + 57344*a^8*b^7*c^4*d^10 - 4096*a^9*b^6*c^3*d^11 - 4096*a^10*b^5*c^2*d^12)*2i)/(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))*(-(a*b^3)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(3/4)*1i)*(-(a*b^3)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(1/4)*1i - (x^(1/2)*(17*a^6*b^7*d^7 + 108*a^5*b^8*c*d^6 + 81*a^2*b^11*c^4*d^3 + 108*a^3*b^10*c^3*d^4 + 198*a^4*b^9*c^2*d^5))/(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))*(-(a*b^3)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(1/4)*1i))*(-(a*b^3)/(16*a^8*d^8 + 16*b^8*c^8 + 448*a^2*b^6*c^6*d^2 - 896*a^3*b^5*c^5*d^3 + 1120*a^4*b^4*c^4*d^4 - 896*a^5*b^3*c^3*d^5 + 448*a^6*b^2*c^2*d^6 - 128*a*b^7*c^7*d - 128*a^7*b*c*d^7))^(1/4) - atan(-(((((x^(1/2)*(256*a^13*b^4*d^15 - 512*a^12*b^5*c*d^14 + 4096*a^2*b^15*c^11*d^4 - 30464*a^3*b^14*c^10*d^5 + 97792*a^4*b^13*c^9*d^6 - 176896*a^5*b^12*c^8*d^7 + 198656*a^6*b^11*c^7*d^8 - 146944*a^7*b^10*c^6*d^9 + 78848*a^8*b^9*c^5*d^10 - 36352*a^9*b^8*c^4*d^11 + 14336*a^10*b^7*c^3*d^12 - 2816*a^11*b^6*c^2*d^13))/(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) - (2*(-(a^4*d^4 + 81*b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 108*a*b^3*c^3*d + 12*a^3*b*c*d^3)/(4096*b^8*c^11*d + 4096*a^8*c^3*d^9 - 32768*a*b^7*c^10*d^2 - 32768*a^7*b*c^4*d^8 + 114688*a^2*b^6*c^9*d^3 - 229376*a^3*b^5*c^8*d^4 + 286720*a^4*b^4*c^7*d^5 - 229376*a^5*b^3*c^6*d^6 + 114688*a^6*b^2*c^5*d^7))^(1/4)*(1024*a^11*b^4*c*d^13 + 4096*a^2*b^13*c^10*d^4 - 31744*a^3*b^12*c^9*d^5 + 106496*a^4*b^11*c^8*d^6 - 200704*a^5*b^10*c^7*d^7 + 229376*a^6*b^9*c^6*d^8 - 157696*a^7*b^8*c^5*d^9 + 57344*a^8*b^7*c^4*d^10 - 4096*a^9*b^6*c^3*d^11 - 4096*a^10*b^5*c^2*d^12))/(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))*(-(a^4*d^4 + 81*b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 108*a*b^3*c^3*d + 12*a^3*b*c*d^3)/(4096*b^8*c^11*d + 4096*a^8*c^3*d^9 - 32768*a*b^7*c^10*d^2 - 32768*a^7*b*c^4*d^8 + 114688*a^2*b^6*c^9*d^3 - 229376*a^3*b^5*c^8*d^4 + 286720*a^4*b^4*c^7*d^5 - 229376*a^5*b^3*c^6*d^6 + 114688*a^6*b^2*c^5*d^7))^(3/4) - (2*(51*a^4*b^7*c*d^5 - a^5*b^6*d^6 + 81*a^2*b^9*c^3*d^3 + 189*a^3*b^8*c^2*d^4))/(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))*(-(a^4*d^4 + 81*b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 108*a*b^3*c^3*d + 12*a^3*b*c*d^3)/(4096*b^8*c^11*d + 4096*a^8*c^3*d^9 - 32768*a*b^7*c^10*d^2 - 32768*a^7*b*c^4*d^8 + 114688*a^2*b^6*c^9*d^3 - 229376*a^3*b^5*c^8*d^4 + 286720*a^4*b^4*c^7*d^5 - 229376*a^5*b^3*c^6*d^6 + 114688*a^6*b^2*c^5*d^7))^(1/4) + (x^(1/2)*(17*a^6*b^7*d^7 + 108*a^5*b^8*c*d^6 + 81*a^2*b^11*c^4*d^3 + 108*a^3*b^10*c^3*d^4 + 198*a^4*b^9*c^2*d^5))/(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))*(-(a^4*d^4 + 81*b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 108*a*b^3*c^3*d + 12*a^3*b*c*d^3)/(4096*b^8*c^11*d + 4096*a^8*c^3*d^9 - 32768*a*b^7*c^10*d^2 - 32768*a^7*b*c^4*d^8 + 114688*a^2*b^6*c^9*d^3 - 229376*a^3*b^5*c^8*d^4 + 286720*a^4*b^4*c^7*d^5 - 229376*a^5*b^3*c^6*d^6 + 114688*a^6*b^2*c^5*d^7))^(1/4)*1i + ((((x^(1/2)*(256*a^13*b^4*d^15 - 512*a^12*b^5*c*d^14 + 4096*a^2*b^15*c^11*d^4 - 30464*a^3*b^14*c^10*d^5 + 97792*a^4*b^13*c^9*d^6 - 176896*a^5*b^12*c^8*d^7 + 198656*a^6*b^11*c^7*d^8 - 146944*a^7*b^10*c^6*d^9 + 78848*a^8*b^9*c^5*d^10 - 36352*a^9*b^8*c^4*d^11 + 14336*a^10*b^7*c^3*d^12 - 2816*a^11*b^6*c^2*d^13))/(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) + (2*(-(a^4*d^4 + 81*b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 108*a*b^3*c^3*d + 12*a^3*b*c*d^3)/(4096*b^8*c^11*d + 4096*a^8*c^3*d^9 - 32768*a*b^7*c^10*d^2 - 32768*a^7*b*c^4*d^8 + 114688*a^2*b^6*c^9*d^3 - 229376*a^3*b^5*c^8*d^4 + 286720*a^4*b^4*c^7*d^5 - 229376*a^5*b^3*c^6*d^6 + 114688*a^6*b^2*c^5*d^7))^(1/4)*(1024*a^11*b^4*c*d^13 + 4096*a^2*b^13*c^10*d^4 - 31744*a^3*b^12*c^9*d^5 + 106496*a^4*b^11*c^8*d^6 - 200704*a^5*b^10*c^7*d^7 + 229376*a^6*b^9*c^6*d^8 - 157696*a^7*b^8*c^5*d^9 + 57344*a^8*b^7*c^4*d^10 - 4096*a^9*b^6*c^3*d^11 - 4096*a^10*b^5*c^2*d^12))/(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))*(-(a^4*d^4 + 81*b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 108*a*b^3*c^3*d + 12*a^3*b*c*d^3)/(4096*b^8*c^11*d + 4096*a^8*c^3*d^9 - 32768*a*b^7*c^10*d^2 - 32768*a^7*b*c^4*d^8 + 114688*a^2*b^6*c^9*d^3 - 229376*a^3*b^5*c^8*d^4 + 286720*a^4*b^4*c^7*d^5 - 229376*a^5*b^3*c^6*d^6 + 114688*a^6*b^2*c^5*d^7))^(3/4) + (2*(51*a^4*b^7*c*d^5 - a^5*b^6*d^6 + 81*a^2*b^9*c^3*d^3 + 189*a^3*b^8*c^2*d^4))/(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))*(-(a^4*d^4 + 81*b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 108*a*b^3*c^3*d + 12*a^3*b*c*d^3)/(4096*b^8*c^11*d + 4096*a^8*c^3*d^9 - 32768*a*b^7*c^10*d^2 - 32768*a^7*b*c^4*d^8 + 114688*a^2*b^6*c^9*d^3 - 229376*a^3*b^5*c^8*d^4 + 286720*a^4*b^4*c^7*d^5 - 229376*a^5*b^3*c^6*d^6 + 114688*a^6*b^2*c^5*d^7))^(1/4) + (x^(1/2)*(17*a^6*b^7*d^7 + 108*a^5*b^8*c*d^6 + 81*a^2*b^11*c^4*d^3 + 108*a^3*b^10*c^3*d^4 + 198*a^4*b^9*c^2*d^5))/(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))*(-(a^4*d^4 + 81*b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 108*a*b^3*c^3*d + 12*a^3*b*c*d^3)/(4096*b^8*c^11*d + 4096*a^8*c^3*d^9 - 32768*a*b^7*c^10*d^2 - 32768*a^7*b*c^4*d^8 + 114688*a^2*b^6*c^9*d^3 - 229376*a^3*b^5*c^8*d^4 + 286720*a^4*b^4*c^7*d^5 - 229376*a^5*b^3*c^6*d^6 + 114688*a^6*b^2*c^5*d^7))^(1/4)*1i)/(((((x^(1/2)*(256*a^13*b^4*d^15 - 512*a^12*b^5*c*d^14 + 4096*a^2*b^15*c^11*d^4 - 30464*a^3*b^14*c^10*d^5 + 97792*a^4*b^13*c^9*d^6 - 176896*a^5*b^12*c^8*d^7 + 198656*a^6*b^11*c^7*d^8 - 146944*a^7*b^10*c^6*d^9 + 78848*a^8*b^9*c^5*d^10 - 36352*a^9*b^8*c^4*d^11 + 14336*a^10*b^7*c^3*d^12 - 2816*a^11*b^6*c^2*d^13))/(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) - (2*(-(a^4*d^4 + 81*b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 108*a*b^3*c^3*d + 12*a^3*b*c*d^3)/(4096*b^8*c^11*d + 4096*a^8*c^3*d^9 - 32768*a*b^7*c^10*d^2 - 32768*a^7*b*c^4*d^8 + 114688*a^2*b^6*c^9*d^3 - 229376*a^3*b^5*c^8*d^4 + 286720*a^4*b^4*c^7*d^5 - 229376*a^5*b^3*c^6*d^6 + 114688*a^6*b^2*c^5*d^7))^(1/4)*(1024*a^11*b^4*c*d^13 + 4096*a^2*b^13*c^10*d^4 - 31744*a^3*b^12*c^9*d^5 + 106496*a^4*b^11*c^8*d^6 - 200704*a^5*b^10*c^7*d^7 + 229376*a^6*b^9*c^6*d^8 - 157696*a^7*b^8*c^5*d^9 + 57344*a^8*b^7*c^4*d^10 - 4096*a^9*b^6*c^3*d^11 - 4096*a^10*b^5*c^2*d^12))/(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))*(-(a^4*d^4 + 81*b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 108*a*b^3*c^3*d + 12*a^3*b*c*d^3)/(4096*b^8*c^11*d + 4096*a^8*c^3*d^9 - 32768*a*b^7*c^10*d^2 - 32768*a^7*b*c^4*d^8 + 114688*a^2*b^6*c^9*d^3 - 229376*a^3*b^5*c^8*d^4 + 286720*a^4*b^4*c^7*d^5 - 229376*a^5*b^3*c^6*d^6 + 114688*a^6*b^2*c^5*d^7))^(3/4) - (2*(51*a^4*b^7*c*d^5 - a^5*b^6*d^6 + 81*a^2*b^9*c^3*d^3 + 189*a^3*b^8*c^2*d^4))/(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))*(-(a^4*d^4 + 81*b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 108*a*b^3*c^3*d + 12*a^3*b*c*d^3)/(4096*b^8*c^11*d + 4096*a^8*c^3*d^9 - 32768*a*b^7*c^10*d^2 - 32768*a^7*b*c^4*d^8 + 114688*a^2*b^6*c^9*d^3 - 229376*a^3*b^5*c^8*d^4 + 286720*a^4*b^4*c^7*d^5 - 229376*a^5*b^3*c^6*d^6 + 114688*a^6*b^2*c^5*d^7))^(1/4) + (x^(1/2)*(17*a^6*b^7*d^7 + 108*a^5*b^8*c*d^6 + 81*a^2*b^11*c^4*d^3 + 108*a^3*b^10*c^3*d^4 + 198*a^4*b^9*c^2*d^5))/(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))*(-(a^4*d^4 + 81*b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 108*a*b^3*c^3*d + 12*a^3*b*c*d^3)/(4096*b^8*c^11*d + 4096*a^8*c^3*d^9 - 32768*a*b^7*c^10*d^2 - 32768*a^7*b*c^4*d^8 + 114688*a^2*b^6*c^9*d^3 - 229376*a^3*b^5*c^8*d^4 + 286720*a^4*b^4*c^7*d^5 - 229376*a^5*b^3*c^6*d^6 + 114688*a^6*b^2*c^5*d^7))^(1/4) - ((((x^(1/2)*(256*a^13*b^4*d^15 - 512*a^12*b^5*c*d^14 + 4096*a^2*b^15*c^11*d^4 - 30464*a^3*b^14*c^10*d^5 + 97792*a^4*b^13*c^9*d^6 - 176896*a^5*b^12*c^8*d^7 + 198656*a^6*b^11*c^7*d^8 - 146944*a^7*b^10*c^6*d^9 + 78848*a^8*b^9*c^5*d^10 - 36352*a^9*b^8*c^4*d^11 + 14336*a^10*b^7*c^3*d^12 - 2816*a^11*b^6*c^2*d^13))/(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) + (2*(-(a^4*d^4 + 81*b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 108*a*b^3*c^3*d + 12*a^3*b*c*d^3)/(4096*b^8*c^11*d + 4096*a^8*c^3*d^9 - 32768*a*b^7*c^10*d^2 - 32768*a^7*b*c^4*d^8 + 114688*a^2*b^6*c^9*d^3 - 229376*a^3*b^5*c^8*d^4 + 286720*a^4*b^4*c^7*d^5 - 229376*a^5*b^3*c^6*d^6 + 114688*a^6*b^2*c^5*d^7))^(1/4)*(1024*a^11*b^4*c*d^13 + 4096*a^2*b^13*c^10*d^4 - 31744*a^3*b^12*c^9*d^5 + 106496*a^4*b^11*c^8*d^6 - 200704*a^5*b^10*c^7*d^7 + 229376*a^6*b^9*c^6*d^8 - 157696*a^7*b^8*c^5*d^9 + 57344*a^8*b^7*c^4*d^10 - 4096*a^9*b^6*c^3*d^11 - 4096*a^10*b^5*c^2*d^12))/(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))*(-(a^4*d^4 + 81*b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 108*a*b^3*c^3*d + 12*a^3*b*c*d^3)/(4096*b^8*c^11*d + 4096*a^8*c^3*d^9 - 32768*a*b^7*c^10*d^2 - 32768*a^7*b*c^4*d^8 + 114688*a^2*b^6*c^9*d^3 - 229376*a^3*b^5*c^8*d^4 + 286720*a^4*b^4*c^7*d^5 - 229376*a^5*b^3*c^6*d^6 + 114688*a^6*b^2*c^5*d^7))^(3/4) + (2*(51*a^4*b^7*c*d^5 - a^5*b^6*d^6 + 81*a^2*b^9*c^3*d^3 + 189*a^3*b^8*c^2*d^4))/(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))*(-(a^4*d^4 + 81*b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 108*a*b^3*c^3*d + 12*a^3*b*c*d^3)/(4096*b^8*c^11*d + 4096*a^8*c^3*d^9 - 32768*a*b^7*c^10*d^2 - 32768*a^7*b*c^4*d^8 + 114688*a^2*b^6*c^9*d^3 - 229376*a^3*b^5*c^8*d^4 + 286720*a^4*b^4*c^7*d^5 - 229376*a^5*b^3*c^6*d^6 + 114688*a^6*b^2*c^5*d^7))^(1/4) + (x^(1/2)*(17*a^6*b^7*d^7 + 108*a^5*b^8*c*d^6 + 81*a^2*b^11*c^4*d^3 + 108*a^3*b^10*c^3*d^4 + 198*a^4*b^9*c^2*d^5))/(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))*(-(a^4*d^4 + 81*b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 108*a*b^3*c^3*d + 12*a^3*b*c*d^3)/(4096*b^8*c^11*d + 4096*a^8*c^3*d^9 - 32768*a*b^7*c^10*d^2 - 32768*a^7*b*c^4*d^8 + 114688*a^2*b^6*c^9*d^3 - 229376*a^3*b^5*c^8*d^4 + 286720*a^4*b^4*c^7*d^5 - 229376*a^5*b^3*c^6*d^6 + 114688*a^6*b^2*c^5*d^7))^(1/4)))*(-(a^4*d^4 + 81*b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 108*a*b^3*c^3*d + 12*a^3*b*c*d^3)/(4096*b^8*c^11*d + 4096*a^8*c^3*d^9 - 32768*a*b^7*c^10*d^2 - 32768*a^7*b*c^4*d^8 + 114688*a^2*b^6*c^9*d^3 - 229376*a^3*b^5*c^8*d^4 + 286720*a^4*b^4*c^7*d^5 - 229376*a^5*b^3*c^6*d^6 + 114688*a^6*b^2*c^5*d^7))^(1/4)*2i - 2*atan(-(((((x^(1/2)*(256*a^13*b^4*d^15 - 512*a^12*b^5*c*d^14 + 4096*a^2*b^15*c^11*d^4 - 30464*a^3*b^14*c^10*d^5 + 97792*a^4*b^13*c^9*d^6 - 176896*a^5*b^12*c^8*d^7 + 198656*a^6*b^11*c^7*d^8 - 146944*a^7*b^10*c^6*d^9 + 78848*a^8*b^9*c^5*d^10 - 36352*a^9*b^8*c^4*d^11 + 14336*a^10*b^7*c^3*d^12 - 2816*a^11*b^6*c^2*d^13))/(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) - ((-(a^4*d^4 + 81*b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 108*a*b^3*c^3*d + 12*a^3*b*c*d^3)/(4096*b^8*c^11*d + 4096*a^8*c^3*d^9 - 32768*a*b^7*c^10*d^2 - 32768*a^7*b*c^4*d^8 + 114688*a^2*b^6*c^9*d^3 - 229376*a^3*b^5*c^8*d^4 + 286720*a^4*b^4*c^7*d^5 - 229376*a^5*b^3*c^6*d^6 + 114688*a^6*b^2*c^5*d^7))^(1/4)*(1024*a^11*b^4*c*d^13 + 4096*a^2*b^13*c^10*d^4 - 31744*a^3*b^12*c^9*d^5 + 106496*a^4*b^11*c^8*d^6 - 200704*a^5*b^10*c^7*d^7 + 229376*a^6*b^9*c^6*d^8 - 157696*a^7*b^8*c^5*d^9 + 57344*a^8*b^7*c^4*d^10 - 4096*a^9*b^6*c^3*d^11 - 4096*a^10*b^5*c^2*d^12)*2i)/(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))*(-(a^4*d^4 + 81*b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 108*a*b^3*c^3*d + 12*a^3*b*c*d^3)/(4096*b^8*c^11*d + 4096*a^8*c^3*d^9 - 32768*a*b^7*c^10*d^2 - 32768*a^7*b*c^4*d^8 + 114688*a^2*b^6*c^9*d^3 - 229376*a^3*b^5*c^8*d^4 + 286720*a^4*b^4*c^7*d^5 - 229376*a^5*b^3*c^6*d^6 + 114688*a^6*b^2*c^5*d^7))^(3/4)*1i + (2*(51*a^4*b^7*c*d^5 - a^5*b^6*d^6 + 81*a^2*b^9*c^3*d^3 + 189*a^3*b^8*c^2*d^4))/(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))*(-(a^4*d^4 + 81*b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 108*a*b^3*c^3*d + 12*a^3*b*c*d^3)/(4096*b^8*c^11*d + 4096*a^8*c^3*d^9 - 32768*a*b^7*c^10*d^2 - 32768*a^7*b*c^4*d^8 + 114688*a^2*b^6*c^9*d^3 - 229376*a^3*b^5*c^8*d^4 + 286720*a^4*b^4*c^7*d^5 - 229376*a^5*b^3*c^6*d^6 + 114688*a^6*b^2*c^5*d^7))^(1/4)*1i - (x^(1/2)*(17*a^6*b^7*d^7 + 108*a^5*b^8*c*d^6 + 81*a^2*b^11*c^4*d^3 + 108*a^3*b^10*c^3*d^4 + 198*a^4*b^9*c^2*d^5))/(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))*(-(a^4*d^4 + 81*b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 108*a*b^3*c^3*d + 12*a^3*b*c*d^3)/(4096*b^8*c^11*d + 4096*a^8*c^3*d^9 - 32768*a*b^7*c^10*d^2 - 32768*a^7*b*c^4*d^8 + 114688*a^2*b^6*c^9*d^3 - 229376*a^3*b^5*c^8*d^4 + 286720*a^4*b^4*c^7*d^5 - 229376*a^5*b^3*c^6*d^6 + 114688*a^6*b^2*c^5*d^7))^(1/4) + ((((x^(1/2)*(256*a^13*b^4*d^15 - 512*a^12*b^5*c*d^14 + 4096*a^2*b^15*c^11*d^4 - 30464*a^3*b^14*c^10*d^5 + 97792*a^4*b^13*c^9*d^6 - 176896*a^5*b^12*c^8*d^7 + 198656*a^6*b^11*c^7*d^8 - 146944*a^7*b^10*c^6*d^9 + 78848*a^8*b^9*c^5*d^10 - 36352*a^9*b^8*c^4*d^11 + 14336*a^10*b^7*c^3*d^12 - 2816*a^11*b^6*c^2*d^13))/(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) + ((-(a^4*d^4 + 81*b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 108*a*b^3*c^3*d + 12*a^3*b*c*d^3)/(4096*b^8*c^11*d + 4096*a^8*c^3*d^9 - 32768*a*b^7*c^10*d^2 - 32768*a^7*b*c^4*d^8 + 114688*a^2*b^6*c^9*d^3 - 229376*a^3*b^5*c^8*d^4 + 286720*a^4*b^4*c^7*d^5 - 229376*a^5*b^3*c^6*d^6 + 114688*a^6*b^2*c^5*d^7))^(1/4)*(1024*a^11*b^4*c*d^13 + 4096*a^2*b^13*c^10*d^4 - 31744*a^3*b^12*c^9*d^5 + 106496*a^4*b^11*c^8*d^6 - 200704*a^5*b^10*c^7*d^7 + 229376*a^6*b^9*c^6*d^8 - 157696*a^7*b^8*c^5*d^9 + 57344*a^8*b^7*c^4*d^10 - 4096*a^9*b^6*c^3*d^11 - 4096*a^10*b^5*c^2*d^12)*2i)/(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))*(-(a^4*d^4 + 81*b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 108*a*b^3*c^3*d + 12*a^3*b*c*d^3)/(4096*b^8*c^11*d + 4096*a^8*c^3*d^9 - 32768*a*b^7*c^10*d^2 - 32768*a^7*b*c^4*d^8 + 114688*a^2*b^6*c^9*d^3 - 229376*a^3*b^5*c^8*d^4 + 286720*a^4*b^4*c^7*d^5 - 229376*a^5*b^3*c^6*d^6 + 114688*a^6*b^2*c^5*d^7))^(3/4)*1i - (2*(51*a^4*b^7*c*d^5 - a^5*b^6*d^6 + 81*a^2*b^9*c^3*d^3 + 189*a^3*b^8*c^2*d^4))/(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))*(-(a^4*d^4 + 81*b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 108*a*b^3*c^3*d + 12*a^3*b*c*d^3)/(4096*b^8*c^11*d + 4096*a^8*c^3*d^9 - 32768*a*b^7*c^10*d^2 - 32768*a^7*b*c^4*d^8 + 114688*a^2*b^6*c^9*d^3 - 229376*a^3*b^5*c^8*d^4 + 286720*a^4*b^4*c^7*d^5 - 229376*a^5*b^3*c^6*d^6 + 114688*a^6*b^2*c^5*d^7))^(1/4)*1i - (x^(1/2)*(17*a^6*b^7*d^7 + 108*a^5*b^8*c*d^6 + 81*a^2*b^11*c^4*d^3 + 108*a^3*b^10*c^3*d^4 + 198*a^4*b^9*c^2*d^5))/(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))*(-(a^4*d^4 + 81*b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 108*a*b^3*c^3*d + 12*a^3*b*c*d^3)/(4096*b^8*c^11*d + 4096*a^8*c^3*d^9 - 32768*a*b^7*c^10*d^2 - 32768*a^7*b*c^4*d^8 + 114688*a^2*b^6*c^9*d^3 - 229376*a^3*b^5*c^8*d^4 + 286720*a^4*b^4*c^7*d^5 - 229376*a^5*b^3*c^6*d^6 + 114688*a^6*b^2*c^5*d^7))^(1/4))/(((((x^(1/2)*(256*a^13*b^4*d^15 - 512*a^12*b^5*c*d^14 + 4096*a^2*b^15*c^11*d^4 - 30464*a^3*b^14*c^10*d^5 + 97792*a^4*b^13*c^9*d^6 - 176896*a^5*b^12*c^8*d^7 + 198656*a^6*b^11*c^7*d^8 - 146944*a^7*b^10*c^6*d^9 + 78848*a^8*b^9*c^5*d^10 - 36352*a^9*b^8*c^4*d^11 + 14336*a^10*b^7*c^3*d^12 - 2816*a^11*b^6*c^2*d^13))/(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) - ((-(a^4*d^4 + 81*b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 108*a*b^3*c^3*d + 12*a^3*b*c*d^3)/(4096*b^8*c^11*d + 4096*a^8*c^3*d^9 - 32768*a*b^7*c^10*d^2 - 32768*a^7*b*c^4*d^8 + 114688*a^2*b^6*c^9*d^3 - 229376*a^3*b^5*c^8*d^4 + 286720*a^4*b^4*c^7*d^5 - 229376*a^5*b^3*c^6*d^6 + 114688*a^6*b^2*c^5*d^7))^(1/4)*(1024*a^11*b^4*c*d^13 + 4096*a^2*b^13*c^10*d^4 - 31744*a^3*b^12*c^9*d^5 + 106496*a^4*b^11*c^8*d^6 - 200704*a^5*b^10*c^7*d^7 + 229376*a^6*b^9*c^6*d^8 - 157696*a^7*b^8*c^5*d^9 + 57344*a^8*b^7*c^4*d^10 - 4096*a^9*b^6*c^3*d^11 - 4096*a^10*b^5*c^2*d^12)*2i)/(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))*(-(a^4*d^4 + 81*b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 108*a*b^3*c^3*d + 12*a^3*b*c*d^3)/(4096*b^8*c^11*d + 4096*a^8*c^3*d^9 - 32768*a*b^7*c^10*d^2 - 32768*a^7*b*c^4*d^8 + 114688*a^2*b^6*c^9*d^3 - 229376*a^3*b^5*c^8*d^4 + 286720*a^4*b^4*c^7*d^5 - 229376*a^5*b^3*c^6*d^6 + 114688*a^6*b^2*c^5*d^7))^(3/4)*1i + (2*(51*a^4*b^7*c*d^5 - a^5*b^6*d^6 + 81*a^2*b^9*c^3*d^3 + 189*a^3*b^8*c^2*d^4))/(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))*(-(a^4*d^4 + 81*b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 108*a*b^3*c^3*d + 12*a^3*b*c*d^3)/(4096*b^8*c^11*d + 4096*a^8*c^3*d^9 - 32768*a*b^7*c^10*d^2 - 32768*a^7*b*c^4*d^8 + 114688*a^2*b^6*c^9*d^3 - 229376*a^3*b^5*c^8*d^4 + 286720*a^4*b^4*c^7*d^5 - 229376*a^5*b^3*c^6*d^6 + 114688*a^6*b^2*c^5*d^7))^(1/4)*1i - (x^(1/2)*(17*a^6*b^7*d^7 + 108*a^5*b^8*c*d^6 + 81*a^2*b^11*c^4*d^3 + 108*a^3*b^10*c^3*d^4 + 198*a^4*b^9*c^2*d^5))/(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))*(-(a^4*d^4 + 81*b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 108*a*b^3*c^3*d + 12*a^3*b*c*d^3)/(4096*b^8*c^11*d + 4096*a^8*c^3*d^9 - 32768*a*b^7*c^10*d^2 - 32768*a^7*b*c^4*d^8 + 114688*a^2*b^6*c^9*d^3 - 229376*a^3*b^5*c^8*d^4 + 286720*a^4*b^4*c^7*d^5 - 229376*a^5*b^3*c^6*d^6 + 114688*a^6*b^2*c^5*d^7))^(1/4)*1i - ((((x^(1/2)*(256*a^13*b^4*d^15 - 512*a^12*b^5*c*d^14 + 4096*a^2*b^15*c^11*d^4 - 30464*a^3*b^14*c^10*d^5 + 97792*a^4*b^13*c^9*d^6 - 176896*a^5*b^12*c^8*d^7 + 198656*a^6*b^11*c^7*d^8 - 146944*a^7*b^10*c^6*d^9 + 78848*a^8*b^9*c^5*d^10 - 36352*a^9*b^8*c^4*d^11 + 14336*a^10*b^7*c^3*d^12 - 2816*a^11*b^6*c^2*d^13))/(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) + ((-(a^4*d^4 + 81*b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 108*a*b^3*c^3*d + 12*a^3*b*c*d^3)/(4096*b^8*c^11*d + 4096*a^8*c^3*d^9 - 32768*a*b^7*c^10*d^2 - 32768*a^7*b*c^4*d^8 + 114688*a^2*b^6*c^9*d^3 - 229376*a^3*b^5*c^8*d^4 + 286720*a^4*b^4*c^7*d^5 - 229376*a^5*b^3*c^6*d^6 + 114688*a^6*b^2*c^5*d^7))^(1/4)*(1024*a^11*b^4*c*d^13 + 4096*a^2*b^13*c^10*d^4 - 31744*a^3*b^12*c^9*d^5 + 106496*a^4*b^11*c^8*d^6 - 200704*a^5*b^10*c^7*d^7 + 229376*a^6*b^9*c^6*d^8 - 157696*a^7*b^8*c^5*d^9 + 57344*a^8*b^7*c^4*d^10 - 4096*a^9*b^6*c^3*d^11 - 4096*a^10*b^5*c^2*d^12)*2i)/(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))*(-(a^4*d^4 + 81*b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 108*a*b^3*c^3*d + 12*a^3*b*c*d^3)/(4096*b^8*c^11*d + 4096*a^8*c^3*d^9 - 32768*a*b^7*c^10*d^2 - 32768*a^7*b*c^4*d^8 + 114688*a^2*b^6*c^9*d^3 - 229376*a^3*b^5*c^8*d^4 + 286720*a^4*b^4*c^7*d^5 - 229376*a^5*b^3*c^6*d^6 + 114688*a^6*b^2*c^5*d^7))^(3/4)*1i - (2*(51*a^4*b^7*c*d^5 - a^5*b^6*d^6 + 81*a^2*b^9*c^3*d^3 + 189*a^3*b^8*c^2*d^4))/(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))*(-(a^4*d^4 + 81*b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 108*a*b^3*c^3*d + 12*a^3*b*c*d^3)/(4096*b^8*c^11*d + 4096*a^8*c^3*d^9 - 32768*a*b^7*c^10*d^2 - 32768*a^7*b*c^4*d^8 + 114688*a^2*b^6*c^9*d^3 - 229376*a^3*b^5*c^8*d^4 + 286720*a^4*b^4*c^7*d^5 - 229376*a^5*b^3*c^6*d^6 + 114688*a^6*b^2*c^5*d^7))^(1/4)*1i - (x^(1/2)*(17*a^6*b^7*d^7 + 108*a^5*b^8*c*d^6 + 81*a^2*b^11*c^4*d^3 + 108*a^3*b^10*c^3*d^4 + 198*a^4*b^9*c^2*d^5))/(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))*(-(a^4*d^4 + 81*b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 108*a*b^3*c^3*d + 12*a^3*b*c*d^3)/(4096*b^8*c^11*d + 4096*a^8*c^3*d^9 - 32768*a*b^7*c^10*d^2 - 32768*a^7*b*c^4*d^8 + 114688*a^2*b^6*c^9*d^3 - 229376*a^3*b^5*c^8*d^4 + 286720*a^4*b^4*c^7*d^5 - 229376*a^5*b^3*c^6*d^6 + 114688*a^6*b^2*c^5*d^7))^(1/4)*1i))*(-(a^4*d^4 + 81*b^4*c^4 + 54*a^2*b^2*c^2*d^2 + 108*a*b^3*c^3*d + 12*a^3*b*c*d^3)/(4096*b^8*c^11*d + 4096*a^8*c^3*d^9 - 32768*a*b^7*c^10*d^2 - 32768*a^7*b*c^4*d^8 + 114688*a^2*b^6*c^9*d^3 - 229376*a^3*b^5*c^8*d^4 + 286720*a^4*b^4*c^7*d^5 - 229376*a^5*b^3*c^6*d^6 + 114688*a^6*b^2*c^5*d^7))^(1/4) - x^(1/2)/(2*(c + d*x^2)*(a*d - b*c))","B"
475,1,19453,536,2.385839,"\text{Not used}","int(x^(1/2)/((a + b*x^2)*(c + d*x^2)^2),x)","2\,\mathrm{atan}\left(\frac{{\left(-\frac{b^5}{16\,a^9\,d^8-128\,a^8\,b\,c\,d^7+448\,a^7\,b^2\,c^2\,d^6-896\,a^6\,b^3\,c^3\,d^5+1120\,a^5\,b^4\,c^4\,d^4-896\,a^4\,b^5\,c^5\,d^3+448\,a^3\,b^6\,c^6\,d^2-128\,a^2\,b^7\,c^7\,d+16\,a\,b^8\,c^8}\right)}^{1/4}\,\left({\left(-\frac{b^5}{16\,a^9\,d^8-128\,a^8\,b\,c\,d^7+448\,a^7\,b^2\,c^2\,d^6-896\,a^6\,b^3\,c^3\,d^5+1120\,a^5\,b^4\,c^4\,d^4-896\,a^4\,b^5\,c^5\,d^3+448\,a^3\,b^6\,c^6\,d^2-128\,a^2\,b^7\,c^7\,d+16\,a\,b^8\,c^8}\right)}^{3/4}\,\left(\frac{\sqrt{x}\,{\left(-\frac{b^5}{16\,a^9\,d^8-128\,a^8\,b\,c\,d^7+448\,a^7\,b^2\,c^2\,d^6-896\,a^6\,b^3\,c^3\,d^5+1120\,a^5\,b^4\,c^4\,d^4-896\,a^4\,b^5\,c^5\,d^3+448\,a^3\,b^6\,c^6\,d^2-128\,a^2\,b^7\,c^7\,d+16\,a\,b^8\,c^8}\right)}^{1/4}\,\left(256\,a^{13}\,b^4\,c\,d^{16}-4608\,a^{12}\,b^5\,c^2\,d^{15}+34048\,a^{11}\,b^6\,c^3\,d^{14}-137216\,a^{10}\,b^7\,c^4\,d^{13}+344576\,a^9\,b^8\,c^5\,d^{12}-584704\,a^8\,b^9\,c^6\,d^{11}+713216\,a^7\,b^{10}\,c^7\,d^{10}-661504\,a^6\,b^{11}\,c^8\,d^9+486656\,a^5\,b^{12}\,c^9\,d^8-283136\,a^4\,b^{13}\,c^{10}\,d^7+121088\,a^3\,b^{14}\,c^{11}\,d^6-32768\,a^2\,b^{15}\,c^{12}\,d^5+4096\,a\,b^{16}\,c^{13}\,d^4\right)}{a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8}+\frac{\left(32\,a^{13}\,b^4\,d^{16}-704\,a^{12}\,b^5\,c\,d^{15}+6432\,a^{11}\,b^6\,c^2\,d^{14}-32000\,a^{10}\,b^7\,c^3\,d^{13}+96320\,a^9\,b^8\,c^4\,d^{12}-183424\,a^8\,b^9\,c^5\,d^{11}+219968\,a^7\,b^{10}\,c^6\,d^{10}-150784\,a^6\,b^{11}\,c^7\,d^9+29600\,a^5\,b^{12}\,c^8\,d^8+41280\,a^4\,b^{13}\,c^9\,d^7-39008\,a^3\,b^{14}\,c^{10}\,d^6+14336\,a^2\,b^{15}\,c^{11}\,d^5-2048\,a\,b^{16}\,c^{12}\,d^4\right)\,1{}\mathrm{i}}{-a^7\,c^2\,d^7+7\,a^6\,b\,c^3\,d^6-21\,a^5\,b^2\,c^4\,d^5+35\,a^4\,b^3\,c^5\,d^4-35\,a^3\,b^4\,c^6\,d^3+21\,a^2\,b^5\,c^7\,d^2-7\,a\,b^6\,c^8\,d+b^7\,c^9}\right)-\frac{\sqrt{x}\,\left(-a^5\,b^8\,d^9+4\,a^4\,b^9\,c\,d^8+10\,a^3\,b^{10}\,c^2\,d^7+100\,a^2\,b^{11}\,c^3\,d^6-625\,a\,b^{12}\,c^4\,d^5\right)}{a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8}\right)-{\left(-\frac{b^5}{16\,a^9\,d^8-128\,a^8\,b\,c\,d^7+448\,a^7\,b^2\,c^2\,d^6-896\,a^6\,b^3\,c^3\,d^5+1120\,a^5\,b^4\,c^4\,d^4-896\,a^4\,b^5\,c^5\,d^3+448\,a^3\,b^6\,c^6\,d^2-128\,a^2\,b^7\,c^7\,d+16\,a\,b^8\,c^8}\right)}^{1/4}\,\left({\left(-\frac{b^5}{16\,a^9\,d^8-128\,a^8\,b\,c\,d^7+448\,a^7\,b^2\,c^2\,d^6-896\,a^6\,b^3\,c^3\,d^5+1120\,a^5\,b^4\,c^4\,d^4-896\,a^4\,b^5\,c^5\,d^3+448\,a^3\,b^6\,c^6\,d^2-128\,a^2\,b^7\,c^7\,d+16\,a\,b^8\,c^8}\right)}^{3/4}\,\left(-\frac{\sqrt{x}\,{\left(-\frac{b^5}{16\,a^9\,d^8-128\,a^8\,b\,c\,d^7+448\,a^7\,b^2\,c^2\,d^6-896\,a^6\,b^3\,c^3\,d^5+1120\,a^5\,b^4\,c^4\,d^4-896\,a^4\,b^5\,c^5\,d^3+448\,a^3\,b^6\,c^6\,d^2-128\,a^2\,b^7\,c^7\,d+16\,a\,b^8\,c^8}\right)}^{1/4}\,\left(256\,a^{13}\,b^4\,c\,d^{16}-4608\,a^{12}\,b^5\,c^2\,d^{15}+34048\,a^{11}\,b^6\,c^3\,d^{14}-137216\,a^{10}\,b^7\,c^4\,d^{13}+344576\,a^9\,b^8\,c^5\,d^{12}-584704\,a^8\,b^9\,c^6\,d^{11}+713216\,a^7\,b^{10}\,c^7\,d^{10}-661504\,a^6\,b^{11}\,c^8\,d^9+486656\,a^5\,b^{12}\,c^9\,d^8-283136\,a^4\,b^{13}\,c^{10}\,d^7+121088\,a^3\,b^{14}\,c^{11}\,d^6-32768\,a^2\,b^{15}\,c^{12}\,d^5+4096\,a\,b^{16}\,c^{13}\,d^4\right)}{a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8}+\frac{\left(32\,a^{13}\,b^4\,d^{16}-704\,a^{12}\,b^5\,c\,d^{15}+6432\,a^{11}\,b^6\,c^2\,d^{14}-32000\,a^{10}\,b^7\,c^3\,d^{13}+96320\,a^9\,b^8\,c^4\,d^{12}-183424\,a^8\,b^9\,c^5\,d^{11}+219968\,a^7\,b^{10}\,c^6\,d^{10}-150784\,a^6\,b^{11}\,c^7\,d^9+29600\,a^5\,b^{12}\,c^8\,d^8+41280\,a^4\,b^{13}\,c^9\,d^7-39008\,a^3\,b^{14}\,c^{10}\,d^6+14336\,a^2\,b^{15}\,c^{11}\,d^5-2048\,a\,b^{16}\,c^{12}\,d^4\right)\,1{}\mathrm{i}}{-a^7\,c^2\,d^7+7\,a^6\,b\,c^3\,d^6-21\,a^5\,b^2\,c^4\,d^5+35\,a^4\,b^3\,c^5\,d^4-35\,a^3\,b^4\,c^6\,d^3+21\,a^2\,b^5\,c^7\,d^2-7\,a\,b^6\,c^8\,d+b^7\,c^9}\right)+\frac{\sqrt{x}\,\left(-a^5\,b^8\,d^9+4\,a^4\,b^9\,c\,d^8+10\,a^3\,b^{10}\,c^2\,d^7+100\,a^2\,b^{11}\,c^3\,d^6-625\,a\,b^{12}\,c^4\,d^5\right)}{a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8}\right)}{{\left(-\frac{b^5}{16\,a^9\,d^8-128\,a^8\,b\,c\,d^7+448\,a^7\,b^2\,c^2\,d^6-896\,a^6\,b^3\,c^3\,d^5+1120\,a^5\,b^4\,c^4\,d^4-896\,a^4\,b^5\,c^5\,d^3+448\,a^3\,b^6\,c^6\,d^2-128\,a^2\,b^7\,c^7\,d+16\,a\,b^8\,c^8}\right)}^{1/4}\,\left({\left(-\frac{b^5}{16\,a^9\,d^8-128\,a^8\,b\,c\,d^7+448\,a^7\,b^2\,c^2\,d^6-896\,a^6\,b^3\,c^3\,d^5+1120\,a^5\,b^4\,c^4\,d^4-896\,a^4\,b^5\,c^5\,d^3+448\,a^3\,b^6\,c^6\,d^2-128\,a^2\,b^7\,c^7\,d+16\,a\,b^8\,c^8}\right)}^{3/4}\,\left(\frac{\sqrt{x}\,{\left(-\frac{b^5}{16\,a^9\,d^8-128\,a^8\,b\,c\,d^7+448\,a^7\,b^2\,c^2\,d^6-896\,a^6\,b^3\,c^3\,d^5+1120\,a^5\,b^4\,c^4\,d^4-896\,a^4\,b^5\,c^5\,d^3+448\,a^3\,b^6\,c^6\,d^2-128\,a^2\,b^7\,c^7\,d+16\,a\,b^8\,c^8}\right)}^{1/4}\,\left(256\,a^{13}\,b^4\,c\,d^{16}-4608\,a^{12}\,b^5\,c^2\,d^{15}+34048\,a^{11}\,b^6\,c^3\,d^{14}-137216\,a^{10}\,b^7\,c^4\,d^{13}+344576\,a^9\,b^8\,c^5\,d^{12}-584704\,a^8\,b^9\,c^6\,d^{11}+713216\,a^7\,b^{10}\,c^7\,d^{10}-661504\,a^6\,b^{11}\,c^8\,d^9+486656\,a^5\,b^{12}\,c^9\,d^8-283136\,a^4\,b^{13}\,c^{10}\,d^7+121088\,a^3\,b^{14}\,c^{11}\,d^6-32768\,a^2\,b^{15}\,c^{12}\,d^5+4096\,a\,b^{16}\,c^{13}\,d^4\right)}{a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8}+\frac{\left(32\,a^{13}\,b^4\,d^{16}-704\,a^{12}\,b^5\,c\,d^{15}+6432\,a^{11}\,b^6\,c^2\,d^{14}-32000\,a^{10}\,b^7\,c^3\,d^{13}+96320\,a^9\,b^8\,c^4\,d^{12}-183424\,a^8\,b^9\,c^5\,d^{11}+219968\,a^7\,b^{10}\,c^6\,d^{10}-150784\,a^6\,b^{11}\,c^7\,d^9+29600\,a^5\,b^{12}\,c^8\,d^8+41280\,a^4\,b^{13}\,c^9\,d^7-39008\,a^3\,b^{14}\,c^{10}\,d^6+14336\,a^2\,b^{15}\,c^{11}\,d^5-2048\,a\,b^{16}\,c^{12}\,d^4\right)\,1{}\mathrm{i}}{-a^7\,c^2\,d^7+7\,a^6\,b\,c^3\,d^6-21\,a^5\,b^2\,c^4\,d^5+35\,a^4\,b^3\,c^5\,d^4-35\,a^3\,b^4\,c^6\,d^3+21\,a^2\,b^5\,c^7\,d^2-7\,a\,b^6\,c^8\,d+b^7\,c^9}\right)\,1{}\mathrm{i}-\frac{\sqrt{x}\,\left(-a^5\,b^8\,d^9+4\,a^4\,b^9\,c\,d^8+10\,a^3\,b^{10}\,c^2\,d^7+100\,a^2\,b^{11}\,c^3\,d^6-625\,a\,b^{12}\,c^4\,d^5\right)\,1{}\mathrm{i}}{a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8}\right)+{\left(-\frac{b^5}{16\,a^9\,d^8-128\,a^8\,b\,c\,d^7+448\,a^7\,b^2\,c^2\,d^6-896\,a^6\,b^3\,c^3\,d^5+1120\,a^5\,b^4\,c^4\,d^4-896\,a^4\,b^5\,c^5\,d^3+448\,a^3\,b^6\,c^6\,d^2-128\,a^2\,b^7\,c^7\,d+16\,a\,b^8\,c^8}\right)}^{1/4}\,\left({\left(-\frac{b^5}{16\,a^9\,d^8-128\,a^8\,b\,c\,d^7+448\,a^7\,b^2\,c^2\,d^6-896\,a^6\,b^3\,c^3\,d^5+1120\,a^5\,b^4\,c^4\,d^4-896\,a^4\,b^5\,c^5\,d^3+448\,a^3\,b^6\,c^6\,d^2-128\,a^2\,b^7\,c^7\,d+16\,a\,b^8\,c^8}\right)}^{3/4}\,\left(-\frac{\sqrt{x}\,{\left(-\frac{b^5}{16\,a^9\,d^8-128\,a^8\,b\,c\,d^7+448\,a^7\,b^2\,c^2\,d^6-896\,a^6\,b^3\,c^3\,d^5+1120\,a^5\,b^4\,c^4\,d^4-896\,a^4\,b^5\,c^5\,d^3+448\,a^3\,b^6\,c^6\,d^2-128\,a^2\,b^7\,c^7\,d+16\,a\,b^8\,c^8}\right)}^{1/4}\,\left(256\,a^{13}\,b^4\,c\,d^{16}-4608\,a^{12}\,b^5\,c^2\,d^{15}+34048\,a^{11}\,b^6\,c^3\,d^{14}-137216\,a^{10}\,b^7\,c^4\,d^{13}+344576\,a^9\,b^8\,c^5\,d^{12}-584704\,a^8\,b^9\,c^6\,d^{11}+713216\,a^7\,b^{10}\,c^7\,d^{10}-661504\,a^6\,b^{11}\,c^8\,d^9+486656\,a^5\,b^{12}\,c^9\,d^8-283136\,a^4\,b^{13}\,c^{10}\,d^7+121088\,a^3\,b^{14}\,c^{11}\,d^6-32768\,a^2\,b^{15}\,c^{12}\,d^5+4096\,a\,b^{16}\,c^{13}\,d^4\right)}{a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8}+\frac{\left(32\,a^{13}\,b^4\,d^{16}-704\,a^{12}\,b^5\,c\,d^{15}+6432\,a^{11}\,b^6\,c^2\,d^{14}-32000\,a^{10}\,b^7\,c^3\,d^{13}+96320\,a^9\,b^8\,c^4\,d^{12}-183424\,a^8\,b^9\,c^5\,d^{11}+219968\,a^7\,b^{10}\,c^6\,d^{10}-150784\,a^6\,b^{11}\,c^7\,d^9+29600\,a^5\,b^{12}\,c^8\,d^8+41280\,a^4\,b^{13}\,c^9\,d^7-39008\,a^3\,b^{14}\,c^{10}\,d^6+14336\,a^2\,b^{15}\,c^{11}\,d^5-2048\,a\,b^{16}\,c^{12}\,d^4\right)\,1{}\mathrm{i}}{-a^7\,c^2\,d^7+7\,a^6\,b\,c^3\,d^6-21\,a^5\,b^2\,c^4\,d^5+35\,a^4\,b^3\,c^5\,d^4-35\,a^3\,b^4\,c^6\,d^3+21\,a^2\,b^5\,c^7\,d^2-7\,a\,b^6\,c^8\,d+b^7\,c^9}\right)\,1{}\mathrm{i}+\frac{\sqrt{x}\,\left(-a^5\,b^8\,d^9+4\,a^4\,b^9\,c\,d^8+10\,a^3\,b^{10}\,c^2\,d^7+100\,a^2\,b^{11}\,c^3\,d^6-625\,a\,b^{12}\,c^4\,d^5\right)\,1{}\mathrm{i}}{a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8}\right)-\frac{5\,a^4\,b^9\,d^8-75\,a^3\,b^{10}\,c\,d^7+375\,a^2\,b^{11}\,c^2\,d^6-625\,a\,b^{12}\,c^3\,d^5}{-a^7\,c^2\,d^7+7\,a^6\,b\,c^3\,d^6-21\,a^5\,b^2\,c^4\,d^5+35\,a^4\,b^3\,c^5\,d^4-35\,a^3\,b^4\,c^6\,d^3+21\,a^2\,b^5\,c^7\,d^2-7\,a\,b^6\,c^8\,d+b^7\,c^9}}\right)\,{\left(-\frac{b^5}{16\,a^9\,d^8-128\,a^8\,b\,c\,d^7+448\,a^7\,b^2\,c^2\,d^6-896\,a^6\,b^3\,c^3\,d^5+1120\,a^5\,b^4\,c^4\,d^4-896\,a^4\,b^5\,c^5\,d^3+448\,a^3\,b^6\,c^6\,d^2-128\,a^2\,b^7\,c^7\,d+16\,a\,b^8\,c^8}\right)}^{1/4}+2\,\mathrm{atan}\left(\frac{\left(\left(\frac{\sqrt{x}\,{\left(-\frac{a^4\,d^5-20\,a^3\,b\,c\,d^4+150\,a^2\,b^2\,c^2\,d^3-500\,a\,b^3\,c^3\,d^2+625\,b^4\,c^4\,d}{4096\,a^8\,c^5\,d^8-32768\,a^7\,b\,c^6\,d^7+114688\,a^6\,b^2\,c^7\,d^6-229376\,a^5\,b^3\,c^8\,d^5+286720\,a^4\,b^4\,c^9\,d^4-229376\,a^3\,b^5\,c^{10}\,d^3+114688\,a^2\,b^6\,c^{11}\,d^2-32768\,a\,b^7\,c^{12}\,d+4096\,b^8\,c^{13}}\right)}^{1/4}\,\left(256\,a^{13}\,b^4\,c\,d^{16}-4608\,a^{12}\,b^5\,c^2\,d^{15}+34048\,a^{11}\,b^6\,c^3\,d^{14}-137216\,a^{10}\,b^7\,c^4\,d^{13}+344576\,a^9\,b^8\,c^5\,d^{12}-584704\,a^8\,b^9\,c^6\,d^{11}+713216\,a^7\,b^{10}\,c^7\,d^{10}-661504\,a^6\,b^{11}\,c^8\,d^9+486656\,a^5\,b^{12}\,c^9\,d^8-283136\,a^4\,b^{13}\,c^{10}\,d^7+121088\,a^3\,b^{14}\,c^{11}\,d^6-32768\,a^2\,b^{15}\,c^{12}\,d^5+4096\,a\,b^{16}\,c^{13}\,d^4\right)}{a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8}+\frac{\left(32\,a^{13}\,b^4\,d^{16}-704\,a^{12}\,b^5\,c\,d^{15}+6432\,a^{11}\,b^6\,c^2\,d^{14}-32000\,a^{10}\,b^7\,c^3\,d^{13}+96320\,a^9\,b^8\,c^4\,d^{12}-183424\,a^8\,b^9\,c^5\,d^{11}+219968\,a^7\,b^{10}\,c^6\,d^{10}-150784\,a^6\,b^{11}\,c^7\,d^9+29600\,a^5\,b^{12}\,c^8\,d^8+41280\,a^4\,b^{13}\,c^9\,d^7-39008\,a^3\,b^{14}\,c^{10}\,d^6+14336\,a^2\,b^{15}\,c^{11}\,d^5-2048\,a\,b^{16}\,c^{12}\,d^4\right)\,1{}\mathrm{i}}{-a^7\,c^2\,d^7+7\,a^6\,b\,c^3\,d^6-21\,a^5\,b^2\,c^4\,d^5+35\,a^4\,b^3\,c^5\,d^4-35\,a^3\,b^4\,c^6\,d^3+21\,a^2\,b^5\,c^7\,d^2-7\,a\,b^6\,c^8\,d+b^7\,c^9}\right)\,{\left(-\frac{a^4\,d^5-20\,a^3\,b\,c\,d^4+150\,a^2\,b^2\,c^2\,d^3-500\,a\,b^3\,c^3\,d^2+625\,b^4\,c^4\,d}{4096\,a^8\,c^5\,d^8-32768\,a^7\,b\,c^6\,d^7+114688\,a^6\,b^2\,c^7\,d^6-229376\,a^5\,b^3\,c^8\,d^5+286720\,a^4\,b^4\,c^9\,d^4-229376\,a^3\,b^5\,c^{10}\,d^3+114688\,a^2\,b^6\,c^{11}\,d^2-32768\,a\,b^7\,c^{12}\,d+4096\,b^8\,c^{13}}\right)}^{3/4}-\frac{\sqrt{x}\,\left(-a^5\,b^8\,d^9+4\,a^4\,b^9\,c\,d^8+10\,a^3\,b^{10}\,c^2\,d^7+100\,a^2\,b^{11}\,c^3\,d^6-625\,a\,b^{12}\,c^4\,d^5\right)}{a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8}\right)\,{\left(-\frac{a^4\,d^5-20\,a^3\,b\,c\,d^4+150\,a^2\,b^2\,c^2\,d^3-500\,a\,b^3\,c^3\,d^2+625\,b^4\,c^4\,d}{4096\,a^8\,c^5\,d^8-32768\,a^7\,b\,c^6\,d^7+114688\,a^6\,b^2\,c^7\,d^6-229376\,a^5\,b^3\,c^8\,d^5+286720\,a^4\,b^4\,c^9\,d^4-229376\,a^3\,b^5\,c^{10}\,d^3+114688\,a^2\,b^6\,c^{11}\,d^2-32768\,a\,b^7\,c^{12}\,d+4096\,b^8\,c^{13}}\right)}^{1/4}-\left(\left(-\frac{\sqrt{x}\,{\left(-\frac{a^4\,d^5-20\,a^3\,b\,c\,d^4+150\,a^2\,b^2\,c^2\,d^3-500\,a\,b^3\,c^3\,d^2+625\,b^4\,c^4\,d}{4096\,a^8\,c^5\,d^8-32768\,a^7\,b\,c^6\,d^7+114688\,a^6\,b^2\,c^7\,d^6-229376\,a^5\,b^3\,c^8\,d^5+286720\,a^4\,b^4\,c^9\,d^4-229376\,a^3\,b^5\,c^{10}\,d^3+114688\,a^2\,b^6\,c^{11}\,d^2-32768\,a\,b^7\,c^{12}\,d+4096\,b^8\,c^{13}}\right)}^{1/4}\,\left(256\,a^{13}\,b^4\,c\,d^{16}-4608\,a^{12}\,b^5\,c^2\,d^{15}+34048\,a^{11}\,b^6\,c^3\,d^{14}-137216\,a^{10}\,b^7\,c^4\,d^{13}+344576\,a^9\,b^8\,c^5\,d^{12}-584704\,a^8\,b^9\,c^6\,d^{11}+713216\,a^7\,b^{10}\,c^7\,d^{10}-661504\,a^6\,b^{11}\,c^8\,d^9+486656\,a^5\,b^{12}\,c^9\,d^8-283136\,a^4\,b^{13}\,c^{10}\,d^7+121088\,a^3\,b^{14}\,c^{11}\,d^6-32768\,a^2\,b^{15}\,c^{12}\,d^5+4096\,a\,b^{16}\,c^{13}\,d^4\right)}{a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8}+\frac{\left(32\,a^{13}\,b^4\,d^{16}-704\,a^{12}\,b^5\,c\,d^{15}+6432\,a^{11}\,b^6\,c^2\,d^{14}-32000\,a^{10}\,b^7\,c^3\,d^{13}+96320\,a^9\,b^8\,c^4\,d^{12}-183424\,a^8\,b^9\,c^5\,d^{11}+219968\,a^7\,b^{10}\,c^6\,d^{10}-150784\,a^6\,b^{11}\,c^7\,d^9+29600\,a^5\,b^{12}\,c^8\,d^8+41280\,a^4\,b^{13}\,c^9\,d^7-39008\,a^3\,b^{14}\,c^{10}\,d^6+14336\,a^2\,b^{15}\,c^{11}\,d^5-2048\,a\,b^{16}\,c^{12}\,d^4\right)\,1{}\mathrm{i}}{-a^7\,c^2\,d^7+7\,a^6\,b\,c^3\,d^6-21\,a^5\,b^2\,c^4\,d^5+35\,a^4\,b^3\,c^5\,d^4-35\,a^3\,b^4\,c^6\,d^3+21\,a^2\,b^5\,c^7\,d^2-7\,a\,b^6\,c^8\,d+b^7\,c^9}\right)\,{\left(-\frac{a^4\,d^5-20\,a^3\,b\,c\,d^4+150\,a^2\,b^2\,c^2\,d^3-500\,a\,b^3\,c^3\,d^2+625\,b^4\,c^4\,d}{4096\,a^8\,c^5\,d^8-32768\,a^7\,b\,c^6\,d^7+114688\,a^6\,b^2\,c^7\,d^6-229376\,a^5\,b^3\,c^8\,d^5+286720\,a^4\,b^4\,c^9\,d^4-229376\,a^3\,b^5\,c^{10}\,d^3+114688\,a^2\,b^6\,c^{11}\,d^2-32768\,a\,b^7\,c^{12}\,d+4096\,b^8\,c^{13}}\right)}^{3/4}+\frac{\sqrt{x}\,\left(-a^5\,b^8\,d^9+4\,a^4\,b^9\,c\,d^8+10\,a^3\,b^{10}\,c^2\,d^7+100\,a^2\,b^{11}\,c^3\,d^6-625\,a\,b^{12}\,c^4\,d^5\right)}{a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8}\right)\,{\left(-\frac{a^4\,d^5-20\,a^3\,b\,c\,d^4+150\,a^2\,b^2\,c^2\,d^3-500\,a\,b^3\,c^3\,d^2+625\,b^4\,c^4\,d}{4096\,a^8\,c^5\,d^8-32768\,a^7\,b\,c^6\,d^7+114688\,a^6\,b^2\,c^7\,d^6-229376\,a^5\,b^3\,c^8\,d^5+286720\,a^4\,b^4\,c^9\,d^4-229376\,a^3\,b^5\,c^{10}\,d^3+114688\,a^2\,b^6\,c^{11}\,d^2-32768\,a\,b^7\,c^{12}\,d+4096\,b^8\,c^{13}}\right)}^{1/4}}{\left(\left(\frac{\sqrt{x}\,{\left(-\frac{a^4\,d^5-20\,a^3\,b\,c\,d^4+150\,a^2\,b^2\,c^2\,d^3-500\,a\,b^3\,c^3\,d^2+625\,b^4\,c^4\,d}{4096\,a^8\,c^5\,d^8-32768\,a^7\,b\,c^6\,d^7+114688\,a^6\,b^2\,c^7\,d^6-229376\,a^5\,b^3\,c^8\,d^5+286720\,a^4\,b^4\,c^9\,d^4-229376\,a^3\,b^5\,c^{10}\,d^3+114688\,a^2\,b^6\,c^{11}\,d^2-32768\,a\,b^7\,c^{12}\,d+4096\,b^8\,c^{13}}\right)}^{1/4}\,\left(256\,a^{13}\,b^4\,c\,d^{16}-4608\,a^{12}\,b^5\,c^2\,d^{15}+34048\,a^{11}\,b^6\,c^3\,d^{14}-137216\,a^{10}\,b^7\,c^4\,d^{13}+344576\,a^9\,b^8\,c^5\,d^{12}-584704\,a^8\,b^9\,c^6\,d^{11}+713216\,a^7\,b^{10}\,c^7\,d^{10}-661504\,a^6\,b^{11}\,c^8\,d^9+486656\,a^5\,b^{12}\,c^9\,d^8-283136\,a^4\,b^{13}\,c^{10}\,d^7+121088\,a^3\,b^{14}\,c^{11}\,d^6-32768\,a^2\,b^{15}\,c^{12}\,d^5+4096\,a\,b^{16}\,c^{13}\,d^4\right)}{a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8}+\frac{\left(32\,a^{13}\,b^4\,d^{16}-704\,a^{12}\,b^5\,c\,d^{15}+6432\,a^{11}\,b^6\,c^2\,d^{14}-32000\,a^{10}\,b^7\,c^3\,d^{13}+96320\,a^9\,b^8\,c^4\,d^{12}-183424\,a^8\,b^9\,c^5\,d^{11}+219968\,a^7\,b^{10}\,c^6\,d^{10}-150784\,a^6\,b^{11}\,c^7\,d^9+29600\,a^5\,b^{12}\,c^8\,d^8+41280\,a^4\,b^{13}\,c^9\,d^7-39008\,a^3\,b^{14}\,c^{10}\,d^6+14336\,a^2\,b^{15}\,c^{11}\,d^5-2048\,a\,b^{16}\,c^{12}\,d^4\right)\,1{}\mathrm{i}}{-a^7\,c^2\,d^7+7\,a^6\,b\,c^3\,d^6-21\,a^5\,b^2\,c^4\,d^5+35\,a^4\,b^3\,c^5\,d^4-35\,a^3\,b^4\,c^6\,d^3+21\,a^2\,b^5\,c^7\,d^2-7\,a\,b^6\,c^8\,d+b^7\,c^9}\right)\,{\left(-\frac{a^4\,d^5-20\,a^3\,b\,c\,d^4+150\,a^2\,b^2\,c^2\,d^3-500\,a\,b^3\,c^3\,d^2+625\,b^4\,c^4\,d}{4096\,a^8\,c^5\,d^8-32768\,a^7\,b\,c^6\,d^7+114688\,a^6\,b^2\,c^7\,d^6-229376\,a^5\,b^3\,c^8\,d^5+286720\,a^4\,b^4\,c^9\,d^4-229376\,a^3\,b^5\,c^{10}\,d^3+114688\,a^2\,b^6\,c^{11}\,d^2-32768\,a\,b^7\,c^{12}\,d+4096\,b^8\,c^{13}}\right)}^{3/4}\,1{}\mathrm{i}-\frac{\sqrt{x}\,\left(-a^5\,b^8\,d^9+4\,a^4\,b^9\,c\,d^8+10\,a^3\,b^{10}\,c^2\,d^7+100\,a^2\,b^{11}\,c^3\,d^6-625\,a\,b^{12}\,c^4\,d^5\right)\,1{}\mathrm{i}}{a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8}\right)\,{\left(-\frac{a^4\,d^5-20\,a^3\,b\,c\,d^4+150\,a^2\,b^2\,c^2\,d^3-500\,a\,b^3\,c^3\,d^2+625\,b^4\,c^4\,d}{4096\,a^8\,c^5\,d^8-32768\,a^7\,b\,c^6\,d^7+114688\,a^6\,b^2\,c^7\,d^6-229376\,a^5\,b^3\,c^8\,d^5+286720\,a^4\,b^4\,c^9\,d^4-229376\,a^3\,b^5\,c^{10}\,d^3+114688\,a^2\,b^6\,c^{11}\,d^2-32768\,a\,b^7\,c^{12}\,d+4096\,b^8\,c^{13}}\right)}^{1/4}+\left(\left(-\frac{\sqrt{x}\,{\left(-\frac{a^4\,d^5-20\,a^3\,b\,c\,d^4+150\,a^2\,b^2\,c^2\,d^3-500\,a\,b^3\,c^3\,d^2+625\,b^4\,c^4\,d}{4096\,a^8\,c^5\,d^8-32768\,a^7\,b\,c^6\,d^7+114688\,a^6\,b^2\,c^7\,d^6-229376\,a^5\,b^3\,c^8\,d^5+286720\,a^4\,b^4\,c^9\,d^4-229376\,a^3\,b^5\,c^{10}\,d^3+114688\,a^2\,b^6\,c^{11}\,d^2-32768\,a\,b^7\,c^{12}\,d+4096\,b^8\,c^{13}}\right)}^{1/4}\,\left(256\,a^{13}\,b^4\,c\,d^{16}-4608\,a^{12}\,b^5\,c^2\,d^{15}+34048\,a^{11}\,b^6\,c^3\,d^{14}-137216\,a^{10}\,b^7\,c^4\,d^{13}+344576\,a^9\,b^8\,c^5\,d^{12}-584704\,a^8\,b^9\,c^6\,d^{11}+713216\,a^7\,b^{10}\,c^7\,d^{10}-661504\,a^6\,b^{11}\,c^8\,d^9+486656\,a^5\,b^{12}\,c^9\,d^8-283136\,a^4\,b^{13}\,c^{10}\,d^7+121088\,a^3\,b^{14}\,c^{11}\,d^6-32768\,a^2\,b^{15}\,c^{12}\,d^5+4096\,a\,b^{16}\,c^{13}\,d^4\right)}{a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8}+\frac{\left(32\,a^{13}\,b^4\,d^{16}-704\,a^{12}\,b^5\,c\,d^{15}+6432\,a^{11}\,b^6\,c^2\,d^{14}-32000\,a^{10}\,b^7\,c^3\,d^{13}+96320\,a^9\,b^8\,c^4\,d^{12}-183424\,a^8\,b^9\,c^5\,d^{11}+219968\,a^7\,b^{10}\,c^6\,d^{10}-150784\,a^6\,b^{11}\,c^7\,d^9+29600\,a^5\,b^{12}\,c^8\,d^8+41280\,a^4\,b^{13}\,c^9\,d^7-39008\,a^3\,b^{14}\,c^{10}\,d^6+14336\,a^2\,b^{15}\,c^{11}\,d^5-2048\,a\,b^{16}\,c^{12}\,d^4\right)\,1{}\mathrm{i}}{-a^7\,c^2\,d^7+7\,a^6\,b\,c^3\,d^6-21\,a^5\,b^2\,c^4\,d^5+35\,a^4\,b^3\,c^5\,d^4-35\,a^3\,b^4\,c^6\,d^3+21\,a^2\,b^5\,c^7\,d^2-7\,a\,b^6\,c^8\,d+b^7\,c^9}\right)\,{\left(-\frac{a^4\,d^5-20\,a^3\,b\,c\,d^4+150\,a^2\,b^2\,c^2\,d^3-500\,a\,b^3\,c^3\,d^2+625\,b^4\,c^4\,d}{4096\,a^8\,c^5\,d^8-32768\,a^7\,b\,c^6\,d^7+114688\,a^6\,b^2\,c^7\,d^6-229376\,a^5\,b^3\,c^8\,d^5+286720\,a^4\,b^4\,c^9\,d^4-229376\,a^3\,b^5\,c^{10}\,d^3+114688\,a^2\,b^6\,c^{11}\,d^2-32768\,a\,b^7\,c^{12}\,d+4096\,b^8\,c^{13}}\right)}^{3/4}\,1{}\mathrm{i}+\frac{\sqrt{x}\,\left(-a^5\,b^8\,d^9+4\,a^4\,b^9\,c\,d^8+10\,a^3\,b^{10}\,c^2\,d^7+100\,a^2\,b^{11}\,c^3\,d^6-625\,a\,b^{12}\,c^4\,d^5\right)\,1{}\mathrm{i}}{a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8}\right)\,{\left(-\frac{a^4\,d^5-20\,a^3\,b\,c\,d^4+150\,a^2\,b^2\,c^2\,d^3-500\,a\,b^3\,c^3\,d^2+625\,b^4\,c^4\,d}{4096\,a^8\,c^5\,d^8-32768\,a^7\,b\,c^6\,d^7+114688\,a^6\,b^2\,c^7\,d^6-229376\,a^5\,b^3\,c^8\,d^5+286720\,a^4\,b^4\,c^9\,d^4-229376\,a^3\,b^5\,c^{10}\,d^3+114688\,a^2\,b^6\,c^{11}\,d^2-32768\,a\,b^7\,c^{12}\,d+4096\,b^8\,c^{13}}\right)}^{1/4}-\frac{5\,a^4\,b^9\,d^8-75\,a^3\,b^{10}\,c\,d^7+375\,a^2\,b^{11}\,c^2\,d^6-625\,a\,b^{12}\,c^3\,d^5}{-a^7\,c^2\,d^7+7\,a^6\,b\,c^3\,d^6-21\,a^5\,b^2\,c^4\,d^5+35\,a^4\,b^3\,c^5\,d^4-35\,a^3\,b^4\,c^6\,d^3+21\,a^2\,b^5\,c^7\,d^2-7\,a\,b^6\,c^8\,d+b^7\,c^9}}\right)\,{\left(-\frac{a^4\,d^5-20\,a^3\,b\,c\,d^4+150\,a^2\,b^2\,c^2\,d^3-500\,a\,b^3\,c^3\,d^2+625\,b^4\,c^4\,d}{4096\,a^8\,c^5\,d^8-32768\,a^7\,b\,c^6\,d^7+114688\,a^6\,b^2\,c^7\,d^6-229376\,a^5\,b^3\,c^8\,d^5+286720\,a^4\,b^4\,c^9\,d^4-229376\,a^3\,b^5\,c^{10}\,d^3+114688\,a^2\,b^6\,c^{11}\,d^2-32768\,a\,b^7\,c^{12}\,d+4096\,b^8\,c^{13}}\right)}^{1/4}+\frac{d\,x^{3/2}}{2\,c\,\left(d\,x^2+c\right)\,\left(a\,d-b\,c\right)}-\mathrm{atan}\left(\frac{{\left(-\frac{b^5}{16\,a^9\,d^8-128\,a^8\,b\,c\,d^7+448\,a^7\,b^2\,c^2\,d^6-896\,a^6\,b^3\,c^3\,d^5+1120\,a^5\,b^4\,c^4\,d^4-896\,a^4\,b^5\,c^5\,d^3+448\,a^3\,b^6\,c^6\,d^2-128\,a^2\,b^7\,c^7\,d+16\,a\,b^8\,c^8}\right)}^{1/4}\,\left({\left(-\frac{b^5}{16\,a^9\,d^8-128\,a^8\,b\,c\,d^7+448\,a^7\,b^2\,c^2\,d^6-896\,a^6\,b^3\,c^3\,d^5+1120\,a^5\,b^4\,c^4\,d^4-896\,a^4\,b^5\,c^5\,d^3+448\,a^3\,b^6\,c^6\,d^2-128\,a^2\,b^7\,c^7\,d+16\,a\,b^8\,c^8}\right)}^{3/4}\,\left(\frac{32\,a^{13}\,b^4\,d^{16}-704\,a^{12}\,b^5\,c\,d^{15}+6432\,a^{11}\,b^6\,c^2\,d^{14}-32000\,a^{10}\,b^7\,c^3\,d^{13}+96320\,a^9\,b^8\,c^4\,d^{12}-183424\,a^8\,b^9\,c^5\,d^{11}+219968\,a^7\,b^{10}\,c^6\,d^{10}-150784\,a^6\,b^{11}\,c^7\,d^9+29600\,a^5\,b^{12}\,c^8\,d^8+41280\,a^4\,b^{13}\,c^9\,d^7-39008\,a^3\,b^{14}\,c^{10}\,d^6+14336\,a^2\,b^{15}\,c^{11}\,d^5-2048\,a\,b^{16}\,c^{12}\,d^4}{-a^7\,c^2\,d^7+7\,a^6\,b\,c^3\,d^6-21\,a^5\,b^2\,c^4\,d^5+35\,a^4\,b^3\,c^5\,d^4-35\,a^3\,b^4\,c^6\,d^3+21\,a^2\,b^5\,c^7\,d^2-7\,a\,b^6\,c^8\,d+b^7\,c^9}+\frac{\sqrt{x}\,{\left(-\frac{b^5}{16\,a^9\,d^8-128\,a^8\,b\,c\,d^7+448\,a^7\,b^2\,c^2\,d^6-896\,a^6\,b^3\,c^3\,d^5+1120\,a^5\,b^4\,c^4\,d^4-896\,a^4\,b^5\,c^5\,d^3+448\,a^3\,b^6\,c^6\,d^2-128\,a^2\,b^7\,c^7\,d+16\,a\,b^8\,c^8}\right)}^{1/4}\,\left(256\,a^{13}\,b^4\,c\,d^{16}-4608\,a^{12}\,b^5\,c^2\,d^{15}+34048\,a^{11}\,b^6\,c^3\,d^{14}-137216\,a^{10}\,b^7\,c^4\,d^{13}+344576\,a^9\,b^8\,c^5\,d^{12}-584704\,a^8\,b^9\,c^6\,d^{11}+713216\,a^7\,b^{10}\,c^7\,d^{10}-661504\,a^6\,b^{11}\,c^8\,d^9+486656\,a^5\,b^{12}\,c^9\,d^8-283136\,a^4\,b^{13}\,c^{10}\,d^7+121088\,a^3\,b^{14}\,c^{11}\,d^6-32768\,a^2\,b^{15}\,c^{12}\,d^5+4096\,a\,b^{16}\,c^{13}\,d^4\right)}{a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8}\right)\,1{}\mathrm{i}-\frac{\sqrt{x}\,\left(-a^5\,b^8\,d^9+4\,a^4\,b^9\,c\,d^8+10\,a^3\,b^{10}\,c^2\,d^7+100\,a^2\,b^{11}\,c^3\,d^6-625\,a\,b^{12}\,c^4\,d^5\right)\,1{}\mathrm{i}}{a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8}\right)-{\left(-\frac{b^5}{16\,a^9\,d^8-128\,a^8\,b\,c\,d^7+448\,a^7\,b^2\,c^2\,d^6-896\,a^6\,b^3\,c^3\,d^5+1120\,a^5\,b^4\,c^4\,d^4-896\,a^4\,b^5\,c^5\,d^3+448\,a^3\,b^6\,c^6\,d^2-128\,a^2\,b^7\,c^7\,d+16\,a\,b^8\,c^8}\right)}^{1/4}\,\left({\left(-\frac{b^5}{16\,a^9\,d^8-128\,a^8\,b\,c\,d^7+448\,a^7\,b^2\,c^2\,d^6-896\,a^6\,b^3\,c^3\,d^5+1120\,a^5\,b^4\,c^4\,d^4-896\,a^4\,b^5\,c^5\,d^3+448\,a^3\,b^6\,c^6\,d^2-128\,a^2\,b^7\,c^7\,d+16\,a\,b^8\,c^8}\right)}^{3/4}\,\left(\frac{32\,a^{13}\,b^4\,d^{16}-704\,a^{12}\,b^5\,c\,d^{15}+6432\,a^{11}\,b^6\,c^2\,d^{14}-32000\,a^{10}\,b^7\,c^3\,d^{13}+96320\,a^9\,b^8\,c^4\,d^{12}-183424\,a^8\,b^9\,c^5\,d^{11}+219968\,a^7\,b^{10}\,c^6\,d^{10}-150784\,a^6\,b^{11}\,c^7\,d^9+29600\,a^5\,b^{12}\,c^8\,d^8+41280\,a^4\,b^{13}\,c^9\,d^7-39008\,a^3\,b^{14}\,c^{10}\,d^6+14336\,a^2\,b^{15}\,c^{11}\,d^5-2048\,a\,b^{16}\,c^{12}\,d^4}{-a^7\,c^2\,d^7+7\,a^6\,b\,c^3\,d^6-21\,a^5\,b^2\,c^4\,d^5+35\,a^4\,b^3\,c^5\,d^4-35\,a^3\,b^4\,c^6\,d^3+21\,a^2\,b^5\,c^7\,d^2-7\,a\,b^6\,c^8\,d+b^7\,c^9}-\frac{\sqrt{x}\,{\left(-\frac{b^5}{16\,a^9\,d^8-128\,a^8\,b\,c\,d^7+448\,a^7\,b^2\,c^2\,d^6-896\,a^6\,b^3\,c^3\,d^5+1120\,a^5\,b^4\,c^4\,d^4-896\,a^4\,b^5\,c^5\,d^3+448\,a^3\,b^6\,c^6\,d^2-128\,a^2\,b^7\,c^7\,d+16\,a\,b^8\,c^8}\right)}^{1/4}\,\left(256\,a^{13}\,b^4\,c\,d^{16}-4608\,a^{12}\,b^5\,c^2\,d^{15}+34048\,a^{11}\,b^6\,c^3\,d^{14}-137216\,a^{10}\,b^7\,c^4\,d^{13}+344576\,a^9\,b^8\,c^5\,d^{12}-584704\,a^8\,b^9\,c^6\,d^{11}+713216\,a^7\,b^{10}\,c^7\,d^{10}-661504\,a^6\,b^{11}\,c^8\,d^9+486656\,a^5\,b^{12}\,c^9\,d^8-283136\,a^4\,b^{13}\,c^{10}\,d^7+121088\,a^3\,b^{14}\,c^{11}\,d^6-32768\,a^2\,b^{15}\,c^{12}\,d^5+4096\,a\,b^{16}\,c^{13}\,d^4\right)}{a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8}\right)\,1{}\mathrm{i}+\frac{\sqrt{x}\,\left(-a^5\,b^8\,d^9+4\,a^4\,b^9\,c\,d^8+10\,a^3\,b^{10}\,c^2\,d^7+100\,a^2\,b^{11}\,c^3\,d^6-625\,a\,b^{12}\,c^4\,d^5\right)\,1{}\mathrm{i}}{a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8}\right)}{{\left(-\frac{b^5}{16\,a^9\,d^8-128\,a^8\,b\,c\,d^7+448\,a^7\,b^2\,c^2\,d^6-896\,a^6\,b^3\,c^3\,d^5+1120\,a^5\,b^4\,c^4\,d^4-896\,a^4\,b^5\,c^5\,d^3+448\,a^3\,b^6\,c^6\,d^2-128\,a^2\,b^7\,c^7\,d+16\,a\,b^8\,c^8}\right)}^{1/4}\,\left({\left(-\frac{b^5}{16\,a^9\,d^8-128\,a^8\,b\,c\,d^7+448\,a^7\,b^2\,c^2\,d^6-896\,a^6\,b^3\,c^3\,d^5+1120\,a^5\,b^4\,c^4\,d^4-896\,a^4\,b^5\,c^5\,d^3+448\,a^3\,b^6\,c^6\,d^2-128\,a^2\,b^7\,c^7\,d+16\,a\,b^8\,c^8}\right)}^{3/4}\,\left(\frac{32\,a^{13}\,b^4\,d^{16}-704\,a^{12}\,b^5\,c\,d^{15}+6432\,a^{11}\,b^6\,c^2\,d^{14}-32000\,a^{10}\,b^7\,c^3\,d^{13}+96320\,a^9\,b^8\,c^4\,d^{12}-183424\,a^8\,b^9\,c^5\,d^{11}+219968\,a^7\,b^{10}\,c^6\,d^{10}-150784\,a^6\,b^{11}\,c^7\,d^9+29600\,a^5\,b^{12}\,c^8\,d^8+41280\,a^4\,b^{13}\,c^9\,d^7-39008\,a^3\,b^{14}\,c^{10}\,d^6+14336\,a^2\,b^{15}\,c^{11}\,d^5-2048\,a\,b^{16}\,c^{12}\,d^4}{-a^7\,c^2\,d^7+7\,a^6\,b\,c^3\,d^6-21\,a^5\,b^2\,c^4\,d^5+35\,a^4\,b^3\,c^5\,d^4-35\,a^3\,b^4\,c^6\,d^3+21\,a^2\,b^5\,c^7\,d^2-7\,a\,b^6\,c^8\,d+b^7\,c^9}+\frac{\sqrt{x}\,{\left(-\frac{b^5}{16\,a^9\,d^8-128\,a^8\,b\,c\,d^7+448\,a^7\,b^2\,c^2\,d^6-896\,a^6\,b^3\,c^3\,d^5+1120\,a^5\,b^4\,c^4\,d^4-896\,a^4\,b^5\,c^5\,d^3+448\,a^3\,b^6\,c^6\,d^2-128\,a^2\,b^7\,c^7\,d+16\,a\,b^8\,c^8}\right)}^{1/4}\,\left(256\,a^{13}\,b^4\,c\,d^{16}-4608\,a^{12}\,b^5\,c^2\,d^{15}+34048\,a^{11}\,b^6\,c^3\,d^{14}-137216\,a^{10}\,b^7\,c^4\,d^{13}+344576\,a^9\,b^8\,c^5\,d^{12}-584704\,a^8\,b^9\,c^6\,d^{11}+713216\,a^7\,b^{10}\,c^7\,d^{10}-661504\,a^6\,b^{11}\,c^8\,d^9+486656\,a^5\,b^{12}\,c^9\,d^8-283136\,a^4\,b^{13}\,c^{10}\,d^7+121088\,a^3\,b^{14}\,c^{11}\,d^6-32768\,a^2\,b^{15}\,c^{12}\,d^5+4096\,a\,b^{16}\,c^{13}\,d^4\right)}{a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8}\right)-\frac{\sqrt{x}\,\left(-a^5\,b^8\,d^9+4\,a^4\,b^9\,c\,d^8+10\,a^3\,b^{10}\,c^2\,d^7+100\,a^2\,b^{11}\,c^3\,d^6-625\,a\,b^{12}\,c^4\,d^5\right)}{a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8}\right)+{\left(-\frac{b^5}{16\,a^9\,d^8-128\,a^8\,b\,c\,d^7+448\,a^7\,b^2\,c^2\,d^6-896\,a^6\,b^3\,c^3\,d^5+1120\,a^5\,b^4\,c^4\,d^4-896\,a^4\,b^5\,c^5\,d^3+448\,a^3\,b^6\,c^6\,d^2-128\,a^2\,b^7\,c^7\,d+16\,a\,b^8\,c^8}\right)}^{1/4}\,\left({\left(-\frac{b^5}{16\,a^9\,d^8-128\,a^8\,b\,c\,d^7+448\,a^7\,b^2\,c^2\,d^6-896\,a^6\,b^3\,c^3\,d^5+1120\,a^5\,b^4\,c^4\,d^4-896\,a^4\,b^5\,c^5\,d^3+448\,a^3\,b^6\,c^6\,d^2-128\,a^2\,b^7\,c^7\,d+16\,a\,b^8\,c^8}\right)}^{3/4}\,\left(\frac{32\,a^{13}\,b^4\,d^{16}-704\,a^{12}\,b^5\,c\,d^{15}+6432\,a^{11}\,b^6\,c^2\,d^{14}-32000\,a^{10}\,b^7\,c^3\,d^{13}+96320\,a^9\,b^8\,c^4\,d^{12}-183424\,a^8\,b^9\,c^5\,d^{11}+219968\,a^7\,b^{10}\,c^6\,d^{10}-150784\,a^6\,b^{11}\,c^7\,d^9+29600\,a^5\,b^{12}\,c^8\,d^8+41280\,a^4\,b^{13}\,c^9\,d^7-39008\,a^3\,b^{14}\,c^{10}\,d^6+14336\,a^2\,b^{15}\,c^{11}\,d^5-2048\,a\,b^{16}\,c^{12}\,d^4}{-a^7\,c^2\,d^7+7\,a^6\,b\,c^3\,d^6-21\,a^5\,b^2\,c^4\,d^5+35\,a^4\,b^3\,c^5\,d^4-35\,a^3\,b^4\,c^6\,d^3+21\,a^2\,b^5\,c^7\,d^2-7\,a\,b^6\,c^8\,d+b^7\,c^9}-\frac{\sqrt{x}\,{\left(-\frac{b^5}{16\,a^9\,d^8-128\,a^8\,b\,c\,d^7+448\,a^7\,b^2\,c^2\,d^6-896\,a^6\,b^3\,c^3\,d^5+1120\,a^5\,b^4\,c^4\,d^4-896\,a^4\,b^5\,c^5\,d^3+448\,a^3\,b^6\,c^6\,d^2-128\,a^2\,b^7\,c^7\,d+16\,a\,b^8\,c^8}\right)}^{1/4}\,\left(256\,a^{13}\,b^4\,c\,d^{16}-4608\,a^{12}\,b^5\,c^2\,d^{15}+34048\,a^{11}\,b^6\,c^3\,d^{14}-137216\,a^{10}\,b^7\,c^4\,d^{13}+344576\,a^9\,b^8\,c^5\,d^{12}-584704\,a^8\,b^9\,c^6\,d^{11}+713216\,a^7\,b^{10}\,c^7\,d^{10}-661504\,a^6\,b^{11}\,c^8\,d^9+486656\,a^5\,b^{12}\,c^9\,d^8-283136\,a^4\,b^{13}\,c^{10}\,d^7+121088\,a^3\,b^{14}\,c^{11}\,d^6-32768\,a^2\,b^{15}\,c^{12}\,d^5+4096\,a\,b^{16}\,c^{13}\,d^4\right)}{a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8}\right)+\frac{\sqrt{x}\,\left(-a^5\,b^8\,d^9+4\,a^4\,b^9\,c\,d^8+10\,a^3\,b^{10}\,c^2\,d^7+100\,a^2\,b^{11}\,c^3\,d^6-625\,a\,b^{12}\,c^4\,d^5\right)}{a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8}\right)+\frac{5\,a^4\,b^9\,d^8-75\,a^3\,b^{10}\,c\,d^7+375\,a^2\,b^{11}\,c^2\,d^6-625\,a\,b^{12}\,c^3\,d^5}{-a^7\,c^2\,d^7+7\,a^6\,b\,c^3\,d^6-21\,a^5\,b^2\,c^4\,d^5+35\,a^4\,b^3\,c^5\,d^4-35\,a^3\,b^4\,c^6\,d^3+21\,a^2\,b^5\,c^7\,d^2-7\,a\,b^6\,c^8\,d+b^7\,c^9}}\right)\,{\left(-\frac{b^5}{16\,a^9\,d^8-128\,a^8\,b\,c\,d^7+448\,a^7\,b^2\,c^2\,d^6-896\,a^6\,b^3\,c^3\,d^5+1120\,a^5\,b^4\,c^4\,d^4-896\,a^4\,b^5\,c^5\,d^3+448\,a^3\,b^6\,c^6\,d^2-128\,a^2\,b^7\,c^7\,d+16\,a\,b^8\,c^8}\right)}^{1/4}\,2{}\mathrm{i}-\mathrm{atan}\left(\frac{\left(\left(\frac{32\,a^{13}\,b^4\,d^{16}-704\,a^{12}\,b^5\,c\,d^{15}+6432\,a^{11}\,b^6\,c^2\,d^{14}-32000\,a^{10}\,b^7\,c^3\,d^{13}+96320\,a^9\,b^8\,c^4\,d^{12}-183424\,a^8\,b^9\,c^5\,d^{11}+219968\,a^7\,b^{10}\,c^6\,d^{10}-150784\,a^6\,b^{11}\,c^7\,d^9+29600\,a^5\,b^{12}\,c^8\,d^8+41280\,a^4\,b^{13}\,c^9\,d^7-39008\,a^3\,b^{14}\,c^{10}\,d^6+14336\,a^2\,b^{15}\,c^{11}\,d^5-2048\,a\,b^{16}\,c^{12}\,d^4}{-a^7\,c^2\,d^7+7\,a^6\,b\,c^3\,d^6-21\,a^5\,b^2\,c^4\,d^5+35\,a^4\,b^3\,c^5\,d^4-35\,a^3\,b^4\,c^6\,d^3+21\,a^2\,b^5\,c^7\,d^2-7\,a\,b^6\,c^8\,d+b^7\,c^9}+\frac{\sqrt{x}\,{\left(-\frac{a^4\,d^5-20\,a^3\,b\,c\,d^4+150\,a^2\,b^2\,c^2\,d^3-500\,a\,b^3\,c^3\,d^2+625\,b^4\,c^4\,d}{4096\,a^8\,c^5\,d^8-32768\,a^7\,b\,c^6\,d^7+114688\,a^6\,b^2\,c^7\,d^6-229376\,a^5\,b^3\,c^8\,d^5+286720\,a^4\,b^4\,c^9\,d^4-229376\,a^3\,b^5\,c^{10}\,d^3+114688\,a^2\,b^6\,c^{11}\,d^2-32768\,a\,b^7\,c^{12}\,d+4096\,b^8\,c^{13}}\right)}^{1/4}\,\left(256\,a^{13}\,b^4\,c\,d^{16}-4608\,a^{12}\,b^5\,c^2\,d^{15}+34048\,a^{11}\,b^6\,c^3\,d^{14}-137216\,a^{10}\,b^7\,c^4\,d^{13}+344576\,a^9\,b^8\,c^5\,d^{12}-584704\,a^8\,b^9\,c^6\,d^{11}+713216\,a^7\,b^{10}\,c^7\,d^{10}-661504\,a^6\,b^{11}\,c^8\,d^9+486656\,a^5\,b^{12}\,c^9\,d^8-283136\,a^4\,b^{13}\,c^{10}\,d^7+121088\,a^3\,b^{14}\,c^{11}\,d^6-32768\,a^2\,b^{15}\,c^{12}\,d^5+4096\,a\,b^{16}\,c^{13}\,d^4\right)}{a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8}\right)\,{\left(-\frac{a^4\,d^5-20\,a^3\,b\,c\,d^4+150\,a^2\,b^2\,c^2\,d^3-500\,a\,b^3\,c^3\,d^2+625\,b^4\,c^4\,d}{4096\,a^8\,c^5\,d^8-32768\,a^7\,b\,c^6\,d^7+114688\,a^6\,b^2\,c^7\,d^6-229376\,a^5\,b^3\,c^8\,d^5+286720\,a^4\,b^4\,c^9\,d^4-229376\,a^3\,b^5\,c^{10}\,d^3+114688\,a^2\,b^6\,c^{11}\,d^2-32768\,a\,b^7\,c^{12}\,d+4096\,b^8\,c^{13}}\right)}^{3/4}\,1{}\mathrm{i}-\frac{\sqrt{x}\,\left(-a^5\,b^8\,d^9+4\,a^4\,b^9\,c\,d^8+10\,a^3\,b^{10}\,c^2\,d^7+100\,a^2\,b^{11}\,c^3\,d^6-625\,a\,b^{12}\,c^4\,d^5\right)\,1{}\mathrm{i}}{a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8}\right)\,{\left(-\frac{a^4\,d^5-20\,a^3\,b\,c\,d^4+150\,a^2\,b^2\,c^2\,d^3-500\,a\,b^3\,c^3\,d^2+625\,b^4\,c^4\,d}{4096\,a^8\,c^5\,d^8-32768\,a^7\,b\,c^6\,d^7+114688\,a^6\,b^2\,c^7\,d^6-229376\,a^5\,b^3\,c^8\,d^5+286720\,a^4\,b^4\,c^9\,d^4-229376\,a^3\,b^5\,c^{10}\,d^3+114688\,a^2\,b^6\,c^{11}\,d^2-32768\,a\,b^7\,c^{12}\,d+4096\,b^8\,c^{13}}\right)}^{1/4}-\left(\left(\frac{32\,a^{13}\,b^4\,d^{16}-704\,a^{12}\,b^5\,c\,d^{15}+6432\,a^{11}\,b^6\,c^2\,d^{14}-32000\,a^{10}\,b^7\,c^3\,d^{13}+96320\,a^9\,b^8\,c^4\,d^{12}-183424\,a^8\,b^9\,c^5\,d^{11}+219968\,a^7\,b^{10}\,c^6\,d^{10}-150784\,a^6\,b^{11}\,c^7\,d^9+29600\,a^5\,b^{12}\,c^8\,d^8+41280\,a^4\,b^{13}\,c^9\,d^7-39008\,a^3\,b^{14}\,c^{10}\,d^6+14336\,a^2\,b^{15}\,c^{11}\,d^5-2048\,a\,b^{16}\,c^{12}\,d^4}{-a^7\,c^2\,d^7+7\,a^6\,b\,c^3\,d^6-21\,a^5\,b^2\,c^4\,d^5+35\,a^4\,b^3\,c^5\,d^4-35\,a^3\,b^4\,c^6\,d^3+21\,a^2\,b^5\,c^7\,d^2-7\,a\,b^6\,c^8\,d+b^7\,c^9}-\frac{\sqrt{x}\,{\left(-\frac{a^4\,d^5-20\,a^3\,b\,c\,d^4+150\,a^2\,b^2\,c^2\,d^3-500\,a\,b^3\,c^3\,d^2+625\,b^4\,c^4\,d}{4096\,a^8\,c^5\,d^8-32768\,a^7\,b\,c^6\,d^7+114688\,a^6\,b^2\,c^7\,d^6-229376\,a^5\,b^3\,c^8\,d^5+286720\,a^4\,b^4\,c^9\,d^4-229376\,a^3\,b^5\,c^{10}\,d^3+114688\,a^2\,b^6\,c^{11}\,d^2-32768\,a\,b^7\,c^{12}\,d+4096\,b^8\,c^{13}}\right)}^{1/4}\,\left(256\,a^{13}\,b^4\,c\,d^{16}-4608\,a^{12}\,b^5\,c^2\,d^{15}+34048\,a^{11}\,b^6\,c^3\,d^{14}-137216\,a^{10}\,b^7\,c^4\,d^{13}+344576\,a^9\,b^8\,c^5\,d^{12}-584704\,a^8\,b^9\,c^6\,d^{11}+713216\,a^7\,b^{10}\,c^7\,d^{10}-661504\,a^6\,b^{11}\,c^8\,d^9+486656\,a^5\,b^{12}\,c^9\,d^8-283136\,a^4\,b^{13}\,c^{10}\,d^7+121088\,a^3\,b^{14}\,c^{11}\,d^6-32768\,a^2\,b^{15}\,c^{12}\,d^5+4096\,a\,b^{16}\,c^{13}\,d^4\right)}{a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8}\right)\,{\left(-\frac{a^4\,d^5-20\,a^3\,b\,c\,d^4+150\,a^2\,b^2\,c^2\,d^3-500\,a\,b^3\,c^3\,d^2+625\,b^4\,c^4\,d}{4096\,a^8\,c^5\,d^8-32768\,a^7\,b\,c^6\,d^7+114688\,a^6\,b^2\,c^7\,d^6-229376\,a^5\,b^3\,c^8\,d^5+286720\,a^4\,b^4\,c^9\,d^4-229376\,a^3\,b^5\,c^{10}\,d^3+114688\,a^2\,b^6\,c^{11}\,d^2-32768\,a\,b^7\,c^{12}\,d+4096\,b^8\,c^{13}}\right)}^{3/4}\,1{}\mathrm{i}+\frac{\sqrt{x}\,\left(-a^5\,b^8\,d^9+4\,a^4\,b^9\,c\,d^8+10\,a^3\,b^{10}\,c^2\,d^7+100\,a^2\,b^{11}\,c^3\,d^6-625\,a\,b^{12}\,c^4\,d^5\right)\,1{}\mathrm{i}}{a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8}\right)\,{\left(-\frac{a^4\,d^5-20\,a^3\,b\,c\,d^4+150\,a^2\,b^2\,c^2\,d^3-500\,a\,b^3\,c^3\,d^2+625\,b^4\,c^4\,d}{4096\,a^8\,c^5\,d^8-32768\,a^7\,b\,c^6\,d^7+114688\,a^6\,b^2\,c^7\,d^6-229376\,a^5\,b^3\,c^8\,d^5+286720\,a^4\,b^4\,c^9\,d^4-229376\,a^3\,b^5\,c^{10}\,d^3+114688\,a^2\,b^6\,c^{11}\,d^2-32768\,a\,b^7\,c^{12}\,d+4096\,b^8\,c^{13}}\right)}^{1/4}}{\left(\left(\frac{32\,a^{13}\,b^4\,d^{16}-704\,a^{12}\,b^5\,c\,d^{15}+6432\,a^{11}\,b^6\,c^2\,d^{14}-32000\,a^{10}\,b^7\,c^3\,d^{13}+96320\,a^9\,b^8\,c^4\,d^{12}-183424\,a^8\,b^9\,c^5\,d^{11}+219968\,a^7\,b^{10}\,c^6\,d^{10}-150784\,a^6\,b^{11}\,c^7\,d^9+29600\,a^5\,b^{12}\,c^8\,d^8+41280\,a^4\,b^{13}\,c^9\,d^7-39008\,a^3\,b^{14}\,c^{10}\,d^6+14336\,a^2\,b^{15}\,c^{11}\,d^5-2048\,a\,b^{16}\,c^{12}\,d^4}{-a^7\,c^2\,d^7+7\,a^6\,b\,c^3\,d^6-21\,a^5\,b^2\,c^4\,d^5+35\,a^4\,b^3\,c^5\,d^4-35\,a^3\,b^4\,c^6\,d^3+21\,a^2\,b^5\,c^7\,d^2-7\,a\,b^6\,c^8\,d+b^7\,c^9}+\frac{\sqrt{x}\,{\left(-\frac{a^4\,d^5-20\,a^3\,b\,c\,d^4+150\,a^2\,b^2\,c^2\,d^3-500\,a\,b^3\,c^3\,d^2+625\,b^4\,c^4\,d}{4096\,a^8\,c^5\,d^8-32768\,a^7\,b\,c^6\,d^7+114688\,a^6\,b^2\,c^7\,d^6-229376\,a^5\,b^3\,c^8\,d^5+286720\,a^4\,b^4\,c^9\,d^4-229376\,a^3\,b^5\,c^{10}\,d^3+114688\,a^2\,b^6\,c^{11}\,d^2-32768\,a\,b^7\,c^{12}\,d+4096\,b^8\,c^{13}}\right)}^{1/4}\,\left(256\,a^{13}\,b^4\,c\,d^{16}-4608\,a^{12}\,b^5\,c^2\,d^{15}+34048\,a^{11}\,b^6\,c^3\,d^{14}-137216\,a^{10}\,b^7\,c^4\,d^{13}+344576\,a^9\,b^8\,c^5\,d^{12}-584704\,a^8\,b^9\,c^6\,d^{11}+713216\,a^7\,b^{10}\,c^7\,d^{10}-661504\,a^6\,b^{11}\,c^8\,d^9+486656\,a^5\,b^{12}\,c^9\,d^8-283136\,a^4\,b^{13}\,c^{10}\,d^7+121088\,a^3\,b^{14}\,c^{11}\,d^6-32768\,a^2\,b^{15}\,c^{12}\,d^5+4096\,a\,b^{16}\,c^{13}\,d^4\right)}{a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8}\right)\,{\left(-\frac{a^4\,d^5-20\,a^3\,b\,c\,d^4+150\,a^2\,b^2\,c^2\,d^3-500\,a\,b^3\,c^3\,d^2+625\,b^4\,c^4\,d}{4096\,a^8\,c^5\,d^8-32768\,a^7\,b\,c^6\,d^7+114688\,a^6\,b^2\,c^7\,d^6-229376\,a^5\,b^3\,c^8\,d^5+286720\,a^4\,b^4\,c^9\,d^4-229376\,a^3\,b^5\,c^{10}\,d^3+114688\,a^2\,b^6\,c^{11}\,d^2-32768\,a\,b^7\,c^{12}\,d+4096\,b^8\,c^{13}}\right)}^{3/4}-\frac{\sqrt{x}\,\left(-a^5\,b^8\,d^9+4\,a^4\,b^9\,c\,d^8+10\,a^3\,b^{10}\,c^2\,d^7+100\,a^2\,b^{11}\,c^3\,d^6-625\,a\,b^{12}\,c^4\,d^5\right)}{a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8}\right)\,{\left(-\frac{a^4\,d^5-20\,a^3\,b\,c\,d^4+150\,a^2\,b^2\,c^2\,d^3-500\,a\,b^3\,c^3\,d^2+625\,b^4\,c^4\,d}{4096\,a^8\,c^5\,d^8-32768\,a^7\,b\,c^6\,d^7+114688\,a^6\,b^2\,c^7\,d^6-229376\,a^5\,b^3\,c^8\,d^5+286720\,a^4\,b^4\,c^9\,d^4-229376\,a^3\,b^5\,c^{10}\,d^3+114688\,a^2\,b^6\,c^{11}\,d^2-32768\,a\,b^7\,c^{12}\,d+4096\,b^8\,c^{13}}\right)}^{1/4}+\left(\left(\frac{32\,a^{13}\,b^4\,d^{16}-704\,a^{12}\,b^5\,c\,d^{15}+6432\,a^{11}\,b^6\,c^2\,d^{14}-32000\,a^{10}\,b^7\,c^3\,d^{13}+96320\,a^9\,b^8\,c^4\,d^{12}-183424\,a^8\,b^9\,c^5\,d^{11}+219968\,a^7\,b^{10}\,c^6\,d^{10}-150784\,a^6\,b^{11}\,c^7\,d^9+29600\,a^5\,b^{12}\,c^8\,d^8+41280\,a^4\,b^{13}\,c^9\,d^7-39008\,a^3\,b^{14}\,c^{10}\,d^6+14336\,a^2\,b^{15}\,c^{11}\,d^5-2048\,a\,b^{16}\,c^{12}\,d^4}{-a^7\,c^2\,d^7+7\,a^6\,b\,c^3\,d^6-21\,a^5\,b^2\,c^4\,d^5+35\,a^4\,b^3\,c^5\,d^4-35\,a^3\,b^4\,c^6\,d^3+21\,a^2\,b^5\,c^7\,d^2-7\,a\,b^6\,c^8\,d+b^7\,c^9}-\frac{\sqrt{x}\,{\left(-\frac{a^4\,d^5-20\,a^3\,b\,c\,d^4+150\,a^2\,b^2\,c^2\,d^3-500\,a\,b^3\,c^3\,d^2+625\,b^4\,c^4\,d}{4096\,a^8\,c^5\,d^8-32768\,a^7\,b\,c^6\,d^7+114688\,a^6\,b^2\,c^7\,d^6-229376\,a^5\,b^3\,c^8\,d^5+286720\,a^4\,b^4\,c^9\,d^4-229376\,a^3\,b^5\,c^{10}\,d^3+114688\,a^2\,b^6\,c^{11}\,d^2-32768\,a\,b^7\,c^{12}\,d+4096\,b^8\,c^{13}}\right)}^{1/4}\,\left(256\,a^{13}\,b^4\,c\,d^{16}-4608\,a^{12}\,b^5\,c^2\,d^{15}+34048\,a^{11}\,b^6\,c^3\,d^{14}-137216\,a^{10}\,b^7\,c^4\,d^{13}+344576\,a^9\,b^8\,c^5\,d^{12}-584704\,a^8\,b^9\,c^6\,d^{11}+713216\,a^7\,b^{10}\,c^7\,d^{10}-661504\,a^6\,b^{11}\,c^8\,d^9+486656\,a^5\,b^{12}\,c^9\,d^8-283136\,a^4\,b^{13}\,c^{10}\,d^7+121088\,a^3\,b^{14}\,c^{11}\,d^6-32768\,a^2\,b^{15}\,c^{12}\,d^5+4096\,a\,b^{16}\,c^{13}\,d^4\right)}{a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8}\right)\,{\left(-\frac{a^4\,d^5-20\,a^3\,b\,c\,d^4+150\,a^2\,b^2\,c^2\,d^3-500\,a\,b^3\,c^3\,d^2+625\,b^4\,c^4\,d}{4096\,a^8\,c^5\,d^8-32768\,a^7\,b\,c^6\,d^7+114688\,a^6\,b^2\,c^7\,d^6-229376\,a^5\,b^3\,c^8\,d^5+286720\,a^4\,b^4\,c^9\,d^4-229376\,a^3\,b^5\,c^{10}\,d^3+114688\,a^2\,b^6\,c^{11}\,d^2-32768\,a\,b^7\,c^{12}\,d+4096\,b^8\,c^{13}}\right)}^{3/4}+\frac{\sqrt{x}\,\left(-a^5\,b^8\,d^9+4\,a^4\,b^9\,c\,d^8+10\,a^3\,b^{10}\,c^2\,d^7+100\,a^2\,b^{11}\,c^3\,d^6-625\,a\,b^{12}\,c^4\,d^5\right)}{a^6\,c^2\,d^6-6\,a^5\,b\,c^3\,d^5+15\,a^4\,b^2\,c^4\,d^4-20\,a^3\,b^3\,c^5\,d^3+15\,a^2\,b^4\,c^6\,d^2-6\,a\,b^5\,c^7\,d+b^6\,c^8}\right)\,{\left(-\frac{a^4\,d^5-20\,a^3\,b\,c\,d^4+150\,a^2\,b^2\,c^2\,d^3-500\,a\,b^3\,c^3\,d^2+625\,b^4\,c^4\,d}{4096\,a^8\,c^5\,d^8-32768\,a^7\,b\,c^6\,d^7+114688\,a^6\,b^2\,c^7\,d^6-229376\,a^5\,b^3\,c^8\,d^5+286720\,a^4\,b^4\,c^9\,d^4-229376\,a^3\,b^5\,c^{10}\,d^3+114688\,a^2\,b^6\,c^{11}\,d^2-32768\,a\,b^7\,c^{12}\,d+4096\,b^8\,c^{13}}\right)}^{1/4}+\frac{5\,a^4\,b^9\,d^8-75\,a^3\,b^{10}\,c\,d^7+375\,a^2\,b^{11}\,c^2\,d^6-625\,a\,b^{12}\,c^3\,d^5}{-a^7\,c^2\,d^7+7\,a^6\,b\,c^3\,d^6-21\,a^5\,b^2\,c^4\,d^5+35\,a^4\,b^3\,c^5\,d^4-35\,a^3\,b^4\,c^6\,d^3+21\,a^2\,b^5\,c^7\,d^2-7\,a\,b^6\,c^8\,d+b^7\,c^9}}\right)\,{\left(-\frac{a^4\,d^5-20\,a^3\,b\,c\,d^4+150\,a^2\,b^2\,c^2\,d^3-500\,a\,b^3\,c^3\,d^2+625\,b^4\,c^4\,d}{4096\,a^8\,c^5\,d^8-32768\,a^7\,b\,c^6\,d^7+114688\,a^6\,b^2\,c^7\,d^6-229376\,a^5\,b^3\,c^8\,d^5+286720\,a^4\,b^4\,c^9\,d^4-229376\,a^3\,b^5\,c^{10}\,d^3+114688\,a^2\,b^6\,c^{11}\,d^2-32768\,a\,b^7\,c^{12}\,d+4096\,b^8\,c^{13}}\right)}^{1/4}\,2{}\mathrm{i}","Not used",1,"2*atan(((-b^5/(16*a^9*d^8 + 16*a*b^8*c^8 - 128*a^2*b^7*c^7*d + 448*a^3*b^6*c^6*d^2 - 896*a^4*b^5*c^5*d^3 + 1120*a^5*b^4*c^4*d^4 - 896*a^6*b^3*c^3*d^5 + 448*a^7*b^2*c^2*d^6 - 128*a^8*b*c*d^7))^(1/4)*((-b^5/(16*a^9*d^8 + 16*a*b^8*c^8 - 128*a^2*b^7*c^7*d + 448*a^3*b^6*c^6*d^2 - 896*a^4*b^5*c^5*d^3 + 1120*a^5*b^4*c^4*d^4 - 896*a^6*b^3*c^3*d^5 + 448*a^7*b^2*c^2*d^6 - 128*a^8*b*c*d^7))^(3/4)*(((32*a^13*b^4*d^16 - 2048*a*b^16*c^12*d^4 - 704*a^12*b^5*c*d^15 + 14336*a^2*b^15*c^11*d^5 - 39008*a^3*b^14*c^10*d^6 + 41280*a^4*b^13*c^9*d^7 + 29600*a^5*b^12*c^8*d^8 - 150784*a^6*b^11*c^7*d^9 + 219968*a^7*b^10*c^6*d^10 - 183424*a^8*b^9*c^5*d^11 + 96320*a^9*b^8*c^4*d^12 - 32000*a^10*b^7*c^3*d^13 + 6432*a^11*b^6*c^2*d^14)*1i)/(b^7*c^9 - a^7*c^2*d^7 + 7*a^6*b*c^3*d^6 + 21*a^2*b^5*c^7*d^2 - 35*a^3*b^4*c^6*d^3 + 35*a^4*b^3*c^5*d^4 - 21*a^5*b^2*c^4*d^5 - 7*a*b^6*c^8*d) + (x^(1/2)*(-b^5/(16*a^9*d^8 + 16*a*b^8*c^8 - 128*a^2*b^7*c^7*d + 448*a^3*b^6*c^6*d^2 - 896*a^4*b^5*c^5*d^3 + 1120*a^5*b^4*c^4*d^4 - 896*a^6*b^3*c^3*d^5 + 448*a^7*b^2*c^2*d^6 - 128*a^8*b*c*d^7))^(1/4)*(4096*a*b^16*c^13*d^4 + 256*a^13*b^4*c*d^16 - 32768*a^2*b^15*c^12*d^5 + 121088*a^3*b^14*c^11*d^6 - 283136*a^4*b^13*c^10*d^7 + 486656*a^5*b^12*c^9*d^8 - 661504*a^6*b^11*c^8*d^9 + 713216*a^7*b^10*c^7*d^10 - 584704*a^8*b^9*c^6*d^11 + 344576*a^9*b^8*c^5*d^12 - 137216*a^10*b^7*c^4*d^13 + 34048*a^11*b^6*c^3*d^14 - 4608*a^12*b^5*c^2*d^15))/(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d)) - (x^(1/2)*(4*a^4*b^9*c*d^8 - 625*a*b^12*c^4*d^5 - a^5*b^8*d^9 + 100*a^2*b^11*c^3*d^6 + 10*a^3*b^10*c^2*d^7))/(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d)) - (-b^5/(16*a^9*d^8 + 16*a*b^8*c^8 - 128*a^2*b^7*c^7*d + 448*a^3*b^6*c^6*d^2 - 896*a^4*b^5*c^5*d^3 + 1120*a^5*b^4*c^4*d^4 - 896*a^6*b^3*c^3*d^5 + 448*a^7*b^2*c^2*d^6 - 128*a^8*b*c*d^7))^(1/4)*((-b^5/(16*a^9*d^8 + 16*a*b^8*c^8 - 128*a^2*b^7*c^7*d + 448*a^3*b^6*c^6*d^2 - 896*a^4*b^5*c^5*d^3 + 1120*a^5*b^4*c^4*d^4 - 896*a^6*b^3*c^3*d^5 + 448*a^7*b^2*c^2*d^6 - 128*a^8*b*c*d^7))^(3/4)*(((32*a^13*b^4*d^16 - 2048*a*b^16*c^12*d^4 - 704*a^12*b^5*c*d^15 + 14336*a^2*b^15*c^11*d^5 - 39008*a^3*b^14*c^10*d^6 + 41280*a^4*b^13*c^9*d^7 + 29600*a^5*b^12*c^8*d^8 - 150784*a^6*b^11*c^7*d^9 + 219968*a^7*b^10*c^6*d^10 - 183424*a^8*b^9*c^5*d^11 + 96320*a^9*b^8*c^4*d^12 - 32000*a^10*b^7*c^3*d^13 + 6432*a^11*b^6*c^2*d^14)*1i)/(b^7*c^9 - a^7*c^2*d^7 + 7*a^6*b*c^3*d^6 + 21*a^2*b^5*c^7*d^2 - 35*a^3*b^4*c^6*d^3 + 35*a^4*b^3*c^5*d^4 - 21*a^5*b^2*c^4*d^5 - 7*a*b^6*c^8*d) - (x^(1/2)*(-b^5/(16*a^9*d^8 + 16*a*b^8*c^8 - 128*a^2*b^7*c^7*d + 448*a^3*b^6*c^6*d^2 - 896*a^4*b^5*c^5*d^3 + 1120*a^5*b^4*c^4*d^4 - 896*a^6*b^3*c^3*d^5 + 448*a^7*b^2*c^2*d^6 - 128*a^8*b*c*d^7))^(1/4)*(4096*a*b^16*c^13*d^4 + 256*a^13*b^4*c*d^16 - 32768*a^2*b^15*c^12*d^5 + 121088*a^3*b^14*c^11*d^6 - 283136*a^4*b^13*c^10*d^7 + 486656*a^5*b^12*c^9*d^8 - 661504*a^6*b^11*c^8*d^9 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39008*a^3*b^14*c^10*d^6 + 41280*a^4*b^13*c^9*d^7 + 29600*a^5*b^12*c^8*d^8 - 150784*a^6*b^11*c^7*d^9 + 219968*a^7*b^10*c^6*d^10 - 183424*a^8*b^9*c^5*d^11 + 96320*a^9*b^8*c^4*d^12 - 32000*a^10*b^7*c^3*d^13 + 6432*a^11*b^6*c^2*d^14)*1i)/(b^7*c^9 - a^7*c^2*d^7 + 7*a^6*b*c^3*d^6 + 21*a^2*b^5*c^7*d^2 - 35*a^3*b^4*c^6*d^3 + 35*a^4*b^3*c^5*d^4 - 21*a^5*b^2*c^4*d^5 - 7*a*b^6*c^8*d) + (x^(1/2)*(-b^5/(16*a^9*d^8 + 16*a*b^8*c^8 - 128*a^2*b^7*c^7*d + 448*a^3*b^6*c^6*d^2 - 896*a^4*b^5*c^5*d^3 + 1120*a^5*b^4*c^4*d^4 - 896*a^6*b^3*c^3*d^5 + 448*a^7*b^2*c^2*d^6 - 128*a^8*b*c*d^7))^(1/4)*(4096*a*b^16*c^13*d^4 + 256*a^13*b^4*c*d^16 - 32768*a^2*b^15*c^12*d^5 + 121088*a^3*b^14*c^11*d^6 - 283136*a^4*b^13*c^10*d^7 + 486656*a^5*b^12*c^9*d^8 - 661504*a^6*b^11*c^8*d^9 + 713216*a^7*b^10*c^7*d^10 - 584704*a^8*b^9*c^6*d^11 + 344576*a^9*b^8*c^5*d^12 - 137216*a^10*b^7*c^4*d^13 + 34048*a^11*b^6*c^3*d^14 - 4608*a^12*b^5*c^2*d^15))/(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d))*1i - (x^(1/2)*(4*a^4*b^9*c*d^8 - 625*a*b^12*c^4*d^5 - a^5*b^8*d^9 + 100*a^2*b^11*c^3*d^6 + 10*a^3*b^10*c^2*d^7)*1i)/(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d)) + (-b^5/(16*a^9*d^8 + 16*a*b^8*c^8 - 128*a^2*b^7*c^7*d + 448*a^3*b^6*c^6*d^2 - 896*a^4*b^5*c^5*d^3 + 1120*a^5*b^4*c^4*d^4 - 896*a^6*b^3*c^3*d^5 + 448*a^7*b^2*c^2*d^6 - 128*a^8*b*c*d^7))^(1/4)*((-b^5/(16*a^9*d^8 + 16*a*b^8*c^8 - 128*a^2*b^7*c^7*d + 448*a^3*b^6*c^6*d^2 - 896*a^4*b^5*c^5*d^3 + 1120*a^5*b^4*c^4*d^4 - 896*a^6*b^3*c^3*d^5 + 448*a^7*b^2*c^2*d^6 - 128*a^8*b*c*d^7))^(3/4)*(((32*a^13*b^4*d^16 - 2048*a*b^16*c^12*d^4 - 704*a^12*b^5*c*d^15 + 14336*a^2*b^15*c^11*d^5 - 39008*a^3*b^14*c^10*d^6 + 41280*a^4*b^13*c^9*d^7 + 29600*a^5*b^12*c^8*d^8 - 150784*a^6*b^11*c^7*d^9 + 219968*a^7*b^10*c^6*d^10 - 183424*a^8*b^9*c^5*d^11 + 96320*a^9*b^8*c^4*d^12 - 32000*a^10*b^7*c^3*d^13 + 6432*a^11*b^6*c^2*d^14)*1i)/(b^7*c^9 - a^7*c^2*d^7 + 7*a^6*b*c^3*d^6 + 21*a^2*b^5*c^7*d^2 - 35*a^3*b^4*c^6*d^3 + 35*a^4*b^3*c^5*d^4 - 21*a^5*b^2*c^4*d^5 - 7*a*b^6*c^8*d) - (x^(1/2)*(-b^5/(16*a^9*d^8 + 16*a*b^8*c^8 - 128*a^2*b^7*c^7*d + 448*a^3*b^6*c^6*d^2 - 896*a^4*b^5*c^5*d^3 + 1120*a^5*b^4*c^4*d^4 - 896*a^6*b^3*c^3*d^5 + 448*a^7*b^2*c^2*d^6 - 128*a^8*b*c*d^7))^(1/4)*(4096*a*b^16*c^13*d^4 + 256*a^13*b^4*c*d^16 - 32768*a^2*b^15*c^12*d^5 + 121088*a^3*b^14*c^11*d^6 - 283136*a^4*b^13*c^10*d^7 + 486656*a^5*b^12*c^9*d^8 - 661504*a^6*b^11*c^8*d^9 + 713216*a^7*b^10*c^7*d^10 - 584704*a^8*b^9*c^6*d^11 + 344576*a^9*b^8*c^5*d^12 - 137216*a^10*b^7*c^4*d^13 + 34048*a^11*b^6*c^3*d^14 - 4608*a^12*b^5*c^2*d^15))/(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d))*1i + (x^(1/2)*(4*a^4*b^9*c*d^8 - 625*a*b^12*c^4*d^5 - a^5*b^8*d^9 + 100*a^2*b^11*c^3*d^6 + 10*a^3*b^10*c^2*d^7)*1i)/(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d)) - (5*a^4*b^9*d^8 - 625*a*b^12*c^3*d^5 - 75*a^3*b^10*c*d^7 + 375*a^2*b^11*c^2*d^6)/(b^7*c^9 - a^7*c^2*d^7 + 7*a^6*b*c^3*d^6 + 21*a^2*b^5*c^7*d^2 - 35*a^3*b^4*c^6*d^3 + 35*a^4*b^3*c^5*d^4 - 21*a^5*b^2*c^4*d^5 - 7*a*b^6*c^8*d)))*(-b^5/(16*a^9*d^8 + 16*a*b^8*c^8 - 128*a^2*b^7*c^7*d + 448*a^3*b^6*c^6*d^2 - 896*a^4*b^5*c^5*d^3 + 1120*a^5*b^4*c^4*d^4 - 896*a^6*b^3*c^3*d^5 + 448*a^7*b^2*c^2*d^6 - 128*a^8*b*c*d^7))^(1/4) - atan(((-b^5/(16*a^9*d^8 + 16*a*b^8*c^8 - 128*a^2*b^7*c^7*d + 448*a^3*b^6*c^6*d^2 - 896*a^4*b^5*c^5*d^3 + 1120*a^5*b^4*c^4*d^4 - 896*a^6*b^3*c^3*d^5 + 448*a^7*b^2*c^2*d^6 - 128*a^8*b*c*d^7))^(1/4)*((-b^5/(16*a^9*d^8 + 16*a*b^8*c^8 - 128*a^2*b^7*c^7*d + 448*a^3*b^6*c^6*d^2 - 896*a^4*b^5*c^5*d^3 + 1120*a^5*b^4*c^4*d^4 - 896*a^6*b^3*c^3*d^5 + 448*a^7*b^2*c^2*d^6 - 128*a^8*b*c*d^7))^(3/4)*((32*a^13*b^4*d^16 - 2048*a*b^16*c^12*d^4 - 704*a^12*b^5*c*d^15 + 14336*a^2*b^15*c^11*d^5 - 39008*a^3*b^14*c^10*d^6 + 41280*a^4*b^13*c^9*d^7 + 29600*a^5*b^12*c^8*d^8 - 150784*a^6*b^11*c^7*d^9 + 219968*a^7*b^10*c^6*d^10 - 183424*a^8*b^9*c^5*d^11 + 96320*a^9*b^8*c^4*d^12 - 32000*a^10*b^7*c^3*d^13 + 6432*a^11*b^6*c^2*d^14)/(b^7*c^9 - a^7*c^2*d^7 + 7*a^6*b*c^3*d^6 + 21*a^2*b^5*c^7*d^2 - 35*a^3*b^4*c^6*d^3 + 35*a^4*b^3*c^5*d^4 - 21*a^5*b^2*c^4*d^5 - 7*a*b^6*c^8*d) + (x^(1/2)*(-b^5/(16*a^9*d^8 + 16*a*b^8*c^8 - 128*a^2*b^7*c^7*d + 448*a^3*b^6*c^6*d^2 - 896*a^4*b^5*c^5*d^3 + 1120*a^5*b^4*c^4*d^4 - 896*a^6*b^3*c^3*d^5 + 448*a^7*b^2*c^2*d^6 - 128*a^8*b*c*d^7))^(1/4)*(4096*a*b^16*c^13*d^4 + 256*a^13*b^4*c*d^16 - 32768*a^2*b^15*c^12*d^5 + 121088*a^3*b^14*c^11*d^6 - 283136*a^4*b^13*c^10*d^7 + 486656*a^5*b^12*c^9*d^8 - 661504*a^6*b^11*c^8*d^9 + 713216*a^7*b^10*c^7*d^10 - 584704*a^8*b^9*c^6*d^11 + 344576*a^9*b^8*c^5*d^12 - 137216*a^10*b^7*c^4*d^13 + 34048*a^11*b^6*c^3*d^14 - 4608*a^12*b^5*c^2*d^15))/(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d))*1i - (x^(1/2)*(4*a^4*b^9*c*d^8 - 625*a*b^12*c^4*d^5 - a^5*b^8*d^9 + 100*a^2*b^11*c^3*d^6 + 10*a^3*b^10*c^2*d^7)*1i)/(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d)) - (-b^5/(16*a^9*d^8 + 16*a*b^8*c^8 - 128*a^2*b^7*c^7*d + 448*a^3*b^6*c^6*d^2 - 896*a^4*b^5*c^5*d^3 + 1120*a^5*b^4*c^4*d^4 - 896*a^6*b^3*c^3*d^5 + 448*a^7*b^2*c^2*d^6 - 128*a^8*b*c*d^7))^(1/4)*((-b^5/(16*a^9*d^8 + 16*a*b^8*c^8 - 128*a^2*b^7*c^7*d + 448*a^3*b^6*c^6*d^2 - 896*a^4*b^5*c^5*d^3 + 1120*a^5*b^4*c^4*d^4 - 896*a^6*b^3*c^3*d^5 + 448*a^7*b^2*c^2*d^6 - 128*a^8*b*c*d^7))^(3/4)*((32*a^13*b^4*d^16 - 2048*a*b^16*c^12*d^4 - 704*a^12*b^5*c*d^15 + 14336*a^2*b^15*c^11*d^5 - 39008*a^3*b^14*c^10*d^6 + 41280*a^4*b^13*c^9*d^7 + 29600*a^5*b^12*c^8*d^8 - 150784*a^6*b^11*c^7*d^9 + 219968*a^7*b^10*c^6*d^10 - 183424*a^8*b^9*c^5*d^11 + 96320*a^9*b^8*c^4*d^12 - 32000*a^10*b^7*c^3*d^13 + 6432*a^11*b^6*c^2*d^14)/(b^7*c^9 - a^7*c^2*d^7 + 7*a^6*b*c^3*d^6 + 21*a^2*b^5*c^7*d^2 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16*a*b^8*c^8 - 128*a^2*b^7*c^7*d + 448*a^3*b^6*c^6*d^2 - 896*a^4*b^5*c^5*d^3 + 1120*a^5*b^4*c^4*d^4 - 896*a^6*b^3*c^3*d^5 + 448*a^7*b^2*c^2*d^6 - 128*a^8*b*c*d^7))^(1/4)*((-b^5/(16*a^9*d^8 + 16*a*b^8*c^8 - 128*a^2*b^7*c^7*d + 448*a^3*b^6*c^6*d^2 - 896*a^4*b^5*c^5*d^3 + 1120*a^5*b^4*c^4*d^4 - 896*a^6*b^3*c^3*d^5 + 448*a^7*b^2*c^2*d^6 - 128*a^8*b*c*d^7))^(3/4)*((32*a^13*b^4*d^16 - 2048*a*b^16*c^12*d^4 - 704*a^12*b^5*c*d^15 + 14336*a^2*b^15*c^11*d^5 - 39008*a^3*b^14*c^10*d^6 + 41280*a^4*b^13*c^9*d^7 + 29600*a^5*b^12*c^8*d^8 - 150784*a^6*b^11*c^7*d^9 + 219968*a^7*b^10*c^6*d^10 - 183424*a^8*b^9*c^5*d^11 + 96320*a^9*b^8*c^4*d^12 - 32000*a^10*b^7*c^3*d^13 + 6432*a^11*b^6*c^2*d^14)/(b^7*c^9 - a^7*c^2*d^7 + 7*a^6*b*c^3*d^6 + 21*a^2*b^5*c^7*d^2 - 35*a^3*b^4*c^6*d^3 + 35*a^4*b^3*c^5*d^4 - 21*a^5*b^2*c^4*d^5 - 7*a*b^6*c^8*d) + (x^(1/2)*(-b^5/(16*a^9*d^8 + 16*a*b^8*c^8 - 128*a^2*b^7*c^7*d + 448*a^3*b^6*c^6*d^2 - 896*a^4*b^5*c^5*d^3 + 1120*a^5*b^4*c^4*d^4 - 896*a^6*b^3*c^3*d^5 + 448*a^7*b^2*c^2*d^6 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896*a^4*b^5*c^5*d^3 + 1120*a^5*b^4*c^4*d^4 - 896*a^6*b^3*c^3*d^5 + 448*a^7*b^2*c^2*d^6 - 128*a^8*b*c*d^7))^(3/4)*((32*a^13*b^4*d^16 - 2048*a*b^16*c^12*d^4 - 704*a^12*b^5*c*d^15 + 14336*a^2*b^15*c^11*d^5 - 39008*a^3*b^14*c^10*d^6 + 41280*a^4*b^13*c^9*d^7 + 29600*a^5*b^12*c^8*d^8 - 150784*a^6*b^11*c^7*d^9 + 219968*a^7*b^10*c^6*d^10 - 183424*a^8*b^9*c^5*d^11 + 96320*a^9*b^8*c^4*d^12 - 32000*a^10*b^7*c^3*d^13 + 6432*a^11*b^6*c^2*d^14)/(b^7*c^9 - a^7*c^2*d^7 + 7*a^6*b*c^3*d^6 + 21*a^2*b^5*c^7*d^2 - 35*a^3*b^4*c^6*d^3 + 35*a^4*b^3*c^5*d^4 - 21*a^5*b^2*c^4*d^5 - 7*a*b^6*c^8*d) - (x^(1/2)*(-b^5/(16*a^9*d^8 + 16*a*b^8*c^8 - 128*a^2*b^7*c^7*d + 448*a^3*b^6*c^6*d^2 - 896*a^4*b^5*c^5*d^3 + 1120*a^5*b^4*c^4*d^4 - 896*a^6*b^3*c^3*d^5 + 448*a^7*b^2*c^2*d^6 - 128*a^8*b*c*d^7))^(1/4)*(4096*a*b^16*c^13*d^4 + 256*a^13*b^4*c*d^16 - 32768*a^2*b^15*c^12*d^5 + 121088*a^3*b^14*c^11*d^6 - 283136*a^4*b^13*c^10*d^7 + 486656*a^5*b^12*c^9*d^8 - 661504*a^6*b^11*c^8*d^9 + 713216*a^7*b^10*c^7*d^10 - 584704*a^8*b^9*c^6*d^11 + 344576*a^9*b^8*c^5*d^12 - 137216*a^10*b^7*c^4*d^13 + 34048*a^11*b^6*c^3*d^14 - 4608*a^12*b^5*c^2*d^15))/(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d)) + (x^(1/2)*(4*a^4*b^9*c*d^8 - 625*a*b^12*c^4*d^5 - a^5*b^8*d^9 + 100*a^2*b^11*c^3*d^6 + 10*a^3*b^10*c^2*d^7))/(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d)) + (5*a^4*b^9*d^8 - 625*a*b^12*c^3*d^5 - 75*a^3*b^10*c*d^7 + 375*a^2*b^11*c^2*d^6)/(b^7*c^9 - a^7*c^2*d^7 + 7*a^6*b*c^3*d^6 + 21*a^2*b^5*c^7*d^2 - 35*a^3*b^4*c^6*d^3 + 35*a^4*b^3*c^5*d^4 - 21*a^5*b^2*c^4*d^5 - 7*a*b^6*c^8*d)))*(-b^5/(16*a^9*d^8 + 16*a*b^8*c^8 - 128*a^2*b^7*c^7*d + 448*a^3*b^6*c^6*d^2 - 896*a^4*b^5*c^5*d^3 + 1120*a^5*b^4*c^4*d^4 - 896*a^6*b^3*c^3*d^5 + 448*a^7*b^2*c^2*d^6 - 128*a^8*b*c*d^7))^(1/4)*2i - atan(((((32*a^13*b^4*d^16 - 2048*a*b^16*c^12*d^4 - 704*a^12*b^5*c*d^15 + 14336*a^2*b^15*c^11*d^5 - 39008*a^3*b^14*c^10*d^6 + 41280*a^4*b^13*c^9*d^7 + 29600*a^5*b^12*c^8*d^8 - 150784*a^6*b^11*c^7*d^9 + 219968*a^7*b^10*c^6*d^10 - 183424*a^8*b^9*c^5*d^11 + 96320*a^9*b^8*c^4*d^12 - 32000*a^10*b^7*c^3*d^13 + 6432*a^11*b^6*c^2*d^14)/(b^7*c^9 - a^7*c^2*d^7 + 7*a^6*b*c^3*d^6 + 21*a^2*b^5*c^7*d^2 - 35*a^3*b^4*c^6*d^3 + 35*a^4*b^3*c^5*d^4 - 21*a^5*b^2*c^4*d^5 - 7*a*b^6*c^8*d) + (x^(1/2)*(-(a^4*d^5 + 625*b^4*c^4*d - 500*a*b^3*c^3*d^2 + 150*a^2*b^2*c^2*d^3 - 20*a^3*b*c*d^4)/(4096*b^8*c^13 + 4096*a^8*c^5*d^8 - 32768*a^7*b*c^6*d^7 + 114688*a^2*b^6*c^11*d^2 - 229376*a^3*b^5*c^10*d^3 + 286720*a^4*b^4*c^9*d^4 - 229376*a^5*b^3*c^8*d^5 + 114688*a^6*b^2*c^7*d^6 - 32768*a*b^7*c^12*d))^(1/4)*(4096*a*b^16*c^13*d^4 + 256*a^13*b^4*c*d^16 - 32768*a^2*b^15*c^12*d^5 + 121088*a^3*b^14*c^11*d^6 - 283136*a^4*b^13*c^10*d^7 + 486656*a^5*b^12*c^9*d^8 - 661504*a^6*b^11*c^8*d^9 + 713216*a^7*b^10*c^7*d^10 - 584704*a^8*b^9*c^6*d^11 + 344576*a^9*b^8*c^5*d^12 - 137216*a^10*b^7*c^4*d^13 + 34048*a^11*b^6*c^3*d^14 - 4608*a^12*b^5*c^2*d^15))/(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d))*(-(a^4*d^5 + 625*b^4*c^4*d - 500*a*b^3*c^3*d^2 + 150*a^2*b^2*c^2*d^3 - 20*a^3*b*c*d^4)/(4096*b^8*c^13 + 4096*a^8*c^5*d^8 - 32768*a^7*b*c^6*d^7 + 114688*a^2*b^6*c^11*d^2 - 229376*a^3*b^5*c^10*d^3 + 286720*a^4*b^4*c^9*d^4 - 229376*a^5*b^3*c^8*d^5 + 114688*a^6*b^2*c^7*d^6 - 32768*a*b^7*c^12*d))^(3/4)*1i - (x^(1/2)*(4*a^4*b^9*c*d^8 - 625*a*b^12*c^4*d^5 - a^5*b^8*d^9 + 100*a^2*b^11*c^3*d^6 + 10*a^3*b^10*c^2*d^7)*1i)/(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d))*(-(a^4*d^5 + 625*b^4*c^4*d - 500*a*b^3*c^3*d^2 + 150*a^2*b^2*c^2*d^3 - 20*a^3*b*c*d^4)/(4096*b^8*c^13 + 4096*a^8*c^5*d^8 - 32768*a^7*b*c^6*d^7 + 114688*a^2*b^6*c^11*d^2 - 229376*a^3*b^5*c^10*d^3 + 286720*a^4*b^4*c^9*d^4 - 229376*a^5*b^3*c^8*d^5 + 114688*a^6*b^2*c^7*d^6 - 32768*a*b^7*c^12*d))^(1/4) - (((32*a^13*b^4*d^16 - 2048*a*b^16*c^12*d^4 - 704*a^12*b^5*c*d^15 + 14336*a^2*b^15*c^11*d^5 - 39008*a^3*b^14*c^10*d^6 + 41280*a^4*b^13*c^9*d^7 + 29600*a^5*b^12*c^8*d^8 - 150784*a^6*b^11*c^7*d^9 + 219968*a^7*b^10*c^6*d^10 - 183424*a^8*b^9*c^5*d^11 + 96320*a^9*b^8*c^4*d^12 - 32000*a^10*b^7*c^3*d^13 + 6432*a^11*b^6*c^2*d^14)/(b^7*c^9 - a^7*c^2*d^7 + 7*a^6*b*c^3*d^6 + 21*a^2*b^5*c^7*d^2 - 35*a^3*b^4*c^6*d^3 + 35*a^4*b^3*c^5*d^4 - 21*a^5*b^2*c^4*d^5 - 7*a*b^6*c^8*d) - (x^(1/2)*(-(a^4*d^5 + 625*b^4*c^4*d - 500*a*b^3*c^3*d^2 + 150*a^2*b^2*c^2*d^3 - 20*a^3*b*c*d^4)/(4096*b^8*c^13 + 4096*a^8*c^5*d^8 - 32768*a^7*b*c^6*d^7 + 114688*a^2*b^6*c^11*d^2 - 229376*a^3*b^5*c^10*d^3 + 286720*a^4*b^4*c^9*d^4 - 229376*a^5*b^3*c^8*d^5 + 114688*a^6*b^2*c^7*d^6 - 32768*a*b^7*c^12*d))^(1/4)*(4096*a*b^16*c^13*d^4 + 256*a^13*b^4*c*d^16 - 32768*a^2*b^15*c^12*d^5 + 121088*a^3*b^14*c^11*d^6 - 283136*a^4*b^13*c^10*d^7 + 486656*a^5*b^12*c^9*d^8 - 661504*a^6*b^11*c^8*d^9 + 713216*a^7*b^10*c^7*d^10 - 584704*a^8*b^9*c^6*d^11 + 344576*a^9*b^8*c^5*d^12 - 137216*a^10*b^7*c^4*d^13 + 34048*a^11*b^6*c^3*d^14 - 4608*a^12*b^5*c^2*d^15))/(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d))*(-(a^4*d^5 + 625*b^4*c^4*d - 500*a*b^3*c^3*d^2 + 150*a^2*b^2*c^2*d^3 - 20*a^3*b*c*d^4)/(4096*b^8*c^13 + 4096*a^8*c^5*d^8 - 32768*a^7*b*c^6*d^7 + 114688*a^2*b^6*c^11*d^2 - 229376*a^3*b^5*c^10*d^3 + 286720*a^4*b^4*c^9*d^4 - 229376*a^5*b^3*c^8*d^5 + 114688*a^6*b^2*c^7*d^6 - 32768*a*b^7*c^12*d))^(3/4)*1i + (x^(1/2)*(4*a^4*b^9*c*d^8 - 625*a*b^12*c^4*d^5 - a^5*b^8*d^9 + 100*a^2*b^11*c^3*d^6 + 10*a^3*b^10*c^2*d^7)*1i)/(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d))*(-(a^4*d^5 + 625*b^4*c^4*d - 500*a*b^3*c^3*d^2 + 150*a^2*b^2*c^2*d^3 - 20*a^3*b*c*d^4)/(4096*b^8*c^13 + 4096*a^8*c^5*d^8 - 32768*a^7*b*c^6*d^7 + 114688*a^2*b^6*c^11*d^2 - 229376*a^3*b^5*c^10*d^3 + 286720*a^4*b^4*c^9*d^4 - 229376*a^5*b^3*c^8*d^5 + 114688*a^6*b^2*c^7*d^6 - 32768*a*b^7*c^12*d))^(1/4))/((((32*a^13*b^4*d^16 - 2048*a*b^16*c^12*d^4 - 704*a^12*b^5*c*d^15 + 14336*a^2*b^15*c^11*d^5 - 39008*a^3*b^14*c^10*d^6 + 41280*a^4*b^13*c^9*d^7 + 29600*a^5*b^12*c^8*d^8 - 150784*a^6*b^11*c^7*d^9 + 219968*a^7*b^10*c^6*d^10 - 183424*a^8*b^9*c^5*d^11 + 96320*a^9*b^8*c^4*d^12 - 32000*a^10*b^7*c^3*d^13 + 6432*a^11*b^6*c^2*d^14)/(b^7*c^9 - a^7*c^2*d^7 + 7*a^6*b*c^3*d^6 + 21*a^2*b^5*c^7*d^2 - 35*a^3*b^4*c^6*d^3 + 35*a^4*b^3*c^5*d^4 - 21*a^5*b^2*c^4*d^5 - 7*a*b^6*c^8*d) + (x^(1/2)*(-(a^4*d^5 + 625*b^4*c^4*d - 500*a*b^3*c^3*d^2 + 150*a^2*b^2*c^2*d^3 - 20*a^3*b*c*d^4)/(4096*b^8*c^13 + 4096*a^8*c^5*d^8 - 32768*a^7*b*c^6*d^7 + 114688*a^2*b^6*c^11*d^2 - 229376*a^3*b^5*c^10*d^3 + 286720*a^4*b^4*c^9*d^4 - 229376*a^5*b^3*c^8*d^5 + 114688*a^6*b^2*c^7*d^6 - 32768*a*b^7*c^12*d))^(1/4)*(4096*a*b^16*c^13*d^4 + 256*a^13*b^4*c*d^16 - 32768*a^2*b^15*c^12*d^5 + 121088*a^3*b^14*c^11*d^6 - 283136*a^4*b^13*c^10*d^7 + 486656*a^5*b^12*c^9*d^8 - 661504*a^6*b^11*c^8*d^9 + 713216*a^7*b^10*c^7*d^10 - 584704*a^8*b^9*c^6*d^11 + 344576*a^9*b^8*c^5*d^12 - 137216*a^10*b^7*c^4*d^13 + 34048*a^11*b^6*c^3*d^14 - 4608*a^12*b^5*c^2*d^15))/(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d))*(-(a^4*d^5 + 625*b^4*c^4*d - 500*a*b^3*c^3*d^2 + 150*a^2*b^2*c^2*d^3 - 20*a^3*b*c*d^4)/(4096*b^8*c^13 + 4096*a^8*c^5*d^8 - 32768*a^7*b*c^6*d^7 + 114688*a^2*b^6*c^11*d^2 - 229376*a^3*b^5*c^10*d^3 + 286720*a^4*b^4*c^9*d^4 - 229376*a^5*b^3*c^8*d^5 + 114688*a^6*b^2*c^7*d^6 - 32768*a*b^7*c^12*d))^(3/4) - (x^(1/2)*(4*a^4*b^9*c*d^8 - 625*a*b^12*c^4*d^5 - a^5*b^8*d^9 + 100*a^2*b^11*c^3*d^6 + 10*a^3*b^10*c^2*d^7))/(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d))*(-(a^4*d^5 + 625*b^4*c^4*d - 500*a*b^3*c^3*d^2 + 150*a^2*b^2*c^2*d^3 - 20*a^3*b*c*d^4)/(4096*b^8*c^13 + 4096*a^8*c^5*d^8 - 32768*a^7*b*c^6*d^7 + 114688*a^2*b^6*c^11*d^2 - 229376*a^3*b^5*c^10*d^3 + 286720*a^4*b^4*c^9*d^4 - 229376*a^5*b^3*c^8*d^5 + 114688*a^6*b^2*c^7*d^6 - 32768*a*b^7*c^12*d))^(1/4) + (((32*a^13*b^4*d^16 - 2048*a*b^16*c^12*d^4 - 704*a^12*b^5*c*d^15 + 14336*a^2*b^15*c^11*d^5 - 39008*a^3*b^14*c^10*d^6 + 41280*a^4*b^13*c^9*d^7 + 29600*a^5*b^12*c^8*d^8 - 150784*a^6*b^11*c^7*d^9 + 219968*a^7*b^10*c^6*d^10 - 183424*a^8*b^9*c^5*d^11 + 96320*a^9*b^8*c^4*d^12 - 32000*a^10*b^7*c^3*d^13 + 6432*a^11*b^6*c^2*d^14)/(b^7*c^9 - a^7*c^2*d^7 + 7*a^6*b*c^3*d^6 + 21*a^2*b^5*c^7*d^2 - 35*a^3*b^4*c^6*d^3 + 35*a^4*b^3*c^5*d^4 - 21*a^5*b^2*c^4*d^5 - 7*a*b^6*c^8*d) - (x^(1/2)*(-(a^4*d^5 + 625*b^4*c^4*d - 500*a*b^3*c^3*d^2 + 150*a^2*b^2*c^2*d^3 - 20*a^3*b*c*d^4)/(4096*b^8*c^13 + 4096*a^8*c^5*d^8 - 32768*a^7*b*c^6*d^7 + 114688*a^2*b^6*c^11*d^2 - 229376*a^3*b^5*c^10*d^3 + 286720*a^4*b^4*c^9*d^4 - 229376*a^5*b^3*c^8*d^5 + 114688*a^6*b^2*c^7*d^6 - 32768*a*b^7*c^12*d))^(1/4)*(4096*a*b^16*c^13*d^4 + 256*a^13*b^4*c*d^16 - 32768*a^2*b^15*c^12*d^5 + 121088*a^3*b^14*c^11*d^6 - 283136*a^4*b^13*c^10*d^7 + 486656*a^5*b^12*c^9*d^8 - 661504*a^6*b^11*c^8*d^9 + 713216*a^7*b^10*c^7*d^10 - 584704*a^8*b^9*c^6*d^11 + 344576*a^9*b^8*c^5*d^12 - 137216*a^10*b^7*c^4*d^13 + 34048*a^11*b^6*c^3*d^14 - 4608*a^12*b^5*c^2*d^15))/(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d))*(-(a^4*d^5 + 625*b^4*c^4*d - 500*a*b^3*c^3*d^2 + 150*a^2*b^2*c^2*d^3 - 20*a^3*b*c*d^4)/(4096*b^8*c^13 + 4096*a^8*c^5*d^8 - 32768*a^7*b*c^6*d^7 + 114688*a^2*b^6*c^11*d^2 - 229376*a^3*b^5*c^10*d^3 + 286720*a^4*b^4*c^9*d^4 - 229376*a^5*b^3*c^8*d^5 + 114688*a^6*b^2*c^7*d^6 - 32768*a*b^7*c^12*d))^(3/4) + (x^(1/2)*(4*a^4*b^9*c*d^8 - 625*a*b^12*c^4*d^5 - a^5*b^8*d^9 + 100*a^2*b^11*c^3*d^6 + 10*a^3*b^10*c^2*d^7))/(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d))*(-(a^4*d^5 + 625*b^4*c^4*d - 500*a*b^3*c^3*d^2 + 150*a^2*b^2*c^2*d^3 - 20*a^3*b*c*d^4)/(4096*b^8*c^13 + 4096*a^8*c^5*d^8 - 32768*a^7*b*c^6*d^7 + 114688*a^2*b^6*c^11*d^2 - 229376*a^3*b^5*c^10*d^3 + 286720*a^4*b^4*c^9*d^4 - 229376*a^5*b^3*c^8*d^5 + 114688*a^6*b^2*c^7*d^6 - 32768*a*b^7*c^12*d))^(1/4) + (5*a^4*b^9*d^8 - 625*a*b^12*c^3*d^5 - 75*a^3*b^10*c*d^7 + 375*a^2*b^11*c^2*d^6)/(b^7*c^9 - a^7*c^2*d^7 + 7*a^6*b*c^3*d^6 + 21*a^2*b^5*c^7*d^2 - 35*a^3*b^4*c^6*d^3 + 35*a^4*b^3*c^5*d^4 - 21*a^5*b^2*c^4*d^5 - 7*a*b^6*c^8*d)))*(-(a^4*d^5 + 625*b^4*c^4*d - 500*a*b^3*c^3*d^2 + 150*a^2*b^2*c^2*d^3 - 20*a^3*b*c*d^4)/(4096*b^8*c^13 + 4096*a^8*c^5*d^8 - 32768*a^7*b*c^6*d^7 + 114688*a^2*b^6*c^11*d^2 - 229376*a^3*b^5*c^10*d^3 + 286720*a^4*b^4*c^9*d^4 - 229376*a^5*b^3*c^8*d^5 + 114688*a^6*b^2*c^7*d^6 - 32768*a*b^7*c^12*d))^(1/4)*2i + 2*atan((((((32*a^13*b^4*d^16 - 2048*a*b^16*c^12*d^4 - 704*a^12*b^5*c*d^15 + 14336*a^2*b^15*c^11*d^5 - 39008*a^3*b^14*c^10*d^6 + 41280*a^4*b^13*c^9*d^7 + 29600*a^5*b^12*c^8*d^8 - 150784*a^6*b^11*c^7*d^9 + 219968*a^7*b^10*c^6*d^10 - 183424*a^8*b^9*c^5*d^11 + 96320*a^9*b^8*c^4*d^12 - 32000*a^10*b^7*c^3*d^13 + 6432*a^11*b^6*c^2*d^14)*1i)/(b^7*c^9 - a^7*c^2*d^7 + 7*a^6*b*c^3*d^6 + 21*a^2*b^5*c^7*d^2 - 35*a^3*b^4*c^6*d^3 + 35*a^4*b^3*c^5*d^4 - 21*a^5*b^2*c^4*d^5 - 7*a*b^6*c^8*d) + (x^(1/2)*(-(a^4*d^5 + 625*b^4*c^4*d - 500*a*b^3*c^3*d^2 + 150*a^2*b^2*c^2*d^3 - 20*a^3*b*c*d^4)/(4096*b^8*c^13 + 4096*a^8*c^5*d^8 - 32768*a^7*b*c^6*d^7 + 114688*a^2*b^6*c^11*d^2 - 229376*a^3*b^5*c^10*d^3 + 286720*a^4*b^4*c^9*d^4 - 229376*a^5*b^3*c^8*d^5 + 114688*a^6*b^2*c^7*d^6 - 32768*a*b^7*c^12*d))^(1/4)*(4096*a*b^16*c^13*d^4 + 256*a^13*b^4*c*d^16 - 32768*a^2*b^15*c^12*d^5 + 121088*a^3*b^14*c^11*d^6 - 283136*a^4*b^13*c^10*d^7 + 486656*a^5*b^12*c^9*d^8 - 661504*a^6*b^11*c^8*d^9 + 713216*a^7*b^10*c^7*d^10 - 584704*a^8*b^9*c^6*d^11 + 344576*a^9*b^8*c^5*d^12 - 137216*a^10*b^7*c^4*d^13 + 34048*a^11*b^6*c^3*d^14 - 4608*a^12*b^5*c^2*d^15))/(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d))*(-(a^4*d^5 + 625*b^4*c^4*d - 500*a*b^3*c^3*d^2 + 150*a^2*b^2*c^2*d^3 - 20*a^3*b*c*d^4)/(4096*b^8*c^13 + 4096*a^8*c^5*d^8 - 32768*a^7*b*c^6*d^7 + 114688*a^2*b^6*c^11*d^2 - 229376*a^3*b^5*c^10*d^3 + 286720*a^4*b^4*c^9*d^4 - 229376*a^5*b^3*c^8*d^5 + 114688*a^6*b^2*c^7*d^6 - 32768*a*b^7*c^12*d))^(3/4) - (x^(1/2)*(4*a^4*b^9*c*d^8 - 625*a*b^12*c^4*d^5 - a^5*b^8*d^9 + 100*a^2*b^11*c^3*d^6 + 10*a^3*b^10*c^2*d^7))/(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d))*(-(a^4*d^5 + 625*b^4*c^4*d - 500*a*b^3*c^3*d^2 + 150*a^2*b^2*c^2*d^3 - 20*a^3*b*c*d^4)/(4096*b^8*c^13 + 4096*a^8*c^5*d^8 - 32768*a^7*b*c^6*d^7 + 114688*a^2*b^6*c^11*d^2 - 229376*a^3*b^5*c^10*d^3 + 286720*a^4*b^4*c^9*d^4 - 229376*a^5*b^3*c^8*d^5 + 114688*a^6*b^2*c^7*d^6 - 32768*a*b^7*c^12*d))^(1/4) - ((((32*a^13*b^4*d^16 - 2048*a*b^16*c^12*d^4 - 704*a^12*b^5*c*d^15 + 14336*a^2*b^15*c^11*d^5 - 39008*a^3*b^14*c^10*d^6 + 41280*a^4*b^13*c^9*d^7 + 29600*a^5*b^12*c^8*d^8 - 150784*a^6*b^11*c^7*d^9 + 219968*a^7*b^10*c^6*d^10 - 183424*a^8*b^9*c^5*d^11 + 96320*a^9*b^8*c^4*d^12 - 32000*a^10*b^7*c^3*d^13 + 6432*a^11*b^6*c^2*d^14)*1i)/(b^7*c^9 - a^7*c^2*d^7 + 7*a^6*b*c^3*d^6 + 21*a^2*b^5*c^7*d^2 - 35*a^3*b^4*c^6*d^3 + 35*a^4*b^3*c^5*d^4 - 21*a^5*b^2*c^4*d^5 - 7*a*b^6*c^8*d) - (x^(1/2)*(-(a^4*d^5 + 625*b^4*c^4*d - 500*a*b^3*c^3*d^2 + 150*a^2*b^2*c^2*d^3 - 20*a^3*b*c*d^4)/(4096*b^8*c^13 + 4096*a^8*c^5*d^8 - 32768*a^7*b*c^6*d^7 + 114688*a^2*b^6*c^11*d^2 - 229376*a^3*b^5*c^10*d^3 + 286720*a^4*b^4*c^9*d^4 - 229376*a^5*b^3*c^8*d^5 + 114688*a^6*b^2*c^7*d^6 - 32768*a*b^7*c^12*d))^(1/4)*(4096*a*b^16*c^13*d^4 + 256*a^13*b^4*c*d^16 - 32768*a^2*b^15*c^12*d^5 + 121088*a^3*b^14*c^11*d^6 - 283136*a^4*b^13*c^10*d^7 + 486656*a^5*b^12*c^9*d^8 - 661504*a^6*b^11*c^8*d^9 + 713216*a^7*b^10*c^7*d^10 - 584704*a^8*b^9*c^6*d^11 + 344576*a^9*b^8*c^5*d^12 - 137216*a^10*b^7*c^4*d^13 + 34048*a^11*b^6*c^3*d^14 - 4608*a^12*b^5*c^2*d^15))/(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d))*(-(a^4*d^5 + 625*b^4*c^4*d - 500*a*b^3*c^3*d^2 + 150*a^2*b^2*c^2*d^3 - 20*a^3*b*c*d^4)/(4096*b^8*c^13 + 4096*a^8*c^5*d^8 - 32768*a^7*b*c^6*d^7 + 114688*a^2*b^6*c^11*d^2 - 229376*a^3*b^5*c^10*d^3 + 286720*a^4*b^4*c^9*d^4 - 229376*a^5*b^3*c^8*d^5 + 114688*a^6*b^2*c^7*d^6 - 32768*a*b^7*c^12*d))^(3/4) + (x^(1/2)*(4*a^4*b^9*c*d^8 - 625*a*b^12*c^4*d^5 - a^5*b^8*d^9 + 100*a^2*b^11*c^3*d^6 + 10*a^3*b^10*c^2*d^7))/(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d))*(-(a^4*d^5 + 625*b^4*c^4*d - 500*a*b^3*c^3*d^2 + 150*a^2*b^2*c^2*d^3 - 20*a^3*b*c*d^4)/(4096*b^8*c^13 + 4096*a^8*c^5*d^8 - 32768*a^7*b*c^6*d^7 + 114688*a^2*b^6*c^11*d^2 - 229376*a^3*b^5*c^10*d^3 + 286720*a^4*b^4*c^9*d^4 - 229376*a^5*b^3*c^8*d^5 + 114688*a^6*b^2*c^7*d^6 - 32768*a*b^7*c^12*d))^(1/4))/(((((32*a^13*b^4*d^16 - 2048*a*b^16*c^12*d^4 - 704*a^12*b^5*c*d^15 + 14336*a^2*b^15*c^11*d^5 - 39008*a^3*b^14*c^10*d^6 + 41280*a^4*b^13*c^9*d^7 + 29600*a^5*b^12*c^8*d^8 - 150784*a^6*b^11*c^7*d^9 + 219968*a^7*b^10*c^6*d^10 - 183424*a^8*b^9*c^5*d^11 + 96320*a^9*b^8*c^4*d^12 - 32000*a^10*b^7*c^3*d^13 + 6432*a^11*b^6*c^2*d^14)*1i)/(b^7*c^9 - a^7*c^2*d^7 + 7*a^6*b*c^3*d^6 + 21*a^2*b^5*c^7*d^2 - 35*a^3*b^4*c^6*d^3 + 35*a^4*b^3*c^5*d^4 - 21*a^5*b^2*c^4*d^5 - 7*a*b^6*c^8*d) + (x^(1/2)*(-(a^4*d^5 + 625*b^4*c^4*d - 500*a*b^3*c^3*d^2 + 150*a^2*b^2*c^2*d^3 - 20*a^3*b*c*d^4)/(4096*b^8*c^13 + 4096*a^8*c^5*d^8 - 32768*a^7*b*c^6*d^7 + 114688*a^2*b^6*c^11*d^2 - 229376*a^3*b^5*c^10*d^3 + 286720*a^4*b^4*c^9*d^4 - 229376*a^5*b^3*c^8*d^5 + 114688*a^6*b^2*c^7*d^6 - 32768*a*b^7*c^12*d))^(1/4)*(4096*a*b^16*c^13*d^4 + 256*a^13*b^4*c*d^16 - 32768*a^2*b^15*c^12*d^5 + 121088*a^3*b^14*c^11*d^6 - 283136*a^4*b^13*c^10*d^7 + 486656*a^5*b^12*c^9*d^8 - 661504*a^6*b^11*c^8*d^9 + 713216*a^7*b^10*c^7*d^10 - 584704*a^8*b^9*c^6*d^11 + 344576*a^9*b^8*c^5*d^12 - 137216*a^10*b^7*c^4*d^13 + 34048*a^11*b^6*c^3*d^14 - 4608*a^12*b^5*c^2*d^15))/(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d))*(-(a^4*d^5 + 625*b^4*c^4*d - 500*a*b^3*c^3*d^2 + 150*a^2*b^2*c^2*d^3 - 20*a^3*b*c*d^4)/(4096*b^8*c^13 + 4096*a^8*c^5*d^8 - 32768*a^7*b*c^6*d^7 + 114688*a^2*b^6*c^11*d^2 - 229376*a^3*b^5*c^10*d^3 + 286720*a^4*b^4*c^9*d^4 - 229376*a^5*b^3*c^8*d^5 + 114688*a^6*b^2*c^7*d^6 - 32768*a*b^7*c^12*d))^(3/4)*1i - (x^(1/2)*(4*a^4*b^9*c*d^8 - 625*a*b^12*c^4*d^5 - a^5*b^8*d^9 + 100*a^2*b^11*c^3*d^6 + 10*a^3*b^10*c^2*d^7)*1i)/(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d))*(-(a^4*d^5 + 625*b^4*c^4*d - 500*a*b^3*c^3*d^2 + 150*a^2*b^2*c^2*d^3 - 20*a^3*b*c*d^4)/(4096*b^8*c^13 + 4096*a^8*c^5*d^8 - 32768*a^7*b*c^6*d^7 + 114688*a^2*b^6*c^11*d^2 - 229376*a^3*b^5*c^10*d^3 + 286720*a^4*b^4*c^9*d^4 - 229376*a^5*b^3*c^8*d^5 + 114688*a^6*b^2*c^7*d^6 - 32768*a*b^7*c^12*d))^(1/4) + ((((32*a^13*b^4*d^16 - 2048*a*b^16*c^12*d^4 - 704*a^12*b^5*c*d^15 + 14336*a^2*b^15*c^11*d^5 - 39008*a^3*b^14*c^10*d^6 + 41280*a^4*b^13*c^9*d^7 + 29600*a^5*b^12*c^8*d^8 - 150784*a^6*b^11*c^7*d^9 + 219968*a^7*b^10*c^6*d^10 - 183424*a^8*b^9*c^5*d^11 + 96320*a^9*b^8*c^4*d^12 - 32000*a^10*b^7*c^3*d^13 + 6432*a^11*b^6*c^2*d^14)*1i)/(b^7*c^9 - a^7*c^2*d^7 + 7*a^6*b*c^3*d^6 + 21*a^2*b^5*c^7*d^2 - 35*a^3*b^4*c^6*d^3 + 35*a^4*b^3*c^5*d^4 - 21*a^5*b^2*c^4*d^5 - 7*a*b^6*c^8*d) - (x^(1/2)*(-(a^4*d^5 + 625*b^4*c^4*d - 500*a*b^3*c^3*d^2 + 150*a^2*b^2*c^2*d^3 - 20*a^3*b*c*d^4)/(4096*b^8*c^13 + 4096*a^8*c^5*d^8 - 32768*a^7*b*c^6*d^7 + 114688*a^2*b^6*c^11*d^2 - 229376*a^3*b^5*c^10*d^3 + 286720*a^4*b^4*c^9*d^4 - 229376*a^5*b^3*c^8*d^5 + 114688*a^6*b^2*c^7*d^6 - 32768*a*b^7*c^12*d))^(1/4)*(4096*a*b^16*c^13*d^4 + 256*a^13*b^4*c*d^16 - 32768*a^2*b^15*c^12*d^5 + 121088*a^3*b^14*c^11*d^6 - 283136*a^4*b^13*c^10*d^7 + 486656*a^5*b^12*c^9*d^8 - 661504*a^6*b^11*c^8*d^9 + 713216*a^7*b^10*c^7*d^10 - 584704*a^8*b^9*c^6*d^11 + 344576*a^9*b^8*c^5*d^12 - 137216*a^10*b^7*c^4*d^13 + 34048*a^11*b^6*c^3*d^14 - 4608*a^12*b^5*c^2*d^15))/(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d))*(-(a^4*d^5 + 625*b^4*c^4*d - 500*a*b^3*c^3*d^2 + 150*a^2*b^2*c^2*d^3 - 20*a^3*b*c*d^4)/(4096*b^8*c^13 + 4096*a^8*c^5*d^8 - 32768*a^7*b*c^6*d^7 + 114688*a^2*b^6*c^11*d^2 - 229376*a^3*b^5*c^10*d^3 + 286720*a^4*b^4*c^9*d^4 - 229376*a^5*b^3*c^8*d^5 + 114688*a^6*b^2*c^7*d^6 - 32768*a*b^7*c^12*d))^(3/4)*1i + (x^(1/2)*(4*a^4*b^9*c*d^8 - 625*a*b^12*c^4*d^5 - a^5*b^8*d^9 + 100*a^2*b^11*c^3*d^6 + 10*a^3*b^10*c^2*d^7)*1i)/(b^6*c^8 + a^6*c^2*d^6 - 6*a^5*b*c^3*d^5 + 15*a^2*b^4*c^6*d^2 - 20*a^3*b^3*c^5*d^3 + 15*a^4*b^2*c^4*d^4 - 6*a*b^5*c^7*d))*(-(a^4*d^5 + 625*b^4*c^4*d - 500*a*b^3*c^3*d^2 + 150*a^2*b^2*c^2*d^3 - 20*a^3*b*c*d^4)/(4096*b^8*c^13 + 4096*a^8*c^5*d^8 - 32768*a^7*b*c^6*d^7 + 114688*a^2*b^6*c^11*d^2 - 229376*a^3*b^5*c^10*d^3 + 286720*a^4*b^4*c^9*d^4 - 229376*a^5*b^3*c^8*d^5 + 114688*a^6*b^2*c^7*d^6 - 32768*a*b^7*c^12*d))^(1/4) - (5*a^4*b^9*d^8 - 625*a*b^12*c^3*d^5 - 75*a^3*b^10*c*d^7 + 375*a^2*b^11*c^2*d^6)/(b^7*c^9 - a^7*c^2*d^7 + 7*a^6*b*c^3*d^6 + 21*a^2*b^5*c^7*d^2 - 35*a^3*b^4*c^6*d^3 + 35*a^4*b^3*c^5*d^4 - 21*a^5*b^2*c^4*d^5 - 7*a*b^6*c^8*d)))*(-(a^4*d^5 + 625*b^4*c^4*d - 500*a*b^3*c^3*d^2 + 150*a^2*b^2*c^2*d^3 - 20*a^3*b*c*d^4)/(4096*b^8*c^13 + 4096*a^8*c^5*d^8 - 32768*a^7*b*c^6*d^7 + 114688*a^2*b^6*c^11*d^2 - 229376*a^3*b^5*c^10*d^3 + 286720*a^4*b^4*c^9*d^4 - 229376*a^5*b^3*c^8*d^5 + 114688*a^6*b^2*c^7*d^6 - 32768*a*b^7*c^12*d))^(1/4) + (d*x^(3/2))/(2*c*(c + d*x^2)*(a*d - b*c))","B"
476,1,21987,536,2.733704,"\text{Not used}","int(1/(x^(1/2)*(a + b*x^2)*(c + d*x^2)^2),x)","2\,\mathrm{atan}\left(\frac{{\left(-\frac{b^7}{16\,a^{11}\,d^8-128\,a^{10}\,b\,c\,d^7+448\,a^9\,b^2\,c^2\,d^6-896\,a^8\,b^3\,c^3\,d^5+1120\,a^7\,b^4\,c^4\,d^4-896\,a^6\,b^5\,c^5\,d^3+448\,a^5\,b^6\,c^6\,d^2-128\,a^4\,b^7\,c^7\,d+16\,a^3\,b^8\,c^8}\right)}^{1/4}\,\left(\frac{\sqrt{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)}{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}}+{\left(-\frac{b^7}{16\,a^{11}\,d^8-128\,a^{10}\,b\,c\,d^7+448\,a^9\,b^2\,c^2\,d^6-896\,a^8\,b^3\,c^3\,d^5+1120\,a^7\,b^4\,c^4\,d^4-896\,a^6\,b^5\,c^5\,d^3+448\,a^5\,b^6\,c^6\,d^2-128\,a^4\,b^7\,c^7\,d+16\,a^3\,b^8\,c^8}\right)}^{1/4}\,\left(\frac{2\,\left(81\,a^4\,b^7\,d^{10}-675\,a^3\,b^8\,c\,d^9+1971\,a^2\,b^9\,c^2\,d^8-2145\,a\,b^{10}\,c^3\,d^7+448\,b^{11}\,c^4\,d^6\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}-{\left(-\frac{b^7}{16\,a^{11}\,d^8-128\,a^{10}\,b\,c\,d^7+448\,a^9\,b^2\,c^2\,d^6-896\,a^8\,b^3\,c^3\,d^5+1120\,a^7\,b^4\,c^4\,d^4-896\,a^6\,b^5\,c^5\,d^3+448\,a^5\,b^6\,c^6\,d^2-128\,a^4\,b^7\,c^7\,d+16\,a^3\,b^8\,c^8}\right)}^{3/4}\,\left(\frac{\sqrt{x}\,\left(2304\,a^{13}\,b^4\,c^2\,d^{17}-29184\,a^{12}\,b^5\,c^3\,d^{16}+163072\,a^{11}\,b^6\,c^4\,d^{15}-530432\,a^{10}\,b^7\,c^5\,d^{14}+1114624\,a^9\,b^8\,c^6\,d^{13}-1580032\,a^8\,b^9\,c^7\,d^{12}+1511936\,a^7\,b^{10}\,c^8\,d^{11}-907264\,a^6\,b^{11}\,c^9\,d^{10}+210176\,a^5\,b^{12}\,c^{10}\,d^9+175616\,a^4\,b^{13}\,c^{11}\,d^8-216832\,a^3\,b^{14}\,c^{12}\,d^7+114688\,a^2\,b^{15}\,c^{13}\,d^6-32768\,a\,b^{16}\,c^{14}\,d^5+4096\,b^{17}\,c^{15}\,d^4\right)}{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}}+\frac{{\left(-\frac{b^7}{16\,a^{11}\,d^8-128\,a^{10}\,b\,c\,d^7+448\,a^9\,b^2\,c^2\,d^6-896\,a^8\,b^3\,c^3\,d^5+1120\,a^7\,b^4\,c^4\,d^4-896\,a^6\,b^5\,c^5\,d^3+448\,a^5\,b^6\,c^6\,d^2-128\,a^4\,b^7\,c^7\,d+16\,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)\,2{}\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)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)-{\left(-\frac{b^7}{16\,a^{11}\,d^8-128\,a^{10}\,b\,c\,d^7+448\,a^9\,b^2\,c^2\,d^6-896\,a^8\,b^3\,c^3\,d^5+1120\,a^7\,b^4\,c^4\,d^4-896\,a^6\,b^5\,c^5\,d^3+448\,a^5\,b^6\,c^6\,d^2-128\,a^4\,b^7\,c^7\,d+16\,a^3\,b^8\,c^8}\right)}^{1/4}\,\left(-\frac{\sqrt{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)}{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}}+{\left(-\frac{b^7}{16\,a^{11}\,d^8-128\,a^{10}\,b\,c\,d^7+448\,a^9\,b^2\,c^2\,d^6-896\,a^8\,b^3\,c^3\,d^5+1120\,a^7\,b^4\,c^4\,d^4-896\,a^6\,b^5\,c^5\,d^3+448\,a^5\,b^6\,c^6\,d^2-128\,a^4\,b^7\,c^7\,d+16\,a^3\,b^8\,c^8}\right)}^{1/4}\,\left(\frac{2\,\left(81\,a^4\,b^7\,d^{10}-675\,a^3\,b^8\,c\,d^9+1971\,a^2\,b^9\,c^2\,d^8-2145\,a\,b^{10}\,c^3\,d^7+448\,b^{11}\,c^4\,d^6\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}-{\left(-\frac{b^7}{16\,a^{11}\,d^8-128\,a^{10}\,b\,c\,d^7+448\,a^9\,b^2\,c^2\,d^6-896\,a^8\,b^3\,c^3\,d^5+1120\,a^7\,b^4\,c^4\,d^4-896\,a^6\,b^5\,c^5\,d^3+448\,a^5\,b^6\,c^6\,d^2-128\,a^4\,b^7\,c^7\,d+16\,a^3\,b^8\,c^8}\right)}^{3/4}\,\left(-\frac{\sqrt{x}\,\left(2304\,a^{13}\,b^4\,c^2\,d^{17}-29184\,a^{12}\,b^5\,c^3\,d^{16}+163072\,a^{11}\,b^6\,c^4\,d^{15}-530432\,a^{10}\,b^7\,c^5\,d^{14}+1114624\,a^9\,b^8\,c^6\,d^{13}-1580032\,a^8\,b^9\,c^7\,d^{12}+1511936\,a^7\,b^{10}\,c^8\,d^{11}-907264\,a^6\,b^{11}\,c^9\,d^{10}+210176\,a^5\,b^{12}\,c^{10}\,d^9+175616\,a^4\,b^{13}\,c^{11}\,d^8-216832\,a^3\,b^{14}\,c^{12}\,d^7+114688\,a^2\,b^{15}\,c^{13}\,d^6-32768\,a\,b^{16}\,c^{14}\,d^5+4096\,b^{17}\,c^{15}\,d^4\right)}{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}}+\frac{{\left(-\frac{b^7}{16\,a^{11}\,d^8-128\,a^{10}\,b\,c\,d^7+448\,a^9\,b^2\,c^2\,d^6-896\,a^8\,b^3\,c^3\,d^5+1120\,a^7\,b^4\,c^4\,d^4-896\,a^6\,b^5\,c^5\,d^3+448\,a^5\,b^6\,c^6\,d^2-128\,a^4\,b^7\,c^7\,d+16\,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)\,2{}\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)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)}{{\left(-\frac{b^7}{16\,a^{11}\,d^8-128\,a^{10}\,b\,c\,d^7+448\,a^9\,b^2\,c^2\,d^6-896\,a^8\,b^3\,c^3\,d^5+1120\,a^7\,b^4\,c^4\,d^4-896\,a^6\,b^5\,c^5\,d^3+448\,a^5\,b^6\,c^6\,d^2-128\,a^4\,b^7\,c^7\,d+16\,a^3\,b^8\,c^8}\right)}^{1/4}\,\left(\frac{\sqrt{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)}{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}}+{\left(-\frac{b^7}{16\,a^{11}\,d^8-128\,a^{10}\,b\,c\,d^7+448\,a^9\,b^2\,c^2\,d^6-896\,a^8\,b^3\,c^3\,d^5+1120\,a^7\,b^4\,c^4\,d^4-896\,a^6\,b^5\,c^5\,d^3+448\,a^5\,b^6\,c^6\,d^2-128\,a^4\,b^7\,c^7\,d+16\,a^3\,b^8\,c^8}\right)}^{1/4}\,\left(\frac{2\,\left(81\,a^4\,b^7\,d^{10}-675\,a^3\,b^8\,c\,d^9+1971\,a^2\,b^9\,c^2\,d^8-2145\,a\,b^{10}\,c^3\,d^7+448\,b^{11}\,c^4\,d^6\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}-{\left(-\frac{b^7}{16\,a^{11}\,d^8-128\,a^{10}\,b\,c\,d^7+448\,a^9\,b^2\,c^2\,d^6-896\,a^8\,b^3\,c^3\,d^5+1120\,a^7\,b^4\,c^4\,d^4-896\,a^6\,b^5\,c^5\,d^3+448\,a^5\,b^6\,c^6\,d^2-128\,a^4\,b^7\,c^7\,d+16\,a^3\,b^8\,c^8}\right)}^{3/4}\,\left(\frac{\sqrt{x}\,\left(2304\,a^{13}\,b^4\,c^2\,d^{17}-29184\,a^{12}\,b^5\,c^3\,d^{16}+163072\,a^{11}\,b^6\,c^4\,d^{15}-530432\,a^{10}\,b^7\,c^5\,d^{14}+1114624\,a^9\,b^8\,c^6\,d^{13}-1580032\,a^8\,b^9\,c^7\,d^{12}+1511936\,a^7\,b^{10}\,c^8\,d^{11}-907264\,a^6\,b^{11}\,c^9\,d^{10}+210176\,a^5\,b^{12}\,c^{10}\,d^9+175616\,a^4\,b^{13}\,c^{11}\,d^8-216832\,a^3\,b^{14}\,c^{12}\,d^7+114688\,a^2\,b^{15}\,c^{13}\,d^6-32768\,a\,b^{16}\,c^{14}\,d^5+4096\,b^{17}\,c^{15}\,d^4\right)}{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}}+\frac{{\left(-\frac{b^7}{16\,a^{11}\,d^8-128\,a^{10}\,b\,c\,d^7+448\,a^9\,b^2\,c^2\,d^6-896\,a^8\,b^3\,c^3\,d^5+1120\,a^7\,b^4\,c^4\,d^4-896\,a^6\,b^5\,c^5\,d^3+448\,a^5\,b^6\,c^6\,d^2-128\,a^4\,b^7\,c^7\,d+16\,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)\,2{}\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)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}+{\left(-\frac{b^7}{16\,a^{11}\,d^8-128\,a^{10}\,b\,c\,d^7+448\,a^9\,b^2\,c^2\,d^6-896\,a^8\,b^3\,c^3\,d^5+1120\,a^7\,b^4\,c^4\,d^4-896\,a^6\,b^5\,c^5\,d^3+448\,a^5\,b^6\,c^6\,d^2-128\,a^4\,b^7\,c^7\,d+16\,a^3\,b^8\,c^8}\right)}^{1/4}\,\left(-\frac{\sqrt{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)}{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}}+{\left(-\frac{b^7}{16\,a^{11}\,d^8-128\,a^{10}\,b\,c\,d^7+448\,a^9\,b^2\,c^2\,d^6-896\,a^8\,b^3\,c^3\,d^5+1120\,a^7\,b^4\,c^4\,d^4-896\,a^6\,b^5\,c^5\,d^3+448\,a^5\,b^6\,c^6\,d^2-128\,a^4\,b^7\,c^7\,d+16\,a^3\,b^8\,c^8}\right)}^{1/4}\,\left(\frac{2\,\left(81\,a^4\,b^7\,d^{10}-675\,a^3\,b^8\,c\,d^9+1971\,a^2\,b^9\,c^2\,d^8-2145\,a\,b^{10}\,c^3\,d^7+448\,b^{11}\,c^4\,d^6\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}-{\left(-\frac{b^7}{16\,a^{11}\,d^8-128\,a^{10}\,b\,c\,d^7+448\,a^9\,b^2\,c^2\,d^6-896\,a^8\,b^3\,c^3\,d^5+1120\,a^7\,b^4\,c^4\,d^4-896\,a^6\,b^5\,c^5\,d^3+448\,a^5\,b^6\,c^6\,d^2-128\,a^4\,b^7\,c^7\,d+16\,a^3\,b^8\,c^8}\right)}^{3/4}\,\left(-\frac{\sqrt{x}\,\left(2304\,a^{13}\,b^4\,c^2\,d^{17}-29184\,a^{12}\,b^5\,c^3\,d^{16}+163072\,a^{11}\,b^6\,c^4\,d^{15}-530432\,a^{10}\,b^7\,c^5\,d^{14}+1114624\,a^9\,b^8\,c^6\,d^{13}-1580032\,a^8\,b^9\,c^7\,d^{12}+1511936\,a^7\,b^{10}\,c^8\,d^{11}-907264\,a^6\,b^{11}\,c^9\,d^{10}+210176\,a^5\,b^{12}\,c^{10}\,d^9+175616\,a^4\,b^{13}\,c^{11}\,d^8-216832\,a^3\,b^{14}\,c^{12}\,d^7+114688\,a^2\,b^{15}\,c^{13}\,d^6-32768\,a\,b^{16}\,c^{14}\,d^5+4096\,b^{17}\,c^{15}\,d^4\right)}{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}}+\frac{{\left(-\frac{b^7}{16\,a^{11}\,d^8-128\,a^{10}\,b\,c\,d^7+448\,a^9\,b^2\,c^2\,d^6-896\,a^8\,b^3\,c^3\,d^5+1120\,a^7\,b^4\,c^4\,d^4-896\,a^6\,b^5\,c^5\,d^3+448\,a^5\,b^6\,c^6\,d^2-128\,a^4\,b^7\,c^7\,d+16\,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)\,2{}\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)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}\right)\,{\left(-\frac{b^7}{16\,a^{11}\,d^8-128\,a^{10}\,b\,c\,d^7+448\,a^9\,b^2\,c^2\,d^6-896\,a^8\,b^3\,c^3\,d^5+1120\,a^7\,b^4\,c^4\,d^4-896\,a^6\,b^5\,c^5\,d^3+448\,a^5\,b^6\,c^6\,d^2-128\,a^4\,b^7\,c^7\,d+16\,a^3\,b^8\,c^8}\right)}^{1/4}-2\,\mathrm{atan}\left(\frac{\left(-\frac{\sqrt{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)}{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}}+\left(\frac{2\,\left(81\,a^4\,b^7\,d^{10}-675\,a^3\,b^8\,c\,d^9+1971\,a^2\,b^9\,c^2\,d^8-2145\,a\,b^{10}\,c^3\,d^7+448\,b^{11}\,c^4\,d^6\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}+\left(\frac{\sqrt{x}\,\left(2304\,a^{13}\,b^4\,c^2\,d^{17}-29184\,a^{12}\,b^5\,c^3\,d^{16}+163072\,a^{11}\,b^6\,c^4\,d^{15}-530432\,a^{10}\,b^7\,c^5\,d^{14}+1114624\,a^9\,b^8\,c^6\,d^{13}-1580032\,a^8\,b^9\,c^7\,d^{12}+1511936\,a^7\,b^{10}\,c^8\,d^{11}-907264\,a^6\,b^{11}\,c^9\,d^{10}+210176\,a^5\,b^{12}\,c^{10}\,d^9+175616\,a^4\,b^{13}\,c^{11}\,d^8-216832\,a^3\,b^{14}\,c^{12}\,d^7+114688\,a^2\,b^{15}\,c^{13}\,d^6-32768\,a\,b^{16}\,c^{14}\,d^5+4096\,b^{17}\,c^{15}\,d^4\right)}{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}}-\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}{4096\,a^8\,c^7\,d^8-32768\,a^7\,b\,c^8\,d^7+114688\,a^6\,b^2\,c^9\,d^6-229376\,a^5\,b^3\,c^{10}\,d^5+286720\,a^4\,b^4\,c^{11}\,d^4-229376\,a^3\,b^5\,c^{12}\,d^3+114688\,a^2\,b^6\,c^{13}\,d^2-32768\,a\,b^7\,c^{14}\,d+4096\,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)\,2{}\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)\,{\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}{4096\,a^8\,c^7\,d^8-32768\,a^7\,b\,c^8\,d^7+114688\,a^6\,b^2\,c^9\,d^6-229376\,a^5\,b^3\,c^{10}\,d^5+286720\,a^4\,b^4\,c^{11}\,d^4-229376\,a^3\,b^5\,c^{12}\,d^3+114688\,a^2\,b^6\,c^{13}\,d^2-32768\,a\,b^7\,c^{14}\,d+4096\,b^8\,c^{15}}\right)}^{3/4}\,1{}\mathrm{i}\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}{4096\,a^8\,c^7\,d^8-32768\,a^7\,b\,c^8\,d^7+114688\,a^6\,b^2\,c^9\,d^6-229376\,a^5\,b^3\,c^{10}\,d^5+286720\,a^4\,b^4\,c^{11}\,d^4-229376\,a^3\,b^5\,c^{12}\,d^3+114688\,a^2\,b^6\,c^{13}\,d^2-32768\,a\,b^7\,c^{14}\,d+4096\,b^8\,c^{15}}\right)}^{1/4}\,1{}\mathrm{i}\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}{4096\,a^8\,c^7\,d^8-32768\,a^7\,b\,c^8\,d^7+114688\,a^6\,b^2\,c^9\,d^6-229376\,a^5\,b^3\,c^{10}\,d^5+286720\,a^4\,b^4\,c^{11}\,d^4-229376\,a^3\,b^5\,c^{12}\,d^3+114688\,a^2\,b^6\,c^{13}\,d^2-32768\,a\,b^7\,c^{14}\,d+4096\,b^8\,c^{15}}\right)}^{1/4}+\left(-\frac{\sqrt{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)}{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}}+\left(-\frac{2\,\left(81\,a^4\,b^7\,d^{10}-675\,a^3\,b^8\,c\,d^9+1971\,a^2\,b^9\,c^2\,d^8-2145\,a\,b^{10}\,c^3\,d^7+448\,b^{11}\,c^4\,d^6\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}+\left(\frac{\sqrt{x}\,\left(2304\,a^{13}\,b^4\,c^2\,d^{17}-29184\,a^{12}\,b^5\,c^3\,d^{16}+163072\,a^{11}\,b^6\,c^4\,d^{15}-530432\,a^{10}\,b^7\,c^5\,d^{14}+1114624\,a^9\,b^8\,c^6\,d^{13}-1580032\,a^8\,b^9\,c^7\,d^{12}+1511936\,a^7\,b^{10}\,c^8\,d^{11}-907264\,a^6\,b^{11}\,c^9\,d^{10}+210176\,a^5\,b^{12}\,c^{10}\,d^9+175616\,a^4\,b^{13}\,c^{11}\,d^8-216832\,a^3\,b^{14}\,c^{12}\,d^7+114688\,a^2\,b^{15}\,c^{13}\,d^6-32768\,a\,b^{16}\,c^{14}\,d^5+4096\,b^{17}\,c^{15}\,d^4\right)}{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}}+\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}{4096\,a^8\,c^7\,d^8-32768\,a^7\,b\,c^8\,d^7+114688\,a^6\,b^2\,c^9\,d^6-229376\,a^5\,b^3\,c^{10}\,d^5+286720\,a^4\,b^4\,c^{11}\,d^4-229376\,a^3\,b^5\,c^{12}\,d^3+114688\,a^2\,b^6\,c^{13}\,d^2-32768\,a\,b^7\,c^{14}\,d+4096\,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)\,2{}\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)\,{\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}{4096\,a^8\,c^7\,d^8-32768\,a^7\,b\,c^8\,d^7+114688\,a^6\,b^2\,c^9\,d^6-229376\,a^5\,b^3\,c^{10}\,d^5+286720\,a^4\,b^4\,c^{11}\,d^4-229376\,a^3\,b^5\,c^{12}\,d^3+114688\,a^2\,b^6\,c^{13}\,d^2-32768\,a\,b^7\,c^{14}\,d+4096\,b^8\,c^{15}}\right)}^{3/4}\,1{}\mathrm{i}\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}{4096\,a^8\,c^7\,d^8-32768\,a^7\,b\,c^8\,d^7+114688\,a^6\,b^2\,c^9\,d^6-229376\,a^5\,b^3\,c^{10}\,d^5+286720\,a^4\,b^4\,c^{11}\,d^4-229376\,a^3\,b^5\,c^{12}\,d^3+114688\,a^2\,b^6\,c^{13}\,d^2-32768\,a\,b^7\,c^{14}\,d+4096\,b^8\,c^{15}}\right)}^{1/4}\,1{}\mathrm{i}\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}{4096\,a^8\,c^7\,d^8-32768\,a^7\,b\,c^8\,d^7+114688\,a^6\,b^2\,c^9\,d^6-229376\,a^5\,b^3\,c^{10}\,d^5+286720\,a^4\,b^4\,c^{11}\,d^4-229376\,a^3\,b^5\,c^{12}\,d^3+114688\,a^2\,b^6\,c^{13}\,d^2-32768\,a\,b^7\,c^{14}\,d+4096\,b^8\,c^{15}}\right)}^{1/4}}{\left(-\frac{\sqrt{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)}{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}}+\left(\frac{2\,\left(81\,a^4\,b^7\,d^{10}-675\,a^3\,b^8\,c\,d^9+1971\,a^2\,b^9\,c^2\,d^8-2145\,a\,b^{10}\,c^3\,d^7+448\,b^{11}\,c^4\,d^6\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}+\left(\frac{\sqrt{x}\,\left(2304\,a^{13}\,b^4\,c^2\,d^{17}-29184\,a^{12}\,b^5\,c^3\,d^{16}+163072\,a^{11}\,b^6\,c^4\,d^{15}-530432\,a^{10}\,b^7\,c^5\,d^{14}+1114624\,a^9\,b^8\,c^6\,d^{13}-1580032\,a^8\,b^9\,c^7\,d^{12}+1511936\,a^7\,b^{10}\,c^8\,d^{11}-907264\,a^6\,b^{11}\,c^9\,d^{10}+210176\,a^5\,b^{12}\,c^{10}\,d^9+175616\,a^4\,b^{13}\,c^{11}\,d^8-216832\,a^3\,b^{14}\,c^{12}\,d^7+114688\,a^2\,b^{15}\,c^{13}\,d^6-32768\,a\,b^{16}\,c^{14}\,d^5+4096\,b^{17}\,c^{15}\,d^4\right)}{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}}-\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}{4096\,a^8\,c^7\,d^8-32768\,a^7\,b\,c^8\,d^7+114688\,a^6\,b^2\,c^9\,d^6-229376\,a^5\,b^3\,c^{10}\,d^5+286720\,a^4\,b^4\,c^{11}\,d^4-229376\,a^3\,b^5\,c^{12}\,d^3+114688\,a^2\,b^6\,c^{13}\,d^2-32768\,a\,b^7\,c^{14}\,d+4096\,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)\,2{}\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)\,{\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}{4096\,a^8\,c^7\,d^8-32768\,a^7\,b\,c^8\,d^7+114688\,a^6\,b^2\,c^9\,d^6-229376\,a^5\,b^3\,c^{10}\,d^5+286720\,a^4\,b^4\,c^{11}\,d^4-229376\,a^3\,b^5\,c^{12}\,d^3+114688\,a^2\,b^6\,c^{13}\,d^2-32768\,a\,b^7\,c^{14}\,d+4096\,b^8\,c^{15}}\right)}^{3/4}\,1{}\mathrm{i}\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}{4096\,a^8\,c^7\,d^8-32768\,a^7\,b\,c^8\,d^7+114688\,a^6\,b^2\,c^9\,d^6-229376\,a^5\,b^3\,c^{10}\,d^5+286720\,a^4\,b^4\,c^{11}\,d^4-229376\,a^3\,b^5\,c^{12}\,d^3+114688\,a^2\,b^6\,c^{13}\,d^2-32768\,a\,b^7\,c^{14}\,d+4096\,b^8\,c^{15}}\right)}^{1/4}\,1{}\mathrm{i}\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}{4096\,a^8\,c^7\,d^8-32768\,a^7\,b\,c^8\,d^7+114688\,a^6\,b^2\,c^9\,d^6-229376\,a^5\,b^3\,c^{10}\,d^5+286720\,a^4\,b^4\,c^{11}\,d^4-229376\,a^3\,b^5\,c^{12}\,d^3+114688\,a^2\,b^6\,c^{13}\,d^2-32768\,a\,b^7\,c^{14}\,d+4096\,b^8\,c^{15}}\right)}^{1/4}\,1{}\mathrm{i}-\left(-\frac{\sqrt{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)}{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}}+\left(-\frac{2\,\left(81\,a^4\,b^7\,d^{10}-675\,a^3\,b^8\,c\,d^9+1971\,a^2\,b^9\,c^2\,d^8-2145\,a\,b^{10}\,c^3\,d^7+448\,b^{11}\,c^4\,d^6\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}+\left(\frac{\sqrt{x}\,\left(2304\,a^{13}\,b^4\,c^2\,d^{17}-29184\,a^{12}\,b^5\,c^3\,d^{16}+163072\,a^{11}\,b^6\,c^4\,d^{15}-530432\,a^{10}\,b^7\,c^5\,d^{14}+1114624\,a^9\,b^8\,c^6\,d^{13}-1580032\,a^8\,b^9\,c^7\,d^{12}+1511936\,a^7\,b^{10}\,c^8\,d^{11}-907264\,a^6\,b^{11}\,c^9\,d^{10}+210176\,a^5\,b^{12}\,c^{10}\,d^9+175616\,a^4\,b^{13}\,c^{11}\,d^8-216832\,a^3\,b^{14}\,c^{12}\,d^7+114688\,a^2\,b^{15}\,c^{13}\,d^6-32768\,a\,b^{16}\,c^{14}\,d^5+4096\,b^{17}\,c^{15}\,d^4\right)}{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}}+\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}{4096\,a^8\,c^7\,d^8-32768\,a^7\,b\,c^8\,d^7+114688\,a^6\,b^2\,c^9\,d^6-229376\,a^5\,b^3\,c^{10}\,d^5+286720\,a^4\,b^4\,c^{11}\,d^4-229376\,a^3\,b^5\,c^{12}\,d^3+114688\,a^2\,b^6\,c^{13}\,d^2-32768\,a\,b^7\,c^{14}\,d+4096\,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)\,2{}\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)\,{\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}{4096\,a^8\,c^7\,d^8-32768\,a^7\,b\,c^8\,d^7+114688\,a^6\,b^2\,c^9\,d^6-229376\,a^5\,b^3\,c^{10}\,d^5+286720\,a^4\,b^4\,c^{11}\,d^4-229376\,a^3\,b^5\,c^{12}\,d^3+114688\,a^2\,b^6\,c^{13}\,d^2-32768\,a\,b^7\,c^{14}\,d+4096\,b^8\,c^{15}}\right)}^{3/4}\,1{}\mathrm{i}\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}{4096\,a^8\,c^7\,d^8-32768\,a^7\,b\,c^8\,d^7+114688\,a^6\,b^2\,c^9\,d^6-229376\,a^5\,b^3\,c^{10}\,d^5+286720\,a^4\,b^4\,c^{11}\,d^4-229376\,a^3\,b^5\,c^{12}\,d^3+114688\,a^2\,b^6\,c^{13}\,d^2-32768\,a\,b^7\,c^{14}\,d+4096\,b^8\,c^{15}}\right)}^{1/4}\,1{}\mathrm{i}\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}{4096\,a^8\,c^7\,d^8-32768\,a^7\,b\,c^8\,d^7+114688\,a^6\,b^2\,c^9\,d^6-229376\,a^5\,b^3\,c^{10}\,d^5+286720\,a^4\,b^4\,c^{11}\,d^4-229376\,a^3\,b^5\,c^{12}\,d^3+114688\,a^2\,b^6\,c^{13}\,d^2-32768\,a\,b^7\,c^{14}\,d+4096\,b^8\,c^{15}}\right)}^{1/4}\,1{}\mathrm{i}}\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}{4096\,a^8\,c^7\,d^8-32768\,a^7\,b\,c^8\,d^7+114688\,a^6\,b^2\,c^9\,d^6-229376\,a^5\,b^3\,c^{10}\,d^5+286720\,a^4\,b^4\,c^{11}\,d^4-229376\,a^3\,b^5\,c^{12}\,d^3+114688\,a^2\,b^6\,c^{13}\,d^2-32768\,a\,b^7\,c^{14}\,d+4096\,b^8\,c^{15}}\right)}^{1/4}+\frac{d\,\sqrt{x}}{2\,c\,\left(d\,x^2+c\right)\,\left(a\,d-b\,c\right)}+\mathrm{atan}\left(\frac{{\left(-\frac{b^7}{16\,a^{11}\,d^8-128\,a^{10}\,b\,c\,d^7+448\,a^9\,b^2\,c^2\,d^6-896\,a^8\,b^3\,c^3\,d^5+1120\,a^7\,b^4\,c^4\,d^4-896\,a^6\,b^5\,c^5\,d^3+448\,a^5\,b^6\,c^6\,d^2-128\,a^4\,b^7\,c^7\,d+16\,a^3\,b^8\,c^8}\right)}^{1/4}\,\left({\left(-\frac{b^7}{16\,a^{11}\,d^8-128\,a^{10}\,b\,c\,d^7+448\,a^9\,b^2\,c^2\,d^6-896\,a^8\,b^3\,c^3\,d^5+1120\,a^7\,b^4\,c^4\,d^4-896\,a^6\,b^5\,c^5\,d^3+448\,a^5\,b^6\,c^6\,d^2-128\,a^4\,b^7\,c^7\,d+16\,a^3\,b^8\,c^8}\right)}^{1/4}\,\left(\frac{2\,\left(81\,a^4\,b^7\,d^{10}-675\,a^3\,b^8\,c\,d^9+1971\,a^2\,b^9\,c^2\,d^8-2145\,a\,b^{10}\,c^3\,d^7+448\,b^{11}\,c^4\,d^6\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}+{\left(-\frac{b^7}{16\,a^{11}\,d^8-128\,a^{10}\,b\,c\,d^7+448\,a^9\,b^2\,c^2\,d^6-896\,a^8\,b^3\,c^3\,d^5+1120\,a^7\,b^4\,c^4\,d^4-896\,a^6\,b^5\,c^5\,d^3+448\,a^5\,b^6\,c^6\,d^2-128\,a^4\,b^7\,c^7\,d+16\,a^3\,b^8\,c^8}\right)}^{3/4}\,\left(\frac{2\,{\left(-\frac{b^7}{16\,a^{11}\,d^8-128\,a^{10}\,b\,c\,d^7+448\,a^9\,b^2\,c^2\,d^6-896\,a^8\,b^3\,c^3\,d^5+1120\,a^7\,b^4\,c^4\,d^4-896\,a^6\,b^5\,c^5\,d^3+448\,a^5\,b^6\,c^6\,d^2-128\,a^4\,b^7\,c^7\,d+16\,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{\sqrt{x}\,\left(2304\,a^{13}\,b^4\,c^2\,d^{17}-29184\,a^{12}\,b^5\,c^3\,d^{16}+163072\,a^{11}\,b^6\,c^4\,d^{15}-530432\,a^{10}\,b^7\,c^5\,d^{14}+1114624\,a^9\,b^8\,c^6\,d^{13}-1580032\,a^8\,b^9\,c^7\,d^{12}+1511936\,a^7\,b^{10}\,c^8\,d^{11}-907264\,a^6\,b^{11}\,c^9\,d^{10}+210176\,a^5\,b^{12}\,c^{10}\,d^9+175616\,a^4\,b^{13}\,c^{11}\,d^8-216832\,a^3\,b^{14}\,c^{12}\,d^7+114688\,a^2\,b^{15}\,c^{13}\,d^6-32768\,a\,b^{16}\,c^{14}\,d^5+4096\,b^{17}\,c^{15}\,d^4\right)}{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{\sqrt{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)}{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)\,1{}\mathrm{i}-{\left(-\frac{b^7}{16\,a^{11}\,d^8-128\,a^{10}\,b\,c\,d^7+448\,a^9\,b^2\,c^2\,d^6-896\,a^8\,b^3\,c^3\,d^5+1120\,a^7\,b^4\,c^4\,d^4-896\,a^6\,b^5\,c^5\,d^3+448\,a^5\,b^6\,c^6\,d^2-128\,a^4\,b^7\,c^7\,d+16\,a^3\,b^8\,c^8}\right)}^{1/4}\,\left({\left(-\frac{b^7}{16\,a^{11}\,d^8-128\,a^{10}\,b\,c\,d^7+448\,a^9\,b^2\,c^2\,d^6-896\,a^8\,b^3\,c^3\,d^5+1120\,a^7\,b^4\,c^4\,d^4-896\,a^6\,b^5\,c^5\,d^3+448\,a^5\,b^6\,c^6\,d^2-128\,a^4\,b^7\,c^7\,d+16\,a^3\,b^8\,c^8}\right)}^{1/4}\,\left(\frac{2\,\left(81\,a^4\,b^7\,d^{10}-675\,a^3\,b^8\,c\,d^9+1971\,a^2\,b^9\,c^2\,d^8-2145\,a\,b^{10}\,c^3\,d^7+448\,b^{11}\,c^4\,d^6\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}+{\left(-\frac{b^7}{16\,a^{11}\,d^8-128\,a^{10}\,b\,c\,d^7+448\,a^9\,b^2\,c^2\,d^6-896\,a^8\,b^3\,c^3\,d^5+1120\,a^7\,b^4\,c^4\,d^4-896\,a^6\,b^5\,c^5\,d^3+448\,a^5\,b^6\,c^6\,d^2-128\,a^4\,b^7\,c^7\,d+16\,a^3\,b^8\,c^8}\right)}^{3/4}\,\left(\frac{2\,{\left(-\frac{b^7}{16\,a^{11}\,d^8-128\,a^{10}\,b\,c\,d^7+448\,a^9\,b^2\,c^2\,d^6-896\,a^8\,b^3\,c^3\,d^5+1120\,a^7\,b^4\,c^4\,d^4-896\,a^6\,b^5\,c^5\,d^3+448\,a^5\,b^6\,c^6\,d^2-128\,a^4\,b^7\,c^7\,d+16\,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{\sqrt{x}\,\left(2304\,a^{13}\,b^4\,c^2\,d^{17}-29184\,a^{12}\,b^5\,c^3\,d^{16}+163072\,a^{11}\,b^6\,c^4\,d^{15}-530432\,a^{10}\,b^7\,c^5\,d^{14}+1114624\,a^9\,b^8\,c^6\,d^{13}-1580032\,a^8\,b^9\,c^7\,d^{12}+1511936\,a^7\,b^{10}\,c^8\,d^{11}-907264\,a^6\,b^{11}\,c^9\,d^{10}+210176\,a^5\,b^{12}\,c^{10}\,d^9+175616\,a^4\,b^{13}\,c^{11}\,d^8-216832\,a^3\,b^{14}\,c^{12}\,d^7+114688\,a^2\,b^{15}\,c^{13}\,d^6-32768\,a\,b^{16}\,c^{14}\,d^5+4096\,b^{17}\,c^{15}\,d^4\right)}{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{\sqrt{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)}{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)\,1{}\mathrm{i}}{{\left(-\frac{b^7}{16\,a^{11}\,d^8-128\,a^{10}\,b\,c\,d^7+448\,a^9\,b^2\,c^2\,d^6-896\,a^8\,b^3\,c^3\,d^5+1120\,a^7\,b^4\,c^4\,d^4-896\,a^6\,b^5\,c^5\,d^3+448\,a^5\,b^6\,c^6\,d^2-128\,a^4\,b^7\,c^7\,d+16\,a^3\,b^8\,c^8}\right)}^{1/4}\,\left({\left(-\frac{b^7}{16\,a^{11}\,d^8-128\,a^{10}\,b\,c\,d^7+448\,a^9\,b^2\,c^2\,d^6-896\,a^8\,b^3\,c^3\,d^5+1120\,a^7\,b^4\,c^4\,d^4-896\,a^6\,b^5\,c^5\,d^3+448\,a^5\,b^6\,c^6\,d^2-128\,a^4\,b^7\,c^7\,d+16\,a^3\,b^8\,c^8}\right)}^{1/4}\,\left(\frac{2\,\left(81\,a^4\,b^7\,d^{10}-675\,a^3\,b^8\,c\,d^9+1971\,a^2\,b^9\,c^2\,d^8-2145\,a\,b^{10}\,c^3\,d^7+448\,b^{11}\,c^4\,d^6\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}+{\left(-\frac{b^7}{16\,a^{11}\,d^8-128\,a^{10}\,b\,c\,d^7+448\,a^9\,b^2\,c^2\,d^6-896\,a^8\,b^3\,c^3\,d^5+1120\,a^7\,b^4\,c^4\,d^4-896\,a^6\,b^5\,c^5\,d^3+448\,a^5\,b^6\,c^6\,d^2-128\,a^4\,b^7\,c^7\,d+16\,a^3\,b^8\,c^8}\right)}^{3/4}\,\left(\frac{2\,{\left(-\frac{b^7}{16\,a^{11}\,d^8-128\,a^{10}\,b\,c\,d^7+448\,a^9\,b^2\,c^2\,d^6-896\,a^8\,b^3\,c^3\,d^5+1120\,a^7\,b^4\,c^4\,d^4-896\,a^6\,b^5\,c^5\,d^3+448\,a^5\,b^6\,c^6\,d^2-128\,a^4\,b^7\,c^7\,d+16\,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{\sqrt{x}\,\left(2304\,a^{13}\,b^4\,c^2\,d^{17}-29184\,a^{12}\,b^5\,c^3\,d^{16}+163072\,a^{11}\,b^6\,c^4\,d^{15}-530432\,a^{10}\,b^7\,c^5\,d^{14}+1114624\,a^9\,b^8\,c^6\,d^{13}-1580032\,a^8\,b^9\,c^7\,d^{12}+1511936\,a^7\,b^{10}\,c^8\,d^{11}-907264\,a^6\,b^{11}\,c^9\,d^{10}+210176\,a^5\,b^{12}\,c^{10}\,d^9+175616\,a^4\,b^{13}\,c^{11}\,d^8-216832\,a^3\,b^{14}\,c^{12}\,d^7+114688\,a^2\,b^{15}\,c^{13}\,d^6-32768\,a\,b^{16}\,c^{14}\,d^5+4096\,b^{17}\,c^{15}\,d^4\right)}{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{\sqrt{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)}{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)+{\left(-\frac{b^7}{16\,a^{11}\,d^8-128\,a^{10}\,b\,c\,d^7+448\,a^9\,b^2\,c^2\,d^6-896\,a^8\,b^3\,c^3\,d^5+1120\,a^7\,b^4\,c^4\,d^4-896\,a^6\,b^5\,c^5\,d^3+448\,a^5\,b^6\,c^6\,d^2-128\,a^4\,b^7\,c^7\,d+16\,a^3\,b^8\,c^8}\right)}^{1/4}\,\left({\left(-\frac{b^7}{16\,a^{11}\,d^8-128\,a^{10}\,b\,c\,d^7+448\,a^9\,b^2\,c^2\,d^6-896\,a^8\,b^3\,c^3\,d^5+1120\,a^7\,b^4\,c^4\,d^4-896\,a^6\,b^5\,c^5\,d^3+448\,a^5\,b^6\,c^6\,d^2-128\,a^4\,b^7\,c^7\,d+16\,a^3\,b^8\,c^8}\right)}^{1/4}\,\left(\frac{2\,\left(81\,a^4\,b^7\,d^{10}-675\,a^3\,b^8\,c\,d^9+1971\,a^2\,b^9\,c^2\,d^8-2145\,a\,b^{10}\,c^3\,d^7+448\,b^{11}\,c^4\,d^6\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}+{\left(-\frac{b^7}{16\,a^{11}\,d^8-128\,a^{10}\,b\,c\,d^7+448\,a^9\,b^2\,c^2\,d^6-896\,a^8\,b^3\,c^3\,d^5+1120\,a^7\,b^4\,c^4\,d^4-896\,a^6\,b^5\,c^5\,d^3+448\,a^5\,b^6\,c^6\,d^2-128\,a^4\,b^7\,c^7\,d+16\,a^3\,b^8\,c^8}\right)}^{3/4}\,\left(\frac{2\,{\left(-\frac{b^7}{16\,a^{11}\,d^8-128\,a^{10}\,b\,c\,d^7+448\,a^9\,b^2\,c^2\,d^6-896\,a^8\,b^3\,c^3\,d^5+1120\,a^7\,b^4\,c^4\,d^4-896\,a^6\,b^5\,c^5\,d^3+448\,a^5\,b^6\,c^6\,d^2-128\,a^4\,b^7\,c^7\,d+16\,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{\sqrt{x}\,\left(2304\,a^{13}\,b^4\,c^2\,d^{17}-29184\,a^{12}\,b^5\,c^3\,d^{16}+163072\,a^{11}\,b^6\,c^4\,d^{15}-530432\,a^{10}\,b^7\,c^5\,d^{14}+1114624\,a^9\,b^8\,c^6\,d^{13}-1580032\,a^8\,b^9\,c^7\,d^{12}+1511936\,a^7\,b^{10}\,c^8\,d^{11}-907264\,a^6\,b^{11}\,c^9\,d^{10}+210176\,a^5\,b^{12}\,c^{10}\,d^9+175616\,a^4\,b^{13}\,c^{11}\,d^8-216832\,a^3\,b^{14}\,c^{12}\,d^7+114688\,a^2\,b^{15}\,c^{13}\,d^6-32768\,a\,b^{16}\,c^{14}\,d^5+4096\,b^{17}\,c^{15}\,d^4\right)}{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{\sqrt{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)}{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}{16\,a^{11}\,d^8-128\,a^{10}\,b\,c\,d^7+448\,a^9\,b^2\,c^2\,d^6-896\,a^8\,b^3\,c^3\,d^5+1120\,a^7\,b^4\,c^4\,d^4-896\,a^6\,b^5\,c^5\,d^3+448\,a^5\,b^6\,c^6\,d^2-128\,a^4\,b^7\,c^7\,d+16\,a^3\,b^8\,c^8}\right)}^{1/4}\,2{}\mathrm{i}-\mathrm{atan}\left(\frac{\left(\left(\left(\frac{\sqrt{x}\,\left(2304\,a^{13}\,b^4\,c^2\,d^{17}-29184\,a^{12}\,b^5\,c^3\,d^{16}+163072\,a^{11}\,b^6\,c^4\,d^{15}-530432\,a^{10}\,b^7\,c^5\,d^{14}+1114624\,a^9\,b^8\,c^6\,d^{13}-1580032\,a^8\,b^9\,c^7\,d^{12}+1511936\,a^7\,b^{10}\,c^8\,d^{11}-907264\,a^6\,b^{11}\,c^9\,d^{10}+210176\,a^5\,b^{12}\,c^{10}\,d^9+175616\,a^4\,b^{13}\,c^{11}\,d^8-216832\,a^3\,b^{14}\,c^{12}\,d^7+114688\,a^2\,b^{15}\,c^{13}\,d^6-32768\,a\,b^{16}\,c^{14}\,d^5+4096\,b^{17}\,c^{15}\,d^4\right)}{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}}-\frac{2\,{\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}{4096\,a^8\,c^7\,d^8-32768\,a^7\,b\,c^8\,d^7+114688\,a^6\,b^2\,c^9\,d^6-229376\,a^5\,b^3\,c^{10}\,d^5+286720\,a^4\,b^4\,c^{11}\,d^4-229376\,a^3\,b^5\,c^{12}\,d^3+114688\,a^2\,b^6\,c^{13}\,d^2-32768\,a\,b^7\,c^{14}\,d+4096\,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}\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}{4096\,a^8\,c^7\,d^8-32768\,a^7\,b\,c^8\,d^7+114688\,a^6\,b^2\,c^9\,d^6-229376\,a^5\,b^3\,c^{10}\,d^5+286720\,a^4\,b^4\,c^{11}\,d^4-229376\,a^3\,b^5\,c^{12}\,d^3+114688\,a^2\,b^6\,c^{13}\,d^2-32768\,a\,b^7\,c^{14}\,d+4096\,b^8\,c^{15}}\right)}^{3/4}-\frac{2\,\left(81\,a^4\,b^7\,d^{10}-675\,a^3\,b^8\,c\,d^9+1971\,a^2\,b^9\,c^2\,d^8-2145\,a\,b^{10}\,c^3\,d^7+448\,b^{11}\,c^4\,d^6\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}\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}{4096\,a^8\,c^7\,d^8-32768\,a^7\,b\,c^8\,d^7+114688\,a^6\,b^2\,c^9\,d^6-229376\,a^5\,b^3\,c^{10}\,d^5+286720\,a^4\,b^4\,c^{11}\,d^4-229376\,a^3\,b^5\,c^{12}\,d^3+114688\,a^2\,b^6\,c^{13}\,d^2-32768\,a\,b^7\,c^{14}\,d+4096\,b^8\,c^{15}}\right)}^{1/4}+\frac{\sqrt{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)}{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)\,{\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}{4096\,a^8\,c^7\,d^8-32768\,a^7\,b\,c^8\,d^7+114688\,a^6\,b^2\,c^9\,d^6-229376\,a^5\,b^3\,c^{10}\,d^5+286720\,a^4\,b^4\,c^{11}\,d^4-229376\,a^3\,b^5\,c^{12}\,d^3+114688\,a^2\,b^6\,c^{13}\,d^2-32768\,a\,b^7\,c^{14}\,d+4096\,b^8\,c^{15}}\right)}^{1/4}\,1{}\mathrm{i}+\left(\left(\left(\frac{\sqrt{x}\,\left(2304\,a^{13}\,b^4\,c^2\,d^{17}-29184\,a^{12}\,b^5\,c^3\,d^{16}+163072\,a^{11}\,b^6\,c^4\,d^{15}-530432\,a^{10}\,b^7\,c^5\,d^{14}+1114624\,a^9\,b^8\,c^6\,d^{13}-1580032\,a^8\,b^9\,c^7\,d^{12}+1511936\,a^7\,b^{10}\,c^8\,d^{11}-907264\,a^6\,b^{11}\,c^9\,d^{10}+210176\,a^5\,b^{12}\,c^{10}\,d^9+175616\,a^4\,b^{13}\,c^{11}\,d^8-216832\,a^3\,b^{14}\,c^{12}\,d^7+114688\,a^2\,b^{15}\,c^{13}\,d^6-32768\,a\,b^{16}\,c^{14}\,d^5+4096\,b^{17}\,c^{15}\,d^4\right)}{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}}+\frac{2\,{\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}{4096\,a^8\,c^7\,d^8-32768\,a^7\,b\,c^8\,d^7+114688\,a^6\,b^2\,c^9\,d^6-229376\,a^5\,b^3\,c^{10}\,d^5+286720\,a^4\,b^4\,c^{11}\,d^4-229376\,a^3\,b^5\,c^{12}\,d^3+114688\,a^2\,b^6\,c^{13}\,d^2-32768\,a\,b^7\,c^{14}\,d+4096\,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}\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}{4096\,a^8\,c^7\,d^8-32768\,a^7\,b\,c^8\,d^7+114688\,a^6\,b^2\,c^9\,d^6-229376\,a^5\,b^3\,c^{10}\,d^5+286720\,a^4\,b^4\,c^{11}\,d^4-229376\,a^3\,b^5\,c^{12}\,d^3+114688\,a^2\,b^6\,c^{13}\,d^2-32768\,a\,b^7\,c^{14}\,d+4096\,b^8\,c^{15}}\right)}^{3/4}+\frac{2\,\left(81\,a^4\,b^7\,d^{10}-675\,a^3\,b^8\,c\,d^9+1971\,a^2\,b^9\,c^2\,d^8-2145\,a\,b^{10}\,c^3\,d^7+448\,b^{11}\,c^4\,d^6\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}\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}{4096\,a^8\,c^7\,d^8-32768\,a^7\,b\,c^8\,d^7+114688\,a^6\,b^2\,c^9\,d^6-229376\,a^5\,b^3\,c^{10}\,d^5+286720\,a^4\,b^4\,c^{11}\,d^4-229376\,a^3\,b^5\,c^{12}\,d^3+114688\,a^2\,b^6\,c^{13}\,d^2-32768\,a\,b^7\,c^{14}\,d+4096\,b^8\,c^{15}}\right)}^{1/4}+\frac{\sqrt{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)}{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)\,{\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}{4096\,a^8\,c^7\,d^8-32768\,a^7\,b\,c^8\,d^7+114688\,a^6\,b^2\,c^9\,d^6-229376\,a^5\,b^3\,c^{10}\,d^5+286720\,a^4\,b^4\,c^{11}\,d^4-229376\,a^3\,b^5\,c^{12}\,d^3+114688\,a^2\,b^6\,c^{13}\,d^2-32768\,a\,b^7\,c^{14}\,d+4096\,b^8\,c^{15}}\right)}^{1/4}\,1{}\mathrm{i}}{\left(\left(\left(\frac{\sqrt{x}\,\left(2304\,a^{13}\,b^4\,c^2\,d^{17}-29184\,a^{12}\,b^5\,c^3\,d^{16}+163072\,a^{11}\,b^6\,c^4\,d^{15}-530432\,a^{10}\,b^7\,c^5\,d^{14}+1114624\,a^9\,b^8\,c^6\,d^{13}-1580032\,a^8\,b^9\,c^7\,d^{12}+1511936\,a^7\,b^{10}\,c^8\,d^{11}-907264\,a^6\,b^{11}\,c^9\,d^{10}+210176\,a^5\,b^{12}\,c^{10}\,d^9+175616\,a^4\,b^{13}\,c^{11}\,d^8-216832\,a^3\,b^{14}\,c^{12}\,d^7+114688\,a^2\,b^{15}\,c^{13}\,d^6-32768\,a\,b^{16}\,c^{14}\,d^5+4096\,b^{17}\,c^{15}\,d^4\right)}{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}}-\frac{2\,{\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}{4096\,a^8\,c^7\,d^8-32768\,a^7\,b\,c^8\,d^7+114688\,a^6\,b^2\,c^9\,d^6-229376\,a^5\,b^3\,c^{10}\,d^5+286720\,a^4\,b^4\,c^{11}\,d^4-229376\,a^3\,b^5\,c^{12}\,d^3+114688\,a^2\,b^6\,c^{13}\,d^2-32768\,a\,b^7\,c^{14}\,d+4096\,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}\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}{4096\,a^8\,c^7\,d^8-32768\,a^7\,b\,c^8\,d^7+114688\,a^6\,b^2\,c^9\,d^6-229376\,a^5\,b^3\,c^{10}\,d^5+286720\,a^4\,b^4\,c^{11}\,d^4-229376\,a^3\,b^5\,c^{12}\,d^3+114688\,a^2\,b^6\,c^{13}\,d^2-32768\,a\,b^7\,c^{14}\,d+4096\,b^8\,c^{15}}\right)}^{3/4}-\frac{2\,\left(81\,a^4\,b^7\,d^{10}-675\,a^3\,b^8\,c\,d^9+1971\,a^2\,b^9\,c^2\,d^8-2145\,a\,b^{10}\,c^3\,d^7+448\,b^{11}\,c^4\,d^6\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}\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}{4096\,a^8\,c^7\,d^8-32768\,a^7\,b\,c^8\,d^7+114688\,a^6\,b^2\,c^9\,d^6-229376\,a^5\,b^3\,c^{10}\,d^5+286720\,a^4\,b^4\,c^{11}\,d^4-229376\,a^3\,b^5\,c^{12}\,d^3+114688\,a^2\,b^6\,c^{13}\,d^2-32768\,a\,b^7\,c^{14}\,d+4096\,b^8\,c^{15}}\right)}^{1/4}+\frac{\sqrt{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)}{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)\,{\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}{4096\,a^8\,c^7\,d^8-32768\,a^7\,b\,c^8\,d^7+114688\,a^6\,b^2\,c^9\,d^6-229376\,a^5\,b^3\,c^{10}\,d^5+286720\,a^4\,b^4\,c^{11}\,d^4-229376\,a^3\,b^5\,c^{12}\,d^3+114688\,a^2\,b^6\,c^{13}\,d^2-32768\,a\,b^7\,c^{14}\,d+4096\,b^8\,c^{15}}\right)}^{1/4}-\left(\left(\left(\frac{\sqrt{x}\,\left(2304\,a^{13}\,b^4\,c^2\,d^{17}-29184\,a^{12}\,b^5\,c^3\,d^{16}+163072\,a^{11}\,b^6\,c^4\,d^{15}-530432\,a^{10}\,b^7\,c^5\,d^{14}+1114624\,a^9\,b^8\,c^6\,d^{13}-1580032\,a^8\,b^9\,c^7\,d^{12}+1511936\,a^7\,b^{10}\,c^8\,d^{11}-907264\,a^6\,b^{11}\,c^9\,d^{10}+210176\,a^5\,b^{12}\,c^{10}\,d^9+175616\,a^4\,b^{13}\,c^{11}\,d^8-216832\,a^3\,b^{14}\,c^{12}\,d^7+114688\,a^2\,b^{15}\,c^{13}\,d^6-32768\,a\,b^{16}\,c^{14}\,d^5+4096\,b^{17}\,c^{15}\,d^4\right)}{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}}+\frac{2\,{\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}{4096\,a^8\,c^7\,d^8-32768\,a^7\,b\,c^8\,d^7+114688\,a^6\,b^2\,c^9\,d^6-229376\,a^5\,b^3\,c^{10}\,d^5+286720\,a^4\,b^4\,c^{11}\,d^4-229376\,a^3\,b^5\,c^{12}\,d^3+114688\,a^2\,b^6\,c^{13}\,d^2-32768\,a\,b^7\,c^{14}\,d+4096\,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}\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}{4096\,a^8\,c^7\,d^8-32768\,a^7\,b\,c^8\,d^7+114688\,a^6\,b^2\,c^9\,d^6-229376\,a^5\,b^3\,c^{10}\,d^5+286720\,a^4\,b^4\,c^{11}\,d^4-229376\,a^3\,b^5\,c^{12}\,d^3+114688\,a^2\,b^6\,c^{13}\,d^2-32768\,a\,b^7\,c^{14}\,d+4096\,b^8\,c^{15}}\right)}^{3/4}+\frac{2\,\left(81\,a^4\,b^7\,d^{10}-675\,a^3\,b^8\,c\,d^9+1971\,a^2\,b^9\,c^2\,d^8-2145\,a\,b^{10}\,c^3\,d^7+448\,b^{11}\,c^4\,d^6\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}\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}{4096\,a^8\,c^7\,d^8-32768\,a^7\,b\,c^8\,d^7+114688\,a^6\,b^2\,c^9\,d^6-229376\,a^5\,b^3\,c^{10}\,d^5+286720\,a^4\,b^4\,c^{11}\,d^4-229376\,a^3\,b^5\,c^{12}\,d^3+114688\,a^2\,b^6\,c^{13}\,d^2-32768\,a\,b^7\,c^{14}\,d+4096\,b^8\,c^{15}}\right)}^{1/4}+\frac{\sqrt{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)}{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)\,{\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}{4096\,a^8\,c^7\,d^8-32768\,a^7\,b\,c^8\,d^7+114688\,a^6\,b^2\,c^9\,d^6-229376\,a^5\,b^3\,c^{10}\,d^5+286720\,a^4\,b^4\,c^{11}\,d^4-229376\,a^3\,b^5\,c^{12}\,d^3+114688\,a^2\,b^6\,c^{13}\,d^2-32768\,a\,b^7\,c^{14}\,d+4096\,b^8\,c^{15}}\right)}^{1/4}}\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}{4096\,a^8\,c^7\,d^8-32768\,a^7\,b\,c^8\,d^7+114688\,a^6\,b^2\,c^9\,d^6-229376\,a^5\,b^3\,c^{10}\,d^5+286720\,a^4\,b^4\,c^{11}\,d^4-229376\,a^3\,b^5\,c^{12}\,d^3+114688\,a^2\,b^6\,c^{13}\,d^2-32768\,a\,b^7\,c^{14}\,d+4096\,b^8\,c^{15}}\right)}^{1/4}\,2{}\mathrm{i}","Not used",1,"atan(((-b^7/(16*a^11*d^8 + 16*a^3*b^8*c^8 - 128*a^4*b^7*c^7*d + 448*a^5*b^6*c^6*d^2 - 896*a^6*b^5*c^5*d^3 + 1120*a^7*b^4*c^4*d^4 - 896*a^8*b^3*c^3*d^5 + 448*a^9*b^2*c^2*d^6 - 128*a^10*b*c*d^7))^(1/4)*((-b^7/(16*a^11*d^8 + 16*a^3*b^8*c^8 - 128*a^4*b^7*c^7*d + 448*a^5*b^6*c^6*d^2 - 896*a^6*b^5*c^5*d^3 + 1120*a^7*b^4*c^4*d^4 - 896*a^8*b^3*c^3*d^5 + 448*a^9*b^2*c^2*d^6 - 128*a^10*b*c*d^7))^(1/4)*((2*(81*a^4*b^7*d^10 + 448*b^11*c^4*d^6 - 2145*a*b^10*c^3*d^7 - 675*a^3*b^8*c*d^9 + 1971*a^2*b^9*c^2*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) + (-b^7/(16*a^11*d^8 + 16*a^3*b^8*c^8 - 128*a^4*b^7*c^7*d + 448*a^5*b^6*c^6*d^2 - 896*a^6*b^5*c^5*d^3 + 1120*a^7*b^4*c^4*d^4 - 896*a^8*b^3*c^3*d^5 + 448*a^9*b^2*c^2*d^6 - 128*a^10*b*c*d^7))^(3/4)*((2*(-b^7/(16*a^11*d^8 + 16*a^3*b^8*c^8 - 128*a^4*b^7*c^7*d + 448*a^5*b^6*c^6*d^2 - 896*a^6*b^5*c^5*d^3 + 1120*a^7*b^4*c^4*d^4 - 896*a^8*b^3*c^3*d^5 + 448*a^9*b^2*c^2*d^6 - 128*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^(1/2)*(4096*b^17*c^15*d^4 - 32768*a*b^16*c^14*d^5 + 114688*a^2*b^15*c^13*d^6 - 216832*a^3*b^14*c^12*d^7 + 175616*a^4*b^13*c^11*d^8 + 210176*a^5*b^12*c^10*d^9 - 907264*a^6*b^11*c^9*d^10 + 1511936*a^7*b^10*c^8*d^11 - 1580032*a^8*b^9*c^7*d^12 + 1114624*a^9*b^8*c^6*d^13 - 530432*a^10*b^7*c^5*d^14 + 163072*a^11*b^6*c^4*d^15 - 29184*a^12*b^5*c^3*d^16 + 2304*a^13*b^4*c^2*d^17))/(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^(1/2)*(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))/(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 - (-b^7/(16*a^11*d^8 + 16*a^3*b^8*c^8 - 128*a^4*b^7*c^7*d + 448*a^5*b^6*c^6*d^2 - 896*a^6*b^5*c^5*d^3 + 1120*a^7*b^4*c^4*d^4 - 896*a^8*b^3*c^3*d^5 + 448*a^9*b^2*c^2*d^6 - 128*a^10*b*c*d^7))^(1/4)*((-b^7/(16*a^11*d^8 + 16*a^3*b^8*c^8 - 128*a^4*b^7*c^7*d + 448*a^5*b^6*c^6*d^2 - 896*a^6*b^5*c^5*d^3 + 1120*a^7*b^4*c^4*d^4 - 896*a^8*b^3*c^3*d^5 + 448*a^9*b^2*c^2*d^6 - 128*a^10*b*c*d^7))^(1/4)*((2*(81*a^4*b^7*d^10 + 448*b^11*c^4*d^6 - 2145*a*b^10*c^3*d^7 - 675*a^3*b^8*c*d^9 + 1971*a^2*b^9*c^2*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) + (-b^7/(16*a^11*d^8 + 16*a^3*b^8*c^8 - 128*a^4*b^7*c^7*d + 448*a^5*b^6*c^6*d^2 - 896*a^6*b^5*c^5*d^3 + 1120*a^7*b^4*c^4*d^4 - 896*a^8*b^3*c^3*d^5 + 448*a^9*b^2*c^2*d^6 - 128*a^10*b*c*d^7))^(3/4)*((2*(-b^7/(16*a^11*d^8 + 16*a^3*b^8*c^8 - 128*a^4*b^7*c^7*d + 448*a^5*b^6*c^6*d^2 - 896*a^6*b^5*c^5*d^3 + 1120*a^7*b^4*c^4*d^4 - 896*a^8*b^3*c^3*d^5 + 448*a^9*b^2*c^2*d^6 - 128*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^(1/2)*(4096*b^17*c^15*d^4 - 32768*a*b^16*c^14*d^5 + 114688*a^2*b^15*c^13*d^6 - 216832*a^3*b^14*c^12*d^7 + 175616*a^4*b^13*c^11*d^8 + 210176*a^5*b^12*c^10*d^9 - 907264*a^6*b^11*c^9*d^10 + 1511936*a^7*b^10*c^8*d^11 - 1580032*a^8*b^9*c^7*d^12 + 1114624*a^9*b^8*c^6*d^13 - 530432*a^10*b^7*c^5*d^14 + 163072*a^11*b^6*c^4*d^15 - 29184*a^12*b^5*c^3*d^16 + 2304*a^13*b^4*c^2*d^17))/(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^(1/2)*(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))/(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)/((-b^7/(16*a^11*d^8 + 16*a^3*b^8*c^8 - 128*a^4*b^7*c^7*d + 448*a^5*b^6*c^6*d^2 - 896*a^6*b^5*c^5*d^3 + 1120*a^7*b^4*c^4*d^4 - 896*a^8*b^3*c^3*d^5 + 448*a^9*b^2*c^2*d^6 - 128*a^10*b*c*d^7))^(1/4)*((-b^7/(16*a^11*d^8 + 16*a^3*b^8*c^8 - 128*a^4*b^7*c^7*d + 448*a^5*b^6*c^6*d^2 - 896*a^6*b^5*c^5*d^3 + 1120*a^7*b^4*c^4*d^4 - 896*a^8*b^3*c^3*d^5 + 448*a^9*b^2*c^2*d^6 - 128*a^10*b*c*d^7))^(1/4)*((2*(81*a^4*b^7*d^10 + 448*b^11*c^4*d^6 - 2145*a*b^10*c^3*d^7 - 675*a^3*b^8*c*d^9 + 1971*a^2*b^9*c^2*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) + (-b^7/(16*a^11*d^8 + 16*a^3*b^8*c^8 - 128*a^4*b^7*c^7*d + 448*a^5*b^6*c^6*d^2 - 896*a^6*b^5*c^5*d^3 + 1120*a^7*b^4*c^4*d^4 - 896*a^8*b^3*c^3*d^5 + 448*a^9*b^2*c^2*d^6 - 128*a^10*b*c*d^7))^(3/4)*((2*(-b^7/(16*a^11*d^8 + 16*a^3*b^8*c^8 - 128*a^4*b^7*c^7*d + 448*a^5*b^6*c^6*d^2 - 896*a^6*b^5*c^5*d^3 + 1120*a^7*b^4*c^4*d^4 - 896*a^8*b^3*c^3*d^5 + 448*a^9*b^2*c^2*d^6 - 128*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^(1/2)*(4096*b^17*c^15*d^4 - 32768*a*b^16*c^14*d^5 + 114688*a^2*b^15*c^13*d^6 - 216832*a^3*b^14*c^12*d^7 + 175616*a^4*b^13*c^11*d^8 + 210176*a^5*b^12*c^10*d^9 - 907264*a^6*b^11*c^9*d^10 + 1511936*a^7*b^10*c^8*d^11 - 1580032*a^8*b^9*c^7*d^12 + 1114624*a^9*b^8*c^6*d^13 - 530432*a^10*b^7*c^5*d^14 + 163072*a^11*b^6*c^4*d^15 - 29184*a^12*b^5*c^3*d^16 + 2304*a^13*b^4*c^2*d^17))/(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^(1/2)*(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))/(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/(16*a^11*d^8 + 16*a^3*b^8*c^8 - 128*a^4*b^7*c^7*d + 448*a^5*b^6*c^6*d^2 - 896*a^6*b^5*c^5*d^3 + 1120*a^7*b^4*c^4*d^4 - 896*a^8*b^3*c^3*d^5 + 448*a^9*b^2*c^2*d^6 - 128*a^10*b*c*d^7))^(1/4)*((-b^7/(16*a^11*d^8 + 16*a^3*b^8*c^8 - 128*a^4*b^7*c^7*d + 448*a^5*b^6*c^6*d^2 - 896*a^6*b^5*c^5*d^3 + 1120*a^7*b^4*c^4*d^4 - 896*a^8*b^3*c^3*d^5 + 448*a^9*b^2*c^2*d^6 - 128*a^10*b*c*d^7))^(1/4)*((2*(81*a^4*b^7*d^10 + 448*b^11*c^4*d^6 - 2145*a*b^10*c^3*d^7 - 675*a^3*b^8*c*d^9 + 1971*a^2*b^9*c^2*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) + (-b^7/(16*a^11*d^8 + 16*a^3*b^8*c^8 - 128*a^4*b^7*c^7*d + 448*a^5*b^6*c^6*d^2 - 896*a^6*b^5*c^5*d^3 + 1120*a^7*b^4*c^4*d^4 - 896*a^8*b^3*c^3*d^5 + 448*a^9*b^2*c^2*d^6 - 128*a^10*b*c*d^7))^(3/4)*((2*(-b^7/(16*a^11*d^8 + 16*a^3*b^8*c^8 - 128*a^4*b^7*c^7*d + 448*a^5*b^6*c^6*d^2 - 896*a^6*b^5*c^5*d^3 + 1120*a^7*b^4*c^4*d^4 - 896*a^8*b^3*c^3*d^5 + 448*a^9*b^2*c^2*d^6 - 128*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^(1/2)*(4096*b^17*c^15*d^4 - 32768*a*b^16*c^14*d^5 + 114688*a^2*b^15*c^13*d^6 - 216832*a^3*b^14*c^12*d^7 + 175616*a^4*b^13*c^11*d^8 + 210176*a^5*b^12*c^10*d^9 - 907264*a^6*b^11*c^9*d^10 + 1511936*a^7*b^10*c^8*d^11 - 1580032*a^8*b^9*c^7*d^12 + 1114624*a^9*b^8*c^6*d^13 - 530432*a^10*b^7*c^5*d^14 + 163072*a^11*b^6*c^4*d^15 - 29184*a^12*b^5*c^3*d^16 + 2304*a^13*b^4*c^2*d^17))/(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^(1/2)*(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))/(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/(16*a^11*d^8 + 16*a^3*b^8*c^8 - 128*a^4*b^7*c^7*d + 448*a^5*b^6*c^6*d^2 - 896*a^6*b^5*c^5*d^3 + 1120*a^7*b^4*c^4*d^4 - 896*a^8*b^3*c^3*d^5 + 448*a^9*b^2*c^2*d^6 - 128*a^10*b*c*d^7))^(1/4)*2i + 2*atan(((-b^7/(16*a^11*d^8 + 16*a^3*b^8*c^8 - 128*a^4*b^7*c^7*d + 448*a^5*b^6*c^6*d^2 - 896*a^6*b^5*c^5*d^3 + 1120*a^7*b^4*c^4*d^4 - 896*a^8*b^3*c^3*d^5 + 448*a^9*b^2*c^2*d^6 - 128*a^10*b*c*d^7))^(1/4)*((-b^7/(16*a^11*d^8 + 16*a^3*b^8*c^8 - 128*a^4*b^7*c^7*d + 448*a^5*b^6*c^6*d^2 - 896*a^6*b^5*c^5*d^3 + 1120*a^7*b^4*c^4*d^4 - 896*a^8*b^3*c^3*d^5 + 448*a^9*b^2*c^2*d^6 - 128*a^10*b*c*d^7))^(1/4)*((2*(81*a^4*b^7*d^10 + 448*b^11*c^4*d^6 - 2145*a*b^10*c^3*d^7 - 675*a^3*b^8*c*d^9 + 1971*a^2*b^9*c^2*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) - (-b^7/(16*a^11*d^8 + 16*a^3*b^8*c^8 - 128*a^4*b^7*c^7*d + 448*a^5*b^6*c^6*d^2 - 896*a^6*b^5*c^5*d^3 + 1120*a^7*b^4*c^4*d^4 - 896*a^8*b^3*c^3*d^5 + 448*a^9*b^2*c^2*d^6 - 128*a^10*b*c*d^7))^(3/4)*(((-b^7/(16*a^11*d^8 + 16*a^3*b^8*c^8 - 128*a^4*b^7*c^7*d + 448*a^5*b^6*c^6*d^2 - 896*a^6*b^5*c^5*d^3 + 1120*a^7*b^4*c^4*d^4 - 896*a^8*b^3*c^3*d^5 + 448*a^9*b^2*c^2*d^6 - 128*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)*2i)/(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^(1/2)*(4096*b^17*c^15*d^4 - 32768*a*b^16*c^14*d^5 + 114688*a^2*b^15*c^13*d^6 - 216832*a^3*b^14*c^12*d^7 + 175616*a^4*b^13*c^11*d^8 + 210176*a^5*b^12*c^10*d^9 - 907264*a^6*b^11*c^9*d^10 + 1511936*a^7*b^10*c^8*d^11 - 1580032*a^8*b^9*c^7*d^12 + 1114624*a^9*b^8*c^6*d^13 - 530432*a^10*b^7*c^5*d^14 + 163072*a^11*b^6*c^4*d^15 - 29184*a^12*b^5*c^3*d^16 + 2304*a^13*b^4*c^2*d^17))/(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^(1/2)*(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))/(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/(16*a^11*d^8 + 16*a^3*b^8*c^8 - 128*a^4*b^7*c^7*d + 448*a^5*b^6*c^6*d^2 - 896*a^6*b^5*c^5*d^3 + 1120*a^7*b^4*c^4*d^4 - 896*a^8*b^3*c^3*d^5 + 448*a^9*b^2*c^2*d^6 - 128*a^10*b*c*d^7))^(1/4)*((-b^7/(16*a^11*d^8 + 16*a^3*b^8*c^8 - 128*a^4*b^7*c^7*d + 448*a^5*b^6*c^6*d^2 - 896*a^6*b^5*c^5*d^3 + 1120*a^7*b^4*c^4*d^4 - 896*a^8*b^3*c^3*d^5 + 448*a^9*b^2*c^2*d^6 - 128*a^10*b*c*d^7))^(1/4)*((2*(81*a^4*b^7*d^10 + 448*b^11*c^4*d^6 - 2145*a*b^10*c^3*d^7 - 675*a^3*b^8*c*d^9 + 1971*a^2*b^9*c^2*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) - (-b^7/(16*a^11*d^8 + 16*a^3*b^8*c^8 - 128*a^4*b^7*c^7*d + 448*a^5*b^6*c^6*d^2 - 896*a^6*b^5*c^5*d^3 + 1120*a^7*b^4*c^4*d^4 - 896*a^8*b^3*c^3*d^5 + 448*a^9*b^2*c^2*d^6 - 128*a^10*b*c*d^7))^(3/4)*(((-b^7/(16*a^11*d^8 + 16*a^3*b^8*c^8 - 128*a^4*b^7*c^7*d + 448*a^5*b^6*c^6*d^2 - 896*a^6*b^5*c^5*d^3 + 1120*a^7*b^4*c^4*d^4 - 896*a^8*b^3*c^3*d^5 + 448*a^9*b^2*c^2*d^6 - 128*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)*2i)/(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^(1/2)*(4096*b^17*c^15*d^4 - 32768*a*b^16*c^14*d^5 + 114688*a^2*b^15*c^13*d^6 - 216832*a^3*b^14*c^12*d^7 + 175616*a^4*b^13*c^11*d^8 + 210176*a^5*b^12*c^10*d^9 - 907264*a^6*b^11*c^9*d^10 + 1511936*a^7*b^10*c^8*d^11 - 1580032*a^8*b^9*c^7*d^12 + 1114624*a^9*b^8*c^6*d^13 - 530432*a^10*b^7*c^5*d^14 + 163072*a^11*b^6*c^4*d^15 - 29184*a^12*b^5*c^3*d^16 + 2304*a^13*b^4*c^2*d^17))/(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^(1/2)*(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))/(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/(16*a^11*d^8 + 16*a^3*b^8*c^8 - 128*a^4*b^7*c^7*d + 448*a^5*b^6*c^6*d^2 - 896*a^6*b^5*c^5*d^3 + 1120*a^7*b^4*c^4*d^4 - 896*a^8*b^3*c^3*d^5 + 448*a^9*b^2*c^2*d^6 - 128*a^10*b*c*d^7))^(1/4)*((-b^7/(16*a^11*d^8 + 16*a^3*b^8*c^8 - 128*a^4*b^7*c^7*d + 448*a^5*b^6*c^6*d^2 - 896*a^6*b^5*c^5*d^3 + 1120*a^7*b^4*c^4*d^4 - 896*a^8*b^3*c^3*d^5 + 448*a^9*b^2*c^2*d^6 - 128*a^10*b*c*d^7))^(1/4)*((2*(81*a^4*b^7*d^10 + 448*b^11*c^4*d^6 - 2145*a*b^10*c^3*d^7 - 675*a^3*b^8*c*d^9 + 1971*a^2*b^9*c^2*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) - (-b^7/(16*a^11*d^8 + 16*a^3*b^8*c^8 - 128*a^4*b^7*c^7*d + 448*a^5*b^6*c^6*d^2 - 896*a^6*b^5*c^5*d^3 + 1120*a^7*b^4*c^4*d^4 - 896*a^8*b^3*c^3*d^5 + 448*a^9*b^2*c^2*d^6 - 128*a^10*b*c*d^7))^(3/4)*(((-b^7/(16*a^11*d^8 + 16*a^3*b^8*c^8 - 128*a^4*b^7*c^7*d + 448*a^5*b^6*c^6*d^2 - 896*a^6*b^5*c^5*d^3 + 1120*a^7*b^4*c^4*d^4 - 896*a^8*b^3*c^3*d^5 + 448*a^9*b^2*c^2*d^6 - 128*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)*2i)/(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^(1/2)*(4096*b^17*c^15*d^4 - 32768*a*b^16*c^14*d^5 + 114688*a^2*b^15*c^13*d^6 - 216832*a^3*b^14*c^12*d^7 + 175616*a^4*b^13*c^11*d^8 + 210176*a^5*b^12*c^10*d^9 - 907264*a^6*b^11*c^9*d^10 + 1511936*a^7*b^10*c^8*d^11 - 1580032*a^8*b^9*c^7*d^12 + 1114624*a^9*b^8*c^6*d^13 - 530432*a^10*b^7*c^5*d^14 + 163072*a^11*b^6*c^4*d^15 - 29184*a^12*b^5*c^3*d^16 + 2304*a^13*b^4*c^2*d^17))/(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^(1/2)*(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))/(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 + (-b^7/(16*a^11*d^8 + 16*a^3*b^8*c^8 - 128*a^4*b^7*c^7*d + 448*a^5*b^6*c^6*d^2 - 896*a^6*b^5*c^5*d^3 + 1120*a^7*b^4*c^4*d^4 - 896*a^8*b^3*c^3*d^5 + 448*a^9*b^2*c^2*d^6 - 128*a^10*b*c*d^7))^(1/4)*((-b^7/(16*a^11*d^8 + 16*a^3*b^8*c^8 - 128*a^4*b^7*c^7*d + 448*a^5*b^6*c^6*d^2 - 896*a^6*b^5*c^5*d^3 + 1120*a^7*b^4*c^4*d^4 - 896*a^8*b^3*c^3*d^5 + 448*a^9*b^2*c^2*d^6 - 128*a^10*b*c*d^7))^(1/4)*((2*(81*a^4*b^7*d^10 + 448*b^11*c^4*d^6 - 2145*a*b^10*c^3*d^7 - 675*a^3*b^8*c*d^9 + 1971*a^2*b^9*c^2*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) - (-b^7/(16*a^11*d^8 + 16*a^3*b^8*c^8 - 128*a^4*b^7*c^7*d + 448*a^5*b^6*c^6*d^2 - 896*a^6*b^5*c^5*d^3 + 1120*a^7*b^4*c^4*d^4 - 896*a^8*b^3*c^3*d^5 + 448*a^9*b^2*c^2*d^6 - 128*a^10*b*c*d^7))^(3/4)*(((-b^7/(16*a^11*d^8 + 16*a^3*b^8*c^8 - 128*a^4*b^7*c^7*d + 448*a^5*b^6*c^6*d^2 - 896*a^6*b^5*c^5*d^3 + 1120*a^7*b^4*c^4*d^4 - 896*a^8*b^3*c^3*d^5 + 448*a^9*b^2*c^2*d^6 - 128*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)*2i)/(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^(1/2)*(4096*b^17*c^15*d^4 - 32768*a*b^16*c^14*d^5 + 114688*a^2*b^15*c^13*d^6 - 216832*a^3*b^14*c^12*d^7 + 175616*a^4*b^13*c^11*d^8 + 210176*a^5*b^12*c^10*d^9 - 907264*a^6*b^11*c^9*d^10 + 1511936*a^7*b^10*c^8*d^11 - 1580032*a^8*b^9*c^7*d^12 + 1114624*a^9*b^8*c^6*d^13 - 530432*a^10*b^7*c^5*d^14 + 163072*a^11*b^6*c^4*d^15 - 29184*a^12*b^5*c^3*d^16 + 2304*a^13*b^4*c^2*d^17))/(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^(1/2)*(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))/(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))*(-b^7/(16*a^11*d^8 + 16*a^3*b^8*c^8 - 128*a^4*b^7*c^7*d + 448*a^5*b^6*c^6*d^2 - 896*a^6*b^5*c^5*d^3 + 1120*a^7*b^4*c^4*d^4 - 896*a^8*b^3*c^3*d^5 + 448*a^9*b^2*c^2*d^6 - 128*a^10*b*c*d^7))^(1/4) - atan((((((x^(1/2)*(4096*b^17*c^15*d^4 - 32768*a*b^16*c^14*d^5 + 114688*a^2*b^15*c^13*d^6 - 216832*a^3*b^14*c^12*d^7 + 175616*a^4*b^13*c^11*d^8 + 210176*a^5*b^12*c^10*d^9 - 907264*a^6*b^11*c^9*d^10 + 1511936*a^7*b^10*c^8*d^11 - 1580032*a^8*b^9*c^7*d^12 + 1114624*a^9*b^8*c^6*d^13 - 530432*a^10*b^7*c^5*d^14 + 163072*a^11*b^6*c^4*d^15 - 29184*a^12*b^5*c^3*d^16 + 2304*a^13*b^4*c^2*d^17))/(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) - (2*(-(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)/(4096*b^8*c^15 + 4096*a^8*c^7*d^8 - 32768*a^7*b*c^8*d^7 + 114688*a^2*b^6*c^13*d^2 - 229376*a^3*b^5*c^12*d^3 + 286720*a^4*b^4*c^11*d^4 - 229376*a^5*b^3*c^10*d^5 + 114688*a^6*b^2*c^9*d^6 - 32768*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))*(-(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)/(4096*b^8*c^15 + 4096*a^8*c^7*d^8 - 32768*a^7*b*c^8*d^7 + 114688*a^2*b^6*c^13*d^2 - 229376*a^3*b^5*c^12*d^3 + 286720*a^4*b^4*c^11*d^4 - 229376*a^5*b^3*c^10*d^5 + 114688*a^6*b^2*c^9*d^6 - 32768*a*b^7*c^14*d))^(3/4) - (2*(81*a^4*b^7*d^10 + 448*b^11*c^4*d^6 - 2145*a*b^10*c^3*d^7 - 675*a^3*b^8*c*d^9 + 1971*a^2*b^9*c^2*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))*(-(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)/(4096*b^8*c^15 + 4096*a^8*c^7*d^8 - 32768*a^7*b*c^8*d^7 + 114688*a^2*b^6*c^13*d^2 - 229376*a^3*b^5*c^12*d^3 + 286720*a^4*b^4*c^11*d^4 - 229376*a^5*b^3*c^10*d^5 + 114688*a^6*b^2*c^9*d^6 - 32768*a*b^7*c^14*d))^(1/4) + (x^(1/2)*(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))/(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)/(4096*b^8*c^15 + 4096*a^8*c^7*d^8 - 32768*a^7*b*c^8*d^7 + 114688*a^2*b^6*c^13*d^2 - 229376*a^3*b^5*c^12*d^3 + 286720*a^4*b^4*c^11*d^4 - 229376*a^5*b^3*c^10*d^5 + 114688*a^6*b^2*c^9*d^6 - 32768*a*b^7*c^14*d))^(1/4)*1i + ((((x^(1/2)*(4096*b^17*c^15*d^4 - 32768*a*b^16*c^14*d^5 + 114688*a^2*b^15*c^13*d^6 - 216832*a^3*b^14*c^12*d^7 + 175616*a^4*b^13*c^11*d^8 + 210176*a^5*b^12*c^10*d^9 - 907264*a^6*b^11*c^9*d^10 + 1511936*a^7*b^10*c^8*d^11 - 1580032*a^8*b^9*c^7*d^12 + 1114624*a^9*b^8*c^6*d^13 - 530432*a^10*b^7*c^5*d^14 + 163072*a^11*b^6*c^4*d^15 - 29184*a^12*b^5*c^3*d^16 + 2304*a^13*b^4*c^2*d^17))/(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) + (2*(-(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)/(4096*b^8*c^15 + 4096*a^8*c^7*d^8 - 32768*a^7*b*c^8*d^7 + 114688*a^2*b^6*c^13*d^2 - 229376*a^3*b^5*c^12*d^3 + 286720*a^4*b^4*c^11*d^4 - 229376*a^5*b^3*c^10*d^5 + 114688*a^6*b^2*c^9*d^6 - 32768*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))*(-(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)/(4096*b^8*c^15 + 4096*a^8*c^7*d^8 - 32768*a^7*b*c^8*d^7 + 114688*a^2*b^6*c^13*d^2 - 229376*a^3*b^5*c^12*d^3 + 286720*a^4*b^4*c^11*d^4 - 229376*a^5*b^3*c^10*d^5 + 114688*a^6*b^2*c^9*d^6 - 32768*a*b^7*c^14*d))^(3/4) + (2*(81*a^4*b^7*d^10 + 448*b^11*c^4*d^6 - 2145*a*b^10*c^3*d^7 - 675*a^3*b^8*c*d^9 + 1971*a^2*b^9*c^2*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))*(-(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)/(4096*b^8*c^15 + 4096*a^8*c^7*d^8 - 32768*a^7*b*c^8*d^7 + 114688*a^2*b^6*c^13*d^2 - 229376*a^3*b^5*c^12*d^3 + 286720*a^4*b^4*c^11*d^4 - 229376*a^5*b^3*c^10*d^5 + 114688*a^6*b^2*c^9*d^6 - 32768*a*b^7*c^14*d))^(1/4) + (x^(1/2)*(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))/(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)/(4096*b^8*c^15 + 4096*a^8*c^7*d^8 - 32768*a^7*b*c^8*d^7 + 114688*a^2*b^6*c^13*d^2 - 229376*a^3*b^5*c^12*d^3 + 286720*a^4*b^4*c^11*d^4 - 229376*a^5*b^3*c^10*d^5 + 114688*a^6*b^2*c^9*d^6 - 32768*a*b^7*c^14*d))^(1/4)*1i)/(((((x^(1/2)*(4096*b^17*c^15*d^4 - 32768*a*b^16*c^14*d^5 + 114688*a^2*b^15*c^13*d^6 - 216832*a^3*b^14*c^12*d^7 + 175616*a^4*b^13*c^11*d^8 + 210176*a^5*b^12*c^10*d^9 - 907264*a^6*b^11*c^9*d^10 + 1511936*a^7*b^10*c^8*d^11 - 1580032*a^8*b^9*c^7*d^12 + 1114624*a^9*b^8*c^6*d^13 - 530432*a^10*b^7*c^5*d^14 + 163072*a^11*b^6*c^4*d^15 - 29184*a^12*b^5*c^3*d^16 + 2304*a^13*b^4*c^2*d^17))/(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) - (2*(-(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)/(4096*b^8*c^15 + 4096*a^8*c^7*d^8 - 32768*a^7*b*c^8*d^7 + 114688*a^2*b^6*c^13*d^2 - 229376*a^3*b^5*c^12*d^3 + 286720*a^4*b^4*c^11*d^4 - 229376*a^5*b^3*c^10*d^5 + 114688*a^6*b^2*c^9*d^6 - 32768*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))*(-(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)/(4096*b^8*c^15 + 4096*a^8*c^7*d^8 - 32768*a^7*b*c^8*d^7 + 114688*a^2*b^6*c^13*d^2 - 229376*a^3*b^5*c^12*d^3 + 286720*a^4*b^4*c^11*d^4 - 229376*a^5*b^3*c^10*d^5 + 114688*a^6*b^2*c^9*d^6 - 32768*a*b^7*c^14*d))^(3/4) - (2*(81*a^4*b^7*d^10 + 448*b^11*c^4*d^6 - 2145*a*b^10*c^3*d^7 - 675*a^3*b^8*c*d^9 + 1971*a^2*b^9*c^2*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))*(-(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)/(4096*b^8*c^15 + 4096*a^8*c^7*d^8 - 32768*a^7*b*c^8*d^7 + 114688*a^2*b^6*c^13*d^2 - 229376*a^3*b^5*c^12*d^3 + 286720*a^4*b^4*c^11*d^4 - 229376*a^5*b^3*c^10*d^5 + 114688*a^6*b^2*c^9*d^6 - 32768*a*b^7*c^14*d))^(1/4) + (x^(1/2)*(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))/(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)/(4096*b^8*c^15 + 4096*a^8*c^7*d^8 - 32768*a^7*b*c^8*d^7 + 114688*a^2*b^6*c^13*d^2 - 229376*a^3*b^5*c^12*d^3 + 286720*a^4*b^4*c^11*d^4 - 229376*a^5*b^3*c^10*d^5 + 114688*a^6*b^2*c^9*d^6 - 32768*a*b^7*c^14*d))^(1/4) - ((((x^(1/2)*(4096*b^17*c^15*d^4 - 32768*a*b^16*c^14*d^5 + 114688*a^2*b^15*c^13*d^6 - 216832*a^3*b^14*c^12*d^7 + 175616*a^4*b^13*c^11*d^8 + 210176*a^5*b^12*c^10*d^9 - 907264*a^6*b^11*c^9*d^10 + 1511936*a^7*b^10*c^8*d^11 - 1580032*a^8*b^9*c^7*d^12 + 1114624*a^9*b^8*c^6*d^13 - 530432*a^10*b^7*c^5*d^14 + 163072*a^11*b^6*c^4*d^15 - 29184*a^12*b^5*c^3*d^16 + 2304*a^13*b^4*c^2*d^17))/(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) + (2*(-(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)/(4096*b^8*c^15 + 4096*a^8*c^7*d^8 - 32768*a^7*b*c^8*d^7 + 114688*a^2*b^6*c^13*d^2 - 229376*a^3*b^5*c^12*d^3 + 286720*a^4*b^4*c^11*d^4 - 229376*a^5*b^3*c^10*d^5 + 114688*a^6*b^2*c^9*d^6 - 32768*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))*(-(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)/(4096*b^8*c^15 + 4096*a^8*c^7*d^8 - 32768*a^7*b*c^8*d^7 + 114688*a^2*b^6*c^13*d^2 - 229376*a^3*b^5*c^12*d^3 + 286720*a^4*b^4*c^11*d^4 - 229376*a^5*b^3*c^10*d^5 + 114688*a^6*b^2*c^9*d^6 - 32768*a*b^7*c^14*d))^(3/4) + (2*(81*a^4*b^7*d^10 + 448*b^11*c^4*d^6 - 2145*a*b^10*c^3*d^7 - 675*a^3*b^8*c*d^9 + 1971*a^2*b^9*c^2*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))*(-(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)/(4096*b^8*c^15 + 4096*a^8*c^7*d^8 - 32768*a^7*b*c^8*d^7 + 114688*a^2*b^6*c^13*d^2 - 229376*a^3*b^5*c^12*d^3 + 286720*a^4*b^4*c^11*d^4 - 229376*a^5*b^3*c^10*d^5 + 114688*a^6*b^2*c^9*d^6 - 32768*a*b^7*c^14*d))^(1/4) + (x^(1/2)*(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))/(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)/(4096*b^8*c^15 + 4096*a^8*c^7*d^8 - 32768*a^7*b*c^8*d^7 + 114688*a^2*b^6*c^13*d^2 - 229376*a^3*b^5*c^12*d^3 + 286720*a^4*b^4*c^11*d^4 - 229376*a^5*b^3*c^10*d^5 + 114688*a^6*b^2*c^9*d^6 - 32768*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)/(4096*b^8*c^15 + 4096*a^8*c^7*d^8 - 32768*a^7*b*c^8*d^7 + 114688*a^2*b^6*c^13*d^2 - 229376*a^3*b^5*c^12*d^3 + 286720*a^4*b^4*c^11*d^4 - 229376*a^5*b^3*c^10*d^5 + 114688*a^6*b^2*c^9*d^6 - 32768*a*b^7*c^14*d))^(1/4)*2i - 2*atan((((((x^(1/2)*(4096*b^17*c^15*d^4 - 32768*a*b^16*c^14*d^5 + 114688*a^2*b^15*c^13*d^6 - 216832*a^3*b^14*c^12*d^7 + 175616*a^4*b^13*c^11*d^8 + 210176*a^5*b^12*c^10*d^9 - 907264*a^6*b^11*c^9*d^10 + 1511936*a^7*b^10*c^8*d^11 - 1580032*a^8*b^9*c^7*d^12 + 1114624*a^9*b^8*c^6*d^13 - 530432*a^10*b^7*c^5*d^14 + 163072*a^11*b^6*c^4*d^15 - 29184*a^12*b^5*c^3*d^16 + 2304*a^13*b^4*c^2*d^17))/(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)/(4096*b^8*c^15 + 4096*a^8*c^7*d^8 - 32768*a^7*b*c^8*d^7 + 114688*a^2*b^6*c^13*d^2 - 229376*a^3*b^5*c^12*d^3 + 286720*a^4*b^4*c^11*d^4 - 229376*a^5*b^3*c^10*d^5 + 114688*a^6*b^2*c^9*d^6 - 32768*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)*2i)/(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)/(4096*b^8*c^15 + 4096*a^8*c^7*d^8 - 32768*a^7*b*c^8*d^7 + 114688*a^2*b^6*c^13*d^2 - 229376*a^3*b^5*c^12*d^3 + 286720*a^4*b^4*c^11*d^4 - 229376*a^5*b^3*c^10*d^5 + 114688*a^6*b^2*c^9*d^6 - 32768*a*b^7*c^14*d))^(3/4)*1i + (2*(81*a^4*b^7*d^10 + 448*b^11*c^4*d^6 - 2145*a*b^10*c^3*d^7 - 675*a^3*b^8*c*d^9 + 1971*a^2*b^9*c^2*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))*(-(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)/(4096*b^8*c^15 + 4096*a^8*c^7*d^8 - 32768*a^7*b*c^8*d^7 + 114688*a^2*b^6*c^13*d^2 - 229376*a^3*b^5*c^12*d^3 + 286720*a^4*b^4*c^11*d^4 - 229376*a^5*b^3*c^10*d^5 + 114688*a^6*b^2*c^9*d^6 - 32768*a*b^7*c^14*d))^(1/4)*1i - (x^(1/2)*(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))/(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)/(4096*b^8*c^15 + 4096*a^8*c^7*d^8 - 32768*a^7*b*c^8*d^7 + 114688*a^2*b^6*c^13*d^2 - 229376*a^3*b^5*c^12*d^3 + 286720*a^4*b^4*c^11*d^4 - 229376*a^5*b^3*c^10*d^5 + 114688*a^6*b^2*c^9*d^6 - 32768*a*b^7*c^14*d))^(1/4) + ((((x^(1/2)*(4096*b^17*c^15*d^4 - 32768*a*b^16*c^14*d^5 + 114688*a^2*b^15*c^13*d^6 - 216832*a^3*b^14*c^12*d^7 + 175616*a^4*b^13*c^11*d^8 + 210176*a^5*b^12*c^10*d^9 - 907264*a^6*b^11*c^9*d^10 + 1511936*a^7*b^10*c^8*d^11 - 1580032*a^8*b^9*c^7*d^12 + 1114624*a^9*b^8*c^6*d^13 - 530432*a^10*b^7*c^5*d^14 + 163072*a^11*b^6*c^4*d^15 - 29184*a^12*b^5*c^3*d^16 + 2304*a^13*b^4*c^2*d^17))/(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)/(4096*b^8*c^15 + 4096*a^8*c^7*d^8 - 32768*a^7*b*c^8*d^7 + 114688*a^2*b^6*c^13*d^2 - 229376*a^3*b^5*c^12*d^3 + 286720*a^4*b^4*c^11*d^4 - 229376*a^5*b^3*c^10*d^5 + 114688*a^6*b^2*c^9*d^6 - 32768*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)*2i)/(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)/(4096*b^8*c^15 + 4096*a^8*c^7*d^8 - 32768*a^7*b*c^8*d^7 + 114688*a^2*b^6*c^13*d^2 - 229376*a^3*b^5*c^12*d^3 + 286720*a^4*b^4*c^11*d^4 - 229376*a^5*b^3*c^10*d^5 + 114688*a^6*b^2*c^9*d^6 - 32768*a*b^7*c^14*d))^(3/4)*1i - (2*(81*a^4*b^7*d^10 + 448*b^11*c^4*d^6 - 2145*a*b^10*c^3*d^7 - 675*a^3*b^8*c*d^9 + 1971*a^2*b^9*c^2*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))*(-(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)/(4096*b^8*c^15 + 4096*a^8*c^7*d^8 - 32768*a^7*b*c^8*d^7 + 114688*a^2*b^6*c^13*d^2 - 229376*a^3*b^5*c^12*d^3 + 286720*a^4*b^4*c^11*d^4 - 229376*a^5*b^3*c^10*d^5 + 114688*a^6*b^2*c^9*d^6 - 32768*a*b^7*c^14*d))^(1/4)*1i - (x^(1/2)*(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))/(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)/(4096*b^8*c^15 + 4096*a^8*c^7*d^8 - 32768*a^7*b*c^8*d^7 + 114688*a^2*b^6*c^13*d^2 - 229376*a^3*b^5*c^12*d^3 + 286720*a^4*b^4*c^11*d^4 - 229376*a^5*b^3*c^10*d^5 + 114688*a^6*b^2*c^9*d^6 - 32768*a*b^7*c^14*d))^(1/4))/(((((x^(1/2)*(4096*b^17*c^15*d^4 - 32768*a*b^16*c^14*d^5 + 114688*a^2*b^15*c^13*d^6 - 216832*a^3*b^14*c^12*d^7 + 175616*a^4*b^13*c^11*d^8 + 210176*a^5*b^12*c^10*d^9 - 907264*a^6*b^11*c^9*d^10 + 1511936*a^7*b^10*c^8*d^11 - 1580032*a^8*b^9*c^7*d^12 + 1114624*a^9*b^8*c^6*d^13 - 530432*a^10*b^7*c^5*d^14 + 163072*a^11*b^6*c^4*d^15 - 29184*a^12*b^5*c^3*d^16 + 2304*a^13*b^4*c^2*d^17))/(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)/(4096*b^8*c^15 + 4096*a^8*c^7*d^8 - 32768*a^7*b*c^8*d^7 + 114688*a^2*b^6*c^13*d^2 - 229376*a^3*b^5*c^12*d^3 + 286720*a^4*b^4*c^11*d^4 - 229376*a^5*b^3*c^10*d^5 + 114688*a^6*b^2*c^9*d^6 - 32768*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)*2i)/(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)/(4096*b^8*c^15 + 4096*a^8*c^7*d^8 - 32768*a^7*b*c^8*d^7 + 114688*a^2*b^6*c^13*d^2 - 229376*a^3*b^5*c^12*d^3 + 286720*a^4*b^4*c^11*d^4 - 229376*a^5*b^3*c^10*d^5 + 114688*a^6*b^2*c^9*d^6 - 32768*a*b^7*c^14*d))^(3/4)*1i + (2*(81*a^4*b^7*d^10 + 448*b^11*c^4*d^6 - 2145*a*b^10*c^3*d^7 - 675*a^3*b^8*c*d^9 + 1971*a^2*b^9*c^2*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))*(-(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)/(4096*b^8*c^15 + 4096*a^8*c^7*d^8 - 32768*a^7*b*c^8*d^7 + 114688*a^2*b^6*c^13*d^2 - 229376*a^3*b^5*c^12*d^3 + 286720*a^4*b^4*c^11*d^4 - 229376*a^5*b^3*c^10*d^5 + 114688*a^6*b^2*c^9*d^6 - 32768*a*b^7*c^14*d))^(1/4)*1i - (x^(1/2)*(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))/(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)/(4096*b^8*c^15 + 4096*a^8*c^7*d^8 - 32768*a^7*b*c^8*d^7 + 114688*a^2*b^6*c^13*d^2 - 229376*a^3*b^5*c^12*d^3 + 286720*a^4*b^4*c^11*d^4 - 229376*a^5*b^3*c^10*d^5 + 114688*a^6*b^2*c^9*d^6 - 32768*a*b^7*c^14*d))^(1/4)*1i - ((((x^(1/2)*(4096*b^17*c^15*d^4 - 32768*a*b^16*c^14*d^5 + 114688*a^2*b^15*c^13*d^6 - 216832*a^3*b^14*c^12*d^7 + 175616*a^4*b^13*c^11*d^8 + 210176*a^5*b^12*c^10*d^9 - 907264*a^6*b^11*c^9*d^10 + 1511936*a^7*b^10*c^8*d^11 - 1580032*a^8*b^9*c^7*d^12 + 1114624*a^9*b^8*c^6*d^13 - 530432*a^10*b^7*c^5*d^14 + 163072*a^11*b^6*c^4*d^15 - 29184*a^12*b^5*c^3*d^16 + 2304*a^13*b^4*c^2*d^17))/(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)/(4096*b^8*c^15 + 4096*a^8*c^7*d^8 - 32768*a^7*b*c^8*d^7 + 114688*a^2*b^6*c^13*d^2 - 229376*a^3*b^5*c^12*d^3 + 286720*a^4*b^4*c^11*d^4 - 229376*a^5*b^3*c^10*d^5 + 114688*a^6*b^2*c^9*d^6 - 32768*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)*2i)/(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)/(4096*b^8*c^15 + 4096*a^8*c^7*d^8 - 32768*a^7*b*c^8*d^7 + 114688*a^2*b^6*c^13*d^2 - 229376*a^3*b^5*c^12*d^3 + 286720*a^4*b^4*c^11*d^4 - 229376*a^5*b^3*c^10*d^5 + 114688*a^6*b^2*c^9*d^6 - 32768*a*b^7*c^14*d))^(3/4)*1i - (2*(81*a^4*b^7*d^10 + 448*b^11*c^4*d^6 - 2145*a*b^10*c^3*d^7 - 675*a^3*b^8*c*d^9 + 1971*a^2*b^9*c^2*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))*(-(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)/(4096*b^8*c^15 + 4096*a^8*c^7*d^8 - 32768*a^7*b*c^8*d^7 + 114688*a^2*b^6*c^13*d^2 - 229376*a^3*b^5*c^12*d^3 + 286720*a^4*b^4*c^11*d^4 - 229376*a^5*b^3*c^10*d^5 + 114688*a^6*b^2*c^9*d^6 - 32768*a*b^7*c^14*d))^(1/4)*1i - (x^(1/2)*(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))/(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)/(4096*b^8*c^15 + 4096*a^8*c^7*d^8 - 32768*a^7*b*c^8*d^7 + 114688*a^2*b^6*c^13*d^2 - 229376*a^3*b^5*c^12*d^3 + 286720*a^4*b^4*c^11*d^4 - 229376*a^5*b^3*c^10*d^5 + 114688*a^6*b^2*c^9*d^6 - 32768*a*b^7*c^14*d))^(1/4)*1i))*(-(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)/(4096*b^8*c^15 + 4096*a^8*c^7*d^8 - 32768*a^7*b*c^8*d^7 + 114688*a^2*b^6*c^13*d^2 - 229376*a^3*b^5*c^12*d^3 + 286720*a^4*b^4*c^11*d^4 - 229376*a^5*b^3*c^10*d^5 + 114688*a^6*b^2*c^9*d^6 - 32768*a*b^7*c^14*d))^(1/4) + (d*x^(1/2))/(2*c*(c + d*x^2)*(a*d - b*c))","B"
477,1,21370,570,4.090567,"\text{Not used}","int(1/(x^(3/2)*(a + b*x^2)*(c + d*x^2)^2),x)","\mathrm{atan}\left(\frac{{\left(-\frac{b^9}{16\,a^{13}\,d^8-128\,a^{12}\,b\,c\,d^7+448\,a^{11}\,b^2\,c^2\,d^6-896\,a^{10}\,b^3\,c^3\,d^5+1120\,a^9\,b^4\,c^4\,d^4-896\,a^8\,b^5\,c^5\,d^3+448\,a^7\,b^6\,c^6\,d^2-128\,a^6\,b^7\,c^7\,d+16\,a^5\,b^8\,c^8}\right)}^{1/4}\,\left({\left(-\frac{b^9}{16\,a^{13}\,d^8-128\,a^{12}\,b\,c\,d^7+448\,a^{11}\,b^2\,c^2\,d^6-896\,a^{10}\,b^3\,c^3\,d^5+1120\,a^9\,b^4\,c^4\,d^4-896\,a^8\,b^5\,c^5\,d^3+448\,a^7\,b^6\,c^6\,d^2-128\,a^6\,b^7\,c^7\,d+16\,a^5\,b^8\,c^8}\right)}^{3/4}\,\left(\sqrt{x}\,{\left(-\frac{b^9}{16\,a^{13}\,d^8-128\,a^{12}\,b\,c\,d^7+448\,a^{11}\,b^2\,c^2\,d^6-896\,a^{10}\,b^3\,c^3\,d^5+1120\,a^9\,b^4\,c^4\,d^4-896\,a^8\,b^5\,c^5\,d^3+448\,a^7\,b^6\,c^6\,d^2-128\,a^6\,b^7\,c^7\,d+16\,a^5\,b^8\,c^8}\right)}^{1/4}\,\left(-52428800\,a^{33}\,b^4\,c^{23}\,d^{25}+975175680\,a^{32}\,b^5\,c^{24}\,d^{24}-8506048512\,a^{31}\,b^6\,c^{25}\,d^{23}+46221230080\,a^{30}\,b^7\,c^{26}\,d^{22}-175279964160\,a^{29}\,b^8\,c^{27}\,d^{21}+492369346560\,a^{28}\,b^9\,c^{28}\,d^{20}-1061108580352\,a^{27}\,b^{10}\,c^{29}\,d^{19}+1792662306816\,a^{26}\,b^{11}\,c^{30}\,d^{18}-2405664030720\,a^{25}\,b^{12}\,c^{31}\,d^{17}+2585348014080\,a^{24}\,b^{13}\,c^{32}\,d^{16}-2241016627200\,a^{23}\,b^{14}\,c^{33}\,d^{15}+1589322448896\,a^{22}\,b^{15}\,c^{34}\,d^{14}-959547703296\,a^{21}\,b^{16}\,c^{35}\,d^{13}+539177779200\,a^{20}\,b^{17}\,c^{36}\,d^{12}-313817825280\,a^{19}\,b^{18}\,c^{37}\,d^{11}+188659793920\,a^{18}\,b^{19}\,c^{38}\,d^{10}-103500742656\,a^{17}\,b^{20}\,c^{39}\,d^9+45971668992\,a^{16}\,b^{21}\,c^{40}\,d^8-15267266560\,a^{15}\,b^{22}\,c^{41}\,d^7+3523215360\,a^{14}\,b^{23}\,c^{42}\,d^6-503316480\,a^{13}\,b^{24}\,c^{43}\,d^5+33554432\,a^{12}\,b^{25}\,c^{44}\,d^4\right)-16777216\,a^{11}\,b^{25}\,c^{42}\,d^4+218103808\,a^{12}\,b^{24}\,c^{41}\,d^5-1308622848\,a^{13}\,b^{23}\,c^{40}\,d^6+4798283776\,a^{14}\,b^{22}\,c^{39}\,d^7-11995709440\,a^{15}\,b^{21}\,c^{38}\,d^8+21783379968\,a^{16}\,b^{20}\,c^{37}\,d^9-31592546304\,a^{17}\,b^{19}\,c^{36}\,d^{10}+48013246464\,a^{18}\,b^{18}\,c^{35}\,d^{11}-103424196608\,a^{19}\,b^{17}\,c^{34}\,d^{12}+253954621440\,a^{20}\,b^{16}\,c^{33}\,d^{13}-531641663488\,a^{21}\,b^{15}\,c^{32}\,d^{14}+875046109184\,a^{22}\,b^{14}\,c^{31}\,d^{15}-1125865488384\,a^{23}\,b^{13}\,c^{30}\,d^{16}+1138334629888\,a^{24}\,b^{12}\,c^{29}\,d^{17}-906425794560\,a^{25}\,b^{11}\,c^{28}\,d^{18}+566347431936\,a^{26}\,b^{10}\,c^{27}\,d^{19}-274688114688\,a^{27}\,b^9\,c^{26}\,d^{20}+101363744768\,a^{28}\,b^8\,c^{25}\,d^{21}-27505197056\,a^{29}\,b^7\,c^{24}\,d^{22}+5174722560\,a^{30}\,b^6\,c^{23}\,d^{23}-602931200\,a^{31}\,b^5\,c^{22}\,d^{24}+32768000\,a^{32}\,b^4\,c^{21}\,d^{25}\right)-\sqrt{x}\,\left(5120000\,a^{23}\,b^{10}\,c^{20}\,d^{20}-72704000\,a^{22}\,b^{11}\,c^{21}\,d^{19}+465100800\,a^{21}\,b^{12}\,c^{22}\,d^{18}-1766236160\,a^{20}\,b^{13}\,c^{23}\,d^{17}+4414717952\,a^{19}\,b^{14}\,c^{24}\,d^{16}-7603863552\,a^{18}\,b^{15}\,c^{25}\,d^{15}+9165979648\,a^{17}\,b^{16}\,c^{26}\,d^{14}-7664386048\,a^{16}\,b^{17}\,c^{27}\,d^{13}+4269711360\,a^{15}\,b^{18}\,c^{28}\,d^{12}-1422057472\,a^{14}\,b^{19}\,c^{29}\,d^{11}+186867712\,a^{13}\,b^{20}\,c^{30}\,d^{10}+32366592\,a^{12}\,b^{21}\,c^{31}\,d^9-10616832\,a^{11}\,b^{22}\,c^{32}\,d^8\right)\right)\,1{}\mathrm{i}+{\left(-\frac{b^9}{16\,a^{13}\,d^8-128\,a^{12}\,b\,c\,d^7+448\,a^{11}\,b^2\,c^2\,d^6-896\,a^{10}\,b^3\,c^3\,d^5+1120\,a^9\,b^4\,c^4\,d^4-896\,a^8\,b^5\,c^5\,d^3+448\,a^7\,b^6\,c^6\,d^2-128\,a^6\,b^7\,c^7\,d+16\,a^5\,b^8\,c^8}\right)}^{1/4}\,\left({\left(-\frac{b^9}{16\,a^{13}\,d^8-128\,a^{12}\,b\,c\,d^7+448\,a^{11}\,b^2\,c^2\,d^6-896\,a^{10}\,b^3\,c^3\,d^5+1120\,a^9\,b^4\,c^4\,d^4-896\,a^8\,b^5\,c^5\,d^3+448\,a^7\,b^6\,c^6\,d^2-128\,a^6\,b^7\,c^7\,d+16\,a^5\,b^8\,c^8}\right)}^{3/4}\,\left(\sqrt{x}\,{\left(-\frac{b^9}{16\,a^{13}\,d^8-128\,a^{12}\,b\,c\,d^7+448\,a^{11}\,b^2\,c^2\,d^6-896\,a^{10}\,b^3\,c^3\,d^5+1120\,a^9\,b^4\,c^4\,d^4-896\,a^8\,b^5\,c^5\,d^3+448\,a^7\,b^6\,c^6\,d^2-128\,a^6\,b^7\,c^7\,d+16\,a^5\,b^8\,c^8}\right)}^{1/4}\,\left(-52428800\,a^{33}\,b^4\,c^{23}\,d^{25}+975175680\,a^{32}\,b^5\,c^{24}\,d^{24}-8506048512\,a^{31}\,b^6\,c^{25}\,d^{23}+46221230080\,a^{30}\,b^7\,c^{26}\,d^{22}-175279964160\,a^{29}\,b^8\,c^{27}\,d^{21}+492369346560\,a^{28}\,b^9\,c^{28}\,d^{20}-1061108580352\,a^{27}\,b^{10}\,c^{29}\,d^{19}+1792662306816\,a^{26}\,b^{11}\,c^{30}\,d^{18}-2405664030720\,a^{25}\,b^{12}\,c^{31}\,d^{17}+2585348014080\,a^{24}\,b^{13}\,c^{32}\,d^{16}-2241016627200\,a^{23}\,b^{14}\,c^{33}\,d^{15}+1589322448896\,a^{22}\,b^{15}\,c^{34}\,d^{14}-959547703296\,a^{21}\,b^{16}\,c^{35}\,d^{13}+539177779200\,a^{20}\,b^{17}\,c^{36}\,d^{12}-313817825280\,a^{19}\,b^{18}\,c^{37}\,d^{11}+188659793920\,a^{18}\,b^{19}\,c^{38}\,d^{10}-103500742656\,a^{17}\,b^{20}\,c^{39}\,d^9+45971668992\,a^{16}\,b^{21}\,c^{40}\,d^8-15267266560\,a^{15}\,b^{22}\,c^{41}\,d^7+3523215360\,a^{14}\,b^{23}\,c^{42}\,d^6-503316480\,a^{13}\,b^{24}\,c^{43}\,d^5+33554432\,a^{12}\,b^{25}\,c^{44}\,d^4\right)+16777216\,a^{11}\,b^{25}\,c^{42}\,d^4-2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554432\,a^{12}\,b^{25}\,c^{44}\,d^4\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)}{29859840\,a^{11}\,b^{21}\,c^{29}\,d^9-228925440\,a^{12}\,b^{20}\,c^{28}\,d^{10}+774144000\,a^{13}\,b^{19}\,c^{27}\,d^{11}-1514700800\,a^{14}\,b^{18}\,c^{26}\,d^{12}+1888665600\,a^{15}\,b^{17}\,c^{25}\,d^{13}-1555415040\,a^{16}\,b^{16}\,c^{24}\,d^{14}+845578240\,a^{17}\,b^{15}\,c^{23}\,d^{15}-292454400\,a^{18}\,b^{14}\,c^{22}\,d^{16}+58368000\,a^{19}\,b^{13}\,c^{21}\,d^{17}-5120000\,a^{20}\,b^{12}\,c^{20}\,d^{18}+{\left(-\frac{b^9}{16\,a^{13}\,d^8-128\,a^{12}\,b\,c\,d^7+448\,a^{11}\,b^2\,c^2\,d^6-896\,a^{10}\,b^3\,c^3\,d^5+1120\,a^9\,b^4\,c^4\,d^4-896\,a^8\,b^5\,c^5\,d^3+448\,a^7\,b^6\,c^6\,d^2-128\,a^6\,b^7\,c^7\,d+16\,a^5\,b^8\,c^8}\right)}^{1/4}\,\left(\sqrt{x}\,\left(5120000\,a^{23}\,b^{10}\,c^{20}\,d^{20}-72704000\,a^{22}\,b^{11}\,c^{21}\,d^{19}+465100800\,a^{21}\,b^{12}\,c^{22}\,d^{18}-1766236160\,a^{20}\,b^{13}\,c^{23}\,d^{17}+4414717952\,a^{19}\,b^{14}\,c^{24}\,d^{16}-7603863552\,a^{18}\,b^{15}\,c^{25}\,d^{15}+9165979648\,a^{17}\,b^{16}\,c^{26}\,d^{14}-7664386048\,a^{16}\,b^{17}\,c^{27}\,d^{13}+4269711360\,a^{15}\,b^{18}\,c^{28}\,d^{12}-1422057472\,a^{14}\,b^{19}\,c^{29}\,d^{11}+186867712\,a^{13}\,b^{20}\,c^{30}\,d^{10}+32366592\,a^{12}\,b^{21}\,c^{31}\,d^9-10616832\,a^{11}\,b^{22}\,c^{32}\,d^8\right)+{\left(-\frac{b^9}{16\,a^{13}\,d^8-128\,a^{12}\,b\,c\,d^7+448\,a^{11}\,b^2\,c^2\,d^6-896\,a^{10}\,b^3\,c^3\,d^5+1120\,a^9\,b^4\,c^4\,d^4-896\,a^8\,b^5\,c^5\,d^3+448\,a^7\,b^6\,c^6\,d^2-128\,a^6\,b^7\,c^7\,d+16\,a^5\,b^8\,c^8}\right)}^{3/4}\,\left(218103808\,a^{12}\,b^{24}\,c^{41}\,d^5-16777216\,a^{11}\,b^{25}\,c^{42}\,d^4-1308622848\,a^{13}\,b^{23}\,c^{40}\,d^6+4798283776\,a^{14}\,b^{22}\,c^{39}\,d^7-11995709440\,a^{15}\,b^{21}\,c^{38}\,d^8+21783379968\,a^{16}\,b^{20}\,c^{37}\,d^9-31592546304\,a^{17}\,b^{19}\,c^{36}\,d^{10}+48013246464\,a^{18}\,b^{18}\,c^{35}\,d^{11}-103424196608\,a^{19}\,b^{17}\,c^{34}\,d^{12}+253954621440\,a^{20}\,b^{16}\,c^{33}\,d^{13}-531641663488\,a^{21}\,b^{15}\,c^{32}\,d^{14}+875046109184\,a^{22}\,b^{14}\,c^{31}\,d^{15}-1125865488384\,a^{23}\,b^{13}\,c^{30}\,d^{16}+1138334629888\,a^{24}\,b^{12}\,c^{29}\,d^{17}-906425794560\,a^{25}\,b^{11}\,c^{28}\,d^{18}+566347431936\,a^{26}\,b^{10}\,c^{27}\,d^{19}-274688114688\,a^{27}\,b^9\,c^{26}\,d^{20}+101363744768\,a^{28}\,b^8\,c^{25}\,d^{21}-27505197056\,a^{29}\,b^7\,c^{24}\,d^{22}+5174722560\,a^{30}\,b^6\,c^{23}\,d^{23}-602931200\,a^{31}\,b^5\,c^{22}\,d^{24}+32768000\,a^{32}\,b^4\,c^{21}\,d^{25}+\sqrt{x}\,{\left(-\frac{b^9}{16\,a^{13}\,d^8-128\,a^{12}\,b\,c\,d^7+448\,a^{11}\,b^2\,c^2\,d^6-896\,a^{10}\,b^3\,c^3\,d^5+1120\,a^9\,b^4\,c^4\,d^4-896\,a^8\,b^5\,c^5\,d^3+448\,a^7\,b^6\,c^6\,d^2-128\,a^6\,b^7\,c^7\,d+16\,a^5\,b^8\,c^8}\right)}^{1/4}\,\left(-52428800\,a^{33}\,b^4\,c^{23}\,d^{25}+975175680\,a^{32}\,b^5\,c^{24}\,d^{24}-8506048512\,a^{31}\,b^6\,c^{25}\,d^{23}+46221230080\,a^{30}\,b^7\,c^{26}\,d^{22}-175279964160\,a^{29}\,b^8\,c^{27}\,d^{21}+492369346560\,a^{28}\,b^9\,c^{28}\,d^{20}-1061108580352\,a^{27}\,b^{10}\,c^{29}\,d^{19}+1792662306816\,a^{26}\,b^{11}\,c^{30}\,d^{18}-2405664030720\,a^{25}\,b^{12}\,c^{31}\,d^{17}+2585348014080\,a^{24}\,b^{13}\,c^{32}\,d^{16}-2241016627200\,a^{23}\,b^{14}\,c^{33}\,d^{15}+1589322448896\,a^{22}\,b^{15}\,c^{34}\,d^{14}-959547703296\,a^{21}\,b^{16}\,c^{35}\,d^{13}+539177779200\,a^{20}\,b^{17}\,c^{36}\,d^{12}-313817825280\,a^{19}\,b^{18}\,c^{37}\,d^{11}+188659793920\,a^{18}\,b^{19}\,c^{38}\,d^{10}-103500742656\,a^{17}\,b^{20}\,c^{39}\,d^9+45971668992\,a^{16}\,b^{21}\,c^{40}\,d^8-15267266560\,a^{15}\,b^{22}\,c^{41}\,d^7+3523215360\,a^{14}\,b^{23}\,c^{42}\,d^6-503316480\,a^{13}\,b^{24}\,c^{43}\,d^5+33554432\,a^{12}\,b^{25}\,c^{44}\,d^4\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}-{\left(-\frac{b^9}{16\,a^{13}\,d^8-128\,a^{12}\,b\,c\,d^7+448\,a^{11}\,b^2\,c^2\,d^6-896\,a^{10}\,b^3\,c^3\,d^5+1120\,a^9\,b^4\,c^4\,d^4-896\,a^8\,b^5\,c^5\,d^3+448\,a^7\,b^6\,c^6\,d^2-128\,a^6\,b^7\,c^7\,d+16\,a^5\,b^8\,c^8}\right)}^{1/4}\,\left(\sqrt{x}\,\left(5120000\,a^{23}\,b^{10}\,c^{20}\,d^{20}-72704000\,a^{22}\,b^{11}\,c^{21}\,d^{19}+465100800\,a^{21}\,b^{12}\,c^{22}\,d^{18}-1766236160\,a^{20}\,b^{13}\,c^{23}\,d^{17}+4414717952\,a^{19}\,b^{14}\,c^{24}\,d^{16}-7603863552\,a^{18}\,b^{15}\,c^{25}\,d^{15}+9165979648\,a^{17}\,b^{16}\,c^{26}\,d^{14}-7664386048\,a^{16}\,b^{17}\,c^{27}\,d^{13}+4269711360\,a^{15}\,b^{18}\,c^{28}\,d^{12}-1422057472\,a^{14}\,b^{19}\,c^{29}\,d^{11}+186867712\,a^{13}\,b^{20}\,c^{30}\,d^{10}+32366592\,a^{12}\,b^{21}\,c^{31}\,d^9-10616832\,a^{11}\,b^{22}\,c^{32}\,d^8\right)+{\left(-\frac{b^9}{16\,a^{13}\,d^8-128\,a^{12}\,b\,c\,d^7+448\,a^{11}\,b^2\,c^2\,d^6-896\,a^{10}\,b^3\,c^3\,d^5+1120\,a^9\,b^4\,c^4\,d^4-896\,a^8\,b^5\,c^5\,d^3+448\,a^7\,b^6\,c^6\,d^2-128\,a^6\,b^7\,c^7\,d+16\,a^5\,b^8\,c^8}\right)}^{3/4}\,\left(16777216\,a^{11}\,b^{25}\,c^{42}\,d^4-218103808\,a^{12}\,b^{24}\,c^{41}\,d^5+1308622848\,a^{13}\,b^{23}\,c^{40}\,d^6-4798283776\,a^{14}\,b^{22}\,c^{39}\,d^7+11995709440\,a^{15}\,b^{21}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616832\,a^{11}\,b^{22}\,c^{32}\,d^8\right)+{\left(-\frac{625\,a^4\,d^9-4500\,a^3\,b\,c\,d^8+12150\,a^2\,b^2\,c^2\,d^7-14580\,a\,b^3\,c^3\,d^6+6561\,b^4\,c^4\,d^5}{4096\,a^8\,c^9\,d^8-32768\,a^7\,b\,c^{10}\,d^7+114688\,a^6\,b^2\,c^{11}\,d^6-229376\,a^5\,b^3\,c^{12}\,d^5+286720\,a^4\,b^4\,c^{13}\,d^4-229376\,a^3\,b^5\,c^{14}\,d^3+114688\,a^2\,b^6\,c^{15}\,d^2-32768\,a\,b^7\,c^{16}\,d+4096\,b^8\,c^{17}}\right)}^{3/4}\,\left(16777216\,a^{11}\,b^{25}\,c^{42}\,d^4-218103808\,a^{12}\,b^{24}\,c^{41}\,d^5+1308622848\,a^{13}\,b^{23}\,c^{40}\,d^6-4798283776\,a^{14}\,b^{22}\,c^{39}\,d^7+11995709440\,a^{15}\,b^{21}\,c^{38}\,d^8-21783379968\,a^{16}\,b^{20}\,c^{37}\,d^9+31592546304\,a^{17}\,b^{19}\,c^{36}\,d^{10}-48013246464\,a^{18}\,b^{18}\,c^{35}\,d^{11}+103424196608\,a^{19}\,b^{17}\,c^{34}\,d^{12}-253954621440\,a^{20}\,b^{16}\,c^{33}\,d^{13}+531641663488\,a^{21}\,b^{15}\,c^{32}\,d^{14}-875046109184\,a^{22}\,b^{14}\,c^{31}\,d^{15}+1125865488384\,a^{23}\,b^{13}\,c^{30}\,d^{16}-1138334629888\,a^{24}\,b^{12}\,c^{29}\,d^{17}+906425794560\,a^{25}\,b^{11}\,c^{28}\,d^{18}-566347431936\,a^{26}\,b^{10}\,c^{27}\,d^{19}+274688114688\,a^{27}\,b^9\,c^{26}\,d^{20}-101363744768\,a^{28}\,b^8\,c^{25}\,d^{21}+27505197056\,a^{29}\,b^7\,c^{24}\,d^{22}-5174722560\,a^{30}\,b^6\,c^{23}\,d^{23}+602931200\,a^{31}\,b^5\,c^{22}\,d^{24}-32768000\,a^{32}\,b^4\,c^{21}\,d^{25}+\sqrt{x}\,{\left(-\frac{625\,a^4\,d^9-4500\,a^3\,b\,c\,d^8+12150\,a^2\,b^2\,c^2\,d^7-14580\,a\,b^3\,c^3\,d^6+6561\,b^4\,c^4\,d^5}{4096\,a^8\,c^9\,d^8-32768\,a^7\,b\,c^{10}\,d^7+114688\,a^6\,b^2\,c^{11}\,d^6-229376\,a^5\,b^3\,c^{12}\,d^5+286720\,a^4\,b^4\,c^{13}\,d^4-229376\,a^3\,b^5\,c^{14}\,d^3+114688\,a^2\,b^6\,c^{15}\,d^2-32768\,a\,b^7\,c^{16}\,d+4096\,b^8\,c^{17}}\right)}^{1/4}\,\left(-52428800\,a^{33}\,b^4\,c^{23}\,d^{25}+975175680\,a^{32}\,b^5\,c^{24}\,d^{24}-8506048512\,a^{31}\,b^6\,c^{25}\,d^{23}+46221230080\,a^{30}\,b^7\,c^{26}\,d^{22}-175279964160\,a^{29}\,b^8\,c^{27}\,d^{21}+492369346560\,a^{28}\,b^9\,c^{28}\,d^{20}-1061108580352\,a^{27}\,b^{10}\,c^{29}\,d^{19}+1792662306816\,a^{26}\,b^{11}\,c^{30}\,d^{18}-2405664030720\,a^{25}\,b^{12}\,c^{31}\,d^{17}+2585348014080\,a^{24}\,b^{13}\,c^{32}\,d^{16}-2241016627200\,a^{23}\,b^{14}\,c^{33}\,d^{15}+1589322448896\,a^{22}\,b^{15}\,c^{34}\,d^{14}-959547703296\,a^{21}\,b^{16}\,c^{35}\,d^{13}+539177779200\,a^{20}\,b^{17}\,c^{36}\,d^{12}-313817825280\,a^{19}\,b^{18}\,c^{37}\,d^{11}+188659793920\,a^{18}\,b^{19}\,c^{38}\,d^{10}-103500742656\,a^{17}\,b^{20}\,c^{39}\,d^9+45971668992\,a^{16}\,b^{21}\,c^{40}\,d^8-15267266560\,a^{15}\,b^{22}\,c^{41}\,d^7+3523215360\,a^{14}\,b^{23}\,c^{42}\,d^6-503316480\,a^{13}\,b^{24}\,c^{43}\,d^5+33554432\,a^{12}\,b^{25}\,c^{44}\,d^4\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}\right)\,{\left(-\frac{625\,a^4\,d^9-4500\,a^3\,b\,c\,d^8+12150\,a^2\,b^2\,c^2\,d^7-14580\,a\,b^3\,c^3\,d^6+6561\,b^4\,c^4\,d^5}{4096\,a^8\,c^9\,d^8-32768\,a^7\,b\,c^{10}\,d^7+114688\,a^6\,b^2\,c^{11}\,d^6-229376\,a^5\,b^3\,c^{12}\,d^5+286720\,a^4\,b^4\,c^{13}\,d^4-229376\,a^3\,b^5\,c^{14}\,d^3+114688\,a^2\,b^6\,c^{15}\,d^2-32768\,a\,b^7\,c^{16}\,d+4096\,b^8\,c^{17}}\right)}^{1/4}","Not used",1,"atan(((-b^9/(16*a^13*d^8 + 16*a^5*b^8*c^8 - 128*a^6*b^7*c^7*d + 448*a^7*b^6*c^6*d^2 - 896*a^8*b^5*c^5*d^3 + 1120*a^9*b^4*c^4*d^4 - 896*a^10*b^3*c^3*d^5 + 448*a^11*b^2*c^2*d^6 - 128*a^12*b*c*d^7))^(1/4)*((-b^9/(16*a^13*d^8 + 16*a^5*b^8*c^8 - 128*a^6*b^7*c^7*d + 448*a^7*b^6*c^6*d^2 - 896*a^8*b^5*c^5*d^3 + 1120*a^9*b^4*c^4*d^4 - 896*a^10*b^3*c^3*d^5 + 448*a^11*b^2*c^2*d^6 - 128*a^12*b*c*d^7))^(3/4)*(x^(1/2)*(-b^9/(16*a^13*d^8 + 16*a^5*b^8*c^8 - 128*a^6*b^7*c^7*d + 448*a^7*b^6*c^6*d^2 - 896*a^8*b^5*c^5*d^3 + 1120*a^9*b^4*c^4*d^4 - 896*a^10*b^3*c^3*d^5 + 448*a^11*b^2*c^2*d^6 - 128*a^12*b*c*d^7))^(1/4)*(33554432*a^12*b^25*c^44*d^4 - 503316480*a^13*b^24*c^43*d^5 + 3523215360*a^14*b^23*c^42*d^6 - 15267266560*a^15*b^22*c^41*d^7 + 45971668992*a^16*b^21*c^40*d^8 - 103500742656*a^17*b^20*c^39*d^9 + 188659793920*a^18*b^19*c^38*d^10 - 313817825280*a^19*b^18*c^37*d^11 + 539177779200*a^20*b^17*c^36*d^12 - 959547703296*a^21*b^16*c^35*d^13 + 1589322448896*a^22*b^15*c^34*d^14 - 2241016627200*a^23*b^14*c^33*d^15 + 2585348014080*a^24*b^13*c^32*d^16 - 2405664030720*a^25*b^12*c^31*d^17 + 1792662306816*a^26*b^11*c^30*d^18 - 1061108580352*a^27*b^10*c^29*d^19 + 492369346560*a^28*b^9*c^28*d^20 - 175279964160*a^29*b^8*c^27*d^21 + 46221230080*a^30*b^7*c^26*d^22 - 8506048512*a^31*b^6*c^25*d^23 + 975175680*a^32*b^5*c^24*d^24 - 52428800*a^33*b^4*c^23*d^25) - 16777216*a^11*b^25*c^42*d^4 + 218103808*a^12*b^24*c^41*d^5 - 1308622848*a^13*b^23*c^40*d^6 + 4798283776*a^14*b^22*c^39*d^7 - 11995709440*a^15*b^21*c^38*d^8 + 21783379968*a^16*b^20*c^37*d^9 - 31592546304*a^17*b^19*c^36*d^10 + 48013246464*a^18*b^18*c^35*d^11 - 103424196608*a^19*b^17*c^34*d^12 + 253954621440*a^20*b^16*c^33*d^13 - 531641663488*a^21*b^15*c^32*d^14 + 875046109184*a^22*b^14*c^31*d^15 - 1125865488384*a^23*b^13*c^30*d^16 + 1138334629888*a^24*b^12*c^29*d^17 - 906425794560*a^25*b^11*c^28*d^18 + 566347431936*a^26*b^10*c^27*d^19 - 274688114688*a^27*b^9*c^26*d^20 + 101363744768*a^28*b^8*c^25*d^21 - 27505197056*a^29*b^7*c^24*d^22 + 5174722560*a^30*b^6*c^23*d^23 - 602931200*a^31*b^5*c^22*d^24 + 32768000*a^32*b^4*c^21*d^25) - x^(1/2)*(32366592*a^12*b^21*c^31*d^9 - 10616832*a^11*b^22*c^32*d^8 + 186867712*a^13*b^20*c^30*d^10 - 1422057472*a^14*b^19*c^29*d^11 + 4269711360*a^15*b^18*c^28*d^12 - 7664386048*a^16*b^17*c^27*d^13 + 9165979648*a^17*b^16*c^26*d^14 - 7603863552*a^18*b^15*c^25*d^15 + 4414717952*a^19*b^14*c^24*d^16 - 1766236160*a^20*b^13*c^23*d^17 + 465100800*a^21*b^12*c^22*d^18 - 72704000*a^22*b^11*c^21*d^19 + 5120000*a^23*b^10*c^20*d^20))*1i + (-b^9/(16*a^13*d^8 + 16*a^5*b^8*c^8 - 128*a^6*b^7*c^7*d + 448*a^7*b^6*c^6*d^2 - 896*a^8*b^5*c^5*d^3 + 1120*a^9*b^4*c^4*d^4 - 896*a^10*b^3*c^3*d^5 + 448*a^11*b^2*c^2*d^6 - 128*a^12*b*c*d^7))^(1/4)*((-b^9/(16*a^13*d^8 + 16*a^5*b^8*c^8 - 128*a^6*b^7*c^7*d + 448*a^7*b^6*c^6*d^2 - 896*a^8*b^5*c^5*d^3 + 1120*a^9*b^4*c^4*d^4 - 896*a^10*b^3*c^3*d^5 + 448*a^11*b^2*c^2*d^6 - 128*a^12*b*c*d^7))^(3/4)*(x^(1/2)*(-b^9/(16*a^13*d^8 + 16*a^5*b^8*c^8 - 128*a^6*b^7*c^7*d + 448*a^7*b^6*c^6*d^2 - 896*a^8*b^5*c^5*d^3 + 1120*a^9*b^4*c^4*d^4 - 896*a^10*b^3*c^3*d^5 + 448*a^11*b^2*c^2*d^6 - 128*a^12*b*c*d^7))^(1/4)*(33554432*a^12*b^25*c^44*d^4 - 503316480*a^13*b^24*c^43*d^5 + 3523215360*a^14*b^23*c^42*d^6 - 15267266560*a^15*b^22*c^41*d^7 + 45971668992*a^16*b^21*c^40*d^8 - 103500742656*a^17*b^20*c^39*d^9 + 188659793920*a^18*b^19*c^38*d^10 - 313817825280*a^19*b^18*c^37*d^11 + 539177779200*a^20*b^17*c^36*d^12 - 959547703296*a^21*b^16*c^35*d^13 + 1589322448896*a^22*b^15*c^34*d^14 - 2241016627200*a^23*b^14*c^33*d^15 + 2585348014080*a^24*b^13*c^32*d^16 - 2405664030720*a^25*b^12*c^31*d^17 + 1792662306816*a^26*b^11*c^30*d^18 - 1061108580352*a^27*b^10*c^29*d^19 + 492369346560*a^28*b^9*c^28*d^20 - 175279964160*a^29*b^8*c^27*d^21 + 46221230080*a^30*b^7*c^26*d^22 - 8506048512*a^31*b^6*c^25*d^23 + 975175680*a^32*b^5*c^24*d^24 - 52428800*a^33*b^4*c^23*d^25) + 16777216*a^11*b^25*c^42*d^4 - 218103808*a^12*b^24*c^41*d^5 + 1308622848*a^13*b^23*c^40*d^6 - 4798283776*a^14*b^22*c^39*d^7 + 11995709440*a^15*b^21*c^38*d^8 - 21783379968*a^16*b^20*c^37*d^9 + 31592546304*a^17*b^19*c^36*d^10 - 48013246464*a^18*b^18*c^35*d^11 + 103424196608*a^19*b^17*c^34*d^12 - 253954621440*a^20*b^16*c^33*d^13 + 531641663488*a^21*b^15*c^32*d^14 - 875046109184*a^22*b^14*c^31*d^15 + 1125865488384*a^23*b^13*c^30*d^16 - 1138334629888*a^24*b^12*c^29*d^17 + 906425794560*a^25*b^11*c^28*d^18 - 566347431936*a^26*b^10*c^27*d^19 + 274688114688*a^27*b^9*c^26*d^20 - 101363744768*a^28*b^8*c^25*d^21 + 27505197056*a^29*b^7*c^24*d^22 - 5174722560*a^30*b^6*c^23*d^23 + 602931200*a^31*b^5*c^22*d^24 - 32768000*a^32*b^4*c^21*d^25) - x^(1/2)*(32366592*a^12*b^21*c^31*d^9 - 10616832*a^11*b^22*c^32*d^8 + 186867712*a^13*b^20*c^30*d^10 - 1422057472*a^14*b^19*c^29*d^11 + 4269711360*a^15*b^18*c^28*d^12 - 7664386048*a^16*b^17*c^27*d^13 + 9165979648*a^17*b^16*c^26*d^14 - 7603863552*a^18*b^15*c^25*d^15 + 4414717952*a^19*b^14*c^24*d^16 - 1766236160*a^20*b^13*c^23*d^17 + 465100800*a^21*b^12*c^22*d^18 - 72704000*a^22*b^11*c^21*d^19 + 5120000*a^23*b^10*c^20*d^20))*1i)/((-b^9/(16*a^13*d^8 + 16*a^5*b^8*c^8 - 128*a^6*b^7*c^7*d + 448*a^7*b^6*c^6*d^2 - 896*a^8*b^5*c^5*d^3 + 1120*a^9*b^4*c^4*d^4 - 896*a^10*b^3*c^3*d^5 + 448*a^11*b^2*c^2*d^6 - 128*a^12*b*c*d^7))^(1/4)*((-b^9/(16*a^13*d^8 + 16*a^5*b^8*c^8 - 128*a^6*b^7*c^7*d + 448*a^7*b^6*c^6*d^2 - 896*a^8*b^5*c^5*d^3 + 1120*a^9*b^4*c^4*d^4 - 896*a^10*b^3*c^3*d^5 + 448*a^11*b^2*c^2*d^6 - 128*a^12*b*c*d^7))^(3/4)*(x^(1/2)*(-b^9/(16*a^13*d^8 + 16*a^5*b^8*c^8 - 128*a^6*b^7*c^7*d + 448*a^7*b^6*c^6*d^2 - 896*a^8*b^5*c^5*d^3 + 1120*a^9*b^4*c^4*d^4 - 896*a^10*b^3*c^3*d^5 + 448*a^11*b^2*c^2*d^6 - 128*a^12*b*c*d^7))^(1/4)*(33554432*a^12*b^25*c^44*d^4 - 503316480*a^13*b^24*c^43*d^5 + 3523215360*a^14*b^23*c^42*d^6 - 15267266560*a^15*b^22*c^41*d^7 + 45971668992*a^16*b^21*c^40*d^8 - 103500742656*a^17*b^20*c^39*d^9 + 188659793920*a^18*b^19*c^38*d^10 - 313817825280*a^19*b^18*c^37*d^11 + 539177779200*a^20*b^17*c^36*d^12 - 959547703296*a^21*b^16*c^35*d^13 + 1589322448896*a^22*b^15*c^34*d^14 - 2241016627200*a^23*b^14*c^33*d^15 + 2585348014080*a^24*b^13*c^32*d^16 - 2405664030720*a^25*b^12*c^31*d^17 + 1792662306816*a^26*b^11*c^30*d^18 - 1061108580352*a^27*b^10*c^29*d^19 + 492369346560*a^28*b^9*c^28*d^20 - 175279964160*a^29*b^8*c^27*d^21 + 46221230080*a^30*b^7*c^26*d^22 - 8506048512*a^31*b^6*c^25*d^23 + 975175680*a^32*b^5*c^24*d^24 - 52428800*a^33*b^4*c^23*d^25) - 16777216*a^11*b^25*c^42*d^4 + 218103808*a^12*b^24*c^41*d^5 - 1308622848*a^13*b^23*c^40*d^6 + 4798283776*a^14*b^22*c^39*d^7 - 11995709440*a^15*b^21*c^38*d^8 + 21783379968*a^16*b^20*c^37*d^9 - 31592546304*a^17*b^19*c^36*d^10 + 48013246464*a^18*b^18*c^35*d^11 - 103424196608*a^19*b^17*c^34*d^12 + 253954621440*a^20*b^16*c^33*d^13 - 531641663488*a^21*b^15*c^32*d^14 + 875046109184*a^22*b^14*c^31*d^15 - 1125865488384*a^23*b^13*c^30*d^16 + 1138334629888*a^24*b^12*c^29*d^17 - 906425794560*a^25*b^11*c^28*d^18 + 566347431936*a^26*b^10*c^27*d^19 - 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128*a^12*b*c*d^7))^(3/4)*(x^(1/2)*(-b^9/(16*a^13*d^8 + 16*a^5*b^8*c^8 - 128*a^6*b^7*c^7*d + 448*a^7*b^6*c^6*d^2 - 896*a^8*b^5*c^5*d^3 + 1120*a^9*b^4*c^4*d^4 - 896*a^10*b^3*c^3*d^5 + 448*a^11*b^2*c^2*d^6 - 128*a^12*b*c*d^7))^(1/4)*(33554432*a^12*b^25*c^44*d^4 - 503316480*a^13*b^24*c^43*d^5 + 3523215360*a^14*b^23*c^42*d^6 - 15267266560*a^15*b^22*c^41*d^7 + 45971668992*a^16*b^21*c^40*d^8 - 103500742656*a^17*b^20*c^39*d^9 + 188659793920*a^18*b^19*c^38*d^10 - 313817825280*a^19*b^18*c^37*d^11 + 539177779200*a^20*b^17*c^36*d^12 - 959547703296*a^21*b^16*c^35*d^13 + 1589322448896*a^22*b^15*c^34*d^14 - 2241016627200*a^23*b^14*c^33*d^15 + 2585348014080*a^24*b^13*c^32*d^16 - 2405664030720*a^25*b^12*c^31*d^17 + 1792662306816*a^26*b^11*c^30*d^18 - 1061108580352*a^27*b^10*c^29*d^19 + 492369346560*a^28*b^9*c^28*d^20 - 175279964160*a^29*b^8*c^27*d^21 + 46221230080*a^30*b^7*c^26*d^22 - 8506048512*a^31*b^6*c^25*d^23 + 975175680*a^32*b^5*c^24*d^24 - 52428800*a^33*b^4*c^23*d^25) + 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229376*a^3*b^5*c^14*d^3 + 286720*a^4*b^4*c^13*d^4 - 229376*a^5*b^3*c^12*d^5 + 114688*a^6*b^2*c^11*d^6 - 32768*a*b^7*c^16*d))^(1/4)*(33554432*a^12*b^25*c^44*d^4 - 503316480*a^13*b^24*c^43*d^5 + 3523215360*a^14*b^23*c^42*d^6 - 15267266560*a^15*b^22*c^41*d^7 + 45971668992*a^16*b^21*c^40*d^8 - 103500742656*a^17*b^20*c^39*d^9 + 188659793920*a^18*b^19*c^38*d^10 - 313817825280*a^19*b^18*c^37*d^11 + 539177779200*a^20*b^17*c^36*d^12 - 959547703296*a^21*b^16*c^35*d^13 + 1589322448896*a^22*b^15*c^34*d^14 - 2241016627200*a^23*b^14*c^33*d^15 + 2585348014080*a^24*b^13*c^32*d^16 - 2405664030720*a^25*b^12*c^31*d^17 + 1792662306816*a^26*b^11*c^30*d^18 - 1061108580352*a^27*b^10*c^29*d^19 + 492369346560*a^28*b^9*c^28*d^20 - 175279964160*a^29*b^8*c^27*d^21 + 46221230080*a^30*b^7*c^26*d^22 - 8506048512*a^31*b^6*c^25*d^23 + 975175680*a^32*b^5*c^24*d^24 - 52428800*a^33*b^4*c^23*d^25)*1i + 16777216*a^11*b^25*c^42*d^4 - 218103808*a^12*b^24*c^41*d^5 + 1308622848*a^13*b^23*c^40*d^6 - 4798283776*a^14*b^22*c^39*d^7 + 11995709440*a^15*b^21*c^38*d^8 - 21783379968*a^16*b^20*c^37*d^9 + 31592546304*a^17*b^19*c^36*d^10 - 48013246464*a^18*b^18*c^35*d^11 + 103424196608*a^19*b^17*c^34*d^12 - 253954621440*a^20*b^16*c^33*d^13 + 531641663488*a^21*b^15*c^32*d^14 - 875046109184*a^22*b^14*c^31*d^15 + 1125865488384*a^23*b^13*c^30*d^16 - 1138334629888*a^24*b^12*c^29*d^17 + 906425794560*a^25*b^11*c^28*d^18 - 566347431936*a^26*b^10*c^27*d^19 + 274688114688*a^27*b^9*c^26*d^20 - 101363744768*a^28*b^8*c^25*d^21 + 27505197056*a^29*b^7*c^24*d^22 - 5174722560*a^30*b^6*c^23*d^23 + 602931200*a^31*b^5*c^22*d^24 - 32768000*a^32*b^4*c^21*d^25)*1i))/((-(625*a^4*d^9 + 6561*b^4*c^4*d^5 - 14580*a*b^3*c^3*d^6 + 12150*a^2*b^2*c^2*d^7 - 4500*a^3*b*c*d^8)/(4096*b^8*c^17 + 4096*a^8*c^9*d^8 - 32768*a^7*b*c^10*d^7 + 114688*a^2*b^6*c^15*d^2 - 229376*a^3*b^5*c^14*d^3 + 286720*a^4*b^4*c^13*d^4 - 229376*a^5*b^3*c^12*d^5 + 114688*a^6*b^2*c^11*d^6 - 32768*a*b^7*c^16*d))^(1/4)*(x^(1/2)*(32366592*a^12*b^21*c^31*d^9 - 10616832*a^11*b^22*c^32*d^8 + 186867712*a^13*b^20*c^30*d^10 - 1422057472*a^14*b^19*c^29*d^11 + 4269711360*a^15*b^18*c^28*d^12 - 7664386048*a^16*b^17*c^27*d^13 + 9165979648*a^17*b^16*c^26*d^14 - 7603863552*a^18*b^15*c^25*d^15 + 4414717952*a^19*b^14*c^24*d^16 - 1766236160*a^20*b^13*c^23*d^17 + 465100800*a^21*b^12*c^22*d^18 - 72704000*a^22*b^11*c^21*d^19 + 5120000*a^23*b^10*c^20*d^20) + (-(625*a^4*d^9 + 6561*b^4*c^4*d^5 - 14580*a*b^3*c^3*d^6 + 12150*a^2*b^2*c^2*d^7 - 4500*a^3*b*c*d^8)/(4096*b^8*c^17 + 4096*a^8*c^9*d^8 - 32768*a^7*b*c^10*d^7 + 114688*a^2*b^6*c^15*d^2 - 229376*a^3*b^5*c^14*d^3 + 286720*a^4*b^4*c^13*d^4 - 229376*a^5*b^3*c^12*d^5 + 114688*a^6*b^2*c^11*d^6 - 32768*a*b^7*c^16*d))^(3/4)*(x^(1/2)*(-(625*a^4*d^9 + 6561*b^4*c^4*d^5 - 14580*a*b^3*c^3*d^6 + 12150*a^2*b^2*c^2*d^7 - 4500*a^3*b*c*d^8)/(4096*b^8*c^17 + 4096*a^8*c^9*d^8 - 32768*a^7*b*c^10*d^7 + 114688*a^2*b^6*c^15*d^2 - 229376*a^3*b^5*c^14*d^3 + 286720*a^4*b^4*c^13*d^4 - 229376*a^5*b^3*c^12*d^5 + 114688*a^6*b^2*c^11*d^6 - 32768*a*b^7*c^16*d))^(1/4)*(33554432*a^12*b^25*c^44*d^4 - 503316480*a^13*b^24*c^43*d^5 + 3523215360*a^14*b^23*c^42*d^6 - 15267266560*a^15*b^22*c^41*d^7 + 45971668992*a^16*b^21*c^40*d^8 - 103500742656*a^17*b^20*c^39*d^9 + 188659793920*a^18*b^19*c^38*d^10 - 313817825280*a^19*b^18*c^37*d^11 + 539177779200*a^20*b^17*c^36*d^12 - 959547703296*a^21*b^16*c^35*d^13 + 1589322448896*a^22*b^15*c^34*d^14 - 2241016627200*a^23*b^14*c^33*d^15 + 2585348014080*a^24*b^13*c^32*d^16 - 2405664030720*a^25*b^12*c^31*d^17 + 1792662306816*a^26*b^11*c^30*d^18 - 1061108580352*a^27*b^10*c^29*d^19 + 492369346560*a^28*b^9*c^28*d^20 - 175279964160*a^29*b^8*c^27*d^21 + 46221230080*a^30*b^7*c^26*d^22 - 8506048512*a^31*b^6*c^25*d^23 + 975175680*a^32*b^5*c^24*d^24 - 52428800*a^33*b^4*c^23*d^25)*1i - 16777216*a^11*b^25*c^42*d^4 + 218103808*a^12*b^24*c^41*d^5 - 1308622848*a^13*b^23*c^40*d^6 + 4798283776*a^14*b^22*c^39*d^7 - 11995709440*a^15*b^21*c^38*d^8 + 21783379968*a^16*b^20*c^37*d^9 - 31592546304*a^17*b^19*c^36*d^10 + 48013246464*a^18*b^18*c^35*d^11 - 103424196608*a^19*b^17*c^34*d^12 + 253954621440*a^20*b^16*c^33*d^13 - 531641663488*a^21*b^15*c^32*d^14 + 875046109184*a^22*b^14*c^31*d^15 - 1125865488384*a^23*b^13*c^30*d^16 + 1138334629888*a^24*b^12*c^29*d^17 - 906425794560*a^25*b^11*c^28*d^18 + 566347431936*a^26*b^10*c^27*d^19 - 274688114688*a^27*b^9*c^26*d^20 + 101363744768*a^28*b^8*c^25*d^21 - 27505197056*a^29*b^7*c^24*d^22 + 5174722560*a^30*b^6*c^23*d^23 - 602931200*a^31*b^5*c^22*d^24 + 32768000*a^32*b^4*c^21*d^25)*1i)*1i - (-(625*a^4*d^9 + 6561*b^4*c^4*d^5 - 14580*a*b^3*c^3*d^6 + 12150*a^2*b^2*c^2*d^7 - 4500*a^3*b*c*d^8)/(4096*b^8*c^17 + 4096*a^8*c^9*d^8 - 32768*a^7*b*c^10*d^7 + 114688*a^2*b^6*c^15*d^2 - 229376*a^3*b^5*c^14*d^3 + 286720*a^4*b^4*c^13*d^4 - 229376*a^5*b^3*c^12*d^5 + 114688*a^6*b^2*c^11*d^6 - 32768*a*b^7*c^16*d))^(1/4)*(x^(1/2)*(32366592*a^12*b^21*c^31*d^9 - 10616832*a^11*b^22*c^32*d^8 + 186867712*a^13*b^20*c^30*d^10 - 1422057472*a^14*b^19*c^29*d^11 + 4269711360*a^15*b^18*c^28*d^12 - 7664386048*a^16*b^17*c^27*d^13 + 9165979648*a^17*b^16*c^26*d^14 - 7603863552*a^18*b^15*c^25*d^15 + 4414717952*a^19*b^14*c^24*d^16 - 1766236160*a^20*b^13*c^23*d^17 + 465100800*a^21*b^12*c^22*d^18 - 72704000*a^22*b^11*c^21*d^19 + 5120000*a^23*b^10*c^20*d^20) + (-(625*a^4*d^9 + 6561*b^4*c^4*d^5 - 14580*a*b^3*c^3*d^6 + 12150*a^2*b^2*c^2*d^7 - 4500*a^3*b*c*d^8)/(4096*b^8*c^17 + 4096*a^8*c^9*d^8 - 32768*a^7*b*c^10*d^7 + 114688*a^2*b^6*c^15*d^2 - 229376*a^3*b^5*c^14*d^3 + 286720*a^4*b^4*c^13*d^4 - 229376*a^5*b^3*c^12*d^5 + 114688*a^6*b^2*c^11*d^6 - 32768*a*b^7*c^16*d))^(3/4)*(x^(1/2)*(-(625*a^4*d^9 + 6561*b^4*c^4*d^5 - 14580*a*b^3*c^3*d^6 + 12150*a^2*b^2*c^2*d^7 - 4500*a^3*b*c*d^8)/(4096*b^8*c^17 + 4096*a^8*c^9*d^8 - 32768*a^7*b*c^10*d^7 + 114688*a^2*b^6*c^15*d^2 - 229376*a^3*b^5*c^14*d^3 + 286720*a^4*b^4*c^13*d^4 - 229376*a^5*b^3*c^12*d^5 + 114688*a^6*b^2*c^11*d^6 - 32768*a*b^7*c^16*d))^(1/4)*(33554432*a^12*b^25*c^44*d^4 - 503316480*a^13*b^24*c^43*d^5 + 3523215360*a^14*b^23*c^42*d^6 - 15267266560*a^15*b^22*c^41*d^7 + 45971668992*a^16*b^21*c^40*d^8 - 103500742656*a^17*b^20*c^39*d^9 + 188659793920*a^18*b^19*c^38*d^10 - 313817825280*a^19*b^18*c^37*d^11 + 539177779200*a^20*b^17*c^36*d^12 - 959547703296*a^21*b^16*c^35*d^13 + 1589322448896*a^22*b^15*c^34*d^14 - 2241016627200*a^23*b^14*c^33*d^15 + 2585348014080*a^24*b^13*c^32*d^16 - 2405664030720*a^25*b^12*c^31*d^17 + 1792662306816*a^26*b^11*c^30*d^18 - 1061108580352*a^27*b^10*c^29*d^19 + 492369346560*a^28*b^9*c^28*d^20 - 175279964160*a^29*b^8*c^27*d^21 + 46221230080*a^30*b^7*c^26*d^22 - 8506048512*a^31*b^6*c^25*d^23 + 975175680*a^32*b^5*c^24*d^24 - 52428800*a^33*b^4*c^23*d^25)*1i + 16777216*a^11*b^25*c^42*d^4 - 218103808*a^12*b^24*c^41*d^5 + 1308622848*a^13*b^23*c^40*d^6 - 4798283776*a^14*b^22*c^39*d^7 + 11995709440*a^15*b^21*c^38*d^8 - 21783379968*a^16*b^20*c^37*d^9 + 31592546304*a^17*b^19*c^36*d^10 - 48013246464*a^18*b^18*c^35*d^11 + 103424196608*a^19*b^17*c^34*d^12 - 253954621440*a^20*b^16*c^33*d^13 + 531641663488*a^21*b^15*c^32*d^14 - 875046109184*a^22*b^14*c^31*d^15 + 1125865488384*a^23*b^13*c^30*d^16 - 1138334629888*a^24*b^12*c^29*d^17 + 906425794560*a^25*b^11*c^28*d^18 - 566347431936*a^26*b^10*c^27*d^19 + 274688114688*a^27*b^9*c^26*d^20 - 101363744768*a^28*b^8*c^25*d^21 + 27505197056*a^29*b^7*c^24*d^22 - 5174722560*a^30*b^6*c^23*d^23 + 602931200*a^31*b^5*c^22*d^24 - 32768000*a^32*b^4*c^21*d^25)*1i)*1i + 29859840*a^11*b^21*c^29*d^9 - 228925440*a^12*b^20*c^28*d^10 + 774144000*a^13*b^19*c^27*d^11 - 1514700800*a^14*b^18*c^26*d^12 + 1888665600*a^15*b^17*c^25*d^13 - 1555415040*a^16*b^16*c^24*d^14 + 845578240*a^17*b^15*c^23*d^15 - 292454400*a^18*b^14*c^22*d^16 + 58368000*a^19*b^13*c^21*d^17 - 5120000*a^20*b^12*c^20*d^18))*(-(625*a^4*d^9 + 6561*b^4*c^4*d^5 - 14580*a*b^3*c^3*d^6 + 12150*a^2*b^2*c^2*d^7 - 4500*a^3*b*c*d^8)/(4096*b^8*c^17 + 4096*a^8*c^9*d^8 - 32768*a^7*b*c^10*d^7 + 114688*a^2*b^6*c^15*d^2 - 229376*a^3*b^5*c^14*d^3 + 286720*a^4*b^4*c^13*d^4 - 229376*a^5*b^3*c^12*d^5 + 114688*a^6*b^2*c^11*d^6 - 32768*a*b^7*c^16*d))^(1/4)","B"
478,1,27743,570,6.584225,"\text{Not used}","int(1/(x^(5/2)*(a + b*x^2)*(c + d*x^2)^2),x)","-\mathrm{atan}\left(\frac{{\left(-\frac{2401\,a^4\,d^{11}-15092\,a^3\,b\,c\,d^{10}+35574\,a^2\,b^2\,c^2\,d^9-37268\,a\,b^3\,c^3\,d^8+14641\,b^4\,c^4\,d^7}{4096\,a^8\,c^{11}\,d^8-32768\,a^7\,b\,c^{12}\,d^7+114688\,a^6\,b^2\,c^{13}\,d^6-229376\,a^5\,b^3\,c^{14}\,d^5+286720\,a^4\,b^4\,c^{15}\,d^4-229376\,a^3\,b^5\,c^{16}\,d^3+114688\,a^2\,b^6\,c^{17}\,d^2-32768\,a\,b^7\,c^{18}\,d+4096\,b^8\,c^{19}}\right)}^{1/4}\,\left(\sqrt{x}\,\left(-19668992\,a^{22}\,b^{11}\,c^{18}\,d^{22}+261316608\,a^{21}\,b^{12}\,c^{19}\,d^{21}-1569906688\,a^{20}\,b^{13}\,c^{20}\,d^{20}+5629976576\,a^{19}\,b^{14}\,c^{21}\,d^{19}-13398917120\,a^{18}\,b^{15}\,c^{22}\,d^{18}+22256009216\,a^{17}\,b^{16}\,c^{23}\,d^{17}-26429997056\,a^{16}\,b^{17}\,c^{24}\,d^{16}+22648012800\,a^{15}\,b^{18}\,c^{25}\,d^{15}-14037065728\,a^{14}\,b^{19}\,c^{26}\,d^{14}+6343680000\,a^{13}\,b^{20}\,c^{27}\,d^{13}-2168807424\,a^{12}\,b^{21}\,c^{28}\,d^{12}+600711168\,a^{11}\,b^{22}\,c^{29}\,d^{11}-131203072\,a^{10}\,b^{23}\,c^{30}\,d^{10}+15859712\,a^9\,b^{24}\,c^{31}\,d^9\right)+{\left(-\frac{2401\,a^4\,d^{11}-15092\,a^3\,b\,c\,d^{10}+35574\,a^2\,b^2\,c^2\,d^9-37268\,a\,b^3\,c^3\,d^8+14641\,b^4\,c^4\,d^7}{4096\,a^8\,c^{11}\,d^8-32768\,a^7\,b\,c^{12}\,d^7+114688\,a^6\,b^2\,c^{13}\,d^6-229376\,a^5\,b^3\,c^{14}\,d^5+286720\,a^4\,b^4\,c^{15}\,d^4-229376\,a^3\,b^5\,c^{16}\,d^3+114688\,a^2\,b^6\,c^{17}\,d^2-32768\,a\,b^7\,c^{18}\,d+4096\,b^8\,c^{19}}\right)}^{1/4}\,\left(11534336\,a^9\,b^{25}\,c^{35}\,d^7-\left({\left(-\frac{2401\,a^4\,d^{11}-15092\,a^3\,b\,c\,d^{10}+35574\,a^2\,b^2\,c^2\,d^9-37268\,a\,b^3\,c^3\,d^8+14641\,b^4\,c^4\,d^7}{4096\,a^8\,c^{11}\,d^8-32768\,a^7\,b\,c^{12}\,d^7+114688\,a^6\,b^2\,c^{13}\,d^6-229376\,a^5\,b^3\,c^{14}\,d^5+286720\,a^4\,b^4\,c^{15}\,d^4-229376\,a^3\,b^5\,c^{16}\,d^3+114688\,a^2\,b^6\,c^{17}\,d^2-32768\,a\,b^7\,c^{18}\,d+4096\,b^8\,c^{19}}\right)}^{1/4}\,\left(-117440512\,a^{34}\,b^4\,c^{25}\,d^{25}+2181038080\,a^{33}\,b^5\,c^{26}\,d^{24}-19109249024\,a^{32}\,b^6\,c^{27}\,d^{23}+104958263296\,a^{31}\,b^7\,c^{28}\,d^{22}-405069103104\,a^{30}\,b^8\,c^{29}\,d^{21}+1167090253824\,a^{29}\,b^9\,c^{30}\,d^{20}-2604562120704\,a^{28}\,b^{10}\,c^{31}\,d^{19}+4613600182272\,a^{27}\,b^{11}\,c^{32}\,d^{18}-6603814207488\,a^{26}\,b^{12}\,c^{33}\,d^{17}+7756643827712\,a^{25}\,b^{13}\,c^{34}\,d^{16}-7600917708800\,a^{24}\,b^{14}\,c^{35}\,d^{15}+6347693228032\,a^{23}\,b^{15}\,c^{36}\,d^{14}-4642121449472\,a^{22}\,b^{16}\,c^{37}\,d^{13}+3052916441088\,a^{21}\,b^{17}\,c^{38}\,d^{12}-1824220250112\,a^{20}\,b^{18}\,c^{39}\,d^{11}+972004786176\,a^{19}\,b^{19}\,c^{40}\,d^{10}-442364854272\,a^{18}\,b^{20}\,c^{41}\,d^9+162973876224\,a^{17}\,b^{21}\,c^{42}\,d^8-45818576896\,a^{16}\,b^{22}\,c^{43}\,d^7+9126805504\,a^{15}\,b^{23}\,c^{44}\,d^6-1140850688\,a^{14}\,b^{24}\,c^{45}\,d^5+67108864\,a^{13}\,b^{25}\,c^{46}\,d^4\right)-\sqrt{x}\,\left(-102760448\,a^{33}\,b^4\,c^{22}\,d^{26}+1864368128\,a^{32}\,b^5\,c^{23}\,d^{25}-15888023552\,a^{31}\,b^6\,c^{24}\,d^{24}+84473282560\,a^{30}\,b^7\,c^{25}\,d^{23}-313859768320\,a^{29}\,b^8\,c^{26}\,d^{22}+864890650624\,a^{28}\,b^9\,c^{27}\,d^{21}-1830545260544\,a^{27}\,b^{10}\,c^{28}\,d^{20}+3039679217664\,a^{26}\,b^{11}\,c^{29}\,d^{19}-4009062563840\,a^{25}\,b^{12}\,c^{30}\,d^{18}+4221965434880\,a^{24}\,b^{13}\,c^{31}\,d^{17}-3542660153344\,a^{23}\,b^{14}\,c^{32}\,d^{16}+2334365057024\,a^{22}\,b^{15}\,c^{33}\,d^{15}-1148861808640\,a^{21}\,b^{16}\,c^{34}\,d^{14}+336173465600\,a^{20}\,b^{17}\,c^{35}\,d^{13}+65011712000\,a^{19}\,b^{18}\,c^{36}\,d^{12}-184331272192\,a^{18}\,b^{19}\,c^{37}\,d^{11}+163810639872\,a^{17}\,b^{20}\,c^{38}\,d^{10}-100510203904\,a^{16}\,b^{21}\,c^{39}\,d^9+45801799680\,a^{15}\,b^{22}\,c^{40}\,d^8-15267266560\,a^{14}\,b^{23}\,c^{41}\,d^7+3523215360\,a^{13}\,b^{24}\,c^{42}\,d^6-503316480\,a^{12}\,b^{25}\,c^{43}\,d^5+33554432\,a^{11}\,b^{26}\,c^{44}\,d^4\right)\right)\,{\left(-\frac{2401\,a^4\,d^{11}-15092\,a^3\,b\,c\,d^{10}+35574\,a^2\,b^2\,c^2\,d^9-37268\,a\,b^3\,c^3\,d^8+14641\,b^4\,c^4\,d^7}{4096\,a^8\,c^{11}\,d^8-32768\,a^7\,b\,c^{12}\,d^7+114688\,a^6\,b^2\,c^{13}\,d^6-229376\,a^5\,b^3\,c^{14}\,d^5+286720\,a^4\,b^4\,c^{15}\,d^4-229376\,a^3\,b^5\,c^{16}\,d^3+114688\,a^2\,b^6\,c^{17}\,d^2-32768\,a\,b^7\,c^{18}\,d+4096\,b^8\,c^{19}}\right)}^{3/4}-111149056\,a^{10}\,b^{24}\,c^{34}\,d^8+481296384\,a^{11}\,b^{23}\,c^{33}\,d^9-1233125376\,a^{12}\,b^{22}\,c^{32}\,d^{10}+1830010880\,a^{13}\,b^{21}\,c^{31}\,d^{11}+391331840\,a^{14}\,b^{20}\,c^{30}\,d^{12}-12820119552\,a^{15}\,b^{19}\,c^{29}\,d^{13}+46592393216\,a^{16}\,b^{18}\,c^{28}\,d^{14}-104394047488\,a^{17}\,b^{17}\,c^{27}\,d^{15}+165297111040\,a^{18}\,b^{16}\,c^{26}\,d^{16}-192702906368\,a^{19}\,b^{15}\,c^{25}\,d^{17}+167824392192\,a^{20}\,b^{14}\,c^{24}\,d^{18}-109211664384\,a^{21}\,b^{13}\,c^{23}\,d^{19}+52444708864\,a^{22}\,b^{12}\,c^{22}\,d^{20}-18062213120\,a^{23}\,b^{11}\,c^{21}\,d^{21}+4224417792\,a^{24}\,b^{10}\,c^{20}\,d^{22}-601309184\,a^{25}\,b^9\,c^{19}\,d^{23}+39337984\,a^{26}\,b^8\,c^{18}\,d^{24}\right)\right)\,1{}\mathrm{i}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28}\,b^9\,c^{27}\,d^{21}-1830545260544\,a^{27}\,b^{10}\,c^{28}\,d^{20}+3039679217664\,a^{26}\,b^{11}\,c^{29}\,d^{19}-4009062563840\,a^{25}\,b^{12}\,c^{30}\,d^{18}+4221965434880\,a^{24}\,b^{13}\,c^{31}\,d^{17}-3542660153344\,a^{23}\,b^{14}\,c^{32}\,d^{16}+2334365057024\,a^{22}\,b^{15}\,c^{33}\,d^{15}-1148861808640\,a^{21}\,b^{16}\,c^{34}\,d^{14}+336173465600\,a^{20}\,b^{17}\,c^{35}\,d^{13}+65011712000\,a^{19}\,b^{18}\,c^{36}\,d^{12}-184331272192\,a^{18}\,b^{19}\,c^{37}\,d^{11}+163810639872\,a^{17}\,b^{20}\,c^{38}\,d^{10}-100510203904\,a^{16}\,b^{21}\,c^{39}\,d^9+45801799680\,a^{15}\,b^{22}\,c^{40}\,d^8-15267266560\,a^{14}\,b^{23}\,c^{41}\,d^7+3523215360\,a^{13}\,b^{24}\,c^{42}\,d^6-503316480\,a^{12}\,b^{25}\,c^{43}\,d^5+33554432\,a^{11}\,b^{26}\,c^{44}\,d^4\right)+{\left(-\frac{b^{11}}{16\,a^{15}\,d^8-128\,a^{14}\,b\,c\,d^7+448\,a^{13}\,b^2\,c^2\,d^6-896\,a^{12}\,b^3\,c^3\,d^5+1120\,a^{11}\,b^4\,c^4\,d^4-896\,a^{10}\,b^5\,c^5\,d^3+448\,a^9\,b^6\,c^6\,d^2-128\,a^8\,b^7\,c^7\,d+16\,a^7\,b^8\,c^8}\right)}^{1/4}\,\left(-117440512\,a^{34}\,b^4\,c^{25}\,d^{25}+2181038080\,a^{33}\,b^5\,c^{26}\,d^{24}-19109249024\,a^{32}\,b^6\,c^{27}\,d^{23}+104958263296\,a^{31}\,b^7\,c^{28}\,d^{22}-405069103104\,a^{30}\,b^8\,c^{29}\,d^{21}+1167090253824\,a^{29}\,b^9\,c^{30}\,d^{20}-2604562120704\,a^{28}\,b^{10}\,c^{31}\,d^{19}+4613600182272\,a^{27}\,b^{11}\,c^{32}\,d^{18}-6603814207488\,a^{26}\,b^{12}\,c^{33}\,d^{17}+7756643827712\,a^{25}\,b^{13}\,c^{34}\,d^{16}-7600917708800\,a^{24}\,b^{14}\,c^{35}\,d^{15}+6347693228032\,a^{23}\,b^{15}\,c^{36}\,d^{14}-4642121449472\,a^{22}\,b^{16}\,c^{37}\,d^{13}+3052916441088\,a^{21}\,b^{17}\,c^{38}\,d^{12}-1824220250112\,a^{20}\,b^{18}\,c^{39}\,d^{11}+972004786176\,a^{19}\,b^{19}\,c^{40}\,d^{10}-442364854272\,a^{18}\,b^{20}\,c^{41}\,d^9+162973876224\,a^{17}\,b^{21}\,c^{42}\,d^8-45818576896\,a^{16}\,b^{22}\,c^{43}\,d^7+9126805504\,a^{15}\,b^{23}\,c^{44}\,d^6-1140850688\,a^{14}\,b^{24}\,c^{45}\,d^5+67108864\,a^{13}\,b^{25}\,c^{46}\,d^4\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}-{\left(-\frac{b^{11}}{16\,a^{15}\,d^8-128\,a^{14}\,b\,c\,d^7+448\,a^{13}\,b^2\,c^2\,d^6-896\,a^{12}\,b^3\,c^3\,d^5+1120\,a^{11}\,b^4\,c^4\,d^4-896\,a^{10}\,b^5\,c^5\,d^3+448\,a^9\,b^6\,c^6\,d^2-128\,a^8\,b^7\,c^7\,d+16\,a^7\,b^8\,c^8}\right)}^{1/4}\,\left(\sqrt{x}\,\left(-19668992\,a^{22}\,b^{11}\,c^{18}\,d^{22}+261316608\,a^{21}\,b^{12}\,c^{19}\,d^{21}-1569906688\,a^{20}\,b^{13}\,c^{20}\,d^{20}+5629976576\,a^{19}\,b^{14}\,c^{21}\,d^{19}-13398917120\,a^{18}\,b^{15}\,c^{22}\,d^{18}+22256009216\,a^{17}\,b^{16}\,c^{23}\,d^{17}-26429997056\,a^{16}\,b^{17}\,c^{24}\,d^{16}+22648012800\,a^{15}\,b^{18}\,c^{25}\,d^{15}-14037065728\,a^{14}\,b^{19}\,c^{26}\,d^{14}+6343680000\,a^{13}\,b^{20}\,c^{27}\,d^{13}-2168807424\,a^{12}\,b^{21}\,c^{28}\,d^{12}+600711168\,a^{11}\,b^{22}\,c^{29}\,d^{11}-131203072\,a^{10}\,b^{23}\,c^{30}\,d^{10}+15859712\,a^9\,b^{24}\,c^{31}\,d^9\right)+{\left(-\frac{b^{11}}{16\,a^{15}\,d^8-128\,a^{14}\,b\,c\,d^7+448\,a^{13}\,b^2\,c^2\,d^6-896\,a^{12}\,b^3\,c^3\,d^5+1120\,a^{11}\,b^4\,c^4\,d^4-896\,a^{10}\,b^5\,c^5\,d^3+448\,a^9\,b^6\,c^6\,d^2-128\,a^8\,b^7\,c^7\,d+16\,a^7\,b^8\,c^8}\right)}^{1/4}\,\left(11534336\,a^9\,b^{25}\,c^{35}\,d^7-111149056\,a^{10}\,b^{24}\,c^{34}\,d^8+481296384\,a^{11}\,b^{23}\,c^{33}\,d^9-1233125376\,a^{12}\,b^{22}\,c^{32}\,d^{10}+1830010880\,a^{13}\,b^{21}\,c^{31}\,d^{11}+391331840\,a^{14}\,b^{20}\,c^{30}\,d^{12}-12820119552\,a^{15}\,b^{19}\,c^{29}\,d^{13}+46592393216\,a^{16}\,b^{18}\,c^{28}\,d^{14}-104394047488\,a^{17}\,b^{17}\,c^{27}\,d^{15}+165297111040\,a^{18}\,b^{16}\,c^{26}\,d^{16}-192702906368\,a^{19}\,b^{15}\,c^{25}\,d^{17}+167824392192\,a^{20}\,b^{14}\,c^{24}\,d^{18}-109211664384\,a^{21}\,b^{13}\,c^{23}\,d^{19}+52444708864\,a^{22}\,b^{12}\,c^{22}\,d^{20}-18062213120\,a^{23}\,b^{11}\,c^{21}\,d^{21}+4224417792\,a^{24}\,b^{10}\,c^{20}\,d^{22}-601309184\,a^{25}\,b^9\,c^{19}\,d^{23}+39337984\,a^{26}\,b^8\,c^{18}\,d^{24}+{\left(-\frac{b^{11}}{16\,a^{15}\,d^8-128\,a^{14}\,b\,c\,d^7+448\,a^{13}\,b^2\,c^2\,d^6-896\,a^{12}\,b^3\,c^3\,d^5+1120\,a^{11}\,b^4\,c^4\,d^4-896\,a^{10}\,b^5\,c^5\,d^3+448\,a^9\,b^6\,c^6\,d^2-128\,a^8\,b^7\,c^7\,d+16\,a^7\,b^8\,c^8}\right)}^{3/4}\,\left(-\sqrt{x}\,\left(-102760448\,a^{33}\,b^4\,c^{22}\,d^{26}+1864368128\,a^{32}\,b^5\,c^{23}\,d^{25}-15888023552\,a^{31}\,b^6\,c^{24}\,d^{24}+84473282560\,a^{30}\,b^7\,c^{25}\,d^{23}-313859768320\,a^{29}\,b^8\,c^{26}\,d^{22}+864890650624\,a^{28}\,b^9\,c^{27}\,d^{21}-1830545260544\,a^{27}\,b^{10}\,c^{28}\,d^{20}+3039679217664\,a^{26}\,b^{11}\,c^{29}\,d^{19}-4009062563840\,a^{25}\,b^{12}\,c^{30}\,d^{18}+4221965434880\,a^{24}\,b^{13}\,c^{31}\,d^{17}-3542660153344\,a^{23}\,b^{14}\,c^{32}\,d^{16}+2334365057024\,a^{22}\,b^{15}\,c^{33}\,d^{15}-1148861808640\,a^{21}\,b^{16}\,c^{34}\,d^{14}+336173465600\,a^{20}\,b^{17}\,c^{35}\,d^{13}+65011712000\,a^{19}\,b^{18}\,c^{36}\,d^{12}-184331272192\,a^{18}\,b^{19}\,c^{37}\,d^{11}+163810639872\,a^{17}\,b^{20}\,c^{38}\,d^{10}-100510203904\,a^{16}\,b^{21}\,c^{39}\,d^9+45801799680\,a^{15}\,b^{22}\,c^{40}\,d^8-15267266560\,a^{14}\,b^{23}\,c^{41}\,d^7+3523215360\,a^{13}\,b^{24}\,c^{42}\,d^6-503316480\,a^{12}\,b^{25}\,c^{43}\,d^5+33554432\,a^{11}\,b^{26}\,c^{44}\,d^4\right)+{\left(-\frac{b^{11}}{16\,a^{15}\,d^8-128\,a^{14}\,b\,c\,d^7+448\,a^{13}\,b^2\,c^2\,d^6-896\,a^{12}\,b^3\,c^3\,d^5+1120\,a^{11}\,b^4\,c^4\,d^4-896\,a^{10}\,b^5\,c^5\,d^3+448\,a^9\,b^6\,c^6\,d^2-128\,a^8\,b^7\,c^7\,d+16\,a^7\,b^8\,c^8}\right)}^{1/4}\,\left(-117440512\,a^{34}\,b^4\,c^{25}\,d^{25}+2181038080\,a^{33}\,b^5\,c^{26}\,d^{24}-19109249024\,a^{32}\,b^6\,c^{27}\,d^{23}+104958263296\,a^{31}\,b^7\,c^{28}\,d^{22}-405069103104\,a^{30}\,b^8\,c^{29}\,d^{21}+1167090253824\,a^{29}\,b^9\,c^{30}\,d^{20}-2604562120704\,a^{28}\,b^{10}\,c^{31}\,d^{19}+4613600182272\,a^{27}\,b^{11}\,c^{32}\,d^{18}-6603814207488\,a^{26}\,b^{12}\,c^{33}\,d^{17}+7756643827712\,a^{25}\,b^{13}\,c^{34}\,d^{16}-7600917708800\,a^{24}\,b^{14}\,c^{35}\,d^{15}+6347693228032\,a^{23}\,b^{15}\,c^{36}\,d^{14}-4642121449472\,a^{22}\,b^{16}\,c^{37}\,d^{13}+3052916441088\,a^{21}\,b^{17}\,c^{38}\,d^{12}-1824220250112\,a^{20}\,b^{18}\,c^{39}\,d^{11}+972004786176\,a^{19}\,b^{19}\,c^{40}\,d^{10}-442364854272\,a^{18}\,b^{20}\,c^{41}\,d^9+162973876224\,a^{17}\,b^{21}\,c^{42}\,d^8-45818576896\,a^{16}\,b^{22}\,c^{43}\,d^7+9126805504\,a^{15}\,b^{23}\,c^{44}\,d^6-1140850688\,a^{14}\,b^{24}\,c^{45}\,d^5+67108864\,a^{13}\,b^{25}\,c^{46}\,d^4\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}\right)\,{\left(-\frac{b^{11}}{16\,a^{15}\,d^8-128\,a^{14}\,b\,c\,d^7+448\,a^{13}\,b^2\,c^2\,d^6-896\,a^{12}\,b^3\,c^3\,d^5+1120\,a^{11}\,b^4\,c^4\,d^4-896\,a^{10}\,b^5\,c^5\,d^3+448\,a^9\,b^6\,c^6\,d^2-128\,a^8\,b^7\,c^7\,d+16\,a^7\,b^8\,c^8}\right)}^{1/4}","Not used",1,"2*atan(((-b^11/(16*a^15*d^8 + 16*a^7*b^8*c^8 - 128*a^8*b^7*c^7*d + 448*a^9*b^6*c^6*d^2 - 896*a^10*b^5*c^5*d^3 + 1120*a^11*b^4*c^4*d^4 - 896*a^12*b^3*c^3*d^5 + 448*a^13*b^2*c^2*d^6 - 128*a^14*b*c*d^7))^(1/4)*(x^(1/2)*(15859712*a^9*b^24*c^31*d^9 - 131203072*a^10*b^23*c^30*d^10 + 600711168*a^11*b^22*c^29*d^11 - 2168807424*a^12*b^21*c^28*d^12 + 6343680000*a^13*b^20*c^27*d^13 - 14037065728*a^14*b^19*c^26*d^14 + 22648012800*a^15*b^18*c^25*d^15 - 26429997056*a^16*b^17*c^24*d^16 + 22256009216*a^17*b^16*c^23*d^17 - 13398917120*a^18*b^15*c^22*d^18 + 5629976576*a^19*b^14*c^21*d^19 - 1569906688*a^20*b^13*c^20*d^20 + 261316608*a^21*b^12*c^19*d^21 - 19668992*a^22*b^11*c^18*d^22) - (-b^11/(16*a^15*d^8 + 16*a^7*b^8*c^8 - 128*a^8*b^7*c^7*d + 448*a^9*b^6*c^6*d^2 - 896*a^10*b^5*c^5*d^3 + 1120*a^11*b^4*c^4*d^4 - 896*a^12*b^3*c^3*d^5 + 448*a^13*b^2*c^2*d^6 - 128*a^14*b*c*d^7))^(1/4)*((-b^11/(16*a^15*d^8 + 16*a^7*b^8*c^8 - 128*a^8*b^7*c^7*d + 448*a^9*b^6*c^6*d^2 - 896*a^10*b^5*c^5*d^3 + 1120*a^11*b^4*c^4*d^4 - 896*a^12*b^3*c^3*d^5 + 448*a^13*b^2*c^2*d^6 - 128*a^14*b*c*d^7))^(3/4)*((-b^11/(16*a^15*d^8 + 16*a^7*b^8*c^8 - 128*a^8*b^7*c^7*d + 448*a^9*b^6*c^6*d^2 - 896*a^10*b^5*c^5*d^3 + 1120*a^11*b^4*c^4*d^4 - 896*a^12*b^3*c^3*d^5 + 448*a^13*b^2*c^2*d^6 - 128*a^14*b*c*d^7))^(1/4)*(67108864*a^13*b^25*c^46*d^4 - 1140850688*a^14*b^24*c^45*d^5 + 9126805504*a^15*b^23*c^44*d^6 - 45818576896*a^16*b^22*c^43*d^7 + 162973876224*a^17*b^21*c^42*d^8 - 442364854272*a^18*b^20*c^41*d^9 + 972004786176*a^19*b^19*c^40*d^10 - 1824220250112*a^20*b^18*c^39*d^11 + 3052916441088*a^21*b^17*c^38*d^12 - 4642121449472*a^22*b^16*c^37*d^13 + 6347693228032*a^23*b^15*c^36*d^14 - 7600917708800*a^24*b^14*c^35*d^15 + 7756643827712*a^25*b^13*c^34*d^16 - 6603814207488*a^26*b^12*c^33*d^17 + 4613600182272*a^27*b^11*c^32*d^18 - 2604562120704*a^28*b^10*c^31*d^19 + 1167090253824*a^29*b^9*c^30*d^20 - 405069103104*a^30*b^8*c^29*d^21 + 104958263296*a^31*b^7*c^28*d^22 - 19109249024*a^32*b^6*c^27*d^23 + 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32768*a*b^7*c^18*d))^(1/4)*(67108864*a^13*b^25*c^46*d^4 - 1140850688*a^14*b^24*c^45*d^5 + 9126805504*a^15*b^23*c^44*d^6 - 45818576896*a^16*b^22*c^43*d^7 + 162973876224*a^17*b^21*c^42*d^8 - 442364854272*a^18*b^20*c^41*d^9 + 972004786176*a^19*b^19*c^40*d^10 - 1824220250112*a^20*b^18*c^39*d^11 + 3052916441088*a^21*b^17*c^38*d^12 - 4642121449472*a^22*b^16*c^37*d^13 + 6347693228032*a^23*b^15*c^36*d^14 - 7600917708800*a^24*b^14*c^35*d^15 + 7756643827712*a^25*b^13*c^34*d^16 - 6603814207488*a^26*b^12*c^33*d^17 + 4613600182272*a^27*b^11*c^32*d^18 - 2604562120704*a^28*b^10*c^31*d^19 + 1167090253824*a^29*b^9*c^30*d^20 - 405069103104*a^30*b^8*c^29*d^21 + 104958263296*a^31*b^7*c^28*d^22 - 19109249024*a^32*b^6*c^27*d^23 + 2181038080*a^33*b^5*c^26*d^24 - 117440512*a^34*b^4*c^25*d^25) + x^(1/2)*(33554432*a^11*b^26*c^44*d^4 - 503316480*a^12*b^25*c^43*d^5 + 3523215360*a^13*b^24*c^42*d^6 - 15267266560*a^14*b^23*c^41*d^7 + 45801799680*a^15*b^22*c^40*d^8 - 100510203904*a^16*b^21*c^39*d^9 + 163810639872*a^17*b^20*c^38*d^10 - 184331272192*a^18*b^19*c^37*d^11 + 65011712000*a^19*b^18*c^36*d^12 + 336173465600*a^20*b^17*c^35*d^13 - 1148861808640*a^21*b^16*c^34*d^14 + 2334365057024*a^22*b^15*c^33*d^15 - 3542660153344*a^23*b^14*c^32*d^16 + 4221965434880*a^24*b^13*c^31*d^17 - 4009062563840*a^25*b^12*c^30*d^18 + 3039679217664*a^26*b^11*c^29*d^19 - 1830545260544*a^27*b^10*c^28*d^20 + 864890650624*a^28*b^9*c^27*d^21 - 313859768320*a^29*b^8*c^26*d^22 + 84473282560*a^30*b^7*c^25*d^23 - 15888023552*a^31*b^6*c^24*d^24 + 1864368128*a^32*b^5*c^23*d^25 - 102760448*a^33*b^4*c^22*d^26))*(-(2401*a^4*d^11 + 14641*b^4*c^4*d^7 - 37268*a*b^3*c^3*d^8 + 35574*a^2*b^2*c^2*d^9 - 15092*a^3*b*c*d^10)/(4096*b^8*c^19 + 4096*a^8*c^11*d^8 - 32768*a^7*b*c^12*d^7 + 114688*a^2*b^6*c^17*d^2 - 229376*a^3*b^5*c^16*d^3 + 286720*a^4*b^4*c^15*d^4 - 229376*a^5*b^3*c^14*d^5 + 114688*a^6*b^2*c^13*d^6 - 32768*a*b^7*c^18*d))^(3/4) - 111149056*a^10*b^24*c^34*d^8 + 481296384*a^11*b^23*c^33*d^9 - 1233125376*a^12*b^22*c^32*d^10 + 1830010880*a^13*b^21*c^31*d^11 + 391331840*a^14*b^20*c^30*d^12 - 12820119552*a^15*b^19*c^29*d^13 + 46592393216*a^16*b^18*c^28*d^14 - 104394047488*a^17*b^17*c^27*d^15 + 165297111040*a^18*b^16*c^26*d^16 - 192702906368*a^19*b^15*c^25*d^17 + 167824392192*a^20*b^14*c^24*d^18 - 109211664384*a^21*b^13*c^23*d^19 + 52444708864*a^22*b^12*c^22*d^20 - 18062213120*a^23*b^11*c^21*d^21 + 4224417792*a^24*b^10*c^20*d^22 - 601309184*a^25*b^9*c^19*d^23 + 39337984*a^26*b^8*c^18*d^24))*1i)/((-(2401*a^4*d^11 + 14641*b^4*c^4*d^7 - 37268*a*b^3*c^3*d^8 + 35574*a^2*b^2*c^2*d^9 - 15092*a^3*b*c*d^10)/(4096*b^8*c^19 + 4096*a^8*c^11*d^8 - 32768*a^7*b*c^12*d^7 + 114688*a^2*b^6*c^17*d^2 - 229376*a^3*b^5*c^16*d^3 + 286720*a^4*b^4*c^15*d^4 - 229376*a^5*b^3*c^14*d^5 + 114688*a^6*b^2*c^13*d^6 - 32768*a*b^7*c^18*d))^(1/4)*(x^(1/2)*(15859712*a^9*b^24*c^31*d^9 - 131203072*a^10*b^23*c^30*d^10 + 600711168*a^11*b^22*c^29*d^11 - 2168807424*a^12*b^21*c^28*d^12 + 6343680000*a^13*b^20*c^27*d^13 - 14037065728*a^14*b^19*c^26*d^14 + 22648012800*a^15*b^18*c^25*d^15 - 26429997056*a^16*b^17*c^24*d^16 + 22256009216*a^17*b^16*c^23*d^17 - 13398917120*a^18*b^15*c^22*d^18 + 5629976576*a^19*b^14*c^21*d^19 - 1569906688*a^20*b^13*c^20*d^20 + 261316608*a^21*b^12*c^19*d^21 - 19668992*a^22*b^11*c^18*d^22) + (-(2401*a^4*d^11 + 14641*b^4*c^4*d^7 - 37268*a*b^3*c^3*d^8 + 35574*a^2*b^2*c^2*d^9 - 15092*a^3*b*c*d^10)/(4096*b^8*c^19 + 4096*a^8*c^11*d^8 - 32768*a^7*b*c^12*d^7 + 114688*a^2*b^6*c^17*d^2 - 229376*a^3*b^5*c^16*d^3 + 286720*a^4*b^4*c^15*d^4 - 229376*a^5*b^3*c^14*d^5 + 114688*a^6*b^2*c^13*d^6 - 32768*a*b^7*c^18*d))^(1/4)*(11534336*a^9*b^25*c^35*d^7 - ((-(2401*a^4*d^11 + 14641*b^4*c^4*d^7 - 37268*a*b^3*c^3*d^8 + 35574*a^2*b^2*c^2*d^9 - 15092*a^3*b*c*d^10)/(4096*b^8*c^19 + 4096*a^8*c^11*d^8 - 32768*a^7*b*c^12*d^7 + 114688*a^2*b^6*c^17*d^2 - 229376*a^3*b^5*c^16*d^3 + 286720*a^4*b^4*c^15*d^4 - 229376*a^5*b^3*c^14*d^5 + 114688*a^6*b^2*c^13*d^6 - 32768*a*b^7*c^18*d))^(1/4)*(67108864*a^13*b^25*c^46*d^4 - 1140850688*a^14*b^24*c^45*d^5 + 9126805504*a^15*b^23*c^44*d^6 - 45818576896*a^16*b^22*c^43*d^7 + 162973876224*a^17*b^21*c^42*d^8 - 442364854272*a^18*b^20*c^41*d^9 + 972004786176*a^19*b^19*c^40*d^10 - 1824220250112*a^20*b^18*c^39*d^11 + 3052916441088*a^21*b^17*c^38*d^12 - 4642121449472*a^22*b^16*c^37*d^13 + 6347693228032*a^23*b^15*c^36*d^14 - 7600917708800*a^24*b^14*c^35*d^15 + 7756643827712*a^25*b^13*c^34*d^16 - 6603814207488*a^26*b^12*c^33*d^17 + 4613600182272*a^27*b^11*c^32*d^18 - 2604562120704*a^28*b^10*c^31*d^19 + 1167090253824*a^29*b^9*c^30*d^20 - 405069103104*a^30*b^8*c^29*d^21 + 104958263296*a^31*b^7*c^28*d^22 - 19109249024*a^32*b^6*c^27*d^23 + 2181038080*a^33*b^5*c^26*d^24 - 117440512*a^34*b^4*c^25*d^25) - x^(1/2)*(33554432*a^11*b^26*c^44*d^4 - 503316480*a^12*b^25*c^43*d^5 + 3523215360*a^13*b^24*c^42*d^6 - 15267266560*a^14*b^23*c^41*d^7 + 45801799680*a^15*b^22*c^40*d^8 - 100510203904*a^16*b^21*c^39*d^9 + 163810639872*a^17*b^20*c^38*d^10 - 184331272192*a^18*b^19*c^37*d^11 + 65011712000*a^19*b^18*c^36*d^12 + 336173465600*a^20*b^17*c^35*d^13 - 1148861808640*a^21*b^16*c^34*d^14 + 2334365057024*a^22*b^15*c^33*d^15 - 3542660153344*a^23*b^14*c^32*d^16 + 4221965434880*a^24*b^13*c^31*d^17 - 4009062563840*a^25*b^12*c^30*d^18 + 3039679217664*a^26*b^11*c^29*d^19 - 1830545260544*a^27*b^10*c^28*d^20 + 864890650624*a^28*b^9*c^27*d^21 - 313859768320*a^29*b^8*c^26*d^22 + 84473282560*a^30*b^7*c^25*d^23 - 15888023552*a^31*b^6*c^24*d^24 + 1864368128*a^32*b^5*c^23*d^25 - 102760448*a^33*b^4*c^22*d^26))*(-(2401*a^4*d^11 + 14641*b^4*c^4*d^7 - 37268*a*b^3*c^3*d^8 + 35574*a^2*b^2*c^2*d^9 - 15092*a^3*b*c*d^10)/(4096*b^8*c^19 + 4096*a^8*c^11*d^8 - 32768*a^7*b*c^12*d^7 + 114688*a^2*b^6*c^17*d^2 - 229376*a^3*b^5*c^16*d^3 + 286720*a^4*b^4*c^15*d^4 - 229376*a^5*b^3*c^14*d^5 + 114688*a^6*b^2*c^13*d^6 - 32768*a*b^7*c^18*d))^(3/4) - 111149056*a^10*b^24*c^34*d^8 + 481296384*a^11*b^23*c^33*d^9 - 1233125376*a^12*b^22*c^32*d^10 + 1830010880*a^13*b^21*c^31*d^11 + 391331840*a^14*b^20*c^30*d^12 - 12820119552*a^15*b^19*c^29*d^13 + 46592393216*a^16*b^18*c^28*d^14 - 104394047488*a^17*b^17*c^27*d^15 + 165297111040*a^18*b^16*c^26*d^16 - 192702906368*a^19*b^15*c^25*d^17 + 167824392192*a^20*b^14*c^24*d^18 - 109211664384*a^21*b^13*c^23*d^19 + 52444708864*a^22*b^12*c^22*d^20 - 18062213120*a^23*b^11*c^21*d^21 + 4224417792*a^24*b^10*c^20*d^22 - 601309184*a^25*b^9*c^19*d^23 + 39337984*a^26*b^8*c^18*d^24)) - (-(2401*a^4*d^11 + 14641*b^4*c^4*d^7 - 37268*a*b^3*c^3*d^8 + 35574*a^2*b^2*c^2*d^9 - 15092*a^3*b*c*d^10)/(4096*b^8*c^19 + 4096*a^8*c^11*d^8 - 32768*a^7*b*c^12*d^7 + 114688*a^2*b^6*c^17*d^2 - 229376*a^3*b^5*c^16*d^3 + 286720*a^4*b^4*c^15*d^4 - 229376*a^5*b^3*c^14*d^5 + 114688*a^6*b^2*c^13*d^6 - 32768*a*b^7*c^18*d))^(1/4)*(x^(1/2)*(15859712*a^9*b^24*c^31*d^9 - 131203072*a^10*b^23*c^30*d^10 + 600711168*a^11*b^22*c^29*d^11 - 2168807424*a^12*b^21*c^28*d^12 + 6343680000*a^13*b^20*c^27*d^13 - 14037065728*a^14*b^19*c^26*d^14 + 22648012800*a^15*b^18*c^25*d^15 - 26429997056*a^16*b^17*c^24*d^16 + 22256009216*a^17*b^16*c^23*d^17 - 13398917120*a^18*b^15*c^22*d^18 + 5629976576*a^19*b^14*c^21*d^19 - 1569906688*a^20*b^13*c^20*d^20 + 261316608*a^21*b^12*c^19*d^21 - 19668992*a^22*b^11*c^18*d^22) - (-(2401*a^4*d^11 + 14641*b^4*c^4*d^7 - 37268*a*b^3*c^3*d^8 + 35574*a^2*b^2*c^2*d^9 - 15092*a^3*b*c*d^10)/(4096*b^8*c^19 + 4096*a^8*c^11*d^8 - 32768*a^7*b*c^12*d^7 + 114688*a^2*b^6*c^17*d^2 - 229376*a^3*b^5*c^16*d^3 + 286720*a^4*b^4*c^15*d^4 - 229376*a^5*b^3*c^14*d^5 + 114688*a^6*b^2*c^13*d^6 - 32768*a*b^7*c^18*d))^(1/4)*(11534336*a^9*b^25*c^35*d^7 - ((-(2401*a^4*d^11 + 14641*b^4*c^4*d^7 - 37268*a*b^3*c^3*d^8 + 35574*a^2*b^2*c^2*d^9 - 15092*a^3*b*c*d^10)/(4096*b^8*c^19 + 4096*a^8*c^11*d^8 - 32768*a^7*b*c^12*d^7 + 114688*a^2*b^6*c^17*d^2 - 229376*a^3*b^5*c^16*d^3 + 286720*a^4*b^4*c^15*d^4 - 229376*a^5*b^3*c^14*d^5 + 114688*a^6*b^2*c^13*d^6 - 32768*a*b^7*c^18*d))^(1/4)*(67108864*a^13*b^25*c^46*d^4 - 1140850688*a^14*b^24*c^45*d^5 + 9126805504*a^15*b^23*c^44*d^6 - 45818576896*a^16*b^22*c^43*d^7 + 162973876224*a^17*b^21*c^42*d^8 - 442364854272*a^18*b^20*c^41*d^9 + 972004786176*a^19*b^19*c^40*d^10 - 1824220250112*a^20*b^18*c^39*d^11 + 3052916441088*a^21*b^17*c^38*d^12 - 4642121449472*a^22*b^16*c^37*d^13 + 6347693228032*a^23*b^15*c^36*d^14 - 7600917708800*a^24*b^14*c^35*d^15 + 7756643827712*a^25*b^13*c^34*d^16 - 6603814207488*a^26*b^12*c^33*d^17 + 4613600182272*a^27*b^11*c^32*d^18 - 2604562120704*a^28*b^10*c^31*d^19 + 1167090253824*a^29*b^9*c^30*d^20 - 405069103104*a^30*b^8*c^29*d^21 + 104958263296*a^31*b^7*c^28*d^22 - 19109249024*a^32*b^6*c^27*d^23 + 2181038080*a^33*b^5*c^26*d^24 - 117440512*a^34*b^4*c^25*d^25) + x^(1/2)*(33554432*a^11*b^26*c^44*d^4 - 503316480*a^12*b^25*c^43*d^5 + 3523215360*a^13*b^24*c^42*d^6 - 15267266560*a^14*b^23*c^41*d^7 + 45801799680*a^15*b^22*c^40*d^8 - 100510203904*a^16*b^21*c^39*d^9 + 163810639872*a^17*b^20*c^38*d^10 - 184331272192*a^18*b^19*c^37*d^11 + 65011712000*a^19*b^18*c^36*d^12 + 336173465600*a^20*b^17*c^35*d^13 - 1148861808640*a^21*b^16*c^34*d^14 + 2334365057024*a^22*b^15*c^33*d^15 - 3542660153344*a^23*b^14*c^32*d^16 + 4221965434880*a^24*b^13*c^31*d^17 - 4009062563840*a^25*b^12*c^30*d^18 + 3039679217664*a^26*b^11*c^29*d^19 - 1830545260544*a^27*b^10*c^28*d^20 + 864890650624*a^28*b^9*c^27*d^21 - 313859768320*a^29*b^8*c^26*d^22 + 84473282560*a^30*b^7*c^25*d^23 - 15888023552*a^31*b^6*c^24*d^24 + 1864368128*a^32*b^5*c^23*d^25 - 102760448*a^33*b^4*c^22*d^26))*(-(2401*a^4*d^11 + 14641*b^4*c^4*d^7 - 37268*a*b^3*c^3*d^8 + 35574*a^2*b^2*c^2*d^9 - 15092*a^3*b*c*d^10)/(4096*b^8*c^19 + 4096*a^8*c^11*d^8 - 32768*a^7*b*c^12*d^7 + 114688*a^2*b^6*c^17*d^2 - 229376*a^3*b^5*c^16*d^3 + 286720*a^4*b^4*c^15*d^4 - 229376*a^5*b^3*c^14*d^5 + 114688*a^6*b^2*c^13*d^6 - 32768*a*b^7*c^18*d))^(3/4) - 111149056*a^10*b^24*c^34*d^8 + 481296384*a^11*b^23*c^33*d^9 - 1233125376*a^12*b^22*c^32*d^10 + 1830010880*a^13*b^21*c^31*d^11 + 391331840*a^14*b^20*c^30*d^12 - 12820119552*a^15*b^19*c^29*d^13 + 46592393216*a^16*b^18*c^28*d^14 - 104394047488*a^17*b^17*c^27*d^15 + 165297111040*a^18*b^16*c^26*d^16 - 192702906368*a^19*b^15*c^25*d^17 + 167824392192*a^20*b^14*c^24*d^18 - 109211664384*a^21*b^13*c^23*d^19 + 52444708864*a^22*b^12*c^22*d^20 - 18062213120*a^23*b^11*c^21*d^21 + 4224417792*a^24*b^10*c^20*d^22 - 601309184*a^25*b^9*c^19*d^23 + 39337984*a^26*b^8*c^18*d^24))))*(-(2401*a^4*d^11 + 14641*b^4*c^4*d^7 - 37268*a*b^3*c^3*d^8 + 35574*a^2*b^2*c^2*d^9 - 15092*a^3*b*c*d^10)/(4096*b^8*c^19 + 4096*a^8*c^11*d^8 - 32768*a^7*b*c^12*d^7 + 114688*a^2*b^6*c^17*d^2 - 229376*a^3*b^5*c^16*d^3 + 286720*a^4*b^4*c^15*d^4 - 229376*a^5*b^3*c^14*d^5 + 114688*a^6*b^2*c^13*d^6 - 32768*a*b^7*c^18*d))^(1/4)*2i","B"
479,1,17850,618,5.835439,"\text{Not used}","int(1/(x^(7/2)*(a + b*x^2)*(c + d*x^2)^2),x)","-\frac{\frac{2}{5\,a\,c}-\frac{2\,x^2\,\left(9\,a\,d+5\,b\,c\right)}{5\,a^2\,c^2}+\frac{d\,x^4\,\left(-9\,a^2\,d^2+4\,a\,b\,c\,d+4\,b^2\,c^2\right)}{2\,a^2\,c^3\,\left(a\,d-b\,c\right)}}{c\,x^{5/2}+d\,x^{9/2}}-2\,\mathrm{atan}\left(\frac{524288\,a^3\,b^{16}\,c^{32}\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{13}-37908\,a^3\,b\,c\,d^{12}+82134\,a^2\,b^2\,c^2\,d^{11}-79092\,a\,b^3\,c^3\,d^{10}+28561\,b^4\,c^4\,d^9}{4096\,a^8\,c^{13}\,d^8-32768\,a^7\,b\,c^{14}\,d^7+114688\,a^6\,b^2\,c^{15}\,d^6-229376\,a^5\,b^3\,c^{16}\,d^5+286720\,a^4\,b^4\,c^{17}\,d^4-229376\,a^3\,b^5\,c^{18}\,d^3+114688\,a^2\,b^6\,c^{19}\,d^2-32768\,a\,b^7\,c^{20}\,d+4096\,b^8\,c^{21}}\right)}^{5/4}+2654208\,a^{19}\,c^{16}\,d^{16}\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{13}-37908\,a^3\,b\,c\,d^{12}+82134\,a^2\,b^2\,c^2\,d^{11}-79092\,a\,b^3\,c^3\,d^{10}+28561\,b^4\,c^4\,d^9}{4096\,a^8\,c^{13}\,d^8-32768\,a^7\,b\,c^{14}\,d^7+114688\,a^6\,b^2\,c^{15}\,d^6-229376\,a^5\,b^3\,c^{16}\,d^5+286720\,a^4\,b^4\,c^{17}\,d^4-229376\,a^3\,b^5\,c^{18}\,d^3+114688\,a^2\,b^6\,c^{19}\,d^2-32768\,a\,b^7\,c^{20}\,d+4096\,b^8\,c^{21}}\right)}^{5/4}+346112\,b^{15}\,c^{18}\,d^6\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{13}-37908\,a^3\,b\,c\,d^{12}+82134\,a^2\,b^2\,c^2\,d^{11}-79092\,a\,b^3\,c^3\,d^{10}+28561\,b^4\,c^4\,d^9}{4096\,a^8\,c^{13}\,d^8-32768\,a^7\,b\,c^{14}\,d^7+114688\,a^6\,b^2\,c^{15}\,d^6-229376\,a^5\,b^3\,c^{16}\,d^5+286720\,a^4\,b^4\,c^{17}\,d^4-229376\,a^3\,b^5\,c^{18}\,d^3+114688\,a^2\,b^6\,c^{19}\,d^2-32768\,a\,b^7\,c^{20}\,d+4096\,b^8\,c^{21}}\right)}^{1/4}-479232\,a\,b^{14}\,c^{17}\,d^7\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{13}-37908\,a^3\,b\,c\,d^{12}+82134\,a^2\,b^2\,c^2\,d^{11}-79092\,a\,b^3\,c^3\,d^{10}+28561\,b^4\,c^4\,d^9}{4096\,a^8\,c^{13}\,d^8-32768\,a^7\,b\,c^{14}\,d^7+114688\,a^6\,b^2\,c^{15}\,d^6-229376\,a^5\,b^3\,c^{16}\,d^5+286720\,a^4\,b^4\,c^{17}\,d^4-229376\,a^3\,b^5\,c^{18}\,d^3+114688\,a^2\,b^6\,c^{19}\,d^2-32768\,a\,b^7\,c^{20}\,d+4096\,b^8\,c^{21}}\right)}^{1/4}-4194304\,a^4\,b^{15}\,c^{31}\,d\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{13}-37908\,a^3\,b\,c\,d^{12}+82134\,a^2\,b^2\,c^2\,d^{11}-79092\,a\,b^3\,c^3\,d^{10}+28561\,b^4\,c^4\,d^9}{4096\,a^8\,c^{13}\,d^8-32768\,a^7\,b\,c^{14}\,d^7+114688\,a^6\,b^2\,c^{15}\,d^6-229376\,a^5\,b^3\,c^{16}\,d^5+286720\,a^4\,b^4\,c^{17}\,d^4-229376\,a^3\,b^5\,c^{18}\,d^3+114688\,a^2\,b^6\,c^{19}\,d^2-32768\,a\,b^7\,c^{20}\,d+4096\,b^8\,c^{21}}\right)}^{5/4}-28901376\,a^{18}\,b\,c^{17}\,d^{15}\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{13}-37908\,a^3\,b\,c\,d^{12}+82134\,a^2\,b^2\,c^2\,d^{11}-79092\,a\,b^3\,c^3\,d^{10}+28561\,b^4\,c^4\,d^9}{4096\,a^8\,c^{13}\,d^8-32768\,a^7\,b\,c^{14}\,d^7+114688\,a^6\,b^2\,c^{15}\,d^6-229376\,a^5\,b^3\,c^{16}\,d^5+286720\,a^4\,b^4\,c^{17}\,d^4-229376\,a^3\,b^5\,c^{18}\,d^3+114688\,a^2\,b^6\,c^{19}\,d^2-32768\,a\,b^7\,c^{20}\,d+4096\,b^8\,c^{21}}\right)}^{5/4}+165888\,a^2\,b^{13}\,c^{16}\,d^8\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{13}-37908\,a^3\,b\,c\,d^{12}+82134\,a^2\,b^2\,c^2\,d^{11}-79092\,a\,b^3\,c^3\,d^{10}+28561\,b^4\,c^4\,d^9}{4096\,a^8\,c^{13}\,d^8-32768\,a^7\,b\,c^{14}\,d^7+114688\,a^6\,b^2\,c^{15}\,d^6-229376\,a^5\,b^3\,c^{16}\,d^5+286720\,a^4\,b^4\,c^{17}\,d^4-229376\,a^3\,b^5\,c^{18}\,d^3+114688\,a^2\,b^6\,c^{19}\,d^2-32768\,a\,b^7\,c^{20}\,d+4096\,b^8\,c^{21}}\right)}^{1/4}+3655808\,a^3\,b^{12}\,c^{15}\,d^9\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{13}-37908\,a^3\,b\,c\,d^{12}+82134\,a^2\,b^2\,c^2\,d^{11}-79092\,a\,b^3\,c^3\,d^{10}+28561\,b^4\,c^4\,d^9}{4096\,a^8\,c^{13}\,d^8-32768\,a^7\,b\,c^{14}\,d^7+114688\,a^6\,b^2\,c^{15}\,d^6-229376\,a^5\,b^3\,c^{16}\,d^5+286720\,a^4\,b^4\,c^{17}\,d^4-229376\,a^3\,b^5\,c^{18}\,d^3+114688\,a^2\,b^6\,c^{19}\,d^2-32768\,a\,b^7\,c^{20}\,d+4096\,b^8\,c^{21}}\right)}^{1/4}-10123776\,a^4\,b^{11}\,c^{14}\,d^{10}\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{13}-37908\,a^3\,b\,c\,d^{12}+82134\,a^2\,b^2\,c^2\,d^{11}-79092\,a\,b^3\,c^3\,d^{10}+28561\,b^4\,c^4\,d^9}{4096\,a^8\,c^{13}\,d^8-32768\,a^7\,b\,c^{14}\,d^7+114688\,a^6\,b^2\,c^{15}\,d^6-229376\,a^5\,b^3\,c^{16}\,d^5+286720\,a^4\,b^4\,c^{17}\,d^4-229376\,a^3\,b^5\,c^{18}\,d^3+114688\,a^2\,b^6\,c^{19}\,d^2-32768\,a\,b^7\,c^{20}\,d+4096\,b^8\,c^{21}}\right)}^{1/4}+10513152\,a^5\,b^{10}\,c^{13}\,d^{11}\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{13}-37908\,a^3\,b\,c\,d^{12}+82134\,a^2\,b^2\,c^2\,d^{11}-79092\,a\,b^3\,c^3\,d^{10}+28561\,b^4\,c^4\,d^9}{4096\,a^8\,c^{13}\,d^8-32768\,a^7\,b\,c^{14}\,d^7+114688\,a^6\,b^2\,c^{15}\,d^6-229376\,a^5\,b^3\,c^{16}\,d^5+286720\,a^4\,b^4\,c^{17}\,d^4-229376\,a^3\,b^5\,c^{18}\,d^3+114688\,a^2\,b^6\,c^{19}\,d^2-32768\,a\,b^7\,c^{20}\,d+4096\,b^8\,c^{21}}\right)}^{1/4}-4852224\,a^6\,b^9\,c^{12}\,d^{12}\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{13}-37908\,a^3\,b\,c\,d^{12}+82134\,a^2\,b^2\,c^2\,d^{11}-79092\,a\,b^3\,c^3\,d^{10}+28561\,b^4\,c^4\,d^9}{4096\,a^8\,c^{13}\,d^8-32768\,a^7\,b\,c^{14}\,d^7+114688\,a^6\,b^2\,c^{15}\,d^6-229376\,a^5\,b^3\,c^{16}\,d^5+286720\,a^4\,b^4\,c^{17}\,d^4-229376\,a^3\,b^5\,c^{18}\,d^3+114688\,a^2\,b^6\,c^{19}\,d^2-32768\,a\,b^7\,c^{20}\,d+4096\,b^8\,c^{21}}\right)}^{1/4}+839808\,a^7\,b^8\,c^{11}\,d^{13}\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{13}-37908\,a^3\,b\,c\,d^{12}+82134\,a^2\,b^2\,c^2\,d^{11}-79092\,a\,b^3\,c^3\,d^{10}+28561\,b^4\,c^4\,d^9}{4096\,a^8\,c^{13}\,d^8-32768\,a^7\,b\,c^{14}\,d^7+114688\,a^6\,b^2\,c^{15}\,d^6-229376\,a^5\,b^3\,c^{16}\,d^5+286720\,a^4\,b^4\,c^{17}\,d^4-229376\,a^3\,b^5\,c^{18}\,d^3+114688\,a^2\,b^6\,c^{19}\,d^2-32768\,a\,b^7\,c^{20}\,d+4096\,b^8\,c^{21}}\right)}^{1/4}+14680064\,a^5\,b^{14}\,c^{30}\,d^2\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{13}-37908\,a^3\,b\,c\,d^{12}+82134\,a^2\,b^2\,c^2\,d^{11}-79092\,a\,b^3\,c^3\,d^{10}+28561\,b^4\,c^4\,d^9}{4096\,a^8\,c^{13}\,d^8-32768\,a^7\,b\,c^{14}\,d^7+114688\,a^6\,b^2\,c^{15}\,d^6-229376\,a^5\,b^3\,c^{16}\,d^5+286720\,a^4\,b^4\,c^{17}\,d^4-229376\,a^3\,b^5\,c^{18}\,d^3+114688\,a^2\,b^6\,c^{19}\,d^2-32768\,a\,b^7\,c^{20}\,d+4096\,b^8\,c^{21}}\right)}^{5/4}-29360128\,a^6\,b^{13}\,c^{29}\,d^3\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{13}-37908\,a^3\,b\,c\,d^{12}+82134\,a^2\,b^2\,c^2\,d^{11}-79092\,a\,b^3\,c^3\,d^{10}+28561\,b^4\,c^4\,d^9}{4096\,a^8\,c^{13}\,d^8-32768\,a^7\,b\,c^{14}\,d^7+114688\,a^6\,b^2\,c^{15}\,d^6-229376\,a^5\,b^3\,c^{16}\,d^5+286720\,a^4\,b^4\,c^{17}\,d^4-229376\,a^3\,b^5\,c^{18}\,d^3+114688\,a^2\,b^6\,c^{19}\,d^2-32768\,a\,b^7\,c^{20}\,d+4096\,b^8\,c^{21}}\right)}^{5/4}+36700160\,a^7\,b^{12}\,c^{28}\,d^4\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{13}-37908\,a^3\,b\,c\,d^{12}+82134\,a^2\,b^2\,c^2\,d^{11}-79092\,a\,b^3\,c^3\,d^{10}+28561\,b^4\,c^4\,d^9}{4096\,a^8\,c^{13}\,d^8-32768\,a^7\,b\,c^{14}\,d^7+114688\,a^6\,b^2\,c^{15}\,d^6-229376\,a^5\,b^3\,c^{16}\,d^5+286720\,a^4\,b^4\,c^{17}\,d^4-229376\,a^3\,b^5\,c^{18}\,d^3+114688\,a^2\,b^6\,c^{19}\,d^2-32768\,a\,b^7\,c^{20}\,d+4096\,b^8\,c^{21}}\right)}^{5/4}-29360128\,a^8\,b^{11}\,c^{27}\,d^5\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{13}-37908\,a^3\,b\,c\,d^{12}+82134\,a^2\,b^2\,c^2\,d^{11}-79092\,a\,b^3\,c^3\,d^{10}+28561\,b^4\,c^4\,d^9}{4096\,a^8\,c^{13}\,d^8-32768\,a^7\,b\,c^{14}\,d^7+114688\,a^6\,b^2\,c^{15}\,d^6-229376\,a^5\,b^3\,c^{16}\,d^5+286720\,a^4\,b^4\,c^{17}\,d^4-229376\,a^3\,b^5\,c^{18}\,d^3+114688\,a^2\,b^6\,c^{19}\,d^2-32768\,a\,b^7\,c^{20}\,d+4096\,b^8\,c^{21}}\right)}^{5/4}+20217856\,a^9\,b^{10}\,c^{26}\,d^6\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{13}-37908\,a^3\,b\,c\,d^{12}+82134\,a^2\,b^2\,c^2\,d^{11}-79092\,a\,b^3\,c^3\,d^{10}+28561\,b^4\,c^4\,d^9}{4096\,a^8\,c^{13}\,d^8-32768\,a^7\,b\,c^{14}\,d^7+114688\,a^6\,b^2\,c^{15}\,d^6-229376\,a^5\,b^3\,c^{16}\,d^5+286720\,a^4\,b^4\,c^{17}\,d^4-229376\,a^3\,b^5\,c^{18}\,d^3+114688\,a^2\,b^6\,c^{19}\,d^2-32768\,a\,b^7\,c^{20}\,d+4096\,b^8\,c^{21}}\right)}^{5/4}-56164352\,a^{10}\,b^9\,c^{25}\,d^7\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{13}-37908\,a^3\,b\,c\,d^{12}+82134\,a^2\,b^2\,c^2\,d^{11}-79092\,a\,b^3\,c^3\,d^{10}+28561\,b^4\,c^4\,d^9}{4096\,a^8\,c^{13}\,d^8-32768\,a^7\,b\,c^{14}\,d^7+114688\,a^6\,b^2\,c^{15}\,d^6-229376\,a^5\,b^3\,c^{16}\,d^5+286720\,a^4\,b^4\,c^{17}\,d^4-229376\,a^3\,b^5\,c^{18}\,d^3+114688\,a^2\,b^6\,c^{19}\,d^2-32768\,a\,b^7\,c^{20}\,d+4096\,b^8\,c^{21}}\right)}^{5/4}+219578368\,a^{11}\,b^8\,c^{24}\,d^8\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{13}-37908\,a^3\,b\,c\,d^{12}+82134\,a^2\,b^2\,c^2\,d^{11}-79092\,a\,b^3\,c^3\,d^{10}+28561\,b^4\,c^4\,d^9}{4096\,a^8\,c^{13}\,d^8-32768\,a^7\,b\,c^{14}\,d^7+114688\,a^6\,b^2\,c^{15}\,d^6-229376\,a^5\,b^3\,c^{16}\,d^5+286720\,a^4\,b^4\,c^{17}\,d^4-229376\,a^3\,b^5\,c^{18}\,d^3+114688\,a^2\,b^6\,c^{19}\,d^2-32768\,a\,b^7\,c^{20}\,d+4096\,b^8\,c^{21}}\right)}^{5/4}-546045952\,a^{12}\,b^7\,c^{23}\,d^9\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{13}-37908\,a^3\,b\,c\,d^{12}+82134\,a^2\,b^2\,c^2\,d^{11}-79092\,a\,b^3\,c^3\,d^{10}+28561\,b^4\,c^4\,d^9}{4096\,a^8\,c^{13}\,d^8-32768\,a^7\,b\,c^{14}\,d^7+114688\,a^6\,b^2\,c^{15}\,d^6-229376\,a^5\,b^3\,c^{16}\,d^5+286720\,a^4\,b^4\,c^{17}\,d^4-229376\,a^3\,b^5\,c^{18}\,d^3+114688\,a^2\,b^6\,c^{19}\,d^2-32768\,a\,b^7\,c^{20}\,d+4096\,b^8\,c^{21}}\right)}^{5/4}+891355136\,a^{13}\,b^6\,c^{22}\,d^{10}\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{13}-37908\,a^3\,b\,c\,d^{12}+82134\,a^2\,b^2\,c^2\,d^{11}-79092\,a\,b^3\,c^3\,d^{10}+28561\,b^4\,c^4\,d^9}{4096\,a^8\,c^{13}\,d^8-32768\,a^7\,b\,c^{14}\,d^7+114688\,a^6\,b^2\,c^{15}\,d^6-229376\,a^5\,b^3\,c^{16}\,d^5+286720\,a^4\,b^4\,c^{17}\,d^4-229376\,a^3\,b^5\,c^{18}\,d^3+114688\,a^2\,b^6\,c^{19}\,d^2-32768\,a\,b^7\,c^{20}\,d+4096\,b^8\,c^{21}}\right)}^{5/4}-995491840\,a^{14}\,b^5\,c^{21}\,d^{11}\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{13}-37908\,a^3\,b\,c\,d^{12}+82134\,a^2\,b^2\,c^2\,d^{11}-79092\,a\,b^3\,c^3\,d^{10}+28561\,b^4\,c^4\,d^9}{4096\,a^8\,c^{13}\,d^8-32768\,a^7\,b\,c^{14}\,d^7+114688\,a^6\,b^2\,c^{15}\,d^6-229376\,a^5\,b^3\,c^{16}\,d^5+286720\,a^4\,b^4\,c^{17}\,d^4-229376\,a^3\,b^5\,c^{18}\,d^3+114688\,a^2\,b^6\,c^{19}\,d^2-32768\,a\,b^7\,c^{20}\,d+4096\,b^8\,c^{21}}\right)}^{5/4}+770244608\,a^{15}\,b^4\,c^{20}\,d^{12}\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{13}-37908\,a^3\,b\,c\,d^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{5/4}-8531968\,a^{20}\,b^7\,c^{12}\,d^9\,\sqrt{x}\,{\left(-\frac{b^{13}}{16\,a^{17}\,d^8-128\,a^{16}\,b\,c\,d^7+448\,a^{15}\,b^2\,c^2\,d^6-896\,a^{14}\,b^3\,c^3\,d^5+1120\,a^{13}\,b^4\,c^4\,d^4-896\,a^{12}\,b^5\,c^5\,d^3+448\,a^{11}\,b^6\,c^6\,d^2-128\,a^{10}\,b^7\,c^7\,d+16\,a^9\,b^8\,c^8}\right)}^{5/4}+13927424\,a^{21}\,b^6\,c^{11}\,d^{10}\,\sqrt{x}\,{\left(-\frac{b^{13}}{16\,a^{17}\,d^8-128\,a^{16}\,b\,c\,d^7+448\,a^{15}\,b^2\,c^2\,d^6-896\,a^{14}\,b^3\,c^3\,d^5+1120\,a^{13}\,b^4\,c^4\,d^4-896\,a^{12}\,b^5\,c^5\,d^3+448\,a^{11}\,b^6\,c^6\,d^2-128\,a^{10}\,b^7\,c^7\,d+16\,a^9\,b^8\,c^8}\right)}^{5/4}-15554560\,a^{22}\,b^5\,c^{10}\,d^{11}\,\sqrt{x}\,{\left(-\frac{b^{13}}{16\,a^{17}\,d^8-128\,a^{16}\,b\,c\,d^7+448\,a^{15}\,b^2\,c^2\,d^6-896\,a^{14}\,b^3\,c^3\,d^5+1120\,a^{13}\,b^4\,c^4\,d^4-896\,a^{12}\,b^5\,c^5\,d^3+448\,a^{11}\,b^6\,c^6\,d^2-128\,a^{10}\,b^7\,c^7\,d+16\,a^9\,b^8\,c^8}\right)}^{5/4}+12035072\,a^{23}\,b^4\,c^9\,d^{12}\,\sqrt{x}\,{\left(-\frac{b^{13}}{16\,a^{17}\,d^8-128\,a^{16}\,b\,c\,d^7+448\,a^{15}\,b^2\,c^2\,d^6-896\,a^{14}\,b^3\,c^3\,d^5+1120\,a^{13}\,b^4\,c^4\,d^4-896\,a^{12}\,b^5\,c^5\,d^3+448\,a^{11}\,b^6\,c^6\,d^2-128\,a^{10}\,b^7\,c^7\,d+16\,a^9\,b^8\,c^8}\right)}^{5/4}-6369280\,a^{24}\,b^3\,c^8\,d^{13}\,\sqrt{x}\,{\left(-\frac{b^{13}}{16\,a^{17}\,d^8-128\,a^{16}\,b\,c\,d^7+448\,a^{15}\,b^2\,c^2\,d^6-896\,a^{14}\,b^3\,c^3\,d^5+1120\,a^{13}\,b^4\,c^4\,d^4-896\,a^{12}\,b^5\,c^5\,d^3+448\,a^{11}\,b^6\,c^6\,d^2-128\,a^{10}\,b^7\,c^7\,d+16\,a^9\,b^8\,c^8}\right)}^{5/4}+2206208\,a^{25}\,b^2\,c^7\,d^{14}\,\sqrt{x}\,{\left(-\frac{b^{13}}{16\,a^{17}\,d^8-128\,a^{16}\,b\,c\,d^7+448\,a^{15}\,b^2\,c^2\,d^6-896\,a^{14}\,b^3\,c^3\,d^5+1120\,a^{13}\,b^4\,c^4\,d^4-896\,a^{12}\,b^5\,c^5\,d^3+448\,a^{11}\,b^6\,c^6\,d^2-128\,a^{10}\,b^7\,c^7\,d+16\,a^9\,b^8\,c^8}\right)}^{5/4}}{-6561\,a^{11}\,b^{11}\,d^{11}+24786\,a^{10}\,b^{12}\,c\,d^{10}-26001\,a^9\,b^{13}\,c^2\,d^9+2304\,a^8\,b^{14}\,c^3\,d^8+2048\,a^7\,b^{15}\,c^4\,d^7+1792\,a^6\,b^{16}\,c^5\,d^6+1536\,a^5\,b^{17}\,c^6\,d^5+1280\,a^4\,b^{18}\,c^7\,d^4+1024\,a^3\,b^{19}\,c^8\,d^3+768\,a^2\,b^{20}\,c^9\,d^2+512\,a\,b^{21}\,c^{10}\,d+256\,b^{22}\,c^{11}}\right)\,{\left(-\frac{b^{13}}{16\,a^{17}\,d^8-128\,a^{16}\,b\,c\,d^7+448\,a^{15}\,b^2\,c^2\,d^6-896\,a^{14}\,b^3\,c^3\,d^5+1120\,a^{13}\,b^4\,c^4\,d^4-896\,a^{12}\,b^5\,c^5\,d^3+448\,a^{11}\,b^6\,c^6\,d^2-128\,a^{10}\,b^7\,c^7\,d+16\,a^9\,b^8\,c^8}\right)}^{1/4}-\mathrm{atan}\left(\frac{a^{11}\,b^{16}\,c^{21}\,\sqrt{x}\,{\left(-\frac{b^{13}}{16\,a^{17}\,d^8-128\,a^{16}\,b\,c\,d^7+448\,a^{15}\,b^2\,c^2\,d^6-896\,a^{14}\,b^3\,c^3\,d^5+1120\,a^{13}\,b^4\,c^4\,d^4-896\,a^{12}\,b^5\,c^5\,d^3+448\,a^{11}\,b^6\,c^6\,d^2-128\,a^{10}\,b^7\,c^7\,d+16\,a^9\,b^8\,c^8}\right)}^{5/4}\,8192{}\mathrm{i}+a^{15}\,b^8\,d^{13}\,\sqrt{x}\,{\left(-\frac{b^{13}}{16\,a^{17}\,d^8-128\,a^{16}\,b\,c\,d^7+448\,a^{15}\,b^2\,c^2\,d^6-896\,a^{14}\,b^3\,c^3\,d^5+1120\,a^{13}\,b^4\,c^4\,d^4-896\,a^{12}\,b^5\,c^5\,d^3+448\,a^{11}\,b^6\,c^6\,d^2-128\,a^{10}\,b^7\,c^7\,d+16\,a^9\,b^8\,c^8}\right)}^{1/4}\,13122{}\mathrm{i}+a^{27}\,c^5\,d^{16}\,\sqrt{x}\,{\left(-\frac{b^{13}}{16\,a^{17}\,d^8-128\,a^{16}\,b\,c\,d^7+448\,a^{15}\,b^2\,c^2\,d^6-896\,a^{14}\,b^3\,c^3\,d^5+1120\,a^{13}\,b^4\,c^4\,d^4-896\,a^{12}\,b^5\,c^5\,d^3+448\,a^{11}\,b^6\,c^6\,d^2-128\,a^{10}\,b^7\,c^7\,d+16\,a^9\,b^8\,c^8}\right)}^{5/4}\,41472{}\mathrm{i}-a^{14}\,b^9\,c\,d^{12}\,\sqrt{x}\,{\left(-\frac{b^{13}}{16\,a^{17}\,d^8-128\,a^{16}\,b\,c\,d^7+448\,a^{15}\,b^2\,c^2\,d^6-896\,a^{14}\,b^3\,c^3\,d^5+1120\,a^{13}\,b^4\,c^4\,d^4-896\,a^{12}\,b^5\,c^5\,d^3+448\,a^{11}\,b^6\,c^6\,d^2-128\,a^{10}\,b^7\,c^7\,d+16\,a^9\,b^8\,c^8}\right)}^{1/4}\,75816{}\mathrm{i}-a^{12}\,b^{15}\,c^{20}\,d\,\sqrt{x}\,{\left(-\frac{b^{13}}{16\,a^{17}\,d^8-128\,a^{16}\,b\,c\,d^7+448\,a^{15}\,b^2\,c^2\,d^6-896\,a^{14}\,b^3\,c^3\,d^5+1120\,a^{13}\,b^4\,c^4\,d^4-896\,a^{12}\,b^5\,c^5\,d^3+448\,a^{11}\,b^6\,c^6\,d^2-128\,a^{10}\,b^7\,c^7\,d+16\,a^9\,b^8\,c^8}\right)}^{5/4}\,65536{}\mathrm{i}-a^{26}\,b\,c^6\,d^{15}\,\sqrt{x}\,{\left(-\frac{b^{13}}{16\,a^{17}\,d^8-128\,a^{16}\,b\,c\,d^7+448\,a^{15}\,b^2\,c^2\,d^6-896\,a^{14}\,b^3\,c^3\,d^5+1120\,a^{13}\,b^4\,c^4\,d^4-896\,a^{12}\,b^5\,c^5\,d^3+448\,a^{11}\,b^6\,c^6\,d^2-128\,a^{10}\,b^7\,c^7\,d+16\,a^9\,b^8\,c^8}\right)}^{5/4}\,451584{}\mathrm{i}+a^8\,b^{15}\,c^7\,d^6\,\sqrt{x}\,{\left(-\frac{b^{13}}{16\,a^{17}\,d^8-128\,a^{16}\,b\,c\,d^7+448\,a^{15}\,b^2\,c^2\,d^6-896\,a^{14}\,b^3\,c^3\,d^5+1120\,a^{13}\,b^4\,c^4\,d^4-896\,a^{12}\,b^5\,c^5\,d^3+448\,a^{11}\,b^6\,c^6\,d^2-128\,a^{10}\,b^7\,c^7\,d+16\,a^9\,b^8\,c^8}\right)}^{1/4}\,5408{}\mathrm{i}-a^9\,b^{14}\,c^6\,d^7\,\sqrt{x}\,{\left(-\frac{b^{13}}{16\,a^{17}\,d^8-128\,a^{16}\,b\,c\,d^7+448\,a^{15}\,b^2\,c^2\,d^6-896\,a^{14}\,b^3\,c^3\,d^5+1120\,a^{13}\,b^4\,c^4\,d^4-896\,a^{12}\,b^5\,c^5\,d^3+448\,a^{11}\,b^6\,c^6\,d^2-128\,a^{10}\,b^7\,c^7\,d+16\,a^9\,b^8\,c^8}\right)}^{1/4}\,7488{}\mathrm{i}+a^{10}\,b^{13}\,c^5\,d^8\,\sqrt{x}\,{\left(-\frac{b^{13}}{16\,a^{17}\,d^8-128\,a^{16}\,b\,c\,d^7+448\,a^{15}\,b^2\,c^2\,d^6-896\,a^{14}\,b^3\,c^3\,d^5+1120\,a^{13}\,b^4\,c^4\,d^4-896\,a^{12}\,b^5\,c^5\,d^3+448\,a^{11}\,b^6\,c^6\,d^2-128\,a^{10}\,b^7\,c^7\,d+16\,a^9\,b^8\,c^8}\right)}^{1/4}\,2592{}\mathrm{i}+a^{11}\,b^{12}\,c^4\,d^9\,\sqrt{x}\,{\left(-\frac{b^{13}}{16\,a^{17}\,d^8-128\,a^{16}\,b\,c\,d^7+448\,a^{15}\,b^2\,c^2\,d^6-896\,a^{14}\,b^3\,c^3\,d^5+1120\,a^{13}\,b^4\,c^4\,d^4-896\,a^{12}\,b^5\,c^5\,d^3+448\,a^{11}\,b^6\,c^6\,d^2-128\,a^{10}\,b^7\,c^7\,d+16\,a^9\,b^8\,c^8}\right)}^{1/4}\,57122{}\mathrm{i}-a^{12}\,b^{11}\,c^3\,d^{10}\,\sqrt{x}\,{\left(-\frac{b^{13}}{16\,a^{17}\,d^8-128\,a^{16}\,b\,c\,d^7+448\,a^{15}\,b^2\,c^2\,d^6-896\,a^{14}\,b^3\,c^3\,d^5+1120\,a^{13}\,b^4\,c^4\,d^4-896\,a^{12}\,b^5\,c^5\,d^3+448\,a^{11}\,b^6\,c^6\,d^2-128\,a^{10}\,b^7\,c^7\,d+16\,a^9\,b^8\,c^8}\right)}^{1/4}\,158184{}\mathrm{i}+a^{13}\,b^{10}\,c^2\,d^{11}\,\sqrt{x}\,{\left(-\frac{b^{13}}{16\,a^{17}\,d^8-128\,a^{16}\,b\,c\,d^7+448\,a^{15}\,b^2\,c^2\,d^6-896\,a^{14}\,b^3\,c^3\,d^5+1120\,a^{13}\,b^4\,c^4\,d^4-896\,a^{12}\,b^5\,c^5\,d^3+448\,a^{11}\,b^6\,c^6\,d^2-128\,a^{10}\,b^7\,c^7\,d+16\,a^9\,b^8\,c^8}\right)}^{1/4}\,164268{}\mathrm{i}+a^{13}\,b^{14}\,c^{19}\,d^2\,\sqrt{x}\,{\left(-\frac{b^{13}}{16\,a^{17}\,d^8-128\,a^{16}\,b\,c\,d^7+448\,a^{15}\,b^2\,c^2\,d^6-896\,a^{14}\,b^3\,c^3\,d^5+1120\,a^{13}\,b^4\,c^4\,d^4-896\,a^{12}\,b^5\,c^5\,d^3+448\,a^{11}\,b^6\,c^6\,d^2-128\,a^{10}\,b^7\,c^7\,d+16\,a^9\,b^8\,c^8}\right)}^{5/4}\,229376{}\mathrm{i}-a^{14}\,b^{13}\,c^{18}\,d^3\,\sqrt{x}\,{\left(-\frac{b^{13}}{16\,a^{17}\,d^8-128\,a^{16}\,b\,c\,d^7+448\,a^{15}\,b^2\,c^2\,d^6-896\,a^{14}\,b^3\,c^3\,d^5+1120\,a^{13}\,b^4\,c^4\,d^4-896\,a^{12}\,b^5\,c^5\,d^3+448\,a^{11}\,b^6\,c^6\,d^2-128\,a^{10}\,b^7\,c^7\,d+16\,a^9\,b^8\,c^8}\right)}^{5/4}\,458752{}\mathrm{i}+a^{15}\,b^{12}\,c^{17}\,d^4\,\sqrt{x}\,{\left(-\frac{b^{13}}{16\,a^{17}\,d^8-128\,a^{16}\,b\,c\,d^7+448\,a^{15}\,b^2\,c^2\,d^6-896\,a^{14}\,b^3\,c^3\,d^5+1120\,a^{13}\,b^4\,c^4\,d^4-896\,a^{12}\,b^5\,c^5\,d^3+448\,a^{11}\,b^6\,c^6\,d^2-128\,a^{10}\,b^7\,c^7\,d+16\,a^9\,b^8\,c^8}\right)}^{5/4}\,573440{}\mathrm{i}-a^{16}\,b^{11}\,c^{16}\,d^5\,\sqrt{x}\,{\left(-\frac{b^{13}}{16\,a^{17}\,d^8-128\,a^{16}\,b\,c\,d^7+448\,a^{15}\,b^2\,c^2\,d^6-896\,a^{14}\,b^3\,c^3\,d^5+1120\,a^{13}\,b^4\,c^4\,d^4-896\,a^{12}\,b^5\,c^5\,d^3+448\,a^{11}\,b^6\,c^6\,d^2-128\,a^{10}\,b^7\,c^7\,d+16\,a^9\,b^8\,c^8}\right)}^{5/4}\,458752{}\mathrm{i}+a^{17}\,b^{10}\,c^{15}\,d^6\,\sqrt{x}\,{\left(-\frac{b^{13}}{16\,a^{17}\,d^8-128\,a^{16}\,b\,c\,d^7+448\,a^{15}\,b^2\,c^2\,d^6-896\,a^{14}\,b^3\,c^3\,d^5+1120\,a^{13}\,b^4\,c^4\,d^4-896\,a^{12}\,b^5\,c^5\,d^3+448\,a^{11}\,b^6\,c^6\,d^2-128\,a^{10}\,b^7\,c^7\,d+16\,a^9\,b^8\,c^8}\right)}^{5/4}\,315904{}\mathrm{i}-a^{18}\,b^9\,c^{14}\,d^7\,\sqrt{x}\,{\left(-\frac{b^{13}}{16\,a^{17}\,d^8-128\,a^{16}\,b\,c\,d^7+448\,a^{15}\,b^2\,c^2\,d^6-896\,a^{14}\,b^3\,c^3\,d^5+1120\,a^{13}\,b^4\,c^4\,d^4-896\,a^{12}\,b^5\,c^5\,d^3+448\,a^{11}\,b^6\,c^6\,d^2-128\,a^{10}\,b^7\,c^7\,d+16\,a^9\,b^8\,c^8}\right)}^{5/4}\,877568{}\mathrm{i}+a^{19}\,b^8\,c^{13}\,d^8\,\sqrt{x}\,{\left(-\frac{b^{13}}{16\,a^{17}\,d^8-128\,a^{16}\,b\,c\,d^7+448\,a^{15}\,b^2\,c^2\,d^6-896\,a^{14}\,b^3\,c^3\,d^5+1120\,a^{13}\,b^4\,c^4\,d^4-896\,a^{12}\,b^5\,c^5\,d^3+448\,a^{11}\,b^6\,c^6\,d^2-128\,a^{10}\,b^7\,c^7\,d+16\,a^9\,b^8\,c^8}\right)}^{5/4}\,3430912{}\mathrm{i}-a^{20}\,b^7\,c^{12}\,d^9\,\sqrt{x}\,{\left(-\frac{b^{13}}{16\,a^{17}\,d^8-128\,a^{16}\,b\,c\,d^7+448\,a^{15}\,b^2\,c^2\,d^6-896\,a^{14}\,b^3\,c^3\,d^5+1120\,a^{13}\,b^4\,c^4\,d^4-896\,a^{12}\,b^5\,c^5\,d^3+448\,a^{11}\,b^6\,c^6\,d^2-128\,a^{10}\,b^7\,c^7\,d+16\,a^9\,b^8\,c^8}\right)}^{5/4}\,8531968{}\mathrm{i}+a^{21}\,b^6\,c^{11}\,d^{10}\,\sqrt{x}\,{\left(-\frac{b^{13}}{16\,a^{17}\,d^8-128\,a^{16}\,b\,c\,d^7+448\,a^{15}\,b^2\,c^2\,d^6-896\,a^{14}\,b^3\,c^3\,d^5+1120\,a^{13}\,b^4\,c^4\,d^4-896\,a^{12}\,b^5\,c^5\,d^3+448\,a^{11}\,b^6\,c^6\,d^2-128\,a^{10}\,b^7\,c^7\,d+16\,a^9\,b^8\,c^8}\right)}^{5/4}\,13927424{}\mathrm{i}-a^{22}\,b^5\,c^{10}\,d^{11}\,\sqrt{x}\,{\left(-\frac{b^{13}}{16\,a^{17}\,d^8-128\,a^{16}\,b\,c\,d^7+448\,a^{15}\,b^2\,c^2\,d^6-896\,a^{14}\,b^3\,c^3\,d^5+1120\,a^{13}\,b^4\,c^4\,d^4-896\,a^{12}\,b^5\,c^5\,d^3+448\,a^{11}\,b^6\,c^6\,d^2-128\,a^{10}\,b^7\,c^7\,d+16\,a^9\,b^8\,c^8}\right)}^{5/4}\,15554560{}\mathrm{i}+a^{23}\,b^4\,c^9\,d^{12}\,\sqrt{x}\,{\left(-\frac{b^{13}}{16\,a^{17}\,d^8-128\,a^{16}\,b\,c\,d^7+448\,a^{15}\,b^2\,c^2\,d^6-896\,a^{14}\,b^3\,c^3\,d^5+1120\,a^{13}\,b^4\,c^4\,d^4-896\,a^{12}\,b^5\,c^5\,d^3+448\,a^{11}\,b^6\,c^6\,d^2-128\,a^{10}\,b^7\,c^7\,d+16\,a^9\,b^8\,c^8}\right)}^{5/4}\,12035072{}\mathrm{i}-a^{24}\,b^3\,c^8\,d^{13}\,\sqrt{x}\,{\left(-\frac{b^{13}}{16\,a^{17}\,d^8-128\,a^{16}\,b\,c\,d^7+448\,a^{15}\,b^2\,c^2\,d^6-896\,a^{14}\,b^3\,c^3\,d^5+1120\,a^{13}\,b^4\,c^4\,d^4-896\,a^{12}\,b^5\,c^5\,d^3+448\,a^{11}\,b^6\,c^6\,d^2-128\,a^{10}\,b^7\,c^7\,d+16\,a^9\,b^8\,c^8}\right)}^{5/4}\,6369280{}\mathrm{i}+a^{25}\,b^2\,c^7\,d^{14}\,\sqrt{x}\,{\left(-\frac{b^{13}}{16\,a^{17}\,d^8-128\,a^{16}\,b\,c\,d^7+448\,a^{15}\,b^2\,c^2\,d^6-896\,a^{14}\,b^3\,c^3\,d^5+1120\,a^{13}\,b^4\,c^4\,d^4-896\,a^{12}\,b^5\,c^5\,d^3+448\,a^{11}\,b^6\,c^6\,d^2-128\,a^{10}\,b^7\,c^7\,d+16\,a^9\,b^8\,c^8}\right)}^{5/4}\,2206208{}\mathrm{i}}{-6561\,a^{11}\,b^{11}\,d^{11}+24786\,a^{10}\,b^{12}\,c\,d^{10}-26001\,a^9\,b^{13}\,c^2\,d^9+2304\,a^8\,b^{14}\,c^3\,d^8+2048\,a^7\,b^{15}\,c^4\,d^7+1792\,a^6\,b^{16}\,c^5\,d^6+1536\,a^5\,b^{17}\,c^6\,d^5+1280\,a^4\,b^{18}\,c^7\,d^4+1024\,a^3\,b^{19}\,c^8\,d^3+768\,a^2\,b^{20}\,c^9\,d^2+512\,a\,b^{21}\,c^{10}\,d+256\,b^{22}\,c^{11}}\right)\,{\left(-\frac{b^{13}}{16\,a^{17}\,d^8-128\,a^{16}\,b\,c\,d^7+448\,a^{15}\,b^2\,c^2\,d^6-896\,a^{14}\,b^3\,c^3\,d^5+1120\,a^{13}\,b^4\,c^4\,d^4-896\,a^{12}\,b^5\,c^5\,d^3+448\,a^{11}\,b^6\,c^6\,d^2-128\,a^{10}\,b^7\,c^7\,d+16\,a^9\,b^8\,c^8}\right)}^{1/4}\,2{}\mathrm{i}","Not used",1,"- (2/(5*a*c) - (2*x^2*(9*a*d + 5*b*c))/(5*a^2*c^2) + (d*x^4*(4*b^2*c^2 - 9*a^2*d^2 + 4*a*b*c*d))/(2*a^2*c^3*(a*d - b*c)))/(c*x^(5/2) + d*x^(9/2)) - 2*atan((524288*a^3*b^16*c^32*x^(1/2)*(-(6561*a^4*d^13 + 28561*b^4*c^4*d^9 - 79092*a*b^3*c^3*d^10 + 82134*a^2*b^2*c^2*d^11 - 37908*a^3*b*c*d^12)/(4096*b^8*c^21 + 4096*a^8*c^13*d^8 - 32768*a^7*b*c^14*d^7 + 114688*a^2*b^6*c^19*d^2 - 229376*a^3*b^5*c^18*d^3 + 286720*a^4*b^4*c^17*d^4 - 229376*a^5*b^3*c^16*d^5 + 114688*a^6*b^2*c^15*d^6 - 32768*a*b^7*c^20*d))^(5/4) + 2654208*a^19*c^16*d^16*x^(1/2)*(-(6561*a^4*d^13 + 28561*b^4*c^4*d^9 - 79092*a*b^3*c^3*d^10 + 82134*a^2*b^2*c^2*d^11 - 37908*a^3*b*c*d^12)/(4096*b^8*c^21 + 4096*a^8*c^13*d^8 - 32768*a^7*b*c^14*d^7 + 114688*a^2*b^6*c^19*d^2 - 229376*a^3*b^5*c^18*d^3 + 286720*a^4*b^4*c^17*d^4 - 229376*a^5*b^3*c^16*d^5 + 114688*a^6*b^2*c^15*d^6 - 32768*a*b^7*c^20*d))^(5/4) + 346112*b^15*c^18*d^6*x^(1/2)*(-(6561*a^4*d^13 + 28561*b^4*c^4*d^9 - 79092*a*b^3*c^3*d^10 + 82134*a^2*b^2*c^2*d^11 - 37908*a^3*b*c*d^12)/(4096*b^8*c^21 + 4096*a^8*c^13*d^8 - 32768*a^7*b*c^14*d^7 + 114688*a^2*b^6*c^19*d^2 - 229376*a^3*b^5*c^18*d^3 + 286720*a^4*b^4*c^17*d^4 - 229376*a^5*b^3*c^16*d^5 + 114688*a^6*b^2*c^15*d^6 - 32768*a*b^7*c^20*d))^(1/4) - 479232*a*b^14*c^17*d^7*x^(1/2)*(-(6561*a^4*d^13 + 28561*b^4*c^4*d^9 - 79092*a*b^3*c^3*d^10 + 82134*a^2*b^2*c^2*d^11 - 37908*a^3*b*c*d^12)/(4096*b^8*c^21 + 4096*a^8*c^13*d^8 - 32768*a^7*b*c^14*d^7 + 114688*a^2*b^6*c^19*d^2 - 229376*a^3*b^5*c^18*d^3 + 286720*a^4*b^4*c^17*d^4 - 229376*a^5*b^3*c^16*d^5 + 114688*a^6*b^2*c^15*d^6 - 32768*a*b^7*c^20*d))^(1/4) - 4194304*a^4*b^15*c^31*d*x^(1/2)*(-(6561*a^4*d^13 + 28561*b^4*c^4*d^9 - 79092*a*b^3*c^3*d^10 + 82134*a^2*b^2*c^2*d^11 - 37908*a^3*b*c*d^12)/(4096*b^8*c^21 + 4096*a^8*c^13*d^8 - 32768*a^7*b*c^14*d^7 + 114688*a^2*b^6*c^19*d^2 - 229376*a^3*b^5*c^18*d^3 + 286720*a^4*b^4*c^17*d^4 - 229376*a^5*b^3*c^16*d^5 + 114688*a^6*b^2*c^15*d^6 - 32768*a*b^7*c^20*d))^(5/4) - 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2048*a^7*b^15*c^4*d^7 + 2304*a^8*b^14*c^3*d^8 - 26001*a^9*b^13*c^2*d^9 + 512*a*b^21*c^10*d))*(-b^13/(16*a^17*d^8 + 16*a^9*b^8*c^8 - 128*a^10*b^7*c^7*d + 448*a^11*b^6*c^6*d^2 - 896*a^12*b^5*c^5*d^3 + 1120*a^13*b^4*c^4*d^4 - 896*a^14*b^3*c^3*d^5 + 448*a^15*b^2*c^2*d^6 - 128*a^16*b*c*d^7))^(1/4) - atan((a^11*b^16*c^21*x^(1/2)*(-b^13/(16*a^17*d^8 + 16*a^9*b^8*c^8 - 128*a^10*b^7*c^7*d + 448*a^11*b^6*c^6*d^2 - 896*a^12*b^5*c^5*d^3 + 1120*a^13*b^4*c^4*d^4 - 896*a^14*b^3*c^3*d^5 + 448*a^15*b^2*c^2*d^6 - 128*a^16*b*c*d^7))^(5/4)*8192i + a^15*b^8*d^13*x^(1/2)*(-b^13/(16*a^17*d^8 + 16*a^9*b^8*c^8 - 128*a^10*b^7*c^7*d + 448*a^11*b^6*c^6*d^2 - 896*a^12*b^5*c^5*d^3 + 1120*a^13*b^4*c^4*d^4 - 896*a^14*b^3*c^3*d^5 + 448*a^15*b^2*c^2*d^6 - 128*a^16*b*c*d^7))^(1/4)*13122i + a^27*c^5*d^16*x^(1/2)*(-b^13/(16*a^17*d^8 + 16*a^9*b^8*c^8 - 128*a^10*b^7*c^7*d + 448*a^11*b^6*c^6*d^2 - 896*a^12*b^5*c^5*d^3 + 1120*a^13*b^4*c^4*d^4 - 896*a^14*b^3*c^3*d^5 + 448*a^15*b^2*c^2*d^6 - 128*a^16*b*c*d^7))^(5/4)*41472i - a^14*b^9*c*d^12*x^(1/2)*(-b^13/(16*a^17*d^8 + 16*a^9*b^8*c^8 - 128*a^10*b^7*c^7*d + 448*a^11*b^6*c^6*d^2 - 896*a^12*b^5*c^5*d^3 + 1120*a^13*b^4*c^4*d^4 - 896*a^14*b^3*c^3*d^5 + 448*a^15*b^2*c^2*d^6 - 128*a^16*b*c*d^7))^(1/4)*75816i - a^12*b^15*c^20*d*x^(1/2)*(-b^13/(16*a^17*d^8 + 16*a^9*b^8*c^8 - 128*a^10*b^7*c^7*d + 448*a^11*b^6*c^6*d^2 - 896*a^12*b^5*c^5*d^3 + 1120*a^13*b^4*c^4*d^4 - 896*a^14*b^3*c^3*d^5 + 448*a^15*b^2*c^2*d^6 - 128*a^16*b*c*d^7))^(5/4)*65536i - a^26*b*c^6*d^15*x^(1/2)*(-b^13/(16*a^17*d^8 + 16*a^9*b^8*c^8 - 128*a^10*b^7*c^7*d + 448*a^11*b^6*c^6*d^2 - 896*a^12*b^5*c^5*d^3 + 1120*a^13*b^4*c^4*d^4 - 896*a^14*b^3*c^3*d^5 + 448*a^15*b^2*c^2*d^6 - 128*a^16*b*c*d^7))^(5/4)*451584i + a^8*b^15*c^7*d^6*x^(1/2)*(-b^13/(16*a^17*d^8 + 16*a^9*b^8*c^8 - 128*a^10*b^7*c^7*d + 448*a^11*b^6*c^6*d^2 - 896*a^12*b^5*c^5*d^3 + 1120*a^13*b^4*c^4*d^4 - 896*a^14*b^3*c^3*d^5 + 448*a^15*b^2*c^2*d^6 - 128*a^16*b*c*d^7))^(1/4)*5408i - a^9*b^14*c^6*d^7*x^(1/2)*(-b^13/(16*a^17*d^8 + 16*a^9*b^8*c^8 - 128*a^10*b^7*c^7*d + 448*a^11*b^6*c^6*d^2 - 896*a^12*b^5*c^5*d^3 + 1120*a^13*b^4*c^4*d^4 - 896*a^14*b^3*c^3*d^5 + 448*a^15*b^2*c^2*d^6 - 128*a^16*b*c*d^7))^(1/4)*7488i + a^10*b^13*c^5*d^8*x^(1/2)*(-b^13/(16*a^17*d^8 + 16*a^9*b^8*c^8 - 128*a^10*b^7*c^7*d + 448*a^11*b^6*c^6*d^2 - 896*a^12*b^5*c^5*d^3 + 1120*a^13*b^4*c^4*d^4 - 896*a^14*b^3*c^3*d^5 + 448*a^15*b^2*c^2*d^6 - 128*a^16*b*c*d^7))^(1/4)*2592i + a^11*b^12*c^4*d^9*x^(1/2)*(-b^13/(16*a^17*d^8 + 16*a^9*b^8*c^8 - 128*a^10*b^7*c^7*d + 448*a^11*b^6*c^6*d^2 - 896*a^12*b^5*c^5*d^3 + 1120*a^13*b^4*c^4*d^4 - 896*a^14*b^3*c^3*d^5 + 448*a^15*b^2*c^2*d^6 - 128*a^16*b*c*d^7))^(1/4)*57122i - a^12*b^11*c^3*d^10*x^(1/2)*(-b^13/(16*a^17*d^8 + 16*a^9*b^8*c^8 - 128*a^10*b^7*c^7*d + 448*a^11*b^6*c^6*d^2 - 896*a^12*b^5*c^5*d^3 + 1120*a^13*b^4*c^4*d^4 - 896*a^14*b^3*c^3*d^5 + 448*a^15*b^2*c^2*d^6 - 128*a^16*b*c*d^7))^(1/4)*158184i + a^13*b^10*c^2*d^11*x^(1/2)*(-b^13/(16*a^17*d^8 + 16*a^9*b^8*c^8 - 128*a^10*b^7*c^7*d + 448*a^11*b^6*c^6*d^2 - 896*a^12*b^5*c^5*d^3 + 1120*a^13*b^4*c^4*d^4 - 896*a^14*b^3*c^3*d^5 + 448*a^15*b^2*c^2*d^6 - 128*a^16*b*c*d^7))^(1/4)*164268i + a^13*b^14*c^19*d^2*x^(1/2)*(-b^13/(16*a^17*d^8 + 16*a^9*b^8*c^8 - 128*a^10*b^7*c^7*d + 448*a^11*b^6*c^6*d^2 - 896*a^12*b^5*c^5*d^3 + 1120*a^13*b^4*c^4*d^4 - 896*a^14*b^3*c^3*d^5 + 448*a^15*b^2*c^2*d^6 - 128*a^16*b*c*d^7))^(5/4)*229376i - a^14*b^13*c^18*d^3*x^(1/2)*(-b^13/(16*a^17*d^8 + 16*a^9*b^8*c^8 - 128*a^10*b^7*c^7*d + 448*a^11*b^6*c^6*d^2 - 896*a^12*b^5*c^5*d^3 + 1120*a^13*b^4*c^4*d^4 - 896*a^14*b^3*c^3*d^5 + 448*a^15*b^2*c^2*d^6 - 128*a^16*b*c*d^7))^(5/4)*458752i + a^15*b^12*c^17*d^4*x^(1/2)*(-b^13/(16*a^17*d^8 + 16*a^9*b^8*c^8 - 128*a^10*b^7*c^7*d + 448*a^11*b^6*c^6*d^2 - 896*a^12*b^5*c^5*d^3 + 1120*a^13*b^4*c^4*d^4 - 896*a^14*b^3*c^3*d^5 + 448*a^15*b^2*c^2*d^6 - 128*a^16*b*c*d^7))^(5/4)*573440i - a^16*b^11*c^16*d^5*x^(1/2)*(-b^13/(16*a^17*d^8 + 16*a^9*b^8*c^8 - 128*a^10*b^7*c^7*d + 448*a^11*b^6*c^6*d^2 - 896*a^12*b^5*c^5*d^3 + 1120*a^13*b^4*c^4*d^4 - 896*a^14*b^3*c^3*d^5 + 448*a^15*b^2*c^2*d^6 - 128*a^16*b*c*d^7))^(5/4)*458752i + a^17*b^10*c^15*d^6*x^(1/2)*(-b^13/(16*a^17*d^8 + 16*a^9*b^8*c^8 - 128*a^10*b^7*c^7*d + 448*a^11*b^6*c^6*d^2 - 896*a^12*b^5*c^5*d^3 + 1120*a^13*b^4*c^4*d^4 - 896*a^14*b^3*c^3*d^5 + 448*a^15*b^2*c^2*d^6 - 128*a^16*b*c*d^7))^(5/4)*315904i - a^18*b^9*c^14*d^7*x^(1/2)*(-b^13/(16*a^17*d^8 + 16*a^9*b^8*c^8 - 128*a^10*b^7*c^7*d + 448*a^11*b^6*c^6*d^2 - 896*a^12*b^5*c^5*d^3 + 1120*a^13*b^4*c^4*d^4 - 896*a^14*b^3*c^3*d^5 + 448*a^15*b^2*c^2*d^6 - 128*a^16*b*c*d^7))^(5/4)*877568i + a^19*b^8*c^13*d^8*x^(1/2)*(-b^13/(16*a^17*d^8 + 16*a^9*b^8*c^8 - 128*a^10*b^7*c^7*d + 448*a^11*b^6*c^6*d^2 - 896*a^12*b^5*c^5*d^3 + 1120*a^13*b^4*c^4*d^4 - 896*a^14*b^3*c^3*d^5 + 448*a^15*b^2*c^2*d^6 - 128*a^16*b*c*d^7))^(5/4)*3430912i - a^20*b^7*c^12*d^9*x^(1/2)*(-b^13/(16*a^17*d^8 + 16*a^9*b^8*c^8 - 128*a^10*b^7*c^7*d + 448*a^11*b^6*c^6*d^2 - 896*a^12*b^5*c^5*d^3 + 1120*a^13*b^4*c^4*d^4 - 896*a^14*b^3*c^3*d^5 + 448*a^15*b^2*c^2*d^6 - 128*a^16*b*c*d^7))^(5/4)*8531968i + a^21*b^6*c^11*d^10*x^(1/2)*(-b^13/(16*a^17*d^8 + 16*a^9*b^8*c^8 - 128*a^10*b^7*c^7*d + 448*a^11*b^6*c^6*d^2 - 896*a^12*b^5*c^5*d^3 + 1120*a^13*b^4*c^4*d^4 - 896*a^14*b^3*c^3*d^5 + 448*a^15*b^2*c^2*d^6 - 128*a^16*b*c*d^7))^(5/4)*13927424i - a^22*b^5*c^10*d^11*x^(1/2)*(-b^13/(16*a^17*d^8 + 16*a^9*b^8*c^8 - 128*a^10*b^7*c^7*d + 448*a^11*b^6*c^6*d^2 - 896*a^12*b^5*c^5*d^3 + 1120*a^13*b^4*c^4*d^4 - 896*a^14*b^3*c^3*d^5 + 448*a^15*b^2*c^2*d^6 - 128*a^16*b*c*d^7))^(5/4)*15554560i + a^23*b^4*c^9*d^12*x^(1/2)*(-b^13/(16*a^17*d^8 + 16*a^9*b^8*c^8 - 128*a^10*b^7*c^7*d + 448*a^11*b^6*c^6*d^2 - 896*a^12*b^5*c^5*d^3 + 1120*a^13*b^4*c^4*d^4 - 896*a^14*b^3*c^3*d^5 + 448*a^15*b^2*c^2*d^6 - 128*a^16*b*c*d^7))^(5/4)*12035072i - a^24*b^3*c^8*d^13*x^(1/2)*(-b^13/(16*a^17*d^8 + 16*a^9*b^8*c^8 - 128*a^10*b^7*c^7*d + 448*a^11*b^6*c^6*d^2 - 896*a^12*b^5*c^5*d^3 + 1120*a^13*b^4*c^4*d^4 - 896*a^14*b^3*c^3*d^5 + 448*a^15*b^2*c^2*d^6 - 128*a^16*b*c*d^7))^(5/4)*6369280i + a^25*b^2*c^7*d^14*x^(1/2)*(-b^13/(16*a^17*d^8 + 16*a^9*b^8*c^8 - 128*a^10*b^7*c^7*d + 448*a^11*b^6*c^6*d^2 - 896*a^12*b^5*c^5*d^3 + 1120*a^13*b^4*c^4*d^4 - 896*a^14*b^3*c^3*d^5 + 448*a^15*b^2*c^2*d^6 - 128*a^16*b*c*d^7))^(5/4)*2206208i)/(256*b^22*c^11 - 6561*a^11*b^11*d^11 + 24786*a^10*b^12*c*d^10 + 768*a^2*b^20*c^9*d^2 + 1024*a^3*b^19*c^8*d^3 + 1280*a^4*b^18*c^7*d^4 + 1536*a^5*b^17*c^6*d^5 + 1792*a^6*b^16*c^5*d^6 + 2048*a^7*b^15*c^4*d^7 + 2304*a^8*b^14*c^3*d^8 - 26001*a^9*b^13*c^2*d^9 + 512*a*b^21*c^10*d))*(-b^13/(16*a^17*d^8 + 16*a^9*b^8*c^8 - 128*a^10*b^7*c^7*d + 448*a^11*b^6*c^6*d^2 - 896*a^12*b^5*c^5*d^3 + 1120*a^13*b^4*c^4*d^4 - 896*a^14*b^3*c^3*d^5 + 448*a^15*b^2*c^2*d^6 - 128*a^16*b*c*d^7))^(1/4)*2i","B"
480,1,35251,631,4.219389,"\text{Not used}","int(x^(7/2)/((a + b*x^2)*(c + d*x^2)^3),x)","-\frac{\frac{x^{5/2}\,\left(9\,a\,d-b\,c\right)}{16\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}+\frac{\sqrt{x}\,\left(3\,b\,c^2+5\,a\,d\,c\right)}{16\,d\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}}{c^2+2\,c\,d\,x^2+d^2\,x^4}+\mathrm{atan}\left(\frac{\left(\left(\frac{-\frac{625\,a^{10}\,b^6\,d^7}{2048}+\frac{148215\,a^9\,b^7\,c\,d^6}{2048}+\frac{997755\,a^8\,b^8\,c^2\,d^5}{2048}+\frac{386451\,a^7\,b^9\,c^3\,d^4}{2048}-\frac{262899\,a^6\,b^{10}\,c^4\,d^3}{2048}+\frac{44901\,a^5\,b^{11}\,c^5\,d^2}{2048}-\frac{3159\,a^4\,b^{12}\,c^6\,d}{2048}+\frac{81\,a^3\,b^{13}\,c^7}{2048}}{a^8\,d^9-8\,a^7\,b\,c\,d^8+28\,a^6\,b^2\,c^2\,d^7-56\,a^5\,b^3\,c^3\,d^6+70\,a^4\,b^4\,c^4\,d^5-56\,a^3\,b^5\,c^5\,d^4+28\,a^2\,b^6\,c^6\,d^3-8\,a\,b^7\,c^7\,d^2+b^8\,c^8\,d}+\left(\frac{{\left(-\frac{a^5\,b^3}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(1280\,a^{16}\,b^4\,c\,d^{18}-6400\,a^{15}\,b^5\,c^2\,d^{17}-23040\,a^{14}\,b^6\,c^3\,d^{16}+309760\,a^{13}\,b^7\,c^4\,d^{15}-1337600\,a^{12}\,b^8\,c^5\,d^{14}+3421440\,a^{11}\,b^9\,c^6\,d^{13}-5913600\,a^{10}\,b^{10}\,c^7\,d^{12}+7265280\,a^9\,b^{11}\,c^8\,d^{11}-6462720\,a^8\,b^{12}\,c^9\,d^{10}+4153600\,a^7\,b^{13}\,c^{10}\,d^9-1886720\,a^6\,b^{14}\,c^{11}\,d^8+576000\,a^5\,b^{15}\,c^{12}\,d^7-106240\,a^4\,b^{16}\,c^{13}\,d^6+8960\,a^3\,b^{17}\,c^{14}\,d^5\right)}{a^8\,d^9-8\,a^7\,b\,c\,d^8+28\,a^6\,b^2\,c^2\,d^7-56\,a^5\,b^3\,c^3\,d^6+70\,a^4\,b^4\,c^4\,d^5-56\,a^3\,b^5\,c^5\,d^4+28\,a^2\,b^6\,c^6\,d^3-8\,a\,b^7\,c^7\,d^2+b^8\,c^8\,d}-\frac{\sqrt{x}\,\left(409600\,a^{19}\,b^4\,d^{20}-17694720\,a^{17}\,b^6\,c^2\,d^{18}+77070336\,a^{16}\,b^7\,c^3\,d^{17}-103612416\,a^{15}\,b^8\,c^4\,d^{16}-116391936\,a^{14}\,b^9\,c^5\,d^{15}+508952576\,a^{13}\,b^{10}\,c^6\,d^{14}-259522560\,a^{12}\,b^{11}\,c^7\,d^{13}-1398177792\,a^{11}\,b^{12}\,c^8\,d^{12}+3714056192\,a^{10}\,b^{13}\,c^9\,d^{11}-4814143488\,a^9\,b^{14}\,c^{10}\,d^{10}+3911712768\,a^8\,b^{15}\,c^{11}\,d^9-2086993920\,a^7\,b^{16}\,c^{12}\,d^8+714080256\,a^6\,b^{17}\,c^{13}\,d^7-141950976\,a^5\,b^{18}\,c^{14}\,d^6+12058624\,a^4\,b^{19}\,c^{15}\,d^5+147456\,a^3\,b^{20}\,c^{16}\,d^4\right)}{4096\,\left(a^{12}\,d^{13}-12\,a^{11}\,b\,c\,d^{12}+66\,a^{10}\,b^2\,c^2\,d^{11}-220\,a^9\,b^3\,c^3\,d^{10}+495\,a^8\,b^4\,c^4\,d^9-792\,a^7\,b^5\,c^5\,d^8+924\,a^6\,b^6\,c^6\,d^7-792\,a^5\,b^7\,c^7\,d^6+495\,a^4\,b^8\,c^8\,d^5-220\,a^3\,b^9\,c^9\,d^4+66\,a^2\,b^{10}\,c^{10}\,d^3-12\,a\,b^{11}\,c^{11}\,d^2+b^{12}\,c^{12}\,d\right)}\right)\,{\left(-\frac{a^5\,b^3}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{3/4}\right)\,{\left(-\frac{a^5\,b^3}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}\,1{}\mathrm{i}-\frac{\sqrt{x}\,\left(26225\,a^{12}\,b^7\,d^8+322200\,a^{11}\,b^8\,c\,d^7+1024380\,a^{10}\,b^9\,c^2\,d^6+328680\,a^9\,b^{10}\,c^3\,d^5+658566\,a^8\,b^{11}\,c^4\,d^4-307800\,a^7\,b^{12}\,c^5\,d^3+48060\,a^6\,b^{13}\,c^6\,d^2-3240\,a^5\,b^{14}\,c^7\,d+81\,a^4\,b^{15}\,c^8\right)\,1{}\mathrm{i}}{4096\,\left(a^{12}\,d^{13}-12\,a^{11}\,b\,c\,d^{12}+66\,a^{10}\,b^2\,c^2\,d^{11}-220\,a^9\,b^3\,c^3\,d^{10}+495\,a^8\,b^4\,c^4\,d^9-792\,a^7\,b^5\,c^5\,d^8+924\,a^6\,b^6\,c^6\,d^7-792\,a^5\,b^7\,c^7\,d^6+495\,a^4\,b^8\,c^8\,d^5-220\,a^3\,b^9\,c^9\,d^4+66\,a^2\,b^{10}\,c^{10}\,d^3-12\,a\,b^{11}\,c^{11}\,d^2+b^{12}\,c^{12}\,d\right)}\right)\,{\left(-\frac{a^5\,b^3}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}-\left(\left(\frac{-\frac{625\,a^{10}\,b^6\,d^7}{2048}+\frac{148215\,a^9\,b^7\,c\,d^6}{2048}+\frac{997755\,a^8\,b^8\,c^2\,d^5}{2048}+\frac{386451\,a^7\,b^9\,c^3\,d^4}{2048}-\frac{262899\,a^6\,b^{10}\,c^4\,d^3}{2048}+\frac{44901\,a^5\,b^{11}\,c^5\,d^2}{2048}-\frac{3159\,a^4\,b^{12}\,c^6\,d}{2048}+\frac{81\,a^3\,b^{13}\,c^7}{2048}}{a^8\,d^9-8\,a^7\,b\,c\,d^8+28\,a^6\,b^2\,c^2\,d^7-56\,a^5\,b^3\,c^3\,d^6+70\,a^4\,b^4\,c^4\,d^5-56\,a^3\,b^5\,c^5\,d^4+28\,a^2\,b^6\,c^6\,d^3-8\,a\,b^7\,c^7\,d^2+b^8\,c^8\,d}+\left(\frac{{\left(-\frac{a^5\,b^3}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(1280\,a^{16}\,b^4\,c\,d^{18}-6400\,a^{15}\,b^5\,c^2\,d^{17}-23040\,a^{14}\,b^6\,c^3\,d^{16}+309760\,a^{13}\,b^7\,c^4\,d^{15}-1337600\,a^{12}\,b^8\,c^5\,d^{14}+3421440\,a^{11}\,b^9\,c^6\,d^{13}-5913600\,a^{10}\,b^{10}\,c^7\,d^{12}+7265280\,a^9\,b^{11}\,c^8\,d^{11}-6462720\,a^8\,b^{12}\,c^9\,d^{10}+4153600\,a^7\,b^{13}\,c^{10}\,d^9-1886720\,a^6\,b^{14}\,c^{11}\,d^8+576000\,a^5\,b^{15}\,c^{12}\,d^7-106240\,a^4\,b^{16}\,c^{13}\,d^6+8960\,a^3\,b^{17}\,c^{14}\,d^5\right)}{a^8\,d^9-8\,a^7\,b\,c\,d^8+28\,a^6\,b^2\,c^2\,d^7-56\,a^5\,b^3\,c^3\,d^6+70\,a^4\,b^4\,c^4\,d^5-56\,a^3\,b^5\,c^5\,d^4+28\,a^2\,b^6\,c^6\,d^3-8\,a\,b^7\,c^7\,d^2+b^8\,c^8\,d}+\frac{\sqrt{x}\,\left(409600\,a^{19}\,b^4\,d^{20}-17694720\,a^{17}\,b^6\,c^2\,d^{18}+77070336\,a^{16}\,b^7\,c^3\,d^{17}-103612416\,a^{15}\,b^8\,c^4\,d^{16}-116391936\,a^{14}\,b^9\,c^5\,d^{15}+508952576\,a^{13}\,b^{10}\,c^6\,d^{14}-259522560\,a^{12}\,b^{11}\,c^7\,d^{13}-1398177792\,a^{11}\,b^{12}\,c^8\,d^{12}+3714056192\,a^{10}\,b^{13}\,c^9\,d^{11}-4814143488\,a^9\,b^{14}\,c^{10}\,d^{10}+3911712768\,a^8\,b^{15}\,c^{11}\,d^9-2086993920\,a^7\,b^{16}\,c^{12}\,d^8+714080256\,a^6\,b^{17}\,c^{13}\,d^7-141950976\,a^5\,b^{18}\,c^{14}\,d^6+12058624\,a^4\,b^{19}\,c^{15}\,d^5+147456\,a^3\,b^{20}\,c^{16}\,d^4\right)}{4096\,\left(a^{12}\,d^{13}-12\,a^{11}\,b\,c\,d^{12}+66\,a^{10}\,b^2\,c^2\,d^{11}-220\,a^9\,b^3\,c^3\,d^{10}+495\,a^8\,b^4\,c^4\,d^9-792\,a^7\,b^5\,c^5\,d^8+924\,a^6\,b^6\,c^6\,d^7-792\,a^5\,b^7\,c^7\,d^6+495\,a^4\,b^8\,c^8\,d^5-220\,a^3\,b^9\,c^9\,d^4+66\,a^2\,b^{10}\,c^{10}\,d^3-12\,a\,b^{11}\,c^{11}\,d^2+b^{12}\,c^{12}\,d\right)}\right)\,{\left(-\frac{a^5\,b^3}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{3/4}\right)\,{\left(-\frac{a^5\,b^3}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}\,1{}\mathrm{i}+\frac{\sqrt{x}\,\left(26225\,a^{12}\,b^7\,d^8+322200\,a^{11}\,b^8\,c\,d^7+1024380\,a^{10}\,b^9\,c^2\,d^6+328680\,a^9\,b^{10}\,c^3\,d^5+658566\,a^8\,b^{11}\,c^4\,d^4-307800\,a^7\,b^{12}\,c^5\,d^3+48060\,a^6\,b^{13}\,c^6\,d^2-3240\,a^5\,b^{14}\,c^7\,d+81\,a^4\,b^{15}\,c^8\right)\,1{}\mathrm{i}}{4096\,\left(a^{12}\,d^{13}-12\,a^{11}\,b\,c\,d^{12}+66\,a^{10}\,b^2\,c^2\,d^{11}-220\,a^9\,b^3\,c^3\,d^{10}+495\,a^8\,b^4\,c^4\,d^9-792\,a^7\,b^5\,c^5\,d^8+924\,a^6\,b^6\,c^6\,d^7-792\,a^5\,b^7\,c^7\,d^6+495\,a^4\,b^8\,c^8\,d^5-220\,a^3\,b^9\,c^9\,d^4+66\,a^2\,b^{10}\,c^{10}\,d^3-12\,a\,b^{11}\,c^{11}\,d^2+b^{12}\,c^{12}\,d\right)}\right)\,{\left(-\frac{a^5\,b^3}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}}{\left(\left(\frac{-\frac{625\,a^{10}\,b^6\,d^7}{2048}+\frac{148215\,a^9\,b^7\,c\,d^6}{2048}+\frac{997755\,a^8\,b^8\,c^2\,d^5}{2048}+\frac{386451\,a^7\,b^9\,c^3\,d^4}{2048}-\frac{262899\,a^6\,b^{10}\,c^4\,d^3}{2048}+\frac{44901\,a^5\,b^{11}\,c^5\,d^2}{2048}-\frac{3159\,a^4\,b^{12}\,c^6\,d}{2048}+\frac{81\,a^3\,b^{13}\,c^7}{2048}}{a^8\,d^9-8\,a^7\,b\,c\,d^8+28\,a^6\,b^2\,c^2\,d^7-56\,a^5\,b^3\,c^3\,d^6+70\,a^4\,b^4\,c^4\,d^5-56\,a^3\,b^5\,c^5\,d^4+28\,a^2\,b^6\,c^6\,d^3-8\,a\,b^7\,c^7\,d^2+b^8\,c^8\,d}+\left(\frac{{\left(-\frac{a^5\,b^3}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(1280\,a^{16}\,b^4\,c\,d^{18}-6400\,a^{15}\,b^5\,c^2\,d^{17}-23040\,a^{14}\,b^6\,c^3\,d^{16}+309760\,a^{13}\,b^7\,c^4\,d^{15}-1337600\,a^{12}\,b^8\,c^5\,d^{14}+3421440\,a^{11}\,b^9\,c^6\,d^{13}-5913600\,a^{10}\,b^{10}\,c^7\,d^{12}+7265280\,a^9\,b^{11}\,c^8\,d^{11}-6462720\,a^8\,b^{12}\,c^9\,d^{10}+4153600\,a^7\,b^{13}\,c^{10}\,d^9-1886720\,a^6\,b^{14}\,c^{11}\,d^8+576000\,a^5\,b^{15}\,c^{12}\,d^7-106240\,a^4\,b^{16}\,c^{13}\,d^6+8960\,a^3\,b^{17}\,c^{14}\,d^5\right)}{a^8\,d^9-8\,a^7\,b\,c\,d^8+28\,a^6\,b^2\,c^2\,d^7-56\,a^5\,b^3\,c^3\,d^6+70\,a^4\,b^4\,c^4\,d^5-56\,a^3\,b^5\,c^5\,d^4+28\,a^2\,b^6\,c^6\,d^3-8\,a\,b^7\,c^7\,d^2+b^8\,c^8\,d}-\frac{\sqrt{x}\,\left(409600\,a^{19}\,b^4\,d^{20}-17694720\,a^{17}\,b^6\,c^2\,d^{18}+77070336\,a^{16}\,b^7\,c^3\,d^{17}-103612416\,a^{15}\,b^8\,c^4\,d^{16}-116391936\,a^{14}\,b^9\,c^5\,d^{15}+508952576\,a^{13}\,b^{10}\,c^6\,d^{14}-259522560\,a^{12}\,b^{11}\,c^7\,d^{13}-1398177792\,a^{11}\,b^{12}\,c^8\,d^{12}+3714056192\,a^{10}\,b^{13}\,c^9\,d^{11}-4814143488\,a^9\,b^{14}\,c^{10}\,d^{10}+3911712768\,a^8\,b^{15}\,c^{11}\,d^9-2086993920\,a^7\,b^{16}\,c^{12}\,d^8+714080256\,a^6\,b^{17}\,c^{13}\,d^7-141950976\,a^5\,b^{18}\,c^{14}\,d^6+12058624\,a^4\,b^{19}\,c^{15}\,d^5+147456\,a^3\,b^{20}\,c^{16}\,d^4\right)}{4096\,\left(a^{12}\,d^{13}-12\,a^{11}\,b\,c\,d^{12}+66\,a^{10}\,b^2\,c^2\,d^{11}-220\,a^9\,b^3\,c^3\,d^{10}+495\,a^8\,b^4\,c^4\,d^9-792\,a^7\,b^5\,c^5\,d^8+924\,a^6\,b^6\,c^6\,d^7-792\,a^5\,b^7\,c^7\,d^6+495\,a^4\,b^8\,c^8\,d^5-220\,a^3\,b^9\,c^9\,d^4+66\,a^2\,b^{10}\,c^{10}\,d^3-12\,a\,b^{11}\,c^{11}\,d^2+b^{12}\,c^{12}\,d\right)}\right)\,{\left(-\frac{a^5\,b^3}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{3/4}\right)\,{\left(-\frac{a^5\,b^3}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}-\frac{\sqrt{x}\,\left(26225\,a^{12}\,b^7\,d^8+322200\,a^{11}\,b^8\,c\,d^7+1024380\,a^{10}\,b^9\,c^2\,d^6+328680\,a^9\,b^{10}\,c^3\,d^5+658566\,a^8\,b^{11}\,c^4\,d^4-307800\,a^7\,b^{12}\,c^5\,d^3+48060\,a^6\,b^{13}\,c^6\,d^2-3240\,a^5\,b^{14}\,c^7\,d+81\,a^4\,b^{15}\,c^8\right)}{4096\,\left(a^{12}\,d^{13}-12\,a^{11}\,b\,c\,d^{12}+66\,a^{10}\,b^2\,c^2\,d^{11}-220\,a^9\,b^3\,c^3\,d^{10}+495\,a^8\,b^4\,c^4\,d^9-792\,a^7\,b^5\,c^5\,d^8+924\,a^6\,b^6\,c^6\,d^7-792\,a^5\,b^7\,c^7\,d^6+495\,a^4\,b^8\,c^8\,d^5-220\,a^3\,b^9\,c^9\,d^4+66\,a^2\,b^{10}\,c^{10}\,d^3-12\,a\,b^{11}\,c^{11}\,d^2+b^{12}\,c^{12}\,d\right)}\right)\,{\left(-\frac{a^5\,b^3}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}+\left(\left(\frac{-\frac{625\,a^{10}\,b^6\,d^7}{2048}+\frac{148215\,a^9\,b^7\,c\,d^6}{2048}+\frac{997755\,a^8\,b^8\,c^2\,d^5}{2048}+\frac{386451\,a^7\,b^9\,c^3\,d^4}{2048}-\frac{262899\,a^6\,b^{10}\,c^4\,d^3}{2048}+\frac{44901\,a^5\,b^{11}\,c^5\,d^2}{2048}-\frac{3159\,a^4\,b^{12}\,c^6\,d}{2048}+\frac{81\,a^3\,b^{13}\,c^7}{2048}}{a^8\,d^9-8\,a^7\,b\,c\,d^8+28\,a^6\,b^2\,c^2\,d^7-56\,a^5\,b^3\,c^3\,d^6+70\,a^4\,b^4\,c^4\,d^5-56\,a^3\,b^5\,c^5\,d^4+28\,a^2\,b^6\,c^6\,d^3-8\,a\,b^7\,c^7\,d^2+b^8\,c^8\,d}+\left(\frac{{\left(-\frac{a^5\,b^3}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(1280\,a^{16}\,b^4\,c\,d^{18}-6400\,a^{15}\,b^5\,c^2\,d^{17}-23040\,a^{14}\,b^6\,c^3\,d^{16}+309760\,a^{13}\,b^7\,c^4\,d^{15}-1337600\,a^{12}\,b^8\,c^5\,d^{14}+3421440\,a^{11}\,b^9\,c^6\,d^{13}-5913600\,a^{10}\,b^{10}\,c^7\,d^{12}+7265280\,a^9\,b^{11}\,c^8\,d^{11}-6462720\,a^8\,b^{12}\,c^9\,d^{10}+4153600\,a^7\,b^{13}\,c^{10}\,d^9-1886720\,a^6\,b^{14}\,c^{11}\,d^8+576000\,a^5\,b^{15}\,c^{12}\,d^7-106240\,a^4\,b^{16}\,c^{13}\,d^6+8960\,a^3\,b^{17}\,c^{14}\,d^5\right)}{a^8\,d^9-8\,a^7\,b\,c\,d^8+28\,a^6\,b^2\,c^2\,d^7-56\,a^5\,b^3\,c^3\,d^6+70\,a^4\,b^4\,c^4\,d^5-56\,a^3\,b^5\,c^5\,d^4+28\,a^2\,b^6\,c^6\,d^3-8\,a\,b^7\,c^7\,d^2+b^8\,c^8\,d}+\frac{\sqrt{x}\,\left(409600\,a^{19}\,b^4\,d^{20}-17694720\,a^{17}\,b^6\,c^2\,d^{18}+77070336\,a^{16}\,b^7\,c^3\,d^{17}-103612416\,a^{15}\,b^8\,c^4\,d^{16}-116391936\,a^{14}\,b^9\,c^5\,d^{15}+508952576\,a^{13}\,b^{10}\,c^6\,d^{14}-259522560\,a^{12}\,b^{11}\,c^7\,d^{13}-1398177792\,a^{11}\,b^{12}\,c^8\,d^{12}+3714056192\,a^{10}\,b^{13}\,c^9\,d^{11}-4814143488\,a^9\,b^{14}\,c^{10}\,d^{10}+3911712768\,a^8\,b^{15}\,c^{11}\,d^9-2086993920\,a^7\,b^{16}\,c^{12}\,d^8+714080256\,a^6\,b^{17}\,c^{13}\,d^7-141950976\,a^5\,b^{18}\,c^{14}\,d^6+12058624\,a^4\,b^{19}\,c^{15}\,d^5+147456\,a^3\,b^{20}\,c^{16}\,d^4\right)}{4096\,\left(a^{12}\,d^{13}-12\,a^{11}\,b\,c\,d^{12}+66\,a^{10}\,b^2\,c^2\,d^{11}-220\,a^9\,b^3\,c^3\,d^{10}+495\,a^8\,b^4\,c^4\,d^9-792\,a^7\,b^5\,c^5\,d^8+924\,a^6\,b^6\,c^6\,d^7-792\,a^5\,b^7\,c^7\,d^6+495\,a^4\,b^8\,c^8\,d^5-220\,a^3\,b^9\,c^9\,d^4+66\,a^2\,b^{10}\,c^{10}\,d^3-12\,a\,b^{11}\,c^{11}\,d^2+b^{12}\,c^{12}\,d\right)}\right)\,{\left(-\frac{a^5\,b^3}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{3/4}\right)\,{\left(-\frac{a^5\,b^3}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}+\frac{\sqrt{x}\,\left(26225\,a^{12}\,b^7\,d^8+322200\,a^{11}\,b^8\,c\,d^7+1024380\,a^{10}\,b^9\,c^2\,d^6+328680\,a^9\,b^{10}\,c^3\,d^5+658566\,a^8\,b^{11}\,c^4\,d^4-307800\,a^7\,b^{12}\,c^5\,d^3+48060\,a^6\,b^{13}\,c^6\,d^2-3240\,a^5\,b^{14}\,c^7\,d+81\,a^4\,b^{15}\,c^8\right)}{4096\,\left(a^{12}\,d^{13}-12\,a^{11}\,b\,c\,d^{12}+66\,a^{10}\,b^2\,c^2\,d^{11}-220\,a^9\,b^3\,c^3\,d^{10}+495\,a^8\,b^4\,c^4\,d^9-792\,a^7\,b^5\,c^5\,d^8+924\,a^6\,b^6\,c^6\,d^7-792\,a^5\,b^7\,c^7\,d^6+495\,a^4\,b^8\,c^8\,d^5-220\,a^3\,b^9\,c^9\,d^4+66\,a^2\,b^{10}\,c^{10}\,d^3-12\,a\,b^{11}\,c^{11}\,d^2+b^{12}\,c^{12}\,d\right)}\right)\,{\left(-\frac{a^5\,b^3}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}}\right)\,{\left(-\frac{a^5\,b^3}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}\,2{}\mathrm{i}-2\,\mathrm{atan}\left(\frac{\left(\left(\frac{\left(-\frac{625\,a^{10}\,b^6\,d^7}{2048}+\frac{148215\,a^9\,b^7\,c\,d^6}{2048}+\frac{997755\,a^8\,b^8\,c^2\,d^5}{2048}+\frac{386451\,a^7\,b^9\,c^3\,d^4}{2048}-\frac{262899\,a^6\,b^{10}\,c^4\,d^3}{2048}+\frac{44901\,a^5\,b^{11}\,c^5\,d^2}{2048}-\frac{3159\,a^4\,b^{12}\,c^6\,d}{2048}+\frac{81\,a^3\,b^{13}\,c^7}{2048}\right)\,1{}\mathrm{i}}{a^8\,d^9-8\,a^7\,b\,c\,d^8+28\,a^6\,b^2\,c^2\,d^7-56\,a^5\,b^3\,c^3\,d^6+70\,a^4\,b^4\,c^4\,d^5-56\,a^3\,b^5\,c^5\,d^4+28\,a^2\,b^6\,c^6\,d^3-8\,a\,b^7\,c^7\,d^2+b^8\,c^8\,d}+\left(\frac{{\left(-\frac{a^5\,b^3}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(1280\,a^{16}\,b^4\,c\,d^{18}-6400\,a^{15}\,b^5\,c^2\,d^{17}-23040\,a^{14}\,b^6\,c^3\,d^{16}+309760\,a^{13}\,b^7\,c^4\,d^{15}-1337600\,a^{12}\,b^8\,c^5\,d^{14}+3421440\,a^{11}\,b^9\,c^6\,d^{13}-5913600\,a^{10}\,b^{10}\,c^7\,d^{12}+7265280\,a^9\,b^{11}\,c^8\,d^{11}-6462720\,a^8\,b^{12}\,c^9\,d^{10}+4153600\,a^7\,b^{13}\,c^{10}\,d^9-1886720\,a^6\,b^{14}\,c^{11}\,d^8+576000\,a^5\,b^{15}\,c^{12}\,d^7-106240\,a^4\,b^{16}\,c^{13}\,d^6+8960\,a^3\,b^{17}\,c^{14}\,d^5\right)}{a^8\,d^9-8\,a^7\,b\,c\,d^8+28\,a^6\,b^2\,c^2\,d^7-56\,a^5\,b^3\,c^3\,d^6+70\,a^4\,b^4\,c^4\,d^5-56\,a^3\,b^5\,c^5\,d^4+28\,a^2\,b^6\,c^6\,d^3-8\,a\,b^7\,c^7\,d^2+b^8\,c^8\,d}-\frac{\sqrt{x}\,\left(409600\,a^{19}\,b^4\,d^{20}-17694720\,a^{17}\,b^6\,c^2\,d^{18}+77070336\,a^{16}\,b^7\,c^3\,d^{17}-103612416\,a^{15}\,b^8\,c^4\,d^{16}-116391936\,a^{14}\,b^9\,c^5\,d^{15}+508952576\,a^{13}\,b^{10}\,c^6\,d^{14}-259522560\,a^{12}\,b^{11}\,c^7\,d^{13}-1398177792\,a^{11}\,b^{12}\,c^8\,d^{12}+3714056192\,a^{10}\,b^{13}\,c^9\,d^{11}-4814143488\,a^9\,b^{14}\,c^{10}\,d^{10}+3911712768\,a^8\,b^{15}\,c^{11}\,d^9-2086993920\,a^7\,b^{16}\,c^{12}\,d^8+714080256\,a^6\,b^{17}\,c^{13}\,d^7-141950976\,a^5\,b^{18}\,c^{14}\,d^6+12058624\,a^4\,b^{19}\,c^{15}\,d^5+147456\,a^3\,b^{20}\,c^{16}\,d^4\right)\,1{}\mathrm{i}}{4096\,\left(a^{12}\,d^{13}-12\,a^{11}\,b\,c\,d^{12}+66\,a^{10}\,b^2\,c^2\,d^{11}-220\,a^9\,b^3\,c^3\,d^{10}+495\,a^8\,b^4\,c^4\,d^9-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,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}-\frac{\sqrt{x}\,\left(26225\,a^{12}\,b^7\,d^8+322200\,a^{11}\,b^8\,c\,d^7+1024380\,a^{10}\,b^9\,c^2\,d^6+328680\,a^9\,b^{10}\,c^3\,d^5+658566\,a^8\,b^{11}\,c^4\,d^4-307800\,a^7\,b^{12}\,c^5\,d^3+48060\,a^6\,b^{13}\,c^6\,d^2-3240\,a^5\,b^{14}\,c^7\,d+81\,a^4\,b^{15}\,c^8\right)}{4096\,\left(a^{12}\,d^{13}-12\,a^{11}\,b\,c\,d^{12}+66\,a^{10}\,b^2\,c^2\,d^{11}-220\,a^9\,b^3\,c^3\,d^{10}+495\,a^8\,b^4\,c^4\,d^9-792\,a^7\,b^5\,c^5\,d^8+924\,a^6\,b^6\,c^6\,d^7-792\,a^5\,b^7\,c^7\,d^6+495\,a^4\,b^8\,c^8\,d^5-220\,a^3\,b^9\,c^9\,d^4+66\,a^2\,b^{10}\,c^{10}\,d^3-12\,a\,b^{11}\,c^{11}\,d^2+b^{12}\,c^{12}\,d\right)}\right)\,{\left(-\frac{a^5\,b^3}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}}{\left(\left(\frac{\left(-\frac{625\,a^{10}\,b^6\,d^7}{2048}+\frac{148215\,a^9\,b^7\,c\,d^6}{2048}+\frac{997755\,a^8\,b^8\,c^2\,d^5}{2048}+\frac{386451\,a^7\,b^9\,c^3\,d^4}{2048}-\frac{262899\,a^6\,b^{10}\,c^4\,d^3}{2048}+\frac{44901\,a^5\,b^{11}\,c^5\,d^2}{2048}-\frac{3159\,a^4\,b^{12}\,c^6\,d}{2048}+\frac{81\,a^3\,b^{13}\,c^7}{2048}\right)\,1{}\mathrm{i}}{a^8\,d^9-8\,a^7\,b\,c\,d^8+28\,a^6\,b^2\,c^2\,d^7-56\,a^5\,b^3\,c^3\,d^6+70\,a^4\,b^4\,c^4\,d^5-56\,a^3\,b^5\,c^5\,d^4+28\,a^2\,b^6\,c^6\,d^3-8\,a\,b^7\,c^7\,d^2+b^8\,c^8\,d}+\left(\frac{{\left(-\frac{a^5\,b^3}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(1280\,a^{16}\,b^4\,c\,d^{18}-6400\,a^{15}\,b^5\,c^2\,d^{17}-23040\,a^{14}\,b^6\,c^3\,d^{16}+309760\,a^{13}\,b^7\,c^4\,d^{15}-1337600\,a^{12}\,b^8\,c^5\,d^{14}+3421440\,a^{11}\,b^9\,c^6\,d^{13}-5913600\,a^{10}\,b^{10}\,c^7\,d^{12}+7265280\,a^9\,b^{11}\,c^8\,d^{11}-6462720\,a^8\,b^{12}\,c^9\,d^{10}+4153600\,a^7\,b^{13}\,c^{10}\,d^9-1886720\,a^6\,b^{14}\,c^{11}\,d^8+576000\,a^5\,b^{15}\,c^{12}\,d^7-106240\,a^4\,b^{16}\,c^{13}\,d^6+8960\,a^3\,b^{17}\,c^{14}\,d^5\right)}{a^8\,d^9-8\,a^7\,b\,c\,d^8+28\,a^6\,b^2\,c^2\,d^7-56\,a^5\,b^3\,c^3\,d^6+70\,a^4\,b^4\,c^4\,d^5-56\,a^3\,b^5\,c^5\,d^4+28\,a^2\,b^6\,c^6\,d^3-8\,a\,b^7\,c^7\,d^2+b^8\,c^8\,d}-\frac{\sqrt{x}\,\left(409600\,a^{19}\,b^4\,d^{20}-17694720\,a^{17}\,b^6\,c^2\,d^{18}+77070336\,a^{16}\,b^7\,c^3\,d^{17}-103612416\,a^{15}\,b^8\,c^4\,d^{16}-116391936\,a^{14}\,b^9\,c^5\,d^{15}+508952576\,a^{13}\,b^{10}\,c^6\,d^{14}-259522560\,a^{12}\,b^{11}\,c^7\,d^{13}-1398177792\,a^{11}\,b^{12}\,c^8\,d^{12}+3714056192\,a^{10}\,b^{13}\,c^9\,d^{11}-4814143488\,a^9\,b^{14}\,c^{10}\,d^{10}+3911712768\,a^8\,b^{15}\,c^{11}\,d^9-2086993920\,a^7\,b^{16}\,c^{12}\,d^8+714080256\,a^6\,b^{17}\,c^{13}\,d^7-141950976\,a^5\,b^{18}\,c^{14}\,d^6+12058624\,a^4\,b^{19}\,c^{15}\,d^5+147456\,a^3\,b^{20}\,c^{16}\,d^4\right)\,1{}\mathrm{i}}{4096\,\left(a^{12}\,d^{13}-12\,a^{11}\,b\,c\,d^{12}+66\,a^{10}\,b^2\,c^2\,d^{11}-220\,a^9\,b^3\,c^3\,d^{10}+495\,a^8\,b^4\,c^4\,d^9-792\,a^7\,b^5\,c^5\,d^8+924\,a^6\,b^6\,c^6\,d^7-792\,a^5\,b^7\,c^7\,d^6+495\,a^4\,b^8\,c^8\,d^5-220\,a^3\,b^9\,c^9\,d^4+66\,a^2\,b^{10}\,c^{10}\,d^3-12\,a\,b^{11}\,c^{11}\,d^2+b^{12}\,c^{12}\,d\right)}\right)\,{\left(-\frac{a^5\,b^3}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{3/4}\,1{}\mathrm{i}\right)\,{\left(-\frac{a^5\,b^3}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}\,1{}\mathrm{i}+\frac{\sqrt{x}\,\left(26225\,a^{12}\,b^7\,d^8+322200\,a^{11}\,b^8\,c\,d^7+1024380\,a^{10}\,b^9\,c^2\,d^6+328680\,a^9\,b^{10}\,c^3\,d^5+658566\,a^8\,b^{11}\,c^4\,d^4-307800\,a^7\,b^{12}\,c^5\,d^3+48060\,a^6\,b^{13}\,c^6\,d^2-3240\,a^5\,b^{14}\,c^7\,d+81\,a^4\,b^{15}\,c^8\right)\,1{}\mathrm{i}}{4096\,\left(a^{12}\,d^{13}-12\,a^{11}\,b\,c\,d^{12}+66\,a^{10}\,b^2\,c^2\,d^{11}-220\,a^9\,b^3\,c^3\,d^{10}+495\,a^8\,b^4\,c^4\,d^9-792\,a^7\,b^5\,c^5\,d^8+924\,a^6\,b^6\,c^6\,d^7-792\,a^5\,b^7\,c^7\,d^6+495\,a^4\,b^8\,c^8\,d^5-220\,a^3\,b^9\,c^9\,d^4+66\,a^2\,b^{10}\,c^{10}\,d^3-12\,a\,b^{11}\,c^{11}\,d^2+b^{12}\,c^{12}\,d\right)}\right)\,{\left(-\frac{a^5\,b^3}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}+\left(\left(\frac{\left(-\frac{625\,a^{10}\,b^6\,d^7}{2048}+\frac{148215\,a^9\,b^7\,c\,d^6}{2048}+\frac{997755\,a^8\,b^8\,c^2\,d^5}{2048}+\frac{386451\,a^7\,b^9\,c^3\,d^4}{2048}-\frac{262899\,a^6\,b^{10}\,c^4\,d^3}{2048}+\frac{44901\,a^5\,b^{11}\,c^5\,d^2}{2048}-\frac{3159\,a^4\,b^{12}\,c^6\,d}{2048}+\frac{81\,a^3\,b^{13}\,c^7}{2048}\right)\,1{}\mathrm{i}}{a^8\,d^9-8\,a^7\,b\,c\,d^8+28\,a^6\,b^2\,c^2\,d^7-56\,a^5\,b^3\,c^3\,d^6+70\,a^4\,b^4\,c^4\,d^5-56\,a^3\,b^5\,c^5\,d^4+28\,a^2\,b^6\,c^6\,d^3-8\,a\,b^7\,c^7\,d^2+b^8\,c^8\,d}+\left(\frac{{\left(-\frac{a^5\,b^3}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(1280\,a^{16}\,b^4\,c\,d^{18}-6400\,a^{15}\,b^5\,c^2\,d^{17}-23040\,a^{14}\,b^6\,c^3\,d^{16}+309760\,a^{13}\,b^7\,c^4\,d^{15}-1337600\,a^{12}\,b^8\,c^5\,d^{14}+3421440\,a^{11}\,b^9\,c^6\,d^{13}-5913600\,a^{10}\,b^{10}\,c^7\,d^{12}+7265280\,a^9\,b^{11}\,c^8\,d^{11}-6462720\,a^8\,b^{12}\,c^9\,d^{10}+4153600\,a^7\,b^{13}\,c^{10}\,d^9-1886720\,a^6\,b^{14}\,c^{11}\,d^8+576000\,a^5\,b^{15}\,c^{12}\,d^7-106240\,a^4\,b^{16}\,c^{13}\,d^6+8960\,a^3\,b^{17}\,c^{14}\,d^5\right)}{a^8\,d^9-8\,a^7\,b\,c\,d^8+28\,a^6\,b^2\,c^2\,d^7-56\,a^5\,b^3\,c^3\,d^6+70\,a^4\,b^4\,c^4\,d^5-56\,a^3\,b^5\,c^5\,d^4+28\,a^2\,b^6\,c^6\,d^3-8\,a\,b^7\,c^7\,d^2+b^8\,c^8\,d}+\frac{\sqrt{x}\,\left(409600\,a^{19}\,b^4\,d^{20}-17694720\,a^{17}\,b^6\,c^2\,d^{18}+77070336\,a^{16}\,b^7\,c^3\,d^{17}-103612416\,a^{15}\,b^8\,c^4\,d^{16}-116391936\,a^{14}\,b^9\,c^5\,d^{15}+508952576\,a^{13}\,b^{10}\,c^6\,d^{14}-259522560\,a^{12}\,b^{11}\,c^7\,d^{13}-1398177792\,a^{11}\,b^{12}\,c^8\,d^{12}+3714056192\,a^{10}\,b^{13}\,c^9\,d^{11}-4814143488\,a^9\,b^{14}\,c^{10}\,d^{10}+3911712768\,a^8\,b^{15}\,c^{11}\,d^9-2086993920\,a^7\,b^{16}\,c^{12}\,d^8+714080256\,a^6\,b^{17}\,c^{13}\,d^7-141950976\,a^5\,b^{18}\,c^{14}\,d^6+12058624\,a^4\,b^{19}\,c^{15}\,d^5+147456\,a^3\,b^{20}\,c^{16}\,d^4\right)\,1{}\mathrm{i}}{4096\,\left(a^{12}\,d^{13}-12\,a^{11}\,b\,c\,d^{12}+66\,a^{10}\,b^2\,c^2\,d^{11}-220\,a^9\,b^3\,c^3\,d^{10}+495\,a^8\,b^4\,c^4\,d^9-792\,a^7\,b^5\,c^5\,d^8+924\,a^6\,b^6\,c^6\,d^7-792\,a^5\,b^7\,c^7\,d^6+495\,a^4\,b^8\,c^8\,d^5-220\,a^3\,b^9\,c^9\,d^4+66\,a^2\,b^{10}\,c^{10}\,d^3-12\,a\,b^{11}\,c^{11}\,d^2+b^{12}\,c^{12}\,d\right)}\right)\,{\left(-\frac{a^5\,b^3}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{3/4}\,1{}\mathrm{i}\right)\,{\left(-\frac{a^5\,b^3}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}\,1{}\mathrm{i}-\frac{\sqrt{x}\,\left(26225\,a^{12}\,b^7\,d^8+322200\,a^{11}\,b^8\,c\,d^7+1024380\,a^{10}\,b^9\,c^2\,d^6+328680\,a^9\,b^{10}\,c^3\,d^5+658566\,a^8\,b^{11}\,c^4\,d^4-307800\,a^7\,b^{12}\,c^5\,d^3+48060\,a^6\,b^{13}\,c^6\,d^2-3240\,a^5\,b^{14}\,c^7\,d+81\,a^4\,b^{15}\,c^8\right)\,1{}\mathrm{i}}{4096\,\left(a^{12}\,d^{13}-12\,a^{11}\,b\,c\,d^{12}+66\,a^{10}\,b^2\,c^2\,d^{11}-220\,a^9\,b^3\,c^3\,d^{10}+495\,a^8\,b^4\,c^4\,d^9-792\,a^7\,b^5\,c^5\,d^8+924\,a^6\,b^6\,c^6\,d^7-792\,a^5\,b^7\,c^7\,d^6+495\,a^4\,b^8\,c^8\,d^5-220\,a^3\,b^9\,c^9\,d^4+66\,a^2\,b^{10}\,c^{10}\,d^3-12\,a\,b^{11}\,c^{11}\,d^2+b^{12}\,c^{12}\,d\right)}\right)\,{\left(-\frac{a^5\,b^3}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}}\right)\,{\left(-\frac{a^5\,b^3}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}-\mathrm{atan}\left(-\frac{\left({\left(-\frac{625\,a^8\,d^8+15000\,a^7\,b\,c\,d^7+133500\,a^6\,b^2\,c^2\,d^6+513000\,a^5\,b^3\,c^3\,d^5+649350\,a^4\,b^4\,c^4\,d^4-307800\,a^3\,b^5\,c^5\,d^3+48060\,a^2\,b^6\,c^6\,d^2-3240\,a\,b^7\,c^7\,d+81\,b^8\,c^8}{16777216\,a^{12}\,c^3\,d^{17}-201326592\,a^{11}\,b\,c^4\,d^{16}+1107296256\,a^{10}\,b^2\,c^5\,d^{15}-3690987520\,a^9\,b^3\,c^6\,d^{14}+8304721920\,a^8\,b^4\,c^7\,d^{13}-13287555072\,a^7\,b^5\,c^8\,d^{12}+15502147584\,a^6\,b^6\,c^9\,d^{11}-13287555072\,a^5\,b^7\,c^{10}\,d^{10}+8304721920\,a^4\,b^8\,c^{11}\,d^9-3690987520\,a^3\,b^9\,c^{12}\,d^8+1107296256\,a^2\,b^{10}\,c^{13}\,d^7-201326592\,a\,b^{11}\,c^{14}\,d^6+16777216\,b^{12}\,c^{15}\,d^5}\right)}^{1/4}\,\left(\frac{-\frac{625\,a^{10}\,b^6\,d^7}{2048}+\frac{148215\,a^9\,b^7\,c\,d^6}{2048}+\frac{997755\,a^8\,b^8\,c^2\,d^5}{2048}+\frac{386451\,a^7\,b^9\,c^3\,d^4}{2048}-\frac{262899\,a^6\,b^{10}\,c^4\,d^3}{2048}+\frac{44901\,a^5\,b^{11}\,c^5\,d^2}{2048}-\frac{3159\,a^4\,b^{12}\,c^6\,d}{2048}+\frac{81\,a^3\,b^{13}\,c^7}{2048}}{a^8\,d^9-8\,a^7\,b\,c\,d^8+28\,a^6\,b^2\,c^2\,d^7-56\,a^5\,b^3\,c^3\,d^6+70\,a^4\,b^4\,c^4\,d^5-56\,a^3\,b^5\,c^5\,d^4+28\,a^2\,b^6\,c^6\,d^3-8\,a\,b^7\,c^7\,d^2+b^8\,c^8\,d}+{\left(-\frac{625\,a^8\,d^8+15000\,a^7\,b\,c\,d^7+133500\,a^6\,b^2\,c^2\,d^6+513000\,a^5\,b^3\,c^3\,d^5+649350\,a^4\,b^4\,c^4\,d^4-307800\,a^3\,b^5\,c^5\,d^3+48060\,a^2\,b^6\,c^6\,d^2-3240\,a\,b^7\,c^7\,d+81\,b^8\,c^8}{16777216\,a^{12}\,c^3\,d^{17}-201326592\,a^{11}\,b\,c^4\,d^{16}+1107296256\,a^{10}\,b^2\,c^5\,d^{15}-3690987520\,a^9\,b^3\,c^6\,d^{14}+8304721920\,a^8\,b^4\,c^7\,d^{13}-13287555072\,a^7\,b^5\,c^8\,d^{12}+15502147584\,a^6\,b^6\,c^9\,d^{11}-13287555072\,a^5\,b^7\,c^{10}\,d^{10}+8304721920\,a^4\,b^8\,c^{11}\,d^9-3690987520\,a^3\,b^9\,c^{12}\,d^8+1107296256\,a^2\,b^{10}\,c^{13}\,d^7-201326592\,a\,b^{11}\,c^{14}\,d^6+16777216\,b^{12}\,c^{15}\,d^5}\right)}^{3/4}\,\left(\frac{{\left(-\frac{625\,a^8\,d^8+15000\,a^7\,b\,c\,d^7+133500\,a^6\,b^2\,c^2\,d^6+513000\,a^5\,b^3\,c^3\,d^5+649350\,a^4\,b^4\,c^4\,d^4-307800\,a^3\,b^5\,c^5\,d^3+48060\,a^2\,b^6\,c^6\,d^2-3240\,a\,b^7\,c^7\,d+81\,b^8\,c^8}{16777216\,a^{12}\,c^3\,d^{17}-201326592\,a^{11}\,b\,c^4\,d^{16}+1107296256\,a^{10}\,b^2\,c^5\,d^{15}-3690987520\,a^9\,b^3\,c^6\,d^{14}+8304721920\,a^8\,b^4\,c^7\,d^{13}-13287555072\,a^7\,b^5\,c^8\,d^{12}+15502147584\,a^6\,b^6\,c^9\,d^{11}-13287555072\,a^5\,b^7\,c^{10}\,d^{10}+8304721920\,a^4\,b^8\,c^{11}\,d^9-3690987520\,a^3\,b^9\,c^{12}\,d^8+1107296256\,a^2\,b^{10}\,c^{13}\,d^7-201326592\,a\,b^{11}\,c^{14}\,d^6+16777216\,b^{12}\,c^{15}\,d^5}\right)}^{1/4}\,\left(1280\,a^{16}\,b^4\,c\,d^{18}-6400\,a^{15}\,b^5\,c^2\,d^{17}-23040\,a^{14}\,b^6\,c^3\,d^{16}+309760\,a^{13}\,b^7\,c^4\,d^{15}-1337600\,a^{12}\,b^8\,c^5\,d^{14}+3421440\,a^{11}\,b^9\,c^6\,d^{13}-5913600\,a^{10}\,b^{10}\,c^7\,d^{12}+7265280\,a^9\,b^{11}\,c^8\,d^{11}-6462720\,a^8\,b^{12}\,c^9\,d^{10}+4153600\,a^7\,b^{13}\,c^{10}\,d^9-1886720\,a^6\,b^{14}\,c^{11}\,d^8+576000\,a^5\,b^{15}\,c^{12}\,d^7-106240\,a^4\,b^{16}\,c^{13}\,d^6+8960\,a^3\,b^{17}\,c^{14}\,d^5\right)}{a^8\,d^9-8\,a^7\,b\,c\,d^8+28\,a^6\,b^2\,c^2\,d^7-56\,a^5\,b^3\,c^3\,d^6+70\,a^4\,b^4\,c^4\,d^5-56\,a^3\,b^5\,c^5\,d^4+28\,a^2\,b^6\,c^6\,d^3-8\,a\,b^7\,c^7\,d^2+b^8\,c^8\,d}-\frac{\sqrt{x}\,\left(409600\,a^{19}\,b^4\,d^{20}-17694720\,a^{17}\,b^6\,c^2\,d^{18}+77070336\,a^{16}\,b^7\,c^3\,d^{17}-103612416\,a^{15}\,b^8\,c^4\,d^{16}-116391936\,a^{14}\,b^9\,c^5\,d^{15}+508952576\,a^{13}\,b^{10}\,c^6\,d^{14}-259522560\,a^{12}\,b^{11}\,c^7\,d^{13}-1398177792\,a^{11}\,b^{12}\,c^8\,d^{12}+3714056192\,a^{10}\,b^{13}\,c^9\,d^{11}-4814143488\,a^9\,b^{14}\,c^{10}\,d^{10}+3911712768\,a^8\,b^{15}\,c^{11}\,d^9-2086993920\,a^7\,b^{16}\,c^{12}\,d^8+714080256\,a^6\,b^{17}\,c^{13}\,d^7-141950976\,a^5\,b^{18}\,c^{14}\,d^6+12058624\,a^4\,b^{19}\,c^{15}\,d^5+147456\,a^3\,b^{20}\,c^{16}\,d^4\right)}{4096\,\left(a^{12}\,d^{13}-12\,a^{11}\,b\,c\,d^{12}+66\,a^{10}\,b^2\,c^2\,d^{11}-220\,a^9\,b^3\,c^3\,d^{10}+495\,a^8\,b^4\,c^4\,d^9-792\,a^7\,b^5\,c^5\,d^8+924\,a^6\,b^6\,c^6\,d^7-792\,a^5\,b^7\,c^7\,d^6+495\,a^4\,b^8\,c^8\,d^5-220\,a^3\,b^9\,c^9\,d^4+66\,a^2\,b^{10}\,c^{10}\,d^3-12\,a\,b^{11}\,c^{11}\,d^2+b^{12}\,c^{12}\,d\right)}\right)\right)\,1{}\mathrm{i}-\frac{\sqrt{x}\,\left(26225\,a^{12}\,b^7\,d^8+322200\,a^{11}\,b^8\,c\,d^7+1024380\,a^{10}\,b^9\,c^2\,d^6+328680\,a^9\,b^{10}\,c^3\,d^5+658566\,a^8\,b^{11}\,c^4\,d^4-307800\,a^7\,b^{12}\,c^5\,d^3+48060\,a^6\,b^{13}\,c^6\,d^2-3240\,a^5\,b^{14}\,c^7\,d+81\,a^4\,b^{15}\,c^8\right)\,1{}\mathrm{i}}{4096\,\left(a^{12}\,d^{13}-12\,a^{11}\,b\,c\,d^{12}+66\,a^{10}\,b^2\,c^2\,d^{11}-220\,a^9\,b^3\,c^3\,d^{10}+495\,a^8\,b^4\,c^4\,d^9-792\,a^7\,b^5\,c^5\,d^8+924\,a^6\,b^6\,c^6\,d^7-792\,a^5\,b^7\,c^7\,d^6+495\,a^4\,b^8\,c^8\,d^5-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eft(26225\,a^{12}\,b^7\,d^8+322200\,a^{11}\,b^8\,c\,d^7+1024380\,a^{10}\,b^9\,c^2\,d^6+328680\,a^9\,b^{10}\,c^3\,d^5+658566\,a^8\,b^{11}\,c^4\,d^4-307800\,a^7\,b^{12}\,c^5\,d^3+48060\,a^6\,b^{13}\,c^6\,d^2-3240\,a^5\,b^{14}\,c^7\,d+81\,a^4\,b^{15}\,c^8\right)\,1{}\mathrm{i}}{4096\,\left(a^{12}\,d^{13}-12\,a^{11}\,b\,c\,d^{12}+66\,a^{10}\,b^2\,c^2\,d^{11}-220\,a^9\,b^3\,c^3\,d^{10}+495\,a^8\,b^4\,c^4\,d^9-792\,a^7\,b^5\,c^5\,d^8+924\,a^6\,b^6\,c^6\,d^7-792\,a^5\,b^7\,c^7\,d^6+495\,a^4\,b^8\,c^8\,d^5-220\,a^3\,b^9\,c^9\,d^4+66\,a^2\,b^{10}\,c^{10}\,d^3-12\,a\,b^{11}\,c^{11}\,d^2+b^{12}\,c^{12}\,d\right)}\right)\,{\left(-\frac{625\,a^8\,d^8+15000\,a^7\,b\,c\,d^7+133500\,a^6\,b^2\,c^2\,d^6+513000\,a^5\,b^3\,c^3\,d^5+649350\,a^4\,b^4\,c^4\,d^4-307800\,a^3\,b^5\,c^5\,d^3+48060\,a^2\,b^6\,c^6\,d^2-3240\,a\,b^7\,c^7\,d+81\,b^8\,c^8}{16777216\,a^{12}\,c^3\,d^{17}-201326592\,a^{11}\,b\,c^4\,d^{16}+1107296256\,a^{10}\,b^2\,c^5\,d^{15}-3690987520\,a^9\,b^3\,c^6\,d^{14}+8304721920\,a^8\,b^4\,c^7\,d^{13}-13287555072\,a^7\,b^5\,c^8\,d^{12}+15502147584\,a^6\,b^6\,c^9\,d^{11}-13287555072\,a^5\,b^7\,c^{10}\,d^{10}+8304721920\,a^4\,b^8\,c^{11}\,d^9-3690987520\,a^3\,b^9\,c^{12}\,d^8+1107296256\,a^2\,b^{10}\,c^{13}\,d^7-201326592\,a\,b^{11}\,c^{14}\,d^6+16777216\,b^{12}\,c^{15}\,d^5}\right)}^{1/4}}{\left({\left(-\frac{625\,a^8\,d^8+15000\,a^7\,b\,c\,d^7+133500\,a^6\,b^2\,c^2\,d^6+513000\,a^5\,b^3\,c^3\,d^5+649350\,a^4\,b^4\,c^4\,d^4-307800\,a^3\,b^5\,c^5\,d^3+48060\,a^2\,b^6\,c^6\,d^2-3240\,a\,b^7\,c^7\,d+81\,b^8\,c^8}{16777216\,a^{12}\,c^3\,d^{17}-201326592\,a^{11}\,b\,c^4\,d^{16}+1107296256\,a^{10}\,b^2\,c^5\,d^{15}-3690987520\,a^9\,b^3\,c^6\,d^{14}+8304721920\,a^8\,b^4\,c^7\,d^{13}-13287555072\,a^7\,b^5\,c^8\,d^{12}+15502147584\,a^6\,b^6\,c^9\,d^{11}-13287555072\,a^5\,b^7\,c^{10}\,d^{10}+8304721920\,a^4\,b^8\,c^{11}\,d^9-3690987520\,a^3\,b^9\,c^{12}\,d^8+1107296256\,a^2\,b^{10}\,c^{13}\,d^7-201326592\,a\,b^{11}\,c^{14}\,d^6+16777216\,b^{12}\,c^{15}\,d^5}\right)}^{1/4}\,\left(\frac{-\frac{625\,a^{10}\,b^6\,d^7}{2048}+\frac{148215\,a^9\,b^7\,c\,d^6}{2048}+\frac{997755\,a^8\,b^8\,c^2\,d^5}{2048}+\frac{386451\,a^7\,b^9\,c^3\,d^4}{2048}-\frac{262899\,a^6\,b^{10}\,c^4\,d^3}{2048}+\frac{44901\,a^5\,b^{11}\,c^5\,d^2}{2048}-\frac{3159\,a^4\,b^{12}\,c^6\,d}{2048}+\frac{81\,a^3\,b^{13}\,c^7}{2048}}{a^8\,d^9-8\,a^7\,b\,c\,d^8+28\,a^6\,b^2\,c^2\,d^7-56\,a^5\,b^3\,c^3\,d^6+70\,a^4\,b^4\,c^4\,d^5-56\,a^3\,b^5\,c^5\,d^4+28\,a^2\,b^6\,c^6\,d^3-8\,a\,b^7\,c^7\,d^2+b^8\,c^8\,d}+{\left(-\frac{625\,a^8\,d^8+15000\,a^7\,b\,c\,d^7+133500\,a^6\,b^2\,c^2\,d^6+513000\,a^5\,b^3\,c^3\,d^5+649350\,a^4\,b^4\,c^4\,d^4-307800\,a^3\,b^5\,c^5\,d^3+48060\,a^2\,b^6\,c^6\,d^2-3240\,a\,b^7\,c^7\,d+81\,b^8\,c^8}{16777216\,a^{12}\,c^3\,d^{17}-201326592\,a^{11}\,b\,c^4\,d^{16}+1107296256\,a^{10}\,b^2\,c^5\,d^{15}-3690987520\,a^9\,b^3\,c^6\,d^{14}+8304721920\,a^8\,b^4\,c^7\,d^{13}-13287555072\,a^7\,b^5\,c^8\,d^{12}+15502147584\,a^6\,b^6\,c^9\,d^{11}-13287555072\,a^5\,b^7\,c^{10}\,d^{10}+8304721920\,a^4\,b^8\,c^{11}\,d^9-3690987520\,a^3\,b^9\,c^{12}\,d^8+1107296256\,a^2\,b^{10}\,c^{13}\,d^7-201326592\,a\,b^{11}\,c^{14}\,d^6+16777216\,b^{12}\,c^{15}\,d^5}\right)}^{3/4}\,\left(\frac{{\left(-\frac{625\,a^8\,d^8+15000\,a^7\,b\,c\,d^7+133500\,a^6\,b^2\,c^2\,d^6+513000\,a^5\,b^3\,c^3\,d^5+649350\,a^4\,b^4\,c^4\,d^4-307800\,a^3\,b^5\,c^5\,d^3+48060\,a^2\,b^6\,c^6\,d^2-3240\,a\,b^7\,c^7\,d+81\,b^8\,c^8}{16777216\,a^{12}\,c^3\,d^{17}-201326592\,a^{11}\,b\,c^4\,d^{16}+1107296256\,a^{10}\,b^2\,c^5\,d^{15}-3690987520\,a^9\,b^3\,c^6\,d^{14}+8304721920\,a^8\,b^4\,c^7\,d^{13}-13287555072\,a^7\,b^5\,c^8\,d^{12}+15502147584\,a^6\,b^6\,c^9\,d^{11}-13287555072\,a^5\,b^7\,c^{10}\,d^{10}+8304721920\,a^4\,b^8\,c^{11}\,d^9-3690987520\,a^3\,b^9\,c^{12}\,d^8+1107296256\,a^2\,b^{10}\,c^{13}\,d^7-201326592\,a\,b^{11}\,c^{14}\,d^6+16777216\,b^{12}\,c^{15}\,d^5}\right)}^{1/4}\,\left(1280\,a^{16}\,b^4\,c\,d^{18}-6400\,a^{15}\,b^5\,c^2\,d^{17}-23040\,a^{14}\,b^6\,c^3\,d^{16}+309760\,a^{13}\,b^7\,c^4\,d^{15}-1337600\,a^{12}\,b^8\,c^5\,d^{14}+3421440\,a^{11}\,b^9\,c^6\,d^{13}-5913600\,a^{10}\,b^{10}\,c^7\,d^{12}+7265280\,a^9\,b^{11}\,c^8\,d^{11}-6462720\,a^8\,b^{12}\,c^9\,d^{10}+4153600\,a^7\,b^{13}\,c^{10}\,d^9-1886720\,a^6\,b^{14}\,c^{11}\,d^8+576000\,a^5\,b^{15}\,c^{12}\,d^7-106240\,a^4\,b^{16}\,c^{13}\,d^6+8960\,a^3\,b^{17}\,c^{14}\,d^5\right)}{a^8\,d^9-8\,a^7\,b\,c\,d^8+28\,a^6\,b^2\,c^2\,d^7-56\,a^5\,b^3\,c^3\,d^6+70\,a^4\,b^4\,c^4\,d^5-56\,a^3\,b^5\,c^5\,d^4+28\,a^2\,b^6\,c^6\,d^3-8\,a\,b^7\,c^7\,d^2+b^8\,c^8\,d}-\frac{\sqrt{x}\,\left(409600\,a^{19}\,b^4\,d^{20}-17694720\,a^{17}\,b^6\,c^2\,d^{18}+77070336\,a^{16}\,b^7\,c^3\,d^{17}-103612416\,a^{15}\,b^8\,c^4\,d^{16}-116391936\,a^{14}\,b^9\,c^5\,d^{15}+508952576\,a^{13}\,b^{10}\,c^6\,d^{14}-259522560\,a^{12}\,b^{11}\,c^7\,d^{13}-1398177792\,a^{11}\,b^{12}\,c^8\,d^{12}+3714056192\,a^{10}\,b^{13}\,c^9\,d^{11}-4814143488\,a^9\,b^{14}\,c^{10}\,d^{10}+3911712768\,a^8\,b^{15}\,c^{11}\,d^9-2086993920\,a^7\,b^{16}\,c^{12}\,d^8+714080256\,a^6\,b^{17}\,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,a^4\,b^{12}\,c^6\,d}{2048}+\frac{81\,a^3\,b^{13}\,c^7}{2048}\right)\,1{}\mathrm{i}}{a^8\,d^9-8\,a^7\,b\,c\,d^8+28\,a^6\,b^2\,c^2\,d^7-56\,a^5\,b^3\,c^3\,d^6+70\,a^4\,b^4\,c^4\,d^5-56\,a^3\,b^5\,c^5\,d^4+28\,a^2\,b^6\,c^6\,d^3-8\,a\,b^7\,c^7\,d^2+b^8\,c^8\,d}+{\left(-\frac{625\,a^8\,d^8+15000\,a^7\,b\,c\,d^7+133500\,a^6\,b^2\,c^2\,d^6+513000\,a^5\,b^3\,c^3\,d^5+649350\,a^4\,b^4\,c^4\,d^4-307800\,a^3\,b^5\,c^5\,d^3+48060\,a^2\,b^6\,c^6\,d^2-3240\,a\,b^7\,c^7\,d+81\,b^8\,c^8}{16777216\,a^{12}\,c^3\,d^{17}-201326592\,a^{11}\,b\,c^4\,d^{16}+1107296256\,a^{10}\,b^2\,c^5\,d^{15}-3690987520\,a^9\,b^3\,c^6\,d^{14}+8304721920\,a^8\,b^4\,c^7\,d^{13}-13287555072\,a^7\,b^5\,c^8\,d^{12}+15502147584\,a^6\,b^6\,c^9\,d^{11}-13287555072\,a^5\,b^7\,c^{10}\,d^{10}+8304721920\,a^4\,b^8\,c^{11}\,d^9-3690987520\,a^3\,b^9\,c^{12}\,d^8+1107296256\,a^2\,b^{10}\,c^{13}\,d^7-201326592\,a\,b^{11}\,c^{14}\,d^6+16777216\,b^{12}\,c^{15}\,d^5}\right)}^{3/4}\,\left(\frac{{\left(-\frac{625\,a^8\,d^8+15000\,a^7\,b\,c\,d^7+133500\,a^6\,b^2\,c^2\,d^6+513000\,a^5\,b^3\,c^3\,d^5+649350\,a^4\,b^4\,c^4\,d^4-307800\,a^3\,b^5\,c^5\,d^3+48060\,a^2\,b^6\,c^6\,d^2-3240\,a\,b^7\,c^7\,d+81\,b^8\,c^8}{16777216\,a^{12}\,c^3\,d^{17}-201326592\,a^{11}\,b\,c^4\,d^{16}+1107296256\,a^{10}\,b^2\,c^5\,d^{15}-3690987520\,a^9\,b^3\,c^6\,d^{14}+8304721920\,a^8\,b^4\,c^7\,d^{13}-13287555072\,a^7\,b^5\,c^8\,d^{12}+15502147584\,a^6\,b^6\,c^9\,d^{11}-13287555072\,a^5\,b^7\,c^{10}\,d^{10}+8304721920\,a^4\,b^8\,c^{11}\,d^9-3690987520\,a^3\,b^9\,c^{12}\,d^8+1107296256\,a^2\,b^{10}\,c^{13}\,d^7-201326592\,a\,b^{11}\,c^{14}\,d^6+16777216\,b^{12}\,c^{15}\,d^5}\right)}^{1/4}\,\left(1280\,a^{16}\,b^4\,c\,d^{18}-6400\,a^{15}\,b^5\,c^2\,d^{17}-23040\,a^{14}\,b^6\,c^3\,d^{16}+309760\,a^{13}\,b^7\,c^4\,d^{15}-1337600\,a^{12}\,b^8\,c^5\,d^{14}+3421440\,a^{11}\,b^9\,c^6\,d^{13}-5913600\,a^{10}\,b^{10}\,c^7\,d^{12}+7265280\,a^9\,b^{11}\,c^8\,d^{11}-6462720\,a^8\,b^{12}\,c^9\,d^{10}+4153600\,a^7\,b^{13}\,c^{10}\,d^9-1886720\,a^6\,b^{14}\,c^{11}\,d^8+576000\,a^5\,b^{15}\,c^{12}\,d^7-106240\,a^4\,b^{16}\,c^{13}\,d^6+8960\,a^3\,b^{17}\,c^{14}\,d^5\right)}{a^8\,d^9-8\,a^7\,b\,c\,d^8+28\,a^6\,b^2\,c^2\,d^7-56\,a^5\,b^3\,c^3\,d^6+70\,a^4\,b^4\,c^4\,d^5-56\,a^3\,b^5\,c^5\,d^4+28\,a^2\,b^6\,c^6\,d^3-8\,a\,b^7\,c^7\,d^2+b^8\,c^8\,d}-\frac{\sqrt{x}\,\left(409600\,a^{19}\,b^4\,d^{20}-17694720\,a^{17}\,b^6\,c^2\,d^{18}+77070336\,a^{16}\,b^7\,c^3\,d^{17}-103612416\,a^{15}\,b^8\,c^4\,d^{16}-116391936\,a^{14}\,b^9\,c^5\,d^{15}+508952576\,a^{13}\,b^{10}\,c^6\,d^{14}-259522560\,a^{12}\,b^{11}\,c^7\,d^{13}-1398177792\,a^{11}\,b^{12}\,c^8\,d^{12}+3714056192\,a^{10}\,b^{13}\,c^9\,d^{11}-4814143488\,a^9\,b^{14}\,c^{10}\,d^{10}+3911712768\,a^8\,b^{15}\,c^{11}\,d^9-2086993920\,a^7\,b^{16}\,c^{12}\,d^8+714080256\,a^6\,b^{17}\,c^{13}\,d^7-141950976\,a^5\,b^{18}\,c^{14}\,d^6+12058624\,a^4\,b^{19}\,c^{15}\,d^5+147456\,a^3\,b^{20}\,c^{16}\,d^4\right)\,1{}\mathrm{i}}{4096\,\left(a^{12}\,d^{13}-12\,a^{11}\,b\,c\,d^{12}+66\,a^{10}\,b^2\,c^2\,d^{11}-220\,a^9\,b^3\,c^3\,d^{10}+495\,a^8\,b^4\,c^4\,d^9-792\,a^7\,b^5\,c^5\,d^8+924\,a^6\,b^6\,c^6\,d^7-792\,a^5\,b^7\,c^7\,d^6+495\,a^4\,b^8\,c^8\,d^5-220\,a^3\,b^9\,c^9\,d^4+66\,a^2\,b^{10}\,c^{10}\,d^3-12\,a\,b^{11}\,c^{11}\,d^2+b^{12}\,c^{12}\,d\right)}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}+\frac{\sqrt{x}\,\left(26225\,a^{12}\,b^7\,d^8+322200\,a^{11}\,b^8\,c\,d^7+1024380\,a^{10}\,b^9\,c^2\,d^6+328680\,a^9\,b^{10}\,c^3\,d^5+658566\,a^8\,b^{11}\,c^4\,d^4-307800\,a^7\,b^{12}\,c^5\,d^3+48060\,a^6\,b^{13}\,c^6\,d^2-3240\,a^5\,b^{14}\,c^7\,d+81\,a^4\,b^{15}\,c^8\right)\,1{}\mathrm{i}}{4096\,\left(a^{12}\,d^{13}-12\,a^{11}\,b\,c\,d^{12}+66\,a^{10}\,b^2\,c^2\,d^{11}-220\,a^9\,b^3\,c^3\,d^{10}+495\,a^8\,b^4\,c^4\,d^9-792\,a^7\,b^5\,c^5\,d^8+924\,a^6\,b^6\,c^6\,d^7-792\,a^5\,b^7\,c^7\,d^6+495\,a^4\,b^8\,c^8\,d^5-220\,a^3\,b^9\,c^9\,d^4+66\,a^2\,b^{10}\,c^{10}\,d^3-12\,a\,b^{11}\,c^{11}\,d^2+b^{12}\,c^{12}\,d\right)}\right)\,{\left(-\frac{625\,a^8\,d^8+15000\,a^7\,b\,c\,d^7+133500\,a^6\,b^2\,c^2\,d^6+513000\,a^5\,b^3\,c^3\,d^5+649350\,a^4\,b^4\,c^4\,d^4-307800\,a^3\,b^5\,c^5\,d^3+48060\,a^2\,b^6\,c^6\,d^2-3240\,a\,b^7\,c^7\,d+81\,b^8\,c^8}{16777216\,a^{12}\,c^3\,d^{17}-201326592\,a^{11}\,b\,c^4\,d^{16}+1107296256\,a^{10}\,b^2\,c^5\,d^{15}-3690987520\,a^9\,b^3\,c^6\,d^{14}+8304721920\,a^8\,b^4\,c^7\,d^{13}-13287555072\,a^7\,b^5\,c^8\,d^{12}+15502147584\,a^6\,b^6\,c^9\,d^{11}-13287555072\,a^5\,b^7\,c^{10}\,d^{10}+8304721920\,a^4\,b^8\,c^{11}\,d^9-3690987520\,a^3\,b^9\,c^{12}\,d^8+1107296256\,a^2\,b^{10}\,c^{13}\,d^7-201326592\,a\,b^{11}\,c^{14}\,d^6+16777216\,b^{12}\,c^{15}\,d^5}\right)}^{1/4}+\left({\left(-\frac{625\,a^8\,d^8+15000\,a^7\,b\,c\,d^7+133500\,a^6\,b^2\,c^2\,d^6+513000\,a^5\,b^3\,c^3\,d^5+649350\,a^4\,b^4\,c^4\,d^4-307800\,a^3\,b^5\,c^5\,d^3+48060\,a^2\,b^6\,c^6\,d^2-3240\,a\,b^7\,c^7\,d+81\,b^8\,c^8}{16777216\,a^{12}\,c^3\,d^{17}-201326592\,a^{11}\,b\,c^4\,d^{16}+1107296256\,a^{10}\,b^2\,c^5\,d^{15}-3690987520\,a^9\,b^3\,c^6\,d^{14}+8304721920\,a^8\,b^4\,c^7\,d^{13}-13287555072\,a^7\,b^5\,c^8\,d^{12}+15502147584\,a^6\,b^6\,c^9\,d^{11}-13287555072\,a^5\,b^7\,c^{10}\,d^{10}+8304721920\,a^4\,b^8\,c^{11}\,d^9-3690987520\,a^3\,b^9\,c^{12}\,d^8+1107296256\,a^2\,b^{10}\,c^{13}\,d^7-201326592\,a\,b^{11}\,c^{14}\,d^6+16777216\,b^{12}\,c^{15}\,d^5}\right)}^{1/4}\,\left(\frac{\left(-\frac{625\,a^{10}\,b^6\,d^7}{2048}+\frac{148215\,a^9\,b^7\,c\,d^6}{2048}+\frac{997755\,a^8\,b^8\,c^2\,d^5}{2048}+\frac{386451\,a^7\,b^9\,c^3\,d^4}{2048}-\frac{262899\,a^6\,b^{10}\,c^4\,d^3}{2048}+\frac{44901\,a^5\,b^{11}\,c^5\,d^2}{2048}-\frac{3159\,a^4\,b^{12}\,c^6\,d}{2048}+\frac{81\,a^3\,b^{13}\,c^7}{2048}\right)\,1{}\mathrm{i}}{a^8\,d^9-8\,a^7\,b\,c\,d^8+28\,a^6\,b^2\,c^2\,d^7-56\,a^5\,b^3\,c^3\,d^6+70\,a^4\,b^4\,c^4\,d^5-56\,a^3\,b^5\,c^5\,d^4+28\,a^2\,b^6\,c^6\,d^3-8\,a\,b^7\,c^7\,d^2+b^8\,c^8\,d}+{\left(-\frac{625\,a^8\,d^8+15000\,a^7\,b\,c\,d^7+133500\,a^6\,b^2\,c^2\,d^6+513000\,a^5\,b^3\,c^3\,d^5+649350\,a^4\,b^4\,c^4\,d^4-307800\,a^3\,b^5\,c^5\,d^3+48060\,a^2\,b^6\,c^6\,d^2-3240\,a\,b^7\,c^7\,d+81\,b^8\,c^8}{16777216\,a^{12}\,c^3\,d^{17}-201326592\,a^{11}\,b\,c^4\,d^{16}+1107296256\,a^{10}\,b^2\,c^5\,d^{15}-3690987520\,a^9\,b^3\,c^6\,d^{14}+8304721920\,a^8\,b^4\,c^7\,d^{13}-13287555072\,a^7\,b^5\,c^8\,d^{12}+15502147584\,a^6\,b^6\,c^9\,d^{11}-13287555072\,a^5\,b^7\,c^{10}\,d^{10}+8304721920\,a^4\,b^8\,c^{11}\,d^9-3690987520\,a^3\,b^9\,c^{12}\,d^8+1107296256\,a^2\,b^{10}\,c^{13}\,d^7-201326592\,a\,b^{11}\,c^{14}\,d^6+16777216\,b^{12}\,c^{15}\,d^5}\right)}^{3/4}\,\left(\frac{{\left(-\frac{625\,a^8\,d^8+15000\,a^7\,b\,c\,d^7+133500\,a^6\,b^2\,c^2\,d^6+513000\,a^5\,b^3\,c^3\,d^5+649350\,a^4\,b^4\,c^4\,d^4-307800\,a^3\,b^5\,c^5\,d^3+48060\,a^2\,b^6\,c^6\,d^2-3240\,a\,b^7\,c^7\,d+81\,b^8\,c^8}{16777216\,a^{12}\,c^3\,d^{17}-201326592\,a^{11}\,b\,c^4\,d^{16}+1107296256\,a^{10}\,b^2\,c^5\,d^{15}-3690987520\,a^9\,b^3\,c^6\,d^{14}+8304721920\,a^8\,b^4\,c^7\,d^{13}-13287555072\,a^7\,b^5\,c^8\,d^{12}+15502147584\,a^6\,b^6\,c^9\,d^{11}-13287555072\,a^5\,b^7\,c^{10}\,d^{10}+8304721920\,a^4\,b^8\,c^{11}\,d^9-3690987520\,a^3\,b^9\,c^{12}\,d^8+1107296256\,a^2\,b^{10}\,c^{13}\,d^7-201326592\,a\,b^{11}\,c^{14}\,d^6+16777216\,b^{12}\,c^{15}\,d^5}\right)}^{1/4}\,\left(1280\,a^{16}\,b^4\,c\,d^{18}-6400\,a^{15}\,b^5\,c^2\,d^{17}-23040\,a^{14}\,b^6\,c^3\,d^{16}+309760\,a^{13}\,b^7\,c^4\,d^{15}-1337600\,a^{12}\,b^8\,c^5\,d^{14}+3421440\,a^{11}\,b^9\,c^6\,d^{13}-5913600\,a^{10}\,b^{10}\,c^7\,d^{12}+7265280\,a^9\,b^{11}\,c^8\,d^{11}-6462720\,a^8\,b^{12}\,c^9\,d^{10}+4153600\,a^7\,b^{13}\,c^{10}\,d^9-1886720\,a^6\,b^{14}\,c^{11}\,d^8+576000\,a^5\,b^{15}\,c^{12}\,d^7-106240\,a^4\,b^{16}\,c^{13}\,d^6+8960\,a^3\,b^{17}\,c^{14}\,d^5\right)}{a^8\,d^9-8\,a^7\,b\,c\,d^8+28\,a^6\,b^2\,c^2\,d^7-56\,a^5\,b^3\,c^3\,d^6+70\,a^4\,b^4\,c^4\,d^5-56\,a^3\,b^5\,c^5\,d^4+28\,a^2\,b^6\,c^6\,d^3-8\,a\,b^7\,c^7\,d^2+b^8\,c^8\,d}+\frac{\sqrt{x}\,\left(409600\,a^{19}\,b^4\,d^{20}-17694720\,a^{17}\,b^6\,c^2\,d^{18}+77070336\,a^{16}\,b^7\,c^3\,d^{17}-103612416\,a^{15}\,b^8\,c^4\,d^{16}-116391936\,a^{14}\,b^9\,c^5\,d^{15}+508952576\,a^{13}\,b^{10}\,c^6\,d^{14}-259522560\,a^{12}\,b^{11}\,c^7\,d^{13}-1398177792\,a^{11}\,b^{12}\,c^8\,d^{12}+3714056192\,a^{10}\,b^{13}\,c^9\,d^{11}-4814143488\,a^9\,b^{14}\,c^{10}\,d^{10}+3911712768\,a^8\,b^{15}\,c^{11}\,d^9-2086993920\,a^7\,b^{16}\,c^{12}\,d^8+714080256\,a^6\,b^{17}\,c^{13}\,d^7-141950976\,a^5\,b^{18}\,c^{14}\,d^6+12058624\,a^4\,b^{19}\,c^{15}\,d^5+147456\,a^3\,b^{20}\,c^{16}\,d^4\right)\,1{}\mathrm{i}}{4096\,\left(a^{12}\,d^{13}-12\,a^{11}\,b\,c\,d^{12}+66\,a^{10}\,b^2\,c^2\,d^{11}-220\,a^9\,b^3\,c^3\,d^{10}+495\,a^8\,b^4\,c^4\,d^9-792\,a^7\,b^5\,c^5\,d^8+924\,a^6\,b^6\,c^6\,d^7-792\,a^5\,b^7\,c^7\,d^6+495\,a^4\,b^8\,c^8\,d^5-220\,a^3\,b^9\,c^9\,d^4+66\,a^2\,b^{10}\,c^{10}\,d^3-12\,a\,b^{11}\,c^{11}\,d^2+b^{12}\,c^{12}\,d\right)}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}-\frac{\sqrt{x}\,\left(26225\,a^{12}\,b^7\,d^8+322200\,a^{11}\,b^8\,c\,d^7+1024380\,a^{10}\,b^9\,c^2\,d^6+328680\,a^9\,b^{10}\,c^3\,d^5+658566\,a^8\,b^{11}\,c^4\,d^4-307800\,a^7\,b^{12}\,c^5\,d^3+48060\,a^6\,b^{13}\,c^6\,d^2-3240\,a^5\,b^{14}\,c^7\,d+81\,a^4\,b^{15}\,c^8\right)\,1{}\mathrm{i}}{4096\,\left(a^{12}\,d^{13}-12\,a^{11}\,b\,c\,d^{12}+66\,a^{10}\,b^2\,c^2\,d^{11}-220\,a^9\,b^3\,c^3\,d^{10}+495\,a^8\,b^4\,c^4\,d^9-792\,a^7\,b^5\,c^5\,d^8+924\,a^6\,b^6\,c^6\,d^7-792\,a^5\,b^7\,c^7\,d^6+495\,a^4\,b^8\,c^8\,d^5-220\,a^3\,b^9\,c^9\,d^4+66\,a^2\,b^{10}\,c^{10}\,d^3-12\,a\,b^{11}\,c^{11}\,d^2+b^{12}\,c^{12}\,d\right)}\right)\,{\left(-\frac{625\,a^8\,d^8+15000\,a^7\,b\,c\,d^7+133500\,a^6\,b^2\,c^2\,d^6+513000\,a^5\,b^3\,c^3\,d^5+649350\,a^4\,b^4\,c^4\,d^4-307800\,a^3\,b^5\,c^5\,d^3+48060\,a^2\,b^6\,c^6\,d^2-3240\,a\,b^7\,c^7\,d+81\,b^8\,c^8}{16777216\,a^{12}\,c^3\,d^{17}-201326592\,a^{11}\,b\,c^4\,d^{16}+1107296256\,a^{10}\,b^2\,c^5\,d^{15}-3690987520\,a^9\,b^3\,c^6\,d^{14}+8304721920\,a^8\,b^4\,c^7\,d^{13}-13287555072\,a^7\,b^5\,c^8\,d^{12}+15502147584\,a^6\,b^6\,c^9\,d^{11}-13287555072\,a^5\,b^7\,c^{10}\,d^{10}+8304721920\,a^4\,b^8\,c^{11}\,d^9-3690987520\,a^3\,b^9\,c^{12}\,d^8+1107296256\,a^2\,b^{10}\,c^{13}\,d^7-201326592\,a\,b^{11}\,c^{14}\,d^6+16777216\,b^{12}\,c^{15}\,d^5}\right)}^{1/4}}\right)\,{\left(-\frac{625\,a^8\,d^8+15000\,a^7\,b\,c\,d^7+133500\,a^6\,b^2\,c^2\,d^6+513000\,a^5\,b^3\,c^3\,d^5+649350\,a^4\,b^4\,c^4\,d^4-307800\,a^3\,b^5\,c^5\,d^3+48060\,a^2\,b^6\,c^6\,d^2-3240\,a\,b^7\,c^7\,d+81\,b^8\,c^8}{16777216\,a^{12}\,c^3\,d^{17}-201326592\,a^{11}\,b\,c^4\,d^{16}+1107296256\,a^{10}\,b^2\,c^5\,d^{15}-3690987520\,a^9\,b^3\,c^6\,d^{14}+8304721920\,a^8\,b^4\,c^7\,d^{13}-13287555072\,a^7\,b^5\,c^8\,d^{12}+15502147584\,a^6\,b^6\,c^9\,d^{11}-13287555072\,a^5\,b^7\,c^{10}\,d^{10}+8304721920\,a^4\,b^8\,c^{11}\,d^9-3690987520\,a^3\,b^9\,c^{12}\,d^8+1107296256\,a^2\,b^{10}\,c^{13}\,d^7-201326592\,a\,b^{11}\,c^{14}\,d^6+16777216\,b^{12}\,c^{15}\,d^5}\right)}^{1/4}","Not used",1,"atan((((((81*a^3*b^13*c^7)/2048 - (625*a^10*b^6*d^7)/2048 - (3159*a^4*b^12*c^6*d)/2048 + (148215*a^9*b^7*c*d^6)/2048 + (44901*a^5*b^11*c^5*d^2)/2048 - (262899*a^6*b^10*c^4*d^3)/2048 + (386451*a^7*b^9*c^3*d^4)/2048 + (997755*a^8*b^8*c^2*d^5)/2048)/(a^8*d^9 + b^8*c^8*d - 8*a*b^7*c^7*d^2 + 28*a^2*b^6*c^6*d^3 - 56*a^3*b^5*c^5*d^4 + 70*a^4*b^4*c^4*d^5 - 56*a^5*b^3*c^3*d^6 + 28*a^6*b^2*c^2*d^7 - 8*a^7*b*c*d^8) + (((-(a^5*b^3)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4)*(1280*a^16*b^4*c*d^18 + 8960*a^3*b^17*c^14*d^5 - 106240*a^4*b^16*c^13*d^6 + 576000*a^5*b^15*c^12*d^7 - 1886720*a^6*b^14*c^11*d^8 + 4153600*a^7*b^13*c^10*d^9 - 6462720*a^8*b^12*c^9*d^10 + 7265280*a^9*b^11*c^8*d^11 - 5913600*a^10*b^10*c^7*d^12 + 3421440*a^11*b^9*c^6*d^13 - 1337600*a^12*b^8*c^5*d^14 + 309760*a^13*b^7*c^4*d^15 - 23040*a^14*b^6*c^3*d^16 - 6400*a^15*b^5*c^2*d^17))/(a^8*d^9 + b^8*c^8*d - 8*a*b^7*c^7*d^2 + 28*a^2*b^6*c^6*d^3 - 56*a^3*b^5*c^5*d^4 + 70*a^4*b^4*c^4*d^5 - 56*a^5*b^3*c^3*d^6 + 28*a^6*b^2*c^2*d^7 - 8*a^7*b*c*d^8) - (x^(1/2)*(409600*a^19*b^4*d^20 + 147456*a^3*b^20*c^16*d^4 + 12058624*a^4*b^19*c^15*d^5 - 141950976*a^5*b^18*c^14*d^6 + 714080256*a^6*b^17*c^13*d^7 - 2086993920*a^7*b^16*c^12*d^8 + 3911712768*a^8*b^15*c^11*d^9 - 4814143488*a^9*b^14*c^10*d^10 + 3714056192*a^10*b^13*c^9*d^11 - 1398177792*a^11*b^12*c^8*d^12 - 259522560*a^12*b^11*c^7*d^13 + 508952576*a^13*b^10*c^6*d^14 - 116391936*a^14*b^9*c^5*d^15 - 103612416*a^15*b^8*c^4*d^16 + 77070336*a^16*b^7*c^3*d^17 - 17694720*a^17*b^6*c^2*d^18))/(4096*(a^12*d^13 + b^12*c^12*d - 12*a*b^11*c^11*d^2 + 66*a^2*b^10*c^10*d^3 - 220*a^3*b^9*c^9*d^4 + 495*a^4*b^8*c^8*d^5 - 792*a^5*b^7*c^7*d^6 + 924*a^6*b^6*c^6*d^7 - 792*a^7*b^5*c^5*d^8 + 495*a^8*b^4*c^4*d^9 - 220*a^9*b^3*c^3*d^10 + 66*a^10*b^2*c^2*d^11 - 12*a^11*b*c*d^12)))*(-(a^5*b^3)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(3/4))*(-(a^5*b^3)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4)*1i - (x^(1/2)*(81*a^4*b^15*c^8 + 26225*a^12*b^7*d^8 - 3240*a^5*b^14*c^7*d + 322200*a^11*b^8*c*d^7 + 48060*a^6*b^13*c^6*d^2 - 307800*a^7*b^12*c^5*d^3 + 658566*a^8*b^11*c^4*d^4 + 328680*a^9*b^10*c^3*d^5 + 1024380*a^10*b^9*c^2*d^6)*1i)/(4096*(a^12*d^13 + b^12*c^12*d - 12*a*b^11*c^11*d^2 + 66*a^2*b^10*c^10*d^3 - 220*a^3*b^9*c^9*d^4 + 495*a^4*b^8*c^8*d^5 - 792*a^5*b^7*c^7*d^6 + 924*a^6*b^6*c^6*d^7 - 792*a^7*b^5*c^5*d^8 + 495*a^8*b^4*c^4*d^9 - 220*a^9*b^3*c^3*d^10 + 66*a^10*b^2*c^2*d^11 - 12*a^11*b*c*d^12)))*(-(a^5*b^3)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4) - ((((81*a^3*b^13*c^7)/2048 - (625*a^10*b^6*d^7)/2048 - (3159*a^4*b^12*c^6*d)/2048 + (148215*a^9*b^7*c*d^6)/2048 + (44901*a^5*b^11*c^5*d^2)/2048 - (262899*a^6*b^10*c^4*d^3)/2048 + (386451*a^7*b^9*c^3*d^4)/2048 + (997755*a^8*b^8*c^2*d^5)/2048)/(a^8*d^9 + b^8*c^8*d - 8*a*b^7*c^7*d^2 + 28*a^2*b^6*c^6*d^3 - 56*a^3*b^5*c^5*d^4 + 70*a^4*b^4*c^4*d^5 - 56*a^5*b^3*c^3*d^6 + 28*a^6*b^2*c^2*d^7 - 8*a^7*b*c*d^8) + (((-(a^5*b^3)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4)*(1280*a^16*b^4*c*d^18 + 8960*a^3*b^17*c^14*d^5 - 106240*a^4*b^16*c^13*d^6 + 576000*a^5*b^15*c^12*d^7 - 1886720*a^6*b^14*c^11*d^8 + 4153600*a^7*b^13*c^10*d^9 - 6462720*a^8*b^12*c^9*d^10 + 7265280*a^9*b^11*c^8*d^11 - 5913600*a^10*b^10*c^7*d^12 + 3421440*a^11*b^9*c^6*d^13 - 1337600*a^12*b^8*c^5*d^14 + 309760*a^13*b^7*c^4*d^15 - 23040*a^14*b^6*c^3*d^16 - 6400*a^15*b^5*c^2*d^17))/(a^8*d^9 + b^8*c^8*d - 8*a*b^7*c^7*d^2 + 28*a^2*b^6*c^6*d^3 - 56*a^3*b^5*c^5*d^4 + 70*a^4*b^4*c^4*d^5 - 56*a^5*b^3*c^3*d^6 + 28*a^6*b^2*c^2*d^7 - 8*a^7*b*c*d^8) + (x^(1/2)*(409600*a^19*b^4*d^20 + 147456*a^3*b^20*c^16*d^4 + 12058624*a^4*b^19*c^15*d^5 - 141950976*a^5*b^18*c^14*d^6 + 714080256*a^6*b^17*c^13*d^7 - 2086993920*a^7*b^16*c^12*d^8 + 3911712768*a^8*b^15*c^11*d^9 - 4814143488*a^9*b^14*c^10*d^10 + 3714056192*a^10*b^13*c^9*d^11 - 1398177792*a^11*b^12*c^8*d^12 - 259522560*a^12*b^11*c^7*d^13 + 508952576*a^13*b^10*c^6*d^14 - 116391936*a^14*b^9*c^5*d^15 - 103612416*a^15*b^8*c^4*d^16 + 77070336*a^16*b^7*c^3*d^17 - 17694720*a^17*b^6*c^2*d^18))/(4096*(a^12*d^13 + b^12*c^12*d - 12*a*b^11*c^11*d^2 + 66*a^2*b^10*c^10*d^3 - 220*a^3*b^9*c^9*d^4 + 495*a^4*b^8*c^8*d^5 - 792*a^5*b^7*c^7*d^6 + 924*a^6*b^6*c^6*d^7 - 792*a^7*b^5*c^5*d^8 + 495*a^8*b^4*c^4*d^9 - 220*a^9*b^3*c^3*d^10 + 66*a^10*b^2*c^2*d^11 - 12*a^11*b*c*d^12)))*(-(a^5*b^3)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(3/4))*(-(a^5*b^3)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4)*1i + (x^(1/2)*(81*a^4*b^15*c^8 + 26225*a^12*b^7*d^8 - 3240*a^5*b^14*c^7*d + 322200*a^11*b^8*c*d^7 + 48060*a^6*b^13*c^6*d^2 - 307800*a^7*b^12*c^5*d^3 + 658566*a^8*b^11*c^4*d^4 + 328680*a^9*b^10*c^3*d^5 + 1024380*a^10*b^9*c^2*d^6)*1i)/(4096*(a^12*d^13 + b^12*c^12*d - 12*a*b^11*c^11*d^2 + 66*a^2*b^10*c^10*d^3 - 220*a^3*b^9*c^9*d^4 + 495*a^4*b^8*c^8*d^5 - 792*a^5*b^7*c^7*d^6 + 924*a^6*b^6*c^6*d^7 - 792*a^7*b^5*c^5*d^8 + 495*a^8*b^4*c^4*d^9 - 220*a^9*b^3*c^3*d^10 + 66*a^10*b^2*c^2*d^11 - 12*a^11*b*c*d^12)))*(-(a^5*b^3)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4))/(((((81*a^3*b^13*c^7)/2048 - (625*a^10*b^6*d^7)/2048 - (3159*a^4*b^12*c^6*d)/2048 + (148215*a^9*b^7*c*d^6)/2048 + (44901*a^5*b^11*c^5*d^2)/2048 - (262899*a^6*b^10*c^4*d^3)/2048 + (386451*a^7*b^9*c^3*d^4)/2048 + (997755*a^8*b^8*c^2*d^5)/2048)/(a^8*d^9 + b^8*c^8*d - 8*a*b^7*c^7*d^2 + 28*a^2*b^6*c^6*d^3 - 56*a^3*b^5*c^5*d^4 + 70*a^4*b^4*c^4*d^5 - 56*a^5*b^3*c^3*d^6 + 28*a^6*b^2*c^2*d^7 - 8*a^7*b*c*d^8) + (((-(a^5*b^3)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4)*(1280*a^16*b^4*c*d^18 + 8960*a^3*b^17*c^14*d^5 - 106240*a^4*b^16*c^13*d^6 + 576000*a^5*b^15*c^12*d^7 - 1886720*a^6*b^14*c^11*d^8 + 4153600*a^7*b^13*c^10*d^9 - 6462720*a^8*b^12*c^9*d^10 + 7265280*a^9*b^11*c^8*d^11 - 5913600*a^10*b^10*c^7*d^12 + 3421440*a^11*b^9*c^6*d^13 - 1337600*a^12*b^8*c^5*d^14 + 309760*a^13*b^7*c^4*d^15 - 23040*a^14*b^6*c^3*d^16 - 6400*a^15*b^5*c^2*d^17))/(a^8*d^9 + b^8*c^8*d - 8*a*b^7*c^7*d^2 + 28*a^2*b^6*c^6*d^3 - 56*a^3*b^5*c^5*d^4 + 70*a^4*b^4*c^4*d^5 - 56*a^5*b^3*c^3*d^6 + 28*a^6*b^2*c^2*d^7 - 8*a^7*b*c*d^8) - (x^(1/2)*(409600*a^19*b^4*d^20 + 147456*a^3*b^20*c^16*d^4 + 12058624*a^4*b^19*c^15*d^5 - 141950976*a^5*b^18*c^14*d^6 + 714080256*a^6*b^17*c^13*d^7 - 2086993920*a^7*b^16*c^12*d^8 + 3911712768*a^8*b^15*c^11*d^9 - 4814143488*a^9*b^14*c^10*d^10 + 3714056192*a^10*b^13*c^9*d^11 - 1398177792*a^11*b^12*c^8*d^12 - 259522560*a^12*b^11*c^7*d^13 + 508952576*a^13*b^10*c^6*d^14 - 116391936*a^14*b^9*c^5*d^15 - 103612416*a^15*b^8*c^4*d^16 + 77070336*a^16*b^7*c^3*d^17 - 17694720*a^17*b^6*c^2*d^18))/(4096*(a^12*d^13 + b^12*c^12*d - 12*a*b^11*c^11*d^2 + 66*a^2*b^10*c^10*d^3 - 220*a^3*b^9*c^9*d^4 + 495*a^4*b^8*c^8*d^5 - 792*a^5*b^7*c^7*d^6 + 924*a^6*b^6*c^6*d^7 - 792*a^7*b^5*c^5*d^8 + 495*a^8*b^4*c^4*d^9 - 220*a^9*b^3*c^3*d^10 + 66*a^10*b^2*c^2*d^11 - 12*a^11*b*c*d^12)))*(-(a^5*b^3)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(3/4))*(-(a^5*b^3)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4) - (x^(1/2)*(81*a^4*b^15*c^8 + 26225*a^12*b^7*d^8 - 3240*a^5*b^14*c^7*d + 322200*a^11*b^8*c*d^7 + 48060*a^6*b^13*c^6*d^2 - 307800*a^7*b^12*c^5*d^3 + 658566*a^8*b^11*c^4*d^4 + 328680*a^9*b^10*c^3*d^5 + 1024380*a^10*b^9*c^2*d^6))/(4096*(a^12*d^13 + b^12*c^12*d - 12*a*b^11*c^11*d^2 + 66*a^2*b^10*c^10*d^3 - 220*a^3*b^9*c^9*d^4 + 495*a^4*b^8*c^8*d^5 - 792*a^5*b^7*c^7*d^6 + 924*a^6*b^6*c^6*d^7 - 792*a^7*b^5*c^5*d^8 + 495*a^8*b^4*c^4*d^9 - 220*a^9*b^3*c^3*d^10 + 66*a^10*b^2*c^2*d^11 - 12*a^11*b*c*d^12)))*(-(a^5*b^3)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4) + ((((81*a^3*b^13*c^7)/2048 - (625*a^10*b^6*d^7)/2048 - (3159*a^4*b^12*c^6*d)/2048 + (148215*a^9*b^7*c*d^6)/2048 + (44901*a^5*b^11*c^5*d^2)/2048 - (262899*a^6*b^10*c^4*d^3)/2048 + (386451*a^7*b^9*c^3*d^4)/2048 + (997755*a^8*b^8*c^2*d^5)/2048)/(a^8*d^9 + b^8*c^8*d - 8*a*b^7*c^7*d^2 + 28*a^2*b^6*c^6*d^3 - 56*a^3*b^5*c^5*d^4 + 70*a^4*b^4*c^4*d^5 - 56*a^5*b^3*c^3*d^6 + 28*a^6*b^2*c^2*d^7 - 8*a^7*b*c*d^8) + (((-(a^5*b^3)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4)*(1280*a^16*b^4*c*d^18 + 8960*a^3*b^17*c^14*d^5 - 106240*a^4*b^16*c^13*d^6 + 576000*a^5*b^15*c^12*d^7 - 1886720*a^6*b^14*c^11*d^8 + 4153600*a^7*b^13*c^10*d^9 - 6462720*a^8*b^12*c^9*d^10 + 7265280*a^9*b^11*c^8*d^11 - 5913600*a^10*b^10*c^7*d^12 + 3421440*a^11*b^9*c^6*d^13 - 1337600*a^12*b^8*c^5*d^14 + 309760*a^13*b^7*c^4*d^15 - 23040*a^14*b^6*c^3*d^16 - 6400*a^15*b^5*c^2*d^17))/(a^8*d^9 + b^8*c^8*d - 8*a*b^7*c^7*d^2 + 28*a^2*b^6*c^6*d^3 - 56*a^3*b^5*c^5*d^4 + 70*a^4*b^4*c^4*d^5 - 56*a^5*b^3*c^3*d^6 + 28*a^6*b^2*c^2*d^7 - 8*a^7*b*c*d^8) + (x^(1/2)*(409600*a^19*b^4*d^20 + 147456*a^3*b^20*c^16*d^4 + 12058624*a^4*b^19*c^15*d^5 - 141950976*a^5*b^18*c^14*d^6 + 714080256*a^6*b^17*c^13*d^7 - 2086993920*a^7*b^16*c^12*d^8 + 3911712768*a^8*b^15*c^11*d^9 - 4814143488*a^9*b^14*c^10*d^10 + 3714056192*a^10*b^13*c^9*d^11 - 1398177792*a^11*b^12*c^8*d^12 - 259522560*a^12*b^11*c^7*d^13 + 508952576*a^13*b^10*c^6*d^14 - 116391936*a^14*b^9*c^5*d^15 - 103612416*a^15*b^8*c^4*d^16 + 77070336*a^16*b^7*c^3*d^17 - 17694720*a^17*b^6*c^2*d^18))/(4096*(a^12*d^13 + b^12*c^12*d - 12*a*b^11*c^11*d^2 + 66*a^2*b^10*c^10*d^3 - 220*a^3*b^9*c^9*d^4 + 495*a^4*b^8*c^8*d^5 - 792*a^5*b^7*c^7*d^6 + 924*a^6*b^6*c^6*d^7 - 792*a^7*b^5*c^5*d^8 + 495*a^8*b^4*c^4*d^9 - 220*a^9*b^3*c^3*d^10 + 66*a^10*b^2*c^2*d^11 - 12*a^11*b*c*d^12)))*(-(a^5*b^3)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(3/4))*(-(a^5*b^3)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4) + (x^(1/2)*(81*a^4*b^15*c^8 + 26225*a^12*b^7*d^8 - 3240*a^5*b^14*c^7*d + 322200*a^11*b^8*c*d^7 + 48060*a^6*b^13*c^6*d^2 - 307800*a^7*b^12*c^5*d^3 + 658566*a^8*b^11*c^4*d^4 + 328680*a^9*b^10*c^3*d^5 + 1024380*a^10*b^9*c^2*d^6))/(4096*(a^12*d^13 + b^12*c^12*d - 12*a*b^11*c^11*d^2 + 66*a^2*b^10*c^10*d^3 - 220*a^3*b^9*c^9*d^4 + 495*a^4*b^8*c^8*d^5 - 792*a^5*b^7*c^7*d^6 + 924*a^6*b^6*c^6*d^7 - 792*a^7*b^5*c^5*d^8 + 495*a^8*b^4*c^4*d^9 - 220*a^9*b^3*c^3*d^10 + 66*a^10*b^2*c^2*d^11 - 12*a^11*b*c*d^12)))*(-(a^5*b^3)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4)))*(-(a^5*b^3)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4)*2i - ((x^(5/2)*(9*a*d - b*c))/(16*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) + (x^(1/2)*(3*b*c^2 + 5*a*c*d))/(16*d*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)))/(c^2 + d^2*x^4 + 2*c*d*x^2) - 2*atan(((((((81*a^3*b^13*c^7)/2048 - (625*a^10*b^6*d^7)/2048 - (3159*a^4*b^12*c^6*d)/2048 + (148215*a^9*b^7*c*d^6)/2048 + (44901*a^5*b^11*c^5*d^2)/2048 - (262899*a^6*b^10*c^4*d^3)/2048 + (386451*a^7*b^9*c^3*d^4)/2048 + (997755*a^8*b^8*c^2*d^5)/2048)*1i)/(a^8*d^9 + b^8*c^8*d - 8*a*b^7*c^7*d^2 + 28*a^2*b^6*c^6*d^3 - 56*a^3*b^5*c^5*d^4 + 70*a^4*b^4*c^4*d^5 - 56*a^5*b^3*c^3*d^6 + 28*a^6*b^2*c^2*d^7 - 8*a^7*b*c*d^8) + (((-(a^5*b^3)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4)*(1280*a^16*b^4*c*d^18 + 8960*a^3*b^17*c^14*d^5 - 106240*a^4*b^16*c^13*d^6 + 576000*a^5*b^15*c^12*d^7 - 1886720*a^6*b^14*c^11*d^8 + 4153600*a^7*b^13*c^10*d^9 - 6462720*a^8*b^12*c^9*d^10 + 7265280*a^9*b^11*c^8*d^11 - 5913600*a^10*b^10*c^7*d^12 + 3421440*a^11*b^9*c^6*d^13 - 1337600*a^12*b^8*c^5*d^14 + 309760*a^13*b^7*c^4*d^15 - 23040*a^14*b^6*c^3*d^16 - 6400*a^15*b^5*c^2*d^17))/(a^8*d^9 + b^8*c^8*d - 8*a*b^7*c^7*d^2 + 28*a^2*b^6*c^6*d^3 - 56*a^3*b^5*c^5*d^4 + 70*a^4*b^4*c^4*d^5 - 56*a^5*b^3*c^3*d^6 + 28*a^6*b^2*c^2*d^7 - 8*a^7*b*c*d^8) - (x^(1/2)*(409600*a^19*b^4*d^20 + 147456*a^3*b^20*c^16*d^4 + 12058624*a^4*b^19*c^15*d^5 - 141950976*a^5*b^18*c^14*d^6 + 714080256*a^6*b^17*c^13*d^7 - 2086993920*a^7*b^16*c^12*d^8 + 3911712768*a^8*b^15*c^11*d^9 - 4814143488*a^9*b^14*c^10*d^10 + 3714056192*a^10*b^13*c^9*d^11 - 1398177792*a^11*b^12*c^8*d^12 - 259522560*a^12*b^11*c^7*d^13 + 508952576*a^13*b^10*c^6*d^14 - 116391936*a^14*b^9*c^5*d^15 - 103612416*a^15*b^8*c^4*d^16 + 77070336*a^16*b^7*c^3*d^17 - 17694720*a^17*b^6*c^2*d^18)*1i)/(4096*(a^12*d^13 + b^12*c^12*d - 12*a*b^11*c^11*d^2 + 66*a^2*b^10*c^10*d^3 - 220*a^3*b^9*c^9*d^4 + 495*a^4*b^8*c^8*d^5 - 792*a^5*b^7*c^7*d^6 + 924*a^6*b^6*c^6*d^7 - 792*a^7*b^5*c^5*d^8 + 495*a^8*b^4*c^4*d^9 - 220*a^9*b^3*c^3*d^10 + 66*a^10*b^2*c^2*d^11 - 12*a^11*b*c*d^12)))*(-(a^5*b^3)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(3/4)*1i)*(-(a^5*b^3)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4) + (x^(1/2)*(81*a^4*b^15*c^8 + 26225*a^12*b^7*d^8 - 3240*a^5*b^14*c^7*d + 322200*a^11*b^8*c*d^7 + 48060*a^6*b^13*c^6*d^2 - 307800*a^7*b^12*c^5*d^3 + 658566*a^8*b^11*c^4*d^4 + 328680*a^9*b^10*c^3*d^5 + 1024380*a^10*b^9*c^2*d^6))/(4096*(a^12*d^13 + b^12*c^12*d - 12*a*b^11*c^11*d^2 + 66*a^2*b^10*c^10*d^3 - 220*a^3*b^9*c^9*d^4 + 495*a^4*b^8*c^8*d^5 - 792*a^5*b^7*c^7*d^6 + 924*a^6*b^6*c^6*d^7 - 792*a^7*b^5*c^5*d^8 + 495*a^8*b^4*c^4*d^9 - 220*a^9*b^3*c^3*d^10 + 66*a^10*b^2*c^2*d^11 - 12*a^11*b*c*d^12)))*(-(a^5*b^3)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4) - (((((81*a^3*b^13*c^7)/2048 - (625*a^10*b^6*d^7)/2048 - (3159*a^4*b^12*c^6*d)/2048 + (148215*a^9*b^7*c*d^6)/2048 + (44901*a^5*b^11*c^5*d^2)/2048 - (262899*a^6*b^10*c^4*d^3)/2048 + (386451*a^7*b^9*c^3*d^4)/2048 + (997755*a^8*b^8*c^2*d^5)/2048)*1i)/(a^8*d^9 + b^8*c^8*d - 8*a*b^7*c^7*d^2 + 28*a^2*b^6*c^6*d^3 - 56*a^3*b^5*c^5*d^4 + 70*a^4*b^4*c^4*d^5 - 56*a^5*b^3*c^3*d^6 + 28*a^6*b^2*c^2*d^7 - 8*a^7*b*c*d^8) + (((-(a^5*b^3)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4)*(1280*a^16*b^4*c*d^18 + 8960*a^3*b^17*c^14*d^5 - 106240*a^4*b^16*c^13*d^6 + 576000*a^5*b^15*c^12*d^7 - 1886720*a^6*b^14*c^11*d^8 + 4153600*a^7*b^13*c^10*d^9 - 6462720*a^8*b^12*c^9*d^10 + 7265280*a^9*b^11*c^8*d^11 - 5913600*a^10*b^10*c^7*d^12 + 3421440*a^11*b^9*c^6*d^13 - 1337600*a^12*b^8*c^5*d^14 + 309760*a^13*b^7*c^4*d^15 - 23040*a^14*b^6*c^3*d^16 - 6400*a^15*b^5*c^2*d^17))/(a^8*d^9 + b^8*c^8*d - 8*a*b^7*c^7*d^2 + 28*a^2*b^6*c^6*d^3 - 56*a^3*b^5*c^5*d^4 + 70*a^4*b^4*c^4*d^5 - 56*a^5*b^3*c^3*d^6 + 28*a^6*b^2*c^2*d^7 - 8*a^7*b*c*d^8) + (x^(1/2)*(409600*a^19*b^4*d^20 + 147456*a^3*b^20*c^16*d^4 + 12058624*a^4*b^19*c^15*d^5 - 141950976*a^5*b^18*c^14*d^6 + 714080256*a^6*b^17*c^13*d^7 - 2086993920*a^7*b^16*c^12*d^8 + 3911712768*a^8*b^15*c^11*d^9 - 4814143488*a^9*b^14*c^10*d^10 + 3714056192*a^10*b^13*c^9*d^11 - 1398177792*a^11*b^12*c^8*d^12 - 259522560*a^12*b^11*c^7*d^13 + 508952576*a^13*b^10*c^6*d^14 - 116391936*a^14*b^9*c^5*d^15 - 103612416*a^15*b^8*c^4*d^16 + 77070336*a^16*b^7*c^3*d^17 - 17694720*a^17*b^6*c^2*d^18)*1i)/(4096*(a^12*d^13 + b^12*c^12*d - 12*a*b^11*c^11*d^2 + 66*a^2*b^10*c^10*d^3 - 220*a^3*b^9*c^9*d^4 + 495*a^4*b^8*c^8*d^5 - 792*a^5*b^7*c^7*d^6 + 924*a^6*b^6*c^6*d^7 - 792*a^7*b^5*c^5*d^8 + 495*a^8*b^4*c^4*d^9 - 220*a^9*b^3*c^3*d^10 + 66*a^10*b^2*c^2*d^11 - 12*a^11*b*c*d^12)))*(-(a^5*b^3)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 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12*a^11*b*c*d^12)))*(-(a^5*b^3)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4))/((((((81*a^3*b^13*c^7)/2048 - (625*a^10*b^6*d^7)/2048 - (3159*a^4*b^12*c^6*d)/2048 + (148215*a^9*b^7*c*d^6)/2048 + (44901*a^5*b^11*c^5*d^2)/2048 - (262899*a^6*b^10*c^4*d^3)/2048 + (386451*a^7*b^9*c^3*d^4)/2048 + (997755*a^8*b^8*c^2*d^5)/2048)*1i)/(a^8*d^9 + b^8*c^8*d - 8*a*b^7*c^7*d^2 + 28*a^2*b^6*c^6*d^3 - 56*a^3*b^5*c^5*d^4 + 70*a^4*b^4*c^4*d^5 - 56*a^5*b^3*c^3*d^6 + 28*a^6*b^2*c^2*d^7 - 8*a^7*b*c*d^8) + (((-(a^5*b^3)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4)*(1280*a^16*b^4*c*d^18 + 8960*a^3*b^17*c^14*d^5 - 106240*a^4*b^16*c^13*d^6 + 576000*a^5*b^15*c^12*d^7 - 1886720*a^6*b^14*c^11*d^8 + 4153600*a^7*b^13*c^10*d^9 - 6462720*a^8*b^12*c^9*d^10 + 7265280*a^9*b^11*c^8*d^11 - 5913600*a^10*b^10*c^7*d^12 + 3421440*a^11*b^9*c^6*d^13 - 1337600*a^12*b^8*c^5*d^14 + 309760*a^13*b^7*c^4*d^15 - 23040*a^14*b^6*c^3*d^16 - 6400*a^15*b^5*c^2*d^17))/(a^8*d^9 + b^8*c^8*d - 8*a*b^7*c^7*d^2 + 28*a^2*b^6*c^6*d^3 - 56*a^3*b^5*c^5*d^4 + 70*a^4*b^4*c^4*d^5 - 56*a^5*b^3*c^3*d^6 + 28*a^6*b^2*c^2*d^7 - 8*a^7*b*c*d^8) - (x^(1/2)*(409600*a^19*b^4*d^20 + 147456*a^3*b^20*c^16*d^4 + 12058624*a^4*b^19*c^15*d^5 - 141950976*a^5*b^18*c^14*d^6 + 714080256*a^6*b^17*c^13*d^7 - 2086993920*a^7*b^16*c^12*d^8 + 3911712768*a^8*b^15*c^11*d^9 - 4814143488*a^9*b^14*c^10*d^10 + 3714056192*a^10*b^13*c^9*d^11 - 1398177792*a^11*b^12*c^8*d^12 - 259522560*a^12*b^11*c^7*d^13 + 508952576*a^13*b^10*c^6*d^14 - 116391936*a^14*b^9*c^5*d^15 - 103612416*a^15*b^8*c^4*d^16 + 77070336*a^16*b^7*c^3*d^17 - 17694720*a^17*b^6*c^2*d^18)*1i)/(4096*(a^12*d^13 + b^12*c^12*d - 12*a*b^11*c^11*d^2 + 66*a^2*b^10*c^10*d^3 - 220*a^3*b^9*c^9*d^4 + 495*a^4*b^8*c^8*d^5 - 792*a^5*b^7*c^7*d^6 + 924*a^6*b^6*c^6*d^7 - 792*a^7*b^5*c^5*d^8 + 495*a^8*b^4*c^4*d^9 - 220*a^9*b^3*c^3*d^10 + 66*a^10*b^2*c^2*d^11 - 12*a^11*b*c*d^12)))*(-(a^5*b^3)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(3/4)*1i)*(-(a^5*b^3)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4)*1i + (x^(1/2)*(81*a^4*b^15*c^8 + 26225*a^12*b^7*d^8 - 3240*a^5*b^14*c^7*d + 322200*a^11*b^8*c*d^7 + 48060*a^6*b^13*c^6*d^2 - 307800*a^7*b^12*c^5*d^3 + 658566*a^8*b^11*c^4*d^4 + 328680*a^9*b^10*c^3*d^5 + 1024380*a^10*b^9*c^2*d^6)*1i)/(4096*(a^12*d^13 + b^12*c^12*d - 12*a*b^11*c^11*d^2 + 66*a^2*b^10*c^10*d^3 - 220*a^3*b^9*c^9*d^4 + 495*a^4*b^8*c^8*d^5 - 792*a^5*b^7*c^7*d^6 + 924*a^6*b^6*c^6*d^7 - 792*a^7*b^5*c^5*d^8 + 495*a^8*b^4*c^4*d^9 - 220*a^9*b^3*c^3*d^10 + 66*a^10*b^2*c^2*d^11 - 12*a^11*b*c*d^12)))*(-(a^5*b^3)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4) + (((((81*a^3*b^13*c^7)/2048 - (625*a^10*b^6*d^7)/2048 - (3159*a^4*b^12*c^6*d)/2048 + (148215*a^9*b^7*c*d^6)/2048 + (44901*a^5*b^11*c^5*d^2)/2048 - (262899*a^6*b^10*c^4*d^3)/2048 + (386451*a^7*b^9*c^3*d^4)/2048 + (997755*a^8*b^8*c^2*d^5)/2048)*1i)/(a^8*d^9 + b^8*c^8*d - 8*a*b^7*c^7*d^2 + 28*a^2*b^6*c^6*d^3 - 56*a^3*b^5*c^5*d^4 + 70*a^4*b^4*c^4*d^5 - 56*a^5*b^3*c^3*d^6 + 28*a^6*b^2*c^2*d^7 - 8*a^7*b*c*d^8) + (((-(a^5*b^3)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4)*(1280*a^16*b^4*c*d^18 + 8960*a^3*b^17*c^14*d^5 - 106240*a^4*b^16*c^13*d^6 + 576000*a^5*b^15*c^12*d^7 - 1886720*a^6*b^14*c^11*d^8 + 4153600*a^7*b^13*c^10*d^9 - 6462720*a^8*b^12*c^9*d^10 + 7265280*a^9*b^11*c^8*d^11 - 5913600*a^10*b^10*c^7*d^12 + 3421440*a^11*b^9*c^6*d^13 - 1337600*a^12*b^8*c^5*d^14 + 309760*a^13*b^7*c^4*d^15 - 23040*a^14*b^6*c^3*d^16 - 6400*a^15*b^5*c^2*d^17))/(a^8*d^9 + b^8*c^8*d - 8*a*b^7*c^7*d^2 + 28*a^2*b^6*c^6*d^3 - 56*a^3*b^5*c^5*d^4 + 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103612416*a^15*b^8*c^4*d^16 + 77070336*a^16*b^7*c^3*d^17 - 17694720*a^17*b^6*c^2*d^18)*1i)/(4096*(a^12*d^13 + b^12*c^12*d - 12*a*b^11*c^11*d^2 + 66*a^2*b^10*c^10*d^3 - 220*a^3*b^9*c^9*d^4 + 495*a^4*b^8*c^8*d^5 - 792*a^5*b^7*c^7*d^6 + 924*a^6*b^6*c^6*d^7 - 792*a^7*b^5*c^5*d^8 + 495*a^8*b^4*c^4*d^9 - 220*a^9*b^3*c^3*d^10 + 66*a^10*b^2*c^2*d^11 - 12*a^11*b*c*d^12)))*1i)*1i + (x^(1/2)*(81*a^4*b^15*c^8 + 26225*a^12*b^7*d^8 - 3240*a^5*b^14*c^7*d + 322200*a^11*b^8*c*d^7 + 48060*a^6*b^13*c^6*d^2 - 307800*a^7*b^12*c^5*d^3 + 658566*a^8*b^11*c^4*d^4 + 328680*a^9*b^10*c^3*d^5 + 1024380*a^10*b^9*c^2*d^6)*1i)/(4096*(a^12*d^13 + b^12*c^12*d - 12*a*b^11*c^11*d^2 + 66*a^2*b^10*c^10*d^3 - 220*a^3*b^9*c^9*d^4 + 495*a^4*b^8*c^8*d^5 - 792*a^5*b^7*c^7*d^6 + 924*a^6*b^6*c^6*d^7 - 792*a^7*b^5*c^5*d^8 + 495*a^8*b^4*c^4*d^9 - 220*a^9*b^3*c^3*d^10 + 66*a^10*b^2*c^2*d^11 - 12*a^11*b*c*d^12)))*(-(625*a^8*d^8 + 81*b^8*c^8 + 48060*a^2*b^6*c^6*d^2 - 307800*a^3*b^5*c^5*d^3 + 649350*a^4*b^4*c^4*d^4 + 513000*a^5*b^3*c^3*d^5 + 133500*a^6*b^2*c^2*d^6 - 3240*a*b^7*c^7*d + 15000*a^7*b*c*d^7)/(16777216*a^12*c^3*d^17 + 16777216*b^12*c^15*d^5 - 201326592*a*b^11*c^14*d^6 - 201326592*a^11*b*c^4*d^16 + 1107296256*a^2*b^10*c^13*d^7 - 3690987520*a^3*b^9*c^12*d^8 + 8304721920*a^4*b^8*c^11*d^9 - 13287555072*a^5*b^7*c^10*d^10 + 15502147584*a^6*b^6*c^9*d^11 - 13287555072*a^7*b^5*c^8*d^12 + 8304721920*a^8*b^4*c^7*d^13 - 3690987520*a^9*b^3*c^6*d^14 + 1107296256*a^10*b^2*c^5*d^15))^(1/4) + ((-(625*a^8*d^8 + 81*b^8*c^8 + 48060*a^2*b^6*c^6*d^2 - 307800*a^3*b^5*c^5*d^3 + 649350*a^4*b^4*c^4*d^4 + 513000*a^5*b^3*c^3*d^5 + 133500*a^6*b^2*c^2*d^6 - 3240*a*b^7*c^7*d + 15000*a^7*b*c*d^7)/(16777216*a^12*c^3*d^17 + 16777216*b^12*c^15*d^5 - 201326592*a*b^11*c^14*d^6 - 201326592*a^11*b*c^4*d^16 + 1107296256*a^2*b^10*c^13*d^7 - 3690987520*a^3*b^9*c^12*d^8 + 8304721920*a^4*b^8*c^11*d^9 - 13287555072*a^5*b^7*c^10*d^10 + 15502147584*a^6*b^6*c^9*d^11 - 13287555072*a^7*b^5*c^8*d^12 + 8304721920*a^8*b^4*c^7*d^13 - 3690987520*a^9*b^3*c^6*d^14 + 1107296256*a^10*b^2*c^5*d^15))^(1/4)*((((81*a^3*b^13*c^7)/2048 - (625*a^10*b^6*d^7)/2048 - (3159*a^4*b^12*c^6*d)/2048 + (148215*a^9*b^7*c*d^6)/2048 + (44901*a^5*b^11*c^5*d^2)/2048 - (262899*a^6*b^10*c^4*d^3)/2048 + (386451*a^7*b^9*c^3*d^4)/2048 + (997755*a^8*b^8*c^2*d^5)/2048)*1i)/(a^8*d^9 + b^8*c^8*d - 8*a*b^7*c^7*d^2 + 28*a^2*b^6*c^6*d^3 - 56*a^3*b^5*c^5*d^4 + 70*a^4*b^4*c^4*d^5 - 56*a^5*b^3*c^3*d^6 + 28*a^6*b^2*c^2*d^7 - 8*a^7*b*c*d^8) + (-(625*a^8*d^8 + 81*b^8*c^8 + 48060*a^2*b^6*c^6*d^2 - 307800*a^3*b^5*c^5*d^3 + 649350*a^4*b^4*c^4*d^4 + 513000*a^5*b^3*c^3*d^5 + 133500*a^6*b^2*c^2*d^6 - 3240*a*b^7*c^7*d + 15000*a^7*b*c*d^7)/(16777216*a^12*c^3*d^17 + 16777216*b^12*c^15*d^5 - 201326592*a*b^11*c^14*d^6 - 201326592*a^11*b*c^4*d^16 + 1107296256*a^2*b^10*c^13*d^7 - 3690987520*a^3*b^9*c^12*d^8 + 8304721920*a^4*b^8*c^11*d^9 - 13287555072*a^5*b^7*c^10*d^10 + 15502147584*a^6*b^6*c^9*d^11 - 13287555072*a^7*b^5*c^8*d^12 + 8304721920*a^8*b^4*c^7*d^13 - 3690987520*a^9*b^3*c^6*d^14 + 1107296256*a^10*b^2*c^5*d^15))^(3/4)*(((-(625*a^8*d^8 + 81*b^8*c^8 + 48060*a^2*b^6*c^6*d^2 - 307800*a^3*b^5*c^5*d^3 + 649350*a^4*b^4*c^4*d^4 + 513000*a^5*b^3*c^3*d^5 + 133500*a^6*b^2*c^2*d^6 - 3240*a*b^7*c^7*d + 15000*a^7*b*c*d^7)/(16777216*a^12*c^3*d^17 + 16777216*b^12*c^15*d^5 - 201326592*a*b^11*c^14*d^6 - 201326592*a^11*b*c^4*d^16 + 1107296256*a^2*b^10*c^13*d^7 - 3690987520*a^3*b^9*c^12*d^8 + 8304721920*a^4*b^8*c^11*d^9 - 13287555072*a^5*b^7*c^10*d^10 + 15502147584*a^6*b^6*c^9*d^11 - 13287555072*a^7*b^5*c^8*d^12 + 8304721920*a^8*b^4*c^7*d^13 - 3690987520*a^9*b^3*c^6*d^14 + 1107296256*a^10*b^2*c^5*d^15))^(1/4)*(1280*a^16*b^4*c*d^18 + 8960*a^3*b^17*c^14*d^5 - 106240*a^4*b^16*c^13*d^6 + 576000*a^5*b^15*c^12*d^7 - 1886720*a^6*b^14*c^11*d^8 + 4153600*a^7*b^13*c^10*d^9 - 6462720*a^8*b^12*c^9*d^10 + 7265280*a^9*b^11*c^8*d^11 - 5913600*a^10*b^10*c^7*d^12 + 3421440*a^11*b^9*c^6*d^13 - 1337600*a^12*b^8*c^5*d^14 + 309760*a^13*b^7*c^4*d^15 - 23040*a^14*b^6*c^3*d^16 - 6400*a^15*b^5*c^2*d^17))/(a^8*d^9 + b^8*c^8*d - 8*a*b^7*c^7*d^2 + 28*a^2*b^6*c^6*d^3 - 56*a^3*b^5*c^5*d^4 + 70*a^4*b^4*c^4*d^5 - 56*a^5*b^3*c^3*d^6 + 28*a^6*b^2*c^2*d^7 - 8*a^7*b*c*d^8) + (x^(1/2)*(409600*a^19*b^4*d^20 + 147456*a^3*b^20*c^16*d^4 + 12058624*a^4*b^19*c^15*d^5 - 141950976*a^5*b^18*c^14*d^6 + 714080256*a^6*b^17*c^13*d^7 - 2086993920*a^7*b^16*c^12*d^8 + 3911712768*a^8*b^15*c^11*d^9 - 4814143488*a^9*b^14*c^10*d^10 + 3714056192*a^10*b^13*c^9*d^11 - 1398177792*a^11*b^12*c^8*d^12 - 259522560*a^12*b^11*c^7*d^13 + 508952576*a^13*b^10*c^6*d^14 - 116391936*a^14*b^9*c^5*d^15 - 103612416*a^15*b^8*c^4*d^16 + 77070336*a^16*b^7*c^3*d^17 - 17694720*a^17*b^6*c^2*d^18)*1i)/(4096*(a^12*d^13 + b^12*c^12*d - 12*a*b^11*c^11*d^2 + 66*a^2*b^10*c^10*d^3 - 220*a^3*b^9*c^9*d^4 + 495*a^4*b^8*c^8*d^5 - 792*a^5*b^7*c^7*d^6 + 924*a^6*b^6*c^6*d^7 - 792*a^7*b^5*c^5*d^8 + 495*a^8*b^4*c^4*d^9 - 220*a^9*b^3*c^3*d^10 + 66*a^10*b^2*c^2*d^11 - 12*a^11*b*c*d^12)))*1i)*1i - (x^(1/2)*(81*a^4*b^15*c^8 + 26225*a^12*b^7*d^8 - 3240*a^5*b^14*c^7*d + 322200*a^11*b^8*c*d^7 + 48060*a^6*b^13*c^6*d^2 - 307800*a^7*b^12*c^5*d^3 + 658566*a^8*b^11*c^4*d^4 + 328680*a^9*b^10*c^3*d^5 + 1024380*a^10*b^9*c^2*d^6)*1i)/(4096*(a^12*d^13 + b^12*c^12*d - 12*a*b^11*c^11*d^2 + 66*a^2*b^10*c^10*d^3 - 220*a^3*b^9*c^9*d^4 + 495*a^4*b^8*c^8*d^5 - 792*a^5*b^7*c^7*d^6 + 924*a^6*b^6*c^6*d^7 - 792*a^7*b^5*c^5*d^8 + 495*a^8*b^4*c^4*d^9 - 220*a^9*b^3*c^3*d^10 + 66*a^10*b^2*c^2*d^11 - 12*a^11*b*c*d^12)))*(-(625*a^8*d^8 + 81*b^8*c^8 + 48060*a^2*b^6*c^6*d^2 - 307800*a^3*b^5*c^5*d^3 + 649350*a^4*b^4*c^4*d^4 + 513000*a^5*b^3*c^3*d^5 + 133500*a^6*b^2*c^2*d^6 - 3240*a*b^7*c^7*d + 15000*a^7*b*c*d^7)/(16777216*a^12*c^3*d^17 + 16777216*b^12*c^15*d^5 - 201326592*a*b^11*c^14*d^6 - 201326592*a^11*b*c^4*d^16 + 1107296256*a^2*b^10*c^13*d^7 - 3690987520*a^3*b^9*c^12*d^8 + 8304721920*a^4*b^8*c^11*d^9 - 13287555072*a^5*b^7*c^10*d^10 + 15502147584*a^6*b^6*c^9*d^11 - 13287555072*a^7*b^5*c^8*d^12 + 8304721920*a^8*b^4*c^7*d^13 - 3690987520*a^9*b^3*c^6*d^14 + 1107296256*a^10*b^2*c^5*d^15))^(1/4)))*(-(625*a^8*d^8 + 81*b^8*c^8 + 48060*a^2*b^6*c^6*d^2 - 307800*a^3*b^5*c^5*d^3 + 649350*a^4*b^4*c^4*d^4 + 513000*a^5*b^3*c^3*d^5 + 133500*a^6*b^2*c^2*d^6 - 3240*a*b^7*c^7*d + 15000*a^7*b*c*d^7)/(16777216*a^12*c^3*d^17 + 16777216*b^12*c^15*d^5 - 201326592*a*b^11*c^14*d^6 - 201326592*a^11*b*c^4*d^16 + 1107296256*a^2*b^10*c^13*d^7 - 3690987520*a^3*b^9*c^12*d^8 + 8304721920*a^4*b^8*c^11*d^9 - 13287555072*a^5*b^7*c^10*d^10 + 15502147584*a^6*b^6*c^9*d^11 - 13287555072*a^7*b^5*c^8*d^12 + 8304721920*a^8*b^4*c^7*d^13 - 3690987520*a^9*b^3*c^6*d^14 + 1107296256*a^10*b^2*c^5*d^15))^(1/4)","B"
481,1,31866,628,4.520623,"\text{Not used}","int(x^(5/2)/((a + b*x^2)*(c + d*x^2)^3),x)","-\mathrm{atan}\left(\frac{\left(\left(\frac{\frac{27\,a^{20}\,b^4\,d^{20}}{16}-\frac{1107\,a^{19}\,b^5\,c\,d^{19}}{16}+\frac{2295\,a^{18}\,b^6\,c^2\,d^{18}}{2}-\frac{20115\,a^{17}\,b^7\,c^3\,d^{17}}{2}+\frac{208665\,a^{16}\,b^8\,c^4\,d^{16}}{4}-\frac{688489\,a^{15}\,b^9\,c^5\,d^{15}}{4}+\frac{744837\,a^{14}\,b^{10}\,c^6\,d^{14}}{2}-\frac{1026465\,a^{13}\,b^{11}\,c^7\,d^{13}}{2}+\frac{2877545\,a^{12}\,b^{12}\,c^8\,d^{12}}{8}+\frac{1117215\,a^{11}\,b^{13}\,c^9\,d^{11}}{8}-\frac{1361943\,a^{10}\,b^{14}\,c^{10}\,d^{10}}{2}+\frac{1760163\,a^9\,b^{15}\,c^{11}\,d^9}{2}-\frac{2723535\,a^8\,b^{16}\,c^{12}\,d^8}{4}+\frac{1382895\,a^7\,b^{17}\,c^{13}\,d^7}{4}-\frac{227605\,a^6\,b^{18}\,c^{14}\,d^6}{2}+\frac{44481\,a^5\,b^{19}\,c^{15}\,d^5}{2}-\frac{31893\,a^4\,b^{20}\,c^{16}\,d^4}{16}+\frac{125\,a^3\,b^{21}\,c^{17}\,d^3}{16}}{a^{14}\,c^2\,d^{14}-14\,a^{13}\,b\,c^3\,d^{13}+91\,a^{12}\,b^2\,c^4\,d^{12}-364\,a^{11}\,b^3\,c^5\,d^{11}+1001\,a^{10}\,b^4\,c^6\,d^{10}-2002\,a^9\,b^5\,c^7\,d^9+3003\,a^8\,b^6\,c^8\,d^8-3432\,a^7\,b^7\,c^9\,d^7+3003\,a^6\,b^8\,c^{10}\,d^6-2002\,a^5\,b^9\,c^{11}\,d^5+1001\,a^4\,b^{10}\,c^{12}\,d^4-364\,a^3\,b^{11}\,c^{13}\,d^3+91\,a^2\,b^{12}\,c^{14}\,d^2-14\,a\,b^{13}\,c^{15}\,d+b^{14}\,c^{16}}-\frac{\sqrt{x}\,{\left(-\frac{a^3\,b^5}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(147456\,a^{19}\,b^4\,c\,d^{20}-4718592\,a^{18}\,b^5\,c^2\,d^{19}+59375616\,a^{17}\,b^6\,c^3\,d^{18}-393216000\,a^{16}\,b^7\,c^4\,d^{17}+1620770816\,a^{15}\,b^8\,c^5\,d^{16}-4594335744\,a^{14}\,b^9\,c^6\,d^{15}+9580707840\,a^{13}\,b^{10}\,c^7\,d^{14}-15479078912\,a^{12}\,b^{11}\,c^8\,d^{13}+20194099200\,a^{11}\,b^{12}\,c^9\,d^{12}-21851799552\,a^{10}\,b^{13}\,c^{10}\,d^{11}+19702087680\,a^9\,b^{14}\,c^{11}\,d^{10}-14511243264\,a^8\,b^{15}\,c^{12}\,d^9+8402436096\,a^7\,b^{16}\,c^{13}\,d^8-3630694400\,a^6\,b^{17}\,c^{14}\,d^7+1089601536\,a^5\,b^{18}\,c^{15}\,d^6-201326592\,a^4\,b^{19}\,c^{16}\,d^5+17186816\,a^3\,b^{20}\,c^{17}\,d^4\right)}{4096\,\left(a^{12}\,c^2\,d^{12}-12\,a^{11}\,b\,c^3\,d^{11}+66\,a^{10}\,b^2\,c^4\,d^{10}-220\,a^9\,b^3\,c^5\,d^9+495\,a^8\,b^4\,c^6\,d^8-792\,a^7\,b^5\,c^7\,d^7+924\,a^6\,b^6\,c^8\,d^6-792\,a^5\,b^7\,c^9\,d^5+495\,a^4\,b^8\,c^{10}\,d^4-220\,a^3\,b^9\,c^{11}\,d^3+66\,a^2\,b^{10}\,c^{12}\,d^2-12\,a\,b^{11}\,c^{13}\,d+b^{12}\,c^{14}\right)}\right)\,{\left(-\frac{a^3\,b^5}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{3/4}\,1{}\mathrm{i}-\frac{\sqrt{x}\,\left(81\,a^{11}\,b^8\,d^9+5976\,a^{10}\,b^9\,c\,d^8-136260\,a^9\,b^{10}\,c^2\,d^7+583080\,a^8\,b^{11}\,c^3\,d^6+956550\,a^7\,b^{12}\,c^4\,d^5+538600\,a^6\,b^{13}\,c^5\,d^4+133500\,a^5\,b^{14}\,c^6\,d^3+15000\,a^4\,b^{15}\,c^7\,d^2+625\,a^3\,b^{16}\,c^8\,d\right)\,1{}\mathrm{i}}{4096\,\left(a^{12}\,c^2\,d^{12}-12\,a^{11}\,b\,c^3\,d^{11}+66\,a^{10}\,b^2\,c^4\,d^{10}-220\,a^9\,b^3\,c^5\,d^9+495\,a^8\,b^4\,c^6\,d^8-792\,a^7\,b^5\,c^7\,d^7+924\,a^6\,b^6\,c^8\,d^6-792\,a^5\,b^7\,c^9\,d^5+495\,a^4\,b^8\,c^{10}\,d^4-220\,a^3\,b^9\,c^{11}\,d^3+66\,a^2\,b^{10}\,c^{12}\,d^2-12\,a\,b^{11}\,c^{13}\,d+b^{12}\,c^{14}\right)}\right)\,{\left(-\frac{a^3\,b^5}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}-\left(\left(\frac{\frac{27\,a^{20}\,b^4\,d^{20}}{16}-\frac{1107\,a^{19}\,b^5\,c\,d^{19}}{16}+\frac{2295\,a^{18}\,b^6\,c^2\,d^{18}}{2}-\frac{20115\,a^{17}\,b^7\,c^3\,d^{17}}{2}+\frac{208665\,a^{16}\,b^8\,c^4\,d^{16}}{4}-\frac{688489\,a^{15}\,b^9\,c^5\,d^{15}}{4}+\frac{744837\,a^{14}\,b^{10}\,c^6\,d^{14}}{2}-\frac{1026465\,a^{13}\,b^{11}\,c^7\,d^{13}}{2}+\frac{2877545\,a^{12}\,b^{12}\,c^8\,d^{12}}{8}+\frac{1117215\,a^{11}\,b^{13}\,c^9\,d^{11}}{8}-\frac{1361943\,a^{10}\,b^{14}\,c^{10}\,d^{10}}{2}+\frac{1760163\,a^9\,b^{15}\,c^{11}\,d^9}{2}-\frac{2723535\,a^8\,b^{16}\,c^{12}\,d^8}{4}+\frac{1382895\,a^7\,b^{17}\,c^{13}\,d^7}{4}-\frac{227605\,a^6\,b^{18}\,c^{14}\,d^6}{2}+\frac{44481\,a^5\,b^{19}\,c^{15}\,d^5}{2}-\frac{31893\,a^4\,b^{20}\,c^{16}\,d^4}{16}+\frac{125\,a^3\,b^{21}\,c^{17}\,d^3}{16}}{a^{14}\,c^2\,d^{14}-14\,a^{13}\,b\,c^3\,d^{13}+91\,a^{12}\,b^2\,c^4\,d^{12}-364\,a^{11}\,b^3\,c^5\,d^{11}+1001\,a^{10}\,b^4\,c^6\,d^{10}-2002\,a^9\,b^5\,c^7\,d^9+3003\,a^8\,b^6\,c^8\,d^8-3432\,a^7\,b^7\,c^9\,d^7+3003\,a^6\,b^8\,c^{10}\,d^6-2002\,a^5\,b^9\,c^{11}\,d^5+1001\,a^4\,b^{10}\,c^{12}\,d^4-364\,a^3\,b^{11}\,c^{13}\,d^3+91\,a^2\,b^{12}\,c^{14}\,d^2-14\,a\,b^{13}\,c^{15}\,d+b^{14}\,c^{16}}+\frac{\sqrt{x}\,{\left(-\frac{a^3\,b^5}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(147456\,a^{19}\,b^4\,c\,d^{20}-4718592\,a^{18}\,b^5\,c^2\,d^{19}+59375616\,a^{17}\,b^6\,c^3\,d^{18}-393216000\,a^{16}\,b^7\,c^4\,d^{17}+1620770816\,a^{15}\,b^8\,c^5\,d^{16}-4594335744\,a^{14}\,b^9\,c^6\,d^{15}+9580707840\,a^{13}\,b^{10}\,c^7\,d^{14}-15479078912\,a^{12}\,b^{11}\,c^8\,d^{13}+20194099200\,a^{11}\,b^{12}\,c^9\,d^{12}-21851799552\,a^{10}\,b^{13}\,c^{10}\,d^{11}+19702087680\,a^9\,b^{14}\,c^{11}\,d^{10}-14511243264\,a^8\,b^{15}\,c^{12}\,d^9+8402436096\,a^7\,b^{16}\,c^{13}\,d^8-3630694400\,a^6\,b^{17}\,c^{14}\,d^7+1089601536\,a^5\,b^{18}\,c^{15}\,d^6-201326592\,a^4\,b^{19}\,c^{16}\,d^5+17186816\,a^3\,b^{20}\,c^{17}\,d^4\right)}{4096\,\left(a^{12}\,c^2\,d^{12}-12\,a^{11}\,b\,c^3\,d^{11}+66\,a^{10}\,b^2\,c^4\,d^{10}-220\,a^9\,b^3\,c^5\,d^9+495\,a^8\,b^4\,c^6\,d^8-792\,a^7\,b^5\,c^7\,d^7+924\,a^6\,b^6\,c^8\,d^6-792\,a^5\,b^7\,c^9\,d^5+495\,a^4\,b^8\,c^{10}\,d^4-220\,a^3\,b^9\,c^{11}\,d^3+66\,a^2\,b^{10}\,c^{12}\,d^2-12\,a\,b^{11}\,c^{13}\,d+b^{12}\,c^{14}\right)}\right)\,{\left(-\frac{a^3\,b^5}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{3/4}\,1{}\mathrm{i}+\frac{\sqrt{x}\,\left(81\,a^{11}\,b^8\,d^9+5976\,a^{10}\,b^9\,c\,d^8-136260\,a^9\,b^{10}\,c^2\,d^7+583080\,a^8\,b^{11}\,c^3\,d^6+956550\,a^7\,b^{12}\,c^4\,d^5+538600\,a^6\,b^{13}\,c^5\,d^4+133500\,a^5\,b^{14}\,c^6\,d^3+15000\,a^4\,b^{15}\,c^7\,d^2+625\,a^3\,b^{16}\,c^8\,d\right)\,1{}\mathrm{i}}{4096\,\left(a^{12}\,c^2\,d^{12}-12\,a^{11}\,b\,c^3\,d^{11}+66\,a^{10}\,b^2\,c^4\,d^{10}-220\,a^9\,b^3\,c^5\,d^9+495\,a^8\,b^4\,c^6\,d^8-792\,a^7\,b^5\,c^7\,d^7+924\,a^6\,b^6\,c^8\,d^6-792\,a^5\,b^7\,c^9\,d^5+495\,a^4\,b^8\,c^{10}\,d^4-220\,a^3\,b^9\,c^{11}\,d^3+66\,a^2\,b^{10}\,c^{12}\,d^2-12\,a\,b^{11}\,c^{13}\,d+b^{12}\,c^{14}\right)}\right)\,{\left(-\frac{a^3\,b^5}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}}{\left(\left(\frac{\frac{27\,a^{20}\,b^4\,d^{20}}{16}-\frac{1107\,a^{19}\,b^5\,c\,d^{19}}{16}+\frac{2295\,a^{18}\,b^6\,c^2\,d^{18}}{2}-\frac{20115\,a^{17}\,b^7\,c^3\,d^{17}}{2}+\frac{208665\,a^{16}\,b^8\,c^4\,d^{16}}{4}-\frac{688489\,a^{15}\,b^9\,c^5\,d^{15}}{4}+\frac{744837\,a^{14}\,b^{10}\,c^6\,d^{14}}{2}-\frac{1026465\,a^{13}\,b^{11}\,c^7\,d^{13}}{2}+\frac{2877545\,a^{12}\,b^{12}\,c^8\,d^{12}}{8}+\frac{1117215\,a^{11}\,b^{13}\,c^9\,d^{11}}{8}-\frac{1361943\,a^{10}\,b^{14}\,c^{10}\,d^{10}}{2}+\frac{1760163\,a^9\,b^{15}\,c^{11}\,d^9}{2}-\frac{2723535\,a^8\,b^{16}\,c^{12}\,d^8}{4}+\frac{1382895\,a^7\,b^{17}\,c^{13}\,d^7}{4}-\frac{227605\,a^6\,b^{18}\,c^{14}\,d^6}{2}+\frac{44481\,a^5\,b^{19}\,c^{15}\,d^5}{2}-\frac{31893\,a^4\,b^{20}\,c^{16}\,d^4}{16}+\frac{125\,a^3\,b^{21}\,c^{17}\,d^3}{16}}{a^{14}\,c^2\,d^{14}-14\,a^{13}\,b\,c^3\,d^{13}+91\,a^{12}\,b^2\,c^4\,d^{12}-364\,a^{11}\,b^3\,c^5\,d^{11}+1001\,a^{10}\,b^4\,c^6\,d^{10}-2002\,a^9\,b^5\,c^7\,d^9+3003\,a^8\,b^6\,c^8\,d^8-3432\,a^7\,b^7\,c^9\,d^7+3003\,a^6\,b^8\,c^{10}\,d^6-2002\,a^5\,b^9\,c^{11}\,d^5+1001\,a^4\,b^{10}\,c^{12}\,d^4-364\,a^3\,b^{11}\,c^{13}\,d^3+91\,a^2\,b^{12}\,c^{14}\,d^2-14\,a\,b^{13}\,c^{15}\,d+b^{14}\,c^{16}}-\frac{\sqrt{x}\,{\left(-\frac{a^3\,b^5}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(147456\,a^{19}\,b^4\,c\,d^{20}-4718592\,a^{18}\,b^5\,c^2\,d^{19}+59375616\,a^{17}\,b^6\,c^3\,d^{18}-393216000\,a^{16}\,b^7\,c^4\,d^{17}+1620770816\,a^{15}\,b^8\,c^5\,d^{16}-4594335744\,a^{14}\,b^9\,c^6\,d^{15}+9580707840\,a^{13}\,b^{10}\,c^7\,d^{14}-15479078912\,a^{12}\,b^{11}\,c^8\,d^{13}+20194099200\,a^{11}\,b^{12}\,c^9\,d^{12}-21851799552\,a^{10}\,b^{13}\,c^{10}\,d^{11}+19702087680\,a^9\,b^{14}\,c^{11}\,d^{10}-14511243264\,a^8\,b^{15}\,c^{12}\,d^9+8402436096\,a^7\,b^{16}\,c^{13}\,d^8-3630694400\,a^6\,b^{17}\,c^{14}\,d^7+1089601536\,a^5\,b^{18}\,c^{15}\,d^6-201326592\,a^4\,b^{19}\,c^{16}\,d^5+17186816\,a^3\,b^{20}\,c^{17}\,d^4\right)}{4096\,\left(a^{12}\,c^2\,d^{12}-12\,a^{11}\,b\,c^3\,d^{11}+66\,a^{10}\,b^2\,c^4\,d^{10}-220\,a^9\,b^3\,c^5\,d^9+495\,a^8\,b^4\,c^6\,d^8-792\,a^7\,b^5\,c^7\,d^7+924\,a^6\,b^6\,c^8\,d^6-792\,a^5\,b^7\,c^9\,d^5+495\,a^4\,b^8\,c^{10}\,d^4-220\,a^3\,b^9\,c^{11}\,d^3+66\,a^2\,b^{10}\,c^{12}\,d^2-12\,a\,b^{11}\,c^{13}\,d+b^{12}\,c^{14}\right)}\right)\,{\left(-\frac{a^3\,b^5}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{3/4}-\frac{\sqrt{x}\,\left(81\,a^{11}\,b^8\,d^9+5976\,a^{10}\,b^9\,c\,d^8-136260\,a^9\,b^{10}\,c^2\,d^7+583080\,a^8\,b^{11}\,c^3\,d^6+956550\,a^7\,b^{12}\,c^4\,d^5+538600\,a^6\,b^{13}\,c^5\,d^4+133500\,a^5\,b^{14}\,c^6\,d^3+15000\,a^4\,b^{15}\,c^7\,d^2+625\,a^3\,b^{16}\,c^8\,d\right)}{4096\,\left(a^{12}\,c^2\,d^{12}-12\,a^{11}\,b\,c^3\,d^{11}+66\,a^{10}\,b^2\,c^4\,d^{10}-220\,a^9\,b^3\,c^5\,d^9+495\,a^8\,b^4\,c^6\,d^8-792\,a^7\,b^5\,c^7\,d^7+924\,a^6\,b^6\,c^8\,d^6-792\,a^5\,b^7\,c^9\,d^5+495\,a^4\,b^8\,c^{10}\,d^4-220\,a^3\,b^9\,c^{11}\,d^3+66\,a^2\,b^{10}\,c^{12}\,d^2-12\,a\,b^{11}\,c^{13}\,d+b^{12}\,c^{14}\right)}\right)\,{\left(-\frac{a^3\,b^5}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}+\left(\left(\frac{\frac{27\,a^{20}\,b^4\,d^{20}}{16}-\frac{1107\,a^{19}\,b^5\,c\,d^{19}}{16}+\frac{2295\,a^{18}\,b^6\,c^2\,d^{18}}{2}-\frac{20115\,a^{17}\,b^7\,c^3\,d^{17}}{2}+\frac{208665\,a^{16}\,b^8\,c^4\,d^{16}}{4}-\frac{688489\,a^{15}\,b^9\,c^5\,d^{15}}{4}+\frac{744837\,a^{14}\,b^{10}\,c^6\,d^{14}}{2}-\frac{1026465\,a^{13}\,b^{11}\,c^7\,d^{13}}{2}+\frac{2877545\,a^{12}\,b^{12}\,c^8\,d^{12}}{8}+\frac{1117215\,a^{11}\,b^{13}\,c^9\,d^{11}}{8}-\frac{1361943\,a^{10}\,b^{14}\,c^{10}\,d^{10}}{2}+\frac{1760163\,a^9\,b^{15}\,c^{11}\,d^9}{2}-\frac{2723535\,a^8\,b^{16}\,c^{12}\,d^8}{4}+\frac{1382895\,a^7\,b^{17}\,c^{13}\,d^7}{4}-\frac{227605\,a^6\,b^{18}\,c^{14}\,d^6}{2}+\frac{44481\,a^5\,b^{19}\,c^{15}\,d^5}{2}-\frac{31893\,a^4\,b^{20}\,c^{16}\,d^4}{16}+\frac{125\,a^3\,b^{21}\,c^{17}\,d^3}{16}}{a^{14}\,c^2\,d^{14}-14\,a^{13}\,b\,c^3\,d^{13}+91\,a^{12}\,b^2\,c^4\,d^{12}-364\,a^{11}\,b^3\,c^5\,d^{11}+1001\,a^{10}\,b^4\,c^6\,d^{10}-2002\,a^9\,b^5\,c^7\,d^9+3003\,a^8\,b^6\,c^8\,d^8-3432\,a^7\,b^7\,c^9\,d^7+3003\,a^6\,b^8\,c^{10}\,d^6-2002\,a^5\,b^9\,c^{11}\,d^5+1001\,a^4\,b^{10}\,c^{12}\,d^4-364\,a^3\,b^{11}\,c^{13}\,d^3+91\,a^2\,b^{12}\,c^{14}\,d^2-14\,a\,b^{13}\,c^{15}\,d+b^{14}\,c^{16}}+\frac{\sqrt{x}\,{\left(-\frac{a^3\,b^5}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(147456\,a^{19}\,b^4\,c\,d^{20}-4718592\,a^{18}\,b^5\,c^2\,d^{19}+59375616\,a^{17}\,b^6\,c^3\,d^{18}-393216000\,a^{16}\,b^7\,c^4\,d^{17}+1620770816\,a^{15}\,b^8\,c^5\,d^{16}-4594335744\,a^{14}\,b^9\,c^6\,d^{15}+9580707840\,a^{13}\,b^{10}\,c^7\,d^{14}-15479078912\,a^{12}\,b^{11}\,c^8\,d^{13}+20194099200\,a^{11}\,b^{12}\,c^9\,d^{12}-21851799552\,a^{10}\,b^{13}\,c^{10}\,d^{11}+19702087680\,a^9\,b^{14}\,c^{11}\,d^{10}-14511243264\,a^8\,b^{15}\,c^{12}\,d^9+8402436096\,a^7\,b^{16}\,c^{13}\,d^8-3630694400\,a^6\,b^{17}\,c^{14}\,d^7+1089601536\,a^5\,b^{18}\,c^{15}\,d^6-201326592\,a^4\,b^{19}\,c^{16}\,d^5+17186816\,a^3\,b^{20}\,c^{17}\,d^4\right)}{4096\,\left(a^{12}\,c^2\,d^{12}-12\,a^{11}\,b\,c^3\,d^{11}+66\,a^{10}\,b^2\,c^4\,d^{10}-220\,a^9\,b^3\,c^5\,d^9+495\,a^8\,b^4\,c^6\,d^8-792\,a^7\,b^5\,c^7\,d^7+924\,a^6\,b^6\,c^8\,d^6-792\,a^5\,b^7\,c^9\,d^5+495\,a^4\,b^8\,c^{10}\,d^4-220\,a^3\,b^9\,c^{11}\,d^3+66\,a^2\,b^{10}\,c^{12}\,d^2-12\,a\,b^{11}\,c^{13}\,d+b^{12}\,c^{14}\right)}\right)\,{\left(-\frac{a^3\,b^5}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{3/4}+\frac{\sqrt{x}\,\left(81\,a^{11}\,b^8\,d^9+5976\,a^{10}\,b^9\,c\,d^8-136260\,a^9\,b^{10}\,c^2\,d^7+583080\,a^8\,b^{11}\,c^3\,d^6+956550\,a^7\,b^{12}\,c^4\,d^5+538600\,a^6\,b^{13}\,c^5\,d^4+133500\,a^5\,b^{14}\,c^6\,d^3+15000\,a^4\,b^{15}\,c^7\,d^2+625\,a^3\,b^{16}\,c^8\,d\right)}{4096\,\left(a^{12}\,c^2\,d^{12}-12\,a^{11}\,b\,c^3\,d^{11}+66\,a^{10}\,b^2\,c^4\,d^{10}-220\,a^9\,b^3\,c^5\,d^9+495\,a^8\,b^4\,c^6\,d^8-792\,a^7\,b^5\,c^7\,d^7+924\,a^6\,b^6\,c^8\,d^6-792\,a^5\,b^7\,c^9\,d^5+495\,a^4\,b^8\,c^{10}\,d^4-220\,a^3\,b^9\,c^{11}\,d^3+66\,a^2\,b^{10}\,c^{12}\,d^2-12\,a\,b^{11}\,c^{13}\,d+b^{12}\,c^{14}\right)}\right)\,{\left(-\frac{a^3\,b^5}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}-\frac{-\frac{945\,a^{11}\,b^9\,d^8}{4096}+\frac{28215\,a^{10}\,b^{10}\,c\,d^7}{4096}-\frac{274725\,a^9\,b^{11}\,c^2\,d^6}{4096}+\frac{810675\,a^8\,b^{12}\,c^3\,d^5}{4096}+\frac{586125\,a^7\,b^{13}\,c^4\,d^4}{4096}+\frac{145125\,a^6\,b^{14}\,c^5\,d^3}{4096}+\frac{15625\,a^5\,b^{15}\,c^6\,d^2}{4096}+\frac{625\,a^4\,b^{16}\,c^7\,d}{4096}}{a^{14}\,c^2\,d^{14}-14\,a^{13}\,b\,c^3\,d^{13}+91\,a^{12}\,b^2\,c^4\,d^{12}-364\,a^{11}\,b^3\,c^5\,d^{11}+1001\,a^{10}\,b^4\,c^6\,d^{10}-2002\,a^9\,b^5\,c^7\,d^9+3003\,a^8\,b^6\,c^8\,d^8-3432\,a^7\,b^7\,c^9\,d^7+3003\,a^6\,b^8\,c^{10}\,d^6-2002\,a^5\,b^9\,c^{11}\,d^5+1001\,a^4\,b^{10}\,c^{12}\,d^4-364\,a^3\,b^{11}\,c^{13}\,d^3+91\,a^2\,b^{12}\,c^{14}\,d^2-14\,a\,b^{13}\,c^{15}\,d+b^{14}\,c^{16}}}\right)\,{\left(-\frac{a^3\,b^5}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}\,2{}\mathrm{i}+2\,\mathrm{atan}\left(\frac{\left(\left(-\frac{\sqrt{x}\,{\left(-\frac{a^3\,b^5}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(147456\,a^{19}\,b^4\,c\,d^{20}-4718592\,a^{18}\,b^5\,c^2\,d^{19}+59375616\,a^{17}\,b^6\,c^3\,d^{18}-393216000\,a^{16}\,b^7\,c^4\,d^{17}+1620770816\,a^{15}\,b^8\,c^5\,d^{16}-4594335744\,a^{14}\,b^9\,c^6\,d^{15}+9580707840\,a^{13}\,b^{10}\,c^7\,d^{14}-15479078912\,a^{12}\,b^{11}\,c^8\,d^{13}+20194099200\,a^{11}\,b^{12}\,c^9\,d^{12}-21851799552\,a^{10}\,b^{13}\,c^{10}\,d^{11}+19702087680\,a^9\,b^{14}\,c^{11}\,d^{10}-14511243264\,a^8\,b^{15}\,c^{12}\,d^9+8402436096\,a^7\,b^{16}\,c^{13}\,d^8-3630694400\,a^6\,b^{17}\,c^{14}\,d^7+1089601536\,a^5\,b^{18}\,c^{15}\,d^6-201326592\,a^4\,b^{19}\,c^{16}\,d^5+17186816\,a^3\,b^{20}\,c^{17}\,d^4\right)}{4096\,\left(a^{12}\,c^2\,d^{12}-12\,a^{11}\,b\,c^3\,d^{11}+66\,a^{10}\,b^2\,c^4\,d^{10}-220\,a^9\,b^3\,c^5\,d^9+495\,a^8\,b^4\,c^6\,d^8-792\,a^7\,b^5\,c^7\,d^7+924\,a^6\,b^6\,c^8\,d^6-792\,a^5\,b^7\,c^9\,d^5+495\,a^4\,b^8\,c^{10}\,d^4-220\,a^3\,b^9\,c^{11}\,d^3+66\,a^2\,b^{10}\,c^{12}\,d^2-12\,a\,b^{11}\,c^{13}\,d+b^{12}\,c^{14}\right)}+\frac{\left(\frac{27\,a^{20}\,b^4\,d^{20}}{16}-\frac{1107\,a^{19}\,b^5\,c\,d^{19}}{16}+\frac{2295\,a^{18}\,b^6\,c^2\,d^{18}}{2}-\frac{20115\,a^{17}\,b^7\,c^3\,d^{17}}{2}+\frac{208665\,a^{16}\,b^8\,c^4\,d^{16}}{4}-\frac{688489\,a^{15}\,b^9\,c^5\,d^{15}}{4}+\frac{744837\,a^{14}\,b^{10}\,c^6\,d^{14}}{2}-\frac{1026465\,a^{13}\,b^{11}\,c^7\,d^{13}}{2}+\frac{2877545\,a^{12}\,b^{12}\,c^8\,d^{12}}{8}+\frac{1117215\,a^{11}\,b^{13}\,c^9\,d^{11}}{8}-\frac{1361943\,a^{10}\,b^{14}\,c^{10}\,d^{10}}{2}+\frac{1760163\,a^9\,b^{15}\,c^{11}\,d^9}{2}-\frac{2723535\,a^8\,b^{16}\,c^{12}\,d^8}{4}+\frac{1382895\,a^7\,b^{17}\,c^{13}\,d^7}{4}-\frac{227605\,a^6\,b^{18}\,c^{14}\,d^6}{2}+\frac{44481\,a^5\,b^{19}\,c^{15}\,d^5}{2}-\frac{31893\,a^4\,b^{20}\,c^{16}\,d^4}{16}+\frac{125\,a^3\,b^{21}\,c^{17}\,d^3}{16}\right)\,1{}\mathrm{i}}{a^{14}\,c^2\,d^{14}-14\,a^{13}\,b\,c^3\,d^{13}+91\,a^{12}\,b^2\,c^4\,d^{12}-364\,a^{11}\,b^3\,c^5\,d^{11}+1001\,a^{10}\,b^4\,c^6\,d^{10}-2002\,a^9\,b^5\,c^7\,d^9+3003\,a^8\,b^6\,c^8\,d^8-3432\,a^7\,b^7\,c^9\,d^7+3003\,a^6\,b^8\,c^{10}\,d^6-2002\,a^5\,b^9\,c^{11}\,d^5+1001\,a^4\,b^{10}\,c^{12}\,d^4-364\,a^3\,b^{11}\,c^{13}\,d^3+91\,a^2\,b^{12}\,c^{14}\,d^2-14\,a\,b^{13}\,c^{15}\,d+b^{14}\,c^{16}}\right)\,{\left(-\frac{a^3\,b^5}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{3/4}-\frac{\sqrt{x}\,\left(81\,a^{11}\,b^8\,d^9+5976\,a^{10}\,b^9\,c\,d^8-136260\,a^9\,b^{10}\,c^2\,d^7+583080\,a^8\,b^{11}\,c^3\,d^6+956550\,a^7\,b^{12}\,c^4\,d^5+538600\,a^6\,b^{13}\,c^5\,d^4+133500\,a^5\,b^{14}\,c^6\,d^3+15000\,a^4\,b^{15}\,c^7\,d^2+625\,a^3\,b^{16}\,c^8\,d\right)}{4096\,\left(a^{12}\,c^2\,d^{12}-12\,a^{11}\,b\,c^3\,d^{11}+66\,a^{10}\,b^2\,c^4\,d^{10}-220\,a^9\,b^3\,c^5\,d^9+495\,a^8\,b^4\,c^6\,d^8-792\,a^7\,b^5\,c^7\,d^7+924\,a^6\,b^6\,c^8\,d^6-792\,a^5\,b^7\,c^9\,d^5+495\,a^4\,b^8\,c^{10}\,d^4-220\,a^3\,b^9\,c^{11}\,d^3+66\,a^2\,b^{10}\,c^{12}\,d^2-12\,a\,b^{11}\,c^{13}\,d+b^{12}\,c^{14}\right)}\right)\,{\left(-\frac{a^3\,b^5}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}-\left(\left(\frac{\sqrt{x}\,{\left(-\frac{a^3\,b^5}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(147456\,a^{19}\,b^4\,c\,d^{20}-4718592\,a^{18}\,b^5\,c^2\,d^{19}+59375616\,a^{17}\,b^6\,c^3\,d^{18}-393216000\,a^{16}\,b^7\,c^4\,d^{17}+1620770816\,a^{15}\,b^8\,c^5\,d^{16}-4594335744\,a^{14}\,b^9\,c^6\,d^{15}+9580707840\,a^{13}\,b^{10}\,c^7\,d^{14}-15479078912\,a^{12}\,b^{11}\,c^8\,d^{13}+20194099200\,a^{11}\,b^{12}\,c^9\,d^{12}-21851799552\,a^{10}\,b^{13}\,c^{10}\,d^{11}+19702087680\,a^9\,b^{14}\,c^{11}\,d^{10}-14511243264\,a^8\,b^{15}\,c^{12}\,d^9+8402436096\,a^7\,b^{16}\,c^{13}\,d^8-3630694400\,a^6\,b^{17}\,c^{14}\,d^7+1089601536\,a^5\,b^{18}\,c^{15}\,d^6-201326592\,a^4\,b^{19}\,c^{16}\,d^5+17186816\,a^3\,b^{20}\,c^{17}\,d^4\right)}{4096\,\left(a^{12}\,c^2\,d^{12}-12\,a^{11}\,b\,c^3\,d^{11}+66\,a^{10}\,b^2\,c^4\,d^{10}-220\,a^9\,b^3\,c^5\,d^9+495\,a^8\,b^4\,c^6\,d^8-792\,a^7\,b^5\,c^7\,d^7+924\,a^6\,b^6\,c^8\,d^6-792\,a^5\,b^7\,c^9\,d^5+495\,a^4\,b^8\,c^{10}\,d^4-220\,a^3\,b^9\,c^{11}\,d^3+66\,a^2\,b^{10}\,c^{12}\,d^2-12\,a\,b^{11}\,c^{13}\,d+b^{12}\,c^{14}\right)}+\frac{\left(\frac{27\,a^{20}\,b^4\,d^{20}}{16}-\frac{1107\,a^{19}\,b^5\,c\,d^{19}}{16}+\frac{2295\,a^{18}\,b^6\,c^2\,d^{18}}{2}-\frac{20115\,a^{17}\,b^7\,c^3\,d^{17}}{2}+\frac{208665\,a^{16}\,b^8\,c^4\,d^{16}}{4}-\frac{688489\,a^{15}\,b^9\,c^5\,d^{15}}{4}+\frac{744837\,a^{14}\,b^{10}\,c^6\,d^{14}}{2}-\frac{1026465\,a^{13}\,b^{11}\,c^7\,d^{13}}{2}+\frac{2877545\,a^{12}\,b^{12}\,c^8\,d^{12}}{8}+\frac{1117215\,a^{11}\,b^{13}\,c^9\,d^{11}}{8}-\frac{1361943\,a^{10}\,b^{14}\,c^{10}\,d^{10}}{2}+\frac{1760163\,a^9\,b^{15}\,c^{11}\,d^9}{2}-\frac{2723535\,a^8\,b^{16}\,c^{12}\,d^8}{4}+\frac{1382895\,a^7\,b^{17}\,c^{13}\,d^7}{4}-\frac{227605\,a^6\,b^{18}\,c^{14}\,d^6}{2}+\frac{44481\,a^5\,b^{19}\,c^{15}\,d^5}{2}-\frac{31893\,a^4\,b^{20}\,c^{16}\,d^4}{16}+\frac{125\,a^3\,b^{21}\,c^{17}\,d^3}{16}\right)\,1{}\mathrm{i}}{a^{14}\,c^2\,d^{14}-14\,a^{13}\,b\,c^3\,d^{13}+91\,a^{12}\,b^2\,c^4\,d^{12}-364\,a^{11}\,b^3\,c^5\,d^{11}+1001\,a^{10}\,b^4\,c^6\,d^{10}-2002\,a^9\,b^5\,c^7\,d^9+3003\,a^8\,b^6\,c^8\,d^8-3432\,a^7\,b^7\,c^9\,d^7+3003\,a^6\,b^8\,c^{10}\,d^6-2002\,a^5\,b^9\,c^{11}\,d^5+1001\,a^4\,b^{10}\,c^{12}\,d^4-364\,a^3\,b^{11}\,c^{13}\,d^3+91\,a^2\,b^{12}\,c^{14}\,d^2-14\,a\,b^{13}\,c^{15}\,d+b^{14}\,c^{16}}\right)\,{\left(-\frac{a^3\,b^5}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{3/4}+\frac{\sqrt{x}\,\left(81\,a^{11}\,b^8\,d^9+5976\,a^{10}\,b^9\,c\,d^8-136260\,a^9\,b^{10}\,c^2\,d^7+583080\,a^8\,b^{11}\,c^3\,d^6+956550\,a^7\,b^{12}\,c^4\,d^5+538600\,a^6\,b^{13}\,c^5\,d^4+133500\,a^5\,b^{14}\,c^6\,d^3+15000\,a^4\,b^{15}\,c^7\,d^2+625\,a^3\,b^{16}\,c^8\,d\right)}{4096\,\left(a^{12}\,c^2\,d^{12}-12\,a^{11}\,b\,c^3\,d^{11}+66\,a^{10}\,b^2\,c^4\,d^{10}-220\,a^9\,b^3\,c^5\,d^9+495\,a^8\,b^4\,c^6\,d^8-792\,a^7\,b^5\,c^7\,d^7+924\,a^6\,b^6\,c^8\,d^6-792\,a^5\,b^7\,c^9\,d^5+495\,a^4\,b^8\,c^{10}\,d^4-220\,a^3\,b^9\,c^{11}\,d^3+66\,a^2\,b^{10}\,c^{12}\,d^2-12\,a\,b^{11}\,c^{13}\,d+b^{12}\,c^{14}\right)}\right)\,{\left(-\frac{a^3\,b^5}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}}{\left(\left(-\frac{\sqrt{x}\,{\left(-\frac{a^3\,b^5}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(147456\,a^{19}\,b^4\,c\,d^{20}-4718592\,a^{18}\,b^5\,c^2\,d^{19}+59375616\,a^{17}\,b^6\,c^3\,d^{18}-393216000\,a^{16}\,b^7\,c^4\,d^{17}+1620770816\,a^{15}\,b^8\,c^5\,d^{16}-4594335744\,a^{14}\,b^9\,c^6\,d^{15}+9580707840\,a^{13}\,b^{10}\,c^7\,d^{14}-15479078912\,a^{12}\,b^{11}\,c^8\,d^{13}+20194099200\,a^{11}\,b^{12}\,c^9\,d^{12}-21851799552\,a^{10}\,b^{13}\,c^{10}\,d^{11}+19702087680\,a^9\,b^{14}\,c^{11}\,d^{10}-14511243264\,a^8\,b^{15}\,c^{12}\,d^9+8402436096\,a^7\,b^{16}\,c^{13}\,d^8-3630694400\,a^6\,b^{17}\,c^{14}\,d^7+1089601536\,a^5\,b^{18}\,c^{15}\,d^6-201326592\,a^4\,b^{19}\,c^{16}\,d^5+17186816\,a^3\,b^{20}\,c^{17}\,d^4\right)}{4096\,\left(a^{12}\,c^2\,d^{12}-12\,a^{11}\,b\,c^3\,d^{11}+66\,a^{10}\,b^2\,c^4\,d^{10}-220\,a^9\,b^3\,c^5\,d^9+495\,a^8\,b^4\,c^6\,d^8-792\,a^7\,b^5\,c^7\,d^7+924\,a^6\,b^6\,c^8\,d^6-792\,a^5\,b^7\,c^9\,d^5+495\,a^4\,b^8\,c^{10}\,d^4-220\,a^3\,b^9\,c^{11}\,d^3+66\,a^2\,b^{10}\,c^{12}\,d^2-12\,a\,b^{11}\,c^{13}\,d+b^{12}\,c^{14}\right)}+\frac{\left(\frac{27\,a^{20}\,b^4\,d^{20}}{16}-\frac{1107\,a^{19}\,b^5\,c\,d^{19}}{16}+\frac{2295\,a^{18}\,b^6\,c^2\,d^{18}}{2}-\frac{20115\,a^{17}\,b^7\,c^3\,d^{17}}{2}+\frac{208665\,a^{16}\,b^8\,c^4\,d^{16}}{4}-\frac{688489\,a^{15}\,b^9\,c^5\,d^{15}}{4}+\frac{744837\,a^{14}\,b^{10}\,c^6\,d^{14}}{2}-\frac{1026465\,a^{13}\,b^{11}\,c^7\,d^{13}}{2}+\frac{2877545\,a^{12}\,b^{12}\,c^8\,d^{12}}{8}+\frac{1117215\,a^{11}\,b^{13}\,c^9\,d^{11}}{8}-\frac{1361943\,a^{10}\,b^{14}\,c^{10}\,d^{10}}{2}+\frac{1760163\,a^9\,b^{15}\,c^{11}\,d^9}{2}-\frac{2723535\,a^8\,b^{16}\,c^{12}\,d^8}{4}+\frac{1382895\,a^7\,b^{17}\,c^{13}\,d^7}{4}-\frac{227605\,a^6\,b^{18}\,c^{14}\,d^6}{2}+\frac{44481\,a^5\,b^{19}\,c^{15}\,d^5}{2}-\frac{31893\,a^4\,b^{20}\,c^{16}\,d^4}{16}+\frac{125\,a^3\,b^{21}\,c^{17}\,d^3}{16}\right)\,1{}\mathrm{i}}{a^{14}\,c^2\,d^{14}-14\,a^{13}\,b\,c^3\,d^{13}+91\,a^{12}\,b^2\,c^4\,d^{12}-364\,a^{11}\,b^3\,c^5\,d^{11}+1001\,a^{10}\,b^4\,c^6\,d^{10}-2002\,a^9\,b^5\,c^7\,d^9+3003\,a^8\,b^6\,c^8\,d^8-3432\,a^7\,b^7\,c^9\,d^7+3003\,a^6\,b^8\,c^{10}\,d^6-2002\,a^5\,b^9\,c^{11}\,d^5+1001\,a^4\,b^{10}\,c^{12}\,d^4-364\,a^3\,b^{11}\,c^{13}\,d^3+91\,a^2\,b^{12}\,c^{14}\,d^2-14\,a\,b^{13}\,c^{15}\,d+b^{14}\,c^{16}}\right)\,{\left(-\frac{a^3\,b^5}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{3/4}\,1{}\mathrm{i}-\frac{\sqrt{x}\,\left(81\,a^{11}\,b^8\,d^9+5976\,a^{10}\,b^9\,c\,d^8-136260\,a^9\,b^{10}\,c^2\,d^7+583080\,a^8\,b^{11}\,c^3\,d^6+956550\,a^7\,b^{12}\,c^4\,d^5+538600\,a^6\,b^{13}\,c^5\,d^4+133500\,a^5\,b^{14}\,c^6\,d^3+15000\,a^4\,b^{15}\,c^7\,d^2+625\,a^3\,b^{16}\,c^8\,d\right)\,1{}\mathrm{i}}{4096\,\left(a^{12}\,c^2\,d^{12}-12\,a^{11}\,b\,c^3\,d^{11}+66\,a^{10}\,b^2\,c^4\,d^{10}-220\,a^9\,b^3\,c^5\,d^9+495\,a^8\,b^4\,c^6\,d^8-792\,a^7\,b^5\,c^7\,d^7+924\,a^6\,b^6\,c^8\,d^6-792\,a^5\,b^7\,c^9\,d^5+495\,a^4\,b^8\,c^{10}\,d^4-220\,a^3\,b^9\,c^{11}\,d^3+66\,a^2\,b^{10}\,c^{12}\,d^2-12\,a\,b^{11}\,c^{13}\,d+b^{12}\,c^{14}\right)}\right)\,{\left(-\frac{a^3\,b^5}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}+\left(\left(\frac{\sqrt{x}\,{\left(-\frac{a^3\,b^5}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(147456\,a^{19}\,b^4\,c\,d^{20}-4718592\,a^{18}\,b^5\,c^2\,d^{19}+59375616\,a^{17}\,b^6\,c^3\,d^{18}-393216000\,a^{16}\,b^7\,c^4\,d^{17}+1620770816\,a^{15}\,b^8\,c^5\,d^{16}-4594335744\,a^{14}\,b^9\,c^6\,d^{15}+9580707840\,a^{13}\,b^{10}\,c^7\,d^{14}-15479078912\,a^{12}\,b^{11}\,c^8\,d^{13}+20194099200\,a^{11}\,b^{12}\,c^9\,d^{12}-21851799552\,a^{10}\,b^{13}\,c^{10}\,d^{11}+19702087680\,a^9\,b^{14}\,c^{11}\,d^{10}-14511243264\,a^8\,b^{15}\,c^{12}\,d^9+8402436096\,a^7\,b^{16}\,c^{13}\,d^8-3630694400\,a^6\,b^{17}\,c^{14}\,d^7+1089601536\,a^5\,b^{18}\,c^{15}\,d^6-201326592\,a^4\,b^{19}\,c^{16}\,d^5+17186816\,a^3\,b^{20}\,c^{17}\,d^4\right)}{4096\,\left(a^{12}\,c^2\,d^{12}-12\,a^{11}\,b\,c^3\,d^{11}+66\,a^{10}\,b^2\,c^4\,d^{10}-220\,a^9\,b^3\,c^5\,d^9+495\,a^8\,b^4\,c^6\,d^8-792\,a^7\,b^5\,c^7\,d^7+924\,a^6\,b^6\,c^8\,d^6-792\,a^5\,b^7\,c^9\,d^5+495\,a^4\,b^8\,c^{10}\,d^4-220\,a^3\,b^9\,c^{11}\,d^3+66\,a^2\,b^{10}\,c^{12}\,d^2-12\,a\,b^{11}\,c^{13}\,d+b^{12}\,c^{14}\right)}+\frac{\left(\frac{27\,a^{20}\,b^4\,d^{20}}{16}-\frac{1107\,a^{19}\,b^5\,c\,d^{19}}{16}+\frac{2295\,a^{18}\,b^6\,c^2\,d^{18}}{2}-\frac{20115\,a^{17}\,b^7\,c^3\,d^{17}}{2}+\frac{208665\,a^{16}\,b^8\,c^4\,d^{16}}{4}-\frac{688489\,a^{15}\,b^9\,c^5\,d^{15}}{4}+\frac{744837\,a^{14}\,b^{10}\,c^6\,d^{14}}{2}-\frac{1026465\,a^{13}\,b^{11}\,c^7\,d^{13}}{2}+\frac{2877545\,a^{12}\,b^{12}\,c^8\,d^{12}}{8}+\frac{1117215\,a^{11}\,b^{13}\,c^9\,d^{11}}{8}-\frac{1361943\,a^{10}\,b^{14}\,c^{10}\,d^{10}}{2}+\frac{1760163\,a^9\,b^{15}\,c^{11}\,d^9}{2}-\frac{2723535\,a^8\,b^{16}\,c^{12}\,d^8}{4}+\frac{1382895\,a^7\,b^{17}\,c^{13}\,d^7}{4}-\frac{227605\,a^6\,b^{18}\,c^{14}\,d^6}{2}+\frac{44481\,a^5\,b^{19}\,c^{15}\,d^5}{2}-\frac{31893\,a^4\,b^{20}\,c^{16}\,d^4}{16}+\frac{125\,a^3\,b^{21}\,c^{17}\,d^3}{16}\right)\,1{}\mathrm{i}}{a^{14}\,c^2\,d^{14}-14\,a^{13}\,b\,c^3\,d^{13}+91\,a^{12}\,b^2\,c^4\,d^{12}-364\,a^{11}\,b^3\,c^5\,d^{11}+1001\,a^{10}\,b^4\,c^6\,d^{10}-2002\,a^9\,b^5\,c^7\,d^9+3003\,a^8\,b^6\,c^8\,d^8-3432\,a^7\,b^7\,c^9\,d^7+3003\,a^6\,b^8\,c^{10}\,d^6-2002\,a^5\,b^9\,c^{11}\,d^5+1001\,a^4\,b^{10}\,c^{12}\,d^4-364\,a^3\,b^{11}\,c^{13}\,d^3+91\,a^2\,b^{12}\,c^{14}\,d^2-14\,a\,b^{13}\,c^{15}\,d+b^{14}\,c^{16}}\right)\,{\left(-\frac{a^3\,b^5}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{3/4}\,1{}\mathrm{i}+\frac{\sqrt{x}\,\left(81\,a^{11}\,b^8\,d^9+5976\,a^{10}\,b^9\,c\,d^8-136260\,a^9\,b^{10}\,c^2\,d^7+583080\,a^8\,b^{11}\,c^3\,d^6+956550\,a^7\,b^{12}\,c^4\,d^5+538600\,a^6\,b^{13}\,c^5\,d^4+133500\,a^5\,b^{14}\,c^6\,d^3+15000\,a^4\,b^{15}\,c^7\,d^2+625\,a^3\,b^{16}\,c^8\,d\right)\,1{}\mathrm{i}}{4096\,\left(a^{12}\,c^2\,d^{12}-12\,a^{11}\,b\,c^3\,d^{11}+66\,a^{10}\,b^2\,c^4\,d^{10}-220\,a^9\,b^3\,c^5\,d^9+495\,a^8\,b^4\,c^6\,d^8-792\,a^7\,b^5\,c^7\,d^7+924\,a^6\,b^6\,c^8\,d^6-792\,a^5\,b^7\,c^9\,d^5+495\,a^4\,b^8\,c^{10}\,d^4-220\,a^3\,b^9\,c^{11}\,d^3+66\,a^2\,b^{10}\,c^{12}\,d^2-12\,a\,b^{11}\,c^{13}\,d+b^{12}\,c^{14}\right)}\right)\,{\left(-\frac{a^3\,b^5}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}+\frac{-\frac{945\,a^{11}\,b^9\,d^8}{4096}+\frac{28215\,a^{10}\,b^{10}\,c\,d^7}{4096}-\frac{274725\,a^9\,b^{11}\,c^2\,d^6}{4096}+\frac{810675\,a^8\,b^{12}\,c^3\,d^5}{4096}+\frac{586125\,a^7\,b^{13}\,c^4\,d^4}{4096}+\frac{145125\,a^6\,b^{14}\,c^5\,d^3}{4096}+\frac{15625\,a^5\,b^{15}\,c^6\,d^2}{4096}+\frac{625\,a^4\,b^{16}\,c^7\,d}{4096}}{a^{14}\,c^2\,d^{14}-14\,a^{13}\,b\,c^3\,d^{13}+91\,a^{12}\,b^2\,c^4\,d^{12}-364\,a^{11}\,b^3\,c^5\,d^{11}+1001\,a^{10}\,b^4\,c^6\,d^{10}-2002\,a^9\,b^5\,c^7\,d^9+3003\,a^8\,b^6\,c^8\,d^8-3432\,a^7\,b^7\,c^9\,d^7+3003\,a^6\,b^8\,c^{10}\,d^6-2002\,a^5\,b^9\,c^{11}\,d^5+1001\,a^4\,b^{10}\,c^{12}\,d^4-364\,a^3\,b^{11}\,c^{13}\,d^3+91\,a^2\,b^{12}\,c^{14}\,d^2-14\,a\,b^{13}\,c^{15}\,d+b^{14}\,c^{16}}}\right)\,{\left(-\frac{a^3\,b^5}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}-\mathrm{atan}\left(\frac{\left(\left(\frac{\frac{27\,a^{20}\,b^4\,d^{20}}{16}-\frac{1107\,a^{19}\,b^5\,c\,d^{19}}{16}+\frac{2295\,a^{18}\,b^6\,c^2\,d^{18}}{2}-\frac{20115\,a^{17}\,b^7\,c^3\,d^{17}}{2}+\frac{208665\,a^{16}\,b^8\,c^4\,d^{16}}{4}-\frac{688489\,a^{15}\,b^9\,c^5\,d^{15}}{4}+\frac{744837\,a^{14}\,b^{10}\,c^6\,d^{14}}{2}-\frac{1026465\,a^{13}\,b^{11}\,c^7\,d^{13}}{2}+\frac{2877545\,a^{12}\,b^{12}\,c^8\,d^{12}}{8}+\frac{1117215\,a^{11}\,b^{13}\,c^9\,d^{11}}{8}-\frac{1361943\,a^{10}\,b^{14}\,c^{10}\,d^{10}}{2}+\frac{1760163\,a^9\,b^{15}\,c^{11}\,d^9}{2}-\frac{2723535\,a^8\,b^{16}\,c^{12}\,d^8}{4}+\frac{1382895\,a^7\,b^{17}\,c^{13}\,d^7}{4}-\frac{227605\,a^6\,b^{18}\,c^{14}\,d^6}{2}+\frac{44481\,a^5\,b^{19}\,c^{15}\,d^5}{2}-\frac{31893\,a^4\,b^{20}\,c^{16}\,d^4}{16}+\frac{125\,a^3\,b^{21}\,c^{17}\,d^3}{16}}{a^{14}\,c^2\,d^{14}-14\,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4}+\left(\left(\frac{\sqrt{x}\,{\left(-\frac{81\,a^8\,d^8-3240\,a^7\,b\,c\,d^7+48060\,a^6\,b^2\,c^2\,d^6-307800\,a^5\,b^3\,c^3\,d^5+649350\,a^4\,b^4\,c^4\,d^4+513000\,a^3\,b^5\,c^5\,d^3+133500\,a^2\,b^6\,c^6\,d^2+15000\,a\,b^7\,c^7\,d+625\,b^8\,c^8}{16777216\,a^{12}\,c^5\,d^{15}-201326592\,a^{11}\,b\,c^6\,d^{14}+1107296256\,a^{10}\,b^2\,c^7\,d^{13}-3690987520\,a^9\,b^3\,c^8\,d^{12}+8304721920\,a^8\,b^4\,c^9\,d^{11}-13287555072\,a^7\,b^5\,c^{10}\,d^{10}+15502147584\,a^6\,b^6\,c^{11}\,d^9-13287555072\,a^5\,b^7\,c^{12}\,d^8+8304721920\,a^4\,b^8\,c^{13}\,d^7-3690987520\,a^3\,b^9\,c^{14}\,d^6+1107296256\,a^2\,b^{10}\,c^{15}\,d^5-201326592\,a\,b^{11}\,c^{16}\,d^4+16777216\,b^{12}\,c^{17}\,d^3}\right)}^{1/4}\,\left(147456\,a^{19}\,b^4\,c\,d^{20}-4718592\,a^{18}\,b^5\,c^2\,d^{19}+59375616\,a^{17}\,b^6\,c^3\,d^{18}-393216000\,a^{16}\,b^7\,c^4\,d^{17}+1620770816\,a^{15}\,b^8\,c^5\,d^{16}-4594335744\,a^{14}\,b^9\,c^6\,d^{15}+9580707840\,a^{13}\,b^{10}\,c^7\,d^{14}-15479078912\,a^{12}\,b^{11}\,c^8\,d^{13}+20194099200\,a^{11}\,b^{12}\,c^9\,d^{12}-21851799552\,a^{10}\,b^{13}\,c^{10}\,d^{11}+19702087680\,a^9\,b^{14}\,c^{11}\,d^{10}-14511243264\,a^8\,b^{15}\,c^{12}\,d^9+8402436096\,a^7\,b^{16}\,c^{13}\,d^8-3630694400\,a^6\,b^{17}\,c^{14}\,d^7+1089601536\,a^5\,b^{18}\,c^{15}\,d^6-201326592\,a^4\,b^{19}\,c^{16}\,d^5+17186816\,a^3\,b^{20}\,c^{17}\,d^4\right)}{4096\,\left(a^{12}\,c^2\,d^{12}-12\,a^{11}\,b\,c^3\,d^{11}+66\,a^{10}\,b^2\,c^4\,d^{10}-220\,a^9\,b^3\,c^5\,d^9+495\,a^8\,b^4\,c^6\,d^8-792\,a^7\,b^5\,c^7\,d^7+924\,a^6\,b^6\,c^8\,d^6-792\,a^5\,b^7\,c^9\,d^5+495\,a^4\,b^8\,c^{10}\,d^4-220\,a^3\,b^9\,c^{11}\,d^3+66\,a^2\,b^{10}\,c^{12}\,d^2-12\,a\,b^{11}\,c^{13}\,d+b^{12}\,c^{14}\right)}+\frac{\left(\frac{27\,a^{20}\,b^4\,d^{20}}{16}-\frac{1107\,a^{19}\,b^5\,c\,d^{19}}{16}+\frac{2295\,a^{18}\,b^6\,c^2\,d^{18}}{2}-\frac{20115\,a^{17}\,b^7\,c^3\,d^{17}}{2}+\frac{208665\,a^{16}\,b^8\,c^4\,d^{16}}{4}-\frac{688489\,a^{15}\,b^9\,c^5\,d^{15}}{4}+\frac{744837\,a^{14}\,b^{10}\,c^6\,d^{14}}{2}-\frac{1026465\,a^{13}\,b^{11}\,c^7\,d^{13}}{2}+\frac{2877545\,a^{12}\,b^{12}\,c^8\,d^{12}}{8}+\frac{1117215\,a^{11}\,b^{13}\,c^9\,d^{11}}{8}-\frac{1361943\,a^{10}\,b^{14}\,c^{10}\,d^{10}}{2}+\frac{1760163\,a^9\,b^{15}\,c^{11}\,d^9}{2}-\frac{2723535\,a^8\,b^{16}\,c^{12}\,d^8}{4}+\frac{1382895\,a^7\,b^{17}\,c^{13}\,d^7}{4}-\frac{227605\,a^6\,b^{18}\,c^{14}\,d^6}{2}+\frac{44481\,a^5\,b^{19}\,c^{15}\,d^5}{2}-\frac{31893\,a^4\,b^{20}\,c^{16}\,d^4}{16}+\frac{125\,a^3\,b^{21}\,c^{17}\,d^3}{16}\right)\,1{}\mathrm{i}}{a^{14}\,c^2\,d^{14}-14\,a^{13}\,b\,c^3\,d^{13}+91\,a^{12}\,b^2\,c^4\,d^{12}-364\,a^{11}\,b^3\,c^5\,d^{11}+1001\,a^{10}\,b^4\,c^6\,d^{10}-2002\,a^9\,b^5\,c^7\,d^9+3003\,a^8\,b^6\,c^8\,d^8-3432\,a^7\,b^7\,c^9\,d^7+3003\,a^6\,b^8\,c^{10}\,d^6-2002\,a^5\,b^9\,c^{11}\,d^5+1001\,a^4\,b^{10}\,c^{12}\,d^4-364\,a^3\,b^{11}\,c^{13}\,d^3+91\,a^2\,b^{12}\,c^{14}\,d^2-14\,a\,b^{13}\,c^{15}\,d+b^{14}\,c^{16}}\right)\,{\left(-\frac{81\,a^8\,d^8-3240\,a^7\,b\,c\,d^7+48060\,a^6\,b^2\,c^2\,d^6-307800\,a^5\,b^3\,c^3\,d^5+649350\,a^4\,b^4\,c^4\,d^4+513000\,a^3\,b^5\,c^5\,d^3+133500\,a^2\,b^6\,c^6\,d^2+15000\,a\,b^7\,c^7\,d+625\,b^8\,c^8}{16777216\,a^{12}\,c^5\,d^{15}-201326592\,a^{11}\,b\,c^6\,d^{14}+1107296256\,a^{10}\,b^2\,c^7\,d^{13}-3690987520\,a^9\,b^3\,c^8\,d^{12}+8304721920\,a^8\,b^4\,c^9\,d^{11}-13287555072\,a^7\,b^5\,c^{10}\,d^{10}+15502147584\,a^6\,b^6\,c^{11}\,d^9-13287555072\,a^5\,b^7\,c^{12}\,d^8+8304721920\,a^4\,b^8\,c^{13}\,d^7-3690987520\,a^3\,b^9\,c^{14}\,d^6+1107296256\,a^2\,b^{10}\,c^{15}\,d^5-201326592\,a\,b^{11}\,c^{16}\,d^4+16777216\,b^{12}\,c^{17}\,d^3}\right)}^{3/4}\,1{}\mathrm{i}+\frac{\sqrt{x}\,\left(81\,a^{11}\,b^8\,d^9+5976\,a^{10}\,b^9\,c\,d^8-136260\,a^9\,b^{10}\,c^2\,d^7+583080\,a^8\,b^{11}\,c^3\,d^6+956550\,a^7\,b^{12}\,c^4\,d^5+538600\,a^6\,b^{13}\,c^5\,d^4+133500\,a^5\,b^{14}\,c^6\,d^3+15000\,a^4\,b^{15}\,c^7\,d^2+625\,a^3\,b^{16}\,c^8\,d\right)\,1{}\mathrm{i}}{4096\,\left(a^{12}\,c^2\,d^{12}-12\,a^{11}\,b\,c^3\,d^{11}+66\,a^{10}\,b^2\,c^4\,d^{10}-220\,a^9\,b^3\,c^5\,d^9+495\,a^8\,b^4\,c^6\,d^8-792\,a^7\,b^5\,c^7\,d^7+924\,a^6\,b^6\,c^8\,d^6-792\,a^5\,b^7\,c^9\,d^5+495\,a^4\,b^8\,c^{10}\,d^4-220\,a^3\,b^9\,c^{11}\,d^3+66\,a^2\,b^{10}\,c^{12}\,d^2-12\,a\,b^{11}\,c^{13}\,d+b^{12}\,c^{14}\right)}\right)\,{\left(-\frac{81\,a^8\,d^8-3240\,a^7\,b\,c\,d^7+48060\,a^6\,b^2\,c^2\,d^6-307800\,a^5\,b^3\,c^3\,d^5+649350\,a^4\,b^4\,c^4\,d^4+513000\,a^3\,b^5\,c^5\,d^3+133500\,a^2\,b^6\,c^6\,d^2+15000\,a\,b^7\,c^7\,d+625\,b^8\,c^8}{16777216\,a^{12}\,c^5\,d^{15}-201326592\,a^{11}\,b\,c^6\,d^{14}+1107296256\,a^{10}\,b^2\,c^7\,d^{13}-3690987520\,a^9\,b^3\,c^8\,d^{12}+8304721920\,a^8\,b^4\,c^9\,d^{11}-13287555072\,a^7\,b^5\,c^{10}\,d^{10}+15502147584\,a^6\,b^6\,c^{11}\,d^9-13287555072\,a^5\,b^7\,c^{12}\,d^8+8304721920\,a^4\,b^8\,c^{13}\,d^7-3690987520\,a^3\,b^9\,c^{14}\,d^6+1107296256\,a^2\,b^{10}\,c^{15}\,d^5-201326592\,a\,b^{11}\,c^{16}\,d^4+16777216\,b^{12}\,c^{17}\,d^3}\right)}^{1/4}+\frac{-\frac{945\,a^{11}\,b^9\,d^8}{4096}+\frac{28215\,a^{10}\,b^{10}\,c\,d^7}{4096}-\frac{274725\,a^9\,b^{11}\,c^2\,d^6}{4096}+\frac{810675\,a^8\,b^{12}\,c^3\,d^5}{4096}+\frac{586125\,a^7\,b^{13}\,c^4\,d^4}{4096}+\frac{145125\,a^6\,b^{14}\,c^5\,d^3}{4096}+\frac{15625\,a^5\,b^{15}\,c^6\,d^2}{4096}+\frac{625\,a^4\,b^{16}\,c^7\,d}{4096}}{a^{14}\,c^2\,d^{14}-14\,a^{13}\,b\,c^3\,d^{13}+91\,a^{12}\,b^2\,c^4\,d^{12}-364\,a^{11}\,b^3\,c^5\,d^{11}+1001\,a^{10}\,b^4\,c^6\,d^{10}-2002\,a^9\,b^5\,c^7\,d^9+3003\,a^8\,b^6\,c^8\,d^8-3432\,a^7\,b^7\,c^9\,d^7+3003\,a^6\,b^8\,c^{10}\,d^6-2002\,a^5\,b^9\,c^{11}\,d^5+1001\,a^4\,b^{10}\,c^{12}\,d^4-364\,a^3\,b^{11}\,c^{13}\,d^3+91\,a^2\,b^{12}\,c^{14}\,d^2-14\,a\,b^{13}\,c^{15}\,d+b^{14}\,c^{16}}}\right)\,{\left(-\frac{81\,a^8\,d^8-3240\,a^7\,b\,c\,d^7+48060\,a^6\,b^2\,c^2\,d^6-307800\,a^5\,b^3\,c^3\,d^5+649350\,a^4\,b^4\,c^4\,d^4+513000\,a^3\,b^5\,c^5\,d^3+133500\,a^2\,b^6\,c^6\,d^2+15000\,a\,b^7\,c^7\,d+625\,b^8\,c^8}{16777216\,a^{12}\,c^5\,d^{15}-201326592\,a^{11}\,b\,c^6\,d^{14}+1107296256\,a^{10}\,b^2\,c^7\,d^{13}-3690987520\,a^9\,b^3\,c^8\,d^{12}+8304721920\,a^8\,b^4\,c^9\,d^{11}-13287555072\,a^7\,b^5\,c^{10}\,d^{10}+15502147584\,a^6\,b^6\,c^{11}\,d^9-13287555072\,a^5\,b^7\,c^{12}\,d^8+8304721920\,a^4\,b^8\,c^{13}\,d^7-3690987520\,a^3\,b^9\,c^{14}\,d^6+1107296256\,a^2\,b^{10}\,c^{15}\,d^5-201326592\,a\,b^{11}\,c^{16}\,d^4+16777216\,b^{12}\,c^{17}\,d^3}\right)}^{1/4}-\frac{\frac{x^{3/2}\,\left(a\,d-9\,b\,c\right)}{16\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}-\frac{d\,x^{7/2}\,\left(3\,a\,d+5\,b\,c\right)}{16\,\left(a^2\,c\,d^2-2\,a\,b\,c^2\,d+b^2\,c^3\right)}}{c^2+2\,c\,d\,x^2+d^2\,x^4}","Not used",1,"2*atan(((((((27*a^20*b^4*d^20)/16 - (1107*a^19*b^5*c*d^19)/16 + (125*a^3*b^21*c^17*d^3)/16 - (31893*a^4*b^20*c^16*d^4)/16 + (44481*a^5*b^19*c^15*d^5)/2 - (227605*a^6*b^18*c^14*d^6)/2 + (1382895*a^7*b^17*c^13*d^7)/4 - (2723535*a^8*b^16*c^12*d^8)/4 + (1760163*a^9*b^15*c^11*d^9)/2 - (1361943*a^10*b^14*c^10*d^10)/2 + (1117215*a^11*b^13*c^9*d^11)/8 + (2877545*a^12*b^12*c^8*d^12)/8 - (1026465*a^13*b^11*c^7*d^13)/2 + (744837*a^14*b^10*c^6*d^14)/2 - (688489*a^15*b^9*c^5*d^15)/4 + (208665*a^16*b^8*c^4*d^16)/4 - (20115*a^17*b^7*c^3*d^17)/2 + (2295*a^18*b^6*c^2*d^18)/2)*1i)/(b^14*c^16 + a^14*c^2*d^14 - 14*a^13*b*c^3*d^13 + 91*a^2*b^12*c^14*d^2 - 364*a^3*b^11*c^13*d^3 + 1001*a^4*b^10*c^12*d^4 - 2002*a^5*b^9*c^11*d^5 + 3003*a^6*b^8*c^10*d^6 - 3432*a^7*b^7*c^9*d^7 + 3003*a^8*b^6*c^8*d^8 - 2002*a^9*b^5*c^7*d^9 + 1001*a^10*b^4*c^6*d^10 - 364*a^11*b^3*c^5*d^11 + 91*a^12*b^2*c^4*d^12 - 14*a*b^13*c^15*d) - (x^(1/2)*(-(a^3*b^5)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4)*(147456*a^19*b^4*c*d^20 + 17186816*a^3*b^20*c^17*d^4 - 201326592*a^4*b^19*c^16*d^5 + 1089601536*a^5*b^18*c^15*d^6 - 3630694400*a^6*b^17*c^14*d^7 + 8402436096*a^7*b^16*c^13*d^8 - 14511243264*a^8*b^15*c^12*d^9 + 19702087680*a^9*b^14*c^11*d^10 - 21851799552*a^10*b^13*c^10*d^11 + 20194099200*a^11*b^12*c^9*d^12 - 15479078912*a^12*b^11*c^8*d^13 + 9580707840*a^13*b^10*c^7*d^14 - 4594335744*a^14*b^9*c^6*d^15 + 1620770816*a^15*b^8*c^5*d^16 - 393216000*a^16*b^7*c^4*d^17 + 59375616*a^17*b^6*c^3*d^18 - 4718592*a^18*b^5*c^2*d^19))/(4096*(b^12*c^14 + a^12*c^2*d^12 - 12*a^11*b*c^3*d^11 + 66*a^2*b^10*c^12*d^2 - 220*a^3*b^9*c^11*d^3 + 495*a^4*b^8*c^10*d^4 - 792*a^5*b^7*c^9*d^5 + 924*a^6*b^6*c^8*d^6 - 792*a^7*b^5*c^7*d^7 + 495*a^8*b^4*c^6*d^8 - 220*a^9*b^3*c^5*d^9 + 66*a^10*b^2*c^4*d^10 - 12*a*b^11*c^13*d)))*(-(a^3*b^5)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(3/4) - (x^(1/2)*(81*a^11*b^8*d^9 + 625*a^3*b^16*c^8*d + 5976*a^10*b^9*c*d^8 + 15000*a^4*b^15*c^7*d^2 + 133500*a^5*b^14*c^6*d^3 + 538600*a^6*b^13*c^5*d^4 + 956550*a^7*b^12*c^4*d^5 + 583080*a^8*b^11*c^3*d^6 - 136260*a^9*b^10*c^2*d^7))/(4096*(b^12*c^14 + a^12*c^2*d^12 - 12*a^11*b*c^3*d^11 + 66*a^2*b^10*c^12*d^2 - 220*a^3*b^9*c^11*d^3 + 495*a^4*b^8*c^10*d^4 - 792*a^5*b^7*c^9*d^5 + 924*a^6*b^6*c^8*d^6 - 792*a^7*b^5*c^7*d^7 + 495*a^8*b^4*c^6*d^8 - 220*a^9*b^3*c^5*d^9 + 66*a^10*b^2*c^4*d^10 - 12*a*b^11*c^13*d)))*(-(a^3*b^5)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4) - (((((27*a^20*b^4*d^20)/16 - (1107*a^19*b^5*c*d^19)/16 + (125*a^3*b^21*c^17*d^3)/16 - (31893*a^4*b^20*c^16*d^4)/16 + (44481*a^5*b^19*c^15*d^5)/2 - (227605*a^6*b^18*c^14*d^6)/2 + (1382895*a^7*b^17*c^13*d^7)/4 - (2723535*a^8*b^16*c^12*d^8)/4 + (1760163*a^9*b^15*c^11*d^9)/2 - (1361943*a^10*b^14*c^10*d^10)/2 + (1117215*a^11*b^13*c^9*d^11)/8 + (2877545*a^12*b^12*c^8*d^12)/8 - (1026465*a^13*b^11*c^7*d^13)/2 + (744837*a^14*b^10*c^6*d^14)/2 - (688489*a^15*b^9*c^5*d^15)/4 + (208665*a^16*b^8*c^4*d^16)/4 - (20115*a^17*b^7*c^3*d^17)/2 + (2295*a^18*b^6*c^2*d^18)/2)*1i)/(b^14*c^16 + a^14*c^2*d^14 - 14*a^13*b*c^3*d^13 + 91*a^2*b^12*c^14*d^2 - 364*a^3*b^11*c^13*d^3 + 1001*a^4*b^10*c^12*d^4 - 2002*a^5*b^9*c^11*d^5 + 3003*a^6*b^8*c^10*d^6 - 3432*a^7*b^7*c^9*d^7 + 3003*a^8*b^6*c^8*d^8 - 2002*a^9*b^5*c^7*d^9 + 1001*a^10*b^4*c^6*d^10 - 364*a^11*b^3*c^5*d^11 + 91*a^12*b^2*c^4*d^12 - 14*a*b^13*c^15*d) + (x^(1/2)*(-(a^3*b^5)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4)*(147456*a^19*b^4*c*d^20 + 17186816*a^3*b^20*c^17*d^4 - 201326592*a^4*b^19*c^16*d^5 + 1089601536*a^5*b^18*c^15*d^6 - 3630694400*a^6*b^17*c^14*d^7 + 8402436096*a^7*b^16*c^13*d^8 - 14511243264*a^8*b^15*c^12*d^9 + 19702087680*a^9*b^14*c^11*d^10 - 21851799552*a^10*b^13*c^10*d^11 + 20194099200*a^11*b^12*c^9*d^12 - 15479078912*a^12*b^11*c^8*d^13 + 9580707840*a^13*b^10*c^7*d^14 - 4594335744*a^14*b^9*c^6*d^15 + 1620770816*a^15*b^8*c^5*d^16 - 393216000*a^16*b^7*c^4*d^17 + 59375616*a^17*b^6*c^3*d^18 - 4718592*a^18*b^5*c^2*d^19))/(4096*(b^12*c^14 + a^12*c^2*d^12 - 12*a^11*b*c^3*d^11 + 66*a^2*b^10*c^12*d^2 - 220*a^3*b^9*c^11*d^3 + 495*a^4*b^8*c^10*d^4 - 792*a^5*b^7*c^9*d^5 + 924*a^6*b^6*c^8*d^6 - 792*a^7*b^5*c^7*d^7 + 495*a^8*b^4*c^6*d^8 - 220*a^9*b^3*c^5*d^9 + 66*a^10*b^2*c^4*d^10 - 12*a*b^11*c^13*d)))*(-(a^3*b^5)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(3/4) + (x^(1/2)*(81*a^11*b^8*d^9 + 625*a^3*b^16*c^8*d + 5976*a^10*b^9*c*d^8 + 15000*a^4*b^15*c^7*d^2 + 133500*a^5*b^14*c^6*d^3 + 538600*a^6*b^13*c^5*d^4 + 956550*a^7*b^12*c^4*d^5 + 583080*a^8*b^11*c^3*d^6 - 136260*a^9*b^10*c^2*d^7))/(4096*(b^12*c^14 + a^12*c^2*d^12 - 12*a^11*b*c^3*d^11 + 66*a^2*b^10*c^12*d^2 - 220*a^3*b^9*c^11*d^3 + 495*a^4*b^8*c^10*d^4 - 792*a^5*b^7*c^9*d^5 + 924*a^6*b^6*c^8*d^6 - 792*a^7*b^5*c^7*d^7 + 495*a^8*b^4*c^6*d^8 - 220*a^9*b^3*c^5*d^9 + 66*a^10*b^2*c^4*d^10 - 12*a*b^11*c^13*d)))*(-(a^3*b^5)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4))/((((((27*a^20*b^4*d^20)/16 - (1107*a^19*b^5*c*d^19)/16 + (125*a^3*b^21*c^17*d^3)/16 - (31893*a^4*b^20*c^16*d^4)/16 + (44481*a^5*b^19*c^15*d^5)/2 - (227605*a^6*b^18*c^14*d^6)/2 + (1382895*a^7*b^17*c^13*d^7)/4 - (2723535*a^8*b^16*c^12*d^8)/4 + (1760163*a^9*b^15*c^11*d^9)/2 - (1361943*a^10*b^14*c^10*d^10)/2 + (1117215*a^11*b^13*c^9*d^11)/8 + (2877545*a^12*b^12*c^8*d^12)/8 - (1026465*a^13*b^11*c^7*d^13)/2 + (744837*a^14*b^10*c^6*d^14)/2 - (688489*a^15*b^9*c^5*d^15)/4 + (208665*a^16*b^8*c^4*d^16)/4 - (20115*a^17*b^7*c^3*d^17)/2 + (2295*a^18*b^6*c^2*d^18)/2)*1i)/(b^14*c^16 + a^14*c^2*d^14 - 14*a^13*b*c^3*d^13 + 91*a^2*b^12*c^14*d^2 - 364*a^3*b^11*c^13*d^3 + 1001*a^4*b^10*c^12*d^4 - 2002*a^5*b^9*c^11*d^5 + 3003*a^6*b^8*c^10*d^6 - 3432*a^7*b^7*c^9*d^7 + 3003*a^8*b^6*c^8*d^8 - 2002*a^9*b^5*c^7*d^9 + 1001*a^10*b^4*c^6*d^10 - 364*a^11*b^3*c^5*d^11 + 91*a^12*b^2*c^4*d^12 - 14*a*b^13*c^15*d) - (x^(1/2)*(-(a^3*b^5)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4)*(147456*a^19*b^4*c*d^20 + 17186816*a^3*b^20*c^17*d^4 - 201326592*a^4*b^19*c^16*d^5 + 1089601536*a^5*b^18*c^15*d^6 - 3630694400*a^6*b^17*c^14*d^7 + 8402436096*a^7*b^16*c^13*d^8 - 14511243264*a^8*b^15*c^12*d^9 + 19702087680*a^9*b^14*c^11*d^10 - 21851799552*a^10*b^13*c^10*d^11 + 20194099200*a^11*b^12*c^9*d^12 - 15479078912*a^12*b^11*c^8*d^13 + 9580707840*a^13*b^10*c^7*d^14 - 4594335744*a^14*b^9*c^6*d^15 + 1620770816*a^15*b^8*c^5*d^16 - 393216000*a^16*b^7*c^4*d^17 + 59375616*a^17*b^6*c^3*d^18 - 4718592*a^18*b^5*c^2*d^19))/(4096*(b^12*c^14 + a^12*c^2*d^12 - 12*a^11*b*c^3*d^11 + 66*a^2*b^10*c^12*d^2 - 220*a^3*b^9*c^11*d^3 + 495*a^4*b^8*c^10*d^4 - 792*a^5*b^7*c^9*d^5 + 924*a^6*b^6*c^8*d^6 - 792*a^7*b^5*c^7*d^7 + 495*a^8*b^4*c^6*d^8 - 220*a^9*b^3*c^5*d^9 + 66*a^10*b^2*c^4*d^10 - 12*a*b^11*c^13*d)))*(-(a^3*b^5)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(3/4)*1i - (x^(1/2)*(81*a^11*b^8*d^9 + 625*a^3*b^16*c^8*d + 5976*a^10*b^9*c*d^8 + 15000*a^4*b^15*c^7*d^2 + 133500*a^5*b^14*c^6*d^3 + 538600*a^6*b^13*c^5*d^4 + 956550*a^7*b^12*c^4*d^5 + 583080*a^8*b^11*c^3*d^6 - 136260*a^9*b^10*c^2*d^7)*1i)/(4096*(b^12*c^14 + a^12*c^2*d^12 - 12*a^11*b*c^3*d^11 + 66*a^2*b^10*c^12*d^2 - 220*a^3*b^9*c^11*d^3 + 495*a^4*b^8*c^10*d^4 - 792*a^5*b^7*c^9*d^5 + 924*a^6*b^6*c^8*d^6 - 792*a^7*b^5*c^7*d^7 + 495*a^8*b^4*c^6*d^8 - 220*a^9*b^3*c^5*d^9 + 66*a^10*b^2*c^4*d^10 - 12*a*b^11*c^13*d)))*(-(a^3*b^5)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4) + (((((27*a^20*b^4*d^20)/16 - (1107*a^19*b^5*c*d^19)/16 + (125*a^3*b^21*c^17*d^3)/16 - (31893*a^4*b^20*c^16*d^4)/16 + (44481*a^5*b^19*c^15*d^5)/2 - (227605*a^6*b^18*c^14*d^6)/2 + (1382895*a^7*b^17*c^13*d^7)/4 - (2723535*a^8*b^16*c^12*d^8)/4 + (1760163*a^9*b^15*c^11*d^9)/2 - (1361943*a^10*b^14*c^10*d^10)/2 + (1117215*a^11*b^13*c^9*d^11)/8 + (2877545*a^12*b^12*c^8*d^12)/8 - (1026465*a^13*b^11*c^7*d^13)/2 + (744837*a^14*b^10*c^6*d^14)/2 - (688489*a^15*b^9*c^5*d^15)/4 + (208665*a^16*b^8*c^4*d^16)/4 - (20115*a^17*b^7*c^3*d^17)/2 + (2295*a^18*b^6*c^2*d^18)/2)*1i)/(b^14*c^16 + a^14*c^2*d^14 - 14*a^13*b*c^3*d^13 + 91*a^2*b^12*c^14*d^2 - 364*a^3*b^11*c^13*d^3 + 1001*a^4*b^10*c^12*d^4 - 2002*a^5*b^9*c^11*d^5 + 3003*a^6*b^8*c^10*d^6 - 3432*a^7*b^7*c^9*d^7 + 3003*a^8*b^6*c^8*d^8 - 2002*a^9*b^5*c^7*d^9 + 1001*a^10*b^4*c^6*d^10 - 364*a^11*b^3*c^5*d^11 + 91*a^12*b^2*c^4*d^12 - 14*a*b^13*c^15*d) + (x^(1/2)*(-(a^3*b^5)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4)*(147456*a^19*b^4*c*d^20 + 17186816*a^3*b^20*c^17*d^4 - 201326592*a^4*b^19*c^16*d^5 + 1089601536*a^5*b^18*c^15*d^6 - 3630694400*a^6*b^17*c^14*d^7 + 8402436096*a^7*b^16*c^13*d^8 - 14511243264*a^8*b^15*c^12*d^9 + 19702087680*a^9*b^14*c^11*d^10 - 21851799552*a^10*b^13*c^10*d^11 + 20194099200*a^11*b^12*c^9*d^12 - 15479078912*a^12*b^11*c^8*d^13 + 9580707840*a^13*b^10*c^7*d^14 - 4594335744*a^14*b^9*c^6*d^15 + 1620770816*a^15*b^8*c^5*d^16 - 393216000*a^16*b^7*c^4*d^17 + 59375616*a^17*b^6*c^3*d^18 - 4718592*a^18*b^5*c^2*d^19))/(4096*(b^12*c^14 + a^12*c^2*d^12 - 12*a^11*b*c^3*d^11 + 66*a^2*b^10*c^12*d^2 - 220*a^3*b^9*c^11*d^3 + 495*a^4*b^8*c^10*d^4 - 792*a^5*b^7*c^9*d^5 + 924*a^6*b^6*c^8*d^6 - 792*a^7*b^5*c^7*d^7 + 495*a^8*b^4*c^6*d^8 - 220*a^9*b^3*c^5*d^9 + 66*a^10*b^2*c^4*d^10 - 12*a*b^11*c^13*d)))*(-(a^3*b^5)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(3/4)*1i + (x^(1/2)*(81*a^11*b^8*d^9 + 625*a^3*b^16*c^8*d + 5976*a^10*b^9*c*d^8 + 15000*a^4*b^15*c^7*d^2 + 133500*a^5*b^14*c^6*d^3 + 538600*a^6*b^13*c^5*d^4 + 956550*a^7*b^12*c^4*d^5 + 583080*a^8*b^11*c^3*d^6 - 136260*a^9*b^10*c^2*d^7)*1i)/(4096*(b^12*c^14 + a^12*c^2*d^12 - 12*a^11*b*c^3*d^11 + 66*a^2*b^10*c^12*d^2 - 220*a^3*b^9*c^11*d^3 + 495*a^4*b^8*c^10*d^4 - 792*a^5*b^7*c^9*d^5 + 924*a^6*b^6*c^8*d^6 - 792*a^7*b^5*c^7*d^7 + 495*a^8*b^4*c^6*d^8 - 220*a^9*b^3*c^5*d^9 + 66*a^10*b^2*c^4*d^10 - 12*a*b^11*c^13*d)))*(-(a^3*b^5)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4) + ((625*a^4*b^16*c^7*d)/4096 - (945*a^11*b^9*d^8)/4096 + (28215*a^10*b^10*c*d^7)/4096 + (15625*a^5*b^15*c^6*d^2)/4096 + (145125*a^6*b^14*c^5*d^3)/4096 + (586125*a^7*b^13*c^4*d^4)/4096 + (810675*a^8*b^12*c^3*d^5)/4096 - (274725*a^9*b^11*c^2*d^6)/4096)/(b^14*c^16 + a^14*c^2*d^14 - 14*a^13*b*c^3*d^13 + 91*a^2*b^12*c^14*d^2 - 364*a^3*b^11*c^13*d^3 + 1001*a^4*b^10*c^12*d^4 - 2002*a^5*b^9*c^11*d^5 + 3003*a^6*b^8*c^10*d^6 - 3432*a^7*b^7*c^9*d^7 + 3003*a^8*b^6*c^8*d^8 - 2002*a^9*b^5*c^7*d^9 + 1001*a^10*b^4*c^6*d^10 - 364*a^11*b^3*c^5*d^11 + 91*a^12*b^2*c^4*d^12 - 14*a*b^13*c^15*d)))*(-(a^3*b^5)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4) - atan((((((27*a^20*b^4*d^20)/16 - (1107*a^19*b^5*c*d^19)/16 + (125*a^3*b^21*c^17*d^3)/16 - (31893*a^4*b^20*c^16*d^4)/16 + (44481*a^5*b^19*c^15*d^5)/2 - (227605*a^6*b^18*c^14*d^6)/2 + (1382895*a^7*b^17*c^13*d^7)/4 - (2723535*a^8*b^16*c^12*d^8)/4 + (1760163*a^9*b^15*c^11*d^9)/2 - (1361943*a^10*b^14*c^10*d^10)/2 + (1117215*a^11*b^13*c^9*d^11)/8 + (2877545*a^12*b^12*c^8*d^12)/8 - (1026465*a^13*b^11*c^7*d^13)/2 + (744837*a^14*b^10*c^6*d^14)/2 - (688489*a^15*b^9*c^5*d^15)/4 + (208665*a^16*b^8*c^4*d^16)/4 - (20115*a^17*b^7*c^3*d^17)/2 + (2295*a^18*b^6*c^2*d^18)/2)/(b^14*c^16 + a^14*c^2*d^14 - 14*a^13*b*c^3*d^13 + 91*a^2*b^12*c^14*d^2 - 364*a^3*b^11*c^13*d^3 + 1001*a^4*b^10*c^12*d^4 - 2002*a^5*b^9*c^11*d^5 + 3003*a^6*b^8*c^10*d^6 - 3432*a^7*b^7*c^9*d^7 + 3003*a^8*b^6*c^8*d^8 - 2002*a^9*b^5*c^7*d^9 + 1001*a^10*b^4*c^6*d^10 - 364*a^11*b^3*c^5*d^11 + 91*a^12*b^2*c^4*d^12 - 14*a*b^13*c^15*d) - (x^(1/2)*(-(a^3*b^5)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4)*(147456*a^19*b^4*c*d^20 + 17186816*a^3*b^20*c^17*d^4 - 201326592*a^4*b^19*c^16*d^5 + 1089601536*a^5*b^18*c^15*d^6 - 3630694400*a^6*b^17*c^14*d^7 + 8402436096*a^7*b^16*c^13*d^8 - 14511243264*a^8*b^15*c^12*d^9 + 19702087680*a^9*b^14*c^11*d^10 - 21851799552*a^10*b^13*c^10*d^11 + 20194099200*a^11*b^12*c^9*d^12 - 15479078912*a^12*b^11*c^8*d^13 + 9580707840*a^13*b^10*c^7*d^14 - 4594335744*a^14*b^9*c^6*d^15 + 1620770816*a^15*b^8*c^5*d^16 - 393216000*a^16*b^7*c^4*d^17 + 59375616*a^17*b^6*c^3*d^18 - 4718592*a^18*b^5*c^2*d^19))/(4096*(b^12*c^14 + a^12*c^2*d^12 - 12*a^11*b*c^3*d^11 + 66*a^2*b^10*c^12*d^2 - 220*a^3*b^9*c^11*d^3 + 495*a^4*b^8*c^10*d^4 - 792*a^5*b^7*c^9*d^5 + 924*a^6*b^6*c^8*d^6 - 792*a^7*b^5*c^7*d^7 + 495*a^8*b^4*c^6*d^8 - 220*a^9*b^3*c^5*d^9 + 66*a^10*b^2*c^4*d^10 - 12*a*b^11*c^13*d)))*(-(a^3*b^5)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(3/4)*1i - (x^(1/2)*(81*a^11*b^8*d^9 + 625*a^3*b^16*c^8*d + 5976*a^10*b^9*c*d^8 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(1760163*a^9*b^15*c^11*d^9)/2 - (1361943*a^10*b^14*c^10*d^10)/2 + (1117215*a^11*b^13*c^9*d^11)/8 + (2877545*a^12*b^12*c^8*d^12)/8 - (1026465*a^13*b^11*c^7*d^13)/2 + (744837*a^14*b^10*c^6*d^14)/2 - (688489*a^15*b^9*c^5*d^15)/4 + (208665*a^16*b^8*c^4*d^16)/4 - (20115*a^17*b^7*c^3*d^17)/2 + (2295*a^18*b^6*c^2*d^18)/2)/(b^14*c^16 + a^14*c^2*d^14 - 14*a^13*b*c^3*d^13 + 91*a^2*b^12*c^14*d^2 - 364*a^3*b^11*c^13*d^3 + 1001*a^4*b^10*c^12*d^4 - 2002*a^5*b^9*c^11*d^5 + 3003*a^6*b^8*c^10*d^6 - 3432*a^7*b^7*c^9*d^7 + 3003*a^8*b^6*c^8*d^8 - 2002*a^9*b^5*c^7*d^9 + 1001*a^10*b^4*c^6*d^10 - 364*a^11*b^3*c^5*d^11 + 91*a^12*b^2*c^4*d^12 - 14*a*b^13*c^15*d) + (x^(1/2)*(-(a^3*b^5)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4)*(147456*a^19*b^4*c*d^20 + 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(31893*a^4*b^20*c^16*d^4)/16 + (44481*a^5*b^19*c^15*d^5)/2 - (227605*a^6*b^18*c^14*d^6)/2 + (1382895*a^7*b^17*c^13*d^7)/4 - (2723535*a^8*b^16*c^12*d^8)/4 + (1760163*a^9*b^15*c^11*d^9)/2 - (1361943*a^10*b^14*c^10*d^10)/2 + (1117215*a^11*b^13*c^9*d^11)/8 + (2877545*a^12*b^12*c^8*d^12)/8 - (1026465*a^13*b^11*c^7*d^13)/2 + (744837*a^14*b^10*c^6*d^14)/2 - (688489*a^15*b^9*c^5*d^15)/4 + (208665*a^16*b^8*c^4*d^16)/4 - (20115*a^17*b^7*c^3*d^17)/2 + (2295*a^18*b^6*c^2*d^18)/2)/(b^14*c^16 + a^14*c^2*d^14 - 14*a^13*b*c^3*d^13 + 91*a^2*b^12*c^14*d^2 - 364*a^3*b^11*c^13*d^3 + 1001*a^4*b^10*c^12*d^4 - 2002*a^5*b^9*c^11*d^5 + 3003*a^6*b^8*c^10*d^6 - 3432*a^7*b^7*c^9*d^7 + 3003*a^8*b^6*c^8*d^8 - 2002*a^9*b^5*c^7*d^9 + 1001*a^10*b^4*c^6*d^10 - 364*a^11*b^3*c^5*d^11 + 91*a^12*b^2*c^4*d^12 - 14*a*b^13*c^15*d) - (x^(1/2)*(-(a^3*b^5)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 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192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4) + ((((27*a^20*b^4*d^20)/16 - (1107*a^19*b^5*c*d^19)/16 + (125*a^3*b^21*c^17*d^3)/16 - (31893*a^4*b^20*c^16*d^4)/16 + (44481*a^5*b^19*c^15*d^5)/2 - (227605*a^6*b^18*c^14*d^6)/2 + (1382895*a^7*b^17*c^13*d^7)/4 - (2723535*a^8*b^16*c^12*d^8)/4 + (1760163*a^9*b^15*c^11*d^9)/2 - (1361943*a^10*b^14*c^10*d^10)/2 + (1117215*a^11*b^13*c^9*d^11)/8 + (2877545*a^12*b^12*c^8*d^12)/8 - (1026465*a^13*b^11*c^7*d^13)/2 + (744837*a^14*b^10*c^6*d^14)/2 - (688489*a^15*b^9*c^5*d^15)/4 + (208665*a^16*b^8*c^4*d^16)/4 - (20115*a^17*b^7*c^3*d^17)/2 + (2295*a^18*b^6*c^2*d^18)/2)/(b^14*c^16 + a^14*c^2*d^14 - 14*a^13*b*c^3*d^13 + 91*a^2*b^12*c^14*d^2 - 364*a^3*b^11*c^13*d^3 + 1001*a^4*b^10*c^12*d^4 - 2002*a^5*b^9*c^11*d^5 + 3003*a^6*b^8*c^10*d^6 - 3432*a^7*b^7*c^9*d^7 + 3003*a^8*b^6*c^8*d^8 - 2002*a^9*b^5*c^7*d^9 + 1001*a^10*b^4*c^6*d^10 - 364*a^11*b^3*c^5*d^11 + 91*a^12*b^2*c^4*d^12 - 14*a*b^13*c^15*d) + (x^(1/2)*(-(a^3*b^5)/(16*a^12*d^12 + 16*b^12*c^12 + 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3690987520*a^3*b^9*c^14*d^6 + 8304721920*a^4*b^8*c^13*d^7 - 13287555072*a^5*b^7*c^12*d^8 + 15502147584*a^6*b^6*c^11*d^9 - 13287555072*a^7*b^5*c^10*d^10 + 8304721920*a^8*b^4*c^9*d^11 - 3690987520*a^9*b^3*c^8*d^12 + 1107296256*a^10*b^2*c^7*d^13))^(1/4))/((((((27*a^20*b^4*d^20)/16 - (1107*a^19*b^5*c*d^19)/16 + (125*a^3*b^21*c^17*d^3)/16 - (31893*a^4*b^20*c^16*d^4)/16 + (44481*a^5*b^19*c^15*d^5)/2 - (227605*a^6*b^18*c^14*d^6)/2 + (1382895*a^7*b^17*c^13*d^7)/4 - (2723535*a^8*b^16*c^12*d^8)/4 + (1760163*a^9*b^15*c^11*d^9)/2 - (1361943*a^10*b^14*c^10*d^10)/2 + (1117215*a^11*b^13*c^9*d^11)/8 + (2877545*a^12*b^12*c^8*d^12)/8 - (1026465*a^13*b^11*c^7*d^13)/2 + (744837*a^14*b^10*c^6*d^14)/2 - (688489*a^15*b^9*c^5*d^15)/4 + (208665*a^16*b^8*c^4*d^16)/4 - (20115*a^17*b^7*c^3*d^17)/2 + (2295*a^18*b^6*c^2*d^18)/2)*1i)/(b^14*c^16 + a^14*c^2*d^14 - 14*a^13*b*c^3*d^13 + 91*a^2*b^12*c^14*d^2 - 364*a^3*b^11*c^13*d^3 + 1001*a^4*b^10*c^12*d^4 - 2002*a^5*b^9*c^11*d^5 + 3003*a^6*b^8*c^10*d^6 - 3432*a^7*b^7*c^9*d^7 + 3003*a^8*b^6*c^8*d^8 - 2002*a^9*b^5*c^7*d^9 + 1001*a^10*b^4*c^6*d^10 - 364*a^11*b^3*c^5*d^11 + 91*a^12*b^2*c^4*d^12 - 14*a*b^13*c^15*d) - (x^(1/2)*(-(81*a^8*d^8 + 625*b^8*c^8 + 133500*a^2*b^6*c^6*d^2 + 513000*a^3*b^5*c^5*d^3 + 649350*a^4*b^4*c^4*d^4 - 307800*a^5*b^3*c^3*d^5 + 48060*a^6*b^2*c^2*d^6 + 15000*a*b^7*c^7*d - 3240*a^7*b*c*d^7)/(16777216*a^12*c^5*d^15 + 16777216*b^12*c^17*d^3 - 201326592*a*b^11*c^16*d^4 - 201326592*a^11*b*c^6*d^14 + 1107296256*a^2*b^10*c^15*d^5 - 3690987520*a^3*b^9*c^14*d^6 + 8304721920*a^4*b^8*c^13*d^7 - 13287555072*a^5*b^7*c^12*d^8 + 15502147584*a^6*b^6*c^11*d^9 - 13287555072*a^7*b^5*c^10*d^10 + 8304721920*a^8*b^4*c^9*d^11 - 3690987520*a^9*b^3*c^8*d^12 + 1107296256*a^10*b^2*c^7*d^13))^(1/4)*(147456*a^19*b^4*c*d^20 + 17186816*a^3*b^20*c^17*d^4 - 201326592*a^4*b^19*c^16*d^5 + 1089601536*a^5*b^18*c^15*d^6 - 3630694400*a^6*b^17*c^14*d^7 + 8402436096*a^7*b^16*c^13*d^8 - 14511243264*a^8*b^15*c^12*d^9 + 19702087680*a^9*b^14*c^11*d^10 - 21851799552*a^10*b^13*c^10*d^11 + 20194099200*a^11*b^12*c^9*d^12 - 15479078912*a^12*b^11*c^8*d^13 + 9580707840*a^13*b^10*c^7*d^14 - 4594335744*a^14*b^9*c^6*d^15 + 1620770816*a^15*b^8*c^5*d^16 - 393216000*a^16*b^7*c^4*d^17 + 59375616*a^17*b^6*c^3*d^18 - 4718592*a^18*b^5*c^2*d^19))/(4096*(b^12*c^14 + a^12*c^2*d^12 - 12*a^11*b*c^3*d^11 + 66*a^2*b^10*c^12*d^2 - 220*a^3*b^9*c^11*d^3 + 495*a^4*b^8*c^10*d^4 - 792*a^5*b^7*c^9*d^5 + 924*a^6*b^6*c^8*d^6 - 792*a^7*b^5*c^7*d^7 + 495*a^8*b^4*c^6*d^8 - 220*a^9*b^3*c^5*d^9 + 66*a^10*b^2*c^4*d^10 - 12*a*b^11*c^13*d)))*(-(81*a^8*d^8 + 625*b^8*c^8 + 133500*a^2*b^6*c^6*d^2 + 513000*a^3*b^5*c^5*d^3 + 649350*a^4*b^4*c^4*d^4 - 307800*a^5*b^3*c^3*d^5 + 48060*a^6*b^2*c^2*d^6 + 15000*a*b^7*c^7*d - 3240*a^7*b*c*d^7)/(16777216*a^12*c^5*d^15 + 16777216*b^12*c^17*d^3 - 201326592*a*b^11*c^16*d^4 - 201326592*a^11*b*c^6*d^14 + 1107296256*a^2*b^10*c^15*d^5 - 3690987520*a^3*b^9*c^14*d^6 + 8304721920*a^4*b^8*c^13*d^7 - 13287555072*a^5*b^7*c^12*d^8 + 15502147584*a^6*b^6*c^11*d^9 - 13287555072*a^7*b^5*c^10*d^10 + 8304721920*a^8*b^4*c^9*d^11 - 3690987520*a^9*b^3*c^8*d^12 + 1107296256*a^10*b^2*c^7*d^13))^(3/4)*1i - (x^(1/2)*(81*a^11*b^8*d^9 + 625*a^3*b^16*c^8*d + 5976*a^10*b^9*c*d^8 + 15000*a^4*b^15*c^7*d^2 + 133500*a^5*b^14*c^6*d^3 + 538600*a^6*b^13*c^5*d^4 + 956550*a^7*b^12*c^4*d^5 + 583080*a^8*b^11*c^3*d^6 - 136260*a^9*b^10*c^2*d^7)*1i)/(4096*(b^12*c^14 + a^12*c^2*d^12 - 12*a^11*b*c^3*d^11 + 66*a^2*b^10*c^12*d^2 - 220*a^3*b^9*c^11*d^3 + 495*a^4*b^8*c^10*d^4 - 792*a^5*b^7*c^9*d^5 + 924*a^6*b^6*c^8*d^6 - 792*a^7*b^5*c^7*d^7 + 495*a^8*b^4*c^6*d^8 - 220*a^9*b^3*c^5*d^9 + 66*a^10*b^2*c^4*d^10 - 12*a*b^11*c^13*d)))*(-(81*a^8*d^8 + 625*b^8*c^8 + 133500*a^2*b^6*c^6*d^2 + 513000*a^3*b^5*c^5*d^3 + 649350*a^4*b^4*c^4*d^4 - 307800*a^5*b^3*c^3*d^5 + 48060*a^6*b^2*c^2*d^6 + 15000*a*b^7*c^7*d - 3240*a^7*b*c*d^7)/(16777216*a^12*c^5*d^15 + 16777216*b^12*c^17*d^3 - 201326592*a*b^11*c^16*d^4 - 201326592*a^11*b*c^6*d^14 + 1107296256*a^2*b^10*c^15*d^5 - 3690987520*a^3*b^9*c^14*d^6 + 8304721920*a^4*b^8*c^13*d^7 - 13287555072*a^5*b^7*c^12*d^8 + 15502147584*a^6*b^6*c^11*d^9 - 13287555072*a^7*b^5*c^10*d^10 + 8304721920*a^8*b^4*c^9*d^11 - 3690987520*a^9*b^3*c^8*d^12 + 1107296256*a^10*b^2*c^7*d^13))^(1/4) + (((((27*a^20*b^4*d^20)/16 - (1107*a^19*b^5*c*d^19)/16 + (125*a^3*b^21*c^17*d^3)/16 - (31893*a^4*b^20*c^16*d^4)/16 + (44481*a^5*b^19*c^15*d^5)/2 - (227605*a^6*b^18*c^14*d^6)/2 + (1382895*a^7*b^17*c^13*d^7)/4 - (2723535*a^8*b^16*c^12*d^8)/4 + (1760163*a^9*b^15*c^11*d^9)/2 - (1361943*a^10*b^14*c^10*d^10)/2 + (1117215*a^11*b^13*c^9*d^11)/8 + (2877545*a^12*b^12*c^8*d^12)/8 - (1026465*a^13*b^11*c^7*d^13)/2 + (744837*a^14*b^10*c^6*d^14)/2 - (688489*a^15*b^9*c^5*d^15)/4 + (208665*a^16*b^8*c^4*d^16)/4 - (20115*a^17*b^7*c^3*d^17)/2 + (2295*a^18*b^6*c^2*d^18)/2)*1i)/(b^14*c^16 + a^14*c^2*d^14 - 14*a^13*b*c^3*d^13 + 91*a^2*b^12*c^14*d^2 - 364*a^3*b^11*c^13*d^3 + 1001*a^4*b^10*c^12*d^4 - 2002*a^5*b^9*c^11*d^5 + 3003*a^6*b^8*c^10*d^6 - 3432*a^7*b^7*c^9*d^7 + 3003*a^8*b^6*c^8*d^8 - 2002*a^9*b^5*c^7*d^9 + 1001*a^10*b^4*c^6*d^10 - 364*a^11*b^3*c^5*d^11 + 91*a^12*b^2*c^4*d^12 - 14*a*b^13*c^15*d) + (x^(1/2)*(-(81*a^8*d^8 + 625*b^8*c^8 + 133500*a^2*b^6*c^6*d^2 + 513000*a^3*b^5*c^5*d^3 + 649350*a^4*b^4*c^4*d^4 - 307800*a^5*b^3*c^3*d^5 + 48060*a^6*b^2*c^2*d^6 + 15000*a*b^7*c^7*d - 3240*a^7*b*c*d^7)/(16777216*a^12*c^5*d^15 + 16777216*b^12*c^17*d^3 - 201326592*a*b^11*c^16*d^4 - 201326592*a^11*b*c^6*d^14 + 1107296256*a^2*b^10*c^15*d^5 - 3690987520*a^3*b^9*c^14*d^6 + 8304721920*a^4*b^8*c^13*d^7 - 13287555072*a^5*b^7*c^12*d^8 + 15502147584*a^6*b^6*c^11*d^9 - 13287555072*a^7*b^5*c^10*d^10 + 8304721920*a^8*b^4*c^9*d^11 - 3690987520*a^9*b^3*c^8*d^12 + 1107296256*a^10*b^2*c^7*d^13))^(1/4)*(147456*a^19*b^4*c*d^20 + 17186816*a^3*b^20*c^17*d^4 - 201326592*a^4*b^19*c^16*d^5 + 1089601536*a^5*b^18*c^15*d^6 - 3630694400*a^6*b^17*c^14*d^7 + 8402436096*a^7*b^16*c^13*d^8 - 14511243264*a^8*b^15*c^12*d^9 + 19702087680*a^9*b^14*c^11*d^10 - 21851799552*a^10*b^13*c^10*d^11 + 20194099200*a^11*b^12*c^9*d^12 - 15479078912*a^12*b^11*c^8*d^13 + 9580707840*a^13*b^10*c^7*d^14 - 4594335744*a^14*b^9*c^6*d^15 + 1620770816*a^15*b^8*c^5*d^16 - 393216000*a^16*b^7*c^4*d^17 + 59375616*a^17*b^6*c^3*d^18 - 4718592*a^18*b^5*c^2*d^19))/(4096*(b^12*c^14 + a^12*c^2*d^12 - 12*a^11*b*c^3*d^11 + 66*a^2*b^10*c^12*d^2 - 220*a^3*b^9*c^11*d^3 + 495*a^4*b^8*c^10*d^4 - 792*a^5*b^7*c^9*d^5 + 924*a^6*b^6*c^8*d^6 - 792*a^7*b^5*c^7*d^7 + 495*a^8*b^4*c^6*d^8 - 220*a^9*b^3*c^5*d^9 + 66*a^10*b^2*c^4*d^10 - 12*a*b^11*c^13*d)))*(-(81*a^8*d^8 + 625*b^8*c^8 + 133500*a^2*b^6*c^6*d^2 + 513000*a^3*b^5*c^5*d^3 + 649350*a^4*b^4*c^4*d^4 - 307800*a^5*b^3*c^3*d^5 + 48060*a^6*b^2*c^2*d^6 + 15000*a*b^7*c^7*d - 3240*a^7*b*c*d^7)/(16777216*a^12*c^5*d^15 + 16777216*b^12*c^17*d^3 - 201326592*a*b^11*c^16*d^4 - 201326592*a^11*b*c^6*d^14 + 1107296256*a^2*b^10*c^15*d^5 - 3690987520*a^3*b^9*c^14*d^6 + 8304721920*a^4*b^8*c^13*d^7 - 13287555072*a^5*b^7*c^12*d^8 + 15502147584*a^6*b^6*c^11*d^9 - 13287555072*a^7*b^5*c^10*d^10 + 8304721920*a^8*b^4*c^9*d^11 - 3690987520*a^9*b^3*c^8*d^12 + 1107296256*a^10*b^2*c^7*d^13))^(3/4)*1i + (x^(1/2)*(81*a^11*b^8*d^9 + 625*a^3*b^16*c^8*d + 5976*a^10*b^9*c*d^8 + 15000*a^4*b^15*c^7*d^2 + 133500*a^5*b^14*c^6*d^3 + 538600*a^6*b^13*c^5*d^4 + 956550*a^7*b^12*c^4*d^5 + 583080*a^8*b^11*c^3*d^6 - 136260*a^9*b^10*c^2*d^7)*1i)/(4096*(b^12*c^14 + a^12*c^2*d^12 - 12*a^11*b*c^3*d^11 + 66*a^2*b^10*c^12*d^2 - 220*a^3*b^9*c^11*d^3 + 495*a^4*b^8*c^10*d^4 - 792*a^5*b^7*c^9*d^5 + 924*a^6*b^6*c^8*d^6 - 792*a^7*b^5*c^7*d^7 + 495*a^8*b^4*c^6*d^8 - 220*a^9*b^3*c^5*d^9 + 66*a^10*b^2*c^4*d^10 - 12*a*b^11*c^13*d)))*(-(81*a^8*d^8 + 625*b^8*c^8 + 133500*a^2*b^6*c^6*d^2 + 513000*a^3*b^5*c^5*d^3 + 649350*a^4*b^4*c^4*d^4 - 307800*a^5*b^3*c^3*d^5 + 48060*a^6*b^2*c^2*d^6 + 15000*a*b^7*c^7*d - 3240*a^7*b*c*d^7)/(16777216*a^12*c^5*d^15 + 16777216*b^12*c^17*d^3 - 201326592*a*b^11*c^16*d^4 - 201326592*a^11*b*c^6*d^14 + 1107296256*a^2*b^10*c^15*d^5 - 3690987520*a^3*b^9*c^14*d^6 + 8304721920*a^4*b^8*c^13*d^7 - 13287555072*a^5*b^7*c^12*d^8 + 15502147584*a^6*b^6*c^11*d^9 - 13287555072*a^7*b^5*c^10*d^10 + 8304721920*a^8*b^4*c^9*d^11 - 3690987520*a^9*b^3*c^8*d^12 + 1107296256*a^10*b^2*c^7*d^13))^(1/4) + ((625*a^4*b^16*c^7*d)/4096 - (945*a^11*b^9*d^8)/4096 + (28215*a^10*b^10*c*d^7)/4096 + (15625*a^5*b^15*c^6*d^2)/4096 + (145125*a^6*b^14*c^5*d^3)/4096 + (586125*a^7*b^13*c^4*d^4)/4096 + (810675*a^8*b^12*c^3*d^5)/4096 - (274725*a^9*b^11*c^2*d^6)/4096)/(b^14*c^16 + a^14*c^2*d^14 - 14*a^13*b*c^3*d^13 + 91*a^2*b^12*c^14*d^2 - 364*a^3*b^11*c^13*d^3 + 1001*a^4*b^10*c^12*d^4 - 2002*a^5*b^9*c^11*d^5 + 3003*a^6*b^8*c^10*d^6 - 3432*a^7*b^7*c^9*d^7 + 3003*a^8*b^6*c^8*d^8 - 2002*a^9*b^5*c^7*d^9 + 1001*a^10*b^4*c^6*d^10 - 364*a^11*b^3*c^5*d^11 + 91*a^12*b^2*c^4*d^12 - 14*a*b^13*c^15*d)))*(-(81*a^8*d^8 + 625*b^8*c^8 + 133500*a^2*b^6*c^6*d^2 + 513000*a^3*b^5*c^5*d^3 + 649350*a^4*b^4*c^4*d^4 - 307800*a^5*b^3*c^3*d^5 + 48060*a^6*b^2*c^2*d^6 + 15000*a*b^7*c^7*d - 3240*a^7*b*c*d^7)/(16777216*a^12*c^5*d^15 + 16777216*b^12*c^17*d^3 - 201326592*a*b^11*c^16*d^4 - 201326592*a^11*b*c^6*d^14 + 1107296256*a^2*b^10*c^15*d^5 - 3690987520*a^3*b^9*c^14*d^6 + 8304721920*a^4*b^8*c^13*d^7 - 13287555072*a^5*b^7*c^12*d^8 + 15502147584*a^6*b^6*c^11*d^9 - 13287555072*a^7*b^5*c^10*d^10 + 8304721920*a^8*b^4*c^9*d^11 - 3690987520*a^9*b^3*c^8*d^12 + 1107296256*a^10*b^2*c^7*d^13))^(1/4) - ((x^(3/2)*(a*d - 9*b*c))/(16*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) - (d*x^(7/2)*(3*a*d + 5*b*c))/(16*(b^2*c^3 + a^2*c*d^2 - 2*a*b*c^2*d)))/(c^2 + d^2*x^4 + 2*c*d*x^2)","B"
482,1,36160,627,4.254526,"\text{Not used}","int(x^(3/2)/((a + b*x^2)*(c + d*x^2)^3),x)","-\mathrm{atan}\left(\frac{\left(\left(\frac{\frac{81\,a^9\,b^7\,d^{10}}{2048}-\frac{1431\,a^8\,b^8\,c\,d^9}{2048}+\frac{6885\,a^7\,b^9\,c^2\,d^8}{2048}+\frac{5709\,a^6\,b^{10}\,c^3\,d^7}{2048}+\frac{18067\,a^5\,b^{11}\,c^4\,d^6}{2048}-\frac{432453\,a^4\,b^{12}\,c^5\,d^5}{2048}-\frac{713097\,a^3\,b^{13}\,c^6\,d^4}{2048}-\frac{194481\,a^2\,b^{14}\,c^7\,d^3}{2048}}{a^8\,c^4\,d^8-8\,a^7\,b\,c^5\,d^7+28\,a^6\,b^2\,c^6\,d^6-56\,a^5\,b^3\,c^7\,d^5+70\,a^4\,b^4\,c^8\,d^4-56\,a^3\,b^5\,c^9\,d^3+28\,a^2\,b^6\,c^{10}\,d^2-8\,a\,b^7\,c^{11}\,d+b^8\,c^{12}}-\left(\frac{{\left(-\frac{a\,b^7}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(-768\,a^{16}\,b^4\,c^4\,d^{18}+12032\,a^{15}\,b^5\,c^5\,d^{17}-76288\,a^{14}\,b^6\,c^6\,d^{16}+256512\,a^{13}\,b^7\,c^7\,d^{15}-459008\,a^{12}\,b^8\,c^8\,d^{14}+199936\,a^{11}\,b^9\,c^9\,d^{13}+1115136\,a^{10}\,b^{10}\,c^{10}\,d^{12}-3277824\,a^9\,b^{11}\,c^{11}\,d^{11}+4958976\,a^8\,b^{12}\,c^{12}\,d^{10}-4925184\,a^7\,b^{13}\,c^{13}\,d^9+3384832\,a^6\,b^{14}\,c^{14}\,d^8-1607168\,a^5\,b^{15}\,c^{15}\,d^7+506112\,a^4\,b^{16}\,c^{16}\,d^6-95488\,a^3\,b^{17}\,c^{17}\,d^5+8192\,a^2\,b^{18}\,c^{18}\,d^4\right)}{a^8\,c^4\,d^8-8\,a^7\,b\,c^5\,d^7+28\,a^6\,b^2\,c^6\,d^6-56\,a^5\,b^3\,c^7\,d^5+70\,a^4\,b^4\,c^8\,d^4-56\,a^3\,b^5\,c^9\,d^3+28\,a^2\,b^6\,c^{10}\,d^2-8\,a\,b^7\,c^{11}\,d+b^8\,c^{12}}-\frac{\sqrt{x}\,\left(147456\,a^{19}\,b^4\,c^2\,d^{21}-3145728\,a^{18}\,b^5\,c^3\,d^{20}+27394048\,a^{17}\,b^6\,c^4\,d^{19}-127401984\,a^{16}\,b^7\,c^5\,d^{18}+343080960\,a^{15}\,b^8\,c^6\,d^{17}-484442112\,a^{14}\,b^9\,c^7\,d^{16}-49938432\,a^{13}\,b^{10}\,c^8\,d^{15}+1989672960\,a^{12}\,b^{11}\,c^9\,d^{14}-5521702912\,a^{11}\,b^{12}\,c^{10}\,d^{13}+9861857280\,a^{10}\,b^{13}\,c^{11}\,d^{12}-13361086464\,a^9\,b^{14}\,c^{12}\,d^{11}+14203486208\,a^8\,b^{15}\,c^{13}\,d^{10}-11738087424\,a^7\,b^{16}\,c^{14}\,d^9+7335837696\,a^6\,b^{17}\,c^{15}\,d^8-3328573440\,a^5\,b^{18}\,c^{16}\,d^7+1030225920\,a^4\,b^{19}\,c^{17}\,d^6-194101248\,a^3\,b^{20}\,c^{18}\,d^5+16777216\,a^2\,b^{21}\,c^{19}\,d^4\right)}{4096\,\left(a^{12}\,c^4\,d^{12}-12\,a^{11}\,b\,c^5\,d^{11}+66\,a^{10}\,b^2\,c^6\,d^{10}-220\,a^9\,b^3\,c^7\,d^9+495\,a^8\,b^4\,c^8\,d^8-792\,a^7\,b^5\,c^9\,d^7+924\,a^6\,b^6\,c^{10}\,d^6-792\,a^5\,b^7\,c^{11}\,d^5+495\,a^4\,b^8\,c^{12}\,d^4-220\,a^3\,b^9\,c^{13}\,d^3+66\,a^2\,b^{10}\,c^{14}\,d^2-12\,a\,b^{11}\,c^{15}\,d+b^{12}\,c^{16}\right)}\right)\,{\left(-\frac{a\,b^7}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{3/4}\right)\,{\left(-\frac{a\,b^7}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}\,1{}\mathrm{i}+\frac{\sqrt{x}\,\left(81\,a^{10}\,b^9\,d^{11}-1512\,a^9\,b^{10}\,c\,d^{10}+17532\,a^8\,b^{11}\,c^2\,d^9-87192\,a^7\,b^{12}\,c^3\,d^8-14266\,a^6\,b^{13}\,c^4\,d^7+610344\,a^5\,b^{14}\,c^5\,d^6+859068\,a^4\,b^{15}\,c^6\,d^5+518616\,a^3\,b^{16}\,c^7\,d^4+194481\,a^2\,b^{17}\,c^8\,d^3\right)\,1{}\mathrm{i}}{4096\,\left(a^{12}\,c^4\,d^{12}-12\,a^{11}\,b\,c^5\,d^{11}+66\,a^{10}\,b^2\,c^6\,d^{10}-220\,a^9\,b^3\,c^7\,d^9+495\,a^8\,b^4\,c^8\,d^8-792\,a^7\,b^5\,c^9\,d^7+924\,a^6\,b^6\,c^{10}\,d^6-792\,a^5\,b^7\,c^{11}\,d^5+495\,a^4\,b^8\,c^{12}\,d^4-220\,a^3\,b^9\,c^{13}\,d^3+66\,a^2\,b^{10}\,c^{14}\,d^2-12\,a\,b^{11}\,c^{15}\,d+b^{12}\,c^{16}\right)}\right)\,{\left(-\frac{a\,b^7}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}-\left(\left(\frac{\frac{81\,a^9\,b^7\,d^{10}}{2048}-\frac{1431\,a^8\,b^8\,c\,d^9}{2048}+\frac{6885\,a^7\,b^9\,c^2\,d^8}{2048}+\frac{5709\,a^6\,b^{10}\,c^3\,d^7}{2048}+\frac{18067\,a^5\,b^{11}\,c^4\,d^6}{2048}-\frac{432453\,a^4\,b^{12}\,c^5\,d^5}{2048}-\frac{713097\,a^3\,b^{13}\,c^6\,d^4}{2048}-\frac{194481\,a^2\,b^{14}\,c^7\,d^3}{2048}}{a^8\,c^4\,d^8-8\,a^7\,b\,c^5\,d^7+28\,a^6\,b^2\,c^6\,d^6-56\,a^5\,b^3\,c^7\,d^5+70\,a^4\,b^4\,c^8\,d^4-56\,a^3\,b^5\,c^9\,d^3+28\,a^2\,b^6\,c^{10}\,d^2-8\,a\,b^7\,c^{11}\,d+b^8\,c^{12}}-\left(\frac{{\left(-\frac{a\,b^7}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(-768\,a^{16}\,b^4\,c^4\,d^{18}+12032\,a^{15}\,b^5\,c^5\,d^{17}-76288\,a^{14}\,b^6\,c^6\,d^{16}+256512\,a^{13}\,b^7\,c^7\,d^{15}-459008\,a^{12}\,b^8\,c^8\,d^{14}+199936\,a^{11}\,b^9\,c^9\,d^{13}+1115136\,a^{10}\,b^{10}\,c^{10}\,d^{12}-3277824\,a^9\,b^{11}\,c^{11}\,d^{11}+4958976\,a^8\,b^{12}\,c^{12}\,d^{10}-4925184\,a^7\,b^{13}\,c^{13}\,d^9+3384832\,a^6\,b^{14}\,c^{14}\,d^8-1607168\,a^5\,b^{15}\,c^{15}\,d^7+506112\,a^4\,b^{16}\,c^{16}\,d^6-95488\,a^3\,b^{17}\,c^{17}\,d^5+8192\,a^2\,b^{18}\,c^{18}\,d^4\right)}{a^8\,c^4\,d^8-8\,a^7\,b\,c^5\,d^7+28\,a^6\,b^2\,c^6\,d^6-56\,a^5\,b^3\,c^7\,d^5+70\,a^4\,b^4\,c^8\,d^4-56\,a^3\,b^5\,c^9\,d^3+28\,a^2\,b^6\,c^{10}\,d^2-8\,a\,b^7\,c^{11}\,d+b^8\,c^{12}}+\frac{\sqrt{x}\,\left(147456\,a^{19}\,b^4\,c^2\,d^{21}-3145728\,a^{18}\,b^5\,c^3\,d^{20}+27394048\,a^{17}\,b^6\,c^4\,d^{19}-127401984\,a^{16}\,b^7\,c^5\,d^{18}+343080960\,a^{15}\,b^8\,c^6\,d^{17}-484442112\,a^{14}\,b^9\,c^7\,d^{16}-49938432\,a^{13}\,b^{10}\,c^8\,d^{15}+1989672960\,a^{12}\,b^{11}\,c^9\,d^{14}-5521702912\,a^{11}\,b^{12}\,c^{10}\,d^{13}+9861857280\,a^{10}\,b^{13}\,c^{11}\,d^{12}-13361086464\,a^9\,b^{14}\,c^{12}\,d^{11}+14203486208\,a^8\,b^{15}\,c^{13}\,d^{10}-11738087424\,a^7\,b^{16}\,c^{14}\,d^9+7335837696\,a^6\,b^{17}\,c^{15}\,d^8-3328573440\,a^5\,b^{18}\,c^{16}\,d^7+1030225920\,a^4\,b^{19}\,c^{17}\,d^6-194101248\,a^3\,b^{20}\,c^{18}\,d^5+16777216\,a^2\,b^{21}\,c^{19}\,d^4\right)}{4096\,\left(a^{12}\,c^4\,d^{12}-12\,a^{11}\,b\,c^5\,d^{11}+66\,a^{10}\,b^2\,c^6\,d^{10}-220\,a^9\,b^3\,c^7\,d^9+495\,a^8\,b^4\,c^8\,d^8-792\,a^7\,b^5\,c^9\,d^7+924\,a^6\,b^6\,c^{10}\,d^6-792\,a^5\,b^7\,c^{11}\,d^5+495\,a^4\,b^8\,c^{12}\,d^4-220\,a^3\,b^9\,c^{13}\,d^3+66\,a^2\,b^{10}\,c^{14}\,d^2-12\,a\,b^{11}\,c^{15}\,d+b^{12}\,c^{16}\right)}\right)\,{\left(-\frac{a\,b^7}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{3/4}\right)\,{\left(-\frac{a\,b^7}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}\,1{}\mathrm{i}-\frac{\sqrt{x}\,\left(81\,a^{10}\,b^9\,d^{11}-1512\,a^9\,b^{10}\,c\,d^{10}+17532\,a^8\,b^{11}\,c^2\,d^9-87192\,a^7\,b^{12}\,c^3\,d^8-14266\,a^6\,b^{13}\,c^4\,d^7+610344\,a^5\,b^{14}\,c^5\,d^6+859068\,a^4\,b^{15}\,c^6\,d^5+518616\,a^3\,b^{16}\,c^7\,d^4+194481\,a^2\,b^{17}\,c^8\,d^3\right)\,1{}\mathrm{i}}{4096\,\left(a^{12}\,c^4\,d^{12}-12\,a^{11}\,b\,c^5\,d^{11}+66\,a^{10}\,b^2\,c^6\,d^{10}-220\,a^9\,b^3\,c^7\,d^9+495\,a^8\,b^4\,c^8\,d^8-792\,a^7\,b^5\,c^9\,d^7+924\,a^6\,b^6\,c^{10}\,d^6-792\,a^5\,b^7\,c^{11}\,d^5+495\,a^4\,b^8\,c^{12}\,d^4-220\,a^3\,b^9\,c^{13}\,d^3+66\,a^2\,b^{10}\,c^{14}\,d^2-12\,a\,b^{11}\,c^{15}\,d+b^{12}\,c^{16}\right)}\right)\,{\left(-\frac{a\,b^7}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}}{\left(\left(\frac{\frac{81\,a^9\,b^7\,d^{10}}{2048}-\frac{1431\,a^8\,b^8\,c\,d^9}{2048}+\frac{6885\,a^7\,b^9\,c^2\,d^8}{2048}+\frac{5709\,a^6\,b^{10}\,c^3\,d^7}{2048}+\frac{18067\,a^5\,b^{11}\,c^4\,d^6}{2048}-\frac{432453\,a^4\,b^{12}\,c^5\,d^5}{2048}-\frac{713097\,a^3\,b^{13}\,c^6\,d^4}{2048}-\frac{194481\,a^2\,b^{14}\,c^7\,d^3}{2048}}{a^8\,c^4\,d^8-8\,a^7\,b\,c^5\,d^7+28\,a^6\,b^2\,c^6\,d^6-56\,a^5\,b^3\,c^7\,d^5+70\,a^4\,b^4\,c^8\,d^4-56\,a^3\,b^5\,c^9\,d^3+28\,a^2\,b^6\,c^{10}\,d^2-8\,a\,b^7\,c^{11}\,d+b^8\,c^{12}}-\left(\frac{{\left(-\frac{a\,b^7}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(-768\,a^{16}\,b^4\,c^4\,d^{18}+12032\,a^{15}\,b^5\,c^5\,d^{17}-76288\,a^{14}\,b^6\,c^6\,d^{16}+256512\,a^{13}\,b^7\,c^7\,d^{15}-459008\,a^{12}\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(147456\,a^{19}\,b^4\,c^2\,d^{21}-3145728\,a^{18}\,b^5\,c^3\,d^{20}+27394048\,a^{17}\,b^6\,c^4\,d^{19}-127401984\,a^{16}\,b^7\,c^5\,d^{18}+343080960\,a^{15}\,b^8\,c^6\,d^{17}-484442112\,a^{14}\,b^9\,c^7\,d^{16}-49938432\,a^{13}\,b^{10}\,c^8\,d^{15}+1989672960\,a^{12}\,b^{11}\,c^9\,d^{14}-5521702912\,a^{11}\,b^{12}\,c^{10}\,d^{13}+9861857280\,a^{10}\,b^{13}\,c^{11}\,d^{12}-13361086464\,a^9\,b^{14}\,c^{12}\,d^{11}+14203486208\,a^8\,b^{15}\,c^{13}\,d^{10}-11738087424\,a^7\,b^{16}\,c^{14}\,d^9+7335837696\,a^6\,b^{17}\,c^{15}\,d^8-3328573440\,a^5\,b^{18}\,c^{16}\,d^7+1030225920\,a^4\,b^{19}\,c^{17}\,d^6-194101248\,a^3\,b^{20}\,c^{18}\,d^5+16777216\,a^2\,b^{21}\,c^{19}\,d^4\right)}{4096\,\left(a^{12}\,c^4\,d^{12}-12\,a^{11}\,b\,c^5\,d^{11}+66\,a^{10}\,b^2\,c^6\,d^{10}-220\,a^9\,b^3\,c^7\,d^9+495\,a^8\,b^4\,c^8\,d^8-792\,a^7\,b^5\,c^9\,d^7+924\,a^6\,b^6\,c^{10}\,d^6-792\,a^5\,b^7\,c^{11}\,d^5+495\,a^4\,b^8\,c^{12}\,d^4-220\,a^3\,b^9\,c^{13}\,d^3+66\,a^2\,b^{10}\,c^{14}\,d^2-12\,a\,b^{11}\,c^{15}\,d+b^{12}\,c^{16}\right)}\right)\,{\left(-\frac{a\,b^7}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{3/4}\right)\,{\left(-\frac{a\,b^7}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}-\frac{\sqrt{x}\,\left(81\,a^{10}\,b^9\,d^{11}-1512\,a^9\,b^{10}\,c\,d^{10}+17532\,a^8\,b^{11}\,c^2\,d^9-87192\,a^7\,b^{12}\,c^3\,d^8-14266\,a^6\,b^{13}\,c^4\,d^7+610344\,a^5\,b^{14}\,c^5\,d^6+859068\,a^4\,b^{15}\,c^6\,d^5+518616\,a^3\,b^{16}\,c^7\,d^4+194481\,a^2\,b^{17}\,c^8\,d^3\right)}{4096\,\left(a^{12}\,c^4\,d^{12}-12\,a^{11}\,b\,c^5\,d^{11}+66\,a^{10}\,b^2\,c^6\,d^{10}-220\,a^9\,b^3\,c^7\,d^9+495\,a^8\,b^4\,c^8\,d^8-792\,a^7\,b^5\,c^9\,d^7+924\,a^6\,b^6\,c^{10}\,d^6-792\,a^5\,b^7\,c^{11}\,d^5+495\,a^4\,b^8\,c^{12}\,d^4-220\,a^3\,b^9\,c^{13}\,d^3+66\,a^2\,b^{10}\,c^{14}\,d^2-12\,a\,b^{11}\,c^{15}\,d+b^{12}\,c^{16}\right)}\right)\,{\left(-\frac{a\,b^7}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}}\right)\,{\left(-\frac{a\,b^7}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}\,2{}\mathrm{i}+2\,\mathrm{atan}\left(\frac{\left(\left(\frac{\left(\frac{81\,a^9\,b^7\,d^{10}}{2048}-\frac{1431\,a^8\,b^8\,c\,d^9}{2048}+\frac{6885\,a^7\,b^9\,c^2\,d^8}{2048}+\frac{5709\,a^6\,b^{10}\,c^3\,d^7}{2048}+\frac{18067\,a^5\,b^{11}\,c^4\,d^6}{2048}-\frac{432453\,a^4\,b^{12}\,c^5\,d^5}{2048}-\frac{713097\,a^3\,b^{13}\,c^6\,d^4}{2048}-\frac{194481\,a^2\,b^{14}\,c^7\,d^3}{2048}\right)\,1{}\mathrm{i}}{a^8\,c^4\,d^8-8\,a^7\,b\,c^5\,d^7+28\,a^6\,b^2\,c^6\,d^6-56\,a^5\,b^3\,c^7\,d^5+70\,a^4\,b^4\,c^8\,d^4-56\,a^3\,b^5\,c^9\,d^3+28\,a^2\,b^6\,c^{10}\,d^2-8\,a\,b^7\,c^{11}\,d+b^8\,c^{12}}-\left(\frac{{\left(-\frac{a\,b^7}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(-768\,a^{16}\,b^4\,c^4\,d^{18}+12032\,a^{15}\,b^5\,c^5\,d^{17}-76288\,a^{14}\,b^6\,c^6\,d^{16}+256512\,a^{13}\,b^7\,c^7\,d^{15}-459008\,a^{12}\,b^8\,c^8\,d^{14}+199936\,a^{11}\,b^9\,c^9\,d^{13}+1115136\,a^{10}\,b^{10}\,c^{10}\,d^{12}-3277824\,a^9\,b^{11}\,c^{11}\,d^{11}+4958976\,a^8\,b^{12}\,c^{12}\,d^{10}-4925184\,a^7\,b^{13}\,c^{13}\,d^9+3384832\,a^6\,b^{14}\,c^{14}\,d^8-1607168\,a^5\,b^{15}\,c^{15}\,d^7+506112\,a^4\,b^{16}\,c^{16}\,d^6-95488\,a^3\,b^{17}\,c^{17}\,d^5+8192\,a^2\,b^{18}\,c^{18}\,d^4\right)}{a^8\,c^4\,d^8-8\,a^7\,b\,c^5\,d^7+28\,a^6\,b^2\,c^6\,d^6-56\,a^5\,b^3\,c^7\,d^5+70\,a^4\,b^4\,c^8\,d^4-56\,a^3\,b^5\,c^9\,d^3+28\,a^2\,b^6\,c^{10}\,d^2-8\,a\,b^7\,c^{11}\,d+b^8\,c^{12}}-\frac{\sqrt{x}\,\left(147456\,a^{19}\,b^4\,c^2\,d^{21}-3145728\,a^{18}\,b^5\,c^3\,d^{20}+27394048\,a^{17}\,b^6\,c^4\,d^{19}-127401984\,a^{16}\,b^7\,c^5\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\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{3/4}\,1{}\mathrm{i}\right)\,{\left(-\frac{a\,b^7}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}\,1{}\mathrm{i}-\frac{\sqrt{x}\,\left(81\,a^{10}\,b^9\,d^{11}-1512\,a^9\,b^{10}\,c\,d^{10}+17532\,a^8\,b^{11}\,c^2\,d^9-87192\,a^7\,b^{12}\,c^3\,d^8-14266\,a^6\,b^{13}\,c^4\,d^7+610344\,a^5\,b^{14}\,c^5\,d^6+859068\,a^4\,b^{15}\,c^6\,d^5+518616\,a^3\,b^{16}\,c^7\,d^4+194481\,a^2\,b^{17}\,c^8\,d^3\right)\,1{}\mathrm{i}}{4096\,\left(a^{12}\,c^4\,d^{12}-12\,a^{11}\,b\,c^5\,d^{11}+66\,a^{10}\,b^2\,c^6\,d^{10}-220\,a^9\,b^3\,c^7\,d^9+495\,a^8\,b^4\,c^8\,d^8-792\,a^7\,b^5\,c^9\,d^7+924\,a^6\,b^6\,c^{10}\,d^6-792\,a^5\,b^7\,c^{11}\,d^5+495\,a^4\,b^8\,c^{12}\,d^4-220\,a^3\,b^9\,c^{13}\,d^3+66\,a^2\,b^{10}\,c^{14}\,d^2-12\,a\,b^{11}\,c^{15}\,d+b^{12}\,c^{16}\right)}\right)\,{\left(-\frac{a\,b^7}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}+\left(\left(\frac{\left(\frac{81\,a^9\,b^7\,d^{10}}{2048}-\frac{1431\,a^8\,b^8\,c\,d^9}{2048}+\frac{6885\,a^7\,b^9\,c^2\,d^8}{2048}+\frac{5709\,a^6\,b^{10}\,c^3\,d^7}{2048}+\frac{18067\,a^5\,b^{11}\,c^4\,d^6}{2048}-\frac{432453\,a^4\,b^{12}\,c^5\,d^5}{2048}-\frac{713097\,a^3\,b^{13}\,c^6\,d^4}{2048}-\frac{194481\,a^2\,b^{14}\,c^7\,d^3}{2048}\right)\,1{}\mathrm{i}}{a^8\,c^4\,d^8-8\,a^7\,b\,c^5\,d^7+28\,a^6\,b^2\,c^6\,d^6-56\,a^5\,b^3\,c^7\,d^5+70\,a^4\,b^4\,c^8\,d^4-56\,a^3\,b^5\,c^9\,d^3+28\,a^2\,b^6\,c^{10}\,d^2-8\,a\,b^7\,c^{11}\,d+b^8\,c^{12}}-\left(\frac{{\left(-\frac{a\,b^7}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(-768\,a^{16}\,b^4\,c^4\,d^{18}+12032\,a^{15}\,b^5\,c^5\,d^{17}-76288\,a^{14}\,b^6\,c^6\,d^{16}+256512\,a^{13}\,b^7\,c^7\,d^{15}-459008\,a^{12}\,b^8\,c^8\,d^{14}+199936\,a^{11}\,b^9\,c^9\,d^{13}+1115136\,a^{10}\,b^{10}\,c^{10}\,d^{12}-3277824\,a^9\,b^{11}\,c^{11}\,d^{11}+4958976\,a^8\,b^{12}\,c^{12}\,d^{10}-4925184\,a^7\,b^{13}\,c^{13}\,d^9+3384832\,a^6\,b^{14}\,c^{14}\,d^8-1607168\,a^5\,b^{15}\,c^{15}\,d^7+506112\,a^4\,b^{16}\,c^{16}\,d^6-95488\,a^3\,b^{17}\,c^{17}\,d^5+8192\,a^2\,b^{18}\,c^{18}\,d^4\right)}{a^8\,c^4\,d^8-8\,a^7\,b\,c^5\,d^7+28\,a^6\,b^2\,c^6\,d^6-56\,a^5\,b^3\,c^7\,d^5+70\,a^4\,b^4\,c^8\,d^4-56\,a^3\,b^5\,c^9\,d^3+28\,a^2\,b^6\,c^{10}\,d^2-8\,a\,b^7\,c^{11}\,d+b^8\,c^{12}}+\frac{\sqrt{x}\,\left(147456\,a^{19}\,b^4\,c^2\,d^{21}-3145728\,a^{18}\,b^5\,c^3\,d^{20}+27394048\,a^{17}\,b^6\,c^4\,d^{19}-127401984\,a^{16}\,b^7\,c^5\,d^{18}+343080960\,a^{15}\,b^8\,c^6\,d^{17}-484442112\,a^{14}\,b^9\,c^7\,d^{16}-49938432\,a^{13}\,b^{10}\,c^8\,d^{15}+1989672960\,a^{12}\,b^{11}\,c^9\,d^{14}-5521702912\,a^{11}\,b^{12}\,c^{10}\,d^{13}+9861857280\,a^{10}\,b^{13}\,c^{11}\,d^{12}-13361086464\,a^9\,b^{14}\,c^{12}\,d^{11}+14203486208\,a^8\,b^{15}\,c^{13}\,d^{10}-11738087424\,a^7\,b^{16}\,c^{14}\,d^9+7335837696\,a^6\,b^{17}\,c^{15}\,d^8-3328573440\,a^5\,b^{18}\,c^{16}\,d^7+1030225920\,a^4\,b^{19}\,c^{17}\,d^6-194101248\,a^3\,b^{20}\,c^{18}\,d^5+16777216\,a^2\,b^{21}\,c^{19}\,d^4\right)\,1{}\mathrm{i}}{4096\,\left(a^{12}\,c^4\,d^{12}-12\,a^{11}\,b\,c^5\,d^{11}+66\,a^{10}\,b^2\,c^6\,d^{10}-220\,a^9\,b^3\,c^7\,d^9+495\,a^8\,b^4\,c^8\,d^8-792\,a^7\,b^5\,c^9\,d^7+924\,a^6\,b^6\,c^{10}\,d^6-792\,a^5\,b^7\,c^{11}\,d^5+495\,a^4\,b^8\,c^{12}\,d^4-220\,a^3\,b^9\,c^{13}\,d^3+66\,a^2\,b^{10}\,c^{14}\,d^2-12\,a\,b^{11}\,c^{15}\,d+b^{12}\,c^{16}\right)}\right)\,{\left(-\frac{a\,b^7}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,c^7\,d^5+7920\,a^4\,b^8\,c^8\,d^4-3520\,a^3\,b^9\,c^9\,d^3+1056\,a^2\,b^{10}\,c^{10}\,d^2-192\,a\,b^{11}\,c^{11}\,d+16\,b^{12}\,c^{12}}\right)}^{3/4}\,1{}\mathrm{i}\right)\,{\left(-\frac{a\,b^7}{16\,a^{12}\,d^{12}-192\,a^{11}\,b\,c\,d^{11}+1056\,a^{10}\,b^2\,c^2\,d^{10}-3520\,a^9\,b^3\,c^3\,d^9+7920\,a^8\,b^4\,c^4\,d^8-12672\,a^7\,b^5\,c^5\,d^7+14784\,a^6\,b^6\,c^6\,d^6-12672\,a^5\,b^7\,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t)}^{3/4}\,\left(\frac{{\left(-\frac{81\,a^8\,d^8-1512\,a^7\,b\,c\,d^7+8316\,a^6\,b^2\,c^2\,d^6-1176\,a^5\,b^3\,c^3\,d^5-85946\,a^4\,b^4\,c^4\,d^4+8232\,a^3\,b^5\,c^5\,d^3+407484\,a^2\,b^6\,c^6\,d^2+518616\,a\,b^7\,c^7\,d+194481\,b^8\,c^8}{16777216\,a^{12}\,c^7\,d^{13}-201326592\,a^{11}\,b\,c^8\,d^{12}+1107296256\,a^{10}\,b^2\,c^9\,d^{11}-3690987520\,a^9\,b^3\,c^{10}\,d^{10}+8304721920\,a^8\,b^4\,c^{11}\,d^9-13287555072\,a^7\,b^5\,c^{12}\,d^8+15502147584\,a^6\,b^6\,c^{13}\,d^7-13287555072\,a^5\,b^7\,c^{14}\,d^6+8304721920\,a^4\,b^8\,c^{15}\,d^5-3690987520\,a^3\,b^9\,c^{16}\,d^4+1107296256\,a^2\,b^{10}\,c^{17}\,d^3-201326592\,a\,b^{11}\,c^{18}\,d^2+16777216\,b^{12}\,c^{19}\,d}\right)}^{1/4}\,\left(-768\,a^{16}\,b^4\,c^4\,d^{18}+12032\,a^{15}\,b^5\,c^5\,d^{17}-76288\,a^{14}\,b^6\,c^6\,d^{16}+256512\,a^{13}\,b^7\,c^7\,d^{15}-459008\,a^{12}\,b^8\,c^8\,d^{14}+199936\,a^{11}\,b^9\,c^9\,d^{13}+1115136\,a^{10}\,b^{10}\,c^{10}\,d^{12}-3277824\,a^9\,b^{11}\,c^{11}\,d^{11}+4958976\,a^8\,b^{12}\,c^{12}\,d^{10}-4925184\,a^7\,b^{13}\,c^{13}\,d^9+3384832\,a^6\,b^{14}\,c^{14}\,d^8-1607168\,a^5\,b^{15}\,c^{15}\,d^7+506112\,a^4\,b^{16}\,c^{16}\,d^6-95488\,a^3\,b^{17}\,c^{17}\,d^5+8192\,a^2\,b^{18}\,c^{18}\,d^4\right)}{a^8\,c^4\,d^8-8\,a^7\,b\,c^5\,d^7+28\,a^6\,b^2\,c^6\,d^6-56\,a^5\,b^3\,c^7\,d^5+70\,a^4\,b^4\,c^8\,d^4-56\,a^3\,b^5\,c^9\,d^3+28\,a^2\,b^6\,c^{10}\,d^2-8\,a\,b^7\,c^{11}\,d+b^8\,c^{12}}-\frac{\sqrt{x}\,\left(147456\,a^{19}\,b^4\,c^2\,d^{21}-3145728\,a^{18}\,b^5\,c^3\,d^{20}+27394048\,a^{17}\,b^6\,c^4\,d^{19}-127401984\,a^{16}\,b^7\,c^5\,d^{18}+343080960\,a^{15}\,b^8\,c^6\,d^{17}-484442112\,a^{14}\,b^9\,c^7\,d^{16}-49938432\,a^{13}\,b^{10}\,c^8\,d^{15}+1989672960\,a^{12}\,b^{11}\,c^9\,d^{14}-5521702912\,a^{11}\,b^{12}\,c^{10}\,d^{13}+9861857280\,a^{10}\,b^{13}\,c^{11}\,d^{12}-13361086464\,a^9\,b^{14}\,c^{12}\,d^{11}+14203486208\,a^8\,b^{15}\,c^{13}\,d^{10}-11738087424\,a^7\,b^{16}\,c^{14}\,d^9+7335837696\,a^6\,b^{17}\,c^{15}\,d^8-3328573440\,a^5\,b^{18}\,c^{16}\,d^7+1030225920\,a^4\,b^{19}\,c^{17}\,d^6-194101248\,a^3\,b^{20}\,c^{18}\,d^5+16777216\,a^2\,b^{21}\,c^{19}\,d^4\right)}{4096\,\left(a^{12}\,c^4\,d^{12}-12\,a^{11}\,b\,c^5\,d^{11}+66\,a^{10}\,b^2\,c^6\,d^{10}-220\,a^9\,b^3\,c^7\,d^9+495\,a^8\,b^4\,c^8\,d^8-792\,a^7\,b^5\,c^9\,d^7+924\,a^6\,b^6\,c^{10}\,d^6-792\,a^5\,b^7\,c^{11}\,d^5+495\,a^4\,b^8\,c^{12}\,d^4-220\,a^3\,b^9\,c^{13}\,d^3+66\,a^2\,b^{10}\,c^{14}\,d^2-12\,a\,b^{11}\,c^{15}\,d+b^{12}\,c^{16}\right)}\right)-\frac{\frac{81\,a^9\,b^7\,d^{10}}{2048}-\frac{1431\,a^8\,b^8\,c\,d^9}{2048}+\frac{6885\,a^7\,b^9\,c^2\,d^8}{2048}+\frac{5709\,a^6\,b^{10}\,c^3\,d^7}{2048}+\frac{18067\,a^5\,b^{11}\,c^4\,d^6}{2048}-\frac{432453\,a^4\,b^{12}\,c^5\,d^5}{2048}-\frac{713097\,a^3\,b^{13}\,c^6\,d^4}{2048}-\frac{194481\,a^2\,b^{14}\,c^7\,d^3}{2048}}{a^8\,c^4\,d^8-8\,a^7\,b\,c^5\,d^7+28\,a^6\,b^2\,c^6\,d^6-56\,a^5\,b^3\,c^7\,d^5+70\,a^4\,b^4\,c^8\,d^4-56\,a^3\,b^5\,c^9\,d^3+28\,a^2\,b^6\,c^{10}\,d^2-8\,a\,b^7\,c^{11}\,d+b^8\,c^{12}}\right)-\frac{\sqrt{x}\,\left(81\,a^{10}\,b^9\,d^{11}-1512\,a^9\,b^{10}\,c\,d^{10}+17532\,a^8\,b^{11}\,c^2\,d^9-87192\,a^7\,b^{12}\,c^3\,d^8-14266\,a^6\,b^{13}\,c^4\,d^7+610344\,a^5\,b^{14}\,c^5\,d^6+859068\,a^4\,b^{15}\,c^6\,d^5+518616\,a^3\,b^{16}\,c^7\,d^4+194481\,a^2\,b^{17}\,c^8\,d^3\right)}{4096\,\left(a^{12}\,c^4\,d^{12}-12\,a^{11}\,b\,c^5\,d^{11}+66\,a^{10}\,b^2\,c^6\,d^{10}-220\,a^9\,b^3\,c^7\,d^9+495\,a^8\,b^4\,c^8\,d^8-792\,a^7\,b^5\,c^9\,d^7+924\,a^6\,b^6\,c^{10}\,d^6-792\,a^5\,b^7\,c^{11}\,d^5+495\,a^4\,b^8\,c^{12}\,d^4-220\,a^3\,b^9\,c^{13}\,d^3+66\,a^2\,b^{10}\,c^{14}\,d^2-12\,a\,b^{11}\,c^{15}\,d+b^{12}\,c^{16}\right)}\right)+{\left(-\frac{81\,a^8\,d^8-1512\,a^7\,b\,c\,d^7+8316\,a^6\,b^2\,c^2\,d^6-1176\,a^5\,b^3\,c^3\,d^5-85946\,a^4\,b^4\,c^4\,d^4+8232\,a^3\,b^5\,c^5\,d^3+407484\,a^2\,b^6\,c^6\,d^2+518616\,a\,b^7\,c^7\,d+194481\,b^8\,c^8}{16777216\,a^{12}\,c^7\,d^{13}-201326592\,a^{11}\,b\,c^8\,d^{12}+1107296256\,a^{10}\,b^2\,c^9\,d^{11}-3690987520\,a^9\,b^3\,c^{10}\,d^{10}+8304721920\,a^8\,b^4\,c^{11}\,d^9-13287555072\,a^7\,b^5\,c^{12}\,d^8+15502147584\,a^6\,b^6\,c^{13}\,d^7-13287555072\,a^5\,b^7\,c^{14}\,d^6+8304721920\,a^4\,b^8\,c^{15}\,d^5-3690987520\,a^3\,b^9\,c^{16}\,d^4+1107296256\,a^2\,b^{10}\,c^{17}\,d^3-201326592\,a\,b^{11}\,c^{18}\,d^2+16777216\,b^{12}\,c^{19}\,d}\right)}^{1/4}\,\left({\left(-\frac{81\,a^8\,d^8-1512\,a^7\,b\,c\,d^7+8316\,a^6\,b^2\,c^2\,d^6-1176\,a^5\,b^3\,c^3\,d^5-85946\,a^4\,b^4\,c^4\,d^4+8232\,a^3\,b^5\,c^5\,d^3+407484\,a^2\,b^6\,c^6\,d^2+518616\,a\,b^7\,c^7\,d+194481\,b^8\,c^8}{16777216\,a^{12}\,c^7\,d^{13}-201326592\,a^{11}\,b\,c^8\,d^{12}+1107296256\,a^{10}\,b^2\,c^9\,d^{11}-3690987520\,a^9\,b^3\,c^{10}\,d^{10}+8304721920\,a^8\,b^4\,c^{11}\,d^9-13287555072\,a^7\,b^5\,c^{12}\,d^8+15502147584\,a^6\,b^6\,c^{13}\,d^7-13287555072\,a^5\,b^7\,c^{14}\,d^6+8304721920\,a^4\,b^8\,c^{15}\,d^5-3690987520\,a^3\,b^9\,c^{16}\,d^4+1107296256\,a^2\,b^{10}\,c^{17}\,d^3-201326592\,a\,b^{11}\,c^{18}\,d^2+16777216\,b^{12}\,c^{19}\,d}\right)}^{1/4}\,\left({\left(-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^{14}\,b^6\,c^6\,d^{16}+256512\,a^{13}\,b^7\,c^7\,d^{15}-459008\,a^{12}\,b^8\,c^8\,d^{14}+199936\,a^{11}\,b^9\,c^9\,d^{13}+1115136\,a^{10}\,b^{10}\,c^{10}\,d^{12}-3277824\,a^9\,b^{11}\,c^{11}\,d^{11}+4958976\,a^8\,b^{12}\,c^{12}\,d^{10}-4925184\,a^7\,b^{13}\,c^{13}\,d^9+3384832\,a^6\,b^{14}\,c^{14}\,d^8-1607168\,a^5\,b^{15}\,c^{15}\,d^7+506112\,a^4\,b^{16}\,c^{16}\,d^6-95488\,a^3\,b^{17}\,c^{17}\,d^5+8192\,a^2\,b^{18}\,c^{18}\,d^4\right)}{a^8\,c^4\,d^8-8\,a^7\,b\,c^5\,d^7+28\,a^6\,b^2\,c^6\,d^6-56\,a^5\,b^3\,c^7\,d^5+70\,a^4\,b^4\,c^8\,d^4-56\,a^3\,b^5\,c^9\,d^3+28\,a^2\,b^6\,c^{10}\,d^2-8\,a\,b^7\,c^{11}\,d+b^8\,c^{12}}+\frac{\sqrt{x}\,\left(147456\,a^{19}\,b^4\,c^2\,d^{21}-3145728\,a^{18}\,b^5\,c^3\,d^{20}+27394048\,a^{17}\,b^6\,c^4\,d^{19}-127401984\,a^{16}\,b^7\,c^5\,d^{18}+343080960\,a^{15}\,b^8\,c^6\,d^{17}-484442112\,a^{14}\,b^9\,c^7\,d^{16}-49938432\,a^{13}\,b^{10}\,c^8\,d^{15}+1989672960\,a^{12}\,b^{11}\,c^9\,d^{14}-5521702912\,a^{11}\,b^{12}\,c^{10}\,d^{13}+9861857280\,a^{10}\,b^{13}\,c^{11}\,d^{12}-13361086464\,a^9\,b^{14}\,c^{12}\,d^{11}+14203486208\,a^8\,b^{15}\,c^{13}\,d^{10}-11738087424\,a^7\,b^{16}\,c^{14}\,d^9+7335837696\,a^6\,b^{17}\,c^{15}\,d^8-3328573440\,a^5\,b^{18}\,c^{16}\,d^7+1030225920\,a^4\,b^{19}\,c^{17}\,d^6-194101248\,a^3\,b^{20}\,c^{18}\,d^5+16777216\,a^2\,b^{21}\,c^{19}\,d^4\right)\,1{}\mathrm{i}}{4096\,\left(a^{12}\,c^4\,d^{12}-12\,a^{11}\,b\,c^5\,d^{11}+66\,a^{10}\,b^2\,c^6\,d^{10}-220\,a^9\,b^3\,c^7\,d^9+495\,a^8\,b^4\,c^8\,d^8-792\,a^7\,b^5\,c^9\,d^7+924\,a^6\,b^6\,c^{10}\,d^6-792\,a^5\,b^7\,c^{11}\,d^5+495\,a^4\,b^8\,c^{12}\,d^4-220\,a^3\,b^9\,c^{13}\,d^3+66\,a^2\,b^{10}\,c^{14}\,d^2-12\,a\,b^{11}\,c^{15}\,d+b^{12}\,c^{16}\right)}\right)\,1{}\mathrm{i}-\frac{\left(\frac{81\,a^9\,b^7\,d^{10}}{2048}-\frac{1431\,a^8\,b^8\,c\,d^9}{2048}+\frac{6885\,a^7\,b^9\,c^2\,d^8}{2048}+\frac{5709\,a^6\,b^{10}\,c^3\,d^7}{2048}+\frac{18067\,a^5\,b^{11}\,c^4\,d^6}{2048}-\frac{432453\,a^4\,b^{12}\,c^5\,d^5}{2048}-\frac{713097\,a^3\,b^{13}\,c^6\,d^4}{2048}-\frac{194481\,a^2\,b^{14}\,c^7\,d^3}{2048}\right)\,1{}\mathrm{i}}{a^8\,c^4\,d^8-8\,a^7\,b\,c^5\,d^7+28\,a^6\,b^2\,c^6\,d^6-56\,a^5\,b^3\,c^7\,d^5+70\,a^4\,b^4\,c^8\,d^4-56\,a^3\,b^5\,c^9\,d^3+28\,a^2\,b^6\,c^{10}\,d^2-8\,a\,b^7\,c^{11}\,d+b^8\,c^{12}}\right)\,1{}\mathrm{i}-\frac{\sqrt{x}\,\left(81\,a^{10}\,b^9\,d^{11}-1512\,a^9\,b^{10}\,c\,d^{10}+17532\,a^8\,b^{11}\,c^2\,d^9-87192\,a^7\,b^{12}\,c^3\,d^8-14266\,a^6\,b^{13}\,c^4\,d^7+610344\,a^5\,b^{14}\,c^5\,d^6+859068\,a^4\,b^{15}\,c^6\,d^5+518616\,a^3\,b^{16}\,c^7\,d^4+194481\,a^2\,b^{17}\,c^8\,d^3\right)\,1{}\mathrm{i}}{4096\,\left(a^{12}\,c^4\,d^{12}-12\,a^{11}\,b\,c^5\,d^{11}+66\,a^{10}\,b^2\,c^6\,d^{10}-220\,a^9\,b^3\,c^7\,d^9+495\,a^8\,b^4\,c^8\,d^8-792\,a^7\,b^5\,c^9\,d^7+924\,a^6\,b^6\,c^{10}\,d^6-792\,a^5\,b^7\,c^{11}\,d^5+495\,a^4\,b^8\,c^{12}\,d^4-220\,a^3\,b^9\,c^{13}\,d^3+66\,a^2\,b^{10}\,c^{14}\,d^2-12\,a\,b^{11}\,c^{15}\,d+b^{12}\,c^{16}\right)}\right)}\right)\,{\left(-\frac{81\,a^8\,d^8-1512\,a^7\,b\,c\,d^7+8316\,a^6\,b^2\,c^2\,d^6-1176\,a^5\,b^3\,c^3\,d^5-85946\,a^4\,b^4\,c^4\,d^4+8232\,a^3\,b^5\,c^5\,d^3+407484\,a^2\,b^6\,c^6\,d^2+518616\,a\,b^7\,c^7\,d+194481\,b^8\,c^8}{16777216\,a^{12}\,c^7\,d^{13}-201326592\,a^{11}\,b\,c^8\,d^{12}+1107296256\,a^{10}\,b^2\,c^9\,d^{11}-3690987520\,a^9\,b^3\,c^{10}\,d^{10}+8304721920\,a^8\,b^4\,c^{11}\,d^9-13287555072\,a^7\,b^5\,c^{12}\,d^8+15502147584\,a^6\,b^6\,c^{13}\,d^7-13287555072\,a^5\,b^7\,c^{14}\,d^6+8304721920\,a^4\,b^8\,c^{15}\,d^5-3690987520\,a^3\,b^9\,c^{16}\,d^4+1107296256\,a^2\,b^{10}\,c^{17}\,d^3-201326592\,a\,b^{11}\,c^{18}\,d^2+16777216\,b^{12}\,c^{19}\,d}\right)}^{1/4}-\frac{\frac{\sqrt{x}\,\left(3\,a\,d-11\,b\,c\right)}{16\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}-\frac{d\,x^{5/2}\,\left(a\,d+7\,b\,c\right)}{16\,\left(a^2\,c\,d^2-2\,a\,b\,c^2\,d+b^2\,c^3\right)}}{c^2+2\,c\,d\,x^2+d^2\,x^4}","Not used",1,"2*atan(((((((81*a^9*b^7*d^10)/2048 - (1431*a^8*b^8*c*d^9)/2048 - (194481*a^2*b^14*c^7*d^3)/2048 - (713097*a^3*b^13*c^6*d^4)/2048 - (432453*a^4*b^12*c^5*d^5)/2048 + (18067*a^5*b^11*c^4*d^6)/2048 + (5709*a^6*b^10*c^3*d^7)/2048 + (6885*a^7*b^9*c^2*d^8)/2048)*1i)/(b^8*c^12 + a^8*c^4*d^8 - 8*a^7*b*c^5*d^7 + 28*a^2*b^6*c^10*d^2 - 56*a^3*b^5*c^9*d^3 + 70*a^4*b^4*c^8*d^4 - 56*a^5*b^3*c^7*d^5 + 28*a^6*b^2*c^6*d^6 - 8*a*b^7*c^11*d) - (((-(a*b^7)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4)*(8192*a^2*b^18*c^18*d^4 - 95488*a^3*b^17*c^17*d^5 + 506112*a^4*b^16*c^16*d^6 - 1607168*a^5*b^15*c^15*d^7 + 3384832*a^6*b^14*c^14*d^8 - 4925184*a^7*b^13*c^13*d^9 + 4958976*a^8*b^12*c^12*d^10 - 3277824*a^9*b^11*c^11*d^11 + 1115136*a^10*b^10*c^10*d^12 + 199936*a^11*b^9*c^9*d^13 - 459008*a^12*b^8*c^8*d^14 + 256512*a^13*b^7*c^7*d^15 - 76288*a^14*b^6*c^6*d^16 + 12032*a^15*b^5*c^5*d^17 - 768*a^16*b^4*c^4*d^18))/(b^8*c^12 + a^8*c^4*d^8 - 8*a^7*b*c^5*d^7 + 28*a^2*b^6*c^10*d^2 - 56*a^3*b^5*c^9*d^3 + 70*a^4*b^4*c^8*d^4 - 56*a^5*b^3*c^7*d^5 + 28*a^6*b^2*c^6*d^6 - 8*a*b^7*c^11*d) - (x^(1/2)*(16777216*a^2*b^21*c^19*d^4 - 194101248*a^3*b^20*c^18*d^5 + 1030225920*a^4*b^19*c^17*d^6 - 3328573440*a^5*b^18*c^16*d^7 + 7335837696*a^6*b^17*c^15*d^8 - 11738087424*a^7*b^16*c^14*d^9 + 14203486208*a^8*b^15*c^13*d^10 - 13361086464*a^9*b^14*c^12*d^11 + 9861857280*a^10*b^13*c^11*d^12 - 5521702912*a^11*b^12*c^10*d^13 + 1989672960*a^12*b^11*c^9*d^14 - 49938432*a^13*b^10*c^8*d^15 - 484442112*a^14*b^9*c^7*d^16 + 343080960*a^15*b^8*c^6*d^17 - 127401984*a^16*b^7*c^5*d^18 + 27394048*a^17*b^6*c^4*d^19 - 3145728*a^18*b^5*c^3*d^20 + 147456*a^19*b^4*c^2*d^21)*1i)/(4096*(b^12*c^16 + a^12*c^4*d^12 - 12*a^11*b*c^5*d^11 + 66*a^2*b^10*c^14*d^2 - 220*a^3*b^9*c^13*d^3 + 495*a^4*b^8*c^12*d^4 - 792*a^5*b^7*c^11*d^5 + 924*a^6*b^6*c^10*d^6 - 792*a^7*b^5*c^9*d^7 + 495*a^8*b^4*c^8*d^8 - 220*a^9*b^3*c^7*d^9 + 66*a^10*b^2*c^6*d^10 - 12*a*b^11*c^15*d)))*(-(a*b^7)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(3/4)*1i)*(-(a*b^7)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4) - (x^(1/2)*(81*a^10*b^9*d^11 - 1512*a^9*b^10*c*d^10 + 194481*a^2*b^17*c^8*d^3 + 518616*a^3*b^16*c^7*d^4 + 859068*a^4*b^15*c^6*d^5 + 610344*a^5*b^14*c^5*d^6 - 14266*a^6*b^13*c^4*d^7 - 87192*a^7*b^12*c^3*d^8 + 17532*a^8*b^11*c^2*d^9))/(4096*(b^12*c^16 + a^12*c^4*d^12 - 12*a^11*b*c^5*d^11 + 66*a^2*b^10*c^14*d^2 - 220*a^3*b^9*c^13*d^3 + 495*a^4*b^8*c^12*d^4 - 792*a^5*b^7*c^11*d^5 + 924*a^6*b^6*c^10*d^6 - 792*a^7*b^5*c^9*d^7 + 495*a^8*b^4*c^8*d^8 - 220*a^9*b^3*c^7*d^9 + 66*a^10*b^2*c^6*d^10 - 12*a*b^11*c^15*d)))*(-(a*b^7)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4) - (((((81*a^9*b^7*d^10)/2048 - (1431*a^8*b^8*c*d^9)/2048 - (194481*a^2*b^14*c^7*d^3)/2048 - (713097*a^3*b^13*c^6*d^4)/2048 - (432453*a^4*b^12*c^5*d^5)/2048 + (18067*a^5*b^11*c^4*d^6)/2048 + (5709*a^6*b^10*c^3*d^7)/2048 + (6885*a^7*b^9*c^2*d^8)/2048)*1i)/(b^8*c^12 + a^8*c^4*d^8 - 8*a^7*b*c^5*d^7 + 28*a^2*b^6*c^10*d^2 - 56*a^3*b^5*c^9*d^3 + 70*a^4*b^4*c^8*d^4 - 56*a^5*b^3*c^7*d^5 + 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1030225920*a^4*b^19*c^17*d^6 - 3328573440*a^5*b^18*c^16*d^7 + 7335837696*a^6*b^17*c^15*d^8 - 11738087424*a^7*b^16*c^14*d^9 + 14203486208*a^8*b^15*c^13*d^10 - 13361086464*a^9*b^14*c^12*d^11 + 9861857280*a^10*b^13*c^11*d^12 - 5521702912*a^11*b^12*c^10*d^13 + 1989672960*a^12*b^11*c^9*d^14 - 49938432*a^13*b^10*c^8*d^15 - 484442112*a^14*b^9*c^7*d^16 + 343080960*a^15*b^8*c^6*d^17 - 127401984*a^16*b^7*c^5*d^18 + 27394048*a^17*b^6*c^4*d^19 - 3145728*a^18*b^5*c^3*d^20 + 147456*a^19*b^4*c^2*d^21)*1i)/(4096*(b^12*c^16 + a^12*c^4*d^12 - 12*a^11*b*c^5*d^11 + 66*a^2*b^10*c^14*d^2 - 220*a^3*b^9*c^13*d^3 + 495*a^4*b^8*c^12*d^4 - 792*a^5*b^7*c^11*d^5 + 924*a^6*b^6*c^10*d^6 - 792*a^7*b^5*c^9*d^7 + 495*a^8*b^4*c^8*d^8 - 220*a^9*b^3*c^7*d^9 + 66*a^10*b^2*c^6*d^10 - 12*a*b^11*c^15*d)))*(-(a*b^7)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(3/4)*1i)*(-(a*b^7)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4) + (x^(1/2)*(81*a^10*b^9*d^11 - 1512*a^9*b^10*c*d^10 + 194481*a^2*b^17*c^8*d^3 + 518616*a^3*b^16*c^7*d^4 + 859068*a^4*b^15*c^6*d^5 + 610344*a^5*b^14*c^5*d^6 - 14266*a^6*b^13*c^4*d^7 - 87192*a^7*b^12*c^3*d^8 + 17532*a^8*b^11*c^2*d^9))/(4096*(b^12*c^16 + a^12*c^4*d^12 - 12*a^11*b*c^5*d^11 + 66*a^2*b^10*c^14*d^2 - 220*a^3*b^9*c^13*d^3 + 495*a^4*b^8*c^12*d^4 - 792*a^5*b^7*c^11*d^5 + 924*a^6*b^6*c^10*d^6 - 792*a^7*b^5*c^9*d^7 + 495*a^8*b^4*c^8*d^8 - 220*a^9*b^3*c^7*d^9 + 66*a^10*b^2*c^6*d^10 - 12*a*b^11*c^15*d)))*(-(a*b^7)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 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506112*a^4*b^16*c^16*d^6 - 1607168*a^5*b^15*c^15*d^7 + 3384832*a^6*b^14*c^14*d^8 - 4925184*a^7*b^13*c^13*d^9 + 4958976*a^8*b^12*c^12*d^10 - 3277824*a^9*b^11*c^11*d^11 + 1115136*a^10*b^10*c^10*d^12 + 199936*a^11*b^9*c^9*d^13 - 459008*a^12*b^8*c^8*d^14 + 256512*a^13*b^7*c^7*d^15 - 76288*a^14*b^6*c^6*d^16 + 12032*a^15*b^5*c^5*d^17 - 768*a^16*b^4*c^4*d^18))/(b^8*c^12 + a^8*c^4*d^8 - 8*a^7*b*c^5*d^7 + 28*a^2*b^6*c^10*d^2 - 56*a^3*b^5*c^9*d^3 + 70*a^4*b^4*c^8*d^4 - 56*a^5*b^3*c^7*d^5 + 28*a^6*b^2*c^6*d^6 - 8*a*b^7*c^11*d) - (x^(1/2)*(16777216*a^2*b^21*c^19*d^4 - 194101248*a^3*b^20*c^18*d^5 + 1030225920*a^4*b^19*c^17*d^6 - 3328573440*a^5*b^18*c^16*d^7 + 7335837696*a^6*b^17*c^15*d^8 - 11738087424*a^7*b^16*c^14*d^9 + 14203486208*a^8*b^15*c^13*d^10 - 13361086464*a^9*b^14*c^12*d^11 + 9861857280*a^10*b^13*c^11*d^12 - 5521702912*a^11*b^12*c^10*d^13 + 1989672960*a^12*b^11*c^9*d^14 - 49938432*a^13*b^10*c^8*d^15 - 484442112*a^14*b^9*c^7*d^16 + 343080960*a^15*b^8*c^6*d^17 - 127401984*a^16*b^7*c^5*d^18 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(x^(1/2)*(81*a^10*b^9*d^11 - 1512*a^9*b^10*c*d^10 + 194481*a^2*b^17*c^8*d^3 + 518616*a^3*b^16*c^7*d^4 + 859068*a^4*b^15*c^6*d^5 + 610344*a^5*b^14*c^5*d^6 - 14266*a^6*b^13*c^4*d^7 - 87192*a^7*b^12*c^3*d^8 + 17532*a^8*b^11*c^2*d^9)*1i)/(4096*(b^12*c^16 + a^12*c^4*d^12 - 12*a^11*b*c^5*d^11 + 66*a^2*b^10*c^14*d^2 - 220*a^3*b^9*c^13*d^3 + 495*a^4*b^8*c^12*d^4 - 792*a^5*b^7*c^11*d^5 + 924*a^6*b^6*c^10*d^6 - 792*a^7*b^5*c^9*d^7 + 495*a^8*b^4*c^8*d^8 - 220*a^9*b^3*c^7*d^9 + 66*a^10*b^2*c^6*d^10 - 12*a*b^11*c^15*d)))*(-(a*b^7)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4) + (((((81*a^9*b^7*d^10)/2048 - (1431*a^8*b^8*c*d^9)/2048 - (194481*a^2*b^14*c^7*d^3)/2048 - (713097*a^3*b^13*c^6*d^4)/2048 - (432453*a^4*b^12*c^5*d^5)/2048 + (18067*a^5*b^11*c^4*d^6)/2048 + (5709*a^6*b^10*c^3*d^7)/2048 + (6885*a^7*b^9*c^2*d^8)/2048)*1i)/(b^8*c^12 + a^8*c^4*d^8 - 8*a^7*b*c^5*d^7 + 28*a^2*b^6*c^10*d^2 - 56*a^3*b^5*c^9*d^3 + 70*a^4*b^4*c^8*d^4 - 56*a^5*b^3*c^7*d^5 + 28*a^6*b^2*c^6*d^6 - 8*a*b^7*c^11*d) - (((-(a*b^7)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4)*(8192*a^2*b^18*c^18*d^4 - 95488*a^3*b^17*c^17*d^5 + 506112*a^4*b^16*c^16*d^6 - 1607168*a^5*b^15*c^15*d^7 + 3384832*a^6*b^14*c^14*d^8 - 4925184*a^7*b^13*c^13*d^9 + 4958976*a^8*b^12*c^12*d^10 - 3277824*a^9*b^11*c^11*d^11 + 1115136*a^10*b^10*c^10*d^12 + 199936*a^11*b^9*c^9*d^13 - 459008*a^12*b^8*c^8*d^14 + 256512*a^13*b^7*c^7*d^15 - 76288*a^14*b^6*c^6*d^16 + 12032*a^15*b^5*c^5*d^17 - 768*a^16*b^4*c^4*d^18))/(b^8*c^12 + a^8*c^4*d^8 - 8*a^7*b*c^5*d^7 + 28*a^2*b^6*c^10*d^2 - 56*a^3*b^5*c^9*d^3 + 70*a^4*b^4*c^8*d^4 - 56*a^5*b^3*c^7*d^5 + 28*a^6*b^2*c^6*d^6 - 8*a*b^7*c^11*d) + (x^(1/2)*(16777216*a^2*b^21*c^19*d^4 - 194101248*a^3*b^20*c^18*d^5 + 1030225920*a^4*b^19*c^17*d^6 - 3328573440*a^5*b^18*c^16*d^7 + 7335837696*a^6*b^17*c^15*d^8 - 11738087424*a^7*b^16*c^14*d^9 + 14203486208*a^8*b^15*c^13*d^10 - 13361086464*a^9*b^14*c^12*d^11 + 9861857280*a^10*b^13*c^11*d^12 - 5521702912*a^11*b^12*c^10*d^13 + 1989672960*a^12*b^11*c^9*d^14 - 49938432*a^13*b^10*c^8*d^15 - 484442112*a^14*b^9*c^7*d^16 + 343080960*a^15*b^8*c^6*d^17 - 127401984*a^16*b^7*c^5*d^18 + 27394048*a^17*b^6*c^4*d^19 - 3145728*a^18*b^5*c^3*d^20 + 147456*a^19*b^4*c^2*d^21)*1i)/(4096*(b^12*c^16 + a^12*c^4*d^12 - 12*a^11*b*c^5*d^11 + 66*a^2*b^10*c^14*d^2 - 220*a^3*b^9*c^13*d^3 + 495*a^4*b^8*c^12*d^4 - 792*a^5*b^7*c^11*d^5 + 924*a^6*b^6*c^10*d^6 - 792*a^7*b^5*c^9*d^7 + 495*a^8*b^4*c^8*d^8 - 220*a^9*b^3*c^7*d^9 + 66*a^10*b^2*c^6*d^10 - 12*a*b^11*c^15*d)))*(-(a*b^7)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(3/4)*1i)*(-(a*b^7)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4)*1i + (x^(1/2)*(81*a^10*b^9*d^11 - 1512*a^9*b^10*c*d^10 + 194481*a^2*b^17*c^8*d^3 + 518616*a^3*b^16*c^7*d^4 + 859068*a^4*b^15*c^6*d^5 + 610344*a^5*b^14*c^5*d^6 - 14266*a^6*b^13*c^4*d^7 - 87192*a^7*b^12*c^3*d^8 + 17532*a^8*b^11*c^2*d^9)*1i)/(4096*(b^12*c^16 + a^12*c^4*d^12 - 12*a^11*b*c^5*d^11 + 66*a^2*b^10*c^14*d^2 - 220*a^3*b^9*c^13*d^3 + 495*a^4*b^8*c^12*d^4 - 792*a^5*b^7*c^11*d^5 + 924*a^6*b^6*c^10*d^6 - 792*a^7*b^5*c^9*d^7 + 495*a^8*b^4*c^8*d^8 - 220*a^9*b^3*c^7*d^9 + 66*a^10*b^2*c^6*d^10 - 12*a*b^11*c^15*d)))*(-(a*b^7)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4)))*(-(a*b^7)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4) - atan((((((81*a^9*b^7*d^10)/2048 - (1431*a^8*b^8*c*d^9)/2048 - (194481*a^2*b^14*c^7*d^3)/2048 - (713097*a^3*b^13*c^6*d^4)/2048 - (432453*a^4*b^12*c^5*d^5)/2048 + (18067*a^5*b^11*c^4*d^6)/2048 + (5709*a^6*b^10*c^3*d^7)/2048 + (6885*a^7*b^9*c^2*d^8)/2048)/(b^8*c^12 + a^8*c^4*d^8 - 8*a^7*b*c^5*d^7 + 28*a^2*b^6*c^10*d^2 - 56*a^3*b^5*c^9*d^3 + 70*a^4*b^4*c^8*d^4 - 56*a^5*b^3*c^7*d^5 + 28*a^6*b^2*c^6*d^6 - 8*a*b^7*c^11*d) - (((-(a*b^7)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4)*(8192*a^2*b^18*c^18*d^4 - 95488*a^3*b^17*c^17*d^5 + 506112*a^4*b^16*c^16*d^6 - 1607168*a^5*b^15*c^15*d^7 + 3384832*a^6*b^14*c^14*d^8 - 4925184*a^7*b^13*c^13*d^9 + 4958976*a^8*b^12*c^12*d^10 - 3277824*a^9*b^11*c^11*d^11 + 1115136*a^10*b^10*c^10*d^12 + 199936*a^11*b^9*c^9*d^13 - 459008*a^12*b^8*c^8*d^14 + 256512*a^13*b^7*c^7*d^15 - 76288*a^14*b^6*c^6*d^16 + 12032*a^15*b^5*c^5*d^17 - 768*a^16*b^4*c^4*d^18))/(b^8*c^12 + a^8*c^4*d^8 - 8*a^7*b*c^5*d^7 + 28*a^2*b^6*c^10*d^2 - 56*a^3*b^5*c^9*d^3 + 70*a^4*b^4*c^8*d^4 - 56*a^5*b^3*c^7*d^5 + 28*a^6*b^2*c^6*d^6 - 8*a*b^7*c^11*d) - (x^(1/2)*(16777216*a^2*b^21*c^19*d^4 - 194101248*a^3*b^20*c^18*d^5 + 1030225920*a^4*b^19*c^17*d^6 - 3328573440*a^5*b^18*c^16*d^7 + 7335837696*a^6*b^17*c^15*d^8 - 11738087424*a^7*b^16*c^14*d^9 + 14203486208*a^8*b^15*c^13*d^10 - 13361086464*a^9*b^14*c^12*d^11 + 9861857280*a^10*b^13*c^11*d^12 - 5521702912*a^11*b^12*c^10*d^13 + 1989672960*a^12*b^11*c^9*d^14 - 49938432*a^13*b^10*c^8*d^15 - 484442112*a^14*b^9*c^7*d^16 + 343080960*a^15*b^8*c^6*d^17 - 127401984*a^16*b^7*c^5*d^18 + 27394048*a^17*b^6*c^4*d^19 - 3145728*a^18*b^5*c^3*d^20 + 147456*a^19*b^4*c^2*d^21))/(4096*(b^12*c^16 + a^12*c^4*d^12 - 12*a^11*b*c^5*d^11 + 66*a^2*b^10*c^14*d^2 - 220*a^3*b^9*c^13*d^3 + 495*a^4*b^8*c^12*d^4 - 792*a^5*b^7*c^11*d^5 + 924*a^6*b^6*c^10*d^6 - 792*a^7*b^5*c^9*d^7 + 495*a^8*b^4*c^8*d^8 - 220*a^9*b^3*c^7*d^9 + 66*a^10*b^2*c^6*d^10 - 12*a*b^11*c^15*d)))*(-(a*b^7)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(3/4))*(-(a*b^7)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4)*1i + (x^(1/2)*(81*a^10*b^9*d^11 - 1512*a^9*b^10*c*d^10 + 194481*a^2*b^17*c^8*d^3 + 518616*a^3*b^16*c^7*d^4 + 859068*a^4*b^15*c^6*d^5 + 610344*a^5*b^14*c^5*d^6 - 14266*a^6*b^13*c^4*d^7 - 87192*a^7*b^12*c^3*d^8 + 17532*a^8*b^11*c^2*d^9)*1i)/(4096*(b^12*c^16 + a^12*c^4*d^12 - 12*a^11*b*c^5*d^11 + 66*a^2*b^10*c^14*d^2 - 220*a^3*b^9*c^13*d^3 + 495*a^4*b^8*c^12*d^4 - 792*a^5*b^7*c^11*d^5 + 924*a^6*b^6*c^10*d^6 - 792*a^7*b^5*c^9*d^7 + 495*a^8*b^4*c^8*d^8 - 220*a^9*b^3*c^7*d^9 + 66*a^10*b^2*c^6*d^10 - 12*a*b^11*c^15*d)))*(-(a*b^7)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4) - ((((81*a^9*b^7*d^10)/2048 - (1431*a^8*b^8*c*d^9)/2048 - (194481*a^2*b^14*c^7*d^3)/2048 - (713097*a^3*b^13*c^6*d^4)/2048 - (432453*a^4*b^12*c^5*d^5)/2048 + (18067*a^5*b^11*c^4*d^6)/2048 + (5709*a^6*b^10*c^3*d^7)/2048 + (6885*a^7*b^9*c^2*d^8)/2048)/(b^8*c^12 + a^8*c^4*d^8 - 8*a^7*b*c^5*d^7 + 28*a^2*b^6*c^10*d^2 - 56*a^3*b^5*c^9*d^3 + 70*a^4*b^4*c^8*d^4 - 56*a^5*b^3*c^7*d^5 + 28*a^6*b^2*c^6*d^6 - 8*a*b^7*c^11*d) - (((-(a*b^7)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4)*(8192*a^2*b^18*c^18*d^4 - 95488*a^3*b^17*c^17*d^5 + 506112*a^4*b^16*c^16*d^6 - 1607168*a^5*b^15*c^15*d^7 + 3384832*a^6*b^14*c^14*d^8 - 4925184*a^7*b^13*c^13*d^9 + 4958976*a^8*b^12*c^12*d^10 - 3277824*a^9*b^11*c^11*d^11 + 1115136*a^10*b^10*c^10*d^12 + 199936*a^11*b^9*c^9*d^13 - 459008*a^12*b^8*c^8*d^14 + 256512*a^13*b^7*c^7*d^15 - 76288*a^14*b^6*c^6*d^16 + 12032*a^15*b^5*c^5*d^17 - 768*a^16*b^4*c^4*d^18))/(b^8*c^12 + a^8*c^4*d^8 - 8*a^7*b*c^5*d^7 + 28*a^2*b^6*c^10*d^2 - 56*a^3*b^5*c^9*d^3 + 70*a^4*b^4*c^8*d^4 - 56*a^5*b^3*c^7*d^5 + 28*a^6*b^2*c^6*d^6 - 8*a*b^7*c^11*d) + (x^(1/2)*(16777216*a^2*b^21*c^19*d^4 - 194101248*a^3*b^20*c^18*d^5 + 1030225920*a^4*b^19*c^17*d^6 - 3328573440*a^5*b^18*c^16*d^7 + 7335837696*a^6*b^17*c^15*d^8 - 11738087424*a^7*b^16*c^14*d^9 + 14203486208*a^8*b^15*c^13*d^10 - 13361086464*a^9*b^14*c^12*d^11 + 9861857280*a^10*b^13*c^11*d^12 - 5521702912*a^11*b^12*c^10*d^13 + 1989672960*a^12*b^11*c^9*d^14 - 49938432*a^13*b^10*c^8*d^15 - 484442112*a^14*b^9*c^7*d^16 + 343080960*a^15*b^8*c^6*d^17 - 127401984*a^16*b^7*c^5*d^18 + 27394048*a^17*b^6*c^4*d^19 - 3145728*a^18*b^5*c^3*d^20 + 147456*a^19*b^4*c^2*d^21))/(4096*(b^12*c^16 + a^12*c^4*d^12 - 12*a^11*b*c^5*d^11 + 66*a^2*b^10*c^14*d^2 - 220*a^3*b^9*c^13*d^3 + 495*a^4*b^8*c^12*d^4 - 792*a^5*b^7*c^11*d^5 + 924*a^6*b^6*c^10*d^6 - 792*a^7*b^5*c^9*d^7 + 495*a^8*b^4*c^8*d^8 - 220*a^9*b^3*c^7*d^9 + 66*a^10*b^2*c^6*d^10 - 12*a*b^11*c^15*d)))*(-(a*b^7)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(3/4))*(-(a*b^7)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4)*1i - (x^(1/2)*(81*a^10*b^9*d^11 - 1512*a^9*b^10*c*d^10 + 194481*a^2*b^17*c^8*d^3 + 518616*a^3*b^16*c^7*d^4 + 859068*a^4*b^15*c^6*d^5 + 610344*a^5*b^14*c^5*d^6 - 14266*a^6*b^13*c^4*d^7 - 87192*a^7*b^12*c^3*d^8 + 17532*a^8*b^11*c^2*d^9)*1i)/(4096*(b^12*c^16 + a^12*c^4*d^12 - 12*a^11*b*c^5*d^11 + 66*a^2*b^10*c^14*d^2 - 220*a^3*b^9*c^13*d^3 + 495*a^4*b^8*c^12*d^4 - 792*a^5*b^7*c^11*d^5 + 924*a^6*b^6*c^10*d^6 - 792*a^7*b^5*c^9*d^7 + 495*a^8*b^4*c^8*d^8 - 220*a^9*b^3*c^7*d^9 + 66*a^10*b^2*c^6*d^10 - 12*a*b^11*c^15*d)))*(-(a*b^7)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4))/(((((81*a^9*b^7*d^10)/2048 - (1431*a^8*b^8*c*d^9)/2048 - (194481*a^2*b^14*c^7*d^3)/2048 - (713097*a^3*b^13*c^6*d^4)/2048 - (432453*a^4*b^12*c^5*d^5)/2048 + (18067*a^5*b^11*c^4*d^6)/2048 + (5709*a^6*b^10*c^3*d^7)/2048 + (6885*a^7*b^9*c^2*d^8)/2048)/(b^8*c^12 + a^8*c^4*d^8 - 8*a^7*b*c^5*d^7 + 28*a^2*b^6*c^10*d^2 - 56*a^3*b^5*c^9*d^3 + 70*a^4*b^4*c^8*d^4 - 56*a^5*b^3*c^7*d^5 + 28*a^6*b^2*c^6*d^6 - 8*a*b^7*c^11*d) - (((-(a*b^7)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4)*(8192*a^2*b^18*c^18*d^4 - 95488*a^3*b^17*c^17*d^5 + 506112*a^4*b^16*c^16*d^6 - 1607168*a^5*b^15*c^15*d^7 + 3384832*a^6*b^14*c^14*d^8 - 4925184*a^7*b^13*c^13*d^9 + 4958976*a^8*b^12*c^12*d^10 - 3277824*a^9*b^11*c^11*d^11 + 1115136*a^10*b^10*c^10*d^12 + 199936*a^11*b^9*c^9*d^13 - 459008*a^12*b^8*c^8*d^14 + 256512*a^13*b^7*c^7*d^15 - 76288*a^14*b^6*c^6*d^16 + 12032*a^15*b^5*c^5*d^17 - 768*a^16*b^4*c^4*d^18))/(b^8*c^12 + a^8*c^4*d^8 - 8*a^7*b*c^5*d^7 + 28*a^2*b^6*c^10*d^2 - 56*a^3*b^5*c^9*d^3 + 70*a^4*b^4*c^8*d^4 - 56*a^5*b^3*c^7*d^5 + 28*a^6*b^2*c^6*d^6 - 8*a*b^7*c^11*d) - (x^(1/2)*(16777216*a^2*b^21*c^19*d^4 - 194101248*a^3*b^20*c^18*d^5 + 1030225920*a^4*b^19*c^17*d^6 - 3328573440*a^5*b^18*c^16*d^7 + 7335837696*a^6*b^17*c^15*d^8 - 11738087424*a^7*b^16*c^14*d^9 + 14203486208*a^8*b^15*c^13*d^10 - 13361086464*a^9*b^14*c^12*d^11 + 9861857280*a^10*b^13*c^11*d^12 - 5521702912*a^11*b^12*c^10*d^13 + 1989672960*a^12*b^11*c^9*d^14 - 49938432*a^13*b^10*c^8*d^15 - 484442112*a^14*b^9*c^7*d^16 + 343080960*a^15*b^8*c^6*d^17 - 127401984*a^16*b^7*c^5*d^18 + 27394048*a^17*b^6*c^4*d^19 - 3145728*a^18*b^5*c^3*d^20 + 147456*a^19*b^4*c^2*d^21))/(4096*(b^12*c^16 + a^12*c^4*d^12 - 12*a^11*b*c^5*d^11 + 66*a^2*b^10*c^14*d^2 - 220*a^3*b^9*c^13*d^3 + 495*a^4*b^8*c^12*d^4 - 792*a^5*b^7*c^11*d^5 + 924*a^6*b^6*c^10*d^6 - 792*a^7*b^5*c^9*d^7 + 495*a^8*b^4*c^8*d^8 - 220*a^9*b^3*c^7*d^9 + 66*a^10*b^2*c^6*d^10 - 12*a*b^11*c^15*d)))*(-(a*b^7)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(3/4))*(-(a*b^7)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4) + (x^(1/2)*(81*a^10*b^9*d^11 - 1512*a^9*b^10*c*d^10 + 194481*a^2*b^17*c^8*d^3 + 518616*a^3*b^16*c^7*d^4 + 859068*a^4*b^15*c^6*d^5 + 610344*a^5*b^14*c^5*d^6 - 14266*a^6*b^13*c^4*d^7 - 87192*a^7*b^12*c^3*d^8 + 17532*a^8*b^11*c^2*d^9))/(4096*(b^12*c^16 + a^12*c^4*d^12 - 12*a^11*b*c^5*d^11 + 66*a^2*b^10*c^14*d^2 - 220*a^3*b^9*c^13*d^3 + 495*a^4*b^8*c^12*d^4 - 792*a^5*b^7*c^11*d^5 + 924*a^6*b^6*c^10*d^6 - 792*a^7*b^5*c^9*d^7 + 495*a^8*b^4*c^8*d^8 - 220*a^9*b^3*c^7*d^9 + 66*a^10*b^2*c^6*d^10 - 12*a*b^11*c^15*d)))*(-(a*b^7)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4) + ((((81*a^9*b^7*d^10)/2048 - (1431*a^8*b^8*c*d^9)/2048 - (194481*a^2*b^14*c^7*d^3)/2048 - (713097*a^3*b^13*c^6*d^4)/2048 - (432453*a^4*b^12*c^5*d^5)/2048 + (18067*a^5*b^11*c^4*d^6)/2048 + (5709*a^6*b^10*c^3*d^7)/2048 + (6885*a^7*b^9*c^2*d^8)/2048)/(b^8*c^12 + a^8*c^4*d^8 - 8*a^7*b*c^5*d^7 + 28*a^2*b^6*c^10*d^2 - 56*a^3*b^5*c^9*d^3 + 70*a^4*b^4*c^8*d^4 - 56*a^5*b^3*c^7*d^5 + 28*a^6*b^2*c^6*d^6 - 8*a*b^7*c^11*d) - (((-(a*b^7)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4)*(8192*a^2*b^18*c^18*d^4 - 95488*a^3*b^17*c^17*d^5 + 506112*a^4*b^16*c^16*d^6 - 1607168*a^5*b^15*c^15*d^7 + 3384832*a^6*b^14*c^14*d^8 - 4925184*a^7*b^13*c^13*d^9 + 4958976*a^8*b^12*c^12*d^10 - 3277824*a^9*b^11*c^11*d^11 + 1115136*a^10*b^10*c^10*d^12 + 199936*a^11*b^9*c^9*d^13 - 459008*a^12*b^8*c^8*d^14 + 256512*a^13*b^7*c^7*d^15 - 76288*a^14*b^6*c^6*d^16 + 12032*a^15*b^5*c^5*d^17 - 768*a^16*b^4*c^4*d^18))/(b^8*c^12 + a^8*c^4*d^8 - 8*a^7*b*c^5*d^7 + 28*a^2*b^6*c^10*d^2 - 56*a^3*b^5*c^9*d^3 + 70*a^4*b^4*c^8*d^4 - 56*a^5*b^3*c^7*d^5 + 28*a^6*b^2*c^6*d^6 - 8*a*b^7*c^11*d) + (x^(1/2)*(16777216*a^2*b^21*c^19*d^4 - 194101248*a^3*b^20*c^18*d^5 + 1030225920*a^4*b^19*c^17*d^6 - 3328573440*a^5*b^18*c^16*d^7 + 7335837696*a^6*b^17*c^15*d^8 - 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192*a^11*b*c*d^11))^(3/4))*(-(a*b^7)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 12672*a^7*b^5*c^5*d^7 + 7920*a^8*b^4*c^4*d^8 - 3520*a^9*b^3*c^3*d^9 + 1056*a^10*b^2*c^2*d^10 - 192*a*b^11*c^11*d - 192*a^11*b*c*d^11))^(1/4) - (x^(1/2)*(81*a^10*b^9*d^11 - 1512*a^9*b^10*c*d^10 + 194481*a^2*b^17*c^8*d^3 + 518616*a^3*b^16*c^7*d^4 + 859068*a^4*b^15*c^6*d^5 + 610344*a^5*b^14*c^5*d^6 - 14266*a^6*b^13*c^4*d^7 - 87192*a^7*b^12*c^3*d^8 + 17532*a^8*b^11*c^2*d^9))/(4096*(b^12*c^16 + a^12*c^4*d^12 - 12*a^11*b*c^5*d^11 + 66*a^2*b^10*c^14*d^2 - 220*a^3*b^9*c^13*d^3 + 495*a^4*b^8*c^12*d^4 - 792*a^5*b^7*c^11*d^5 + 924*a^6*b^6*c^10*d^6 - 792*a^7*b^5*c^9*d^7 + 495*a^8*b^4*c^8*d^8 - 220*a^9*b^3*c^7*d^9 + 66*a^10*b^2*c^6*d^10 - 12*a*b^11*c^15*d)))*(-(a*b^7)/(16*a^12*d^12 + 16*b^12*c^12 + 1056*a^2*b^10*c^10*d^2 - 3520*a^3*b^9*c^9*d^3 + 7920*a^4*b^8*c^8*d^4 - 12672*a^5*b^7*c^7*d^5 + 14784*a^6*b^6*c^6*d^6 - 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220*a^3*b^9*c^13*d^3 + 495*a^4*b^8*c^12*d^4 - 792*a^5*b^7*c^11*d^5 + 924*a^6*b^6*c^10*d^6 - 792*a^7*b^5*c^9*d^7 + 495*a^8*b^4*c^8*d^8 - 220*a^9*b^3*c^7*d^9 + 66*a^10*b^2*c^6*d^10 - 12*a*b^11*c^15*d))) - ((81*a^9*b^7*d^10)/2048 - (1431*a^8*b^8*c*d^9)/2048 - (194481*a^2*b^14*c^7*d^3)/2048 - (713097*a^3*b^13*c^6*d^4)/2048 - (432453*a^4*b^12*c^5*d^5)/2048 + (18067*a^5*b^11*c^4*d^6)/2048 + (5709*a^6*b^10*c^3*d^7)/2048 + (6885*a^7*b^9*c^2*d^8)/2048)/(b^8*c^12 + a^8*c^4*d^8 - 8*a^7*b*c^5*d^7 + 28*a^2*b^6*c^10*d^2 - 56*a^3*b^5*c^9*d^3 + 70*a^4*b^4*c^8*d^4 - 56*a^5*b^3*c^7*d^5 + 28*a^6*b^2*c^6*d^6 - 8*a*b^7*c^11*d))*1i - (x^(1/2)*(81*a^10*b^9*d^11 - 1512*a^9*b^10*c*d^10 + 194481*a^2*b^17*c^8*d^3 + 518616*a^3*b^16*c^7*d^4 + 859068*a^4*b^15*c^6*d^5 + 610344*a^5*b^14*c^5*d^6 - 14266*a^6*b^13*c^4*d^7 - 87192*a^7*b^12*c^3*d^8 + 17532*a^8*b^11*c^2*d^9)*1i)/(4096*(b^12*c^16 + a^12*c^4*d^12 - 12*a^11*b*c^5*d^11 + 66*a^2*b^10*c^14*d^2 - 220*a^3*b^9*c^13*d^3 + 495*a^4*b^8*c^12*d^4 - 792*a^5*b^7*c^11*d^5 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76288*a^14*b^6*c^6*d^16 + 12032*a^15*b^5*c^5*d^17 - 768*a^16*b^4*c^4*d^18))/(b^8*c^12 + a^8*c^4*d^8 - 8*a^7*b*c^5*d^7 + 28*a^2*b^6*c^10*d^2 - 56*a^3*b^5*c^9*d^3 + 70*a^4*b^4*c^8*d^4 - 56*a^5*b^3*c^7*d^5 + 28*a^6*b^2*c^6*d^6 - 8*a*b^7*c^11*d) - (x^(1/2)*(16777216*a^2*b^21*c^19*d^4 - 194101248*a^3*b^20*c^18*d^5 + 1030225920*a^4*b^19*c^17*d^6 - 3328573440*a^5*b^18*c^16*d^7 + 7335837696*a^6*b^17*c^15*d^8 - 11738087424*a^7*b^16*c^14*d^9 + 14203486208*a^8*b^15*c^13*d^10 - 13361086464*a^9*b^14*c^12*d^11 + 9861857280*a^10*b^13*c^11*d^12 - 5521702912*a^11*b^12*c^10*d^13 + 1989672960*a^12*b^11*c^9*d^14 - 49938432*a^13*b^10*c^8*d^15 - 484442112*a^14*b^9*c^7*d^16 + 343080960*a^15*b^8*c^6*d^17 - 127401984*a^16*b^7*c^5*d^18 + 27394048*a^17*b^6*c^4*d^19 - 3145728*a^18*b^5*c^3*d^20 + 147456*a^19*b^4*c^2*d^21)*1i)/(4096*(b^12*c^16 + a^12*c^4*d^12 - 12*a^11*b*c^5*d^11 + 66*a^2*b^10*c^14*d^2 - 220*a^3*b^9*c^13*d^3 + 495*a^4*b^8*c^12*d^4 - 792*a^5*b^7*c^11*d^5 + 924*a^6*b^6*c^10*d^6 - 792*a^7*b^5*c^9*d^7 + 495*a^8*b^4*c^8*d^8 - 220*a^9*b^3*c^7*d^9 + 66*a^10*b^2*c^6*d^10 - 12*a*b^11*c^15*d)))*1i - (((81*a^9*b^7*d^10)/2048 - (1431*a^8*b^8*c*d^9)/2048 - (194481*a^2*b^14*c^7*d^3)/2048 - (713097*a^3*b^13*c^6*d^4)/2048 - (432453*a^4*b^12*c^5*d^5)/2048 + (18067*a^5*b^11*c^4*d^6)/2048 + (5709*a^6*b^10*c^3*d^7)/2048 + (6885*a^7*b^9*c^2*d^8)/2048)*1i)/(b^8*c^12 + a^8*c^4*d^8 - 8*a^7*b*c^5*d^7 + 28*a^2*b^6*c^10*d^2 - 56*a^3*b^5*c^9*d^3 + 70*a^4*b^4*c^8*d^4 - 56*a^5*b^3*c^7*d^5 + 28*a^6*b^2*c^6*d^6 - 8*a*b^7*c^11*d))*1i + (x^(1/2)*(81*a^10*b^9*d^11 - 1512*a^9*b^10*c*d^10 + 194481*a^2*b^17*c^8*d^3 + 518616*a^3*b^16*c^7*d^4 + 859068*a^4*b^15*c^6*d^5 + 610344*a^5*b^14*c^5*d^6 - 14266*a^6*b^13*c^4*d^7 - 87192*a^7*b^12*c^3*d^8 + 17532*a^8*b^11*c^2*d^9)*1i)/(4096*(b^12*c^16 + a^12*c^4*d^12 - 12*a^11*b*c^5*d^11 + 66*a^2*b^10*c^14*d^2 - 220*a^3*b^9*c^13*d^3 + 495*a^4*b^8*c^12*d^4 - 792*a^5*b^7*c^11*d^5 + 924*a^6*b^6*c^10*d^6 - 792*a^7*b^5*c^9*d^7 + 495*a^8*b^4*c^8*d^8 - 220*a^9*b^3*c^7*d^9 + 66*a^10*b^2*c^6*d^10 - 12*a*b^11*c^15*d))) + (-(81*a^8*d^8 + 194481*b^8*c^8 + 407484*a^2*b^6*c^6*d^2 + 8232*a^3*b^5*c^5*d^3 - 85946*a^4*b^4*c^4*d^4 - 1176*a^5*b^3*c^3*d^5 + 8316*a^6*b^2*c^2*d^6 + 518616*a*b^7*c^7*d - 1512*a^7*b*c*d^7)/(16777216*b^12*c^19*d + 16777216*a^12*c^7*d^13 - 201326592*a*b^11*c^18*d^2 - 201326592*a^11*b*c^8*d^12 + 1107296256*a^2*b^10*c^17*d^3 - 3690987520*a^3*b^9*c^16*d^4 + 8304721920*a^4*b^8*c^15*d^5 - 13287555072*a^5*b^7*c^14*d^6 + 15502147584*a^6*b^6*c^13*d^7 - 13287555072*a^7*b^5*c^12*d^8 + 8304721920*a^8*b^4*c^11*d^9 - 3690987520*a^9*b^3*c^10*d^10 + 1107296256*a^10*b^2*c^9*d^11))^(1/4)*((-(81*a^8*d^8 + 194481*b^8*c^8 + 407484*a^2*b^6*c^6*d^2 + 8232*a^3*b^5*c^5*d^3 - 85946*a^4*b^4*c^4*d^4 - 1176*a^5*b^3*c^3*d^5 + 8316*a^6*b^2*c^2*d^6 + 518616*a*b^7*c^7*d - 1512*a^7*b*c*d^7)/(16777216*b^12*c^19*d + 16777216*a^12*c^7*d^13 - 201326592*a*b^11*c^18*d^2 - 201326592*a^11*b*c^8*d^12 + 1107296256*a^2*b^10*c^17*d^3 - 3690987520*a^3*b^9*c^16*d^4 + 8304721920*a^4*b^8*c^15*d^5 - 13287555072*a^5*b^7*c^14*d^6 + 15502147584*a^6*b^6*c^13*d^7 - 13287555072*a^7*b^5*c^12*d^8 + 8304721920*a^8*b^4*c^11*d^9 - 3690987520*a^9*b^3*c^10*d^10 + 1107296256*a^10*b^2*c^9*d^11))^(1/4)*((-(81*a^8*d^8 + 194481*b^8*c^8 + 407484*a^2*b^6*c^6*d^2 + 8232*a^3*b^5*c^5*d^3 - 85946*a^4*b^4*c^4*d^4 - 1176*a^5*b^3*c^3*d^5 + 8316*a^6*b^2*c^2*d^6 + 518616*a*b^7*c^7*d - 1512*a^7*b*c*d^7)/(16777216*b^12*c^19*d + 16777216*a^12*c^7*d^13 - 201326592*a*b^11*c^18*d^2 - 201326592*a^11*b*c^8*d^12 + 1107296256*a^2*b^10*c^17*d^3 - 3690987520*a^3*b^9*c^16*d^4 + 8304721920*a^4*b^8*c^15*d^5 - 13287555072*a^5*b^7*c^14*d^6 + 15502147584*a^6*b^6*c^13*d^7 - 13287555072*a^7*b^5*c^12*d^8 + 8304721920*a^8*b^4*c^11*d^9 - 3690987520*a^9*b^3*c^10*d^10 + 1107296256*a^10*b^2*c^9*d^11))^(3/4)*(((-(81*a^8*d^8 + 194481*b^8*c^8 + 407484*a^2*b^6*c^6*d^2 + 8232*a^3*b^5*c^5*d^3 - 85946*a^4*b^4*c^4*d^4 - 1176*a^5*b^3*c^3*d^5 + 8316*a^6*b^2*c^2*d^6 + 518616*a*b^7*c^7*d - 1512*a^7*b*c*d^7)/(16777216*b^12*c^19*d + 16777216*a^12*c^7*d^13 - 201326592*a*b^11*c^18*d^2 - 201326592*a^11*b*c^8*d^12 + 1107296256*a^2*b^10*c^17*d^3 - 3690987520*a^3*b^9*c^16*d^4 + 8304721920*a^4*b^8*c^15*d^5 - 13287555072*a^5*b^7*c^14*d^6 + 15502147584*a^6*b^6*c^13*d^7 - 13287555072*a^7*b^5*c^12*d^8 + 8304721920*a^8*b^4*c^11*d^9 - 3690987520*a^9*b^3*c^10*d^10 + 1107296256*a^10*b^2*c^9*d^11))^(1/4)*(8192*a^2*b^18*c^18*d^4 - 95488*a^3*b^17*c^17*d^5 + 506112*a^4*b^16*c^16*d^6 - 1607168*a^5*b^15*c^15*d^7 + 3384832*a^6*b^14*c^14*d^8 - 4925184*a^7*b^13*c^13*d^9 + 4958976*a^8*b^12*c^12*d^10 - 3277824*a^9*b^11*c^11*d^11 + 1115136*a^10*b^10*c^10*d^12 + 199936*a^11*b^9*c^9*d^13 - 459008*a^12*b^8*c^8*d^14 + 256512*a^13*b^7*c^7*d^15 - 76288*a^14*b^6*c^6*d^16 + 12032*a^15*b^5*c^5*d^17 - 768*a^16*b^4*c^4*d^18))/(b^8*c^12 + a^8*c^4*d^8 - 8*a^7*b*c^5*d^7 + 28*a^2*b^6*c^10*d^2 - 56*a^3*b^5*c^9*d^3 + 70*a^4*b^4*c^8*d^4 - 56*a^5*b^3*c^7*d^5 + 28*a^6*b^2*c^6*d^6 - 8*a*b^7*c^11*d) + (x^(1/2)*(16777216*a^2*b^21*c^19*d^4 - 194101248*a^3*b^20*c^18*d^5 + 1030225920*a^4*b^19*c^17*d^6 - 3328573440*a^5*b^18*c^16*d^7 + 7335837696*a^6*b^17*c^15*d^8 - 11738087424*a^7*b^16*c^14*d^9 + 14203486208*a^8*b^15*c^13*d^10 - 13361086464*a^9*b^14*c^12*d^11 + 9861857280*a^10*b^13*c^11*d^12 - 5521702912*a^11*b^12*c^10*d^13 + 1989672960*a^12*b^11*c^9*d^14 - 49938432*a^13*b^10*c^8*d^15 - 484442112*a^14*b^9*c^7*d^16 + 343080960*a^15*b^8*c^6*d^17 - 127401984*a^16*b^7*c^5*d^18 + 27394048*a^17*b^6*c^4*d^19 - 3145728*a^18*b^5*c^3*d^20 + 147456*a^19*b^4*c^2*d^21)*1i)/(4096*(b^12*c^16 + a^12*c^4*d^12 - 12*a^11*b*c^5*d^11 + 66*a^2*b^10*c^14*d^2 - 220*a^3*b^9*c^13*d^3 + 495*a^4*b^8*c^12*d^4 - 792*a^5*b^7*c^11*d^5 + 924*a^6*b^6*c^10*d^6 - 792*a^7*b^5*c^9*d^7 + 495*a^8*b^4*c^8*d^8 - 220*a^9*b^3*c^7*d^9 + 66*a^10*b^2*c^6*d^10 - 12*a*b^11*c^15*d)))*1i - (((81*a^9*b^7*d^10)/2048 - (1431*a^8*b^8*c*d^9)/2048 - (194481*a^2*b^14*c^7*d^3)/2048 - (713097*a^3*b^13*c^6*d^4)/2048 - (432453*a^4*b^12*c^5*d^5)/2048 + (18067*a^5*b^11*c^4*d^6)/2048 + (5709*a^6*b^10*c^3*d^7)/2048 + (6885*a^7*b^9*c^2*d^8)/2048)*1i)/(b^8*c^12 + a^8*c^4*d^8 - 8*a^7*b*c^5*d^7 + 28*a^2*b^6*c^10*d^2 - 56*a^3*b^5*c^9*d^3 + 70*a^4*b^4*c^8*d^4 - 56*a^5*b^3*c^7*d^5 + 28*a^6*b^2*c^6*d^6 - 8*a*b^7*c^11*d))*1i - (x^(1/2)*(81*a^10*b^9*d^11 - 1512*a^9*b^10*c*d^10 + 194481*a^2*b^17*c^8*d^3 + 518616*a^3*b^16*c^7*d^4 + 859068*a^4*b^15*c^6*d^5 + 610344*a^5*b^14*c^5*d^6 - 14266*a^6*b^13*c^4*d^7 - 87192*a^7*b^12*c^3*d^8 + 17532*a^8*b^11*c^2*d^9)*1i)/(4096*(b^12*c^16 + a^12*c^4*d^12 - 12*a^11*b*c^5*d^11 + 66*a^2*b^10*c^14*d^2 - 220*a^3*b^9*c^13*d^3 + 495*a^4*b^8*c^12*d^4 - 792*a^5*b^7*c^11*d^5 + 924*a^6*b^6*c^10*d^6 - 792*a^7*b^5*c^9*d^7 + 495*a^8*b^4*c^8*d^8 - 220*a^9*b^3*c^7*d^9 + 66*a^10*b^2*c^6*d^10 - 12*a*b^11*c^15*d)))))*(-(81*a^8*d^8 + 194481*b^8*c^8 + 407484*a^2*b^6*c^6*d^2 + 8232*a^3*b^5*c^5*d^3 - 85946*a^4*b^4*c^4*d^4 - 1176*a^5*b^3*c^3*d^5 + 8316*a^6*b^2*c^2*d^6 + 518616*a*b^7*c^7*d - 1512*a^7*b*c*d^7)/(16777216*b^12*c^19*d + 16777216*a^12*c^7*d^13 - 201326592*a*b^11*c^18*d^2 - 201326592*a^11*b*c^8*d^12 + 1107296256*a^2*b^10*c^17*d^3 - 3690987520*a^3*b^9*c^16*d^4 + 8304721920*a^4*b^8*c^15*d^5 - 13287555072*a^5*b^7*c^14*d^6 + 15502147584*a^6*b^6*c^13*d^7 - 13287555072*a^7*b^5*c^12*d^8 + 8304721920*a^8*b^4*c^11*d^9 - 3690987520*a^9*b^3*c^10*d^10 + 1107296256*a^10*b^2*c^9*d^11))^(1/4) - ((x^(1/2)*(3*a*d - 11*b*c))/(16*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) - (d*x^(5/2)*(a*d + 7*b*c))/(16*(b^2*c^3 + a^2*c*d^2 - 2*a*b*c^2*d)))/(c^2 + d^2*x^4 + 2*c*d*x^2)","B"
483,1,32735,633,4.353537,"\text{Not used}","int(x^(1/2)/((a + b*x^2)*(c + d*x^2)^3),x)","-\mathrm{atan}\left(\frac{\left(\left(\frac{\frac{125\,a^{20}\,b^4\,c\,d^{23}}{16}-\frac{2725\,a^{19}\,b^5\,c^2\,d^{22}}{16}+\frac{3745\,a^{18}\,b^6\,c^3\,d^{21}}{2}-\frac{26949\,a^{17}\,b^7\,c^4\,d^{20}}{2}+\frac{280623\,a^{16}\,b^8\,c^5\,d^{19}}{4}-\frac{1110975\,a^{15}\,b^9\,c^6\,d^{18}}{4}+\frac{1717635\,a^{14}\,b^{10}\,c^7\,d^{17}}{2}-\frac{4207335\,a^{13}\,b^{11}\,c^8\,d^{16}}{2}+\frac{32835743\,a^{12}\,b^{12}\,c^9\,d^{15}}{8}-\frac{50934983\,a^{11}\,b^{13}\,c^{10}\,d^{14}}{8}+\frac{15550975\,a^{10}\,b^{14}\,c^{11}\,d^{13}}{2}-\frac{14638795\,a^9\,b^{15}\,c^{12}\,d^{12}}{2}+\frac{20337495\,a^8\,b^{16}\,c^{13}\,d^{11}}{4}-\frac{9347799\,a^7\,b^{17}\,c^{14}\,d^{10}}{4}+\frac{844557\,a^6\,b^{18}\,c^{15}\,d^9}{2}+\frac{565575\,a^5\,b^{19}\,c^{16}\,d^8}{2}-\frac{4294995\,a^4\,b^{20}\,c^{17}\,d^7}{16}+\frac{1711115\,a^3\,b^{21}\,c^{18}\,d^6}{16}-22528\,a^2\,b^{22}\,c^{19}\,d^5+2048\,a\,b^{23}\,c^{20}\,d^4}{a^{14}\,c^6\,d^{14}-14\,a^{13}\,b\,c^7\,d^{13}+91\,a^{12}\,b^2\,c^8\,d^{12}-364\,a^{11}\,b^3\,c^9\,d^{11}+1001\,a^{10}\,b^4\,c^{10}\,d^{10}-2002\,a^9\,b^5\,c^{11}\,d^9+3003\,a^8\,b^6\,c^{12}\,d^8-3432\,a^7\,b^7\,c^{13}\,d^7+3003\,a^6\,b^8\,c^{14}\,d^6-2002\,a^5\,b^9\,c^{15}\,d^5+1001\,a^4\,b^{10}\,c^{16}\,d^4-364\,a^3\,b^{11}\,c^{17}\,d^3+91\,a^2\,b^{12}\,c^{18}\,d^2-14\,a\,b^{13}\,c^{19}\,d+b^{14}\,c^{20}}-\frac{\sqrt{x}\,{\left(-\frac{b^9}{16\,a^{13}\,d^{12}-192\,a^{12}\,b\,c\,d^{11}+1056\,a^{11}\,b^2\,c^2\,d^{10}-3520\,a^{10}\,b^3\,c^3\,d^9+7920\,a^9\,b^4\,c^4\,d^8-12672\,a^8\,b^5\,c^5\,d^7+14784\,a^7\,b^6\,c^6\,d^6-12672\,a^6\,b^7\,c^7\,d^5+7920\,a^5\,b^8\,c^8\,d^4-3520\,a^4\,b^9\,c^9\,d^3+1056\,a^3\,b^{10}\,c^{10}\,d^2-192\,a^2\,b^{11}\,c^{11}\,d+16\,a\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(409600\,a^{19}\,b^4\,c^3\,d^{22}-7864320\,a^{18}\,b^5\,c^4\,d^{21}+75104256\,a^{17}\,b^6\,c^5\,d^{20}-463470592\,a^{16}\,b^7\,c^6\,d^{19}+2040201216\,a^{15}\,b^8\,c^7\,d^{18}-6723993600\,a^{14}\,b^9\,c^8\,d^{17}+17037131776\,a^{13}\,b^{10}\,c^9\,d^{16}-33731641344\,a^{12}\,b^{11}\,c^{10}\,d^{15}+52807434240\,a^{11}\,b^{12}\,c^{11}\,d^{14}-66085978112\,a^{10}\,b^{13}\,c^{12}\,d^{13}+66935193600\,a^9\,b^{14}\,c^{13}\,d^{12}-55691968512\,a^8\,b^{15}\,c^{14}\,d^{11}+38637076480\,a^7\,b^{16}\,c^{15}\,d^{10}-22493528064\,a^6\,b^{17}\,c^{16}\,d^9+10825629696\,a^5\,b^{18}\,c^{17}\,d^8-4115660800\,a^4\,b^{19}\,c^{18}\,d^7+1140473856\,a^3\,b^{20}\,c^{19}\,d^6-201326592\,a^2\,b^{21}\,c^{20}\,d^5+16777216\,a\,b^{22}\,c^{21}\,d^4\right)}{4096\,\left(a^{12}\,c^6\,d^{12}-12\,a^{11}\,b\,c^7\,d^{11}+66\,a^{10}\,b^2\,c^8\,d^{10}-220\,a^9\,b^3\,c^9\,d^9+495\,a^8\,b^4\,c^{10}\,d^8-792\,a^7\,b^5\,c^{11}\,d^7+924\,a^6\,b^6\,c^{12}\,d^6-792\,a^5\,b^7\,c^{13}\,d^5+495\,a^4\,b^8\,c^{14}\,d^4-220\,a^3\,b^9\,c^{15}\,d^3+66\,a^2\,b^{10}\,c^{16}\,d^2-12\,a\,b^{11}\,c^{17}\,d+b^{12}\,c^{18}\right)}\right)\,{\left(-\frac{b^9}{16\,a^{13}\,d^{12}-192\,a^{12}\,b\,c\,d^{11}+1056\,a^{11}\,b^2\,c^2\,d^{10}-3520\,a^{10}\,b^3\,c^3\,d^9+7920\,a^9\,b^4\,c^4\,d^8-12672\,a^8\,b^5\,c^5\,d^7+14784\,a^7\,b^6\,c^6\,d^6-12672\,a^6\,b^7\,c^7\,d^5+7920\,a^5\,b^8\,c^8\,d^4-3520\,a^4\,b^9\,c^9\,d^3+1056\,a^3\,b^{10}\,c^{10}\,d^2-192\,a^2\,b^{11}\,c^{11}\,d+16\,a\,b^{12}\,c^{12}}\right)}^{3/4}\,1{}\mathrm{i}-\frac{\sqrt{x}\,\left(625\,a^9\,b^{10}\,d^{13}-9000\,a^8\,b^{11}\,c\,d^{12}+71100\,a^7\,b^{12}\,c^2\,d^{11}-334040\,a^6\,b^{13}\,c^3\,d^{10}+1099206\,a^5\,b^{14}\,c^4\,d^9-2444184\,a^4\,b^{15}\,c^5\,d^8+4100220\,a^3\,b^{16}\,c^6\,d^7-4487400\,a^2\,b^{17}\,c^7\,d^6+4100625\,a\,b^{18}\,c^8\,d^5\right)\,1{}\mathrm{i}}{4096\,\left(a^{12}\,c^6\,d^{12}-12\,a^{11}\,b\,c^7\,d^{11}+66\,a^{10}\,b^2\,c^8\,d^{10}-220\,a^9\,b^3\,c^9\,d^9+495\,a^8\,b^4\,c^{10}\,d^8-792\,a^7\,b^5\,c^{11}\,d^7+924\,a^6\,b^6\,c^{12}\,d^6-792\,a^5\,b^7\,c^{13}\,d^5+495\,a^4\,b^8\,c^{14}\,d^4-220\,a^3\,b^9\,c^{15}\,d^3+66\,a^2\,b^{10}\,c^{16}\,d^2-12\,a\,b^{11}\,c^{17}\,d+b^{12}\,c^{18}\right)}\right)\,{\left(-\frac{b^9}{16\,a^{13}\,d^{12}-192\,a^{12}\,b\,c\,d^{11}+1056\,a^{11}\,b^2\,c^2\,d^{10}-3520\,a^{10}\,b^3\,c^3\,d^9+7920\,a^9\,b^4\,c^4\,d^8-12672\,a^8\,b^5\,c^5\,d^7+14784\,a^7\,b^6\,c^6\,d^6-12672\,a^6\,b^7\,c^7\,d^5+7920\,a^5\,b^8\,c^8\,d^4-3520\,a^4\,b^9\,c^9\,d^3+1056\,a^3\,b^{10}\,c^{10}\,d^2-192\,a^2\,b^{11}\,c^{11}\,d+16\,a\,b^{12}\,c^{12}}\right)}^{1/4}-\left(\left(\frac{\frac{125\,a^{20}\,b^4\,c\,d^{23}}{16}-\frac{2725\,a^{19}\,b^5\,c^2\,d^{22}}{16}+\frac{3745\,a^{18}\,b^6\,c^3\,d^{21}}{2}-\frac{26949\,a^{17}\,b^7\,c^4\,d^{20}}{2}+\frac{280623\,a^{16}\,b^8\,c^5\,d^{19}}{4}-\frac{1110975\,a^{15}\,b^9\,c^6\,d^{18}}{4}+\frac{1717635\,a^{14}\,b^{10}\,c^7\,d^{17}}{2}-\frac{4207335\,a^{13}\,b^{11}\,c^8\,d^{16}}{2}+\frac{32835743\,a^{12}\,b^{12}\,c^9\,d^{15}}{8}-\frac{50934983\,a^{11}\,b^{13}\,c^{10}\,d^{14}}{8}+\frac{15550975\,a^{10}\,b^{14}\,c^{11}\,d^{13}}{2}-\frac{14638795\,a^9\,b^{15}\,c^{12}\,d^{12}}{2}+\frac{20337495\,a^8\,b^{16}\,c^{13}\,d^{11}}{4}-\frac{9347799\,a^7\,b^{17}\,c^{14}\,d^{10}}{4}+\frac{844557\,a^6\,b^{18}\,c^{15}\,d^9}{2}+\frac{565575\,a^5\,b^{19}\,c^{16}\,d^8}{2}-\frac{4294995\,a^4\,b^{20}\,c^{17}\,d^7}{16}+\frac{1711115\,a^3\,b^{21}\,c^{18}\,d^6}{16}-22528\,a^2\,b^{22}\,c^{19}\,d^5+2048\,a\,b^{23}\,c^{20}\,d^4}{a^{14}\,c^6\,d^{14}-14\,a^{13}\,b\,c^7\,d^{13}+91\,a^{12}\,b^2\,c^8\,d^{12}-364\,a^{11}\,b^3\,c^9\,d^{11}+1001\,a^{10}\,b^4\,c^{10}\,d^{10}-2002\,a^9\,b^5\,c^{11}\,d^9+3003\,a^8\,b^6\,c^{12}\,d^8-3432\,a^7\,b^7\,c^{13}\,d^7+3003\,a^6\,b^8\,c^{14}\,d^6-2002\,a^5\,b^9\,c^{15}\,d^5+1001\,a^4\,b^{10}\,c^{16}\,d^4-364\,a^3\,b^{11}\,c^{17}\,d^3+91\,a^2\,b^{12}\,c^{18}\,d^2-14\,a\,b^{13}\,c^{19}\,d+b^{14}\,c^{20}}+\frac{\sqrt{x}\,{\left(-\frac{b^9}{16\,a^{13}\,d^{12}-192\,a^{12}\,b\,c\,d^{11}+1056\,a^{11}\,b^2\,c^2\,d^{10}-3520\,a^{10}\,b^3\,c^3\,d^9+7920\,a^9\,b^4\,c^4\,d^8-12672\,a^8\,b^5\,c^5\,d^7+14784\,a^7\,b^6\,c^6\,d^6-12672\,a^6\,b^7\,c^7\,d^5+7920\,a^5\,b^8\,c^8\,d^4-3520\,a^4\,b^9\,c^9\,d^3+1056\,a^3\,b^{10}\,c^{10}\,d^2-192\,a^2\,b^{11}\,c^{11}\,d+16\,a\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(409600\,a^{19}\,b^4\,c^3\,d^{22}-7864320\,a^{18}\,b^5\,c^4\,d^{21}+75104256\,a^{17}\,b^6\,c^5\,d^{20}-463470592\,a^{16}\,b^7\,c^6\,d^{19}+2040201216\,a^{15}\,b^8\,c^7\,d^{18}-6723993600\,a^{14}\,b^9\,c^8\,d^{17}+17037131776\,a^{13}\,b^{10}\,c^9\,d^{16}-33731641344\,a^{12}\,b^{11}\,c^{10}\,d^{15}+52807434240\,a^{11}\,b^{12}\,c^{11}\,d^{14}-66085978112\,a^{10}\,b^{13}\,c^{12}\,d^{13}+66935193600\,a^9\,b^{14}\,c^{13}\,d^{12}-55691968512\,a^8\,b^{15}\,c^{14}\,d^{11}+38637076480\,a^7\,b^{16}\,c^{15}\,d^{10}-22493528064\,a^6\,b^{17}\,c^{16}\,d^9+10825629696\,a^5\,b^{18}\,c^{17}\,d^8-4115660800\,a^4\,b^{19}\,c^{18}\,d^7+1140473856\,a^3\,b^{20}\,c^{19}\,d^6-201326592\,a^2\,b^{21}\,c^{20}\,d^5+16777216\,a\,b^{22}\,c^{21}\,d^4\right)}{4096\,\left(a^{12}\,c^6\,d^{12}-12\,a^{11}\,b\,c^7\,d^{11}+66\,a^{10}\,b^2\,c^8\,d^{10}-220\,a^9\,b^3\,c^9\,d^9+495\,a^8\,b^4\,c^{10}\,d^8-792\,a^7\,b^5\,c^{11}\,d^7+924\,a^6\,b^6\,c^{12}\,d^6-792\,a^5\,b^7\,c^{13}\,d^5+495\,a^4\,b^8\,c^{14}\,d^4-220\,a^3\,b^9\,c^{15}\,d^3+66\,a^2\,b^{10}\,c^{16}\,d^2-12\,a\,b^{11}\,c^{17}\,d+b^{12}\,c^{18}\right)}\right)\,{\left(-\frac{b^9}{16\,a^{13}\,d^{12}-192\,a^{12}\,b\,c\,d^{11}+1056\,a^{11}\,b^2\,c^2\,d^{10}-3520\,a^{10}\,b^3\,c^3\,d^9+7920\,a^9\,b^4\,c^4\,d^8-12672\,a^8\,b^5\,c^5\,d^7+14784\,a^7\,b^6\,c^6\,d^6-12672\,a^6\,b^7\,c^7\,d^5+7920\,a^5\,b^8\,c^8\,d^4-3520\,a^4\,b^9\,c^9\,d^3+1056\,a^3\,b^{10}\,c^{10}\,d^2-192\,a^2\,b^{11}\,c^{11}\,d+16\,a\,b^{12}\,c^{12}}\right)}^{3/4}\,1{}\mathrm{i}+\frac{\sqrt{x}\,\left(625\,a^9\,b^{10}\,d^{13}-9000\,a^8\,b^{11}\,c\,d^{12}+71100\,a^7\,b^{12}\,c^2\,d^{11}-334040\,a^6\,b^{13}\,c^3\,d^{10}+1099206\,a^5\,b^{14}\,c^4\,d^9-2444184\,a^4\,b^{15}\,c^5\,d^8+4100220\,a^3\,b^{16}\,c^6\,d^7-4487400\,a^2\,b^{17}\,c^7\,d^6+4100625\,a\,b^{18}\,c^8\,d^5\right)\,1{}\mathrm{i}}{4096\,\left(a^{12}\,c^6\,d^{12}-12\,a^{11}\,b\,c^7\,d^{11}+66\,a^{10}\,b^2\,c^8\,d^{10}-220\,a^9\,b^3\,c^9\,d^9+495\,a^8\,b^4\,c^{10}\,d^8-792\,a^7\,b^5\,c^{11}\,d^7+924\,a^6\,b^6\,c^{12}\,d^6-792\,a^5\,b^7\,c^{13}\,d^5+495\,a^4\,b^8\,c^{14}\,d^4-220\,a^3\,b^9\,c^{15}\,d^3+66\,a^2\,b^{10}\,c^{16}\,d^2-12\,a\,b^{11}\,c^{17}\,d+b^{12}\,c^{18}\right)}\right)\,{\left(-\frac{b^9}{16\,a^{13}\,d^{12}-192\,a^{12}\,b\,c\,d^{11}+1056\,a^{11}\,b^2\,c^2\,d^{10}-3520\,a^{10}\,b^3\,c^3\,d^9+7920\,a^9\,b^4\,c^4\,d^8-12672\,a^8\,b^5\,c^5\,d^7+14784\,a^7\,b^6\,c^6\,d^6-12672\,a^6\,b^7\,c^7\,d^5+7920\,a^5\,b^8\,c^8\,d^4-3520\,a^4\,b^9\,c^9\,d^3+1056\,a^3\,b^{10}\,c^{10}\,d^2-192\,a^2\,b^{11}\,c^{11}\,d+16\,a\,b^{12}\,c^{12}}\right)}^{1/4}}{\left(\left(\frac{\frac{125\,a^{20}\,b^4\,c\,d^{23}}{16}-\frac{2725\,a^{19}\,b^5\,c^2\,d^{22}}{16}+\frac{3745\,a^{18}\,b^6\,c^3\,d^{21}}{2}-\frac{26949\,a^{17}\,b^7\,c^4\,d^{20}}{2}+\frac{280623\,a^{16}\,b^8\,c^5\,d^{19}}{4}-\frac{1110975\,a^{15}\,b^9\,c^6\,d^{18}}{4}+\frac{1717635\,a^{14}\,b^{10}\,c^7\,d^{17}}{2}-\frac{4207335\,a^{13}\,b^{11}\,c^8\,d^{16}}{2}+\frac{32835743\,a^{12}\,b^{12}\,c^9\,d^{15}}{8}-\frac{50934983\,a^{11}\,b^{13}\,c^{10}\,d^{14}}{8}+\frac{15550975\,a^{10}\,b^{14}\,c^{11}\,d^{13}}{2}-\frac{14638795\,a^9\,b^{15}\,c^{12}\,d^{12}}{2}+\frac{20337495\,a^8\,b^{16}\,c^{13}\,d^{11}}{4}-\frac{9347799\,a^7\,b^{17}\,c^{14}\,d^{10}}{4}+\frac{844557\,a^6\,b^{18}\,c^{15}\,d^9}{2}+\frac{565575\,a^5\,b^{19}\,c^{16}\,d^8}{2}-\frac{4294995\,a^4\,b^{20}\,c^{17}\,d^7}{16}+\frac{1711115\,a^3\,b^{21}\,c^{18}\,d^6}{16}-22528\,a^2\,b^{22}\,c^{19}\,d^5+2048\,a\,b^{23}\,c^{20}\,d^4}{a^{14}\,c^6\,d^{14}-14\,a^{13}\,b\,c^7\,d^{13}+91\,a^{12}\,b^2\,c^8\,d^{12}-364\,a^{11}\,b^3\,c^9\,d^{11}+1001\,a^{10}\,b^4\,c^{10}\,d^{10}-2002\,a^9\,b^5\,c^{11}\,d^9+3003\,a^8\,b^6\,c^{12}\,d^8-3432\,a^7\,b^7\,c^{13}\,d^7+3003\,a^6\,b^8\,c^{14}\,d^6-2002\,a^5\,b^9\,c^{15}\,d^5+1001\,a^4\,b^{10}\,c^{16}\,d^4-364\,a^3\,b^{11}\,c^{17}\,d^3+91\,a^2\,b^{12}\,c^{18}\,d^2-14\,a\,b^{13}\,c^{19}\,d+b^{14}\,c^{20}}-\frac{\sqrt{x}\,{\left(-\frac{b^9}{16\,a^{13}\,d^{12}-192\,a^{12}\,b\,c\,d^{11}+1056\,a^{11}\,b^2\,c^2\,d^{10}-3520\,a^{10}\,b^3\,c^3\,d^9+7920\,a^9\,b^4\,c^4\,d^8-12672\,a^8\,b^5\,c^5\,d^7+14784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^{11}\,b^{13}\,c^{10}\,d^{14}}{8}+\frac{15550975\,a^{10}\,b^{14}\,c^{11}\,d^{13}}{2}-\frac{14638795\,a^9\,b^{15}\,c^{12}\,d^{12}}{2}+\frac{20337495\,a^8\,b^{16}\,c^{13}\,d^{11}}{4}-\frac{9347799\,a^7\,b^{17}\,c^{14}\,d^{10}}{4}+\frac{844557\,a^6\,b^{18}\,c^{15}\,d^9}{2}+\frac{565575\,a^5\,b^{19}\,c^{16}\,d^8}{2}-\frac{4294995\,a^4\,b^{20}\,c^{17}\,d^7}{16}+\frac{1711115\,a^3\,b^{21}\,c^{18}\,d^6}{16}-22528\,a^2\,b^{22}\,c^{19}\,d^5+2048\,a\,b^{23}\,c^{20}\,d^4\right)\,1{}\mathrm{i}}{a^{14}\,c^6\,d^{14}-14\,a^{13}\,b\,c^7\,d^{13}+91\,a^{12}\,b^2\,c^8\,d^{12}-364\,a^{11}\,b^3\,c^9\,d^{11}+1001\,a^{10}\,b^4\,c^{10}\,d^{10}-2002\,a^9\,b^5\,c^{11}\,d^9+3003\,a^8\,b^6\,c^{12}\,d^8-3432\,a^7\,b^7\,c^{13}\,d^7+3003\,a^6\,b^8\,c^{14}\,d^6-2002\,a^5\,b^9\,c^{15}\,d^5+1001\,a^4\,b^{10}\,c^{16}\,d^4-364\,a^3\,b^{11}\,c^{17}\,d^3+91\,a^2\,b^{12}\,c^{18}\,d^2-14\,a\,b^{13}\,c^{19}\,d+b^{14}\,c^{20}}\right)\,{\left(-\frac{b^9}{16\,a^{13}\,d^{12}-192\,a^{12}\,b\,c\,d^{11}+1056\,a^{11}\,b^2\,c^2\,d^{10}-3520\,a^{10}\,b^3\,c^3\,d^9+7920\,a^9\,b^4\,c^4\,d^8-12672\,a^8\,b^5\,c^5\,d^7+14784\,a^7\,b^6\,c^6\,d^6-12672\,a^6\,b^7\,c^7\,d^5+7920\,a^5\,b^8\,c^8\,d^4-3520\,a^4\,b^9\,c^9\,d^3+1056\,a^3\,b^{10}\,c^{10}\,d^2-192\,a^2\,b^{11}\,c^{11}\,d+16\,a\,b^{12}\,c^{12}}\right)}^{3/4}-\frac{\sqrt{x}\,\left(625\,a^9\,b^{10}\,d^{13}-9000\,a^8\,b^{11}\,c\,d^{12}+71100\,a^7\,b^{12}\,c^2\,d^{11}-334040\,a^6\,b^{13}\,c^3\,d^{10}+1099206\,a^5\,b^{14}\,c^4\,d^9-2444184\,a^4\,b^{15}\,c^5\,d^8+4100220\,a^3\,b^{16}\,c^6\,d^7-4487400\,a^2\,b^{17}\,c^7\,d^6+4100625\,a\,b^{18}\,c^8\,d^5\right)}{4096\,\left(a^{12}\,c^6\,d^{12}-12\,a^{11}\,b\,c^7\,d^{11}+66\,a^{10}\,b^2\,c^8\,d^{10}-220\,a^9\,b^3\,c^9\,d^9+495\,a^8\,b^4\,c^{10}\,d^8-792\,a^7\,b^5\,c^{11}\,d^7+924\,a^6\,b^6\,c^{12}\,d^6-792\,a^5\,b^7\,c^{13}\,d^5+495\,a^4\,b^8\,c^{14}\,d^4-220\,a^3\,b^9\,c^{15}\,d^3+66\,a^2\,b^{10}\,c^{16}\,d^2-12\,a\,b^{11}\,c^{17}\,d+b^{12}\,c^{18}\right)}\right)\,{\left(-\frac{b^9}{16\,a^{13}\,d^{12}-192\,a^{12}\,b\,c\,d^{11}+1056\,a^{11}\,b^2\,c^2\,d^{10}-3520\,a^{10}\,b^3\,c^3\,d^9+7920\,a^9\,b^4\,c^4\,d^8-12672\,a^8\,b^5\,c^5\,d^7+14784\,a^7\,b^6\,c^6\,d^6-12672\,a^6\,b^7\,c^7\,d^5+7920\,a^5\,b^8\,c^8\,d^4-3520\,a^4\,b^9\,c^9\,d^3+1056\,a^3\,b^{10}\,c^{10}\,d^2-192\,a^2\,b^{11}\,c^{11}\,d+16\,a\,b^{12}\,c^{12}}\right)}^{1/4}-\left(\left(\frac{\sqrt{x}\,{\left(-\frac{b^9}{16\,a^{13}\,d^{12}-192\,a^{12}\,b\,c\,d^{11}+1056\,a^{11}\,b^2\,c^2\,d^{10}-3520\,a^{10}\,b^3\,c^3\,d^9+7920\,a^9\,b^4\,c^4\,d^8-12672\,a^8\,b^5\,c^5\,d^7+14784\,a^7\,b^6\,c^6\,d^6-12672\,a^6\,b^7\,c^7\,d^5+7920\,a^5\,b^8\,c^8\,d^4-3520\,a^4\,b^9\,c^9\,d^3+1056\,a^3\,b^{10}\,c^{10}\,d^2-192\,a^2\,b^{11}\,c^{11}\,d+16\,a\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(409600\,a^{19}\,b^4\,c^3\,d^{22}-7864320\,a^{18}\,b^5\,c^4\,d^{21}+75104256\,a^{17}\,b^6\,c^5\,d^{20}-463470592\,a^{16}\,b^7\,c^6\,d^{19}+2040201216\,a^{15}\,b^8\,c^7\,d^{18}-6723993600\,a^{14}\,b^9\,c^8\,d^{17}+17037131776\,a^{13}\,b^{10}\,c^9\,d^{16}-33731641344\,a^{12}\,b^{11}\,c^{10}\,d^{15}+52807434240\,a^{11}\,b^{12}\,c^{11}\,d^{14}-66085978112\,a^{10}\,b^{13}\,c^{12}\,d^{13}+66935193600\,a^9\,b^{14}\,c^{13}\,d^{12}-55691968512\,a^8\,b^{15}\,c^{14}\,d^{11}+38637076480\,a^7\,b^{16}\,c^{15}\,d^{10}-22493528064\,a^6\,b^{17}\,c^{16}\,d^9+10825629696\,a^5\,b^{18}\,c^{17}\,d^8-4115660800\,a^4\,b^{19}\,c^{18}\,d^7+1140473856\,a^3\,b^{20}\,c^{19}\,d^6-201326592\,a^2\,b^{21}\,c^{20}\,d^5+16777216\,a\,b^{22}\,c^{21}\,d^4\right)}{4096\,\left(a^{12}\,c^6\,d^{12}-12\,a^{11}\,b\,c^7\,d^{11}+66\,a^{10}\,b^2\,c^8\,d^{10}-220\,a^9\,b^3\,c^9\,d^9+495\,a^8\,b^4\,c^{10}\,d^8-792\,a^7\,b^5\,c^{11}\,d^7+924\,a^6\,b^6\,c^{12}\,d^6-792\,a^5\,b^7\,c^{13}\,d^5+495\,a^4\,b^8\,c^{14}\,d^4-220\,a^3\,b^9\,c^{15}\,d^3+66\,a^2\,b^{10}\,c^{16}\,d^2-12\,a\,b^{11}\,c^{17}\,d+b^{12}\,c^{18}\right)}+\frac{\left(\frac{125\,a^{20}\,b^4\,c\,d^{23}}{16}-\frac{2725\,a^{19}\,b^5\,c^2\,d^{22}}{16}+\frac{3745\,a^{18}\,b^6\,c^3\,d^{21}}{2}-\frac{26949\,a^{17}\,b^7\,c^4\,d^{20}}{2}+\frac{280623\,a^{16}\,b^8\,c^5\,d^{19}}{4}-\frac{1110975\,a^{15}\,b^9\,c^6\,d^{18}}{4}+\frac{1717635\,a^{14}\,b^{10}\,c^7\,d^{17}}{2}-\frac{4207335\,a^{13}\,b^{11}\,c^8\,d^{16}}{2}+\frac{32835743\,a^{12}\,b^{12}\,c^9\,d^{15}}{8}-\frac{50934983\,a^{11}\,b^{13}\,c^{10}\,d^{14}}{8}+\frac{15550975\,a^{10}\,b^{14}\,c^{11}\,d^{13}}{2}-\frac{14638795\,a^9\,b^{15}\,c^{12}\,d^{12}}{2}+\frac{20337495\,a^8\,b^{16}\,c^{13}\,d^{11}}{4}-\frac{9347799\,a^7\,b^{17}\,c^{14}\,d^{10}}{4}+\frac{844557\,a^6\,b^{18}\,c^{15}\,d^9}{2}+\frac{565575\,a^5\,b^{19}\,c^{16}\,d^8}{2}-\frac{4294995\,a^4\,b^{20}\,c^{17}\,d^7}{16}+\frac{1711115\,a^3\,b^{21}\,c^{18}\,d^6}{16}-22528\,a^2\,b^{22}\,c^{19}\,d^5+2048\,a\,b^{23}\,c^{20}\,d^4\right)\,1{}\mathrm{i}}{a^{14}\,c^6\,d^{14}-14\,a^{13}\,b\,c^7\,d^{13}+91\,a^{12}\,b^2\,c^8\,d^{12}-364\,a^{11}\,b^3\,c^9\,d^{11}+1001\,a^{10}\,b^4\,c^{10}\,d^{10}-2002\,a^9\,b^5\,c^{11}\,d^9+3003\,a^8\,b^6\,c^{12}\,d^8-3432\,a^7\,b^7\,c^{13}\,d^7+3003\,a^6\,b^8\,c^{14}\,d^6-2002\,a^5\,b^9\,c^{15}\,d^5+1001\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12}\,c^9\,d^{12}-201326592\,a^{11}\,b\,c^{10}\,d^{11}+1107296256\,a^{10}\,b^2\,c^{11}\,d^{10}-3690987520\,a^9\,b^3\,c^{12}\,d^9+8304721920\,a^8\,b^4\,c^{13}\,d^8-13287555072\,a^7\,b^5\,c^{14}\,d^7+15502147584\,a^6\,b^6\,c^{15}\,d^6-13287555072\,a^5\,b^7\,c^{16}\,d^5+8304721920\,a^4\,b^8\,c^{17}\,d^4-3690987520\,a^3\,b^9\,c^{18}\,d^3+1107296256\,a^2\,b^{10}\,c^{19}\,d^2-201326592\,a\,b^{11}\,c^{20}\,d+16777216\,b^{12}\,c^{21}}\right)}^{1/4}\,\left(409600\,a^{19}\,b^4\,c^3\,d^{22}-7864320\,a^{18}\,b^5\,c^4\,d^{21}+75104256\,a^{17}\,b^6\,c^5\,d^{20}-463470592\,a^{16}\,b^7\,c^6\,d^{19}+2040201216\,a^{15}\,b^8\,c^7\,d^{18}-6723993600\,a^{14}\,b^9\,c^8\,d^{17}+17037131776\,a^{13}\,b^{10}\,c^9\,d^{16}-33731641344\,a^{12}\,b^{11}\,c^{10}\,d^{15}+52807434240\,a^{11}\,b^{12}\,c^{11}\,d^{14}-66085978112\,a^{10}\,b^{13}\,c^{12}\,d^{13}+66935193600\,a^9\,b^{14}\,c^{13}\,d^{12}-55691968512\,a^8\,b^{15}\,c^{14}\,d^{11}+38637076480\,a^7\,b^{16}\,c^{15}\,d^{10}-22493528064\,a^6\,b^{17}\,c^{16}\,d^9+10825629696\,a^5\,b^{18}\,c^{17}\,d^8-4115660800\,a^4\,b^{19}\,c^{18}\,d^7+1140473856\,a^3\,b^{20}\,c^{19}\,d^6-201326592\,a^2\,b^{21}\,c^{20}\,d^5+16777216\,a\,b^{22}\,c^{21}\,d^4\right)}{4096\,\left(a^{12}\,c^6\,d^{12}-12\,a^{11}\,b\,c^7\,d^{11}+66\,a^{10}\,b^2\,c^8\,d^{10}-220\,a^9\,b^3\,c^9\,d^9+495\,a^8\,b^4\,c^{10}\,d^8-792\,a^7\,b^5\,c^{11}\,d^7+924\,a^6\,b^6\,c^{12}\,d^6-792\,a^5\,b^7\,c^{13}\,d^5+495\,a^4\,b^8\,c^{14}\,d^4-220\,a^3\,b^9\,c^{15}\,d^3+66\,a^2\,b^{10}\,c^{16}\,d^2-12\,a\,b^{11}\,c^{17}\,d+b^{12}\,c^{18}\right)}+\frac{\left(\frac{125\,a^{20}\,b^4\,c\,d^{23}}{16}-\frac{2725\,a^{19}\,b^5\,c^2\,d^{22}}{16}+\frac{3745\,a^{18}\,b^6\,c^3\,d^{21}}{2}-\frac{26949\,a^{17}\,b^7\,c^4\,d^{20}}{2}+\frac{280623\,a^{16}\,b^8\,c^5\,d^{19}}{4}-\frac{1110975\,a^{15}\,b^9\,c^6\,d^{18}}{4}+\frac{1717635\,a^{14}\,b^{10}\,c^7\,d^{17}}{2}-\frac{4207335\,a^{13}\,b^{11}\,c^8\,d^{16}}{2}+\frac{32835743\,a^{12}\,b^{12}\,c^9\,d^{15}}{8}-\frac{50934983\,a^{11}\,b^{13}\,c^{10}\,d^{14}}{8}+\frac{15550975\,a^{10}\,b^{14}\,c^{11}\,d^{13}}{2}-\frac{14638795\,a^9\,b^{15}\,c^{12}\,d^{12}}{2}+\frac{20337495\,a^8\,b^{16}\,c^{13}\,d^{11}}{4}-\frac{9347799\,a^7\,b^{17}\,c^{14}\,d^{10}}{4}+\frac{844557\,a^6\,b^{18}\,c^{15}\,d^9}{2}+\frac{565575\,a^5\,b^{19}\,c^{16}\,d^8}{2}-\frac{4294995\,a^4\,b^{20}\,c^{17}\,d^7}{16}+\frac{1711115\,a^3\,b^{21}\,c^{18}\,d^6}{16}-22528\,a^2\,b^{22}\,c^{19}\,d^5+2048\,a\,b^{23}\,c^{20}\,d^4\right)\,1{}\mathrm{i}}{a^{14}\,c^6\,d^{14}-14\,a^{13}\,b\,c^7\,d^{13}+91\,a^{12}\,b^2\,c^8\,d^{12}-364\,a^{11}\,b^3\,c^9\,d^{11}+1001\,a^{10}\,b^4\,c^{10}\,d^{10}-2002\,a^9\,b^5\,c^{11}\,d^9+3003\,a^8\,b^6\,c^{12}\,d^8-3432\,a^7\,b^7\,c^{13}\,d^7+3003\,a^6\,b^8\,c^{14}\,d^6-2002\,a^5\,b^9\,c^{15}\,d^5+1001\,a^4\,b^{10}\,c^{16}\,d^4-364\,a^3\,b^{11}\,c^{17}\,d^3+91\,a^2\,b^{12}\,c^{18}\,d^2-14\,a\,b^{13}\,c^{19}\,d+b^{14}\,c^{20}}\right)\,{\left(-\frac{625\,a^8\,d^9-9000\,a^7\,b\,c\,d^8+71100\,a^6\,b^2\,c^2\,d^7-359640\,a^5\,b^3\,c^3\,d^6+1283526\,a^4\,b^4\,c^4\,d^5-3236760\,a^3\,b^5\,c^5\,d^4+5759100\,a^2\,b^6\,c^6\,d^3-6561000\,a\,b^7\,c^7\,d^2+4100625\,b^8\,c^8\,d}{16777216\,a^{12}\,c^9\,d^{12}-201326592\,a^{11}\,b\,c^{10}\,d^{11}+1107296256\,a^{10}\,b^2\,c^{11}\,d^{10}-3690987520\,a^9\,b^3\,c^{12}\,d^9+8304721920\,a^8\,b^4\,c^{13}\,d^8-13287555072\,a^7\,b^5\,c^{14}\,d^7+15502147584\,a^6\,b^6\,c^{15}\,d^6-13287555072\,a^5\,b^7\,c^{16}\,d^5+8304721920\,a^4\,b^8\,c^{17}\,d^4-3690987520\,a^3\,b^9\,c^{18}\,d^3+1107296256\,a^2\,b^{10}\,c^{19}\,d^2-201326592\,a\,b^{11}\,c^{20}\,d+16777216\,b^{12}\,c^{21}}\right)}^{3/4}\,1{}\mathrm{i}-\frac{\sqrt{x}\,\left(625\,a^9\,b^{10}\,d^{13}-9000\,a^8\,b^{11}\,c\,d^{12}+71100\,a^7\,b^{12}\,c^2\,d^{11}-334040\,a^6\,b^{13}\,c^3\,d^{10}+1099206\,a^5\,b^{14}\,c^4\,d^9-2444184\,a^4\,b^{15}\,c^5\,d^8+4100220\,a^3\,b^{16}\,c^6\,d^7-4487400\,a^2\,b^{17}\,c^7\,d^6+4100625\,a\,b^{18}\,c^8\,d^5\right)\,1{}\mathrm{i}}{4096\,\left(a^{12}\,c^6\,d^{12}-12\,a^{11}\,b\,c^7\,d^{11}+66\,a^{10}\,b^2\,c^8\,d^{10}-220\,a^9\,b^3\,c^9\,d^9+495\,a^8\,b^4\,c^{10}\,d^8-792\,a^7\,b^5\,c^{11}\,d^7+924\,a^6\,b^6\,c^{12}\,d^6-792\,a^5\,b^7\,c^{13}\,d^5+495\,a^4\,b^8\,c^{14}\,d^4-220\,a^3\,b^9\,c^{15}\,d^3+66\,a^2\,b^{10}\,c^{16}\,d^2-12\,a\,b^{11}\,c^{17}\,d+b^{12}\,c^{18}\right)}\right)+{\left(-\frac{625\,a^8\,d^9-9000\,a^7\,b\,c\,d^8+71100\,a^6\,b^2\,c^2\,d^7-359640\,a^5\,b^3\,c^3\,d^6+1283526\,a^4\,b^4\,c^4\,d^5-3236760\,a^3\,b^5\,c^5\,d^4+5759100\,a^2\,b^6\,c^6\,d^3-6561000\,a\,b^7\,c^7\,d^2+4100625\,b^8\,c^8\,d}{16777216\,a^{12}\,c^9\,d^{12}-201326592\,a^{11}\,b\,c^{10}\,d^{11}+1107296256\,a^{10}\,b^2\,c^{11}\,d^{10}-3690987520\,a^9\,b^3\,c^{12}\,d^9+8304721920\,a^8\,b^4\,c^{13}\,d^8-13287555072\,a^7\,b^5\,c^{14}\,d^7+15502147584\,a^6\,b^6\,c^{15}\,d^6-13287555072\,a^5\,b^7\,c^{16}\,d^5+8304721920\,a^4\,b^8\,c^{17}\,d^4-3690987520\,a^3\,b^9\,c^{18}\,d^3+1107296256\,a^2\,b^{10}\,c^{19}\,d^2-201326592\,a\,b^{11}\,c^{20}\,d+16777216\,b^{12}\,c^{21}}\right)}^{1/4}\,\left(\left(\frac{\sqrt{x}\,{\left(-\frac{625\,a^8\,d^9-9000\,a^7\,b\,c\,d^8+71100\,a^6\,b^2\,c^2\,d^7-359640\,a^5\,b^3\,c^3\,d^6+1283526\,a^4\,b^4\,c^4\,d^5-3236760\,a^3\,b^5\,c^5\,d^4+5759100\,a^2\,b^6\,c^6\,d^3-6561000\,a\,b^7\,c^7\,d^2+4100625\,b^8\,c^8\,d}{16777216\,a^{12}\,c^9\,d^{12}-201326592\,a^{11}\,b\,c^{10}\,d^{11}+1107296256\,a^{10}\,b^2\,c^{11}\,d^{10}-3690987520\,a^9\,b^3\,c^{12}\,d^9+8304721920\,a^8\,b^4\,c^{13}\,d^8-13287555072\,a^7\,b^5\,c^{14}\,d^7+15502147584\,a^6\,b^6\,c^{15}\,d^6-13287555072\,a^5\,b^7\,c^{16}\,d^5+8304721920\,a^4\,b^8\,c^{17}\,d^4-3690987520\,a^3\,b^9\,c^{18}\,d^3+1107296256\,a^2\,b^{10}\,c^{19}\,d^2-201326592\,a\,b^{11}\,c^{20}\,d+16777216\,b^{12}\,c^{21}}\right)}^{1/4}\,\left(409600\,a^{19}\,b^4\,c^3\,d^{22}-7864320\,a^{18}\,b^5\,c^4\,d^{21}+75104256\,a^{17}\,b^6\,c^5\,d^{20}-463470592\,a^{16}\,b^7\,c^6\,d^{19}+2040201216\,a^{15}\,b^8\,c^7\,d^{18}-6723993600\,a^{14}\,b^9\,c^8\,d^{17}+17037131776\,a^{13}\,b^{10}\,c^9\,d^{16}-33731641344\,a^{12}\,b^{11}\,c^{10}\,d^{15}+52807434240\,a^{11}\,b^{12}\,c^{11}\,d^{14}-66085978112\,a^{10}\,b^{13}\,c^{12}\,d^{13}+66935193600\,a^9\,b^{14}\,c^{13}\,d^{12}-55691968512\,a^8\,b^{15}\,c^{14}\,d^{11}+38637076480\,a^7\,b^{16}\,c^{15}\,d^{10}-22493528064\,a^6\,b^{17}\,c^{16}\,d^9+10825629696\,a^5\,b^{18}\,c^{17}\,d^8-4115660800\,a^4\,b^{19}\,c^{18}\,d^7+1140473856\,a^3\,b^{20}\,c^{19}\,d^6-201326592\,a^2\,b^{21}\,c^{20}\,d^5+16777216\,a\,b^{22}\,c^{21}\,d^4\right)}{4096\,\left(a^{12}\,c^6\,d^{12}-12\,a^{11}\,b\,c^7\,d^{11}+66\,a^{10}\,b^2\,c^8\,d^{10}-220\,a^9\,b^3\,c^9\,d^9+495\,a^8\,b^4\,c^{10}\,d^8-792\,a^7\,b^5\,c^{11}\,d^7+924\,a^6\,b^6\,c^{12}\,d^6-792\,a^5\,b^7\,c^{13}\,d^5+495\,a^4\,b^8\,c^{14}\,d^4-220\,a^3\,b^9\,c^{15}\,d^3+66\,a^2\,b^{10}\,c^{16}\,d^2-12\,a\,b^{11}\,c^{17}\,d+b^{12}\,c^{18}\right)}+\frac{\left(\frac{125\,a^{20}\,b^4\,c\,d^{23}}{16}-\frac{2725\,a^{19}\,b^5\,c^2\,d^{22}}{16}+\frac{3745\,a^{18}\,b^6\,c^3\,d^{21}}{2}-\frac{26949\,a^{17}\,b^7\,c^4\,d^{20}}{2}+\frac{280623\,a^{16}\,b^8\,c^5\,d^{19}}{4}-\frac{1110975\,a^{15}\,b^9\,c^6\,d^{18}}{4}+\frac{1717635\,a^{14}\,b^{10}\,c^7\,d^{17}}{2}-\frac{4207335\,a^{13}\,b^{11}\,c^8\,d^{16}}{2}+\frac{32835743\,a^{12}\,b^{12}\,c^9\,d^{15}}{8}-\frac{50934983\,a^{11}\,b^{13}\,c^{10}\,d^{14}}{8}+\frac{15550975\,a^{10}\,b^{14}\,c^{11}\,d^{13}}{2}-\frac{14638795\,a^9\,b^{15}\,c^{12}\,d^{12}}{2}+\frac{20337495\,a^8\,b^{16}\,c^{13}\,d^{11}}{4}-\frac{9347799\,a^7\,b^{17}\,c^{14}\,d^{10}}{4}+\frac{844557\,a^6\,b^{18}\,c^{15}\,d^9}{2}+\frac{565575\,a^5\,b^{19}\,c^{16}\,d^8}{2}-\frac{4294995\,a^4\,b^{20}\,c^{17}\,d^7}{16}+\frac{1711115\,a^3\,b^{21}\,c^{18}\,d^6}{16}-22528\,a^2\,b^{22}\,c^{19}\,d^5+2048\,a\,b^{23}\,c^{20}\,d^4\right)\,1{}\mathrm{i}}{a^{14}\,c^6\,d^{14}-14\,a^{13}\,b\,c^7\,d^{13}+91\,a^{12}\,b^2\,c^8\,d^{12}-364\,a^{11}\,b^3\,c^9\,d^{11}+1001\,a^{10}\,b^4\,c^{10}\,d^{10}-2002\,a^9\,b^5\,c^{11}\,d^9+3003\,a^8\,b^6\,c^{12}\,d^8-3432\,a^7\,b^7\,c^{13}\,d^7+3003\,a^6\,b^8\,c^{14}\,d^6-2002\,a^5\,b^9\,c^{15}\,d^5+1001\,a^4\,b^{10}\,c^{16}\,d^4-364\,a^3\,b^{11}\,c^{17}\,d^3+91\,a^2\,b^{12}\,c^{18}\,d^2-14\,a\,b^{13}\,c^{19}\,d+b^{14}\,c^{20}}\right)\,{\left(-\frac{625\,a^8\,d^9-9000\,a^7\,b\,c\,d^8+71100\,a^6\,b^2\,c^2\,d^7-359640\,a^5\,b^3\,c^3\,d^6+1283526\,a^4\,b^4\,c^4\,d^5-3236760\,a^3\,b^5\,c^5\,d^4+5759100\,a^2\,b^6\,c^6\,d^3-6561000\,a\,b^7\,c^7\,d^2+4100625\,b^8\,c^8\,d}{16777216\,a^{12}\,c^9\,d^{12}-201326592\,a^{11}\,b\,c^{10}\,d^{11}+1107296256\,a^{10}\,b^2\,c^{11}\,d^{10}-3690987520\,a^9\,b^3\,c^{12}\,d^9+8304721920\,a^8\,b^4\,c^{13}\,d^8-13287555072\,a^7\,b^5\,c^{14}\,d^7+15502147584\,a^6\,b^6\,c^{15}\,d^6-13287555072\,a^5\,b^7\,c^{16}\,d^5+8304721920\,a^4\,b^8\,c^{17}\,d^4-3690987520\,a^3\,b^9\,c^{18}\,d^3+1107296256\,a^2\,b^{10}\,c^{19}\,d^2-201326592\,a\,b^{11}\,c^{20}\,d+16777216\,b^{12}\,c^{21}}\right)}^{3/4}\,1{}\mathrm{i}+\frac{\sqrt{x}\,\left(625\,a^9\,b^{10}\,d^{13}-9000\,a^8\,b^{11}\,c\,d^{12}+71100\,a^7\,b^{12}\,c^2\,d^{11}-334040\,a^6\,b^{13}\,c^3\,d^{10}+1099206\,a^5\,b^{14}\,c^4\,d^9-2444184\,a^4\,b^{15}\,c^5\,d^8+4100220\,a^3\,b^{16}\,c^6\,d^7-4487400\,a^2\,b^{17}\,c^7\,d^6+4100625\,a\,b^{18}\,c^8\,d^5\right)\,1{}\mathrm{i}}{4096\,\left(a^{12}\,c^6\,d^{12}-12\,a^{11}\,b\,c^7\,d^{11}+66\,a^{10}\,b^2\,c^8\,d^{10}-220\,a^9\,b^3\,c^9\,d^9+495\,a^8\,b^4\,c^{10}\,d^8-792\,a^7\,b^5\,c^{11}\,d^7+924\,a^6\,b^6\,c^{12}\,d^6-792\,a^5\,b^7\,c^{13}\,d^5+495\,a^4\,b^8\,c^{14}\,d^4-220\,a^3\,b^9\,c^{15}\,d^3+66\,a^2\,b^{10}\,c^{16}\,d^2-12\,a\,b^{11}\,c^{17}\,d+b^{12}\,c^{18}\right)}\right)+\frac{\frac{625\,a^8\,b^{12}\,d^{12}}{4096}-\frac{12375\,a^7\,b^{13}\,c\,d^{11}}{4096}+\frac{101925\,a^6\,b^{14}\,c^2\,d^{10}}{4096}-\frac{521235\,a^5\,b^{15}\,c^3\,d^9}{4096}+\frac{1726515\,a^4\,b^{16}\,c^4\,d^8}{4096}-\frac{3881925\,a^3\,b^{17}\,c^5\,d^7}{4096}+\frac{5376375\,a^2\,b^{18}\,c^6\,d^6}{4096}-\frac{4100625\,a\,b^{19}\,c^7\,d^5}{4096}}{a^{14}\,c^6\,d^{14}-14\,a^{13}\,b\,c^7\,d^{13}+91\,a^{12}\,b^2\,c^8\,d^{12}-364\,a^{11}\,b^3\,c^9\,d^{11}+1001\,a^{10}\,b^4\,c^{10}\,d^{10}-2002\,a^9\,b^5\,c^{11}\,d^9+3003\,a^8\,b^6\,c^{12}\,d^8-3432\,a^7\,b^7\,c^{13}\,d^7+3003\,a^6\,b^8\,c^{14}\,d^6-2002\,a^5\,b^9\,c^{15}\,d^5+1001\,a^4\,b^{10}\,c^{16}\,d^4-364\,a^3\,b^{11}\,c^{17}\,d^3+91\,a^2\,b^{12}\,c^{18}\,d^2-14\,a\,b^{13}\,c^{19}\,d+b^{14}\,c^{20}}}\right)\,{\left(-\frac{625\,a^8\,d^9-9000\,a^7\,b\,c\,d^8+71100\,a^6\,b^2\,c^2\,d^7-359640\,a^5\,b^3\,c^3\,d^6+1283526\,a^4\,b^4\,c^4\,d^5-3236760\,a^3\,b^5\,c^5\,d^4+5759100\,a^2\,b^6\,c^6\,d^3-6561000\,a\,b^7\,c^7\,d^2+4100625\,b^8\,c^8\,d}{16777216\,a^{12}\,c^9\,d^{12}-201326592\,a^{11}\,b\,c^{10}\,d^{11}+1107296256\,a^{10}\,b^2\,c^{11}\,d^{10}-3690987520\,a^9\,b^3\,c^{12}\,d^9+8304721920\,a^8\,b^4\,c^{13}\,d^8-13287555072\,a^7\,b^5\,c^{14}\,d^7+15502147584\,a^6\,b^6\,c^{15}\,d^6-13287555072\,a^5\,b^7\,c^{16}\,d^5+8304721920\,a^4\,b^8\,c^{17}\,d^4-3690987520\,a^3\,b^9\,c^{18}\,d^3+1107296256\,a^2\,b^{10}\,c^{19}\,d^2-201326592\,a\,b^{11}\,c^{20}\,d+16777216\,b^{12}\,c^{21}}\right)}^{1/4}","Not used",1,"2*atan((((((2048*a*b^23*c^20*d^4 + (125*a^20*b^4*c*d^23)/16 - 22528*a^2*b^22*c^19*d^5 + (1711115*a^3*b^21*c^18*d^6)/16 - (4294995*a^4*b^20*c^17*d^7)/16 + (565575*a^5*b^19*c^16*d^8)/2 + (844557*a^6*b^18*c^15*d^9)/2 - (9347799*a^7*b^17*c^14*d^10)/4 + (20337495*a^8*b^16*c^13*d^11)/4 - (14638795*a^9*b^15*c^12*d^12)/2 + (15550975*a^10*b^14*c^11*d^13)/2 - (50934983*a^11*b^13*c^10*d^14)/8 + (32835743*a^12*b^12*c^9*d^15)/8 - (4207335*a^13*b^11*c^8*d^16)/2 + (1717635*a^14*b^10*c^7*d^17)/2 - (1110975*a^15*b^9*c^6*d^18)/4 + (280623*a^16*b^8*c^5*d^19)/4 - (26949*a^17*b^7*c^4*d^20)/2 + (3745*a^18*b^6*c^3*d^21)/2 - (2725*a^19*b^5*c^2*d^22)/16)*1i)/(b^14*c^20 + a^14*c^6*d^14 - 14*a^13*b*c^7*d^13 + 91*a^2*b^12*c^18*d^2 - 364*a^3*b^11*c^17*d^3 + 1001*a^4*b^10*c^16*d^4 - 2002*a^5*b^9*c^15*d^5 + 3003*a^6*b^8*c^14*d^6 - 3432*a^7*b^7*c^13*d^7 + 3003*a^8*b^6*c^12*d^8 - 2002*a^9*b^5*c^11*d^9 + 1001*a^10*b^4*c^10*d^10 - 364*a^11*b^3*c^9*d^11 + 91*a^12*b^2*c^8*d^12 - 14*a*b^13*c^19*d) - (x^(1/2)*(-b^9/(16*a^13*d^12 + 16*a*b^12*c^12 - 192*a^2*b^11*c^11*d + 1056*a^3*b^10*c^10*d^2 - 3520*a^4*b^9*c^9*d^3 + 7920*a^5*b^8*c^8*d^4 - 12672*a^6*b^7*c^7*d^5 + 14784*a^7*b^6*c^6*d^6 - 12672*a^8*b^5*c^5*d^7 + 7920*a^9*b^4*c^4*d^8 - 3520*a^10*b^3*c^3*d^9 + 1056*a^11*b^2*c^2*d^10 - 192*a^12*b*c*d^11))^(1/4)*(16777216*a*b^22*c^21*d^4 - 201326592*a^2*b^21*c^20*d^5 + 1140473856*a^3*b^20*c^19*d^6 - 4115660800*a^4*b^19*c^18*d^7 + 10825629696*a^5*b^18*c^17*d^8 - 22493528064*a^6*b^17*c^16*d^9 + 38637076480*a^7*b^16*c^15*d^10 - 55691968512*a^8*b^15*c^14*d^11 + 66935193600*a^9*b^14*c^13*d^12 - 66085978112*a^10*b^13*c^12*d^13 + 52807434240*a^11*b^12*c^11*d^14 - 33731641344*a^12*b^11*c^10*d^15 + 17037131776*a^13*b^10*c^9*d^16 - 6723993600*a^14*b^9*c^8*d^17 + 2040201216*a^15*b^8*c^7*d^18 - 463470592*a^16*b^7*c^6*d^19 + 75104256*a^17*b^6*c^5*d^20 - 7864320*a^18*b^5*c^4*d^21 + 409600*a^19*b^4*c^3*d^22))/(4096*(b^12*c^18 + a^12*c^6*d^12 - 12*a^11*b*c^7*d^11 + 66*a^2*b^10*c^16*d^2 - 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(15550975*a^10*b^14*c^11*d^13)/2 - (50934983*a^11*b^13*c^10*d^14)/8 + (32835743*a^12*b^12*c^9*d^15)/8 - (4207335*a^13*b^11*c^8*d^16)/2 + (1717635*a^14*b^10*c^7*d^17)/2 - (1110975*a^15*b^9*c^6*d^18)/4 + (280623*a^16*b^8*c^5*d^19)/4 - (26949*a^17*b^7*c^4*d^20)/2 + (3745*a^18*b^6*c^3*d^21)/2 - (2725*a^19*b^5*c^2*d^22)/16)*1i)/(b^14*c^20 + a^14*c^6*d^14 - 14*a^13*b*c^7*d^13 + 91*a^2*b^12*c^18*d^2 - 364*a^3*b^11*c^17*d^3 + 1001*a^4*b^10*c^16*d^4 - 2002*a^5*b^9*c^15*d^5 + 3003*a^6*b^8*c^14*d^6 - 3432*a^7*b^7*c^13*d^7 + 3003*a^8*b^6*c^12*d^8 - 2002*a^9*b^5*c^11*d^9 + 1001*a^10*b^4*c^10*d^10 - 364*a^11*b^3*c^9*d^11 + 91*a^12*b^2*c^8*d^12 - 14*a*b^13*c^19*d) - (x^(1/2)*(-b^9/(16*a^13*d^12 + 16*a*b^12*c^12 - 192*a^2*b^11*c^11*d + 1056*a^3*b^10*c^10*d^2 - 3520*a^4*b^9*c^9*d^3 + 7920*a^5*b^8*c^8*d^4 - 12672*a^6*b^7*c^7*d^5 + 14784*a^7*b^6*c^6*d^6 - 12672*a^8*b^5*c^5*d^7 + 7920*a^9*b^4*c^4*d^8 - 3520*a^10*b^3*c^3*d^9 + 1056*a^11*b^2*c^2*d^10 - 192*a^12*b*c*d^11))^(1/4)*(16777216*a*b^22*c^21*d^4 - 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3236760*a^3*b^5*c^5*d^4 + 1283526*a^4*b^4*c^4*d^5 - 359640*a^5*b^3*c^3*d^6 + 71100*a^6*b^2*c^2*d^7 - 9000*a^7*b*c*d^8)/(16777216*b^12*c^21 + 16777216*a^12*c^9*d^12 - 201326592*a^11*b*c^10*d^11 + 1107296256*a^2*b^10*c^19*d^2 - 3690987520*a^3*b^9*c^18*d^3 + 8304721920*a^4*b^8*c^17*d^4 - 13287555072*a^5*b^7*c^16*d^5 + 15502147584*a^6*b^6*c^15*d^6 - 13287555072*a^7*b^5*c^14*d^7 + 8304721920*a^8*b^4*c^13*d^8 - 3690987520*a^9*b^3*c^12*d^9 + 1107296256*a^10*b^2*c^11*d^10 - 201326592*a*b^11*c^20*d))^(3/4) + (x^(1/2)*(625*a^9*b^10*d^13 + 4100625*a*b^18*c^8*d^5 - 9000*a^8*b^11*c*d^12 - 4487400*a^2*b^17*c^7*d^6 + 4100220*a^3*b^16*c^6*d^7 - 2444184*a^4*b^15*c^5*d^8 + 1099206*a^5*b^14*c^4*d^9 - 334040*a^6*b^13*c^3*d^10 + 71100*a^7*b^12*c^2*d^11))/(4096*(b^12*c^18 + a^12*c^6*d^12 - 12*a^11*b*c^7*d^11 + 66*a^2*b^10*c^16*d^2 - 220*a^3*b^9*c^15*d^3 + 495*a^4*b^8*c^14*d^4 - 792*a^5*b^7*c^13*d^5 + 924*a^6*b^6*c^12*d^6 - 792*a^7*b^5*c^11*d^7 + 495*a^8*b^4*c^10*d^8 - 220*a^9*b^3*c^9*d^9 + 66*a^10*b^2*c^8*d^10 - 12*a*b^11*c^17*d))))/((-(625*a^8*d^9 + 4100625*b^8*c^8*d - 6561000*a*b^7*c^7*d^2 + 5759100*a^2*b^6*c^6*d^3 - 3236760*a^3*b^5*c^5*d^4 + 1283526*a^4*b^4*c^4*d^5 - 359640*a^5*b^3*c^3*d^6 + 71100*a^6*b^2*c^2*d^7 - 9000*a^7*b*c*d^8)/(16777216*b^12*c^21 + 16777216*a^12*c^9*d^12 - 201326592*a^11*b*c^10*d^11 + 1107296256*a^2*b^10*c^19*d^2 - 3690987520*a^3*b^9*c^18*d^3 + 8304721920*a^4*b^8*c^17*d^4 - 13287555072*a^5*b^7*c^16*d^5 + 15502147584*a^6*b^6*c^15*d^6 - 13287555072*a^7*b^5*c^14*d^7 + 8304721920*a^8*b^4*c^13*d^8 - 3690987520*a^9*b^3*c^12*d^9 + 1107296256*a^10*b^2*c^11*d^10 - 201326592*a*b^11*c^20*d))^(1/4)*((((2048*a*b^23*c^20*d^4 + (125*a^20*b^4*c*d^23)/16 - 22528*a^2*b^22*c^19*d^5 + (1711115*a^3*b^21*c^18*d^6)/16 - (4294995*a^4*b^20*c^17*d^7)/16 + (565575*a^5*b^19*c^16*d^8)/2 + (844557*a^6*b^18*c^15*d^9)/2 - (9347799*a^7*b^17*c^14*d^10)/4 + (20337495*a^8*b^16*c^13*d^11)/4 - (14638795*a^9*b^15*c^12*d^12)/2 + (15550975*a^10*b^14*c^11*d^13)/2 - (50934983*a^11*b^13*c^10*d^14)/8 + (32835743*a^12*b^12*c^9*d^15)/8 - (4207335*a^13*b^11*c^8*d^16)/2 + (1717635*a^14*b^10*c^7*d^17)/2 - (1110975*a^15*b^9*c^6*d^18)/4 + (280623*a^16*b^8*c^5*d^19)/4 - (26949*a^17*b^7*c^4*d^20)/2 + (3745*a^18*b^6*c^3*d^21)/2 - (2725*a^19*b^5*c^2*d^22)/16)*1i)/(b^14*c^20 + a^14*c^6*d^14 - 14*a^13*b*c^7*d^13 + 91*a^2*b^12*c^18*d^2 - 364*a^3*b^11*c^17*d^3 + 1001*a^4*b^10*c^16*d^4 - 2002*a^5*b^9*c^15*d^5 + 3003*a^6*b^8*c^14*d^6 - 3432*a^7*b^7*c^13*d^7 + 3003*a^8*b^6*c^12*d^8 - 2002*a^9*b^5*c^11*d^9 + 1001*a^10*b^4*c^10*d^10 - 364*a^11*b^3*c^9*d^11 + 91*a^12*b^2*c^8*d^12 - 14*a*b^13*c^19*d) - (x^(1/2)*(-(625*a^8*d^9 + 4100625*b^8*c^8*d - 6561000*a*b^7*c^7*d^2 + 5759100*a^2*b^6*c^6*d^3 - 3236760*a^3*b^5*c^5*d^4 + 1283526*a^4*b^4*c^4*d^5 - 359640*a^5*b^3*c^3*d^6 + 71100*a^6*b^2*c^2*d^7 - 9000*a^7*b*c*d^8)/(16777216*b^12*c^21 + 16777216*a^12*c^9*d^12 - 201326592*a^11*b*c^10*d^11 + 1107296256*a^2*b^10*c^19*d^2 - 3690987520*a^3*b^9*c^18*d^3 + 8304721920*a^4*b^8*c^17*d^4 - 13287555072*a^5*b^7*c^16*d^5 + 15502147584*a^6*b^6*c^15*d^6 - 13287555072*a^7*b^5*c^14*d^7 + 8304721920*a^8*b^4*c^13*d^8 - 3690987520*a^9*b^3*c^12*d^9 + 1107296256*a^10*b^2*c^11*d^10 - 201326592*a*b^11*c^20*d))^(1/4)*(16777216*a*b^22*c^21*d^4 - 201326592*a^2*b^21*c^20*d^5 + 1140473856*a^3*b^20*c^19*d^6 - 4115660800*a^4*b^19*c^18*d^7 + 10825629696*a^5*b^18*c^17*d^8 - 22493528064*a^6*b^17*c^16*d^9 + 38637076480*a^7*b^16*c^15*d^10 - 55691968512*a^8*b^15*c^14*d^11 + 66935193600*a^9*b^14*c^13*d^12 - 66085978112*a^10*b^13*c^12*d^13 + 52807434240*a^11*b^12*c^11*d^14 - 33731641344*a^12*b^11*c^10*d^15 + 17037131776*a^13*b^10*c^9*d^16 - 6723993600*a^14*b^9*c^8*d^17 + 2040201216*a^15*b^8*c^7*d^18 - 463470592*a^16*b^7*c^6*d^19 + 75104256*a^17*b^6*c^5*d^20 - 7864320*a^18*b^5*c^4*d^21 + 409600*a^19*b^4*c^3*d^22))/(4096*(b^12*c^18 + a^12*c^6*d^12 - 12*a^11*b*c^7*d^11 + 66*a^2*b^10*c^16*d^2 - 220*a^3*b^9*c^15*d^3 + 495*a^4*b^8*c^14*d^4 - 792*a^5*b^7*c^13*d^5 + 924*a^6*b^6*c^12*d^6 - 792*a^7*b^5*c^11*d^7 + 495*a^8*b^4*c^10*d^8 - 220*a^9*b^3*c^9*d^9 + 66*a^10*b^2*c^8*d^10 - 12*a*b^11*c^17*d)))*(-(625*a^8*d^9 + 4100625*b^8*c^8*d - 6561000*a*b^7*c^7*d^2 + 5759100*a^2*b^6*c^6*d^3 - 3236760*a^3*b^5*c^5*d^4 + 1283526*a^4*b^4*c^4*d^5 - 359640*a^5*b^3*c^3*d^6 + 71100*a^6*b^2*c^2*d^7 - 9000*a^7*b*c*d^8)/(16777216*b^12*c^21 + 16777216*a^12*c^9*d^12 - 201326592*a^11*b*c^10*d^11 + 1107296256*a^2*b^10*c^19*d^2 - 3690987520*a^3*b^9*c^18*d^3 + 8304721920*a^4*b^8*c^17*d^4 - 13287555072*a^5*b^7*c^16*d^5 + 15502147584*a^6*b^6*c^15*d^6 - 13287555072*a^7*b^5*c^14*d^7 + 8304721920*a^8*b^4*c^13*d^8 - 3690987520*a^9*b^3*c^12*d^9 + 1107296256*a^10*b^2*c^11*d^10 - 201326592*a*b^11*c^20*d))^(3/4)*1i - (x^(1/2)*(625*a^9*b^10*d^13 + 4100625*a*b^18*c^8*d^5 - 9000*a^8*b^11*c*d^12 - 4487400*a^2*b^17*c^7*d^6 + 4100220*a^3*b^16*c^6*d^7 - 2444184*a^4*b^15*c^5*d^8 + 1099206*a^5*b^14*c^4*d^9 - 334040*a^6*b^13*c^3*d^10 + 71100*a^7*b^12*c^2*d^11)*1i)/(4096*(b^12*c^18 + a^12*c^6*d^12 - 12*a^11*b*c^7*d^11 + 66*a^2*b^10*c^16*d^2 - 220*a^3*b^9*c^15*d^3 + 495*a^4*b^8*c^14*d^4 - 792*a^5*b^7*c^13*d^5 + 924*a^6*b^6*c^12*d^6 - 792*a^7*b^5*c^11*d^7 + 495*a^8*b^4*c^10*d^8 - 220*a^9*b^3*c^9*d^9 + 66*a^10*b^2*c^8*d^10 - 12*a*b^11*c^17*d))) + (-(625*a^8*d^9 + 4100625*b^8*c^8*d - 6561000*a*b^7*c^7*d^2 + 5759100*a^2*b^6*c^6*d^3 - 3236760*a^3*b^5*c^5*d^4 + 1283526*a^4*b^4*c^4*d^5 - 359640*a^5*b^3*c^3*d^6 + 71100*a^6*b^2*c^2*d^7 - 9000*a^7*b*c*d^8)/(16777216*b^12*c^21 + 16777216*a^12*c^9*d^12 - 201326592*a^11*b*c^10*d^11 + 1107296256*a^2*b^10*c^19*d^2 - 3690987520*a^3*b^9*c^18*d^3 + 8304721920*a^4*b^8*c^17*d^4 - 13287555072*a^5*b^7*c^16*d^5 + 15502147584*a^6*b^6*c^15*d^6 - 13287555072*a^7*b^5*c^14*d^7 + 8304721920*a^8*b^4*c^13*d^8 - 3690987520*a^9*b^3*c^12*d^9 + 1107296256*a^10*b^2*c^11*d^10 - 201326592*a*b^11*c^20*d))^(1/4)*((((2048*a*b^23*c^20*d^4 + (125*a^20*b^4*c*d^23)/16 - 22528*a^2*b^22*c^19*d^5 + (1711115*a^3*b^21*c^18*d^6)/16 - (4294995*a^4*b^20*c^17*d^7)/16 + (565575*a^5*b^19*c^16*d^8)/2 + (844557*a^6*b^18*c^15*d^9)/2 - (9347799*a^7*b^17*c^14*d^10)/4 + (20337495*a^8*b^16*c^13*d^11)/4 - (14638795*a^9*b^15*c^12*d^12)/2 + (15550975*a^10*b^14*c^11*d^13)/2 - (50934983*a^11*b^13*c^10*d^14)/8 + (32835743*a^12*b^12*c^9*d^15)/8 - (4207335*a^13*b^11*c^8*d^16)/2 + (1717635*a^14*b^10*c^7*d^17)/2 - (1110975*a^15*b^9*c^6*d^18)/4 + (280623*a^16*b^8*c^5*d^19)/4 - (26949*a^17*b^7*c^4*d^20)/2 + (3745*a^18*b^6*c^3*d^21)/2 - (2725*a^19*b^5*c^2*d^22)/16)*1i)/(b^14*c^20 + a^14*c^6*d^14 - 14*a^13*b*c^7*d^13 + 91*a^2*b^12*c^18*d^2 - 364*a^3*b^11*c^17*d^3 + 1001*a^4*b^10*c^16*d^4 - 2002*a^5*b^9*c^15*d^5 + 3003*a^6*b^8*c^14*d^6 - 3432*a^7*b^7*c^13*d^7 + 3003*a^8*b^6*c^12*d^8 - 2002*a^9*b^5*c^11*d^9 + 1001*a^10*b^4*c^10*d^10 - 364*a^11*b^3*c^9*d^11 + 91*a^12*b^2*c^8*d^12 - 14*a*b^13*c^19*d) + (x^(1/2)*(-(625*a^8*d^9 + 4100625*b^8*c^8*d - 6561000*a*b^7*c^7*d^2 + 5759100*a^2*b^6*c^6*d^3 - 3236760*a^3*b^5*c^5*d^4 + 1283526*a^4*b^4*c^4*d^5 - 359640*a^5*b^3*c^3*d^6 + 71100*a^6*b^2*c^2*d^7 - 9000*a^7*b*c*d^8)/(16777216*b^12*c^21 + 16777216*a^12*c^9*d^12 - 201326592*a^11*b*c^10*d^11 + 1107296256*a^2*b^10*c^19*d^2 - 3690987520*a^3*b^9*c^18*d^3 + 8304721920*a^4*b^8*c^17*d^4 - 13287555072*a^5*b^7*c^16*d^5 + 15502147584*a^6*b^6*c^15*d^6 - 13287555072*a^7*b^5*c^14*d^7 + 8304721920*a^8*b^4*c^13*d^8 - 3690987520*a^9*b^3*c^12*d^9 + 1107296256*a^10*b^2*c^11*d^10 - 201326592*a*b^11*c^20*d))^(1/4)*(16777216*a*b^22*c^21*d^4 - 201326592*a^2*b^21*c^20*d^5 + 1140473856*a^3*b^20*c^19*d^6 - 4115660800*a^4*b^19*c^18*d^7 + 10825629696*a^5*b^18*c^17*d^8 - 22493528064*a^6*b^17*c^16*d^9 + 38637076480*a^7*b^16*c^15*d^10 - 55691968512*a^8*b^15*c^14*d^11 + 66935193600*a^9*b^14*c^13*d^12 - 66085978112*a^10*b^13*c^12*d^13 + 52807434240*a^11*b^12*c^11*d^14 - 33731641344*a^12*b^11*c^10*d^15 + 17037131776*a^13*b^10*c^9*d^16 - 6723993600*a^14*b^9*c^8*d^17 + 2040201216*a^15*b^8*c^7*d^18 - 463470592*a^16*b^7*c^6*d^19 + 75104256*a^17*b^6*c^5*d^20 - 7864320*a^18*b^5*c^4*d^21 + 409600*a^19*b^4*c^3*d^22))/(4096*(b^12*c^18 + a^12*c^6*d^12 - 12*a^11*b*c^7*d^11 + 66*a^2*b^10*c^16*d^2 - 220*a^3*b^9*c^15*d^3 + 495*a^4*b^8*c^14*d^4 - 792*a^5*b^7*c^13*d^5 + 924*a^6*b^6*c^12*d^6 - 792*a^7*b^5*c^11*d^7 + 495*a^8*b^4*c^10*d^8 - 220*a^9*b^3*c^9*d^9 + 66*a^10*b^2*c^8*d^10 - 12*a*b^11*c^17*d)))*(-(625*a^8*d^9 + 4100625*b^8*c^8*d - 6561000*a*b^7*c^7*d^2 + 5759100*a^2*b^6*c^6*d^3 - 3236760*a^3*b^5*c^5*d^4 + 1283526*a^4*b^4*c^4*d^5 - 359640*a^5*b^3*c^3*d^6 + 71100*a^6*b^2*c^2*d^7 - 9000*a^7*b*c*d^8)/(16777216*b^12*c^21 + 16777216*a^12*c^9*d^12 - 201326592*a^11*b*c^10*d^11 + 1107296256*a^2*b^10*c^19*d^2 - 3690987520*a^3*b^9*c^18*d^3 + 8304721920*a^4*b^8*c^17*d^4 - 13287555072*a^5*b^7*c^16*d^5 + 15502147584*a^6*b^6*c^15*d^6 - 13287555072*a^7*b^5*c^14*d^7 + 8304721920*a^8*b^4*c^13*d^8 - 3690987520*a^9*b^3*c^12*d^9 + 1107296256*a^10*b^2*c^11*d^10 - 201326592*a*b^11*c^20*d))^(3/4)*1i + (x^(1/2)*(625*a^9*b^10*d^13 + 4100625*a*b^18*c^8*d^5 - 9000*a^8*b^11*c*d^12 - 4487400*a^2*b^17*c^7*d^6 + 4100220*a^3*b^16*c^6*d^7 - 2444184*a^4*b^15*c^5*d^8 + 1099206*a^5*b^14*c^4*d^9 - 334040*a^6*b^13*c^3*d^10 + 71100*a^7*b^12*c^2*d^11)*1i)/(4096*(b^12*c^18 + a^12*c^6*d^12 - 12*a^11*b*c^7*d^11 + 66*a^2*b^10*c^16*d^2 - 220*a^3*b^9*c^15*d^3 + 495*a^4*b^8*c^14*d^4 - 792*a^5*b^7*c^13*d^5 + 924*a^6*b^6*c^12*d^6 - 792*a^7*b^5*c^11*d^7 + 495*a^8*b^4*c^10*d^8 - 220*a^9*b^3*c^9*d^9 + 66*a^10*b^2*c^8*d^10 - 12*a*b^11*c^17*d))) + ((625*a^8*b^12*d^12)/4096 - (4100625*a*b^19*c^7*d^5)/4096 - (12375*a^7*b^13*c*d^11)/4096 + (5376375*a^2*b^18*c^6*d^6)/4096 - (3881925*a^3*b^17*c^5*d^7)/4096 + (1726515*a^4*b^16*c^4*d^8)/4096 - (521235*a^5*b^15*c^3*d^9)/4096 + (101925*a^6*b^14*c^2*d^10)/4096)/(b^14*c^20 + a^14*c^6*d^14 - 14*a^13*b*c^7*d^13 + 91*a^2*b^12*c^18*d^2 - 364*a^3*b^11*c^17*d^3 + 1001*a^4*b^10*c^16*d^4 - 2002*a^5*b^9*c^15*d^5 + 3003*a^6*b^8*c^14*d^6 - 3432*a^7*b^7*c^13*d^7 + 3003*a^8*b^6*c^12*d^8 - 2002*a^9*b^5*c^11*d^9 + 1001*a^10*b^4*c^10*d^10 - 364*a^11*b^3*c^9*d^11 + 91*a^12*b^2*c^8*d^12 - 14*a*b^13*c^19*d)))*(-(625*a^8*d^9 + 4100625*b^8*c^8*d - 6561000*a*b^7*c^7*d^2 + 5759100*a^2*b^6*c^6*d^3 - 3236760*a^3*b^5*c^5*d^4 + 1283526*a^4*b^4*c^4*d^5 - 359640*a^5*b^3*c^3*d^6 + 71100*a^6*b^2*c^2*d^7 - 9000*a^7*b*c*d^8)/(16777216*b^12*c^21 + 16777216*a^12*c^9*d^12 - 201326592*a^11*b*c^10*d^11 + 1107296256*a^2*b^10*c^19*d^2 - 3690987520*a^3*b^9*c^18*d^3 + 8304721920*a^4*b^8*c^17*d^4 - 13287555072*a^5*b^7*c^16*d^5 + 15502147584*a^6*b^6*c^15*d^6 - 13287555072*a^7*b^5*c^14*d^7 + 8304721920*a^8*b^4*c^13*d^8 - 3690987520*a^9*b^3*c^12*d^9 + 1107296256*a^10*b^2*c^11*d^10 - 201326592*a*b^11*c^20*d))^(1/4)","B"
484,1,36997,633,4.414553,"\text{Not used}","int(1/(x^(1/2)*(a + b*x^2)*(c + d*x^2)^3),x)","\mathrm{atan}\left(\frac{{\left(-\frac{b^{11}}{16\,a^{15}\,d^{12}-192\,a^{14}\,b\,c\,d^{11}+1056\,a^{13}\,b^2\,c^2\,d^{10}-3520\,a^{12}\,b^3\,c^3\,d^9+7920\,a^{11}\,b^4\,c^4\,d^8-12672\,a^{10}\,b^5\,c^5\,d^7+14784\,a^9\,b^6\,c^6\,d^6-12672\,a^8\,b^7\,c^7\,d^5+7920\,a^7\,b^8\,c^8\,d^4-3520\,a^6\,b^9\,c^9\,d^3+1056\,a^5\,b^{10}\,c^{10}\,d^2-192\,a^4\,b^{11}\,c^{11}\,d+16\,a^3\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(\left(\frac{\frac{194481\,a^8\,b^8\,d^{14}}{2048}-\frac{2250423\,a^7\,b^9\,c\,d^{13}}{2048}+\frac{12127941\,a^6\,b^{10}\,c^2\,d^{12}}{2048}-\frac{38915667\,a^5\,b^{11}\,c^3\,d^{11}}{2048}+\frac{80271027\,a^4\,b^{12}\,c^4\,d^{10}}{2048}-\frac{106888869\,a^3\,b^{13}\,c^5\,d^9}{2048}+\frac{86420247\,a^2\,b^{14}\,c^6\,d^8}{2048}-\frac{34792593\,a\,b^{15}\,c^7\,d^7}{2048}+1232\,b^{16}\,c^8\,d^6}{a^8\,c^8\,d^8-8\,a^7\,b\,c^9\,d^7+28\,a^6\,b^2\,c^{10}\,d^6-56\,a^5\,b^3\,c^{11}\,d^5+70\,a^4\,b^4\,c^{12}\,d^4-56\,a^3\,b^5\,c^{13}\,d^3+28\,a^2\,b^6\,c^{14}\,d^2-8\,a\,b^7\,c^{15}\,d+b^8\,c^{16}}+\left(\frac{\sqrt{x}\,\left(7225344\,a^{19}\,b^4\,c^4\,d^{23}-132120576\,a^{18}\,b^5\,c^5\,d^{22}+1146224640\,a^{17}\,b^6\,c^6\,d^{21}-6245842944\,a^{16}\,b^7\,c^7\,d^{20}+23871029248\,a^{15}\,b^8\,c^8\,d^{19}-67718086656\,a^{14}\,b^9\,c^9\,d^{18}+147248775168\,a^{13}\,b^{10}\,c^{10}\,d^{17}-249961119744\,a^{12}\,b^{11}\,c^{11}\,d^{16}+334222688256\,a^{11}\,b^{12}\,c^{12}\,d^{15}-352258621440\,a^{10}\,b^{13}\,c^{13}\,d^{14}+289980416000\,a^9\,b^{14}\,c^{14}\,d^{13}-181503787008\,a^8\,b^{15}\,c^{15}\,d^{12}+80192667648\,a^7\,b^{16}\,c^{16}\,d^{11}-18397265920\,a^6\,b^{17}\,c^{17}\,d^{10}-4753588224\,a^5\,b^{18}\,c^{18}\,d^9+6972506112\,a^4\,b^{19}\,c^{19}\,d^8-3593846784\,a^3\,b^{20}\,c^{20}\,d^7+1107296256\,a^2\,b^{21}\,c^{21}\,d^6-201326592\,a\,b^{22}\,c^{22}\,d^5+16777216\,b^{23}\,c^{23}\,d^4\right)}{4096\,\left(a^{12}\,c^8\,d^{12}-12\,a^{11}\,b\,c^9\,d^{11}+66\,a^{10}\,b^2\,c^{10}\,d^{10}-220\,a^9\,b^3\,c^{11}\,d^9+495\,a^8\,b^4\,c^{12}\,d^8-792\,a^7\,b^5\,c^{13}\,d^7+924\,a^6\,b^6\,c^{14}\,d^6-792\,a^5\,b^7\,c^{15}\,d^5+495\,a^4\,b^8\,c^{16}\,d^4-220\,a^3\,b^9\,c^{17}\,d^3+66\,a^2\,b^{10}\,c^{18}\,d^2-12\,a\,b^{11}\,c^{19}\,d+b^{12}\,c^{20}\right)}-\frac{{\left(-\frac{b^{11}}{16\,a^{15}\,d^{12}-192\,a^{14}\,b\,c\,d^{11}+1056\,a^{13}\,b^2\,c^2\,d^{10}-3520\,a^{12}\,b^3\,c^3\,d^9+7920\,a^{11}\,b^4\,c^4\,d^8-12672\,a^{10}\,b^5\,c^5\,d^7+14784\,a^9\,b^6\,c^6\,d^6-12672\,a^8\,b^7\,c^7\,d^5+7920\,a^7\,b^8\,c^8\,d^4-3520\,a^6\,b^9\,c^9\,d^3+1056\,a^5\,b^{10}\,c^{10}\,d^2-192\,a^4\,b^{11}\,c^{11}\,d+16\,a^3\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(5376\,a^{16}\,b^4\,c^7\,d^{19}-76032\,a^{15}\,b^5\,c^8\,d^{18}+501248\,a^{14}\,b^6\,c^9\,d^{17}-2033152\,a^{13}\,b^7\,c^{10}\,d^{16}+5637888\,a^{12}\,b^8\,c^{11}\,d^{15}-11221760\,a^{11}\,b^9\,c^{12}\,d^{14}+16344064\,a^{10}\,b^{10}\,c^{13}\,d^{13}-17335296\,a^9\,b^{11}\,c^{14}\,d^{12}+12866304\,a^8\,b^{12}\,c^{15}\,d^{11}-5803776\,a^7\,b^{13}\,c^{16}\,d^{10}+456192\,a^6\,b^{14}\,c^{17}\,d^9+1427968\,a^5\,b^{15}\,c^{18}\,d^8-1117952\,a^4\,b^{16}\,c^{19}\,d^7+430848\,a^3\,b^{17}\,c^{20}\,d^6-90112\,a^2\,b^{18}\,c^{21}\,d^5+8192\,a\,b^{19}\,c^{22}\,d^4\right)}{a^8\,c^8\,d^8-8\,a^7\,b\,c^9\,d^7+28\,a^6\,b^2\,c^{10}\,d^6-56\,a^5\,b^3\,c^{11}\,d^5+70\,a^4\,b^4\,c^{12}\,d^4-56\,a^3\,b^5\,c^{13}\,d^3+28\,a^2\,b^6\,c^{14}\,d^2-8\,a\,b^7\,c^{15}\,d+b^8\,c^{16}}\right)\,{\left(-\frac{b^{11}}{16\,a^{15}\,d^{12}-192\,a^{14}\,b\,c\,d^{11}+1056\,a^{13}\,b^2\,c^2\,d^{10}-3520\,a^{12}\,b^3\,c^3\,d^9+7920\,a^{11}\,b^4\,c^4\,d^8-12672\,a^{10}\,b^5\,c^5\,d^7+14784\,a^9\,b^6\,c^6\,d^6-12672\,a^8\,b^7\,c^7\,d^5+7920\,a^7\,b^8\,c^8\,d^4-3520\,a^6\,b^9\,c^9\,d^3+1056\,a^5\,b^{10}\,c^{10}\,d^2-192\,a^4\,b^{11}\,c^{11}\,d+16\,a^3\,b^{12}\,c^{12}}\right)}^{3/4}\right)\,{\left(-\frac{b^{11}}{16\,a^{15}\,d^{12}-192\,a^{14}\,b\,c\,d^{11}+1056\,a^{13}\,b^2\,c^2\,d^{10}-3520\,a^{12}\,b^3\,c^3\,d^9+7920\,a^{11}\,b^4\,c^4\,d^8-12672\,a^{10}\,b^5\,c^5\,d^7+14784\,a^9\,b^6\,c^6\,d^6-12672\,a^8\,b^7\,c^7\,d^5+7920\,a^7\,b^8\,c^8\,d^4-3520\,a^6\,b^9\,c^9\,d^3+1056\,a^5\,b^{10}\,c^{10}\,d^2-192\,a^4\,b^{11}\,c^{11}\,d+16\,a^3\,b^{12}\,c^{12}}\right)}^{1/4}\,1{}\mathrm{i}+\frac{\sqrt{x}\,\left(194481\,a^8\,b^{11}\,d^{15}-2444904\,a^7\,b^{12}\,c\,d^{14}+14378364\,a^6\,b^{13}\,c^2\,d^{13}-51043608\,a^5\,b^{14}\,c^3\,d^{12}+119638278\,a^4\,b^{15}\,c^4\,d^{11}-189998424\,a^3\,b^{16}\,c^5\,d^{10}+201081276\,a^2\,b^{17}\,c^6\,d^9-130932648\,a\,b^{18}\,c^7\,d^8+41224337\,b^{19}\,c^8\,d^7\right)\,1{}\mathrm{i}}{4096\,\left(a^{12}\,c^8\,d^{12}-12\,a^{11}\,b\,c^9\,d^{11}+66\,a^{10}\,b^2\,c^{10}\,d^{10}-220\,a^9\,b^3\,c^{11}\,d^9+495\,a^8\,b^4\,c^{12}\,d^8-792\,a^7\,b^5\,c^{13}\,d^7+924\,a^6\,b^6\,c^{14}\,d^6-792\,a^5\,b^7\,c^{15}\,d^5+495\,a^4\,b^8\,c^{16}\,d^4-220\,a^3\,b^9\,c^{17}\,d^3+66\,a^2\,b^{10}\,c^{18}\,d^2-12\,a\,b^{11}\,c^{19}\,d+b^{12}\,c^{20}\right)}\right)-{\left(-\frac{b^{11}}{16\,a^{15}\,d^{12}-192\,a^{14}\,b\,c\,d^{11}+1056\,a^{13}\,b^2\,c^2\,d^{10}-3520\,a^{12}\,b^3\,c^3\,d^9+7920\,a^{11}\,b^4\,c^4\,d^8-12672\,a^{10}\,b^5\,c^5\,d^7+14784\,a^9\,b^6\,c^6\,d^6-12672\,a^8\,b^7\,c^7\,d^5+7920\,a^7\,b^8\,c^8\,d^4-3520\,a^6\,b^9\,c^9\,d^3+1056\,a^5\,b^{10}\,c^{10}\,d^2-192\,a^4\,b^{11}\,c^{11}\,d+16\,a^3\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(\left(\frac{\frac{194481\,a^8\,b^8\,d^{14}}{2048}-\frac{2250423\,a^7\,b^9\,c\,d^{13}}{2048}+\frac{12127941\,a^6\,b^{10}\,c^2\,d^{12}}{2048}-\frac{38915667\,a^5\,b^{11}\,c^3\,d^{11}}{2048}+\frac{80271027\,a^4\,b^{12}\,c^4\,d^{10}}{2048}-\frac{106888869\,a^3\,b^{13}\,c^5\,d^9}{2048}+\frac{86420247\,a^2\,b^{14}\,c^6\,d^8}{2048}-\frac{34792593\,a\,b^{15}\,c^7\,d^7}{2048}+1232\,b^{16}\,c^8\,d^6}{a^8\,c^8\,d^8-8\,a^7\,b\,c^9\,d^7+28\,a^6\,b^2\,c^{10}\,d^6-56\,a^5\,b^3\,c^{11}\,d^5+70\,a^4\,b^4\,c^{12}\,d^4-56\,a^3\,b^5\,c^{13}\,d^3+28\,a^2\,b^6\,c^{14}\,d^2-8\,a\,b^7\,c^{15}\,d+b^8\,c^{16}}-\left(\frac{\sqrt{x}\,\left(7225344\,a^{19}\,b^4\,c^4\,d^{23}-132120576\,a^{18}\,b^5\,c^5\,d^{22}+1146224640\,a^{17}\,b^6\,c^6\,d^{21}-6245842944\,a^{16}\,b^7\,c^7\,d^{20}+23871029248\,a^{15}\,b^8\,c^8\,d^{19}-67718086656\,a^{14}\,b^9\,c^9\,d^{18}+147248775168\,a^{13}\,b^{10}\,c^{10}\,d^{17}-249961119744\,a^{12}\,b^{11}\,c^{11}\,d^{16}+334222688256\,a^{11}\,b^{12}\,c^{12}\,d^{15}-352258621440\,a^{10}\,b^{13}\,c^{13}\,d^{14}+289980416000\,a^9\,b^{14}\,c^{14}\,d^{13}-181503787008\,a^8\,b^{15}\,c^{15}\,d^{12}+80192667648\,a^7\,b^{16}\,c^{16}\,d^{11}-18397265920\,a^6\,b^{17}\,c^{17}\,d^{10}-4753588224\,a^5\,b^{18}\,c^{18}\,d^9+6972506112\,a^4\,b^{19}\,c^{19}\,d^8-3593846784\,a^3\,b^{20}\,c^{20}\,d^7+1107296256\,a^2\,b^{21}\,c^{21}\,d^6-201326592\,a\,b^{22}\,c^{22}\,d^5+16777216\,b^{23}\,c^{23}\,d^4\right)}{4096\,\left(a^{12}\,c^8\,d^{12}-12\,a^{11}\,b\,c^9\,d^{11}+66\,a^{10}\,b^2\,c^{10}\,d^{10}-220\,a^9\,b^3\,c^{11}\,d^9+495\,a^8\,b^4\,c^{12}\,d^8-792\,a^7\,b^5\,c^{13}\,d^7+924\,a^6\,b^6\,c^{14}\,d^6-792\,a^5\,b^7\,c^{15}\,d^5+495\,a^4\,b^8\,c^{16}\,d^4-220\,a^3\,b^9\,c^{17}\,d^3+66\,a^2\,b^{10}\,c^{18}\,d^2-12\,a\,b^{11}\,c^{19}\,d+b^{12}\,c^{20}\right)}+\frac{{\left(-\frac{b^{11}}{16\,a^{15}\,d^{12}-192\,a^{14}\,b\,c\,d^{11}+1056\,a^{13}\,b^2\,c^2\,d^{10}-3520\,a^{12}\,b^3\,c^3\,d^9+7920\,a^{11}\,b^4\,c^4\,d^8-12672\,a^{10}\,b^5\,c^5\,d^7+14784\,a^9\,b^6\,c^6\,d^6-12672\,a^8\,b^7\,c^7\,d^5+7920\,a^7\,b^8\,c^8\,d^4-3520\,a^6\,b^9\,c^9\,d^3+1056\,a^5\,b^{10}\,c^{10}\,d^2-192\,a^4\,b^{11}\,c^{11}\,d+16\,a^3\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(5376\,a^{16}\,b^4\,c^7\,d^{19}-76032\,a^{15}\,b^5\,c^8\,d^{18}+501248\,a^{14}\,b^6\,c^9\,d^{17}-2033152\,a^{13}\,b^7\,c^{10}\,d^{16}+5637888\,a^{12}\,b^8\,c^{11}\,d^{15}-11221760\,a^{11}\,b^9\,c^{12}\,d^{14}+16344064\,a^{10}\,b^{10}\,c^{13}\,d^{13}-17335296\,a^9\,b^{11}\,c^{14}\,d^{12}+12866304\,a^8\,b^{12}\,c^{15}\,d^{11}-5803776\,a^7\,b^{13}\,c^{16}\,d^{10}+456192\,a^6\,b^{14}\,c^{17}\,d^9+1427968\,a^5\,b^{15}\,c^{18}\,d^8-1117952\,a^4\,b^{16}\,c^{19}\,d^7+430848\,a^3\,b^{17}\,c^{20}\,d^6-90112\,a^2\,b^{18}\,c^{21}\,d^5+8192\,a\,b^{19}\,c^{22}\,d^4\right)}{a^8\,c^8\,d^8-8\,a^7\,b\,c^9\,d^7+28\,a^6\,b^2\,c^{10}\,d^6-56\,a^5\,b^3\,c^{11}\,d^5+70\,a^4\,b^4\,c^{12}\,d^4-56\,a^3\,b^5\,c^{13}\,d^3+28\,a^2\,b^6\,c^{14}\,d^2-8\,a\,b^7\,c^{15}\,d+b^8\,c^{16}}\right)\,{\left(-\frac{b^{11}}{16\,a^{15}\,d^{12}-192\,a^{14}\,b\,c\,d^{11}+1056\,a^{13}\,b^2\,c^2\,d^{10}-3520\,a^{12}\,b^3\,c^3\,d^9+7920\,a^{11}\,b^4\,c^4\,d^8-12672\,a^{10}\,b^5\,c^5\,d^7+14784\,a^9\,b^6\,c^6\,d^6-12672\,a^8\,b^7\,c^7\,d^5+7920\,a^7\,b^8\,c^8\,d^4-3520\,a^6\,b^9\,c^9\,d^3+1056\,a^5\,b^{10}\,c^{10}\,d^2-192\,a^4\,b^{11}\,c^{11}\,d+16\,a^3\,b^{12}\,c^{12}}\right)}^{3/4}\right)\,{\left(-\frac{b^{11}}{16\,a^{15}\,d^{12}-192\,a^{14}\,b\,c\,d^{11}+1056\,a^{13}\,b^2\,c^2\,d^{10}-3520\,a^{12}\,b^3\,c^3\,d^9+7920\,a^{11}\,b^4\,c^4\,d^8-12672\,a^{10}\,b^5\,c^5\,d^7+14784\,a^9\,b^6\,c^6\,d^6-12672\,a^8\,b^7\,c^7\,d^5+7920\,a^7\,b^8\,c^8\,d^4-3520\,a^6\,b^9\,c^9\,d^3+1056\,a^5\,b^{10}\,c^{10}\,d^2-192\,a^4\,b^{11}\,c^{11}\,d+16\,a^3\,b^{12}\,c^{12}}\right)}^{1/4}\,1{}\mathrm{i}-\frac{\sqrt{x}\,\left(194481\,a^8\,b^{11}\,d^{15}-2444904\,a^7\,b^{12}\,c\,d^{14}+14378364\,a^6\,b^{13}\,c^2\,d^{13}-51043608\,a^5\,b^{14}\,c^3\,d^{12}+119638278\,a^4\,b^{15}\,c^4\,d^{11}-189998424\,a^3\,b^{16}\,c^5\,d^{10}+201081276\,a^2\,b^{17}\,c^6\,d^9-130932648\,a\,b^{18}\,c^7\,d^8+41224337\,b^{19}\,c^8\,d^7\right)\,1{}\mathrm{i}}{4096\,\left(a^{12}\,c^8\,d^{12}-12\,a^{11}\,b\,c^9\,d^{11}+66\,a^{10}\,b^2\,c^{10}\,d^{10}-220\,a^9\,b^3\,c^{11}\,d^9+495\,a^8\,b^4\,c^{12}\,d^8-792\,a^7\,b^5\,c^{13}\,d^7+924\,a^6\,b^6\,c^{14}\,d^6-792\,a^5\,b^7\,c^{15}\,d^5+495\,a^4\,b^8\,c^{16}\,d^4-220\,a^3\,b^9\,c^{17}\,d^3+66\,a^2\,b^{10}\,c^{18}\,d^2-12\,a\,b^{11}\,c^{19}\,d+b^{12}\,c^{20}\right)}\right)}{{\left(-\frac{b^{11}}{16\,a^{15}\,d^{12}-192\,a^{14}\,b\,c\,d^{11}+1056\,a^{13}\,b^2\,c^2\,d^{10}-3520\,a^{12}\,b^3\,c^3\,d^9+7920\,a^{11}\,b^4\,c^4\,d^8-12672\,a^{10}\,b^5\,c^5\,d^7+14784\,a^9\,b^6\,c^6\,d^6-12672\,a^8\,b^7\,c^7\,d^5+7920\,a^7\,b^8\,c^8\,d^4-3520\,a^6\,b^9\,c^9\,d^3+1056\,a^5\,b^{10}\,c^{10}\,d^2-192\,a^4\,b^{11}\,c^{11}\,d+16\,a^3\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(\left(\frac{\frac{194481\,a^8\,b^8\,d^{14}}{2048}-\frac{2250423\,a^7\,b^9\,c\,d^{13}}{2048}+\frac{12127941\,a^6\,b^{10}\,c^2\,d^{12}}{2048}-\frac{38915667\,a^5\,b^{11}\,c^3\,d^{11}}{2048}+\frac{80271027\,a^4\,b^{12}\,c^4\,d^{10}}{2048}-\frac{106888869\,a^3\,b^{13}\,c^5\,d^9}{2048}+\frac{86420247\,a^2\,b^{14}\,c^6\,d^8}{2048}-\frac{34792593\,a\,b^{15}\,c^7\,d^7}{2048}+1232\,b^{16}\,c^8\,d^6}{a^8\,c^8\,d^8-8\,a^7\,b\,c^9\,d^7+28\,a^6\,b^2\,c^{10}\,d^6-56\,a^5\,b^3\,c^{11}\,d^5+70\,a^4\,b^4\,c^{12}\,d^4-56\,a^3\,b^5\,c^{13}\,d^3+28\,a^2\,b^6\,c^{14}\,d^2-8\,a\,b^7\,c^{15}\,d+b^8\,c^{16}}+\left(\frac{\sqrt{x}\,\left(7225344\,a^{19}\,b^4\,c^4\,d^{23}-132120576\,a^{18}\,b^5\,c^5\,d^{22}+1146224640\,a^{17}\,b^6\,c^6\,d^{21}-6245842944\,a^{16}\,b^7\,c^7\,d^{20}+23871029248\,a^{15}\,b^8\,c^8\,d^{19}-67718086656\,a^{14}\,b^9\,c^9\,d^{18}+147248775168\,a^{13}\,b^{10}\,c^{10}\,d^{17}-249961119744\,a^{12}\,b^{11}\,c^{11}\,d^{16}+334222688256\,a^{11}\,b^{12}\,c^{12}\,d^{15}-352258621440\,a^{10}\,b^{13}\,c^{13}\,d^{14}+289980416000\,a^9\,b^{14}\,c^{14}\,d^{13}-181503787008\,a^8\,b^{15}\,c^{15}\,d^{12}+80192667648\,a^7\,b^{16}\,c^{16}\,d^{11}-18397265920\,a^6\,b^{17}\,c^{17}\,d^{10}-4753588224\,a^5\,b^{18}\,c^{18}\,d^9+6972506112\,a^4\,b^{19}\,c^{19}\,d^8-3593846784\,a^3\,b^{20}\,c^{20}\,d^7+1107296256\,a^2\,b^{21}\,c^{21}\,d^6-201326592\,a\,b^{22}\,c^{22}\,d^5+16777216\,b^{23}\,c^{23}\,d^4\right)}{4096\,\left(a^{12}\,c^8\,d^{12}-12\,a^{11}\,b\,c^9\,d^{11}+66\,a^{10}\,b^2\,c^{10}\,d^{10}-220\,a^9\,b^3\,c^{11}\,d^9+495\,a^8\,b^4\,c^{12}\,d^8-792\,a^7\,b^5\,c^{13}\,d^7+924\,a^6\,b^6\,c^{14}\,d^6-792\,a^5\,b^7\,c^{15}\,d^5+495\,a^4\,b^8\,c^{16}\,d^4-220\,a^3\,b^9\,c^{17}\,d^3+66\,a^2\,b^{10}\,c^{18}\,d^2-12\,a\,b^{11}\,c^{19}\,d+b^{12}\,c^{20}\right)}-\frac{{\left(-\frac{b^{11}}{16\,a^{15}\,d^{12}-192\,a^{14}\,b\,c\,d^{11}+1056\,a^{13}\,b^2\,c^2\,d^{10}-3520\,a^{12}\,b^3\,c^3\,d^9+7920\,a^{11}\,b^4\,c^4\,d^8-12672\,a^{10}\,b^5\,c^5\,d^7+14784\,a^9\,b^6\,c^6\,d^6-12672\,a^8\,b^7\,c^7\,d^5+7920\,a^7\,b^8\,c^8\,d^4-3520\,a^6\,b^9\,c^9\,d^3+1056\,a^5\,b^{10}\,c^{10}\,d^2-192\,a^4\,b^{11}\,c^{11}\,d+16\,a^3\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(5376\,a^{16}\,b^4\,c^7\,d^{19}-76032\,a^{15}\,b^5\,c^8\,d^{18}+501248\,a^{14}\,b^6\,c^9\,d^{17}-2033152\,a^{13}\,b^7\,c^{10}\,d^{16}+5637888\,a^{12}\,b^8\,c^{11}\,d^{15}-11221760\,a^{11}\,b^9\,c^{12}\,d^{14}+16344064\,a^{10}\,b^{10}\,c^{13}\,d^{13}-17335296\,a^9\,b^{11}\,c^{14}\,d^{12}+12866304\,a^8\,b^{12}\,c^{15}\,d^{11}-5803776\,a^7\,b^{13}\,c^{16}\,d^{10}+456192\,a^6\,b^{14}\,c^{17}\,d^9+1427968\,a^5\,b^{15}\,c^{18}\,d^8-1117952\,a^4\,b^{16}\,c^{19}\,d^7+430848\,a^3\,b^{17}\,c^{20}\,d^6-90112\,a^2\,b^{18}\,c^{21}\,d^5+8192\,a\,b^{19}\,c^{22}\,d^4\right)}{a^8\,c^8\,d^8-8\,a^7\,b\,c^9\,d^7+28\,a^6\,b^2\,c^{10}\,d^6-56\,a^5\,b^3\,c^{11}\,d^5+70\,a^4\,b^4\,c^{12}\,d^4-56\,a^3\,b^5\,c^{13}\,d^3+28\,a^2\,b^6\,c^{14}\,d^2-8\,a\,b^7\,c^{15}\,d+b^8\,c^{16}}\right)\,{\left(-\frac{b^{11}}{16\,a^{15}\,d^{12}-192\,a^{14}\,b\,c\,d^{11}+1056\,a^{13}\,b^2\,c^2\,d^{10}-3520\,a^{12}\,b^3\,c^3\,d^9+7920\,a^{11}\,b^4\,c^4\,d^8-12672\,a^{10}\,b^5\,c^5\,d^7+14784\,a^9\,b^6\,c^6\,d^6-12672\,a^8\,b^7\,c^7\,d^5+7920\,a^7\,b^8\,c^8\,d^4-3520\,a^6\,b^9\,c^9\,d^3+1056\,a^5\,b^{10}\,c^{10}\,d^2-192\,a^4\,b^{11}\,c^{11}\,d+16\,a^3\,b^{12}\,c^{12}}\right)}^{3/4}\right)\,{\left(-\frac{b^{11}}{16\,a^{15}\,d^{12}-192\,a^{14}\,b\,c\,d^{11}+1056\,a^{13}\,b^2\,c^2\,d^{10}-3520\,a^{12}\,b^3\,c^3\,d^9+7920\,a^{11}\,b^4\,c^4\,d^8-12672\,a^{10}\,b^5\,c^5\,d^7+14784\,a^9\,b^6\,c^6\,d^6-12672\,a^8\,b^7\,c^7\,d^5+7920\,a^7\,b^8\,c^8\,d^4-3520\,a^6\,b^9\,c^9\,d^3+1056\,a^5\,b^{10}\,c^{10}\,d^2-192\,a^4\,b^{11}\,c^{11}\,d+16\,a^3\,b^{12}\,c^{12}}\right)}^{1/4}+\frac{\sqrt{x}\,\left(194481\,a^8\,b^{11}\,d^{15}-2444904\,a^7\,b^{12}\,c\,d^{14}+14378364\,a^6\,b^{13}\,c^2\,d^{13}-51043608\,a^5\,b^{14}\,c^3\,d^{12}+119638278\,a^4\,b^{15}\,c^4\,d^{11}-189998424\,a^3\,b^{16}\,c^5\,d^{10}+201081276\,a^2\,b^{17}\,c^6\,d^9-130932648\,a\,b^{18}\,c^7\,d^8+41224337\,b^{19}\,c^8\,d^7\right)}{4096\,\left(a^{12}\,c^8\,d^{12}-12\,a^{11}\,b\,c^9\,d^{11}+66\,a^{10}\,b^2\,c^{10}\,d^{10}-220\,a^9\,b^3\,c^{11}\,d^9+495\,a^8\,b^4\,c^{12}\,d^8-792\,a^7\,b^5\,c^{13}\,d^7+924\,a^6\,b^6\,c^{14}\,d^6-792\,a^5\,b^7\,c^{15}\,d^5+495\,a^4\,b^8\,c^{16}\,d^4-220\,a^3\,b^9\,c^{17}\,d^3+66\,a^2\,b^{10}\,c^{18}\,d^2-12\,a\,b^{11}\,c^{19}\,d+b^{12}\,c^{20}\right)}\right)+{\left(-\frac{b^{11}}{16\,a^{15}\,d^{12}-192\,a^{14}\,b\,c\,d^{11}+1056\,a^{13}\,b^2\,c^2\,d^{10}-3520\,a^{12}\,b^3\,c^3\,d^9+7920\,a^{11}\,b^4\,c^4\,d^8-12672\,a^{10}\,b^5\,c^5\,d^7+14784\,a^9\,b^6\,c^6\,d^6-12672\,a^8\,b^7\,c^7\,d^5+7920\,a^7\,b^8\,c^8\,d^4-3520\,a^6\,b^9\,c^9\,d^3+1056\,a^5\,b^{10}\,c^{10}\,d^2-192\,a^4\,b^{11}\,c^{11}\,d+16\,a^3\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(\left(\frac{\frac{194481\,a^8\,b^8\,d^{14}}{2048}-\frac{2250423\,a^7\,b^9\,c\,d^{13}}{2048}+\frac{12127941\,a^6\,b^{10}\,c^2\,d^{12}}{2048}-\frac{38915667\,a^5\,b^{11}\,c^3\,d^{11}}{2048}+\frac{80271027\,a^4\,b^{12}\,c^4\,d^{10}}{2048}-\frac{106888869\,a^3\,b^{13}\,c^5\,d^9}{2048}+\frac{86420247\,a^2\,b^{14}\,c^6\,d^8}{2048}-\frac{34792593\,a\,b^{15}\,c^7\,d^7}{2048}+1232\,b^{16}\,c^8\,d^6}{a^8\,c^8\,d^8-8\,a^7\,b\,c^9\,d^7+28\,a^6\,b^2\,c^{10}\,d^6-56\,a^5\,b^3\,c^{11}\,d^5+70\,a^4\,b^4\,c^{12}\,d^4-56\,a^3\,b^5\,c^{13}\,d^3+28\,a^2\,b^6\,c^{14}\,d^2-8\,a\,b^7\,c^{15}\,d+b^8\,c^{16}}-\left(\frac{\sqrt{x}\,\left(7225344\,a^{19}\,b^4\,c^4\,d^{23}-132120576\,a^{18}\,b^5\,c^5\,d^{22}+1146224640\,a^{17}\,b^6\,c^6\,d^{21}-6245842944\,a^{16}\,b^7\,c^7\,d^{20}+23871029248\,a^{15}\,b^8\,c^8\,d^{19}-67718086656\,a^{14}\,b^9\,c^9\,d^{18}+147248775168\,a^{13}\,b^{10}\,c^{10}\,d^{17}-249961119744\,a^{12}\,b^{11}\,c^{11}\,d^{16}+334222688256\,a^{11}\,b^{12}\,c^{12}\,d^{15}-352258621440\,a^{10}\,b^{13}\,c^{13}\,d^{14}+289980416000\,a^9\,b^{14}\,c^{14}\,d^{13}-181503787008\,a^8\,b^{15}\,c^{15}\,d^{12}+80192667648\,a^7\,b^{16}\,c^{16}\,d^{11}-18397265920\,a^6\,b^{17}\,c^{17}\,d^{10}-4753588224\,a^5\,b^{18}\,c^{18}\,d^9+6972506112\,a^4\,b^{19}\,c^{19}\,d^8-3593846784\,a^3\,b^{20}\,c^{20}\,d^7+1107296256\,a^2\,b^{21}\,c^{21}\,d^6-201326592\,a\,b^{22}\,c^{22}\,d^5+16777216\,b^{23}\,c^{23}\,d^4\right)}{4096\,\left(a^{12}\,c^8\,d^{12}-12\,a^{11}\,b\,c^9\,d^{11}+66\,a^{10}\,b^2\,c^{10}\,d^{10}-220\,a^9\,b^3\,c^{11}\,d^9+495\,a^8\,b^4\,c^{12}\,d^8-792\,a^7\,b^5\,c^{13}\,d^7+924\,a^6\,b^6\,c^{14}\,d^6-792\,a^5\,b^7\,c^{15}\,d^5+495\,a^4\,b^8\,c^{16}\,d^4-220\,a^3\,b^9\,c^{17}\,d^3+66\,a^2\,b^{10}\,c^{18}\,d^2-12\,a\,b^{11}\,c^{19}\,d+b^{12}\,c^{20}\right)}+\frac{{\left(-\frac{b^{11}}{16\,a^{15}\,d^{12}-192\,a^{14}\,b\,c\,d^{11}+1056\,a^{13}\,b^2\,c^2\,d^{10}-3520\,a^{12}\,b^3\,c^3\,d^9+7920\,a^{11}\,b^4\,c^4\,d^8-12672\,a^{10}\,b^5\,c^5\,d^7+14784\,a^9\,b^6\,c^6\,d^6-12672\,a^8\,b^7\,c^7\,d^5+7920\,a^7\,b^8\,c^8\,d^4-3520\,a^6\,b^9\,c^9\,d^3+1056\,a^5\,b^{10}\,c^{10}\,d^2-192\,a^4\,b^{11}\,c^{11}\,d+16\,a^3\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(5376\,a^{16}\,b^4\,c^7\,d^{19}-76032\,a^{15}\,b^5\,c^8\,d^{18}+501248\,a^{14}\,b^6\,c^9\,d^{17}-2033152\,a^{13}\,b^7\,c^{10}\,d^{16}+5637888\,a^{12}\,b^8\,c^{11}\,d^{15}-11221760\,a^{11}\,b^9\,c^{12}\,d^{14}+16344064\,a^{10}\,b^{10}\,c^{13}\,d^{13}-17335296\,a^9\,b^{11}\,c^{14}\,d^{12}+12866304\,a^8\,b^{12}\,c^{15}\,d^{11}-5803776\,a^7\,b^{13}\,c^{16}\,d^{10}+456192\,a^6\,b^{14}\,c^{17}\,d^9+1427968\,a^5\,b^{15}\,c^{18}\,d^8-1117952\,a^4\,b^{16}\,c^{19}\,d^7+430848\,a^3\,b^{17}\,c^{20}\,d^6-90112\,a^2\,b^{18}\,c^{21}\,d^5+8192\,a\,b^{19}\,c^{22}\,d^4\right)}{a^8\,c^8\,d^8-8\,a^7\,b\,c^9\,d^7+28\,a^6\,b^2\,c^{10}\,d^6-56\,a^5\,b^3\,c^{11}\,d^5+70\,a^4\,b^4\,c^{12}\,d^4-56\,a^3\,b^5\,c^{13}\,d^3+28\,a^2\,b^6\,c^{14}\,d^2-8\,a\,b^7\,c^{15}\,d+b^8\,c^{16}}\right)\,{\left(-\frac{b^{11}}{16\,a^{15}\,d^{12}-192\,a^{14}\,b\,c\,d^{11}+1056\,a^{13}\,b^2\,c^2\,d^{10}-3520\,a^{12}\,b^3\,c^3\,d^9+7920\,a^{11}\,b^4\,c^4\,d^8-12672\,a^{10}\,b^5\,c^5\,d^7+14784\,a^9\,b^6\,c^6\,d^6-12672\,a^8\,b^7\,c^7\,d^5+7920\,a^7\,b^8\,c^8\,d^4-3520\,a^6\,b^9\,c^9\,d^3+1056\,a^5\,b^{10}\,c^{10}\,d^2-192\,a^4\,b^{11}\,c^{11}\,d+16\,a^3\,b^{12}\,c^{12}}\right)}^{3/4}\right)\,{\left(-\frac{b^{11}}{16\,a^{15}\,d^{12}-192\,a^{14}\,b\,c\,d^{11}+1056\,a^{13}\,b^2\,c^2\,d^{10}-3520\,a^{12}\,b^3\,c^3\,d^9+7920\,a^{11}\,b^4\,c^4\,d^8-12672\,a^{10}\,b^5\,c^5\,d^7+14784\,a^9\,b^6\,c^6\,d^6-12672\,a^8\,b^7\,c^7\,d^5+7920\,a^7\,b^8\,c^8\,d^4-3520\,a^6\,b^9\,c^9\,d^3+1056\,a^5\,b^{10}\,c^{10}\,d^2-192\,a^4\,b^{11}\,c^{11}\,d+16\,a^3\,b^{12}\,c^{12}}\right)}^{1/4}-\frac{\sqrt{x}\,\left(194481\,a^8\,b^{11}\,d^{15}-2444904\,a^7\,b^{12}\,c\,d^{14}+14378364\,a^6\,b^{13}\,c^2\,d^{13}-51043608\,a^5\,b^{14}\,c^3\,d^{12}+119638278\,a^4\,b^{15}\,c^4\,d^{11}-189998424\,a^3\,b^{16}\,c^5\,d^{10}+201081276\,a^2\,b^{17}\,c^6\,d^9-130932648\,a\,b^{18}\,c^7\,d^8+41224337\,b^{19}\,c^8\,d^7\right)}{4096\,\left(a^{12}\,c^8\,d^{12}-12\,a^{11}\,b\,c^9\,d^{11}+66\,a^{10}\,b^2\,c^{10}\,d^{10}-220\,a^9\,b^3\,c^{11}\,d^9+495\,a^8\,b^4\,c^{12}\,d^8-792\,a^7\,b^5\,c^{13}\,d^7+924\,a^6\,b^6\,c^{14}\,d^6-792\,a^5\,b^7\,c^{15}\,d^5+495\,a^4\,b^8\,c^{16}\,d^4-220\,a^3\,b^9\,c^{17}\,d^3+66\,a^2\,b^{10}\,c^{18}\,d^2-12\,a\,b^{11}\,c^{19}\,d+b^{12}\,c^{20}\right)}\right)}\right)\,{\left(-\frac{b^{11}}{16\,a^{15}\,d^{12}-192\,a^{14}\,b\,c\,d^{11}+1056\,a^{13}\,b^2\,c^2\,d^{10}-3520\,a^{12}\,b^3\,c^3\,d^9+7920\,a^{11}\,b^4\,c^4\,d^8-12672\,a^{10}\,b^5\,c^5\,d^7+14784\,a^9\,b^6\,c^6\,d^6-12672\,a^8\,b^7\,c^7\,d^5+7920\,a^7\,b^8\,c^8\,d^4-3520\,a^6\,b^9\,c^9\,d^3+1056\,a^5\,b^{10}\,c^{10}\,d^2-192\,a^4\,b^{11}\,c^{11}\,d+16\,a^3\,b^{12}\,c^{12}}\right)}^{1/4}\,2{}\mathrm{i}+2\,\mathrm{atan}\left(\frac{{\left(-\frac{b^{11}}{16\,a^{15}\,d^{12}-192\,a^{14}\,b\,c\,d^{11}+1056\,a^{13}\,b^2\,c^2\,d^{10}-3520\,a^{12}\,b^3\,c^3\,d^9+7920\,a^{11}\,b^4\,c^4\,d^8-12672\,a^{10}\,b^5\,c^5\,d^7+14784\,a^9\,b^6\,c^6\,d^6-12672\,a^8\,b^7\,c^7\,d^5+7920\,a^7\,b^8\,c^8\,d^4-3520\,a^6\,b^9\,c^9\,d^3+1056\,a^5\,b^{10}\,c^{10}\,d^2-192\,a^4\,b^{11}\,c^{11}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ght)\,1{}\mathrm{i}}{a^8\,c^8\,d^8-8\,a^7\,b\,c^9\,d^7+28\,a^6\,b^2\,c^{10}\,d^6-56\,a^5\,b^3\,c^{11}\,d^5+70\,a^4\,b^4\,c^{12}\,d^4-56\,a^3\,b^5\,c^{13}\,d^3+28\,a^2\,b^6\,c^{14}\,d^2-8\,a\,b^7\,c^{15}\,d+b^8\,c^{16}}+\left(-\frac{{\left(-\frac{b^{11}}{16\,a^{15}\,d^{12}-192\,a^{14}\,b\,c\,d^{11}+1056\,a^{13}\,b^2\,c^2\,d^{10}-3520\,a^{12}\,b^3\,c^3\,d^9+7920\,a^{11}\,b^4\,c^4\,d^8-12672\,a^{10}\,b^5\,c^5\,d^7+14784\,a^9\,b^6\,c^6\,d^6-12672\,a^8\,b^7\,c^7\,d^5+7920\,a^7\,b^8\,c^8\,d^4-3520\,a^6\,b^9\,c^9\,d^3+1056\,a^5\,b^{10}\,c^{10}\,d^2-192\,a^4\,b^{11}\,c^{11}\,d+16\,a^3\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(5376\,a^{16}\,b^4\,c^7\,d^{19}-76032\,a^{15}\,b^5\,c^8\,d^{18}+501248\,a^{14}\,b^6\,c^9\,d^{17}-2033152\,a^{13}\,b^7\,c^{10}\,d^{16}+5637888\,a^{12}\,b^8\,c^{11}\,d^{15}-11221760\,a^{11}\,b^9\,c^{12}\,d^{14}+16344064\,a^{10}\,b^{10}\,c^{13}\,d^{13}-17335296\,a^9\,b^{11}\,c^{14}\,d^{12}+12866304\,a^8\,b^{12}\,c^{15}\,d^{11}-5803776\,a^7\,b^{13}\,c^{16}\,d^{10}+456192\,a^6\,b^{14}\,c^{17}\,d^9+1427968\,a^5\,b^{15}\,c^{18}\,d^8-1117952\,a^4\,b^{16}\,c^{19}\,d^7+430848\,a^3\,b^{17}\,c^{20}\,d^6-90112\,a^2\,b^{18}\,c^{21}\,d^5+8192\,a\,b^{19}\,c^{22}\,d^4\right)}{a^8\,c^8\,d^8-8\,a^7\,b\,c^9\,d^7+28\,a^6\,b^2\,c^{10}\,d^6-56\,a^5\,b^3\,c^{11}\,d^5+70\,a^4\,b^4\,c^{12}\,d^4-56\,a^3\,b^5\,c^{13}\,d^3+28\,a^2\,b^6\,c^{14}\,d^2-8\,a\,b^7\,c^{15}\,d+b^8\,c^{16}}+\frac{\sqrt{x}\,\left(7225344\,a^{19}\,b^4\,c^4\,d^{23}-132120576\,a^{18}\,b^5\,c^5\,d^{22}+1146224640\,a^{17}\,b^6\,c^6\,d^{21}-6245842944\,a^{16}\,b^7\,c^7\,d^{20}+23871029248\,a^{15}\,b^8\,c^8\,d^{19}-67718086656\,a^{14}\,b^9\,c^9\,d^{18}+147248775168\,a^{13}\,b^{10}\,c^{10}\,d^{17}-249961119744\,a^{12}\,b^{11}\,c^{11}\,d^{16}+334222688256\,a^{11}\,b^{12}\,c^{12}\,d^{15}-352258621440\,a^{10}\,b^{13}\,c^{13}\,d^{14}+289980416000\,a^9\,b^{14}\,c^{14}\,d^{13}-181503787008\,a^8\,b^{15}\,c^{15}\,d^{12}+80192667648\,a^7\,b^{16}\,c^{16}\,d^{11}-18397265920\,a^6\,b^{17}\,c^{17}\,d^{10}-4753588224\,a^5\,b^{18}\,c^{18}\,d^9+6972506112\,a^4\,b^{19}\,c^{19}\,d^8-3593846784\,a^3\,b^{20}\,c^{20}\,d^7+1107296256\,a^2\,b^{21}\,c^{21}\,d^6-201326592\,a\,b^{22}\,c^{22}\,d^5+16777216\,b^{23}\,c^{23}\,d^4\right)\,1{}\mathrm{i}}{4096\,\left(a^{12}\,c^8\,d^{12}-12\,a^{11}\,b\,c^9\,d^{11}+66\,a^{10}\,b^2\,c^{10}\,d^{10}-220\,a^9\,b^3\,c^{11}\,d^9+495\,a^8\,b^4\,c^{12}\,d^8-792\,a^7\,b^5\,c^{13}\,d^7+924\,a^6\,b^6\,c^{14}\,d^6-792\,a^5\,b^7\,c^{15}\,d^5+495\,a^4\,b^8\,c^{16}\,d^4-220\,a^3\,b^9\,c^{17}\,d^3+66\,a^2\,b^{10}\,c^{18}\,d^2-12\,a\,b^{11}\,c^{19}\,d+b^{12}\,c^{20}\right)}\right)\,{\left(-\frac{b^{11}}{16\,a^{15}\,d^{12}-192\,a^{14}\,b\,c\,d^{11}+1056\,a^{13}\,b^2\,c^2\,d^{10}-3520\,a^{12}\,b^3\,c^3\,d^9+7920\,a^{11}\,b^4\,c^4\,d^8-12672\,a^{10}\,b^5\,c^5\,d^7+14784\,a^9\,b^6\,c^6\,d^6-12672\,a^8\,b^7\,c^7\,d^5+7920\,a^7\,b^8\,c^8\,d^4-3520\,a^6\,b^9\,c^9\,d^3+1056\,a^5\,b^{10}\,c^{10}\,d^2-192\,a^4\,b^{11}\,c^{11}\,d+16\,a^3\,b^{12}\,c^{12}}\right)}^{3/4}\,1{}\mathrm{i}\right)\,{\left(-\frac{b^{11}}{16\,a^{15}\,d^{12}-192\,a^{14}\,b\,c\,d^{11}+1056\,a^{13}\,b^2\,c^2\,d^{10}-3520\,a^{12}\,b^3\,c^3\,d^9+7920\,a^{11}\,b^4\,c^4\,d^8-12672\,a^{10}\,b^5\,c^5\,d^7+14784\,a^9\,b^6\,c^6\,d^6-12672\,a^8\,b^7\,c^7\,d^5+7920\,a^7\,b^8\,c^8\,d^4-3520\,a^6\,b^9\,c^9\,d^3+1056\,a^5\,b^{10}\,c^{10}\,d^2-192\,a^4\,b^{11}\,c^{11}\,d+16\,a^3\,b^{12}\,c^{12}}\right)}^{1/4}\,1{}\mathrm{i}-\frac{\sqrt{x}\,\left(194481\,a^8\,b^{11}\,d^{15}-2444904\,a^7\,b^{12}\,c\,d^{14}+14378364\,a^6\,b^{13}\,c^2\,d^{13}-51043608\,a^5\,b^{14}\,c^3\,d^{12}+119638278\,a^4\,b^{15}\,c^4\,d^{11}-189998424\,a^3\,b^{16}\,c^5\,d^{10}+201081276\,a^2\,b^{17}\,c^6\,d^9-130932648\,a\,b^{18}\,c^7\,d^8+41224337\,b^{19}\,c^8\,d^7\right)\,1{}\mathrm{i}}{4096\,\left(a^{12}\,c^8\,d^{12}-12\,a^{11}\,b\,c^9\,d^{11}+66\,a^{10}\,b^2\,c^{10}\,d^{10}-220\,a^9\,b^3\,c^{11}\,d^9+495\,a^8\,b^4\,c^{12}\,d^8-792\,a^7\,b^5\,c^{13}\,d^7+924\,a^6\,b^6\,c^{14}\,d^6-792\,a^5\,b^7\,c^{15}\,d^5+495\,a^4\,b^8\,c^{16}\,d^4-220\,a^3\,b^9\,c^{17}\,d^3+66\,a^2\,b^{10}\,c^{18}\,d^2-12\,a\,b^{11}\,c^{19}\,d+b^{12}\,c^{20}\right)}\right)}\right)\,{\left(-\frac{b^{11}}{16\,a^{15}\,d^{12}-192\,a^{14}\,b\,c\,d^{11}+1056\,a^{13}\,b^2\,c^2\,d^{10}-3520\,a^{12}\,b^3\,c^3\,d^9+7920\,a^{11}\,b^4\,c^4\,d^8-12672\,a^{10}\,b^5\,c^5\,d^7+14784\,a^9\,b^6\,c^6\,d^6-12672\,a^8\,b^7\,c^7\,d^5+7920\,a^7\,b^8\,c^8\,d^4-3520\,a^6\,b^9\,c^9\,d^3+1056\,a^5\,b^{10}\,c^{10}\,d^2-192\,a^4\,b^{11}\,c^{11}\,d+16\,a^3\,b^{12}\,c^{12}}\right)}^{1/4}+\frac{\frac{\sqrt{x}\,\left(11\,a\,d^2-19\,b\,c\,d\right)}{16\,\left(a^2\,c\,d^2-2\,a\,b\,c^2\,d+b^2\,c^3\right)}+\frac{d^2\,x^{5/2}\,\left(7\,a\,d-15\,b\,c\right)}{16\,c\,\left(a^2\,c\,d^2-2\,a\,b\,c^2\,d+b^2\,c^3\right)}}{c^2+2\,c\,d\,x^2+d^2\,x^4}+\mathrm{atan}\left(\frac{\left(\left(\frac{\frac{194481\,a^8\,b^8\,d^{14}}{2048}-\frac{2250423\,a^7\,b^9\,c\,d^{13}}{2048}+\frac{12127941\,a^6\,b^{10}\,c^2\,d^{12}}{2048}-\frac{38915667\,a^5\,b^{11}\,c^3\,d^{11}}{2048}+\frac{80271027\,a^4\,b^{12}\,c^4\,d^{10}}{2048}-\frac{10688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107296256\,a^2\,b^{10}\,c^{21}\,d^2-201326592\,a\,b^{11}\,c^{22}\,d+16777216\,b^{12}\,c^{23}}\right)}^{1/4}\,\left(5376\,a^{16}\,b^4\,c^7\,d^{19}-76032\,a^{15}\,b^5\,c^8\,d^{18}+501248\,a^{14}\,b^6\,c^9\,d^{17}-2033152\,a^{13}\,b^7\,c^{10}\,d^{16}+5637888\,a^{12}\,b^8\,c^{11}\,d^{15}-11221760\,a^{11}\,b^9\,c^{12}\,d^{14}+16344064\,a^{10}\,b^{10}\,c^{13}\,d^{13}-17335296\,a^9\,b^{11}\,c^{14}\,d^{12}+12866304\,a^8\,b^{12}\,c^{15}\,d^{11}-5803776\,a^7\,b^{13}\,c^{16}\,d^{10}+456192\,a^6\,b^{14}\,c^{17}\,d^9+1427968\,a^5\,b^{15}\,c^{18}\,d^8-1117952\,a^4\,b^{16}\,c^{19}\,d^7+430848\,a^3\,b^{17}\,c^{20}\,d^6-90112\,a^2\,b^{18}\,c^{21}\,d^5+8192\,a\,b^{19}\,c^{22}\,d^4\right)}{a^8\,c^8\,d^8-8\,a^7\,b\,c^9\,d^7+28\,a^6\,b^2\,c^{10}\,d^6-56\,a^5\,b^3\,c^{11}\,d^5+70\,a^4\,b^4\,c^{12}\,d^4-56\,a^3\,b^5\,c^{13}\,d^3+28\,a^2\,b^6\,c^{14}\,d^2-8\,a\,b^7\,c^{15}\,d+b^8\,c^{16}}+\frac{\sqrt{x}\,\left(7225344\,a^{19}\,b^4\,c^4\,d^{23}-132120576\,a^{18}\,b^5\,c^5\,d^{22}+1146224640\,a^{17}\,b^6\,c^6\,d^{21}-6245842944\,a^{16}\,b^7\,c^7\,d^{20}+23871029248\,a^{15}\,b^8\,c^8\,d^{19}-67718086656\,a^{14}\,b^9\,c^9\,d^{18}+147248775168\,a^{13}\,b^{10}\,c^{10}\,d^{17}-249961119744\,a^{12}\,b^{11}\,c^{11}\,d^{16}+334222688256\,a^{11}\,b^{12}\,c^{12}\,d^{15}-352258621440\,a^{10}\,b^{13}\,c^{13}\,d^{14}+289980416000\,a^9\,b^{14}\,c^{14}\,d^{13}-181503787008\,a^8\,b^{15}\,c^{15}\,d^{12}+80192667648\,a^7\,b^{16}\,c^{16}\,d^{11}-18397265920\,a^6\,b^{17}\,c^{17}\,d^{10}-4753588224\,a^5\,b^{18}\,c^{18}\,d^9+6972506112\,a^4\,b^{19}\,c^{19}\,d^8-3593846784\,a^3\,b^{20}\,c^{20}\,d^7+1107296256\,a^2\,b^{21}\,c^{21}\,d^6-201326592\,a\,b^{22}\,c^{22}\,d^5+16777216\,b^{23}\,c^{23}\,d^4\right)\,1{}\mathrm{i}}{4096\,\left(a^{12}\,c^8\,d^{12}-12\,a^{11}\,b\,c^9\,d^{11}+66\,a^{10}\,b^2\,c^{10}\,d^{10}-220\,a^9\,b^3\,c^{11}\,d^9+495\,a^8\,b^4\,c^{12}\,d^8-792\,a^7\,b^5\,c^{13}\,d^7+924\,a^6\,b^6\,c^{14}\,d^6-792\,a^5\,b^7\,c^{15}\,d^5+495\,a^4\,b^8\,c^{16}\,d^4-220\,a^3\,b^9\,c^{17}\,d^3+66\,a^2\,b^{10}\,c^{18}\,d^2-12\,a\,b^{11}\,c^{19}\,d+b^{12}\,c^{20}\right)}\right)\,{\left(-\frac{194481\,a^8\,d^{11}-2444904\,a^7\,b\,c\,d^{10}+14378364\,a^6\,b^2\,c^2\,d^9-51043608\,a^5\,b^3\,c^3\,d^8+119186694\,a^4\,b^4\,c^4\,d^7-187159896\,a^3\,b^5\,c^5\,d^6+193309116\,a^2\,b^6\,c^6\,d^5-120524712\,a\,b^7\,c^7\,d^4+35153041\,b^8\,c^8\,d^3}{16777216\,a^{12}\,c^{11}\,d^{12}-201326592\,a^{11}\,b\,c^{12}\,d^{11}+1107296256\,a^{10}\,b^2\,c^{13}\,d^{10}-3690987520\,a^9\,b^3\,c^{14}\,d^9+8304721920\,a^8\,b^4\,c^{15}\,d^8-13287555072\,a^7\,b^5\,c^{16}\,d^7+15502147584\,a^6\,b^6\,c^{17}\,d^6-13287555072\,a^5\,b^7\,c^{18}\,d^5+8304721920\,a^4\,b^8\,c^{19}\,d^4-3690987520\,a^3\,b^9\,c^{20}\,d^3+1107296256\,a^2\,b^{10}\,c^{21}\,d^2-201326592\,a\,b^{11}\,c^{22}\,d+16777216\,b^{12}\,c^{23}}\right)}^{3/4}\,1{}\mathrm{i}\right)\,{\left(-\frac{194481\,a^8\,d^{11}-2444904\,a^7\,b\,c\,d^{10}+14378364\,a^6\,b^2\,c^2\,d^9-51043608\,a^5\,b^3\,c^3\,d^8+119186694\,a^4\,b^4\,c^4\,d^7-187159896\,a^3\,b^5\,c^5\,d^6+193309116\,a^2\,b^6\,c^6\,d^5-120524712\,a\,b^7\,c^7\,d^4+35153041\,b^8\,c^8\,d^3}{16777216\,a^{12}\,c^{11}\,d^{12}-201326592\,a^{11}\,b\,c^{12}\,d^{11}+1107296256\,a^{10}\,b^2\,c^{13}\,d^{10}-3690987520\,a^9\,b^3\,c^{14}\,d^9+8304721920\,a^8\,b^4\,c^{15}\,d^8-13287555072\,a^7\,b^5\,c^{16}\,d^7+15502147584\,a^6\,b^6\,c^{17}\,d^6-13287555072\,a^5\,b^7\,c^{18}\,d^5+8304721920\,a^4\,b^8\,c^{19}\,d^4-3690987520\,a^3\,b^9\,c^{20}\,d^3+1107296256\,a^2\,b^{10}\,c^{21}\,d^2-201326592\,a\,b^{11}\,c^{22}\,d+16777216\,b^{12}\,c^{23}}\right)}^{1/4}\,1{}\mathrm{i}-\frac{\sqrt{x}\,\left(194481\,a^8\,b^{11}\,d^{15}-2444904\,a^7\,b^{12}\,c\,d^{14}+14378364\,a^6\,b^{13}\,c^2\,d^{13}-51043608\,a^5\,b^{14}\,c^3\,d^{12}+119638278\,a^4\,b^{15}\,c^4\,d^{11}-189998424\,a^3\,b^{16}\,c^5\,d^{10}+201081276\,a^2\,b^{17}\,c^6\,d^9-130932648\,a\,b^{18}\,c^7\,d^8+41224337\,b^{19}\,c^8\,d^7\right)\,1{}\mathrm{i}}{4096\,\left(a^{12}\,c^8\,d^{12}-12\,a^{11}\,b\,c^9\,d^{11}+66\,a^{10}\,b^2\,c^{10}\,d^{10}-220\,a^9\,b^3\,c^{11}\,d^9+495\,a^8\,b^4\,c^{12}\,d^8-792\,a^7\,b^5\,c^{13}\,d^7+924\,a^6\,b^6\,c^{14}\,d^6-792\,a^5\,b^7\,c^{15}\,d^5+495\,a^4\,b^8\,c^{16}\,d^4-220\,a^3\,b^9\,c^{17}\,d^3+66\,a^2\,b^{10}\,c^{18}\,d^2-12\,a\,b^{11}\,c^{19}\,d+b^{12}\,c^{20}\right)}\right)\,{\left(-\frac{194481\,a^8\,d^{11}-2444904\,a^7\,b\,c\,d^{10}+14378364\,a^6\,b^2\,c^2\,d^9-51043608\,a^5\,b^3\,c^3\,d^8+119186694\,a^4\,b^4\,c^4\,d^7-187159896\,a^3\,b^5\,c^5\,d^6+193309116\,a^2\,b^6\,c^6\,d^5-120524712\,a\,b^7\,c^7\,d^4+35153041\,b^8\,c^8\,d^3}{16777216\,a^{12}\,c^{11}\,d^{12}-201326592\,a^{11}\,b\,c^{12}\,d^{11}+1107296256\,a^{10}\,b^2\,c^{13}\,d^{10}-3690987520\,a^9\,b^3\,c^{14}\,d^9+8304721920\,a^8\,b^4\,c^{15}\,d^8-13287555072\,a^7\,b^5\,c^{16}\,d^7+15502147584\,a^6\,b^6\,c^{17}\,d^6-13287555072\,a^5\,b^7\,c^{18}\,d^5+8304721920\,a^4\,b^8\,c^{19}\,d^4-3690987520\,a^3\,b^9\,c^{20}\,d^3+1107296256\,a^2\,b^{10}\,c^{21}\,d^2-201326592\,a\,b^{11}\,c^{22}\,d+16777216\,b^{12}\,c^{23}}\right)}^{1/4}}\right)\,{\left(-\frac{194481\,a^8\,d^{11}-2444904\,a^7\,b\,c\,d^{10}+14378364\,a^6\,b^2\,c^2\,d^9-51043608\,a^5\,b^3\,c^3\,d^8+119186694\,a^4\,b^4\,c^4\,d^7-187159896\,a^3\,b^5\,c^5\,d^6+193309116\,a^2\,b^6\,c^6\,d^5-120524712\,a\,b^7\,c^7\,d^4+35153041\,b^8\,c^8\,d^3}{16777216\,a^{12}\,c^{11}\,d^{12}-201326592\,a^{11}\,b\,c^{12}\,d^{11}+1107296256\,a^{10}\,b^2\,c^{13}\,d^{10}-3690987520\,a^9\,b^3\,c^{14}\,d^9+8304721920\,a^8\,b^4\,c^{15}\,d^8-13287555072\,a^7\,b^5\,c^{16}\,d^7+15502147584\,a^6\,b^6\,c^{17}\,d^6-13287555072\,a^5\,b^7\,c^{18}\,d^5+8304721920\,a^4\,b^8\,c^{19}\,d^4-3690987520\,a^3\,b^9\,c^{20}\,d^3+1107296256\,a^2\,b^{10}\,c^{21}\,d^2-201326592\,a\,b^{11}\,c^{22}\,d+16777216\,b^{12}\,c^{23}}\right)}^{1/4}","Not used",1,"atan(((-b^11/(16*a^15*d^12 + 16*a^3*b^12*c^12 - 192*a^4*b^11*c^11*d + 1056*a^5*b^10*c^10*d^2 - 3520*a^6*b^9*c^9*d^3 + 7920*a^7*b^8*c^8*d^4 - 12672*a^8*b^7*c^7*d^5 + 14784*a^9*b^6*c^6*d^6 - 12672*a^10*b^5*c^5*d^7 + 7920*a^11*b^4*c^4*d^8 - 3520*a^12*b^3*c^3*d^9 + 1056*a^13*b^2*c^2*d^10 - 192*a^14*b*c*d^11))^(1/4)*((((194481*a^8*b^8*d^14)/2048 + 1232*b^16*c^8*d^6 - (34792593*a*b^15*c^7*d^7)/2048 - (2250423*a^7*b^9*c*d^13)/2048 + (86420247*a^2*b^14*c^6*d^8)/2048 - (106888869*a^3*b^13*c^5*d^9)/2048 + (80271027*a^4*b^12*c^4*d^10)/2048 - (38915667*a^5*b^11*c^3*d^11)/2048 + (12127941*a^6*b^10*c^2*d^12)/2048)/(b^8*c^16 + a^8*c^8*d^8 - 8*a^7*b*c^9*d^7 + 28*a^2*b^6*c^14*d^2 - 56*a^3*b^5*c^13*d^3 + 70*a^4*b^4*c^12*d^4 - 56*a^5*b^3*c^11*d^5 + 28*a^6*b^2*c^10*d^6 - 8*a*b^7*c^15*d) + ((x^(1/2)*(16777216*b^23*c^23*d^4 - 201326592*a*b^22*c^22*d^5 + 1107296256*a^2*b^21*c^21*d^6 - 3593846784*a^3*b^20*c^20*d^7 + 6972506112*a^4*b^19*c^19*d^8 - 4753588224*a^5*b^18*c^18*d^9 - 18397265920*a^6*b^17*c^17*d^10 + 80192667648*a^7*b^16*c^16*d^11 - 181503787008*a^8*b^15*c^15*d^12 + 289980416000*a^9*b^14*c^14*d^13 - 352258621440*a^10*b^13*c^13*d^14 + 334222688256*a^11*b^12*c^12*d^15 - 249961119744*a^12*b^11*c^11*d^16 + 147248775168*a^13*b^10*c^10*d^17 - 67718086656*a^14*b^9*c^9*d^18 + 23871029248*a^15*b^8*c^8*d^19 - 6245842944*a^16*b^7*c^7*d^20 + 1146224640*a^17*b^6*c^6*d^21 - 132120576*a^18*b^5*c^5*d^22 + 7225344*a^19*b^4*c^4*d^23))/(4096*(b^12*c^20 + a^12*c^8*d^12 - 12*a^11*b*c^9*d^11 + 66*a^2*b^10*c^18*d^2 - 220*a^3*b^9*c^17*d^3 + 495*a^4*b^8*c^16*d^4 - 792*a^5*b^7*c^15*d^5 + 924*a^6*b^6*c^14*d^6 - 792*a^7*b^5*c^13*d^7 + 495*a^8*b^4*c^12*d^8 - 220*a^9*b^3*c^11*d^9 + 66*a^10*b^2*c^10*d^10 - 12*a*b^11*c^19*d)) - ((-b^11/(16*a^15*d^12 + 16*a^3*b^12*c^12 - 192*a^4*b^11*c^11*d + 1056*a^5*b^10*c^10*d^2 - 3520*a^6*b^9*c^9*d^3 + 7920*a^7*b^8*c^8*d^4 - 12672*a^8*b^7*c^7*d^5 + 14784*a^9*b^6*c^6*d^6 - 12672*a^10*b^5*c^5*d^7 + 7920*a^11*b^4*c^4*d^8 - 3520*a^12*b^3*c^3*d^9 + 1056*a^13*b^2*c^2*d^10 - 192*a^14*b*c*d^11))^(1/4)*(8192*a*b^19*c^22*d^4 - 90112*a^2*b^18*c^21*d^5 + 430848*a^3*b^17*c^20*d^6 - 1117952*a^4*b^16*c^19*d^7 + 1427968*a^5*b^15*c^18*d^8 + 456192*a^6*b^14*c^17*d^9 - 5803776*a^7*b^13*c^16*d^10 + 12866304*a^8*b^12*c^15*d^11 - 17335296*a^9*b^11*c^14*d^12 + 16344064*a^10*b^10*c^13*d^13 - 11221760*a^11*b^9*c^12*d^14 + 5637888*a^12*b^8*c^11*d^15 - 2033152*a^13*b^7*c^10*d^16 + 501248*a^14*b^6*c^9*d^17 - 76032*a^15*b^5*c^8*d^18 + 5376*a^16*b^4*c^7*d^19))/(b^8*c^16 + a^8*c^8*d^8 - 8*a^7*b*c^9*d^7 + 28*a^2*b^6*c^14*d^2 - 56*a^3*b^5*c^13*d^3 + 70*a^4*b^4*c^12*d^4 - 56*a^5*b^3*c^11*d^5 + 28*a^6*b^2*c^10*d^6 - 8*a*b^7*c^15*d))*(-b^11/(16*a^15*d^12 + 16*a^3*b^12*c^12 - 192*a^4*b^11*c^11*d + 1056*a^5*b^10*c^10*d^2 - 3520*a^6*b^9*c^9*d^3 + 7920*a^7*b^8*c^8*d^4 - 12672*a^8*b^7*c^7*d^5 + 14784*a^9*b^6*c^6*d^6 - 12672*a^10*b^5*c^5*d^7 + 7920*a^11*b^4*c^4*d^8 - 3520*a^12*b^3*c^3*d^9 + 1056*a^13*b^2*c^2*d^10 - 192*a^14*b*c*d^11))^(3/4))*(-b^11/(16*a^15*d^12 + 16*a^3*b^12*c^12 - 192*a^4*b^11*c^11*d + 1056*a^5*b^10*c^10*d^2 - 3520*a^6*b^9*c^9*d^3 + 7920*a^7*b^8*c^8*d^4 - 12672*a^8*b^7*c^7*d^5 + 14784*a^9*b^6*c^6*d^6 - 12672*a^10*b^5*c^5*d^7 + 7920*a^11*b^4*c^4*d^8 - 3520*a^12*b^3*c^3*d^9 + 1056*a^13*b^2*c^2*d^10 - 192*a^14*b*c*d^11))^(1/4)*1i + (x^(1/2)*(194481*a^8*b^11*d^15 + 41224337*b^19*c^8*d^7 - 130932648*a*b^18*c^7*d^8 - 2444904*a^7*b^12*c*d^14 + 201081276*a^2*b^17*c^6*d^9 - 189998424*a^3*b^16*c^5*d^10 + 119638278*a^4*b^15*c^4*d^11 - 51043608*a^5*b^14*c^3*d^12 + 14378364*a^6*b^13*c^2*d^13)*1i)/(4096*(b^12*c^20 + a^12*c^8*d^12 - 12*a^11*b*c^9*d^11 + 66*a^2*b^10*c^18*d^2 - 220*a^3*b^9*c^17*d^3 + 495*a^4*b^8*c^16*d^4 - 792*a^5*b^7*c^15*d^5 + 924*a^6*b^6*c^14*d^6 - 792*a^7*b^5*c^13*d^7 + 495*a^8*b^4*c^12*d^8 - 220*a^9*b^3*c^11*d^9 + 66*a^10*b^2*c^10*d^10 - 12*a*b^11*c^19*d))) - (-b^11/(16*a^15*d^12 + 16*a^3*b^12*c^12 - 192*a^4*b^11*c^11*d + 1056*a^5*b^10*c^10*d^2 - 3520*a^6*b^9*c^9*d^3 + 7920*a^7*b^8*c^8*d^4 - 12672*a^8*b^7*c^7*d^5 + 14784*a^9*b^6*c^6*d^6 - 12672*a^10*b^5*c^5*d^7 + 7920*a^11*b^4*c^4*d^8 - 3520*a^12*b^3*c^3*d^9 + 1056*a^13*b^2*c^2*d^10 - 192*a^14*b*c*d^11))^(1/4)*((((194481*a^8*b^8*d^14)/2048 + 1232*b^16*c^8*d^6 - (34792593*a*b^15*c^7*d^7)/2048 - (2250423*a^7*b^9*c*d^13)/2048 + (86420247*a^2*b^14*c^6*d^8)/2048 - (106888869*a^3*b^13*c^5*d^9)/2048 + (80271027*a^4*b^12*c^4*d^10)/2048 - (38915667*a^5*b^11*c^3*d^11)/2048 + (12127941*a^6*b^10*c^2*d^12)/2048)/(b^8*c^16 + a^8*c^8*d^8 - 8*a^7*b*c^9*d^7 + 28*a^2*b^6*c^14*d^2 - 56*a^3*b^5*c^13*d^3 + 70*a^4*b^4*c^12*d^4 - 56*a^5*b^3*c^11*d^5 + 28*a^6*b^2*c^10*d^6 - 8*a*b^7*c^15*d) - ((x^(1/2)*(16777216*b^23*c^23*d^4 - 201326592*a*b^22*c^22*d^5 + 1107296256*a^2*b^21*c^21*d^6 - 3593846784*a^3*b^20*c^20*d^7 + 6972506112*a^4*b^19*c^19*d^8 - 4753588224*a^5*b^18*c^18*d^9 - 18397265920*a^6*b^17*c^17*d^10 + 80192667648*a^7*b^16*c^16*d^11 - 181503787008*a^8*b^15*c^15*d^12 + 289980416000*a^9*b^14*c^14*d^13 - 352258621440*a^10*b^13*c^13*d^14 + 334222688256*a^11*b^12*c^12*d^15 - 249961119744*a^12*b^11*c^11*d^16 + 147248775168*a^13*b^10*c^10*d^17 - 67718086656*a^14*b^9*c^9*d^18 + 23871029248*a^15*b^8*c^8*d^19 - 6245842944*a^16*b^7*c^7*d^20 + 1146224640*a^17*b^6*c^6*d^21 - 132120576*a^18*b^5*c^5*d^22 + 7225344*a^19*b^4*c^4*d^23))/(4096*(b^12*c^20 + a^12*c^8*d^12 - 12*a^11*b*c^9*d^11 + 66*a^2*b^10*c^18*d^2 - 220*a^3*b^9*c^17*d^3 + 495*a^4*b^8*c^16*d^4 - 792*a^5*b^7*c^15*d^5 + 924*a^6*b^6*c^14*d^6 - 792*a^7*b^5*c^13*d^7 + 495*a^8*b^4*c^12*d^8 - 220*a^9*b^3*c^11*d^9 + 66*a^10*b^2*c^10*d^10 - 12*a*b^11*c^19*d)) + ((-b^11/(16*a^15*d^12 + 16*a^3*b^12*c^12 - 192*a^4*b^11*c^11*d + 1056*a^5*b^10*c^10*d^2 - 3520*a^6*b^9*c^9*d^3 + 7920*a^7*b^8*c^8*d^4 - 12672*a^8*b^7*c^7*d^5 + 14784*a^9*b^6*c^6*d^6 - 12672*a^10*b^5*c^5*d^7 + 7920*a^11*b^4*c^4*d^8 - 3520*a^12*b^3*c^3*d^9 + 1056*a^13*b^2*c^2*d^10 - 192*a^14*b*c*d^11))^(1/4)*(8192*a*b^19*c^22*d^4 - 90112*a^2*b^18*c^21*d^5 + 430848*a^3*b^17*c^20*d^6 - 1117952*a^4*b^16*c^19*d^7 + 1427968*a^5*b^15*c^18*d^8 + 456192*a^6*b^14*c^17*d^9 - 5803776*a^7*b^13*c^16*d^10 + 12866304*a^8*b^12*c^15*d^11 - 17335296*a^9*b^11*c^14*d^12 + 16344064*a^10*b^10*c^13*d^13 - 11221760*a^11*b^9*c^12*d^14 + 5637888*a^12*b^8*c^11*d^15 - 2033152*a^13*b^7*c^10*d^16 + 501248*a^14*b^6*c^9*d^17 - 76032*a^15*b^5*c^8*d^18 + 5376*a^16*b^4*c^7*d^19))/(b^8*c^16 + a^8*c^8*d^8 - 8*a^7*b*c^9*d^7 + 28*a^2*b^6*c^14*d^2 - 56*a^3*b^5*c^13*d^3 + 70*a^4*b^4*c^12*d^4 - 56*a^5*b^3*c^11*d^5 + 28*a^6*b^2*c^10*d^6 - 8*a*b^7*c^15*d))*(-b^11/(16*a^15*d^12 + 16*a^3*b^12*c^12 - 192*a^4*b^11*c^11*d + 1056*a^5*b^10*c^10*d^2 - 3520*a^6*b^9*c^9*d^3 + 7920*a^7*b^8*c^8*d^4 - 12672*a^8*b^7*c^7*d^5 + 14784*a^9*b^6*c^6*d^6 - 12672*a^10*b^5*c^5*d^7 + 7920*a^11*b^4*c^4*d^8 - 3520*a^12*b^3*c^3*d^9 + 1056*a^13*b^2*c^2*d^10 - 192*a^14*b*c*d^11))^(3/4))*(-b^11/(16*a^15*d^12 + 16*a^3*b^12*c^12 - 192*a^4*b^11*c^11*d + 1056*a^5*b^10*c^10*d^2 - 3520*a^6*b^9*c^9*d^3 + 7920*a^7*b^8*c^8*d^4 - 12672*a^8*b^7*c^7*d^5 + 14784*a^9*b^6*c^6*d^6 - 12672*a^10*b^5*c^5*d^7 + 7920*a^11*b^4*c^4*d^8 - 3520*a^12*b^3*c^3*d^9 + 1056*a^13*b^2*c^2*d^10 - 192*a^14*b*c*d^11))^(1/4)*1i - (x^(1/2)*(194481*a^8*b^11*d^15 + 41224337*b^19*c^8*d^7 - 130932648*a*b^18*c^7*d^8 - 2444904*a^7*b^12*c*d^14 + 201081276*a^2*b^17*c^6*d^9 - 189998424*a^3*b^16*c^5*d^10 + 119638278*a^4*b^15*c^4*d^11 - 51043608*a^5*b^14*c^3*d^12 + 14378364*a^6*b^13*c^2*d^13)*1i)/(4096*(b^12*c^20 + a^12*c^8*d^12 - 12*a^11*b*c^9*d^11 + 66*a^2*b^10*c^18*d^2 - 220*a^3*b^9*c^17*d^3 + 495*a^4*b^8*c^16*d^4 - 792*a^5*b^7*c^15*d^5 + 924*a^6*b^6*c^14*d^6 - 792*a^7*b^5*c^13*d^7 + 495*a^8*b^4*c^12*d^8 - 220*a^9*b^3*c^11*d^9 + 66*a^10*b^2*c^10*d^10 - 12*a*b^11*c^19*d))))/((-b^11/(16*a^15*d^12 + 16*a^3*b^12*c^12 - 192*a^4*b^11*c^11*d + 1056*a^5*b^10*c^10*d^2 - 3520*a^6*b^9*c^9*d^3 + 7920*a^7*b^8*c^8*d^4 - 12672*a^8*b^7*c^7*d^5 + 14784*a^9*b^6*c^6*d^6 - 12672*a^10*b^5*c^5*d^7 + 7920*a^11*b^4*c^4*d^8 - 3520*a^12*b^3*c^3*d^9 + 1056*a^13*b^2*c^2*d^10 - 192*a^14*b*c*d^11))^(1/4)*((((194481*a^8*b^8*d^14)/2048 + 1232*b^16*c^8*d^6 - (34792593*a*b^15*c^7*d^7)/2048 - (2250423*a^7*b^9*c*d^13)/2048 + (86420247*a^2*b^14*c^6*d^8)/2048 - (106888869*a^3*b^13*c^5*d^9)/2048 + (80271027*a^4*b^12*c^4*d^10)/2048 - (38915667*a^5*b^11*c^3*d^11)/2048 + (12127941*a^6*b^10*c^2*d^12)/2048)/(b^8*c^16 + a^8*c^8*d^8 - 8*a^7*b*c^9*d^7 + 28*a^2*b^6*c^14*d^2 - 56*a^3*b^5*c^13*d^3 + 70*a^4*b^4*c^12*d^4 - 56*a^5*b^3*c^11*d^5 + 28*a^6*b^2*c^10*d^6 - 8*a*b^7*c^15*d) + ((x^(1/2)*(16777216*b^23*c^23*d^4 - 201326592*a*b^22*c^22*d^5 + 1107296256*a^2*b^21*c^21*d^6 - 3593846784*a^3*b^20*c^20*d^7 + 6972506112*a^4*b^19*c^19*d^8 - 4753588224*a^5*b^18*c^18*d^9 - 18397265920*a^6*b^17*c^17*d^10 + 80192667648*a^7*b^16*c^16*d^11 - 181503787008*a^8*b^15*c^15*d^12 + 289980416000*a^9*b^14*c^14*d^13 - 352258621440*a^10*b^13*c^13*d^14 + 334222688256*a^11*b^12*c^12*d^15 - 249961119744*a^12*b^11*c^11*d^16 + 147248775168*a^13*b^10*c^10*d^17 - 67718086656*a^14*b^9*c^9*d^18 + 23871029248*a^15*b^8*c^8*d^19 - 6245842944*a^16*b^7*c^7*d^20 + 1146224640*a^17*b^6*c^6*d^21 - 132120576*a^18*b^5*c^5*d^22 + 7225344*a^19*b^4*c^4*d^23))/(4096*(b^12*c^20 + a^12*c^8*d^12 - 12*a^11*b*c^9*d^11 + 66*a^2*b^10*c^18*d^2 - 220*a^3*b^9*c^17*d^3 + 495*a^4*b^8*c^16*d^4 - 792*a^5*b^7*c^15*d^5 + 924*a^6*b^6*c^14*d^6 - 792*a^7*b^5*c^13*d^7 + 495*a^8*b^4*c^12*d^8 - 220*a^9*b^3*c^11*d^9 + 66*a^10*b^2*c^10*d^10 - 12*a*b^11*c^19*d)) - ((-b^11/(16*a^15*d^12 + 16*a^3*b^12*c^12 - 192*a^4*b^11*c^11*d + 1056*a^5*b^10*c^10*d^2 - 3520*a^6*b^9*c^9*d^3 + 7920*a^7*b^8*c^8*d^4 - 12672*a^8*b^7*c^7*d^5 + 14784*a^9*b^6*c^6*d^6 - 12672*a^10*b^5*c^5*d^7 + 7920*a^11*b^4*c^4*d^8 - 3520*a^12*b^3*c^3*d^9 + 1056*a^13*b^2*c^2*d^10 - 192*a^14*b*c*d^11))^(1/4)*(8192*a*b^19*c^22*d^4 - 90112*a^2*b^18*c^21*d^5 + 430848*a^3*b^17*c^20*d^6 - 1117952*a^4*b^16*c^19*d^7 + 1427968*a^5*b^15*c^18*d^8 + 456192*a^6*b^14*c^17*d^9 - 5803776*a^7*b^13*c^16*d^10 + 12866304*a^8*b^12*c^15*d^11 - 17335296*a^9*b^11*c^14*d^12 + 16344064*a^10*b^10*c^13*d^13 - 11221760*a^11*b^9*c^12*d^14 + 5637888*a^12*b^8*c^11*d^15 - 2033152*a^13*b^7*c^10*d^16 + 501248*a^14*b^6*c^9*d^17 - 76032*a^15*b^5*c^8*d^18 + 5376*a^16*b^4*c^7*d^19))/(b^8*c^16 + a^8*c^8*d^8 - 8*a^7*b*c^9*d^7 + 28*a^2*b^6*c^14*d^2 - 56*a^3*b^5*c^13*d^3 + 70*a^4*b^4*c^12*d^4 - 56*a^5*b^3*c^11*d^5 + 28*a^6*b^2*c^10*d^6 - 8*a*b^7*c^15*d))*(-b^11/(16*a^15*d^12 + 16*a^3*b^12*c^12 - 192*a^4*b^11*c^11*d + 1056*a^5*b^10*c^10*d^2 - 3520*a^6*b^9*c^9*d^3 + 7920*a^7*b^8*c^8*d^4 - 12672*a^8*b^7*c^7*d^5 + 14784*a^9*b^6*c^6*d^6 - 12672*a^10*b^5*c^5*d^7 + 7920*a^11*b^4*c^4*d^8 - 3520*a^12*b^3*c^3*d^9 + 1056*a^13*b^2*c^2*d^10 - 192*a^14*b*c*d^11))^(3/4))*(-b^11/(16*a^15*d^12 + 16*a^3*b^12*c^12 - 192*a^4*b^11*c^11*d + 1056*a^5*b^10*c^10*d^2 - 3520*a^6*b^9*c^9*d^3 + 7920*a^7*b^8*c^8*d^4 - 12672*a^8*b^7*c^7*d^5 + 14784*a^9*b^6*c^6*d^6 - 12672*a^10*b^5*c^5*d^7 + 7920*a^11*b^4*c^4*d^8 - 3520*a^12*b^3*c^3*d^9 + 1056*a^13*b^2*c^2*d^10 - 192*a^14*b*c*d^11))^(1/4) + (x^(1/2)*(194481*a^8*b^11*d^15 + 41224337*b^19*c^8*d^7 - 130932648*a*b^18*c^7*d^8 - 2444904*a^7*b^12*c*d^14 + 201081276*a^2*b^17*c^6*d^9 - 189998424*a^3*b^16*c^5*d^10 + 119638278*a^4*b^15*c^4*d^11 - 51043608*a^5*b^14*c^3*d^12 + 14378364*a^6*b^13*c^2*d^13))/(4096*(b^12*c^20 + a^12*c^8*d^12 - 12*a^11*b*c^9*d^11 + 66*a^2*b^10*c^18*d^2 - 220*a^3*b^9*c^17*d^3 + 495*a^4*b^8*c^16*d^4 - 792*a^5*b^7*c^15*d^5 + 924*a^6*b^6*c^14*d^6 - 792*a^7*b^5*c^13*d^7 + 495*a^8*b^4*c^12*d^8 - 220*a^9*b^3*c^11*d^9 + 66*a^10*b^2*c^10*d^10 - 12*a*b^11*c^19*d))) + (-b^11/(16*a^15*d^12 + 16*a^3*b^12*c^12 - 192*a^4*b^11*c^11*d + 1056*a^5*b^10*c^10*d^2 - 3520*a^6*b^9*c^9*d^3 + 7920*a^7*b^8*c^8*d^4 - 12672*a^8*b^7*c^7*d^5 + 14784*a^9*b^6*c^6*d^6 - 12672*a^10*b^5*c^5*d^7 + 7920*a^11*b^4*c^4*d^8 - 3520*a^12*b^3*c^3*d^9 + 1056*a^13*b^2*c^2*d^10 - 192*a^14*b*c*d^11))^(1/4)*((((194481*a^8*b^8*d^14)/2048 + 1232*b^16*c^8*d^6 - (34792593*a*b^15*c^7*d^7)/2048 - (2250423*a^7*b^9*c*d^13)/2048 + (86420247*a^2*b^14*c^6*d^8)/2048 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12*a^11*b*c^9*d^11 + 66*a^2*b^10*c^18*d^2 - 220*a^3*b^9*c^17*d^3 + 495*a^4*b^8*c^16*d^4 - 792*a^5*b^7*c^15*d^5 + 924*a^6*b^6*c^14*d^6 - 792*a^7*b^5*c^13*d^7 + 495*a^8*b^4*c^12*d^8 - 220*a^9*b^3*c^11*d^9 + 66*a^10*b^2*c^10*d^10 - 12*a*b^11*c^19*d)) + ((-b^11/(16*a^15*d^12 + 16*a^3*b^12*c^12 - 192*a^4*b^11*c^11*d + 1056*a^5*b^10*c^10*d^2 - 3520*a^6*b^9*c^9*d^3 + 7920*a^7*b^8*c^8*d^4 - 12672*a^8*b^7*c^7*d^5 + 14784*a^9*b^6*c^6*d^6 - 12672*a^10*b^5*c^5*d^7 + 7920*a^11*b^4*c^4*d^8 - 3520*a^12*b^3*c^3*d^9 + 1056*a^13*b^2*c^2*d^10 - 192*a^14*b*c*d^11))^(1/4)*(8192*a*b^19*c^22*d^4 - 90112*a^2*b^18*c^21*d^5 + 430848*a^3*b^17*c^20*d^6 - 1117952*a^4*b^16*c^19*d^7 + 1427968*a^5*b^15*c^18*d^8 + 456192*a^6*b^14*c^17*d^9 - 5803776*a^7*b^13*c^16*d^10 + 12866304*a^8*b^12*c^15*d^11 - 17335296*a^9*b^11*c^14*d^12 + 16344064*a^10*b^10*c^13*d^13 - 11221760*a^11*b^9*c^12*d^14 + 5637888*a^12*b^8*c^11*d^15 - 2033152*a^13*b^7*c^10*d^16 + 501248*a^14*b^6*c^9*d^17 - 76032*a^15*b^5*c^8*d^18 + 5376*a^16*b^4*c^7*d^19))/(b^8*c^16 + a^8*c^8*d^8 - 8*a^7*b*c^9*d^7 + 28*a^2*b^6*c^14*d^2 - 56*a^3*b^5*c^13*d^3 + 70*a^4*b^4*c^12*d^4 - 56*a^5*b^3*c^11*d^5 + 28*a^6*b^2*c^10*d^6 - 8*a*b^7*c^15*d))*(-b^11/(16*a^15*d^12 + 16*a^3*b^12*c^12 - 192*a^4*b^11*c^11*d + 1056*a^5*b^10*c^10*d^2 - 3520*a^6*b^9*c^9*d^3 + 7920*a^7*b^8*c^8*d^4 - 12672*a^8*b^7*c^7*d^5 + 14784*a^9*b^6*c^6*d^6 - 12672*a^10*b^5*c^5*d^7 + 7920*a^11*b^4*c^4*d^8 - 3520*a^12*b^3*c^3*d^9 + 1056*a^13*b^2*c^2*d^10 - 192*a^14*b*c*d^11))^(3/4))*(-b^11/(16*a^15*d^12 + 16*a^3*b^12*c^12 - 192*a^4*b^11*c^11*d + 1056*a^5*b^10*c^10*d^2 - 3520*a^6*b^9*c^9*d^3 + 7920*a^7*b^8*c^8*d^4 - 12672*a^8*b^7*c^7*d^5 + 14784*a^9*b^6*c^6*d^6 - 12672*a^10*b^5*c^5*d^7 + 7920*a^11*b^4*c^4*d^8 - 3520*a^12*b^3*c^3*d^9 + 1056*a^13*b^2*c^2*d^10 - 192*a^14*b*c*d^11))^(1/4) - (x^(1/2)*(194481*a^8*b^11*d^15 + 41224337*b^19*c^8*d^7 - 130932648*a*b^18*c^7*d^8 - 2444904*a^7*b^12*c*d^14 + 201081276*a^2*b^17*c^6*d^9 - 189998424*a^3*b^16*c^5*d^10 + 119638278*a^4*b^15*c^4*d^11 - 51043608*a^5*b^14*c^3*d^12 + 14378364*a^6*b^13*c^2*d^13))/(4096*(b^12*c^20 + a^12*c^8*d^12 - 12*a^11*b*c^9*d^11 + 66*a^2*b^10*c^18*d^2 - 220*a^3*b^9*c^17*d^3 + 495*a^4*b^8*c^16*d^4 - 792*a^5*b^7*c^15*d^5 + 924*a^6*b^6*c^14*d^6 - 792*a^7*b^5*c^13*d^7 + 495*a^8*b^4*c^12*d^8 - 220*a^9*b^3*c^11*d^9 + 66*a^10*b^2*c^10*d^10 - 12*a*b^11*c^19*d)))))*(-b^11/(16*a^15*d^12 + 16*a^3*b^12*c^12 - 192*a^4*b^11*c^11*d + 1056*a^5*b^10*c^10*d^2 - 3520*a^6*b^9*c^9*d^3 + 7920*a^7*b^8*c^8*d^4 - 12672*a^8*b^7*c^7*d^5 + 14784*a^9*b^6*c^6*d^6 - 12672*a^10*b^5*c^5*d^7 + 7920*a^11*b^4*c^4*d^8 - 3520*a^12*b^3*c^3*d^9 + 1056*a^13*b^2*c^2*d^10 - 192*a^14*b*c*d^11))^(1/4)*2i + 2*atan(((-b^11/(16*a^15*d^12 + 16*a^3*b^12*c^12 - 192*a^4*b^11*c^11*d + 1056*a^5*b^10*c^10*d^2 - 3520*a^6*b^9*c^9*d^3 + 7920*a^7*b^8*c^8*d^4 - 12672*a^8*b^7*c^7*d^5 + 14784*a^9*b^6*c^6*d^6 - 12672*a^10*b^5*c^5*d^7 + 7920*a^11*b^4*c^4*d^8 - 3520*a^12*b^3*c^3*d^9 + 1056*a^13*b^2*c^2*d^10 - 192*a^14*b*c*d^11))^(1/4)*(((((194481*a^8*b^8*d^14)/2048 + 1232*b^16*c^8*d^6 - (34792593*a*b^15*c^7*d^7)/2048 - (2250423*a^7*b^9*c*d^13)/2048 + (86420247*a^2*b^14*c^6*d^8)/2048 - (106888869*a^3*b^13*c^5*d^9)/2048 + (80271027*a^4*b^12*c^4*d^10)/2048 - (38915667*a^5*b^11*c^3*d^11)/2048 + (12127941*a^6*b^10*c^2*d^12)/2048)*1i)/(b^8*c^16 + a^8*c^8*d^8 - 8*a^7*b*c^9*d^7 + 28*a^2*b^6*c^14*d^2 - 56*a^3*b^5*c^13*d^3 + 70*a^4*b^4*c^12*d^4 - 56*a^5*b^3*c^11*d^5 + 28*a^6*b^2*c^10*d^6 - 8*a*b^7*c^15*d) - ((x^(1/2)*(16777216*b^23*c^23*d^4 - 201326592*a*b^22*c^22*d^5 + 1107296256*a^2*b^21*c^21*d^6 - 3593846784*a^3*b^20*c^20*d^7 + 6972506112*a^4*b^19*c^19*d^8 - 4753588224*a^5*b^18*c^18*d^9 - 18397265920*a^6*b^17*c^17*d^10 + 80192667648*a^7*b^16*c^16*d^11 - 181503787008*a^8*b^15*c^15*d^12 + 289980416000*a^9*b^14*c^14*d^13 - 352258621440*a^10*b^13*c^13*d^14 + 334222688256*a^11*b^12*c^12*d^15 - 249961119744*a^12*b^11*c^11*d^16 + 147248775168*a^13*b^10*c^10*d^17 - 67718086656*a^14*b^9*c^9*d^18 + 23871029248*a^15*b^8*c^8*d^19 - 6245842944*a^16*b^7*c^7*d^20 + 1146224640*a^17*b^6*c^6*d^21 - 132120576*a^18*b^5*c^5*d^22 + 7225344*a^19*b^4*c^4*d^23)*1i)/(4096*(b^12*c^20 + a^12*c^8*d^12 - 12*a^11*b*c^9*d^11 + 66*a^2*b^10*c^18*d^2 - 220*a^3*b^9*c^17*d^3 + 495*a^4*b^8*c^16*d^4 - 792*a^5*b^7*c^15*d^5 + 924*a^6*b^6*c^14*d^6 - 792*a^7*b^5*c^13*d^7 + 495*a^8*b^4*c^12*d^8 - 220*a^9*b^3*c^11*d^9 + 66*a^10*b^2*c^10*d^10 - 12*a*b^11*c^19*d)) + ((-b^11/(16*a^15*d^12 + 16*a^3*b^12*c^12 - 192*a^4*b^11*c^11*d + 1056*a^5*b^10*c^10*d^2 - 3520*a^6*b^9*c^9*d^3 + 7920*a^7*b^8*c^8*d^4 - 12672*a^8*b^7*c^7*d^5 + 14784*a^9*b^6*c^6*d^6 - 12672*a^10*b^5*c^5*d^7 + 7920*a^11*b^4*c^4*d^8 - 3520*a^12*b^3*c^3*d^9 + 1056*a^13*b^2*c^2*d^10 - 192*a^14*b*c*d^11))^(1/4)*(8192*a*b^19*c^22*d^4 - 90112*a^2*b^18*c^21*d^5 + 430848*a^3*b^17*c^20*d^6 - 1117952*a^4*b^16*c^19*d^7 + 1427968*a^5*b^15*c^18*d^8 + 456192*a^6*b^14*c^17*d^9 - 5803776*a^7*b^13*c^16*d^10 + 12866304*a^8*b^12*c^15*d^11 - 17335296*a^9*b^11*c^14*d^12 + 16344064*a^10*b^10*c^13*d^13 - 11221760*a^11*b^9*c^12*d^14 + 5637888*a^12*b^8*c^11*d^15 - 2033152*a^13*b^7*c^10*d^16 + 501248*a^14*b^6*c^9*d^17 - 76032*a^15*b^5*c^8*d^18 + 5376*a^16*b^4*c^7*d^19))/(b^8*c^16 + a^8*c^8*d^8 - 8*a^7*b*c^9*d^7 + 28*a^2*b^6*c^14*d^2 - 56*a^3*b^5*c^13*d^3 + 70*a^4*b^4*c^12*d^4 - 56*a^5*b^3*c^11*d^5 + 28*a^6*b^2*c^10*d^6 - 8*a*b^7*c^15*d))*(-b^11/(16*a^15*d^12 + 16*a^3*b^12*c^12 - 192*a^4*b^11*c^11*d + 1056*a^5*b^10*c^10*d^2 - 3520*a^6*b^9*c^9*d^3 + 7920*a^7*b^8*c^8*d^4 - 12672*a^8*b^7*c^7*d^5 + 14784*a^9*b^6*c^6*d^6 - 12672*a^10*b^5*c^5*d^7 + 7920*a^11*b^4*c^4*d^8 - 3520*a^12*b^3*c^3*d^9 + 1056*a^13*b^2*c^2*d^10 - 192*a^14*b*c*d^11))^(3/4)*1i)*(-b^11/(16*a^15*d^12 + 16*a^3*b^12*c^12 - 192*a^4*b^11*c^11*d + 1056*a^5*b^10*c^10*d^2 - 3520*a^6*b^9*c^9*d^3 + 7920*a^7*b^8*c^8*d^4 - 12672*a^8*b^7*c^7*d^5 + 14784*a^9*b^6*c^6*d^6 - 12672*a^10*b^5*c^5*d^7 + 7920*a^11*b^4*c^4*d^8 - 3520*a^12*b^3*c^3*d^9 + 1056*a^13*b^2*c^2*d^10 - 192*a^14*b*c*d^11))^(1/4) + (x^(1/2)*(194481*a^8*b^11*d^15 + 41224337*b^19*c^8*d^7 - 130932648*a*b^18*c^7*d^8 - 2444904*a^7*b^12*c*d^14 + 201081276*a^2*b^17*c^6*d^9 - 189998424*a^3*b^16*c^5*d^10 + 119638278*a^4*b^15*c^4*d^11 - 51043608*a^5*b^14*c^3*d^12 + 14378364*a^6*b^13*c^2*d^13))/(4096*(b^12*c^20 + a^12*c^8*d^12 - 12*a^11*b*c^9*d^11 + 66*a^2*b^10*c^18*d^2 - 220*a^3*b^9*c^17*d^3 + 495*a^4*b^8*c^16*d^4 - 792*a^5*b^7*c^15*d^5 + 924*a^6*b^6*c^14*d^6 - 792*a^7*b^5*c^13*d^7 + 495*a^8*b^4*c^12*d^8 - 220*a^9*b^3*c^11*d^9 + 66*a^10*b^2*c^10*d^10 - 12*a*b^11*c^19*d))) - (-b^11/(16*a^15*d^12 + 16*a^3*b^12*c^12 - 192*a^4*b^11*c^11*d + 1056*a^5*b^10*c^10*d^2 - 3520*a^6*b^9*c^9*d^3 + 7920*a^7*b^8*c^8*d^4 - 12672*a^8*b^7*c^7*d^5 + 14784*a^9*b^6*c^6*d^6 - 12672*a^10*b^5*c^5*d^7 + 7920*a^11*b^4*c^4*d^8 - 3520*a^12*b^3*c^3*d^9 + 1056*a^13*b^2*c^2*d^10 - 192*a^14*b*c*d^11))^(1/4)*(((((194481*a^8*b^8*d^14)/2048 + 1232*b^16*c^8*d^6 - (34792593*a*b^15*c^7*d^7)/2048 - (2250423*a^7*b^9*c*d^13)/2048 + (86420247*a^2*b^14*c^6*d^8)/2048 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119638278*a^4*b^15*c^4*d^11 - 51043608*a^5*b^14*c^3*d^12 + 14378364*a^6*b^13*c^2*d^13))/(4096*(b^12*c^20 + a^12*c^8*d^12 - 12*a^11*b*c^9*d^11 + 66*a^2*b^10*c^18*d^2 - 220*a^3*b^9*c^17*d^3 + 495*a^4*b^8*c^16*d^4 - 792*a^5*b^7*c^15*d^5 + 924*a^6*b^6*c^14*d^6 - 792*a^7*b^5*c^13*d^7 + 495*a^8*b^4*c^12*d^8 - 220*a^9*b^3*c^11*d^9 + 66*a^10*b^2*c^10*d^10 - 12*a*b^11*c^19*d))))/((-b^11/(16*a^15*d^12 + 16*a^3*b^12*c^12 - 192*a^4*b^11*c^11*d + 1056*a^5*b^10*c^10*d^2 - 3520*a^6*b^9*c^9*d^3 + 7920*a^7*b^8*c^8*d^4 - 12672*a^8*b^7*c^7*d^5 + 14784*a^9*b^6*c^6*d^6 - 12672*a^10*b^5*c^5*d^7 + 7920*a^11*b^4*c^4*d^8 - 3520*a^12*b^3*c^3*d^9 + 1056*a^13*b^2*c^2*d^10 - 192*a^14*b*c*d^11))^(1/4)*(((((194481*a^8*b^8*d^14)/2048 + 1232*b^16*c^8*d^6 - (34792593*a*b^15*c^7*d^7)/2048 - (2250423*a^7*b^9*c*d^13)/2048 + (86420247*a^2*b^14*c^6*d^8)/2048 - (106888869*a^3*b^13*c^5*d^9)/2048 + (80271027*a^4*b^12*c^4*d^10)/2048 - (38915667*a^5*b^11*c^3*d^11)/2048 + (12127941*a^6*b^10*c^2*d^12)/2048)*1i)/(b^8*c^16 + 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3520*a^6*b^9*c^9*d^3 + 7920*a^7*b^8*c^8*d^4 - 12672*a^8*b^7*c^7*d^5 + 14784*a^9*b^6*c^6*d^6 - 12672*a^10*b^5*c^5*d^7 + 7920*a^11*b^4*c^4*d^8 - 3520*a^12*b^3*c^3*d^9 + 1056*a^13*b^2*c^2*d^10 - 192*a^14*b*c*d^11))^(1/4)*(8192*a*b^19*c^22*d^4 - 90112*a^2*b^18*c^21*d^5 + 430848*a^3*b^17*c^20*d^6 - 1117952*a^4*b^16*c^19*d^7 + 1427968*a^5*b^15*c^18*d^8 + 456192*a^6*b^14*c^17*d^9 - 5803776*a^7*b^13*c^16*d^10 + 12866304*a^8*b^12*c^15*d^11 - 17335296*a^9*b^11*c^14*d^12 + 16344064*a^10*b^10*c^13*d^13 - 11221760*a^11*b^9*c^12*d^14 + 5637888*a^12*b^8*c^11*d^15 - 2033152*a^13*b^7*c^10*d^16 + 501248*a^14*b^6*c^9*d^17 - 76032*a^15*b^5*c^8*d^18 + 5376*a^16*b^4*c^7*d^19))/(b^8*c^16 + a^8*c^8*d^8 - 8*a^7*b*c^9*d^7 + 28*a^2*b^6*c^14*d^2 - 56*a^3*b^5*c^13*d^3 + 70*a^4*b^4*c^12*d^4 - 56*a^5*b^3*c^11*d^5 + 28*a^6*b^2*c^10*d^6 - 8*a*b^7*c^15*d))*(-b^11/(16*a^15*d^12 + 16*a^3*b^12*c^12 - 192*a^4*b^11*c^11*d + 1056*a^5*b^10*c^10*d^2 - 3520*a^6*b^9*c^9*d^3 + 7920*a^7*b^8*c^8*d^4 - 12672*a^8*b^7*c^7*d^5 + 14784*a^9*b^6*c^6*d^6 - 12672*a^10*b^5*c^5*d^7 + 7920*a^11*b^4*c^4*d^8 - 3520*a^12*b^3*c^3*d^9 + 1056*a^13*b^2*c^2*d^10 - 192*a^14*b*c*d^11))^(3/4)*1i)*(-b^11/(16*a^15*d^12 + 16*a^3*b^12*c^12 - 192*a^4*b^11*c^11*d + 1056*a^5*b^10*c^10*d^2 - 3520*a^6*b^9*c^9*d^3 + 7920*a^7*b^8*c^8*d^4 - 12672*a^8*b^7*c^7*d^5 + 14784*a^9*b^6*c^6*d^6 - 12672*a^10*b^5*c^5*d^7 + 7920*a^11*b^4*c^4*d^8 - 3520*a^12*b^3*c^3*d^9 + 1056*a^13*b^2*c^2*d^10 - 192*a^14*b*c*d^11))^(1/4)*1i - (x^(1/2)*(194481*a^8*b^11*d^15 + 41224337*b^19*c^8*d^7 - 130932648*a*b^18*c^7*d^8 - 2444904*a^7*b^12*c*d^14 + 201081276*a^2*b^17*c^6*d^9 - 189998424*a^3*b^16*c^5*d^10 + 119638278*a^4*b^15*c^4*d^11 - 51043608*a^5*b^14*c^3*d^12 + 14378364*a^6*b^13*c^2*d^13)*1i)/(4096*(b^12*c^20 + a^12*c^8*d^12 - 12*a^11*b*c^9*d^11 + 66*a^2*b^10*c^18*d^2 - 220*a^3*b^9*c^17*d^3 + 495*a^4*b^8*c^16*d^4 - 792*a^5*b^7*c^15*d^5 + 924*a^6*b^6*c^14*d^6 - 792*a^7*b^5*c^13*d^7 + 495*a^8*b^4*c^12*d^8 - 220*a^9*b^3*c^11*d^9 + 66*a^10*b^2*c^10*d^10 - 12*a*b^11*c^19*d)))))*(-b^11/(16*a^15*d^12 + 16*a^3*b^12*c^12 - 192*a^4*b^11*c^11*d + 1056*a^5*b^10*c^10*d^2 - 3520*a^6*b^9*c^9*d^3 + 7920*a^7*b^8*c^8*d^4 - 12672*a^8*b^7*c^7*d^5 + 14784*a^9*b^6*c^6*d^6 - 12672*a^10*b^5*c^5*d^7 + 7920*a^11*b^4*c^4*d^8 - 3520*a^12*b^3*c^3*d^9 + 1056*a^13*b^2*c^2*d^10 - 192*a^14*b*c*d^11))^(1/4) + ((x^(1/2)*(11*a*d^2 - 19*b*c*d))/(16*(b^2*c^3 + a^2*c*d^2 - 2*a*b*c^2*d)) + (d^2*x^(5/2)*(7*a*d - 15*b*c))/(16*c*(b^2*c^3 + a^2*c*d^2 - 2*a*b*c^2*d)))/(c^2 + d^2*x^4 + 2*c*d*x^2) + atan((((((194481*a^8*b^8*d^14)/2048 + 1232*b^16*c^8*d^6 - (34792593*a*b^15*c^7*d^7)/2048 - (2250423*a^7*b^9*c*d^13)/2048 + (86420247*a^2*b^14*c^6*d^8)/2048 - (106888869*a^3*b^13*c^5*d^9)/2048 + (80271027*a^4*b^12*c^4*d^10)/2048 - (38915667*a^5*b^11*c^3*d^11)/2048 + (12127941*a^6*b^10*c^2*d^12)/2048)/(b^8*c^16 + a^8*c^8*d^8 - 8*a^7*b*c^9*d^7 + 28*a^2*b^6*c^14*d^2 - 56*a^3*b^5*c^13*d^3 + 70*a^4*b^4*c^12*d^4 - 56*a^5*b^3*c^11*d^5 + 28*a^6*b^2*c^10*d^6 - 8*a*b^7*c^15*d) + ((x^(1/2)*(16777216*b^23*c^23*d^4 - 201326592*a*b^22*c^22*d^5 + 1107296256*a^2*b^21*c^21*d^6 - 3593846784*a^3*b^20*c^20*d^7 + 6972506112*a^4*b^19*c^19*d^8 - 4753588224*a^5*b^18*c^18*d^9 - 18397265920*a^6*b^17*c^17*d^10 + 80192667648*a^7*b^16*c^16*d^11 - 181503787008*a^8*b^15*c^15*d^12 + 289980416000*a^9*b^14*c^14*d^13 - 352258621440*a^10*b^13*c^13*d^14 + 334222688256*a^11*b^12*c^12*d^15 - 249961119744*a^12*b^11*c^11*d^16 + 147248775168*a^13*b^10*c^10*d^17 - 67718086656*a^14*b^9*c^9*d^18 + 23871029248*a^15*b^8*c^8*d^19 - 6245842944*a^16*b^7*c^7*d^20 + 1146224640*a^17*b^6*c^6*d^21 - 132120576*a^18*b^5*c^5*d^22 + 7225344*a^19*b^4*c^4*d^23))/(4096*(b^12*c^20 + a^12*c^8*d^12 - 12*a^11*b*c^9*d^11 + 66*a^2*b^10*c^18*d^2 - 220*a^3*b^9*c^17*d^3 + 495*a^4*b^8*c^16*d^4 - 792*a^5*b^7*c^15*d^5 + 924*a^6*b^6*c^14*d^6 - 792*a^7*b^5*c^13*d^7 + 495*a^8*b^4*c^12*d^8 - 220*a^9*b^3*c^11*d^9 + 66*a^10*b^2*c^10*d^10 - 12*a*b^11*c^19*d)) - ((-(194481*a^8*d^11 + 35153041*b^8*c^8*d^3 - 120524712*a*b^7*c^7*d^4 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5376*a^16*b^4*c^7*d^19))/(b^8*c^16 + a^8*c^8*d^8 - 8*a^7*b*c^9*d^7 + 28*a^2*b^6*c^14*d^2 - 56*a^3*b^5*c^13*d^3 + 70*a^4*b^4*c^12*d^4 - 56*a^5*b^3*c^11*d^5 + 28*a^6*b^2*c^10*d^6 - 8*a*b^7*c^15*d))*(-(194481*a^8*d^11 + 35153041*b^8*c^8*d^3 - 120524712*a*b^7*c^7*d^4 + 193309116*a^2*b^6*c^6*d^5 - 187159896*a^3*b^5*c^5*d^6 + 119186694*a^4*b^4*c^4*d^7 - 51043608*a^5*b^3*c^3*d^8 + 14378364*a^6*b^2*c^2*d^9 - 2444904*a^7*b*c*d^10)/(16777216*b^12*c^23 + 16777216*a^12*c^11*d^12 - 201326592*a^11*b*c^12*d^11 + 1107296256*a^2*b^10*c^21*d^2 - 3690987520*a^3*b^9*c^20*d^3 + 8304721920*a^4*b^8*c^19*d^4 - 13287555072*a^5*b^7*c^18*d^5 + 15502147584*a^6*b^6*c^17*d^6 - 13287555072*a^7*b^5*c^16*d^7 + 8304721920*a^8*b^4*c^15*d^8 - 3690987520*a^9*b^3*c^14*d^9 + 1107296256*a^10*b^2*c^13*d^10 - 201326592*a*b^11*c^22*d))^(3/4))*(-(194481*a^8*d^11 + 35153041*b^8*c^8*d^3 - 120524712*a*b^7*c^7*d^4 + 193309116*a^2*b^6*c^6*d^5 - 187159896*a^3*b^5*c^5*d^6 + 119186694*a^4*b^4*c^4*d^7 - 51043608*a^5*b^3*c^3*d^8 + 14378364*a^6*b^2*c^2*d^9 - 2444904*a^7*b*c*d^10)/(16777216*b^12*c^23 + 16777216*a^12*c^11*d^12 - 201326592*a^11*b*c^12*d^11 + 1107296256*a^2*b^10*c^21*d^2 - 3690987520*a^3*b^9*c^20*d^3 + 8304721920*a^4*b^8*c^19*d^4 - 13287555072*a^5*b^7*c^18*d^5 + 15502147584*a^6*b^6*c^17*d^6 - 13287555072*a^7*b^5*c^16*d^7 + 8304721920*a^8*b^4*c^15*d^8 - 3690987520*a^9*b^3*c^14*d^9 + 1107296256*a^10*b^2*c^13*d^10 - 201326592*a*b^11*c^22*d))^(1/4)*1i + (x^(1/2)*(194481*a^8*b^11*d^15 + 41224337*b^19*c^8*d^7 - 130932648*a*b^18*c^7*d^8 - 2444904*a^7*b^12*c*d^14 + 201081276*a^2*b^17*c^6*d^9 - 189998424*a^3*b^16*c^5*d^10 + 119638278*a^4*b^15*c^4*d^11 - 51043608*a^5*b^14*c^3*d^12 + 14378364*a^6*b^13*c^2*d^13)*1i)/(4096*(b^12*c^20 + a^12*c^8*d^12 - 12*a^11*b*c^9*d^11 + 66*a^2*b^10*c^18*d^2 - 220*a^3*b^9*c^17*d^3 + 495*a^4*b^8*c^16*d^4 - 792*a^5*b^7*c^15*d^5 + 924*a^6*b^6*c^14*d^6 - 792*a^7*b^5*c^13*d^7 + 495*a^8*b^4*c^12*d^8 - 220*a^9*b^3*c^11*d^9 + 66*a^10*b^2*c^10*d^10 - 12*a*b^11*c^19*d)))*(-(194481*a^8*d^11 + 35153041*b^8*c^8*d^3 - 120524712*a*b^7*c^7*d^4 + 193309116*a^2*b^6*c^6*d^5 - 187159896*a^3*b^5*c^5*d^6 + 119186694*a^4*b^4*c^4*d^7 - 51043608*a^5*b^3*c^3*d^8 + 14378364*a^6*b^2*c^2*d^9 - 2444904*a^7*b*c*d^10)/(16777216*b^12*c^23 + 16777216*a^12*c^11*d^12 - 201326592*a^11*b*c^12*d^11 + 1107296256*a^2*b^10*c^21*d^2 - 3690987520*a^3*b^9*c^20*d^3 + 8304721920*a^4*b^8*c^19*d^4 - 13287555072*a^5*b^7*c^18*d^5 + 15502147584*a^6*b^6*c^17*d^6 - 13287555072*a^7*b^5*c^16*d^7 + 8304721920*a^8*b^4*c^15*d^8 - 3690987520*a^9*b^3*c^14*d^9 + 1107296256*a^10*b^2*c^13*d^10 - 201326592*a*b^11*c^22*d))^(1/4) - ((((194481*a^8*b^8*d^14)/2048 + 1232*b^16*c^8*d^6 - (34792593*a*b^15*c^7*d^7)/2048 - (2250423*a^7*b^9*c*d^13)/2048 + (86420247*a^2*b^14*c^6*d^8)/2048 - (106888869*a^3*b^13*c^5*d^9)/2048 + (80271027*a^4*b^12*c^4*d^10)/2048 - (38915667*a^5*b^11*c^3*d^11)/2048 + (12127941*a^6*b^10*c^2*d^12)/2048)/(b^8*c^16 + a^8*c^8*d^8 - 8*a^7*b*c^9*d^7 + 28*a^2*b^6*c^14*d^2 - 56*a^3*b^5*c^13*d^3 + 70*a^4*b^4*c^12*d^4 - 56*a^5*b^3*c^11*d^5 + 28*a^6*b^2*c^10*d^6 - 8*a*b^7*c^15*d) - ((x^(1/2)*(16777216*b^23*c^23*d^4 - 201326592*a*b^22*c^22*d^5 + 1107296256*a^2*b^21*c^21*d^6 - 3593846784*a^3*b^20*c^20*d^7 + 6972506112*a^4*b^19*c^19*d^8 - 4753588224*a^5*b^18*c^18*d^9 - 18397265920*a^6*b^17*c^17*d^10 + 80192667648*a^7*b^16*c^16*d^11 - 181503787008*a^8*b^15*c^15*d^12 + 289980416000*a^9*b^14*c^14*d^13 - 352258621440*a^10*b^13*c^13*d^14 + 334222688256*a^11*b^12*c^12*d^15 - 249961119744*a^12*b^11*c^11*d^16 + 147248775168*a^13*b^10*c^10*d^17 - 67718086656*a^14*b^9*c^9*d^18 + 23871029248*a^15*b^8*c^8*d^19 - 6245842944*a^16*b^7*c^7*d^20 + 1146224640*a^17*b^6*c^6*d^21 - 132120576*a^18*b^5*c^5*d^22 + 7225344*a^19*b^4*c^4*d^23))/(4096*(b^12*c^20 + a^12*c^8*d^12 - 12*a^11*b*c^9*d^11 + 66*a^2*b^10*c^18*d^2 - 220*a^3*b^9*c^17*d^3 + 495*a^4*b^8*c^16*d^4 - 792*a^5*b^7*c^15*d^5 + 924*a^6*b^6*c^14*d^6 - 792*a^7*b^5*c^13*d^7 + 495*a^8*b^4*c^12*d^8 - 220*a^9*b^3*c^11*d^9 + 66*a^10*b^2*c^10*d^10 - 12*a*b^11*c^19*d)) + ((-(194481*a^8*d^11 + 35153041*b^8*c^8*d^3 - 120524712*a*b^7*c^7*d^4 + 193309116*a^2*b^6*c^6*d^5 - 187159896*a^3*b^5*c^5*d^6 + 119186694*a^4*b^4*c^4*d^7 - 51043608*a^5*b^3*c^3*d^8 + 14378364*a^6*b^2*c^2*d^9 - 2444904*a^7*b*c*d^10)/(16777216*b^12*c^23 + 16777216*a^12*c^11*d^12 - 201326592*a^11*b*c^12*d^11 + 1107296256*a^2*b^10*c^21*d^2 - 3690987520*a^3*b^9*c^20*d^3 + 8304721920*a^4*b^8*c^19*d^4 - 13287555072*a^5*b^7*c^18*d^5 + 15502147584*a^6*b^6*c^17*d^6 - 13287555072*a^7*b^5*c^16*d^7 + 8304721920*a^8*b^4*c^15*d^8 - 3690987520*a^9*b^3*c^14*d^9 + 1107296256*a^10*b^2*c^13*d^10 - 201326592*a*b^11*c^22*d))^(1/4)*(8192*a*b^19*c^22*d^4 - 90112*a^2*b^18*c^21*d^5 + 430848*a^3*b^17*c^20*d^6 - 1117952*a^4*b^16*c^19*d^7 + 1427968*a^5*b^15*c^18*d^8 + 456192*a^6*b^14*c^17*d^9 - 5803776*a^7*b^13*c^16*d^10 + 12866304*a^8*b^12*c^15*d^11 - 17335296*a^9*b^11*c^14*d^12 + 16344064*a^10*b^10*c^13*d^13 - 11221760*a^11*b^9*c^12*d^14 + 5637888*a^12*b^8*c^11*d^15 - 2033152*a^13*b^7*c^10*d^16 + 501248*a^14*b^6*c^9*d^17 - 76032*a^15*b^5*c^8*d^18 + 5376*a^16*b^4*c^7*d^19))/(b^8*c^16 + a^8*c^8*d^8 - 8*a^7*b*c^9*d^7 + 28*a^2*b^6*c^14*d^2 - 56*a^3*b^5*c^13*d^3 + 70*a^4*b^4*c^12*d^4 - 56*a^5*b^3*c^11*d^5 + 28*a^6*b^2*c^10*d^6 - 8*a*b^7*c^15*d))*(-(194481*a^8*d^11 + 35153041*b^8*c^8*d^3 - 120524712*a*b^7*c^7*d^4 + 193309116*a^2*b^6*c^6*d^5 - 187159896*a^3*b^5*c^5*d^6 + 119186694*a^4*b^4*c^4*d^7 - 51043608*a^5*b^3*c^3*d^8 + 14378364*a^6*b^2*c^2*d^9 - 2444904*a^7*b*c*d^10)/(16777216*b^12*c^23 + 16777216*a^12*c^11*d^12 - 201326592*a^11*b*c^12*d^11 + 1107296256*a^2*b^10*c^21*d^2 - 3690987520*a^3*b^9*c^20*d^3 + 8304721920*a^4*b^8*c^19*d^4 - 13287555072*a^5*b^7*c^18*d^5 + 15502147584*a^6*b^6*c^17*d^6 - 13287555072*a^7*b^5*c^16*d^7 + 8304721920*a^8*b^4*c^15*d^8 - 3690987520*a^9*b^3*c^14*d^9 + 1107296256*a^10*b^2*c^13*d^10 - 201326592*a*b^11*c^22*d))^(3/4))*(-(194481*a^8*d^11 + 35153041*b^8*c^8*d^3 - 120524712*a*b^7*c^7*d^4 + 193309116*a^2*b^6*c^6*d^5 - 187159896*a^3*b^5*c^5*d^6 + 119186694*a^4*b^4*c^4*d^7 - 51043608*a^5*b^3*c^3*d^8 + 14378364*a^6*b^2*c^2*d^9 - 2444904*a^7*b*c*d^10)/(16777216*b^12*c^23 + 16777216*a^12*c^11*d^12 - 201326592*a^11*b*c^12*d^11 + 1107296256*a^2*b^10*c^21*d^2 - 3690987520*a^3*b^9*c^20*d^3 + 8304721920*a^4*b^8*c^19*d^4 - 13287555072*a^5*b^7*c^18*d^5 + 15502147584*a^6*b^6*c^17*d^6 - 13287555072*a^7*b^5*c^16*d^7 + 8304721920*a^8*b^4*c^15*d^8 - 3690987520*a^9*b^3*c^14*d^9 + 1107296256*a^10*b^2*c^13*d^10 - 201326592*a*b^11*c^22*d))^(1/4)*1i - (x^(1/2)*(194481*a^8*b^11*d^15 + 41224337*b^19*c^8*d^7 - 130932648*a*b^18*c^7*d^8 - 2444904*a^7*b^12*c*d^14 + 201081276*a^2*b^17*c^6*d^9 - 189998424*a^3*b^16*c^5*d^10 + 119638278*a^4*b^15*c^4*d^11 - 51043608*a^5*b^14*c^3*d^12 + 14378364*a^6*b^13*c^2*d^13)*1i)/(4096*(b^12*c^20 + a^12*c^8*d^12 - 12*a^11*b*c^9*d^11 + 66*a^2*b^10*c^18*d^2 - 220*a^3*b^9*c^17*d^3 + 495*a^4*b^8*c^16*d^4 - 792*a^5*b^7*c^15*d^5 + 924*a^6*b^6*c^14*d^6 - 792*a^7*b^5*c^13*d^7 + 495*a^8*b^4*c^12*d^8 - 220*a^9*b^3*c^11*d^9 + 66*a^10*b^2*c^10*d^10 - 12*a*b^11*c^19*d)))*(-(194481*a^8*d^11 + 35153041*b^8*c^8*d^3 - 120524712*a*b^7*c^7*d^4 + 193309116*a^2*b^6*c^6*d^5 - 187159896*a^3*b^5*c^5*d^6 + 119186694*a^4*b^4*c^4*d^7 - 51043608*a^5*b^3*c^3*d^8 + 14378364*a^6*b^2*c^2*d^9 - 2444904*a^7*b*c*d^10)/(16777216*b^12*c^23 + 16777216*a^12*c^11*d^12 - 201326592*a^11*b*c^12*d^11 + 1107296256*a^2*b^10*c^21*d^2 - 3690987520*a^3*b^9*c^20*d^3 + 8304721920*a^4*b^8*c^19*d^4 - 13287555072*a^5*b^7*c^18*d^5 + 15502147584*a^6*b^6*c^17*d^6 - 13287555072*a^7*b^5*c^16*d^7 + 8304721920*a^8*b^4*c^15*d^8 - 3690987520*a^9*b^3*c^14*d^9 + 1107296256*a^10*b^2*c^13*d^10 - 201326592*a*b^11*c^22*d))^(1/4))/(((((194481*a^8*b^8*d^14)/2048 + 1232*b^16*c^8*d^6 - (34792593*a*b^15*c^7*d^7)/2048 - (2250423*a^7*b^9*c*d^13)/2048 + (86420247*a^2*b^14*c^6*d^8)/2048 - (106888869*a^3*b^13*c^5*d^9)/2048 + (80271027*a^4*b^12*c^4*d^10)/2048 - (38915667*a^5*b^11*c^3*d^11)/2048 + (12127941*a^6*b^10*c^2*d^12)/2048)/(b^8*c^16 + a^8*c^8*d^8 - 8*a^7*b*c^9*d^7 + 28*a^2*b^6*c^14*d^2 - 56*a^3*b^5*c^13*d^3 + 70*a^4*b^4*c^12*d^4 - 56*a^5*b^3*c^11*d^5 + 28*a^6*b^2*c^10*d^6 - 8*a*b^7*c^15*d) + ((x^(1/2)*(16777216*b^23*c^23*d^4 - 201326592*a*b^22*c^22*d^5 + 1107296256*a^2*b^21*c^21*d^6 - 3593846784*a^3*b^20*c^20*d^7 + 6972506112*a^4*b^19*c^19*d^8 - 4753588224*a^5*b^18*c^18*d^9 - 18397265920*a^6*b^17*c^17*d^10 + 80192667648*a^7*b^16*c^16*d^11 - 181503787008*a^8*b^15*c^15*d^12 + 289980416000*a^9*b^14*c^14*d^13 - 352258621440*a^10*b^13*c^13*d^14 + 334222688256*a^11*b^12*c^12*d^15 - 249961119744*a^12*b^11*c^11*d^16 + 147248775168*a^13*b^10*c^10*d^17 - 67718086656*a^14*b^9*c^9*d^18 + 23871029248*a^15*b^8*c^8*d^19 - 6245842944*a^16*b^7*c^7*d^20 + 1146224640*a^17*b^6*c^6*d^21 - 132120576*a^18*b^5*c^5*d^22 + 7225344*a^19*b^4*c^4*d^23))/(4096*(b^12*c^20 + a^12*c^8*d^12 - 12*a^11*b*c^9*d^11 + 66*a^2*b^10*c^18*d^2 - 220*a^3*b^9*c^17*d^3 + 495*a^4*b^8*c^16*d^4 - 792*a^5*b^7*c^15*d^5 + 924*a^6*b^6*c^14*d^6 - 792*a^7*b^5*c^13*d^7 + 495*a^8*b^4*c^12*d^8 - 220*a^9*b^3*c^11*d^9 + 66*a^10*b^2*c^10*d^10 - 12*a*b^11*c^19*d)) - ((-(194481*a^8*d^11 + 35153041*b^8*c^8*d^3 - 120524712*a*b^7*c^7*d^4 + 193309116*a^2*b^6*c^6*d^5 - 187159896*a^3*b^5*c^5*d^6 + 119186694*a^4*b^4*c^4*d^7 - 51043608*a^5*b^3*c^3*d^8 + 14378364*a^6*b^2*c^2*d^9 - 2444904*a^7*b*c*d^10)/(16777216*b^12*c^23 + 16777216*a^12*c^11*d^12 - 201326592*a^11*b*c^12*d^11 + 1107296256*a^2*b^10*c^21*d^2 - 3690987520*a^3*b^9*c^20*d^3 + 8304721920*a^4*b^8*c^19*d^4 - 13287555072*a^5*b^7*c^18*d^5 + 15502147584*a^6*b^6*c^17*d^6 - 13287555072*a^7*b^5*c^16*d^7 + 8304721920*a^8*b^4*c^15*d^8 - 3690987520*a^9*b^3*c^14*d^9 + 1107296256*a^10*b^2*c^13*d^10 - 201326592*a*b^11*c^22*d))^(1/4)*(8192*a*b^19*c^22*d^4 - 90112*a^2*b^18*c^21*d^5 + 430848*a^3*b^17*c^20*d^6 - 1117952*a^4*b^16*c^19*d^7 + 1427968*a^5*b^15*c^18*d^8 + 456192*a^6*b^14*c^17*d^9 - 5803776*a^7*b^13*c^16*d^10 + 12866304*a^8*b^12*c^15*d^11 - 17335296*a^9*b^11*c^14*d^12 + 16344064*a^10*b^10*c^13*d^13 - 11221760*a^11*b^9*c^12*d^14 + 5637888*a^12*b^8*c^11*d^15 - 2033152*a^13*b^7*c^10*d^16 + 501248*a^14*b^6*c^9*d^17 - 76032*a^15*b^5*c^8*d^18 + 5376*a^16*b^4*c^7*d^19))/(b^8*c^16 + a^8*c^8*d^8 - 8*a^7*b*c^9*d^7 + 28*a^2*b^6*c^14*d^2 - 56*a^3*b^5*c^13*d^3 + 70*a^4*b^4*c^12*d^4 - 56*a^5*b^3*c^11*d^5 + 28*a^6*b^2*c^10*d^6 - 8*a*b^7*c^15*d))*(-(194481*a^8*d^11 + 35153041*b^8*c^8*d^3 - 120524712*a*b^7*c^7*d^4 + 193309116*a^2*b^6*c^6*d^5 - 187159896*a^3*b^5*c^5*d^6 + 119186694*a^4*b^4*c^4*d^7 - 51043608*a^5*b^3*c^3*d^8 + 14378364*a^6*b^2*c^2*d^9 - 2444904*a^7*b*c*d^10)/(16777216*b^12*c^23 + 16777216*a^12*c^11*d^12 - 201326592*a^11*b*c^12*d^11 + 1107296256*a^2*b^10*c^21*d^2 - 3690987520*a^3*b^9*c^20*d^3 + 8304721920*a^4*b^8*c^19*d^4 - 13287555072*a^5*b^7*c^18*d^5 + 15502147584*a^6*b^6*c^17*d^6 - 13287555072*a^7*b^5*c^16*d^7 + 8304721920*a^8*b^4*c^15*d^8 - 3690987520*a^9*b^3*c^14*d^9 + 1107296256*a^10*b^2*c^13*d^10 - 201326592*a*b^11*c^22*d))^(3/4))*(-(194481*a^8*d^11 + 35153041*b^8*c^8*d^3 - 120524712*a*b^7*c^7*d^4 + 193309116*a^2*b^6*c^6*d^5 - 187159896*a^3*b^5*c^5*d^6 + 119186694*a^4*b^4*c^4*d^7 - 51043608*a^5*b^3*c^3*d^8 + 14378364*a^6*b^2*c^2*d^9 - 2444904*a^7*b*c*d^10)/(16777216*b^12*c^23 + 16777216*a^12*c^11*d^12 - 201326592*a^11*b*c^12*d^11 + 1107296256*a^2*b^10*c^21*d^2 - 3690987520*a^3*b^9*c^20*d^3 + 8304721920*a^4*b^8*c^19*d^4 - 13287555072*a^5*b^7*c^18*d^5 + 15502147584*a^6*b^6*c^17*d^6 - 13287555072*a^7*b^5*c^16*d^7 + 8304721920*a^8*b^4*c^15*d^8 - 3690987520*a^9*b^3*c^14*d^9 + 1107296256*a^10*b^2*c^13*d^10 - 201326592*a*b^11*c^22*d))^(1/4) + (x^(1/2)*(194481*a^8*b^11*d^15 + 41224337*b^19*c^8*d^7 - 130932648*a*b^18*c^7*d^8 - 2444904*a^7*b^12*c*d^14 + 201081276*a^2*b^17*c^6*d^9 - 189998424*a^3*b^16*c^5*d^10 + 119638278*a^4*b^15*c^4*d^11 - 51043608*a^5*b^14*c^3*d^12 + 14378364*a^6*b^13*c^2*d^13))/(4096*(b^12*c^20 + a^12*c^8*d^12 - 12*a^11*b*c^9*d^11 + 66*a^2*b^10*c^18*d^2 - 220*a^3*b^9*c^17*d^3 + 495*a^4*b^8*c^16*d^4 - 792*a^5*b^7*c^15*d^5 + 924*a^6*b^6*c^14*d^6 - 792*a^7*b^5*c^13*d^7 + 495*a^8*b^4*c^12*d^8 - 220*a^9*b^3*c^11*d^9 + 66*a^10*b^2*c^10*d^10 - 12*a*b^11*c^19*d)))*(-(194481*a^8*d^11 + 35153041*b^8*c^8*d^3 - 120524712*a*b^7*c^7*d^4 + 193309116*a^2*b^6*c^6*d^5 - 187159896*a^3*b^5*c^5*d^6 + 119186694*a^4*b^4*c^4*d^7 - 51043608*a^5*b^3*c^3*d^8 + 14378364*a^6*b^2*c^2*d^9 - 2444904*a^7*b*c*d^10)/(16777216*b^12*c^23 + 16777216*a^12*c^11*d^12 - 201326592*a^11*b*c^12*d^11 + 1107296256*a^2*b^10*c^21*d^2 - 3690987520*a^3*b^9*c^20*d^3 + 8304721920*a^4*b^8*c^19*d^4 - 13287555072*a^5*b^7*c^18*d^5 + 15502147584*a^6*b^6*c^17*d^6 - 13287555072*a^7*b^5*c^16*d^7 + 8304721920*a^8*b^4*c^15*d^8 - 3690987520*a^9*b^3*c^14*d^9 + 1107296256*a^10*b^2*c^13*d^10 - 201326592*a*b^11*c^22*d))^(1/4) + ((((194481*a^8*b^8*d^14)/2048 + 1232*b^16*c^8*d^6 - (34792593*a*b^15*c^7*d^7)/2048 - (2250423*a^7*b^9*c*d^13)/2048 + (86420247*a^2*b^14*c^6*d^8)/2048 - (106888869*a^3*b^13*c^5*d^9)/2048 + (80271027*a^4*b^12*c^4*d^10)/2048 - (38915667*a^5*b^11*c^3*d^11)/2048 + (12127941*a^6*b^10*c^2*d^12)/2048)/(b^8*c^16 + a^8*c^8*d^8 - 8*a^7*b*c^9*d^7 + 28*a^2*b^6*c^14*d^2 - 56*a^3*b^5*c^13*d^3 + 70*a^4*b^4*c^12*d^4 - 56*a^5*b^3*c^11*d^5 + 28*a^6*b^2*c^10*d^6 - 8*a*b^7*c^15*d) - ((x^(1/2)*(16777216*b^23*c^23*d^4 - 201326592*a*b^22*c^22*d^5 + 1107296256*a^2*b^21*c^21*d^6 - 3593846784*a^3*b^20*c^20*d^7 + 6972506112*a^4*b^19*c^19*d^8 - 4753588224*a^5*b^18*c^18*d^9 - 18397265920*a^6*b^17*c^17*d^10 + 80192667648*a^7*b^16*c^16*d^11 - 181503787008*a^8*b^15*c^15*d^12 + 289980416000*a^9*b^14*c^14*d^13 - 352258621440*a^10*b^13*c^13*d^14 + 334222688256*a^11*b^12*c^12*d^15 - 249961119744*a^12*b^11*c^11*d^16 + 147248775168*a^13*b^10*c^10*d^17 - 67718086656*a^14*b^9*c^9*d^18 + 23871029248*a^15*b^8*c^8*d^19 - 6245842944*a^16*b^7*c^7*d^20 + 1146224640*a^17*b^6*c^6*d^21 - 132120576*a^18*b^5*c^5*d^22 + 7225344*a^19*b^4*c^4*d^23))/(4096*(b^12*c^20 + a^12*c^8*d^12 - 12*a^11*b*c^9*d^11 + 66*a^2*b^10*c^18*d^2 - 220*a^3*b^9*c^17*d^3 + 495*a^4*b^8*c^16*d^4 - 792*a^5*b^7*c^15*d^5 + 924*a^6*b^6*c^14*d^6 - 792*a^7*b^5*c^13*d^7 + 495*a^8*b^4*c^12*d^8 - 220*a^9*b^3*c^11*d^9 + 66*a^10*b^2*c^10*d^10 - 12*a*b^11*c^19*d)) + ((-(194481*a^8*d^11 + 35153041*b^8*c^8*d^3 - 120524712*a*b^7*c^7*d^4 + 193309116*a^2*b^6*c^6*d^5 - 187159896*a^3*b^5*c^5*d^6 + 119186694*a^4*b^4*c^4*d^7 - 51043608*a^5*b^3*c^3*d^8 + 14378364*a^6*b^2*c^2*d^9 - 2444904*a^7*b*c*d^10)/(16777216*b^12*c^23 + 16777216*a^12*c^11*d^12 - 201326592*a^11*b*c^12*d^11 + 1107296256*a^2*b^10*c^21*d^2 - 3690987520*a^3*b^9*c^20*d^3 + 8304721920*a^4*b^8*c^19*d^4 - 13287555072*a^5*b^7*c^18*d^5 + 15502147584*a^6*b^6*c^17*d^6 - 13287555072*a^7*b^5*c^16*d^7 + 8304721920*a^8*b^4*c^15*d^8 - 3690987520*a^9*b^3*c^14*d^9 + 1107296256*a^10*b^2*c^13*d^10 - 201326592*a*b^11*c^22*d))^(1/4)*(8192*a*b^19*c^22*d^4 - 90112*a^2*b^18*c^21*d^5 + 430848*a^3*b^17*c^20*d^6 - 1117952*a^4*b^16*c^19*d^7 + 1427968*a^5*b^15*c^18*d^8 + 456192*a^6*b^14*c^17*d^9 - 5803776*a^7*b^13*c^16*d^10 + 12866304*a^8*b^12*c^15*d^11 - 17335296*a^9*b^11*c^14*d^12 + 16344064*a^10*b^10*c^13*d^13 - 11221760*a^11*b^9*c^12*d^14 + 5637888*a^12*b^8*c^11*d^15 - 2033152*a^13*b^7*c^10*d^16 + 501248*a^14*b^6*c^9*d^17 - 76032*a^15*b^5*c^8*d^18 + 5376*a^16*b^4*c^7*d^19))/(b^8*c^16 + a^8*c^8*d^8 - 8*a^7*b*c^9*d^7 + 28*a^2*b^6*c^14*d^2 - 56*a^3*b^5*c^13*d^3 + 70*a^4*b^4*c^12*d^4 - 56*a^5*b^3*c^11*d^5 + 28*a^6*b^2*c^10*d^6 - 8*a*b^7*c^15*d))*(-(194481*a^8*d^11 + 35153041*b^8*c^8*d^3 - 120524712*a*b^7*c^7*d^4 + 193309116*a^2*b^6*c^6*d^5 - 187159896*a^3*b^5*c^5*d^6 + 119186694*a^4*b^4*c^4*d^7 - 51043608*a^5*b^3*c^3*d^8 + 14378364*a^6*b^2*c^2*d^9 - 2444904*a^7*b*c*d^10)/(16777216*b^12*c^23 + 16777216*a^12*c^11*d^12 - 201326592*a^11*b*c^12*d^11 + 1107296256*a^2*b^10*c^21*d^2 - 3690987520*a^3*b^9*c^20*d^3 + 8304721920*a^4*b^8*c^19*d^4 - 13287555072*a^5*b^7*c^18*d^5 + 15502147584*a^6*b^6*c^17*d^6 - 13287555072*a^7*b^5*c^16*d^7 + 8304721920*a^8*b^4*c^15*d^8 - 3690987520*a^9*b^3*c^14*d^9 + 1107296256*a^10*b^2*c^13*d^10 - 201326592*a*b^11*c^22*d))^(3/4))*(-(194481*a^8*d^11 + 35153041*b^8*c^8*d^3 - 120524712*a*b^7*c^7*d^4 + 193309116*a^2*b^6*c^6*d^5 - 187159896*a^3*b^5*c^5*d^6 + 119186694*a^4*b^4*c^4*d^7 - 51043608*a^5*b^3*c^3*d^8 + 14378364*a^6*b^2*c^2*d^9 - 2444904*a^7*b*c*d^10)/(16777216*b^12*c^23 + 16777216*a^12*c^11*d^12 - 201326592*a^11*b*c^12*d^11 + 1107296256*a^2*b^10*c^21*d^2 - 3690987520*a^3*b^9*c^20*d^3 + 8304721920*a^4*b^8*c^19*d^4 - 13287555072*a^5*b^7*c^18*d^5 + 15502147584*a^6*b^6*c^17*d^6 - 13287555072*a^7*b^5*c^16*d^7 + 8304721920*a^8*b^4*c^15*d^8 - 3690987520*a^9*b^3*c^14*d^9 + 1107296256*a^10*b^2*c^13*d^10 - 201326592*a*b^11*c^22*d))^(1/4) - (x^(1/2)*(194481*a^8*b^11*d^15 + 41224337*b^19*c^8*d^7 - 130932648*a*b^18*c^7*d^8 - 2444904*a^7*b^12*c*d^14 + 201081276*a^2*b^17*c^6*d^9 - 189998424*a^3*b^16*c^5*d^10 + 119638278*a^4*b^15*c^4*d^11 - 51043608*a^5*b^14*c^3*d^12 + 14378364*a^6*b^13*c^2*d^13))/(4096*(b^12*c^20 + a^12*c^8*d^12 - 12*a^11*b*c^9*d^11 + 66*a^2*b^10*c^18*d^2 - 220*a^3*b^9*c^17*d^3 + 495*a^4*b^8*c^16*d^4 - 792*a^5*b^7*c^15*d^5 + 924*a^6*b^6*c^14*d^6 - 792*a^7*b^5*c^13*d^7 + 495*a^8*b^4*c^12*d^8 - 220*a^9*b^3*c^11*d^9 + 66*a^10*b^2*c^10*d^10 - 12*a*b^11*c^19*d)))*(-(194481*a^8*d^11 + 35153041*b^8*c^8*d^3 - 120524712*a*b^7*c^7*d^4 + 193309116*a^2*b^6*c^6*d^5 - 187159896*a^3*b^5*c^5*d^6 + 119186694*a^4*b^4*c^4*d^7 - 51043608*a^5*b^3*c^3*d^8 + 14378364*a^6*b^2*c^2*d^9 - 2444904*a^7*b*c*d^10)/(16777216*b^12*c^23 + 16777216*a^12*c^11*d^12 - 201326592*a^11*b*c^12*d^11 + 1107296256*a^2*b^10*c^21*d^2 - 3690987520*a^3*b^9*c^20*d^3 + 8304721920*a^4*b^8*c^19*d^4 - 13287555072*a^5*b^7*c^18*d^5 + 15502147584*a^6*b^6*c^17*d^6 - 13287555072*a^7*b^5*c^16*d^7 + 8304721920*a^8*b^4*c^15*d^8 - 3690987520*a^9*b^3*c^14*d^9 + 1107296256*a^10*b^2*c^13*d^10 - 201326592*a*b^11*c^22*d))^(1/4)))*(-(194481*a^8*d^11 + 35153041*b^8*c^8*d^3 - 120524712*a*b^7*c^7*d^4 + 193309116*a^2*b^6*c^6*d^5 - 187159896*a^3*b^5*c^5*d^6 + 119186694*a^4*b^4*c^4*d^7 - 51043608*a^5*b^3*c^3*d^8 + 14378364*a^6*b^2*c^2*d^9 - 2444904*a^7*b*c*d^10)/(16777216*b^12*c^23 + 16777216*a^12*c^11*d^12 - 201326592*a^11*b*c^12*d^11 + 1107296256*a^2*b^10*c^21*d^2 - 3690987520*a^3*b^9*c^20*d^3 + 8304721920*a^4*b^8*c^19*d^4 - 13287555072*a^5*b^7*c^18*d^5 + 15502147584*a^6*b^6*c^17*d^6 - 13287555072*a^7*b^5*c^16*d^7 + 8304721920*a^8*b^4*c^15*d^8 - 3690987520*a^9*b^3*c^14*d^9 + 1107296256*a^10*b^2*c^13*d^10 - 201326592*a*b^11*c^22*d))^(1/4)*2i + 2*atan(((((((194481*a^8*b^8*d^14)/2048 + 1232*b^16*c^8*d^6 - (34792593*a*b^15*c^7*d^7)/2048 - (2250423*a^7*b^9*c*d^13)/2048 + (86420247*a^2*b^14*c^6*d^8)/2048 - (106888869*a^3*b^13*c^5*d^9)/2048 + (80271027*a^4*b^12*c^4*d^10)/2048 - (38915667*a^5*b^11*c^3*d^11)/2048 + (12127941*a^6*b^10*c^2*d^12)/2048)*1i)/(b^8*c^16 + a^8*c^8*d^8 - 8*a^7*b*c^9*d^7 + 28*a^2*b^6*c^14*d^2 - 56*a^3*b^5*c^13*d^3 + 70*a^4*b^4*c^12*d^4 - 56*a^5*b^3*c^11*d^5 + 28*a^6*b^2*c^10*d^6 - 8*a*b^7*c^15*d) - ((x^(1/2)*(16777216*b^23*c^23*d^4 - 201326592*a*b^22*c^22*d^5 + 1107296256*a^2*b^21*c^21*d^6 - 3593846784*a^3*b^20*c^20*d^7 + 6972506112*a^4*b^19*c^19*d^8 - 4753588224*a^5*b^18*c^18*d^9 - 18397265920*a^6*b^17*c^17*d^10 + 80192667648*a^7*b^16*c^16*d^11 - 181503787008*a^8*b^15*c^15*d^12 + 289980416000*a^9*b^14*c^14*d^13 - 352258621440*a^10*b^13*c^13*d^14 + 334222688256*a^11*b^12*c^12*d^15 - 249961119744*a^12*b^11*c^11*d^16 + 147248775168*a^13*b^10*c^10*d^17 - 67718086656*a^14*b^9*c^9*d^18 + 23871029248*a^15*b^8*c^8*d^19 - 6245842944*a^16*b^7*c^7*d^20 + 1146224640*a^17*b^6*c^6*d^21 - 132120576*a^18*b^5*c^5*d^22 + 7225344*a^19*b^4*c^4*d^23)*1i)/(4096*(b^12*c^20 + a^12*c^8*d^12 - 12*a^11*b*c^9*d^11 + 66*a^2*b^10*c^18*d^2 - 220*a^3*b^9*c^17*d^3 + 495*a^4*b^8*c^16*d^4 - 792*a^5*b^7*c^15*d^5 + 924*a^6*b^6*c^14*d^6 - 792*a^7*b^5*c^13*d^7 + 495*a^8*b^4*c^12*d^8 - 220*a^9*b^3*c^11*d^9 + 66*a^10*b^2*c^10*d^10 - 12*a*b^11*c^19*d)) + ((-(194481*a^8*d^11 + 35153041*b^8*c^8*d^3 - 120524712*a*b^7*c^7*d^4 + 193309116*a^2*b^6*c^6*d^5 - 187159896*a^3*b^5*c^5*d^6 + 119186694*a^4*b^4*c^4*d^7 - 51043608*a^5*b^3*c^3*d^8 + 14378364*a^6*b^2*c^2*d^9 - 2444904*a^7*b*c*d^10)/(16777216*b^12*c^23 + 16777216*a^12*c^11*d^12 - 201326592*a^11*b*c^12*d^11 + 1107296256*a^2*b^10*c^21*d^2 - 3690987520*a^3*b^9*c^20*d^3 + 8304721920*a^4*b^8*c^19*d^4 - 13287555072*a^5*b^7*c^18*d^5 + 15502147584*a^6*b^6*c^17*d^6 - 13287555072*a^7*b^5*c^16*d^7 + 8304721920*a^8*b^4*c^15*d^8 - 3690987520*a^9*b^3*c^14*d^9 + 1107296256*a^10*b^2*c^13*d^10 - 201326592*a*b^11*c^22*d))^(1/4)*(8192*a*b^19*c^22*d^4 - 90112*a^2*b^18*c^21*d^5 + 430848*a^3*b^17*c^20*d^6 - 1117952*a^4*b^16*c^19*d^7 + 1427968*a^5*b^15*c^18*d^8 + 456192*a^6*b^14*c^17*d^9 - 5803776*a^7*b^13*c^16*d^10 + 12866304*a^8*b^12*c^15*d^11 - 17335296*a^9*b^11*c^14*d^12 + 16344064*a^10*b^10*c^13*d^13 - 11221760*a^11*b^9*c^12*d^14 + 5637888*a^12*b^8*c^11*d^15 - 2033152*a^13*b^7*c^10*d^16 + 501248*a^14*b^6*c^9*d^17 - 76032*a^15*b^5*c^8*d^18 + 5376*a^16*b^4*c^7*d^19))/(b^8*c^16 + a^8*c^8*d^8 - 8*a^7*b*c^9*d^7 + 28*a^2*b^6*c^14*d^2 - 56*a^3*b^5*c^13*d^3 + 70*a^4*b^4*c^12*d^4 - 56*a^5*b^3*c^11*d^5 + 28*a^6*b^2*c^10*d^6 - 8*a*b^7*c^15*d))*(-(194481*a^8*d^11 + 35153041*b^8*c^8*d^3 - 120524712*a*b^7*c^7*d^4 + 193309116*a^2*b^6*c^6*d^5 - 187159896*a^3*b^5*c^5*d^6 + 119186694*a^4*b^4*c^4*d^7 - 51043608*a^5*b^3*c^3*d^8 + 14378364*a^6*b^2*c^2*d^9 - 2444904*a^7*b*c*d^10)/(16777216*b^12*c^23 + 16777216*a^12*c^11*d^12 - 201326592*a^11*b*c^12*d^11 + 1107296256*a^2*b^10*c^21*d^2 - 3690987520*a^3*b^9*c^20*d^3 + 8304721920*a^4*b^8*c^19*d^4 - 13287555072*a^5*b^7*c^18*d^5 + 15502147584*a^6*b^6*c^17*d^6 - 13287555072*a^7*b^5*c^16*d^7 + 8304721920*a^8*b^4*c^15*d^8 - 3690987520*a^9*b^3*c^14*d^9 + 1107296256*a^10*b^2*c^13*d^10 - 201326592*a*b^11*c^22*d))^(3/4)*1i)*(-(194481*a^8*d^11 + 35153041*b^8*c^8*d^3 - 120524712*a*b^7*c^7*d^4 + 193309116*a^2*b^6*c^6*d^5 - 187159896*a^3*b^5*c^5*d^6 + 119186694*a^4*b^4*c^4*d^7 - 51043608*a^5*b^3*c^3*d^8 + 14378364*a^6*b^2*c^2*d^9 - 2444904*a^7*b*c*d^10)/(16777216*b^12*c^23 + 16777216*a^12*c^11*d^12 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((x^(1/2)*(16777216*b^23*c^23*d^4 - 201326592*a*b^22*c^22*d^5 + 1107296256*a^2*b^21*c^21*d^6 - 3593846784*a^3*b^20*c^20*d^7 + 6972506112*a^4*b^19*c^19*d^8 - 4753588224*a^5*b^18*c^18*d^9 - 18397265920*a^6*b^17*c^17*d^10 + 80192667648*a^7*b^16*c^16*d^11 - 181503787008*a^8*b^15*c^15*d^12 + 289980416000*a^9*b^14*c^14*d^13 - 352258621440*a^10*b^13*c^13*d^14 + 334222688256*a^11*b^12*c^12*d^15 - 249961119744*a^12*b^11*c^11*d^16 + 147248775168*a^13*b^10*c^10*d^17 - 67718086656*a^14*b^9*c^9*d^18 + 23871029248*a^15*b^8*c^8*d^19 - 6245842944*a^16*b^7*c^7*d^20 + 1146224640*a^17*b^6*c^6*d^21 - 132120576*a^18*b^5*c^5*d^22 + 7225344*a^19*b^4*c^4*d^23)*1i)/(4096*(b^12*c^20 + a^12*c^8*d^12 - 12*a^11*b*c^9*d^11 + 66*a^2*b^10*c^18*d^2 - 220*a^3*b^9*c^17*d^3 + 495*a^4*b^8*c^16*d^4 - 792*a^5*b^7*c^15*d^5 + 924*a^6*b^6*c^14*d^6 - 792*a^7*b^5*c^13*d^7 + 495*a^8*b^4*c^12*d^8 - 220*a^9*b^3*c^11*d^9 + 66*a^10*b^2*c^10*d^10 - 12*a*b^11*c^19*d)) - ((-(194481*a^8*d^11 + 35153041*b^8*c^8*d^3 - 120524712*a*b^7*c^7*d^4 + 193309116*a^2*b^6*c^6*d^5 - 187159896*a^3*b^5*c^5*d^6 + 119186694*a^4*b^4*c^4*d^7 - 51043608*a^5*b^3*c^3*d^8 + 14378364*a^6*b^2*c^2*d^9 - 2444904*a^7*b*c*d^10)/(16777216*b^12*c^23 + 16777216*a^12*c^11*d^12 - 201326592*a^11*b*c^12*d^11 + 1107296256*a^2*b^10*c^21*d^2 - 3690987520*a^3*b^9*c^20*d^3 + 8304721920*a^4*b^8*c^19*d^4 - 13287555072*a^5*b^7*c^18*d^5 + 15502147584*a^6*b^6*c^17*d^6 - 13287555072*a^7*b^5*c^16*d^7 + 8304721920*a^8*b^4*c^15*d^8 - 3690987520*a^9*b^3*c^14*d^9 + 1107296256*a^10*b^2*c^13*d^10 - 201326592*a*b^11*c^22*d))^(1/4)*(8192*a*b^19*c^22*d^4 - 90112*a^2*b^18*c^21*d^5 + 430848*a^3*b^17*c^20*d^6 - 1117952*a^4*b^16*c^19*d^7 + 1427968*a^5*b^15*c^18*d^8 + 456192*a^6*b^14*c^17*d^9 - 5803776*a^7*b^13*c^16*d^10 + 12866304*a^8*b^12*c^15*d^11 - 17335296*a^9*b^11*c^14*d^12 + 16344064*a^10*b^10*c^13*d^13 - 11221760*a^11*b^9*c^12*d^14 + 5637888*a^12*b^8*c^11*d^15 - 2033152*a^13*b^7*c^10*d^16 + 501248*a^14*b^6*c^9*d^17 - 76032*a^15*b^5*c^8*d^18 + 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14378364*a^6*b^2*c^2*d^9 - 2444904*a^7*b*c*d^10)/(16777216*b^12*c^23 + 16777216*a^12*c^11*d^12 - 201326592*a^11*b*c^12*d^11 + 1107296256*a^2*b^10*c^21*d^2 - 3690987520*a^3*b^9*c^20*d^3 + 8304721920*a^4*b^8*c^19*d^4 - 13287555072*a^5*b^7*c^18*d^5 + 15502147584*a^6*b^6*c^17*d^6 - 13287555072*a^7*b^5*c^16*d^7 + 8304721920*a^8*b^4*c^15*d^8 - 3690987520*a^9*b^3*c^14*d^9 + 1107296256*a^10*b^2*c^13*d^10 - 201326592*a*b^11*c^22*d))^(1/4) - (x^(1/2)*(194481*a^8*b^11*d^15 + 41224337*b^19*c^8*d^7 - 130932648*a*b^18*c^7*d^8 - 2444904*a^7*b^12*c*d^14 + 201081276*a^2*b^17*c^6*d^9 - 189998424*a^3*b^16*c^5*d^10 + 119638278*a^4*b^15*c^4*d^11 - 51043608*a^5*b^14*c^3*d^12 + 14378364*a^6*b^13*c^2*d^13))/(4096*(b^12*c^20 + a^12*c^8*d^12 - 12*a^11*b*c^9*d^11 + 66*a^2*b^10*c^18*d^2 - 220*a^3*b^9*c^17*d^3 + 495*a^4*b^8*c^16*d^4 - 792*a^5*b^7*c^15*d^5 + 924*a^6*b^6*c^14*d^6 - 792*a^7*b^5*c^13*d^7 + 495*a^8*b^4*c^12*d^8 - 220*a^9*b^3*c^11*d^9 + 66*a^10*b^2*c^10*d^10 - 12*a*b^11*c^19*d)))*(-(194481*a^8*d^11 + 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70*a^4*b^4*c^12*d^4 - 56*a^5*b^3*c^11*d^5 + 28*a^6*b^2*c^10*d^6 - 8*a*b^7*c^15*d) - ((x^(1/2)*(16777216*b^23*c^23*d^4 - 201326592*a*b^22*c^22*d^5 + 1107296256*a^2*b^21*c^21*d^6 - 3593846784*a^3*b^20*c^20*d^7 + 6972506112*a^4*b^19*c^19*d^8 - 4753588224*a^5*b^18*c^18*d^9 - 18397265920*a^6*b^17*c^17*d^10 + 80192667648*a^7*b^16*c^16*d^11 - 181503787008*a^8*b^15*c^15*d^12 + 289980416000*a^9*b^14*c^14*d^13 - 352258621440*a^10*b^13*c^13*d^14 + 334222688256*a^11*b^12*c^12*d^15 - 249961119744*a^12*b^11*c^11*d^16 + 147248775168*a^13*b^10*c^10*d^17 - 67718086656*a^14*b^9*c^9*d^18 + 23871029248*a^15*b^8*c^8*d^19 - 6245842944*a^16*b^7*c^7*d^20 + 1146224640*a^17*b^6*c^6*d^21 - 132120576*a^18*b^5*c^5*d^22 + 7225344*a^19*b^4*c^4*d^23)*1i)/(4096*(b^12*c^20 + a^12*c^8*d^12 - 12*a^11*b*c^9*d^11 + 66*a^2*b^10*c^18*d^2 - 220*a^3*b^9*c^17*d^3 + 495*a^4*b^8*c^16*d^4 - 792*a^5*b^7*c^15*d^5 + 924*a^6*b^6*c^14*d^6 - 792*a^7*b^5*c^13*d^7 + 495*a^8*b^4*c^12*d^8 - 220*a^9*b^3*c^11*d^9 + 66*a^10*b^2*c^10*d^10 - 12*a*b^11*c^19*d)) + ((-(194481*a^8*d^11 + 35153041*b^8*c^8*d^3 - 120524712*a*b^7*c^7*d^4 + 193309116*a^2*b^6*c^6*d^5 - 187159896*a^3*b^5*c^5*d^6 + 119186694*a^4*b^4*c^4*d^7 - 51043608*a^5*b^3*c^3*d^8 + 14378364*a^6*b^2*c^2*d^9 - 2444904*a^7*b*c*d^10)/(16777216*b^12*c^23 + 16777216*a^12*c^11*d^12 - 201326592*a^11*b*c^12*d^11 + 1107296256*a^2*b^10*c^21*d^2 - 3690987520*a^3*b^9*c^20*d^3 + 8304721920*a^4*b^8*c^19*d^4 - 13287555072*a^5*b^7*c^18*d^5 + 15502147584*a^6*b^6*c^17*d^6 - 13287555072*a^7*b^5*c^16*d^7 + 8304721920*a^8*b^4*c^15*d^8 - 3690987520*a^9*b^3*c^14*d^9 + 1107296256*a^10*b^2*c^13*d^10 - 201326592*a*b^11*c^22*d))^(1/4)*(8192*a*b^19*c^22*d^4 - 90112*a^2*b^18*c^21*d^5 + 430848*a^3*b^17*c^20*d^6 - 1117952*a^4*b^16*c^19*d^7 + 1427968*a^5*b^15*c^18*d^8 + 456192*a^6*b^14*c^17*d^9 - 5803776*a^7*b^13*c^16*d^10 + 12866304*a^8*b^12*c^15*d^11 - 17335296*a^9*b^11*c^14*d^12 + 16344064*a^10*b^10*c^13*d^13 - 11221760*a^11*b^9*c^12*d^14 + 5637888*a^12*b^8*c^11*d^15 - 2033152*a^13*b^7*c^10*d^16 + 501248*a^14*b^6*c^9*d^17 - 76032*a^15*b^5*c^8*d^18 + 5376*a^16*b^4*c^7*d^19))/(b^8*c^16 + a^8*c^8*d^8 - 8*a^7*b*c^9*d^7 + 28*a^2*b^6*c^14*d^2 - 56*a^3*b^5*c^13*d^3 + 70*a^4*b^4*c^12*d^4 - 56*a^5*b^3*c^11*d^5 + 28*a^6*b^2*c^10*d^6 - 8*a*b^7*c^15*d))*(-(194481*a^8*d^11 + 35153041*b^8*c^8*d^3 - 120524712*a*b^7*c^7*d^4 + 193309116*a^2*b^6*c^6*d^5 - 187159896*a^3*b^5*c^5*d^6 + 119186694*a^4*b^4*c^4*d^7 - 51043608*a^5*b^3*c^3*d^8 + 14378364*a^6*b^2*c^2*d^9 - 2444904*a^7*b*c*d^10)/(16777216*b^12*c^23 + 16777216*a^12*c^11*d^12 - 201326592*a^11*b*c^12*d^11 + 1107296256*a^2*b^10*c^21*d^2 - 3690987520*a^3*b^9*c^20*d^3 + 8304721920*a^4*b^8*c^19*d^4 - 13287555072*a^5*b^7*c^18*d^5 + 15502147584*a^6*b^6*c^17*d^6 - 13287555072*a^7*b^5*c^16*d^7 + 8304721920*a^8*b^4*c^15*d^8 - 3690987520*a^9*b^3*c^14*d^9 + 1107296256*a^10*b^2*c^13*d^10 - 201326592*a*b^11*c^22*d))^(3/4)*1i)*(-(194481*a^8*d^11 + 35153041*b^8*c^8*d^3 - 120524712*a*b^7*c^7*d^4 + 193309116*a^2*b^6*c^6*d^5 - 187159896*a^3*b^5*c^5*d^6 + 119186694*a^4*b^4*c^4*d^7 - 51043608*a^5*b^3*c^3*d^8 + 14378364*a^6*b^2*c^2*d^9 - 2444904*a^7*b*c*d^10)/(16777216*b^12*c^23 + 16777216*a^12*c^11*d^12 - 201326592*a^11*b*c^12*d^11 + 1107296256*a^2*b^10*c^21*d^2 - 3690987520*a^3*b^9*c^20*d^3 + 8304721920*a^4*b^8*c^19*d^4 - 13287555072*a^5*b^7*c^18*d^5 + 15502147584*a^6*b^6*c^17*d^6 - 13287555072*a^7*b^5*c^16*d^7 + 8304721920*a^8*b^4*c^15*d^8 - 3690987520*a^9*b^3*c^14*d^9 + 1107296256*a^10*b^2*c^13*d^10 - 201326592*a*b^11*c^22*d))^(1/4)*1i + (x^(1/2)*(194481*a^8*b^11*d^15 + 41224337*b^19*c^8*d^7 - 130932648*a*b^18*c^7*d^8 - 2444904*a^7*b^12*c*d^14 + 201081276*a^2*b^17*c^6*d^9 - 189998424*a^3*b^16*c^5*d^10 + 119638278*a^4*b^15*c^4*d^11 - 51043608*a^5*b^14*c^3*d^12 + 14378364*a^6*b^13*c^2*d^13)*1i)/(4096*(b^12*c^20 + a^12*c^8*d^12 - 12*a^11*b*c^9*d^11 + 66*a^2*b^10*c^18*d^2 - 220*a^3*b^9*c^17*d^3 + 495*a^4*b^8*c^16*d^4 - 792*a^5*b^7*c^15*d^5 + 924*a^6*b^6*c^14*d^6 - 792*a^7*b^5*c^13*d^7 + 495*a^8*b^4*c^12*d^8 - 220*a^9*b^3*c^11*d^9 + 66*a^10*b^2*c^10*d^10 - 12*a*b^11*c^19*d)))*(-(194481*a^8*d^11 + 35153041*b^8*c^8*d^3 - 120524712*a*b^7*c^7*d^4 + 193309116*a^2*b^6*c^6*d^5 - 187159896*a^3*b^5*c^5*d^6 + 119186694*a^4*b^4*c^4*d^7 - 51043608*a^5*b^3*c^3*d^8 + 14378364*a^6*b^2*c^2*d^9 - 2444904*a^7*b*c*d^10)/(16777216*b^12*c^23 + 16777216*a^12*c^11*d^12 - 201326592*a^11*b*c^12*d^11 + 1107296256*a^2*b^10*c^21*d^2 - 3690987520*a^3*b^9*c^20*d^3 + 8304721920*a^4*b^8*c^19*d^4 - 13287555072*a^5*b^7*c^18*d^5 + 15502147584*a^6*b^6*c^17*d^6 - 13287555072*a^7*b^5*c^16*d^7 + 8304721920*a^8*b^4*c^15*d^8 - 3690987520*a^9*b^3*c^14*d^9 + 1107296256*a^10*b^2*c^13*d^10 - 201326592*a*b^11*c^22*d))^(1/4) + (((((194481*a^8*b^8*d^14)/2048 + 1232*b^16*c^8*d^6 - (34792593*a*b^15*c^7*d^7)/2048 - (2250423*a^7*b^9*c*d^13)/2048 + (86420247*a^2*b^14*c^6*d^8)/2048 - (106888869*a^3*b^13*c^5*d^9)/2048 + (80271027*a^4*b^12*c^4*d^10)/2048 - (38915667*a^5*b^11*c^3*d^11)/2048 + (12127941*a^6*b^10*c^2*d^12)/2048)*1i)/(b^8*c^16 + a^8*c^8*d^8 - 8*a^7*b*c^9*d^7 + 28*a^2*b^6*c^14*d^2 - 56*a^3*b^5*c^13*d^3 + 70*a^4*b^4*c^12*d^4 - 56*a^5*b^3*c^11*d^5 + 28*a^6*b^2*c^10*d^6 - 8*a*b^7*c^15*d) + ((x^(1/2)*(16777216*b^23*c^23*d^4 - 201326592*a*b^22*c^22*d^5 + 1107296256*a^2*b^21*c^21*d^6 - 3593846784*a^3*b^20*c^20*d^7 + 6972506112*a^4*b^19*c^19*d^8 - 4753588224*a^5*b^18*c^18*d^9 - 18397265920*a^6*b^17*c^17*d^10 + 80192667648*a^7*b^16*c^16*d^11 - 181503787008*a^8*b^15*c^15*d^12 + 289980416000*a^9*b^14*c^14*d^13 - 352258621440*a^10*b^13*c^13*d^14 + 334222688256*a^11*b^12*c^12*d^15 - 249961119744*a^12*b^11*c^11*d^16 + 147248775168*a^13*b^10*c^10*d^17 - 67718086656*a^14*b^9*c^9*d^18 + 23871029248*a^15*b^8*c^8*d^19 - 6245842944*a^16*b^7*c^7*d^20 + 1146224640*a^17*b^6*c^6*d^21 - 132120576*a^18*b^5*c^5*d^22 + 7225344*a^19*b^4*c^4*d^23)*1i)/(4096*(b^12*c^20 + a^12*c^8*d^12 - 12*a^11*b*c^9*d^11 + 66*a^2*b^10*c^18*d^2 - 220*a^3*b^9*c^17*d^3 + 495*a^4*b^8*c^16*d^4 - 792*a^5*b^7*c^15*d^5 + 924*a^6*b^6*c^14*d^6 - 792*a^7*b^5*c^13*d^7 + 495*a^8*b^4*c^12*d^8 - 220*a^9*b^3*c^11*d^9 + 66*a^10*b^2*c^10*d^10 - 12*a*b^11*c^19*d)) - ((-(194481*a^8*d^11 + 35153041*b^8*c^8*d^3 - 120524712*a*b^7*c^7*d^4 + 193309116*a^2*b^6*c^6*d^5 - 187159896*a^3*b^5*c^5*d^6 + 119186694*a^4*b^4*c^4*d^7 - 51043608*a^5*b^3*c^3*d^8 + 14378364*a^6*b^2*c^2*d^9 - 2444904*a^7*b*c*d^10)/(16777216*b^12*c^23 + 16777216*a^12*c^11*d^12 - 201326592*a^11*b*c^12*d^11 + 1107296256*a^2*b^10*c^21*d^2 - 3690987520*a^3*b^9*c^20*d^3 + 8304721920*a^4*b^8*c^19*d^4 - 13287555072*a^5*b^7*c^18*d^5 + 15502147584*a^6*b^6*c^17*d^6 - 13287555072*a^7*b^5*c^16*d^7 + 8304721920*a^8*b^4*c^15*d^8 - 3690987520*a^9*b^3*c^14*d^9 + 1107296256*a^10*b^2*c^13*d^10 - 201326592*a*b^11*c^22*d))^(1/4)*(8192*a*b^19*c^22*d^4 - 90112*a^2*b^18*c^21*d^5 + 430848*a^3*b^17*c^20*d^6 - 1117952*a^4*b^16*c^19*d^7 + 1427968*a^5*b^15*c^18*d^8 + 456192*a^6*b^14*c^17*d^9 - 5803776*a^7*b^13*c^16*d^10 + 12866304*a^8*b^12*c^15*d^11 - 17335296*a^9*b^11*c^14*d^12 + 16344064*a^10*b^10*c^13*d^13 - 11221760*a^11*b^9*c^12*d^14 + 5637888*a^12*b^8*c^11*d^15 - 2033152*a^13*b^7*c^10*d^16 + 501248*a^14*b^6*c^9*d^17 - 76032*a^15*b^5*c^8*d^18 + 5376*a^16*b^4*c^7*d^19))/(b^8*c^16 + a^8*c^8*d^8 - 8*a^7*b*c^9*d^7 + 28*a^2*b^6*c^14*d^2 - 56*a^3*b^5*c^13*d^3 + 70*a^4*b^4*c^12*d^4 - 56*a^5*b^3*c^11*d^5 + 28*a^6*b^2*c^10*d^6 - 8*a*b^7*c^15*d))*(-(194481*a^8*d^11 + 35153041*b^8*c^8*d^3 - 120524712*a*b^7*c^7*d^4 + 193309116*a^2*b^6*c^6*d^5 - 187159896*a^3*b^5*c^5*d^6 + 119186694*a^4*b^4*c^4*d^7 - 51043608*a^5*b^3*c^3*d^8 + 14378364*a^6*b^2*c^2*d^9 - 2444904*a^7*b*c*d^10)/(16777216*b^12*c^23 + 16777216*a^12*c^11*d^12 - 201326592*a^11*b*c^12*d^11 + 1107296256*a^2*b^10*c^21*d^2 - 3690987520*a^3*b^9*c^20*d^3 + 8304721920*a^4*b^8*c^19*d^4 - 13287555072*a^5*b^7*c^18*d^5 + 15502147584*a^6*b^6*c^17*d^6 - 13287555072*a^7*b^5*c^16*d^7 + 8304721920*a^8*b^4*c^15*d^8 - 3690987520*a^9*b^3*c^14*d^9 + 1107296256*a^10*b^2*c^13*d^10 - 201326592*a*b^11*c^22*d))^(3/4)*1i)*(-(194481*a^8*d^11 + 35153041*b^8*c^8*d^3 - 120524712*a*b^7*c^7*d^4 + 193309116*a^2*b^6*c^6*d^5 - 187159896*a^3*b^5*c^5*d^6 + 119186694*a^4*b^4*c^4*d^7 - 51043608*a^5*b^3*c^3*d^8 + 14378364*a^6*b^2*c^2*d^9 - 2444904*a^7*b*c*d^10)/(16777216*b^12*c^23 + 16777216*a^12*c^11*d^12 - 201326592*a^11*b*c^12*d^11 + 1107296256*a^2*b^10*c^21*d^2 - 3690987520*a^3*b^9*c^20*d^3 + 8304721920*a^4*b^8*c^19*d^4 - 13287555072*a^5*b^7*c^18*d^5 + 15502147584*a^6*b^6*c^17*d^6 - 13287555072*a^7*b^5*c^16*d^7 + 8304721920*a^8*b^4*c^15*d^8 - 3690987520*a^9*b^3*c^14*d^9 + 1107296256*a^10*b^2*c^13*d^10 - 201326592*a*b^11*c^22*d))^(1/4)*1i - (x^(1/2)*(194481*a^8*b^11*d^15 + 41224337*b^19*c^8*d^7 - 130932648*a*b^18*c^7*d^8 - 2444904*a^7*b^12*c*d^14 + 201081276*a^2*b^17*c^6*d^9 - 189998424*a^3*b^16*c^5*d^10 + 119638278*a^4*b^15*c^4*d^11 - 51043608*a^5*b^14*c^3*d^12 + 14378364*a^6*b^13*c^2*d^13)*1i)/(4096*(b^12*c^20 + a^12*c^8*d^12 - 12*a^11*b*c^9*d^11 + 66*a^2*b^10*c^18*d^2 - 220*a^3*b^9*c^17*d^3 + 495*a^4*b^8*c^16*d^4 - 792*a^5*b^7*c^15*d^5 + 924*a^6*b^6*c^14*d^6 - 792*a^7*b^5*c^13*d^7 + 495*a^8*b^4*c^12*d^8 - 220*a^9*b^3*c^11*d^9 + 66*a^10*b^2*c^10*d^10 - 12*a*b^11*c^19*d)))*(-(194481*a^8*d^11 + 35153041*b^8*c^8*d^3 - 120524712*a*b^7*c^7*d^4 + 193309116*a^2*b^6*c^6*d^5 - 187159896*a^3*b^5*c^5*d^6 + 119186694*a^4*b^4*c^4*d^7 - 51043608*a^5*b^3*c^3*d^8 + 14378364*a^6*b^2*c^2*d^9 - 2444904*a^7*b*c*d^10)/(16777216*b^12*c^23 + 16777216*a^12*c^11*d^12 - 201326592*a^11*b*c^12*d^11 + 1107296256*a^2*b^10*c^21*d^2 - 3690987520*a^3*b^9*c^20*d^3 + 8304721920*a^4*b^8*c^19*d^4 - 13287555072*a^5*b^7*c^18*d^5 + 15502147584*a^6*b^6*c^17*d^6 - 13287555072*a^7*b^5*c^16*d^7 + 8304721920*a^8*b^4*c^15*d^8 - 3690987520*a^9*b^3*c^14*d^9 + 1107296256*a^10*b^2*c^13*d^10 - 201326592*a*b^11*c^22*d))^(1/4)))*(-(194481*a^8*d^11 + 35153041*b^8*c^8*d^3 - 120524712*a*b^7*c^7*d^4 + 193309116*a^2*b^6*c^6*d^5 - 187159896*a^3*b^5*c^5*d^6 + 119186694*a^4*b^4*c^4*d^7 - 51043608*a^5*b^3*c^3*d^8 + 14378364*a^6*b^2*c^2*d^9 - 2444904*a^7*b*c*d^10)/(16777216*b^12*c^23 + 16777216*a^12*c^11*d^12 - 201326592*a^11*b*c^12*d^11 + 1107296256*a^2*b^10*c^21*d^2 - 3690987520*a^3*b^9*c^20*d^3 + 8304721920*a^4*b^8*c^19*d^4 - 13287555072*a^5*b^7*c^18*d^5 + 15502147584*a^6*b^6*c^17*d^6 - 13287555072*a^7*b^5*c^16*d^7 + 8304721920*a^8*b^4*c^15*d^8 - 3690987520*a^9*b^3*c^14*d^9 + 1107296256*a^10*b^2*c^13*d^10 - 201326592*a*b^11*c^22*d))^(1/4)","B"
485,1,33717,681,10.854918,"\text{Not used}","int(1/(x^(3/2)*(a + b*x^2)*(c + d*x^2)^3),x)","\mathrm{atan}\left(\frac{a^{21}\,c^{16}\,d^{20}\,\sqrt{x}\,{\left(-\frac{4100625\,a^8\,d^{13}-47385000\,a^7\,b\,c\,d^{12}+247981500\,a^6\,b^2\,c^2\,d^{11}-765063000\,a^5\,b^3\,c^3\,d^{10}+1519673350\,a^4\,b^4\,c^4\,d^9-1989163800\,a^3\,b^5\,c^5\,d^8+1676354940\,a^2\,b^6\,c^6\,d^7-832838760\,a\,b^7\,c^7\,d^6+187388721\,b^8\,c^8\,d^5}{16777216\,a^{12}\,c^{13}\,d^{12}-201326592\,a^{11}\,b\,c^{14}\,d^{11}+1107296256\,a^{10}\,b^2\,c^{15}\,d^{10}-3690987520\,a^9\,b^3\,c^{16}\,d^9+8304721920\,a^8\,b^4\,c^{17}\,d^8-13287555072\,a^7\,b^5\,c^{18}\,d^7+15502147584\,a^6\,b^6\,c^{19}\,d^6-13287555072\,a^5\,b^7\,c^{20}\,d^5+8304721920\,a^4\,b^8\,c^{21}\,d^4-3690987520\,a^3\,b^9\,c^{22}\,d^3+1107296256\,a^2\,b^{10}\,c^{23}\,d^2-201326592\,a\,b^{11}\,c^{24}\,d+16777216\,b^{12}\,c^{25}}\right)}^{5/4}\,2174327193600{}\mathrm{i}+b^{17}\,c^{20}\,d^4\,\sqrt{x}\,{\left(-\frac{4100625\,a^8\,d^{13}-47385000\,a^7\,b\,c\,d^{12}+247981500\,a^6\,b^2\,c^2\,d^{11}-765063000\,a^5\,b^3\,c^3\,d^{10}+1519673350\,a^4\,b^4\,c^4\,d^9-1989163800\,a^3\,b^5\,c^5\,d^8+1676354940\,a^2\,b^6\,c^6\,d^7-832838760\,a\,b^7\,c^7\,d^6+187388721\,b^8\,c^8\,d^5}{16777216\,a^{12}\,c^{13}\,d^{12}-201326592\,a^{11}\,b\,c^{14}\,d^{11}+1107296256\,a^{10}\,b^2\,c^{15}\,d^{10}-3690987520\,a^9\,b^3\,c^{16}\,d^9+8304721920\,a^8\,b^4\,c^{17}\,d^8-13287555072\,a^7\,b^5\,c^{18}\,d^7+15502147584\,a^6\,b^6\,c^{19}\,d^6-13287555072\,a^5\,b^7\,c^{20}\,d^5+8304721920\,a^4\,b^8\,c^{21}\,d^4-3690987520\,a^3\,b^9\,c^{22}\,d^3+1107296256\,a^2\,b^{10}\,c^{23}\,d^2-201326592\,a\,b^{11}\,c^{24}\,d+16777216\,b^{12}\,c^{25}}\right)}^{1/4}\,918653239296{}\mathrm{i}+a\,b^{20}\,c^{36}\,\sqrt{x}\,{\left(-\frac{4100625\,a^8\,d^{13}-47385000\,a^7\,b\,c\,d^{12}+247981500\,a^6\,b^2\,c^2\,d^{11}-765063000\,a^5\,b^3\,c^3\,d^{10}+1519673350\,a^4\,b^4\,c^4\,d^9-1989163800\,a^3\,b^5\,c^5\,d^8+1676354940\,a^2\,b^6\,c^6\,d^7-832838760\,a\,b^7\,c^7\,d^6+187388721\,b^8\,c^8\,d^5}{16777216\,a^{12}\,c^{13}\,d^{12}-201326592\,a^{11}\,b\,c^{14}\,d^{11}+1107296256\,a^{10}\,b^2\,c^{15}\,d^{10}-3690987520\,a^9\,b^3\,c^{16}\,d^9+8304721920\,a^8\,b^4\,c^{17}\,d^8-13287555072\,a^7\,b^5\,c^{18}\,d^7+15502147584\,a^6\,b^6\,c^{19}\,d^6-13287555072\,a^5\,b^7\,c^{20}\,d^5+8304721920\,a^4\,b^8\,c^{21}\,d^4-3690987520\,a^3\,b^9\,c^{22}\,d^3+1107296256\,a^2\,b^{10}\,c^{23}\,d^2-201326592\,a\,b^{11}\,c^{24}\,d+16777216\,b^{12}\,c^{25}}\right)}^{5/4}\,1099511627776{}\mathrm{i}+a\,b^{16}\,c^{19}\,d^5\,\sqrt{x}\,{\left(-\frac{4100625\,a^8\,d^{13}-47385000\,a^7\,b\,c\,d^{12}+247981500\,a^6\,b^2\,c^2\,d^{11}-765063000\,a^5\,b^3\,c^3\,d^{10}+1519673350\,a^4\,b^4\,c^4\,d^9-1989163800\,a^3\,b^5\,c^5\,d^8+1676354940\,a^2\,b^6\,c^6\,d^7-832838760\,a\,b^7\,c^7\,d^6+187388721\,b^8\,c^8\,d^5}{16777216\,a^{12}\,c^{13}\,d^{12}-201326592\,a^{11}\,b\,c^{14}\,d^{11}+1107296256\,a^{10}\,b^2\,c^{15}\,d^{10}-3690987520\,a^9\,b^3\,c^{16}\,d^9+8304721920\,a^8\,b^4\,c^{17}\,d^8-13287555072\,a^7\,b^5\,c^{18}\,d^7+15502147584\,a^6\,b^6\,c^{19}\,d^6-13287555072\,a^5\,b^7\,c^{20}\,d^5+8304721920\,a^4\,b^8\,c^{21}\,d^4-3690987520\,a^3\,b^9\,c^{22}\,d^3+1107296256\,a^2\,b^{10}\,c^{23}\,d^2-201326592\,a\,b^{11}\,c^{24}\,d+16777216\,b^{12}\,c^{25}}\right)}^{1/4}\,10239255576576{}\mathrm{i}-a^2\,b^{19}\,c^{35}\,d\,\sqrt{x}\,{\left(-\frac{4100625\,a^8\,d^{13}-47385000\,a^7\,b\,c\,d^{12}+247981500\,a^6\,b^2\,c^2\,d^{11}-765063000\,a^5\,b^3\,c^3\,d^{10}+1519673350\,a^4\,b^4\,c^4\,d^9-1989163800\,a^3\,b^5\,c^5\,d^8+1676354940\,a^2\,b^6\,c^6\,d^7-832838760\,a\,b^7\,c^7\,d^6+187388721\,b^8\,c^8\,d^5}{16777216\,a^{12}\,c^{13}\,d^{12}-201326592\,a^{11}\,b\,c^{14}\,d^{11}+1107296256\,a^{10}\,b^2\,c^{15}\,d^{10}-3690987520\,a^9\,b^3\,c^{16}\,d^9+8304721920\,a^8\,b^4\,c^{17}\,d^8-13287555072\,a^7\,b^5\,c^{18}\,d^7+15502147584\,a^6\,b^6\,c^{19}\,d^6-13287555072\,a^5\,b^7\,c^{20}\,d^5+8304721920\,a^4\,b^8\,c^{21}\,d^4-3690987520\,a^3\,b^9\,c^{22}\,d^3+1107296256\,a^2\,b^{10}\,c^{23}\,d^2-201326592\,a\,b^{11}\,c^{24}\,d+16777216\,b^{12}\,c^{25}}\right)}^{5/4}\,13194139533312{}\mathrm{i}-a^{20}\,b\,c^{17}\,d^{19}\,\sqrt{x}\,{\left(-\frac{4100625\,a^8\,d^{13}-47385000\,a^7\,b\,c\,d^{12}+247981500\,a^6\,b^2\,c^2\,d^{11}-765063000\,a^5\,b^3\,c^3\,d^{10}+1519673350\,a^4\,b^4\,c^4\,d^9-1989163800\,a^3\,b^5\,c^5\,d^8+1676354940\,a^2\,b^6\,c^6\,d^7-832838760\,a\,b^7\,c^7\,d^6+187388721\,b^8\,c^8\,d^5}{16777216\,a^{12}\,c^{13}\,d^{12}-201326592\,a^{11}\,b\,c^{14}\,d^{11}+1107296256\,a^{10}\,b^2\,c^{15}\,d^{10}-3690987520\,a^9\,b^3\,c^{16}\,d^9+8304721920\,a^8\,b^4\,c^{17}\,d^8-13287555072\,a^7\,b^5\,c^{18}\,d^7+15502147584\,a^6\,b^6\,c^{19}\,d^6-13287555072\,a^5\,b^7\,c^{20}\,d^5+8304721920\,a^4\,b^8\,c^{21}\,d^4-3690987520\,a^3\,b^9\,c^{22}\,d^3+1107296256\,a^2\,b^{10}\,c^{23}\,d^2-201326592\,a\,b^{11}\,c^{24}\,d+16777216\,b^{12}\,c^{25}}\right)}^{5/4}\,38654705664000{}\mathrm{i}-a^2\,b^{15}\,c^{18}\,d^6\,\sqrt{x}\,{\left(-\frac{4100625\,a^8\,d^{13}-47385000\,a^7\,b\,c\,d^{12}+247981500\,a^6\,b^2\,c^2\,d^{11}-765063000\,a^5\,b^3\,c^3\,d^{10}+1519673350\,a^4\,b^4\,c^4\,d^9-1989163800\,a^3\,b^5\,c^5\,d^8+1676354940\,a^2\,b^6\,c^6\,d^7-832838760\,a\,b^7\,c^7\,d^6+187388721\,b^8\,c^8\,d^5}{16777216\,a^{12}\,c^{13}\,d^{12}-201326592\,a^{11}\,b\,c^{14}\,d^{11}+1107296256\,a^{10}\,b^2\,c^{15}\,d^{10}-3690987520\,a^9\,b^3\,c^{16}\,d^9+8304721920\,a^8\,b^4\,c^{17}\,d^8-13287555072\,a^7\,b^5\,c^{18}\,d^7+15502147584\,a^6\,b^6\,c^{19}\,d^6-13287555072\,a^5\,b^7\,c^{20}\,d^5+8304721920\,a^4\,b^8\,c^{21}\,d^4-3690987520\,a^3\,b^9\,c^{22}\,d^3+1107296256\,a^2\,b^{10}\,c^{23}\,d^2-201326592\,a\,b^{11}\,c^{24}\,d+16777216\,b^{12}\,c^{25}}\right)}^{1/4}\,52740124835840{}\mathrm{i}+a^3\,b^{14}\,c^{17}\,d^7\,\sqrt{x}\,{\left(-\frac{4100625\,a^8\,d^{13}-47385000\,a^7\,b\,c\,d^{12}+247981500\,a^6\,b^2\,c^2\,d^{11}-765063000\,a^5\,b^3\,c^3\,d^{10}+1519673350\,a^4\,b^4\,c^4\,d^9-1989163800\,a^3\,b^5\,c^5\,d^8+1676354940\,a^2\,b^6\,c^6\,d^7-832838760\,a\,b^7\,c^7\,d^6+187388721\,b^8\,c^8\,d^5}{16777216\,a^{12}\,c^{13}\,d^{12}-201326592\,a^{11}\,b\,c^{14}\,d^{11}+1107296256\,a^{10}\,b^2\,c^{15}\,d^{10}-3690987520\,a^9\,b^3\,c^{16}\,d^9+8304721920\,a^8\,b^4\,c^{17}\,d^8-13287555072\,a^7\,b^5\,c^{18}\,d^7+15502147584\,a^6\,b^6\,c^{19}\,d^6-13287555072\,a^5\,b^7\,c^{20}\,d^5+8304721920\,a^4\,b^8\,c^{21}\,d^4-3690987520\,a^3\,b^9\,c^{22}\,d^3+1107296256\,a^2\,b^{10}\,c^{23}\,d^2-201326592\,a\,b^{11}\,c^{24}\,d+16777216\,b^{12}\,c^{25}}\right)}^{1/4}\,109076423639040{}\mathrm{i}-a^4\,b^{13}\,c^{16}\,d^8\,\sqrt{x}\,{\left(-\frac{4100625\,a^8\,d^{13}-47385000\,a^7\,b\,c\,d^{12}+247981500\,a^6\,b^2\,c^2\,d^{11}-765063000\,a^5\,b^3\,c^3\,d^{10}+1519673350\,a^4\,b^4\,c^4\,d^9-1989163800\,a^3\,b^5\,c^5\,d^8+1676354940\,a^2\,b^6\,c^6\,d^7-832838760\,a\,b^7\,c^7\,d^6+187388721\,b^8\,c^8\,d^5}{16777216\,a^{12}\,c^{13}\,d^{12}-201326592\,a^{11}\,b\,c^{14}\,d^{11}+1107296256\,a^{10}\,b^2\,c^{15}\,d^{10}-3690987520\,a^9\,b^3\,c^{16}\,d^9+8304721920\,a^8\,b^4\,c^{17}\,d^8-13287555072\,a^7\,b^5\,c^{18}\,d^7+15502147584\,a^6\,b^6\,c^{19}\,d^6-13287555072\,a^5\,b^7\,c^{20}\,d^5+8304721920\,a^4\,b^8\,c^{21}\,d^4-3690987520\,a^3\,b^9\,c^{22}\,d^3+1107296256\,a^2\,b^{10}\,c^{23}\,d^2-201326592\,a\,b^{11}\,c^{24}\,d+16777216\,b^{12}\,c^{25}}\right)}^{1/4}\,130225943347200{}\mathrm{i}+a^5\,b^{12}\,c^{15}\,d^9\,\sqrt{x}\,{\left(-\frac{4100625\,a^8\,d^{13}-47385000\,a^7\,b\,c\,d^{12}+247981500\,a^6\,b^2\,c^2\,d^{11}-765063000\,a^5\,b^3\,c^3\,d^{10}+1519673350\,a^4\,b^4\,c^4\,d^9-1989163800\,a^3\,b^5\,c^5\,d^8+1676354940\,a^2\,b^6\,c^6\,d^7-832838760\,a\,b^7\,c^7\,d^6+187388721\,b^8\,c^8\,d^5}{16777216\,a^{12}\,c^{13}\,d^{12}-201326592\,a^{11}\,b\,c^{14}\,d^{11}+1107296256\,a^{10}\,b^2\,c^{15}\,d^{10}-3690987520\,a^9\,b^3\,c^{16}\,d^9+8304721920\,a^8\,b^4\,c^{17}\,d^8-13287555072\,a^7\,b^5\,c^{18}\,d^7+15502147584\,a^6\,b^6\,c^{19}\,d^6-13287555072\,a^5\,b^7\,c^{20}\,d^5+8304721920\,a^4\,b^8\,c^{21}\,d^4-3690987520\,a^3\,b^9\,c^{22}\,d^3+1107296256\,a^2\,b^{10}\,c^{23}\,d^2-201326592\,a\,b^{11}\,c^{24}\,d+16777216\,b^{12}\,c^{25}}\right)}^{1/4}\,99593312665600{}\mathrm{i}-a^6\,b^{11}\,c^{14}\,d^{10}\,\sqrt{x}\,{\left(-\frac{4100625\,a^8\,d^{13}-47385000\,a^7\,b\,c\,d^{12}+247981500\,a^6\,b^2\,c^2\,d^{11}-765063000\,a^5\,b^3\,c^3\,d^{10}+1519673350\,a^4\,b^4\,c^4\,d^9-1989163800\,a^3\,b^5\,c^5\,d^8+1676354940\,a^2\,b^6\,c^6\,d^7-832838760\,a\,b^7\,c^7\,d^6+187388721\,b^8\,c^8\,d^5}{16777216\,a^{12}\,c^{13}\,d^{12}-201326592\,a^{11}\,b\,c^{14}\,d^{11}+1107296256\,a^{10}\,b^2\,c^{15}\,d^{10}-3690987520\,a^9\,b^3\,c^{16}\,d^9+8304721920\,a^8\,b^4\,c^{17}\,d^8-13287555072\,a^7\,b^5\,c^{18}\,d^7+15502147584\,a^6\,b^6\,c^{19}\,d^6-13287555072\,a^5\,b^7\,c^{20}\,d^5+8304721920\,a^4\,b^8\,c^{21}\,d^4-3690987520\,a^3\,b^9\,c^{22}\,d^3+1107296256\,a^2\,b^{10}\,c^{23}\,d^2-201326592\,a\,b^{11}\,c^{24}\,d+16777216\,b^{12}\,c^{25}}\right)}^{1/4}\,50139168768000{}\mathrm{i}+a^7\,b^{10}\,c^{13}\,d^{11}\,\sqrt{x}\,{\left(-\frac{4100625\,a^8\,d^{13}-47385000\,a^7\,b\,c\,d^{12}+247981500\,a^6\,b^2\,c^2\,d^{11}-765063000\,a^5\,b^3\,c^3\,d^{10}+1519673350\,a^4\,b^4\,c^4\,d^9-1989163800\,a^3\,b^5\,c^5\,d^8+1676354940\,a^2\,b^6\,c^6\,d^7-832838760\,a\,b^7\,c^7\,d^6+187388721\,b^8\,c^8\,d^5}{16777216\,a^{12}\,c^{13}\,d^{12}-201326592\,a^{11}\,b\,c^{14}\,d^{11}+1107296256\,a^{10}\,b^2\,c^{15}\,d^{10}-3690987520\,a^9\,b^3\,c^{16}\,d^9+8304721920\,a^8\,b^4\,c^{17}\,d^8-13287555072\,a^7\,b^5\,c^{18}\,d^7+15502147584\,a^6\,b^6\,c^{19}\,d^6-13287555072\,a^5\,b^7\,c^{20}\,d^5+8304721920\,a^4\,b^8\,c^{21}\,d^4-3690987520\,a^3\,b^9\,c^{22}\,d^3+1107296256\,a^2\,b^{10}\,c^{23}\,d^2-201326592\,a\,b^{11}\,c^{24}\,d+16777216\,b^{12}\,c^{25}}\right)}^{1/4}\,16251715584000{}\mathrm{i}-a^8\,b^9\,c^{12}\,d^{12}\,\sqrt{x}\,{\left(-\frac{4100625\,a^8\,d^{13}-47385000\,a^7\,b\,c\,d^{12}+247981500\,a^6\,b^2\,c^2\,d^{11}-765063000\,a^5\,b^3\,c^3\,d^{10}+1519673350\,a^4\,b^4\,c^4\,d^9-1989163800\,a^3\,b^5\,c^5\,d^8+1676354940\,a^2\,b^6\,c^6\,d^7-832838760\,a\,b^7\,c^7\,d^6+187388721\,b^8\,c^8\,d^5}{16777216\,a^{12}\,c^{13}\,d^{12}-201326592\,a^{11}\,b\,c^{14}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2}\,c^{42}\,d^{30}-910688569282163512962973696\,a^{37}\,b^{13}\,c^{43}\,d^{29}+2041552487767277748019527680\,a^{36}\,b^{14}\,c^{44}\,d^{28}-3963723814398261058758246400\,a^{35}\,b^{15}\,c^{45}\,d^{27}+6703228082495101562834124800\,a^{34}\,b^{16}\,c^{46}\,d^{26}-9915254214005035782929121280\,a^{33}\,b^{17}\,c^{47}\,d^{25}+12864666662378251575193763840\,a^{32}\,b^{18}\,c^{48}\,d^{24}-14666481047173052905774120960\,a^{31}\,b^{19}\,c^{49}\,d^{23}+14704312650164876038740377600\,a^{30}\,b^{20}\,c^{50}\,d^{22}-12966109559707844614920601600\,a^{29}\,b^{21}\,c^{51}\,d^{21}+10053745593205095687740456960\,a^{28}\,b^{22}\,c^{52}\,d^{20}-6855830429358878767993323520\,a^{27}\,b^{23}\,c^{53}\,d^{19}+4119286127977833519707586560\,a^{26}\,b^{24}\,c^{54}\,d^{18}-2194458800584304697435750400\,a^{25}\,b^{25}\,c^{55}\,d^{17}+1052056219870198056039219200\,a^{24}\,b^{26}\,c^{56}\,d^{16}-466650996519299420897935360\,a^{23}\,b^{27}\,c^{57}\,d^{15}+198753207063509910306160640\,a^{22}\,b^{28}\,c^{58}\,d^{14}-83405832293258492567879680\,a^{21}\,b^{29}\,c^{59}\,d^{13}+34096448785847177707520000\,a^{20}\,b^{30}\,c^{60}\,d^{12}-12966583542852067073720320\,a^{19}\,b^{31}\,c^{61}\,d^{11}+4341880678999181785825280\,a^{18}\,b^{32}\,c^{62}\,d^{10}-1220386399802376518107136\,a^{17}\,b^{33}\,c^{63}\,d^9+276025423003154095538176\,a^{16}\,b^{34}\,c^{64}\,d^8-47961534591644834201600\,a^{15}\,b^{35}\,c^{65}\,d^7+5995191823955604275200\,a^{14}\,b^{36}\,c^{66}\,d^6-479615345916448342016\,a^{13}\,b^{37}\,c^{67}\,d^5+18446744073709551616\,a^{12}\,b^{38}\,c^{68}\,d^4\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}\right)\,{\left(-\frac{4100625\,a^8\,d^{13}-47385000\,a^7\,b\,c\,d^{12}+247981500\,a^6\,b^2\,c^2\,d^{11}-765063000\,a^5\,b^3\,c^3\,d^{10}+1519673350\,a^4\,b^4\,c^4\,d^9-1989163800\,a^3\,b^5\,c^5\,d^8+1676354940\,a^2\,b^6\,c^6\,d^7-832838760\,a\,b^7\,c^7\,d^6+187388721\,b^8\,c^8\,d^5}{16777216\,a^{12}\,c^{13}\,d^{12}-201326592\,a^{11}\,b\,c^{14}\,d^{11}+1107296256\,a^{10}\,b^2\,c^{15}\,d^{10}-3690987520\,a^9\,b^3\,c^{16}\,d^9+8304721920\,a^8\,b^4\,c^{17}\,d^8-13287555072\,a^7\,b^5\,c^{18}\,d^7+15502147584\,a^6\,b^6\,c^{19}\,d^6-13287555072\,a^5\,b^7\,c^{20}\,d^5+8304721920\,a^4\,b^8\,c^{21}\,d^4-3690987520\,a^3\,b^9\,c^{22}\,d^3+1107296256\,a^2\,b^{10}\,c^{23}\,d^2-201326592\,a\,b^{11}\,c^{24}\,d+16777216\,b^{12}\,c^{25}}\right)}^{1/4}","Not 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8605396720616721741816791040*a^30*b^19*c^46*d^23 + 7767500088979055902405427200*a^31*b^18*c^45*d^24 - 6135496566696171932913500160*a^32*b^17*c^44*d^25 + 4236422046382466798589050880*a^33*b^16*c^43*d^26 - 2550980661067485441771438080*a^34*b^15*c^42*d^27 + 1334575022384247271808040960*a^35*b^14*c^41*d^28 - 603343239457650202481000448*a^36*b^13*c^40*d^29 + 233967123641003163353350144*a^37*b^12*c^39*d^30 - 77049527429528415176228864*a^38*b^11*c^38*d^31 + 21258749850480450394390528*a^39*b^10*c^37*d^32 - 4823899363819901975265280*a^40*b^9*c^36*d^33 + 876898617974708020183040*a^41*b^8*c^35*d^34 - 122811796684756379238400*a^42*b^7*c^34*d^35 + 12444332416601319014400*a^43*b^6*c^33*d^36 - 812231229670686720000*a^44*b^5*c^32*d^37 + 25649407252758528000*a^45*b^4*c^31*d^38)*1i)*1i - 149684329919262228480*a^11*b^34*c^48*d^9 + 2374404370680061624320*a^12*b^33*c^47*d^10 - 17808722627439624192000*a^13*b^32*c^46*d^11 + 83960295795175519682560*a^14*b^31*c^45*d^12 - 278998813302985850880000*a^15*b^30*c^44*d^13 + 694438771802419400540160*a^16*b^29*c^43*d^14 - 1342951722708271932375040*a^17*b^28*c^42*d^15 + 2065391322938120916172800*a^18*b^27*c^41*d^16 - 2564218746215699966853120*a^19*b^26*c^40*d^17 + 2593338871410901332787200*a^20*b^25*c^39*d^18 - 2146065846150812380692480*a^21*b^24*c^38*d^19 + 1453625441569727022366720*a^22*b^23*c^37*d^20 - 802881124954933087436800*a^23*b^22*c^36*d^21 + 358581985606139180482560*a^24*b^21*c^35*d^22 - 127660361818125316915200*a^25*b^20*c^34*d^23 + 35417419405750750412800*a^26*b^19*c^33*d^24 - 7386837561454362624000*a^27*b^18*c^32*d^25 + 1090533977896255488000*a^28*b^17*c^31*d^26 - 101695892037304320000*a^29*b^16*c^30*d^27 + 4508684868648960000*a^30*b^15*c^29*d^28))*(-(4100625*a^8*d^13 + 187388721*b^8*c^8*d^5 - 832838760*a*b^7*c^7*d^6 + 1676354940*a^2*b^6*c^6*d^7 - 1989163800*a^3*b^5*c^5*d^8 + 1519673350*a^4*b^4*c^4*d^9 - 765063000*a^5*b^3*c^3*d^10 + 247981500*a^6*b^2*c^2*d^11 - 47385000*a^7*b*c*d^12)/(16777216*b^12*c^25 + 16777216*a^12*c^13*d^12 - 201326592*a^11*b*c^14*d^11 + 1107296256*a^2*b^10*c^23*d^2 - 3690987520*a^3*b^9*c^22*d^3 + 8304721920*a^4*b^8*c^21*d^4 - 13287555072*a^5*b^7*c^20*d^5 + 15502147584*a^6*b^6*c^19*d^6 - 13287555072*a^7*b^5*c^18*d^7 + 8304721920*a^8*b^4*c^17*d^8 - 3690987520*a^9*b^3*c^16*d^9 + 1107296256*a^10*b^2*c^15*d^10 - 201326592*a*b^11*c^24*d))^(1/4)","B"
486,1,44524,681,10.807543,"\text{Not used}","int(1/(x^(5/2)*(a + b*x^2)*(c + d*x^2)^3),x)","\mathrm{atan}\left(\frac{{\left(-\frac{35153041\,a^8\,d^{15}-383487720\,a^7\,b\,c\,d^{14}+1870125180\,a^6\,b^2\,c^2\,d^{13}-5317666200\,a^5\,b^3\,c^3\,d^{12}+9636798150\,a^4\,b^4\,c^4\,d^{11}-11394999000\,a^3\,b^5\,c^5\,d^{10}+8587309500\,a^2\,b^6\,c^6\,d^9-3773385000\,a\,b^7\,c^7\,d^8+741200625\,b^8\,c^8\,d^7}{16777216\,a^{12}\,c^{15}\,d^{12}-201326592\,a^{11}\,b\,c^{16}\,d^{11}+1107296256\,a^{10}\,b^2\,c^{17}\,d^{10}-3690987520\,a^9\,b^3\,c^{18}\,d^9+8304721920\,a^8\,b^4\,c^{19}\,d^8-13287555072\,a^7\,b^5\,c^{20}\,d^7+15502147584\,a^6\,b^6\,c^{21}\,d^6-13287555072\,a^5\,b^7\,c^{22}\,d^5+8304721920\,a^4\,b^8\,c^{23}\,d^4-3690987520\,a^3\,b^9\,c^{24}\,d^3+1107296256\,a^2\,b^{10}\,c^{25}\,d^2-201326592\,a\,b^{11}\,c^{26}\,d+16777216\,b^{12}\,c^{27}}\right)}^{1/4}\,\left({\left(-\frac{35153041\,a^8\,d^{15}-383487720\,a^7\,b\,c\,d^{14}+1870125180\,a^6\,b^2\,c^2\,d^{13}-5317666200\,a^5\,b^3\,c^3\,d^{12}+9636798150\,a^4\,b^4\,c^4\,d^{11}-11394999000\,a^3\,b^5\,c^5\,d^{10}+8587309500\,a^2\,b^6\,c^6\,d^9-3773385000\,a\,b^7\,c^7\,d^8+741200625\,b^8\,c^8\,d^7}{16777216\,a^{12}\,c^{15}\,d^{12}-201326592\,a^{11}\,b\,c^{16}\,d^{11}+1107296256\,a^{10}\,b^2\,c^{17}\,d^{10}-3690987520\,a^9\,b^3\,c^{18}\,d^9+8304721920\,a^8\,b^4\,c^{19}\,d^8-13287555072\,a^7\,b^5\,c^{20}\,d^7+15502147584\,a^6\,b^6\,c^{21}\,d^6-13287555072\,a^5\,b^7\,c^{22}\,d^5+8304721920\,a^4\,b^8\,c^{23}\,d^4-3690987520\,a^3\,b^9\,c^{24}\,d^3+1107296256\,a^2\,b^{10}\,c^{25}\,d^2-201326592\,a\,b^{11}\,c^{26}\,d+16777216\,b^{12}\,c^{27}}\right)}^{1/4}\,\left({\left(-\frac{35153041\,a^8\,d^{15}-383487720\,a^7\,b\,c\,d^{14}+1870125180\,a^6\,b^2\,c^2\,d^{13}-5317666200\,a^5\,b^3\,c^3\,d^{12}+9636798150\,a^4\,b^4\,c^4\,d^{11}-11394999000\,a^3\,b^5\,c^5\,d^{10}+8587309500\,a^2\,b^6\,c^6\,d^9-3773385000\,a\,b^7\,c^7\,d^8+741200625\,b^8\,c^8\,d^7}{16777216\,a^{12}\,c^{15}\,d^{12}-201326592\,a^{11}\,b\,c^{16}\,d^{11}+1107296256\,a^{10}\,b^2\,c^{17}\,d^{10}-3690987520\,a^9\,b^3\,c^{18}\,d^9+8304721920\,a^8\,b^4\,c^{19}\,d^8-13287555072\,a^7\,b^5\,c^{20}\,d^7+15502147584\,a^6\,b^6\,c^{21}\,d^6-13287555072\,a^5\,b^7\,c^{22}\,d^5+8304721920\,a^4\,b^8\,c^{23}\,d^4-3690987520\,a^3\,b^9\,c^{24}\,d^3+1107296256\,a^2\,b^{10}\,c^{25}\,d^2-201326592\,a\,b^{11}\,c^{26}\,d+16777216\,b^{12}\,c^{27}}\right)}^{3/4}\,\left(\sqrt{x}\,\left(106807368762718683136\,a^{46}\,b^4\,c^{33}\,d^{39}-3359577235627333124096\,a^{45}\,b^5\,c^{34}\,d^{38}+51111802530990496153600\,a^{44}\,b^6\,c^{35}\,d^{37}-500844593983932480880640\,a^{43}\,b^7\,c^{36}\,d^{36}+3551400405635812871372800\,a^{42}\,b^8\,c^{37}\,d^{35}-19409595119210898894356480\,a^{41}\,b^9\,c^{38}\,d^{34}+85038075959446046066606080\,a^{40}\,b^{10}\,c^{39}\,d^{33}-306693733103726739901644800\,a^{39}\,b^{11}\,c^{40}\,d^{32}+927828632312674738870681600\,a^{38}\,b^{12}\,c^{41}\,d^{31}-2387248399405916166169821184\,a^{37}\,b^{13}\,c^{42}\,d^{30}+5278011312905736232783314944\,a^{36}\,b^{14}\,c^{43}\,d^{29}-10105200492115418262179676160\,a^{35}\,b^{15}\,c^{44}\,d^{28}+16850754961433442876234137600\,a^{34}\,b^{16}\,c^{45}\,d^{27}-24575140799491012895231180800\,a^{33}\,b^{17}\,c^{46}\,d^{26}+31433146498544749041648926720\,a^{32}\,b^{18}\,c^{47}\,d^{25}-35316718238336158489724846080\,a^{31}\,b^{19}\,c^{48}\,d^{24}+34870163031766389952882933760\,a^{30}\,b^{20}\,c^{49}\,d^{23}-30231538828274701475145318400\,a^{29}\,b^{21}\,c^{50}\,d^{22}+22962658463246519625580544000\,a^{28}\,b^{22}\,c^{51}\,d^{21}-15215326043975142249374679040\,a^{27}\,b^{23}\,c^{52}\,d^{20}+8727322757849829186700574720\,a^{26}\,b^{24}\,c^{53}\,d^{19}-4269437167365872814842183680\,a^{25}\,b^{25}\,c^{54}\,d^{18}+1723753001020797184743833600\,a^{24}\,b^{26}\,c^{55}\,d^{17}-523234066593179210717593600\,a^{23}\,b^{27}\,c^{56}\,d^{16}+72781112360087761599856640\,a^{22}\,b^{28}\,c^{57}\,d^{15}+43611606538557895133364224\,a^{21}\,b^{29}\,c^{58}\,d^{14}-46637619173392487079215104\,a^{20}\,b^{30}\,c^{59}\,d^{13}+27104869321333056471040000\,a^{19}\,b^{31}\,c^{60}\,d^{12}-11941164077799654041845760\,a^{18}\,b^{32}\,c^{61}\,d^{11}+4232993998288506144686080\,a^{17}\,b^{33}\,c^{62}\,d^{10}-1212936383169193658286080\,a^{16}\,b^{34}\,c^{63}\,d^9+275778823901957796659200\,a^{15}\,b^{35}\,c^{64}\,d^8-47961534591644834201600\,a^{14}\,b^{36}\,c^{65}\,d^7+5995191823955604275200\,a^{13}\,b^{37}\,c^{66}\,d^6-479615345916448342016\,a^{12}\,b^{38}\,c^{67}\,d^5+18446744073709551616\,a^{11}\,b^{39}\,c^{68}\,d^4\right)+{\left(-\frac{35153041\,a^8\,d^{15}-383487720\,a^7\,b\,c\,d^{14}+1870125180\,a^6\,b^2\,c^2\,d^{13}-5317666200\,a^5\,b^3\,c^3\,d^{12}+9636798150\,a^4\,b^4\,c^4\,d^{11}-11394999000\,a^3\,b^5\,c^5\,d^{10}+8587309500\,a^2\,b^6\,c^6\,d^9-3773385000\,a\,b^7\,c^7\,d^8+741200625\,b^8\,c^8\,d^7}{16777216\,a^{12}\,c^{15}\,d^{12}-201326592\,a^{11}\,b\,c^{16}\,d^{11}+1107296256\,a^{10}\,b^2\,c^{17}\,d^{10}-3690987520\,a^9\,b^3\,c^{18}\,d^9+8304721920\,a^8\,b^4\,c^{19}\,d^8-13287555072\,a^7\,b^5\,c^{20}\,d^7+15502147584\,a^6\,b^6\,c^{21}\,d^6-13287555072\,a^5\,b^7\,c^{22}\,d^5+8304721920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1080394184249474617790431232*a^22*b^25*c^43*d^20 + 1524725339928630029153468416*a^23*b^24*c^42*d^21 - 1834102420924176937716285440*a^24*b^23*c^41*d^22 + 1888062742223171008426147840*a^25*b^22*c^40*d^23 - 1666588213584359199850102784*a^26*b^21*c^39*d^24 + 1261562453800014779376467968*a^27*b^20*c^38*d^25 - 817528072151542384572760064*a^28*b^19*c^37*d^26 + 451847698934426396681830400*a^29*b^18*c^36*d^27 - 211721890947778234390937600*a^30*b^17*c^35*d^28 + 83366248780838000977248256*a^31*b^16*c^34*d^29 - 27241266624044306322685952*a^32*b^15*c^33*d^30 + 7257515800860571589410816*a^33*b^14*c^32*d^31 - 1536699518639901947985920*a^34*b^13*c^31*d^32 + 248859486128715197317120*a^35*b^12*c^30*d^33 - 28961642042172523937792*a^36*b^11*c^29*d^34 + 2157438443758953693184*a^37*b^10*c^28*d^35 - 77302354662372933632*a^38*b^9*c^27*d^36)*1i)*1i - (-b^15/(16*a^19*d^12 + 16*a^7*b^12*c^12 - 192*a^8*b^11*c^11*d + 1056*a^9*b^10*c^10*d^2 - 3520*a^10*b^9*c^9*d^3 + 7920*a^11*b^8*c^8*d^4 - 12672*a^12*b^7*c^7*d^5 + 14784*a^13*b^6*c^6*d^6 - 12672*a^14*b^5*c^5*d^7 + 7920*a^15*b^4*c^4*d^8 - 3520*a^16*b^3*c^3*d^9 + 1056*a^17*b^2*c^2*d^10 - 192*a^18*b*c*d^11))^(1/4)*(x^(1/2)*(30652624963790438400*a^9*b^37*c^51*d^9 - 507161613037259980800*a^10*b^36*c^50*d^10 + 4774956969550613053440*a^11*b^35*c^49*d^11 - 34948190471081762488320*a^12*b^34*c^48*d^12 + 208409962786483628670976*a^13*b^33*c^47*d^13 - 990271368055602664177664*a^14*b^32*c^46*d^14 + 3711631588079120800546816*a^15*b^31*c^45*d^15 - 11050795179720929846493184*a^16*b^30*c^44*d^16 + 26487755718620581216649216*a^17*b^29*c^43*d^17 - 51805174836472540920020992*a^18*b^28*c^42*d^18 + 83617663209148864427720704*a^19*b^27*c^41*d^19 - 112350430315654120415952896*a^20*b^26*c^40*d^20 + 126417217514830317658046464*a^21*b^25*c^39*d^21 - 119537906081128203174281216*a^22*b^24*c^38*d^22 + 95089864774620999552335872*a^23*b^23*c^37*d^23 - 63545506634457987380412416*a^24*b^22*c^36*d^24 + 35529578846146774008070144*a^25*b^21*c^35*d^25 - 16501565732136655819636736*a^26*b^20*c^34*d^26 + 6295808856090071441342464*a^27*b^19*c^33*d^27 - 1940847984249953081884672*a^28*b^18*c^32*d^28 + 471738031694568778366976*a^29*b^17*c^31*d^29 - 87073083559063809163264*a^30*b^16*c^30*d^30 + 11476570419434950230016*a^31*b^15*c^29*d^31 - 962765689885917446144*a^32*b^14*c^28*d^32 + 38651177331186466816*a^33*b^13*c^27*d^33) - (-b^15/(16*a^19*d^12 + 16*a^7*b^12*c^12 - 192*a^8*b^11*c^11*d + 1056*a^9*b^10*c^10*d^2 - 3520*a^10*b^9*c^9*d^3 + 7920*a^11*b^8*c^8*d^4 - 12672*a^12*b^7*c^7*d^5 + 14784*a^13*b^6*c^6*d^6 - 12672*a^14*b^5*c^5*d^7 + 7920*a^15*b^4*c^4*d^8 - 3520*a^16*b^3*c^3*d^9 + 1056*a^17*b^2*c^2*d^10 - 192*a^18*b*c*d^11))^(1/4)*((x^(1/2)*(18446744073709551616*a^11*b^39*c^68*d^4 - 479615345916448342016*a^12*b^38*c^67*d^5 + 5995191823955604275200*a^13*b^37*c^66*d^6 - 47961534591644834201600*a^14*b^36*c^65*d^7 + 275778823901957796659200*a^15*b^35*c^64*d^8 - 1212936383169193658286080*a^16*b^34*c^63*d^9 + 4232993998288506144686080*a^17*b^33*c^62*d^10 - 11941164077799654041845760*a^18*b^32*c^61*d^11 + 27104869321333056471040000*a^19*b^31*c^60*d^12 - 46637619173392487079215104*a^20*b^30*c^59*d^13 + 43611606538557895133364224*a^21*b^29*c^58*d^14 + 72781112360087761599856640*a^22*b^28*c^57*d^15 - 523234066593179210717593600*a^23*b^27*c^56*d^16 + 1723753001020797184743833600*a^24*b^26*c^55*d^17 - 4269437167365872814842183680*a^25*b^25*c^54*d^18 + 8727322757849829186700574720*a^26*b^24*c^53*d^19 - 15215326043975142249374679040*a^27*b^23*c^52*d^20 + 22962658463246519625580544000*a^28*b^22*c^51*d^21 - 30231538828274701475145318400*a^29*b^21*c^50*d^22 + 34870163031766389952882933760*a^30*b^20*c^49*d^23 - 35316718238336158489724846080*a^31*b^19*c^48*d^24 + 31433146498544749041648926720*a^32*b^18*c^47*d^25 - 24575140799491012895231180800*a^33*b^17*c^46*d^26 + 16850754961433442876234137600*a^34*b^16*c^45*d^27 - 10105200492115418262179676160*a^35*b^15*c^44*d^28 + 5278011312905736232783314944*a^36*b^14*c^43*d^29 - 2387248399405916166169821184*a^37*b^13*c^42*d^30 + 927828632312674738870681600*a^38*b^12*c^41*d^31 - 306693733103726739901644800*a^39*b^11*c^40*d^32 + 85038075959446046066606080*a^40*b^10*c^39*d^33 - 19409595119210898894356480*a^41*b^9*c^38*d^34 + 3551400405635812871372800*a^42*b^8*c^37*d^35 - 500844593983932480880640*a^43*b^7*c^36*d^36 + 51111802530990496153600*a^44*b^6*c^35*d^37 - 3359577235627333124096*a^45*b^5*c^34*d^38 + 106807368762718683136*a^46*b^4*c^33*d^39) + (-b^15/(16*a^19*d^12 + 16*a^7*b^12*c^12 - 192*a^8*b^11*c^11*d + 1056*a^9*b^10*c^10*d^2 - 3520*a^10*b^9*c^9*d^3 + 7920*a^11*b^8*c^8*d^4 - 12672*a^12*b^7*c^7*d^5 + 14784*a^13*b^6*c^6*d^6 - 12672*a^14*b^5*c^5*d^7 + 7920*a^15*b^4*c^4*d^8 - 3520*a^16*b^3*c^3*d^9 + 1056*a^17*b^2*c^2*d^10 - 192*a^18*b*c*d^11))^(1/4)*(36893488147419103232*a^13*b^38*c^71*d^4 - 1069911156275153993728*a^14*b^37*c^70*d^5 + 14978756187852155912192*a^15*b^36*c^69*d^6 - 134999037738929532960768*a^16*b^35*c^68*d^7 + 882016079904862321508352*a^17*b^34*c^67*d^8 - 4465630463459278708539392*a^18*b^33*c^66*d^9 + 18321125205332103390035968*a^19*b^32*c^65*d^10 - 63021545228377166868119552*a^20*b^31*c^64*d^11 + 187018029382071665408606208*a^21*b^30*c^63*d^12 - 490713180393588600090918912*a^22*b^29*c^62*d^13 + 1161438545048511890042388480*a^23*b^28*c^61*d^14 - 2512974056309066269898833920*a^24*b^27*c^60*d^15 + 4997541469898172697285754880*a^25*b^26*c^59*d^16 - 9119889428539397211967979520*a^26*b^25*c^58*d^17 + 15181544306461039744285409280*a^27*b^24*c^57*d^18 - 22888317982577902576352624640*a^28*b^23*c^56*d^19 + 31049708276802113763866050560*a^29*b^22*c^55*d^20 - 37706614244767692268335267840*a^30*b^21*c^54*d^21 + 40833216619792283792163471360*a^31*b^20*c^53*d^22 - 39312168062751093709382615040*a^32*b^19*c^52*d^23 + 33557805042801128843488788480*a^33*b^18*c^51*d^24 - 25329188887155786370693201920*a^34*b^17*c^50*d^25 + 16851463310911481777624186880*a^35*b^16*c^49*d^26 - 9843609097631363291959787520*a^36*b^15*c^48*d^27 + 5023816147465636127472353280*a^37*b^14*c^47*d^28 - 2226054577272365612261179392*a^38*b^13*c^46*d^29 + 849419752718963326077370368*a^39*b^12*c^45*d^30 - 276172923601113041340465152*a^40*b^11*c^44*d^31 + 75441341408208223215812608*a^41*b^10*c^43*d^32 - 16988052798101408932954112*a^42*b^9*c^42*d^33 + 3070410975444256772063232*a^43*b^8*c^41*d^34 - 428198505575496787427328*a^44*b^7*c^40*d^35 + 43254156088335077998592*a^45*b^6*c^39*d^36 - 2816587235754527162368*a^46*b^5*c^38*d^37 + 88774955854727217152*a^47*b^4*c^37*d^38)*1i)*(-b^15/(16*a^19*d^12 + 16*a^7*b^12*c^12 - 192*a^8*b^11*c^11*d + 1056*a^9*b^10*c^10*d^2 - 3520*a^10*b^9*c^9*d^3 + 7920*a^11*b^8*c^8*d^4 - 12672*a^12*b^7*c^7*d^5 + 14784*a^13*b^6*c^6*d^6 - 12672*a^14*b^5*c^5*d^7 + 7920*a^15*b^4*c^4*d^8 - 3520*a^16*b^3*c^3*d^9 + 1056*a^17*b^2*c^2*d^10 - 192*a^18*b*c*d^11))^(3/4)*1i + 11889503016258109440*a^9*b^38*c^56*d^7 - 217253646024352727040*a^10*b^37*c^55*d^8 + 1879766455667426066432*a^11*b^36*c^54*d^9 - 10237150327374383939584*a^12*b^35*c^53*d^10 + 37711511320670913953792*a^13*b^34*c^52*d^11 - 77353208427556875796480*a^14*b^33*c^51*d^12 - 127627238172719495249920*a^15*b^32*c^50*d^13 + 2130084466030987427446784*a^16*b^31*c^49*d^14 - 11885048527140028256616448*a^17*b^30*c^48*d^15 + 45690531361686842972831744*a^18*b^29*c^47*d^16 - 135851929384595950057553920*a^19*b^28*c^46*d^17 + 326376775711477371051704320*a^20*b^27*c^45*d^18 - 648353352496064059760705536*a^21*b^26*c^44*d^19 + 1080394184249474617790431232*a^22*b^25*c^43*d^20 - 1524725339928630029153468416*a^23*b^24*c^42*d^21 + 1834102420924176937716285440*a^24*b^23*c^41*d^22 - 1888062742223171008426147840*a^25*b^22*c^40*d^23 + 1666588213584359199850102784*a^26*b^21*c^39*d^24 - 1261562453800014779376467968*a^27*b^20*c^38*d^25 + 817528072151542384572760064*a^28*b^19*c^37*d^26 - 451847698934426396681830400*a^29*b^18*c^36*d^27 + 211721890947778234390937600*a^30*b^17*c^35*d^28 - 83366248780838000977248256*a^31*b^16*c^34*d^29 + 27241266624044306322685952*a^32*b^15*c^33*d^30 - 7257515800860571589410816*a^33*b^14*c^32*d^31 + 1536699518639901947985920*a^34*b^13*c^31*d^32 - 248859486128715197317120*a^35*b^12*c^30*d^33 + 28961642042172523937792*a^36*b^11*c^29*d^34 - 2157438443758953693184*a^37*b^10*c^28*d^35 + 77302354662372933632*a^38*b^9*c^27*d^36)*1i)*1i))*(-b^15/(16*a^19*d^12 + 16*a^7*b^12*c^12 - 192*a^8*b^11*c^11*d + 1056*a^9*b^10*c^10*d^2 - 3520*a^10*b^9*c^9*d^3 + 7920*a^11*b^8*c^8*d^4 - 12672*a^12*b^7*c^7*d^5 + 14784*a^13*b^6*c^6*d^6 - 12672*a^14*b^5*c^5*d^7 + 7920*a^15*b^4*c^4*d^8 - 3520*a^16*b^3*c^3*d^9 + 1056*a^17*b^2*c^2*d^10 - 192*a^18*b*c*d^11))^(1/4) - (2/(3*a*c) + (x^2*(121*a^2*d^3 + 64*b^2*c^2*d - 209*a*b*c*d^2))/(48*a*c*(b^2*c^3 + a^2*c*d^2 - 2*a*b*c^2*d)) + (d^2*x^4*(77*a^2*d^2 + 32*b^2*c^2 - 133*a*b*c*d))/(48*a*c^2*(b^2*c^3 + a^2*c*d^2 - 2*a*b*c^2*d)))/(c^2*x^(3/2) + d^2*x^(11/2) + 2*c*d*x^(7/2))","B"
487,1,36917,743,12.545524,"\text{Not used}","int(1/(x^(7/2)*(a + b*x^2)*(c + d*x^2)^3),x)","-2\,\mathrm{atan}\left(\frac{33554432\,a^{11}\,b^{22}\,c^{29}\,\sqrt{x}\,{\left(-\frac{b^{17}}{16\,a^{21}\,d^{12}-192\,a^{20}\,b\,c\,d^{11}+1056\,a^{19}\,b^2\,c^2\,d^{10}-3520\,a^{18}\,b^3\,c^3\,d^9+7920\,a^{17}\,b^4\,c^4\,d^8-12672\,a^{16}\,b^5\,c^5\,d^7+14784\,a^{15}\,b^6\,c^6\,d^6-12672\,a^{14}\,b^7\,c^7\,d^5+7920\,a^{13}\,b^8\,c^8\,d^4-3520\,a^{12}\,b^9\,c^9\,d^3+1056\,a^{11}\,b^{10}\,c^{10}\,d^2-192\,a^{10}\,b^{11}\,c^{11}\,d+16\,a^9\,b^{12}\,c^{12}}\right)}^{5/4}+374777442\,a^{19}\,b^{10}\,d^{17}\,\sqrt{x}\,{\left(-\frac{b^{17}}{16\,a^{21}\,d^{12}-192\,a^{20}\,b\,c\,d^{11}+1056\,a^{19}\,b^2\,c^2\,d^{10}-3520\,a^{18}\,b^3\,c^3\,d^9+7920\,a^{17}\,b^4\,c^4\,d^8-12672\,a^{16}\,b^5\,c^5\,d^7+14784\,a^{15}\,b^6\,c^6\,d^6-12672\,a^{14}\,b^7\,c^7\,d^5+7920\,a^{13}\,b^8\,c^8\,d^4-3520\,a^{12}\,b^9\,c^9\,d^3+1056\,a^{11}\,b^{10}\,c^{10}\,d^2-192\,a^{10}\,b^{11}\,c^{11}\,d+16\,a^9\,b^{12}\,c^{12}}\right)}^{1/4}+448561152\,a^{33}\,c^7\,d^{22}\,\sqrt{x}\,{\left(-\frac{b^{17}}{16\,a^{21}\,d^{12}-192\,a^{20}\,b\,c\,d^{11}+1056\,a^{19}\,b^2\,c^2\,d^{10}-3520\,a^{18}\,b^3\,c^3\,d^9+7920\,a^{17}\,b^4\,c^4\,d^8-12672\,a^{16}\,b^5\,c^5\,d^7+14784\,a^{15}\,b^6\,c^6\,d^6-12672\,a^{14}\,b^7\,c^7\,d^5+7920\,a^{13}\,b^8\,c^8\,d^4-3520\,a^{12}\,b^9\,c^9\,d^3+1056\,a^{11}\,b^{10}\,c^{10}\,d^2-192\,a^{10}\,b^{11}\,c^{11}\,d+16\,a^9\,b^{12}\,c^{12}}\right)}^{5/4}+100026368\,a^8\,b^{21}\,c^{11}\,d^6\,\sqrt{x}\,{\left(-\frac{b^{17}}{16\,a^{21}\,d^{12}-192\,a^{20}\,b\,c\,d^{11}+1056\,a^{19}\,b^2\,c^2\,d^{10}-3520\,a^{18}\,b^3\,c^3\,d^9+7920\,a^{17}\,b^4\,c^4\,d^8-12672\,a^{16}\,b^5\,c^5\,d^7+14784\,a^{15}\,b^6\,c^6\,d^6-12672\,a^{14}\,b^7\,c^7\,d^5+7920\,a^{13}\,b^8\,c^8\,d^4-3520\,a^{12}\,b^9\,c^9\,d^3+1056\,a^{11}\,b^{10}\,c^{10}\,d^2-192\,a^{10}\,b^{11}\,c^{11}\,d+16\,a^9\,b^{12}\,c^{12}}\right)}^{1/4}-276996096\,a^9\,b^{20}\,c^{10}\,d^7\,\sqrt{x}\,{\left(-\frac{b^{17}}{16\,a^{21}\,d^{12}-192\,a^{20}\,b\,c\,d^{11}+1056\,a^{19}\,b^2\,c^2\,d^{10}-3520\,a^{18}\,b^3\,c^3\,d^9+7920\,a^{17}\,b^4\,c^4\,d^8-12672\,a^{16}\,b^5\,c^5\,d^7+14784\,a^{15}\,b^6\,c^6\,d^6-12672\,a^{14}\,b^7\,c^7\,d^5+7920\,a^{13}\,b^8\,c^8\,d^4-3520\,a^{12}\,b^9\,c^9\,d^3+1056\,a^{11}\,b^{10}\,c^{10}\,d^2-192\,a^{10}\,b^{11}\,c^{11}\,d+16\,a^9\,b^{12}\,c^{12}}\right)}^{1/4}+297676800\,a^{10}\,b^{19}\,c^9\,d^8\,\sqrt{x}\,{\left(-\frac{b^{17}}{16\,a^{21}\,d^{12}-192\,a^{20}\,b\,c\,d^{11}+1056\,a^{19}\,b^2\,c^2\,d^{10}-3520\,a^{18}\,b^3\,c^3\,d^9+7920\,a^{17}\,b^4\,c^4\,d^8-12672\,a^{16}\,b^5\,c^5\,d^7+14784\,a^{15}\,b^6\,c^6\,d^6-12672\,a^{14}\,b^7\,c^7\,d^5+7920\,a^{13}\,b^8\,c^8\,d^4-3520\,a^{12}\,b^9\,c^9\,d^3+1056\,a^{11}\,b^{10}\,c^{10}\,d^2-192\,a^{10}\,b^{11}\,c^{11}\,d+16\,a^9\,b^{12}\,c^{12}}\right)}^{1/4}+4624241570\,a^{11}\,b^{18}\,c^8\,d^9\,\sqrt{x}\,{\left(-\frac{b^{17}}{16\,a^{21}\,d^{12}-192\,a^{20}\,b\,c\,d^{11}+1056\,a^{19}\,b^2\,c^2\,d^{10}-3520\,a^{18}\,b^3\,c^3\,d^9+7920\,a^{17}\,b^4\,c^4\,d^8-12672\,a^{16}\,b^5\,c^5\,d^7+14784\,a^{15}\,b^6\,c^6\,d^6-12672\,a^{14}\,b^7\,c^7\,d^5+7920\,a^{13}\,b^8\,c^8\,d^4-3520\,a^{12}\,b^9\,c^9\,d^3+1056\,a^{11}\,b^{10}\,c^{10}\,d^2-192\,a^{10}\,b^{11}\,c^{11}\,d+16\,a^9\,b^{12}\,c^{12}}\right)}^{1/4}-26395336656\,a^{12}\,b^{17}\,c^7\,d^{10}\,\sqrt{x}\,{\left(-\frac{b^{17}}{16\,a^{21}\,d^{12}-192\,a^{20}\,b\,c\,d^{11}+1056\,a^{19}\,b^2\,c^2\,d^{10}-3520\,a^{18}\,b^3\,c^3\,d^9+7920\,a^{17}\,b^4\,c^4\,d^8-12672\,a^{16}\,b^5\,c^5\,d^7+14784\,a^{15}\,b^6\,c^6\,d^6-12672\,a^{14}\,b^7\,c^7\,d^5+7920\,a^{13}\,b^8\,c^8\,d^4-3520\,a^{12}\,b^9\,c^9\,d^3+1056\,a^{11}\,b^{10}\,c^{10}\,d^2-192\,a^{10}\,b^{11}\,c^{11}\,d+16\,a^9\,b^{12}\,c^{12}}\right)}^{1/4}+64982364408\,a^{13}\,b^{16}\,c^6\,d^{11}\,\sqrt{x}\,{\left(-\frac{b^{17}}{16\,a^{21}\,d^{12}-192\,a^{20}\,b\,c\,d^{11}+1056\,a^{19}\,b^2\,c^2\,d^{10}-3520\,a^{18}\,b^3\,c^3\,d^9+7920\,a^{17}\,b^4\,c^4\,d^8-12672\,a^{16}\,b^5\,c^5\,d^7+14784\,a^{15}\,b^6\,c^6\,d^6-12672\,a^{14}\,b^7\,c^7\,d^5+7920\,a^{13}\,b^8\,c^8\,d^4-3520\,a^{12}\,b^9\,c^9\,d^3+1056\,a^{11}\,b^{10}\,c^{10}\,d^2-192\,a^{10}\,b^{11}\,c^{11}\,d+16\,a^9\,b^{12}\,c^{12}}\right)}^{1/4}-92624356656\,a^{14}\,b^{15}\,c^5\,d^{12}\,\sqrt{x}\,{\left(-\frac{b^{17}}{16\,a^{21}\,d^{12}-192\,a^{20}\,b\,c\,d^{11}+1056\,a^{19}\,b^2\,c^2\,d^{10}-3520\,a^{18}\,b^3\,c^3\,d^9+7920\,a^{17}\,b^4\,c^4\,d^8-12672\,a^{16}\,b^5\,c^5\,d^7+14784\,a^{15}\,b^6\,c^6\,d^6-12672\,a^{14}\,b^7\,c^7\,d^5+7920\,a^{13}\,b^8\,c^8\,d^4-3520\,a^{12}\,b^9\,c^9\,d^3+1056\,a^{11}\,b^{10}\,c^{10}\,d^2-192\,a^{10}\,b^{11}\,c^{11}\,d+16\,a^9\,b^{12}\,c^{12}}\right)}^{1/4}+83665919628\,a^{15}\,b^{14}\,c^4\,d^{13}\,\sqrt{x}\,{\left(-\frac{b^{17}}{16\,a^{21}\,d^{12}-192\,a^{20}\,b\,c\,d^{11}+1056\,a^{19}\,b^2\,c^2\,d^{10}-3520\,a^{18}\,b^3\,c^3\,d^9+7920\,a^{17}\,b^4\,c^4\,d^8-12672\,a^{16}\,b^5\,c^5\,d^7+14784\,a^{15}\,b^6\,c^6\,d^6-12672\,a^{14}\,b^7\,c^7\,d^5+7920\,a^{13}\,b^8\,c^8\,d^4-3520\,a^{12}\,b^9\,c^9\,d^3+1056\,a^{11}\,b^{10}\,c^{10}\,d^2-192\,a^{10}\,b^{11}\,c^{11}\,d+16\,a^9\,b^{12}\,c^{12}}\right)}^{1/4}-49036424112\,a^{16}\,b^{13}\,c^3\,d^{14}\,\sqrt{x}\,{\left(-\frac{b^{17}}{16\,a^{21}\,d^{12}-192\,a^{20}\,b\,c\,d^{11}+1056\,a^{19}\,b^2\,c^2\,d^{10}-3520\,a^{18}\,b^3\,c^3\,d^9+7920\,a^{17}\,b^4\,c^4\,d^8-12672\,a^{16}\,b^5\,c^5\,d^7+14784\,a^{15}\,b^6\,c^6\,d^6-12672\,a^{14}\,b^7\,c^7\,d^5+7920\,a^{13}\,b^8\,c^8\,d^4-3520\,a^{12}\,b^9\,c^9\,d^3+1056\,a^{11}\,b^{10}\,c^{10}\,d^2-192\,a^{10}\,b^{11}\,c^{11}\,d+16\,a^9\,b^{12}\,c^{12}}\right)}^{1/4}+18213050232\,a^{17}\,b^{12}\,c^2\,d^{15}\,\sqrt{x}\,{\left(-\frac{b^{17}}{16\,a^{21}\,d^{12}-192\,a^{20}\,b\,c\,d^{11}+1056\,a^{19}\,b^2\,c^2\,d^{10}-3520\,a^{18}\,b^3\,c^3\,d^9+7920\,a^{17}\,b^4\,c^4\,d^8-12672\,a^{16}\,b^5\,c^5\,d^7+14784\,a^{15}\,b^6\,c^6\,d^6-12672\,a^{14}\,b^7\,c^7\,d^5+7920\,a^{13}\,b^8\,c^8\,d^4-3520\,a^{12}\,b^9\,c^9\,d^3+1056\,a^{11}\,b^{10}\,c^{10}\,d^2-192\,a^{10}\,b^{11}\,c^{11}\,d+16\,a^9\,b^{12}\,c^{12}}\right)}^{1/4}+2214592512\,a^{13}\,b^{20}\,c^{27}\,d^2\,\sqrt{x}\,{\left(-\frac{b^{17}}{16\,a^{21}\,d^{12}-192\,a^{20}\,b\,c\,d^{11}+1056\,a^{19}\,b^2\,c^2\,d^{10}-3520\,a^{18}\,b^3\,c^3\,d^9+7920\,a^{17}\,b^4\,c^4\,d^8-12672\,a^{16}\,b^5\,c^5\,d^7+14784\,a^{15}\,b^6\,c^6\,d^6-12672\,a^{14}\,b^7\,c^7\,d^5+7920\,a^{13}\,b^8\,c^8\,d^4-3520\,a^{12}\,b^9\,c^9\,d^3+1056\,a^{11}\,b^{10}\,c^{10}\,d^2-192\,a^{10}\,b^{11}\,c^{11}\,d+16\,a^9\,b^{12}\,c^{12}}\right)}^{5/4}-7381975040\,a^{14}\,b^{19}\,c^{26}\,d^3\,\sqrt{x}\,{\left(-\frac{b^{17}}{16\,a^{21}\,d^{12}-192\,a^{20}\,b\,c\,d^{11}+1056\,a^{19}\,b^2\,c^2\,d^{10}-3520\,a^{18}\,b^3\,c^3\,d^9+7920\,a^{17}\,b^4\,c^4\,d^8-12672\,a^{16}\,b^5\,c^5\,d^7+14784\,a^{15}\,b^6\,c^6\,d^6-12672\,a^{14}\,b^7\,c^7\,d^5+7920\,a^{13}\,b^8\,c^8\,d^4-3520\,a^{12}\,b^9\,c^9\,d^3+1056\,a^{11}\,b^{10}\,c^{10}\,d^2-192\,a^{10}\,b^{11}\,c^{11}\,d+16\,a^9\,b^{12}\,c^{12}}\right)}^{5/4}+16609443840\,a^{15}\,b^{18}\,c^{25}\,d^4\,\sqrt{x}\,{\left(-\frac{b^{17}}{16\,a^{21}\,d^{12}-192\,a^{20}\,b\,c\,d^{11}+1056\,a^{19}\,b^2\,c^2\,d^{10}-3520\,a^{18}\,b^3\,c^3\,d^9+7920\,a^{17}\,b^4\,c^4\,d^8-12672\,a^{16}\,b^5\,c^5\,d^7+14784\,a^{15}\,b^6\,c^6\,d^6-12672\,a^{14}\,b^7\,c^7\,d^5+7920\,a^{13}\,b^8\,c^8\,d^4-3520\,a^{12}\,b^9\,c^9\,d^3+1056\,a^{11}\,b^{10}\,c^{10}\,d^2-192\,a^{10}\,b^{11}\,c^{11}\,d+16\,a^9\,b^{12}\,c^{12}}\right)}^{5/4}-26575110144\,a^{16}\,b^{17}\,c^{24}\,d^5\,\sqrt{x}\,{\left(-\frac{b^{17}}{16\,a^{21}\,d^{12}-192\,a^{20}\,b\,c\,d^{11}+1056\,a^{19}\,b^2\,c^2\,d^{10}-3520\,a^{18}\,b^3\,c^3\,d^9+7920\,a^{17}\,b^4\,c^4\,d^8-12672\,a^{16}\,b^5\,c^5\,d^7+14784\,a^{15}\,b^6\,c^6\,d^6-12672\,a^{14}\,b^7\,c^7\,d^5+7920\,a^{13}\,b^8\,c^8\,d^4-3520\,a^{12}\,b^9\,c^9\,d^3+1056\,a^{11}\,b^{10}\,c^{10}\,d^2-192\,a^{10}\,b^{11}\,c^{11}\,d+16\,a^9\,b^{12}\,c^{12}}\right)}^{5/4}+32604717056\,a^{17}\,b^{16}\,c^{23}\,d^6\,\sqrt{x}\,{\left(-\frac{b^{17}}{16\,a^{21}\,d^{12}-192\,a^{20}\,b\,c\,d^{11}+1056\,a^{19}\,b^2\,c^2\,d^{10}-3520\,a^{18}\,b^3\,c^3\,d^9+7920\,a^{17}\,b^4\,c^4\,d^8-12672\,a^{16}\,b^5\,c^5\,d^7+14784\,a^{15}\,b^6\,c^6\,d^6-12672\,a^{14}\,b^7\,c^7\,d^5+7920\,a^{13}\,b^8\,c^8\,d^4-3520\,a^{12}\,b^9\,c^9\,d^3+1056\,a^{11}\,b^{10}\,c^{10}\,d^2-192\,a^{10}\,b^{11}\,c^{11}\,d+16\,a^9\,b^{12}\,c^{12}}\right)}^{5/4}-50212110336\,a^{18}\,b^{15}\,c^{22}\,d^7\,\sqrt{x}\,{\left(-\frac{b^{17}}{16\,a^{21}\,d^{12}-192\,a^{20}\,b\,c\,d^{11}+1056\,a^{19}\,b^2\,c^2\,d^{10}-3520\,a^{18}\,b^3\,c^3\,d^9+7920\,a^{17}\,b^4\,c^4\,d^8-12672\,a^{16}\,b^5\,c^5\,d^7+14784\,a^{15}\,b^6\,c^6\,d^6-12672\,a^{14}\,b^7\,c^7\,d^5+7920\,a^{13}\,b^8\,c^8\,d^4-3520\,a^{12}\,b^9\,c^9\,d^3+1056\,a^{11}\,b^{10}\,c^{10}\,d^2-192\,a^{10}\,b^{11}\,c^{11}\,d+16\,a^9\,b^{12}\,c^{12}}\right)}^{5/4}+180183367680\,a^{19}\,b^{14}\,c^{21}\,d^8\,\sqrt{x}\,{\left(-\frac{b^{17}}{16\,a^{21}\,d^{12}-192\,a^{20}\,b\,c\,d^{11}+1056\,a^{19}\,b^2\,c^2\,d^{10}-3520\,a^{18}\,b^3\,c^3\,d^9+7920\,a^{17}\,b^4\,c^4\,d^8-12672\,a^{16}\,b^5\,c^5\,d^7+14784\,a^{15}\,b^6\,c^6\,d^6-12672\,a^{14}\,b^7\,c^7\,d^5+7920\,a^{13}\,b^8\,c^8\,d^4-3520\,a^{12}\,b^9\,c^9\,d^3+1056\,a^{11}\,b^{10}\,c^{10}\,d^2-192\,a^{10}\,b^{11}\,c^{11}\,d+16\,a^9\,b^{12}\,c^{12}}\right)}^{5/4}-711482933248\,a^{20}\,b^{13}\,c^{20}\,d^9\,\sqrt{x}\,{\left(-\frac{b^{17}}{16\,a^{21}\,d^{12}-192\,a^{20}\,b\,c\,d^{11}+1056\,a^{19}\,b^2\,c^2\,d^{10}-3520\,a^{18}\,b^3\,c^3\,d^9+7920\,a^{17}\,b^4\,c^4\,d^8-12672\,a^{16}\,b^5\,c^5\,d^7+14784\,a^{15}\,b^6\,c^6\,d^6-12672\,a^{14}\,b^7\,c^7\,d^5+7920\,a^{13}\,b^8\,c^8\,d^4-3520\,a^{12}\,b^9\,c^9\,d^3+1056\,a^{11}\,b^{10}\,c^{10}\,d^2-192\,a^{10}\,b^{11}\,c^{11}\,d+16\,a^9\,b^{12}\,c^{12}}\right)}^{5/4}+2112400785408\,a^{21}\,b^{12}\,c^{19}\,d^{10}\,\sqrt{x}\,{\left(-\frac{b^{17}}{16\,a^{21}\,d^{12}-192\,a^{20}\,b\,c\,d^{11}+1056\,a^{19}\,b^2\,c^2\,d^{10}-3520\,a^{18}\,b^3\,c^3\,d^9+7920\,a^{17}\,b^4\,c^4\,d^8-12672\,a^{16}\,b^5\,c^5\,d^7+14784\,a^{15}\,b^6\,c^6\,d^6-12672\,a^{14}\,b^7\,c^7\,d^5+7920\,a^{13}\,b^8\,c^8\,d^4-3520\,a^{12}\,b^9\,c^9\,d^3+1056\,a^{11}\,b^{10}\,c^{10}\,d^2-192\,a^{10}\,b^{11}\,c^{11}\,d+16\,a^9\,b^{12}\,c^{12}}\right)}^{5/4}-4669808050176\,a^{22}\,b^{11}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thrm{i}+a^{23}\,b^2\,c^{23}\,d^{20}\,\sqrt{x}\,{\left(-\frac{187388721\,a^8\,d^{17}-1960374312\,a^7\,b\,c\,d^{16}+9106525116\,a^6\,b^2\,c^2\,d^{15}-24518212056\,a^5\,b^3\,c^3\,d^{14}+41832959814\,a^4\,b^4\,c^4\,d^{13}-46312178328\,a^3\,b^5\,c^5\,d^{12}+32491182204\,a^2\,b^6\,c^6\,d^{11}-13211685864\,a\,b^7\,c^7\,d^{10}+2385443281\,b^8\,c^8\,d^9}{16777216\,a^{12}\,c^{17}\,d^{12}-201326592\,a^{11}\,b\,c^{18}\,d^{11}+1107296256\,a^{10}\,b^2\,c^{19}\,d^{10}-3690987520\,a^9\,b^3\,c^{20}\,d^9+8304721920\,a^8\,b^4\,c^{21}\,d^8-13287555072\,a^7\,b^5\,c^{22}\,d^7+15502147584\,a^6\,b^6\,c^{23}\,d^6-13287555072\,a^5\,b^7\,c^{24}\,d^5+8304721920\,a^4\,b^8\,c^{25}\,d^4-3690987520\,a^3\,b^9\,c^{26}\,d^3+1107296256\,a^2\,b^{10}\,c^{27}\,d^2-201326592\,a\,b^{11}\,c^{28}\,d+16777216\,b^{12}\,c^{29}}\right)}^{5/4}\,2048776709603328{}\mathrm{i}-a\,b^{20}\,c^{24}\,d^7\,\sqrt{x}\,{\left(-\frac{187388721\,a^8\,d^{17}-1960374312\,a^7\,b\,c\,d^{16}+9106525116\,a^6\,b^2\,c^2\,d^{15}-24518212056\,a^5\,b^3\,c^3\,d^{14}+41832959814\,a^4\,b^4\,c^4\,d^{13}-46312178328\,a^3\,b^5\,c^5\,d^{12}+32491182204\,a^2\,b^6\,c^6\,d^{11}-13211685864\,a\,b^7\,c^7\,d^{10}+2385443281\,b^8\,c^8\,d^9}{16777216\,a^{12}\,c^{17}\,d^{12}-201326592\,a^{11}\,b\,c^{18}\,d^{11}+1107296256\,a^{10}\,b^2\,c^{19}\,d^{10}-3690987520\,a^9\,b^3\,c^{20}\,d^9+8304721920\,a^8\,b^4\,c^{21}\,d^8-13287555072\,a^7\,b^5\,c^{22}\,d^7+15502147584\,a^6\,b^6\,c^{23}\,d^6-13287555072\,a^5\,b^7\,c^{24}\,d^5+8304721920\,a^4\,b^8\,c^{25}\,d^4-3690987520\,a^3\,b^9\,c^{26}\,d^3+1107296256\,a^2\,b^{10}\,c^{27}\,d^2-201326592\,a\,b^{11}\,c^{28}\,d+16777216\,b^{12}\,c^{29}}\right)}^{1/4}\,9076608073728{}\mathrm{i}-a^4\,b^{21}\,c^{42}\,d\,\sqrt{x}\,{\left(-\frac{187388721\,a^8\,d^{17}-1960374312\,a^7\,b\,c\,d^{16}+9106525116\,a^6\,b^2\,c^2\,d^{15}-24518212056\,a^5\,b^3\,c^3\,d^{14}+41832959814\,a^4\,b^4\,c^4\,d^{13}-46312178328\,a^3\,b^5\,c^5\,d^{12}+32491182204\,a^2\,b^6\,c^6\,d^{11}-13211685864\,a\,b^7\,c^7\,d^{10}+2385443281\,b^8\,c^8\,d^9}{16777216\,a^{12}\,c^{17}\,d^{12}-201326592\,a^{11}\,b\,c^{18}\,d^{11}+1107296256\,a^{10}\,b^2\,c^{19}\,d^{10}-3690987520\,a^9\,b^3\,c^{20}\,d^9+8304721920\,a^8\,b^4\,c^{21}\,d^8-13287555072\,a^7\,b^5\,c^{22}\,d^7+15502147584\,a^6\,b^6\,c^{23}\,d^6-13287555072\,a^5\,b^7\,c^{24}\,d^5+8304721920\,a^4\,b^8\,c^{25}\,d^4-3690987520\,a^3\,b^9\,c^{26}\,d^3+1107296256\,a^2\,b^{10}\,c^{27}\,d^2-201326592\,a\,b^{11}\,c^{28}\,d+16777216\,b^{12}\,c^{29}}\right)}^{5/4}\,13194139533312{}\mathrm{i}-a^{24}\,b\,c^{22}\,d^{21}\,\sqrt{x}\,{\left(-\frac{187388721\,a^8\,d^{17}-1960374312\,a^7\,b\,c\,d^{16}+9106525116\,a^6\,b^2\,c^2\,d^{15}-24518212056\,a^5\,b^3\,c^3\,d^{14}+41832959814\,a^4\,b^4\,c^4\,d^{13}-46312178328\,a^3\,b^5\,c^5\,d^{12}+32491182204\,a^2\,b^6\,c^6\,d^{11}-13211685864\,a\,b^7\,c^7\,d^{10}+2385443281\,b^8\,c^8\,d^9}{16777216\,a^{12}\,c^{17}\,d^{12}-201326592\,a^{11}\,b\,c^{18}\,d^{11}+1107296256\,a^{10}\,b^2\,c^{19}\,d^{10}-3690987520\,a^9\,b^3\,c^{20}\,d^9+8304721920\,a^8\,b^4\,c^{21}\,d^8-13287555072\,a^7\,b^5\,c^{22}\,d^7+15502147584\,a^6\,b^6\,c^{23}\,d^6-13287555072\,a^5\,b^7\,c^{24}\,d^5+8304721920\,a^4\,b^8\,c^{25}\,d^4-3690987520\,a^3\,b^9\,c^{26}\,d^3+1107296256\,a^2\,b^{10}\,c^{27}\,d^2-201326592\,a\,b^{11}\,c^{28}\,d+16777216\,b^{12}\,c^{29}}\right)}^{5/4}\,253265631510528{}\mathrm{i}}{300124211606973\,a^{20}\,d^{28}-4594209085368279\,a^{19}\,b\,c\,d^{27}+32396642626079979\,a^{18}\,b^2\,c^2\,d^{26}-138920444110237257\,a^{17}\,b^3\,c^3\,d^{25}+402590417597719650\,a^{16}\,b^4\,c^4\,d^{24}-828236972743874694\,a^{15}\,b^5\,c^5\,d^{23}+1235024770525419510\,a^{14}\,b^6\,c^6\,d^{22}-1335978873710775378\,a^{13}\,b^7\,c^7\,d^{21}+1028670489683926929\,a^{12}\,b^8\,c^8\,d^{20}-537854694138813555\,a^{11}\,b^9\,c^9\,d^{19}+172320214465160559\,a^{10}\,b^{10}\,c^{10}\,d^{18}-25743035408641173\,a^9\,b^{11}\,c^{11}\,d^{17}+4532264239104\,a^8\,b^{12}\,c^{12}\,d^{16}+3991098359808\,a^7\,b^{13}\,c^{13}\,d^{15}+3484292218880\,a^6\,b^{14}\,c^{14}\,d^{14}+3011845816320\,a^5\,b^{15}\,c^{15}\,d^{13}+2573759152128\,a^4\,b^{16}\,c^{16}\,d^{12}+490619273216\,a^3\,b^{17}\,c^{17}\,d^{11}+9939358580736\,a^2\,b^{18}\,c^{18}\,d^{10}-13059442606080\,a\,b^{19}\,c^{19}\,d^9+11318183591936\,b^{20}\,c^{20}\,d^8}\right)\,{\left(-\frac{187388721\,a^8\,d^{17}-1960374312\,a^7\,b\,c\,d^{16}+9106525116\,a^6\,b^2\,c^2\,d^{15}-24518212056\,a^5\,b^3\,c^3\,d^{14}+41832959814\,a^4\,b^4\,c^4\,d^{13}-46312178328\,a^3\,b^5\,c^5\,d^{12}+32491182204\,a^2\,b^6\,c^6\,d^{11}-13211685864\,a\,b^7\,c^7\,d^{10}+2385443281\,b^8\,c^8\,d^9}{16777216\,a^{12}\,c^{17}\,d^{12}-201326592\,a^{11}\,b\,c^{18}\,d^{11}+1107296256\,a^{10}\,b^2\,c^{19}\,d^{10}-3690987520\,a^9\,b^3\,c^{20}\,d^9+8304721920\,a^8\,b^4\,c^{21}\,d^8-13287555072\,a^7\,b^5\,c^{22}\,d^7+15502147584\,a^6\,b^6\,c^{23}\,d^6-13287555072\,a^5\,b^7\,c^{24}\,d^5+8304721920\,a^4\,b^8\,c^{25}\,d^4-3690987520\,a^3\,b^9\,c^{26}\,d^3+1107296256\,a^2\,b^{10}\,c^{27}\,d^2-201326592\,a\,b^{11}\,c^{28}\,d+16777216\,b^{12}\,c^{29}}\right)}^{1/4}\,2{}\mathrm{i}+\frac{\frac{2\,x^2\,\left(13\,a\,d+5\,b\,c\right)}{5\,a^2\,c^2}-\frac{2}{5\,a\,c}+\frac{x^4\,\left(1053\,a^3\,d^4-1701\,a^2\,b\,c\,d^3+288\,a\,b^2\,c^2\,d^2+320\,b^3\,c^3\,d\right)}{80\,a^2\,c^2\,\left(a^2\,c\,d^2-2\,a\,b\,c^2\,d+b^2\,c^3\right)}+\frac{d^2\,x^6\,\left(117\,a^3\,d^3-189\,a^2\,b\,c\,d^2+32\,a\,b^2\,c^2\,d+32\,b^3\,c^3\right)}{16\,a^2\,c^3\,\left(a^2\,c\,d^2-2\,a\,b\,c^2\,d+b^2\,c^3\right)}}{c^2\,x^{5/2}+d^2\,x^{13/2}+2\,c\,d\,x^{9/2}}","Not 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7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(5/4) - 315126448128*a^30*b^3*c^10*d^19*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(5/4) + 62523703296*a^31*b^2*c^9*d^20*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(5/4) - 3920748624*a^18*b^11*c*d^16*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(1/4) - 402653184*a^12*b^21*c^28*d*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(5/4) - 7729053696*a^32*b*c^8*d^21*x^(1/2)*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(5/4))/(1048576*b^28*c^14 + 187388721*a^14*b^14*d^14 - 1398208149*a^13*b^15*c*d^13 + 6291456*a^2*b^26*c^12*d^2 + 10485760*a^3*b^25*c^11*d^3 + 15728640*a^4*b^24*c^10*d^4 + 22020096*a^5*b^23*c^9*d^5 + 29360128*a^6*b^22*c^8*d^6 + 37748736*a^7*b^21*c^7*d^7 + 47185920*a^8*b^20*c^6*d^8 - 2327771601*a^9*b^19*c^5*d^9 + 6124562037*a^10*b^18*c^4*d^10 - 7086995370*a^11*b^17*c^3*d^11 + 4349734506*a^12*b^16*c^2*d^12 + 3145728*a*b^27*c^13*d))*(-b^17/(16*a^21*d^12 + 16*a^9*b^12*c^12 - 192*a^10*b^11*c^11*d + 1056*a^11*b^10*c^10*d^2 - 3520*a^12*b^9*c^9*d^3 + 7920*a^13*b^8*c^8*d^4 - 12672*a^14*b^7*c^7*d^5 + 14784*a^15*b^6*c^6*d^6 - 12672*a^16*b^5*c^5*d^7 + 7920*a^17*b^4*c^4*d^8 - 3520*a^18*b^3*c^3*d^9 + 1056*a^19*b^2*c^2*d^10 - 192*a^20*b*c*d^11))^(1/4)","B"
488,1,34921,624,3.984888,"\text{Not used}","int(x^(7/2)/((a + b*x^2)^2*(c + d*x^2)^2),x)","\mathrm{atan}\left(\frac{{\left(-\frac{625\,a^4\,c\,d^4+1500\,a^3\,b\,c^2\,d^3+1350\,a^2\,b^2\,c^3\,d^2+540\,a\,b^3\,c^4\,d+81\,b^4\,c^5}{4096\,a^{12}\,d^{13}-49152\,a^{11}\,b\,c\,d^{12}+270336\,a^{10}\,b^2\,c^2\,d^{11}-901120\,a^9\,b^3\,c^3\,d^{10}+2027520\,a^8\,b^4\,c^4\,d^9-3244032\,a^7\,b^5\,c^5\,d^8+3784704\,a^6\,b^6\,c^6\,d^7-3244032\,a^5\,b^7\,c^7\,d^6+2027520\,a^4\,b^8\,c^8\,d^5-901120\,a^3\,b^9\,c^9\,d^4+270336\,a^2\,b^{10}\,c^{10}\,d^3-49152\,a\,b^{11}\,c^{11}\,d^2+4096\,b^{12}\,c^{12}\,d}\right)}^{1/4}\,\left({\left(-\frac{625\,a^4\,c\,d^4+1500\,a^3\,b\,c^2\,d^3+1350\,a^2\,b^2\,c^3\,d^2+540\,a\,b^3\,c^4\,d+81\,b^4\,c^5}{4096\,a^{12}\,d^{13}-49152\,a^{11}\,b\,c\,d^{12}+270336\,a^{10}\,b^2\,c^2\,d^{11}-901120\,a^9\,b^3\,c^3\,d^{10}+2027520\,a^8\,b^4\,c^4\,d^9-3244032\,a^7\,b^5\,c^5\,d^8+3784704\,a^6\,b^6\,c^6\,d^7-3244032\,a^5\,b^7\,c^7\,d^6+2027520\,a^4\,b^8\,c^8\,d^5-901120\,a^3\,b^9\,c^9\,d^4+270336\,a^2\,b^{10}\,c^{10}\,d^3-49152\,a\,b^{11}\,c^{11}\,d^2+4096\,b^{12}\,c^{12}\,d}\right)}^{1/4}\,\left(\frac{\frac{405\,a^8\,b^3\,c^2\,d^9}{2}+1674\,a^7\,b^4\,c^3\,d^8+\frac{9843\,a^6\,b^5\,c^4\,d^7}{2}+6884\,a^5\,b^6\,c^5\,d^6+\frac{9843\,a^4\,b^7\,c^6\,d^5}{2}+1674\,a^3\,b^8\,c^7\,d^4+\frac{405\,a^2\,b^9\,c^8\,d^3}{2}}{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}+{\left(-\frac{625\,a^4\,c\,d^4+1500\,a^3\,b\,c^2\,d^3+1350\,a^2\,b^2\,c^3\,d^2+540\,a\,b^3\,c^4\,d+81\,b^4\,c^5}{4096\,a^{12}\,d^{13}-49152\,a^{11}\,b\,c\,d^{12}+270336\,a^{10}\,b^2\,c^2\,d^{11}-901120\,a^9\,b^3\,c^3\,d^{10}+2027520\,a^8\,b^4\,c^4\,d^9-3244032\,a^7\,b^5\,c^5\,d^8+3784704\,a^6\,b^6\,c^6\,d^7-3244032\,a^5\,b^7\,c^7\,d^6+2027520\,a^4\,b^8\,c^8\,d^5-901120\,a^3\,b^9\,c^9\,d^4+270336\,a^2\,b^{10}\,c^{10}\,d^3-49152\,a\,b^{11}\,c^{11}\,d^2+4096\,b^{12}\,c^{12}\,d}\right)}^{3/4}\,\left(\frac{\sqrt{x}\,\left(102400\,a^{17}\,b^4\,c^2\,d^{19}-1069056\,a^{16}\,b^5\,c^3\,d^{18}+5001216\,a^{15}\,b^6\,c^4\,d^{17}-13799424\,a^{14}\,b^7\,c^5\,d^{16}+24858624\,a^{13}\,b^8\,c^6\,d^{15}-30412800\,a^{12}\,b^9\,c^7\,d^{14}+24645632\,a^{11}\,b^{10}\,c^8\,d^{13}-9326592\,a^{10}\,b^{11}\,c^9\,d^{12}-9326592\,a^9\,b^{12}\,c^{10}\,d^{11}+24645632\,a^8\,b^{13}\,c^{11}\,d^{10}-30412800\,a^7\,b^{14}\,c^{12}\,d^9+24858624\,a^6\,b^{15}\,c^{13}\,d^8-13799424\,a^5\,b^{16}\,c^{14}\,d^7+5001216\,a^4\,b^{17}\,c^{15}\,d^6-1069056\,a^3\,b^{18}\,c^{16}\,d^5+102400\,a^2\,b^{19}\,c^{17}\,d^4\right)}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}+\frac{{\left(-\frac{625\,a^4\,c\,d^4+1500\,a^3\,b\,c^2\,d^3+1350\,a^2\,b^2\,c^3\,d^2+540\,a\,b^3\,c^4\,d+81\,b^4\,c^5}{4096\,a^{12}\,d^{13}-49152\,a^{11}\,b\,c\,d^{12}+270336\,a^{10}\,b^2\,c^2\,d^{11}-901120\,a^9\,b^3\,c^3\,d^{10}+2027520\,a^8\,b^4\,c^4\,d^9-3244032\,a^7\,b^5\,c^5\,d^8+3784704\,a^6\,b^6\,c^6\,d^7-3244032\,a^5\,b^7\,c^7\,d^6+2027520\,a^4\,b^8\,c^8\,d^5-901120\,a^3\,b^9\,c^9\,d^4+270336\,a^2\,b^{10}\,c^{10}\,d^3-49152\,a\,b^{11}\,c^{11}\,d^2+4096\,b^{12}\,c^{12}\,d}\right)}^{1/4}\,\left(10240\,a^{15}\,b^4\,c^2\,d^{17}-112640\,a^{14}\,b^5\,c^3\,d^{16}+552960\,a^{13}\,b^6\,c^4\,d^{15}-1576960\,a^{12}\,b^7\,c^5\,d^{14}+2816000\,a^{11}\,b^8\,c^6\,d^{13}-3041280\,a^{10}\,b^9\,c^7\,d^{12}+1351680\,a^9\,b^{10}\,c^8\,d^{11}+1351680\,a^8\,b^{11}\,c^9\,d^{10}-3041280\,a^7\,b^{12}\,c^{10}\,d^9+2816000\,a^6\,b^{13}\,c^{11}\,d^8-1576960\,a^5\,b^{14}\,c^{12}\,d^7+552960\,a^4\,b^{15}\,c^{13}\,d^6-112640\,a^3\,b^{16}\,c^{14}\,d^5+10240\,a^2\,b^{17}\,c^{15}\,d^4\right)}{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)\right)\,1{}\mathrm{i}+\frac{\sqrt{x}\,\left(2025\,a^{10}\,b^3\,c^2\,d^{11}+15930\,a^9\,b^4\,c^3\,d^{10}+56304\,a^8\,b^5\,c^4\,d^9+115110\,a^7\,b^6\,c^5\,d^8+145550\,a^6\,b^7\,c^6\,d^7+115110\,a^5\,b^8\,c^7\,d^6+56304\,a^4\,b^9\,c^8\,d^5+15930\,a^3\,b^{10}\,c^9\,d^4+2025\,a^2\,b^{11}\,c^{10}\,d^3\right)\,1{}\mathrm{i}}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)-{\left(-\frac{625\,a^4\,c\,d^4+1500\,a^3\,b\,c^2\,d^3+1350\,a^2\,b^2\,c^3\,d^2+540\,a\,b^3\,c^4\,d+81\,b^4\,c^5}{4096\,a^{12}\,d^{13}-49152\,a^{11}\,b\,c\,d^{12}+270336\,a^{10}\,b^2\,c^2\,d^{11}-901120\,a^9\,b^3\,c^3\,d^{10}+2027520\,a^8\,b^4\,c^4\,d^9-3244032\,a^7\,b^5\,c^5\,d^8+3784704\,a^6\,b^6\,c^6\,d^7-3244032\,a^5\,b^7\,c^7\,d^6+2027520\,a^4\,b^8\,c^8\,d^5-901120\,a^3\,b^9\,c^9\,d^4+270336\,a^2\,b^{10}\,c^{10}\,d^3-49152\,a\,b^{11}\,c^{11}\,d^2+4096\,b^{12}\,c^{12}\,d}\right)}^{1/4}\,\left({\left(-\frac{625\,a^4\,c\,d^4+1500\,a^3\,b\,c^2\,d^3+1350\,a^2\,b^2\,c^3\,d^2+540\,a\,b^3\,c^4\,d+81\,b^4\,c^5}{4096\,a^{12}\,d^{13}-49152\,a^{11}\,b\,c\,d^{12}+270336\,a^{10}\,b^2\,c^2\,d^{11}-901120\,a^9\,b^3\,c^3\,d^{10}+2027520\,a^8\,b^4\,c^4\,d^9-3244032\,a^7\,b^5\,c^5\,d^8+3784704\,a^6\,b^6\,c^6\,d^7-3244032\,a^5\,b^7\,c^7\,d^6+2027520\,a^4\,b^8\,c^8\,d^5-901120\,a^3\,b^9\,c^9\,d^4+270336\,a^2\,b^{10}\,c^{10}\,d^3-49152\,a\,b^{11}\,c^{11}\,d^2+4096\,b^{12}\,c^{12}\,d}\right)}^{1/4}\,\left(\frac{\frac{405\,a^8\,b^3\,c^2\,d^9}{2}+1674\,a^7\,b^4\,c^3\,d^8+\frac{9843\,a^6\,b^5\,c^4\,d^7}{2}+6884\,a^5\,b^6\,c^5\,d^6+\frac{9843\,a^4\,b^7\,c^6\,d^5}{2}+1674\,a^3\,b^8\,c^7\,d^4+\frac{405\,a^2\,b^9\,c^8\,d^3}{2}}{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}-{\left(-\frac{625\,a^4\,c\,d^4+1500\,a^3\,b\,c^2\,d^3+1350\,a^2\,b^2\,c^3\,d^2+540\,a\,b^3\,c^4\,d+81\,b^4\,c^5}{4096\,a^{12}\,d^{13}-49152\,a^{11}\,b\,c\,d^{12}+270336\,a^{10}\,b^2\,c^2\,d^{11}-901120\,a^9\,b^3\,c^3\,d^{10}+2027520\,a^8\,b^4\,c^4\,d^9-3244032\,a^7\,b^5\,c^5\,d^8+3784704\,a^6\,b^6\,c^6\,d^7-3244032\,a^5\,b^7\,c^7\,d^6+2027520\,a^4\,b^8\,c^8\,d^5-901120\,a^3\,b^9\,c^9\,d^4+270336\,a^2\,b^{10}\,c^{10}\,d^3-49152\,a\,b^{11}\,c^{11}\,d^2+4096\,b^{12}\,c^{12}\,d}\right)}^{3/4}\,\left(\frac{\sqrt{x}\,\left(102400\,a^{17}\,b^4\,c^2\,d^{19}-1069056\,a^{16}\,b^5\,c^3\,d^{18}+5001216\,a^{15}\,b^6\,c^4\,d^{17}-13799424\,a^{14}\,b^7\,c^5\,d^{16}+24858624\,a^{13}\,b^8\,c^6\,d^{15}-30412800\,a^{12}\,b^9\,c^7\,d^{14}+24645632\,a^{11}\,b^{10}\,c^8\,d^{13}-9326592\,a^{10}\,b^{11}\,c^9\,d^{12}-9326592\,a^9\,b^{12}\,c^{10}\,d^{11}+24645632\,a^8\,b^{13}\,c^{11}\,d^{10}-30412800\,a^7\,b^{14}\,c^{12}\,d^9+24858624\,a^6\,b^{15}\,c^{13}\,d^8-13799424\,a^5\,b^{16}\,c^{14}\,d^7+5001216\,a^4\,b^{17}\,c^{15}\,d^6-1069056\,a^3\,b^{18}\,c^{16}\,d^5+102400\,a^2\,b^{19}\,c^{17}\,d^4\right)}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}-\frac{{\left(-\frac{625\,a^4\,c\,d^4+1500\,a^3\,b\,c^2\,d^3+1350\,a^2\,b^2\,c^3\,d^2+540\,a\,b^3\,c^4\,d+81\,b^4\,c^5}{4096\,a^{12}\,d^{13}-49152\,a^{11}\,b\,c\,d^{12}+270336\,a^{10}\,b^2\,c^2\,d^{11}-901120\,a^9\,b^3\,c^3\,d^{10}+2027520\,a^8\,b^4\,c^4\,d^9-3244032\,a^7\,b^5\,c^5\,d^8+3784704\,a^6\,b^6\,c^6\,d^7-3244032\,a^5\,b^7\,c^7\,d^6+2027520\,a^4\,b^8\,c^8\,d^5-901120\,a^3\,b^9\,c^9\,d^4+270336\,a^2\,b^{10}\,c^{10}\,d^3-49152\,a\,b^{11}\,c^{11}\,d^2+4096\,b^{12}\,c^{12}\,d}\right)}^{1/4}\,\left(10240\,a^{15}\,b^4\,c^2\,d^{17}-112640\,a^{14}\,b^5\,c^3\,d^{16}+552960\,a^{13}\,b^6\,c^4\,d^{15}-1576960\,a^{12}\,b^7\,c^5\,d^{14}+2816000\,a^{11}\,b^8\,c^6\,d^{13}-3041280\,a^{10}\,b^9\,c^7\,d^{12}+1351680\,a^9\,b^{10}\,c^8\,d^{11}+1351680\,a^8\,b^{11}\,c^9\,d^{10}-3041280\,a^7\,b^{12}\,c^{10}\,d^9+2816000\,a^6\,b^{13}\,c^{11}\,d^8-1576960\,a^5\,b^{14}\,c^{12}\,d^7+552960\,a^4\,b^{15}\,c^{13}\,d^6-112640\,a^3\,b^{16}\,c^{14}\,d^5+10240\,a^2\,b^{17}\,c^{15}\,d^4\right)}{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)\right)\,1{}\mathrm{i}-\frac{\sqrt{x}\,\left(2025\,a^{10}\,b^3\,c^2\,d^{11}+15930\,a^9\,b^4\,c^3\,d^{10}+56304\,a^8\,b^5\,c^4\,d^9+115110\,a^7\,b^6\,c^5\,d^8+145550\,a^6\,b^7\,c^6\,d^7+115110\,a^5\,b^8\,c^7\,d^6+56304\,a^4\,b^9\,c^8\,d^5+15930\,a^3\,b^{10}\,c^9\,d^4+2025\,a^2\,b^{11}\,c^{10}\,d^3\right)\,1{}\mathrm{i}}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)}{{\left(-\frac{625\,a^4\,c\,d^4+1500\,a^3\,b\,c^2\,d^3+1350\,a^2\,b^2\,c^3\,d^2+540\,a\,b^3\,c^4\,d+81\,b^4\,c^5}{4096\,a^{12}\,d^{13}-49152\,a^{11}\,b\,c\,d^{12}+270336\,a^{10}\,b^2\,c^2\,d^{11}-901120\,a^9\,b^3\,c^3\,d^{10}+2027520\,a^8\,b^4\,c^4\,d^9-3244032\,a^7\,b^5\,c^5\,d^8+3784704\,a^6\,b^6\,c^6\,d^7-3244032\,a^5\,b^7\,c^7\,d^6+2027520\,a^4\,b^8\,c^8\,d^5-901120\,a^3\,b^9\,c^9\,d^4+270336\,a^2\,b^{10}\,c^{10}\,d^3-49152\,a\,b^{11}\,c^{11}\,d^2+4096\,b^{12}\,c^{12}\,d}\right)}^{1/4}\,\left({\left(-\frac{625\,a^4\,c\,d^4+1500\,a^3\,b\,c^2\,d^3+1350\,a^2\,b^2\,c^3\,d^2+540\,a\,b^3\,c^4\,d+81\,b^4\,c^5}{4096\,a^{12}\,d^{13}-49152\,a^{11}\,b\,c\,d^{12}+270336\,a^{10}\,b^2\,c^2\,d^{11}-901120\,a^9\,b^3\,c^3\,d^{10}+2027520\,a^8\,b^4\,c^4\,d^9-3244032\,a^7\,b^5\,c^5\,d^8+3784704\,a^6\,b^6\,c^6\,d^7-3244032\,a^5\,b^7\,c^7\,d^6+2027520\,a^4\,b^8\,c^8\,d^5-901120\,a^3\,b^9\,c^9\,d^4+270336\,a^2\,b^{10}\,c^{10}\,d^3-49152\,a\,b^{11}\,c^{11}\,d^2+4096\,b^{12}\,c^{12}\,d}\right)}^{1/4}\,\left(\frac{\frac{405\,a^8\,b^3\,c^2\,d^9}{2}+1674\,a^7\,b^4\,c^3\,d^8+\frac{9843\,a^6\,b^5\,c^4\,d^7}{2}+6884\,a^5\,b^6\,c^5\,d^6+\frac{9843\,a^4\,b^7\,c^6\,d^5}{2}+1674\,a^3\,b^8\,c^7\,d^4+\frac{405\,a^2\,b^9\,c^8\,d^3}{2}}{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}+{\left(-\frac{625\,a^4\,c\,d^4+1500\,a^3\,b\,c^2\,d^3+1350\,a^2\,b^2\,c^3\,d^2+540\,a\,b^3\,c^4\,d+81\,b^4\,c^5}{4096\,a^{12}\,d^{13}-49152\,a^{11}\,b\,c\,d^{12}+270336\,a^{10}\,b^2\,c^2\,d^{11}-901120\,a^9\,b^3\,c^3\,d^{10}+2027520\,a^8\,b^4\,c^4\,d^9-3244032\,a^7\,b^5\,c^5\,d^8+3784704\,a^6\,b^6\,c^6\,d^7-3244032\,a^5\,b^7\,c^7\,d^6+2027520\,a^4\,b^8\,c^8\,d^5-901120\,a^3\,b^9\,c^9\,d^4+270336\,a^2\,b^{10}\,c^{10}\,d^3-49152\,a\,b^{11}\,c^{11}\,d^2+4096\,b^{12}\,c^{12}\,d}\right)}^{3/4}\,\left(\frac{\sqrt{x}\,\left(102400\,a^{17}\,b^4\,c^2\,d^{19}-1069056\,a^{16}\,b^5\,c^3\,d^{18}+5001216\,a^{15}\,b^6\,c^4\,d^{17}-13799424\,a^{14}\,b^7\,c^5\,d^{16}+24858624\,a^{13}\,b^8\,c^6\,d^{15}-30412800\,a^{12}\,b^9\,c^7\,d^{14}+24645632\,a^{11}\,b^{10}\,c^8\,d^{13}-9326592\,a^{10}\,b^{11}\,c^9\,d^{12}-9326592\,a^9\,b^{12}\,c^{10}\,d^{11}+24645632\,a^8\,b^{13}\,c^{11}\,d^{10}-30412800\,a^7\,b^{14}\,c^{12}\,d^9+24858624\,a^6\,b^{15}\,c^{13}\,d^8-13799424\,a^5\,b^{16}\,c^{14}\,d^7+5001216\,a^4\,b^{17}\,c^{15}\,d^6-1069056\,a^3\,b^{18}\,c^{16}\,d^5+102400\,a^2\,b^{19}\,c^{17}\,d^4\right)}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}+\frac{{\left(-\frac{625\,a^4\,c\,d^4+1500\,a^3\,b\,c^2\,d^3+1350\,a^2\,b^2\,c^3\,d^2+540\,a\,b^3\,c^4\,d+81\,b^4\,c^5}{4096\,a^{12}\,d^{13}-49152\,a^{11}\,b\,c\,d^{12}+270336\,a^{10}\,b^2\,c^2\,d^{11}-901120\,a^9\,b^3\,c^3\,d^{10}+2027520\,a^8\,b^4\,c^4\,d^9-3244032\,a^7\,b^5\,c^5\,d^8+3784704\,a^6\,b^6\,c^6\,d^7-3244032\,a^5\,b^7\,c^7\,d^6+2027520\,a^4\,b^8\,c^8\,d^5-901120\,a^3\,b^9\,c^9\,d^4+270336\,a^2\,b^{10}\,c^{10}\,d^3-49152\,a\,b^{11}\,c^{11}\,d^2+4096\,b^{12}\,c^{12}\,d}\right)}^{1/4}\,\left(10240\,a^{15}\,b^4\,c^2\,d^{17}-112640\,a^{14}\,b^5\,c^3\,d^{16}+552960\,a^{13}\,b^6\,c^4\,d^{15}-1576960\,a^{12}\,b^7\,c^5\,d^{14}+2816000\,a^{11}\,b^8\,c^6\,d^{13}-3041280\,a^{10}\,b^9\,c^7\,d^{12}+1351680\,a^9\,b^{10}\,c^8\,d^{11}+1351680\,a^8\,b^{11}\,c^9\,d^{10}-3041280\,a^7\,b^{12}\,c^{10}\,d^9+2816000\,a^6\,b^{13}\,c^{11}\,d^8-1576960\,a^5\,b^{14}\,c^{12}\,d^7+552960\,a^4\,b^{15}\,c^{13}\,d^6-112640\,a^3\,b^{16}\,c^{14}\,d^5+10240\,a^2\,b^{17}\,c^{15}\,d^4\right)}{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)\right)+\frac{\sqrt{x}\,\left(2025\,a^{10}\,b^3\,c^2\,d^{11}+15930\,a^9\,b^4\,c^3\,d^{10}+56304\,a^8\,b^5\,c^4\,d^9+115110\,a^7\,b^6\,c^5\,d^8+145550\,a^6\,b^7\,c^6\,d^7+115110\,a^5\,b^8\,c^7\,d^6+56304\,a^4\,b^9\,c^8\,d^5+15930\,a^3\,b^{10}\,c^9\,d^4+2025\,a^2\,b^{11}\,c^{10}\,d^3\right)}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)+{\left(-\frac{625\,a^4\,c\,d^4+1500\,a^3\,b\,c^2\,d^3+1350\,a^2\,b^2\,c^3\,d^2+540\,a\,b^3\,c^4\,d+81\,b^4\,c^5}{4096\,a^{12}\,d^{13}-49152\,a^{11}\,b\,c\,d^{12}+270336\,a^{10}\,b^2\,c^2\,d^{11}-901120\,a^9\,b^3\,c^3\,d^{10}+2027520\,a^8\,b^4\,c^4\,d^9-3244032\,a^7\,b^5\,c^5\,d^8+3784704\,a^6\,b^6\,c^6\,d^7-3244032\,a^5\,b^7\,c^7\,d^6+2027520\,a^4\,b^8\,c^8\,d^5-901120\,a^3\,b^9\,c^9\,d^4+270336\,a^2\,b^{10}\,c^{10}\,d^3-49152\,a\,b^{11}\,c^{11}\,d^2+4096\,b^{12}\,c^{12}\,d}\right)}^{1/4}\,\left({\left(-\frac{625\,a^4\,c\,d^4+1500\,a^3\,b\,c^2\,d^3+1350\,a^2\,b^2\,c^3\,d^2+540\,a\,b^3\,c^4\,d+81\,b^4\,c^5}{4096\,a^{12}\,d^{13}-49152\,a^{11}\,b\,c\,d^{12}+270336\,a^{10}\,b^2\,c^2\,d^{11}-901120\,a^9\,b^3\,c^3\,d^{10}+2027520\,a^8\,b^4\,c^4\,d^9-3244032\,a^7\,b^5\,c^5\,d^8+3784704\,a^6\,b^6\,c^6\,d^7-3244032\,a^5\,b^7\,c^7\,d^6+2027520\,a^4\,b^8\,c^8\,d^5-901120\,a^3\,b^9\,c^9\,d^4+270336\,a^2\,b^{10}\,c^{10}\,d^3-49152\,a\,b^{11}\,c^{11}\,d^2+4096\,b^{12}\,c^{12}\,d}\right)}^{1/4}\,\left(\frac{\frac{405\,a^8\,b^3\,c^2\,d^9}{2}+1674\,a^7\,b^4\,c^3\,d^8+\frac{9843\,a^6\,b^5\,c^4\,d^7}{2}+6884\,a^5\,b^6\,c^5\,d^6+\frac{9843\,a^4\,b^7\,c^6\,d^5}{2}+1674\,a^3\,b^8\,c^7\,d^4+\frac{405\,a^2\,b^9\,c^8\,d^3}{2}}{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}-{\left(-\frac{625\,a^4\,c\,d^4+1500\,a^3\,b\,c^2\,d^3+1350\,a^2\,b^2\,c^3\,d^2+540\,a\,b^3\,c^4\,d+81\,b^4\,c^5}{4096\,a^{12}\,d^{13}-49152\,a^{11}\,b\,c\,d^{12}+270336\,a^{10}\,b^2\,c^2\,d^{11}-901120\,a^9\,b^3\,c^3\,d^{10}+2027520\,a^8\,b^4\,c^4\,d^9-3244032\,a^7\,b^5\,c^5\,d^8+3784704\,a^6\,b^6\,c^6\,d^7-3244032\,a^5\,b^7\,c^7\,d^6+2027520\,a^4\,b^8\,c^8\,d^5-901120\,a^3\,b^9\,c^9\,d^4+270336\,a^2\,b^{10}\,c^{10}\,d^3-49152\,a\,b^{11}\,c^{11}\,d^2+4096\,b^{12}\,c^{12}\,d}\right)}^{3/4}\,\left(\frac{\sqrt{x}\,\left(102400\,a^{17}\,b^4\,c^2\,d^{19}-1069056\,a^{16}\,b^5\,c^3\,d^{18}+5001216\,a^{15}\,b^6\,c^4\,d^{17}-13799424\,a^{14}\,b^7\,c^5\,d^{16}+24858624\,a^{13}\,b^8\,c^6\,d^{15}-30412800\,a^{12}\,b^9\,c^7\,d^{14}+24645632\,a^{11}\,b^{10}\,c^8\,d^{13}-9326592\,a^{10}\,b^{11}\,c^9\,d^{12}-9326592\,a^9\,b^{12}\,c^{10}\,d^{11}+24645632\,a^8\,b^{13}\,c^{11}\,d^{10}-30412800\,a^7\,b^{14}\,c^{12}\,d^9+24858624\,a^6\,b^{15}\,c^{13}\,d^8-13799424\,a^5\,b^{16}\,c^{14}\,d^7+5001216\,a^4\,b^{17}\,c^{15}\,d^6-1069056\,a^3\,b^{18}\,c^{16}\,d^5+102400\,a^2\,b^{19}\,c^{17}\,d^4\right)}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}-\frac{{\left(-\frac{625\,a^4\,c\,d^4+1500\,a^3\,b\,c^2\,d^3+1350\,a^2\,b^2\,c^3\,d^2+540\,a\,b^3\,c^4\,d+81\,b^4\,c^5}{4096\,a^{12}\,d^{13}-49152\,a^{11}\,b\,c\,d^{12}+270336\,a^{10}\,b^2\,c^2\,d^{11}-901120\,a^9\,b^3\,c^3\,d^{10}+2027520\,a^8\,b^4\,c^4\,d^9-3244032\,a^7\,b^5\,c^5\,d^8+3784704\,a^6\,b^6\,c^6\,d^7-3244032\,a^5\,b^7\,c^7\,d^6+2027520\,a^4\,b^8\,c^8\,d^5-901120\,a^3\,b^9\,c^9\,d^4+270336\,a^2\,b^{10}\,c^{10}\,d^3-49152\,a\,b^{11}\,c^{11}\,d^2+4096\,b^{12}\,c^{12}\,d}\right)}^{1/4}\,\left(10240\,a^{15}\,b^4\,c^2\,d^{17}-112640\,a^{14}\,b^5\,c^3\,d^{16}+552960\,a^{13}\,b^6\,c^4\,d^{15}-1576960\,a^{12}\,b^7\,c^5\,d^{14}+2816000\,a^{11}\,b^8\,c^6\,d^{13}-3041280\,a^{10}\,b^9\,c^7\,d^{12}+1351680\,a^9\,b^{10}\,c^8\,d^{11}+1351680\,a^8\,b^{11}\,c^9\,d^{10}-3041280\,a^7\,b^{12}\,c^{10}\,d^9+2816000\,a^6\,b^{13}\,c^{11}\,d^8-1576960\,a^5\,b^{14}\,c^{12}\,d^7+552960\,a^4\,b^{15}\,c^{13}\,d^6-112640\,a^3\,b^{16}\,c^{14}\,d^5+10240\,a^2\,b^{17}\,c^{15}\,d^4\right)}{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)\right)-\frac{\sqrt{x}\,\left(2025\,a^{10}\,b^3\,c^2\,d^{11}+15930\,a^9\,b^4\,c^3\,d^{10}+56304\,a^8\,b^5\,c^4\,d^9+115110\,a^7\,b^6\,c^5\,d^8+145550\,a^6\,b^7\,c^6\,d^7+115110\,a^5\,b^8\,c^7\,d^6+56304\,a^4\,b^9\,c^8\,d^5+15930\,a^3\,b^{10}\,c^9\,d^4+2025\,a^2\,b^{11}\,c^{10}\,d^3\right)}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)}\right)\,{\left(-\frac{625\,a^4\,c\,d^4+1500\,a^3\,b\,c^2\,d^3+1350\,a^2\,b^2\,c^3\,d^2+540\,a\,b^3\,c^4\,d+81\,b^4\,c^5}{4096\,a^{12}\,d^{13}-49152\,a^{11}\,b\,c\,d^{12}+270336\,a^{10}\,b^2\,c^2\,d^{11}-901120\,a^9\,b^3\,c^3\,d^{10}+2027520\,a^8\,b^4\,c^4\,d^9-3244032\,a^7\,b^5\,c^5\,d^8+3784704\,a^6\,b^6\,c^6\,d^7-3244032\,a^5\,b^7\,c^7\,d^6+2027520\,a^4\,b^8\,c^8\,d^5-901120\,a^3\,b^9\,c^9\,d^4+270336\,a^2\,b^{10}\,c^{10}\,d^3-49152\,a\,b^{11}\,c^{11}\,d^2+4096\,b^{12}\,c^{12}\,d}\right)}^{1/4}\,2{}\mathrm{i}-2\,\mathrm{atan}\left(\frac{{\left(-\frac{625\,a^4\,c\,d^4+1500\,a^3\,b\,c^2\,d^3+1350\,a^2\,b^2\,c^3\,d^2+540\,a\,b^3\,c^4\,d+81\,b^4\,c^5}{4096\,a^{12}\,d^{13}-49152\,a^{11}\,b\,c\,d^{12}+270336\,a^{10}\,b^2\,c^2\,d^{11}-901120\,a^9\,b^3\,c^3\,d^{10}+2027520\,a^8\,b^4\,c^4\,d^9-3244032\,a^7\,b^5\,c^5\,d^8+3784704\,a^6\,b^6\,c^6\,d^7-3244032\,a^5\,b^7\,c^7\,d^6+2027520\,a^4\,b^8\,c^8\,d^5-901120\,a^3\,b^9\,c^9\,d^4+270336\,a^2\,b^{10}\,c^{10}\,d^3-49152\,a\,b^{11}\,c^{11}\,d^2+4096\,b^{12}\,c^{12}\,d}\right)}^{1/4}\,\left({\left(-\frac{625\,a^4\,c\,d^4+1500\,a^3\,b\,c^2\,d^3+1350\,a^2\,b^2\,c^3\,d^2+540\,a\,b^3\,c^4\,d+81\,b^4\,c^5}{4096\,a^{12}\,d^{13}-49152\,a^{11}\,b\,c\,d^{12}+270336\,a^{10}\,b^2\,c^2\,d^{11}-901120\,a^9\,b^3\,c^3\,d^{10}+2027520\,a^8\,b^4\,c^4\,d^9-3244032\,a^7\,b^5\,c^5\,d^8+3784704\,a^6\,b^6\,c^6\,d^7-3244032\,a^5\,b^7\,c^7\,d^6+2027520\,a^4\,b^8\,c^8\,d^5-901120\,a^3\,b^9\,c^9\,d^4+270336\,a^2\,b^{10}\,c^{10}\,d^3-49152\,a\,b^{11}\,c^{11}\,d^2+4096\,b^{12}\,c^{12}\,d}\right)}^{1/4}\,\left(\frac{\left(\frac{405\,a^8\,b^3\,c^2\,d^9}{2}+1674\,a^7\,b^4\,c^3\,d^8+\frac{9843\,a^6\,b^5\,c^4\,d^7}{2}+6884\,a^5\,b^6\,c^5\,d^6+\frac{9843\,a^4\,b^7\,c^6\,d^5}{2}+1674\,a^3\,b^8\,c^7\,d^4+\frac{405\,a^2\,b^9\,c^8\,d^3}{2}\right)\,1{}\mathrm{i}}{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}+{\left(-\frac{625\,a^4\,c\,d^4+1500\,a^3\,b\,c^2\,d^3+1350\,a^2\,b^2\,c^3\,d^2+540\,a\,b^3\,c^4\,d+81\,b^4\,c^5}{4096\,a^{12}\,d^{13}-49152\,a^{11}\,b\,c\,d^{12}+270336\,a^{10}\,b^2\,c^2\,d^{11}-901120\,a^9\,b^3\,c^3\,d^{10}+2027520\,a^8\,b^4\,c^4\,d^9-3244032\,a^7\,b^5\,c^5\,d^8+3784704\,a^6\,b^6\,c^6\,d^7-3244032\,a^5\,b^7\,c^7\,d^6+2027520\,a^4\,b^8\,c^8\,d^5-901120\,a^3\,b^9\,c^9\,d^4+270336\,a^2\,b^{10}\,c^{10}\,d^3-49152\,a\,b^{11}\,c^{11}\,d^2+4096\,b^{12}\,c^{12}\,d}\right)}^{3/4}\,\left(\frac{{\left(-\frac{625\,a^4\,c\,d^4+1500\,a^3\,b\,c^2\,d^3+1350\,a^2\,b^2\,c^3\,d^2+540\,a\,b^3\,c^4\,d+81\,b^4\,c^5}{4096\,a^{12}\,d^{13}-49152\,a^{11}\,b\,c\,d^{12}+270336\,a^{10}\,b^2\,c^2\,d^{11}-901120\,a^9\,b^3\,c^3\,d^{10}+2027520\,a^8\,b^4\,c^4\,d^9-3244032\,a^7\,b^5\,c^5\,d^8+3784704\,a^6\,b^6\,c^6\,d^7-3244032\,a^5\,b^7\,c^7\,d^6+2027520\,a^4\,b^8\,c^8\,d^5-901120\,a^3\,b^9\,c^9\,d^4+270336\,a^2\,b^{10}\,c^{10}\,d^3-49152\,a\,b^{11}\,c^{11}\,d^2+4096\,b^{12}\,c^{12}\,d}\right)}^{1/4}\,\left(10240\,a^{15}\,b^4\,c^2\,d^{17}-112640\,a^{14}\,b^5\,c^3\,d^{16}+552960\,a^{13}\,b^6\,c^4\,d^{15}-1576960\,a^{12}\,b^7\,c^5\,d^{14}+2816000\,a^{11}\,b^8\,c^6\,d^{13}-3041280\,a^{10}\,b^9\,c^7\,d^{12}+1351680\,a^9\,b^{10}\,c^8\,d^{11}+1351680\,a^8\,b^{11}\,c^9\,d^{10}-3041280\,a^7\,b^{12}\,c^{10}\,d^9+2816000\,a^6\,b^{13}\,c^{11}\,d^8-1576960\,a^5\,b^{14}\,c^{12}\,d^7+552960\,a^4\,b^{15}\,c^{13}\,d^6-112640\,a^3\,b^{16}\,c^{14}\,d^5+10240\,a^2\,b^{17}\,c^{15}\,d^4\right)}{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}+\frac{\sqrt{x}\,\left(102400\,a^{17}\,b^4\,c^2\,d^{19}-1069056\,a^{16}\,b^5\,c^3\,d^{18}+5001216\,a^{15}\,b^6\,c^4\,d^{17}-13799424\,a^{14}\,b^7\,c^5\,d^{16}+24858624\,a^{13}\,b^8\,c^6\,d^{15}-30412800\,a^{12}\,b^9\,c^7\,d^{14}+24645632\,a^{11}\,b^{10}\,c^8\,d^{13}-9326592\,a^{10}\,b^{11}\,c^9\,d^{12}-9326592\,a^9\,b^{12}\,c^{10}\,d^{11}+24645632\,a^8\,b^{13}\,c^{11}\,d^{10}-30412800\,a^7\,b^{14}\,c^{12}\,d^9+24858624\,a^6\,b^{15}\,c^{13}\,d^8-13799424\,a^5\,b^{16}\,c^{14}\,d^7+5001216\,a^4\,b^{17}\,c^{15}\,d^6-1069056\,a^3\,b^{18}\,c^{16}\,d^5+102400\,a^2\,b^{19}\,c^{17}\,d^4\right)\,1{}\mathrm{i}}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)\,1{}\mathrm{i}\right)-\frac{\sqrt{x}\,\left(2025\,a^{10}\,b^3\,c^2\,d^{11}+15930\,a^9\,b^4\,c^3\,d^{10}+56304\,a^8\,b^5\,c^4\,d^9+115110\,a^7\,b^6\,c^5\,d^8+145550\,a^6\,b^7\,c^6\,d^7+115110\,a^5\,b^8\,c^7\,d^6+56304\,a^4\,b^9\,c^8\,d^5+15930\,a^3\,b^{10}\,c^9\,d^4+2025\,a^2\,b^{11}\,c^{10}\,d^3\right)}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)-{\left(-\frac{625\,a^4\,c\,d^4+1500\,a^3\,b\,c^2\,d^3+1350\,a^2\,b^2\,c^3\,d^2+540\,a\,b^3\,c^4\,d+81\,b^4\,c^5}{4096\,a^{12}\,d^{13}-49152\,a^{11}\,b\,c\,d^{12}+270336\,a^{10}\,b^2\,c^2\,d^{11}-901120\,a^9\,b^3\,c^3\,d^{10}+2027520\,a^8\,b^4\,c^4\,d^9-3244032\,a^7\,b^5\,c^5\,d^8+3784704\,a^6\,b^6\,c^6\,d^7-3244032\,a^5\,b^7\,c^7\,d^6+2027520\,a^4\,b^8\,c^8\,d^5-901120\,a^3\,b^9\,c^9\,d^4+270336\,a^2\,b^{10}\,c^{10}\,d^3-49152\,a\,b^{11}\,c^{11}\,d^2+4096\,b^{12}\,c^{12}\,d}\right)}^{1/4}\,\left({\left(-\frac{625\,a^4\,c\,d^4+1500\,a^3\,b\,c^2\,d^3+1350\,a^2\,b^2\,c^3\,d^2+540\,a\,b^3\,c^4\,d+81\,b^4\,c^5}{4096\,a^{12}\,d^{13}-49152\,a^{11}\,b\,c\,d^{12}+270336\,a^{10}\,b^2\,c^2\,d^{11}-901120\,a^9\,b^3\,c^3\,d^{10}+2027520\,a^8\,b^4\,c^4\,d^9-3244032\,a^7\,b^5\,c^5\,d^8+3784704\,a^6\,b^6\,c^6\,d^7-3244032\,a^5\,b^7\,c^7\,d^6+2027520\,a^4\,b^8\,c^8\,d^5-901120\,a^3\,b^9\,c^9\,d^4+270336\,a^2\,b^{10}\,c^{10}\,d^3-49152\,a\,b^{11}\,c^{11}\,d^2+4096\,b^{12}\,c^{12}\,d}\right)}^{1/4}\,\left(\frac{\left(\frac{405\,a^8\,b^3\,c^2\,d^9}{2}+1674\,a^7\,b^4\,c^3\,d^8+\frac{9843\,a^6\,b^5\,c^4\,d^7}{2}+6884\,a^5\,b^6\,c^5\,d^6+\frac{9843\,a^4\,b^7\,c^6\,d^5}{2}+1674\,a^3\,b^8\,c^7\,d^4+\frac{405\,a^2\,b^9\,c^8\,d^3}{2}\right)\,1{}\mathrm{i}}{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}-{\left(-\frac{625\,a^4\,c\,d^4+1500\,a^3\,b\,c^2\,d^3+1350\,a^2\,b^2\,c^3\,d^2+540\,a\,b^3\,c^4\,d+81\,b^4\,c^5}{4096\,a^{12}\,d^{13}-49152\,a^{11}\,b\,c\,d^{12}+270336\,a^{10}\,b^2\,c^2\,d^{11}-901120\,a^9\,b^3\,c^3\,d^{10}+2027520\,a^8\,b^4\,c^4\,d^9-3244032\,a^7\,b^5\,c^5\,d^8+3784704\,a^6\,b^6\,c^6\,d^7-3244032\,a^5\,b^7\,c^7\,d^6+2027520\,a^4\,b^8\,c^8\,d^5-901120\,a^3\,b^9\,c^9\,d^4+270336\,a^2\,b^{10}\,c^{10}\,d^3-49152\,a\,b^{11}\,c^{11}\,d^2+4096\,b^{12}\,c^{12}\,d}\right)}^{3/4}\,\left(-\frac{{\left(-\frac{625\,a^4\,c\,d^4+1500\,a^3\,b\,c^2\,d^3+1350\,a^2\,b^2\,c^3\,d^2+540\,a\,b^3\,c^4\,d+81\,b^4\,c^5}{4096\,a^{12}\,d^{13}-49152\,a^{11}\,b\,c\,d^{12}+270336\,a^{10}\,b^2\,c^2\,d^{11}-901120\,a^9\,b^3\,c^3\,d^{10}+2027520\,a^8\,b^4\,c^4\,d^9-3244032\,a^7\,b^5\,c^5\,d^8+3784704\,a^6\,b^6\,c^6\,d^7-3244032\,a^5\,b^7\,c^7\,d^6+2027520\,a^4\,b^8\,c^8\,d^5-901120\,a^3\,b^9\,c^9\,d^4+270336\,a^2\,b^{10}\,c^{10}\,d^3-49152\,a\,b^{11}\,c^{11}\,d^2+4096\,b^{12}\,c^{12}\,d}\right)}^{1/4}\,\left(10240\,a^{15}\,b^4\,c^2\,d^{17}-112640\,a^{14}\,b^5\,c^3\,d^{16}+552960\,a^{13}\,b^6\,c^4\,d^{15}-1576960\,a^{12}\,b^7\,c^5\,d^{14}+2816000\,a^{11}\,b^8\,c^6\,d^{13}-3041280\,a^{10}\,b^9\,c^7\,d^{12}+1351680\,a^9\,b^{10}\,c^8\,d^{11}+1351680\,a^8\,b^{11}\,c^9\,d^{10}-3041280\,a^7\,b^{12}\,c^{10}\,d^9+2816000\,a^6\,b^{13}\,c^{11}\,d^8-1576960\,a^5\,b^{14}\,c^{12}\,d^7+552960\,a^4\,b^{15}\,c^{13}\,d^6-112640\,a^3\,b^{16}\,c^{14}\,d^5+10240\,a^2\,b^{17}\,c^{15}\,d^4\right)}{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}+\frac{\sqrt{x}\,\left(102400\,a^{17}\,b^4\,c^2\,d^{19}-1069056\,a^{16}\,b^5\,c^3\,d^{18}+5001216\,a^{15}\,b^6\,c^4\,d^{17}-13799424\,a^{14}\,b^7\,c^5\,d^{16}+24858624\,a^{13}\,b^8\,c^6\,d^{15}-30412800\,a^{12}\,b^9\,c^7\,d^{14}+24645632\,a^{11}\,b^{10}\,c^8\,d^{13}-9326592\,a^{10}\,b^{11}\,c^9\,d^{12}-9326592\,a^9\,b^{12}\,c^{10}\,d^{11}+24645632\,a^8\,b^{13}\,c^{11}\,d^{10}-30412800\,a^7\,b^{14}\,c^{12}\,d^9+24858624\,a^6\,b^{15}\,c^{13}\,d^8-13799424\,a^5\,b^{16}\,c^{14}\,d^7+5001216\,a^4\,b^{17}\,c^{15}\,d^6-1069056\,a^3\,b^{18}\,c^{16}\,d^5+102400\,a^2\,b^{19}\,c^{17}\,d^4\right)\,1{}\mathrm{i}}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)\,1{}\mathrm{i}\right)+\frac{\sqrt{x}\,\left(2025\,a^{10}\,b^3\,c^2\,d^{11}+15930\,a^9\,b^4\,c^3\,d^{10}+56304\,a^8\,b^5\,c^4\,d^9+115110\,a^7\,b^6\,c^5\,d^8+145550\,a^6\,b^7\,c^6\,d^7+115110\,a^5\,b^8\,c^7\,d^6+56304\,a^4\,b^9\,c^8\,d^5+15930\,a^3\,b^{10}\,c^9\,d^4+2025\,a^2\,b^{11}\,c^{10}\,d^3\right)}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)}{{\left(-\frac{625\,a^4\,c\,d^4+1500\,a^3\,b\,c^2\,d^3+1350\,a^2\,b^2\,c^3\,d^2+540\,a\,b^3\,c^4\,d+81\,b^4\,c^5}{4096\,a^{12}\,d^{13}-49152\,a^{11}\,b\,c\,d^{12}+270336\,a^{10}\,b^2\,c^2\,d^{11}-901120\,a^9\,b^3\,c^3\,d^{10}+2027520\,a^8\,b^4\,c^4\,d^9-3244032\,a^7\,b^5\,c^5\,d^8+3784704\,a^6\,b^6\,c^6\,d^7-3244032\,a^5\,b^7\,c^7\,d^6+2027520\,a^4\,b^8\,c^8\,d^5-901120\,a^3\,b^9\,c^9\,d^4+270336\,a^2\,b^{10}\,c^{10}\,d^3-49152\,a\,b^{11}\,c^{11}\,d^2+4096\,b^{12}\,c^{12}\,d}\right)}^{1/4}\,\left({\left(-\frac{625\,a^4\,c\,d^4+1500\,a^3\,b\,c^2\,d^3+1350\,a^2\,b^2\,c^3\,d^2+540\,a\,b^3\,c^4\,d+81\,b^4\,c^5}{4096\,a^{12}\,d^{13}-49152\,a^{11}\,b\,c\,d^{12}+270336\,a^{10}\,b^2\,c^2\,d^{11}-901120\,a^9\,b^3\,c^3\,d^{10}+2027520\,a^8\,b^4\,c^4\,d^9-3244032\,a^7\,b^5\,c^5\,d^8+3784704\,a^6\,b^6\,c^6\,d^7-3244032\,a^5\,b^7\,c^7\,d^6+2027520\,a^4\,b^8\,c^8\,d^5-901120\,a^3\,b^9\,c^9\,d^4+270336\,a^2\,b^{10}\,c^{10}\,d^3-49152\,a\,b^{11}\,c^{11}\,d^2+4096\,b^{12}\,c^{12}\,d}\right)}^{1/4}\,\left(\frac{\left(\frac{405\,a^8\,b^3\,c^2\,d^9}{2}+1674\,a^7\,b^4\,c^3\,d^8+\frac{9843\,a^6\,b^5\,c^4\,d^7}{2}+6884\,a^5\,b^6\,c^5\,d^6+\frac{9843\,a^4\,b^7\,c^6\,d^5}{2}+1674\,a^3\,b^8\,c^7\,d^4+\frac{405\,a^2\,b^9\,c^8\,d^3}{2}\right)\,1{}\mathrm{i}}{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}+{\left(-\frac{625\,a^4\,c\,d^4+1500\,a^3\,b\,c^2\,d^3+1350\,a^2\,b^2\,c^3\,d^2+540\,a\,b^3\,c^4\,d+81\,b^4\,c^5}{4096\,a^{12}\,d^{13}-49152\,a^{11}\,b\,c\,d^{12}+270336\,a^{10}\,b^2\,c^2\,d^{11}-901120\,a^9\,b^3\,c^3\,d^{10}+2027520\,a^8\,b^4\,c^4\,d^9-3244032\,a^7\,b^5\,c^5\,d^8+3784704\,a^6\,b^6\,c^6\,d^7-3244032\,a^5\,b^7\,c^7\,d^6+2027520\,a^4\,b^8\,c^8\,d^5-901120\,a^3\,b^9\,c^9\,d^4+270336\,a^2\,b^{10}\,c^{10}\,d^3-49152\,a\,b^{11}\,c^{11}\,d^2+4096\,b^{12}\,c^{12}\,d}\right)}^{3/4}\,\left(\frac{{\left(-\frac{625\,a^4\,c\,d^4+1500\,a^3\,b\,c^2\,d^3+1350\,a^2\,b^2\,c^3\,d^2+540\,a\,b^3\,c^4\,d+81\,b^4\,c^5}{4096\,a^{12}\,d^{13}-49152\,a^{11}\,b\,c\,d^{12}+270336\,a^{10}\,b^2\,c^2\,d^{11}-901120\,a^9\,b^3\,c^3\,d^{10}+2027520\,a^8\,b^4\,c^4\,d^9-3244032\,a^7\,b^5\,c^5\,d^8+3784704\,a^6\,b^6\,c^6\,d^7-3244032\,a^5\,b^7\,c^7\,d^6+2027520\,a^4\,b^8\,c^8\,d^5-901120\,a^3\,b^9\,c^9\,d^4+270336\,a^2\,b^{10}\,c^{10}\,d^3-49152\,a\,b^{11}\,c^{11}\,d^2+4096\,b^{12}\,c^{12}\,d}\right)}^{1/4}\,\left(10240\,a^{15}\,b^4\,c^2\,d^{17}-112640\,a^{14}\,b^5\,c^3\,d^{16}+552960\,a^{13}\,b^6\,c^4\,d^{15}-1576960\,a^{12}\,b^7\,c^5\,d^{14}+2816000\,a^{11}\,b^8\,c^6\,d^{13}-3041280\,a^{10}\,b^9\,c^7\,d^{12}+1351680\,a^9\,b^{10}\,c^8\,d^{11}+1351680\,a^8\,b^{11}\,c^9\,d^{10}-3041280\,a^7\,b^{12}\,c^{10}\,d^9+2816000\,a^6\,b^{13}\,c^{11}\,d^8-1576960\,a^5\,b^{14}\,c^{12}\,d^7+552960\,a^4\,b^{15}\,c^{13}\,d^6-112640\,a^3\,b^{16}\,c^{14}\,d^5+10240\,a^2\,b^{17}\,c^{15}\,d^4\right)}{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}+\frac{\sqrt{x}\,\left(102400\,a^{17}\,b^4\,c^2\,d^{19}-1069056\,a^{16}\,b^5\,c^3\,d^{18}+5001216\,a^{15}\,b^6\,c^4\,d^{17}-13799424\,a^{14}\,b^7\,c^5\,d^{16}+24858624\,a^{13}\,b^8\,c^6\,d^{15}-30412800\,a^{12}\,b^9\,c^7\,d^{14}+24645632\,a^{11}\,b^{10}\,c^8\,d^{13}-9326592\,a^{10}\,b^{11}\,c^9\,d^{12}-9326592\,a^9\,b^{12}\,c^{10}\,d^{11}+24645632\,a^8\,b^{13}\,c^{11}\,d^{10}-30412800\,a^7\,b^{14}\,c^{12}\,d^9+24858624\,a^6\,b^{15}\,c^{13}\,d^8-13799424\,a^5\,b^{16}\,c^{14}\,d^7+5001216\,a^4\,b^{17}\,c^{15}\,d^6-1069056\,a^3\,b^{18}\,c^{16}\,d^5+102400\,a^2\,b^{19}\,c^{17}\,d^4\right)\,1{}\mathrm{i}}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}-\frac{\sqrt{x}\,\left(2025\,a^{10}\,b^3\,c^2\,d^{11}+15930\,a^9\,b^4\,c^3\,d^{10}+56304\,a^8\,b^5\,c^4\,d^9+115110\,a^7\,b^6\,c^5\,d^8+145550\,a^6\,b^7\,c^6\,d^7+115110\,a^5\,b^8\,c^7\,d^6+56304\,a^4\,b^9\,c^8\,d^5+15930\,a^3\,b^{10}\,c^9\,d^4+2025\,a^2\,b^{11}\,c^{10}\,d^3\right)\,1{}\mathrm{i}}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)+{\left(-\frac{625\,a^4\,c\,d^4+1500\,a^3\,b\,c^2\,d^3+1350\,a^2\,b^2\,c^3\,d^2+540\,a\,b^3\,c^4\,d+81\,b^4\,c^5}{4096\,a^{12}\,d^{13}-49152\,a^{11}\,b\,c\,d^{12}+270336\,a^{10}\,b^2\,c^2\,d^{11}-901120\,a^9\,b^3\,c^3\,d^{10}+2027520\,a^8\,b^4\,c^4\,d^9-3244032\,a^7\,b^5\,c^5\,d^8+3784704\,a^6\,b^6\,c^6\,d^7-3244032\,a^5\,b^7\,c^7\,d^6+2027520\,a^4\,b^8\,c^8\,d^5-901120\,a^3\,b^9\,c^9\,d^4+270336\,a^2\,b^{10}\,c^{10}\,d^3-49152\,a\,b^{11}\,c^{11}\,d^2+4096\,b^{12}\,c^{12}\,d}\right)}^{1/4}\,\left({\left(-\frac{625\,a^4\,c\,d^4+1500\,a^3\,b\,c^2\,d^3+1350\,a^2\,b^2\,c^3\,d^2+540\,a\,b^3\,c^4\,d+81\,b^4\,c^5}{4096\,a^{12}\,d^{13}-49152\,a^{11}\,b\,c\,d^{12}+270336\,a^{10}\,b^2\,c^2\,d^{11}-901120\,a^9\,b^3\,c^3\,d^{10}+2027520\,a^8\,b^4\,c^4\,d^9-3244032\,a^7\,b^5\,c^5\,d^8+3784704\,a^6\,b^6\,c^6\,d^7-3244032\,a^5\,b^7\,c^7\,d^6+2027520\,a^4\,b^8\,c^8\,d^5-901120\,a^3\,b^9\,c^9\,d^4+270336\,a^2\,b^{10}\,c^{10}\,d^3-49152\,a\,b^{11}\,c^{11}\,d^2+4096\,b^{12}\,c^{12}\,d}\right)}^{1/4}\,\left(\frac{\left(\frac{405\,a^8\,b^3\,c^2\,d^9}{2}+1674\,a^7\,b^4\,c^3\,d^8+\frac{9843\,a^6\,b^5\,c^4\,d^7}{2}+6884\,a^5\,b^6\,c^5\,d^6+\frac{9843\,a^4\,b^7\,c^6\,d^5}{2}+1674\,a^3\,b^8\,c^7\,d^4+\frac{405\,a^2\,b^9\,c^8\,d^3}{2}\right)\,1{}\mathrm{i}}{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}-{\left(-\frac{625\,a^4\,c\,d^4+1500\,a^3\,b\,c^2\,d^3+1350\,a^2\,b^2\,c^3\,d^2+540\,a\,b^3\,c^4\,d+81\,b^4\,c^5}{4096\,a^{12}\,d^{13}-49152\,a^{11}\,b\,c\,d^{12}+270336\,a^{10}\,b^2\,c^2\,d^{11}-901120\,a^9\,b^3\,c^3\,d^{10}+2027520\,a^8\,b^4\,c^4\,d^9-3244032\,a^7\,b^5\,c^5\,d^8+3784704\,a^6\,b^6\,c^6\,d^7-3244032\,a^5\,b^7\,c^7\,d^6+2027520\,a^4\,b^8\,c^8\,d^5-901120\,a^3\,b^9\,c^9\,d^4+270336\,a^2\,b^{10}\,c^{10}\,d^3-49152\,a\,b^{11}\,c^{11}\,d^2+4096\,b^{12}\,c^{12}\,d}\right)}^{3/4}\,\left(-\frac{{\left(-\frac{625\,a^4\,c\,d^4+1500\,a^3\,b\,c^2\,d^3+1350\,a^2\,b^2\,c^3\,d^2+540\,a\,b^3\,c^4\,d+81\,b^4\,c^5}{4096\,a^{12}\,d^{13}-49152\,a^{11}\,b\,c\,d^{12}+270336\,a^{10}\,b^2\,c^2\,d^{11}-901120\,a^9\,b^3\,c^3\,d^{10}+2027520\,a^8\,b^4\,c^4\,d^9-3244032\,a^7\,b^5\,c^5\,d^8+3784704\,a^6\,b^6\,c^6\,d^7-3244032\,a^5\,b^7\,c^7\,d^6+2027520\,a^4\,b^8\,c^8\,d^5-901120\,a^3\,b^9\,c^9\,d^4+270336\,a^2\,b^{10}\,c^{10}\,d^3-49152\,a\,b^{11}\,c^{11}\,d^2+4096\,b^{12}\,c^{12}\,d}\right)}^{1/4}\,\left(10240\,a^{15}\,b^4\,c^2\,d^{17}-112640\,a^{14}\,b^5\,c^3\,d^{16}+552960\,a^{13}\,b^6\,c^4\,d^{15}-1576960\,a^{12}\,b^7\,c^5\,d^{14}+2816000\,a^{11}\,b^8\,c^6\,d^{13}-3041280\,a^{10}\,b^9\,c^7\,d^{12}+1351680\,a^9\,b^{10}\,c^8\,d^{11}+1351680\,a^8\,b^{11}\,c^9\,d^{10}-3041280\,a^7\,b^{12}\,c^{10}\,d^9+2816000\,a^6\,b^{13}\,c^{11}\,d^8-1576960\,a^5\,b^{14}\,c^{12}\,d^7+552960\,a^4\,b^{15}\,c^{13}\,d^6-112640\,a^3\,b^{16}\,c^{14}\,d^5+10240\,a^2\,b^{17}\,c^{15}\,d^4\right)}{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}+\frac{\sqrt{x}\,\left(102400\,a^{17}\,b^4\,c^2\,d^{19}-1069056\,a^{16}\,b^5\,c^3\,d^{18}+5001216\,a^{15}\,b^6\,c^4\,d^{17}-13799424\,a^{14}\,b^7\,c^5\,d^{16}+24858624\,a^{13}\,b^8\,c^6\,d^{15}-30412800\,a^{12}\,b^9\,c^7\,d^{14}+24645632\,a^{11}\,b^{10}\,c^8\,d^{13}-9326592\,a^{10}\,b^{11}\,c^9\,d^{12}-9326592\,a^9\,b^{12}\,c^{10}\,d^{11}+24645632\,a^8\,b^{13}\,c^{11}\,d^{10}-30412800\,a^7\,b^{14}\,c^{12}\,d^9+24858624\,a^6\,b^{15}\,c^{13}\,d^8-13799424\,a^5\,b^{16}\,c^{14}\,d^7+5001216\,a^4\,b^{17}\,c^{15}\,d^6-1069056\,a^3\,b^{18}\,c^{16}\,d^5+102400\,a^2\,b^{19}\,c^{17}\,d^4\right)\,1{}\mathrm{i}}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}+\frac{\sqrt{x}\,\left(2025\,a^{10}\,b^3\,c^2\,d^{11}+15930\,a^9\,b^4\,c^3\,d^{10}+56304\,a^8\,b^5\,c^4\,d^9+115110\,a^7\,b^6\,c^5\,d^8+145550\,a^6\,b^7\,c^6\,d^7+115110\,a^5\,b^8\,c^7\,d^6+56304\,a^4\,b^9\,c^8\,d^5+15930\,a^3\,b^{10}\,c^9\,d^4+2025\,a^2\,b^{11}\,c^{10}\,d^3\right)\,1{}\mathrm{i}}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)}\right)\,{\left(-\frac{625\,a^4\,c\,d^4+1500\,a^3\,b\,c^2\,d^3+1350\,a^2\,b^2\,c^3\,d^2+540\,a\,b^3\,c^4\,d+81\,b^4\,c^5}{4096\,a^{12}\,d^{13}-49152\,a^{11}\,b\,c\,d^{12}+270336\,a^{10}\,b^2\,c^2\,d^{11}-901120\,a^9\,b^3\,c^3\,d^{10}+2027520\,a^8\,b^4\,c^4\,d^9-3244032\,a^7\,b^5\,c^5\,d^8+3784704\,a^6\,b^6\,c^6\,d^7-3244032\,a^5\,b^7\,c^7\,d^6+2027520\,a^4\,b^8\,c^8\,d^5-901120\,a^3\,b^9\,c^9\,d^4+270336\,a^2\,b^{10}\,c^{10}\,d^3-49152\,a\,b^{11}\,c^{11}\,d^2+4096\,b^{12}\,c^{12}\,d}\right)}^{1/4}+\frac{\frac{x^{5/2}\,\left(a\,d+b\,c\right)}{2\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}+\frac{a\,c\,\sqrt{x}}{a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2}}{b\,d\,x^4+\left(a\,d+b\,c\right)\,x^2+a\,c}+\mathrm{atan}\left(\frac{{\left(-\frac{81\,a^5\,d^4+540\,a^4\,b\,c\,d^3+1350\,a^3\,b^2\,c^2\,d^2+1500\,a^2\,b^3\,c^3\,d+625\,a\,b^4\,c^4}{4096\,a^{12}\,b\,d^{12}-49152\,a^{11}\,b^2\,c\,d^{11}+270336\,a^{10}\,b^3\,c^2\,d^{10}-901120\,a^9\,b^4\,c^3\,d^9+2027520\,a^8\,b^5\,c^4\,d^8-3244032\,a^7\,b^6\,c^5\,d^7+3784704\,a^6\,b^7\,c^6\,d^6-3244032\,a^5\,b^8\,c^7\,d^5+2027520\,a^4\,b^9\,c^8\,d^4-901120\,a^3\,b^{10}\,c^9\,d^3+270336\,a^2\,b^{11}\,c^{10}\,d^2-49152\,a\,b^{12}\,c^{11}\,d+4096\,b^{13}\,c^{12}}\right)}^{1/4}\,\left({\left(-\frac{81\,a^5\,d^4+540\,a^4\,b\,c\,d^3+1350\,a^3\,b^2\,c^2\,d^2+1500\,a^2\,b^3\,c^3\,d+625\,a\,b^4\,c^4}{4096\,a^{12}\,b\,d^{12}-49152\,a^{11}\,b^2\,c\,d^{11}+270336\,a^{10}\,b^3\,c^2\,d^{10}-901120\,a^9\,b^4\,c^3\,d^9+2027520\,a^8\,b^5\,c^4\,d^8-3244032\,a^7\,b^6\,c^5\,d^7+3784704\,a^6\,b^7\,c^6\,d^6-3244032\,a^5\,b^8\,c^7\,d^5+2027520\,a^4\,b^9\,c^8\,d^4-901120\,a^3\,b^{10}\,c^9\,d^3+270336\,a^2\,b^{11}\,c^{10}\,d^2-49152\,a\,b^{12}\,c^{11}\,d+4096\,b^{13}\,c^{12}}\right)}^{1/4}\,\left(\frac{\frac{405\,a^8\,b^3\,c^2\,d^9}{2}+1674\,a^7\,b^4\,c^3\,d^8+\frac{9843\,a^6\,b^5\,c^4\,d^7}{2}+6884\,a^5\,b^6\,c^5\,d^6+\frac{9843\,a^4\,b^7\,c^6\,d^5}{2}+1674\,a^3\,b^8\,c^7\,d^4+\frac{405\,a^2\,b^9\,c^8\,d^3}{2}}{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}+{\left(-\frac{81\,a^5\,d^4+540\,a^4\,b\,c\,d^3+1350\,a^3\,b^2\,c^2\,d^2+1500\,a^2\,b^3\,c^3\,d+625\,a\,b^4\,c^4}{4096\,a^{12}\,b\,d^{12}-49152\,a^{11}\,b^2\,c\,d^{11}+270336\,a^{10}\,b^3\,c^2\,d^{10}-901120\,a^9\,b^4\,c^3\,d^9+2027520\,a^8\,b^5\,c^4\,d^8-3244032\,a^7\,b^6\,c^5\,d^7+3784704\,a^6\,b^7\,c^6\,d^6-3244032\,a^5\,b^8\,c^7\,d^5+2027520\,a^4\,b^9\,c^8\,d^4-901120\,a^3\,b^{10}\,c^9\,d^3+270336\,a^2\,b^{11}\,c^{10}\,d^2-49152\,a\,b^{12}\,c^{11}\,d+4096\,b^{13}\,c^{12}}\right)}^{3/4}\,\left(\frac{\sqrt{x}\,\left(102400\,a^{17}\,b^4\,c^2\,d^{19}-1069056\,a^{16}\,b^5\,c^3\,d^{18}+5001216\,a^{15}\,b^6\,c^4\,d^{17}-13799424\,a^{14}\,b^7\,c^5\,d^{16}+24858624\,a^{13}\,b^8\,c^6\,d^{15}-30412800\,a^{12}\,b^9\,c^7\,d^{14}+24645632\,a^{11}\,b^{10}\,c^8\,d^{13}-9326592\,a^{10}\,b^{11}\,c^9\,d^{12}-9326592\,a^9\,b^{12}\,c^{10}\,d^{11}+24645632\,a^8\,b^{13}\,c^{11}\,d^{10}-30412800\,a^7\,b^{14}\,c^{12}\,d^9+24858624\,a^6\,b^{15}\,c^{13}\,d^8-13799424\,a^5\,b^{16}\,c^{14}\,d^7+5001216\,a^4\,b^{17}\,c^{15}\,d^6-1069056\,a^3\,b^{18}\,c^{16}\,d^5+102400\,a^2\,b^{19}\,c^{17}\,d^4\right)}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}+\frac{{\left(-\frac{81\,a^5\,d^4+540\,a^4\,b\,c\,d^3+1350\,a^3\,b^2\,c^2\,d^2+1500\,a^2\,b^3\,c^3\,d+625\,a\,b^4\,c^4}{4096\,a^{12}\,b\,d^{12}-49152\,a^{11}\,b^2\,c\,d^{11}+270336\,a^{10}\,b^3\,c^2\,d^{10}-901120\,a^9\,b^4\,c^3\,d^9+2027520\,a^8\,b^5\,c^4\,d^8-3244032\,a^7\,b^6\,c^5\,d^7+3784704\,a^6\,b^7\,c^6\,d^6-3244032\,a^5\,b^8\,c^7\,d^5+2027520\,a^4\,b^9\,c^8\,d^4-901120\,a^3\,b^{10}\,c^9\,d^3+270336\,a^2\,b^{11}\,c^{10}\,d^2-49152\,a\,b^{12}\,c^{11}\,d+4096\,b^{13}\,c^{12}}\right)}^{1/4}\,\left(10240\,a^{15}\,b^4\,c^2\,d^{17}-112640\,a^{14}\,b^5\,c^3\,d^{16}+552960\,a^{13}\,b^6\,c^4\,d^{15}-1576960\,a^{12}\,b^7\,c^5\,d^{14}+2816000\,a^{11}\,b^8\,c^6\,d^{13}-3041280\,a^{10}\,b^9\,c^7\,d^{12}+1351680\,a^9\,b^{10}\,c^8\,d^{11}+1351680\,a^8\,b^{11}\,c^9\,d^{10}-3041280\,a^7\,b^{12}\,c^{10}\,d^9+2816000\,a^6\,b^{13}\,c^{11}\,d^8-1576960\,a^5\,b^{14}\,c^{12}\,d^7+552960\,a^4\,b^{15}\,c^{13}\,d^6-112640\,a^3\,b^{16}\,c^{14}\,d^5+10240\,a^2\,b^{17}\,c^{15}\,d^4\right)}{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)\right)\,1{}\mathrm{i}+\frac{\sqrt{x}\,\left(2025\,a^{10}\,b^3\,c^2\,d^{11}+15930\,a^9\,b^4\,c^3\,d^{10}+56304\,a^8\,b^5\,c^4\,d^9+115110\,a^7\,b^6\,c^5\,d^8+145550\,a^6\,b^7\,c^6\,d^7+115110\,a^5\,b^8\,c^7\,d^6+56304\,a^4\,b^9\,c^8\,d^5+15930\,a^3\,b^{10}\,c^9\,d^4+2025\,a^2\,b^{11}\,c^{10}\,d^3\right)\,1{}\mathrm{i}}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)-{\left(-\frac{81\,a^5\,d^4+540\,a^4\,b\,c\,d^3+1350\,a^3\,b^2\,c^2\,d^2+1500\,a^2\,b^3\,c^3\,d+625\,a\,b^4\,c^4}{4096\,a^{12}\,b\,d^{12}-49152\,a^{11}\,b^2\,c\,d^{11}+270336\,a^{10}\,b^3\,c^2\,d^{10}-901120\,a^9\,b^4\,c^3\,d^9+2027520\,a^8\,b^5\,c^4\,d^8-3244032\,a^7\,b^6\,c^5\,d^7+3784704\,a^6\,b^7\,c^6\,d^6-3244032\,a^5\,b^8\,c^7\,d^5+2027520\,a^4\,b^9\,c^8\,d^4-901120\,a^3\,b^{10}\,c^9\,d^3+270336\,a^2\,b^{11}\,c^{10}\,d^2-49152\,a\,b^{12}\,c^{11}\,d+4096\,b^{13}\,c^{12}}\right)}^{1/4}\,\left({\left(-\frac{81\,a^5\,d^4+540\,a^4\,b\,c\,d^3+1350\,a^3\,b^2\,c^2\,d^2+1500\,a^2\,b^3\,c^3\,d+625\,a\,b^4\,c^4}{4096\,a^{12}\,b\,d^{12}-49152\,a^{11}\,b^2\,c\,d^{11}+270336\,a^{10}\,b^3\,c^2\,d^{10}-901120\,a^9\,b^4\,c^3\,d^9+2027520\,a^8\,b^5\,c^4\,d^8-3244032\,a^7\,b^6\,c^5\,d^7+3784704\,a^6\,b^7\,c^6\,d^6-3244032\,a^5\,b^8\,c^7\,d^5+2027520\,a^4\,b^9\,c^8\,d^4-901120\,a^3\,b^{10}\,c^9\,d^3+270336\,a^2\,b^{11}\,c^{10}\,d^2-49152\,a\,b^{12}\,c^{11}\,d+4096\,b^{13}\,c^{12}}\right)}^{1/4}\,\left(\frac{\frac{405\,a^8\,b^3\,c^2\,d^9}{2}+1674\,a^7\,b^4\,c^3\,d^8+\frac{9843\,a^6\,b^5\,c^4\,d^7}{2}+6884\,a^5\,b^6\,c^5\,d^6+\frac{9843\,a^4\,b^7\,c^6\,d^5}{2}+1674\,a^3\,b^8\,c^7\,d^4+\frac{405\,a^2\,b^9\,c^8\,d^3}{2}}{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}-{\left(-\frac{81\,a^5\,d^4+540\,a^4\,b\,c\,d^3+1350\,a^3\,b^2\,c^2\,d^2+1500\,a^2\,b^3\,c^3\,d+625\,a\,b^4\,c^4}{4096\,a^{12}\,b\,d^{12}-49152\,a^{11}\,b^2\,c\,d^{11}+270336\,a^{10}\,b^3\,c^2\,d^{10}-901120\,a^9\,b^4\,c^3\,d^9+2027520\,a^8\,b^5\,c^4\,d^8-3244032\,a^7\,b^6\,c^5\,d^7+3784704\,a^6\,b^7\,c^6\,d^6-3244032\,a^5\,b^8\,c^7\,d^5+2027520\,a^4\,b^9\,c^8\,d^4-901120\,a^3\,b^{10}\,c^9\,d^3+270336\,a^2\,b^{11}\,c^{10}\,d^2-49152\,a\,b^{12}\,c^{11}\,d+4096\,b^{13}\,c^{12}}\right)}^{3/4}\,\left(\frac{\sqrt{x}\,\left(102400\,a^{17}\,b^4\,c^2\,d^{19}-1069056\,a^{16}\,b^5\,c^3\,d^{18}+5001216\,a^{15}\,b^6\,c^4\,d^{17}-13799424\,a^{14}\,b^7\,c^5\,d^{16}+24858624\,a^{13}\,b^8\,c^6\,d^{15}-30412800\,a^{12}\,b^9\,c^7\,d^{14}+24645632\,a^{11}\,b^{10}\,c^8\,d^{13}-9326592\,a^{10}\,b^{11}\,c^9\,d^{12}-9326592\,a^9\,b^{12}\,c^{10}\,d^{11}+24645632\,a^8\,b^{13}\,c^{11}\,d^{10}-30412800\,a^7\,b^{14}\,c^{12}\,d^9+24858624\,a^6\,b^{15}\,c^{13}\,d^8-13799424\,a^5\,b^{16}\,c^{14}\,d^7+5001216\,a^4\,b^{17}\,c^{15}\,d^6-1069056\,a^3\,b^{18}\,c^{16}\,d^5+102400\,a^2\,b^{19}\,c^{17}\,d^4\right)}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}-\frac{{\left(-\frac{81\,a^5\,d^4+540\,a^4\,b\,c\,d^3+1350\,a^3\,b^2\,c^2\,d^2+1500\,a^2\,b^3\,c^3\,d+625\,a\,b^4\,c^4}{4096\,a^{12}\,b\,d^{12}-49152\,a^{11}\,b^2\,c\,d^{11}+270336\,a^{10}\,b^3\,c^2\,d^{10}-901120\,a^9\,b^4\,c^3\,d^9+2027520\,a^8\,b^5\,c^4\,d^8-3244032\,a^7\,b^6\,c^5\,d^7+3784704\,a^6\,b^7\,c^6\,d^6-3244032\,a^5\,b^8\,c^7\,d^5+2027520\,a^4\,b^9\,c^8\,d^4-901120\,a^3\,b^{10}\,c^9\,d^3+270336\,a^2\,b^{11}\,c^{10}\,d^2-49152\,a\,b^{12}\,c^{11}\,d+4096\,b^{13}\,c^{12}}\right)}^{1/4}\,\left(10240\,a^{15}\,b^4\,c^2\,d^{17}-112640\,a^{14}\,b^5\,c^3\,d^{16}+552960\,a^{13}\,b^6\,c^4\,d^{15}-1576960\,a^{12}\,b^7\,c^5\,d^{14}+2816000\,a^{11}\,b^8\,c^6\,d^{13}-3041280\,a^{10}\,b^9\,c^7\,d^{12}+1351680\,a^9\,b^{10}\,c^8\,d^{11}+1351680\,a^8\,b^{11}\,c^9\,d^{10}-3041280\,a^7\,b^{12}\,c^{10}\,d^9+2816000\,a^6\,b^{13}\,c^{11}\,d^8-1576960\,a^5\,b^{14}\,c^{12}\,d^7+552960\,a^4\,b^{15}\,c^{13}\,d^6-112640\,a^3\,b^{16}\,c^{14}\,d^5+10240\,a^2\,b^{17}\,c^{15}\,d^4\right)}{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)\right)\,1{}\mathrm{i}-\frac{\sqrt{x}\,\left(2025\,a^{10}\,b^3\,c^2\,d^{11}+15930\,a^9\,b^4\,c^3\,d^{10}+56304\,a^8\,b^5\,c^4\,d^9+115110\,a^7\,b^6\,c^5\,d^8+145550\,a^6\,b^7\,c^6\,d^7+115110\,a^5\,b^8\,c^7\,d^6+56304\,a^4\,b^9\,c^8\,d^5+15930\,a^3\,b^{10}\,c^9\,d^4+2025\,a^2\,b^{11}\,c^{10}\,d^3\right)\,1{}\mathrm{i}}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)}{{\left(-\frac{81\,a^5\,d^4+540\,a^4\,b\,c\,d^3+1350\,a^3\,b^2\,c^2\,d^2+1500\,a^2\,b^3\,c^3\,d+625\,a\,b^4\,c^4}{4096\,a^{12}\,b\,d^{12}-49152\,a^{11}\,b^2\,c\,d^{11}+270336\,a^{10}\,b^3\,c^2\,d^{10}-901120\,a^9\,b^4\,c^3\,d^9+2027520\,a^8\,b^5\,c^4\,d^8-3244032\,a^7\,b^6\,c^5\,d^7+3784704\,a^6\,b^7\,c^6\,d^6-3244032\,a^5\,b^8\,c^7\,d^5+2027520\,a^4\,b^9\,c^8\,d^4-901120\,a^3\,b^{10}\,c^9\,d^3+270336\,a^2\,b^{11}\,c^{10}\,d^2-49152\,a\,b^{12}\,c^{11}\,d+4096\,b^{13}\,c^{12}}\right)}^{1/4}\,\left({\left(-\frac{81\,a^5\,d^4+540\,a^4\,b\,c\,d^3+1350\,a^3\,b^2\,c^2\,d^2+1500\,a^2\,b^3\,c^3\,d+625\,a\,b^4\,c^4}{4096\,a^{12}\,b\,d^{12}-49152\,a^{11}\,b^2\,c\,d^{11}+270336\,a^{10}\,b^3\,c^2\,d^{10}-901120\,a^9\,b^4\,c^3\,d^9+2027520\,a^8\,b^5\,c^4\,d^8-3244032\,a^7\,b^6\,c^5\,d^7+3784704\,a^6\,b^7\,c^6\,d^6-3244032\,a^5\,b^8\,c^7\,d^5+2027520\,a^4\,b^9\,c^8\,d^4-901120\,a^3\,b^{10}\,c^9\,d^3+270336\,a^2\,b^{11}\,c^{10}\,d^2-49152\,a\,b^{12}\,c^{11}\,d+4096\,b^{13}\,c^{12}}\right)}^{1/4}\,\left(\frac{\frac{405\,a^8\,b^3\,c^2\,d^9}{2}+1674\,a^7\,b^4\,c^3\,d^8+\frac{9843\,a^6\,b^5\,c^4\,d^7}{2}+6884\,a^5\,b^6\,c^5\,d^6+\frac{9843\,a^4\,b^7\,c^6\,d^5}{2}+1674\,a^3\,b^8\,c^7\,d^4+\frac{405\,a^2\,b^9\,c^8\,d^3}{2}}{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}+{\left(-\frac{81\,a^5\,d^4+540\,a^4\,b\,c\,d^3+1350\,a^3\,b^2\,c^2\,d^2+1500\,a^2\,b^3\,c^3\,d+625\,a\,b^4\,c^4}{4096\,a^{12}\,b\,d^{12}-49152\,a^{11}\,b^2\,c\,d^{11}+270336\,a^{10}\,b^3\,c^2\,d^{10}-901120\,a^9\,b^4\,c^3\,d^9+2027520\,a^8\,b^5\,c^4\,d^8-3244032\,a^7\,b^6\,c^5\,d^7+3784704\,a^6\,b^7\,c^6\,d^6-3244032\,a^5\,b^8\,c^7\,d^5+2027520\,a^4\,b^9\,c^8\,d^4-901120\,a^3\,b^{10}\,c^9\,d^3+270336\,a^2\,b^{11}\,c^{10}\,d^2-49152\,a\,b^{12}\,c^{11}\,d+4096\,b^{13}\,c^{12}}\right)}^{3/4}\,\left(\frac{\sqrt{x}\,\left(102400\,a^{17}\,b^4\,c^2\,d^{19}-1069056\,a^{16}\,b^5\,c^3\,d^{18}+5001216\,a^{15}\,b^6\,c^4\,d^{17}-13799424\,a^{14}\,b^7\,c^5\,d^{16}+24858624\,a^{13}\,b^8\,c^6\,d^{15}-30412800\,a^{12}\,b^9\,c^7\,d^{14}+24645632\,a^{11}\,b^{10}\,c^8\,d^{13}-9326592\,a^{10}\,b^{11}\,c^9\,d^{12}-9326592\,a^9\,b^{12}\,c^{10}\,d^{11}+24645632\,a^8\,b^{13}\,c^{11}\,d^{10}-30412800\,a^7\,b^{14}\,c^{12}\,d^9+24858624\,a^6\,b^{15}\,c^{13}\,d^8-13799424\,a^5\,b^{16}\,c^{14}\,d^7+5001216\,a^4\,b^{17}\,c^{15}\,d^6-1069056\,a^3\,b^{18}\,c^{16}\,d^5+102400\,a^2\,b^{19}\,c^{17}\,d^4\right)}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}+\frac{{\left(-\frac{81\,a^5\,d^4+540\,a^4\,b\,c\,d^3+1350\,a^3\,b^2\,c^2\,d^2+1500\,a^2\,b^3\,c^3\,d+625\,a\,b^4\,c^4}{4096\,a^{12}\,b\,d^{12}-49152\,a^{11}\,b^2\,c\,d^{11}+270336\,a^{10}\,b^3\,c^2\,d^{10}-901120\,a^9\,b^4\,c^3\,d^9+2027520\,a^8\,b^5\,c^4\,d^8-3244032\,a^7\,b^6\,c^5\,d^7+3784704\,a^6\,b^7\,c^6\,d^6-3244032\,a^5\,b^8\,c^7\,d^5+2027520\,a^4\,b^9\,c^8\,d^4-901120\,a^3\,b^{10}\,c^9\,d^3+270336\,a^2\,b^{11}\,c^{10}\,d^2-49152\,a\,b^{12}\,c^{11}\,d+4096\,b^{13}\,c^{12}}\right)}^{1/4}\,\left(10240\,a^{15}\,b^4\,c^2\,d^{17}-112640\,a^{14}\,b^5\,c^3\,d^{16}+552960\,a^{13}\,b^6\,c^4\,d^{15}-1576960\,a^{12}\,b^7\,c^5\,d^{14}+2816000\,a^{11}\,b^8\,c^6\,d^{13}-3041280\,a^{10}\,b^9\,c^7\,d^{12}+1351680\,a^9\,b^{10}\,c^8\,d^{11}+1351680\,a^8\,b^{11}\,c^9\,d^{10}-3041280\,a^7\,b^{12}\,c^{10}\,d^9+2816000\,a^6\,b^{13}\,c^{11}\,d^8-1576960\,a^5\,b^{14}\,c^{12}\,d^7+552960\,a^4\,b^{15}\,c^{13}\,d^6-112640\,a^3\,b^{16}\,c^{14}\,d^5+10240\,a^2\,b^{17}\,c^{15}\,d^4\right)}{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)\right)+\frac{\sqrt{x}\,\left(2025\,a^{10}\,b^3\,c^2\,d^{11}+15930\,a^9\,b^4\,c^3\,d^{10}+56304\,a^8\,b^5\,c^4\,d^9+115110\,a^7\,b^6\,c^5\,d^8+145550\,a^6\,b^7\,c^6\,d^7+115110\,a^5\,b^8\,c^7\,d^6+56304\,a^4\,b^9\,c^8\,d^5+15930\,a^3\,b^{10}\,c^9\,d^4+2025\,a^2\,b^{11}\,c^{10}\,d^3\right)}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)+{\left(-\frac{81\,a^5\,d^4+540\,a^4\,b\,c\,d^3+1350\,a^3\,b^2\,c^2\,d^2+1500\,a^2\,b^3\,c^3\,d+625\,a\,b^4\,c^4}{4096\,a^{12}\,b\,d^{12}-49152\,a^{11}\,b^2\,c\,d^{11}+270336\,a^{10}\,b^3\,c^2\,d^{10}-901120\,a^9\,b^4\,c^3\,d^9+2027520\,a^8\,b^5\,c^4\,d^8-3244032\,a^7\,b^6\,c^5\,d^7+3784704\,a^6\,b^7\,c^6\,d^6-3244032\,a^5\,b^8\,c^7\,d^5+2027520\,a^4\,b^9\,c^8\,d^4-901120\,a^3\,b^{10}\,c^9\,d^3+270336\,a^2\,b^{11}\,c^{10}\,d^2-49152\,a\,b^{12}\,c^{11}\,d+4096\,b^{13}\,c^{12}}\right)}^{1/4}\,\left({\left(-\frac{81\,a^5\,d^4+540\,a^4\,b\,c\,d^3+1350\,a^3\,b^2\,c^2\,d^2+1500\,a^2\,b^3\,c^3\,d+625\,a\,b^4\,c^4}{4096\,a^{12}\,b\,d^{12}-49152\,a^{11}\,b^2\,c\,d^{11}+270336\,a^{10}\,b^3\,c^2\,d^{10}-901120\,a^9\,b^4\,c^3\,d^9+2027520\,a^8\,b^5\,c^4\,d^8-3244032\,a^7\,b^6\,c^5\,d^7+3784704\,a^6\,b^7\,c^6\,d^6-3244032\,a^5\,b^8\,c^7\,d^5+2027520\,a^4\,b^9\,c^8\,d^4-901120\,a^3\,b^{10}\,c^9\,d^3+270336\,a^2\,b^{11}\,c^{10}\,d^2-49152\,a\,b^{12}\,c^{11}\,d+4096\,b^{13}\,c^{12}}\right)}^{1/4}\,\left(\frac{\frac{405\,a^8\,b^3\,c^2\,d^9}{2}+1674\,a^7\,b^4\,c^3\,d^8+\frac{9843\,a^6\,b^5\,c^4\,d^7}{2}+6884\,a^5\,b^6\,c^5\,d^6+\frac{9843\,a^4\,b^7\,c^6\,d^5}{2}+1674\,a^3\,b^8\,c^7\,d^4+\frac{405\,a^2\,b^9\,c^8\,d^3}{2}}{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}-{\left(-\frac{81\,a^5\,d^4+540\,a^4\,b\,c\,d^3+1350\,a^3\,b^2\,c^2\,d^2+1500\,a^2\,b^3\,c^3\,d+625\,a\,b^4\,c^4}{4096\,a^{12}\,b\,d^{12}-49152\,a^{11}\,b^2\,c\,d^{11}+270336\,a^{10}\,b^3\,c^2\,d^{10}-901120\,a^9\,b^4\,c^3\,d^9+2027520\,a^8\,b^5\,c^4\,d^8-3244032\,a^7\,b^6\,c^5\,d^7+3784704\,a^6\,b^7\,c^6\,d^6-3244032\,a^5\,b^8\,c^7\,d^5+2027520\,a^4\,b^9\,c^8\,d^4-901120\,a^3\,b^{10}\,c^9\,d^3+270336\,a^2\,b^{11}\,c^{10}\,d^2-49152\,a\,b^{12}\,c^{11}\,d+4096\,b^{13}\,c^{12}}\right)}^{3/4}\,\left(\frac{\sqrt{x}\,\left(102400\,a^{17}\,b^4\,c^2\,d^{19}-1069056\,a^{16}\,b^5\,c^3\,d^{18}+5001216\,a^{15}\,b^6\,c^4\,d^{17}-13799424\,a^{14}\,b^7\,c^5\,d^{16}+24858624\,a^{13}\,b^8\,c^6\,d^{15}-30412800\,a^{12}\,b^9\,c^7\,d^{14}+24645632\,a^{11}\,b^{10}\,c^8\,d^{13}-9326592\,a^{10}\,b^{11}\,c^9\,d^{12}-9326592\,a^9\,b^{12}\,c^{10}\,d^{11}+24645632\,a^8\,b^{13}\,c^{11}\,d^{10}-30412800\,a^7\,b^{14}\,c^{12}\,d^9+24858624\,a^6\,b^{15}\,c^{13}\,d^8-13799424\,a^5\,b^{16}\,c^{14}\,d^7+5001216\,a^4\,b^{17}\,c^{15}\,d^6-1069056\,a^3\,b^{18}\,c^{16}\,d^5+102400\,a^2\,b^{19}\,c^{17}\,d^4\right)}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}-\frac{{\left(-\frac{81\,a^5\,d^4+540\,a^4\,b\,c\,d^3+1350\,a^3\,b^2\,c^2\,d^2+1500\,a^2\,b^3\,c^3\,d+625\,a\,b^4\,c^4}{4096\,a^{12}\,b\,d^{12}-49152\,a^{11}\,b^2\,c\,d^{11}+270336\,a^{10}\,b^3\,c^2\,d^{10}-901120\,a^9\,b^4\,c^3\,d^9+2027520\,a^8\,b^5\,c^4\,d^8-3244032\,a^7\,b^6\,c^5\,d^7+3784704\,a^6\,b^7\,c^6\,d^6-3244032\,a^5\,b^8\,c^7\,d^5+2027520\,a^4\,b^9\,c^8\,d^4-901120\,a^3\,b^{10}\,c^9\,d^3+270336\,a^2\,b^{11}\,c^{10}\,d^2-49152\,a\,b^{12}\,c^{11}\,d+4096\,b^{13}\,c^{12}}\right)}^{1/4}\,\left(10240\,a^{15}\,b^4\,c^2\,d^{17}-112640\,a^{14}\,b^5\,c^3\,d^{16}+552960\,a^{13}\,b^6\,c^4\,d^{15}-1576960\,a^{12}\,b^7\,c^5\,d^{14}+2816000\,a^{11}\,b^8\,c^6\,d^{13}-3041280\,a^{10}\,b^9\,c^7\,d^{12}+1351680\,a^9\,b^{10}\,c^8\,d^{11}+1351680\,a^8\,b^{11}\,c^9\,d^{10}-3041280\,a^7\,b^{12}\,c^{10}\,d^9+2816000\,a^6\,b^{13}\,c^{11}\,d^8-1576960\,a^5\,b^{14}\,c^{12}\,d^7+552960\,a^4\,b^{15}\,c^{13}\,d^6-112640\,a^3\,b^{16}\,c^{14}\,d^5+10240\,a^2\,b^{17}\,c^{15}\,d^4\right)}{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)\right)-\frac{\sqrt{x}\,\left(2025\,a^{10}\,b^3\,c^2\,d^{11}+15930\,a^9\,b^4\,c^3\,d^{10}+56304\,a^8\,b^5\,c^4\,d^9+115110\,a^7\,b^6\,c^5\,d^8+145550\,a^6\,b^7\,c^6\,d^7+115110\,a^5\,b^8\,c^7\,d^6+56304\,a^4\,b^9\,c^8\,d^5+15930\,a^3\,b^{10}\,c^9\,d^4+2025\,a^2\,b^{11}\,c^{10}\,d^3\right)}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)}\right)\,{\left(-\frac{81\,a^5\,d^4+540\,a^4\,b\,c\,d^3+1350\,a^3\,b^2\,c^2\,d^2+1500\,a^2\,b^3\,c^3\,d+625\,a\,b^4\,c^4}{4096\,a^{12}\,b\,d^{12}-49152\,a^{11}\,b^2\,c\,d^{11}+270336\,a^{10}\,b^3\,c^2\,d^{10}-901120\,a^9\,b^4\,c^3\,d^9+2027520\,a^8\,b^5\,c^4\,d^8-3244032\,a^7\,b^6\,c^5\,d^7+3784704\,a^6\,b^7\,c^6\,d^6-3244032\,a^5\,b^8\,c^7\,d^5+2027520\,a^4\,b^9\,c^8\,d^4-901120\,a^3\,b^{10}\,c^9\,d^3+270336\,a^2\,b^{11}\,c^{10}\,d^2-49152\,a\,b^{12}\,c^{11}\,d+4096\,b^{13}\,c^{12}}\right)}^{1/4}\,2{}\mathrm{i}-2\,\mathrm{atan}\left(\frac{{\left(-\frac{81\,a^5\,d^4+540\,a^4\,b\,c\,d^3+1350\,a^3\,b^2\,c^2\,d^2+1500\,a^2\,b^3\,c^3\,d+625\,a\,b^4\,c^4}{4096\,a^{12}\,b\,d^{12}-49152\,a^{11}\,b^2\,c\,d^{11}+270336\,a^{10}\,b^3\,c^2\,d^{10}-901120\,a^9\,b^4\,c^3\,d^9+2027520\,a^8\,b^5\,c^4\,d^8-3244032\,a^7\,b^6\,c^5\,d^7+3784704\,a^6\,b^7\,c^6\,d^6-3244032\,a^5\,b^8\,c^7\,d^5+2027520\,a^4\,b^9\,c^8\,d^4-901120\,a^3\,b^{10}\,c^9\,d^3+270336\,a^2\,b^{11}\,c^{10}\,d^2-49152\,a\,b^{12}\,c^{11}\,d+4096\,b^{13}\,c^{12}}\right)}^{1/4}\,\left({\left(-\frac{81\,a^5\,d^4+540\,a^4\,b\,c\,d^3+1350\,a^3\,b^2\,c^2\,d^2+1500\,a^2\,b^3\,c^3\,d+625\,a\,b^4\,c^4}{4096\,a^{12}\,b\,d^{12}-49152\,a^{11}\,b^2\,c\,d^{11}+270336\,a^{10}\,b^3\,c^2\,d^{10}-901120\,a^9\,b^4\,c^3\,d^9+2027520\,a^8\,b^5\,c^4\,d^8-3244032\,a^7\,b^6\,c^5\,d^7+3784704\,a^6\,b^7\,c^6\,d^6-3244032\,a^5\,b^8\,c^7\,d^5+2027520\,a^4\,b^9\,c^8\,d^4-901120\,a^3\,b^{10}\,c^9\,d^3+270336\,a^2\,b^{11}\,c^{10}\,d^2-49152\,a\,b^{12}\,c^{11}\,d+4096\,b^{13}\,c^{12}}\right)}^{1/4}\,\left(\frac{\left(\frac{405\,a^8\,b^3\,c^2\,d^9}{2}+1674\,a^7\,b^4\,c^3\,d^8+\frac{9843\,a^6\,b^5\,c^4\,d^7}{2}+6884\,a^5\,b^6\,c^5\,d^6+\frac{9843\,a^4\,b^7\,c^6\,d^5}{2}+1674\,a^3\,b^8\,c^7\,d^4+\frac{405\,a^2\,b^9\,c^8\,d^3}{2}\right)\,1{}\mathrm{i}}{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}+{\left(-\frac{81\,a^5\,d^4+540\,a^4\,b\,c\,d^3+1350\,a^3\,b^2\,c^2\,d^2+1500\,a^2\,b^3\,c^3\,d+625\,a\,b^4\,c^4}{4096\,a^{12}\,b\,d^{12}-49152\,a^{11}\,b^2\,c\,d^{11}+270336\,a^{10}\,b^3\,c^2\,d^{10}-901120\,a^9\,b^4\,c^3\,d^9+2027520\,a^8\,b^5\,c^4\,d^8-3244032\,a^7\,b^6\,c^5\,d^7+3784704\,a^6\,b^7\,c^6\,d^6-3244032\,a^5\,b^8\,c^7\,d^5+2027520\,a^4\,b^9\,c^8\,d^4-901120\,a^3\,b^{10}\,c^9\,d^3+270336\,a^2\,b^{11}\,c^{10}\,d^2-49152\,a\,b^{12}\,c^{11}\,d+4096\,b^{13}\,c^{12}}\right)}^{3/4}\,\left(\frac{{\left(-\frac{81\,a^5\,d^4+540\,a^4\,b\,c\,d^3+1350\,a^3\,b^2\,c^2\,d^2+1500\,a^2\,b^3\,c^3\,d+625\,a\,b^4\,c^4}{4096\,a^{12}\,b\,d^{12}-49152\,a^{11}\,b^2\,c\,d^{11}+270336\,a^{10}\,b^3\,c^2\,d^{10}-901120\,a^9\,b^4\,c^3\,d^9+2027520\,a^8\,b^5\,c^4\,d^8-3244032\,a^7\,b^6\,c^5\,d^7+3784704\,a^6\,b^7\,c^6\,d^6-3244032\,a^5\,b^8\,c^7\,d^5+2027520\,a^4\,b^9\,c^8\,d^4-901120\,a^3\,b^{10}\,c^9\,d^3+270336\,a^2\,b^{11}\,c^{10}\,d^2-49152\,a\,b^{12}\,c^{11}\,d+4096\,b^{13}\,c^{12}}\right)}^{1/4}\,\left(10240\,a^{15}\,b^4\,c^2\,d^{17}-112640\,a^{14}\,b^5\,c^3\,d^{16}+552960\,a^{13}\,b^6\,c^4\,d^{15}-1576960\,a^{12}\,b^7\,c^5\,d^{14}+2816000\,a^{11}\,b^8\,c^6\,d^{13}-3041280\,a^{10}\,b^9\,c^7\,d^{12}+1351680\,a^9\,b^{10}\,c^8\,d^{11}+1351680\,a^8\,b^{11}\,c^9\,d^{10}-3041280\,a^7\,b^{12}\,c^{10}\,d^9+2816000\,a^6\,b^{13}\,c^{11}\,d^8-1576960\,a^5\,b^{14}\,c^{12}\,d^7+552960\,a^4\,b^{15}\,c^{13}\,d^6-112640\,a^3\,b^{16}\,c^{14}\,d^5+10240\,a^2\,b^{17}\,c^{15}\,d^4\right)}{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}+\frac{\sqrt{x}\,\left(102400\,a^{17}\,b^4\,c^2\,d^{19}-1069056\,a^{16}\,b^5\,c^3\,d^{18}+5001216\,a^{15}\,b^6\,c^4\,d^{17}-13799424\,a^{14}\,b^7\,c^5\,d^{16}+24858624\,a^{13}\,b^8\,c^6\,d^{15}-30412800\,a^{12}\,b^9\,c^7\,d^{14}+24645632\,a^{11}\,b^{10}\,c^8\,d^{13}-9326592\,a^{10}\,b^{11}\,c^9\,d^{12}-9326592\,a^9\,b^{12}\,c^{10}\,d^{11}+24645632\,a^8\,b^{13}\,c^{11}\,d^{10}-30412800\,a^7\,b^{14}\,c^{12}\,d^9+24858624\,a^6\,b^{15}\,c^{13}\,d^8-13799424\,a^5\,b^{16}\,c^{14}\,d^7+5001216\,a^4\,b^{17}\,c^{15}\,d^6-1069056\,a^3\,b^{18}\,c^{16}\,d^5+102400\,a^2\,b^{19}\,c^{17}\,d^4\right)\,1{}\mathrm{i}}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)\,1{}\mathrm{i}\right)-\frac{\sqrt{x}\,\left(2025\,a^{10}\,b^3\,c^2\,d^{11}+15930\,a^9\,b^4\,c^3\,d^{10}+56304\,a^8\,b^5\,c^4\,d^9+115110\,a^7\,b^6\,c^5\,d^8+145550\,a^6\,b^7\,c^6\,d^7+115110\,a^5\,b^8\,c^7\,d^6+56304\,a^4\,b^9\,c^8\,d^5+15930\,a^3\,b^{10}\,c^9\,d^4+2025\,a^2\,b^{11}\,c^{10}\,d^3\right)}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)-{\left(-\frac{81\,a^5\,d^4+540\,a^4\,b\,c\,d^3+1350\,a^3\,b^2\,c^2\,d^2+1500\,a^2\,b^3\,c^3\,d+625\,a\,b^4\,c^4}{4096\,a^{12}\,b\,d^{12}-49152\,a^{11}\,b^2\,c\,d^{11}+270336\,a^{10}\,b^3\,c^2\,d^{10}-901120\,a^9\,b^4\,c^3\,d^9+2027520\,a^8\,b^5\,c^4\,d^8-3244032\,a^7\,b^6\,c^5\,d^7+3784704\,a^6\,b^7\,c^6\,d^6-3244032\,a^5\,b^8\,c^7\,d^5+2027520\,a^4\,b^9\,c^8\,d^4-901120\,a^3\,b^{10}\,c^9\,d^3+270336\,a^2\,b^{11}\,c^{10}\,d^2-49152\,a\,b^{12}\,c^{11}\,d+4096\,b^{13}\,c^{12}}\right)}^{1/4}\,\left({\left(-\frac{81\,a^5\,d^4+540\,a^4\,b\,c\,d^3+1350\,a^3\,b^2\,c^2\,d^2+1500\,a^2\,b^3\,c^3\,d+625\,a\,b^4\,c^4}{4096\,a^{12}\,b\,d^{12}-49152\,a^{11}\,b^2\,c\,d^{11}+270336\,a^{10}\,b^3\,c^2\,d^{10}-901120\,a^9\,b^4\,c^3\,d^9+2027520\,a^8\,b^5\,c^4\,d^8-3244032\,a^7\,b^6\,c^5\,d^7+3784704\,a^6\,b^7\,c^6\,d^6-3244032\,a^5\,b^8\,c^7\,d^5+2027520\,a^4\,b^9\,c^8\,d^4-901120\,a^3\,b^{10}\,c^9\,d^3+270336\,a^2\,b^{11}\,c^{10}\,d^2-49152\,a\,b^{12}\,c^{11}\,d+4096\,b^{13}\,c^{12}}\right)}^{1/4}\,\left(\frac{\left(\frac{405\,a^8\,b^3\,c^2\,d^9}{2}+1674\,a^7\,b^4\,c^3\,d^8+\frac{9843\,a^6\,b^5\,c^4\,d^7}{2}+6884\,a^5\,b^6\,c^5\,d^6+\frac{9843\,a^4\,b^7\,c^6\,d^5}{2}+1674\,a^3\,b^8\,c^7\,d^4+\frac{405\,a^2\,b^9\,c^8\,d^3}{2}\right)\,1{}\mathrm{i}}{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}-{\left(-\frac{81\,a^5\,d^4+540\,a^4\,b\,c\,d^3+1350\,a^3\,b^2\,c^2\,d^2+1500\,a^2\,b^3\,c^3\,d+625\,a\,b^4\,c^4}{4096\,a^{12}\,b\,d^{12}-49152\,a^{11}\,b^2\,c\,d^{11}+270336\,a^{10}\,b^3\,c^2\,d^{10}-901120\,a^9\,b^4\,c^3\,d^9+2027520\,a^8\,b^5\,c^4\,d^8-3244032\,a^7\,b^6\,c^5\,d^7+3784704\,a^6\,b^7\,c^6\,d^6-3244032\,a^5\,b^8\,c^7\,d^5+2027520\,a^4\,b^9\,c^8\,d^4-901120\,a^3\,b^{10}\,c^9\,d^3+270336\,a^2\,b^{11}\,c^{10}\,d^2-49152\,a\,b^{12}\,c^{11}\,d+4096\,b^{13}\,c^{12}}\right)}^{3/4}\,\left(-\frac{{\left(-\frac{81\,a^5\,d^4+540\,a^4\,b\,c\,d^3+1350\,a^3\,b^2\,c^2\,d^2+1500\,a^2\,b^3\,c^3\,d+625\,a\,b^4\,c^4}{4096\,a^{12}\,b\,d^{12}-49152\,a^{11}\,b^2\,c\,d^{11}+270336\,a^{10}\,b^3\,c^2\,d^{10}-901120\,a^9\,b^4\,c^3\,d^9+2027520\,a^8\,b^5\,c^4\,d^8-3244032\,a^7\,b^6\,c^5\,d^7+3784704\,a^6\,b^7\,c^6\,d^6-3244032\,a^5\,b^8\,c^7\,d^5+2027520\,a^4\,b^9\,c^8\,d^4-901120\,a^3\,b^{10}\,c^9\,d^3+270336\,a^2\,b^{11}\,c^{10}\,d^2-49152\,a\,b^{12}\,c^{11}\,d+4096\,b^{13}\,c^{12}}\right)}^{1/4}\,\left(10240\,a^{15}\,b^4\,c^2\,d^{17}-112640\,a^{14}\,b^5\,c^3\,d^{16}+552960\,a^{13}\,b^6\,c^4\,d^{15}-1576960\,a^{12}\,b^7\,c^5\,d^{14}+2816000\,a^{11}\,b^8\,c^6\,d^{13}-3041280\,a^{10}\,b^9\,c^7\,d^{12}+1351680\,a^9\,b^{10}\,c^8\,d^{11}+1351680\,a^8\,b^{11}\,c^9\,d^{10}-3041280\,a^7\,b^{12}\,c^{10}\,d^9+2816000\,a^6\,b^{13}\,c^{11}\,d^8-1576960\,a^5\,b^{14}\,c^{12}\,d^7+552960\,a^4\,b^{15}\,c^{13}\,d^6-112640\,a^3\,b^{16}\,c^{14}\,d^5+10240\,a^2\,b^{17}\,c^{15}\,d^4\right)}{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}+\frac{\sqrt{x}\,\left(102400\,a^{17}\,b^4\,c^2\,d^{19}-1069056\,a^{16}\,b^5\,c^3\,d^{18}+5001216\,a^{15}\,b^6\,c^4\,d^{17}-13799424\,a^{14}\,b^7\,c^5\,d^{16}+24858624\,a^{13}\,b^8\,c^6\,d^{15}-30412800\,a^{12}\,b^9\,c^7\,d^{14}+24645632\,a^{11}\,b^{10}\,c^8\,d^{13}-9326592\,a^{10}\,b^{11}\,c^9\,d^{12}-9326592\,a^9\,b^{12}\,c^{10}\,d^{11}+24645632\,a^8\,b^{13}\,c^{11}\,d^{10}-30412800\,a^7\,b^{14}\,c^{12}\,d^9+24858624\,a^6\,b^{15}\,c^{13}\,d^8-13799424\,a^5\,b^{16}\,c^{14}\,d^7+5001216\,a^4\,b^{17}\,c^{15}\,d^6-1069056\,a^3\,b^{18}\,c^{16}\,d^5+102400\,a^2\,b^{19}\,c^{17}\,d^4\right)\,1{}\mathrm{i}}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)\,1{}\mathrm{i}\right)+\frac{\sqrt{x}\,\left(2025\,a^{10}\,b^3\,c^2\,d^{11}+15930\,a^9\,b^4\,c^3\,d^{10}+56304\,a^8\,b^5\,c^4\,d^9+115110\,a^7\,b^6\,c^5\,d^8+145550\,a^6\,b^7\,c^6\,d^7+115110\,a^5\,b^8\,c^7\,d^6+56304\,a^4\,b^9\,c^8\,d^5+15930\,a^3\,b^{10}\,c^9\,d^4+2025\,a^2\,b^{11}\,c^{10}\,d^3\right)}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)}{{\left(-\frac{81\,a^5\,d^4+540\,a^4\,b\,c\,d^3+1350\,a^3\,b^2\,c^2\,d^2+1500\,a^2\,b^3\,c^3\,d+625\,a\,b^4\,c^4}{4096\,a^{12}\,b\,d^{12}-49152\,a^{11}\,b^2\,c\,d^{11}+270336\,a^{10}\,b^3\,c^2\,d^{10}-901120\,a^9\,b^4\,c^3\,d^9+2027520\,a^8\,b^5\,c^4\,d^8-3244032\,a^7\,b^6\,c^5\,d^7+3784704\,a^6\,b^7\,c^6\,d^6-3244032\,a^5\,b^8\,c^7\,d^5+2027520\,a^4\,b^9\,c^8\,d^4-901120\,a^3\,b^{10}\,c^9\,d^3+270336\,a^2\,b^{11}\,c^{10}\,d^2-49152\,a\,b^{12}\,c^{11}\,d+4096\,b^{13}\,c^{12}}\right)}^{1/4}\,\left({\left(-\frac{81\,a^5\,d^4+540\,a^4\,b\,c\,d^3+1350\,a^3\,b^2\,c^2\,d^2+1500\,a^2\,b^3\,c^3\,d+625\,a\,b^4\,c^4}{4096\,a^{12}\,b\,d^{12}-49152\,a^{11}\,b^2\,c\,d^{11}+270336\,a^{10}\,b^3\,c^2\,d^{10}-901120\,a^9\,b^4\,c^3\,d^9+2027520\,a^8\,b^5\,c^4\,d^8-3244032\,a^7\,b^6\,c^5\,d^7+3784704\,a^6\,b^7\,c^6\,d^6-3244032\,a^5\,b^8\,c^7\,d^5+2027520\,a^4\,b^9\,c^8\,d^4-901120\,a^3\,b^{10}\,c^9\,d^3+270336\,a^2\,b^{11}\,c^{10}\,d^2-49152\,a\,b^{12}\,c^{11}\,d+4096\,b^{13}\,c^{12}}\right)}^{1/4}\,\left(\frac{\left(\frac{405\,a^8\,b^3\,c^2\,d^9}{2}+1674\,a^7\,b^4\,c^3\,d^8+\frac{9843\,a^6\,b^5\,c^4\,d^7}{2}+6884\,a^5\,b^6\,c^5\,d^6+\frac{9843\,a^4\,b^7\,c^6\,d^5}{2}+1674\,a^3\,b^8\,c^7\,d^4+\frac{405\,a^2\,b^9\,c^8\,d^3}{2}\right)\,1{}\mathrm{i}}{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}+{\left(-\frac{81\,a^5\,d^4+540\,a^4\,b\,c\,d^3+1350\,a^3\,b^2\,c^2\,d^2+1500\,a^2\,b^3\,c^3\,d+625\,a\,b^4\,c^4}{4096\,a^{12}\,b\,d^{12}-49152\,a^{11}\,b^2\,c\,d^{11}+270336\,a^{10}\,b^3\,c^2\,d^{10}-901120\,a^9\,b^4\,c^3\,d^9+2027520\,a^8\,b^5\,c^4\,d^8-3244032\,a^7\,b^6\,c^5\,d^7+3784704\,a^6\,b^7\,c^6\,d^6-3244032\,a^5\,b^8\,c^7\,d^5+2027520\,a^4\,b^9\,c^8\,d^4-901120\,a^3\,b^{10}\,c^9\,d^3+270336\,a^2\,b^{11}\,c^{10}\,d^2-49152\,a\,b^{12}\,c^{11}\,d+4096\,b^{13}\,c^{12}}\right)}^{3/4}\,\left(\frac{{\left(-\frac{81\,a^5\,d^4+540\,a^4\,b\,c\,d^3+1350\,a^3\,b^2\,c^2\,d^2+1500\,a^2\,b^3\,c^3\,d+625\,a\,b^4\,c^4}{4096\,a^{12}\,b\,d^{12}-49152\,a^{11}\,b^2\,c\,d^{11}+270336\,a^{10}\,b^3\,c^2\,d^{10}-901120\,a^9\,b^4\,c^3\,d^9+2027520\,a^8\,b^5\,c^4\,d^8-3244032\,a^7\,b^6\,c^5\,d^7+3784704\,a^6\,b^7\,c^6\,d^6-3244032\,a^5\,b^8\,c^7\,d^5+2027520\,a^4\,b^9\,c^8\,d^4-901120\,a^3\,b^{10}\,c^9\,d^3+270336\,a^2\,b^{11}\,c^{10}\,d^2-49152\,a\,b^{12}\,c^{11}\,d+4096\,b^{13}\,c^{12}}\right)}^{1/4}\,\left(10240\,a^{15}\,b^4\,c^2\,d^{17}-112640\,a^{14}\,b^5\,c^3\,d^{16}+552960\,a^{13}\,b^6\,c^4\,d^{15}-1576960\,a^{12}\,b^7\,c^5\,d^{14}+2816000\,a^{11}\,b^8\,c^6\,d^{13}-3041280\,a^{10}\,b^9\,c^7\,d^{12}+1351680\,a^9\,b^{10}\,c^8\,d^{11}+1351680\,a^8\,b^{11}\,c^9\,d^{10}-3041280\,a^7\,b^{12}\,c^{10}\,d^9+2816000\,a^6\,b^{13}\,c^{11}\,d^8-1576960\,a^5\,b^{14}\,c^{12}\,d^7+552960\,a^4\,b^{15}\,c^{13}\,d^6-112640\,a^3\,b^{16}\,c^{14}\,d^5+10240\,a^2\,b^{17}\,c^{15}\,d^4\right)}{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}+\frac{\sqrt{x}\,\left(102400\,a^{17}\,b^4\,c^2\,d^{19}-1069056\,a^{16}\,b^5\,c^3\,d^{18}+5001216\,a^{15}\,b^6\,c^4\,d^{17}-13799424\,a^{14}\,b^7\,c^5\,d^{16}+24858624\,a^{13}\,b^8\,c^6\,d^{15}-30412800\,a^{12}\,b^9\,c^7\,d^{14}+24645632\,a^{11}\,b^{10}\,c^8\,d^{13}-9326592\,a^{10}\,b^{11}\,c^9\,d^{12}-9326592\,a^9\,b^{12}\,c^{10}\,d^{11}+24645632\,a^8\,b^{13}\,c^{11}\,d^{10}-30412800\,a^7\,b^{14}\,c^{12}\,d^9+24858624\,a^6\,b^{15}\,c^{13}\,d^8-13799424\,a^5\,b^{16}\,c^{14}\,d^7+5001216\,a^4\,b^{17}\,c^{15}\,d^6-1069056\,a^3\,b^{18}\,c^{16}\,d^5+102400\,a^2\,b^{19}\,c^{17}\,d^4\right)\,1{}\mathrm{i}}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}-\frac{\sqrt{x}\,\left(2025\,a^{10}\,b^3\,c^2\,d^{11}+15930\,a^9\,b^4\,c^3\,d^{10}+56304\,a^8\,b^5\,c^4\,d^9+115110\,a^7\,b^6\,c^5\,d^8+145550\,a^6\,b^7\,c^6\,d^7+115110\,a^5\,b^8\,c^7\,d^6+56304\,a^4\,b^9\,c^8\,d^5+15930\,a^3\,b^{10}\,c^9\,d^4+2025\,a^2\,b^{11}\,c^{10}\,d^3\right)\,1{}\mathrm{i}}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)+{\left(-\frac{81\,a^5\,d^4+540\,a^4\,b\,c\,d^3+1350\,a^3\,b^2\,c^2\,d^2+1500\,a^2\,b^3\,c^3\,d+625\,a\,b^4\,c^4}{4096\,a^{12}\,b\,d^{12}-49152\,a^{11}\,b^2\,c\,d^{11}+270336\,a^{10}\,b^3\,c^2\,d^{10}-901120\,a^9\,b^4\,c^3\,d^9+2027520\,a^8\,b^5\,c^4\,d^8-3244032\,a^7\,b^6\,c^5\,d^7+3784704\,a^6\,b^7\,c^6\,d^6-3244032\,a^5\,b^8\,c^7\,d^5+2027520\,a^4\,b^9\,c^8\,d^4-901120\,a^3\,b^{10}\,c^9\,d^3+270336\,a^2\,b^{11}\,c^{10}\,d^2-49152\,a\,b^{12}\,c^{11}\,d+4096\,b^{13}\,c^{12}}\right)}^{1/4}\,\left({\left(-\frac{81\,a^5\,d^4+540\,a^4\,b\,c\,d^3+1350\,a^3\,b^2\,c^2\,d^2+1500\,a^2\,b^3\,c^3\,d+625\,a\,b^4\,c^4}{4096\,a^{12}\,b\,d^{12}-49152\,a^{11}\,b^2\,c\,d^{11}+270336\,a^{10}\,b^3\,c^2\,d^{10}-901120\,a^9\,b^4\,c^3\,d^9+2027520\,a^8\,b^5\,c^4\,d^8-3244032\,a^7\,b^6\,c^5\,d^7+3784704\,a^6\,b^7\,c^6\,d^6-3244032\,a^5\,b^8\,c^7\,d^5+2027520\,a^4\,b^9\,c^8\,d^4-901120\,a^3\,b^{10}\,c^9\,d^3+270336\,a^2\,b^{11}\,c^{10}\,d^2-49152\,a\,b^{12}\,c^{11}\,d+4096\,b^{13}\,c^{12}}\right)}^{1/4}\,\left(\frac{\left(\frac{405\,a^8\,b^3\,c^2\,d^9}{2}+1674\,a^7\,b^4\,c^3\,d^8+\frac{9843\,a^6\,b^5\,c^4\,d^7}{2}+6884\,a^5\,b^6\,c^5\,d^6+\frac{9843\,a^4\,b^7\,c^6\,d^5}{2}+1674\,a^3\,b^8\,c^7\,d^4+\frac{405\,a^2\,b^9\,c^8\,d^3}{2}\right)\,1{}\mathrm{i}}{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}-{\left(-\frac{81\,a^5\,d^4+540\,a^4\,b\,c\,d^3+1350\,a^3\,b^2\,c^2\,d^2+1500\,a^2\,b^3\,c^3\,d+625\,a\,b^4\,c^4}{4096\,a^{12}\,b\,d^{12}-49152\,a^{11}\,b^2\,c\,d^{11}+270336\,a^{10}\,b^3\,c^2\,d^{10}-901120\,a^9\,b^4\,c^3\,d^9+2027520\,a^8\,b^5\,c^4\,d^8-3244032\,a^7\,b^6\,c^5\,d^7+3784704\,a^6\,b^7\,c^6\,d^6-3244032\,a^5\,b^8\,c^7\,d^5+2027520\,a^4\,b^9\,c^8\,d^4-901120\,a^3\,b^{10}\,c^9\,d^3+270336\,a^2\,b^{11}\,c^{10}\,d^2-49152\,a\,b^{12}\,c^{11}\,d+4096\,b^{13}\,c^{12}}\right)}^{3/4}\,\left(-\frac{{\left(-\frac{81\,a^5\,d^4+540\,a^4\,b\,c\,d^3+1350\,a^3\,b^2\,c^2\,d^2+1500\,a^2\,b^3\,c^3\,d+625\,a\,b^4\,c^4}{4096\,a^{12}\,b\,d^{12}-49152\,a^{11}\,b^2\,c\,d^{11}+270336\,a^{10}\,b^3\,c^2\,d^{10}-901120\,a^9\,b^4\,c^3\,d^9+2027520\,a^8\,b^5\,c^4\,d^8-3244032\,a^7\,b^6\,c^5\,d^7+3784704\,a^6\,b^7\,c^6\,d^6-3244032\,a^5\,b^8\,c^7\,d^5+2027520\,a^4\,b^9\,c^8\,d^4-901120\,a^3\,b^{10}\,c^9\,d^3+270336\,a^2\,b^{11}\,c^{10}\,d^2-49152\,a\,b^{12}\,c^{11}\,d+4096\,b^{13}\,c^{12}}\right)}^{1/4}\,\left(10240\,a^{15}\,b^4\,c^2\,d^{17}-112640\,a^{14}\,b^5\,c^3\,d^{16}+552960\,a^{13}\,b^6\,c^4\,d^{15}-1576960\,a^{12}\,b^7\,c^5\,d^{14}+2816000\,a^{11}\,b^8\,c^6\,d^{13}-3041280\,a^{10}\,b^9\,c^7\,d^{12}+1351680\,a^9\,b^{10}\,c^8\,d^{11}+1351680\,a^8\,b^{11}\,c^9\,d^{10}-3041280\,a^7\,b^{12}\,c^{10}\,d^9+2816000\,a^6\,b^{13}\,c^{11}\,d^8-1576960\,a^5\,b^{14}\,c^{12}\,d^7+552960\,a^4\,b^{15}\,c^{13}\,d^6-112640\,a^3\,b^{16}\,c^{14}\,d^5+10240\,a^2\,b^{17}\,c^{15}\,d^4\right)}{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}+\frac{\sqrt{x}\,\left(102400\,a^{17}\,b^4\,c^2\,d^{19}-1069056\,a^{16}\,b^5\,c^3\,d^{18}+5001216\,a^{15}\,b^6\,c^4\,d^{17}-13799424\,a^{14}\,b^7\,c^5\,d^{16}+24858624\,a^{13}\,b^8\,c^6\,d^{15}-30412800\,a^{12}\,b^9\,c^7\,d^{14}+24645632\,a^{11}\,b^{10}\,c^8\,d^{13}-9326592\,a^{10}\,b^{11}\,c^9\,d^{12}-9326592\,a^9\,b^{12}\,c^{10}\,d^{11}+24645632\,a^8\,b^{13}\,c^{11}\,d^{10}-30412800\,a^7\,b^{14}\,c^{12}\,d^9+24858624\,a^6\,b^{15}\,c^{13}\,d^8-13799424\,a^5\,b^{16}\,c^{14}\,d^7+5001216\,a^4\,b^{17}\,c^{15}\,d^6-1069056\,a^3\,b^{18}\,c^{16}\,d^5+102400\,a^2\,b^{19}\,c^{17}\,d^4\right)\,1{}\mathrm{i}}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}+\frac{\sqrt{x}\,\left(2025\,a^{10}\,b^3\,c^2\,d^{11}+15930\,a^9\,b^4\,c^3\,d^{10}+56304\,a^8\,b^5\,c^4\,d^9+115110\,a^7\,b^6\,c^5\,d^8+145550\,a^6\,b^7\,c^6\,d^7+115110\,a^5\,b^8\,c^7\,d^6+56304\,a^4\,b^9\,c^8\,d^5+15930\,a^3\,b^{10}\,c^9\,d^4+2025\,a^2\,b^{11}\,c^{10}\,d^3\right)\,1{}\mathrm{i}}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)}\right)\,{\left(-\frac{81\,a^5\,d^4+540\,a^4\,b\,c\,d^3+1350\,a^3\,b^2\,c^2\,d^2+1500\,a^2\,b^3\,c^3\,d+625\,a\,b^4\,c^4}{4096\,a^{12}\,b\,d^{12}-49152\,a^{11}\,b^2\,c\,d^{11}+270336\,a^{10}\,b^3\,c^2\,d^{10}-901120\,a^9\,b^4\,c^3\,d^9+2027520\,a^8\,b^5\,c^4\,d^8-3244032\,a^7\,b^6\,c^5\,d^7+3784704\,a^6\,b^7\,c^6\,d^6-3244032\,a^5\,b^8\,c^7\,d^5+2027520\,a^4\,b^9\,c^8\,d^4-901120\,a^3\,b^{10}\,c^9\,d^3+270336\,a^2\,b^{11}\,c^{10}\,d^2-49152\,a\,b^{12}\,c^{11}\,d+4096\,b^{13}\,c^{12}}\right)}^{1/4}","Not used",1,"atan(((-(81*b^4*c^5 + 625*a^4*c*d^4 + 1500*a^3*b*c^2*d^3 + 1350*a^2*b^2*c^3*d^2 + 540*a*b^3*c^4*d)/(4096*a^12*d^13 + 4096*b^12*c^12*d - 49152*a*b^11*c^11*d^2 + 270336*a^2*b^10*c^10*d^3 - 901120*a^3*b^9*c^9*d^4 + 2027520*a^4*b^8*c^8*d^5 - 3244032*a^5*b^7*c^7*d^6 + 3784704*a^6*b^6*c^6*d^7 - 3244032*a^7*b^5*c^5*d^8 + 2027520*a^8*b^4*c^4*d^9 - 901120*a^9*b^3*c^3*d^10 + 270336*a^10*b^2*c^2*d^11 - 49152*a^11*b*c*d^12))^(1/4)*((-(81*b^4*c^5 + 625*a^4*c*d^4 + 1500*a^3*b*c^2*d^3 + 1350*a^2*b^2*c^3*d^2 + 540*a*b^3*c^4*d)/(4096*a^12*d^13 + 4096*b^12*c^12*d - 49152*a*b^11*c^11*d^2 + 270336*a^2*b^10*c^10*d^3 - 901120*a^3*b^9*c^9*d^4 + 2027520*a^4*b^8*c^8*d^5 - 3244032*a^5*b^7*c^7*d^6 + 3784704*a^6*b^6*c^6*d^7 - 3244032*a^7*b^5*c^5*d^8 + 2027520*a^8*b^4*c^4*d^9 - 901120*a^9*b^3*c^3*d^10 + 270336*a^10*b^2*c^2*d^11 - 49152*a^11*b*c*d^12))^(1/4)*(((405*a^2*b^9*c^8*d^3)/2 + 1674*a^3*b^8*c^7*d^4 + (9843*a^4*b^7*c^6*d^5)/2 + 6884*a^5*b^6*c^5*d^6 + (9843*a^6*b^5*c^4*d^7)/2 + 1674*a^7*b^4*c^3*d^8 + (405*a^8*b^3*c^2*d^9)/2)/(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) + (-(81*b^4*c^5 + 625*a^4*c*d^4 + 1500*a^3*b*c^2*d^3 + 1350*a^2*b^2*c^3*d^2 + 540*a*b^3*c^4*d)/(4096*a^12*d^13 + 4096*b^12*c^12*d - 49152*a*b^11*c^11*d^2 + 270336*a^2*b^10*c^10*d^3 - 901120*a^3*b^9*c^9*d^4 + 2027520*a^4*b^8*c^8*d^5 - 3244032*a^5*b^7*c^7*d^6 + 3784704*a^6*b^6*c^6*d^7 - 3244032*a^7*b^5*c^5*d^8 + 2027520*a^8*b^4*c^4*d^9 - 901120*a^9*b^3*c^3*d^10 + 270336*a^10*b^2*c^2*d^11 - 49152*a^11*b*c*d^12))^(3/4)*((x^(1/2)*(102400*a^2*b^19*c^17*d^4 - 1069056*a^3*b^18*c^16*d^5 + 5001216*a^4*b^17*c^15*d^6 - 13799424*a^5*b^16*c^14*d^7 + 24858624*a^6*b^15*c^13*d^8 - 30412800*a^7*b^14*c^12*d^9 + 24645632*a^8*b^13*c^11*d^10 - 9326592*a^9*b^12*c^10*d^11 - 9326592*a^10*b^11*c^9*d^12 + 24645632*a^11*b^10*c^8*d^13 - 30412800*a^12*b^9*c^7*d^14 + 24858624*a^13*b^8*c^6*d^15 - 13799424*a^14*b^7*c^5*d^16 + 5001216*a^15*b^6*c^4*d^17 - 1069056*a^16*b^5*c^3*d^18 + 102400*a^17*b^4*c^2*d^19))/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)) + ((-(81*b^4*c^5 + 625*a^4*c*d^4 + 1500*a^3*b*c^2*d^3 + 1350*a^2*b^2*c^3*d^2 + 540*a*b^3*c^4*d)/(4096*a^12*d^13 + 4096*b^12*c^12*d - 49152*a*b^11*c^11*d^2 + 270336*a^2*b^10*c^10*d^3 - 901120*a^3*b^9*c^9*d^4 + 2027520*a^4*b^8*c^8*d^5 - 3244032*a^5*b^7*c^7*d^6 + 3784704*a^6*b^6*c^6*d^7 - 3244032*a^7*b^5*c^5*d^8 + 2027520*a^8*b^4*c^4*d^9 - 901120*a^9*b^3*c^3*d^10 + 270336*a^10*b^2*c^2*d^11 - 49152*a^11*b*c*d^12))^(1/4)*(10240*a^2*b^17*c^15*d^4 - 112640*a^3*b^16*c^14*d^5 + 552960*a^4*b^15*c^13*d^6 - 1576960*a^5*b^14*c^12*d^7 + 2816000*a^6*b^13*c^11*d^8 - 3041280*a^7*b^12*c^10*d^9 + 1351680*a^8*b^11*c^9*d^10 + 1351680*a^9*b^10*c^8*d^11 - 3041280*a^10*b^9*c^7*d^12 + 2816000*a^11*b^8*c^6*d^13 - 1576960*a^12*b^7*c^5*d^14 + 552960*a^13*b^6*c^4*d^15 - 112640*a^14*b^5*c^3*d^16 + 10240*a^15*b^4*c^2*d^17))/(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)))*1i + (x^(1/2)*(2025*a^2*b^11*c^10*d^3 + 15930*a^3*b^10*c^9*d^4 + 56304*a^4*b^9*c^8*d^5 + 115110*a^5*b^8*c^7*d^6 + 145550*a^6*b^7*c^6*d^7 + 115110*a^7*b^6*c^5*d^8 + 56304*a^8*b^5*c^4*d^9 + 15930*a^9*b^4*c^3*d^10 + 2025*a^10*b^3*c^2*d^11)*1i)/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11))) - (-(81*b^4*c^5 + 625*a^4*c*d^4 + 1500*a^3*b*c^2*d^3 + 1350*a^2*b^2*c^3*d^2 + 540*a*b^3*c^4*d)/(4096*a^12*d^13 + 4096*b^12*c^12*d - 49152*a*b^11*c^11*d^2 + 270336*a^2*b^10*c^10*d^3 - 901120*a^3*b^9*c^9*d^4 + 2027520*a^4*b^8*c^8*d^5 - 3244032*a^5*b^7*c^7*d^6 + 3784704*a^6*b^6*c^6*d^7 - 3244032*a^7*b^5*c^5*d^8 + 2027520*a^8*b^4*c^4*d^9 - 901120*a^9*b^3*c^3*d^10 + 270336*a^10*b^2*c^2*d^11 - 49152*a^11*b*c*d^12))^(1/4)*((-(81*b^4*c^5 + 625*a^4*c*d^4 + 1500*a^3*b*c^2*d^3 + 1350*a^2*b^2*c^3*d^2 + 540*a*b^3*c^4*d)/(4096*a^12*d^13 + 4096*b^12*c^12*d - 49152*a*b^11*c^11*d^2 + 270336*a^2*b^10*c^10*d^3 - 901120*a^3*b^9*c^9*d^4 + 2027520*a^4*b^8*c^8*d^5 - 3244032*a^5*b^7*c^7*d^6 + 3784704*a^6*b^6*c^6*d^7 - 3244032*a^7*b^5*c^5*d^8 + 2027520*a^8*b^4*c^4*d^9 - 901120*a^9*b^3*c^3*d^10 + 270336*a^10*b^2*c^2*d^11 - 49152*a^11*b*c*d^12))^(1/4)*(((405*a^2*b^9*c^8*d^3)/2 + 1674*a^3*b^8*c^7*d^4 + (9843*a^4*b^7*c^6*d^5)/2 + 6884*a^5*b^6*c^5*d^6 + (9843*a^6*b^5*c^4*d^7)/2 + 1674*a^7*b^4*c^3*d^8 + (405*a^8*b^3*c^2*d^9)/2)/(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) - (-(81*b^4*c^5 + 625*a^4*c*d^4 + 1500*a^3*b*c^2*d^3 + 1350*a^2*b^2*c^3*d^2 + 540*a*b^3*c^4*d)/(4096*a^12*d^13 + 4096*b^12*c^12*d - 49152*a*b^11*c^11*d^2 + 270336*a^2*b^10*c^10*d^3 - 901120*a^3*b^9*c^9*d^4 + 2027520*a^4*b^8*c^8*d^5 - 3244032*a^5*b^7*c^7*d^6 + 3784704*a^6*b^6*c^6*d^7 - 3244032*a^7*b^5*c^5*d^8 + 2027520*a^8*b^4*c^4*d^9 - 901120*a^9*b^3*c^3*d^10 + 270336*a^10*b^2*c^2*d^11 - 49152*a^11*b*c*d^12))^(3/4)*((x^(1/2)*(102400*a^2*b^19*c^17*d^4 - 1069056*a^3*b^18*c^16*d^5 + 5001216*a^4*b^17*c^15*d^6 - 13799424*a^5*b^16*c^14*d^7 + 24858624*a^6*b^15*c^13*d^8 - 30412800*a^7*b^14*c^12*d^9 + 24645632*a^8*b^13*c^11*d^10 - 9326592*a^9*b^12*c^10*d^11 - 9326592*a^10*b^11*c^9*d^12 + 24645632*a^11*b^10*c^8*d^13 - 30412800*a^12*b^9*c^7*d^14 + 24858624*a^13*b^8*c^6*d^15 - 13799424*a^14*b^7*c^5*d^16 + 5001216*a^15*b^6*c^4*d^17 - 1069056*a^16*b^5*c^3*d^18 + 102400*a^17*b^4*c^2*d^19))/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)) - ((-(81*b^4*c^5 + 625*a^4*c*d^4 + 1500*a^3*b*c^2*d^3 + 1350*a^2*b^2*c^3*d^2 + 540*a*b^3*c^4*d)/(4096*a^12*d^13 + 4096*b^12*c^12*d - 49152*a*b^11*c^11*d^2 + 270336*a^2*b^10*c^10*d^3 - 901120*a^3*b^9*c^9*d^4 + 2027520*a^4*b^8*c^8*d^5 - 3244032*a^5*b^7*c^7*d^6 + 3784704*a^6*b^6*c^6*d^7 - 3244032*a^7*b^5*c^5*d^8 + 2027520*a^8*b^4*c^4*d^9 - 901120*a^9*b^3*c^3*d^10 + 270336*a^10*b^2*c^2*d^11 - 49152*a^11*b*c*d^12))^(1/4)*(10240*a^2*b^17*c^15*d^4 - 112640*a^3*b^16*c^14*d^5 + 552960*a^4*b^15*c^13*d^6 - 1576960*a^5*b^14*c^12*d^7 + 2816000*a^6*b^13*c^11*d^8 - 3041280*a^7*b^12*c^10*d^9 + 1351680*a^8*b^11*c^9*d^10 + 1351680*a^9*b^10*c^8*d^11 - 3041280*a^10*b^9*c^7*d^12 + 2816000*a^11*b^8*c^6*d^13 - 1576960*a^12*b^7*c^5*d^14 + 552960*a^13*b^6*c^4*d^15 - 112640*a^14*b^5*c^3*d^16 + 10240*a^15*b^4*c^2*d^17))/(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)))*1i - (x^(1/2)*(2025*a^2*b^11*c^10*d^3 + 15930*a^3*b^10*c^9*d^4 + 56304*a^4*b^9*c^8*d^5 + 115110*a^5*b^8*c^7*d^6 + 145550*a^6*b^7*c^6*d^7 + 115110*a^7*b^6*c^5*d^8 + 56304*a^8*b^5*c^4*d^9 + 15930*a^9*b^4*c^3*d^10 + 2025*a^10*b^3*c^2*d^11)*1i)/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11))))/((-(81*b^4*c^5 + 625*a^4*c*d^4 + 1500*a^3*b*c^2*d^3 + 1350*a^2*b^2*c^3*d^2 + 540*a*b^3*c^4*d)/(4096*a^12*d^13 + 4096*b^12*c^12*d - 49152*a*b^11*c^11*d^2 + 270336*a^2*b^10*c^10*d^3 - 901120*a^3*b^9*c^9*d^4 + 2027520*a^4*b^8*c^8*d^5 - 3244032*a^5*b^7*c^7*d^6 + 3784704*a^6*b^6*c^6*d^7 - 3244032*a^7*b^5*c^5*d^8 + 2027520*a^8*b^4*c^4*d^9 - 901120*a^9*b^3*c^3*d^10 + 270336*a^10*b^2*c^2*d^11 - 49152*a^11*b*c*d^12))^(1/4)*((-(81*b^4*c^5 + 625*a^4*c*d^4 + 1500*a^3*b*c^2*d^3 + 1350*a^2*b^2*c^3*d^2 + 540*a*b^3*c^4*d)/(4096*a^12*d^13 + 4096*b^12*c^12*d - 49152*a*b^11*c^11*d^2 + 270336*a^2*b^10*c^10*d^3 - 901120*a^3*b^9*c^9*d^4 + 2027520*a^4*b^8*c^8*d^5 - 3244032*a^5*b^7*c^7*d^6 + 3784704*a^6*b^6*c^6*d^7 - 3244032*a^7*b^5*c^5*d^8 + 2027520*a^8*b^4*c^4*d^9 - 901120*a^9*b^3*c^3*d^10 + 270336*a^10*b^2*c^2*d^11 - 49152*a^11*b*c*d^12))^(1/4)*(((405*a^2*b^9*c^8*d^3)/2 + 1674*a^3*b^8*c^7*d^4 + (9843*a^4*b^7*c^6*d^5)/2 + 6884*a^5*b^6*c^5*d^6 + (9843*a^6*b^5*c^4*d^7)/2 + 1674*a^7*b^4*c^3*d^8 + (405*a^8*b^3*c^2*d^9)/2)/(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) + (-(81*b^4*c^5 + 625*a^4*c*d^4 + 1500*a^3*b*c^2*d^3 + 1350*a^2*b^2*c^3*d^2 + 540*a*b^3*c^4*d)/(4096*a^12*d^13 + 4096*b^12*c^12*d - 49152*a*b^11*c^11*d^2 + 270336*a^2*b^10*c^10*d^3 - 901120*a^3*b^9*c^9*d^4 + 2027520*a^4*b^8*c^8*d^5 - 3244032*a^5*b^7*c^7*d^6 + 3784704*a^6*b^6*c^6*d^7 - 3244032*a^7*b^5*c^5*d^8 + 2027520*a^8*b^4*c^4*d^9 - 901120*a^9*b^3*c^3*d^10 + 270336*a^10*b^2*c^2*d^11 - 49152*a^11*b*c*d^12))^(3/4)*((x^(1/2)*(102400*a^2*b^19*c^17*d^4 - 1069056*a^3*b^18*c^16*d^5 + 5001216*a^4*b^17*c^15*d^6 - 13799424*a^5*b^16*c^14*d^7 + 24858624*a^6*b^15*c^13*d^8 - 30412800*a^7*b^14*c^12*d^9 + 24645632*a^8*b^13*c^11*d^10 - 9326592*a^9*b^12*c^10*d^11 - 9326592*a^10*b^11*c^9*d^12 + 24645632*a^11*b^10*c^8*d^13 - 30412800*a^12*b^9*c^7*d^14 + 24858624*a^13*b^8*c^6*d^15 - 13799424*a^14*b^7*c^5*d^16 + 5001216*a^15*b^6*c^4*d^17 - 1069056*a^16*b^5*c^3*d^18 + 102400*a^17*b^4*c^2*d^19))/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)) + ((-(81*b^4*c^5 + 625*a^4*c*d^4 + 1500*a^3*b*c^2*d^3 + 1350*a^2*b^2*c^3*d^2 + 540*a*b^3*c^4*d)/(4096*a^12*d^13 + 4096*b^12*c^12*d - 49152*a*b^11*c^11*d^2 + 270336*a^2*b^10*c^10*d^3 - 901120*a^3*b^9*c^9*d^4 + 2027520*a^4*b^8*c^8*d^5 - 3244032*a^5*b^7*c^7*d^6 + 3784704*a^6*b^6*c^6*d^7 - 3244032*a^7*b^5*c^5*d^8 + 2027520*a^8*b^4*c^4*d^9 - 901120*a^9*b^3*c^3*d^10 + 270336*a^10*b^2*c^2*d^11 - 49152*a^11*b*c*d^12))^(1/4)*(10240*a^2*b^17*c^15*d^4 - 112640*a^3*b^16*c^14*d^5 + 552960*a^4*b^15*c^13*d^6 - 1576960*a^5*b^14*c^12*d^7 + 2816000*a^6*b^13*c^11*d^8 - 3041280*a^7*b^12*c^10*d^9 + 1351680*a^8*b^11*c^9*d^10 + 1351680*a^9*b^10*c^8*d^11 - 3041280*a^10*b^9*c^7*d^12 + 2816000*a^11*b^8*c^6*d^13 - 1576960*a^12*b^7*c^5*d^14 + 552960*a^13*b^6*c^4*d^15 - 112640*a^14*b^5*c^3*d^16 + 10240*a^15*b^4*c^2*d^17))/(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))) + (x^(1/2)*(2025*a^2*b^11*c^10*d^3 + 15930*a^3*b^10*c^9*d^4 + 56304*a^4*b^9*c^8*d^5 + 115110*a^5*b^8*c^7*d^6 + 145550*a^6*b^7*c^6*d^7 + 115110*a^7*b^6*c^5*d^8 + 56304*a^8*b^5*c^4*d^9 + 15930*a^9*b^4*c^3*d^10 + 2025*a^10*b^3*c^2*d^11))/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11))) + (-(81*b^4*c^5 + 625*a^4*c*d^4 + 1500*a^3*b*c^2*d^3 + 1350*a^2*b^2*c^3*d^2 + 540*a*b^3*c^4*d)/(4096*a^12*d^13 + 4096*b^12*c^12*d - 49152*a*b^11*c^11*d^2 + 270336*a^2*b^10*c^10*d^3 - 901120*a^3*b^9*c^9*d^4 + 2027520*a^4*b^8*c^8*d^5 - 3244032*a^5*b^7*c^7*d^6 + 3784704*a^6*b^6*c^6*d^7 - 3244032*a^7*b^5*c^5*d^8 + 2027520*a^8*b^4*c^4*d^9 - 901120*a^9*b^3*c^3*d^10 + 270336*a^10*b^2*c^2*d^11 - 49152*a^11*b*c*d^12))^(1/4)*((-(81*b^4*c^5 + 625*a^4*c*d^4 + 1500*a^3*b*c^2*d^3 + 1350*a^2*b^2*c^3*d^2 + 540*a*b^3*c^4*d)/(4096*a^12*d^13 + 4096*b^12*c^12*d - 49152*a*b^11*c^11*d^2 + 270336*a^2*b^10*c^10*d^3 - 901120*a^3*b^9*c^9*d^4 + 2027520*a^4*b^8*c^8*d^5 - 3244032*a^5*b^7*c^7*d^6 + 3784704*a^6*b^6*c^6*d^7 - 3244032*a^7*b^5*c^5*d^8 + 2027520*a^8*b^4*c^4*d^9 - 901120*a^9*b^3*c^3*d^10 + 270336*a^10*b^2*c^2*d^11 - 49152*a^11*b*c*d^12))^(1/4)*(((405*a^2*b^9*c^8*d^3)/2 + 1674*a^3*b^8*c^7*d^4 + (9843*a^4*b^7*c^6*d^5)/2 + 6884*a^5*b^6*c^5*d^6 + (9843*a^6*b^5*c^4*d^7)/2 + 1674*a^7*b^4*c^3*d^8 + (405*a^8*b^3*c^2*d^9)/2)/(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) - (-(81*b^4*c^5 + 625*a^4*c*d^4 + 1500*a^3*b*c^2*d^3 + 1350*a^2*b^2*c^3*d^2 + 540*a*b^3*c^4*d)/(4096*a^12*d^13 + 4096*b^12*c^12*d - 49152*a*b^11*c^11*d^2 + 270336*a^2*b^10*c^10*d^3 - 901120*a^3*b^9*c^9*d^4 + 2027520*a^4*b^8*c^8*d^5 - 3244032*a^5*b^7*c^7*d^6 + 3784704*a^6*b^6*c^6*d^7 - 3244032*a^7*b^5*c^5*d^8 + 2027520*a^8*b^4*c^4*d^9 - 901120*a^9*b^3*c^3*d^10 + 270336*a^10*b^2*c^2*d^11 - 49152*a^11*b*c*d^12))^(3/4)*((x^(1/2)*(102400*a^2*b^19*c^17*d^4 - 1069056*a^3*b^18*c^16*d^5 + 5001216*a^4*b^17*c^15*d^6 - 13799424*a^5*b^16*c^14*d^7 + 24858624*a^6*b^15*c^13*d^8 - 30412800*a^7*b^14*c^12*d^9 + 24645632*a^8*b^13*c^11*d^10 - 9326592*a^9*b^12*c^10*d^11 - 9326592*a^10*b^11*c^9*d^12 + 24645632*a^11*b^10*c^8*d^13 - 30412800*a^12*b^9*c^7*d^14 + 24858624*a^13*b^8*c^6*d^15 - 13799424*a^14*b^7*c^5*d^16 + 5001216*a^15*b^6*c^4*d^17 - 1069056*a^16*b^5*c^3*d^18 + 102400*a^17*b^4*c^2*d^19))/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)) - ((-(81*b^4*c^5 + 625*a^4*c*d^4 + 1500*a^3*b*c^2*d^3 + 1350*a^2*b^2*c^3*d^2 + 540*a*b^3*c^4*d)/(4096*a^12*d^13 + 4096*b^12*c^12*d - 49152*a*b^11*c^11*d^2 + 270336*a^2*b^10*c^10*d^3 - 901120*a^3*b^9*c^9*d^4 + 2027520*a^4*b^8*c^8*d^5 - 3244032*a^5*b^7*c^7*d^6 + 3784704*a^6*b^6*c^6*d^7 - 3244032*a^7*b^5*c^5*d^8 + 2027520*a^8*b^4*c^4*d^9 - 901120*a^9*b^3*c^3*d^10 + 270336*a^10*b^2*c^2*d^11 - 49152*a^11*b*c*d^12))^(1/4)*(10240*a^2*b^17*c^15*d^4 - 112640*a^3*b^16*c^14*d^5 + 552960*a^4*b^15*c^13*d^6 - 1576960*a^5*b^14*c^12*d^7 + 2816000*a^6*b^13*c^11*d^8 - 3041280*a^7*b^12*c^10*d^9 + 1351680*a^8*b^11*c^9*d^10 + 1351680*a^9*b^10*c^8*d^11 - 3041280*a^10*b^9*c^7*d^12 + 2816000*a^11*b^8*c^6*d^13 - 1576960*a^12*b^7*c^5*d^14 + 552960*a^13*b^6*c^4*d^15 - 112640*a^14*b^5*c^3*d^16 + 10240*a^15*b^4*c^2*d^17))/(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))) - (x^(1/2)*(2025*a^2*b^11*c^10*d^3 + 15930*a^3*b^10*c^9*d^4 + 56304*a^4*b^9*c^8*d^5 + 115110*a^5*b^8*c^7*d^6 + 145550*a^6*b^7*c^6*d^7 + 115110*a^7*b^6*c^5*d^8 + 56304*a^8*b^5*c^4*d^9 + 15930*a^9*b^4*c^3*d^10 + 2025*a^10*b^3*c^2*d^11))/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)))))*(-(81*b^4*c^5 + 625*a^4*c*d^4 + 1500*a^3*b*c^2*d^3 + 1350*a^2*b^2*c^3*d^2 + 540*a*b^3*c^4*d)/(4096*a^12*d^13 + 4096*b^12*c^12*d - 49152*a*b^11*c^11*d^2 + 270336*a^2*b^10*c^10*d^3 - 901120*a^3*b^9*c^9*d^4 + 2027520*a^4*b^8*c^8*d^5 - 3244032*a^5*b^7*c^7*d^6 + 3784704*a^6*b^6*c^6*d^7 - 3244032*a^7*b^5*c^5*d^8 + 2027520*a^8*b^4*c^4*d^9 - 901120*a^9*b^3*c^3*d^10 + 270336*a^10*b^2*c^2*d^11 - 49152*a^11*b*c*d^12))^(1/4)*2i - 2*atan(((-(81*b^4*c^5 + 625*a^4*c*d^4 + 1500*a^3*b*c^2*d^3 + 1350*a^2*b^2*c^3*d^2 + 540*a*b^3*c^4*d)/(4096*a^12*d^13 + 4096*b^12*c^12*d - 49152*a*b^11*c^11*d^2 + 270336*a^2*b^10*c^10*d^3 - 901120*a^3*b^9*c^9*d^4 + 2027520*a^4*b^8*c^8*d^5 - 3244032*a^5*b^7*c^7*d^6 + 3784704*a^6*b^6*c^6*d^7 - 3244032*a^7*b^5*c^5*d^8 + 2027520*a^8*b^4*c^4*d^9 - 901120*a^9*b^3*c^3*d^10 + 270336*a^10*b^2*c^2*d^11 - 49152*a^11*b*c*d^12))^(1/4)*((-(81*b^4*c^5 + 625*a^4*c*d^4 + 1500*a^3*b*c^2*d^3 + 1350*a^2*b^2*c^3*d^2 + 540*a*b^3*c^4*d)/(4096*a^12*d^13 + 4096*b^12*c^12*d - 49152*a*b^11*c^11*d^2 + 270336*a^2*b^10*c^10*d^3 - 901120*a^3*b^9*c^9*d^4 + 2027520*a^4*b^8*c^8*d^5 - 3244032*a^5*b^7*c^7*d^6 + 3784704*a^6*b^6*c^6*d^7 - 3244032*a^7*b^5*c^5*d^8 + 2027520*a^8*b^4*c^4*d^9 - 901120*a^9*b^3*c^3*d^10 + 270336*a^10*b^2*c^2*d^11 - 49152*a^11*b*c*d^12))^(1/4)*((((405*a^2*b^9*c^8*d^3)/2 + 1674*a^3*b^8*c^7*d^4 + (9843*a^4*b^7*c^6*d^5)/2 + 6884*a^5*b^6*c^5*d^6 + (9843*a^6*b^5*c^4*d^7)/2 + 1674*a^7*b^4*c^3*d^8 + (405*a^8*b^3*c^2*d^9)/2)*1i)/(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) + (-(81*b^4*c^5 + 625*a^4*c*d^4 + 1500*a^3*b*c^2*d^3 + 1350*a^2*b^2*c^3*d^2 + 540*a*b^3*c^4*d)/(4096*a^12*d^13 + 4096*b^12*c^12*d - 49152*a*b^11*c^11*d^2 + 270336*a^2*b^10*c^10*d^3 - 901120*a^3*b^9*c^9*d^4 + 2027520*a^4*b^8*c^8*d^5 - 3244032*a^5*b^7*c^7*d^6 + 3784704*a^6*b^6*c^6*d^7 - 3244032*a^7*b^5*c^5*d^8 + 2027520*a^8*b^4*c^4*d^9 - 901120*a^9*b^3*c^3*d^10 + 270336*a^10*b^2*c^2*d^11 - 49152*a^11*b*c*d^12))^(3/4)*((x^(1/2)*(102400*a^2*b^19*c^17*d^4 - 1069056*a^3*b^18*c^16*d^5 + 5001216*a^4*b^17*c^15*d^6 - 13799424*a^5*b^16*c^14*d^7 + 24858624*a^6*b^15*c^13*d^8 - 30412800*a^7*b^14*c^12*d^9 + 24645632*a^8*b^13*c^11*d^10 - 9326592*a^9*b^12*c^10*d^11 - 9326592*a^10*b^11*c^9*d^12 + 24645632*a^11*b^10*c^8*d^13 - 30412800*a^12*b^9*c^7*d^14 + 24858624*a^13*b^8*c^6*d^15 - 13799424*a^14*b^7*c^5*d^16 + 5001216*a^15*b^6*c^4*d^17 - 1069056*a^16*b^5*c^3*d^18 + 102400*a^17*b^4*c^2*d^19)*1i)/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)) + ((-(81*b^4*c^5 + 625*a^4*c*d^4 + 1500*a^3*b*c^2*d^3 + 1350*a^2*b^2*c^3*d^2 + 540*a*b^3*c^4*d)/(4096*a^12*d^13 + 4096*b^12*c^12*d - 49152*a*b^11*c^11*d^2 + 270336*a^2*b^10*c^10*d^3 - 901120*a^3*b^9*c^9*d^4 + 2027520*a^4*b^8*c^8*d^5 - 3244032*a^5*b^7*c^7*d^6 + 3784704*a^6*b^6*c^6*d^7 - 3244032*a^7*b^5*c^5*d^8 + 2027520*a^8*b^4*c^4*d^9 - 901120*a^9*b^3*c^3*d^10 + 270336*a^10*b^2*c^2*d^11 - 49152*a^11*b*c*d^12))^(1/4)*(10240*a^2*b^17*c^15*d^4 - 112640*a^3*b^16*c^14*d^5 + 552960*a^4*b^15*c^13*d^6 - 1576960*a^5*b^14*c^12*d^7 + 2816000*a^6*b^13*c^11*d^8 - 3041280*a^7*b^12*c^10*d^9 + 1351680*a^8*b^11*c^9*d^10 + 1351680*a^9*b^10*c^8*d^11 - 3041280*a^10*b^9*c^7*d^12 + 2816000*a^11*b^8*c^6*d^13 - 1576960*a^12*b^7*c^5*d^14 + 552960*a^13*b^6*c^4*d^15 - 112640*a^14*b^5*c^3*d^16 + 10240*a^15*b^4*c^2*d^17))/(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))*1i) - (x^(1/2)*(2025*a^2*b^11*c^10*d^3 + 15930*a^3*b^10*c^9*d^4 + 56304*a^4*b^9*c^8*d^5 + 115110*a^5*b^8*c^7*d^6 + 145550*a^6*b^7*c^6*d^7 + 115110*a^7*b^6*c^5*d^8 + 56304*a^8*b^5*c^4*d^9 + 15930*a^9*b^4*c^3*d^10 + 2025*a^10*b^3*c^2*d^11))/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11))) - (-(81*b^4*c^5 + 625*a^4*c*d^4 + 1500*a^3*b*c^2*d^3 + 1350*a^2*b^2*c^3*d^2 + 540*a*b^3*c^4*d)/(4096*a^12*d^13 + 4096*b^12*c^12*d - 49152*a*b^11*c^11*d^2 + 270336*a^2*b^10*c^10*d^3 - 901120*a^3*b^9*c^9*d^4 + 2027520*a^4*b^8*c^8*d^5 - 3244032*a^5*b^7*c^7*d^6 + 3784704*a^6*b^6*c^6*d^7 - 3244032*a^7*b^5*c^5*d^8 + 2027520*a^8*b^4*c^4*d^9 - 901120*a^9*b^3*c^3*d^10 + 270336*a^10*b^2*c^2*d^11 - 49152*a^11*b*c*d^12))^(1/4)*((-(81*b^4*c^5 + 625*a^4*c*d^4 + 1500*a^3*b*c^2*d^3 + 1350*a^2*b^2*c^3*d^2 + 540*a*b^3*c^4*d)/(4096*a^12*d^13 + 4096*b^12*c^12*d - 49152*a*b^11*c^11*d^2 + 270336*a^2*b^10*c^10*d^3 - 901120*a^3*b^9*c^9*d^4 + 2027520*a^4*b^8*c^8*d^5 - 3244032*a^5*b^7*c^7*d^6 + 3784704*a^6*b^6*c^6*d^7 - 3244032*a^7*b^5*c^5*d^8 + 2027520*a^8*b^4*c^4*d^9 - 901120*a^9*b^3*c^3*d^10 + 270336*a^10*b^2*c^2*d^11 - 49152*a^11*b*c*d^12))^(1/4)*((((405*a^2*b^9*c^8*d^3)/2 + 1674*a^3*b^8*c^7*d^4 + (9843*a^4*b^7*c^6*d^5)/2 + 6884*a^5*b^6*c^5*d^6 + (9843*a^6*b^5*c^4*d^7)/2 + 1674*a^7*b^4*c^3*d^8 + (405*a^8*b^3*c^2*d^9)/2)*1i)/(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) - (-(81*b^4*c^5 + 625*a^4*c*d^4 + 1500*a^3*b*c^2*d^3 + 1350*a^2*b^2*c^3*d^2 + 540*a*b^3*c^4*d)/(4096*a^12*d^13 + 4096*b^12*c^12*d - 49152*a*b^11*c^11*d^2 + 270336*a^2*b^10*c^10*d^3 - 901120*a^3*b^9*c^9*d^4 + 2027520*a^4*b^8*c^8*d^5 - 3244032*a^5*b^7*c^7*d^6 + 3784704*a^6*b^6*c^6*d^7 - 3244032*a^7*b^5*c^5*d^8 + 2027520*a^8*b^4*c^4*d^9 - 901120*a^9*b^3*c^3*d^10 + 270336*a^10*b^2*c^2*d^11 - 49152*a^11*b*c*d^12))^(3/4)*((x^(1/2)*(102400*a^2*b^19*c^17*d^4 - 1069056*a^3*b^18*c^16*d^5 + 5001216*a^4*b^17*c^15*d^6 - 13799424*a^5*b^16*c^14*d^7 + 24858624*a^6*b^15*c^13*d^8 - 30412800*a^7*b^14*c^12*d^9 + 24645632*a^8*b^13*c^11*d^10 - 9326592*a^9*b^12*c^10*d^11 - 9326592*a^10*b^11*c^9*d^12 + 24645632*a^11*b^10*c^8*d^13 - 30412800*a^12*b^9*c^7*d^14 + 24858624*a^13*b^8*c^6*d^15 - 13799424*a^14*b^7*c^5*d^16 + 5001216*a^15*b^6*c^4*d^17 - 1069056*a^16*b^5*c^3*d^18 + 102400*a^17*b^4*c^2*d^19)*1i)/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)) - ((-(81*b^4*c^5 + 625*a^4*c*d^4 + 1500*a^3*b*c^2*d^3 + 1350*a^2*b^2*c^3*d^2 + 540*a*b^3*c^4*d)/(4096*a^12*d^13 + 4096*b^12*c^12*d - 49152*a*b^11*c^11*d^2 + 270336*a^2*b^10*c^10*d^3 - 901120*a^3*b^9*c^9*d^4 + 2027520*a^4*b^8*c^8*d^5 - 3244032*a^5*b^7*c^7*d^6 + 3784704*a^6*b^6*c^6*d^7 - 3244032*a^7*b^5*c^5*d^8 + 2027520*a^8*b^4*c^4*d^9 - 901120*a^9*b^3*c^3*d^10 + 270336*a^10*b^2*c^2*d^11 - 49152*a^11*b*c*d^12))^(1/4)*(10240*a^2*b^17*c^15*d^4 - 112640*a^3*b^16*c^14*d^5 + 552960*a^4*b^15*c^13*d^6 - 1576960*a^5*b^14*c^12*d^7 + 2816000*a^6*b^13*c^11*d^8 - 3041280*a^7*b^12*c^10*d^9 + 1351680*a^8*b^11*c^9*d^10 + 1351680*a^9*b^10*c^8*d^11 - 3041280*a^10*b^9*c^7*d^12 + 2816000*a^11*b^8*c^6*d^13 - 1576960*a^12*b^7*c^5*d^14 + 552960*a^13*b^6*c^4*d^15 - 112640*a^14*b^5*c^3*d^16 + 10240*a^15*b^4*c^2*d^17))/(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))*1i) + (x^(1/2)*(2025*a^2*b^11*c^10*d^3 + 15930*a^3*b^10*c^9*d^4 + 56304*a^4*b^9*c^8*d^5 + 115110*a^5*b^8*c^7*d^6 + 145550*a^6*b^7*c^6*d^7 + 115110*a^7*b^6*c^5*d^8 + 56304*a^8*b^5*c^4*d^9 + 15930*a^9*b^4*c^3*d^10 + 2025*a^10*b^3*c^2*d^11))/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11))))/((-(81*b^4*c^5 + 625*a^4*c*d^4 + 1500*a^3*b*c^2*d^3 + 1350*a^2*b^2*c^3*d^2 + 540*a*b^3*c^4*d)/(4096*a^12*d^13 + 4096*b^12*c^12*d - 49152*a*b^11*c^11*d^2 + 270336*a^2*b^10*c^10*d^3 - 901120*a^3*b^9*c^9*d^4 + 2027520*a^4*b^8*c^8*d^5 - 3244032*a^5*b^7*c^7*d^6 + 3784704*a^6*b^6*c^6*d^7 - 3244032*a^7*b^5*c^5*d^8 + 2027520*a^8*b^4*c^4*d^9 - 901120*a^9*b^3*c^3*d^10 + 270336*a^10*b^2*c^2*d^11 - 49152*a^11*b*c*d^12))^(1/4)*((-(81*b^4*c^5 + 625*a^4*c*d^4 + 1500*a^3*b*c^2*d^3 + 1350*a^2*b^2*c^3*d^2 + 540*a*b^3*c^4*d)/(4096*a^12*d^13 + 4096*b^12*c^12*d - 49152*a*b^11*c^11*d^2 + 270336*a^2*b^10*c^10*d^3 - 901120*a^3*b^9*c^9*d^4 + 2027520*a^4*b^8*c^8*d^5 - 3244032*a^5*b^7*c^7*d^6 + 3784704*a^6*b^6*c^6*d^7 - 3244032*a^7*b^5*c^5*d^8 + 2027520*a^8*b^4*c^4*d^9 - 901120*a^9*b^3*c^3*d^10 + 270336*a^10*b^2*c^2*d^11 - 49152*a^11*b*c*d^12))^(1/4)*((((405*a^2*b^9*c^8*d^3)/2 + 1674*a^3*b^8*c^7*d^4 + (9843*a^4*b^7*c^6*d^5)/2 + 6884*a^5*b^6*c^5*d^6 + (9843*a^6*b^5*c^4*d^7)/2 + 1674*a^7*b^4*c^3*d^8 + (405*a^8*b^3*c^2*d^9)/2)*1i)/(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) + (-(81*b^4*c^5 + 625*a^4*c*d^4 + 1500*a^3*b*c^2*d^3 + 1350*a^2*b^2*c^3*d^2 + 540*a*b^3*c^4*d)/(4096*a^12*d^13 + 4096*b^12*c^12*d - 49152*a*b^11*c^11*d^2 + 270336*a^2*b^10*c^10*d^3 - 901120*a^3*b^9*c^9*d^4 + 2027520*a^4*b^8*c^8*d^5 - 3244032*a^5*b^7*c^7*d^6 + 3784704*a^6*b^6*c^6*d^7 - 3244032*a^7*b^5*c^5*d^8 + 2027520*a^8*b^4*c^4*d^9 - 901120*a^9*b^3*c^3*d^10 + 270336*a^10*b^2*c^2*d^11 - 49152*a^11*b*c*d^12))^(3/4)*((x^(1/2)*(102400*a^2*b^19*c^17*d^4 - 1069056*a^3*b^18*c^16*d^5 + 5001216*a^4*b^17*c^15*d^6 - 13799424*a^5*b^16*c^14*d^7 + 24858624*a^6*b^15*c^13*d^8 - 30412800*a^7*b^14*c^12*d^9 + 24645632*a^8*b^13*c^11*d^10 - 9326592*a^9*b^12*c^10*d^11 - 9326592*a^10*b^11*c^9*d^12 + 24645632*a^11*b^10*c^8*d^13 - 30412800*a^12*b^9*c^7*d^14 + 24858624*a^13*b^8*c^6*d^15 - 13799424*a^14*b^7*c^5*d^16 + 5001216*a^15*b^6*c^4*d^17 - 1069056*a^16*b^5*c^3*d^18 + 102400*a^17*b^4*c^2*d^19)*1i)/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)) + ((-(81*b^4*c^5 + 625*a^4*c*d^4 + 1500*a^3*b*c^2*d^3 + 1350*a^2*b^2*c^3*d^2 + 540*a*b^3*c^4*d)/(4096*a^12*d^13 + 4096*b^12*c^12*d - 49152*a*b^11*c^11*d^2 + 270336*a^2*b^10*c^10*d^3 - 901120*a^3*b^9*c^9*d^4 + 2027520*a^4*b^8*c^8*d^5 - 3244032*a^5*b^7*c^7*d^6 + 3784704*a^6*b^6*c^6*d^7 - 3244032*a^7*b^5*c^5*d^8 + 2027520*a^8*b^4*c^4*d^9 - 901120*a^9*b^3*c^3*d^10 + 270336*a^10*b^2*c^2*d^11 - 49152*a^11*b*c*d^12))^(1/4)*(10240*a^2*b^17*c^15*d^4 - 112640*a^3*b^16*c^14*d^5 + 552960*a^4*b^15*c^13*d^6 - 1576960*a^5*b^14*c^12*d^7 + 2816000*a^6*b^13*c^11*d^8 - 3041280*a^7*b^12*c^10*d^9 + 1351680*a^8*b^11*c^9*d^10 + 1351680*a^9*b^10*c^8*d^11 - 3041280*a^10*b^9*c^7*d^12 + 2816000*a^11*b^8*c^6*d^13 - 1576960*a^12*b^7*c^5*d^14 + 552960*a^13*b^6*c^4*d^15 - 112640*a^14*b^5*c^3*d^16 + 10240*a^15*b^4*c^2*d^17))/(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))*1i)*1i - (x^(1/2)*(2025*a^2*b^11*c^10*d^3 + 15930*a^3*b^10*c^9*d^4 + 56304*a^4*b^9*c^8*d^5 + 115110*a^5*b^8*c^7*d^6 + 145550*a^6*b^7*c^6*d^7 + 115110*a^7*b^6*c^5*d^8 + 56304*a^8*b^5*c^4*d^9 + 15930*a^9*b^4*c^3*d^10 + 2025*a^10*b^3*c^2*d^11)*1i)/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11))) + (-(81*b^4*c^5 + 625*a^4*c*d^4 + 1500*a^3*b*c^2*d^3 + 1350*a^2*b^2*c^3*d^2 + 540*a*b^3*c^4*d)/(4096*a^12*d^13 + 4096*b^12*c^12*d - 49152*a*b^11*c^11*d^2 + 270336*a^2*b^10*c^10*d^3 - 901120*a^3*b^9*c^9*d^4 + 2027520*a^4*b^8*c^8*d^5 - 3244032*a^5*b^7*c^7*d^6 + 3784704*a^6*b^6*c^6*d^7 - 3244032*a^7*b^5*c^5*d^8 + 2027520*a^8*b^4*c^4*d^9 - 901120*a^9*b^3*c^3*d^10 + 270336*a^10*b^2*c^2*d^11 - 49152*a^11*b*c*d^12))^(1/4)*((-(81*b^4*c^5 + 625*a^4*c*d^4 + 1500*a^3*b*c^2*d^3 + 1350*a^2*b^2*c^3*d^2 + 540*a*b^3*c^4*d)/(4096*a^12*d^13 + 4096*b^12*c^12*d - 49152*a*b^11*c^11*d^2 + 270336*a^2*b^10*c^10*d^3 - 901120*a^3*b^9*c^9*d^4 + 2027520*a^4*b^8*c^8*d^5 - 3244032*a^5*b^7*c^7*d^6 + 3784704*a^6*b^6*c^6*d^7 - 3244032*a^7*b^5*c^5*d^8 + 2027520*a^8*b^4*c^4*d^9 - 901120*a^9*b^3*c^3*d^10 + 270336*a^10*b^2*c^2*d^11 - 49152*a^11*b*c*d^12))^(1/4)*((((405*a^2*b^9*c^8*d^3)/2 + 1674*a^3*b^8*c^7*d^4 + (9843*a^4*b^7*c^6*d^5)/2 + 6884*a^5*b^6*c^5*d^6 + (9843*a^6*b^5*c^4*d^7)/2 + 1674*a^7*b^4*c^3*d^8 + (405*a^8*b^3*c^2*d^9)/2)*1i)/(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) - (-(81*b^4*c^5 + 625*a^4*c*d^4 + 1500*a^3*b*c^2*d^3 + 1350*a^2*b^2*c^3*d^2 + 540*a*b^3*c^4*d)/(4096*a^12*d^13 + 4096*b^12*c^12*d - 49152*a*b^11*c^11*d^2 + 270336*a^2*b^10*c^10*d^3 - 901120*a^3*b^9*c^9*d^4 + 2027520*a^4*b^8*c^8*d^5 - 3244032*a^5*b^7*c^7*d^6 + 3784704*a^6*b^6*c^6*d^7 - 3244032*a^7*b^5*c^5*d^8 + 2027520*a^8*b^4*c^4*d^9 - 901120*a^9*b^3*c^3*d^10 + 270336*a^10*b^2*c^2*d^11 - 49152*a^11*b*c*d^12))^(3/4)*((x^(1/2)*(102400*a^2*b^19*c^17*d^4 - 1069056*a^3*b^18*c^16*d^5 + 5001216*a^4*b^17*c^15*d^6 - 13799424*a^5*b^16*c^14*d^7 + 24858624*a^6*b^15*c^13*d^8 - 30412800*a^7*b^14*c^12*d^9 + 24645632*a^8*b^13*c^11*d^10 - 9326592*a^9*b^12*c^10*d^11 - 9326592*a^10*b^11*c^9*d^12 + 24645632*a^11*b^10*c^8*d^13 - 30412800*a^12*b^9*c^7*d^14 + 24858624*a^13*b^8*c^6*d^15 - 13799424*a^14*b^7*c^5*d^16 + 5001216*a^15*b^6*c^4*d^17 - 1069056*a^16*b^5*c^3*d^18 + 102400*a^17*b^4*c^2*d^19)*1i)/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)) - ((-(81*b^4*c^5 + 625*a^4*c*d^4 + 1500*a^3*b*c^2*d^3 + 1350*a^2*b^2*c^3*d^2 + 540*a*b^3*c^4*d)/(4096*a^12*d^13 + 4096*b^12*c^12*d - 49152*a*b^11*c^11*d^2 + 270336*a^2*b^10*c^10*d^3 - 901120*a^3*b^9*c^9*d^4 + 2027520*a^4*b^8*c^8*d^5 - 3244032*a^5*b^7*c^7*d^6 + 3784704*a^6*b^6*c^6*d^7 - 3244032*a^7*b^5*c^5*d^8 + 2027520*a^8*b^4*c^4*d^9 - 901120*a^9*b^3*c^3*d^10 + 270336*a^10*b^2*c^2*d^11 - 49152*a^11*b*c*d^12))^(1/4)*(10240*a^2*b^17*c^15*d^4 - 112640*a^3*b^16*c^14*d^5 + 552960*a^4*b^15*c^13*d^6 - 1576960*a^5*b^14*c^12*d^7 + 2816000*a^6*b^13*c^11*d^8 - 3041280*a^7*b^12*c^10*d^9 + 1351680*a^8*b^11*c^9*d^10 + 1351680*a^9*b^10*c^8*d^11 - 3041280*a^10*b^9*c^7*d^12 + 2816000*a^11*b^8*c^6*d^13 - 1576960*a^12*b^7*c^5*d^14 + 552960*a^13*b^6*c^4*d^15 - 112640*a^14*b^5*c^3*d^16 + 10240*a^15*b^4*c^2*d^17))/(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))*1i)*1i + (x^(1/2)*(2025*a^2*b^11*c^10*d^3 + 15930*a^3*b^10*c^9*d^4 + 56304*a^4*b^9*c^8*d^5 + 115110*a^5*b^8*c^7*d^6 + 145550*a^6*b^7*c^6*d^7 + 115110*a^7*b^6*c^5*d^8 + 56304*a^8*b^5*c^4*d^9 + 15930*a^9*b^4*c^3*d^10 + 2025*a^10*b^3*c^2*d^11)*1i)/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)))))*(-(81*b^4*c^5 + 625*a^4*c*d^4 + 1500*a^3*b*c^2*d^3 + 1350*a^2*b^2*c^3*d^2 + 540*a*b^3*c^4*d)/(4096*a^12*d^13 + 4096*b^12*c^12*d - 49152*a*b^11*c^11*d^2 + 270336*a^2*b^10*c^10*d^3 - 901120*a^3*b^9*c^9*d^4 + 2027520*a^4*b^8*c^8*d^5 - 3244032*a^5*b^7*c^7*d^6 + 3784704*a^6*b^6*c^6*d^7 - 3244032*a^7*b^5*c^5*d^8 + 2027520*a^8*b^4*c^4*d^9 - 901120*a^9*b^3*c^3*d^10 + 270336*a^10*b^2*c^2*d^11 - 49152*a^11*b*c*d^12))^(1/4) + ((x^(5/2)*(a*d + b*c))/(2*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) + (a*c*x^(1/2))/(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/(a*c + x^2*(a*d + b*c) + b*d*x^4) + atan(((-(81*a^5*d^4 + 625*a*b^4*c^4 + 1500*a^2*b^3*c^3*d + 1350*a^3*b^2*c^2*d^2 + 540*a^4*b*c*d^3)/(4096*b^13*c^12 + 4096*a^12*b*d^12 - 49152*a^11*b^2*c*d^11 + 270336*a^2*b^11*c^10*d^2 - 901120*a^3*b^10*c^9*d^3 + 2027520*a^4*b^9*c^8*d^4 - 3244032*a^5*b^8*c^7*d^5 + 3784704*a^6*b^7*c^6*d^6 - 3244032*a^7*b^6*c^5*d^7 + 2027520*a^8*b^5*c^4*d^8 - 901120*a^9*b^4*c^3*d^9 + 270336*a^10*b^3*c^2*d^10 - 49152*a*b^12*c^11*d))^(1/4)*((-(81*a^5*d^4 + 625*a*b^4*c^4 + 1500*a^2*b^3*c^3*d + 1350*a^3*b^2*c^2*d^2 + 540*a^4*b*c*d^3)/(4096*b^13*c^12 + 4096*a^12*b*d^12 - 49152*a^11*b^2*c*d^11 + 270336*a^2*b^11*c^10*d^2 - 901120*a^3*b^10*c^9*d^3 + 2027520*a^4*b^9*c^8*d^4 - 3244032*a^5*b^8*c^7*d^5 + 3784704*a^6*b^7*c^6*d^6 - 3244032*a^7*b^6*c^5*d^7 + 2027520*a^8*b^5*c^4*d^8 - 901120*a^9*b^4*c^3*d^9 + 270336*a^10*b^3*c^2*d^10 - 49152*a*b^12*c^11*d))^(1/4)*(((405*a^2*b^9*c^8*d^3)/2 + 1674*a^3*b^8*c^7*d^4 + (9843*a^4*b^7*c^6*d^5)/2 + 6884*a^5*b^6*c^5*d^6 + (9843*a^6*b^5*c^4*d^7)/2 + 1674*a^7*b^4*c^3*d^8 + (405*a^8*b^3*c^2*d^9)/2)/(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) + (-(81*a^5*d^4 + 625*a*b^4*c^4 + 1500*a^2*b^3*c^3*d + 1350*a^3*b^2*c^2*d^2 + 540*a^4*b*c*d^3)/(4096*b^13*c^12 + 4096*a^12*b*d^12 - 49152*a^11*b^2*c*d^11 + 270336*a^2*b^11*c^10*d^2 - 901120*a^3*b^10*c^9*d^3 + 2027520*a^4*b^9*c^8*d^4 - 3244032*a^5*b^8*c^7*d^5 + 3784704*a^6*b^7*c^6*d^6 - 3244032*a^7*b^6*c^5*d^7 + 2027520*a^8*b^5*c^4*d^8 - 901120*a^9*b^4*c^3*d^9 + 270336*a^10*b^3*c^2*d^10 - 49152*a*b^12*c^11*d))^(3/4)*((x^(1/2)*(102400*a^2*b^19*c^17*d^4 - 1069056*a^3*b^18*c^16*d^5 + 5001216*a^4*b^17*c^15*d^6 - 13799424*a^5*b^16*c^14*d^7 + 24858624*a^6*b^15*c^13*d^8 - 30412800*a^7*b^14*c^12*d^9 + 24645632*a^8*b^13*c^11*d^10 - 9326592*a^9*b^12*c^10*d^11 - 9326592*a^10*b^11*c^9*d^12 + 24645632*a^11*b^10*c^8*d^13 - 30412800*a^12*b^9*c^7*d^14 + 24858624*a^13*b^8*c^6*d^15 - 13799424*a^14*b^7*c^5*d^16 + 5001216*a^15*b^6*c^4*d^17 - 1069056*a^16*b^5*c^3*d^18 + 102400*a^17*b^4*c^2*d^19))/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)) + ((-(81*a^5*d^4 + 625*a*b^4*c^4 + 1500*a^2*b^3*c^3*d + 1350*a^3*b^2*c^2*d^2 + 540*a^4*b*c*d^3)/(4096*b^13*c^12 + 4096*a^12*b*d^12 - 49152*a^11*b^2*c*d^11 + 270336*a^2*b^11*c^10*d^2 - 901120*a^3*b^10*c^9*d^3 + 2027520*a^4*b^9*c^8*d^4 - 3244032*a^5*b^8*c^7*d^5 + 3784704*a^6*b^7*c^6*d^6 - 3244032*a^7*b^6*c^5*d^7 + 2027520*a^8*b^5*c^4*d^8 - 901120*a^9*b^4*c^3*d^9 + 270336*a^10*b^3*c^2*d^10 - 49152*a*b^12*c^11*d))^(1/4)*(10240*a^2*b^17*c^15*d^4 - 112640*a^3*b^16*c^14*d^5 + 552960*a^4*b^15*c^13*d^6 - 1576960*a^5*b^14*c^12*d^7 + 2816000*a^6*b^13*c^11*d^8 - 3041280*a^7*b^12*c^10*d^9 + 1351680*a^8*b^11*c^9*d^10 + 1351680*a^9*b^10*c^8*d^11 - 3041280*a^10*b^9*c^7*d^12 + 2816000*a^11*b^8*c^6*d^13 - 1576960*a^12*b^7*c^5*d^14 + 552960*a^13*b^6*c^4*d^15 - 112640*a^14*b^5*c^3*d^16 + 10240*a^15*b^4*c^2*d^17))/(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)))*1i + (x^(1/2)*(2025*a^2*b^11*c^10*d^3 + 15930*a^3*b^10*c^9*d^4 + 56304*a^4*b^9*c^8*d^5 + 115110*a^5*b^8*c^7*d^6 + 145550*a^6*b^7*c^6*d^7 + 115110*a^7*b^6*c^5*d^8 + 56304*a^8*b^5*c^4*d^9 + 15930*a^9*b^4*c^3*d^10 + 2025*a^10*b^3*c^2*d^11)*1i)/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11))) - (-(81*a^5*d^4 + 625*a*b^4*c^4 + 1500*a^2*b^3*c^3*d + 1350*a^3*b^2*c^2*d^2 + 540*a^4*b*c*d^3)/(4096*b^13*c^12 + 4096*a^12*b*d^12 - 49152*a^11*b^2*c*d^11 + 270336*a^2*b^11*c^10*d^2 - 901120*a^3*b^10*c^9*d^3 + 2027520*a^4*b^9*c^8*d^4 - 3244032*a^5*b^8*c^7*d^5 + 3784704*a^6*b^7*c^6*d^6 - 3244032*a^7*b^6*c^5*d^7 + 2027520*a^8*b^5*c^4*d^8 - 901120*a^9*b^4*c^3*d^9 + 270336*a^10*b^3*c^2*d^10 - 49152*a*b^12*c^11*d))^(1/4)*((-(81*a^5*d^4 + 625*a*b^4*c^4 + 1500*a^2*b^3*c^3*d + 1350*a^3*b^2*c^2*d^2 + 540*a^4*b*c*d^3)/(4096*b^13*c^12 + 4096*a^12*b*d^12 - 49152*a^11*b^2*c*d^11 + 270336*a^2*b^11*c^10*d^2 - 901120*a^3*b^10*c^9*d^3 + 2027520*a^4*b^9*c^8*d^4 - 3244032*a^5*b^8*c^7*d^5 + 3784704*a^6*b^7*c^6*d^6 - 3244032*a^7*b^6*c^5*d^7 + 2027520*a^8*b^5*c^4*d^8 - 901120*a^9*b^4*c^3*d^9 + 270336*a^10*b^3*c^2*d^10 - 49152*a*b^12*c^11*d))^(1/4)*(((405*a^2*b^9*c^8*d^3)/2 + 1674*a^3*b^8*c^7*d^4 + (9843*a^4*b^7*c^6*d^5)/2 + 6884*a^5*b^6*c^5*d^6 + (9843*a^6*b^5*c^4*d^7)/2 + 1674*a^7*b^4*c^3*d^8 + (405*a^8*b^3*c^2*d^9)/2)/(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) - (-(81*a^5*d^4 + 625*a*b^4*c^4 + 1500*a^2*b^3*c^3*d + 1350*a^3*b^2*c^2*d^2 + 540*a^4*b*c*d^3)/(4096*b^13*c^12 + 4096*a^12*b*d^12 - 49152*a^11*b^2*c*d^11 + 270336*a^2*b^11*c^10*d^2 - 901120*a^3*b^10*c^9*d^3 + 2027520*a^4*b^9*c^8*d^4 - 3244032*a^5*b^8*c^7*d^5 + 3784704*a^6*b^7*c^6*d^6 - 3244032*a^7*b^6*c^5*d^7 + 2027520*a^8*b^5*c^4*d^8 - 901120*a^9*b^4*c^3*d^9 + 270336*a^10*b^3*c^2*d^10 - 49152*a*b^12*c^11*d))^(3/4)*((x^(1/2)*(102400*a^2*b^19*c^17*d^4 - 1069056*a^3*b^18*c^16*d^5 + 5001216*a^4*b^17*c^15*d^6 - 13799424*a^5*b^16*c^14*d^7 + 24858624*a^6*b^15*c^13*d^8 - 30412800*a^7*b^14*c^12*d^9 + 24645632*a^8*b^13*c^11*d^10 - 9326592*a^9*b^12*c^10*d^11 - 9326592*a^10*b^11*c^9*d^12 + 24645632*a^11*b^10*c^8*d^13 - 30412800*a^12*b^9*c^7*d^14 + 24858624*a^13*b^8*c^6*d^15 - 13799424*a^14*b^7*c^5*d^16 + 5001216*a^15*b^6*c^4*d^17 - 1069056*a^16*b^5*c^3*d^18 + 102400*a^17*b^4*c^2*d^19))/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)) - ((-(81*a^5*d^4 + 625*a*b^4*c^4 + 1500*a^2*b^3*c^3*d + 1350*a^3*b^2*c^2*d^2 + 540*a^4*b*c*d^3)/(4096*b^13*c^12 + 4096*a^12*b*d^12 - 49152*a^11*b^2*c*d^11 + 270336*a^2*b^11*c^10*d^2 - 901120*a^3*b^10*c^9*d^3 + 2027520*a^4*b^9*c^8*d^4 - 3244032*a^5*b^8*c^7*d^5 + 3784704*a^6*b^7*c^6*d^6 - 3244032*a^7*b^6*c^5*d^7 + 2027520*a^8*b^5*c^4*d^8 - 901120*a^9*b^4*c^3*d^9 + 270336*a^10*b^3*c^2*d^10 - 49152*a*b^12*c^11*d))^(1/4)*(10240*a^2*b^17*c^15*d^4 - 112640*a^3*b^16*c^14*d^5 + 552960*a^4*b^15*c^13*d^6 - 1576960*a^5*b^14*c^12*d^7 + 2816000*a^6*b^13*c^11*d^8 - 3041280*a^7*b^12*c^10*d^9 + 1351680*a^8*b^11*c^9*d^10 + 1351680*a^9*b^10*c^8*d^11 - 3041280*a^10*b^9*c^7*d^12 + 2816000*a^11*b^8*c^6*d^13 - 1576960*a^12*b^7*c^5*d^14 + 552960*a^13*b^6*c^4*d^15 - 112640*a^14*b^5*c^3*d^16 + 10240*a^15*b^4*c^2*d^17))/(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)))*1i - (x^(1/2)*(2025*a^2*b^11*c^10*d^3 + 15930*a^3*b^10*c^9*d^4 + 56304*a^4*b^9*c^8*d^5 + 115110*a^5*b^8*c^7*d^6 + 145550*a^6*b^7*c^6*d^7 + 115110*a^7*b^6*c^5*d^8 + 56304*a^8*b^5*c^4*d^9 + 15930*a^9*b^4*c^3*d^10 + 2025*a^10*b^3*c^2*d^11)*1i)/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11))))/((-(81*a^5*d^4 + 625*a*b^4*c^4 + 1500*a^2*b^3*c^3*d + 1350*a^3*b^2*c^2*d^2 + 540*a^4*b*c*d^3)/(4096*b^13*c^12 + 4096*a^12*b*d^12 - 49152*a^11*b^2*c*d^11 + 270336*a^2*b^11*c^10*d^2 - 901120*a^3*b^10*c^9*d^3 + 2027520*a^4*b^9*c^8*d^4 - 3244032*a^5*b^8*c^7*d^5 + 3784704*a^6*b^7*c^6*d^6 - 3244032*a^7*b^6*c^5*d^7 + 2027520*a^8*b^5*c^4*d^8 - 901120*a^9*b^4*c^3*d^9 + 270336*a^10*b^3*c^2*d^10 - 49152*a*b^12*c^11*d))^(1/4)*((-(81*a^5*d^4 + 625*a*b^4*c^4 + 1500*a^2*b^3*c^3*d + 1350*a^3*b^2*c^2*d^2 + 540*a^4*b*c*d^3)/(4096*b^13*c^12 + 4096*a^12*b*d^12 - 49152*a^11*b^2*c*d^11 + 270336*a^2*b^11*c^10*d^2 - 901120*a^3*b^10*c^9*d^3 + 2027520*a^4*b^9*c^8*d^4 - 3244032*a^5*b^8*c^7*d^5 + 3784704*a^6*b^7*c^6*d^6 - 3244032*a^7*b^6*c^5*d^7 + 2027520*a^8*b^5*c^4*d^8 - 901120*a^9*b^4*c^3*d^9 + 270336*a^10*b^3*c^2*d^10 - 49152*a*b^12*c^11*d))^(1/4)*(((405*a^2*b^9*c^8*d^3)/2 + 1674*a^3*b^8*c^7*d^4 + (9843*a^4*b^7*c^6*d^5)/2 + 6884*a^5*b^6*c^5*d^6 + (9843*a^6*b^5*c^4*d^7)/2 + 1674*a^7*b^4*c^3*d^8 + (405*a^8*b^3*c^2*d^9)/2)/(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) + (-(81*a^5*d^4 + 625*a*b^4*c^4 + 1500*a^2*b^3*c^3*d + 1350*a^3*b^2*c^2*d^2 + 540*a^4*b*c*d^3)/(4096*b^13*c^12 + 4096*a^12*b*d^12 - 49152*a^11*b^2*c*d^11 + 270336*a^2*b^11*c^10*d^2 - 901120*a^3*b^10*c^9*d^3 + 2027520*a^4*b^9*c^8*d^4 - 3244032*a^5*b^8*c^7*d^5 + 3784704*a^6*b^7*c^6*d^6 - 3244032*a^7*b^6*c^5*d^7 + 2027520*a^8*b^5*c^4*d^8 - 901120*a^9*b^4*c^3*d^9 + 270336*a^10*b^3*c^2*d^10 - 49152*a*b^12*c^11*d))^(3/4)*((x^(1/2)*(102400*a^2*b^19*c^17*d^4 - 1069056*a^3*b^18*c^16*d^5 + 5001216*a^4*b^17*c^15*d^6 - 13799424*a^5*b^16*c^14*d^7 + 24858624*a^6*b^15*c^13*d^8 - 30412800*a^7*b^14*c^12*d^9 + 24645632*a^8*b^13*c^11*d^10 - 9326592*a^9*b^12*c^10*d^11 - 9326592*a^10*b^11*c^9*d^12 + 24645632*a^11*b^10*c^8*d^13 - 30412800*a^12*b^9*c^7*d^14 + 24858624*a^13*b^8*c^6*d^15 - 13799424*a^14*b^7*c^5*d^16 + 5001216*a^15*b^6*c^4*d^17 - 1069056*a^16*b^5*c^3*d^18 + 102400*a^17*b^4*c^2*d^19))/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)) + ((-(81*a^5*d^4 + 625*a*b^4*c^4 + 1500*a^2*b^3*c^3*d + 1350*a^3*b^2*c^2*d^2 + 540*a^4*b*c*d^3)/(4096*b^13*c^12 + 4096*a^12*b*d^12 - 49152*a^11*b^2*c*d^11 + 270336*a^2*b^11*c^10*d^2 - 901120*a^3*b^10*c^9*d^3 + 2027520*a^4*b^9*c^8*d^4 - 3244032*a^5*b^8*c^7*d^5 + 3784704*a^6*b^7*c^6*d^6 - 3244032*a^7*b^6*c^5*d^7 + 2027520*a^8*b^5*c^4*d^8 - 901120*a^9*b^4*c^3*d^9 + 270336*a^10*b^3*c^2*d^10 - 49152*a*b^12*c^11*d))^(1/4)*(10240*a^2*b^17*c^15*d^4 - 112640*a^3*b^16*c^14*d^5 + 552960*a^4*b^15*c^13*d^6 - 1576960*a^5*b^14*c^12*d^7 + 2816000*a^6*b^13*c^11*d^8 - 3041280*a^7*b^12*c^10*d^9 + 1351680*a^8*b^11*c^9*d^10 + 1351680*a^9*b^10*c^8*d^11 - 3041280*a^10*b^9*c^7*d^12 + 2816000*a^11*b^8*c^6*d^13 - 1576960*a^12*b^7*c^5*d^14 + 552960*a^13*b^6*c^4*d^15 - 112640*a^14*b^5*c^3*d^16 + 10240*a^15*b^4*c^2*d^17))/(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))) + (x^(1/2)*(2025*a^2*b^11*c^10*d^3 + 15930*a^3*b^10*c^9*d^4 + 56304*a^4*b^9*c^8*d^5 + 115110*a^5*b^8*c^7*d^6 + 145550*a^6*b^7*c^6*d^7 + 115110*a^7*b^6*c^5*d^8 + 56304*a^8*b^5*c^4*d^9 + 15930*a^9*b^4*c^3*d^10 + 2025*a^10*b^3*c^2*d^11))/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11))) + (-(81*a^5*d^4 + 625*a*b^4*c^4 + 1500*a^2*b^3*c^3*d + 1350*a^3*b^2*c^2*d^2 + 540*a^4*b*c*d^3)/(4096*b^13*c^12 + 4096*a^12*b*d^12 - 49152*a^11*b^2*c*d^11 + 270336*a^2*b^11*c^10*d^2 - 901120*a^3*b^10*c^9*d^3 + 2027520*a^4*b^9*c^8*d^4 - 3244032*a^5*b^8*c^7*d^5 + 3784704*a^6*b^7*c^6*d^6 - 3244032*a^7*b^6*c^5*d^7 + 2027520*a^8*b^5*c^4*d^8 - 901120*a^9*b^4*c^3*d^9 + 270336*a^10*b^3*c^2*d^10 - 49152*a*b^12*c^11*d))^(1/4)*((-(81*a^5*d^4 + 625*a*b^4*c^4 + 1500*a^2*b^3*c^3*d + 1350*a^3*b^2*c^2*d^2 + 540*a^4*b*c*d^3)/(4096*b^13*c^12 + 4096*a^12*b*d^12 - 49152*a^11*b^2*c*d^11 + 270336*a^2*b^11*c^10*d^2 - 901120*a^3*b^10*c^9*d^3 + 2027520*a^4*b^9*c^8*d^4 - 3244032*a^5*b^8*c^7*d^5 + 3784704*a^6*b^7*c^6*d^6 - 3244032*a^7*b^6*c^5*d^7 + 2027520*a^8*b^5*c^4*d^8 - 901120*a^9*b^4*c^3*d^9 + 270336*a^10*b^3*c^2*d^10 - 49152*a*b^12*c^11*d))^(1/4)*(((405*a^2*b^9*c^8*d^3)/2 + 1674*a^3*b^8*c^7*d^4 + (9843*a^4*b^7*c^6*d^5)/2 + 6884*a^5*b^6*c^5*d^6 + (9843*a^6*b^5*c^4*d^7)/2 + 1674*a^7*b^4*c^3*d^8 + (405*a^8*b^3*c^2*d^9)/2)/(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) - (-(81*a^5*d^4 + 625*a*b^4*c^4 + 1500*a^2*b^3*c^3*d + 1350*a^3*b^2*c^2*d^2 + 540*a^4*b*c*d^3)/(4096*b^13*c^12 + 4096*a^12*b*d^12 - 49152*a^11*b^2*c*d^11 + 270336*a^2*b^11*c^10*d^2 - 901120*a^3*b^10*c^9*d^3 + 2027520*a^4*b^9*c^8*d^4 - 3244032*a^5*b^8*c^7*d^5 + 3784704*a^6*b^7*c^6*d^6 - 3244032*a^7*b^6*c^5*d^7 + 2027520*a^8*b^5*c^4*d^8 - 901120*a^9*b^4*c^3*d^9 + 270336*a^10*b^3*c^2*d^10 - 49152*a*b^12*c^11*d))^(3/4)*((x^(1/2)*(102400*a^2*b^19*c^17*d^4 - 1069056*a^3*b^18*c^16*d^5 + 5001216*a^4*b^17*c^15*d^6 - 13799424*a^5*b^16*c^14*d^7 + 24858624*a^6*b^15*c^13*d^8 - 30412800*a^7*b^14*c^12*d^9 + 24645632*a^8*b^13*c^11*d^10 - 9326592*a^9*b^12*c^10*d^11 - 9326592*a^10*b^11*c^9*d^12 + 24645632*a^11*b^10*c^8*d^13 - 30412800*a^12*b^9*c^7*d^14 + 24858624*a^13*b^8*c^6*d^15 - 13799424*a^14*b^7*c^5*d^16 + 5001216*a^15*b^6*c^4*d^17 - 1069056*a^16*b^5*c^3*d^18 + 102400*a^17*b^4*c^2*d^19))/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)) - ((-(81*a^5*d^4 + 625*a*b^4*c^4 + 1500*a^2*b^3*c^3*d + 1350*a^3*b^2*c^2*d^2 + 540*a^4*b*c*d^3)/(4096*b^13*c^12 + 4096*a^12*b*d^12 - 49152*a^11*b^2*c*d^11 + 270336*a^2*b^11*c^10*d^2 - 901120*a^3*b^10*c^9*d^3 + 2027520*a^4*b^9*c^8*d^4 - 3244032*a^5*b^8*c^7*d^5 + 3784704*a^6*b^7*c^6*d^6 - 3244032*a^7*b^6*c^5*d^7 + 2027520*a^8*b^5*c^4*d^8 - 901120*a^9*b^4*c^3*d^9 + 270336*a^10*b^3*c^2*d^10 - 49152*a*b^12*c^11*d))^(1/4)*(10240*a^2*b^17*c^15*d^4 - 112640*a^3*b^16*c^14*d^5 + 552960*a^4*b^15*c^13*d^6 - 1576960*a^5*b^14*c^12*d^7 + 2816000*a^6*b^13*c^11*d^8 - 3041280*a^7*b^12*c^10*d^9 + 1351680*a^8*b^11*c^9*d^10 + 1351680*a^9*b^10*c^8*d^11 - 3041280*a^10*b^9*c^7*d^12 + 2816000*a^11*b^8*c^6*d^13 - 1576960*a^12*b^7*c^5*d^14 + 552960*a^13*b^6*c^4*d^15 - 112640*a^14*b^5*c^3*d^16 + 10240*a^15*b^4*c^2*d^17))/(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))) - (x^(1/2)*(2025*a^2*b^11*c^10*d^3 + 15930*a^3*b^10*c^9*d^4 + 56304*a^4*b^9*c^8*d^5 + 115110*a^5*b^8*c^7*d^6 + 145550*a^6*b^7*c^6*d^7 + 115110*a^7*b^6*c^5*d^8 + 56304*a^8*b^5*c^4*d^9 + 15930*a^9*b^4*c^3*d^10 + 2025*a^10*b^3*c^2*d^11))/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)))))*(-(81*a^5*d^4 + 625*a*b^4*c^4 + 1500*a^2*b^3*c^3*d + 1350*a^3*b^2*c^2*d^2 + 540*a^4*b*c*d^3)/(4096*b^13*c^12 + 4096*a^12*b*d^12 - 49152*a^11*b^2*c*d^11 + 270336*a^2*b^11*c^10*d^2 - 901120*a^3*b^10*c^9*d^3 + 2027520*a^4*b^9*c^8*d^4 - 3244032*a^5*b^8*c^7*d^5 + 3784704*a^6*b^7*c^6*d^6 - 3244032*a^7*b^6*c^5*d^7 + 2027520*a^8*b^5*c^4*d^8 - 901120*a^9*b^4*c^3*d^9 + 270336*a^10*b^3*c^2*d^10 - 49152*a*b^12*c^11*d))^(1/4)*2i - 2*atan(((-(81*a^5*d^4 + 625*a*b^4*c^4 + 1500*a^2*b^3*c^3*d + 1350*a^3*b^2*c^2*d^2 + 540*a^4*b*c*d^3)/(4096*b^13*c^12 + 4096*a^12*b*d^12 - 49152*a^11*b^2*c*d^11 + 270336*a^2*b^11*c^10*d^2 - 901120*a^3*b^10*c^9*d^3 + 2027520*a^4*b^9*c^8*d^4 - 3244032*a^5*b^8*c^7*d^5 + 3784704*a^6*b^7*c^6*d^6 - 3244032*a^7*b^6*c^5*d^7 + 2027520*a^8*b^5*c^4*d^8 - 901120*a^9*b^4*c^3*d^9 + 270336*a^10*b^3*c^2*d^10 - 49152*a*b^12*c^11*d))^(1/4)*((-(81*a^5*d^4 + 625*a*b^4*c^4 + 1500*a^2*b^3*c^3*d + 1350*a^3*b^2*c^2*d^2 + 540*a^4*b*c*d^3)/(4096*b^13*c^12 + 4096*a^12*b*d^12 - 49152*a^11*b^2*c*d^11 + 270336*a^2*b^11*c^10*d^2 - 901120*a^3*b^10*c^9*d^3 + 2027520*a^4*b^9*c^8*d^4 - 3244032*a^5*b^8*c^7*d^5 + 3784704*a^6*b^7*c^6*d^6 - 3244032*a^7*b^6*c^5*d^7 + 2027520*a^8*b^5*c^4*d^8 - 901120*a^9*b^4*c^3*d^9 + 270336*a^10*b^3*c^2*d^10 - 49152*a*b^12*c^11*d))^(1/4)*((((405*a^2*b^9*c^8*d^3)/2 + 1674*a^3*b^8*c^7*d^4 + (9843*a^4*b^7*c^6*d^5)/2 + 6884*a^5*b^6*c^5*d^6 + (9843*a^6*b^5*c^4*d^7)/2 + 1674*a^7*b^4*c^3*d^8 + (405*a^8*b^3*c^2*d^9)/2)*1i)/(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) + (-(81*a^5*d^4 + 625*a*b^4*c^4 + 1500*a^2*b^3*c^3*d + 1350*a^3*b^2*c^2*d^2 + 540*a^4*b*c*d^3)/(4096*b^13*c^12 + 4096*a^12*b*d^12 - 49152*a^11*b^2*c*d^11 + 270336*a^2*b^11*c^10*d^2 - 901120*a^3*b^10*c^9*d^3 + 2027520*a^4*b^9*c^8*d^4 - 3244032*a^5*b^8*c^7*d^5 + 3784704*a^6*b^7*c^6*d^6 - 3244032*a^7*b^6*c^5*d^7 + 2027520*a^8*b^5*c^4*d^8 - 901120*a^9*b^4*c^3*d^9 + 270336*a^10*b^3*c^2*d^10 - 49152*a*b^12*c^11*d))^(3/4)*((x^(1/2)*(102400*a^2*b^19*c^17*d^4 - 1069056*a^3*b^18*c^16*d^5 + 5001216*a^4*b^17*c^15*d^6 - 13799424*a^5*b^16*c^14*d^7 + 24858624*a^6*b^15*c^13*d^8 - 30412800*a^7*b^14*c^12*d^9 + 24645632*a^8*b^13*c^11*d^10 - 9326592*a^9*b^12*c^10*d^11 - 9326592*a^10*b^11*c^9*d^12 + 24645632*a^11*b^10*c^8*d^13 - 30412800*a^12*b^9*c^7*d^14 + 24858624*a^13*b^8*c^6*d^15 - 13799424*a^14*b^7*c^5*d^16 + 5001216*a^15*b^6*c^4*d^17 - 1069056*a^16*b^5*c^3*d^18 + 102400*a^17*b^4*c^2*d^19)*1i)/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)) + ((-(81*a^5*d^4 + 625*a*b^4*c^4 + 1500*a^2*b^3*c^3*d + 1350*a^3*b^2*c^2*d^2 + 540*a^4*b*c*d^3)/(4096*b^13*c^12 + 4096*a^12*b*d^12 - 49152*a^11*b^2*c*d^11 + 270336*a^2*b^11*c^10*d^2 - 901120*a^3*b^10*c^9*d^3 + 2027520*a^4*b^9*c^8*d^4 - 3244032*a^5*b^8*c^7*d^5 + 3784704*a^6*b^7*c^6*d^6 - 3244032*a^7*b^6*c^5*d^7 + 2027520*a^8*b^5*c^4*d^8 - 901120*a^9*b^4*c^3*d^9 + 270336*a^10*b^3*c^2*d^10 - 49152*a*b^12*c^11*d))^(1/4)*(10240*a^2*b^17*c^15*d^4 - 112640*a^3*b^16*c^14*d^5 + 552960*a^4*b^15*c^13*d^6 - 1576960*a^5*b^14*c^12*d^7 + 2816000*a^6*b^13*c^11*d^8 - 3041280*a^7*b^12*c^10*d^9 + 1351680*a^8*b^11*c^9*d^10 + 1351680*a^9*b^10*c^8*d^11 - 3041280*a^10*b^9*c^7*d^12 + 2816000*a^11*b^8*c^6*d^13 - 1576960*a^12*b^7*c^5*d^14 + 552960*a^13*b^6*c^4*d^15 - 112640*a^14*b^5*c^3*d^16 + 10240*a^15*b^4*c^2*d^17))/(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))*1i) - (x^(1/2)*(2025*a^2*b^11*c^10*d^3 + 15930*a^3*b^10*c^9*d^4 + 56304*a^4*b^9*c^8*d^5 + 115110*a^5*b^8*c^7*d^6 + 145550*a^6*b^7*c^6*d^7 + 115110*a^7*b^6*c^5*d^8 + 56304*a^8*b^5*c^4*d^9 + 15930*a^9*b^4*c^3*d^10 + 2025*a^10*b^3*c^2*d^11))/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11))) - (-(81*a^5*d^4 + 625*a*b^4*c^4 + 1500*a^2*b^3*c^3*d + 1350*a^3*b^2*c^2*d^2 + 540*a^4*b*c*d^3)/(4096*b^13*c^12 + 4096*a^12*b*d^12 - 49152*a^11*b^2*c*d^11 + 270336*a^2*b^11*c^10*d^2 - 901120*a^3*b^10*c^9*d^3 + 2027520*a^4*b^9*c^8*d^4 - 3244032*a^5*b^8*c^7*d^5 + 3784704*a^6*b^7*c^6*d^6 - 3244032*a^7*b^6*c^5*d^7 + 2027520*a^8*b^5*c^4*d^8 - 901120*a^9*b^4*c^3*d^9 + 270336*a^10*b^3*c^2*d^10 - 49152*a*b^12*c^11*d))^(1/4)*((-(81*a^5*d^4 + 625*a*b^4*c^4 + 1500*a^2*b^3*c^3*d + 1350*a^3*b^2*c^2*d^2 + 540*a^4*b*c*d^3)/(4096*b^13*c^12 + 4096*a^12*b*d^12 - 49152*a^11*b^2*c*d^11 + 270336*a^2*b^11*c^10*d^2 - 901120*a^3*b^10*c^9*d^3 + 2027520*a^4*b^9*c^8*d^4 - 3244032*a^5*b^8*c^7*d^5 + 3784704*a^6*b^7*c^6*d^6 - 3244032*a^7*b^6*c^5*d^7 + 2027520*a^8*b^5*c^4*d^8 - 901120*a^9*b^4*c^3*d^9 + 270336*a^10*b^3*c^2*d^10 - 49152*a*b^12*c^11*d))^(1/4)*((((405*a^2*b^9*c^8*d^3)/2 + 1674*a^3*b^8*c^7*d^4 + (9843*a^4*b^7*c^6*d^5)/2 + 6884*a^5*b^6*c^5*d^6 + (9843*a^6*b^5*c^4*d^7)/2 + 1674*a^7*b^4*c^3*d^8 + (405*a^8*b^3*c^2*d^9)/2)*1i)/(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) - (-(81*a^5*d^4 + 625*a*b^4*c^4 + 1500*a^2*b^3*c^3*d + 1350*a^3*b^2*c^2*d^2 + 540*a^4*b*c*d^3)/(4096*b^13*c^12 + 4096*a^12*b*d^12 - 49152*a^11*b^2*c*d^11 + 270336*a^2*b^11*c^10*d^2 - 901120*a^3*b^10*c^9*d^3 + 2027520*a^4*b^9*c^8*d^4 - 3244032*a^5*b^8*c^7*d^5 + 3784704*a^6*b^7*c^6*d^6 - 3244032*a^7*b^6*c^5*d^7 + 2027520*a^8*b^5*c^4*d^8 - 901120*a^9*b^4*c^3*d^9 + 270336*a^10*b^3*c^2*d^10 - 49152*a*b^12*c^11*d))^(3/4)*((x^(1/2)*(102400*a^2*b^19*c^17*d^4 - 1069056*a^3*b^18*c^16*d^5 + 5001216*a^4*b^17*c^15*d^6 - 13799424*a^5*b^16*c^14*d^7 + 24858624*a^6*b^15*c^13*d^8 - 30412800*a^7*b^14*c^12*d^9 + 24645632*a^8*b^13*c^11*d^10 - 9326592*a^9*b^12*c^10*d^11 - 9326592*a^10*b^11*c^9*d^12 + 24645632*a^11*b^10*c^8*d^13 - 30412800*a^12*b^9*c^7*d^14 + 24858624*a^13*b^8*c^6*d^15 - 13799424*a^14*b^7*c^5*d^16 + 5001216*a^15*b^6*c^4*d^17 - 1069056*a^16*b^5*c^3*d^18 + 102400*a^17*b^4*c^2*d^19)*1i)/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)) - ((-(81*a^5*d^4 + 625*a*b^4*c^4 + 1500*a^2*b^3*c^3*d + 1350*a^3*b^2*c^2*d^2 + 540*a^4*b*c*d^3)/(4096*b^13*c^12 + 4096*a^12*b*d^12 - 49152*a^11*b^2*c*d^11 + 270336*a^2*b^11*c^10*d^2 - 901120*a^3*b^10*c^9*d^3 + 2027520*a^4*b^9*c^8*d^4 - 3244032*a^5*b^8*c^7*d^5 + 3784704*a^6*b^7*c^6*d^6 - 3244032*a^7*b^6*c^5*d^7 + 2027520*a^8*b^5*c^4*d^8 - 901120*a^9*b^4*c^3*d^9 + 270336*a^10*b^3*c^2*d^10 - 49152*a*b^12*c^11*d))^(1/4)*(10240*a^2*b^17*c^15*d^4 - 112640*a^3*b^16*c^14*d^5 + 552960*a^4*b^15*c^13*d^6 - 1576960*a^5*b^14*c^12*d^7 + 2816000*a^6*b^13*c^11*d^8 - 3041280*a^7*b^12*c^10*d^9 + 1351680*a^8*b^11*c^9*d^10 + 1351680*a^9*b^10*c^8*d^11 - 3041280*a^10*b^9*c^7*d^12 + 2816000*a^11*b^8*c^6*d^13 - 1576960*a^12*b^7*c^5*d^14 + 552960*a^13*b^6*c^4*d^15 - 112640*a^14*b^5*c^3*d^16 + 10240*a^15*b^4*c^2*d^17))/(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))*1i) + (x^(1/2)*(2025*a^2*b^11*c^10*d^3 + 15930*a^3*b^10*c^9*d^4 + 56304*a^4*b^9*c^8*d^5 + 115110*a^5*b^8*c^7*d^6 + 145550*a^6*b^7*c^6*d^7 + 115110*a^7*b^6*c^5*d^8 + 56304*a^8*b^5*c^4*d^9 + 15930*a^9*b^4*c^3*d^10 + 2025*a^10*b^3*c^2*d^11))/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11))))/((-(81*a^5*d^4 + 625*a*b^4*c^4 + 1500*a^2*b^3*c^3*d + 1350*a^3*b^2*c^2*d^2 + 540*a^4*b*c*d^3)/(4096*b^13*c^12 + 4096*a^12*b*d^12 - 49152*a^11*b^2*c*d^11 + 270336*a^2*b^11*c^10*d^2 - 901120*a^3*b^10*c^9*d^3 + 2027520*a^4*b^9*c^8*d^4 - 3244032*a^5*b^8*c^7*d^5 + 3784704*a^6*b^7*c^6*d^6 - 3244032*a^7*b^6*c^5*d^7 + 2027520*a^8*b^5*c^4*d^8 - 901120*a^9*b^4*c^3*d^9 + 270336*a^10*b^3*c^2*d^10 - 49152*a*b^12*c^11*d))^(1/4)*((-(81*a^5*d^4 + 625*a*b^4*c^4 + 1500*a^2*b^3*c^3*d + 1350*a^3*b^2*c^2*d^2 + 540*a^4*b*c*d^3)/(4096*b^13*c^12 + 4096*a^12*b*d^12 - 49152*a^11*b^2*c*d^11 + 270336*a^2*b^11*c^10*d^2 - 901120*a^3*b^10*c^9*d^3 + 2027520*a^4*b^9*c^8*d^4 - 3244032*a^5*b^8*c^7*d^5 + 3784704*a^6*b^7*c^6*d^6 - 3244032*a^7*b^6*c^5*d^7 + 2027520*a^8*b^5*c^4*d^8 - 901120*a^9*b^4*c^3*d^9 + 270336*a^10*b^3*c^2*d^10 - 49152*a*b^12*c^11*d))^(1/4)*((((405*a^2*b^9*c^8*d^3)/2 + 1674*a^3*b^8*c^7*d^4 + (9843*a^4*b^7*c^6*d^5)/2 + 6884*a^5*b^6*c^5*d^6 + (9843*a^6*b^5*c^4*d^7)/2 + 1674*a^7*b^4*c^3*d^8 + (405*a^8*b^3*c^2*d^9)/2)*1i)/(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) + (-(81*a^5*d^4 + 625*a*b^4*c^4 + 1500*a^2*b^3*c^3*d + 1350*a^3*b^2*c^2*d^2 + 540*a^4*b*c*d^3)/(4096*b^13*c^12 + 4096*a^12*b*d^12 - 49152*a^11*b^2*c*d^11 + 270336*a^2*b^11*c^10*d^2 - 901120*a^3*b^10*c^9*d^3 + 2027520*a^4*b^9*c^8*d^4 - 3244032*a^5*b^8*c^7*d^5 + 3784704*a^6*b^7*c^6*d^6 - 3244032*a^7*b^6*c^5*d^7 + 2027520*a^8*b^5*c^4*d^8 - 901120*a^9*b^4*c^3*d^9 + 270336*a^10*b^3*c^2*d^10 - 49152*a*b^12*c^11*d))^(3/4)*((x^(1/2)*(102400*a^2*b^19*c^17*d^4 - 1069056*a^3*b^18*c^16*d^5 + 5001216*a^4*b^17*c^15*d^6 - 13799424*a^5*b^16*c^14*d^7 + 24858624*a^6*b^15*c^13*d^8 - 30412800*a^7*b^14*c^12*d^9 + 24645632*a^8*b^13*c^11*d^10 - 9326592*a^9*b^12*c^10*d^11 - 9326592*a^10*b^11*c^9*d^12 + 24645632*a^11*b^10*c^8*d^13 - 30412800*a^12*b^9*c^7*d^14 + 24858624*a^13*b^8*c^6*d^15 - 13799424*a^14*b^7*c^5*d^16 + 5001216*a^15*b^6*c^4*d^17 - 1069056*a^16*b^5*c^3*d^18 + 102400*a^17*b^4*c^2*d^19)*1i)/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)) + ((-(81*a^5*d^4 + 625*a*b^4*c^4 + 1500*a^2*b^3*c^3*d + 1350*a^3*b^2*c^2*d^2 + 540*a^4*b*c*d^3)/(4096*b^13*c^12 + 4096*a^12*b*d^12 - 49152*a^11*b^2*c*d^11 + 270336*a^2*b^11*c^10*d^2 - 901120*a^3*b^10*c^9*d^3 + 2027520*a^4*b^9*c^8*d^4 - 3244032*a^5*b^8*c^7*d^5 + 3784704*a^6*b^7*c^6*d^6 - 3244032*a^7*b^6*c^5*d^7 + 2027520*a^8*b^5*c^4*d^8 - 901120*a^9*b^4*c^3*d^9 + 270336*a^10*b^3*c^2*d^10 - 49152*a*b^12*c^11*d))^(1/4)*(10240*a^2*b^17*c^15*d^4 - 112640*a^3*b^16*c^14*d^5 + 552960*a^4*b^15*c^13*d^6 - 1576960*a^5*b^14*c^12*d^7 + 2816000*a^6*b^13*c^11*d^8 - 3041280*a^7*b^12*c^10*d^9 + 1351680*a^8*b^11*c^9*d^10 + 1351680*a^9*b^10*c^8*d^11 - 3041280*a^10*b^9*c^7*d^12 + 2816000*a^11*b^8*c^6*d^13 - 1576960*a^12*b^7*c^5*d^14 + 552960*a^13*b^6*c^4*d^15 - 112640*a^14*b^5*c^3*d^16 + 10240*a^15*b^4*c^2*d^17))/(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))*1i)*1i - (x^(1/2)*(2025*a^2*b^11*c^10*d^3 + 15930*a^3*b^10*c^9*d^4 + 56304*a^4*b^9*c^8*d^5 + 115110*a^5*b^8*c^7*d^6 + 145550*a^6*b^7*c^6*d^7 + 115110*a^7*b^6*c^5*d^8 + 56304*a^8*b^5*c^4*d^9 + 15930*a^9*b^4*c^3*d^10 + 2025*a^10*b^3*c^2*d^11)*1i)/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11))) + (-(81*a^5*d^4 + 625*a*b^4*c^4 + 1500*a^2*b^3*c^3*d + 1350*a^3*b^2*c^2*d^2 + 540*a^4*b*c*d^3)/(4096*b^13*c^12 + 4096*a^12*b*d^12 - 49152*a^11*b^2*c*d^11 + 270336*a^2*b^11*c^10*d^2 - 901120*a^3*b^10*c^9*d^3 + 2027520*a^4*b^9*c^8*d^4 - 3244032*a^5*b^8*c^7*d^5 + 3784704*a^6*b^7*c^6*d^6 - 3244032*a^7*b^6*c^5*d^7 + 2027520*a^8*b^5*c^4*d^8 - 901120*a^9*b^4*c^3*d^9 + 270336*a^10*b^3*c^2*d^10 - 49152*a*b^12*c^11*d))^(1/4)*((-(81*a^5*d^4 + 625*a*b^4*c^4 + 1500*a^2*b^3*c^3*d + 1350*a^3*b^2*c^2*d^2 + 540*a^4*b*c*d^3)/(4096*b^13*c^12 + 4096*a^12*b*d^12 - 49152*a^11*b^2*c*d^11 + 270336*a^2*b^11*c^10*d^2 - 901120*a^3*b^10*c^9*d^3 + 2027520*a^4*b^9*c^8*d^4 - 3244032*a^5*b^8*c^7*d^5 + 3784704*a^6*b^7*c^6*d^6 - 3244032*a^7*b^6*c^5*d^7 + 2027520*a^8*b^5*c^4*d^8 - 901120*a^9*b^4*c^3*d^9 + 270336*a^10*b^3*c^2*d^10 - 49152*a*b^12*c^11*d))^(1/4)*((((405*a^2*b^9*c^8*d^3)/2 + 1674*a^3*b^8*c^7*d^4 + (9843*a^4*b^7*c^6*d^5)/2 + 6884*a^5*b^6*c^5*d^6 + (9843*a^6*b^5*c^4*d^7)/2 + 1674*a^7*b^4*c^3*d^8 + (405*a^8*b^3*c^2*d^9)/2)*1i)/(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) - (-(81*a^5*d^4 + 625*a*b^4*c^4 + 1500*a^2*b^3*c^3*d + 1350*a^3*b^2*c^2*d^2 + 540*a^4*b*c*d^3)/(4096*b^13*c^12 + 4096*a^12*b*d^12 - 49152*a^11*b^2*c*d^11 + 270336*a^2*b^11*c^10*d^2 - 901120*a^3*b^10*c^9*d^3 + 2027520*a^4*b^9*c^8*d^4 - 3244032*a^5*b^8*c^7*d^5 + 3784704*a^6*b^7*c^6*d^6 - 3244032*a^7*b^6*c^5*d^7 + 2027520*a^8*b^5*c^4*d^8 - 901120*a^9*b^4*c^3*d^9 + 270336*a^10*b^3*c^2*d^10 - 49152*a*b^12*c^11*d))^(3/4)*((x^(1/2)*(102400*a^2*b^19*c^17*d^4 - 1069056*a^3*b^18*c^16*d^5 + 5001216*a^4*b^17*c^15*d^6 - 13799424*a^5*b^16*c^14*d^7 + 24858624*a^6*b^15*c^13*d^8 - 30412800*a^7*b^14*c^12*d^9 + 24645632*a^8*b^13*c^11*d^10 - 9326592*a^9*b^12*c^10*d^11 - 9326592*a^10*b^11*c^9*d^12 + 24645632*a^11*b^10*c^8*d^13 - 30412800*a^12*b^9*c^7*d^14 + 24858624*a^13*b^8*c^6*d^15 - 13799424*a^14*b^7*c^5*d^16 + 5001216*a^15*b^6*c^4*d^17 - 1069056*a^16*b^5*c^3*d^18 + 102400*a^17*b^4*c^2*d^19)*1i)/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)) - ((-(81*a^5*d^4 + 625*a*b^4*c^4 + 1500*a^2*b^3*c^3*d + 1350*a^3*b^2*c^2*d^2 + 540*a^4*b*c*d^3)/(4096*b^13*c^12 + 4096*a^12*b*d^12 - 49152*a^11*b^2*c*d^11 + 270336*a^2*b^11*c^10*d^2 - 901120*a^3*b^10*c^9*d^3 + 2027520*a^4*b^9*c^8*d^4 - 3244032*a^5*b^8*c^7*d^5 + 3784704*a^6*b^7*c^6*d^6 - 3244032*a^7*b^6*c^5*d^7 + 2027520*a^8*b^5*c^4*d^8 - 901120*a^9*b^4*c^3*d^9 + 270336*a^10*b^3*c^2*d^10 - 49152*a*b^12*c^11*d))^(1/4)*(10240*a^2*b^17*c^15*d^4 - 112640*a^3*b^16*c^14*d^5 + 552960*a^4*b^15*c^13*d^6 - 1576960*a^5*b^14*c^12*d^7 + 2816000*a^6*b^13*c^11*d^8 - 3041280*a^7*b^12*c^10*d^9 + 1351680*a^8*b^11*c^9*d^10 + 1351680*a^9*b^10*c^8*d^11 - 3041280*a^10*b^9*c^7*d^12 + 2816000*a^11*b^8*c^6*d^13 - 1576960*a^12*b^7*c^5*d^14 + 552960*a^13*b^6*c^4*d^15 - 112640*a^14*b^5*c^3*d^16 + 10240*a^15*b^4*c^2*d^17))/(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))*1i)*1i + (x^(1/2)*(2025*a^2*b^11*c^10*d^3 + 15930*a^3*b^10*c^9*d^4 + 56304*a^4*b^9*c^8*d^5 + 115110*a^5*b^8*c^7*d^6 + 145550*a^6*b^7*c^6*d^7 + 115110*a^7*b^6*c^5*d^8 + 56304*a^8*b^5*c^4*d^9 + 15930*a^9*b^4*c^3*d^10 + 2025*a^10*b^3*c^2*d^11)*1i)/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)))))*(-(81*a^5*d^4 + 625*a*b^4*c^4 + 1500*a^2*b^3*c^3*d + 1350*a^3*b^2*c^2*d^2 + 540*a^4*b*c*d^3)/(4096*b^13*c^12 + 4096*a^12*b*d^12 - 49152*a^11*b^2*c*d^11 + 270336*a^2*b^11*c^10*d^2 - 901120*a^3*b^10*c^9*d^3 + 2027520*a^4*b^9*c^8*d^4 - 3244032*a^5*b^8*c^7*d^5 + 3784704*a^6*b^7*c^6*d^6 - 3244032*a^7*b^6*c^5*d^7 + 2027520*a^8*b^5*c^4*d^8 - 901120*a^9*b^4*c^3*d^9 + 270336*a^10*b^3*c^2*d^10 - 49152*a*b^12*c^11*d))^(1/4)","B"
489,1,30956,609,3.965022,"\text{Not used}","int(x^(5/2)/((a + b*x^2)^2*(c + d*x^2)^2),x)","-\frac{\frac{x^{3/2}\,\left(a\,d+b\,c\right)}{2\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}+\frac{b\,d\,x^{7/2}}{a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2}}{b\,d\,x^4+\left(a\,d+b\,c\right)\,x^2+a\,c}-\mathrm{atan}\left(\frac{\left({\left(-\frac{625\,a^4\,b\,d^4+1500\,a^3\,b^2\,c\,d^3+1350\,a^2\,b^3\,c^2\,d^2+540\,a\,b^4\,c^3\,d+81\,b^5\,c^4}{4096\,a^{13}\,d^{12}-49152\,a^{12}\,b\,c\,d^{11}+270336\,a^{11}\,b^2\,c^2\,d^{10}-901120\,a^{10}\,b^3\,c^3\,d^9+2027520\,a^9\,b^4\,c^4\,d^8-3244032\,a^8\,b^5\,c^5\,d^7+3784704\,a^7\,b^6\,c^6\,d^6-3244032\,a^6\,b^7\,c^7\,d^5+2027520\,a^5\,b^8\,c^8\,d^4-901120\,a^4\,b^9\,c^9\,d^3+270336\,a^3\,b^{10}\,c^{10}\,d^2-49152\,a^2\,b^{11}\,c^{11}\,d+4096\,a\,b^{12}\,c^{12}}\right)}^{3/4}\,\left(\frac{864\,a^{17}\,b^4\,c\,d^{20}-5184\,a^{16}\,b^5\,c^2\,d^{19}+3200\,a^{15}\,b^6\,c^3\,d^{18}+56640\,a^{14}\,b^7\,c^4\,d^{17}-220800\,a^{13}\,b^8\,c^5\,d^{16}+369088\,a^{12}\,b^9\,c^6\,d^{15}-240768\,a^{11}\,b^{10}\,c^7\,d^{14}-158400\,a^{10}\,b^{11}\,c^8\,d^{13}+390720\,a^9\,b^{12}\,c^9\,d^{12}-158400\,a^8\,b^{13}\,c^{10}\,d^{11}-240768\,a^7\,b^{14}\,c^{11}\,d^{10}+369088\,a^6\,b^{15}\,c^{12}\,d^9-220800\,a^5\,b^{16}\,c^{13}\,d^8+56640\,a^4\,b^{17}\,c^{14}\,d^7+3200\,a^3\,b^{18}\,c^{15}\,d^6-5184\,a^2\,b^{19}\,c^{16}\,d^5+864\,a\,b^{20}\,c^{17}\,d^4}{a^{14}\,d^{14}-14\,a^{13}\,b\,c\,d^{13}+91\,a^{12}\,b^2\,c^2\,d^{12}-364\,a^{11}\,b^3\,c^3\,d^{11}+1001\,a^{10}\,b^4\,c^4\,d^{10}-2002\,a^9\,b^5\,c^5\,d^9+3003\,a^8\,b^6\,c^6\,d^8-3432\,a^7\,b^7\,c^7\,d^7+3003\,a^6\,b^8\,c^8\,d^6-2002\,a^5\,b^9\,c^9\,d^5+1001\,a^4\,b^{10}\,c^{10}\,d^4-364\,a^3\,b^{11}\,c^{11}\,d^3+91\,a^2\,b^{12}\,c^{12}\,d^2-14\,a\,b^{13}\,c^{13}\,d+b^{14}\,c^{14}}-\frac{\sqrt{x}\,{\left(-\frac{625\,a^4\,b\,d^4+1500\,a^3\,b^2\,c\,d^3+1350\,a^2\,b^3\,c^2\,d^2+540\,a\,b^4\,c^3\,d+81\,b^5\,c^4}{4096\,a^{13}\,d^{12}-49152\,a^{12}\,b\,c\,d^{11}+270336\,a^{11}\,b^2\,c^2\,d^{10}-901120\,a^{10}\,b^3\,c^3\,d^9+2027520\,a^9\,b^4\,c^4\,d^8-3244032\,a^8\,b^5\,c^5\,d^7+3784704\,a^7\,b^6\,c^6\,d^6-3244032\,a^6\,b^7\,c^7\,d^5+2027520\,a^5\,b^8\,c^8\,d^4-901120\,a^4\,b^9\,c^9\,d^3+270336\,a^3\,b^{10}\,c^{10}\,d^2-49152\,a^2\,b^{11}\,c^{11}\,d+4096\,a\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(36864\,a^{17}\,b^4\,c\,d^{20}-319488\,a^{16}\,b^5\,c^2\,d^{19}+1163264\,a^{15}\,b^6\,c^3\,d^{18}-2334720\,a^{14}\,b^7\,c^4\,d^{17}+3293184\,a^{13}\,b^8\,c^5\,d^{16}-5758976\,a^{12}\,b^9\,c^6\,d^{15}+13516800\,a^{11}\,b^{10}\,c^7\,d^{14}-25141248\,a^{10}\,b^{11}\,c^8\,d^{13}+31088640\,a^9\,b^{12}\,c^9\,d^{12}-25141248\,a^8\,b^{13}\,c^{10}\,d^{11}+13516800\,a^7\,b^{14}\,c^{11}\,d^{10}-5758976\,a^6\,b^{15}\,c^{12}\,d^9+3293184\,a^5\,b^{16}\,c^{13}\,d^8-2334720\,a^4\,b^{17}\,c^{14}\,d^7+1163264\,a^3\,b^{18}\,c^{15}\,d^6-319488\,a^2\,b^{19}\,c^{16}\,d^5+36864\,a\,b^{20}\,c^{17}\,d^4\right)}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)\,1{}\mathrm{i}-\frac{\sqrt{x}\,\left(5625\,a^8\,b^5\,c\,d^{12}+34275\,a^7\,b^6\,c^2\,d^{11}+88705\,a^6\,b^7\,c^3\,d^{10}+133539\,a^5\,b^8\,c^4\,d^9+133539\,a^4\,b^9\,c^5\,d^8+88705\,a^3\,b^{10}\,c^6\,d^7+34275\,a^2\,b^{11}\,c^7\,d^6+5625\,a\,b^{12}\,c^8\,d^5\right)\,1{}\mathrm{i}}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)\,{\left(-\frac{625\,a^4\,b\,d^4+1500\,a^3\,b^2\,c\,d^3+1350\,a^2\,b^3\,c^2\,d^2+540\,a\,b^4\,c^3\,d+81\,b^5\,c^4}{4096\,a^{13}\,d^{12}-49152\,a^{12}\,b\,c\,d^{11}+270336\,a^{11}\,b^2\,c^2\,d^{10}-901120\,a^{10}\,b^3\,c^3\,d^9+2027520\,a^9\,b^4\,c^4\,d^8-3244032\,a^8\,b^5\,c^5\,d^7+3784704\,a^7\,b^6\,c^6\,d^6-3244032\,a^6\,b^7\,c^7\,d^5+2027520\,a^5\,b^8\,c^8\,d^4-901120\,a^4\,b^9\,c^9\,d^3+270336\,a^3\,b^{10}\,c^{10}\,d^2-49152\,a^2\,b^{11}\,c^{11}\,d+4096\,a\,b^{12}\,c^{12}}\right)}^{1/4}-\left({\left(-\frac{625\,a^4\,b\,d^4+1500\,a^3\,b^2\,c\,d^3+1350\,a^2\,b^3\,c^2\,d^2+540\,a\,b^4\,c^3\,d+81\,b^5\,c^4}{4096\,a^{13}\,d^{12}-49152\,a^{12}\,b\,c\,d^{11}+270336\,a^{11}\,b^2\,c^2\,d^{10}-901120\,a^{10}\,b^3\,c^3\,d^9+2027520\,a^9\,b^4\,c^4\,d^8-3244032\,a^8\,b^5\,c^5\,d^7+3784704\,a^7\,b^6\,c^6\,d^6-3244032\,a^6\,b^7\,c^7\,d^5+2027520\,a^5\,b^8\,c^8\,d^4-901120\,a^4\,b^9\,c^9\,d^3+270336\,a^3\,b^{10}\,c^{10}\,d^2-49152\,a^2\,b^{11}\,c^{11}\,d+4096\,a\,b^{12}\,c^{12}}\right)}^{3/4}\,\left(\frac{864\,a^{17}\,b^4\,c\,d^{20}-5184\,a^{16}\,b^5\,c^2\,d^{19}+3200\,a^{15}\,b^6\,c^3\,d^{18}+56640\,a^{14}\,b^7\,c^4\,d^{17}-220800\,a^{13}\,b^8\,c^5\,d^{16}+369088\,a^{12}\,b^9\,c^6\,d^{15}-240768\,a^{11}\,b^{10}\,c^7\,d^{14}-158400\,a^{10}\,b^{11}\,c^8\,d^{13}+390720\,a^9\,b^{12}\,c^9\,d^{12}-158400\,a^8\,b^{13}\,c^{10}\,d^{11}-240768\,a^7\,b^{14}\,c^{11}\,d^{10}+369088\,a^6\,b^{15}\,c^{12}\,d^9-220800\,a^5\,b^{16}\,c^{13}\,d^8+56640\,a^4\,b^{17}\,c^{14}\,d^7+3200\,a^3\,b^{18}\,c^{15}\,d^6-5184\,a^2\,b^{19}\,c^{16}\,d^5+864\,a\,b^{20}\,c^{17}\,d^4}{a^{14}\,d^{14}-14\,a^{13}\,b\,c\,d^{13}+91\,a^{12}\,b^2\,c^2\,d^{12}-364\,a^{11}\,b^3\,c^3\,d^{11}+1001\,a^{10}\,b^4\,c^4\,d^{10}-2002\,a^9\,b^5\,c^5\,d^9+3003\,a^8\,b^6\,c^6\,d^8-3432\,a^7\,b^7\,c^7\,d^7+3003\,a^6\,b^8\,c^8\,d^6-2002\,a^5\,b^9\,c^9\,d^5+1001\,a^4\,b^{10}\,c^{10}\,d^4-364\,a^3\,b^{11}\,c^{11}\,d^3+91\,a^2\,b^{12}\,c^{12}\,d^2-14\,a\,b^{13}\,c^{13}\,d+b^{14}\,c^{14}}+\frac{\sqrt{x}\,{\left(-\frac{625\,a^4\,b\,d^4+1500\,a^3\,b^2\,c\,d^3+1350\,a^2\,b^3\,c^2\,d^2+540\,a\,b^4\,c^3\,d+81\,b^5\,c^4}{4096\,a^{13}\,d^{12}-49152\,a^{12}\,b\,c\,d^{11}+270336\,a^{11}\,b^2\,c^2\,d^{10}-901120\,a^{10}\,b^3\,c^3\,d^9+2027520\,a^9\,b^4\,c^4\,d^8-3244032\,a^8\,b^5\,c^5\,d^7+3784704\,a^7\,b^6\,c^6\,d^6-3244032\,a^6\,b^7\,c^7\,d^5+2027520\,a^5\,b^8\,c^8\,d^4-901120\,a^4\,b^9\,c^9\,d^3+270336\,a^3\,b^{10}\,c^{10}\,d^2-49152\,a^2\,b^{11}\,c^{11}\,d+4096\,a\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(36864\,a^{17}\,b^4\,c\,d^{20}-319488\,a^{16}\,b^5\,c^2\,d^{19}+1163264\,a^{15}\,b^6\,c^3\,d^{18}-2334720\,a^{14}\,b^7\,c^4\,d^{17}+3293184\,a^{13}\,b^8\,c^5\,d^{16}-5758976\,a^{12}\,b^9\,c^6\,d^{15}+13516800\,a^{11}\,b^{10}\,c^7\,d^{14}-25141248\,a^{10}\,b^{11}\,c^8\,d^{13}+31088640\,a^9\,b^{12}\,c^9\,d^{12}-25141248\,a^8\,b^{13}\,c^{10}\,d^{11}+13516800\,a^7\,b^{14}\,c^{11}\,d^{10}-5758976\,a^6\,b^{15}\,c^{12}\,d^9+3293184\,a^5\,b^{16}\,c^{13}\,d^8-2334720\,a^4\,b^{17}\,c^{14}\,d^7+1163264\,a^3\,b^{18}\,c^{15}\,d^6-319488\,a^2\,b^{19}\,c^{16}\,d^5+36864\,a\,b^{20}\,c^{17}\,d^4\right)}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)\,1{}\mathrm{i}+\frac{\sqrt{x}\,\left(5625\,a^8\,b^5\,c\,d^{12}+34275\,a^7\,b^6\,c^2\,d^{11}+88705\,a^6\,b^7\,c^3\,d^{10}+133539\,a^5\,b^8\,c^4\,d^9+133539\,a^4\,b^9\,c^5\,d^8+88705\,a^3\,b^{10}\,c^6\,d^7+34275\,a^2\,b^{11}\,c^7\,d^6+5625\,a\,b^{12}\,c^8\,d^5\right)\,1{}\mathrm{i}}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)\,{\left(-\frac{625\,a^4\,b\,d^4+1500\,a^3\,b^2\,c\,d^3+1350\,a^2\,b^3\,c^2\,d^2+540\,a\,b^4\,c^3\,d+81\,b^5\,c^4}{4096\,a^{13}\,d^{12}-49152\,a^{12}\,b\,c\,d^{11}+270336\,a^{11}\,b^2\,c^2\,d^{10}-901120\,a^{10}\,b^3\,c^3\,d^9+2027520\,a^9\,b^4\,c^4\,d^8-3244032\,a^8\,b^5\,c^5\,d^7+3784704\,a^7\,b^6\,c^6\,d^6-3244032\,a^6\,b^7\,c^7\,d^5+2027520\,a^5\,b^8\,c^8\,d^4-901120\,a^4\,b^9\,c^9\,d^3+270336\,a^3\,b^{10}\,c^{10}\,d^2-49152\,a^2\,b^{11}\,c^{11}\,d+4096\,a\,b^{12}\,c^{12}}\right)}^{1/4}}{\left({\left(-\frac{625\,a^4\,b\,d^4+1500\,a^3\,b^2\,c\,d^3+1350\,a^2\,b^3\,c^2\,d^2+540\,a\,b^4\,c^3\,d+81\,b^5\,c^4}{4096\,a^{13}\,d^{12}-49152\,a^{12}\,b\,c\,d^{11}+270336\,a^{11}\,b^2\,c^2\,d^{10}-901120\,a^{10}\,b^3\,c^3\,d^9+2027520\,a^9\,b^4\,c^4\,d^8-3244032\,a^8\,b^5\,c^5\,d^7+3784704\,a^7\,b^6\,c^6\,d^6-3244032\,a^6\,b^7\,c^7\,d^5+2027520\,a^5\,b^8\,c^8\,d^4-901120\,a^4\,b^9\,c^9\,d^3+270336\,a^3\,b^{10}\,c^{10}\,d^2-49152\,a^2\,b^{11}\,c^{11}\,d+4096\,a\,b^{12}\,c^{12}}\right)}^{3/4}\,\left(\frac{864\,a^{17}\,b^4\,c\,d^{20}-5184\,a^{16}\,b^5\,c^2\,d^{19}+3200\,a^{15}\,b^6\,c^3\,d^{18}+56640\,a^{14}\,b^7\,c^4\,d^{17}-220800\,a^{13}\,b^8\,c^5\,d^{16}+369088\,a^{12}\,b^9\,c^6\,d^{15}-240768\,a^{11}\,b^{10}\,c^7\,d^{14}-158400\,a^{10}\,b^{11}\,c^8\,d^{13}+390720\,a^9\,b^{12}\,c^9\,d^{12}-158400\,a^8\,b^{13}\,c^{10}\,d^{11}-240768\,a^7\,b^{14}\,c^{11}\,d^{10}+369088\,a^6\,b^{15}\,c^{12}\,d^9-220800\,a^5\,b^{16}\,c^{13}\,d^8+56640\,a^4\,b^{17}\,c^{14}\,d^7+3200\,a^3\,b^{18}\,c^{15}\,d^6-5184\,a^2\,b^{19}\,c^{16}\,d^5+864\,a\,b^{20}\,c^{17}\,d^4}{a^{14}\,d^{14}-14\,a^{13}\,b\,c\,d^{13}+91\,a^{12}\,b^2\,c^2\,d^{12}-364\,a^{11}\,b^3\,c^3\,d^{11}+1001\,a^{10}\,b^4\,c^4\,d^{10}-2002\,a^9\,b^5\,c^5\,d^9+3003\,a^8\,b^6\,c^6\,d^8-3432\,a^7\,b^7\,c^7\,d^7+3003\,a^6\,b^8\,c^8\,d^6-2002\,a^5\,b^9\,c^9\,d^5+1001\,a^4\,b^{10}\,c^{10}\,d^4-364\,a^3\,b^{11}\,c^{11}\,d^3+91\,a^2\,b^{12}\,c^{12}\,d^2-14\,a\,b^{13}\,c^{13}\,d+b^{14}\,c^{14}}-\frac{\sqrt{x}\,{\left(-\frac{625\,a^4\,b\,d^4+1500\,a^3\,b^2\,c\,d^3+1350\,a^2\,b^3\,c^2\,d^2+540\,a\,b^4\,c^3\,d+81\,b^5\,c^4}{4096\,a^{13}\,d^{12}-49152\,a^{12}\,b\,c\,d^{11}+270336\,a^{11}\,b^2\,c^2\,d^{10}-901120\,a^{10}\,b^3\,c^3\,d^9+2027520\,a^9\,b^4\,c^4\,d^8-3244032\,a^8\,b^5\,c^5\,d^7+3784704\,a^7\,b^6\,c^6\,d^6-3244032\,a^6\,b^7\,c^7\,d^5+2027520\,a^5\,b^8\,c^8\,d^4-901120\,a^4\,b^9\,c^9\,d^3+270336\,a^3\,b^{10}\,c^{10}\,d^2-49152\,a^2\,b^{11}\,c^{11}\,d+4096\,a\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(36864\,a^{17}\,b^4\,c\,d^{20}-319488\,a^{16}\,b^5\,c^2\,d^{19}+1163264\,a^{15}\,b^6\,c^3\,d^{18}-2334720\,a^{14}\,b^7\,c^4\,d^{17}+3293184\,a^{13}\,b^8\,c^5\,d^{16}-5758976\,a^{12}\,b^9\,c^6\,d^{15}+13516800\,a^{11}\,b^{10}\,c^7\,d^{14}-25141248\,a^{10}\,b^{11}\,c^8\,d^{13}+31088640\,a^9\,b^{12}\,c^9\,d^{12}-25141248\,a^8\,b^{13}\,c^{10}\,d^{11}+13516800\,a^7\,b^{14}\,c^{11}\,d^{10}-5758976\,a^6\,b^{15}\,c^{12}\,d^9+3293184\,a^5\,b^{16}\,c^{13}\,d^8-2334720\,a^4\,b^{17}\,c^{14}\,d^7+1163264\,a^3\,b^{18}\,c^{15}\,d^6-319488\,a^2\,b^{19}\,c^{16}\,d^5+36864\,a\,b^{20}\,c^{17}\,d^4\right)}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)-\frac{\sqrt{x}\,\left(5625\,a^8\,b^5\,c\,d^{12}+34275\,a^7\,b^6\,c^2\,d^{11}+88705\,a^6\,b^7\,c^3\,d^{10}+133539\,a^5\,b^8\,c^4\,d^9+133539\,a^4\,b^9\,c^5\,d^8+88705\,a^3\,b^{10}\,c^6\,d^7+34275\,a^2\,b^{11}\,c^7\,d^6+5625\,a\,b^{12}\,c^8\,d^5\right)}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)\,{\left(-\frac{625\,a^4\,b\,d^4+1500\,a^3\,b^2\,c\,d^3+1350\,a^2\,b^3\,c^2\,d^2+540\,a\,b^4\,c^3\,d+81\,b^5\,c^4}{4096\,a^{13}\,d^{12}-49152\,a^{12}\,b\,c\,d^{11}+270336\,a^{11}\,b^2\,c^2\,d^{10}-901120\,a^{10}\,b^3\,c^3\,d^9+2027520\,a^9\,b^4\,c^4\,d^8-3244032\,a^8\,b^5\,c^5\,d^7+3784704\,a^7\,b^6\,c^6\,d^6-3244032\,a^6\,b^7\,c^7\,d^5+2027520\,a^5\,b^8\,c^8\,d^4-901120\,a^4\,b^9\,c^9\,d^3+270336\,a^3\,b^{10}\,c^{10}\,d^2-49152\,a^2\,b^{11}\,c^{11}\,d+4096\,a\,b^{12}\,c^{12}}\right)}^{1/4}+\left({\left(-\frac{625\,a^4\,b\,d^4+1500\,a^3\,b^2\,c\,d^3+1350\,a^2\,b^3\,c^2\,d^2+540\,a\,b^4\,c^3\,d+81\,b^5\,c^4}{4096\,a^{13}\,d^{12}-49152\,a^{12}\,b\,c\,d^{11}+270336\,a^{11}\,b^2\,c^2\,d^{10}-901120\,a^{10}\,b^3\,c^3\,d^9+2027520\,a^9\,b^4\,c^4\,d^8-3244032\,a^8\,b^5\,c^5\,d^7+3784704\,a^7\,b^6\,c^6\,d^6-3244032\,a^6\,b^7\,c^7\,d^5+2027520\,a^5\,b^8\,c^8\,d^4-901120\,a^4\,b^9\,c^9\,d^3+270336\,a^3\,b^{10}\,c^{10}\,d^2-49152\,a^2\,b^{11}\,c^{11}\,d+4096\,a\,b^{12}\,c^{12}}\right)}^{3/4}\,\left(\frac{864\,a^{17}\,b^4\,c\,d^{20}-5184\,a^{16}\,b^5\,c^2\,d^{19}+3200\,a^{15}\,b^6\,c^3\,d^{18}+56640\,a^{14}\,b^7\,c^4\,d^{17}-220800\,a^{13}\,b^8\,c^5\,d^{16}+369088\,a^{12}\,b^9\,c^6\,d^{15}-240768\,a^{11}\,b^{10}\,c^7\,d^{14}-158400\,a^{10}\,b^{11}\,c^8\,d^{13}+390720\,a^9\,b^{12}\,c^9\,d^{12}-158400\,a^8\,b^{13}\,c^{10}\,d^{11}-240768\,a^7\,b^{14}\,c^{11}\,d^{10}+369088\,a^6\,b^{15}\,c^{12}\,d^9-220800\,a^5\,b^{16}\,c^{13}\,d^8+56640\,a^4\,b^{17}\,c^{14}\,d^7+3200\,a^3\,b^{18}\,c^{15}\,d^6-5184\,a^2\,b^{19}\,c^{16}\,d^5+864\,a\,b^{20}\,c^{17}\,d^4}{a^{14}\,d^{14}-14\,a^{13}\,b\,c\,d^{13}+91\,a^{12}\,b^2\,c^2\,d^{12}-364\,a^{11}\,b^3\,c^3\,d^{11}+1001\,a^{10}\,b^4\,c^4\,d^{10}-2002\,a^9\,b^5\,c^5\,d^9+3003\,a^8\,b^6\,c^6\,d^8-3432\,a^7\,b^7\,c^7\,d^7+3003\,a^6\,b^8\,c^8\,d^6-2002\,a^5\,b^9\,c^9\,d^5+1001\,a^4\,b^{10}\,c^{10}\,d^4-364\,a^3\,b^{11}\,c^{11}\,d^3+91\,a^2\,b^{12}\,c^{12}\,d^2-14\,a\,b^{13}\,c^{13}\,d+b^{14}\,c^{14}}+\frac{\sqrt{x}\,{\left(-\frac{625\,a^4\,b\,d^4+1500\,a^3\,b^2\,c\,d^3+1350\,a^2\,b^3\,c^2\,d^2+540\,a\,b^4\,c^3\,d+81\,b^5\,c^4}{4096\,a^{13}\,d^{12}-49152\,a^{12}\,b\,c\,d^{11}+270336\,a^{11}\,b^2\,c^2\,d^{10}-901120\,a^{10}\,b^3\,c^3\,d^9+2027520\,a^9\,b^4\,c^4\,d^8-3244032\,a^8\,b^5\,c^5\,d^7+3784704\,a^7\,b^6\,c^6\,d^6-3244032\,a^6\,b^7\,c^7\,d^5+2027520\,a^5\,b^8\,c^8\,d^4-901120\,a^4\,b^9\,c^9\,d^3+270336\,a^3\,b^{10}\,c^{10}\,d^2-49152\,a^2\,b^{11}\,c^{11}\,d+4096\,a\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(36864\,a^{17}\,b^4\,c\,d^{20}-319488\,a^{16}\,b^5\,c^2\,d^{19}+1163264\,a^{15}\,b^6\,c^3\,d^{18}-2334720\,a^{14}\,b^7\,c^4\,d^{17}+3293184\,a^{13}\,b^8\,c^5\,d^{16}-5758976\,a^{12}\,b^9\,c^6\,d^{15}+13516800\,a^{11}\,b^{10}\,c^7\,d^{14}-25141248\,a^{10}\,b^{11}\,c^8\,d^{13}+31088640\,a^9\,b^{12}\,c^9\,d^{12}-25141248\,a^8\,b^{13}\,c^{10}\,d^{11}+13516800\,a^7\,b^{14}\,c^{11}\,d^{10}-5758976\,a^6\,b^{15}\,c^{12}\,d^9+3293184\,a^5\,b^{16}\,c^{13}\,d^8-2334720\,a^4\,b^{17}\,c^{14}\,d^7+1163264\,a^3\,b^{18}\,c^{15}\,d^6-319488\,a^2\,b^{19}\,c^{16}\,d^5+36864\,a\,b^{20}\,c^{17}\,d^4\right)}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)+\frac{\sqrt{x}\,\left(5625\,a^8\,b^5\,c\,d^{12}+34275\,a^7\,b^6\,c^2\,d^{11}+88705\,a^6\,b^7\,c^3\,d^{10}+133539\,a^5\,b^8\,c^4\,d^9+133539\,a^4\,b^9\,c^5\,d^8+88705\,a^3\,b^{10}\,c^6\,d^7+34275\,a^2\,b^{11}\,c^7\,d^6+5625\,a\,b^{12}\,c^8\,d^5\right)}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)\,{\left(-\frac{625\,a^4\,b\,d^4+1500\,a^3\,b^2\,c\,d^3+1350\,a^2\,b^3\,c^2\,d^2+540\,a\,b^4\,c^3\,d+81\,b^5\,c^4}{4096\,a^{13}\,d^{12}-49152\,a^{12}\,b\,c\,d^{11}+270336\,a^{11}\,b^2\,c^2\,d^{10}-901120\,a^{10}\,b^3\,c^3\,d^9+2027520\,a^9\,b^4\,c^4\,d^8-3244032\,a^8\,b^5\,c^5\,d^7+3784704\,a^7\,b^6\,c^6\,d^6-3244032\,a^6\,b^7\,c^7\,d^5+2027520\,a^5\,b^8\,c^8\,d^4-901120\,a^4\,b^9\,c^9\,d^3+270336\,a^3\,b^{10}\,c^{10}\,d^2-49152\,a^2\,b^{11}\,c^{11}\,d+4096\,a\,b^{12}\,c^{12}}\right)}^{1/4}+\frac{\frac{16875\,a^8\,b^5\,c\,d^{12}}{64}+\frac{131625\,a^7\,b^6\,c^2\,d^{11}}{64}+\frac{425475\,a^6\,b^7\,c^3\,d^{10}}{64}+\frac{736745\,a^5\,b^8\,c^4\,d^9}{64}+\frac{736745\,a^4\,b^9\,c^5\,d^8}{64}+\frac{425475\,a^3\,b^{10}\,c^6\,d^7}{64}+\frac{131625\,a^2\,b^{11}\,c^7\,d^6}{64}+\frac{16875\,a\,b^{12}\,c^8\,d^5}{64}}{a^{14}\,d^{14}-14\,a^{13}\,b\,c\,d^{13}+91\,a^{12}\,b^2\,c^2\,d^{12}-364\,a^{11}\,b^3\,c^3\,d^{11}+1001\,a^{10}\,b^4\,c^4\,d^{10}-2002\,a^9\,b^5\,c^5\,d^9+3003\,a^8\,b^6\,c^6\,d^8-3432\,a^7\,b^7\,c^7\,d^7+3003\,a^6\,b^8\,c^8\,d^6-2002\,a^5\,b^9\,c^9\,d^5+1001\,a^4\,b^{10}\,c^{10}\,d^4-364\,a^3\,b^{11}\,c^{11}\,d^3+91\,a^2\,b^{12}\,c^{12}\,d^2-14\,a\,b^{13}\,c^{13}\,d+b^{14}\,c^{14}}}\right)\,{\left(-\frac{625\,a^4\,b\,d^4+1500\,a^3\,b^2\,c\,d^3+1350\,a^2\,b^3\,c^2\,d^2+540\,a\,b^4\,c^3\,d+81\,b^5\,c^4}{4096\,a^{13}\,d^{12}-49152\,a^{12}\,b\,c\,d^{11}+270336\,a^{11}\,b^2\,c^2\,d^{10}-901120\,a^{10}\,b^3\,c^3\,d^9+2027520\,a^9\,b^4\,c^4\,d^8-3244032\,a^8\,b^5\,c^5\,d^7+3784704\,a^7\,b^6\,c^6\,d^6-3244032\,a^6\,b^7\,c^7\,d^5+2027520\,a^5\,b^8\,c^8\,d^4-901120\,a^4\,b^9\,c^9\,d^3+270336\,a^3\,b^{10}\,c^{10}\,d^2-49152\,a^2\,b^{11}\,c^{11}\,d+4096\,a\,b^{12}\,c^{12}}\right)}^{1/4}\,2{}\mathrm{i}+2\,\mathrm{atan}\left(\frac{\left({\left(-\frac{625\,a^4\,b\,d^4+1500\,a^3\,b^2\,c\,d^3+1350\,a^2\,b^3\,c^2\,d^2+540\,a\,b^4\,c^3\,d+81\,b^5\,c^4}{4096\,a^{13}\,d^{12}-49152\,a^{12}\,b\,c\,d^{11}+270336\,a^{11}\,b^2\,c^2\,d^{10}-901120\,a^{10}\,b^3\,c^3\,d^9+2027520\,a^9\,b^4\,c^4\,d^8-3244032\,a^8\,b^5\,c^5\,d^7+3784704\,a^7\,b^6\,c^6\,d^6-3244032\,a^6\,b^7\,c^7\,d^5+2027520\,a^5\,b^8\,c^8\,d^4-901120\,a^4\,b^9\,c^9\,d^3+270336\,a^3\,b^{10}\,c^{10}\,d^2-49152\,a^2\,b^{11}\,c^{11}\,d+4096\,a\,b^{12}\,c^{12}}\right)}^{3/4}\,\left(-\frac{\sqrt{x}\,{\left(-\frac{625\,a^4\,b\,d^4+1500\,a^3\,b^2\,c\,d^3+1350\,a^2\,b^3\,c^2\,d^2+540\,a\,b^4\,c^3\,d+81\,b^5\,c^4}{4096\,a^{13}\,d^{12}-49152\,a^{12}\,b\,c\,d^{11}+270336\,a^{11}\,b^2\,c^2\,d^{10}-901120\,a^{10}\,b^3\,c^3\,d^9+2027520\,a^9\,b^4\,c^4\,d^8-3244032\,a^8\,b^5\,c^5\,d^7+3784704\,a^7\,b^6\,c^6\,d^6-3244032\,a^6\,b^7\,c^7\,d^5+2027520\,a^5\,b^8\,c^8\,d^4-901120\,a^4\,b^9\,c^9\,d^3+270336\,a^3\,b^{10}\,c^{10}\,d^2-49152\,a^2\,b^{11}\,c^{11}\,d+4096\,a\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(36864\,a^{17}\,b^4\,c\,d^{20}-319488\,a^{16}\,b^5\,c^2\,d^{19}+1163264\,a^{15}\,b^6\,c^3\,d^{18}-2334720\,a^{14}\,b^7\,c^4\,d^{17}+3293184\,a^{13}\,b^8\,c^5\,d^{16}-5758976\,a^{12}\,b^9\,c^6\,d^{15}+13516800\,a^{11}\,b^{10}\,c^7\,d^{14}-25141248\,a^{10}\,b^{11}\,c^8\,d^{13}+31088640\,a^9\,b^{12}\,c^9\,d^{12}-25141248\,a^8\,b^{13}\,c^{10}\,d^{11}+13516800\,a^7\,b^{14}\,c^{11}\,d^{10}-5758976\,a^6\,b^{15}\,c^{12}\,d^9+3293184\,a^5\,b^{16}\,c^{13}\,d^8-2334720\,a^4\,b^{17}\,c^{14}\,d^7+1163264\,a^3\,b^{18}\,c^{15}\,d^6-319488\,a^2\,b^{19}\,c^{16}\,d^5+36864\,a\,b^{20}\,c^{17}\,d^4\right)}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}+\frac{\left(864\,a^{17}\,b^4\,c\,d^{20}-5184\,a^{16}\,b^5\,c^2\,d^{19}+3200\,a^{15}\,b^6\,c^3\,d^{18}+56640\,a^{14}\,b^7\,c^4\,d^{17}-220800\,a^{13}\,b^8\,c^5\,d^{16}+369088\,a^{12}\,b^9\,c^6\,d^{15}-240768\,a^{11}\,b^{10}\,c^7\,d^{14}-158400\,a^{10}\,b^{11}\,c^8\,d^{13}+390720\,a^9\,b^{12}\,c^9\,d^{12}-158400\,a^8\,b^{13}\,c^{10}\,d^{11}-240768\,a^7\,b^{14}\,c^{11}\,d^{10}+369088\,a^6\,b^{15}\,c^{12}\,d^9-220800\,a^5\,b^{16}\,c^{13}\,d^8+56640\,a^4\,b^{17}\,c^{14}\,d^7+3200\,a^3\,b^{18}\,c^{15}\,d^6-5184\,a^2\,b^{19}\,c^{16}\,d^5+864\,a\,b^{20}\,c^{17}\,d^4\right)\,1{}\mathrm{i}}{a^{14}\,d^{14}-14\,a^{13}\,b\,c\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350\,a^2\,b^3\,c^2\,d^2+540\,a\,b^4\,c^3\,d+81\,b^5\,c^4}{4096\,a^{13}\,d^{12}-49152\,a^{12}\,b\,c\,d^{11}+270336\,a^{11}\,b^2\,c^2\,d^{10}-901120\,a^{10}\,b^3\,c^3\,d^9+2027520\,a^9\,b^4\,c^4\,d^8-3244032\,a^8\,b^5\,c^5\,d^7+3784704\,a^7\,b^6\,c^6\,d^6-3244032\,a^6\,b^7\,c^7\,d^5+2027520\,a^5\,b^8\,c^8\,d^4-901120\,a^4\,b^9\,c^9\,d^3+270336\,a^3\,b^{10}\,c^{10}\,d^2-49152\,a^2\,b^{11}\,c^{11}\,d+4096\,a\,b^{12}\,c^{12}}\right)}^{1/4}}{\left({\left(-\frac{625\,a^4\,b\,d^4+1500\,a^3\,b^2\,c\,d^3+1350\,a^2\,b^3\,c^2\,d^2+540\,a\,b^4\,c^3\,d+81\,b^5\,c^4}{4096\,a^{13}\,d^{12}-49152\,a^{12}\,b\,c\,d^{11}+270336\,a^{11}\,b^2\,c^2\,d^{10}-901120\,a^{10}\,b^3\,c^3\,d^9+2027520\,a^9\,b^4\,c^4\,d^8-3244032\,a^8\,b^5\,c^5\,d^7+3784704\,a^7\,b^6\,c^6\,d^6-3244032\,a^6\,b^7\,c^7\,d^5+2027520\,a^5\,b^8\,c^8\,d^4-901120\,a^4\,b^9\,c^9\,d^3+270336\,a^3\,b^{10}\,c^{10}\,d^2-49152\,a^2\,b^{11}\,c^{11}\,d+4096\,a\,b^{12}\,c^{12}}\right)}^{3/4}\,\left(-\frac{\sqrt{x}\,{\left(-\frac{625\,a^4\,b\,d^4+1500\,a^3\,b^2\,c\,d^3+1350\,a^2\,b^3\,c^2\,d^2+540\,a\,b^4\,c^3\,d+81\,b^5\,c^4}{4096\,a^{13}\,d^{12}-49152\,a^{12}\,b\,c\,d^{11}+270336\,a^{11}\,b^2\,c^2\,d^{10}-901120\,a^{10}\,b^3\,c^3\,d^9+2027520\,a^9\,b^4\,c^4\,d^8-3244032\,a^8\,b^5\,c^5\,d^7+3784704\,a^7\,b^6\,c^6\,d^6-3244032\,a^6\,b^7\,c^7\,d^5+2027520\,a^5\,b^8\,c^8\,d^4-901120\,a^4\,b^9\,c^9\,d^3+270336\,a^3\,b^{10}\,c^{10}\,d^2-49152\,a^2\,b^{11}\,c^{11}\,d+4096\,a\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(36864\,a^{17}\,b^4\,c\,d^{20}-319488\,a^{16}\,b^5\,c^2\,d^{19}+1163264\,a^{15}\,b^6\,c^3\,d^{18}-2334720\,a^{14}\,b^7\,c^4\,d^{17}+3293184\,a^{13}\,b^8\,c^5\,d^{16}-5758976\,a^{12}\,b^9\,c^6\,d^{15}+13516800\,a^{11}\,b^{10}\,c^7\,d^{14}-25141248\,a^{10}\,b^{11}\,c^8\,d^{13}+31088640\,a^9\,b^{12}\,c^9\,d^{12}-25141248\,a^8\,b^{13}\,c^{10}\,d^{11}+13516800\,a^7\,b^{14}\,c^{11}\,d^{10}-5758976\,a^6\,b^{15}\,c^{12}\,d^9+3293184\,a^5\,b^{16}\,c^{13}\,d^8-2334720\,a^4\,b^{17}\,c^{14}\,d^7+1163264\,a^3\,b^{18}\,c^{15}\,d^6-319488\,a^2\,b^{19}\,c^{16}\,d^5+36864\,a\,b^{20}\,c^{17}\,d^4\right)}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}+\frac{\left(864\,a^{17}\,b^4\,c\,d^{20}-5184\,a^{16}\,b^5\,c^2\,d^{19}+3200\,a^{15}\,b^6\,c^3\,d^{18}+56640\,a^{14}\,b^7\,c^4\,d^{17}-220800\,a^{13}\,b^8\,c^5\,d^{16}+369088\,a^{12}\,b^9\,c^6\,d^{15}-240768\,a^{11}\,b^{10}\,c^7\,d^{14}-158400\,a^{10}\,b^{11}\,c^8\,d^{13}+390720\,a^9\,b^{12}\,c^9\,d^{12}-158400\,a^8\,b^{13}\,c^{10}\,d^{11}-240768\,a^7\,b^{14}\,c^{11}\,d^{10}+369088\,a^6\,b^{15}\,c^{12}\,d^9-220800\,a^5\,b^{16}\,c^{13}\,d^8+56640\,a^4\,b^{17}\,c^{14}\,d^7+3200\,a^3\,b^{18}\,c^{15}\,d^6-5184\,a^2\,b^{19}\,c^{16}\,d^5+864\,a\,b^{20}\,c^{17}\,d^4\right)\,1{}\mathrm{i}}{a^{14}\,d^{14}-14\,a^{13}\,b\,c\,d^{13}+91\,a^{12}\,b^2\,c^2\,d^{12}-364\,a^{11}\,b^3\,c^3\,d^{11}+1001\,a^{10}\,b^4\,c^4\,d^{10}-2002\,a^9\,b^5\,c^5\,d^9+3003\,a^8\,b^6\,c^6\,d^8-3432\,a^7\,b^7\,c^7\,d^7+3003\,a^6\,b^8\,c^8\,d^6-2002\,a^5\,b^9\,c^9\,d^5+1001\,a^4\,b^{10}\,c^{10}\,d^4-364\,a^3\,b^{11}\,c^{11}\,d^3+91\,a^2\,b^{12}\,c^{12}\,d^2-14\,a\,b^{13}\,c^{13}\,d+b^{14}\,c^{14}}\right)\,1{}\mathrm{i}-\frac{\sqrt{x}\,\left(5625\,a^8\,b^5\,c\,d^{12}+34275\,a^7\,b^6\,c^2\,d^{11}+88705\,a^6\,b^7\,c^3\,d^{10}+133539\,a^5\,b^8\,c^4\,d^9+133539\,a^4\,b^9\,c^5\,d^8+88705\,a^3\,b^{10}\,c^6\,d^7+34275\,a^2\,b^{11}\,c^7\,d^6+5625\,a\,b^{12}\,c^8\,d^5\right)\,1{}\mathrm{i}}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)\,{\left(-\frac{625\,a^4\,b\,d^4+1500\,a^3\,b^2\,c\,d^3+1350\,a^2\,b^3\,c^2\,d^2+540\,a\,b^4\,c^3\,d+81\,b^5\,c^4}{4096\,a^{13}\,d^{12}-49152\,a^{12}\,b\,c\,d^{11}+270336\,a^{11}\,b^2\,c^2\,d^{10}-901120\,a^{10}\,b^3\,c^3\,d^9+2027520\,a^9\,b^4\,c^4\,d^8-3244032\,a^8\,b^5\,c^5\,d^7+3784704\,a^7\,b^6\,c^6\,d^6-3244032\,a^6\,b^7\,c^7\,d^5+2027520\,a^5\,b^8\,c^8\,d^4-901120\,a^4\,b^9\,c^9\,d^3+270336\,a^3\,b^{10}\,c^{10}\,d^2-49152\,a^2\,b^{11}\,c^{11}\,d+4096\,a\,b^{12}\,c^{12}}\right)}^{1/4}+\left({\left(-\frac{625\,a^4\,b\,d^4+1500\,a^3\,b^2\,c\,d^3+1350\,a^2\,b^3\,c^2\,d^2+540\,a\,b^4\,c^3\,d+81\,b^5\,c^4}{4096\,a^{13}\,d^{12}-49152\,a^{12}\,b\,c\,d^{11}+270336\,a^{11}\,b^2\,c^2\,d^{10}-901120\,a^{10}\,b^3\,c^3\,d^9+2027520\,a^9\,b^4\,c^4\,d^8-3244032\,a^8\,b^5\,c^5\,d^7+3784704\,a^7\,b^6\,c^6\,d^6-3244032\,a^6\,b^7\,c^7\,d^5+2027520\,a^5\,b^8\,c^8\,d^4-901120\,a^4\,b^9\,c^9\,d^3+270336\,a^3\,b^{10}\,c^{10}\,d^2-49152\,a^2\,b^{11}\,c^{11}\,d+4096\,a\,b^{12}\,c^{12}}\right)}^{3/4}\,\left(\frac{\sqrt{x}\,{\left(-\frac{625\,a^4\,b\,d^4+1500\,a^3\,b^2\,c\,d^3+1350\,a^2\,b^3\,c^2\,d^2+540\,a\,b^4\,c^3\,d+81\,b^5\,c^4}{4096\,a^{13}\,d^{12}-49152\,a^{12}\,b\,c\,d^{11}+270336\,a^{11}\,b^2\,c^2\,d^{10}-901120\,a^{10}\,b^3\,c^3\,d^9+2027520\,a^9\,b^4\,c^4\,d^8-3244032\,a^8\,b^5\,c^5\,d^7+3784704\,a^7\,b^6\,c^6\,d^6-3244032\,a^6\,b^7\,c^7\,d^5+2027520\,a^5\,b^8\,c^8\,d^4-901120\,a^4\,b^9\,c^9\,d^3+270336\,a^3\,b^{10}\,c^{10}\,d^2-49152\,a^2\,b^{11}\,c^{11}\,d+4096\,a\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(36864\,a^{17}\,b^4\,c\,d^{20}-319488\,a^{16}\,b^5\,c^2\,d^{19}+1163264\,a^{15}\,b^6\,c^3\,d^{18}-2334720\,a^{14}\,b^7\,c^4\,d^{17}+3293184\,a^{13}\,b^8\,c^5\,d^{16}-5758976\,a^{12}\,b^9\,c^6\,d^{15}+13516800\,a^{11}\,b^{10}\,c^7\,d^{14}-25141248\,a^{10}\,b^{11}\,c^8\,d^{13}+31088640\,a^9\,b^{12}\,c^9\,d^{12}-25141248\,a^8\,b^{13}\,c^{10}\,d^{11}+13516800\,a^7\,b^{14}\,c^{11}\,d^{10}-5758976\,a^6\,b^{15}\,c^{12}\,d^9+3293184\,a^5\,b^{16}\,c^{13}\,d^8-2334720\,a^4\,b^{17}\,c^{14}\,d^7+1163264\,a^3\,b^{18}\,c^{15}\,d^6-319488\,a^2\,b^{19}\,c^{16}\,d^5+36864\,a\,b^{20}\,c^{17}\,d^4\right)}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}+\frac{\left(864\,a^{17}\,b^4\,c\,d^{20}-5184\,a^{16}\,b^5\,c^2\,d^{19}+3200\,a^{15}\,b^6\,c^3\,d^{18}+56640\,a^{14}\,b^7\,c^4\,d^{17}-220800\,a^{13}\,b^8\,c^5\,d^{16}+369088\,a^{12}\,b^9\,c^6\,d^{15}-240768\,a^{11}\,b^{10}\,c^7\,d^{14}-158400\,a^{10}\,b^{11}\,c^8\,d^{13}+390720\,a^9\,b^{12}\,c^9\,d^{12}-158400\,a^8\,b^{13}\,c^{10}\,d^{11}-240768\,a^7\,b^{14}\,c^{11}\,d^{10}+369088\,a^6\,b^{15}\,c^{12}\,d^9-220800\,a^5\,b^{16}\,c^{13}\,d^8+56640\,a^4\,b^{17}\,c^{14}\,d^7+3200\,a^3\,b^{18}\,c^{15}\,d^6-5184\,a^2\,b^{19}\,c^{16}\,d^5+864\,a\,b^{20}\,c^{17}\,d^4\right)\,1{}\mathrm{i}}{a^{14}\,d^{14}-14\,a^{13}\,b\,c\,d^{13}+91\,a^{12}\,b^2\,c^2\,d^{12}-364\,a^{11}\,b^3\,c^3\,d^{11}+1001\,a^{10}\,b^4\,c^4\,d^{10}-2002\,a^9\,b^5\,c^5\,d^9+3003\,a^8\,b^6\,c^6\,d^8-3432\,a^7\,b^7\,c^7\,d^7+3003\,a^6\,b^8\,c^8\,d^6-2002\,a^5\,b^9\,c^9\,d^5+1001\,a^4\,b^{10}\,c^{10}\,d^4-364\,a^3\,b^{11}\,c^{11}\,d^3+91\,a^2\,b^{12}\,c^{12}\,d^2-14\,a\,b^{13}\,c^{13}\,d+b^{14}\,c^{14}}\right)\,1{}\mathrm{i}+\frac{\sqrt{x}\,\left(5625\,a^8\,b^5\,c\,d^{12}+34275\,a^7\,b^6\,c^2\,d^{11}+88705\,a^6\,b^7\,c^3\,d^{10}+133539\,a^5\,b^8\,c^4\,d^9+133539\,a^4\,b^9\,c^5\,d^8+88705\,a^3\,b^{10}\,c^6\,d^7+34275\,a^2\,b^{11}\,c^7\,d^6+5625\,a\,b^{12}\,c^8\,d^5\right)\,1{}\mathrm{i}}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)\,{\left(-\frac{625\,a^4\,b\,d^4+1500\,a^3\,b^2\,c\,d^3+1350\,a^2\,b^3\,c^2\,d^2+540\,a\,b^4\,c^3\,d+81\,b^5\,c^4}{4096\,a^{13}\,d^{12}-49152\,a^{12}\,b\,c\,d^{11}+270336\,a^{11}\,b^2\,c^2\,d^{10}-901120\,a^{10}\,b^3\,c^3\,d^9+2027520\,a^9\,b^4\,c^4\,d^8-3244032\,a^8\,b^5\,c^5\,d^7+3784704\,a^7\,b^6\,c^6\,d^6-3244032\,a^6\,b^7\,c^7\,d^5+2027520\,a^5\,b^8\,c^8\,d^4-901120\,a^4\,b^9\,c^9\,d^3+270336\,a^3\,b^{10}\,c^{10}\,d^2-49152\,a^2\,b^{11}\,c^{11}\,d+4096\,a\,b^{12}\,c^{12}}\right)}^{1/4}-\frac{\frac{16875\,a^8\,b^5\,c\,d^{12}}{64}+\frac{131625\,a^7\,b^6\,c^2\,d^{11}}{64}+\frac{425475\,a^6\,b^7\,c^3\,d^{10}}{64}+\frac{736745\,a^5\,b^8\,c^4\,d^9}{64}+\frac{736745\,a^4\,b^9\,c^5\,d^8}{64}+\frac{425475\,a^3\,b^{10}\,c^6\,d^7}{64}+\frac{131625\,a^2\,b^{11}\,c^7\,d^6}{64}+\frac{16875\,a\,b^{12}\,c^8\,d^5}{64}}{a^{14}\,d^{14}-14\,a^{13}\,b\,c\,d^{13}+91\,a^{12}\,b^2\,c^2\,d^{12}-364\,a^{11}\,b^3\,c^3\,d^{11}+1001\,a^{10}\,b^4\,c^4\,d^{10}-2002\,a^9\,b^5\,c^5\,d^9+3003\,a^8\,b^6\,c^6\,d^8-3432\,a^7\,b^7\,c^7\,d^7+3003\,a^6\,b^8\,c^8\,d^6-2002\,a^5\,b^9\,c^9\,d^5+1001\,a^4\,b^{10}\,c^{10}\,d^4-364\,a^3\,b^{11}\,c^{11}\,d^3+91\,a^2\,b^{12}\,c^{12}\,d^2-14\,a\,b^{13}\,c^{13}\,d+b^{14}\,c^{14}}}\right)\,{\left(-\frac{625\,a^4\,b\,d^4+1500\,a^3\,b^2\,c\,d^3+1350\,a^2\,b^3\,c^2\,d^2+540\,a\,b^4\,c^3\,d+81\,b^5\,c^4}{4096\,a^{13}\,d^{12}-49152\,a^{12}\,b\,c\,d^{11}+270336\,a^{11}\,b^2\,c^2\,d^{10}-901120\,a^{10}\,b^3\,c^3\,d^9+2027520\,a^9\,b^4\,c^4\,d^8-3244032\,a^8\,b^5\,c^5\,d^7+3784704\,a^7\,b^6\,c^6\,d^6-3244032\,a^6\,b^7\,c^7\,d^5+2027520\,a^5\,b^8\,c^8\,d^4-901120\,a^4\,b^9\,c^9\,d^3+270336\,a^3\,b^{10}\,c^{10}\,d^2-49152\,a^2\,b^{11}\,c^{11}\,d+4096\,a\,b^{12}\,c^{12}}\right)}^{1/4}-\mathrm{atan}\left(\frac{\left({\left(-\frac{81\,a^4\,d^5+540\,a^3\,b\,c\,d^4+1350\,a^2\,b^2\,c^2\,d^3+1500\,a\,b^3\,c^3\,d^2+625\,b^4\,c^4\,d}{4096\,a^{12}\,c\,d^{12}-49152\,a^{11}\,b\,c^2\,d^{11}+270336\,a^{10}\,b^2\,c^3\,d^{10}-901120\,a^9\,b^3\,c^4\,d^9+2027520\,a^8\,b^4\,c^5\,d^8-3244032\,a^7\,b^5\,c^6\,d^7+3784704\,a^6\,b^6\,c^7\,d^6-3244032\,a^5\,b^7\,c^8\,d^5+2027520\,a^4\,b^8\,c^9\,d^4-901120\,a^3\,b^9\,c^{10}\,d^3+270336\,a^2\,b^{10}\,c^{11}\,d^2-49152\,a\,b^{11}\,c^{12}\,d+4096\,b^{12}\,c^{13}}\right)}^{3/4}\,\left(\frac{864\,a^{17}\,b^4\,c\,d^{20}-5184\,a^{16}\,b^5\,c^2\,d^{19}+3200\,a^{15}\,b^6\,c^3\,d^{18}+56640\,a^{14}\,b^7\,c^4\,d^{17}-220800\,a^{13}\,b^8\,c^5\,d^{16}+369088\,a^{12}\,b^9\,c^6\,d^{15}-240768\,a^{11}\,b^{10}\,c^7\,d^{14}-158400\,a^{10}\,b^{11}\,c^8\,d^{13}+390720\,a^9\,b^{12}\,c^9\,d^{12}-158400\,a^8\,b^{13}\,c^{10}\,d^{11}-240768\,a^7\,b^{14}\,c^{11}\,d^{10}+369088\,a^6\,b^{15}\,c^{12}\,d^9-220800\,a^5\,b^{16}\,c^{13}\,d^8+56640\,a^4\,b^{17}\,c^{14}\,d^7+3200\,a^3\,b^{18}\,c^{15}\,d^6-5184\,a^2\,b^{19}\,c^{16}\,d^5+864\,a\,b^{20}\,c^{17}\,d^4}{a^{14}\,d^{14}-14\,a^{13}\,b\,c\,d^{13}+91\,a^{12}\,b^2\,c^2\,d^{12}-364\,a^{11}\,b^3\,c^3\,d^{11}+1001\,a^{10}\,b^4\,c^4\,d^{10}-2002\,a^9\,b^5\,c^5\,d^9+3003\,a^8\,b^6\,c^6\,d^8-3432\,a^7\,b^7\,c^7\,d^7+3003\,a^6\,b^8\,c^8\,d^6-2002\,a^5\,b^9\,c^9\,d^5+1001\,a^4\,b^{10}\,c^{10}\,d^4-364\,a^3\,b^{11}\,c^{11}\,d^3+91\,a^2\,b^{12}\,c^{12}\,d^2-14\,a\,b^{13}\,c^{13}\,d+b^{14}\,c^{14}}-\frac{\sqrt{x}\,{\left(-\frac{81\,a^4\,d^5+540\,a^3\,b\,c\,d^4+1350\,a^2\,b^2\,c^2\,d^3+1500\,a\,b^3\,c^3\,d^2+625\,b^4\,c^4\,d}{4096\,a^{12}\,c\,d^{12}-49152\,a^{11}\,b\,c^2\,d^{11}+270336\,a^{10}\,b^2\,c^3\,d^{10}-901120\,a^9\,b^3\,c^4\,d^9+2027520\,a^8\,b^4\,c^5\,d^8-3244032\,a^7\,b^5\,c^6\,d^7+3784704\,a^6\,b^6\,c^7\,d^6-3244032\,a^5\,b^7\,c^8\,d^5+2027520\,a^4\,b^8\,c^9\,d^4-901120\,a^3\,b^9\,c^{10}\,d^3+270336\,a^2\,b^{10}\,c^{11}\,d^2-49152\,a\,b^{11}\,c^{12}\,d+4096\,b^{12}\,c^{13}}\right)}^{1/4}\,\left(36864\,a^{17}\,b^4\,c\,d^{20}-319488\,a^{16}\,b^5\,c^2\,d^{19}+1163264\,a^{15}\,b^6\,c^3\,d^{18}-2334720\,a^{14}\,b^7\,c^4\,d^{17}+3293184\,a^{13}\,b^8\,c^5\,d^{16}-5758976\,a^{12}\,b^9\,c^6\,d^{15}+13516800\,a^{11}\,b^{10}\,c^7\,d^{14}-25141248\,a^{10}\,b^{11}\,c^8\,d^{13}+31088640\,a^9\,b^{12}\,c^9\,d^{12}-25141248\,a^8\,b^{13}\,c^{10}\,d^{11}+13516800\,a^7\,b^{14}\,c^{11}\,d^{10}-5758976\,a^6\,b^{15}\,c^{12}\,d^9+3293184\,a^5\,b^{16}\,c^{13}\,d^8-2334720\,a^4\,b^{17}\,c^{14}\,d^7+1163264\,a^3\,b^{18}\,c^{15}\,d^6-319488\,a^2\,b^{19}\,c^{16}\,d^5+36864\,a\,b^{20}\,c^{17}\,d^4\right)}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)\,1{}\mathrm{i}-\frac{\sqrt{x}\,\left(5625\,a^8\,b^5\,c\,d^{12}+34275\,a^7\,b^6\,c^2\,d^{11}+88705\,a^6\,b^7\,c^3\,d^{10}+133539\,a^5\,b^8\,c^4\,d^9+133539\,a^4\,b^9\,c^5\,d^8+88705\,a^3\,b^{10}\,c^6\,d^7+34275\,a^2\,b^{11}\,c^7\,d^6+5625\,a\,b^{12}\,c^8\,d^5\right)\,1{}\mathrm{i}}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)\,{\left(-\frac{81\,a^4\,d^5+540\,a^3\,b\,c\,d^4+1350\,a^2\,b^2\,c^2\,d^3+1500\,a\,b^3\,c^3\,d^2+625\,b^4\,c^4\,d}{4096\,a^{12}\,c\,d^{12}-49152\,a^{11}\,b\,c^2\,d^{11}+270336\,a^{10}\,b^2\,c^3\,d^{10}-901120\,a^9\,b^3\,c^4\,d^9+2027520\,a^8\,b^4\,c^5\,d^8-3244032\,a^7\,b^5\,c^6\,d^7+3784704\,a^6\,b^6\,c^7\,d^6-3244032\,a^5\,b^7\,c^8\,d^5+2027520\,a^4\,b^8\,c^9\,d^4-901120\,a^3\,b^9\,c^{10}\,d^3+270336\,a^2\,b^{10}\,c^{11}\,d^2-49152\,a\,b^{11}\,c^{12}\,d+4096\,b^{12}\,c^{13}}\right)}^{1/4}-\left({\left(-\frac{81\,a^4\,d^5+540\,a^3\,b\,c\,d^4+1350\,a^2\,b^2\,c^2\,d^3+1500\,a\,b^3\,c^3\,d^2+625\,b^4\,c^4\,d}{4096\,a^{12}\,c\,d^{12}-49152\,a^{11}\,b\,c^2\,d^{11}+270336\,a^{10}\,b^2\,c^3\,d^{10}-901120\,a^9\,b^3\,c^4\,d^9+2027520\,a^8\,b^4\,c^5\,d^8-3244032\,a^7\,b^5\,c^6\,d^7+3784704\,a^6\,b^6\,c^7\,d^6-3244032\,a^5\,b^7\,c^8\,d^5+2027520\,a^4\,b^8\,c^9\,d^4-901120\,a^3\,b^9\,c^{10}\,d^3+270336\,a^2\,b^{10}\,c^{11}\,d^2-49152\,a\,b^{11}\,c^{12}\,d+4096\,b^{12}\,c^{13}}\right)}^{3/4}\,\left(\frac{864\,a^{17}\,b^4\,c\,d^{20}-5184\,a^{16}\,b^5\,c^2\,d^{19}+3200\,a^{15}\,b^6\,c^3\,d^{18}+56640\,a^{14}\,b^7\,c^4\,d^{17}-220800\,a^{13}\,b^8\,c^5\,d^{16}+369088\,a^{12}\,b^9\,c^6\,d^{15}-240768\,a^{11}\,b^{10}\,c^7\,d^{14}-158400\,a^{10}\,b^{11}\,c^8\,d^{13}+390720\,a^9\,b^{12}\,c^9\,d^{12}-158400\,a^8\,b^{13}\,c^{10}\,d^{11}-240768\,a^7\,b^{14}\,c^{11}\,d^{10}+369088\,a^6\,b^{15}\,c^{12}\,d^9-220800\,a^5\,b^{16}\,c^{13}\,d^8+56640\,a^4\,b^{17}\,c^{14}\,d^7+3200\,a^3\,b^{18}\,c^{15}\,d^6-5184\,a^2\,b^{19}\,c^{16}\,d^5+864\,a\,b^{20}\,c^{17}\,d^4}{a^{14}\,d^{14}-14\,a^{13}\,b\,c\,d^{13}+91\,a^{12}\,b^2\,c^2\,d^{12}-364\,a^{11}\,b^3\,c^3\,d^{11}+1001\,a^{10}\,b^4\,c^4\,d^{10}-2002\,a^9\,b^5\,c^5\,d^9+3003\,a^8\,b^6\,c^6\,d^8-3432\,a^7\,b^7\,c^7\,d^7+3003\,a^6\,b^8\,c^8\,d^6-2002\,a^5\,b^9\,c^9\,d^5+1001\,a^4\,b^{10}\,c^{10}\,d^4-364\,a^3\,b^{11}\,c^{11}\,d^3+91\,a^2\,b^{12}\,c^{12}\,d^2-14\,a\,b^{13}\,c^{13}\,d+b^{14}\,c^{14}}+\frac{\sqrt{x}\,{\left(-\frac{81\,a^4\,d^5+540\,a^3\,b\,c\,d^4+1350\,a^2\,b^2\,c^2\,d^3+1500\,a\,b^3\,c^3\,d^2+625\,b^4\,c^4\,d}{4096\,a^{12}\,c\,d^{12}-49152\,a^{11}\,b\,c^2\,d^{11}+270336\,a^{10}\,b^2\,c^3\,d^{10}-901120\,a^9\,b^3\,c^4\,d^9+2027520\,a^8\,b^4\,c^5\,d^8-3244032\,a^7\,b^5\,c^6\,d^7+3784704\,a^6\,b^6\,c^7\,d^6-3244032\,a^5\,b^7\,c^8\,d^5+2027520\,a^4\,b^8\,c^9\,d^4-901120\,a^3\,b^9\,c^{10}\,d^3+270336\,a^2\,b^{10}\,c^{11}\,d^2-49152\,a\,b^{11}\,c^{12}\,d+4096\,b^{12}\,c^{13}}\right)}^{1/4}\,\left(36864\,a^{17}\,b^4\,c\,d^{20}-319488\,a^{16}\,b^5\,c^2\,d^{19}+1163264\,a^{15}\,b^6\,c^3\,d^{18}-2334720\,a^{14}\,b^7\,c^4\,d^{17}+3293184\,a^{13}\,b^8\,c^5\,d^{16}-5758976\,a^{12}\,b^9\,c^6\,d^{15}+13516800\,a^{11}\,b^{10}\,c^7\,d^{14}-25141248\,a^{10}\,b^{11}\,c^8\,d^{13}+31088640\,a^9\,b^{12}\,c^9\,d^{12}-25141248\,a^8\,b^{13}\,c^{10}\,d^{11}+13516800\,a^7\,b^{14}\,c^{11}\,d^{10}-5758976\,a^6\,b^{15}\,c^{12}\,d^9+3293184\,a^5\,b^{16}\,c^{13}\,d^8-2334720\,a^4\,b^{17}\,c^{14}\,d^7+1163264\,a^3\,b^{18}\,c^{15}\,d^6-319488\,a^2\,b^{19}\,c^{16}\,d^5+36864\,a\,b^{20}\,c^{17}\,d^4\right)}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)\,1{}\mathrm{i}+\frac{\sqrt{x}\,\left(5625\,a^8\,b^5\,c\,d^{12}+34275\,a^7\,b^6\,c^2\,d^{11}+88705\,a^6\,b^7\,c^3\,d^{10}+133539\,a^5\,b^8\,c^4\,d^9+133539\,a^4\,b^9\,c^5\,d^8+88705\,a^3\,b^{10}\,c^6\,d^7+34275\,a^2\,b^{11}\,c^7\,d^6+5625\,a\,b^{12}\,c^8\,d^5\right)\,1{}\mathrm{i}}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)\,{\left(-\frac{81\,a^4\,d^5+540\,a^3\,b\,c\,d^4+1350\,a^2\,b^2\,c^2\,d^3+1500\,a\,b^3\,c^3\,d^2+625\,b^4\,c^4\,d}{4096\,a^{12}\,c\,d^{12}-49152\,a^{11}\,b\,c^2\,d^{11}+270336\,a^{10}\,b^2\,c^3\,d^{10}-901120\,a^9\,b^3\,c^4\,d^9+2027520\,a^8\,b^4\,c^5\,d^8-3244032\,a^7\,b^5\,c^6\,d^7+3784704\,a^6\,b^6\,c^7\,d^6-3244032\,a^5\,b^7\,c^8\,d^5+2027520\,a^4\,b^8\,c^9\,d^4-901120\,a^3\,b^9\,c^{10}\,d^3+270336\,a^2\,b^{10}\,c^{11}\,d^2-49152\,a\,b^{11}\,c^{12}\,d+4096\,b^{12}\,c^{13}}\right)}^{1/4}}{\left({\left(-\frac{81\,a^4\,d^5+540\,a^3\,b\,c\,d^4+1350\,a^2\,b^2\,c^2\,d^3+1500\,a\,b^3\,c^3\,d^2+625\,b^4\,c^4\,d}{4096\,a^{12}\,c\,d^{12}-49152\,a^{11}\,b\,c^2\,d^{11}+270336\,a^{10}\,b^2\,c^3\,d^{10}-901120\,a^9\,b^3\,c^4\,d^9+2027520\,a^8\,b^4\,c^5\,d^8-3244032\,a^7\,b^5\,c^6\,d^7+3784704\,a^6\,b^6\,c^7\,d^6-3244032\,a^5\,b^7\,c^8\,d^5+2027520\,a^4\,b^8\,c^9\,d^4-901120\,a^3\,b^9\,c^{10}\,d^3+270336\,a^2\,b^{10}\,c^{11}\,d^2-49152\,a\,b^{11}\,c^{12}\,d+4096\,b^{12}\,c^{13}}\right)}^{3/4}\,\left(\frac{864\,a^{17}\,b^4\,c\,d^{20}-5184\,a^{16}\,b^5\,c^2\,d^{19}+3200\,a^{15}\,b^6\,c^3\,d^{18}+56640\,a^{14}\,b^7\,c^4\,d^{17}-220800\,a^{13}\,b^8\,c^5\,d^{16}+369088\,a^{12}\,b^9\,c^6\,d^{15}-240768\,a^{11}\,b^{10}\,c^7\,d^{14}-158400\,a^{10}\,b^{11}\,c^8\,d^{13}+390720\,a^9\,b^{12}\,c^9\,d^{12}-158400\,a^8\,b^{13}\,c^{10}\,d^{11}-240768\,a^7\,b^{14}\,c^{11}\,d^{10}+369088\,a^6\,b^{15}\,c^{12}\,d^9-220800\,a^5\,b^{16}\,c^{13}\,d^8+56640\,a^4\,b^{17}\,c^{14}\,d^7+3200\,a^3\,b^{18}\,c^{15}\,d^6-5184\,a^2\,b^{19}\,c^{16}\,d^5+864\,a\,b^{20}\,c^{17}\,d^4}{a^{14}\,d^{14}-14\,a^{13}\,b\,c\,d^{13}+91\,a^{12}\,b^2\,c^2\,d^{12}-364\,a^{11}\,b^3\,c^3\,d^{11}+1001\,a^{10}\,b^4\,c^4\,d^{10}-2002\,a^9\,b^5\,c^5\,d^9+3003\,a^8\,b^6\,c^6\,d^8-3432\,a^7\,b^7\,c^7\,d^7+3003\,a^6\,b^8\,c^8\,d^6-2002\,a^5\,b^9\,c^9\,d^5+1001\,a^4\,b^{10}\,c^{10}\,d^4-364\,a^3\,b^{11}\,c^{11}\,d^3+91\,a^2\,b^{12}\,c^{12}\,d^2-14\,a\,b^{13}\,c^{13}\,d+b^{14}\,c^{14}}-\frac{\sqrt{x}\,{\left(-\frac{81\,a^4\,d^5+540\,a^3\,b\,c\,d^4+1350\,a^2\,b^2\,c^2\,d^3+1500\,a\,b^3\,c^3\,d^2+625\,b^4\,c^4\,d}{4096\,a^{12}\,c\,d^{12}-49152\,a^{11}\,b\,c^2\,d^{11}+270336\,a^{10}\,b^2\,c^3\,d^{10}-901120\,a^9\,b^3\,c^4\,d^9+2027520\,a^8\,b^4\,c^5\,d^8-3244032\,a^7\,b^5\,c^6\,d^7+3784704\,a^6\,b^6\,c^7\,d^6-3244032\,a^5\,b^7\,c^8\,d^5+2027520\,a^4\,b^8\,c^9\,d^4-901120\,a^3\,b^9\,c^{10}\,d^3+270336\,a^2\,b^{10}\,c^{11}\,d^2-49152\,a\,b^{11}\,c^{12}\,d+4096\,b^{12}\,c^{13}}\right)}^{1/4}\,\left(36864\,a^{17}\,b^4\,c\,d^{20}-319488\,a^{16}\,b^5\,c^2\,d^{19}+1163264\,a^{15}\,b^6\,c^3\,d^{18}-2334720\,a^{14}\,b^7\,c^4\,d^{17}+3293184\,a^{13}\,b^8\,c^5\,d^{16}-5758976\,a^{12}\,b^9\,c^6\,d^{15}+13516800\,a^{11}\,b^{10}\,c^7\,d^{14}-25141248\,a^{10}\,b^{11}\,c^8\,d^{13}+31088640\,a^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5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)\,{\left(-\frac{81\,a^4\,d^5+540\,a^3\,b\,c\,d^4+1350\,a^2\,b^2\,c^2\,d^3+1500\,a\,b^3\,c^3\,d^2+625\,b^4\,c^4\,d}{4096\,a^{12}\,c\,d^{12}-49152\,a^{11}\,b\,c^2\,d^{11}+270336\,a^{10}\,b^2\,c^3\,d^{10}-901120\,a^9\,b^3\,c^4\,d^9+2027520\,a^8\,b^4\,c^5\,d^8-3244032\,a^7\,b^5\,c^6\,d^7+3784704\,a^6\,b^6\,c^7\,d^6-3244032\,a^5\,b^7\,c^8\,d^5+2027520\,a^4\,b^8\,c^9\,d^4-901120\,a^3\,b^9\,c^{10}\,d^3+270336\,a^2\,b^{10}\,c^{11}\,d^2-49152\,a\,b^{11}\,c^{12}\,d+4096\,b^{12}\,c^{13}}\right)}^{1/4}+\frac{\frac{16875\,a^8\,b^5\,c\,d^{12}}{64}+\frac{131625\,a^7\,b^6\,c^2\,d^{11}}{64}+\frac{425475\,a^6\,b^7\,c^3\,d^{10}}{64}+\frac{736745\,a^5\,b^8\,c^4\,d^9}{64}+\frac{736745\,a^4\,b^9\,c^5\,d^8}{64}+\frac{425475\,a^3\,b^{10}\,c^6\,d^7}{64}+\frac{131625\,a^2\,b^{11}\,c^7\,d^6}{64}+\frac{16875\,a\,b^{12}\,c^8\,d^5}{64}}{a^{14}\,d^{14}-14\,a^{13}\,b\,c\,d^{13}+91\,a^{12}\,b^2\,c^2\,d^{12}-364\,a^{11}\,b^3\,c^3\,d^{11}+1001\,a^{10}\,b^4\,c^4\,d^{10}-2002\,a^9\,b^5\,c^5\,d^9+3003\,a^8\,b^6\,c^6\,d^8-3432\,a^7\,b^7\,c^7\,d^7+3003\,a^6\,b^8\,c^8\,d^6-2002\,a^5\,b^9\,c^9\,d^5+1001\,a^4\,b^{10}\,c^{10}\,d^4-364\,a^3\,b^{11}\,c^{11}\,d^3+91\,a^2\,b^{12}\,c^{12}\,d^2-14\,a\,b^{13}\,c^{13}\,d+b^{14}\,c^{14}}}\right)\,{\left(-\frac{81\,a^4\,d^5+540\,a^3\,b\,c\,d^4+1350\,a^2\,b^2\,c^2\,d^3+1500\,a\,b^3\,c^3\,d^2+625\,b^4\,c^4\,d}{4096\,a^{12}\,c\,d^{12}-49152\,a^{11}\,b\,c^2\,d^{11}+270336\,a^{10}\,b^2\,c^3\,d^{10}-901120\,a^9\,b^3\,c^4\,d^9+2027520\,a^8\,b^4\,c^5\,d^8-3244032\,a^7\,b^5\,c^6\,d^7+3784704\,a^6\,b^6\,c^7\,d^6-3244032\,a^5\,b^7\,c^8\,d^5+2027520\,a^4\,b^8\,c^9\,d^4-901120\,a^3\,b^9\,c^{10}\,d^3+270336\,a^2\,b^{10}\,c^{11}\,d^2-49152\,a\,b^{11}\,c^{12}\,d+4096\,b^{12}\,c^{13}}\right)}^{1/4}\,2{}\mathrm{i}+2\,\mathrm{atan}\left(\frac{\left({\left(-\frac{81\,a^4\,d^5+540\,a^3\,b\,c\,d^4+1350\,a^2\,b^2\,c^2\,d^3+1500\,a\,b^3\,c^3\,d^2+625\,b^4\,c^4\,d}{4096\,a^{12}\,c\,d^{12}-49152\,a^{11}\,b\,c^2\,d^{11}+270336\,a^{10}\,b^2\,c^3\,d^{10}-901120\,a^9\,b^3\,c^4\,d^9+2027520\,a^8\,b^4\,c^5\,d^8-3244032\,a^7\,b^5\,c^6\,d^7+3784704\,a^6\,b^6\,c^7\,d^6-3244032\,a^5\,b^7\,c^8\,d^5+2027520\,a^4\,b^8\,c^9\,d^4-901120\,a^3\,b^9\,c^{10}\,d^3+270336\,a^2\,b^{10}\,c^{11}\,d^2-49152\,a\,b^{11}\,c^{12}\,d+4096\,b^{12}\,c^{13}}\right)}^{3/4}\,\left(-\frac{\sqrt{x}\,{\left(-\frac{81\,a^4\,d^5+540\,a^3\,b\,c\,d^4+1350\,a^2\,b^2\,c^2\,d^3+1500\,a\,b^3\,c^3\,d^2+625\,b^4\,c^4\,d}{4096\,a^{12}\,c\,d^{12}-49152\,a^{11}\,b\,c^2\,d^{11}+270336\,a^{10}\,b^2\,c^3\,d^{10}-901120\,a^9\,b^3\,c^4\,d^9+2027520\,a^8\,b^4\,c^5\,d^8-3244032\,a^7\,b^5\,c^6\,d^7+3784704\,a^6\,b^6\,c^7\,d^6-3244032\,a^5\,b^7\,c^8\,d^5+2027520\,a^4\,b^8\,c^9\,d^4-901120\,a^3\,b^9\,c^{10}\,d^3+270336\,a^2\,b^{10}\,c^{11}\,d^2-49152\,a\,b^{11}\,c^{12}\,d+4096\,b^{12}\,c^{13}}\right)}^{1/4}\,\left(36864\,a^{17}\,b^4\,c\,d^{20}-319488\,a^{16}\,b^5\,c^2\,d^{19}+1163264\,a^{15}\,b^6\,c^3\,d^{18}-2334720\,a^{14}\,b^7\,c^4\,d^{17}+3293184\,a^{13}\,b^8\,c^5\,d^{16}-5758976\,a^{12}\,b^9\,c^6\,d^{15}+13516800\,a^{11}\,b^{10}\,c^7\,d^{14}-25141248\,a^{10}\,b^{11}\,c^8\,d^{13}+31088640\,a^9\,b^{12}\,c^9\,d^{12}-25141248\,a^8\,b^{13}\,c^{10}\,d^{11}+13516800\,a^7\,b^{14}\,c^{11}\,d^{10}-5758976\,a^6\,b^{15}\,c^{12}\,d^9+3293184\,a^5\,b^{16}\,c^{13}\,d^8-2334720\,a^4\,b^{17}\,c^{14}\,d^7+1163264\,a^3\,b^{18}\,c^{15}\,d^6-319488\,a^2\,b^{19}\,c^{16}\,d^5+36864\,a\,b^{20}\,c^{17}\,d^4\right)}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}+\frac{\left(864\,a^{17}\,b^4\,c\,d^{20}-5184\,a^{16}\,b^5\,c^2\,d^{19}+3200\,a^{15}\,b^6\,c^3\,d^{18}+56640\,a^{14}\,b^7\,c^4\,d^{17}-220800\,a^{13}\,b^8\,c^5\,d^{16}+369088\,a^{12}\,b^9\,c^6\,d^{15}-240768\,a^{11}\,b^{10}\,c^7\,d^{14}-158400\,a^{10}\,b^{11}\,c^8\,d^{13}+390720\,a^9\,b^{12}\,c^9\,d^{12}-158400\,a^8\,b^{13}\,c^{10}\,d^{11}-240768\,a^7\,b^{14}\,c^{11}\,d^{10}+369088\,a^6\,b^{15}\,c^{12}\,d^9-220800\,a^5\,b^{16}\,c^{13}\,d^8+56640\,a^4\,b^{17}\,c^{14}\,d^7+3200\,a^3\,b^{18}\,c^{15}\,d^6-5184\,a^2\,b^{19}\,c^{16}\,d^5+864\,a\,b^{20}\,c^{17}\,d^4\right)\,1{}\mathrm{i}}{a^{14}\,d^{14}-14\,a^{13}\,b\,c\,d^{13}+91\,a^{12}\,b^2\,c^2\,d^{12}-364\,a^{11}\,b^3\,c^3\,d^{11}+1001\,a^{10}\,b^4\,c^4\,d^{10}-2002\,a^9\,b^5\,c^5\,d^9+3003\,a^8\,b^6\,c^6\,d^8-3432\,a^7\,b^7\,c^7\,d^7+3003\,a^6\,b^8\,c^8\,d^6-2002\,a^5\,b^9\,c^9\,d^5+1001\,a^4\,b^{10}\,c^{10}\,d^4-364\,a^3\,b^{11}\,c^{11}\,d^3+91\,a^2\,b^{12}\,c^{12}\,d^2-14\,a\,b^{13}\,c^{13}\,d+b^{14}\,c^{14}}\right)-\frac{\sqrt{x}\,\left(5625\,a^8\,b^5\,c\,d^{12}+34275\,a^7\,b^6\,c^2\,d^{11}+88705\,a^6\,b^7\,c^3\,d^{10}+133539\,a^5\,b^8\,c^4\,d^9+133539\,a^4\,b^9\,c^5\,d^8+88705\,a^3\,b^{10}\,c^6\,d^7+34275\,a^2\,b^{11}\,c^7\,d^6+5625\,a\,b^{12}\,c^8\,d^5\right)}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)\,{\left(-\frac{81\,a^4\,d^5+540\,a^3\,b\,c\,d^4+1350\,a^2\,b^2\,c^2\,d^3+1500\,a\,b^3\,c^3\,d^2+625\,b^4\,c^4\,d}{4096\,a^{12}\,c\,d^{12}-49152\,a^{11}\,b\,c^2\,d^{11}+270336\,a^{10}\,b^2\,c^3\,d^{10}-901120\,a^9\,b^3\,c^4\,d^9+2027520\,a^8\,b^4\,c^5\,d^8-3244032\,a^7\,b^5\,c^6\,d^7+3784704\,a^6\,b^6\,c^7\,d^6-3244032\,a^5\,b^7\,c^8\,d^5+2027520\,a^4\,b^8\,c^9\,d^4-901120\,a^3\,b^9\,c^{10}\,d^3+270336\,a^2\,b^{10}\,c^{11}\,d^2-49152\,a\,b^{11}\,c^{12}\,d+4096\,b^{12}\,c^{13}}\right)}^{1/4}-\left({\left(-\frac{81\,a^4\,d^5+540\,a^3\,b\,c\,d^4+1350\,a^2\,b^2\,c^2\,d^3+1500\,a\,b^3\,c^3\,d^2+625\,b^4\,c^4\,d}{4096\,a^{12}\,c\,d^{12}-49152\,a^{11}\,b\,c^2\,d^{11}+270336\,a^{10}\,b^2\,c^3\,d^{10}-901120\,a^9\,b^3\,c^4\,d^9+2027520\,a^8\,b^4\,c^5\,d^8-3244032\,a^7\,b^5\,c^6\,d^7+3784704\,a^6\,b^6\,c^7\,d^6-3244032\,a^5\,b^7\,c^8\,d^5+2027520\,a^4\,b^8\,c^9\,d^4-901120\,a^3\,b^9\,c^{10}\,d^3+270336\,a^2\,b^{10}\,c^{11}\,d^2-49152\,a\,b^{11}\,c^{12}\,d+4096\,b^{12}\,c^{13}}\right)}^{3/4}\,\left(\frac{\sqrt{x}\,{\left(-\frac{81\,a^4\,d^5+540\,a^3\,b\,c\,d^4+1350\,a^2\,b^2\,c^2\,d^3+1500\,a\,b^3\,c^3\,d^2+625\,b^4\,c^4\,d}{4096\,a^{12}\,c\,d^{12}-49152\,a^{11}\,b\,c^2\,d^{11}+270336\,a^{10}\,b^2\,c^3\,d^{10}-901120\,a^9\,b^3\,c^4\,d^9+2027520\,a^8\,b^4\,c^5\,d^8-3244032\,a^7\,b^5\,c^6\,d^7+3784704\,a^6\,b^6\,c^7\,d^6-3244032\,a^5\,b^7\,c^8\,d^5+2027520\,a^4\,b^8\,c^9\,d^4-901120\,a^3\,b^9\,c^{10}\,d^3+270336\,a^2\,b^{10}\,c^{11}\,d^2-49152\,a\,b^{11}\,c^{12}\,d+4096\,b^{12}\,c^{13}}\right)}^{1/4}\,\left(36864\,a^{17}\,b^4\,c\,d^{20}-319488\,a^{16}\,b^5\,c^2\,d^{19}+1163264\,a^{15}\,b^6\,c^3\,d^{18}-2334720\,a^{14}\,b^7\,c^4\,d^{17}+3293184\,a^{13}\,b^8\,c^5\,d^{16}-5758976\,a^{12}\,b^9\,c^6\,d^{15}+13516800\,a^{11}\,b^{10}\,c^7\,d^{14}-25141248\,a^{10}\,b^{11}\,c^8\,d^{13}+31088640\,a^9\,b^{12}\,c^9\,d^{12}-25141248\,a^8\,b^{13}\,c^{10}\,d^{11}+13516800\,a^7\,b^{14}\,c^{11}\,d^{10}-5758976\,a^6\,b^{15}\,c^{12}\,d^9+3293184\,a^5\,b^{16}\,c^{13}\,d^8-2334720\,a^4\,b^{17}\,c^{14}\,d^7+1163264\,a^3\,b^{18}\,c^{15}\,d^6-319488\,a^2\,b^{19}\,c^{16}\,d^5+36864\,a\,b^{20}\,c^{17}\,d^4\right)}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}+\frac{\left(864\,a^{17}\,b^4\,c\,d^{20}-5184\,a^{16}\,b^5\,c^2\,d^{19}+3200\,a^{15}\,b^6\,c^3\,d^{18}+56640\,a^{14}\,b^7\,c^4\,d^{17}-220800\,a^{13}\,b^8\,c^5\,d^{16}+369088\,a^{12}\,b^9\,c^6\,d^{15}-240768\,a^{11}\,b^{10}\,c^7\,d^{14}-158400\,a^{10}\,b^{11}\,c^8\,d^{13}+390720\,a^9\,b^{12}\,c^9\,d^{12}-158400\,a^8\,b^{13}\,c^{10}\,d^{11}-240768\,a^7\,b^{14}\,c^{11}\,d^{10}+369088\,a^6\,b^{15}\,c^{12}\,d^9-220800\,a^5\,b^{16}\,c^{13}\,d^8+56640\,a^4\,b^{17}\,c^{14}\,d^7+3200\,a^3\,b^{18}\,c^{15}\,d^6-5184\,a^2\,b^{19}\,c^{16}\,d^5+864\,a\,b^{20}\,c^{17}\,d^4\right)\,1{}\mathrm{i}}{a^{14}\,d^{14}-14\,a^{13}\,b\,c\,d^{13}+91\,a^{12}\,b^2\,c^2\,d^{12}-364\,a^{11}\,b^3\,c^3\,d^{11}+1001\,a^{10}\,b^4\,c^4\,d^{10}-2002\,a^9\,b^5\,c^5\,d^9+3003\,a^8\,b^6\,c^6\,d^8-3432\,a^7\,b^7\,c^7\,d^7+3003\,a^6\,b^8\,c^8\,d^6-2002\,a^5\,b^9\,c^9\,d^5+1001\,a^4\,b^{10}\,c^{10}\,d^4-364\,a^3\,b^{11}\,c^{11}\,d^3+91\,a^2\,b^{12}\,c^{12}\,d^2-14\,a\,b^{13}\,c^{13}\,d+b^{14}\,c^{14}}\right)+\frac{\sqrt{x}\,\left(5625\,a^8\,b^5\,c\,d^{12}+34275\,a^7\,b^6\,c^2\,d^{11}+88705\,a^6\,b^7\,c^3\,d^{10}+133539\,a^5\,b^8\,c^4\,d^9+133539\,a^4\,b^9\,c^5\,d^8+88705\,a^3\,b^{10}\,c^6\,d^7+34275\,a^2\,b^{11}\,c^7\,d^6+5625\,a\,b^{12}\,c^8\,d^5\right)}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)\,{\left(-\frac{81\,a^4\,d^5+540\,a^3\,b\,c\,d^4+1350\,a^2\,b^2\,c^2\,d^3+1500\,a\,b^3\,c^3\,d^2+625\,b^4\,c^4\,d}{4096\,a^{12}\,c\,d^{12}-49152\,a^{11}\,b\,c^2\,d^{11}+270336\,a^{10}\,b^2\,c^3\,d^{10}-901120\,a^9\,b^3\,c^4\,d^9+2027520\,a^8\,b^4\,c^5\,d^8-3244032\,a^7\,b^5\,c^6\,d^7+3784704\,a^6\,b^6\,c^7\,d^6-3244032\,a^5\,b^7\,c^8\,d^5+2027520\,a^4\,b^8\,c^9\,d^4-901120\,a^3\,b^9\,c^{10}\,d^3+270336\,a^2\,b^{10}\,c^{11}\,d^2-49152\,a\,b^{11}\,c^{12}\,d+4096\,b^{12}\,c^{13}}\right)}^{1/4}}{\left({\left(-\frac{81\,a^4\,d^5+540\,a^3\,b\,c\,d^4+1350\,a^2\,b^2\,c^2\,d^3+1500\,a\,b^3\,c^3\,d^2+625\,b^4\,c^4\,d}{4096\,a^{12}\,c\,d^{12}-49152\,a^{11}\,b\,c^2\,d^{11}+270336\,a^{10}\,b^2\,c^3\,d^{10}-901120\,a^9\,b^3\,c^4\,d^9+2027520\,a^8\,b^4\,c^5\,d^8-3244032\,a^7\,b^5\,c^6\,d^7+3784704\,a^6\,b^6\,c^7\,d^6-3244032\,a^5\,b^7\,c^8\,d^5+2027520\,a^4\,b^8\,c^9\,d^4-901120\,a^3\,b^9\,c^{10}\,d^3+270336\,a^2\,b^{10}\,c^{11}\,d^2-49152\,a\,b^{11}\,c^{12}\,d+4096\,b^{12}\,c^{13}}\right)}^{3/4}\,\left(-\frac{\sqrt{x}\,{\left(-\frac{81\,a^4\,d^5+540\,a^3\,b\,c\,d^4+1350\,a^2\,b^2\,c^2\,d^3+1500\,a\,b^3\,c^3\,d^2+625\,b^4\,c^4\,d}{4096\,a^{12}\,c\,d^{12}-49152\,a^{11}\,b\,c^2\,d^{11}+270336\,a^{10}\,b^2\,c^3\,d^{10}-901120\,a^9\,b^3\,c^4\,d^9+2027520\,a^8\,b^4\,c^5\,d^8-3244032\,a^7\,b^5\,c^6\,d^7+3784704\,a^6\,b^6\,c^7\,d^6-3244032\,a^5\,b^7\,c^8\,d^5+2027520\,a^4\,b^8\,c^9\,d^4-901120\,a^3\,b^9\,c^{10}\,d^3+270336\,a^2\,b^{10}\,c^{11}\,d^2-49152\,a\,b^{11}\,c^{12}\,d+4096\,b^{12}\,c^{13}}\right)}^{1/4}\,\left(36864\,a^{17}\,b^4\,c\,d^{20}-319488\,a^{16}\,b^5\,c^2\,d^{19}+1163264\,a^{15}\,b^6\,c^3\,d^{18}-2334720\,a^{14}\,b^7\,c^4\,d^{17}+3293184\,a^{13}\,b^8\,c^5\,d^{16}-5758976\,a^{12}\,b^9\,c^6\,d^{15}+13516800\,a^{11}\,b^{10}\,c^7\,d^{14}-25141248\,a^{10}\,b^{11}\,c^8\,d^{13}+31088640\,a^9\,b^{12}\,c^9\,d^{12}-25141248\,a^8\,b^{13}\,c^{10}\,d^{11}+13516800\,a^7\,b^{14}\,c^{11}\,d^{10}-5758976\,a^6\,b^{15}\,c^{12}\,d^9+3293184\,a^5\,b^{16}\,c^{13}\,d^8-2334720\,a^4\,b^{17}\,c^{14}\,d^7+1163264\,a^3\,b^{18}\,c^{15}\,d^6-319488\,a^2\,b^{19}\,c^{16}\,d^5+36864\,a\,b^{20}\,c^{17}\,d^4\right)}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}+\frac{\left(864\,a^{17}\,b^4\,c\,d^{20}-5184\,a^{16}\,b^5\,c^2\,d^{19}+3200\,a^{15}\,b^6\,c^3\,d^{18}+56640\,a^{14}\,b^7\,c^4\,d^{17}-220800\,a^{13}\,b^8\,c^5\,d^{16}+369088\,a^{12}\,b^9\,c^6\,d^{15}-240768\,a^{11}\,b^{10}\,c^7\,d^{14}-158400\,a^{10}\,b^{11}\,c^8\,d^{13}+390720\,a^9\,b^{12}\,c^9\,d^{12}-158400\,a^8\,b^{13}\,c^{10}\,d^{11}-240768\,a^7\,b^{14}\,c^{11}\,d^{10}+369088\,a^6\,b^{15}\,c^{12}\,d^9-220800\,a^5\,b^{16}\,c^{13}\,d^8+56640\,a^4\,b^{17}\,c^{14}\,d^7+3200\,a^3\,b^{18}\,c^{15}\,d^6-5184\,a^2\,b^{19}\,c^{16}\,d^5+864\,a\,b^{20}\,c^{17}\,d^4\right)\,1{}\mathrm{i}}{a^{14}\,d^{14}-14\,a^{13}\,b\,c\,d^{13}+91\,a^{12}\,b^2\,c^2\,d^{12}-364\,a^{11}\,b^3\,c^3\,d^{11}+1001\,a^{10}\,b^4\,c^4\,d^{10}-2002\,a^9\,b^5\,c^5\,d^9+3003\,a^8\,b^6\,c^6\,d^8-3432\,a^7\,b^7\,c^7\,d^7+3003\,a^6\,b^8\,c^8\,d^6-2002\,a^5\,b^9\,c^9\,d^5+1001\,a^4\,b^{10}\,c^{10}\,d^4-364\,a^3\,b^{11}\,c^{11}\,d^3+91\,a^2\,b^{12}\,c^{12}\,d^2-14\,a\,b^{13}\,c^{13}\,d+b^{14}\,c^{14}}\right)\,1{}\mathrm{i}-\frac{\sqrt{x}\,\left(5625\,a^8\,b^5\,c\,d^{12}+34275\,a^7\,b^6\,c^2\,d^{11}+88705\,a^6\,b^7\,c^3\,d^{10}+133539\,a^5\,b^8\,c^4\,d^9+133539\,a^4\,b^9\,c^5\,d^8+88705\,a^3\,b^{10}\,c^6\,d^7+34275\,a^2\,b^{11}\,c^7\,d^6+5625\,a\,b^{12}\,c^8\,d^5\right)\,1{}\mathrm{i}}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)\,{\left(-\frac{81\,a^4\,d^5+540\,a^3\,b\,c\,d^4+1350\,a^2\,b^2\,c^2\,d^3+1500\,a\,b^3\,c^3\,d^2+625\,b^4\,c^4\,d}{4096\,a^{12}\,c\,d^{12}-49152\,a^{11}\,b\,c^2\,d^{11}+270336\,a^{10}\,b^2\,c^3\,d^{10}-901120\,a^9\,b^3\,c^4\,d^9+2027520\,a^8\,b^4\,c^5\,d^8-3244032\,a^7\,b^5\,c^6\,d^7+3784704\,a^6\,b^6\,c^7\,d^6-3244032\,a^5\,b^7\,c^8\,d^5+2027520\,a^4\,b^8\,c^9\,d^4-901120\,a^3\,b^9\,c^{10}\,d^3+270336\,a^2\,b^{10}\,c^{11}\,d^2-49152\,a\,b^{11}\,c^{12}\,d+4096\,b^{12}\,c^{13}}\right)}^{1/4}+\left({\left(-\frac{81\,a^4\,d^5+540\,a^3\,b\,c\,d^4+1350\,a^2\,b^2\,c^2\,d^3+1500\,a\,b^3\,c^3\,d^2+625\,b^4\,c^4\,d}{4096\,a^{12}\,c\,d^{12}-49152\,a^{11}\,b\,c^2\,d^{11}+270336\,a^{10}\,b^2\,c^3\,d^{10}-901120\,a^9\,b^3\,c^4\,d^9+2027520\,a^8\,b^4\,c^5\,d^8-3244032\,a^7\,b^5\,c^6\,d^7+3784704\,a^6\,b^6\,c^7\,d^6-3244032\,a^5\,b^7\,c^8\,d^5+2027520\,a^4\,b^8\,c^9\,d^4-901120\,a^3\,b^9\,c^{10}\,d^3+270336\,a^2\,b^{10}\,c^{11}\,d^2-49152\,a\,b^{11}\,c^{12}\,d+4096\,b^{12}\,c^{13}}\right)}^{3/4}\,\left(\frac{\sqrt{x}\,{\left(-\frac{81\,a^4\,d^5+540\,a^3\,b\,c\,d^4+1350\,a^2\,b^2\,c^2\,d^3+1500\,a\,b^3\,c^3\,d^2+625\,b^4\,c^4\,d}{4096\,a^{12}\,c\,d^{12}-49152\,a^{11}\,b\,c^2\,d^{11}+270336\,a^{10}\,b^2\,c^3\,d^{10}-901120\,a^9\,b^3\,c^4\,d^9+2027520\,a^8\,b^4\,c^5\,d^8-3244032\,a^7\,b^5\,c^6\,d^7+3784704\,a^6\,b^6\,c^7\,d^6-3244032\,a^5\,b^7\,c^8\,d^5+2027520\,a^4\,b^8\,c^9\,d^4-901120\,a^3\,b^9\,c^{10}\,d^3+270336\,a^2\,b^{10}\,c^{11}\,d^2-49152\,a\,b^{11}\,c^{12}\,d+4096\,b^{12}\,c^{13}}\right)}^{1/4}\,\left(36864\,a^{17}\,b^4\,c\,d^{20}-319488\,a^{16}\,b^5\,c^2\,d^{19}+1163264\,a^{15}\,b^6\,c^3\,d^{18}-2334720\,a^{14}\,b^7\,c^4\,d^{17}+3293184\,a^{13}\,b^8\,c^5\,d^{16}-5758976\,a^{12}\,b^9\,c^6\,d^{15}+13516800\,a^{11}\,b^{10}\,c^7\,d^{14}-25141248\,a^{10}\,b^{11}\,c^8\,d^{13}+31088640\,a^9\,b^{12}\,c^9\,d^{12}-25141248\,a^8\,b^{13}\,c^{10}\,d^{11}+13516800\,a^7\,b^{14}\,c^{11}\,d^{10}-5758976\,a^6\,b^{15}\,c^{12}\,d^9+3293184\,a^5\,b^{16}\,c^{13}\,d^8-2334720\,a^4\,b^{17}\,c^{14}\,d^7+1163264\,a^3\,b^{18}\,c^{15}\,d^6-319488\,a^2\,b^{19}\,c^{16}\,d^5+36864\,a\,b^{20}\,c^{17}\,d^4\right)}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}+\frac{\left(864\,a^{17}\,b^4\,c\,d^{20}-5184\,a^{16}\,b^5\,c^2\,d^{19}+3200\,a^{15}\,b^6\,c^3\,d^{18}+56640\,a^{14}\,b^7\,c^4\,d^{17}-220800\,a^{13}\,b^8\,c^5\,d^{16}+369088\,a^{12}\,b^9\,c^6\,d^{15}-240768\,a^{11}\,b^{10}\,c^7\,d^{14}-158400\,a^{10}\,b^{11}\,c^8\,d^{13}+390720\,a^9\,b^{12}\,c^9\,d^{12}-158400\,a^8\,b^{13}\,c^{10}\,d^{11}-240768\,a^7\,b^{14}\,c^{11}\,d^{10}+369088\,a^6\,b^{15}\,c^{12}\,d^9-220800\,a^5\,b^{16}\,c^{13}\,d^8+56640\,a^4\,b^{17}\,c^{14}\,d^7+3200\,a^3\,b^{18}\,c^{15}\,d^6-5184\,a^2\,b^{19}\,c^{16}\,d^5+864\,a\,b^{20}\,c^{17}\,d^4\right)\,1{}\mathrm{i}}{a^{14}\,d^{14}-14\,a^{13}\,b\,c\,d^{13}+91\,a^{12}\,b^2\,c^2\,d^{12}-364\,a^{11}\,b^3\,c^3\,d^{11}+1001\,a^{10}\,b^4\,c^4\,d^{10}-2002\,a^9\,b^5\,c^5\,d^9+3003\,a^8\,b^6\,c^6\,d^8-3432\,a^7\,b^7\,c^7\,d^7+3003\,a^6\,b^8\,c^8\,d^6-2002\,a^5\,b^9\,c^9\,d^5+1001\,a^4\,b^{10}\,c^{10}\,d^4-364\,a^3\,b^{11}\,c^{11}\,d^3+91\,a^2\,b^{12}\,c^{12}\,d^2-14\,a\,b^{13}\,c^{13}\,d+b^{14}\,c^{14}}\right)\,1{}\mathrm{i}+\frac{\sqrt{x}\,\left(5625\,a^8\,b^5\,c\,d^{12}+34275\,a^7\,b^6\,c^2\,d^{11}+88705\,a^6\,b^7\,c^3\,d^{10}+133539\,a^5\,b^8\,c^4\,d^9+133539\,a^4\,b^9\,c^5\,d^8+88705\,a^3\,b^{10}\,c^6\,d^7+34275\,a^2\,b^{11}\,c^7\,d^6+5625\,a\,b^{12}\,c^8\,d^5\right)\,1{}\mathrm{i}}{16\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)\,{\left(-\frac{81\,a^4\,d^5+540\,a^3\,b\,c\,d^4+1350\,a^2\,b^2\,c^2\,d^3+1500\,a\,b^3\,c^3\,d^2+625\,b^4\,c^4\,d}{4096\,a^{12}\,c\,d^{12}-49152\,a^{11}\,b\,c^2\,d^{11}+270336\,a^{10}\,b^2\,c^3\,d^{10}-901120\,a^9\,b^3\,c^4\,d^9+2027520\,a^8\,b^4\,c^5\,d^8-3244032\,a^7\,b^5\,c^6\,d^7+3784704\,a^6\,b^6\,c^7\,d^6-3244032\,a^5\,b^7\,c^8\,d^5+2027520\,a^4\,b^8\,c^9\,d^4-901120\,a^3\,b^9\,c^{10}\,d^3+270336\,a^2\,b^{10}\,c^{11}\,d^2-49152\,a\,b^{11}\,c^{12}\,d+4096\,b^{12}\,c^{13}}\right)}^{1/4}-\frac{\frac{16875\,a^8\,b^5\,c\,d^{12}}{64}+\frac{131625\,a^7\,b^6\,c^2\,d^{11}}{64}+\frac{425475\,a^6\,b^7\,c^3\,d^{10}}{64}+\frac{736745\,a^5\,b^8\,c^4\,d^9}{64}+\frac{736745\,a^4\,b^9\,c^5\,d^8}{64}+\frac{425475\,a^3\,b^{10}\,c^6\,d^7}{64}+\frac{131625\,a^2\,b^{11}\,c^7\,d^6}{64}+\frac{16875\,a\,b^{12}\,c^8\,d^5}{64}}{a^{14}\,d^{14}-14\,a^{13}\,b\,c\,d^{13}+91\,a^{12}\,b^2\,c^2\,d^{12}-364\,a^{11}\,b^3\,c^3\,d^{11}+1001\,a^{10}\,b^4\,c^4\,d^{10}-2002\,a^9\,b^5\,c^5\,d^9+3003\,a^8\,b^6\,c^6\,d^8-3432\,a^7\,b^7\,c^7\,d^7+3003\,a^6\,b^8\,c^8\,d^6-2002\,a^5\,b^9\,c^9\,d^5+1001\,a^4\,b^{10}\,c^{10}\,d^4-364\,a^3\,b^{11}\,c^{11}\,d^3+91\,a^2\,b^{12}\,c^{12}\,d^2-14\,a\,b^{13}\,c^{13}\,d+b^{14}\,c^{14}}}\right)\,{\left(-\frac{81\,a^4\,d^5+540\,a^3\,b\,c\,d^4+1350\,a^2\,b^2\,c^2\,d^3+1500\,a\,b^3\,c^3\,d^2+625\,b^4\,c^4\,d}{4096\,a^{12}\,c\,d^{12}-49152\,a^{11}\,b\,c^2\,d^{11}+270336\,a^{10}\,b^2\,c^3\,d^{10}-901120\,a^9\,b^3\,c^4\,d^9+2027520\,a^8\,b^4\,c^5\,d^8-3244032\,a^7\,b^5\,c^6\,d^7+3784704\,a^6\,b^6\,c^7\,d^6-3244032\,a^5\,b^7\,c^8\,d^5+2027520\,a^4\,b^8\,c^9\,d^4-901120\,a^3\,b^9\,c^{10}\,d^3+270336\,a^2\,b^{10}\,c^{11}\,d^2-49152\,a\,b^{11}\,c^{12}\,d+4096\,b^{12}\,c^{13}}\right)}^{1/4}","Not used",1,"2*atan((((-(81*b^5*c^4 + 625*a^4*b*d^4 + 1500*a^3*b^2*c*d^3 + 1350*a^2*b^3*c^2*d^2 + 540*a*b^4*c^3*d)/(4096*a^13*d^12 + 4096*a*b^12*c^12 - 49152*a^2*b^11*c^11*d + 270336*a^3*b^10*c^10*d^2 - 901120*a^4*b^9*c^9*d^3 + 2027520*a^5*b^8*c^8*d^4 - 3244032*a^6*b^7*c^7*d^5 + 3784704*a^7*b^6*c^6*d^6 - 3244032*a^8*b^5*c^5*d^7 + 2027520*a^9*b^4*c^4*d^8 - 901120*a^10*b^3*c^3*d^9 + 270336*a^11*b^2*c^2*d^10 - 49152*a^12*b*c*d^11))^(3/4)*(((864*a*b^20*c^17*d^4 + 864*a^17*b^4*c*d^20 - 5184*a^2*b^19*c^16*d^5 + 3200*a^3*b^18*c^15*d^6 + 56640*a^4*b^17*c^14*d^7 - 220800*a^5*b^16*c^13*d^8 + 369088*a^6*b^15*c^12*d^9 - 240768*a^7*b^14*c^11*d^10 - 158400*a^8*b^13*c^10*d^11 + 390720*a^9*b^12*c^9*d^12 - 158400*a^10*b^11*c^8*d^13 - 240768*a^11*b^10*c^7*d^14 + 369088*a^12*b^9*c^6*d^15 - 220800*a^13*b^8*c^5*d^16 + 56640*a^14*b^7*c^4*d^17 + 3200*a^15*b^6*c^3*d^18 - 5184*a^16*b^5*c^2*d^19)*1i)/(a^14*d^14 + b^14*c^14 + 91*a^2*b^12*c^12*d^2 - 364*a^3*b^11*c^11*d^3 + 1001*a^4*b^10*c^10*d^4 - 2002*a^5*b^9*c^9*d^5 + 3003*a^6*b^8*c^8*d^6 - 3432*a^7*b^7*c^7*d^7 + 3003*a^8*b^6*c^6*d^8 - 2002*a^9*b^5*c^5*d^9 + 1001*a^10*b^4*c^4*d^10 - 364*a^11*b^3*c^3*d^11 + 91*a^12*b^2*c^2*d^12 - 14*a*b^13*c^13*d - 14*a^13*b*c*d^13) - (x^(1/2)*(-(81*b^5*c^4 + 625*a^4*b*d^4 + 1500*a^3*b^2*c*d^3 + 1350*a^2*b^3*c^2*d^2 + 540*a*b^4*c^3*d)/(4096*a^13*d^12 + 4096*a*b^12*c^12 - 49152*a^2*b^11*c^11*d + 270336*a^3*b^10*c^10*d^2 - 901120*a^4*b^9*c^9*d^3 + 2027520*a^5*b^8*c^8*d^4 - 3244032*a^6*b^7*c^7*d^5 + 3784704*a^7*b^6*c^6*d^6 - 3244032*a^8*b^5*c^5*d^7 + 2027520*a^9*b^4*c^4*d^8 - 901120*a^10*b^3*c^3*d^9 + 270336*a^11*b^2*c^2*d^10 - 49152*a^12*b*c*d^11))^(1/4)*(36864*a*b^20*c^17*d^4 + 36864*a^17*b^4*c*d^20 - 319488*a^2*b^19*c^16*d^5 + 1163264*a^3*b^18*c^15*d^6 - 2334720*a^4*b^17*c^14*d^7 + 3293184*a^5*b^16*c^13*d^8 - 5758976*a^6*b^15*c^12*d^9 + 13516800*a^7*b^14*c^11*d^10 - 25141248*a^8*b^13*c^10*d^11 + 31088640*a^9*b^12*c^9*d^12 - 25141248*a^10*b^11*c^8*d^13 + 13516800*a^11*b^10*c^7*d^14 - 5758976*a^12*b^9*c^6*d^15 + 3293184*a^13*b^8*c^5*d^16 - 2334720*a^14*b^7*c^4*d^17 + 1163264*a^15*b^6*c^3*d^18 - 319488*a^16*b^5*c^2*d^19))/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11))) - (x^(1/2)*(5625*a*b^12*c^8*d^5 + 5625*a^8*b^5*c*d^12 + 34275*a^2*b^11*c^7*d^6 + 88705*a^3*b^10*c^6*d^7 + 133539*a^4*b^9*c^5*d^8 + 133539*a^5*b^8*c^4*d^9 + 88705*a^6*b^7*c^3*d^10 + 34275*a^7*b^6*c^2*d^11))/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)))*(-(81*b^5*c^4 + 625*a^4*b*d^4 + 1500*a^3*b^2*c*d^3 + 1350*a^2*b^3*c^2*d^2 + 540*a*b^4*c^3*d)/(4096*a^13*d^12 + 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319488*a^2*b^19*c^16*d^5 + 1163264*a^3*b^18*c^15*d^6 - 2334720*a^4*b^17*c^14*d^7 + 3293184*a^5*b^16*c^13*d^8 - 5758976*a^6*b^15*c^12*d^9 + 13516800*a^7*b^14*c^11*d^10 - 25141248*a^8*b^13*c^10*d^11 + 31088640*a^9*b^12*c^9*d^12 - 25141248*a^10*b^11*c^8*d^13 + 13516800*a^11*b^10*c^7*d^14 - 5758976*a^12*b^9*c^6*d^15 + 3293184*a^13*b^8*c^5*d^16 - 2334720*a^14*b^7*c^4*d^17 + 1163264*a^15*b^6*c^3*d^18 - 319488*a^16*b^5*c^2*d^19))/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11))) + (x^(1/2)*(5625*a*b^12*c^8*d^5 + 5625*a^8*b^5*c*d^12 + 34275*a^2*b^11*c^7*d^6 + 88705*a^3*b^10*c^6*d^7 + 133539*a^4*b^9*c^5*d^8 + 133539*a^5*b^8*c^4*d^9 + 88705*a^6*b^7*c^3*d^10 + 34275*a^7*b^6*c^2*d^11))/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)))*(-(81*b^5*c^4 + 625*a^4*b*d^4 + 1500*a^3*b^2*c*d^3 + 1350*a^2*b^3*c^2*d^2 + 540*a*b^4*c^3*d)/(4096*a^13*d^12 + 4096*a*b^12*c^12 - 49152*a^2*b^11*c^11*d + 270336*a^3*b^10*c^10*d^2 - 901120*a^4*b^9*c^9*d^3 + 2027520*a^5*b^8*c^8*d^4 - 3244032*a^6*b^7*c^7*d^5 + 3784704*a^7*b^6*c^6*d^6 - 3244032*a^8*b^5*c^5*d^7 + 2027520*a^9*b^4*c^4*d^8 - 901120*a^10*b^3*c^3*d^9 + 270336*a^11*b^2*c^2*d^10 - 49152*a^12*b*c*d^11))^(1/4))/(((-(81*b^5*c^4 + 625*a^4*b*d^4 + 1500*a^3*b^2*c*d^3 + 1350*a^2*b^3*c^2*d^2 + 540*a*b^4*c^3*d)/(4096*a^13*d^12 + 4096*a*b^12*c^12 - 49152*a^2*b^11*c^11*d + 270336*a^3*b^10*c^10*d^2 - 901120*a^4*b^9*c^9*d^3 + 2027520*a^5*b^8*c^8*d^4 - 3244032*a^6*b^7*c^7*d^5 + 3784704*a^7*b^6*c^6*d^6 - 3244032*a^8*b^5*c^5*d^7 + 2027520*a^9*b^4*c^4*d^8 - 901120*a^10*b^3*c^3*d^9 + 270336*a^11*b^2*c^2*d^10 - 49152*a^12*b*c*d^11))^(3/4)*(((864*a*b^20*c^17*d^4 + 864*a^17*b^4*c*d^20 - 5184*a^2*b^19*c^16*d^5 + 3200*a^3*b^18*c^15*d^6 + 56640*a^4*b^17*c^14*d^7 - 220800*a^5*b^16*c^13*d^8 + 369088*a^6*b^15*c^12*d^9 - 240768*a^7*b^14*c^11*d^10 - 158400*a^8*b^13*c^10*d^11 + 390720*a^9*b^12*c^9*d^12 - 158400*a^10*b^11*c^8*d^13 - 240768*a^11*b^10*c^7*d^14 + 369088*a^12*b^9*c^6*d^15 - 220800*a^13*b^8*c^5*d^16 + 56640*a^14*b^7*c^4*d^17 + 3200*a^15*b^6*c^3*d^18 - 5184*a^16*b^5*c^2*d^19)*1i)/(a^14*d^14 + b^14*c^14 + 91*a^2*b^12*c^12*d^2 - 364*a^3*b^11*c^11*d^3 + 1001*a^4*b^10*c^10*d^4 - 2002*a^5*b^9*c^9*d^5 + 3003*a^6*b^8*c^8*d^6 - 3432*a^7*b^7*c^7*d^7 + 3003*a^8*b^6*c^6*d^8 - 2002*a^9*b^5*c^5*d^9 + 1001*a^10*b^4*c^4*d^10 - 364*a^11*b^3*c^3*d^11 + 91*a^12*b^2*c^2*d^12 - 14*a*b^13*c^13*d - 14*a^13*b*c*d^13) - (x^(1/2)*(-(81*b^5*c^4 + 625*a^4*b*d^4 + 1500*a^3*b^2*c*d^3 + 1350*a^2*b^3*c^2*d^2 + 540*a*b^4*c^3*d)/(4096*a^13*d^12 + 4096*a*b^12*c^12 - 49152*a^2*b^11*c^11*d + 270336*a^3*b^10*c^10*d^2 - 901120*a^4*b^9*c^9*d^3 + 2027520*a^5*b^8*c^8*d^4 - 3244032*a^6*b^7*c^7*d^5 + 3784704*a^7*b^6*c^6*d^6 - 3244032*a^8*b^5*c^5*d^7 + 2027520*a^9*b^4*c^4*d^8 - 901120*a^10*b^3*c^3*d^9 + 270336*a^11*b^2*c^2*d^10 - 49152*a^12*b*c*d^11))^(1/4)*(36864*a*b^20*c^17*d^4 + 36864*a^17*b^4*c*d^20 - 319488*a^2*b^19*c^16*d^5 + 1163264*a^3*b^18*c^15*d^6 - 2334720*a^4*b^17*c^14*d^7 + 3293184*a^5*b^16*c^13*d^8 - 5758976*a^6*b^15*c^12*d^9 + 13516800*a^7*b^14*c^11*d^10 - 25141248*a^8*b^13*c^10*d^11 + 31088640*a^9*b^12*c^9*d^12 - 25141248*a^10*b^11*c^8*d^13 + 13516800*a^11*b^10*c^7*d^14 - 5758976*a^12*b^9*c^6*d^15 + 3293184*a^13*b^8*c^5*d^16 - 2334720*a^14*b^7*c^4*d^17 + 1163264*a^15*b^6*c^3*d^18 - 319488*a^16*b^5*c^2*d^19))/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)))*1i - (x^(1/2)*(5625*a*b^12*c^8*d^5 + 5625*a^8*b^5*c*d^12 + 34275*a^2*b^11*c^7*d^6 + 88705*a^3*b^10*c^6*d^7 + 133539*a^4*b^9*c^5*d^8 + 133539*a^5*b^8*c^4*d^9 + 88705*a^6*b^7*c^3*d^10 + 34275*a^7*b^6*c^2*d^11)*1i)/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)))*(-(81*b^5*c^4 + 625*a^4*b*d^4 + 1500*a^3*b^2*c*d^3 + 1350*a^2*b^3*c^2*d^2 + 540*a*b^4*c^3*d)/(4096*a^13*d^12 + 4096*a*b^12*c^12 - 49152*a^2*b^11*c^11*d + 270336*a^3*b^10*c^10*d^2 - 901120*a^4*b^9*c^9*d^3 + 2027520*a^5*b^8*c^8*d^4 - 3244032*a^6*b^7*c^7*d^5 + 3784704*a^7*b^6*c^6*d^6 - 3244032*a^8*b^5*c^5*d^7 + 2027520*a^9*b^4*c^4*d^8 - 901120*a^10*b^3*c^3*d^9 + 270336*a^11*b^2*c^2*d^10 - 49152*a^12*b*c*d^11))^(1/4) + ((-(81*b^5*c^4 + 625*a^4*b*d^4 + 1500*a^3*b^2*c*d^3 + 1350*a^2*b^3*c^2*d^2 + 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3784704*a^7*b^6*c^6*d^6 - 3244032*a^8*b^5*c^5*d^7 + 2027520*a^9*b^4*c^4*d^8 - 901120*a^10*b^3*c^3*d^9 + 270336*a^11*b^2*c^2*d^10 - 49152*a^12*b*c*d^11))^(1/4)*(36864*a*b^20*c^17*d^4 + 36864*a^17*b^4*c*d^20 - 319488*a^2*b^19*c^16*d^5 + 1163264*a^3*b^18*c^15*d^6 - 2334720*a^4*b^17*c^14*d^7 + 3293184*a^5*b^16*c^13*d^8 - 5758976*a^6*b^15*c^12*d^9 + 13516800*a^7*b^14*c^11*d^10 - 25141248*a^8*b^13*c^10*d^11 + 31088640*a^9*b^12*c^9*d^12 - 25141248*a^10*b^11*c^8*d^13 + 13516800*a^11*b^10*c^7*d^14 - 5758976*a^12*b^9*c^6*d^15 + 3293184*a^13*b^8*c^5*d^16 - 2334720*a^14*b^7*c^4*d^17 + 1163264*a^15*b^6*c^3*d^18 - 319488*a^16*b^5*c^2*d^19))/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)))*1i + (x^(1/2)*(5625*a*b^12*c^8*d^5 + 5625*a^8*b^5*c*d^12 + 34275*a^2*b^11*c^7*d^6 + 88705*a^3*b^10*c^6*d^7 + 133539*a^4*b^9*c^5*d^8 + 133539*a^5*b^8*c^4*d^9 + 88705*a^6*b^7*c^3*d^10 + 34275*a^7*b^6*c^2*d^11)*1i)/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)))*(-(81*b^5*c^4 + 625*a^4*b*d^4 + 1500*a^3*b^2*c*d^3 + 1350*a^2*b^3*c^2*d^2 + 540*a*b^4*c^3*d)/(4096*a^13*d^12 + 4096*a*b^12*c^12 - 49152*a^2*b^11*c^11*d + 270336*a^3*b^10*c^10*d^2 - 901120*a^4*b^9*c^9*d^3 + 2027520*a^5*b^8*c^8*d^4 - 3244032*a^6*b^7*c^7*d^5 + 3784704*a^7*b^6*c^6*d^6 - 3244032*a^8*b^5*c^5*d^7 + 2027520*a^9*b^4*c^4*d^8 - 901120*a^10*b^3*c^3*d^9 + 270336*a^11*b^2*c^2*d^10 - 49152*a^12*b*c*d^11))^(1/4))/(((-(81*b^5*c^4 + 625*a^4*b*d^4 + 1500*a^3*b^2*c*d^3 + 1350*a^2*b^3*c^2*d^2 + 540*a*b^4*c^3*d)/(4096*a^13*d^12 + 4096*a*b^12*c^12 - 49152*a^2*b^11*c^11*d + 270336*a^3*b^10*c^10*d^2 - 901120*a^4*b^9*c^9*d^3 + 2027520*a^5*b^8*c^8*d^4 - 3244032*a^6*b^7*c^7*d^5 + 3784704*a^7*b^6*c^6*d^6 - 3244032*a^8*b^5*c^5*d^7 + 2027520*a^9*b^4*c^4*d^8 - 901120*a^10*b^3*c^3*d^9 + 270336*a^11*b^2*c^2*d^10 - 49152*a^12*b*c*d^11))^(3/4)*((864*a*b^20*c^17*d^4 + 864*a^17*b^4*c*d^20 - 5184*a^2*b^19*c^16*d^5 + 3200*a^3*b^18*c^15*d^6 + 56640*a^4*b^17*c^14*d^7 - 220800*a^5*b^16*c^13*d^8 + 369088*a^6*b^15*c^12*d^9 - 240768*a^7*b^14*c^11*d^10 - 158400*a^8*b^13*c^10*d^11 + 390720*a^9*b^12*c^9*d^12 - 158400*a^10*b^11*c^8*d^13 - 240768*a^11*b^10*c^7*d^14 + 369088*a^12*b^9*c^6*d^15 - 220800*a^13*b^8*c^5*d^16 + 56640*a^14*b^7*c^4*d^17 + 3200*a^15*b^6*c^3*d^18 - 5184*a^16*b^5*c^2*d^19)/(a^14*d^14 + b^14*c^14 + 91*a^2*b^12*c^12*d^2 - 364*a^3*b^11*c^11*d^3 + 1001*a^4*b^10*c^10*d^4 - 2002*a^5*b^9*c^9*d^5 + 3003*a^6*b^8*c^8*d^6 - 3432*a^7*b^7*c^7*d^7 + 3003*a^8*b^6*c^6*d^8 - 2002*a^9*b^5*c^5*d^9 + 1001*a^10*b^4*c^4*d^10 - 364*a^11*b^3*c^3*d^11 + 91*a^12*b^2*c^2*d^12 - 14*a*b^13*c^13*d - 14*a^13*b*c*d^13) - (x^(1/2)*(-(81*b^5*c^4 + 625*a^4*b*d^4 + 1500*a^3*b^2*c*d^3 + 1350*a^2*b^3*c^2*d^2 + 540*a*b^4*c^3*d)/(4096*a^13*d^12 + 4096*a*b^12*c^12 - 49152*a^2*b^11*c^11*d + 270336*a^3*b^10*c^10*d^2 - 901120*a^4*b^9*c^9*d^3 + 2027520*a^5*b^8*c^8*d^4 - 3244032*a^6*b^7*c^7*d^5 + 3784704*a^7*b^6*c^6*d^6 - 3244032*a^8*b^5*c^5*d^7 + 2027520*a^9*b^4*c^4*d^8 - 901120*a^10*b^3*c^3*d^9 + 270336*a^11*b^2*c^2*d^10 - 49152*a^12*b*c*d^11))^(1/4)*(36864*a*b^20*c^17*d^4 + 36864*a^17*b^4*c*d^20 - 319488*a^2*b^19*c^16*d^5 + 1163264*a^3*b^18*c^15*d^6 - 2334720*a^4*b^17*c^14*d^7 + 3293184*a^5*b^16*c^13*d^8 - 5758976*a^6*b^15*c^12*d^9 + 13516800*a^7*b^14*c^11*d^10 - 25141248*a^8*b^13*c^10*d^11 + 31088640*a^9*b^12*c^9*d^12 - 25141248*a^10*b^11*c^8*d^13 + 13516800*a^11*b^10*c^7*d^14 - 5758976*a^12*b^9*c^6*d^15 + 3293184*a^13*b^8*c^5*d^16 - 2334720*a^14*b^7*c^4*d^17 + 1163264*a^15*b^6*c^3*d^18 - 319488*a^16*b^5*c^2*d^19))/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11))) - (x^(1/2)*(5625*a*b^12*c^8*d^5 + 5625*a^8*b^5*c*d^12 + 34275*a^2*b^11*c^7*d^6 + 88705*a^3*b^10*c^6*d^7 + 133539*a^4*b^9*c^5*d^8 + 133539*a^5*b^8*c^4*d^9 + 88705*a^6*b^7*c^3*d^10 + 34275*a^7*b^6*c^2*d^11))/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)))*(-(81*b^5*c^4 + 625*a^4*b*d^4 + 1500*a^3*b^2*c*d^3 + 1350*a^2*b^3*c^2*d^2 + 540*a*b^4*c^3*d)/(4096*a^13*d^12 + 4096*a*b^12*c^12 - 49152*a^2*b^11*c^11*d + 270336*a^3*b^10*c^10*d^2 - 901120*a^4*b^9*c^9*d^3 + 2027520*a^5*b^8*c^8*d^4 - 3244032*a^6*b^7*c^7*d^5 + 3784704*a^7*b^6*c^6*d^6 - 3244032*a^8*b^5*c^5*d^7 + 2027520*a^9*b^4*c^4*d^8 - 901120*a^10*b^3*c^3*d^9 + 270336*a^11*b^2*c^2*d^10 - 49152*a^12*b*c*d^11))^(1/4) + ((-(81*b^5*c^4 + 625*a^4*b*d^4 + 1500*a^3*b^2*c*d^3 + 1350*a^2*b^3*c^2*d^2 + 540*a*b^4*c^3*d)/(4096*a^13*d^12 + 4096*a*b^12*c^12 - 49152*a^2*b^11*c^11*d + 270336*a^3*b^10*c^10*d^2 - 901120*a^4*b^9*c^9*d^3 + 2027520*a^5*b^8*c^8*d^4 - 3244032*a^6*b^7*c^7*d^5 + 3784704*a^7*b^6*c^6*d^6 - 3244032*a^8*b^5*c^5*d^7 + 2027520*a^9*b^4*c^4*d^8 - 901120*a^10*b^3*c^3*d^9 + 270336*a^11*b^2*c^2*d^10 - 49152*a^12*b*c*d^11))^(3/4)*((864*a*b^20*c^17*d^4 + 864*a^17*b^4*c*d^20 - 5184*a^2*b^19*c^16*d^5 + 3200*a^3*b^18*c^15*d^6 + 56640*a^4*b^17*c^14*d^7 - 220800*a^5*b^16*c^13*d^8 + 369088*a^6*b^15*c^12*d^9 - 240768*a^7*b^14*c^11*d^10 - 158400*a^8*b^13*c^10*d^11 + 390720*a^9*b^12*c^9*d^12 - 158400*a^10*b^11*c^8*d^13 - 240768*a^11*b^10*c^7*d^14 + 369088*a^12*b^9*c^6*d^15 - 220800*a^13*b^8*c^5*d^16 + 56640*a^14*b^7*c^4*d^17 + 3200*a^15*b^6*c^3*d^18 - 5184*a^16*b^5*c^2*d^19)/(a^14*d^14 + b^14*c^14 + 91*a^2*b^12*c^12*d^2 - 364*a^3*b^11*c^11*d^3 + 1001*a^4*b^10*c^10*d^4 - 2002*a^5*b^9*c^9*d^5 + 3003*a^6*b^8*c^8*d^6 - 3432*a^7*b^7*c^7*d^7 + 3003*a^8*b^6*c^6*d^8 - 2002*a^9*b^5*c^5*d^9 + 1001*a^10*b^4*c^4*d^10 - 364*a^11*b^3*c^3*d^11 + 91*a^12*b^2*c^2*d^12 - 14*a*b^13*c^13*d - 14*a^13*b*c*d^13) + (x^(1/2)*(-(81*b^5*c^4 + 625*a^4*b*d^4 + 1500*a^3*b^2*c*d^3 + 1350*a^2*b^3*c^2*d^2 + 540*a*b^4*c^3*d)/(4096*a^13*d^12 + 4096*a*b^12*c^12 - 49152*a^2*b^11*c^11*d + 270336*a^3*b^10*c^10*d^2 - 901120*a^4*b^9*c^9*d^3 + 2027520*a^5*b^8*c^8*d^4 - 3244032*a^6*b^7*c^7*d^5 + 3784704*a^7*b^6*c^6*d^6 - 3244032*a^8*b^5*c^5*d^7 + 2027520*a^9*b^4*c^4*d^8 - 901120*a^10*b^3*c^3*d^9 + 270336*a^11*b^2*c^2*d^10 - 49152*a^12*b*c*d^11))^(1/4)*(36864*a*b^20*c^17*d^4 + 36864*a^17*b^4*c*d^20 - 319488*a^2*b^19*c^16*d^5 + 1163264*a^3*b^18*c^15*d^6 - 2334720*a^4*b^17*c^14*d^7 + 3293184*a^5*b^16*c^13*d^8 - 5758976*a^6*b^15*c^12*d^9 + 13516800*a^7*b^14*c^11*d^10 - 25141248*a^8*b^13*c^10*d^11 + 31088640*a^9*b^12*c^9*d^12 - 25141248*a^10*b^11*c^8*d^13 + 13516800*a^11*b^10*c^7*d^14 - 5758976*a^12*b^9*c^6*d^15 + 3293184*a^13*b^8*c^5*d^16 - 2334720*a^14*b^7*c^4*d^17 + 1163264*a^15*b^6*c^3*d^18 - 319488*a^16*b^5*c^2*d^19))/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11))) + (x^(1/2)*(5625*a*b^12*c^8*d^5 + 5625*a^8*b^5*c*d^12 + 34275*a^2*b^11*c^7*d^6 + 88705*a^3*b^10*c^6*d^7 + 133539*a^4*b^9*c^5*d^8 + 133539*a^5*b^8*c^4*d^9 + 88705*a^6*b^7*c^3*d^10 + 34275*a^7*b^6*c^2*d^11))/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)))*(-(81*b^5*c^4 + 625*a^4*b*d^4 + 1500*a^3*b^2*c*d^3 + 1350*a^2*b^3*c^2*d^2 + 540*a*b^4*c^3*d)/(4096*a^13*d^12 + 4096*a*b^12*c^12 - 49152*a^2*b^11*c^11*d + 270336*a^3*b^10*c^10*d^2 - 901120*a^4*b^9*c^9*d^3 + 2027520*a^5*b^8*c^8*d^4 - 3244032*a^6*b^7*c^7*d^5 + 3784704*a^7*b^6*c^6*d^6 - 3244032*a^8*b^5*c^5*d^7 + 2027520*a^9*b^4*c^4*d^8 - 901120*a^10*b^3*c^3*d^9 + 270336*a^11*b^2*c^2*d^10 - 49152*a^12*b*c*d^11))^(1/4) + ((16875*a*b^12*c^8*d^5)/64 + (16875*a^8*b^5*c*d^12)/64 + (131625*a^2*b^11*c^7*d^6)/64 + (425475*a^3*b^10*c^6*d^7)/64 + (736745*a^4*b^9*c^5*d^8)/64 + (736745*a^5*b^8*c^4*d^9)/64 + (425475*a^6*b^7*c^3*d^10)/64 + (131625*a^7*b^6*c^2*d^11)/64)/(a^14*d^14 + b^14*c^14 + 91*a^2*b^12*c^12*d^2 - 364*a^3*b^11*c^11*d^3 + 1001*a^4*b^10*c^10*d^4 - 2002*a^5*b^9*c^9*d^5 + 3003*a^6*b^8*c^8*d^6 - 3432*a^7*b^7*c^7*d^7 + 3003*a^8*b^6*c^6*d^8 - 2002*a^9*b^5*c^5*d^9 + 1001*a^10*b^4*c^4*d^10 - 364*a^11*b^3*c^3*d^11 + 91*a^12*b^2*c^2*d^12 - 14*a*b^13*c^13*d - 14*a^13*b*c*d^13)))*(-(81*b^5*c^4 + 625*a^4*b*d^4 + 1500*a^3*b^2*c*d^3 + 1350*a^2*b^3*c^2*d^2 + 540*a*b^4*c^3*d)/(4096*a^13*d^12 + 4096*a*b^12*c^12 - 49152*a^2*b^11*c^11*d + 270336*a^3*b^10*c^10*d^2 - 901120*a^4*b^9*c^9*d^3 + 2027520*a^5*b^8*c^8*d^4 - 3244032*a^6*b^7*c^7*d^5 + 3784704*a^7*b^6*c^6*d^6 - 3244032*a^8*b^5*c^5*d^7 + 2027520*a^9*b^4*c^4*d^8 - 901120*a^10*b^3*c^3*d^9 + 270336*a^11*b^2*c^2*d^10 - 49152*a^12*b*c*d^11))^(1/4)*2i - ((x^(3/2)*(a*d + b*c))/(2*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) + (b*d*x^(7/2))/(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/(a*c + x^2*(a*d + b*c) + b*d*x^4) - atan((((-(81*a^4*d^5 + 625*b^4*c^4*d + 1500*a*b^3*c^3*d^2 + 1350*a^2*b^2*c^2*d^3 + 540*a^3*b*c*d^4)/(4096*b^12*c^13 + 4096*a^12*c*d^12 - 49152*a^11*b*c^2*d^11 + 270336*a^2*b^10*c^11*d^2 - 901120*a^3*b^9*c^10*d^3 + 2027520*a^4*b^8*c^9*d^4 - 3244032*a^5*b^7*c^8*d^5 + 3784704*a^6*b^6*c^7*d^6 - 3244032*a^7*b^5*c^6*d^7 + 2027520*a^8*b^4*c^5*d^8 - 901120*a^9*b^3*c^4*d^9 + 270336*a^10*b^2*c^3*d^10 - 49152*a*b^11*c^12*d))^(3/4)*((864*a*b^20*c^17*d^4 + 864*a^17*b^4*c*d^20 - 5184*a^2*b^19*c^16*d^5 + 3200*a^3*b^18*c^15*d^6 + 56640*a^4*b^17*c^14*d^7 - 220800*a^5*b^16*c^13*d^8 + 369088*a^6*b^15*c^12*d^9 - 240768*a^7*b^14*c^11*d^10 - 158400*a^8*b^13*c^10*d^11 + 390720*a^9*b^12*c^9*d^12 - 158400*a^10*b^11*c^8*d^13 - 240768*a^11*b^10*c^7*d^14 + 369088*a^12*b^9*c^6*d^15 - 220800*a^13*b^8*c^5*d^16 + 56640*a^14*b^7*c^4*d^17 + 3200*a^15*b^6*c^3*d^18 - 5184*a^16*b^5*c^2*d^19)/(a^14*d^14 + b^14*c^14 + 91*a^2*b^12*c^12*d^2 - 364*a^3*b^11*c^11*d^3 + 1001*a^4*b^10*c^10*d^4 - 2002*a^5*b^9*c^9*d^5 + 3003*a^6*b^8*c^8*d^6 - 3432*a^7*b^7*c^7*d^7 + 3003*a^8*b^6*c^6*d^8 - 2002*a^9*b^5*c^5*d^9 + 1001*a^10*b^4*c^4*d^10 - 364*a^11*b^3*c^3*d^11 + 91*a^12*b^2*c^2*d^12 - 14*a*b^13*c^13*d - 14*a^13*b*c*d^13) - (x^(1/2)*(-(81*a^4*d^5 + 625*b^4*c^4*d + 1500*a*b^3*c^3*d^2 + 1350*a^2*b^2*c^2*d^3 + 540*a^3*b*c*d^4)/(4096*b^12*c^13 + 4096*a^12*c*d^12 - 49152*a^11*b*c^2*d^11 + 270336*a^2*b^10*c^11*d^2 - 901120*a^3*b^9*c^10*d^3 + 2027520*a^4*b^8*c^9*d^4 - 3244032*a^5*b^7*c^8*d^5 + 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88705*a^3*b^10*c^6*d^7 + 133539*a^4*b^9*c^5*d^8 + 133539*a^5*b^8*c^4*d^9 + 88705*a^6*b^7*c^3*d^10 + 34275*a^7*b^6*c^2*d^11)*1i)/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)))*(-(81*a^4*d^5 + 625*b^4*c^4*d + 1500*a*b^3*c^3*d^2 + 1350*a^2*b^2*c^2*d^3 + 540*a^3*b*c*d^4)/(4096*b^12*c^13 + 4096*a^12*c*d^12 - 49152*a^11*b*c^2*d^11 + 270336*a^2*b^10*c^11*d^2 - 901120*a^3*b^9*c^10*d^3 + 2027520*a^4*b^8*c^9*d^4 - 3244032*a^5*b^7*c^8*d^5 + 3784704*a^6*b^6*c^7*d^6 - 3244032*a^7*b^5*c^6*d^7 + 2027520*a^8*b^4*c^5*d^8 - 901120*a^9*b^3*c^4*d^9 + 270336*a^10*b^2*c^3*d^10 - 49152*a*b^11*c^12*d))^(1/4) - ((-(81*a^4*d^5 + 625*b^4*c^4*d + 1500*a*b^3*c^3*d^2 + 1350*a^2*b^2*c^2*d^3 + 540*a^3*b*c*d^4)/(4096*b^12*c^13 + 4096*a^12*c*d^12 - 49152*a^11*b*c^2*d^11 + 270336*a^2*b^10*c^11*d^2 - 901120*a^3*b^9*c^10*d^3 + 2027520*a^4*b^8*c^9*d^4 - 3244032*a^5*b^7*c^8*d^5 + 3784704*a^6*b^6*c^7*d^6 - 3244032*a^7*b^5*c^6*d^7 + 2027520*a^8*b^4*c^5*d^8 - 901120*a^9*b^3*c^4*d^9 + 270336*a^10*b^2*c^3*d^10 - 49152*a*b^11*c^12*d))^(3/4)*((864*a*b^20*c^17*d^4 + 864*a^17*b^4*c*d^20 - 5184*a^2*b^19*c^16*d^5 + 3200*a^3*b^18*c^15*d^6 + 56640*a^4*b^17*c^14*d^7 - 220800*a^5*b^16*c^13*d^8 + 369088*a^6*b^15*c^12*d^9 - 240768*a^7*b^14*c^11*d^10 - 158400*a^8*b^13*c^10*d^11 + 390720*a^9*b^12*c^9*d^12 - 158400*a^10*b^11*c^8*d^13 - 240768*a^11*b^10*c^7*d^14 + 369088*a^12*b^9*c^6*d^15 - 220800*a^13*b^8*c^5*d^16 + 56640*a^14*b^7*c^4*d^17 + 3200*a^15*b^6*c^3*d^18 - 5184*a^16*b^5*c^2*d^19)/(a^14*d^14 + b^14*c^14 + 91*a^2*b^12*c^12*d^2 - 364*a^3*b^11*c^11*d^3 + 1001*a^4*b^10*c^10*d^4 - 2002*a^5*b^9*c^9*d^5 + 3003*a^6*b^8*c^8*d^6 - 3432*a^7*b^7*c^7*d^7 + 3003*a^8*b^6*c^6*d^8 - 2002*a^9*b^5*c^5*d^9 + 1001*a^10*b^4*c^4*d^10 - 364*a^11*b^3*c^3*d^11 + 91*a^12*b^2*c^2*d^12 - 14*a*b^13*c^13*d - 14*a^13*b*c*d^13) + (x^(1/2)*(-(81*a^4*d^5 + 625*b^4*c^4*d + 1500*a*b^3*c^3*d^2 + 1350*a^2*b^2*c^2*d^3 + 540*a^3*b*c*d^4)/(4096*b^12*c^13 + 4096*a^12*c*d^12 - 49152*a^11*b*c^2*d^11 + 270336*a^2*b^10*c^11*d^2 - 901120*a^3*b^9*c^10*d^3 + 2027520*a^4*b^8*c^9*d^4 - 3244032*a^5*b^7*c^8*d^5 + 3784704*a^6*b^6*c^7*d^6 - 3244032*a^7*b^5*c^6*d^7 + 2027520*a^8*b^4*c^5*d^8 - 901120*a^9*b^3*c^4*d^9 + 270336*a^10*b^2*c^3*d^10 - 49152*a*b^11*c^12*d))^(1/4)*(36864*a*b^20*c^17*d^4 + 36864*a^17*b^4*c*d^20 - 319488*a^2*b^19*c^16*d^5 + 1163264*a^3*b^18*c^15*d^6 - 2334720*a^4*b^17*c^14*d^7 + 3293184*a^5*b^16*c^13*d^8 - 5758976*a^6*b^15*c^12*d^9 + 13516800*a^7*b^14*c^11*d^10 - 25141248*a^8*b^13*c^10*d^11 + 31088640*a^9*b^12*c^9*d^12 - 25141248*a^10*b^11*c^8*d^13 + 13516800*a^11*b^10*c^7*d^14 - 5758976*a^12*b^9*c^6*d^15 + 3293184*a^13*b^8*c^5*d^16 - 2334720*a^14*b^7*c^4*d^17 + 1163264*a^15*b^6*c^3*d^18 - 319488*a^16*b^5*c^2*d^19))/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)))*1i + (x^(1/2)*(5625*a*b^12*c^8*d^5 + 5625*a^8*b^5*c*d^12 + 34275*a^2*b^11*c^7*d^6 + 88705*a^3*b^10*c^6*d^7 + 133539*a^4*b^9*c^5*d^8 + 133539*a^5*b^8*c^4*d^9 + 88705*a^6*b^7*c^3*d^10 + 34275*a^7*b^6*c^2*d^11)*1i)/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)))*(-(81*a^4*d^5 + 625*b^4*c^4*d + 1500*a*b^3*c^3*d^2 + 1350*a^2*b^2*c^2*d^3 + 540*a^3*b*c*d^4)/(4096*b^12*c^13 + 4096*a^12*c*d^12 - 49152*a^11*b*c^2*d^11 + 270336*a^2*b^10*c^11*d^2 - 901120*a^3*b^9*c^10*d^3 + 2027520*a^4*b^8*c^9*d^4 - 3244032*a^5*b^7*c^8*d^5 + 3784704*a^6*b^6*c^7*d^6 - 3244032*a^7*b^5*c^6*d^7 + 2027520*a^8*b^4*c^5*d^8 - 901120*a^9*b^3*c^4*d^9 + 270336*a^10*b^2*c^3*d^10 - 49152*a*b^11*c^12*d))^(1/4))/(((-(81*a^4*d^5 + 625*b^4*c^4*d + 1500*a*b^3*c^3*d^2 + 1350*a^2*b^2*c^2*d^3 + 540*a^3*b*c*d^4)/(4096*b^12*c^13 + 4096*a^12*c*d^12 - 49152*a^11*b*c^2*d^11 + 270336*a^2*b^10*c^11*d^2 - 901120*a^3*b^9*c^10*d^3 + 2027520*a^4*b^8*c^9*d^4 - 3244032*a^5*b^7*c^8*d^5 + 3784704*a^6*b^6*c^7*d^6 - 3244032*a^7*b^5*c^6*d^7 + 2027520*a^8*b^4*c^5*d^8 - 901120*a^9*b^3*c^4*d^9 + 270336*a^10*b^2*c^3*d^10 - 49152*a*b^11*c^12*d))^(3/4)*((864*a*b^20*c^17*d^4 + 864*a^17*b^4*c*d^20 - 5184*a^2*b^19*c^16*d^5 + 3200*a^3*b^18*c^15*d^6 + 56640*a^4*b^17*c^14*d^7 - 220800*a^5*b^16*c^13*d^8 + 369088*a^6*b^15*c^12*d^9 - 240768*a^7*b^14*c^11*d^10 - 158400*a^8*b^13*c^10*d^11 + 390720*a^9*b^12*c^9*d^12 - 158400*a^10*b^11*c^8*d^13 - 240768*a^11*b^10*c^7*d^14 + 369088*a^12*b^9*c^6*d^15 - 220800*a^13*b^8*c^5*d^16 + 56640*a^14*b^7*c^4*d^17 + 3200*a^15*b^6*c^3*d^18 - 5184*a^16*b^5*c^2*d^19)/(a^14*d^14 + b^14*c^14 + 91*a^2*b^12*c^12*d^2 - 364*a^3*b^11*c^11*d^3 + 1001*a^4*b^10*c^10*d^4 - 2002*a^5*b^9*c^9*d^5 + 3003*a^6*b^8*c^8*d^6 - 3432*a^7*b^7*c^7*d^7 + 3003*a^8*b^6*c^6*d^8 - 2002*a^9*b^5*c^5*d^9 + 1001*a^10*b^4*c^4*d^10 - 364*a^11*b^3*c^3*d^11 + 91*a^12*b^2*c^2*d^12 - 14*a*b^13*c^13*d - 14*a^13*b*c*d^13) - (x^(1/2)*(-(81*a^4*d^5 + 625*b^4*c^4*d + 1500*a*b^3*c^3*d^2 + 1350*a^2*b^2*c^2*d^3 + 540*a^3*b*c*d^4)/(4096*b^12*c^13 + 4096*a^12*c*d^12 - 49152*a^11*b*c^2*d^11 + 270336*a^2*b^10*c^11*d^2 - 901120*a^3*b^9*c^10*d^3 + 2027520*a^4*b^8*c^9*d^4 - 3244032*a^5*b^7*c^8*d^5 + 3784704*a^6*b^6*c^7*d^6 - 3244032*a^7*b^5*c^6*d^7 + 2027520*a^8*b^4*c^5*d^8 - 901120*a^9*b^3*c^4*d^9 + 270336*a^10*b^2*c^3*d^10 - 49152*a*b^11*c^12*d))^(1/4)*(36864*a*b^20*c^17*d^4 + 36864*a^17*b^4*c*d^20 - 319488*a^2*b^19*c^16*d^5 + 1163264*a^3*b^18*c^15*d^6 - 2334720*a^4*b^17*c^14*d^7 + 3293184*a^5*b^16*c^13*d^8 - 5758976*a^6*b^15*c^12*d^9 + 13516800*a^7*b^14*c^11*d^10 - 25141248*a^8*b^13*c^10*d^11 + 31088640*a^9*b^12*c^9*d^12 - 25141248*a^10*b^11*c^8*d^13 + 13516800*a^11*b^10*c^7*d^14 - 5758976*a^12*b^9*c^6*d^15 + 3293184*a^13*b^8*c^5*d^16 - 2334720*a^14*b^7*c^4*d^17 + 1163264*a^15*b^6*c^3*d^18 - 319488*a^16*b^5*c^2*d^19))/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11))) - (x^(1/2)*(5625*a*b^12*c^8*d^5 + 5625*a^8*b^5*c*d^12 + 34275*a^2*b^11*c^7*d^6 + 88705*a^3*b^10*c^6*d^7 + 133539*a^4*b^9*c^5*d^8 + 133539*a^5*b^8*c^4*d^9 + 88705*a^6*b^7*c^3*d^10 + 34275*a^7*b^6*c^2*d^11))/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)))*(-(81*a^4*d^5 + 625*b^4*c^4*d + 1500*a*b^3*c^3*d^2 + 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49152*a*b^11*c^12*d))^(1/4)*(36864*a*b^20*c^17*d^4 + 36864*a^17*b^4*c*d^20 - 319488*a^2*b^19*c^16*d^5 + 1163264*a^3*b^18*c^15*d^6 - 2334720*a^4*b^17*c^14*d^7 + 3293184*a^5*b^16*c^13*d^8 - 5758976*a^6*b^15*c^12*d^9 + 13516800*a^7*b^14*c^11*d^10 - 25141248*a^8*b^13*c^10*d^11 + 31088640*a^9*b^12*c^9*d^12 - 25141248*a^10*b^11*c^8*d^13 + 13516800*a^11*b^10*c^7*d^14 - 5758976*a^12*b^9*c^6*d^15 + 3293184*a^13*b^8*c^5*d^16 - 2334720*a^14*b^7*c^4*d^17 + 1163264*a^15*b^6*c^3*d^18 - 319488*a^16*b^5*c^2*d^19))/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11))) + (x^(1/2)*(5625*a*b^12*c^8*d^5 + 5625*a^8*b^5*c*d^12 + 34275*a^2*b^11*c^7*d^6 + 88705*a^3*b^10*c^6*d^7 + 133539*a^4*b^9*c^5*d^8 + 133539*a^5*b^8*c^4*d^9 + 88705*a^6*b^7*c^3*d^10 + 34275*a^7*b^6*c^2*d^11))/(16*(a^12*d^12 + 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66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11))) - (x^(1/2)*(5625*a*b^12*c^8*d^5 + 5625*a^8*b^5*c*d^12 + 34275*a^2*b^11*c^7*d^6 + 88705*a^3*b^10*c^6*d^7 + 133539*a^4*b^9*c^5*d^8 + 133539*a^5*b^8*c^4*d^9 + 88705*a^6*b^7*c^3*d^10 + 34275*a^7*b^6*c^2*d^11))/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)))*(-(81*a^4*d^5 + 625*b^4*c^4*d + 1500*a*b^3*c^3*d^2 + 1350*a^2*b^2*c^2*d^3 + 540*a^3*b*c*d^4)/(4096*b^12*c^13 + 4096*a^12*c*d^12 - 49152*a^11*b*c^2*d^11 + 270336*a^2*b^10*c^11*d^2 - 901120*a^3*b^9*c^10*d^3 + 2027520*a^4*b^8*c^9*d^4 - 3244032*a^5*b^7*c^8*d^5 + 3784704*a^6*b^6*c^7*d^6 - 3244032*a^7*b^5*c^6*d^7 + 2027520*a^8*b^4*c^5*d^8 - 901120*a^9*b^3*c^4*d^9 + 270336*a^10*b^2*c^3*d^10 - 49152*a*b^11*c^12*d))^(1/4) - ((-(81*a^4*d^5 + 625*b^4*c^4*d + 1500*a*b^3*c^3*d^2 + 1350*a^2*b^2*c^2*d^3 + 540*a^3*b*c*d^4)/(4096*b^12*c^13 + 4096*a^12*c*d^12 - 49152*a^11*b*c^2*d^11 + 270336*a^2*b^10*c^11*d^2 - 901120*a^3*b^9*c^10*d^3 + 2027520*a^4*b^8*c^9*d^4 - 3244032*a^5*b^7*c^8*d^5 + 3784704*a^6*b^6*c^7*d^6 - 3244032*a^7*b^5*c^6*d^7 + 2027520*a^8*b^4*c^5*d^8 - 901120*a^9*b^3*c^4*d^9 + 270336*a^10*b^2*c^3*d^10 - 49152*a*b^11*c^12*d))^(3/4)*(((864*a*b^20*c^17*d^4 + 864*a^17*b^4*c*d^20 - 5184*a^2*b^19*c^16*d^5 + 3200*a^3*b^18*c^15*d^6 + 56640*a^4*b^17*c^14*d^7 - 220800*a^5*b^16*c^13*d^8 + 369088*a^6*b^15*c^12*d^9 - 240768*a^7*b^14*c^11*d^10 - 158400*a^8*b^13*c^10*d^11 + 390720*a^9*b^12*c^9*d^12 - 158400*a^10*b^11*c^8*d^13 - 240768*a^11*b^10*c^7*d^14 + 369088*a^12*b^9*c^6*d^15 - 220800*a^13*b^8*c^5*d^16 + 56640*a^14*b^7*c^4*d^17 + 3200*a^15*b^6*c^3*d^18 - 5184*a^16*b^5*c^2*d^19)*1i)/(a^14*d^14 + b^14*c^14 + 91*a^2*b^12*c^12*d^2 - 364*a^3*b^11*c^11*d^3 + 1001*a^4*b^10*c^10*d^4 - 2002*a^5*b^9*c^9*d^5 + 3003*a^6*b^8*c^8*d^6 - 3432*a^7*b^7*c^7*d^7 + 3003*a^8*b^6*c^6*d^8 - 2002*a^9*b^5*c^5*d^9 + 1001*a^10*b^4*c^4*d^10 - 364*a^11*b^3*c^3*d^11 + 91*a^12*b^2*c^2*d^12 - 14*a*b^13*c^13*d - 14*a^13*b*c*d^13) + (x^(1/2)*(-(81*a^4*d^5 + 625*b^4*c^4*d + 1500*a*b^3*c^3*d^2 + 1350*a^2*b^2*c^2*d^3 + 540*a^3*b*c*d^4)/(4096*b^12*c^13 + 4096*a^12*c*d^12 - 49152*a^11*b*c^2*d^11 + 270336*a^2*b^10*c^11*d^2 - 901120*a^3*b^9*c^10*d^3 + 2027520*a^4*b^8*c^9*d^4 - 3244032*a^5*b^7*c^8*d^5 + 3784704*a^6*b^6*c^7*d^6 - 3244032*a^7*b^5*c^6*d^7 + 2027520*a^8*b^4*c^5*d^8 - 901120*a^9*b^3*c^4*d^9 + 270336*a^10*b^2*c^3*d^10 - 49152*a*b^11*c^12*d))^(1/4)*(36864*a*b^20*c^17*d^4 + 36864*a^17*b^4*c*d^20 - 319488*a^2*b^19*c^16*d^5 + 1163264*a^3*b^18*c^15*d^6 - 2334720*a^4*b^17*c^14*d^7 + 3293184*a^5*b^16*c^13*d^8 - 5758976*a^6*b^15*c^12*d^9 + 13516800*a^7*b^14*c^11*d^10 - 25141248*a^8*b^13*c^10*d^11 + 31088640*a^9*b^12*c^9*d^12 - 25141248*a^10*b^11*c^8*d^13 + 13516800*a^11*b^10*c^7*d^14 - 5758976*a^12*b^9*c^6*d^15 + 3293184*a^13*b^8*c^5*d^16 - 2334720*a^14*b^7*c^4*d^17 + 1163264*a^15*b^6*c^3*d^18 - 319488*a^16*b^5*c^2*d^19))/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11))) + (x^(1/2)*(5625*a*b^12*c^8*d^5 + 5625*a^8*b^5*c*d^12 + 34275*a^2*b^11*c^7*d^6 + 88705*a^3*b^10*c^6*d^7 + 133539*a^4*b^9*c^5*d^8 + 133539*a^5*b^8*c^4*d^9 + 88705*a^6*b^7*c^3*d^10 + 34275*a^7*b^6*c^2*d^11))/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)))*(-(81*a^4*d^5 + 625*b^4*c^4*d + 1500*a*b^3*c^3*d^2 + 1350*a^2*b^2*c^2*d^3 + 540*a^3*b*c*d^4)/(4096*b^12*c^13 + 4096*a^12*c*d^12 - 49152*a^11*b*c^2*d^11 + 270336*a^2*b^10*c^11*d^2 - 901120*a^3*b^9*c^10*d^3 + 2027520*a^4*b^8*c^9*d^4 - 3244032*a^5*b^7*c^8*d^5 + 3784704*a^6*b^6*c^7*d^6 - 3244032*a^7*b^5*c^6*d^7 + 2027520*a^8*b^4*c^5*d^8 - 901120*a^9*b^3*c^4*d^9 + 270336*a^10*b^2*c^3*d^10 - 49152*a*b^11*c^12*d))^(1/4))/(((-(81*a^4*d^5 + 625*b^4*c^4*d + 1500*a*b^3*c^3*d^2 + 1350*a^2*b^2*c^2*d^3 + 540*a^3*b*c*d^4)/(4096*b^12*c^13 + 4096*a^12*c*d^12 - 49152*a^11*b*c^2*d^11 + 270336*a^2*b^10*c^11*d^2 - 901120*a^3*b^9*c^10*d^3 + 2027520*a^4*b^8*c^9*d^4 - 3244032*a^5*b^7*c^8*d^5 + 3784704*a^6*b^6*c^7*d^6 - 3244032*a^7*b^5*c^6*d^7 + 2027520*a^8*b^4*c^5*d^8 - 901120*a^9*b^3*c^4*d^9 + 270336*a^10*b^2*c^3*d^10 - 49152*a*b^11*c^12*d))^(3/4)*(((864*a*b^20*c^17*d^4 + 864*a^17*b^4*c*d^20 - 5184*a^2*b^19*c^16*d^5 + 3200*a^3*b^18*c^15*d^6 + 56640*a^4*b^17*c^14*d^7 - 220800*a^5*b^16*c^13*d^8 + 369088*a^6*b^15*c^12*d^9 - 240768*a^7*b^14*c^11*d^10 - 158400*a^8*b^13*c^10*d^11 + 390720*a^9*b^12*c^9*d^12 - 158400*a^10*b^11*c^8*d^13 - 240768*a^11*b^10*c^7*d^14 + 369088*a^12*b^9*c^6*d^15 - 220800*a^13*b^8*c^5*d^16 + 56640*a^14*b^7*c^4*d^17 + 3200*a^15*b^6*c^3*d^18 - 5184*a^16*b^5*c^2*d^19)*1i)/(a^14*d^14 + b^14*c^14 + 91*a^2*b^12*c^12*d^2 - 364*a^3*b^11*c^11*d^3 + 1001*a^4*b^10*c^10*d^4 - 2002*a^5*b^9*c^9*d^5 + 3003*a^6*b^8*c^8*d^6 - 3432*a^7*b^7*c^7*d^7 + 3003*a^8*b^6*c^6*d^8 - 2002*a^9*b^5*c^5*d^9 + 1001*a^10*b^4*c^4*d^10 - 364*a^11*b^3*c^3*d^11 + 91*a^12*b^2*c^2*d^12 - 14*a*b^13*c^13*d - 14*a^13*b*c*d^13) - (x^(1/2)*(-(81*a^4*d^5 + 625*b^4*c^4*d + 1500*a*b^3*c^3*d^2 + 1350*a^2*b^2*c^2*d^3 + 540*a^3*b*c*d^4)/(4096*b^12*c^13 + 4096*a^12*c*d^12 - 49152*a^11*b*c^2*d^11 + 270336*a^2*b^10*c^11*d^2 - 901120*a^3*b^9*c^10*d^3 + 2027520*a^4*b^8*c^9*d^4 - 3244032*a^5*b^7*c^8*d^5 + 3784704*a^6*b^6*c^7*d^6 - 3244032*a^7*b^5*c^6*d^7 + 2027520*a^8*b^4*c^5*d^8 - 901120*a^9*b^3*c^4*d^9 + 270336*a^10*b^2*c^3*d^10 - 49152*a*b^11*c^12*d))^(1/4)*(36864*a*b^20*c^17*d^4 + 36864*a^17*b^4*c*d^20 - 319488*a^2*b^19*c^16*d^5 + 1163264*a^3*b^18*c^15*d^6 - 2334720*a^4*b^17*c^14*d^7 + 3293184*a^5*b^16*c^13*d^8 - 5758976*a^6*b^15*c^12*d^9 + 13516800*a^7*b^14*c^11*d^10 - 25141248*a^8*b^13*c^10*d^11 + 31088640*a^9*b^12*c^9*d^12 - 25141248*a^10*b^11*c^8*d^13 + 13516800*a^11*b^10*c^7*d^14 - 5758976*a^12*b^9*c^6*d^15 + 3293184*a^13*b^8*c^5*d^16 - 2334720*a^14*b^7*c^4*d^17 + 1163264*a^15*b^6*c^3*d^18 - 319488*a^16*b^5*c^2*d^19))/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)))*1i - (x^(1/2)*(5625*a*b^12*c^8*d^5 + 5625*a^8*b^5*c*d^12 + 34275*a^2*b^11*c^7*d^6 + 88705*a^3*b^10*c^6*d^7 + 133539*a^4*b^9*c^5*d^8 + 133539*a^5*b^8*c^4*d^9 + 88705*a^6*b^7*c^3*d^10 + 34275*a^7*b^6*c^2*d^11)*1i)/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)))*(-(81*a^4*d^5 + 625*b^4*c^4*d + 1500*a*b^3*c^3*d^2 + 1350*a^2*b^2*c^2*d^3 + 540*a^3*b*c*d^4)/(4096*b^12*c^13 + 4096*a^12*c*d^12 - 49152*a^11*b*c^2*d^11 + 270336*a^2*b^10*c^11*d^2 - 901120*a^3*b^9*c^10*d^3 + 2027520*a^4*b^8*c^9*d^4 - 3244032*a^5*b^7*c^8*d^5 + 3784704*a^6*b^6*c^7*d^6 - 3244032*a^7*b^5*c^6*d^7 + 2027520*a^8*b^4*c^5*d^8 - 901120*a^9*b^3*c^4*d^9 + 270336*a^10*b^2*c^3*d^10 - 49152*a*b^11*c^12*d))^(1/4) + ((-(81*a^4*d^5 + 625*b^4*c^4*d + 1500*a*b^3*c^3*d^2 + 1350*a^2*b^2*c^2*d^3 + 540*a^3*b*c*d^4)/(4096*b^12*c^13 + 4096*a^12*c*d^12 - 49152*a^11*b*c^2*d^11 + 270336*a^2*b^10*c^11*d^2 - 901120*a^3*b^9*c^10*d^3 + 2027520*a^4*b^8*c^9*d^4 - 3244032*a^5*b^7*c^8*d^5 + 3784704*a^6*b^6*c^7*d^6 - 3244032*a^7*b^5*c^6*d^7 + 2027520*a^8*b^4*c^5*d^8 - 901120*a^9*b^3*c^4*d^9 + 270336*a^10*b^2*c^3*d^10 - 49152*a*b^11*c^12*d))^(3/4)*(((864*a*b^20*c^17*d^4 + 864*a^17*b^4*c*d^20 - 5184*a^2*b^19*c^16*d^5 + 3200*a^3*b^18*c^15*d^6 + 56640*a^4*b^17*c^14*d^7 - 220800*a^5*b^16*c^13*d^8 + 369088*a^6*b^15*c^12*d^9 - 240768*a^7*b^14*c^11*d^10 - 158400*a^8*b^13*c^10*d^11 + 390720*a^9*b^12*c^9*d^12 - 158400*a^10*b^11*c^8*d^13 - 240768*a^11*b^10*c^7*d^14 + 369088*a^12*b^9*c^6*d^15 - 220800*a^13*b^8*c^5*d^16 + 56640*a^14*b^7*c^4*d^17 + 3200*a^15*b^6*c^3*d^18 - 5184*a^16*b^5*c^2*d^19)*1i)/(a^14*d^14 + b^14*c^14 + 91*a^2*b^12*c^12*d^2 - 364*a^3*b^11*c^11*d^3 + 1001*a^4*b^10*c^10*d^4 - 2002*a^5*b^9*c^9*d^5 + 3003*a^6*b^8*c^8*d^6 - 3432*a^7*b^7*c^7*d^7 + 3003*a^8*b^6*c^6*d^8 - 2002*a^9*b^5*c^5*d^9 + 1001*a^10*b^4*c^4*d^10 - 364*a^11*b^3*c^3*d^11 + 91*a^12*b^2*c^2*d^12 - 14*a*b^13*c^13*d - 14*a^13*b*c*d^13) + (x^(1/2)*(-(81*a^4*d^5 + 625*b^4*c^4*d + 1500*a*b^3*c^3*d^2 + 1350*a^2*b^2*c^2*d^3 + 540*a^3*b*c*d^4)/(4096*b^12*c^13 + 4096*a^12*c*d^12 - 49152*a^11*b*c^2*d^11 + 270336*a^2*b^10*c^11*d^2 - 901120*a^3*b^9*c^10*d^3 + 2027520*a^4*b^8*c^9*d^4 - 3244032*a^5*b^7*c^8*d^5 + 3784704*a^6*b^6*c^7*d^6 - 3244032*a^7*b^5*c^6*d^7 + 2027520*a^8*b^4*c^5*d^8 - 901120*a^9*b^3*c^4*d^9 + 270336*a^10*b^2*c^3*d^10 - 49152*a*b^11*c^12*d))^(1/4)*(36864*a*b^20*c^17*d^4 + 36864*a^17*b^4*c*d^20 - 319488*a^2*b^19*c^16*d^5 + 1163264*a^3*b^18*c^15*d^6 - 2334720*a^4*b^17*c^14*d^7 + 3293184*a^5*b^16*c^13*d^8 - 5758976*a^6*b^15*c^12*d^9 + 13516800*a^7*b^14*c^11*d^10 - 25141248*a^8*b^13*c^10*d^11 + 31088640*a^9*b^12*c^9*d^12 - 25141248*a^10*b^11*c^8*d^13 + 13516800*a^11*b^10*c^7*d^14 - 5758976*a^12*b^9*c^6*d^15 + 3293184*a^13*b^8*c^5*d^16 - 2334720*a^14*b^7*c^4*d^17 + 1163264*a^15*b^6*c^3*d^18 - 319488*a^16*b^5*c^2*d^19))/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)))*1i + (x^(1/2)*(5625*a*b^12*c^8*d^5 + 5625*a^8*b^5*c*d^12 + 34275*a^2*b^11*c^7*d^6 + 88705*a^3*b^10*c^6*d^7 + 133539*a^4*b^9*c^5*d^8 + 133539*a^5*b^8*c^4*d^9 + 88705*a^6*b^7*c^3*d^10 + 34275*a^7*b^6*c^2*d^11)*1i)/(16*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)))*(-(81*a^4*d^5 + 625*b^4*c^4*d + 1500*a*b^3*c^3*d^2 + 1350*a^2*b^2*c^2*d^3 + 540*a^3*b*c*d^4)/(4096*b^12*c^13 + 4096*a^12*c*d^12 - 49152*a^11*b*c^2*d^11 + 270336*a^2*b^10*c^11*d^2 - 901120*a^3*b^9*c^10*d^3 + 2027520*a^4*b^8*c^9*d^4 - 3244032*a^5*b^7*c^8*d^5 + 3784704*a^6*b^6*c^7*d^6 - 3244032*a^7*b^5*c^6*d^7 + 2027520*a^8*b^4*c^5*d^8 - 901120*a^9*b^3*c^4*d^9 + 270336*a^10*b^2*c^3*d^10 - 49152*a*b^11*c^12*d))^(1/4) - ((16875*a*b^12*c^8*d^5)/64 + (16875*a^8*b^5*c*d^12)/64 + (131625*a^2*b^11*c^7*d^6)/64 + (425475*a^3*b^10*c^6*d^7)/64 + (736745*a^4*b^9*c^5*d^8)/64 + (736745*a^5*b^8*c^4*d^9)/64 + (425475*a^6*b^7*c^3*d^10)/64 + (131625*a^7*b^6*c^2*d^11)/64)/(a^14*d^14 + b^14*c^14 + 91*a^2*b^12*c^12*d^2 - 364*a^3*b^11*c^11*d^3 + 1001*a^4*b^10*c^10*d^4 - 2002*a^5*b^9*c^9*d^5 + 3003*a^6*b^8*c^8*d^6 - 3432*a^7*b^7*c^7*d^7 + 3003*a^8*b^6*c^6*d^8 - 2002*a^9*b^5*c^5*d^9 + 1001*a^10*b^4*c^4*d^10 - 364*a^11*b^3*c^3*d^11 + 91*a^12*b^2*c^2*d^12 - 14*a*b^13*c^13*d - 14*a^13*b*c*d^13)))*(-(81*a^4*d^5 + 625*b^4*c^4*d + 1500*a*b^3*c^3*d^2 + 1350*a^2*b^2*c^2*d^3 + 540*a^3*b*c*d^4)/(4096*b^12*c^13 + 4096*a^12*c*d^12 - 49152*a^11*b*c^2*d^11 + 270336*a^2*b^10*c^11*d^2 - 901120*a^3*b^9*c^10*d^3 + 2027520*a^4*b^8*c^9*d^4 - 3244032*a^5*b^7*c^8*d^5 + 3784704*a^6*b^6*c^7*d^6 - 3244032*a^7*b^5*c^6*d^7 + 2027520*a^8*b^4*c^5*d^8 - 901120*a^9*b^3*c^4*d^9 + 270336*a^10*b^2*c^3*d^10 - 49152*a*b^11*c^12*d))^(1/4)","B"
490,1,34586,601,3.788455,"\text{Not used}","int(x^(3/2)/((a + b*x^2)^2*(c + d*x^2)^2),x)","-\frac{\frac{\sqrt{x}\,\left(a\,d+b\,c\right)}{2\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}+\frac{b\,d\,x^{5/2}}{a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2}}{b\,d\,x^4+\left(a\,d+b\,c\right)\,x^2+a\,c}-\mathrm{atan}\left(-\frac{\left(\left(\left(\frac{\sqrt{x}\,\left(2048\,a^{17}\,b^4\,d^{21}+4096\,a^{16}\,b^5\,c\,d^{20}-108544\,a^{15}\,b^6\,c^2\,d^{19}+337920\,a^{14}\,b^7\,c^3\,d^{18}+153600\,a^{13}\,b^8\,c^4\,d^{17}-3225600\,a^{12}\,b^9\,c^5\,d^{16}+8648704\,a^{11}\,b^{10}\,c^6\,d^{15}-11106304\,a^{10}\,b^{11}\,c^7\,d^{14}+5294080\,a^9\,b^{12}\,c^8\,d^{13}+5294080\,a^8\,b^{13}\,c^9\,d^{12}-11106304\,a^7\,b^{14}\,c^{10}\,d^{11}+8648704\,a^6\,b^{15}\,c^{11}\,d^{10}-3225600\,a^5\,b^{16}\,c^{12}\,d^9+153600\,a^4\,b^{17}\,c^{13}\,d^8+337920\,a^3\,b^{18}\,c^{14}\,d^7-108544\,a^2\,b^{19}\,c^{15}\,d^6+4096\,a\,b^{20}\,c^{16}\,d^5+2048\,b^{21}\,c^{17}\,d^4\right)}{8\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}+\frac{{\left(-\frac{2401\,a^4\,b^3\,d^4+1372\,a^3\,b^4\,c\,d^3+294\,a^2\,b^5\,c^2\,d^2+28\,a\,b^6\,c^3\,d+b^7\,c^4}{4096\,a^{15}\,d^{12}-49152\,a^{14}\,b\,c\,d^{11}+270336\,a^{13}\,b^2\,c^2\,d^{10}-901120\,a^{12}\,b^3\,c^3\,d^9+2027520\,a^{11}\,b^4\,c^4\,d^8-3244032\,a^{10}\,b^5\,c^5\,d^7+3784704\,a^9\,b^6\,c^6\,d^6-3244032\,a^8\,b^7\,c^7\,d^5+2027520\,a^7\,b^8\,c^8\,d^4-901120\,a^6\,b^9\,c^9\,d^3+270336\,a^5\,b^{10}\,c^{10}\,d^2-49152\,a^4\,b^{11}\,c^{11}\,d+4096\,a^3\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(-2048\,a^{15}\,b^4\,c\,d^{18}+8192\,a^{14}\,b^5\,c^2\,d^{17}+59392\,a^{13}\,b^6\,c^3\,d^{16}-606208\,a^{12}\,b^7\,c^4\,d^{15}+2455552\,a^{11}\,b^8\,c^5\,d^{14}-6037504\,a^{10}\,b^9\,c^6\,d^{13}+10070016\,a^9\,b^{10}\,c^7\,d^{12}-11894784\,a^8\,b^{11}\,c^8\,d^{11}+10070016\,a^7\,b^{12}\,c^9\,d^{10}-6037504\,a^6\,b^{13}\,c^{10}\,d^9+2455552\,a^5\,b^{14}\,c^{11}\,d^8-606208\,a^4\,b^{15}\,c^{12}\,d^7+59392\,a^3\,b^{16}\,c^{13}\,d^6+8192\,a^2\,b^{17}\,c^{14}\,d^5-2048\,a\,b^{18}\,c^{15}\,d^4\right)}{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)\,{\left(-\frac{2401\,a^4\,b^3\,d^4+1372\,a^3\,b^4\,c\,d^3+294\,a^2\,b^5\,c^2\,d^2+28\,a\,b^6\,c^3\,d+b^7\,c^4}{4096\,a^{15}\,d^{12}-49152\,a^{14}\,b\,c\,d^{11}+270336\,a^{13}\,b^2\,c^2\,d^{10}-901120\,a^{12}\,b^3\,c^3\,d^9+2027520\,a^{11}\,b^4\,c^4\,d^8-3244032\,a^{10}\,b^5\,c^5\,d^7+3784704\,a^9\,b^6\,c^6\,d^6-3244032\,a^8\,b^7\,c^7\,d^5+2027520\,a^7\,b^8\,c^8\,d^4-901120\,a^6\,b^9\,c^9\,d^3+270336\,a^5\,b^{10}\,c^{10}\,d^2-49152\,a^4\,b^{11}\,c^{11}\,d+4096\,a^3\,b^{12}\,c^{12}}\right)}^{3/4}-\frac{-\frac{7\,a^5\,b^6\,d^{11}}{2}+\frac{2197\,a^4\,b^7\,c\,d^{10}}{2}+9145\,a^3\,b^8\,c^2\,d^9+9145\,a^2\,b^9\,c^3\,d^8+\frac{2197\,a\,b^{10}\,c^4\,d^7}{2}-\frac{7\,b^{11}\,c^5\,d^6}{2}}{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)\,{\left(-\frac{2401\,a^4\,b^3\,d^4+1372\,a^3\,b^4\,c\,d^3+294\,a^2\,b^5\,c^2\,d^2+28\,a\,b^6\,c^3\,d+b^7\,c^4}{4096\,a^{15}\,d^{12}-49152\,a^{14}\,b\,c\,d^{11}+270336\,a^{13}\,b^2\,c^2\,d^{10}-901120\,a^{12}\,b^3\,c^3\,d^9+2027520\,a^{11}\,b^4\,c^4\,d^8-3244032\,a^{10}\,b^5\,c^5\,d^7+3784704\,a^9\,b^6\,c^6\,d^6-3244032\,a^8\,b^7\,c^7\,d^5+2027520\,a^7\,b^8\,c^8\,d^4-901120\,a^6\,b^9\,c^9\,d^3+270336\,a^5\,b^{10}\,c^{10}\,d^2-49152\,a^4\,b^{11}\,c^{11}\,d+4096\,a^3\,b^{12}\,c^{12}}\right)}^{1/4}\,1{}\mathrm{i}+\frac{\sqrt{x}\,\left(1225\,a^6\,b^7\,d^{13}+18186\,a^5\,b^8\,c\,d^{12}+75975\,a^4\,b^9\,c^2\,d^{11}+71372\,a^3\,b^{10}\,c^3\,d^{10}+75975\,a^2\,b^{11}\,c^4\,d^9+18186\,a\,b^{12}\,c^5\,d^8+1225\,b^{13}\,c^6\,d^7\right)\,1{}\mathrm{i}}{8\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)\,{\left(-\frac{2401\,a^4\,b^3\,d^4+1372\,a^3\,b^4\,c\,d^3+294\,a^2\,b^5\,c^2\,d^2+28\,a\,b^6\,c^3\,d+b^7\,c^4}{4096\,a^{15}\,d^{12}-49152\,a^{14}\,b\,c\,d^{11}+270336\,a^{13}\,b^2\,c^2\,d^{10}-901120\,a^{12}\,b^3\,c^3\,d^9+2027520\,a^{11}\,b^4\,c^4\,d^8-3244032\,a^{10}\,b^5\,c^5\,d^7+3784704\,a^9\,b^6\,c^6\,d^6-3244032\,a^8\,b^7\,c^7\,d^5+2027520\,a^7\,b^8\,c^8\,d^4-901120\,a^6\,b^9\,c^9\,d^3+270336\,a^5\,b^{10}\,c^{10}\,d^2-49152\,a^4\,b^{11}\,c^{11}\,d+4096\,a^3\,b^{12}\,c^{12}}\right)}^{1/4}+\left(\left(\left(\frac{\sqrt{x}\,\left(2048\,a^{17}\,b^4\,d^{21}+4096\,a^{16}\,b^5\,c\,d^{20}-108544\,a^{15}\,b^6\,c^2\,d^{19}+337920\,a^{14}\,b^7\,c^3\,d^{18}+153600\,a^{13}\,b^8\,c^4\,d^{17}-3225600\,a^{12}\,b^9\,c^5\,d^{16}+8648704\,a^{11}\,b^{10}\,c^6\,d^{15}-11106304\,a^{10}\,b^{11}\,c^7\,d^{14}+5294080\,a^9\,b^{12}\,c^8\,d^{13}+5294080\,a^8\,b^{13}\,c^9\,d^{12}-11106304\,a^7\,b^{14}\,c^{10}\,d^{11}+8648704\,a^6\,b^{15}\,c^{11}\,d^{10}-3225600\,a^5\,b^{16}\,c^{12}\,d^9+153600\,a^4\,b^{17}\,c^{13}\,d^8+337920\,a^3\,b^{18}\,c^{14}\,d^7-108544\,a^2\,b^{19}\,c^{15}\,d^6+4096\,a\,b^{20}\,c^{16}\,d^5+2048\,b^{21}\,c^{17}\,d^4\right)}{8\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}-\frac{{\left(-\frac{2401\,a^4\,b^3\,d^4+1372\,a^3\,b^4\,c\,d^3+294\,a^2\,b^5\,c^2\,d^2+28\,a\,b^6\,c^3\,d+b^7\,c^4}{4096\,a^{15}\,d^{12}-49152\,a^{14}\,b\,c\,d^{11}+270336\,a^{13}\,b^2\,c^2\,d^{10}-901120\,a^{12}\,b^3\,c^3\,d^9+2027520\,a^{11}\,b^4\,c^4\,d^8-3244032\,a^{10}\,b^5\,c^5\,d^7+3784704\,a^9\,b^6\,c^6\,d^6-3244032\,a^8\,b^7\,c^7\,d^5+2027520\,a^7\,b^8\,c^8\,d^4-901120\,a^6\,b^9\,c^9\,d^3+270336\,a^5\,b^{10}\,c^{10}\,d^2-49152\,a^4\,b^{11}\,c^{11}\,d+4096\,a^3\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(-2048\,a^{15}\,b^4\,c\,d^{18}+8192\,a^{14}\,b^5\,c^2\,d^{17}+59392\,a^{13}\,b^6\,c^3\,d^{16}-606208\,a^{12}\,b^7\,c^4\,d^{15}+2455552\,a^{11}\,b^8\,c^5\,d^{14}-6037504\,a^{10}\,b^9\,c^6\,d^{13}+10070016\,a^9\,b^{10}\,c^7\,d^{12}-11894784\,a^8\,b^{11}\,c^8\,d^{11}+10070016\,a^7\,b^{12}\,c^9\,d^{10}-6037504\,a^6\,b^{13}\,c^{10}\,d^9+2455552\,a^5\,b^{14}\,c^{11}\,d^8-606208\,a^4\,b^{15}\,c^{12}\,d^7+59392\,a^3\,b^{16}\,c^{13}\,d^6+8192\,a^2\,b^{17}\,c^{14}\,d^5-2048\,a\,b^{18}\,c^{15}\,d^4\right)}{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)\,{\left(-\frac{2401\,a^4\,b^3\,d^4+1372\,a^3\,b^4\,c\,d^3+294\,a^2\,b^5\,c^2\,d^2+28\,a\,b^6\,c^3\,d+b^7\,c^4}{4096\,a^{15}\,d^{12}-49152\,a^{14}\,b\,c\,d^{11}+270336\,a^{13}\,b^2\,c^2\,d^{10}-901120\,a^{12}\,b^3\,c^3\,d^9+2027520\,a^{11}\,b^4\,c^4\,d^8-3244032\,a^{10}\,b^5\,c^5\,d^7+3784704\,a^9\,b^6\,c^6\,d^6-3244032\,a^8\,b^7\,c^7\,d^5+2027520\,a^7\,b^8\,c^8\,d^4-901120\,a^6\,b^9\,c^9\,d^3+270336\,a^5\,b^{10}\,c^{10}\,d^2-49152\,a^4\,b^{11}\,c^{11}\,d+4096\,a^3\,b^{12}\,c^{12}}\right)}^{3/4}+\frac{-\frac{7\,a^5\,b^6\,d^{11}}{2}+\frac{2197\,a^4\,b^7\,c\,d^{10}}{2}+9145\,a^3\,b^8\,c^2\,d^9+9145\,a^2\,b^9\,c^3\,d^8+\frac{2197\,a\,b^{10}\,c^4\,d^7}{2}-\frac{7\,b^{11}\,c^5\,d^6}{2}}{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)\,{\left(-\frac{2401\,a^4\,b^3\,d^4+1372\,a^3\,b^4\,c\,d^3+294\,a^2\,b^5\,c^2\,d^2+28\,a\,b^6\,c^3\,d+b^7\,c^4}{4096\,a^{15}\,d^{12}-49152\,a^{14}\,b\,c\,d^{11}+270336\,a^{13}\,b^2\,c^2\,d^{10}-901120\,a^{12}\,b^3\,c^3\,d^9+2027520\,a^{11}\,b^4\,c^4\,d^8-3244032\,a^{10}\,b^5\,c^5\,d^7+3784704\,a^9\,b^6\,c^6\,d^6-3244032\,a^8\,b^7\,c^7\,d^5+2027520\,a^7\,b^8\,c^8\,d^4-901120\,a^6\,b^9\,c^9\,d^3+270336\,a^5\,b^{10}\,c^{10}\,d^2-49152\,a^4\,b^{11}\,c^{11}\,d+4096\,a^3\,b^{12}\,c^{12}}\right)}^{1/4}\,1{}\mathrm{i}+\frac{\sqrt{x}\,\left(1225\,a^6\,b^7\,d^{13}+18186\,a^5\,b^8\,c\,d^{12}+75975\,a^4\,b^9\,c^2\,d^{11}+71372\,a^3\,b^{10}\,c^3\,d^{10}+75975\,a^2\,b^{11}\,c^4\,d^9+18186\,a\,b^{12}\,c^5\,d^8+1225\,b^{13}\,c^6\,d^7\right)\,1{}\mathrm{i}}{8\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)\,{\left(-\frac{2401\,a^4\,b^3\,d^4+1372\,a^3\,b^4\,c\,d^3+294\,a^2\,b^5\,c^2\,d^2+28\,a\,b^6\,c^3\,d+b^7\,c^4}{4096\,a^{15}\,d^{12}-49152\,a^{14}\,b\,c\,d^{11}+270336\,a^{13}\,b^2\,c^2\,d^{10}-901120\,a^{12}\,b^3\,c^3\,d^9+2027520\,a^{11}\,b^4\,c^4\,d^8-3244032\,a^{10}\,b^5\,c^5\,d^7+3784704\,a^9\,b^6\,c^6\,d^6-3244032\,a^8\,b^7\,c^7\,d^5+2027520\,a^7\,b^8\,c^8\,d^4-901120\,a^6\,b^9\,c^9\,d^3+270336\,a^5\,b^{10}\,c^{10}\,d^2-49152\,a^4\,b^{11}\,c^{11}\,d+4096\,a^3\,b^{12}\,c^{12}}\right)}^{1/4}}{\left(\left(\left(\frac{\sqrt{x}\,\left(2048\,a^{17}\,b^4\,d^{21}+4096\,a^{16}\,b^5\,c\,d^{20}-108544\,a^{15}\,b^6\,c^2\,d^{19}+337920\,a^{14}\,b^7\,c^3\,d^{18}+153600\,a^{13}\,b^8\,c^4\,d^{17}-3225600\,a^{12}\,b^9\,c^5\,d^{16}+8648704\,a^{11}\,b^{10}\,c^6\,d^{15}-11106304\,a^{10}\,b^{11}\,c^7\,d^{14}+5294080\,a^9\,b^{12}\,c^8\,d^{13}+5294080\,a^8\,b^{13}\,c^9\,d^{12}-11106304\,a^7\,b^{14}\,c^{10}\,d^{11}+8648704\,a^6\,b^{15}\,c^{11}\,d^{10}-3225600\,a^5\,b^{16}\,c^{12}\,d^9+153600\,a^4\,b^{17}\,c^{13}\,d^8+337920\,a^3\,b^{18}\,c^{14}\,d^7-108544\,a^2\,b^{19}\,c^{15}\,d^6+4096\,a\,b^{20}\,c^{16}\,d^5+2048\,b^{21}\,c^{17}\,d^4\right)}{8\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}+\frac{{\left(-\frac{2401\,a^4\,b^3\,d^4+1372\,a^3\,b^4\,c\,d^3+294\,a^2\,b^5\,c^2\,d^2+28\,a\,b^6\,c^3\,d+b^7\,c^4}{4096\,a^{15}\,d^{12}-49152\,a^{14}\,b\,c\,d^{11}+270336\,a^{13}\,b^2\,c^2\,d^{10}-901120\,a^{12}\,b^3\,c^3\,d^9+2027520\,a^{11}\,b^4\,c^4\,d^8-3244032\,a^{10}\,b^5\,c^5\,d^7+3784704\,a^9\,b^6\,c^6\,d^6-3244032\,a^8\,b^7\,c^7\,d^5+2027520\,a^7\,b^8\,c^8\,d^4-901120\,a^6\,b^9\,c^9\,d^3+270336\,a^5\,b^{10}\,c^{10}\,d^2-49152\,a^4\,b^{11}\,c^{11}\,d+4096\,a^3\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(-2048\,a^{15}\,b^4\,c\,d^{18}+8192\,a^{14}\,b^5\,c^2\,d^{17}+59392\,a^{13}\,b^6\,c^3\,d^{16}-606208\,a^{12}\,b^7\,c^4\,d^{15}+2455552\,a^{11}\,b^8\,c^5\,d^{14}-6037504\,a^{10}\,b^9\,c^6\,d^{13}+10070016\,a^9\,b^{10}\,c^7\,d^{12}-11894784\,a^8\,b^{11}\,c^8\,d^{11}+10070016\,a^7\,b^{12}\,c^9\,d^{10}-6037504\,a^6\,b^{13}\,c^{10}\,d^9+2455552\,a^5\,b^{14}\,c^{11}\,d^8-606208\,a^4\,b^{15}\,c^{12}\,d^7+59392\,a^3\,b^{16}\,c^{13}\,d^6+8192\,a^2\,b^{17}\,c^{14}\,d^5-2048\,a\,b^{18}\,c^{15}\,d^4\right)}{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)\,{\left(-\frac{2401\,a^4\,b^3\,d^4+1372\,a^3\,b^4\,c\,d^3+294\,a^2\,b^5\,c^2\,d^2+28\,a\,b^6\,c^3\,d+b^7\,c^4}{4096\,a^{15}\,d^{12}-49152\,a^{14}\,b\,c\,d^{11}+270336\,a^{13}\,b^2\,c^2\,d^{10}-901120\,a^{12}\,b^3\,c^3\,d^9+2027520\,a^{11}\,b^4\,c^4\,d^8-3244032\,a^{10}\,b^5\,c^5\,d^7+3784704\,a^9\,b^6\,c^6\,d^6-3244032\,a^8\,b^7\,c^7\,d^5+2027520\,a^7\,b^8\,c^8\,d^4-901120\,a^6\,b^9\,c^9\,d^3+270336\,a^5\,b^{10}\,c^{10}\,d^2-49152\,a^4\,b^{11}\,c^{11}\,d+4096\,a^3\,b^{12}\,c^{12}}\right)}^{3/4}-\frac{-\frac{7\,a^5\,b^6\,d^{11}}{2}+\frac{2197\,a^4\,b^7\,c\,d^{10}}{2}+9145\,a^3\,b^8\,c^2\,d^9+9145\,a^2\,b^9\,c^3\,d^8+\frac{2197\,a\,b^{10}\,c^4\,d^7}{2}-\frac{7\,b^{11}\,c^5\,d^6}{2}}{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)\,{\left(-\frac{2401\,a^4\,b^3\,d^4+1372\,a^3\,b^4\,c\,d^3+294\,a^2\,b^5\,c^2\,d^2+28\,a\,b^6\,c^3\,d+b^7\,c^4}{4096\,a^{15}\,d^{12}-49152\,a^{14}\,b\,c\,d^{11}+270336\,a^{13}\,b^2\,c^2\,d^{10}-901120\,a^{12}\,b^3\,c^3\,d^9+2027520\,a^{11}\,b^4\,c^4\,d^8-3244032\,a^{10}\,b^5\,c^5\,d^7+3784704\,a^9\,b^6\,c^6\,d^6-3244032\,a^8\,b^7\,c^7\,d^5+2027520\,a^7\,b^8\,c^8\,d^4-901120\,a^6\,b^9\,c^9\,d^3+270336\,a^5\,b^{10}\,c^{10}\,d^2-49152\,a^4\,b^{11}\,c^{11}\,d+4096\,a^3\,b^{12}\,c^{12}}\right)}^{1/4}+\frac{\sqrt{x}\,\left(1225\,a^6\,b^7\,d^{13}+18186\,a^5\,b^8\,c\,d^{12}+75975\,a^4\,b^9\,c^2\,d^{11}+71372\,a^3\,b^{10}\,c^3\,d^{10}+75975\,a^2\,b^{11}\,c^4\,d^9+18186\,a\,b^{12}\,c^5\,d^8+1225\,b^{13}\,c^6\,d^7\right)}{8\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)\,{\left(-\frac{2401\,a^4\,b^3\,d^4+1372\,a^3\,b^4\,c\,d^3+294\,a^2\,b^5\,c^2\,d^2+28\,a\,b^6\,c^3\,d+b^7\,c^4}{4096\,a^{15}\,d^{12}-49152\,a^{14}\,b\,c\,d^{11}+270336\,a^{13}\,b^2\,c^2\,d^{10}-901120\,a^{12}\,b^3\,c^3\,d^9+2027520\,a^{11}\,b^4\,c^4\,d^8-3244032\,a^{10}\,b^5\,c^5\,d^7+3784704\,a^9\,b^6\,c^6\,d^6-3244032\,a^8\,b^7\,c^7\,d^5+2027520\,a^7\,b^8\,c^8\,d^4-901120\,a^6\,b^9\,c^9\,d^3+270336\,a^5\,b^{10}\,c^{10}\,d^2-49152\,a^4\,b^{11}\,c^{11}\,d+4096\,a^3\,b^{12}\,c^{12}}\right)}^{1/4}-\left(\left(\left(\frac{\sqrt{x}\,\left(2048\,a^{17}\,b^4\,d^{21}+4096\,a^{16}\,b^5\,c\,d^{20}-108544\,a^{15}\,b^6\,c^2\,d^{19}+337920\,a^{14}\,b^7\,c^3\,d^{18}+153600\,a^{13}\,b^8\,c^4\,d^{17}-3225600\,a^{12}\,b^9\,c^5\,d^{16}+8648704\,a^{11}\,b^{10}\,c^6\,d^{15}-11106304\,a^{10}\,b^{11}\,c^7\,d^{14}+5294080\,a^9\,b^{12}\,c^8\,d^{13}+5294080\,a^8\,b^{13}\,c^9\,d^{12}-11106304\,a^7\,b^{14}\,c^{10}\,d^{11}+8648704\,a^6\,b^{15}\,c^{11}\,d^{10}-3225600\,a^5\,b^{16}\,c^{12}\,d^9+153600\,a^4\,b^{17}\,c^{13}\,d^8+337920\,a^3\,b^{18}\,c^{14}\,d^7-108544\,a^2\,b^{19}\,c^{15}\,d^6+4096\,a\,b^{20}\,c^{16}\,d^5+2048\,b^{21}\,c^{17}\,d^4\right)}{8\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}-\frac{{\left(-\frac{2401\,a^4\,b^3\,d^4+1372\,a^3\,b^4\,c\,d^3+294\,a^2\,b^5\,c^2\,d^2+28\,a\,b^6\,c^3\,d+b^7\,c^4}{4096\,a^{15}\,d^{12}-49152\,a^{14}\,b\,c\,d^{11}+270336\,a^{13}\,b^2\,c^2\,d^{10}-901120\,a^{12}\,b^3\,c^3\,d^9+2027520\,a^{11}\,b^4\,c^4\,d^8-3244032\,a^{10}\,b^5\,c^5\,d^7+3784704\,a^9\,b^6\,c^6\,d^6-3244032\,a^8\,b^7\,c^7\,d^5+2027520\,a^7\,b^8\,c^8\,d^4-901120\,a^6\,b^9\,c^9\,d^3+270336\,a^5\,b^{10}\,c^{10}\,d^2-49152\,a^4\,b^{11}\,c^{11}\,d+4096\,a^3\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(-2048\,a^{15}\,b^4\,c\,d^{18}+8192\,a^{14}\,b^5\,c^2\,d^{17}+59392\,a^{13}\,b^6\,c^3\,d^{16}-606208\,a^{12}\,b^7\,c^4\,d^{15}+2455552\,a^{11}\,b^8\,c^5\,d^{14}-6037504\,a^{10}\,b^9\,c^6\,d^{13}+10070016\,a^9\,b^{10}\,c^7\,d^{12}-11894784\,a^8\,b^{11}\,c^8\,d^{11}+10070016\,a^7\,b^{12}\,c^9\,d^{10}-6037504\,a^6\,b^{13}\,c^{10}\,d^9+2455552\,a^5\,b^{14}\,c^{11}\,d^8-606208\,a^4\,b^{15}\,c^{12}\,d^7+59392\,a^3\,b^{16}\,c^{13}\,d^6+8192\,a^2\,b^{17}\,c^{14}\,d^5-2048\,a\,b^{18}\,c^{15}\,d^4\right)}{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)\,{\left(-\frac{2401\,a^4\,b^3\,d^4+1372\,a^3\,b^4\,c\,d^3+294\,a^2\,b^5\,c^2\,d^2+28\,a\,b^6\,c^3\,d+b^7\,c^4}{4096\,a^{15}\,d^{12}-49152\,a^{14}\,b\,c\,d^{11}+270336\,a^{13}\,b^2\,c^2\,d^{10}-901120\,a^{12}\,b^3\,c^3\,d^9+2027520\,a^{11}\,b^4\,c^4\,d^8-3244032\,a^{10}\,b^5\,c^5\,d^7+3784704\,a^9\,b^6\,c^6\,d^6-3244032\,a^8\,b^7\,c^7\,d^5+2027520\,a^7\,b^8\,c^8\,d^4-901120\,a^6\,b^9\,c^9\,d^3+270336\,a^5\,b^{10}\,c^{10}\,d^2-49152\,a^4\,b^{11}\,c^{11}\,d+4096\,a^3\,b^{12}\,c^{12}}\right)}^{3/4}+\frac{-\frac{7\,a^5\,b^6\,d^{11}}{2}+\frac{2197\,a^4\,b^7\,c\,d^{10}}{2}+9145\,a^3\,b^8\,c^2\,d^9+9145\,a^2\,b^9\,c^3\,d^8+\frac{2197\,a\,b^{10}\,c^4\,d^7}{2}-\frac{7\,b^{11}\,c^5\,d^6}{2}}{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)\,{\left(-\frac{2401\,a^4\,b^3\,d^4+1372\,a^3\,b^4\,c\,d^3+294\,a^2\,b^5\,c^2\,d^2+28\,a\,b^6\,c^3\,d+b^7\,c^4}{4096\,a^{15}\,d^{12}-49152\,a^{14}\,b\,c\,d^{11}+270336\,a^{13}\,b^2\,c^2\,d^{10}-901120\,a^{12}\,b^3\,c^3\,d^9+2027520\,a^{11}\,b^4\,c^4\,d^8-3244032\,a^{10}\,b^5\,c^5\,d^7+3784704\,a^9\,b^6\,c^6\,d^6-3244032\,a^8\,b^7\,c^7\,d^5+2027520\,a^7\,b^8\,c^8\,d^4-901120\,a^6\,b^9\,c^9\,d^3+270336\,a^5\,b^{10}\,c^{10}\,d^2-49152\,a^4\,b^{11}\,c^{11}\,d+4096\,a^3\,b^{12}\,c^{12}}\right)}^{1/4}+\frac{\sqrt{x}\,\left(1225\,a^6\,b^7\,d^{13}+18186\,a^5\,b^8\,c\,d^{12}+75975\,a^4\,b^9\,c^2\,d^{11}+71372\,a^3\,b^{10}\,c^3\,d^{10}+75975\,a^2\,b^{11}\,c^4\,d^9+18186\,a\,b^{12}\,c^5\,d^8+1225\,b^{13}\,c^6\,d^7\right)}{8\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)\,{\left(-\frac{2401\,a^4\,b^3\,d^4+1372\,a^3\,b^4\,c\,d^3+294\,a^2\,b^5\,c^2\,d^2+28\,a\,b^6\,c^3\,d+b^7\,c^4}{4096\,a^{15}\,d^{12}-49152\,a^{14}\,b\,c\,d^{11}+270336\,a^{13}\,b^2\,c^2\,d^{10}-901120\,a^{12}\,b^3\,c^3\,d^9+2027520\,a^{11}\,b^4\,c^4\,d^8-3244032\,a^{10}\,b^5\,c^5\,d^7+3784704\,a^9\,b^6\,c^6\,d^6-3244032\,a^8\,b^7\,c^7\,d^5+2027520\,a^7\,b^8\,c^8\,d^4-901120\,a^6\,b^9\,c^9\,d^3+270336\,a^5\,b^{10}\,c^{10}\,d^2-49152\,a^4\,b^{11}\,c^{11}\,d+4096\,a^3\,b^{12}\,c^{12}}\right)}^{1/4}}\right)\,{\left(-\frac{2401\,a^4\,b^3\,d^4+1372\,a^3\,b^4\,c\,d^3+294\,a^2\,b^5\,c^2\,d^2+28\,a\,b^6\,c^3\,d+b^7\,c^4}{4096\,a^{15}\,d^{12}-49152\,a^{14}\,b\,c\,d^{11}+270336\,a^{13}\,b^2\,c^2\,d^{10}-901120\,a^{12}\,b^3\,c^3\,d^9+2027520\,a^{11}\,b^4\,c^4\,d^8-3244032\,a^{10}\,b^5\,c^5\,d^7+3784704\,a^9\,b^6\,c^6\,d^6-3244032\,a^8\,b^7\,c^7\,d^5+2027520\,a^7\,b^8\,c^8\,d^4-901120\,a^6\,b^9\,c^9\,d^3+270336\,a^5\,b^{10}\,c^{10}\,d^2-49152\,a^4\,b^{11}\,c^{11}\,d+4096\,a^3\,b^{12}\,c^{12}}\right)}^{1/4}\,2{}\mathrm{i}+2\,\mathrm{atan}\left(-\frac{\left(\left(\left(\frac{{\left(-\frac{2401\,a^4\,b^3\,d^4+1372\,a^3\,b^4\,c\,d^3+294\,a^2\,b^5\,c^2\,d^2+28\,a\,b^6\,c^3\,d+b^7\,c^4}{4096\,a^{15}\,d^{12}-49152\,a^{14}\,b\,c\,d^{11}+270336\,a^{13}\,b^2\,c^2\,d^{10}-901120\,a^{12}\,b^3\,c^3\,d^9+2027520\,a^{11}\,b^4\,c^4\,d^8-3244032\,a^{10}\,b^5\,c^5\,d^7+3784704\,a^9\,b^6\,c^6\,d^6-3244032\,a^8\,b^7\,c^7\,d^5+2027520\,a^7\,b^8\,c^8\,d^4-901120\,a^6\,b^9\,c^9\,d^3+270336\,a^5\,b^{10}\,c^{10}\,d^2-49152\,a^4\,b^{11}\,c^{11}\,d+4096\,a^3\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(-2048\,a^{15}\,b^4\,c\,d^{18}+8192\,a^{14}\,b^5\,c^2\,d^{17}+59392\,a^{13}\,b^6\,c^3\,d^{16}-606208\,a^{12}\,b^7\,c^4\,d^{15}+2455552\,a^{11}\,b^8\,c^5\,d^{14}-6037504\,a^{10}\,b^9\,c^6\,d^{13}+10070016\,a^9\,b^{10}\,c^7\,d^{12}-11894784\,a^8\,b^{11}\,c^8\,d^{11}+10070016\,a^7\,b^{12}\,c^9\,d^{10}-6037504\,a^6\,b^{13}\,c^{10}\,d^9+2455552\,a^5\,b^{14}\,c^{11}\,d^8-606208\,a^4\,b^{15}\,c^{12}\,d^7+59392\,a^3\,b^{16}\,c^{13}\,d^6+8192\,a^2\,b^{17}\,c^{14}\,d^5-2048\,a\,b^{18}\,c^{15}\,d^4\right)}{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}+\frac{\sqrt{x}\,\left(2048\,a^{17}\,b^4\,d^{21}+4096\,a^{16}\,b^5\,c\,d^{20}-108544\,a^{15}\,b^6\,c^2\,d^{19}+337920\,a^{14}\,b^7\,c^3\,d^{18}+153600\,a^{13}\,b^8\,c^4\,d^{17}-3225600\,a^{12}\,b^9\,c^5\,d^{16}+8648704\,a^{11}\,b^{10}\,c^6\,d^{15}-11106304\,a^{10}\,b^{11}\,c^7\,d^{14}+5294080\,a^9\,b^{12}\,c^8\,d^{13}+5294080\,a^8\,b^{13}\,c^9\,d^{12}-11106304\,a^7\,b^{14}\,c^{10}\,d^{11}+8648704\,a^6\,b^{15}\,c^{11}\,d^{10}-3225600\,a^5\,b^{16}\,c^{12}\,d^9+153600\,a^4\,b^{17}\,c^{13}\,d^8+337920\,a^3\,b^{18}\,c^{14}\,d^7-108544\,a^2\,b^{19}\,c^{15}\,d^6+4096\,a\,b^{20}\,c^{16}\,d^5+2048\,b^{21}\,c^{17}\,d^4\right)\,1{}\mathrm{i}}{8\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)\,{\left(-\frac{2401\,a^4\,b^3\,d^4+1372\,a^3\,b^4\,c\,d^3+294\,a^2\,b^5\,c^2\,d^2+28\,a\,b^6\,c^3\,d+b^7\,c^4}{4096\,a^{15}\,d^{12}-49152\,a^{14}\,b\,c\,d^{11}+270336\,a^{13}\,b^2\,c^2\,d^{10}-901120\,a^{12}\,b^3\,c^3\,d^9+2027520\,a^{11}\,b^4\,c^4\,d^8-3244032\,a^{10}\,b^5\,c^5\,d^7+3784704\,a^9\,b^6\,c^6\,d^6-3244032\,a^8\,b^7\,c^7\,d^5+2027520\,a^7\,b^8\,c^8\,d^4-901120\,a^6\,b^9\,c^9\,d^3+270336\,a^5\,b^{10}\,c^{10}\,d^2-49152\,a^4\,b^{11}\,c^{11}\,d+4096\,a^3\,b^{12}\,c^{12}}\right)}^{3/4}\,1{}\mathrm{i}-\frac{\left(-\frac{7\,a^5\,b^6\,d^{11}}{2}+\frac{2197\,a^4\,b^7\,c\,d^{10}}{2}+9145\,a^3\,b^8\,c^2\,d^9+9145\,a^2\,b^9\,c^3\,d^8+\frac{2197\,a\,b^{10}\,c^4\,d^7}{2}-\frac{7\,b^{11}\,c^5\,d^6}{2}\right)\,1{}\mathrm{i}}{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)\,{\left(-\frac{2401\,a^4\,b^3\,d^4+1372\,a^3\,b^4\,c\,d^3+294\,a^2\,b^5\,c^2\,d^2+28\,a\,b^6\,c^3\,d+b^7\,c^4}{4096\,a^{15}\,d^{12}-49152\,a^{14}\,b\,c\,d^{11}+270336\,a^{13}\,b^2\,c^2\,d^{10}-901120\,a^{12}\,b^3\,c^3\,d^9+2027520\,a^{11}\,b^4\,c^4\,d^8-3244032\,a^{10}\,b^5\,c^5\,d^7+3784704\,a^9\,b^6\,c^6\,d^6-3244032\,a^8\,b^7\,c^7\,d^5+2027520\,a^7\,b^8\,c^8\,d^4-901120\,a^6\,b^9\,c^9\,d^3+270336\,a^5\,b^{10}\,c^{10}\,d^2-49152\,a^4\,b^{11}\,c^{11}\,d+4096\,a^3\,b^{12}\,c^{12}}\right)}^{1/4}-\frac{\sqrt{x}\,\left(1225\,a^6\,b^7\,d^{13}+18186\,a^5\,b^8\,c\,d^{12}+75975\,a^4\,b^9\,c^2\,d^{11}+71372\,a^3\,b^{10}\,c^3\,d^{10}+75975\,a^2\,b^{11}\,c^4\,d^9+18186\,a\,b^{12}\,c^5\,d^8+1225\,b^{13}\,c^6\,d^7\right)}{8\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)\,{\left(-\frac{2401\,a^4\,b^3\,d^4+1372\,a^3\,b^4\,c\,d^3+294\,a^2\,b^5\,c^2\,d^2+28\,a\,b^6\,c^3\,d+b^7\,c^4}{4096\,a^{15}\,d^{12}-49152\,a^{14}\,b\,c\,d^{11}+270336\,a^{13}\,b^2\,c^2\,d^{10}-901120\,a^{12}\,b^3\,c^3\,d^9+2027520\,a^{11}\,b^4\,c^4\,d^8-3244032\,a^{10}\,b^5\,c^5\,d^7+3784704\,a^9\,b^6\,c^6\,d^6-3244032\,a^8\,b^7\,c^7\,d^5+2027520\,a^7\,b^8\,c^8\,d^4-901120\,a^6\,b^9\,c^9\,d^3+270336\,a^5\,b^{10}\,c^{10}\,d^2-49152\,a^4\,b^{11}\,c^{11}\,d+4096\,a^3\,b^{12}\,c^{12}}\right)}^{1/4}+\left(\left(\left(-\frac{{\left(-\frac{2401\,a^4\,b^3\,d^4+1372\,a^3\,b^4\,c\,d^3+294\,a^2\,b^5\,c^2\,d^2+28\,a\,b^6\,c^3\,d+b^7\,c^4}{4096\,a^{15}\,d^{12}-49152\,a^{14}\,b\,c\,d^{11}+270336\,a^{13}\,b^2\,c^2\,d^{10}-901120\,a^{12}\,b^3\,c^3\,d^9+2027520\,a^{11}\,b^4\,c^4\,d^8-3244032\,a^{10}\,b^5\,c^5\,d^7+3784704\,a^9\,b^6\,c^6\,d^6-3244032\,a^8\,b^7\,c^7\,d^5+2027520\,a^7\,b^8\,c^8\,d^4-901120\,a^6\,b^9\,c^9\,d^3+270336\,a^5\,b^{10}\,c^{10}\,d^2-49152\,a^4\,b^{11}\,c^{11}\,d+4096\,a^3\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(-2048\,a^{15}\,b^4\,c\,d^{18}+8192\,a^{14}\,b^5\,c^2\,d^{17}+59392\,a^{13}\,b^6\,c^3\,d^{16}-606208\,a^{12}\,b^7\,c^4\,d^{15}+2455552\,a^{11}\,b^8\,c^5\,d^{14}-6037504\,a^{10}\,b^9\,c^6\,d^{13}+10070016\,a^9\,b^{10}\,c^7\,d^{12}-11894784\,a^8\,b^{11}\,c^8\,d^{11}+10070016\,a^7\,b^{12}\,c^9\,d^{10}-6037504\,a^6\,b^{13}\,c^{10}\,d^9+2455552\,a^5\,b^{14}\,c^{11}\,d^8-606208\,a^4\,b^{15}\,c^{12}\,d^7+59392\,a^3\,b^{16}\,c^{13}\,d^6+8192\,a^2\,b^{17}\,c^{14}\,d^5-2048\,a\,b^{18}\,c^{15}\,d^4\right)}{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}+\frac{\sqrt{x}\,\left(2048\,a^{17}\,b^4\,d^{21}+4096\,a^{16}\,b^5\,c\,d^{20}-108544\,a^{15}\,b^6\,c^2\,d^{19}+337920\,a^{14}\,b^7\,c^3\,d^{18}+153600\,a^{13}\,b^8\,c^4\,d^{17}-3225600\,a^{12}\,b^9\,c^5\,d^{16}+8648704\,a^{11}\,b^{10}\,c^6\,d^{15}-11106304\,a^{10}\,b^{11}\,c^7\,d^{14}+5294080\,a^9\,b^{12}\,c^8\,d^{13}+5294080\,a^8\,b^{13}\,c^9\,d^{12}-11106304\,a^7\,b^{14}\,c^{10}\,d^{11}+8648704\,a^6\,b^{15}\,c^{11}\,d^{10}-3225600\,a^5\,b^{16}\,c^{12}\,d^9+153600\,a^4\,b^{17}\,c^{13}\,d^8+337920\,a^3\,b^{18}\,c^{14}\,d^7-108544\,a^2\,b^{19}\,c^{15}\,d^6+4096\,a\,b^{20}\,c^{16}\,d^5+2048\,b^{21}\,c^{17}\,d^4\right)\,1{}\mathrm{i}}{8\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)\,{\left(-\frac{2401\,a^4\,b^3\,d^4+1372\,a^3\,b^4\,c\,d^3+294\,a^2\,b^5\,c^2\,d^2+28\,a\,b^6\,c^3\,d+b^7\,c^4}{4096\,a^{15}\,d^{12}-49152\,a^{14}\,b\,c\,d^{11}+270336\,a^{13}\,b^2\,c^2\,d^{10}-901120\,a^{12}\,b^3\,c^3\,d^9+2027520\,a^{11}\,b^4\,c^4\,d^8-3244032\,a^{10}\,b^5\,c^5\,d^7+3784704\,a^9\,b^6\,c^6\,d^6-3244032\,a^8\,b^7\,c^7\,d^5+2027520\,a^7\,b^8\,c^8\,d^4-901120\,a^6\,b^9\,c^9\,d^3+270336\,a^5\,b^{10}\,c^{10}\,d^2-49152\,a^4\,b^{11}\,c^{11}\,d+4096\,a^3\,b^{12}\,c^{12}}\right)}^{3/4}\,1{}\mathrm{i}+\frac{\left(-\frac{7\,a^5\,b^6\,d^{11}}{2}+\frac{2197\,a^4\,b^7\,c\,d^{10}}{2}+9145\,a^3\,b^8\,c^2\,d^9+9145\,a^2\,b^9\,c^3\,d^8+\frac{2197\,a\,b^{10}\,c^4\,d^7}{2}-\frac{7\,b^{11}\,c^5\,d^6}{2}\right)\,1{}\mathrm{i}}{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)\,{\left(-\frac{2401\,a^4\,b^3\,d^4+1372\,a^3\,b^4\,c\,d^3+294\,a^2\,b^5\,c^2\,d^2+28\,a\,b^6\,c^3\,d+b^7\,c^4}{4096\,a^{15}\,d^{12}-49152\,a^{14}\,b\,c\,d^{11}+270336\,a^{13}\,b^2\,c^2\,d^{10}-901120\,a^{12}\,b^3\,c^3\,d^9+2027520\,a^{11}\,b^4\,c^4\,d^8-3244032\,a^{10}\,b^5\,c^5\,d^7+3784704\,a^9\,b^6\,c^6\,d^6-3244032\,a^8\,b^7\,c^7\,d^5+2027520\,a^7\,b^8\,c^8\,d^4-901120\,a^6\,b^9\,c^9\,d^3+270336\,a^5\,b^{10}\,c^{10}\,d^2-49152\,a^4\,b^{11}\,c^{11}\,d+4096\,a^3\,b^{12}\,c^{12}}\right)}^{1/4}-\frac{\sqrt{x}\,\left(1225\,a^6\,b^7\,d^{13}+18186\,a^5\,b^8\,c\,d^{12}+75975\,a^4\,b^9\,c^2\,d^{11}+71372\,a^3\,b^{10}\,c^3\,d^{10}+75975\,a^2\,b^{11}\,c^4\,d^9+18186\,a\,b^{12}\,c^5\,d^8+1225\,b^{13}\,c^6\,d^7\right)}{8\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)\,{\left(-\frac{2401\,a^4\,b^3\,d^4+1372\,a^3\,b^4\,c\,d^3+294\,a^2\,b^5\,c^2\,d^2+28\,a\,b^6\,c^3\,d+b^7\,c^4}{4096\,a^{15}\,d^{12}-49152\,a^{14}\,b\,c\,d^{11}+270336\,a^{13}\,b^2\,c^2\,d^{10}-901120\,a^{12}\,b^3\,c^3\,d^9+2027520\,a^{11}\,b^4\,c^4\,d^8-3244032\,a^{10}\,b^5\,c^5\,d^7+3784704\,a^9\,b^6\,c^6\,d^6-3244032\,a^8\,b^7\,c^7\,d^5+2027520\,a^7\,b^8\,c^8\,d^4-901120\,a^6\,b^9\,c^9\,d^3+270336\,a^5\,b^{10}\,c^{10}\,d^2-49152\,a^4\,b^{11}\,c^{11}\,d+4096\,a^3\,b^{12}\,c^{12}}\right)}^{1/4}}{\left(\left(\left(\frac{{\left(-\frac{2401\,a^4\,b^3\,d^4+1372\,a^3\,b^4\,c\,d^3+294\,a^2\,b^5\,c^2\,d^2+28\,a\,b^6\,c^3\,d+b^7\,c^4}{4096\,a^{15}\,d^{12}-49152\,a^{14}\,b\,c\,d^{11}+270336\,a^{13}\,b^2\,c^2\,d^{10}-901120\,a^{12}\,b^3\,c^3\,d^9+2027520\,a^{11}\,b^4\,c^4\,d^8-3244032\,a^{10}\,b^5\,c^5\,d^7+3784704\,a^9\,b^6\,c^6\,d^6-3244032\,a^8\,b^7\,c^7\,d^5+2027520\,a^7\,b^8\,c^8\,d^4-901120\,a^6\,b^9\,c^9\,d^3+270336\,a^5\,b^{10}\,c^{10}\,d^2-49152\,a^4\,b^{11}\,c^{11}\,d+4096\,a^3\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(-2048\,a^{15}\,b^4\,c\,d^{18}+8192\,a^{14}\,b^5\,c^2\,d^{17}+59392\,a^{13}\,b^6\,c^3\,d^{16}-606208\,a^{12}\,b^7\,c^4\,d^{15}+2455552\,a^{11}\,b^8\,c^5\,d^{14}-6037504\,a^{10}\,b^9\,c^6\,d^{13}+10070016\,a^9\,b^{10}\,c^7\,d^{12}-11894784\,a^8\,b^{11}\,c^8\,d^{11}+10070016\,a^7\,b^{12}\,c^9\,d^{10}-6037504\,a^6\,b^{13}\,c^{10}\,d^9+2455552\,a^5\,b^{14}\,c^{11}\,d^8-606208\,a^4\,b^{15}\,c^{12}\,d^7+59392\,a^3\,b^{16}\,c^{13}\,d^6+8192\,a^2\,b^{17}\,c^{14}\,d^5-2048\,a\,b^{18}\,c^{15}\,d^4\right)}{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}+\frac{\sqrt{x}\,\left(2048\,a^{17}\,b^4\,d^{21}+4096\,a^{16}\,b^5\,c\,d^{20}-108544\,a^{15}\,b^6\,c^2\,d^{19}+337920\,a^{14}\,b^7\,c^3\,d^{18}+153600\,a^{13}\,b^8\,c^4\,d^{17}-3225600\,a^{12}\,b^9\,c^5\,d^{16}+8648704\,a^{11}\,b^{10}\,c^6\,d^{15}-11106304\,a^{10}\,b^{11}\,c^7\,d^{14}+5294080\,a^9\,b^{12}\,c^8\,d^{13}+5294080\,a^8\,b^{13}\,c^9\,d^{12}-11106304\,a^7\,b^{14}\,c^{10}\,d^{11}+8648704\,a^6\,b^{15}\,c^{11}\,d^{10}-3225600\,a^5\,b^{16}\,c^{12}\,d^9+153600\,a^4\,b^{17}\,c^{13}\,d^8+337920\,a^3\,b^{18}\,c^{14}\,d^7-108544\,a^2\,b^{19}\,c^{15}\,d^6+4096\,a\,b^{20}\,c^{16}\,d^5+2048\,b^{21}\,c^{17}\,d^4\right)\,1{}\mathrm{i}}{8\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)\,{\left(-\frac{2401\,a^4\,b^3\,d^4+1372\,a^3\,b^4\,c\,d^3+294\,a^2\,b^5\,c^2\,d^2+28\,a\,b^6\,c^3\,d+b^7\,c^4}{4096\,a^{15}\,d^{12}-49152\,a^{14}\,b\,c\,d^{11}+270336\,a^{13}\,b^2\,c^2\,d^{10}-901120\,a^{12}\,b^3\,c^3\,d^9+2027520\,a^{11}\,b^4\,c^4\,d^8-3244032\,a^{10}\,b^5\,c^5\,d^7+3784704\,a^9\,b^6\,c^6\,d^6-3244032\,a^8\,b^7\,c^7\,d^5+2027520\,a^7\,b^8\,c^8\,d^4-901120\,a^6\,b^9\,c^9\,d^3+270336\,a^5\,b^{10}\,c^{10}\,d^2-49152\,a^4\,b^{11}\,c^{11}\,d+4096\,a^3\,b^{12}\,c^{12}}\right)}^{3/4}\,1{}\mathrm{i}-\frac{\left(-\frac{7\,a^5\,b^6\,d^{11}}{2}+\frac{2197\,a^4\,b^7\,c\,d^{10}}{2}+9145\,a^3\,b^8\,c^2\,d^9+9145\,a^2\,b^9\,c^3\,d^8+\frac{2197\,a\,b^{10}\,c^4\,d^7}{2}-\frac{7\,b^{11}\,c^5\,d^6}{2}\right)\,1{}\mathrm{i}}{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)\,{\left(-\frac{2401\,a^4\,b^3\,d^4+1372\,a^3\,b^4\,c\,d^3+294\,a^2\,b^5\,c^2\,d^2+28\,a\,b^6\,c^3\,d+b^7\,c^4}{4096\,a^{15}\,d^{12}-49152\,a^{14}\,b\,c\,d^{11}+270336\,a^{13}\,b^2\,c^2\,d^{10}-901120\,a^{12}\,b^3\,c^3\,d^9+2027520\,a^{11}\,b^4\,c^4\,d^8-3244032\,a^{10}\,b^5\,c^5\,d^7+3784704\,a^9\,b^6\,c^6\,d^6-3244032\,a^8\,b^7\,c^7\,d^5+2027520\,a^7\,b^8\,c^8\,d^4-901120\,a^6\,b^9\,c^9\,d^3+270336\,a^5\,b^{10}\,c^{10}\,d^2-49152\,a^4\,b^{11}\,c^{11}\,d+4096\,a^3\,b^{12}\,c^{12}}\right)}^{1/4}\,1{}\mathrm{i}-\frac{\sqrt{x}\,\left(1225\,a^6\,b^7\,d^{13}+18186\,a^5\,b^8\,c\,d^{12}+75975\,a^4\,b^9\,c^2\,d^{11}+71372\,a^3\,b^{10}\,c^3\,d^{10}+75975\,a^2\,b^{11}\,c^4\,d^9+18186\,a\,b^{12}\,c^5\,d^8+1225\,b^{13}\,c^6\,d^7\right)\,1{}\mathrm{i}}{8\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)\,{\left(-\frac{2401\,a^4\,b^3\,d^4+1372\,a^3\,b^4\,c\,d^3+294\,a^2\,b^5\,c^2\,d^2+28\,a\,b^6\,c^3\,d+b^7\,c^4}{4096\,a^{15}\,d^{12}-49152\,a^{14}\,b\,c\,d^{11}+270336\,a^{13}\,b^2\,c^2\,d^{10}-901120\,a^{12}\,b^3\,c^3\,d^9+2027520\,a^{11}\,b^4\,c^4\,d^8-3244032\,a^{10}\,b^5\,c^5\,d^7+3784704\,a^9\,b^6\,c^6\,d^6-3244032\,a^8\,b^7\,c^7\,d^5+2027520\,a^7\,b^8\,c^8\,d^4-901120\,a^6\,b^9\,c^9\,d^3+270336\,a^5\,b^{10}\,c^{10}\,d^2-49152\,a^4\,b^{11}\,c^{11}\,d+4096\,a^3\,b^{12}\,c^{12}}\right)}^{1/4}-\left(\left(\left(-\frac{{\left(-\frac{2401\,a^4\,b^3\,d^4+1372\,a^3\,b^4\,c\,d^3+294\,a^2\,b^5\,c^2\,d^2+28\,a\,b^6\,c^3\,d+b^7\,c^4}{4096\,a^{15}\,d^{12}-49152\,a^{14}\,b\,c\,d^{11}+270336\,a^{13}\,b^2\,c^2\,d^{10}-901120\,a^{12}\,b^3\,c^3\,d^9+2027520\,a^{11}\,b^4\,c^4\,d^8-3244032\,a^{10}\,b^5\,c^5\,d^7+3784704\,a^9\,b^6\,c^6\,d^6-3244032\,a^8\,b^7\,c^7\,d^5+2027520\,a^7\,b^8\,c^8\,d^4-901120\,a^6\,b^9\,c^9\,d^3+270336\,a^5\,b^{10}\,c^{10}\,d^2-49152\,a^4\,b^{11}\,c^{11}\,d+4096\,a^3\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(-2048\,a^{15}\,b^4\,c\,d^{18}+8192\,a^{14}\,b^5\,c^2\,d^{17}+59392\,a^{13}\,b^6\,c^3\,d^{16}-606208\,a^{12}\,b^7\,c^4\,d^{15}+2455552\,a^{11}\,b^8\,c^5\,d^{14}-6037504\,a^{10}\,b^9\,c^6\,d^{13}+10070016\,a^9\,b^{10}\,c^7\,d^{12}-11894784\,a^8\,b^{11}\,c^8\,d^{11}+10070016\,a^7\,b^{12}\,c^9\,d^{10}-6037504\,a^6\,b^{13}\,c^{10}\,d^9+2455552\,a^5\,b^{14}\,c^{11}\,d^8-606208\,a^4\,b^{15}\,c^{12}\,d^7+59392\,a^3\,b^{16}\,c^{13}\,d^6+8192\,a^2\,b^{17}\,c^{14}\,d^5-2048\,a\,b^{18}\,c^{15}\,d^4\right)}{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}+\frac{\sqrt{x}\,\left(2048\,a^{17}\,b^4\,d^{21}+4096\,a^{16}\,b^5\,c\,d^{20}-108544\,a^{15}\,b^6\,c^2\,d^{19}+337920\,a^{14}\,b^7\,c^3\,d^{18}+153600\,a^{13}\,b^8\,c^4\,d^{17}-3225600\,a^{12}\,b^9\,c^5\,d^{16}+8648704\,a^{11}\,b^{10}\,c^6\,d^{15}-11106304\,a^{10}\,b^{11}\,c^7\,d^{14}+5294080\,a^9\,b^{12}\,c^8\,d^{13}+5294080\,a^8\,b^{13}\,c^9\,d^{12}-11106304\,a^7\,b^{14}\,c^{10}\,d^{11}+8648704\,a^6\,b^{15}\,c^{11}\,d^{10}-3225600\,a^5\,b^{16}\,c^{12}\,d^9+153600\,a^4\,b^{17}\,c^{13}\,d^8+337920\,a^3\,b^{18}\,c^{14}\,d^7-108544\,a^2\,b^{19}\,c^{15}\,d^6+4096\,a\,b^{20}\,c^{16}\,d^5+2048\,b^{21}\,c^{17}\,d^4\right)\,1{}\mathrm{i}}{8\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)\,{\left(-\frac{2401\,a^4\,b^3\,d^4+1372\,a^3\,b^4\,c\,d^3+294\,a^2\,b^5\,c^2\,d^2+28\,a\,b^6\,c^3\,d+b^7\,c^4}{4096\,a^{15}\,d^{12}-49152\,a^{14}\,b\,c\,d^{11}+270336\,a^{13}\,b^2\,c^2\,d^{10}-901120\,a^{12}\,b^3\,c^3\,d^9+2027520\,a^{11}\,b^4\,c^4\,d^8-3244032\,a^{10}\,b^5\,c^5\,d^7+3784704\,a^9\,b^6\,c^6\,d^6-3244032\,a^8\,b^7\,c^7\,d^5+2027520\,a^7\,b^8\,c^8\,d^4-901120\,a^6\,b^9\,c^9\,d^3+270336\,a^5\,b^{10}\,c^{10}\,d^2-49152\,a^4\,b^{11}\,c^{11}\,d+4096\,a^3\,b^{12}\,c^{12}}\right)}^{3/4}\,1{}\mathrm{i}+\frac{\left(-\frac{7\,a^5\,b^6\,d^{11}}{2}+\frac{2197\,a^4\,b^7\,c\,d^{10}}{2}+9145\,a^3\,b^8\,c^2\,d^9+9145\,a^2\,b^9\,c^3\,d^8+\frac{2197\,a\,b^{10}\,c^4\,d^7}{2}-\frac{7\,b^{11}\,c^5\,d^6}{2}\right)\,1{}\mathrm{i}}{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)\,{\left(-\frac{2401\,a^4\,b^3\,d^4+1372\,a^3\,b^4\,c\,d^3+294\,a^2\,b^5\,c^2\,d^2+28\,a\,b^6\,c^3\,d+b^7\,c^4}{4096\,a^{15}\,d^{12}-49152\,a^{14}\,b\,c\,d^{11}+270336\,a^{13}\,b^2\,c^2\,d^{10}-901120\,a^{12}\,b^3\,c^3\,d^9+2027520\,a^{11}\,b^4\,c^4\,d^8-3244032\,a^{10}\,b^5\,c^5\,d^7+3784704\,a^9\,b^6\,c^6\,d^6-3244032\,a^8\,b^7\,c^7\,d^5+2027520\,a^7\,b^8\,c^8\,d^4-901120\,a^6\,b^9\,c^9\,d^3+270336\,a^5\,b^{10}\,c^{10}\,d^2-49152\,a^4\,b^{11}\,c^{11}\,d+4096\,a^3\,b^{12}\,c^{12}}\right)}^{1/4}\,1{}\mathrm{i}-\frac{\sqrt{x}\,\left(1225\,a^6\,b^7\,d^{13}+18186\,a^5\,b^8\,c\,d^{12}+75975\,a^4\,b^9\,c^2\,d^{11}+71372\,a^3\,b^{10}\,c^3\,d^{10}+75975\,a^2\,b^{11}\,c^4\,d^9+18186\,a\,b^{12}\,c^5\,d^8+1225\,b^{13}\,c^6\,d^7\right)\,1{}\mathrm{i}}{8\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)\,{\left(-\frac{2401\,a^4\,b^3\,d^4+1372\,a^3\,b^4\,c\,d^3+294\,a^2\,b^5\,c^2\,d^2+28\,a\,b^6\,c^3\,d+b^7\,c^4}{4096\,a^{15}\,d^{12}-49152\,a^{14}\,b\,c\,d^{11}+270336\,a^{13}\,b^2\,c^2\,d^{10}-901120\,a^{12}\,b^3\,c^3\,d^9+2027520\,a^{11}\,b^4\,c^4\,d^8-3244032\,a^{10}\,b^5\,c^5\,d^7+3784704\,a^9\,b^6\,c^6\,d^6-3244032\,a^8\,b^7\,c^7\,d^5+2027520\,a^7\,b^8\,c^8\,d^4-901120\,a^6\,b^9\,c^9\,d^3+270336\,a^5\,b^{10}\,c^{10}\,d^2-49152\,a^4\,b^{11}\,c^{11}\,d+4096\,a^3\,b^{12}\,c^{12}}\right)}^{1/4}}\right)\,{\left(-\frac{2401\,a^4\,b^3\,d^4+1372\,a^3\,b^4\,c\,d^3+294\,a^2\,b^5\,c^2\,d^2+28\,a\,b^6\,c^3\,d+b^7\,c^4}{4096\,a^{15}\,d^{12}-49152\,a^{14}\,b\,c\,d^{11}+270336\,a^{13}\,b^2\,c^2\,d^{10}-901120\,a^{12}\,b^3\,c^3\,d^9+2027520\,a^{11}\,b^4\,c^4\,d^8-3244032\,a^{10}\,b^5\,c^5\,d^7+3784704\,a^9\,b^6\,c^6\,d^6-3244032\,a^8\,b^7\,c^7\,d^5+2027520\,a^7\,b^8\,c^8\,d^4-901120\,a^6\,b^9\,c^9\,d^3+270336\,a^5\,b^{10}\,c^{10}\,d^2-49152\,a^4\,b^{11}\,c^{11}\,d+4096\,a^3\,b^{12}\,c^{12}}\right)}^{1/4}-\mathrm{atan}\left(-\frac{\left(\left(\left(\frac{\sqrt{x}\,\left(2048\,a^{17}\,b^4\,d^{21}+4096\,a^{16}\,b^5\,c\,d^{20}-108544\,a^{15}\,b^6\,c^2\,d^{19}+337920\,a^{14}\,b^7\,c^3\,d^{18}+153600\,a^{13}\,b^8\,c^4\,d^{17}-3225600\,a^{12}\,b^9\,c^5\,d^{16}+8648704\,a^{11}\,b^{10}\,c^6\,d^{15}-11106304\,a^{10}\,b^{11}\,c^7\,d^{14}+5294080\,a^9\,b^{12}\,c^8\,d^{13}+5294080\,a^8\,b^{13}\,c^9\,d^{12}-11106304\,a^7\,b^{14}\,c^{10}\,d^{11}+8648704\,a^6\,b^{15}\,c^{11}\,d^{10}-3225600\,a^5\,b^{16}\,c^{12}\,d^9+153600\,a^4\,b^{17}\,c^{13}\,d^8+337920\,a^3\,b^{18}\,c^{14}\,d^7-108544\,a^2\,b^{19}\,c^{15}\,d^6+4096\,a\,b^{20}\,c^{16}\,d^5+2048\,b^{21}\,c^{17}\,d^4\right)}{8\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}+\frac{{\left(-\frac{a^4\,d^7+28\,a^3\,b\,c\,d^6+294\,a^2\,b^2\,c^2\,d^5+1372\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{4096\,a^{12}\,c^3\,d^{12}-49152\,a^{11}\,b\,c^4\,d^{11}+270336\,a^{10}\,b^2\,c^5\,d^{10}-901120\,a^9\,b^3\,c^6\,d^9+2027520\,a^8\,b^4\,c^7\,d^8-3244032\,a^7\,b^5\,c^8\,d^7+3784704\,a^6\,b^6\,c^9\,d^6-3244032\,a^5\,b^7\,c^{10}\,d^5+2027520\,a^4\,b^8\,c^{11}\,d^4-901120\,a^3\,b^9\,c^{12}\,d^3+270336\,a^2\,b^{10}\,c^{13}\,d^2-49152\,a\,b^{11}\,c^{14}\,d+4096\,b^{12}\,c^{15}}\right)}^{1/4}\,\left(-2048\,a^{15}\,b^4\,c\,d^{18}+8192\,a^{14}\,b^5\,c^2\,d^{17}+59392\,a^{13}\,b^6\,c^3\,d^{16}-606208\,a^{12}\,b^7\,c^4\,d^{15}+2455552\,a^{11}\,b^8\,c^5\,d^{14}-6037504\,a^{10}\,b^9\,c^6\,d^{13}+10070016\,a^9\,b^{10}\,c^7\,d^{12}-11894784\,a^8\,b^{11}\,c^8\,d^{11}+10070016\,a^7\,b^{12}\,c^9\,d^{10}-6037504\,a^6\,b^{13}\,c^{10}\,d^9+2455552\,a^5\,b^{14}\,c^{11}\,d^8-606208\,a^4\,b^{15}\,c^{12}\,d^7+59392\,a^3\,b^{16}\,c^{13}\,d^6+8192\,a^2\,b^{17}\,c^{14}\,d^5-2048\,a\,b^{18}\,c^{15}\,d^4\right)}{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)\,{\left(-\frac{a^4\,d^7+28\,a^3\,b\,c\,d^6+294\,a^2\,b^2\,c^2\,d^5+1372\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{4096\,a^{12}\,c^3\,d^{12}-49152\,a^{11}\,b\,c^4\,d^{11}+270336\,a^{10}\,b^2\,c^5\,d^{10}-901120\,a^9\,b^3\,c^6\,d^9+2027520\,a^8\,b^4\,c^7\,d^8-3244032\,a^7\,b^5\,c^8\,d^7+3784704\,a^6\,b^6\,c^9\,d^6-3244032\,a^5\,b^7\,c^{10}\,d^5+2027520\,a^4\,b^8\,c^{11}\,d^4-901120\,a^3\,b^9\,c^{12}\,d^3+270336\,a^2\,b^{10}\,c^{13}\,d^2-49152\,a\,b^{11}\,c^{14}\,d+4096\,b^{12}\,c^{15}}\right)}^{3/4}-\frac{-\frac{7\,a^5\,b^6\,d^{11}}{2}+\frac{2197\,a^4\,b^7\,c\,d^{10}}{2}+9145\,a^3\,b^8\,c^2\,d^9+9145\,a^2\,b^9\,c^3\,d^8+\frac{2197\,a\,b^{10}\,c^4\,d^7}{2}-\frac{7\,b^{11}\,c^5\,d^6}{2}}{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)\,{\left(-\frac{a^4\,d^7+28\,a^3\,b\,c\,d^6+294\,a^2\,b^2\,c^2\,d^5+1372\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{4096\,a^{12}\,c^3\,d^{12}-49152\,a^{11}\,b\,c^4\,d^{11}+270336\,a^{10}\,b^2\,c^5\,d^{10}-901120\,a^9\,b^3\,c^6\,d^9+2027520\,a^8\,b^4\,c^7\,d^8-3244032\,a^7\,b^5\,c^8\,d^7+3784704\,a^6\,b^6\,c^9\,d^6-3244032\,a^5\,b^7\,c^{10}\,d^5+2027520\,a^4\,b^8\,c^{11}\,d^4-901120\,a^3\,b^9\,c^{12}\,d^3+270336\,a^2\,b^{10}\,c^{13}\,d^2-49152\,a\,b^{11}\,c^{14}\,d+4096\,b^{12}\,c^{15}}\right)}^{1/4}\,1{}\mathrm{i}+\frac{\sqrt{x}\,\left(1225\,a^6\,b^7\,d^{13}+18186\,a^5\,b^8\,c\,d^{12}+75975\,a^4\,b^9\,c^2\,d^{11}+71372\,a^3\,b^{10}\,c^3\,d^{10}+75975\,a^2\,b^{11}\,c^4\,d^9+18186\,a\,b^{12}\,c^5\,d^8+1225\,b^{13}\,c^6\,d^7\right)\,1{}\mathrm{i}}{8\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)\,{\left(-\frac{a^4\,d^7+28\,a^3\,b\,c\,d^6+294\,a^2\,b^2\,c^2\,d^5+1372\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{4096\,a^{12}\,c^3\,d^{12}-49152\,a^{11}\,b\,c^4\,d^{11}+270336\,a^{10}\,b^2\,c^5\,d^{10}-901120\,a^9\,b^3\,c^6\,d^9+2027520\,a^8\,b^4\,c^7\,d^8-3244032\,a^7\,b^5\,c^8\,d^7+3784704\,a^6\,b^6\,c^9\,d^6-3244032\,a^5\,b^7\,c^{10}\,d^5+2027520\,a^4\,b^8\,c^{11}\,d^4-901120\,a^3\,b^9\,c^{12}\,d^3+270336\,a^2\,b^{10}\,c^{13}\,d^2-49152\,a\,b^{11}\,c^{14}\,d+4096\,b^{12}\,c^{15}}\right)}^{1/4}+\left(\left(\left(\frac{\sqrt{x}\,\left(2048\,a^{17}\,b^4\,d^{21}+4096\,a^{16}\,b^5\,c\,d^{20}-108544\,a^{15}\,b^6\,c^2\,d^{19}+337920\,a^{14}\,b^7\,c^3\,d^{18}+153600\,a^{13}\,b^8\,c^4\,d^{17}-3225600\,a^{12}\,b^9\,c^5\,d^{16}+8648704\,a^{11}\,b^{10}\,c^6\,d^{15}-11106304\,a^{10}\,b^{11}\,c^7\,d^{14}+5294080\,a^9\,b^{12}\,c^8\,d^{13}+5294080\,a^8\,b^{13}\,c^9\,d^{12}-11106304\,a^7\,b^{14}\,c^{10}\,d^{11}+8648704\,a^6\,b^{15}\,c^{11}\,d^{10}-3225600\,a^5\,b^{16}\,c^{12}\,d^9+153600\,a^4\,b^{17}\,c^{13}\,d^8+337920\,a^3\,b^{18}\,c^{14}\,d^7-108544\,a^2\,b^{19}\,c^{15}\,d^6+4096\,a\,b^{20}\,c^{16}\,d^5+2048\,b^{21}\,c^{17}\,d^4\right)}{8\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}-\frac{{\left(-\frac{a^4\,d^7+28\,a^3\,b\,c\,d^6+294\,a^2\,b^2\,c^2\,d^5+1372\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{4096\,a^{12}\,c^3\,d^{12}-49152\,a^{11}\,b\,c^4\,d^{11}+270336\,a^{10}\,b^2\,c^5\,d^{10}-901120\,a^9\,b^3\,c^6\,d^9+2027520\,a^8\,b^4\,c^7\,d^8-3244032\,a^7\,b^5\,c^8\,d^7+3784704\,a^6\,b^6\,c^9\,d^6-3244032\,a^5\,b^7\,c^{10}\,d^5+2027520\,a^4\,b^8\,c^{11}\,d^4-901120\,a^3\,b^9\,c^{12}\,d^3+270336\,a^2\,b^{10}\,c^{13}\,d^2-49152\,a\,b^{11}\,c^{14}\,d+4096\,b^{12}\,c^{15}}\right)}^{1/4}\,\left(-2048\,a^{15}\,b^4\,c\,d^{18}+8192\,a^{14}\,b^5\,c^2\,d^{17}+59392\,a^{13}\,b^6\,c^3\,d^{16}-606208\,a^{12}\,b^7\,c^4\,d^{15}+2455552\,a^{11}\,b^8\,c^5\,d^{14}-6037504\,a^{10}\,b^9\,c^6\,d^{13}+10070016\,a^9\,b^{10}\,c^7\,d^{12}-11894784\,a^8\,b^{11}\,c^8\,d^{11}+10070016\,a^7\,b^{12}\,c^9\,d^{10}-6037504\,a^6\,b^{13}\,c^{10}\,d^9+2455552\,a^5\,b^{14}\,c^{11}\,d^8-606208\,a^4\,b^{15}\,c^{12}\,d^7+59392\,a^3\,b^{16}\,c^{13}\,d^6+8192\,a^2\,b^{17}\,c^{14}\,d^5-2048\,a\,b^{18}\,c^{15}\,d^4\right)}{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)\,{\left(-\frac{a^4\,d^7+28\,a^3\,b\,c\,d^6+294\,a^2\,b^2\,c^2\,d^5+1372\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{4096\,a^{12}\,c^3\,d^{12}-49152\,a^{11}\,b\,c^4\,d^{11}+270336\,a^{10}\,b^2\,c^5\,d^{10}-901120\,a^9\,b^3\,c^6\,d^9+2027520\,a^8\,b^4\,c^7\,d^8-3244032\,a^7\,b^5\,c^8\,d^7+3784704\,a^6\,b^6\,c^9\,d^6-3244032\,a^5\,b^7\,c^{10}\,d^5+2027520\,a^4\,b^8\,c^{11}\,d^4-901120\,a^3\,b^9\,c^{12}\,d^3+270336\,a^2\,b^{10}\,c^{13}\,d^2-49152\,a\,b^{11}\,c^{14}\,d+4096\,b^{12}\,c^{15}}\right)}^{3/4}+\frac{-\frac{7\,a^5\,b^6\,d^{11}}{2}+\frac{2197\,a^4\,b^7\,c\,d^{10}}{2}+9145\,a^3\,b^8\,c^2\,d^9+9145\,a^2\,b^9\,c^3\,d^8+\frac{2197\,a\,b^{10}\,c^4\,d^7}{2}-\frac{7\,b^{11}\,c^5\,d^6}{2}}{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)\,{\left(-\frac{a^4\,d^7+28\,a^3\,b\,c\,d^6+294\,a^2\,b^2\,c^2\,d^5+1372\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{4096\,a^{12}\,c^3\,d^{12}-49152\,a^{11}\,b\,c^4\,d^{11}+270336\,a^{10}\,b^2\,c^5\,d^{10}-901120\,a^9\,b^3\,c^6\,d^9+2027520\,a^8\,b^4\,c^7\,d^8-3244032\,a^7\,b^5\,c^8\,d^7+3784704\,a^6\,b^6\,c^9\,d^6-3244032\,a^5\,b^7\,c^{10}\,d^5+2027520\,a^4\,b^8\,c^{11}\,d^4-901120\,a^3\,b^9\,c^{12}\,d^3+270336\,a^2\,b^{10}\,c^{13}\,d^2-49152\,a\,b^{11}\,c^{14}\,d+4096\,b^{12}\,c^{15}}\right)}^{1/4}\,1{}\mathrm{i}+\frac{\sqrt{x}\,\left(1225\,a^6\,b^7\,d^{13}+18186\,a^5\,b^8\,c\,d^{12}+75975\,a^4\,b^9\,c^2\,d^{11}+71372\,a^3\,b^{10}\,c^3\,d^{10}+75975\,a^2\,b^{11}\,c^4\,d^9+18186\,a\,b^{12}\,c^5\,d^8+1225\,b^{13}\,c^6\,d^7\right)\,1{}\mathrm{i}}{8\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)\,{\left(-\frac{a^4\,d^7+28\,a^3\,b\,c\,d^6+294\,a^2\,b^2\,c^2\,d^5+1372\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{4096\,a^{12}\,c^3\,d^{12}-49152\,a^{11}\,b\,c^4\,d^{11}+270336\,a^{10}\,b^2\,c^5\,d^{10}-901120\,a^9\,b^3\,c^6\,d^9+2027520\,a^8\,b^4\,c^7\,d^8-3244032\,a^7\,b^5\,c^8\,d^7+3784704\,a^6\,b^6\,c^9\,d^6-3244032\,a^5\,b^7\,c^{10}\,d^5+2027520\,a^4\,b^8\,c^{11}\,d^4-901120\,a^3\,b^9\,c^{12}\,d^3+270336\,a^2\,b^{10}\,c^{13}\,d^2-49152\,a\,b^{11}\,c^{14}\,d+4096\,b^{12}\,c^{15}}\right)}^{1/4}}{\left(\left(\left(\frac{\sqrt{x}\,\left(2048\,a^{17}\,b^4\,d^{21}+4096\,a^{16}\,b^5\,c\,d^{20}-108544\,a^{15}\,b^6\,c^2\,d^{19}+337920\,a^{14}\,b^7\,c^3\,d^{18}+153600\,a^{13}\,b^8\,c^4\,d^{17}-3225600\,a^{12}\,b^9\,c^5\,d^{16}+8648704\,a^{11}\,b^{10}\,c^6\,d^{15}-11106304\,a^{10}\,b^{11}\,c^7\,d^{14}+5294080\,a^9\,b^{12}\,c^8\,d^{13}+5294080\,a^8\,b^{13}\,c^9\,d^{12}-11106304\,a^7\,b^{14}\,c^{10}\,d^{11}+8648704\,a^6\,b^{15}\,c^{11}\,d^{10}-3225600\,a^5\,b^{16}\,c^{12}\,d^9+153600\,a^4\,b^{17}\,c^{13}\,d^8+337920\,a^3\,b^{18}\,c^{14}\,d^7-108544\,a^2\,b^{19}\,c^{15}\,d^6+4096\,a\,b^{20}\,c^{16}\,d^5+2048\,b^{21}\,c^{17}\,d^4\right)}{8\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}+\frac{{\left(-\frac{a^4\,d^7+28\,a^3\,b\,c\,d^6+294\,a^2\,b^2\,c^2\,d^5+1372\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{4096\,a^{12}\,c^3\,d^{12}-49152\,a^{11}\,b\,c^4\,d^{11}+270336\,a^{10}\,b^2\,c^5\,d^{10}-901120\,a^9\,b^3\,c^6\,d^9+2027520\,a^8\,b^4\,c^7\,d^8-3244032\,a^7\,b^5\,c^8\,d^7+3784704\,a^6\,b^6\,c^9\,d^6-3244032\,a^5\,b^7\,c^{10}\,d^5+2027520\,a^4\,b^8\,c^{11}\,d^4-901120\,a^3\,b^9\,c^{12}\,d^3+270336\,a^2\,b^{10}\,c^{13}\,d^2-49152\,a\,b^{11}\,c^{14}\,d+4096\,b^{12}\,c^{15}}\right)}^{1/4}\,\left(-2048\,a^{15}\,b^4\,c\,d^{18}+8192\,a^{14}\,b^5\,c^2\,d^{17}+59392\,a^{13}\,b^6\,c^3\,d^{16}-606208\,a^{12}\,b^7\,c^4\,d^{15}+2455552\,a^{11}\,b^8\,c^5\,d^{14}-6037504\,a^{10}\,b^9\,c^6\,d^{13}+10070016\,a^9\,b^{10}\,c^7\,d^{12}-11894784\,a^8\,b^{11}\,c^8\,d^{11}+10070016\,a^7\,b^{12}\,c^9\,d^{10}-6037504\,a^6\,b^{13}\,c^{10}\,d^9+2455552\,a^5\,b^{14}\,c^{11}\,d^8-606208\,a^4\,b^{15}\,c^{12}\,d^7+59392\,a^3\,b^{16}\,c^{13}\,d^6+8192\,a^2\,b^{17}\,c^{14}\,d^5-2048\,a\,b^{18}\,c^{15}\,d^4\right)}{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)\,{\left(-\frac{a^4\,d^7+28\,a^3\,b\,c\,d^6+294\,a^2\,b^2\,c^2\,d^5+1372\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{4096\,a^{12}\,c^3\,d^{12}-49152\,a^{11}\,b\,c^4\,d^{11}+270336\,a^{10}\,b^2\,c^5\,d^{10}-901120\,a^9\,b^3\,c^6\,d^9+2027520\,a^8\,b^4\,c^7\,d^8-3244032\,a^7\,b^5\,c^8\,d^7+3784704\,a^6\,b^6\,c^9\,d^6-3244032\,a^5\,b^7\,c^{10}\,d^5+2027520\,a^4\,b^8\,c^{11}\,d^4-901120\,a^3\,b^9\,c^{12}\,d^3+270336\,a^2\,b^{10}\,c^{13}\,d^2-49152\,a\,b^{11}\,c^{14}\,d+4096\,b^{12}\,c^{15}}\right)}^{3/4}-\frac{-\frac{7\,a^5\,b^6\,d^{11}}{2}+\frac{2197\,a^4\,b^7\,c\,d^{10}}{2}+9145\,a^3\,b^8\,c^2\,d^9+9145\,a^2\,b^9\,c^3\,d^8+\frac{2197\,a\,b^{10}\,c^4\,d^7}{2}-\frac{7\,b^{11}\,c^5\,d^6}{2}}{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)\,{\left(-\frac{a^4\,d^7+28\,a^3\,b\,c\,d^6+294\,a^2\,b^2\,c^2\,d^5+1372\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{4096\,a^{12}\,c^3\,d^{12}-49152\,a^{11}\,b\,c^4\,d^{11}+270336\,a^{10}\,b^2\,c^5\,d^{10}-901120\,a^9\,b^3\,c^6\,d^9+2027520\,a^8\,b^4\,c^7\,d^8-3244032\,a^7\,b^5\,c^8\,d^7+3784704\,a^6\,b^6\,c^9\,d^6-3244032\,a^5\,b^7\,c^{10}\,d^5+2027520\,a^4\,b^8\,c^{11}\,d^4-901120\,a^3\,b^9\,c^{12}\,d^3+270336\,a^2\,b^{10}\,c^{13}\,d^2-49152\,a\,b^{11}\,c^{14}\,d+4096\,b^{12}\,c^{15}}\right)}^{1/4}+\frac{\sqrt{x}\,\left(1225\,a^6\,b^7\,d^{13}+18186\,a^5\,b^8\,c\,d^{12}+75975\,a^4\,b^9\,c^2\,d^{11}+71372\,a^3\,b^{10}\,c^3\,d^{10}+75975\,a^2\,b^{11}\,c^4\,d^9+18186\,a\,b^{12}\,c^5\,d^8+1225\,b^{13}\,c^6\,d^7\right)}{8\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)\,{\left(-\frac{a^4\,d^7+28\,a^3\,b\,c\,d^6+294\,a^2\,b^2\,c^2\,d^5+1372\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{4096\,a^{12}\,c^3\,d^{12}-49152\,a^{11}\,b\,c^4\,d^{11}+270336\,a^{10}\,b^2\,c^5\,d^{10}-901120\,a^9\,b^3\,c^6\,d^9+2027520\,a^8\,b^4\,c^7\,d^8-3244032\,a^7\,b^5\,c^8\,d^7+3784704\,a^6\,b^6\,c^9\,d^6-3244032\,a^5\,b^7\,c^{10}\,d^5+2027520\,a^4\,b^8\,c^{11}\,d^4-901120\,a^3\,b^9\,c^{12}\,d^3+270336\,a^2\,b^{10}\,c^{13}\,d^2-49152\,a\,b^{11}\,c^{14}\,d+4096\,b^{12}\,c^{15}}\right)}^{1/4}-\left(\left(\left(\frac{\sqrt{x}\,\left(2048\,a^{17}\,b^4\,d^{21}+4096\,a^{16}\,b^5\,c\,d^{20}-108544\,a^{15}\,b^6\,c^2\,d^{19}+337920\,a^{14}\,b^7\,c^3\,d^{18}+153600\,a^{13}\,b^8\,c^4\,d^{17}-3225600\,a^{12}\,b^9\,c^5\,d^{16}+8648704\,a^{11}\,b^{10}\,c^6\,d^{15}-11106304\,a^{10}\,b^{11}\,c^7\,d^{14}+5294080\,a^9\,b^{12}\,c^8\,d^{13}+5294080\,a^8\,b^{13}\,c^9\,d^{12}-11106304\,a^7\,b^{14}\,c^{10}\,d^{11}+8648704\,a^6\,b^{15}\,c^{11}\,d^{10}-3225600\,a^5\,b^{16}\,c^{12}\,d^9+153600\,a^4\,b^{17}\,c^{13}\,d^8+337920\,a^3\,b^{18}\,c^{14}\,d^7-108544\,a^2\,b^{19}\,c^{15}\,d^6+4096\,a\,b^{20}\,c^{16}\,d^5+2048\,b^{21}\,c^{17}\,d^4\right)}{8\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}-\frac{{\left(-\frac{a^4\,d^7+28\,a^3\,b\,c\,d^6+294\,a^2\,b^2\,c^2\,d^5+1372\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{4096\,a^{12}\,c^3\,d^{12}-49152\,a^{11}\,b\,c^4\,d^{11}+270336\,a^{10}\,b^2\,c^5\,d^{10}-901120\,a^9\,b^3\,c^6\,d^9+2027520\,a^8\,b^4\,c^7\,d^8-3244032\,a^7\,b^5\,c^8\,d^7+3784704\,a^6\,b^6\,c^9\,d^6-3244032\,a^5\,b^7\,c^{10}\,d^5+2027520\,a^4\,b^8\,c^{11}\,d^4-901120\,a^3\,b^9\,c^{12}\,d^3+270336\,a^2\,b^{10}\,c^{13}\,d^2-49152\,a\,b^{11}\,c^{14}\,d+4096\,b^{12}\,c^{15}}\right)}^{1/4}\,\left(-2048\,a^{15}\,b^4\,c\,d^{18}+8192\,a^{14}\,b^5\,c^2\,d^{17}+59392\,a^{13}\,b^6\,c^3\,d^{16}-606208\,a^{12}\,b^7\,c^4\,d^{15}+2455552\,a^{11}\,b^8\,c^5\,d^{14}-6037504\,a^{10}\,b^9\,c^6\,d^{13}+10070016\,a^9\,b^{10}\,c^7\,d^{12}-11894784\,a^8\,b^{11}\,c^8\,d^{11}+10070016\,a^7\,b^{12}\,c^9\,d^{10}-6037504\,a^6\,b^{13}\,c^{10}\,d^9+2455552\,a^5\,b^{14}\,c^{11}\,d^8-606208\,a^4\,b^{15}\,c^{12}\,d^7+59392\,a^3\,b^{16}\,c^{13}\,d^6+8192\,a^2\,b^{17}\,c^{14}\,d^5-2048\,a\,b^{18}\,c^{15}\,d^4\right)}{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)\,{\left(-\frac{a^4\,d^7+28\,a^3\,b\,c\,d^6+294\,a^2\,b^2\,c^2\,d^5+1372\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{4096\,a^{12}\,c^3\,d^{12}-49152\,a^{11}\,b\,c^4\,d^{11}+270336\,a^{10}\,b^2\,c^5\,d^{10}-901120\,a^9\,b^3\,c^6\,d^9+2027520\,a^8\,b^4\,c^7\,d^8-3244032\,a^7\,b^5\,c^8\,d^7+3784704\,a^6\,b^6\,c^9\,d^6-3244032\,a^5\,b^7\,c^{10}\,d^5+2027520\,a^4\,b^8\,c^{11}\,d^4-901120\,a^3\,b^9\,c^{12}\,d^3+270336\,a^2\,b^{10}\,c^{13}\,d^2-49152\,a\,b^{11}\,c^{14}\,d+4096\,b^{12}\,c^{15}}\right)}^{3/4}+\frac{-\frac{7\,a^5\,b^6\,d^{11}}{2}+\frac{2197\,a^4\,b^7\,c\,d^{10}}{2}+9145\,a^3\,b^8\,c^2\,d^9+9145\,a^2\,b^9\,c^3\,d^8+\frac{2197\,a\,b^{10}\,c^4\,d^7}{2}-\frac{7\,b^{11}\,c^5\,d^6}{2}}{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)\,{\left(-\frac{a^4\,d^7+28\,a^3\,b\,c\,d^6+294\,a^2\,b^2\,c^2\,d^5+1372\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{4096\,a^{12}\,c^3\,d^{12}-49152\,a^{11}\,b\,c^4\,d^{11}+270336\,a^{10}\,b^2\,c^5\,d^{10}-901120\,a^9\,b^3\,c^6\,d^9+2027520\,a^8\,b^4\,c^7\,d^8-3244032\,a^7\,b^5\,c^8\,d^7+3784704\,a^6\,b^6\,c^9\,d^6-3244032\,a^5\,b^7\,c^{10}\,d^5+2027520\,a^4\,b^8\,c^{11}\,d^4-901120\,a^3\,b^9\,c^{12}\,d^3+270336\,a^2\,b^{10}\,c^{13}\,d^2-49152\,a\,b^{11}\,c^{14}\,d+4096\,b^{12}\,c^{15}}\right)}^{1/4}+\frac{\sqrt{x}\,\left(1225\,a^6\,b^7\,d^{13}+18186\,a^5\,b^8\,c\,d^{12}+75975\,a^4\,b^9\,c^2\,d^{11}+71372\,a^3\,b^{10}\,c^3\,d^{10}+75975\,a^2\,b^{11}\,c^4\,d^9+18186\,a\,b^{12}\,c^5\,d^8+1225\,b^{13}\,c^6\,d^7\right)}{8\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)\,{\left(-\frac{a^4\,d^7+28\,a^3\,b\,c\,d^6+294\,a^2\,b^2\,c^2\,d^5+1372\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{4096\,a^{12}\,c^3\,d^{12}-49152\,a^{11}\,b\,c^4\,d^{11}+270336\,a^{10}\,b^2\,c^5\,d^{10}-901120\,a^9\,b^3\,c^6\,d^9+2027520\,a^8\,b^4\,c^7\,d^8-3244032\,a^7\,b^5\,c^8\,d^7+3784704\,a^6\,b^6\,c^9\,d^6-3244032\,a^5\,b^7\,c^{10}\,d^5+2027520\,a^4\,b^8\,c^{11}\,d^4-901120\,a^3\,b^9\,c^{12}\,d^3+270336\,a^2\,b^{10}\,c^{13}\,d^2-49152\,a\,b^{11}\,c^{14}\,d+4096\,b^{12}\,c^{15}}\right)}^{1/4}}\right)\,{\left(-\frac{a^4\,d^7+28\,a^3\,b\,c\,d^6+294\,a^2\,b^2\,c^2\,d^5+1372\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{4096\,a^{12}\,c^3\,d^{12}-49152\,a^{11}\,b\,c^4\,d^{11}+270336\,a^{10}\,b^2\,c^5\,d^{10}-901120\,a^9\,b^3\,c^6\,d^9+2027520\,a^8\,b^4\,c^7\,d^8-3244032\,a^7\,b^5\,c^8\,d^7+3784704\,a^6\,b^6\,c^9\,d^6-3244032\,a^5\,b^7\,c^{10}\,d^5+2027520\,a^4\,b^8\,c^{11}\,d^4-901120\,a^3\,b^9\,c^{12}\,d^3+270336\,a^2\,b^{10}\,c^{13}\,d^2-49152\,a\,b^{11}\,c^{14}\,d+4096\,b^{12}\,c^{15}}\right)}^{1/4}\,2{}\mathrm{i}+2\,\mathrm{atan}\left(-\frac{\left(\left(\left(\frac{{\left(-\frac{a^4\,d^7+28\,a^3\,b\,c\,d^6+294\,a^2\,b^2\,c^2\,d^5+1372\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{4096\,a^{12}\,c^3\,d^{12}-49152\,a^{11}\,b\,c^4\,d^{11}+270336\,a^{10}\,b^2\,c^5\,d^{10}-901120\,a^9\,b^3\,c^6\,d^9+2027520\,a^8\,b^4\,c^7\,d^8-3244032\,a^7\,b^5\,c^8\,d^7+3784704\,a^6\,b^6\,c^9\,d^6-3244032\,a^5\,b^7\,c^{10}\,d^5+2027520\,a^4\,b^8\,c^{11}\,d^4-901120\,a^3\,b^9\,c^{12}\,d^3+270336\,a^2\,b^{10}\,c^{13}\,d^2-49152\,a\,b^{11}\,c^{14}\,d+4096\,b^{12}\,c^{15}}\right)}^{1/4}\,\left(-2048\,a^{15}\,b^4\,c\,d^{18}+8192\,a^{14}\,b^5\,c^2\,d^{17}+59392\,a^{13}\,b^6\,c^3\,d^{16}-606208\,a^{12}\,b^7\,c^4\,d^{15}+2455552\,a^{11}\,b^8\,c^5\,d^{14}-6037504\,a^{10}\,b^9\,c^6\,d^{13}+10070016\,a^9\,b^{10}\,c^7\,d^{12}-11894784\,a^8\,b^{11}\,c^8\,d^{11}+10070016\,a^7\,b^{12}\,c^9\,d^{10}-6037504\,a^6\,b^{13}\,c^{10}\,d^9+2455552\,a^5\,b^{14}\,c^{11}\,d^8-606208\,a^4\,b^{15}\,c^{12}\,d^7+59392\,a^3\,b^{16}\,c^{13}\,d^6+8192\,a^2\,b^{17}\,c^{14}\,d^5-2048\,a\,b^{18}\,c^{15}\,d^4\right)}{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}+\frac{\sqrt{x}\,\left(2048\,a^{17}\,b^4\,d^{21}+4096\,a^{16}\,b^5\,c\,d^{20}-108544\,a^{15}\,b^6\,c^2\,d^{19}+337920\,a^{14}\,b^7\,c^3\,d^{18}+153600\,a^{13}\,b^8\,c^4\,d^{17}-3225600\,a^{12}\,b^9\,c^5\,d^{16}+8648704\,a^{11}\,b^{10}\,c^6\,d^{15}-11106304\,a^{10}\,b^{11}\,c^7\,d^{14}+5294080\,a^9\,b^{12}\,c^8\,d^{13}+5294080\,a^8\,b^{13}\,c^9\,d^{12}-11106304\,a^7\,b^{14}\,c^{10}\,d^{11}+8648704\,a^6\,b^{15}\,c^{11}\,d^{10}-3225600\,a^5\,b^{16}\,c^{12}\,d^9+153600\,a^4\,b^{17}\,c^{13}\,d^8+337920\,a^3\,b^{18}\,c^{14}\,d^7-108544\,a^2\,b^{19}\,c^{15}\,d^6+4096\,a\,b^{20}\,c^{16}\,d^5+2048\,b^{21}\,c^{17}\,d^4\right)\,1{}\mathrm{i}}{8\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)\,{\left(-\frac{a^4\,d^7+28\,a^3\,b\,c\,d^6+294\,a^2\,b^2\,c^2\,d^5+1372\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{4096\,a^{12}\,c^3\,d^{12}-49152\,a^{11}\,b\,c^4\,d^{11}+270336\,a^{10}\,b^2\,c^5\,d^{10}-901120\,a^9\,b^3\,c^6\,d^9+2027520\,a^8\,b^4\,c^7\,d^8-3244032\,a^7\,b^5\,c^8\,d^7+3784704\,a^6\,b^6\,c^9\,d^6-3244032\,a^5\,b^7\,c^{10}\,d^5+2027520\,a^4\,b^8\,c^{11}\,d^4-901120\,a^3\,b^9\,c^{12}\,d^3+270336\,a^2\,b^{10}\,c^{13}\,d^2-49152\,a\,b^{11}\,c^{14}\,d+4096\,b^{12}\,c^{15}}\right)}^{3/4}\,1{}\mathrm{i}-\frac{\left(-\frac{7\,a^5\,b^6\,d^{11}}{2}+\frac{2197\,a^4\,b^7\,c\,d^{10}}{2}+9145\,a^3\,b^8\,c^2\,d^9+9145\,a^2\,b^9\,c^3\,d^8+\frac{2197\,a\,b^{10}\,c^4\,d^7}{2}-\frac{7\,b^{11}\,c^5\,d^6}{2}\right)\,1{}\mathrm{i}}{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)\,{\left(-\frac{a^4\,d^7+28\,a^3\,b\,c\,d^6+294\,a^2\,b^2\,c^2\,d^5+1372\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{4096\,a^{12}\,c^3\,d^{12}-49152\,a^{11}\,b\,c^4\,d^{11}+270336\,a^{10}\,b^2\,c^5\,d^{10}-901120\,a^9\,b^3\,c^6\,d^9+2027520\,a^8\,b^4\,c^7\,d^8-3244032\,a^7\,b^5\,c^8\,d^7+3784704\,a^6\,b^6\,c^9\,d^6-3244032\,a^5\,b^7\,c^{10}\,d^5+2027520\,a^4\,b^8\,c^{11}\,d^4-901120\,a^3\,b^9\,c^{12}\,d^3+270336\,a^2\,b^{10}\,c^{13}\,d^2-49152\,a\,b^{11}\,c^{14}\,d+4096\,b^{12}\,c^{15}}\right)}^{1/4}-\frac{\sqrt{x}\,\left(1225\,a^6\,b^7\,d^{13}+18186\,a^5\,b^8\,c\,d^{12}+75975\,a^4\,b^9\,c^2\,d^{11}+71372\,a^3\,b^{10}\,c^3\,d^{10}+75975\,a^2\,b^{11}\,c^4\,d^9+18186\,a\,b^{12}\,c^5\,d^8+1225\,b^{13}\,c^6\,d^7\right)}{8\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)\,{\left(-\frac{a^4\,d^7+28\,a^3\,b\,c\,d^6+294\,a^2\,b^2\,c^2\,d^5+1372\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{4096\,a^{12}\,c^3\,d^{12}-49152\,a^{11}\,b\,c^4\,d^{11}+270336\,a^{10}\,b^2\,c^5\,d^{10}-901120\,a^9\,b^3\,c^6\,d^9+2027520\,a^8\,b^4\,c^7\,d^8-3244032\,a^7\,b^5\,c^8\,d^7+3784704\,a^6\,b^6\,c^9\,d^6-3244032\,a^5\,b^7\,c^{10}\,d^5+2027520\,a^4\,b^8\,c^{11}\,d^4-901120\,a^3\,b^9\,c^{12}\,d^3+270336\,a^2\,b^{10}\,c^{13}\,d^2-49152\,a\,b^{11}\,c^{14}\,d+4096\,b^{12}\,c^{15}}\right)}^{1/4}+\left(\left(\left(-\frac{{\left(-\frac{a^4\,d^7+28\,a^3\,b\,c\,d^6+294\,a^2\,b^2\,c^2\,d^5+1372\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{4096\,a^{12}\,c^3\,d^{12}-49152\,a^{11}\,b\,c^4\,d^{11}+270336\,a^{10}\,b^2\,c^5\,d^{10}-901120\,a^9\,b^3\,c^6\,d^9+2027520\,a^8\,b^4\,c^7\,d^8-3244032\,a^7\,b^5\,c^8\,d^7+3784704\,a^6\,b^6\,c^9\,d^6-3244032\,a^5\,b^7\,c^{10}\,d^5+2027520\,a^4\,b^8\,c^{11}\,d^4-901120\,a^3\,b^9\,c^{12}\,d^3+270336\,a^2\,b^{10}\,c^{13}\,d^2-49152\,a\,b^{11}\,c^{14}\,d+4096\,b^{12}\,c^{15}}\right)}^{1/4}\,\left(-2048\,a^{15}\,b^4\,c\,d^{18}+8192\,a^{14}\,b^5\,c^2\,d^{17}+59392\,a^{13}\,b^6\,c^3\,d^{16}-606208\,a^{12}\,b^7\,c^4\,d^{15}+2455552\,a^{11}\,b^8\,c^5\,d^{14}-6037504\,a^{10}\,b^9\,c^6\,d^{13}+10070016\,a^9\,b^{10}\,c^7\,d^{12}-11894784\,a^8\,b^{11}\,c^8\,d^{11}+10070016\,a^7\,b^{12}\,c^9\,d^{10}-6037504\,a^6\,b^{13}\,c^{10}\,d^9+2455552\,a^5\,b^{14}\,c^{11}\,d^8-606208\,a^4\,b^{15}\,c^{12}\,d^7+59392\,a^3\,b^{16}\,c^{13}\,d^6+8192\,a^2\,b^{17}\,c^{14}\,d^5-2048\,a\,b^{18}\,c^{15}\,d^4\right)}{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}+\frac{\sqrt{x}\,\left(2048\,a^{17}\,b^4\,d^{21}+4096\,a^{16}\,b^5\,c\,d^{20}-108544\,a^{15}\,b^6\,c^2\,d^{19}+337920\,a^{14}\,b^7\,c^3\,d^{18}+153600\,a^{13}\,b^8\,c^4\,d^{17}-3225600\,a^{12}\,b^9\,c^5\,d^{16}+8648704\,a^{11}\,b^{10}\,c^6\,d^{15}-11106304\,a^{10}\,b^{11}\,c^7\,d^{14}+5294080\,a^9\,b^{12}\,c^8\,d^{13}+5294080\,a^8\,b^{13}\,c^9\,d^{12}-11106304\,a^7\,b^{14}\,c^{10}\,d^{11}+8648704\,a^6\,b^{15}\,c^{11}\,d^{10}-3225600\,a^5\,b^{16}\,c^{12}\,d^9+153600\,a^4\,b^{17}\,c^{13}\,d^8+337920\,a^3\,b^{18}\,c^{14}\,d^7-108544\,a^2\,b^{19}\,c^{15}\,d^6+4096\,a\,b^{20}\,c^{16}\,d^5+2048\,b^{21}\,c^{17}\,d^4\right)\,1{}\mathrm{i}}{8\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)\,{\left(-\frac{a^4\,d^7+28\,a^3\,b\,c\,d^6+294\,a^2\,b^2\,c^2\,d^5+1372\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{4096\,a^{12}\,c^3\,d^{12}-49152\,a^{11}\,b\,c^4\,d^{11}+270336\,a^{10}\,b^2\,c^5\,d^{10}-901120\,a^9\,b^3\,c^6\,d^9+2027520\,a^8\,b^4\,c^7\,d^8-3244032\,a^7\,b^5\,c^8\,d^7+3784704\,a^6\,b^6\,c^9\,d^6-3244032\,a^5\,b^7\,c^{10}\,d^5+2027520\,a^4\,b^8\,c^{11}\,d^4-901120\,a^3\,b^9\,c^{12}\,d^3+270336\,a^2\,b^{10}\,c^{13}\,d^2-49152\,a\,b^{11}\,c^{14}\,d+4096\,b^{12}\,c^{15}}\right)}^{3/4}\,1{}\mathrm{i}+\frac{\left(-\frac{7\,a^5\,b^6\,d^{11}}{2}+\frac{2197\,a^4\,b^7\,c\,d^{10}}{2}+9145\,a^3\,b^8\,c^2\,d^9+9145\,a^2\,b^9\,c^3\,d^8+\frac{2197\,a\,b^{10}\,c^4\,d^7}{2}-\frac{7\,b^{11}\,c^5\,d^6}{2}\right)\,1{}\mathrm{i}}{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)\,{\left(-\frac{a^4\,d^7+28\,a^3\,b\,c\,d^6+294\,a^2\,b^2\,c^2\,d^5+1372\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{4096\,a^{12}\,c^3\,d^{12}-49152\,a^{11}\,b\,c^4\,d^{11}+270336\,a^{10}\,b^2\,c^5\,d^{10}-901120\,a^9\,b^3\,c^6\,d^9+2027520\,a^8\,b^4\,c^7\,d^8-3244032\,a^7\,b^5\,c^8\,d^7+3784704\,a^6\,b^6\,c^9\,d^6-3244032\,a^5\,b^7\,c^{10}\,d^5+2027520\,a^4\,b^8\,c^{11}\,d^4-901120\,a^3\,b^9\,c^{12}\,d^3+270336\,a^2\,b^{10}\,c^{13}\,d^2-49152\,a\,b^{11}\,c^{14}\,d+4096\,b^{12}\,c^{15}}\right)}^{1/4}-\frac{\sqrt{x}\,\left(1225\,a^6\,b^7\,d^{13}+18186\,a^5\,b^8\,c\,d^{12}+75975\,a^4\,b^9\,c^2\,d^{11}+71372\,a^3\,b^{10}\,c^3\,d^{10}+75975\,a^2\,b^{11}\,c^4\,d^9+18186\,a\,b^{12}\,c^5\,d^8+1225\,b^{13}\,c^6\,d^7\right)}{8\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)\,{\left(-\frac{a^4\,d^7+28\,a^3\,b\,c\,d^6+294\,a^2\,b^2\,c^2\,d^5+1372\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{4096\,a^{12}\,c^3\,d^{12}-49152\,a^{11}\,b\,c^4\,d^{11}+270336\,a^{10}\,b^2\,c^5\,d^{10}-901120\,a^9\,b^3\,c^6\,d^9+2027520\,a^8\,b^4\,c^7\,d^8-3244032\,a^7\,b^5\,c^8\,d^7+3784704\,a^6\,b^6\,c^9\,d^6-3244032\,a^5\,b^7\,c^{10}\,d^5+2027520\,a^4\,b^8\,c^{11}\,d^4-901120\,a^3\,b^9\,c^{12}\,d^3+270336\,a^2\,b^{10}\,c^{13}\,d^2-49152\,a\,b^{11}\,c^{14}\,d+4096\,b^{12}\,c^{15}}\right)}^{1/4}}{\left(\left(\left(\frac{{\left(-\frac{a^4\,d^7+28\,a^3\,b\,c\,d^6+294\,a^2\,b^2\,c^2\,d^5+1372\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{4096\,a^{12}\,c^3\,d^{12}-49152\,a^{11}\,b\,c^4\,d^{11}+270336\,a^{10}\,b^2\,c^5\,d^{10}-901120\,a^9\,b^3\,c^6\,d^9+2027520\,a^8\,b^4\,c^7\,d^8-3244032\,a^7\,b^5\,c^8\,d^7+3784704\,a^6\,b^6\,c^9\,d^6-3244032\,a^5\,b^7\,c^{10}\,d^5+2027520\,a^4\,b^8\,c^{11}\,d^4-901120\,a^3\,b^9\,c^{12}\,d^3+270336\,a^2\,b^{10}\,c^{13}\,d^2-49152\,a\,b^{11}\,c^{14}\,d+4096\,b^{12}\,c^{15}}\right)}^{1/4}\,\left(-2048\,a^{15}\,b^4\,c\,d^{18}+8192\,a^{14}\,b^5\,c^2\,d^{17}+59392\,a^{13}\,b^6\,c^3\,d^{16}-606208\,a^{12}\,b^7\,c^4\,d^{15}+2455552\,a^{11}\,b^8\,c^5\,d^{14}-6037504\,a^{10}\,b^9\,c^6\,d^{13}+10070016\,a^9\,b^{10}\,c^7\,d^{12}-11894784\,a^8\,b^{11}\,c^8\,d^{11}+10070016\,a^7\,b^{12}\,c^9\,d^{10}-6037504\,a^6\,b^{13}\,c^{10}\,d^9+2455552\,a^5\,b^{14}\,c^{11}\,d^8-606208\,a^4\,b^{15}\,c^{12}\,d^7+59392\,a^3\,b^{16}\,c^{13}\,d^6+8192\,a^2\,b^{17}\,c^{14}\,d^5-2048\,a\,b^{18}\,c^{15}\,d^4\right)}{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}+\frac{\sqrt{x}\,\left(2048\,a^{17}\,b^4\,d^{21}+4096\,a^{16}\,b^5\,c\,d^{20}-108544\,a^{15}\,b^6\,c^2\,d^{19}+337920\,a^{14}\,b^7\,c^3\,d^{18}+153600\,a^{13}\,b^8\,c^4\,d^{17}-3225600\,a^{12}\,b^9\,c^5\,d^{16}+8648704\,a^{11}\,b^{10}\,c^6\,d^{15}-11106304\,a^{10}\,b^{11}\,c^7\,d^{14}+5294080\,a^9\,b^{12}\,c^8\,d^{13}+5294080\,a^8\,b^{13}\,c^9\,d^{12}-11106304\,a^7\,b^{14}\,c^{10}\,d^{11}+8648704\,a^6\,b^{15}\,c^{11}\,d^{10}-3225600\,a^5\,b^{16}\,c^{12}\,d^9+153600\,a^4\,b^{17}\,c^{13}\,d^8+337920\,a^3\,b^{18}\,c^{14}\,d^7-108544\,a^2\,b^{19}\,c^{15}\,d^6+4096\,a\,b^{20}\,c^{16}\,d^5+2048\,b^{21}\,c^{17}\,d^4\right)\,1{}\mathrm{i}}{8\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)\,{\left(-\frac{a^4\,d^7+28\,a^3\,b\,c\,d^6+294\,a^2\,b^2\,c^2\,d^5+1372\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{4096\,a^{12}\,c^3\,d^{12}-49152\,a^{11}\,b\,c^4\,d^{11}+270336\,a^{10}\,b^2\,c^5\,d^{10}-901120\,a^9\,b^3\,c^6\,d^9+2027520\,a^8\,b^4\,c^7\,d^8-3244032\,a^7\,b^5\,c^8\,d^7+3784704\,a^6\,b^6\,c^9\,d^6-3244032\,a^5\,b^7\,c^{10}\,d^5+2027520\,a^4\,b^8\,c^{11}\,d^4-901120\,a^3\,b^9\,c^{12}\,d^3+270336\,a^2\,b^{10}\,c^{13}\,d^2-49152\,a\,b^{11}\,c^{14}\,d+4096\,b^{12}\,c^{15}}\right)}^{3/4}\,1{}\mathrm{i}-\frac{\left(-\frac{7\,a^5\,b^6\,d^{11}}{2}+\frac{2197\,a^4\,b^7\,c\,d^{10}}{2}+9145\,a^3\,b^8\,c^2\,d^9+9145\,a^2\,b^9\,c^3\,d^8+\frac{2197\,a\,b^{10}\,c^4\,d^7}{2}-\frac{7\,b^{11}\,c^5\,d^6}{2}\right)\,1{}\mathrm{i}}{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)\,{\left(-\frac{a^4\,d^7+28\,a^3\,b\,c\,d^6+294\,a^2\,b^2\,c^2\,d^5+1372\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{4096\,a^{12}\,c^3\,d^{12}-49152\,a^{11}\,b\,c^4\,d^{11}+270336\,a^{10}\,b^2\,c^5\,d^{10}-901120\,a^9\,b^3\,c^6\,d^9+2027520\,a^8\,b^4\,c^7\,d^8-3244032\,a^7\,b^5\,c^8\,d^7+3784704\,a^6\,b^6\,c^9\,d^6-3244032\,a^5\,b^7\,c^{10}\,d^5+2027520\,a^4\,b^8\,c^{11}\,d^4-901120\,a^3\,b^9\,c^{12}\,d^3+270336\,a^2\,b^{10}\,c^{13}\,d^2-49152\,a\,b^{11}\,c^{14}\,d+4096\,b^{12}\,c^{15}}\right)}^{1/4}\,1{}\mathrm{i}-\frac{\sqrt{x}\,\left(1225\,a^6\,b^7\,d^{13}+18186\,a^5\,b^8\,c\,d^{12}+75975\,a^4\,b^9\,c^2\,d^{11}+71372\,a^3\,b^{10}\,c^3\,d^{10}+75975\,a^2\,b^{11}\,c^4\,d^9+18186\,a\,b^{12}\,c^5\,d^8+1225\,b^{13}\,c^6\,d^7\right)\,1{}\mathrm{i}}{8\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)\,{\left(-\frac{a^4\,d^7+28\,a^3\,b\,c\,d^6+294\,a^2\,b^2\,c^2\,d^5+1372\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{4096\,a^{12}\,c^3\,d^{12}-49152\,a^{11}\,b\,c^4\,d^{11}+270336\,a^{10}\,b^2\,c^5\,d^{10}-901120\,a^9\,b^3\,c^6\,d^9+2027520\,a^8\,b^4\,c^7\,d^8-3244032\,a^7\,b^5\,c^8\,d^7+3784704\,a^6\,b^6\,c^9\,d^6-3244032\,a^5\,b^7\,c^{10}\,d^5+2027520\,a^4\,b^8\,c^{11}\,d^4-901120\,a^3\,b^9\,c^{12}\,d^3+270336\,a^2\,b^{10}\,c^{13}\,d^2-49152\,a\,b^{11}\,c^{14}\,d+4096\,b^{12}\,c^{15}}\right)}^{1/4}-\left(\left(\left(-\frac{{\left(-\frac{a^4\,d^7+28\,a^3\,b\,c\,d^6+294\,a^2\,b^2\,c^2\,d^5+1372\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{4096\,a^{12}\,c^3\,d^{12}-49152\,a^{11}\,b\,c^4\,d^{11}+270336\,a^{10}\,b^2\,c^5\,d^{10}-901120\,a^9\,b^3\,c^6\,d^9+2027520\,a^8\,b^4\,c^7\,d^8-3244032\,a^7\,b^5\,c^8\,d^7+3784704\,a^6\,b^6\,c^9\,d^6-3244032\,a^5\,b^7\,c^{10}\,d^5+2027520\,a^4\,b^8\,c^{11}\,d^4-901120\,a^3\,b^9\,c^{12}\,d^3+270336\,a^2\,b^{10}\,c^{13}\,d^2-49152\,a\,b^{11}\,c^{14}\,d+4096\,b^{12}\,c^{15}}\right)}^{1/4}\,\left(-2048\,a^{15}\,b^4\,c\,d^{18}+8192\,a^{14}\,b^5\,c^2\,d^{17}+59392\,a^{13}\,b^6\,c^3\,d^{16}-606208\,a^{12}\,b^7\,c^4\,d^{15}+2455552\,a^{11}\,b^8\,c^5\,d^{14}-6037504\,a^{10}\,b^9\,c^6\,d^{13}+10070016\,a^9\,b^{10}\,c^7\,d^{12}-11894784\,a^8\,b^{11}\,c^8\,d^{11}+10070016\,a^7\,b^{12}\,c^9\,d^{10}-6037504\,a^6\,b^{13}\,c^{10}\,d^9+2455552\,a^5\,b^{14}\,c^{11}\,d^8-606208\,a^4\,b^{15}\,c^{12}\,d^7+59392\,a^3\,b^{16}\,c^{13}\,d^6+8192\,a^2\,b^{17}\,c^{14}\,d^5-2048\,a\,b^{18}\,c^{15}\,d^4\right)}{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}+\frac{\sqrt{x}\,\left(2048\,a^{17}\,b^4\,d^{21}+4096\,a^{16}\,b^5\,c\,d^{20}-108544\,a^{15}\,b^6\,c^2\,d^{19}+337920\,a^{14}\,b^7\,c^3\,d^{18}+153600\,a^{13}\,b^8\,c^4\,d^{17}-3225600\,a^{12}\,b^9\,c^5\,d^{16}+8648704\,a^{11}\,b^{10}\,c^6\,d^{15}-11106304\,a^{10}\,b^{11}\,c^7\,d^{14}+5294080\,a^9\,b^{12}\,c^8\,d^{13}+5294080\,a^8\,b^{13}\,c^9\,d^{12}-11106304\,a^7\,b^{14}\,c^{10}\,d^{11}+8648704\,a^6\,b^{15}\,c^{11}\,d^{10}-3225600\,a^5\,b^{16}\,c^{12}\,d^9+153600\,a^4\,b^{17}\,c^{13}\,d^8+337920\,a^3\,b^{18}\,c^{14}\,d^7-108544\,a^2\,b^{19}\,c^{15}\,d^6+4096\,a\,b^{20}\,c^{16}\,d^5+2048\,b^{21}\,c^{17}\,d^4\right)\,1{}\mathrm{i}}{8\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)\,{\left(-\frac{a^4\,d^7+28\,a^3\,b\,c\,d^6+294\,a^2\,b^2\,c^2\,d^5+1372\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{4096\,a^{12}\,c^3\,d^{12}-49152\,a^{11}\,b\,c^4\,d^{11}+270336\,a^{10}\,b^2\,c^5\,d^{10}-901120\,a^9\,b^3\,c^6\,d^9+2027520\,a^8\,b^4\,c^7\,d^8-3244032\,a^7\,b^5\,c^8\,d^7+3784704\,a^6\,b^6\,c^9\,d^6-3244032\,a^5\,b^7\,c^{10}\,d^5+2027520\,a^4\,b^8\,c^{11}\,d^4-901120\,a^3\,b^9\,c^{12}\,d^3+270336\,a^2\,b^{10}\,c^{13}\,d^2-49152\,a\,b^{11}\,c^{14}\,d+4096\,b^{12}\,c^{15}}\right)}^{3/4}\,1{}\mathrm{i}+\frac{\left(-\frac{7\,a^5\,b^6\,d^{11}}{2}+\frac{2197\,a^4\,b^7\,c\,d^{10}}{2}+9145\,a^3\,b^8\,c^2\,d^9+9145\,a^2\,b^9\,c^3\,d^8+\frac{2197\,a\,b^{10}\,c^4\,d^7}{2}-\frac{7\,b^{11}\,c^5\,d^6}{2}\right)\,1{}\mathrm{i}}{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)\,{\left(-\frac{a^4\,d^7+28\,a^3\,b\,c\,d^6+294\,a^2\,b^2\,c^2\,d^5+1372\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{4096\,a^{12}\,c^3\,d^{12}-49152\,a^{11}\,b\,c^4\,d^{11}+270336\,a^{10}\,b^2\,c^5\,d^{10}-901120\,a^9\,b^3\,c^6\,d^9+2027520\,a^8\,b^4\,c^7\,d^8-3244032\,a^7\,b^5\,c^8\,d^7+3784704\,a^6\,b^6\,c^9\,d^6-3244032\,a^5\,b^7\,c^{10}\,d^5+2027520\,a^4\,b^8\,c^{11}\,d^4-901120\,a^3\,b^9\,c^{12}\,d^3+270336\,a^2\,b^{10}\,c^{13}\,d^2-49152\,a\,b^{11}\,c^{14}\,d+4096\,b^{12}\,c^{15}}\right)}^{1/4}\,1{}\mathrm{i}-\frac{\sqrt{x}\,\left(1225\,a^6\,b^7\,d^{13}+18186\,a^5\,b^8\,c\,d^{12}+75975\,a^4\,b^9\,c^2\,d^{11}+71372\,a^3\,b^{10}\,c^3\,d^{10}+75975\,a^2\,b^{11}\,c^4\,d^9+18186\,a\,b^{12}\,c^5\,d^8+1225\,b^{13}\,c^6\,d^7\right)\,1{}\mathrm{i}}{8\,\left(a^{12}\,d^{12}-12\,a^{11}\,b\,c\,d^{11}+66\,a^{10}\,b^2\,c^2\,d^{10}-220\,a^9\,b^3\,c^3\,d^9+495\,a^8\,b^4\,c^4\,d^8-792\,a^7\,b^5\,c^5\,d^7+924\,a^6\,b^6\,c^6\,d^6-792\,a^5\,b^7\,c^7\,d^5+495\,a^4\,b^8\,c^8\,d^4-220\,a^3\,b^9\,c^9\,d^3+66\,a^2\,b^{10}\,c^{10}\,d^2-12\,a\,b^{11}\,c^{11}\,d+b^{12}\,c^{12}\right)}\right)\,{\left(-\frac{a^4\,d^7+28\,a^3\,b\,c\,d^6+294\,a^2\,b^2\,c^2\,d^5+1372\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{4096\,a^{12}\,c^3\,d^{12}-49152\,a^{11}\,b\,c^4\,d^{11}+270336\,a^{10}\,b^2\,c^5\,d^{10}-901120\,a^9\,b^3\,c^6\,d^9+2027520\,a^8\,b^4\,c^7\,d^8-3244032\,a^7\,b^5\,c^8\,d^7+3784704\,a^6\,b^6\,c^9\,d^6-3244032\,a^5\,b^7\,c^{10}\,d^5+2027520\,a^4\,b^8\,c^{11}\,d^4-901120\,a^3\,b^9\,c^{12}\,d^3+270336\,a^2\,b^{10}\,c^{13}\,d^2-49152\,a\,b^{11}\,c^{14}\,d+4096\,b^{12}\,c^{15}}\right)}^{1/4}}\right)\,{\left(-\frac{a^4\,d^7+28\,a^3\,b\,c\,d^6+294\,a^2\,b^2\,c^2\,d^5+1372\,a\,b^3\,c^3\,d^4+2401\,b^4\,c^4\,d^3}{4096\,a^{12}\,c^3\,d^{12}-49152\,a^{11}\,b\,c^4\,d^{11}+270336\,a^{10}\,b^2\,c^5\,d^{10}-901120\,a^9\,b^3\,c^6\,d^9+2027520\,a^8\,b^4\,c^7\,d^8-3244032\,a^7\,b^5\,c^8\,d^7+3784704\,a^6\,b^6\,c^9\,d^6-3244032\,a^5\,b^7\,c^{10}\,d^5+2027520\,a^4\,b^8\,c^{11}\,d^4-901120\,a^3\,b^9\,c^{12}\,d^3+270336\,a^2\,b^{10}\,c^{13}\,d^2-49152\,a\,b^{11}\,c^{14}\,d+4096\,b^{12}\,c^{15}}\right)}^{1/4}","Not used",1,"2*atan(-(((((x^(1/2)*(2048*a^17*b^4*d^21 + 2048*b^21*c^17*d^4 + 4096*a*b^20*c^16*d^5 + 4096*a^16*b^5*c*d^20 - 108544*a^2*b^19*c^15*d^6 + 337920*a^3*b^18*c^14*d^7 + 153600*a^4*b^17*c^13*d^8 - 3225600*a^5*b^16*c^12*d^9 + 8648704*a^6*b^15*c^11*d^10 - 11106304*a^7*b^14*c^10*d^11 + 5294080*a^8*b^13*c^9*d^12 + 5294080*a^9*b^12*c^8*d^13 - 11106304*a^10*b^11*c^7*d^14 + 8648704*a^11*b^10*c^6*d^15 - 3225600*a^12*b^9*c^5*d^16 + 153600*a^13*b^8*c^4*d^17 + 337920*a^14*b^7*c^3*d^18 - 108544*a^15*b^6*c^2*d^19)*1i)/(8*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)) + ((-(b^7*c^4 + 2401*a^4*b^3*d^4 + 1372*a^3*b^4*c*d^3 + 294*a^2*b^5*c^2*d^2 + 28*a*b^6*c^3*d)/(4096*a^15*d^12 + 4096*a^3*b^12*c^12 - 49152*a^4*b^11*c^11*d + 270336*a^5*b^10*c^10*d^2 - 901120*a^6*b^9*c^9*d^3 + 2027520*a^7*b^8*c^8*d^4 - 3244032*a^8*b^7*c^7*d^5 + 3784704*a^9*b^6*c^6*d^6 - 3244032*a^10*b^5*c^5*d^7 + 2027520*a^11*b^4*c^4*d^8 - 901120*a^12*b^3*c^3*d^9 + 270336*a^13*b^2*c^2*d^10 - 49152*a^14*b*c*d^11))^(1/4)*(8192*a^2*b^17*c^14*d^5 - 2048*a^15*b^4*c*d^18 - 2048*a*b^18*c^15*d^4 + 59392*a^3*b^16*c^13*d^6 - 606208*a^4*b^15*c^12*d^7 + 2455552*a^5*b^14*c^11*d^8 - 6037504*a^6*b^13*c^10*d^9 + 10070016*a^7*b^12*c^9*d^10 - 11894784*a^8*b^11*c^8*d^11 + 10070016*a^9*b^10*c^7*d^12 - 6037504*a^10*b^9*c^6*d^13 + 2455552*a^11*b^8*c^5*d^14 - 606208*a^12*b^7*c^4*d^15 + 59392*a^13*b^6*c^3*d^16 + 8192*a^14*b^5*c^2*d^17))/(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^7*c^4 + 2401*a^4*b^3*d^4 + 1372*a^3*b^4*c*d^3 + 294*a^2*b^5*c^2*d^2 + 28*a*b^6*c^3*d)/(4096*a^15*d^12 + 4096*a^3*b^12*c^12 - 49152*a^4*b^11*c^11*d + 270336*a^5*b^10*c^10*d^2 - 901120*a^6*b^9*c^9*d^3 + 2027520*a^7*b^8*c^8*d^4 - 3244032*a^8*b^7*c^7*d^5 + 3784704*a^9*b^6*c^6*d^6 - 3244032*a^10*b^5*c^5*d^7 + 2027520*a^11*b^4*c^4*d^8 - 901120*a^12*b^3*c^3*d^9 + 270336*a^13*b^2*c^2*d^10 - 49152*a^14*b*c*d^11))^(3/4)*1i - (((2197*a*b^10*c^4*d^7)/2 - (7*b^11*c^5*d^6)/2 - (7*a^5*b^6*d^11)/2 + (2197*a^4*b^7*c*d^10)/2 + 9145*a^2*b^9*c^3*d^8 + 9145*a^3*b^8*c^2*d^9)*1i)/(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^7*c^4 + 2401*a^4*b^3*d^4 + 1372*a^3*b^4*c*d^3 + 294*a^2*b^5*c^2*d^2 + 28*a*b^6*c^3*d)/(4096*a^15*d^12 + 4096*a^3*b^12*c^12 - 49152*a^4*b^11*c^11*d + 270336*a^5*b^10*c^10*d^2 - 901120*a^6*b^9*c^9*d^3 + 2027520*a^7*b^8*c^8*d^4 - 3244032*a^8*b^7*c^7*d^5 + 3784704*a^9*b^6*c^6*d^6 - 3244032*a^10*b^5*c^5*d^7 + 2027520*a^11*b^4*c^4*d^8 - 901120*a^12*b^3*c^3*d^9 + 270336*a^13*b^2*c^2*d^10 - 49152*a^14*b*c*d^11))^(1/4) - (x^(1/2)*(1225*a^6*b^7*d^13 + 1225*b^13*c^6*d^7 + 18186*a*b^12*c^5*d^8 + 18186*a^5*b^8*c*d^12 + 75975*a^2*b^11*c^4*d^9 + 71372*a^3*b^10*c^3*d^10 + 75975*a^4*b^9*c^2*d^11))/(8*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)))*(-(b^7*c^4 + 2401*a^4*b^3*d^4 + 1372*a^3*b^4*c*d^3 + 294*a^2*b^5*c^2*d^2 + 28*a*b^6*c^3*d)/(4096*a^15*d^12 + 4096*a^3*b^12*c^12 - 49152*a^4*b^11*c^11*d + 270336*a^5*b^10*c^10*d^2 - 901120*a^6*b^9*c^9*d^3 + 2027520*a^7*b^8*c^8*d^4 - 3244032*a^8*b^7*c^7*d^5 + 3784704*a^9*b^6*c^6*d^6 - 3244032*a^10*b^5*c^5*d^7 + 2027520*a^11*b^4*c^4*d^8 - 901120*a^12*b^3*c^3*d^9 + 270336*a^13*b^2*c^2*d^10 - 49152*a^14*b*c*d^11))^(1/4) + ((((x^(1/2)*(2048*a^17*b^4*d^21 + 2048*b^21*c^17*d^4 + 4096*a*b^20*c^16*d^5 + 4096*a^16*b^5*c*d^20 - 108544*a^2*b^19*c^15*d^6 + 337920*a^3*b^18*c^14*d^7 + 153600*a^4*b^17*c^13*d^8 - 3225600*a^5*b^16*c^12*d^9 + 8648704*a^6*b^15*c^11*d^10 - 11106304*a^7*b^14*c^10*d^11 + 5294080*a^8*b^13*c^9*d^12 + 5294080*a^9*b^12*c^8*d^13 - 11106304*a^10*b^11*c^7*d^14 + 8648704*a^11*b^10*c^6*d^15 - 3225600*a^12*b^9*c^5*d^16 + 153600*a^13*b^8*c^4*d^17 + 337920*a^14*b^7*c^3*d^18 - 108544*a^15*b^6*c^2*d^19)*1i)/(8*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)) - ((-(b^7*c^4 + 2401*a^4*b^3*d^4 + 1372*a^3*b^4*c*d^3 + 294*a^2*b^5*c^2*d^2 + 28*a*b^6*c^3*d)/(4096*a^15*d^12 + 4096*a^3*b^12*c^12 - 49152*a^4*b^11*c^11*d + 270336*a^5*b^10*c^10*d^2 - 901120*a^6*b^9*c^9*d^3 + 2027520*a^7*b^8*c^8*d^4 - 3244032*a^8*b^7*c^7*d^5 + 3784704*a^9*b^6*c^6*d^6 - 3244032*a^10*b^5*c^5*d^7 + 2027520*a^11*b^4*c^4*d^8 - 901120*a^12*b^3*c^3*d^9 + 270336*a^13*b^2*c^2*d^10 - 49152*a^14*b*c*d^11))^(1/4)*(8192*a^2*b^17*c^14*d^5 - 2048*a^15*b^4*c*d^18 - 2048*a*b^18*c^15*d^4 + 59392*a^3*b^16*c^13*d^6 - 606208*a^4*b^15*c^12*d^7 + 2455552*a^5*b^14*c^11*d^8 - 6037504*a^6*b^13*c^10*d^9 + 10070016*a^7*b^12*c^9*d^10 - 11894784*a^8*b^11*c^8*d^11 + 10070016*a^9*b^10*c^7*d^12 - 6037504*a^10*b^9*c^6*d^13 + 2455552*a^11*b^8*c^5*d^14 - 606208*a^12*b^7*c^4*d^15 + 59392*a^13*b^6*c^3*d^16 + 8192*a^14*b^5*c^2*d^17))/(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^7*c^4 + 2401*a^4*b^3*d^4 + 1372*a^3*b^4*c*d^3 + 294*a^2*b^5*c^2*d^2 + 28*a*b^6*c^3*d)/(4096*a^15*d^12 + 4096*a^3*b^12*c^12 - 49152*a^4*b^11*c^11*d + 270336*a^5*b^10*c^10*d^2 - 901120*a^6*b^9*c^9*d^3 + 2027520*a^7*b^8*c^8*d^4 - 3244032*a^8*b^7*c^7*d^5 + 3784704*a^9*b^6*c^6*d^6 - 3244032*a^10*b^5*c^5*d^7 + 2027520*a^11*b^4*c^4*d^8 - 901120*a^12*b^3*c^3*d^9 + 270336*a^13*b^2*c^2*d^10 - 49152*a^14*b*c*d^11))^(3/4)*1i + (((2197*a*b^10*c^4*d^7)/2 - (7*b^11*c^5*d^6)/2 - (7*a^5*b^6*d^11)/2 + (2197*a^4*b^7*c*d^10)/2 + 9145*a^2*b^9*c^3*d^8 + 9145*a^3*b^8*c^2*d^9)*1i)/(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^7*c^4 + 2401*a^4*b^3*d^4 + 1372*a^3*b^4*c*d^3 + 294*a^2*b^5*c^2*d^2 + 28*a*b^6*c^3*d)/(4096*a^15*d^12 + 4096*a^3*b^12*c^12 - 49152*a^4*b^11*c^11*d + 270336*a^5*b^10*c^10*d^2 - 901120*a^6*b^9*c^9*d^3 + 2027520*a^7*b^8*c^8*d^4 - 3244032*a^8*b^7*c^7*d^5 + 3784704*a^9*b^6*c^6*d^6 - 3244032*a^10*b^5*c^5*d^7 + 2027520*a^11*b^4*c^4*d^8 - 901120*a^12*b^3*c^3*d^9 + 270336*a^13*b^2*c^2*d^10 - 49152*a^14*b*c*d^11))^(1/4) - (x^(1/2)*(1225*a^6*b^7*d^13 + 1225*b^13*c^6*d^7 + 18186*a*b^12*c^5*d^8 + 18186*a^5*b^8*c*d^12 + 75975*a^2*b^11*c^4*d^9 + 71372*a^3*b^10*c^3*d^10 + 75975*a^4*b^9*c^2*d^11))/(8*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)))*(-(b^7*c^4 + 2401*a^4*b^3*d^4 + 1372*a^3*b^4*c*d^3 + 294*a^2*b^5*c^2*d^2 + 28*a*b^6*c^3*d)/(4096*a^15*d^12 + 4096*a^3*b^12*c^12 - 49152*a^4*b^11*c^11*d + 270336*a^5*b^10*c^10*d^2 - 901120*a^6*b^9*c^9*d^3 + 2027520*a^7*b^8*c^8*d^4 - 3244032*a^8*b^7*c^7*d^5 + 3784704*a^9*b^6*c^6*d^6 - 3244032*a^10*b^5*c^5*d^7 + 2027520*a^11*b^4*c^4*d^8 - 901120*a^12*b^3*c^3*d^9 + 270336*a^13*b^2*c^2*d^10 - 49152*a^14*b*c*d^11))^(1/4))/(((((x^(1/2)*(2048*a^17*b^4*d^21 + 2048*b^21*c^17*d^4 + 4096*a*b^20*c^16*d^5 + 4096*a^16*b^5*c*d^20 - 108544*a^2*b^19*c^15*d^6 + 337920*a^3*b^18*c^14*d^7 + 153600*a^4*b^17*c^13*d^8 - 3225600*a^5*b^16*c^12*d^9 + 8648704*a^6*b^15*c^11*d^10 - 11106304*a^7*b^14*c^10*d^11 + 5294080*a^8*b^13*c^9*d^12 + 5294080*a^9*b^12*c^8*d^13 - 11106304*a^10*b^11*c^7*d^14 + 8648704*a^11*b^10*c^6*d^15 - 3225600*a^12*b^9*c^5*d^16 + 153600*a^13*b^8*c^4*d^17 + 337920*a^14*b^7*c^3*d^18 - 108544*a^15*b^6*c^2*d^19)*1i)/(8*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)) + ((-(b^7*c^4 + 2401*a^4*b^3*d^4 + 1372*a^3*b^4*c*d^3 + 294*a^2*b^5*c^2*d^2 + 28*a*b^6*c^3*d)/(4096*a^15*d^12 + 4096*a^3*b^12*c^12 - 49152*a^4*b^11*c^11*d + 270336*a^5*b^10*c^10*d^2 - 901120*a^6*b^9*c^9*d^3 + 2027520*a^7*b^8*c^8*d^4 - 3244032*a^8*b^7*c^7*d^5 + 3784704*a^9*b^6*c^6*d^6 - 3244032*a^10*b^5*c^5*d^7 + 2027520*a^11*b^4*c^4*d^8 - 901120*a^12*b^3*c^3*d^9 + 270336*a^13*b^2*c^2*d^10 - 49152*a^14*b*c*d^11))^(1/4)*(8192*a^2*b^17*c^14*d^5 - 2048*a^15*b^4*c*d^18 - 2048*a*b^18*c^15*d^4 + 59392*a^3*b^16*c^13*d^6 - 606208*a^4*b^15*c^12*d^7 + 2455552*a^5*b^14*c^11*d^8 - 6037504*a^6*b^13*c^10*d^9 + 10070016*a^7*b^12*c^9*d^10 - 11894784*a^8*b^11*c^8*d^11 + 10070016*a^9*b^10*c^7*d^12 - 6037504*a^10*b^9*c^6*d^13 + 2455552*a^11*b^8*c^5*d^14 - 606208*a^12*b^7*c^4*d^15 + 59392*a^13*b^6*c^3*d^16 + 8192*a^14*b^5*c^2*d^17))/(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^7*c^4 + 2401*a^4*b^3*d^4 + 1372*a^3*b^4*c*d^3 + 294*a^2*b^5*c^2*d^2 + 28*a*b^6*c^3*d)/(4096*a^15*d^12 + 4096*a^3*b^12*c^12 - 49152*a^4*b^11*c^11*d + 270336*a^5*b^10*c^10*d^2 - 901120*a^6*b^9*c^9*d^3 + 2027520*a^7*b^8*c^8*d^4 - 3244032*a^8*b^7*c^7*d^5 + 3784704*a^9*b^6*c^6*d^6 - 3244032*a^10*b^5*c^5*d^7 + 2027520*a^11*b^4*c^4*d^8 - 901120*a^12*b^3*c^3*d^9 + 270336*a^13*b^2*c^2*d^10 - 49152*a^14*b*c*d^11))^(3/4)*1i - (((2197*a*b^10*c^4*d^7)/2 - (7*b^11*c^5*d^6)/2 - (7*a^5*b^6*d^11)/2 + (2197*a^4*b^7*c*d^10)/2 + 9145*a^2*b^9*c^3*d^8 + 9145*a^3*b^8*c^2*d^9)*1i)/(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^7*c^4 + 2401*a^4*b^3*d^4 + 1372*a^3*b^4*c*d^3 + 294*a^2*b^5*c^2*d^2 + 28*a*b^6*c^3*d)/(4096*a^15*d^12 + 4096*a^3*b^12*c^12 - 49152*a^4*b^11*c^11*d + 270336*a^5*b^10*c^10*d^2 - 901120*a^6*b^9*c^9*d^3 + 2027520*a^7*b^8*c^8*d^4 - 3244032*a^8*b^7*c^7*d^5 + 3784704*a^9*b^6*c^6*d^6 - 3244032*a^10*b^5*c^5*d^7 + 2027520*a^11*b^4*c^4*d^8 - 901120*a^12*b^3*c^3*d^9 + 270336*a^13*b^2*c^2*d^10 - 49152*a^14*b*c*d^11))^(1/4)*1i - (x^(1/2)*(1225*a^6*b^7*d^13 + 1225*b^13*c^6*d^7 + 18186*a*b^12*c^5*d^8 + 18186*a^5*b^8*c*d^12 + 75975*a^2*b^11*c^4*d^9 + 71372*a^3*b^10*c^3*d^10 + 75975*a^4*b^9*c^2*d^11)*1i)/(8*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)))*(-(b^7*c^4 + 2401*a^4*b^3*d^4 + 1372*a^3*b^4*c*d^3 + 294*a^2*b^5*c^2*d^2 + 28*a*b^6*c^3*d)/(4096*a^15*d^12 + 4096*a^3*b^12*c^12 - 49152*a^4*b^11*c^11*d + 270336*a^5*b^10*c^10*d^2 - 901120*a^6*b^9*c^9*d^3 + 2027520*a^7*b^8*c^8*d^4 - 3244032*a^8*b^7*c^7*d^5 + 3784704*a^9*b^6*c^6*d^6 - 3244032*a^10*b^5*c^5*d^7 + 2027520*a^11*b^4*c^4*d^8 - 901120*a^12*b^3*c^3*d^9 + 270336*a^13*b^2*c^2*d^10 - 49152*a^14*b*c*d^11))^(1/4) - ((((x^(1/2)*(2048*a^17*b^4*d^21 + 2048*b^21*c^17*d^4 + 4096*a*b^20*c^16*d^5 + 4096*a^16*b^5*c*d^20 - 108544*a^2*b^19*c^15*d^6 + 337920*a^3*b^18*c^14*d^7 + 153600*a^4*b^17*c^13*d^8 - 3225600*a^5*b^16*c^12*d^9 + 8648704*a^6*b^15*c^11*d^10 - 11106304*a^7*b^14*c^10*d^11 + 5294080*a^8*b^13*c^9*d^12 + 5294080*a^9*b^12*c^8*d^13 - 11106304*a^10*b^11*c^7*d^14 + 8648704*a^11*b^10*c^6*d^15 - 3225600*a^12*b^9*c^5*d^16 + 153600*a^13*b^8*c^4*d^17 + 337920*a^14*b^7*c^3*d^18 - 108544*a^15*b^6*c^2*d^19)*1i)/(8*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)) - ((-(b^7*c^4 + 2401*a^4*b^3*d^4 + 1372*a^3*b^4*c*d^3 + 294*a^2*b^5*c^2*d^2 + 28*a*b^6*c^3*d)/(4096*a^15*d^12 + 4096*a^3*b^12*c^12 - 49152*a^4*b^11*c^11*d + 270336*a^5*b^10*c^10*d^2 - 901120*a^6*b^9*c^9*d^3 + 2027520*a^7*b^8*c^8*d^4 - 3244032*a^8*b^7*c^7*d^5 + 3784704*a^9*b^6*c^6*d^6 - 3244032*a^10*b^5*c^5*d^7 + 2027520*a^11*b^4*c^4*d^8 - 901120*a^12*b^3*c^3*d^9 + 270336*a^13*b^2*c^2*d^10 - 49152*a^14*b*c*d^11))^(1/4)*(8192*a^2*b^17*c^14*d^5 - 2048*a^15*b^4*c*d^18 - 2048*a*b^18*c^15*d^4 + 59392*a^3*b^16*c^13*d^6 - 606208*a^4*b^15*c^12*d^7 + 2455552*a^5*b^14*c^11*d^8 - 6037504*a^6*b^13*c^10*d^9 + 10070016*a^7*b^12*c^9*d^10 - 11894784*a^8*b^11*c^8*d^11 + 10070016*a^9*b^10*c^7*d^12 - 6037504*a^10*b^9*c^6*d^13 + 2455552*a^11*b^8*c^5*d^14 - 606208*a^12*b^7*c^4*d^15 + 59392*a^13*b^6*c^3*d^16 + 8192*a^14*b^5*c^2*d^17))/(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^7*c^4 + 2401*a^4*b^3*d^4 + 1372*a^3*b^4*c*d^3 + 294*a^2*b^5*c^2*d^2 + 28*a*b^6*c^3*d)/(4096*a^15*d^12 + 4096*a^3*b^12*c^12 - 49152*a^4*b^11*c^11*d + 270336*a^5*b^10*c^10*d^2 - 901120*a^6*b^9*c^9*d^3 + 2027520*a^7*b^8*c^8*d^4 - 3244032*a^8*b^7*c^7*d^5 + 3784704*a^9*b^6*c^6*d^6 - 3244032*a^10*b^5*c^5*d^7 + 2027520*a^11*b^4*c^4*d^8 - 901120*a^12*b^3*c^3*d^9 + 270336*a^13*b^2*c^2*d^10 - 49152*a^14*b*c*d^11))^(3/4)*1i + (((2197*a*b^10*c^4*d^7)/2 - (7*b^11*c^5*d^6)/2 - (7*a^5*b^6*d^11)/2 + (2197*a^4*b^7*c*d^10)/2 + 9145*a^2*b^9*c^3*d^8 + 9145*a^3*b^8*c^2*d^9)*1i)/(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^7*c^4 + 2401*a^4*b^3*d^4 + 1372*a^3*b^4*c*d^3 + 294*a^2*b^5*c^2*d^2 + 28*a*b^6*c^3*d)/(4096*a^15*d^12 + 4096*a^3*b^12*c^12 - 49152*a^4*b^11*c^11*d + 270336*a^5*b^10*c^10*d^2 - 901120*a^6*b^9*c^9*d^3 + 2027520*a^7*b^8*c^8*d^4 - 3244032*a^8*b^7*c^7*d^5 + 3784704*a^9*b^6*c^6*d^6 - 3244032*a^10*b^5*c^5*d^7 + 2027520*a^11*b^4*c^4*d^8 - 901120*a^12*b^3*c^3*d^9 + 270336*a^13*b^2*c^2*d^10 - 49152*a^14*b*c*d^11))^(1/4)*1i - (x^(1/2)*(1225*a^6*b^7*d^13 + 1225*b^13*c^6*d^7 + 18186*a*b^12*c^5*d^8 + 18186*a^5*b^8*c*d^12 + 75975*a^2*b^11*c^4*d^9 + 71372*a^3*b^10*c^3*d^10 + 75975*a^4*b^9*c^2*d^11)*1i)/(8*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)))*(-(b^7*c^4 + 2401*a^4*b^3*d^4 + 1372*a^3*b^4*c*d^3 + 294*a^2*b^5*c^2*d^2 + 28*a*b^6*c^3*d)/(4096*a^15*d^12 + 4096*a^3*b^12*c^12 - 49152*a^4*b^11*c^11*d + 270336*a^5*b^10*c^10*d^2 - 901120*a^6*b^9*c^9*d^3 + 2027520*a^7*b^8*c^8*d^4 - 3244032*a^8*b^7*c^7*d^5 + 3784704*a^9*b^6*c^6*d^6 - 3244032*a^10*b^5*c^5*d^7 + 2027520*a^11*b^4*c^4*d^8 - 901120*a^12*b^3*c^3*d^9 + 270336*a^13*b^2*c^2*d^10 - 49152*a^14*b*c*d^11))^(1/4)))*(-(b^7*c^4 + 2401*a^4*b^3*d^4 + 1372*a^3*b^4*c*d^3 + 294*a^2*b^5*c^2*d^2 + 28*a*b^6*c^3*d)/(4096*a^15*d^12 + 4096*a^3*b^12*c^12 - 49152*a^4*b^11*c^11*d + 270336*a^5*b^10*c^10*d^2 - 901120*a^6*b^9*c^9*d^3 + 2027520*a^7*b^8*c^8*d^4 - 3244032*a^8*b^7*c^7*d^5 + 3784704*a^9*b^6*c^6*d^6 - 3244032*a^10*b^5*c^5*d^7 + 2027520*a^11*b^4*c^4*d^8 - 901120*a^12*b^3*c^3*d^9 + 270336*a^13*b^2*c^2*d^10 - 49152*a^14*b*c*d^11))^(1/4) - atan(-(((((x^(1/2)*(2048*a^17*b^4*d^21 + 2048*b^21*c^17*d^4 + 4096*a*b^20*c^16*d^5 + 4096*a^16*b^5*c*d^20 - 108544*a^2*b^19*c^15*d^6 + 337920*a^3*b^18*c^14*d^7 + 153600*a^4*b^17*c^13*d^8 - 3225600*a^5*b^16*c^12*d^9 + 8648704*a^6*b^15*c^11*d^10 - 11106304*a^7*b^14*c^10*d^11 + 5294080*a^8*b^13*c^9*d^12 + 5294080*a^9*b^12*c^8*d^13 - 11106304*a^10*b^11*c^7*d^14 + 8648704*a^11*b^10*c^6*d^15 - 3225600*a^12*b^9*c^5*d^16 + 153600*a^13*b^8*c^4*d^17 + 337920*a^14*b^7*c^3*d^18 - 108544*a^15*b^6*c^2*d^19))/(8*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)) + ((-(b^7*c^4 + 2401*a^4*b^3*d^4 + 1372*a^3*b^4*c*d^3 + 294*a^2*b^5*c^2*d^2 + 28*a*b^6*c^3*d)/(4096*a^15*d^12 + 4096*a^3*b^12*c^12 - 49152*a^4*b^11*c^11*d + 270336*a^5*b^10*c^10*d^2 - 901120*a^6*b^9*c^9*d^3 + 2027520*a^7*b^8*c^8*d^4 - 3244032*a^8*b^7*c^7*d^5 + 3784704*a^9*b^6*c^6*d^6 - 3244032*a^10*b^5*c^5*d^7 + 2027520*a^11*b^4*c^4*d^8 - 901120*a^12*b^3*c^3*d^9 + 270336*a^13*b^2*c^2*d^10 - 49152*a^14*b*c*d^11))^(1/4)*(8192*a^2*b^17*c^14*d^5 - 2048*a^15*b^4*c*d^18 - 2048*a*b^18*c^15*d^4 + 59392*a^3*b^16*c^13*d^6 - 606208*a^4*b^15*c^12*d^7 + 2455552*a^5*b^14*c^11*d^8 - 6037504*a^6*b^13*c^10*d^9 + 10070016*a^7*b^12*c^9*d^10 - 11894784*a^8*b^11*c^8*d^11 + 10070016*a^9*b^10*c^7*d^12 - 6037504*a^10*b^9*c^6*d^13 + 2455552*a^11*b^8*c^5*d^14 - 606208*a^12*b^7*c^4*d^15 + 59392*a^13*b^6*c^3*d^16 + 8192*a^14*b^5*c^2*d^17))/(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^7*c^4 + 2401*a^4*b^3*d^4 + 1372*a^3*b^4*c*d^3 + 294*a^2*b^5*c^2*d^2 + 28*a*b^6*c^3*d)/(4096*a^15*d^12 + 4096*a^3*b^12*c^12 - 49152*a^4*b^11*c^11*d + 270336*a^5*b^10*c^10*d^2 - 901120*a^6*b^9*c^9*d^3 + 2027520*a^7*b^8*c^8*d^4 - 3244032*a^8*b^7*c^7*d^5 + 3784704*a^9*b^6*c^6*d^6 - 3244032*a^10*b^5*c^5*d^7 + 2027520*a^11*b^4*c^4*d^8 - 901120*a^12*b^3*c^3*d^9 + 270336*a^13*b^2*c^2*d^10 - 49152*a^14*b*c*d^11))^(3/4) - ((2197*a*b^10*c^4*d^7)/2 - (7*b^11*c^5*d^6)/2 - (7*a^5*b^6*d^11)/2 + (2197*a^4*b^7*c*d^10)/2 + 9145*a^2*b^9*c^3*d^8 + 9145*a^3*b^8*c^2*d^9)/(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^7*c^4 + 2401*a^4*b^3*d^4 + 1372*a^3*b^4*c*d^3 + 294*a^2*b^5*c^2*d^2 + 28*a*b^6*c^3*d)/(4096*a^15*d^12 + 4096*a^3*b^12*c^12 - 49152*a^4*b^11*c^11*d + 270336*a^5*b^10*c^10*d^2 - 901120*a^6*b^9*c^9*d^3 + 2027520*a^7*b^8*c^8*d^4 - 3244032*a^8*b^7*c^7*d^5 + 3784704*a^9*b^6*c^6*d^6 - 3244032*a^10*b^5*c^5*d^7 + 2027520*a^11*b^4*c^4*d^8 - 901120*a^12*b^3*c^3*d^9 + 270336*a^13*b^2*c^2*d^10 - 49152*a^14*b*c*d^11))^(1/4)*1i + (x^(1/2)*(1225*a^6*b^7*d^13 + 1225*b^13*c^6*d^7 + 18186*a*b^12*c^5*d^8 + 18186*a^5*b^8*c*d^12 + 75975*a^2*b^11*c^4*d^9 + 71372*a^3*b^10*c^3*d^10 + 75975*a^4*b^9*c^2*d^11)*1i)/(8*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)))*(-(b^7*c^4 + 2401*a^4*b^3*d^4 + 1372*a^3*b^4*c*d^3 + 294*a^2*b^5*c^2*d^2 + 28*a*b^6*c^3*d)/(4096*a^15*d^12 + 4096*a^3*b^12*c^12 - 49152*a^4*b^11*c^11*d + 270336*a^5*b^10*c^10*d^2 - 901120*a^6*b^9*c^9*d^3 + 2027520*a^7*b^8*c^8*d^4 - 3244032*a^8*b^7*c^7*d^5 + 3784704*a^9*b^6*c^6*d^6 - 3244032*a^10*b^5*c^5*d^7 + 2027520*a^11*b^4*c^4*d^8 - 901120*a^12*b^3*c^3*d^9 + 270336*a^13*b^2*c^2*d^10 - 49152*a^14*b*c*d^11))^(1/4) + ((((x^(1/2)*(2048*a^17*b^4*d^21 + 2048*b^21*c^17*d^4 + 4096*a*b^20*c^16*d^5 + 4096*a^16*b^5*c*d^20 - 108544*a^2*b^19*c^15*d^6 + 337920*a^3*b^18*c^14*d^7 + 153600*a^4*b^17*c^13*d^8 - 3225600*a^5*b^16*c^12*d^9 + 8648704*a^6*b^15*c^11*d^10 - 11106304*a^7*b^14*c^10*d^11 + 5294080*a^8*b^13*c^9*d^12 + 5294080*a^9*b^12*c^8*d^13 - 11106304*a^10*b^11*c^7*d^14 + 8648704*a^11*b^10*c^6*d^15 - 3225600*a^12*b^9*c^5*d^16 + 153600*a^13*b^8*c^4*d^17 + 337920*a^14*b^7*c^3*d^18 - 108544*a^15*b^6*c^2*d^19))/(8*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)) - ((-(b^7*c^4 + 2401*a^4*b^3*d^4 + 1372*a^3*b^4*c*d^3 + 294*a^2*b^5*c^2*d^2 + 28*a*b^6*c^3*d)/(4096*a^15*d^12 + 4096*a^3*b^12*c^12 - 49152*a^4*b^11*c^11*d + 270336*a^5*b^10*c^10*d^2 - 901120*a^6*b^9*c^9*d^3 + 2027520*a^7*b^8*c^8*d^4 - 3244032*a^8*b^7*c^7*d^5 + 3784704*a^9*b^6*c^6*d^6 - 3244032*a^10*b^5*c^5*d^7 + 2027520*a^11*b^4*c^4*d^8 - 901120*a^12*b^3*c^3*d^9 + 270336*a^13*b^2*c^2*d^10 - 49152*a^14*b*c*d^11))^(1/4)*(8192*a^2*b^17*c^14*d^5 - 2048*a^15*b^4*c*d^18 - 2048*a*b^18*c^15*d^4 + 59392*a^3*b^16*c^13*d^6 - 606208*a^4*b^15*c^12*d^7 + 2455552*a^5*b^14*c^11*d^8 - 6037504*a^6*b^13*c^10*d^9 + 10070016*a^7*b^12*c^9*d^10 - 11894784*a^8*b^11*c^8*d^11 + 10070016*a^9*b^10*c^7*d^12 - 6037504*a^10*b^9*c^6*d^13 + 2455552*a^11*b^8*c^5*d^14 - 606208*a^12*b^7*c^4*d^15 + 59392*a^13*b^6*c^3*d^16 + 8192*a^14*b^5*c^2*d^17))/(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^7*c^4 + 2401*a^4*b^3*d^4 + 1372*a^3*b^4*c*d^3 + 294*a^2*b^5*c^2*d^2 + 28*a*b^6*c^3*d)/(4096*a^15*d^12 + 4096*a^3*b^12*c^12 - 49152*a^4*b^11*c^11*d + 270336*a^5*b^10*c^10*d^2 - 901120*a^6*b^9*c^9*d^3 + 2027520*a^7*b^8*c^8*d^4 - 3244032*a^8*b^7*c^7*d^5 + 3784704*a^9*b^6*c^6*d^6 - 3244032*a^10*b^5*c^5*d^7 + 2027520*a^11*b^4*c^4*d^8 - 901120*a^12*b^3*c^3*d^9 + 270336*a^13*b^2*c^2*d^10 - 49152*a^14*b*c*d^11))^(3/4) + ((2197*a*b^10*c^4*d^7)/2 - (7*b^11*c^5*d^6)/2 - (7*a^5*b^6*d^11)/2 + (2197*a^4*b^7*c*d^10)/2 + 9145*a^2*b^9*c^3*d^8 + 9145*a^3*b^8*c^2*d^9)/(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^7*c^4 + 2401*a^4*b^3*d^4 + 1372*a^3*b^4*c*d^3 + 294*a^2*b^5*c^2*d^2 + 28*a*b^6*c^3*d)/(4096*a^15*d^12 + 4096*a^3*b^12*c^12 - 49152*a^4*b^11*c^11*d + 270336*a^5*b^10*c^10*d^2 - 901120*a^6*b^9*c^9*d^3 + 2027520*a^7*b^8*c^8*d^4 - 3244032*a^8*b^7*c^7*d^5 + 3784704*a^9*b^6*c^6*d^6 - 3244032*a^10*b^5*c^5*d^7 + 2027520*a^11*b^4*c^4*d^8 - 901120*a^12*b^3*c^3*d^9 + 270336*a^13*b^2*c^2*d^10 - 49152*a^14*b*c*d^11))^(1/4)*1i + (x^(1/2)*(1225*a^6*b^7*d^13 + 1225*b^13*c^6*d^7 + 18186*a*b^12*c^5*d^8 + 18186*a^5*b^8*c*d^12 + 75975*a^2*b^11*c^4*d^9 + 71372*a^3*b^10*c^3*d^10 + 75975*a^4*b^9*c^2*d^11)*1i)/(8*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)))*(-(b^7*c^4 + 2401*a^4*b^3*d^4 + 1372*a^3*b^4*c*d^3 + 294*a^2*b^5*c^2*d^2 + 28*a*b^6*c^3*d)/(4096*a^15*d^12 + 4096*a^3*b^12*c^12 - 49152*a^4*b^11*c^11*d + 270336*a^5*b^10*c^10*d^2 - 901120*a^6*b^9*c^9*d^3 + 2027520*a^7*b^8*c^8*d^4 - 3244032*a^8*b^7*c^7*d^5 + 3784704*a^9*b^6*c^6*d^6 - 3244032*a^10*b^5*c^5*d^7 + 2027520*a^11*b^4*c^4*d^8 - 901120*a^12*b^3*c^3*d^9 + 270336*a^13*b^2*c^2*d^10 - 49152*a^14*b*c*d^11))^(1/4))/(((((x^(1/2)*(2048*a^17*b^4*d^21 + 2048*b^21*c^17*d^4 + 4096*a*b^20*c^16*d^5 + 4096*a^16*b^5*c*d^20 - 108544*a^2*b^19*c^15*d^6 + 337920*a^3*b^18*c^14*d^7 + 153600*a^4*b^17*c^13*d^8 - 3225600*a^5*b^16*c^12*d^9 + 8648704*a^6*b^15*c^11*d^10 - 11106304*a^7*b^14*c^10*d^11 + 5294080*a^8*b^13*c^9*d^12 + 5294080*a^9*b^12*c^8*d^13 - 11106304*a^10*b^11*c^7*d^14 + 8648704*a^11*b^10*c^6*d^15 - 3225600*a^12*b^9*c^5*d^16 + 153600*a^13*b^8*c^4*d^17 + 337920*a^14*b^7*c^3*d^18 - 108544*a^15*b^6*c^2*d^19))/(8*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)) + ((-(b^7*c^4 + 2401*a^4*b^3*d^4 + 1372*a^3*b^4*c*d^3 + 294*a^2*b^5*c^2*d^2 + 28*a*b^6*c^3*d)/(4096*a^15*d^12 + 4096*a^3*b^12*c^12 - 49152*a^4*b^11*c^11*d + 270336*a^5*b^10*c^10*d^2 - 901120*a^6*b^9*c^9*d^3 + 2027520*a^7*b^8*c^8*d^4 - 3244032*a^8*b^7*c^7*d^5 + 3784704*a^9*b^6*c^6*d^6 - 3244032*a^10*b^5*c^5*d^7 + 2027520*a^11*b^4*c^4*d^8 - 901120*a^12*b^3*c^3*d^9 + 270336*a^13*b^2*c^2*d^10 - 49152*a^14*b*c*d^11))^(1/4)*(8192*a^2*b^17*c^14*d^5 - 2048*a^15*b^4*c*d^18 - 2048*a*b^18*c^15*d^4 + 59392*a^3*b^16*c^13*d^6 - 606208*a^4*b^15*c^12*d^7 + 2455552*a^5*b^14*c^11*d^8 - 6037504*a^6*b^13*c^10*d^9 + 10070016*a^7*b^12*c^9*d^10 - 11894784*a^8*b^11*c^8*d^11 + 10070016*a^9*b^10*c^7*d^12 - 6037504*a^10*b^9*c^6*d^13 + 2455552*a^11*b^8*c^5*d^14 - 606208*a^12*b^7*c^4*d^15 + 59392*a^13*b^6*c^3*d^16 + 8192*a^14*b^5*c^2*d^17))/(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^7*c^4 + 2401*a^4*b^3*d^4 + 1372*a^3*b^4*c*d^3 + 294*a^2*b^5*c^2*d^2 + 28*a*b^6*c^3*d)/(4096*a^15*d^12 + 4096*a^3*b^12*c^12 - 49152*a^4*b^11*c^11*d + 270336*a^5*b^10*c^10*d^2 - 901120*a^6*b^9*c^9*d^3 + 2027520*a^7*b^8*c^8*d^4 - 3244032*a^8*b^7*c^7*d^5 + 3784704*a^9*b^6*c^6*d^6 - 3244032*a^10*b^5*c^5*d^7 + 2027520*a^11*b^4*c^4*d^8 - 901120*a^12*b^3*c^3*d^9 + 270336*a^13*b^2*c^2*d^10 - 49152*a^14*b*c*d^11))^(3/4) - ((2197*a*b^10*c^4*d^7)/2 - (7*b^11*c^5*d^6)/2 - (7*a^5*b^6*d^11)/2 + (2197*a^4*b^7*c*d^10)/2 + 9145*a^2*b^9*c^3*d^8 + 9145*a^3*b^8*c^2*d^9)/(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^7*c^4 + 2401*a^4*b^3*d^4 + 1372*a^3*b^4*c*d^3 + 294*a^2*b^5*c^2*d^2 + 28*a*b^6*c^3*d)/(4096*a^15*d^12 + 4096*a^3*b^12*c^12 - 49152*a^4*b^11*c^11*d + 270336*a^5*b^10*c^10*d^2 - 901120*a^6*b^9*c^9*d^3 + 2027520*a^7*b^8*c^8*d^4 - 3244032*a^8*b^7*c^7*d^5 + 3784704*a^9*b^6*c^6*d^6 - 3244032*a^10*b^5*c^5*d^7 + 2027520*a^11*b^4*c^4*d^8 - 901120*a^12*b^3*c^3*d^9 + 270336*a^13*b^2*c^2*d^10 - 49152*a^14*b*c*d^11))^(1/4) + (x^(1/2)*(1225*a^6*b^7*d^13 + 1225*b^13*c^6*d^7 + 18186*a*b^12*c^5*d^8 + 18186*a^5*b^8*c*d^12 + 75975*a^2*b^11*c^4*d^9 + 71372*a^3*b^10*c^3*d^10 + 75975*a^4*b^9*c^2*d^11))/(8*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)))*(-(b^7*c^4 + 2401*a^4*b^3*d^4 + 1372*a^3*b^4*c*d^3 + 294*a^2*b^5*c^2*d^2 + 28*a*b^6*c^3*d)/(4096*a^15*d^12 + 4096*a^3*b^12*c^12 - 49152*a^4*b^11*c^11*d + 270336*a^5*b^10*c^10*d^2 - 901120*a^6*b^9*c^9*d^3 + 2027520*a^7*b^8*c^8*d^4 - 3244032*a^8*b^7*c^7*d^5 + 3784704*a^9*b^6*c^6*d^6 - 3244032*a^10*b^5*c^5*d^7 + 2027520*a^11*b^4*c^4*d^8 - 901120*a^12*b^3*c^3*d^9 + 270336*a^13*b^2*c^2*d^10 - 49152*a^14*b*c*d^11))^(1/4) - ((((x^(1/2)*(2048*a^17*b^4*d^21 + 2048*b^21*c^17*d^4 + 4096*a*b^20*c^16*d^5 + 4096*a^16*b^5*c*d^20 - 108544*a^2*b^19*c^15*d^6 + 337920*a^3*b^18*c^14*d^7 + 153600*a^4*b^17*c^13*d^8 - 3225600*a^5*b^16*c^12*d^9 + 8648704*a^6*b^15*c^11*d^10 - 11106304*a^7*b^14*c^10*d^11 + 5294080*a^8*b^13*c^9*d^12 + 5294080*a^9*b^12*c^8*d^13 - 11106304*a^10*b^11*c^7*d^14 + 8648704*a^11*b^10*c^6*d^15 - 3225600*a^12*b^9*c^5*d^16 + 153600*a^13*b^8*c^4*d^17 + 337920*a^14*b^7*c^3*d^18 - 108544*a^15*b^6*c^2*d^19))/(8*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)) - ((-(b^7*c^4 + 2401*a^4*b^3*d^4 + 1372*a^3*b^4*c*d^3 + 294*a^2*b^5*c^2*d^2 + 28*a*b^6*c^3*d)/(4096*a^15*d^12 + 4096*a^3*b^12*c^12 - 49152*a^4*b^11*c^11*d + 270336*a^5*b^10*c^10*d^2 - 901120*a^6*b^9*c^9*d^3 + 2027520*a^7*b^8*c^8*d^4 - 3244032*a^8*b^7*c^7*d^5 + 3784704*a^9*b^6*c^6*d^6 - 3244032*a^10*b^5*c^5*d^7 + 2027520*a^11*b^4*c^4*d^8 - 901120*a^12*b^3*c^3*d^9 + 270336*a^13*b^2*c^2*d^10 - 49152*a^14*b*c*d^11))^(1/4)*(8192*a^2*b^17*c^14*d^5 - 2048*a^15*b^4*c*d^18 - 2048*a*b^18*c^15*d^4 + 59392*a^3*b^16*c^13*d^6 - 606208*a^4*b^15*c^12*d^7 + 2455552*a^5*b^14*c^11*d^8 - 6037504*a^6*b^13*c^10*d^9 + 10070016*a^7*b^12*c^9*d^10 - 11894784*a^8*b^11*c^8*d^11 + 10070016*a^9*b^10*c^7*d^12 - 6037504*a^10*b^9*c^6*d^13 + 2455552*a^11*b^8*c^5*d^14 - 606208*a^12*b^7*c^4*d^15 + 59392*a^13*b^6*c^3*d^16 + 8192*a^14*b^5*c^2*d^17))/(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^7*c^4 + 2401*a^4*b^3*d^4 + 1372*a^3*b^4*c*d^3 + 294*a^2*b^5*c^2*d^2 + 28*a*b^6*c^3*d)/(4096*a^15*d^12 + 4096*a^3*b^12*c^12 - 49152*a^4*b^11*c^11*d + 270336*a^5*b^10*c^10*d^2 - 901120*a^6*b^9*c^9*d^3 + 2027520*a^7*b^8*c^8*d^4 - 3244032*a^8*b^7*c^7*d^5 + 3784704*a^9*b^6*c^6*d^6 - 3244032*a^10*b^5*c^5*d^7 + 2027520*a^11*b^4*c^4*d^8 - 901120*a^12*b^3*c^3*d^9 + 270336*a^13*b^2*c^2*d^10 - 49152*a^14*b*c*d^11))^(3/4) + ((2197*a*b^10*c^4*d^7)/2 - (7*b^11*c^5*d^6)/2 - (7*a^5*b^6*d^11)/2 + (2197*a^4*b^7*c*d^10)/2 + 9145*a^2*b^9*c^3*d^8 + 9145*a^3*b^8*c^2*d^9)/(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^7*c^4 + 2401*a^4*b^3*d^4 + 1372*a^3*b^4*c*d^3 + 294*a^2*b^5*c^2*d^2 + 28*a*b^6*c^3*d)/(4096*a^15*d^12 + 4096*a^3*b^12*c^12 - 49152*a^4*b^11*c^11*d + 270336*a^5*b^10*c^10*d^2 - 901120*a^6*b^9*c^9*d^3 + 2027520*a^7*b^8*c^8*d^4 - 3244032*a^8*b^7*c^7*d^5 + 3784704*a^9*b^6*c^6*d^6 - 3244032*a^10*b^5*c^5*d^7 + 2027520*a^11*b^4*c^4*d^8 - 901120*a^12*b^3*c^3*d^9 + 270336*a^13*b^2*c^2*d^10 - 49152*a^14*b*c*d^11))^(1/4) + (x^(1/2)*(1225*a^6*b^7*d^13 + 1225*b^13*c^6*d^7 + 18186*a*b^12*c^5*d^8 + 18186*a^5*b^8*c*d^12 + 75975*a^2*b^11*c^4*d^9 + 71372*a^3*b^10*c^3*d^10 + 75975*a^4*b^9*c^2*d^11))/(8*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)))*(-(b^7*c^4 + 2401*a^4*b^3*d^4 + 1372*a^3*b^4*c*d^3 + 294*a^2*b^5*c^2*d^2 + 28*a*b^6*c^3*d)/(4096*a^15*d^12 + 4096*a^3*b^12*c^12 - 49152*a^4*b^11*c^11*d + 270336*a^5*b^10*c^10*d^2 - 901120*a^6*b^9*c^9*d^3 + 2027520*a^7*b^8*c^8*d^4 - 3244032*a^8*b^7*c^7*d^5 + 3784704*a^9*b^6*c^6*d^6 - 3244032*a^10*b^5*c^5*d^7 + 2027520*a^11*b^4*c^4*d^8 - 901120*a^12*b^3*c^3*d^9 + 270336*a^13*b^2*c^2*d^10 - 49152*a^14*b*c*d^11))^(1/4)))*(-(b^7*c^4 + 2401*a^4*b^3*d^4 + 1372*a^3*b^4*c*d^3 + 294*a^2*b^5*c^2*d^2 + 28*a*b^6*c^3*d)/(4096*a^15*d^12 + 4096*a^3*b^12*c^12 - 49152*a^4*b^11*c^11*d + 270336*a^5*b^10*c^10*d^2 - 901120*a^6*b^9*c^9*d^3 + 2027520*a^7*b^8*c^8*d^4 - 3244032*a^8*b^7*c^7*d^5 + 3784704*a^9*b^6*c^6*d^6 - 3244032*a^10*b^5*c^5*d^7 + 2027520*a^11*b^4*c^4*d^8 - 901120*a^12*b^3*c^3*d^9 + 270336*a^13*b^2*c^2*d^10 - 49152*a^14*b*c*d^11))^(1/4)*2i - ((x^(1/2)*(a*d + b*c))/(2*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) + (b*d*x^(5/2))/(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/(a*c + x^2*(a*d + b*c) + b*d*x^4) - atan(-(((((x^(1/2)*(2048*a^17*b^4*d^21 + 2048*b^21*c^17*d^4 + 4096*a*b^20*c^16*d^5 + 4096*a^16*b^5*c*d^20 - 108544*a^2*b^19*c^15*d^6 + 337920*a^3*b^18*c^14*d^7 + 153600*a^4*b^17*c^13*d^8 - 3225600*a^5*b^16*c^12*d^9 + 8648704*a^6*b^15*c^11*d^10 - 11106304*a^7*b^14*c^10*d^11 + 5294080*a^8*b^13*c^9*d^12 + 5294080*a^9*b^12*c^8*d^13 - 11106304*a^10*b^11*c^7*d^14 + 8648704*a^11*b^10*c^6*d^15 - 3225600*a^12*b^9*c^5*d^16 + 153600*a^13*b^8*c^4*d^17 + 337920*a^14*b^7*c^3*d^18 - 108544*a^15*b^6*c^2*d^19))/(8*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)) + ((-(a^4*d^7 + 2401*b^4*c^4*d^3 + 1372*a*b^3*c^3*d^4 + 294*a^2*b^2*c^2*d^5 + 28*a^3*b*c*d^6)/(4096*b^12*c^15 + 4096*a^12*c^3*d^12 - 49152*a^11*b*c^4*d^11 + 270336*a^2*b^10*c^13*d^2 - 901120*a^3*b^9*c^12*d^3 + 2027520*a^4*b^8*c^11*d^4 - 3244032*a^5*b^7*c^10*d^5 + 3784704*a^6*b^6*c^9*d^6 - 3244032*a^7*b^5*c^8*d^7 + 2027520*a^8*b^4*c^7*d^8 - 901120*a^9*b^3*c^6*d^9 + 270336*a^10*b^2*c^5*d^10 - 49152*a*b^11*c^14*d))^(1/4)*(8192*a^2*b^17*c^14*d^5 - 2048*a^15*b^4*c*d^18 - 2048*a*b^18*c^15*d^4 + 59392*a^3*b^16*c^13*d^6 - 606208*a^4*b^15*c^12*d^7 + 2455552*a^5*b^14*c^11*d^8 - 6037504*a^6*b^13*c^10*d^9 + 10070016*a^7*b^12*c^9*d^10 - 11894784*a^8*b^11*c^8*d^11 + 10070016*a^9*b^10*c^7*d^12 - 6037504*a^10*b^9*c^6*d^13 + 2455552*a^11*b^8*c^5*d^14 - 606208*a^12*b^7*c^4*d^15 + 59392*a^13*b^6*c^3*d^16 + 8192*a^14*b^5*c^2*d^17))/(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))*(-(a^4*d^7 + 2401*b^4*c^4*d^3 + 1372*a*b^3*c^3*d^4 + 294*a^2*b^2*c^2*d^5 + 28*a^3*b*c*d^6)/(4096*b^12*c^15 + 4096*a^12*c^3*d^12 - 49152*a^11*b*c^4*d^11 + 270336*a^2*b^10*c^13*d^2 - 901120*a^3*b^9*c^12*d^3 + 2027520*a^4*b^8*c^11*d^4 - 3244032*a^5*b^7*c^10*d^5 + 3784704*a^6*b^6*c^9*d^6 - 3244032*a^7*b^5*c^8*d^7 + 2027520*a^8*b^4*c^7*d^8 - 901120*a^9*b^3*c^6*d^9 + 270336*a^10*b^2*c^5*d^10 - 49152*a*b^11*c^14*d))^(3/4) - ((2197*a*b^10*c^4*d^7)/2 - (7*b^11*c^5*d^6)/2 - (7*a^5*b^6*d^11)/2 + (2197*a^4*b^7*c*d^10)/2 + 9145*a^2*b^9*c^3*d^8 + 9145*a^3*b^8*c^2*d^9)/(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))*(-(a^4*d^7 + 2401*b^4*c^4*d^3 + 1372*a*b^3*c^3*d^4 + 294*a^2*b^2*c^2*d^5 + 28*a^3*b*c*d^6)/(4096*b^12*c^15 + 4096*a^12*c^3*d^12 - 49152*a^11*b*c^4*d^11 + 270336*a^2*b^10*c^13*d^2 - 901120*a^3*b^9*c^12*d^3 + 2027520*a^4*b^8*c^11*d^4 - 3244032*a^5*b^7*c^10*d^5 + 3784704*a^6*b^6*c^9*d^6 - 3244032*a^7*b^5*c^8*d^7 + 2027520*a^8*b^4*c^7*d^8 - 901120*a^9*b^3*c^6*d^9 + 270336*a^10*b^2*c^5*d^10 - 49152*a*b^11*c^14*d))^(1/4)*1i + (x^(1/2)*(1225*a^6*b^7*d^13 + 1225*b^13*c^6*d^7 + 18186*a*b^12*c^5*d^8 + 18186*a^5*b^8*c*d^12 + 75975*a^2*b^11*c^4*d^9 + 71372*a^3*b^10*c^3*d^10 + 75975*a^4*b^9*c^2*d^11)*1i)/(8*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)))*(-(a^4*d^7 + 2401*b^4*c^4*d^3 + 1372*a*b^3*c^3*d^4 + 294*a^2*b^2*c^2*d^5 + 28*a^3*b*c*d^6)/(4096*b^12*c^15 + 4096*a^12*c^3*d^12 - 49152*a^11*b*c^4*d^11 + 270336*a^2*b^10*c^13*d^2 - 901120*a^3*b^9*c^12*d^3 + 2027520*a^4*b^8*c^11*d^4 - 3244032*a^5*b^7*c^10*d^5 + 3784704*a^6*b^6*c^9*d^6 - 3244032*a^7*b^5*c^8*d^7 + 2027520*a^8*b^4*c^7*d^8 - 901120*a^9*b^3*c^6*d^9 + 270336*a^10*b^2*c^5*d^10 - 49152*a*b^11*c^14*d))^(1/4) + ((((x^(1/2)*(2048*a^17*b^4*d^21 + 2048*b^21*c^17*d^4 + 4096*a*b^20*c^16*d^5 + 4096*a^16*b^5*c*d^20 - 108544*a^2*b^19*c^15*d^6 + 337920*a^3*b^18*c^14*d^7 + 153600*a^4*b^17*c^13*d^8 - 3225600*a^5*b^16*c^12*d^9 + 8648704*a^6*b^15*c^11*d^10 - 11106304*a^7*b^14*c^10*d^11 + 5294080*a^8*b^13*c^9*d^12 + 5294080*a^9*b^12*c^8*d^13 - 11106304*a^10*b^11*c^7*d^14 + 8648704*a^11*b^10*c^6*d^15 - 3225600*a^12*b^9*c^5*d^16 + 153600*a^13*b^8*c^4*d^17 + 337920*a^14*b^7*c^3*d^18 - 108544*a^15*b^6*c^2*d^19))/(8*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)) - ((-(a^4*d^7 + 2401*b^4*c^4*d^3 + 1372*a*b^3*c^3*d^4 + 294*a^2*b^2*c^2*d^5 + 28*a^3*b*c*d^6)/(4096*b^12*c^15 + 4096*a^12*c^3*d^12 - 49152*a^11*b*c^4*d^11 + 270336*a^2*b^10*c^13*d^2 - 901120*a^3*b^9*c^12*d^3 + 2027520*a^4*b^8*c^11*d^4 - 3244032*a^5*b^7*c^10*d^5 + 3784704*a^6*b^6*c^9*d^6 - 3244032*a^7*b^5*c^8*d^7 + 2027520*a^8*b^4*c^7*d^8 - 901120*a^9*b^3*c^6*d^9 + 270336*a^10*b^2*c^5*d^10 - 49152*a*b^11*c^14*d))^(1/4)*(8192*a^2*b^17*c^14*d^5 - 2048*a^15*b^4*c*d^18 - 2048*a*b^18*c^15*d^4 + 59392*a^3*b^16*c^13*d^6 - 606208*a^4*b^15*c^12*d^7 + 2455552*a^5*b^14*c^11*d^8 - 6037504*a^6*b^13*c^10*d^9 + 10070016*a^7*b^12*c^9*d^10 - 11894784*a^8*b^11*c^8*d^11 + 10070016*a^9*b^10*c^7*d^12 - 6037504*a^10*b^9*c^6*d^13 + 2455552*a^11*b^8*c^5*d^14 - 606208*a^12*b^7*c^4*d^15 + 59392*a^13*b^6*c^3*d^16 + 8192*a^14*b^5*c^2*d^17))/(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))*(-(a^4*d^7 + 2401*b^4*c^4*d^3 + 1372*a*b^3*c^3*d^4 + 294*a^2*b^2*c^2*d^5 + 28*a^3*b*c*d^6)/(4096*b^12*c^15 + 4096*a^12*c^3*d^12 - 49152*a^11*b*c^4*d^11 + 270336*a^2*b^10*c^13*d^2 - 901120*a^3*b^9*c^12*d^3 + 2027520*a^4*b^8*c^11*d^4 - 3244032*a^5*b^7*c^10*d^5 + 3784704*a^6*b^6*c^9*d^6 - 3244032*a^7*b^5*c^8*d^7 + 2027520*a^8*b^4*c^7*d^8 - 901120*a^9*b^3*c^6*d^9 + 270336*a^10*b^2*c^5*d^10 - 49152*a*b^11*c^14*d))^(3/4) + ((2197*a*b^10*c^4*d^7)/2 - (7*b^11*c^5*d^6)/2 - (7*a^5*b^6*d^11)/2 + (2197*a^4*b^7*c*d^10)/2 + 9145*a^2*b^9*c^3*d^8 + 9145*a^3*b^8*c^2*d^9)/(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))*(-(a^4*d^7 + 2401*b^4*c^4*d^3 + 1372*a*b^3*c^3*d^4 + 294*a^2*b^2*c^2*d^5 + 28*a^3*b*c*d^6)/(4096*b^12*c^15 + 4096*a^12*c^3*d^12 - 49152*a^11*b*c^4*d^11 + 270336*a^2*b^10*c^13*d^2 - 901120*a^3*b^9*c^12*d^3 + 2027520*a^4*b^8*c^11*d^4 - 3244032*a^5*b^7*c^10*d^5 + 3784704*a^6*b^6*c^9*d^6 - 3244032*a^7*b^5*c^8*d^7 + 2027520*a^8*b^4*c^7*d^8 - 901120*a^9*b^3*c^6*d^9 + 270336*a^10*b^2*c^5*d^10 - 49152*a*b^11*c^14*d))^(1/4)*1i + (x^(1/2)*(1225*a^6*b^7*d^13 + 1225*b^13*c^6*d^7 + 18186*a*b^12*c^5*d^8 + 18186*a^5*b^8*c*d^12 + 75975*a^2*b^11*c^4*d^9 + 71372*a^3*b^10*c^3*d^10 + 75975*a^4*b^9*c^2*d^11)*1i)/(8*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)))*(-(a^4*d^7 + 2401*b^4*c^4*d^3 + 1372*a*b^3*c^3*d^4 + 294*a^2*b^2*c^2*d^5 + 28*a^3*b*c*d^6)/(4096*b^12*c^15 + 4096*a^12*c^3*d^12 - 49152*a^11*b*c^4*d^11 + 270336*a^2*b^10*c^13*d^2 - 901120*a^3*b^9*c^12*d^3 + 2027520*a^4*b^8*c^11*d^4 - 3244032*a^5*b^7*c^10*d^5 + 3784704*a^6*b^6*c^9*d^6 - 3244032*a^7*b^5*c^8*d^7 + 2027520*a^8*b^4*c^7*d^8 - 901120*a^9*b^3*c^6*d^9 + 270336*a^10*b^2*c^5*d^10 - 49152*a*b^11*c^14*d))^(1/4))/(((((x^(1/2)*(2048*a^17*b^4*d^21 + 2048*b^21*c^17*d^4 + 4096*a*b^20*c^16*d^5 + 4096*a^16*b^5*c*d^20 - 108544*a^2*b^19*c^15*d^6 + 337920*a^3*b^18*c^14*d^7 + 153600*a^4*b^17*c^13*d^8 - 3225600*a^5*b^16*c^12*d^9 + 8648704*a^6*b^15*c^11*d^10 - 11106304*a^7*b^14*c^10*d^11 + 5294080*a^8*b^13*c^9*d^12 + 5294080*a^9*b^12*c^8*d^13 - 11106304*a^10*b^11*c^7*d^14 + 8648704*a^11*b^10*c^6*d^15 - 3225600*a^12*b^9*c^5*d^16 + 153600*a^13*b^8*c^4*d^17 + 337920*a^14*b^7*c^3*d^18 - 108544*a^15*b^6*c^2*d^19))/(8*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)) + ((-(a^4*d^7 + 2401*b^4*c^4*d^3 + 1372*a*b^3*c^3*d^4 + 294*a^2*b^2*c^2*d^5 + 28*a^3*b*c*d^6)/(4096*b^12*c^15 + 4096*a^12*c^3*d^12 - 49152*a^11*b*c^4*d^11 + 270336*a^2*b^10*c^13*d^2 - 901120*a^3*b^9*c^12*d^3 + 2027520*a^4*b^8*c^11*d^4 - 3244032*a^5*b^7*c^10*d^5 + 3784704*a^6*b^6*c^9*d^6 - 3244032*a^7*b^5*c^8*d^7 + 2027520*a^8*b^4*c^7*d^8 - 901120*a^9*b^3*c^6*d^9 + 270336*a^10*b^2*c^5*d^10 - 49152*a*b^11*c^14*d))^(1/4)*(8192*a^2*b^17*c^14*d^5 - 2048*a^15*b^4*c*d^18 - 2048*a*b^18*c^15*d^4 + 59392*a^3*b^16*c^13*d^6 - 606208*a^4*b^15*c^12*d^7 + 2455552*a^5*b^14*c^11*d^8 - 6037504*a^6*b^13*c^10*d^9 + 10070016*a^7*b^12*c^9*d^10 - 11894784*a^8*b^11*c^8*d^11 + 10070016*a^9*b^10*c^7*d^12 - 6037504*a^10*b^9*c^6*d^13 + 2455552*a^11*b^8*c^5*d^14 - 606208*a^12*b^7*c^4*d^15 + 59392*a^13*b^6*c^3*d^16 + 8192*a^14*b^5*c^2*d^17))/(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))*(-(a^4*d^7 + 2401*b^4*c^4*d^3 + 1372*a*b^3*c^3*d^4 + 294*a^2*b^2*c^2*d^5 + 28*a^3*b*c*d^6)/(4096*b^12*c^15 + 4096*a^12*c^3*d^12 - 49152*a^11*b*c^4*d^11 + 270336*a^2*b^10*c^13*d^2 - 901120*a^3*b^9*c^12*d^3 + 2027520*a^4*b^8*c^11*d^4 - 3244032*a^5*b^7*c^10*d^5 + 3784704*a^6*b^6*c^9*d^6 - 3244032*a^7*b^5*c^8*d^7 + 2027520*a^8*b^4*c^7*d^8 - 901120*a^9*b^3*c^6*d^9 + 270336*a^10*b^2*c^5*d^10 - 49152*a*b^11*c^14*d))^(3/4) - ((2197*a*b^10*c^4*d^7)/2 - (7*b^11*c^5*d^6)/2 - (7*a^5*b^6*d^11)/2 + (2197*a^4*b^7*c*d^10)/2 + 9145*a^2*b^9*c^3*d^8 + 9145*a^3*b^8*c^2*d^9)/(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))*(-(a^4*d^7 + 2401*b^4*c^4*d^3 + 1372*a*b^3*c^3*d^4 + 294*a^2*b^2*c^2*d^5 + 28*a^3*b*c*d^6)/(4096*b^12*c^15 + 4096*a^12*c^3*d^12 - 49152*a^11*b*c^4*d^11 + 270336*a^2*b^10*c^13*d^2 - 901120*a^3*b^9*c^12*d^3 + 2027520*a^4*b^8*c^11*d^4 - 3244032*a^5*b^7*c^10*d^5 + 3784704*a^6*b^6*c^9*d^6 - 3244032*a^7*b^5*c^8*d^7 + 2027520*a^8*b^4*c^7*d^8 - 901120*a^9*b^3*c^6*d^9 + 270336*a^10*b^2*c^5*d^10 - 49152*a*b^11*c^14*d))^(1/4) + (x^(1/2)*(1225*a^6*b^7*d^13 + 1225*b^13*c^6*d^7 + 18186*a*b^12*c^5*d^8 + 18186*a^5*b^8*c*d^12 + 75975*a^2*b^11*c^4*d^9 + 71372*a^3*b^10*c^3*d^10 + 75975*a^4*b^9*c^2*d^11))/(8*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)))*(-(a^4*d^7 + 2401*b^4*c^4*d^3 + 1372*a*b^3*c^3*d^4 + 294*a^2*b^2*c^2*d^5 + 28*a^3*b*c*d^6)/(4096*b^12*c^15 + 4096*a^12*c^3*d^12 - 49152*a^11*b*c^4*d^11 + 270336*a^2*b^10*c^13*d^2 - 901120*a^3*b^9*c^12*d^3 + 2027520*a^4*b^8*c^11*d^4 - 3244032*a^5*b^7*c^10*d^5 + 3784704*a^6*b^6*c^9*d^6 - 3244032*a^7*b^5*c^8*d^7 + 2027520*a^8*b^4*c^7*d^8 - 901120*a^9*b^3*c^6*d^9 + 270336*a^10*b^2*c^5*d^10 - 49152*a*b^11*c^14*d))^(1/4) - ((((x^(1/2)*(2048*a^17*b^4*d^21 + 2048*b^21*c^17*d^4 + 4096*a*b^20*c^16*d^5 + 4096*a^16*b^5*c*d^20 - 108544*a^2*b^19*c^15*d^6 + 337920*a^3*b^18*c^14*d^7 + 153600*a^4*b^17*c^13*d^8 - 3225600*a^5*b^16*c^12*d^9 + 8648704*a^6*b^15*c^11*d^10 - 11106304*a^7*b^14*c^10*d^11 + 5294080*a^8*b^13*c^9*d^12 + 5294080*a^9*b^12*c^8*d^13 - 11106304*a^10*b^11*c^7*d^14 + 8648704*a^11*b^10*c^6*d^15 - 3225600*a^12*b^9*c^5*d^16 + 153600*a^13*b^8*c^4*d^17 + 337920*a^14*b^7*c^3*d^18 - 108544*a^15*b^6*c^2*d^19))/(8*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)) - ((-(a^4*d^7 + 2401*b^4*c^4*d^3 + 1372*a*b^3*c^3*d^4 + 294*a^2*b^2*c^2*d^5 + 28*a^3*b*c*d^6)/(4096*b^12*c^15 + 4096*a^12*c^3*d^12 - 49152*a^11*b*c^4*d^11 + 270336*a^2*b^10*c^13*d^2 - 901120*a^3*b^9*c^12*d^3 + 2027520*a^4*b^8*c^11*d^4 - 3244032*a^5*b^7*c^10*d^5 + 3784704*a^6*b^6*c^9*d^6 - 3244032*a^7*b^5*c^8*d^7 + 2027520*a^8*b^4*c^7*d^8 - 901120*a^9*b^3*c^6*d^9 + 270336*a^10*b^2*c^5*d^10 - 49152*a*b^11*c^14*d))^(1/4)*(8192*a^2*b^17*c^14*d^5 - 2048*a^15*b^4*c*d^18 - 2048*a*b^18*c^15*d^4 + 59392*a^3*b^16*c^13*d^6 - 606208*a^4*b^15*c^12*d^7 + 2455552*a^5*b^14*c^11*d^8 - 6037504*a^6*b^13*c^10*d^9 + 10070016*a^7*b^12*c^9*d^10 - 11894784*a^8*b^11*c^8*d^11 + 10070016*a^9*b^10*c^7*d^12 - 6037504*a^10*b^9*c^6*d^13 + 2455552*a^11*b^8*c^5*d^14 - 606208*a^12*b^7*c^4*d^15 + 59392*a^13*b^6*c^3*d^16 + 8192*a^14*b^5*c^2*d^17))/(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))*(-(a^4*d^7 + 2401*b^4*c^4*d^3 + 1372*a*b^3*c^3*d^4 + 294*a^2*b^2*c^2*d^5 + 28*a^3*b*c*d^6)/(4096*b^12*c^15 + 4096*a^12*c^3*d^12 - 49152*a^11*b*c^4*d^11 + 270336*a^2*b^10*c^13*d^2 - 901120*a^3*b^9*c^12*d^3 + 2027520*a^4*b^8*c^11*d^4 - 3244032*a^5*b^7*c^10*d^5 + 3784704*a^6*b^6*c^9*d^6 - 3244032*a^7*b^5*c^8*d^7 + 2027520*a^8*b^4*c^7*d^8 - 901120*a^9*b^3*c^6*d^9 + 270336*a^10*b^2*c^5*d^10 - 49152*a*b^11*c^14*d))^(3/4) + ((2197*a*b^10*c^4*d^7)/2 - (7*b^11*c^5*d^6)/2 - (7*a^5*b^6*d^11)/2 + (2197*a^4*b^7*c*d^10)/2 + 9145*a^2*b^9*c^3*d^8 + 9145*a^3*b^8*c^2*d^9)/(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))*(-(a^4*d^7 + 2401*b^4*c^4*d^3 + 1372*a*b^3*c^3*d^4 + 294*a^2*b^2*c^2*d^5 + 28*a^3*b*c*d^6)/(4096*b^12*c^15 + 4096*a^12*c^3*d^12 - 49152*a^11*b*c^4*d^11 + 270336*a^2*b^10*c^13*d^2 - 901120*a^3*b^9*c^12*d^3 + 2027520*a^4*b^8*c^11*d^4 - 3244032*a^5*b^7*c^10*d^5 + 3784704*a^6*b^6*c^9*d^6 - 3244032*a^7*b^5*c^8*d^7 + 2027520*a^8*b^4*c^7*d^8 - 901120*a^9*b^3*c^6*d^9 + 270336*a^10*b^2*c^5*d^10 - 49152*a*b^11*c^14*d))^(1/4) + (x^(1/2)*(1225*a^6*b^7*d^13 + 1225*b^13*c^6*d^7 + 18186*a*b^12*c^5*d^8 + 18186*a^5*b^8*c*d^12 + 75975*a^2*b^11*c^4*d^9 + 71372*a^3*b^10*c^3*d^10 + 75975*a^4*b^9*c^2*d^11))/(8*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)))*(-(a^4*d^7 + 2401*b^4*c^4*d^3 + 1372*a*b^3*c^3*d^4 + 294*a^2*b^2*c^2*d^5 + 28*a^3*b*c*d^6)/(4096*b^12*c^15 + 4096*a^12*c^3*d^12 - 49152*a^11*b*c^4*d^11 + 270336*a^2*b^10*c^13*d^2 - 901120*a^3*b^9*c^12*d^3 + 2027520*a^4*b^8*c^11*d^4 - 3244032*a^5*b^7*c^10*d^5 + 3784704*a^6*b^6*c^9*d^6 - 3244032*a^7*b^5*c^8*d^7 + 2027520*a^8*b^4*c^7*d^8 - 901120*a^9*b^3*c^6*d^9 + 270336*a^10*b^2*c^5*d^10 - 49152*a*b^11*c^14*d))^(1/4)))*(-(a^4*d^7 + 2401*b^4*c^4*d^3 + 1372*a*b^3*c^3*d^4 + 294*a^2*b^2*c^2*d^5 + 28*a^3*b*c*d^6)/(4096*b^12*c^15 + 4096*a^12*c^3*d^12 - 49152*a^11*b*c^4*d^11 + 270336*a^2*b^10*c^13*d^2 - 901120*a^3*b^9*c^12*d^3 + 2027520*a^4*b^8*c^11*d^4 - 3244032*a^5*b^7*c^10*d^5 + 3784704*a^6*b^6*c^9*d^6 - 3244032*a^7*b^5*c^8*d^7 + 2027520*a^8*b^4*c^7*d^8 - 901120*a^9*b^3*c^6*d^9 + 270336*a^10*b^2*c^5*d^10 - 49152*a*b^11*c^14*d))^(1/4)*2i + 2*atan(-(((((x^(1/2)*(2048*a^17*b^4*d^21 + 2048*b^21*c^17*d^4 + 4096*a*b^20*c^16*d^5 + 4096*a^16*b^5*c*d^20 - 108544*a^2*b^19*c^15*d^6 + 337920*a^3*b^18*c^14*d^7 + 153600*a^4*b^17*c^13*d^8 - 3225600*a^5*b^16*c^12*d^9 + 8648704*a^6*b^15*c^11*d^10 - 11106304*a^7*b^14*c^10*d^11 + 5294080*a^8*b^13*c^9*d^12 + 5294080*a^9*b^12*c^8*d^13 - 11106304*a^10*b^11*c^7*d^14 + 8648704*a^11*b^10*c^6*d^15 - 3225600*a^12*b^9*c^5*d^16 + 153600*a^13*b^8*c^4*d^17 + 337920*a^14*b^7*c^3*d^18 - 108544*a^15*b^6*c^2*d^19)*1i)/(8*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)) + ((-(a^4*d^7 + 2401*b^4*c^4*d^3 + 1372*a*b^3*c^3*d^4 + 294*a^2*b^2*c^2*d^5 + 28*a^3*b*c*d^6)/(4096*b^12*c^15 + 4096*a^12*c^3*d^12 - 49152*a^11*b*c^4*d^11 + 270336*a^2*b^10*c^13*d^2 - 901120*a^3*b^9*c^12*d^3 + 2027520*a^4*b^8*c^11*d^4 - 3244032*a^5*b^7*c^10*d^5 + 3784704*a^6*b^6*c^9*d^6 - 3244032*a^7*b^5*c^8*d^7 + 2027520*a^8*b^4*c^7*d^8 - 901120*a^9*b^3*c^6*d^9 + 270336*a^10*b^2*c^5*d^10 - 49152*a*b^11*c^14*d))^(1/4)*(8192*a^2*b^17*c^14*d^5 - 2048*a^15*b^4*c*d^18 - 2048*a*b^18*c^15*d^4 + 59392*a^3*b^16*c^13*d^6 - 606208*a^4*b^15*c^12*d^7 + 2455552*a^5*b^14*c^11*d^8 - 6037504*a^6*b^13*c^10*d^9 + 10070016*a^7*b^12*c^9*d^10 - 11894784*a^8*b^11*c^8*d^11 + 10070016*a^9*b^10*c^7*d^12 - 6037504*a^10*b^9*c^6*d^13 + 2455552*a^11*b^8*c^5*d^14 - 606208*a^12*b^7*c^4*d^15 + 59392*a^13*b^6*c^3*d^16 + 8192*a^14*b^5*c^2*d^17))/(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))*(-(a^4*d^7 + 2401*b^4*c^4*d^3 + 1372*a*b^3*c^3*d^4 + 294*a^2*b^2*c^2*d^5 + 28*a^3*b*c*d^6)/(4096*b^12*c^15 + 4096*a^12*c^3*d^12 - 49152*a^11*b*c^4*d^11 + 270336*a^2*b^10*c^13*d^2 - 901120*a^3*b^9*c^12*d^3 + 2027520*a^4*b^8*c^11*d^4 - 3244032*a^5*b^7*c^10*d^5 + 3784704*a^6*b^6*c^9*d^6 - 3244032*a^7*b^5*c^8*d^7 + 2027520*a^8*b^4*c^7*d^8 - 901120*a^9*b^3*c^6*d^9 + 270336*a^10*b^2*c^5*d^10 - 49152*a*b^11*c^14*d))^(3/4)*1i - (((2197*a*b^10*c^4*d^7)/2 - (7*b^11*c^5*d^6)/2 - (7*a^5*b^6*d^11)/2 + (2197*a^4*b^7*c*d^10)/2 + 9145*a^2*b^9*c^3*d^8 + 9145*a^3*b^8*c^2*d^9)*1i)/(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))*(-(a^4*d^7 + 2401*b^4*c^4*d^3 + 1372*a*b^3*c^3*d^4 + 294*a^2*b^2*c^2*d^5 + 28*a^3*b*c*d^6)/(4096*b^12*c^15 + 4096*a^12*c^3*d^12 - 49152*a^11*b*c^4*d^11 + 270336*a^2*b^10*c^13*d^2 - 901120*a^3*b^9*c^12*d^3 + 2027520*a^4*b^8*c^11*d^4 - 3244032*a^5*b^7*c^10*d^5 + 3784704*a^6*b^6*c^9*d^6 - 3244032*a^7*b^5*c^8*d^7 + 2027520*a^8*b^4*c^7*d^8 - 901120*a^9*b^3*c^6*d^9 + 270336*a^10*b^2*c^5*d^10 - 49152*a*b^11*c^14*d))^(1/4) - (x^(1/2)*(1225*a^6*b^7*d^13 + 1225*b^13*c^6*d^7 + 18186*a*b^12*c^5*d^8 + 18186*a^5*b^8*c*d^12 + 75975*a^2*b^11*c^4*d^9 + 71372*a^3*b^10*c^3*d^10 + 75975*a^4*b^9*c^2*d^11))/(8*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)))*(-(a^4*d^7 + 2401*b^4*c^4*d^3 + 1372*a*b^3*c^3*d^4 + 294*a^2*b^2*c^2*d^5 + 28*a^3*b*c*d^6)/(4096*b^12*c^15 + 4096*a^12*c^3*d^12 - 49152*a^11*b*c^4*d^11 + 270336*a^2*b^10*c^13*d^2 - 901120*a^3*b^9*c^12*d^3 + 2027520*a^4*b^8*c^11*d^4 - 3244032*a^5*b^7*c^10*d^5 + 3784704*a^6*b^6*c^9*d^6 - 3244032*a^7*b^5*c^8*d^7 + 2027520*a^8*b^4*c^7*d^8 - 901120*a^9*b^3*c^6*d^9 + 270336*a^10*b^2*c^5*d^10 - 49152*a*b^11*c^14*d))^(1/4) + ((((x^(1/2)*(2048*a^17*b^4*d^21 + 2048*b^21*c^17*d^4 + 4096*a*b^20*c^16*d^5 + 4096*a^16*b^5*c*d^20 - 108544*a^2*b^19*c^15*d^6 + 337920*a^3*b^18*c^14*d^7 + 153600*a^4*b^17*c^13*d^8 - 3225600*a^5*b^16*c^12*d^9 + 8648704*a^6*b^15*c^11*d^10 - 11106304*a^7*b^14*c^10*d^11 + 5294080*a^8*b^13*c^9*d^12 + 5294080*a^9*b^12*c^8*d^13 - 11106304*a^10*b^11*c^7*d^14 + 8648704*a^11*b^10*c^6*d^15 - 3225600*a^12*b^9*c^5*d^16 + 153600*a^13*b^8*c^4*d^17 + 337920*a^14*b^7*c^3*d^18 - 108544*a^15*b^6*c^2*d^19)*1i)/(8*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)) - ((-(a^4*d^7 + 2401*b^4*c^4*d^3 + 1372*a*b^3*c^3*d^4 + 294*a^2*b^2*c^2*d^5 + 28*a^3*b*c*d^6)/(4096*b^12*c^15 + 4096*a^12*c^3*d^12 - 49152*a^11*b*c^4*d^11 + 270336*a^2*b^10*c^13*d^2 - 901120*a^3*b^9*c^12*d^3 + 2027520*a^4*b^8*c^11*d^4 - 3244032*a^5*b^7*c^10*d^5 + 3784704*a^6*b^6*c^9*d^6 - 3244032*a^7*b^5*c^8*d^7 + 2027520*a^8*b^4*c^7*d^8 - 901120*a^9*b^3*c^6*d^9 + 270336*a^10*b^2*c^5*d^10 - 49152*a*b^11*c^14*d))^(1/4)*(8192*a^2*b^17*c^14*d^5 - 2048*a^15*b^4*c*d^18 - 2048*a*b^18*c^15*d^4 + 59392*a^3*b^16*c^13*d^6 - 606208*a^4*b^15*c^12*d^7 + 2455552*a^5*b^14*c^11*d^8 - 6037504*a^6*b^13*c^10*d^9 + 10070016*a^7*b^12*c^9*d^10 - 11894784*a^8*b^11*c^8*d^11 + 10070016*a^9*b^10*c^7*d^12 - 6037504*a^10*b^9*c^6*d^13 + 2455552*a^11*b^8*c^5*d^14 - 606208*a^12*b^7*c^4*d^15 + 59392*a^13*b^6*c^3*d^16 + 8192*a^14*b^5*c^2*d^17))/(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))*(-(a^4*d^7 + 2401*b^4*c^4*d^3 + 1372*a*b^3*c^3*d^4 + 294*a^2*b^2*c^2*d^5 + 28*a^3*b*c*d^6)/(4096*b^12*c^15 + 4096*a^12*c^3*d^12 - 49152*a^11*b*c^4*d^11 + 270336*a^2*b^10*c^13*d^2 - 901120*a^3*b^9*c^12*d^3 + 2027520*a^4*b^8*c^11*d^4 - 3244032*a^5*b^7*c^10*d^5 + 3784704*a^6*b^6*c^9*d^6 - 3244032*a^7*b^5*c^8*d^7 + 2027520*a^8*b^4*c^7*d^8 - 901120*a^9*b^3*c^6*d^9 + 270336*a^10*b^2*c^5*d^10 - 49152*a*b^11*c^14*d))^(3/4)*1i + (((2197*a*b^10*c^4*d^7)/2 - (7*b^11*c^5*d^6)/2 - (7*a^5*b^6*d^11)/2 + (2197*a^4*b^7*c*d^10)/2 + 9145*a^2*b^9*c^3*d^8 + 9145*a^3*b^8*c^2*d^9)*1i)/(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))*(-(a^4*d^7 + 2401*b^4*c^4*d^3 + 1372*a*b^3*c^3*d^4 + 294*a^2*b^2*c^2*d^5 + 28*a^3*b*c*d^6)/(4096*b^12*c^15 + 4096*a^12*c^3*d^12 - 49152*a^11*b*c^4*d^11 + 270336*a^2*b^10*c^13*d^2 - 901120*a^3*b^9*c^12*d^3 + 2027520*a^4*b^8*c^11*d^4 - 3244032*a^5*b^7*c^10*d^5 + 3784704*a^6*b^6*c^9*d^6 - 3244032*a^7*b^5*c^8*d^7 + 2027520*a^8*b^4*c^7*d^8 - 901120*a^9*b^3*c^6*d^9 + 270336*a^10*b^2*c^5*d^10 - 49152*a*b^11*c^14*d))^(1/4) - (x^(1/2)*(1225*a^6*b^7*d^13 + 1225*b^13*c^6*d^7 + 18186*a*b^12*c^5*d^8 + 18186*a^5*b^8*c*d^12 + 75975*a^2*b^11*c^4*d^9 + 71372*a^3*b^10*c^3*d^10 + 75975*a^4*b^9*c^2*d^11))/(8*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)))*(-(a^4*d^7 + 2401*b^4*c^4*d^3 + 1372*a*b^3*c^3*d^4 + 294*a^2*b^2*c^2*d^5 + 28*a^3*b*c*d^6)/(4096*b^12*c^15 + 4096*a^12*c^3*d^12 - 49152*a^11*b*c^4*d^11 + 270336*a^2*b^10*c^13*d^2 - 901120*a^3*b^9*c^12*d^3 + 2027520*a^4*b^8*c^11*d^4 - 3244032*a^5*b^7*c^10*d^5 + 3784704*a^6*b^6*c^9*d^6 - 3244032*a^7*b^5*c^8*d^7 + 2027520*a^8*b^4*c^7*d^8 - 901120*a^9*b^3*c^6*d^9 + 270336*a^10*b^2*c^5*d^10 - 49152*a*b^11*c^14*d))^(1/4))/(((((x^(1/2)*(2048*a^17*b^4*d^21 + 2048*b^21*c^17*d^4 + 4096*a*b^20*c^16*d^5 + 4096*a^16*b^5*c*d^20 - 108544*a^2*b^19*c^15*d^6 + 337920*a^3*b^18*c^14*d^7 + 153600*a^4*b^17*c^13*d^8 - 3225600*a^5*b^16*c^12*d^9 + 8648704*a^6*b^15*c^11*d^10 - 11106304*a^7*b^14*c^10*d^11 + 5294080*a^8*b^13*c^9*d^12 + 5294080*a^9*b^12*c^8*d^13 - 11106304*a^10*b^11*c^7*d^14 + 8648704*a^11*b^10*c^6*d^15 - 3225600*a^12*b^9*c^5*d^16 + 153600*a^13*b^8*c^4*d^17 + 337920*a^14*b^7*c^3*d^18 - 108544*a^15*b^6*c^2*d^19)*1i)/(8*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)) + ((-(a^4*d^7 + 2401*b^4*c^4*d^3 + 1372*a*b^3*c^3*d^4 + 294*a^2*b^2*c^2*d^5 + 28*a^3*b*c*d^6)/(4096*b^12*c^15 + 4096*a^12*c^3*d^12 - 49152*a^11*b*c^4*d^11 + 270336*a^2*b^10*c^13*d^2 - 901120*a^3*b^9*c^12*d^3 + 2027520*a^4*b^8*c^11*d^4 - 3244032*a^5*b^7*c^10*d^5 + 3784704*a^6*b^6*c^9*d^6 - 3244032*a^7*b^5*c^8*d^7 + 2027520*a^8*b^4*c^7*d^8 - 901120*a^9*b^3*c^6*d^9 + 270336*a^10*b^2*c^5*d^10 - 49152*a*b^11*c^14*d))^(1/4)*(8192*a^2*b^17*c^14*d^5 - 2048*a^15*b^4*c*d^18 - 2048*a*b^18*c^15*d^4 + 59392*a^3*b^16*c^13*d^6 - 606208*a^4*b^15*c^12*d^7 + 2455552*a^5*b^14*c^11*d^8 - 6037504*a^6*b^13*c^10*d^9 + 10070016*a^7*b^12*c^9*d^10 - 11894784*a^8*b^11*c^8*d^11 + 10070016*a^9*b^10*c^7*d^12 - 6037504*a^10*b^9*c^6*d^13 + 2455552*a^11*b^8*c^5*d^14 - 606208*a^12*b^7*c^4*d^15 + 59392*a^13*b^6*c^3*d^16 + 8192*a^14*b^5*c^2*d^17))/(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))*(-(a^4*d^7 + 2401*b^4*c^4*d^3 + 1372*a*b^3*c^3*d^4 + 294*a^2*b^2*c^2*d^5 + 28*a^3*b*c*d^6)/(4096*b^12*c^15 + 4096*a^12*c^3*d^12 - 49152*a^11*b*c^4*d^11 + 270336*a^2*b^10*c^13*d^2 - 901120*a^3*b^9*c^12*d^3 + 2027520*a^4*b^8*c^11*d^4 - 3244032*a^5*b^7*c^10*d^5 + 3784704*a^6*b^6*c^9*d^6 - 3244032*a^7*b^5*c^8*d^7 + 2027520*a^8*b^4*c^7*d^8 - 901120*a^9*b^3*c^6*d^9 + 270336*a^10*b^2*c^5*d^10 - 49152*a*b^11*c^14*d))^(3/4)*1i - (((2197*a*b^10*c^4*d^7)/2 - (7*b^11*c^5*d^6)/2 - (7*a^5*b^6*d^11)/2 + (2197*a^4*b^7*c*d^10)/2 + 9145*a^2*b^9*c^3*d^8 + 9145*a^3*b^8*c^2*d^9)*1i)/(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))*(-(a^4*d^7 + 2401*b^4*c^4*d^3 + 1372*a*b^3*c^3*d^4 + 294*a^2*b^2*c^2*d^5 + 28*a^3*b*c*d^6)/(4096*b^12*c^15 + 4096*a^12*c^3*d^12 - 49152*a^11*b*c^4*d^11 + 270336*a^2*b^10*c^13*d^2 - 901120*a^3*b^9*c^12*d^3 + 2027520*a^4*b^8*c^11*d^4 - 3244032*a^5*b^7*c^10*d^5 + 3784704*a^6*b^6*c^9*d^6 - 3244032*a^7*b^5*c^8*d^7 + 2027520*a^8*b^4*c^7*d^8 - 901120*a^9*b^3*c^6*d^9 + 270336*a^10*b^2*c^5*d^10 - 49152*a*b^11*c^14*d))^(1/4)*1i - (x^(1/2)*(1225*a^6*b^7*d^13 + 1225*b^13*c^6*d^7 + 18186*a*b^12*c^5*d^8 + 18186*a^5*b^8*c*d^12 + 75975*a^2*b^11*c^4*d^9 + 71372*a^3*b^10*c^3*d^10 + 75975*a^4*b^9*c^2*d^11)*1i)/(8*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)))*(-(a^4*d^7 + 2401*b^4*c^4*d^3 + 1372*a*b^3*c^3*d^4 + 294*a^2*b^2*c^2*d^5 + 28*a^3*b*c*d^6)/(4096*b^12*c^15 + 4096*a^12*c^3*d^12 - 49152*a^11*b*c^4*d^11 + 270336*a^2*b^10*c^13*d^2 - 901120*a^3*b^9*c^12*d^3 + 2027520*a^4*b^8*c^11*d^4 - 3244032*a^5*b^7*c^10*d^5 + 3784704*a^6*b^6*c^9*d^6 - 3244032*a^7*b^5*c^8*d^7 + 2027520*a^8*b^4*c^7*d^8 - 901120*a^9*b^3*c^6*d^9 + 270336*a^10*b^2*c^5*d^10 - 49152*a*b^11*c^14*d))^(1/4) - ((((x^(1/2)*(2048*a^17*b^4*d^21 + 2048*b^21*c^17*d^4 + 4096*a*b^20*c^16*d^5 + 4096*a^16*b^5*c*d^20 - 108544*a^2*b^19*c^15*d^6 + 337920*a^3*b^18*c^14*d^7 + 153600*a^4*b^17*c^13*d^8 - 3225600*a^5*b^16*c^12*d^9 + 8648704*a^6*b^15*c^11*d^10 - 11106304*a^7*b^14*c^10*d^11 + 5294080*a^8*b^13*c^9*d^12 + 5294080*a^9*b^12*c^8*d^13 - 11106304*a^10*b^11*c^7*d^14 + 8648704*a^11*b^10*c^6*d^15 - 3225600*a^12*b^9*c^5*d^16 + 153600*a^13*b^8*c^4*d^17 + 337920*a^14*b^7*c^3*d^18 - 108544*a^15*b^6*c^2*d^19)*1i)/(8*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)) - ((-(a^4*d^7 + 2401*b^4*c^4*d^3 + 1372*a*b^3*c^3*d^4 + 294*a^2*b^2*c^2*d^5 + 28*a^3*b*c*d^6)/(4096*b^12*c^15 + 4096*a^12*c^3*d^12 - 49152*a^11*b*c^4*d^11 + 270336*a^2*b^10*c^13*d^2 - 901120*a^3*b^9*c^12*d^3 + 2027520*a^4*b^8*c^11*d^4 - 3244032*a^5*b^7*c^10*d^5 + 3784704*a^6*b^6*c^9*d^6 - 3244032*a^7*b^5*c^8*d^7 + 2027520*a^8*b^4*c^7*d^8 - 901120*a^9*b^3*c^6*d^9 + 270336*a^10*b^2*c^5*d^10 - 49152*a*b^11*c^14*d))^(1/4)*(8192*a^2*b^17*c^14*d^5 - 2048*a^15*b^4*c*d^18 - 2048*a*b^18*c^15*d^4 + 59392*a^3*b^16*c^13*d^6 - 606208*a^4*b^15*c^12*d^7 + 2455552*a^5*b^14*c^11*d^8 - 6037504*a^6*b^13*c^10*d^9 + 10070016*a^7*b^12*c^9*d^10 - 11894784*a^8*b^11*c^8*d^11 + 10070016*a^9*b^10*c^7*d^12 - 6037504*a^10*b^9*c^6*d^13 + 2455552*a^11*b^8*c^5*d^14 - 606208*a^12*b^7*c^4*d^15 + 59392*a^13*b^6*c^3*d^16 + 8192*a^14*b^5*c^2*d^17))/(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))*(-(a^4*d^7 + 2401*b^4*c^4*d^3 + 1372*a*b^3*c^3*d^4 + 294*a^2*b^2*c^2*d^5 + 28*a^3*b*c*d^6)/(4096*b^12*c^15 + 4096*a^12*c^3*d^12 - 49152*a^11*b*c^4*d^11 + 270336*a^2*b^10*c^13*d^2 - 901120*a^3*b^9*c^12*d^3 + 2027520*a^4*b^8*c^11*d^4 - 3244032*a^5*b^7*c^10*d^5 + 3784704*a^6*b^6*c^9*d^6 - 3244032*a^7*b^5*c^8*d^7 + 2027520*a^8*b^4*c^7*d^8 - 901120*a^9*b^3*c^6*d^9 + 270336*a^10*b^2*c^5*d^10 - 49152*a*b^11*c^14*d))^(3/4)*1i + (((2197*a*b^10*c^4*d^7)/2 - (7*b^11*c^5*d^6)/2 - (7*a^5*b^6*d^11)/2 + (2197*a^4*b^7*c*d^10)/2 + 9145*a^2*b^9*c^3*d^8 + 9145*a^3*b^8*c^2*d^9)*1i)/(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))*(-(a^4*d^7 + 2401*b^4*c^4*d^3 + 1372*a*b^3*c^3*d^4 + 294*a^2*b^2*c^2*d^5 + 28*a^3*b*c*d^6)/(4096*b^12*c^15 + 4096*a^12*c^3*d^12 - 49152*a^11*b*c^4*d^11 + 270336*a^2*b^10*c^13*d^2 - 901120*a^3*b^9*c^12*d^3 + 2027520*a^4*b^8*c^11*d^4 - 3244032*a^5*b^7*c^10*d^5 + 3784704*a^6*b^6*c^9*d^6 - 3244032*a^7*b^5*c^8*d^7 + 2027520*a^8*b^4*c^7*d^8 - 901120*a^9*b^3*c^6*d^9 + 270336*a^10*b^2*c^5*d^10 - 49152*a*b^11*c^14*d))^(1/4)*1i - (x^(1/2)*(1225*a^6*b^7*d^13 + 1225*b^13*c^6*d^7 + 18186*a*b^12*c^5*d^8 + 18186*a^5*b^8*c*d^12 + 75975*a^2*b^11*c^4*d^9 + 71372*a^3*b^10*c^3*d^10 + 75975*a^4*b^9*c^2*d^11)*1i)/(8*(a^12*d^12 + b^12*c^12 + 66*a^2*b^10*c^10*d^2 - 220*a^3*b^9*c^9*d^3 + 495*a^4*b^8*c^8*d^4 - 792*a^5*b^7*c^7*d^5 + 924*a^6*b^6*c^6*d^6 - 792*a^7*b^5*c^5*d^7 + 495*a^8*b^4*c^4*d^8 - 220*a^9*b^3*c^3*d^9 + 66*a^10*b^2*c^2*d^10 - 12*a*b^11*c^11*d - 12*a^11*b*c*d^11)))*(-(a^4*d^7 + 2401*b^4*c^4*d^3 + 1372*a*b^3*c^3*d^4 + 294*a^2*b^2*c^2*d^5 + 28*a^3*b*c*d^6)/(4096*b^12*c^15 + 4096*a^12*c^3*d^12 - 49152*a^11*b*c^4*d^11 + 270336*a^2*b^10*c^13*d^2 - 901120*a^3*b^9*c^12*d^3 + 2027520*a^4*b^8*c^11*d^4 - 3244032*a^5*b^7*c^10*d^5 + 3784704*a^6*b^6*c^9*d^6 - 3244032*a^7*b^5*c^8*d^7 + 2027520*a^8*b^4*c^7*d^8 - 901120*a^9*b^3*c^6*d^9 + 270336*a^10*b^2*c^5*d^10 - 49152*a*b^11*c^14*d))^(1/4)))*(-(a^4*d^7 + 2401*b^4*c^4*d^3 + 1372*a*b^3*c^3*d^4 + 294*a^2*b^2*c^2*d^5 + 28*a^3*b*c*d^6)/(4096*b^12*c^15 + 4096*a^12*c^3*d^12 - 49152*a^11*b*c^4*d^11 + 270336*a^2*b^10*c^13*d^2 - 901120*a^3*b^9*c^12*d^3 + 2027520*a^4*b^8*c^11*d^4 - 3244032*a^5*b^7*c^10*d^5 + 3784704*a^6*b^6*c^9*d^6 - 3244032*a^7*b^5*c^8*d^7 + 2027520*a^8*b^4*c^7*d^8 - 901120*a^9*b^3*c^6*d^9 + 270336*a^10*b^2*c^5*d^10 - 49152*a*b^11*c^14*d))^(1/4)","B"
491,1,32506,624,4.559976,"\text{Not used}","int(x^(1/2)/((a + b*x^2)^2*(c + d*x^2)^2),x)","-\mathrm{atan}\left(\frac{\left(\left(\frac{32\,a^{19}\,b^4\,d^{23}-1216\,a^{18}\,b^5\,c\,d^{22}+19040\,a^{17}\,b^6\,c^2\,d^{21}-161664\,a^{16}\,b^7\,c^3\,d^{20}+837408\,a^{15}\,b^8\,c^4\,d^{19}-2842656\,a^{14}\,b^9\,c^5\,d^{18}+6564768\,a^{13}\,b^{10}\,c^6\,d^{17}-10331040\,a^{12}\,b^{11}\,c^7\,d^{16}+10374112\,a^{11}\,b^{12}\,c^8\,d^{15}-4458784\,a^{10}\,b^{13}\,c^9\,d^{14}-4458784\,a^9\,b^{14}\,c^{10}\,d^{13}+10374112\,a^8\,b^{15}\,c^{11}\,d^{12}-10331040\,a^7\,b^{16}\,c^{12}\,d^{11}+6564768\,a^6\,b^{17}\,c^{13}\,d^{10}-2842656\,a^5\,b^{18}\,c^{14}\,d^9+837408\,a^4\,b^{19}\,c^{15}\,d^8-161664\,a^3\,b^{20}\,c^{16}\,d^7+19040\,a^2\,b^{21}\,c^{17}\,d^6-1216\,a\,b^{22}\,c^{18}\,d^5+32\,b^{23}\,c^{19}\,d^4}{a^{16}\,c^2\,d^{14}-14\,a^{15}\,b\,c^3\,d^{13}+91\,a^{14}\,b^2\,c^4\,d^{12}-364\,a^{13}\,b^3\,c^5\,d^{11}+1001\,a^{12}\,b^4\,c^6\,d^{10}-2002\,a^{11}\,b^5\,c^7\,d^9+3003\,a^{10}\,b^6\,c^8\,d^8-3432\,a^9\,b^7\,c^9\,d^7+3003\,a^8\,b^8\,c^{10}\,d^6-2002\,a^7\,b^9\,c^{11}\,d^5+1001\,a^6\,b^{10}\,c^{12}\,d^4-364\,a^5\,b^{11}\,c^{13}\,d^3+91\,a^4\,b^{12}\,c^{14}\,d^2-14\,a^3\,b^{13}\,c^{15}\,d+a^2\,b^{14}\,c^{16}}-\frac{\sqrt{x}\,{\left(-\frac{a^4\,d^9-36\,a^3\,b\,c\,d^8+486\,a^2\,b^2\,c^2\,d^7-2916\,a\,b^3\,c^3\,d^6+6561\,b^4\,c^4\,d^5}{4096\,a^{12}\,c^5\,d^{12}-49152\,a^{11}\,b\,c^6\,d^{11}+270336\,a^{10}\,b^2\,c^7\,d^{10}-901120\,a^9\,b^3\,c^8\,d^9+2027520\,a^8\,b^4\,c^9\,d^8-3244032\,a^7\,b^5\,c^{10}\,d^7+3784704\,a^6\,b^6\,c^{11}\,d^6-3244032\,a^5\,b^7\,c^{12}\,d^5+2027520\,a^4\,b^8\,c^{13}\,d^4-901120\,a^3\,b^9\,c^{14}\,d^3+270336\,a^2\,b^{10}\,c^{15}\,d^2-49152\,a\,b^{11}\,c^{16}\,d+4096\,b^{12}\,c^{17}}\right)}^{1/4}\,\left(4096\,a^{19}\,b^4\,c\,d^{22}-122880\,a^{18}\,b^5\,c^2\,d^{21}+1486848\,a^{17}\,b^6\,c^3\,d^{20}-9748480\,a^{16}\,b^7\,c^4\,d^{19}+40476672\,a^{15}\,b^8\,c^5\,d^{18}-116785152\,a^{14}\,b^9\,c^6\,d^{17}+249192448\,a^{13}\,b^{10}\,c^7\,d^{16}-412041216\,a^{12}\,b^{11}\,c^8\,d^{15}+547700736\,a^{11}\,b^{12}\,c^9\,d^{14}-600326144\,a^{10}\,b^{13}\,c^{10}\,d^{13}+547700736\,a^9\,b^{14}\,c^{11}\,d^{12}-412041216\,a^8\,b^{15}\,c^{12}\,d^{11}+249192448\,a^7\,b^{16}\,c^{13}\,d^{10}-116785152\,a^6\,b^{17}\,c^{14}\,d^9+40476672\,a^5\,b^{18}\,c^{15}\,d^8-9748480\,a^4\,b^{19}\,c^{16}\,d^7+1486848\,a^3\,b^{20}\,c^{17}\,d^6-122880\,a^2\,b^{21}\,c^{18}\,d^5+4096\,a\,b^{22}\,c^{19}\,d^4\right)}{16\,\left(a^{14}\,c^2\,d^{12}-12\,a^{13}\,b\,c^3\,d^{11}+66\,a^{12}\,b^2\,c^4\,d^{10}-220\,a^{11}\,b^3\,c^5\,d^9+495\,a^{10}\,b^4\,c^6\,d^8-792\,a^9\,b^5\,c^7\,d^7+924\,a^8\,b^6\,c^8\,d^6-792\,a^7\,b^7\,c^9\,d^5+495\,a^6\,b^8\,c^{10}\,d^4-220\,a^5\,b^9\,c^{11}\,d^3+66\,a^4\,b^{10}\,c^{12}\,d^2-12\,a^3\,b^{11}\,c^{13}\,d+a^2\,b^{12}\,c^{14}\right)}\right)\,{\left(-\frac{a^4\,d^9-36\,a^3\,b\,c\,d^8+486\,a^2\,b^2\,c^2\,d^7-2916\,a\,b^3\,c^3\,d^6+6561\,b^4\,c^4\,d^5}{4096\,a^{12}\,c^5\,d^{12}-49152\,a^{11}\,b\,c^6\,d^{11}+270336\,a^{10}\,b^2\,c^7\,d^{10}-901120\,a^9\,b^3\,c^8\,d^9+2027520\,a^8\,b^4\,c^9\,d^8-3244032\,a^7\,b^5\,c^{10}\,d^7+3784704\,a^6\,b^6\,c^{11}\,d^6-3244032\,a^5\,b^7\,c^{12}\,d^5+2027520\,a^4\,b^8\,c^{13}\,d^4-901120\,a^3\,b^9\,c^{14}\,d^3+270336\,a^2\,b^{10}\,c^{15}\,d^2-49152\,a\,b^{11}\,c^{16}\,d+4096\,b^{12}\,c^{17}}\right)}^{3/4}\,1{}\mathrm{i}-\frac{\sqrt{x}\,\left(81\,a^7\,b^8\,d^{15}+3627\,a^6\,b^9\,c\,d^{14}-80999\,a^5\,b^{10}\,c^2\,d^{13}+339435\,a^4\,b^{11}\,c^3\,d^{12}+339435\,a^3\,b^{12}\,c^4\,d^{11}-80999\,a^2\,b^{13}\,c^5\,d^{10}+3627\,a\,b^{14}\,c^6\,d^9+81\,b^{15}\,c^7\,d^8\right)\,1{}\mathrm{i}}{16\,\left(a^{14}\,c^2\,d^{12}-12\,a^{13}\,b\,c^3\,d^{11}+66\,a^{12}\,b^2\,c^4\,d^{10}-220\,a^{11}\,b^3\,c^5\,d^9+495\,a^{10}\,b^4\,c^6\,d^8-792\,a^9\,b^5\,c^7\,d^7+924\,a^8\,b^6\,c^8\,d^6-792\,a^7\,b^7\,c^9\,d^5+495\,a^6\,b^8\,c^{10}\,d^4-220\,a^5\,b^9\,c^{11}\,d^3+66\,a^4\,b^{10}\,c^{12}\,d^2-12\,a^3\,b^{11}\,c^{13}\,d+a^2\,b^{12}\,c^{14}\right)}\right)\,{\left(-\frac{a^4\,d^9-36\,a^3\,b\,c\,d^8+486\,a^2\,b^2\,c^2\,d^7-2916\,a\,b^3\,c^3\,d^6+6561\,b^4\,c^4\,d^5}{4096\,a^{12}\,c^5\,d^{12}-49152\,a^{11}\,b\,c^6\,d^{11}+270336\,a^{10}\,b^2\,c^7\,d^{10}-901120\,a^9\,b^3\,c^8\,d^9+2027520\,a^8\,b^4\,c^9\,d^8-3244032\,a^7\,b^5\,c^{10}\,d^7+3784704\,a^6\,b^6\,c^{11}\,d^6-3244032\,a^5\,b^7\,c^{12}\,d^5+2027520\,a^4\,b^8\,c^{13}\,d^4-901120\,a^3\,b^9\,c^{14}\,d^3+270336\,a^2\,b^{10}\,c^{15}\,d^2-49152\,a\,b^{11}\,c^{16}\,d+4096\,b^{12}\,c^{17}}\right)}^{1/4}-\left(\left(\frac{32\,a^{19}\,b^4\,d^{23}-1216\,a^{18}\,b^5\,c\,d^{22}+19040\,a^{17}\,b^6\,c^2\,d^{21}-161664\,a^{16}\,b^7\,c^3\,d^{20}+837408\,a^{15}\,b^8\,c^4\,d^{19}-2842656\,a^{14}\,b^9\,c^5\,d^{18}+6564768\,a^{13}\,b^{10}\,c^6\,d^{17}-10331040\,a^{12}\,b^{11}\,c^7\,d^{16}+10374112\,a^{11}\,b^{12}\,c^8\,d^{15}-4458784\,a^{10}\,b^{13}\,c^9\,d^{14}-4458784\,a^9\,b^{14}\,c^{10}\,d^{13}+10374112\,a^8\,b^{15}\,c^{11}\,d^{12}-10331040\,a^7\,b^{16}\,c^{12}\,d^{11}+6564768\,a^6\,b^{17}\,c^{13}\,d^{10}-2842656\,a^5\,b^{18}\,c^{14}\,d^9+837408\,a^4\,b^{19}\,c^{15}\,d^8-161664\,a^3\,b^{20}\,c^{16}\,d^7+19040\,a^2\,b^{21}\,c^{17}\,d^6-1216\,a\,b^{22}\,c^{18}\,d^5+32\,b^{23}\,c^{19}\,d^4}{a^{16}\,c^2\,d^{14}-14\,a^{15}\,b\,c^3\,d^{13}+91\,a^{14}\,b^2\,c^4\,d^{12}-364\,a^{13}\,b^3\,c^5\,d^{11}+1001\,a^{12}\,b^4\,c^6\,d^{10}-2002\,a^{11}\,b^5\,c^7\,d^9+3003\,a^{10}\,b^6\,c^8\,d^8-3432\,a^9\,b^7\,c^9\,d^7+3003\,a^8\,b^8\,c^{10}\,d^6-2002\,a^7\,b^9\,c^{11}\,d^5+1001\,a^6\,b^{10}\,c^{12}\,d^4-364\,a^5\,b^{11}\,c^{13}\,d^3+91\,a^4\,b^{12}\,c^{14}\,d^2-14\,a^3\,b^{13}\,c^{15}\,d+a^2\,b^{14}\,c^{16}}+\frac{\sqrt{x}\,{\left(-\frac{a^4\,d^9-36\,a^3\,b\,c\,d^8+486\,a^2\,b^2\,c^2\,d^7-2916\,a\,b^3\,c^3\,d^6+6561\,b^4\,c^4\,d^5}{4096\,a^{12}\,c^5\,d^{12}-49152\,a^{11}\,b\,c^6\,d^{11}+270336\,a^{10}\,b^2\,c^7\,d^{10}-901120\,a^9\,b^3\,c^8\,d^9+2027520\,a^8\,b^4\,c^9\,d^8-3244032\,a^7\,b^5\,c^{10}\,d^7+3784704\,a^6\,b^6\,c^{11}\,d^6-3244032\,a^5\,b^7\,c^{12}\,d^5+2027520\,a^4\,b^8\,c^{13}\,d^4-901120\,a^3\,b^9\,c^{14}\,d^3+270336\,a^2\,b^{10}\,c^{15}\,d^2-49152\,a\,b^{11}\,c^{16}\,d+4096\,b^{12}\,c^{17}}\right)}^{1/4}\,\left(4096\,a^{19}\,b^4\,c\,d^{22}-122880\,a^{18}\,b^5\,c^2\,d^{21}+1486848\,a^{17}\,b^6\,c^3\,d^{20}-9748480\,a^{16}\,b^7\,c^4\,d^{19}+40476672\,a^{15}\,b^8\,c^5\,d^{18}-116785152\,a^{14}\,b^9\,c^6\,d^{17}+249192448\,a^{13}\,b^{10}\,c^7\,d^{16}-412041216\,a^{12}\,b^{11}\,c^8\,d^{15}+547700736\,a^{11}\,b^{12}\,c^9\,d^{14}-600326144\,a^{10}\,b^{13}\,c^{10}\,d^{13}+547700736\,a^9\,b^{14}\,c^{11}\,d^{12}-412041216\,a^8\,b^{15}\,c^{12}\,d^{11}+249192448\,a^7\,b^{16}\,c^{13}\,d^{10}-116785152\,a^6\,b^{17}\,c^{14}\,d^9+40476672\,a^5\,b^{18}\,c^{15}\,d^8-9748480\,a^4\,b^{19}\,c^{16}\,d^7+1486848\,a^3\,b^{20}\,c^{17}\,d^6-122880\,a^2\,b^{21}\,c^{18}\,d^5+4096\,a\,b^{22}\,c^{19}\,d^4\right)}{16\,\left(a^{14}\,c^2\,d^{12}-12\,a^{13}\,b\,c^3\,d^{11}+66\,a^{12}\,b^2\,c^4\,d^{10}-220\,a^{11}\,b^3\,c^5\,d^9+495\,a^{10}\,b^4\,c^6\,d^8-792\,a^9\,b^5\,c^7\,d^7+924\,a^8\,b^6\,c^8\,d^6-792\,a^7\,b^7\,c^9\,d^5+495\,a^6\,b^8\,c^{10}\,d^4-220\,a^5\,b^9\,c^{11}\,d^3+66\,a^4\,b^{10}\,c^{12}\,d^2-12\,a^3\,b^{11}\,c^{13}\,d+a^2\,b^{12}\,c^{14}\right)}\right)\,{\left(-\frac{a^4\,d^9-36\,a^3\,b\,c\,d^8+486\,a^2\,b^2\,c^2\,d^7-2916\,a\,b^3\,c^3\,d^6+6561\,b^4\,c^4\,d^5}{4096\,a^{12}\,c^5\,d^{12}-49152\,a^{11}\,b\,c^6\,d^{11}+270336\,a^{10}\,b^2\,c^7\,d^{10}-901120\,a^9\,b^3\,c^8\,d^9+2027520\,a^8\,b^4\,c^9\,d^8-3244032\,a^7\,b^5\,c^{10}\,d^7+3784704\,a^6\,b^6\,c^{11}\,d^6-3244032\,a^5\,b^7\,c^{12}\,d^5+2027520\,a^4\,b^8\,c^{13}\,d^4-901120\,a^3\,b^9\,c^{14}\,d^3+270336\,a^2\,b^{10}\,c^{15}\,d^2-49152\,a\,b^{11}\,c^{16}\,d+4096\,b^{12}\,c^{17}}\right)}^{3/4}\,1{}\mathrm{i}+\frac{\sqrt{x}\,\left(81\,a^7\,b^8\,d^{15}+3627\,a^6\,b^9\,c\,d^{14}-80999\,a^5\,b^{10}\,c^2\,d^{13}+339435\,a^4\,b^{11}\,c^3\,d^{12}+339435\,a^3\,b^{12}\,c^4\,d^{11}-80999\,a^2\,b^{13}\,c^5\,d^{10}+3627\,a\,b^{14}\,c^6\,d^9+81\,b^{15}\,c^7\,d^8\right)\,1{}\mathrm{i}}{16\,\left(a^{14}\,c^2\,d^{12}-12\,a^{13}\,b\,c^3\,d^{11}+66\,a^{12}\,b^2\,c^4\,d^{10}-220\,a^{11}\,b^3\,c^5\,d^9+495\,a^{10}\,b^4\,c^6\,d^8-792\,a^9\,b^5\,c^7\,d^7+924\,a^8\,b^6\,c^8\,d^6-792\,a^7\,b^7\,c^9\,d^5+495\,a^6\,b^8\,c^{10}\,d^4-220\,a^5\,b^9\,c^{11}\,d^3+66\,a^4\,b^{10}\,c^{12}\,d^2-12\,a^3\,b^{11}\,c^{13}\,d+a^2\,b^{12}\,c^{14}\right)}\right)\,{\left(-\frac{a^4\,d^9-36\,a^3\,b\,c\,d^8+486\,a^2\,b^2\,c^2\,d^7-2916\,a\,b^3\,c^3\,d^6+6561\,b^4\,c^4\,d^5}{4096\,a^{12}\,c^5\,d^{12}-49152\,a^{11}\,b\,c^6\,d^{11}+270336\,a^{10}\,b^2\,c^7\,d^{10}-901120\,a^9\,b^3\,c^8\,d^9+2027520\,a^8\,b^4\,c^9\,d^8-3244032\,a^7\,b^5\,c^{10}\,d^7+3784704\,a^6\,b^6\,c^{11}\,d^6-3244032\,a^5\,b^7\,c^{12}\,d^5+2027520\,a^4\,b^8\,c^{13}\,d^4-901120\,a^3\,b^9\,c^{14}\,d^3+270336\,a^2\,b^{10}\,c^{15}\,d^2-49152\,a\,b^{11}\,c^{16}\,d+4096\,b^{12}\,c^{17}}\right)}^{1/4}}{\frac{\frac{3645\,a^6\,b^9\,d^{15}}{32}-\frac{49815\,a^5\,b^{10}\,c\,d^{14}}{16}+\frac{918675\,a^4\,b^{11}\,c^2\,d^{13}}{32}-\frac{739025\,a^3\,b^{12}\,c^3\,d^{12}}{8}+\frac{918675\,a^2\,b^{13}\,c^4\,d^{11}}{32}-\frac{49815\,a\,b^{14}\,c^5\,d^{10}}{16}+\frac{3645\,b^{15}\,c^6\,d^9}{32}}{a^{16}\,c^2\,d^{14}-14\,a^{15}\,b\,c^3\,d^{13}+91\,a^{14}\,b^2\,c^4\,d^{12}-364\,a^{13}\,b^3\,c^5\,d^{11}+1001\,a^{12}\,b^4\,c^6\,d^{10}-2002\,a^{11}\,b^5\,c^7\,d^9+3003\,a^{10}\,b^6\,c^8\,d^8-3432\,a^9\,b^7\,c^9\,d^7+3003\,a^8\,b^8\,c^{10}\,d^6-2002\,a^7\,b^9\,c^{11}\,d^5+1001\,a^6\,b^{10}\,c^{12}\,d^4-364\,a^5\,b^{11}\,c^{13}\,d^3+91\,a^4\,b^{12}\,c^{14}\,d^2-14\,a^3\,b^{13}\,c^{15}\,d+a^2\,b^{14}\,c^{16}}+\left(\left(\frac{32\,a^{19}\,b^4\,d^{23}-1216\,a^{18}\,b^5\,c\,d^{22}+19040\,a^{17}\,b^6\,c^2\,d^{21}-161664\,a^{16}\,b^7\,c^3\,d^{20}+837408\,a^{15}\,b^8\,c^4\,d^{19}-2842656\,a^{14}\,b^9\,c^5\,d^{18}+6564768\,a^{13}\,b^{10}\,c^6\,d^{17}-10331040\,a^{12}\,b^{11}\,c^7\,d^{16}+10374112\,a^{11}\,b^{12}\,c^8\,d^{15}-4458784\,a^{10}\,b^{13}\,c^9\,d^{14}-4458784\,a^9\,b^{14}\,c^{10}\,d^{13}+10374112\,a^8\,b^{15}\,c^{11}\,d^{12}-10331040\,a^7\,b^{16}\,c^{12}\,d^{11}+6564768\,a^6\,b^{17}\,c^{13}\,d^{10}-2842656\,a^5\,b^{18}\,c^{14}\,d^9+837408\,a^4\,b^{19}\,c^{15}\,d^8-161664\,a^3\,b^{20}\,c^{16}\,d^7+19040\,a^2\,b^{21}\,c^{17}\,d^6-1216\,a\,b^{22}\,c^{18}\,d^5+32\,b^{23}\,c^{19}\,d^4}{a^{16}\,c^2\,d^{14}-14\,a^{15}\,b\,c^3\,d^{13}+91\,a^{14}\,b^2\,c^4\,d^{12}-364\,a^{13}\,b^3\,c^5\,d^{11}+1001\,a^{12}\,b^4\,c^6\,d^{10}-2002\,a^{11}\,b^5\,c^7\,d^9+3003\,a^{10}\,b^6\,c^8\,d^8-3432\,a^9\,b^7\,c^9\,d^7+3003\,a^8\,b^8\,c^{10}\,d^6-2002\,a^7\,b^9\,c^{11}\,d^5+1001\,a^6\,b^{10}\,c^{12}\,d^4-364\,a^5\,b^{11}\,c^{13}\,d^3+91\,a^4\,b^{12}\,c^{14}\,d^2-14\,a^3\,b^{13}\,c^{15}\,d+a^2\,b^{14}\,c^{16}}-\frac{\sqrt{x}\,{\left(-\frac{a^4\,d^9-36\,a^3\,b\,c\,d^8+486\,a^2\,b^2\,c^2\,d^7-2916\,a\,b^3\,c^3\,d^6+6561\,b^4\,c^4\,d^5}{4096\,a^{12}\,c^5\,d^{12}-49152\,a^{11}\,b\,c^6\,d^{11}+270336\,a^{10}\,b^2\,c^7\,d^{10}-901120\,a^9\,b^3\,c^8\,d^9+2027520\,a^8\,b^4\,c^9\,d^8-3244032\,a^7\,b^5\,c^{10}\,d^7+3784704\,a^6\,b^6\,c^{11}\,d^6-3244032\,a^5\,b^7\,c^{12}\,d^5+2027520\,a^4\,b^8\,c^{13}\,d^4-901120\,a^3\,b^9\,c^{14}\,d^3+270336\,a^2\,b^{10}\,c^{15}\,d^2-49152\,a\,b^{11}\,c^{16}\,d+4096\,b^{12}\,c^{17}}\right)}^{1/4}\,\left(4096\,a^{19}\,b^4\,c\,d^{22}-122880\,a^{18}\,b^5\,c^2\,d^{21}+1486848\,a^{17}\,b^6\,c^3\,d^{20}-9748480\,a^{16}\,b^7\,c^4\,d^{19}+40476672\,a^{15}\,b^8\,c^5\,d^{18}-116785152\,a^{14}\,b^9\,c^6\,d^{17}+249192448\,a^{13}\,b^{10}\,c^7\,d^{16}-412041216\,a^{12}\,b^{11}\,c^8\,d^{15}+547700736\,a^{11}\,b^{12}\,c^9\,d^{14}-600326144\,a^{10}\,b^{13}\,c^{10}\,d^{13}+547700736\,a^9\,b^{14}\,c^{11}\,d^{12}-412041216\,a^8\,b^{15}\,c^{12}\,d^{11}+249192448\,a^7\,b^{16}\,c^{13}\,d^{10}-116785152\,a^6\,b^{17}\,c^{14}\,d^9+40476672\,a^5\,b^{18}\,c^{15}\,d^8-9748480\,a^4\,b^{19}\,c^{16}\,d^7+1486848\,a^3\,b^{20}\,c^{17}\,d^6-122880\,a^2\,b^{21}\,c^{18}\,d^5+4096\,a\,b^{22}\,c^{19}\,d^4\right)}{16\,\left(a^{14}\,c^2\,d^{12}-12\,a^{13}\,b\,c^3\,d^{11}+66\,a^{12}\,b^2\,c^4\,d^{10}-220\,a^{11}\,b^3\,c^5\,d^9+495\,a^{10}\,b^4\,c^6\,d^8-792\,a^9\,b^5\,c^7\,d^7+924\,a^8\,b^6\,c^8\,d^6-792\,a^7\,b^7\,c^9\,d^5+495\,a^6\,b^8\,c^{10}\,d^4-220\,a^5\,b^9\,c^{11}\,d^3+66\,a^4\,b^{10}\,c^{12}\,d^2-12\,a^3\,b^{11}\,c^{13}\,d+a^2\,b^{12}\,c^{14}\right)}\right)\,{\left(-\frac{a^4\,d^9-36\,a^3\,b\,c\,d^8+486\,a^2\,b^2\,c^2\,d^7-2916\,a\,b^3\,c^3\,d^6+6561\,b^4\,c^4\,d^5}{4096\,a^{12}\,c^5\,d^{12}-49152\,a^{11}\,b\,c^6\,d^{11}+270336\,a^{10}\,b^2\,c^7\,d^{10}-901120\,a^9\,b^3\,c^8\,d^9+2027520\,a^8\,b^4\,c^9\,d^8-3244032\,a^7\,b^5\,c^{10}\,d^7+3784704\,a^6\,b^6\,c^{11}\,d^6-3244032\,a^5\,b^7\,c^{12}\,d^5+2027520\,a^4\,b^8\,c^{13}\,d^4-901120\,a^3\,b^9\,c^{14}\,d^3+270336\,a^2\,b^{10}\,c^{15}\,d^2-49152\,a\,b^{11}\,c^{16}\,d+4096\,b^{12}\,c^{17}}\right)}^{3/4}-\frac{\sqrt{x}\,\left(81\,a^7\,b^8\,d^{15}+3627\,a^6\,b^9\,c\,d^{14}-80999\,a^5\,b^{10}\,c^2\,d^{13}+339435\,a^4\,b^{11}\,c^3\,d^{12}+339435\,a^3\,b^{12}\,c^4\,d^{11}-80999\,a^2\,b^{13}\,c^5\,d^{10}+3627\,a\,b^{14}\,c^6\,d^9+81\,b^{15}\,c^7\,d^8\right)}{16\,\left(a^{14}\,c^2\,d^{12}-12\,a^{13}\,b\,c^3\,d^{11}+66\,a^{12}\,b^2\,c^4\,d^{10}-220\,a^{11}\,b^3\,c^5\,d^9+495\,a^{10}\,b^4\,c^6\,d^8-792\,a^9\,b^5\,c^7\,d^7+924\,a^8\,b^6\,c^8\,d^6-792\,a^7\,b^7\,c^9\,d^5+495\,a^6\,b^8\,c^{10}\,d^4-220\,a^5\,b^9\,c^{11}\,d^3+66\,a^4\,b^{10}\,c^{12}\,d^2-12\,a^3\,b^{11}\,c^{13}\,d+a^2\,b^{12}\,c^{14}\right)}\right)\,{\left(-\frac{a^4\,d^9-36\,a^3\,b\,c\,d^8+486\,a^2\,b^2\,c^2\,d^7-2916\,a\,b^3\,c^3\,d^6+6561\,b^4\,c^4\,d^5}{4096\,a^{12}\,c^5\,d^{12}-49152\,a^{11}\,b\,c^6\,d^{11}+270336\,a^{10}\,b^2\,c^7\,d^{10}-901120\,a^9\,b^3\,c^8\,d^9+2027520\,a^8\,b^4\,c^9\,d^8-3244032\,a^7\,b^5\,c^{10}\,d^7+3784704\,a^6\,b^6\,c^{11}\,d^6-3244032\,a^5\,b^7\,c^{12}\,d^5+2027520\,a^4\,b^8\,c^{13}\,d^4-901120\,a^3\,b^9\,c^{14}\,d^3+270336\,a^2\,b^{10}\,c^{15}\,d^2-49152\,a\,b^{11}\,c^{16}\,d+4096\,b^{12}\,c^{17}}\right)}^{1/4}+\left(\left(\frac{32\,a^{19}\,b^4\,d^{23}-1216\,a^{18}\,b^5\,c\,d^{22}+19040\,a^{17}\,b^6\,c^2\,d^{21}-161664\,a^{16}\,b^7\,c^3\,d^{20}+837408\,a^{15}\,b^8\,c^4\,d^{19}-2842656\,a^{14}\,b^9\,c^5\,d^{18}+6564768\,a^{13}\,b^{10}\,c^6\,d^{17}-10331040\,a^{12}\,b^{11}\,c^7\,d^{16}+10374112\,a^{11}\,b^{12}\,c^8\,d^{15}-4458784\,a^{10}\,b^{13}\,c^9\,d^{14}-4458784\,a^9\,b^{14}\,c^{10}\,d^{13}+10374112\,a^8\,b^{15}\,c^{11}\,d^{12}-10331040\,a^7\,b^{16}\,c^{12}\,d^{11}+6564768\,a^6\,b^{17}\,c^{13}\,d^{10}-2842656\,a^5\,b^{18}\,c^{14}\,d^9+837408\,a^4\,b^{19}\,c^{15}\,d^8-161664\,a^3\,b^{20}\,c^{16}\,d^7+19040\,a^2\,b^{21}\,c^{17}\,d^6-1216\,a\,b^{22}\,c^{18}\,d^5+32\,b^{23}\,c^{19}\,d^4}{a^{16}\,c^2\,d^{14}-14\,a^{15}\,b\,c^3\,d^{13}+91\,a^{14}\,b^2\,c^4\,d^{12}-364\,a^{13}\,b^3\,c^5\,d^{11}+1001\,a^{12}\,b^4\,c^6\,d^{10}-2002\,a^{11}\,b^5\,c^7\,d^9+3003\,a^{10}\,b^6\,c^8\,d^8-3432\,a^9\,b^7\,c^9\,d^7+3003\,a^8\,b^8\,c^{10}\,d^6-2002\,a^7\,b^9\,c^{11}\,d^5+1001\,a^6\,b^{10}\,c^{12}\,d^4-364\,a^5\,b^{11}\,c^{13}\,d^3+91\,a^4\,b^{12}\,c^{14}\,d^2-14\,a^3\,b^{13}\,c^{15}\,d+a^2\,b^{14}\,c^{16}}+\frac{\sqrt{x}\,{\left(-\frac{a^4\,d^9-36\,a^3\,b\,c\,d^8+486\,a^2\,b^2\,c^2\,d^7-2916\,a\,b^3\,c^3\,d^6+6561\,b^4\,c^4\,d^5}{4096\,a^{12}\,c^5\,d^{12}-49152\,a^{11}\,b\,c^6\,d^{11}+270336\,a^{10}\,b^2\,c^7\,d^{10}-901120\,a^9\,b^3\,c^8\,d^9+2027520\,a^8\,b^4\,c^9\,d^8-3244032\,a^7\,b^5\,c^{10}\,d^7+3784704\,a^6\,b^6\,c^{11}\,d^6-3244032\,a^5\,b^7\,c^{12}\,d^5+2027520\,a^4\,b^8\,c^{13}\,d^4-901120\,a^3\,b^9\,c^{14}\,d^3+270336\,a^2\,b^{10}\,c^{15}\,d^2-49152\,a\,b^{11}\,c^{16}\,d+4096\,b^{12}\,c^{17}}\right)}^{1/4}\,\left(4096\,a^{19}\,b^4\,c\,d^{22}-122880\,a^{18}\,b^5\,c^2\,d^{21}+1486848\,a^{17}\,b^6\,c^3\,d^{20}-9748480\,a^{16}\,b^7\,c^4\,d^{19}+40476672\,a^{15}\,b^8\,c^5\,d^{18}-116785152\,a^{14}\,b^9\,c^6\,d^{17}+249192448\,a^{13}\,b^{10}\,c^7\,d^{16}-412041216\,a^{12}\,b^{11}\,c^8\,d^{15}+547700736\,a^{11}\,b^{12}\,c^9\,d^{14}-600326144\,a^{10}\,b^{13}\,c^{10}\,d^{13}+547700736\,a^9\,b^{14}\,c^{11}\,d^{12}-412041216\,a^8\,b^{15}\,c^{12}\,d^{11}+249192448\,a^7\,b^{16}\,c^{13}\,d^{10}-116785152\,a^6\,b^{17}\,c^{14}\,d^9+40476672\,a^5\,b^{18}\,c^{15}\,d^8-9748480\,a^4\,b^{19}\,c^{16}\,d^7+1486848\,a^3\,b^{20}\,c^{17}\,d^6-122880\,a^2\,b^{21}\,c^{18}\,d^5+4096\,a\,b^{22}\,c^{19}\,d^4\right)}{16\,\left(a^{14}\,c^2\,d^{12}-12\,a^{13}\,b\,c^3\,d^{11}+66\,a^{12}\,b^2\,c^4\,d^{10}-220\,a^{11}\,b^3\,c^5\,d^9+495\,a^{10}\,b^4\,c^6\,d^8-792\,a^9\,b^5\,c^7\,d^7+924\,a^8\,b^6\,c^8\,d^6-792\,a^7\,b^7\,c^9\,d^5+495\,a^6\,b^8\,c^{10}\,d^4-220\,a^5\,b^9\,c^{11}\,d^3+66\,a^4\,b^{10}\,c^{12}\,d^2-12\,a^3\,b^{11}\,c^{13}\,d+a^2\,b^{12}\,c^{14}\right)}\right)\,{\left(-\frac{a^4\,d^9-36\,a^3\,b\,c\,d^8+486\,a^2\,b^2\,c^2\,d^7-2916\,a\,b^3\,c^3\,d^6+6561\,b^4\,c^4\,d^5}{4096\,a^{12}\,c^5\,d^{12}-49152\,a^{11}\,b\,c^6\,d^{11}+270336\,a^{10}\,b^2\,c^7\,d^{10}-901120\,a^9\,b^3\,c^8\,d^9+2027520\,a^8\,b^4\,c^9\,d^8-3244032\,a^7\,b^5\,c^{10}\,d^7+3784704\,a^6\,b^6\,c^{11}\,d^6-3244032\,a^5\,b^7\,c^{12}\,d^5+2027520\,a^4\,b^8\,c^{13}\,d^4-901120\,a^3\,b^9\,c^{14}\,d^3+270336\,a^2\,b^{10}\,c^{15}\,d^2-49152\,a\,b^{11}\,c^{16}\,d+4096\,b^{12}\,c^{17}}\right)}^{3/4}+\frac{\sqrt{x}\,\left(81\,a^7\,b^8\,d^{15}+3627\,a^6\,b^9\,c\,d^{14}-80999\,a^5\,b^{10}\,c^2\,d^{13}+339435\,a^4\,b^{11}\,c^3\,d^{12}+339435\,a^3\,b^{12}\,c^4\,d^{11}-80999\,a^2\,b^{13}\,c^5\,d^{10}+3627\,a\,b^{14}\,c^6\,d^9+81\,b^{15}\,c^7\,d^8\right)}{16\,\left(a^{14}\,c^2\,d^{12}-12\,a^{13}\,b\,c^3\,d^{11}+66\,a^{12}\,b^2\,c^4\,d^{10}-220\,a^{11}\,b^3\,c^5\,d^9+495\,a^{10}\,b^4\,c^6\,d^8-792\,a^9\,b^5\,c^7\,d^7+924\,a^8\,b^6\,c^8\,d^6-792\,a^7\,b^7\,c^9\,d^5+495\,a^6\,b^8\,c^{10}\,d^4-220\,a^5\,b^9\,c^{11}\,d^3+66\,a^4\,b^{10}\,c^{12}\,d^2-12\,a^3\,b^{11}\,c^{13}\,d+a^2\,b^{12}\,c^{14}\right)}\right)\,{\left(-\frac{a^4\,d^9-36\,a^3\,b\,c\,d^8+486\,a^2\,b^2\,c^2\,d^7-2916\,a\,b^3\,c^3\,d^6+6561\,b^4\,c^4\,d^5}{4096\,a^{12}\,c^5\,d^{12}-49152\,a^{11}\,b\,c^6\,d^{11}+270336\,a^{10}\,b^2\,c^7\,d^{10}-901120\,a^9\,b^3\,c^8\,d^9+2027520\,a^8\,b^4\,c^9\,d^8-3244032\,a^7\,b^5\,c^{10}\,d^7+3784704\,a^6\,b^6\,c^{11}\,d^6-3244032\,a^5\,b^7\,c^{12}\,d^5+2027520\,a^4\,b^8\,c^{13}\,d^4-901120\,a^3\,b^9\,c^{14}\,d^3+270336\,a^2\,b^{10}\,c^{15}\,d^2-49152\,a\,b^{11}\,c^{16}\,d+4096\,b^{12}\,c^{17}}\right)}^{1/4}}\right)\,{\left(-\frac{a^4\,d^9-36\,a^3\,b\,c\,d^8+486\,a^2\,b^2\,c^2\,d^7-2916\,a\,b^3\,c^3\,d^6+6561\,b^4\,c^4\,d^5}{4096\,a^{12}\,c^5\,d^{12}-49152\,a^{11}\,b\,c^6\,d^{11}+270336\,a^{10}\,b^2\,c^7\,d^{10}-901120\,a^9\,b^3\,c^8\,d^9+2027520\,a^8\,b^4\,c^9\,d^8-3244032\,a^7\,b^5\,c^{10}\,d^7+3784704\,a^6\,b^6\,c^{11}\,d^6-3244032\,a^5\,b^7\,c^{12}\,d^5+2027520\,a^4\,b^8\,c^{13}\,d^4-901120\,a^3\,b^9\,c^{14}\,d^3+270336\,a^2\,b^{10}\,c^{15}\,d^2-49152\,a\,b^{11}\,c^{16}\,d+4096\,b^{12}\,c^{17}}\right)}^{1/4}\,2{}\mathrm{i}+2\,\mathrm{atan}\left(\frac{\left(\left(-\frac{\sqrt{x}\,{\left(-\frac{a^4\,d^9-36\,a^3\,b\,c\,d^8+486\,a^2\,b^2\,c^2\,d^7-2916\,a\,b^3\,c^3\,d^6+6561\,b^4\,c^4\,d^5}{4096\,a^{12}\,c^5\,d^{12}-49152\,a^{11}\,b\,c^6\,d^{11}+270336\,a^{10}\,b^2\,c^7\,d^{10}-901120\,a^9\,b^3\,c^8\,d^9+2027520\,a^8\,b^4\,c^9\,d^8-3244032\,a^7\,b^5\,c^{10}\,d^7+3784704\,a^6\,b^6\,c^{11}\,d^6-3244032\,a^5\,b^7\,c^{12}\,d^5+2027520\,a^4\,b^8\,c^{13}\,d^4-901120\,a^3\,b^9\,c^{14}\,d^3+270336\,a^2\,b^{10}\,c^{15}\,d^2-49152\,a\,b^{11}\,c^{16}\,d+4096\,b^{12}\,c^{17}}\right)}^{1/4}\,\left(4096\,a^{19}\,b^4\,c\,d^{22}-122880\,a^{18}\,b^5\,c^2\,d^{21}+1486848\,a^{17}\,b^6\,c^3\,d^{20}-9748480\,a^{16}\,b^7\,c^4\,d^{19}+40476672\,a^{15}\,b^8\,c^5\,d^{18}-116785152\,a^{14}\,b^9\,c^6\,d^{17}+249192448\,a^{13}\,b^{10}\,c^7\,d^{16}-412041216\,a^{12}\,b^{11}\,c^8\,d^{15}+547700736\,a^{11}\,b^{12}\,c^9\,d^{14}-600326144\,a^{10}\,b^{13}\,c^{10}\,d^{13}+547700736\,a^9\,b^{14}\,c^{11}\,d^{12}-412041216\,a^8\,b^{15}\,c^{12}\,d^{11}+249192448\,a^7\,b^{16}\,c^{13}\,d^{10}-116785152\,a^6\,b^{17}\,c^{14}\,d^9+40476672\,a^5\,b^{18}\,c^{15}\,d^8-9748480\,a^4\,b^{19}\,c^{16}\,d^7+1486848\,a^3\,b^{20}\,c^{17}\,d^6-122880\,a^2\,b^{21}\,c^{18}\,d^5+4096\,a\,b^{22}\,c^{19}\,d^4\right)}{16\,\left(a^{14}\,c^2\,d^{12}-12\,a^{13}\,b\,c^3\,d^{11}+66\,a^{12}\,b^2\,c^4\,d^{10}-220\,a^{11}\,b^3\,c^5\,d^9+495\,a^{10}\,b^4\,c^6\,d^8-792\,a^9\,b^5\,c^7\,d^7+924\,a^8\,b^6\,c^8\,d^6-792\,a^7\,b^7\,c^9\,d^5+495\,a^6\,b^8\,c^{10}\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c^2\,d^7-2916\,a\,b^3\,c^3\,d^6+6561\,b^4\,c^4\,d^5}{4096\,a^{12}\,c^5\,d^{12}-49152\,a^{11}\,b\,c^6\,d^{11}+270336\,a^{10}\,b^2\,c^7\,d^{10}-901120\,a^9\,b^3\,c^8\,d^9+2027520\,a^8\,b^4\,c^9\,d^8-3244032\,a^7\,b^5\,c^{10}\,d^7+3784704\,a^6\,b^6\,c^{11}\,d^6-3244032\,a^5\,b^7\,c^{12}\,d^5+2027520\,a^4\,b^8\,c^{13}\,d^4-901120\,a^3\,b^9\,c^{14}\,d^3+270336\,a^2\,b^{10}\,c^{15}\,d^2-49152\,a\,b^{11}\,c^{16}\,d+4096\,b^{12}\,c^{17}}\right)}^{3/4}\,1{}\mathrm{i}+\frac{\sqrt{x}\,\left(81\,a^7\,b^8\,d^{15}+3627\,a^6\,b^9\,c\,d^{14}-80999\,a^5\,b^{10}\,c^2\,d^{13}+339435\,a^4\,b^{11}\,c^3\,d^{12}+339435\,a^3\,b^{12}\,c^4\,d^{11}-80999\,a^2\,b^{13}\,c^5\,d^{10}+3627\,a\,b^{14}\,c^6\,d^9+81\,b^{15}\,c^7\,d^8\right)\,1{}\mathrm{i}}{16\,\left(a^{14}\,c^2\,d^{12}-12\,a^{13}\,b\,c^3\,d^{11}+66\,a^{12}\,b^2\,c^4\,d^{10}-220\,a^{11}\,b^3\,c^5\,d^9+495\,a^{10}\,b^4\,c^6\,d^8-792\,a^9\,b^5\,c^7\,d^7+924\,a^8\,b^6\,c^8\,d^6-792\,a^7\,b^7\,c^9\,d^5+495\,a^6\,b^8\,c^{10}\,d^4-220\,a^5\,b^9\,c^{11}\,d^3+66\,a^4\,b^{10}\,c^{12}\,d^2-12\,a^3\,b^{11}\,c^{13}\,d+a^2\,b^{12}\,c^{14}\right)}\right)\,{\left(-\frac{a^4\,d^9-36\,a^3\,b\,c\,d^8+486\,a^2\,b^2\,c^2\,d^7-2916\,a\,b^3\,c^3\,d^6+6561\,b^4\,c^4\,d^5}{4096\,a^{12}\,c^5\,d^{12}-49152\,a^{11}\,b\,c^6\,d^{11}+270336\,a^{10}\,b^2\,c^7\,d^{10}-901120\,a^9\,b^3\,c^8\,d^9+2027520\,a^8\,b^4\,c^9\,d^8-3244032\,a^7\,b^5\,c^{10}\,d^7+3784704\,a^6\,b^6\,c^{11}\,d^6-3244032\,a^5\,b^7\,c^{12}\,d^5+2027520\,a^4\,b^8\,c^{13}\,d^4-901120\,a^3\,b^9\,c^{14}\,d^3+270336\,a^2\,b^{10}\,c^{15}\,d^2-49152\,a\,b^{11}\,c^{16}\,d+4096\,b^{12}\,c^{17}}\right)}^{1/4}}\right)\,{\left(-\frac{a^4\,d^9-36\,a^3\,b\,c\,d^8+486\,a^2\,b^2\,c^2\,d^7-2916\,a\,b^3\,c^3\,d^6+6561\,b^4\,c^4\,d^5}{4096\,a^{12}\,c^5\,d^{12}-49152\,a^{11}\,b\,c^6\,d^{11}+270336\,a^{10}\,b^2\,c^7\,d^{10}-901120\,a^9\,b^3\,c^8\,d^9+2027520\,a^8\,b^4\,c^9\,d^8-3244032\,a^7\,b^5\,c^{10}\,d^7+3784704\,a^6\,b^6\,c^{11}\,d^6-3244032\,a^5\,b^7\,c^{12}\,d^5+2027520\,a^4\,b^8\,c^{13}\,d^4-901120\,a^3\,b^9\,c^{14}\,d^3+270336\,a^2\,b^{10}\,c^{15}\,d^2-49152\,a\,b^{11}\,c^{16}\,d+4096\,b^{12}\,c^{17}}\right)}^{1/4}+\frac{\frac{x^{3/2}\,\left(a^2\,d^2+b^2\,c^2\right)}{2\,a\,c\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}+\frac{b\,d\,x^{7/2}\,\left(a\,d+b\,c\right)}{2\,a\,c\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}}{b\,d\,x^4+\left(a\,d+b\,c\right)\,x^2+a\,c}-\mathrm{atan}\left(\frac{\left(\left(\frac{32\,a^{19}\,b^4\,d^{23}-1216\,a^{18}\,b^5\,c\,d^{22}+19040\,a^{17}\,b^6\,c^2\,d^{21}-161664\,a^{16}\,b^7\,c^3\,d^{20}+837408\,a^{15}\,b^8\,c^4\,d^{19}-2842656\,a^{14}\,b^9\,c^5\,d^{18}+6564768\,a^{13}\,b^{10}\,c^6\,d^{17}-10331040\,a^{12}\,b^{11}\,c^7\,d^{16}+10374112\,a^{11}\,b^{12}\,c^8\,d^{15}-4458784\,a^{10}\,b^{13}\,c^9\,d^{14}-4458784\,a^9\,b^{14}\,c^{10}\,d^{13}+10374112\,a^8\,b^{15}\,c^{11}\,d^{12}-10331040\,a^7\,b^{16}\,c^{12}\,d^{11}+6564768\,a^6\,b^{17}\,c^{13}\,d^{10}-2842656\,a^5\,b^{18}\,c^{14}\,d^9+837408\,a^4\,b^{19}\,c^{15}\,d^8-161664\,a^3\,b^{20}\,c^{16}\,d^7+19040\,a^2\,b^{21}\,c^{17}\,d^6-1216\,a\,b^{22}\,c^{18}\,d^5+32\,b^{23}\,c^{19}\,d^4}{a^{16}\,c^2\,d^{14}-14\,a^{15}\,b\,c^3\,d^{13}+91\,a^{14}\,b^2\,c^4\,d^{12}-364\,a^{13}\,b^3\,c^5\,d^{11}+1001\,a^{12}\,b^4\,c^6\,d^{10}-2002\,a^{11}\,b^5\,c^7\,d^9+3003\,a^{10}\,b^6\,c^8\,d^8-3432\,a^9\,b^7\,c^9\,d^7+3003\,a^8\,b^8\,c^{10}\,d^6-2002\,a^7\,b^9\,c^{11}\,d^5+1001\,a^6\,b^{10}\,c^{12}\,d^4-364\,a^5\,b^{11}\,c^{13}\,d^3+91\,a^4\,b^{12}\,c^{14}\,d^2-14\,a^3\,b^{13}\,c^{15}\,d+a^2\,b^{14}\,c^{16}}-\frac{\sqrt{x}\,{\left(-\frac{6561\,a^4\,b^5\,d^4-2916\,a^3\,b^6\,c\,d^3+486\,a^2\,b^7\,c^2\,d^2-36\,a\,b^8\,c^3\,d+b^9\,c^4}{4096\,a^{17}\,d^{12}-49152\,a^{16}\,b\,c\,d^{11}+270336\,a^{15}\,b^2\,c^2\,d^{10}-901120\,a^{14}\,b^3\,c^3\,d^9+2027520\,a^{13}\,b^4\,c^4\,d^8-3244032\,a^{12}\,b^5\,c^5\,d^7+3784704\,a^{11}\,b^6\,c^6\,d^6-3244032\,a^{10}\,b^7\,c^7\,d^5+2027520\,a^9\,b^8\,c^8\,d^4-901120\,a^8\,b^9\,c^9\,d^3+270336\,a^7\,b^{10}\,c^{10}\,d^2-49152\,a^6\,b^{11}\,c^{11}\,d+4096\,a^5\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(4096\,a^{19}\,b^4\,c\,d^{22}-122880\,a^{18}\,b^5\,c^2\,d^{21}+1486848\,a^{17}\,b^6\,c^3\,d^{20}-9748480\,a^{16}\,b^7\,c^4\,d^{19}+40476672\,a^{15}\,b^8\,c^5\,d^{18}-116785152\,a^{14}\,b^9\,c^6\,d^{17}+249192448\,a^{13}\,b^{10}\,c^7\,d^{16}-412041216\,a^{12}\,b^{11}\,c^8\,d^{15}+547700736\,a^{11}\,b^{12}\,c^9\,d^{14}-600326144\,a^{10}\,b^{13}\,c^{10}\,d^{13}+547700736\,a^9\,b^{14}\,c^{11}\,d^{12}-412041216\,a^8\,b^{15}\,c^{12}\,d^{11}+249192448\,a^7\,b^{16}\,c^{13}\,d^{10}-116785152\,a^6\,b^{17}\,c^{14}\,d^9+40476672\,a^5\,b^{18}\,c^{15}\,d^8-9748480\,a^4\,b^{19}\,c^{16}\,d^7+1486848\,a^3\,b^{20}\,c^{17}\,d^6-122880\,a^2\,b^{21}\,c^{18}\,d^5+4096\,a\,b^{22}\,c^{19}\,d^4\right)}{16\,\left(a^{14}\,c^2\,d^{12}-12\,a^{13}\,b\,c^3\,d^{11}+66\,a^{12}\,b^2\,c^4\,d^{10}-220\,a^{11}\,b^3\,c^5\,d^9+495\,a^{10}\,b^4\,c^6\,d^8-792\,a^9\,b^5\,c^7\,d^7+924\,a^8\,b^6\,c^8\,d^6-792\,a^7\,b^7\,c^9\,d^5+495\,a^6\,b^8\,c^{10}\,d^4-220\,a^5\,b^9\,c^{11}\,d^3+66\,a^4\,b^{10}\,c^{12}\,d^2-12\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10}\,c^2\,d^{13}+339435\,a^4\,b^{11}\,c^3\,d^{12}+339435\,a^3\,b^{12}\,c^4\,d^{11}-80999\,a^2\,b^{13}\,c^5\,d^{10}+3627\,a\,b^{14}\,c^6\,d^9+81\,b^{15}\,c^7\,d^8\right)}{16\,\left(a^{14}\,c^2\,d^{12}-12\,a^{13}\,b\,c^3\,d^{11}+66\,a^{12}\,b^2\,c^4\,d^{10}-220\,a^{11}\,b^3\,c^5\,d^9+495\,a^{10}\,b^4\,c^6\,d^8-792\,a^9\,b^5\,c^7\,d^7+924\,a^8\,b^6\,c^8\,d^6-792\,a^7\,b^7\,c^9\,d^5+495\,a^6\,b^8\,c^{10}\,d^4-220\,a^5\,b^9\,c^{11}\,d^3+66\,a^4\,b^{10}\,c^{12}\,d^2-12\,a^3\,b^{11}\,c^{13}\,d+a^2\,b^{12}\,c^{14}\right)}\right)\,{\left(-\frac{6561\,a^4\,b^5\,d^4-2916\,a^3\,b^6\,c\,d^3+486\,a^2\,b^7\,c^2\,d^2-36\,a\,b^8\,c^3\,d+b^9\,c^4}{4096\,a^{17}\,d^{12}-49152\,a^{16}\,b\,c\,d^{11}+270336\,a^{15}\,b^2\,c^2\,d^{10}-901120\,a^{14}\,b^3\,c^3\,d^9+2027520\,a^{13}\,b^4\,c^4\,d^8-3244032\,a^{12}\,b^5\,c^5\,d^7+3784704\,a^{11}\,b^6\,c^6\,d^6-3244032\,a^{10}\,b^7\,c^7\,d^5+2027520\,a^9\,b^8\,c^8\,d^4-901120\,a^8\,b^9\,c^9\,d^3+270336\,a^7\,b^{10}\,c^{10}\,d^2-49152\,a^6\,b^{11}\,c^{11}\,d+4096\,a^5\,b^{12}\,c^{12}}\right)}^{1/4}+\left(\left(\frac{32\,a^{19}\,b^4\,d^{23}-1216\,a^{18}\,b^5\,c\,d^{22}+19040\,a^{17}\,b^6\,c^2\,d^{21}-161664\,a^{16}\,b^7\,c^3\,d^{20}+837408\,a^{15}\,b^8\,c^4\,d^{19}-2842656\,a^{14}\,b^9\,c^5\,d^{18}+6564768\,a^{13}\,b^{10}\,c^6\,d^{17}-10331040\,a^{12}\,b^{11}\,c^7\,d^{16}+10374112\,a^{11}\,b^{12}\,c^8\,d^{15}-4458784\,a^{10}\,b^{13}\,c^9\,d^{14}-4458784\,a^9\,b^{14}\,c^{10}\,d^{13}+10374112\,a^8\,b^{15}\,c^{11}\,d^{12}-10331040\,a^7\,b^{16}\,c^{12}\,d^{11}+6564768\,a^6\,b^{17}\,c^{13}\,d^{10}-2842656\,a^5\,b^{18}\,c^{14}\,d^9+837408\,a^4\,b^{19}\,c^{15}\,d^8-161664\,a^3\,b^{20}\,c^{16}\,d^7+19040\,a^2\,b^{21}\,c^{17}\,d^6-1216\,a\,b^{22}\,c^{18}\,d^5+32\,b^{23}\,c^{19}\,d^4}{a^{16}\,c^2\,d^{14}-14\,a^{15}\,b\,c^3\,d^{13}+91\,a^{14}\,b^2\,c^4\,d^{12}-364\,a^{13}\,b^3\,c^5\,d^{11}+1001\,a^{12}\,b^4\,c^6\,d^{10}-2002\,a^{11}\,b^5\,c^7\,d^9+3003\,a^{10}\,b^6\,c^8\,d^8-3432\,a^9\,b^7\,c^9\,d^7+3003\,a^8\,b^8\,c^{10}\,d^6-2002\,a^7\,b^9\,c^{11}\,d^5+1001\,a^6\,b^{10}\,c^{12}\,d^4-364\,a^5\,b^{11}\,c^{13}\,d^3+91\,a^4\,b^{12}\,c^{14}\,d^2-14\,a^3\,b^{13}\,c^{15}\,d+a^2\,b^{14}\,c^{16}}+\frac{\sqrt{x}\,{\left(-\frac{6561\,a^4\,b^5\,d^4-2916\,a^3\,b^6\,c\,d^3+486\,a^2\,b^7\,c^2\,d^2-36\,a\,b^8\,c^3\,d+b^9\,c^4}{4096\,a^{17}\,d^{12}-49152\,a^{16}\,b\,c\,d^{11}+270336\,a^{15}\,b^2\,c^2\,d^{10}-901120\,a^{14}\,b^3\,c^3\,d^9+2027520\,a^{13}\,b^4\,c^4\,d^8-3244032\,a^{12}\,b^5\,c^5\,d^7+3784704\,a^{11}\,b^6\,c^6\,d^6-3244032\,a^{10}\,b^7\,c^7\,d^5+2027520\,a^9\,b^8\,c^8\,d^4-901120\,a^8\,b^9\,c^9\,d^3+270336\,a^7\,b^{10}\,c^{10}\,d^2-49152\,a^6\,b^{11}\,c^{11}\,d+4096\,a^5\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(4096\,a^{19}\,b^4\,c\,d^{22}-122880\,a^{18}\,b^5\,c^2\,d^{21}+1486848\,a^{17}\,b^6\,c^3\,d^{20}-9748480\,a^{16}\,b^7\,c^4\,d^{19}+40476672\,a^{15}\,b^8\,c^5\,d^{18}-116785152\,a^{14}\,b^9\,c^6\,d^{17}+249192448\,a^{13}\,b^{10}\,c^7\,d^{16}-412041216\,a^{12}\,b^{11}\,c^8\,d^{15}+547700736\,a^{11}\,b^{12}\,c^9\,d^{14}-600326144\,a^{10}\,b^{13}\,c^{10}\,d^{13}+547700736\,a^9\,b^{14}\,c^{11}\,d^{12}-412041216\,a^8\,b^{15}\,c^{12}\,d^{11}+249192448\,a^7\,b^{16}\,c^{13}\,d^{10}-116785152\,a^6\,b^{17}\,c^{14}\,d^9+40476672\,a^5\,b^{18}\,c^{15}\,d^8-9748480\,a^4\,b^{19}\,c^{16}\,d^7+1486848\,a^3\,b^{20}\,c^{17}\,d^6-122880\,a^2\,b^{21}\,c^{18}\,d^5+4096\,a\,b^{22}\,c^{19}\,d^4\right)}{16\,\left(a^{14}\,c^2\,d^{12}-12\,a^{13}\,b\,c^3\,d^{11}+66\,a^{12}\,b^2\,c^4\,d^{10}-220\,a^{11}\,b^3\,c^5\,d^9+495\,a^{10}\,b^4\,c^6\,d^8-792\,a^9\,b^5\,c^7\,d^7+924\,a^8\,b^6\,c^8\,d^6-792\,a^7\,b^7\,c^9\,d^5+495\,a^6\,b^8\,c^{10}\,d^4-220\,a^5\,b^9\,c^{11}\,d^3+66\,a^4\,b^{10}\,c^{12}\,d^2-12\,a^3\,b^{11}\,c^{13}\,d+a^2\,b^{12}\,c^{14}\right)}\right)\,{\left(-\frac{6561\,a^4\,b^5\,d^4-2916\,a^3\,b^6\,c\,d^3+486\,a^2\,b^7\,c^2\,d^2-36\,a\,b^8\,c^3\,d+b^9\,c^4}{4096\,a^{17}\,d^{12}-49152\,a^{16}\,b\,c\,d^{11}+270336\,a^{15}\,b^2\,c^2\,d^{10}-901120\,a^{14}\,b^3\,c^3\,d^9+2027520\,a^{13}\,b^4\,c^4\,d^8-3244032\,a^{12}\,b^5\,c^5\,d^7+3784704\,a^{11}\,b^6\,c^6\,d^6-3244032\,a^{10}\,b^7\,c^7\,d^5+2027520\,a^9\,b^8\,c^8\,d^4-901120\,a^8\,b^9\,c^9\,d^3+270336\,a^7\,b^{10}\,c^{10}\,d^2-49152\,a^6\,b^{11}\,c^{11}\,d+4096\,a^5\,b^{12}\,c^{12}}\right)}^{3/4}+\frac{\sqrt{x}\,\left(81\,a^7\,b^8\,d^{15}+3627\,a^6\,b^9\,c\,d^{14}-80999\,a^5\,b^{10}\,c^2\,d^{13}+339435\,a^4\,b^{11}\,c^3\,d^{12}+339435\,a^3\,b^{12}\,c^4\,d^{11}-80999\,a^2\,b^{13}\,c^5\,d^{10}+3627\,a\,b^{14}\,c^6\,d^9+81\,b^{15}\,c^7\,d^8\right)}{16\,\left(a^{14}\,c^2\,d^{12}-12\,a^{13}\,b\,c^3\,d^{11}+66\,a^{12}\,b^2\,c^4\,d^{10}-220\,a^{11}\,b^3\,c^5\,d^9+495\,a^{10}\,b^4\,c^6\,d^8-792\,a^9\,b^5\,c^7\,d^7+924\,a^8\,b^6\,c^8\,d^6-792\,a^7\,b^7\,c^9\,d^5+495\,a^6\,b^8\,c^{10}\,d^4-220\,a^5\,b^9\,c^{11}\,d^3+66\,a^4\,b^{10}\,c^{12}\,d^2-12\,a^3\,b^{11}\,c^{13}\,d+a^2\,b^{12}\,c^{14}\right)}\right)\,{\left(-\frac{6561\,a^4\,b^5\,d^4-2916\,a^3\,b^6\,c\,d^3+486\,a^2\,b^7\,c^2\,d^2-36\,a\,b^8\,c^3\,d+b^9\,c^4}{4096\,a^{17}\,d^{12}-49152\,a^{16}\,b\,c\,d^{11}+270336\,a^{15}\,b^2\,c^2\,d^{10}-901120\,a^{14}\,b^3\,c^3\,d^9+2027520\,a^{13}\,b^4\,c^4\,d^8-3244032\,a^{12}\,b^5\,c^5\,d^7+3784704\,a^{11}\,b^6\,c^6\,d^6-3244032\,a^{10}\,b^7\,c^7\,d^5+2027520\,a^9\,b^8\,c^8\,d^4-901120\,a^8\,b^9\,c^9\,d^3+270336\,a^7\,b^{10}\,c^{10}\,d^2-49152\,a^6\,b^{11}\,c^{11}\,d+4096\,a^5\,b^{12}\,c^{12}}\right)}^{1/4}}\right)\,{\left(-\frac{6561\,a^4\,b^5\,d^4-2916\,a^3\,b^6\,c\,d^3+486\,a^2\,b^7\,c^2\,d^2-36\,a\,b^8\,c^3\,d+b^9\,c^4}{4096\,a^{17}\,d^{12}-49152\,a^{16}\,b\,c\,d^{11}+270336\,a^{15}\,b^2\,c^2\,d^{10}-901120\,a^{14}\,b^3\,c^3\,d^9+2027520\,a^{13}\,b^4\,c^4\,d^8-3244032\,a^{12}\,b^5\,c^5\,d^7+3784704\,a^{11}\,b^6\,c^6\,d^6-3244032\,a^{10}\,b^7\,c^7\,d^5+2027520\,a^9\,b^8\,c^8\,d^4-901120\,a^8\,b^9\,c^9\,d^3+270336\,a^7\,b^{10}\,c^{10}\,d^2-49152\,a^6\,b^{11}\,c^{11}\,d+4096\,a^5\,b^{12}\,c^{12}}\right)}^{1/4}\,2{}\mathrm{i}+2\,\mathrm{atan}\left(\frac{\left(\left(-\frac{\sqrt{x}\,{\left(-\frac{6561\,a^4\,b^5\,d^4-2916\,a^3\,b^6\,c\,d^3+486\,a^2\,b^7\,c^2\,d^2-36\,a\,b^8\,c^3\,d+b^9\,c^4}{4096\,a^{17}\,d^{12}-49152\,a^{16}\,b\,c\,d^{11}+270336\,a^{15}\,b^2\,c^2\,d^{10}-901120\,a^{14}\,b^3\,c^3\,d^9+2027520\,a^{13}\,b^4\,c^4\,d^8-3244032\,a^{12}\,b^5\,c^5\,d^7+3784704\,a^{11}\,b^6\,c^6\,d^6-3244032\,a^{10}\,b^7\,c^7\,d^5+2027520\,a^9\,b^8\,c^8\,d^4-901120\,a^8\,b^9\,c^9\,d^3+270336\,a^7\,b^{10}\,c^{10}\,d^2-49152\,a^6\,b^{11}\,c^{11}\,d+4096\,a^5\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(4096\,a^{19}\,b^4\,c\,d^{22}-122880\,a^{18}\,b^5\,c^2\,d^{21}+1486848\,a^{17}\,b^6\,c^3\,d^{20}-9748480\,a^{16}\,b^7\,c^4\,d^{19}+40476672\,a^{15}\,b^8\,c^5\,d^{18}-116785152\,a^{14}\,b^9\,c^6\,d^{17}+249192448\,a^{13}\,b^{10}\,c^7\,d^{16}-412041216\,a^{12}\,b^{11}\,c^8\,d^{15}+547700736\,a^{11}\,b^{12}\,c^9\,d^{14}-600326144\,a^{10}\,b^{13}\,c^{10}\,d^{13}+547700736\,a^9\,b^{14}\,c^{11}\,d^{12}-412041216\,a^8\,b^{15}\,c^{12}\,d^{11}+249192448\,a^7\,b^{16}\,c^{13}\,d^{10}-116785152\,a^6\,b^{17}\,c^{14}\,d^9+40476672\,a^5\,b^{18}\,c^{15}\,d^8-9748480\,a^4\,b^{19}\,c^{16}\,d^7+1486848\,a^3\,b^{20}\,c^{17}\,d^6-122880\,a^2\,b^{21}\,c^{18}\,d^5+4096\,a\,b^{22}\,c^{19}\,d^4\right)}{16\,\left(a^{14}\,c^2\,d^{12}-12\,a^{13}\,b\,c^3\,d^{11}+66\,a^{12}\,b^2\,c^4\,d^{10}-220\,a^{11}\,b^3\,c^5\,d^9+495\,a^{10}\,b^4\,c^6\,d^8-792\,a^9\,b^5\,c^7\,d^7+924\,a^8\,b^6\,c^8\,d^6-792\,a^7\,b^7\,c^9\,d^5+495\,a^6\,b^8\,c^{10}\,d^4-220\,a^5\,b^9\,c^{11}\,d^3+66\,a^4\,b^{10}\,c^{12}\,d^2-12\,a^3\,b^{11}\,c^{13}\,d+a^2\,b^{12}\,c^{14}\right)}+\frac{\left(32\,a^{19}\,b^4\,d^{23}-1216\,a^{18}\,b^5\,c\,d^{22}+19040\,a^{17}\,b^6\,c^2\,d^{21}-161664\,a^{16}\,b^7\,c^3\,d^{20}+837408\,a^{15}\,b^8\,c^4\,d^{19}-2842656\,a^{14}\,b^9\,c^5\,d^{18}+6564768\,a^{13}\,b^{10}\,c^6\,d^{17}-10331040\,a^{12}\,b^{11}\,c^7\,d^{16}+10374112\,a^{11}\,b^{12}\,c^8\,d^{15}-4458784\,a^{10}\,b^{13}\,c^9\,d^{14}-4458784\,a^9\,b^{14}\,c^{10}\,d^{13}+10374112\,a^8\,b^{15}\,c^{11}\,d^{12}-10331040\,a^7\,b^{16}\,c^{12}\,d^{11}+6564768\,a^6\,b^{17}\,c^{13}\,d^{10}-2842656\,a^5\,b^{18}\,c^{14}\,d^9+837408\,a^4\,b^{19}\,c^{15}\,d^8-161664\,a^3\,b^{20}\,c^{16}\,d^7+19040\,a^2\,b^{21}\,c^{17}\,d^6-1216\,a\,b^{22}\,c^{18}\,d^5+32\,b^{23}\,c^{19}\,d^4\right)\,1{}\mathrm{i}}{a^{16}\,c^2\,d^{14}-14\,a^{15}\,b\,c^3\,d^{13}+91\,a^{14}\,b^2\,c^4\,d^{12}-364\,a^{13}\,b^3\,c^5\,d^{11}+1001\,a^{12}\,b^4\,c^6\,d^{10}-2002\,a^{11}\,b^5\,c^7\,d^9+3003\,a^{10}\,b^6\,c^8\,d^8-3432\,a^9\,b^7\,c^9\,d^7+3003\,a^8\,b^8\,c^{10}\,d^6-2002\,a^7\,b^9\,c^{11}\,d^5+1001\,a^6\,b^{10}\,c^{12}\,d^4-364\,a^5\,b^{11}\,c^{13}\,d^3+91\,a^4\,b^{12}\,c^{14}\,d^2-14\,a^3\,b^{13}\,c^{15}\,d+a^2\,b^{14}\,c^{16}}\right)\,{\left(-\frac{6561\,a^4\,b^5\,d^4-2916\,a^3\,b^6\,c\,d^3+486\,a^2\,b^7\,c^2\,d^2-36\,a\,b^8\,c^3\,d+b^9\,c^4}{4096\,a^{17}\,d^{12}-49152\,a^{16}\,b\,c\,d^{11}+270336\,a^{15}\,b^2\,c^2\,d^{10}-901120\,a^{14}\,b^3\,c^3\,d^9+2027520\,a^{13}\,b^4\,c^4\,d^8-3244032\,a^{12}\,b^5\,c^5\,d^7+3784704\,a^{11}\,b^6\,c^6\,d^6-3244032\,a^{10}\,b^7\,c^7\,d^5+2027520\,a^9\,b^8\,c^8\,d^4-901120\,a^8\,b^9\,c^9\,d^3+270336\,a^7\,b^{10}\,c^{10}\,d^2-49152\,a^6\,b^{11}\,c^{11}\,d+4096\,a^5\,b^{12}\,c^{12}}\right)}^{3/4}-\frac{\sqrt{x}\,\left(81\,a^7\,b^8\,d^{15}+3627\,a^6\,b^9\,c\,d^{14}-80999\,a^5\,b^{10}\,c^2\,d^{13}+339435\,a^4\,b^{11}\,c^3\,d^{12}+339435\,a^3\,b^{12}\,c^4\,d^{11}-80999\,a^2\,b^{13}\,c^5\,d^{10}+3627\,a\,b^{14}\,c^6\,d^9+81\,b^{15}\,c^7\,d^8\right)}{16\,\left(a^{14}\,c^2\,d^{12}-12\,a^{13}\,b\,c^3\,d^{11}+66\,a^{12}\,b^2\,c^4\,d^{10}-220\,a^{11}\,b^3\,c^5\,d^9+495\,a^{10}\,b^4\,c^6\,d^8-792\,a^9\,b^5\,c^7\,d^7+924\,a^8\,b^6\,c^8\,d^6-792\,a^7\,b^7\,c^9\,d^5+495\,a^6\,b^8\,c^{10}\,d^4-220\,a^5\,b^9\,c^{11}\,d^3+66\,a^4\,b^{10}\,c^{12}\,d^2-12\,a^3\,b^{11}\,c^{13}\,d+a^2\,b^{12}\,c^{14}\right)}\right)\,{\left(-\frac{6561\,a^4\,b^5\,d^4-2916\,a^3\,b^6\,c\,d^3+486\,a^2\,b^7\,c^2\,d^2-36\,a\,b^8\,c^3\,d+b^9\,c^4}{4096\,a^{17}\,d^{12}-49152\,a^{16}\,b\,c\,d^{11}+270336\,a^{15}\,b^2\,c^2\,d^{10}-901120\,a^{14}\,b^3\,c^3\,d^9+2027520\,a^{13}\,b^4\,c^4\,d^8-3244032\,a^{12}\,b^5\,c^5\,d^7+3784704\,a^{11}\,b^6\,c^6\,d^6-3244032\,a^{10}\,b^7\,c^7\,d^5+2027520\,a^9\,b^8\,c^8\,d^4-901120\,a^8\,b^9\,c^9\,d^3+270336\,a^7\,b^{10}\,c^{10}\,d^2-49152\,a^6\,b^{11}\,c^{11}\,d+4096\,a^5\,b^{12}\,c^{12}}\right)}^{1/4}-\left(\left(\frac{\sqrt{x}\,{\left(-\frac{6561\,a^4\,b^5\,d^4-2916\,a^3\,b^6\,c\,d^3+486\,a^2\,b^7\,c^2\,d^2-36\,a\,b^8\,c^3\,d+b^9\,c^4}{4096\,a^{17}\,d^{12}-49152\,a^{16}\,b\,c\,d^{11}+270336\,a^{15}\,b^2\,c^2\,d^{10}-901120\,a^{14}\,b^3\,c^3\,d^9+2027520\,a^{13}\,b^4\,c^4\,d^8-3244032\,a^{12}\,b^5\,c^5\,d^7+3784704\,a^{11}\,b^6\,c^6\,d^6-3244032\,a^{10}\,b^7\,c^7\,d^5+2027520\,a^9\,b^8\,c^8\,d^4-901120\,a^8\,b^9\,c^9\,d^3+270336\,a^7\,b^{10}\,c^{10}\,d^2-49152\,a^6\,b^{11}\,c^{11}\,d+4096\,a^5\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(4096\,a^{19}\,b^4\,c\,d^{22}-122880\,a^{18}\,b^5\,c^2\,d^{21}+1486848\,a^{17}\,b^6\,c^3\,d^{20}-9748480\,a^{16}\,b^7\,c^4\,d^{19}+40476672\,a^{15}\,b^8\,c^5\,d^{18}-116785152\,a^{14}\,b^9\,c^6\,d^{17}+249192448\,a^{13}\,b^{10}\,c^7\,d^{16}-412041216\,a^{12}\,b^{11}\,c^8\,d^{15}+547700736\,a^{11}\,b^{12}\,c^9\,d^{14}-600326144\,a^{10}\,b^{13}\,c^{10}\,d^{13}+547700736\,a^9\,b^{14}\,c^{11}\,d^{12}-412041216\,a^8\,b^{15}\,c^{12}\,d^{11}+249192448\,a^7\,b^{16}\,c^{13}\,d^{10}-116785152\,a^6\,b^{17}\,c^{14}\,d^9+40476672\,a^5\,b^{18}\,c^{15}\,d^8-9748480\,a^4\,b^{19}\,c^{16}\,d^7+1486848\,a^3\,b^{20}\,c^{17}\,d^6-122880\,a^2\,b^{21}\,c^{18}\,d^5+4096\,a\,b^{22}\,c^{19}\,d^4\right)}{16\,\left(a^{14}\,c^2\,d^{12}-12\,a^{13}\,b\,c^3\,d^{11}+66\,a^{12}\,b^2\,c^4\,d^{10}-220\,a^{11}\,b^3\,c^5\,d^9+495\,a^{10}\,b^4\,c^6\,d^8-792\,a^9\,b^5\,c^7\,d^7+924\,a^8\,b^6\,c^8\,d^6-792\,a^7\,b^7\,c^9\,d^5+495\,a^6\,b^8\,c^{10}\,d^4-220\,a^5\,b^9\,c^{11}\,d^3+66\,a^4\,b^{10}\,c^{12}\,d^2-12\,a^3\,b^{11}\,c^{13}\,d+a^2\,b^{12}\,c^{14}\right)}+\frac{\left(32\,a^{19}\,b^4\,d^{23}-1216\,a^{18}\,b^5\,c\,d^{22}+19040\,a^{17}\,b^6\,c^2\,d^{21}-161664\,a^{16}\,b^7\,c^3\,d^{20}+837408\,a^{15}\,b^8\,c^4\,d^{19}-2842656\,a^{14}\,b^9\,c^5\,d^{18}+6564768\,a^{13}\,b^{10}\,c^6\,d^{17}-10331040\,a^{12}\,b^{11}\,c^7\,d^{16}+10374112\,a^{11}\,b^{12}\,c^8\,d^{15}-4458784\,a^{10}\,b^{13}\,c^9\,d^{14}-4458784\,a^9\,b^{14}\,c^{10}\,d^{13}+10374112\,a^8\,b^{15}\,c^{11}\,d^{12}-10331040\,a^7\,b^{16}\,c^{12}\,d^{11}+6564768\,a^6\,b^{17}\,c^{13}\,d^{10}-2842656\,a^5\,b^{18}\,c^{14}\,d^9+837408\,a^4\,b^{19}\,c^{15}\,d^8-161664\,a^3\,b^{20}\,c^{16}\,d^7+19040\,a^2\,b^{21}\,c^{17}\,d^6-1216\,a\,b^{22}\,c^{18}\,d^5+32\,b^{23}\,c^{19}\,d^4\right)\,1{}\mathrm{i}}{a^{16}\,c^2\,d^{14}-14\,a^{15}\,b\,c^3\,d^{13}+91\,a^{14}\,b^2\,c^4\,d^{12}-364\,a^{13}\,b^3\,c^5\,d^{11}+1001\,a^{12}\,b^4\,c^6\,d^{10}-2002\,a^{11}\,b^5\,c^7\,d^9+3003\,a^{10}\,b^6\,c^8\,d^8-3432\,a^9\,b^7\,c^9\,d^7+3003\,a^8\,b^8\,c^{10}\,d^6-2002\,a^7\,b^9\,c^{11}\,d^5+1001\,a^6\,b^{10}\,c^{12}\,d^4-364\,a^5\,b^{11}\,c^{13}\,d^3+91\,a^4\,b^{12}\,c^{14}\,d^2-14\,a^3\,b^{13}\,c^{15}\,d+a^2\,b^{14}\,c^{16}}\right)\,{\left(-\frac{6561\,a^4\,b^5\,d^4-2916\,a^3\,b^6\,c\,d^3+486\,a^2\,b^7\,c^2\,d^2-36\,a\,b^8\,c^3\,d+b^9\,c^4}{4096\,a^{17}\,d^{12}-49152\,a^{16}\,b\,c\,d^{11}+270336\,a^{15}\,b^2\,c^2\,d^{10}-901120\,a^{14}\,b^3\,c^3\,d^9+2027520\,a^{13}\,b^4\,c^4\,d^8-3244032\,a^{12}\,b^5\,c^5\,d^7+3784704\,a^{11}\,b^6\,c^6\,d^6-3244032\,a^{10}\,b^7\,c^7\,d^5+2027520\,a^9\,b^8\,c^8\,d^4-901120\,a^8\,b^9\,c^9\,d^3+270336\,a^7\,b^{10}\,c^{10}\,d^2-49152\,a^6\,b^{11}\,c^{11}\,d+4096\,a^5\,b^{12}\,c^{12}}\right)}^{3/4}+\frac{\sqrt{x}\,\left(81\,a^7\,b^8\,d^{15}+3627\,a^6\,b^9\,c\,d^{14}-80999\,a^5\,b^{10}\,c^2\,d^{13}+339435\,a^4\,b^{11}\,c^3\,d^{12}+339435\,a^3\,b^{12}\,c^4\,d^{11}-80999\,a^2\,b^{13}\,c^5\,d^{10}+3627\,a\,b^{14}\,c^6\,d^9+81\,b^{15}\,c^7\,d^8\right)}{16\,\left(a^{14}\,c^2\,d^{12}-12\,a^{13}\,b\,c^3\,d^{11}+66\,a^{12}\,b^2\,c^4\,d^{10}-220\,a^{11}\,b^3\,c^5\,d^9+495\,a^{10}\,b^4\,c^6\,d^8-792\,a^9\,b^5\,c^7\,d^7+924\,a^8\,b^6\,c^8\,d^6-792\,a^7\,b^7\,c^9\,d^5+495\,a^6\,b^8\,c^{10}\,d^4-220\,a^5\,b^9\,c^{11}\,d^3+66\,a^4\,b^{10}\,c^{12}\,d^2-12\,a^3\,b^{11}\,c^{13}\,d+a^2\,b^{12}\,c^{14}\right)}\right)\,{\left(-\frac{6561\,a^4\,b^5\,d^4-2916\,a^3\,b^6\,c\,d^3+486\,a^2\,b^7\,c^2\,d^2-36\,a\,b^8\,c^3\,d+b^9\,c^4}{4096\,a^{17}\,d^{12}-49152\,a^{16}\,b\,c\,d^{11}+270336\,a^{15}\,b^2\,c^2\,d^{10}-901120\,a^{14}\,b^3\,c^3\,d^9+2027520\,a^{13}\,b^4\,c^4\,d^8-3244032\,a^{12}\,b^5\,c^5\,d^7+3784704\,a^{11}\,b^6\,c^6\,d^6-3244032\,a^{10}\,b^7\,c^7\,d^5+2027520\,a^9\,b^8\,c^8\,d^4-901120\,a^8\,b^9\,c^9\,d^3+270336\,a^7\,b^{10}\,c^{10}\,d^2-49152\,a^6\,b^{11}\,c^{11}\,d+4096\,a^5\,b^{12}\,c^{12}}\right)}^{1/4}}{-\frac{\frac{3645\,a^6\,b^9\,d^{15}}{32}-\frac{49815\,a^5\,b^{10}\,c\,d^{14}}{16}+\frac{918675\,a^4\,b^{11}\,c^2\,d^{13}}{32}-\frac{739025\,a^3\,b^{12}\,c^3\,d^{12}}{8}+\frac{918675\,a^2\,b^{13}\,c^4\,d^{11}}{32}-\frac{49815\,a\,b^{14}\,c^5\,d^{10}}{16}+\frac{3645\,b^{15}\,c^6\,d^9}{32}}{a^{16}\,c^2\,d^{14}-14\,a^{15}\,b\,c^3\,d^{13}+91\,a^{14}\,b^2\,c^4\,d^{12}-364\,a^{13}\,b^3\,c^5\,d^{11}+1001\,a^{12}\,b^4\,c^6\,d^{10}-2002\,a^{11}\,b^5\,c^7\,d^9+3003\,a^{10}\,b^6\,c^8\,d^8-3432\,a^9\,b^7\,c^9\,d^7+3003\,a^8\,b^8\,c^{10}\,d^6-2002\,a^7\,b^9\,c^{11}\,d^5+1001\,a^6\,b^{10}\,c^{12}\,d^4-364\,a^5\,b^{11}\,c^{13}\,d^3+91\,a^4\,b^{12}\,c^{14}\,d^2-14\,a^3\,b^{13}\,c^{15}\,d+a^2\,b^{14}\,c^{16}}+\left(\left(-\frac{\sqrt{x}\,{\left(-\frac{6561\,a^4\,b^5\,d^4-2916\,a^3\,b^6\,c\,d^3+486\,a^2\,b^7\,c^2\,d^2-36\,a\,b^8\,c^3\,d+b^9\,c^4}{4096\,a^{17}\,d^{12}-49152\,a^{16}\,b\,c\,d^{11}+270336\,a^{15}\,b^2\,c^2\,d^{10}-901120\,a^{14}\,b^3\,c^3\,d^9+2027520\,a^{13}\,b^4\,c^4\,d^8-3244032\,a^{12}\,b^5\,c^5\,d^7+3784704\,a^{11}\,b^6\,c^6\,d^6-3244032\,a^{10}\,b^7\,c^7\,d^5+2027520\,a^9\,b^8\,c^8\,d^4-901120\,a^8\,b^9\,c^9\,d^3+270336\,a^7\,b^{10}\,c^{10}\,d^2-49152\,a^6\,b^{11}\,c^{11}\,d+4096\,a^5\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(4096\,a^{19}\,b^4\,c\,d^{22}-122880\,a^{18}\,b^5\,c^2\,d^{21}+1486848\,a^{17}\,b^6\,c^3\,d^{20}-9748480\,a^{16}\,b^7\,c^4\,d^{19}+40476672\,a^{15}\,b^8\,c^5\,d^{18}-116785152\,a^{14}\,b^9\,c^6\,d^{17}+249192448\,a^{13}\,b^{10}\,c^7\,d^{16}-412041216\,a^{12}\,b^{11}\,c^8\,d^{15}+547700736\,a^{11}\,b^{12}\,c^9\,d^{14}-600326144\,a^{10}\,b^{13}\,c^{10}\,d^{13}+547700736\,a^9\,b^{14}\,c^{11}\,d^{12}-412041216\,a^8\,b^{15}\,c^{12}\,d^{11}+249192448\,a^7\,b^{16}\,c^{13}\,d^{10}-116785152\,a^6\,b^{17}\,c^{14}\,d^9+40476672\,a^5\,b^{18}\,c^{15}\,d^8-9748480\,a^4\,b^{19}\,c^{16}\,d^7+1486848\,a^3\,b^{20}\,c^{17}\,d^6-122880\,a^2\,b^{21}\,c^{18}\,d^5+4096\,a\,b^{22}\,c^{19}\,d^4\right)}{16\,\left(a^{14}\,c^2\,d^{12}-12\,a^{13}\,b\,c^3\,d^{11}+66\,a^{12}\,b^2\,c^4\,d^{10}-220\,a^{11}\,b^3\,c^5\,d^9+495\,a^{10}\,b^4\,c^6\,d^8-792\,a^9\,b^5\,c^7\,d^7+924\,a^8\,b^6\,c^8\,d^6-792\,a^7\,b^7\,c^9\,d^5+495\,a^6\,b^8\,c^{10}\,d^4-220\,a^5\,b^9\,c^{11}\,d^3+66\,a^4\,b^{10}\,c^{12}\,d^2-12\,a^3\,b^{11}\,c^{13}\,d+a^2\,b^{12}\,c^{14}\right)}+\frac{\left(32\,a^{19}\,b^4\,d^{23}-1216\,a^{18}\,b^5\,c\,d^{22}+19040\,a^{17}\,b^6\,c^2\,d^{21}-161664\,a^{16}\,b^7\,c^3\,d^{20}+837408\,a^{15}\,b^8\,c^4\,d^{19}-2842656\,a^{14}\,b^9\,c^5\,d^{18}+6564768\,a^{13}\,b^{10}\,c^6\,d^{17}-10331040\,a^{12}\,b^{11}\,c^7\,d^{16}+10374112\,a^{11}\,b^{12}\,c^8\,d^{15}-4458784\,a^{10}\,b^{13}\,c^9\,d^{14}-4458784\,a^9\,b^{14}\,c^{10}\,d^{13}+10374112\,a^8\,b^{15}\,c^{11}\,d^{12}-10331040\,a^7\,b^{16}\,c^{12}\,d^{11}+6564768\,a^6\,b^{17}\,c^{13}\,d^{10}-2842656\,a^5\,b^{18}\,c^{14}\,d^9+837408\,a^4\,b^{19}\,c^{15}\,d^8-161664\,a^3\,b^{20}\,c^{16}\,d^7+19040\,a^2\,b^{21}\,c^{17}\,d^6-1216\,a\,b^{22}\,c^{18}\,d^5+32\,b^{23}\,c^{19}\,d^4\right)\,1{}\mathrm{i}}{a^{16}\,c^2\,d^{14}-14\,a^{15}\,b\,c^3\,d^{13}+91\,a^{14}\,b^2\,c^4\,d^{12}-364\,a^{13}\,b^3\,c^5\,d^{11}+1001\,a^{12}\,b^4\,c^6\,d^{10}-2002\,a^{11}\,b^5\,c^7\,d^9+3003\,a^{10}\,b^6\,c^8\,d^8-3432\,a^9\,b^7\,c^9\,d^7+3003\,a^8\,b^8\,c^{10}\,d^6-2002\,a^7\,b^9\,c^{11}\,d^5+1001\,a^6\,b^{10}\,c^{12}\,d^4-364\,a^5\,b^{11}\,c^{13}\,d^3+91\,a^4\,b^{12}\,c^{14}\,d^2-14\,a^3\,b^{13}\,c^{15}\,d+a^2\,b^{14}\,c^{16}}\right)\,{\left(-\frac{6561\,a^4\,b^5\,d^4-2916\,a^3\,b^6\,c\,d^3+486\,a^2\,b^7\,c^2\,d^2-36\,a\,b^8\,c^3\,d+b^9\,c^4}{4096\,a^{17}\,d^{12}-49152\,a^{16}\,b\,c\,d^{11}+270336\,a^{15}\,b^2\,c^2\,d^{10}-901120\,a^{14}\,b^3\,c^3\,d^9+2027520\,a^{13}\,b^4\,c^4\,d^8-3244032\,a^{12}\,b^5\,c^5\,d^7+3784704\,a^{11}\,b^6\,c^6\,d^6-3244032\,a^{10}\,b^7\,c^7\,d^5+2027520\,a^9\,b^8\,c^8\,d^4-901120\,a^8\,b^9\,c^9\,d^3+270336\,a^7\,b^{10}\,c^{10}\,d^2-49152\,a^6\,b^{11}\,c^{11}\,d+4096\,a^5\,b^{12}\,c^{12}}\right)}^{3/4}\,1{}\mathrm{i}-\frac{\sqrt{x}\,\left(81\,a^7\,b^8\,d^{15}+3627\,a^6\,b^9\,c\,d^{14}-80999\,a^5\,b^{10}\,c^2\,d^{13}+339435\,a^4\,b^{11}\,c^3\,d^{12}+339435\,a^3\,b^{12}\,c^4\,d^{11}-80999\,a^2\,b^{13}\,c^5\,d^{10}+3627\,a\,b^{14}\,c^6\,d^9+81\,b^{15}\,c^7\,d^8\right)\,1{}\mathrm{i}}{16\,\left(a^{14}\,c^2\,d^{12}-12\,a^{13}\,b\,c^3\,d^{11}+66\,a^{12}\,b^2\,c^4\,d^{10}-220\,a^{11}\,b^3\,c^5\,d^9+495\,a^{10}\,b^4\,c^6\,d^8-792\,a^9\,b^5\,c^7\,d^7+924\,a^8\,b^6\,c^8\,d^6-792\,a^7\,b^7\,c^9\,d^5+495\,a^6\,b^8\,c^{10}\,d^4-220\,a^5\,b^9\,c^{11}\,d^3+66\,a^4\,b^{10}\,c^{12}\,d^2-12\,a^3\,b^{11}\,c^{13}\,d+a^2\,b^{12}\,c^{14}\right)}\right)\,{\left(-\frac{6561\,a^4\,b^5\,d^4-2916\,a^3\,b^6\,c\,d^3+486\,a^2\,b^7\,c^2\,d^2-36\,a\,b^8\,c^3\,d+b^9\,c^4}{4096\,a^{17}\,d^{12}-49152\,a^{16}\,b\,c\,d^{11}+270336\,a^{15}\,b^2\,c^2\,d^{10}-901120\,a^{14}\,b^3\,c^3\,d^9+2027520\,a^{13}\,b^4\,c^4\,d^8-3244032\,a^{12}\,b^5\,c^5\,d^7+3784704\,a^{11}\,b^6\,c^6\,d^6-3244032\,a^{10}\,b^7\,c^7\,d^5+2027520\,a^9\,b^8\,c^8\,d^4-901120\,a^8\,b^9\,c^9\,d^3+270336\,a^7\,b^{10}\,c^{10}\,d^2-49152\,a^6\,b^{11}\,c^{11}\,d+4096\,a^5\,b^{12}\,c^{12}}\right)}^{1/4}+\left(\left(\frac{\sqrt{x}\,{\left(-\frac{6561\,a^4\,b^5\,d^4-2916\,a^3\,b^6\,c\,d^3+486\,a^2\,b^7\,c^2\,d^2-36\,a\,b^8\,c^3\,d+b^9\,c^4}{4096\,a^{17}\,d^{12}-49152\,a^{16}\,b\,c\,d^{11}+270336\,a^{15}\,b^2\,c^2\,d^{10}-901120\,a^{14}\,b^3\,c^3\,d^9+2027520\,a^{13}\,b^4\,c^4\,d^8-3244032\,a^{12}\,b^5\,c^5\,d^7+3784704\,a^{11}\,b^6\,c^6\,d^6-3244032\,a^{10}\,b^7\,c^7\,d^5+2027520\,a^9\,b^8\,c^8\,d^4-901120\,a^8\,b^9\,c^9\,d^3+270336\,a^7\,b^{10}\,c^{10}\,d^2-49152\,a^6\,b^{11}\,c^{11}\,d+4096\,a^5\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(4096\,a^{19}\,b^4\,c\,d^{22}-122880\,a^{18}\,b^5\,c^2\,d^{21}+1486848\,a^{17}\,b^6\,c^3\,d^{20}-9748480\,a^{16}\,b^7\,c^4\,d^{19}+40476672\,a^{15}\,b^8\,c^5\,d^{18}-116785152\,a^{14}\,b^9\,c^6\,d^{17}+249192448\,a^{13}\,b^{10}\,c^7\,d^{16}-412041216\,a^{12}\,b^{11}\,c^8\,d^{15}+547700736\,a^{11}\,b^{12}\,c^9\,d^{14}-600326144\,a^{10}\,b^{13}\,c^{10}\,d^{13}+547700736\,a^9\,b^{14}\,c^{11}\,d^{12}-412041216\,a^8\,b^{15}\,c^{12}\,d^{11}+249192448\,a^7\,b^{16}\,c^{13}\,d^{10}-116785152\,a^6\,b^{17}\,c^{14}\,d^9+40476672\,a^5\,b^{18}\,c^{15}\,d^8-9748480\,a^4\,b^{19}\,c^{16}\,d^7+1486848\,a^3\,b^{20}\,c^{17}\,d^6-122880\,a^2\,b^{21}\,c^{18}\,d^5+4096\,a\,b^{22}\,c^{19}\,d^4\right)}{16\,\left(a^{14}\,c^2\,d^{12}-12\,a^{13}\,b\,c^3\,d^{11}+66\,a^{12}\,b^2\,c^4\,d^{10}-220\,a^{11}\,b^3\,c^5\,d^9+495\,a^{10}\,b^4\,c^6\,d^8-792\,a^9\,b^5\,c^7\,d^7+924\,a^8\,b^6\,c^8\,d^6-792\,a^7\,b^7\,c^9\,d^5+495\,a^6\,b^8\,c^{10}\,d^4-220\,a^5\,b^9\,c^{11}\,d^3+66\,a^4\,b^{10}\,c^{12}\,d^2-12\,a^3\,b^{11}\,c^{13}\,d+a^2\,b^{12}\,c^{14}\right)}+\frac{\left(32\,a^{19}\,b^4\,d^{23}-1216\,a^{18}\,b^5\,c\,d^{22}+19040\,a^{17}\,b^6\,c^2\,d^{21}-161664\,a^{16}\,b^7\,c^3\,d^{20}+837408\,a^{15}\,b^8\,c^4\,d^{19}-2842656\,a^{14}\,b^9\,c^5\,d^{18}+6564768\,a^{13}\,b^{10}\,c^6\,d^{17}-10331040\,a^{12}\,b^{11}\,c^7\,d^{16}+10374112\,a^{11}\,b^{12}\,c^8\,d^{15}-4458784\,a^{10}\,b^{13}\,c^9\,d^{14}-4458784\,a^9\,b^{14}\,c^{10}\,d^{13}+10374112\,a^8\,b^{15}\,c^{11}\,d^{12}-10331040\,a^7\,b^{16}\,c^{12}\,d^{11}+6564768\,a^6\,b^{17}\,c^{13}\,d^{10}-2842656\,a^5\,b^{18}\,c^{14}\,d^9+837408\,a^4\,b^{19}\,c^{15}\,d^8-161664\,a^3\,b^{20}\,c^{16}\,d^7+19040\,a^2\,b^{21}\,c^{17}\,d^6-1216\,a\,b^{22}\,c^{18}\,d^5+32\,b^{23}\,c^{19}\,d^4\right)\,1{}\mathrm{i}}{a^{16}\,c^2\,d^{14}-14\,a^{15}\,b\,c^3\,d^{13}+91\,a^{14}\,b^2\,c^4\,d^{12}-364\,a^{13}\,b^3\,c^5\,d^{11}+1001\,a^{12}\,b^4\,c^6\,d^{10}-2002\,a^{11}\,b^5\,c^7\,d^9+3003\,a^{10}\,b^6\,c^8\,d^8-3432\,a^9\,b^7\,c^9\,d^7+3003\,a^8\,b^8\,c^{10}\,d^6-2002\,a^7\,b^9\,c^{11}\,d^5+1001\,a^6\,b^{10}\,c^{12}\,d^4-364\,a^5\,b^{11}\,c^{13}\,d^3+91\,a^4\,b^{12}\,c^{14}\,d^2-14\,a^3\,b^{13}\,c^{15}\,d+a^2\,b^{14}\,c^{16}}\right)\,{\left(-\frac{6561\,a^4\,b^5\,d^4-2916\,a^3\,b^6\,c\,d^3+486\,a^2\,b^7\,c^2\,d^2-36\,a\,b^8\,c^3\,d+b^9\,c^4}{4096\,a^{17}\,d^{12}-49152\,a^{16}\,b\,c\,d^{11}+270336\,a^{15}\,b^2\,c^2\,d^{10}-901120\,a^{14}\,b^3\,c^3\,d^9+2027520\,a^{13}\,b^4\,c^4\,d^8-3244032\,a^{12}\,b^5\,c^5\,d^7+3784704\,a^{11}\,b^6\,c^6\,d^6-3244032\,a^{10}\,b^7\,c^7\,d^5+2027520\,a^9\,b^8\,c^8\,d^4-901120\,a^8\,b^9\,c^9\,d^3+270336\,a^7\,b^{10}\,c^{10}\,d^2-49152\,a^6\,b^{11}\,c^{11}\,d+4096\,a^5\,b^{12}\,c^{12}}\right)}^{3/4}\,1{}\mathrm{i}+\frac{\sqrt{x}\,\left(81\,a^7\,b^8\,d^{15}+3627\,a^6\,b^9\,c\,d^{14}-80999\,a^5\,b^{10}\,c^2\,d^{13}+339435\,a^4\,b^{11}\,c^3\,d^{12}+339435\,a^3\,b^{12}\,c^4\,d^{11}-80999\,a^2\,b^{13}\,c^5\,d^{10}+3627\,a\,b^{14}\,c^6\,d^9+81\,b^{15}\,c^7\,d^8\right)\,1{}\mathrm{i}}{16\,\left(a^{14}\,c^2\,d^{12}-12\,a^{13}\,b\,c^3\,d^{11}+66\,a^{12}\,b^2\,c^4\,d^{10}-220\,a^{11}\,b^3\,c^5\,d^9+495\,a^{10}\,b^4\,c^6\,d^8-792\,a^9\,b^5\,c^7\,d^7+924\,a^8\,b^6\,c^8\,d^6-792\,a^7\,b^7\,c^9\,d^5+495\,a^6\,b^8\,c^{10}\,d^4-220\,a^5\,b^9\,c^{11}\,d^3+66\,a^4\,b^{10}\,c^{12}\,d^2-12\,a^3\,b^{11}\,c^{13}\,d+a^2\,b^{12}\,c^{14}\right)}\right)\,{\left(-\frac{6561\,a^4\,b^5\,d^4-2916\,a^3\,b^6\,c\,d^3+486\,a^2\,b^7\,c^2\,d^2-36\,a\,b^8\,c^3\,d+b^9\,c^4}{4096\,a^{17}\,d^{12}-49152\,a^{16}\,b\,c\,d^{11}+270336\,a^{15}\,b^2\,c^2\,d^{10}-901120\,a^{14}\,b^3\,c^3\,d^9+2027520\,a^{13}\,b^4\,c^4\,d^8-3244032\,a^{12}\,b^5\,c^5\,d^7+3784704\,a^{11}\,b^6\,c^6\,d^6-3244032\,a^{10}\,b^7\,c^7\,d^5+2027520\,a^9\,b^8\,c^8\,d^4-901120\,a^8\,b^9\,c^9\,d^3+270336\,a^7\,b^{10}\,c^{10}\,d^2-49152\,a^6\,b^{11}\,c^{11}\,d+4096\,a^5\,b^{12}\,c^{12}}\right)}^{1/4}}\right)\,{\left(-\frac{6561\,a^4\,b^5\,d^4-2916\,a^3\,b^6\,c\,d^3+486\,a^2\,b^7\,c^2\,d^2-36\,a\,b^8\,c^3\,d+b^9\,c^4}{4096\,a^{17}\,d^{12}-49152\,a^{16}\,b\,c\,d^{11}+270336\,a^{15}\,b^2\,c^2\,d^{10}-901120\,a^{14}\,b^3\,c^3\,d^9+2027520\,a^{13}\,b^4\,c^4\,d^8-3244032\,a^{12}\,b^5\,c^5\,d^7+3784704\,a^{11}\,b^6\,c^6\,d^6-3244032\,a^{10}\,b^7\,c^7\,d^5+2027520\,a^9\,b^8\,c^8\,d^4-901120\,a^8\,b^9\,c^9\,d^3+270336\,a^7\,b^{10}\,c^{10}\,d^2-49152\,a^6\,b^{11}\,c^{11}\,d+4096\,a^5\,b^{12}\,c^{12}}\right)}^{1/4}","Not used",1,"2*atan((((((32*a^19*b^4*d^23 + 32*b^23*c^19*d^4 - 1216*a*b^22*c^18*d^5 - 1216*a^18*b^5*c*d^22 + 19040*a^2*b^21*c^17*d^6 - 161664*a^3*b^20*c^16*d^7 + 837408*a^4*b^19*c^15*d^8 - 2842656*a^5*b^18*c^14*d^9 + 6564768*a^6*b^17*c^13*d^10 - 10331040*a^7*b^16*c^12*d^11 + 10374112*a^8*b^15*c^11*d^12 - 4458784*a^9*b^14*c^10*d^13 - 4458784*a^10*b^13*c^9*d^14 + 10374112*a^11*b^12*c^8*d^15 - 10331040*a^12*b^11*c^7*d^16 + 6564768*a^13*b^10*c^6*d^17 - 2842656*a^14*b^9*c^5*d^18 + 837408*a^15*b^8*c^4*d^19 - 161664*a^16*b^7*c^3*d^20 + 19040*a^17*b^6*c^2*d^21)*1i)/(a^2*b^14*c^16 + a^16*c^2*d^14 - 14*a^3*b^13*c^15*d - 14*a^15*b*c^3*d^13 + 91*a^4*b^12*c^14*d^2 - 364*a^5*b^11*c^13*d^3 + 1001*a^6*b^10*c^12*d^4 - 2002*a^7*b^9*c^11*d^5 + 3003*a^8*b^8*c^10*d^6 - 3432*a^9*b^7*c^9*d^7 + 3003*a^10*b^6*c^8*d^8 - 2002*a^11*b^5*c^7*d^9 + 1001*a^12*b^4*c^6*d^10 - 364*a^13*b^3*c^5*d^11 + 91*a^14*b^2*c^4*d^12) - (x^(1/2)*(-(a^4*d^9 + 6561*b^4*c^4*d^5 - 2916*a*b^3*c^3*d^6 + 486*a^2*b^2*c^2*d^7 - 36*a^3*b*c*d^8)/(4096*b^12*c^17 + 4096*a^12*c^5*d^12 - 49152*a^11*b*c^6*d^11 + 270336*a^2*b^10*c^15*d^2 - 901120*a^3*b^9*c^14*d^3 + 2027520*a^4*b^8*c^13*d^4 - 3244032*a^5*b^7*c^12*d^5 + 3784704*a^6*b^6*c^11*d^6 - 3244032*a^7*b^5*c^10*d^7 + 2027520*a^8*b^4*c^9*d^8 - 901120*a^9*b^3*c^8*d^9 + 270336*a^10*b^2*c^7*d^10 - 49152*a*b^11*c^16*d))^(1/4)*(4096*a*b^22*c^19*d^4 + 4096*a^19*b^4*c*d^22 - 122880*a^2*b^21*c^18*d^5 + 1486848*a^3*b^20*c^17*d^6 - 9748480*a^4*b^19*c^16*d^7 + 40476672*a^5*b^18*c^15*d^8 - 116785152*a^6*b^17*c^14*d^9 + 249192448*a^7*b^16*c^13*d^10 - 412041216*a^8*b^15*c^12*d^11 + 547700736*a^9*b^14*c^11*d^12 - 600326144*a^10*b^13*c^10*d^13 + 547700736*a^11*b^12*c^9*d^14 - 412041216*a^12*b^11*c^8*d^15 + 249192448*a^13*b^10*c^7*d^16 - 116785152*a^14*b^9*c^6*d^17 + 40476672*a^15*b^8*c^5*d^18 - 9748480*a^16*b^7*c^4*d^19 + 1486848*a^17*b^6*c^3*d^20 - 122880*a^18*b^5*c^2*d^21))/(16*(a^2*b^12*c^14 + a^14*c^2*d^12 - 12*a^3*b^11*c^13*d - 12*a^13*b*c^3*d^11 + 66*a^4*b^10*c^12*d^2 - 220*a^5*b^9*c^11*d^3 + 495*a^6*b^8*c^10*d^4 - 792*a^7*b^7*c^9*d^5 + 924*a^8*b^6*c^8*d^6 - 792*a^9*b^5*c^7*d^7 + 495*a^10*b^4*c^6*d^8 - 220*a^11*b^3*c^5*d^9 + 66*a^12*b^2*c^4*d^10)))*(-(a^4*d^9 + 6561*b^4*c^4*d^5 - 2916*a*b^3*c^3*d^6 + 486*a^2*b^2*c^2*d^7 - 36*a^3*b*c*d^8)/(4096*b^12*c^17 + 4096*a^12*c^5*d^12 - 49152*a^11*b*c^6*d^11 + 270336*a^2*b^10*c^15*d^2 - 901120*a^3*b^9*c^14*d^3 + 2027520*a^4*b^8*c^13*d^4 - 3244032*a^5*b^7*c^12*d^5 + 3784704*a^6*b^6*c^11*d^6 - 3244032*a^7*b^5*c^10*d^7 + 2027520*a^8*b^4*c^9*d^8 - 901120*a^9*b^3*c^8*d^9 + 270336*a^10*b^2*c^7*d^10 - 49152*a*b^11*c^16*d))^(3/4) - (x^(1/2)*(81*a^7*b^8*d^15 + 81*b^15*c^7*d^8 + 3627*a*b^14*c^6*d^9 + 3627*a^6*b^9*c*d^14 - 80999*a^2*b^13*c^5*d^10 + 339435*a^3*b^12*c^4*d^11 + 339435*a^4*b^11*c^3*d^12 - 80999*a^5*b^10*c^2*d^13))/(16*(a^2*b^12*c^14 + a^14*c^2*d^12 - 12*a^3*b^11*c^13*d - 12*a^13*b*c^3*d^11 + 66*a^4*b^10*c^12*d^2 - 220*a^5*b^9*c^11*d^3 + 495*a^6*b^8*c^10*d^4 - 792*a^7*b^7*c^9*d^5 + 924*a^8*b^6*c^8*d^6 - 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2027520*a^8*b^4*c^9*d^8 - 901120*a^9*b^3*c^8*d^9 + 270336*a^10*b^2*c^7*d^10 - 49152*a*b^11*c^16*d))^(3/4) + (x^(1/2)*(81*a^7*b^8*d^15 + 81*b^15*c^7*d^8 + 3627*a*b^14*c^6*d^9 + 3627*a^6*b^9*c*d^14 - 80999*a^2*b^13*c^5*d^10 + 339435*a^3*b^12*c^4*d^11 + 339435*a^4*b^11*c^3*d^12 - 80999*a^5*b^10*c^2*d^13))/(16*(a^2*b^12*c^14 + a^14*c^2*d^12 - 12*a^3*b^11*c^13*d - 12*a^13*b*c^3*d^11 + 66*a^4*b^10*c^12*d^2 - 220*a^5*b^9*c^11*d^3 + 495*a^6*b^8*c^10*d^4 - 792*a^7*b^7*c^9*d^5 + 924*a^8*b^6*c^8*d^6 - 792*a^9*b^5*c^7*d^7 + 495*a^10*b^4*c^6*d^8 - 220*a^11*b^3*c^5*d^9 + 66*a^12*b^2*c^4*d^10)))*(-(a^4*d^9 + 6561*b^4*c^4*d^5 - 2916*a*b^3*c^3*d^6 + 486*a^2*b^2*c^2*d^7 - 36*a^3*b*c*d^8)/(4096*b^12*c^17 + 4096*a^12*c^5*d^12 - 49152*a^11*b*c^6*d^11 + 270336*a^2*b^10*c^15*d^2 - 901120*a^3*b^9*c^14*d^3 + 2027520*a^4*b^8*c^13*d^4 - 3244032*a^5*b^7*c^12*d^5 + 3784704*a^6*b^6*c^11*d^6 - 3244032*a^7*b^5*c^10*d^7 + 2027520*a^8*b^4*c^9*d^8 - 901120*a^9*b^3*c^8*d^9 + 270336*a^10*b^2*c^7*d^10 - 49152*a*b^11*c^16*d))^(1/4))/(((((32*a^19*b^4*d^23 + 32*b^23*c^19*d^4 - 1216*a*b^22*c^18*d^5 - 1216*a^18*b^5*c*d^22 + 19040*a^2*b^21*c^17*d^6 - 161664*a^3*b^20*c^16*d^7 + 837408*a^4*b^19*c^15*d^8 - 2842656*a^5*b^18*c^14*d^9 + 6564768*a^6*b^17*c^13*d^10 - 10331040*a^7*b^16*c^12*d^11 + 10374112*a^8*b^15*c^11*d^12 - 4458784*a^9*b^14*c^10*d^13 - 4458784*a^10*b^13*c^9*d^14 + 10374112*a^11*b^12*c^8*d^15 - 10331040*a^12*b^11*c^7*d^16 + 6564768*a^13*b^10*c^6*d^17 - 2842656*a^14*b^9*c^5*d^18 + 837408*a^15*b^8*c^4*d^19 - 161664*a^16*b^7*c^3*d^20 + 19040*a^17*b^6*c^2*d^21)*1i)/(a^2*b^14*c^16 + a^16*c^2*d^14 - 14*a^3*b^13*c^15*d - 14*a^15*b*c^3*d^13 + 91*a^4*b^12*c^14*d^2 - 364*a^5*b^11*c^13*d^3 + 1001*a^6*b^10*c^12*d^4 - 2002*a^7*b^9*c^11*d^5 + 3003*a^8*b^8*c^10*d^6 - 3432*a^9*b^7*c^9*d^7 + 3003*a^10*b^6*c^8*d^8 - 2002*a^11*b^5*c^7*d^9 + 1001*a^12*b^4*c^6*d^10 - 364*a^13*b^3*c^5*d^11 + 91*a^14*b^2*c^4*d^12) - (x^(1/2)*(-(a^4*d^9 + 6561*b^4*c^4*d^5 - 2916*a*b^3*c^3*d^6 + 486*a^2*b^2*c^2*d^7 - 36*a^3*b*c*d^8)/(4096*b^12*c^17 + 4096*a^12*c^5*d^12 - 49152*a^11*b*c^6*d^11 + 270336*a^2*b^10*c^15*d^2 - 901120*a^3*b^9*c^14*d^3 + 2027520*a^4*b^8*c^13*d^4 - 3244032*a^5*b^7*c^12*d^5 + 3784704*a^6*b^6*c^11*d^6 - 3244032*a^7*b^5*c^10*d^7 + 2027520*a^8*b^4*c^9*d^8 - 901120*a^9*b^3*c^8*d^9 + 270336*a^10*b^2*c^7*d^10 - 49152*a*b^11*c^16*d))^(1/4)*(4096*a*b^22*c^19*d^4 + 4096*a^19*b^4*c*d^22 - 122880*a^2*b^21*c^18*d^5 + 1486848*a^3*b^20*c^17*d^6 - 9748480*a^4*b^19*c^16*d^7 + 40476672*a^5*b^18*c^15*d^8 - 116785152*a^6*b^17*c^14*d^9 + 249192448*a^7*b^16*c^13*d^10 - 412041216*a^8*b^15*c^12*d^11 + 547700736*a^9*b^14*c^11*d^12 - 600326144*a^10*b^13*c^10*d^13 + 547700736*a^11*b^12*c^9*d^14 - 412041216*a^12*b^11*c^8*d^15 + 249192448*a^13*b^10*c^7*d^16 - 116785152*a^14*b^9*c^6*d^17 + 40476672*a^15*b^8*c^5*d^18 - 9748480*a^16*b^7*c^4*d^19 + 1486848*a^17*b^6*c^3*d^20 - 122880*a^18*b^5*c^2*d^21))/(16*(a^2*b^12*c^14 + a^14*c^2*d^12 - 12*a^3*b^11*c^13*d - 12*a^13*b*c^3*d^11 + 66*a^4*b^10*c^12*d^2 - 220*a^5*b^9*c^11*d^3 + 495*a^6*b^8*c^10*d^4 - 792*a^7*b^7*c^9*d^5 + 924*a^8*b^6*c^8*d^6 - 792*a^9*b^5*c^7*d^7 + 495*a^10*b^4*c^6*d^8 - 220*a^11*b^3*c^5*d^9 + 66*a^12*b^2*c^4*d^10)))*(-(a^4*d^9 + 6561*b^4*c^4*d^5 - 2916*a*b^3*c^3*d^6 + 486*a^2*b^2*c^2*d^7 - 36*a^3*b*c*d^8)/(4096*b^12*c^17 + 4096*a^12*c^5*d^12 - 49152*a^11*b*c^6*d^11 + 270336*a^2*b^10*c^15*d^2 - 901120*a^3*b^9*c^14*d^3 + 2027520*a^4*b^8*c^13*d^4 - 3244032*a^5*b^7*c^12*d^5 + 3784704*a^6*b^6*c^11*d^6 - 3244032*a^7*b^5*c^10*d^7 + 2027520*a^8*b^4*c^9*d^8 - 901120*a^9*b^3*c^8*d^9 + 270336*a^10*b^2*c^7*d^10 - 49152*a*b^11*c^16*d))^(3/4)*1i - (x^(1/2)*(81*a^7*b^8*d^15 + 81*b^15*c^7*d^8 + 3627*a*b^14*c^6*d^9 + 3627*a^6*b^9*c*d^14 - 80999*a^2*b^13*c^5*d^10 + 339435*a^3*b^12*c^4*d^11 + 339435*a^4*b^11*c^3*d^12 - 80999*a^5*b^10*c^2*d^13)*1i)/(16*(a^2*b^12*c^14 + a^14*c^2*d^12 - 12*a^3*b^11*c^13*d - 12*a^13*b*c^3*d^11 + 66*a^4*b^10*c^12*d^2 - 220*a^5*b^9*c^11*d^3 + 495*a^6*b^8*c^10*d^4 - 792*a^7*b^7*c^9*d^5 + 924*a^8*b^6*c^8*d^6 - 792*a^9*b^5*c^7*d^7 + 495*a^10*b^4*c^6*d^8 - 220*a^11*b^3*c^5*d^9 + 66*a^12*b^2*c^4*d^10)))*(-(a^4*d^9 + 6561*b^4*c^4*d^5 - 2916*a*b^3*c^3*d^6 + 486*a^2*b^2*c^2*d^7 - 36*a^3*b*c*d^8)/(4096*b^12*c^17 + 4096*a^12*c^5*d^12 - 49152*a^11*b*c^6*d^11 + 270336*a^2*b^10*c^15*d^2 - 901120*a^3*b^9*c^14*d^3 + 2027520*a^4*b^8*c^13*d^4 - 3244032*a^5*b^7*c^12*d^5 + 3784704*a^6*b^6*c^11*d^6 - 3244032*a^7*b^5*c^10*d^7 + 2027520*a^8*b^4*c^9*d^8 - 901120*a^9*b^3*c^8*d^9 + 270336*a^10*b^2*c^7*d^10 - 49152*a*b^11*c^16*d))^(1/4) - ((3645*a^6*b^9*d^15)/32 + (3645*b^15*c^6*d^9)/32 - (49815*a*b^14*c^5*d^10)/16 - (49815*a^5*b^10*c*d^14)/16 + (918675*a^2*b^13*c^4*d^11)/32 - (739025*a^3*b^12*c^3*d^12)/8 + (918675*a^4*b^11*c^2*d^13)/32)/(a^2*b^14*c^16 + a^16*c^2*d^14 - 14*a^3*b^13*c^15*d - 14*a^15*b*c^3*d^13 + 91*a^4*b^12*c^14*d^2 - 364*a^5*b^11*c^13*d^3 + 1001*a^6*b^10*c^12*d^4 - 2002*a^7*b^9*c^11*d^5 + 3003*a^8*b^8*c^10*d^6 - 3432*a^9*b^7*c^9*d^7 + 3003*a^10*b^6*c^8*d^8 - 2002*a^11*b^5*c^7*d^9 + 1001*a^12*b^4*c^6*d^10 - 364*a^13*b^3*c^5*d^11 + 91*a^14*b^2*c^4*d^12) + ((((32*a^19*b^4*d^23 + 32*b^23*c^19*d^4 - 1216*a*b^22*c^18*d^5 - 1216*a^18*b^5*c*d^22 + 19040*a^2*b^21*c^17*d^6 - 161664*a^3*b^20*c^16*d^7 + 837408*a^4*b^19*c^15*d^8 - 2842656*a^5*b^18*c^14*d^9 + 6564768*a^6*b^17*c^13*d^10 - 10331040*a^7*b^16*c^12*d^11 + 10374112*a^8*b^15*c^11*d^12 - 4458784*a^9*b^14*c^10*d^13 - 4458784*a^10*b^13*c^9*d^14 + 10374112*a^11*b^12*c^8*d^15 - 10331040*a^12*b^11*c^7*d^16 + 6564768*a^13*b^10*c^6*d^17 - 2842656*a^14*b^9*c^5*d^18 + 837408*a^15*b^8*c^4*d^19 - 161664*a^16*b^7*c^3*d^20 + 19040*a^17*b^6*c^2*d^21)*1i)/(a^2*b^14*c^16 + a^16*c^2*d^14 - 14*a^3*b^13*c^15*d - 14*a^15*b*c^3*d^13 + 91*a^4*b^12*c^14*d^2 - 364*a^5*b^11*c^13*d^3 + 1001*a^6*b^10*c^12*d^4 - 2002*a^7*b^9*c^11*d^5 + 3003*a^8*b^8*c^10*d^6 - 3432*a^9*b^7*c^9*d^7 + 3003*a^10*b^6*c^8*d^8 - 2002*a^11*b^5*c^7*d^9 + 1001*a^12*b^4*c^6*d^10 - 364*a^13*b^3*c^5*d^11 + 91*a^14*b^2*c^4*d^12) + (x^(1/2)*(-(a^4*d^9 + 6561*b^4*c^4*d^5 - 2916*a*b^3*c^3*d^6 + 486*a^2*b^2*c^2*d^7 - 36*a^3*b*c*d^8)/(4096*b^12*c^17 + 4096*a^12*c^5*d^12 - 49152*a^11*b*c^6*d^11 + 270336*a^2*b^10*c^15*d^2 - 901120*a^3*b^9*c^14*d^3 + 2027520*a^4*b^8*c^13*d^4 - 3244032*a^5*b^7*c^12*d^5 + 3784704*a^6*b^6*c^11*d^6 - 3244032*a^7*b^5*c^10*d^7 + 2027520*a^8*b^4*c^9*d^8 - 901120*a^9*b^3*c^8*d^9 + 270336*a^10*b^2*c^7*d^10 - 49152*a*b^11*c^16*d))^(1/4)*(4096*a*b^22*c^19*d^4 + 4096*a^19*b^4*c*d^22 - 122880*a^2*b^21*c^18*d^5 + 1486848*a^3*b^20*c^17*d^6 - 9748480*a^4*b^19*c^16*d^7 + 40476672*a^5*b^18*c^15*d^8 - 116785152*a^6*b^17*c^14*d^9 + 249192448*a^7*b^16*c^13*d^10 - 412041216*a^8*b^15*c^12*d^11 + 547700736*a^9*b^14*c^11*d^12 - 600326144*a^10*b^13*c^10*d^13 + 547700736*a^11*b^12*c^9*d^14 - 412041216*a^12*b^11*c^8*d^15 + 249192448*a^13*b^10*c^7*d^16 - 116785152*a^14*b^9*c^6*d^17 + 40476672*a^15*b^8*c^5*d^18 - 9748480*a^16*b^7*c^4*d^19 + 1486848*a^17*b^6*c^3*d^20 - 122880*a^18*b^5*c^2*d^21))/(16*(a^2*b^12*c^14 + a^14*c^2*d^12 - 12*a^3*b^11*c^13*d - 12*a^13*b*c^3*d^11 + 66*a^4*b^10*c^12*d^2 - 220*a^5*b^9*c^11*d^3 + 495*a^6*b^8*c^10*d^4 - 792*a^7*b^7*c^9*d^5 + 924*a^8*b^6*c^8*d^6 - 792*a^9*b^5*c^7*d^7 + 495*a^10*b^4*c^6*d^8 - 220*a^11*b^3*c^5*d^9 + 66*a^12*b^2*c^4*d^10)))*(-(a^4*d^9 + 6561*b^4*c^4*d^5 - 2916*a*b^3*c^3*d^6 + 486*a^2*b^2*c^2*d^7 - 36*a^3*b*c*d^8)/(4096*b^12*c^17 + 4096*a^12*c^5*d^12 - 49152*a^11*b*c^6*d^11 + 270336*a^2*b^10*c^15*d^2 - 901120*a^3*b^9*c^14*d^3 + 2027520*a^4*b^8*c^13*d^4 - 3244032*a^5*b^7*c^12*d^5 + 3784704*a^6*b^6*c^11*d^6 - 3244032*a^7*b^5*c^10*d^7 + 2027520*a^8*b^4*c^9*d^8 - 901120*a^9*b^3*c^8*d^9 + 270336*a^10*b^2*c^7*d^10 - 49152*a*b^11*c^16*d))^(3/4)*1i + (x^(1/2)*(81*a^7*b^8*d^15 + 81*b^15*c^7*d^8 + 3627*a*b^14*c^6*d^9 + 3627*a^6*b^9*c*d^14 - 80999*a^2*b^13*c^5*d^10 + 339435*a^3*b^12*c^4*d^11 + 339435*a^4*b^11*c^3*d^12 - 80999*a^5*b^10*c^2*d^13)*1i)/(16*(a^2*b^12*c^14 + a^14*c^2*d^12 - 12*a^3*b^11*c^13*d - 12*a^13*b*c^3*d^11 + 66*a^4*b^10*c^12*d^2 - 220*a^5*b^9*c^11*d^3 + 495*a^6*b^8*c^10*d^4 - 792*a^7*b^7*c^9*d^5 + 924*a^8*b^6*c^8*d^6 - 792*a^9*b^5*c^7*d^7 + 495*a^10*b^4*c^6*d^8 - 220*a^11*b^3*c^5*d^9 + 66*a^12*b^2*c^4*d^10)))*(-(a^4*d^9 + 6561*b^4*c^4*d^5 - 2916*a*b^3*c^3*d^6 + 486*a^2*b^2*c^2*d^7 - 36*a^3*b*c*d^8)/(4096*b^12*c^17 + 4096*a^12*c^5*d^12 - 49152*a^11*b*c^6*d^11 + 270336*a^2*b^10*c^15*d^2 - 901120*a^3*b^9*c^14*d^3 + 2027520*a^4*b^8*c^13*d^4 - 3244032*a^5*b^7*c^12*d^5 + 3784704*a^6*b^6*c^11*d^6 - 3244032*a^7*b^5*c^10*d^7 + 2027520*a^8*b^4*c^9*d^8 - 901120*a^9*b^3*c^8*d^9 + 270336*a^10*b^2*c^7*d^10 - 49152*a*b^11*c^16*d))^(1/4)))*(-(a^4*d^9 + 6561*b^4*c^4*d^5 - 2916*a*b^3*c^3*d^6 + 486*a^2*b^2*c^2*d^7 - 36*a^3*b*c*d^8)/(4096*b^12*c^17 + 4096*a^12*c^5*d^12 - 49152*a^11*b*c^6*d^11 + 270336*a^2*b^10*c^15*d^2 - 901120*a^3*b^9*c^14*d^3 + 2027520*a^4*b^8*c^13*d^4 - 3244032*a^5*b^7*c^12*d^5 + 3784704*a^6*b^6*c^11*d^6 - 3244032*a^7*b^5*c^10*d^7 + 2027520*a^8*b^4*c^9*d^8 - 901120*a^9*b^3*c^8*d^9 + 270336*a^10*b^2*c^7*d^10 - 49152*a*b^11*c^16*d))^(1/4) - atan(((((32*a^19*b^4*d^23 + 32*b^23*c^19*d^4 - 1216*a*b^22*c^18*d^5 - 1216*a^18*b^5*c*d^22 + 19040*a^2*b^21*c^17*d^6 - 161664*a^3*b^20*c^16*d^7 + 837408*a^4*b^19*c^15*d^8 - 2842656*a^5*b^18*c^14*d^9 + 6564768*a^6*b^17*c^13*d^10 - 10331040*a^7*b^16*c^12*d^11 + 10374112*a^8*b^15*c^11*d^12 - 4458784*a^9*b^14*c^10*d^13 - 4458784*a^10*b^13*c^9*d^14 + 10374112*a^11*b^12*c^8*d^15 - 10331040*a^12*b^11*c^7*d^16 + 6564768*a^13*b^10*c^6*d^17 - 2842656*a^14*b^9*c^5*d^18 + 837408*a^15*b^8*c^4*d^19 - 161664*a^16*b^7*c^3*d^20 + 19040*a^17*b^6*c^2*d^21)/(a^2*b^14*c^16 + a^16*c^2*d^14 - 14*a^3*b^13*c^15*d - 14*a^15*b*c^3*d^13 + 91*a^4*b^12*c^14*d^2 - 364*a^5*b^11*c^13*d^3 + 1001*a^6*b^10*c^12*d^4 - 2002*a^7*b^9*c^11*d^5 + 3003*a^8*b^8*c^10*d^6 - 3432*a^9*b^7*c^9*d^7 + 3003*a^10*b^6*c^8*d^8 - 2002*a^11*b^5*c^7*d^9 + 1001*a^12*b^4*c^6*d^10 - 364*a^13*b^3*c^5*d^11 + 91*a^14*b^2*c^4*d^12) - (x^(1/2)*(-(a^4*d^9 + 6561*b^4*c^4*d^5 - 2916*a*b^3*c^3*d^6 + 486*a^2*b^2*c^2*d^7 - 36*a^3*b*c*d^8)/(4096*b^12*c^17 + 4096*a^12*c^5*d^12 - 49152*a^11*b*c^6*d^11 + 270336*a^2*b^10*c^15*d^2 - 901120*a^3*b^9*c^14*d^3 + 2027520*a^4*b^8*c^13*d^4 - 3244032*a^5*b^7*c^12*d^5 + 3784704*a^6*b^6*c^11*d^6 - 3244032*a^7*b^5*c^10*d^7 + 2027520*a^8*b^4*c^9*d^8 - 901120*a^9*b^3*c^8*d^9 + 270336*a^10*b^2*c^7*d^10 - 49152*a*b^11*c^16*d))^(1/4)*(4096*a*b^22*c^19*d^4 + 4096*a^19*b^4*c*d^22 - 122880*a^2*b^21*c^18*d^5 + 1486848*a^3*b^20*c^17*d^6 - 9748480*a^4*b^19*c^16*d^7 + 40476672*a^5*b^18*c^15*d^8 - 116785152*a^6*b^17*c^14*d^9 + 249192448*a^7*b^16*c^13*d^10 - 412041216*a^8*b^15*c^12*d^11 + 547700736*a^9*b^14*c^11*d^12 - 600326144*a^10*b^13*c^10*d^13 + 547700736*a^11*b^12*c^9*d^14 - 412041216*a^12*b^11*c^8*d^15 + 249192448*a^13*b^10*c^7*d^16 - 116785152*a^14*b^9*c^6*d^17 + 40476672*a^15*b^8*c^5*d^18 - 9748480*a^16*b^7*c^4*d^19 + 1486848*a^17*b^6*c^3*d^20 - 122880*a^18*b^5*c^2*d^21))/(16*(a^2*b^12*c^14 + a^14*c^2*d^12 - 12*a^3*b^11*c^13*d - 12*a^13*b*c^3*d^11 + 66*a^4*b^10*c^12*d^2 - 220*a^5*b^9*c^11*d^3 + 495*a^6*b^8*c^10*d^4 - 792*a^7*b^7*c^9*d^5 + 924*a^8*b^6*c^8*d^6 - 792*a^9*b^5*c^7*d^7 + 495*a^10*b^4*c^6*d^8 - 220*a^11*b^3*c^5*d^9 + 66*a^12*b^2*c^4*d^10)))*(-(a^4*d^9 + 6561*b^4*c^4*d^5 - 2916*a*b^3*c^3*d^6 + 486*a^2*b^2*c^2*d^7 - 36*a^3*b*c*d^8)/(4096*b^12*c^17 + 4096*a^12*c^5*d^12 - 49152*a^11*b*c^6*d^11 + 270336*a^2*b^10*c^15*d^2 - 901120*a^3*b^9*c^14*d^3 + 2027520*a^4*b^8*c^13*d^4 - 3244032*a^5*b^7*c^12*d^5 + 3784704*a^6*b^6*c^11*d^6 - 3244032*a^7*b^5*c^10*d^7 + 2027520*a^8*b^4*c^9*d^8 - 901120*a^9*b^3*c^8*d^9 + 270336*a^10*b^2*c^7*d^10 - 49152*a*b^11*c^16*d))^(3/4)*1i - (x^(1/2)*(81*a^7*b^8*d^15 + 81*b^15*c^7*d^8 + 3627*a*b^14*c^6*d^9 + 3627*a^6*b^9*c*d^14 - 80999*a^2*b^13*c^5*d^10 + 339435*a^3*b^12*c^4*d^11 + 339435*a^4*b^11*c^3*d^12 - 80999*a^5*b^10*c^2*d^13)*1i)/(16*(a^2*b^12*c^14 + a^14*c^2*d^12 - 12*a^3*b^11*c^13*d - 12*a^13*b*c^3*d^11 + 66*a^4*b^10*c^12*d^2 - 220*a^5*b^9*c^11*d^3 + 495*a^6*b^8*c^10*d^4 - 792*a^7*b^7*c^9*d^5 + 924*a^8*b^6*c^8*d^6 - 792*a^9*b^5*c^7*d^7 + 495*a^10*b^4*c^6*d^8 - 220*a^11*b^3*c^5*d^9 + 66*a^12*b^2*c^4*d^10)))*(-(a^4*d^9 + 6561*b^4*c^4*d^5 - 2916*a*b^3*c^3*d^6 + 486*a^2*b^2*c^2*d^7 - 36*a^3*b*c*d^8)/(4096*b^12*c^17 + 4096*a^12*c^5*d^12 - 49152*a^11*b*c^6*d^11 + 270336*a^2*b^10*c^15*d^2 - 901120*a^3*b^9*c^14*d^3 + 2027520*a^4*b^8*c^13*d^4 - 3244032*a^5*b^7*c^12*d^5 + 3784704*a^6*b^6*c^11*d^6 - 3244032*a^7*b^5*c^10*d^7 + 2027520*a^8*b^4*c^9*d^8 - 901120*a^9*b^3*c^8*d^9 + 270336*a^10*b^2*c^7*d^10 - 49152*a*b^11*c^16*d))^(1/4) - (((32*a^19*b^4*d^23 + 32*b^23*c^19*d^4 - 1216*a*b^22*c^18*d^5 - 1216*a^18*b^5*c*d^22 + 19040*a^2*b^21*c^17*d^6 - 161664*a^3*b^20*c^16*d^7 + 837408*a^4*b^19*c^15*d^8 - 2842656*a^5*b^18*c^14*d^9 + 6564768*a^6*b^17*c^13*d^10 - 10331040*a^7*b^16*c^12*d^11 + 10374112*a^8*b^15*c^11*d^12 - 4458784*a^9*b^14*c^10*d^13 - 4458784*a^10*b^13*c^9*d^14 + 10374112*a^11*b^12*c^8*d^15 - 10331040*a^12*b^11*c^7*d^16 + 6564768*a^13*b^10*c^6*d^17 - 2842656*a^14*b^9*c^5*d^18 + 837408*a^15*b^8*c^4*d^19 - 161664*a^16*b^7*c^3*d^20 + 19040*a^17*b^6*c^2*d^21)/(a^2*b^14*c^16 + a^16*c^2*d^14 - 14*a^3*b^13*c^15*d - 14*a^15*b*c^3*d^13 + 91*a^4*b^12*c^14*d^2 - 364*a^5*b^11*c^13*d^3 + 1001*a^6*b^10*c^12*d^4 - 2002*a^7*b^9*c^11*d^5 + 3003*a^8*b^8*c^10*d^6 - 3432*a^9*b^7*c^9*d^7 + 3003*a^10*b^6*c^8*d^8 - 2002*a^11*b^5*c^7*d^9 + 1001*a^12*b^4*c^6*d^10 - 364*a^13*b^3*c^5*d^11 + 91*a^14*b^2*c^4*d^12) + (x^(1/2)*(-(a^4*d^9 + 6561*b^4*c^4*d^5 - 2916*a*b^3*c^3*d^6 + 486*a^2*b^2*c^2*d^7 - 36*a^3*b*c*d^8)/(4096*b^12*c^17 + 4096*a^12*c^5*d^12 - 49152*a^11*b*c^6*d^11 + 270336*a^2*b^10*c^15*d^2 - 901120*a^3*b^9*c^14*d^3 + 2027520*a^4*b^8*c^13*d^4 - 3244032*a^5*b^7*c^12*d^5 + 3784704*a^6*b^6*c^11*d^6 - 3244032*a^7*b^5*c^10*d^7 + 2027520*a^8*b^4*c^9*d^8 - 901120*a^9*b^3*c^8*d^9 + 270336*a^10*b^2*c^7*d^10 - 49152*a*b^11*c^16*d))^(1/4)*(4096*a*b^22*c^19*d^4 + 4096*a^19*b^4*c*d^22 - 122880*a^2*b^21*c^18*d^5 + 1486848*a^3*b^20*c^17*d^6 - 9748480*a^4*b^19*c^16*d^7 + 40476672*a^5*b^18*c^15*d^8 - 116785152*a^6*b^17*c^14*d^9 + 249192448*a^7*b^16*c^13*d^10 - 412041216*a^8*b^15*c^12*d^11 + 547700736*a^9*b^14*c^11*d^12 - 600326144*a^10*b^13*c^10*d^13 + 547700736*a^11*b^12*c^9*d^14 - 412041216*a^12*b^11*c^8*d^15 + 249192448*a^13*b^10*c^7*d^16 - 116785152*a^14*b^9*c^6*d^17 + 40476672*a^15*b^8*c^5*d^18 - 9748480*a^16*b^7*c^4*d^19 + 1486848*a^17*b^6*c^3*d^20 - 122880*a^18*b^5*c^2*d^21))/(16*(a^2*b^12*c^14 + a^14*c^2*d^12 - 12*a^3*b^11*c^13*d - 12*a^13*b*c^3*d^11 + 66*a^4*b^10*c^12*d^2 - 220*a^5*b^9*c^11*d^3 + 495*a^6*b^8*c^10*d^4 - 792*a^7*b^7*c^9*d^5 + 924*a^8*b^6*c^8*d^6 - 792*a^9*b^5*c^7*d^7 + 495*a^10*b^4*c^6*d^8 - 220*a^11*b^3*c^5*d^9 + 66*a^12*b^2*c^4*d^10)))*(-(a^4*d^9 + 6561*b^4*c^4*d^5 - 2916*a*b^3*c^3*d^6 + 486*a^2*b^2*c^2*d^7 - 36*a^3*b*c*d^8)/(4096*b^12*c^17 + 4096*a^12*c^5*d^12 - 49152*a^11*b*c^6*d^11 + 270336*a^2*b^10*c^15*d^2 - 901120*a^3*b^9*c^14*d^3 + 2027520*a^4*b^8*c^13*d^4 - 3244032*a^5*b^7*c^12*d^5 + 3784704*a^6*b^6*c^11*d^6 - 3244032*a^7*b^5*c^10*d^7 + 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49152*a*b^11*c^16*d))^(1/4))/(((3645*a^6*b^9*d^15)/32 + (3645*b^15*c^6*d^9)/32 - (49815*a*b^14*c^5*d^10)/16 - (49815*a^5*b^10*c*d^14)/16 + (918675*a^2*b^13*c^4*d^11)/32 - (739025*a^3*b^12*c^3*d^12)/8 + (918675*a^4*b^11*c^2*d^13)/32)/(a^2*b^14*c^16 + a^16*c^2*d^14 - 14*a^3*b^13*c^15*d - 14*a^15*b*c^3*d^13 + 91*a^4*b^12*c^14*d^2 - 364*a^5*b^11*c^13*d^3 + 1001*a^6*b^10*c^12*d^4 - 2002*a^7*b^9*c^11*d^5 + 3003*a^8*b^8*c^10*d^6 - 3432*a^9*b^7*c^9*d^7 + 3003*a^10*b^6*c^8*d^8 - 2002*a^11*b^5*c^7*d^9 + 1001*a^12*b^4*c^6*d^10 - 364*a^13*b^3*c^5*d^11 + 91*a^14*b^2*c^4*d^12) + (((32*a^19*b^4*d^23 + 32*b^23*c^19*d^4 - 1216*a*b^22*c^18*d^5 - 1216*a^18*b^5*c*d^22 + 19040*a^2*b^21*c^17*d^6 - 161664*a^3*b^20*c^16*d^7 + 837408*a^4*b^19*c^15*d^8 - 2842656*a^5*b^18*c^14*d^9 + 6564768*a^6*b^17*c^13*d^10 - 10331040*a^7*b^16*c^12*d^11 + 10374112*a^8*b^15*c^11*d^12 - 4458784*a^9*b^14*c^10*d^13 - 4458784*a^10*b^13*c^9*d^14 + 10374112*a^11*b^12*c^8*d^15 - 10331040*a^12*b^11*c^7*d^16 + 6564768*a^13*b^10*c^6*d^17 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9748480*a^4*b^19*c^16*d^7 + 40476672*a^5*b^18*c^15*d^8 - 116785152*a^6*b^17*c^14*d^9 + 249192448*a^7*b^16*c^13*d^10 - 412041216*a^8*b^15*c^12*d^11 + 547700736*a^9*b^14*c^11*d^12 - 600326144*a^10*b^13*c^10*d^13 + 547700736*a^11*b^12*c^9*d^14 - 412041216*a^12*b^11*c^8*d^15 + 249192448*a^13*b^10*c^7*d^16 - 116785152*a^14*b^9*c^6*d^17 + 40476672*a^15*b^8*c^5*d^18 - 9748480*a^16*b^7*c^4*d^19 + 1486848*a^17*b^6*c^3*d^20 - 122880*a^18*b^5*c^2*d^21))/(16*(a^2*b^12*c^14 + a^14*c^2*d^12 - 12*a^3*b^11*c^13*d - 12*a^13*b*c^3*d^11 + 66*a^4*b^10*c^12*d^2 - 220*a^5*b^9*c^11*d^3 + 495*a^6*b^8*c^10*d^4 - 792*a^7*b^7*c^9*d^5 + 924*a^8*b^6*c^8*d^6 - 792*a^9*b^5*c^7*d^7 + 495*a^10*b^4*c^6*d^8 - 220*a^11*b^3*c^5*d^9 + 66*a^12*b^2*c^4*d^10)))*(-(a^4*d^9 + 6561*b^4*c^4*d^5 - 2916*a*b^3*c^3*d^6 + 486*a^2*b^2*c^2*d^7 - 36*a^3*b*c*d^8)/(4096*b^12*c^17 + 4096*a^12*c^5*d^12 - 49152*a^11*b*c^6*d^11 + 270336*a^2*b^10*c^15*d^2 - 901120*a^3*b^9*c^14*d^3 + 2027520*a^4*b^8*c^13*d^4 - 3244032*a^5*b^7*c^12*d^5 + 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901120*a^9*b^3*c^8*d^9 + 270336*a^10*b^2*c^7*d^10 - 49152*a*b^11*c^16*d))^(1/4) + (((32*a^19*b^4*d^23 + 32*b^23*c^19*d^4 - 1216*a*b^22*c^18*d^5 - 1216*a^18*b^5*c*d^22 + 19040*a^2*b^21*c^17*d^6 - 161664*a^3*b^20*c^16*d^7 + 837408*a^4*b^19*c^15*d^8 - 2842656*a^5*b^18*c^14*d^9 + 6564768*a^6*b^17*c^13*d^10 - 10331040*a^7*b^16*c^12*d^11 + 10374112*a^8*b^15*c^11*d^12 - 4458784*a^9*b^14*c^10*d^13 - 4458784*a^10*b^13*c^9*d^14 + 10374112*a^11*b^12*c^8*d^15 - 10331040*a^12*b^11*c^7*d^16 + 6564768*a^13*b^10*c^6*d^17 - 2842656*a^14*b^9*c^5*d^18 + 837408*a^15*b^8*c^4*d^19 - 161664*a^16*b^7*c^3*d^20 + 19040*a^17*b^6*c^2*d^21)/(a^2*b^14*c^16 + a^16*c^2*d^14 - 14*a^3*b^13*c^15*d - 14*a^15*b*c^3*d^13 + 91*a^4*b^12*c^14*d^2 - 364*a^5*b^11*c^13*d^3 + 1001*a^6*b^10*c^12*d^4 - 2002*a^7*b^9*c^11*d^5 + 3003*a^8*b^8*c^10*d^6 - 3432*a^9*b^7*c^9*d^7 + 3003*a^10*b^6*c^8*d^8 - 2002*a^11*b^5*c^7*d^9 + 1001*a^12*b^4*c^6*d^10 - 364*a^13*b^3*c^5*d^11 + 91*a^14*b^2*c^4*d^12) + (x^(1/2)*(-(a^4*d^9 + 6561*b^4*c^4*d^5 - 2916*a*b^3*c^3*d^6 + 486*a^2*b^2*c^2*d^7 - 36*a^3*b*c*d^8)/(4096*b^12*c^17 + 4096*a^12*c^5*d^12 - 49152*a^11*b*c^6*d^11 + 270336*a^2*b^10*c^15*d^2 - 901120*a^3*b^9*c^14*d^3 + 2027520*a^4*b^8*c^13*d^4 - 3244032*a^5*b^7*c^12*d^5 + 3784704*a^6*b^6*c^11*d^6 - 3244032*a^7*b^5*c^10*d^7 + 2027520*a^8*b^4*c^9*d^8 - 901120*a^9*b^3*c^8*d^9 + 270336*a^10*b^2*c^7*d^10 - 49152*a*b^11*c^16*d))^(1/4)*(4096*a*b^22*c^19*d^4 + 4096*a^19*b^4*c*d^22 - 122880*a^2*b^21*c^18*d^5 + 1486848*a^3*b^20*c^17*d^6 - 9748480*a^4*b^19*c^16*d^7 + 40476672*a^5*b^18*c^15*d^8 - 116785152*a^6*b^17*c^14*d^9 + 249192448*a^7*b^16*c^13*d^10 - 412041216*a^8*b^15*c^12*d^11 + 547700736*a^9*b^14*c^11*d^12 - 600326144*a^10*b^13*c^10*d^13 + 547700736*a^11*b^12*c^9*d^14 - 412041216*a^12*b^11*c^8*d^15 + 249192448*a^13*b^10*c^7*d^16 - 116785152*a^14*b^9*c^6*d^17 + 40476672*a^15*b^8*c^5*d^18 - 9748480*a^16*b^7*c^4*d^19 + 1486848*a^17*b^6*c^3*d^20 - 122880*a^18*b^5*c^2*d^21))/(16*(a^2*b^12*c^14 + a^14*c^2*d^12 - 12*a^3*b^11*c^13*d - 12*a^13*b*c^3*d^11 + 66*a^4*b^10*c^12*d^2 - 220*a^5*b^9*c^11*d^3 + 495*a^6*b^8*c^10*d^4 - 792*a^7*b^7*c^9*d^5 + 924*a^8*b^6*c^8*d^6 - 792*a^9*b^5*c^7*d^7 + 495*a^10*b^4*c^6*d^8 - 220*a^11*b^3*c^5*d^9 + 66*a^12*b^2*c^4*d^10)))*(-(a^4*d^9 + 6561*b^4*c^4*d^5 - 2916*a*b^3*c^3*d^6 + 486*a^2*b^2*c^2*d^7 - 36*a^3*b*c*d^8)/(4096*b^12*c^17 + 4096*a^12*c^5*d^12 - 49152*a^11*b*c^6*d^11 + 270336*a^2*b^10*c^15*d^2 - 901120*a^3*b^9*c^14*d^3 + 2027520*a^4*b^8*c^13*d^4 - 3244032*a^5*b^7*c^12*d^5 + 3784704*a^6*b^6*c^11*d^6 - 3244032*a^7*b^5*c^10*d^7 + 2027520*a^8*b^4*c^9*d^8 - 901120*a^9*b^3*c^8*d^9 + 270336*a^10*b^2*c^7*d^10 - 49152*a*b^11*c^16*d))^(3/4) + (x^(1/2)*(81*a^7*b^8*d^15 + 81*b^15*c^7*d^8 + 3627*a*b^14*c^6*d^9 + 3627*a^6*b^9*c*d^14 - 80999*a^2*b^13*c^5*d^10 + 339435*a^3*b^12*c^4*d^11 + 339435*a^4*b^11*c^3*d^12 - 80999*a^5*b^10*c^2*d^13))/(16*(a^2*b^12*c^14 + a^14*c^2*d^12 - 12*a^3*b^11*c^13*d - 12*a^13*b*c^3*d^11 + 66*a^4*b^10*c^12*d^2 - 220*a^5*b^9*c^11*d^3 + 495*a^6*b^8*c^10*d^4 - 792*a^7*b^7*c^9*d^5 + 924*a^8*b^6*c^8*d^6 - 792*a^9*b^5*c^7*d^7 + 495*a^10*b^4*c^6*d^8 - 220*a^11*b^3*c^5*d^9 + 66*a^12*b^2*c^4*d^10)))*(-(a^4*d^9 + 6561*b^4*c^4*d^5 - 2916*a*b^3*c^3*d^6 + 486*a^2*b^2*c^2*d^7 - 36*a^3*b*c*d^8)/(4096*b^12*c^17 + 4096*a^12*c^5*d^12 - 49152*a^11*b*c^6*d^11 + 270336*a^2*b^10*c^15*d^2 - 901120*a^3*b^9*c^14*d^3 + 2027520*a^4*b^8*c^13*d^4 - 3244032*a^5*b^7*c^12*d^5 + 3784704*a^6*b^6*c^11*d^6 - 3244032*a^7*b^5*c^10*d^7 + 2027520*a^8*b^4*c^9*d^8 - 901120*a^9*b^3*c^8*d^9 + 270336*a^10*b^2*c^7*d^10 - 49152*a*b^11*c^16*d))^(1/4)))*(-(a^4*d^9 + 6561*b^4*c^4*d^5 - 2916*a*b^3*c^3*d^6 + 486*a^2*b^2*c^2*d^7 - 36*a^3*b*c*d^8)/(4096*b^12*c^17 + 4096*a^12*c^5*d^12 - 49152*a^11*b*c^6*d^11 + 270336*a^2*b^10*c^15*d^2 - 901120*a^3*b^9*c^14*d^3 + 2027520*a^4*b^8*c^13*d^4 - 3244032*a^5*b^7*c^12*d^5 + 3784704*a^6*b^6*c^11*d^6 - 3244032*a^7*b^5*c^10*d^7 + 2027520*a^8*b^4*c^9*d^8 - 901120*a^9*b^3*c^8*d^9 + 270336*a^10*b^2*c^7*d^10 - 49152*a*b^11*c^16*d))^(1/4)*2i + ((x^(3/2)*(a^2*d^2 + b^2*c^2))/(2*a*c*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) + (b*d*x^(7/2)*(a*d + b*c))/(2*a*c*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)))/(a*c + x^2*(a*d + b*c) + b*d*x^4) - atan(((((32*a^19*b^4*d^23 + 32*b^23*c^19*d^4 - 1216*a*b^22*c^18*d^5 - 1216*a^18*b^5*c*d^22 + 19040*a^2*b^21*c^17*d^6 - 161664*a^3*b^20*c^16*d^7 + 837408*a^4*b^19*c^15*d^8 - 2842656*a^5*b^18*c^14*d^9 + 6564768*a^6*b^17*c^13*d^10 - 10331040*a^7*b^16*c^12*d^11 + 10374112*a^8*b^15*c^11*d^12 - 4458784*a^9*b^14*c^10*d^13 - 4458784*a^10*b^13*c^9*d^14 + 10374112*a^11*b^12*c^8*d^15 - 10331040*a^12*b^11*c^7*d^16 + 6564768*a^13*b^10*c^6*d^17 - 2842656*a^14*b^9*c^5*d^18 + 837408*a^15*b^8*c^4*d^19 - 161664*a^16*b^7*c^3*d^20 + 19040*a^17*b^6*c^2*d^21)/(a^2*b^14*c^16 + a^16*c^2*d^14 - 14*a^3*b^13*c^15*d - 14*a^15*b*c^3*d^13 + 91*a^4*b^12*c^14*d^2 - 364*a^5*b^11*c^13*d^3 + 1001*a^6*b^10*c^12*d^4 - 2002*a^7*b^9*c^11*d^5 + 3003*a^8*b^8*c^10*d^6 - 3432*a^9*b^7*c^9*d^7 + 3003*a^10*b^6*c^8*d^8 - 2002*a^11*b^5*c^7*d^9 + 1001*a^12*b^4*c^6*d^10 - 364*a^13*b^3*c^5*d^11 + 91*a^14*b^2*c^4*d^12) - (x^(1/2)*(-(b^9*c^4 + 6561*a^4*b^5*d^4 - 2916*a^3*b^6*c*d^3 + 486*a^2*b^7*c^2*d^2 - 36*a*b^8*c^3*d)/(4096*a^17*d^12 + 4096*a^5*b^12*c^12 - 49152*a^6*b^11*c^11*d + 270336*a^7*b^10*c^10*d^2 - 901120*a^8*b^9*c^9*d^3 + 2027520*a^9*b^8*c^8*d^4 - 3244032*a^10*b^7*c^7*d^5 + 3784704*a^11*b^6*c^6*d^6 - 3244032*a^12*b^5*c^5*d^7 + 2027520*a^13*b^4*c^4*d^8 - 901120*a^14*b^3*c^3*d^9 + 270336*a^15*b^2*c^2*d^10 - 49152*a^16*b*c*d^11))^(1/4)*(4096*a*b^22*c^19*d^4 + 4096*a^19*b^4*c*d^22 - 122880*a^2*b^21*c^18*d^5 + 1486848*a^3*b^20*c^17*d^6 - 9748480*a^4*b^19*c^16*d^7 + 40476672*a^5*b^18*c^15*d^8 - 116785152*a^6*b^17*c^14*d^9 + 249192448*a^7*b^16*c^13*d^10 - 412041216*a^8*b^15*c^12*d^11 + 547700736*a^9*b^14*c^11*d^12 - 600326144*a^10*b^13*c^10*d^13 + 547700736*a^11*b^12*c^9*d^14 - 412041216*a^12*b^11*c^8*d^15 + 249192448*a^13*b^10*c^7*d^16 - 116785152*a^14*b^9*c^6*d^17 + 40476672*a^15*b^8*c^5*d^18 - 9748480*a^16*b^7*c^4*d^19 + 1486848*a^17*b^6*c^3*d^20 - 122880*a^18*b^5*c^2*d^21))/(16*(a^2*b^12*c^14 + a^14*c^2*d^12 - 12*a^3*b^11*c^13*d - 12*a^13*b*c^3*d^11 + 66*a^4*b^10*c^12*d^2 - 220*a^5*b^9*c^11*d^3 + 495*a^6*b^8*c^10*d^4 - 792*a^7*b^7*c^9*d^5 + 924*a^8*b^6*c^8*d^6 - 792*a^9*b^5*c^7*d^7 + 495*a^10*b^4*c^6*d^8 - 220*a^11*b^3*c^5*d^9 + 66*a^12*b^2*c^4*d^10)))*(-(b^9*c^4 + 6561*a^4*b^5*d^4 - 2916*a^3*b^6*c*d^3 + 486*a^2*b^7*c^2*d^2 - 36*a*b^8*c^3*d)/(4096*a^17*d^12 + 4096*a^5*b^12*c^12 - 49152*a^6*b^11*c^11*d + 270336*a^7*b^10*c^10*d^2 - 901120*a^8*b^9*c^9*d^3 + 2027520*a^9*b^8*c^8*d^4 - 3244032*a^10*b^7*c^7*d^5 + 3784704*a^11*b^6*c^6*d^6 - 3244032*a^12*b^5*c^5*d^7 + 2027520*a^13*b^4*c^4*d^8 - 901120*a^14*b^3*c^3*d^9 + 270336*a^15*b^2*c^2*d^10 - 49152*a^16*b*c*d^11))^(3/4)*1i - (x^(1/2)*(81*a^7*b^8*d^15 + 81*b^15*c^7*d^8 + 3627*a*b^14*c^6*d^9 + 3627*a^6*b^9*c*d^14 - 80999*a^2*b^13*c^5*d^10 + 339435*a^3*b^12*c^4*d^11 + 339435*a^4*b^11*c^3*d^12 - 80999*a^5*b^10*c^2*d^13)*1i)/(16*(a^2*b^12*c^14 + a^14*c^2*d^12 - 12*a^3*b^11*c^13*d - 12*a^13*b*c^3*d^11 + 66*a^4*b^10*c^12*d^2 - 220*a^5*b^9*c^11*d^3 + 495*a^6*b^8*c^10*d^4 - 792*a^7*b^7*c^9*d^5 + 924*a^8*b^6*c^8*d^6 - 792*a^9*b^5*c^7*d^7 + 495*a^10*b^4*c^6*d^8 - 220*a^11*b^3*c^5*d^9 + 66*a^12*b^2*c^4*d^10)))*(-(b^9*c^4 + 6561*a^4*b^5*d^4 - 2916*a^3*b^6*c*d^3 + 486*a^2*b^7*c^2*d^2 - 36*a*b^8*c^3*d)/(4096*a^17*d^12 + 4096*a^5*b^12*c^12 - 49152*a^6*b^11*c^11*d + 270336*a^7*b^10*c^10*d^2 - 901120*a^8*b^9*c^9*d^3 + 2027520*a^9*b^8*c^8*d^4 - 3244032*a^10*b^7*c^7*d^5 + 3784704*a^11*b^6*c^6*d^6 - 3244032*a^12*b^5*c^5*d^7 + 2027520*a^13*b^4*c^4*d^8 - 901120*a^14*b^3*c^3*d^9 + 270336*a^15*b^2*c^2*d^10 - 49152*a^16*b*c*d^11))^(1/4) - (((32*a^19*b^4*d^23 + 32*b^23*c^19*d^4 - 1216*a*b^22*c^18*d^5 - 1216*a^18*b^5*c*d^22 + 19040*a^2*b^21*c^17*d^6 - 161664*a^3*b^20*c^16*d^7 + 837408*a^4*b^19*c^15*d^8 - 2842656*a^5*b^18*c^14*d^9 + 6564768*a^6*b^17*c^13*d^10 - 10331040*a^7*b^16*c^12*d^11 + 10374112*a^8*b^15*c^11*d^12 - 4458784*a^9*b^14*c^10*d^13 - 4458784*a^10*b^13*c^9*d^14 + 10374112*a^11*b^12*c^8*d^15 - 10331040*a^12*b^11*c^7*d^16 + 6564768*a^13*b^10*c^6*d^17 - 2842656*a^14*b^9*c^5*d^18 + 837408*a^15*b^8*c^4*d^19 - 161664*a^16*b^7*c^3*d^20 + 19040*a^17*b^6*c^2*d^21)/(a^2*b^14*c^16 + a^16*c^2*d^14 - 14*a^3*b^13*c^15*d - 14*a^15*b*c^3*d^13 + 91*a^4*b^12*c^14*d^2 - 364*a^5*b^11*c^13*d^3 + 1001*a^6*b^10*c^12*d^4 - 2002*a^7*b^9*c^11*d^5 + 3003*a^8*b^8*c^10*d^6 - 3432*a^9*b^7*c^9*d^7 + 3003*a^10*b^6*c^8*d^8 - 2002*a^11*b^5*c^7*d^9 + 1001*a^12*b^4*c^6*d^10 - 364*a^13*b^3*c^5*d^11 + 91*a^14*b^2*c^4*d^12) + (x^(1/2)*(-(b^9*c^4 + 6561*a^4*b^5*d^4 - 2916*a^3*b^6*c*d^3 + 486*a^2*b^7*c^2*d^2 - 36*a*b^8*c^3*d)/(4096*a^17*d^12 + 4096*a^5*b^12*c^12 - 49152*a^6*b^11*c^11*d + 270336*a^7*b^10*c^10*d^2 - 901120*a^8*b^9*c^9*d^3 + 2027520*a^9*b^8*c^8*d^4 - 3244032*a^10*b^7*c^7*d^5 + 3784704*a^11*b^6*c^6*d^6 - 3244032*a^12*b^5*c^5*d^7 + 2027520*a^13*b^4*c^4*d^8 - 901120*a^14*b^3*c^3*d^9 + 270336*a^15*b^2*c^2*d^10 - 49152*a^16*b*c*d^11))^(1/4)*(4096*a*b^22*c^19*d^4 + 4096*a^19*b^4*c*d^22 - 122880*a^2*b^21*c^18*d^5 + 1486848*a^3*b^20*c^17*d^6 - 9748480*a^4*b^19*c^16*d^7 + 40476672*a^5*b^18*c^15*d^8 - 116785152*a^6*b^17*c^14*d^9 + 249192448*a^7*b^16*c^13*d^10 - 412041216*a^8*b^15*c^12*d^11 + 547700736*a^9*b^14*c^11*d^12 - 600326144*a^10*b^13*c^10*d^13 + 547700736*a^11*b^12*c^9*d^14 - 412041216*a^12*b^11*c^8*d^15 + 249192448*a^13*b^10*c^7*d^16 - 116785152*a^14*b^9*c^6*d^17 + 40476672*a^15*b^8*c^5*d^18 - 9748480*a^16*b^7*c^4*d^19 + 1486848*a^17*b^6*c^3*d^20 - 122880*a^18*b^5*c^2*d^21))/(16*(a^2*b^12*c^14 + a^14*c^2*d^12 - 12*a^3*b^11*c^13*d - 12*a^13*b*c^3*d^11 + 66*a^4*b^10*c^12*d^2 - 220*a^5*b^9*c^11*d^3 + 495*a^6*b^8*c^10*d^4 - 792*a^7*b^7*c^9*d^5 + 924*a^8*b^6*c^8*d^6 - 792*a^9*b^5*c^7*d^7 + 495*a^10*b^4*c^6*d^8 - 220*a^11*b^3*c^5*d^9 + 66*a^12*b^2*c^4*d^10)))*(-(b^9*c^4 + 6561*a^4*b^5*d^4 - 2916*a^3*b^6*c*d^3 + 486*a^2*b^7*c^2*d^2 - 36*a*b^8*c^3*d)/(4096*a^17*d^12 + 4096*a^5*b^12*c^12 - 49152*a^6*b^11*c^11*d + 270336*a^7*b^10*c^10*d^2 - 901120*a^8*b^9*c^9*d^3 + 2027520*a^9*b^8*c^8*d^4 - 3244032*a^10*b^7*c^7*d^5 + 3784704*a^11*b^6*c^6*d^6 - 3244032*a^12*b^5*c^5*d^7 + 2027520*a^13*b^4*c^4*d^8 - 901120*a^14*b^3*c^3*d^9 + 270336*a^15*b^2*c^2*d^10 - 49152*a^16*b*c*d^11))^(3/4)*1i + (x^(1/2)*(81*a^7*b^8*d^15 + 81*b^15*c^7*d^8 + 3627*a*b^14*c^6*d^9 + 3627*a^6*b^9*c*d^14 - 80999*a^2*b^13*c^5*d^10 + 339435*a^3*b^12*c^4*d^11 + 339435*a^4*b^11*c^3*d^12 - 80999*a^5*b^10*c^2*d^13)*1i)/(16*(a^2*b^12*c^14 + a^14*c^2*d^12 - 12*a^3*b^11*c^13*d - 12*a^13*b*c^3*d^11 + 66*a^4*b^10*c^12*d^2 - 220*a^5*b^9*c^11*d^3 + 495*a^6*b^8*c^10*d^4 - 792*a^7*b^7*c^9*d^5 + 924*a^8*b^6*c^8*d^6 - 792*a^9*b^5*c^7*d^7 + 495*a^10*b^4*c^6*d^8 - 220*a^11*b^3*c^5*d^9 + 66*a^12*b^2*c^4*d^10)))*(-(b^9*c^4 + 6561*a^4*b^5*d^4 - 2916*a^3*b^6*c*d^3 + 486*a^2*b^7*c^2*d^2 - 36*a*b^8*c^3*d)/(4096*a^17*d^12 + 4096*a^5*b^12*c^12 - 49152*a^6*b^11*c^11*d + 270336*a^7*b^10*c^10*d^2 - 901120*a^8*b^9*c^9*d^3 + 2027520*a^9*b^8*c^8*d^4 - 3244032*a^10*b^7*c^7*d^5 + 3784704*a^11*b^6*c^6*d^6 - 3244032*a^12*b^5*c^5*d^7 + 2027520*a^13*b^4*c^4*d^8 - 901120*a^14*b^3*c^3*d^9 + 270336*a^15*b^2*c^2*d^10 - 49152*a^16*b*c*d^11))^(1/4))/(((3645*a^6*b^9*d^15)/32 + (3645*b^15*c^6*d^9)/32 - (49815*a*b^14*c^5*d^10)/16 - (49815*a^5*b^10*c*d^14)/16 + (918675*a^2*b^13*c^4*d^11)/32 - (739025*a^3*b^12*c^3*d^12)/8 + (918675*a^4*b^11*c^2*d^13)/32)/(a^2*b^14*c^16 + a^16*c^2*d^14 - 14*a^3*b^13*c^15*d - 14*a^15*b*c^3*d^13 + 91*a^4*b^12*c^14*d^2 - 364*a^5*b^11*c^13*d^3 + 1001*a^6*b^10*c^12*d^4 - 2002*a^7*b^9*c^11*d^5 + 3003*a^8*b^8*c^10*d^6 - 3432*a^9*b^7*c^9*d^7 + 3003*a^10*b^6*c^8*d^8 - 2002*a^11*b^5*c^7*d^9 + 1001*a^12*b^4*c^6*d^10 - 364*a^13*b^3*c^5*d^11 + 91*a^14*b^2*c^4*d^12) + (((32*a^19*b^4*d^23 + 32*b^23*c^19*d^4 - 1216*a*b^22*c^18*d^5 - 1216*a^18*b^5*c*d^22 + 19040*a^2*b^21*c^17*d^6 - 161664*a^3*b^20*c^16*d^7 + 837408*a^4*b^19*c^15*d^8 - 2842656*a^5*b^18*c^14*d^9 + 6564768*a^6*b^17*c^13*d^10 - 10331040*a^7*b^16*c^12*d^11 + 10374112*a^8*b^15*c^11*d^12 - 4458784*a^9*b^14*c^10*d^13 - 4458784*a^10*b^13*c^9*d^14 + 10374112*a^11*b^12*c^8*d^15 - 10331040*a^12*b^11*c^7*d^16 + 6564768*a^13*b^10*c^6*d^17 - 2842656*a^14*b^9*c^5*d^18 + 837408*a^15*b^8*c^4*d^19 - 161664*a^16*b^7*c^3*d^20 + 19040*a^17*b^6*c^2*d^21)/(a^2*b^14*c^16 + a^16*c^2*d^14 - 14*a^3*b^13*c^15*d - 14*a^15*b*c^3*d^13 + 91*a^4*b^12*c^14*d^2 - 364*a^5*b^11*c^13*d^3 + 1001*a^6*b^10*c^12*d^4 - 2002*a^7*b^9*c^11*d^5 + 3003*a^8*b^8*c^10*d^6 - 3432*a^9*b^7*c^9*d^7 + 3003*a^10*b^6*c^8*d^8 - 2002*a^11*b^5*c^7*d^9 + 1001*a^12*b^4*c^6*d^10 - 364*a^13*b^3*c^5*d^11 + 91*a^14*b^2*c^4*d^12) - (x^(1/2)*(-(b^9*c^4 + 6561*a^4*b^5*d^4 - 2916*a^3*b^6*c*d^3 + 486*a^2*b^7*c^2*d^2 - 36*a*b^8*c^3*d)/(4096*a^17*d^12 + 4096*a^5*b^12*c^12 - 49152*a^6*b^11*c^11*d + 270336*a^7*b^10*c^10*d^2 - 901120*a^8*b^9*c^9*d^3 + 2027520*a^9*b^8*c^8*d^4 - 3244032*a^10*b^7*c^7*d^5 + 3784704*a^11*b^6*c^6*d^6 - 3244032*a^12*b^5*c^5*d^7 + 2027520*a^13*b^4*c^4*d^8 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116785152*a^14*b^9*c^6*d^17 + 40476672*a^15*b^8*c^5*d^18 - 9748480*a^16*b^7*c^4*d^19 + 1486848*a^17*b^6*c^3*d^20 - 122880*a^18*b^5*c^2*d^21))/(16*(a^2*b^12*c^14 + a^14*c^2*d^12 - 12*a^3*b^11*c^13*d - 12*a^13*b*c^3*d^11 + 66*a^4*b^10*c^12*d^2 - 220*a^5*b^9*c^11*d^3 + 495*a^6*b^8*c^10*d^4 - 792*a^7*b^7*c^9*d^5 + 924*a^8*b^6*c^8*d^6 - 792*a^9*b^5*c^7*d^7 + 495*a^10*b^4*c^6*d^8 - 220*a^11*b^3*c^5*d^9 + 66*a^12*b^2*c^4*d^10)))*(-(b^9*c^4 + 6561*a^4*b^5*d^4 - 2916*a^3*b^6*c*d^3 + 486*a^2*b^7*c^2*d^2 - 36*a*b^8*c^3*d)/(4096*a^17*d^12 + 4096*a^5*b^12*c^12 - 49152*a^6*b^11*c^11*d + 270336*a^7*b^10*c^10*d^2 - 901120*a^8*b^9*c^9*d^3 + 2027520*a^9*b^8*c^8*d^4 - 3244032*a^10*b^7*c^7*d^5 + 3784704*a^11*b^6*c^6*d^6 - 3244032*a^12*b^5*c^5*d^7 + 2027520*a^13*b^4*c^4*d^8 - 901120*a^14*b^3*c^3*d^9 + 270336*a^15*b^2*c^2*d^10 - 49152*a^16*b*c*d^11))^(3/4) + (x^(1/2)*(81*a^7*b^8*d^15 + 81*b^15*c^7*d^8 + 3627*a*b^14*c^6*d^9 + 3627*a^6*b^9*c*d^14 - 80999*a^2*b^13*c^5*d^10 + 339435*a^3*b^12*c^4*d^11 + 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3244032*a^10*b^7*c^7*d^5 + 3784704*a^11*b^6*c^6*d^6 - 3244032*a^12*b^5*c^5*d^7 + 2027520*a^13*b^4*c^4*d^8 - 901120*a^14*b^3*c^3*d^9 + 270336*a^15*b^2*c^2*d^10 - 49152*a^16*b*c*d^11))^(1/4)*2i + 2*atan((((((32*a^19*b^4*d^23 + 32*b^23*c^19*d^4 - 1216*a*b^22*c^18*d^5 - 1216*a^18*b^5*c*d^22 + 19040*a^2*b^21*c^17*d^6 - 161664*a^3*b^20*c^16*d^7 + 837408*a^4*b^19*c^15*d^8 - 2842656*a^5*b^18*c^14*d^9 + 6564768*a^6*b^17*c^13*d^10 - 10331040*a^7*b^16*c^12*d^11 + 10374112*a^8*b^15*c^11*d^12 - 4458784*a^9*b^14*c^10*d^13 - 4458784*a^10*b^13*c^9*d^14 + 10374112*a^11*b^12*c^8*d^15 - 10331040*a^12*b^11*c^7*d^16 + 6564768*a^13*b^10*c^6*d^17 - 2842656*a^14*b^9*c^5*d^18 + 837408*a^15*b^8*c^4*d^19 - 161664*a^16*b^7*c^3*d^20 + 19040*a^17*b^6*c^2*d^21)*1i)/(a^2*b^14*c^16 + a^16*c^2*d^14 - 14*a^3*b^13*c^15*d - 14*a^15*b*c^3*d^13 + 91*a^4*b^12*c^14*d^2 - 364*a^5*b^11*c^13*d^3 + 1001*a^6*b^10*c^12*d^4 - 2002*a^7*b^9*c^11*d^5 + 3003*a^8*b^8*c^10*d^6 - 3432*a^9*b^7*c^9*d^7 + 3003*a^10*b^6*c^8*d^8 - 2002*a^11*b^5*c^7*d^9 + 1001*a^12*b^4*c^6*d^10 - 364*a^13*b^3*c^5*d^11 + 91*a^14*b^2*c^4*d^12) - (x^(1/2)*(-(b^9*c^4 + 6561*a^4*b^5*d^4 - 2916*a^3*b^6*c*d^3 + 486*a^2*b^7*c^2*d^2 - 36*a*b^8*c^3*d)/(4096*a^17*d^12 + 4096*a^5*b^12*c^12 - 49152*a^6*b^11*c^11*d + 270336*a^7*b^10*c^10*d^2 - 901120*a^8*b^9*c^9*d^3 + 2027520*a^9*b^8*c^8*d^4 - 3244032*a^10*b^7*c^7*d^5 + 3784704*a^11*b^6*c^6*d^6 - 3244032*a^12*b^5*c^5*d^7 + 2027520*a^13*b^4*c^4*d^8 - 901120*a^14*b^3*c^3*d^9 + 270336*a^15*b^2*c^2*d^10 - 49152*a^16*b*c*d^11))^(1/4)*(4096*a*b^22*c^19*d^4 + 4096*a^19*b^4*c*d^22 - 122880*a^2*b^21*c^18*d^5 + 1486848*a^3*b^20*c^17*d^6 - 9748480*a^4*b^19*c^16*d^7 + 40476672*a^5*b^18*c^15*d^8 - 116785152*a^6*b^17*c^14*d^9 + 249192448*a^7*b^16*c^13*d^10 - 412041216*a^8*b^15*c^12*d^11 + 547700736*a^9*b^14*c^11*d^12 - 600326144*a^10*b^13*c^10*d^13 + 547700736*a^11*b^12*c^9*d^14 - 412041216*a^12*b^11*c^8*d^15 + 249192448*a^13*b^10*c^7*d^16 - 116785152*a^14*b^9*c^6*d^17 + 40476672*a^15*b^8*c^5*d^18 - 9748480*a^16*b^7*c^4*d^19 + 1486848*a^17*b^6*c^3*d^20 - 122880*a^18*b^5*c^2*d^21))/(16*(a^2*b^12*c^14 + a^14*c^2*d^12 - 12*a^3*b^11*c^13*d - 12*a^13*b*c^3*d^11 + 66*a^4*b^10*c^12*d^2 - 220*a^5*b^9*c^11*d^3 + 495*a^6*b^8*c^10*d^4 - 792*a^7*b^7*c^9*d^5 + 924*a^8*b^6*c^8*d^6 - 792*a^9*b^5*c^7*d^7 + 495*a^10*b^4*c^6*d^8 - 220*a^11*b^3*c^5*d^9 + 66*a^12*b^2*c^4*d^10)))*(-(b^9*c^4 + 6561*a^4*b^5*d^4 - 2916*a^3*b^6*c*d^3 + 486*a^2*b^7*c^2*d^2 - 36*a*b^8*c^3*d)/(4096*a^17*d^12 + 4096*a^5*b^12*c^12 - 49152*a^6*b^11*c^11*d + 270336*a^7*b^10*c^10*d^2 - 901120*a^8*b^9*c^9*d^3 + 2027520*a^9*b^8*c^8*d^4 - 3244032*a^10*b^7*c^7*d^5 + 3784704*a^11*b^6*c^6*d^6 - 3244032*a^12*b^5*c^5*d^7 + 2027520*a^13*b^4*c^4*d^8 - 901120*a^14*b^3*c^3*d^9 + 270336*a^15*b^2*c^2*d^10 - 49152*a^16*b*c*d^11))^(3/4) - (x^(1/2)*(81*a^7*b^8*d^15 + 81*b^15*c^7*d^8 + 3627*a*b^14*c^6*d^9 + 3627*a^6*b^9*c*d^14 - 80999*a^2*b^13*c^5*d^10 + 339435*a^3*b^12*c^4*d^11 + 339435*a^4*b^11*c^3*d^12 - 80999*a^5*b^10*c^2*d^13))/(16*(a^2*b^12*c^14 + a^14*c^2*d^12 - 12*a^3*b^11*c^13*d - 12*a^13*b*c^3*d^11 + 66*a^4*b^10*c^12*d^2 - 220*a^5*b^9*c^11*d^3 + 495*a^6*b^8*c^10*d^4 - 792*a^7*b^7*c^9*d^5 + 924*a^8*b^6*c^8*d^6 - 792*a^9*b^5*c^7*d^7 + 495*a^10*b^4*c^6*d^8 - 220*a^11*b^3*c^5*d^9 + 66*a^12*b^2*c^4*d^10)))*(-(b^9*c^4 + 6561*a^4*b^5*d^4 - 2916*a^3*b^6*c*d^3 + 486*a^2*b^7*c^2*d^2 - 36*a*b^8*c^3*d)/(4096*a^17*d^12 + 4096*a^5*b^12*c^12 - 49152*a^6*b^11*c^11*d + 270336*a^7*b^10*c^10*d^2 - 901120*a^8*b^9*c^9*d^3 + 2027520*a^9*b^8*c^8*d^4 - 3244032*a^10*b^7*c^7*d^5 + 3784704*a^11*b^6*c^6*d^6 - 3244032*a^12*b^5*c^5*d^7 + 2027520*a^13*b^4*c^4*d^8 - 901120*a^14*b^3*c^3*d^9 + 270336*a^15*b^2*c^2*d^10 - 49152*a^16*b*c*d^11))^(1/4) - ((((32*a^19*b^4*d^23 + 32*b^23*c^19*d^4 - 1216*a*b^22*c^18*d^5 - 1216*a^18*b^5*c*d^22 + 19040*a^2*b^21*c^17*d^6 - 161664*a^3*b^20*c^16*d^7 + 837408*a^4*b^19*c^15*d^8 - 2842656*a^5*b^18*c^14*d^9 + 6564768*a^6*b^17*c^13*d^10 - 10331040*a^7*b^16*c^12*d^11 + 10374112*a^8*b^15*c^11*d^12 - 4458784*a^9*b^14*c^10*d^13 - 4458784*a^10*b^13*c^9*d^14 + 10374112*a^11*b^12*c^8*d^15 - 10331040*a^12*b^11*c^7*d^16 + 6564768*a^13*b^10*c^6*d^17 - 2842656*a^14*b^9*c^5*d^18 + 837408*a^15*b^8*c^4*d^19 - 161664*a^16*b^7*c^3*d^20 + 19040*a^17*b^6*c^2*d^21)*1i)/(a^2*b^14*c^16 + a^16*c^2*d^14 - 14*a^3*b^13*c^15*d - 14*a^15*b*c^3*d^13 + 91*a^4*b^12*c^14*d^2 - 364*a^5*b^11*c^13*d^3 + 1001*a^6*b^10*c^12*d^4 - 2002*a^7*b^9*c^11*d^5 + 3003*a^8*b^8*c^10*d^6 - 3432*a^9*b^7*c^9*d^7 + 3003*a^10*b^6*c^8*d^8 - 2002*a^11*b^5*c^7*d^9 + 1001*a^12*b^4*c^6*d^10 - 364*a^13*b^3*c^5*d^11 + 91*a^14*b^2*c^4*d^12) + (x^(1/2)*(-(b^9*c^4 + 6561*a^4*b^5*d^4 - 2916*a^3*b^6*c*d^3 + 486*a^2*b^7*c^2*d^2 - 36*a*b^8*c^3*d)/(4096*a^17*d^12 + 4096*a^5*b^12*c^12 - 49152*a^6*b^11*c^11*d + 270336*a^7*b^10*c^10*d^2 - 901120*a^8*b^9*c^9*d^3 + 2027520*a^9*b^8*c^8*d^4 - 3244032*a^10*b^7*c^7*d^5 + 3784704*a^11*b^6*c^6*d^6 - 3244032*a^12*b^5*c^5*d^7 + 2027520*a^13*b^4*c^4*d^8 - 901120*a^14*b^3*c^3*d^9 + 270336*a^15*b^2*c^2*d^10 - 49152*a^16*b*c*d^11))^(1/4)*(4096*a*b^22*c^19*d^4 + 4096*a^19*b^4*c*d^22 - 122880*a^2*b^21*c^18*d^5 + 1486848*a^3*b^20*c^17*d^6 - 9748480*a^4*b^19*c^16*d^7 + 40476672*a^5*b^18*c^15*d^8 - 116785152*a^6*b^17*c^14*d^9 + 249192448*a^7*b^16*c^13*d^10 - 412041216*a^8*b^15*c^12*d^11 + 547700736*a^9*b^14*c^11*d^12 - 600326144*a^10*b^13*c^10*d^13 + 547700736*a^11*b^12*c^9*d^14 - 412041216*a^12*b^11*c^8*d^15 + 249192448*a^13*b^10*c^7*d^16 - 116785152*a^14*b^9*c^6*d^17 + 40476672*a^15*b^8*c^5*d^18 - 9748480*a^16*b^7*c^4*d^19 + 1486848*a^17*b^6*c^3*d^20 - 122880*a^18*b^5*c^2*d^21))/(16*(a^2*b^12*c^14 + a^14*c^2*d^12 - 12*a^3*b^11*c^13*d - 12*a^13*b*c^3*d^11 + 66*a^4*b^10*c^12*d^2 - 220*a^5*b^9*c^11*d^3 + 495*a^6*b^8*c^10*d^4 - 792*a^7*b^7*c^9*d^5 + 924*a^8*b^6*c^8*d^6 - 792*a^9*b^5*c^7*d^7 + 495*a^10*b^4*c^6*d^8 - 220*a^11*b^3*c^5*d^9 + 66*a^12*b^2*c^4*d^10)))*(-(b^9*c^4 + 6561*a^4*b^5*d^4 - 2916*a^3*b^6*c*d^3 + 486*a^2*b^7*c^2*d^2 - 36*a*b^8*c^3*d)/(4096*a^17*d^12 + 4096*a^5*b^12*c^12 - 49152*a^6*b^11*c^11*d + 270336*a^7*b^10*c^10*d^2 - 901120*a^8*b^9*c^9*d^3 + 2027520*a^9*b^8*c^8*d^4 - 3244032*a^10*b^7*c^7*d^5 + 3784704*a^11*b^6*c^6*d^6 - 3244032*a^12*b^5*c^5*d^7 + 2027520*a^13*b^4*c^4*d^8 - 901120*a^14*b^3*c^3*d^9 + 270336*a^15*b^2*c^2*d^10 - 49152*a^16*b*c*d^11))^(3/4) + (x^(1/2)*(81*a^7*b^8*d^15 + 81*b^15*c^7*d^8 + 3627*a*b^14*c^6*d^9 + 3627*a^6*b^9*c*d^14 - 80999*a^2*b^13*c^5*d^10 + 339435*a^3*b^12*c^4*d^11 + 339435*a^4*b^11*c^3*d^12 - 80999*a^5*b^10*c^2*d^13))/(16*(a^2*b^12*c^14 + a^14*c^2*d^12 - 12*a^3*b^11*c^13*d - 12*a^13*b*c^3*d^11 + 66*a^4*b^10*c^12*d^2 - 220*a^5*b^9*c^11*d^3 + 495*a^6*b^8*c^10*d^4 - 792*a^7*b^7*c^9*d^5 + 924*a^8*b^6*c^8*d^6 - 792*a^9*b^5*c^7*d^7 + 495*a^10*b^4*c^6*d^8 - 220*a^11*b^3*c^5*d^9 + 66*a^12*b^2*c^4*d^10)))*(-(b^9*c^4 + 6561*a^4*b^5*d^4 - 2916*a^3*b^6*c*d^3 + 486*a^2*b^7*c^2*d^2 - 36*a*b^8*c^3*d)/(4096*a^17*d^12 + 4096*a^5*b^12*c^12 - 49152*a^6*b^11*c^11*d + 270336*a^7*b^10*c^10*d^2 - 901120*a^8*b^9*c^9*d^3 + 2027520*a^9*b^8*c^8*d^4 - 3244032*a^10*b^7*c^7*d^5 + 3784704*a^11*b^6*c^6*d^6 - 3244032*a^12*b^5*c^5*d^7 + 2027520*a^13*b^4*c^4*d^8 - 901120*a^14*b^3*c^3*d^9 + 270336*a^15*b^2*c^2*d^10 - 49152*a^16*b*c*d^11))^(1/4))/(((((32*a^19*b^4*d^23 + 32*b^23*c^19*d^4 - 1216*a*b^22*c^18*d^5 - 1216*a^18*b^5*c*d^22 + 19040*a^2*b^21*c^17*d^6 - 161664*a^3*b^20*c^16*d^7 + 837408*a^4*b^19*c^15*d^8 - 2842656*a^5*b^18*c^14*d^9 + 6564768*a^6*b^17*c^13*d^10 - 10331040*a^7*b^16*c^12*d^11 + 10374112*a^8*b^15*c^11*d^12 - 4458784*a^9*b^14*c^10*d^13 - 4458784*a^10*b^13*c^9*d^14 + 10374112*a^11*b^12*c^8*d^15 - 10331040*a^12*b^11*c^7*d^16 + 6564768*a^13*b^10*c^6*d^17 - 2842656*a^14*b^9*c^5*d^18 + 837408*a^15*b^8*c^4*d^19 - 161664*a^16*b^7*c^3*d^20 + 19040*a^17*b^6*c^2*d^21)*1i)/(a^2*b^14*c^16 + a^16*c^2*d^14 - 14*a^3*b^13*c^15*d - 14*a^15*b*c^3*d^13 + 91*a^4*b^12*c^14*d^2 - 364*a^5*b^11*c^13*d^3 + 1001*a^6*b^10*c^12*d^4 - 2002*a^7*b^9*c^11*d^5 + 3003*a^8*b^8*c^10*d^6 - 3432*a^9*b^7*c^9*d^7 + 3003*a^10*b^6*c^8*d^8 - 2002*a^11*b^5*c^7*d^9 + 1001*a^12*b^4*c^6*d^10 - 364*a^13*b^3*c^5*d^11 + 91*a^14*b^2*c^4*d^12) - (x^(1/2)*(-(b^9*c^4 + 6561*a^4*b^5*d^4 - 2916*a^3*b^6*c*d^3 + 486*a^2*b^7*c^2*d^2 - 36*a*b^8*c^3*d)/(4096*a^17*d^12 + 4096*a^5*b^12*c^12 - 49152*a^6*b^11*c^11*d + 270336*a^7*b^10*c^10*d^2 - 901120*a^8*b^9*c^9*d^3 + 2027520*a^9*b^8*c^8*d^4 - 3244032*a^10*b^7*c^7*d^5 + 3784704*a^11*b^6*c^6*d^6 - 3244032*a^12*b^5*c^5*d^7 + 2027520*a^13*b^4*c^4*d^8 - 901120*a^14*b^3*c^3*d^9 + 270336*a^15*b^2*c^2*d^10 - 49152*a^16*b*c*d^11))^(1/4)*(4096*a*b^22*c^19*d^4 + 4096*a^19*b^4*c*d^22 - 122880*a^2*b^21*c^18*d^5 + 1486848*a^3*b^20*c^17*d^6 - 9748480*a^4*b^19*c^16*d^7 + 40476672*a^5*b^18*c^15*d^8 - 116785152*a^6*b^17*c^14*d^9 + 249192448*a^7*b^16*c^13*d^10 - 412041216*a^8*b^15*c^12*d^11 + 547700736*a^9*b^14*c^11*d^12 - 600326144*a^10*b^13*c^10*d^13 + 547700736*a^11*b^12*c^9*d^14 - 412041216*a^12*b^11*c^8*d^15 + 249192448*a^13*b^10*c^7*d^16 - 116785152*a^14*b^9*c^6*d^17 + 40476672*a^15*b^8*c^5*d^18 - 9748480*a^16*b^7*c^4*d^19 + 1486848*a^17*b^6*c^3*d^20 - 122880*a^18*b^5*c^2*d^21))/(16*(a^2*b^12*c^14 + a^14*c^2*d^12 - 12*a^3*b^11*c^13*d - 12*a^13*b*c^3*d^11 + 66*a^4*b^10*c^12*d^2 - 220*a^5*b^9*c^11*d^3 + 495*a^6*b^8*c^10*d^4 - 792*a^7*b^7*c^9*d^5 + 924*a^8*b^6*c^8*d^6 - 792*a^9*b^5*c^7*d^7 + 495*a^10*b^4*c^6*d^8 - 220*a^11*b^3*c^5*d^9 + 66*a^12*b^2*c^4*d^10)))*(-(b^9*c^4 + 6561*a^4*b^5*d^4 - 2916*a^3*b^6*c*d^3 + 486*a^2*b^7*c^2*d^2 - 36*a*b^8*c^3*d)/(4096*a^17*d^12 + 4096*a^5*b^12*c^12 - 49152*a^6*b^11*c^11*d + 270336*a^7*b^10*c^10*d^2 - 901120*a^8*b^9*c^9*d^3 + 2027520*a^9*b^8*c^8*d^4 - 3244032*a^10*b^7*c^7*d^5 + 3784704*a^11*b^6*c^6*d^6 - 3244032*a^12*b^5*c^5*d^7 + 2027520*a^13*b^4*c^4*d^8 - 901120*a^14*b^3*c^3*d^9 + 270336*a^15*b^2*c^2*d^10 - 49152*a^16*b*c*d^11))^(3/4)*1i - (x^(1/2)*(81*a^7*b^8*d^15 + 81*b^15*c^7*d^8 + 3627*a*b^14*c^6*d^9 + 3627*a^6*b^9*c*d^14 - 80999*a^2*b^13*c^5*d^10 + 339435*a^3*b^12*c^4*d^11 + 339435*a^4*b^11*c^3*d^12 - 80999*a^5*b^10*c^2*d^13)*1i)/(16*(a^2*b^12*c^14 + a^14*c^2*d^12 - 12*a^3*b^11*c^13*d - 12*a^13*b*c^3*d^11 + 66*a^4*b^10*c^12*d^2 - 220*a^5*b^9*c^11*d^3 + 495*a^6*b^8*c^10*d^4 - 792*a^7*b^7*c^9*d^5 + 924*a^8*b^6*c^8*d^6 - 792*a^9*b^5*c^7*d^7 + 495*a^10*b^4*c^6*d^8 - 220*a^11*b^3*c^5*d^9 + 66*a^12*b^2*c^4*d^10)))*(-(b^9*c^4 + 6561*a^4*b^5*d^4 - 2916*a^3*b^6*c*d^3 + 486*a^2*b^7*c^2*d^2 - 36*a*b^8*c^3*d)/(4096*a^17*d^12 + 4096*a^5*b^12*c^12 - 49152*a^6*b^11*c^11*d + 270336*a^7*b^10*c^10*d^2 - 901120*a^8*b^9*c^9*d^3 + 2027520*a^9*b^8*c^8*d^4 - 3244032*a^10*b^7*c^7*d^5 + 3784704*a^11*b^6*c^6*d^6 - 3244032*a^12*b^5*c^5*d^7 + 2027520*a^13*b^4*c^4*d^8 - 901120*a^14*b^3*c^3*d^9 + 270336*a^15*b^2*c^2*d^10 - 49152*a^16*b*c*d^11))^(1/4) - ((3645*a^6*b^9*d^15)/32 + (3645*b^15*c^6*d^9)/32 - (49815*a*b^14*c^5*d^10)/16 - (49815*a^5*b^10*c*d^14)/16 + (918675*a^2*b^13*c^4*d^11)/32 - (739025*a^3*b^12*c^3*d^12)/8 + (918675*a^4*b^11*c^2*d^13)/32)/(a^2*b^14*c^16 + a^16*c^2*d^14 - 14*a^3*b^13*c^15*d - 14*a^15*b*c^3*d^13 + 91*a^4*b^12*c^14*d^2 - 364*a^5*b^11*c^13*d^3 + 1001*a^6*b^10*c^12*d^4 - 2002*a^7*b^9*c^11*d^5 + 3003*a^8*b^8*c^10*d^6 - 3432*a^9*b^7*c^9*d^7 + 3003*a^10*b^6*c^8*d^8 - 2002*a^11*b^5*c^7*d^9 + 1001*a^12*b^4*c^6*d^10 - 364*a^13*b^3*c^5*d^11 + 91*a^14*b^2*c^4*d^12) + ((((32*a^19*b^4*d^23 + 32*b^23*c^19*d^4 - 1216*a*b^22*c^18*d^5 - 1216*a^18*b^5*c*d^22 + 19040*a^2*b^21*c^17*d^6 - 161664*a^3*b^20*c^16*d^7 + 837408*a^4*b^19*c^15*d^8 - 2842656*a^5*b^18*c^14*d^9 + 6564768*a^6*b^17*c^13*d^10 - 10331040*a^7*b^16*c^12*d^11 + 10374112*a^8*b^15*c^11*d^12 - 4458784*a^9*b^14*c^10*d^13 - 4458784*a^10*b^13*c^9*d^14 + 10374112*a^11*b^12*c^8*d^15 - 10331040*a^12*b^11*c^7*d^16 + 6564768*a^13*b^10*c^6*d^17 - 2842656*a^14*b^9*c^5*d^18 + 837408*a^15*b^8*c^4*d^19 - 161664*a^16*b^7*c^3*d^20 + 19040*a^17*b^6*c^2*d^21)*1i)/(a^2*b^14*c^16 + a^16*c^2*d^14 - 14*a^3*b^13*c^15*d - 14*a^15*b*c^3*d^13 + 91*a^4*b^12*c^14*d^2 - 364*a^5*b^11*c^13*d^3 + 1001*a^6*b^10*c^12*d^4 - 2002*a^7*b^9*c^11*d^5 + 3003*a^8*b^8*c^10*d^6 - 3432*a^9*b^7*c^9*d^7 + 3003*a^10*b^6*c^8*d^8 - 2002*a^11*b^5*c^7*d^9 + 1001*a^12*b^4*c^6*d^10 - 364*a^13*b^3*c^5*d^11 + 91*a^14*b^2*c^4*d^12) + (x^(1/2)*(-(b^9*c^4 + 6561*a^4*b^5*d^4 - 2916*a^3*b^6*c*d^3 + 486*a^2*b^7*c^2*d^2 - 36*a*b^8*c^3*d)/(4096*a^17*d^12 + 4096*a^5*b^12*c^12 - 49152*a^6*b^11*c^11*d + 270336*a^7*b^10*c^10*d^2 - 901120*a^8*b^9*c^9*d^3 + 2027520*a^9*b^8*c^8*d^4 - 3244032*a^10*b^7*c^7*d^5 + 3784704*a^11*b^6*c^6*d^6 - 3244032*a^12*b^5*c^5*d^7 + 2027520*a^13*b^4*c^4*d^8 - 901120*a^14*b^3*c^3*d^9 + 270336*a^15*b^2*c^2*d^10 - 49152*a^16*b*c*d^11))^(1/4)*(4096*a*b^22*c^19*d^4 + 4096*a^19*b^4*c*d^22 - 122880*a^2*b^21*c^18*d^5 + 1486848*a^3*b^20*c^17*d^6 - 9748480*a^4*b^19*c^16*d^7 + 40476672*a^5*b^18*c^15*d^8 - 116785152*a^6*b^17*c^14*d^9 + 249192448*a^7*b^16*c^13*d^10 - 412041216*a^8*b^15*c^12*d^11 + 547700736*a^9*b^14*c^11*d^12 - 600326144*a^10*b^13*c^10*d^13 + 547700736*a^11*b^12*c^9*d^14 - 412041216*a^12*b^11*c^8*d^15 + 249192448*a^13*b^10*c^7*d^16 - 116785152*a^14*b^9*c^6*d^17 + 40476672*a^15*b^8*c^5*d^18 - 9748480*a^16*b^7*c^4*d^19 + 1486848*a^17*b^6*c^3*d^20 - 122880*a^18*b^5*c^2*d^21))/(16*(a^2*b^12*c^14 + a^14*c^2*d^12 - 12*a^3*b^11*c^13*d - 12*a^13*b*c^3*d^11 + 66*a^4*b^10*c^12*d^2 - 220*a^5*b^9*c^11*d^3 + 495*a^6*b^8*c^10*d^4 - 792*a^7*b^7*c^9*d^5 + 924*a^8*b^6*c^8*d^6 - 792*a^9*b^5*c^7*d^7 + 495*a^10*b^4*c^6*d^8 - 220*a^11*b^3*c^5*d^9 + 66*a^12*b^2*c^4*d^10)))*(-(b^9*c^4 + 6561*a^4*b^5*d^4 - 2916*a^3*b^6*c*d^3 + 486*a^2*b^7*c^2*d^2 - 36*a*b^8*c^3*d)/(4096*a^17*d^12 + 4096*a^5*b^12*c^12 - 49152*a^6*b^11*c^11*d + 270336*a^7*b^10*c^10*d^2 - 901120*a^8*b^9*c^9*d^3 + 2027520*a^9*b^8*c^8*d^4 - 3244032*a^10*b^7*c^7*d^5 + 3784704*a^11*b^6*c^6*d^6 - 3244032*a^12*b^5*c^5*d^7 + 2027520*a^13*b^4*c^4*d^8 - 901120*a^14*b^3*c^3*d^9 + 270336*a^15*b^2*c^2*d^10 - 49152*a^16*b*c*d^11))^(3/4)*1i + (x^(1/2)*(81*a^7*b^8*d^15 + 81*b^15*c^7*d^8 + 3627*a*b^14*c^6*d^9 + 3627*a^6*b^9*c*d^14 - 80999*a^2*b^13*c^5*d^10 + 339435*a^3*b^12*c^4*d^11 + 339435*a^4*b^11*c^3*d^12 - 80999*a^5*b^10*c^2*d^13)*1i)/(16*(a^2*b^12*c^14 + a^14*c^2*d^12 - 12*a^3*b^11*c^13*d - 12*a^13*b*c^3*d^11 + 66*a^4*b^10*c^12*d^2 - 220*a^5*b^9*c^11*d^3 + 495*a^6*b^8*c^10*d^4 - 792*a^7*b^7*c^9*d^5 + 924*a^8*b^6*c^8*d^6 - 792*a^9*b^5*c^7*d^7 + 495*a^10*b^4*c^6*d^8 - 220*a^11*b^3*c^5*d^9 + 66*a^12*b^2*c^4*d^10)))*(-(b^9*c^4 + 6561*a^4*b^5*d^4 - 2916*a^3*b^6*c*d^3 + 486*a^2*b^7*c^2*d^2 - 36*a*b^8*c^3*d)/(4096*a^17*d^12 + 4096*a^5*b^12*c^12 - 49152*a^6*b^11*c^11*d + 270336*a^7*b^10*c^10*d^2 - 901120*a^8*b^9*c^9*d^3 + 2027520*a^9*b^8*c^8*d^4 - 3244032*a^10*b^7*c^7*d^5 + 3784704*a^11*b^6*c^6*d^6 - 3244032*a^12*b^5*c^5*d^7 + 2027520*a^13*b^4*c^4*d^8 - 901120*a^14*b^3*c^3*d^9 + 270336*a^15*b^2*c^2*d^10 - 49152*a^16*b*c*d^11))^(1/4)))*(-(b^9*c^4 + 6561*a^4*b^5*d^4 - 2916*a^3*b^6*c*d^3 + 486*a^2*b^7*c^2*d^2 - 36*a*b^8*c^3*d)/(4096*a^17*d^12 + 4096*a^5*b^12*c^12 - 49152*a^6*b^11*c^11*d + 270336*a^7*b^10*c^10*d^2 - 901120*a^8*b^9*c^9*d^3 + 2027520*a^9*b^8*c^8*d^4 - 3244032*a^10*b^7*c^7*d^5 + 3784704*a^11*b^6*c^6*d^6 - 3244032*a^12*b^5*c^5*d^7 + 2027520*a^13*b^4*c^4*d^8 - 901120*a^14*b^3*c^3*d^9 + 270336*a^15*b^2*c^2*d^10 - 49152*a^16*b*c*d^11))^(1/4)","B"
492,1,37332,628,5.069920,"\text{Not used}","int(1/(x^(1/2)*(a + b*x^2)^2*(c + d*x^2)^2),x)","\frac{\frac{\sqrt{x}\,\left(a^2\,d^2+b^2\,c^2\right)}{2\,a\,c\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}+\frac{b\,d\,x^{5/2}\,\left(a\,d+b\,c\right)}{2\,a\,c\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}}{b\,d\,x^4+\left(a\,d+b\,c\right)\,x^2+a\,c}-\mathrm{atan}\left(\frac{\left(\left(\left(\frac{\sqrt{x}\,\left(36864\,a^{21}\,b^4\,c^2\,d^{23}-712704\,a^{20}\,b^5\,c^3\,d^{22}+6172672\,a^{19}\,b^6\,c^4\,d^{21}-31899648\,a^{18}\,b^7\,c^5\,d^{20}+110432256\,a^{17}\,b^8\,c^6\,d^{19}-271552512\,a^{16}\,b^9\,c^7\,d^{18}+487280640\,a^{15}\,b^{10}\,c^8\,d^{17}-635523072\,a^{14}\,b^{11}\,c^9\,d^{16}+562982912\,a^{13}\,b^{12}\,c^{10}\,d^{15}-227217408\,a^{12}\,b^{13}\,c^{11}\,d^{14}-227217408\,a^{11}\,b^{14}\,c^{12}\,d^{13}+562982912\,a^{10}\,b^{15}\,c^{13}\,d^{12}-635523072\,a^9\,b^{16}\,c^{14}\,d^{11}+487280640\,a^8\,b^{17}\,c^{15}\,d^{10}-271552512\,a^7\,b^{18}\,c^{16}\,d^9+110432256\,a^6\,b^{19}\,c^{17}\,d^8-31899648\,a^5\,b^{20}\,c^{18}\,d^7+6172672\,a^4\,b^{21}\,c^{19}\,d^6-712704\,a^3\,b^{22}\,c^{20}\,d^5+36864\,a^2\,b^{23}\,c^{21}\,d^4\right)}{16\,\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}{4096\,a^{19}\,d^{12}-49152\,a^{18}\,b\,c\,d^{11}+270336\,a^{17}\,b^2\,c^2\,d^{10}-901120\,a^{16}\,b^3\,c^3\,d^9+2027520\,a^{15}\,b^4\,c^4\,d^8-3244032\,a^{14}\,b^5\,c^5\,d^7+3784704\,a^{13}\,b^6\,c^6\,d^6-3244032\,a^{12}\,b^7\,c^7\,d^5+2027520\,a^{11}\,b^8\,c^8\,d^4-901120\,a^{10}\,b^9\,c^9\,d^3+270336\,a^9\,b^{10}\,c^{10}\,d^2-49152\,a^8\,b^{11}\,c^{11}\,d+4096\,a^7\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(6144\,a^{19}\,b^4\,c^4\,d^{19}-90112\,a^{18}\,b^5\,c^5\,d^{18}+585728\,a^{17}\,b^6\,c^6\,d^{17}-2230272\,a^{16}\,b^7\,c^7\,d^{16}+5490688\,a^{15}\,b^8\,c^8\,d^{15}-8966144\,a^{14}\,b^9\,c^9\,d^{14}+9191424\,a^{13}\,b^{10}\,c^{10}\,d^{13}-3987456\,a^{12}\,b^{11}\,c^{11}\,d^{12}-3987456\,a^{11}\,b^{12}\,c^{12}\,d^{11}+9191424\,a^{10}\,b^{13}\,c^{13}\,d^{10}-8966144\,a^9\,b^{14}\,c^{14}\,d^9+5490688\,a^8\,b^{15}\,c^{15}\,d^8-2230272\,a^7\,b^{16}\,c^{16}\,d^7+585728\,a^6\,b^{17}\,c^{17}\,d^6-90112\,a^5\,b^{18}\,c^{18}\,d^5+6144\,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)\,{\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}{4096\,a^{19}\,d^{12}-49152\,a^{18}\,b\,c\,d^{11}+270336\,a^{17}\,b^2\,c^2\,d^{10}-901120\,a^{16}\,b^3\,c^3\,d^9+2027520\,a^{15}\,b^4\,c^4\,d^8-3244032\,a^{14}\,b^5\,c^5\,d^7+3784704\,a^{13}\,b^6\,c^6\,d^6-3244032\,a^{12}\,b^7\,c^7\,d^5+2027520\,a^{11}\,b^8\,c^8\,d^4-901120\,a^{10}\,b^9\,c^9\,d^3+270336\,a^9\,b^{10}\,c^{10}\,d^2-49152\,a^8\,b^{11}\,c^{11}\,d+4096\,a^7\,b^{12}\,c^{12}}\right)}^{3/4}+\frac{\frac{891\,a^8\,b^7\,d^{15}}{2}-6210\,a^7\,b^8\,c\,d^{14}+31509\,a^6\,b^9\,c^2\,d^{13}-66138\,a^5\,b^{10}\,c^3\,d^{12}+60307\,a^4\,b^{11}\,c^4\,d^{11}-66138\,a^3\,b^{12}\,c^5\,d^{10}+31509\,a^2\,b^{13}\,c^6\,d^9-6210\,a\,b^{14}\,c^7\,d^8+\frac{891\,b^{15}\,c^8\,d^7}{2}}{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)\,{\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}{4096\,a^{19}\,d^{12}-49152\,a^{18}\,b\,c\,d^{11}+270336\,a^{17}\,b^2\,c^2\,d^{10}-901120\,a^{16}\,b^3\,c^3\,d^9+2027520\,a^{15}\,b^4\,c^4\,d^8-3244032\,a^{14}\,b^5\,c^5\,d^7+3784704\,a^{13}\,b^6\,c^6\,d^6-3244032\,a^{12}\,b^7\,c^7\,d^5+2027520\,a^{11}\,b^8\,c^8\,d^4-901120\,a^{10}\,b^9\,c^9\,d^3+270336\,a^9\,b^{10}\,c^{10}\,d^2-49152\,a^8\,b^{11}\,c^{11}\,d+4096\,a^7\,b^{12}\,c^{12}}\right)}^{1/4}\,1{}\mathrm{i}+\frac{\sqrt{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}}{16\,\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}{4096\,a^{19}\,d^{12}-49152\,a^{18}\,b\,c\,d^{11}+270336\,a^{17}\,b^2\,c^2\,d^{10}-901120\,a^{16}\,b^3\,c^3\,d^9+2027520\,a^{15}\,b^4\,c^4\,d^8-3244032\,a^{14}\,b^5\,c^5\,d^7+3784704\,a^{13}\,b^6\,c^6\,d^6-3244032\,a^{12}\,b^7\,c^7\,d^5+2027520\,a^{11}\,b^8\,c^8\,d^4-901120\,a^{10}\,b^9\,c^9\,d^3+270336\,a^9\,b^{10}\,c^{10}\,d^2-49152\,a^8\,b^{11}\,c^{11}\,d+4096\,a^7\,b^{12}\,c^{12}}\right)}^{1/4}+\left(\left(\left(\frac{\sqrt{x}\,\left(36864\,a^{21}\,b^4\,c^2\,d^{23}-712704\,a^{20}\,b^5\,c^3\,d^{22}+6172672\,a^{19}\,b^6\,c^4\,d^{21}-31899648\,a^{18}\,b^7\,c^5\,d^{20}+110432256\,a^{17}\,b^8\,c^6\,d^{19}-271552512\,a^{16}\,b^9\,c^7\,d^{18}+487280640\,a^{15}\,b^{10}\,c^8\,d^{17}-635523072\,a^{14}\,b^{11}\,c^9\,d^{16}+562982912\,a^{13}\,b^{12}\,c^{10}\,d^{15}-227217408\,a^{12}\,b^{13}\,c^{11}\,d^{14}-227217408\,a^{11}\,b^{14}\,c^{12}\,d^{13}+562982912\,a^{10}\,b^{15}\,c^{13}\,d^{12}-635523072\,a^9\,b^{16}\,c^{14}\,d^{11}+487280640\,a^8\,b^{17}\,c^{15}\,d^{10}-271552512\,a^7\,b^{18}\,c^{16}\,d^9+110432256\,a^6\,b^{19}\,c^{17}\,d^8-31899648\,a^5\,b^{20}\,c^{18}\,d^7+6172672\,a^4\,b^{21}\,c^{19}\,d^6-712704\,a^3\,b^{22}\,c^{20}\,d^5+36864\,a^2\,b^{23}\,c^{21}\,d^4\right)}{16\,\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}{4096\,a^{19}\,d^{12}-49152\,a^{18}\,b\,c\,d^{11}+270336\,a^{17}\,b^2\,c^2\,d^{10}-901120\,a^{16}\,b^3\,c^3\,d^9+2027520\,a^{15}\,b^4\,c^4\,d^8-3244032\,a^{14}\,b^5\,c^5\,d^7+3784704\,a^{13}\,b^6\,c^6\,d^6-3244032\,a^{12}\,b^7\,c^7\,d^5+2027520\,a^{11}\,b^8\,c^8\,d^4-901120\,a^{10}\,b^9\,c^9\,d^3+270336\,a^9\,b^{10}\,c^{10}\,d^2-49152\,a^8\,b^{11}\,c^{11}\,d+4096\,a^7\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(6144\,a^{19}\,b^4\,c^4\,d^{19}-90112\,a^{18}\,b^5\,c^5\,d^{18}+585728\,a^{17}\,b^6\,c^6\,d^{17}-2230272\,a^{16}\,b^7\,c^7\,d^{16}+5490688\,a^{15}\,b^8\,c^8\,d^{15}-8966144\,a^{14}\,b^9\,c^9\,d^{14}+9191424\,a^{13}\,b^{10}\,c^{10}\,d^{13}-3987456\,a^{12}\,b^{11}\,c^{11}\,d^{12}-3987456\,a^{11}\,b^{12}\,c^{12}\,d^{11}+9191424\,a^{10}\,b^{13}\,c^{13}\,d^{10}-8966144\,a^9\,b^{14}\,c^{14}\,d^9+5490688\,a^8\,b^{15}\,c^{15}\,d^8-2230272\,a^7\,b^{16}\,c^{16}\,d^7+585728\,a^6\,b^{17}\,c^{17}\,d^6-90112\,a^5\,b^{18}\,c^{18}\,d^5+6144\,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)\,{\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}{4096\,a^{19}\,d^{12}-49152\,a^{18}\,b\,c\,d^{11}+270336\,a^{17}\,b^2\,c^2\,d^{10}-901120\,a^{16}\,b^3\,c^3\,d^9+2027520\,a^{15}\,b^4\,c^4\,d^8-3244032\,a^{14}\,b^5\,c^5\,d^7+3784704\,a^{13}\,b^6\,c^6\,d^6-3244032\,a^{12}\,b^7\,c^7\,d^5+2027520\,a^{11}\,b^8\,c^8\,d^4-901120\,a^{10}\,b^9\,c^9\,d^3+270336\,a^9\,b^{10}\,c^{10}\,d^2-49152\,a^8\,b^{11}\,c^{11}\,d+4096\,a^7\,b^{12}\,c^{12}}\right)}^{3/4}-\frac{\frac{891\,a^8\,b^7\,d^{15}}{2}-6210\,a^7\,b^8\,c\,d^{14}+31509\,a^6\,b^9\,c^2\,d^{13}-66138\,a^5\,b^{10}\,c^3\,d^{12}+60307\,a^4\,b^{11}\,c^4\,d^{11}-66138\,a^3\,b^{12}\,c^5\,d^{10}+31509\,a^2\,b^{13}\,c^6\,d^9-6210\,a\,b^{14}\,c^7\,d^8+\frac{891\,b^{15}\,c^8\,d^7}{2}}{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)\,{\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}{4096\,a^{19}\,d^{12}-49152\,a^{18}\,b\,c\,d^{11}+270336\,a^{17}\,b^2\,c^2\,d^{10}-901120\,a^{16}\,b^3\,c^3\,d^9+2027520\,a^{15}\,b^4\,c^4\,d^8-3244032\,a^{14}\,b^5\,c^5\,d^7+3784704\,a^{13}\,b^6\,c^6\,d^6-3244032\,a^{12}\,b^7\,c^7\,d^5+2027520\,a^{11}\,b^8\,c^8\,d^4-901120\,a^{10}\,b^9\,c^9\,d^3+270336\,a^9\,b^{10}\,c^{10}\,d^2-49152\,a^8\,b^{11}\,c^{11}\,d+4096\,a^7\,b^{12}\,c^{12}}\right)}^{1/4}\,1{}\mathrm{i}+\frac{\sqrt{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}}{16\,\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^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1}-149094\,a\,b^{16}\,c^7\,d^{10}+9801\,b^{17}\,c^8\,d^9\right)}{16\,\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}{4096\,a^{19}\,d^{12}-49152\,a^{18}\,b\,c\,d^{11}+270336\,a^{17}\,b^2\,c^2\,d^{10}-901120\,a^{16}\,b^3\,c^3\,d^9+2027520\,a^{15}\,b^4\,c^4\,d^8-3244032\,a^{14}\,b^5\,c^5\,d^7+3784704\,a^{13}\,b^6\,c^6\,d^6-3244032\,a^{12}\,b^7\,c^7\,d^5+2027520\,a^{11}\,b^8\,c^8\,d^4-901120\,a^{10}\,b^9\,c^9\,d^3+270336\,a^9\,b^{10}\,c^{10}\,d^2-49152\,a^8\,b^{11}\,c^{11}\,d+4096\,a^7\,b^{12}\,c^{12}}\right)}^{1/4}-\left(\left(\left(\frac{\sqrt{x}\,\left(36864\,a^{21}\,b^4\,c^2\,d^{23}-712704\,a^{20}\,b^5\,c^3\,d^{22}+6172672\,a^{19}\,b^6\,c^4\,d^{21}-31899648\,a^{18}\,b^7\,c^5\,d^{20}+110432256\,a^{17}\,b^8\,c^6\,d^{19}-271552512\,a^{16}\,b^9\,c^7\,d^{18}+487280640\,a^{15}\,b^{10}\,c^8\,d^{17}-635523072\,a^{14}\,b^{11}\,c^9\,d^{16}+562982912\,a^{13}\,b^{12}\,c^{10}\,d^{15}-227217408\,a^{12}\,b^{13}\,c^{11}\,d^{14}-227217408\,a^{11}\,b^{14}\,c^{12}\,d^{13}+562982912\,a^{10}\,b^{15}\,c^{13}\,d^{12}-635523072\,a^9\,b^{16}\,c^{14}\,d^{11}+487280640\,a^8\,b^{17}\,c^{15}\,d^{10}-271552512\,a^7\,b^{18}\,c^{16}\,d^9+110432256\,a^6\,b^{19}\,c^{17}\,d^8-31899648\,a^5\,b^{20}\,c^{18}\,d^7+6172672\,a^4\,b^{21}\,c^{19}\,d^6-712704\,a^3\,b^{22}\,c^{20}\,d^5+36864\,a^2\,b^{23}\,c^{21}\,d^4\right)}{16\,\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}{4096\,a^{19}\,d^{12}-49152\,a^{18}\,b\,c\,d^{11}+270336\,a^{17}\,b^2\,c^2\,d^{10}-901120\,a^{16}\,b^3\,c^3\,d^9+2027520\,a^{15}\,b^4\,c^4\,d^8-3244032\,a^{14}\,b^5\,c^5\,d^7+3784704\,a^{13}\,b^6\,c^6\,d^6-3244032\,a^{12}\,b^7\,c^7\,d^5+2027520\,a^{11}\,b^8\,c^8\,d^4-901120\,a^{10}\,b^9\,c^9\,d^3+270336\,a^9\,b^{10}\,c^{10}\,d^2-49152\,a^8\,b^{11}\,c^{11}\,d+4096\,a^7\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(6144\,a^{19}\,b^4\,c^4\,d^{19}-90112\,a^{18}\,b^5\,c^5\,d^{18}+585728\,a^{17}\,b^6\,c^6\,d^{17}-2230272\,a^{16}\,b^7\,c^7\,d^{16}+5490688\,a^{15}\,b^8\,c^8\,d^{15}-8966144\,a^{14}\,b^9\,c^9\,d^{14}+9191424\,a^{13}\,b^{10}\,c^{10}\,d^{13}-3987456\,a^{12}\,b^{11}\,c^{11}\,d^{12}-3987456\,a^{11}\,b^{12}\,c^{12}\,d^{11}+9191424\,a^{10}\,b^{13}\,c^{13}\,d^{10}-8966144\,a^9\,b^{14}\,c^{14}\,d^9+5490688\,a^8\,b^{15}\,c^{15}\,d^8-2230272\,a^7\,b^{16}\,c^{16}\,d^7+585728\,a^6\,b^{17}\,c^{17}\,d^6-90112\,a^5\,b^{18}\,c^{18}\,d^5+6144\,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)\,{\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}{4096\,a^{19}\,d^{12}-49152\,a^{18}\,b\,c\,d^{11}+270336\,a^{17}\,b^2\,c^2\,d^{10}-901120\,a^{16}\,b^3\,c^3\,d^9+2027520\,a^{15}\,b^4\,c^4\,d^8-3244032\,a^{14}\,b^5\,c^5\,d^7+3784704\,a^{13}\,b^6\,c^6\,d^6-3244032\,a^{12}\,b^7\,c^7\,d^5+2027520\,a^{11}\,b^8\,c^8\,d^4-901120\,a^{10}\,b^9\,c^9\,d^3+270336\,a^9\,b^{10}\,c^{10}\,d^2-49152\,a^8\,b^{11}\,c^{11}\,d+4096\,a^7\,b^{12}\,c^{12}}\right)}^{3/4}-\frac{\frac{891\,a^8\,b^7\,d^{15}}{2}-6210\,a^7\,b^8\,c\,d^{14}+31509\,a^6\,b^9\,c^2\,d^{13}-66138\,a^5\,b^{10}\,c^3\,d^{12}+60307\,a^4\,b^{11}\,c^4\,d^{11}-66138\,a^3\,b^{12}\,c^5\,d^{10}+31509\,a^2\,b^{13}\,c^6\,d^9-6210\,a\,b^{14}\,c^7\,d^8+\frac{891\,b^{15}\,c^8\,d^7}{2}}{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)\,{\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}{4096\,a^{19}\,d^{12}-49152\,a^{18}\,b\,c\,d^{11}+270336\,a^{17}\,b^2\,c^2\,d^{10}-901120\,a^{16}\,b^3\,c^3\,d^9+2027520\,a^{15}\,b^4\,c^4\,d^8-3244032\,a^{14}\,b^5\,c^5\,d^7+3784704\,a^{13}\,b^6\,c^6\,d^6-3244032\,a^{12}\,b^7\,c^7\,d^5+2027520\,a^{11}\,b^8\,c^8\,d^4-901120\,a^{10}\,b^9\,c^9\,d^3+270336\,a^9\,b^{10}\,c^{10}\,d^2-49152\,a^8\,b^{11}\,c^{11}\,d+4096\,a^7\,b^{12}\,c^{12}}\right)}^{1/4}+\frac{\sqrt{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)}{16\,\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}{4096\,a^{19}\,d^{12}-49152\,a^{18}\,b\,c\,d^{11}+270336\,a^{17}\,b^2\,c^2\,d^{10}-901120\,a^{16}\,b^3\,c^3\,d^9+2027520\,a^{15}\,b^4\,c^4\,d^8-3244032\,a^{14}\,b^5\,c^5\,d^7+3784704\,a^{13}\,b^6\,c^6\,d^6-3244032\,a^{12}\,b^7\,c^7\,d^5+2027520\,a^{11}\,b^8\,c^8\,d^4-901120\,a^{10}\,b^9\,c^9\,d^3+270336\,a^9\,b^{10}\,c^{10}\,d^2-49152\,a^8\,b^{11}\,c^{11}\,d+4096\,a^7\,b^{12}\,c^{12}}\right)}^{1/4}}\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}{4096\,a^{19}\,d^{12}-49152\,a^{18}\,b\,c\,d^{11}+270336\,a^{17}\,b^2\,c^2\,d^{10}-901120\,a^{16}\,b^3\,c^3\,d^9+2027520\,a^{15}\,b^4\,c^4\,d^8-3244032\,a^{14}\,b^5\,c^5\,d^7+3784704\,a^{13}\,b^6\,c^6\,d^6-3244032\,a^{12}\,b^7\,c^7\,d^5+2027520\,a^{11}\,b^8\,c^8\,d^4-901120\,a^{10}\,b^9\,c^9\,d^3+270336\,a^9\,b^{10}\,c^{10}\,d^2-49152\,a^8\,b^{11}\,c^{11}\,d+4096\,a^7\,b^{12}\,c^{12}}\right)}^{1/4}\,2{}\mathrm{i}+2\,\mathrm{atan}\left(\frac{\left(\left(\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}{4096\,a^{19}\,d^{12}-49152\,a^{18}\,b\,c\,d^{11}+270336\,a^{17}\,b^2\,c^2\,d^{10}-901120\,a^{16}\,b^3\,c^3\,d^9+2027520\,a^{15}\,b^4\,c^4\,d^8-3244032\,a^{14}\,b^5\,c^5\,d^7+3784704\,a^{13}\,b^6\,c^6\,d^6-3244032\,a^{12}\,b^7\,c^7\,d^5+2027520\,a^{11}\,b^8\,c^8\,d^4-901120\,a^{10}\,b^9\,c^9\,d^3+270336\,a^9\,b^{10}\,c^{10}\,d^2-49152\,a^8\,b^{11}\,c^{11}\,d+4096\,a^7\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(6144\,a^{19}\,b^4\,c^4\,d^{19}-90112\,a^{18}\,b^5\,c^5\,d^{18}+585728\,a^{17}\,b^6\,c^6\,d^{17}-2230272\,a^{16}\,b^7\,c^7\,d^{16}+5490688\,a^{15}\,b^8\,c^8\,d^{15}-8966144\,a^{14}\,b^9\,c^9\,d^{14}+9191424\,a^{13}\,b^{10}\,c^{10}\,d^{13}-3987456\,a^{12}\,b^{11}\,c^{11}\,d^{12}-3987456\,a^{11}\,b^{12}\,c^{12}\,d^{11}+9191424\,a^{10}\,b^{13}\,c^{13}\,d^{10}-8966144\,a^9\,b^{14}\,c^{14}\,d^9+5490688\,a^8\,b^{15}\,c^{15}\,d^8-2230272\,a^7\,b^{16}\,c^{16}\,d^7+585728\,a^6\,b^{17}\,c^{17}\,d^6-90112\,a^5\,b^{18}\,c^{18}\,d^5+6144\,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{\sqrt{x}\,\left(36864\,a^{21}\,b^4\,c^2\,d^{23}-712704\,a^{20}\,b^5\,c^3\,d^{22}+6172672\,a^{19}\,b^6\,c^4\,d^{21}-31899648\,a^{18}\,b^7\,c^5\,d^{20}+110432256\,a^{17}\,b^8\,c^6\,d^{19}-271552512\,a^{16}\,b^9\,c^7\,d^{18}+487280640\,a^{15}\,b^{10}\,c^8\,d^{17}-635523072\,a^{14}\,b^{11}\,c^9\,d^{16}+562982912\,a^{13}\,b^{12}\,c^{10}\,d^{15}-227217408\,a^{12}\,b^{13}\,c^{11}\,d^{14}-227217408\,a^{11}\,b^{14}\,c^{12}\,d^{13}+562982912\,a^{10}\,b^{15}\,c^{13}\,d^{12}-635523072\,a^9\,b^{16}\,c^{14}\,d^{11}+487280640\,a^8\,b^{17}\,c^{15}\,d^{10}-271552512\,a^7\,b^{18}\,c^{16}\,d^9+110432256\,a^6\,b^{19}\,c^{17}\,d^8-31899648\,a^5\,b^{20}\,c^{18}\,d^7+6172672\,a^4\,b^{21}\,c^{19}\,d^6-712704\,a^3\,b^{22}\,c^{20}\,d^5+36864\,a^2\,b^{23}\,c^{21}\,d^4\right)\,1{}\mathrm{i}}{16\,\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}{4096\,a^{19}\,d^{12}-49152\,a^{18}\,b\,c\,d^{11}+270336\,a^{17}\,b^2\,c^2\,d^{10}-901120\,a^{16}\,b^3\,c^3\,d^9+2027520\,a^{15}\,b^4\,c^4\,d^8-3244032\,a^{14}\,b^5\,c^5\,d^7+3784704\,a^{13}\,b^6\,c^6\,d^6-3244032\,a^{12}\,b^7\,c^7\,d^5+2027520\,a^{11}\,b^8\,c^8\,d^4-901120\,a^{10}\,b^9\,c^9\,d^3+270336\,a^9\,b^{10}\,c^{10}\,d^2-49152\,a^8\,b^{11}\,c^{11}\,d+4096\,a^7\,b^{12}\,c^{12}}\right)}^{3/4}\,1{}\mathrm{i}+\frac{\left(\frac{891\,a^8\,b^7\,d^{15}}{2}-6210\,a^7\,b^8\,c\,d^{14}+31509\,a^6\,b^9\,c^2\,d^{13}-66138\,a^5\,b^{10}\,c^3\,d^{12}+60307\,a^4\,b^{11}\,c^4\,d^{11}-66138\,a^3\,b^{12}\,c^5\,d^{10}+31509\,a^2\,b^{13}\,c^6\,d^9-6210\,a\,b^{14}\,c^7\,d^8+\frac{891\,b^{15}\,c^8\,d^7}{2}\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)\,{\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}{4096\,a^{19}\,d^{12}-49152\,a^{18}\,b\,c\,d^{11}+270336\,a^{17}\,b^2\,c^2\,d^{10}-901120\,a^{16}\,b^3\,c^3\,d^9+2027520\,a^{15}\,b^4\,c^4\,d^8-3244032\,a^{14}\,b^5\,c^5\,d^7+3784704\,a^{13}\,b^6\,c^6\,d^6-3244032\,a^{12}\,b^7\,c^7\,d^5+2027520\,a^{11}\,b^8\,c^8\,d^4-901120\,a^{10}\,b^9\,c^9\,d^3+270336\,a^9\,b^{10}\,c^{10}\,d^2-49152\,a^8\,b^{11}\,c^{11}\,d+4096\,a^7\,b^{12}\,c^{12}}\right)}^{1/4}-\frac{\sqrt{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)}{16\,\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}{4096\,a^{19}\,d^{12}-49152\,a^{18}\,b\,c\,d^{11}+270336\,a^{17}\,b^2\,c^2\,d^{10}-901120\,a^{16}\,b^3\,c^3\,d^9+2027520\,a^{15}\,b^4\,c^4\,d^8-3244032\,a^{14}\,b^5\,c^5\,d^7+3784704\,a^{13}\,b^6\,c^6\,d^6-3244032\,a^{12}\,b^7\,c^7\,d^5+2027520\,a^{11}\,b^8\,c^8\,d^4-901120\,a^{10}\,b^9\,c^9\,d^3+270336\,a^9\,b^{10}\,c^{10}\,d^2-49152\,a^8\,b^{11}\,c^{11}\,d+4096\,a^7\,b^{12}\,c^{12}}\right)}^{1/4}+\left(\left(\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}{4096\,a^{19}\,d^{12}-49152\,a^{18}\,b\,c\,d^{11}+270336\,a^{17}\,b^2\,c^2\,d^{10}-901120\,a^{16}\,b^3\,c^3\,d^9+2027520\,a^{15}\,b^4\,c^4\,d^8-3244032\,a^{14}\,b^5\,c^5\,d^7+3784704\,a^{13}\,b^6\,c^6\,d^6-3244032\,a^{12}\,b^7\,c^7\,d^5+2027520\,a^{11}\,b^8\,c^8\,d^4-901120\,a^{10}\,b^9\,c^9\,d^3+270336\,a^9\,b^{10}\,c^{10}\,d^2-49152\,a^8\,b^{11}\,c^{11}\,d+4096\,a^7\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(6144\,a^{19}\,b^4\,c^4\,d^{19}-90112\,a^{18}\,b^5\,c^5\,d^{18}+585728\,a^{17}\,b^6\,c^6\,d^{17}-2230272\,a^{16}\,b^7\,c^7\,d^{16}+5490688\,a^{15}\,b^8\,c^8\,d^{15}-8966144\,a^{14}\,b^9\,c^9\,d^{14}+9191424\,a^{13}\,b^{10}\,c^{10}\,d^{13}-3987456\,a^{12}\,b^{11}\,c^{11}\,d^{12}-3987456\,a^{11}\,b^{12}\,c^{12}\,d^{11}+9191424\,a^{10}\,b^{13}\,c^{13}\,d^{10}-8966144\,a^9\,b^{14}\,c^{14}\,d^9+5490688\,a^8\,b^{15}\,c^{15}\,d^8-2230272\,a^7\,b^{16}\,c^{16}\,d^7+585728\,a^6\,b^{17}\,c^{17}\,d^6-90112\,a^5\,b^{18}\,c^{18}\,d^5+6144\,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{\sqrt{x}\,\left(36864\,a^{21}\,b^4\,c^2\,d^{23}-712704\,a^{20}\,b^5\,c^3\,d^{22}+6172672\,a^{19}\,b^6\,c^4\,d^{21}-31899648\,a^{18}\,b^7\,c^5\,d^{20}+110432256\,a^{17}\,b^8\,c^6\,d^{19}-271552512\,a^{16}\,b^9\,c^7\,d^{18}+487280640\,a^{15}\,b^{10}\,c^8\,d^{17}-635523072\,a^{14}\,b^{11}\,c^9\,d^{16}+562982912\,a^{13}\,b^{12}\,c^{10}\,d^{15}-227217408\,a^{12}\,b^{13}\,c^{11}\,d^{14}-227217408\,a^{11}\,b^{14}\,c^{12}\,d^{13}+562982912\,a^{10}\,b^{15}\,c^{13}\,d^{12}-635523072\,a^9\,b^{16}\,c^{14}\,d^{11}+487280640\,a^8\,b^{17}\,c^{15}\,d^{10}-271552512\,a^7\,b^{18}\,c^{16}\,d^9+110432256\,a^6\,b^{19}\,c^{17}\,d^8-31899648\,a^5\,b^{20}\,c^{18}\,d^7+6172672\,a^4\,b^{21}\,c^{19}\,d^6-712704\,a^3\,b^{22}\,c^{20}\,d^5+36864\,a^2\,b^{23}\,c^{21}\,d^4\right)\,1{}\mathrm{i}}{16\,\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}{4096\,a^{19}\,d^{12}-49152\,a^{18}\,b\,c\,d^{11}+270336\,a^{17}\,b^2\,c^2\,d^{10}-901120\,a^{16}\,b^3\,c^3\,d^9+2027520\,a^{15}\,b^4\,c^4\,d^8-3244032\,a^{14}\,b^5\,c^5\,d^7+3784704\,a^{13}\,b^6\,c^6\,d^6-3244032\,a^{12}\,b^7\,c^7\,d^5+2027520\,a^{11}\,b^8\,c^8\,d^4-901120\,a^{10}\,b^9\,c^9\,d^3+270336\,a^9\,b^{10}\,c^{10}\,d^2-49152\,a^8\,b^{11}\,c^{11}\,d+4096\,a^7\,b^{12}\,c^{12}}\right)}^{3/4}\,1{}\mathrm{i}-\frac{\left(\frac{891\,a^8\,b^7\,d^{15}}{2}-6210\,a^7\,b^8\,c\,d^{14}+31509\,a^6\,b^9\,c^2\,d^{13}-66138\,a^5\,b^{10}\,c^3\,d^{12}+60307\,a^4\,b^{11}\,c^4\,d^{11}-66138\,a^3\,b^{12}\,c^5\,d^{10}+31509\,a^2\,b^{13}\,c^6\,d^9-6210\,a\,b^{14}\,c^7\,d^8+\frac{891\,b^{15}\,c^8\,d^7}{2}\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)\,{\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}{4096\,a^{19}\,d^{12}-49152\,a^{18}\,b\,c\,d^{11}+270336\,a^{17}\,b^2\,c^2\,d^{10}-901120\,a^{16}\,b^3\,c^3\,d^9+2027520\,a^{15}\,b^4\,c^4\,d^8-3244032\,a^{14}\,b^5\,c^5\,d^7+3784704\,a^{13}\,b^6\,c^6\,d^6-3244032\,a^{12}\,b^7\,c^7\,d^5+2027520\,a^{11}\,b^8\,c^8\,d^4-901120\,a^{10}\,b^9\,c^9\,d^3+270336\,a^9\,b^{10}\,c^{10}\,d^2-49152\,a^8\,b^{11}\,c^{11}\,d+4096\,a^7\,b^{12}\,c^{12}}\right)}^{1/4}-\frac{\sqrt{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)}{16\,\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}{4096\,a^{19}\,d^{12}-49152\,a^{18}\,b\,c\,d^{11}+270336\,a^{17}\,b^2\,c^2\,d^{10}-901120\,a^{16}\,b^3\,c^3\,d^9+2027520\,a^{15}\,b^4\,c^4\,d^8-3244032\,a^{14}\,b^5\,c^5\,d^7+3784704\,a^{13}\,b^6\,c^6\,d^6-3244032\,a^{12}\,b^7\,c^7\,d^5+2027520\,a^{11}\,b^8\,c^8\,d^4-901120\,a^{10}\,b^9\,c^9\,d^3+270336\,a^9\,b^{10}\,c^{10}\,d^2-49152\,a^8\,b^{11}\,c^{11}\,d+4096\,a^7\,b^{12}\,c^{12}}\right)}^{1/4}}{\left(\left(\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}{4096\,a^{19}\,d^{12}-49152\,a^{18}\,b\,c\,d^{11}+270336\,a^{17}\,b^2\,c^2\,d^{10}-901120\,a^{16}\,b^3\,c^3\,d^9+2027520\,a^{15}\,b^4\,c^4\,d^8-3244032\,a^{14}\,b^5\,c^5\,d^7+3784704\,a^{13}\,b^6\,c^6\,d^6-3244032\,a^{12}\,b^7\,c^7\,d^5+2027520\,a^{11}\,b^8\,c^8\,d^4-901120\,a^{10}\,b^9\,c^9\,d^3+270336\,a^9\,b^{10}\,c^{10}\,d^2-49152\,a^8\,b^{11}\,c^{11}\,d+4096\,a^7\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(6144\,a^{19}\,b^4\,c^4\,d^{19}-90112\,a^{18}\,b^5\,c^5\,d^{18}+585728\,a^{17}\,b^6\,c^6\,d^{17}-2230272\,a^{16}\,b^7\,c^7\,d^{16}+5490688\,a^{15}\,b^8\,c^8\,d^{15}-8966144\,a^{14}\,b^9\,c^9\,d^{14}+9191424\,a^{13}\,b^{10}\,c^{10}\,d^{13}-3987456\,a^{12}\,b^{11}\,c^{11}\,d^{12}-3987456\,a^{11}\,b^{12}\,c^{12}\,d^{11}+9191424\,a^{10}\,b^{13}\,c^{13}\,d^{10}-8966144\,a^9\,b^{14}\,c^{14}\,d^9+5490688\,a^8\,b^{15}\,c^{15}\,d^8-2230272\,a^7\,b^{16}\,c^{16}\,d^7+585728\,a^6\,b^{17}\,c^{17}\,d^6-90112\,a^5\,b^{18}\,c^{18}\,d^5+6144\,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{\sqrt{x}\,\left(36864\,a^{21}\,b^4\,c^2\,d^{23}-712704\,a^{20}\,b^5\,c^3\,d^{22}+6172672\,a^{19}\,b^6\,c^4\,d^{21}-31899648\,a^{18}\,b^7\,c^5\,d^{20}+110432256\,a^{17}\,b^8\,c^6\,d^{19}-271552512\,a^{16}\,b^9\,c^7\,d^{18}+487280640\,a^{15}\,b^{10}\,c^8\,d^{17}-635523072\,a^{14}\,b^{11}\,c^9\,d^{16}+562982912\,a^{13}\,b^{12}\,c^{10}\,d^{15}-227217408\,a^{12}\,b^{13}\,c^{11}\,d^{14}-227217408\,a^{11}\,b^{14}\,c^{12}\,d^{13}+562982912\,a^{10}\,b^{15}\,c^{13}\,d^{12}-635523072\,a^9\,b^{16}\,c^{14}\,d^{11}+487280640\,a^8\,b^{17}\,c^{15}\,d^{10}-271552512\,a^7\,b^{18}\,c^{16}\,d^9+110432256\,a^6\,b^{19}\,c^{17}\,d^8-31899648\,a^5\,b^{20}\,c^{18}\,d^7+6172672\,a^4\,b^{21}\,c^{19}\,d^6-712704\,a^3\,b^{22}\,c^{20}\,d^5+36864\,a^2\,b^{23}\,c^{21}\,d^4\right)\,1{}\mathrm{i}}{16\,\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}{4096\,a^{19}\,d^{12}-49152\,a^{18}\,b\,c\,d^{11}+270336\,a^{17}\,b^2\,c^2\,d^{10}-901120\,a^{16}\,b^3\,c^3\,d^9+2027520\,a^{15}\,b^4\,c^4\,d^8-3244032\,a^{14}\,b^5\,c^5\,d^7+3784704\,a^{13}\,b^6\,c^6\,d^6-3244032\,a^{12}\,b^7\,c^7\,d^5+2027520\,a^{11}\,b^8\,c^8\,d^4-901120\,a^{10}\,b^9\,c^9\,d^3+270336\,a^9\,b^{10}\,c^{10}\,d^2-49152\,a^8\,b^{11}\,c^{11}\,d+4096\,a^7\,b^{12}\,c^{12}}\right)}^{3/4}\,1{}\mathrm{i}+\frac{\left(\frac{891\,a^8\,b^7\,d^{15}}{2}-6210\,a^7\,b^8\,c\,d^{14}+31509\,a^6\,b^9\,c^2\,d^{13}-66138\,a^5\,b^{10}\,c^3\,d^{12}+60307\,a^4\,b^{11}\,c^4\,d^{11}-66138\,a^3\,b^{12}\,c^5\,d^{10}+31509\,a^2\,b^{13}\,c^6\,d^9-6210\,a\,b^{14}\,c^7\,d^8+\frac{891\,b^{15}\,c^8\,d^7}{2}\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)\,{\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}{4096\,a^{19}\,d^{12}-49152\,a^{18}\,b\,c\,d^{11}+270336\,a^{17}\,b^2\,c^2\,d^{10}-901120\,a^{16}\,b^3\,c^3\,d^9+2027520\,a^{15}\,b^4\,c^4\,d^8-3244032\,a^{14}\,b^5\,c^5\,d^7+3784704\,a^{13}\,b^6\,c^6\,d^6-3244032\,a^{12}\,b^7\,c^7\,d^5+2027520\,a^{11}\,b^8\,c^8\,d^4-901120\,a^{10}\,b^9\,c^9\,d^3+270336\,a^9\,b^{10}\,c^{10}\,d^2-49152\,a^8\,b^{11}\,c^{11}\,d+4096\,a^7\,b^{12}\,c^{12}}\right)}^{1/4}\,1{}\mathrm{i}-\frac{\sqrt{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}}{16\,\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}{4096\,a^{19}\,d^{12}-49152\,a^{18}\,b\,c\,d^{11}+270336\,a^{17}\,b^2\,c^2\,d^{10}-901120\,a^{16}\,b^3\,c^3\,d^9+2027520\,a^{15}\,b^4\,c^4\,d^8-3244032\,a^{14}\,b^5\,c^5\,d^7+3784704\,a^{13}\,b^6\,c^6\,d^6-3244032\,a^{12}\,b^7\,c^7\,d^5+2027520\,a^{11}\,b^8\,c^8\,d^4-901120\,a^{10}\,b^9\,c^9\,d^3+270336\,a^9\,b^{10}\,c^{10}\,d^2-49152\,a^8\,b^{11}\,c^{11}\,d+4096\,a^7\,b^{12}\,c^{12}}\right)}^{1/4}-\left(\left(\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}{4096\,a^{19}\,d^{12}-49152\,a^{18}\,b\,c\,d^{11}+270336\,a^{17}\,b^2\,c^2\,d^{10}-901120\,a^{16}\,b^3\,c^3\,d^9+2027520\,a^{15}\,b^4\,c^4\,d^8-3244032\,a^{14}\,b^5\,c^5\,d^7+3784704\,a^{13}\,b^6\,c^6\,d^6-3244032\,a^{12}\,b^7\,c^7\,d^5+2027520\,a^{11}\,b^8\,c^8\,d^4-901120\,a^{10}\,b^9\,c^9\,d^3+270336\,a^9\,b^{10}\,c^{10}\,d^2-49152\,a^8\,b^{11}\,c^{11}\,d+4096\,a^7\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(6144\,a^{19}\,b^4\,c^4\,d^{19}-90112\,a^{18}\,b^5\,c^5\,d^{18}+585728\,a^{17}\,b^6\,c^6\,d^{17}-2230272\,a^{16}\,b^7\,c^7\,d^{16}+5490688\,a^{15}\,b^8\,c^8\,d^{15}-8966144\,a^{14}\,b^9\,c^9\,d^{14}+9191424\,a^{13}\,b^{10}\,c^{10}\,d^{13}-3987456\,a^{12}\,b^{11}\,c^{11}\,d^{12}-3987456\,a^{11}\,b^{12}\,c^{12}\,d^{11}+9191424\,a^{10}\,b^{13}\,c^{13}\,d^{10}-8966144\,a^9\,b^{14}\,c^{14}\,d^9+5490688\,a^8\,b^{15}\,c^{15}\,d^8-2230272\,a^7\,b^{16}\,c^{16}\,d^7+585728\,a^6\,b^{17}\,c^{17}\,d^6-90112\,a^5\,b^{18}\,c^{18}\,d^5+6144\,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{\sqrt{x}\,\left(36864\,a^{21}\,b^4\,c^2\,d^{23}-712704\,a^{20}\,b^5\,c^3\,d^{22}+6172672\,a^{19}\,b^6\,c^4\,d^{21}-31899648\,a^{18}\,b^7\,c^5\,d^{20}+110432256\,a^{17}\,b^8\,c^6\,d^{19}-271552512\,a^{16}\,b^9\,c^7\,d^{18}+487280640\,a^{15}\,b^{10}\,c^8\,d^{17}-635523072\,a^{14}\,b^{11}\,c^9\,d^{16}+562982912\,a^{13}\,b^{12}\,c^{10}\,d^{15}-227217408\,a^{12}\,b^{13}\,c^{11}\,d^{14}-227217408\,a^{11}\,b^{14}\,c^{12}\,d^{13}+562982912\,a^{10}\,b^{15}\,c^{13}\,d^{12}-635523072\,a^9\,b^{16}\,c^{14}\,d^{11}+487280640\,a^8\,b^{17}\,c^{15}\,d^{10}-271552512\,a^7\,b^{18}\,c^{16}\,d^9+110432256\,a^6\,b^{19}\,c^{17}\,d^8-31899648\,a^5\,b^{20}\,c^{18}\,d^7+6172672\,a^4\,b^{21}\,c^{19}\,d^6-712704\,a^3\,b^{22}\,c^{20}\,d^5+36864\,a^2\,b^{23}\,c^{21}\,d^4\right)\,1{}\mathrm{i}}{16\,\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}{4096\,a^{19}\,d^{12}-49152\,a^{18}\,b\,c\,d^{11}+270336\,a^{17}\,b^2\,c^2\,d^{10}-901120\,a^{16}\,b^3\,c^3\,d^9+2027520\,a^{15}\,b^4\,c^4\,d^8-3244032\,a^{14}\,b^5\,c^5\,d^7+3784704\,a^{13}\,b^6\,c^6\,d^6-3244032\,a^{12}\,b^7\,c^7\,d^5+2027520\,a^{11}\,b^8\,c^8\,d^4-901120\,a^{10}\,b^9\,c^9\,d^3+270336\,a^9\,b^{10}\,c^{10}\,d^2-49152\,a^8\,b^{11}\,c^{11}\,d+4096\,a^7\,b^{12}\,c^{12}}\right)}^{3/4}\,1{}\mathrm{i}-\frac{\left(\frac{891\,a^8\,b^7\,d^{15}}{2}-6210\,a^7\,b^8\,c\,d^{14}+31509\,a^6\,b^9\,c^2\,d^{13}-66138\,a^5\,b^{10}\,c^3\,d^{12}+60307\,a^4\,b^{11}\,c^4\,d^{11}-66138\,a^3\,b^{12}\,c^5\,d^{10}+31509\,a^2\,b^{13}\,c^6\,d^9-6210\,a\,b^{14}\,c^7\,d^8+\frac{891\,b^{15}\,c^8\,d^7}{2}\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)\,{\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}{4096\,a^{19}\,d^{12}-49152\,a^{18}\,b\,c\,d^{11}+270336\,a^{17}\,b^2\,c^2\,d^{10}-901120\,a^{16}\,b^3\,c^3\,d^9+2027520\,a^{15}\,b^4\,c^4\,d^8-3244032\,a^{14}\,b^5\,c^5\,d^7+3784704\,a^{13}\,b^6\,c^6\,d^6-3244032\,a^{12}\,b^7\,c^7\,d^5+2027520\,a^{11}\,b^8\,c^8\,d^4-901120\,a^{10}\,b^9\,c^9\,d^3+270336\,a^9\,b^{10}\,c^{10}\,d^2-49152\,a^8\,b^{11}\,c^{11}\,d+4096\,a^7\,b^{12}\,c^{12}}\right)}^{1/4}\,1{}\mathrm{i}-\frac{\sqrt{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}}{16\,\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}{4096\,a^{19}\,d^{12}-49152\,a^{18}\,b\,c\,d^{11}+270336\,a^{17}\,b^2\,c^2\,d^{10}-901120\,a^{16}\,b^3\,c^3\,d^9+2027520\,a^{15}\,b^4\,c^4\,d^8-3244032\,a^{14}\,b^5\,c^5\,d^7+3784704\,a^{13}\,b^6\,c^6\,d^6-3244032\,a^{12}\,b^7\,c^7\,d^5+2027520\,a^{11}\,b^8\,c^8\,d^4-901120\,a^{10}\,b^9\,c^9\,d^3+270336\,a^9\,b^{10}\,c^{10}\,d^2-49152\,a^8\,b^{11}\,c^{11}\,d+4096\,a^7\,b^{12}\,c^{12}}\right)}^{1/4}}\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}{4096\,a^{19}\,d^{12}-49152\,a^{18}\,b\,c\,d^{11}+270336\,a^{17}\,b^2\,c^2\,d^{10}-901120\,a^{16}\,b^3\,c^3\,d^9+2027520\,a^{15}\,b^4\,c^4\,d^8-3244032\,a^{14}\,b^5\,c^5\,d^7+3784704\,a^{13}\,b^6\,c^6\,d^6-3244032\,a^{12}\,b^7\,c^7\,d^5+2027520\,a^{11}\,b^8\,c^8\,d^4-901120\,a^{10}\,b^9\,c^9\,d^3+270336\,a^9\,b^{10}\,c^{10}\,d^2-49152\,a^8\,b^{11}\,c^{11}\,d+4096\,a^7\,b^{12}\,c^{12}}\right)}^{1/4}-\mathrm{atan}\left(\frac{\left(\left(\left(\frac{\sqrt{x}\,\left(36864\,a^{21}\,b^4\,c^2\,d^{23}-712704\,a^{20}\,b^5\,c^3\,d^{22}+6172672\,a^{19}\,b^6\,c^4\,d^{21}-31899648\,a^{18}\,b^7\,c^5\,d^{20}+110432256\,a^{17}\,b^8\,c^6\,d^{19}-271552512\,a^{16}\,b^9\,c^7\,d^{18}+487280640\,a^{15}\,b^{10}\,c^8\,d^{17}-635523072\,a^{14}\,b^{11}\,c^9\,d^{16}+562982912\,a^{13}\,b^{12}\,c^{10}\,d^{15}-227217408\,a^{12}\,b^{13}\,c^{11}\,d^{14}-227217408\,a^{11}\,b^{14}\,c^{12}\,d^{13}+562982912\,a^{10}\,b^{15}\,c^{13}\,d^{12}-635523072\,a^9\,b^{16}\,c^{14}\,d^{11}+487280640\,a^8\,b^{17}\,c^{15}\,d^{10}-271552512\,a^7\,b^{18}\,c^{16}\,d^9+110432256\,a^6\,b^{19}\,c^{17}\,d^8-31899648\,a^5\,b^{20}\,c^{18}\,d^7+6172672\,a^4\,b^{21}\,c^{19}\,d^6-712704\,a^3\,b^{22}\,c^{20}\,d^5+36864\,a^2\,b^{23}\,c^{21}\,d^4\right)}{16\,\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}{4096\,a^{12}\,c^7\,d^{12}-49152\,a^{11}\,b\,c^8\,d^{11}+270336\,a^{10}\,b^2\,c^9\,d^{10}-901120\,a^9\,b^3\,c^{10}\,d^9+2027520\,a^8\,b^4\,c^{11}\,d^8-3244032\,a^7\,b^5\,c^{12}\,d^7+3784704\,a^6\,b^6\,c^{13}\,d^6-3244032\,a^5\,b^7\,c^{14}\,d^5+2027520\,a^4\,b^8\,c^{15}\,d^4-901120\,a^3\,b^9\,c^{16}\,d^3+270336\,a^2\,b^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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}{4096\,a^{12}\,c^7\,d^{12}-49152\,a^{11}\,b\,c^8\,d^{11}+270336\,a^{10}\,b^2\,c^9\,d^{10}-901120\,a^9\,b^3\,c^{10}\,d^9+2027520\,a^8\,b^4\,c^{11}\,d^8-3244032\,a^7\,b^5\,c^{12}\,d^7+3784704\,a^6\,b^6\,c^{13}\,d^6-3244032\,a^5\,b^7\,c^{14}\,d^5+2027520\,a^4\,b^8\,c^{15}\,d^4-901120\,a^3\,b^9\,c^{16}\,d^3+270336\,a^2\,b^{10}\,c^{17}\,d^2-49152\,a\,b^{11}\,c^{18}\,d+4096\,b^{12}\,c^{19}}\right)}^{1/4}\,\left(6144\,a^{19}\,b^4\,c^4\,d^{19}-90112\,a^{18}\,b^5\,c^5\,d^{18}+585728\,a^{17}\,b^6\,c^6\,d^{17}-2230272\,a^{16}\,b^7\,c^7\,d^{16}+5490688\,a^{15}\,b^8\,c^8\,d^{15}-8966144\,a^{14}\,b^9\,c^9\,d^{14}+9191424\,a^{13}\,b^{10}\,c^{10}\,d^{13}-3987456\,a^{12}\,b^{11}\,c^{11}\,d^{12}-3987456\,a^{11}\,b^{12}\,c^{12}\,d^{11}+9191424\,a^{10}\,b^{13}\,c^{13}\,d^{10}-8966144\,a^9\,b^{14}\,c^{14}\,d^9+5490688\,a^8\,b^{15}\,c^{15}\,d^8-2230272\,a^7\,b^{16}\,c^{16}\,d^7+585728\,a^6\,b^{17}\,c^{17}\,d^6-90112\,a^5\,b^{18}\,c^{18}\,d^5+6144\,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)\,{\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}{4096\,a^{12}\,c^7\,d^{12}-49152\,a^{11}\,b\,c^8\,d^{11}+270336\,a^{10}\,b^2\,c^9\,d^{10}-901120\,a^9\,b^3\,c^{10}\,d^9+2027520\,a^8\,b^4\,c^{11}\,d^8-3244032\,a^7\,b^5\,c^{12}\,d^7+3784704\,a^6\,b^6\,c^{13}\,d^6-3244032\,a^5\,b^7\,c^{14}\,d^5+2027520\,a^4\,b^8\,c^{15}\,d^4-901120\,a^3\,b^9\,c^{16}\,d^3+270336\,a^2\,b^{10}\,c^{17}\,d^2-49152\,a\,b^{11}\,c^{18}\,d+4096\,b^{12}\,c^{19}}\right)}^{3/4}+\frac{\frac{891\,a^8\,b^7\,d^{15}}{2}-6210\,a^7\,b^8\,c\,d^{14}+31509\,a^6\,b^9\,c^2\,d^{13}-66138\,a^5\,b^{10}\,c^3\,d^{12}+60307\,a^4\,b^{11}\,c^4\,d^{11}-66138\,a^3\,b^{12}\,c^5\,d^{10}+31509\,a^2\,b^{13}\,c^6\,d^9-6210\,a\,b^{14}\,c^7\,d^8+\frac{891\,b^{15}\,c^8\,d^7}{2}}{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)\,{\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}{4096\,a^{12}\,c^7\,d^{12}-49152\,a^{11}\,b\,c^8\,d^{11}+270336\,a^{10}\,b^2\,c^9\,d^{10}-901120\,a^9\,b^3\,c^{10}\,d^9+2027520\,a^8\,b^4\,c^{11}\,d^8-3244032\,a^7\,b^5\,c^{12}\,d^7+3784704\,a^6\,b^6\,c^{13}\,d^6-3244032\,a^5\,b^7\,c^{14}\,d^5+2027520\,a^4\,b^8\,c^{15}\,d^4-901120\,a^3\,b^9\,c^{16}\,d^3+270336\,a^2\,b^{10}\,c^{17}\,d^2-49152\,a\,b^{11}\,c^{18}\,d+4096\,b^{12}\,c^{19}}\right)}^{1/4}+\frac{\sqrt{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)}{16\,\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}{4096\,a^{12}\,c^7\,d^{12}-49152\,a^{11}\,b\,c^8\,d^{11}+270336\,a^{10}\,b^2\,c^9\,d^{10}-901120\,a^9\,b^3\,c^{10}\,d^9+2027520\,a^8\,b^4\,c^{11}\,d^8-3244032\,a^7\,b^5\,c^{12}\,d^7+3784704\,a^6\,b^6\,c^{13}\,d^6-3244032\,a^5\,b^7\,c^{14}\,d^5+2027520\,a^4\,b^8\,c^{15}\,d^4-901120\,a^3\,b^9\,c^{16}\,d^3+270336\,a^2\,b^{10}\,c^{17}\,d^2-49152\,a\,b^{11}\,c^{18}\,d+4096\,b^{12}\,c^{19}}\right)}^{1/4}-\left(\left(\left(\frac{\sqrt{x}\,\left(36864\,a^{21}\,b^4\,c^2\,d^{23}-712704\,a^{20}\,b^5\,c^3\,d^{22}+6172672\,a^{19}\,b^6\,c^4\,d^{21}-31899648\,a^{18}\,b^7\,c^5\,d^{20}+110432256\,a^{17}\,b^8\,c^6\,d^{19}-271552512\,a^{16}\,b^9\,c^7\,d^{18}+487280640\,a^{15}\,b^{10}\,c^8\,d^{17}-635523072\,a^{14}\,b^{11}\,c^9\,d^{16}+562982912\,a^{13}\,b^{12}\,c^{10}\,d^{15}-227217408\,a^{12}\,b^{13}\,c^{11}\,d^{14}-227217408\,a^{11}\,b^{14}\,c^{12}\,d^{13}+562982912\,a^{10}\,b^{15}\,c^{13}\,d^{12}-635523072\,a^9\,b^{16}\,c^{14}\,d^{11}+487280640\,a^8\,b^{17}\,c^{15}\,d^{10}-271552512\,a^7\,b^{18}\,c^{16}\,d^9+110432256\,a^6\,b^{19}\,c^{17}\,d^8-31899648\,a^5\,b^{20}\,c^{18}\,d^7+6172672\,a^4\,b^{21}\,c^{19}\,d^6-712704\,a^3\,b^{22}\,c^{20}\,d^5+36864\,a^2\,b^{23}\,c^{21}\,d^4\right)}{16\,\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\,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\,c^{16}\,d^3+270336\,a^2\,b^{10}\,c^{17}\,d^2-49152\,a\,b^{11}\,c^{18}\,d+4096\,b^{12}\,c^{19}}\right)}^{1/4}+\left(\left(\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}{4096\,a^{12}\,c^7\,d^{12}-49152\,a^{11}\,b\,c^8\,d^{11}+270336\,a^{10}\,b^2\,c^9\,d^{10}-901120\,a^9\,b^3\,c^{10}\,d^9+2027520\,a^8\,b^4\,c^{11}\,d^8-3244032\,a^7\,b^5\,c^{12}\,d^7+3784704\,a^6\,b^6\,c^{13}\,d^6-3244032\,a^5\,b^7\,c^{14}\,d^5+2027520\,a^4\,b^8\,c^{15}\,d^4-901120\,a^3\,b^9\,c^{16}\,d^3+270336\,a^2\,b^{10}\,c^{17}\,d^2-49152\,a\,b^{11}\,c^{18}\,d+4096\,b^{12}\,c^{19}}\right)}^{1/4}\,\left(6144\,a^{19}\,b^4\,c^4\,d^{19}-90112\,a^{18}\,b^5\,c^5\,d^{18}+585728\,a^{17}\,b^6\,c^6\,d^{17}-2230272\,a^{16}\,b^7\,c^7\,d^{16}+5490688\,a^{15}\,b^8\,c^8\,d^{15}-8966144\,a^{14}\,b^9\,c^9\,d^{14}+9191424\,a^{13}\,b^{10}\,c^{10}\,d^{13}-3987456\,a^{12}\,b^{11}\,c^{11}\,d^{12}-3987456\,a^{11}\,b^{12}\,c^{12}\,d^{11}+9191424\,a^{10}\,b^{13}\,c^{13}\,d^{10}-8966144\,a^9\,b^{14}\,c^{14}\,d^9+5490688\,a^8\,b^{15}\,c^{15}\,d^8-2230272\,a^7\,b^{16}\,c^{16}\,d^7+585728\,a^6\,b^{17}\,c^{17}\,d^6-90112\,a^5\,b^{18}\,c^{18}\,d^5+6144\,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{\sqrt{x}\,\left(36864\,a^{21}\,b^4\,c^2\,d^{23}-712704\,a^{20}\,b^5\,c^3\,d^{22}+6172672\,a^{19}\,b^6\,c^4\,d^{21}-31899648\,a^{18}\,b^7\,c^5\,d^{20}+110432256\,a^{17}\,b^8\,c^6\,d^{19}-271552512\,a^{16}\,b^9\,c^7\,d^{18}+487280640\,a^{15}\,b^{10}\,c^8\,d^{17}-635523072\,a^{14}\,b^{11}\,c^9\,d^{16}+562982912\,a^{13}\,b^{12}\,c^{10}\,d^{15}-227217408\,a^{12}\,b^{13}\,c^{11}\,d^{14}-227217408\,a^{11}\,b^{14}\,c^{12}\,d^{13}+562982912\,a^{10}\,b^{15}\,c^{13}\,d^{12}-635523072\,a^9\,b^{16}\,c^{14}\,d^{11}+487280640\,a^8\,b^{17}\,c^{15}\,d^{10}-271552512\,a^7\,b^{18}\,c^{16}\,d^9+110432256\,a^6\,b^{19}\,c^{17}\,d^8-31899648\,a^5\,b^{20}\,c^{18}\,d^7+6172672\,a^4\,b^{21}\,c^{19}\,d^6-712704\,a^3\,b^{22}\,c^{20}\,d^5+36864\,a^2\,b^{23}\,c^{21}\,d^4\right)\,1{}\mathrm{i}}{16\,\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}{4096\,a^{12}\,c^7\,d^{12}-49152\,a^{11}\,b\,c^8\,d^{11}+270336\,a^{10}\,b^2\,c^9\,d^{10}-901120\,a^9\,b^3\,c^{10}\,d^9+2027520\,a^8\,b^4\,c^{11}\,d^8-3244032\,a^7\,b^5\,c^{12}\,d^7+3784704\,a^6\,b^6\,c^{13}\,d^6-3244032\,a^5\,b^7\,c^{14}\,d^5+2027520\,a^4\,b^8\,c^{15}\,d^4-901120\,a^3\,b^9\,c^{16}\,d^3+270336\,a^2\,b^{10}\,c^{17}\,d^2-49152\,a\,b^{11}\,c^{18}\,d+4096\,b^{12}\,c^{19}}\right)}^{3/4}\,1{}\mathrm{i}-\frac{\left(\frac{891\,a^8\,b^7\,d^{15}}{2}-6210\,a^7\,b^8\,c\,d^{14}+31509\,a^6\,b^9\,c^2\,d^{13}-66138\,a^5\,b^{10}\,c^3\,d^{12}+60307\,a^4\,b^{11}\,c^4\,d^{11}-66138\,a^3\,b^{12}\,c^5\,d^{10}+31509\,a^2\,b^{13}\,c^6\,d^9-6210\,a\,b^{14}\,c^7\,d^8+\frac{891\,b^{15}\,c^8\,d^7}{2}\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)\,{\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}{4096\,a^{12}\,c^7\,d^{12}-49152\,a^{11}\,b\,c^8\,d^{11}+270336\,a^{10}\,b^2\,c^9\,d^{10}-901120\,a^9\,b^3\,c^{10}\,d^9+2027520\,a^8\,b^4\,c^{11}\,d^8-3244032\,a^7\,b^5\,c^{12}\,d^7+3784704\,a^6\,b^6\,c^{13}\,d^6-3244032\,a^5\,b^7\,c^{14}\,d^5+2027520\,a^4\,b^8\,c^{15}\,d^4-901120\,a^3\,b^9\,c^{16}\,d^3+270336\,a^2\,b^{10}\,c^{17}\,d^2-49152\,a\,b^{11}\,c^{18}\,d+4096\,b^{12}\,c^{19}}\right)}^{1/4}-\frac{\sqrt{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)}{16\,\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}{4096\,a^{12}\,c^7\,d^{12}-49152\,a^{11}\,b\,c^8\,d^{11}+270336\,a^{10}\,b^2\,c^9\,d^{10}-901120\,a^9\,b^3\,c^{10}\,d^9+2027520\,a^8\,b^4\,c^{11}\,d^8-3244032\,a^7\,b^5\,c^{12}\,d^7+3784704\,a^6\,b^6\,c^{13}\,d^6-3244032\,a^5\,b^7\,c^{14}\,d^5+2027520\,a^4\,b^8\,c^{15}\,d^4-901120\,a^3\,b^9\,c^{16}\,d^3+270336\,a^2\,b^{10}\,c^{17}\,d^2-49152\,a\,b^{11}\,c^{18}\,d+4096\,b^{12}\,c^{19}}\right)}^{1/4}}{\left(\left(\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}{4096\,a^{12}\,c^7\,d^{12}-49152\,a^{11}\,b\,c^8\,d^{11}+270336\,a^{10}\,b^2\,c^9\,d^{10}-901120\,a^9\,b^3\,c^{10}\,d^9+2027520\,a^8\,b^4\,c^{11}\,d^8-3244032\,a^7\,b^5\,c^{12}\,d^7+3784704\,a^6\,b^6\,c^{13}\,d^6-3244032\,a^5\,b^7\,c^{14}\,d^5+2027520\,a^4\,b^8\,c^{15}\,d^4-901120\,a^3\,b^9\,c^{16}\,d^3+270336\,a^2\,b^{10}\,c^{17}\,d^2-49152\,a\,b^{11}\,c^{18}\,d+4096\,b^{12}\,c^{19}}\right)}^{1/4}\,\left(6144\,a^{19}\,b^4\,c^4\,d^{19}-90112\,a^{18}\,b^5\,c^5\,d^{18}+585728\,a^{17}\,b^6\,c^6\,d^{17}-2230272\,a^{16}\,b^7\,c^7\,d^{16}+5490688\,a^{15}\,b^8\,c^8\,d^{15}-8966144\,a^{14}\,b^9\,c^9\,d^{14}+9191424\,a^{13}\,b^{10}\,c^{10}\,d^{13}-3987456\,a^{12}\,b^{11}\,c^{11}\,d^{12}-3987456\,a^{11}\,b^{12}\,c^{12}\,d^{11}+9191424\,a^{10}\,b^{13}\,c^{13}\,d^{10}-8966144\,a^9\,b^{14}\,c^{14}\,d^9+5490688\,a^8\,b^{15}\,c^{15}\,d^8-2230272\,a^7\,b^{16}\,c^{16}\,d^7+585728\,a^6\,b^{17}\,c^{17}\,d^6-90112\,a^5\,b^{18}\,c^{18}\,d^5+6144\,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{\sqrt{x}\,\left(36864\,a^{21}\,b^4\,c^2\,d^{23}-712704\,a^{20}\,b^5\,c^3\,d^{22}+6172672\,a^{19}\,b^6\,c^4\,d^{21}-31899648\,a^{18}\,b^7\,c^5\,d^{20}+110432256\,a^{17}\,b^8\,c^6\,d^{19}-271552512\,a^{16}\,b^9\,c^7\,d^{18}+487280640\,a^{15}\,b^{10}\,c^8\,d^{17}-635523072\,a^{14}\,b^{11}\,c^9\,d^{16}+562982912\,a^{13}\,b^{12}\,c^{10}\,d^{15}-227217408\,a^{12}\,b^{13}\,c^{11}\,d^{14}-227217408\,a^{11}\,b^{14}\,c^{12}\,d^{13}+562982912\,a^{10}\,b^{15}\,c^{13}\,d^{12}-635523072\,a^9\,b^{16}\,c^{14}\,d^{11}+487280640\,a^8\,b^{17}\,c^{15}\,d^{10}-271552512\,a^7\,b^{18}\,c^{16}\,d^9+110432256\,a^6\,b^{19}\,c^{17}\,d^8-31899648\,a^5\,b^{20}\,c^{18}\,d^7+6172672\,a^4\,b^{21}\,c^{19}\,d^6-712704\,a^3\,b^{22}\,c^{20}\,d^5+36864\,a^2\,b^{23}\,c^{21}\,d^4\right)\,1{}\mathrm{i}}{16\,\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}{4096\,a^{12}\,c^7\,d^{12}-49152\,a^{11}\,b\,c^8\,d^{11}+270336\,a^{10}\,b^2\,c^9\,d^{10}-901120\,a^9\,b^3\,c^{10}\,d^9+2027520\,a^8\,b^4\,c^{11}\,d^8-3244032\,a^7\,b^5\,c^{12}\,d^7+3784704\,a^6\,b^6\,c^{13}\,d^6-3244032\,a^5\,b^7\,c^{14}\,d^5+2027520\,a^4\,b^8\,c^{15}\,d^4-901120\,a^3\,b^9\,c^{16}\,d^3+270336\,a^2\,b^{10}\,c^{17}\,d^2-49152\,a\,b^{11}\,c^{18}\,d+4096\,b^{12}\,c^{19}}\right)}^{3/4}\,1{}\mathrm{i}+\frac{\left(\frac{891\,a^8\,b^7\,d^{15}}{2}-6210\,a^7\,b^8\,c\,d^{14}+31509\,a^6\,b^9\,c^2\,d^{13}-66138\,a^5\,b^{10}\,c^3\,d^{12}+60307\,a^4\,b^{11}\,c^4\,d^{11}-66138\,a^3\,b^{12}\,c^5\,d^{10}+31509\,a^2\,b^{13}\,c^6\,d^9-6210\,a\,b^{14}\,c^7\,d^8+\frac{891\,b^{15}\,c^8\,d^7}{2}\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)\,{\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}{4096\,a^{12}\,c^7\,d^{12}-49152\,a^{11}\,b\,c^8\,d^{11}+270336\,a^{10}\,b^2\,c^9\,d^{10}-901120\,a^9\,b^3\,c^{10}\,d^9+2027520\,a^8\,b^4\,c^{11}\,d^8-3244032\,a^7\,b^5\,c^{12}\,d^7+3784704\,a^6\,b^6\,c^{13}\,d^6-3244032\,a^5\,b^7\,c^{14}\,d^5+2027520\,a^4\,b^8\,c^{15}\,d^4-901120\,a^3\,b^9\,c^{16}\,d^3+270336\,a^2\,b^{10}\,c^{17}\,d^2-49152\,a\,b^{11}\,c^{18}\,d+4096\,b^{12}\,c^{19}}\right)}^{1/4}\,1{}\mathrm{i}-\frac{\sqrt{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}}{16\,\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}{4096\,a^{12}\,c^7\,d^{12}-49152\,a^{11}\,b\,c^8\,d^{11}+270336\,a^{10}\,b^2\,c^9\,d^{10}-901120\,a^9\,b^3\,c^{10}\,d^9+2027520\,a^8\,b^4\,c^{11}\,d^8-3244032\,a^7\,b^5\,c^{12}\,d^7+3784704\,a^6\,b^6\,c^{13}\,d^6-3244032\,a^5\,b^7\,c^{14}\,d^5+2027520\,a^4\,b^8\,c^{15}\,d^4-901120\,a^3\,b^9\,c^{16}\,d^3+270336\,a^2\,b^{10}\,c^{17}\,d^2-49152\,a\,b^{11}\,c^{18}\,d+4096\,b^{12}\,c^{19}}\right)}^{1/4}-\left(\left(\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}{4096\,a^{12}\,c^7\,d^{12}-49152\,a^{11}\,b\,c^8\,d^{11}+270336\,a^{10}\,b^2\,c^9\,d^{10}-901120\,a^9\,b^3\,c^{10}\,d^9+2027520\,a^8\,b^4\,c^{11}\,d^8-3244032\,a^7\,b^5\,c^{12}\,d^7+3784704\,a^6\,b^6\,c^{13}\,d^6-3244032\,a^5\,b^7\,c^{14}\,d^5+2027520\,a^4\,b^8\,c^{15}\,d^4-901120\,a^3\,b^9\,c^{16}\,d^3+270336\,a^2\,b^{10}\,c^{17}\,d^2-49152\,a\,b^{11}\,c^{18}\,d+4096\,b^{12}\,c^{19}}\right)}^{1/4}\,\left(6144\,a^{19}\,b^4\,c^4\,d^{19}-90112\,a^{18}\,b^5\,c^5\,d^{18}+585728\,a^{17}\,b^6\,c^6\,d^{17}-2230272\,a^{16}\,b^7\,c^7\,d^{16}+5490688\,a^{15}\,b^8\,c^8\,d^{15}-8966144\,a^{14}\,b^9\,c^9\,d^{14}+9191424\,a^{13}\,b^{10}\,c^{10}\,d^{13}-3987456\,a^{12}\,b^{11}\,c^{11}\,d^{12}-3987456\,a^{11}\,b^{12}\,c^{12}\,d^{11}+9191424\,a^{10}\,b^{13}\,c^{13}\,d^{10}-8966144\,a^9\,b^{14}\,c^{14}\,d^9+5490688\,a^8\,b^{15}\,c^{15}\,d^8-2230272\,a^7\,b^{16}\,c^{16}\,d^7+585728\,a^6\,b^{17}\,c^{17}\,d^6-90112\,a^5\,b^{18}\,c^{18}\,d^5+6144\,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{\sqrt{x}\,\left(36864\,a^{21}\,b^4\,c^2\,d^{23}-712704\,a^{20}\,b^5\,c^3\,d^{22}+6172672\,a^{19}\,b^6\,c^4\,d^{21}-31899648\,a^{18}\,b^7\,c^5\,d^{20}+110432256\,a^{17}\,b^8\,c^6\,d^{19}-271552512\,a^{16}\,b^9\,c^7\,d^{18}+487280640\,a^{15}\,b^{10}\,c^8\,d^{17}-635523072\,a^{14}\,b^{11}\,c^9\,d^{16}+562982912\,a^{13}\,b^{12}\,c^{10}\,d^{15}-227217408\,a^{12}\,b^{13}\,c^{11}\,d^{14}-227217408\,a^{11}\,b^{14}\,c^{12}\,d^{13}+562982912\,a^{10}\,b^{15}\,c^{13}\,d^{12}-635523072\,a^9\,b^{16}\,c^{14}\,d^{11}+487280640\,a^8\,b^{17}\,c^{15}\,d^{10}-271552512\,a^7\,b^{18}\,c^{16}\,d^9+110432256\,a^6\,b^{19}\,c^{17}\,d^8-31899648\,a^5\,b^{20}\,c^{18}\,d^7+6172672\,a^4\,b^{21}\,c^{19}\,d^6-712704\,a^3\,b^{22}\,c^{20}\,d^5+36864\,a^2\,b^{23}\,c^{21}\,d^4\right)\,1{}\mathrm{i}}{16\,\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}{4096\,a^{12}\,c^7\,d^{12}-49152\,a^{11}\,b\,c^8\,d^{11}+270336\,a^{10}\,b^2\,c^9\,d^{10}-901120\,a^9\,b^3\,c^{10}\,d^9+2027520\,a^8\,b^4\,c^{11}\,d^8-3244032\,a^7\,b^5\,c^{12}\,d^7+3784704\,a^6\,b^6\,c^{13}\,d^6-3244032\,a^5\,b^7\,c^{14}\,d^5+2027520\,a^4\,b^8\,c^{15}\,d^4-901120\,a^3\,b^9\,c^{16}\,d^3+270336\,a^2\,b^{10}\,c^{17}\,d^2-49152\,a\,b^{11}\,c^{18}\,d+4096\,b^{12}\,c^{19}}\right)}^{3/4}\,1{}\mathrm{i}-\frac{\left(\frac{891\,a^8\,b^7\,d^{15}}{2}-6210\,a^7\,b^8\,c\,d^{14}+31509\,a^6\,b^9\,c^2\,d^{13}-66138\,a^5\,b^{10}\,c^3\,d^{12}+60307\,a^4\,b^{11}\,c^4\,d^{11}-66138\,a^3\,b^{12}\,c^5\,d^{10}+31509\,a^2\,b^{13}\,c^6\,d^9-6210\,a\,b^{14}\,c^7\,d^8+\frac{891\,b^{15}\,c^8\,d^7}{2}\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)\,{\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}{4096\,a^{12}\,c^7\,d^{12}-49152\,a^{11}\,b\,c^8\,d^{11}+270336\,a^{10}\,b^2\,c^9\,d^{10}-901120\,a^9\,b^3\,c^{10}\,d^9+2027520\,a^8\,b^4\,c^{11}\,d^8-3244032\,a^7\,b^5\,c^{12}\,d^7+3784704\,a^6\,b^6\,c^{13}\,d^6-3244032\,a^5\,b^7\,c^{14}\,d^5+2027520\,a^4\,b^8\,c^{15}\,d^4-901120\,a^3\,b^9\,c^{16}\,d^3+270336\,a^2\,b^{10}\,c^{17}\,d^2-49152\,a\,b^{11}\,c^{18}\,d+4096\,b^{12}\,c^{19}}\right)}^{1/4}\,1{}\mathrm{i}-\frac{\sqrt{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}}{16\,\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}{4096\,a^{12}\,c^7\,d^{12}-49152\,a^{11}\,b\,c^8\,d^{11}+270336\,a^{10}\,b^2\,c^9\,d^{10}-901120\,a^9\,b^3\,c^{10}\,d^9+2027520\,a^8\,b^4\,c^{11}\,d^8-3244032\,a^7\,b^5\,c^{12}\,d^7+3784704\,a^6\,b^6\,c^{13}\,d^6-3244032\,a^5\,b^7\,c^{14}\,d^5+2027520\,a^4\,b^8\,c^{15}\,d^4-901120\,a^3\,b^9\,c^{16}\,d^3+270336\,a^2\,b^{10}\,c^{17}\,d^2-49152\,a\,b^{11}\,c^{18}\,d+4096\,b^{12}\,c^{19}}\right)}^{1/4}}\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}{4096\,a^{12}\,c^7\,d^{12}-49152\,a^{11}\,b\,c^8\,d^{11}+270336\,a^{10}\,b^2\,c^9\,d^{10}-901120\,a^9\,b^3\,c^{10}\,d^9+2027520\,a^8\,b^4\,c^{11}\,d^8-3244032\,a^7\,b^5\,c^{12}\,d^7+3784704\,a^6\,b^6\,c^{13}\,d^6-3244032\,a^5\,b^7\,c^{14}\,d^5+2027520\,a^4\,b^8\,c^{15}\,d^4-901120\,a^3\,b^9\,c^{16}\,d^3+270336\,a^2\,b^{10}\,c^{17}\,d^2-49152\,a\,b^{11}\,c^{18}\,d+4096\,b^{12}\,c^{19}}\right)}^{1/4}","Not used",1,"((x^(1/2)*(a^2*d^2 + b^2*c^2))/(2*a*c*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) + (b*d*x^(5/2)*(a*d + b*c))/(2*a*c*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)))/(a*c + x^2*(a*d + b*c) + b*d*x^4) - atan((((((x^(1/2)*(36864*a^2*b^23*c^21*d^4 - 712704*a^3*b^22*c^20*d^5 + 6172672*a^4*b^21*c^19*d^6 - 31899648*a^5*b^20*c^18*d^7 + 110432256*a^6*b^19*c^17*d^8 - 271552512*a^7*b^18*c^16*d^9 + 487280640*a^8*b^17*c^15*d^10 - 635523072*a^9*b^16*c^14*d^11 + 562982912*a^10*b^15*c^13*d^12 - 227217408*a^11*b^14*c^12*d^13 - 227217408*a^12*b^13*c^11*d^14 + 562982912*a^13*b^12*c^10*d^15 - 635523072*a^14*b^11*c^9*d^16 + 487280640*a^15*b^10*c^8*d^17 - 271552512*a^16*b^9*c^7*d^18 + 110432256*a^17*b^8*c^6*d^19 - 31899648*a^18*b^7*c^5*d^20 + 6172672*a^19*b^6*c^4*d^21 - 712704*a^20*b^5*c^3*d^22 + 36864*a^21*b^4*c^2*d^23))/(16*(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)/(4096*a^19*d^12 + 4096*a^7*b^12*c^12 - 49152*a^8*b^11*c^11*d + 270336*a^9*b^10*c^10*d^2 - 901120*a^10*b^9*c^9*d^3 + 2027520*a^11*b^8*c^8*d^4 - 3244032*a^12*b^7*c^7*d^5 + 3784704*a^13*b^6*c^6*d^6 - 3244032*a^14*b^5*c^5*d^7 + 2027520*a^15*b^4*c^4*d^8 - 901120*a^16*b^3*c^3*d^9 + 270336*a^17*b^2*c^2*d^10 - 49152*a^18*b*c*d^11))^(1/4)*(6144*a^4*b^19*c^19*d^4 - 90112*a^5*b^18*c^18*d^5 + 585728*a^6*b^17*c^17*d^6 - 2230272*a^7*b^16*c^16*d^7 + 5490688*a^8*b^15*c^15*d^8 - 8966144*a^9*b^14*c^14*d^9 + 9191424*a^10*b^13*c^13*d^10 - 3987456*a^11*b^12*c^12*d^11 - 3987456*a^12*b^11*c^11*d^12 + 9191424*a^13*b^10*c^10*d^13 - 8966144*a^14*b^9*c^9*d^14 + 5490688*a^15*b^8*c^8*d^15 - 2230272*a^16*b^7*c^7*d^16 + 585728*a^17*b^6*c^6*d^17 - 90112*a^18*b^5*c^5*d^18 + 6144*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))*(-(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)/(4096*a^19*d^12 + 4096*a^7*b^12*c^12 - 49152*a^8*b^11*c^11*d + 270336*a^9*b^10*c^10*d^2 - 901120*a^10*b^9*c^9*d^3 + 2027520*a^11*b^8*c^8*d^4 - 3244032*a^12*b^7*c^7*d^5 + 3784704*a^13*b^6*c^6*d^6 - 3244032*a^14*b^5*c^5*d^7 + 2027520*a^15*b^4*c^4*d^8 - 901120*a^16*b^3*c^3*d^9 + 270336*a^17*b^2*c^2*d^10 - 49152*a^18*b*c*d^11))^(3/4) + ((891*a^8*b^7*d^15)/2 + (891*b^15*c^8*d^7)/2 - 6210*a*b^14*c^7*d^8 - 6210*a^7*b^8*c*d^14 + 31509*a^2*b^13*c^6*d^9 - 66138*a^3*b^12*c^5*d^10 + 60307*a^4*b^11*c^4*d^11 - 66138*a^5*b^10*c^3*d^12 + 31509*a^6*b^9*c^2*d^13)/(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*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)/(4096*a^19*d^12 + 4096*a^7*b^12*c^12 - 49152*a^8*b^11*c^11*d + 270336*a^9*b^10*c^10*d^2 - 901120*a^10*b^9*c^9*d^3 + 2027520*a^11*b^8*c^8*d^4 - 3244032*a^12*b^7*c^7*d^5 + 3784704*a^13*b^6*c^6*d^6 - 3244032*a^14*b^5*c^5*d^7 + 2027520*a^15*b^4*c^4*d^8 - 901120*a^16*b^3*c^3*d^9 + 270336*a^17*b^2*c^2*d^10 - 49152*a^18*b*c*d^11))^(1/4)*1i + (x^(1/2)*(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)/(16*(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)/(4096*a^19*d^12 + 4096*a^7*b^12*c^12 - 49152*a^8*b^11*c^11*d + 270336*a^9*b^10*c^10*d^2 - 901120*a^10*b^9*c^9*d^3 + 2027520*a^11*b^8*c^8*d^4 - 3244032*a^12*b^7*c^7*d^5 + 3784704*a^13*b^6*c^6*d^6 - 3244032*a^14*b^5*c^5*d^7 + 2027520*a^15*b^4*c^4*d^8 - 901120*a^16*b^3*c^3*d^9 + 270336*a^17*b^2*c^2*d^10 - 49152*a^18*b*c*d^11))^(1/4) + ((((x^(1/2)*(36864*a^2*b^23*c^21*d^4 - 712704*a^3*b^22*c^20*d^5 + 6172672*a^4*b^21*c^19*d^6 - 31899648*a^5*b^20*c^18*d^7 + 110432256*a^6*b^19*c^17*d^8 - 271552512*a^7*b^18*c^16*d^9 + 487280640*a^8*b^17*c^15*d^10 - 635523072*a^9*b^16*c^14*d^11 + 562982912*a^10*b^15*c^13*d^12 - 227217408*a^11*b^14*c^12*d^13 - 227217408*a^12*b^13*c^11*d^14 + 562982912*a^13*b^12*c^10*d^15 - 635523072*a^14*b^11*c^9*d^16 + 487280640*a^15*b^10*c^8*d^17 - 271552512*a^16*b^9*c^7*d^18 + 110432256*a^17*b^8*c^6*d^19 - 31899648*a^18*b^7*c^5*d^20 + 6172672*a^19*b^6*c^4*d^21 - 712704*a^20*b^5*c^3*d^22 + 36864*a^21*b^4*c^2*d^23))/(16*(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)/(4096*a^19*d^12 + 4096*a^7*b^12*c^12 - 49152*a^8*b^11*c^11*d + 270336*a^9*b^10*c^10*d^2 - 901120*a^10*b^9*c^9*d^3 + 2027520*a^11*b^8*c^8*d^4 - 3244032*a^12*b^7*c^7*d^5 + 3784704*a^13*b^6*c^6*d^6 - 3244032*a^14*b^5*c^5*d^7 + 2027520*a^15*b^4*c^4*d^8 - 901120*a^16*b^3*c^3*d^9 + 270336*a^17*b^2*c^2*d^10 - 49152*a^18*b*c*d^11))^(1/4)*(6144*a^4*b^19*c^19*d^4 - 90112*a^5*b^18*c^18*d^5 + 585728*a^6*b^17*c^17*d^6 - 2230272*a^7*b^16*c^16*d^7 + 5490688*a^8*b^15*c^15*d^8 - 8966144*a^9*b^14*c^14*d^9 + 9191424*a^10*b^13*c^13*d^10 - 3987456*a^11*b^12*c^12*d^11 - 3987456*a^12*b^11*c^11*d^12 + 9191424*a^13*b^10*c^10*d^13 - 8966144*a^14*b^9*c^9*d^14 + 5490688*a^15*b^8*c^8*d^15 - 2230272*a^16*b^7*c^7*d^16 + 585728*a^17*b^6*c^6*d^17 - 90112*a^18*b^5*c^5*d^18 + 6144*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))*(-(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)/(4096*a^19*d^12 + 4096*a^7*b^12*c^12 - 49152*a^8*b^11*c^11*d + 270336*a^9*b^10*c^10*d^2 - 901120*a^10*b^9*c^9*d^3 + 2027520*a^11*b^8*c^8*d^4 - 3244032*a^12*b^7*c^7*d^5 + 3784704*a^13*b^6*c^6*d^6 - 3244032*a^14*b^5*c^5*d^7 + 2027520*a^15*b^4*c^4*d^8 - 901120*a^16*b^3*c^3*d^9 + 270336*a^17*b^2*c^2*d^10 - 49152*a^18*b*c*d^11))^(3/4) - ((891*a^8*b^7*d^15)/2 + (891*b^15*c^8*d^7)/2 - 6210*a*b^14*c^7*d^8 - 6210*a^7*b^8*c*d^14 + 31509*a^2*b^13*c^6*d^9 - 66138*a^3*b^12*c^5*d^10 + 60307*a^4*b^11*c^4*d^11 - 66138*a^5*b^10*c^3*d^12 + 31509*a^6*b^9*c^2*d^13)/(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*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)/(4096*a^19*d^12 + 4096*a^7*b^12*c^12 - 49152*a^8*b^11*c^11*d + 270336*a^9*b^10*c^10*d^2 - 901120*a^10*b^9*c^9*d^3 + 2027520*a^11*b^8*c^8*d^4 - 3244032*a^12*b^7*c^7*d^5 + 3784704*a^13*b^6*c^6*d^6 - 3244032*a^14*b^5*c^5*d^7 + 2027520*a^15*b^4*c^4*d^8 - 901120*a^16*b^3*c^3*d^9 + 270336*a^17*b^2*c^2*d^10 - 49152*a^18*b*c*d^11))^(1/4)*1i + (x^(1/2)*(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)/(16*(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)/(4096*a^19*d^12 + 4096*a^7*b^12*c^12 - 49152*a^8*b^11*c^11*d + 270336*a^9*b^10*c^10*d^2 - 901120*a^10*b^9*c^9*d^3 + 2027520*a^11*b^8*c^8*d^4 - 3244032*a^12*b^7*c^7*d^5 + 3784704*a^13*b^6*c^6*d^6 - 3244032*a^14*b^5*c^5*d^7 + 2027520*a^15*b^4*c^4*d^8 - 901120*a^16*b^3*c^3*d^9 + 270336*a^17*b^2*c^2*d^10 - 49152*a^18*b*c*d^11))^(1/4))/(((((x^(1/2)*(36864*a^2*b^23*c^21*d^4 - 712704*a^3*b^22*c^20*d^5 + 6172672*a^4*b^21*c^19*d^6 - 31899648*a^5*b^20*c^18*d^7 + 110432256*a^6*b^19*c^17*d^8 - 271552512*a^7*b^18*c^16*d^9 + 487280640*a^8*b^17*c^15*d^10 - 635523072*a^9*b^16*c^14*d^11 + 562982912*a^10*b^15*c^13*d^12 - 227217408*a^11*b^14*c^12*d^13 - 227217408*a^12*b^13*c^11*d^14 + 562982912*a^13*b^12*c^10*d^15 - 635523072*a^14*b^11*c^9*d^16 + 487280640*a^15*b^10*c^8*d^17 - 271552512*a^16*b^9*c^7*d^18 + 110432256*a^17*b^8*c^6*d^19 - 31899648*a^18*b^7*c^5*d^20 + 6172672*a^19*b^6*c^4*d^21 - 712704*a^20*b^5*c^3*d^22 + 36864*a^21*b^4*c^2*d^23))/(16*(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)/(4096*a^19*d^12 + 4096*a^7*b^12*c^12 - 49152*a^8*b^11*c^11*d + 270336*a^9*b^10*c^10*d^2 - 901120*a^10*b^9*c^9*d^3 + 2027520*a^11*b^8*c^8*d^4 - 3244032*a^12*b^7*c^7*d^5 + 3784704*a^13*b^6*c^6*d^6 - 3244032*a^14*b^5*c^5*d^7 + 2027520*a^15*b^4*c^4*d^8 - 901120*a^16*b^3*c^3*d^9 + 270336*a^17*b^2*c^2*d^10 - 49152*a^18*b*c*d^11))^(1/4)*(6144*a^4*b^19*c^19*d^4 - 90112*a^5*b^18*c^18*d^5 + 585728*a^6*b^17*c^17*d^6 - 2230272*a^7*b^16*c^16*d^7 + 5490688*a^8*b^15*c^15*d^8 - 8966144*a^9*b^14*c^14*d^9 + 9191424*a^10*b^13*c^13*d^10 - 3987456*a^11*b^12*c^12*d^11 - 3987456*a^12*b^11*c^11*d^12 + 9191424*a^13*b^10*c^10*d^13 - 8966144*a^14*b^9*c^9*d^14 + 5490688*a^15*b^8*c^8*d^15 - 2230272*a^16*b^7*c^7*d^16 + 585728*a^17*b^6*c^6*d^17 - 90112*a^18*b^5*c^5*d^18 + 6144*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))*(-(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)/(4096*a^19*d^12 + 4096*a^7*b^12*c^12 - 49152*a^8*b^11*c^11*d + 270336*a^9*b^10*c^10*d^2 - 901120*a^10*b^9*c^9*d^3 + 2027520*a^11*b^8*c^8*d^4 - 3244032*a^12*b^7*c^7*d^5 + 3784704*a^13*b^6*c^6*d^6 - 3244032*a^14*b^5*c^5*d^7 + 2027520*a^15*b^4*c^4*d^8 - 901120*a^16*b^3*c^3*d^9 + 270336*a^17*b^2*c^2*d^10 - 49152*a^18*b*c*d^11))^(3/4) + ((891*a^8*b^7*d^15)/2 + (891*b^15*c^8*d^7)/2 - 6210*a*b^14*c^7*d^8 - 6210*a^7*b^8*c*d^14 + 31509*a^2*b^13*c^6*d^9 - 66138*a^3*b^12*c^5*d^10 + 60307*a^4*b^11*c^4*d^11 - 66138*a^5*b^10*c^3*d^12 + 31509*a^6*b^9*c^2*d^13)/(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*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)/(4096*a^19*d^12 + 4096*a^7*b^12*c^12 - 49152*a^8*b^11*c^11*d + 270336*a^9*b^10*c^10*d^2 - 901120*a^10*b^9*c^9*d^3 + 2027520*a^11*b^8*c^8*d^4 - 3244032*a^12*b^7*c^7*d^5 + 3784704*a^13*b^6*c^6*d^6 - 3244032*a^14*b^5*c^5*d^7 + 2027520*a^15*b^4*c^4*d^8 - 901120*a^16*b^3*c^3*d^9 + 270336*a^17*b^2*c^2*d^10 - 49152*a^18*b*c*d^11))^(1/4) + (x^(1/2)*(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))/(16*(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)/(4096*a^19*d^12 + 4096*a^7*b^12*c^12 - 49152*a^8*b^11*c^11*d + 270336*a^9*b^10*c^10*d^2 - 901120*a^10*b^9*c^9*d^3 + 2027520*a^11*b^8*c^8*d^4 - 3244032*a^12*b^7*c^7*d^5 + 3784704*a^13*b^6*c^6*d^6 - 3244032*a^14*b^5*c^5*d^7 + 2027520*a^15*b^4*c^4*d^8 - 901120*a^16*b^3*c^3*d^9 + 270336*a^17*b^2*c^2*d^10 - 49152*a^18*b*c*d^11))^(1/4) - ((((x^(1/2)*(36864*a^2*b^23*c^21*d^4 - 712704*a^3*b^22*c^20*d^5 + 6172672*a^4*b^21*c^19*d^6 - 31899648*a^5*b^20*c^18*d^7 + 110432256*a^6*b^19*c^17*d^8 - 271552512*a^7*b^18*c^16*d^9 + 487280640*a^8*b^17*c^15*d^10 - 635523072*a^9*b^16*c^14*d^11 + 562982912*a^10*b^15*c^13*d^12 - 227217408*a^11*b^14*c^12*d^13 - 227217408*a^12*b^13*c^11*d^14 + 562982912*a^13*b^12*c^10*d^15 - 635523072*a^14*b^11*c^9*d^16 + 487280640*a^15*b^10*c^8*d^17 - 271552512*a^16*b^9*c^7*d^18 + 110432256*a^17*b^8*c^6*d^19 - 31899648*a^18*b^7*c^5*d^20 + 6172672*a^19*b^6*c^4*d^21 - 712704*a^20*b^5*c^3*d^22 + 36864*a^21*b^4*c^2*d^23))/(16*(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)/(4096*a^19*d^12 + 4096*a^7*b^12*c^12 - 49152*a^8*b^11*c^11*d + 270336*a^9*b^10*c^10*d^2 - 901120*a^10*b^9*c^9*d^3 + 2027520*a^11*b^8*c^8*d^4 - 3244032*a^12*b^7*c^7*d^5 + 3784704*a^13*b^6*c^6*d^6 - 3244032*a^14*b^5*c^5*d^7 + 2027520*a^15*b^4*c^4*d^8 - 901120*a^16*b^3*c^3*d^9 + 270336*a^17*b^2*c^2*d^10 - 49152*a^18*b*c*d^11))^(1/4)*(6144*a^4*b^19*c^19*d^4 - 90112*a^5*b^18*c^18*d^5 + 585728*a^6*b^17*c^17*d^6 - 2230272*a^7*b^16*c^16*d^7 + 5490688*a^8*b^15*c^15*d^8 - 8966144*a^9*b^14*c^14*d^9 + 9191424*a^10*b^13*c^13*d^10 - 3987456*a^11*b^12*c^12*d^11 - 3987456*a^12*b^11*c^11*d^12 + 9191424*a^13*b^10*c^10*d^13 - 8966144*a^14*b^9*c^9*d^14 + 5490688*a^15*b^8*c^8*d^15 - 2230272*a^16*b^7*c^7*d^16 + 585728*a^17*b^6*c^6*d^17 - 90112*a^18*b^5*c^5*d^18 + 6144*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))*(-(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)/(4096*a^19*d^12 + 4096*a^7*b^12*c^12 - 49152*a^8*b^11*c^11*d + 270336*a^9*b^10*c^10*d^2 - 901120*a^10*b^9*c^9*d^3 + 2027520*a^11*b^8*c^8*d^4 - 3244032*a^12*b^7*c^7*d^5 + 3784704*a^13*b^6*c^6*d^6 - 3244032*a^14*b^5*c^5*d^7 + 2027520*a^15*b^4*c^4*d^8 - 901120*a^16*b^3*c^3*d^9 + 270336*a^17*b^2*c^2*d^10 - 49152*a^18*b*c*d^11))^(3/4) - ((891*a^8*b^7*d^15)/2 + (891*b^15*c^8*d^7)/2 - 6210*a*b^14*c^7*d^8 - 6210*a^7*b^8*c*d^14 + 31509*a^2*b^13*c^6*d^9 - 66138*a^3*b^12*c^5*d^10 + 60307*a^4*b^11*c^4*d^11 - 66138*a^5*b^10*c^3*d^12 + 31509*a^6*b^9*c^2*d^13)/(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*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)/(4096*a^19*d^12 + 4096*a^7*b^12*c^12 - 49152*a^8*b^11*c^11*d + 270336*a^9*b^10*c^10*d^2 - 901120*a^10*b^9*c^9*d^3 + 2027520*a^11*b^8*c^8*d^4 - 3244032*a^12*b^7*c^7*d^5 + 3784704*a^13*b^6*c^6*d^6 - 3244032*a^14*b^5*c^5*d^7 + 2027520*a^15*b^4*c^4*d^8 - 901120*a^16*b^3*c^3*d^9 + 270336*a^17*b^2*c^2*d^10 - 49152*a^18*b*c*d^11))^(1/4) + (x^(1/2)*(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))/(16*(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)/(4096*a^19*d^12 + 4096*a^7*b^12*c^12 - 49152*a^8*b^11*c^11*d + 270336*a^9*b^10*c^10*d^2 - 901120*a^10*b^9*c^9*d^3 + 2027520*a^11*b^8*c^8*d^4 - 3244032*a^12*b^7*c^7*d^5 + 3784704*a^13*b^6*c^6*d^6 - 3244032*a^14*b^5*c^5*d^7 + 2027520*a^15*b^4*c^4*d^8 - 901120*a^16*b^3*c^3*d^9 + 270336*a^17*b^2*c^2*d^10 - 49152*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)/(4096*a^19*d^12 + 4096*a^7*b^12*c^12 - 49152*a^8*b^11*c^11*d + 270336*a^9*b^10*c^10*d^2 - 901120*a^10*b^9*c^9*d^3 + 2027520*a^11*b^8*c^8*d^4 - 3244032*a^12*b^7*c^7*d^5 + 3784704*a^13*b^6*c^6*d^6 - 3244032*a^14*b^5*c^5*d^7 + 2027520*a^15*b^4*c^4*d^8 - 901120*a^16*b^3*c^3*d^9 + 270336*a^17*b^2*c^2*d^10 - 49152*a^18*b*c*d^11))^(1/4)*2i + 2*atan((((((x^(1/2)*(36864*a^2*b^23*c^21*d^4 - 712704*a^3*b^22*c^20*d^5 + 6172672*a^4*b^21*c^19*d^6 - 31899648*a^5*b^20*c^18*d^7 + 110432256*a^6*b^19*c^17*d^8 - 271552512*a^7*b^18*c^16*d^9 + 487280640*a^8*b^17*c^15*d^10 - 635523072*a^9*b^16*c^14*d^11 + 562982912*a^10*b^15*c^13*d^12 - 227217408*a^11*b^14*c^12*d^13 - 227217408*a^12*b^13*c^11*d^14 + 562982912*a^13*b^12*c^10*d^15 - 635523072*a^14*b^11*c^9*d^16 + 487280640*a^15*b^10*c^8*d^17 - 271552512*a^16*b^9*c^7*d^18 + 110432256*a^17*b^8*c^6*d^19 - 31899648*a^18*b^7*c^5*d^20 + 6172672*a^19*b^6*c^4*d^21 - 712704*a^20*b^5*c^3*d^22 + 36864*a^21*b^4*c^2*d^23)*1i)/(16*(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)/(4096*a^19*d^12 + 4096*a^7*b^12*c^12 - 49152*a^8*b^11*c^11*d + 270336*a^9*b^10*c^10*d^2 - 901120*a^10*b^9*c^9*d^3 + 2027520*a^11*b^8*c^8*d^4 - 3244032*a^12*b^7*c^7*d^5 + 3784704*a^13*b^6*c^6*d^6 - 3244032*a^14*b^5*c^5*d^7 + 2027520*a^15*b^4*c^4*d^8 - 901120*a^16*b^3*c^3*d^9 + 270336*a^17*b^2*c^2*d^10 - 49152*a^18*b*c*d^11))^(1/4)*(6144*a^4*b^19*c^19*d^4 - 90112*a^5*b^18*c^18*d^5 + 585728*a^6*b^17*c^17*d^6 - 2230272*a^7*b^16*c^16*d^7 + 5490688*a^8*b^15*c^15*d^8 - 8966144*a^9*b^14*c^14*d^9 + 9191424*a^10*b^13*c^13*d^10 - 3987456*a^11*b^12*c^12*d^11 - 3987456*a^12*b^11*c^11*d^12 + 9191424*a^13*b^10*c^10*d^13 - 8966144*a^14*b^9*c^9*d^14 + 5490688*a^15*b^8*c^8*d^15 - 2230272*a^16*b^7*c^7*d^16 + 585728*a^17*b^6*c^6*d^17 - 90112*a^18*b^5*c^5*d^18 + 6144*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))*(-(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)/(4096*a^19*d^12 + 4096*a^7*b^12*c^12 - 49152*a^8*b^11*c^11*d + 270336*a^9*b^10*c^10*d^2 - 901120*a^10*b^9*c^9*d^3 + 2027520*a^11*b^8*c^8*d^4 - 3244032*a^12*b^7*c^7*d^5 + 3784704*a^13*b^6*c^6*d^6 - 3244032*a^14*b^5*c^5*d^7 + 2027520*a^15*b^4*c^4*d^8 - 901120*a^16*b^3*c^3*d^9 + 270336*a^17*b^2*c^2*d^10 - 49152*a^18*b*c*d^11))^(3/4)*1i + (((891*a^8*b^7*d^15)/2 + (891*b^15*c^8*d^7)/2 - 6210*a*b^14*c^7*d^8 - 6210*a^7*b^8*c*d^14 + 31509*a^2*b^13*c^6*d^9 - 66138*a^3*b^12*c^5*d^10 + 60307*a^4*b^11*c^4*d^11 - 66138*a^5*b^10*c^3*d^12 + 31509*a^6*b^9*c^2*d^13)*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*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)/(4096*a^19*d^12 + 4096*a^7*b^12*c^12 - 49152*a^8*b^11*c^11*d + 270336*a^9*b^10*c^10*d^2 - 901120*a^10*b^9*c^9*d^3 + 2027520*a^11*b^8*c^8*d^4 - 3244032*a^12*b^7*c^7*d^5 + 3784704*a^13*b^6*c^6*d^6 - 3244032*a^14*b^5*c^5*d^7 + 2027520*a^15*b^4*c^4*d^8 - 901120*a^16*b^3*c^3*d^9 + 270336*a^17*b^2*c^2*d^10 - 49152*a^18*b*c*d^11))^(1/4) - (x^(1/2)*(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))/(16*(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)/(4096*a^19*d^12 + 4096*a^7*b^12*c^12 - 49152*a^8*b^11*c^11*d + 270336*a^9*b^10*c^10*d^2 - 901120*a^10*b^9*c^9*d^3 + 2027520*a^11*b^8*c^8*d^4 - 3244032*a^12*b^7*c^7*d^5 + 3784704*a^13*b^6*c^6*d^6 - 3244032*a^14*b^5*c^5*d^7 + 2027520*a^15*b^4*c^4*d^8 - 901120*a^16*b^3*c^3*d^9 + 270336*a^17*b^2*c^2*d^10 - 49152*a^18*b*c*d^11))^(1/4) + ((((x^(1/2)*(36864*a^2*b^23*c^21*d^4 - 712704*a^3*b^22*c^20*d^5 + 6172672*a^4*b^21*c^19*d^6 - 31899648*a^5*b^20*c^18*d^7 + 110432256*a^6*b^19*c^17*d^8 - 271552512*a^7*b^18*c^16*d^9 + 487280640*a^8*b^17*c^15*d^10 - 635523072*a^9*b^16*c^14*d^11 + 562982912*a^10*b^15*c^13*d^12 - 227217408*a^11*b^14*c^12*d^13 - 227217408*a^12*b^13*c^11*d^14 + 562982912*a^13*b^12*c^10*d^15 - 635523072*a^14*b^11*c^9*d^16 + 487280640*a^15*b^10*c^8*d^17 - 271552512*a^16*b^9*c^7*d^18 + 110432256*a^17*b^8*c^6*d^19 - 31899648*a^18*b^7*c^5*d^20 + 6172672*a^19*b^6*c^4*d^21 - 712704*a^20*b^5*c^3*d^22 + 36864*a^21*b^4*c^2*d^23)*1i)/(16*(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)/(4096*a^19*d^12 + 4096*a^7*b^12*c^12 - 49152*a^8*b^11*c^11*d + 270336*a^9*b^10*c^10*d^2 - 901120*a^10*b^9*c^9*d^3 + 2027520*a^11*b^8*c^8*d^4 - 3244032*a^12*b^7*c^7*d^5 + 3784704*a^13*b^6*c^6*d^6 - 3244032*a^14*b^5*c^5*d^7 + 2027520*a^15*b^4*c^4*d^8 - 901120*a^16*b^3*c^3*d^9 + 270336*a^17*b^2*c^2*d^10 - 49152*a^18*b*c*d^11))^(1/4)*(6144*a^4*b^19*c^19*d^4 - 90112*a^5*b^18*c^18*d^5 + 585728*a^6*b^17*c^17*d^6 - 2230272*a^7*b^16*c^16*d^7 + 5490688*a^8*b^15*c^15*d^8 - 8966144*a^9*b^14*c^14*d^9 + 9191424*a^10*b^13*c^13*d^10 - 3987456*a^11*b^12*c^12*d^11 - 3987456*a^12*b^11*c^11*d^12 + 9191424*a^13*b^10*c^10*d^13 - 8966144*a^14*b^9*c^9*d^14 + 5490688*a^15*b^8*c^8*d^15 - 2230272*a^16*b^7*c^7*d^16 + 585728*a^17*b^6*c^6*d^17 - 90112*a^18*b^5*c^5*d^18 + 6144*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))*(-(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)/(4096*a^19*d^12 + 4096*a^7*b^12*c^12 - 49152*a^8*b^11*c^11*d + 270336*a^9*b^10*c^10*d^2 - 901120*a^10*b^9*c^9*d^3 + 2027520*a^11*b^8*c^8*d^4 - 3244032*a^12*b^7*c^7*d^5 + 3784704*a^13*b^6*c^6*d^6 - 3244032*a^14*b^5*c^5*d^7 + 2027520*a^15*b^4*c^4*d^8 - 901120*a^16*b^3*c^3*d^9 + 270336*a^17*b^2*c^2*d^10 - 49152*a^18*b*c*d^11))^(3/4)*1i - (((891*a^8*b^7*d^15)/2 + (891*b^15*c^8*d^7)/2 - 6210*a*b^14*c^7*d^8 - 6210*a^7*b^8*c*d^14 + 31509*a^2*b^13*c^6*d^9 - 66138*a^3*b^12*c^5*d^10 + 60307*a^4*b^11*c^4*d^11 - 66138*a^5*b^10*c^3*d^12 + 31509*a^6*b^9*c^2*d^13)*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*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)/(4096*a^19*d^12 + 4096*a^7*b^12*c^12 - 49152*a^8*b^11*c^11*d + 270336*a^9*b^10*c^10*d^2 - 901120*a^10*b^9*c^9*d^3 + 2027520*a^11*b^8*c^8*d^4 - 3244032*a^12*b^7*c^7*d^5 + 3784704*a^13*b^6*c^6*d^6 - 3244032*a^14*b^5*c^5*d^7 + 2027520*a^15*b^4*c^4*d^8 - 901120*a^16*b^3*c^3*d^9 + 270336*a^17*b^2*c^2*d^10 - 49152*a^18*b*c*d^11))^(1/4) - (x^(1/2)*(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))/(16*(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)/(4096*a^19*d^12 + 4096*a^7*b^12*c^12 - 49152*a^8*b^11*c^11*d + 270336*a^9*b^10*c^10*d^2 - 901120*a^10*b^9*c^9*d^3 + 2027520*a^11*b^8*c^8*d^4 - 3244032*a^12*b^7*c^7*d^5 + 3784704*a^13*b^6*c^6*d^6 - 3244032*a^14*b^5*c^5*d^7 + 2027520*a^15*b^4*c^4*d^8 - 901120*a^16*b^3*c^3*d^9 + 270336*a^17*b^2*c^2*d^10 - 49152*a^18*b*c*d^11))^(1/4))/(((((x^(1/2)*(36864*a^2*b^23*c^21*d^4 - 712704*a^3*b^22*c^20*d^5 + 6172672*a^4*b^21*c^19*d^6 - 31899648*a^5*b^20*c^18*d^7 + 110432256*a^6*b^19*c^17*d^8 - 271552512*a^7*b^18*c^16*d^9 + 487280640*a^8*b^17*c^15*d^10 - 635523072*a^9*b^16*c^14*d^11 + 562982912*a^10*b^15*c^13*d^12 - 227217408*a^11*b^14*c^12*d^13 - 227217408*a^12*b^13*c^11*d^14 + 562982912*a^13*b^12*c^10*d^15 - 635523072*a^14*b^11*c^9*d^16 + 487280640*a^15*b^10*c^8*d^17 - 271552512*a^16*b^9*c^7*d^18 + 110432256*a^17*b^8*c^6*d^19 - 31899648*a^18*b^7*c^5*d^20 + 6172672*a^19*b^6*c^4*d^21 - 712704*a^20*b^5*c^3*d^22 + 36864*a^21*b^4*c^2*d^23)*1i)/(16*(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)/(4096*a^19*d^12 + 4096*a^7*b^12*c^12 - 49152*a^8*b^11*c^11*d + 270336*a^9*b^10*c^10*d^2 - 901120*a^10*b^9*c^9*d^3 + 2027520*a^11*b^8*c^8*d^4 - 3244032*a^12*b^7*c^7*d^5 + 3784704*a^13*b^6*c^6*d^6 - 3244032*a^14*b^5*c^5*d^7 + 2027520*a^15*b^4*c^4*d^8 - 901120*a^16*b^3*c^3*d^9 + 270336*a^17*b^2*c^2*d^10 - 49152*a^18*b*c*d^11))^(1/4)*(6144*a^4*b^19*c^19*d^4 - 90112*a^5*b^18*c^18*d^5 + 585728*a^6*b^17*c^17*d^6 - 2230272*a^7*b^16*c^16*d^7 + 5490688*a^8*b^15*c^15*d^8 - 8966144*a^9*b^14*c^14*d^9 + 9191424*a^10*b^13*c^13*d^10 - 3987456*a^11*b^12*c^12*d^11 - 3987456*a^12*b^11*c^11*d^12 + 9191424*a^13*b^10*c^10*d^13 - 8966144*a^14*b^9*c^9*d^14 + 5490688*a^15*b^8*c^8*d^15 - 2230272*a^16*b^7*c^7*d^16 + 585728*a^17*b^6*c^6*d^17 - 90112*a^18*b^5*c^5*d^18 + 6144*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))*(-(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)/(4096*a^19*d^12 + 4096*a^7*b^12*c^12 - 49152*a^8*b^11*c^11*d + 270336*a^9*b^10*c^10*d^2 - 901120*a^10*b^9*c^9*d^3 + 2027520*a^11*b^8*c^8*d^4 - 3244032*a^12*b^7*c^7*d^5 + 3784704*a^13*b^6*c^6*d^6 - 3244032*a^14*b^5*c^5*d^7 + 2027520*a^15*b^4*c^4*d^8 - 901120*a^16*b^3*c^3*d^9 + 270336*a^17*b^2*c^2*d^10 - 49152*a^18*b*c*d^11))^(3/4)*1i + (((891*a^8*b^7*d^15)/2 + (891*b^15*c^8*d^7)/2 - 6210*a*b^14*c^7*d^8 - 6210*a^7*b^8*c*d^14 + 31509*a^2*b^13*c^6*d^9 - 66138*a^3*b^12*c^5*d^10 + 60307*a^4*b^11*c^4*d^11 - 66138*a^5*b^10*c^3*d^12 + 31509*a^6*b^9*c^2*d^13)*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*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)/(4096*a^19*d^12 + 4096*a^7*b^12*c^12 - 49152*a^8*b^11*c^11*d + 270336*a^9*b^10*c^10*d^2 - 901120*a^10*b^9*c^9*d^3 + 2027520*a^11*b^8*c^8*d^4 - 3244032*a^12*b^7*c^7*d^5 + 3784704*a^13*b^6*c^6*d^6 - 3244032*a^14*b^5*c^5*d^7 + 2027520*a^15*b^4*c^4*d^8 - 901120*a^16*b^3*c^3*d^9 + 270336*a^17*b^2*c^2*d^10 - 49152*a^18*b*c*d^11))^(1/4)*1i - (x^(1/2)*(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)/(16*(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)/(4096*a^19*d^12 + 4096*a^7*b^12*c^12 - 49152*a^8*b^11*c^11*d + 270336*a^9*b^10*c^10*d^2 - 901120*a^10*b^9*c^9*d^3 + 2027520*a^11*b^8*c^8*d^4 - 3244032*a^12*b^7*c^7*d^5 + 3784704*a^13*b^6*c^6*d^6 - 3244032*a^14*b^5*c^5*d^7 + 2027520*a^15*b^4*c^4*d^8 - 901120*a^16*b^3*c^3*d^9 + 270336*a^17*b^2*c^2*d^10 - 49152*a^18*b*c*d^11))^(1/4) - ((((x^(1/2)*(36864*a^2*b^23*c^21*d^4 - 712704*a^3*b^22*c^20*d^5 + 6172672*a^4*b^21*c^19*d^6 - 31899648*a^5*b^20*c^18*d^7 + 110432256*a^6*b^19*c^17*d^8 - 271552512*a^7*b^18*c^16*d^9 + 487280640*a^8*b^17*c^15*d^10 - 635523072*a^9*b^16*c^14*d^11 + 562982912*a^10*b^15*c^13*d^12 - 227217408*a^11*b^14*c^12*d^13 - 227217408*a^12*b^13*c^11*d^14 + 562982912*a^13*b^12*c^10*d^15 - 635523072*a^14*b^11*c^9*d^16 + 487280640*a^15*b^10*c^8*d^17 - 271552512*a^16*b^9*c^7*d^18 + 110432256*a^17*b^8*c^6*d^19 - 31899648*a^18*b^7*c^5*d^20 + 6172672*a^19*b^6*c^4*d^21 - 712704*a^20*b^5*c^3*d^22 + 36864*a^21*b^4*c^2*d^23)*1i)/(16*(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)/(4096*a^19*d^12 + 4096*a^7*b^12*c^12 - 49152*a^8*b^11*c^11*d + 270336*a^9*b^10*c^10*d^2 - 901120*a^10*b^9*c^9*d^3 + 2027520*a^11*b^8*c^8*d^4 - 3244032*a^12*b^7*c^7*d^5 + 3784704*a^13*b^6*c^6*d^6 - 3244032*a^14*b^5*c^5*d^7 + 2027520*a^15*b^4*c^4*d^8 - 901120*a^16*b^3*c^3*d^9 + 270336*a^17*b^2*c^2*d^10 - 49152*a^18*b*c*d^11))^(1/4)*(6144*a^4*b^19*c^19*d^4 - 90112*a^5*b^18*c^18*d^5 + 585728*a^6*b^17*c^17*d^6 - 2230272*a^7*b^16*c^16*d^7 + 5490688*a^8*b^15*c^15*d^8 - 8966144*a^9*b^14*c^14*d^9 + 9191424*a^10*b^13*c^13*d^10 - 3987456*a^11*b^12*c^12*d^11 - 3987456*a^12*b^11*c^11*d^12 + 9191424*a^13*b^10*c^10*d^13 - 8966144*a^14*b^9*c^9*d^14 + 5490688*a^15*b^8*c^8*d^15 - 2230272*a^16*b^7*c^7*d^16 + 585728*a^17*b^6*c^6*d^17 - 90112*a^18*b^5*c^5*d^18 + 6144*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))*(-(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)/(4096*a^19*d^12 + 4096*a^7*b^12*c^12 - 49152*a^8*b^11*c^11*d + 270336*a^9*b^10*c^10*d^2 - 901120*a^10*b^9*c^9*d^3 + 2027520*a^11*b^8*c^8*d^4 - 3244032*a^12*b^7*c^7*d^5 + 3784704*a^13*b^6*c^6*d^6 - 3244032*a^14*b^5*c^5*d^7 + 2027520*a^15*b^4*c^4*d^8 - 901120*a^16*b^3*c^3*d^9 + 270336*a^17*b^2*c^2*d^10 - 49152*a^18*b*c*d^11))^(3/4)*1i - (((891*a^8*b^7*d^15)/2 + (891*b^15*c^8*d^7)/2 - 6210*a*b^14*c^7*d^8 - 6210*a^7*b^8*c*d^14 + 31509*a^2*b^13*c^6*d^9 - 66138*a^3*b^12*c^5*d^10 + 60307*a^4*b^11*c^4*d^11 - 66138*a^5*b^10*c^3*d^12 + 31509*a^6*b^9*c^2*d^13)*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*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)/(4096*a^19*d^12 + 4096*a^7*b^12*c^12 - 49152*a^8*b^11*c^11*d + 270336*a^9*b^10*c^10*d^2 - 901120*a^10*b^9*c^9*d^3 + 2027520*a^11*b^8*c^8*d^4 - 3244032*a^12*b^7*c^7*d^5 + 3784704*a^13*b^6*c^6*d^6 - 3244032*a^14*b^5*c^5*d^7 + 2027520*a^15*b^4*c^4*d^8 - 901120*a^16*b^3*c^3*d^9 + 270336*a^17*b^2*c^2*d^10 - 49152*a^18*b*c*d^11))^(1/4)*1i - (x^(1/2)*(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)/(16*(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)/(4096*a^19*d^12 + 4096*a^7*b^12*c^12 - 49152*a^8*b^11*c^11*d + 270336*a^9*b^10*c^10*d^2 - 901120*a^10*b^9*c^9*d^3 + 2027520*a^11*b^8*c^8*d^4 - 3244032*a^12*b^7*c^7*d^5 + 3784704*a^13*b^6*c^6*d^6 - 3244032*a^14*b^5*c^5*d^7 + 2027520*a^15*b^4*c^4*d^8 - 901120*a^16*b^3*c^3*d^9 + 270336*a^17*b^2*c^2*d^10 - 49152*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)/(4096*a^19*d^12 + 4096*a^7*b^12*c^12 - 49152*a^8*b^11*c^11*d + 270336*a^9*b^10*c^10*d^2 - 901120*a^10*b^9*c^9*d^3 + 2027520*a^11*b^8*c^8*d^4 - 3244032*a^12*b^7*c^7*d^5 + 3784704*a^13*b^6*c^6*d^6 - 3244032*a^14*b^5*c^5*d^7 + 2027520*a^15*b^4*c^4*d^8 - 901120*a^16*b^3*c^3*d^9 + 270336*a^17*b^2*c^2*d^10 - 49152*a^18*b*c*d^11))^(1/4) - atan((((((x^(1/2)*(36864*a^2*b^23*c^21*d^4 - 712704*a^3*b^22*c^20*d^5 + 6172672*a^4*b^21*c^19*d^6 - 31899648*a^5*b^20*c^18*d^7 + 110432256*a^6*b^19*c^17*d^8 - 271552512*a^7*b^18*c^16*d^9 + 487280640*a^8*b^17*c^15*d^10 - 635523072*a^9*b^16*c^14*d^11 + 562982912*a^10*b^15*c^13*d^12 - 227217408*a^11*b^14*c^12*d^13 - 227217408*a^12*b^13*c^11*d^14 + 562982912*a^13*b^12*c^10*d^15 - 635523072*a^14*b^11*c^9*d^16 + 487280640*a^15*b^10*c^8*d^17 - 271552512*a^16*b^9*c^7*d^18 + 110432256*a^17*b^8*c^6*d^19 - 31899648*a^18*b^7*c^5*d^20 + 6172672*a^19*b^6*c^4*d^21 - 712704*a^20*b^5*c^3*d^22 + 36864*a^21*b^4*c^2*d^23))/(16*(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)/(4096*b^12*c^19 + 4096*a^12*c^7*d^12 - 49152*a^11*b*c^8*d^11 + 270336*a^2*b^10*c^17*d^2 - 901120*a^3*b^9*c^16*d^3 + 2027520*a^4*b^8*c^15*d^4 - 3244032*a^5*b^7*c^14*d^5 + 3784704*a^6*b^6*c^13*d^6 - 3244032*a^7*b^5*c^12*d^7 + 2027520*a^8*b^4*c^11*d^8 - 901120*a^9*b^3*c^10*d^9 + 270336*a^10*b^2*c^9*d^10 - 49152*a*b^11*c^18*d))^(1/4)*(6144*a^4*b^19*c^19*d^4 - 90112*a^5*b^18*c^18*d^5 + 585728*a^6*b^17*c^17*d^6 - 2230272*a^7*b^16*c^16*d^7 + 5490688*a^8*b^15*c^15*d^8 - 8966144*a^9*b^14*c^14*d^9 + 9191424*a^10*b^13*c^13*d^10 - 3987456*a^11*b^12*c^12*d^11 - 3987456*a^12*b^11*c^11*d^12 + 9191424*a^13*b^10*c^10*d^13 - 8966144*a^14*b^9*c^9*d^14 + 5490688*a^15*b^8*c^8*d^15 - 2230272*a^16*b^7*c^7*d^16 + 585728*a^17*b^6*c^6*d^17 - 90112*a^18*b^5*c^5*d^18 + 6144*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))*(-(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)/(4096*b^12*c^19 + 4096*a^12*c^7*d^12 - 49152*a^11*b*c^8*d^11 + 270336*a^2*b^10*c^17*d^2 - 901120*a^3*b^9*c^16*d^3 + 2027520*a^4*b^8*c^15*d^4 - 3244032*a^5*b^7*c^14*d^5 + 3784704*a^6*b^6*c^13*d^6 - 3244032*a^7*b^5*c^12*d^7 + 2027520*a^8*b^4*c^11*d^8 - 901120*a^9*b^3*c^10*d^9 + 270336*a^10*b^2*c^9*d^10 - 49152*a*b^11*c^18*d))^(3/4) + ((891*a^8*b^7*d^15)/2 + (891*b^15*c^8*d^7)/2 - 6210*a*b^14*c^7*d^8 - 6210*a^7*b^8*c*d^14 + 31509*a^2*b^13*c^6*d^9 - 66138*a^3*b^12*c^5*d^10 + 60307*a^4*b^11*c^4*d^11 - 66138*a^5*b^10*c^3*d^12 + 31509*a^6*b^9*c^2*d^13)/(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)/(4096*b^12*c^19 + 4096*a^12*c^7*d^12 - 49152*a^11*b*c^8*d^11 + 270336*a^2*b^10*c^17*d^2 - 901120*a^3*b^9*c^16*d^3 + 2027520*a^4*b^8*c^15*d^4 - 3244032*a^5*b^7*c^14*d^5 + 3784704*a^6*b^6*c^13*d^6 - 3244032*a^7*b^5*c^12*d^7 + 2027520*a^8*b^4*c^11*d^8 - 901120*a^9*b^3*c^10*d^9 + 270336*a^10*b^2*c^9*d^10 - 49152*a*b^11*c^18*d))^(1/4)*1i + (x^(1/2)*(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)/(16*(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)/(4096*b^12*c^19 + 4096*a^12*c^7*d^12 - 49152*a^11*b*c^8*d^11 + 270336*a^2*b^10*c^17*d^2 - 901120*a^3*b^9*c^16*d^3 + 2027520*a^4*b^8*c^15*d^4 - 3244032*a^5*b^7*c^14*d^5 + 3784704*a^6*b^6*c^13*d^6 - 3244032*a^7*b^5*c^12*d^7 + 2027520*a^8*b^4*c^11*d^8 - 901120*a^9*b^3*c^10*d^9 + 270336*a^10*b^2*c^9*d^10 - 49152*a*b^11*c^18*d))^(1/4) + ((((x^(1/2)*(36864*a^2*b^23*c^21*d^4 - 712704*a^3*b^22*c^20*d^5 + 6172672*a^4*b^21*c^19*d^6 - 31899648*a^5*b^20*c^18*d^7 + 110432256*a^6*b^19*c^17*d^8 - 271552512*a^7*b^18*c^16*d^9 + 487280640*a^8*b^17*c^15*d^10 - 635523072*a^9*b^16*c^14*d^11 + 562982912*a^10*b^15*c^13*d^12 - 227217408*a^11*b^14*c^12*d^13 - 227217408*a^12*b^13*c^11*d^14 + 562982912*a^13*b^12*c^10*d^15 - 635523072*a^14*b^11*c^9*d^16 + 487280640*a^15*b^10*c^8*d^17 - 271552512*a^16*b^9*c^7*d^18 + 110432256*a^17*b^8*c^6*d^19 - 31899648*a^18*b^7*c^5*d^20 + 6172672*a^19*b^6*c^4*d^21 - 712704*a^20*b^5*c^3*d^22 + 36864*a^21*b^4*c^2*d^23))/(16*(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)/(4096*b^12*c^19 + 4096*a^12*c^7*d^12 - 49152*a^11*b*c^8*d^11 + 270336*a^2*b^10*c^17*d^2 - 901120*a^3*b^9*c^16*d^3 + 2027520*a^4*b^8*c^15*d^4 - 3244032*a^5*b^7*c^14*d^5 + 3784704*a^6*b^6*c^13*d^6 - 3244032*a^7*b^5*c^12*d^7 + 2027520*a^8*b^4*c^11*d^8 - 901120*a^9*b^3*c^10*d^9 + 270336*a^10*b^2*c^9*d^10 - 49152*a*b^11*c^18*d))^(1/4)*(6144*a^4*b^19*c^19*d^4 - 90112*a^5*b^18*c^18*d^5 + 585728*a^6*b^17*c^17*d^6 - 2230272*a^7*b^16*c^16*d^7 + 5490688*a^8*b^15*c^15*d^8 - 8966144*a^9*b^14*c^14*d^9 + 9191424*a^10*b^13*c^13*d^10 - 3987456*a^11*b^12*c^12*d^11 - 3987456*a^12*b^11*c^11*d^12 + 9191424*a^13*b^10*c^10*d^13 - 8966144*a^14*b^9*c^9*d^14 + 5490688*a^15*b^8*c^8*d^15 - 2230272*a^16*b^7*c^7*d^16 + 585728*a^17*b^6*c^6*d^17 - 90112*a^18*b^5*c^5*d^18 + 6144*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))*(-(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)/(4096*b^12*c^19 + 4096*a^12*c^7*d^12 - 49152*a^11*b*c^8*d^11 + 270336*a^2*b^10*c^17*d^2 - 901120*a^3*b^9*c^16*d^3 + 2027520*a^4*b^8*c^15*d^4 - 3244032*a^5*b^7*c^14*d^5 + 3784704*a^6*b^6*c^13*d^6 - 3244032*a^7*b^5*c^12*d^7 + 2027520*a^8*b^4*c^11*d^8 - 901120*a^9*b^3*c^10*d^9 + 270336*a^10*b^2*c^9*d^10 - 49152*a*b^11*c^18*d))^(3/4) - ((891*a^8*b^7*d^15)/2 + (891*b^15*c^8*d^7)/2 - 6210*a*b^14*c^7*d^8 - 6210*a^7*b^8*c*d^14 + 31509*a^2*b^13*c^6*d^9 - 66138*a^3*b^12*c^5*d^10 + 60307*a^4*b^11*c^4*d^11 - 66138*a^5*b^10*c^3*d^12 + 31509*a^6*b^9*c^2*d^13)/(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)/(4096*b^12*c^19 + 4096*a^12*c^7*d^12 - 49152*a^11*b*c^8*d^11 + 270336*a^2*b^10*c^17*d^2 - 901120*a^3*b^9*c^16*d^3 + 2027520*a^4*b^8*c^15*d^4 - 3244032*a^5*b^7*c^14*d^5 + 3784704*a^6*b^6*c^13*d^6 - 3244032*a^7*b^5*c^12*d^7 + 2027520*a^8*b^4*c^11*d^8 - 901120*a^9*b^3*c^10*d^9 + 270336*a^10*b^2*c^9*d^10 - 49152*a*b^11*c^18*d))^(1/4)*1i + (x^(1/2)*(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)/(16*(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)/(4096*b^12*c^19 + 4096*a^12*c^7*d^12 - 49152*a^11*b*c^8*d^11 + 270336*a^2*b^10*c^17*d^2 - 901120*a^3*b^9*c^16*d^3 + 2027520*a^4*b^8*c^15*d^4 - 3244032*a^5*b^7*c^14*d^5 + 3784704*a^6*b^6*c^13*d^6 - 3244032*a^7*b^5*c^12*d^7 + 2027520*a^8*b^4*c^11*d^8 - 901120*a^9*b^3*c^10*d^9 + 270336*a^10*b^2*c^9*d^10 - 49152*a*b^11*c^18*d))^(1/4))/(((((x^(1/2)*(36864*a^2*b^23*c^21*d^4 - 712704*a^3*b^22*c^20*d^5 + 6172672*a^4*b^21*c^19*d^6 - 31899648*a^5*b^20*c^18*d^7 + 110432256*a^6*b^19*c^17*d^8 - 271552512*a^7*b^18*c^16*d^9 + 487280640*a^8*b^17*c^15*d^10 - 635523072*a^9*b^16*c^14*d^11 + 562982912*a^10*b^15*c^13*d^12 - 227217408*a^11*b^14*c^12*d^13 - 227217408*a^12*b^13*c^11*d^14 + 562982912*a^13*b^12*c^10*d^15 - 635523072*a^14*b^11*c^9*d^16 + 487280640*a^15*b^10*c^8*d^17 - 271552512*a^16*b^9*c^7*d^18 + 110432256*a^17*b^8*c^6*d^19 - 31899648*a^18*b^7*c^5*d^20 + 6172672*a^19*b^6*c^4*d^21 - 712704*a^20*b^5*c^3*d^22 + 36864*a^21*b^4*c^2*d^23))/(16*(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)/(4096*b^12*c^19 + 4096*a^12*c^7*d^12 - 49152*a^11*b*c^8*d^11 + 270336*a^2*b^10*c^17*d^2 - 901120*a^3*b^9*c^16*d^3 + 2027520*a^4*b^8*c^15*d^4 - 3244032*a^5*b^7*c^14*d^5 + 3784704*a^6*b^6*c^13*d^6 - 3244032*a^7*b^5*c^12*d^7 + 2027520*a^8*b^4*c^11*d^8 - 901120*a^9*b^3*c^10*d^9 + 270336*a^10*b^2*c^9*d^10 - 49152*a*b^11*c^18*d))^(1/4)*(6144*a^4*b^19*c^19*d^4 - 90112*a^5*b^18*c^18*d^5 + 585728*a^6*b^17*c^17*d^6 - 2230272*a^7*b^16*c^16*d^7 + 5490688*a^8*b^15*c^15*d^8 - 8966144*a^9*b^14*c^14*d^9 + 9191424*a^10*b^13*c^13*d^10 - 3987456*a^11*b^12*c^12*d^11 - 3987456*a^12*b^11*c^11*d^12 + 9191424*a^13*b^10*c^10*d^13 - 8966144*a^14*b^9*c^9*d^14 + 5490688*a^15*b^8*c^8*d^15 - 2230272*a^16*b^7*c^7*d^16 + 585728*a^17*b^6*c^6*d^17 - 90112*a^18*b^5*c^5*d^18 + 6144*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))*(-(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)/(4096*b^12*c^19 + 4096*a^12*c^7*d^12 - 49152*a^11*b*c^8*d^11 + 270336*a^2*b^10*c^17*d^2 - 901120*a^3*b^9*c^16*d^3 + 2027520*a^4*b^8*c^15*d^4 - 3244032*a^5*b^7*c^14*d^5 + 3784704*a^6*b^6*c^13*d^6 - 3244032*a^7*b^5*c^12*d^7 + 2027520*a^8*b^4*c^11*d^8 - 901120*a^9*b^3*c^10*d^9 + 270336*a^10*b^2*c^9*d^10 - 49152*a*b^11*c^18*d))^(3/4) + ((891*a^8*b^7*d^15)/2 + (891*b^15*c^8*d^7)/2 - 6210*a*b^14*c^7*d^8 - 6210*a^7*b^8*c*d^14 + 31509*a^2*b^13*c^6*d^9 - 66138*a^3*b^12*c^5*d^10 + 60307*a^4*b^11*c^4*d^11 - 66138*a^5*b^10*c^3*d^12 + 31509*a^6*b^9*c^2*d^13)/(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)/(4096*b^12*c^19 + 4096*a^12*c^7*d^12 - 49152*a^11*b*c^8*d^11 + 270336*a^2*b^10*c^17*d^2 - 901120*a^3*b^9*c^16*d^3 + 2027520*a^4*b^8*c^15*d^4 - 3244032*a^5*b^7*c^14*d^5 + 3784704*a^6*b^6*c^13*d^6 - 3244032*a^7*b^5*c^12*d^7 + 2027520*a^8*b^4*c^11*d^8 - 901120*a^9*b^3*c^10*d^9 + 270336*a^10*b^2*c^9*d^10 - 49152*a*b^11*c^18*d))^(1/4) + (x^(1/2)*(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))/(16*(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)/(4096*b^12*c^19 + 4096*a^12*c^7*d^12 - 49152*a^11*b*c^8*d^11 + 270336*a^2*b^10*c^17*d^2 - 901120*a^3*b^9*c^16*d^3 + 2027520*a^4*b^8*c^15*d^4 - 3244032*a^5*b^7*c^14*d^5 + 3784704*a^6*b^6*c^13*d^6 - 3244032*a^7*b^5*c^12*d^7 + 2027520*a^8*b^4*c^11*d^8 - 901120*a^9*b^3*c^10*d^9 + 270336*a^10*b^2*c^9*d^10 - 49152*a*b^11*c^18*d))^(1/4) - ((((x^(1/2)*(36864*a^2*b^23*c^21*d^4 - 712704*a^3*b^22*c^20*d^5 + 6172672*a^4*b^21*c^19*d^6 - 31899648*a^5*b^20*c^18*d^7 + 110432256*a^6*b^19*c^17*d^8 - 271552512*a^7*b^18*c^16*d^9 + 487280640*a^8*b^17*c^15*d^10 - 635523072*a^9*b^16*c^14*d^11 + 562982912*a^10*b^15*c^13*d^12 - 227217408*a^11*b^14*c^12*d^13 - 227217408*a^12*b^13*c^11*d^14 + 562982912*a^13*b^12*c^10*d^15 - 635523072*a^14*b^11*c^9*d^16 + 487280640*a^15*b^10*c^8*d^17 - 271552512*a^16*b^9*c^7*d^18 + 110432256*a^17*b^8*c^6*d^19 - 31899648*a^18*b^7*c^5*d^20 + 6172672*a^19*b^6*c^4*d^21 - 712704*a^20*b^5*c^3*d^22 + 36864*a^21*b^4*c^2*d^23))/(16*(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)/(4096*b^12*c^19 + 4096*a^12*c^7*d^12 - 49152*a^11*b*c^8*d^11 + 270336*a^2*b^10*c^17*d^2 - 901120*a^3*b^9*c^16*d^3 + 2027520*a^4*b^8*c^15*d^4 - 3244032*a^5*b^7*c^14*d^5 + 3784704*a^6*b^6*c^13*d^6 - 3244032*a^7*b^5*c^12*d^7 + 2027520*a^8*b^4*c^11*d^8 - 901120*a^9*b^3*c^10*d^9 + 270336*a^10*b^2*c^9*d^10 - 49152*a*b^11*c^18*d))^(1/4)*(6144*a^4*b^19*c^19*d^4 - 90112*a^5*b^18*c^18*d^5 + 585728*a^6*b^17*c^17*d^6 - 2230272*a^7*b^16*c^16*d^7 + 5490688*a^8*b^15*c^15*d^8 - 8966144*a^9*b^14*c^14*d^9 + 9191424*a^10*b^13*c^13*d^10 - 3987456*a^11*b^12*c^12*d^11 - 3987456*a^12*b^11*c^11*d^12 + 9191424*a^13*b^10*c^10*d^13 - 8966144*a^14*b^9*c^9*d^14 + 5490688*a^15*b^8*c^8*d^15 - 2230272*a^16*b^7*c^7*d^16 + 585728*a^17*b^6*c^6*d^17 - 90112*a^18*b^5*c^5*d^18 + 6144*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))*(-(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)/(4096*b^12*c^19 + 4096*a^12*c^7*d^12 - 49152*a^11*b*c^8*d^11 + 270336*a^2*b^10*c^17*d^2 - 901120*a^3*b^9*c^16*d^3 + 2027520*a^4*b^8*c^15*d^4 - 3244032*a^5*b^7*c^14*d^5 + 3784704*a^6*b^6*c^13*d^6 - 3244032*a^7*b^5*c^12*d^7 + 2027520*a^8*b^4*c^11*d^8 - 901120*a^9*b^3*c^10*d^9 + 270336*a^10*b^2*c^9*d^10 - 49152*a*b^11*c^18*d))^(3/4) - ((891*a^8*b^7*d^15)/2 + (891*b^15*c^8*d^7)/2 - 6210*a*b^14*c^7*d^8 - 6210*a^7*b^8*c*d^14 + 31509*a^2*b^13*c^6*d^9 - 66138*a^3*b^12*c^5*d^10 + 60307*a^4*b^11*c^4*d^11 - 66138*a^5*b^10*c^3*d^12 + 31509*a^6*b^9*c^2*d^13)/(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)/(4096*b^12*c^19 + 4096*a^12*c^7*d^12 - 49152*a^11*b*c^8*d^11 + 270336*a^2*b^10*c^17*d^2 - 901120*a^3*b^9*c^16*d^3 + 2027520*a^4*b^8*c^15*d^4 - 3244032*a^5*b^7*c^14*d^5 + 3784704*a^6*b^6*c^13*d^6 - 3244032*a^7*b^5*c^12*d^7 + 2027520*a^8*b^4*c^11*d^8 - 901120*a^9*b^3*c^10*d^9 + 270336*a^10*b^2*c^9*d^10 - 49152*a*b^11*c^18*d))^(1/4) + (x^(1/2)*(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))/(16*(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)/(4096*b^12*c^19 + 4096*a^12*c^7*d^12 - 49152*a^11*b*c^8*d^11 + 270336*a^2*b^10*c^17*d^2 - 901120*a^3*b^9*c^16*d^3 + 2027520*a^4*b^8*c^15*d^4 - 3244032*a^5*b^7*c^14*d^5 + 3784704*a^6*b^6*c^13*d^6 - 3244032*a^7*b^5*c^12*d^7 + 2027520*a^8*b^4*c^11*d^8 - 901120*a^9*b^3*c^10*d^9 + 270336*a^10*b^2*c^9*d^10 - 49152*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)/(4096*b^12*c^19 + 4096*a^12*c^7*d^12 - 49152*a^11*b*c^8*d^11 + 270336*a^2*b^10*c^17*d^2 - 901120*a^3*b^9*c^16*d^3 + 2027520*a^4*b^8*c^15*d^4 - 3244032*a^5*b^7*c^14*d^5 + 3784704*a^6*b^6*c^13*d^6 - 3244032*a^7*b^5*c^12*d^7 + 2027520*a^8*b^4*c^11*d^8 - 901120*a^9*b^3*c^10*d^9 + 270336*a^10*b^2*c^9*d^10 - 49152*a*b^11*c^18*d))^(1/4)*2i + 2*atan((((((x^(1/2)*(36864*a^2*b^23*c^21*d^4 - 712704*a^3*b^22*c^20*d^5 + 6172672*a^4*b^21*c^19*d^6 - 31899648*a^5*b^20*c^18*d^7 + 110432256*a^6*b^19*c^17*d^8 - 271552512*a^7*b^18*c^16*d^9 + 487280640*a^8*b^17*c^15*d^10 - 635523072*a^9*b^16*c^14*d^11 + 562982912*a^10*b^15*c^13*d^12 - 227217408*a^11*b^14*c^12*d^13 - 227217408*a^12*b^13*c^11*d^14 + 562982912*a^13*b^12*c^10*d^15 - 635523072*a^14*b^11*c^9*d^16 + 487280640*a^15*b^10*c^8*d^17 - 271552512*a^16*b^9*c^7*d^18 + 110432256*a^17*b^8*c^6*d^19 - 31899648*a^18*b^7*c^5*d^20 + 6172672*a^19*b^6*c^4*d^21 - 712704*a^20*b^5*c^3*d^22 + 36864*a^21*b^4*c^2*d^23)*1i)/(16*(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)/(4096*b^12*c^19 + 4096*a^12*c^7*d^12 - 49152*a^11*b*c^8*d^11 + 270336*a^2*b^10*c^17*d^2 - 901120*a^3*b^9*c^16*d^3 + 2027520*a^4*b^8*c^15*d^4 - 3244032*a^5*b^7*c^14*d^5 + 3784704*a^6*b^6*c^13*d^6 - 3244032*a^7*b^5*c^12*d^7 + 2027520*a^8*b^4*c^11*d^8 - 901120*a^9*b^3*c^10*d^9 + 270336*a^10*b^2*c^9*d^10 - 49152*a*b^11*c^18*d))^(1/4)*(6144*a^4*b^19*c^19*d^4 - 90112*a^5*b^18*c^18*d^5 + 585728*a^6*b^17*c^17*d^6 - 2230272*a^7*b^16*c^16*d^7 + 5490688*a^8*b^15*c^15*d^8 - 8966144*a^9*b^14*c^14*d^9 + 9191424*a^10*b^13*c^13*d^10 - 3987456*a^11*b^12*c^12*d^11 - 3987456*a^12*b^11*c^11*d^12 + 9191424*a^13*b^10*c^10*d^13 - 8966144*a^14*b^9*c^9*d^14 + 5490688*a^15*b^8*c^8*d^15 - 2230272*a^16*b^7*c^7*d^16 + 585728*a^17*b^6*c^6*d^17 - 90112*a^18*b^5*c^5*d^18 + 6144*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))*(-(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)/(4096*b^12*c^19 + 4096*a^12*c^7*d^12 - 49152*a^11*b*c^8*d^11 + 270336*a^2*b^10*c^17*d^2 - 901120*a^3*b^9*c^16*d^3 + 2027520*a^4*b^8*c^15*d^4 - 3244032*a^5*b^7*c^14*d^5 + 3784704*a^6*b^6*c^13*d^6 - 3244032*a^7*b^5*c^12*d^7 + 2027520*a^8*b^4*c^11*d^8 - 901120*a^9*b^3*c^10*d^9 + 270336*a^10*b^2*c^9*d^10 - 49152*a*b^11*c^18*d))^(3/4)*1i + (((891*a^8*b^7*d^15)/2 + (891*b^15*c^8*d^7)/2 - 6210*a*b^14*c^7*d^8 - 6210*a^7*b^8*c*d^14 + 31509*a^2*b^13*c^6*d^9 - 66138*a^3*b^12*c^5*d^10 + 60307*a^4*b^11*c^4*d^11 - 66138*a^5*b^10*c^3*d^12 + 31509*a^6*b^9*c^2*d^13)*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)/(4096*b^12*c^19 + 4096*a^12*c^7*d^12 - 49152*a^11*b*c^8*d^11 + 270336*a^2*b^10*c^17*d^2 - 901120*a^3*b^9*c^16*d^3 + 2027520*a^4*b^8*c^15*d^4 - 3244032*a^5*b^7*c^14*d^5 + 3784704*a^6*b^6*c^13*d^6 - 3244032*a^7*b^5*c^12*d^7 + 2027520*a^8*b^4*c^11*d^8 - 901120*a^9*b^3*c^10*d^9 + 270336*a^10*b^2*c^9*d^10 - 49152*a*b^11*c^18*d))^(1/4) - (x^(1/2)*(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))/(16*(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)/(4096*b^12*c^19 + 4096*a^12*c^7*d^12 - 49152*a^11*b*c^8*d^11 + 270336*a^2*b^10*c^17*d^2 - 901120*a^3*b^9*c^16*d^3 + 2027520*a^4*b^8*c^15*d^4 - 3244032*a^5*b^7*c^14*d^5 + 3784704*a^6*b^6*c^13*d^6 - 3244032*a^7*b^5*c^12*d^7 + 2027520*a^8*b^4*c^11*d^8 - 901120*a^9*b^3*c^10*d^9 + 270336*a^10*b^2*c^9*d^10 - 49152*a*b^11*c^18*d))^(1/4) + ((((x^(1/2)*(36864*a^2*b^23*c^21*d^4 - 712704*a^3*b^22*c^20*d^5 + 6172672*a^4*b^21*c^19*d^6 - 31899648*a^5*b^20*c^18*d^7 + 110432256*a^6*b^19*c^17*d^8 - 271552512*a^7*b^18*c^16*d^9 + 487280640*a^8*b^17*c^15*d^10 - 635523072*a^9*b^16*c^14*d^11 + 562982912*a^10*b^15*c^13*d^12 - 227217408*a^11*b^14*c^12*d^13 - 227217408*a^12*b^13*c^11*d^14 + 562982912*a^13*b^12*c^10*d^15 - 635523072*a^14*b^11*c^9*d^16 + 487280640*a^15*b^10*c^8*d^17 - 271552512*a^16*b^9*c^7*d^18 + 110432256*a^17*b^8*c^6*d^19 - 31899648*a^18*b^7*c^5*d^20 + 6172672*a^19*b^6*c^4*d^21 - 712704*a^20*b^5*c^3*d^22 + 36864*a^21*b^4*c^2*d^23)*1i)/(16*(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)/(4096*b^12*c^19 + 4096*a^12*c^7*d^12 - 49152*a^11*b*c^8*d^11 + 270336*a^2*b^10*c^17*d^2 - 901120*a^3*b^9*c^16*d^3 + 2027520*a^4*b^8*c^15*d^4 - 3244032*a^5*b^7*c^14*d^5 + 3784704*a^6*b^6*c^13*d^6 - 3244032*a^7*b^5*c^12*d^7 + 2027520*a^8*b^4*c^11*d^8 - 901120*a^9*b^3*c^10*d^9 + 270336*a^10*b^2*c^9*d^10 - 49152*a*b^11*c^18*d))^(1/4)*(6144*a^4*b^19*c^19*d^4 - 90112*a^5*b^18*c^18*d^5 + 585728*a^6*b^17*c^17*d^6 - 2230272*a^7*b^16*c^16*d^7 + 5490688*a^8*b^15*c^15*d^8 - 8966144*a^9*b^14*c^14*d^9 + 9191424*a^10*b^13*c^13*d^10 - 3987456*a^11*b^12*c^12*d^11 - 3987456*a^12*b^11*c^11*d^12 + 9191424*a^13*b^10*c^10*d^13 - 8966144*a^14*b^9*c^9*d^14 + 5490688*a^15*b^8*c^8*d^15 - 2230272*a^16*b^7*c^7*d^16 + 585728*a^17*b^6*c^6*d^17 - 90112*a^18*b^5*c^5*d^18 + 6144*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))*(-(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)/(4096*b^12*c^19 + 4096*a^12*c^7*d^12 - 49152*a^11*b*c^8*d^11 + 270336*a^2*b^10*c^17*d^2 - 901120*a^3*b^9*c^16*d^3 + 2027520*a^4*b^8*c^15*d^4 - 3244032*a^5*b^7*c^14*d^5 + 3784704*a^6*b^6*c^13*d^6 - 3244032*a^7*b^5*c^12*d^7 + 2027520*a^8*b^4*c^11*d^8 - 901120*a^9*b^3*c^10*d^9 + 270336*a^10*b^2*c^9*d^10 - 49152*a*b^11*c^18*d))^(3/4)*1i - (((891*a^8*b^7*d^15)/2 + (891*b^15*c^8*d^7)/2 - 6210*a*b^14*c^7*d^8 - 6210*a^7*b^8*c*d^14 + 31509*a^2*b^13*c^6*d^9 - 66138*a^3*b^12*c^5*d^10 + 60307*a^4*b^11*c^4*d^11 - 66138*a^5*b^10*c^3*d^12 + 31509*a^6*b^9*c^2*d^13)*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)/(4096*b^12*c^19 + 4096*a^12*c^7*d^12 - 49152*a^11*b*c^8*d^11 + 270336*a^2*b^10*c^17*d^2 - 901120*a^3*b^9*c^16*d^3 + 2027520*a^4*b^8*c^15*d^4 - 3244032*a^5*b^7*c^14*d^5 + 3784704*a^6*b^6*c^13*d^6 - 3244032*a^7*b^5*c^12*d^7 + 2027520*a^8*b^4*c^11*d^8 - 901120*a^9*b^3*c^10*d^9 + 270336*a^10*b^2*c^9*d^10 - 49152*a*b^11*c^18*d))^(1/4) - (x^(1/2)*(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))/(16*(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)/(4096*b^12*c^19 + 4096*a^12*c^7*d^12 - 49152*a^11*b*c^8*d^11 + 270336*a^2*b^10*c^17*d^2 - 901120*a^3*b^9*c^16*d^3 + 2027520*a^4*b^8*c^15*d^4 - 3244032*a^5*b^7*c^14*d^5 + 3784704*a^6*b^6*c^13*d^6 - 3244032*a^7*b^5*c^12*d^7 + 2027520*a^8*b^4*c^11*d^8 - 901120*a^9*b^3*c^10*d^9 + 270336*a^10*b^2*c^9*d^10 - 49152*a*b^11*c^18*d))^(1/4))/(((((x^(1/2)*(36864*a^2*b^23*c^21*d^4 - 712704*a^3*b^22*c^20*d^5 + 6172672*a^4*b^21*c^19*d^6 - 31899648*a^5*b^20*c^18*d^7 + 110432256*a^6*b^19*c^17*d^8 - 271552512*a^7*b^18*c^16*d^9 + 487280640*a^8*b^17*c^15*d^10 - 635523072*a^9*b^16*c^14*d^11 + 562982912*a^10*b^15*c^13*d^12 - 227217408*a^11*b^14*c^12*d^13 - 227217408*a^12*b^13*c^11*d^14 + 562982912*a^13*b^12*c^10*d^15 - 635523072*a^14*b^11*c^9*d^16 + 487280640*a^15*b^10*c^8*d^17 - 271552512*a^16*b^9*c^7*d^18 + 110432256*a^17*b^8*c^6*d^19 - 31899648*a^18*b^7*c^5*d^20 + 6172672*a^19*b^6*c^4*d^21 - 712704*a^20*b^5*c^3*d^22 + 36864*a^21*b^4*c^2*d^23)*1i)/(16*(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)/(4096*b^12*c^19 + 4096*a^12*c^7*d^12 - 49152*a^11*b*c^8*d^11 + 270336*a^2*b^10*c^17*d^2 - 901120*a^3*b^9*c^16*d^3 + 2027520*a^4*b^8*c^15*d^4 - 3244032*a^5*b^7*c^14*d^5 + 3784704*a^6*b^6*c^13*d^6 - 3244032*a^7*b^5*c^12*d^7 + 2027520*a^8*b^4*c^11*d^8 - 901120*a^9*b^3*c^10*d^9 + 270336*a^10*b^2*c^9*d^10 - 49152*a*b^11*c^18*d))^(1/4)*(6144*a^4*b^19*c^19*d^4 - 90112*a^5*b^18*c^18*d^5 + 585728*a^6*b^17*c^17*d^6 - 2230272*a^7*b^16*c^16*d^7 + 5490688*a^8*b^15*c^15*d^8 - 8966144*a^9*b^14*c^14*d^9 + 9191424*a^10*b^13*c^13*d^10 - 3987456*a^11*b^12*c^12*d^11 - 3987456*a^12*b^11*c^11*d^12 + 9191424*a^13*b^10*c^10*d^13 - 8966144*a^14*b^9*c^9*d^14 + 5490688*a^15*b^8*c^8*d^15 - 2230272*a^16*b^7*c^7*d^16 + 585728*a^17*b^6*c^6*d^17 - 90112*a^18*b^5*c^5*d^18 + 6144*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))*(-(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)/(4096*b^12*c^19 + 4096*a^12*c^7*d^12 - 49152*a^11*b*c^8*d^11 + 270336*a^2*b^10*c^17*d^2 - 901120*a^3*b^9*c^16*d^3 + 2027520*a^4*b^8*c^15*d^4 - 3244032*a^5*b^7*c^14*d^5 + 3784704*a^6*b^6*c^13*d^6 - 3244032*a^7*b^5*c^12*d^7 + 2027520*a^8*b^4*c^11*d^8 - 901120*a^9*b^3*c^10*d^9 + 270336*a^10*b^2*c^9*d^10 - 49152*a*b^11*c^18*d))^(3/4)*1i + (((891*a^8*b^7*d^15)/2 + (891*b^15*c^8*d^7)/2 - 6210*a*b^14*c^7*d^8 - 6210*a^7*b^8*c*d^14 + 31509*a^2*b^13*c^6*d^9 - 66138*a^3*b^12*c^5*d^10 + 60307*a^4*b^11*c^4*d^11 - 66138*a^5*b^10*c^3*d^12 + 31509*a^6*b^9*c^2*d^13)*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)/(4096*b^12*c^19 + 4096*a^12*c^7*d^12 - 49152*a^11*b*c^8*d^11 + 270336*a^2*b^10*c^17*d^2 - 901120*a^3*b^9*c^16*d^3 + 2027520*a^4*b^8*c^15*d^4 - 3244032*a^5*b^7*c^14*d^5 + 3784704*a^6*b^6*c^13*d^6 - 3244032*a^7*b^5*c^12*d^7 + 2027520*a^8*b^4*c^11*d^8 - 901120*a^9*b^3*c^10*d^9 + 270336*a^10*b^2*c^9*d^10 - 49152*a*b^11*c^18*d))^(1/4)*1i - (x^(1/2)*(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)/(16*(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)/(4096*b^12*c^19 + 4096*a^12*c^7*d^12 - 49152*a^11*b*c^8*d^11 + 270336*a^2*b^10*c^17*d^2 - 901120*a^3*b^9*c^16*d^3 + 2027520*a^4*b^8*c^15*d^4 - 3244032*a^5*b^7*c^14*d^5 + 3784704*a^6*b^6*c^13*d^6 - 3244032*a^7*b^5*c^12*d^7 + 2027520*a^8*b^4*c^11*d^8 - 901120*a^9*b^3*c^10*d^9 + 270336*a^10*b^2*c^9*d^10 - 49152*a*b^11*c^18*d))^(1/4) - ((((x^(1/2)*(36864*a^2*b^23*c^21*d^4 - 712704*a^3*b^22*c^20*d^5 + 6172672*a^4*b^21*c^19*d^6 - 31899648*a^5*b^20*c^18*d^7 + 110432256*a^6*b^19*c^17*d^8 - 271552512*a^7*b^18*c^16*d^9 + 487280640*a^8*b^17*c^15*d^10 - 635523072*a^9*b^16*c^14*d^11 + 562982912*a^10*b^15*c^13*d^12 - 227217408*a^11*b^14*c^12*d^13 - 227217408*a^12*b^13*c^11*d^14 + 562982912*a^13*b^12*c^10*d^15 - 635523072*a^14*b^11*c^9*d^16 + 487280640*a^15*b^10*c^8*d^17 - 271552512*a^16*b^9*c^7*d^18 + 110432256*a^17*b^8*c^6*d^19 - 31899648*a^18*b^7*c^5*d^20 + 6172672*a^19*b^6*c^4*d^21 - 712704*a^20*b^5*c^3*d^22 + 36864*a^21*b^4*c^2*d^23)*1i)/(16*(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)/(4096*b^12*c^19 + 4096*a^12*c^7*d^12 - 49152*a^11*b*c^8*d^11 + 270336*a^2*b^10*c^17*d^2 - 901120*a^3*b^9*c^16*d^3 + 2027520*a^4*b^8*c^15*d^4 - 3244032*a^5*b^7*c^14*d^5 + 3784704*a^6*b^6*c^13*d^6 - 3244032*a^7*b^5*c^12*d^7 + 2027520*a^8*b^4*c^11*d^8 - 901120*a^9*b^3*c^10*d^9 + 270336*a^10*b^2*c^9*d^10 - 49152*a*b^11*c^18*d))^(1/4)*(6144*a^4*b^19*c^19*d^4 - 90112*a^5*b^18*c^18*d^5 + 585728*a^6*b^17*c^17*d^6 - 2230272*a^7*b^16*c^16*d^7 + 5490688*a^8*b^15*c^15*d^8 - 8966144*a^9*b^14*c^14*d^9 + 9191424*a^10*b^13*c^13*d^10 - 3987456*a^11*b^12*c^12*d^11 - 3987456*a^12*b^11*c^11*d^12 + 9191424*a^13*b^10*c^10*d^13 - 8966144*a^14*b^9*c^9*d^14 + 5490688*a^15*b^8*c^8*d^15 - 2230272*a^16*b^7*c^7*d^16 + 585728*a^17*b^6*c^6*d^17 - 90112*a^18*b^5*c^5*d^18 + 6144*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))*(-(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)/(4096*b^12*c^19 + 4096*a^12*c^7*d^12 - 49152*a^11*b*c^8*d^11 + 270336*a^2*b^10*c^17*d^2 - 901120*a^3*b^9*c^16*d^3 + 2027520*a^4*b^8*c^15*d^4 - 3244032*a^5*b^7*c^14*d^5 + 3784704*a^6*b^6*c^13*d^6 - 3244032*a^7*b^5*c^12*d^7 + 2027520*a^8*b^4*c^11*d^8 - 901120*a^9*b^3*c^10*d^9 + 270336*a^10*b^2*c^9*d^10 - 49152*a*b^11*c^18*d))^(3/4)*1i - (((891*a^8*b^7*d^15)/2 + (891*b^15*c^8*d^7)/2 - 6210*a*b^14*c^7*d^8 - 6210*a^7*b^8*c*d^14 + 31509*a^2*b^13*c^6*d^9 - 66138*a^3*b^12*c^5*d^10 + 60307*a^4*b^11*c^4*d^11 - 66138*a^5*b^10*c^3*d^12 + 31509*a^6*b^9*c^2*d^13)*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)/(4096*b^12*c^19 + 4096*a^12*c^7*d^12 - 49152*a^11*b*c^8*d^11 + 270336*a^2*b^10*c^17*d^2 - 901120*a^3*b^9*c^16*d^3 + 2027520*a^4*b^8*c^15*d^4 - 3244032*a^5*b^7*c^14*d^5 + 3784704*a^6*b^6*c^13*d^6 - 3244032*a^7*b^5*c^12*d^7 + 2027520*a^8*b^4*c^11*d^8 - 901120*a^9*b^3*c^10*d^9 + 270336*a^10*b^2*c^9*d^10 - 49152*a*b^11*c^18*d))^(1/4)*1i - (x^(1/2)*(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)/(16*(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)/(4096*b^12*c^19 + 4096*a^12*c^7*d^12 - 49152*a^11*b*c^8*d^11 + 270336*a^2*b^10*c^17*d^2 - 901120*a^3*b^9*c^16*d^3 + 2027520*a^4*b^8*c^15*d^4 - 3244032*a^5*b^7*c^14*d^5 + 3784704*a^6*b^6*c^13*d^6 - 3244032*a^7*b^5*c^12*d^7 + 2027520*a^8*b^4*c^11*d^8 - 901120*a^9*b^3*c^10*d^9 + 270336*a^10*b^2*c^9*d^10 - 49152*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)/(4096*b^12*c^19 + 4096*a^12*c^7*d^12 - 49152*a^11*b*c^8*d^11 + 270336*a^2*b^10*c^17*d^2 - 901120*a^3*b^9*c^16*d^3 + 2027520*a^4*b^8*c^15*d^4 - 3244032*a^5*b^7*c^14*d^5 + 3784704*a^6*b^6*c^13*d^6 - 3244032*a^7*b^5*c^12*d^7 + 2027520*a^8*b^4*c^11*d^8 - 901120*a^9*b^3*c^10*d^9 + 270336*a^10*b^2*c^9*d^10 - 49152*a*b^11*c^18*d))^(1/4)","B"
493,1,33548,676,12.376259,"\text{Not used}","int(1/(x^(3/2)*(a + b*x^2)^2*(c + d*x^2)^2),x)","2\,\mathrm{atan}\left(\frac{\left(-\sqrt{x}\,\left(54080000\,a^{43}\,b^{10}\,c^{20}\,d^{33}-1361152000\,a^{42}\,b^{11}\,c^{21}\,d^{32}+16011852800\,a^{41}\,b^{12}\,c^{22}\,d^{31}-116736734720\,a^{40}\,b^{13}\,c^{23}\,d^{30}+589861462528\,a^{39}\,b^{14}\,c^{24}\,d^{29}-2187899577344\,a^{38}\,b^{15}\,c^{25}\,d^{28}+6149347117056\,a^{37}\,b^{16}\,c^{26}\,d^{27}-13298820601344\,a^{36}\,b^{17}\,c^{27}\,d^{26}+22133436343296\,a^{35}\,b^{18}\,c^{28}\,d^{25}-27715689750528\,a^{34}\,b^{19}\,c^{29}\,d^{24}+24077503776768\,a^{33}\,b^{20}\,c^{30}\,d^{23}-9645706816512\,a^{32}\,b^{21}\,c^{31}\,d^{22}-9645706816512\,a^{31}\,b^{22}\,c^{32}\,d^{21}+24077503776768\,a^{30}\,b^{23}\,c^{33}\,d^{20}-27715689750528\,a^{29}\,b^{24}\,c^{34}\,d^{19}+22133436343296\,a^{28}\,b^{25}\,c^{35}\,d^{18}-13298820601344\,a^{27}\,b^{26}\,c^{36}\,d^{17}+6149347117056\,a^{26}\,b^{27}\,c^{37}\,d^{16}-2187899577344\,a^{25}\,b^{28}\,c^{38}\,d^{15}+589861462528\,a^{24}\,b^{29}\,c^{39}\,d^{14}-116736734720\,a^{23}\,b^{30}\,c^{40}\,d^{13}+16011852800\,a^{22}\,b^{31}\,c^{41}\,d^{12}-1361152000\,a^{21}\,b^{32}\,c^{42}\,d^{11}+54080000\,a^{20}\,b^{33}\,c^{43}\,d^{10}\right)+{\left(-\frac{625\,a^4\,d^{13}-6500\,a^3\,b\,c\,d^{12}+25350\,a^2\,b^2\,c^2\,d^{11}-43940\,a\,b^3\,c^3\,d^{10}+28561\,b^4\,c^4\,d^9}{4096\,a^{12}\,c^9\,d^{12}-49152\,a^{11}\,b\,c^{10}\,d^{11}+270336\,a^{10}\,b^2\,c^{11}\,d^{10}-901120\,a^9\,b^3\,c^{12}\,d^9+2027520\,a^8\,b^4\,c^{13}\,d^8-3244032\,a^7\,b^5\,c^{14}\,d^7+3784704\,a^6\,b^6\,c^{15}\,d^6-3244032\,a^5\,b^7\,c^{16}\,d^5+2027520\,a^4\,b^8\,c^{17}\,d^4-901120\,a^3\,b^9\,c^{18}\,d^3+270336\,a^2\,b^{10}\,c^{19}\,d^2-49152\,a\,b^{11}\,c^{20}\,d+4096\,b^{12}\,c^{21}}\right)}^{3/4}\,\left(1009254400\,a^{22}\,b^{37}\,c^{54}\,d^5-32768000\,a^{21}\,b^{38}\,c^{55}\,d^4-14833418240\,a^{23}\,b^{36}\,c^{53}\,d^6+138556735488\,a^{24}\,b^{35}\,c^{52}\,d^7-924185001984\,a^{25}\,b^{34}\,c^{51}\,d^8+4688465362944\,a^{26}\,b^{33}\,c^{50}\,d^9-18812623126528\,a^{27}\,b^{32}\,c^{49}\,d^{10}+61295191654400\,a^{28}\,b^{31}\,c^{48}\,d^{11}-165189260410880\,a^{29}\,b^{30}\,c^{47}\,d^{12}+373165003898880\,a^{30}\,b^{29}\,c^{46}\,d^{13}-713540118773760\,a^{31}\,b^{28}\,c^{45}\,d^{14}+1163349301657600\,a^{32}\,b^{27}\,c^{44}\,d^{15}-1627141704253440\,a^{33}\,b^{26}\,c^{43}\,d^{16}+1966197351383040\,a^{34}\,b^{25}\,c^{42}\,d^{17}-2079216623943680\,a^{35}\,b^{24}\,c^{41}\,d^{18}+1981073955225600\,a^{36}\,b^{23}\,c^{40}\,d^{19}-1807512431493120\,a^{37}\,b^{22}\,c^{39}\,d^{20}+1724885956034560\,a^{38}\,b^{21}\,c^{38}\,d^{21}-1807512431493120\,a^{39}\,b^{20}\,c^{37}\,d^{22}+1981073955225600\,a^{40}\,b^{19}\,c^{36}\,d^{23}-2079216623943680\,a^{41}\,b^{18}\,c^{35}\,d^{24}+1966197351383040\,a^{42}\,b^{17}\,c^{34}\,d^{25}-1627141704253440\,a^{43}\,b^{16}\,c^{33}\,d^{26}+1163349301657600\,a^{44}\,b^{15}\,c^{32}\,d^{27}-713540118773760\,a^{45}\,b^{14}\,c^{31}\,d^{28}+373165003898880\,a^{46}\,b^{13}\,c^{30}\,d^{29}-165189260410880\,a^{47}\,b^{12}\,c^{29}\,d^{30}+61295191654400\,a^{48}\,b^{11}\,c^{28}\,d^{31}-18812623126528\,a^{49}\,b^{10}\,c^{27}\,d^{32}+4688465362944\,a^{50}\,b^9\,c^{26}\,d^{33}-924185001984\,a^{51}\,b^8\,c^{25}\,d^{34}+138556735488\,a^{52}\,b^7\,c^{24}\,d^{35}-14833418240\,a^{53}\,b^6\,c^{23}\,d^{36}+1009254400\,a^{54}\,b^5\,c^{22}\,d^{37}-32768000\,a^{55}\,b^4\,c^{21}\,d^{38}+\sqrt{x}\,{\left(-\frac{625\,a^4\,d^{13}-6500\,a^3\,b\,c\,d^{12}+25350\,a^2\,b^2\,c^2\,d^{11}-43940\,a\,b^3\,c^3\,d^{10}+28561\,b^4\,c^4\,d^9}{4096\,a^{12}\,c^9\,d^{12}-49152\,a^{11}\,b\,c^{10}\,d^{11}+270336\,a^{10}\,b^2\,c^{11}\,d^{10}-901120\,a^9\,b^3\,c^{12}\,d^9+2027520\,a^8\,b^4\,c^{13}\,d^8-3244032\,a^7\,b^5\,c^{14}\,d^7+3784704\,a^6\,b^6\,c^{15}\,d^6-3244032\,a^5\,b^7\,c^{16}\,d^5+2027520\,a^4\,b^8\,c^{17}\,d^4-901120\,a^3\,b^9\,c^{18}\,d^3+270336\,a^2\,b^{10}\,c^{19}\,d^2-49152\,a\,b^{11}\,c^{20}\,d+4096\,b^{12}\,c^{21}}\right)}^{1/4}\,\left(52428800\,a^{57}\,b^4\,c^{23}\,d^{38}-1635778560\,a^{56}\,b^5\,c^{24}\,d^{37}+24482152448\,a^{55}\,b^6\,c^{25}\,d^{36}-234134437888\,a^{54}\,b^7\,c^{26}\,d^{35}+1607834009600\,a^{53}\,b^8\,c^{27}\,d^{34}-8446069964800\,a^{52}\,b^9\,c^{28}\,d^{33}+35303182041088\,a^{51}\,b^{10}\,c^{29}\,d^{32}-120578363097088\,a^{50}\,b^{11}\,c^{30}\,d^{31}+342964201062400\,a^{49}\,b^{12}\,c^{31}\,d^{30}-823887134720000\,a^{48}\,b^{13}\,c^{32}\,d^{29}+1690057100492800\,a^{47}\,b^{14}\,c^{33}\,d^{28}-2988135038320640\,a^{46}\,b^{15}\,c^{34}\,d^{27}+4595616128696320\,a^{45}\,b^{16}\,c^{35}\,d^{26}-6215915829985280\,a^{44}\,b^{17}\,c^{36}\,d^{25}+7509830061260800\,a^{43}\,b^{18}\,c^{37}\,d^{24}-8292025971507200\,a^{42}\,b^{19}\,c^{38}\,d^{23}+8624070071418880\,a^{41}\,b^{20}\,c^{39}\,d^{22}-8700497871503360\,a^{40}\,b^{21}\,c^{40}\,d^{21}+8624070071418880\,a^{39}\,b^{22}\,c^{41}\,d^{20}-8292025971507200\,a^{38}\,b^{23}\,c^{42}\,d^{19}+7509830061260800\,a^{37}\,b^{24}\,c^{43}\,d^{18}-6215915829985280\,a^{36}\,b^{25}\,c^{44}\,d^{17}+4595616128696320\,a^{35}\,b^{26}\,c^{45}\,d^{16}-2988135038320640\,a^{34}\,b^{27}\,c^{46}\,d^{15}+169005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,b^9\,c^9\,d^3+270336\,a^{11}\,b^{10}\,c^{10}\,d^2-49152\,a^{10}\,b^{11}\,c^{11}\,d+4096\,a^9\,b^{12}\,c^{12}}\right)}^{5/4}\,8184070144{}\mathrm{i}+a^{23}\,b^8\,c^{11}\,d^{12}\,\sqrt{x}\,{\left(-\frac{28561\,a^4\,b^9\,d^4-43940\,a^3\,b^{10}\,c\,d^3+25350\,a^2\,b^{11}\,c^2\,d^2-6500\,a\,b^{12}\,c^3\,d+625\,b^{13}\,c^4}{4096\,a^{21}\,d^{12}-49152\,a^{20}\,b\,c\,d^{11}+270336\,a^{19}\,b^2\,c^2\,d^{10}-901120\,a^{18}\,b^3\,c^3\,d^9+2027520\,a^{17}\,b^4\,c^4\,d^8-3244032\,a^{16}\,b^5\,c^5\,d^7+3784704\,a^{15}\,b^6\,c^6\,d^6-3244032\,a^{14}\,b^7\,c^7\,d^5+2027520\,a^{13}\,b^8\,c^8\,d^4-901120\,a^{12}\,b^9\,c^9\,d^3+270336\,a^{11}\,b^{10}\,c^{10}\,d^2-49152\,a^{10}\,b^{11}\,c^{11}\,d+4096\,a^9\,b^{12}\,c^{12}}\right)}^{5/4}\,9313648640{}\mathrm{i}-a^{24}\,b^7\,c^{10}\,d^{13}\,\sqrt{x}\,{\left(-\frac{28561\,a^4\,b^9\,d^4-43940\,a^3\,b^{10}\,c\,d^3+25350\,a^2\,b^{11}\,c^2\,d^2-6500\,a\,b^{12}\,c^3\,d+625\,b^{13}\,c^4}{4096\,a^{21}\,d^{12}-49152\,a^{20}\,b\,c\,d^{11}+270336\,a^{19}\,b^2\,c^2\,d^{10}-901120\,a^{18}\,b^3\,c^3\,d^9+2027520\,a^{17}\,b^4\,c^4\,d^8-3244032\,a^{16}\,b^5\,c^5\,d^7+3784704\,a^{15}\,b^6\,c^6\,d^6-3244032\,a^{14}\,b^7\,c^7\,d^5+2027520\,a^{13}\,b^8\,c^8\,d^4-901120\,a^{12}\,b^9\,c^9\,d^3+270336\,a^{11}\,b^{10}\,c^{10}\,d^2-49152\,a^{10}\,b^{11}\,c^{11}\,d+4096\,a^9\,b^{12}\,c^{12}}\right)}^{5/4}\,9041543168{}\mathrm{i}+a^{25}\,b^6\,c^9\,d^{14}\,\sqrt{x}\,{\left(-\frac{28561\,a^4\,b^9\,d^4-43940\,a^3\,b^{10}\,c\,d^3+25350\,a^2\,b^{11}\,c^2\,d^2-6500\,a\,b^{12}\,c^3\,d+625\,b^{13}\,c^4}{4096\,a^{21}\,d^{12}-49152\,a^{20}\,b\,c\,d^{11}+270336\,a^{19}\,b^2\,c^2\,d^{10}-901120\,a^{18}\,b^3\,c^3\,d^9+2027520\,a^{17}\,b^4\,c^4\,d^8-3244032\,a^{16}\,b^5\,c^5\,d^7+3784704\,a^{15}\,b^6\,c^6\,d^6-3244032\,a^{14}\,b^7\,c^7\,d^5+2027520\,a^{13}\,b^8\,c^8\,d^4-901120\,a^{12}\,b^9\,c^9\,d^3+270336\,a^{11}\,b^{10}\,c^{10}\,d^2-49152\,a^{10}\,b^{11}\,c^{11}\,d+4096\,a^9\,b^{12}\,c^{12}}\right)}^{5/4}\,6877478912{}\mathrm{i}-a^{26}\,b^5\,c^8\,d^{15}\,\sqrt{x}\,{\left(-\frac{28561\,a^4\,b^9\,d^4-43940\,a^3\,b^{10}\,c\,d^3+25350\,a^2\,b^{11}\,c^2\,d^2-6500\,a\,b^{12}\,c^3\,d+625\,b^{13}\,c^4}{4096\,a^{21}\,d^{12}-49152\,a^{20}\,b\,c\,d^{11}+270336\,a^{19}\,b^2\,c^2\,d^{10}-901120\,a^{18}\,b^3\,c^3\,d^9+2027520\,a^{17}\,b^4\,c^4\,d^8-3244032\,a^{16}\,b^5\,c^5\,d^7+3784704\,a^{15}\,b^6\,c^6\,d^6-3244032\,a^{14}\,b^7\,c^7\,d^5+2027520\,a^{13}\,b^8\,c^8\,d^4-901120\,a^{12}\,b^9\,c^9\,d^3+270336\,a^{11}\,b^{10}\,c^{10}\,d^2-49152\,a^{10}\,b^{11}\,c^{11}\,d+4096\,a^9\,b^{12}\,c^{12}}\right)}^{5/4}\,3975741440{}\mathrm{i}+a^{27}\,b^4\,c^7\,d^{16}\,\sqrt{x}\,{\left(-\frac{28561\,a^4\,b^9\,d^4-43940\,a^3\,b^{10}\,c\,d^3+25350\,a^2\,b^{11}\,c^2\,d^2-6500\,a\,b^{12}\,c^3\,d+625\,b^{13}\,c^4}{4096\,a^{21}\,d^{12}-49152\,a^{20}\,b\,c\,d^{11}+270336\,a^{19}\,b^2\,c^2\,d^{10}-901120\,a^{18}\,b^3\,c^3\,d^9+2027520\,a^{17}\,b^4\,c^4\,d^8-3244032\,a^{16}\,b^5\,c^5\,d^7+3784704\,a^{15}\,b^6\,c^6\,d^6-3244032\,a^{14}\,b^7\,c^7\,d^5+2027520\,a^{13}\,b^8\,c^8\,d^4-901120\,a^{12}\,b^9\,c^9\,d^3+270336\,a^{11}\,b^{10}\,c^{10}\,d^2-49152\,a^{10}\,b^{11}\,c^{11}\,d+4096\,a^9\,b^{12}\,c^{12}}\right)}^{5/4}\,1708163072{}\mathrm{i}-a^{28}\,b^3\,c^6\,d^{17}\,\sqrt{x}\,{\left(-\frac{28561\,a^4\,b^9\,d^4-43940\,a^3\,b^{10}\,c\,d^3+25350\,a^2\,b^{11}\,c^2\,d^2-6500\,a\,b^{12}\,c^3\,d+625\,b^{13}\,c^4}{4096\,a^{21}\,d^{12}-49152\,a^{20}\,b\,c\,d^{11}+270336\,a^{19}\,b^2\,c^2\,d^{10}-901120\,a^{18}\,b^3\,c^3\,d^9+2027520\,a^{17}\,b^4\,c^4\,d^8-3244032\,a^{16}\,b^5\,c^5\,d^7+3784704\,a^{15}\,b^6\,c^6\,d^6-3244032\,a^{14}\,b^7\,c^7\,d^5+2027520\,a^{13}\,b^8\,c^8\,d^4-901120\,a^{12}\,b^9\,c^9\,d^3+270336\,a^{11}\,b^{10}\,c^{10}\,d^2-49152\,a^{10}\,b^{11}\,c^{11}\,d+4096\,a^9\,b^{12}\,c^{12}}\right)}^{5/4}\,527826944{}\mathrm{i}+a^{29}\,b^2\,c^5\,d^{18}\,\sqrt{x}\,{\left(-\frac{28561\,a^4\,b^9\,d^4-43940\,a^3\,b^{10}\,c\,d^3+25350\,a^2\,b^{11}\,c^2\,d^2-6500\,a\,b^{12}\,c^3\,d+625\,b^{13}\,c^4}{4096\,a^{21}\,d^{12}-49152\,a^{20}\,b\,c\,d^{11}+270336\,a^{19}\,b^2\,c^2\,d^{10}-901120\,a^{18}\,b^3\,c^3\,d^9+2027520\,a^{17}\,b^4\,c^4\,d^8-3244032\,a^{16}\,b^5\,c^5\,d^7+3784704\,a^{15}\,b^6\,c^6\,d^6-3244032\,a^{14}\,b^7\,c^7\,d^5+2027520\,a^{13}\,b^8\,c^8\,d^4-901120\,a^{12}\,b^9\,c^9\,d^3+270336\,a^{11}\,b^{10}\,c^{10}\,d^2-49152\,a^{10}\,b^{11}\,c^{11}\,d+4096\,a^9\,b^{12}\,c^{12}}\right)}^{5/4}\,110723072{}\mathrm{i}}{-1373125\,a^{13}\,b^8\,d^{13}+11745500\,a^{12}\,b^9\,c\,d^{12}-33424950\,a^{11}\,b^{10}\,c^2\,d^{11}+30329580\,a^{10}\,b^{11}\,c^3\,d^{10}+3343923\,a^9\,b^{12}\,c^4\,d^9+4030464\,a^8\,b^{13}\,c^5\,d^8-950272\,a^7\,b^{14}\,c^6\,d^7-8028160\,a^6\,b^{15}\,c^7\,d^6-17203200\,a^5\,b^{16}\,c^8\,d^5+34273125\,a^4\,b^{17}\,c^9\,d^4-22537500\,a^3\,b^{18}\,c^{10}\,d^3+7293750\,a^2\,b^{19}\,c^{11}\,d^2-1187500\,a\,b^{20}\,c^{12}\,d+78125\,b^{21}\,c^{13}}\right)\,{\left(-\frac{28561\,a^4\,b^9\,d^4-43940\,a^3\,b^{10}\,c\,d^3+25350\,a^2\,b^{11}\,c^2\,d^2-6500\,a\,b^{12}\,c^3\,d+625\,b^{13}\,c^4}{4096\,a^{21}\,d^{12}-49152\,a^{20}\,b\,c\,d^{11}+270336\,a^{19}\,b^2\,c^2\,d^{10}-901120\,a^{18}\,b^3\,c^3\,d^9+2027520\,a^{17}\,b^4\,c^4\,d^8-3244032\,a^{16}\,b^5\,c^5\,d^7+3784704\,a^{15}\,b^6\,c^6\,d^6-3244032\,a^{14}\,b^7\,c^7\,d^5+2027520\,a^{13}\,b^8\,c^8\,d^4-901120\,a^{12}\,b^9\,c^9\,d^3+270336\,a^{11}\,b^{10}\,c^{10}\,d^2-49152\,a^{10}\,b^{11}\,c^{11}\,d+4096\,a^9\,b^{12}\,c^{12}}\right)}^{1/4}\,2{}\mathrm{i}","Not used",1,"atan((((-(625*a^4*d^13 + 28561*b^4*c^4*d^9 - 43940*a*b^3*c^3*d^10 + 25350*a^2*b^2*c^2*d^11 - 6500*a^3*b*c*d^12)/(4096*b^12*c^21 + 4096*a^12*c^9*d^12 - 49152*a^11*b*c^10*d^11 + 270336*a^2*b^10*c^19*d^2 - 901120*a^3*b^9*c^18*d^3 + 2027520*a^4*b^8*c^17*d^4 - 3244032*a^5*b^7*c^16*d^5 + 3784704*a^6*b^6*c^15*d^6 - 3244032*a^7*b^5*c^14*d^7 + 2027520*a^8*b^4*c^13*d^8 - 901120*a^9*b^3*c^12*d^9 + 270336*a^10*b^2*c^11*d^10 - 49152*a*b^11*c^20*d))^(3/4)*(x^(1/2)*(-(625*a^4*d^13 + 28561*b^4*c^4*d^9 - 43940*a*b^3*c^3*d^10 + 25350*a^2*b^2*c^2*d^11 - 6500*a^3*b*c*d^12)/(4096*b^12*c^21 + 4096*a^12*c^9*d^12 - 49152*a^11*b*c^10*d^11 + 270336*a^2*b^10*c^19*d^2 - 901120*a^3*b^9*c^18*d^3 + 2027520*a^4*b^8*c^17*d^4 - 3244032*a^5*b^7*c^16*d^5 + 3784704*a^6*b^6*c^15*d^6 - 3244032*a^7*b^5*c^14*d^7 + 2027520*a^8*b^4*c^13*d^8 - 901120*a^9*b^3*c^12*d^9 + 270336*a^10*b^2*c^11*d^10 - 49152*a*b^11*c^20*d))^(1/4)*(52428800*a^23*b^38*c^57*d^4 - 1635778560*a^24*b^37*c^56*d^5 + 24482152448*a^25*b^36*c^55*d^6 - 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x^(1/2)*(54080000*a^20*b^33*c^43*d^10 - 1361152000*a^21*b^32*c^42*d^11 + 16011852800*a^22*b^31*c^41*d^12 - 116736734720*a^23*b^30*c^40*d^13 + 589861462528*a^24*b^29*c^39*d^14 - 2187899577344*a^25*b^28*c^38*d^15 + 6149347117056*a^26*b^27*c^37*d^16 - 13298820601344*a^27*b^26*c^36*d^17 + 22133436343296*a^28*b^25*c^35*d^18 - 27715689750528*a^29*b^24*c^34*d^19 + 24077503776768*a^30*b^23*c^33*d^20 - 9645706816512*a^31*b^22*c^32*d^21 - 9645706816512*a^32*b^21*c^31*d^22 + 24077503776768*a^33*b^20*c^30*d^23 - 27715689750528*a^34*b^19*c^29*d^24 + 22133436343296*a^35*b^18*c^28*d^25 - 13298820601344*a^36*b^17*c^27*d^26 + 6149347117056*a^37*b^16*c^26*d^27 - 2187899577344*a^38*b^15*c^25*d^28 + 589861462528*a^39*b^14*c^24*d^29 - 116736734720*a^40*b^13*c^23*d^30 + 16011852800*a^41*b^12*c^22*d^31 - 1361152000*a^42*b^11*c^21*d^32 + 54080000*a^43*b^10*c^20*d^33))*(-(625*a^4*d^13 + 28561*b^4*c^4*d^9 - 43940*a*b^3*c^3*d^10 + 25350*a^2*b^2*c^2*d^11 - 6500*a^3*b*c*d^12)/(4096*b^12*c^21 + 4096*a^12*c^9*d^12 - 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49152*a^10*b^11*c^11*d + 270336*a^11*b^10*c^10*d^2 - 901120*a^12*b^9*c^9*d^3 + 2027520*a^13*b^8*c^8*d^4 - 3244032*a^14*b^7*c^7*d^5 + 3784704*a^15*b^6*c^6*d^6 - 3244032*a^16*b^5*c^5*d^7 + 2027520*a^17*b^4*c^4*d^8 - 901120*a^18*b^3*c^3*d^9 + 270336*a^19*b^2*c^2*d^10 - 49152*a^20*b*c*d^11))^(5/4)*8184070144i + a^23*b^8*c^11*d^12*x^(1/2)*(-(625*b^13*c^4 + 28561*a^4*b^9*d^4 - 43940*a^3*b^10*c*d^3 + 25350*a^2*b^11*c^2*d^2 - 6500*a*b^12*c^3*d)/(4096*a^21*d^12 + 4096*a^9*b^12*c^12 - 49152*a^10*b^11*c^11*d + 270336*a^11*b^10*c^10*d^2 - 901120*a^12*b^9*c^9*d^3 + 2027520*a^13*b^8*c^8*d^4 - 3244032*a^14*b^7*c^7*d^5 + 3784704*a^15*b^6*c^6*d^6 - 3244032*a^16*b^5*c^5*d^7 + 2027520*a^17*b^4*c^4*d^8 - 901120*a^18*b^3*c^3*d^9 + 270336*a^19*b^2*c^2*d^10 - 49152*a^20*b*c*d^11))^(5/4)*9313648640i - a^24*b^7*c^10*d^13*x^(1/2)*(-(625*b^13*c^4 + 28561*a^4*b^9*d^4 - 43940*a^3*b^10*c*d^3 + 25350*a^2*b^11*c^2*d^2 - 6500*a*b^12*c^3*d)/(4096*a^21*d^12 + 4096*a^9*b^12*c^12 - 49152*a^10*b^11*c^11*d + 270336*a^11*b^10*c^10*d^2 - 901120*a^12*b^9*c^9*d^3 + 2027520*a^13*b^8*c^8*d^4 - 3244032*a^14*b^7*c^7*d^5 + 3784704*a^15*b^6*c^6*d^6 - 3244032*a^16*b^5*c^5*d^7 + 2027520*a^17*b^4*c^4*d^8 - 901120*a^18*b^3*c^3*d^9 + 270336*a^19*b^2*c^2*d^10 - 49152*a^20*b*c*d^11))^(5/4)*9041543168i + a^25*b^6*c^9*d^14*x^(1/2)*(-(625*b^13*c^4 + 28561*a^4*b^9*d^4 - 43940*a^3*b^10*c*d^3 + 25350*a^2*b^11*c^2*d^2 - 6500*a*b^12*c^3*d)/(4096*a^21*d^12 + 4096*a^9*b^12*c^12 - 49152*a^10*b^11*c^11*d + 270336*a^11*b^10*c^10*d^2 - 901120*a^12*b^9*c^9*d^3 + 2027520*a^13*b^8*c^8*d^4 - 3244032*a^14*b^7*c^7*d^5 + 3784704*a^15*b^6*c^6*d^6 - 3244032*a^16*b^5*c^5*d^7 + 2027520*a^17*b^4*c^4*d^8 - 901120*a^18*b^3*c^3*d^9 + 270336*a^19*b^2*c^2*d^10 - 49152*a^20*b*c*d^11))^(5/4)*6877478912i - a^26*b^5*c^8*d^15*x^(1/2)*(-(625*b^13*c^4 + 28561*a^4*b^9*d^4 - 43940*a^3*b^10*c*d^3 + 25350*a^2*b^11*c^2*d^2 - 6500*a*b^12*c^3*d)/(4096*a^21*d^12 + 4096*a^9*b^12*c^12 - 49152*a^10*b^11*c^11*d + 270336*a^11*b^10*c^10*d^2 - 901120*a^12*b^9*c^9*d^3 + 2027520*a^13*b^8*c^8*d^4 - 3244032*a^14*b^7*c^7*d^5 + 3784704*a^15*b^6*c^6*d^6 - 3244032*a^16*b^5*c^5*d^7 + 2027520*a^17*b^4*c^4*d^8 - 901120*a^18*b^3*c^3*d^9 + 270336*a^19*b^2*c^2*d^10 - 49152*a^20*b*c*d^11))^(5/4)*3975741440i + a^27*b^4*c^7*d^16*x^(1/2)*(-(625*b^13*c^4 + 28561*a^4*b^9*d^4 - 43940*a^3*b^10*c*d^3 + 25350*a^2*b^11*c^2*d^2 - 6500*a*b^12*c^3*d)/(4096*a^21*d^12 + 4096*a^9*b^12*c^12 - 49152*a^10*b^11*c^11*d + 270336*a^11*b^10*c^10*d^2 - 901120*a^12*b^9*c^9*d^3 + 2027520*a^13*b^8*c^8*d^4 - 3244032*a^14*b^7*c^7*d^5 + 3784704*a^15*b^6*c^6*d^6 - 3244032*a^16*b^5*c^5*d^7 + 2027520*a^17*b^4*c^4*d^8 - 901120*a^18*b^3*c^3*d^9 + 270336*a^19*b^2*c^2*d^10 - 49152*a^20*b*c*d^11))^(5/4)*1708163072i - a^28*b^3*c^6*d^17*x^(1/2)*(-(625*b^13*c^4 + 28561*a^4*b^9*d^4 - 43940*a^3*b^10*c*d^3 + 25350*a^2*b^11*c^2*d^2 - 6500*a*b^12*c^3*d)/(4096*a^21*d^12 + 4096*a^9*b^12*c^12 - 49152*a^10*b^11*c^11*d + 270336*a^11*b^10*c^10*d^2 - 901120*a^12*b^9*c^9*d^3 + 2027520*a^13*b^8*c^8*d^4 - 3244032*a^14*b^7*c^7*d^5 + 3784704*a^15*b^6*c^6*d^6 - 3244032*a^16*b^5*c^5*d^7 + 2027520*a^17*b^4*c^4*d^8 - 901120*a^18*b^3*c^3*d^9 + 270336*a^19*b^2*c^2*d^10 - 49152*a^20*b*c*d^11))^(5/4)*527826944i + a^29*b^2*c^5*d^18*x^(1/2)*(-(625*b^13*c^4 + 28561*a^4*b^9*d^4 - 43940*a^3*b^10*c*d^3 + 25350*a^2*b^11*c^2*d^2 - 6500*a*b^12*c^3*d)/(4096*a^21*d^12 + 4096*a^9*b^12*c^12 - 49152*a^10*b^11*c^11*d + 270336*a^11*b^10*c^10*d^2 - 901120*a^12*b^9*c^9*d^3 + 2027520*a^13*b^8*c^8*d^4 - 3244032*a^14*b^7*c^7*d^5 + 3784704*a^15*b^6*c^6*d^6 - 3244032*a^16*b^5*c^5*d^7 + 2027520*a^17*b^4*c^4*d^8 - 901120*a^18*b^3*c^3*d^9 + 270336*a^19*b^2*c^2*d^10 - 49152*a^20*b*c*d^11))^(5/4)*110723072i)/(78125*b^21*c^13 - 1373125*a^13*b^8*d^13 + 11745500*a^12*b^9*c*d^12 + 7293750*a^2*b^19*c^11*d^2 - 22537500*a^3*b^18*c^10*d^3 + 34273125*a^4*b^17*c^9*d^4 - 17203200*a^5*b^16*c^8*d^5 - 8028160*a^6*b^15*c^7*d^6 - 950272*a^7*b^14*c^6*d^7 + 4030464*a^8*b^13*c^5*d^8 + 3343923*a^9*b^12*c^4*d^9 + 30329580*a^10*b^11*c^3*d^10 - 33424950*a^11*b^10*c^2*d^11 - 1187500*a*b^20*c^12*d))*(-(625*b^13*c^4 + 28561*a^4*b^9*d^4 - 43940*a^3*b^10*c*d^3 + 25350*a^2*b^11*c^2*d^2 - 6500*a*b^12*c^3*d)/(4096*a^21*d^12 + 4096*a^9*b^12*c^12 - 49152*a^10*b^11*c^11*d + 270336*a^11*b^10*c^10*d^2 - 901120*a^12*b^9*c^9*d^3 + 2027520*a^13*b^8*c^8*d^4 - 3244032*a^14*b^7*c^7*d^5 + 3784704*a^15*b^6*c^6*d^6 - 3244032*a^16*b^5*c^5*d^7 + 2027520*a^17*b^4*c^4*d^8 - 901120*a^18*b^3*c^3*d^9 + 270336*a^19*b^2*c^2*d^10 - 49152*a^20*b*c*d^11))^(1/4)*2i - (2/(a*c) + (x^2*(5*a^3*d^3 + 5*b^3*c^3 - 4*a*b^2*c^2*d - 4*a^2*b*c*d^2))/(2*a^2*c^2*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) + (b*d*x^4*(5*a^2*d^2 + 5*b^2*c^2 - 8*a*b*c*d))/(2*a^2*c^2*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)))/(x^(5/2)*(a*d + b*c) + a*c*x^(1/2) + b*d*x^(9/2))","B"
494,1,44436,676,10.589333,"\text{Not used}","int(1/(x^(5/2)*(a + b*x^2)^2*(c + d*x^2)^2),x)","\mathrm{atan}\left(\frac{\left({\left(-\frac{50625\,a^4\,b^{11}\,d^4-94500\,a^3\,b^{12}\,c\,d^3+66150\,a^2\,b^{13}\,c^2\,d^2-20580\,a\,b^{14}\,c^3\,d+2401\,b^{15}\,c^4}{4096\,a^{23}\,d^{12}-49152\,a^{22}\,b\,c\,d^{11}+270336\,a^{21}\,b^2\,c^2\,d^{10}-901120\,a^{20}\,b^3\,c^3\,d^9+2027520\,a^{19}\,b^4\,c^4\,d^8-3244032\,a^{18}\,b^5\,c^5\,d^7+3784704\,a^{17}\,b^6\,c^6\,d^6-3244032\,a^{16}\,b^7\,c^7\,d^5+2027520\,a^{15}\,b^8\,c^8\,d^4-901120\,a^{14}\,b^9\,c^9\,d^3+270336\,a^{13}\,b^{10}\,c^{10}\,d^2-49152\,a^{12}\,b^{11}\,c^{11}\,d+4096\,a^{11}\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(\left({\left(-\frac{50625\,a^4\,b^{11}\,d^4-94500\,a^3\,b^{12}\,c\,d^3+66150\,a^2\,b^{13}\,c^2\,d^2-20580\,a\,b^{14}\,c^3\,d+2401\,b^{15}\,c^4}{4096\,a^{23}\,d^{12}-49152\,a^{22}\,b\,c\,d^{11}+270336\,a^{21}\,b^2\,c^2\,d^{10}-901120\,a^{20}\,b^3\,c^3\,d^9+2027520\,a^{19}\,b^4\,c^4\,d^8-3244032\,a^{18}\,b^5\,c^5\,d^7+3784704\,a^{17}\,b^6\,c^6\,d^6-3244032\,a^{16}\,b^7\,c^7\,d^5+2027520\,a^{15}\,b^8\,c^8\,d^4-901120\,a^{14}\,b^9\,c^9\,d^3+270336\,a^{13}\,b^{10}\,c^{10}\,d^2-49152\,a^{12}\,b^{11}\,c^{11}\,d+4096\,a^{11}\,b^{12}\,c^{12}}\right)}^{1/4}\,\left(117440512\,a^{59}\,b^4\,c^{25}\,d^{38}-3657433088\,a^{58}\,b^5\,c^{26}\,d^{37}+54978936832\,a^{57}\,b^6\,c^{27}\,d^{36}-531300876288\,a^{56}\,b^7\,c^{28}\,d^{35}+3709140467712\,a^{55}\,b^8\,c^{29}\,d^{34}-19931198390272\,a^{54}\,b^9\,c^{30}\,d^{33}+85777845321728\,a^{53}\,b^{10}\,c^{31}\,d^{32}-303808739540992\,a^{52}\,b^{11}\,c^{32}\,d^{31}+903261116694528\,a^{51}\,b^{12}\,c^{33}\,d^{30}-2288995975299072\,a^{50}\,b^{13}\,c^{34}\,d^{29}+5006182506823680\,a^{49}\,b^{14}\,c^{35}\,d^{28}-9552410255032320\,a^{48}\,b^{15}\,c^{36}\,d^{27}+16064830746132480\,a^{47}\,b^{16}\,c^{37}\,d^{26}-24054442827448320\,a^{46}\,b^{17}\,c^{38}\,d^{25}+32403938271559680\,a^{45}\,b^{18}\,c^{39}\,d^{24}-39685869262602240\,a^{44}\,b^{19}\,c^{40}\,d^{23}+44611437078773760\,a^{43}\,b^{20}\,c^{41}\,d^{22}-46346397171056640\,a^{42}\,b^{21}\,c^{42}\,d^{21}+44611437078773760\,a^{41}\,b^{22}\,c^{43}\,d^{20}-39685869262602240\,a^{40}\,b^{23}\,c^{44}\,d^{19}+32403938271559680\,a^{39}\,b^{24}\,c^{45}\,d^{18}-24054442827448320\,a^{38}\,b^{25}\,c^{46}\,d^{17}+16064830746132480\,a^{37}\,b^{26}\,c^{47}\,d^{16}-9552410255032320\,a^{36}\,b^{27}\,c^{48}\,d^{15}+5006182506823680\,a^{35}\,b^{28}\,c^{49}\,d^{14}-2288995975299072\,a^{34}\,b^{29}\,c^{50}\,d^{13}+903261116694528\,a^{33}\,b^{30}\,c^{51}\,d^{12}-303808739540992\,a^{32}\,b^{31}\,c^{52}\,d^{11}+85777845321728\,a^{31}\,b^{32}\,c^{53}\,d^{10}-19931198390272\,a^{30}\,b^{33}\,c^{54}\,d^9+3709140467712\,a^{29}\,b^{34}\,c^{55}\,d^8-531300876288\,a^{28}\,b^{35}\,c^{56}\,d^7+54978936832\,a^{27}\,b^{36}\,c^{57}\,d^6-3657433088\,a^{26}\,b^{37}\,c^{58}\,d^5+117440512\,a^{25}\,b^{38}\,c^{59}\,d^4\right)+\sqrt{x}\,\left(102760448\,a^{57}\,b^4\,c^{22}\,d^{39}-3112173568\,a^{56}\,b^5\,c^{23}\,d^{38}+45319454720\,a^{55}\,b^6\,c^{24}\,d^{37}-422576128000\,a^{54}\,b^7\,c^{25}\,d^{36}+2834667929600\,a^{53}\,b^8\,c^{26}\,d^{35}-14570424893440\,a^{52}\,b^9\,c^{27}\,d^{34}+59682471280640\,a^{51}\,b^{10}\,c^{28}\,d^{33}-200027983052800\,a^{50}\,b^{11}\,c^{29}\,d^{32}+558859896750080\,a^{49}\,b^{12}\,c^{30}\,d^{31}-1319333141676032\,a^{48}\,b^{13}\,c^{31}\,d^{30}+2657695282757632\,a^{47}\,b^{14}\,c^{32}\,d^{29}-4599356881633280\,a^{46}\,b^{15}\,c^{33}\,d^{28}+6863546220544000\,a^{45}\,b^{16}\,c^{34}\,d^{27}-8828557564313600\,a^{44}\,b^{17}\,c^{35}\,d^{26}+9711406085570560\,a^{43}\,b^{18}\,c^{36}\,d^{25}-8904303328624640\,a^{42}\,b^{19}\,c^{37}\,d^{24}+6275554166702080\,a^{41}\,b^{20}\,c^{38}\,d^{23}-2263049201254400\,a^{40}\,b^{21}\,c^{39}\,d^{22}-2263049201254400\,a^{39}\,b^{22}\,c^{40}\,d^{21}+6275554166702080\,a^{38}\,b^{23}\,c^{41}\,d^{20}-8904303328624640\,a^{37}\,b^{24}\,c^{42}\,d^{19}+9711406085570560\,a^{36}\,b^{25}\,c^{43}\,d^{18}-8828557564313600\,a^{35}\,b^{26}\,c^{44}\,d^{17}+6863546220544000\,a^{34}\,b^{27}\,c^{45}\,d^{16}-4599356881633280\,a^{33}\,b^{28}\,c^{46}\,d^{15}+2657695282757632\,a^{32}\,b^{29}\,c^{47}\,d^{14}-1319333141676032\,a^{31}\,b^{30}\,c^{48}\,d^{13}+558859896750080\,a^{30}\,b^{31}\,c^{49}\,d^{12}-200027983052800\,a^{29}\,b^{32}\,c^{50}\,d^{11}+59682471280640\,a^{28}\,b^{33}\,c^{51}\,d^{10}-14570424893440\,a^{27}\,b^{34}\,c^{52}\,d^9+2834667929600\,a^{26}\,b^{35}\,c^{53}\,d^8-422576128000\,a^{25}\,b^{36}\,c^{54}\,d^7+45319454720\,a^{24}\,b^{37}\,c^{55}\,d^6-3112173568\,a^{23}\,b^{38}\,c^{56}\,d^5+102760448\,a^{22}\,b^{39}\,c^{57}\,d^4\right)\right)\,{\left(-\frac{50625\,a^4\,b^{11}\,d^4-94500\,a^3\,b^{12}\,c\,d^3+66150\,a^2\,b^{13}\,c^2\,d^2-20580\,a\,b^{14}\,c^3\,d+2401\,b^{15}\,c^4}{4096\,a^{23}\,d^{12}-49152\,a^{22}\,b\,c\,d^{11}+270336\,a^{21}\,b^2\,c^2\,d^{10}-901120\,a^{20}\,b^3\,c^3\,d^9+2027520\,a^{19}\,b^4\,c^4\,d^8-3244032\,a^{18}\,b^5\,c^5\,d^7+3784704\,a^{17}\,b^6\,c^6\,d^6-3244032\,a^{16}\,b^7\,c^7\,d^5+2027520\,a^{15}\,b^8\,c^8\,d^4-901120\,a^{14}\,b^9\,c^9\,d^3+270336\,a^{13}\,b^{10}\,c^{10}\,d^2-49152\,a^{12}\,b^{11}\,c^{11}\,d+40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used",1,"atan((((-(2401*b^15*c^4 + 50625*a^4*b^11*d^4 - 94500*a^3*b^12*c*d^3 + 66150*a^2*b^13*c^2*d^2 - 20580*a*b^14*c^3*d)/(4096*a^23*d^12 + 4096*a^11*b^12*c^12 - 49152*a^12*b^11*c^11*d + 270336*a^13*b^10*c^10*d^2 - 901120*a^14*b^9*c^9*d^3 + 2027520*a^15*b^8*c^8*d^4 - 3244032*a^16*b^7*c^7*d^5 + 3784704*a^17*b^6*c^6*d^6 - 3244032*a^18*b^5*c^5*d^7 + 2027520*a^19*b^4*c^4*d^8 - 901120*a^20*b^3*c^3*d^9 + 270336*a^21*b^2*c^2*d^10 - 49152*a^22*b*c*d^11))^(1/4)*(((-(2401*b^15*c^4 + 50625*a^4*b^11*d^4 - 94500*a^3*b^12*c*d^3 + 66150*a^2*b^13*c^2*d^2 - 20580*a*b^14*c^3*d)/(4096*a^23*d^12 + 4096*a^11*b^12*c^12 - 49152*a^12*b^11*c^11*d + 270336*a^13*b^10*c^10*d^2 - 901120*a^14*b^9*c^9*d^3 + 2027520*a^15*b^8*c^8*d^4 - 3244032*a^16*b^7*c^7*d^5 + 3784704*a^17*b^6*c^6*d^6 - 3244032*a^18*b^5*c^5*d^7 + 2027520*a^19*b^4*c^4*d^8 - 901120*a^20*b^3*c^3*d^9 + 270336*a^21*b^2*c^2*d^10 - 49152*a^22*b*c*d^11))^(1/4)*(117440512*a^25*b^38*c^59*d^4 - 3657433088*a^26*b^37*c^58*d^5 + 54978936832*a^27*b^36*c^57*d^6 - 531300876288*a^28*b^35*c^56*d^7 + 3709140467712*a^29*b^34*c^55*d^8 - 19931198390272*a^30*b^33*c^54*d^9 + 85777845321728*a^31*b^32*c^53*d^10 - 303808739540992*a^32*b^31*c^52*d^11 + 903261116694528*a^33*b^30*c^51*d^12 - 2288995975299072*a^34*b^29*c^50*d^13 + 5006182506823680*a^35*b^28*c^49*d^14 - 9552410255032320*a^36*b^27*c^48*d^15 + 16064830746132480*a^37*b^26*c^47*d^16 - 24054442827448320*a^38*b^25*c^46*d^17 + 32403938271559680*a^39*b^24*c^45*d^18 - 39685869262602240*a^40*b^23*c^44*d^19 + 44611437078773760*a^41*b^22*c^43*d^20 - 46346397171056640*a^42*b^21*c^42*d^21 + 44611437078773760*a^43*b^20*c^41*d^22 - 39685869262602240*a^44*b^19*c^40*d^23 + 32403938271559680*a^45*b^18*c^39*d^24 - 24054442827448320*a^46*b^17*c^38*d^25 + 16064830746132480*a^47*b^16*c^37*d^26 - 9552410255032320*a^48*b^15*c^36*d^27 + 5006182506823680*a^49*b^14*c^35*d^28 - 2288995975299072*a^50*b^13*c^34*d^29 + 903261116694528*a^51*b^12*c^33*d^30 - 303808739540992*a^52*b^11*c^32*d^31 + 85777845321728*a^53*b^10*c^31*d^32 - 19931198390272*a^54*b^9*c^30*d^33 + 3709140467712*a^55*b^8*c^29*d^34 - 531300876288*a^56*b^7*c^28*d^35 + 54978936832*a^57*b^6*c^27*d^36 - 3657433088*a^58*b^5*c^26*d^37 + 117440512*a^59*b^4*c^25*d^38) + x^(1/2)*(102760448*a^22*b^39*c^57*d^4 - 3112173568*a^23*b^38*c^56*d^5 + 45319454720*a^24*b^37*c^55*d^6 - 422576128000*a^25*b^36*c^54*d^7 + 2834667929600*a^26*b^35*c^53*d^8 - 14570424893440*a^27*b^34*c^52*d^9 + 59682471280640*a^28*b^33*c^51*d^10 - 200027983052800*a^29*b^32*c^50*d^11 + 558859896750080*a^30*b^31*c^49*d^12 - 1319333141676032*a^31*b^30*c^48*d^13 + 2657695282757632*a^32*b^29*c^47*d^14 - 4599356881633280*a^33*b^28*c^46*d^15 + 6863546220544000*a^34*b^27*c^45*d^16 - 8828557564313600*a^35*b^26*c^44*d^17 + 9711406085570560*a^36*b^25*c^43*d^18 - 8904303328624640*a^37*b^24*c^42*d^19 + 6275554166702080*a^38*b^23*c^41*d^20 - 2263049201254400*a^39*b^22*c^40*d^21 - 2263049201254400*a^40*b^21*c^39*d^22 + 6275554166702080*a^41*b^20*c^38*d^23 - 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6501304320*a^41*b^12*c^19*d^34 + 276595200*a^42*b^11*c^18*d^35))*(-(2401*b^15*c^4 + 50625*a^4*b^11*d^4 - 94500*a^3*b^12*c*d^3 + 66150*a^2*b^13*c^2*d^2 - 20580*a*b^14*c^3*d)/(4096*a^23*d^12 + 4096*a^11*b^12*c^12 - 49152*a^12*b^11*c^11*d + 270336*a^13*b^10*c^10*d^2 - 901120*a^14*b^9*c^9*d^3 + 2027520*a^15*b^8*c^8*d^4 - 3244032*a^16*b^7*c^7*d^5 + 3784704*a^17*b^6*c^6*d^6 - 3244032*a^18*b^5*c^5*d^7 + 2027520*a^19*b^4*c^4*d^8 - 901120*a^20*b^3*c^3*d^9 + 270336*a^21*b^2*c^2*d^10 - 49152*a^22*b*c*d^11))^(1/4)*1i - ((-(2401*b^15*c^4 + 50625*a^4*b^11*d^4 - 94500*a^3*b^12*c*d^3 + 66150*a^2*b^13*c^2*d^2 - 20580*a*b^14*c^3*d)/(4096*a^23*d^12 + 4096*a^11*b^12*c^12 - 49152*a^12*b^11*c^11*d + 270336*a^13*b^10*c^10*d^2 - 901120*a^14*b^9*c^9*d^3 + 2027520*a^15*b^8*c^8*d^4 - 3244032*a^16*b^7*c^7*d^5 + 3784704*a^17*b^6*c^6*d^6 - 3244032*a^18*b^5*c^5*d^7 + 2027520*a^19*b^4*c^4*d^8 - 901120*a^20*b^3*c^3*d^9 + 270336*a^21*b^2*c^2*d^10 - 49152*a^22*b*c*d^11))^(1/4)*(((-(2401*b^15*c^4 + 50625*a^4*b^11*d^4 - 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71869242368*a^20*b^33*c^40*d^13 - 496940910592*a^21*b^32*c^39*d^14 + 2412258434048*a^22*b^31*c^38*d^15 - 8751989614592*a^23*b^30*c^37*d^16 + 24696348863488*a^24*b^29*c^36*d^17 - 55777785276416*a^25*b^28*c^35*d^18 + 103251559480832*a^26*b^27*c^34*d^19 - 160243801919488*a^27*b^26*c^33*d^20 + 213523293304832*a^28*b^25*c^32*d^21 - 250272765841408*a^29*b^24*c^31*d^22 + 263188357892096*a^30*b^23*c^30*d^23 - 250272765841408*a^31*b^22*c^29*d^24 + 213523293304832*a^32*b^21*c^28*d^25 - 160243801919488*a^33*b^20*c^27*d^26 + 103251559480832*a^34*b^19*c^26*d^27 - 55777785276416*a^35*b^18*c^25*d^28 + 24696348863488*a^36*b^17*c^24*d^29 - 8751989614592*a^37*b^16*c^23*d^30 + 2412258434048*a^38*b^15*c^22*d^31 - 496940910592*a^39*b^14*c^21*d^32 + 71869242368*a^40*b^13*c^20*d^33 - 6501304320*a^41*b^12*c^19*d^34 + 276595200*a^42*b^11*c^18*d^35))*1i + (-(2401*a^4*d^15 + 50625*b^4*c^4*d^11 - 94500*a*b^3*c^3*d^12 + 66150*a^2*b^2*c^2*d^13 - 20580*a^3*b*c*d^14)/(4096*b^12*c^23 + 4096*a^12*c^11*d^12 - 49152*a^11*b*c^12*d^11 + 270336*a^2*b^10*c^21*d^2 - 901120*a^3*b^9*c^20*d^3 + 2027520*a^4*b^8*c^19*d^4 - 3244032*a^5*b^7*c^18*d^5 + 3784704*a^6*b^6*c^17*d^6 - 3244032*a^7*b^5*c^16*d^7 + 2027520*a^8*b^4*c^15*d^8 - 901120*a^9*b^3*c^14*d^9 + 270336*a^10*b^2*c^13*d^10 - 49152*a*b^11*c^22*d))^(1/4)*((-(2401*a^4*d^15 + 50625*b^4*c^4*d^11 - 94500*a*b^3*c^3*d^12 + 66150*a^2*b^2*c^2*d^13 - 20580*a^3*b*c*d^14)/(4096*b^12*c^23 + 4096*a^12*c^11*d^12 - 49152*a^11*b*c^12*d^11 + 270336*a^2*b^10*c^21*d^2 - 901120*a^3*b^9*c^20*d^3 + 2027520*a^4*b^8*c^19*d^4 - 3244032*a^5*b^7*c^18*d^5 + 3784704*a^6*b^6*c^17*d^6 - 3244032*a^7*b^5*c^16*d^7 + 2027520*a^8*b^4*c^15*d^8 - 901120*a^9*b^3*c^14*d^9 + 270336*a^10*b^2*c^13*d^10 - 49152*a*b^11*c^22*d))^(1/4)*(147517440*a^18*b^37*c^47*d^8 - ((-(2401*a^4*d^15 + 50625*b^4*c^4*d^11 - 94500*a*b^3*c^3*d^12 + 66150*a^2*b^2*c^2*d^13 - 20580*a^3*b*c*d^14)/(4096*b^12*c^23 + 4096*a^12*c^11*d^12 - 49152*a^11*b*c^12*d^11 + 270336*a^2*b^10*c^21*d^2 - 901120*a^3*b^9*c^20*d^3 + 2027520*a^4*b^8*c^19*d^4 - 3244032*a^5*b^7*c^18*d^5 + 3784704*a^6*b^6*c^17*d^6 - 3244032*a^7*b^5*c^16*d^7 + 2027520*a^8*b^4*c^15*d^8 - 901120*a^9*b^3*c^14*d^9 + 270336*a^10*b^2*c^13*d^10 - 49152*a*b^11*c^22*d))^(1/4)*(117440512*a^25*b^38*c^59*d^4 - 3657433088*a^26*b^37*c^58*d^5 + 54978936832*a^27*b^36*c^57*d^6 - 531300876288*a^28*b^35*c^56*d^7 + 3709140467712*a^29*b^34*c^55*d^8 - 19931198390272*a^30*b^33*c^54*d^9 + 85777845321728*a^31*b^32*c^53*d^10 - 303808739540992*a^32*b^31*c^52*d^11 + 903261116694528*a^33*b^30*c^51*d^12 - 2288995975299072*a^34*b^29*c^50*d^13 + 5006182506823680*a^35*b^28*c^49*d^14 - 9552410255032320*a^36*b^27*c^48*d^15 + 16064830746132480*a^37*b^26*c^47*d^16 - 24054442827448320*a^38*b^25*c^46*d^17 + 32403938271559680*a^39*b^24*c^45*d^18 - 39685869262602240*a^40*b^23*c^44*d^19 + 44611437078773760*a^41*b^22*c^43*d^20 - 46346397171056640*a^42*b^21*c^42*d^21 + 44611437078773760*a^43*b^20*c^41*d^22 - 39685869262602240*a^44*b^19*c^40*d^23 + 32403938271559680*a^45*b^18*c^39*d^24 - 24054442827448320*a^46*b^17*c^38*d^25 + 16064830746132480*a^47*b^16*c^37*d^26 - 9552410255032320*a^48*b^15*c^36*d^27 + 5006182506823680*a^49*b^14*c^35*d^28 - 2288995975299072*a^50*b^13*c^34*d^29 + 903261116694528*a^51*b^12*c^33*d^30 - 303808739540992*a^52*b^11*c^32*d^31 + 85777845321728*a^53*b^10*c^31*d^32 - 19931198390272*a^54*b^9*c^30*d^33 + 3709140467712*a^55*b^8*c^29*d^34 - 531300876288*a^56*b^7*c^28*d^35 + 54978936832*a^57*b^6*c^27*d^36 - 3657433088*a^58*b^5*c^26*d^37 + 117440512*a^59*b^4*c^25*d^38)*1i - x^(1/2)*(102760448*a^22*b^39*c^57*d^4 - 3112173568*a^23*b^38*c^56*d^5 + 45319454720*a^24*b^37*c^55*d^6 - 422576128000*a^25*b^36*c^54*d^7 + 2834667929600*a^26*b^35*c^53*d^8 - 14570424893440*a^27*b^34*c^52*d^9 + 59682471280640*a^28*b^33*c^51*d^10 - 200027983052800*a^29*b^32*c^50*d^11 + 558859896750080*a^30*b^31*c^49*d^12 - 1319333141676032*a^31*b^30*c^48*d^13 + 2657695282757632*a^32*b^29*c^47*d^14 - 4599356881633280*a^33*b^28*c^46*d^15 + 6863546220544000*a^34*b^27*c^45*d^16 - 8828557564313600*a^35*b^26*c^44*d^17 + 9711406085570560*a^36*b^25*c^43*d^18 - 8904303328624640*a^37*b^24*c^42*d^19 + 6275554166702080*a^38*b^23*c^41*d^20 - 2263049201254400*a^39*b^22*c^40*d^21 - 2263049201254400*a^40*b^21*c^39*d^22 + 6275554166702080*a^41*b^20*c^38*d^23 - 8904303328624640*a^42*b^19*c^37*d^24 + 9711406085570560*a^43*b^18*c^36*d^25 - 8828557564313600*a^44*b^17*c^35*d^26 + 6863546220544000*a^45*b^16*c^34*d^27 - 4599356881633280*a^46*b^15*c^33*d^28 + 2657695282757632*a^47*b^14*c^32*d^29 - 1319333141676032*a^48*b^13*c^31*d^30 + 558859896750080*a^49*b^12*c^30*d^31 - 200027983052800*a^50*b^11*c^29*d^32 + 59682471280640*a^51*b^10*c^28*d^33 - 14570424893440*a^52*b^9*c^27*d^34 + 2834667929600*a^53*b^8*c^26*d^35 - 422576128000*a^54*b^7*c^25*d^36 + 45319454720*a^55*b^6*c^24*d^37 - 3112173568*a^56*b^5*c^23*d^38 + 102760448*a^57*b^4*c^22*d^39))*(-(2401*a^4*d^15 + 50625*b^4*c^4*d^11 - 94500*a*b^3*c^3*d^12 + 66150*a^2*b^2*c^2*d^13 - 20580*a^3*b*c*d^14)/(4096*b^12*c^23 + 4096*a^12*c^11*d^12 - 49152*a^11*b*c^12*d^11 + 270336*a^2*b^10*c^21*d^2 - 901120*a^3*b^9*c^20*d^3 + 2027520*a^4*b^8*c^19*d^4 - 3244032*a^5*b^7*c^18*d^5 + 3784704*a^6*b^6*c^17*d^6 - 3244032*a^7*b^5*c^16*d^7 + 2027520*a^8*b^4*c^15*d^8 - 901120*a^9*b^3*c^14*d^9 + 270336*a^10*b^2*c^13*d^10 - 49152*a*b^11*c^22*d))^(3/4)*1i - 3841073152*a^19*b^36*c^46*d^9 + 47382401024*a^20*b^35*c^45*d^10 - 368463757312*a^21*b^34*c^44*d^11 + 2027474309120*a^22*b^33*c^43*d^12 - 8398939463680*a^23*b^32*c^42*d^13 + 27207328280576*a^24*b^31*c^41*d^14 - 70656513052672*a^25*b^30*c^40*d^15 + 149590069231616*a^26*b^29*c^39*d^16 - 261008589107200*a^27*b^28*c^38*d^17 + 377325278126080*a^28*b^27*c^37*d^18 - 450764657864704*a^29*b^26*c^36*d^19 + 436168221851648*a^30*b^25*c^35*d^20 - 317115551617024*a^31*b^24*c^34*d^21 + 115950654218240*a^32*b^23*c^33*d^22 + 115950654218240*a^33*b^22*c^32*d^23 - 317115551617024*a^34*b^21*c^31*d^24 + 436168221851648*a^35*b^20*c^30*d^25 - 450764657864704*a^36*b^19*c^29*d^26 + 377325278126080*a^37*b^18*c^28*d^27 - 261008589107200*a^38*b^17*c^27*d^28 + 149590069231616*a^39*b^16*c^26*d^29 - 70656513052672*a^40*b^15*c^25*d^30 + 27207328280576*a^41*b^14*c^24*d^31 - 8398939463680*a^42*b^13*c^23*d^32 + 2027474309120*a^43*b^12*c^22*d^33 - 368463757312*a^44*b^11*c^21*d^34 + 47382401024*a^45*b^10*c^20*d^35 - 3841073152*a^46*b^9*c^19*d^36 + 147517440*a^47*b^8*c^18*d^37)*1i - x^(1/2)*(276595200*a^18*b^35*c^42*d^11 - 6501304320*a^19*b^34*c^41*d^12 + 71869242368*a^20*b^33*c^40*d^13 - 496940910592*a^21*b^32*c^39*d^14 + 2412258434048*a^22*b^31*c^38*d^15 - 8751989614592*a^23*b^30*c^37*d^16 + 24696348863488*a^24*b^29*c^36*d^17 - 55777785276416*a^25*b^28*c^35*d^18 + 103251559480832*a^26*b^27*c^34*d^19 - 160243801919488*a^27*b^26*c^33*d^20 + 213523293304832*a^28*b^25*c^32*d^21 - 250272765841408*a^29*b^24*c^31*d^22 + 263188357892096*a^30*b^23*c^30*d^23 - 250272765841408*a^31*b^22*c^29*d^24 + 213523293304832*a^32*b^21*c^28*d^25 - 160243801919488*a^33*b^20*c^27*d^26 + 103251559480832*a^34*b^19*c^26*d^27 - 55777785276416*a^35*b^18*c^25*d^28 + 24696348863488*a^36*b^17*c^24*d^29 - 8751989614592*a^37*b^16*c^23*d^30 + 2412258434048*a^38*b^15*c^22*d^31 - 496940910592*a^39*b^14*c^21*d^32 + 71869242368*a^40*b^13*c^20*d^33 - 6501304320*a^41*b^12*c^19*d^34 + 276595200*a^42*b^11*c^18*d^35))*1i))*(-(2401*a^4*d^15 + 50625*b^4*c^4*d^11 - 94500*a*b^3*c^3*d^12 + 66150*a^2*b^2*c^2*d^13 - 20580*a^3*b*c*d^14)/(4096*b^12*c^23 + 4096*a^12*c^11*d^12 - 49152*a^11*b*c^12*d^11 + 270336*a^2*b^10*c^21*d^2 - 901120*a^3*b^9*c^20*d^3 + 2027520*a^4*b^8*c^19*d^4 - 3244032*a^5*b^7*c^18*d^5 + 3784704*a^6*b^6*c^17*d^6 - 3244032*a^7*b^5*c^16*d^7 + 2027520*a^8*b^4*c^15*d^8 - 901120*a^9*b^3*c^14*d^9 + 270336*a^10*b^2*c^13*d^10 - 49152*a*b^11*c^22*d))^(1/4) - (2/(3*a*c) + (x^2*(7*a^3*d^3 + 7*b^3*c^3 - 4*a*b^2*c^2*d - 4*a^2*b*c*d^2))/(6*a^2*c^2*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) + (b*d*x^4*(7*a^2*d^2 + 7*b^2*c^2 - 8*a*b*c*d))/(6*a^2*c^2*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)))/(x^(7/2)*(a*d + b*c) + a*c*x^(3/2) + b*d*x^(11/2))","B"
495,1,36571,731,14.273191,"\text{Not used}","int(1/(x^(7/2)*(a + b*x^2)^2*(c + d*x^2)^2),x)","2\,\mathrm{atan}\left(\frac{2654208\,a^{16}\,b^{22}\,c^{27}\,\sqrt{x}\,{\left(-\frac{83521\,a^4\,b^{13}\,d^4-176868\,a^3\,b^{14}\,c\,d^3+140454\,a^2\,b^{15}\,c^2\,d^2-49572\,a\,b^{16}\,c^3\,d+6561\,b^{17}\,c^4}{4096\,a^{25}\,d^{12}-49152\,a^{24}\,b\,c\,d^{11}+270336\,a^{23}\,b^2\,c^2\,d^{10}-901120\,a^{22}\,b^3\,c^3\,d^9+2027520\,a^{21}\,b^4\,c^4\,d^8-3244032\,a^{20}\,b^5\,c^5\,d^7+3784704\,a^{19}\,b^6\,c^6\,d^6-3244032\,a^{18}\,b^7\,c^7\,d^5+2027520\,a^{17}\,b^8\,c^8\,d^4-901120\,a^{16}\,b^9\,c^9\,d^3+270336\,a^{15}\,b^{10}\,c^{10}\,d^2-49152\,a^{14}\,b^{11}\,c^{11}\,d+4096\,a^{13}\,b^{12}\,c^{12}}\right)}^{5/4}+15169032\,a^{22}\,b^8\,d^{19}\,\sqrt{x}\,{\left(-\frac{83521\,a^4\,b^{13}\,d^4-176868\,a^3\,b^{14}\,c\,d^3+140454\,a^2\,b^{15}\,c^2\,d^2-49572\,a\,b^{16}\,c^3\,d+6561\,b^{17}\,c^4}{4096\,a^{25}\,d^{12}-49152\,a^{24}\,b\,c\,d^{11}+270336\,a^{23}\,b^2\,c^2\,d^{10}-901120\,a^{22}\,b^3\,c^3\,d^9+2027520\,a^{21}\,b^4\,c^4\,d^8-3244032\,a^{20}\,b^5\,c^5\,d^7+3784704\,a^{19}\,b^6\,c^6\,d^6-3244032\,a^{18}\,b^7\,c^7\,d^5+2027520\,a^{17}\,b^8\,c^8\,d^4-901120\,a^{16}\,b^9\,c^9\,d^3+270336\,a^{15}\,b^{10}\,c^{10}\,d^2-49152\,a^{14}\,b^{11}\,c^{11}\,d+4096\,a^{13}\,b^{12}\,c^{12}}\right)}^{1/4}+2654208\,a^{38}\,c^5\,d^{22}\,\sqrt{x}\,{\left(-\frac{83521\,a^4\,b^{13}\,d^4-176868\,a^3\,b^{14}\,c\,d^3+140454\,a^2\,b^{15}\,c^2\,d^2-49572\,a\,b^{16}\,c^3\,d+6561\,b^{17}\,c^4}{4096\,a^{25}\,d^{12}-49152\,a^{24}\,b\,c\,d^{11}+270336\,a^{23}\,b^2\,c^2\,d^{10}-901120\,a^{22}\,b^3\,c^3\,d^9+2027520\,a^{21}\,b^4\,c^4\,d^8-3244032\,a^{20}\,b^5\,c^5\,d^7+3784704\,a^{19}\,b^6\,c^6\,d^6-3244032\,a^{18}\,b^7\,c^7\,d^5+2027520\,a^{17}\,b^8\,c^8\,d^4-901120\,a^{16}\,b^9\,c^9\,d^3+270336\,a^{15}\,b^{10}\,c^{10}\,d^2-49152\,a^{14}\,b^{11}\,c^{11}\,d+4096\,a^{13}\,b^{12}\,c^{12}}\right)}^{5/4}-130671792\,a^{21}\,b^9\,c\,d^{18}\,\sqrt{x}\,{\left(-\frac{83521\,a^4\,b^{13}\,d^4-176868\,a^3\,b^{14}\,c\,d^3+140454\,a^2\,b^{15}\,c^2\,d^2-49572\,a\,b^{16}\,c^3\,d+6561\,b^{17}\,c^4}{4096\,a^{25}\,d^{12}-49152\,a^{24}\,b\,c\,d^{11}+270336\,a^{23}\,b^2\,c^2\,d^{10}-901120\,a^{22}\,b^3\,c^3\,d^9+2027520\,a^{21}\,b^4\,c^4\,d^8-3244032\,a^{20}\,b^5\,c^5\,d^7+3784704\,a^{19}\,b^6\,c^6\,d^6-3244032\,a^{18}\,b^7\,c^7\,d^5+2027520\,a^{17}\,b^8\,c^8\,d^4-901120\,a^{16}\,b^9\,c^9\,d^3+270336\,a^{15}\,b^{10}\,c^{10}\,d^2-49152\,a^{14}\,b^{11}\,c^{11}\,d+4096\,a^{13}\,b^{12}\,c^{12}}\right)}^{1/4}-41877504\,a^{17}\,b^{21}\,c^{26}\,d\,\sqrt{x}\,{\left(-\frac{83521\,a^4\,b^{13}\,d^4-176868\,a^3\,b^{14}\,c\,d^3+140454\,a^2\,b^{15}\,c^2\,d^2-49572\,a\,b^{16}\,c^3\,d+6561\,b^{17}\,c^4}{4096\,a^{25}\,d^{12}-49152\,a^{24}\,b\,c\,d^{11}+270336\,a^{23}\,b^2\,c^2\,d^{10}-901120\,a^{22}\,b^3\,c^3\,d^9+2027520\,a^{21}\,b^4\,c^4\,d^8-3244032\,a^{20}\,b^5\,c^5\,d^7+3784704\,a^{19}\,b^6\,c^6\,d^6-3244032\,a^{18}\,b^7\,c^7\,d^5+2027520\,a^{17}\,b^8\,c^8\,d^4-901120\,a^{16}\,b^9\,c^9\,d^3+270336\,a^{15}\,b^{10}\,c^{10}\,d^2-49152\,a^{14}\,b^{11}\,c^{11}\,d+4096\,a^{13}\,b^{12}\,c^{12}}\right)}^{5/4}-41877504\,a^{37}\,b\,c^6\,d^{21}\,\sqrt{x}\,{\left(-\frac{83521\,a^4\,b^{13}\,d^4-176868\,a^3\,b^{14}\,c\,d^3+140454\,a^2\,b^{15}\,c^2\,d^2-49572\,a\,b^{16}\,c^3\,d+6561\,b^{17}\,c^4}{4096\,a^{25}\,d^{12}-49152\,a^{24}\,b\,c\,d^{11}+270336\,a^{23}\,b^2\,c^2\,d^{10}-901120\,a^{22}\,b^3\,c^3\,d^9+2027520\,a^{21}\,b^4\,c^4\,d^8-3244032\,a^{20}\,b^5\,c^5\,d^7+3784704\,a^{19}\,b^6\,c^6\,d^6-3244032\,a^{18}\,b^7\,c^7\,d^5+2027520\,a^{17}\,b^8\,c^8\,d^4-901120\,a^{16}\,b^9\,c^9\,d^3+270336\,a^{15}\,b^{10}\,c^{10}\,d^2-49152\,a^{14}\,b^{11}\,c^{11}\,d+4096\,a^{13}\,b^{12}\,c^{12}}\right)}^{5/4}+15169032\,a^{11}\,b^{19}\,c^{11}\,d^8\,\sqrt{x}\,{\left(-\frac{83521\,a^4\,b^{13}\,d^4-176868\,a^3\,b^{14}\,c\,d^3+140454\,a^2\,b^{15}\,c^2\,d^2-49572\,a\,b^{16}\,c^3\,d+6561\,b^{17}\,c^4}{4096\,a^{25}\,d^{12}-49152\,a^{24}\,b\,c\,d^{11}+270336\,a^{23}\,b^2\,c^2\,d^{10}-901120\,a^{22}\,b^3\,c^3\,d^9+2027520\,a^{21}\,b^4\,c^4\,d^8-3244032\,a^{20}\,b^5\,c^5\,d^7+3784704\,a^{19}\,b^6\,c^6\,d^6-3244032\,a^{18}\,b^7\,c^7\,d^5+2027520\,a^{17}\,b^8\,c^8\,d^4-901120\,a^{16}\,b^9\,c^9\,d^3+270336\,a^{15}\,b^{10}\,c^{10}\,d^2-49152\,a^{14}\,b^{11}\,c^{11}\,d+4096\,a^{13}\,b^{12}\,c^{12}}\right)}^{1/4}-130671792\,a^{12}\,b^{18}\,c^{10}\,d^9\,\sqrt{x}\,{\left(-\frac{83521\,a^4\,b^{13}\,d^4-176868\,a^3\,b^{14}\,c\,d^3+140454\,a^2\,b^{15}\,c^2\,d^2-49572\,a\,b^{16}\,c^3\,d+6561\,b^{17}\,c^4}{4096\,a^{25}\,d^{12}-49152\,a^{24}\,b\,c\,d^{11}+270336\,a^{23}\,b^2\,c^2\,d^{10}-901120\,a^{22}\,b^3\,c^3\,d^9+2027520\,a^{21}\,b^4\,c^4\,d^8-3244032\,a^{20}\,b^5\,c^5\,d^7+3784704\,a^{19}\,b^6\,c^6\,d^6-3244032\,a^{18}\,b^7\,c^7\,d^5+2027520\,a^{17}\,b^8\,c^8\,d^4-901120\,a^{16}\,b^9\,c^9\,d^3+270336\,a^{15}\,b^{10}\,c^{10}\,d^2-49152\,a^{14}\,b^{11}\,c^{11}\,d+4096\,a^{13}\,b^{12}\,c^{12}}\right)}^{1/4}+450333432\,a^{13}\,b^{17}\,c^9\,d^{10}\,\sqrt{x}\,{\left(-\frac{83521\,a^4\,b^{13}\,d^4-176868\,a^3\,b^{14}\,c\,d^3+140454\,a^2\,b^{15}\,c^2\,d^2-49572\,a\,b^{16}\,c^3\,d+6561\,b^{17}\,c^4}{4096\,a^{25}\,d^{12}-49152\,a^{24}\,b\,c\,d^{11}+270336\,a^{23}\,b^2\,c^2\,d^{10}-901120\,a^{22}\,b^3\,c^3\,d^9+2027520\,a^{21}\,b^4\,c^4\,d^8-3244032\,a^{20}\,b^5\,c^5\,d^7+3784704\,a^{19}\,b^6\,c^6\,d^6-3244032\,a^{18}\,b^7\,c^7\,d^5+2027520\,a^{17}\,b^8\,c^8\,d^4-901120\,a^{16}\,b^9\,c^9\,d^3+270336\,a^{15}\,b^{10}\,c^{10}\,d^2-49152\,a^{14}\,b^{11}\,c^{11}\,d+4096\,a^{13}\,b^{12}\,c^{12}}\right)}^{1/4}-784872864\,a^{14}\,b^{16}\,c^8\,d^{11}\,\sqrt{x}\,{\left(-\frac{83521\,a^4\,b^{13}\,d^4-176868\,a^3\,b^{14}\,c\,d^3+140454\,a^2\,b^{15}\,c^2\,d^2-49572\,a\,b^{16}\,c^3\,d+6561\,b^{17}\,c^4}{4096\,a^{25}\,d^{12}-49152\,a^{24}\,b\,c\,d^{11}+270336\,a^{23}\,b^2\,c^2\,d^{10}-901120\,a^{22}\,b^3\,c^3\,d^9+2027520\,a^{21}\,b^4\,c^4\,d^8-3244032\,a^{20}\,b^5\,c^5\,d^7+3784704\,a^{19}\,b^6\,c^6\,d^6-3244032\,a^{18}\,b^7\,c^7\,d^5+2027520\,a^{17}\,b^8\,c^8\,d^4-901120\,a^{16}\,b^9\,c^9\,d^3+270336\,a^{15}\,b^{10}\,c^{10}\,d^2-49152\,a^{14}\,b^{11}\,c^{11}\,d+4096\,a^{13}\,b^{12}\,c^{12}}\right)}^{1/4}+717087608\,a^{15}\,b^{15}\,c^7\,d^{12}\,\sqrt{x}\,{\left(-\frac{83521\,a^4\,b^{13}\,d^4-176868\,a^3\,b^{14}\,c\,d^3+140454\,a^2\,b^{15}\,c^2\,d^2-49572\,a\,b^{16}\,c^3\,d+6561\,b^{17}\,c^4}{4096\,a^{25}\,d^{12}-49152\,a^{24}\,b\,c\,d^{11}+270336\,a^{23}\,b^2\,c^2\,d^{10}-901120\,a^{22}\,b^3\,c^3\,d^9+2027520\,a^{21}\,b^4\,c^4\,d^8-3244032\,a^{20}\,b^5\,c^5\,d^7+3784704\,a^{19}\,b^6\,c^6\,d^6-3244032\,a^{18}\,b^7\,c^7\,d^5+2027520\,a^{17}\,b^8\,c^8\,d^4-901120\,a^{16}\,b^9\,c^9\,d^3+270336\,a^{15}\,b^{10}\,c^{10}\,d^2-49152\,a^{14}\,b^{11}\,c^{11}\,d+4096\,a^{13}\,b^{12}\,c^{12}}\right)}^{1/4}-264948264\,a^{16}\,b^{14}\,c^6\,d^{13}\,\sqrt{x}\,{\left(-\frac{83521\,a^4\,b^{13}\,d^4-176868\,a^3\,b^{14}\,c\,d^3+140454\,a^2\,b^{15}\,c^2\,d^2-49572\,a\,b^{16}\,c^3\,d+6561\,b^{17}\,c^4}{4096\,a^{25}\,d^{12}-49152\,a^{24}\,b\,c\,d^{11}+270336\,a^{23}\,b^2\,c^2\,d^{10}-901120\,a^{22}\,b^3\,c^3\,d^9+2027520\,a^{21}\,b^4\,c^4\,d^8-3244032\,a^{20}\,b^5\,c^5\,d^7+3784704\,a^{19}\,b^6\,c^6\,d^6-3244032\,a^{18}\,b^7\,c^7\,d^5+2027520\,a^{17}\,b^8\,c^8\,d^4-901120\,a^{16}\,b^9\,c^9\,d^3+270336\,a^{15}\,b^{10}\,c^{10}\,d^2-49152\,a^{14}\,b^{11}\,c^{11}\,d+4096\,a^{13}\,b^{12}\,c^{12}}\right)}^{1/4}-264948264\,a^{17}\,b^{13}\,c^5\,d^{14}\,\sqrt{x}\,{\left(-\frac{83521\,a^4\,b^{13}\,d^4-176868\,a^3\,b^{14}\,c\,d^3+140454\,a^2\,b^{15}\,c^2\,d^2-49572\,a\,b^{16}\,c^3\,d+6561\,b^{17}\,c^4}{4096\,a^{25}\,d^{12}-49152\,a^{24}\,b\,c\,d^{11}+270336\,a^{23}\,b^2\,c^2\,d^{10}-901120\,a^{22}\,b^3\,c^3\,d^9+2027520\,a^{21}\,b^4\,c^4\,d^8-3244032\,a^{20}\,b^5\,c^5\,d^7+3784704\,a^{19}\,b^6\,c^6\,d^6-3244032\,a^{18}\,b^7\,c^7\,d^5+2027520\,a^{17}\,b^8\,c^8\,d^4-901120\,a^{16}\,b^9\,c^9\,d^3+270336\,a^{15}\,b^{10}\,c^{10}\,d^2-49152\,a^{14}\,b^{11}\,c^{11}\,d+4096\,a^{13}\,b^{12}\,c^{12}}\right)}^{1/4}+717087608\,a^{18}\,b^{12}\,c^4\,d^{15}\,\sqrt{x}\,{\left(-\frac{83521\,a^4\,b^{13}\,d^4-176868\,a^3\,b^{14}\,c\,d^3+140454\,a^2\,b^{15}\,c^2\,d^2-49572\,a\,b^{16}\,c^3\,d+6561\,b^{17}\,c^4}{4096\,a^{25}\,d^{12}-49152\,a^{24}\,b\,c\,d^{11}+270336\,a^{23}\,b^2\,c^2\,d^{10}-901120\,a^{22}\,b^3\,c^3\,d^9+2027520\,a^{21}\,b^4\,c^4\,d^8-3244032\,a^{20}\,b^5\,c^5\,d^7+3784704\,a^{19}\,b^6\,c^6\,d^6-3244032\,a^{18}\,b^7\,c^7\,d^5+2027520\,a^{17}\,b^8\,c^8\,d^4-901120\,a^{16}\,b^9\,c^9\,d^3+270336\,a^{15}\,b^{10}\,c^{10}\,d^2-49152\,a^{14}\,b^{11}\,c^{11}\,d+4096\,a^{13}\,b^{12}\,c^{12}}\right)}^{1/4}-784872864\,a^{19}\,b^{11}\,c^3\,d^{16}\,\sqrt{x}\,{\left(-\frac{83521\,a^4\,b^{13}\,d^4-176868\,a^3\,b^{14}\,c\,d^3+140454\,a^2\,b^{15}\,c^2\,d^2-49572\,a\,b^{16}\,c^3\,d+6561\,b^{17}\,c^4}{4096\,a^{25}\,d^{12}-49152\,a^{24}\,b\,c\,d^{11}+270336\,a^{23}\,b^2\,c^2\,d^{10}-901120\,a^{22}\,b^3\,c^3\,d^9+2027520\,a^{21}\,b^4\,c^4\,d^8-3244032\,a^{20}\,b^5\,c^5\,d^7+3784704\,a^{19}\,b^6\,c^6\,d^6-3244032\,a^{18}\,b^7\,c^7\,d^5+2027520\,a^{17}\,b^8\,c^8\,d^4-901120\,a^{16}\,b^9\,c^9\,d^3+270336\,a^{15}\,b^{10}\,c^{10}\,d^2-49152\,a^{14}\,b^{11}\,c^{11}\,d+4096\,a^{13}\,b^{12}\,c^{12}}\right)}^{1/4}+450333432\,a^{20}\,b^{10}\,c^2\,d^{17}\,\sqrt{x}\,{\left(-\frac{83521\,a^4\,b^{13}\,d^4-176868\,a^3\,b^{14}\,c\,d^3+140454\,a^2\,b^{15}\,c^2\,d^2-49572\,a\,b^{16}\,c^3\,d+6561\,b^{17}\,c^4}{4096\,a^{25}\,d^{12}-49152\,a^{24}\,b\,c\,d^{11}+270336\,a^{23}\,b^2\,c^2\,d^{10}-901120\,a^{22}\,b^3\,c^3\,d^9+2027520\,a^{21}\,b^4\,c^4\,d^8-3244032\,a^{20}\,b^5\,c^5\,d^7+3784704\,a^{19}\,b^6\,c^6\,d^6-3244032\,a^{18}\,b^7\,c^7\,d^5+2027520\,a^{17}\,b^8\,c^8\,d^4-901120\,a^{16}\,b^9\,c^9\,d^3+270336\,a^{15}\,b^{10}\,c^{10}\,d^2-49152\,a^{14}\,b^{11}\,c^{11}\,d+4096\,a^{13}\,b^{12}\,c^{12}}\right)}^{1/4}+304971776\,a^{18}\,b^{20}\,c^{25}\,d^2\,\sqrt{x}\,{\left(-\frac{83521\,a^4\,b^{13}\,d^4-176868\,a^3\,b^{14}\,c\,d^3+140454\,a^2\,b^{15}\,c^2\,d^2-49572\,a\,b^{16}\,c^3\,d+6561\,b^{17}\,c^4}{4096\,a^{25}\,d^{12}-49152\,a^{24}\,b\,c\,d^{11}+270336\,a^{23}\,b^2\,c^2\,d^{10}-901120\,a^{22}\,b^3\,c^3\,d^9+2027520\,a^{21}\,b^4\,c^4\,d^8-3244032\,a^{20}\,b^5\,c^5\,d^7+3784704\,a^{19}\,b^6\,c^6\,d^6-324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\frac{2654208\,a^5\,b^{22}\,c^{38}\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{17}-49572\,a^3\,b\,c\,d^{16}+140454\,a^2\,b^2\,c^2\,d^{15}-176868\,a\,b^3\,c^3\,d^{14}+83521\,b^4\,c^4\,d^{13}}{4096\,a^{12}\,c^{13}\,d^{12}-49152\,a^{11}\,b\,c^{14}\,d^{11}+270336\,a^{10}\,b^2\,c^{15}\,d^{10}-901120\,a^9\,b^3\,c^{16}\,d^9+2027520\,a^8\,b^4\,c^{17}\,d^8-3244032\,a^7\,b^5\,c^{18}\,d^7+3784704\,a^6\,b^6\,c^{19}\,d^6-3244032\,a^5\,b^7\,c^{20}\,d^5+2027520\,a^4\,b^8\,c^{21}\,d^4-901120\,a^3\,b^9\,c^{22}\,d^3+270336\,a^2\,b^{10}\,c^{23}\,d^2-49152\,a\,b^{11}\,c^{24}\,d+4096\,b^{12}\,c^{25}}\right)}^{5/4}+2654208\,a^{27}\,c^{16}\,d^{22}\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{17}-49572\,a^3\,b\,c\,d^{16}+140454\,a^2\,b^2\,c^2\,d^{15}-176868\,a\,b^3\,c^3\,d^{14}+83521\,b^4\,c^4\,d^{13}}{4096\,a^{12}\,c^{13}\,d^{12}-49152\,a^{11}\,b\,c^{14}\,d^{11}+270336\,a^{10}\,b^2\,c^{15}\,d^{10}-901120\,a^9\,b^3\,c^{16}\,d^9+2027520\,a^8\,b^4\,c^{17}\,d^8-3244032\,a^7\,b^5\,c^{18}\,d^7+3784704\,a^6\,b^6\,c^{19}\,d^6-3244032\,a^5\,b^7\,c^{20}\,d^5+2027520\,a^4\,b^8\,c^{21}\,d^4-901120\,a^3\,b^9\,c^{22}\,d^3+270336\,a^2\,b^{10}\,c^{23}\,d^2-49152\,a\,b^{11}\,c^{24}\,d+4096\,b^{12}\,c^{25}}\right)}^{5/4}+15169032\,b^{19}\,c^{22}\,d^8\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{17}-49572\,a^3\,b\,c\,d^{16}+140454\,a^2\,b^2\,c^2\,d^{15}-176868\,a\,b^3\,c^3\,d^{14}+83521\,b^4\,c^4\,d^{13}}{4096\,a^{12}\,c^{13}\,d^{12}-49152\,a^{11}\,b\,c^{14}\,d^{11}+270336\,a^{10}\,b^2\,c^{15}\,d^{10}-901120\,a^9\,b^3\,c^{16}\,d^9+2027520\,a^8\,b^4\,c^{17}\,d^8-3244032\,a^7\,b^5\,c^{18}\,d^7+3784704\,a^6\,b^6\,c^{19}\,d^6-3244032\,a^5\,b^7\,c^{20}\,d^5+2027520\,a^4\,b^8\,c^{21}\,d^4-901120\,a^3\,b^9\,c^{22}\,d^3+270336\,a^2\,b^{10}\,c^{23}\,d^2-49152\,a\,b^{11}\,c^{24}\,d+4096\,b^{12}\,c^{25}}\right)}^{1/4}-130671792\,a\,b^{18}\,c^{21}\,d^9\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{17}-49572\,a^3\,b\,c\,d^{16}+140454\,a^2\,b^2\,c^2\,d^{15}-176868\,a\,b^3\,c^3\,d^{14}+83521\,b^4\,c^4\,d^{13}}{4096\,a^{12}\,c^{13}\,d^{12}-49152\,a^{11}\,b\,c^{14}\,d^{11}+270336\,a^{10}\,b^2\,c^{15}\,d^{10}-901120\,a^9\,b^3\,c^{16}\,d^9+2027520\,a^8\,b^4\,c^{17}\,d^8-3244032\,a^7\,b^5\,c^{18}\,d^7+3784704\,a^6\,b^6\,c^{19}\,d^6-3244032\,a^5\,b^7\,c^{20}\,d^5+2027520\,a^4\,b^8\,c^{21}\,d^4-901120\,a^3\,b^9\,c^{22}\,d^3+270336\,a^2\,b^{10}\,c^{23}\,d^2-49152\,a\,b^{11}\,c^{24}\,d+4096\,b^{12}\,c^{25}}\right)}^{1/4}-41877504\,a^6\,b^{21}\,c^{37}\,d\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{17}-49572\,a^3\,b\,c\,d^{16}+140454\,a^2\,b^2\,c^2\,d^{15}-176868\,a\,b^3\,c^3\,d^{14}+83521\,b^4\,c^4\,d^{13}}{4096\,a^{12}\,c^{13}\,d^{12}-49152\,a^{11}\,b\,c^{14}\,d^{11}+270336\,a^{10}\,b^2\,c^{15}\,d^{10}-901120\,a^9\,b^3\,c^{16}\,d^9+2027520\,a^8\,b^4\,c^{17}\,d^8-3244032\,a^7\,b^5\,c^{18}\,d^7+3784704\,a^6\,b^6\,c^{19}\,d^6-3244032\,a^5\,b^7\,c^{20}\,d^5+2027520\,a^4\,b^8\,c^{21}\,d^4-901120\,a^3\,b^9\,c^{22}\,d^3+270336\,a^2\,b^{10}\,c^{23}\,d^2-49152\,a\,b^{11}\,c^{24}\,d+4096\,b^{12}\,c^{25}}\right)}^{5/4}-41877504\,a^{26}\,b\,c^{17}\,d^{21}\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{17}-49572\,a^3\,b\,c\,d^{16}+140454\,a^2\,b^2\,c^2\,d^{15}-176868\,a\,b^3\,c^3\,d^{14}+83521\,b^4\,c^4\,d^{13}}{4096\,a^{12}\,c^{13}\,d^{12}-49152\,a^{11}\,b\,c^{14}\,d^{11}+270336\,a^{10}\,b^2\,c^{15}\,d^{10}-901120\,a^9\,b^3\,c^{16}\,d^9+2027520\,a^8\,b^4\,c^{17}\,d^8-3244032\,a^7\,b^5\,c^{18}\,d^7+3784704\,a^6\,b^6\,c^{19}\,d^6-3244032\,a^5\,b^7\,c^{20}\,d^5+2027520\,a^4\,b^8\,c^{21}\,d^4-901120\,a^3\,b^9\,c^{22}\,d^3+270336\,a^2\,b^{10}\,c^{23}\,d^2-49152\,a\,b^{11}\,c^{24}\,d+4096\,b^{12}\,c^{25}}\right)}^{5/4}+450333432\,a^2\,b^{17}\,c^{20}\,d^{10}\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{17}-49572\,a^3\,b\,c\,d^{16}+140454\,a^2\,b^2\,c^2\,d^{15}-176868\,a\,b^3\,c^3\,d^{14}+83521\,b^4\,c^4\,d^{13}}{4096\,a^{12}\,c^{13}\,d^{12}-49152\,a^{11}\,b\,c^{14}\,d^{11}+270336\,a^{10}\,b^2\,c^{15}\,d^{10}-901120\,a^9\,b^3\,c^{16}\,d^9+2027520\,a^8\,b^4\,c^{17}\,d^8-3244032\,a^7\,b^5\,c^{18}\,d^7+3784704\,a^6\,b^6\,c^{19}\,d^6-3244032\,a^5\,b^7\,c^{20}\,d^5+2027520\,a^4\,b^8\,c^{21}\,d^4-901120\,a^3\,b^9\,c^{22}\,d^3+270336\,a^2\,b^{10}\,c^{23}\,d^2-49152\,a\,b^{11}\,c^{24}\,d+4096\,b^{12}\,c^{25}}\right)}^{1/4}-784872864\,a^3\,b^{16}\,c^{19}\,d^{11}\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{17}-49572\,a^3\,b\,c\,d^{16}+140454\,a^2\,b^2\,c^2\,d^{15}-176868\,a\,b^3\,c^3\,d^{14}+83521\,b^4\,c^4\,d^{13}}{4096\,a^{12}\,c^{13}\,d^{12}-49152\,a^{11}\,b\,c^{14}\,d^{11}+270336\,a^{10}\,b^2\,c^{15}\,d^{10}-901120\,a^9\,b^3\,c^{16}\,d^9+2027520\,a^8\,b^4\,c^{17}\,d^8-3244032\,a^7\,b^5\,c^{18}\,d^7+3784704\,a^6\,b^6\,c^{19}\,d^6-3244032\,a^5\,b^7\,c^{20}\,d^5+2027520\,a^4\,b^8\,c^{21}\,d^4-901120\,a^3\,b^9\,c^{22}\,d^3+270336\,a^2\,b^{10}\,c^{23}\,d^2-49152\,a\,b^{11}\,c^{24}\,d+4096\,b^{12}\,c^{25}}\right)}^{1/4}+717087608\,a^4\,b^{15}\,c^{18}\,d^{12}\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{17}-49572\,a^3\,b\,c\,d^{16}+140454\,a^2\,b^2\,c^2\,d^{15}-176868\,a\,b^3\,c^3\,d^{14}+83521\,b^4\,c^4\,d^{13}}{4096\,a^{12}\,c^{13}\,d^{12}-49152\,a^{11}\,b\,c^{14}\,d^{11}+270336\,a^{10}\,b^2\,c^{15}\,d^{10}-901120\,a^9\,b^3\,c^{16}\,d^9+2027520\,a^8\,b^4\,c^{17}\,d^8-3244032\,a^7\,b^5\,c^{18}\,d^7+3784704\,a^6\,b^6\,c^{19}\,d^6-3244032\,a^5\,b^7\,c^{20}\,d^5+2027520\,a^4\,b^8\,c^{21}\,d^4-901120\,a^3\,b^9\,c^{22}\,d^3+270336\,a^2\,b^{10}\,c^{23}\,d^2-49152\,a\,b^{11}\,c^{24}\,d+4096\,b^{12}\,c^{25}}\right)}^{1/4}-264948264\,a^5\,b^{14}\,c^{17}\,d^{13}\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{17}-49572\,a^3\,b\,c\,d^{16}+140454\,a^2\,b^2\,c^2\,d^{15}-176868\,a\,b^3\,c^3\,d^{14}+83521\,b^4\,c^4\,d^{13}}{4096\,a^{12}\,c^{13}\,d^{12}-49152\,a^{11}\,b\,c^{14}\,d^{11}+270336\,a^{10}\,b^2\,c^{15}\,d^{10}-901120\,a^9\,b^3\,c^{16}\,d^9+2027520\,a^8\,b^4\,c^{17}\,d^8-3244032\,a^7\,b^5\,c^{18}\,d^7+3784704\,a^6\,b^6\,c^{19}\,d^6-3244032\,a^5\,b^7\,c^{20}\,d^5+2027520\,a^4\,b^8\,c^{21}\,d^4-901120\,a^3\,b^9\,c^{22}\,d^3+270336\,a^2\,b^{10}\,c^{23}\,d^2-49152\,a\,b^{11}\,c^{24}\,d+4096\,b^{12}\,c^{25}}\right)}^{1/4}-264948264\,a^6\,b^{13}\,c^{16}\,d^{14}\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{17}-49572\,a^3\,b\,c\,d^{16}+140454\,a^2\,b^2\,c^2\,d^{15}-176868\,a\,b^3\,c^3\,d^{14}+83521\,b^4\,c^4\,d^{13}}{4096\,a^{12}\,c^{13}\,d^{12}-49152\,a^{11}\,b\,c^{14}\,d^{11}+270336\,a^{10}\,b^2\,c^{15}\,d^{10}-901120\,a^9\,b^3\,c^{16}\,d^9+2027520\,a^8\,b^4\,c^{17}\,d^8-3244032\,a^7\,b^5\,c^{18}\,d^7+3784704\,a^6\,b^6\,c^{19}\,d^6-3244032\,a^5\,b^7\,c^{20}\,d^5+2027520\,a^4\,b^8\,c^{21}\,d^4-901120\,a^3\,b^9\,c^{22}\,d^3+270336\,a^2\,b^{10}\,c^{23}\,d^2-49152\,a\,b^{11}\,c^{24}\,d+4096\,b^{12}\,c^{25}}\right)}^{1/4}+717087608\,a^7\,b^{12}\,c^{15}\,d^{15}\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{17}-49572\,a^3\,b\,c\,d^{16}+140454\,a^2\,b^2\,c^2\,d^{15}-176868\,a\,b^3\,c^3\,d^{14}+83521\,b^4\,c^4\,d^{13}}{4096\,a^{12}\,c^{13}\,d^{12}-49152\,a^{11}\,b\,c^{14}\,d^{11}+270336\,a^{10}\,b^2\,c^{15}\,d^{10}-901120\,a^9\,b^3\,c^{16}\,d^9+2027520\,a^8\,b^4\,c^{17}\,d^8-3244032\,a^7\,b^5\,c^{18}\,d^7+3784704\,a^6\,b^6\,c^{19}\,d^6-3244032\,a^5\,b^7\,c^{20}\,d^5+2027520\,a^4\,b^8\,c^{21}\,d^4-901120\,a^3\,b^9\,c^{22}\,d^3+270336\,a^2\,b^{10}\,c^{23}\,d^2-49152\,a\,b^{11}\,c^{24}\,d+4096\,b^{12}\,c^{25}}\right)}^{1/4}-784872864\,a^8\,b^{11}\,c^{14}\,d^{16}\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{17}-49572\,a^3\,b\,c\,d^{16}+140454\,a^2\,b^2\,c^2\,d^{15}-176868\,a\,b^3\,c^3\,d^{14}+83521\,b^4\,c^4\,d^{13}}{4096\,a^{12}\,c^{13}\,d^{12}-49152\,a^{11}\,b\,c^{14}\,d^{11}+270336\,a^{10}\,b^2\,c^{15}\,d^{10}-901120\,a^9\,b^3\,c^{16}\,d^9+2027520\,a^8\,b^4\,c^{17}\,d^8-3244032\,a^7\,b^5\,c^{18}\,d^7+3784704\,a^6\,b^6\,c^{19}\,d^6-3244032\,a^5\,b^7\,c^{20}\,d^5+2027520\,a^4\,b^8\,c^{21}\,d^4-901120\,a^3\,b^9\,c^{22}\,d^3+270336\,a^2\,b^{10}\,c^{23}\,d^2-49152\,a\,b^{11}\,c^{24}\,d+4096\,b^{12}\,c^{25}}\right)}^{1/4}+450333432\,a^9\,b^{10}\,c^{13}\,d^{17}\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{17}-49572\,a^3\,b\,c\,d^{16}+140454\,a^2\,b^2\,c^2\,d^{15}-176868\,a\,b^3\,c^3\,d^{14}+83521\,b^4\,c^4\,d^{13}}{4096\,a^{12}\,c^{13}\,d^{12}-49152\,a^{11}\,b\,c^{14}\,d^{11}+270336\,a^{10}\,b^2\,c^{15}\,d^{10}-901120\,a^9\,b^3\,c^{16}\,d^9+2027520\,a^8\,b^4\,c^{17}\,d^8-3244032\,a^7\,b^5\,c^{18}\,d^7+3784704\,a^6\,b^6\,c^{19}\,d^6-3244032\,a^5\,b^7\,c^{20}\,d^5+2027520\,a^4\,b^8\,c^{21}\,d^4-901120\,a^3\,b^9\,c^{22}\,d^3+270336\,a^2\,b^{10}\,c^{23}\,d^2-49152\,a\,b^{11}\,c^{24}\,d+4096\,b^{12}\,c^{25}}\right)}^{1/4}-130671792\,a^{10}\,b^9\,c^{12}\,d^{18}\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{17}-49572\,a^3\,b\,c\,d^{16}+140454\,a^2\,b^2\,c^2\,d^{15}-176868\,a\,b^3\,c^3\,d^{14}+83521\,b^4\,c^4\,d^{13}}{4096\,a^{12}\,c^{13}\,d^{12}-49152\,a^{11}\,b\,c^{14}\,d^{11}+270336\,a^{10}\,b^2\,c^{15}\,d^{10}-901120\,a^9\,b^3\,c^{16}\,d^9+2027520\,a^8\,b^4\,c^{17}\,d^8-3244032\,a^7\,b^5\,c^{18}\,d^7+3784704\,a^6\,b^6\,c^{19}\,d^6-3244032\,a^5\,b^7\,c^{20}\,d^5+2027520\,a^4\,b^8\,c^{21}\,d^4-901120\,a^3\,b^9\,c^{22}\,d^3+270336\,a^2\,b^{10}\,c^{23}\,d^2-49152\,a\,b^{11}\,c^{24}\,d+4096\,b^{12}\,c^{25}}\right)}^{1/4}+15169032\,a^{11}\,b^8\,c^{11}\,d^{19}\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{17}-49572\,a^3\,b\,c\,d^{16}+140454\,a^2\,b^2\,c^2\,d^{15}-176868\,a\,b^3\,c^3\,d^{14}+83521\,b^4\,c^4\,d^{13}}{4096\,a^{12}\,c^{13}\,d^{12}-49152\,a^{11}\,b\,c^{14}\,d^{11}+270336\,a^{10}\,b^2\,c^{15}\,d^{10}-901120\,a^9\,b^3\,c^{16}\,d^9+2027520\,a^8\,b^4\,c^{17}\,d^8-3244032\,a^7\,b^5\,c^{18}\,d^7+3784704\,a^6\,b^6\,c^{19}\,d^6-3244032\,a^5\,b^7\,c^{20}\,d^5+2027520\,a^4\,b^8\,c^{21}\,d^4-901120\,a^3\,b^9\,c^{22}\,d^3+270336\,a^2\,b^{10}\,c^{23}\,d^2-49152\,a\,b^{11}\,c^{24}\,d+4096\,b^{12}\,c^{25}}\right)}^{1/4}+304971776\,a^7\,b^{20}\,c^{36}\,d^2\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{17}-49572\,a^3\,b\,c\,d^{16}+140454\,a^2\,b^2\,c^2\,d^{15}-176868\,a\,b^3\,c^3\,d^{14}+83521\,b^4\,c^4\,d^{13}}{4096\,a^{12}\,c^{13}\,d^{12}-49152\,a^{11}\,b\,c^{14}\,d^{11}+270336\,a^{10}\,b^2\,c^{15}\,d^{10}-901120\,a^9\,b^3\,c^{16}\,d^9+2027520\,a^8\,b^4\,c^{17}\,d^8-3244032\,a^7\,b^5\,c^{18}\,d^7+3784704\,a^6\,b^6\,c^{19}\,d^6-3244032\,a^5\,b^7\,c^{20}\,d^5+2027520\,a^4\,b^8\,c^{21}\,d^4-901120\,a^3\,b^9\,c^{22}\,d^3+270336\,a^2\,b^{10}\,c^{23}\,d^2-49152\,a\,b^{11}\,c^{24}\,d+4096\,b^{12}\,c^{25}}\right)}^{5/4}-1359347712\,a^8\,b^{19}\,c^{35}\,d^3\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{17}-49572\,a^3\,b\,c\,d^{16}+140454\,a^2\,b^2\,c^2\,d^{15}-176868\,a\,b^3\,c^3\,d^{14}+83521\,b^4\,c^4\,d^{13}}{4096\,a^{12}\,c^{13}\,d^{12}-49152\,a^{11}\,b\,c^{14}\,d^{11}+270336\,a^{10}\,b^2\,c^{15}\,d^{10}-901120\,a^9\,b^3\,c^{16}\,d^9+2027520\,a^8\,b^4\,c^{17}\,d^8-3244032\,a^7\,b^5\,c^{18}\,d^7+3784704\,a^6\,b^6\,c^{19}\,d^6-3244032\,a^5\,b^7\,c^{20}\,d^5+2027520\,a^4\,b^8\,c^{21}\,d^4-901120\,a^3\,b^9\,c^{22}\,d^3+270336\,a^2\,b^{10}\,c^{23}\,d^2-49152\,a\,b^{11}\,c^{24}\,d+4096\,b^{12}\,c^{25}}\right)}^{5/4}+4144791552\,a^9\,b^{18}\,c^{34}\,d^4\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{17}-49572\,a^3\,b\,c\,d^{16}+140454\,a^2\,b^2\,c^2\,d^{15}-176868\,a\,b^3\,c^3\,d^{14}+83521\,b^4\,c^4\,d^{13}}{4096\,a^{12}\,c^{13}\,d^{12}-49152\,a^{11}\,b\,c^{14}\,d^{11}+270336\,a^{10}\,b^2\,c^{15}\,d^{10}-901120\,a^9\,b^3\,c^{16}\,d^9+2027520\,a^8\,b^4\,c^{17}\,d^8-3244032\,a^7\,b^5\,c^{18}\,d^7+3784704\,a^6\,b^6\,c^{19}\,d^6-3244032\,a^5\,b^7\,c^{20}\,d^5+2027520\,a^4\,b^8\,c^{21}\,d^4-901120\,a^3\,b^9\,c^{22}\,d^3+270336\,a^2\,b^{10}\,c^{23}\,d^2-49152\,a\,b^{11}\,c^{24}\,d+4096\,b^{12}\,c^{25}}\right)}^{5/4}-9148891136\,a^{10}\,b^{17}\,c^{33}\,d^5\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{17}-49572\,a^3\,b\,c\,d^{16}+140454\,a^2\,b^2\,c^2\,d^{15}-176868\,a\,b^3\,c^3\,d^{14}+83521\,b^4\,c^4\,d^{13}}{4096\,a^{12}\,c^{13}\,d^{12}-49152\,a^{11}\,b\,c^{14}\,d^{11}+270336\,a^{10}\,b^2\,c^{15}\,d^{10}-901120\,a^9\,b^3\,c^{16}\,d^9+2027520\,a^8\,b^4\,c^{17}\,d^8-3244032\,a^7\,b^5\,c^{18}\,d^7+3784704\,a^6\,b^6\,c^{19}\,d^6-3244032\,a^5\,b^7\,c^{20}\,d^5+2027520\,a^4\,b^8\,c^{21}\,d^4-901120\,a^3\,b^9\,c^{22}\,d^3+270336\,a^2\,b^{10}\,c^{23}\,d^2-49152\,a\,b^{11}\,c^{24}\,d+4096\,b^{12}\,c^{25}}\right)}^{5/4}+15081504768\,a^{11}\,b^{16}\,c^{32}\,d^6\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{17}-49572\,a^3\,b\,c\,d^{16}+140454\,a^2\,b^2\,c^2\,d^{15}-176868\,a\,b^3\,c^3\,d^{14}+83521\,b^4\,c^4\,d^{13}}{4096\,a^{12}\,c^{13}\,d^{12}-49152\,a^{11}\,b\,c^{14}\,d^{11}+270336\,a^{10}\,b^2\,c^{15}\,d^{10}-901120\,a^9\,b^3\,c^{16}\,d^9+2027520\,a^8\,b^4\,c^{17}\,d^8-3244032\,a^7\,b^5\,c^{18}\,d^7+3784704\,a^6\,b^6\,c^{19}\,d^6-3244032\,a^5\,b^7\,c^{20}\,d^5+2027520\,a^4\,b^8\,c^{21}\,d^4-901120\,a^3\,b^9\,c^{22}\,d^3+270336\,a^2\,b^{10}\,c^{23}\,d^2-49152\,a\,b^{11}\,c^{24}\,d+4096\,b^{12}\,c^{25}}\right)}^{5/4}-18867290112\,a^{12}\,b^{15}\,c^{31}\,d^7\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{17}-49572\,a^3\,b\,c\,d^{16}+140454\,a^2\,b^2\,c^2\,d^{15}-176868\,a\,b^3\,c^3\,d^{14}+83521\,b^4\,c^4\,d^{13}}{4096\,a^{12}\,c^{13}\,d^{12}-49152\,a^{11}\,b\,c^{14}\,d^{11}+270336\,a^{10}\,b^2\,c^{15}\,d^{10}-901120\,a^9\,b^3\,c^{16}\,d^9+2027520\,a^8\,b^4\,c^{17}\,d^8-3244032\,a^7\,b^5\,c^{18}\,d^7+3784704\,a^6\,b^6\,c^{19}\,d^6-3244032\,a^5\,b^7\,c^{20}\,d^5+2027520\,a^4\,b^8\,c^{21}\,d^4-901120\,a^3\,b^9\,c^{22}\,d^3+270336\,a^2\,b^{10}\,c^{23}\,d^2-49152\,a\,b^{11}\,c^{24}\,d+4096\,b^{12}\,c^{25}}\right)}^{5/4}+18014928896\,a^{13}\,b^{14}\,c^{30}\,d^8\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{17}-49572\,a^3\,b\,c\,d^{16}+140454\,a^2\,b^2\,c^2\,d^{15}-176868\,a\,b^3\,c^3\,d^{14}+83521\,b^4\,c^4\,d^{13}}{4096\,a^{12}\,c^{13}\,d^{12}-49152\,a^{11}\,b\,c^{14}\,d^{11}+270336\,a^{10}\,b^2\,c^{15}\,d^{10}-901120\,a^9\,b^3\,c^{16}\,d^9+2027520\,a^8\,b^4\,c^{17}\,d^8-3244032\,a^7\,b^5\,c^{18}\,d^7+3784704\,a^6\,b^6\,c^{19}\,d^6-3244032\,a^5\,b^7\,c^{20}\,d^5+2027520\,a^4\,b^8\,c^{21}\,d^4-901120\,a^3\,b^9\,c^{22}\,d^3+270336\,a^2\,b^{10}\,c^{23}\,d^2-49152\,a\,b^{11}\,c^{24}\,d+4096\,b^{12}\,c^{25}}\right)}^{5/4}-13171163136\,a^{14}\,b^{13}\,c^{29}\,d^9\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{17}-49572\,a^3\,b\,c\,d^{16}+140454\,a^2\,b^2\,c^2\,d^{15}-176868\,a\,b^3\,c^3\,d^{14}+83521\,b^4\,c^4\,d^{13}}{4096\,a^{12}\,c^{13}\,d^{12}-49152\,a^{11}\,b\,c^{14}\,d^{11}+270336\,a^{10}\,b^2\,c^{15}\,d^{10}-901120\,a^9\,b^3\,c^{16}\,d^9+2027520\,a^8\,b^4\,c^{17}\,d^8-3244032\,a^7\,b^5\,c^{18}\,d^7+3784704\,a^6\,b^6\,c^{19}\,d^6-3244032\,a^5\,b^7\,c^{20}\,d^5+2027520\,a^4\,b^8\,c^{21}\,d^4-901120\,a^3\,b^9\,c^{22}\,d^3+270336\,a^2\,b^{10}\,c^{23}\,d^2-49152\,a\,b^{11}\,c^{24}\,d+4096\,b^{12}\,c^{25}}\right)}^{5/4}+7816740864\,a^{15}\,b^{12}\,c^{28}\,d^{10}\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{17}-49572\,a^3\,b\,c\,d^{16}+140454\,a^2\,b^2\,c^2\,d^{15}-176868\,a\,b^3\,c^3\,d^{14}+83521\,b^4\,c^4\,d^{13}}{4096\,a^{12}\,c^{13}\,d^{12}-49152\,a^{11}\,b\,c^{14}\,d^{11}+270336\,a^{10}\,b^2\,c^{15}\,d^{10}-901120\,a^9\,b^3\,c^{16}\,d^9+2027520\,a^8\,b^4\,c^{17}\,d^8-3244032\,a^7\,b^5\,c^{18}\,d^7+3784704\,a^6\,b^6\,c^{19}\,d^6-3244032\,a^5\,b^7\,c^{20}\,d^5+2027520\,a^4\,b^8\,c^{21}\,d^4-901120\,a^3\,b^9\,c^{22}\,d^3+270336\,a^2\,b^{10}\,c^{23}\,d^2-49152\,a\,b^{11}\,c^{24}\,d+4096\,b^{12}\,c^{25}}\right)}^{5/4}-5554044928\,a^{16}\,b^{11}\,c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{}\mathrm{i}-a^{12}\,b^{15}\,c^{31}\,d^7\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{17}-49572\,a^3\,b\,c\,d^{16}+140454\,a^2\,b^2\,c^2\,d^{15}-176868\,a\,b^3\,c^3\,d^{14}+83521\,b^4\,c^4\,d^{13}}{4096\,a^{12}\,c^{13}\,d^{12}-49152\,a^{11}\,b\,c^{14}\,d^{11}+270336\,a^{10}\,b^2\,c^{15}\,d^{10}-901120\,a^9\,b^3\,c^{16}\,d^9+2027520\,a^8\,b^4\,c^{17}\,d^8-3244032\,a^7\,b^5\,c^{18}\,d^7+3784704\,a^6\,b^6\,c^{19}\,d^6-3244032\,a^5\,b^7\,c^{20}\,d^5+2027520\,a^4\,b^8\,c^{21}\,d^4-901120\,a^3\,b^9\,c^{22}\,d^3+270336\,a^2\,b^{10}\,c^{23}\,d^2-49152\,a\,b^{11}\,c^{24}\,d+4096\,b^{12}\,c^{25}}\right)}^{5/4}\,18867290112{}\mathrm{i}+a^{13}\,b^{14}\,c^{30}\,d^8\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{17}-49572\,a^3\,b\,c\,d^{16}+140454\,a^2\,b^2\,c^2\,d^{15}-176868\,a\,b^3\,c^3\,d^{14}+83521\,b^4\,c^4\,d^{13}}{4096\,a^{12}\,c^{13}\,d^{12}-49152\,a^{11}\,b\,c^{14}\,d^{11}+270336\,a^{10}\,b^2\,c^{15}\,d^{10}-901120\,a^9\,b^3\,c^{16}\,d^9+2027520\,a^8\,b^4\,c^{17}\,d^8-3244032\,a^7\,b^5\,c^{18}\,d^7+3784704\,a^6\,b^6\,c^{19}\,d^6-3244032\,a^5\,b^7\,c^{20}\,d^5+2027520\,a^4\,b^8\,c^{21}\,d^4-901120\,a^3\,b^9\,c^{22}\,d^3+270336\,a^2\,b^{10}\,c^{23}\,d^2-49152\,a\,b^{11}\,c^{24}\,d+4096\,b^{12}\,c^{25}}\right)}^{5/4}\,18014928896{}\mathrm{i}-a^{14}\,b^{13}\,c^{29}\,d^9\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{17}-49572\,a^3\,b\,c\,d^{16}+140454\,a^2\,b^2\,c^2\,d^{15}-176868\,a\,b^3\,c^3\,d^{14}+83521\,b^4\,c^4\,d^{13}}{4096\,a^{12}\,c^{13}\,d^{12}-49152\,a^{11}\,b\,c^{14}\,d^{11}+270336\,a^{10}\,b^2\,c^{15}\,d^{10}-901120\,a^9\,b^3\,c^{16}\,d^9+2027520\,a^8\,b^4\,c^{17}\,d^8-3244032\,a^7\,b^5\,c^{18}\,d^7+3784704\,a^6\,b^6\,c^{19}\,d^6-3244032\,a^5\,b^7\,c^{20}\,d^5+2027520\,a^4\,b^8\,c^{21}\,d^4-901120\,a^3\,b^9\,c^{22}\,d^3+270336\,a^2\,b^{10}\,c^{23}\,d^2-49152\,a\,b^{11}\,c^{24}\,d+4096\,b^{12}\,c^{25}}\right)}^{5/4}\,13171163136{}\mathrm{i}+a^{15}\,b^{12}\,c^{28}\,d^{10}\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{17}-49572\,a^3\,b\,c\,d^{16}+140454\,a^2\,b^2\,c^2\,d^{15}-176868\,a\,b^3\,c^3\,d^{14}+83521\,b^4\,c^4\,d^{13}}{4096\,a^{12}\,c^{13}\,d^{12}-49152\,a^{11}\,b\,c^{14}\,d^{11}+270336\,a^{10}\,b^2\,c^{15}\,d^{10}-901120\,a^9\,b^3\,c^{16}\,d^9+2027520\,a^8\,b^4\,c^{17}\,d^8-3244032\,a^7\,b^5\,c^{18}\,d^7+3784704\,a^6\,b^6\,c^{19}\,d^6-3244032\,a^5\,b^7\,c^{20}\,d^5+2027520\,a^4\,b^8\,c^{21}\,d^4-901120\,a^3\,b^9\,c^{22}\,d^3+270336\,a^2\,b^{10}\,c^{23}\,d^2-49152\,a\,b^{11}\,c^{24}\,d+4096\,b^{12}\,c^{25}}\right)}^{5/4}\,7816740864{}\mathrm{i}-a^{16}\,b^{11}\,c^{27}\,d^{11}\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{17}-49572\,a^3\,b\,c\,d^{16}+140454\,a^2\,b^2\,c^2\,d^{15}-176868\,a\,b^3\,c^3\,d^{14}+83521\,b^4\,c^4\,d^{13}}{4096\,a^{12}\,c^{13}\,d^{12}-49152\,a^{11}\,b\,c^{14}\,d^{11}+270336\,a^{10}\,b^2\,c^{15}\,d^{10}-901120\,a^9\,b^3\,c^{16}\,d^9+2027520\,a^8\,b^4\,c^{17}\,d^8-3244032\,a^7\,b^5\,c^{18}\,d^7+3784704\,a^6\,b^6\,c^{19}\,d^6-3244032\,a^5\,b^7\,c^{20}\,d^5+2027520\,a^4\,b^8\,c^{21}\,d^4-901120\,a^3\,b^9\,c^{22}\,d^3+270336\,a^2\,b^{10}\,c^{23}\,d^2-49152\,a\,b^{11}\,c^{24}\,d+4096\,b^{12}\,c^{25}}\right)}^{5/4}\,5554044928{}\mathrm{i}+a^{17}\,b^{10}\,c^{26}\,d^{12}\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{17}-49572\,a^3\,b\,c\,d^{16}+140454\,a^2\,b^2\,c^2\,d^{15}-176868\,a\,b^3\,c^3\,d^{14}+83521\,b^4\,c^4\,d^{13}}{4096\,a^{12}\,c^{13}\,d^{12}-49152\,a^{11}\,b\,c^{14}\,d^{11}+270336\,a^{10}\,b^2\,c^{15}\,d^{10}-901120\,a^9\,b^3\,c^{16}\,d^9+2027520\,a^8\,b^4\,c^{17}\,d^8-3244032\,a^7\,b^5\,c^{18}\,d^7+3784704\,a^6\,b^6\,c^{19}\,d^6-3244032\,a^5\,b^7\,c^{20}\,d^5+2027520\,a^4\,b^8\,c^{21}\,d^4-901120\,a^3\,b^9\,c^{22}\,d^3+270336\,a^2\,b^{10}\,c^{23}\,d^2-49152\,a\,b^{11}\,c^{24}\,d+4096\,b^{12}\,c^{25}}\right)}^{5/4}\,7816740864{}\mathrm{i}-a^{18}\,b^9\,c^{25}\,d^{13}\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{17}-49572\,a^3\,b\,c\,d^{16}+140454\,a^2\,b^2\,c^2\,d^{15}-176868\,a\,b^3\,c^3\,d^{14}+83521\,b^4\,c^4\,d^{13}}{4096\,a^{12}\,c^{13}\,d^{12}-49152\,a^{11}\,b\,c^{14}\,d^{11}+270336\,a^{10}\,b^2\,c^{15}\,d^{10}-901120\,a^9\,b^3\,c^{16}\,d^9+2027520\,a^8\,b^4\,c^{17}\,d^8-3244032\,a^7\,b^5\,c^{18}\,d^7+3784704\,a^6\,b^6\,c^{19}\,d^6-3244032\,a^5\,b^7\,c^{20}\,d^5+2027520\,a^4\,b^8\,c^{21}\,d^4-901120\,a^3\,b^9\,c^{22}\,d^3+270336\,a^2\,b^{10}\,c^{23}\,d^2-49152\,a\,b^{11}\,c^{24}\,d+4096\,b^{12}\,c^{25}}\right)}^{5/4}\,13171163136{}\mathrm{i}+a^{19}\,b^8\,c^{24}\,d^{14}\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{17}-49572\,a^3\,b\,c\,d^{16}+140454\,a^2\,b^2\,c^2\,d^{15}-176868\,a\,b^3\,c^3\,d^{14}+83521\,b^4\,c^4\,d^{13}}{4096\,a^{12}\,c^{13}\,d^{12}-49152\,a^{11}\,b\,c^{14}\,d^{11}+270336\,a^{10}\,b^2\,c^{15}\,d^{10}-901120\,a^9\,b^3\,c^{16}\,d^9+2027520\,a^8\,b^4\,c^{17}\,d^8-3244032\,a^7\,b^5\,c^{18}\,d^7+3784704\,a^6\,b^6\,c^{19}\,d^6-3244032\,a^5\,b^7\,c^{20}\,d^5+2027520\,a^4\,b^8\,c^{21}\,d^4-901120\,a^3\,b^9\,c^{22}\,d^3+270336\,a^2\,b^{10}\,c^{23}\,d^2-49152\,a\,b^{11}\,c^{24}\,d+4096\,b^{12}\,c^{25}}\right)}^{5/4}\,18014928896{}\mathrm{i}-a^{20}\,b^7\,c^{23}\,d^{15}\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{17}-49572\,a^3\,b\,c\,d^{16}+140454\,a^2\,b^2\,c^2\,d^{15}-176868\,a\,b^3\,c^3\,d^{14}+83521\,b^4\,c^4\,d^{13}}{4096\,a^{12}\,c^{13}\,d^{12}-49152\,a^{11}\,b\,c^{14}\,d^{11}+270336\,a^{10}\,b^2\,c^{15}\,d^{10}-901120\,a^9\,b^3\,c^{16}\,d^9+2027520\,a^8\,b^4\,c^{17}\,d^8-3244032\,a^7\,b^5\,c^{18}\,d^7+3784704\,a^6\,b^6\,c^{19}\,d^6-3244032\,a^5\,b^7\,c^{20}\,d^5+2027520\,a^4\,b^8\,c^{21}\,d^4-901120\,a^3\,b^9\,c^{22}\,d^3+270336\,a^2\,b^{10}\,c^{23}\,d^2-49152\,a\,b^{11}\,c^{24}\,d+4096\,b^{12}\,c^{25}}\right)}^{5/4}\,18867290112{}\mathrm{i}+a^{21}\,b^6\,c^{22}\,d^{16}\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{17}-49572\,a^3\,b\,c\,d^{16}+140454\,a^2\,b^2\,c^2\,d^{15}-176868\,a\,b^3\,c^3\,d^{14}+83521\,b^4\,c^4\,d^{13}}{4096\,a^{12}\,c^{13}\,d^{12}-49152\,a^{11}\,b\,c^{14}\,d^{11}+270336\,a^{10}\,b^2\,c^{15}\,d^{10}-901120\,a^9\,b^3\,c^{16}\,d^9+2027520\,a^8\,b^4\,c^{17}\,d^8-3244032\,a^7\,b^5\,c^{18}\,d^7+3784704\,a^6\,b^6\,c^{19}\,d^6-3244032\,a^5\,b^7\,c^{20}\,d^5+2027520\,a^4\,b^8\,c^{21}\,d^4-901120\,a^3\,b^9\,c^{22}\,d^3+270336\,a^2\,b^{10}\,c^{23}\,d^2-49152\,a\,b^{11}\,c^{24}\,d+4096\,b^{12}\,c^{25}}\right)}^{5/4}\,15081504768{}\mathrm{i}-a^{22}\,b^5\,c^{21}\,d^{17}\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{17}-49572\,a^3\,b\,c\,d^{16}+140454\,a^2\,b^2\,c^2\,d^{15}-176868\,a\,b^3\,c^3\,d^{14}+83521\,b^4\,c^4\,d^{13}}{4096\,a^{12}\,c^{13}\,d^{12}-49152\,a^{11}\,b\,c^{14}\,d^{11}+270336\,a^{10}\,b^2\,c^{15}\,d^{10}-901120\,a^9\,b^3\,c^{16}\,d^9+2027520\,a^8\,b^4\,c^{17}\,d^8-3244032\,a^7\,b^5\,c^{18}\,d^7+3784704\,a^6\,b^6\,c^{19}\,d^6-3244032\,a^5\,b^7\,c^{20}\,d^5+2027520\,a^4\,b^8\,c^{21}\,d^4-901120\,a^3\,b^9\,c^{22}\,d^3+270336\,a^2\,b^{10}\,c^{23}\,d^2-49152\,a\,b^{11}\,c^{24}\,d+4096\,b^{12}\,c^{25}}\right)}^{5/4}\,9148891136{}\mathrm{i}+a^{23}\,b^4\,c^{20}\,d^{18}\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{17}-49572\,a^3\,b\,c\,d^{16}+140454\,a^2\,b^2\,c^2\,d^{15}-176868\,a\,b^3\,c^3\,d^{14}+83521\,b^4\,c^4\,d^{13}}{4096\,a^{12}\,c^{13}\,d^{12}-49152\,a^{11}\,b\,c^{14}\,d^{11}+270336\,a^{10}\,b^2\,c^{15}\,d^{10}-901120\,a^9\,b^3\,c^{16}\,d^9+2027520\,a^8\,b^4\,c^{17}\,d^8-3244032\,a^7\,b^5\,c^{18}\,d^7+3784704\,a^6\,b^6\,c^{19}\,d^6-3244032\,a^5\,b^7\,c^{20}\,d^5+2027520\,a^4\,b^8\,c^{21}\,d^4-901120\,a^3\,b^9\,c^{22}\,d^3+270336\,a^2\,b^{10}\,c^{23}\,d^2-49152\,a\,b^{11}\,c^{24}\,d+4096\,b^{12}\,c^{25}}\right)}^{5/4}\,4144791552{}\mathrm{i}-a^{24}\,b^3\,c^{19}\,d^{19}\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{17}-49572\,a^3\,b\,c\,d^{16}+140454\,a^2\,b^2\,c^2\,d^{15}-176868\,a\,b^3\,c^3\,d^{14}+83521\,b^4\,c^4\,d^{13}}{4096\,a^{12}\,c^{13}\,d^{12}-49152\,a^{11}\,b\,c^{14}\,d^{11}+270336\,a^{10}\,b^2\,c^{15}\,d^{10}-901120\,a^9\,b^3\,c^{16}\,d^9+2027520\,a^8\,b^4\,c^{17}\,d^8-3244032\,a^7\,b^5\,c^{18}\,d^7+3784704\,a^6\,b^6\,c^{19}\,d^6-3244032\,a^5\,b^7\,c^{20}\,d^5+2027520\,a^4\,b^8\,c^{21}\,d^4-901120\,a^3\,b^9\,c^{22}\,d^3+270336\,a^2\,b^{10}\,c^{23}\,d^2-49152\,a\,b^{11}\,c^{24}\,d+4096\,b^{12}\,c^{25}}\right)}^{5/4}\,1359347712{}\mathrm{i}+a^{25}\,b^2\,c^{18}\,d^{20}\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,d^{17}-49572\,a^3\,b\,c\,d^{16}+140454\,a^2\,b^2\,c^2\,d^{15}-176868\,a\,b^3\,c^3\,d^{14}+83521\,b^4\,c^4\,d^{13}}{4096\,a^{12}\,c^{13}\,d^{12}-49152\,a^{11}\,b\,c^{14}\,d^{11}+270336\,a^{10}\,b^2\,c^{15}\,d^{10}-901120\,a^9\,b^3\,c^{16}\,d^9+2027520\,a^8\,b^4\,c^{17}\,d^8-3244032\,a^7\,b^5\,c^{18}\,d^7+3784704\,a^6\,b^6\,c^{19}\,d^6-3244032\,a^5\,b^7\,c^{20}\,d^5+2027520\,a^4\,b^8\,c^{21}\,d^4-901120\,a^3\,b^9\,c^{22}\,d^3+270336\,a^2\,b^{10}\,c^{23}\,d^2-49152\,a\,b^{11}\,c^{24}\,d+4096\,b^{12}\,c^{25}}\right)}^{5/4}\,304971776{}\mathrm{i}}{-4782969\,a^{17}\,d^{28}+48892572\,a^{16}\,b\,c\,d^{27}-197341758\,a^{15}\,b^2\,c^2\,d^{26}+384710796\,a^{14}\,b^3\,c^3\,d^{25}-335988081\,a^{13}\,b^4\,c^4\,d^{24}+55738368\,a^{12}\,b^5\,c^5\,d^{23}+39223296\,a^{11}\,b^6\,c^6\,d^{22}+24805376\,a^{10}\,b^7\,c^7\,d^{21}+12484608\,a^9\,b^8\,c^8\,d^{20}+2260992\,a^8\,b^9\,c^9\,d^{19}-5865472\,a^7\,b^{10}\,c^{10}\,d^{18}-11894784\,a^6\,b^{11}\,c^{11}\,d^{17}-15826944\,a^5\,b^{12}\,c^{12}\,d^{16}+43224857\,a^4\,b^{13}\,c^{13}\,d^{15}-308701404\,a^3\,b^{14}\,c^{14}\,d^{14}+413141310\,a^2\,b^{15}\,c^{15}\,d^{13}-198040140\,a\,b^{16}\,c^{16}\,d^{12}+32234193\,b^{17}\,c^{17}\,d^{11}}\right)\,{\left(-\frac{6561\,a^4\,d^{17}-49572\,a^3\,b\,c\,d^{16}+140454\,a^2\,b^2\,c^2\,d^{15}-176868\,a\,b^3\,c^3\,d^{14}+83521\,b^4\,c^4\,d^{13}}{4096\,a^{12}\,c^{13}\,d^{12}-49152\,a^{11}\,b\,c^{14}\,d^{11}+270336\,a^{10}\,b^2\,c^{15}\,d^{10}-901120\,a^9\,b^3\,c^{16}\,d^9+2027520\,a^8\,b^4\,c^{17}\,d^8-3244032\,a^7\,b^5\,c^{18}\,d^7+3784704\,a^6\,b^6\,c^{19}\,d^6-3244032\,a^5\,b^7\,c^{20}\,d^5+2027520\,a^4\,b^8\,c^{21}\,d^4-901120\,a^3\,b^9\,c^{22}\,d^3+270336\,a^2\,b^{10}\,c^{23}\,d^2-49152\,a\,b^{11}\,c^{24}\,d+4096\,b^{12}\,c^{25}}\right)}^{1/4}\,2{}\mathrm{i}","Not used",1,"2*atan((2654208*a^16*b^22*c^27*x^(1/2)*(-(6561*b^17*c^4 + 83521*a^4*b^13*d^4 - 176868*a^3*b^14*c*d^3 + 140454*a^2*b^15*c^2*d^2 - 49572*a*b^16*c^3*d)/(4096*a^25*d^12 + 4096*a^13*b^12*c^12 - 49152*a^14*b^11*c^11*d + 270336*a^15*b^10*c^10*d^2 - 901120*a^16*b^9*c^9*d^3 + 2027520*a^17*b^8*c^8*d^4 - 3244032*a^18*b^7*c^7*d^5 + 3784704*a^19*b^6*c^6*d^6 - 3244032*a^20*b^5*c^5*d^7 + 2027520*a^21*b^4*c^4*d^8 - 901120*a^22*b^3*c^3*d^9 + 270336*a^23*b^2*c^2*d^10 - 49152*a^24*b*c*d^11))^(5/4) + 15169032*a^22*b^8*d^19*x^(1/2)*(-(6561*b^17*c^4 + 83521*a^4*b^13*d^4 - 176868*a^3*b^14*c*d^3 + 140454*a^2*b^15*c^2*d^2 - 49572*a*b^16*c^3*d)/(4096*a^25*d^12 + 4096*a^13*b^12*c^12 - 49152*a^14*b^11*c^11*d + 270336*a^15*b^10*c^10*d^2 - 901120*a^16*b^9*c^9*d^3 + 2027520*a^17*b^8*c^8*d^4 - 3244032*a^18*b^7*c^7*d^5 + 3784704*a^19*b^6*c^6*d^6 - 3244032*a^20*b^5*c^5*d^7 + 2027520*a^21*b^4*c^4*d^8 - 901120*a^22*b^3*c^3*d^9 + 270336*a^23*b^2*c^2*d^10 - 49152*a^24*b*c*d^11))^(1/4) + 2654208*a^38*c^5*d^22*x^(1/2)*(-(6561*b^17*c^4 + 83521*a^4*b^13*d^4 - 176868*a^3*b^14*c*d^3 + 140454*a^2*b^15*c^2*d^2 - 49572*a*b^16*c^3*d)/(4096*a^25*d^12 + 4096*a^13*b^12*c^12 - 49152*a^14*b^11*c^11*d + 270336*a^15*b^10*c^10*d^2 - 901120*a^16*b^9*c^9*d^3 + 2027520*a^17*b^8*c^8*d^4 - 3244032*a^18*b^7*c^7*d^5 + 3784704*a^19*b^6*c^6*d^6 - 3244032*a^20*b^5*c^5*d^7 + 2027520*a^21*b^4*c^4*d^8 - 901120*a^22*b^3*c^3*d^9 + 270336*a^23*b^2*c^2*d^10 - 49152*a^24*b*c*d^11))^(5/4) - 130671792*a^21*b^9*c*d^18*x^(1/2)*(-(6561*b^17*c^4 + 83521*a^4*b^13*d^4 - 176868*a^3*b^14*c*d^3 + 140454*a^2*b^15*c^2*d^2 - 49572*a*b^16*c^3*d)/(4096*a^25*d^12 + 4096*a^13*b^12*c^12 - 49152*a^14*b^11*c^11*d + 270336*a^15*b^10*c^10*d^2 - 901120*a^16*b^9*c^9*d^3 + 2027520*a^17*b^8*c^8*d^4 - 3244032*a^18*b^7*c^7*d^5 + 3784704*a^19*b^6*c^6*d^6 - 3244032*a^20*b^5*c^5*d^7 + 2027520*a^21*b^4*c^4*d^8 - 901120*a^22*b^3*c^3*d^9 + 270336*a^23*b^2*c^2*d^10 - 49152*a^24*b*c*d^11))^(1/4) - 41877504*a^17*b^21*c^26*d*x^(1/2)*(-(6561*b^17*c^4 + 83521*a^4*b^13*d^4 - 176868*a^3*b^14*c*d^3 + 140454*a^2*b^15*c^2*d^2 - 49572*a*b^16*c^3*d)/(4096*a^25*d^12 + 4096*a^13*b^12*c^12 - 49152*a^14*b^11*c^11*d + 270336*a^15*b^10*c^10*d^2 - 901120*a^16*b^9*c^9*d^3 + 2027520*a^17*b^8*c^8*d^4 - 3244032*a^18*b^7*c^7*d^5 + 3784704*a^19*b^6*c^6*d^6 - 3244032*a^20*b^5*c^5*d^7 + 2027520*a^21*b^4*c^4*d^8 - 901120*a^22*b^3*c^3*d^9 + 270336*a^23*b^2*c^2*d^10 - 49152*a^24*b*c*d^11))^(5/4) - 41877504*a^37*b*c^6*d^21*x^(1/2)*(-(6561*b^17*c^4 + 83521*a^4*b^13*d^4 - 176868*a^3*b^14*c*d^3 + 140454*a^2*b^15*c^2*d^2 - 49572*a*b^16*c^3*d)/(4096*a^25*d^12 + 4096*a^13*b^12*c^12 - 49152*a^14*b^11*c^11*d + 270336*a^15*b^10*c^10*d^2 - 901120*a^16*b^9*c^9*d^3 + 2027520*a^17*b^8*c^8*d^4 - 3244032*a^18*b^7*c^7*d^5 + 3784704*a^19*b^6*c^6*d^6 - 3244032*a^20*b^5*c^5*d^7 + 2027520*a^21*b^4*c^4*d^8 - 901120*a^22*b^3*c^3*d^9 + 270336*a^23*b^2*c^2*d^10 - 49152*a^24*b*c*d^11))^(5/4) + 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49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(5/4)*4144791552i - a^10*b^17*c^33*d^5*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(5/4)*9148891136i + a^11*b^16*c^32*d^6*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(5/4)*15081504768i - a^12*b^15*c^31*d^7*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(5/4)*18867290112i + a^13*b^14*c^30*d^8*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(5/4)*18014928896i - a^14*b^13*c^29*d^9*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(5/4)*13171163136i + a^15*b^12*c^28*d^10*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(5/4)*7816740864i - a^16*b^11*c^27*d^11*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(5/4)*5554044928i + a^17*b^10*c^26*d^12*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(5/4)*7816740864i - a^18*b^9*c^25*d^13*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(5/4)*13171163136i + a^19*b^8*c^24*d^14*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(5/4)*18014928896i - a^20*b^7*c^23*d^15*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(5/4)*18867290112i + a^21*b^6*c^22*d^16*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(5/4)*15081504768i - a^22*b^5*c^21*d^17*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(5/4)*9148891136i + a^23*b^4*c^20*d^18*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(5/4)*4144791552i - a^24*b^3*c^19*d^19*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(5/4)*1359347712i + a^25*b^2*c^18*d^20*x^(1/2)*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(5/4)*304971776i)/(32234193*b^17*c^17*d^11 - 4782969*a^17*d^28 - 198040140*a*b^16*c^16*d^12 + 413141310*a^2*b^15*c^15*d^13 - 308701404*a^3*b^14*c^14*d^14 + 43224857*a^4*b^13*c^13*d^15 - 15826944*a^5*b^12*c^12*d^16 - 11894784*a^6*b^11*c^11*d^17 - 5865472*a^7*b^10*c^10*d^18 + 2260992*a^8*b^9*c^9*d^19 + 12484608*a^9*b^8*c^8*d^20 + 24805376*a^10*b^7*c^7*d^21 + 39223296*a^11*b^6*c^6*d^22 + 55738368*a^12*b^5*c^5*d^23 - 335988081*a^13*b^4*c^4*d^24 + 384710796*a^14*b^3*c^3*d^25 - 197341758*a^15*b^2*c^2*d^26 + 48892572*a^16*b*c*d^27))*(-(6561*a^4*d^17 + 83521*b^4*c^4*d^13 - 176868*a*b^3*c^3*d^14 + 140454*a^2*b^2*c^2*d^15 - 49572*a^3*b*c*d^16)/(4096*b^12*c^25 + 4096*a^12*c^13*d^12 - 49152*a^11*b*c^14*d^11 + 270336*a^2*b^10*c^23*d^2 - 901120*a^3*b^9*c^22*d^3 + 2027520*a^4*b^8*c^21*d^4 - 3244032*a^5*b^7*c^20*d^5 + 3784704*a^6*b^6*c^19*d^6 - 3244032*a^7*b^5*c^18*d^7 + 2027520*a^8*b^4*c^17*d^8 - 901120*a^9*b^3*c^16*d^9 + 270336*a^10*b^2*c^15*d^10 - 49152*a*b^11*c^24*d))^(1/4)*2i","B"
496,1,48950,718,7.731908,"\text{Not used}","int(x^(7/2)/((a + b*x^2)^2*(c + d*x^2)^3),x)","-\frac{\frac{x^{5/2}\,\left(9\,a^2\,d^2+28\,a\,b\,c\,d+11\,b^2\,c^2\right)}{16\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)}+\frac{c\,\sqrt{x}\,\left(5\,d\,a^2+19\,b\,c\,a\right)}{16\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)}+\frac{b\,d\,x^{9/2}\,\left(17\,a\,d+7\,b\,c\right)}{16\,\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^2+x^2\,\left(b\,c^2+2\,a\,d\,c\right)+x^4\,\left(a\,d^2+2\,b\,c\,d\right)+b\,d^2\,x^6}-\mathrm{atan}\left(-\frac{\left(\left(\frac{-\frac{4375\,a^{10}\,b^6\,d^{11}}{8192}+\frac{1473515\,a^9\,b^7\,c\,d^{10}}{2048}+\frac{6507125\,a^8\,b^8\,c^2\,d^9}{512}+\frac{84943363\,a^7\,b^9\,c^3\,d^8}{2048}+\frac{218830061\,a^6\,b^{10}\,c^4\,d^7}{4096}+\frac{69456793\,a^5\,b^{11}\,c^5\,d^6}{2048}+\frac{11560479\,a^4\,b^{12}\,c^6\,d^5}{1024}+\frac{3824793\,a^3\,b^{13}\,c^7\,d^4}{2048}+\frac{972405\,a^2\,b^{14}\,c^8\,d^3}{8192}}{a^{13}\,d^{13}-13\,a^{12}\,b\,c\,d^{12}+78\,a^{11}\,b^2\,c^2\,d^{11}-286\,a^{10}\,b^3\,c^3\,d^{10}+715\,a^9\,b^4\,c^4\,d^9-1287\,a^8\,b^5\,c^5\,d^8+1716\,a^7\,b^6\,c^6\,d^7-1716\,a^6\,b^7\,c^7\,d^6+1287\,a^5\,b^8\,c^8\,d^5-715\,a^4\,b^9\,c^9\,d^4+286\,a^3\,b^{10}\,c^{10}\,d^3-78\,a^2\,b^{11}\,c^{11}\,d^2+13\,a\,b^{12}\,c^{12}\,d-b^{13}\,c^{13}}+{\left(-\frac{625\,a^8\,d^8+35000\,a^7\,b\,c\,d^7+745500\,a^6\,b^2\,c^2\,d^6+7301000\,a^5\,b^3\,c^3\,d^5+30250150\,a^4\,b^4\,c^4\,d^4+30664200\,a^3\,b^5\,c^5\,d^3+13150620\,a^2\,b^6\,c^6\,d^2+2593080\,a\,b^7\,c^7\,d+194481\,b^8\,c^8}{16777216\,a^{16}\,c^3\,d^{17}-268435456\,a^{15}\,b\,c^4\,d^{16}+2013265920\,a^{14}\,b^2\,c^5\,d^{15}-9395240960\,a^{13}\,b^3\,c^6\,d^{14}+30534533120\,a^{12}\,b^4\,c^7\,d^{13}-73282879488\,a^{11}\,b^5\,c^8\,d^{12}+134351945728\,a^{10}\,b^6\,c^9\,d^{11}-191931351040\,a^9\,b^7\,c^{10}\,d^{10}+215922769920\,a^8\,b^8\,c^{11}\,d^9-191931351040\,a^7\,b^9\,c^{12}\,d^8+134351945728\,a^6\,b^{10}\,c^{13}\,d^7-73282879488\,a^5\,b^{11}\,c^{14}\,d^6+30534533120\,a^4\,b^{12}\,c^{15}\,d^5-9395240960\,a^3\,b^{13}\,c^{16}\,d^4+2013265920\,a^2\,b^{14}\,c^{17}\,d^3-268435456\,a\,b^{15}\,c^{18}\,d^2+16777216\,b^{16}\,c^{19}\,d}\right)}^{3/4}\,\left(\frac{{\left(-\frac{625\,a^8\,d^8+35000\,a^7\,b\,c\,d^7+745500\,a^6\,b^2\,c^2\,d^6+7301000\,a^5\,b^3\,c^3\,d^5+30250150\,a^4\,b^4\,c^4\,d^4+30664200\,a^3\,b^5\,c^5\,d^3+13150620\,a^2\,b^6\,c^6\,d^2+2593080\,a\,b^7\,c^7\,d+194481\,b^8\,c^8}{16777216\,a^{16}\,c^3\,d^{17}-268435456\,a^{15}\,b\,c^4\,d^{16}+2013265920\,a^{14}\,b^2\,c^5\,d^{15}-9395240960\,a^{13}\,b^3\,c^6\,d^{14}+30534533120\,a^{12}\,b^4\,c^7\,d^{13}-73282879488\,a^{11}\,b^5\,c^8\,d^{12}+134351945728\,a^{10}\,b^6\,c^9\,d^{11}-191931351040\,a^9\,b^7\,c^{10}\,d^{10}+215922769920\,a^8\,b^8\,c^{11}\,d^9-191931351040\,a^7\,b^9\,c^{12}\,d^8+134351945728\,a^6\,b^{10}\,c^{13}\,d^7-73282879488\,a^5\,b^{11}\,c^{14}\,d^6+30534533120\,a^4\,b^{12}\,c^{15}\,d^5-9395240960\,a^3\,b^{13}\,c^{16}\,d^4+2013265920\,a^2\,b^{14}\,c^{17}\,d^3-268435456\,a\,b^{15}\,c^{18}\,d^2+16777216\,b^{16}\,c^{19}\,d}\right)}^{1/4}\,\left(1280\,a^{20}\,b^4\,c\,d^{22}-1280\,a^{19}\,b^5\,c^2\,d^{21}-143360\,a^{18}\,b^6\,c^3\,d^{20}+1423360\,a^{17}\,b^7\,c^4\,d^{19}-7193600\,a^{16}\,b^8\,c^5\,d^{18}+23618560\,a^{15}\,b^9\,c^6\,d^{17}-54978560\,a^{14}\,b^{10}\,c^7\,d^{16}+94382080\,a^{13}\,b^{11}\,c^8\,d^{15}-121172480\,a^{12}\,b^{12}\,c^9\,d^{14}+115315200\,a^{11}\,b^{13}\,c^{10}\,d^{13}-77608960\,a^{10}\,b^{14}\,c^{11}\,d^{12}+31016960\,a^9\,b^{15}\,c^{12}\,d^{11}+465920\,a^8\,b^{16}\,c^{13}\,d^{10}-10501120\,a^7\,b^{17}\,c^{14}\,d^9+8038400\,a^6\,b^{18}\,c^{15}\,d^8-3450880\,a^5\,b^{19}\,c^{16}\,d^7+922880\,a^4\,b^{20}\,c^{17}\,d^6-144640\,a^3\,b^{21}\,c^{18}\,d^5+10240\,a^2\,b^{22}\,c^{19}\,d^4\right)}{a^{13}\,d^{13}-13\,a^{12}\,b\,c\,d^{12}+78\,a^{11}\,b^2\,c^2\,d^{11}-286\,a^{10}\,b^3\,c^3\,d^{10}+715\,a^9\,b^4\,c^4\,d^9-1287\,a^8\,b^5\,c^5\,d^8+1716\,a^7\,b^6\,c^6\,d^7-1716\,a^6\,b^7\,c^7\,d^6+1287\,a^5\,b^8\,c^8\,d^5-715\,a^4\,b^9\,c^9\,d^4+286\,a^3\,b^{10}\,c^{10}\,d^3-78\,a^2\,b^{11}\,c^{11}\,d^2+13\,a\,b^{12}\,c^{12}\,d-b^{13}\,c^{13}}-\frac{\sqrt{x}\,\left(6553600\,a^{23}\,b^4\,d^{25}+78643200\,a^{22}\,b^5\,c\,d^{24}-810024960\,a^{21}\,b^6\,c^2\,d^{23}-1490026496\,a^{20}\,b^7\,c^3\,d^{22}+45719224320\,a^{19}\,b^8\,c^4\,d^{21}-273892245504\,a^{18}\,b^9\,c^5\,d^{20}+945071063040\,a^{17}\,b^{10}\,c^6\,d^{19}-2229880750080\,a^{16}\,b^{11}\,c^7\,d^{18}+3867903787008\,a^{15}\,b^{12}\,c^8\,d^{17}-5154201927680\,a^{14}\,b^{13}\,c^9\,d^{16}+5470166188032\,a^{13}\,b^{14}\,c^{10}\,d^{15}-4783425454080\,a^{12}\,b^{15}\,c^{11}\,d^{14}+3520229539840\,a^{11}\,b^{16}\,c^{12}\,d^{13}-2125492912128\,a^{10}\,b^{17}\,c^{13}\,d^{12}+910845542400\,a^9\,b^{18}\,c^{14}\,d^{11}-105331556352\,a^8\,b^{19}\,c^{15}\,d^{10}-218396098560\,a^7\,b^{20}\,c^{16}\,d^9+210842419200\,a^6\,b^{21}\,c^{17}\,d^8-104224784384\,a^5\,b^{22}\,c^{18}\,d^7+31284264960\,a^4\,b^{23}\,c^{19}\,d^6-5420875776\,a^3\,b^{24}\,c^{20}\,d^5+419430400\,a^2\,b^{25}\,c^{21}\,d^4\right)}{65536\,\left(a^{18}\,d^{18}-18\,a^{17}\,b\,c\,d^{17}+153\,a^{16}\,b^2\,c^2\,d^{16}-816\,a^{15}\,b^3\,c^3\,d^{15}+3060\,a^{14}\,b^4\,c^4\,d^{14}-8568\,a^{13}\,b^5\,c^5\,d^{13}+18564\,a^{12}\,b^6\,c^6\,d^{12}-31824\,a^{11}\,b^7\,c^7\,d^{11}+43758\,a^{10}\,b^8\,c^8\,d^{10}-48620\,a^9\,b^9\,c^9\,d^9+43758\,a^8\,b^{10}\,c^{10}\,d^8-31824\,a^7\,b^{11}\,c^{11}\,d^7+18564\,a^6\,b^{12}\,c^{12}\,d^6-8568\,a^5\,b^{13}\,c^{13}\,d^5+3060\,a^4\,b^{14}\,c^{14}\,d^4-816\,a^3\,b^{15}\,c^{15}\,d^3+153\,a^2\,b^{16}\,c^{16}\,d^2-18\,a\,b^{17}\,c^{17}\,d+b^{18}\,c^{18}\right)}\right)\right)\,{\left(-\frac{625\,a^8\,d^8+35000\,a^7\,b\,c\,d^7+745500\,a^6\,b^2\,c^2\,d^6+7301000\,a^5\,b^3\,c^3\,d^5+30250150\,a^4\,b^4\,c^4\,d^4+30664200\,a^3\,b^5\,c^5\,d^3+13150620\,a^2\,b^6\,c^6\,d^2+2593080\,a\,b^7\,c^7\,d+194481\,b^8\,c^8}{16777216\,a^{16}\,c^3\,d^{17}-268435456\,a^{15}\,b\,c^4\,d^{16}+2013265920\,a^{14}\,b^2\,c^5\,d^{15}-9395240960\,a^{13}\,b^3\,c^6\,d^{14}+30534533120\,a^{12}\,b^4\,c^7\,d^{13}-73282879488\,a^{11}\,b^5\,c^8\,d^{12}+134351945728\,a^{10}\,b^6\,c^9\,d^{11}-191931351040\,a^9\,b^7\,c^{10}\,d^{10}+215922769920\,a^8\,b^8\,c^{11}\,d^9-191931351040\,a^7\,b^9\,c^{12}\,d^8+134351945728\,a^6\,b^{10}\,c^{13}\,d^7-73282879488\,a^5\,b^{11}\,c^{14}\,d^6+30534533120\,a^4\,b^{12}\,c^{15}\,d^5-9395240960\,a^3\,b^{13}\,c^{16}\,d^4+2013265920\,a^2\,b^{14}\,c^{17}\,d^3-268435456\,a\,b^{15}\,c^{18}\,d^2+16777216\,b^{16}\,c^{19}\,d}\right)}^{1/4}\,1{}\mathrm{i}-\frac{\sqrt{x}\,\left(3872225\,a^{12}\,b^7\,d^{13}+120299550\,a^{11}\,b^8\,c\,d^{12}+1143306165\,a^{10}\,b^9\,c^2\,d^{11}+3440955560\,a^9\,b^{10}\,c^3\,d^{10}+5932052274\,a^8\,b^{11}\,c^4\,d^9+6551813940\,a^7\,b^{12}\,c^5\,d^8+4617534530\,a^6\,b^{13}\,c^6\,d^7+2030593320\,a^5\,b^{14}\,c^7\,d^6+537450669\,a^4\,b^{15}\,c^8\,d^5+78440670\,a^3\,b^{16}\,c^9\,d^4+4862025\,a^2\,b^{17}\,c^{10}\,d^3\right)\,1{}\mathrm{i}}{65536\,\left(a^{18}\,d^{18}-18\,a^{17}\,b\,c\,d^{17}+153\,a^{16}\,b^2\,c^2\,d^{16}-816\,a^{15}\,b^3\,c^3\,d^{15}+3060\,a^{14}\,b^4\,c^4\,d^{14}-8568\,a^{13}\,b^5\,c^5\,d^{13}+18564\,a^{12}\,b^6\,c^6\,d^{12}-31824\,a^{11}\,b^7\,c^7\,d^{11}+43758\,a^{10}\,b^8\,c^8\,d^{10}-48620\,a^9\,b^9\,c^9\,d^9+43758\,a^8\,b^{10}\,c^{10}\,d^8-31824\,a^7\,b^{11}\,c^{11}\,d^7+18564\,a^6\,b^{12}\,c^{12}\,d^6-8568\,a^5\,b^{13}\,c^{13}\,d^5+3060\,a^4\,b^{14}\,c^{14}\,d^4-816\,a^3\,b^{15}\,c^{15}\,d^3+153\,a^2\,b^{16}\,c^{16}\,d^2-18\,a\,b^{17}\,c^{17}\,d+b^{18}\,c^{18}\right)}\right)\,{\left(-\frac{625\,a^8\,d^8+35000\,a^7\,b\,c\,d^7+745500\,a^6\,b^2\,c^2\,d^6+7301000\,a^5\,b^3\,c^3\,d^5+30250150\,a^4\,b^4\,c^4\,d^4+30664200\,a^3\,b^5\,c^5\,d^3+13150620\,a^2\,b^6\,c^6\,d^2+2593080\,a\,b^7\,c^7\,d+194481\,b^8\,c^8}{16777216\,a^{16}\,c^3\,d^{17}-268435456\,a^{15}\,b\,c^4\,d^{16}+2013265920\,a^{14}\,b^2\,c^5\,d^{15}-9395240960\,a^{13}\,b^3\,c^6\,d^{14}+30534533120\,a^{12}\,b^4\,c^7\,d^{13}-73282879488\,a^{11}\,b^5\,c^8\,d^{12}+134351945728\,a^{10}\,b^6\,c^9\,d^{11}-191931351040\,a^9\,b^7\,c^{10}\,d^{10}+215922769920\,a^8\,b^8\,c^{11}\,d^9-191931351040\,a^7\,b^9\,c^{12}\,d^8+134351945728\,a^6\,b^{10}\,c^{13}\,d^7-73282879488\,a^5\,b^{11}\,c^{14}\,d^6+30534533120\,a^4\,b^{12}\,c^{15}\,d^5-9395240960\,a^3\,b^{13}\,c^{16}\,d^4+2013265920\,a^2\,b^{14}\,c^{17}\,d^3-268435456\,a\,b^{15}\,c^{18}\,d^2+16777216\,b^{16}\,c^{19}\,d}\right)}^{1/4}-\left(\left(\frac{-\frac{4375\,a^{10}\,b^6\,d^{11}}{8192}+\frac{1473515\,a^9\,b^7\,c\,d^{10}}{2048}+\frac{6507125\,a^8\,b^8\,c^2\,d^9}{512}+\frac{84943363\,a^7\,b^9\,c^3\,d^8}{2048}+\frac{218830061\,a^6\,b^{10}\,c^4\,d^7}{4096}+\frac{69456793\,a^5\,b^{11}\,c^5\,d^6}{2048}+\frac{11560479\,a^4\,b^{12}\,c^6\,d^5}{1024}+\frac{3824793\,a^3\,b^{13}\,c^7\,d^4}{2048}+\frac{972405\,a^2\,b^{14}\,c^8\,d^3}{8192}}{a^{13}\,d^{13}-13\,a^{12}\,b\,c\,d^{12}+78\,a^{11}\,b^2\,c^2\,d^{11}-286\,a^{10}\,b^3\,c^3\,d^{10}+715\,a^9\,b^4\,c^4\,d^9-1287\,a^8\,b^5\,c^5\,d^8+1716\,a^7\,b^6\,c^6\,d^7-1716\,a^6\,b^7\,c^7\,d^6+1287\,a^5\,b^8\,c^8\,d^5-715\,a^4\,b^9\,c^9\,d^4+286\,a^3\,b^{10}\,c^{10}\,d^3-78\,a^2\,b^{11}\,c^{11}\,d^2+13\,a\,b^{12}\,c^{12}\,d-b^{13}\,c^{13}}+{\left(-\frac{625\,a^8\,d^8+35000\,a^7\,b\,c\,d^7+745500\,a^6\,b^2\,c^2\,d^6+7301000\,a^5\,b^3\,c^3\,d^5+30250150\,a^4\,b^4\,c^4\,d^4+30664200\,a^3\,b^5\,c^5\,d^3+13150620\,a^2\,b^6\,c^6\,d^2+2593080\,a\,b^7\,c^7\,d+194481\,b^8\,c^8}{16777216\,a^{16}\,c^3\,d^{17}-268435456\,a^{15}\,b\,c^4\,d^{16}+2013265920\,a^{14}\,b^2\,c^5\,d^{15}-9395240960\,a^{13}\,b^3\,c^6\,d^{14}+30534533120\,a^{12}\,b^4\,c^7\,d^{13}-73282879488\,a^{11}\,b^5\,c^8\,d^{12}+134351945728\,a^{10}\,b^6\,c^9\,d^{11}-191931351040\,a^9\,b^7\,c^{10}\,d^{10}+215922769920\,a^8\,b^8\,c^{11}\,d^9-191931351040\,a^7\,b^9\,c^{12}\,d^8+134351945728\,a^6\,b^{10}\,c^{13}\,d^7-73282879488\,a^5\,b^{11}\,c^{14}\,d^6+30534533120\,a^4\,b^{12}\,c^{15}\,d^5-9395240960\,a^3\,b^{13}\,c^{16}\,d^4+2013265920\,a^2\,b^{14}\,c^{17}\,d^3-268435456\,a\,b^{15}\,c^{18}\,d^2+16777216\,b^{16}\,c^{19}\,d}\right)}^{3/4}\,\left(\frac{{\left(-\frac{625\,a^8\,d^8+35000\,a^7\,b\,c\,d^7+745500\,a^6\,b^2\,c^2\,d^6+7301000\,a^5\,b^3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3}\,d^5+3060\,a^4\,b^{14}\,c^{14}\,d^4-816\,a^3\,b^{15}\,c^{15}\,d^3+153\,a^2\,b^{16}\,c^{16}\,d^2-18\,a\,b^{17}\,c^{17}\,d+b^{18}\,c^{18}\right)}\right)\,{\left(-\frac{625\,a^8\,d^8+35000\,a^7\,b\,c\,d^7+745500\,a^6\,b^2\,c^2\,d^6+7301000\,a^5\,b^3\,c^3\,d^5+30250150\,a^4\,b^4\,c^4\,d^4+30664200\,a^3\,b^5\,c^5\,d^3+13150620\,a^2\,b^6\,c^6\,d^2+2593080\,a\,b^7\,c^7\,d+194481\,b^8\,c^8}{16777216\,a^{16}\,c^3\,d^{17}-268435456\,a^{15}\,b\,c^4\,d^{16}+2013265920\,a^{14}\,b^2\,c^5\,d^{15}-9395240960\,a^{13}\,b^3\,c^6\,d^{14}+30534533120\,a^{12}\,b^4\,c^7\,d^{13}-73282879488\,a^{11}\,b^5\,c^8\,d^{12}+134351945728\,a^{10}\,b^6\,c^9\,d^{11}-191931351040\,a^9\,b^7\,c^{10}\,d^{10}+215922769920\,a^8\,b^8\,c^{11}\,d^9-191931351040\,a^7\,b^9\,c^{12}\,d^8+134351945728\,a^6\,b^{10}\,c^{13}\,d^7-73282879488\,a^5\,b^{11}\,c^{14}\,d^6+30534533120\,a^4\,b^{12}\,c^{15}\,d^5-9395240960\,a^3\,b^{13}\,c^{16}\,d^4+2013265920\,a^2\,b^{14}\,c^{17}\,d^3-268435456\,a\,b^{15}\,c^{18}\,d^2+16777216\,b^{16}\,c^{19}\,d}\right)}^{1/4}}{\left(\left(\frac{-\frac{4375\,a^{10}\,b^6\,d^{11}}{8192}+\frac{1473515\,a^9\,b^7\,c\,d^{10}}{2048}+\frac{6507125\,a^8\,b^8\,c^2\,d^9}{512}+\frac{84943363\,a^7\,b^9\,c^3\,d^8}{2048}+\frac{218830061\,a^6\,b^{10}\,c^4\,d^7}{4096}+\frac{69456793\,a^5\,b^{11}\,c^5\,d^6}{2048}+\frac{11560479\,a^4\,b^{12}\,c^6\,d^5}{1024}+\frac{3824793\,a^3\,b^{13}\,c^7\,d^4}{2048}+\frac{972405\,a^2\,b^{14}\,c^8\,d^3}{8192}}{a^{13}\,d^{13}-13\,a^{12}\,b\,c\,d^{12}+78\,a^{11}\,b^2\,c^2\,d^{11}-286\,a^{10}\,b^3\,c^3\,d^{10}+715\,a^9\,b^4\,c^4\,d^9-1287\,a^8\,b^5\,c^5\,d^8+1716\,a^7\,b^6\,c^6\,d^7-1716\,a^6\,b^7\,c^7\,d^6+1287\,a^5\,b^8\,c^8\,d^5-715\,a^4\,b^9\,c^9\,d^4+286\,a^3\,b^{10}\,c^{10}\,d^3-78\,a^2\,b^{11}\,c^{11}\,d^2+13\,a\,b^{12}\,c^{12}\,d-b^{13}\,c^{13}}+{\left(-\frac{625\,a^8\,d^8+35000\,a^7\,b\,c\,d^7+745500\,a^6\,b^2\,c^2\,d^6+7301000\,a^5\,b^3\,c^3\,d^5+30250150\,a^4\,b^4\,c^4\,d^4+30664200\,a^3\,b^5\,c^5\,d^3+13150620\,a^2\,b^6\,c^6\,d^2+2593080\,a\,b^7\,c^7\,d+194481\,b^8\,c^8}{16777216\,a^{16}\,c^3\,d^{17}-268435456\,a^{15}\,b\,c^4\,d^{16}+2013265920\,a^{14}\,b^2\,c^5\,d^{15}-9395240960\,a^{13}\,b^3\,c^6\,d^{14}+30534533120\,a^{12}\,b^4\,c^7\,d^{13}-73282879488\,a^{11}\,b^5\,c^8\,d^{12}+134351945728\,a^{10}\,b^6\,c^9\,d^{11}-191931351040\,a^9\,b^7\,c^{10}\,d^{10}+215922769920\,a^8\,b^8\,c^{11}\,d^9-191931351040\,a^7\,b^9\,c^{12}\,d^8+134351945728\,a^6\,b^{10}\,c^{13}\,d^7-73282879488\,a^5\,b^{11}\,c^{14}\,d^6+30534533120\,a^4\,b^{12}\,c^{15}\,d^5-9395240960\,a^3\,b^{13}\,c^{16}\,d^4+2013265920\,a^2\,b^{14}\,c^{17}\,d^3-268435456\,a\,b^{15}\,c^{18}\,d^2+16777216\,b^{16}\,c^{19}\,d}\right)}^{3/4}\,\left(\frac{{\left(-\frac{625\,a^8\,d^8+35000\,a^7\,b\,c\,d^7+745500\,a^6\,b^2\,c^2\,d^6+7301000\,a^5\,b^3\,c^3\,d^5+30250150\,a^4\,b^4\,c^4\,d^4+30664200\,a^3\,b^5\,c^5\,d^3+13150620\,a^2\,b^6\,c^6\,d^2+2593080\,a\,b^7\,c^7\,d+194481\,b^8\,c^8}{16777216\,a^{16}\,c^3\,d^{17}-268435456\,a^{15}\,b\,c^4\,d^{16}+2013265920\,a^{14}\,b^2\,c^5\,d^{15}-9395240960\,a^{13}\,b^3\,c^6\,d^{14}+30534533120\,a^{12}\,b^4\,c^7\,d^{13}-73282879488\,a^{11}\,b^5\,c^8\,d^{12}+134351945728\,a^{10}\,b^6\,c^9\,d^{11}-191931351040\,a^9\,b^7\,c^{10}\,d^{10}+215922769920\,a^8\,b^8\,c^{11}\,d^9-191931351040\,a^7\,b^9\,c^{12}\,d^8+134351945728\,a^6\,b^{10}\,c^{13}\,d^7-73282879488\,a^5\,b^{11}\,c^{14}\,d^6+30534533120\,a^4\,b^{12}\,c^{15}\,d^5-9395240960\,a^3\,b^{13}\,c^{16}\,d^4+2013265920\,a^2\,b^{14}\,c^{17}\,d^3-268435456\,a\,b^{15}\,c^{18}\,d^2+16777216\,b^{16}\,c^{19}\,d}\right)}^{1/4}\,\left(1280\,a^{20}\,b^4\,c\,d^{22}-1280\,a^{19}\,b^5\,c^2\,d^{21}-143360\,a^{18}\,b^6\,c^3\,d^{20}+1423360\,a^{17}\,b^7\,c^4\,d^{19}-7193600\,a^{16}\,b^8\,c^5\,d^{18}+23618560\,a^{15}\,b^9\,c^6\,d^{17}-54978560\,a^{14}\,b^{10}\,c^7\,d^{16}+94382080\,a^{13}\,b^{11}\,c^8\,d^{15}-121172480\,a^{12}\,b^{12}\,c^9\,d^{14}+115315200\,a^{11}\,b^{13}\,c^{10}\,d^{13}-77608960\,a^{10}\,b^{14}\,c^{11}\,d^{12}+31016960\,a^9\,b^{15}\,c^{12}\,d^{11}+465920\,a^8\,b^{16}\,c^{13}\,d^{10}-10501120\,a^7\,b^{17}\,c^{14}\,d^9+8038400\,a^6\,b^{18}\,c^{15}\,d^8-3450880\,a^5\,b^{19}\,c^{16}\,d^7+922880\,a^4\,b^{20}\,c^{17}\,d^6-144640\,a^3\,b^{21}\,c^{18}\,d^5+10240\,a^2\,b^{22}\,c^{19}\,d^4\right)}{a^{13}\,d^{13}-13\,a^{12}\,b\,c\,d^{12}+78\,a^{11}\,b^2\,c^2\,d^{11}-286\,a^{10}\,b^3\,c^3\,d^{10}+715\,a^9\,b^4\,c^4\,d^9-1287\,a^8\,b^5\,c^5\,d^8+1716\,a^7\,b^6\,c^6\,d^7-1716\,a^6\,b^7\,c^7\,d^6+1287\,a^5\,b^8\,c^8\,d^5-715\,a^4\,b^9\,c^9\,d^4+286\,a^3\,b^{10}\,c^{10}\,d^3-78\,a^2\,b^{11}\,c^{11}\,d^2+13\,a\,b^{12}\,c^{12}\,d-b^{13}\,c^{13}}-\frac{\sqrt{x}\,\left(6553600\,a^{23}\,b^4\,d^{25}+78643200\,a^{22}\,b^5\,c\,d^{24}-810024960\,a^{21}\,b^6\,c^2\,d^{23}-1490026496\,a^{20}\,b^7\,c^3\,d^{22}+45719224320\,a^{19}\,b^8\,c^4\,d^{21}-273892245504\,a^{18}\,b^9\,c^5\,d^{20}+945071063040\,a^{17}\,b^{10}\,c^6\,d^{19}-2229880750080\,a^{16}\,b^{11}\,c^7\,d^{18}+3867903787008\,a^{15}\,b^{12}\,c^8\,d^{17}-5154201927680\,a^{14}\,b^{13}\,c^9\,d^{16}+5470166188032\,a^{13}\,b^{14}\,c^{10}\,d^{15}-4783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}\,d^2-65536\,a\,b^{15}\,c^{15}\,d+4096\,b^{16}\,c^{16}}\right)}^{1/4}\,\left({\left(-\frac{2401\,a^5\,b^3\,d^4+6860\,a^4\,b^4\,c\,d^3+7350\,a^3\,b^5\,c^2\,d^2+3500\,a^2\,b^6\,c^3\,d+625\,a\,b^7\,c^4}{4096\,a^{16}\,d^{16}-65536\,a^{15}\,b\,c\,d^{15}+491520\,a^{14}\,b^2\,c^2\,d^{14}-2293760\,a^{13}\,b^3\,c^3\,d^{13}+7454720\,a^{12}\,b^4\,c^4\,d^{12}-17891328\,a^{11}\,b^5\,c^5\,d^{11}+32800768\,a^{10}\,b^6\,c^6\,d^{10}-46858240\,a^9\,b^7\,c^7\,d^9+52715520\,a^8\,b^8\,c^8\,d^8-46858240\,a^7\,b^9\,c^9\,d^7+32800768\,a^6\,b^{10}\,c^{10}\,d^6-17891328\,a^5\,b^{11}\,c^{11}\,d^5+7454720\,a^4\,b^{12}\,c^{12}\,d^4-2293760\,a^3\,b^{13}\,c^{13}\,d^3+491520\,a^2\,b^{14}\,c^{14}\,d^2-65536\,a\,b^{15}\,c^{15}\,d+4096\,b^{16}\,c^{16}}\right)}^{1/4}\,\left(\frac{-\frac{4375\,a^{10}\,b^6\,d^{11}}{8192}+\frac{1473515\,a^9\,b^7\,c\,d^{10}}{2048}+\frac{6507125\,a^8\,b^8\,c^2\,d^9}{512}+\frac{84943363\,a^7\,b^9\,c^3\,d^8}{2048}+\frac{218830061\,a^6\,b^{10}\,c^4\,d^7}{4096}+\frac{69456793\,a^5\,b^{11}\,c^5\,d^6}{2048}+\frac{11560479\,a^4\,b^{12}\,c^6\,d^5}{1024}+\frac{3824793\,a^3\,b^{13}\,c^7\,d^4}{2048}+\frac{972405\,a^2\,b^{14}\,c^8\,d^3}{8192}}{a^{13}\,d^{13}-13\,a^{12}\,b\,c\,d^{12}+78\,a^{11}\,b^2\,c^2\,d^{11}-286\,a^{10}\,b^3\,c^3\,d^{10}+715\,a^9\,b^4\,c^4\,d^9-1287\,a^8\,b^5\,c^5\,d^8+1716\,a^7\,b^6\,c^6\,d^7-1716\,a^6\,b^7\,c^7\,d^6+1287\,a^5\,b^8\,c^8\,d^5-715\,a^4\,b^9\,c^9\,d^4+286\,a^3\,b^{10}\,c^{10}\,d^3-78\,a^2\,b^{11}\,c^{11}\,d^2+13\,a\,b^{12}\,c^{12}\,d-b^{13}\,c^{13}}+{\left(-\frac{2401\,a^5\,b^3\,d^4+6860\,a^4\,b^4\,c\,d^3+7350\,a^3\,b^5\,c^2\,d^2+3500\,a^2\,b^6\,c^3\,d+625\,a\,b^7\,c^4}{4096\,a^{16}\,d^{16}-65536\,a^{15}\,b\,c\,d^{15}+491520\,a^{14}\,b^2\,c^2\,d^{14}-2293760\,a^{13}\,b^3\,c^3\,d^{13}+7454720\,a^{12}\,b^4\,c^4\,d^{12}-17891328\,a^{11}\,b^5\,c^5\,d^{11}+32800768\,a^{10}\,b^6\,c^6\,d^{10}-46858240\,a^9\,b^7\,c^7\,d^9+52715520\,a^8\,b^8\,c^8\,d^8-46858240\,a^7\,b^9\,c^9\,d^7+32800768\,a^6\,b^{10}\,c^{10}\,d^6-17891328\,a^5\,b^{11}\,c^{11}\,d^5+7454720\,a^4\,b^{12}\,c^{12}\,d^4-2293760\,a^3\,b^{13}\,c^{13}\,d^3+491520\,a^2\,b^{14}\,c^{14}\,d^2-65536\,a\,b^{15}\,c^{15}\,d+4096\,b^{16}\,c^{16}}\right)}^{3/4}\,\left(\frac{\sqrt{x}\,\left(6553600\,a^{23}\,b^4\,d^{25}+78643200\,a^{22}\,b^5\,c\,d^{24}-810024960\,a^{21}\,b^6\,c^2\,d^{23}-1490026496\,a^{20}\,b^7\,c^3\,d^{22}+45719224320\,a^{19}\,b^8\,c^4\,d^{21}-273892245504\,a^{18}\,b^9\,c^5\,d^{20}+945071063040\,a^{17}\,b^{10}\,c^6\,d^{19}-2229880750080\,a^{16}\,b^{11}\,c^7\,d^{18}+3867903787008\,a^{15}\,b^{12}\,c^8\,d^{17}-5154201927680\,a^{14}\,b^{13}\,c^9\,d^{16}+5470166188032\,a^{13}\,b^{14}\,c^{10}\,d^{15}-4783425454080\,a^{12}\,b^{15}\,c^{11}\,d^{14}+3520229539840\,a^{11}\,b^{16}\,c^{12}\,d^{13}-2125492912128\,a^{10}\,b^{17}\,c^{13}\,d^{12}+910845542400\,a^9\,b^{18}\,c^{14}\,d^{11}-105331556352\,a^8\,b^{19}\,c^{15}\,d^{10}-218396098560\,a^7\,b^{20}\,c^{16}\,d^9+210842419200\,a^6\,b^{21}\,c^{17}\,d^8-104224784384\,a^5\,b^{22}\,c^{18}\,d^7+31284264960\,a^4\,b^{23}\,c^{19}\,d^6-5420875776\,a^3\,b^{24}\,c^{20}\,d^5+419430400\,a^2\,b^{25}\,c^{21}\,d^4\right)}{65536\,\left(a^{18}\,d^{18}-18\,a^{17}\,b\,c\,d^{17}+153\,a^{16}\,b^2\,c^2\,d^{16}-816\,a^{15}\,b^3\,c^3\,d^{15}+3060\,a^{14}\,b^4\,c^4\,d^{14}-8568\,a^{13}\,b^5\,c^5\,d^{13}+18564\,a^{12}\,b^6\,c^6\,d^{12}-31824\,a^{11}\,b^7\,c^7\,d^{11}+43758\,a^{10}\,b^8\,c^8\,d^{10}-48620\,a^9\,b^9\,c^9\,d^9+43758\,a^8\,b^{10}\,c^{10}\,d^8-31824\,a^7\,b^{11}\,c^{11}\,d^7+18564\,a^6\,b^{12}\,c^{12}\,d^6-8568\,a^5\,b^{13}\,c^{13}\,d^5+3060\,a^4\,b^{14}\,c^{14}\,d^4-816\,a^3\,b^{15}\,c^{15}\,d^3+153\,a^2\,b^{16}\,c^{16}\,d^2-18\,a\,b^{17}\,c^{17}\,d+b^{18}\,c^{18}\right)}+\frac{{\left(-\frac{2401\,a^5\,b^3\,d^4+6860\,a^4\,b^4\,c\,d^3+7350\,a^3\,b^5\,c^2\,d^2+3500\,a^2\,b^6\,c^3\,d+625\,a\,b^7\,c^4}{4096\,a^{16}\,d^{16}-65536\,a^{15}\,b\,c\,d^{15}+491520\,a^{14}\,b^2\,c^2\,d^{14}-2293760\,a^{13}\,b^3\,c^3\,d^{13}+7454720\,a^{12}\,b^4\,c^4\,d^{12}-17891328\,a^{11}\,b^5\,c^5\,d^{11}+32800768\,a^{10}\,b^6\,c^6\,d^{10}-46858240\,a^9\,b^7\,c^7\,d^9+52715520\,a^8\,b^8\,c^8\,d^8-46858240\,a^7\,b^9\,c^9\,d^7+32800768\,a^6\,b^{10}\,c^{10}\,d^6-17891328\,a^5\,b^{11}\,c^{11}\,d^5+7454720\,a^4\,b^{12}\,c^{12}\,d^4-2293760\,a^3\,b^{13}\,c^{13}\,d^3+491520\,a^2\,b^{14}\,c^{14}\,d^2-65536\,a\,b^{15}\,c^{15}\,d+4096\,b^{16}\,c^{16}}\right)}^{1/4}\,\left(1280\,a^{20}\,b^4\,c\,d^{22}-1280\,a^{19}\,b^5\,c^2\,d^{21}-143360\,a^{18}\,b^6\,c^3\,d^{20}+1423360\,a^{17}\,b^7\,c^4\,d^{19}-7193600\,a^{16}\,b^8\,c^5\,d^{18}+23618560\,a^{15}\,b^9\,c^6\,d^{17}-54978560\,a^{14}\,b^{10}\,c^7\,d^{16}+94382080\,a^{13}\,b^{11}\,c^8\,d^{15}-121172480\,a^{12}\,b^{12}\,c^9\,d^{14}+115315200\,a^{11}\,b^{13}\,c^{10}\,d^{13}-77608960\,a^{10}\,b^{14}\,c^{11}\,d^{12}+31016960\,a^9\,b^{15}\,c^{12}\,d^{11}+465920\,a^8\,b^{16}\,c^{13}\,d^{10}-10501120\,a^7\,b^{17}\,c^{14}\,d^9+8038400\,a^6\,b^{18}\,c^{15}\,d^8-3450880\,a^5\,b^{19}\,c^{16}\,d^7+922880\,a^4\,b^{20}\,c^{17}\,d^6-144640\,a^3\,b^{21}\,c^{18}\,d^5+10240\,a^2\,b^{22}\,c^{19}\,d^4\right)}{a^{13}\,d^{13}-13\,a^{12}\,b\,c\,d^{12}+78\,a^{11}\,b^2\,c^2\,d^{11}-286\,a^{10}\,b^3\,c^3\,d^{10}+715\,a^9\,b^4\,c^4\,d^9-1287\,a^8\,b^5\,c^5\,d^8+1716\,a^7\,b^6\,c^6\,d^7-1716\,a^6\,b^7\,c^7\,d^6+1287\,a^5\,b^8\,c^8\,d^5-715\,a^4\,b^9\,c^9\,d^4+286\,a^3\,b^{10}\,c^{10}\,d^3-78\,a^2\,b^{11}\,c^{11}\,d^2+13\,a\,b^{12}\,c^{12}\,d-b^{13}\,c^{13}}\right)\right)\,1{}\mathrm{i}+\frac{\sqrt{x}\,\left(3872225\,a^{12}\,b^7\,d^{13}+120299550\,a^{11}\,b^8\,c\,d^{12}+1143306165\,a^{10}\,b^9\,c^2\,d^{11}+3440955560\,a^9\,b^{10}\,c^3\,d^{10}+5932052274\,a^8\,b^{11}\,c^4\,d^9+6551813940\,a^7\,b^{12}\,c^5\,d^8+4617534530\,a^6\,b^{13}\,c^6\,d^7+2030593320\,a^5\,b^{14}\,c^7\,d^6+537450669\,a^4\,b^{15}\,c^8\,d^5+78440670\,a^3\,b^{16}\,c^9\,d^4+4862025\,a^2\,b^{17}\,c^{10}\,d^3\right)\,1{}\mathrm{i}}{65536\,\left(a^{18}\,d^{18}-18\,a^{17}\,b\,c\,d^{17}+153\,a^{16}\,b^2\,c^2\,d^{16}-816\,a^{15}\,b^3\,c^3\,d^{15}+3060\,a^{14}\,b^4\,c^4\,d^{14}-8568\,a^{13}\,b^5\,c^5\,d^{13}+18564\,a^{12}\,b^6\,c^6\,d^{12}-31824\,a^{11}\,b^7\,c^7\,d^{11}+43758\,a^{10}\,b^8\,c^8\,d^{10}-48620\,a^9\,b^9\,c^9\,d^9+43758\,a^8\,b^{10}\,c^{10}\,d^8-31824\,a^7\,b^{11}\,c^{11}\,d^7+18564\,a^6\,b^{12}\,c^{12}\,d^6-8568\,a^5\,b^{13}\,c^{13}\,d^5+3060\,a^4\,b^{14}\,c^{14}\,d^4-816\,a^3\,b^{15}\,c^{15}\,d^3+153\,a^2\,b^{16}\,c^{16}\,d^2-18\,a\,b^{17}\,c^{17}\,d+b^{18}\,c^{18}\right)}\right)-{\left(-\frac{2401\,a^5\,b^3\,d^4+6860\,a^4\,b^4\,c\,d^3+7350\,a^3\,b^5\,c^2\,d^2+3500\,a^2\,b^6\,c^3\,d+625\,a\,b^7\,c^4}{4096\,a^{16}\,d^{16}-65536\,a^{15}\,b\,c\,d^{15}+491520\,a^{14}\,b^2\,c^2\,d^{14}-2293760\,a^{13}\,b^3\,c^3\,d^{13}+7454720\,a^{12}\,b^4\,c^4\,d^{12}-17891328\,a^{11}\,b^5\,c^5\,d^{11}+32800768\,a^{10}\,b^6\,c^6\,d^{10}-46858240\,a^9\,b^7\,c^7\,d^9+52715520\,a^8\,b^8\,c^8\,d^8-46858240\,a^7\,b^9\,c^9\,d^7+32800768\,a^6\,b^{10}\,c^{10}\,d^6-17891328\,a^5\,b^{11}\,c^{11}\,d^5+7454720\,a^4\,b^{12}\,c^{12}\,d^4-2293760\,a^3\,b^{13}\,c^{13}\,d^3+491520\,a^2\,b^{14}\,c^{14}\,d^2-65536\,a\,b^{15}\,c^{15}\,d+4096\,b^{16}\,c^{16}}\right)}^{1/4}\,\left({\left(-\frac{2401\,a^5\,b^3\,d^4+6860\,a^4\,b^4\,c\,d^3+7350\,a^3\,b^5\,c^2\,d^2+3500\,a^2\,b^6\,c^3\,d+625\,a\,b^7\,c^4}{4096\,a^{16}\,d^{16}-65536\,a^{15}\,b\,c\,d^{15}+491520\,a^{14}\,b^2\,c^2\,d^{14}-2293760\,a^{13}\,b^3\,c^3\,d^{13}+7454720\,a^{12}\,b^4\,c^4\,d^{12}-17891328\,a^{11}\,b^5\,c^5\,d^{11}+32800768\,a^{10}\,b^6\,c^6\,d^{10}-46858240\,a^9\,b^7\,c^7\,d^9+52715520\,a^8\,b^8\,c^8\,d^8-46858240\,a^7\,b^9\,c^9\,d^7+32800768\,a^6\,b^{10}\,c^{10}\,d^6-17891328\,a^5\,b^{11}\,c^{11}\,d^5+7454720\,a^4\,b^{12}\,c^{12}\,d^4-2293760\,a^3\,b^{13}\,c^{13}\,d^3+491520\,a^2\,b^{14}\,c^{14}\,d^2-65536\,a\,b^{15}\,c^{15}\,d+4096\,b^{16}\,c^{16}}\right)}^{1/4}\,\left(\frac{-\frac{4375\,a^{10}\,b^6\,d^{11}}{8192}+\frac{1473515\,a^9\,b^7\,c\,d^{10}}{2048}+\frac{6507125\,a^8\,b^8\,c^2\,d^9}{512}+\frac{84943363\,a^7\,b^9\,c^3\,d^8}{2048}+\frac{218830061\,a^6\,b^{10}\,c^4\,d^7}{4096}+\frac{69456793\,a^5\,b^{11}\,c^5\,d^6}{2048}+\frac{11560479\,a^4\,b^{12}\,c^6\,d^5}{1024}+\frac{3824793\,a^3\,b^{13}\,c^7\,d^4}{2048}+\frac{972405\,a^2\,b^{14}\,c^8\,d^3}{8192}}{a^{13}\,d^{13}-13\,a^{12}\,b\,c\,d^{12}+78\,a^{11}\,b^2\,c^2\,d^{11}-286\,a^{10}\,b^3\,c^3\,d^{10}+715\,a^9\,b^4\,c^4\,d^9-1287\,a^8\,b^5\,c^5\,d^8+1716\,a^7\,b^6\,c^6\,d^7-1716\,a^6\,b^7\,c^7\,d^6+1287\,a^5\,b^8\,c^8\,d^5-715\,a^4\,b^9\,c^9\,d^4+286\,a^3\,b^{10}\,c^{10}\,d^3-78\,a^2\,b^{11}\,c^{11}\,d^2+13\,a\,b^{12}\,c^{12}\,d-b^{13}\,c^{13}}-{\left(-\frac{2401\,a^5\,b^3\,d^4+6860\,a^4\,b^4\,c\,d^3+7350\,a^3\,b^5\,c^2\,d^2+3500\,a^2\,b^6\,c^3\,d+625\,a\,b^7\,c^4}{4096\,a^{16}\,d^{16}-65536\,a^{15}\,b\,c\,d^{15}+491520\,a^{14}\,b^2\,c^2\,d^{14}-2293760\,a^{13}\,b^3\,c^3\,d^{13}+7454720\,a^{12}\,b^4\,c^4\,d^{12}-17891328\,a^{11}\,b^5\,c^5\,d^{11}+32800768\,a^{10}\,b^6\,c^6\,d^{10}-46858240\,a^9\,b^7\,c^7\,d^9+52715520\,a^8\,b^8\,c^8\,d^8-46858240\,a^7\,b^9\,c^9\,d^7+32800768\,a^6\,b^{10}\,c^{10}\,d^6-17891328\,a^5\,b^{11}\,c^{11}\,d^5+7454720\,a^4\,b^{12}\,c^{12}\,d^4-2293760\,a^3\,b^{13}\,c^{13}\,d^3+491520\,a^2\,b^{14}\,c^{14}\,d^2-65536\,a\,b^{15}\,c^{15}\,d+4096\,b^{16}\,c^{16}}\right)}^{3/4}\,\left(\frac{\sqrt{x}\,\left(6553600\,a^{23}\,b^4\,d^{25}+78643200\,a^{22}\,b^5\,c\,d^{24}-810024960\,a^{21}\,b^6\,c^2\,d^{23}-1490026496\,a^{20}\,b^7\,c^3\,d^{22}+45719224320\,a^{19}\,b^8\,c^4\,d^{21}-273892245504\,a^{18}\,b^9\,c^5\,d^{20}+945071063040\,a^{17}\,b^{10}\,c^6\,d^{19}-2229880750080\,a^{16}\,b^{11}\,c^7\,d^{18}+3867903787008\,a^{15}\,b^{12}\,c^8\,d^{17}-5154201927680\,a^{14}\,b^{13}\,c^9\,d^{16}+5470166188032\,a^{13}\,b^{14}\,c^{10}\,d^{15}-4783425454080\,a^{12}\,b^{15}\,c^{11}\,d^{14}+3520229539840\,a^{11}\,b^{16}\,c^{12}\,d^{13}-2125492912128\,a^{10}\,b^{17}\,c^{13}\,d^{12}+910845542400\,a^9\,b^{18}\,c^{14}\,d^{11}-105331556352\,a^8\,b^{19}\,c^{15}\,d^{10}-218396098560\,a^7\,b^{20}\,c^{16}\,d^9+210842419200\,a^6\,b^{21}\,c^{17}\,d^8-104224784384\,a^5\,b^{22}\,c^{18}\,d^7+31284264960\,a^4\,b^{23}\,c^{19}\,d^6-5420875776\,a^3\,b^{24}\,c^{20}\,d^5+419430400\,a^2\,b^{25}\,c^{21}\,d^4\right)}{65536\,\left(a^{18}\,d^{18}-18\,a^{17}\,b\,c\,d^{17}+153\,a^{16}\,b^2\,c^2\,d^{16}-816\,a^{15}\,b^3\,c^3\,d^{15}+3060\,a^{14}\,b^4\,c^4\,d^{14}-8568\,a^{13}\,b^5\,c^5\,d^{13}+18564\,a^{12}\,b^6\,c^6\,d^{12}-31824\,a^{11}\,b^7\,c^7\,d^{11}+43758\,a^{10}\,b^8\,c^8\,d^{10}-48620\,a^9\,b^9\,c^9\,d^9+43758\,a^8\,b^{10}\,c^{10}\,d^8-31824\,a^7\,b^{11}\,c^{11}\,d^7+18564\,a^6\,b^{12}\,c^{12}\,d^6-8568\,a^5\,b^{13}\,c^{13}\,d^5+3060\,a^4\,b^{14}\,c^{14}\,d^4-816\,a^3\,b^{15}\,c^{15}\,d^3+153\,a^2\,b^{16}\,c^{16}\,d^2-18\,a\,b^{17}\,c^{17}\,d+b^{18}\,c^{18}\right)}-\frac{{\left(-\frac{2401\,a^5\,b^3\,d^4+6860\,a^4\,b^4\,c\,d^3+7350\,a^3\,b^5\,c^2\,d^2+3500\,a^2\,b^6\,c^3\,d+625\,a\,b^7\,c^4}{4096\,a^{16}\,d^{16}-65536\,a^{15}\,b\,c\,d^{15}+491520\,a^{14}\,b^2\,c^2\,d^{14}-2293760\,a^{13}\,b^3\,c^3\,d^{13}+7454720\,a^{12}\,b^4\,c^4\,d^{12}-17891328\,a^{11}\,b^5\,c^5\,d^{11}+32800768\,a^{10}\,b^6\,c^6\,d^{10}-46858240\,a^9\,b^7\,c^7\,d^9+52715520\,a^8\,b^8\,c^8\,d^8-46858240\,a^7\,b^9\,c^9\,d^7+32800768\,a^6\,b^{10}\,c^{10}\,d^6-17891328\,a^5\,b^{11}\,c^{11}\,d^5+7454720\,a^4\,b^{12}\,c^{12}\,d^4-2293760\,a^3\,b^{13}\,c^{13}\,d^3+491520\,a^2\,b^{14}\,c^{14}\,d^2-65536\,a\,b^{15}\,c^{15}\,d+4096\,b^{16}\,c^{16}}\right)}^{1/4}\,\left(1280\,a^{20}\,b^4\,c\,d^{22}-1280\,a^{19}\,b^5\,c^2\,d^{21}-143360\,a^{18}\,b^6\,c^3\,d^{20}+1423360\,a^{17}\,b^7\,c^4\,d^{19}-7193600\,a^{16}\,b^8\,c^5\,d^{18}+23618560\,a^{15}\,b^9\,c^6\,d^{17}-54978560\,a^{14}\,b^{10}\,c^7\,d^{16}+94382080\,a^{13}\,b^{11}\,c^8\,d^{15}-121172480\,a^{12}\,b^{12}\,c^9\,d^{14}+115315200\,a^{11}\,b^{13}\,c^{10}\,d^{13}-77608960\,a^{10}\,b^{14}\,c^{11}\,d^{12}+31016960\,a^9\,b^{15}\,c^{12}\,d^{11}+465920\,a^8\,b^{16}\,c^{13}\,d^{10}-10501120\,a^7\,b^{17}\,c^{14}\,d^9+8038400\,a^6\,b^{18}\,c^{15}\,d^8-3450880\,a^5\,b^{19}\,c^{16}\,d^7+922880\,a^4\,b^{20}\,c^{17}\,d^6-144640\,a^3\,b^{21}\,c^{18}\,d^5+10240\,a^2\,b^{22}\,c^{19}\,d^4\right)}{a^{13}\,d^{13}-13\,a^{12}\,b\,c\,d^{12}+78\,a^{11}\,b^2\,c^2\,d^{11}-286\,a^{10}\,b^3\,c^3\,d^{10}+715\,a^9\,b^4\,c^4\,d^9-1287\,a^8\,b^5\,c^5\,d^8+1716\,a^7\,b^6\,c^6\,d^7-1716\,a^6\,b^7\,c^7\,d^6+1287\,a^5\,b^8\,c^8\,d^5-715\,a^4\,b^9\,c^9\,d^4+286\,a^3\,b^{10}\,c^{10}\,d^3-78\,a^2\,b^{11}\,c^{11}\,d^2+13\,a\,b^{12}\,c^{12}\,d-b^{13}\,c^{13}}\right)\right)\,1{}\mathrm{i}-\frac{\sqrt{x}\,\left(3872225\,a^{12}\,b^7\,d^{13}+120299550\,a^{11}\,b^8\,c\,d^{12}+1143306165\,a^{10}\,b^9\,c^2\,d^{11}+3440955560\,a^9\,b^{10}\,c^3\,d^{10}+5932052274\,a^8\,b^{11}\,c^4\,d^9+6551813940\,a^7\,b^{12}\,c^5\,d^8+4617534530\,a^6\,b^{13}\,c^6\,d^7+2030593320\,a^5\,b^{14}\,c^7\,d^6+537450669\,a^4\,b^{15}\,c^8\,d^5+78440670\,a^3\,b^{16}\,c^9\,d^4+4862025\,a^2\,b^{17}\,c^{10}\,d^3\right)\,1{}\mathrm{i}}{65536\,\left(a^{18}\,d^{18}-18\,a^{17}\,b\,c\,d^{17}+153\,a^{16}\,b^2\,c^2\,d^{16}-816\,a^{15}\,b^3\,c^3\,d^{15}+3060\,a^{14}\,b^4\,c^4\,d^{14}-8568\,a^{13}\,b^5\,c^5\,d^{13}+18564\,a^{12}\,b^6\,c^6\,d^{12}-31824\,a^{11}\,b^7\,c^7\,d^{11}+43758\,a^{10}\,b^8\,c^8\,d^{10}-48620\,a^9\,b^9\,c^9\,d^9+43758\,a^8\,b^{10}\,c^{10}\,d^8-31824\,a^7\,b^{11}\,c^{11}\,d^7+18564\,a^6\,b^{12}\,c^{12}\,d^6-8568\,a^5\,b^{13}\,c^{13}\,d^5+3060\,a^4\,b^{14}\,c^{14}\,d^4-816\,a^3\,b^{15}\,c^{15}\,d^3+153\,a^2\,b^{16}\,c^{16}\,d^2-18\,a\,b^{17}\,c^{17}\,d+b^{18}\,c^{18}\right)}\right)}{{\left(-\frac{2401\,a^5\,b^3\,d^4+6860\,a^4\,b^4\,c\,d^3+7350\,a^3\,b^5\,c^2\,d^2+3500\,a^2\,b^6\,c^3\,d+625\,a\,b^7\,c^4}{4096\,a^{16}\,d^{16}-65536\,a^{15}\,b\,c\,d^{15}+491520\,a^{14}\,b^2\,c^2\,d^{14}-2293760\,a^{13}\,b^3\,c^3\,d^{13}+7454720\,a^{12}\,b^4\,c^4\,d^{12}-17891328\,a^{11}\,b^5\,c^5\,d^{11}+32800768\,a^{10}\,b^6\,c^6\,d^{10}-46858240\,a^9\,b^7\,c^7\,d^9+52715520\,a^8\,b^8\,c^8\,d^8-46858240\,a^7\,b^9\,c^9\,d^7+32800768\,a^6\,b^{10}\,c^{10}\,d^6-17891328\,a^5\,b^{11}\,c^{11}\,d^5+7454720\,a^4\,b^{12}\,c^{12}\,d^4-2293760\,a^3\,b^{13}\,c^{13}\,d^3+491520\,a^2\,b^{14}\,c^{14}\,d^2-65536\,a\,b^{15}\,c^{15}\,d+4096\,b^{16}\,c^{16}}\right)}^{1/4}\,\left({\left(-\frac{2401\,a^5\,b^3\,d^4+6860\,a^4\,b^4\,c\,d^3+7350\,a^3\,b^5\,c^2\,d^2+3500\,a^2\,b^6\,c^3\,d+625\,a\,b^7\,c^4}{4096\,a^{16}\,d^{16}-65536\,a^{15}\,b\,c\,d^{15}+491520\,a^{14}\,b^2\,c^2\,d^{14}-2293760\,a^{13}\,b^3\,c^3\,d^{13}+7454720\,a^{12}\,b^4\,c^4\,d^{12}-17891328\,a^{11}\,b^5\,c^5\,d^{11}+32800768\,a^{10}\,b^6\,c^6\,d^{10}-46858240\,a^9\,b^7\,c^7\,d^9+52715520\,a^8\,b^8\,c^8\,d^8-46858240\,a^7\,b^9\,c^9\,d^7+32800768\,a^6\,b^{10}\,c^{10}\,d^6-17891328\,a^5\,b^{11}\,c^{11}\,d^5+7454720\,a^4\,b^{12}\,c^{12}\,d^4-2293760\,a^3\,b^{13}\,c^{13}\,d^3+491520\,a^2\,b^{14}\,c^{14}\,d^2-65536\,a\,b^{15}\,c^{15}\,d+4096\,b^{16}\,c^{16}}\right)}^{1/4}\,\left(\frac{-\frac{4375\,a^{10}\,b^6\,d^{11}}{8192}+\frac{1473515\,a^9\,b^7\,c\,d^{10}}{2048}+\frac{6507125\,a^8\,b^8\,c^2\,d^9}{512}+\frac{84943363\,a^7\,b^9\,c^3\,d^8}{2048}+\frac{218830061\,a^6\,b^{10}\,c^4\,d^7}{4096}+\frac{69456793\,a^5\,b^{11}\,c^5\,d^6}{2048}+\frac{11560479\,a^4\,b^{12}\,c^6\,d^5}{1024}+\frac{3824793\,a^3\,b^{13}\,c^7\,d^4}{2048}+\frac{972405\,a^2\,b^{14}\,c^8\,d^3}{8192}}{a^{13}\,d^{13}-13\,a^{12}\,b\,c\,d^{12}+78\,a^{11}\,b^2\,c^2\,d^{11}-286\,a^{10}\,b^3\,c^3\,d^{10}+715\,a^9\,b^4\,c^4\,d^9-1287\,a^8\,b^5\,c^5\,d^8+1716\,a^7\,b^6\,c^6\,d^7-1716\,a^6\,b^7\,c^7\,d^6+1287\,a^5\,b^8\,c^8\,d^5-715\,a^4\,b^9\,c^9\,d^4+286\,a^3\,b^{10}\,c^{10}\,d^3-78\,a^2\,b^{11}\,c^{11}\,d^2+13\,a\,b^{12}\,c^{12}\,d-b^{13}\,c^{13}}+{\left(-\frac{2401\,a^5\,b^3\,d^4+6860\,a^4\,b^4\,c\,d^3+7350\,a^3\,b^5\,c^2\,d^2+3500\,a^2\,b^6\,c^3\,d+625\,a\,b^7\,c^4}{4096\,a^{16}\,d^{16}-65536\,a^{15}\,b\,c\,d^{15}+491520\,a^{14}\,b^2\,c^2\,d^{14}-2293760\,a^{13}\,b^3\,c^3\,d^{13}+7454720\,a^{12}\,b^4\,c^4\,d^{12}-17891328\,a^{11}\,b^5\,c^5\,d^{11}+32800768\,a^{10}\,b^6\,c^6\,d^{10}-46858240\,a^9\,b^7\,c^7\,d^9+52715520\,a^8\,b^8\,c^8\,d^8-46858240\,a^7\,b^9\,c^9\,d^7+32800768\,a^6\,b^{10}\,c^{10}\,d^6-17891328\,a^5\,b^{11}\,c^{11}\,d^5+7454720\,a^4\,b^{12}\,c^{12}\,d^4-2293760\,a^3\,b^{13}\,c^{13}\,d^3+491520\,a^2\,b^{14}\,c^{14}\,d^2-65536\,a\,b^{15}\,c^{15}\,d+4096\,b^{16}\,c^{16}}\right)}^{3/4}\,\left(\frac{\sqrt{x}\,\left(6553600\,a^{23}\,b^4\,d^{25}+78643200\,a^{22}\,b^5\,c\,d^{24}-810024960\,a^{21}\,b^6\,c^2\,d^{23}-1490026496\,a^{20}\,b^7\,c^3\,d^{22}+45719224320\,a^{19}\,b^8\,c^4\,d^{21}-273892245504\,a^{18}\,b^9\,c^5\,d^{20}+945071063040\,a^{17}\,b^{10}\,c^6\,d^{19}-2229880750080\,a^{16}\,b^{11}\,c^7\,d^{18}+3867903787008\,a^{15}\,b^{12}\,c^8\,d^{17}-5154201927680\,a^{14}\,b^{13}\,c^9\,d^{16}+5470166188032\,a^{13}\,b^{14}\,c^{10}\,d^{15}-4783425454080\,a^{12}\,b^{15}\,c^{11}\,d^{14}+3520229539840\,a^{11}\,b^{16}\,c^{12}\,d^{13}-2125492912128\,a^{10}\,b^{17}\,c^{13}\,d^{12}+910845542400\,a^9\,b^{18}\,c^{14}\,d^{11}-105331556352\,a^8\,b^{19}\,c^{15}\,d^{10}-218396098560\,a^7\,b^{20}\,c^{16}\,d^9+210842419200\,a^6\,b^{21}\,c^{17}\,d^8-104224784384\,a^5\,b^{22}\,c^{18}\,d^7+31284264960\,a^4\,b^{23}\,c^{19}\,d^6-5420875776\,a^3\,b^{24}\,c^{20}\,d^5+419430400\,a^2\,b^{25}\,c^{21}\,d^4\right)}{65536\,\left(a^{18}\,d^{18}-18\,a^{17}\,b\,c\,d^{17}+153\,a^{16}\,b^2\,c^2\,d^{16}-816\,a^{15}\,b^3\,c^3\,d^{15}+3060\,a^{14}\,b^4\,c^4\,d^{14}-8568\,a^{13}\,b^5\,c^5\,d^{13}+18564\,a^{12}\,b^6\,c^6\,d^{12}-31824\,a^{11}\,b^7\,c^7\,d^{11}+43758\,a^{10}\,b^8\,c^8\,d^{10}-48620\,a^9\,b^9\,c^9\,d^9+43758\,a^8\,b^{10}\,c^{10}\,d^8-31824\,a^7\,b^{11}\,c^{11}\,d^7+18564\,a^6\,b^{12}\,c^{12}\,d^6-8568\,a^5\,b^{13}\,c^{13}\,d^5+3060\,a^4\,b^{14}\,c^{14}\,d^4-816\,a^3\,b^{15}\,c^{15}\,d^3+153\,a^2\,b^{16}\,c^{16}\,d^2-18\,a\,b^{17}\,c^{17}\,d+b^{18}\,c^{18}\right)}+\frac{{\left(-\frac{2401\,a^5\,b^3\,d^4+6860\,a^4\,b^4\,c\,d^3+7350\,a^3\,b^5\,c^2\,d^2+3500\,a^2\,b^6\,c^3\,d+625\,a\,b^7\,c^4}{4096\,a^{16}\,d^{16}-65536\,a^{15}\,b\,c\,d^{15}+491520\,a^{14}\,b^2\,c^2\,d^{14}-2293760\,a^{13}\,b^3\,c^3\,d^{13}+7454720\,a^{12}\,b^4\,c^4\,d^{12}-17891328\,a^{11}\,b^5\,c^5\,d^{11}+32800768\,a^{10}\,b^6\,c^6\,d^{10}-46858240\,a^9\,b^7\,c^7\,d^9+52715520\,a^8\,b^8\,c^8\,d^8-46858240\,a^7\,b^9\,c^9\,d^7+32800768\,a^6\,b^{10}\,c^{10}\,d^6-17891328\,a^5\,b^{11}\,c^{11}\,d^5+7454720\,a^4\,b^{12}\,c^{12}\,d^4-2293760\,a^3\,b^{13}\,c^{13}\,d^3+491520\,a^2\,b^{14}\,c^{14}\,d^2-65536\,a\,b^{15}\,c^{15}\,d+4096\,b^{16}\,c^{16}}\right)}^{1/4}\,\left(1280\,a^{20}\,b^4\,c\,d^{22}-1280\,a^{19}\,b^5\,c^2\,d^{21}-143360\,a^{18}\,b^6\,c^3\,d^{20}+1423360\,a^{17}\,b^7\,c^4\,d^{19}-7193600\,a^{16}\,b^8\,c^5\,d^{18}+23618560\,a^{15}\,b^9\,c^6\,d^{17}-54978560\,a^{14}\,b^{10}\,c^7\,d^{16}+94382080\,a^{13}\,b^{11}\,c^8\,d^{15}-121172480\,a^{12}\,b^{12}\,c^9\,d^{14}+115315200\,a^{11}\,b^{13}\,c^{10}\,d^{13}-77608960\,a^{10}\,b^{14}\,c^{11}\,d^{12}+31016960\,a^9\,b^{15}\,c^{12}\,d^{11}+465920\,a^8\,b^{16}\,c^{13}\,d^{10}-10501120\,a^7\,b^{17}\,c^{14}\,d^9+8038400\,a^6\,b^{18}\,c^{15}\,d^8-3450880\,a^5\,b^{19}\,c^{16}\,d^7+922880\,a^4\,b^{20}\,c^{17}\,d^6-144640\,a^3\,b^{21}\,c^{18}\,d^5+10240\,a^2\,b^{22}\,c^{19}\,d^4\right)}{a^{13}\,d^{13}-13\,a^{12}\,b\,c\,d^{12}+78\,a^{11}\,b^2\,c^2\,d^{11}-286\,a^{10}\,b^3\,c^3\,d^{10}+715\,a^9\,b^4\,c^4\,d^9-1287\,a^8\,b^5\,c^5\,d^8+1716\,a^7\,b^6\,c^6\,d^7-1716\,a^6\,b^7\,c^7\,d^6+1287\,a^5\,b^8\,c^8\,d^5-715\,a^4\,b^9\,c^9\,d^4+286\,a^3\,b^{10}\,c^{10}\,d^3-78\,a^2\,b^{11}\,c^{11}\,d^2+13\,a\,b^{12}\,c^{12}\,d-b^{13}\,c^{13}}\right)\right)+\frac{\sqrt{x}\,\left(3872225\,a^{12}\,b^7\,d^{13}+120299550\,a^{11}\,b^8\,c\,d^{12}+1143306165\,a^{10}\,b^9\,c^2\,d^{11}+3440955560\,a^9\,b^{10}\,c^3\,d^{10}+5932052274\,a^8\,b^{11}\,c^4\,d^9+6551813940\,a^7\,b^{12}\,c^5\,d^8+4617534530\,a^6\,b^{13}\,c^6\,d^7+2030593320\,a^5\,b^{14}\,c^7\,d^6+537450669\,a^4\,b^{15}\,c^8\,d^5+78440670\,a^3\,b^{16}\,c^9\,d^4+4862025\,a^2\,b^{17}\,c^{10}\,d^3\right)}{65536\,\left(a^{18}\,d^{18}-18\,a^{17}\,b\,c\,d^{17}+153\,a^{16}\,b^2\,c^2\,d^{16}-816\,a^{15}\,b^3\,c^3\,d^{15}+3060\,a^{14}\,b^4\,c^4\,d^{14}-8568\,a^{13}\,b^5\,c^5\,d^{13}+18564\,a^{12}\,b^6\,c^6\,d^{12}-31824\,a^{11}\,b^7\,c^7\,d^{11}+43758\,a^{10}\,b^8\,c^8\,d^{10}-48620\,a^9\,b^9\,c^9\,d^9+43758\,a^8\,b^{10}\,c^{10}\,d^8-31824\,a^7\,b^{11}\,c^{11}\,d^7+18564\,a^6\,b^{12}\,c^{12}\,d^6-8568\,a^5\,b^{13}\,c^{13}\,d^5+3060\,a^4\,b^{14}\,c^{14}\,d^4-816\,a^3\,b^{15}\,c^{15}\,d^3+153\,a^2\,b^{16}\,c^{16}\,d^2-18\,a\,b^{17}\,c^{17}\,d+b^{18}\,c^{18}\right)}\right)+{\left(-\frac{2401\,a^5\,b^3\,d^4+6860\,a^4\,b^4\,c\,d^3+7350\,a^3\,b^5\,c^2\,d^2+3500\,a^2\,b^6\,c^3\,d+625\,a\,b^7\,c^4}{4096\,a^{16}\,d^{16}-65536\,a^{15}\,b\,c\,d^{15}+491520\,a^{14}\,b^2\,c^2\,d^{14}-2293760\,a^{13}\,b^3\,c^3\,d^{13}+7454720\,a^{12}\,b^4\,c^4\,d^{12}-17891328\,a^{11}\,b^5\,c^5\,d^{11}+32800768\,a^{10}\,b^6\,c^6\,d^{10}-46858240\,a^9\,b^7\,c^7\,d^9+52715520\,a^8\,b^8\,c^8\,d^8-46858240\,a^7\,b^9\,c^9\,d^7+32800768\,a^6\,b^{10}\,c^{10}\,d^6-17891328\,a^5\,b^{11}\,c^{11}\,d^5+7454720\,a^4\,b^{12}\,c^{12}\,d^4-2293760\,a^3\,b^{13}\,c^{13}\,d^3+491520\,a^2\,b^{14}\,c^{14}\,d^2-65536\,a\,b^{15}\,c^{15}\,d+4096\,b^{16}\,c^{16}}\right)}^{1/4}\,\left({\left(-\frac{2401\,a^5\,b^3\,d^4+6860\,a^4\,b^4\,c\,d^3+7350\,a^3\,b^5\,c^2\,d^2+3500\,a^2\,b^6\,c^3\,d+625\,a\,b^7\,c^4}{4096\,a^{16}\,d^{16}-65536\,a^{15}\,b\,c\,d^{15}+491520\,a^{14}\,b^2\,c^2\,d^{14}-2293760\,a^{13}\,b^3\,c^3\,d^{13}+7454720\,a^{12}\,b^4\,c^4\,d^{12}-17891328\,a^{11}\,b^5\,c^5\,d^{11}+32800768\,a^{10}\,b^6\,c^6\,d^{10}-46858240\,a^9\,b^7\,c^7\,d^9+52715520\,a^8\,b^8\,c^8\,d^8-46858240\,a^7\,b^9\,c^9\,d^7+32800768\,a^6\,b^{10}\,c^{10}\,d^6-17891328\,a^5\,b^{11}\,c^{11}\,d^5+7454720\,a^4\,b^{12}\,c^{12}\,d^4-2293760\,a^3\,b^{13}\,c^{13}\,d^3+491520\,a^2\,b^{14}\,c^{14}\,d^2-65536\,a\,b^{15}\,c^{15}\,d+4096\,b^{16}\,c^{16}}\right)}^{1/4}\,\left(\frac{-\frac{4375\,a^{10}\,b^6\,d^{11}}{8192}+\frac{1473515\,a^9\,b^7\,c\,d^{10}}{2048}+\frac{6507125\,a^8\,b^8\,c^2\,d^9}{512}+\frac{84943363\,a^7\,b^9\,c^3\,d^8}{2048}+\frac{218830061\,a^6\,b^{10}\,c^4\,d^7}{4096}+\frac{69456793\,a^5\,b^{11}\,c^5\,d^6}{2048}+\frac{11560479\,a^4\,b^{12}\,c^6\,d^5}{1024}+\frac{3824793\,a^3\,b^{13}\,c^7\,d^4}{2048}+\frac{972405\,a^2\,b^{14}\,c^8\,d^3}{8192}}{a^{13}\,d^{13}-13\,a^{12}\,b\,c\,d^{12}+78\,a^{11}\,b^2\,c^2\,d^{11}-286\,a^{10}\,b^3\,c^3\,d^{10}+715\,a^9\,b^4\,c^4\,d^9-1287\,a^8\,b^5\,c^5\,d^8+1716\,a^7\,b^6\,c^6\,d^7-1716\,a^6\,b^7\,c^7\,d^6+1287\,a^5\,b^8\,c^8\,d^5-715\,a^4\,b^9\,c^9\,d^4+286\,a^3\,b^{10}\,c^{10}\,d^3-78\,a^2\,b^{11}\,c^{11}\,d^2+13\,a\,b^{12}\,c^{12}\,d-b^{13}\,c^{13}}-{\left(-\frac{2401\,a^5\,b^3\,d^4+6860\,a^4\,b^4\,c\,d^3+7350\,a^3\,b^5\,c^2\,d^2+3500\,a^2\,b^6\,c^3\,d+625\,a\,b^7\,c^4}{4096\,a^{16}\,d^{16}-65536\,a^{15}\,b\,c\,d^{15}+491520\,a^{14}\,b^2\,c^2\,d^{14}-2293760\,a^{13}\,b^3\,c^3\,d^{13}+7454720\,a^{12}\,b^4\,c^4\,d^{12}-17891328\,a^{11}\,b^5\,c^5\,d^{11}+32800768\,a^{10}\,b^6\,c^6\,d^{10}-46858240\,a^9\,b^7\,c^7\,d^9+52715520\,a^8\,b^8\,c^8\,d^8-46858240\,a^7\,b^9\,c^9\,d^7+32800768\,a^6\,b^{10}\,c^{10}\,d^6-17891328\,a^5\,b^{11}\,c^{11}\,d^5+7454720\,a^4\,b^{12}\,c^{12}\,d^4-2293760\,a^3\,b^{13}\,c^{13}\,d^3+491520\,a^2\,b^{14}\,c^{14}\,d^2-65536\,a\,b^{15}\,c^{15}\,d+4096\,b^{16}\,c^{16}}\right)}^{3/4}\,\left(\frac{\sqrt{x}\,\left(6553600\,a^{23}\,b^4\,d^{25}+78643200\,a^{22}\,b^5\,c\,d^{24}-810024960\,a^{21}\,b^6\,c^2\,d^{23}-1490026496\,a^{20}\,b^7\,c^3\,d^{22}+45719224320\,a^{19}\,b^8\,c^4\,d^{21}-273892245504\,a^{18}\,b^9\,c^5\,d^{20}+945071063040\,a^{17}\,b^{10}\,c^6\,d^{19}-2229880750080\,a^{16}\,b^{11}\,c^7\,d^{18}+3867903787008\,a^{15}\,b^{12}\,c^8\,d^{17}-5154201927680\,a^{14}\,b^{13}\,c^9\,d^{16}+5470166188032\,a^{13}\,b^{14}\,c^{10}\,d^{15}-4783425454080\,a^{12}\,b^{15}\,c^{11}\,d^{14}+3520229539840\,a^{11}\,b^{16}\,c^{12}\,d^{13}-2125492912128\,a^{10}\,b^{17}\,c^{13}\,d^{12}+910845542400\,a^9\,b^{18}\,c^{14}\,d^{11}-105331556352\,a^8\,b^{19}\,c^{15}\,d^{10}-218396098560\,a^7\,b^{20}\,c^{16}\,d^9+210842419200\,a^6\,b^{21}\,c^{17}\,d^8-104224784384\,a^5\,b^{22}\,c^{18}\,d^7+31284264960\,a^4\,b^{23}\,c^{19}\,d^6-5420875776\,a^3\,b^{24}\,c^{20}\,d^5+419430400\,a^2\,b^{25}\,c^{21}\,d^4\right)}{65536\,\left(a^{18}\,d^{18}-18\,a^{17}\,b\,c\,d^{17}+153\,a^{16}\,b^2\,c^2\,d^{16}-816\,a^{15}\,b^3\,c^3\,d^{15}+3060\,a^{14}\,b^4\,c^4\,d^{14}-8568\,a^{13}\,b^5\,c^5\,d^{13}+18564\,a^{12}\,b^6\,c^6\,d^{12}-31824\,a^{11}\,b^7\,c^7\,d^{11}+43758\,a^{10}\,b^8\,c^8\,d^{10}-48620\,a^9\,b^9\,c^9\,d^9+43758\,a^8\,b^{10}\,c^{10}\,d^8-31824\,a^7\,b^{11}\,c^{11}\,d^7+18564\,a^6\,b^{12}\,c^{12}\,d^6-8568\,a^5\,b^{13}\,c^{13}\,d^5+3060\,a^4\,b^{14}\,c^{14}\,d^4-816\,a^3\,b^{15}\,c^{15}\,d^3+153\,a^2\,b^{16}\,c^{16}\,d^2-18\,a\,b^{17}\,c^{17}\,d+b^{18}\,c^{18}\right)}-\frac{{\left(-\frac{2401\,a^5\,b^3\,d^4+6860\,a^4\,b^4\,c\,d^3+7350\,a^3\,b^5\,c^2\,d^2+3500\,a^2\,b^6\,c^3\,d+625\,a\,b^7\,c^4}{4096\,a^{16}\,d^{16}-65536\,a^{15}\,b\,c\,d^{15}+491520\,a^{14}\,b^2\,c^2\,d^{14}-2293760\,a^{13}\,b^3\,c^3\,d^{13}+7454720\,a^{12}\,b^4\,c^4\,d^{12}-17891328\,a^{11}\,b^5\,c^5\,d^{11}+32800768\,a^{10}\,b^6\,c^6\,d^{10}-46858240\,a^9\,b^7\,c^7\,d^9+52715520\,a^8\,b^8\,c^8\,d^8-46858240\,a^7\,b^9\,c^9\,d^7+32800768\,a^6\,b^{10}\,c^{10}\,d^6-17891328\,a^5\,b^{11}\,c^{11}\,d^5+7454720\,a^4\,b^{12}\,c^{12}\,d^4-2293760\,a^3\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91520\,a^{14}\,b^2\,c^2\,d^{14}-2293760\,a^{13}\,b^3\,c^3\,d^{13}+7454720\,a^{12}\,b^4\,c^4\,d^{12}-17891328\,a^{11}\,b^5\,c^5\,d^{11}+32800768\,a^{10}\,b^6\,c^6\,d^{10}-46858240\,a^9\,b^7\,c^7\,d^9+52715520\,a^8\,b^8\,c^8\,d^8-46858240\,a^7\,b^9\,c^9\,d^7+32800768\,a^6\,b^{10}\,c^{10}\,d^6-17891328\,a^5\,b^{11}\,c^{11}\,d^5+7454720\,a^4\,b^{12}\,c^{12}\,d^4-2293760\,a^3\,b^{13}\,c^{13}\,d^3+491520\,a^2\,b^{14}\,c^{14}\,d^2-65536\,a\,b^{15}\,c^{15}\,d+4096\,b^{16}\,c^{16}}\right)}^{1/4}\,\left({\left(-\frac{2401\,a^5\,b^3\,d^4+6860\,a^4\,b^4\,c\,d^3+7350\,a^3\,b^5\,c^2\,d^2+3500\,a^2\,b^6\,c^3\,d+625\,a\,b^7\,c^4}{4096\,a^{16}\,d^{16}-65536\,a^{15}\,b\,c\,d^{15}+491520\,a^{14}\,b^2\,c^2\,d^{14}-2293760\,a^{13}\,b^3\,c^3\,d^{13}+7454720\,a^{12}\,b^4\,c^4\,d^{12}-17891328\,a^{11}\,b^5\,c^5\,d^{11}+32800768\,a^{10}\,b^6\,c^6\,d^{10}-46858240\,a^9\,b^7\,c^7\,d^9+52715520\,a^8\,b^8\,c^8\,d^8-46858240\,a^7\,b^9\,c^9\,d^7+32800768\,a^6\,b^{10}\,c^{10}\,d^6-17891328\,a^5\,b^{11}\,c^{11}\,d^5+7454720\,a^4\,b^{12}\,c^{12}\,d^4-2293760\,a^3\,b^{13}\,c^{13}\,d^3+491520\,a^2\,b^{14}\,c^{14}\,d^2-65536\,a\,b^{15}\,c^{15}\,d+4096\,b^{16}\,c^{16}}\right)}^{1/4}\,\left(\frac{\left(-\frac{4375\,a^{10}\,b^6\,d^{11}}{8192}+\frac{1473515\,a^9\,b^7\,c\,d^{10}}{2048}+\frac{6507125\,a^8\,b^8\,c^2\,d^9}{512}+\frac{84943363\,a^7\,b^9\,c^3\,d^8}{2048}+\frac{218830061\,a^6\,b^{10}\,c^4\,d^7}{4096}+\frac{69456793\,a^5\,b^{11}\,c^5\,d^6}{2048}+\frac{11560479\,a^4\,b^{12}\,c^6\,d^5}{1024}+\frac{3824793\,a^3\,b^{13}\,c^7\,d^4}{2048}+\frac{972405\,a^2\,b^{14}\,c^8\,d^3}{8192}\right)\,1{}\mathrm{i}}{a^{13}\,d^{13}-13\,a^{12}\,b\,c\,d^{12}+78\,a^{11}\,b^2\,c^2\,d^{11}-286\,a^{10}\,b^3\,c^3\,d^{10}+715\,a^9\,b^4\,c^4\,d^9-1287\,a^8\,b^5\,c^5\,d^8+1716\,a^7\,b^6\,c^6\,d^7-1716\,a^6\,b^7\,c^7\,d^6+1287\,a^5\,b^8\,c^8\,d^5-715\,a^4\,b^9\,c^9\,d^4+286\,a^3\,b^{10}\,c^{10}\,d^3-78\,a^2\,b^{11}\,c^{11}\,d^2+13\,a\,b^{12}\,c^{12}\,d-b^{13}\,c^{13}}-{\left(-\frac{2401\,a^5\,b^3\,d^4+6860\,a^4\,b^4\,c\,d^3+7350\,a^3\,b^5\,c^2\,d^2+3500\,a^2\,b^6\,c^3\,d+625\,a\,b^7\,c^4}{4096\,a^{16}\,d^{16}-65536\,a^{15}\,b\,c\,d^{15}+491520\,a^{14}\,b^2\,c^2\,d^{14}-2293760\,a^{13}\,b^3\,c^3\,d^{13}+7454720\,a^{12}\,b^4\,c^4\,d^{12}-17891328\,a^{11}\,b^5\,c^5\,d^{11}+32800768\,a^{10}\,b^6\,c^6\,d^{10}-46858240\,a^9\,b^7\,c^7\,d^9+52715520\,a^8\,b^8\,c^8\,d^8-46858240\,a^7\,b^9\,c^9\,d^7+32800768\,a^6\,b^{10}\,c^{10}\,d^6-17891328\,a^5\,b^{11}\,c^{11}\,d^5+7454720\,a^4\,b^{12}\,c^{12}\,d^4-2293760\,a^3\,b^{13}\,c^{13}\,d^3+491520\,a^2\,b^{14}\,c^{14}\,d^2-65536\,a\,b^{15}\,c^{15}\,d+4096\,b^{16}\,c^{16}}\right)}^{3/4}\,\left(-\frac{{\left(-\frac{2401\,a^5\,b^3\,d^4+6860\,a^4\,b^4\,c\,d^3+7350\,a^3\,b^5\,c^2\,d^2+3500\,a^2\,b^6\,c^3\,d+625\,a\,b^7\,c^4}{4096\,a^{16}\,d^{16}-65536\,a^{15}\,b\,c\,d^{15}+491520\,a^{14}\,b^2\,c^2\,d^{14}-2293760\,a^{13}\,b^3\,c^3\,d^{13}+7454720\,a^{12}\,b^4\,c^4\,d^{12}-17891328\,a^{11}\,b^5\,c^5\,d^{11}+32800768\,a^{10}\,b^6\,c^6\,d^{10}-46858240\,a^9\,b^7\,c^7\,d^9+52715520\,a^8\,b^8\,c^8\,d^8-46858240\,a^7\,b^9\,c^9\,d^7+32800768\,a^6\,b^{10}\,c^{10}\,d^6-17891328\,a^5\,b^{11}\,c^{11}\,d^5+7454720\,a^4\,b^{12}\,c^{12}\,d^4-2293760\,a^3\,b^{13}\,c^{13}\,d^3+491520\,a^2\,b^{14}\,c^{14}\,d^2-65536\,a\,b^{15}\,c^{15}\,d+4096\,b^{16}\,c^{16}}\right)}^{1/4}\,\left(1280\,a^{20}\,b^4\,c\,d^{22}-1280\,a^{19}\,b^5\,c^2\,d^{21}-143360\,a^{18}\,b^6\,c^3\,d^{20}+1423360\,a^{17}\,b^7\,c^4\,d^{19}-7193600\,a^{16}\,b^8\,c^5\,d^{18}+23618560\,a^{15}\,b^9\,c^6\,d^{17}-54978560\,a^{14}\,b^{10}\,c^7\,d^{16}+94382080\,a^{13}\,b^{11}\,c^8\,d^{15}-121172480\,a^{12}\,b^{12}\,c^9\,d^{14}+115315200\,a^{11}\,b^{13}\,c^{10}\,d^{13}-77608960\,a^{10}\,b^{14}\,c^{11}\,d^{12}+31016960\,a^9\,b^{15}\,c^{12}\,d^{11}+465920\,a^8\,b^{16}\,c^{13}\,d^{10}-10501120\,a^7\,b^{17}\,c^{14}\,d^9+8038400\,a^6\,b^{18}\,c^{15}\,d^8-3450880\,a^5\,b^{19}\,c^{16}\,d^7+922880\,a^4\,b^{20}\,c^{17}\,d^6-144640\,a^3\,b^{21}\,c^{18}\,d^5+10240\,a^2\,b^{22}\,c^{19}\,d^4\right)}{a^{13}\,d^{13}-13\,a^{12}\,b\,c\,d^{12}+78\,a^{11}\,b^2\,c^2\,d^{11}-286\,a^{10}\,b^3\,c^3\,d^{10}+715\,a^9\,b^4\,c^4\,d^9-1287\,a^8\,b^5\,c^5\,d^8+1716\,a^7\,b^6\,c^6\,d^7-1716\,a^6\,b^7\,c^7\,d^6+1287\,a^5\,b^8\,c^8\,d^5-715\,a^4\,b^9\,c^9\,d^4+286\,a^3\,b^{10}\,c^{10}\,d^3-78\,a^2\,b^{11}\,c^{11}\,d^2+13\,a\,b^{12}\,c^{12}\,d-b^{13}\,c^{13}}+\frac{\sqrt{x}\,\left(6553600\,a^{23}\,b^4\,d^{25}+78643200\,a^{22}\,b^5\,c\,d^{24}-810024960\,a^{21}\,b^6\,c^2\,d^{23}-1490026496\,a^{20}\,b^7\,c^3\,d^{22}+45719224320\,a^{19}\,b^8\,c^4\,d^{21}-273892245504\,a^{18}\,b^9\,c^5\,d^{20}+945071063040\,a^{17}\,b^{10}\,c^6\,d^{19}-2229880750080\,a^{16}\,b^{11}\,c^7\,d^{18}+3867903787008\,a^{15}\,b^{12}\,c^8\,d^{17}-5154201927680\,a^{14}\,b^{13}\,c^9\,d^{16}+5470166188032\,a^{13}\,b^{14}\,c^{10}\,d^{15}-4783425454080\,a^{12}\,b^{15}\,c^{11}\,d^{14}+3520229539840\,a^{11}\,b^{16}\,c^{12}\,d^{13}-2125492912128\,a^{10}\,b^{17}\,c^{13}\,d^{12}+910845542400\,a^9\,b^{18}\,c^{14}\,d^{11}-105331556352\,a^8\,b^{19}\,c^{15}\,d^{10}-218396098560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8240\,a^7\,b^9\,c^9\,d^7+32800768\,a^6\,b^{10}\,c^{10}\,d^6-17891328\,a^5\,b^{11}\,c^{11}\,d^5+7454720\,a^4\,b^{12}\,c^{12}\,d^4-2293760\,a^3\,b^{13}\,c^{13}\,d^3+491520\,a^2\,b^{14}\,c^{14}\,d^2-65536\,a\,b^{15}\,c^{15}\,d+4096\,b^{16}\,c^{16}}\right)}^{1/4}\,\left(1280\,a^{20}\,b^4\,c\,d^{22}-1280\,a^{19}\,b^5\,c^2\,d^{21}-143360\,a^{18}\,b^6\,c^3\,d^{20}+1423360\,a^{17}\,b^7\,c^4\,d^{19}-7193600\,a^{16}\,b^8\,c^5\,d^{18}+23618560\,a^{15}\,b^9\,c^6\,d^{17}-54978560\,a^{14}\,b^{10}\,c^7\,d^{16}+94382080\,a^{13}\,b^{11}\,c^8\,d^{15}-121172480\,a^{12}\,b^{12}\,c^9\,d^{14}+115315200\,a^{11}\,b^{13}\,c^{10}\,d^{13}-77608960\,a^{10}\,b^{14}\,c^{11}\,d^{12}+31016960\,a^9\,b^{15}\,c^{12}\,d^{11}+465920\,a^8\,b^{16}\,c^{13}\,d^{10}-10501120\,a^7\,b^{17}\,c^{14}\,d^9+8038400\,a^6\,b^{18}\,c^{15}\,d^8-3450880\,a^5\,b^{19}\,c^{16}\,d^7+922880\,a^4\,b^{20}\,c^{17}\,d^6-144640\,a^3\,b^{21}\,c^{18}\,d^5+10240\,a^2\,b^{22}\,c^{19}\,d^4\right)}{a^{13}\,d^{13}-13\,a^{12}\,b\,c\,d^{12}+78\,a^{11}\,b^2\,c^2\,d^{11}-286\,a^{10}\,b^3\,c^3\,d^{10}+715\,a^9\,b^4\,c^4\,d^9-1287\,a^8\,b^5\,c^5\,d^8+1716\,a^7\,b^6\,c^6\,d^7-1716\,a^6\,b^7\,c^7\,d^6+1287\,a^5\,b^8\,c^8\,d^5-715\,a^4\,b^9\,c^9\,d^4+286\,a^3\,b^{10}\,c^{10}\,d^3-78\,a^2\,b^{11}\,c^{11}\,d^2+13\,a\,b^{12}\,c^{12}\,d-b^{13}\,c^{13}}+\frac{\sqrt{x}\,\left(6553600\,a^{23}\,b^4\,d^{25}+78643200\,a^{22}\,b^5\,c\,d^{24}-810024960\,a^{21}\,b^6\,c^2\,d^{23}-1490026496\,a^{20}\,b^7\,c^3\,d^{22}+45719224320\,a^{19}\,b^8\,c^4\,d^{21}-273892245504\,a^{18}\,b^9\,c^5\,d^{20}+945071063040\,a^{17}\,b^{10}\,c^6\,d^{19}-2229880750080\,a^{16}\,b^{11}\,c^7\,d^{18}+3867903787008\,a^{15}\,b^{12}\,c^8\,d^{17}-5154201927680\,a^{14}\,b^{13}\,c^9\,d^{16}+5470166188032\,a^{13}\,b^{14}\,c^{10}\,d^{15}-4783425454080\,a^{12}\,b^{15}\,c^{11}\,d^{14}+3520229539840\,a^{11}\,b^{16}\,c^{12}\,d^{13}-2125492912128\,a^{10}\,b^{17}\,c^{13}\,d^{12}+910845542400\,a^9\,b^{18}\,c^{14}\,d^{11}-105331556352\,a^8\,b^{19}\,c^{15}\,d^{10}-218396098560\,a^7\,b^{20}\,c^{16}\,d^9+210842419200\,a^6\,b^{21}\,c^{17}\,d^8-104224784384\,a^5\,b^{22}\,c^{18}\,d^7+31284264960\,a^4\,b^{23}\,c^{19}\,d^6-5420875776\,a^3\,b^{24}\,c^{20}\,d^5+419430400\,a^2\,b^{25}\,c^{21}\,d^4\right)\,1{}\mathrm{i}}{65536\,\left(a^{18}\,d^{18}-18\,a^{17}\,b\,c\,d^{17}+153\,a^{16}\,b^2\,c^2\,d^{16}-816\,a^{15}\,b^3\,c^3\,d^{15}+3060\,a^{14}\,b^4\,c^4\,d^{14}-8568\,a^{13}\,b^5\,c^5\,d^{13}+18564\,a^{12}\,b^6\,c^6\,d^{12}-31824\,a^{11}\,b^7\,c^7\,d^{11}+43758\,a^{10}\,b^8\,c^8\,d^{10}-48620\,a^9\,b^9\,c^9\,d^9+43758\,a^8\,b^{10}\,c^{10}\,d^8-31824\,a^7\,b^{11}\,c^{11}\,d^7+18564\,a^6\,b^{12}\,c^{12}\,d^6-8568\,a^5\,b^{13}\,c^{13}\,d^5+3060\,a^4\,b^{14}\,c^{14}\,d^4-816\,a^3\,b^{15}\,c^{15}\,d^3+153\,a^2\,b^{16}\,c^{16}\,d^2-18\,a\,b^{17}\,c^{17}\,d+b^{18}\,c^{18}\right)}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}-\frac{\sqrt{x}\,\left(3872225\,a^{12}\,b^7\,d^{13}+120299550\,a^{11}\,b^8\,c\,d^{12}+1143306165\,a^{10}\,b^9\,c^2\,d^{11}+3440955560\,a^9\,b^{10}\,c^3\,d^{10}+5932052274\,a^8\,b^{11}\,c^4\,d^9+6551813940\,a^7\,b^{12}\,c^5\,d^8+4617534530\,a^6\,b^{13}\,c^6\,d^7+2030593320\,a^5\,b^{14}\,c^7\,d^6+537450669\,a^4\,b^{15}\,c^8\,d^5+78440670\,a^3\,b^{16}\,c^9\,d^4+4862025\,a^2\,b^{17}\,c^{10}\,d^3\right)\,1{}\mathrm{i}}{65536\,\left(a^{18}\,d^{18}-18\,a^{17}\,b\,c\,d^{17}+153\,a^{16}\,b^2\,c^2\,d^{16}-816\,a^{15}\,b^3\,c^3\,d^{15}+3060\,a^{14}\,b^4\,c^4\,d^{14}-8568\,a^{13}\,b^5\,c^5\,d^{13}+18564\,a^{12}\,b^6\,c^6\,d^{12}-31824\,a^{11}\,b^7\,c^7\,d^{11}+43758\,a^{10}\,b^8\,c^8\,d^{10}-48620\,a^9\,b^9\,c^9\,d^9+43758\,a^8\,b^{10}\,c^{10}\,d^8-31824\,a^7\,b^{11}\,c^{11}\,d^7+18564\,a^6\,b^{12}\,c^{12}\,d^6-8568\,a^5\,b^{13}\,c^{13}\,d^5+3060\,a^4\,b^{14}\,c^{14}\,d^4-816\,a^3\,b^{15}\,c^{15}\,d^3+153\,a^2\,b^{16}\,c^{16}\,d^2-18\,a\,b^{17}\,c^{17}\,d+b^{18}\,c^{18}\right)}\right)+{\left(-\frac{2401\,a^5\,b^3\,d^4+6860\,a^4\,b^4\,c\,d^3+7350\,a^3\,b^5\,c^2\,d^2+3500\,a^2\,b^6\,c^3\,d+625\,a\,b^7\,c^4}{4096\,a^{16}\,d^{16}-65536\,a^{15}\,b\,c\,d^{15}+491520\,a^{14}\,b^2\,c^2\,d^{14}-2293760\,a^{13}\,b^3\,c^3\,d^{13}+7454720\,a^{12}\,b^4\,c^4\,d^{12}-17891328\,a^{11}\,b^5\,c^5\,d^{11}+32800768\,a^{10}\,b^6\,c^6\,d^{10}-46858240\,a^9\,b^7\,c^7\,d^9+52715520\,a^8\,b^8\,c^8\,d^8-46858240\,a^7\,b^9\,c^9\,d^7+32800768\,a^6\,b^{10}\,c^{10}\,d^6-17891328\,a^5\,b^{11}\,c^{11}\,d^5+7454720\,a^4\,b^{12}\,c^{12}\,d^4-2293760\,a^3\,b^{13}\,c^{13}\,d^3+491520\,a^2\,b^{14}\,c^{14}\,d^2-65536\,a\,b^{15}\,c^{15}\,d+4096\,b^{16}\,c^{16}}\right)}^{1/4}\,\left({\left(-\frac{2401\,a^5\,b^3\,d^4+6860\,a^4\,b^4\,c\,d^3+7350\,a^3\,b^5\,c^2\,d^2+3500\,a^2\,b^6\,c^3\,d+625\,a\,b^7\,c^4}{4096\,a^{16}\,d^{16}-65536\,a^{15}\,b\,c\,d^{15}+491520\,a^{14}\,b^2\,c^2\,d^{14}-2293760\,a^{13}\,b^3\,c^3\,d^{13}+7454720\,a^{12}\,b^4\,c^4\,d^{12}-17891328\,a^{11}\,b^5\,c^5\,d^{11}+32800768\,a^{10}\,b^6\,c^6\,d^{10}-46858240\,a^9\,b^7\,c^7\,d^9+52715520\,a^8\,b^8\,c^8\,d^8-46858240\,a^7\,b^9\,c^9\,d^7+32800768\,a^6\,b^{10}\,c^{10}\,d^6-17891328\,a^5\,b^{11}\,c^{11}\,d^5+7454720\,a^4\,b^{12}\,c^{12}\,d^4-2293760\,a^3\,b^{13}\,c^{13}\,d^3+491520\,a^2\,b^{14}\,c^{14}\,d^2-65536\,a\,b^{15}\,c^{15}\,d+4096\,b^{16}\,c^{16}}\right)}^{1/4}\,\left(\frac{\left(-\frac{4375\,a^{10}\,b^6\,d^{11}}{8192}+\frac{1473515\,a^9\,b^7\,c\,d^{10}}{2048}+\frac{6507125\,a^8\,b^8\,c^2\,d^9}{512}+\frac{84943363\,a^7\,b^9\,c^3\,d^8}{2048}+\frac{218830061\,a^6\,b^{10}\,c^4\,d^7}{4096}+\frac{69456793\,a^5\,b^{11}\,c^5\,d^6}{2048}+\frac{11560479\,a^4\,b^{12}\,c^6\,d^5}{1024}+\frac{3824793\,a^3\,b^{13}\,c^7\,d^4}{2048}+\frac{972405\,a^2\,b^{14}\,c^8\,d^3}{8192}\right)\,1{}\mathrm{i}}{a^{13}\,d^{13}-13\,a^{12}\,b\,c\,d^{12}+78\,a^{11}\,b^2\,c^2\,d^{11}-286\,a^{10}\,b^3\,c^3\,d^{10}+715\,a^9\,b^4\,c^4\,d^9-1287\,a^8\,b^5\,c^5\,d^8+1716\,a^7\,b^6\,c^6\,d^7-1716\,a^6\,b^7\,c^7\,d^6+1287\,a^5\,b^8\,c^8\,d^5-715\,a^4\,b^9\,c^9\,d^4+286\,a^3\,b^{10}\,c^{10}\,d^3-78\,a^2\,b^{11}\,c^{11}\,d^2+13\,a\,b^{12}\,c^{12}\,d-b^{13}\,c^{13}}-{\left(-\frac{2401\,a^5\,b^3\,d^4+6860\,a^4\,b^4\,c\,d^3+7350\,a^3\,b^5\,c^2\,d^2+3500\,a^2\,b^6\,c^3\,d+625\,a\,b^7\,c^4}{4096\,a^{16}\,d^{16}-65536\,a^{15}\,b\,c\,d^{15}+491520\,a^{14}\,b^2\,c^2\,d^{14}-2293760\,a^{13}\,b^3\,c^3\,d^{13}+7454720\,a^{12}\,b^4\,c^4\,d^{12}-17891328\,a^{11}\,b^5\,c^5\,d^{11}+32800768\,a^{10}\,b^6\,c^6\,d^{10}-46858240\,a^9\,b^7\,c^7\,d^9+52715520\,a^8\,b^8\,c^8\,d^8-46858240\,a^7\,b^9\,c^9\,d^7+32800768\,a^6\,b^{10}\,c^{10}\,d^6-17891328\,a^5\,b^{11}\,c^{11}\,d^5+7454720\,a^4\,b^{12}\,c^{12}\,d^4-2293760\,a^3\,b^{13}\,c^{13}\,d^3+491520\,a^2\,b^{14}\,c^{14}\,d^2-65536\,a\,b^{15}\,c^{15}\,d+4096\,b^{16}\,c^{16}}\right)}^{3/4}\,\left(-\frac{{\left(-\frac{2401\,a^5\,b^3\,d^4+6860\,a^4\,b^4\,c\,d^3+7350\,a^3\,b^5\,c^2\,d^2+3500\,a^2\,b^6\,c^3\,d+625\,a\,b^7\,c^4}{4096\,a^{16}\,d^{16}-65536\,a^{15}\,b\,c\,d^{15}+491520\,a^{14}\,b^2\,c^2\,d^{14}-2293760\,a^{13}\,b^3\,c^3\,d^{13}+7454720\,a^{12}\,b^4\,c^4\,d^{12}-17891328\,a^{11}\,b^5\,c^5\,d^{11}+32800768\,a^{10}\,b^6\,c^6\,d^{10}-46858240\,a^9\,b^7\,c^7\,d^9+52715520\,a^8\,b^8\,c^8\,d^8-46858240\,a^7\,b^9\,c^9\,d^7+32800768\,a^6\,b^{10}\,c^{10}\,d^6-17891328\,a^5\,b^{11}\,c^{11}\,d^5+7454720\,a^4\,b^{12}\,c^{12}\,d^4-2293760\,a^3\,b^{13}\,c^{13}\,d^3+491520\,a^2\,b^{14}\,c^{14}\,d^2-65536\,a\,b^{15}\,c^{15}\,d+4096\,b^{16}\,c^{16}}\right)}^{1/4}\,\left(1280\,a^{20}\,b^4\,c\,d^{22}-1280\,a^{19}\,b^5\,c^2\,d^{21}-143360\,a^{18}\,b^6\,c^3\,d^{20}+1423360\,a^{17}\,b^7\,c^4\,d^{19}-7193600\,a^{16}\,b^8\,c^5\,d^{18}+23618560\,a^{15}\,b^9\,c^6\,d^{17}-54978560\,a^{14}\,b^{10}\,c^7\,d^{16}+94382080\,a^{13}\,b^{11}\,c^8\,d^{15}-121172480\,a^{12}\,b^{12}\,c^9\,d^{14}+115315200\,a^{11}\,b^{13}\,c^{10}\,d^{13}-77608960\,a^{10}\,b^{14}\,c^{11}\,d^{12}+31016960\,a^9\,b^{15}\,c^{12}\,d^{11}+465920\,a^8\,b^{16}\,c^{13}\,d^{10}-10501120\,a^7\,b^{17}\,c^{14}\,d^9+8038400\,a^6\,b^{18}\,c^{15}\,d^8-3450880\,a^5\,b^{19}\,c^{16}\,d^7+922880\,a^4\,b^{20}\,c^{17}\,d^6-144640\,a^3\,b^{21}\,c^{18}\,d^5+10240\,a^2\,b^{22}\,c^{19}\,d^4\right)}{a^{13}\,d^{13}-13\,a^{12}\,b\,c\,d^{12}+78\,a^{11}\,b^2\,c^2\,d^{11}-286\,a^{10}\,b^3\,c^3\,d^{10}+715\,a^9\,b^4\,c^4\,d^9-1287\,a^8\,b^5\,c^5\,d^8+1716\,a^7\,b^6\,c^6\,d^7-1716\,a^6\,b^7\,c^7\,d^6+1287\,a^5\,b^8\,c^8\,d^5-715\,a^4\,b^9\,c^9\,d^4+286\,a^3\,b^{10}\,c^{10}\,d^3-78\,a^2\,b^{11}\,c^{11}\,d^2+13\,a\,b^{12}\,c^{12}\,d-b^{13}\,c^{13}}+\frac{\sqrt{x}\,\left(6553600\,a^{23}\,b^4\,d^{25}+78643200\,a^{22}\,b^5\,c\,d^{24}-810024960\,a^{21}\,b^6\,c^2\,d^{23}-1490026496\,a^{20}\,b^7\,c^3\,d^{22}+45719224320\,a^{19}\,b^8\,c^4\,d^{21}-273892245504\,a^{18}\,b^9\,c^5\,d^{20}+945071063040\,a^{17}\,b^{10}\,c^6\,d^{19}-2229880750080\,a^{16}\,b^{11}\,c^7\,d^{18}+3867903787008\,a^{15}\,b^{12}\,c^8\,d^{17}-5154201927680\,a^{14}\,b^{13}\,c^9\,d^{16}+5470166188032\,a^{13}\,b^{14}\,c^{10}\,d^{15}-4783425454080\,a^{12}\,b^{15}\,c^{11}\,d^{14}+3520229539840\,a^{11}\,b^{16}\,c^{12}\,d^{13}-2125492912128\,a^{10}\,b^{17}\,c^{13}\,d^{12}+910845542400\,a^9\,b^{18}\,c^{14}\,d^{11}-105331556352\,a^8\,b^{19}\,c^{15}\,d^{10}-218396098560\,a^7\,b^{20}\,c^{16}\,d^9+210842419200\,a^6\,b^{21}\,c^{17}\,d^8-104224784384\,a^5\,b^{22}\,c^{18}\,d^7+31284264960\,a^4\,b^{23}\,c^{19}\,d^6-5420875776\,a^3\,b^{24}\,c^{20}\,d^5+419430400\,a^2\,b^{25}\,c^{21}\,d^4\right)\,1{}\mathrm{i}}{65536\,\left(a^{18}\,d^{18}-18\,a^{17}\,b\,c\,d^{17}+153\,a^{16}\,b^2\,c^2\,d^{16}-816\,a^{15}\,b^3\,c^3\,d^{15}+3060\,a^{14}\,b^4\,c^4\,d^{14}-8568\,a^{13}\,b^5\,c^5\,d^{13}+18564\,a^{12}\,b^6\,c^6\,d^{12}-31824\,a^{11}\,b^7\,c^7\,d^{11}+43758\,a^{10}\,b^8\,c^8\,d^{10}-48620\,a^9\,b^9\,c^9\,d^9+43758\,a^8\,b^{10}\,c^{10}\,d^8-31824\,a^7\,b^{11}\,c^{11}\,d^7+18564\,a^6\,b^{12}\,c^{12}\,d^6-8568\,a^5\,b^{13}\,c^{13}\,d^5+3060\,a^4\,b^{14}\,c^{14}\,d^4-816\,a^3\,b^{15}\,c^{15}\,d^3+153\,a^2\,b^{16}\,c^{16}\,d^2-18\,a\,b^{17}\,c^{17}\,d+b^{18}\,c^{18}\right)}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}+\frac{\sqrt{x}\,\left(3872225\,a^{12}\,b^7\,d^{13}+120299550\,a^{11}\,b^8\,c\,d^{12}+1143306165\,a^{10}\,b^9\,c^2\,d^{11}+3440955560\,a^9\,b^{10}\,c^3\,d^{10}+5932052274\,a^8\,b^{11}\,c^4\,d^9+6551813940\,a^7\,b^{12}\,c^5\,d^8+4617534530\,a^6\,b^{13}\,c^6\,d^7+2030593320\,a^5\,b^{14}\,c^7\,d^6+537450669\,a^4\,b^{15}\,c^8\,d^5+78440670\,a^3\,b^{16}\,c^9\,d^4+4862025\,a^2\,b^{17}\,c^{10}\,d^3\right)\,1{}\mathrm{i}}{65536\,\left(a^{18}\,d^{18}-18\,a^{17}\,b\,c\,d^{17}+153\,a^{16}\,b^2\,c^2\,d^{16}-816\,a^{15}\,b^3\,c^3\,d^{15}+3060\,a^{14}\,b^4\,c^4\,d^{14}-8568\,a^{13}\,b^5\,c^5\,d^{13}+18564\,a^{12}\,b^6\,c^6\,d^{12}-31824\,a^{11}\,b^7\,c^7\,d^{11}+43758\,a^{10}\,b^8\,c^8\,d^{10}-48620\,a^9\,b^9\,c^9\,d^9+43758\,a^8\,b^{10}\,c^{10}\,d^8-31824\,a^7\,b^{11}\,c^{11}\,d^7+18564\,a^6\,b^{12}\,c^{12}\,d^6-8568\,a^5\,b^{13}\,c^{13}\,d^5+3060\,a^4\,b^{14}\,c^{14}\,d^4-816\,a^3\,b^{15}\,c^{15}\,d^3+153\,a^2\,b^{16}\,c^{16}\,d^2-18\,a\,b^{17}\,c^{17}\,d+b^{18}\,c^{18}\right)}\right)}\right)\,{\left(-\frac{2401\,a^5\,b^3\,d^4+6860\,a^4\,b^4\,c\,d^3+7350\,a^3\,b^5\,c^2\,d^2+3500\,a^2\,b^6\,c^3\,d+625\,a\,b^7\,c^4}{4096\,a^{16}\,d^{16}-65536\,a^{15}\,b\,c\,d^{15}+491520\,a^{14}\,b^2\,c^2\,d^{14}-2293760\,a^{13}\,b^3\,c^3\,d^{13}+7454720\,a^{12}\,b^4\,c^4\,d^{12}-17891328\,a^{11}\,b^5\,c^5\,d^{11}+32800768\,a^{10}\,b^6\,c^6\,d^{10}-46858240\,a^9\,b^7\,c^7\,d^9+52715520\,a^8\,b^8\,c^8\,d^8-46858240\,a^7\,b^9\,c^9\,d^7+32800768\,a^6\,b^{10}\,c^{10}\,d^6-17891328\,a^5\,b^{11}\,c^{11}\,d^5+7454720\,a^4\,b^{12}\,c^{12}\,d^4-2293760\,a^3\,b^{13}\,c^{13}\,d^3+491520\,a^2\,b^{14}\,c^{14}\,d^2-65536\,a\,b^{15}\,c^{15}\,d+4096\,b^{16}\,c^{16}}\right)}^{1/4}","Not used",1,"2*atan(-((((((1473515*a^9*b^7*c*d^10)/2048 - (4375*a^10*b^6*d^11)/8192 + (972405*a^2*b^14*c^8*d^3)/8192 + (3824793*a^3*b^13*c^7*d^4)/2048 + (11560479*a^4*b^12*c^6*d^5)/1024 + (69456793*a^5*b^11*c^5*d^6)/2048 + (218830061*a^6*b^10*c^4*d^7)/4096 + (84943363*a^7*b^9*c^3*d^8)/2048 + (6507125*a^8*b^8*c^2*d^9)/512)*1i)/(a^13*d^13 - b^13*c^13 - 78*a^2*b^11*c^11*d^2 + 286*a^3*b^10*c^10*d^3 - 715*a^4*b^9*c^9*d^4 + 1287*a^5*b^8*c^8*d^5 - 1716*a^6*b^7*c^7*d^6 + 1716*a^7*b^6*c^6*d^7 - 1287*a^8*b^5*c^5*d^8 + 715*a^9*b^4*c^4*d^9 - 286*a^10*b^3*c^3*d^10 + 78*a^11*b^2*c^2*d^11 + 13*a*b^12*c^12*d - 13*a^12*b*c*d^12) + (-(625*a^8*d^8 + 194481*b^8*c^8 + 13150620*a^2*b^6*c^6*d^2 + 30664200*a^3*b^5*c^5*d^3 + 30250150*a^4*b^4*c^4*d^4 + 7301000*a^5*b^3*c^3*d^5 + 745500*a^6*b^2*c^2*d^6 + 2593080*a*b^7*c^7*d + 35000*a^7*b*c*d^7)/(16777216*b^16*c^19*d + 16777216*a^16*c^3*d^17 - 268435456*a*b^15*c^18*d^2 - 268435456*a^15*b*c^4*d^16 + 2013265920*a^2*b^14*c^17*d^3 - 9395240960*a^3*b^13*c^16*d^4 + 30534533120*a^4*b^12*c^15*d^5 - 73282879488*a^5*b^11*c^14*d^6 + 134351945728*a^6*b^10*c^13*d^7 - 191931351040*a^7*b^9*c^12*d^8 + 215922769920*a^8*b^8*c^11*d^9 - 191931351040*a^9*b^7*c^10*d^10 + 134351945728*a^10*b^6*c^9*d^11 - 73282879488*a^11*b^5*c^8*d^12 + 30534533120*a^12*b^4*c^7*d^13 - 9395240960*a^13*b^3*c^6*d^14 + 2013265920*a^14*b^2*c^5*d^15))^(3/4)*(((-(625*a^8*d^8 + 194481*b^8*c^8 + 13150620*a^2*b^6*c^6*d^2 + 30664200*a^3*b^5*c^5*d^3 + 30250150*a^4*b^4*c^4*d^4 + 7301000*a^5*b^3*c^3*d^5 + 745500*a^6*b^2*c^2*d^6 + 2593080*a*b^7*c^7*d + 35000*a^7*b*c*d^7)/(16777216*b^16*c^19*d + 16777216*a^16*c^3*d^17 - 268435456*a*b^15*c^18*d^2 - 268435456*a^15*b*c^4*d^16 + 2013265920*a^2*b^14*c^17*d^3 - 9395240960*a^3*b^13*c^16*d^4 + 30534533120*a^4*b^12*c^15*d^5 - 73282879488*a^5*b^11*c^14*d^6 + 134351945728*a^6*b^10*c^13*d^7 - 191931351040*a^7*b^9*c^12*d^8 + 215922769920*a^8*b^8*c^11*d^9 - 191931351040*a^9*b^7*c^10*d^10 + 134351945728*a^10*b^6*c^9*d^11 - 73282879488*a^11*b^5*c^8*d^12 + 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104224784384*a^5*b^22*c^18*d^7 + 210842419200*a^6*b^21*c^17*d^8 - 218396098560*a^7*b^20*c^16*d^9 - 105331556352*a^8*b^19*c^15*d^10 + 910845542400*a^9*b^18*c^14*d^11 - 2125492912128*a^10*b^17*c^13*d^12 + 3520229539840*a^11*b^16*c^12*d^13 - 4783425454080*a^12*b^15*c^11*d^14 + 5470166188032*a^13*b^14*c^10*d^15 - 5154201927680*a^14*b^13*c^9*d^16 + 3867903787008*a^15*b^12*c^8*d^17 - 2229880750080*a^16*b^11*c^7*d^18 + 945071063040*a^17*b^10*c^6*d^19 - 273892245504*a^18*b^9*c^5*d^20 + 45719224320*a^19*b^8*c^4*d^21 - 1490026496*a^20*b^7*c^3*d^22 - 810024960*a^21*b^6*c^2*d^23)*1i)/(65536*(a^18*d^18 + b^18*c^18 + 153*a^2*b^16*c^16*d^2 - 816*a^3*b^15*c^15*d^3 + 3060*a^4*b^14*c^14*d^4 - 8568*a^5*b^13*c^13*d^5 + 18564*a^6*b^12*c^12*d^6 - 31824*a^7*b^11*c^11*d^7 + 43758*a^8*b^10*c^10*d^8 - 48620*a^9*b^9*c^9*d^9 + 43758*a^10*b^8*c^8*d^10 - 31824*a^11*b^7*c^7*d^11 + 18564*a^12*b^6*c^6*d^12 - 8568*a^13*b^5*c^5*d^13 + 3060*a^14*b^4*c^4*d^14 - 816*a^15*b^3*c^3*d^15 + 153*a^16*b^2*c^2*d^16 - 18*a*b^17*c^17*d - 18*a^17*b*c*d^17)) + ((-(625*a*b^7*c^4 + 2401*a^5*b^3*d^4 + 3500*a^2*b^6*c^3*d + 6860*a^4*b^4*c*d^3 + 7350*a^3*b^5*c^2*d^2)/(4096*a^16*d^16 + 4096*b^16*c^16 + 491520*a^2*b^14*c^14*d^2 - 2293760*a^3*b^13*c^13*d^3 + 7454720*a^4*b^12*c^12*d^4 - 17891328*a^5*b^11*c^11*d^5 + 32800768*a^6*b^10*c^10*d^6 - 46858240*a^7*b^9*c^9*d^7 + 52715520*a^8*b^8*c^8*d^8 - 46858240*a^9*b^7*c^7*d^9 + 32800768*a^10*b^6*c^6*d^10 - 17891328*a^11*b^5*c^5*d^11 + 7454720*a^12*b^4*c^4*d^12 - 2293760*a^13*b^3*c^3*d^13 + 491520*a^14*b^2*c^2*d^14 - 65536*a*b^15*c^15*d - 65536*a^15*b*c*d^15))^(1/4)*(1280*a^20*b^4*c*d^22 + 10240*a^2*b^22*c^19*d^4 - 144640*a^3*b^21*c^18*d^5 + 922880*a^4*b^20*c^17*d^6 - 3450880*a^5*b^19*c^16*d^7 + 8038400*a^6*b^18*c^15*d^8 - 10501120*a^7*b^17*c^14*d^9 + 465920*a^8*b^16*c^13*d^10 + 31016960*a^9*b^15*c^12*d^11 - 77608960*a^10*b^14*c^11*d^12 + 115315200*a^11*b^13*c^10*d^13 - 121172480*a^12*b^12*c^9*d^14 + 94382080*a^13*b^11*c^8*d^15 - 54978560*a^14*b^10*c^7*d^16 + 23618560*a^15*b^9*c^6*d^17 - 7193600*a^16*b^8*c^5*d^18 + 1423360*a^17*b^7*c^4*d^19 - 143360*a^18*b^6*c^3*d^20 - 1280*a^19*b^5*c^2*d^21))/(a^13*d^13 - b^13*c^13 - 78*a^2*b^11*c^11*d^2 + 286*a^3*b^10*c^10*d^3 - 715*a^4*b^9*c^9*d^4 + 1287*a^5*b^8*c^8*d^5 - 1716*a^6*b^7*c^7*d^6 + 1716*a^7*b^6*c^6*d^7 - 1287*a^8*b^5*c^5*d^8 + 715*a^9*b^4*c^4*d^9 - 286*a^10*b^3*c^3*d^10 + 78*a^11*b^2*c^2*d^11 + 13*a*b^12*c^12*d - 13*a^12*b*c*d^12))*1i)*1i - (x^(1/2)*(3872225*a^12*b^7*d^13 + 120299550*a^11*b^8*c*d^12 + 4862025*a^2*b^17*c^10*d^3 + 78440670*a^3*b^16*c^9*d^4 + 537450669*a^4*b^15*c^8*d^5 + 2030593320*a^5*b^14*c^7*d^6 + 4617534530*a^6*b^13*c^6*d^7 + 6551813940*a^7*b^12*c^5*d^8 + 5932052274*a^8*b^11*c^4*d^9 + 3440955560*a^9*b^10*c^3*d^10 + 1143306165*a^10*b^9*c^2*d^11)*1i)/(65536*(a^18*d^18 + b^18*c^18 + 153*a^2*b^16*c^16*d^2 - 816*a^3*b^15*c^15*d^3 + 3060*a^4*b^14*c^14*d^4 - 8568*a^5*b^13*c^13*d^5 + 18564*a^6*b^12*c^12*d^6 - 31824*a^7*b^11*c^11*d^7 + 43758*a^8*b^10*c^10*d^8 - 48620*a^9*b^9*c^9*d^9 + 43758*a^10*b^8*c^8*d^10 - 31824*a^11*b^7*c^7*d^11 + 18564*a^12*b^6*c^6*d^12 - 8568*a^13*b^5*c^5*d^13 + 3060*a^14*b^4*c^4*d^14 - 816*a^15*b^3*c^3*d^15 + 153*a^16*b^2*c^2*d^16 - 18*a*b^17*c^17*d - 18*a^17*b*c*d^17))) + (-(625*a*b^7*c^4 + 2401*a^5*b^3*d^4 + 3500*a^2*b^6*c^3*d + 6860*a^4*b^4*c*d^3 + 7350*a^3*b^5*c^2*d^2)/(4096*a^16*d^16 + 4096*b^16*c^16 + 491520*a^2*b^14*c^14*d^2 - 2293760*a^3*b^13*c^13*d^3 + 7454720*a^4*b^12*c^12*d^4 - 17891328*a^5*b^11*c^11*d^5 + 32800768*a^6*b^10*c^10*d^6 - 46858240*a^7*b^9*c^9*d^7 + 52715520*a^8*b^8*c^8*d^8 - 46858240*a^9*b^7*c^7*d^9 + 32800768*a^10*b^6*c^6*d^10 - 17891328*a^11*b^5*c^5*d^11 + 7454720*a^12*b^4*c^4*d^12 - 2293760*a^13*b^3*c^3*d^13 + 491520*a^14*b^2*c^2*d^14 - 65536*a*b^15*c^15*d - 65536*a^15*b*c*d^15))^(1/4)*((-(625*a*b^7*c^4 + 2401*a^5*b^3*d^4 + 3500*a^2*b^6*c^3*d + 6860*a^4*b^4*c*d^3 + 7350*a^3*b^5*c^2*d^2)/(4096*a^16*d^16 + 4096*b^16*c^16 + 491520*a^2*b^14*c^14*d^2 - 2293760*a^3*b^13*c^13*d^3 + 7454720*a^4*b^12*c^12*d^4 - 17891328*a^5*b^11*c^11*d^5 + 32800768*a^6*b^10*c^10*d^6 - 46858240*a^7*b^9*c^9*d^7 + 52715520*a^8*b^8*c^8*d^8 - 46858240*a^9*b^7*c^7*d^9 + 32800768*a^10*b^6*c^6*d^10 - 17891328*a^11*b^5*c^5*d^11 + 7454720*a^12*b^4*c^4*d^12 - 2293760*a^13*b^3*c^3*d^13 + 491520*a^14*b^2*c^2*d^14 - 65536*a*b^15*c^15*d - 65536*a^15*b*c*d^15))^(1/4)*((((1473515*a^9*b^7*c*d^10)/2048 - (4375*a^10*b^6*d^11)/8192 + (972405*a^2*b^14*c^8*d^3)/8192 + (3824793*a^3*b^13*c^7*d^4)/2048 + (11560479*a^4*b^12*c^6*d^5)/1024 + (69456793*a^5*b^11*c^5*d^6)/2048 + (218830061*a^6*b^10*c^4*d^7)/4096 + (84943363*a^7*b^9*c^3*d^8)/2048 + (6507125*a^8*b^8*c^2*d^9)/512)*1i)/(a^13*d^13 - b^13*c^13 - 78*a^2*b^11*c^11*d^2 + 286*a^3*b^10*c^10*d^3 - 715*a^4*b^9*c^9*d^4 + 1287*a^5*b^8*c^8*d^5 - 1716*a^6*b^7*c^7*d^6 + 1716*a^7*b^6*c^6*d^7 - 1287*a^8*b^5*c^5*d^8 + 715*a^9*b^4*c^4*d^9 - 286*a^10*b^3*c^3*d^10 + 78*a^11*b^2*c^2*d^11 + 13*a*b^12*c^12*d - 13*a^12*b*c*d^12) - (-(625*a*b^7*c^4 + 2401*a^5*b^3*d^4 + 3500*a^2*b^6*c^3*d + 6860*a^4*b^4*c*d^3 + 7350*a^3*b^5*c^2*d^2)/(4096*a^16*d^16 + 4096*b^16*c^16 + 491520*a^2*b^14*c^14*d^2 - 2293760*a^3*b^13*c^13*d^3 + 7454720*a^4*b^12*c^12*d^4 - 17891328*a^5*b^11*c^11*d^5 + 32800768*a^6*b^10*c^10*d^6 - 46858240*a^7*b^9*c^9*d^7 + 52715520*a^8*b^8*c^8*d^8 - 46858240*a^9*b^7*c^7*d^9 + 32800768*a^10*b^6*c^6*d^10 - 17891328*a^11*b^5*c^5*d^11 + 7454720*a^12*b^4*c^4*d^12 - 2293760*a^13*b^3*c^3*d^13 + 491520*a^14*b^2*c^2*d^14 - 65536*a*b^15*c^15*d - 65536*a^15*b*c*d^15))^(3/4)*((x^(1/2)*(6553600*a^23*b^4*d^25 + 78643200*a^22*b^5*c*d^24 + 419430400*a^2*b^25*c^21*d^4 - 5420875776*a^3*b^24*c^20*d^5 + 31284264960*a^4*b^23*c^19*d^6 - 104224784384*a^5*b^22*c^18*d^7 + 210842419200*a^6*b^21*c^17*d^8 - 218396098560*a^7*b^20*c^16*d^9 - 105331556352*a^8*b^19*c^15*d^10 + 910845542400*a^9*b^18*c^14*d^11 - 2125492912128*a^10*b^17*c^13*d^12 + 3520229539840*a^11*b^16*c^12*d^13 - 4783425454080*a^12*b^15*c^11*d^14 + 5470166188032*a^13*b^14*c^10*d^15 - 5154201927680*a^14*b^13*c^9*d^16 + 3867903787008*a^15*b^12*c^8*d^17 - 2229880750080*a^16*b^11*c^7*d^18 + 945071063040*a^17*b^10*c^6*d^19 - 273892245504*a^18*b^9*c^5*d^20 + 45719224320*a^19*b^8*c^4*d^21 - 1490026496*a^20*b^7*c^3*d^22 - 810024960*a^21*b^6*c^2*d^23)*1i)/(65536*(a^18*d^18 + b^18*c^18 + 153*a^2*b^16*c^16*d^2 - 816*a^3*b^15*c^15*d^3 + 3060*a^4*b^14*c^14*d^4 - 8568*a^5*b^13*c^13*d^5 + 18564*a^6*b^12*c^12*d^6 - 31824*a^7*b^11*c^11*d^7 + 43758*a^8*b^10*c^10*d^8 - 48620*a^9*b^9*c^9*d^9 + 43758*a^10*b^8*c^8*d^10 - 31824*a^11*b^7*c^7*d^11 + 18564*a^12*b^6*c^6*d^12 - 8568*a^13*b^5*c^5*d^13 + 3060*a^14*b^4*c^4*d^14 - 816*a^15*b^3*c^3*d^15 + 153*a^16*b^2*c^2*d^16 - 18*a*b^17*c^17*d - 18*a^17*b*c*d^17)) - ((-(625*a*b^7*c^4 + 2401*a^5*b^3*d^4 + 3500*a^2*b^6*c^3*d + 6860*a^4*b^4*c*d^3 + 7350*a^3*b^5*c^2*d^2)/(4096*a^16*d^16 + 4096*b^16*c^16 + 491520*a^2*b^14*c^14*d^2 - 2293760*a^3*b^13*c^13*d^3 + 7454720*a^4*b^12*c^12*d^4 - 17891328*a^5*b^11*c^11*d^5 + 32800768*a^6*b^10*c^10*d^6 - 46858240*a^7*b^9*c^9*d^7 + 52715520*a^8*b^8*c^8*d^8 - 46858240*a^9*b^7*c^7*d^9 + 32800768*a^10*b^6*c^6*d^10 - 17891328*a^11*b^5*c^5*d^11 + 7454720*a^12*b^4*c^4*d^12 - 2293760*a^13*b^3*c^3*d^13 + 491520*a^14*b^2*c^2*d^14 - 65536*a*b^15*c^15*d - 65536*a^15*b*c*d^15))^(1/4)*(1280*a^20*b^4*c*d^22 + 10240*a^2*b^22*c^19*d^4 - 144640*a^3*b^21*c^18*d^5 + 922880*a^4*b^20*c^17*d^6 - 3450880*a^5*b^19*c^16*d^7 + 8038400*a^6*b^18*c^15*d^8 - 10501120*a^7*b^17*c^14*d^9 + 465920*a^8*b^16*c^13*d^10 + 31016960*a^9*b^15*c^12*d^11 - 77608960*a^10*b^14*c^11*d^12 + 115315200*a^11*b^13*c^10*d^13 - 121172480*a^12*b^12*c^9*d^14 + 94382080*a^13*b^11*c^8*d^15 - 54978560*a^14*b^10*c^7*d^16 + 23618560*a^15*b^9*c^6*d^17 - 7193600*a^16*b^8*c^5*d^18 + 1423360*a^17*b^7*c^4*d^19 - 143360*a^18*b^6*c^3*d^20 - 1280*a^19*b^5*c^2*d^21))/(a^13*d^13 - b^13*c^13 - 78*a^2*b^11*c^11*d^2 + 286*a^3*b^10*c^10*d^3 - 715*a^4*b^9*c^9*d^4 + 1287*a^5*b^8*c^8*d^5 - 1716*a^6*b^7*c^7*d^6 + 1716*a^7*b^6*c^6*d^7 - 1287*a^8*b^5*c^5*d^8 + 715*a^9*b^4*c^4*d^9 - 286*a^10*b^3*c^3*d^10 + 78*a^11*b^2*c^2*d^11 + 13*a*b^12*c^12*d - 13*a^12*b*c*d^12))*1i)*1i + (x^(1/2)*(3872225*a^12*b^7*d^13 + 120299550*a^11*b^8*c*d^12 + 4862025*a^2*b^17*c^10*d^3 + 78440670*a^3*b^16*c^9*d^4 + 537450669*a^4*b^15*c^8*d^5 + 2030593320*a^5*b^14*c^7*d^6 + 4617534530*a^6*b^13*c^6*d^7 + 6551813940*a^7*b^12*c^5*d^8 + 5932052274*a^8*b^11*c^4*d^9 + 3440955560*a^9*b^10*c^3*d^10 + 1143306165*a^10*b^9*c^2*d^11)*1i)/(65536*(a^18*d^18 + b^18*c^18 + 153*a^2*b^16*c^16*d^2 - 816*a^3*b^15*c^15*d^3 + 3060*a^4*b^14*c^14*d^4 - 8568*a^5*b^13*c^13*d^5 + 18564*a^6*b^12*c^12*d^6 - 31824*a^7*b^11*c^11*d^7 + 43758*a^8*b^10*c^10*d^8 - 48620*a^9*b^9*c^9*d^9 + 43758*a^10*b^8*c^8*d^10 - 31824*a^11*b^7*c^7*d^11 + 18564*a^12*b^6*c^6*d^12 - 8568*a^13*b^5*c^5*d^13 + 3060*a^14*b^4*c^4*d^14 - 816*a^15*b^3*c^3*d^15 + 153*a^16*b^2*c^2*d^16 - 18*a*b^17*c^17*d - 18*a^17*b*c*d^17)))))*(-(625*a*b^7*c^4 + 2401*a^5*b^3*d^4 + 3500*a^2*b^6*c^3*d + 6860*a^4*b^4*c*d^3 + 7350*a^3*b^5*c^2*d^2)/(4096*a^16*d^16 + 4096*b^16*c^16 + 491520*a^2*b^14*c^14*d^2 - 2293760*a^3*b^13*c^13*d^3 + 7454720*a^4*b^12*c^12*d^4 - 17891328*a^5*b^11*c^11*d^5 + 32800768*a^6*b^10*c^10*d^6 - 46858240*a^7*b^9*c^9*d^7 + 52715520*a^8*b^8*c^8*d^8 - 46858240*a^9*b^7*c^7*d^9 + 32800768*a^10*b^6*c^6*d^10 - 17891328*a^11*b^5*c^5*d^11 + 7454720*a^12*b^4*c^4*d^12 - 2293760*a^13*b^3*c^3*d^13 + 491520*a^14*b^2*c^2*d^14 - 65536*a*b^15*c^15*d - 65536*a^15*b*c*d^15))^(1/4)","B"
497,1,44169,703,7.631412,"\text{Not used}","int(x^(5/2)/((a + b*x^2)^2*(c + d*x^2)^3),x)","-\mathrm{atan}\left(\frac{\left(\left(\frac{-\frac{27\,a^{24}\,b^4\,d^{27}}{16}+\frac{1863\,a^{23}\,b^5\,c\,d^{26}}{16}-\frac{24867\,a^{22}\,b^6\,c^2\,d^{25}}{8}+\frac{327267\,a^{21}\,b^7\,c^3\,d^{24}}{8}-\frac{4658715\,a^{20}\,b^8\,c^4\,d^{23}}{16}+\frac{19723743\,a^{19}\,b^9\,c^5\,d^{22}}{16}-\frac{6325749\,a^{18}\,b^{10}\,c^6\,d^{21}}{2}+\frac{8300637\,a^{17}\,b^{11}\,c^7\,d^{20}}{2}+\frac{14462037\,a^{16}\,b^{12}\,c^8\,d^{19}}{8}-\frac{166924665\,a^{15}\,b^{13}\,c^9\,d^{18}}{8}+\frac{196146927\,a^{14}\,b^{14}\,c^{10}\,d^{17}}{4}-\frac{274240863\,a^{13}\,b^{15}\,c^{11}\,d^{16}}{4}+\frac{501573033\,a^{12}\,b^{16}\,c^{12}\,d^{15}}{8}-\frac{279642213\,a^{11}\,b^{17}\,c^{13}\,d^{14}}{8}+\frac{12854835\,a^{10}\,b^{18}\,c^{14}\,d^{13}}{2}+\frac{13320261\,a^9\,b^{19}\,c^{15}\,d^{12}}{2}-\frac{93270447\,a^8\,b^{20}\,c^{16}\,d^{11}}{16}+\frac{22410891\,a^7\,b^{21}\,c^{17}\,d^{10}}{16}+\frac{5105997\,a^6\,b^{22}\,c^{18}\,d^9}{8}-\frac{4585005\,a^5\,b^{23}\,c^{19}\,d^8}{8}+\frac{2587113\,a^4\,b^{24}\,c^{20}\,d^7}{16}-\frac{132597\,a^3\,b^{25}\,c^{21}\,d^6}{16}-5184\,a^2\,b^{26}\,c^{22}\,d^5+864\,a\,b^{27}\,c^{23}\,d^4}{-a^{21}\,c^2\,d^{21}+21\,a^{20}\,b\,c^3\,d^{20}-210\,a^{19}\,b^2\,c^4\,d^{19}+1330\,a^{18}\,b^3\,c^5\,d^{18}-5985\,a^{17}\,b^4\,c^6\,d^{17}+20349\,a^{16}\,b^5\,c^7\,d^{16}-54264\,a^{15}\,b^6\,c^8\,d^{15}+116280\,a^{14}\,b^7\,c^9\,d^{14}-203490\,a^{13}\,b^8\,c^{10}\,d^{13}+293930\,a^{12}\,b^9\,c^{11}\,d^{12}-352716\,a^{11}\,b^{10}\,c^{12}\,d^{11}+352716\,a^{10}\,b^{11}\,c^{13}\,d^{10}-293930\,a^9\,b^{12}\,c^{14}\,d^9+203490\,a^8\,b^{13}\,c^{15}\,d^8-116280\,a^7\,b^{14}\,c^{16}\,d^7+54264\,a^6\,b^{15}\,c^{17}\,d^6-20349\,a^5\,b^{16}\,c^{18}\,d^5+5985\,a^4\,b^{17}\,c^{19}\,d^4-1330\,a^3\,b^{18}\,c^{20}\,d^3+210\,a^2\,b^{19}\,c^{21}\,d^2-21\,a\,b^{20}\,c^{22}\,d+b^{21}\,c^{23}}-\frac{9\,\sqrt{x}\,{\left(-\frac{81\,a^8\,d^9-5832\,a^7\,b\,c\,d^8+152604\,a^6\,b^2\,c^2\,d^7-1627128\,a^5\,b^3\,c^3\,d^6+3888486\,a^4\,b^4\,c^4\,d^5+24406920\,a^3\,b^5\,c^5\,d^4+34335900\,a^2\,b^6\,c^6\,d^3+19683000\,a\,b^7\,c^7\,d^2+4100625\,b^8\,c^8\,d}{16777216\,a^{16}\,c^5\,d^{16}-268435456\,a^{15}\,b\,c^6\,d^{15}+2013265920\,a^{14}\,b^2\,c^7\,d^{14}-9395240960\,a^{13}\,b^3\,c^8\,d^{13}+30534533120\,a^{12}\,b^4\,c^9\,d^{12}-73282879488\,a^{11}\,b^5\,c^{10}\,d^{11}+134351945728\,a^{10}\,b^6\,c^{11}\,d^{10}-191931351040\,a^9\,b^7\,c^{12}\,d^9+215922769920\,a^8\,b^8\,c^{13}\,d^8-191931351040\,a^7\,b^9\,c^{14}\,d^7+134351945728\,a^6\,b^{10}\,c^{15}\,d^6-73282879488\,a^5\,b^{11}\,c^{16}\,d^5+30534533120\,a^4\,b^{12}\,c^{17}\,d^4-9395240960\,a^3\,b^{13}\,c^{18}\,d^3+2013265920\,a^2\,b^{14}\,c^{19}\,d^2-268435456\,a\,b^{15}\,c^{20}\,d+16777216\,b^{16}\,c^{21}}\right)}^{1/4}\,\left(262144\,a^{23}\,b^4\,c\,d^{26}-13631488\,a^{22}\,b^5\,c^2\,d^{25}+259522560\,a^{21}\,b^6\,c^3\,d^{24}-2370830336\,a^{20}\,b^7\,c^4\,d^{23}+12955418624\,a^{19}\,b^8\,c^5\,d^{22}-47752151040\,a^{18}\,b^9\,c^6\,d^{21}+127919980544\,a^{17}\,b^{10}\,c^7\,d^{20}-263356153856\,a^{16}\,b^{11}\,c^8\,d^{19}+437990719488\,a^{15}\,b^{12}\,c^9\,d^{18}-615914668032\,a^{14}\,b^{13}\,c^{10}\,d^{17}+754870910976\,a^{13}\,b^{14}\,c^{11}\,d^{16}-805866307584\,a^{12}\,b^{15}\,c^{12}\,d^{15}+724629454848\,a^{11}\,b^{16}\,c^{13}\,d^{14}-518906707968\,a^{10}\,b^{17}\,c^{14}\,d^{13}+273093230592\,a^9\,b^{18}\,c^{15}\,d^{12}-89661636608\,a^8\,b^{19}\,c^{16}\,d^{11}+6940786688\,a^7\,b^{20}\,c^{17}\,d^{10}+8081375232\,a^6\,b^{21}\,c^{18}\,d^9-2827485184\,a^5\,b^{22}\,c^{19}\,d^8-533725184\,a^4\,b^{23}\,c^{20}\,d^7+612630528\,a^3\,b^{24}\,c^{21}\,d^6-167772160\,a^2\,b^{25}\,c^{22}\,d^5+16777216\,a\,b^{26}\,c^{23}\,d^4\right)}{65536\,\left(a^{18}\,c^2\,d^{18}-18\,a^{17}\,b\,c^3\,d^{17}+153\,a^{16}\,b^2\,c^4\,d^{16}-816\,a^{15}\,b^3\,c^5\,d^{15}+3060\,a^{14}\,b^4\,c^6\,d^{14}-8568\,a^{13}\,b^5\,c^7\,d^{13}+18564\,a^{12}\,b^6\,c^8\,d^{12}-31824\,a^{11}\,b^7\,c^9\,d^{11}+43758\,a^{10}\,b^8\,c^{10}\,d^{10}-48620\,a^9\,b^9\,c^{11}\,d^9+43758\,a^8\,b^{10}\,c^{12}\,d^8-31824\,a^7\,b^{11}\,c^{13}\,d^7+18564\,a^6\,b^{12}\,c^{14}\,d^6-8568\,a^5\,b^{13}\,c^{15}\,d^5+3060\,a^4\,b^{14}\,c^{16}\,d^4-816\,a^3\,b^{15}\,c^{17}\,d^3+153\,a^2\,b^{16}\,c^{18}\,d^2-18\,a\,b^{17}\,c^{19}\,d+b^{18}\,c^{20}\right)}\right)\,{\left(-\frac{81\,a^8\,d^9-5832\,a^7\,b\,c\,d^8+152604\,a^6\,b^2\,c^2\,d^7-1627128\,a^5\,b^3\,c^3\,d^6+3888486\,a^4\,b^4\,c^4\,d^5+24406920\,a^3\,b^5\,c^5\,d^4+34335900\,a^2\,b^6\,c^6\,d^3+19683000\,a\,b^7\,c^7\,d^2+4100625\,b^8\,c^8\,d}{16777216\,a^{16}\,c^5\,d^{16}-268435456\,a^{15}\,b\,c^6\,d^{15}+2013265920\,a^{14}\,b^2\,c^7\,d^{14}-9395240960\,a^{13}\,b^3\,c^8\,d^{13}+30534533120\,a^{12}\,b^4\,c^9\,d^{12}-73282879488\,a^{11}\,b^5\,c^{10}\,d^{11}+134351945728\,a^{10}\,b^6\,c^{11}\,d^{10}-191931351040\,a^9\,b^7\,c^{12}\,d^9+215922769920\,a^8\,b^8\,c^{13}\,d^8-191931351040\,a^7\,b^9\,c^{14}\,d^7+134351945728\,a^6\,b^{10}\,c^{15}\,d^6-73282879488\,a^5\,b^{11}\,c^{16}\,d^5+30534533120\,a^4\,b^{12}\,c^{17}\,d^4-9395240960\,a^3\,b^{13}\,c^{18}\,d^3+2013265920\,a^2\,b^{14}\,c^{19}\,d^2-268435456\,a\,b^{15}\,c^{20}\,d+16777216\,b^{16}\,c^{21}}\right)}^{3/4}\,1{}\mathrm{i}-\frac{\sqrt{x}\,\left(729\,a^{11}\,b^8\,d^{15}+367902\,a^{10}\,b^9\,c\,d^{14}-13218147\,a^9\,b^{10}\,c^2\,d^{13}+89841960\,a^8\,b^{11}\,c^3\,d^{12}+406721250\,a^7\,b^{12}\,c^4\,d^{11}+718242228\,a^6\,b^{13}\,c^5\,d^{10}+754592274\,a^5\,b^{14}\,c^6\,d^9+505671336\,a^4\,b^{15}\,c^7\,d^8+206135685\,a^3\,b^{16}\,c^8\,d^7+45453150\,a^2\,b^{17}\,c^9\,d^6+4100625\,a\,b^{18}\,c^{10}\,d^5\right)\,9{}\mathrm{i}}{65536\,\left(a^{18}\,c^2\,d^{18}-18\,a^{17}\,b\,c^3\,d^{17}+153\,a^{16}\,b^2\,c^4\,d^{16}-816\,a^{15}\,b^3\,c^5\,d^{15}+3060\,a^{14}\,b^4\,c^6\,d^{14}-8568\,a^{13}\,b^5\,c^7\,d^{13}+18564\,a^{12}\,b^6\,c^8\,d^{12}-31824\,a^{11}\,b^7\,c^9\,d^{11}+43758\,a^{10}\,b^8\,c^{10}\,d^{10}-48620\,a^9\,b^9\,c^{11}\,d^9+43758\,a^8\,b^{10}\,c^{12}\,d^8-31824\,a^7\,b^{11}\,c^{13}\,d^7+18564\,a^6\,b^{12}\,c^{14}\,d^6-8568\,a^5\,b^{13}\,c^{15}\,d^5+3060\,a^4\,b^{14}\,c^{16}\,d^4-816\,a^3\,b^{15}\,c^{17}\,d^3+153\,a^2\,b^{16}\,c^{18}\,d^2-18\,a\,b^{17}\,c^{19}\,d+b^{18}\,c^{20}\right)}\right)\,{\left(-\frac{81\,a^8\,d^9-5832\,a^7\,b\,c\,d^8+152604\,a^6\,b^2\,c^2\,d^7-1627128\,a^5\,b^3\,c^3\,d^6+3888486\,a^4\,b^4\,c^4\,d^5+24406920\,a^3\,b^5\,c^5\,d^4+34335900\,a^2\,b^6\,c^6\,d^3+19683000\,a\,b^7\,c^7\,d^2+4100625\,b^8\,c^8\,d}{16777216\,a^{16}\,c^5\,d^{16}-268435456\,a^{15}\,b\,c^6\,d^{15}+2013265920\,a^{14}\,b^2\,c^7\,d^{14}-9395240960\,a^{13}\,b^3\,c^8\,d^{13}+30534533120\,a^{12}\,b^4\,c^9\,d^{12}-73282879488\,a^{11}\,b^5\,c^{10}\,d^{11}+134351945728\,a^{10}\,b^6\,c^{11}\,d^{10}-191931351040\,a^9\,b^7\,c^{12}\,d^9+215922769920\,a^8\,b^8\,c^{13}\,d^8-191931351040\,a^7\,b^9\,c^{14}\,d^7+134351945728\,a^6\,b^{10}\,c^{15}\,d^6-73282879488\,a^5\,b^{11}\,c^{16}\,d^5+30534533120\,a^4\,b^{12}\,c^{17}\,d^4-9395240960\,a^3\,b^{13}\,c^{18}\,d^3+2013265920\,a^2\,b^{14}\,c^{19}\,d^2-268435456\,a\,b^{15}\,c^{20}\,d+16777216\,b^{16}\,c^{21}}\right)}^{1/4}-\left(\left(\frac{-\frac{27\,a^{24}\,b^4\,d^{27}}{16}+\frac{1863\,a^{23}\,b^5\,c\,d^{26}}{16}-\frac{24867\,a^{22}\,b^6\,c^2\,d^{25}}{8}+\frac{327267\,a^{21}\,b^7\,c^3\,d^{24}}{8}-\frac{4658715\,a^{20}\,b^8\,c^4\,d^{23}}{16}+\frac{19723743\,a^{19}\,b^9\,c^5\,d^{22}}{16}-\frac{6325749\,a^{18}\,b^{10}\,c^6\,d^{21}}{2}+\frac{8300637\,a^{17}\,b^{11}\,c^7\,d^{20}}{2}+\frac{14462037\,a^{16}\,b^{12}\,c^8\,d^{19}}{8}-\frac{166924665\,a^{15}\,b^{13}\,c^9\,d^{18}}{8}+\frac{196146927\,a^{14}\,b^{14}\,c^{10}\,d^{17}}{4}-\frac{274240863\,a^{13}\,b^{15}\,c^{11}\,d^{16}}{4}+\frac{501573033\,a^{12}\,b^{16}\,c^{12}\,d^{15}}{8}-\frac{279642213\,a^{11}\,b^{17}\,c^{13}\,d^{14}}{8}+\frac{12854835\,a^{10}\,b^{18}\,c^{14}\,d^{13}}{2}+\frac{13320261\,a^9\,b^{19}\,c^{15}\,d^{12}}{2}-\frac{93270447\,a^8\,b^{20}\,c^{16}\,d^{11}}{16}+\frac{22410891\,a^7\,b^{21}\,c^{17}\,d^{10}}{16}+\frac{5105997\,a^6\,b^{22}\,c^{18}\,d^9}{8}-\frac{4585005\,a^5\,b^{23}\,c^{19}\,d^8}{8}+\frac{2587113\,a^4\,b^{24}\,c^{20}\,d^7}{16}-\frac{132597\,a^3\,b^{25}\,c^{21}\,d^6}{16}-5184\,a^2\,b^{26}\,c^{22}\,d^5+864\,a\,b^{27}\,c^{23}\,d^4}{-a^{21}\,c^2\,d^{21}+21\,a^{20}\,b\,c^3\,d^{20}-210\,a^{19}\,b^2\,c^4\,d^{19}+1330\,a^{18}\,b^3\,c^5\,d^{18}-5985\,a^{17}\,b^4\,c^6\,d^{17}+20349\,a^{16}\,b^5\,c^7\,d^{16}-54264\,a^{15}\,b^6\,c^8\,d^{15}+116280\,a^{14}\,b^7\,c^9\,d^{14}-203490\,a^{13}\,b^8\,c^{10}\,d^{13}+293930\,a^{12}\,b^9\,c^{11}\,d^{12}-352716\,a^{11}\,b^{10}\,c^{12}\,d^{11}+352716\,a^{10}\,b^{11}\,c^{13}\,d^{10}-293930\,a^9\,b^{12}\,c^{14}\,d^9+203490\,a^8\,b^{13}\,c^{15}\,d^8-116280\,a^7\,b^{14}\,c^{16}\,d^7+54264\,a^6\,b^{15}\,c^{17}\,d^6-20349\,a^5\,b^{16}\,c^{18}\,d^5+5985\,a^4\,b^{17}\,c^{19}\,d^4-1330\,a^3\,b^{18}\,c^{20}\,d^3+210\,a^2\,b^{19}\,c^{21}\,d^2-21\,a\,b^{20}\,c^{22}\,d+b^{21}\,c^{23}}+\frac{9\,\sqrt{x}\,{\left(-\frac{81\,a^8\,d^9-5832\,a^7\,b\,c\,d^8+152604\,a^6\,b^2\,c^2\,d^7-1627128\,a^5\,b^3\,c^3\,d^6+3888486\,a^4\,b^4\,c^4\,d^5+24406920\,a^3\,b^5\,c^5\,d^4+34335900\,a^2\,b^6\,c^6\,d^3+19683000\,a\,b^7\,c^7\,d^2+4100625\,b^8\,c^8\,d}{16777216\,a^{16}\,c^5\,d^{16}-268435456\,a^{15}\,b\,c^6\,d^{15}+2013265920\,a^{14}\,b^2\,c^7\,d^{14}-9395240960\,a^{13}\,b^3\,c^8\,d^{13}+30534533120\,a^{12}\,b^4\,c^9\,d^{12}-73282879488\,a^{11}\,b^5\,c^{10}\,d^{11}+134351945728\,a^{10}\,b^6\,c^{11}\,d^{10}-191931351040\,a^9\,b^7\,c^{12}\,d^9+215922769920\,a^8\,b^8\,c^{13}\,d^8-191931351040\,a^7\,b^9\,c^{14}\,d^7+134351945728\,a^6\,b^{10}\,c^{15}\,d^6-73282879488\,a^5\,b^{11}\,c^{16}\,d^5+30534533120\,a^4\,b^{12}\,c^{17}\,d^4-9395240960\,a^3\,b^{13}\,c^{18}\,d^3+2013265920\,a^2\,b^{14}\,c^{19}\,d^2-268435456\,a\,b^{15}\,c^{20}\,d+16777216\,b^{16}\,c^{21}}\right)}^{1/4}\,\left(262144\,a^{23}\,b^4\,c\,d^{26}-13631488\,a^{22}\,b^5\,c^2\,d^{25}+259522560\,a^{21}\,b^6\,c^3\,d^{24}-2370830336\,a^{20}\,b^7\,c^4\,d^{23}+12955418624\,a^{19}\,b^8\,c^5\,d^{22}-47752151040\,a^{18}\,b^9\,c^6\,d^{21}+127919980544\,a^{17}\,b^{10}\,c^7\,d^{20}-263356153856\,a^{16}\,b^{11}\,c^8\,d^{19}+437990719488\,a^{15}\,b^{12}\,c^9\,d^{18}-615914668032\,a^{14}\,b^{13}\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8\,b^{13}\,c^{15}\,d^8-116280\,a^7\,b^{14}\,c^{16}\,d^7+54264\,a^6\,b^{15}\,c^{17}\,d^6-20349\,a^5\,b^{16}\,c^{18}\,d^5+5985\,a^4\,b^{17}\,c^{19}\,d^4-1330\,a^3\,b^{18}\,c^{20}\,d^3+210\,a^2\,b^{19}\,c^{21}\,d^2-21\,a\,b^{20}\,c^{22}\,d+b^{21}\,c^{23}}\right)\,1{}\mathrm{i}-\frac{\sqrt{x}\,\left(729\,a^{11}\,b^8\,d^{15}+367902\,a^{10}\,b^9\,c\,d^{14}-13218147\,a^9\,b^{10}\,c^2\,d^{13}+89841960\,a^8\,b^{11}\,c^3\,d^{12}+406721250\,a^7\,b^{12}\,c^4\,d^{11}+718242228\,a^6\,b^{13}\,c^5\,d^{10}+754592274\,a^5\,b^{14}\,c^6\,d^9+505671336\,a^4\,b^{15}\,c^7\,d^8+206135685\,a^3\,b^{16}\,c^8\,d^7+45453150\,a^2\,b^{17}\,c^9\,d^6+4100625\,a\,b^{18}\,c^{10}\,d^5\right)\,9{}\mathrm{i}}{65536\,\left(a^{18}\,c^2\,d^{18}-18\,a^{17}\,b\,c^3\,d^{17}+153\,a^{16}\,b^2\,c^4\,d^{16}-816\,a^{15}\,b^3\,c^5\,d^{15}+3060\,a^{14}\,b^4\,c^6\,d^{14}-8568\,a^{13}\,b^5\,c^7\,d^{13}+18564\,a^{12}\,b^6\,c^8\,d^{12}-31824\,a^{11}\,b^7\,c^9\,d^{11}+43758\,a^{10}\,b^8\,c^{10}\,d^{10}-48620\,a^9\,b^9\,c^{11}\,d^9+43758\,a^8\,b^{10}\,c^{12}\,d^8-31824\,a^7\,b^{11}\,c^{13}\,d^7+18564\,a^6\,b^{12}\,c^{14}\,d^6-8568\,a^5\,b^{13}\,c^{15}\,d^5+3060\,a^4\,b^{14}\,c^{16}\,d^4-816\,a^3\,b^{15}\,c^{17}\,d^3+153\,a^2\,b^{16}\,c^{18}\,d^2-18\,a\,b^{17}\,c^{19}\,d+b^{18}\,c^{20}\right)}\right)+{\left(-\frac{6561\,a^4\,b^5\,d^4+8748\,a^3\,b^6\,c\,d^3+4374\,a^2\,b^7\,c^2\,d^2+972\,a\,b^8\,c^3\,d+81\,b^9\,c^4}{4096\,a^{17}\,d^{16}-65536\,a^{16}\,b\,c\,d^{15}+491520\,a^{15}\,b^2\,c^2\,d^{14}-2293760\,a^{14}\,b^3\,c^3\,d^{13}+7454720\,a^{13}\,b^4\,c^4\,d^{12}-17891328\,a^{12}\,b^5\,c^5\,d^{11}+32800768\,a^{11}\,b^6\,c^6\,d^{10}-46858240\,a^{10}\,b^7\,c^7\,d^9+52715520\,a^9\,b^8\,c^8\,d^8-46858240\,a^8\,b^9\,c^9\,d^7+32800768\,a^7\,b^{10}\,c^{10}\,d^6-17891328\,a^6\,b^{11}\,c^{11}\,d^5+7454720\,a^5\,b^{12}\,c^{12}\,d^4-2293760\,a^4\,b^{13}\,c^{13}\,d^3+491520\,a^3\,b^{14}\,c^{14}\,d^2-65536\,a^2\,b^{15}\,c^{15}\,d+4096\,a\,b^{16}\,c^{16}}\right)}^{1/4}\,\left({\left(-\frac{6561\,a^4\,b^5\,d^4+8748\,a^3\,b^6\,c\,d^3+4374\,a^2\,b^7\,c^2\,d^2+972\,a\,b^8\,c^3\,d+81\,b^9\,c^4}{4096\,a^{17}\,d^{16}-65536\,a^{16}\,b\,c\,d^{15}+491520\,a^{15}\,b^2\,c^2\,d^{14}-2293760\,a^{14}\,b^3\,c^3\,d^{13}+7454720\,a^{13}\,b^4\,c^4\,d^{12}-17891328\,a^{12}\,b^5\,c^5\,d^{11}+32800768\,a^{11}\,b^6\,c^6\,d^{10}-46858240\,a^{10}\,b^7\,c^7\,d^9+52715520\,a^9\,b^8\,c^8\,d^8-46858240\,a^8\,b^9\,c^9\,d^7+32800768\,a^7\,b^{10}\,c^{10}\,d^6-17891328\,a^6\,b^{11}\,c^{11}\,d^5+7454720\,a^5\,b^{12}\,c^{12}\,d^4-2293760\,a^4\,b^{13}\,c^{13}\,d^3+491520\,a^3\,b^{14}\,c^{14}\,d^2-65536\,a^2\,b^{15}\,c^{15}\,d+4096\,a\,b^{16}\,c^{16}}\right)}^{3/4}\,\left(\frac{9\,\sqrt{x}\,{\left(-\frac{6561\,a^4\,b^5\,d^4+8748\,a^3\,b^6\,c\,d^3+4374\,a^2\,b^7\,c^2\,d^2+972\,a\,b^8\,c^3\,d+81\,b^9\,c^4}{4096\,a^{17}\,d^{16}-65536\,a^{16}\,b\,c\,d^{15}+491520\,a^{15}\,b^2\,c^2\,d^{14}-2293760\,a^{14}\,b^3\,c^3\,d^{13}+7454720\,a^{13}\,b^4\,c^4\,d^{12}-17891328\,a^{12}\,b^5\,c^5\,d^{11}+32800768\,a^{11}\,b^6\,c^6\,d^{10}-46858240\,a^{10}\,b^7\,c^7\,d^9+52715520\,a^9\,b^8\,c^8\,d^8-46858240\,a^8\,b^9\,c^9\,d^7+32800768\,a^7\,b^{10}\,c^{10}\,d^6-17891328\,a^6\,b^{11}\,c^{11}\,d^5+7454720\,a^5\,b^{12}\,c^{12}\,d^4-2293760\,a^4\,b^{13}\,c^{13}\,d^3+491520\,a^3\,b^{14}\,c^{14}\,d^2-65536\,a^2\,b^{15}\,c^{15}\,d+4096\,a\,b^{16}\,c^{16}}\right)}^{1/4}\,\left(262144\,a^{23}\,b^4\,c\,d^{26}-13631488\,a^{22}\,b^5\,c^2\,d^{25}+259522560\,a^{21}\,b^6\,c^3\,d^{24}-2370830336\,a^{20}\,b^7\,c^4\,d^{23}+12955418624\,a^{19}\,b^8\,c^5\,d^{22}-47752151040\,a^{18}\,b^9\,c^6\,d^{21}+127919980544\,a^{17}\,b^{10}\,c^7\,d^{20}-263356153856\,a^{16}\,b^{11}\,c^8\,d^{19}+437990719488\,a^{15}\,b^{12}\,c^9\,d^{18}-615914668032\,a^{14}\,b^{13}\,c^{10}\,d^{17}+754870910976\,a^{13}\,b^{14}\,c^{11}\,d^{16}-805866307584\,a^{12}\,b^{15}\,c^{12}\,d^{15}+724629454848\,a^{11}\,b^{16}\,c^{13}\,d^{14}-518906707968\,a^{10}\,b^{17}\,c^{14}\,d^{13}+273093230592\,a^9\,b^{18}\,c^{15}\,d^{12}-89661636608\,a^8\,b^{19}\,c^{16}\,d^{11}+6940786688\,a^7\,b^{20}\,c^{17}\,d^{10}+8081375232\,a^6\,b^{21}\,c^{18}\,d^9-2827485184\,a^5\,b^{22}\,c^{19}\,d^8-533725184\,a^4\,b^{23}\,c^{20}\,d^7+612630528\,a^3\,b^{24}\,c^{21}\,d^6-167772160\,a^2\,b^{25}\,c^{22}\,d^5+16777216\,a\,b^{26}\,c^{23}\,d^4\right)}{65536\,\left(a^{18}\,c^2\,d^{18}-18\,a^{17}\,b\,c^3\,d^{17}+153\,a^{16}\,b^2\,c^4\,d^{16}-816\,a^{15}\,b^3\,c^5\,d^{15}+3060\,a^{14}\,b^4\,c^6\,d^{14}-8568\,a^{13}\,b^5\,c^7\,d^{13}+18564\,a^{12}\,b^6\,c^8\,d^{12}-31824\,a^{11}\,b^7\,c^9\,d^{11}+43758\,a^{10}\,b^8\,c^{10}\,d^{10}-48620\,a^9\,b^9\,c^{11}\,d^9+43758\,a^8\,b^{10}\,c^{12}\,d^8-31824\,a^7\,b^{11}\,c^{13}\,d^7+18564\,a^6\,b^{12}\,c^{14}\,d^6-8568\,a^5\,b^{13}\,c^{15}\,d^5+3060\,a^4\,b^{14}\,c^{16}\,d^4-816\,a^3\,b^{15}\,c^{17}\,d^3+153\,a^2\,b^{16}\,c^{18}\,d^2-18\,a\,b^{17}\,c^{19}\,d+b^{18}\,c^{20}\right)}+\frac{\left(-\frac{27\,a^{24}\,b^4\,d^{27}}{16}+\frac{1863\,a^{23}\,b^5\,c\,d^{26}}{16}-\frac{24867\,a^{22}\,b^6\,c^2\,d^{25}}{8}+\frac{327267\,a^{21}\,b^7\,c^3\,d^{24}}{8}-\frac{4658715\,a^{20}\,b^8\,c^4\,d^{23}}{16}+\frac{19723743\,a^{19}\,b^9\,c^5\,d^{22}}{16}-\frac{6325749\,a^{18}\,b^{10}\,c^6\,d^{21}}{2}+\frac{8300637\,a^{17}\,b^{11}\,c^7\,d^{20}}{2}+\frac{14462037\,a^{16}\,b^{12}\,c^8\,d^{19}}{8}-\frac{166924665\,a^{15}\,b^{13}\,c^9\,d^{18}}{8}+\frac{196146927\,a^{14}\,b^{14}\,c^{10}\,d^{17}}{4}-\frac{274240863\,a^{13}\,b^{15}\,c^{11}\,d^{16}}{4}+\frac{501573033\,a^{12}\,b^{16}\,c^{12}\,d^{15}}{8}-\frac{279642213\,a^{11}\,b^{17}\,c^{13}\,d^{14}}{8}+\frac{12854835\,a^{10}\,b^{18}\,c^{14}\,d^{13}}{2}+\frac{13320261\,a^9\,b^{19}\,c^{15}\,d^{12}}{2}-\frac{93270447\,a^8\,b^{20}\,c^{16}\,d^{11}}{16}+\frac{22410891\,a^7\,b^{21}\,c^{17}\,d^{10}}{16}+\frac{5105997\,a^6\,b^{22}\,c^{18}\,d^9}{8}-\frac{4585005\,a^5\,b^{23}\,c^{19}\,d^8}{8}+\frac{2587113\,a^4\,b^{24}\,c^{20}\,d^7}{16}-\frac{132597\,a^3\,b^{25}\,c^{21}\,d^6}{16}-5184\,a^2\,b^{26}\,c^{22}\,d^5+864\,a\,b^{27}\,c^{23}\,d^4\right)\,1{}\mathrm{i}}{-a^{21}\,c^2\,d^{21}+21\,a^{20}\,b\,c^3\,d^{20}-210\,a^{19}\,b^2\,c^4\,d^{19}+1330\,a^{18}\,b^3\,c^5\,d^{18}-5985\,a^{17}\,b^4\,c^6\,d^{17}+20349\,a^{16}\,b^5\,c^7\,d^{16}-54264\,a^{15}\,b^6\,c^8\,d^{15}+116280\,a^{14}\,b^7\,c^9\,d^{14}-203490\,a^{13}\,b^8\,c^{10}\,d^{13}+293930\,a^{12}\,b^9\,c^{11}\,d^{12}-352716\,a^{11}\,b^{10}\,c^{12}\,d^{11}+352716\,a^{10}\,b^{11}\,c^{13}\,d^{10}-293930\,a^9\,b^{12}\,c^{14}\,d^9+203490\,a^8\,b^{13}\,c^{15}\,d^8-116280\,a^7\,b^{14}\,c^{16}\,d^7+54264\,a^6\,b^{15}\,c^{17}\,d^6-20349\,a^5\,b^{16}\,c^{18}\,d^5+5985\,a^4\,b^{17}\,c^{19}\,d^4-1330\,a^3\,b^{18}\,c^{20}\,d^3+210\,a^2\,b^{19}\,c^{21}\,d^2-21\,a\,b^{20}\,c^{22}\,d+b^{21}\,c^{23}}\right)\,1{}\mathrm{i}+\frac{\sqrt{x}\,\left(729\,a^{11}\,b^8\,d^{15}+367902\,a^{10}\,b^9\,c\,d^{14}-13218147\,a^9\,b^{10}\,c^2\,d^{13}+89841960\,a^8\,b^{11}\,c^3\,d^{12}+406721250\,a^7\,b^{12}\,c^4\,d^{11}+718242228\,a^6\,b^{13}\,c^5\,d^{10}+754592274\,a^5\,b^{14}\,c^6\,d^9+505671336\,a^4\,b^{15}\,c^7\,d^8+206135685\,a^3\,b^{16}\,c^8\,d^7+45453150\,a^2\,b^{17}\,c^9\,d^6+4100625\,a\,b^{18}\,c^{10}\,d^5\right)\,9{}\mathrm{i}}{65536\,\left(a^{18}\,c^2\,d^{18}-18\,a^{17}\,b\,c^3\,d^{17}+153\,a^{16}\,b^2\,c^4\,d^{16}-816\,a^{15}\,b^3\,c^5\,d^{15}+3060\,a^{14}\,b^4\,c^6\,d^{14}-8568\,a^{13}\,b^5\,c^7\,d^{13}+18564\,a^{12}\,b^6\,c^8\,d^{12}-31824\,a^{11}\,b^7\,c^9\,d^{11}+43758\,a^{10}\,b^8\,c^{10}\,d^{10}-48620\,a^9\,b^9\,c^{11}\,d^9+43758\,a^8\,b^{10}\,c^{12}\,d^8-31824\,a^7\,b^{11}\,c^{13}\,d^7+18564\,a^6\,b^{12}\,c^{14}\,d^6-8568\,a^5\,b^{13}\,c^{15}\,d^5+3060\,a^4\,b^{14}\,c^{16}\,d^4-816\,a^3\,b^{15}\,c^{17}\,d^3+153\,a^2\,b^{16}\,c^{18}\,d^2-18\,a\,b^{17}\,c^{19}\,d+b^{18}\,c^{20}\right)}\right)-\frac{-\frac{1476225\,a^{11}\,b^9\,d^{15}}{262144}+\frac{38677095\,a^{10}\,b^{10}\,c\,d^{14}}{131072}-\frac{1242292545\,a^9\,b^{11}\,c^2\,d^{13}}{262144}+\frac{512796825\,a^8\,b^{12}\,c^3\,d^{12}}{32768}+\frac{14608558575\,a^7\,b^{13}\,c^4\,d^{11}}{131072}+\frac{14064979725\,a^6\,b^{14}\,c^5\,d^{10}}{65536}+\frac{27140987115\,a^5\,b^{15}\,c^6\,d^9}{131072}+\frac{3714477345\,a^4\,b^{16}\,c^7\,d^8}{32768}+\frac{9357790275\,a^3\,b^{17}\,c^8\,d^7}{262144}+\frac{789780375\,a^2\,b^{18}\,c^9\,d^6}{131072}+\frac{110716875\,a\,b^{19}\,c^{10}\,d^5}{262144}}{-a^{21}\,c^2\,d^{21}+21\,a^{20}\,b\,c^3\,d^{20}-210\,a^{19}\,b^2\,c^4\,d^{19}+1330\,a^{18}\,b^3\,c^5\,d^{18}-5985\,a^{17}\,b^4\,c^6\,d^{17}+20349\,a^{16}\,b^5\,c^7\,d^{16}-54264\,a^{15}\,b^6\,c^8\,d^{15}+116280\,a^{14}\,b^7\,c^9\,d^{14}-203490\,a^{13}\,b^8\,c^{10}\,d^{13}+293930\,a^{12}\,b^9\,c^{11}\,d^{12}-352716\,a^{11}\,b^{10}\,c^{12}\,d^{11}+352716\,a^{10}\,b^{11}\,c^{13}\,d^{10}-293930\,a^9\,b^{12}\,c^{14}\,d^9+203490\,a^8\,b^{13}\,c^{15}\,d^8-116280\,a^7\,b^{14}\,c^{16}\,d^7+54264\,a^6\,b^{15}\,c^{17}\,d^6-20349\,a^5\,b^{16}\,c^{18}\,d^5+5985\,a^4\,b^{17}\,c^{19}\,d^4-1330\,a^3\,b^{18}\,c^{20}\,d^3+210\,a^2\,b^{19}\,c^{21}\,d^2-21\,a\,b^{20}\,c^{22}\,d+b^{21}\,c^{23}}}\right)\,{\left(-\frac{6561\,a^4\,b^5\,d^4+8748\,a^3\,b^6\,c\,d^3+4374\,a^2\,b^7\,c^2\,d^2+972\,a\,b^8\,c^3\,d+81\,b^9\,c^4}{4096\,a^{17}\,d^{16}-65536\,a^{16}\,b\,c\,d^{15}+491520\,a^{15}\,b^2\,c^2\,d^{14}-2293760\,a^{14}\,b^3\,c^3\,d^{13}+7454720\,a^{13}\,b^4\,c^4\,d^{12}-17891328\,a^{12}\,b^5\,c^5\,d^{11}+32800768\,a^{11}\,b^6\,c^6\,d^{10}-46858240\,a^{10}\,b^7\,c^7\,d^9+52715520\,a^9\,b^8\,c^8\,d^8-46858240\,a^8\,b^9\,c^9\,d^7+32800768\,a^7\,b^{10}\,c^{10}\,d^6-17891328\,a^6\,b^{11}\,c^{11}\,d^5+7454720\,a^5\,b^{12}\,c^{12}\,d^4-2293760\,a^4\,b^{13}\,c^{13}\,d^3+491520\,a^3\,b^{14}\,c^{14}\,d^2-65536\,a^2\,b^{15}\,c^{15}\,d+4096\,a\,b^{16}\,c^{16}}\right)}^{1/4}","Not used",1,"2*atan((((((864*a*b^27*c^23*d^4 - (27*a^24*b^4*d^27)/16 + (1863*a^23*b^5*c*d^26)/16 - 5184*a^2*b^26*c^22*d^5 - (132597*a^3*b^25*c^21*d^6)/16 + (2587113*a^4*b^24*c^20*d^7)/16 - (4585005*a^5*b^23*c^19*d^8)/8 + (5105997*a^6*b^22*c^18*d^9)/8 + (22410891*a^7*b^21*c^17*d^10)/16 - (93270447*a^8*b^20*c^16*d^11)/16 + (13320261*a^9*b^19*c^15*d^12)/2 + (12854835*a^10*b^18*c^14*d^13)/2 - (279642213*a^11*b^17*c^13*d^14)/8 + (501573033*a^12*b^16*c^12*d^15)/8 - (274240863*a^13*b^15*c^11*d^16)/4 + (196146927*a^14*b^14*c^10*d^17)/4 - (166924665*a^15*b^13*c^9*d^18)/8 + (14462037*a^16*b^12*c^8*d^19)/8 + (8300637*a^17*b^11*c^7*d^20)/2 - (6325749*a^18*b^10*c^6*d^21)/2 + (19723743*a^19*b^9*c^5*d^22)/16 - (4658715*a^20*b^8*c^4*d^23)/16 + (327267*a^21*b^7*c^3*d^24)/8 - (24867*a^22*b^6*c^2*d^25)/8)*1i)/(b^21*c^23 - a^21*c^2*d^21 + 21*a^20*b*c^3*d^20 + 210*a^2*b^19*c^21*d^2 - 1330*a^3*b^18*c^20*d^3 + 5985*a^4*b^17*c^19*d^4 - 20349*a^5*b^16*c^18*d^5 + 54264*a^6*b^15*c^17*d^6 - 116280*a^7*b^14*c^16*d^7 + 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(x^(3/2)*(8*b^2*c^2 - a^2*d^2 + 17*a*b*c*d))/(16*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)) + (3*b*d*x^(11/2)*(a*d^2 + 7*b*c*d))/(16*(b^3*c^4 - a^3*c*d^3 + 3*a^2*b*c^2*d^2 - 3*a*b^2*c^3*d)))/(a*c^2 + x^2*(b*c^2 + 2*a*c*d) + x^4*(a*d^2 + 2*b*c*d) + b*d^2*x^6) - atan(((-(81*b^9*c^4 + 6561*a^4*b^5*d^4 + 8748*a^3*b^6*c*d^3 + 4374*a^2*b^7*c^2*d^2 + 972*a*b^8*c^3*d)/(4096*a^17*d^16 + 4096*a*b^16*c^16 - 65536*a^2*b^15*c^15*d + 491520*a^3*b^14*c^14*d^2 - 2293760*a^4*b^13*c^13*d^3 + 7454720*a^5*b^12*c^12*d^4 - 17891328*a^6*b^11*c^11*d^5 + 32800768*a^7*b^10*c^10*d^6 - 46858240*a^8*b^9*c^9*d^7 + 52715520*a^9*b^8*c^8*d^8 - 46858240*a^10*b^7*c^7*d^9 + 32800768*a^11*b^6*c^6*d^10 - 17891328*a^12*b^5*c^5*d^11 + 7454720*a^13*b^4*c^4*d^12 - 2293760*a^14*b^3*c^3*d^13 + 491520*a^15*b^2*c^2*d^14 - 65536*a^16*b*c*d^15))^(1/4)*((-(81*b^9*c^4 + 6561*a^4*b^5*d^4 + 8748*a^3*b^6*c*d^3 + 4374*a^2*b^7*c^2*d^2 + 972*a*b^8*c^3*d)/(4096*a^17*d^16 + 4096*a*b^16*c^16 - 65536*a^2*b^15*c^15*d + 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(8300637*a^17*b^11*c^7*d^20)/2 - (6325749*a^18*b^10*c^6*d^21)/2 + (19723743*a^19*b^9*c^5*d^22)/16 - (4658715*a^20*b^8*c^4*d^23)/16 + (327267*a^21*b^7*c^3*d^24)/8 - (24867*a^22*b^6*c^2*d^25)/8)/(b^21*c^23 - a^21*c^2*d^21 + 21*a^20*b*c^3*d^20 + 210*a^2*b^19*c^21*d^2 - 1330*a^3*b^18*c^20*d^3 + 5985*a^4*b^17*c^19*d^4 - 20349*a^5*b^16*c^18*d^5 + 54264*a^6*b^15*c^17*d^6 - 116280*a^7*b^14*c^16*d^7 + 203490*a^8*b^13*c^15*d^8 - 293930*a^9*b^12*c^14*d^9 + 352716*a^10*b^11*c^13*d^10 - 352716*a^11*b^10*c^12*d^11 + 293930*a^12*b^9*c^11*d^12 - 203490*a^13*b^8*c^10*d^13 + 116280*a^14*b^7*c^9*d^14 - 54264*a^15*b^6*c^8*d^15 + 20349*a^16*b^5*c^7*d^16 - 5985*a^17*b^4*c^6*d^17 + 1330*a^18*b^3*c^5*d^18 - 210*a^19*b^2*c^4*d^19 - 21*a*b^20*c^22*d) - (9*x^(1/2)*(-(81*b^9*c^4 + 6561*a^4*b^5*d^4 + 8748*a^3*b^6*c*d^3 + 4374*a^2*b^7*c^2*d^2 + 972*a*b^8*c^3*d)/(4096*a^17*d^16 + 4096*a*b^16*c^16 - 65536*a^2*b^15*c^15*d + 491520*a^3*b^14*c^14*d^2 - 2293760*a^4*b^13*c^13*d^3 + 7454720*a^5*b^12*c^12*d^4 - 17891328*a^6*b^11*c^11*d^5 + 32800768*a^7*b^10*c^10*d^6 - 46858240*a^8*b^9*c^9*d^7 + 52715520*a^9*b^8*c^8*d^8 - 46858240*a^10*b^7*c^7*d^9 + 32800768*a^11*b^6*c^6*d^10 - 17891328*a^12*b^5*c^5*d^11 + 7454720*a^13*b^4*c^4*d^12 - 2293760*a^14*b^3*c^3*d^13 + 491520*a^15*b^2*c^2*d^14 - 65536*a^16*b*c*d^15))^(1/4)*(16777216*a*b^26*c^23*d^4 + 262144*a^23*b^4*c*d^26 - 167772160*a^2*b^25*c^22*d^5 + 612630528*a^3*b^24*c^21*d^6 - 533725184*a^4*b^23*c^20*d^7 - 2827485184*a^5*b^22*c^19*d^8 + 8081375232*a^6*b^21*c^18*d^9 + 6940786688*a^7*b^20*c^17*d^10 - 89661636608*a^8*b^19*c^16*d^11 + 273093230592*a^9*b^18*c^15*d^12 - 518906707968*a^10*b^17*c^14*d^13 + 724629454848*a^11*b^16*c^13*d^14 - 805866307584*a^12*b^15*c^12*d^15 + 754870910976*a^13*b^14*c^11*d^16 - 615914668032*a^14*b^13*c^10*d^17 + 437990719488*a^15*b^12*c^9*d^18 - 263356153856*a^16*b^11*c^8*d^19 + 127919980544*a^17*b^10*c^7*d^20 - 47752151040*a^18*b^9*c^6*d^21 + 12955418624*a^19*b^8*c^5*d^22 - 2370830336*a^20*b^7*c^4*d^23 + 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293930*a^9*b^12*c^14*d^9 + 352716*a^10*b^11*c^13*d^10 - 352716*a^11*b^10*c^12*d^11 + 293930*a^12*b^9*c^11*d^12 - 203490*a^13*b^8*c^10*d^13 + 116280*a^14*b^7*c^9*d^14 - 54264*a^15*b^6*c^8*d^15 + 20349*a^16*b^5*c^7*d^16 - 5985*a^17*b^4*c^6*d^17 + 1330*a^18*b^3*c^5*d^18 - 210*a^19*b^2*c^4*d^19 - 21*a*b^20*c^22*d) - (9*x^(1/2)*(-(81*b^9*c^4 + 6561*a^4*b^5*d^4 + 8748*a^3*b^6*c*d^3 + 4374*a^2*b^7*c^2*d^2 + 972*a*b^8*c^3*d)/(4096*a^17*d^16 + 4096*a*b^16*c^16 - 65536*a^2*b^15*c^15*d + 491520*a^3*b^14*c^14*d^2 - 2293760*a^4*b^13*c^13*d^3 + 7454720*a^5*b^12*c^12*d^4 - 17891328*a^6*b^11*c^11*d^5 + 32800768*a^7*b^10*c^10*d^6 - 46858240*a^8*b^9*c^9*d^7 + 52715520*a^9*b^8*c^8*d^8 - 46858240*a^10*b^7*c^7*d^9 + 32800768*a^11*b^6*c^6*d^10 - 17891328*a^12*b^5*c^5*d^11 + 7454720*a^13*b^4*c^4*d^12 - 2293760*a^14*b^3*c^3*d^13 + 491520*a^15*b^2*c^2*d^14 - 65536*a^16*b*c*d^15))^(1/4)*(16777216*a*b^26*c^23*d^4 + 262144*a^23*b^4*c*d^26 - 167772160*a^2*b^25*c^22*d^5 + 612630528*a^3*b^24*c^21*d^6 - 533725184*a^4*b^23*c^20*d^7 - 2827485184*a^5*b^22*c^19*d^8 + 8081375232*a^6*b^21*c^18*d^9 + 6940786688*a^7*b^20*c^17*d^10 - 89661636608*a^8*b^19*c^16*d^11 + 273093230592*a^9*b^18*c^15*d^12 - 518906707968*a^10*b^17*c^14*d^13 + 724629454848*a^11*b^16*c^13*d^14 - 805866307584*a^12*b^15*c^12*d^15 + 754870910976*a^13*b^14*c^11*d^16 - 615914668032*a^14*b^13*c^10*d^17 + 437990719488*a^15*b^12*c^9*d^18 - 263356153856*a^16*b^11*c^8*d^19 + 127919980544*a^17*b^10*c^7*d^20 - 47752151040*a^18*b^9*c^6*d^21 + 12955418624*a^19*b^8*c^5*d^22 - 2370830336*a^20*b^7*c^4*d^23 + 259522560*a^21*b^6*c^3*d^24 - 13631488*a^22*b^5*c^2*d^25))/(65536*(b^18*c^20 + a^18*c^2*d^18 - 18*a^17*b*c^3*d^17 + 153*a^2*b^16*c^18*d^2 - 816*a^3*b^15*c^17*d^3 + 3060*a^4*b^14*c^16*d^4 - 8568*a^5*b^13*c^15*d^5 + 18564*a^6*b^12*c^14*d^6 - 31824*a^7*b^11*c^13*d^7 + 43758*a^8*b^10*c^12*d^8 - 48620*a^9*b^9*c^11*d^9 + 43758*a^10*b^8*c^10*d^10 - 31824*a^11*b^7*c^9*d^11 + 18564*a^12*b^6*c^8*d^12 - 8568*a^13*b^5*c^7*d^13 + 3060*a^14*b^4*c^6*d^14 - 816*a^15*b^3*c^5*d^15 + 153*a^16*b^2*c^4*d^16 - 18*a*b^17*c^19*d)))*1i - (x^(1/2)*(729*a^11*b^8*d^15 + 4100625*a*b^18*c^10*d^5 + 367902*a^10*b^9*c*d^14 + 45453150*a^2*b^17*c^9*d^6 + 206135685*a^3*b^16*c^8*d^7 + 505671336*a^4*b^15*c^7*d^8 + 754592274*a^5*b^14*c^6*d^9 + 718242228*a^6*b^13*c^5*d^10 + 406721250*a^7*b^12*c^4*d^11 + 89841960*a^8*b^11*c^3*d^12 - 13218147*a^9*b^10*c^2*d^13)*9i)/(65536*(b^18*c^20 + a^18*c^2*d^18 - 18*a^17*b*c^3*d^17 + 153*a^2*b^16*c^18*d^2 - 816*a^3*b^15*c^17*d^3 + 3060*a^4*b^14*c^16*d^4 - 8568*a^5*b^13*c^15*d^5 + 18564*a^6*b^12*c^14*d^6 - 31824*a^7*b^11*c^13*d^7 + 43758*a^8*b^10*c^12*d^8 - 48620*a^9*b^9*c^11*d^9 + 43758*a^10*b^8*c^10*d^10 - 31824*a^11*b^7*c^9*d^11 + 18564*a^12*b^6*c^8*d^12 - 8568*a^13*b^5*c^7*d^13 + 3060*a^14*b^4*c^6*d^14 - 816*a^15*b^3*c^5*d^15 + 153*a^16*b^2*c^4*d^16 - 18*a*b^17*c^19*d))) + (-(81*b^9*c^4 + 6561*a^4*b^5*d^4 + 8748*a^3*b^6*c*d^3 + 4374*a^2*b^7*c^2*d^2 + 972*a*b^8*c^3*d)/(4096*a^17*d^16 + 4096*a*b^16*c^16 - 65536*a^2*b^15*c^15*d + 491520*a^3*b^14*c^14*d^2 - 2293760*a^4*b^13*c^13*d^3 + 7454720*a^5*b^12*c^12*d^4 - 17891328*a^6*b^11*c^11*d^5 + 32800768*a^7*b^10*c^10*d^6 - 46858240*a^8*b^9*c^9*d^7 + 52715520*a^9*b^8*c^8*d^8 - 46858240*a^10*b^7*c^7*d^9 + 32800768*a^11*b^6*c^6*d^10 - 17891328*a^12*b^5*c^5*d^11 + 7454720*a^13*b^4*c^4*d^12 - 2293760*a^14*b^3*c^3*d^13 + 491520*a^15*b^2*c^2*d^14 - 65536*a^16*b*c*d^15))^(1/4)*((-(81*b^9*c^4 + 6561*a^4*b^5*d^4 + 8748*a^3*b^6*c*d^3 + 4374*a^2*b^7*c^2*d^2 + 972*a*b^8*c^3*d)/(4096*a^17*d^16 + 4096*a*b^16*c^16 - 65536*a^2*b^15*c^15*d + 491520*a^3*b^14*c^14*d^2 - 2293760*a^4*b^13*c^13*d^3 + 7454720*a^5*b^12*c^12*d^4 - 17891328*a^6*b^11*c^11*d^5 + 32800768*a^7*b^10*c^10*d^6 - 46858240*a^8*b^9*c^9*d^7 + 52715520*a^9*b^8*c^8*d^8 - 46858240*a^10*b^7*c^7*d^9 + 32800768*a^11*b^6*c^6*d^10 - 17891328*a^12*b^5*c^5*d^11 + 7454720*a^13*b^4*c^4*d^12 - 2293760*a^14*b^3*c^3*d^13 + 491520*a^15*b^2*c^2*d^14 - 65536*a^16*b*c*d^15))^(3/4)*(((864*a*b^27*c^23*d^4 - (27*a^24*b^4*d^27)/16 + (1863*a^23*b^5*c*d^26)/16 - 5184*a^2*b^26*c^22*d^5 - (132597*a^3*b^25*c^21*d^6)/16 + (2587113*a^4*b^24*c^20*d^7)/16 - (4585005*a^5*b^23*c^19*d^8)/8 + (5105997*a^6*b^22*c^18*d^9)/8 + (22410891*a^7*b^21*c^17*d^10)/16 - (93270447*a^8*b^20*c^16*d^11)/16 + (13320261*a^9*b^19*c^15*d^12)/2 + (12854835*a^10*b^18*c^14*d^13)/2 - (279642213*a^11*b^17*c^13*d^14)/8 + (501573033*a^12*b^16*c^12*d^15)/8 - (274240863*a^13*b^15*c^11*d^16)/4 + (196146927*a^14*b^14*c^10*d^17)/4 - (166924665*a^15*b^13*c^9*d^18)/8 + (14462037*a^16*b^12*c^8*d^19)/8 + (8300637*a^17*b^11*c^7*d^20)/2 - (6325749*a^18*b^10*c^6*d^21)/2 + (19723743*a^19*b^9*c^5*d^22)/16 - (4658715*a^20*b^8*c^4*d^23)/16 + (327267*a^21*b^7*c^3*d^24)/8 - (24867*a^22*b^6*c^2*d^25)/8)*1i)/(b^21*c^23 - a^21*c^2*d^21 + 21*a^20*b*c^3*d^20 + 210*a^2*b^19*c^21*d^2 - 1330*a^3*b^18*c^20*d^3 + 5985*a^4*b^17*c^19*d^4 - 20349*a^5*b^16*c^18*d^5 + 54264*a^6*b^15*c^17*d^6 - 116280*a^7*b^14*c^16*d^7 + 203490*a^8*b^13*c^15*d^8 - 293930*a^9*b^12*c^14*d^9 + 352716*a^10*b^11*c^13*d^10 - 352716*a^11*b^10*c^12*d^11 + 293930*a^12*b^9*c^11*d^12 - 203490*a^13*b^8*c^10*d^13 + 116280*a^14*b^7*c^9*d^14 - 54264*a^15*b^6*c^8*d^15 + 20349*a^16*b^5*c^7*d^16 - 5985*a^17*b^4*c^6*d^17 + 1330*a^18*b^3*c^5*d^18 - 210*a^19*b^2*c^4*d^19 - 21*a*b^20*c^22*d) + (9*x^(1/2)*(-(81*b^9*c^4 + 6561*a^4*b^5*d^4 + 8748*a^3*b^6*c*d^3 + 4374*a^2*b^7*c^2*d^2 + 972*a*b^8*c^3*d)/(4096*a^17*d^16 + 4096*a*b^16*c^16 - 65536*a^2*b^15*c^15*d + 491520*a^3*b^14*c^14*d^2 - 2293760*a^4*b^13*c^13*d^3 + 7454720*a^5*b^12*c^12*d^4 - 17891328*a^6*b^11*c^11*d^5 + 32800768*a^7*b^10*c^10*d^6 - 46858240*a^8*b^9*c^9*d^7 + 52715520*a^9*b^8*c^8*d^8 - 46858240*a^10*b^7*c^7*d^9 + 32800768*a^11*b^6*c^6*d^10 - 17891328*a^12*b^5*c^5*d^11 + 7454720*a^13*b^4*c^4*d^12 - 2293760*a^14*b^3*c^3*d^13 + 491520*a^15*b^2*c^2*d^14 - 65536*a^16*b*c*d^15))^(1/4)*(16777216*a*b^26*c^23*d^4 + 262144*a^23*b^4*c*d^26 - 167772160*a^2*b^25*c^22*d^5 + 612630528*a^3*b^24*c^21*d^6 - 533725184*a^4*b^23*c^20*d^7 - 2827485184*a^5*b^22*c^19*d^8 + 8081375232*a^6*b^21*c^18*d^9 + 6940786688*a^7*b^20*c^17*d^10 - 89661636608*a^8*b^19*c^16*d^11 + 273093230592*a^9*b^18*c^15*d^12 - 518906707968*a^10*b^17*c^14*d^13 + 724629454848*a^11*b^16*c^13*d^14 - 805866307584*a^12*b^15*c^12*d^15 + 754870910976*a^13*b^14*c^11*d^16 - 615914668032*a^14*b^13*c^10*d^17 + 437990719488*a^15*b^12*c^9*d^18 - 263356153856*a^16*b^11*c^8*d^19 + 127919980544*a^17*b^10*c^7*d^20 - 47752151040*a^18*b^9*c^6*d^21 + 12955418624*a^19*b^8*c^5*d^22 - 2370830336*a^20*b^7*c^4*d^23 + 259522560*a^21*b^6*c^3*d^24 - 13631488*a^22*b^5*c^2*d^25))/(65536*(b^18*c^20 + a^18*c^2*d^18 - 18*a^17*b*c^3*d^17 + 153*a^2*b^16*c^18*d^2 - 816*a^3*b^15*c^17*d^3 + 3060*a^4*b^14*c^16*d^4 - 8568*a^5*b^13*c^15*d^5 + 18564*a^6*b^12*c^14*d^6 - 31824*a^7*b^11*c^13*d^7 + 43758*a^8*b^10*c^12*d^8 - 48620*a^9*b^9*c^11*d^9 + 43758*a^10*b^8*c^10*d^10 - 31824*a^11*b^7*c^9*d^11 + 18564*a^12*b^6*c^8*d^12 - 8568*a^13*b^5*c^7*d^13 + 3060*a^14*b^4*c^6*d^14 - 816*a^15*b^3*c^5*d^15 + 153*a^16*b^2*c^4*d^16 - 18*a*b^17*c^19*d)))*1i + (x^(1/2)*(729*a^11*b^8*d^15 + 4100625*a*b^18*c^10*d^5 + 367902*a^10*b^9*c*d^14 + 45453150*a^2*b^17*c^9*d^6 + 206135685*a^3*b^16*c^8*d^7 + 505671336*a^4*b^15*c^7*d^8 + 754592274*a^5*b^14*c^6*d^9 + 718242228*a^6*b^13*c^5*d^10 + 406721250*a^7*b^12*c^4*d^11 + 89841960*a^8*b^11*c^3*d^12 - 13218147*a^9*b^10*c^2*d^13)*9i)/(65536*(b^18*c^20 + a^18*c^2*d^18 - 18*a^17*b*c^3*d^17 + 153*a^2*b^16*c^18*d^2 - 816*a^3*b^15*c^17*d^3 + 3060*a^4*b^14*c^16*d^4 - 8568*a^5*b^13*c^15*d^5 + 18564*a^6*b^12*c^14*d^6 - 31824*a^7*b^11*c^13*d^7 + 43758*a^8*b^10*c^12*d^8 - 48620*a^9*b^9*c^11*d^9 + 43758*a^10*b^8*c^10*d^10 - 31824*a^11*b^7*c^9*d^11 + 18564*a^12*b^6*c^8*d^12 - 8568*a^13*b^5*c^7*d^13 + 3060*a^14*b^4*c^6*d^14 - 816*a^15*b^3*c^5*d^15 + 153*a^16*b^2*c^4*d^16 - 18*a*b^17*c^19*d))) - ((110716875*a*b^19*c^10*d^5)/262144 - (1476225*a^11*b^9*d^15)/262144 + (38677095*a^10*b^10*c*d^14)/131072 + (789780375*a^2*b^18*c^9*d^6)/131072 + (9357790275*a^3*b^17*c^8*d^7)/262144 + (3714477345*a^4*b^16*c^7*d^8)/32768 + (27140987115*a^5*b^15*c^6*d^9)/131072 + (14064979725*a^6*b^14*c^5*d^10)/65536 + (14608558575*a^7*b^13*c^4*d^11)/131072 + (512796825*a^8*b^12*c^3*d^12)/32768 - (1242292545*a^9*b^11*c^2*d^13)/262144)/(b^21*c^23 - a^21*c^2*d^21 + 21*a^20*b*c^3*d^20 + 210*a^2*b^19*c^21*d^2 - 1330*a^3*b^18*c^20*d^3 + 5985*a^4*b^17*c^19*d^4 - 20349*a^5*b^16*c^18*d^5 + 54264*a^6*b^15*c^17*d^6 - 116280*a^7*b^14*c^16*d^7 + 203490*a^8*b^13*c^15*d^8 - 293930*a^9*b^12*c^14*d^9 + 352716*a^10*b^11*c^13*d^10 - 352716*a^11*b^10*c^12*d^11 + 293930*a^12*b^9*c^11*d^12 - 203490*a^13*b^8*c^10*d^13 + 116280*a^14*b^7*c^9*d^14 - 54264*a^15*b^6*c^8*d^15 + 20349*a^16*b^5*c^7*d^16 - 5985*a^17*b^4*c^6*d^17 + 1330*a^18*b^3*c^5*d^18 - 210*a^19*b^2*c^4*d^19 - 21*a*b^20*c^22*d)))*(-(81*b^9*c^4 + 6561*a^4*b^5*d^4 + 8748*a^3*b^6*c*d^3 + 4374*a^2*b^7*c^2*d^2 + 972*a*b^8*c^3*d)/(4096*a^17*d^16 + 4096*a*b^16*c^16 - 65536*a^2*b^15*c^15*d + 491520*a^3*b^14*c^14*d^2 - 2293760*a^4*b^13*c^13*d^3 + 7454720*a^5*b^12*c^12*d^4 - 17891328*a^6*b^11*c^11*d^5 + 32800768*a^7*b^10*c^10*d^6 - 46858240*a^8*b^9*c^9*d^7 + 52715520*a^9*b^8*c^8*d^8 - 46858240*a^10*b^7*c^7*d^9 + 32800768*a^11*b^6*c^6*d^10 - 17891328*a^12*b^5*c^5*d^11 + 7454720*a^13*b^4*c^4*d^12 - 2293760*a^14*b^3*c^3*d^13 + 491520*a^15*b^2*c^2*d^14 - 65536*a^16*b*c*d^15))^(1/4)","B"
498,1,50125,703,7.006217,"\text{Not used}","int(x^(3/2)/((a + b*x^2)^2*(c + d*x^2)^3),x)","\frac{\frac{\sqrt{x}\,\left(-3\,a^2\,d^2+19\,a\,b\,c\,d+8\,b^2\,c^2\right)}{16\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)}+\frac{x^{5/2}\,\left(a^2\,d^3+12\,a\,b\,c\,d^2+35\,b^2\,c^2\,d\right)}{16\,c\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)}+\frac{b\,d\,x^{9/2}\,\left(a\,d^2+23\,b\,c\,d\right)}{16\,c\,\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^2+x^2\,\left(b\,c^2+2\,a\,d\,c\right)+x^4\,\left(a\,d^2+2\,b\,c\,d\right)+b\,d^2\,x^6}+2\,\mathrm{atan}\left(\frac{{\left(-\frac{81\,a^8\,d^{11}-2376\,a^7\,b\,c\,d^{10}+17820\,a^6\,b^2\,c^2\,d^9+55176\,a^5\,b^3\,c^3\,d^8-787226\,a^4\,b^4\,c^4\,d^7-1416184\,a^3\,b^5\,c^5\,d^6+11739420\,a^2\,b^6\,c^6\,d^5+40174904\,a\,b^7\,c^7\,d^4+35153041\,b^8\,c^8\,d^3}{16777216\,a^{16}\,c^7\,d^{16}-268435456\,a^{15}\,b\,c^8\,d^{15}+2013265920\,a^{14}\,b^2\,c^9\,d^{14}-9395240960\,a^{13}\,b^3\,c^{10}\,d^{13}+30534533120\,a^{12}\,b^4\,c^{11}\,d^{12}-73282879488\,a^{11}\,b^5\,c^{12}\,d^{11}+134351945728\,a^{10}\,b^6\,c^{13}\,d^{10}-191931351040\,a^9\,b^7\,c^{14}\,d^9+215922769920\,a^8\,b^8\,c^{15}\,d^8-191931351040\,a^7\,b^9\,c^{16}\,d^7+134351945728\,a^6\,b^{10}\,c^{17}\,d^6-73282879488\,a^5\,b^{11}\,c^{18}\,d^5+30534533120\,a^4\,b^{12}\,c^{19}\,d^4-9395240960\,a^3\,b^{13}\,c^{20}\,d^3+2013265920\,a^2\,b^{14}\,c^{21}\,d^2-268435456\,a\,b^{15}\,c^{22}\,d+16777216\,b^{16}\,c^{23}}\right)}^{1/4}\,\left({\left(-\frac{81\,a^8\,d^{11}-2376\,a^7\,b\,c\,d^{10}+17820\,a^6\,b^2\,c^2\,d^9+55176\,a^5\,b^3\,c^3\,d^8-787226\,a^4\,b^4\,c^4\,d^7-1416184\,a^3\,b^5\,c^5\,d^6+11739420\,a^2\,b^6\,c^6\,d^5+40174904\,a\,b^7\,c^7\,d^4+35153041\,b^8\,c^8\,d^3}{16777216\,a^{16}\,c^7\,d^{16}-268435456\,a^{15}\,b\,c^8\,d^{15}+2013265920\,a^{14}\,b^2\,c^9\,d^{14}-9395240960\,a^{13}\,b^3\,c^{10}\,d^{13}+30534533120\,a^{12}\,b^4\,c^{11}\,d^{12}-73282879488\,a^{11}\,b^5\,c^{12}\,d^{11}+134351945728\,a^{10}\,b^6\,c^{13}\,d^{10}-191931351040\,a^9\,b^7\,c^{14}\,d^9+215922769920\,a^8\,b^8\,c^{15}\,d^8-191931351040\,a^7\,b^9\,c^{16}\,d^7+134351945728\,a^6\,b^{10}\,c^{17}\,d^6-73282879488\,a^5\,b^{11}\,c^{18}\,d^5+30534533120\,a^4\,b^{12}\,c^{19}\,d^4-9395240960\,a^3\,b^{13}\,c^{20}\,d^3+2013265920\,a^2\,b^{14}\,c^{21}\,d^2-268435456\,a\,b^{15}\,c^{22}\,d+16777216\,b^{16}\,c^{23}}\right)}^{1/4}\,\left(\frac{\left(\frac{891\,a^9\,b^7\,d^{15}}{8192}-\frac{6291\,a^8\,b^8\,c\,d^{14}}{2048}+\frac{5265\,a^7\,b^9\,c^2\,d^{13}}{256}+\frac{198309\,a^6\,b^{10}\,c^3\,d^{12}}{2048}+\frac{7338751\,a^5\,b^{11}\,c^4\,d^{11}}{4096}-\frac{39606577\,a^4\,b^{12}\,c^5\,d^{10}}{2048}-\frac{83346257\,a^3\,b^{13}\,c^6\,d^9}{1024}-\frac{107777537\,a^2\,b^{14}\,c^7\,d^8}{2048}-\frac{33367697\,a\,b^{15}\,c^8\,d^7}{8192}+\frac{77\,b^{16}\,c^9\,d^6}{16}\right)\,1{}\mathrm{i}}{-a^{13}\,c^4\,d^{13}+13\,a^{12}\,b\,c^5\,d^{12}-78\,a^{11}\,b^2\,c^6\,d^{11}+286\,a^{10}\,b^3\,c^7\,d^{10}-715\,a^9\,b^4\,c^8\,d^9+1287\,a^8\,b^5\,c^9\,d^8-1716\,a^7\,b^6\,c^{10}\,d^7+1716\,a^6\,b^7\,c^{11}\,d^6-1287\,a^5\,b^8\,c^{12}\,d^5+715\,a^4\,b^9\,c^{13}\,d^4-286\,a^3\,b^{10}\,c^{14}\,d^3+78\,a^2\,b^{11}\,c^{15}\,d^2-13\,a\,b^{12}\,c^{16}\,d+b^{13}\,c^{17}}+{\left(-\frac{81\,a^8\,d^{11}-2376\,a^7\,b\,c\,d^{10}+17820\,a^6\,b^2\,c^2\,d^9+55176\,a^5\,b^3\,c^3\,d^8-787226\,a^4\,b^4\,c^4\,d^7-1416184\,a^3\,b^5\,c^5\,d^6+11739420\,a^2\,b^6\,c^6\,d^5+40174904\,a\,b^7\,c^7\,d^4+35153041\,b^8\,c^8\,d^3}{16777216\,a^{16}\,c^7\,d^{16}-268435456\,a^{15}\,b\,c^8\,d^{15}+2013265920\,a^{14}\,b^2\,c^9\,d^{14}-9395240960\,a^{13}\,b^3\,c^{10}\,d^{13}+30534533120\,a^{12}\,b^4\,c^{11}\,d^{12}-73282879488\,a^{11}\,b^5\,c^{12}\,d^{11}+134351945728\,a^{10}\,b^6\,c^{13}\,d^{10}-191931351040\,a^9\,b^7\,c^{14}\,d^9+215922769920\,a^8\,b^8\,c^{15}\,d^8-191931351040\,a^7\,b^9\,c^{16}\,d^7+134351945728\,a^6\,b^{10}\,c^{17}\,d^6-73282879488\,a^5\,b^{11}\,c^{18}\,d^5+30534533120\,a^4\,b^{12}\,c^{19}\,d^4-9395240960\,a^3\,b^{13}\,c^{20}\,d^3+2013265920\,a^2\,b^{14}\,c^{21}\,d^2-268435456\,a\,b^{15}\,c^{22}\,d+16777216\,b^{16}\,c^{23}}\right)}^{3/4}\,\left(\frac{{\left(-\frac{81\,a^8\,d^{11}-2376\,a^7\,b\,c\,d^{10}+17820\,a^6\,b^2\,c^2\,d^9+55176\,a^5\,b^3\,c^3\,d^8-787226\,a^4\,b^4\,c^4\,d^7-1416184\,a^3\,b^5\,c^5\,d^6+11739420\,a^2\,b^6\,c^6\,d^5+40174904\,a\,b^7\,c^7\,d^4+35153041\,b^8\,c^8\,d^3}{16777216\,a^{16}\,c^7\,d^{16}-268435456\,a^{15}\,b\,c^8\,d^{15}+2013265920\,a^{14}\,b^2\,c^9\,d^{14}-9395240960\,a^{13}\,b^3\,c^{10}\,d^{13}+30534533120\,a^{12}\,b^4\,c^{11}\,d^{12}-73282879488\,a^{11}\,b^5\,c^{12}\,d^{11}+134351945728\,a^{10}\,b^6\,c^{13}\,d^{10}-191931351040\,a^9\,b^7\,c^{14}\,d^9+215922769920\,a^8\,b^8\,c^{15}\,d^8-191931351040\,a^7\,b^9\,c^{16}\,d^7+134351945728\,a^6\,b^{10}\,c^{17}\,d^6-73282879488\,a^5\,b^{11}\,c^{18}\,d^5+30534533120\,a^4\,b^{12}\,c^{19}\,d^4-9395240960\,a^3\,b^{13}\,c^{20}\,d^3+2013265920\,a^2\,b^{14}\,c^{21}\,d^2-268435456\,a\,b^{15}\,c^{22}\,d+16777216\,b^{16}\,c^{23}}\right)}^{1/4}\,\left(768\,a^{20}\,b^4\,c^4\,d^{23}-17152\,a^{19}\,b^5\,c^5\,d^{22}+145408\,a^{18}\,b^6\,c^6\,d^{21}-622592\,a^{17}\,b^7\,c^7\,d^{20}+1205248\,a^{16}\,b^8\,c^8\,d^{19}+1309696\,a^{15}\,b^9\,c^9\,d^{18}-16185344\,a^{14}\,b^{10}\,c^{10}\,d^{17}+55883776\,a^{13}\,b^{11}\,c^{11}\,d^{16}-122330624\,a^{12}\,b^{12}\,c^{12}\,d^{15}+193363456\,a^{11}\,b^{13}\,c^{13}\,d^{14}-231069696\,a^{10}\,b^{14}\,c^{14}\,d^{13}+212486144\,a^9\,b^{15}\,c^{15}\,d^{12}-150731776\,a^8\,b^{16}\,c^{16}\,d^{11}+81665024\,a^7\,b^{17}\,c^{17}\,d^{10}-32966656\,a^6\,b^{18}\,c^{18}\,d^9+9439232\,a^5\,b^{19}\,c^{19}\,d^8-1723648\,a^4\,b^{20}\,c^{20}\,d^7+142592\,a^3\,b^{21}\,c^{21}\,d^6+8192\,a^2\,b^{22}\,c^{22}\,d^5-2048\,a\,b^{23}\,c^{23}\,d^4\right)}{-a^{13}\,c^4\,d^{13}+13\,a^{12}\,b\,c^5\,d^{12}-78\,a^{11}\,b^2\,c^6\,d^{11}+286\,a^{10}\,b^3\,c^7\,d^{10}-715\,a^9\,b^4\,c^8\,d^9+1287\,a^8\,b^5\,c^9\,d^8-1716\,a^7\,b^6\,c^{10}\,d^7+1716\,a^6\,b^7\,c^{11}\,d^6-1287\,a^5\,b^8\,c^{12}\,d^5+715\,a^4\,b^9\,c^{13}\,d^4-286\,a^3\,b^{10}\,c^{14}\,d^3+78\,a^2\,b^{11}\,c^{15}\,d^2-13\,a\,b^{12}\,c^{16}\,d+b^{13}\,c^{17}}-\frac{\sqrt{x}\,\left(2359296\,a^{23}\,b^4\,c^2\,d^{27}-72351744\,a^{22}\,b^5\,c^3\,d^{26}+842530816\,a^{21}\,b^6\,c^4\,d^{25}-4677697536\,a^{20}\,b^7\,c^5\,d^{24}+11707613184\,a^{19}\,b^8\,c^6\,d^{23}+7226785792\,a^{18}\,b^9\,c^7\,d^{22}-162426519552\,a^{17}\,b^{10}\,c^8\,d^{21}+654475001856\,a^{16}\,b^{11}\,c^9\,d^{20}-1671068909568\,a^{15}\,b^{12}\,c^{10}\,d^{19}+3274973380608\,a^{14}\,b^{13}\,c^{11}\,d^{18}-5429806497792\,a^{13}\,b^{14}\,c^{12}\,d^{17}+7971285237760\,a^{12}\,b^{15}\,c^{13}\,d^{16}-10296755748864\,a^{11}\,b^{16}\,c^{14}\,d^{15}+11280643522560\,a^{10}\,b^{17}\,c^{15}\,d^{14}-10068131053568\,a^9\,b^{18}\,c^{16}\,d^{13}+7070048845824\,a^8\,b^{19}\,c^{17}\,d^{12}-3770791231488\,a^7\,b^{20}\,c^{18}\,d^{11}+1452876496896\,a^6\,b^{21}\,c^{19}\,d^{10}-366041628672\,a^5\,b^{22}\,c^{20}\,d^9+43464523776\,a^4\,b^{23}\,c^{21}\,d^8+3970170880\,a^3\,b^{24}\,c^{22}\,d^7-1862270976\,a^2\,b^{25}\,c^{23}\,d^6+100663296\,a\,b^{26}\,c^{24}\,d^5+16777216\,b^{27}\,c^{25}\,d^4\right)\,1{}\mathrm{i}}{65536\,\left(a^{18}\,c^4\,d^{18}-18\,a^{17}\,b\,c^5\,d^{17}+153\,a^{16}\,b^2\,c^6\,d^{16}-816\,a^{15}\,b^3\,c^7\,d^{15}+3060\,a^{14}\,b^4\,c^8\,d^{14}-8568\,a^{13}\,b^5\,c^9\,d^{13}+18564\,a^{12}\,b^6\,c^{10}\,d^{12}-31824\,a^{11}\,b^7\,c^{11}\,d^{11}+43758\,a^{10}\,b^8\,c^{12}\,d^{10}-48620\,a^9\,b^9\,c^{13}\,d^9+43758\,a^8\,b^{10}\,c^{14}\,d^8-31824\,a^7\,b^{11}\,c^{15}\,d^7+18564\,a^6\,b^{12}\,c^{16}\,d^6-8568\,a^5\,b^{13}\,c^{17}\,d^5+3060\,a^4\,b^{14}\,c^{18}\,d^4-816\,a^3\,b^{15}\,c^{19}\,d^3+153\,a^2\,b^{16}\,c^{20}\,d^2-18\,a\,b^{17}\,c^{21}\,d+b^{18}\,c^{22}\right)}\right)\,1{}\mathrm{i}\right)+\frac{\sqrt{x}\,\left(9801\,a^{10}\,b^9\,d^{17}-285714\,a^9\,b^{10}\,c\,d^{16}+10537245\,a^8\,b^{11}\,c^2\,d^{15}-113554584\,a^7\,b^{12}\,c^3\,d^{14}-117967102\,a^6\,b^{13}\,c^4\,d^{13}+2987403540\,a^5\,b^{14}\,c^5\,d^{12}+8099206482\,a^4\,b^{15}\,c^6\,d^{11}+7295711720\,a^3\,b^{16}\,c^7\,d^{10}+5434132341\,a^2\,b^{17}\,c^8\,d^9+830454702\,a\,b^{18}\,c^9\,d^8+35532497\,b^{19}\,c^{10}\,d^7\right)}{65536\,\left(a^{18}\,c^4\,d^{18}-18\,a^{17}\,b\,c^5\,d^{17}+153\,a^{16}\,b^2\,c^6\,d^{16}-816\,a^{15}\,b^3\,c^7\,d^{15}+3060\,a^{14}\,b^4\,c^8\,d^{14}-8568\,a^{13}\,b^5\,c^9\,d^{13}+18564\,a^{12}\,b^6\,c^{10}\,d^{12}-31824\,a^{11}\,b^7\,c^{11}\,d^{11}+43758\,a^{10}\,b^8\,c^{12}\,d^{10}-48620\,a^9\,b^9\,c^{13}\,d^9+43758\,a^8\,b^{10}\,c^{14}\,d^8-31824\,a^7\,b^{11}\,c^{15}\,d^7+18564\,a^6\,b^{12}\,c^{16}\,d^6-8568\,a^5\,b^{13}\,c^{17}\,d^5+3060\,a^4\,b^{14}\,c^{18}\,d^4-816\,a^3\,b^{15}\,c^{19}\,d^3+153\,a^2\,b^{16}\,c^{20}\,d^2-18\,a\,b^{17}\,c^{21}\,d+b^{18}\,c^{22}\right)}\right)-{\left(-\frac{81\,a^8\,d^{11}-2376\,a^7\,b\,c\,d^{10}+17820\,a^6\,b^2\,c^2\,d^9+55176\,a^5\,b^3\,c^3\,d^8-787226\,a^4\,b^4\,c^4\,d^7-1416184\,a^3\,b^5\,c^5\,d^6+11739420\,a^2\,b^6\,c^6\,d^5+40174904\,a\,b^7\,c^7\,d^4+35153041\,b^8\,c^8\,d^3}{16777216\,a^{16}\,c^7\,d^{16}-268435456\,a^{15}\,b\,c^8\,d^{15}+2013265920\,a^{14}\,b^2\,c^9\,d^{14}-9395240960\,a^{13}\,b^3\,c^{10}\,d^{13}+30534533120\,a^{12}\,b^4\,c^{11}\,d^{12}-73282879488\,a^{11}\,b^5\,c^{12}\,d^{11}+134351945728\,a^{10}\,b^6\,c^{13}\,d^{10}-191931351040\,a^9\,b^7\,c^{14}\,d^9+215922769920\,a^8\,b^8\,c^{15}\,d^8-191931351040\,a^7\,b^9\,c^{16}\,d^7+134351945728\,a^6\,b^{10}\,c^{17}\,d^6-73282879488\,a^5\,b^{11}\,c^{18}\,d^5+30534533120\,a^4\,b^{12}\,c^{19}\,d^4-9395240960\,a^3\,b^{13}\,c^{20}\,d^3+2013265920\,a^2\,b^{14}\,c^{21}\,d^2-268435456\,a\,b^{15}\,c^{22}\,d+16777216\,b^{16}\,c^{23}}\right)}^{1/4}\,\left({\left(-\frac{81\,a^8\,d^{11}-2376\,a^7\,b\,c\,d^{10}+17820\,a^6\,b^2\,c^2\,d^9+55176\,a^5\,b^3\,c^3\,d^8-787226\,a^4\,b^4\,c^4\,d^7-1416184\,a^3\,b^5\,c^5\,d^6+11739420\,a^2\,b^6\,c^6\,d^5+40174904\,a\,b^7\,c^7\,d^4+35153041\,b^8\,c^8\,d^3}{16777216\,a^{16}\,c^7\,d^{16}-268435456\,a^{15}\,b\,c^8\,d^{15}+2013265920\,a^{14}\,b^2\,c^9\,d^{14}-9395240960\,a^{13}\,b^3\,c^{10}\,d^{13}+30534533120\,a^{12}\,b^4\,c^{11}\,d^{12}-73282879488\,a^{11}\,b^5\,c^{12}\,d^{11}+134351945728\,a^{10}\,b^6\,c^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1}\,c^{11}\,d^5+7454720\,a^7\,b^{12}\,c^{12}\,d^4-2293760\,a^6\,b^{13}\,c^{13}\,d^3+491520\,a^5\,b^{14}\,c^{14}\,d^2-65536\,a^4\,b^{15}\,c^{15}\,d+4096\,a^3\,b^{16}\,c^{16}}\right)}^{3/4}+\frac{\frac{891\,a^9\,b^7\,d^{15}}{8192}-\frac{6291\,a^8\,b^8\,c\,d^{14}}{2048}+\frac{5265\,a^7\,b^9\,c^2\,d^{13}}{256}+\frac{198309\,a^6\,b^{10}\,c^3\,d^{12}}{2048}+\frac{7338751\,a^5\,b^{11}\,c^4\,d^{11}}{4096}-\frac{39606577\,a^4\,b^{12}\,c^5\,d^{10}}{2048}-\frac{83346257\,a^3\,b^{13}\,c^6\,d^9}{1024}-\frac{107777537\,a^2\,b^{14}\,c^7\,d^8}{2048}-\frac{33367697\,a\,b^{15}\,c^8\,d^7}{8192}+\frac{77\,b^{16}\,c^9\,d^6}{16}}{-a^{13}\,c^4\,d^{13}+13\,a^{12}\,b\,c^5\,d^{12}-78\,a^{11}\,b^2\,c^6\,d^{11}+286\,a^{10}\,b^3\,c^7\,d^{10}-715\,a^9\,b^4\,c^8\,d^9+1287\,a^8\,b^5\,c^9\,d^8-1716\,a^7\,b^6\,c^{10}\,d^7+1716\,a^6\,b^7\,c^{11}\,d^6-1287\,a^5\,b^8\,c^{12}\,d^5+715\,a^4\,b^9\,c^{13}\,d^4-286\,a^3\,b^{10}\,c^{14}\,d^3+78\,a^2\,b^{11}\,c^{15}\,d^2-13\,a\,b^{12}\,c^{16}\,d+b^{13}\,c^{17}}\right)\,{\left(-\frac{14641\,a^4\,b^7\,d^4+5324\,a^3\,b^8\,c\,d^3+726\,a^2\,b^9\,c^2\,d^2+44\,a\,b^{10}\,c^3\,d+b^{11}\,c^4}{4096\,a^{19}\,d^{16}-65536\,a^{18}\,b\,c\,d^{15}+491520\,a^{17}\,b^2\,c^2\,d^{14}-2293760\,a^{16}\,b^3\,c^3\,d^{13}+7454720\,a^{15}\,b^4\,c^4\,d^{12}-17891328\,a^{14}\,b^5\,c^5\,d^{11}+32800768\,a^{13}\,b^6\,c^6\,d^{10}-46858240\,a^{12}\,b^7\,c^7\,d^9+52715520\,a^{11}\,b^8\,c^8\,d^8-46858240\,a^{10}\,b^9\,c^9\,d^7+32800768\,a^9\,b^{10}\,c^{10}\,d^6-17891328\,a^8\,b^{11}\,c^{11}\,d^5+7454720\,a^7\,b^{12}\,c^{12}\,d^4-2293760\,a^6\,b^{13}\,c^{13}\,d^3+491520\,a^5\,b^{14}\,c^{14}\,d^2-65536\,a^4\,b^{15}\,c^{15}\,d+4096\,a^3\,b^{16}\,c^{16}}\right)}^{1/4}+\frac{\sqrt{x}\,\left(9801\,a^{10}\,b^9\,d^{17}-285714\,a^9\,b^{10}\,c\,d^{16}+10537245\,a^8\,b^{11}\,c^2\,d^{15}-113554584\,a^7\,b^{12}\,c^3\,d^{14}-117967102\,a^6\,b^{13}\,c^4\,d^{13}+2987403540\,a^5\,b^{14}\,c^5\,d^{12}+8099206482\,a^4\,b^{15}\,c^6\,d^{11}+7295711720\,a^3\,b^{16}\,c^7\,d^{10}+5434132341\,a^2\,b^{17}\,c^8\,d^9+830454702\,a\,b^{18}\,c^9\,d^8+35532497\,b^{19}\,c^{10}\,d^7\right)}{65536\,\left(a^{18}\,c^4\,d^{18}-18\,a^{17}\,b\,c^5\,d^{17}+153\,a^{16}\,b^2\,c^6\,d^{16}-816\,a^{15}\,b^3\,c^7\,d^{15}+3060\,a^{14}\,b^4\,c^8\,d^{14}-8568\,a^{13}\,b^5\,c^9\,d^{13}+18564\,a^{12}\,b^6\,c^{10}\,d^{12}-31824\,a^{11}\,b^7\,c^{11}\,d^{11}+43758\,a^{10}\,b^8\,c^{12}\,d^{10}-48620\,a^9\,b^9\,c^{13}\,d^9+43758\,a^8\,b^{10}\,c^{14}\,d^8-31824\,a^7\,b^{11}\,c^{15}\,d^7+18564\,a^6\,b^{12}\,c^{16}\,d^6-8568\,a^5\,b^{13}\,c^{17}\,d^5+3060\,a^4\,b^{14}\,c^{18}\,d^4-816\,a^3\,b^{15}\,c^{19}\,d^3+153\,a^2\,b^{16}\,c^{20}\,d^2-18\,a\,b^{17}\,c^{21}\,d+b^{18}\,c^{22}\right)}\right)}\right)\,{\left(-\frac{14641\,a^4\,b^7\,d^4+5324\,a^3\,b^8\,c\,d^3+726\,a^2\,b^9\,c^2\,d^2+44\,a\,b^{10}\,c^3\,d+b^{11}\,c^4}{4096\,a^{19}\,d^{16}-65536\,a^{18}\,b\,c\,d^{15}+491520\,a^{17}\,b^2\,c^2\,d^{14}-2293760\,a^{16}\,b^3\,c^3\,d^{13}+7454720\,a^{15}\,b^4\,c^4\,d^{12}-17891328\,a^{14}\,b^5\,c^5\,d^{11}+32800768\,a^{13}\,b^6\,c^6\,d^{10}-46858240\,a^{12}\,b^7\,c^7\,d^9+52715520\,a^{11}\,b^8\,c^8\,d^8-46858240\,a^{10}\,b^9\,c^9\,d^7+32800768\,a^9\,b^{10}\,c^{10}\,d^6-17891328\,a^8\,b^{11}\,c^{11}\,d^5+7454720\,a^7\,b^{12}\,c^{12}\,d^4-2293760\,a^6\,b^{13}\,c^{13}\,d^3+491520\,a^5\,b^{14}\,c^{14}\,d^2-65536\,a^4\,b^{15}\,c^{15}\,d+4096\,a^3\,b^{16}\,c^{16}}\right)}^{1/4}\,2{}\mathrm{i}+2\,\mathrm{atan}\left(\frac{{\left(-\frac{14641\,a^4\,b^7\,d^4+5324\,a^3\,b^8\,c\,d^3+726\,a^2\,b^9\,c^2\,d^2+44\,a\,b^{10}\,c^3\,d+b^{11}\,c^4}{4096\,a^{19}\,d^{16}-65536\,a^{18}\,b\,c\,d^{15}+491520\,a^{17}\,b^2\,c^2\,d^{14}-2293760\,a^{16}\,b^3\,c^3\,d^{13}+7454720\,a^{15}\,b^4\,c^4\,d^{12}-17891328\,a^{14}\,b^5\,c^5\,d^{11}+32800768\,a^{13}\,b^6\,c^6\,d^{10}-46858240\,a^{12}\,b^7\,c^7\,d^9+52715520\,a^{11}\,b^8\,c^8\,d^8-46858240\,a^{10}\,b^9\,c^9\,d^7+32800768\,a^9\,b^{10}\,c^{10}\,d^6-17891328\,a^8\,b^{11}\,c^{11}\,d^5+7454720\,a^7\,b^{12}\,c^{12}\,d^4-2293760\,a^6\,b^{13}\,c^{13}\,d^3+491520\,a^5\,b^{14}\,c^{14}\,d^2-65536\,a^4\,b^{15}\,c^{15}\,d+4096\,a^3\,b^{16}\,c^{16}}\right)}^{1/4}\,\left(\left(\left(\frac{{\left(-\frac{14641\,a^4\,b^7\,d^4+5324\,a^3\,b^8\,c\,d^3+726\,a^2\,b^9\,c^2\,d^2+44\,a\,b^{10}\,c^3\,d+b^{11}\,c^4}{4096\,a^{19}\,d^{16}-65536\,a^{18}\,b\,c\,d^{15}+491520\,a^{17}\,b^2\,c^2\,d^{14}-2293760\,a^{16}\,b^3\,c^3\,d^{13}+7454720\,a^{15}\,b^4\,c^4\,d^{12}-17891328\,a^{14}\,b^5\,c^5\,d^{11}+32800768\,a^{13}\,b^6\,c^6\,d^{10}-46858240\,a^{12}\,b^7\,c^7\,d^9+52715520\,a^{11}\,b^8\,c^8\,d^8-46858240\,a^{10}\,b^9\,c^9\,d^7+32800768\,a^9\,b^{10}\,c^{10}\,d^6-17891328\,a^8\,b^{11}\,c^{11}\,d^5+7454720\,a^7\,b^{12}\,c^{12}\,d^4-2293760\,a^6\,b^{13}\,c^{13}\,d^3+491520\,a^5\,b^{14}\,c^{14}\,d^2-65536\,a^4\,b^{15}\,c^{15}\,d+4096\,a^3\,b^{16}\,c^{16}}\right)}^{1/4}\,\left(768\,a^{20}\,b^4\,c^4\,d^{23}-17152\,a^{19}\,b^5\,c^5\,d^{22}+145408\,a^{18}\,b^6\,c^6\,d^{21}-622592\,a^{17}\,b^7\,c^7\,d^{20}+1205248\,a^{16}\,b^8\,c^8\,d^{19}+1309696\,a^{15}\,b^9\,c^9\,d^{18}-16185344\,a^{14}\,b^{10}\,c^{10}\,d^{17}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2}\,c^{16}\,d^6-8568\,a^5\,b^{13}\,c^{17}\,d^5+3060\,a^4\,b^{14}\,c^{18}\,d^4-816\,a^3\,b^{15}\,c^{19}\,d^3+153\,a^2\,b^{16}\,c^{20}\,d^2-18\,a\,b^{17}\,c^{21}\,d+b^{18}\,c^{22}\right)}\right)+{\left(-\frac{14641\,a^4\,b^7\,d^4+5324\,a^3\,b^8\,c\,d^3+726\,a^2\,b^9\,c^2\,d^2+44\,a\,b^{10}\,c^3\,d+b^{11}\,c^4}{4096\,a^{19}\,d^{16}-65536\,a^{18}\,b\,c\,d^{15}+491520\,a^{17}\,b^2\,c^2\,d^{14}-2293760\,a^{16}\,b^3\,c^3\,d^{13}+7454720\,a^{15}\,b^4\,c^4\,d^{12}-17891328\,a^{14}\,b^5\,c^5\,d^{11}+32800768\,a^{13}\,b^6\,c^6\,d^{10}-46858240\,a^{12}\,b^7\,c^7\,d^9+52715520\,a^{11}\,b^8\,c^8\,d^8-46858240\,a^{10}\,b^9\,c^9\,d^7+32800768\,a^9\,b^{10}\,c^{10}\,d^6-17891328\,a^8\,b^{11}\,c^{11}\,d^5+7454720\,a^7\,b^{12}\,c^{12}\,d^4-2293760\,a^6\,b^{13}\,c^{13}\,d^3+491520\,a^5\,b^{14}\,c^{14}\,d^2-65536\,a^4\,b^{15}\,c^{15}\,d+4096\,a^3\,b^{16}\,c^{16}}\right)}^{1/4}\,\left(\left(\left(\frac{{\left(-\frac{14641\,a^4\,b^7\,d^4+5324\,a^3\,b^8\,c\,d^3+726\,a^2\,b^9\,c^2\,d^2+44\,a\,b^{10}\,c^3\,d+b^{11}\,c^4}{4096\,a^{19}\,d^{16}-65536\,a^{18}\,b\,c\,d^{15}+491520\,a^{17}\,b^2\,c^2\,d^{14}-2293760\,a^{16}\,b^3\,c^3\,d^{13}+7454720\,a^{15}\,b^4\,c^4\,d^{12}-17891328\,a^{14}\,b^5\,c^5\,d^{11}+32800768\,a^{13}\,b^6\,c^6\,d^{10}-46858240\,a^{12}\,b^7\,c^7\,d^9+52715520\,a^{11}\,b^8\,c^8\,d^8-46858240\,a^{10}\,b^9\,c^9\,d^7+32800768\,a^9\,b^{10}\,c^{10}\,d^6-17891328\,a^8\,b^{11}\,c^{11}\,d^5+7454720\,a^7\,b^{12}\,c^{12}\,d^4-2293760\,a^6\,b^{13}\,c^{13}\,d^3+491520\,a^5\,b^{14}\,c^{14}\,d^2-65536\,a^4\,b^{15}\,c^{15}\,d+4096\,a^3\,b^{16}\,c^{16}}\right)}^{1/4}\,\left(768\,a^{20}\,b^4\,c^4\,d^{23}-17152\,a^{19}\,b^5\,c^5\,d^{22}+145408\,a^{18}\,b^6\,c^6\,d^{21}-622592\,a^{17}\,b^7\,c^7\,d^{20}+1205248\,a^{16}\,b^8\,c^8\,d^{19}+1309696\,a^{15}\,b^9\,c^9\,d^{18}-16185344\,a^{14}\,b^{10}\,c^{10}\,d^{17}+55883776\,a^{13}\,b^{11}\,c^{11}\,d^{16}-122330624\,a^{12}\,b^{12}\,c^{12}\,d^{15}+193363456\,a^{11}\,b^{13}\,c^{13}\,d^{14}-231069696\,a^{10}\,b^{14}\,c^{14}\,d^{13}+212486144\,a^9\,b^{15}\,c^{15}\,d^{12}-150731776\,a^8\,b^{16}\,c^{16}\,d^{11}+81665024\,a^7\,b^{17}\,c^{17}\,d^{10}-32966656\,a^6\,b^{18}\,c^{18}\,d^9+9439232\,a^5\,b^{19}\,c^{19}\,d^8-1723648\,a^4\,b^{20}\,c^{20}\,d^7+142592\,a^3\,b^{21}\,c^{21}\,d^6+8192\,a^2\,b^{22}\,c^{22}\,d^5-2048\,a\,b^{23}\,c^{23}\,d^4\right)}{-a^{13}\,c^4\,d^{13}+13\,a^{12}\,b\,c^5\,d^{12}-78\,a^{11}\,b^2\,c^6\,d^{11}+286\,a^{10}\,b^3\,c^7\,d^{10}-715\,a^9\,b^4\,c^8\,d^9+1287\,a^8\,b^5\,c^9\,d^8-1716\,a^7\,b^6\,c^{10}\,d^7+1716\,a^6\,b^7\,c^{11}\,d^6-1287\,a^5\,b^8\,c^{12}\,d^5+715\,a^4\,b^9\,c^{13}\,d^4-286\,a^3\,b^{10}\,c^{14}\,d^3+78\,a^2\,b^{11}\,c^{15}\,d^2-13\,a\,b^{12}\,c^{16}\,d+b^{13}\,c^{17}}+\frac{\sqrt{x}\,\left(2359296\,a^{23}\,b^4\,c^2\,d^{27}-72351744\,a^{22}\,b^5\,c^3\,d^{26}+842530816\,a^{21}\,b^6\,c^4\,d^{25}-4677697536\,a^{20}\,b^7\,c^5\,d^{24}+11707613184\,a^{19}\,b^8\,c^6\,d^{23}+7226785792\,a^{18}\,b^9\,c^7\,d^{22}-162426519552\,a^{17}\,b^{10}\,c^8\,d^{21}+654475001856\,a^{16}\,b^{11}\,c^9\,d^{20}-1671068909568\,a^{15}\,b^{12}\,c^{10}\,d^{19}+3274973380608\,a^{14}\,b^{13}\,c^{11}\,d^{18}-5429806497792\,a^{13}\,b^{14}\,c^{12}\,d^{17}+7971285237760\,a^{12}\,b^{15}\,c^{13}\,d^{16}-10296755748864\,a^{11}\,b^{16}\,c^{14}\,d^{15}+11280643522560\,a^{10}\,b^{17}\,c^{15}\,d^{14}-10068131053568\,a^9\,b^{18}\,c^{16}\,d^{13}+7070048845824\,a^8\,b^{19}\,c^{17}\,d^{12}-3770791231488\,a^7\,b^{20}\,c^{18}\,d^{11}+1452876496896\,a^6\,b^{21}\,c^{19}\,d^{10}-366041628672\,a^5\,b^{22}\,c^{20}\,d^9+43464523776\,a^4\,b^{23}\,c^{21}\,d^8+3970170880\,a^3\,b^{24}\,c^{22}\,d^7-1862270976\,a^2\,b^{25}\,c^{23}\,d^6+100663296\,a\,b^{26}\,c^{24}\,d^5+16777216\,b^{27}\,c^{25}\,d^4\right)\,1{}\mathrm{i}}{65536\,\left(a^{18}\,c^4\,d^{18}-18\,a^{17}\,b\,c^5\,d^{17}+153\,a^{16}\,b^2\,c^6\,d^{16}-816\,a^{15}\,b^3\,c^7\,d^{15}+3060\,a^{14}\,b^4\,c^8\,d^{14}-8568\,a^{13}\,b^5\,c^9\,d^{13}+18564\,a^{12}\,b^6\,c^{10}\,d^{12}-31824\,a^{11}\,b^7\,c^{11}\,d^{11}+43758\,a^{10}\,b^8\,c^{12}\,d^{10}-48620\,a^9\,b^9\,c^{13}\,d^9+43758\,a^8\,b^{10}\,c^{14}\,d^8-31824\,a^7\,b^{11}\,c^{15}\,d^7+18564\,a^6\,b^{12}\,c^{16}\,d^6-8568\,a^5\,b^{13}\,c^{17}\,d^5+3060\,a^4\,b^{14}\,c^{18}\,d^4-816\,a^3\,b^{15}\,c^{19}\,d^3+153\,a^2\,b^{16}\,c^{20}\,d^2-18\,a\,b^{17}\,c^{21}\,d+b^{18}\,c^{22}\right)}\right)\,{\left(-\frac{14641\,a^4\,b^7\,d^4+5324\,a^3\,b^8\,c\,d^3+726\,a^2\,b^9\,c^2\,d^2+44\,a\,b^{10}\,c^3\,d+b^{11}\,c^4}{4096\,a^{19}\,d^{16}-65536\,a^{18}\,b\,c\,d^{15}+491520\,a^{17}\,b^2\,c^2\,d^{14}-2293760\,a^{16}\,b^3\,c^3\,d^{13}+7454720\,a^{15}\,b^4\,c^4\,d^{12}-17891328\,a^{14}\,b^5\,c^5\,d^{11}+32800768\,a^{13}\,b^6\,c^6\,d^{10}-46858240\,a^{12}\,b^7\,c^7\,d^9+52715520\,a^{11}\,b^8\,c^8\,d^8-46858240\,a^{10}\,b^9\,c^9\,d^7+32800768\,a^9\,b^{10}\,c^{10}\,d^6-17891328\,a^8\,b^{11}\,c^{11}\,d^5+7454720\,a^7\,b^{12}\,c^{12}\,d^4-2293760\,a^6\,b^{13}\,c^{13}\,d^3+491520\,a^5\,b^{14}\,c^{14}\,d^2-65536\,a^4\,b^{15}\,c^{15}\,d+4096\,a^3\,b^{16}\,c^{16}}\right)}^{3/4}\,1{}\mathrm{i}+\frac{\left(\frac{891\,a^9\,b^7\,d^{15}}{8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0}-191931351040\,a^9\,b^7\,c^{14}\,d^9+215922769920\,a^8\,b^8\,c^{15}\,d^8-191931351040\,a^7\,b^9\,c^{16}\,d^7+134351945728\,a^6\,b^{10}\,c^{17}\,d^6-73282879488\,a^5\,b^{11}\,c^{18}\,d^5+30534533120\,a^4\,b^{12}\,c^{19}\,d^4-9395240960\,a^3\,b^{13}\,c^{20}\,d^3+2013265920\,a^2\,b^{14}\,c^{21}\,d^2-268435456\,a\,b^{15}\,c^{22}\,d+16777216\,b^{16}\,c^{23}}\right)}^{1/4}-\frac{\sqrt{x}\,\left(9801\,a^{10}\,b^9\,d^{17}-285714\,a^9\,b^{10}\,c\,d^{16}+10537245\,a^8\,b^{11}\,c^2\,d^{15}-113554584\,a^7\,b^{12}\,c^3\,d^{14}-117967102\,a^6\,b^{13}\,c^4\,d^{13}+2987403540\,a^5\,b^{14}\,c^5\,d^{12}+8099206482\,a^4\,b^{15}\,c^6\,d^{11}+7295711720\,a^3\,b^{16}\,c^7\,d^{10}+5434132341\,a^2\,b^{17}\,c^8\,d^9+830454702\,a\,b^{18}\,c^9\,d^8+35532497\,b^{19}\,c^{10}\,d^7\right)}{65536\,\left(a^{18}\,c^4\,d^{18}-18\,a^{17}\,b\,c^5\,d^{17}+153\,a^{16}\,b^2\,c^6\,d^{16}-816\,a^{15}\,b^3\,c^7\,d^{15}+3060\,a^{14}\,b^4\,c^8\,d^{14}-8568\,a^{13}\,b^5\,c^9\,d^{13}+18564\,a^{12}\,b^6\,c^{10}\,d^{12}-31824\,a^{11}\,b^7\,c^{11}\,d^{11}+43758\,a^{10}\,b^8\,c^{12}\,d^{10}-48620\,a^9\,b^9\,c^{13}\,d^9+43758\,a^8\,b^{10}\,c^{14}\,d^8-31824\,a^7\,b^{11}\,c^{15}\,d^7+18564\,a^6\,b^{12}\,c^{16}\,d^6-8568\,a^5\,b^{13}\,c^{17}\,d^5+3060\,a^4\,b^{14}\,c^{18}\,d^4-816\,a^3\,b^{15}\,c^{19}\,d^3+153\,a^2\,b^{16}\,c^{20}\,d^2-18\,a\,b^{17}\,c^{21}\,d+b^{18}\,c^{22}\right)}\right)\,{\left(-\frac{81\,a^8\,d^{11}-2376\,a^7\,b\,c\,d^{10}+17820\,a^6\,b^2\,c^2\,d^9+55176\,a^5\,b^3\,c^3\,d^8-787226\,a^4\,b^4\,c^4\,d^7-1416184\,a^3\,b^5\,c^5\,d^6+11739420\,a^2\,b^6\,c^6\,d^5+40174904\,a\,b^7\,c^7\,d^4+35153041\,b^8\,c^8\,d^3}{16777216\,a^{16}\,c^7\,d^{16}-268435456\,a^{15}\,b\,c^8\,d^{15}+2013265920\,a^{14}\,b^2\,c^9\,d^{14}-9395240960\,a^{13}\,b^3\,c^{10}\,d^{13}+30534533120\,a^{12}\,b^4\,c^{11}\,d^{12}-73282879488\,a^{11}\,b^5\,c^{12}\,d^{11}+134351945728\,a^{10}\,b^6\,c^{13}\,d^{10}-191931351040\,a^9\,b^7\,c^{14}\,d^9+215922769920\,a^8\,b^8\,c^{15}\,d^8-191931351040\,a^7\,b^9\,c^{16}\,d^7+134351945728\,a^6\,b^{10}\,c^{17}\,d^6-73282879488\,a^5\,b^{11}\,c^{18}\,d^5+30534533120\,a^4\,b^{12}\,c^{19}\,d^4-9395240960\,a^3\,b^{13}\,c^{20}\,d^3+2013265920\,a^2\,b^{14}\,c^{21}\,d^2-268435456\,a\,b^{15}\,c^{22}\,d+16777216\,b^{16}\,c^{23}}\right)}^{1/4}+\left(\left(\frac{891\,a^9\,b^7\,d^{15}-25164\,a^8\,b^8\,c\,d^{14}+168480\,a^7\,b^9\,c^2\,d^{13}+793236\,a^6\,b^{10}\,c^3\,d^{12}+14677502\,a^5\,b^{11}\,c^4\,d^{11}-158426308\,a^4\,b^{12}\,c^5\,d^{10}-666770056\,a^3\,b^{13}\,c^6\,d^9-431110148\,a^2\,b^{14}\,c^7\,d^8-33367697\,a\,b^{15}\,c^8\,d^7+39424\,b^{16}\,c^9\,d^6}{8192\,\left(-a^{13}\,c^4\,d^{13}+13\,a^{12}\,b\,c^5\,d^{12}-78\,a^{11}\,b^2\,c^6\,d^{11}+286\,a^{10}\,b^3\,c^7\,d^{10}-715\,a^9\,b^4\,c^8\,d^9+1287\,a^8\,b^5\,c^9\,d^8-1716\,a^7\,b^6\,c^{10}\,d^7+1716\,a^6\,b^7\,c^{11}\,d^6-1287\,a^5\,b^8\,c^{12}\,d^5+715\,a^4\,b^9\,c^{13}\,d^4-286\,a^3\,b^{10}\,c^{14}\,d^3+78\,a^2\,b^{11}\,c^{15}\,d^2-13\,a\,b^{12}\,c^{16}\,d+b^{13}\,c^{17}\right)}+\left(\frac{{\left(-\frac{81\,a^8\,d^{11}-2376\,a^7\,b\,c\,d^{10}+17820\,a^6\,b^2\,c^2\,d^9+55176\,a^5\,b^3\,c^3\,d^8-787226\,a^4\,b^4\,c^4\,d^7-1416184\,a^3\,b^5\,c^5\,d^6+11739420\,a^2\,b^6\,c^6\,d^5+40174904\,a\,b^7\,c^7\,d^4+35153041\,b^8\,c^8\,d^3}{16777216\,a^{16}\,c^7\,d^{16}-268435456\,a^{15}\,b\,c^8\,d^{15}+2013265920\,a^{14}\,b^2\,c^9\,d^{14}-9395240960\,a^{13}\,b^3\,c^{10}\,d^{13}+30534533120\,a^{12}\,b^4\,c^{11}\,d^{12}-73282879488\,a^{11}\,b^5\,c^{12}\,d^{11}+134351945728\,a^{10}\,b^6\,c^{13}\,d^{10}-191931351040\,a^9\,b^7\,c^{14}\,d^9+215922769920\,a^8\,b^8\,c^{15}\,d^8-191931351040\,a^7\,b^9\,c^{16}\,d^7+134351945728\,a^6\,b^{10}\,c^{17}\,d^6-73282879488\,a^5\,b^{11}\,c^{18}\,d^5+30534533120\,a^4\,b^{12}\,c^{19}\,d^4-9395240960\,a^3\,b^{13}\,c^{20}\,d^3+2013265920\,a^2\,b^{14}\,c^{21}\,d^2-268435456\,a\,b^{15}\,c^{22}\,d+16777216\,b^{16}\,c^{23}}\right)}^{1/4}\,\left(6291456\,a^{20}\,b^4\,c^4\,d^{23}-140509184\,a^{19}\,b^5\,c^5\,d^{22}+1191182336\,a^{18}\,b^6\,c^6\,d^{21}-5100273664\,a^{17}\,b^7\,c^7\,d^{20}+9873391616\,a^{16}\,b^8\,c^8\,d^{19}+10729029632\,a^{15}\,b^9\,c^9\,d^{18}-132590338048\,a^{14}\,b^{10}\,c^{10}\,d^{17}+457799892992\,a^{13}\,b^{11}\,c^{11}\,d^{16}-1002132471808\,a^{12}\,b^{12}\,c^{12}\,d^{15}+1584033431552\,a^{11}\,b^{13}\,c^{13}\,d^{14}-1892922949632\,a^{10}\,b^{14}\,c^{14}\,d^{13}+1740686491648\,a^9\,b^{15}\,c^{15}\,d^{12}-1234794708992\,a^8\,b^{16}\,c^{16}\,d^{11}+668999876608\,a^7\,b^{17}\,c^{17}\,d^{10}-270062845952\,a^6\,b^{18}\,c^{18}\,d^9+77326188544\,a^5\,b^{19}\,c^{19}\,d^8-14120124416\,a^4\,b^{20}\,c^{20}\,d^7+1168113664\,a^3\,b^{21}\,c^{21}\,d^6+67108864\,a^2\,b^{22}\,c^{22}\,d^5-16777216\,a\,b^{23}\,c^{23}\,d^4\right)}{8192\,\left(-a^{13}\,c^4\,d^{13}+13\,a^{12}\,b\,c^5\,d^{12}-78\,a^{11}\,b^2\,c^6\,d^{11}+286\,a^{10}\,b^3\,c^7\,d^{10}-715\,a^9\,b^4\,c^8\,d^9+1287\,a^8\,b^5\,c^9\,d^8-1716\,a^7\,b^6\,c^{10}\,d^7+1716\,a^6\,b^7\,c^{11}\,d^6-1287\,a^5\,b^8\,c^{12}\,d^5+715\,a^4\,b^9\,c^{13}\,d^4-286\,a^3\,b^{10}\,c^{14}\,d^3+78\,a^2\,b^{11}\,c^{15}\,d^2-13\,a\,b^{12}\,c^{16}\,d+b^{13}\,c^{17}\right)}+\frac{\sqrt{x}\,\left(2359296\,a^{23}\,b^4\,c^2\,d^{27}-72351744\,a^{22}\,b^5\,c^3\,d^{26}+842530816\,a^{21}\,b^6\,c^4\,d^{25}-4677697536\,a^{20}\,b^7\,c^5\,d^{24}+11707613184\,a^{19}\,b^8\,c^6\,d^{23}+7226785792\,a^{18}\,b^9\,c^7\,d^{22}-162426519552\,a^{17}\,b^{10}\,c^8\,d^{21}+654475001856\,a^{16}\,b^{11}\,c^9\,d^{20}-1671068909568\,a^{15}\,b^{12}\,c^{10}\,d^{19}+3274973380608\,a^{14}\,b^{13}\,c^{11}\,d^{18}-5429806497792\,a^{13}\,b^{14}\,c^{12}\,d^{17}+7971285237760\,a^{12}\,b^{15}\,c^{13}\,d^{16}-10296755748864\,a^{11}\,b^{16}\,c^{14}\,d^{15}+11280643522560\,a^{10}\,b^{17}\,c^{15}\,d^{14}-10068131053568\,a^9\,b^{18}\,c^{16}\,d^{13}+7070048845824\,a^8\,b^{19}\,c^{17}\,d^{12}-3770791231488\,a^7\,b^{20}\,c^{18}\,d^{11}+1452876496896\,a^6\,b^{21}\,c^{19}\,d^{10}-366041628672\,a^5\,b^{22}\,c^{20}\,d^9+43464523776\,a^4\,b^{23}\,c^{21}\,d^8+3970170880\,a^3\,b^{24}\,c^{22}\,d^7-1862270976\,a^2\,b^{25}\,c^{23}\,d^6+100663296\,a\,b^{26}\,c^{24}\,d^5+16777216\,b^{27}\,c^{25}\,d^4\right)}{65536\,\left(a^{18}\,c^4\,d^{18}-18\,a^{17}\,b\,c^5\,d^{17}+153\,a^{16}\,b^2\,c^6\,d^{16}-816\,a^{15}\,b^3\,c^7\,d^{15}+3060\,a^{14}\,b^4\,c^8\,d^{14}-8568\,a^{13}\,b^5\,c^9\,d^{13}+18564\,a^{12}\,b^6\,c^{10}\,d^{12}-31824\,a^{11}\,b^7\,c^{11}\,d^{11}+43758\,a^{10}\,b^8\,c^{12}\,d^{10}-48620\,a^9\,b^9\,c^{13}\,d^9+43758\,a^8\,b^{10}\,c^{14}\,d^8-31824\,a^7\,b^{11}\,c^{15}\,d^7+18564\,a^6\,b^{12}\,c^{16}\,d^6-8568\,a^5\,b^{13}\,c^{17}\,d^5+3060\,a^4\,b^{14}\,c^{18}\,d^4-816\,a^3\,b^{15}\,c^{19}\,d^3+153\,a^2\,b^{16}\,c^{20}\,d^2-18\,a\,b^{17}\,c^{21}\,d+b^{18}\,c^{22}\right)}\right)\,{\left(-\frac{81\,a^8\,d^{11}-2376\,a^7\,b\,c\,d^{10}+17820\,a^6\,b^2\,c^2\,d^9+55176\,a^5\,b^3\,c^3\,d^8-787226\,a^4\,b^4\,c^4\,d^7-1416184\,a^3\,b^5\,c^5\,d^6+11739420\,a^2\,b^6\,c^6\,d^5+40174904\,a\,b^7\,c^7\,d^4+35153041\,b^8\,c^8\,d^3}{16777216\,a^{16}\,c^7\,d^{16}-268435456\,a^{15}\,b\,c^8\,d^{15}+2013265920\,a^{14}\,b^2\,c^9\,d^{14}-9395240960\,a^{13}\,b^3\,c^{10}\,d^{13}+30534533120\,a^{12}\,b^4\,c^{11}\,d^{12}-73282879488\,a^{11}\,b^5\,c^{12}\,d^{11}+134351945728\,a^{10}\,b^6\,c^{13}\,d^{10}-191931351040\,a^9\,b^7\,c^{14}\,d^9+215922769920\,a^8\,b^8\,c^{15}\,d^8-191931351040\,a^7\,b^9\,c^{16}\,d^7+134351945728\,a^6\,b^{10}\,c^{17}\,d^6-73282879488\,a^5\,b^{11}\,c^{18}\,d^5+30534533120\,a^4\,b^{12}\,c^{19}\,d^4-9395240960\,a^3\,b^{13}\,c^{20}\,d^3+2013265920\,a^2\,b^{14}\,c^{21}\,d^2-268435456\,a\,b^{15}\,c^{22}\,d+16777216\,b^{16}\,c^{23}}\right)}^{3/4}\right)\,{\left(-\frac{81\,a^8\,d^{11}-2376\,a^7\,b\,c\,d^{10}+17820\,a^6\,b^2\,c^2\,d^9+55176\,a^5\,b^3\,c^3\,d^8-787226\,a^4\,b^4\,c^4\,d^7-1416184\,a^3\,b^5\,c^5\,d^6+11739420\,a^2\,b^6\,c^6\,d^5+40174904\,a\,b^7\,c^7\,d^4+35153041\,b^8\,c^8\,d^3}{16777216\,a^{16}\,c^7\,d^{16}-268435456\,a^{15}\,b\,c^8\,d^{15}+2013265920\,a^{14}\,b^2\,c^9\,d^{14}-9395240960\,a^{13}\,b^3\,c^{10}\,d^{13}+30534533120\,a^{12}\,b^4\,c^{11}\,d^{12}-73282879488\,a^{11}\,b^5\,c^{12}\,d^{11}+134351945728\,a^{10}\,b^6\,c^{13}\,d^{10}-191931351040\,a^9\,b^7\,c^{14}\,d^9+215922769920\,a^8\,b^8\,c^{15}\,d^8-191931351040\,a^7\,b^9\,c^{16}\,d^7+134351945728\,a^6\,b^{10}\,c^{17}\,d^6-73282879488\,a^5\,b^{11}\,c^{18}\,d^5+30534533120\,a^4\,b^{12}\,c^{19}\,d^4-9395240960\,a^3\,b^{13}\,c^{20}\,d^3+2013265920\,a^2\,b^{14}\,c^{21}\,d^2-268435456\,a\,b^{15}\,c^{22}\,d+16777216\,b^{16}\,c^{23}}\right)}^{1/4}+\frac{\sqrt{x}\,\left(9801\,a^{10}\,b^9\,d^{17}-285714\,a^9\,b^{10}\,c\,d^{16}+10537245\,a^8\,b^{11}\,c^2\,d^{15}-113554584\,a^7\,b^{12}\,c^3\,d^{14}-117967102\,a^6\,b^{13}\,c^4\,d^{13}+2987403540\,a^5\,b^{14}\,c^5\,d^{12}+8099206482\,a^4\,b^{15}\,c^6\,d^{11}+7295711720\,a^3\,b^{16}\,c^7\,d^{10}+5434132341\,a^2\,b^{17}\,c^8\,d^9+830454702\,a\,b^{18}\,c^9\,d^8+35532497\,b^{19}\,c^{10}\,d^7\right)}{65536\,\left(a^{18}\,c^4\,d^{18}-18\,a^{17}\,b\,c^5\,d^{17}+153\,a^{16}\,b^2\,c^6\,d^{16}-816\,a^{15}\,b^3\,c^7\,d^{15}+3060\,a^{14}\,b^4\,c^8\,d^{14}-8568\,a^{13}\,b^5\,c^9\,d^{13}+18564\,a^{12}\,b^6\,c^{10}\,d^{12}-31824\,a^{11}\,b^7\,c^{11}\,d^{11}+43758\,a^{10}\,b^8\,c^{12}\,d^{10}-48620\,a^9\,b^9\,c^{13}\,d^9+43758\,a^8\,b^{10}\,c^{14}\,d^8-31824\,a^7\,b^{11}\,c^{15}\,d^7+18564\,a^6\,b^{12}\,c^{16}\,d^6-8568\,a^5\,b^{13}\,c^{17}\,d^5+3060\,a^4\,b^{14}\,c^{18}\,d^4-816\,a^3\,b^{15}\,c^{19}\,d^3+153\,a^2\,b^{16}\,c^{20}\,d^2-18\,a\,b^{17}\,c^{21}\,d+b^{18}\,c^{22}\right)}\right)\,{\left(-\frac{81\,a^8\,d^{11}-2376\,a^7\,b\,c\,d^{10}+17820\,a^6\,b^2\,c^2\,d^9+55176\,a^5\,b^3\,c^3\,d^8-787226\,a^4\,b^4\,c^4\,d^7-1416184\,a^3\,b^5\,c^5\,d^6+11739420\,a^2\,b^6\,c^6\,d^5+40174904\,a\,b^7\,c^7\,d^4+35153041\,b^8\,c^8\,d^3}{16777216\,a^{16}\,c^7\,d^{16}-268435456\,a^{15}\,b\,c^8\,d^{15}+2013265920\,a^{14}\,b^2\,c^9\,d^{14}-9395240960\,a^{13}\,b^3\,c^{10}\,d^{13}+30534533120\,a^{12}\,b^4\,c^{11}\,d^{12}-73282879488\,a^{11}\,b^5\,c^{12}\,d^{11}+134351945728\,a^{10}\,b^6\,c^{13}\,d^{10}-191931351040\,a^9\,b^7\,c^{14}\,d^9+215922769920\,a^8\,b^8\,c^{15}\,d^8-191931351040\,a^7\,b^9\,c^{16}\,d^7+134351945728\,a^6\,b^{10}\,c^{17}\,d^6-73282879488\,a^5\,b^{11}\,c^{18}\,d^5+30534533120\,a^4\,b^{12}\,c^{19}\,d^4-9395240960\,a^3\,b^{13}\,c^{20}\,d^3+2013265920\,a^2\,b^{14}\,c^{21}\,d^2-268435456\,a\,b^{15}\,c^{22}\,d+16777216\,b^{16}\,c^{23}}\right)}^{1/4}}\right)\,{\left(-\frac{81\,a^8\,d^{11}-2376\,a^7\,b\,c\,d^{10}+17820\,a^6\,b^2\,c^2\,d^9+55176\,a^5\,b^3\,c^3\,d^8-787226\,a^4\,b^4\,c^4\,d^7-1416184\,a^3\,b^5\,c^5\,d^6+11739420\,a^2\,b^6\,c^6\,d^5+40174904\,a\,b^7\,c^7\,d^4+35153041\,b^8\,c^8\,d^3}{16777216\,a^{16}\,c^7\,d^{16}-268435456\,a^{15}\,b\,c^8\,d^{15}+2013265920\,a^{14}\,b^2\,c^9\,d^{14}-9395240960\,a^{13}\,b^3\,c^{10}\,d^{13}+30534533120\,a^{12}\,b^4\,c^{11}\,d^{12}-73282879488\,a^{11}\,b^5\,c^{12}\,d^{11}+134351945728\,a^{10}\,b^6\,c^{13}\,d^{10}-191931351040\,a^9\,b^7\,c^{14}\,d^9+215922769920\,a^8\,b^8\,c^{15}\,d^8-191931351040\,a^7\,b^9\,c^{16}\,d^7+134351945728\,a^6\,b^{10}\,c^{17}\,d^6-73282879488\,a^5\,b^{11}\,c^{18}\,d^5+30534533120\,a^4\,b^{12}\,c^{19}\,d^4-9395240960\,a^3\,b^{13}\,c^{20}\,d^3+2013265920\,a^2\,b^{14}\,c^{21}\,d^2-268435456\,a\,b^{15}\,c^{22}\,d+16777216\,b^{16}\,c^{23}}\right)}^{1/4}\,2{}\mathrm{i}","Not 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73282879488*a^11*b^5*c^12*d^11 + 30534533120*a^12*b^4*c^11*d^12 - 9395240960*a^13*b^3*c^10*d^13 + 2013265920*a^14*b^2*c^9*d^14 - 268435456*a*b^15*c^22*d))^(3/4))*(-(81*a^8*d^11 + 35153041*b^8*c^8*d^3 + 40174904*a*b^7*c^7*d^4 + 11739420*a^2*b^6*c^6*d^5 - 1416184*a^3*b^5*c^5*d^6 - 787226*a^4*b^4*c^4*d^7 + 55176*a^5*b^3*c^3*d^8 + 17820*a^6*b^2*c^2*d^9 - 2376*a^7*b*c*d^10)/(16777216*b^16*c^23 + 16777216*a^16*c^7*d^16 - 268435456*a^15*b*c^8*d^15 + 2013265920*a^2*b^14*c^21*d^2 - 9395240960*a^3*b^13*c^20*d^3 + 30534533120*a^4*b^12*c^19*d^4 - 73282879488*a^5*b^11*c^18*d^5 + 134351945728*a^6*b^10*c^17*d^6 - 191931351040*a^7*b^9*c^16*d^7 + 215922769920*a^8*b^8*c^15*d^8 - 191931351040*a^9*b^7*c^14*d^9 + 134351945728*a^10*b^6*c^13*d^10 - 73282879488*a^11*b^5*c^12*d^11 + 30534533120*a^12*b^4*c^11*d^12 - 9395240960*a^13*b^3*c^10*d^13 + 2013265920*a^14*b^2*c^9*d^14 - 268435456*a*b^15*c^22*d))^(1/4) + (x^(1/2)*(9801*a^10*b^9*d^17 + 35532497*b^19*c^10*d^7 + 830454702*a*b^18*c^9*d^8 - 285714*a^9*b^10*c*d^16 + 5434132341*a^2*b^17*c^8*d^9 + 7295711720*a^3*b^16*c^7*d^10 + 8099206482*a^4*b^15*c^6*d^11 + 2987403540*a^5*b^14*c^5*d^12 - 117967102*a^6*b^13*c^4*d^13 - 113554584*a^7*b^12*c^3*d^14 + 10537245*a^8*b^11*c^2*d^15))/(65536*(b^18*c^22 + a^18*c^4*d^18 - 18*a^17*b*c^5*d^17 + 153*a^2*b^16*c^20*d^2 - 816*a^3*b^15*c^19*d^3 + 3060*a^4*b^14*c^18*d^4 - 8568*a^5*b^13*c^17*d^5 + 18564*a^6*b^12*c^16*d^6 - 31824*a^7*b^11*c^15*d^7 + 43758*a^8*b^10*c^14*d^8 - 48620*a^9*b^9*c^13*d^9 + 43758*a^10*b^8*c^12*d^10 - 31824*a^11*b^7*c^11*d^11 + 18564*a^12*b^6*c^10*d^12 - 8568*a^13*b^5*c^9*d^13 + 3060*a^14*b^4*c^8*d^14 - 816*a^15*b^3*c^7*d^15 + 153*a^16*b^2*c^6*d^16 - 18*a*b^17*c^21*d)))*(-(81*a^8*d^11 + 35153041*b^8*c^8*d^3 + 40174904*a*b^7*c^7*d^4 + 11739420*a^2*b^6*c^6*d^5 - 1416184*a^3*b^5*c^5*d^6 - 787226*a^4*b^4*c^4*d^7 + 55176*a^5*b^3*c^3*d^8 + 17820*a^6*b^2*c^2*d^9 - 2376*a^7*b*c*d^10)/(16777216*b^16*c^23 + 16777216*a^16*c^7*d^16 - 268435456*a^15*b*c^8*d^15 + 2013265920*a^2*b^14*c^21*d^2 - 9395240960*a^3*b^13*c^20*d^3 + 30534533120*a^4*b^12*c^19*d^4 - 73282879488*a^5*b^11*c^18*d^5 + 134351945728*a^6*b^10*c^17*d^6 - 191931351040*a^7*b^9*c^16*d^7 + 215922769920*a^8*b^8*c^15*d^8 - 191931351040*a^9*b^7*c^14*d^9 + 134351945728*a^10*b^6*c^13*d^10 - 73282879488*a^11*b^5*c^12*d^11 + 30534533120*a^12*b^4*c^11*d^12 - 9395240960*a^13*b^3*c^10*d^13 + 2013265920*a^14*b^2*c^9*d^14 - 268435456*a*b^15*c^22*d))^(1/4)))*(-(81*a^8*d^11 + 35153041*b^8*c^8*d^3 + 40174904*a*b^7*c^7*d^4 + 11739420*a^2*b^6*c^6*d^5 - 1416184*a^3*b^5*c^5*d^6 - 787226*a^4*b^4*c^4*d^7 + 55176*a^5*b^3*c^3*d^8 + 17820*a^6*b^2*c^2*d^9 - 2376*a^7*b*c*d^10)/(16777216*b^16*c^23 + 16777216*a^16*c^7*d^16 - 268435456*a^15*b*c^8*d^15 + 2013265920*a^2*b^14*c^21*d^2 - 9395240960*a^3*b^13*c^20*d^3 + 30534533120*a^4*b^12*c^19*d^4 - 73282879488*a^5*b^11*c^18*d^5 + 134351945728*a^6*b^10*c^17*d^6 - 191931351040*a^7*b^9*c^16*d^7 + 215922769920*a^8*b^8*c^15*d^8 - 191931351040*a^9*b^7*c^14*d^9 + 134351945728*a^10*b^6*c^13*d^10 - 73282879488*a^11*b^5*c^12*d^11 + 30534533120*a^12*b^4*c^11*d^12 - 9395240960*a^13*b^3*c^10*d^13 + 2013265920*a^14*b^2*c^9*d^14 - 268435456*a*b^15*c^22*d))^(1/4)*2i","B"
499,1,45858,739,9.581238,"\text{Not used}","int(x^(1/2)/((a + b*x^2)^2*(c + d*x^2)^3),x)","\frac{\frac{x^{7/2}\,\left(-5\,a^3\,d^4+12\,a^2\,b\,c\,d^3+25\,a\,b^2\,c^2\,d^2+16\,b^3\,c^3\,d\right)}{16\,a\,c\,\left(-a^3\,c\,d^3+3\,a^2\,b\,c^2\,d^2-3\,a\,b^2\,c^3\,d+b^3\,c^4\right)}-\frac{x^{3/2}\,\left(-9\,a^3\,d^3+25\,a^2\,b\,c\,d^2+8\,b^3\,c^3\right)}{16\,a\,c\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)}+\frac{b\,d^2\,x^{11/2}\,\left(-5\,a^2\,d^2+21\,a\,b\,c\,d+8\,b^2\,c^2\right)}{16\,a\,c\,\left(-a^3\,c\,d^3+3\,a^2\,b\,c^2\,d^2-3\,a\,b^2\,c^3\,d+b^3\,c^4\right)}}{a\,c^2+x^2\,\left(b\,c^2+2\,a\,d\,c\right)+x^4\,\left(a\,d^2+2\,b\,c\,d\right)+b\,d^2\,x^6}-\mathrm{atan}\left(\frac{{\left(-\frac{625\,a^8\,d^{13}-13000\,a^7\,b\,c\,d^{12}+159900\,a^6\,b^2\,c^2\,d^{11}-1264120\,a^5\,b^3\,c^3\,d^{10}+7255846\,a^4\,b^4\,c^4\,d^9-29580408\,a^3\,b^5\,c^5\,d^8+87554844\,a^2\,b^6\,c^6\,d^7-166567752\,a\,b^7\,c^7\,d^6+187388721\,b^8\,c^8\,d^5}{16777216\,a^{16}\,c^9\,d^{16}-268435456\,a^{15}\,b\,c^{10}\,d^{15}+2013265920\,a^{14}\,b^2\,c^{11}\,d^{14}-9395240960\,a^{13}\,b^3\,c^{12}\,d^{13}+30534533120\,a^{12}\,b^4\,c^{13}\,d^{12}-73282879488\,a^{11}\,b^5\,c^{14}\,d^{11}+134351945728\,a^{10}\,b^6\,c^{15}\,d^{10}-191931351040\,a^9\,b^7\,c^{16}\,d^9+215922769920\,a^8\,b^8\,c^{17}\,d^8-191931351040\,a^7\,b^9\,c^{18}\,d^7+134351945728\,a^6\,b^{10}\,c^{19}\,d^6-73282879488\,a^5\,b^{11}\,c^{20}\,d^5+30534533120\,a^4\,b^{12}\,c^{21}\,d^4-9395240960\,a^3\,b^{13}\,c^{22}\,d^3+2013265920\,a^2\,b^{14}\,c^{23}\,d^2-268435456\,a\,b^{15}\,c^{24}\,d+16777216\,b^{16}\,c^{25}}\right)}^{1/4}\,\left({\left(-\frac{625\,a^8\,d^{13}-13000\,a^7\,b\,c\,d^{12}+159900\,a^6\,b^2\,c^2\,d^{11}-1264120\,a^5\,b^3\,c^3\,d^{10}+7255846\,a^4\,b^4\,c^4\,d^9-29580408\,a^3\,b^5\,c^5\,d^8+87554844\,a^2\,b^6\,c^6\,d^7-166567752\,a\,b^7\,c^7\,d^6+187388721\,b^8\,c^8\,d^5}{16777216\,a^{16}\,c^9\,d^{16}-268435456\,a^{15}\,b\,c^{10}\,d^{15}+2013265920\,a^{14}\,b^2\,c^{11}\,d^{14}-9395240960\,a^{13}\,b^3\,c^{12}\,d^{13}+30534533120\,a^{12}\,b^4\,c^{13}\,d^{12}-73282879488\,a^{11}\,b^5\,c^{14}\,d^{11}+134351945728\,a^{10}\,b^6\,c^{15}\,d^{10}-191931351040\,a^9\,b^7\,c^{16}\,d^9+215922769920\,a^8\,b^8\,c^{17}\,d^8-191931351040\,a^7\,b^9\,c^{18}\,d^7+134351945728\,a^6\,b^{10}\,c^{19}\,d^6-73282879488\,a^5\,b^{11}\,c^{20}\,d^5+30534533120\,a^4\,b^{12}\,c^{21}\,d^4-9395240960\,a^3\,b^{13}\,c^{22}\,d^3+2013265920\,a^2\,b^{14}\,c^{23}\,d^2-268435456\,a\,b^{15}\,c^{24}\,d+16777216\,b^{16}\,c^{25}}\right)}^{3/4}\,\left(\frac{-\frac{125\,a^{26}\,b^4\,c\,d^{30}}{16}+\frac{3825\,a^{25}\,b^5\,c^2\,d^{29}}{16}-\frac{30645\,a^{24}\,b^6\,c^3\,d^{28}}{8}+\frac{327093\,a^{23}\,b^7\,c^4\,d^{27}}{8}-\frac{5119101\,a^{22}\,b^8\,c^5\,d^{26}}{16}+\frac{30778137\,a^{21}\,b^9\,c^6\,d^{25}}{16}-\frac{18239091\,a^{20}\,b^{10}\,c^7\,d^{24}}{2}+\frac{69181515\,a^{19}\,b^{11}\,c^8\,d^{23}}{2}-\frac{845943917\,a^{18}\,b^{12}\,c^9\,d^{22}}{8}+\frac{2088923057\,a^{17}\,b^{13}\,c^{10}\,d^{21}}{8}-\frac{2079521847\,a^{16}\,b^{14}\,c^{11}\,d^{20}}{4}+\frac{3315895143\,a^{15}\,b^{15}\,c^{12}\,d^{19}}{4}-\frac{8341892385\,a^{14}\,b^{16}\,c^{13}\,d^{18}}{8}+\frac{8002341693\,a^{13}\,b^{17}\,c^{14}\,d^{17}}{8}-\frac{1337499867\,a^{12}\,b^{18}\,c^{15}\,d^{16}}{2}+\frac{409977699\,a^{11}\,b^{19}\,c^{16}\,d^{15}}{2}+\frac{2530187127\,a^{10}\,b^{20}\,c^{17}\,d^{14}}{16}-\frac{4711274035\,a^9\,b^{21}\,c^{18}\,d^{13}}{16}+\frac{1980689243\,a^8\,b^{22}\,c^{19}\,d^{12}}{8}-\frac{1116788283\,a^7\,b^{23}\,c^{20}\,d^{11}}{8}+\frac{903579807\,a^6\,b^{24}\,c^{21}\,d^{10}}{16}-\frac{263413683\,a^5\,b^{25}\,c^{22}\,d^9}{16}+3369600\,a^4\,b^{26}\,c^{23}\,d^8-459264\,a^3\,b^{27}\,c^{24}\,d^7+38304\,a^2\,b^{28}\,c^{25}\,d^6-1728\,a\,b^{29}\,c^{26}\,d^5+32\,b^{30}\,c^{27}\,d^4}{-a^{23}\,c^6\,d^{21}+21\,a^{22}\,b\,c^7\,d^{20}-210\,a^{21}\,b^2\,c^8\,d^{19}+1330\,a^{20}\,b^3\,c^9\,d^{18}-5985\,a^{19}\,b^4\,c^{10}\,d^{17}+20349\,a^{18}\,b^5\,c^{11}\,d^{16}-54264\,a^{17}\,b^6\,c^{12}\,d^{15}+116280\,a^{16}\,b^7\,c^{13}\,d^{14}-203490\,a^{15}\,b^8\,c^{14}\,d^{13}+293930\,a^{14}\,b^9\,c^{15}\,d^{12}-352716\,a^{13}\,b^{10}\,c^{16}\,d^{11}+352716\,a^{12}\,b^{11}\,c^{17}\,d^{10}-293930\,a^{11}\,b^{12}\,c^{18}\,d^9+203490\,a^{10}\,b^{13}\,c^{19}\,d^8-116280\,a^9\,b^{14}\,c^{20}\,d^7+54264\,a^8\,b^{15}\,c^{21}\,d^6-20349\,a^7\,b^{16}\,c^{22}\,d^5+5985\,a^6\,b^{17}\,c^{23}\,d^4-1330\,a^5\,b^{18}\,c^{24}\,d^3+210\,a^4\,b^{19}\,c^{25}\,d^2-21\,a^3\,b^{20}\,c^{26}\,d+a^2\,b^{21}\,c^{27}}-\frac{\sqrt{x}\,{\left(-\frac{625\,a^8\,d^{13}-13000\,a^7\,b\,c\,d^{12}+159900\,a^6\,b^2\,c^2\,d^{11}-1264120\,a^5\,b^3\,c^3\,d^{10}+7255846\,a^4\,b^4\,c^4\,d^9-29580408\,a^3\,b^5\,c^5\,d^8+87554844\,a^2\,b^6\,c^6\,d^7-166567752\,a\,b^7\,c^7\,d^6+187388721\,b^8\,c^8\,d^5}{16777216\,a^{16}\,c^9\,d^{16}-268435456\,a^{15}\,b\,c^{10}\,d^{15}+2013265920\,a^{14}\,b^2\,c^{11}\,d^{14}-9395240960\,a^{13}\,b^3\,c^{12}\,d^{13}+30534533120\,a^{12}\,b^4\,c^{13}\,d^{12}-73282879488\,a^{11}\,b^5\,c^{14}\,d^{11}+134351945728\,a^{10}\,b^6\,c^{15}\,d^{10}-191931351040\,a^9\,b^7\,c^{16}\,d^9+215922769920\,a^8\,b^8\,c^{17}\,d^8-191931351040\,a^7\,b^9\,c^{18}\,d^7+134351945728\,a^6\,b^{10}\,c^{19}\,d^6-73282879488\,a^5\,b^{11}\,c^{20}\,d^5+30534533120\,a^4\,b^{12}\,c^{21}\,d^4-9395240960\,a^3\,b^{13}\,c^{22}\,d^3+2013265920\,a^2\,b^{14}\,c^{23}\,d^2-268435456\,a\,b^{15}\,c^{24}\,d+16777216\,b^{16}\,c^{25}}\right)}^{1/4}\,\left(6553600\,a^{25}\,b^4\,c^3\,d^{28}-173015040\,a^{24}\,b^5\,c^4\,d^{27}+2360868864\,a^{23}\,b^6\,c^5\,d^{26}-21186478080\,a^{22}\,b^7\,c^6\,d^{25}+137272492032\,a^{21}\,b^8\,c^7\,d^{24}-672468566016\,a^{20}\,b^9\,c^8\,d^{23}+2557512515584\,a^{19}\,b^{10}\,c^9\,d^{22}-7692575834112\,a^{18}\,b^{11}\,c^{10}\,d^{21}+18584022024192\,a^{17}\,b^{12}\,c^{11}\,d^{20}-36574941151232\,a^{16}\,b^{13}\,c^{12}\,d^{19}+59448946065408\,a^{15}\,b^{14}\,c^{13}\,d^{18}-80877025492992\,a^{14}\,b^{15}\,c^{14}\,d^{17}+93255551680512\,a^{13}\,b^{16}\,c^{15}\,d^{16}-92068449878016\,a^{12}\,b^{17}\,c^{16}\,d^{15}+78238275600384\,a^{11}\,b^{18}\,c^{17}\,d^{14}-57098809376768\,a^{10}\,b^{19}\,c^{18}\,d^{13}+35394969403392\,a^9\,b^{20}\,c^{19}\,d^{12}-18278639468544\,a^8\,b^{21}\,c^{20}\,d^{11}+7656663678976\,a^7\,b^{22}\,c^{21}\,d^{10}-2513987174400\,a^6\,b^{23}\,c^{22}\,d^9+618641227776\,a^5\,b^{24}\,c^{23}\,d^8-107105746944\,a^4\,b^{25}\,c^{24}\,d^7+11827937280\,a^3\,b^{26}\,c^{25}\,d^6-704643072\,a^2\,b^{27}\,c^{26}\,d^5+16777216\,a\,b^{28}\,c^{27}\,d^4\right)}{65536\,\left(a^{20}\,c^6\,d^{18}-18\,a^{19}\,b\,c^7\,d^{17}+153\,a^{18}\,b^2\,c^8\,d^{16}-816\,a^{17}\,b^3\,c^9\,d^{15}+3060\,a^{16}\,b^4\,c^{10}\,d^{14}-8568\,a^{15}\,b^5\,c^{11}\,d^{13}+18564\,a^{14}\,b^6\,c^{12}\,d^{12}-31824\,a^{13}\,b^7\,c^{13}\,d^{11}+43758\,a^{12}\,b^8\,c^{14}\,d^{10}-48620\,a^{11}\,b^9\,c^{15}\,d^9+43758\,a^{10}\,b^{10}\,c^{16}\,d^8-31824\,a^9\,b^{11}\,c^{17}\,d^7+18564\,a^8\,b^{12}\,c^{18}\,d^6-8568\,a^7\,b^{13}\,c^{19}\,d^5+3060\,a^6\,b^{14}\,c^{20}\,d^4-816\,a^5\,b^{15}\,c^{21}\,d^3+153\,a^4\,b^{16}\,c^{22}\,d^2-18\,a^3\,b^{17}\,c^{23}\,d+a^2\,b^{18}\,c^{24}\right)}\right)\,1{}\mathrm{i}-\frac{\sqrt{x}\,\left(105625\,a^{11}\,b^{10}\,d^{19}-2213250\,a^{10}\,b^{11}\,c\,d^{18}+27361725\,a^9\,b^{12}\,c^2\,d^{17}-172109080\,a^8\,b^{13}\,c^3\,d^{16}+769949154\,a^7\,b^{14}\,c^4\,d^{15}-1666839564\,a^6\,b^{15}\,c^5\,d^{14}+3396941522\,a^5\,b^{16}\,c^6\,d^{13}-1891277400\,a^4\,b^{17}\,c^7\,d^{12}+27986891205\,a^3\,b^{18}\,c^8\,d^{11}-4129947458\,a^2\,b^{19}\,c^9\,d^{10}+141442353\,a\,b^{20}\,c^{10}\,d^9+876096\,b^{21}\,c^{11}\,d^8\right)\,1{}\mathrm{i}}{65536\,\left(a^{20}\,c^6\,d^{18}-18\,a^{19}\,b\,c^7\,d^{17}+153\,a^{18}\,b^2\,c^8\,d^{16}-816\,a^{17}\,b^3\,c^9\,d^{15}+3060\,a^{16}\,b^4\,c^{10}\,d^{14}-8568\,a^{15}\,b^5\,c^{11}\,d^{13}+18564\,a^{14}\,b^6\,c^{12}\,d^{12}-31824\,a^{13}\,b^7\,c^{13}\,d^{11}+43758\,a^{12}\,b^8\,c^{14}\,d^{10}-48620\,a^{11}\,b^9\,c^{15}\,d^9+43758\,a^{10}\,b^{10}\,c^{16}\,d^8-31824\,a^9\,b^{11}\,c^{17}\,d^7+18564\,a^8\,b^{12}\,c^{18}\,d^6-8568\,a^7\,b^{13}\,c^{19}\,d^5+3060\,a^6\,b^{14}\,c^{20}\,d^4-816\,a^5\,b^{15}\,c^{21}\,d^3+153\,a^4\,b^{16}\,c^{22}\,d^2-18\,a^3\,b^{17}\,c^{23}\,d+a^2\,b^{18}\,c^{24}\right)}\right)-{\left(-\frac{625\,a^8\,d^{13}-13000\,a^7\,b\,c\,d^{12}+159900\,a^6\,b^2\,c^2\,d^{11}-1264120\,a^5\,b^3\,c^3\,d^{10}+7255846\,a^4\,b^4\,c^4\,d^9-29580408\,a^3\,b^5\,c^5\,d^8+87554844\,a^2\,b^6\,c^6\,d^7-166567752\,a\,b^7\,c^7\,d^6+187388721\,b^8\,c^8\,d^5}{16777216\,a^{16}\,c^9\,d^{16}-268435456\,a^{15}\,b\,c^{10}\,d^{15}+2013265920\,a^{14}\,b^2\,c^{11}\,d^{14}-9395240960\,a^{13}\,b^3\,c^{12}\,d^{13}+30534533120\,a^{12}\,b^4\,c^{13}\,d^{12}-73282879488\,a^{11}\,b^5\,c^{14}\,d^{11}+134351945728\,a^{10}\,b^6\,c^{15}\,d^{10}-191931351040\,a^9\,b^7\,c^{16}\,d^9+215922769920\,a^8\,b^8\,c^{17}\,d^8-191931351040\,a^7\,b^9\,c^{18}\,d^7+134351945728\,a^6\,b^{10}\,c^{19}\,d^6-73282879488\,a^5\,b^{11}\,c^{20}\,d^5+30534533120\,a^4\,b^{12}\,c^{21}\,d^4-9395240960\,a^3\,b^{13}\,c^{22}\,d^3+2013265920\,a^2\,b^{14}\,c^{23}\,d^2-268435456\,a\,b^{15}\,c^{24}\,d+16777216\,b^{16}\,c^{25}}\right)}^{1/4}\,\left({\left(-\frac{625\,a^8\,d^{13}-13000\,a^7\,b\,c\,d^{12}+159900\,a^6\,b^2\,c^2\,d^{11}-1264120\,a^5\,b^3\,c^3\,d^{10}+7255846\,a^4\,b^4\,c^4\,d^9-29580408\,a^3\,b^5\,c^5\,d^8+87554844\,a^2\,b^6\,c^6\,d^7-166567752\,a\,b^7\,c^7\,d^6+187388721\,b^8\,c^8\,d^5}{16777216\,a^{16}\,c^9\,d^{16}-268435456\,a^{15}\,b\,c^{10}\,d^{15}+2013265920\,a^{14}\,b^2\,c^{11}\,d^{14}-9395240960\,a^{13}\,b^3\,c^{12}\,d^{13}+30534533120\,a^{12}\,b^4\,c^{13}\,d^{12}-73282879488\,a^{11}\,b^5\,c^{14}\,d^{11}+134351945728\,a^{10}\,b^6\,c^{15}\,d^{10}-191931351040\,a^9\,b^7\,c^{16}\,d^9+215922769920\,a^8\,b^8\,c^{17}\,d^8-191931351040\,a^7\,b^9\,c^{18}\,d^7+134351945728\,a^6\,b^{10}\,c^{19}\,d^6-73282879488\,a^5\,b^{11}\,c^{20}\,d^5+30534533120\,a^4\,b^{12}\,c^{21}\,d^4-9395240960\,a^3\,b^{13}\,c^{22}\,d^3+2013265920\,a^2\,b^{14}\,c^{23}\,d^2-268435456\,a\,b^{15}\,c^{24}\,d+16777216\,b^{16}\,c^{25}}\right)}^{3/4}\,\left(\frac{-\frac{125\,a^{26}\,b^4\,c\,d^{30}}{16}+\frac{3825\,a^{25}\,b^5\,c^2\,d^{29}}{16}-\frac{30645\,a^{24}\,b^6\,c^3\,d^{28}}{8}+\frac{327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28\,a^{10}\,b^{11}\,c^{11}\,d^5+7454720\,a^9\,b^{12}\,c^{12}\,d^4-2293760\,a^8\,b^{13}\,c^{13}\,d^3+491520\,a^7\,b^{14}\,c^{14}\,d^2-65536\,a^6\,b^{15}\,c^{15}\,d+4096\,a^5\,b^{16}\,c^{16}}\right)}^{1/4}+\left(\left(\frac{\sqrt{x}\,{\left(-\frac{28561\,a^4\,b^9\,d^4-8788\,a^3\,b^{10}\,c\,d^3+1014\,a^2\,b^{11}\,c^2\,d^2-52\,a\,b^{12}\,c^3\,d+b^{13}\,c^4}{4096\,a^{21}\,d^{16}-65536\,a^{20}\,b\,c\,d^{15}+491520\,a^{19}\,b^2\,c^2\,d^{14}-2293760\,a^{18}\,b^3\,c^3\,d^{13}+7454720\,a^{17}\,b^4\,c^4\,d^{12}-17891328\,a^{16}\,b^5\,c^5\,d^{11}+32800768\,a^{15}\,b^6\,c^6\,d^{10}-46858240\,a^{14}\,b^7\,c^7\,d^9+52715520\,a^{13}\,b^8\,c^8\,d^8-46858240\,a^{12}\,b^9\,c^9\,d^7+32800768\,a^{11}\,b^{10}\,c^{10}\,d^6-17891328\,a^{10}\,b^{11}\,c^{11}\,d^5+7454720\,a^9\,b^{12}\,c^{12}\,d^4-2293760\,a^8\,b^{13}\,c^{13}\,d^3+491520\,a^7\,b^{14}\,c^{14}\,d^2-65536\,a^6\,b^{15}\,c^{15}\,d+4096\,a^5\,b^{16}\,c^{16}}\right)}^{1/4}\,\left(6553600\,a^{25}\,b^4\,c^3\,d^{28}-173015040\,a^{24}\,b^5\,c^4\,d^{27}+2360868864\,a^{23}\,b^6\,c^5\,d^{26}-21186478080\,a^{22}\,b^7\,c^6\,d^{25}+137272492032\,a^{21}\,b^8\,c^7\,d^{24}-672468566016\,a^{20}\,b^9\,c^8\,d^{23}+2557512515584\,a^{19}\,b^{10}\,c^9\,d^{22}-7692575834112\,a^{18}\,b^{11}\,c^{10}\,d^{21}+18584022024192\,a^{17}\,b^{12}\,c^{11}\,d^{20}-36574941151232\,a^{16}\,b^{13}\,c^{12}\,d^{19}+59448946065408\,a^{15}\,b^{14}\,c^{13}\,d^{18}-80877025492992\,a^{14}\,b^{15}\,c^{14}\,d^{17}+93255551680512\,a^{13}\,b^{16}\,c^{15}\,d^{16}-92068449878016\,a^{12}\,b^{17}\,c^{16}\,d^{15}+78238275600384\,a^{11}\,b^{18}\,c^{17}\,d^{14}-57098809376768\,a^{10}\,b^{19}\,c^{18}\,d^{13}+35394969403392\,a^9\,b^{20}\,c^{19}\,d^{12}-18278639468544\,a^8\,b^{21}\,c^{20}\,d^{11}+7656663678976\,a^7\,b^{22}\,c^{21}\,d^{10}-2513987174400\,a^6\,b^{23}\,c^{22}\,d^9+618641227776\,a^5\,b^{24}\,c^{23}\,d^8-107105746944\,a^4\,b^{25}\,c^{24}\,d^7+11827937280\,a^3\,b^{26}\,c^{25}\,d^6-704643072\,a^2\,b^{27}\,c^{26}\,d^5+16777216\,a\,b^{28}\,c^{27}\,d^4\right)}{65536\,\left(a^{20}\,c^6\,d^{18}-18\,a^{19}\,b\,c^7\,d^{17}+153\,a^{18}\,b^2\,c^8\,d^{16}-816\,a^{17}\,b^3\,c^9\,d^{15}+3060\,a^{16}\,b^4\,c^{10}\,d^{14}-8568\,a^{15}\,b^5\,c^{11}\,d^{13}+18564\,a^{14}\,b^6\,c^{12}\,d^{12}-31824\,a^{13}\,b^7\,c^{13}\,d^{11}+43758\,a^{12}\,b^8\,c^{14}\,d^{10}-48620\,a^{11}\,b^9\,c^{15}\,d^9+43758\,a^{10}\,b^{10}\,c^{16}\,d^8-31824\,a^9\,b^{11}\,c^{17}\,d^7+18564\,a^8\,b^{12}\,c^{18}\,d^6-8568\,a^7\,b^{13}\,c^{19}\,d^5+3060\,a^6\,b^{14}\,c^{20}\,d^4-816\,a^5\,b^{15}\,c^{21}\,d^3+153\,a^4\,b^{16}\,c^{22}\,d^2-18\,a^3\,b^{17}\,c^{23}\,d+a^2\,b^{18}\,c^{24}\right)}+\frac{\left(-\frac{125\,a^{26}\,b^4\,c\,d^{30}}{16}+\frac{3825\,a^{25}\,b^5\,c^2\,d^{29}}{16}-\frac{30645\,a^{24}\,b^6\,c^3\,d^{28}}{8}+\frac{327093\,a^{23}\,b^7\,c^4\,d^{27}}{8}-\frac{5119101\,a^{22}\,b^8\,c^5\,d^{26}}{16}+\frac{30778137\,a^{21}\,b^9\,c^6\,d^{25}}{16}-\frac{18239091\,a^{20}\,b^{10}\,c^7\,d^{24}}{2}+\frac{69181515\,a^{19}\,b^{11}\,c^8\,d^{23}}{2}-\frac{845943917\,a^{18}\,b^{12}\,c^9\,d^{22}}{8}+\frac{2088923057\,a^{17}\,b^{13}\,c^{10}\,d^{21}}{8}-\frac{2079521847\,a^{16}\,b^{14}\,c^{11}\,d^{20}}{4}+\frac{3315895143\,a^{15}\,b^{15}\,c^{12}\,d^{19}}{4}-\frac{8341892385\,a^{14}\,b^{16}\,c^{13}\,d^{18}}{8}+\frac{8002341693\,a^{13}\,b^{17}\,c^{14}\,d^{17}}{8}-\frac{1337499867\,a^{12}\,b^{18}\,c^{15}\,d^{16}}{2}+\frac{409977699\,a^{11}\,b^{19}\,c^{16}\,d^{15}}{2}+\frac{2530187127\,a^{10}\,b^{20}\,c^{17}\,d^{14}}{16}-\frac{4711274035\,a^9\,b^{21}\,c^{18}\,d^{13}}{16}+\frac{1980689243\,a^8\,b^{22}\,c^{19}\,d^{12}}{8}-\frac{1116788283\,a^7\,b^{23}\,c^{20}\,d^{11}}{8}+\frac{903579807\,a^6\,b^{24}\,c^{21}\,d^{10}}{16}-\frac{263413683\,a^5\,b^{25}\,c^{22}\,d^9}{16}+3369600\,a^4\,b^{26}\,c^{23}\,d^8-459264\,a^3\,b^{27}\,c^{24}\,d^7+38304\,a^2\,b^{28}\,c^{25}\,d^6-1728\,a\,b^{29}\,c^{26}\,d^5+32\,b^{30}\,c^{27}\,d^4\right)\,1{}\mathrm{i}}{-a^{23}\,c^6\,d^{21}+21\,a^{22}\,b\,c^7\,d^{20}-210\,a^{21}\,b^2\,c^8\,d^{19}+1330\,a^{20}\,b^3\,c^9\,d^{18}-5985\,a^{19}\,b^4\,c^{10}\,d^{17}+20349\,a^{18}\,b^5\,c^{11}\,d^{16}-54264\,a^{17}\,b^6\,c^{12}\,d^{15}+116280\,a^{16}\,b^7\,c^{13}\,d^{14}-203490\,a^{15}\,b^8\,c^{14}\,d^{13}+293930\,a^{14}\,b^9\,c^{15}\,d^{12}-352716\,a^{13}\,b^{10}\,c^{16}\,d^{11}+352716\,a^{12}\,b^{11}\,c^{17}\,d^{10}-293930\,a^{11}\,b^{12}\,c^{18}\,d^9+203490\,a^{10}\,b^{13}\,c^{19}\,d^8-116280\,a^9\,b^{14}\,c^{20}\,d^7+54264\,a^8\,b^{15}\,c^{21}\,d^6-20349\,a^7\,b^{16}\,c^{22}\,d^5+5985\,a^6\,b^{17}\,c^{23}\,d^4-1330\,a^5\,b^{18}\,c^{24}\,d^3+210\,a^4\,b^{19}\,c^{25}\,d^2-21\,a^3\,b^{20}\,c^{26}\,d+a^2\,b^{21}\,c^{27}}\right)\,{\left(-\frac{28561\,a^4\,b^9\,d^4-8788\,a^3\,b^{10}\,c\,d^3+1014\,a^2\,b^{11}\,c^2\,d^2-52\,a\,b^{12}\,c^3\,d+b^{13}\,c^4}{4096\,a^{21}\,d^{16}-65536\,a^{20}\,b\,c\,d^{15}+491520\,a^{19}\,b^2\,c^2\,d^{14}-2293760\,a^{18}\,b^3\,c^3\,d^{13}+7454720\,a^{17}\,b^4\,c^4\,d^{12}-17891328\,a^{16}\,b^5\,c^5\,d^{11}+32800768\,a^{15}\,b^6\,c^6\,d^{10}-46858240\,a^{14}\,b^7\,c^7\,d^9+52715520\,a^{13}\,b^8\,c^8\,d^8-46858240\,a^{12}\,b^9\,c^9\,d^7+32800768\,a^{11}\,b^{10}\,c^{10}\,d^6-17891328\,a^{10}\,b^{11}\,c^{11}\,d^5+7454720\,a^9\,b^{12}\,c^{12}\,d^4-2293760\,a^8\,b^{13}\,c^{13}\,d^3+491520\,a^7\,b^{14}\,c^{14}\,d^2-65536\,a^6\,b^{15}\,c^{15}\,d+4096\,a^5\,b^{16}\,c^{16}}\right)}^{3/4}\,1{}\mathrm{i}+\frac{\sqrt{x}\,\left(105625\,a^{11}\,b^{10}\,d^{19}-2213250\,a^{10}\,b^{11}\,c\,d^{18}+27361725\,a^9\,b^{12}\,c^2\,d^{17}-172109080\,a^8\,b^{13}\,c^3\,d^{16}+769949154\,a^7\,b^{14}\,c^4\,d^{15}-1666839564\,a^6\,b^{15}\,c^5\,d^{14}+3396941522\,a^5\,b^{16}\,c^6\,d^{13}-1891277400\,a^4\,b^{17}\,c^7\,d^{12}+27986891205\,a^3\,b^{18}\,c^8\,d^{11}-4129947458\,a^2\,b^{19}\,c^9\,d^{10}+141442353\,a\,b^{20}\,c^{10}\,d^9+876096\,b^{21}\,c^{11}\,d^8\right)\,1{}\mathrm{i}}{65536\,\left(a^{20}\,c^6\,d^{18}-18\,a^{19}\,b\,c^7\,d^{17}+153\,a^{18}\,b^2\,c^8\,d^{16}-816\,a^{17}\,b^3\,c^9\,d^{15}+3060\,a^{16}\,b^4\,c^{10}\,d^{14}-8568\,a^{15}\,b^5\,c^{11}\,d^{13}+18564\,a^{14}\,b^6\,c^{12}\,d^{12}-31824\,a^{13}\,b^7\,c^{13}\,d^{11}+43758\,a^{12}\,b^8\,c^{14}\,d^{10}-48620\,a^{11}\,b^9\,c^{15}\,d^9+43758\,a^{10}\,b^{10}\,c^{16}\,d^8-31824\,a^9\,b^{11}\,c^{17}\,d^7+18564\,a^8\,b^{12}\,c^{18}\,d^6-8568\,a^7\,b^{13}\,c^{19}\,d^5+3060\,a^6\,b^{14}\,c^{20}\,d^4-816\,a^5\,b^{15}\,c^{21}\,d^3+153\,a^4\,b^{16}\,c^{22}\,d^2-18\,a^3\,b^{17}\,c^{23}\,d+a^2\,b^{18}\,c^{24}\right)}\right)\,{\left(-\frac{28561\,a^4\,b^9\,d^4-8788\,a^3\,b^{10}\,c\,d^3+1014\,a^2\,b^{11}\,c^2\,d^2-52\,a\,b^{12}\,c^3\,d+b^{13}\,c^4}{4096\,a^{21}\,d^{16}-65536\,a^{20}\,b\,c\,d^{15}+491520\,a^{19}\,b^2\,c^2\,d^{14}-2293760\,a^{18}\,b^3\,c^3\,d^{13}+7454720\,a^{17}\,b^4\,c^4\,d^{12}-17891328\,a^{16}\,b^5\,c^5\,d^{11}+32800768\,a^{15}\,b^6\,c^6\,d^{10}-46858240\,a^{14}\,b^7\,c^7\,d^9+52715520\,a^{13}\,b^8\,c^8\,d^8-46858240\,a^{12}\,b^9\,c^9\,d^7+32800768\,a^{11}\,b^{10}\,c^{10}\,d^6-17891328\,a^{10}\,b^{11}\,c^{11}\,d^5+7454720\,a^9\,b^{12}\,c^{12}\,d^4-2293760\,a^8\,b^{13}\,c^{13}\,d^3+491520\,a^7\,b^{14}\,c^{14}\,d^2-65536\,a^6\,b^{15}\,c^{15}\,d+4096\,a^5\,b^{16}\,c^{16}}\right)}^{1/4}}\right)\,{\left(-\frac{28561\,a^4\,b^9\,d^4-8788\,a^3\,b^{10}\,c\,d^3+1014\,a^2\,b^{11}\,c^2\,d^2-52\,a\,b^{12}\,c^3\,d+b^{13}\,c^4}{4096\,a^{21}\,d^{16}-65536\,a^{20}\,b\,c\,d^{15}+491520\,a^{19}\,b^2\,c^2\,d^{14}-2293760\,a^{18}\,b^3\,c^3\,d^{13}+7454720\,a^{17}\,b^4\,c^4\,d^{12}-17891328\,a^{16}\,b^5\,c^5\,d^{11}+32800768\,a^{15}\,b^6\,c^6\,d^{10}-46858240\,a^{14}\,b^7\,c^7\,d^9+52715520\,a^{13}\,b^8\,c^8\,d^8-46858240\,a^{12}\,b^9\,c^9\,d^7+32800768\,a^{11}\,b^{10}\,c^{10}\,d^6-17891328\,a^{10}\,b^{11}\,c^{11}\,d^5+7454720\,a^9\,b^{12}\,c^{12}\,d^4-2293760\,a^8\,b^{13}\,c^{13}\,d^3+491520\,a^7\,b^{14}\,c^{14}\,d^2-65536\,a^6\,b^{15}\,c^{15}\,d+4096\,a^5\,b^{16}\,c^{16}}\right)}^{1/4}","Not used",1,"((x^(7/2)*(16*b^3*c^3*d - 5*a^3*d^4 + 25*a*b^2*c^2*d^2 + 12*a^2*b*c*d^3))/(16*a*c*(b^3*c^4 - a^3*c*d^3 + 3*a^2*b*c^2*d^2 - 3*a*b^2*c^3*d)) - (x^(3/2)*(8*b^3*c^3 - 9*a^3*d^3 + 25*a^2*b*c*d^2))/(16*a*c*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)) + (b*d^2*x^(11/2)*(8*b^2*c^2 - 5*a^2*d^2 + 21*a*b*c*d))/(16*a*c*(b^3*c^4 - a^3*c*d^3 + 3*a^2*b*c^2*d^2 - 3*a*b^2*c^3*d)))/(a*c^2 + x^2*(b*c^2 + 2*a*c*d) + x^4*(a*d^2 + 2*b*c*d) + b*d^2*x^6) - atan(((-(625*a^8*d^13 + 187388721*b^8*c^8*d^5 - 166567752*a*b^7*c^7*d^6 + 87554844*a^2*b^6*c^6*d^7 - 29580408*a^3*b^5*c^5*d^8 + 7255846*a^4*b^4*c^4*d^9 - 1264120*a^5*b^3*c^3*d^10 + 159900*a^6*b^2*c^2*d^11 - 13000*a^7*b*c*d^12)/(16777216*b^16*c^25 + 16777216*a^16*c^9*d^16 - 268435456*a^15*b*c^10*d^15 + 2013265920*a^2*b^14*c^23*d^2 - 9395240960*a^3*b^13*c^22*d^3 + 30534533120*a^4*b^12*c^21*d^4 - 73282879488*a^5*b^11*c^20*d^5 + 134351945728*a^6*b^10*c^19*d^6 - 191931351040*a^7*b^9*c^18*d^7 + 215922769920*a^8*b^8*c^17*d^8 - 191931351040*a^9*b^7*c^16*d^9 + 134351945728*a^10*b^6*c^15*d^10 - 73282879488*a^11*b^5*c^14*d^11 + 30534533120*a^12*b^4*c^13*d^12 - 9395240960*a^13*b^3*c^12*d^13 + 2013265920*a^14*b^2*c^11*d^14 - 268435456*a*b^15*c^24*d))^(1/4)*((-(625*a^8*d^13 + 187388721*b^8*c^8*d^5 - 166567752*a*b^7*c^7*d^6 + 87554844*a^2*b^6*c^6*d^7 - 29580408*a^3*b^5*c^5*d^8 + 7255846*a^4*b^4*c^4*d^9 - 1264120*a^5*b^3*c^3*d^10 + 159900*a^6*b^2*c^2*d^11 - 13000*a^7*b*c*d^12)/(16777216*b^16*c^25 + 16777216*a^16*c^9*d^16 - 268435456*a^15*b*c^10*d^15 + 2013265920*a^2*b^14*c^23*d^2 - 9395240960*a^3*b^13*c^22*d^3 + 30534533120*a^4*b^12*c^21*d^4 - 73282879488*a^5*b^11*c^20*d^5 + 134351945728*a^6*b^10*c^19*d^6 - 191931351040*a^7*b^9*c^18*d^7 + 215922769920*a^8*b^8*c^17*d^8 - 191931351040*a^9*b^7*c^16*d^9 + 134351945728*a^10*b^6*c^15*d^10 - 73282879488*a^11*b^5*c^14*d^11 + 30534533120*a^12*b^4*c^13*d^12 - 9395240960*a^13*b^3*c^12*d^13 + 2013265920*a^14*b^2*c^11*d^14 - 268435456*a*b^15*c^24*d))^(3/4)*((32*b^30*c^27*d^4 - 1728*a*b^29*c^26*d^5 - (125*a^26*b^4*c*d^30)/16 + 38304*a^2*b^28*c^25*d^6 - 459264*a^3*b^27*c^24*d^7 + 3369600*a^4*b^26*c^23*d^8 - (263413683*a^5*b^25*c^22*d^9)/16 + (903579807*a^6*b^24*c^21*d^10)/16 - (1116788283*a^7*b^23*c^20*d^11)/8 + (1980689243*a^8*b^22*c^19*d^12)/8 - (4711274035*a^9*b^21*c^18*d^13)/16 + (2530187127*a^10*b^20*c^17*d^14)/16 + (409977699*a^11*b^19*c^16*d^15)/2 - (1337499867*a^12*b^18*c^15*d^16)/2 + (8002341693*a^13*b^17*c^14*d^17)/8 - (8341892385*a^14*b^16*c^13*d^18)/8 + (3315895143*a^15*b^15*c^12*d^19)/4 - (2079521847*a^16*b^14*c^11*d^20)/4 + (2088923057*a^17*b^13*c^10*d^21)/8 - (845943917*a^18*b^12*c^9*d^22)/8 + (69181515*a^19*b^11*c^8*d^23)/2 - (18239091*a^20*b^10*c^7*d^24)/2 + (30778137*a^21*b^9*c^6*d^25)/16 - (5119101*a^22*b^8*c^5*d^26)/16 + (327093*a^23*b^7*c^4*d^27)/8 - (30645*a^24*b^6*c^3*d^28)/8 + (3825*a^25*b^5*c^2*d^29)/16)/(a^2*b^21*c^27 - a^23*c^6*d^21 - 21*a^3*b^20*c^26*d + 21*a^22*b*c^7*d^20 + 210*a^4*b^19*c^25*d^2 - 1330*a^5*b^18*c^24*d^3 + 5985*a^6*b^17*c^23*d^4 - 20349*a^7*b^16*c^22*d^5 + 54264*a^8*b^15*c^21*d^6 - 116280*a^9*b^14*c^20*d^7 + 203490*a^10*b^13*c^19*d^8 - 293930*a^11*b^12*c^18*d^9 + 352716*a^12*b^11*c^17*d^10 - 352716*a^13*b^10*c^16*d^11 + 293930*a^14*b^9*c^15*d^12 - 203490*a^15*b^8*c^14*d^13 + 116280*a^16*b^7*c^13*d^14 - 54264*a^17*b^6*c^12*d^15 + 20349*a^18*b^5*c^11*d^16 - 5985*a^19*b^4*c^10*d^17 + 1330*a^20*b^3*c^9*d^18 - 210*a^21*b^2*c^8*d^19) - (x^(1/2)*(-(625*a^8*d^13 + 187388721*b^8*c^8*d^5 - 166567752*a*b^7*c^7*d^6 + 87554844*a^2*b^6*c^6*d^7 - 29580408*a^3*b^5*c^5*d^8 + 7255846*a^4*b^4*c^4*d^9 - 1264120*a^5*b^3*c^3*d^10 + 159900*a^6*b^2*c^2*d^11 - 13000*a^7*b*c*d^12)/(16777216*b^16*c^25 + 16777216*a^16*c^9*d^16 - 268435456*a^15*b*c^10*d^15 + 2013265920*a^2*b^14*c^23*d^2 - 9395240960*a^3*b^13*c^22*d^3 + 30534533120*a^4*b^12*c^21*d^4 - 73282879488*a^5*b^11*c^20*d^5 + 134351945728*a^6*b^10*c^19*d^6 - 191931351040*a^7*b^9*c^18*d^7 + 215922769920*a^8*b^8*c^17*d^8 - 191931351040*a^9*b^7*c^16*d^9 + 134351945728*a^10*b^6*c^15*d^10 - 73282879488*a^11*b^5*c^14*d^11 + 30534533120*a^12*b^4*c^13*d^12 - 9395240960*a^13*b^3*c^12*d^13 + 2013265920*a^14*b^2*c^11*d^14 - 268435456*a*b^15*c^24*d))^(1/4)*(16777216*a*b^28*c^27*d^4 - 704643072*a^2*b^27*c^26*d^5 + 11827937280*a^3*b^26*c^25*d^6 - 107105746944*a^4*b^25*c^24*d^7 + 618641227776*a^5*b^24*c^23*d^8 - 2513987174400*a^6*b^23*c^22*d^9 + 7656663678976*a^7*b^22*c^21*d^10 - 18278639468544*a^8*b^21*c^20*d^11 + 35394969403392*a^9*b^20*c^19*d^12 - 57098809376768*a^10*b^19*c^18*d^13 + 78238275600384*a^11*b^18*c^17*d^14 - 92068449878016*a^12*b^17*c^16*d^15 + 93255551680512*a^13*b^16*c^15*d^16 - 80877025492992*a^14*b^15*c^14*d^17 + 59448946065408*a^15*b^14*c^13*d^18 - 36574941151232*a^16*b^13*c^12*d^19 + 18584022024192*a^17*b^12*c^11*d^20 - 7692575834112*a^18*b^11*c^10*d^21 + 2557512515584*a^19*b^10*c^9*d^22 - 672468566016*a^20*b^9*c^8*d^23 + 137272492032*a^21*b^8*c^7*d^24 - 21186478080*a^22*b^7*c^6*d^25 + 2360868864*a^23*b^6*c^5*d^26 - 173015040*a^24*b^5*c^4*d^27 + 6553600*a^25*b^4*c^3*d^28))/(65536*(a^2*b^18*c^24 + a^20*c^6*d^18 - 18*a^3*b^17*c^23*d - 18*a^19*b*c^7*d^17 + 153*a^4*b^16*c^22*d^2 - 816*a^5*b^15*c^21*d^3 + 3060*a^6*b^14*c^20*d^4 - 8568*a^7*b^13*c^19*d^5 + 18564*a^8*b^12*c^18*d^6 - 31824*a^9*b^11*c^17*d^7 + 43758*a^10*b^10*c^16*d^8 - 48620*a^11*b^9*c^15*d^9 + 43758*a^12*b^8*c^14*d^10 - 31824*a^13*b^7*c^13*d^11 + 18564*a^14*b^6*c^12*d^12 - 8568*a^15*b^5*c^11*d^13 + 3060*a^16*b^4*c^10*d^14 - 816*a^17*b^3*c^9*d^15 + 153*a^18*b^2*c^8*d^16)))*1i - (x^(1/2)*(105625*a^11*b^10*d^19 + 876096*b^21*c^11*d^8 + 141442353*a*b^20*c^10*d^9 - 2213250*a^10*b^11*c*d^18 - 4129947458*a^2*b^19*c^9*d^10 + 27986891205*a^3*b^18*c^8*d^11 - 1891277400*a^4*b^17*c^7*d^12 + 3396941522*a^5*b^16*c^6*d^13 - 1666839564*a^6*b^15*c^5*d^14 + 769949154*a^7*b^14*c^4*d^15 - 172109080*a^8*b^13*c^3*d^16 + 27361725*a^9*b^12*c^2*d^17)*1i)/(65536*(a^2*b^18*c^24 + a^20*c^6*d^18 - 18*a^3*b^17*c^23*d - 18*a^19*b*c^7*d^17 + 153*a^4*b^16*c^22*d^2 - 816*a^5*b^15*c^21*d^3 + 3060*a^6*b^14*c^20*d^4 - 8568*a^7*b^13*c^19*d^5 + 18564*a^8*b^12*c^18*d^6 - 31824*a^9*b^11*c^17*d^7 + 43758*a^10*b^10*c^16*d^8 - 48620*a^11*b^9*c^15*d^9 + 43758*a^12*b^8*c^14*d^10 - 31824*a^13*b^7*c^13*d^11 + 18564*a^14*b^6*c^12*d^12 - 8568*a^15*b^5*c^11*d^13 + 3060*a^16*b^4*c^10*d^14 - 816*a^17*b^3*c^9*d^15 + 153*a^18*b^2*c^8*d^16))) - (-(625*a^8*d^13 + 187388721*b^8*c^8*d^5 - 166567752*a*b^7*c^7*d^6 + 87554844*a^2*b^6*c^6*d^7 - 29580408*a^3*b^5*c^5*d^8 + 7255846*a^4*b^4*c^4*d^9 - 1264120*a^5*b^3*c^3*d^10 + 159900*a^6*b^2*c^2*d^11 - 13000*a^7*b*c*d^12)/(16777216*b^16*c^25 + 16777216*a^16*c^9*d^16 - 268435456*a^15*b*c^10*d^15 + 2013265920*a^2*b^14*c^23*d^2 - 9395240960*a^3*b^13*c^22*d^3 + 30534533120*a^4*b^12*c^21*d^4 - 73282879488*a^5*b^11*c^20*d^5 + 134351945728*a^6*b^10*c^19*d^6 - 191931351040*a^7*b^9*c^18*d^7 + 215922769920*a^8*b^8*c^17*d^8 - 191931351040*a^9*b^7*c^16*d^9 + 134351945728*a^10*b^6*c^15*d^10 - 73282879488*a^11*b^5*c^14*d^11 + 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31824*a^9*b^11*c^17*d^7 + 43758*a^10*b^10*c^16*d^8 - 48620*a^11*b^9*c^15*d^9 + 43758*a^12*b^8*c^14*d^10 - 31824*a^13*b^7*c^13*d^11 + 18564*a^14*b^6*c^12*d^12 - 8568*a^15*b^5*c^11*d^13 + 3060*a^16*b^4*c^10*d^14 - 816*a^17*b^3*c^9*d^15 + 153*a^18*b^2*c^8*d^16)))*(-(b^13*c^4 + 28561*a^4*b^9*d^4 - 8788*a^3*b^10*c*d^3 + 1014*a^2*b^11*c^2*d^2 - 52*a*b^12*c^3*d)/(4096*a^21*d^16 + 4096*a^5*b^16*c^16 - 65536*a^6*b^15*c^15*d + 491520*a^7*b^14*c^14*d^2 - 2293760*a^8*b^13*c^13*d^3 + 7454720*a^9*b^12*c^12*d^4 - 17891328*a^10*b^11*c^11*d^5 + 32800768*a^11*b^10*c^10*d^6 - 46858240*a^12*b^9*c^9*d^7 + 52715520*a^13*b^8*c^8*d^8 - 46858240*a^14*b^7*c^7*d^9 + 32800768*a^15*b^6*c^6*d^10 - 17891328*a^16*b^5*c^5*d^11 + 7454720*a^17*b^4*c^4*d^12 - 2293760*a^18*b^3*c^3*d^13 + 491520*a^19*b^2*c^2*d^14 - 65536*a^20*b*c*d^15))^(3/4)*1i - (x^(1/2)*(105625*a^11*b^10*d^19 + 876096*b^21*c^11*d^8 + 141442353*a*b^20*c^10*d^9 - 2213250*a^10*b^11*c*d^18 - 4129947458*a^2*b^19*c^9*d^10 + 27986891205*a^3*b^18*c^8*d^11 - 1891277400*a^4*b^17*c^7*d^12 + 3396941522*a^5*b^16*c^6*d^13 - 1666839564*a^6*b^15*c^5*d^14 + 769949154*a^7*b^14*c^4*d^15 - 172109080*a^8*b^13*c^3*d^16 + 27361725*a^9*b^12*c^2*d^17)*1i)/(65536*(a^2*b^18*c^24 + a^20*c^6*d^18 - 18*a^3*b^17*c^23*d - 18*a^19*b*c^7*d^17 + 153*a^4*b^16*c^22*d^2 - 816*a^5*b^15*c^21*d^3 + 3060*a^6*b^14*c^20*d^4 - 8568*a^7*b^13*c^19*d^5 + 18564*a^8*b^12*c^18*d^6 - 31824*a^9*b^11*c^17*d^7 + 43758*a^10*b^10*c^16*d^8 - 48620*a^11*b^9*c^15*d^9 + 43758*a^12*b^8*c^14*d^10 - 31824*a^13*b^7*c^13*d^11 + 18564*a^14*b^6*c^12*d^12 - 8568*a^15*b^5*c^11*d^13 + 3060*a^16*b^4*c^10*d^14 - 816*a^17*b^3*c^9*d^15 + 153*a^18*b^2*c^8*d^16)))*(-(b^13*c^4 + 28561*a^4*b^9*d^4 - 8788*a^3*b^10*c*d^3 + 1014*a^2*b^11*c^2*d^2 - 52*a*b^12*c^3*d)/(4096*a^21*d^16 + 4096*a^5*b^16*c^16 - 65536*a^6*b^15*c^15*d + 491520*a^7*b^14*c^14*d^2 - 2293760*a^8*b^13*c^13*d^3 + 7454720*a^9*b^12*c^12*d^4 - 17891328*a^10*b^11*c^11*d^5 + 32800768*a^11*b^10*c^10*d^6 - 46858240*a^12*b^9*c^9*d^7 + 52715520*a^13*b^8*c^8*d^8 - 46858240*a^14*b^7*c^7*d^9 + 32800768*a^15*b^6*c^6*d^10 - 17891328*a^16*b^5*c^5*d^11 + 7454720*a^17*b^4*c^4*d^12 - 2293760*a^18*b^3*c^3*d^13 + 491520*a^19*b^2*c^2*d^14 - 65536*a^20*b*c*d^15))^(1/4) - ((1373125*a^10*b^12*d^19)/262144 + (200201625*b^22*c^10*d^9)/262144 - (3974669595*a*b^21*c^9*d^10)/131072 - (28032875*a^9*b^13*c*d^18)/131072 + (107080445745*a^2*b^20*c^8*d^11)/262144 - (64244120525*a^3*b^19*c^7*d^12)/32768 + (171099678425*a^4*b^18*c^6*d^13)/131072 - (35353616025*a^5*b^17*c^5*d^14)/65536 + (18119512885*a^6*b^16*c^4*d^15)/131072 - (820327045*a^7*b^15*c^3*d^16)/32768 + (756189525*a^8*b^14*c^2*d^17)/262144)/(a^2*b^21*c^27 - a^23*c^6*d^21 - 21*a^3*b^20*c^26*d + 21*a^22*b*c^7*d^20 + 210*a^4*b^19*c^25*d^2 - 1330*a^5*b^18*c^24*d^3 + 5985*a^6*b^17*c^23*d^4 - 20349*a^7*b^16*c^22*d^5 + 54264*a^8*b^15*c^21*d^6 - 116280*a^9*b^14*c^20*d^7 + 203490*a^10*b^13*c^19*d^8 - 293930*a^11*b^12*c^18*d^9 + 352716*a^12*b^11*c^17*d^10 - 352716*a^13*b^10*c^16*d^11 + 293930*a^14*b^9*c^15*d^12 - 203490*a^15*b^8*c^14*d^13 + 116280*a^16*b^7*c^13*d^14 - 54264*a^17*b^6*c^12*d^15 + 20349*a^18*b^5*c^11*d^16 - 5985*a^19*b^4*c^10*d^17 + 1330*a^20*b^3*c^9*d^18 - 210*a^21*b^2*c^8*d^19) + ((((32*b^30*c^27*d^4 - 1728*a*b^29*c^26*d^5 - (125*a^26*b^4*c*d^30)/16 + 38304*a^2*b^28*c^25*d^6 - 459264*a^3*b^27*c^24*d^7 + 3369600*a^4*b^26*c^23*d^8 - (263413683*a^5*b^25*c^22*d^9)/16 + (903579807*a^6*b^24*c^21*d^10)/16 - (1116788283*a^7*b^23*c^20*d^11)/8 + (1980689243*a^8*b^22*c^19*d^12)/8 - (4711274035*a^9*b^21*c^18*d^13)/16 + (2530187127*a^10*b^20*c^17*d^14)/16 + (409977699*a^11*b^19*c^16*d^15)/2 - (1337499867*a^12*b^18*c^15*d^16)/2 + (8002341693*a^13*b^17*c^14*d^17)/8 - (8341892385*a^14*b^16*c^13*d^18)/8 + (3315895143*a^15*b^15*c^12*d^19)/4 - (2079521847*a^16*b^14*c^11*d^20)/4 + (2088923057*a^17*b^13*c^10*d^21)/8 - (845943917*a^18*b^12*c^9*d^22)/8 + (69181515*a^19*b^11*c^8*d^23)/2 - (18239091*a^20*b^10*c^7*d^24)/2 + (30778137*a^21*b^9*c^6*d^25)/16 - (5119101*a^22*b^8*c^5*d^26)/16 + (327093*a^23*b^7*c^4*d^27)/8 - (30645*a^24*b^6*c^3*d^28)/8 + (3825*a^25*b^5*c^2*d^29)/16)*1i)/(a^2*b^21*c^27 - a^23*c^6*d^21 - 21*a^3*b^20*c^26*d + 21*a^22*b*c^7*d^20 + 210*a^4*b^19*c^25*d^2 - 1330*a^5*b^18*c^24*d^3 + 5985*a^6*b^17*c^23*d^4 - 20349*a^7*b^16*c^22*d^5 + 54264*a^8*b^15*c^21*d^6 - 116280*a^9*b^14*c^20*d^7 + 203490*a^10*b^13*c^19*d^8 - 293930*a^11*b^12*c^18*d^9 + 352716*a^12*b^11*c^17*d^10 - 352716*a^13*b^10*c^16*d^11 + 293930*a^14*b^9*c^15*d^12 - 203490*a^15*b^8*c^14*d^13 + 116280*a^16*b^7*c^13*d^14 - 54264*a^17*b^6*c^12*d^15 + 20349*a^18*b^5*c^11*d^16 - 5985*a^19*b^4*c^10*d^17 + 1330*a^20*b^3*c^9*d^18 - 210*a^21*b^2*c^8*d^19) + (x^(1/2)*(-(b^13*c^4 + 28561*a^4*b^9*d^4 - 8788*a^3*b^10*c*d^3 + 1014*a^2*b^11*c^2*d^2 - 52*a*b^12*c^3*d)/(4096*a^21*d^16 + 4096*a^5*b^16*c^16 - 65536*a^6*b^15*c^15*d + 491520*a^7*b^14*c^14*d^2 - 2293760*a^8*b^13*c^13*d^3 + 7454720*a^9*b^12*c^12*d^4 - 17891328*a^10*b^11*c^11*d^5 + 32800768*a^11*b^10*c^10*d^6 - 46858240*a^12*b^9*c^9*d^7 + 52715520*a^13*b^8*c^8*d^8 - 46858240*a^14*b^7*c^7*d^9 + 32800768*a^15*b^6*c^6*d^10 - 17891328*a^16*b^5*c^5*d^11 + 7454720*a^17*b^4*c^4*d^12 - 2293760*a^18*b^3*c^3*d^13 + 491520*a^19*b^2*c^2*d^14 - 65536*a^20*b*c*d^15))^(1/4)*(16777216*a*b^28*c^27*d^4 - 704643072*a^2*b^27*c^26*d^5 + 11827937280*a^3*b^26*c^25*d^6 - 107105746944*a^4*b^25*c^24*d^7 + 618641227776*a^5*b^24*c^23*d^8 - 2513987174400*a^6*b^23*c^22*d^9 + 7656663678976*a^7*b^22*c^21*d^10 - 18278639468544*a^8*b^21*c^20*d^11 + 35394969403392*a^9*b^20*c^19*d^12 - 57098809376768*a^10*b^19*c^18*d^13 + 78238275600384*a^11*b^18*c^17*d^14 - 92068449878016*a^12*b^17*c^16*d^15 + 93255551680512*a^13*b^16*c^15*d^16 - 80877025492992*a^14*b^15*c^14*d^17 + 59448946065408*a^15*b^14*c^13*d^18 - 36574941151232*a^16*b^13*c^12*d^19 + 18584022024192*a^17*b^12*c^11*d^20 - 7692575834112*a^18*b^11*c^10*d^21 + 2557512515584*a^19*b^10*c^9*d^22 - 672468566016*a^20*b^9*c^8*d^23 + 137272492032*a^21*b^8*c^7*d^24 - 21186478080*a^22*b^7*c^6*d^25 + 2360868864*a^23*b^6*c^5*d^26 - 173015040*a^24*b^5*c^4*d^27 + 6553600*a^25*b^4*c^3*d^28))/(65536*(a^2*b^18*c^24 + a^20*c^6*d^18 - 18*a^3*b^17*c^23*d - 18*a^19*b*c^7*d^17 + 153*a^4*b^16*c^22*d^2 - 816*a^5*b^15*c^21*d^3 + 3060*a^6*b^14*c^20*d^4 - 8568*a^7*b^13*c^19*d^5 + 18564*a^8*b^12*c^18*d^6 - 31824*a^9*b^11*c^17*d^7 + 43758*a^10*b^10*c^16*d^8 - 48620*a^11*b^9*c^15*d^9 + 43758*a^12*b^8*c^14*d^10 - 31824*a^13*b^7*c^13*d^11 + 18564*a^14*b^6*c^12*d^12 - 8568*a^15*b^5*c^11*d^13 + 3060*a^16*b^4*c^10*d^14 - 816*a^17*b^3*c^9*d^15 + 153*a^18*b^2*c^8*d^16)))*(-(b^13*c^4 + 28561*a^4*b^9*d^4 - 8788*a^3*b^10*c*d^3 + 1014*a^2*b^11*c^2*d^2 - 52*a*b^12*c^3*d)/(4096*a^21*d^16 + 4096*a^5*b^16*c^16 - 65536*a^6*b^15*c^15*d + 491520*a^7*b^14*c^14*d^2 - 2293760*a^8*b^13*c^13*d^3 + 7454720*a^9*b^12*c^12*d^4 - 17891328*a^10*b^11*c^11*d^5 + 32800768*a^11*b^10*c^10*d^6 - 46858240*a^12*b^9*c^9*d^7 + 52715520*a^13*b^8*c^8*d^8 - 46858240*a^14*b^7*c^7*d^9 + 32800768*a^15*b^6*c^6*d^10 - 17891328*a^16*b^5*c^5*d^11 + 7454720*a^17*b^4*c^4*d^12 - 2293760*a^18*b^3*c^3*d^13 + 491520*a^19*b^2*c^2*d^14 - 65536*a^20*b*c*d^15))^(3/4)*1i + (x^(1/2)*(105625*a^11*b^10*d^19 + 876096*b^21*c^11*d^8 + 141442353*a*b^20*c^10*d^9 - 2213250*a^10*b^11*c*d^18 - 4129947458*a^2*b^19*c^9*d^10 + 27986891205*a^3*b^18*c^8*d^11 - 1891277400*a^4*b^17*c^7*d^12 + 3396941522*a^5*b^16*c^6*d^13 - 1666839564*a^6*b^15*c^5*d^14 + 769949154*a^7*b^14*c^4*d^15 - 172109080*a^8*b^13*c^3*d^16 + 27361725*a^9*b^12*c^2*d^17)*1i)/(65536*(a^2*b^18*c^24 + a^20*c^6*d^18 - 18*a^3*b^17*c^23*d - 18*a^19*b*c^7*d^17 + 153*a^4*b^16*c^22*d^2 - 816*a^5*b^15*c^21*d^3 + 3060*a^6*b^14*c^20*d^4 - 8568*a^7*b^13*c^19*d^5 + 18564*a^8*b^12*c^18*d^6 - 31824*a^9*b^11*c^17*d^7 + 43758*a^10*b^10*c^16*d^8 - 48620*a^11*b^9*c^15*d^9 + 43758*a^12*b^8*c^14*d^10 - 31824*a^13*b^7*c^13*d^11 + 18564*a^14*b^6*c^12*d^12 - 8568*a^15*b^5*c^11*d^13 + 3060*a^16*b^4*c^10*d^14 - 816*a^17*b^3*c^9*d^15 + 153*a^18*b^2*c^8*d^16)))*(-(b^13*c^4 + 28561*a^4*b^9*d^4 - 8788*a^3*b^10*c*d^3 + 1014*a^2*b^11*c^2*d^2 - 52*a*b^12*c^3*d)/(4096*a^21*d^16 + 4096*a^5*b^16*c^16 - 65536*a^6*b^15*c^15*d + 491520*a^7*b^14*c^14*d^2 - 2293760*a^8*b^13*c^13*d^3 + 7454720*a^9*b^12*c^12*d^4 - 17891328*a^10*b^11*c^11*d^5 + 32800768*a^11*b^10*c^10*d^6 - 46858240*a^12*b^9*c^9*d^7 + 52715520*a^13*b^8*c^8*d^8 - 46858240*a^14*b^7*c^7*d^9 + 32800768*a^15*b^6*c^6*d^10 - 17891328*a^16*b^5*c^5*d^11 + 7454720*a^17*b^4*c^4*d^12 - 2293760*a^18*b^3*c^3*d^13 + 491520*a^19*b^2*c^2*d^14 - 65536*a^20*b*c*d^15))^(1/4)))*(-(b^13*c^4 + 28561*a^4*b^9*d^4 - 8788*a^3*b^10*c*d^3 + 1014*a^2*b^11*c^2*d^2 - 52*a*b^12*c^3*d)/(4096*a^21*d^16 + 4096*a^5*b^16*c^16 - 65536*a^6*b^15*c^15*d + 491520*a^7*b^14*c^14*d^2 - 2293760*a^8*b^13*c^13*d^3 + 7454720*a^9*b^12*c^12*d^4 - 17891328*a^10*b^11*c^11*d^5 + 32800768*a^11*b^10*c^10*d^6 - 46858240*a^12*b^9*c^9*d^7 + 52715520*a^13*b^8*c^8*d^8 - 46858240*a^14*b^7*c^7*d^9 + 32800768*a^15*b^6*c^6*d^10 - 17891328*a^16*b^5*c^5*d^11 + 7454720*a^17*b^4*c^4*d^12 - 2293760*a^18*b^3*c^3*d^13 + 491520*a^19*b^2*c^2*d^14 - 65536*a^20*b*c*d^15))^(1/4)","B"
500,1,150312,739,16.832621,"\text{Not used}","int(1/(x^(1/2)*(a + b*x^2)^2*(c + 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23871332023900569600*a^26*b^13*c^24*d^19 + 15516365815535370240*a^27*b^12*c^23*d^20 - 8866494751734497280*a^28*b^11*c^22*d^21 + 4433247375867248640*a^29*b^10*c^21*d^22 - 1927498859072716800*a^30*b^9*c^20*d^23 + 722812072152268800*a^31*b^8*c^19*d^24 - 231299863088726016*a^32*b^7*c^18*d^25 + 62273040062349312*a^33*b^6*c^17*d^26 - 13838453347188736*a^34*b^5*c^16*d^27 + 2471152383426560*a^35*b^4*c^15*d^28 - 340848604610560*a^36*b^3*c^14*d^29 + 34084860461056*a^37*b^2*c^13*d^30))^(1/4)*1i + (9*x^(1/2)*(4862025*a^12*b^11*d^21 + 15681600*b^23*c^12*d^9 - 330739200*a*b^22*c^11*d^10 - 85293810*a^11*b^12*c*d^20 + 3444241905*a^2*b^21*c^10*d^11 - 19611374130*a^3*b^20*c^9*d^12 + 56099130741*a^4*b^19*c^8*d^13 - 73884775320*a^5*b^18*c^7*d^14 + 60509855250*a^6*b^17*c^6*d^15 - 33837158700*a^7*b^16*c^5*d^16 + 13445660610*a^8*b^15*c^4*d^17 - 3774337560*a^9*b^14*c^3*d^18 + 722155581*a^10*b^13*c^2*d^19))/(65536*(a^4*b^18*c^26 + a^22*c^8*d^18 - 18*a^5*b^17*c^25*d - 18*a^21*b*c^9*d^17 + 153*a^6*b^16*c^24*d^2 - 816*a^7*b^15*c^23*d^3 + 3060*a^8*b^14*c^22*d^4 - 8568*a^9*b^13*c^21*d^5 + 18564*a^10*b^12*c^20*d^6 - 31824*a^11*b^11*c^19*d^7 + 43758*a^12*b^10*c^18*d^8 - 48620*a^13*b^9*c^17*d^9 + 43758*a^14*b^8*c^16*d^10 - 31824*a^15*b^7*c^15*d^11 + 18564*a^16*b^6*c^14*d^12 - 8568*a^17*b^5*c^13*d^13 + 3060*a^18*b^4*c^12*d^14 - 816*a^19*b^3*c^11*d^15 + 153*a^20*b^2*c^10*d^16)))*1i))*(-((158640570309279744*a^62*d^62 + 461689330549653504*b^62*c^62 + 1143142782440942075904*a^2*b^60*c^60*d^2 - 25023561715791219916800*a^3*b^59*c^59*d^3 + 392117365329126217482240*a^4*b^58*c^58*d^4 - 4690198490643886824751104*a^5*b^57*c^57*d^5 + 44594910394380994297724928*a^6*b^56*c^56*d^6 - 346602278587137521765842944*a^7*b^55*c^55*d^7 + 2247504424575830750669045760*a^8*b^54*c^54*d^8 - 12350275985199266166472704000*a^9*b^53*c^53*d^9 + 58231240117103771404688424960*a^10*b^52*c^52*d^10 - 238022522313714176288222085120*a^11*b^51*c^51*d^11 + 851128269824272461500629647360*a^12*b^50*c^50*d^12 - 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48092805215322280459690440055062528*a^30*b^32*c^32*d^30 - 59264887465626927586633770646634496*a^31*b^31*c^31*d^31 + 68586599768084153161669916447735808*a^32*b^30*c^30*d^32 - 73974197164791541927858637824327680*a^33*b^29*c^29*d^33 + 73965997892283818508917976575508480*a^34*b^28*c^28*d^34 - 68335704761988738252796495977775104*a^35*b^27*c^27*d^35 + 58219427824782390172272112611360768*a^36*b^26*c^26*d^36 - 45688108560967442735282995681296384*a^37*b^25*c^25*d^37 + 33004306099634531959911507013140480*a^38*b^24*c^24*d^38 - 21937255814019282279521941129789440*a^39*b^23*c^23*d^39 + 13411283618120781029280868454105088*a^40*b^22*c^22*d^40 - 7537663576430440382672512877592576*a^41*b^21*c^21*d^41 + 3892412049497521843004374964502528*a^42*b^20*c^20*d^42 - 1845284865146033724645937218846720*a^43*b^19*c^19*d^43 + 802242695487291496905120122142720*a^44*b^18*c^18*d^44 - 319410517078400510775218487164928*a^45*b^17*c^17*d^45 + 116263619225964311813956237787136*a^46*b^16*c^16*d^46 - 38606608474448543697499060174848*a^47*b^15*c^15*d^47 + 11664498576526727219629743144960*a^48*b^14*c^14*d^48 - 3196489115423809113423033139200*a^49*b^13*c^13*d^49 + 791409982329733215668467138560*a^50*b^12*c^12*d^50 - 176199485733388663821717995520*a^51*b^11*c^11*d^51 + 35073618030151357707960975360*a^52*b^10*c^10*d^52 - 6197909674539500954745569280*a^53*b^9*c^9*d^53 + 963722299349432543100272640*a^54*b^8*c^8*d^54 - 130383980335571997403643904*a^55*b^7*c^7*d^55 + 15126732643705401196412928*a^56*b^6*c^6*d^56 - 1476009532413734912262144*a^57*b^5*c^5*d^57 + 117913206827103100600320*a^58*b^4*c^4*d^58 - 7412982469913298862080*a^59*b^3*c^3*d^59 + 344295363448368267264*a^60*b^2*c^2*d^60 - 33241631799575052288*a*b^61*c^61*d - 10515603517643685888*a^61*b*c*d^61)^(1/2) + 398297088*a^31*d^31 + 679477248*b^31*c^31 + 400891576320*a^2*b^29*c^29*d^2 - 3981736673280*a^3*b^28*c^28*d^3 + 26937875496960*a^4*b^27*c^27*d^4 - 132340424638464*a^5*b^26*c^26*d^5 + 491512097931264*a^6*b^25*c^25*d^6 - 1416415142246400*a^7*b^24*c^24*d^7 + 3209681400053760*a^8*b^23*c^23*d^8 - 5685622110904320*a^9*b^22*c^22*d^9 + 7454556262416384*a^10*b^21*c^21*d^10 - 5436179592966144*a^11*b^20*c^20*d^11 - 4665413760860160*a^12*b^19*c^19*d^12 + 26292873905971200*a^13*b^18*c^18*d^13 - 58696011926323200*a^14*b^17*c^17*d^14 + 94544944805836800*a^15*b^16*c^16*d^15 - 121670839126425600*a^16*b^15*c^15*d^16 + 129462901032960000*a^17*b^14*c^14*d^17 - 115561503891947520*a^18*b^13*c^13*d^18 + 87113445112995840*a^19*b^12*c^12*d^19 - 55609782114484224*a^20*b^11*c^11*d^20 + 30067181023739904*a^21*b^10*c^10*d^21 - 13742000583966720*a^22*b^9*c^9*d^22 + 5286598571980800*a^23*b^8*c^8*d^23 - 1699967106662400*a^24*b^7*c^7*d^24 + 452124225183744*a^25*b^6*c^6*d^25 - 97916547907584*a^26*b^5*c^5*d^26 + 16871335464960*a^27*b^4*c^4*d^27 - 2231346216960*a^28*b^3*c^3*d^28 + 213454725120*a^29*b^2*c^2*d^29 - 24461180928*a*b^30*c^30*d - 13200703488*a^30*b*c*d^30)/(68719476736*a^7*b^32*c^43 + 68719476736*a^39*c^11*d^32 - 2199023255552*a^8*b^31*c^42*d - 2199023255552*a^38*b*c^12*d^31 + 34084860461056*a^9*b^30*c^41*d^2 - 340848604610560*a^10*b^29*c^40*d^3 + 2471152383426560*a^11*b^28*c^39*d^4 - 13838453347188736*a^12*b^27*c^38*d^5 + 62273040062349312*a^13*b^26*c^37*d^6 - 231299863088726016*a^14*b^25*c^36*d^7 + 722812072152268800*a^15*b^24*c^35*d^8 - 1927498859072716800*a^16*b^23*c^34*d^9 + 4433247375867248640*a^17*b^22*c^33*d^10 - 8866494751734497280*a^18*b^21*c^32*d^11 + 15516365815535370240*a^19*b^20*c^31*d^12 - 23871332023900569600*a^20*b^19*c^30*d^13 + 32396807746722201600*a^21*b^18*c^29*d^14 - 38876169296066641920*a^22*b^17*c^28*d^15 + 41305929877070807040*a^23*b^16*c^27*d^16 - 38876169296066641920*a^24*b^15*c^26*d^17 + 32396807746722201600*a^25*b^14*c^25*d^18 - 23871332023900569600*a^26*b^13*c^24*d^19 + 15516365815535370240*a^27*b^12*c^23*d^20 - 8866494751734497280*a^28*b^11*c^22*d^21 + 4433247375867248640*a^29*b^10*c^21*d^22 - 1927498859072716800*a^30*b^9*c^20*d^23 + 722812072152268800*a^31*b^8*c^19*d^24 - 231299863088726016*a^32*b^7*c^18*d^25 + 62273040062349312*a^33*b^6*c^17*d^26 - 13838453347188736*a^34*b^5*c^16*d^27 + 2471152383426560*a^35*b^4*c^15*d^28 - 340848604610560*a^36*b^3*c^14*d^29 + 34084860461056*a^37*b^2*c^13*d^30))^(1/4)","B"
501,1,127276,805,24.918345,"\text{Not used}","int(1/(x^(3/2)*(a + b*x^2)^2*(c + 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8866494751734497280*a^30*b^11*c^24*d^21 + 4433247375867248640*a^31*b^10*c^23*d^22 - 1927498859072716800*a^32*b^9*c^22*d^23 + 722812072152268800*a^33*b^8*c^21*d^24 - 231299863088726016*a^34*b^7*c^20*d^25 + 62273040062349312*a^35*b^6*c^19*d^26 - 13838453347188736*a^36*b^5*c^18*d^27 + 2471152383426560*a^37*b^4*c^17*d^28 - 340848604610560*a^38*b^3*c^16*d^29 + 34084860461056*a^39*b^2*c^15*d^30))^(1/4) - (2/(a*c) + (x^2*(81*a^4*d^4 - 40*b^4*c^4 + 96*a^2*b^2*c^2*d^2 + 32*a*b^3*c^3*d - 193*a^3*b*c*d^3))/(16*a^2*c^2*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)) + (x^4*(80*b^4*c^4*d - 45*a^4*d^5 - 160*a*b^3*c^3*d^2 + 129*a^2*b^2*c^2*d^3 + 44*a^3*b*c*d^4))/(16*a^2*c^2*(b^3*c^4 - a^3*c*d^3 + 3*a^2*b*c^2*d^2 - 3*a*b^2*c^3*d)) - (b*d^2*x^6*(45*a^3*d^3 - 40*b^3*c^3 + 96*a*b^2*c^2*d - 125*a^2*b*c*d^2))/(16*a^2*c^2*(b^3*c^4 - a^3*c*d^3 + 3*a^2*b*c^2*d^2 - 3*a*b^2*c^3*d)))/(x^(5/2)*(b*c^2 + 2*a*c*d) + x^(9/2)*(a*d^2 + 2*b*c*d) + a*c^2*x^(1/2) + b*d^2*x^(13/2))","B"
502,1,180372,805,19.057603,"\text{Not used}","int(1/(x^(5/2)*(a + b*x^2)^2*(c + d*x^2)^3),x)","\mathrm{atan}\left(\frac{\left(\sqrt{x}\,\left(-872067188534894657536\,a^{53}\,b^{13}\,c^{27}\,d^{46}+31006369751209579905024\,a^{52}\,b^{14}\,c^{28}\,d^{45}-534037861185724002336768\,a^{51}\,b^{15}\,c^{29}\,d^{44}+5931528400797457427988480\,a^{50}\,b^{16}\,c^{30}\,d^{43}-47717950421254308290887680\,a^{49}\,b^{17}\,c^{31}\,d^{42}+296084339424033093684559872\,a^{48}\,b^{18}\,c^{32}\,d^{41}-1473449639082715479512449024\,a^{47}\,b^{19}\,c^{33}\,d^{40}+6037825951797032255320227840\,a^{46}\,b^{20}\,c^{34}\,d^{39}-20757436699772395749793333248\,a^{45}\,b^{21}\,c^{35}\,d^{38}+60699171433471101739298979840\,a^{44}\,b^{22}\,c^{36}\,d^{37}-152543196968133650922715742208\,a^{43}\,b^{23}\,c^{37}\,d^{36}+332065764335584004230153764864\,a^{42}\,b^{24}\,c^{38}\,d^{35}-629956523592774331698776113152\,a^{41}\,b^{25}\,c^{39}\,d^{34}+1046409458758522347995126562816\,a^{40}\,b^{26}\,c^{40}\,d^{33}-1527649406048366621262568488960\,a^{39}\,b^{27}\,c^{41}\,d^{32}+1966204854457469918399988498432\,a^{38}\,b^{28}\,c^{42}\,d^{31}-2237449183565830435563494178816\,a^{37}\,b^{29}\,c^{43}\,d^{30}+2257905973104023956972306956288\,a^{36}\,b^{30}\,c^{44}\,d^{29}-2028143345719314676074795761664\,a^{35}\,b^{31}\,c^{45}\,d^{28}+1629690593600095833823295569920\,a^{34}\,b^{32}\,c^{46}\,d^{27}-1179424943892680059222782640128\,a^{33}\,b^{33}\,c^{47}\,d^{26}+775321096823109302674935250944\,a^{32}\,b^{34}\,c^{48}\,d^{25}-467106577738876991145070559232\,a^{31}\,b^{35}\,c^{49}\,d^{24}+259595474982835164713400139776\,a^{30}\,b^{36}\,c^{50}\,d^{23}-133143680796215491474489344000\,a^{29}\,b^{37}\,c^{51}\,d^{22}+62528004036875405150857986048\,a^{28}\,b^{38}\,c^{52}\,d^{21}-26475613142538536817178705920\,a^{27}\,b^{39}\,c^{53}\,d^{20}+9904866981547362725832687616\,a^{26}\,b^{40}\,c^{54}\,d^{19}-3201588318340888739356606464\,a^{25}\,b^{41}\,c^{55}\,d^{18}+873231122236416493313064960\,a^{24}\,b^{42}\,c^{56}\,d^{17}-195811106815542077297786880\,a^{23}\,b^{43}\,c^{57}\,d^{16}+34982076529826233401212928\,a^{22}\,b^{44}\,c^{58}\,d^{15}-4772189938359453553262592\,a^{21}\,b^{45}\,c^{59}\,d^{14}+465808355868544602210304\,a^{20}\,b^{46}\,c^{60}\,d^{13}-28925330217666430894080\,a^{19}\,b^{47}\,c^{61}\,d^{12}+857712418202478182400\,a^{18}\,b^{48}\,c^{62}\,d^{11}\right)+{\left(-\frac{\sqrt{\frac{{\left(143986855936\,a^{35}\,d^{35}-4293426249728\,a^{34}\,b\,c\,d^{34}+61554295914496\,a^{33}\,b^2\,c^2\,d^{33}-564292849139712\,a^{32}\,b^3\,c^3\,d^{32}+3711306051231744\,a^{31}\,b^4\,c^4\,d^{31}-18626082598846464\,a^{30}\,b^5\,c^5\,d^{30}+74080636676358144\,a^{29}\,b^6\,c^6\,d^{29}-239385911340269568\,a^{28}\,b^7\,c^7\,d^{28}+639329497516732416\,a^{27}\,b^8\,c^8\,d^{27}-1428045479666450432\,a^{26}\,b^9\,c^9\,d^{26}+2689585093637472256\,a^{25}\,b^{10}\,c^{10}\,d^{25}-4293767561145810944\,a^{24}\,b^{11}\,c^{11}\,d^{24}+5827091540545486848\,a^{23}\,b^{12}\,c^{12}\,d^{23}-6727518677746384896\,a^{22}\,b^{13}\,c^{13}\,d^{22}+6599213688440389632\,a^{21}\,b^{14}\,c^{14}\,d^{21}-5481339136181731328\,a^{20}\,b^{15}\,c^{15}\,d^{20}+3832850809857372160\,a^{19}\,b^{16}\,c^{16}\,d^{19}-2236571458836070400\,a^{18}\,b^{17}\,c^{17}\,d^{18}+1074443231596134400\,a^{17}\,b^{18}\,c^{18}\,d^{17}-413241453930905600\,a^{16}\,b^{19}\,c^{19}\,d^{16}+112491276045524992\,a^{15}\,b^{20}\,c^{20}\,d^{15}+4937158577455104\,a^{14}\,b^{21}\,c^{21}\,d^{14}-54384137459908608\,a^{13}\,b^{22}\,c^{22}\,d^{13}+80709771031904256\,a^{12}\,b^{23}\,c^{23}\,d^{12}-90502742771167232\,a^{11}\,b^{24}\,c^{24}\,d^{11}+82612272492445696\,a^{10}\,b^{25}\,c^{25}\,d^{10}-61812801970110464\,a^9\,b^{26}\,c^{26}\,d^9+37834420899545088\,a^8\,b^{27}\,c^{27}\,d^8-18829534178574336\,a^7\,b^{28}\,c^{28}\,d^7+7540414907154432\,a^6\,b^{29}\,c^{29}\,d^6-2390715430600704\,a^5\,b^{30}\,c^{30}\,d^5+585644510281728\,a^4\,b^{31}\,c^{31}\,d^4-106752016121856\,a^3\,b^{32}\,c^{32}\,d^3+13612059983872\,a^2\,b^{33}\,c^{33}\,d^2-1081861996544\,a\,b^{34}\,c^{34}\,d+40282095616\,b^{35}\,c^{35}\right)}^2}{4}-\left(4581179456161\,a^{12}\,b^{15}\,d^{23}-70054782497084\,a^{11}\,b^{16}\,c\,d^{22}+492873253157362\,a^{10}\,b^{17}\,c^2\,d^{21}-2094206929053932\,a^9\,b^{18}\,c^3\,d^{20}+5941572716242975\,a^8\,b^{19}\,c^4\,d^{19}-11760839441437688\,a^7\,b^{20}\,c^5\,d^{18}+16492413880109692\,a^6\,b^{21}\,c^6\,d^{17}-16316203958046776\,a^5\,b^{22}\,c^7\,d^{16}+11150130570636271\,a^4\,b^{23}\,c^8\,d^{15}-5065427904712140\,a^3\,b^{24}\,c^9\,d^{14}+1442203904732850\,a^2\,b^{25}\,c^{10}\,d^{13}-231121882561500\,a\,b^{26}\,c^{11}\,d^{12}+15840599000625\,b^{27}\,c^{12}\,d^{11}\right)\,\left(68719476736\,a^{43}\,c^{15}\,d^{32}-2199023255552\,a^{42}\,b\,c^{16}\,d^{31}+34084860461056\,a^{41}\,b^2\,c^{17}\,d^{30}-340848604610560\,a^{40}\,b^3\,c^{18}\,d^{29}+2471152383426560\,a^{39}\,b^4\,c^{19}\,d^{28}-13838453347188736\,a^{38}\,b^5\,c^{20}\,d^{27}+62273040062349312\,a^{37}\,b^6\,c^{21}\,d^{26}-231299863088726016\,a^{36}\,b^7\,c^{22}\,d^{25}+722812072152268800\,a^{35}\,b^8\,c^{23}\,d^{24}-1927498859072716800\,a^{34}\,b^9\,c^{24}\,d^{23}+4433247375867248640\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496*a^13*b^30*c^45*d^2 - 4960*a^14*b^29*c^44*d^3 + 35960*a^15*b^28*c^43*d^4 - 201376*a^16*b^27*c^42*d^5 + 906192*a^17*b^26*c^41*d^6 - 3365856*a^18*b^25*c^40*d^7 + 10518300*a^19*b^24*c^39*d^8 - 28048800*a^20*b^23*c^38*d^9 + 64512240*a^21*b^22*c^37*d^10 - 129024480*a^22*b^21*c^36*d^11 + 225792840*a^23*b^20*c^35*d^12 - 347373600*a^24*b^19*c^34*d^13 + 471435600*a^25*b^18*c^33*d^14 - 565722720*a^26*b^17*c^32*d^15 + 601080390*a^27*b^16*c^31*d^16 - 565722720*a^28*b^15*c^30*d^17 + 471435600*a^29*b^14*c^29*d^18 - 347373600*a^30*b^13*c^28*d^19 + 225792840*a^31*b^12*c^27*d^20 - 129024480*a^32*b^11*c^26*d^21 + 64512240*a^33*b^10*c^25*d^22 - 28048800*a^34*b^9*c^24*d^23 + 10518300*a^35*b^8*c^23*d^24 - 3365856*a^36*b^7*c^22*d^25 + 906192*a^37*b^6*c^21*d^26 - 201376*a^38*b^5*c^20*d^27 + 35960*a^39*b^4*c^19*d^28 - 4960*a^40*b^3*c^18*d^29 + 496*a^41*b^2*c^17*d^30)))^(1/4)*1i))*(-(71993427968*a^35*d^35 - ((143986855936*a^35*d^35 + 40282095616*b^35*c^35 + 13612059983872*a^2*b^33*c^33*d^2 - 106752016121856*a^3*b^32*c^32*d^3 + 585644510281728*a^4*b^31*c^31*d^4 - 2390715430600704*a^5*b^30*c^30*d^5 + 7540414907154432*a^6*b^29*c^29*d^6 - 18829534178574336*a^7*b^28*c^28*d^7 + 37834420899545088*a^8*b^27*c^27*d^8 - 61812801970110464*a^9*b^26*c^26*d^9 + 82612272492445696*a^10*b^25*c^25*d^10 - 90502742771167232*a^11*b^24*c^24*d^11 + 80709771031904256*a^12*b^23*c^23*d^12 - 54384137459908608*a^13*b^22*c^22*d^13 + 4937158577455104*a^14*b^21*c^21*d^14 + 112491276045524992*a^15*b^20*c^20*d^15 - 413241453930905600*a^16*b^19*c^19*d^16 + 1074443231596134400*a^17*b^18*c^18*d^17 - 2236571458836070400*a^18*b^17*c^17*d^18 + 3832850809857372160*a^19*b^16*c^16*d^19 - 5481339136181731328*a^20*b^15*c^15*d^20 + 6599213688440389632*a^21*b^14*c^14*d^21 - 6727518677746384896*a^22*b^13*c^13*d^22 + 5827091540545486848*a^23*b^12*c^12*d^23 - 4293767561145810944*a^24*b^11*c^11*d^24 + 2689585093637472256*a^25*b^10*c^10*d^25 - 1428045479666450432*a^26*b^9*c^9*d^26 + 639329497516732416*a^27*b^8*c^8*d^27 - 239385911340269568*a^28*b^7*c^7*d^28 + 74080636676358144*a^29*b^6*c^6*d^29 - 18626082598846464*a^30*b^5*c^5*d^30 + 3711306051231744*a^31*b^4*c^4*d^31 - 564292849139712*a^32*b^3*c^3*d^32 + 61554295914496*a^33*b^2*c^2*d^33 - 1081861996544*a*b^34*c^34*d - 4293426249728*a^34*b*c*d^34)^2/4 - (4581179456161*a^12*b^15*d^23 + 15840599000625*b^27*c^12*d^11 - 231121882561500*a*b^26*c^11*d^12 - 70054782497084*a^11*b^16*c*d^22 + 1442203904732850*a^2*b^25*c^10*d^13 - 5065427904712140*a^3*b^24*c^9*d^14 + 11150130570636271*a^4*b^23*c^8*d^15 - 16316203958046776*a^5*b^22*c^7*d^16 + 16492413880109692*a^6*b^21*c^6*d^17 - 11760839441437688*a^7*b^20*c^5*d^18 + 5941572716242975*a^8*b^19*c^4*d^19 - 2094206929053932*a^9*b^18*c^3*d^20 + 492873253157362*a^10*b^17*c^2*d^21)*(68719476736*a^11*b^32*c^47 + 68719476736*a^43*c^15*d^32 - 2199023255552*a^12*b^31*c^46*d - 2199023255552*a^42*b*c^16*d^31 + 34084860461056*a^13*b^30*c^45*d^2 - 340848604610560*a^14*b^29*c^44*d^3 + 2471152383426560*a^15*b^28*c^43*d^4 - 13838453347188736*a^16*b^27*c^42*d^5 + 62273040062349312*a^17*b^26*c^41*d^6 - 231299863088726016*a^18*b^25*c^40*d^7 + 722812072152268800*a^19*b^24*c^39*d^8 - 1927498859072716800*a^20*b^23*c^38*d^9 + 4433247375867248640*a^21*b^22*c^37*d^10 - 8866494751734497280*a^22*b^21*c^36*d^11 + 15516365815535370240*a^23*b^20*c^35*d^12 - 23871332023900569600*a^24*b^19*c^34*d^13 + 32396807746722201600*a^25*b^18*c^33*d^14 - 38876169296066641920*a^26*b^17*c^32*d^15 + 41305929877070807040*a^27*b^16*c^31*d^16 - 38876169296066641920*a^28*b^15*c^30*d^17 + 32396807746722201600*a^29*b^14*c^29*d^18 - 23871332023900569600*a^30*b^13*c^28*d^19 + 15516365815535370240*a^31*b^12*c^27*d^20 - 8866494751734497280*a^32*b^11*c^26*d^21 + 4433247375867248640*a^33*b^10*c^25*d^22 - 1927498859072716800*a^34*b^9*c^24*d^23 + 722812072152268800*a^35*b^8*c^23*d^24 - 231299863088726016*a^36*b^7*c^22*d^25 + 62273040062349312*a^37*b^6*c^21*d^26 - 13838453347188736*a^38*b^5*c^20*d^27 + 2471152383426560*a^39*b^4*c^19*d^28 - 340848604610560*a^40*b^3*c^18*d^29 + 34084860461056*a^41*b^2*c^17*d^30))^(1/2) + 20141047808*b^35*c^35 + 6806029991936*a^2*b^33*c^33*d^2 - 53376008060928*a^3*b^32*c^32*d^3 + 292822255140864*a^4*b^31*c^31*d^4 - 1195357715300352*a^5*b^30*c^30*d^5 + 3770207453577216*a^6*b^29*c^29*d^6 - 9414767089287168*a^7*b^28*c^28*d^7 + 18917210449772544*a^8*b^27*c^27*d^8 - 30906400985055232*a^9*b^26*c^26*d^9 + 41306136246222848*a^10*b^25*c^25*d^10 - 45251371385583616*a^11*b^24*c^24*d^11 + 40354885515952128*a^12*b^23*c^23*d^12 - 27192068729954304*a^13*b^22*c^22*d^13 + 2468579288727552*a^14*b^21*c^21*d^14 + 56245638022762496*a^15*b^20*c^20*d^15 - 206620726965452800*a^16*b^19*c^19*d^16 + 537221615798067200*a^17*b^18*c^18*d^17 - 1118285729418035200*a^18*b^17*c^17*d^18 + 1916425404928686080*a^19*b^16*c^16*d^19 - 2740669568090865664*a^20*b^15*c^15*d^20 + 3299606844220194816*a^21*b^14*c^14*d^21 - 3363759338873192448*a^22*b^13*c^13*d^22 + 2913545770272743424*a^23*b^12*c^12*d^23 - 2146883780572905472*a^24*b^11*c^11*d^24 + 1344792546818736128*a^25*b^10*c^10*d^25 - 714022739833225216*a^26*b^9*c^9*d^26 + 319664748758366208*a^27*b^8*c^8*d^27 - 119692955670134784*a^28*b^7*c^7*d^28 + 37040318338179072*a^29*b^6*c^6*d^29 - 9313041299423232*a^30*b^5*c^5*d^30 + 1855653025615872*a^31*b^4*c^4*d^31 - 282146424569856*a^32*b^3*c^3*d^32 + 30777147957248*a^33*b^2*c^2*d^33 - 540930998272*a*b^34*c^34*d - 2146713124864*a^34*b*c*d^34)/(68719476736*(a^11*b^32*c^47 + a^43*c^15*d^32 - 32*a^12*b^31*c^46*d - 32*a^42*b*c^16*d^31 + 496*a^13*b^30*c^45*d^2 - 4960*a^14*b^29*c^44*d^3 + 35960*a^15*b^28*c^43*d^4 - 201376*a^16*b^27*c^42*d^5 + 906192*a^17*b^26*c^41*d^6 - 3365856*a^18*b^25*c^40*d^7 + 10518300*a^19*b^24*c^39*d^8 - 28048800*a^20*b^23*c^38*d^9 + 64512240*a^21*b^22*c^37*d^10 - 129024480*a^22*b^21*c^36*d^11 + 225792840*a^23*b^20*c^35*d^12 - 347373600*a^24*b^19*c^34*d^13 + 471435600*a^25*b^18*c^33*d^14 - 565722720*a^26*b^17*c^32*d^15 + 601080390*a^27*b^16*c^31*d^16 - 565722720*a^28*b^15*c^30*d^17 + 471435600*a^29*b^14*c^29*d^18 - 347373600*a^30*b^13*c^28*d^19 + 225792840*a^31*b^12*c^27*d^20 - 129024480*a^32*b^11*c^26*d^21 + 64512240*a^33*b^10*c^25*d^22 - 28048800*a^34*b^9*c^24*d^23 + 10518300*a^35*b^8*c^23*d^24 - 3365856*a^36*b^7*c^22*d^25 + 906192*a^37*b^6*c^21*d^26 - 201376*a^38*b^5*c^20*d^27 + 35960*a^39*b^4*c^19*d^28 - 4960*a^40*b^3*c^18*d^29 + 496*a^41*b^2*c^17*d^30)))^(1/4) - (2/(3*a*c) - (x^4*(112*b^4*c^4*d - 77*a^4*d^5 - 160*a*b^3*c^3*d^2 + 201*a^2*b^2*c^2*d^3 + 68*a^3*b*c*d^4))/(48*a^2*c^3*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)) + (x^2*(121*a^4*d^4 - 56*b^4*c^4 + 96*a^2*b^2*c^2*d^2 + 32*a*b^3*c^3*d - 265*a^3*b*c*d^3))/(48*a^2*c^2*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)) + (b*d*x^6*(77*a^3*d^4 - 56*b^3*c^3*d + 96*a*b^2*c^2*d^2 - 189*a^2*b*c*d^3))/(48*a^2*c^3*(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2)))/(x^(7/2)*(b*c^2 + 2*a*c*d) + x^(11/2)*(a*d^2 + 2*b*c*d) + a*c^2*x^(3/2) + b*d^2*x^(15/2))","B"
503,1,143600,881,22.140721,"\text{Not used}","int(1/(x^(7/2)*(a + b*x^2)^2*(c + 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32396807746722201600*a^27*b^18*c^35*d^14 - 38876169296066641920*a^28*b^17*c^34*d^15 + 41305929877070807040*a^29*b^16*c^33*d^16 - 38876169296066641920*a^30*b^15*c^32*d^17 + 32396807746722201600*a^31*b^14*c^31*d^18 - 23871332023900569600*a^32*b^13*c^30*d^19 + 15516365815535370240*a^33*b^12*c^29*d^20 - 8866494751734497280*a^34*b^11*c^28*d^21 + 4433247375867248640*a^35*b^10*c^27*d^22 - 1927498859072716800*a^36*b^9*c^26*d^23 + 722812072152268800*a^37*b^8*c^25*d^24 - 231299863088726016*a^38*b^7*c^24*d^25 + 62273040062349312*a^39*b^6*c^23*d^26 - 13838453347188736*a^40*b^5*c^22*d^27 + 2471152383426560*a^41*b^4*c^21*d^28 - 340848604610560*a^42*b^3*c^20*d^29 + 34084860461056*a^43*b^2*c^19*d^30))^(1/2) + 16621372440576*a^2*b^35*c^35*d^2 - 124026341031936*a^3*b^34*c^34*d^3 + 649958717915136*a^4*b^33*c^33*d^4 - 2543843228516352*a^5*b^32*c^32*d^5 + 7718627797106688*a^6*b^31*c^31*d^6 - 18600075416567808*a^7*b^30*c^30*d^7 + 36167749025660928*a^8*b^29*c^29*d^8 - 57330958029815808*a^9*b^28*c^28*d^9 + 74515250191269888*a^10*b^27*c^27*d^10 - 79579326172889088*a^11*b^26*c^26*d^11 + 69732511764185088*a^12*b^25*c^25*d^12 - 49845375656294400*a^13*b^24*c^24*d^13 + 28173849246646272*a^14*b^23*c^23*d^14 - 6771862489227264*a^15*b^22*c^22*d^15 - 35351260229615616*a^16*b^21*c^21*d^16 + 175204558709526528*a^17*b^20*c^20*d^17 - 590253517884506112*a^18*b^19*c^19*d^18 + 1561215302787538944*a^19*b^18*c^18*d^19 - 3346011544839634944*a^20*b^17*c^17*d^20 + 5916130635628541952*a^21*b^16*c^16*d^21 - 8737333381308579840*a^22*b^15*c^15*d^22 + 10871659607848206336*a^23*b^14*c^14*d^23 - 11462371182372225024*a^24*b^13*c^13*d^24 + 10274468596079321088*a^25*b^12*c^12*d^25 - 7839134030538768384*a^26*b^11*c^11*d^26 + 5086592011760910336*a^27*b^10*c^10*d^27 - 2798565459902300160*a^28*b^9*c^9*d^28 + 1298533136315185152*a^29*b^8*c^8*d^29 - 503942981543903232*a^30*b^7*c^7*d^30 + 161618590114652160*a^31*b^6*c^6*d^31 - 42100124556607488*a^32*b^5*c^5*d^32 + 8686591868473344*a^33*b^4*c^4*d^33 - 1366716850716672*a^34*b^3*c^3*d^34 + 154123481161728*a^35*b^2*c^2*d^35 - 1394287312896*a*b^36*c^36*d - 11099869986816*a^36*b*c*d^36)/(68719476736*(a^13*b^32*c^49 + a^45*c^17*d^32 - 32*a^14*b^31*c^48*d - 32*a^44*b*c^18*d^31 + 496*a^15*b^30*c^47*d^2 - 4960*a^16*b^29*c^46*d^3 + 35960*a^17*b^28*c^45*d^4 - 201376*a^18*b^27*c^44*d^5 + 906192*a^19*b^26*c^43*d^6 - 3365856*a^20*b^25*c^42*d^7 + 10518300*a^21*b^24*c^41*d^8 - 28048800*a^22*b^23*c^40*d^9 + 64512240*a^23*b^22*c^39*d^10 - 129024480*a^24*b^21*c^38*d^11 + 225792840*a^25*b^20*c^37*d^12 - 347373600*a^26*b^19*c^36*d^13 + 471435600*a^27*b^18*c^35*d^14 - 565722720*a^28*b^17*c^34*d^15 + 601080390*a^29*b^16*c^33*d^16 - 565722720*a^30*b^15*c^32*d^17 + 471435600*a^31*b^14*c^31*d^18 - 347373600*a^32*b^13*c^30*d^19 + 225792840*a^33*b^12*c^29*d^20 - 129024480*a^34*b^11*c^28*d^21 + 64512240*a^35*b^10*c^27*d^22 - 28048800*a^36*b^9*c^26*d^23 + 10518300*a^37*b^8*c^25*d^24 - 3365856*a^38*b^7*c^24*d^25 + 906192*a^39*b^6*c^23*d^26 - 201376*a^40*b^5*c^22*d^27 + 35960*a^41*b^4*c^21*d^28 - 4960*a^42*b^3*c^20*d^29 + 496*a^43*b^2*c^19*d^30)))^(1/4)*1i + 41028394776665109037056*a^29*b^48*c^68*d^15 - 1210739885076097825505280*a^30*b^47*c^67*d^16 + 17243628768780949747924992*a^31*b^46*c^66*d^17 - 158081319004444765483696128*a^32*b^45*c^65*d^18 + 1049494986915760527133114368*a^33*b^44*c^64*d^19 - 5380683046490354438136397824*a^34*b^43*c^63*d^20 + 22176160052724101903372255232*a^35*b^42*c^62*d^21 - 75486313325241636679770439680*a^36*b^41*c^61*d^22 + 216288375615109659684325294080*a^37*b^40*c^60*d^23 - 528818181695424054504437317632*a^38*b^39*c^59*d^24 + 1114222690302433619242395893760*a^39*b^38*c^58*d^25 - 2037545055293058005529639518208*a^40*b^37*c^57*d^26 + 3249918857904337975850827776000*a^41*b^36*c^56*d^27 - 4536394700759564584125915463680*a^42*b^35*c^55*d^28 + 5552435240283931429496420302848*a^43*b^34*c^54*d^29 - 5964290825683224886861470105600*a^44*b^33*c^53*d^30 + 5621639355410781338712284332032*a^45*b^32*c^52*d^31 - 4644077108074496901042866749440*a^46*b^31*c^51*d^32 + 3355360862716129153108295024640*a^47*b^30*c^50*d^33 - 2113405281704782215093506015232*a^48*b^29*c^49*d^34 + 1155283596049337948225918730240*a^49*b^28*c^48*d^35 - 544829519870376944469402451968*a^50*b^27*c^47*d^36 + 219926172037899117268712816640*a^51*b^26*c^46*d^37 - 75201916274561138554746961920*a^52*b^25*c^45*d^38 + 21483948869172056418164932608*a^53*b^24*c^44*d^39 - 5032346201606164325320359936*a^54*b^23*c^43*d^40 + 941275744618015035796488192*a^55*b^22*c^42*d^41 - 135189136301093329947328512*a^56*b^21*c^41*d^42 + 13999140307267180988203008*a^57*b^20*c^40*d^43 - 930460907799665663016960*a^58*b^19*c^39*d^44 + 29814064299214639202304*a^59*b^18*c^38*d^45))*(-(383772100608*a^37*d^37 + 55037657088*b^37*c^37 + ((767544201216*a^37*d^37 + 110075314176*b^37*c^37 + 33242744881152*a^2*b^35*c^35*d^2 - 248052682063872*a^3*b^34*c^34*d^3 + 1299917435830272*a^4*b^33*c^33*d^4 - 5087686457032704*a^5*b^32*c^32*d^5 + 15437255594213376*a^6*b^31*c^31*d^6 - 37200150833135616*a^7*b^30*c^30*d^7 + 72335498051321856*a^8*b^29*c^29*d^8 - 114661916059631616*a^9*b^28*c^28*d^9 + 149030500382539776*a^10*b^27*c^27*d^10 - 159158652345778176*a^11*b^26*c^26*d^11 + 139465023528370176*a^12*b^25*c^25*d^12 - 99690751312588800*a^13*b^24*c^24*d^13 + 56347698493292544*a^14*b^23*c^23*d^14 - 13543724978454528*a^15*b^22*c^22*d^15 - 70702520459231232*a^16*b^21*c^21*d^16 + 350409117419053056*a^17*b^20*c^20*d^17 - 1180507035769012224*a^18*b^19*c^19*d^18 + 3122430605575077888*a^19*b^18*c^18*d^19 - 6692023089679269888*a^20*b^17*c^17*d^20 + 11832261271257083904*a^21*b^16*c^16*d^21 - 17474666762617159680*a^22*b^15*c^15*d^22 + 21743319215696412672*a^23*b^14*c^14*d^23 - 22924742364744450048*a^24*b^13*c^13*d^24 + 20548937192158642176*a^25*b^12*c^12*d^25 - 15678268061077536768*a^26*b^11*c^11*d^26 + 10173184023521820672*a^27*b^10*c^10*d^27 - 5597130919804600320*a^28*b^9*c^9*d^28 + 2597066272630370304*a^29*b^8*c^8*d^29 - 1007885963087806464*a^30*b^7*c^7*d^30 + 323237180229304320*a^31*b^6*c^6*d^31 - 84200249113214976*a^32*b^5*c^5*d^32 + 17373183736946688*a^33*b^4*c^4*d^33 - 2733433701433344*a^34*b^3*c^3*d^34 + 308246962323456*a^35*b^2*c^2*d^35 - 2788574625792*a*b^36*c^36*d - 22199739973632*a^36*b*c*d^36)^2/4 - (36443545848801*a^12*b^17*d^25 + 106571947510161*b^29*c^12*d^13 - 1446035052490812*a*b^28*c^11*d^14 - 533437396380252*a^11*b^18*c*d^24 + 8550655952661522*a^2*b^27*c^10*d^15 - 29104520578391916*a^3*b^26*c^9*d^16 + 63613900184394735*a^4*b^25*c^8*d^17 - 94521216268814328*a^5*b^24*c^7*d^18 + 98620802659391292*a^6*b^23*c^6*d^19 - 73370651908486968*a^7*b^22*c^5*d^20 + 38907153228163455*a^8*b^21*c^4*d^21 - 14432588165402316*a^9*b^20*c^3*d^22 + 3574683057023442*a^10*b^19*c^2*d^23)*(68719476736*a^13*b^32*c^49 + 68719476736*a^45*c^17*d^32 - 2199023255552*a^14*b^31*c^48*d - 2199023255552*a^44*b*c^18*d^31 + 34084860461056*a^15*b^30*c^47*d^2 - 340848604610560*a^16*b^29*c^46*d^3 + 2471152383426560*a^17*b^28*c^45*d^4 - 13838453347188736*a^18*b^27*c^44*d^5 + 62273040062349312*a^19*b^26*c^43*d^6 - 231299863088726016*a^20*b^25*c^42*d^7 + 722812072152268800*a^21*b^24*c^41*d^8 - 1927498859072716800*a^22*b^23*c^40*d^9 + 4433247375867248640*a^23*b^22*c^39*d^10 - 8866494751734497280*a^24*b^21*c^38*d^11 + 15516365815535370240*a^25*b^20*c^37*d^12 - 23871332023900569600*a^26*b^19*c^36*d^13 + 32396807746722201600*a^27*b^18*c^35*d^14 - 38876169296066641920*a^28*b^17*c^34*d^15 + 41305929877070807040*a^29*b^16*c^33*d^16 - 38876169296066641920*a^30*b^15*c^32*d^17 + 32396807746722201600*a^31*b^14*c^31*d^18 - 23871332023900569600*a^32*b^13*c^30*d^19 + 15516365815535370240*a^33*b^12*c^29*d^20 - 8866494751734497280*a^34*b^11*c^28*d^21 + 4433247375867248640*a^35*b^10*c^27*d^22 - 1927498859072716800*a^36*b^9*c^26*d^23 + 722812072152268800*a^37*b^8*c^25*d^24 - 231299863088726016*a^38*b^7*c^24*d^25 + 62273040062349312*a^39*b^6*c^23*d^26 - 13838453347188736*a^40*b^5*c^22*d^27 + 2471152383426560*a^41*b^4*c^21*d^28 - 340848604610560*a^42*b^3*c^20*d^29 + 34084860461056*a^43*b^2*c^19*d^30))^(1/2) + 16621372440576*a^2*b^35*c^35*d^2 - 124026341031936*a^3*b^34*c^34*d^3 + 649958717915136*a^4*b^33*c^33*d^4 - 2543843228516352*a^5*b^32*c^32*d^5 + 7718627797106688*a^6*b^31*c^31*d^6 - 18600075416567808*a^7*b^30*c^30*d^7 + 36167749025660928*a^8*b^29*c^29*d^8 - 57330958029815808*a^9*b^28*c^28*d^9 + 74515250191269888*a^10*b^27*c^27*d^10 - 79579326172889088*a^11*b^26*c^26*d^11 + 69732511764185088*a^12*b^25*c^25*d^12 - 49845375656294400*a^13*b^24*c^24*d^13 + 28173849246646272*a^14*b^23*c^23*d^14 - 6771862489227264*a^15*b^22*c^22*d^15 - 35351260229615616*a^16*b^21*c^21*d^16 + 175204558709526528*a^17*b^20*c^20*d^17 - 590253517884506112*a^18*b^19*c^19*d^18 + 1561215302787538944*a^19*b^18*c^18*d^19 - 3346011544839634944*a^20*b^17*c^17*d^20 + 5916130635628541952*a^21*b^16*c^16*d^21 - 8737333381308579840*a^22*b^15*c^15*d^22 + 10871659607848206336*a^23*b^14*c^14*d^23 - 11462371182372225024*a^24*b^13*c^13*d^24 + 10274468596079321088*a^25*b^12*c^12*d^25 - 7839134030538768384*a^26*b^11*c^11*d^26 + 5086592011760910336*a^27*b^10*c^10*d^27 - 2798565459902300160*a^28*b^9*c^9*d^28 + 1298533136315185152*a^29*b^8*c^8*d^29 - 503942981543903232*a^30*b^7*c^7*d^30 + 161618590114652160*a^31*b^6*c^6*d^31 - 42100124556607488*a^32*b^5*c^5*d^32 + 8686591868473344*a^33*b^4*c^4*d^33 - 1366716850716672*a^34*b^3*c^3*d^34 + 154123481161728*a^35*b^2*c^2*d^35 - 1394287312896*a*b^36*c^36*d - 11099869986816*a^36*b*c*d^36)/(68719476736*(a^13*b^32*c^49 + a^45*c^17*d^32 - 32*a^14*b^31*c^48*d - 32*a^44*b*c^18*d^31 + 496*a^15*b^30*c^47*d^2 - 4960*a^16*b^29*c^46*d^3 + 35960*a^17*b^28*c^45*d^4 - 201376*a^18*b^27*c^44*d^5 + 906192*a^19*b^26*c^43*d^6 - 3365856*a^20*b^25*c^42*d^7 + 10518300*a^21*b^24*c^41*d^8 - 28048800*a^22*b^23*c^40*d^9 + 64512240*a^23*b^22*c^39*d^10 - 129024480*a^24*b^21*c^38*d^11 + 225792840*a^25*b^20*c^37*d^12 - 347373600*a^26*b^19*c^36*d^13 + 471435600*a^27*b^18*c^35*d^14 - 565722720*a^28*b^17*c^34*d^15 + 601080390*a^29*b^16*c^33*d^16 - 565722720*a^30*b^15*c^32*d^17 + 471435600*a^31*b^14*c^31*d^18 - 347373600*a^32*b^13*c^30*d^19 + 225792840*a^33*b^12*c^29*d^20 - 129024480*a^34*b^11*c^28*d^21 + 64512240*a^35*b^10*c^27*d^22 - 28048800*a^36*b^9*c^26*d^23 + 10518300*a^37*b^8*c^25*d^24 - 3365856*a^38*b^7*c^24*d^25 + 906192*a^39*b^6*c^23*d^26 - 201376*a^40*b^5*c^22*d^27 + 35960*a^41*b^4*c^21*d^28 - 4960*a^42*b^3*c^20*d^29 + 496*a^43*b^2*c^19*d^30)))^(1/4)","B"
504,1,96,103,0.643561,"\text{Not used}","int(x^5*(A + B*x^2)*(a + b*x^2)^(1/2),x)","\sqrt{b\,x^2+a}\,\left(\frac{B\,x^8}{9}-\frac{16\,B\,a^4-24\,A\,a^3\,b}{315\,b^4}+\frac{x^6\,\left(45\,A\,b^4+5\,B\,a\,b^3\right)}{315\,b^4}-\frac{4\,a^2\,x^2\,\left(3\,A\,b-2\,B\,a\right)}{315\,b^3}+\frac{a\,x^4\,\left(3\,A\,b-2\,B\,a\right)}{105\,b^2}\right)","Not used",1,"(a + b*x^2)^(1/2)*((B*x^8)/9 - (16*B*a^4 - 24*A*a^3*b)/(315*b^4) + (x^6*(45*A*b^4 + 5*B*a*b^3))/(315*b^4) - (4*a^2*x^2*(3*A*b - 2*B*a))/(315*b^3) + (a*x^4*(3*A*b - 2*B*a))/(105*b^2))","B"
505,0,-1,155,0.000000,"\text{Not used}","int(x^4*(A + B*x^2)*(a + b*x^2)^(1/2),x)","\int x^4\,\left(B\,x^2+A\right)\,\sqrt{b\,x^2+a} \,d x","Not used",1,"int(x^4*(A + B*x^2)*(a + b*x^2)^(1/2), x)","F"
506,1,76,73,0.556370,"\text{Not used}","int(x^3*(A + B*x^2)*(a + b*x^2)^(1/2),x)","\sqrt{b\,x^2+a}\,\left(\frac{B\,x^6}{7}+\frac{8\,B\,a^3-14\,A\,a^2\,b}{105\,b^3}+\frac{x^4\,\left(21\,A\,b^3+3\,B\,a\,b^2\right)}{105\,b^3}+\frac{a\,x^2\,\left(7\,A\,b-4\,B\,a\right)}{105\,b^2}\right)","Not used",1,"(a + b*x^2)^(1/2)*((B*x^6)/7 + (8*B*a^3 - 14*A*a^2*b)/(105*b^3) + (x^4*(21*A*b^3 + 3*B*a*b^2))/(105*b^3) + (a*x^2*(7*A*b - 4*B*a))/(105*b^2))","B"
507,0,-1,122,0.000000,"\text{Not used}","int(x^2*(A + B*x^2)*(a + b*x^2)^(1/2),x)","\int x^2\,\left(B\,x^2+A\right)\,\sqrt{b\,x^2+a} \,d x","Not used",1,"int(x^2*(A + B*x^2)*(a + b*x^2)^(1/2), x)","F"
508,1,53,46,0.536608,"\text{Not used}","int(x*(A + B*x^2)*(a + b*x^2)^(1/2),x)","\sqrt{b\,x^2+a}\,\left(\frac{B\,x^4}{5}-\frac{2\,B\,a^2-5\,A\,a\,b}{15\,b^2}+\frac{x^2\,\left(5\,A\,b^2+B\,a\,b\right)}{15\,b^2}\right)","Not used",1,"(a + b*x^2)^(1/2)*((B*x^4)/5 - (2*B*a^2 - 5*A*a*b)/(15*b^2) + (x^2*(5*A*b^2 + B*a*b))/(15*b^2))","B"
509,0,-1,87,0.000000,"\text{Not used}","int((A + B*x^2)*(a + b*x^2)^(1/2),x)","\int \left(B\,x^2+A\right)\,\sqrt{b\,x^2+a} \,d x","Not used",1,"int((A + B*x^2)*(a + b*x^2)^(1/2), x)","F"
510,1,47,59,0.880755,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^(1/2))/x,x)","A\,\sqrt{b\,x^2+a}+\frac{B\,{\left(b\,x^2+a\right)}^{3/2}}{3\,b}-A\,\sqrt{a}\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)","Not used",1,"A*(a + b*x^2)^(1/2) + (B*(a + b*x^2)^(3/2))/(3*b) - A*a^(1/2)*atanh((a + b*x^2)^(1/2)/a^(1/2))","B"
511,1,94,84,1.262357,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^(1/2))/x^2,x)","\frac{B\,x\,\sqrt{b\,x^2+a}}{2}-\frac{A\,\sqrt{b\,x^2+a}}{x}+\frac{B\,a\,\ln\left(\sqrt{b}\,x+\sqrt{b\,x^2+a}\right)}{2\,\sqrt{b}}-\frac{A\,\sqrt{b}\,\mathrm{asin}\left(\frac{\sqrt{b}\,x\,1{}\mathrm{i}}{\sqrt{a}}\right)\,\sqrt{b\,x^2+a}\,1{}\mathrm{i}}{\sqrt{a}\,\sqrt{\frac{b\,x^2}{a}+1}}","Not used",1,"(B*x*(a + b*x^2)^(1/2))/2 - (A*(a + b*x^2)^(1/2))/x + (B*a*log(b^(1/2)*x + (a + b*x^2)^(1/2)))/(2*b^(1/2)) - (A*b^(1/2)*asin((b^(1/2)*x*1i)/a^(1/2))*(a + b*x^2)^(1/2)*1i)/(a^(1/2)*((b*x^2)/a + 1)^(1/2))","B"
512,1,68,84,1.347214,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^(1/2))/x^3,x)","B\,\sqrt{b\,x^2+a}-\frac{A\,\sqrt{b\,x^2+a}}{2\,x^2}-B\,\sqrt{a}\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)-\frac{A\,b\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{2\,\sqrt{a}}","Not used",1,"B*(a + b*x^2)^(1/2) - (A*(a + b*x^2)^(1/2))/(2*x^2) - B*a^(1/2)*atanh((a + b*x^2)^(1/2)/a^(1/2)) - (A*b*atanh((a + b*x^2)^(1/2)/a^(1/2)))/(2*a^(1/2))","B"
513,1,76,66,1.466676,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^(1/2))/x^4,x)","-\frac{B\,\sqrt{b\,x^2+a}}{x}-\frac{A\,{\left(b\,x^2+a\right)}^{3/2}}{3\,a\,x^3}-\frac{B\,\sqrt{b}\,\mathrm{asin}\left(\frac{\sqrt{b}\,x\,1{}\mathrm{i}}{\sqrt{a}}\right)\,\sqrt{b\,x^2+a}\,1{}\mathrm{i}}{\sqrt{a}\,\sqrt{\frac{b\,x^2}{a}+1}}","Not used",1,"- (B*(a + b*x^2)^(1/2))/x - (A*(a + b*x^2)^(3/2))/(3*a*x^3) - (B*b^(1/2)*asin((b^(1/2)*x*1i)/a^(1/2))*(a + b*x^2)^(1/2)*1i)/(a^(1/2)*((b*x^2)/a + 1)^(1/2))","B"
514,1,93,88,1.696964,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^(1/2))/x^5,x)","\frac{A\,b^2\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{8\,a^{3/2}}-\frac{B\,\sqrt{b\,x^2+a}}{2\,x^2}-\frac{A\,\sqrt{b\,x^2+a}}{8\,x^4}-\frac{A\,{\left(b\,x^2+a\right)}^{3/2}}{8\,a\,x^4}-\frac{B\,b\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{2\,\sqrt{a}}","Not used",1,"(A*b^2*atanh((a + b*x^2)^(1/2)/a^(1/2)))/(8*a^(3/2)) - (B*(a + b*x^2)^(1/2))/(2*x^2) - (A*(a + b*x^2)^(1/2))/(8*x^4) - (A*(a + b*x^2)^(3/2))/(8*a*x^4) - (B*b*atanh((a + b*x^2)^(1/2)/a^(1/2)))/(2*a^(1/2))","B"
515,1,97,53,0.896416,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^(1/2))/x^6,x)","\frac{\left(A\,b^2+B\,a\,b\right)\,\sqrt{b\,x^2+a}}{5\,a^2\,x}-\frac{\left(5\,B\,a^2+A\,b\,a\right)\,\sqrt{b\,x^2+a}}{15\,a^2\,x^3}-\frac{A\,\sqrt{b\,x^2+a}}{5\,x^5}-\frac{b\,\sqrt{b\,x^2+a}\,\left(A\,b+8\,B\,a\right)}{15\,a^2\,x}","Not used",1,"((A*b^2 + B*a*b)*(a + b*x^2)^(1/2))/(5*a^2*x) - ((5*B*a^2 + A*a*b)*(a + b*x^2)^(1/2))/(15*a^2*x^3) - (A*(a + b*x^2)^(1/2))/(5*x^5) - (b*(a + b*x^2)^(1/2)*(A*b + 8*B*a))/(15*a^2*x)","B"
516,1,134,120,2.200156,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^(1/2))/x^7,x)","\frac{B\,b^2\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{8\,a^{3/2}}-\frac{B\,\sqrt{b\,x^2+a}}{8\,x^4}-\frac{A\,\sqrt{b\,x^2+a}}{16\,x^6}-\frac{A\,{\left(b\,x^2+a\right)}^{3/2}}{6\,a\,x^6}+\frac{A\,{\left(b\,x^2+a\right)}^{5/2}}{16\,a^2\,x^6}-\frac{B\,{\left(b\,x^2+a\right)}^{3/2}}{8\,a\,x^4}+\frac{A\,b^3\,\mathrm{atan}\left(\frac{\sqrt{b\,x^2+a}\,1{}\mathrm{i}}{\sqrt{a}}\right)\,1{}\mathrm{i}}{16\,a^{5/2}}","Not used",1,"(A*b^3*atan(((a + b*x^2)^(1/2)*1i)/a^(1/2))*1i)/(16*a^(5/2)) - (B*(a + b*x^2)^(1/2))/(8*x^4) - (A*(a + b*x^2)^(1/2))/(16*x^6) + (B*b^2*atanh((a + b*x^2)^(1/2)/a^(1/2)))/(8*a^(3/2)) - (A*(a + b*x^2)^(3/2))/(6*a*x^6) + (A*(a + b*x^2)^(5/2))/(16*a^2*x^6) - (B*(a + b*x^2)^(3/2))/(8*a*x^4)","B"
517,1,132,84,1.093647,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^(1/2))/x^8,x)","\frac{4\,A\,b^2\,\sqrt{b\,x^2+a}}{105\,a^2\,x^3}-\frac{B\,\sqrt{b\,x^2+a}}{5\,x^5}-\frac{A\,b\,\sqrt{b\,x^2+a}}{35\,a\,x^5}-\frac{B\,b\,\sqrt{b\,x^2+a}}{15\,a\,x^3}-\frac{A\,\sqrt{b\,x^2+a}}{7\,x^7}-\frac{8\,A\,b^3\,\sqrt{b\,x^2+a}}{105\,a^3\,x}+\frac{2\,B\,b^2\,\sqrt{b\,x^2+a}}{15\,a^2\,x}","Not used",1,"(4*A*b^2*(a + b*x^2)^(1/2))/(105*a^2*x^3) - (B*(a + b*x^2)^(1/2))/(5*x^5) - (A*b*(a + b*x^2)^(1/2))/(35*a*x^5) - (B*b*(a + b*x^2)^(1/2))/(15*a*x^3) - (A*(a + b*x^2)^(1/2))/(7*x^7) - (8*A*b^3*(a + b*x^2)^(1/2))/(105*a^3*x) + (2*B*b^2*(a + b*x^2)^(1/2))/(15*a^2*x)","B"
518,1,173,156,2.679744,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^(1/2))/x^9,x)","\frac{55\,A\,{\left(b\,x^2+a\right)}^{5/2}}{384\,a^2\,x^8}-\frac{B\,\sqrt{b\,x^2+a}}{16\,x^6}-\frac{73\,A\,{\left(b\,x^2+a\right)}^{3/2}}{384\,a\,x^8}-\frac{5\,A\,\sqrt{b\,x^2+a}}{128\,x^8}-\frac{5\,A\,{\left(b\,x^2+a\right)}^{7/2}}{128\,a^3\,x^8}-\frac{B\,{\left(b\,x^2+a\right)}^{3/2}}{6\,a\,x^6}+\frac{B\,{\left(b\,x^2+a\right)}^{5/2}}{16\,a^2\,x^6}-\frac{A\,b^4\,\mathrm{atan}\left(\frac{\sqrt{b\,x^2+a}\,1{}\mathrm{i}}{\sqrt{a}}\right)\,5{}\mathrm{i}}{128\,a^{7/2}}+\frac{B\,b^3\,\mathrm{atan}\left(\frac{\sqrt{b\,x^2+a}\,1{}\mathrm{i}}{\sqrt{a}}\right)\,1{}\mathrm{i}}{16\,a^{5/2}}","Not used",1,"(B*b^3*atan(((a + b*x^2)^(1/2)*1i)/a^(1/2))*1i)/(16*a^(5/2)) - (B*(a + b*x^2)^(1/2))/(16*x^6) - (A*b^4*atan(((a + b*x^2)^(1/2)*1i)/a^(1/2))*5i)/(128*a^(7/2)) - (5*A*(a + b*x^2)^(1/2))/(128*x^8) - (73*A*(a + b*x^2)^(3/2))/(384*a*x^8) + (55*A*(a + b*x^2)^(5/2))/(384*a^2*x^8) - (5*A*(a + b*x^2)^(7/2))/(128*a^3*x^8) - (B*(a + b*x^2)^(3/2))/(6*a*x^6) + (B*(a + b*x^2)^(5/2))/(16*a^2*x^6)","B"
519,1,174,117,1.462717,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^(1/2))/x^10,x)","\frac{2\,A\,b^2\,\sqrt{b\,x^2+a}}{105\,a^2\,x^5}-\frac{B\,\sqrt{b\,x^2+a}}{7\,x^7}-\frac{A\,b\,\sqrt{b\,x^2+a}}{63\,a\,x^7}-\frac{B\,b\,\sqrt{b\,x^2+a}}{35\,a\,x^5}-\frac{A\,\sqrt{b\,x^2+a}}{9\,x^9}-\frac{8\,A\,b^3\,\sqrt{b\,x^2+a}}{315\,a^3\,x^3}+\frac{16\,A\,b^4\,\sqrt{b\,x^2+a}}{315\,a^4\,x}+\frac{4\,B\,b^2\,\sqrt{b\,x^2+a}}{105\,a^2\,x^3}-\frac{8\,B\,b^3\,\sqrt{b\,x^2+a}}{105\,a^3\,x}","Not used",1,"(2*A*b^2*(a + b*x^2)^(1/2))/(105*a^2*x^5) - (B*(a + b*x^2)^(1/2))/(7*x^7) - (A*b*(a + b*x^2)^(1/2))/(63*a*x^7) - (B*b*(a + b*x^2)^(1/2))/(35*a*x^5) - (A*(a + b*x^2)^(1/2))/(9*x^9) - (8*A*b^3*(a + b*x^2)^(1/2))/(315*a^3*x^3) + (16*A*b^4*(a + b*x^2)^(1/2))/(315*a^4*x) + (4*B*b^2*(a + b*x^2)^(1/2))/(105*a^2*x^3) - (8*B*b^3*(a + b*x^2)^(1/2))/(105*a^3*x)","B"
520,1,209,189,3.497407,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^(1/2))/x^11,x)","\frac{7\,A\,{\left(b\,x^2+a\right)}^{5/2}}{30\,a^2\,x^{10}}-\frac{5\,B\,\sqrt{b\,x^2+a}}{128\,x^8}-\frac{79\,A\,{\left(b\,x^2+a\right)}^{3/2}}{384\,a\,x^{10}}-\frac{7\,A\,\sqrt{b\,x^2+a}}{256\,x^{10}}-\frac{49\,A\,{\left(b\,x^2+a\right)}^{7/2}}{384\,a^3\,x^{10}}+\frac{7\,A\,{\left(b\,x^2+a\right)}^{9/2}}{256\,a^4\,x^{10}}-\frac{73\,B\,{\left(b\,x^2+a\right)}^{3/2}}{384\,a\,x^8}+\frac{55\,B\,{\left(b\,x^2+a\right)}^{5/2}}{384\,a^2\,x^8}-\frac{5\,B\,{\left(b\,x^2+a\right)}^{7/2}}{128\,a^3\,x^8}+\frac{A\,b^5\,\mathrm{atan}\left(\frac{\sqrt{b\,x^2+a}\,1{}\mathrm{i}}{\sqrt{a}}\right)\,7{}\mathrm{i}}{256\,a^{9/2}}-\frac{B\,b^4\,\mathrm{atan}\left(\frac{\sqrt{b\,x^2+a}\,1{}\mathrm{i}}{\sqrt{a}}\right)\,5{}\mathrm{i}}{128\,a^{7/2}}","Not used",1,"(A*b^5*atan(((a + b*x^2)^(1/2)*1i)/a^(1/2))*7i)/(256*a^(9/2)) - (5*B*(a + b*x^2)^(1/2))/(128*x^8) - (7*A*(a + b*x^2)^(1/2))/(256*x^10) - (B*b^4*atan(((a + b*x^2)^(1/2)*1i)/a^(1/2))*5i)/(128*a^(7/2)) - (79*A*(a + b*x^2)^(3/2))/(384*a*x^10) + (7*A*(a + b*x^2)^(5/2))/(30*a^2*x^10) - (49*A*(a + b*x^2)^(7/2))/(384*a^3*x^10) + (7*A*(a + b*x^2)^(9/2))/(256*a^4*x^10) - (73*B*(a + b*x^2)^(3/2))/(384*a*x^8) + (55*B*(a + b*x^2)^(5/2))/(384*a^2*x^8) - (5*B*(a + b*x^2)^(7/2))/(128*a^3*x^8)","B"
521,1,117,103,0.742395,"\text{Not used}","int(x^5*(A + B*x^2)*(a + b*x^2)^(3/2),x)","\sqrt{b\,x^2+a}\,\left(\frac{x^8\,\left(385\,A\,b^5+420\,B\,a\,b^4\right)}{3465\,b^4}-\frac{48\,B\,a^5-88\,A\,a^4\,b}{3465\,b^4}+\frac{B\,b\,x^{10}}{11}+\frac{a^2\,x^4\,\left(11\,A\,b-6\,B\,a\right)}{1155\,b^2}-\frac{4\,a^3\,x^2\,\left(11\,A\,b-6\,B\,a\right)}{3465\,b^3}+\frac{a\,x^6\,\left(110\,A\,b+3\,B\,a\right)}{693\,b}\right)","Not used",1,"(a + b*x^2)^(1/2)*((x^8*(385*A*b^5 + 420*B*a*b^4))/(3465*b^4) - (48*B*a^5 - 88*A*a^4*b)/(3465*b^4) + (B*b*x^10)/11 + (a^2*x^4*(11*A*b - 6*B*a))/(1155*b^2) - (4*a^3*x^2*(11*A*b - 6*B*a))/(3465*b^3) + (a*x^6*(110*A*b + 3*B*a))/(693*b))","B"
522,0,-1,188,0.000000,"\text{Not used}","int(x^4*(A + B*x^2)*(a + b*x^2)^(3/2),x)","\int x^4\,\left(B\,x^2+A\right)\,{\left(b\,x^2+a\right)}^{3/2} \,d x","Not used",1,"int(x^4*(A + B*x^2)*(a + b*x^2)^(3/2), x)","F"
523,1,96,73,0.626634,"\text{Not used}","int(x^3*(A + B*x^2)*(a + b*x^2)^(3/2),x)","\sqrt{b\,x^2+a}\,\left(\frac{8\,B\,a^4-18\,A\,a^3\,b}{315\,b^3}+\frac{x^6\,\left(45\,A\,b^4+50\,B\,a\,b^3\right)}{315\,b^3}+\frac{B\,b\,x^8}{9}+\frac{a^2\,x^2\,\left(9\,A\,b-4\,B\,a\right)}{315\,b^2}+\frac{a\,x^4\,\left(24\,A\,b+B\,a\right)}{105\,b}\right)","Not used",1,"(a + b*x^2)^(1/2)*((8*B*a^4 - 18*A*a^3*b)/(315*b^3) + (x^6*(45*A*b^4 + 50*B*a*b^3))/(315*b^3) + (B*b*x^8)/9 + (a^2*x^2*(9*A*b - 4*B*a))/(315*b^2) + (a*x^4*(24*A*b + B*a))/(105*b))","B"
524,0,-1,155,0.000000,"\text{Not used}","int(x^2*(A + B*x^2)*(a + b*x^2)^(3/2),x)","\int x^2\,\left(B\,x^2+A\right)\,{\left(b\,x^2+a\right)}^{3/2} \,d x","Not used",1,"int(x^2*(A + B*x^2)*(a + b*x^2)^(3/2), x)","F"
525,1,76,46,0.562813,"\text{Not used}","int(x*(A + B*x^2)*(a + b*x^2)^(3/2),x)","\sqrt{b\,x^2+a}\,\left(\frac{x^4\,\left(7\,A\,b^3+8\,B\,a\,b^2\right)}{35\,b^2}-\frac{2\,B\,a^3-7\,A\,a^2\,b}{35\,b^2}+\frac{B\,b\,x^6}{7}+\frac{a\,x^2\,\left(14\,A\,b+B\,a\right)}{35\,b}\right)","Not used",1,"(a + b*x^2)^(1/2)*((x^4*(7*A*b^3 + 8*B*a*b^2))/(35*b^2) - (2*B*a^3 - 7*A*a^2*b)/(35*b^2) + (B*b*x^6)/7 + (a*x^2*(14*A*b + B*a))/(35*b))","B"
526,0,-1,118,0.000000,"\text{Not used}","int((A + B*x^2)*(a + b*x^2)^(3/2),x)","\int \left(B\,x^2+A\right)\,{\left(b\,x^2+a\right)}^{3/2} \,d x","Not used",1,"int((A + B*x^2)*(a + b*x^2)^(3/2), x)","F"
527,1,60,76,0.971644,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^(3/2))/x,x)","\frac{A\,{\left(b\,x^2+a\right)}^{3/2}}{3}+\frac{B\,{\left(b\,x^2+a\right)}^{5/2}}{5\,b}-A\,a^{3/2}\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)+A\,a\,\sqrt{b\,x^2+a}","Not used",1,"(A*(a + b*x^2)^(3/2))/3 + (B*(a + b*x^2)^(5/2))/(5*b) - A*a^(3/2)*atanh((a + b*x^2)^(1/2)/a^(1/2)) + A*a*(a + b*x^2)^(1/2)","B"
528,1,80,109,1.503586,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^(3/2))/x^2,x)","\frac{B\,x\,{\left(b\,x^2+a\right)}^{3/2}\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{2},\frac{1}{2};\ \frac{3}{2};\ -\frac{b\,x^2}{a}\right)}{{\left(\frac{b\,x^2}{a}+1\right)}^{3/2}}-\frac{A\,{\left(b\,x^2+a\right)}^{3/2}\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{2},-\frac{1}{2};\ \frac{1}{2};\ -\frac{b\,x^2}{a}\right)}{x\,{\left(\frac{b\,x^2}{a}+1\right)}^{3/2}}","Not used",1,"(B*x*(a + b*x^2)^(3/2)*hypergeom([-3/2, 1/2], 3/2, -(b*x^2)/a))/((b*x^2)/a + 1)^(3/2) - (A*(a + b*x^2)^(3/2)*hypergeom([-3/2, -1/2], 1/2, -(b*x^2)/a))/(x*((b*x^2)/a + 1)^(3/2))","B"
529,1,94,110,1.490717,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^(3/2))/x^3,x)","\frac{B\,{\left(b\,x^2+a\right)}^{3/2}}{3}-B\,a^{3/2}\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)+A\,b\,\sqrt{b\,x^2+a}+B\,a\,\sqrt{b\,x^2+a}-\frac{A\,a\,\sqrt{b\,x^2+a}}{2\,x^2}-\frac{3\,A\,\sqrt{a}\,b\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{2}","Not used",1,"(B*(a + b*x^2)^(3/2))/3 - B*a^(3/2)*atanh((a + b*x^2)^(1/2)/a^(1/2)) + A*b*(a + b*x^2)^(1/2) + B*a*(a + b*x^2)^(1/2) - (A*a*(a + b*x^2)^(1/2))/(2*x^2) - (3*A*a^(1/2)*b*atanh((a + b*x^2)^(1/2)/a^(1/2)))/2","B"
530,0,-1,119,0.000000,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^(3/2))/x^4,x)","\int \frac{\left(B\,x^2+A\right)\,{\left(b\,x^2+a\right)}^{3/2}}{x^4} \,d x","Not used",1,"int(((A + B*x^2)*(a + b*x^2)^(3/2))/x^4, x)","F"
531,1,104,115,1.903372,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^(3/2))/x^5,x)","B\,b\,\sqrt{b\,x^2+a}-\frac{5\,A\,{\left(b\,x^2+a\right)}^{3/2}}{8\,x^4}-\frac{3\,A\,b^2\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{8\,\sqrt{a}}+\frac{3\,A\,a\,\sqrt{b\,x^2+a}}{8\,x^4}-\frac{B\,a\,\sqrt{b\,x^2+a}}{2\,x^2}-\frac{3\,B\,\sqrt{a}\,b\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{2}","Not used",1,"B*b*(a + b*x^2)^(1/2) - (5*A*(a + b*x^2)^(3/2))/(8*x^4) - (3*A*b^2*atanh((a + b*x^2)^(1/2)/a^(1/2)))/(8*a^(1/2)) + (3*A*a*(a + b*x^2)^(1/2))/(8*x^4) - (B*a*(a + b*x^2)^(1/2))/(2*x^2) - (3*B*a^(1/2)*b*atanh((a + b*x^2)^(1/2)/a^(1/2)))/2","B"
532,0,-1,86,0.000000,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^(3/2))/x^6,x)","\int \frac{\left(B\,x^2+A\right)\,{\left(b\,x^2+a\right)}^{3/2}}{x^6} \,d x","Not used",1,"int(((A + B*x^2)*(a + b*x^2)^(3/2))/x^6, x)","F"
533,1,130,120,2.626043,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^(3/2))/x^7,x)","\frac{A\,a\,\sqrt{b\,x^2+a}}{16\,x^6}-\frac{5\,B\,{\left(b\,x^2+a\right)}^{3/2}}{8\,x^4}-\frac{3\,B\,b^2\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{8\,\sqrt{a}}-\frac{A\,{\left(b\,x^2+a\right)}^{3/2}}{6\,x^6}+\frac{3\,B\,a\,\sqrt{b\,x^2+a}}{8\,x^4}-\frac{A\,{\left(b\,x^2+a\right)}^{5/2}}{16\,a\,x^6}-\frac{A\,b^3\,\mathrm{atan}\left(\frac{\sqrt{b\,x^2+a}\,1{}\mathrm{i}}{\sqrt{a}}\right)\,1{}\mathrm{i}}{16\,a^{3/2}}","Not used",1,"(A*a*(a + b*x^2)^(1/2))/(16*x^6) - (5*B*(a + b*x^2)^(3/2))/(8*x^4) - (A*b^3*atan(((a + b*x^2)^(1/2)*1i)/a^(1/2))*1i)/(16*a^(3/2)) - (3*B*b^2*atanh((a + b*x^2)^(1/2)/a^(1/2)))/(8*a^(1/2)) - (A*(a + b*x^2)^(3/2))/(6*x^6) + (3*B*a*(a + b*x^2)^(1/2))/(8*x^4) - (A*(a + b*x^2)^(5/2))/(16*a*x^6)","B"
534,1,128,53,1.517664,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^(3/2))/x^8,x)","\frac{2\,A\,b^3\,\sqrt{b\,x^2+a}}{35\,a^2\,x}-\frac{8\,A\,b\,\sqrt{b\,x^2+a}}{35\,x^5}-\frac{B\,a\,\sqrt{b\,x^2+a}}{5\,x^5}-\frac{2\,B\,b\,\sqrt{b\,x^2+a}}{5\,x^3}-\frac{A\,b^2\,\sqrt{b\,x^2+a}}{35\,a\,x^3}-\frac{A\,a\,\sqrt{b\,x^2+a}}{7\,x^7}-\frac{B\,b^2\,\sqrt{b\,x^2+a}}{5\,a\,x}","Not used",1,"(2*A*b^3*(a + b*x^2)^(1/2))/(35*a^2*x) - (8*A*b*(a + b*x^2)^(1/2))/(35*x^5) - (B*a*(a + b*x^2)^(1/2))/(5*x^5) - (2*B*b*(a + b*x^2)^(1/2))/(5*x^3) - (A*b^2*(a + b*x^2)^(1/2))/(35*a*x^3) - (A*a*(a + b*x^2)^(1/2))/(7*x^7) - (B*b^2*(a + b*x^2)^(1/2))/(5*a*x)","B"
535,1,169,156,3.570678,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^(3/2))/x^9,x)","\frac{3\,A\,a\,\sqrt{b\,x^2+a}}{128\,x^8}-\frac{B\,{\left(b\,x^2+a\right)}^{3/2}}{6\,x^6}-\frac{11\,A\,{\left(b\,x^2+a\right)}^{3/2}}{128\,x^8}+\frac{B\,a\,\sqrt{b\,x^2+a}}{16\,x^6}-\frac{11\,A\,{\left(b\,x^2+a\right)}^{5/2}}{128\,a\,x^8}+\frac{3\,A\,{\left(b\,x^2+a\right)}^{7/2}}{128\,a^2\,x^8}-\frac{B\,{\left(b\,x^2+a\right)}^{5/2}}{16\,a\,x^6}+\frac{A\,b^4\,\mathrm{atan}\left(\frac{\sqrt{b\,x^2+a}\,1{}\mathrm{i}}{\sqrt{a}}\right)\,3{}\mathrm{i}}{128\,a^{5/2}}-\frac{B\,b^3\,\mathrm{atan}\left(\frac{\sqrt{b\,x^2+a}\,1{}\mathrm{i}}{\sqrt{a}}\right)\,1{}\mathrm{i}}{16\,a^{3/2}}","Not used",1,"(A*b^4*atan(((a + b*x^2)^(1/2)*1i)/a^(1/2))*3i)/(128*a^(5/2)) - (B*(a + b*x^2)^(3/2))/(6*x^6) - (11*A*(a + b*x^2)^(3/2))/(128*x^8) - (B*b^3*atan(((a + b*x^2)^(1/2)*1i)/a^(1/2))*1i)/(16*a^(3/2)) + (3*A*a*(a + b*x^2)^(1/2))/(128*x^8) + (B*a*(a + b*x^2)^(1/2))/(16*x^6) - (11*A*(a + b*x^2)^(5/2))/(128*a*x^8) + (3*A*(a + b*x^2)^(7/2))/(128*a^2*x^8) - (B*(a + b*x^2)^(5/2))/(16*a*x^6)","B"
536,1,170,84,2.134390,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^(3/2))/x^10,x)","\frac{4\,A\,b^3\,\sqrt{b\,x^2+a}}{315\,a^2\,x^3}-\frac{10\,A\,b\,\sqrt{b\,x^2+a}}{63\,x^7}-\frac{B\,a\,\sqrt{b\,x^2+a}}{7\,x^7}-\frac{8\,B\,b\,\sqrt{b\,x^2+a}}{35\,x^5}-\frac{A\,b^2\,\sqrt{b\,x^2+a}}{105\,a\,x^5}-\frac{A\,a\,\sqrt{b\,x^2+a}}{9\,x^9}-\frac{8\,A\,b^4\,\sqrt{b\,x^2+a}}{315\,a^3\,x}-\frac{B\,b^2\,\sqrt{b\,x^2+a}}{35\,a\,x^3}+\frac{2\,B\,b^3\,\sqrt{b\,x^2+a}}{35\,a^2\,x}","Not used",1,"(4*A*b^3*(a + b*x^2)^(1/2))/(315*a^2*x^3) - (10*A*b*(a + b*x^2)^(1/2))/(63*x^7) - (B*a*(a + b*x^2)^(1/2))/(7*x^7) - (8*B*b*(a + b*x^2)^(1/2))/(35*x^5) - (A*b^2*(a + b*x^2)^(1/2))/(105*a*x^5) - (A*a*(a + b*x^2)^(1/2))/(9*x^9) - (8*A*b^4*(a + b*x^2)^(1/2))/(315*a^3*x) - (B*b^2*(a + b*x^2)^(1/2))/(35*a*x^3) + (2*B*b^3*(a + b*x^2)^(1/2))/(35*a^2*x)","B"
537,1,205,184,4.888846,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^(3/2))/x^11,x)","\frac{3\,A\,a\,\sqrt{b\,x^2+a}}{256\,x^{10}}-\frac{11\,B\,{\left(b\,x^2+a\right)}^{3/2}}{128\,x^8}-\frac{7\,A\,{\left(b\,x^2+a\right)}^{3/2}}{128\,x^{10}}+\frac{3\,B\,a\,\sqrt{b\,x^2+a}}{128\,x^8}-\frac{A\,{\left(b\,x^2+a\right)}^{5/2}}{10\,a\,x^{10}}+\frac{7\,A\,{\left(b\,x^2+a\right)}^{7/2}}{128\,a^2\,x^{10}}-\frac{3\,A\,{\left(b\,x^2+a\right)}^{9/2}}{256\,a^3\,x^{10}}-\frac{11\,B\,{\left(b\,x^2+a\right)}^{5/2}}{128\,a\,x^8}+\frac{3\,B\,{\left(b\,x^2+a\right)}^{7/2}}{128\,a^2\,x^8}-\frac{A\,b^5\,\mathrm{atan}\left(\frac{\sqrt{b\,x^2+a}\,1{}\mathrm{i}}{\sqrt{a}}\right)\,3{}\mathrm{i}}{256\,a^{7/2}}+\frac{B\,b^4\,\mathrm{atan}\left(\frac{\sqrt{b\,x^2+a}\,1{}\mathrm{i}}{\sqrt{a}}\right)\,3{}\mathrm{i}}{128\,a^{5/2}}","Not used",1,"(B*b^4*atan(((a + b*x^2)^(1/2)*1i)/a^(1/2))*3i)/(128*a^(5/2)) - (11*B*(a + b*x^2)^(3/2))/(128*x^8) - (A*b^5*atan(((a + b*x^2)^(1/2)*1i)/a^(1/2))*3i)/(256*a^(7/2)) - (7*A*(a + b*x^2)^(3/2))/(128*x^10) + (3*A*a*(a + b*x^2)^(1/2))/(256*x^10) + (3*B*a*(a + b*x^2)^(1/2))/(128*x^8) - (A*(a + b*x^2)^(5/2))/(10*a*x^10) + (7*A*(a + b*x^2)^(7/2))/(128*a^2*x^10) - (3*A*(a + b*x^2)^(9/2))/(256*a^3*x^10) - (11*B*(a + b*x^2)^(5/2))/(128*a*x^8) + (3*B*(a + b*x^2)^(7/2))/(128*a^2*x^8)","B"
538,1,136,103,0.815417,"\text{Not used}","int(x^5*(A + B*x^2)*(a + b*x^2)^(5/2),x)","\sqrt{b\,x^2+a}\,\left(\frac{B\,b^2\,x^{12}}{13}-\frac{48\,B\,a^6-104\,A\,a^5\,b}{9009\,b^4}+\frac{x^{10}\,\left(819\,A\,b^6+1701\,B\,a\,b^5\right)}{9009\,b^4}+\frac{a\,x^8\,\left(299\,A\,b+159\,B\,a\right)}{1287}+\frac{a^3\,x^4\,\left(13\,A\,b-6\,B\,a\right)}{3003\,b^2}-\frac{4\,a^4\,x^2\,\left(13\,A\,b-6\,B\,a\right)}{9009\,b^3}+\frac{a^2\,x^6\,\left(1469\,A\,b+15\,B\,a\right)}{9009\,b}\right)","Not used",1,"(a + b*x^2)^(1/2)*((B*b^2*x^12)/13 - (48*B*a^6 - 104*A*a^5*b)/(9009*b^4) + (x^10*(819*A*b^6 + 1701*B*a*b^5))/(9009*b^4) + (a*x^8*(299*A*b + 159*B*a))/1287 + (a^3*x^4*(13*A*b - 6*B*a))/(3003*b^2) - (4*a^4*x^2*(13*A*b - 6*B*a))/(9009*b^3) + (a^2*x^6*(1469*A*b + 15*B*a))/(9009*b))","B"
539,0,-1,221,0.000000,"\text{Not used}","int(x^4*(A + B*x^2)*(a + b*x^2)^(5/2),x)","\int x^4\,\left(B\,x^2+A\right)\,{\left(b\,x^2+a\right)}^{5/2} \,d x","Not used",1,"int(x^4*(A + B*x^2)*(a + b*x^2)^(5/2), x)","F"
540,1,115,73,0.689276,"\text{Not used}","int(x^3*(A + B*x^2)*(a + b*x^2)^(5/2),x)","\sqrt{b\,x^2+a}\,\left(\frac{8\,B\,a^5-22\,A\,a^4\,b}{693\,b^3}+\frac{B\,b^2\,x^{10}}{11}+\frac{x^8\,\left(77\,A\,b^5+161\,B\,a\,b^4\right)}{693\,b^3}+\frac{a\,x^6\,\left(209\,A\,b+113\,B\,a\right)}{693}+\frac{a^3\,x^2\,\left(11\,A\,b-4\,B\,a\right)}{693\,b^2}+\frac{a^2\,x^4\,\left(55\,A\,b+B\,a\right)}{231\,b}\right)","Not used",1,"(a + b*x^2)^(1/2)*((8*B*a^5 - 22*A*a^4*b)/(693*b^3) + (B*b^2*x^10)/11 + (x^8*(77*A*b^5 + 161*B*a*b^4))/(693*b^3) + (a*x^6*(209*A*b + 113*B*a))/693 + (a^3*x^2*(11*A*b - 4*B*a))/(693*b^2) + (a^2*x^4*(55*A*b + B*a))/(231*b))","B"
541,0,-1,188,0.000000,"\text{Not used}","int(x^2*(A + B*x^2)*(a + b*x^2)^(5/2),x)","\int x^2\,\left(B\,x^2+A\right)\,{\left(b\,x^2+a\right)}^{5/2} \,d x","Not used",1,"int(x^2*(A + B*x^2)*(a + b*x^2)^(5/2), x)","F"
542,1,44,46,0.674857,"\text{Not used}","int(x*(A + B*x^2)*(a + b*x^2)^(5/2),x)","\frac{7\,B\,{\left(b\,x^2+a\right)}^{9/2}+9\,A\,b\,{\left(b\,x^2+a\right)}^{7/2}-9\,B\,a\,{\left(b\,x^2+a\right)}^{7/2}}{63\,b^2}","Not used",1,"(7*B*(a + b*x^2)^(9/2) + 9*A*b*(a + b*x^2)^(7/2) - 9*B*a*(a + b*x^2)^(7/2))/(63*b^2)","B"
543,0,-1,149,0.000000,"\text{Not used}","int((A + B*x^2)*(a + b*x^2)^(5/2),x)","\int \left(B\,x^2+A\right)\,{\left(b\,x^2+a\right)}^{5/2} \,d x","Not used",1,"int((A + B*x^2)*(a + b*x^2)^(5/2), x)","F"
544,1,78,95,1.034583,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^(5/2))/x,x)","\frac{A\,{\left(b\,x^2+a\right)}^{5/2}}{5}+A\,a^2\,\sqrt{b\,x^2+a}+\frac{B\,{\left(b\,x^2+a\right)}^{7/2}}{7\,b}+\frac{A\,a\,{\left(b\,x^2+a\right)}^{3/2}}{3}+A\,a^{5/2}\,\mathrm{atan}\left(\frac{\sqrt{b\,x^2+a}\,1{}\mathrm{i}}{\sqrt{a}}\right)\,1{}\mathrm{i}","Not used",1,"(A*(a + b*x^2)^(5/2))/5 + A*a^2*(a + b*x^2)^(1/2) + (B*(a + b*x^2)^(7/2))/(7*b) + A*a^(5/2)*atan(((a + b*x^2)^(1/2)*1i)/a^(1/2))*1i + (A*a*(a + b*x^2)^(3/2))/3","B"
545,1,80,136,1.916446,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^(5/2))/x^2,x)","\frac{B\,x\,{\left(b\,x^2+a\right)}^{5/2}\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{2},\frac{1}{2};\ \frac{3}{2};\ -\frac{b\,x^2}{a}\right)}{{\left(\frac{b\,x^2}{a}+1\right)}^{5/2}}-\frac{A\,{\left(b\,x^2+a\right)}^{5/2}\,{{}}_2{\mathrm{F}}_1\left(-\frac{5}{2},-\frac{1}{2};\ \frac{1}{2};\ -\frac{b\,x^2}{a}\right)}{x\,{\left(\frac{b\,x^2}{a}+1\right)}^{5/2}}","Not used",1,"(B*x*(a + b*x^2)^(5/2)*hypergeom([-5/2, 1/2], 3/2, -(b*x^2)/a))/((b*x^2)/a + 1)^(5/2) - (A*(a + b*x^2)^(5/2)*hypergeom([-5/2, -1/2], 1/2, -(b*x^2)/a))/(x*((b*x^2)/a + 1)^(5/2))","B"
546,1,132,135,1.854353,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^(5/2))/x^3,x)","\frac{B\,{\left(b\,x^2+a\right)}^{5/2}}{5}+B\,a^2\,\sqrt{b\,x^2+a}+B\,a^{5/2}\,\mathrm{atan}\left(\frac{\sqrt{b\,x^2+a}\,1{}\mathrm{i}}{\sqrt{a}}\right)\,1{}\mathrm{i}+\frac{A\,b\,{\left(b\,x^2+a\right)}^{3/2}}{3}+\frac{B\,a\,{\left(b\,x^2+a\right)}^{3/2}}{3}+2\,A\,a\,b\,\sqrt{b\,x^2+a}-\frac{A\,a^2\,\sqrt{b\,x^2+a}}{2\,x^2}+\frac{A\,a^{3/2}\,b\,\mathrm{atan}\left(\frac{\sqrt{b\,x^2+a}\,1{}\mathrm{i}}{\sqrt{a}}\right)\,5{}\mathrm{i}}{2}","Not used",1,"(B*(a + b*x^2)^(5/2))/5 + B*a^2*(a + b*x^2)^(1/2) + B*a^(5/2)*atan(((a + b*x^2)^(1/2)*1i)/a^(1/2))*1i + (A*b*(a + b*x^2)^(3/2))/3 + (B*a*(a + b*x^2)^(3/2))/3 + 2*A*a*b*(a + b*x^2)^(1/2) - (A*a^2*(a + b*x^2)^(1/2))/(2*x^2) + (A*a^(3/2)*b*atan(((a + b*x^2)^(1/2)*1i)/a^(1/2))*5i)/2","B"
547,0,-1,146,0.000000,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^(5/2))/x^4,x)","\int \frac{\left(B\,x^2+A\right)\,{\left(b\,x^2+a\right)}^{5/2}}{x^4} \,d x","Not used",1,"int(((A + B*x^2)*(a + b*x^2)^(5/2))/x^4, x)","F"
548,1,144,143,2.585562,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^(5/2))/x^5,x)","A\,b^2\,\sqrt{b\,x^2+a}+\frac{B\,b\,{\left(b\,x^2+a\right)}^{3/2}}{3}+2\,B\,a\,b\,\sqrt{b\,x^2+a}+\frac{A\,\sqrt{a}\,b^2\,\mathrm{atan}\left(\frac{\sqrt{b\,x^2+a}\,1{}\mathrm{i}}{\sqrt{a}}\right)\,15{}\mathrm{i}}{8}-\frac{9\,A\,a\,{\left(b\,x^2+a\right)}^{3/2}}{8\,x^4}+\frac{7\,A\,a^2\,\sqrt{b\,x^2+a}}{8\,x^4}-\frac{B\,a^2\,\sqrt{b\,x^2+a}}{2\,x^2}+\frac{B\,a^{3/2}\,b\,\mathrm{atan}\left(\frac{\sqrt{b\,x^2+a}\,1{}\mathrm{i}}{\sqrt{a}}\right)\,5{}\mathrm{i}}{2}","Not used",1,"A*b^2*(a + b*x^2)^(1/2) + (B*b*(a + b*x^2)^(3/2))/3 + 2*B*a*b*(a + b*x^2)^(1/2) + (A*a^(1/2)*b^2*atan(((a + b*x^2)^(1/2)*1i)/a^(1/2))*15i)/8 - (9*A*a*(a + b*x^2)^(3/2))/(8*x^4) + (7*A*a^2*(a + b*x^2)^(1/2))/(8*x^4) - (B*a^2*(a + b*x^2)^(1/2))/(2*x^2) + (B*a^(3/2)*b*atan(((a + b*x^2)^(1/2)*1i)/a^(1/2))*5i)/2","B"
549,0,-1,152,0.000000,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^(5/2))/x^6,x)","\int \frac{\left(B\,x^2+A\right)\,{\left(b\,x^2+a\right)}^{5/2}}{x^6} \,d x","Not used",1,"int(((A + B*x^2)*(a + b*x^2)^(5/2))/x^6, x)","F"
550,1,150,149,3.368558,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^(5/2))/x^7,x)","B\,b^2\,\sqrt{b\,x^2+a}-\frac{11\,A\,{\left(b\,x^2+a\right)}^{5/2}}{16\,x^6}+\frac{5\,A\,a\,{\left(b\,x^2+a\right)}^{3/2}}{6\,x^6}-\frac{9\,B\,a\,{\left(b\,x^2+a\right)}^{3/2}}{8\,x^4}-\frac{5\,A\,a^2\,\sqrt{b\,x^2+a}}{16\,x^6}+\frac{7\,B\,a^2\,\sqrt{b\,x^2+a}}{8\,x^4}+\frac{A\,b^3\,\mathrm{atan}\left(\frac{\sqrt{b\,x^2+a}\,1{}\mathrm{i}}{\sqrt{a}}\right)\,5{}\mathrm{i}}{16\,\sqrt{a}}+\frac{B\,\sqrt{a}\,b^2\,\mathrm{atan}\left(\frac{\sqrt{b\,x^2+a}\,1{}\mathrm{i}}{\sqrt{a}}\right)\,15{}\mathrm{i}}{8}","Not used",1,"B*b^2*(a + b*x^2)^(1/2) - (11*A*(a + b*x^2)^(5/2))/(16*x^6) + (A*b^3*atan(((a + b*x^2)^(1/2)*1i)/a^(1/2))*5i)/(16*a^(1/2)) + (B*a^(1/2)*b^2*atan(((a + b*x^2)^(1/2)*1i)/a^(1/2))*15i)/8 + (5*A*a*(a + b*x^2)^(3/2))/(6*x^6) - (9*B*a*(a + b*x^2)^(3/2))/(8*x^4) - (5*A*a^2*(a + b*x^2)^(1/2))/(16*x^6) + (7*B*a^2*(a + b*x^2)^(1/2))/(8*x^4)","B"
551,0,-1,108,0.000000,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^(5/2))/x^8,x)","\int \frac{\left(B\,x^2+A\right)\,{\left(b\,x^2+a\right)}^{5/2}}{x^8} \,d x","Not used",1,"int(((A + B*x^2)*(a + b*x^2)^(5/2))/x^8, x)","F"
552,1,169,152,4.581073,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^(5/2))/x^9,x)","\frac{55\,A\,a\,{\left(b\,x^2+a\right)}^{3/2}}{384\,x^8}-\frac{11\,B\,{\left(b\,x^2+a\right)}^{5/2}}{16\,x^6}-\frac{73\,A\,{\left(b\,x^2+a\right)}^{5/2}}{384\,x^8}+\frac{5\,B\,a\,{\left(b\,x^2+a\right)}^{3/2}}{6\,x^6}-\frac{5\,A\,a^2\,\sqrt{b\,x^2+a}}{128\,x^8}-\frac{5\,A\,{\left(b\,x^2+a\right)}^{7/2}}{128\,a\,x^8}-\frac{5\,B\,a^2\,\sqrt{b\,x^2+a}}{16\,x^6}-\frac{A\,b^4\,\mathrm{atan}\left(\frac{\sqrt{b\,x^2+a}\,1{}\mathrm{i}}{\sqrt{a}}\right)\,5{}\mathrm{i}}{128\,a^{3/2}}+\frac{B\,b^3\,\mathrm{atan}\left(\frac{\sqrt{b\,x^2+a}\,1{}\mathrm{i}}{\sqrt{a}}\right)\,5{}\mathrm{i}}{16\,\sqrt{a}}","Not used",1,"(B*b^3*atan(((a + b*x^2)^(1/2)*1i)/a^(1/2))*5i)/(16*a^(1/2)) - (11*B*(a + b*x^2)^(5/2))/(16*x^6) - (A*b^4*atan(((a + b*x^2)^(1/2)*1i)/a^(1/2))*5i)/(128*a^(3/2)) - (73*A*(a + b*x^2)^(5/2))/(384*x^8) + (55*A*a*(a + b*x^2)^(3/2))/(384*x^8) + (5*B*a*(a + b*x^2)^(3/2))/(6*x^6) - (5*A*a^2*(a + b*x^2)^(1/2))/(128*x^8) - (5*A*(a + b*x^2)^(7/2))/(128*a*x^8) - (5*B*a^2*(a + b*x^2)^(1/2))/(16*x^6)","B"
553,1,170,53,2.718157,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^(5/2))/x^10,x)","\frac{2\,A\,b^4\,\sqrt{b\,x^2+a}}{63\,a^2\,x}-\frac{5\,A\,b^2\,\sqrt{b\,x^2+a}}{21\,x^5}-\frac{B\,a^2\,\sqrt{b\,x^2+a}}{7\,x^7}-\frac{3\,B\,b^2\,\sqrt{b\,x^2+a}}{7\,x^3}-\frac{A\,b^3\,\sqrt{b\,x^2+a}}{63\,a\,x^3}-\frac{A\,a^2\,\sqrt{b\,x^2+a}}{9\,x^9}-\frac{B\,b^3\,\sqrt{b\,x^2+a}}{7\,a\,x}-\frac{19\,A\,a\,b\,\sqrt{b\,x^2+a}}{63\,x^7}-\frac{3\,B\,a\,b\,\sqrt{b\,x^2+a}}{7\,x^5}","Not used",1,"(2*A*b^4*(a + b*x^2)^(1/2))/(63*a^2*x) - (5*A*b^2*(a + b*x^2)^(1/2))/(21*x^5) - (B*a^2*(a + b*x^2)^(1/2))/(7*x^7) - (3*B*b^2*(a + b*x^2)^(1/2))/(7*x^3) - (A*b^3*(a + b*x^2)^(1/2))/(63*a*x^3) - (A*a^2*(a + b*x^2)^(1/2))/(9*x^9) - (B*b^3*(a + b*x^2)^(1/2))/(7*a*x) - (19*A*a*b*(a + b*x^2)^(1/2))/(63*x^7) - (3*B*a*b*(a + b*x^2)^(1/2))/(7*x^5)","B"
554,1,205,189,6.059599,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^(5/2))/x^11,x)","\frac{7\,A\,a\,{\left(b\,x^2+a\right)}^{3/2}}{128\,x^{10}}-\frac{73\,B\,{\left(b\,x^2+a\right)}^{5/2}}{384\,x^8}-\frac{A\,{\left(b\,x^2+a\right)}^{5/2}}{10\,x^{10}}+\frac{55\,B\,a\,{\left(b\,x^2+a\right)}^{3/2}}{384\,x^8}-\frac{3\,A\,a^2\,\sqrt{b\,x^2+a}}{256\,x^{10}}-\frac{7\,A\,{\left(b\,x^2+a\right)}^{7/2}}{128\,a\,x^{10}}+\frac{3\,A\,{\left(b\,x^2+a\right)}^{9/2}}{256\,a^2\,x^{10}}-\frac{5\,B\,a^2\,\sqrt{b\,x^2+a}}{128\,x^8}-\frac{5\,B\,{\left(b\,x^2+a\right)}^{7/2}}{128\,a\,x^8}+\frac{A\,b^5\,\mathrm{atan}\left(\frac{\sqrt{b\,x^2+a}\,1{}\mathrm{i}}{\sqrt{a}}\right)\,3{}\mathrm{i}}{256\,a^{5/2}}-\frac{B\,b^4\,\mathrm{atan}\left(\frac{\sqrt{b\,x^2+a}\,1{}\mathrm{i}}{\sqrt{a}}\right)\,5{}\mathrm{i}}{128\,a^{3/2}}","Not used",1,"(A*b^5*atan(((a + b*x^2)^(1/2)*1i)/a^(1/2))*3i)/(256*a^(5/2)) - (73*B*(a + b*x^2)^(5/2))/(384*x^8) - (A*(a + b*x^2)^(5/2))/(10*x^10) - (B*b^4*atan(((a + b*x^2)^(1/2)*1i)/a^(1/2))*5i)/(128*a^(3/2)) + (7*A*a*(a + b*x^2)^(3/2))/(128*x^10) + (55*B*a*(a + b*x^2)^(3/2))/(384*x^8) - (3*A*a^2*(a + b*x^2)^(1/2))/(256*x^10) - (7*A*(a + b*x^2)^(7/2))/(128*a*x^10) + (3*A*(a + b*x^2)^(9/2))/(256*a^2*x^10) - (5*B*a^2*(a + b*x^2)^(1/2))/(128*x^8) - (5*B*(a + b*x^2)^(7/2))/(128*a*x^8)","B"
555,1,80,100,0.665755,"\text{Not used}","int((x^5*(A + B*x^2))/(a + b*x^2)^(1/2),x)","-\sqrt{b\,x^2+a}\,\left(\frac{48\,B\,a^3-56\,A\,a^2\,b}{105\,b^4}-\frac{B\,x^6}{7\,b}-\frac{x^4\,\left(21\,A\,b^3-18\,B\,a\,b^2\right)}{105\,b^4}+\frac{4\,a\,x^2\,\left(7\,A\,b-6\,B\,a\right)}{105\,b^3}\right)","Not used",1,"-(a + b*x^2)^(1/2)*((48*B*a^3 - 56*A*a^2*b)/(105*b^4) - (B*x^6)/(7*b) - (x^4*(21*A*b^3 - 18*B*a*b^2))/(105*b^4) + (4*a*x^2*(7*A*b - 6*B*a))/(105*b^3))","B"
556,0,-1,122,0.000000,"\text{Not used}","int((x^4*(A + B*x^2))/(a + b*x^2)^(1/2),x)","\int \frac{x^4\,\left(B\,x^2+A\right)}{\sqrt{b\,x^2+a}} \,d x","Not used",1,"int((x^4*(A + B*x^2))/(a + b*x^2)^(1/2), x)","F"
557,1,57,71,0.596844,"\text{Not used}","int((x^3*(A + B*x^2))/(a + b*x^2)^(1/2),x)","\sqrt{b\,x^2+a}\,\left(\frac{8\,B\,a^2-10\,A\,a\,b}{15\,b^3}+\frac{x^2\,\left(5\,A\,b^2-4\,B\,a\,b\right)}{15\,b^3}+\frac{B\,x^4}{5\,b}\right)","Not used",1,"(a + b*x^2)^(1/2)*((8*B*a^2 - 10*A*a*b)/(15*b^3) + (x^2*(5*A*b^2 - 4*B*a*b))/(15*b^3) + (B*x^4)/(5*b))","B"
558,0,-1,89,0.000000,"\text{Not used}","int((x^2*(A + B*x^2))/(a + b*x^2)^(1/2),x)","\int \frac{x^2\,\left(B\,x^2+A\right)}{\sqrt{b\,x^2+a}} \,d x","Not used",1,"int((x^2*(A + B*x^2))/(a + b*x^2)^(1/2), x)","F"
559,1,34,43,0.567522,"\text{Not used}","int((x*(A + B*x^2))/(a + b*x^2)^(1/2),x)","\left(\frac{3\,A\,b-2\,B\,a}{3\,b^2}+\frac{B\,x^2}{3\,b}\right)\,\sqrt{b\,x^2+a}","Not used",1,"((3*A*b - 2*B*a)/(3*b^2) + (B*x^2)/(3*b))*(a + b*x^2)^(1/2)","B"
560,1,86,58,1.070872,"\text{Not used}","int((A + B*x^2)/(a + b*x^2)^(1/2),x)","\left\{\begin{array}{cl} \frac{B\,x^3+3\,A\,x}{3\,\sqrt{a}} & \text{\ if\ \ }b=0\\ \frac{A\,\ln\left(\sqrt{b}\,x+\sqrt{b\,x^2+a}\right)}{\sqrt{b}}-\frac{B\,a\,\ln\left(2\,\sqrt{b}\,x+2\,\sqrt{b\,x^2+a}\right)}{2\,b^{3/2}}+\frac{B\,x\,\sqrt{b\,x^2+a}}{2\,b} & \text{\ if\ \ }b\neq 0 \end{array}\right.","Not used",1,"piecewise(b == 0, (3*A*x + B*x^3)/(3*a^(1/2)), b ~= 0, (A*log(b^(1/2)*x + (a + b*x^2)^(1/2)))/b^(1/2) - (B*a*log(2*b^(1/2)*x + 2*(a + b*x^2)^(1/2)))/(2*b^(3/2)) + (B*x*(a + b*x^2)^(1/2))/(2*b))","B"
561,1,35,43,1.017723,"\text{Not used}","int((A + B*x^2)/(x*(a + b*x^2)^(1/2)),x)","\frac{B\,\sqrt{b\,x^2+a}}{b}-\frac{A\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{\sqrt{a}}","Not used",1,"(B*(a + b*x^2)^(1/2))/b - (A*atanh((a + b*x^2)^(1/2)/a^(1/2)))/a^(1/2)","B"
562,1,40,47,0.736947,"\text{Not used}","int((A + B*x^2)/(x^2*(a + b*x^2)^(1/2)),x)","\frac{B\,\ln\left(\sqrt{b}\,x+\sqrt{b\,x^2+a}\right)}{\sqrt{b}}-\frac{A\,\sqrt{b\,x^2+a}}{a\,x}","Not used",1,"(B*log(b^(1/2)*x + (a + b*x^2)^(1/2)))/b^(1/2) - (A*(a + b*x^2)^(1/2))/(a*x)","B"
563,1,60,58,1.341658,"\text{Not used}","int((A + B*x^2)/(x^3*(a + b*x^2)^(1/2)),x)","\frac{A\,b\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{2\,a^{3/2}}-\frac{A\,\sqrt{b\,x^2+a}}{2\,a\,x^2}-\frac{B\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{\sqrt{a}}","Not used",1,"(A*b*atanh((a + b*x^2)^(1/2)/a^(1/2)))/(2*a^(3/2)) - (A*(a + b*x^2)^(1/2))/(2*a*x^2) - (B*atanh((a + b*x^2)^(1/2)/a^(1/2)))/a^(1/2)","B"
564,1,35,53,0.577778,"\text{Not used}","int((A + B*x^2)/(x^4*(a + b*x^2)^(1/2)),x)","-\frac{\sqrt{b\,x^2+a}\,\left(A\,a-2\,A\,b\,x^2+3\,B\,a\,x^2\right)}{3\,a^2\,x^3}","Not used",1,"-((a + b*x^2)^(1/2)*(A*a - 2*A*b*x^2 + 3*B*a*x^2))/(3*a^2*x^3)","B"
565,1,99,90,1.533188,"\text{Not used}","int((A + B*x^2)/(x^5*(a + b*x^2)^(1/2)),x)","\frac{3\,A\,{\left(b\,x^2+a\right)}^{3/2}}{8\,a^2\,x^4}-\frac{5\,A\,\sqrt{b\,x^2+a}}{8\,a\,x^4}-\frac{3\,A\,b^2\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{8\,a^{5/2}}-\frac{B\,\sqrt{b\,x^2+a}}{2\,a\,x^2}+\frac{B\,b\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{2\,a^{3/2}}","Not used",1,"(3*A*(a + b*x^2)^(3/2))/(8*a^2*x^4) - (5*A*(a + b*x^2)^(1/2))/(8*a*x^4) - (3*A*b^2*atanh((a + b*x^2)^(1/2)/a^(1/2)))/(8*a^(5/2)) - (B*(a + b*x^2)^(1/2))/(2*a*x^2) + (B*b*atanh((a + b*x^2)^(1/2)/a^(1/2)))/(2*a^(3/2))","B"
566,1,58,84,0.682321,"\text{Not used}","int((A + B*x^2)/(x^6*(a + b*x^2)^(1/2)),x)","-\frac{\sqrt{b\,x^2+a}\,\left(5\,B\,a^2\,x^2+3\,A\,a^2-10\,B\,a\,b\,x^4-4\,A\,a\,b\,x^2+8\,A\,b^2\,x^4\right)}{15\,a^3\,x^5}","Not used",1,"-((a + b*x^2)^(1/2)*(3*A*a^2 + 5*B*a^2*x^2 + 8*A*b^2*x^4 - 4*A*a*b*x^2 - 10*B*a*b*x^4))/(15*a^3*x^5)","B"
567,1,140,123,1.678608,"\text{Not used}","int((A + B*x^2)/(x^7*(a + b*x^2)^(1/2)),x)","\frac{5\,A\,{\left(b\,x^2+a\right)}^{3/2}}{6\,a^2\,x^6}-\frac{11\,A\,\sqrt{b\,x^2+a}}{16\,a\,x^6}-\frac{3\,B\,b^2\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{8\,a^{5/2}}-\frac{5\,A\,{\left(b\,x^2+a\right)}^{5/2}}{16\,a^3\,x^6}-\frac{5\,B\,\sqrt{b\,x^2+a}}{8\,a\,x^4}+\frac{3\,B\,{\left(b\,x^2+a\right)}^{3/2}}{8\,a^2\,x^4}-\frac{A\,b^3\,\mathrm{atan}\left(\frac{\sqrt{b\,x^2+a}\,1{}\mathrm{i}}{\sqrt{a}}\right)\,5{}\mathrm{i}}{16\,a^{7/2}}","Not used",1,"(5*A*(a + b*x^2)^(3/2))/(6*a^2*x^6) - (3*B*b^2*atanh((a + b*x^2)^(1/2)/a^(1/2)))/(8*a^(5/2)) - (11*A*(a + b*x^2)^(1/2))/(16*a*x^6) - (A*b^3*atan(((a + b*x^2)^(1/2)*1i)/a^(1/2))*5i)/(16*a^(7/2)) - (5*A*(a + b*x^2)^(5/2))/(16*a^3*x^6) - (5*B*(a + b*x^2)^(1/2))/(8*a*x^4) + (3*B*(a + b*x^2)^(3/2))/(8*a^2*x^4)","B"
568,1,105,117,0.733359,"\text{Not used}","int((A + B*x^2)/(x^8*(a + b*x^2)^(1/2)),x)","\frac{\sqrt{b\,x^2+a}\,\left(6\,A\,b-7\,B\,a\right)}{35\,a^2\,x^5}+\frac{\sqrt{b\,x^2+a}\,\left(48\,A\,b^3-56\,B\,a\,b^2\right)}{105\,a^4\,x}-\frac{\left(24\,A\,b^2-28\,B\,a\,b\right)\,\sqrt{b\,x^2+a}}{105\,a^3\,x^3}-\frac{A\,\sqrt{b\,x^2+a}}{7\,a\,x^7}","Not used",1,"((a + b*x^2)^(1/2)*(6*A*b - 7*B*a))/(35*a^2*x^5) + ((a + b*x^2)^(1/2)*(48*A*b^3 - 56*B*a*b^2))/(105*a^4*x) - ((24*A*b^2 - 28*B*a*b)*(a + b*x^2)^(1/2))/(105*a^3*x^3) - (A*(a + b*x^2)^(1/2))/(7*a*x^7)","B"
569,0,-1,152,0.000000,"\text{Not used}","int((x^6*(A + B*x^2))/(a + b*x^2)^(3/2),x)","\int \frac{x^6\,\left(B\,x^2+A\right)}{{\left(b\,x^2+a\right)}^{3/2}} \,d x","Not used",1,"int((x^6*(A + B*x^2))/(a + b*x^2)^(3/2), x)","F"
570,1,89,99,0.819145,"\text{Not used}","int((x^5*(A + B*x^2))/(a + b*x^2)^(3/2),x)","\frac{\frac{B\,{\left(b\,x^2+a\right)}^3}{5}+B\,a^3+\frac{A\,b\,{\left(b\,x^2+a\right)}^2}{3}-B\,a\,{\left(b\,x^2+a\right)}^2+3\,B\,a^2\,\left(b\,x^2+a\right)-A\,a^2\,b-2\,A\,a\,b\,\left(b\,x^2+a\right)}{b^4\,\sqrt{b\,x^2+a}}","Not used",1,"((B*(a + b*x^2)^3)/5 + B*a^3 + (A*b*(a + b*x^2)^2)/3 - B*a*(a + b*x^2)^2 + 3*B*a^2*(a + b*x^2) - A*a^2*b - 2*A*a*b*(a + b*x^2))/(b^4*(a + b*x^2)^(1/2))","B"
571,0,-1,119,0.000000,"\text{Not used}","int((x^4*(A + B*x^2))/(a + b*x^2)^(3/2),x)","\int \frac{x^4\,\left(B\,x^2+A\right)}{{\left(b\,x^2+a\right)}^{3/2}} \,d x","Not used",1,"int((x^4*(A + B*x^2))/(a + b*x^2)^(3/2), x)","F"
572,1,59,67,0.679323,"\text{Not used}","int((x^3*(A + B*x^2))/(a + b*x^2)^(3/2),x)","\frac{B\,{\left(b\,x^2+a\right)}^2-3\,B\,a^2+3\,A\,b\,\left(b\,x^2+a\right)-6\,B\,a\,\left(b\,x^2+a\right)+3\,A\,a\,b}{3\,b^3\,\sqrt{b\,x^2+a}}","Not used",1,"(B*(a + b*x^2)^2 - 3*B*a^2 + 3*A*b*(a + b*x^2) - 6*B*a*(a + b*x^2) + 3*A*a*b)/(3*b^3*(a + b*x^2)^(1/2))","B"
573,0,-1,83,0.000000,"\text{Not used}","int((x^2*(A + B*x^2))/(a + b*x^2)^(3/2),x)","\int \frac{x^2\,\left(B\,x^2+A\right)}{{\left(b\,x^2+a\right)}^{3/2}} \,d x","Not used",1,"int((x^2*(A + B*x^2))/(a + b*x^2)^(3/2), x)","F"
574,1,30,41,0.595249,"\text{Not used}","int((x*(A + B*x^2))/(a + b*x^2)^(3/2),x)","\frac{B\,a-A\,b+B\,\left(b\,x^2+a\right)}{b^2\,\sqrt{b\,x^2+a}}","Not used",1,"(B*a - A*b + B*(a + b*x^2))/(b^2*(a + b*x^2)^(1/2))","B"
575,1,53,54,0.772447,"\text{Not used}","int((A + B*x^2)/(a + b*x^2)^(3/2),x)","\frac{B\,\ln\left(\sqrt{b}\,x+\sqrt{b\,x^2+a}\right)}{b^{3/2}}+\frac{A\,x}{a\,\sqrt{b\,x^2+a}}-\frac{B\,x}{b\,\sqrt{b\,x^2+a}}","Not used",1,"(B*log(b^(1/2)*x + (a + b*x^2)^(1/2)))/b^(3/2) + (A*x)/(a*(a + b*x^2)^(1/2)) - (B*x)/(b*(a + b*x^2)^(1/2))","B"
576,1,50,53,1.058214,"\text{Not used}","int((A + B*x^2)/(x*(a + b*x^2)^(3/2)),x)","\frac{A}{a\,\sqrt{b\,x^2+a}}-\frac{B}{b\,\sqrt{b\,x^2+a}}-\frac{A\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{a^{3/2}}","Not used",1,"A/(a*(a + b*x^2)^(1/2)) - B/(b*(a + b*x^2)^(1/2)) - (A*atanh((a + b*x^2)^(1/2)/a^(1/2)))/a^(3/2)","B"
577,1,46,47,0.538483,"\text{Not used}","int((A + B*x^2)/(x^2*(a + b*x^2)^(3/2)),x)","-\frac{\sqrt{b\,x^2+a}\,\left(\frac{A}{a}-x^2\,\left(\frac{B}{a}-\frac{2\,A\,b}{a^2}\right)\right)}{b\,x^3+a\,x}","Not used",1,"-((a + b*x^2)^(1/2)*(A/a - x^2*(B/a - (2*A*b)/a^2)))/(a*x + b*x^3)","B"
578,1,90,86,1.440110,"\text{Not used}","int((A + B*x^2)/(x^3*(a + b*x^2)^(3/2)),x)","\frac{B}{a\,\sqrt{b\,x^2+a}}-\frac{B\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{a^{3/2}}-\frac{3\,A\,b}{2\,a^2\,\sqrt{b\,x^2+a}}-\frac{A}{2\,a\,x^2\,\sqrt{b\,x^2+a}}+\frac{3\,A\,b\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{2\,a^{5/2}}","Not used",1,"B/(a*(a + b*x^2)^(1/2)) - (B*atanh((a + b*x^2)^(1/2)/a^(1/2)))/a^(3/2) - (3*A*b)/(2*a^2*(a + b*x^2)^(1/2)) - A/(2*a*x^2*(a + b*x^2)^(1/2)) + (3*A*b*atanh((a + b*x^2)^(1/2)/a^(1/2)))/(2*a^(5/2))","B"
579,1,57,82,0.664658,"\text{Not used}","int((A + B*x^2)/(x^4*(a + b*x^2)^(3/2)),x)","-\frac{3\,B\,a^2\,x^2+A\,a^2+6\,B\,a\,b\,x^4-4\,A\,a\,b\,x^2-8\,A\,b^2\,x^4}{3\,a^3\,x^3\,\sqrt{b\,x^2+a}}","Not used",1,"-(A*a^2 + 3*B*a^2*x^2 - 8*A*b^2*x^4 - 4*A*a*b*x^2 + 6*B*a*b*x^4)/(3*a^3*x^3*(a + b*x^2)^(1/2))","B"
580,1,134,118,1.906947,"\text{Not used}","int((A + B*x^2)/(x^5*(a + b*x^2)^(3/2)),x)","\frac{15\,A\,b^2}{8\,a^3\,\sqrt{b\,x^2+a}}-\frac{3\,B\,b}{2\,a^2\,\sqrt{b\,x^2+a}}-\frac{15\,A\,b^2\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{8\,a^{7/2}}-\frac{A}{4\,a\,x^4\,\sqrt{b\,x^2+a}}-\frac{B}{2\,a\,x^2\,\sqrt{b\,x^2+a}}+\frac{3\,B\,b\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{2\,a^{5/2}}+\frac{5\,A\,b}{8\,a^2\,x^2\,\sqrt{b\,x^2+a}}","Not used",1,"(15*A*b^2)/(8*a^3*(a + b*x^2)^(1/2)) - (3*B*b)/(2*a^2*(a + b*x^2)^(1/2)) - (15*A*b^2*atanh((a + b*x^2)^(1/2)/a^(1/2)))/(8*a^(7/2)) - A/(4*a*x^4*(a + b*x^2)^(1/2)) - B/(2*a*x^2*(a + b*x^2)^(1/2)) + (3*B*b*atanh((a + b*x^2)^(1/2)/a^(1/2)))/(2*a^(5/2)) + (5*A*b)/(8*a^2*x^2*(a + b*x^2)^(1/2))","B"
581,1,82,115,0.826271,"\text{Not used}","int((A + B*x^2)/(x^6*(a + b*x^2)^(3/2)),x)","-\frac{5\,B\,a^3\,x^2+3\,A\,a^3-20\,B\,a^2\,b\,x^4-6\,A\,a^2\,b\,x^2-40\,B\,a\,b^2\,x^6+24\,A\,a\,b^2\,x^4+48\,A\,b^3\,x^6}{15\,a^4\,x^5\,\sqrt{b\,x^2+a}}","Not used",1,"-(3*A*a^3 + 5*B*a^3*x^2 + 48*A*b^3*x^6 - 6*A*a^2*b*x^2 + 24*A*a*b^2*x^4 - 20*B*a^2*b*x^4 - 40*B*a*b^2*x^6)/(15*a^4*x^5*(a + b*x^2)^(1/2))","B"
582,1,178,153,2.245857,"\text{Not used}","int((A + B*x^2)/(x^7*(a + b*x^2)^(3/2)),x)","\frac{35\,A\,b^3\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{16\,a^{9/2}}-\frac{15\,B\,b^2\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{8\,a^{7/2}}-\frac{35\,A\,b^3}{16\,a^4\,\sqrt{b\,x^2+a}}+\frac{15\,B\,b^2}{8\,a^3\,\sqrt{b\,x^2+a}}-\frac{A}{6\,a\,x^6\,\sqrt{b\,x^2+a}}-\frac{B}{4\,a\,x^4\,\sqrt{b\,x^2+a}}+\frac{7\,A\,b}{24\,a^2\,x^4\,\sqrt{b\,x^2+a}}+\frac{5\,B\,b}{8\,a^2\,x^2\,\sqrt{b\,x^2+a}}-\frac{35\,A\,b^2}{48\,a^3\,x^2\,\sqrt{b\,x^2+a}}","Not used",1,"(35*A*b^3*atanh((a + b*x^2)^(1/2)/a^(1/2)))/(16*a^(9/2)) - (15*B*b^2*atanh((a + b*x^2)^(1/2)/a^(1/2)))/(8*a^(7/2)) - (35*A*b^3)/(16*a^4*(a + b*x^2)^(1/2)) + (15*B*b^2)/(8*a^3*(a + b*x^2)^(1/2)) - A/(6*a*x^6*(a + b*x^2)^(1/2)) - B/(4*a*x^4*(a + b*x^2)^(1/2)) + (7*A*b)/(24*a^2*x^4*(a + b*x^2)^(1/2)) + (5*B*b)/(8*a^2*x^2*(a + b*x^2)^(1/2)) - (35*A*b^2)/(48*a^3*x^2*(a + b*x^2)^(1/2))","B"
583,1,148,148,1.073635,"\text{Not used}","int((A + B*x^2)/(x^8*(a + b*x^2)^(3/2)),x)","-\frac{x^2\,\left(\frac{58\,A\,b^4-42\,B\,a\,b^3}{35\,a^5}-\frac{2\,b^3\,\left(93\,A\,b-77\,B\,a\right)}{35\,a^5}\right)-\frac{b^2\,\left(93\,A\,b-77\,B\,a\right)}{35\,a^4}}{x\,\sqrt{b\,x^2+a}}-\frac{\left(7\,B\,a^2-13\,A\,a\,b\right)\,\sqrt{b\,x^2+a}}{35\,a^4\,x^5}-\frac{A\,\sqrt{b\,x^2+a}}{7\,a^2\,x^7}-\frac{b\,\sqrt{b\,x^2+a}\,\left(29\,A\,b-21\,B\,a\right)}{35\,a^4\,x^3}","Not used",1,"- (x^2*((58*A*b^4 - 42*B*a*b^3)/(35*a^5) - (2*b^3*(93*A*b - 77*B*a))/(35*a^5)) - (b^2*(93*A*b - 77*B*a))/(35*a^4))/(x*(a + b*x^2)^(1/2)) - ((7*B*a^2 - 13*A*a*b)*(a + b*x^2)^(1/2))/(35*a^4*x^5) - (A*(a + b*x^2)^(1/2))/(7*a^2*x^7) - (b*(a + b*x^2)^(1/2)*(29*A*b - 21*B*a))/(35*a^4*x^3)","B"
584,1,122,128,1.004806,"\text{Not used}","int((x^7*(A + B*x^2))/(a + b*x^2)^(5/2),x)","\frac{3\,B\,{\left(b\,x^2+a\right)}^4-5\,B\,a^4+90\,B\,a^2\,{\left(b\,x^2+a\right)}^2+5\,A\,b\,{\left(b\,x^2+a\right)}^3-20\,B\,a\,{\left(b\,x^2+a\right)}^3+60\,B\,a^3\,\left(b\,x^2+a\right)+5\,A\,a^3\,b-45\,A\,a\,b\,{\left(b\,x^2+a\right)}^2-45\,A\,a^2\,b\,\left(b\,x^2+a\right)}{15\,b^5\,{\left(b\,x^2+a\right)}^{3/2}}","Not used",1,"(3*B*(a + b*x^2)^4 - 5*B*a^4 + 90*B*a^2*(a + b*x^2)^2 + 5*A*b*(a + b*x^2)^3 - 20*B*a*(a + b*x^2)^3 + 60*B*a^3*(a + b*x^2) + 5*A*a^3*b - 45*A*a*b*(a + b*x^2)^2 - 45*A*a^2*b*(a + b*x^2))/(15*b^5*(a + b*x^2)^(3/2))","B"
585,0,-1,149,0.000000,"\text{Not used}","int((x^6*(A + B*x^2))/(a + b*x^2)^(5/2),x)","\int \frac{x^6\,\left(B\,x^2+A\right)}{{\left(b\,x^2+a\right)}^{5/2}} \,d x","Not used",1,"int((x^6*(A + B*x^2))/(a + b*x^2)^(5/2), x)","F"
586,1,89,97,0.862280,"\text{Not used}","int((x^5*(A + B*x^2))/(a + b*x^2)^(5/2),x)","\frac{B\,{\left(b\,x^2+a\right)}^3+B\,a^3+3\,A\,b\,{\left(b\,x^2+a\right)}^2-9\,B\,a\,{\left(b\,x^2+a\right)}^2-9\,B\,a^2\,\left(b\,x^2+a\right)-A\,a^2\,b+6\,A\,a\,b\,\left(b\,x^2+a\right)}{3\,b^4\,{\left(b\,x^2+a\right)}^{3/2}}","Not used",1,"(B*(a + b*x^2)^3 + B*a^3 + 3*A*b*(a + b*x^2)^2 - 9*B*a*(a + b*x^2)^2 - 9*B*a^2*(a + b*x^2) - A*a^2*b + 6*A*a*b*(a + b*x^2))/(3*b^4*(a + b*x^2)^(3/2))","B"
587,0,-1,114,0.000000,"\text{Not used}","int((x^4*(A + B*x^2))/(a + b*x^2)^(5/2),x)","\int \frac{x^4\,\left(B\,x^2+A\right)}{{\left(b\,x^2+a\right)}^{5/2}} \,d x","Not used",1,"int((x^4*(A + B*x^2))/(a + b*x^2)^(5/2), x)","F"
588,1,59,68,0.667891,"\text{Not used}","int((x^3*(A + B*x^2))/(a + b*x^2)^(5/2),x)","\frac{3\,B\,{\left(b\,x^2+a\right)}^2-B\,a^2-3\,A\,b\,\left(b\,x^2+a\right)+6\,B\,a\,\left(b\,x^2+a\right)+A\,a\,b}{3\,b^3\,{\left(b\,x^2+a\right)}^{3/2}}","Not used",1,"(3*B*(a + b*x^2)^2 - B*a^2 - 3*A*b*(a + b*x^2) + 6*B*a*(a + b*x^2) + A*a*b)/(3*b^3*(a + b*x^2)^(3/2))","B"
589,0,-1,77,0.000000,"\text{Not used}","int((x^2*(A + B*x^2))/(a + b*x^2)^(5/2),x)","\int \frac{x^2\,\left(B\,x^2+A\right)}{{\left(b\,x^2+a\right)}^{5/2}} \,d x","Not used",1,"int((x^2*(A + B*x^2))/(a + b*x^2)^(5/2), x)","F"
590,1,32,44,0.542126,"\text{Not used}","int((x*(A + B*x^2))/(a + b*x^2)^(5/2),x)","-\frac{A\,b-B\,a+3\,B\,\left(b\,x^2+a\right)}{3\,b^2\,{\left(b\,x^2+a\right)}^{3/2}}","Not used",1,"-(A*b - B*a + 3*B*(a + b*x^2))/(3*b^2*(a + b*x^2)^(3/2))","B"
591,1,33,47,0.552465,"\text{Not used}","int((A + B*x^2)/(a + b*x^2)^(5/2),x)","\frac{3\,A\,a\,x+2\,A\,b\,x^3+B\,a\,x^3}{3\,a^2\,{\left(b\,x^2+a\right)}^{3/2}}","Not used",1,"(3*A*a*x + 2*A*b*x^3 + B*a*x^3)/(3*a^2*(a + b*x^2)^(3/2))","B"
592,1,65,72,1.114001,"\text{Not used}","int((A + B*x^2)/(x*(a + b*x^2)^(5/2)),x)","\frac{\frac{A}{3\,a}+\frac{A\,\left(b\,x^2+a\right)}{a^2}}{{\left(b\,x^2+a\right)}^{3/2}}-\frac{B}{3\,b\,{\left(b\,x^2+a\right)}^{3/2}}-\frac{A\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{a^{5/2}}","Not used",1,"(A/(3*a) + (A*(a + b*x^2))/a^2)/(a + b*x^2)^(3/2) - B/(3*b*(a + b*x^2)^(3/2)) - (A*atanh((a + b*x^2)^(1/2)/a^(1/2)))/a^(5/2)","B"
593,1,68,77,0.619347,"\text{Not used}","int((A + B*x^2)/(x^2*(a + b*x^2)^(5/2)),x)","\frac{A\,a^2-8\,A\,{\left(b\,x^2+a\right)}^2+B\,a^2\,x^2+4\,A\,a\,\left(b\,x^2+a\right)+2\,B\,a\,x^2\,\left(b\,x^2+a\right)}{3\,a^3\,x\,{\left(b\,x^2+a\right)}^{3/2}}","Not used",1,"(A*a^2 - 8*A*(a + b*x^2)^2 + B*a^2*x^2 + 4*A*a*(a + b*x^2) + 2*B*a*x^2*(a + b*x^2))/(3*a^3*x*(a + b*x^2)^(3/2))","B"
594,1,126,113,1.546180,"\text{Not used}","int((A + B*x^2)/(x^3*(a + b*x^2)^(5/2)),x)","\frac{\frac{B}{3\,a}+\frac{B\,\left(b\,x^2+a\right)}{a^2}}{{\left(b\,x^2+a\right)}^{3/2}}-\frac{B\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{a^{5/2}}-\frac{10\,A\,b}{3\,a^2\,{\left(b\,x^2+a\right)}^{3/2}}-\frac{A}{2\,a\,x^2\,{\left(b\,x^2+a\right)}^{3/2}}+\frac{5\,A\,b\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{2\,a^{7/2}}-\frac{5\,A\,b^2\,x^2}{2\,a^3\,{\left(b\,x^2+a\right)}^{3/2}}","Not used",1,"(B/(3*a) + (B*(a + b*x^2))/a^2)/(a + b*x^2)^(3/2) - (B*atanh((a + b*x^2)^(1/2)/a^(1/2)))/a^(5/2) - (10*A*b)/(3*a^2*(a + b*x^2)^(3/2)) - A/(2*a*x^2*(a + b*x^2)^(3/2)) + (5*A*b*atanh((a + b*x^2)^(1/2)/a^(1/2)))/(2*a^(7/2)) - (5*A*b^2*x^2)/(2*a^3*(a + b*x^2)^(3/2))","B"
595,1,123,108,0.761855,"\text{Not used}","int((A + B*x^2)/(x^4*(a + b*x^2)^(5/2)),x)","-\frac{16\,A\,{\left(b\,x^2+a\right)}^3+A\,a^3+B\,a^3\,x^2-24\,A\,a\,{\left(b\,x^2+a\right)}^2+6\,A\,a^2\,\left(b\,x^2+a\right)-8\,B\,a\,x^2\,{\left(b\,x^2+a\right)}^2+4\,B\,a^2\,x^2\,\left(b\,x^2+a\right)}{{\left(b\,x^2+a\right)}^{3/2}\,\left(\frac{3\,a^5\,x}{b}-\frac{3\,a^4\,x\,\left(b\,x^2+a\right)}{b}\right)}","Not used",1,"-(16*A*(a + b*x^2)^3 + A*a^3 + B*a^3*x^2 - 24*A*a*(a + b*x^2)^2 + 6*A*a^2*(a + b*x^2) - 8*B*a*x^2*(a + b*x^2)^2 + 4*B*a^2*x^2*(a + b*x^2))/((a + b*x^2)^(3/2)*((3*a^5*x)/b - (3*a^4*x*(a + b*x^2))/b))","B"
596,1,176,146,2.017384,"\text{Not used}","int((A + B*x^2)/(x^5*(a + b*x^2)^(5/2)),x)","\frac{35\,A\,b^2}{6\,a^3\,{\left(b\,x^2+a\right)}^{3/2}}-\frac{10\,B\,b}{3\,a^2\,{\left(b\,x^2+a\right)}^{3/2}}-\frac{35\,A\,b^2\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{8\,a^{9/2}}-\frac{A}{4\,a\,x^4\,{\left(b\,x^2+a\right)}^{3/2}}-\frac{B}{2\,a\,x^2\,{\left(b\,x^2+a\right)}^{3/2}}+\frac{5\,B\,b\,\mathrm{atanh}\left(\frac{\sqrt{b\,x^2+a}}{\sqrt{a}}\right)}{2\,a^{7/2}}+\frac{7\,A\,b}{8\,a^2\,x^2\,{\left(b\,x^2+a\right)}^{3/2}}+\frac{35\,A\,b^3\,x^2}{8\,a^4\,{\left(b\,x^2+a\right)}^{3/2}}-\frac{5\,B\,b^2\,x^2}{2\,a^3\,{\left(b\,x^2+a\right)}^{3/2}}","Not used",1,"(35*A*b^2)/(6*a^3*(a + b*x^2)^(3/2)) - (10*B*b)/(3*a^2*(a + b*x^2)^(3/2)) - (35*A*b^2*atanh((a + b*x^2)^(1/2)/a^(1/2)))/(8*a^(9/2)) - A/(4*a*x^4*(a + b*x^2)^(3/2)) - B/(2*a*x^2*(a + b*x^2)^(3/2)) + (5*B*b*atanh((a + b*x^2)^(1/2)/a^(1/2)))/(2*a^(7/2)) + (7*A*b)/(8*a^2*x^2*(a + b*x^2)^(3/2)) + (35*A*b^3*x^2)/(8*a^4*(a + b*x^2)^(3/2)) - (5*B*b^2*x^2)/(2*a^3*(a + b*x^2)^(3/2))","B"
597,1,231,146,0.999128,"\text{Not used}","int((A + B*x^2)/(x^6*(a + b*x^2)^(5/2)),x)","\frac{\frac{a\,\left(\frac{b^2\,\left(73\,A\,b-40\,B\,a\right)}{18\,a^4}+\frac{b^2\,\left(86\,A\,b-35\,B\,a\right)}{30\,a^4}+\frac{a\,\left(\frac{28\,A\,b^4-10\,B\,a\,b^3}{45\,a^5}-\frac{b^3\,\left(86\,A\,b-35\,B\,a\right)}{18\,a^5}\right)}{b}\right)}{b}-\frac{b\,\left(73\,A\,b-40\,B\,a\right)}{30\,a^3}}{x\,{\left(b\,x^2+a\right)}^{3/2}}+\frac{x^2\,\left(\frac{28\,A\,b^3-10\,B\,a\,b^2}{15\,a^5}-\frac{2\,b^2\,\left(26\,A\,b-15\,B\,a\right)}{5\,a^5}\right)-\frac{b\,\left(26\,A\,b-15\,B\,a\right)}{5\,a^4}}{x\,\sqrt{b\,x^2+a}}-\frac{\sqrt{b\,x^2+a}\,\left(5\,B\,a^3-14\,A\,a^2\,b\right)}{15\,a^6\,x^3}-\frac{A\,\sqrt{b\,x^2+a}}{5\,a^3\,x^5}","Not used",1,"((a*((b^2*(73*A*b - 40*B*a))/(18*a^4) + (b^2*(86*A*b - 35*B*a))/(30*a^4) + (a*((28*A*b^4 - 10*B*a*b^3)/(45*a^5) - (b^3*(86*A*b - 35*B*a))/(18*a^5)))/b))/b - (b*(73*A*b - 40*B*a))/(30*a^3))/(x*(a + b*x^2)^(3/2)) + (x^2*((28*A*b^3 - 10*B*a*b^2)/(15*a^5) - (2*b^2*(26*A*b - 15*B*a))/(5*a^5)) - (b*(26*A*b - 15*B*a))/(5*a^4))/(x*(a + b*x^2)^(1/2)) - ((a + b*x^2)^(1/2)*(5*B*a^3 - 14*A*a^2*b))/(15*a^6*x^3) - (A*(a + b*x^2)^(1/2))/(5*a^3*x^5)","B"
598,1,171,157,0.755834,"\text{Not used}","int(x^5*(a + b*x^2)^2*(c + d*x^2)^(1/2),x)","\sqrt{d\,x^2+c}\,\left(\frac{264\,a^2\,c^3\,d^2-352\,a\,b\,c^4\,d+128\,b^2\,c^5}{3465\,d^5}+\frac{b^2\,x^{10}}{11}+\frac{x^6\,\left(495\,a^2\,d^5+110\,a\,b\,c\,d^4-40\,b^2\,c^2\,d^3\right)}{3465\,d^5}+\frac{b\,x^8\,\left(22\,a\,d+b\,c\right)}{99\,d}+\frac{c\,x^4\,\left(33\,a^2\,d^2-44\,a\,b\,c\,d+16\,b^2\,c^2\right)}{1155\,d^3}-\frac{4\,c^2\,x^2\,\left(33\,a^2\,d^2-44\,a\,b\,c\,d+16\,b^2\,c^2\right)}{3465\,d^4}\right)","Not used",1,"(c + d*x^2)^(1/2)*((128*b^2*c^5 + 264*a^2*c^3*d^2 - 352*a*b*c^4*d)/(3465*d^5) + (b^2*x^10)/11 + (x^6*(495*a^2*d^5 - 40*b^2*c^2*d^3 + 110*a*b*c*d^4))/(3465*d^5) + (b*x^8*(22*a*d + b*c))/(99*d) + (c*x^4*(33*a^2*d^2 + 16*b^2*c^2 - 44*a*b*c*d))/(1155*d^3) - (4*c^2*x^2*(33*a^2*d^2 + 16*b^2*c^2 - 44*a*b*c*d))/(3465*d^4))","B"
599,1,137,114,0.653984,"\text{Not used}","int(x^3*(a + b*x^2)^2*(c + d*x^2)^(1/2),x)","\sqrt{d\,x^2+c}\,\left(\frac{b^2\,x^8}{9}-\frac{42\,a^2\,c^2\,d^2-48\,a\,b\,c^3\,d+16\,b^2\,c^4}{315\,d^4}+\frac{x^4\,\left(63\,a^2\,d^4+18\,a\,b\,c\,d^3-6\,b^2\,c^2\,d^2\right)}{315\,d^4}+\frac{b\,x^6\,\left(18\,a\,d+b\,c\right)}{63\,d}+\frac{c\,x^2\,\left(21\,a^2\,d^2-24\,a\,b\,c\,d+8\,b^2\,c^2\right)}{315\,d^3}\right)","Not used",1,"(c + d*x^2)^(1/2)*((b^2*x^8)/9 - (16*b^2*c^4 + 42*a^2*c^2*d^2 - 48*a*b*c^3*d)/(315*d^4) + (x^4*(63*a^2*d^4 - 6*b^2*c^2*d^2 + 18*a*b*c*d^3))/(315*d^4) + (b*x^6*(18*a*d + b*c))/(63*d) + (c*x^2*(21*a^2*d^2 + 8*b^2*c^2 - 24*a*b*c*d))/(315*d^3))","B"
600,1,101,77,0.625880,"\text{Not used}","int(x*(a + b*x^2)^2*(c + d*x^2)^(1/2),x)","\sqrt{d\,x^2+c}\,\left(\frac{35\,a^2\,c\,d^2-28\,a\,b\,c^2\,d+8\,b^2\,c^3}{105\,d^3}+\frac{b^2\,x^6}{7}+\frac{x^2\,\left(35\,a^2\,d^3+14\,a\,b\,c\,d^2-4\,b^2\,c^2\,d\right)}{105\,d^3}+\frac{b\,x^4\,\left(14\,a\,d+b\,c\right)}{35\,d}\right)","Not used",1,"(c + d*x^2)^(1/2)*((8*b^2*c^3 + 35*a^2*c*d^2 - 28*a*b*c^2*d)/(105*d^3) + (b^2*x^6)/7 + (x^2*(35*a^2*d^3 - 4*b^2*c^2*d + 14*a*b*c*d^2))/(105*d^3) + (b*x^4*(14*a*d + b*c))/(35*d))","B"
601,1,135,92,0.694713,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^(1/2))/x,x)","\sqrt{d\,x^2+c}\,\left(\frac{{\left(a\,d-b\,c\right)}^2}{d^2}-c\,\left(\frac{2\,b^2\,c-2\,a\,b\,d}{d^2}-\frac{b^2\,c}{d^2}\right)\right)-\left(\frac{2\,b^2\,c-2\,a\,b\,d}{3\,d^2}-\frac{b^2\,c}{3\,d^2}\right)\,{\left(d\,x^2+c\right)}^{3/2}+\frac{b^2\,{\left(d\,x^2+c\right)}^{5/2}}{5\,d^2}+a^2\,\sqrt{c}\,\mathrm{atan}\left(\frac{\sqrt{d\,x^2+c}\,1{}\mathrm{i}}{\sqrt{c}}\right)\,1{}\mathrm{i}","Not used",1,"(c + d*x^2)^(1/2)*((a*d - b*c)^2/d^2 - c*((2*b^2*c - 2*a*b*d)/d^2 - (b^2*c)/d^2)) - ((2*b^2*c - 2*a*b*d)/(3*d^2) - (b^2*c)/(3*d^2))*(c + d*x^2)^(3/2) + a^2*c^(1/2)*atan(((c + d*x^2)^(1/2)*1i)/c^(1/2))*1i + (b^2*(c + d*x^2)^(5/2))/(5*d^2)","B"
602,1,103,109,1.058991,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^(1/2))/x^3,x)","\frac{b^2\,{\left(d\,x^2+c\right)}^{3/2}}{3\,d}-\left(\frac{2\,b^2\,c-2\,a\,b\,d}{d}-\frac{2\,b^2\,c}{d}\right)\,\sqrt{d\,x^2+c}-\frac{a^2\,\sqrt{d\,x^2+c}}{2\,x^2}+\frac{a\,\mathrm{atan}\left(\frac{\sqrt{d\,x^2+c}\,1{}\mathrm{i}}{\sqrt{c}}\right)\,\left(a\,d+4\,b\,c\right)\,1{}\mathrm{i}}{2\,\sqrt{c}}","Not used",1,"(b^2*(c + d*x^2)^(3/2))/(3*d) - ((2*b^2*c - 2*a*b*d)/d - (2*b^2*c)/d)*(c + d*x^2)^(1/2) - (a^2*(c + d*x^2)^(1/2))/(2*x^2) + (a*atan(((c + d*x^2)^(1/2)*1i)/c^(1/2))*(a*d + 4*b*c)*1i)/(2*c^(1/2))","B"
603,1,137,143,1.328460,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^(1/2))/x^5,x)","b^2\,\sqrt{d\,x^2+c}-\frac{\left(\frac{a^2\,d^2}{8}-a\,b\,c\,d\right)\,\sqrt{d\,x^2+c}+\frac{\left(a^2\,d^2+8\,b\,c\,a\,d\right)\,{\left(d\,x^2+c\right)}^{3/2}}{8\,c}}{{\left(d\,x^2+c\right)}^2-2\,c\,\left(d\,x^2+c\right)+c^2}-\frac{\mathrm{atanh}\left(\frac{\sqrt{d\,x^2+c}}{\sqrt{c}}\right)\,\left(-a^2\,d^2+8\,a\,b\,c\,d+8\,b^2\,c^2\right)}{8\,c^{3/2}}","Not used",1,"b^2*(c + d*x^2)^(1/2) - (((a^2*d^2)/8 - a*b*c*d)*(c + d*x^2)^(1/2) + ((a^2*d^2 + 8*a*b*c*d)*(c + d*x^2)^(3/2))/(8*c))/((c + d*x^2)^2 - 2*c*(c + d*x^2) + c^2) - (atanh((c + d*x^2)^(1/2)/c^(1/2))*(8*b^2*c^2 - a^2*d^2 + 8*a*b*c*d))/(8*c^(3/2))","B"
604,1,193,149,1.838389,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^(1/2))/x^7,x)","\frac{\sqrt{d\,x^2+c}\,\left(\frac{a^2\,d^3}{16}-\frac{a\,b\,c\,d^2}{4}+\frac{b^2\,c^2\,d}{2}\right)+\frac{{\left(d\,x^2+c\right)}^{3/2}\,\left(a^2\,d^3-6\,b^2\,c^2\,d\right)}{6\,c}+\frac{{\left(d\,x^2+c\right)}^{5/2}\,\left(-a^2\,d^3+4\,a\,b\,c\,d^2+8\,b^2\,c^2\,d\right)}{16\,c^2}}{3\,c\,{\left(d\,x^2+c\right)}^2-3\,c^2\,\left(d\,x^2+c\right)-{\left(d\,x^2+c\right)}^3+c^3}-\frac{d\,\mathrm{atanh}\left(\frac{\sqrt{d\,x^2+c}}{\sqrt{c}}\right)\,\left(a^2\,d^2-4\,a\,b\,c\,d+8\,b^2\,c^2\right)}{16\,c^{5/2}}","Not used",1,"((c + d*x^2)^(1/2)*((a^2*d^3)/16 + (b^2*c^2*d)/2 - (a*b*c*d^2)/4) + ((c + d*x^2)^(3/2)*(a^2*d^3 - 6*b^2*c^2*d))/(6*c) + ((c + d*x^2)^(5/2)*(8*b^2*c^2*d - a^2*d^3 + 4*a*b*c*d^2))/(16*c^2))/(3*c*(c + d*x^2)^2 - 3*c^2*(c + d*x^2) - (c + d*x^2)^3 + c^3) - (d*atanh((c + d*x^2)^(1/2)/c^(1/2))*(a^2*d^2 + 8*b^2*c^2 - 4*a*b*c*d))/(16*c^(5/2))","B"
605,0,-1,191,0.000000,"\text{Not used}","int(x^2*(a + b*x^2)^2*(c + d*x^2)^(1/2),x)","\int x^2\,{\left(b\,x^2+a\right)}^2\,\sqrt{d\,x^2+c} \,d x","Not used",1,"int(x^2*(a + b*x^2)^2*(c + d*x^2)^(1/2), x)","F"
606,0,-1,149,0.000000,"\text{Not used}","int((a + b*x^2)^2*(c + d*x^2)^(1/2),x)","\int {\left(b\,x^2+a\right)}^2\,\sqrt{d\,x^2+c} \,d x","Not used",1,"int((a + b*x^2)^2*(c + d*x^2)^(1/2), x)","F"
607,0,-1,133,0.000000,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^(1/2))/x^2,x)","\int \frac{{\left(b\,x^2+a\right)}^2\,\sqrt{d\,x^2+c}}{x^2} \,d x","Not used",1,"int(((a + b*x^2)^2*(c + d*x^2)^(1/2))/x^2, x)","F"
608,0,-1,111,0.000000,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^(1/2))/x^4,x)","\int \frac{{\left(b\,x^2+a\right)}^2\,\sqrt{d\,x^2+c}}{x^4} \,d x","Not used",1,"int(((a + b*x^2)^2*(c + d*x^2)^(1/2))/x^4, x)","F"
609,0,-1,103,0.000000,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^(1/2))/x^6,x)","\int \frac{{\left(b\,x^2+a\right)}^2\,\sqrt{d\,x^2+c}}{x^6} \,d x","Not used",1,"int(((a + b*x^2)^2*(c + d*x^2)^(1/2))/x^6, x)","F"
610,1,181,99,1.632497,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^(1/2))/x^8,x)","\frac{4\,a^2\,d^2\,\sqrt{d\,x^2+c}}{105\,c^2\,x^3}-\frac{b^2\,\sqrt{d\,x^2+c}}{3\,x^3}-\frac{2\,a\,b\,\sqrt{d\,x^2+c}}{5\,x^5}-\frac{a^2\,\sqrt{d\,x^2+c}}{7\,x^7}-\frac{8\,a^2\,d^3\,\sqrt{d\,x^2+c}}{105\,c^3\,x}-\frac{a^2\,d\,\sqrt{d\,x^2+c}}{35\,c\,x^5}-\frac{b^2\,d\,\sqrt{d\,x^2+c}}{3\,c\,x}+\frac{4\,a\,b\,d^2\,\sqrt{d\,x^2+c}}{15\,c^2\,x}-\frac{2\,a\,b\,d\,\sqrt{d\,x^2+c}}{15\,c\,x^3}","Not used",1,"(4*a^2*d^2*(c + d*x^2)^(1/2))/(105*c^2*x^3) - (b^2*(c + d*x^2)^(1/2))/(3*x^3) - (2*a*b*(c + d*x^2)^(1/2))/(5*x^5) - (a^2*(c + d*x^2)^(1/2))/(7*x^7) - (8*a^2*d^3*(c + d*x^2)^(1/2))/(105*c^3*x) - (a^2*d*(c + d*x^2)^(1/2))/(35*c*x^5) - (b^2*d*(c + d*x^2)^(1/2))/(3*c*x) + (4*a*b*d^2*(c + d*x^2)^(1/2))/(15*c^2*x) - (2*a*b*d*(c + d*x^2)^(1/2))/(15*c*x^3)","B"
611,1,249,143,2.291389,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^(1/2))/x^10,x)","\frac{2\,a^2\,d^2\,\sqrt{d\,x^2+c}}{105\,c^2\,x^5}-\frac{b^2\,\sqrt{d\,x^2+c}}{5\,x^5}-\frac{2\,a\,b\,\sqrt{d\,x^2+c}}{7\,x^7}-\frac{a^2\,\sqrt{d\,x^2+c}}{9\,x^9}-\frac{8\,a^2\,d^3\,\sqrt{d\,x^2+c}}{315\,c^3\,x^3}+\frac{16\,a^2\,d^4\,\sqrt{d\,x^2+c}}{315\,c^4\,x}+\frac{2\,b^2\,d^2\,\sqrt{d\,x^2+c}}{15\,c^2\,x}-\frac{a^2\,d\,\sqrt{d\,x^2+c}}{63\,c\,x^7}-\frac{b^2\,d\,\sqrt{d\,x^2+c}}{15\,c\,x^3}+\frac{8\,a\,b\,d^2\,\sqrt{d\,x^2+c}}{105\,c^2\,x^3}-\frac{16\,a\,b\,d^3\,\sqrt{d\,x^2+c}}{105\,c^3\,x}-\frac{2\,a\,b\,d\,\sqrt{d\,x^2+c}}{35\,c\,x^5}","Not used",1,"(2*a^2*d^2*(c + d*x^2)^(1/2))/(105*c^2*x^5) - (b^2*(c + d*x^2)^(1/2))/(5*x^5) - (2*a*b*(c + d*x^2)^(1/2))/(7*x^7) - (a^2*(c + d*x^2)^(1/2))/(9*x^9) - (8*a^2*d^3*(c + d*x^2)^(1/2))/(315*c^3*x^3) + (16*a^2*d^4*(c + d*x^2)^(1/2))/(315*c^4*x) + (2*b^2*d^2*(c + d*x^2)^(1/2))/(15*c^2*x) - (a^2*d*(c + d*x^2)^(1/2))/(63*c*x^7) - (b^2*d*(c + d*x^2)^(1/2))/(15*c*x^3) + (8*a*b*d^2*(c + d*x^2)^(1/2))/(105*c^2*x^3) - (16*a*b*d^3*(c + d*x^2)^(1/2))/(105*c^3*x) - (2*a*b*d*(c + d*x^2)^(1/2))/(35*c*x^5)","B"
612,1,317,189,2.990788,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^(1/2))/x^12,x)","\frac{8\,a^2\,d^2\,\sqrt{d\,x^2+c}}{693\,c^2\,x^7}-\frac{b^2\,\sqrt{d\,x^2+c}}{7\,x^7}-\frac{2\,a\,b\,\sqrt{d\,x^2+c}}{9\,x^9}-\frac{a^2\,\sqrt{d\,x^2+c}}{11\,x^{11}}-\frac{16\,a^2\,d^3\,\sqrt{d\,x^2+c}}{1155\,c^3\,x^5}+\frac{64\,a^2\,d^4\,\sqrt{d\,x^2+c}}{3465\,c^4\,x^3}-\frac{128\,a^2\,d^5\,\sqrt{d\,x^2+c}}{3465\,c^5\,x}+\frac{4\,b^2\,d^2\,\sqrt{d\,x^2+c}}{105\,c^2\,x^3}-\frac{8\,b^2\,d^3\,\sqrt{d\,x^2+c}}{105\,c^3\,x}-\frac{a^2\,d\,\sqrt{d\,x^2+c}}{99\,c\,x^9}-\frac{b^2\,d\,\sqrt{d\,x^2+c}}{35\,c\,x^5}+\frac{4\,a\,b\,d^2\,\sqrt{d\,x^2+c}}{105\,c^2\,x^5}-\frac{16\,a\,b\,d^3\,\sqrt{d\,x^2+c}}{315\,c^3\,x^3}+\frac{32\,a\,b\,d^4\,\sqrt{d\,x^2+c}}{315\,c^4\,x}-\frac{2\,a\,b\,d\,\sqrt{d\,x^2+c}}{63\,c\,x^7}","Not used",1,"(8*a^2*d^2*(c + d*x^2)^(1/2))/(693*c^2*x^7) - (b^2*(c + d*x^2)^(1/2))/(7*x^7) - (2*a*b*(c + d*x^2)^(1/2))/(9*x^9) - (a^2*(c + d*x^2)^(1/2))/(11*x^11) - (16*a^2*d^3*(c + d*x^2)^(1/2))/(1155*c^3*x^5) + (64*a^2*d^4*(c + d*x^2)^(1/2))/(3465*c^4*x^3) - (128*a^2*d^5*(c + d*x^2)^(1/2))/(3465*c^5*x) + (4*b^2*d^2*(c + d*x^2)^(1/2))/(105*c^2*x^3) - (8*b^2*d^3*(c + d*x^2)^(1/2))/(105*c^3*x) - (a^2*d*(c + d*x^2)^(1/2))/(99*c*x^9) - (b^2*d*(c + d*x^2)^(1/2))/(35*c*x^5) + (4*a*b*d^2*(c + d*x^2)^(1/2))/(105*c^2*x^5) - (16*a*b*d^3*(c + d*x^2)^(1/2))/(315*c^3*x^3) + (32*a*b*d^4*(c + d*x^2)^(1/2))/(315*c^4*x) - (2*a*b*d*(c + d*x^2)^(1/2))/(63*c*x^7)","B"
613,0,-1,281,0.000000,"\text{Not used}","int(x^4*(a + b*x^2)^2*(c + d*x^2)^(3/2),x)","\int x^4\,{\left(b\,x^2+a\right)}^2\,{\left(d\,x^2+c\right)}^{3/2} \,d x","Not used",1,"int(x^4*(a + b*x^2)^2*(c + d*x^2)^(3/2), x)","F"
614,1,170,114,0.822973,"\text{Not used}","int(x^3*(a + b*x^2)^2*(c + d*x^2)^(3/2),x)","\sqrt{d\,x^2+c}\,\left(\frac{x^6\,\left(495\,a^2\,d^5+1100\,a\,b\,c\,d^4+15\,b^2\,c^2\,d^3\right)}{3465\,d^4}-\frac{198\,a^2\,c^3\,d^2-176\,a\,b\,c^4\,d+48\,b^2\,c^5}{3465\,d^4}+\frac{2\,b\,x^8\,\left(11\,a\,d+6\,b\,c\right)}{99}+\frac{b^2\,d\,x^{10}}{11}+\frac{2\,c\,x^4\,\left(132\,a^2\,d^2+11\,a\,b\,c\,d-3\,b^2\,c^2\right)}{1155\,d^2}+\frac{c^2\,x^2\,\left(99\,a^2\,d^2-88\,a\,b\,c\,d+24\,b^2\,c^2\right)}{3465\,d^3}\right)","Not used",1,"(c + d*x^2)^(1/2)*((x^6*(495*a^2*d^5 + 15*b^2*c^2*d^3 + 1100*a*b*c*d^4))/(3465*d^4) - (48*b^2*c^5 + 198*a^2*c^3*d^2 - 176*a*b*c^4*d)/(3465*d^4) + (2*b*x^8*(11*a*d + 6*b*c))/99 + (b^2*d*x^10)/11 + (2*c*x^4*(132*a^2*d^2 - 3*b^2*c^2 + 11*a*b*c*d))/(1155*d^2) + (c^2*x^2*(99*a^2*d^2 + 24*b^2*c^2 - 88*a*b*c*d))/(3465*d^3))","B"
615,0,-1,235,0.000000,"\text{Not used}","int(x^2*(a + b*x^2)^2*(c + d*x^2)^(3/2),x)","\int x^2\,{\left(b\,x^2+a\right)}^2\,{\left(d\,x^2+c\right)}^{3/2} \,d x","Not used",1,"int(x^2*(a + b*x^2)^2*(c + d*x^2)^(3/2), x)","F"
616,1,136,77,0.726461,"\text{Not used}","int(x*(a + b*x^2)^2*(c + d*x^2)^(3/2),x)","\sqrt{d\,x^2+c}\,\left(\frac{63\,a^2\,c^2\,d^2-36\,a\,b\,c^3\,d+8\,b^2\,c^4}{315\,d^3}+\frac{x^4\,\left(63\,a^2\,d^4+144\,a\,b\,c\,d^3+3\,b^2\,c^2\,d^2\right)}{315\,d^3}+\frac{2\,b\,x^6\,\left(9\,a\,d+5\,b\,c\right)}{63}+\frac{b^2\,d\,x^8}{9}+\frac{2\,c\,x^2\,\left(63\,a^2\,d^2+9\,a\,b\,c\,d-2\,b^2\,c^2\right)}{315\,d^2}\right)","Not used",1,"(c + d*x^2)^(1/2)*((8*b^2*c^4 + 63*a^2*c^2*d^2 - 36*a*b*c^3*d)/(315*d^3) + (x^4*(63*a^2*d^4 + 3*b^2*c^2*d^2 + 144*a*b*c*d^3))/(315*d^3) + (2*b*x^6*(9*a*d + 5*b*c))/63 + (b^2*d*x^8)/9 + (2*c*x^2*(63*a^2*d^2 - 2*b^2*c^2 + 9*a*b*c*d))/(315*d^2))","B"
617,0,-1,196,0.000000,"\text{Not used}","int((a + b*x^2)^2*(c + d*x^2)^(3/2),x)","\int {\left(b\,x^2+a\right)}^2\,{\left(d\,x^2+c\right)}^{3/2} \,d x","Not used",1,"int((a + b*x^2)^2*(c + d*x^2)^(3/2), x)","F"
618,1,191,111,0.702600,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^(3/2))/x,x)","{\left(d\,x^2+c\right)}^{3/2}\,\left(\frac{{\left(a\,d-b\,c\right)}^2}{3\,d^2}-\frac{c\,\left(\frac{2\,b^2\,c-2\,a\,b\,d}{d^2}-\frac{b^2\,c}{d^2}\right)}{3}\right)-\left(\frac{2\,b^2\,c-2\,a\,b\,d}{5\,d^2}-\frac{b^2\,c}{5\,d^2}\right)\,{\left(d\,x^2+c\right)}^{5/2}+\frac{b^2\,{\left(d\,x^2+c\right)}^{7/2}}{7\,d^2}+c\,\sqrt{d\,x^2+c}\,\left(\frac{{\left(a\,d-b\,c\right)}^2}{d^2}-c\,\left(\frac{2\,b^2\,c-2\,a\,b\,d}{d^2}-\frac{b^2\,c}{d^2}\right)\right)+a^2\,c^{3/2}\,\mathrm{atan}\left(\frac{\sqrt{d\,x^2+c}\,1{}\mathrm{i}}{\sqrt{c}}\right)\,1{}\mathrm{i}","Not used",1,"(c + d*x^2)^(3/2)*((a*d - b*c)^2/(3*d^2) - (c*((2*b^2*c - 2*a*b*d)/d^2 - (b^2*c)/d^2))/3) - ((2*b^2*c - 2*a*b*d)/(5*d^2) - (b^2*c)/(5*d^2))*(c + d*x^2)^(5/2) + a^2*c^(3/2)*atan(((c + d*x^2)^(1/2)*1i)/c^(1/2))*1i + (b^2*(c + d*x^2)^(7/2))/(7*d^2) + c*(c + d*x^2)^(1/2)*((a*d - b*c)^2/d^2 - c*((2*b^2*c - 2*a*b*d)/d^2 - (b^2*c)/d^2))","B"
619,0,-1,175,0.000000,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^(3/2))/x^2,x)","\int \frac{{\left(b\,x^2+a\right)}^2\,{\left(d\,x^2+c\right)}^{3/2}}{x^2} \,d x","Not used",1,"int(((a + b*x^2)^2*(c + d*x^2)^(3/2))/x^2, x)","F"
620,1,201,136,1.167050,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^(3/2))/x^3,x)","\frac{b^2\,{\left(d\,x^2+c\right)}^{5/2}}{5\,d}-\left(\frac{2\,b^2\,c-2\,a\,b\,d}{3\,d}-\frac{2\,b^2\,c}{3\,d}\right)\,{\left(d\,x^2+c\right)}^{3/2}-\sqrt{d\,x^2+c}\,\left(2\,c\,\left(\frac{2\,b^2\,c-2\,a\,b\,d}{d}-\frac{2\,b^2\,c}{d}\right)-\frac{{\left(a\,d-b\,c\right)}^2}{d}+\frac{b^2\,c^2}{d}\right)-\frac{a^2\,c\,\sqrt{d\,x^2+c}}{2\,x^2}+2\,a\,\mathrm{atan}\left(\frac{2\,a\,\sqrt{d\,x^2+c}\,\left(3\,a\,d+4\,b\,c\right)\,\sqrt{-\frac{c}{16}}}{\frac{3\,d\,a^2\,c}{2}+2\,b\,a\,c^2}\right)\,\left(3\,a\,d+4\,b\,c\right)\,\sqrt{-\frac{c}{16}}","Not used",1,"(b^2*(c + d*x^2)^(5/2))/(5*d) - ((2*b^2*c - 2*a*b*d)/(3*d) - (2*b^2*c)/(3*d))*(c + d*x^2)^(3/2) - (c + d*x^2)^(1/2)*(2*c*((2*b^2*c - 2*a*b*d)/d - (2*b^2*c)/d) - (a*d - b*c)^2/d + (b^2*c^2)/d) - (a^2*c*(c + d*x^2)^(1/2))/(2*x^2) + 2*a*atan((2*a*(c + d*x^2)^(1/2)*(3*a*d + 4*b*c)*(-c/16)^(1/2))/(2*a*b*c^2 + (3*a^2*c*d)/2))*(3*a*d + 4*b*c)*(-c/16)^(1/2)","B"
621,0,-1,184,0.000000,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^(3/2))/x^4,x)","\int \frac{{\left(b\,x^2+a\right)}^2\,{\left(d\,x^2+c\right)}^{3/2}}{x^4} \,d x","Not used",1,"int(((a + b*x^2)^2*(c + d*x^2)^(3/2))/x^4, x)","F"
622,1,208,181,1.645227,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^(3/2))/x^5,x)","\frac{\sqrt{d\,x^2+c}\,\left(\frac{3\,a^2\,c\,d^2}{8}+b\,a\,c^2\,d\right)-\left(\frac{5\,a^2\,d^2}{8}+b\,c\,a\,d\right)\,{\left(d\,x^2+c\right)}^{3/2}}{{\left(d\,x^2+c\right)}^2-2\,c\,\left(d\,x^2+c\right)+c^2}+\sqrt{d\,x^2+c}\,\left(c\,b^2+2\,a\,d\,b\right)+\frac{b^2\,{\left(d\,x^2+c\right)}^{3/2}}{3}+\frac{\mathrm{atan}\left(\frac{\sqrt{d\,x^2+c}\,\left(3\,a^2\,d^2+24\,a\,b\,c\,d+8\,b^2\,c^2\right)\,1{}\mathrm{i}}{4\,\sqrt{c}\,\left(\frac{3\,a^2\,d^2}{4}+6\,a\,b\,c\,d+2\,b^2\,c^2\right)}\right)\,\left(3\,a^2\,d^2+24\,a\,b\,c\,d+8\,b^2\,c^2\right)\,1{}\mathrm{i}}{8\,\sqrt{c}}","Not used",1,"((c + d*x^2)^(1/2)*((3*a^2*c*d^2)/8 + a*b*c^2*d) - ((5*a^2*d^2)/8 + a*b*c*d)*(c + d*x^2)^(3/2))/((c + d*x^2)^2 - 2*c*(c + d*x^2) + c^2) + (c + d*x^2)^(1/2)*(b^2*c + 2*a*b*d) + (b^2*(c + d*x^2)^(3/2))/3 + (atan(((c + d*x^2)^(1/2)*(3*a^2*d^2 + 8*b^2*c^2 + 24*a*b*c*d)*1i)/(4*c^(1/2)*((3*a^2*d^2)/4 + 2*b^2*c^2 + 6*a*b*c*d)))*(3*a^2*d^2 + 8*b^2*c^2 + 24*a*b*c*d)*1i)/(8*c^(1/2))","B"
623,0,-1,147,0.000000,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^(3/2))/x^6,x)","\int \frac{{\left(b\,x^2+a\right)}^2\,{\left(d\,x^2+c\right)}^{3/2}}{x^6} \,d x","Not used",1,"int(((a + b*x^2)^2*(c + d*x^2)^(3/2))/x^6, x)","F"
624,1,215,187,2.345173,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^(3/2))/x^7,x)","\frac{\sqrt{d\,x^2+c}\,\left(-\frac{a^2\,c\,d^3}{16}+\frac{3\,a\,b\,c^2\,d^2}{4}+\frac{b^2\,c^3\,d}{2}\right)-{\left(d\,x^2+c\right)}^{3/2}\,\left(-\frac{a^2\,d^3}{6}+2\,a\,b\,c\,d^2+b^2\,c^2\,d\right)+\frac{{\left(d\,x^2+c\right)}^{5/2}\,\left(a^2\,d^3+20\,a\,b\,c\,d^2+8\,b^2\,c^2\,d\right)}{16\,c}}{3\,c\,{\left(d\,x^2+c\right)}^2-3\,c^2\,\left(d\,x^2+c\right)-{\left(d\,x^2+c\right)}^3+c^3}+b^2\,d\,\sqrt{d\,x^2+c}-\frac{d\,\mathrm{atanh}\left(\frac{\sqrt{d\,x^2+c}}{\sqrt{c}}\right)\,\left(-a^2\,d^2+12\,a\,b\,c\,d+24\,b^2\,c^2\right)}{16\,c^{3/2}}","Not used",1,"((c + d*x^2)^(1/2)*((b^2*c^3*d)/2 - (a^2*c*d^3)/16 + (3*a*b*c^2*d^2)/4) - (c + d*x^2)^(3/2)*(b^2*c^2*d - (a^2*d^3)/6 + 2*a*b*c*d^2) + ((c + d*x^2)^(5/2)*(a^2*d^3 + 8*b^2*c^2*d + 20*a*b*c*d^2))/(16*c))/(3*c*(c + d*x^2)^2 - 3*c^2*(c + d*x^2) - (c + d*x^2)^3 + c^3) + b^2*d*(c + d*x^2)^(1/2) - (d*atanh((c + d*x^2)^(1/2)/c^(1/2))*(24*b^2*c^2 - a^2*d^2 + 12*a*b*c*d))/(16*c^(3/2))","B"
625,1,207,114,0.918485,"\text{Not used}","int(x^3*(a + b*x^2)^2*(c + d*x^2)^(5/2),x)","\sqrt{d\,x^2+c}\,\left(\frac{x^8\,\left(1001\,a^2\,d^6+4186\,a\,b\,c\,d^5+1113\,b^2\,c^2\,d^4\right)}{9009\,d^4}-\frac{286\,a^2\,c^4\,d^2-208\,a\,b\,c^5\,d+48\,b^2\,c^6}{9009\,d^4}+\frac{b^2\,d^2\,x^{12}}{13}+\frac{c\,x^6\,\left(2717\,a^2\,d^2+2938\,a\,b\,c\,d+15\,b^2\,c^2\right)}{9009\,d}+\frac{b\,d\,x^{10}\,\left(26\,a\,d+27\,b\,c\right)}{143}+\frac{c^3\,x^2\,\left(143\,a^2\,d^2-104\,a\,b\,c\,d+24\,b^2\,c^2\right)}{9009\,d^3}+\frac{c^2\,x^4\,\left(715\,a^2\,d^2+26\,a\,b\,c\,d-6\,b^2\,c^2\right)}{3003\,d^2}\right)","Not used",1,"(c + d*x^2)^(1/2)*((x^8*(1001*a^2*d^6 + 1113*b^2*c^2*d^4 + 4186*a*b*c*d^5))/(9009*d^4) - (48*b^2*c^6 + 286*a^2*c^4*d^2 - 208*a*b*c^5*d)/(9009*d^4) + (b^2*d^2*x^12)/13 + (c*x^6*(2717*a^2*d^2 + 15*b^2*c^2 + 2938*a*b*c*d))/(9009*d) + (b*d*x^10*(26*a*d + 27*b*c))/143 + (c^3*x^2*(143*a^2*d^2 + 24*b^2*c^2 - 104*a*b*c*d))/(9009*d^3) + (c^2*x^4*(715*a^2*d^2 - 6*b^2*c^2 + 26*a*b*c*d))/(3003*d^2))","B"
626,0,-1,281,0.000000,"\text{Not used}","int(x^2*(a + b*x^2)^2*(c + d*x^2)^(5/2),x)","\int x^2\,{\left(b\,x^2+a\right)}^2\,{\left(d\,x^2+c\right)}^{5/2} \,d x","Not used",1,"int(x^2*(a + b*x^2)^2*(c + d*x^2)^(5/2), x)","F"
627,1,98,77,0.797320,"\text{Not used}","int(x*(a + b*x^2)^2*(c + d*x^2)^(5/2),x)","\frac{d\,\left(\frac{2\,a\,b\,{\left(d\,x^2+c\right)}^{9/2}}{9}-\frac{2\,a\,b\,c\,{\left(d\,x^2+c\right)}^{7/2}}{7}\right)+\frac{b^2\,{\left(d\,x^2+c\right)}^{11/2}}{11}-\frac{2\,b^2\,c\,{\left(d\,x^2+c\right)}^{9/2}}{9}+\frac{a^2\,d^2\,{\left(d\,x^2+c\right)}^{7/2}}{7}+\frac{b^2\,c^2\,{\left(d\,x^2+c\right)}^{7/2}}{7}}{d^3}","Not used",1,"(d*((2*a*b*(c + d*x^2)^(9/2))/9 - (2*a*b*c*(c + d*x^2)^(7/2))/7) + (b^2*(c + d*x^2)^(11/2))/11 - (2*b^2*c*(c + d*x^2)^(9/2))/9 + (a^2*d^2*(c + d*x^2)^(7/2))/7 + (b^2*c^2*(c + d*x^2)^(7/2))/7)/d^3","B"
628,0,-1,240,0.000000,"\text{Not used}","int((a + b*x^2)^2*(c + d*x^2)^(5/2),x)","\int {\left(b\,x^2+a\right)}^2\,{\left(d\,x^2+c\right)}^{5/2} \,d x","Not used",1,"int((a + b*x^2)^2*(c + d*x^2)^(5/2), x)","F"
629,1,249,132,0.774657,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^(5/2))/x,x)","{\left(d\,x^2+c\right)}^{5/2}\,\left(\frac{{\left(a\,d-b\,c\right)}^2}{5\,d^2}-\frac{c\,\left(\frac{2\,b^2\,c-2\,a\,b\,d}{d^2}-\frac{b^2\,c}{d^2}\right)}{5}\right)-\left(\frac{2\,b^2\,c-2\,a\,b\,d}{7\,d^2}-\frac{b^2\,c}{7\,d^2}\right)\,{\left(d\,x^2+c\right)}^{7/2}+c^2\,\sqrt{d\,x^2+c}\,\left(\frac{{\left(a\,d-b\,c\right)}^2}{d^2}-c\,\left(\frac{2\,b^2\,c-2\,a\,b\,d}{d^2}-\frac{b^2\,c}{d^2}\right)\right)+\frac{b^2\,{\left(d\,x^2+c\right)}^{9/2}}{9\,d^2}+\frac{c\,{\left(d\,x^2+c\right)}^{3/2}\,\left(\frac{{\left(a\,d-b\,c\right)}^2}{d^2}-c\,\left(\frac{2\,b^2\,c-2\,a\,b\,d}{d^2}-\frac{b^2\,c}{d^2}\right)\right)}{3}+a^2\,c^{5/2}\,\mathrm{atan}\left(\frac{\sqrt{d\,x^2+c}\,1{}\mathrm{i}}{\sqrt{c}}\right)\,1{}\mathrm{i}","Not used",1,"(c + d*x^2)^(5/2)*((a*d - b*c)^2/(5*d^2) - (c*((2*b^2*c - 2*a*b*d)/d^2 - (b^2*c)/d^2))/5) - ((2*b^2*c - 2*a*b*d)/(7*d^2) - (b^2*c)/(7*d^2))*(c + d*x^2)^(7/2) + a^2*c^(5/2)*atan(((c + d*x^2)^(1/2)*1i)/c^(1/2))*1i + c^2*(c + d*x^2)^(1/2)*((a*d - b*c)^2/d^2 - c*((2*b^2*c - 2*a*b*d)/d^2 - (b^2*c)/d^2)) + (b^2*(c + d*x^2)^(9/2))/(9*d^2) + (c*(c + d*x^2)^(3/2)*((a*d - b*c)^2/d^2 - c*((2*b^2*c - 2*a*b*d)/d^2 - (b^2*c)/d^2)))/3","B"
630,0,-1,217,0.000000,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^(5/2))/x^2,x)","\int \frac{{\left(b\,x^2+a\right)}^2\,{\left(d\,x^2+c\right)}^{5/2}}{x^2} \,d x","Not used",1,"int(((a + b*x^2)^2*(c + d*x^2)^(5/2))/x^2, x)","F"
631,1,274,162,1.450835,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^(5/2))/x^3,x)","\sqrt{d\,x^2+c}\,\left(c^2\,\left(\frac{2\,b^2\,c-2\,a\,b\,d}{d}-\frac{2\,b^2\,c}{d}\right)-2\,c\,\left(2\,c\,\left(\frac{2\,b^2\,c-2\,a\,b\,d}{d}-\frac{2\,b^2\,c}{d}\right)-\frac{{\left(a\,d-b\,c\right)}^2}{d}+\frac{b^2\,c^2}{d}\right)\right)-\left(\frac{2\,b^2\,c-2\,a\,b\,d}{5\,d}-\frac{2\,b^2\,c}{5\,d}\right)\,{\left(d\,x^2+c\right)}^{5/2}-{\left(d\,x^2+c\right)}^{3/2}\,\left(\frac{2\,c\,\left(\frac{2\,b^2\,c-2\,a\,b\,d}{d}-\frac{2\,b^2\,c}{d}\right)}{3}-\frac{{\left(a\,d-b\,c\right)}^2}{3\,d}+\frac{b^2\,c^2}{3\,d}\right)+\frac{b^2\,{\left(d\,x^2+c\right)}^{7/2}}{7\,d}-\frac{a^2\,c^2\,\sqrt{d\,x^2+c}}{2\,x^2}+\frac{a\,c^{3/2}\,\mathrm{atan}\left(\frac{\sqrt{d\,x^2+c}\,1{}\mathrm{i}}{\sqrt{c}}\right)\,\left(5\,a\,d+4\,b\,c\right)\,1{}\mathrm{i}}{2}","Not used",1,"(c + d*x^2)^(1/2)*(c^2*((2*b^2*c - 2*a*b*d)/d - (2*b^2*c)/d) - 2*c*(2*c*((2*b^2*c - 2*a*b*d)/d - (2*b^2*c)/d) - (a*d - b*c)^2/d + (b^2*c^2)/d)) - ((2*b^2*c - 2*a*b*d)/(5*d) - (2*b^2*c)/(5*d))*(c + d*x^2)^(5/2) - (c + d*x^2)^(3/2)*((2*c*((2*b^2*c - 2*a*b*d)/d - (2*b^2*c)/d))/3 - (a*d - b*c)^2/(3*d) + (b^2*c^2)/(3*d)) + (b^2*(c + d*x^2)^(7/2))/(7*d) + (a*c^(3/2)*atan(((c + d*x^2)^(1/2)*1i)/c^(1/2))*(5*a*d + 4*b*c)*1i)/2 - (a^2*c^2*(c + d*x^2)^(1/2))/(2*x^2)","B"
632,0,-1,223,0.000000,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^(5/2))/x^4,x)","\int \frac{{\left(b\,x^2+a\right)}^2\,{\left(d\,x^2+c\right)}^{5/2}}{x^4} \,d x","Not used",1,"int(((a + b*x^2)^2*(c + d*x^2)^(5/2))/x^4, x)","F"
633,1,262,222,1.884795,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^(5/2))/x^5,x)","{\left(d\,x^2+c\right)}^{3/2}\,\left(\frac{c\,b^2}{3}+\frac{2\,a\,d\,b}{3}\right)-\frac{{\left(d\,x^2+c\right)}^{3/2}\,\left(\frac{9\,a^2\,c\,d^2}{8}+b\,a\,c^2\,d\right)-\left(\frac{7\,a^2\,c^2\,d^2}{8}+b\,a\,c^3\,d\right)\,\sqrt{d\,x^2+c}}{{\left(d\,x^2+c\right)}^2-2\,c\,\left(d\,x^2+c\right)+c^2}+\sqrt{d\,x^2+c}\,\left({\left(a\,d-b\,c\right)}^2+3\,c\,\left(c\,b^2+2\,a\,d\,b\right)-3\,b^2\,c^2\right)+\frac{b^2\,{\left(d\,x^2+c\right)}^{5/2}}{5}+2\,\mathrm{atan}\left(\frac{2\,\sqrt{d\,x^2+c}\,\sqrt{-\frac{c}{256}}\,\left(15\,a^2\,d^2+40\,a\,b\,c\,d+8\,b^2\,c^2\right)}{\frac{15\,a^2\,c\,d^2}{8}+5\,a\,b\,c^2\,d+b^2\,c^3}\right)\,\sqrt{-\frac{c}{256}}\,\left(15\,a^2\,d^2+40\,a\,b\,c\,d+8\,b^2\,c^2\right)","Not used",1,"(c + d*x^2)^(3/2)*((b^2*c)/3 + (2*a*b*d)/3) - ((c + d*x^2)^(3/2)*((9*a^2*c*d^2)/8 + a*b*c^2*d) - ((7*a^2*c^2*d^2)/8 + a*b*c^3*d)*(c + d*x^2)^(1/2))/((c + d*x^2)^2 - 2*c*(c + d*x^2) + c^2) + (c + d*x^2)^(1/2)*((a*d - b*c)^2 + 3*c*(b^2*c + 2*a*b*d) - 3*b^2*c^2) + (b^2*(c + d*x^2)^(5/2))/5 + 2*atan((2*(c + d*x^2)^(1/2)*(-c/256)^(1/2)*(15*a^2*d^2 + 8*b^2*c^2 + 40*a*b*c*d))/(b^2*c^3 + (15*a^2*c*d^2)/8 + 5*a*b*c^2*d))*(-c/256)^(1/2)*(15*a^2*d^2 + 8*b^2*c^2 + 40*a*b*c*d)","B"
634,0,-1,228,0.000000,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^(5/2))/x^6,x)","\int \frac{{\left(b\,x^2+a\right)}^2\,{\left(d\,x^2+c\right)}^{5/2}}{x^6} \,d x","Not used",1,"int(((a + b*x^2)^2*(c + d*x^2)^(5/2))/x^6, x)","F"
635,1,301,222,2.723116,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^(5/2))/x^7,x)","\frac{\sqrt{d\,x^2+c}\,\left(\frac{5\,a^2\,c^2\,d^3}{16}+\frac{7\,a\,b\,c^3\,d^2}{4}+\frac{b^2\,c^4\,d}{2}\right)-{\left(d\,x^2+c\right)}^{3/2}\,\left(\frac{5\,a^2\,c\,d^3}{6}+4\,a\,b\,c^2\,d^2+b^2\,c^3\,d\right)+{\left(d\,x^2+c\right)}^{5/2}\,\left(\frac{11\,a^2\,d^3}{16}+\frac{9\,a\,b\,c\,d^2}{4}+\frac{b^2\,c^2\,d}{2}\right)}{3\,c\,{\left(d\,x^2+c\right)}^2-3\,c^2\,\left(d\,x^2+c\right)-{\left(d\,x^2+c\right)}^3+c^3}+\left(2\,b\,d\,\left(a\,d-b\,c\right)+4\,b^2\,c\,d\right)\,\sqrt{d\,x^2+c}+\frac{b^2\,d\,{\left(d\,x^2+c\right)}^{3/2}}{3}+\frac{d\,\mathrm{atan}\left(\frac{d\,\sqrt{d\,x^2+c}\,\left(a^2\,d^2+12\,a\,b\,c\,d+8\,b^2\,c^2\right)\,5{}\mathrm{i}}{8\,\sqrt{c}\,\left(\frac{5\,a^2\,d^3}{8}+\frac{15\,a\,b\,c\,d^2}{2}+5\,b^2\,c^2\,d\right)}\right)\,\left(a^2\,d^2+12\,a\,b\,c\,d+8\,b^2\,c^2\right)\,5{}\mathrm{i}}{16\,\sqrt{c}}","Not used",1,"((c + d*x^2)^(1/2)*((b^2*c^4*d)/2 + (5*a^2*c^2*d^3)/16 + (7*a*b*c^3*d^2)/4) - (c + d*x^2)^(3/2)*((5*a^2*c*d^3)/6 + b^2*c^3*d + 4*a*b*c^2*d^2) + (c + d*x^2)^(5/2)*((11*a^2*d^3)/16 + (b^2*c^2*d)/2 + (9*a*b*c*d^2)/4))/(3*c*(c + d*x^2)^2 - 3*c^2*(c + d*x^2) - (c + d*x^2)^3 + c^3) + (2*b*d*(a*d - b*c) + 4*b^2*c*d)*(c + d*x^2)^(1/2) + (b^2*d*(c + d*x^2)^(3/2))/3 + (d*atan((d*(c + d*x^2)^(1/2)*(a^2*d^2 + 8*b^2*c^2 + 12*a*b*c*d)*5i)/(8*c^(1/2)*((5*a^2*d^3)/8 + 5*b^2*c^2*d + (15*a*b*c*d^2)/2)))*(a^2*d^2 + 8*b^2*c^2 + 12*a*b*c*d)*5i)/(16*c^(1/2))","B"
636,0,-1,194,0.000000,"\text{Not used}","int((x^4*(a + b*x^2)^2)/(c + d*x^2)^(1/2),x)","\int \frac{x^4\,{\left(b\,x^2+a\right)}^2}{\sqrt{d\,x^2+c}} \,d x","Not used",1,"int((x^4*(a + b*x^2)^2)/(c + d*x^2)^(1/2), x)","F"
637,1,105,112,0.664327,"\text{Not used}","int((x^3*(a + b*x^2)^2)/(c + d*x^2)^(1/2),x)","\sqrt{d\,x^2+c}\,\left(\frac{b^2\,x^6}{7\,d}-\frac{70\,a^2\,c\,d^2-112\,a\,b\,c^2\,d+48\,b^2\,c^3}{105\,d^4}+\frac{x^2\,\left(35\,a^2\,d^3-56\,a\,b\,c\,d^2+24\,b^2\,c^2\,d\right)}{105\,d^4}+\frac{2\,b\,x^4\,\left(7\,a\,d-3\,b\,c\right)}{35\,d^2}\right)","Not used",1,"(c + d*x^2)^(1/2)*((b^2*x^6)/(7*d) - (48*b^2*c^3 + 70*a^2*c*d^2 - 112*a*b*c^2*d)/(105*d^4) + (x^2*(35*a^2*d^3 + 24*b^2*c^2*d - 56*a*b*c*d^2))/(105*d^4) + (2*b*x^4*(7*a*d - 3*b*c))/(35*d^2))","B"
638,0,-1,146,0.000000,"\text{Not used}","int((x^2*(a + b*x^2)^2)/(c + d*x^2)^(1/2),x)","\int \frac{x^2\,{\left(b\,x^2+a\right)}^2}{\sqrt{d\,x^2+c}} \,d x","Not used",1,"int((x^2*(a + b*x^2)^2)/(c + d*x^2)^(1/2), x)","F"
639,1,68,74,0.654996,"\text{Not used}","int((x*(a + b*x^2)^2)/(c + d*x^2)^(1/2),x)","\sqrt{d\,x^2+c}\,\left(\frac{15\,a^2\,d^2-20\,a\,b\,c\,d+8\,b^2\,c^2}{15\,d^3}+\frac{b^2\,x^4}{5\,d}+\frac{2\,b\,x^2\,\left(5\,a\,d-2\,b\,c\right)}{15\,d^2}\right)","Not used",1,"(c + d*x^2)^(1/2)*((15*a^2*d^2 + 8*b^2*c^2 - 20*a*b*c*d)/(15*d^3) + (b^2*x^4)/(5*d) + (2*b*x^2*(5*a*d - 2*b*c))/(15*d^2))","B"
640,0,-1,107,0.000000,"\text{Not used}","int((a + b*x^2)^2/(c + d*x^2)^(1/2),x)","\int \frac{{\left(b\,x^2+a\right)}^2}{\sqrt{d\,x^2+c}} \,d x","Not used",1,"int((a + b*x^2)^2/(c + d*x^2)^(1/2), x)","F"
641,1,77,75,0.717619,"\text{Not used}","int((a + b*x^2)^2/(x*(c + d*x^2)^(1/2)),x)","\frac{b^2\,{\left(d\,x^2+c\right)}^{3/2}}{3\,d^2}-\frac{a^2\,\mathrm{atanh}\left(\frac{\sqrt{d\,x^2+c}}{\sqrt{c}}\right)}{\sqrt{c}}-\left(\frac{2\,b^2\,c-2\,a\,b\,d}{d^2}-\frac{b^2\,c}{d^2}\right)\,\sqrt{d\,x^2+c}","Not used",1,"(b^2*(c + d*x^2)^(3/2))/(3*d^2) - (a^2*atanh((c + d*x^2)^(1/2)/c^(1/2)))/c^(1/2) - ((2*b^2*c - 2*a*b*d)/d^2 - (b^2*c)/d^2)*(c + d*x^2)^(1/2)","B"
642,1,125,82,1.464316,"\text{Not used}","int((a + b*x^2)^2/(x^2*(c + d*x^2)^(1/2)),x)","\left\{\begin{array}{cl} \frac{-a^2+2\,a\,b\,x^2+\frac{b^2\,x^4}{3}}{\sqrt{c}\,x} & \text{\ if\ \ }d=0\\ \frac{2\,a\,b\,\ln\left(\sqrt{d}\,x+\sqrt{d\,x^2+c}\right)}{\sqrt{d}}+\frac{b^2\,x\,\sqrt{d\,x^2+c}}{2\,d}-\frac{a^2\,\sqrt{d\,x^2+c}}{c\,x}-\frac{b^2\,c\,\ln\left(2\,\sqrt{d}\,x+2\,\sqrt{d\,x^2+c}\right)}{2\,d^{3/2}} & \text{\ if\ \ }d\neq 0 \end{array}\right.","Not used",1,"piecewise(d == 0, (- a^2 + (b^2*x^4)/3 + 2*a*b*x^2)/(c^(1/2)*x), d ~= 0, (2*a*b*log(d^(1/2)*x + (c + d*x^2)^(1/2)))/d^(1/2) + (b^2*x*(c + d*x^2)^(1/2))/(2*d) - (a^2*(c + d*x^2)^(1/2))/(c*x) - (b^2*c*log(2*d^(1/2)*x + 2*(c + d*x^2)^(1/2)))/(2*d^(3/2)))","B"
643,1,65,80,0.936429,"\text{Not used}","int((a + b*x^2)^2/(x^3*(c + d*x^2)^(1/2)),x)","\frac{b^2\,\sqrt{d\,x^2+c}}{d}+\frac{a\,\mathrm{atanh}\left(\frac{\sqrt{d\,x^2+c}}{\sqrt{c}}\right)\,\left(a\,d-4\,b\,c\right)}{2\,c^{3/2}}-\frac{a^2\,\sqrt{d\,x^2+c}}{2\,c\,x^2}","Not used",1,"(b^2*(c + d*x^2)^(1/2))/d + (a*atanh((c + d*x^2)^(1/2)/c^(1/2))*(a*d - 4*b*c))/(2*c^(3/2)) - (a^2*(c + d*x^2)^(1/2))/(2*c*x^2)","B"
644,0,-1,84,0.000000,"\text{Not used}","int((a + b*x^2)^2/(x^4*(c + d*x^2)^(1/2)),x)","\int \frac{{\left(b\,x^2+a\right)}^2}{x^4\,\sqrt{d\,x^2+c}} \,d x","Not used",1,"int((a + b*x^2)^2/(x^4*(c + d*x^2)^(1/2)), x)","F"
645,1,129,106,1.062972,"\text{Not used}","int((a + b*x^2)^2/(x^5*(c + d*x^2)^(1/2)),x)","-\frac{\frac{\left(5\,a^2\,d^2-8\,a\,b\,c\,d\right)\,\sqrt{d\,x^2+c}}{8\,c}-\frac{\left(3\,a^2\,d^2-8\,a\,b\,c\,d\right)\,{\left(d\,x^2+c\right)}^{3/2}}{8\,c^2}}{{\left(d\,x^2+c\right)}^2-2\,c\,\left(d\,x^2+c\right)+c^2}-\frac{\mathrm{atanh}\left(\frac{\sqrt{d\,x^2+c}}{\sqrt{c}}\right)\,\left(3\,a^2\,d^2-8\,a\,b\,c\,d+8\,b^2\,c^2\right)}{8\,c^{5/2}}","Not used",1,"- (((5*a^2*d^2 - 8*a*b*c*d)*(c + d*x^2)^(1/2))/(8*c) - ((3*a^2*d^2 - 8*a*b*c*d)*(c + d*x^2)^(3/2))/(8*c^2))/((c + d*x^2)^2 - 2*c*(c + d*x^2) + c^2) - (atanh((c + d*x^2)^(1/2)/c^(1/2))*(3*a^2*d^2 + 8*b^2*c^2 - 8*a*b*c*d))/(8*c^(5/2))","B"
646,1,77,99,0.726506,"\text{Not used}","int((a + b*x^2)^2/(x^6*(c + d*x^2)^(1/2)),x)","-\frac{\sqrt{d\,x^2+c}\,\left(3\,a^2\,c^2-4\,a^2\,c\,d\,x^2+8\,a^2\,d^2\,x^4+10\,a\,b\,c^2\,x^2-20\,a\,b\,c\,d\,x^4+15\,b^2\,c^2\,x^4\right)}{15\,c^3\,x^5}","Not used",1,"-((c + d*x^2)^(1/2)*(3*a^2*c^2 + 8*a^2*d^2*x^4 + 15*b^2*c^2*x^4 + 10*a*b*c^2*x^2 - 4*a^2*c*d*x^2 - 20*a*b*c*d*x^4))/(15*c^3*x^5)","B"
647,1,207,151,1.147872,"\text{Not used}","int((a + b*x^2)^2/(x^7*(c + d*x^2)^(1/2)),x)","\frac{\frac{{\left(d\,x^2+c\right)}^{5/2}\,\left(5\,a^2\,d^3-12\,a\,b\,c\,d^2+8\,b^2\,c^2\,d\right)}{16\,c^3}-\frac{{\left(d\,x^2+c\right)}^{3/2}\,\left(5\,a^2\,d^3-12\,a\,b\,c\,d^2+6\,b^2\,c^2\,d\right)}{6\,c^2}+\frac{\sqrt{d\,x^2+c}\,\left(11\,a^2\,d^3-20\,a\,b\,c\,d^2+8\,b^2\,c^2\,d\right)}{16\,c}}{3\,c\,{\left(d\,x^2+c\right)}^2-3\,c^2\,\left(d\,x^2+c\right)-{\left(d\,x^2+c\right)}^3+c^3}+\frac{d\,\mathrm{atanh}\left(\frac{\sqrt{d\,x^2+c}}{\sqrt{c}}\right)\,\left(5\,a^2\,d^2-12\,a\,b\,c\,d+8\,b^2\,c^2\right)}{16\,c^{7/2}}","Not used",1,"(((c + d*x^2)^(5/2)*(5*a^2*d^3 + 8*b^2*c^2*d - 12*a*b*c*d^2))/(16*c^3) - ((c + d*x^2)^(3/2)*(5*a^2*d^3 + 6*b^2*c^2*d - 12*a*b*c*d^2))/(6*c^2) + ((c + d*x^2)^(1/2)*(11*a^2*d^3 + 8*b^2*c^2*d - 20*a*b*c*d^2))/(16*c))/(3*c*(c + d*x^2)^2 - 3*c^2*(c + d*x^2) - (c + d*x^2)^3 + c^3) + (d*atanh((c + d*x^2)^(1/2)/c^(1/2))*(5*a^2*d^2 + 8*b^2*c^2 - 12*a*b*c*d))/(16*c^(7/2))","B"
648,0,-1,197,0.000000,"\text{Not used}","int((x^4*(a + b*x^2)^2)/(c + d*x^2)^(3/2),x)","\int \frac{x^4\,{\left(b\,x^2+a\right)}^2}{{\left(d\,x^2+c\right)}^{3/2}} \,d x","Not used",1,"int((x^4*(a + b*x^2)^2)/(c + d*x^2)^(3/2), x)","F"
649,1,107,108,0.884645,"\text{Not used}","int((x^3*(a + b*x^2)^2)/(c + d*x^2)^(3/2),x)","\frac{30\,a^2\,c\,d^2+15\,a^2\,d^3\,x^2-80\,a\,b\,c^2\,d-40\,a\,b\,c\,d^2\,x^2+10\,a\,b\,d^3\,x^4+48\,b^2\,c^3+24\,b^2\,c^2\,d\,x^2-6\,b^2\,c\,d^2\,x^4+3\,b^2\,d^3\,x^6}{15\,d^4\,\sqrt{d\,x^2+c}}","Not used",1,"(48*b^2*c^3 + 30*a^2*c*d^2 + 15*a^2*d^3*x^2 + 3*b^2*d^3*x^6 + 24*b^2*c^2*d*x^2 - 6*b^2*c*d^2*x^4 - 80*a*b*c^2*d + 10*a*b*d^3*x^4 - 40*a*b*c*d^2*x^2)/(15*d^4*(c + d*x^2)^(1/2))","B"
650,0,-1,152,0.000000,"\text{Not used}","int((x^2*(a + b*x^2)^2)/(c + d*x^2)^(3/2),x)","\int \frac{x^2\,{\left(b\,x^2+a\right)}^2}{{\left(d\,x^2+c\right)}^{3/2}} \,d x","Not used",1,"int((x^2*(a + b*x^2)^2)/(c + d*x^2)^(3/2), x)","F"
651,1,75,73,0.673952,"\text{Not used}","int((x*(a + b*x^2)^2)/(c + d*x^2)^(3/2),x)","\frac{b^2\,{\left(d\,x^2+c\right)}^2-3\,a^2\,d^2-3\,b^2\,c^2-6\,b^2\,c\,\left(d\,x^2+c\right)+6\,a\,b\,d\,\left(d\,x^2+c\right)+6\,a\,b\,c\,d}{3\,d^3\,\sqrt{d\,x^2+c}}","Not used",1,"(b^2*(c + d*x^2)^2 - 3*a^2*d^2 - 3*b^2*c^2 - 6*b^2*c*(c + d*x^2) + 6*a*b*d*(c + d*x^2) + 6*a*b*c*d)/(3*d^3*(c + d*x^2)^(1/2))","B"
652,0,-1,106,0.000000,"\text{Not used}","int((a + b*x^2)^2/(c + d*x^2)^(3/2),x)","\int \frac{{\left(b\,x^2+a\right)}^2}{{\left(d\,x^2+c\right)}^{3/2}} \,d x","Not used",1,"int((a + b*x^2)^2/(c + d*x^2)^(3/2), x)","F"
653,1,76,75,0.862605,"\text{Not used}","int((a + b*x^2)^2/(x*(c + d*x^2)^(3/2)),x)","\frac{b^2\,\sqrt{d\,x^2+c}}{d^2}-\frac{a^2\,\mathrm{atanh}\left(\frac{\sqrt{d\,x^2+c}}{\sqrt{c}}\right)}{c^{3/2}}+\frac{a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2}{c\,d^2\,\sqrt{d\,x^2+c}}","Not used",1,"(b^2*(c + d*x^2)^(1/2))/d^2 - (a^2*atanh((c + d*x^2)^(1/2)/c^(1/2)))/c^(3/2) + (a^2*d^2 + b^2*c^2 - 2*a*b*c*d)/(c*d^2*(c + d*x^2)^(1/2))","B"
654,0,-1,91,0.000000,"\text{Not used}","int((a + b*x^2)^2/(x^2*(c + d*x^2)^(3/2)),x)","\int \frac{{\left(b\,x^2+a\right)}^2}{x^2\,{\left(d\,x^2+c\right)}^{3/2}} \,d x","Not used",1,"int((a + b*x^2)^2/(x^2*(c + d*x^2)^(3/2)), x)","F"
655,1,119,103,1.079624,"\text{Not used}","int((a + b*x^2)^2/(x^3*(c + d*x^2)^(3/2)),x)","\frac{\frac{a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2}{c}-\frac{\left(d\,x^2+c\right)\,\left(3\,a^2\,d^2-4\,a\,b\,c\,d+2\,b^2\,c^2\right)}{2\,c^2}}{d\,{\left(d\,x^2+c\right)}^{3/2}-c\,d\,\sqrt{d\,x^2+c}}+\frac{a\,\mathrm{atanh}\left(\frac{\sqrt{d\,x^2+c}}{\sqrt{c}}\right)\,\left(3\,a\,d-4\,b\,c\right)}{2\,c^{5/2}}","Not used",1,"((a^2*d^2 + b^2*c^2 - 2*a*b*c*d)/c - ((c + d*x^2)*(3*a^2*d^2 + 2*b^2*c^2 - 4*a*b*c*d))/(2*c^2))/(d*(c + d*x^2)^(3/2) - c*d*(c + d*x^2)^(1/2)) + (a*atanh((c + d*x^2)^(1/2)/c^(1/2))*(3*a*d - 4*b*c))/(2*c^(5/2))","B"
656,1,76,97,0.760074,"\text{Not used}","int((a + b*x^2)^2/(x^4*(c + d*x^2)^(3/2)),x)","-\frac{a^2\,c^2-4\,a^2\,c\,d\,x^2-8\,a^2\,d^2\,x^4+6\,a\,b\,c^2\,x^2+12\,a\,b\,c\,d\,x^4-3\,b^2\,c^2\,x^4}{3\,c^3\,x^3\,\sqrt{d\,x^2+c}}","Not used",1,"-(a^2*c^2 - 8*a^2*d^2*x^4 - 3*b^2*c^2*x^4 + 6*a*b*c^2*x^2 - 4*a^2*c*d*x^2 + 12*a*b*c*d*x^4)/(3*c^3*x^3*(c + d*x^2)^(1/2))","B"
657,1,179,145,1.063517,"\text{Not used}","int((a + b*x^2)^2/(x^5*(c + d*x^2)^(3/2)),x)","\frac{\frac{a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2}{c}-\frac{\left(d\,x^2+c\right)\,\left(25\,a^2\,d^2-40\,a\,b\,c\,d+16\,b^2\,c^2\right)}{8\,c^2}+\frac{{\left(d\,x^2+c\right)}^2\,\left(15\,a^2\,d^2-24\,a\,b\,c\,d+8\,b^2\,c^2\right)}{8\,c^3}}{{\left(d\,x^2+c\right)}^{5/2}-2\,c\,{\left(d\,x^2+c\right)}^{3/2}+c^2\,\sqrt{d\,x^2+c}}-\frac{\mathrm{atanh}\left(\frac{\sqrt{d\,x^2+c}}{\sqrt{c}}\right)\,\left(15\,a^2\,d^2-24\,a\,b\,c\,d+8\,b^2\,c^2\right)}{8\,c^{7/2}}","Not used",1,"((a^2*d^2 + b^2*c^2 - 2*a*b*c*d)/c - ((c + d*x^2)*(25*a^2*d^2 + 16*b^2*c^2 - 40*a*b*c*d))/(8*c^2) + ((c + d*x^2)^2*(15*a^2*d^2 + 8*b^2*c^2 - 24*a*b*c*d))/(8*c^3))/((c + d*x^2)^(5/2) - 2*c*(c + d*x^2)^(3/2) + c^2*(c + d*x^2)^(1/2)) - (atanh((c + d*x^2)^(1/2)/c^(1/2))*(15*a^2*d^2 + 8*b^2*c^2 - 24*a*b*c*d))/(8*c^(7/2))","B"
658,1,116,141,0.846663,"\text{Not used}","int((a + b*x^2)^2/(x^6*(c + d*x^2)^(3/2)),x)","-\frac{3\,a^2\,c^3-6\,a^2\,c^2\,d\,x^2+24\,a^2\,c\,d^2\,x^4+48\,a^2\,d^3\,x^6+10\,a\,b\,c^3\,x^2-40\,a\,b\,c^2\,d\,x^4-80\,a\,b\,c\,d^2\,x^6+15\,b^2\,c^3\,x^4+30\,b^2\,c^2\,d\,x^6}{15\,c^4\,x^5\,\sqrt{d\,x^2+c}}","Not used",1,"-(3*a^2*c^3 + 15*b^2*c^3*x^4 + 48*a^2*d^3*x^6 - 6*a^2*c^2*d*x^2 + 24*a^2*c*d^2*x^4 + 30*b^2*c^2*d*x^6 + 10*a*b*c^3*x^2 - 40*a*b*c^2*d*x^4 - 80*a*b*c*d^2*x^6)/(15*c^4*x^5*(c + d*x^2)^(1/2))","B"
659,1,246,190,1.340298,"\text{Not used}","int((a + b*x^2)^2/(x^7*(c + d*x^2)^(3/2)),x)","\frac{d\,\mathrm{atanh}\left(\frac{\sqrt{d\,x^2+c}}{\sqrt{c}}\right)\,\left(35\,a^2\,d^2-60\,a\,b\,c\,d+24\,b^2\,c^2\right)}{16\,c^{9/2}}-\frac{\frac{a^2\,d^3-2\,a\,b\,c\,d^2+b^2\,c^2\,d}{c}-\frac{\left(d\,x^2+c\right)\,\left(77\,a^2\,d^3-132\,a\,b\,c\,d^2+56\,b^2\,c^2\,d\right)}{16\,c^2}+\frac{{\left(d\,x^2+c\right)}^2\,\left(35\,a^2\,d^3-60\,a\,b\,c\,d^2+24\,b^2\,c^2\,d\right)}{6\,c^3}-\frac{{\left(d\,x^2+c\right)}^3\,\left(35\,a^2\,d^3-60\,a\,b\,c\,d^2+24\,b^2\,c^2\,d\right)}{16\,c^4}}{3\,c\,{\left(d\,x^2+c\right)}^{5/2}-{\left(d\,x^2+c\right)}^{7/2}+c^3\,\sqrt{d\,x^2+c}-3\,c^2\,{\left(d\,x^2+c\right)}^{3/2}}","Not used",1,"(d*atanh((c + d*x^2)^(1/2)/c^(1/2))*(35*a^2*d^2 + 24*b^2*c^2 - 60*a*b*c*d))/(16*c^(9/2)) - ((a^2*d^3 + b^2*c^2*d - 2*a*b*c*d^2)/c - ((c + d*x^2)*(77*a^2*d^3 + 56*b^2*c^2*d - 132*a*b*c*d^2))/(16*c^2) + ((c + d*x^2)^2*(35*a^2*d^3 + 24*b^2*c^2*d - 60*a*b*c*d^2))/(6*c^3) - ((c + d*x^2)^3*(35*a^2*d^3 + 24*b^2*c^2*d - 60*a*b*c*d^2))/(16*c^4))/(3*c*(c + d*x^2)^(5/2) - (c + d*x^2)^(7/2) + c^3*(c + d*x^2)^(1/2) - 3*c^2*(c + d*x^2)^(3/2))","B"
660,0,-1,202,0.000000,"\text{Not used}","int((x^4*(a + b*x^2)^2)/(c + d*x^2)^(5/2),x)","\int \frac{x^4\,{\left(b\,x^2+a\right)}^2}{{\left(d\,x^2+c\right)}^{5/2}} \,d x","Not used",1,"int((x^4*(a + b*x^2)^2)/(c + d*x^2)^(5/2), x)","F"
661,1,107,110,0.779751,"\text{Not used}","int((x^3*(a + b*x^2)^2)/(c + d*x^2)^(5/2),x)","-\frac{2\,a^2\,c\,d^2+3\,a^2\,d^3\,x^2-16\,a\,b\,c^2\,d-24\,a\,b\,c\,d^2\,x^2-6\,a\,b\,d^3\,x^4+16\,b^2\,c^3+24\,b^2\,c^2\,d\,x^2+6\,b^2\,c\,d^2\,x^4-b^2\,d^3\,x^6}{3\,d^4\,{\left(d\,x^2+c\right)}^{3/2}}","Not used",1,"-(16*b^2*c^3 + 2*a^2*c*d^2 + 3*a^2*d^3*x^2 - b^2*d^3*x^6 + 24*b^2*c^2*d*x^2 + 6*b^2*c*d^2*x^4 - 16*a*b*c^2*d - 6*a*b*d^3*x^4 - 24*a*b*c*d^2*x^2)/(3*d^4*(c + d*x^2)^(3/2))","B"
662,0,-1,121,0.000000,"\text{Not used}","int((x^2*(a + b*x^2)^2)/(c + d*x^2)^(5/2),x)","\int \frac{x^2\,{\left(b\,x^2+a\right)}^2}{{\left(d\,x^2+c\right)}^{5/2}} \,d x","Not used",1,"int((x^2*(a + b*x^2)^2)/(c + d*x^2)^(5/2), x)","F"
663,1,76,72,0.629310,"\text{Not used}","int((x*(a + b*x^2)^2)/(c + d*x^2)^(5/2),x)","\frac{3\,b^2\,{\left(d\,x^2+c\right)}^2-a^2\,d^2-b^2\,c^2+6\,b^2\,c\,\left(d\,x^2+c\right)-6\,a\,b\,d\,\left(d\,x^2+c\right)+2\,a\,b\,c\,d}{3\,d^3\,{\left(d\,x^2+c\right)}^{3/2}}","Not used",1,"(3*b^2*(c + d*x^2)^2 - a^2*d^2 - b^2*c^2 + 6*b^2*c*(c + d*x^2) - 6*a*b*d*(c + d*x^2) + 2*a*b*c*d)/(3*d^3*(c + d*x^2)^(3/2))","B"
664,0,-1,105,0.000000,"\text{Not used}","int((a + b*x^2)^2/(c + d*x^2)^(5/2),x)","\int \frac{{\left(b\,x^2+a\right)}^2}{{\left(d\,x^2+c\right)}^{5/2}} \,d x","Not used",1,"int((a + b*x^2)^2/(c + d*x^2)^(5/2), x)","F"
665,1,90,88,0.803249,"\text{Not used}","int((a + b*x^2)^2/(x*(c + d*x^2)^(5/2)),x)","\frac{\frac{a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2}{3\,c}+\frac{\left(a^2\,d^2-b^2\,c^2\right)\,\left(d\,x^2+c\right)}{c^2}}{d^2\,{\left(d\,x^2+c\right)}^{3/2}}-\frac{a^2\,\mathrm{atanh}\left(\frac{\sqrt{d\,x^2+c}}{\sqrt{c}}\right)}{c^{5/2}}","Not used",1,"((a^2*d^2 + b^2*c^2 - 2*a*b*c*d)/(3*c) + ((a^2*d^2 - b^2*c^2)*(c + d*x^2))/c^2)/(d^2*(c + d*x^2)^(3/2)) - (a^2*atanh((c + d*x^2)^(1/2)/c^(1/2)))/c^(5/2)","B"
666,1,77,90,0.646577,"\text{Not used}","int((a + b*x^2)^2/(x^2*(c + d*x^2)^(5/2)),x)","-\frac{3\,a^2\,c^2+12\,a^2\,c\,d\,x^2+8\,a^2\,d^2\,x^4-6\,a\,b\,c^2\,x^2-4\,a\,b\,c\,d\,x^4-b^2\,c^2\,x^4}{3\,c^3\,x\,{\left(d\,x^2+c\right)}^{3/2}}","Not used",1,"-(3*a^2*c^2 + 8*a^2*d^2*x^4 - b^2*c^2*x^4 - 6*a*b*c^2*x^2 + 12*a^2*c*d*x^2 - 4*a*b*c*d*x^4)/(3*c^3*x*(c + d*x^2)^(3/2))","B"
667,1,147,131,0.897134,"\text{Not used}","int((a + b*x^2)^2/(x^3*(c + d*x^2)^(5/2)),x)","\frac{a\,\mathrm{atanh}\left(\frac{\sqrt{d\,x^2+c}}{\sqrt{c}}\right)\,\left(5\,a\,d-4\,b\,c\right)}{2\,c^{7/2}}-\frac{\frac{\left(d\,x^2+c\right)\,\left(-5\,a^2\,d^2+4\,a\,b\,c\,d+b^2\,c^2\right)}{3\,c^2}-\frac{a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2}{3\,c}+\frac{d\,{\left(d\,x^2+c\right)}^2\,\left(5\,a^2\,d-4\,a\,b\,c\right)}{2\,c^3}}{d\,{\left(d\,x^2+c\right)}^{5/2}-c\,d\,{\left(d\,x^2+c\right)}^{3/2}}","Not used",1,"(a*atanh((c + d*x^2)^(1/2)/c^(1/2))*(5*a*d - 4*b*c))/(2*c^(7/2)) - (((c + d*x^2)*(b^2*c^2 - 5*a^2*d^2 + 4*a*b*c*d))/(3*c^2) - (a^2*d^2 + b^2*c^2 - 2*a*b*c*d)/(3*c) + (d*(c + d*x^2)^2*(5*a^2*d - 4*a*b*c))/(2*c^3))/(d*(c + d*x^2)^(5/2) - c*d*(c + d*x^2)^(3/2))","B"
668,1,187,131,0.733187,"\text{Not used}","int((a + b*x^2)^2/(x^4*(c + d*x^2)^(5/2)),x)","\frac{b^2\,c^4\,x^2-a^2\,c^3\,d-16\,a^2\,d\,{\left(d\,x^2+c\right)}^3+2\,a\,b\,c^4+b^2\,c^3\,x^2\,\left(d\,x^2+c\right)+16\,a\,b\,c\,{\left(d\,x^2+c\right)}^3+6\,a\,b\,c^3\,\left(d\,x^2+c\right)-2\,b^2\,c^2\,x^2\,{\left(d\,x^2+c\right)}^2-24\,a\,b\,c^2\,{\left(d\,x^2+c\right)}^2+24\,a^2\,c\,d\,{\left(d\,x^2+c\right)}^2-6\,a^2\,c^2\,d\,\left(d\,x^2+c\right)}{{\left(d\,x^2+c\right)}^{3/2}\,\left(3\,c^5\,x-3\,c^4\,x\,\left(d\,x^2+c\right)\right)}","Not used",1,"(b^2*c^4*x^2 - a^2*c^3*d - 16*a^2*d*(c + d*x^2)^3 + 2*a*b*c^4 + b^2*c^3*x^2*(c + d*x^2) + 16*a*b*c*(c + d*x^2)^3 + 6*a*b*c^3*(c + d*x^2) - 2*b^2*c^2*x^2*(c + d*x^2)^2 - 24*a*b*c^2*(c + d*x^2)^2 + 24*a^2*c*d*(c + d*x^2)^2 - 6*a^2*c^2*d*(c + d*x^2))/((c + d*x^2)^(3/2)*(3*c^5*x - 3*c^4*x*(c + d*x^2)))","B"
669,1,216,185,1.109982,"\text{Not used}","int((a + b*x^2)^2/(x^5*(c + d*x^2)^(5/2)),x)","\frac{\frac{a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2}{3\,c}+\frac{\left(d\,x^2+c\right)\,\left(7\,a^2\,d^2-8\,a\,b\,c\,d+b^2\,c^2\right)}{3\,c^2}-\frac{5\,{\left(d\,x^2+c\right)}^2\,\left(35\,a^2\,d^2-40\,a\,b\,c\,d+8\,b^2\,c^2\right)}{24\,c^3}+\frac{{\left(d\,x^2+c\right)}^3\,\left(35\,a^2\,d^2-40\,a\,b\,c\,d+8\,b^2\,c^2\right)}{8\,c^4}}{{\left(d\,x^2+c\right)}^{7/2}-2\,c\,{\left(d\,x^2+c\right)}^{5/2}+c^2\,{\left(d\,x^2+c\right)}^{3/2}}-\frac{\mathrm{atanh}\left(\frac{\sqrt{d\,x^2+c}}{\sqrt{c}}\right)\,\left(35\,a^2\,d^2-40\,a\,b\,c\,d+8\,b^2\,c^2\right)}{8\,c^{9/2}}","Not used",1,"((a^2*d^2 + b^2*c^2 - 2*a*b*c*d)/(3*c) + ((c + d*x^2)*(7*a^2*d^2 + b^2*c^2 - 8*a*b*c*d))/(3*c^2) - (5*(c + d*x^2)^2*(35*a^2*d^2 + 8*b^2*c^2 - 40*a*b*c*d))/(24*c^3) + ((c + d*x^2)^3*(35*a^2*d^2 + 8*b^2*c^2 - 40*a*b*c*d))/(8*c^4))/((c + d*x^2)^(7/2) - 2*c*(c + d*x^2)^(5/2) + c^2*(c + d*x^2)^(3/2)) - (atanh((c + d*x^2)^(1/2)/c^(1/2))*(35*a^2*d^2 + 8*b^2*c^2 - 40*a*b*c*d))/(8*c^(9/2))","B"
670,1,298,183,0.979235,"\text{Not used}","int((a + b*x^2)^2/(x^6*(c + d*x^2)^(5/2)),x)","\frac{2\,a\,\sqrt{d\,x^2+c}\,\left(7\,a\,d-5\,b\,c\right)}{15\,c^4\,x^3}-\frac{\frac{73\,a^2\,c^2\,d^2-80\,a\,b\,c^3\,d+15\,b^2\,c^4}{30\,c^5}-\frac{c\,\left(\frac{d\,\left(73\,a^2\,c^2\,d^2-80\,a\,b\,c^3\,d+15\,b^2\,c^4\right)}{18\,c^6}+\frac{c\,\left(\frac{4\,a\,d^3\,\left(7\,a\,d-5\,b\,c\right)}{45\,c^5}-\frac{a\,d^3\,\left(43\,a\,d-35\,b\,c\right)}{9\,c^5}\right)}{d}+\frac{a\,d^2\,\left(43\,a\,d-35\,b\,c\right)}{15\,c^4}\right)}{d}}{x\,{\left(d\,x^2+c\right)}^{3/2}}-\frac{a^2\,\sqrt{d\,x^2+c}}{5\,c^3\,x^5}-\frac{x^2\,\left(\frac{2\,d\,\left(78\,a^2\,c\,d^2-90\,a\,b\,c^2\,d+20\,b^2\,c^3\right)}{15\,c^6}-\frac{4\,a\,d^2\,\left(7\,a\,d-5\,b\,c\right)}{15\,c^5}\right)+\frac{78\,a^2\,c\,d^2-90\,a\,b\,c^2\,d+20\,b^2\,c^3}{15\,c^5}}{x\,\sqrt{d\,x^2+c}}","Not used",1,"(2*a*(c + d*x^2)^(1/2)*(7*a*d - 5*b*c))/(15*c^4*x^3) - ((15*b^2*c^4 + 73*a^2*c^2*d^2 - 80*a*b*c^3*d)/(30*c^5) - (c*((d*(15*b^2*c^4 + 73*a^2*c^2*d^2 - 80*a*b*c^3*d))/(18*c^6) + (c*((4*a*d^3*(7*a*d - 5*b*c))/(45*c^5) - (a*d^3*(43*a*d - 35*b*c))/(9*c^5)))/d + (a*d^2*(43*a*d - 35*b*c))/(15*c^4)))/d)/(x*(c + d*x^2)^(3/2)) - (a^2*(c + d*x^2)^(1/2))/(5*c^3*x^5) - (x^2*((2*d*(20*b^2*c^3 + 78*a^2*c*d^2 - 90*a*b*c^2*d))/(15*c^6) - (4*a*d^2*(7*a*d - 5*b*c))/(15*c^5)) + (20*b^2*c^3 + 78*a^2*c*d^2 - 90*a*b*c^2*d)/(15*c^5))/(x*(c + d*x^2)^(1/2))","B"
671,1,51,72,0.647711,"\text{Not used}","int(x^5/((a + b*x^2)*(d*x^2)^(1/2)),x)","\frac{{\left(x^2\right)}^{3/2}}{3\,b\,\sqrt{d}}+\frac{a^{3/2}\,\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{x^2}}{\sqrt{a}}\right)}{b^{5/2}\,\sqrt{d}}-\frac{a\,\sqrt{x^2}}{b^2\,\sqrt{d}}","Not used",1,"(x^2)^(3/2)/(3*b*d^(1/2)) + (a^(3/2)*atan((b^(1/2)*(x^2)^(1/2))/a^(1/2)))/(b^(5/2)*d^(1/2)) - (a*(x^2)^(1/2))/(b^2*d^(1/2))","B"
672,1,37,52,0.617561,"\text{Not used}","int(x^3/((a + b*x^2)*(d*x^2)^(1/2)),x)","\frac{\sqrt{x^2}}{b\,\sqrt{d}}-\frac{\sqrt{a}\,\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{x^2}}{\sqrt{a}}\right)}{b^{3/2}\,\sqrt{d}}","Not used",1,"(x^2)^(1/2)/(b*d^(1/2)) - (a^(1/2)*atan((b^(1/2)*(x^2)^(1/2))/a^(1/2)))/(b^(3/2)*d^(1/2))","B"
673,1,23,34,0.608895,"\text{Not used}","int(x/((a + b*x^2)*(d*x^2)^(1/2)),x)","\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{x^2}}{\sqrt{a}}\right)}{\sqrt{a}\,\sqrt{b}\,\sqrt{d}}","Not used",1,"atan((b^(1/2)*(x^2)^(1/2))/a^(1/2))/(a^(1/2)*b^(1/2)*d^(1/2))","B"
674,1,38,50,0.620213,"\text{Not used}","int(1/(x*(a + b*x^2)*(d*x^2)^(1/2)),x)","-\frac{1}{a\,\sqrt{d}\,\sqrt{x^2}}-\frac{\sqrt{b}\,\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{x^2}}{\sqrt{a}}\right)}{a^{3/2}\,\sqrt{d}}","Not used",1,"- 1/(a*d^(1/2)*(x^2)^(1/2)) - (b^(1/2)*atan((b^(1/2)*(x^2)^(1/2))/a^(1/2)))/(a^(3/2)*d^(1/2))","B"
675,1,53,68,0.633111,"\text{Not used}","int(1/(x^3*(a + b*x^2)*(d*x^2)^(1/2)),x)","\frac{b^{3/2}\,\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{x^2}}{\sqrt{a}}\right)}{a^{5/2}\,\sqrt{d}}-\frac{1}{3\,a\,\sqrt{d}\,{\left(x^2\right)}^{3/2}}+\frac{b\,x^2}{a^2\,\sqrt{d}\,{\left(x^2\right)}^{3/2}}","Not used",1,"(b^(3/2)*atan((b^(1/2)*(x^2)^(1/2))/a^(1/2)))/(a^(5/2)*d^(1/2)) - 1/(3*a*d^(1/2)*(x^2)^(3/2)) + (b*x^2)/(a^2*d^(1/2)*(x^2)^(3/2))","B"
676,0,-1,157,0.000000,"\text{Not used}","int((x^4*(c + d*x^2)^(1/2))/(a + b*x^2),x)","\int \frac{x^4\,\sqrt{d\,x^2+c}}{b\,x^2+a} \,d x","Not used",1,"int((x^4*(c + d*x^2)^(1/2))/(a + b*x^2), x)","F"
677,1,86,88,0.592246,"\text{Not used}","int((x^3*(c + d*x^2)^(1/2))/(a + b*x^2),x)","\frac{{\left(d\,x^2+c\right)}^{3/2}}{3\,b\,d}-\frac{a\,\sqrt{d\,x^2+c}}{b^2}+\frac{a\,\mathrm{atan}\left(\frac{a\,\sqrt{b}\,\sqrt{d\,x^2+c}\,\sqrt{a\,d-b\,c}}{a^2\,d-a\,b\,c}\right)\,\sqrt{a\,d-b\,c}}{b^{5/2}}","Not used",1,"(c + d*x^2)^(3/2)/(3*b*d) - (a*(c + d*x^2)^(1/2))/b^2 + (a*atan((a*b^(1/2)*(c + d*x^2)^(1/2)*(a*d - b*c)^(1/2))/(a^2*d - a*b*c))*(a*d - b*c)^(1/2))/b^(5/2)","B"
678,0,-1,112,0.000000,"\text{Not used}","int((x^2*(c + d*x^2)^(1/2))/(a + b*x^2),x)","\int \frac{x^2\,\sqrt{d\,x^2+c}}{b\,x^2+a} \,d x","Not used",1,"int((x^2*(c + d*x^2)^(1/2))/(a + b*x^2), x)","F"
679,1,53,65,0.585578,"\text{Not used}","int((x*(c + d*x^2)^(1/2))/(a + b*x^2),x)","\frac{\sqrt{d\,x^2+c}}{b}-\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d\,x^2+c}}{\sqrt{a\,d-b\,c}}\right)\,\sqrt{a\,d-b\,c}}{b^{3/2}}","Not used",1,"(c + d*x^2)^(1/2)/b - (atan((b^(1/2)*(c + d*x^2)^(1/2))/(a*d - b*c)^(1/2))*(a*d - b*c)^(1/2))/b^(3/2)","B"
680,0,-1,81,0.000000,"\text{Not used}","int((c + d*x^2)^(1/2)/(a + b*x^2),x)","\left\{\begin{array}{cl} \frac{\sqrt{-d}\,\mathrm{asin}\left(x\,\sqrt{-\frac{d}{c}}\right)}{a} & \text{\ if\ \ }\left(\left(c+a\,d=0\wedge b=-1\right)\vee a\,d=b\,c\right)\wedge d<0\\ \frac{\sqrt{d}\,\ln\left(2\,\sqrt{d}\,x+2\,\sqrt{d\,x^2+c}\right)}{b}+\frac{\mathrm{atan}\left(\frac{x\,\sqrt{b\,c-a\,d}}{\sqrt{a}\,\sqrt{d\,x^2+c}}\right)\,\sqrt{b\,c-a\,d}}{\sqrt{a}\,b} & \text{\ if\ \ }c\neq 0\wedge \left(\left(\left(c+a\,d\neq 0\vee b\neq -1\right)\wedge a\,d\neq b\,c\right)\vee \neg d<0\right)\\ \int \frac{\sqrt{d\,x^2+c}}{b\,x^2+a} \,d x & \text{\ if\ \ }\left(\left(\left(\left(c+a\,d=0\wedge b=-1\right)\vee a\,d=b\,c\right)\wedge d<0\right)\vee c=0\right)\wedge \left(\left(\left(c+a\,d\neq 0\vee b\neq -1\right)\wedge a\,d\neq b\,c\right)\vee \neg d<0\right) \end{array}\right.","Not used",1,"piecewise((c + a*d == 0 & b == -1 | a*d == b*c) & d < 0, ((-d)^(1/2)*asin(x*(-d/c)^(1/2)))/a, c ~= 0 & ((c + a*d ~= 0 | b ~= -1) & a*d ~= b*c | ~d < 0), (d^(1/2)*log(2*d^(1/2)*x + 2*(c + d*x^2)^(1/2)))/b + (atan((x*(- a*d + b*c)^(1/2))/(a^(1/2)*(c + d*x^2)^(1/2)))*(- a*d + b*c)^(1/2))/(a^(1/2)*b), ((c + a*d == 0 & b == -1 | a*d == b*c) & d < 0 | c == 0) & ((c + a*d ~= 0 | b ~= -1) & a*d ~= b*c | ~d < 0), int((c + d*x^2)^(1/2)/(a + b*x^2), x))","F"
681,1,103,80,0.725168,"\text{Not used}","int((c + d*x^2)^(1/2)/(x*(a + b*x^2)),x)","\frac{\mathrm{atanh}\left(\frac{2\,a\,b^2\,c\,d^3\,\sqrt{d\,x^2+c}\,\sqrt{b^2\,c-a\,b\,d}}{2\,a\,b^3\,c^2\,d^3-2\,a^2\,b^2\,c\,d^4}\right)\,\sqrt{b^2\,c-a\,b\,d}}{a\,b}-\frac{\sqrt{c}\,\mathrm{atanh}\left(\frac{\sqrt{d\,x^2+c}}{\sqrt{c}}\right)}{a}","Not used",1,"(atanh((2*a*b^2*c*d^3*(c + d*x^2)^(1/2)*(b^2*c - a*b*d)^(1/2))/(2*a*b^3*c^2*d^3 - 2*a^2*b^2*c*d^4))*(b^2*c - a*b*d)^(1/2))/(a*b) - (c^(1/2)*atanh((c + d*x^2)^(1/2)/c^(1/2)))/a","B"
682,0,-1,70,0.000000,"\text{Not used}","int((c + d*x^2)^(1/2)/(x^2*(a + b*x^2)),x)","\int \frac{\sqrt{d\,x^2+c}}{x^2\,\left(b\,x^2+a\right)} \,d x","Not used",1,"int((c + d*x^2)^(1/2)/(x^2*(a + b*x^2)), x)","F"
683,1,268,113,0.992315,"\text{Not used}","int((c + d*x^2)^(1/2)/(x^3*(a + b*x^2)),x)","\frac{\mathrm{atanh}\left(\frac{b^3\,d^4\,\sqrt{d\,x^2+c}\,\sqrt{b^2\,c-a\,b\,d}}{2\,\left(\frac{a\,b^3\,d^5}{2}-\frac{b^4\,c\,d^4}{2}\right)}\right)\,\sqrt{b^2\,c-a\,b\,d}}{a^2}-\frac{\sqrt{d\,x^2+c}}{2\,a\,x^2}-\frac{\mathrm{atanh}\left(\frac{b^4\,\sqrt{c}\,d^4\,\sqrt{d\,x^2+c}}{2\,\left(\frac{b^4\,c\,d^4}{2}-\frac{3\,a\,b^3\,d^5}{4}+\frac{a^2\,b^2\,d^6}{4\,c}\right)}-\frac{3\,b^3\,d^5\,\sqrt{d\,x^2+c}}{4\,\sqrt{c}\,\left(\frac{a\,b^2\,d^6}{4\,c}-\frac{3\,b^3\,d^5}{4}+\frac{b^4\,c\,d^4}{2\,a}\right)}+\frac{b^2\,d^6\,\sqrt{d\,x^2+c}}{4\,c^{3/2}\,\left(\frac{b^2\,d^6}{4\,c}-\frac{3\,b^3\,d^5}{4\,a}+\frac{b^4\,c\,d^4}{2\,a^2}\right)}\right)\,\left(a\,d-2\,b\,c\right)}{2\,a^2\,\sqrt{c}}","Not used",1,"(atanh((b^3*d^4*(c + d*x^2)^(1/2)*(b^2*c - a*b*d)^(1/2))/(2*((a*b^3*d^5)/2 - (b^4*c*d^4)/2)))*(b^2*c - a*b*d)^(1/2))/a^2 - (c + d*x^2)^(1/2)/(2*a*x^2) - (atanh((b^4*c^(1/2)*d^4*(c + d*x^2)^(1/2))/(2*((b^4*c*d^4)/2 - (3*a*b^3*d^5)/4 + (a^2*b^2*d^6)/(4*c))) - (3*b^3*d^5*(c + d*x^2)^(1/2))/(4*c^(1/2)*((a*b^2*d^6)/(4*c) - (3*b^3*d^5)/4 + (b^4*c*d^4)/(2*a))) + (b^2*d^6*(c + d*x^2)^(1/2))/(4*c^(3/2)*((b^2*d^6)/(4*c) - (3*b^3*d^5)/(4*a) + (b^4*c*d^4)/(2*a^2))))*(a*d - 2*b*c))/(2*a^2*c^(1/2))","B"
684,0,-1,105,0.000000,"\text{Not used}","int((c + d*x^2)^(1/2)/(x^4*(a + b*x^2)),x)","\int \frac{\sqrt{d\,x^2+c}}{x^4\,\left(b\,x^2+a\right)} \,d x","Not used",1,"int((c + d*x^2)^(1/2)/(x^4*(a + b*x^2)), x)","F"
685,0,-1,210,0.000000,"\text{Not used}","int((x^4*(c + d*x^2)^(3/2))/(a + b*x^2),x)","\int \frac{x^4\,{\left(d\,x^2+c\right)}^{3/2}}{b\,x^2+a} \,d x","Not used",1,"int((x^4*(c + d*x^2)^(3/2))/(a + b*x^2), x)","F"
686,1,179,115,0.654913,"\text{Not used}","int((x^3*(c + d*x^2)^(3/2))/(a + b*x^2),x)","\frac{{\left(d\,x^2+c\right)}^{5/2}}{5\,b\,d}-{\left(d\,x^2+c\right)}^{3/2}\,\left(\frac{c}{3\,b\,d}+\frac{a\,d^2-b\,c\,d}{3\,b^2\,d^2}\right)-\frac{a\,\mathrm{atan}\left(\frac{a\,\sqrt{b}\,\sqrt{d\,x^2+c}\,{\left(a\,d-b\,c\right)}^{3/2}}{a^3\,d^2-2\,a^2\,b\,c\,d+a\,b^2\,c^2}\right)\,{\left(a\,d-b\,c\right)}^{3/2}}{b^{7/2}}+\frac{\sqrt{d\,x^2+c}\,\left(a\,d^2-b\,c\,d\right)\,\left(\frac{c}{b\,d}+\frac{a\,d^2-b\,c\,d}{b^2\,d^2}\right)}{b\,d}","Not used",1,"(c + d*x^2)^(5/2)/(5*b*d) - (c + d*x^2)^(3/2)*(c/(3*b*d) + (a*d^2 - b*c*d)/(3*b^2*d^2)) - (a*atan((a*b^(1/2)*(c + d*x^2)^(1/2)*(a*d - b*c)^(3/2))/(a^3*d^2 + a*b^2*c^2 - 2*a^2*b*c*d))*(a*d - b*c)^(3/2))/b^(7/2) + ((c + d*x^2)^(1/2)*(a*d^2 - b*c*d)*(c/(b*d) + (a*d^2 - b*c*d)/(b^2*d^2)))/(b*d)","B"
687,0,-1,158,0.000000,"\text{Not used}","int((x^2*(c + d*x^2)^(3/2))/(a + b*x^2),x)","\int \frac{x^2\,{\left(d\,x^2+c\right)}^{3/2}}{b\,x^2+a} \,d x","Not used",1,"int((x^2*(c + d*x^2)^(3/2))/(a + b*x^2), x)","F"
688,1,98,91,0.622999,"\text{Not used}","int((x*(c + d*x^2)^(3/2))/(a + b*x^2),x)","\frac{{\left(d\,x^2+c\right)}^{3/2}}{3\,b}-\frac{\sqrt{d\,x^2+c}\,\left(a\,d-b\,c\right)}{b^2}+\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d\,x^2+c}\,{\left(a\,d-b\,c\right)}^{3/2}}{a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2}\right)\,{\left(a\,d-b\,c\right)}^{3/2}}{b^{5/2}}","Not used",1,"(c + d*x^2)^(3/2)/(3*b) - ((c + d*x^2)^(1/2)*(a*d - b*c))/b^2 + (atan((b^(1/2)*(c + d*x^2)^(1/2)*(a*d - b*c)^(3/2))/(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))*(a*d - b*c)^(3/2))/b^(5/2)","B"
689,0,-1,113,0.000000,"\text{Not used}","int((c + d*x^2)^(3/2)/(a + b*x^2),x)","\int \frac{{\left(d\,x^2+c\right)}^{3/2}}{b\,x^2+a} \,d x","Not used",1,"int((c + d*x^2)^(3/2)/(a + b*x^2), x)","F"
690,1,711,96,0.805845,"\text{Not used}","int((c + d*x^2)^(3/2)/(x*(a + b*x^2)),x)","\frac{d\,\sqrt{d\,x^2+c}}{b}-\frac{\mathrm{atanh}\left(\frac{2\,a^3\,d^6\,\sqrt{d\,x^2+c}\,\sqrt{c^3}}{2\,a^3\,c^2\,d^6-8\,a^2\,b\,c^3\,d^5+12\,a\,b^2\,c^4\,d^4-6\,b^3\,c^5\,d^3}+\frac{8\,a^2\,c\,d^5\,\sqrt{d\,x^2+c}\,\sqrt{c^3}}{8\,a^2\,c^3\,d^5+6\,b^2\,c^5\,d^3-\frac{2\,a^3\,c^2\,d^6}{b}-12\,a\,b\,c^4\,d^4}+\frac{6\,b^2\,c^3\,d^3\,\sqrt{d\,x^2+c}\,\sqrt{c^3}}{8\,a^2\,c^3\,d^5+6\,b^2\,c^5\,d^3-\frac{2\,a^3\,c^2\,d^6}{b}-12\,a\,b\,c^4\,d^4}-\frac{12\,a\,b\,c^2\,d^4\,\sqrt{d\,x^2+c}\,\sqrt{c^3}}{8\,a^2\,c^3\,d^5+6\,b^2\,c^5\,d^3-\frac{2\,a^3\,c^2\,d^6}{b}-12\,a\,b\,c^4\,d^4}\right)\,\sqrt{c^3}}{a}+\frac{\mathrm{atanh}\left(\frac{6\,c^3\,d^3\,\sqrt{d\,x^2+c}\,\sqrt{-a^3\,b^3\,d^3+3\,a^2\,b^4\,c\,d^2-3\,a\,b^5\,c^2\,d+b^6\,c^3}}{6\,b^3\,c^5\,d^3-10\,a^3\,c^2\,d^6-18\,a\,b^2\,c^4\,d^4+20\,a^2\,b\,c^3\,d^5+\frac{2\,a^4\,c\,d^7}{b}}-\frac{6\,a\,c^2\,d^4\,\sqrt{d\,x^2+c}\,\sqrt{-a^3\,b^3\,d^3+3\,a^2\,b^4\,c\,d^2-3\,a\,b^5\,c^2\,d+b^6\,c^3}}{2\,a^4\,c\,d^7-10\,a^3\,b\,c^2\,d^6+20\,a^2\,b^2\,c^3\,d^5-18\,a\,b^3\,c^4\,d^4+6\,b^4\,c^5\,d^3}+\frac{2\,a^2\,c\,d^5\,\sqrt{d\,x^2+c}\,\sqrt{-a^3\,b^3\,d^3+3\,a^2\,b^4\,c\,d^2-3\,a\,b^5\,c^2\,d+b^6\,c^3}}{2\,a^4\,b\,c\,d^7-10\,a^3\,b^2\,c^2\,d^6+20\,a^2\,b^3\,c^3\,d^5-18\,a\,b^4\,c^4\,d^4+6\,b^5\,c^5\,d^3}\right)\,\sqrt{-b^3\,{\left(a\,d-b\,c\right)}^3}}{a\,b^3}","Not used",1,"(d*(c + d*x^2)^(1/2))/b - (atanh((2*a^3*d^6*(c + d*x^2)^(1/2)*(c^3)^(1/2))/(2*a^3*c^2*d^6 - 6*b^3*c^5*d^3 + 12*a*b^2*c^4*d^4 - 8*a^2*b*c^3*d^5) + (8*a^2*c*d^5*(c + d*x^2)^(1/2)*(c^3)^(1/2))/(8*a^2*c^3*d^5 + 6*b^2*c^5*d^3 - (2*a^3*c^2*d^6)/b - 12*a*b*c^4*d^4) + (6*b^2*c^3*d^3*(c + d*x^2)^(1/2)*(c^3)^(1/2))/(8*a^2*c^3*d^5 + 6*b^2*c^5*d^3 - (2*a^3*c^2*d^6)/b - 12*a*b*c^4*d^4) - (12*a*b*c^2*d^4*(c + d*x^2)^(1/2)*(c^3)^(1/2))/(8*a^2*c^3*d^5 + 6*b^2*c^5*d^3 - (2*a^3*c^2*d^6)/b - 12*a*b*c^4*d^4))*(c^3)^(1/2))/a + (atanh((6*c^3*d^3*(c + d*x^2)^(1/2)*(b^6*c^3 - a^3*b^3*d^3 + 3*a^2*b^4*c*d^2 - 3*a*b^5*c^2*d)^(1/2))/(6*b^3*c^5*d^3 - 10*a^3*c^2*d^6 - 18*a*b^2*c^4*d^4 + 20*a^2*b*c^3*d^5 + (2*a^4*c*d^7)/b) - (6*a*c^2*d^4*(c + d*x^2)^(1/2)*(b^6*c^3 - a^3*b^3*d^3 + 3*a^2*b^4*c*d^2 - 3*a*b^5*c^2*d)^(1/2))/(2*a^4*c*d^7 + 6*b^4*c^5*d^3 - 18*a*b^3*c^4*d^4 - 10*a^3*b*c^2*d^6 + 20*a^2*b^2*c^3*d^5) + (2*a^2*c*d^5*(c + d*x^2)^(1/2)*(b^6*c^3 - a^3*b^3*d^3 + 3*a^2*b^4*c*d^2 - 3*a*b^5*c^2*d)^(1/2))/(6*b^5*c^5*d^3 - 18*a*b^4*c^4*d^4 + 20*a^2*b^3*c^3*d^5 - 10*a^3*b^2*c^2*d^6 + 2*a^4*b*c*d^7))*(-b^3*(a*d - b*c)^3)^(1/2))/(a*b^3)","B"
691,0,-1,102,0.000000,"\text{Not used}","int((c + d*x^2)^(3/2)/(x^2*(a + b*x^2)),x)","\int \frac{{\left(d\,x^2+c\right)}^{3/2}}{x^2\,\left(b\,x^2+a\right)} \,d x","Not used",1,"int((c + d*x^2)^(3/2)/(x^2*(a + b*x^2)), x)","F"
692,1,560,114,1.159381,"\text{Not used}","int((c + d*x^2)^(3/2)/(x^3*(a + b*x^2)),x)","-\frac{c\,\sqrt{d\,x^2+c}}{2\,a\,x^2}-\frac{\sqrt{c}\,\mathrm{atanh}\left(\frac{29\,b^2\,c^{3/2}\,d^6\,\sqrt{d\,x^2+c}}{4\,\left(\frac{29\,b^2\,c^2\,d^6}{4}-3\,a\,b\,c\,d^7-\frac{23\,b^3\,c^3\,d^5}{4\,a}+\frac{3\,b^4\,c^4\,d^4}{2\,a^2}\right)}+\frac{23\,b^3\,c^{5/2}\,d^5\,\sqrt{d\,x^2+c}}{4\,\left(\frac{23\,b^3\,c^3\,d^5}{4}-\frac{29\,a\,b^2\,c^2\,d^6}{4}-\frac{3\,b^4\,c^4\,d^4}{2\,a}+3\,a^2\,b\,c\,d^7\right)}+\frac{3\,b^4\,c^{7/2}\,d^4\,\sqrt{d\,x^2+c}}{2\,\left(-3\,a^3\,b\,c\,d^7+\frac{29\,a^2\,b^2\,c^2\,d^6}{4}-\frac{23\,a\,b^3\,c^3\,d^5}{4}+\frac{3\,b^4\,c^4\,d^4}{2}\right)}-\frac{3\,a\,b\,\sqrt{c}\,d^7\,\sqrt{d\,x^2+c}}{\frac{29\,b^2\,c^2\,d^6}{4}-3\,a\,b\,c\,d^7-\frac{23\,b^3\,c^3\,d^5}{4\,a}+\frac{3\,b^4\,c^4\,d^4}{2\,a^2}}\right)\,\left(3\,a\,d-2\,b\,c\right)}{2\,a^2}-\frac{\mathrm{atanh}\left(\frac{3\,b^2\,c^2\,d^4\,\sqrt{d\,x^2+c}\,\sqrt{-a^3\,b\,d^3+3\,a^2\,b^2\,c\,d^2-3\,a\,b^3\,c^2\,d+b^4\,c^3}}{2\,\left(-2\,a^3\,b\,c\,d^7+\frac{11\,a^2\,b^2\,c^2\,d^6}{2}-5\,a\,b^3\,c^3\,d^5+\frac{3\,b^4\,c^4\,d^4}{2}\right)}+\frac{2\,b\,c\,d^5\,\sqrt{d\,x^2+c}\,\sqrt{-a^3\,b\,d^3+3\,a^2\,b^2\,c\,d^2-3\,a\,b^3\,c^2\,d+b^4\,c^3}}{5\,b^3\,c^3\,d^5-\frac{11\,a\,b^2\,c^2\,d^6}{2}-\frac{3\,b^4\,c^4\,d^4}{2\,a}+2\,a^2\,b\,c\,d^7}\right)\,\sqrt{-b\,{\left(a\,d-b\,c\right)}^3}}{a^2\,b}","Not used",1,"- (c*(c + d*x^2)^(1/2))/(2*a*x^2) - (c^(1/2)*atanh((29*b^2*c^(3/2)*d^6*(c + d*x^2)^(1/2))/(4*((29*b^2*c^2*d^6)/4 - 3*a*b*c*d^7 - (23*b^3*c^3*d^5)/(4*a) + (3*b^4*c^4*d^4)/(2*a^2))) + (23*b^3*c^(5/2)*d^5*(c + d*x^2)^(1/2))/(4*((23*b^3*c^3*d^5)/4 - (29*a*b^2*c^2*d^6)/4 - (3*b^4*c^4*d^4)/(2*a) + 3*a^2*b*c*d^7)) + (3*b^4*c^(7/2)*d^4*(c + d*x^2)^(1/2))/(2*((3*b^4*c^4*d^4)/2 - (23*a*b^3*c^3*d^5)/4 + (29*a^2*b^2*c^2*d^6)/4 - 3*a^3*b*c*d^7)) - (3*a*b*c^(1/2)*d^7*(c + d*x^2)^(1/2))/((29*b^2*c^2*d^6)/4 - 3*a*b*c*d^7 - (23*b^3*c^3*d^5)/(4*a) + (3*b^4*c^4*d^4)/(2*a^2)))*(3*a*d - 2*b*c))/(2*a^2) - (atanh((3*b^2*c^2*d^4*(c + d*x^2)^(1/2)*(b^4*c^3 - a^3*b*d^3 + 3*a^2*b^2*c*d^2 - 3*a*b^3*c^2*d)^(1/2))/(2*((3*b^4*c^4*d^4)/2 - 5*a*b^3*c^3*d^5 + (11*a^2*b^2*c^2*d^6)/2 - 2*a^3*b*c*d^7)) + (2*b*c*d^5*(c + d*x^2)^(1/2)*(b^4*c^3 - a^3*b*d^3 + 3*a^2*b^2*c*d^2 - 3*a*b^3*c^2*d)^(1/2))/(5*b^3*c^3*d^5 - (11*a*b^2*c^2*d^6)/2 - (3*b^4*c^4*d^4)/(2*a) + 2*a^2*b*c*d^7))*(-b*(a*d - b*c)^3)^(1/2))/(a^2*b)","B"
693,0,-1,102,0.000000,"\text{Not used}","int((c + d*x^2)^(3/2)/(x^4*(a + b*x^2)),x)","\int \frac{{\left(d\,x^2+c\right)}^{3/2}}{x^4\,\left(b\,x^2+a\right)} \,d x","Not used",1,"int((c + d*x^2)^(3/2)/(x^4*(a + b*x^2)), x)","F"
694,0,-1,291,0.000000,"\text{Not used}","int((x^4*(c + d*x^2)^(5/2))/(a + b*x^2),x)","\int \frac{x^4\,{\left(d\,x^2+c\right)}^{5/2}}{b\,x^2+a} \,d x","Not used",1,"int((x^4*(c + d*x^2)^(5/2))/(a + b*x^2), x)","F"
695,1,251,144,0.603075,"\text{Not used}","int((x^3*(c + d*x^2)^(5/2))/(a + b*x^2),x)","\frac{{\left(d\,x^2+c\right)}^{7/2}}{7\,b\,d}-{\left(d\,x^2+c\right)}^{5/2}\,\left(\frac{c}{5\,b\,d}+\frac{a\,d^2-b\,c\,d}{5\,b^2\,d^2}\right)+\frac{a\,\mathrm{atan}\left(\frac{a\,\sqrt{b}\,\sqrt{d\,x^2+c}\,{\left(a\,d-b\,c\right)}^{5/2}}{a^4\,d^3-3\,a^3\,b\,c\,d^2+3\,a^2\,b^2\,c^2\,d-a\,b^3\,c^3}\right)\,{\left(a\,d-b\,c\right)}^{5/2}}{b^{9/2}}+\frac{{\left(d\,x^2+c\right)}^{3/2}\,\left(a\,d^2-b\,c\,d\right)\,\left(\frac{c}{b\,d}+\frac{a\,d^2-b\,c\,d}{b^2\,d^2}\right)}{3\,b\,d}-\frac{\sqrt{d\,x^2+c}\,{\left(a\,d^2-b\,c\,d\right)}^2\,\left(\frac{c}{b\,d}+\frac{a\,d^2-b\,c\,d}{b^2\,d^2}\right)}{b^2\,d^2}","Not used",1,"(c + d*x^2)^(7/2)/(7*b*d) - (c + d*x^2)^(5/2)*(c/(5*b*d) + (a*d^2 - b*c*d)/(5*b^2*d^2)) + (a*atan((a*b^(1/2)*(c + d*x^2)^(1/2)*(a*d - b*c)^(5/2))/(a^4*d^3 - a*b^3*c^3 + 3*a^2*b^2*c^2*d - 3*a^3*b*c*d^2))*(a*d - b*c)^(5/2))/b^(9/2) + ((c + d*x^2)^(3/2)*(a*d^2 - b*c*d)*(c/(b*d) + (a*d^2 - b*c*d)/(b^2*d^2)))/(3*b*d) - ((c + d*x^2)^(1/2)*(a*d^2 - b*c*d)^2*(c/(b*d) + (a*d^2 - b*c*d)/(b^2*d^2)))/(b^2*d^2)","B"
696,0,-1,217,0.000000,"\text{Not used}","int((x^2*(c + d*x^2)^(5/2))/(a + b*x^2),x)","\int \frac{x^2\,{\left(d\,x^2+c\right)}^{5/2}}{b\,x^2+a} \,d x","Not used",1,"int((x^2*(c + d*x^2)^(5/2))/(a + b*x^2), x)","F"
697,1,137,119,0.605037,"\text{Not used}","int((x*(c + d*x^2)^(5/2))/(a + b*x^2),x)","\frac{{\left(d\,x^2+c\right)}^{5/2}}{5\,b}-\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d\,x^2+c}\,{\left(a\,d-b\,c\right)}^{5/2}}{a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3}\right)\,{\left(a\,d-b\,c\right)}^{5/2}}{b^{7/2}}-\frac{{\left(d\,x^2+c\right)}^{3/2}\,\left(a\,d-b\,c\right)}{3\,b^2}+\frac{\sqrt{d\,x^2+c}\,{\left(a\,d-b\,c\right)}^2}{b^3}","Not used",1,"(c + d*x^2)^(5/2)/(5*b) - (atan((b^(1/2)*(c + d*x^2)^(1/2)*(a*d - b*c)^(5/2))/(a^3*d^3 - b^3*c^3 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2))*(a*d - b*c)^(5/2))/b^(7/2) - ((c + d*x^2)^(3/2)*(a*d - b*c))/(3*b^2) + ((c + d*x^2)^(1/2)*(a*d - b*c)^2)/b^3","B"
698,0,-1,156,0.000000,"\text{Not used}","int((c + d*x^2)^(5/2)/(a + b*x^2),x)","\int \frac{{\left(d\,x^2+c\right)}^{5/2}}{b\,x^2+a} \,d x","Not used",1,"int((c + d*x^2)^(5/2)/(a + b*x^2), x)","F"
699,1,2094,124,0.999608,"\text{Not used}","int((c + d*x^2)^(5/2)/(x*(a + b*x^2)),x)","\frac{d\,{\left(d\,x^2+c\right)}^{3/2}}{3\,b}-\frac{d\,\sqrt{d\,x^2+c}\,\left(a\,d-2\,b\,c\right)}{b^2}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{c^5}\,\left(\frac{2\,\sqrt{d\,x^2+c}\,\left(a^6\,d^8-6\,a^5\,b\,c\,d^7+15\,a^4\,b^2\,c^2\,d^6-20\,a^3\,b^3\,c^3\,d^5+15\,a^2\,b^4\,c^4\,d^4-6\,a\,b^5\,c^5\,d^3+2\,b^6\,c^6\,d^2\right)}{b^3}+\frac{\left(\frac{4\,a^4\,b^3\,c\,d^5-12\,a^3\,b^4\,c^2\,d^4+8\,a^2\,b^5\,c^3\,d^3}{b^3}+\frac{\left(4\,a^3\,b^5\,d^3-8\,a^2\,b^6\,c\,d^2\right)\,\sqrt{d\,x^2+c}\,\sqrt{c^5}}{a\,b^3}\right)\,\sqrt{c^5}}{2\,a}\right)\,1{}\mathrm{i}}{2\,a}+\frac{\sqrt{c^5}\,\left(\frac{2\,\sqrt{d\,x^2+c}\,\left(a^6\,d^8-6\,a^5\,b\,c\,d^7+15\,a^4\,b^2\,c^2\,d^6-20\,a^3\,b^3\,c^3\,d^5+15\,a^2\,b^4\,c^4\,d^4-6\,a\,b^5\,c^5\,d^3+2\,b^6\,c^6\,d^2\right)}{b^3}-\frac{\left(\frac{4\,a^4\,b^3\,c\,d^5-12\,a^3\,b^4\,c^2\,d^4+8\,a^2\,b^5\,c^3\,d^3}{b^3}-\frac{\left(4\,a^3\,b^5\,d^3-8\,a^2\,b^6\,c\,d^2\right)\,\sqrt{d\,x^2+c}\,\sqrt{c^5}}{a\,b^3}\right)\,\sqrt{c^5}}{2\,a}\right)\,1{}\mathrm{i}}{2\,a}}{\frac{2\,\left(a^5\,c^3\,d^8-6\,a^4\,b\,c^4\,d^7+15\,a^3\,b^2\,c^5\,d^6-19\,a^2\,b^3\,c^6\,d^5+12\,a\,b^4\,c^7\,d^4-3\,b^5\,c^8\,d^3\right)}{b^3}-\frac{\sqrt{c^5}\,\left(\frac{2\,\sqrt{d\,x^2+c}\,\left(a^6\,d^8-6\,a^5\,b\,c\,d^7+15\,a^4\,b^2\,c^2\,d^6-20\,a^3\,b^3\,c^3\,d^5+15\,a^2\,b^4\,c^4\,d^4-6\,a\,b^5\,c^5\,d^3+2\,b^6\,c^6\,d^2\right)}{b^3}+\frac{\left(\frac{4\,a^4\,b^3\,c\,d^5-12\,a^3\,b^4\,c^2\,d^4+8\,a^2\,b^5\,c^3\,d^3}{b^3}+\frac{\left(4\,a^3\,b^5\,d^3-8\,a^2\,b^6\,c\,d^2\right)\,\sqrt{d\,x^2+c}\,\sqrt{c^5}}{a\,b^3}\right)\,\sqrt{c^5}}{2\,a}\right)}{2\,a}+\frac{\sqrt{c^5}\,\left(\frac{2\,\sqrt{d\,x^2+c}\,\left(a^6\,d^8-6\,a^5\,b\,c\,d^7+15\,a^4\,b^2\,c^2\,d^6-20\,a^3\,b^3\,c^3\,d^5+15\,a^2\,b^4\,c^4\,d^4-6\,a\,b^5\,c^5\,d^3+2\,b^6\,c^6\,d^2\right)}{b^3}-\frac{\left(\frac{4\,a^4\,b^3\,c\,d^5-12\,a^3\,b^4\,c^2\,d^4+8\,a^2\,b^5\,c^3\,d^3}{b^3}-\frac{\left(4\,a^3\,b^5\,d^3-8\,a^2\,b^6\,c\,d^2\right)\,\sqrt{d\,x^2+c}\,\sqrt{c^5}}{a\,b^3}\right)\,\sqrt{c^5}}{2\,a}\right)}{2\,a}}\right)\,\sqrt{c^5}\,1{}\mathrm{i}}{a}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^5}\,\left(\frac{2\,\sqrt{d\,x^2+c}\,\left(a^6\,d^8-6\,a^5\,b\,c\,d^7+15\,a^4\,b^2\,c^2\,d^6-20\,a^3\,b^3\,c^3\,d^5+15\,a^2\,b^4\,c^4\,d^4-6\,a\,b^5\,c^5\,d^3+2\,b^6\,c^6\,d^2\right)}{b^3}+\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^5}\,\left(\frac{4\,a^4\,b^3\,c\,d^5-12\,a^3\,b^4\,c^2\,d^4+8\,a^2\,b^5\,c^3\,d^3}{b^3}+\frac{\left(4\,a^3\,b^5\,d^3-8\,a^2\,b^6\,c\,d^2\right)\,\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^5}\,\sqrt{d\,x^2+c}}{a\,b^8}\right)}{2\,a\,b^5}\right)\,1{}\mathrm{i}}{2\,a\,b^5}+\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^5}\,\left(\frac{2\,\sqrt{d\,x^2+c}\,\left(a^6\,d^8-6\,a^5\,b\,c\,d^7+15\,a^4\,b^2\,c^2\,d^6-20\,a^3\,b^3\,c^3\,d^5+15\,a^2\,b^4\,c^4\,d^4-6\,a\,b^5\,c^5\,d^3+2\,b^6\,c^6\,d^2\right)}{b^3}-\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^5}\,\left(\frac{4\,a^4\,b^3\,c\,d^5-12\,a^3\,b^4\,c^2\,d^4+8\,a^2\,b^5\,c^3\,d^3}{b^3}-\frac{\left(4\,a^3\,b^5\,d^3-8\,a^2\,b^6\,c\,d^2\right)\,\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^5}\,\sqrt{d\,x^2+c}}{a\,b^8}\right)}{2\,a\,b^5}\right)\,1{}\mathrm{i}}{2\,a\,b^5}}{\frac{2\,\left(a^5\,c^3\,d^8-6\,a^4\,b\,c^4\,d^7+15\,a^3\,b^2\,c^5\,d^6-19\,a^2\,b^3\,c^6\,d^5+12\,a\,b^4\,c^7\,d^4-3\,b^5\,c^8\,d^3\right)}{b^3}-\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^5}\,\left(\frac{2\,\sqrt{d\,x^2+c}\,\left(a^6\,d^8-6\,a^5\,b\,c\,d^7+15\,a^4\,b^2\,c^2\,d^6-20\,a^3\,b^3\,c^3\,d^5+15\,a^2\,b^4\,c^4\,d^4-6\,a\,b^5\,c^5\,d^3+2\,b^6\,c^6\,d^2\right)}{b^3}+\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^5}\,\left(\frac{4\,a^4\,b^3\,c\,d^5-12\,a^3\,b^4\,c^2\,d^4+8\,a^2\,b^5\,c^3\,d^3}{b^3}+\frac{\left(4\,a^3\,b^5\,d^3-8\,a^2\,b^6\,c\,d^2\right)\,\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^5}\,\sqrt{d\,x^2+c}}{a\,b^8}\right)}{2\,a\,b^5}\right)}{2\,a\,b^5}+\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^5}\,\left(\frac{2\,\sqrt{d\,x^2+c}\,\left(a^6\,d^8-6\,a^5\,b\,c\,d^7+15\,a^4\,b^2\,c^2\,d^6-20\,a^3\,b^3\,c^3\,d^5+15\,a^2\,b^4\,c^4\,d^4-6\,a\,b^5\,c^5\,d^3+2\,b^6\,c^6\,d^2\right)}{b^3}-\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^5}\,\left(\frac{4\,a^4\,b^3\,c\,d^5-12\,a^3\,b^4\,c^2\,d^4+8\,a^2\,b^5\,c^3\,d^3}{b^3}-\frac{\left(4\,a^3\,b^5\,d^3-8\,a^2\,b^6\,c\,d^2\right)\,\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^5}\,\sqrt{d\,x^2+c}}{a\,b^8}\right)}{2\,a\,b^5}\right)}{2\,a\,b^5}}\right)\,\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^5}\,1{}\mathrm{i}}{a\,b^5}","Not used",1,"(atan((((c^5)^(1/2)*((2*(c + d*x^2)^(1/2)*(a^6*d^8 + 2*b^6*c^6*d^2 - 6*a*b^5*c^5*d^3 + 15*a^2*b^4*c^4*d^4 - 20*a^3*b^3*c^3*d^5 + 15*a^4*b^2*c^2*d^6 - 6*a^5*b*c*d^7))/b^3 + (((4*a^4*b^3*c*d^5 + 8*a^2*b^5*c^3*d^3 - 12*a^3*b^4*c^2*d^4)/b^3 + ((4*a^3*b^5*d^3 - 8*a^2*b^6*c*d^2)*(c + d*x^2)^(1/2)*(c^5)^(1/2))/(a*b^3))*(c^5)^(1/2))/(2*a))*1i)/(2*a) + ((c^5)^(1/2)*((2*(c + d*x^2)^(1/2)*(a^6*d^8 + 2*b^6*c^6*d^2 - 6*a*b^5*c^5*d^3 + 15*a^2*b^4*c^4*d^4 - 20*a^3*b^3*c^3*d^5 + 15*a^4*b^2*c^2*d^6 - 6*a^5*b*c*d^7))/b^3 - (((4*a^4*b^3*c*d^5 + 8*a^2*b^5*c^3*d^3 - 12*a^3*b^4*c^2*d^4)/b^3 - ((4*a^3*b^5*d^3 - 8*a^2*b^6*c*d^2)*(c + d*x^2)^(1/2)*(c^5)^(1/2))/(a*b^3))*(c^5)^(1/2))/(2*a))*1i)/(2*a))/((2*(a^5*c^3*d^8 - 3*b^5*c^8*d^3 + 12*a*b^4*c^7*d^4 - 6*a^4*b*c^4*d^7 - 19*a^2*b^3*c^6*d^5 + 15*a^3*b^2*c^5*d^6))/b^3 - ((c^5)^(1/2)*((2*(c + d*x^2)^(1/2)*(a^6*d^8 + 2*b^6*c^6*d^2 - 6*a*b^5*c^5*d^3 + 15*a^2*b^4*c^4*d^4 - 20*a^3*b^3*c^3*d^5 + 15*a^4*b^2*c^2*d^6 - 6*a^5*b*c*d^7))/b^3 + (((4*a^4*b^3*c*d^5 + 8*a^2*b^5*c^3*d^3 - 12*a^3*b^4*c^2*d^4)/b^3 + ((4*a^3*b^5*d^3 - 8*a^2*b^6*c*d^2)*(c + d*x^2)^(1/2)*(c^5)^(1/2))/(a*b^3))*(c^5)^(1/2))/(2*a)))/(2*a) + ((c^5)^(1/2)*((2*(c + d*x^2)^(1/2)*(a^6*d^8 + 2*b^6*c^6*d^2 - 6*a*b^5*c^5*d^3 + 15*a^2*b^4*c^4*d^4 - 20*a^3*b^3*c^3*d^5 + 15*a^4*b^2*c^2*d^6 - 6*a^5*b*c*d^7))/b^3 - (((4*a^4*b^3*c*d^5 + 8*a^2*b^5*c^3*d^3 - 12*a^3*b^4*c^2*d^4)/b^3 - ((4*a^3*b^5*d^3 - 8*a^2*b^6*c*d^2)*(c + d*x^2)^(1/2)*(c^5)^(1/2))/(a*b^3))*(c^5)^(1/2))/(2*a)))/(2*a)))*(c^5)^(1/2)*1i)/a + (d*(c + d*x^2)^(3/2))/(3*b) + (atan((((-b^5*(a*d - b*c)^5)^(1/2)*((2*(c + d*x^2)^(1/2)*(a^6*d^8 + 2*b^6*c^6*d^2 - 6*a*b^5*c^5*d^3 + 15*a^2*b^4*c^4*d^4 - 20*a^3*b^3*c^3*d^5 + 15*a^4*b^2*c^2*d^6 - 6*a^5*b*c*d^7))/b^3 + ((-b^5*(a*d - b*c)^5)^(1/2)*((4*a^4*b^3*c*d^5 + 8*a^2*b^5*c^3*d^3 - 12*a^3*b^4*c^2*d^4)/b^3 + ((4*a^3*b^5*d^3 - 8*a^2*b^6*c*d^2)*(-b^5*(a*d - b*c)^5)^(1/2)*(c + d*x^2)^(1/2))/(a*b^8)))/(2*a*b^5))*1i)/(2*a*b^5) + ((-b^5*(a*d - b*c)^5)^(1/2)*((2*(c + d*x^2)^(1/2)*(a^6*d^8 + 2*b^6*c^6*d^2 - 6*a*b^5*c^5*d^3 + 15*a^2*b^4*c^4*d^4 - 20*a^3*b^3*c^3*d^5 + 15*a^4*b^2*c^2*d^6 - 6*a^5*b*c*d^7))/b^3 - ((-b^5*(a*d - b*c)^5)^(1/2)*((4*a^4*b^3*c*d^5 + 8*a^2*b^5*c^3*d^3 - 12*a^3*b^4*c^2*d^4)/b^3 - ((4*a^3*b^5*d^3 - 8*a^2*b^6*c*d^2)*(-b^5*(a*d - b*c)^5)^(1/2)*(c + d*x^2)^(1/2))/(a*b^8)))/(2*a*b^5))*1i)/(2*a*b^5))/((2*(a^5*c^3*d^8 - 3*b^5*c^8*d^3 + 12*a*b^4*c^7*d^4 - 6*a^4*b*c^4*d^7 - 19*a^2*b^3*c^6*d^5 + 15*a^3*b^2*c^5*d^6))/b^3 - ((-b^5*(a*d - b*c)^5)^(1/2)*((2*(c + d*x^2)^(1/2)*(a^6*d^8 + 2*b^6*c^6*d^2 - 6*a*b^5*c^5*d^3 + 15*a^2*b^4*c^4*d^4 - 20*a^3*b^3*c^3*d^5 + 15*a^4*b^2*c^2*d^6 - 6*a^5*b*c*d^7))/b^3 + ((-b^5*(a*d - b*c)^5)^(1/2)*((4*a^4*b^3*c*d^5 + 8*a^2*b^5*c^3*d^3 - 12*a^3*b^4*c^2*d^4)/b^3 + ((4*a^3*b^5*d^3 - 8*a^2*b^6*c*d^2)*(-b^5*(a*d - b*c)^5)^(1/2)*(c + d*x^2)^(1/2))/(a*b^8)))/(2*a*b^5)))/(2*a*b^5) + ((-b^5*(a*d - b*c)^5)^(1/2)*((2*(c + d*x^2)^(1/2)*(a^6*d^8 + 2*b^6*c^6*d^2 - 6*a*b^5*c^5*d^3 + 15*a^2*b^4*c^4*d^4 - 20*a^3*b^3*c^3*d^5 + 15*a^4*b^2*c^2*d^6 - 6*a^5*b*c*d^7))/b^3 - ((-b^5*(a*d - b*c)^5)^(1/2)*((4*a^4*b^3*c*d^5 + 8*a^2*b^5*c^3*d^3 - 12*a^3*b^4*c^2*d^4)/b^3 - ((4*a^3*b^5*d^3 - 8*a^2*b^6*c*d^2)*(-b^5*(a*d - b*c)^5)^(1/2)*(c + d*x^2)^(1/2))/(a*b^8)))/(2*a*b^5)))/(2*a*b^5)))*(-b^5*(a*d - b*c)^5)^(1/2)*1i)/(a*b^5) - (d*(c + d*x^2)^(1/2)*(a*d - 2*b*c))/b^2","B"
700,0,-1,145,0.000000,"\text{Not used}","int((c + d*x^2)^(5/2)/(x^2*(a + b*x^2)),x)","\int \frac{{\left(d\,x^2+c\right)}^{5/2}}{x^2\,\left(b\,x^2+a\right)} \,d x","Not used",1,"int((c + d*x^2)^(5/2)/(x^2*(a + b*x^2)), x)","F"
701,1,1428,144,1.367809,"\text{Not used}","int((c + d*x^2)^(5/2)/(x^3*(a + b*x^2)),x)","\frac{d^2\,\sqrt{d\,x^2+c}}{b}-\frac{b\,c^2\,d\,\sqrt{d\,x^2+c}}{2\,a\,\left(b\,\left(d\,x^2+c\right)-b\,c\right)}+\frac{\mathrm{atan}\left(\frac{a^3\,d^9\,\sqrt{d\,x^2+c}\,\sqrt{c^3}\,5{}\mathrm{i}}{5\,a^3\,c^2\,d^9-\frac{395\,b^3\,c^5\,d^6}{4}+87\,a\,b^2\,c^4\,d^7-32\,a^2\,b\,c^3\,d^8+\frac{185\,b^4\,c^6\,d^5}{4\,a}-\frac{15\,b^5\,c^7\,d^4}{2\,a^2}}+\frac{a^2\,c\,d^8\,\sqrt{d\,x^2+c}\,\sqrt{c^3}\,32{}\mathrm{i}}{32\,a^2\,c^3\,d^8+\frac{395\,b^2\,c^5\,d^6}{4}-\frac{185\,b^3\,c^6\,d^5}{4\,a}-\frac{5\,a^3\,c^2\,d^9}{b}+\frac{15\,b^4\,c^7\,d^4}{2\,a^2}-87\,a\,b\,c^4\,d^7}+\frac{b^2\,c^3\,d^6\,\sqrt{d\,x^2+c}\,\sqrt{c^3}\,395{}\mathrm{i}}{4\,\left(32\,a^2\,c^3\,d^8+\frac{395\,b^2\,c^5\,d^6}{4}-\frac{185\,b^3\,c^6\,d^5}{4\,a}-\frac{5\,a^3\,c^2\,d^9}{b}+\frac{15\,b^4\,c^7\,d^4}{2\,a^2}-87\,a\,b\,c^4\,d^7\right)}-\frac{b^3\,c^4\,d^5\,\sqrt{d\,x^2+c}\,\sqrt{c^3}\,185{}\mathrm{i}}{4\,\left(32\,a^3\,c^3\,d^8-\frac{185\,b^3\,c^6\,d^5}{4}+\frac{395\,a\,b^2\,c^5\,d^6}{4}-87\,a^2\,b\,c^4\,d^7+\frac{15\,b^4\,c^7\,d^4}{2\,a}-\frac{5\,a^4\,c^2\,d^9}{b}\right)}+\frac{b^4\,c^5\,d^4\,\sqrt{d\,x^2+c}\,\sqrt{c^3}\,15{}\mathrm{i}}{2\,\left(32\,a^4\,c^3\,d^8+\frac{15\,b^4\,c^7\,d^4}{2}-\frac{185\,a\,b^3\,c^6\,d^5}{4}-87\,a^3\,b\,c^4\,d^7+\frac{395\,a^2\,b^2\,c^5\,d^6}{4}-\frac{5\,a^5\,c^2\,d^9}{b}\right)}-\frac{a\,b\,c^2\,d^7\,\sqrt{d\,x^2+c}\,\sqrt{c^3}\,87{}\mathrm{i}}{32\,a^2\,c^3\,d^8+\frac{395\,b^2\,c^5\,d^6}{4}-\frac{185\,b^3\,c^6\,d^5}{4\,a}-\frac{5\,a^3\,c^2\,d^9}{b}+\frac{15\,b^4\,c^7\,d^4}{2\,a^2}-87\,a\,b\,c^4\,d^7}\right)\,\left(5\,a\,d-2\,b\,c\right)\,\sqrt{c^3}\,1{}\mathrm{i}}{2\,a^2}-\frac{\mathrm{atan}\left(\frac{c^3\,d^5\,\sqrt{d\,x^2+c}\,\sqrt{-a^5\,b^3\,d^5+5\,a^4\,b^4\,c\,d^4-10\,a^3\,b^5\,c^2\,d^3+10\,a^2\,b^6\,c^3\,d^2-5\,a\,b^7\,c^4\,d+b^8\,c^5}\,20{}\mathrm{i}}{\frac{185\,a\,b^3\,c^5\,d^6}{2}-\frac{85\,b^4\,c^6\,d^5}{2}-16\,a^4\,c^2\,d^9+56\,a^3\,b\,c^3\,d^8+\frac{2\,a^5\,c\,d^{10}}{b}-\frac{199\,a^2\,b^2\,c^4\,d^7}{2}+\frac{15\,b^5\,c^7\,d^4}{2\,a}}-\frac{c^2\,d^6\,\sqrt{d\,x^2+c}\,\sqrt{-a^5\,b^3\,d^5+5\,a^4\,b^4\,c\,d^4-10\,a^3\,b^5\,c^2\,d^3+10\,a^2\,b^6\,c^3\,d^2-5\,a\,b^7\,c^4\,d+b^8\,c^5}\,10{}\mathrm{i}}{2\,a^4\,c\,d^{10}+\frac{185\,b^4\,c^5\,d^6}{2}-\frac{199\,a\,b^3\,c^4\,d^7}{2}-16\,a^3\,b\,c^2\,d^9+56\,a^2\,b^2\,c^3\,d^8-\frac{85\,b^5\,c^6\,d^5}{2\,a}+\frac{15\,b^6\,c^7\,d^4}{2\,a^2}}-\frac{c^4\,d^4\,\sqrt{d\,x^2+c}\,\sqrt{-a^5\,b^3\,d^5+5\,a^4\,b^4\,c\,d^4-10\,a^3\,b^5\,c^2\,d^3+10\,a^2\,b^6\,c^3\,d^2-5\,a\,b^7\,c^4\,d+b^8\,c^5}\,15{}\mathrm{i}}{2\,\left(56\,a^4\,c^3\,d^8+\frac{15\,b^4\,c^7\,d^4}{2}-\frac{85\,a\,b^3\,c^6\,d^5}{2}-\frac{199\,a^3\,b\,c^4\,d^7}{2}+\frac{2\,a^6\,c\,d^{10}}{b^2}+\frac{185\,a^2\,b^2\,c^5\,d^6}{2}-\frac{16\,a^5\,c^2\,d^9}{b}\right)}+\frac{a\,c\,d^7\,\sqrt{d\,x^2+c}\,\sqrt{-a^5\,b^3\,d^5+5\,a^4\,b^4\,c\,d^4-10\,a^3\,b^5\,c^2\,d^3+10\,a^2\,b^6\,c^3\,d^2-5\,a\,b^7\,c^4\,d+b^8\,c^5}\,2{}\mathrm{i}}{\frac{185\,b^5\,c^5\,d^6}{2}-\frac{199\,a\,b^4\,c^4\,d^7}{2}+56\,a^2\,b^3\,c^3\,d^8-16\,a^3\,b^2\,c^2\,d^9-\frac{85\,b^6\,c^6\,d^5}{2\,a}+\frac{15\,b^7\,c^7\,d^4}{2\,a^2}+2\,a^4\,b\,c\,d^{10}}\right)\,\sqrt{-b^3\,{\left(a\,d-b\,c\right)}^5}\,1{}\mathrm{i}}{a^2\,b^3}","Not used",1,"(d^2*(c + d*x^2)^(1/2))/b + (atan((a^3*d^9*(c + d*x^2)^(1/2)*(c^3)^(1/2)*5i)/(5*a^3*c^2*d^9 - (395*b^3*c^5*d^6)/4 + 87*a*b^2*c^4*d^7 - 32*a^2*b*c^3*d^8 + (185*b^4*c^6*d^5)/(4*a) - (15*b^5*c^7*d^4)/(2*a^2)) + (a^2*c*d^8*(c + d*x^2)^(1/2)*(c^3)^(1/2)*32i)/(32*a^2*c^3*d^8 + (395*b^2*c^5*d^6)/4 - (185*b^3*c^6*d^5)/(4*a) - (5*a^3*c^2*d^9)/b + (15*b^4*c^7*d^4)/(2*a^2) - 87*a*b*c^4*d^7) + (b^2*c^3*d^6*(c + d*x^2)^(1/2)*(c^3)^(1/2)*395i)/(4*(32*a^2*c^3*d^8 + (395*b^2*c^5*d^6)/4 - (185*b^3*c^6*d^5)/(4*a) - (5*a^3*c^2*d^9)/b + (15*b^4*c^7*d^4)/(2*a^2) - 87*a*b*c^4*d^7)) - (b^3*c^4*d^5*(c + d*x^2)^(1/2)*(c^3)^(1/2)*185i)/(4*(32*a^3*c^3*d^8 - (185*b^3*c^6*d^5)/4 + (395*a*b^2*c^5*d^6)/4 - 87*a^2*b*c^4*d^7 + (15*b^4*c^7*d^4)/(2*a) - (5*a^4*c^2*d^9)/b)) + (b^4*c^5*d^4*(c + d*x^2)^(1/2)*(c^3)^(1/2)*15i)/(2*(32*a^4*c^3*d^8 + (15*b^4*c^7*d^4)/2 - (185*a*b^3*c^6*d^5)/4 - 87*a^3*b*c^4*d^7 + (395*a^2*b^2*c^5*d^6)/4 - (5*a^5*c^2*d^9)/b)) - (a*b*c^2*d^7*(c + d*x^2)^(1/2)*(c^3)^(1/2)*87i)/(32*a^2*c^3*d^8 + (395*b^2*c^5*d^6)/4 - (185*b^3*c^6*d^5)/(4*a) - (5*a^3*c^2*d^9)/b + (15*b^4*c^7*d^4)/(2*a^2) - 87*a*b*c^4*d^7))*(5*a*d - 2*b*c)*(c^3)^(1/2)*1i)/(2*a^2) - (atan((c^3*d^5*(c + d*x^2)^(1/2)*(b^8*c^5 - a^5*b^3*d^5 + 5*a^4*b^4*c*d^4 + 10*a^2*b^6*c^3*d^2 - 10*a^3*b^5*c^2*d^3 - 5*a*b^7*c^4*d)^(1/2)*20i)/((185*a*b^3*c^5*d^6)/2 - (85*b^4*c^6*d^5)/2 - 16*a^4*c^2*d^9 + 56*a^3*b*c^3*d^8 + (2*a^5*c*d^10)/b - (199*a^2*b^2*c^4*d^7)/2 + (15*b^5*c^7*d^4)/(2*a)) - (c^2*d^6*(c + d*x^2)^(1/2)*(b^8*c^5 - a^5*b^3*d^5 + 5*a^4*b^4*c*d^4 + 10*a^2*b^6*c^3*d^2 - 10*a^3*b^5*c^2*d^3 - 5*a*b^7*c^4*d)^(1/2)*10i)/(2*a^4*c*d^10 + (185*b^4*c^5*d^6)/2 - (199*a*b^3*c^4*d^7)/2 - 16*a^3*b*c^2*d^9 + 56*a^2*b^2*c^3*d^8 - (85*b^5*c^6*d^5)/(2*a) + (15*b^6*c^7*d^4)/(2*a^2)) - (c^4*d^4*(c + d*x^2)^(1/2)*(b^8*c^5 - a^5*b^3*d^5 + 5*a^4*b^4*c*d^4 + 10*a^2*b^6*c^3*d^2 - 10*a^3*b^5*c^2*d^3 - 5*a*b^7*c^4*d)^(1/2)*15i)/(2*(56*a^4*c^3*d^8 + (15*b^4*c^7*d^4)/2 - (85*a*b^3*c^6*d^5)/2 - (199*a^3*b*c^4*d^7)/2 + (2*a^6*c*d^10)/b^2 + (185*a^2*b^2*c^5*d^6)/2 - (16*a^5*c^2*d^9)/b)) + (a*c*d^7*(c + d*x^2)^(1/2)*(b^8*c^5 - a^5*b^3*d^5 + 5*a^4*b^4*c*d^4 + 10*a^2*b^6*c^3*d^2 - 10*a^3*b^5*c^2*d^3 - 5*a*b^7*c^4*d)^(1/2)*2i)/((185*b^5*c^5*d^6)/2 - (199*a*b^4*c^4*d^7)/2 + 56*a^2*b^3*c^3*d^8 - 16*a^3*b^2*c^2*d^9 - (85*b^6*c^6*d^5)/(2*a) + (15*b^7*c^7*d^4)/(2*a^2) + 2*a^4*b*c*d^10))*(-b^3*(a*d - b*c)^5)^(1/2)*1i)/(a^2*b^3) - (b*c^2*d*(c + d*x^2)^(1/2))/(2*a*(b*(c + d*x^2) - b*c))","B"
702,0,-1,130,0.000000,"\text{Not used}","int((c + d*x^2)^(5/2)/(x^4*(a + b*x^2)),x)","\int \frac{{\left(d\,x^2+c\right)}^{5/2}}{x^4\,\left(b\,x^2+a\right)} \,d x","Not used",1,"int((c + d*x^2)^(5/2)/(x^4*(a + b*x^2)), x)","F"
703,1,100,100,0.688508,"\text{Not used}","int(x^5/((a + b*x^2)*(c + d*x^2)^(1/2)),x)","\frac{{\left(d\,x^2+c\right)}^{3/2}}{3\,b\,d^2}-\left(\frac{2\,c}{b\,d^2}+\frac{a\,d^3-b\,c\,d^2}{b^2\,d^4}\right)\,\sqrt{d\,x^2+c}+\frac{a^2\,\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d\,x^2+c}}{\sqrt{a\,d-b\,c}}\right)}{b^{5/2}\,\sqrt{a\,d-b\,c}}","Not used",1,"(c + d*x^2)^(3/2)/(3*b*d^2) - ((2*c)/(b*d^2) + (a*d^3 - b*c*d^2)/(b^2*d^4))*(c + d*x^2)^(1/2) + (a^2*atan((b^(1/2)*(c + d*x^2)^(1/2))/(a*d - b*c)^(1/2)))/(b^(5/2)*(a*d - b*c)^(1/2))","B"
704,1,57,68,0.636660,"\text{Not used}","int(x^3/((a + b*x^2)*(c + d*x^2)^(1/2)),x)","\frac{\sqrt{d\,x^2+c}}{b\,d}-\frac{a\,\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d\,x^2+c}}{\sqrt{a\,d-b\,c}}\right)}{b^{3/2}\,\sqrt{a\,d-b\,c}}","Not used",1,"(c + d*x^2)^(1/2)/(b*d) - (a*atan((b^(1/2)*(c + d*x^2)^(1/2))/(a*d - b*c)^(1/2)))/(b^(3/2)*(a*d - b*c)^(1/2))","B"
705,1,39,49,0.647958,"\text{Not used}","int(x/((a + b*x^2)*(c + d*x^2)^(1/2)),x)","\frac{\mathrm{atan}\left(\frac{b\,\sqrt{d\,x^2+c}}{\sqrt{a\,b\,d-b^2\,c}}\right)}{\sqrt{a\,b\,d-b^2\,c}}","Not used",1,"atan((b*(c + d*x^2)^(1/2))/(a*b*d - b^2*c)^(1/2))/(a*b*d - b^2*c)^(1/2)","B"
706,1,651,80,0.881228,"\text{Not used}","int(1/(x*(a + b*x^2)*(c + d*x^2)^(1/2)),x)","-\frac{\mathrm{atanh}\left(\frac{\sqrt{d\,x^2+c}}{\sqrt{c}}\right)}{a\,\sqrt{c}}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{b^2\,c-a\,b\,d}\,\left(2\,b^3\,d^2\,\sqrt{d\,x^2+c}-\frac{\sqrt{b^2\,c-a\,b\,d}\,\left(2\,a^2\,b^2\,d^3-\frac{\left(8\,a^3\,b^2\,d^3-16\,a^2\,b^3\,c\,d^2\right)\,\sqrt{d\,x^2+c}\,\sqrt{b^2\,c-a\,b\,d}}{4\,\left(a^2\,d-a\,b\,c\right)}\right)}{2\,\left(a^2\,d-a\,b\,c\right)}\right)\,1{}\mathrm{i}}{a^2\,d-a\,b\,c}+\frac{\sqrt{b^2\,c-a\,b\,d}\,\left(2\,b^3\,d^2\,\sqrt{d\,x^2+c}+\frac{\sqrt{b^2\,c-a\,b\,d}\,\left(2\,a^2\,b^2\,d^3+\frac{\left(8\,a^3\,b^2\,d^3-16\,a^2\,b^3\,c\,d^2\right)\,\sqrt{d\,x^2+c}\,\sqrt{b^2\,c-a\,b\,d}}{4\,\left(a^2\,d-a\,b\,c\right)}\right)}{2\,\left(a^2\,d-a\,b\,c\right)}\right)\,1{}\mathrm{i}}{a^2\,d-a\,b\,c}}{\frac{\sqrt{b^2\,c-a\,b\,d}\,\left(2\,b^3\,d^2\,\sqrt{d\,x^2+c}-\frac{\sqrt{b^2\,c-a\,b\,d}\,\left(2\,a^2\,b^2\,d^3-\frac{\left(8\,a^3\,b^2\,d^3-16\,a^2\,b^3\,c\,d^2\right)\,\sqrt{d\,x^2+c}\,\sqrt{b^2\,c-a\,b\,d}}{4\,\left(a^2\,d-a\,b\,c\right)}\right)}{2\,\left(a^2\,d-a\,b\,c\right)}\right)}{a^2\,d-a\,b\,c}-\frac{\sqrt{b^2\,c-a\,b\,d}\,\left(2\,b^3\,d^2\,\sqrt{d\,x^2+c}+\frac{\sqrt{b^2\,c-a\,b\,d}\,\left(2\,a^2\,b^2\,d^3+\frac{\left(8\,a^3\,b^2\,d^3-16\,a^2\,b^3\,c\,d^2\right)\,\sqrt{d\,x^2+c}\,\sqrt{b^2\,c-a\,b\,d}}{4\,\left(a^2\,d-a\,b\,c\right)}\right)}{2\,\left(a^2\,d-a\,b\,c\right)}\right)}{a^2\,d-a\,b\,c}}\right)\,\sqrt{b^2\,c-a\,b\,d}\,1{}\mathrm{i}}{a^2\,d-a\,b\,c}","Not used",1,"- atanh((c + d*x^2)^(1/2)/c^(1/2))/(a*c^(1/2)) - (atan((((b^2*c - a*b*d)^(1/2)*(2*b^3*d^2*(c + d*x^2)^(1/2) - ((b^2*c - a*b*d)^(1/2)*(2*a^2*b^2*d^3 - ((8*a^3*b^2*d^3 - 16*a^2*b^3*c*d^2)*(c + d*x^2)^(1/2)*(b^2*c - a*b*d)^(1/2))/(4*(a^2*d - a*b*c))))/(2*(a^2*d - a*b*c)))*1i)/(a^2*d - a*b*c) + ((b^2*c - a*b*d)^(1/2)*(2*b^3*d^2*(c + d*x^2)^(1/2) + ((b^2*c - a*b*d)^(1/2)*(2*a^2*b^2*d^3 + ((8*a^3*b^2*d^3 - 16*a^2*b^3*c*d^2)*(c + d*x^2)^(1/2)*(b^2*c - a*b*d)^(1/2))/(4*(a^2*d - a*b*c))))/(2*(a^2*d - a*b*c)))*1i)/(a^2*d - a*b*c))/(((b^2*c - a*b*d)^(1/2)*(2*b^3*d^2*(c + d*x^2)^(1/2) - ((b^2*c - a*b*d)^(1/2)*(2*a^2*b^2*d^3 - ((8*a^3*b^2*d^3 - 16*a^2*b^3*c*d^2)*(c + d*x^2)^(1/2)*(b^2*c - a*b*d)^(1/2))/(4*(a^2*d - a*b*c))))/(2*(a^2*d - a*b*c))))/(a^2*d - a*b*c) - ((b^2*c - a*b*d)^(1/2)*(2*b^3*d^2*(c + d*x^2)^(1/2) + ((b^2*c - a*b*d)^(1/2)*(2*a^2*b^2*d^3 + ((8*a^3*b^2*d^3 - 16*a^2*b^3*c*d^2)*(c + d*x^2)^(1/2)*(b^2*c - a*b*d)^(1/2))/(4*(a^2*d - a*b*c))))/(2*(a^2*d - a*b*c))))/(a^2*d - a*b*c)))*(b^2*c - a*b*d)^(1/2)*1i)/(a^2*d - a*b*c)","B"
707,1,396,115,1.111947,"\text{Not used}","int(1/(x^3*(a + b*x^2)*(c + d*x^2)^(1/2)),x)","\frac{\ln\left(\sqrt{d\,x^2+c}\,{\left(b^4\,c-a\,b^3\,d\right)}^{3/2}+b^6\,c^2+a^2\,b^4\,d^2-2\,a\,b^5\,c\,d\right)\,\sqrt{b^4\,c-a\,b^3\,d}}{2\,a^3\,d-2\,a^2\,b\,c}-\frac{\ln\left(\sqrt{d\,x^2+c}\,{\left(b^4\,c-a\,b^3\,d\right)}^{3/2}-b^6\,c^2-a^2\,b^4\,d^2+2\,a\,b^5\,c\,d\right)\,\sqrt{b^4\,c-a\,b^3\,d}}{2\,\left(a^3\,d-a^2\,b\,c\right)}-\frac{\sqrt{d\,x^2+c}}{2\,a\,c\,x^2}-\frac{\mathrm{atan}\left(\frac{b^4\,d^4\,\sqrt{d\,x^2+c}\,3{}\mathrm{i}}{2\,\sqrt{c^3}\,\left(\frac{3\,b^4\,d^4}{2\,c}+\frac{5\,a\,b^3\,d^5}{4\,c^2}+\frac{a^2\,b^2\,d^6}{4\,c^3}\right)}+\frac{b^2\,d^6\,\sqrt{d\,x^2+c}\,1{}\mathrm{i}}{4\,\sqrt{c^3}\,\left(\frac{5\,b^3\,d^5}{4\,a}+\frac{b^2\,d^6}{4\,c}+\frac{3\,b^4\,c\,d^4}{2\,a^2}\right)}+\frac{b^3\,d^5\,\sqrt{d\,x^2+c}\,5{}\mathrm{i}}{4\,\sqrt{c^3}\,\left(\frac{3\,b^4\,d^4}{2\,a}+\frac{5\,b^3\,d^5}{4\,c}+\frac{a\,b^2\,d^6}{4\,c^2}\right)}\right)\,\left(a\,d+2\,b\,c\right)\,1{}\mathrm{i}}{2\,a^2\,\sqrt{c^3}}","Not used",1,"(log((c + d*x^2)^(1/2)*(b^4*c - a*b^3*d)^(3/2) + b^6*c^2 + a^2*b^4*d^2 - 2*a*b^5*c*d)*(b^4*c - a*b^3*d)^(1/2))/(2*a^3*d - 2*a^2*b*c) - (log((c + d*x^2)^(1/2)*(b^4*c - a*b^3*d)^(3/2) - b^6*c^2 - a^2*b^4*d^2 + 2*a*b^5*c*d)*(b^4*c - a*b^3*d)^(1/2))/(2*(a^3*d - a^2*b*c)) - (c + d*x^2)^(1/2)/(2*a*c*x^2) - (atan((b^4*d^4*(c + d*x^2)^(1/2)*3i)/(2*(c^3)^(1/2)*((3*b^4*d^4)/(2*c) + (5*a*b^3*d^5)/(4*c^2) + (a^2*b^2*d^6)/(4*c^3))) + (b^2*d^6*(c + d*x^2)^(1/2)*1i)/(4*(c^3)^(1/2)*((5*b^3*d^5)/(4*a) + (b^2*d^6)/(4*c) + (3*b^4*c*d^4)/(2*a^2))) + (b^3*d^5*(c + d*x^2)^(1/2)*5i)/(4*(c^3)^(1/2)*((3*b^4*d^4)/(2*a) + (5*b^3*d^5)/(4*c) + (a*b^2*d^6)/(4*c^2))))*(a*d + 2*b*c)*1i)/(2*a^2*(c^3)^(1/2))","B"
708,0,-1,114,0.000000,"\text{Not used}","int(x^4/((a + b*x^2)*(c + d*x^2)^(1/2)),x)","\int \frac{x^4}{\left(b\,x^2+a\right)\,\sqrt{d\,x^2+c}} \,d x","Not used",1,"int(x^4/((a + b*x^2)*(c + d*x^2)^(1/2)), x)","F"
709,0,-1,82,0.000000,"\text{Not used}","int(x^2/((a + b*x^2)*(c + d*x^2)^(1/2)),x)","\int \frac{x^2}{\left(b\,x^2+a\right)\,\sqrt{d\,x^2+c}} \,d x","Not used",1,"int(x^2/((a + b*x^2)*(c + d*x^2)^(1/2)), x)","F"
710,0,-1,49,0.000000,"\text{Not used}","int(1/((a + b*x^2)*(c + d*x^2)^(1/2)),x)","\left\{\begin{array}{cl} \frac{\mathrm{atan}\left(\frac{x\,\sqrt{b\,c-a\,d}}{\sqrt{a}\,\sqrt{d\,x^2+c}}\right)}{\sqrt{-a\,\left(a\,d-b\,c\right)}} & \text{\ if\ \ }0<b\,c-a\,d\\ \frac{\ln\left(\frac{\sqrt{a\,\left(d\,x^2+c\right)}+x\,\sqrt{a\,d-b\,c}}{\sqrt{a\,\left(d\,x^2+c\right)}-x\,\sqrt{a\,d-b\,c}}\right)}{2\,\sqrt{a\,\left(a\,d-b\,c\right)}} & \text{\ if\ \ }b\,c-a\,d<0\\ \int \frac{1}{\left(b\,x^2+a\right)\,\sqrt{d\,x^2+c}} \,d x & \text{\ if\ \ }b\,c-a\,d\notin \mathbb{R}\vee a\,d=b\,c \end{array}\right.","Not used",1,"piecewise(0 < - a*d + b*c, atan((x*(- a*d + b*c)^(1/2))/(a^(1/2)*(c + d*x^2)^(1/2)))/(-a*(a*d - b*c))^(1/2), - a*d + b*c < 0, log(((a*(c + d*x^2))^(1/2) + x*(a*d - b*c)^(1/2))/((a*(c + d*x^2))^(1/2) - x*(a*d - b*c)^(1/2)))/(2*(a*(a*d - b*c))^(1/2)), ~in(- a*d + b*c, 'real') | a*d == b*c, int(1/((a + b*x^2)*(c + d*x^2)^(1/2)), x))","F"
711,0,-1,74,0.000000,"\text{Not used}","int(1/(x^2*(a + b*x^2)*(c + d*x^2)^(1/2)),x)","\int \frac{1}{x^2\,\left(b\,x^2+a\right)\,\sqrt{d\,x^2+c}} \,d x","Not used",1,"int(1/(x^2*(a + b*x^2)*(c + d*x^2)^(1/2)), x)","F"
712,0,-1,110,0.000000,"\text{Not used}","int(1/(x^4*(a + b*x^2)*(c + d*x^2)^(1/2)),x)","\int \frac{1}{x^4\,\left(b\,x^2+a\right)\,\sqrt{d\,x^2+c}} \,d x","Not used",1,"int(1/(x^4*(a + b*x^2)*(c + d*x^2)^(1/2)), x)","F"
713,0,-1,109,0.000000,"\text{Not used}","int(x^4/((a + b*x^2)*(c + d*x^2)^(3/2)),x)","\int \frac{x^4}{\left(b\,x^2+a\right)\,{\left(d\,x^2+c\right)}^{3/2}} \,d x","Not used",1,"int(x^4/((a + b*x^2)*(c + d*x^2)^(3/2)), x)","F"
714,1,64,77,0.755079,"\text{Not used}","int(x^3/((a + b*x^2)*(c + d*x^2)^(3/2)),x)","\frac{c}{d\,\sqrt{d\,x^2+c}\,\left(a\,d-b\,c\right)}+\frac{a\,\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d\,x^2+c}}{\sqrt{a\,d-b\,c}}\right)}{\sqrt{b}\,{\left(a\,d-b\,c\right)}^{3/2}}","Not used",1,"c/(d*(c + d*x^2)^(1/2)*(a*d - b*c)) + (a*atan((b^(1/2)*(c + d*x^2)^(1/2))/(a*d - b*c)^(1/2)))/(b^(1/2)*(a*d - b*c)^(3/2))","B"
715,0,-1,74,0.000000,"\text{Not used}","int(x^2/((a + b*x^2)*(c + d*x^2)^(3/2)),x)","\int \frac{x^2}{\left(b\,x^2+a\right)\,{\left(d\,x^2+c\right)}^{3/2}} \,d x","Not used",1,"int(x^2/((a + b*x^2)*(c + d*x^2)^(3/2)), x)","F"
716,1,61,72,0.735074,"\text{Not used}","int(x/((a + b*x^2)*(c + d*x^2)^(3/2)),x)","-\frac{1}{\sqrt{d\,x^2+c}\,\left(a\,d-b\,c\right)}-\frac{\sqrt{b}\,\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d\,x^2+c}}{\sqrt{a\,d-b\,c}}\right)}{{\left(a\,d-b\,c\right)}^{3/2}}","Not used",1,"- 1/((c + d*x^2)^(1/2)*(a*d - b*c)) - (b^(1/2)*atan((b^(1/2)*(c + d*x^2)^(1/2))/(a*d - b*c)^(1/2)))/(a*d - b*c)^(3/2)","B"
717,0,-1,79,0.000000,"\text{Not used}","int(1/((a + b*x^2)*(c + d*x^2)^(3/2)),x)","\int \frac{1}{\left(b\,x^2+a\right)\,{\left(d\,x^2+c\right)}^{3/2}} \,d x","Not used",1,"int(1/((a + b*x^2)*(c + d*x^2)^(3/2)), x)","F"
718,1,2296,107,1.415096,"\text{Not used}","int(1/(x*(a + b*x^2)*(c + d*x^2)^(3/2)),x)","-\frac{d}{\sqrt{d\,x^2+c}\,\left(b\,c^2-a\,c\,d\right)}-\frac{\mathrm{atanh}\left(\frac{6\,b^7\,c^7\,d^3\,\sqrt{d\,x^2+c}}{\sqrt{c^3}\,\left(-2\,a^5\,b^2\,c\,d^8+12\,a^4\,b^3\,c^2\,d^7-30\,a^3\,b^4\,c^3\,d^6+38\,a^2\,b^5\,c^4\,d^5-24\,a\,b^6\,c^5\,d^4+6\,b^7\,c^6\,d^3\right)}-\frac{24\,a\,b^6\,c^6\,d^4\,\sqrt{d\,x^2+c}}{\sqrt{c^3}\,\left(-2\,a^5\,b^2\,c\,d^8+12\,a^4\,b^3\,c^2\,d^7-30\,a^3\,b^4\,c^3\,d^6+38\,a^2\,b^5\,c^4\,d^5-24\,a\,b^6\,c^5\,d^4+6\,b^7\,c^6\,d^3\right)}+\frac{38\,a^2\,b^5\,c^5\,d^5\,\sqrt{d\,x^2+c}}{\sqrt{c^3}\,\left(-2\,a^5\,b^2\,c\,d^8+12\,a^4\,b^3\,c^2\,d^7-30\,a^3\,b^4\,c^3\,d^6+38\,a^2\,b^5\,c^4\,d^5-24\,a\,b^6\,c^5\,d^4+6\,b^7\,c^6\,d^3\right)}-\frac{30\,a^3\,b^4\,c^4\,d^6\,\sqrt{d\,x^2+c}}{\sqrt{c^3}\,\left(-2\,a^5\,b^2\,c\,d^8+12\,a^4\,b^3\,c^2\,d^7-30\,a^3\,b^4\,c^3\,d^6+38\,a^2\,b^5\,c^4\,d^5-24\,a\,b^6\,c^5\,d^4+6\,b^7\,c^6\,d^3\right)}+\frac{12\,a^4\,b^3\,c^3\,d^7\,\sqrt{d\,x^2+c}}{\sqrt{c^3}\,\left(-2\,a^5\,b^2\,c\,d^8+12\,a^4\,b^3\,c^2\,d^7-30\,a^3\,b^4\,c^3\,d^6+38\,a^2\,b^5\,c^4\,d^5-24\,a\,b^6\,c^5\,d^4+6\,b^7\,c^6\,d^3\right)}-\frac{2\,a^5\,b^2\,c^2\,d^8\,\sqrt{d\,x^2+c}}{\sqrt{c^3}\,\left(-2\,a^5\,b^2\,c\,d^8+12\,a^4\,b^3\,c^2\,d^7-30\,a^3\,b^4\,c^3\,d^6+38\,a^2\,b^5\,c^4\,d^5-24\,a\,b^6\,c^5\,d^4+6\,b^7\,c^6\,d^3\right)}\right)}{a\,\sqrt{c^3}}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-b^3\,{\left(a\,d-b\,c\right)}^3}\,\left(\frac{\sqrt{d\,x^2+c}\,\left(-2\,a^5\,b^3\,c^3\,d^7+10\,a^4\,b^4\,c^4\,d^6-22\,a^3\,b^5\,c^5\,d^5+26\,a^2\,b^6\,c^6\,d^4-16\,a\,b^7\,c^7\,d^3+4\,b^8\,c^8\,d^2\right)}{2}-\frac{\sqrt{-b^3\,{\left(a\,d-b\,c\right)}^3}\,\left(18\,a^3\,b^6\,c^8\,d^4-4\,a^2\,b^7\,c^9\,d^3-32\,a^4\,b^5\,c^7\,d^5+28\,a^5\,b^4\,c^6\,d^6-12\,a^6\,b^3\,c^5\,d^7+2\,a^7\,b^2\,c^4\,d^8+\frac{\sqrt{-b^3\,{\left(a\,d-b\,c\right)}^3}\,\sqrt{d\,x^2+c}\,\left(8\,a^8\,b^2\,c^5\,d^8-56\,a^7\,b^3\,c^6\,d^7+160\,a^6\,b^4\,c^7\,d^6-240\,a^5\,b^5\,c^8\,d^5+200\,a^4\,b^6\,c^9\,d^4-88\,a^3\,b^7\,c^{10}\,d^3+16\,a^2\,b^8\,c^{11}\,d^2\right)}{4\,a\,{\left(a\,d-b\,c\right)}^3}\right)}{2\,a\,{\left(a\,d-b\,c\right)}^3}\right)\,1{}\mathrm{i}}{a\,{\left(a\,d-b\,c\right)}^3}+\frac{\sqrt{-b^3\,{\left(a\,d-b\,c\right)}^3}\,\left(\frac{\sqrt{d\,x^2+c}\,\left(-2\,a^5\,b^3\,c^3\,d^7+10\,a^4\,b^4\,c^4\,d^6-22\,a^3\,b^5\,c^5\,d^5+26\,a^2\,b^6\,c^6\,d^4-16\,a\,b^7\,c^7\,d^3+4\,b^8\,c^8\,d^2\right)}{2}-\frac{\sqrt{-b^3\,{\left(a\,d-b\,c\right)}^3}\,\left(4\,a^2\,b^7\,c^9\,d^3-18\,a^3\,b^6\,c^8\,d^4+32\,a^4\,b^5\,c^7\,d^5-28\,a^5\,b^4\,c^6\,d^6+12\,a^6\,b^3\,c^5\,d^7-2\,a^7\,b^2\,c^4\,d^8+\frac{\sqrt{-b^3\,{\left(a\,d-b\,c\right)}^3}\,\sqrt{d\,x^2+c}\,\left(8\,a^8\,b^2\,c^5\,d^8-56\,a^7\,b^3\,c^6\,d^7+160\,a^6\,b^4\,c^7\,d^6-240\,a^5\,b^5\,c^8\,d^5+200\,a^4\,b^6\,c^9\,d^4-88\,a^3\,b^7\,c^{10}\,d^3+16\,a^2\,b^8\,c^{11}\,d^2\right)}{4\,a\,{\left(a\,d-b\,c\right)}^3}\right)}{2\,a\,{\left(a\,d-b\,c\right)}^3}\right)\,1{}\mathrm{i}}{a\,{\left(a\,d-b\,c\right)}^3}}{2\,b^7\,c^6\,d^3-6\,a\,b^6\,c^5\,d^4+6\,a^2\,b^5\,c^4\,d^5-2\,a^3\,b^4\,c^3\,d^6+\frac{\sqrt{-b^3\,{\left(a\,d-b\,c\right)}^3}\,\left(\frac{\sqrt{d\,x^2+c}\,\left(-2\,a^5\,b^3\,c^3\,d^7+10\,a^4\,b^4\,c^4\,d^6-22\,a^3\,b^5\,c^5\,d^5+26\,a^2\,b^6\,c^6\,d^4-16\,a\,b^7\,c^7\,d^3+4\,b^8\,c^8\,d^2\right)}{2}-\frac{\sqrt{-b^3\,{\left(a\,d-b\,c\right)}^3}\,\left(18\,a^3\,b^6\,c^8\,d^4-4\,a^2\,b^7\,c^9\,d^3-32\,a^4\,b^5\,c^7\,d^5+28\,a^5\,b^4\,c^6\,d^6-12\,a^6\,b^3\,c^5\,d^7+2\,a^7\,b^2\,c^4\,d^8+\frac{\sqrt{-b^3\,{\left(a\,d-b\,c\right)}^3}\,\sqrt{d\,x^2+c}\,\left(8\,a^8\,b^2\,c^5\,d^8-56\,a^7\,b^3\,c^6\,d^7+160\,a^6\,b^4\,c^7\,d^6-240\,a^5\,b^5\,c^8\,d^5+200\,a^4\,b^6\,c^9\,d^4-88\,a^3\,b^7\,c^{10}\,d^3+16\,a^2\,b^8\,c^{11}\,d^2\right)}{4\,a\,{\left(a\,d-b\,c\right)}^3}\right)}{2\,a\,{\left(a\,d-b\,c\right)}^3}\right)}{a\,{\left(a\,d-b\,c\right)}^3}-\frac{\sqrt{-b^3\,{\left(a\,d-b\,c\right)}^3}\,\left(\frac{\sqrt{d\,x^2+c}\,\left(-2\,a^5\,b^3\,c^3\,d^7+10\,a^4\,b^4\,c^4\,d^6-22\,a^3\,b^5\,c^5\,d^5+26\,a^2\,b^6\,c^6\,d^4-16\,a\,b^7\,c^7\,d^3+4\,b^8\,c^8\,d^2\right)}{2}-\frac{\sqrt{-b^3\,{\left(a\,d-b\,c\right)}^3}\,\left(4\,a^2\,b^7\,c^9\,d^3-18\,a^3\,b^6\,c^8\,d^4+32\,a^4\,b^5\,c^7\,d^5-28\,a^5\,b^4\,c^6\,d^6+12\,a^6\,b^3\,c^5\,d^7-2\,a^7\,b^2\,c^4\,d^8+\frac{\sqrt{-b^3\,{\left(a\,d-b\,c\right)}^3}\,\sqrt{d\,x^2+c}\,\left(8\,a^8\,b^2\,c^5\,d^8-56\,a^7\,b^3\,c^6\,d^7+160\,a^6\,b^4\,c^7\,d^6-240\,a^5\,b^5\,c^8\,d^5+200\,a^4\,b^6\,c^9\,d^4-88\,a^3\,b^7\,c^{10}\,d^3+16\,a^2\,b^8\,c^{11}\,d^2\right)}{4\,a\,{\left(a\,d-b\,c\right)}^3}\right)}{2\,a\,{\left(a\,d-b\,c\right)}^3}\right)}{a\,{\left(a\,d-b\,c\right)}^3}}\right)\,\sqrt{-b^3\,{\left(a\,d-b\,c\right)}^3}\,1{}\mathrm{i}}{a\,{\left(a\,d-b\,c\right)}^3}","Not used",1,"(atan((((-b^3*(a*d - b*c)^3)^(1/2)*(((c + d*x^2)^(1/2)*(4*b^8*c^8*d^2 - 16*a*b^7*c^7*d^3 + 26*a^2*b^6*c^6*d^4 - 22*a^3*b^5*c^5*d^5 + 10*a^4*b^4*c^4*d^6 - 2*a^5*b^3*c^3*d^7))/2 - ((-b^3*(a*d - b*c)^3)^(1/2)*(18*a^3*b^6*c^8*d^4 - 4*a^2*b^7*c^9*d^3 - 32*a^4*b^5*c^7*d^5 + 28*a^5*b^4*c^6*d^6 - 12*a^6*b^3*c^5*d^7 + 2*a^7*b^2*c^4*d^8 + ((-b^3*(a*d - b*c)^3)^(1/2)*(c + d*x^2)^(1/2)*(16*a^2*b^8*c^11*d^2 - 88*a^3*b^7*c^10*d^3 + 200*a^4*b^6*c^9*d^4 - 240*a^5*b^5*c^8*d^5 + 160*a^6*b^4*c^7*d^6 - 56*a^7*b^3*c^6*d^7 + 8*a^8*b^2*c^5*d^8))/(4*a*(a*d - b*c)^3)))/(2*a*(a*d - b*c)^3))*1i)/(a*(a*d - b*c)^3) + ((-b^3*(a*d - b*c)^3)^(1/2)*(((c + d*x^2)^(1/2)*(4*b^8*c^8*d^2 - 16*a*b^7*c^7*d^3 + 26*a^2*b^6*c^6*d^4 - 22*a^3*b^5*c^5*d^5 + 10*a^4*b^4*c^4*d^6 - 2*a^5*b^3*c^3*d^7))/2 - ((-b^3*(a*d - b*c)^3)^(1/2)*(4*a^2*b^7*c^9*d^3 - 18*a^3*b^6*c^8*d^4 + 32*a^4*b^5*c^7*d^5 - 28*a^5*b^4*c^6*d^6 + 12*a^6*b^3*c^5*d^7 - 2*a^7*b^2*c^4*d^8 + ((-b^3*(a*d - b*c)^3)^(1/2)*(c + d*x^2)^(1/2)*(16*a^2*b^8*c^11*d^2 - 88*a^3*b^7*c^10*d^3 + 200*a^4*b^6*c^9*d^4 - 240*a^5*b^5*c^8*d^5 + 160*a^6*b^4*c^7*d^6 - 56*a^7*b^3*c^6*d^7 + 8*a^8*b^2*c^5*d^8))/(4*a*(a*d - b*c)^3)))/(2*a*(a*d - b*c)^3))*1i)/(a*(a*d - b*c)^3))/(2*b^7*c^6*d^3 - 6*a*b^6*c^5*d^4 + 6*a^2*b^5*c^4*d^5 - 2*a^3*b^4*c^3*d^6 + ((-b^3*(a*d - b*c)^3)^(1/2)*(((c + d*x^2)^(1/2)*(4*b^8*c^8*d^2 - 16*a*b^7*c^7*d^3 + 26*a^2*b^6*c^6*d^4 - 22*a^3*b^5*c^5*d^5 + 10*a^4*b^4*c^4*d^6 - 2*a^5*b^3*c^3*d^7))/2 - ((-b^3*(a*d - b*c)^3)^(1/2)*(18*a^3*b^6*c^8*d^4 - 4*a^2*b^7*c^9*d^3 - 32*a^4*b^5*c^7*d^5 + 28*a^5*b^4*c^6*d^6 - 12*a^6*b^3*c^5*d^7 + 2*a^7*b^2*c^4*d^8 + ((-b^3*(a*d - b*c)^3)^(1/2)*(c + d*x^2)^(1/2)*(16*a^2*b^8*c^11*d^2 - 88*a^3*b^7*c^10*d^3 + 200*a^4*b^6*c^9*d^4 - 240*a^5*b^5*c^8*d^5 + 160*a^6*b^4*c^7*d^6 - 56*a^7*b^3*c^6*d^7 + 8*a^8*b^2*c^5*d^8))/(4*a*(a*d - b*c)^3)))/(2*a*(a*d - b*c)^3)))/(a*(a*d - b*c)^3) - ((-b^3*(a*d - b*c)^3)^(1/2)*(((c + d*x^2)^(1/2)*(4*b^8*c^8*d^2 - 16*a*b^7*c^7*d^3 + 26*a^2*b^6*c^6*d^4 - 22*a^3*b^5*c^5*d^5 + 10*a^4*b^4*c^4*d^6 - 2*a^5*b^3*c^3*d^7))/2 - ((-b^3*(a*d - b*c)^3)^(1/2)*(4*a^2*b^7*c^9*d^3 - 18*a^3*b^6*c^8*d^4 + 32*a^4*b^5*c^7*d^5 - 28*a^5*b^4*c^6*d^6 + 12*a^6*b^3*c^5*d^7 - 2*a^7*b^2*c^4*d^8 + ((-b^3*(a*d - b*c)^3)^(1/2)*(c + d*x^2)^(1/2)*(16*a^2*b^8*c^11*d^2 - 88*a^3*b^7*c^10*d^3 + 200*a^4*b^6*c^9*d^4 - 240*a^5*b^5*c^8*d^5 + 160*a^6*b^4*c^7*d^6 - 56*a^7*b^3*c^6*d^7 + 8*a^8*b^2*c^5*d^8))/(4*a*(a*d - b*c)^3)))/(2*a*(a*d - b*c)^3)))/(a*(a*d - b*c)^3)))*(-b^3*(a*d - b*c)^3)^(1/2)*1i)/(a*(a*d - b*c)^3) - atanh((6*b^7*c^7*d^3*(c + d*x^2)^(1/2))/((c^3)^(1/2)*(6*b^7*c^6*d^3 - 24*a*b^6*c^5*d^4 - 2*a^5*b^2*c*d^8 + 38*a^2*b^5*c^4*d^5 - 30*a^3*b^4*c^3*d^6 + 12*a^4*b^3*c^2*d^7)) - (24*a*b^6*c^6*d^4*(c + d*x^2)^(1/2))/((c^3)^(1/2)*(6*b^7*c^6*d^3 - 24*a*b^6*c^5*d^4 - 2*a^5*b^2*c*d^8 + 38*a^2*b^5*c^4*d^5 - 30*a^3*b^4*c^3*d^6 + 12*a^4*b^3*c^2*d^7)) + (38*a^2*b^5*c^5*d^5*(c + d*x^2)^(1/2))/((c^3)^(1/2)*(6*b^7*c^6*d^3 - 24*a*b^6*c^5*d^4 - 2*a^5*b^2*c*d^8 + 38*a^2*b^5*c^4*d^5 - 30*a^3*b^4*c^3*d^6 + 12*a^4*b^3*c^2*d^7)) - (30*a^3*b^4*c^4*d^6*(c + d*x^2)^(1/2))/((c^3)^(1/2)*(6*b^7*c^6*d^3 - 24*a*b^6*c^5*d^4 - 2*a^5*b^2*c*d^8 + 38*a^2*b^5*c^4*d^5 - 30*a^3*b^4*c^3*d^6 + 12*a^4*b^3*c^2*d^7)) + (12*a^4*b^3*c^3*d^7*(c + d*x^2)^(1/2))/((c^3)^(1/2)*(6*b^7*c^6*d^3 - 24*a*b^6*c^5*d^4 - 2*a^5*b^2*c*d^8 + 38*a^2*b^5*c^4*d^5 - 30*a^3*b^4*c^3*d^6 + 12*a^4*b^3*c^2*d^7)) - (2*a^5*b^2*c^2*d^8*(c + d*x^2)^(1/2))/((c^3)^(1/2)*(6*b^7*c^6*d^3 - 24*a*b^6*c^5*d^4 - 2*a^5*b^2*c*d^8 + 38*a^2*b^5*c^4*d^5 - 30*a^3*b^4*c^3*d^6 + 12*a^4*b^3*c^2*d^7)))/(a*(c^3)^(1/2)) - d/((c + d*x^2)^(1/2)*(b*c^2 - a*c*d))","B"
719,0,-1,124,0.000000,"\text{Not used}","int(1/(x^2*(a + b*x^2)*(c + d*x^2)^(3/2)),x)","\int \frac{1}{x^2\,\left(b\,x^2+a\right)\,{\left(d\,x^2+c\right)}^{3/2}} \,d x","Not used",1,"int(1/(x^2*(a + b*x^2)*(c + d*x^2)^(3/2)), x)","F"
720,1,3025,156,1.979343,"\text{Not used}","int(1/(x^3*(a + b*x^2)*(c + d*x^2)^(3/2)),x)","\frac{\frac{d^2}{b\,c^2-a\,c\,d}+\frac{d\,\left(d\,x^2+c\right)\,\left(3\,a\,d-b\,c\right)}{2\,a\,c^2\,\left(a\,d-b\,c\right)}}{c\,\sqrt{d\,x^2+c}-{\left(d\,x^2+c\right)}^{3/2}}+\frac{\mathrm{atanh}\left(\frac{440\,a^4\,b^8\,c^{11}\,d^5\,\sqrt{d\,x^2+c}}{\sqrt{c^5}\,\left(216\,a^{10}\,b^2\,c^3\,d^{11}-864\,a^9\,b^3\,c^4\,d^{10}+936\,a^8\,b^4\,c^5\,d^9+496\,a^7\,b^5\,c^6\,d^8-1464\,a^6\,b^6\,c^7\,d^7+480\,a^5\,b^7\,c^8\,d^6+440\,a^4\,b^8\,c^9\,d^5-240\,a^3\,b^9\,c^{10}\,d^4\right)}-\frac{240\,a^3\,b^9\,c^{12}\,d^4\,\sqrt{d\,x^2+c}}{\sqrt{c^5}\,\left(216\,a^{10}\,b^2\,c^3\,d^{11}-864\,a^9\,b^3\,c^4\,d^{10}+936\,a^8\,b^4\,c^5\,d^9+496\,a^7\,b^5\,c^6\,d^8-1464\,a^6\,b^6\,c^7\,d^7+480\,a^5\,b^7\,c^8\,d^6+440\,a^4\,b^8\,c^9\,d^5-240\,a^3\,b^9\,c^{10}\,d^4\right)}+\frac{480\,a^5\,b^7\,c^{10}\,d^6\,\sqrt{d\,x^2+c}}{\sqrt{c^5}\,\left(216\,a^{10}\,b^2\,c^3\,d^{11}-864\,a^9\,b^3\,c^4\,d^{10}+936\,a^8\,b^4\,c^5\,d^9+496\,a^7\,b^5\,c^6\,d^8-1464\,a^6\,b^6\,c^7\,d^7+480\,a^5\,b^7\,c^8\,d^6+440\,a^4\,b^8\,c^9\,d^5-240\,a^3\,b^9\,c^{10}\,d^4\right)}-\frac{1464\,a^6\,b^6\,c^9\,d^7\,\sqrt{d\,x^2+c}}{\sqrt{c^5}\,\left(216\,a^{10}\,b^2\,c^3\,d^{11}-864\,a^9\,b^3\,c^4\,d^{10}+936\,a^8\,b^4\,c^5\,d^9+496\,a^7\,b^5\,c^6\,d^8-1464\,a^6\,b^6\,c^7\,d^7+480\,a^5\,b^7\,c^8\,d^6+440\,a^4\,b^8\,c^9\,d^5-240\,a^3\,b^9\,c^{10}\,d^4\right)}+\frac{496\,a^7\,b^5\,c^8\,d^8\,\sqrt{d\,x^2+c}}{\sqrt{c^5}\,\left(216\,a^{10}\,b^2\,c^3\,d^{11}-864\,a^9\,b^3\,c^4\,d^{10}+936\,a^8\,b^4\,c^5\,d^9+496\,a^7\,b^5\,c^6\,d^8-1464\,a^6\,b^6\,c^7\,d^7+480\,a^5\,b^7\,c^8\,d^6+440\,a^4\,b^8\,c^9\,d^5-240\,a^3\,b^9\,c^{10}\,d^4\right)}+\frac{936\,a^8\,b^4\,c^7\,d^9\,\sqrt{d\,x^2+c}}{\sqrt{c^5}\,\left(216\,a^{10}\,b^2\,c^3\,d^{11}-864\,a^9\,b^3\,c^4\,d^{10}+936\,a^8\,b^4\,c^5\,d^9+496\,a^7\,b^5\,c^6\,d^8-1464\,a^6\,b^6\,c^7\,d^7+480\,a^5\,b^7\,c^8\,d^6+440\,a^4\,b^8\,c^9\,d^5-240\,a^3\,b^9\,c^{10}\,d^4\right)}-\frac{864\,a^9\,b^3\,c^6\,d^{10}\,\sqrt{d\,x^2+c}}{\sqrt{c^5}\,\left(216\,a^{10}\,b^2\,c^3\,d^{11}-864\,a^9\,b^3\,c^4\,d^{10}+936\,a^8\,b^4\,c^5\,d^9+496\,a^7\,b^5\,c^6\,d^8-1464\,a^6\,b^6\,c^7\,d^7+480\,a^5\,b^7\,c^8\,d^6+440\,a^4\,b^8\,c^9\,d^5-240\,a^3\,b^9\,c^{10}\,d^4\right)}+\frac{216\,a^{10}\,b^2\,c^5\,d^{11}\,\sqrt{d\,x^2+c}}{\sqrt{c^5}\,\left(216\,a^{10}\,b^2\,c^3\,d^{11}-864\,a^9\,b^3\,c^4\,d^{10}+936\,a^8\,b^4\,c^5\,d^9+496\,a^7\,b^5\,c^6\,d^8-1464\,a^6\,b^6\,c^7\,d^7+480\,a^5\,b^7\,c^8\,d^6+440\,a^4\,b^8\,c^9\,d^5-240\,a^3\,b^9\,c^{10}\,d^4\right)}\right)\,\left(3\,a\,d+2\,b\,c\right)}{2\,a^2\,\sqrt{c^5}}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^3}\,\left(\frac{\sqrt{d\,x^2+c}\,\left(-144\,a^{10}\,b^3\,c^6\,d^9+528\,a^9\,b^4\,c^7\,d^8-544\,a^8\,b^5\,c^8\,d^7-160\,a^7\,b^6\,c^9\,d^6+496\,a^6\,b^7\,c^{10}\,d^5+16\,a^5\,b^8\,c^{11}\,d^4-320\,a^4\,b^9\,c^{12}\,d^3+128\,a^3\,b^{10}\,c^{13}\,d^2\right)}{2}-\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^3}\,\left(416\,a^8\,b^6\,c^{12}\,d^5-32\,a^6\,b^8\,c^{14}\,d^3-1024\,a^9\,b^5\,c^{11}\,d^6+1056\,a^{10}\,b^4\,c^{10}\,d^7-512\,a^{11}\,b^3\,c^9\,d^8+96\,a^{12}\,b^2\,c^8\,d^9+\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^3}\,\sqrt{d\,x^2+c}\,\left(256\,a^{13}\,b^2\,c^{10}\,d^8-1792\,a^{12}\,b^3\,c^{11}\,d^7+5120\,a^{11}\,b^4\,c^{12}\,d^6-7680\,a^{10}\,b^5\,c^{13}\,d^5+6400\,a^9\,b^6\,c^{14}\,d^4-2816\,a^8\,b^7\,c^{15}\,d^3+512\,a^7\,b^8\,c^{16}\,d^2\right)}{4\,a^2\,{\left(a\,d-b\,c\right)}^3}\right)}{2\,a^2\,{\left(a\,d-b\,c\right)}^3}\right)\,1{}\mathrm{i}}{a^2\,{\left(a\,d-b\,c\right)}^3}+\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^3}\,\left(\frac{\sqrt{d\,x^2+c}\,\left(-144\,a^{10}\,b^3\,c^6\,d^9+528\,a^9\,b^4\,c^7\,d^8-544\,a^8\,b^5\,c^8\,d^7-160\,a^7\,b^6\,c^9\,d^6+496\,a^6\,b^7\,c^{10}\,d^5+16\,a^5\,b^8\,c^{11}\,d^4-320\,a^4\,b^9\,c^{12}\,d^3+128\,a^3\,b^{10}\,c^{13}\,d^2\right)}{2}-\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^3}\,\left(32\,a^6\,b^8\,c^{14}\,d^3-416\,a^8\,b^6\,c^{12}\,d^5+1024\,a^9\,b^5\,c^{11}\,d^6-1056\,a^{10}\,b^4\,c^{10}\,d^7+512\,a^{11}\,b^3\,c^9\,d^8-96\,a^{12}\,b^2\,c^8\,d^9+\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^3}\,\sqrt{d\,x^2+c}\,\left(256\,a^{13}\,b^2\,c^{10}\,d^8-1792\,a^{12}\,b^3\,c^{11}\,d^7+5120\,a^{11}\,b^4\,c^{12}\,d^6-7680\,a^{10}\,b^5\,c^{13}\,d^5+6400\,a^9\,b^6\,c^{14}\,d^4-2816\,a^8\,b^7\,c^{15}\,d^3+512\,a^7\,b^8\,c^{16}\,d^2\right)}{4\,a^2\,{\left(a\,d-b\,c\right)}^3}\right)}{2\,a^2\,{\left(a\,d-b\,c\right)}^3}\right)\,1{}\mathrm{i}}{a^2\,{\left(a\,d-b\,c\right)}^3}}{32\,a^2\,b^{10}\,c^{11}\,d^3-144\,a^3\,b^9\,c^{10}\,d^4+96\,a^4\,b^8\,c^9\,d^5+256\,a^5\,b^7\,c^8\,d^6-384\,a^6\,b^6\,c^7\,d^7+144\,a^7\,b^5\,c^6\,d^8-\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^3}\,\left(\frac{\sqrt{d\,x^2+c}\,\left(-144\,a^{10}\,b^3\,c^6\,d^9+528\,a^9\,b^4\,c^7\,d^8-544\,a^8\,b^5\,c^8\,d^7-160\,a^7\,b^6\,c^9\,d^6+496\,a^6\,b^7\,c^{10}\,d^5+16\,a^5\,b^8\,c^{11}\,d^4-320\,a^4\,b^9\,c^{12}\,d^3+128\,a^3\,b^{10}\,c^{13}\,d^2\right)}{2}-\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^3}\,\left(416\,a^8\,b^6\,c^{12}\,d^5-32\,a^6\,b^8\,c^{14}\,d^3-1024\,a^9\,b^5\,c^{11}\,d^6+1056\,a^{10}\,b^4\,c^{10}\,d^7-512\,a^{11}\,b^3\,c^9\,d^8+96\,a^{12}\,b^2\,c^8\,d^9+\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^3}\,\sqrt{d\,x^2+c}\,\left(256\,a^{13}\,b^2\,c^{10}\,d^8-1792\,a^{12}\,b^3\,c^{11}\,d^7+5120\,a^{11}\,b^4\,c^{12}\,d^6-7680\,a^{10}\,b^5\,c^{13}\,d^5+6400\,a^9\,b^6\,c^{14}\,d^4-2816\,a^8\,b^7\,c^{15}\,d^3+512\,a^7\,b^8\,c^{16}\,d^2\right)}{4\,a^2\,{\left(a\,d-b\,c\right)}^3}\right)}{2\,a^2\,{\left(a\,d-b\,c\right)}^3}\right)}{a^2\,{\left(a\,d-b\,c\right)}^3}+\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^3}\,\left(\frac{\sqrt{d\,x^2+c}\,\left(-144\,a^{10}\,b^3\,c^6\,d^9+528\,a^9\,b^4\,c^7\,d^8-544\,a^8\,b^5\,c^8\,d^7-160\,a^7\,b^6\,c^9\,d^6+496\,a^6\,b^7\,c^{10}\,d^5+16\,a^5\,b^8\,c^{11}\,d^4-320\,a^4\,b^9\,c^{12}\,d^3+128\,a^3\,b^{10}\,c^{13}\,d^2\right)}{2}-\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^3}\,\left(32\,a^6\,b^8\,c^{14}\,d^3-416\,a^8\,b^6\,c^{12}\,d^5+1024\,a^9\,b^5\,c^{11}\,d^6-1056\,a^{10}\,b^4\,c^{10}\,d^7+512\,a^{11}\,b^3\,c^9\,d^8-96\,a^{12}\,b^2\,c^8\,d^9+\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^3}\,\sqrt{d\,x^2+c}\,\left(256\,a^{13}\,b^2\,c^{10}\,d^8-1792\,a^{12}\,b^3\,c^{11}\,d^7+5120\,a^{11}\,b^4\,c^{12}\,d^6-7680\,a^{10}\,b^5\,c^{13}\,d^5+6400\,a^9\,b^6\,c^{14}\,d^4-2816\,a^8\,b^7\,c^{15}\,d^3+512\,a^7\,b^8\,c^{16}\,d^2\right)}{4\,a^2\,{\left(a\,d-b\,c\right)}^3}\right)}{2\,a^2\,{\left(a\,d-b\,c\right)}^3}\right)}{a^2\,{\left(a\,d-b\,c\right)}^3}}\right)\,\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^3}\,1{}\mathrm{i}}{a^2\,{\left(a\,d-b\,c\right)}^3}","Not used",1,"(d^2/(b*c^2 - a*c*d) + (d*(c + d*x^2)*(3*a*d - b*c))/(2*a*c^2*(a*d - b*c)))/(c*(c + d*x^2)^(1/2) - (c + d*x^2)^(3/2)) + (atan((((-b^5*(a*d - b*c)^3)^(1/2)*(((c + d*x^2)^(1/2)*(128*a^3*b^10*c^13*d^2 - 320*a^4*b^9*c^12*d^3 + 16*a^5*b^8*c^11*d^4 + 496*a^6*b^7*c^10*d^5 - 160*a^7*b^6*c^9*d^6 - 544*a^8*b^5*c^8*d^7 + 528*a^9*b^4*c^7*d^8 - 144*a^10*b^3*c^6*d^9))/2 - ((-b^5*(a*d - b*c)^3)^(1/2)*(416*a^8*b^6*c^12*d^5 - 32*a^6*b^8*c^14*d^3 - 1024*a^9*b^5*c^11*d^6 + 1056*a^10*b^4*c^10*d^7 - 512*a^11*b^3*c^9*d^8 + 96*a^12*b^2*c^8*d^9 + ((-b^5*(a*d - b*c)^3)^(1/2)*(c + d*x^2)^(1/2)*(512*a^7*b^8*c^16*d^2 - 2816*a^8*b^7*c^15*d^3 + 6400*a^9*b^6*c^14*d^4 - 7680*a^10*b^5*c^13*d^5 + 5120*a^11*b^4*c^12*d^6 - 1792*a^12*b^3*c^11*d^7 + 256*a^13*b^2*c^10*d^8))/(4*a^2*(a*d - b*c)^3)))/(2*a^2*(a*d - b*c)^3))*1i)/(a^2*(a*d - b*c)^3) + ((-b^5*(a*d - b*c)^3)^(1/2)*(((c + d*x^2)^(1/2)*(128*a^3*b^10*c^13*d^2 - 320*a^4*b^9*c^12*d^3 + 16*a^5*b^8*c^11*d^4 + 496*a^6*b^7*c^10*d^5 - 160*a^7*b^6*c^9*d^6 - 544*a^8*b^5*c^8*d^7 + 528*a^9*b^4*c^7*d^8 - 144*a^10*b^3*c^6*d^9))/2 - ((-b^5*(a*d - b*c)^3)^(1/2)*(32*a^6*b^8*c^14*d^3 - 416*a^8*b^6*c^12*d^5 + 1024*a^9*b^5*c^11*d^6 - 1056*a^10*b^4*c^10*d^7 + 512*a^11*b^3*c^9*d^8 - 96*a^12*b^2*c^8*d^9 + ((-b^5*(a*d - b*c)^3)^(1/2)*(c + d*x^2)^(1/2)*(512*a^7*b^8*c^16*d^2 - 2816*a^8*b^7*c^15*d^3 + 6400*a^9*b^6*c^14*d^4 - 7680*a^10*b^5*c^13*d^5 + 5120*a^11*b^4*c^12*d^6 - 1792*a^12*b^3*c^11*d^7 + 256*a^13*b^2*c^10*d^8))/(4*a^2*(a*d - b*c)^3)))/(2*a^2*(a*d - b*c)^3))*1i)/(a^2*(a*d - b*c)^3))/(32*a^2*b^10*c^11*d^3 - 144*a^3*b^9*c^10*d^4 + 96*a^4*b^8*c^9*d^5 + 256*a^5*b^7*c^8*d^6 - 384*a^6*b^6*c^7*d^7 + 144*a^7*b^5*c^6*d^8 - ((-b^5*(a*d - b*c)^3)^(1/2)*(((c + d*x^2)^(1/2)*(128*a^3*b^10*c^13*d^2 - 320*a^4*b^9*c^12*d^3 + 16*a^5*b^8*c^11*d^4 + 496*a^6*b^7*c^10*d^5 - 160*a^7*b^6*c^9*d^6 - 544*a^8*b^5*c^8*d^7 + 528*a^9*b^4*c^7*d^8 - 144*a^10*b^3*c^6*d^9))/2 - ((-b^5*(a*d - b*c)^3)^(1/2)*(416*a^8*b^6*c^12*d^5 - 32*a^6*b^8*c^14*d^3 - 1024*a^9*b^5*c^11*d^6 + 1056*a^10*b^4*c^10*d^7 - 512*a^11*b^3*c^9*d^8 + 96*a^12*b^2*c^8*d^9 + ((-b^5*(a*d - b*c)^3)^(1/2)*(c + d*x^2)^(1/2)*(512*a^7*b^8*c^16*d^2 - 2816*a^8*b^7*c^15*d^3 + 6400*a^9*b^6*c^14*d^4 - 7680*a^10*b^5*c^13*d^5 + 5120*a^11*b^4*c^12*d^6 - 1792*a^12*b^3*c^11*d^7 + 256*a^13*b^2*c^10*d^8))/(4*a^2*(a*d - b*c)^3)))/(2*a^2*(a*d - b*c)^3)))/(a^2*(a*d - b*c)^3) + ((-b^5*(a*d - b*c)^3)^(1/2)*(((c + d*x^2)^(1/2)*(128*a^3*b^10*c^13*d^2 - 320*a^4*b^9*c^12*d^3 + 16*a^5*b^8*c^11*d^4 + 496*a^6*b^7*c^10*d^5 - 160*a^7*b^6*c^9*d^6 - 544*a^8*b^5*c^8*d^7 + 528*a^9*b^4*c^7*d^8 - 144*a^10*b^3*c^6*d^9))/2 - ((-b^5*(a*d - b*c)^3)^(1/2)*(32*a^6*b^8*c^14*d^3 - 416*a^8*b^6*c^12*d^5 + 1024*a^9*b^5*c^11*d^6 - 1056*a^10*b^4*c^10*d^7 + 512*a^11*b^3*c^9*d^8 - 96*a^12*b^2*c^8*d^9 + ((-b^5*(a*d - b*c)^3)^(1/2)*(c + d*x^2)^(1/2)*(512*a^7*b^8*c^16*d^2 - 2816*a^8*b^7*c^15*d^3 + 6400*a^9*b^6*c^14*d^4 - 7680*a^10*b^5*c^13*d^5 + 5120*a^11*b^4*c^12*d^6 - 1792*a^12*b^3*c^11*d^7 + 256*a^13*b^2*c^10*d^8))/(4*a^2*(a*d - b*c)^3)))/(2*a^2*(a*d - b*c)^3)))/(a^2*(a*d - b*c)^3)))*(-b^5*(a*d - b*c)^3)^(1/2)*1i)/(a^2*(a*d - b*c)^3) + (atanh((440*a^4*b^8*c^11*d^5*(c + d*x^2)^(1/2))/((c^5)^(1/2)*(440*a^4*b^8*c^9*d^5 - 240*a^3*b^9*c^10*d^4 + 480*a^5*b^7*c^8*d^6 - 1464*a^6*b^6*c^7*d^7 + 496*a^7*b^5*c^6*d^8 + 936*a^8*b^4*c^5*d^9 - 864*a^9*b^3*c^4*d^10 + 216*a^10*b^2*c^3*d^11)) - (240*a^3*b^9*c^12*d^4*(c + d*x^2)^(1/2))/((c^5)^(1/2)*(440*a^4*b^8*c^9*d^5 - 240*a^3*b^9*c^10*d^4 + 480*a^5*b^7*c^8*d^6 - 1464*a^6*b^6*c^7*d^7 + 496*a^7*b^5*c^6*d^8 + 936*a^8*b^4*c^5*d^9 - 864*a^9*b^3*c^4*d^10 + 216*a^10*b^2*c^3*d^11)) + (480*a^5*b^7*c^10*d^6*(c + d*x^2)^(1/2))/((c^5)^(1/2)*(440*a^4*b^8*c^9*d^5 - 240*a^3*b^9*c^10*d^4 + 480*a^5*b^7*c^8*d^6 - 1464*a^6*b^6*c^7*d^7 + 496*a^7*b^5*c^6*d^8 + 936*a^8*b^4*c^5*d^9 - 864*a^9*b^3*c^4*d^10 + 216*a^10*b^2*c^3*d^11)) - (1464*a^6*b^6*c^9*d^7*(c + d*x^2)^(1/2))/((c^5)^(1/2)*(440*a^4*b^8*c^9*d^5 - 240*a^3*b^9*c^10*d^4 + 480*a^5*b^7*c^8*d^6 - 1464*a^6*b^6*c^7*d^7 + 496*a^7*b^5*c^6*d^8 + 936*a^8*b^4*c^5*d^9 - 864*a^9*b^3*c^4*d^10 + 216*a^10*b^2*c^3*d^11)) + (496*a^7*b^5*c^8*d^8*(c + d*x^2)^(1/2))/((c^5)^(1/2)*(440*a^4*b^8*c^9*d^5 - 240*a^3*b^9*c^10*d^4 + 480*a^5*b^7*c^8*d^6 - 1464*a^6*b^6*c^7*d^7 + 496*a^7*b^5*c^6*d^8 + 936*a^8*b^4*c^5*d^9 - 864*a^9*b^3*c^4*d^10 + 216*a^10*b^2*c^3*d^11)) + (936*a^8*b^4*c^7*d^9*(c + d*x^2)^(1/2))/((c^5)^(1/2)*(440*a^4*b^8*c^9*d^5 - 240*a^3*b^9*c^10*d^4 + 480*a^5*b^7*c^8*d^6 - 1464*a^6*b^6*c^7*d^7 + 496*a^7*b^5*c^6*d^8 + 936*a^8*b^4*c^5*d^9 - 864*a^9*b^3*c^4*d^10 + 216*a^10*b^2*c^3*d^11)) - (864*a^9*b^3*c^6*d^10*(c + d*x^2)^(1/2))/((c^5)^(1/2)*(440*a^4*b^8*c^9*d^5 - 240*a^3*b^9*c^10*d^4 + 480*a^5*b^7*c^8*d^6 - 1464*a^6*b^6*c^7*d^7 + 496*a^7*b^5*c^6*d^8 + 936*a^8*b^4*c^5*d^9 - 864*a^9*b^3*c^4*d^10 + 216*a^10*b^2*c^3*d^11)) + (216*a^10*b^2*c^5*d^11*(c + d*x^2)^(1/2))/((c^5)^(1/2)*(440*a^4*b^8*c^9*d^5 - 240*a^3*b^9*c^10*d^4 + 480*a^5*b^7*c^8*d^6 - 1464*a^6*b^6*c^7*d^7 + 496*a^7*b^5*c^6*d^8 + 936*a^8*b^4*c^5*d^9 - 864*a^9*b^3*c^4*d^10 + 216*a^10*b^2*c^3*d^11)))*(3*a*d + 2*b*c))/(2*a^2*(c^5)^(1/2))","B"
721,0,-1,176,0.000000,"\text{Not used}","int(1/(x^4*(a + b*x^2)*(c + d*x^2)^(3/2)),x)","\int \frac{1}{x^4\,\left(b\,x^2+a\right)\,{\left(d\,x^2+c\right)}^{3/2}} \,d x","Not used",1,"int(1/(x^4*(a + b*x^2)*(c + d*x^2)^(3/2)), x)","F"
722,0,-1,117,0.000000,"\text{Not used}","int(x^4/((a + b*x^2)*(c + d*x^2)^(5/2)),x)","\int \frac{x^4}{\left(b\,x^2+a\right)\,{\left(d\,x^2+c\right)}^{5/2}} \,d x","Not used",1,"int(x^4/((a + b*x^2)*(c + d*x^2)^(5/2)), x)","F"
723,1,110,103,0.927050,"\text{Not used}","int(x^3/((a + b*x^2)*(c + d*x^2)^(5/2)),x)","\frac{\frac{c}{3\,\left(a\,d-b\,c\right)}-\frac{a\,d\,\left(d\,x^2+c\right)}{{\left(a\,d-b\,c\right)}^2}}{d\,{\left(d\,x^2+c\right)}^{3/2}}-\frac{a\,\sqrt{b}\,\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d\,x^2+c}\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}{{\left(a\,d-b\,c\right)}^{5/2}}\right)}{{\left(a\,d-b\,c\right)}^{5/2}}","Not used",1,"(c/(3*(a*d - b*c)) - (a*d*(c + d*x^2))/(a*d - b*c)^2)/(d*(c + d*x^2)^(3/2)) - (a*b^(1/2)*atan((b^(1/2)*(c + d*x^2)^(1/2)*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/(a*d - b*c)^(5/2)))/(a*d - b*c)^(5/2)","B"
724,0,-1,115,0.000000,"\text{Not used}","int(x^2/((a + b*x^2)*(c + d*x^2)^(5/2)),x)","\int \frac{x^2}{\left(b\,x^2+a\right)\,{\left(d\,x^2+c\right)}^{5/2}} \,d x","Not used",1,"int(x^2/((a + b*x^2)*(c + d*x^2)^(5/2)), x)","F"
725,1,103,98,0.850213,"\text{Not used}","int(x/((a + b*x^2)*(c + d*x^2)^(5/2)),x)","\frac{b^{3/2}\,\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d\,x^2+c}\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}{{\left(a\,d-b\,c\right)}^{5/2}}\right)}{{\left(a\,d-b\,c\right)}^{5/2}}-\frac{\frac{1}{3\,\left(a\,d-b\,c\right)}-\frac{b\,\left(d\,x^2+c\right)}{{\left(a\,d-b\,c\right)}^2}}{{\left(d\,x^2+c\right)}^{3/2}}","Not used",1,"(b^(3/2)*atan((b^(1/2)*(c + d*x^2)^(1/2)*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/(a*d - b*c)^(5/2)))/(a*d - b*c)^(5/2) - (1/(3*(a*d - b*c)) - (b*(c + d*x^2))/(a*d - b*c)^2)/(c + d*x^2)^(3/2)","B"
726,0,-1,122,0.000000,"\text{Not used}","int(1/((a + b*x^2)*(c + d*x^2)^(5/2)),x)","\int \frac{1}{\left(b\,x^2+a\right)\,{\left(d\,x^2+c\right)}^{5/2}} \,d x","Not used",1,"int(1/((a + b*x^2)*(c + d*x^2)^(5/2)), x)","F"
727,1,4558,145,2.480768,"\text{Not used}","int(1/(x*(a + b*x^2)*(c + d*x^2)^(5/2)),x)","-\frac{\frac{d}{3\,\left(b\,c^2-a\,c\,d\right)}-\frac{d\,\left(d\,x^2+c\right)\,\left(a\,d-2\,b\,c\right)}{{\left(b\,c^2-a\,c\,d\right)}^2}}{{\left(d\,x^2+c\right)}^{3/2}}-\frac{\mathrm{atanh}\left(\frac{10\,b^{12}\,c^{15}\,d^3\,\sqrt{d\,x^2+c}}{\sqrt{c^5}\,\left(2\,a^{10}\,b^2\,c^3\,d^{13}-22\,a^9\,b^3\,c^4\,d^{12}+110\,a^8\,b^4\,c^5\,d^{11}-330\,a^7\,b^5\,c^6\,d^{10}+660\,a^6\,b^6\,c^7\,d^9-922\,a^5\,b^7\,c^8\,d^8+912\,a^4\,b^8\,c^9\,d^7-630\,a^3\,b^9\,c^{10}\,d^6+290\,a^2\,b^{10}\,c^{11}\,d^5-80\,a\,b^{11}\,c^{12}\,d^4+10\,b^{12}\,c^{13}\,d^3\right)}+\frac{290\,a^2\,b^{10}\,c^{13}\,d^5\,\sqrt{d\,x^2+c}}{\sqrt{c^5}\,\left(2\,a^{10}\,b^2\,c^3\,d^{13}-22\,a^9\,b^3\,c^4\,d^{12}+110\,a^8\,b^4\,c^5\,d^{11}-330\,a^7\,b^5\,c^6\,d^{10}+660\,a^6\,b^6\,c^7\,d^9-922\,a^5\,b^7\,c^8\,d^8+912\,a^4\,b^8\,c^9\,d^7-630\,a^3\,b^9\,c^{10}\,d^6+290\,a^2\,b^{10}\,c^{11}\,d^5-80\,a\,b^{11}\,c^{12}\,d^4+10\,b^{12}\,c^{13}\,d^3\right)}-\frac{630\,a^3\,b^9\,c^{12}\,d^6\,\sqrt{d\,x^2+c}}{\sqrt{c^5}\,\left(2\,a^{10}\,b^2\,c^3\,d^{13}-22\,a^9\,b^3\,c^4\,d^{12}+110\,a^8\,b^4\,c^5\,d^{11}-330\,a^7\,b^5\,c^6\,d^{10}+660\,a^6\,b^6\,c^7\,d^9-922\,a^5\,b^7\,c^8\,d^8+912\,a^4\,b^8\,c^9\,d^7-630\,a^3\,b^9\,c^{10}\,d^6+290\,a^2\,b^{10}\,c^{11}\,d^5-80\,a\,b^{11}\,c^{12}\,d^4+10\,b^{12}\,c^{13}\,d^3\right)}+\frac{912\,a^4\,b^8\,c^{11}\,d^7\,\sqrt{d\,x^2+c}}{\sqrt{c^5}\,\left(2\,a^{10}\,b^2\,c^3\,d^{13}-22\,a^9\,b^3\,c^4\,d^{12}+110\,a^8\,b^4\,c^5\,d^{11}-330\,a^7\,b^5\,c^6\,d^{10}+660\,a^6\,b^6\,c^7\,d^9-922\,a^5\,b^7\,c^8\,d^8+912\,a^4\,b^8\,c^9\,d^7-630\,a^3\,b^9\,c^{10}\,d^6+290\,a^2\,b^{10}\,c^{11}\,d^5-80\,a\,b^{11}\,c^{12}\,d^4+10\,b^{12}\,c^{13}\,d^3\right)}-\frac{922\,a^5\,b^7\,c^{10}\,d^8\,\sqrt{d\,x^2+c}}{\sqrt{c^5}\,\left(2\,a^{10}\,b^2\,c^3\,d^{13}-22\,a^9\,b^3\,c^4\,d^{12}+110\,a^8\,b^4\,c^5\,d^{11}-330\,a^7\,b^5\,c^6\,d^{10}+660\,a^6\,b^6\,c^7\,d^9-922\,a^5\,b^7\,c^8\,d^8+912\,a^4\,b^8\,c^9\,d^7-630\,a^3\,b^9\,c^{10}\,d^6+290\,a^2\,b^{10}\,c^{11}\,d^5-80\,a\,b^{11}\,c^{12}\,d^4+10\,b^{12}\,c^{13}\,d^3\right)}+\frac{660\,a^6\,b^6\,c^9\,d^9\,\sqrt{d\,x^2+c}}{\sqrt{c^5}\,\left(2\,a^{10}\,b^2\,c^3\,d^{13}-22\,a^9\,b^3\,c^4\,d^{12}+110\,a^8\,b^4\,c^5\,d^{11}-330\,a^7\,b^5\,c^6\,d^{10}+660\,a^6\,b^6\,c^7\,d^9-922\,a^5\,b^7\,c^8\,d^8+912\,a^4\,b^8\,c^9\,d^7-630\,a^3\,b^9\,c^{10}\,d^6+290\,a^2\,b^{10}\,c^{11}\,d^5-80\,a\,b^{11}\,c^{12}\,d^4+10\,b^{12}\,c^{13}\,d^3\right)}-\frac{330\,a^7\,b^5\,c^8\,d^{10}\,\sqrt{d\,x^2+c}}{\sqrt{c^5}\,\left(2\,a^{10}\,b^2\,c^3\,d^{13}-22\,a^9\,b^3\,c^4\,d^{12}+110\,a^8\,b^4\,c^5\,d^{11}-330\,a^7\,b^5\,c^6\,d^{10}+660\,a^6\,b^6\,c^7\,d^9-922\,a^5\,b^7\,c^8\,d^8+912\,a^4\,b^8\,c^9\,d^7-630\,a^3\,b^9\,c^{10}\,d^6+290\,a^2\,b^{10}\,c^{11}\,d^5-80\,a\,b^{11}\,c^{12}\,d^4+10\,b^{12}\,c^{13}\,d^3\right)}+\frac{110\,a^8\,b^4\,c^7\,d^{11}\,\sqrt{d\,x^2+c}}{\sqrt{c^5}\,\left(2\,a^{10}\,b^2\,c^3\,d^{13}-22\,a^9\,b^3\,c^4\,d^{12}+110\,a^8\,b^4\,c^5\,d^{11}-330\,a^7\,b^5\,c^6\,d^{10}+660\,a^6\,b^6\,c^7\,d^9-922\,a^5\,b^7\,c^8\,d^8+912\,a^4\,b^8\,c^9\,d^7-630\,a^3\,b^9\,c^{10}\,d^6+290\,a^2\,b^{10}\,c^{11}\,d^5-80\,a\,b^{11}\,c^{12}\,d^4+10\,b^{12}\,c^{13}\,d^3\right)}-\frac{22\,a^9\,b^3\,c^6\,d^{12}\,\sqrt{d\,x^2+c}}{\sqrt{c^5}\,\left(2\,a^{10}\,b^2\,c^3\,d^{13}-22\,a^9\,b^3\,c^4\,d^{12}+110\,a^8\,b^4\,c^5\,d^{11}-330\,a^7\,b^5\,c^6\,d^{10}+660\,a^6\,b^6\,c^7\,d^9-922\,a^5\,b^7\,c^8\,d^8+912\,a^4\,b^8\,c^9\,d^7-630\,a^3\,b^9\,c^{10}\,d^6+290\,a^2\,b^{10}\,c^{11}\,d^5-80\,a\,b^{11}\,c^{12}\,d^4+10\,b^{12}\,c^{13}\,d^3\right)}+\frac{2\,a^{10}\,b^2\,c^5\,d^{13}\,\sqrt{d\,x^2+c}}{\sqrt{c^5}\,\left(2\,a^{10}\,b^2\,c^3\,d^{13}-22\,a^9\,b^3\,c^4\,d^{12}+110\,a^8\,b^4\,c^5\,d^{11}-330\,a^7\,b^5\,c^6\,d^{10}+660\,a^6\,b^6\,c^7\,d^9-922\,a^5\,b^7\,c^8\,d^8+912\,a^4\,b^8\,c^9\,d^7-630\,a^3\,b^9\,c^{10}\,d^6+290\,a^2\,b^{10}\,c^{11}\,d^5-80\,a\,b^{11}\,c^{12}\,d^4+10\,b^{12}\,c^{13}\,d^3\right)}-\frac{80\,a\,b^{11}\,c^{14}\,d^4\,\sqrt{d\,x^2+c}}{\sqrt{c^5}\,\left(2\,a^{10}\,b^2\,c^3\,d^{13}-22\,a^9\,b^3\,c^4\,d^{12}+110\,a^8\,b^4\,c^5\,d^{11}-330\,a^7\,b^5\,c^6\,d^{10}+660\,a^6\,b^6\,c^7\,d^9-922\,a^5\,b^7\,c^8\,d^8+912\,a^4\,b^8\,c^9\,d^7-630\,a^3\,b^9\,c^{10}\,d^6+290\,a^2\,b^{10}\,c^{11}\,d^5-80\,a\,b^{11}\,c^{12}\,d^4+10\,b^{12}\,c^{13}\,d^3\right)}\right)}{a\,\sqrt{c^5}}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^5}\,\left(\frac{\sqrt{d\,x^2+c}\,\left(2\,a^{10}\,b^3\,c^6\,d^{12}-20\,a^9\,b^4\,c^7\,d^{11}+90\,a^8\,b^5\,c^8\,d^{10}-240\,a^7\,b^6\,c^9\,d^9+422\,a^6\,b^7\,c^{10}\,d^8-516\,a^5\,b^8\,c^{11}\,d^7+450\,a^4\,b^9\,c^{12}\,d^6-280\,a^3\,b^{10}\,c^{13}\,d^5+120\,a^2\,b^{11}\,c^{14}\,d^4-32\,a\,b^{12}\,c^{15}\,d^3+4\,b^{13}\,c^{16}\,d^2\right)}{2}+\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^5}\,\left(6\,a^2\,b^{12}\,c^{18}\,d^3-54\,a^3\,b^{11}\,c^{17}\,d^4+218\,a^4\,b^{10}\,c^{16}\,d^5-520\,a^5\,b^9\,c^{15}\,d^6+812\,a^6\,b^8\,c^{14}\,d^7-868\,a^7\,b^7\,c^{13}\,d^8+644\,a^8\,b^6\,c^{12}\,d^9-328\,a^9\,b^5\,c^{11}\,d^{10}+110\,a^{10}\,b^4\,c^{10}\,d^{11}-22\,a^{11}\,b^3\,c^9\,d^{12}+2\,a^{12}\,b^2\,c^8\,d^{13}-\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^5}\,\sqrt{d\,x^2+c}\,\left(-8\,a^{13}\,b^2\,c^{10}\,d^{13}+96\,a^{12}\,b^3\,c^{11}\,d^{12}-520\,a^{11}\,b^4\,c^{12}\,d^{11}+1680\,a^{10}\,b^5\,c^{13}\,d^{10}-3600\,a^9\,b^6\,c^{14}\,d^9+5376\,a^8\,b^7\,c^{15}\,d^8-5712\,a^7\,b^8\,c^{16}\,d^7+4320\,a^6\,b^9\,c^{17}\,d^6-2280\,a^5\,b^{10}\,c^{18}\,d^5+800\,a^4\,b^{11}\,c^{19}\,d^4-168\,a^3\,b^{12}\,c^{20}\,d^3+16\,a^2\,b^{13}\,c^{21}\,d^2\right)}{4\,a\,{\left(a\,d-b\,c\right)}^5}\right)}{2\,a\,{\left(a\,d-b\,c\right)}^5}\right)\,1{}\mathrm{i}}{a\,{\left(a\,d-b\,c\right)}^5}+\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^5}\,\left(\frac{\sqrt{d\,x^2+c}\,\left(2\,a^{10}\,b^3\,c^6\,d^{12}-20\,a^9\,b^4\,c^7\,d^{11}+90\,a^8\,b^5\,c^8\,d^{10}-240\,a^7\,b^6\,c^9\,d^9+422\,a^6\,b^7\,c^{10}\,d^8-516\,a^5\,b^8\,c^{11}\,d^7+450\,a^4\,b^9\,c^{12}\,d^6-280\,a^3\,b^{10}\,c^{13}\,d^5+120\,a^2\,b^{11}\,c^{14}\,d^4-32\,a\,b^{12}\,c^{15}\,d^3+4\,b^{13}\,c^{16}\,d^2\right)}{2}-\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^5}\,\left(6\,a^2\,b^{12}\,c^{18}\,d^3-54\,a^3\,b^{11}\,c^{17}\,d^4+218\,a^4\,b^{10}\,c^{16}\,d^5-520\,a^5\,b^9\,c^{15}\,d^6+812\,a^6\,b^8\,c^{14}\,d^7-868\,a^7\,b^7\,c^{13}\,d^8+644\,a^8\,b^6\,c^{12}\,d^9-328\,a^9\,b^5\,c^{11}\,d^{10}+110\,a^{10}\,b^4\,c^{10}\,d^{11}-22\,a^{11}\,b^3\,c^9\,d^{12}+2\,a^{12}\,b^2\,c^8\,d^{13}+\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^5}\,\sqrt{d\,x^2+c}\,\left(-8\,a^{13}\,b^2\,c^{10}\,d^{13}+96\,a^{12}\,b^3\,c^{11}\,d^{12}-520\,a^{11}\,b^4\,c^{12}\,d^{11}+1680\,a^{10}\,b^5\,c^{13}\,d^{10}-3600\,a^9\,b^6\,c^{14}\,d^9+5376\,a^8\,b^7\,c^{15}\,d^8-5712\,a^7\,b^8\,c^{16}\,d^7+4320\,a^6\,b^9\,c^{17}\,d^6-2280\,a^5\,b^{10}\,c^{18}\,d^5+800\,a^4\,b^{11}\,c^{19}\,d^4-168\,a^3\,b^{12}\,c^{20}\,d^3+16\,a^2\,b^{13}\,c^{21}\,d^2\right)}{4\,a\,{\left(a\,d-b\,c\right)}^5}\right)}{2\,a\,{\left(a\,d-b\,c\right)}^5}\right)\,1{}\mathrm{i}}{a\,{\left(a\,d-b\,c\right)}^5}}{4\,b^{12}\,c^{13}\,d^3-26\,a\,b^{11}\,c^{12}\,d^4+72\,a^2\,b^{10}\,c^{11}\,d^5-110\,a^3\,b^9\,c^{10}\,d^6+100\,a^4\,b^8\,c^9\,d^7-54\,a^5\,b^7\,c^8\,d^8+16\,a^6\,b^6\,c^7\,d^9-2\,a^7\,b^5\,c^6\,d^{10}+\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^5}\,\left(\frac{\sqrt{d\,x^2+c}\,\left(2\,a^{10}\,b^3\,c^6\,d^{12}-20\,a^9\,b^4\,c^7\,d^{11}+90\,a^8\,b^5\,c^8\,d^{10}-240\,a^7\,b^6\,c^9\,d^9+422\,a^6\,b^7\,c^{10}\,d^8-516\,a^5\,b^8\,c^{11}\,d^7+450\,a^4\,b^9\,c^{12}\,d^6-280\,a^3\,b^{10}\,c^{13}\,d^5+120\,a^2\,b^{11}\,c^{14}\,d^4-32\,a\,b^{12}\,c^{15}\,d^3+4\,b^{13}\,c^{16}\,d^2\right)}{2}+\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^5}\,\left(6\,a^2\,b^{12}\,c^{18}\,d^3-54\,a^3\,b^{11}\,c^{17}\,d^4+218\,a^4\,b^{10}\,c^{16}\,d^5-520\,a^5\,b^9\,c^{15}\,d^6+812\,a^6\,b^8\,c^{14}\,d^7-868\,a^7\,b^7\,c^{13}\,d^8+644\,a^8\,b^6\,c^{12}\,d^9-328\,a^9\,b^5\,c^{11}\,d^{10}+110\,a^{10}\,b^4\,c^{10}\,d^{11}-22\,a^{11}\,b^3\,c^9\,d^{12}+2\,a^{12}\,b^2\,c^8\,d^{13}-\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^5}\,\sqrt{d\,x^2+c}\,\left(-8\,a^{13}\,b^2\,c^{10}\,d^{13}+96\,a^{12}\,b^3\,c^{11}\,d^{12}-520\,a^{11}\,b^4\,c^{12}\,d^{11}+1680\,a^{10}\,b^5\,c^{13}\,d^{10}-3600\,a^9\,b^6\,c^{14}\,d^9+5376\,a^8\,b^7\,c^{15}\,d^8-5712\,a^7\,b^8\,c^{16}\,d^7+4320\,a^6\,b^9\,c^{17}\,d^6-2280\,a^5\,b^{10}\,c^{18}\,d^5+800\,a^4\,b^{11}\,c^{19}\,d^4-168\,a^3\,b^{12}\,c^{20}\,d^3+16\,a^2\,b^{13}\,c^{21}\,d^2\right)}{4\,a\,{\left(a\,d-b\,c\right)}^5}\right)}{2\,a\,{\left(a\,d-b\,c\right)}^5}\right)}{a\,{\left(a\,d-b\,c\right)}^5}-\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^5}\,\left(\frac{\sqrt{d\,x^2+c}\,\left(2\,a^{10}\,b^3\,c^6\,d^{12}-20\,a^9\,b^4\,c^7\,d^{11}+90\,a^8\,b^5\,c^8\,d^{10}-240\,a^7\,b^6\,c^9\,d^9+422\,a^6\,b^7\,c^{10}\,d^8-516\,a^5\,b^8\,c^{11}\,d^7+450\,a^4\,b^9\,c^{12}\,d^6-280\,a^3\,b^{10}\,c^{13}\,d^5+120\,a^2\,b^{11}\,c^{14}\,d^4-32\,a\,b^{12}\,c^{15}\,d^3+4\,b^{13}\,c^{16}\,d^2\right)}{2}-\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^5}\,\left(6\,a^2\,b^{12}\,c^{18}\,d^3-54\,a^3\,b^{11}\,c^{17}\,d^4+218\,a^4\,b^{10}\,c^{16}\,d^5-520\,a^5\,b^9\,c^{15}\,d^6+812\,a^6\,b^8\,c^{14}\,d^7-868\,a^7\,b^7\,c^{13}\,d^8+644\,a^8\,b^6\,c^{12}\,d^9-328\,a^9\,b^5\,c^{11}\,d^{10}+110\,a^{10}\,b^4\,c^{10}\,d^{11}-22\,a^{11}\,b^3\,c^9\,d^{12}+2\,a^{12}\,b^2\,c^8\,d^{13}+\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^5}\,\sqrt{d\,x^2+c}\,\left(-8\,a^{13}\,b^2\,c^{10}\,d^{13}+96\,a^{12}\,b^3\,c^{11}\,d^{12}-520\,a^{11}\,b^4\,c^{12}\,d^{11}+1680\,a^{10}\,b^5\,c^{13}\,d^{10}-3600\,a^9\,b^6\,c^{14}\,d^9+5376\,a^8\,b^7\,c^{15}\,d^8-5712\,a^7\,b^8\,c^{16}\,d^7+4320\,a^6\,b^9\,c^{17}\,d^6-2280\,a^5\,b^{10}\,c^{18}\,d^5+800\,a^4\,b^{11}\,c^{19}\,d^4-168\,a^3\,b^{12}\,c^{20}\,d^3+16\,a^2\,b^{13}\,c^{21}\,d^2\right)}{4\,a\,{\left(a\,d-b\,c\right)}^5}\right)}{2\,a\,{\left(a\,d-b\,c\right)}^5}\right)}{a\,{\left(a\,d-b\,c\right)}^5}}\right)\,\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^5}\,1{}\mathrm{i}}{a\,{\left(a\,d-b\,c\right)}^5}","Not used",1,"(atan((((-b^5*(a*d - b*c)^5)^(1/2)*(((c + d*x^2)^(1/2)*(4*b^13*c^16*d^2 - 32*a*b^12*c^15*d^3 + 120*a^2*b^11*c^14*d^4 - 280*a^3*b^10*c^13*d^5 + 450*a^4*b^9*c^12*d^6 - 516*a^5*b^8*c^11*d^7 + 422*a^6*b^7*c^10*d^8 - 240*a^7*b^6*c^9*d^9 + 90*a^8*b^5*c^8*d^10 - 20*a^9*b^4*c^7*d^11 + 2*a^10*b^3*c^6*d^12))/2 + ((-b^5*(a*d - b*c)^5)^(1/2)*(6*a^2*b^12*c^18*d^3 - 54*a^3*b^11*c^17*d^4 + 218*a^4*b^10*c^16*d^5 - 520*a^5*b^9*c^15*d^6 + 812*a^6*b^8*c^14*d^7 - 868*a^7*b^7*c^13*d^8 + 644*a^8*b^6*c^12*d^9 - 328*a^9*b^5*c^11*d^10 + 110*a^10*b^4*c^10*d^11 - 22*a^11*b^3*c^9*d^12 + 2*a^12*b^2*c^8*d^13 - ((-b^5*(a*d - b*c)^5)^(1/2)*(c + d*x^2)^(1/2)*(16*a^2*b^13*c^21*d^2 - 168*a^3*b^12*c^20*d^3 + 800*a^4*b^11*c^19*d^4 - 2280*a^5*b^10*c^18*d^5 + 4320*a^6*b^9*c^17*d^6 - 5712*a^7*b^8*c^16*d^7 + 5376*a^8*b^7*c^15*d^8 - 3600*a^9*b^6*c^14*d^9 + 1680*a^10*b^5*c^13*d^10 - 520*a^11*b^4*c^12*d^11 + 96*a^12*b^3*c^11*d^12 - 8*a^13*b^2*c^10*d^13))/(4*a*(a*d - b*c)^5)))/(2*a*(a*d - b*c)^5))*1i)/(a*(a*d - b*c)^5) + ((-b^5*(a*d - b*c)^5)^(1/2)*(((c + d*x^2)^(1/2)*(4*b^13*c^16*d^2 - 32*a*b^12*c^15*d^3 + 120*a^2*b^11*c^14*d^4 - 280*a^3*b^10*c^13*d^5 + 450*a^4*b^9*c^12*d^6 - 516*a^5*b^8*c^11*d^7 + 422*a^6*b^7*c^10*d^8 - 240*a^7*b^6*c^9*d^9 + 90*a^8*b^5*c^8*d^10 - 20*a^9*b^4*c^7*d^11 + 2*a^10*b^3*c^6*d^12))/2 - ((-b^5*(a*d - b*c)^5)^(1/2)*(6*a^2*b^12*c^18*d^3 - 54*a^3*b^11*c^17*d^4 + 218*a^4*b^10*c^16*d^5 - 520*a^5*b^9*c^15*d^6 + 812*a^6*b^8*c^14*d^7 - 868*a^7*b^7*c^13*d^8 + 644*a^8*b^6*c^12*d^9 - 328*a^9*b^5*c^11*d^10 + 110*a^10*b^4*c^10*d^11 - 22*a^11*b^3*c^9*d^12 + 2*a^12*b^2*c^8*d^13 + ((-b^5*(a*d - b*c)^5)^(1/2)*(c + d*x^2)^(1/2)*(16*a^2*b^13*c^21*d^2 - 168*a^3*b^12*c^20*d^3 + 800*a^4*b^11*c^19*d^4 - 2280*a^5*b^10*c^18*d^5 + 4320*a^6*b^9*c^17*d^6 - 5712*a^7*b^8*c^16*d^7 + 5376*a^8*b^7*c^15*d^8 - 3600*a^9*b^6*c^14*d^9 + 1680*a^10*b^5*c^13*d^10 - 520*a^11*b^4*c^12*d^11 + 96*a^12*b^3*c^11*d^12 - 8*a^13*b^2*c^10*d^13))/(4*a*(a*d - b*c)^5)))/(2*a*(a*d - b*c)^5))*1i)/(a*(a*d - b*c)^5))/(4*b^12*c^13*d^3 - 26*a*b^11*c^12*d^4 + 72*a^2*b^10*c^11*d^5 - 110*a^3*b^9*c^10*d^6 + 100*a^4*b^8*c^9*d^7 - 54*a^5*b^7*c^8*d^8 + 16*a^6*b^6*c^7*d^9 - 2*a^7*b^5*c^6*d^10 + ((-b^5*(a*d - b*c)^5)^(1/2)*(((c + d*x^2)^(1/2)*(4*b^13*c^16*d^2 - 32*a*b^12*c^15*d^3 + 120*a^2*b^11*c^14*d^4 - 280*a^3*b^10*c^13*d^5 + 450*a^4*b^9*c^12*d^6 - 516*a^5*b^8*c^11*d^7 + 422*a^6*b^7*c^10*d^8 - 240*a^7*b^6*c^9*d^9 + 90*a^8*b^5*c^8*d^10 - 20*a^9*b^4*c^7*d^11 + 2*a^10*b^3*c^6*d^12))/2 + ((-b^5*(a*d - b*c)^5)^(1/2)*(6*a^2*b^12*c^18*d^3 - 54*a^3*b^11*c^17*d^4 + 218*a^4*b^10*c^16*d^5 - 520*a^5*b^9*c^15*d^6 + 812*a^6*b^8*c^14*d^7 - 868*a^7*b^7*c^13*d^8 + 644*a^8*b^6*c^12*d^9 - 328*a^9*b^5*c^11*d^10 + 110*a^10*b^4*c^10*d^11 - 22*a^11*b^3*c^9*d^12 + 2*a^12*b^2*c^8*d^13 - ((-b^5*(a*d - b*c)^5)^(1/2)*(c + d*x^2)^(1/2)*(16*a^2*b^13*c^21*d^2 - 168*a^3*b^12*c^20*d^3 + 800*a^4*b^11*c^19*d^4 - 2280*a^5*b^10*c^18*d^5 + 4320*a^6*b^9*c^17*d^6 - 5712*a^7*b^8*c^16*d^7 + 5376*a^8*b^7*c^15*d^8 - 3600*a^9*b^6*c^14*d^9 + 1680*a^10*b^5*c^13*d^10 - 520*a^11*b^4*c^12*d^11 + 96*a^12*b^3*c^11*d^12 - 8*a^13*b^2*c^10*d^13))/(4*a*(a*d - b*c)^5)))/(2*a*(a*d - b*c)^5)))/(a*(a*d - b*c)^5) - ((-b^5*(a*d - b*c)^5)^(1/2)*(((c + d*x^2)^(1/2)*(4*b^13*c^16*d^2 - 32*a*b^12*c^15*d^3 + 120*a^2*b^11*c^14*d^4 - 280*a^3*b^10*c^13*d^5 + 450*a^4*b^9*c^12*d^6 - 516*a^5*b^8*c^11*d^7 + 422*a^6*b^7*c^10*d^8 - 240*a^7*b^6*c^9*d^9 + 90*a^8*b^5*c^8*d^10 - 20*a^9*b^4*c^7*d^11 + 2*a^10*b^3*c^6*d^12))/2 - ((-b^5*(a*d - b*c)^5)^(1/2)*(6*a^2*b^12*c^18*d^3 - 54*a^3*b^11*c^17*d^4 + 218*a^4*b^10*c^16*d^5 - 520*a^5*b^9*c^15*d^6 + 812*a^6*b^8*c^14*d^7 - 868*a^7*b^7*c^13*d^8 + 644*a^8*b^6*c^12*d^9 - 328*a^9*b^5*c^11*d^10 + 110*a^10*b^4*c^10*d^11 - 22*a^11*b^3*c^9*d^12 + 2*a^12*b^2*c^8*d^13 + ((-b^5*(a*d - b*c)^5)^(1/2)*(c + d*x^2)^(1/2)*(16*a^2*b^13*c^21*d^2 - 168*a^3*b^12*c^20*d^3 + 800*a^4*b^11*c^19*d^4 - 2280*a^5*b^10*c^18*d^5 + 4320*a^6*b^9*c^17*d^6 - 5712*a^7*b^8*c^16*d^7 + 5376*a^8*b^7*c^15*d^8 - 3600*a^9*b^6*c^14*d^9 + 1680*a^10*b^5*c^13*d^10 - 520*a^11*b^4*c^12*d^11 + 96*a^12*b^3*c^11*d^12 - 8*a^13*b^2*c^10*d^13))/(4*a*(a*d - b*c)^5)))/(2*a*(a*d - b*c)^5)))/(a*(a*d - b*c)^5)))*(-b^5*(a*d - b*c)^5)^(1/2)*1i)/(a*(a*d - b*c)^5) - atanh((10*b^12*c^15*d^3*(c + d*x^2)^(1/2))/((c^5)^(1/2)*(10*b^12*c^13*d^3 - 80*a*b^11*c^12*d^4 + 290*a^2*b^10*c^11*d^5 - 630*a^3*b^9*c^10*d^6 + 912*a^4*b^8*c^9*d^7 - 922*a^5*b^7*c^8*d^8 + 660*a^6*b^6*c^7*d^9 - 330*a^7*b^5*c^6*d^10 + 110*a^8*b^4*c^5*d^11 - 22*a^9*b^3*c^4*d^12 + 2*a^10*b^2*c^3*d^13)) + (290*a^2*b^10*c^13*d^5*(c + d*x^2)^(1/2))/((c^5)^(1/2)*(10*b^12*c^13*d^3 - 80*a*b^11*c^12*d^4 + 290*a^2*b^10*c^11*d^5 - 630*a^3*b^9*c^10*d^6 + 912*a^4*b^8*c^9*d^7 - 922*a^5*b^7*c^8*d^8 + 660*a^6*b^6*c^7*d^9 - 330*a^7*b^5*c^6*d^10 + 110*a^8*b^4*c^5*d^11 - 22*a^9*b^3*c^4*d^12 + 2*a^10*b^2*c^3*d^13)) - (630*a^3*b^9*c^12*d^6*(c + d*x^2)^(1/2))/((c^5)^(1/2)*(10*b^12*c^13*d^3 - 80*a*b^11*c^12*d^4 + 290*a^2*b^10*c^11*d^5 - 630*a^3*b^9*c^10*d^6 + 912*a^4*b^8*c^9*d^7 - 922*a^5*b^7*c^8*d^8 + 660*a^6*b^6*c^7*d^9 - 330*a^7*b^5*c^6*d^10 + 110*a^8*b^4*c^5*d^11 - 22*a^9*b^3*c^4*d^12 + 2*a^10*b^2*c^3*d^13)) + (912*a^4*b^8*c^11*d^7*(c + d*x^2)^(1/2))/((c^5)^(1/2)*(10*b^12*c^13*d^3 - 80*a*b^11*c^12*d^4 + 290*a^2*b^10*c^11*d^5 - 630*a^3*b^9*c^10*d^6 + 912*a^4*b^8*c^9*d^7 - 922*a^5*b^7*c^8*d^8 + 660*a^6*b^6*c^7*d^9 - 330*a^7*b^5*c^6*d^10 + 110*a^8*b^4*c^5*d^11 - 22*a^9*b^3*c^4*d^12 + 2*a^10*b^2*c^3*d^13)) - (922*a^5*b^7*c^10*d^8*(c + d*x^2)^(1/2))/((c^5)^(1/2)*(10*b^12*c^13*d^3 - 80*a*b^11*c^12*d^4 + 290*a^2*b^10*c^11*d^5 - 630*a^3*b^9*c^10*d^6 + 912*a^4*b^8*c^9*d^7 - 922*a^5*b^7*c^8*d^8 + 660*a^6*b^6*c^7*d^9 - 330*a^7*b^5*c^6*d^10 + 110*a^8*b^4*c^5*d^11 - 22*a^9*b^3*c^4*d^12 + 2*a^10*b^2*c^3*d^13)) + (660*a^6*b^6*c^9*d^9*(c + d*x^2)^(1/2))/((c^5)^(1/2)*(10*b^12*c^13*d^3 - 80*a*b^11*c^12*d^4 + 290*a^2*b^10*c^11*d^5 - 630*a^3*b^9*c^10*d^6 + 912*a^4*b^8*c^9*d^7 - 922*a^5*b^7*c^8*d^8 + 660*a^6*b^6*c^7*d^9 - 330*a^7*b^5*c^6*d^10 + 110*a^8*b^4*c^5*d^11 - 22*a^9*b^3*c^4*d^12 + 2*a^10*b^2*c^3*d^13)) - (330*a^7*b^5*c^8*d^10*(c + d*x^2)^(1/2))/((c^5)^(1/2)*(10*b^12*c^13*d^3 - 80*a*b^11*c^12*d^4 + 290*a^2*b^10*c^11*d^5 - 630*a^3*b^9*c^10*d^6 + 912*a^4*b^8*c^9*d^7 - 922*a^5*b^7*c^8*d^8 + 660*a^6*b^6*c^7*d^9 - 330*a^7*b^5*c^6*d^10 + 110*a^8*b^4*c^5*d^11 - 22*a^9*b^3*c^4*d^12 + 2*a^10*b^2*c^3*d^13)) + (110*a^8*b^4*c^7*d^11*(c + d*x^2)^(1/2))/((c^5)^(1/2)*(10*b^12*c^13*d^3 - 80*a*b^11*c^12*d^4 + 290*a^2*b^10*c^11*d^5 - 630*a^3*b^9*c^10*d^6 + 912*a^4*b^8*c^9*d^7 - 922*a^5*b^7*c^8*d^8 + 660*a^6*b^6*c^7*d^9 - 330*a^7*b^5*c^6*d^10 + 110*a^8*b^4*c^5*d^11 - 22*a^9*b^3*c^4*d^12 + 2*a^10*b^2*c^3*d^13)) - (22*a^9*b^3*c^6*d^12*(c + d*x^2)^(1/2))/((c^5)^(1/2)*(10*b^12*c^13*d^3 - 80*a*b^11*c^12*d^4 + 290*a^2*b^10*c^11*d^5 - 630*a^3*b^9*c^10*d^6 + 912*a^4*b^8*c^9*d^7 - 922*a^5*b^7*c^8*d^8 + 660*a^6*b^6*c^7*d^9 - 330*a^7*b^5*c^6*d^10 + 110*a^8*b^4*c^5*d^11 - 22*a^9*b^3*c^4*d^12 + 2*a^10*b^2*c^3*d^13)) + (2*a^10*b^2*c^5*d^13*(c + d*x^2)^(1/2))/((c^5)^(1/2)*(10*b^12*c^13*d^3 - 80*a*b^11*c^12*d^4 + 290*a^2*b^10*c^11*d^5 - 630*a^3*b^9*c^10*d^6 + 912*a^4*b^8*c^9*d^7 - 922*a^5*b^7*c^8*d^8 + 660*a^6*b^6*c^7*d^9 - 330*a^7*b^5*c^6*d^10 + 110*a^8*b^4*c^5*d^11 - 22*a^9*b^3*c^4*d^12 + 2*a^10*b^2*c^3*d^13)) - (80*a*b^11*c^14*d^4*(c + d*x^2)^(1/2))/((c^5)^(1/2)*(10*b^12*c^13*d^3 - 80*a*b^11*c^12*d^4 + 290*a^2*b^10*c^11*d^5 - 630*a^3*b^9*c^10*d^6 + 912*a^4*b^8*c^9*d^7 - 922*a^5*b^7*c^8*d^8 + 660*a^6*b^6*c^7*d^9 - 330*a^7*b^5*c^6*d^10 + 110*a^8*b^4*c^5*d^11 - 22*a^9*b^3*c^4*d^12 + 2*a^10*b^2*c^3*d^13)))/(a*(c^5)^(1/2)) - (d/(3*(b*c^2 - a*c*d)) - (d*(c + d*x^2)*(a*d - 2*b*c))/(b*c^2 - a*c*d)^2)/(c + d*x^2)^(3/2)","B"
728,0,-1,178,0.000000,"\text{Not used}","int(1/(x^2*(a + b*x^2)*(c + d*x^2)^(5/2)),x)","\int \frac{1}{x^2\,\left(b\,x^2+a\right)\,{\left(d\,x^2+c\right)}^{5/2}} \,d x","Not used",1,"int(1/(x^2*(a + b*x^2)*(c + d*x^2)^(5/2)), x)","F"
729,1,5409,211,3.420463,"\text{Not used}","int(1/(x^3*(a + b*x^2)*(c + d*x^2)^(5/2)),x)","-\frac{\frac{d^2\,\left(d\,x^2+c\right)\,\left(5\,a\,d-8\,b\,c\right)}{3\,{\left(b\,c^2-a\,c\,d\right)}^2}-\frac{d^2}{3\,\left(b\,c^2-a\,c\,d\right)}+\frac{d\,{\left(d\,x^2+c\right)}^2\,\left(5\,a^2\,d^2-8\,a\,b\,c\,d+b^2\,c^2\right)}{2\,a\,c^2\,\left(b\,c^2-a\,c\,d\right)\,\left(a\,d-b\,c\right)}}{c\,{\left(d\,x^2+c\right)}^{3/2}-{\left(d\,x^2+c\right)}^{5/2}}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\sqrt{d\,x^2+c}\,\left(400\,a^{15}\,b^3\,c^9\,d^{14}-3680\,a^{14}\,b^4\,c^{10}\,d^{13}+14864\,a^{13}\,b^5\,c^{11}\,d^{12}-34240\,a^{12}\,b^6\,c^{12}\,d^{11}+48480\,a^{11}\,b^7\,c^{13}\,d^{10}-41280\,a^{10}\,b^8\,c^{14}\,d^9+16864\,a^9\,b^9\,c^{15}\,d^8+2688\,a^8\,b^{10}\,c^{16}\,d^7-6000\,a^7\,b^{11}\,c^{17}\,d^6+1440\,a^6\,b^{12}\,c^{18}\,d^5+1040\,a^5\,b^{13}\,c^{19}\,d^4-704\,a^4\,b^{14}\,c^{20}\,d^3+128\,a^3\,b^{15}\,c^{21}\,d^2\right)+\frac{\left(5\,a\,d+2\,b\,c\right)\,\left(64\,a^6\,b^{13}\,c^{23}\,d^3+64\,a^7\,b^{12}\,c^{22}\,d^4-3648\,a^8\,b^{11}\,c^{21}\,d^5+19520\,a^9\,b^{10}\,c^{20}\,d^6-53632\,a^{10}\,b^9\,c^{19}\,d^7+92288\,a^{11}\,b^8\,c^{18}\,d^8-106624\,a^{12}\,b^7\,c^{17}\,d^9+84608\,a^{13}\,b^6\,c^{16}\,d^{10}-45760\,a^{14}\,b^5\,c^{15}\,d^{11}+16192\,a^{15}\,b^4\,c^{14}\,d^{12}-3392\,a^{16}\,b^3\,c^{13}\,d^{13}+320\,a^{17}\,b^2\,c^{12}\,d^{14}-\frac{\sqrt{d\,x^2+c}\,\left(5\,a\,d+2\,b\,c\right)\,\left(-256\,a^{18}\,b^2\,c^{15}\,d^{13}+3072\,a^{17}\,b^3\,c^{16}\,d^{12}-16640\,a^{16}\,b^4\,c^{17}\,d^{11}+53760\,a^{15}\,b^5\,c^{18}\,d^{10}-115200\,a^{14}\,b^6\,c^{19}\,d^9+172032\,a^{13}\,b^7\,c^{20}\,d^8-182784\,a^{12}\,b^8\,c^{21}\,d^7+138240\,a^{11}\,b^9\,c^{22}\,d^6-72960\,a^{10}\,b^{10}\,c^{23}\,d^5+25600\,a^9\,b^{11}\,c^{24}\,d^4-5376\,a^8\,b^{12}\,c^{25}\,d^3+512\,a^7\,b^{13}\,c^{26}\,d^2\right)}{4\,a^2\,\sqrt{c^7}}\right)}{4\,a^2\,\sqrt{c^7}}\right)\,\left(5\,a\,d+2\,b\,c\right)\,1{}\mathrm{i}}{4\,a^2\,\sqrt{c^7}}+\frac{\left(\sqrt{d\,x^2+c}\,\left(400\,a^{15}\,b^3\,c^9\,d^{14}-3680\,a^{14}\,b^4\,c^{10}\,d^{13}+14864\,a^{13}\,b^5\,c^{11}\,d^{12}-34240\,a^{12}\,b^6\,c^{12}\,d^{11}+48480\,a^{11}\,b^7\,c^{13}\,d^{10}-41280\,a^{10}\,b^8\,c^{14}\,d^9+16864\,a^9\,b^9\,c^{15}\,d^8+2688\,a^8\,b^{10}\,c^{16}\,d^7-6000\,a^7\,b^{11}\,c^{17}\,d^6+1440\,a^6\,b^{12}\,c^{18}\,d^5+1040\,a^5\,b^{13}\,c^{19}\,d^4-704\,a^4\,b^{14}\,c^{20}\,d^3+128\,a^3\,b^{15}\,c^{21}\,d^2\right)-\frac{\left(5\,a\,d+2\,b\,c\right)\,\left(64\,a^6\,b^{13}\,c^{23}\,d^3+64\,a^7\,b^{12}\,c^{22}\,d^4-3648\,a^8\,b^{11}\,c^{21}\,d^5+19520\,a^9\,b^{10}\,c^{20}\,d^6-53632\,a^{10}\,b^9\,c^{19}\,d^7+92288\,a^{11}\,b^8\,c^{18}\,d^8-106624\,a^{12}\,b^7\,c^{17}\,d^9+84608\,a^{13}\,b^6\,c^{16}\,d^{10}-45760\,a^{14}\,b^5\,c^{15}\,d^{11}+16192\,a^{15}\,b^4\,c^{14}\,d^{12}-3392\,a^{16}\,b^3\,c^{13}\,d^{13}+320\,a^{17}\,b^2\,c^{12}\,d^{14}+\frac{\sqrt{d\,x^2+c}\,\left(5\,a\,d+2\,b\,c\right)\,\left(-256\,a^{18}\,b^2\,c^{15}\,d^{13}+3072\,a^{17}\,b^3\,c^{16}\,d^{12}-16640\,a^{16}\,b^4\,c^{17}\,d^{11}+53760\,a^{15}\,b^5\,c^{18}\,d^{10}-115200\,a^{14}\,b^6\,c^{19}\,d^9+172032\,a^{13}\,b^7\,c^{20}\,d^8-182784\,a^{12}\,b^8\,c^{21}\,d^7+138240\,a^{11}\,b^9\,c^{22}\,d^6-72960\,a^{10}\,b^{10}\,c^{23}\,d^5+25600\,a^9\,b^{11}\,c^{24}\,d^4-5376\,a^8\,b^{12}\,c^{25}\,d^3+512\,a^7\,b^{13}\,c^{26}\,d^2\right)}{4\,a^2\,\sqrt{c^7}}\right)}{4\,a^2\,\sqrt{c^7}}\right)\,\left(5\,a\,d+2\,b\,c\right)\,1{}\mathrm{i}}{4\,a^2\,\sqrt{c^7}}}{32\,a^2\,b^{15}\,c^{18}\,d^3-368\,a^3\,b^{14}\,c^{17}\,d^4+1056\,a^4\,b^{13}\,c^{16}\,d^5-5600\,a^6\,b^{11}\,c^{14}\,d^7+12768\,a^7\,b^{10}\,c^{13}\,d^8-14112\,a^8\,b^9\,c^{12}\,d^9+8704\,a^9\,b^8\,c^{11}\,d^{10}-2880\,a^{10}\,b^7\,c^{10}\,d^{11}+400\,a^{11}\,b^6\,c^9\,d^{12}-\frac{\left(\sqrt{d\,x^2+c}\,\left(400\,a^{15}\,b^3\,c^9\,d^{14}-3680\,a^{14}\,b^4\,c^{10}\,d^{13}+14864\,a^{13}\,b^5\,c^{11}\,d^{12}-34240\,a^{12}\,b^6\,c^{12}\,d^{11}+48480\,a^{11}\,b^7\,c^{13}\,d^{10}-41280\,a^{10}\,b^8\,c^{14}\,d^9+16864\,a^9\,b^9\,c^{15}\,d^8+2688\,a^8\,b^{10}\,c^{16}\,d^7-6000\,a^7\,b^{11}\,c^{17}\,d^6+1440\,a^6\,b^{12}\,c^{18}\,d^5+1040\,a^5\,b^{13}\,c^{19}\,d^4-704\,a^4\,b^{14}\,c^{20}\,d^3+128\,a^3\,b^{15}\,c^{21}\,d^2\right)+\frac{\left(5\,a\,d+2\,b\,c\right)\,\left(64\,a^6\,b^{13}\,c^{23}\,d^3+64\,a^7\,b^{12}\,c^{22}\,d^4-3648\,a^8\,b^{11}\,c^{21}\,d^5+19520\,a^9\,b^{10}\,c^{20}\,d^6-53632\,a^{10}\,b^9\,c^{19}\,d^7+92288\,a^{11}\,b^8\,c^{18}\,d^8-106624\,a^{12}\,b^7\,c^{17}\,d^9+84608\,a^{13}\,b^6\,c^{16}\,d^{10}-45760\,a^{14}\,b^5\,c^{15}\,d^{11}+16192\,a^{15}\,b^4\,c^{14}\,d^{12}-3392\,a^{16}\,b^3\,c^{13}\,d^{13}+320\,a^{17}\,b^2\,c^{12}\,d^{14}-\frac{\sqrt{d\,x^2+c}\,\left(5\,a\,d+2\,b\,c\right)\,\left(-256\,a^{18}\,b^2\,c^{15}\,d^{13}+3072\,a^{17}\,b^3\,c^{16}\,d^{12}-16640\,a^{16}\,b^4\,c^{17}\,d^{11}+53760\,a^{15}\,b^5\,c^{18}\,d^{10}-115200\,a^{14}\,b^6\,c^{19}\,d^9+172032\,a^{13}\,b^7\,c^{20}\,d^8-182784\,a^{12}\,b^8\,c^{21}\,d^7+138240\,a^{11}\,b^9\,c^{22}\,d^6-72960\,a^{10}\,b^{10}\,c^{23}\,d^5+25600\,a^9\,b^{11}\,c^{24}\,d^4-5376\,a^8\,b^{12}\,c^{25}\,d^3+512\,a^7\,b^{13}\,c^{26}\,d^2\right)}{4\,a^2\,\sqrt{c^7}}\right)}{4\,a^2\,\sqrt{c^7}}\right)\,\left(5\,a\,d+2\,b\,c\right)}{4\,a^2\,\sqrt{c^7}}+\frac{\left(\sqrt{d\,x^2+c}\,\left(400\,a^{15}\,b^3\,c^9\,d^{14}-3680\,a^{14}\,b^4\,c^{10}\,d^{13}+14864\,a^{13}\,b^5\,c^{11}\,d^{12}-34240\,a^{12}\,b^6\,c^{12}\,d^{11}+48480\,a^{11}\,b^7\,c^{13}\,d^{10}-41280\,a^{10}\,b^8\,c^{14}\,d^9+16864\,a^9\,b^9\,c^{15}\,d^8+2688\,a^8\,b^{10}\,c^{16}\,d^7-6000\,a^7\,b^{11}\,c^{17}\,d^6+1440\,a^6\,b^{12}\,c^{18}\,d^5+1040\,a^5\,b^{13}\,c^{19}\,d^4-704\,a^4\,b^{14}\,c^{20}\,d^3+128\,a^3\,b^{15}\,c^{21}\,d^2\right)-\frac{\left(5\,a\,d+2\,b\,c\right)\,\left(64\,a^6\,b^{13}\,c^{23}\,d^3+64\,a^7\,b^{12}\,c^{22}\,d^4-3648\,a^8\,b^{11}\,c^{21}\,d^5+19520\,a^9\,b^{10}\,c^{20}\,d^6-53632\,a^{10}\,b^9\,c^{19}\,d^7+92288\,a^{11}\,b^8\,c^{18}\,d^8-106624\,a^{12}\,b^7\,c^{17}\,d^9+84608\,a^{13}\,b^6\,c^{16}\,d^{10}-45760\,a^{14}\,b^5\,c^{15}\,d^{11}+16192\,a^{15}\,b^4\,c^{14}\,d^{12}-3392\,a^{16}\,b^3\,c^{13}\,d^{13}+320\,a^{17}\,b^2\,c^{12}\,d^{14}+\frac{\sqrt{d\,x^2+c}\,\left(5\,a\,d+2\,b\,c\right)\,\left(-256\,a^{18}\,b^2\,c^{15}\,d^{13}+3072\,a^{17}\,b^3\,c^{16}\,d^{12}-16640\,a^{16}\,b^4\,c^{17}\,d^{11}+53760\,a^{15}\,b^5\,c^{18}\,d^{10}-115200\,a^{14}\,b^6\,c^{19}\,d^9+172032\,a^{13}\,b^7\,c^{20}\,d^8-182784\,a^{12}\,b^8\,c^{21}\,d^7+138240\,a^{11}\,b^9\,c^{22}\,d^6-72960\,a^{10}\,b^{10}\,c^{23}\,d^5+25600\,a^9\,b^{11}\,c^{24}\,d^4-5376\,a^8\,b^{12}\,c^{25}\,d^3+512\,a^7\,b^{13}\,c^{26}\,d^2\right)}{4\,a^2\,\sqrt{c^7}}\right)}{4\,a^2\,\sqrt{c^7}}\right)\,\left(5\,a\,d+2\,b\,c\right)}{4\,a^2\,\sqrt{c^7}}}\right)\,\left(5\,a\,d+2\,b\,c\right)\,1{}\mathrm{i}}{2\,a^2\,\sqrt{c^7}}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-b^7\,{\left(a\,d-b\,c\right)}^5}\,\left(\frac{\sqrt{d\,x^2+c}\,\left(400\,a^{15}\,b^3\,c^9\,d^{14}-3680\,a^{14}\,b^4\,c^{10}\,d^{13}+14864\,a^{13}\,b^5\,c^{11}\,d^{12}-34240\,a^{12}\,b^6\,c^{12}\,d^{11}+48480\,a^{11}\,b^7\,c^{13}\,d^{10}-41280\,a^{10}\,b^8\,c^{14}\,d^9+16864\,a^9\,b^9\,c^{15}\,d^8+2688\,a^8\,b^{10}\,c^{16}\,d^7-6000\,a^7\,b^{11}\,c^{17}\,d^6+1440\,a^6\,b^{12}\,c^{18}\,d^5+1040\,a^5\,b^{13}\,c^{19}\,d^4-704\,a^4\,b^{14}\,c^{20}\,d^3+128\,a^3\,b^{15}\,c^{21}\,d^2\right)}{2}+\frac{\sqrt{-b^7\,{\left(a\,d-b\,c\right)}^5}\,\left(32\,a^6\,b^{13}\,c^{23}\,d^3+32\,a^7\,b^{12}\,c^{22}\,d^4-1824\,a^8\,b^{11}\,c^{21}\,d^5+9760\,a^9\,b^{10}\,c^{20}\,d^6-26816\,a^{10}\,b^9\,c^{19}\,d^7+46144\,a^{11}\,b^8\,c^{18}\,d^8-53312\,a^{12}\,b^7\,c^{17}\,d^9+42304\,a^{13}\,b^6\,c^{16}\,d^{10}-22880\,a^{14}\,b^5\,c^{15}\,d^{11}+8096\,a^{15}\,b^4\,c^{14}\,d^{12}-1696\,a^{16}\,b^3\,c^{13}\,d^{13}+160\,a^{17}\,b^2\,c^{12}\,d^{14}-\frac{\sqrt{-b^7\,{\left(a\,d-b\,c\right)}^5}\,\sqrt{d\,x^2+c}\,\left(-256\,a^{18}\,b^2\,c^{15}\,d^{13}+3072\,a^{17}\,b^3\,c^{16}\,d^{12}-16640\,a^{16}\,b^4\,c^{17}\,d^{11}+53760\,a^{15}\,b^5\,c^{18}\,d^{10}-115200\,a^{14}\,b^6\,c^{19}\,d^9+172032\,a^{13}\,b^7\,c^{20}\,d^8-182784\,a^{12}\,b^8\,c^{21}\,d^7+138240\,a^{11}\,b^9\,c^{22}\,d^6-72960\,a^{10}\,b^{10}\,c^{23}\,d^5+25600\,a^9\,b^{11}\,c^{24}\,d^4-5376\,a^8\,b^{12}\,c^{25}\,d^3+512\,a^7\,b^{13}\,c^{26}\,d^2\right)}{4\,a^2\,{\left(a\,d-b\,c\right)}^5}\right)}{2\,a^2\,{\left(a\,d-b\,c\right)}^5}\right)\,1{}\mathrm{i}}{a^2\,{\left(a\,d-b\,c\right)}^5}+\frac{\sqrt{-b^7\,{\left(a\,d-b\,c\right)}^5}\,\left(\frac{\sqrt{d\,x^2+c}\,\left(400\,a^{15}\,b^3\,c^9\,d^{14}-3680\,a^{14}\,b^4\,c^{10}\,d^{13}+14864\,a^{13}\,b^5\,c^{11}\,d^{12}-34240\,a^{12}\,b^6\,c^{12}\,d^{11}+48480\,a^{11}\,b^7\,c^{13}\,d^{10}-41280\,a^{10}\,b^8\,c^{14}\,d^9+16864\,a^9\,b^9\,c^{15}\,d^8+2688\,a^8\,b^{10}\,c^{16}\,d^7-6000\,a^7\,b^{11}\,c^{17}\,d^6+1440\,a^6\,b^{12}\,c^{18}\,d^5+1040\,a^5\,b^{13}\,c^{19}\,d^4-704\,a^4\,b^{14}\,c^{20}\,d^3+128\,a^3\,b^{15}\,c^{21}\,d^2\right)}{2}-\frac{\sqrt{-b^7\,{\left(a\,d-b\,c\right)}^5}\,\left(32\,a^6\,b^{13}\,c^{23}\,d^3+32\,a^7\,b^{12}\,c^{22}\,d^4-1824\,a^8\,b^{11}\,c^{21}\,d^5+9760\,a^9\,b^{10}\,c^{20}\,d^6-26816\,a^{10}\,b^9\,c^{19}\,d^7+46144\,a^{11}\,b^8\,c^{18}\,d^8-53312\,a^{12}\,b^7\,c^{17}\,d^9+42304\,a^{13}\,b^6\,c^{16}\,d^{10}-22880\,a^{14}\,b^5\,c^{15}\,d^{11}+8096\,a^{15}\,b^4\,c^{14}\,d^{12}-1696\,a^{16}\,b^3\,c^{13}\,d^{13}+160\,a^{17}\,b^2\,c^{12}\,d^{14}+\frac{\sqrt{-b^7\,{\left(a\,d-b\,c\right)}^5}\,\sqrt{d\,x^2+c}\,\left(-256\,a^{18}\,b^2\,c^{15}\,d^{13}+3072\,a^{17}\,b^3\,c^{16}\,d^{12}-16640\,a^{16}\,b^4\,c^{17}\,d^{11}+53760\,a^{15}\,b^5\,c^{18}\,d^{10}-115200\,a^{14}\,b^6\,c^{19}\,d^9+172032\,a^{13}\,b^7\,c^{20}\,d^8-182784\,a^{12}\,b^8\,c^{21}\,d^7+138240\,a^{11}\,b^9\,c^{22}\,d^6-72960\,a^{10}\,b^{10}\,c^{23}\,d^5+25600\,a^9\,b^{11}\,c^{24}\,d^4-5376\,a^8\,b^{12}\,c^{25}\,d^3+512\,a^7\,b^{13}\,c^{26}\,d^2\right)}{4\,a^2\,{\left(a\,d-b\,c\right)}^5}\right)}{2\,a^2\,{\left(a\,d-b\,c\right)}^5}\right)\,1{}\mathrm{i}}{a^2\,{\left(a\,d-b\,c\right)}^5}}{\frac{\sqrt{-b^7\,{\left(a\,d-b\,c\right)}^5}\,\left(\frac{\sqrt{d\,x^2+c}\,\left(400\,a^{15}\,b^3\,c^9\,d^{14}-3680\,a^{14}\,b^4\,c^{10}\,d^{13}+14864\,a^{13}\,b^5\,c^{11}\,d^{12}-34240\,a^{12}\,b^6\,c^{12}\,d^{11}+48480\,a^{11}\,b^7\,c^{13}\,d^{10}-41280\,a^{10}\,b^8\,c^{14}\,d^9+16864\,a^9\,b^9\,c^{15}\,d^8+2688\,a^8\,b^{10}\,c^{16}\,d^7-6000\,a^7\,b^{11}\,c^{17}\,d^6+1440\,a^6\,b^{12}\,c^{18}\,d^5+1040\,a^5\,b^{13}\,c^{19}\,d^4-704\,a^4\,b^{14}\,c^{20}\,d^3+128\,a^3\,b^{15}\,c^{21}\,d^2\right)}{2}-\frac{\sqrt{-b^7\,{\left(a\,d-b\,c\right)}^5}\,\left(32\,a^6\,b^{13}\,c^{23}\,d^3+32\,a^7\,b^{12}\,c^{22}\,d^4-1824\,a^8\,b^{11}\,c^{21}\,d^5+9760\,a^9\,b^{10}\,c^{20}\,d^6-26816\,a^{10}\,b^9\,c^{19}\,d^7+46144\,a^{11}\,b^8\,c^{18}\,d^8-53312\,a^{12}\,b^7\,c^{17}\,d^9+42304\,a^{13}\,b^6\,c^{16}\,d^{10}-22880\,a^{14}\,b^5\,c^{15}\,d^{11}+8096\,a^{15}\,b^4\,c^{14}\,d^{12}-1696\,a^{16}\,b^3\,c^{13}\,d^{13}+160\,a^{17}\,b^2\,c^{12}\,d^{14}+\frac{\sqrt{-b^7\,{\left(a\,d-b\,c\right)}^5}\,\sqrt{d\,x^2+c}\,\left(-256\,a^{18}\,b^2\,c^{15}\,d^{13}+3072\,a^{17}\,b^3\,c^{16}\,d^{12}-16640\,a^{16}\,b^4\,c^{17}\,d^{11}+53760\,a^{15}\,b^5\,c^{18}\,d^{10}-115200\,a^{14}\,b^6\,c^{19}\,d^9+172032\,a^{13}\,b^7\,c^{20}\,d^8-182784\,a^{12}\,b^8\,c^{21}\,d^7+138240\,a^{11}\,b^9\,c^{22}\,d^6-72960\,a^{10}\,b^{10}\,c^{23}\,d^5+25600\,a^9\,b^{11}\,c^{24}\,d^4-5376\,a^8\,b^{12}\,c^{25}\,d^3+512\,a^7\,b^{13}\,c^{26}\,d^2\right)}{4\,a^2\,{\left(a\,d-b\,c\right)}^5}\right)}{2\,a^2\,{\left(a\,d-b\,c\right)}^5}\right)}{a^2\,{\left(a\,d-b\,c\right)}^5}-\frac{\sqrt{-b^7\,{\left(a\,d-b\,c\right)}^5}\,\left(\frac{\sqrt{d\,x^2+c}\,\left(400\,a^{15}\,b^3\,c^9\,d^{14}-3680\,a^{14}\,b^4\,c^{10}\,d^{13}+14864\,a^{13}\,b^5\,c^{11}\,d^{12}-34240\,a^{12}\,b^6\,c^{12}\,d^{11}+48480\,a^{11}\,b^7\,c^{13}\,d^{10}-41280\,a^{10}\,b^8\,c^{14}\,d^9+16864\,a^9\,b^9\,c^{15}\,d^8+2688\,a^8\,b^{10}\,c^{16}\,d^7-6000\,a^7\,b^{11}\,c^{17}\,d^6+1440\,a^6\,b^{12}\,c^{18}\,d^5+1040\,a^5\,b^{13}\,c^{19}\,d^4-704\,a^4\,b^{14}\,c^{20}\,d^3+128\,a^3\,b^{15}\,c^{21}\,d^2\right)}{2}+\frac{\sqrt{-b^7\,{\left(a\,d-b\,c\right)}^5}\,\left(32\,a^6\,b^{13}\,c^{23}\,d^3+32\,a^7\,b^{12}\,c^{22}\,d^4-1824\,a^8\,b^{11}\,c^{21}\,d^5+9760\,a^9\,b^{10}\,c^{20}\,d^6-26816\,a^{10}\,b^9\,c^{19}\,d^7+46144\,a^{11}\,b^8\,c^{18}\,d^8-53312\,a^{12}\,b^7\,c^{17}\,d^9+42304\,a^{13}\,b^6\,c^{16}\,d^{10}-22880\,a^{14}\,b^5\,c^{15}\,d^{11}+8096\,a^{15}\,b^4\,c^{14}\,d^{12}-1696\,a^{16}\,b^3\,c^{13}\,d^{13}+160\,a^{17}\,b^2\,c^{12}\,d^{14}-\frac{\sqrt{-b^7\,{\left(a\,d-b\,c\right)}^5}\,\sqrt{d\,x^2+c}\,\left(-256\,a^{18}\,b^2\,c^{15}\,d^{13}+3072\,a^{17}\,b^3\,c^{16}\,d^{12}-16640\,a^{16}\,b^4\,c^{17}\,d^{11}+53760\,a^{15}\,b^5\,c^{18}\,d^{10}-115200\,a^{14}\,b^6\,c^{19}\,d^9+172032\,a^{13}\,b^7\,c^{20}\,d^8-182784\,a^{12}\,b^8\,c^{21}\,d^7+138240\,a^{11}\,b^9\,c^{22}\,d^6-72960\,a^{10}\,b^{10}\,c^{23}\,d^5+25600\,a^9\,b^{11}\,c^{24}\,d^4-5376\,a^8\,b^{12}\,c^{25}\,d^3+512\,a^7\,b^{13}\,c^{26}\,d^2\right)}{4\,a^2\,{\left(a\,d-b\,c\right)}^5}\right)}{2\,a^2\,{\left(a\,d-b\,c\right)}^5}\right)}{a^2\,{\left(a\,d-b\,c\right)}^5}+32\,a^2\,b^{15}\,c^{18}\,d^3-368\,a^3\,b^{14}\,c^{17}\,d^4+1056\,a^4\,b^{13}\,c^{16}\,d^5-5600\,a^6\,b^{11}\,c^{14}\,d^7+12768\,a^7\,b^{10}\,c^{13}\,d^8-14112\,a^8\,b^9\,c^{12}\,d^9+8704\,a^9\,b^8\,c^{11}\,d^{10}-2880\,a^{10}\,b^7\,c^{10}\,d^{11}+400\,a^{11}\,b^6\,c^9\,d^{12}}\right)\,\sqrt{-b^7\,{\left(a\,d-b\,c\right)}^5}\,1{}\mathrm{i}}{a^2\,{\left(a\,d-b\,c\right)}^5}","Not used",1,"(atan(((((c + d*x^2)^(1/2)*(128*a^3*b^15*c^21*d^2 - 704*a^4*b^14*c^20*d^3 + 1040*a^5*b^13*c^19*d^4 + 1440*a^6*b^12*c^18*d^5 - 6000*a^7*b^11*c^17*d^6 + 2688*a^8*b^10*c^16*d^7 + 16864*a^9*b^9*c^15*d^8 - 41280*a^10*b^8*c^14*d^9 + 48480*a^11*b^7*c^13*d^10 - 34240*a^12*b^6*c^12*d^11 + 14864*a^13*b^5*c^11*d^12 - 3680*a^14*b^4*c^10*d^13 + 400*a^15*b^3*c^9*d^14) + ((5*a*d + 2*b*c)*(64*a^6*b^13*c^23*d^3 + 64*a^7*b^12*c^22*d^4 - 3648*a^8*b^11*c^21*d^5 + 19520*a^9*b^10*c^20*d^6 - 53632*a^10*b^9*c^19*d^7 + 92288*a^11*b^8*c^18*d^8 - 106624*a^12*b^7*c^17*d^9 + 84608*a^13*b^6*c^16*d^10 - 45760*a^14*b^5*c^15*d^11 + 16192*a^15*b^4*c^14*d^12 - 3392*a^16*b^3*c^13*d^13 + 320*a^17*b^2*c^12*d^14 - ((c + d*x^2)^(1/2)*(5*a*d + 2*b*c)*(512*a^7*b^13*c^26*d^2 - 5376*a^8*b^12*c^25*d^3 + 25600*a^9*b^11*c^24*d^4 - 72960*a^10*b^10*c^23*d^5 + 138240*a^11*b^9*c^22*d^6 - 182784*a^12*b^8*c^21*d^7 + 172032*a^13*b^7*c^20*d^8 - 115200*a^14*b^6*c^19*d^9 + 53760*a^15*b^5*c^18*d^10 - 16640*a^16*b^4*c^17*d^11 + 3072*a^17*b^3*c^16*d^12 - 256*a^18*b^2*c^15*d^13))/(4*a^2*(c^7)^(1/2))))/(4*a^2*(c^7)^(1/2)))*(5*a*d + 2*b*c)*1i)/(4*a^2*(c^7)^(1/2)) + (((c + d*x^2)^(1/2)*(128*a^3*b^15*c^21*d^2 - 704*a^4*b^14*c^20*d^3 + 1040*a^5*b^13*c^19*d^4 + 1440*a^6*b^12*c^18*d^5 - 6000*a^7*b^11*c^17*d^6 + 2688*a^8*b^10*c^16*d^7 + 16864*a^9*b^9*c^15*d^8 - 41280*a^10*b^8*c^14*d^9 + 48480*a^11*b^7*c^13*d^10 - 34240*a^12*b^6*c^12*d^11 + 14864*a^13*b^5*c^11*d^12 - 3680*a^14*b^4*c^10*d^13 + 400*a^15*b^3*c^9*d^14) - ((5*a*d + 2*b*c)*(64*a^6*b^13*c^23*d^3 + 64*a^7*b^12*c^22*d^4 - 3648*a^8*b^11*c^21*d^5 + 19520*a^9*b^10*c^20*d^6 - 53632*a^10*b^9*c^19*d^7 + 92288*a^11*b^8*c^18*d^8 - 106624*a^12*b^7*c^17*d^9 + 84608*a^13*b^6*c^16*d^10 - 45760*a^14*b^5*c^15*d^11 + 16192*a^15*b^4*c^14*d^12 - 3392*a^16*b^3*c^13*d^13 + 320*a^17*b^2*c^12*d^14 + ((c + d*x^2)^(1/2)*(5*a*d + 2*b*c)*(512*a^7*b^13*c^26*d^2 - 5376*a^8*b^12*c^25*d^3 + 25600*a^9*b^11*c^24*d^4 - 72960*a^10*b^10*c^23*d^5 + 138240*a^11*b^9*c^22*d^6 - 182784*a^12*b^8*c^21*d^7 + 172032*a^13*b^7*c^20*d^8 - 115200*a^14*b^6*c^19*d^9 + 53760*a^15*b^5*c^18*d^10 - 16640*a^16*b^4*c^17*d^11 + 3072*a^17*b^3*c^16*d^12 - 256*a^18*b^2*c^15*d^13))/(4*a^2*(c^7)^(1/2))))/(4*a^2*(c^7)^(1/2)))*(5*a*d + 2*b*c)*1i)/(4*a^2*(c^7)^(1/2)))/(32*a^2*b^15*c^18*d^3 - 368*a^3*b^14*c^17*d^4 + 1056*a^4*b^13*c^16*d^5 - 5600*a^6*b^11*c^14*d^7 + 12768*a^7*b^10*c^13*d^8 - 14112*a^8*b^9*c^12*d^9 + 8704*a^9*b^8*c^11*d^10 - 2880*a^10*b^7*c^10*d^11 + 400*a^11*b^6*c^9*d^12 - (((c + d*x^2)^(1/2)*(128*a^3*b^15*c^21*d^2 - 704*a^4*b^14*c^20*d^3 + 1040*a^5*b^13*c^19*d^4 + 1440*a^6*b^12*c^18*d^5 - 6000*a^7*b^11*c^17*d^6 + 2688*a^8*b^10*c^16*d^7 + 16864*a^9*b^9*c^15*d^8 - 41280*a^10*b^8*c^14*d^9 + 48480*a^11*b^7*c^13*d^10 - 34240*a^12*b^6*c^12*d^11 + 14864*a^13*b^5*c^11*d^12 - 3680*a^14*b^4*c^10*d^13 + 400*a^15*b^3*c^9*d^14) + ((5*a*d + 2*b*c)*(64*a^6*b^13*c^23*d^3 + 64*a^7*b^12*c^22*d^4 - 3648*a^8*b^11*c^21*d^5 + 19520*a^9*b^10*c^20*d^6 - 53632*a^10*b^9*c^19*d^7 + 92288*a^11*b^8*c^18*d^8 - 106624*a^12*b^7*c^17*d^9 + 84608*a^13*b^6*c^16*d^10 - 45760*a^14*b^5*c^15*d^11 + 16192*a^15*b^4*c^14*d^12 - 3392*a^16*b^3*c^13*d^13 + 320*a^17*b^2*c^12*d^14 - ((c + d*x^2)^(1/2)*(5*a*d + 2*b*c)*(512*a^7*b^13*c^26*d^2 - 5376*a^8*b^12*c^25*d^3 + 25600*a^9*b^11*c^24*d^4 - 72960*a^10*b^10*c^23*d^5 + 138240*a^11*b^9*c^22*d^6 - 182784*a^12*b^8*c^21*d^7 + 172032*a^13*b^7*c^20*d^8 - 115200*a^14*b^6*c^19*d^9 + 53760*a^15*b^5*c^18*d^10 - 16640*a^16*b^4*c^17*d^11 + 3072*a^17*b^3*c^16*d^12 - 256*a^18*b^2*c^15*d^13))/(4*a^2*(c^7)^(1/2))))/(4*a^2*(c^7)^(1/2)))*(5*a*d + 2*b*c))/(4*a^2*(c^7)^(1/2)) + (((c + d*x^2)^(1/2)*(128*a^3*b^15*c^21*d^2 - 704*a^4*b^14*c^20*d^3 + 1040*a^5*b^13*c^19*d^4 + 1440*a^6*b^12*c^18*d^5 - 6000*a^7*b^11*c^17*d^6 + 2688*a^8*b^10*c^16*d^7 + 16864*a^9*b^9*c^15*d^8 - 41280*a^10*b^8*c^14*d^9 + 48480*a^11*b^7*c^13*d^10 - 34240*a^12*b^6*c^12*d^11 + 14864*a^13*b^5*c^11*d^12 - 3680*a^14*b^4*c^10*d^13 + 400*a^15*b^3*c^9*d^14) - ((5*a*d + 2*b*c)*(64*a^6*b^13*c^23*d^3 + 64*a^7*b^12*c^22*d^4 - 3648*a^8*b^11*c^21*d^5 + 19520*a^9*b^10*c^20*d^6 - 53632*a^10*b^9*c^19*d^7 + 92288*a^11*b^8*c^18*d^8 - 106624*a^12*b^7*c^17*d^9 + 84608*a^13*b^6*c^16*d^10 - 45760*a^14*b^5*c^15*d^11 + 16192*a^15*b^4*c^14*d^12 - 3392*a^16*b^3*c^13*d^13 + 320*a^17*b^2*c^12*d^14 + ((c + d*x^2)^(1/2)*(5*a*d + 2*b*c)*(512*a^7*b^13*c^26*d^2 - 5376*a^8*b^12*c^25*d^3 + 25600*a^9*b^11*c^24*d^4 - 72960*a^10*b^10*c^23*d^5 + 138240*a^11*b^9*c^22*d^6 - 182784*a^12*b^8*c^21*d^7 + 172032*a^13*b^7*c^20*d^8 - 115200*a^14*b^6*c^19*d^9 + 53760*a^15*b^5*c^18*d^10 - 16640*a^16*b^4*c^17*d^11 + 3072*a^17*b^3*c^16*d^12 - 256*a^18*b^2*c^15*d^13))/(4*a^2*(c^7)^(1/2))))/(4*a^2*(c^7)^(1/2)))*(5*a*d + 2*b*c))/(4*a^2*(c^7)^(1/2))))*(5*a*d + 2*b*c)*1i)/(2*a^2*(c^7)^(1/2)) - ((d^2*(c + d*x^2)*(5*a*d - 8*b*c))/(3*(b*c^2 - a*c*d)^2) - d^2/(3*(b*c^2 - a*c*d)) + (d*(c + d*x^2)^2*(5*a^2*d^2 + b^2*c^2 - 8*a*b*c*d))/(2*a*c^2*(b*c^2 - a*c*d)*(a*d - b*c)))/(c*(c + d*x^2)^(3/2) - (c + d*x^2)^(5/2)) + (atan((((-b^7*(a*d - b*c)^5)^(1/2)*(((c + d*x^2)^(1/2)*(128*a^3*b^15*c^21*d^2 - 704*a^4*b^14*c^20*d^3 + 1040*a^5*b^13*c^19*d^4 + 1440*a^6*b^12*c^18*d^5 - 6000*a^7*b^11*c^17*d^6 + 2688*a^8*b^10*c^16*d^7 + 16864*a^9*b^9*c^15*d^8 - 41280*a^10*b^8*c^14*d^9 + 48480*a^11*b^7*c^13*d^10 - 34240*a^12*b^6*c^12*d^11 + 14864*a^13*b^5*c^11*d^12 - 3680*a^14*b^4*c^10*d^13 + 400*a^15*b^3*c^9*d^14))/2 + ((-b^7*(a*d - b*c)^5)^(1/2)*(32*a^6*b^13*c^23*d^3 + 32*a^7*b^12*c^22*d^4 - 1824*a^8*b^11*c^21*d^5 + 9760*a^9*b^10*c^20*d^6 - 26816*a^10*b^9*c^19*d^7 + 46144*a^11*b^8*c^18*d^8 - 53312*a^12*b^7*c^17*d^9 + 42304*a^13*b^6*c^16*d^10 - 22880*a^14*b^5*c^15*d^11 + 8096*a^15*b^4*c^14*d^12 - 1696*a^16*b^3*c^13*d^13 + 160*a^17*b^2*c^12*d^14 - ((-b^7*(a*d - b*c)^5)^(1/2)*(c + d*x^2)^(1/2)*(512*a^7*b^13*c^26*d^2 - 5376*a^8*b^12*c^25*d^3 + 25600*a^9*b^11*c^24*d^4 - 72960*a^10*b^10*c^23*d^5 + 138240*a^11*b^9*c^22*d^6 - 182784*a^12*b^8*c^21*d^7 + 172032*a^13*b^7*c^20*d^8 - 115200*a^14*b^6*c^19*d^9 + 53760*a^15*b^5*c^18*d^10 - 16640*a^16*b^4*c^17*d^11 + 3072*a^17*b^3*c^16*d^12 - 256*a^18*b^2*c^15*d^13))/(4*a^2*(a*d - b*c)^5)))/(2*a^2*(a*d - b*c)^5))*1i)/(a^2*(a*d - b*c)^5) + ((-b^7*(a*d - b*c)^5)^(1/2)*(((c + d*x^2)^(1/2)*(128*a^3*b^15*c^21*d^2 - 704*a^4*b^14*c^20*d^3 + 1040*a^5*b^13*c^19*d^4 + 1440*a^6*b^12*c^18*d^5 - 6000*a^7*b^11*c^17*d^6 + 2688*a^8*b^10*c^16*d^7 + 16864*a^9*b^9*c^15*d^8 - 41280*a^10*b^8*c^14*d^9 + 48480*a^11*b^7*c^13*d^10 - 34240*a^12*b^6*c^12*d^11 + 14864*a^13*b^5*c^11*d^12 - 3680*a^14*b^4*c^10*d^13 + 400*a^15*b^3*c^9*d^14))/2 - ((-b^7*(a*d - b*c)^5)^(1/2)*(32*a^6*b^13*c^23*d^3 + 32*a^7*b^12*c^22*d^4 - 1824*a^8*b^11*c^21*d^5 + 9760*a^9*b^10*c^20*d^6 - 26816*a^10*b^9*c^19*d^7 + 46144*a^11*b^8*c^18*d^8 - 53312*a^12*b^7*c^17*d^9 + 42304*a^13*b^6*c^16*d^10 - 22880*a^14*b^5*c^15*d^11 + 8096*a^15*b^4*c^14*d^12 - 1696*a^16*b^3*c^13*d^13 + 160*a^17*b^2*c^12*d^14 + ((-b^7*(a*d - b*c)^5)^(1/2)*(c + d*x^2)^(1/2)*(512*a^7*b^13*c^26*d^2 - 5376*a^8*b^12*c^25*d^3 + 25600*a^9*b^11*c^24*d^4 - 72960*a^10*b^10*c^23*d^5 + 138240*a^11*b^9*c^22*d^6 - 182784*a^12*b^8*c^21*d^7 + 172032*a^13*b^7*c^20*d^8 - 115200*a^14*b^6*c^19*d^9 + 53760*a^15*b^5*c^18*d^10 - 16640*a^16*b^4*c^17*d^11 + 3072*a^17*b^3*c^16*d^12 - 256*a^18*b^2*c^15*d^13))/(4*a^2*(a*d - b*c)^5)))/(2*a^2*(a*d - b*c)^5))*1i)/(a^2*(a*d - b*c)^5))/(((-b^7*(a*d - b*c)^5)^(1/2)*(((c + d*x^2)^(1/2)*(128*a^3*b^15*c^21*d^2 - 704*a^4*b^14*c^20*d^3 + 1040*a^5*b^13*c^19*d^4 + 1440*a^6*b^12*c^18*d^5 - 6000*a^7*b^11*c^17*d^6 + 2688*a^8*b^10*c^16*d^7 + 16864*a^9*b^9*c^15*d^8 - 41280*a^10*b^8*c^14*d^9 + 48480*a^11*b^7*c^13*d^10 - 34240*a^12*b^6*c^12*d^11 + 14864*a^13*b^5*c^11*d^12 - 3680*a^14*b^4*c^10*d^13 + 400*a^15*b^3*c^9*d^14))/2 - ((-b^7*(a*d - b*c)^5)^(1/2)*(32*a^6*b^13*c^23*d^3 + 32*a^7*b^12*c^22*d^4 - 1824*a^8*b^11*c^21*d^5 + 9760*a^9*b^10*c^20*d^6 - 26816*a^10*b^9*c^19*d^7 + 46144*a^11*b^8*c^18*d^8 - 53312*a^12*b^7*c^17*d^9 + 42304*a^13*b^6*c^16*d^10 - 22880*a^14*b^5*c^15*d^11 + 8096*a^15*b^4*c^14*d^12 - 1696*a^16*b^3*c^13*d^13 + 160*a^17*b^2*c^12*d^14 + ((-b^7*(a*d - b*c)^5)^(1/2)*(c + d*x^2)^(1/2)*(512*a^7*b^13*c^26*d^2 - 5376*a^8*b^12*c^25*d^3 + 25600*a^9*b^11*c^24*d^4 - 72960*a^10*b^10*c^23*d^5 + 138240*a^11*b^9*c^22*d^6 - 182784*a^12*b^8*c^21*d^7 + 172032*a^13*b^7*c^20*d^8 - 115200*a^14*b^6*c^19*d^9 + 53760*a^15*b^5*c^18*d^10 - 16640*a^16*b^4*c^17*d^11 + 3072*a^17*b^3*c^16*d^12 - 256*a^18*b^2*c^15*d^13))/(4*a^2*(a*d - b*c)^5)))/(2*a^2*(a*d - b*c)^5)))/(a^2*(a*d - b*c)^5) - ((-b^7*(a*d - b*c)^5)^(1/2)*(((c + d*x^2)^(1/2)*(128*a^3*b^15*c^21*d^2 - 704*a^4*b^14*c^20*d^3 + 1040*a^5*b^13*c^19*d^4 + 1440*a^6*b^12*c^18*d^5 - 6000*a^7*b^11*c^17*d^6 + 2688*a^8*b^10*c^16*d^7 + 16864*a^9*b^9*c^15*d^8 - 41280*a^10*b^8*c^14*d^9 + 48480*a^11*b^7*c^13*d^10 - 34240*a^12*b^6*c^12*d^11 + 14864*a^13*b^5*c^11*d^12 - 3680*a^14*b^4*c^10*d^13 + 400*a^15*b^3*c^9*d^14))/2 + ((-b^7*(a*d - b*c)^5)^(1/2)*(32*a^6*b^13*c^23*d^3 + 32*a^7*b^12*c^22*d^4 - 1824*a^8*b^11*c^21*d^5 + 9760*a^9*b^10*c^20*d^6 - 26816*a^10*b^9*c^19*d^7 + 46144*a^11*b^8*c^18*d^8 - 53312*a^12*b^7*c^17*d^9 + 42304*a^13*b^6*c^16*d^10 - 22880*a^14*b^5*c^15*d^11 + 8096*a^15*b^4*c^14*d^12 - 1696*a^16*b^3*c^13*d^13 + 160*a^17*b^2*c^12*d^14 - ((-b^7*(a*d - b*c)^5)^(1/2)*(c + d*x^2)^(1/2)*(512*a^7*b^13*c^26*d^2 - 5376*a^8*b^12*c^25*d^3 + 25600*a^9*b^11*c^24*d^4 - 72960*a^10*b^10*c^23*d^5 + 138240*a^11*b^9*c^22*d^6 - 182784*a^12*b^8*c^21*d^7 + 172032*a^13*b^7*c^20*d^8 - 115200*a^14*b^6*c^19*d^9 + 53760*a^15*b^5*c^18*d^10 - 16640*a^16*b^4*c^17*d^11 + 3072*a^17*b^3*c^16*d^12 - 256*a^18*b^2*c^15*d^13))/(4*a^2*(a*d - b*c)^5)))/(2*a^2*(a*d - b*c)^5)))/(a^2*(a*d - b*c)^5) + 32*a^2*b^15*c^18*d^3 - 368*a^3*b^14*c^17*d^4 + 1056*a^4*b^13*c^16*d^5 - 5600*a^6*b^11*c^14*d^7 + 12768*a^7*b^10*c^13*d^8 - 14112*a^8*b^9*c^12*d^9 + 8704*a^9*b^8*c^11*d^10 - 2880*a^10*b^7*c^10*d^11 + 400*a^11*b^6*c^9*d^12))*(-b^7*(a*d - b*c)^5)^(1/2)*1i)/(a^2*(a*d - b*c)^5)","B"
730,0,-1,245,0.000000,"\text{Not used}","int(1/(x^4*(a + b*x^2)*(c + d*x^2)^(5/2)),x)","\int \frac{1}{x^4\,\left(b\,x^2+a\right)\,{\left(d\,x^2+c\right)}^{5/2}} \,d x","Not used",1,"int(1/(x^4*(a + b*x^2)*(c + d*x^2)^(5/2)), x)","F"
731,0,-1,150,0.000000,"\text{Not used}","int((x^4*(c + d*x^2)^(1/2))/(a + b*x^2)^2,x)","\int \frac{x^4\,\sqrt{d\,x^2+c}}{{\left(b\,x^2+a\right)}^2} \,d x","Not used",1,"int((x^4*(c + d*x^2)^(1/2))/(a + b*x^2)^2, x)","F"
732,1,102,136,0.901952,"\text{Not used}","int((x^3*(c + d*x^2)^(1/2))/(a + b*x^2)^2,x)","\frac{\sqrt{d\,x^2+c}}{b^2}-\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d\,x^2+c}}{\sqrt{a\,d-b\,c}}\right)\,\left(3\,a\,d-2\,b\,c\right)}{2\,b^{5/2}\,\sqrt{a\,d-b\,c}}+\frac{a\,d\,\sqrt{d\,x^2+c}}{2\,\left(b^3\,\left(d\,x^2+c\right)-b^3\,c+a\,b^2\,d\right)}","Not used",1,"(c + d*x^2)^(1/2)/b^2 - (atan((b^(1/2)*(c + d*x^2)^(1/2))/(a*d - b*c)^(1/2))*(3*a*d - 2*b*c))/(2*b^(5/2)*(a*d - b*c)^(1/2)) + (a*d*(c + d*x^2)^(1/2))/(2*(b^3*(c + d*x^2) - b^3*c + a*b^2*d))","B"
733,0,-1,120,0.000000,"\text{Not used}","int((x^2*(c + d*x^2)^(1/2))/(a + b*x^2)^2,x)","\int \frac{x^2\,\sqrt{d\,x^2+c}}{{\left(b\,x^2+a\right)}^2} \,d x","Not used",1,"int((x^2*(c + d*x^2)^(1/2))/(a + b*x^2)^2, x)","F"
734,1,70,80,0.737610,"\text{Not used}","int((x*(c + d*x^2)^(1/2))/(a + b*x^2)^2,x)","\frac{d\,\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d\,x^2+c}}{\sqrt{a\,d-b\,c}}\right)}{2\,b^{3/2}\,\sqrt{a\,d-b\,c}}-\frac{d\,\sqrt{d\,x^2+c}}{2\,\left(d\,b^2\,x^2+a\,d\,b\right)}","Not used",1,"(d*atan((b^(1/2)*(c + d*x^2)^(1/2))/(a*d - b*c)^(1/2)))/(2*b^(3/2)*(a*d - b*c)^(1/2)) - (d*(c + d*x^2)^(1/2))/(2*(b^2*d*x^2 + a*b*d))","B"
735,0,-1,82,0.000000,"\text{Not used}","int((c + d*x^2)^(1/2)/(a + b*x^2)^2,x)","\int \frac{\sqrt{d\,x^2+c}}{{\left(b\,x^2+a\right)}^2} \,d x","Not used",1,"int((c + d*x^2)^(1/2)/(a + b*x^2)^2, x)","F"
736,1,996,119,1.157219,"\text{Not used}","int((c + d*x^2)^(1/2)/(x*(a + b*x^2)^2),x)","\frac{d\,\sqrt{d\,x^2+c}}{2\,a\,\left(b\,\left(d\,x^2+c\right)+a\,d-b\,c\right)}-\frac{\sqrt{c}\,\mathrm{atanh}\left(\frac{\sqrt{d\,x^2+c}}{\sqrt{c}}\right)}{a^2}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\sqrt{d\,x^2+c}\,\left(a^2\,b\,d^4-4\,a\,b^2\,c\,d^3+8\,b^3\,c^2\,d^2\right)}{2\,a^2}-\frac{\left(2\,a\,b^2\,c\,d^3-\frac{\left(16\,a^5\,b^2\,d^3-32\,a^4\,b^3\,c\,d^2\right)\,\sqrt{d\,x^2+c}\,\sqrt{-b\,\left(a\,d-b\,c\right)}\,\left(a\,d-2\,b\,c\right)}{8\,a^2\,\left(a^2\,b^2\,c-a^3\,b\,d\right)}\right)\,\sqrt{-b\,\left(a\,d-b\,c\right)}\,\left(a\,d-2\,b\,c\right)}{4\,\left(a^2\,b^2\,c-a^3\,b\,d\right)}\right)\,\sqrt{-b\,\left(a\,d-b\,c\right)}\,\left(a\,d-2\,b\,c\right)\,1{}\mathrm{i}}{4\,\left(a^2\,b^2\,c-a^3\,b\,d\right)}+\frac{\left(\frac{\sqrt{d\,x^2+c}\,\left(a^2\,b\,d^4-4\,a\,b^2\,c\,d^3+8\,b^3\,c^2\,d^2\right)}{2\,a^2}+\frac{\left(2\,a\,b^2\,c\,d^3+\frac{\left(16\,a^5\,b^2\,d^3-32\,a^4\,b^3\,c\,d^2\right)\,\sqrt{d\,x^2+c}\,\sqrt{-b\,\left(a\,d-b\,c\right)}\,\left(a\,d-2\,b\,c\right)}{8\,a^2\,\left(a^2\,b^2\,c-a^3\,b\,d\right)}\right)\,\sqrt{-b\,\left(a\,d-b\,c\right)}\,\left(a\,d-2\,b\,c\right)}{4\,\left(a^2\,b^2\,c-a^3\,b\,d\right)}\right)\,\sqrt{-b\,\left(a\,d-b\,c\right)}\,\left(a\,d-2\,b\,c\right)\,1{}\mathrm{i}}{4\,\left(a^2\,b^2\,c-a^3\,b\,d\right)}}{\frac{b^2\,c^2\,d^3-\frac{a\,b\,c\,d^4}{2}}{a^3}+\frac{\left(\frac{\sqrt{d\,x^2+c}\,\left(a^2\,b\,d^4-4\,a\,b^2\,c\,d^3+8\,b^3\,c^2\,d^2\right)}{2\,a^2}-\frac{\left(2\,a\,b^2\,c\,d^3-\frac{\left(16\,a^5\,b^2\,d^3-32\,a^4\,b^3\,c\,d^2\right)\,\sqrt{d\,x^2+c}\,\sqrt{-b\,\left(a\,d-b\,c\right)}\,\left(a\,d-2\,b\,c\right)}{8\,a^2\,\left(a^2\,b^2\,c-a^3\,b\,d\right)}\right)\,\sqrt{-b\,\left(a\,d-b\,c\right)}\,\left(a\,d-2\,b\,c\right)}{4\,\left(a^2\,b^2\,c-a^3\,b\,d\right)}\right)\,\sqrt{-b\,\left(a\,d-b\,c\right)}\,\left(a\,d-2\,b\,c\right)}{4\,\left(a^2\,b^2\,c-a^3\,b\,d\right)}-\frac{\left(\frac{\sqrt{d\,x^2+c}\,\left(a^2\,b\,d^4-4\,a\,b^2\,c\,d^3+8\,b^3\,c^2\,d^2\right)}{2\,a^2}+\frac{\left(2\,a\,b^2\,c\,d^3+\frac{\left(16\,a^5\,b^2\,d^3-32\,a^4\,b^3\,c\,d^2\right)\,\sqrt{d\,x^2+c}\,\sqrt{-b\,\left(a\,d-b\,c\right)}\,\left(a\,d-2\,b\,c\right)}{8\,a^2\,\left(a^2\,b^2\,c-a^3\,b\,d\right)}\right)\,\sqrt{-b\,\left(a\,d-b\,c\right)}\,\left(a\,d-2\,b\,c\right)}{4\,\left(a^2\,b^2\,c-a^3\,b\,d\right)}\right)\,\sqrt{-b\,\left(a\,d-b\,c\right)}\,\left(a\,d-2\,b\,c\right)}{4\,\left(a^2\,b^2\,c-a^3\,b\,d\right)}}\right)\,\sqrt{-b\,\left(a\,d-b\,c\right)}\,\left(a\,d-2\,b\,c\right)\,1{}\mathrm{i}}{2\,\left(a^2\,b^2\,c-a^3\,b\,d\right)}","Not used",1,"(d*(c + d*x^2)^(1/2))/(2*a*(b*(c + d*x^2) + a*d - b*c)) - (c^(1/2)*atanh((c + d*x^2)^(1/2)/c^(1/2)))/a^2 - (atan((((((c + d*x^2)^(1/2)*(a^2*b*d^4 + 8*b^3*c^2*d^2 - 4*a*b^2*c*d^3))/(2*a^2) - ((2*a*b^2*c*d^3 - ((16*a^5*b^2*d^3 - 32*a^4*b^3*c*d^2)*(c + d*x^2)^(1/2)*(-b*(a*d - b*c))^(1/2)*(a*d - 2*b*c))/(8*a^2*(a^2*b^2*c - a^3*b*d)))*(-b*(a*d - b*c))^(1/2)*(a*d - 2*b*c))/(4*(a^2*b^2*c - a^3*b*d)))*(-b*(a*d - b*c))^(1/2)*(a*d - 2*b*c)*1i)/(4*(a^2*b^2*c - a^3*b*d)) + ((((c + d*x^2)^(1/2)*(a^2*b*d^4 + 8*b^3*c^2*d^2 - 4*a*b^2*c*d^3))/(2*a^2) + ((2*a*b^2*c*d^3 + ((16*a^5*b^2*d^3 - 32*a^4*b^3*c*d^2)*(c + d*x^2)^(1/2)*(-b*(a*d - b*c))^(1/2)*(a*d - 2*b*c))/(8*a^2*(a^2*b^2*c - a^3*b*d)))*(-b*(a*d - b*c))^(1/2)*(a*d - 2*b*c))/(4*(a^2*b^2*c - a^3*b*d)))*(-b*(a*d - b*c))^(1/2)*(a*d - 2*b*c)*1i)/(4*(a^2*b^2*c - a^3*b*d)))/((b^2*c^2*d^3 - (a*b*c*d^4)/2)/a^3 + ((((c + d*x^2)^(1/2)*(a^2*b*d^4 + 8*b^3*c^2*d^2 - 4*a*b^2*c*d^3))/(2*a^2) - ((2*a*b^2*c*d^3 - ((16*a^5*b^2*d^3 - 32*a^4*b^3*c*d^2)*(c + d*x^2)^(1/2)*(-b*(a*d - b*c))^(1/2)*(a*d - 2*b*c))/(8*a^2*(a^2*b^2*c - a^3*b*d)))*(-b*(a*d - b*c))^(1/2)*(a*d - 2*b*c))/(4*(a^2*b^2*c - a^3*b*d)))*(-b*(a*d - b*c))^(1/2)*(a*d - 2*b*c))/(4*(a^2*b^2*c - a^3*b*d)) - ((((c + d*x^2)^(1/2)*(a^2*b*d^4 + 8*b^3*c^2*d^2 - 4*a*b^2*c*d^3))/(2*a^2) + ((2*a*b^2*c*d^3 + ((16*a^5*b^2*d^3 - 32*a^4*b^3*c*d^2)*(c + d*x^2)^(1/2)*(-b*(a*d - b*c))^(1/2)*(a*d - 2*b*c))/(8*a^2*(a^2*b^2*c - a^3*b*d)))*(-b*(a*d - b*c))^(1/2)*(a*d - 2*b*c))/(4*(a^2*b^2*c - a^3*b*d)))*(-b*(a*d - b*c))^(1/2)*(a*d - 2*b*c))/(4*(a^2*b^2*c - a^3*b*d))))*(-b*(a*d - b*c))^(1/2)*(a*d - 2*b*c)*1i)/(2*(a^2*b^2*c - a^3*b*d))","B"
737,0,-1,113,0.000000,"\text{Not used}","int((c + d*x^2)^(1/2)/(x^2*(a + b*x^2)^2),x)","\int \frac{\sqrt{d\,x^2+c}}{x^2\,{\left(b\,x^2+a\right)}^2} \,d x","Not used",1,"int((c + d*x^2)^(1/2)/(x^2*(a + b*x^2)^2), x)","F"
738,1,1193,159,1.689469,"\text{Not used}","int((c + d*x^2)^(1/2)/(x^3*(a + b*x^2)^2),x)","\frac{\mathrm{atanh}\left(\frac{b^2\,d^6\,\sqrt{d\,x^2+c}}{4\,c^{3/2}\,\left(\frac{b^3\,d^5}{a}-\frac{b^2\,d^6}{4\,c}\right)}-\frac{b^3\,d^5\,\sqrt{d\,x^2+c}}{\sqrt{c}\,\left(b^3\,d^5-\frac{a\,b^2\,d^6}{4\,c}\right)}\right)\,\left(a\,d-4\,b\,c\right)}{2\,a^3\,\sqrt{c}}-\frac{\frac{b\,d\,{\left(d\,x^2+c\right)}^{3/2}}{a^2}+\frac{d\,\sqrt{d\,x^2+c}\,\left(a\,d-2\,b\,c\right)}{2\,a^2}}{\left(d\,x^2+c\right)\,\left(a\,d-2\,b\,c\right)+b\,{\left(d\,x^2+c\right)}^2+b\,c^2-a\,c\,d}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-b\,\left(a\,d-b\,c\right)}\,\left(\frac{\sqrt{d\,x^2+c}\,\left(5\,a^2\,b^3\,d^4-16\,a\,b^4\,c\,d^3+16\,b^5\,c^2\,d^2\right)}{a^4}-\frac{\left(\frac{2\,a^7\,b^2\,d^4-4\,a^6\,b^3\,c\,d^3}{a^6}-\frac{\left(8\,a^7\,b^2\,d^3-16\,a^6\,b^3\,c\,d^2\right)\,\sqrt{d\,x^2+c}\,\sqrt{-b\,\left(a\,d-b\,c\right)}\,\left(3\,a\,d-4\,b\,c\right)}{4\,a^4\,\left(a^4\,d-a^3\,b\,c\right)}\right)\,\sqrt{-b\,\left(a\,d-b\,c\right)}\,\left(3\,a\,d-4\,b\,c\right)}{4\,\left(a^4\,d-a^3\,b\,c\right)}\right)\,\left(3\,a\,d-4\,b\,c\right)\,1{}\mathrm{i}}{4\,\left(a^4\,d-a^3\,b\,c\right)}+\frac{\sqrt{-b\,\left(a\,d-b\,c\right)}\,\left(\frac{\sqrt{d\,x^2+c}\,\left(5\,a^2\,b^3\,d^4-16\,a\,b^4\,c\,d^3+16\,b^5\,c^2\,d^2\right)}{a^4}+\frac{\left(\frac{2\,a^7\,b^2\,d^4-4\,a^6\,b^3\,c\,d^3}{a^6}+\frac{\left(8\,a^7\,b^2\,d^3-16\,a^6\,b^3\,c\,d^2\right)\,\sqrt{d\,x^2+c}\,\sqrt{-b\,\left(a\,d-b\,c\right)}\,\left(3\,a\,d-4\,b\,c\right)}{4\,a^4\,\left(a^4\,d-a^3\,b\,c\right)}\right)\,\sqrt{-b\,\left(a\,d-b\,c\right)}\,\left(3\,a\,d-4\,b\,c\right)}{4\,\left(a^4\,d-a^3\,b\,c\right)}\right)\,\left(3\,a\,d-4\,b\,c\right)\,1{}\mathrm{i}}{4\,\left(a^4\,d-a^3\,b\,c\right)}}{\frac{\frac{3\,a^2\,b^3\,d^5}{2}-8\,a\,b^4\,c\,d^4+8\,b^5\,c^2\,d^3}{a^6}-\frac{\sqrt{-b\,\left(a\,d-b\,c\right)}\,\left(\frac{\sqrt{d\,x^2+c}\,\left(5\,a^2\,b^3\,d^4-16\,a\,b^4\,c\,d^3+16\,b^5\,c^2\,d^2\right)}{a^4}-\frac{\left(\frac{2\,a^7\,b^2\,d^4-4\,a^6\,b^3\,c\,d^3}{a^6}-\frac{\left(8\,a^7\,b^2\,d^3-16\,a^6\,b^3\,c\,d^2\right)\,\sqrt{d\,x^2+c}\,\sqrt{-b\,\left(a\,d-b\,c\right)}\,\left(3\,a\,d-4\,b\,c\right)}{4\,a^4\,\left(a^4\,d-a^3\,b\,c\right)}\right)\,\sqrt{-b\,\left(a\,d-b\,c\right)}\,\left(3\,a\,d-4\,b\,c\right)}{4\,\left(a^4\,d-a^3\,b\,c\right)}\right)\,\left(3\,a\,d-4\,b\,c\right)}{4\,\left(a^4\,d-a^3\,b\,c\right)}+\frac{\sqrt{-b\,\left(a\,d-b\,c\right)}\,\left(\frac{\sqrt{d\,x^2+c}\,\left(5\,a^2\,b^3\,d^4-16\,a\,b^4\,c\,d^3+16\,b^5\,c^2\,d^2\right)}{a^4}+\frac{\left(\frac{2\,a^7\,b^2\,d^4-4\,a^6\,b^3\,c\,d^3}{a^6}+\frac{\left(8\,a^7\,b^2\,d^3-16\,a^6\,b^3\,c\,d^2\right)\,\sqrt{d\,x^2+c}\,\sqrt{-b\,\left(a\,d-b\,c\right)}\,\left(3\,a\,d-4\,b\,c\right)}{4\,a^4\,\left(a^4\,d-a^3\,b\,c\right)}\right)\,\sqrt{-b\,\left(a\,d-b\,c\right)}\,\left(3\,a\,d-4\,b\,c\right)}{4\,\left(a^4\,d-a^3\,b\,c\right)}\right)\,\left(3\,a\,d-4\,b\,c\right)}{4\,\left(a^4\,d-a^3\,b\,c\right)}}\right)\,\sqrt{-b\,\left(a\,d-b\,c\right)}\,\left(3\,a\,d-4\,b\,c\right)\,1{}\mathrm{i}}{2\,\left(a^4\,d-a^3\,b\,c\right)}","Not used",1,"(atan((((-b*(a*d - b*c))^(1/2)*(((c + d*x^2)^(1/2)*(5*a^2*b^3*d^4 + 16*b^5*c^2*d^2 - 16*a*b^4*c*d^3))/a^4 - (((2*a^7*b^2*d^4 - 4*a^6*b^3*c*d^3)/a^6 - ((8*a^7*b^2*d^3 - 16*a^6*b^3*c*d^2)*(c + d*x^2)^(1/2)*(-b*(a*d - b*c))^(1/2)*(3*a*d - 4*b*c))/(4*a^4*(a^4*d - a^3*b*c)))*(-b*(a*d - b*c))^(1/2)*(3*a*d - 4*b*c))/(4*(a^4*d - a^3*b*c)))*(3*a*d - 4*b*c)*1i)/(4*(a^4*d - a^3*b*c)) + ((-b*(a*d - b*c))^(1/2)*(((c + d*x^2)^(1/2)*(5*a^2*b^3*d^4 + 16*b^5*c^2*d^2 - 16*a*b^4*c*d^3))/a^4 + (((2*a^7*b^2*d^4 - 4*a^6*b^3*c*d^3)/a^6 + ((8*a^7*b^2*d^3 - 16*a^6*b^3*c*d^2)*(c + d*x^2)^(1/2)*(-b*(a*d - b*c))^(1/2)*(3*a*d - 4*b*c))/(4*a^4*(a^4*d - a^3*b*c)))*(-b*(a*d - b*c))^(1/2)*(3*a*d - 4*b*c))/(4*(a^4*d - a^3*b*c)))*(3*a*d - 4*b*c)*1i)/(4*(a^4*d - a^3*b*c)))/(((3*a^2*b^3*d^5)/2 + 8*b^5*c^2*d^3 - 8*a*b^4*c*d^4)/a^6 - ((-b*(a*d - b*c))^(1/2)*(((c + d*x^2)^(1/2)*(5*a^2*b^3*d^4 + 16*b^5*c^2*d^2 - 16*a*b^4*c*d^3))/a^4 - (((2*a^7*b^2*d^4 - 4*a^6*b^3*c*d^3)/a^6 - ((8*a^7*b^2*d^3 - 16*a^6*b^3*c*d^2)*(c + d*x^2)^(1/2)*(-b*(a*d - b*c))^(1/2)*(3*a*d - 4*b*c))/(4*a^4*(a^4*d - a^3*b*c)))*(-b*(a*d - b*c))^(1/2)*(3*a*d - 4*b*c))/(4*(a^4*d - a^3*b*c)))*(3*a*d - 4*b*c))/(4*(a^4*d - a^3*b*c)) + ((-b*(a*d - b*c))^(1/2)*(((c + d*x^2)^(1/2)*(5*a^2*b^3*d^4 + 16*b^5*c^2*d^2 - 16*a*b^4*c*d^3))/a^4 + (((2*a^7*b^2*d^4 - 4*a^6*b^3*c*d^3)/a^6 + ((8*a^7*b^2*d^3 - 16*a^6*b^3*c*d^2)*(c + d*x^2)^(1/2)*(-b*(a*d - b*c))^(1/2)*(3*a*d - 4*b*c))/(4*a^4*(a^4*d - a^3*b*c)))*(-b*(a*d - b*c))^(1/2)*(3*a*d - 4*b*c))/(4*(a^4*d - a^3*b*c)))*(3*a*d - 4*b*c))/(4*(a^4*d - a^3*b*c))))*(-b*(a*d - b*c))^(1/2)*(3*a*d - 4*b*c)*1i)/(2*(a^4*d - a^3*b*c)) - ((b*d*(c + d*x^2)^(3/2))/a^2 + (d*(c + d*x^2)^(1/2)*(a*d - 2*b*c))/(2*a^2))/((c + d*x^2)*(a*d - 2*b*c) + b*(c + d*x^2)^2 + b*c^2 - a*c*d) + (atanh((b^2*d^6*(c + d*x^2)^(1/2))/(4*c^(3/2)*((b^3*d^5)/a - (b^2*d^6)/(4*c))) - (b^3*d^5*(c + d*x^2)^(1/2))/(c^(1/2)*(b^3*d^5 - (a*b^2*d^6)/(4*c))))*(a*d - 4*b*c))/(2*a^3*c^(1/2))","B"
739,0,-1,147,0.000000,"\text{Not used}","int((c + d*x^2)^(1/2)/(x^4*(a + b*x^2)^2),x)","\int \frac{\sqrt{d\,x^2+c}}{x^4\,{\left(b\,x^2+a\right)}^2} \,d x","Not used",1,"int((c + d*x^2)^(1/2)/(x^4*(a + b*x^2)^2), x)","F"
740,0,-1,197,0.000000,"\text{Not used}","int((x^4*(c + d*x^2)^(3/2))/(a + b*x^2)^2,x)","\int \frac{x^4\,{\left(d\,x^2+c\right)}^{3/2}}{{\left(b\,x^2+a\right)}^2} \,d x","Not used",1,"int((x^4*(c + d*x^2)^(3/2))/(a + b*x^2)^2, x)","F"
741,1,183,163,0.986332,"\text{Not used}","int((x^3*(c + d*x^2)^(3/2))/(a + b*x^2)^2,x)","\frac{{\left(d\,x^2+c\right)}^{3/2}}{3\,b^2}-\sqrt{d\,x^2+c}\,\left(\frac{c}{b^2}-\frac{2\,b^2\,c-2\,a\,b\,d}{b^4}\right)-\frac{\left(\frac{a^2\,d^2}{2}-\frac{a\,b\,c\,d}{2}\right)\,\sqrt{d\,x^2+c}}{b^4\,\left(d\,x^2+c\right)-b^4\,c+a\,b^3\,d}+\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d\,x^2+c}\,\sqrt{a\,d-b\,c}\,\left(5\,a\,d-2\,b\,c\right)}{5\,a^2\,d^2-7\,a\,b\,c\,d+2\,b^2\,c^2}\right)\,\sqrt{a\,d-b\,c}\,\left(5\,a\,d-2\,b\,c\right)}{2\,b^{7/2}}","Not used",1,"(c + d*x^2)^(3/2)/(3*b^2) - (c + d*x^2)^(1/2)*(c/b^2 - (2*b^2*c - 2*a*b*d)/b^4) - (((a^2*d^2)/2 - (a*b*c*d)/2)*(c + d*x^2)^(1/2))/(b^4*(c + d*x^2) - b^4*c + a*b^3*d) + (atan((b^(1/2)*(c + d*x^2)^(1/2)*(a*d - b*c)^(1/2)*(5*a*d - 2*b*c))/(5*a^2*d^2 + 2*b^2*c^2 - 7*a*b*c*d))*(a*d - b*c)^(1/2)*(5*a*d - 2*b*c))/(2*b^(7/2))","B"
742,0,-1,149,0.000000,"\text{Not used}","int((x^2*(c + d*x^2)^(3/2))/(a + b*x^2)^2,x)","\int \frac{x^2\,{\left(d\,x^2+c\right)}^{3/2}}{{\left(b\,x^2+a\right)}^2} \,d x","Not used",1,"int((x^2*(c + d*x^2)^(3/2))/(a + b*x^2)^2, x)","F"
743,1,117,99,0.904844,"\text{Not used}","int((x*(c + d*x^2)^(3/2))/(a + b*x^2)^2,x)","\frac{\sqrt{d\,x^2+c}\,\left(\frac{a\,d^2}{2}-\frac{b\,c\,d}{2}\right)}{b^3\,\left(d\,x^2+c\right)-b^3\,c+a\,b^2\,d}+\frac{d\,\sqrt{d\,x^2+c}}{b^2}-\frac{3\,d\,\mathrm{atan}\left(\frac{\sqrt{b}\,d\,\sqrt{d\,x^2+c}\,\sqrt{a\,d-b\,c}}{a\,d^2-b\,c\,d}\right)\,\sqrt{a\,d-b\,c}}{2\,b^{5/2}}","Not used",1,"((c + d*x^2)^(1/2)*((a*d^2)/2 - (b*c*d)/2))/(b^3*(c + d*x^2) - b^3*c + a*b^2*d) + (d*(c + d*x^2)^(1/2))/b^2 - (3*d*atan((b^(1/2)*d*(c + d*x^2)^(1/2)*(a*d - b*c)^(1/2))/(a*d^2 - b*c*d))*(a*d - b*c)^(1/2))/(2*b^(5/2))","B"
744,0,-1,131,0.000000,"\text{Not used}","int((c + d*x^2)^(3/2)/(a + b*x^2)^2,x)","\int \frac{{\left(d\,x^2+c\right)}^{3/2}}{{\left(b\,x^2+a\right)}^2} \,d x","Not used",1,"int((c + d*x^2)^(3/2)/(a + b*x^2)^2, x)","F"
745,1,488,129,1.101385,"\text{Not used}","int((c + d*x^2)^(3/2)/(x*(a + b*x^2)^2),x)","-\frac{\mathrm{atanh}\left(\frac{d^6\,\sqrt{d\,x^2+c}\,\sqrt{c^3}}{2\,\left(\frac{c^2\,d^6}{2}+\frac{b\,c^3\,d^5}{a}-\frac{3\,b^2\,c^4\,d^4}{2\,a^2}\right)}+\frac{c\,d^5\,\sqrt{d\,x^2+c}\,\sqrt{c^3}}{c^3\,d^5+\frac{a\,c^2\,d^6}{2\,b}-\frac{3\,b\,c^4\,d^4}{2\,a}}-\frac{3\,b\,c^2\,d^4\,\sqrt{d\,x^2+c}\,\sqrt{c^3}}{2\,\left(a\,c^3\,d^5-\frac{3\,b\,c^4\,d^4}{2}+\frac{a^2\,c^2\,d^6}{2\,b}\right)}\right)\,\sqrt{c^3}}{a^2}-\frac{\mathrm{atanh}\left(\frac{5\,c^2\,d^5\,\sqrt{d\,x^2+c}\,\sqrt{b^4\,c-a\,b^3\,d}}{4\,\left(\frac{a^2\,c\,d^7}{4}+\frac{b^2\,c^3\,d^5}{4}-\frac{3\,b^3\,c^4\,d^4}{2\,a}+a\,b\,c^2\,d^6\right)}+\frac{3\,c^3\,d^4\,\sqrt{d\,x^2+c}\,\sqrt{b^4\,c-a\,b^3\,d}}{2\,\left(a^2\,c^2\,d^6-\frac{3\,b^2\,c^4\,d^4}{2}+\frac{a^3\,c\,d^7}{4\,b}+\frac{a\,b\,c^3\,d^5}{4}\right)}+\frac{c\,d^6\,\sqrt{d\,x^2+c}\,\sqrt{b^4\,c-a\,b^3\,d}}{4\,\left(b^2\,c^2\,d^6+\frac{a\,b\,c\,d^7}{4}+\frac{b^3\,c^3\,d^5}{4\,a}-\frac{3\,b^4\,c^4\,d^4}{2\,a^2}\right)}\right)\,\left(a\,d+2\,b\,c\right)\,\sqrt{-b^3\,\left(a\,d-b\,c\right)}}{2\,a^2\,b^3}-\frac{d\,\sqrt{d\,x^2+c}\,\left(a\,d-b\,c\right)}{2\,a\,b\,\left(b\,\left(d\,x^2+c\right)+a\,d-b\,c\right)}","Not used",1,"- (atanh((d^6*(c + d*x^2)^(1/2)*(c^3)^(1/2))/(2*((c^2*d^6)/2 + (b*c^3*d^5)/a - (3*b^2*c^4*d^4)/(2*a^2))) + (c*d^5*(c + d*x^2)^(1/2)*(c^3)^(1/2))/(c^3*d^5 + (a*c^2*d^6)/(2*b) - (3*b*c^4*d^4)/(2*a)) - (3*b*c^2*d^4*(c + d*x^2)^(1/2)*(c^3)^(1/2))/(2*(a*c^3*d^5 - (3*b*c^4*d^4)/2 + (a^2*c^2*d^6)/(2*b))))*(c^3)^(1/2))/a^2 - (atanh((5*c^2*d^5*(c + d*x^2)^(1/2)*(b^4*c - a*b^3*d)^(1/2))/(4*((a^2*c*d^7)/4 + (b^2*c^3*d^5)/4 - (3*b^3*c^4*d^4)/(2*a) + a*b*c^2*d^6)) + (3*c^3*d^4*(c + d*x^2)^(1/2)*(b^4*c - a*b^3*d)^(1/2))/(2*(a^2*c^2*d^6 - (3*b^2*c^4*d^4)/2 + (a^3*c*d^7)/(4*b) + (a*b*c^3*d^5)/4)) + (c*d^6*(c + d*x^2)^(1/2)*(b^4*c - a*b^3*d)^(1/2))/(4*(b^2*c^2*d^6 + (a*b*c*d^7)/4 + (b^3*c^3*d^5)/(4*a) - (3*b^4*c^4*d^4)/(2*a^2))))*(a*d + 2*b*c)*(-b^3*(a*d - b*c))^(1/2))/(2*a^2*b^3) - (d*(c + d*x^2)^(1/2)*(a*d - b*c))/(2*a*b*(b*(c + d*x^2) + a*d - b*c))","B"
746,0,-1,128,0.000000,"\text{Not used}","int((c + d*x^2)^(3/2)/(x^2*(a + b*x^2)^2),x)","\int \frac{{\left(d\,x^2+c\right)}^{3/2}}{x^2\,{\left(b\,x^2+a\right)}^2} \,d x","Not used",1,"int((c + d*x^2)^(3/2)/(x^2*(a + b*x^2)^2), x)","F"
747,1,441,170,1.737136,"\text{Not used}","int((c + d*x^2)^(3/2)/(x^3*(a + b*x^2)^2),x)","\frac{\mathrm{atanh}\left(\frac{b^2\,c^2\,d^5\,\sqrt{d\,x^2+c}\,\sqrt{b^2\,c-a\,b\,d}}{\frac{a^2\,b\,c\,d^7}{4}-\frac{5\,a\,b^2\,c^2\,d^6}{4}+b^3\,c^3\,d^5}-\frac{b\,c\,d^6\,\sqrt{d\,x^2+c}\,\sqrt{b^2\,c-a\,b\,d}}{4\,\left(\frac{a\,b\,c\,d^7}{4}-\frac{5\,b^2\,c^2\,d^6}{4}+\frac{b^3\,c^3\,d^5}{a}\right)}\right)\,\sqrt{-b\,\left(a\,d-b\,c\right)}\,\left(a\,d-4\,b\,c\right)}{2\,a^3\,b}-\frac{\sqrt{c}\,\mathrm{atanh}\left(\frac{3\,b\,\sqrt{c}\,d^7\,\sqrt{d\,x^2+c}}{4\,\left(\frac{3\,b\,c\,d^7}{4}-\frac{7\,b^2\,c^2\,d^6}{4\,a}+\frac{b^3\,c^3\,d^5}{a^2}\right)}-\frac{7\,b^2\,c^{3/2}\,d^6\,\sqrt{d\,x^2+c}}{4\,\left(\frac{3\,a\,b\,c\,d^7}{4}-\frac{7\,b^2\,c^2\,d^6}{4}+\frac{b^3\,c^3\,d^5}{a}\right)}+\frac{b^3\,c^{5/2}\,d^5\,\sqrt{d\,x^2+c}}{\frac{3\,a^2\,b\,c\,d^7}{4}-\frac{7\,a\,b^2\,c^2\,d^6}{4}+b^3\,c^3\,d^5}\right)\,\left(3\,a\,d-4\,b\,c\right)}{2\,a^3}-\frac{\frac{\left(a\,c\,d^2-b\,c^2\,d\right)\,\sqrt{d\,x^2+c}}{a^2}-\frac{d\,{\left(d\,x^2+c\right)}^{3/2}\,\left(a\,d-2\,b\,c\right)}{2\,a^2}}{\left(d\,x^2+c\right)\,\left(a\,d-2\,b\,c\right)+b\,{\left(d\,x^2+c\right)}^2+b\,c^2-a\,c\,d}","Not used",1,"(atanh((b^2*c^2*d^5*(c + d*x^2)^(1/2)*(b^2*c - a*b*d)^(1/2))/(b^3*c^3*d^5 - (5*a*b^2*c^2*d^6)/4 + (a^2*b*c*d^7)/4) - (b*c*d^6*(c + d*x^2)^(1/2)*(b^2*c - a*b*d)^(1/2))/(4*((a*b*c*d^7)/4 - (5*b^2*c^2*d^6)/4 + (b^3*c^3*d^5)/a)))*(-b*(a*d - b*c))^(1/2)*(a*d - 4*b*c))/(2*a^3*b) - (c^(1/2)*atanh((3*b*c^(1/2)*d^7*(c + d*x^2)^(1/2))/(4*((3*b*c*d^7)/4 - (7*b^2*c^2*d^6)/(4*a) + (b^3*c^3*d^5)/a^2)) - (7*b^2*c^(3/2)*d^6*(c + d*x^2)^(1/2))/(4*((3*a*b*c*d^7)/4 - (7*b^2*c^2*d^6)/4 + (b^3*c^3*d^5)/a)) + (b^3*c^(5/2)*d^5*(c + d*x^2)^(1/2))/(b^3*c^3*d^5 - (7*a*b^2*c^2*d^6)/4 + (3*a^2*b*c*d^7)/4))*(3*a*d - 4*b*c))/(2*a^3) - (((a*c*d^2 - b*c^2*d)*(c + d*x^2)^(1/2))/a^2 - (d*(c + d*x^2)^(3/2)*(a*d - 2*b*c))/(2*a^2))/((c + d*x^2)*(a*d - 2*b*c) + b*(c + d*x^2)^2 + b*c^2 - a*c*d)","B"
748,0,-1,166,0.000000,"\text{Not used}","int((c + d*x^2)^(3/2)/(x^4*(a + b*x^2)^2),x)","\int \frac{{\left(d\,x^2+c\right)}^{3/2}}{x^4\,{\left(b\,x^2+a\right)}^2} \,d x","Not used",1,"int((c + d*x^2)^(3/2)/(x^4*(a + b*x^2)^2), x)","F"
749,0,-1,258,0.000000,"\text{Not used}","int((x^4*(c + d*x^2)^(5/2))/(a + b*x^2)^2,x)","\int \frac{x^4\,{\left(d\,x^2+c\right)}^{5/2}}{{\left(b\,x^2+a\right)}^2} \,d x","Not used",1,"int((x^4*(c + d*x^2)^(5/2))/(a + b*x^2)^2, x)","F"
750,1,276,198,1.171724,"\text{Not used}","int((x^3*(c + d*x^2)^(5/2))/(a + b*x^2)^2,x)","\frac{{\left(d\,x^2+c\right)}^{5/2}}{5\,b^2}-\sqrt{d\,x^2+c}\,\left(\frac{{\left(a\,d-b\,c\right)}^2}{b^4}+\frac{\left(2\,b^2\,c-2\,a\,b\,d\right)\,\left(\frac{c}{b^2}-\frac{2\,b^2\,c-2\,a\,b\,d}{b^4}\right)}{b^2}\right)-{\left(d\,x^2+c\right)}^{3/2}\,\left(\frac{c}{3\,b^2}-\frac{2\,b^2\,c-2\,a\,b\,d}{3\,b^4}\right)+\frac{\sqrt{d\,x^2+c}\,\left(\frac{a^3\,d^3}{2}-a^2\,b\,c\,d^2+\frac{a\,b^2\,c^2\,d}{2}\right)}{b^5\,\left(d\,x^2+c\right)-b^5\,c+a\,b^4\,d}-\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d\,x^2+c}\,{\left(a\,d-b\,c\right)}^{3/2}\,\left(7\,a\,d-2\,b\,c\right)}{7\,a^3\,d^3-16\,a^2\,b\,c\,d^2+11\,a\,b^2\,c^2\,d-2\,b^3\,c^3}\right)\,{\left(a\,d-b\,c\right)}^{3/2}\,\left(7\,a\,d-2\,b\,c\right)}{2\,b^{9/2}}","Not used",1,"(c + d*x^2)^(5/2)/(5*b^2) - (c + d*x^2)^(1/2)*((a*d - b*c)^2/b^4 + ((2*b^2*c - 2*a*b*d)*(c/b^2 - (2*b^2*c - 2*a*b*d)/b^4))/b^2) - (c + d*x^2)^(3/2)*(c/(3*b^2) - (2*b^2*c - 2*a*b*d)/(3*b^4)) + ((c + d*x^2)^(1/2)*((a^3*d^3)/2 + (a*b^2*c^2*d)/2 - a^2*b*c*d^2))/(b^5*(c + d*x^2) - b^5*c + a*b^4*d) - (atan((b^(1/2)*(c + d*x^2)^(1/2)*(a*d - b*c)^(3/2)*(7*a*d - 2*b*c))/(7*a^3*d^3 - 2*b^3*c^3 + 11*a*b^2*c^2*d - 16*a^2*b*c*d^2))*(a*d - b*c)^(3/2)*(7*a*d - 2*b*c))/(2*b^(9/2))","B"
751,0,-1,195,0.000000,"\text{Not used}","int((x^2*(c + d*x^2)^(5/2))/(a + b*x^2)^2,x)","\int \frac{x^2\,{\left(d\,x^2+c\right)}^{5/2}}{{\left(b\,x^2+a\right)}^2} \,d x","Not used",1,"int((x^2*(c + d*x^2)^(5/2))/(a + b*x^2)^2, x)","F"
752,1,172,126,1.035659,"\text{Not used}","int((x*(c + d*x^2)^(5/2))/(a + b*x^2)^2,x)","\frac{d\,{\left(d\,x^2+c\right)}^{3/2}}{3\,b^2}-\frac{\sqrt{d\,x^2+c}\,\left(\frac{a^2\,d^3}{2}-a\,b\,c\,d^2+\frac{b^2\,c^2\,d}{2}\right)}{b^4\,\left(d\,x^2+c\right)-b^4\,c+a\,b^3\,d}+\frac{5\,d\,\mathrm{atan}\left(\frac{\sqrt{b}\,d\,\sqrt{d\,x^2+c}\,{\left(a\,d-b\,c\right)}^{3/2}}{a^2\,d^3-2\,a\,b\,c\,d^2+b^2\,c^2\,d}\right)\,{\left(a\,d-b\,c\right)}^{3/2}}{2\,b^{7/2}}+\frac{d\,\sqrt{d\,x^2+c}\,\left(2\,b^2\,c-2\,a\,b\,d\right)}{b^4}","Not used",1,"(d*(c + d*x^2)^(3/2))/(3*b^2) - ((c + d*x^2)^(1/2)*((a^2*d^3)/2 + (b^2*c^2*d)/2 - a*b*c*d^2))/(b^4*(c + d*x^2) - b^4*c + a*b^3*d) + (5*d*atan((b^(1/2)*d*(c + d*x^2)^(1/2)*(a*d - b*c)^(3/2))/(a^2*d^3 + b^2*c^2*d - 2*a*b*c*d^2))*(a*d - b*c)^(3/2))/(2*b^(7/2)) + (d*(c + d*x^2)^(1/2)*(2*b^2*c - 2*a*b*d))/b^4","B"
753,0,-1,174,0.000000,"\text{Not used}","int((c + d*x^2)^(5/2)/(a + b*x^2)^2,x)","\int \frac{{\left(d\,x^2+c\right)}^{5/2}}{{\left(b\,x^2+a\right)}^2} \,d x","Not used",1,"int((c + d*x^2)^(5/2)/(a + b*x^2)^2, x)","F"
754,1,1321,160,1.309675,"\text{Not used}","int((c + d*x^2)^(5/2)/(x*(a + b*x^2)^2),x)","\frac{d^2\,\sqrt{d\,x^2+c}}{b^2}+\frac{\mathrm{atan}\left(\frac{a^2\,d^8\,\sqrt{d\,x^2+c}\,\sqrt{c^5}\,9{}\mathrm{i}}{2\,\left(\frac{9\,a^2\,c^3\,d^8}{2}+5\,b^2\,c^5\,d^6+\frac{10\,b^3\,c^6\,d^5}{a}-\frac{15\,b^4\,c^7\,d^4}{2\,a^2}-12\,a\,b\,c^4\,d^7\right)}+\frac{c^2\,d^6\,\sqrt{d\,x^2+c}\,\sqrt{c^5}\,5{}\mathrm{i}}{5\,c^5\,d^6-\frac{12\,a\,c^4\,d^7}{b}+\frac{10\,b\,c^6\,d^5}{a}-\frac{15\,b^2\,c^7\,d^4}{2\,a^2}+\frac{9\,a^2\,c^3\,d^8}{2\,b^2}}+\frac{c^3\,d^5\,\sqrt{d\,x^2+c}\,\sqrt{c^5}\,10{}\mathrm{i}}{10\,c^6\,d^5+\frac{5\,a\,c^5\,d^6}{b}-\frac{15\,b\,c^7\,d^4}{2\,a}-\frac{12\,a^2\,c^4\,d^7}{b^2}+\frac{9\,a^3\,c^3\,d^8}{2\,b^3}}-\frac{a\,c\,d^7\,\sqrt{d\,x^2+c}\,\sqrt{c^5}\,12{}\mathrm{i}}{5\,b\,c^5\,d^6-12\,a\,c^4\,d^7+\frac{10\,b^2\,c^6\,d^5}{a}+\frac{9\,a^2\,c^3\,d^8}{2\,b}-\frac{15\,b^3\,c^7\,d^4}{2\,a^2}}-\frac{b\,c^4\,d^4\,\sqrt{d\,x^2+c}\,\sqrt{c^5}\,15{}\mathrm{i}}{2\,\left(10\,a\,c^6\,d^5-\frac{15\,b\,c^7\,d^4}{2}+\frac{5\,a^2\,c^5\,d^6}{b}-\frac{12\,a^3\,c^4\,d^7}{b^2}+\frac{9\,a^4\,c^3\,d^8}{2\,b^3}\right)}\right)\,\sqrt{c^5}\,1{}\mathrm{i}}{a^2}+\frac{\sqrt{d\,x^2+c}\,\left(a^2\,d^3-2\,a\,b\,c\,d^2+b^2\,c^2\,d\right)}{2\,a\,\left(b^3\,\left(d\,x^2+c\right)-b^3\,c+a\,b^2\,d\right)}-\frac{\mathrm{atan}\left(\frac{c^4\,d^5\,\sqrt{d\,x^2+c}\,\sqrt{-a^3\,b^5\,d^3+3\,a^2\,b^6\,c\,d^2-3\,a\,b^7\,c^2\,d+b^8\,c^3}\,35{}\mathrm{i}}{4\,\left(9\,a^3\,b\,c^3\,d^8-\frac{25\,b^4\,c^6\,d^5}{4}-\frac{85\,a\,b^3\,c^5\,d^6}{4}-\frac{81\,a^4\,c^2\,d^9}{4}+\frac{27\,a^5\,c\,d^{10}}{4\,b}+\frac{49\,a^2\,b^2\,c^4\,d^7}{2}+\frac{15\,b^5\,c^7\,d^4}{2\,a}\right)}-\frac{c^3\,d^6\,\sqrt{d\,x^2+c}\,\sqrt{-a^3\,b^5\,d^3+3\,a^2\,b^6\,c\,d^2-3\,a\,b^7\,c^2\,d+b^8\,c^3}\,45{}\mathrm{i}}{4\,\left(\frac{27\,a^4\,c\,d^{10}}{4}-\frac{85\,b^4\,c^5\,d^6}{4}+\frac{49\,a\,b^3\,c^4\,d^7}{2}-\frac{81\,a^3\,b\,c^2\,d^9}{4}+9\,a^2\,b^2\,c^3\,d^8-\frac{25\,b^5\,c^6\,d^5}{4\,a}+\frac{15\,b^6\,c^7\,d^4}{2\,a^2}\right)}+\frac{c^5\,d^4\,\sqrt{d\,x^2+c}\,\sqrt{-a^3\,b^5\,d^3+3\,a^2\,b^6\,c\,d^2-3\,a\,b^7\,c^2\,d+b^8\,c^3}\,15{}\mathrm{i}}{2\,\left(9\,a^4\,c^3\,d^8+\frac{15\,b^4\,c^7\,d^4}{2}-\frac{25\,a\,b^3\,c^6\,d^5}{4}+\frac{49\,a^3\,b\,c^4\,d^7}{2}+\frac{27\,a^6\,c\,d^{10}}{4\,b^2}-\frac{85\,a^2\,b^2\,c^5\,d^6}{4}-\frac{81\,a^5\,c^2\,d^9}{4\,b}\right)}+\frac{a^2\,c\,d^8\,\sqrt{d\,x^2+c}\,\sqrt{-a^3\,b^5\,d^3+3\,a^2\,b^6\,c\,d^2-3\,a\,b^7\,c^2\,d+b^8\,c^3}\,27{}\mathrm{i}}{4\,\left(\frac{49\,a\,b^5\,c^4\,d^7}{2}-\frac{85\,b^6\,c^5\,d^6}{4}+\frac{27\,a^4\,b^2\,c\,d^{10}}{4}+9\,a^2\,b^4\,c^3\,d^8-\frac{81\,a^3\,b^3\,c^2\,d^9}{4}-\frac{25\,b^7\,c^6\,d^5}{4\,a}+\frac{15\,b^8\,c^7\,d^4}{2\,a^2}\right)}-\frac{a\,c^2\,d^7\,\sqrt{d\,x^2+c}\,\sqrt{-a^3\,b^5\,d^3+3\,a^2\,b^6\,c\,d^2-3\,a\,b^7\,c^2\,d+b^8\,c^3}\,27{}\mathrm{i}}{4\,\left(\frac{49\,a\,b^4\,c^4\,d^7}{2}-\frac{85\,b^5\,c^5\,d^6}{4}+9\,a^2\,b^3\,c^3\,d^8-\frac{81\,a^3\,b^2\,c^2\,d^9}{4}-\frac{25\,b^6\,c^6\,d^5}{4\,a}+\frac{15\,b^7\,c^7\,d^4}{2\,a^2}+\frac{27\,a^4\,b\,c\,d^{10}}{4}\right)}\right)\,\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^3}\,\left(3\,a\,d+2\,b\,c\right)\,1{}\mathrm{i}}{2\,a^2\,b^5}","Not used",1,"(d^2*(c + d*x^2)^(1/2))/b^2 + (atan((a^2*d^8*(c + d*x^2)^(1/2)*(c^5)^(1/2)*9i)/(2*((9*a^2*c^3*d^8)/2 + 5*b^2*c^5*d^6 + (10*b^3*c^6*d^5)/a - (15*b^4*c^7*d^4)/(2*a^2) - 12*a*b*c^4*d^7)) + (c^2*d^6*(c + d*x^2)^(1/2)*(c^5)^(1/2)*5i)/(5*c^5*d^6 - (12*a*c^4*d^7)/b + (10*b*c^6*d^5)/a - (15*b^2*c^7*d^4)/(2*a^2) + (9*a^2*c^3*d^8)/(2*b^2)) + (c^3*d^5*(c + d*x^2)^(1/2)*(c^5)^(1/2)*10i)/(10*c^6*d^5 + (5*a*c^5*d^6)/b - (15*b*c^7*d^4)/(2*a) - (12*a^2*c^4*d^7)/b^2 + (9*a^3*c^3*d^8)/(2*b^3)) - (a*c*d^7*(c + d*x^2)^(1/2)*(c^5)^(1/2)*12i)/(5*b*c^5*d^6 - 12*a*c^4*d^7 + (10*b^2*c^6*d^5)/a + (9*a^2*c^3*d^8)/(2*b) - (15*b^3*c^7*d^4)/(2*a^2)) - (b*c^4*d^4*(c + d*x^2)^(1/2)*(c^5)^(1/2)*15i)/(2*(10*a*c^6*d^5 - (15*b*c^7*d^4)/2 + (5*a^2*c^5*d^6)/b - (12*a^3*c^4*d^7)/b^2 + (9*a^4*c^3*d^8)/(2*b^3))))*(c^5)^(1/2)*1i)/a^2 + ((c + d*x^2)^(1/2)*(a^2*d^3 + b^2*c^2*d - 2*a*b*c*d^2))/(2*a*(b^3*(c + d*x^2) - b^3*c + a*b^2*d)) - (atan((c^4*d^5*(c + d*x^2)^(1/2)*(b^8*c^3 - a^3*b^5*d^3 + 3*a^2*b^6*c*d^2 - 3*a*b^7*c^2*d)^(1/2)*35i)/(4*(9*a^3*b*c^3*d^8 - (25*b^4*c^6*d^5)/4 - (85*a*b^3*c^5*d^6)/4 - (81*a^4*c^2*d^9)/4 + (27*a^5*c*d^10)/(4*b) + (49*a^2*b^2*c^4*d^7)/2 + (15*b^5*c^7*d^4)/(2*a))) - (c^3*d^6*(c + d*x^2)^(1/2)*(b^8*c^3 - a^3*b^5*d^3 + 3*a^2*b^6*c*d^2 - 3*a*b^7*c^2*d)^(1/2)*45i)/(4*((27*a^4*c*d^10)/4 - (85*b^4*c^5*d^6)/4 + (49*a*b^3*c^4*d^7)/2 - (81*a^3*b*c^2*d^9)/4 + 9*a^2*b^2*c^3*d^8 - (25*b^5*c^6*d^5)/(4*a) + (15*b^6*c^7*d^4)/(2*a^2))) + (c^5*d^4*(c + d*x^2)^(1/2)*(b^8*c^3 - a^3*b^5*d^3 + 3*a^2*b^6*c*d^2 - 3*a*b^7*c^2*d)^(1/2)*15i)/(2*(9*a^4*c^3*d^8 + (15*b^4*c^7*d^4)/2 - (25*a*b^3*c^6*d^5)/4 + (49*a^3*b*c^4*d^7)/2 + (27*a^6*c*d^10)/(4*b^2) - (85*a^2*b^2*c^5*d^6)/4 - (81*a^5*c^2*d^9)/(4*b))) + (a^2*c*d^8*(c + d*x^2)^(1/2)*(b^8*c^3 - a^3*b^5*d^3 + 3*a^2*b^6*c*d^2 - 3*a*b^7*c^2*d)^(1/2)*27i)/(4*((49*a*b^5*c^4*d^7)/2 - (85*b^6*c^5*d^6)/4 + (27*a^4*b^2*c*d^10)/4 + 9*a^2*b^4*c^3*d^8 - (81*a^3*b^3*c^2*d^9)/4 - (25*b^7*c^6*d^5)/(4*a) + (15*b^8*c^7*d^4)/(2*a^2))) - (a*c^2*d^7*(c + d*x^2)^(1/2)*(b^8*c^3 - a^3*b^5*d^3 + 3*a^2*b^6*c*d^2 - 3*a*b^7*c^2*d)^(1/2)*27i)/(4*((49*a*b^4*c^4*d^7)/2 - (85*b^5*c^5*d^6)/4 + 9*a^2*b^3*c^3*d^8 - (81*a^3*b^2*c^2*d^9)/4 - (25*b^6*c^6*d^5)/(4*a) + (15*b^7*c^7*d^4)/(2*a^2) + (27*a^4*b*c*d^10)/4)))*(-b^5*(a*d - b*c)^3)^(1/2)*(3*a*d + 2*b*c)*1i)/(2*a^2*b^5)","B"
755,0,-1,168,0.000000,"\text{Not used}","int((c + d*x^2)^(5/2)/(x^2*(a + b*x^2)^2),x)","\int \frac{{\left(d\,x^2+c\right)}^{5/2}}{x^2\,{\left(b\,x^2+a\right)}^2} \,d x","Not used",1,"int((c + d*x^2)^(5/2)/(x^2*(a + b*x^2)^2), x)","F"
756,1,1152,180,1.989836,"\text{Not used}","int((c + d*x^2)^(5/2)/(x^3*(a + b*x^2)^2),x)","\frac{\frac{\sqrt{d\,x^2+c}\,\left(a^2\,c\,d^3-3\,a\,b\,c^2\,d^2+2\,b^2\,c^3\,d\right)}{2\,a^2\,b}-\frac{d\,{\left(d\,x^2+c\right)}^{3/2}\,\left(a^2\,d^2-2\,a\,b\,c\,d+2\,b^2\,c^2\right)}{2\,a^2\,b}}{\left(d\,x^2+c\right)\,\left(a\,d-2\,b\,c\right)+b\,{\left(d\,x^2+c\right)}^2+b\,c^2-a\,c\,d}-\frac{\mathrm{atanh}\left(\frac{5\,d^9\,\sqrt{d\,x^2+c}\,\sqrt{c^3}}{4\,\left(\frac{5\,c^2\,d^9}{4}+\frac{4\,b\,c^3\,d^8}{a}-\frac{33\,b^2\,c^4\,d^7}{2\,a^2}+\frac{65\,b^3\,c^5\,d^6}{4\,a^3}-\frac{5\,b^4\,c^6\,d^5}{a^4}\right)}+\frac{4\,c\,d^8\,\sqrt{d\,x^2+c}\,\sqrt{c^3}}{4\,c^3\,d^8+\frac{5\,a\,c^2\,d^9}{4\,b}-\frac{33\,b\,c^4\,d^7}{2\,a}+\frac{65\,b^2\,c^5\,d^6}{4\,a^2}-\frac{5\,b^3\,c^6\,d^5}{a^3}}+\frac{65\,b^2\,c^3\,d^6\,\sqrt{d\,x^2+c}\,\sqrt{c^3}}{4\,\left(4\,a^2\,c^3\,d^8+\frac{65\,b^2\,c^5\,d^6}{4}-\frac{5\,b^3\,c^6\,d^5}{a}+\frac{5\,a^3\,c^2\,d^9}{4\,b}-\frac{33\,a\,b\,c^4\,d^7}{2}\right)}-\frac{5\,b^3\,c^4\,d^5\,\sqrt{d\,x^2+c}\,\sqrt{c^3}}{4\,a^3\,c^3\,d^8-5\,b^3\,c^6\,d^5+\frac{65\,a\,b^2\,c^5\,d^6}{4}-\frac{33\,a^2\,b\,c^4\,d^7}{2}+\frac{5\,a^4\,c^2\,d^9}{4\,b}}-\frac{33\,b\,c^2\,d^7\,\sqrt{d\,x^2+c}\,\sqrt{c^3}}{2\,\left(4\,a\,c^3\,d^8-\frac{33\,b\,c^4\,d^7}{2}+\frac{65\,b^2\,c^5\,d^6}{4\,a}+\frac{5\,a^2\,c^2\,d^9}{4\,b}-\frac{5\,b^3\,c^6\,d^5}{a^2}\right)}\right)\,\left(5\,a\,d-4\,b\,c\right)\,\sqrt{c^3}}{2\,a^3}-\frac{\mathrm{atanh}\left(\frac{15\,c^3\,d^6\,\sqrt{d\,x^2+c}\,\sqrt{-a^3\,b^3\,d^3+3\,a^2\,b^4\,c\,d^2-3\,a\,b^5\,c^2\,d+b^6\,c^3}}{4\,\left(\frac{7\,a^3\,c^2\,d^9}{4}+\frac{55\,b^3\,c^5\,d^6}{4}-\frac{41\,a\,b^2\,c^4\,d^7}{4}-\frac{a^2\,b\,c^3\,d^8}{2}+\frac{a^4\,c\,d^{10}}{4\,b}-\frac{5\,b^4\,c^6\,d^5}{a}\right)}+\frac{9\,c^2\,d^7\,\sqrt{d\,x^2+c}\,\sqrt{-a^3\,b^3\,d^3+3\,a^2\,b^4\,c\,d^2-3\,a\,b^5\,c^2\,d+b^6\,c^3}}{4\,\left(\frac{a^3\,c\,d^{10}}{4}-\frac{41\,b^3\,c^4\,d^7}{4}-\frac{a\,b^2\,c^3\,d^8}{2}+\frac{7\,a^2\,b\,c^2\,d^9}{4}+\frac{55\,b^4\,c^5\,d^6}{4\,a}-\frac{5\,b^5\,c^6\,d^5}{a^2}\right)}+\frac{5\,c^4\,d^5\,\sqrt{d\,x^2+c}\,\sqrt{-a^3\,b^3\,d^3+3\,a^2\,b^4\,c\,d^2-3\,a\,b^5\,c^2\,d+b^6\,c^3}}{\frac{a^3\,c^3\,d^8}{2}+5\,b^3\,c^6\,d^5-\frac{55\,a\,b^2\,c^5\,d^6}{4}+\frac{41\,a^2\,b\,c^4\,d^7}{4}-\frac{a^5\,c\,d^{10}}{4\,b^2}-\frac{7\,a^4\,c^2\,d^9}{4\,b}}-\frac{c\,d^8\,\sqrt{d\,x^2+c}\,\sqrt{-a^3\,b^3\,d^3+3\,a^2\,b^4\,c\,d^2-3\,a\,b^5\,c^2\,d+b^6\,c^3}}{4\,\left(\frac{b^3\,c^3\,d^8}{2}-\frac{7\,a\,b^2\,c^2\,d^9}{4}+\frac{41\,b^4\,c^4\,d^7}{4\,a}-\frac{55\,b^5\,c^5\,d^6}{4\,a^2}+\frac{5\,b^6\,c^6\,d^5}{a^3}-\frac{a^2\,b\,c\,d^{10}}{4}\right)}\right)\,\sqrt{-b^3\,{\left(a\,d-b\,c\right)}^3}\,\left(a\,d+4\,b\,c\right)}{2\,a^3\,b^3}","Not used",1,"(((c + d*x^2)^(1/2)*(a^2*c*d^3 + 2*b^2*c^3*d - 3*a*b*c^2*d^2))/(2*a^2*b) - (d*(c + d*x^2)^(3/2)*(a^2*d^2 + 2*b^2*c^2 - 2*a*b*c*d))/(2*a^2*b))/((c + d*x^2)*(a*d - 2*b*c) + b*(c + d*x^2)^2 + b*c^2 - a*c*d) - (atanh((5*d^9*(c + d*x^2)^(1/2)*(c^3)^(1/2))/(4*((5*c^2*d^9)/4 + (4*b*c^3*d^8)/a - (33*b^2*c^4*d^7)/(2*a^2) + (65*b^3*c^5*d^6)/(4*a^3) - (5*b^4*c^6*d^5)/a^4)) + (4*c*d^8*(c + d*x^2)^(1/2)*(c^3)^(1/2))/(4*c^3*d^8 + (5*a*c^2*d^9)/(4*b) - (33*b*c^4*d^7)/(2*a) + (65*b^2*c^5*d^6)/(4*a^2) - (5*b^3*c^6*d^5)/a^3) + (65*b^2*c^3*d^6*(c + d*x^2)^(1/2)*(c^3)^(1/2))/(4*(4*a^2*c^3*d^8 + (65*b^2*c^5*d^6)/4 - (5*b^3*c^6*d^5)/a + (5*a^3*c^2*d^9)/(4*b) - (33*a*b*c^4*d^7)/2)) - (5*b^3*c^4*d^5*(c + d*x^2)^(1/2)*(c^3)^(1/2))/(4*a^3*c^3*d^8 - 5*b^3*c^6*d^5 + (65*a*b^2*c^5*d^6)/4 - (33*a^2*b*c^4*d^7)/2 + (5*a^4*c^2*d^9)/(4*b)) - (33*b*c^2*d^7*(c + d*x^2)^(1/2)*(c^3)^(1/2))/(2*(4*a*c^3*d^8 - (33*b*c^4*d^7)/2 + (65*b^2*c^5*d^6)/(4*a) + (5*a^2*c^2*d^9)/(4*b) - (5*b^3*c^6*d^5)/a^2)))*(5*a*d - 4*b*c)*(c^3)^(1/2))/(2*a^3) - (atanh((15*c^3*d^6*(c + d*x^2)^(1/2)*(b^6*c^3 - a^3*b^3*d^3 + 3*a^2*b^4*c*d^2 - 3*a*b^5*c^2*d)^(1/2))/(4*((7*a^3*c^2*d^9)/4 + (55*b^3*c^5*d^6)/4 - (41*a*b^2*c^4*d^7)/4 - (a^2*b*c^3*d^8)/2 + (a^4*c*d^10)/(4*b) - (5*b^4*c^6*d^5)/a)) + (9*c^2*d^7*(c + d*x^2)^(1/2)*(b^6*c^3 - a^3*b^3*d^3 + 3*a^2*b^4*c*d^2 - 3*a*b^5*c^2*d)^(1/2))/(4*((a^3*c*d^10)/4 - (41*b^3*c^4*d^7)/4 - (a*b^2*c^3*d^8)/2 + (7*a^2*b*c^2*d^9)/4 + (55*b^4*c^5*d^6)/(4*a) - (5*b^5*c^6*d^5)/a^2)) + (5*c^4*d^5*(c + d*x^2)^(1/2)*(b^6*c^3 - a^3*b^3*d^3 + 3*a^2*b^4*c*d^2 - 3*a*b^5*c^2*d)^(1/2))/((a^3*c^3*d^8)/2 + 5*b^3*c^6*d^5 - (55*a*b^2*c^5*d^6)/4 + (41*a^2*b*c^4*d^7)/4 - (a^5*c*d^10)/(4*b^2) - (7*a^4*c^2*d^9)/(4*b)) - (c*d^8*(c + d*x^2)^(1/2)*(b^6*c^3 - a^3*b^3*d^3 + 3*a^2*b^4*c*d^2 - 3*a*b^5*c^2*d)^(1/2))/(4*((b^3*c^3*d^8)/2 - (7*a*b^2*c^2*d^9)/4 + (41*b^4*c^4*d^7)/(4*a) - (55*b^5*c^5*d^6)/(4*a^2) + (5*b^6*c^6*d^5)/a^3 - (a^2*b*c*d^10)/4)))*(-b^3*(a*d - b*c)^3)^(1/2)*(a*d + 4*b*c))/(2*a^3*b^3)","B"
757,0,-1,176,0.000000,"\text{Not used}","int((c + d*x^2)^(5/2)/(x^4*(a + b*x^2)^2),x)","\int \frac{{\left(d\,x^2+c\right)}^{5/2}}{x^4\,{\left(b\,x^2+a\right)}^2} \,d x","Not used",1,"int((c + d*x^2)^(5/2)/(x^4*(a + b*x^2)^2), x)","F"
758,0,-1,132,0.000000,"\text{Not used}","int(x^4/((a + b*x^2)^2*(c + d*x^2)^(1/2)),x)","\int \frac{x^4}{{\left(b\,x^2+a\right)}^2\,\sqrt{d\,x^2+c}} \,d x","Not used",1,"int(x^4/((a + b*x^2)^2*(c + d*x^2)^(1/2)), x)","F"
759,1,93,99,0.892313,"\text{Not used}","int(x^3/((a + b*x^2)^2*(c + d*x^2)^(1/2)),x)","\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d\,x^2+c}}{\sqrt{a\,d-b\,c}}\right)\,\left(a\,d-2\,b\,c\right)}{2\,b^{3/2}\,{\left(a\,d-b\,c\right)}^{3/2}}-\frac{a\,d\,\sqrt{d\,x^2+c}}{2\,b\,\left(a\,d-b\,c\right)\,\left(b\,\left(d\,x^2+c\right)+a\,d-b\,c\right)}","Not used",1,"(atan((b^(1/2)*(c + d*x^2)^(1/2))/(a*d - b*c)^(1/2))*(a*d - 2*b*c))/(2*b^(3/2)*(a*d - b*c)^(3/2)) - (a*d*(c + d*x^2)^(1/2))/(2*b*(a*d - b*c)*(b*(c + d*x^2) + a*d - b*c))","B"
760,0,-1,89,0.000000,"\text{Not used}","int(x^2/((a + b*x^2)^2*(c + d*x^2)^(1/2)),x)","\int \frac{x^2}{{\left(b\,x^2+a\right)}^2\,\sqrt{d\,x^2+c}} \,d x","Not used",1,"int(x^2/((a + b*x^2)^2*(c + d*x^2)^(1/2)), x)","F"
761,1,82,87,0.785083,"\text{Not used}","int(x/((a + b*x^2)^2*(c + d*x^2)^(1/2)),x)","\frac{d\,\sqrt{d\,x^2+c}}{2\,\left(a\,d-b\,c\right)\,\left(b\,\left(d\,x^2+c\right)+a\,d-b\,c\right)}+\frac{d\,\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d\,x^2+c}}{\sqrt{a\,d-b\,c}}\right)}{2\,\sqrt{b}\,{\left(a\,d-b\,c\right)}^{3/2}}","Not used",1,"(d*(c + d*x^2)^(1/2))/(2*(a*d - b*c)*(b*(c + d*x^2) + a*d - b*c)) + (d*atan((b^(1/2)*(c + d*x^2)^(1/2))/(a*d - b*c)^(1/2)))/(2*b^(1/2)*(a*d - b*c)^(3/2))","B"
762,0,-1,100,0.000000,"\text{Not used}","int(1/((a + b*x^2)^2*(c + d*x^2)^(1/2)),x)","\int \frac{1}{{\left(b\,x^2+a\right)}^2\,\sqrt{d\,x^2+c}} \,d x","Not used",1,"int(1/((a + b*x^2)^2*(c + d*x^2)^(1/2)), x)","F"
763,1,3023,130,1.936937,"\text{Not used}","int(1/(x*(a + b*x^2)^2*(c + d*x^2)^(1/2)),x)","-\frac{b\,d\,\sqrt{d\,x^2+c}}{2\,\left(a^2\,d-a\,b\,c\right)\,\left(b\,\left(d\,x^2+c\right)+a\,d-b\,c\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\frac{4\,a^6\,b^2\,d^5-6\,a^5\,b^3\,c\,d^4+2\,a^4\,b^4\,c^2\,d^3}{2\,\left(a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2\right)}-\frac{\sqrt{d\,x^2+c}\,\left(16\,a^7\,b^2\,d^5-64\,a^6\,b^3\,c\,d^4+80\,a^5\,b^4\,c^2\,d^3-32\,a^4\,b^5\,c^3\,d^2\right)}{8\,a^2\,\sqrt{c}\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}}{2\,a^2\,\sqrt{c}}-\frac{\sqrt{d\,x^2+c}\,\left(13\,a^2\,b^3\,d^4-20\,a\,b^4\,c\,d^3+8\,b^5\,c^2\,d^2\right)}{4\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}\right)\,1{}\mathrm{i}}{a^2\,\sqrt{c}}-\frac{\left(\frac{\frac{4\,a^6\,b^2\,d^5-6\,a^5\,b^3\,c\,d^4+2\,a^4\,b^4\,c^2\,d^3}{2\,\left(a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2\right)}+\frac{\sqrt{d\,x^2+c}\,\left(16\,a^7\,b^2\,d^5-64\,a^6\,b^3\,c\,d^4+80\,a^5\,b^4\,c^2\,d^3-32\,a^4\,b^5\,c^3\,d^2\right)}{8\,a^2\,\sqrt{c}\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}}{2\,a^2\,\sqrt{c}}+\frac{\sqrt{d\,x^2+c}\,\left(13\,a^2\,b^3\,d^4-20\,a\,b^4\,c\,d^3+8\,b^5\,c^2\,d^2\right)}{4\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}\right)\,1{}\mathrm{i}}{a^2\,\sqrt{c}}}{\frac{\frac{3\,a\,b^3\,d^4}{2}-b^4\,c\,d^3}{a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2}+\frac{\frac{\frac{4\,a^6\,b^2\,d^5-6\,a^5\,b^3\,c\,d^4+2\,a^4\,b^4\,c^2\,d^3}{2\,\left(a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2\right)}-\frac{\sqrt{d\,x^2+c}\,\left(16\,a^7\,b^2\,d^5-64\,a^6\,b^3\,c\,d^4+80\,a^5\,b^4\,c^2\,d^3-32\,a^4\,b^5\,c^3\,d^2\right)}{8\,a^2\,\sqrt{c}\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}}{2\,a^2\,\sqrt{c}}-\frac{\sqrt{d\,x^2+c}\,\left(13\,a^2\,b^3\,d^4-20\,a\,b^4\,c\,d^3+8\,b^5\,c^2\,d^2\right)}{4\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}}{a^2\,\sqrt{c}}+\frac{\frac{\frac{4\,a^6\,b^2\,d^5-6\,a^5\,b^3\,c\,d^4+2\,a^4\,b^4\,c^2\,d^3}{2\,\left(a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2\right)}+\frac{\sqrt{d\,x^2+c}\,\left(16\,a^7\,b^2\,d^5-64\,a^6\,b^3\,c\,d^4+80\,a^5\,b^4\,c^2\,d^3-32\,a^4\,b^5\,c^3\,d^2\right)}{8\,a^2\,\sqrt{c}\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}}{2\,a^2\,\sqrt{c}}+\frac{\sqrt{d\,x^2+c}\,\left(13\,a^2\,b^3\,d^4-20\,a\,b^4\,c\,d^3+8\,b^5\,c^2\,d^2\right)}{4\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}}{a^2\,\sqrt{c}}}\right)\,1{}\mathrm{i}}{a^2\,\sqrt{c}}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\sqrt{d\,x^2+c}\,\left(13\,a^2\,b^3\,d^4-20\,a\,b^4\,c\,d^3+8\,b^5\,c^2\,d^2\right)}{2\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}-\frac{\left(\frac{4\,a^6\,b^2\,d^5-6\,a^5\,b^3\,c\,d^4+2\,a^4\,b^4\,c^2\,d^3}{a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2}-\frac{\sqrt{d\,x^2+c}\,\left(3\,a\,d-2\,b\,c\right)\,\sqrt{-b\,{\left(a\,d-b\,c\right)}^3}\,\left(16\,a^7\,b^2\,d^5-64\,a^6\,b^3\,c\,d^4+80\,a^5\,b^4\,c^2\,d^3-32\,a^4\,b^5\,c^3\,d^2\right)}{8\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)\,\left(a^5\,d^3-3\,a^4\,b\,c\,d^2+3\,a^3\,b^2\,c^2\,d-a^2\,b^3\,c^3\right)}\right)\,\left(3\,a\,d-2\,b\,c\right)\,\sqrt{-b\,{\left(a\,d-b\,c\right)}^3}}{4\,\left(a^5\,d^3-3\,a^4\,b\,c\,d^2+3\,a^3\,b^2\,c^2\,d-a^2\,b^3\,c^3\right)}\right)\,\left(3\,a\,d-2\,b\,c\right)\,\sqrt{-b\,{\left(a\,d-b\,c\right)}^3}\,1{}\mathrm{i}}{4\,\left(a^5\,d^3-3\,a^4\,b\,c\,d^2+3\,a^3\,b^2\,c^2\,d-a^2\,b^3\,c^3\right)}+\frac{\left(\frac{\sqrt{d\,x^2+c}\,\left(13\,a^2\,b^3\,d^4-20\,a\,b^4\,c\,d^3+8\,b^5\,c^2\,d^2\right)}{2\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}+\frac{\left(\frac{4\,a^6\,b^2\,d^5-6\,a^5\,b^3\,c\,d^4+2\,a^4\,b^4\,c^2\,d^3}{a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2}+\frac{\sqrt{d\,x^2+c}\,\left(3\,a\,d-2\,b\,c\right)\,\sqrt{-b\,{\left(a\,d-b\,c\right)}^3}\,\left(16\,a^7\,b^2\,d^5-64\,a^6\,b^3\,c\,d^4+80\,a^5\,b^4\,c^2\,d^3-32\,a^4\,b^5\,c^3\,d^2\right)}{8\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)\,\left(a^5\,d^3-3\,a^4\,b\,c\,d^2+3\,a^3\,b^2\,c^2\,d-a^2\,b^3\,c^3\right)}\right)\,\left(3\,a\,d-2\,b\,c\right)\,\sqrt{-b\,{\left(a\,d-b\,c\right)}^3}}{4\,\left(a^5\,d^3-3\,a^4\,b\,c\,d^2+3\,a^3\,b^2\,c^2\,d-a^2\,b^3\,c^3\right)}\right)\,\left(3\,a\,d-2\,b\,c\right)\,\sqrt{-b\,{\left(a\,d-b\,c\right)}^3}\,1{}\mathrm{i}}{4\,\left(a^5\,d^3-3\,a^4\,b\,c\,d^2+3\,a^3\,b^2\,c^2\,d-a^2\,b^3\,c^3\right)}}{\frac{\frac{3\,a\,b^3\,d^4}{2}-b^4\,c\,d^3}{a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2}-\frac{\left(\frac{\sqrt{d\,x^2+c}\,\left(13\,a^2\,b^3\,d^4-20\,a\,b^4\,c\,d^3+8\,b^5\,c^2\,d^2\right)}{2\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}-\frac{\left(\frac{4\,a^6\,b^2\,d^5-6\,a^5\,b^3\,c\,d^4+2\,a^4\,b^4\,c^2\,d^3}{a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2}-\frac{\sqrt{d\,x^2+c}\,\left(3\,a\,d-2\,b\,c\right)\,\sqrt{-b\,{\left(a\,d-b\,c\right)}^3}\,\left(16\,a^7\,b^2\,d^5-64\,a^6\,b^3\,c\,d^4+80\,a^5\,b^4\,c^2\,d^3-32\,a^4\,b^5\,c^3\,d^2\right)}{8\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)\,\left(a^5\,d^3-3\,a^4\,b\,c\,d^2+3\,a^3\,b^2\,c^2\,d-a^2\,b^3\,c^3\right)}\right)\,\left(3\,a\,d-2\,b\,c\right)\,\sqrt{-b\,{\left(a\,d-b\,c\right)}^3}}{4\,\left(a^5\,d^3-3\,a^4\,b\,c\,d^2+3\,a^3\,b^2\,c^2\,d-a^2\,b^3\,c^3\right)}\right)\,\left(3\,a\,d-2\,b\,c\right)\,\sqrt{-b\,{\left(a\,d-b\,c\right)}^3}}{4\,\left(a^5\,d^3-3\,a^4\,b\,c\,d^2+3\,a^3\,b^2\,c^2\,d-a^2\,b^3\,c^3\right)}+\frac{\left(\frac{\sqrt{d\,x^2+c}\,\left(13\,a^2\,b^3\,d^4-20\,a\,b^4\,c\,d^3+8\,b^5\,c^2\,d^2\right)}{2\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}+\frac{\left(\frac{4\,a^6\,b^2\,d^5-6\,a^5\,b^3\,c\,d^4+2\,a^4\,b^4\,c^2\,d^3}{a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2}+\frac{\sqrt{d\,x^2+c}\,\left(3\,a\,d-2\,b\,c\right)\,\sqrt{-b\,{\left(a\,d-b\,c\right)}^3}\,\left(16\,a^7\,b^2\,d^5-64\,a^6\,b^3\,c\,d^4+80\,a^5\,b^4\,c^2\,d^3-32\,a^4\,b^5\,c^3\,d^2\right)}{8\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)\,\left(a^5\,d^3-3\,a^4\,b\,c\,d^2+3\,a^3\,b^2\,c^2\,d-a^2\,b^3\,c^3\right)}\right)\,\left(3\,a\,d-2\,b\,c\right)\,\sqrt{-b\,{\left(a\,d-b\,c\right)}^3}}{4\,\left(a^5\,d^3-3\,a^4\,b\,c\,d^2+3\,a^3\,b^2\,c^2\,d-a^2\,b^3\,c^3\right)}\right)\,\left(3\,a\,d-2\,b\,c\right)\,\sqrt{-b\,{\left(a\,d-b\,c\right)}^3}}{4\,\left(a^5\,d^3-3\,a^4\,b\,c\,d^2+3\,a^3\,b^2\,c^2\,d-a^2\,b^3\,c^3\right)}}\right)\,\left(3\,a\,d-2\,b\,c\right)\,\sqrt{-b\,{\left(a\,d-b\,c\right)}^3}\,1{}\mathrm{i}}{2\,\left(a^5\,d^3-3\,a^4\,b\,c\,d^2+3\,a^3\,b^2\,c^2\,d-a^2\,b^3\,c^3\right)}","Not used",1,"(atan((((((c + d*x^2)^(1/2)*(13*a^2*b^3*d^4 + 8*b^5*c^2*d^2 - 20*a*b^4*c*d^3))/(2*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)) - (((4*a^6*b^2*d^5 - 6*a^5*b^3*c*d^4 + 2*a^4*b^4*c^2*d^3)/(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d) - ((c + d*x^2)^(1/2)*(3*a*d - 2*b*c)*(-b*(a*d - b*c)^3)^(1/2)*(16*a^7*b^2*d^5 - 64*a^6*b^3*c*d^4 - 32*a^4*b^5*c^3*d^2 + 80*a^5*b^4*c^2*d^3))/(8*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)*(a^5*d^3 - a^2*b^3*c^3 + 3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2)))*(3*a*d - 2*b*c)*(-b*(a*d - b*c)^3)^(1/2))/(4*(a^5*d^3 - a^2*b^3*c^3 + 3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2)))*(3*a*d - 2*b*c)*(-b*(a*d - b*c)^3)^(1/2)*1i)/(4*(a^5*d^3 - a^2*b^3*c^3 + 3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2)) + ((((c + d*x^2)^(1/2)*(13*a^2*b^3*d^4 + 8*b^5*c^2*d^2 - 20*a*b^4*c*d^3))/(2*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)) + (((4*a^6*b^2*d^5 - 6*a^5*b^3*c*d^4 + 2*a^4*b^4*c^2*d^3)/(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d) + ((c + d*x^2)^(1/2)*(3*a*d - 2*b*c)*(-b*(a*d - b*c)^3)^(1/2)*(16*a^7*b^2*d^5 - 64*a^6*b^3*c*d^4 - 32*a^4*b^5*c^3*d^2 + 80*a^5*b^4*c^2*d^3))/(8*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)*(a^5*d^3 - a^2*b^3*c^3 + 3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2)))*(3*a*d - 2*b*c)*(-b*(a*d - b*c)^3)^(1/2))/(4*(a^5*d^3 - a^2*b^3*c^3 + 3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2)))*(3*a*d - 2*b*c)*(-b*(a*d - b*c)^3)^(1/2)*1i)/(4*(a^5*d^3 - a^2*b^3*c^3 + 3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2)))/(((3*a*b^3*d^4)/2 - b^4*c*d^3)/(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d) - ((((c + d*x^2)^(1/2)*(13*a^2*b^3*d^4 + 8*b^5*c^2*d^2 - 20*a*b^4*c*d^3))/(2*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)) - (((4*a^6*b^2*d^5 - 6*a^5*b^3*c*d^4 + 2*a^4*b^4*c^2*d^3)/(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d) - ((c + d*x^2)^(1/2)*(3*a*d - 2*b*c)*(-b*(a*d - b*c)^3)^(1/2)*(16*a^7*b^2*d^5 - 64*a^6*b^3*c*d^4 - 32*a^4*b^5*c^3*d^2 + 80*a^5*b^4*c^2*d^3))/(8*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)*(a^5*d^3 - a^2*b^3*c^3 + 3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2)))*(3*a*d - 2*b*c)*(-b*(a*d - b*c)^3)^(1/2))/(4*(a^5*d^3 - a^2*b^3*c^3 + 3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2)))*(3*a*d - 2*b*c)*(-b*(a*d - b*c)^3)^(1/2))/(4*(a^5*d^3 - a^2*b^3*c^3 + 3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2)) + ((((c + d*x^2)^(1/2)*(13*a^2*b^3*d^4 + 8*b^5*c^2*d^2 - 20*a*b^4*c*d^3))/(2*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)) + (((4*a^6*b^2*d^5 - 6*a^5*b^3*c*d^4 + 2*a^4*b^4*c^2*d^3)/(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d) + ((c + d*x^2)^(1/2)*(3*a*d - 2*b*c)*(-b*(a*d - b*c)^3)^(1/2)*(16*a^7*b^2*d^5 - 64*a^6*b^3*c*d^4 - 32*a^4*b^5*c^3*d^2 + 80*a^5*b^4*c^2*d^3))/(8*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)*(a^5*d^3 - a^2*b^3*c^3 + 3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2)))*(3*a*d - 2*b*c)*(-b*(a*d - b*c)^3)^(1/2))/(4*(a^5*d^3 - a^2*b^3*c^3 + 3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2)))*(3*a*d - 2*b*c)*(-b*(a*d - b*c)^3)^(1/2))/(4*(a^5*d^3 - a^2*b^3*c^3 + 3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2))))*(3*a*d - 2*b*c)*(-b*(a*d - b*c)^3)^(1/2)*1i)/(2*(a^5*d^3 - a^2*b^3*c^3 + 3*a^3*b^2*c^2*d - 3*a^4*b*c*d^2)) - (atan((((((4*a^6*b^2*d^5 - 6*a^5*b^3*c*d^4 + 2*a^4*b^4*c^2*d^3)/(2*(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d)) - ((c + d*x^2)^(1/2)*(16*a^7*b^2*d^5 - 64*a^6*b^3*c*d^4 - 32*a^4*b^5*c^3*d^2 + 80*a^5*b^4*c^2*d^3))/(8*a^2*c^(1/2)*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)))/(2*a^2*c^(1/2)) - ((c + d*x^2)^(1/2)*(13*a^2*b^3*d^4 + 8*b^5*c^2*d^2 - 20*a*b^4*c*d^3))/(4*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)))*1i)/(a^2*c^(1/2)) - ((((4*a^6*b^2*d^5 - 6*a^5*b^3*c*d^4 + 2*a^4*b^4*c^2*d^3)/(2*(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d)) + ((c + d*x^2)^(1/2)*(16*a^7*b^2*d^5 - 64*a^6*b^3*c*d^4 - 32*a^4*b^5*c^3*d^2 + 80*a^5*b^4*c^2*d^3))/(8*a^2*c^(1/2)*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)))/(2*a^2*c^(1/2)) + ((c + d*x^2)^(1/2)*(13*a^2*b^3*d^4 + 8*b^5*c^2*d^2 - 20*a*b^4*c*d^3))/(4*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)))*1i)/(a^2*c^(1/2)))/(((3*a*b^3*d^4)/2 - b^4*c*d^3)/(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d) + (((4*a^6*b^2*d^5 - 6*a^5*b^3*c*d^4 + 2*a^4*b^4*c^2*d^3)/(2*(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d)) - ((c + d*x^2)^(1/2)*(16*a^7*b^2*d^5 - 64*a^6*b^3*c*d^4 - 32*a^4*b^5*c^3*d^2 + 80*a^5*b^4*c^2*d^3))/(8*a^2*c^(1/2)*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)))/(2*a^2*c^(1/2)) - ((c + d*x^2)^(1/2)*(13*a^2*b^3*d^4 + 8*b^5*c^2*d^2 - 20*a*b^4*c*d^3))/(4*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)))/(a^2*c^(1/2)) + (((4*a^6*b^2*d^5 - 6*a^5*b^3*c*d^4 + 2*a^4*b^4*c^2*d^3)/(2*(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d)) + ((c + d*x^2)^(1/2)*(16*a^7*b^2*d^5 - 64*a^6*b^3*c*d^4 - 32*a^4*b^5*c^3*d^2 + 80*a^5*b^4*c^2*d^3))/(8*a^2*c^(1/2)*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)))/(2*a^2*c^(1/2)) + ((c + d*x^2)^(1/2)*(13*a^2*b^3*d^4 + 8*b^5*c^2*d^2 - 20*a*b^4*c*d^3))/(4*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)))/(a^2*c^(1/2))))*1i)/(a^2*c^(1/2)) - (b*d*(c + d*x^2)^(1/2))/(2*(a^2*d - a*b*c)*(b*(c + d*x^2) + a*d - b*c))","B"
764,0,-1,147,0.000000,"\text{Not used}","int(1/(x^2*(a + b*x^2)^2*(c + d*x^2)^(1/2)),x)","\int \frac{1}{x^2\,{\left(b\,x^2+a\right)}^2\,\sqrt{d\,x^2+c}} \,d x","Not used",1,"int(1/(x^2*(a + b*x^2)^2*(c + d*x^2)^(1/2)), x)","F"
765,1,3837,185,2.852826,"\text{Not used}","int(1/(x^3*(a + b*x^2)^2*(c + d*x^2)^(1/2)),x)","\frac{\frac{\sqrt{d\,x^2+c}\,\left(a^2\,d^3-2\,a\,b\,c\,d^2+2\,b^2\,c^2\,d\right)}{2\,a^2\,\left(b\,c^2-a\,c\,d\right)}+\frac{b\,{\left(d\,x^2+c\right)}^{3/2}\,\left(a\,d^2-2\,b\,c\,d\right)}{2\,a^2\,\left(b\,c^2-a\,c\,d\right)}}{\left(d\,x^2+c\right)\,\left(a\,d-2\,b\,c\right)+b\,{\left(d\,x^2+c\right)}^2+b\,c^2-a\,c\,d}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-b^3\,{\left(a\,d-b\,c\right)}^3}\,\left(5\,a\,d-4\,b\,c\right)\,\left(\frac{\sqrt{d\,x^2+c}\,\left(a^4\,b^3\,d^6+6\,a^3\,b^4\,c\,d^5+26\,a^2\,b^5\,c^2\,d^4-64\,a\,b^6\,c^3\,d^3+32\,b^7\,c^4\,d^2\right)}{2\,\left(a^6\,c^2\,d^2-2\,a^5\,b\,c^3\,d+a^4\,b^2\,c^4\right)}+\frac{\sqrt{-b^3\,{\left(a\,d-b\,c\right)}^3}\,\left(5\,a\,d-4\,b\,c\right)\,\left(\frac{2\,a^9\,b^2\,c\,d^6+2\,a^8\,b^3\,c^2\,d^5-8\,a^7\,b^4\,c^3\,d^4+4\,a^6\,b^5\,c^4\,d^3}{a^8\,c^2\,d^2-2\,a^7\,b\,c^3\,d+a^6\,b^2\,c^4}-\frac{\sqrt{-b^3\,{\left(a\,d-b\,c\right)}^3}\,\sqrt{d\,x^2+c}\,\left(5\,a\,d-4\,b\,c\right)\,\left(-16\,a^9\,b^2\,c^2\,d^5+64\,a^8\,b^3\,c^3\,d^4-80\,a^7\,b^4\,c^4\,d^3+32\,a^6\,b^5\,c^5\,d^2\right)}{8\,\left(a^6\,c^2\,d^2-2\,a^5\,b\,c^3\,d+a^4\,b^2\,c^4\right)\,\left(a^6\,d^3-3\,a^5\,b\,c\,d^2+3\,a^4\,b^2\,c^2\,d-a^3\,b^3\,c^3\right)}\right)}{4\,\left(a^6\,d^3-3\,a^5\,b\,c\,d^2+3\,a^4\,b^2\,c^2\,d-a^3\,b^3\,c^3\right)}\right)\,1{}\mathrm{i}}{4\,\left(a^6\,d^3-3\,a^5\,b\,c\,d^2+3\,a^4\,b^2\,c^2\,d-a^3\,b^3\,c^3\right)}+\frac{\sqrt{-b^3\,{\left(a\,d-b\,c\right)}^3}\,\left(5\,a\,d-4\,b\,c\right)\,\left(\frac{\sqrt{d\,x^2+c}\,\left(a^4\,b^3\,d^6+6\,a^3\,b^4\,c\,d^5+26\,a^2\,b^5\,c^2\,d^4-64\,a\,b^6\,c^3\,d^3+32\,b^7\,c^4\,d^2\right)}{2\,\left(a^6\,c^2\,d^2-2\,a^5\,b\,c^3\,d+a^4\,b^2\,c^4\right)}-\frac{\sqrt{-b^3\,{\left(a\,d-b\,c\right)}^3}\,\left(5\,a\,d-4\,b\,c\right)\,\left(\frac{2\,a^9\,b^2\,c\,d^6+2\,a^8\,b^3\,c^2\,d^5-8\,a^7\,b^4\,c^3\,d^4+4\,a^6\,b^5\,c^4\,d^3}{a^8\,c^2\,d^2-2\,a^7\,b\,c^3\,d+a^6\,b^2\,c^4}+\frac{\sqrt{-b^3\,{\left(a\,d-b\,c\right)}^3}\,\sqrt{d\,x^2+c}\,\left(5\,a\,d-4\,b\,c\right)\,\left(-16\,a^9\,b^2\,c^2\,d^5+64\,a^8\,b^3\,c^3\,d^4-80\,a^7\,b^4\,c^4\,d^3+32\,a^6\,b^5\,c^5\,d^2\right)}{8\,\left(a^6\,c^2\,d^2-2\,a^5\,b\,c^3\,d+a^4\,b^2\,c^4\right)\,\left(a^6\,d^3-3\,a^5\,b\,c\,d^2+3\,a^4\,b^2\,c^2\,d-a^3\,b^3\,c^3\right)}\right)}{4\,\left(a^6\,d^3-3\,a^5\,b\,c\,d^2+3\,a^4\,b^2\,c^2\,d-a^3\,b^3\,c^3\right)}\right)\,1{}\mathrm{i}}{4\,\left(a^6\,d^3-3\,a^5\,b\,c\,d^2+3\,a^4\,b^2\,c^2\,d-a^3\,b^3\,c^3\right)}}{\frac{\frac{5\,a^3\,b^4\,d^6}{4}+\frac{3\,a^2\,b^5\,c\,d^5}{2}-12\,a\,b^6\,c^2\,d^4+8\,b^7\,c^3\,d^3}{a^8\,c^2\,d^2-2\,a^7\,b\,c^3\,d+a^6\,b^2\,c^4}-\frac{\sqrt{-b^3\,{\left(a\,d-b\,c\right)}^3}\,\left(5\,a\,d-4\,b\,c\right)\,\left(\frac{\sqrt{d\,x^2+c}\,\left(a^4\,b^3\,d^6+6\,a^3\,b^4\,c\,d^5+26\,a^2\,b^5\,c^2\,d^4-64\,a\,b^6\,c^3\,d^3+32\,b^7\,c^4\,d^2\right)}{2\,\left(a^6\,c^2\,d^2-2\,a^5\,b\,c^3\,d+a^4\,b^2\,c^4\right)}+\frac{\sqrt{-b^3\,{\left(a\,d-b\,c\right)}^3}\,\left(5\,a\,d-4\,b\,c\right)\,\left(\frac{2\,a^9\,b^2\,c\,d^6+2\,a^8\,b^3\,c^2\,d^5-8\,a^7\,b^4\,c^3\,d^4+4\,a^6\,b^5\,c^4\,d^3}{a^8\,c^2\,d^2-2\,a^7\,b\,c^3\,d+a^6\,b^2\,c^4}-\frac{\sqrt{-b^3\,{\left(a\,d-b\,c\right)}^3}\,\sqrt{d\,x^2+c}\,\left(5\,a\,d-4\,b\,c\right)\,\left(-16\,a^9\,b^2\,c^2\,d^5+64\,a^8\,b^3\,c^3\,d^4-80\,a^7\,b^4\,c^4\,d^3+32\,a^6\,b^5\,c^5\,d^2\right)}{8\,\left(a^6\,c^2\,d^2-2\,a^5\,b\,c^3\,d+a^4\,b^2\,c^4\right)\,\left(a^6\,d^3-3\,a^5\,b\,c\,d^2+3\,a^4\,b^2\,c^2\,d-a^3\,b^3\,c^3\right)}\right)}{4\,\left(a^6\,d^3-3\,a^5\,b\,c\,d^2+3\,a^4\,b^2\,c^2\,d-a^3\,b^3\,c^3\right)}\right)}{4\,\left(a^6\,d^3-3\,a^5\,b\,c\,d^2+3\,a^4\,b^2\,c^2\,d-a^3\,b^3\,c^3\right)}+\frac{\sqrt{-b^3\,{\left(a\,d-b\,c\right)}^3}\,\left(5\,a\,d-4\,b\,c\right)\,\left(\frac{\sqrt{d\,x^2+c}\,\left(a^4\,b^3\,d^6+6\,a^3\,b^4\,c\,d^5+26\,a^2\,b^5\,c^2\,d^4-64\,a\,b^6\,c^3\,d^3+32\,b^7\,c^4\,d^2\right)}{2\,\left(a^6\,c^2\,d^2-2\,a^5\,b\,c^3\,d+a^4\,b^2\,c^4\right)}-\frac{\sqrt{-b^3\,{\left(a\,d-b\,c\right)}^3}\,\left(5\,a\,d-4\,b\,c\right)\,\left(\frac{2\,a^9\,b^2\,c\,d^6+2\,a^8\,b^3\,c^2\,d^5-8\,a^7\,b^4\,c^3\,d^4+4\,a^6\,b^5\,c^4\,d^3}{a^8\,c^2\,d^2-2\,a^7\,b\,c^3\,d+a^6\,b^2\,c^4}+\frac{\sqrt{-b^3\,{\left(a\,d-b\,c\right)}^3}\,\sqrt{d\,x^2+c}\,\left(5\,a\,d-4\,b\,c\right)\,\left(-16\,a^9\,b^2\,c^2\,d^5+64\,a^8\,b^3\,c^3\,d^4-80\,a^7\,b^4\,c^4\,d^3+32\,a^6\,b^5\,c^5\,d^2\right)}{8\,\left(a^6\,c^2\,d^2-2\,a^5\,b\,c^3\,d+a^4\,b^2\,c^4\right)\,\left(a^6\,d^3-3\,a^5\,b\,c\,d^2+3\,a^4\,b^2\,c^2\,d-a^3\,b^3\,c^3\right)}\right)}{4\,\left(a^6\,d^3-3\,a^5\,b\,c\,d^2+3\,a^4\,b^2\,c^2\,d-a^3\,b^3\,c^3\right)}\right)}{4\,\left(a^6\,d^3-3\,a^5\,b\,c\,d^2+3\,a^4\,b^2\,c^2\,d-a^3\,b^3\,c^3\right)}}\right)\,\sqrt{-b^3\,{\left(a\,d-b\,c\right)}^3}\,\left(5\,a\,d-4\,b\,c\right)\,1{}\mathrm{i}}{2\,\left(a^6\,d^3-3\,a^5\,b\,c\,d^2+3\,a^4\,b^2\,c^2\,d-a^3\,b^3\,c^3\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\sqrt{d\,x^2+c}\,\left(a^4\,b^3\,d^6+6\,a^3\,b^4\,c\,d^5+26\,a^2\,b^5\,c^2\,d^4-64\,a\,b^6\,c^3\,d^3+32\,b^7\,c^4\,d^2\right)}{2\,\left(a^6\,c^2\,d^2-2\,a^5\,b\,c^3\,d+a^4\,b^2\,c^4\right)}+\frac{\left(\frac{2\,a^9\,b^2\,c\,d^6+2\,a^8\,b^3\,c^2\,d^5-8\,a^7\,b^4\,c^3\,d^4+4\,a^6\,b^5\,c^4\,d^3}{a^8\,c^2\,d^2-2\,a^7\,b\,c^3\,d+a^6\,b^2\,c^4}-\frac{\sqrt{d\,x^2+c}\,\left(a\,d+4\,b\,c\right)\,\left(-16\,a^9\,b^2\,c^2\,d^5+64\,a^8\,b^3\,c^3\,d^4-80\,a^7\,b^4\,c^4\,d^3+32\,a^6\,b^5\,c^5\,d^2\right)}{8\,a^3\,\sqrt{c^3}\,\left(a^6\,c^2\,d^2-2\,a^5\,b\,c^3\,d+a^4\,b^2\,c^4\right)}\right)\,\left(a\,d+4\,b\,c\right)}{4\,a^3\,\sqrt{c^3}}\right)\,\left(a\,d+4\,b\,c\right)\,1{}\mathrm{i}}{4\,a^3\,\sqrt{c^3}}+\frac{\left(\frac{\sqrt{d\,x^2+c}\,\left(a^4\,b^3\,d^6+6\,a^3\,b^4\,c\,d^5+26\,a^2\,b^5\,c^2\,d^4-64\,a\,b^6\,c^3\,d^3+32\,b^7\,c^4\,d^2\right)}{2\,\left(a^6\,c^2\,d^2-2\,a^5\,b\,c^3\,d+a^4\,b^2\,c^4\right)}-\frac{\left(\frac{2\,a^9\,b^2\,c\,d^6+2\,a^8\,b^3\,c^2\,d^5-8\,a^7\,b^4\,c^3\,d^4+4\,a^6\,b^5\,c^4\,d^3}{a^8\,c^2\,d^2-2\,a^7\,b\,c^3\,d+a^6\,b^2\,c^4}+\frac{\sqrt{d\,x^2+c}\,\left(a\,d+4\,b\,c\right)\,\left(-16\,a^9\,b^2\,c^2\,d^5+64\,a^8\,b^3\,c^3\,d^4-80\,a^7\,b^4\,c^4\,d^3+32\,a^6\,b^5\,c^5\,d^2\right)}{8\,a^3\,\sqrt{c^3}\,\left(a^6\,c^2\,d^2-2\,a^5\,b\,c^3\,d+a^4\,b^2\,c^4\right)}\right)\,\left(a\,d+4\,b\,c\right)}{4\,a^3\,\sqrt{c^3}}\right)\,\left(a\,d+4\,b\,c\right)\,1{}\mathrm{i}}{4\,a^3\,\sqrt{c^3}}}{\frac{\frac{5\,a^3\,b^4\,d^6}{4}+\frac{3\,a^2\,b^5\,c\,d^5}{2}-12\,a\,b^6\,c^2\,d^4+8\,b^7\,c^3\,d^3}{a^8\,c^2\,d^2-2\,a^7\,b\,c^3\,d+a^6\,b^2\,c^4}-\frac{\left(\frac{\sqrt{d\,x^2+c}\,\left(a^4\,b^3\,d^6+6\,a^3\,b^4\,c\,d^5+26\,a^2\,b^5\,c^2\,d^4-64\,a\,b^6\,c^3\,d^3+32\,b^7\,c^4\,d^2\right)}{2\,\left(a^6\,c^2\,d^2-2\,a^5\,b\,c^3\,d+a^4\,b^2\,c^4\right)}+\frac{\left(\frac{2\,a^9\,b^2\,c\,d^6+2\,a^8\,b^3\,c^2\,d^5-8\,a^7\,b^4\,c^3\,d^4+4\,a^6\,b^5\,c^4\,d^3}{a^8\,c^2\,d^2-2\,a^7\,b\,c^3\,d+a^6\,b^2\,c^4}-\frac{\sqrt{d\,x^2+c}\,\left(a\,d+4\,b\,c\right)\,\left(-16\,a^9\,b^2\,c^2\,d^5+64\,a^8\,b^3\,c^3\,d^4-80\,a^7\,b^4\,c^4\,d^3+32\,a^6\,b^5\,c^5\,d^2\right)}{8\,a^3\,\sqrt{c^3}\,\left(a^6\,c^2\,d^2-2\,a^5\,b\,c^3\,d+a^4\,b^2\,c^4\right)}\right)\,\left(a\,d+4\,b\,c\right)}{4\,a^3\,\sqrt{c^3}}\right)\,\left(a\,d+4\,b\,c\right)}{4\,a^3\,\sqrt{c^3}}+\frac{\left(\frac{\sqrt{d\,x^2+c}\,\left(a^4\,b^3\,d^6+6\,a^3\,b^4\,c\,d^5+26\,a^2\,b^5\,c^2\,d^4-64\,a\,b^6\,c^3\,d^3+32\,b^7\,c^4\,d^2\right)}{2\,\left(a^6\,c^2\,d^2-2\,a^5\,b\,c^3\,d+a^4\,b^2\,c^4\right)}-\frac{\left(\frac{2\,a^9\,b^2\,c\,d^6+2\,a^8\,b^3\,c^2\,d^5-8\,a^7\,b^4\,c^3\,d^4+4\,a^6\,b^5\,c^4\,d^3}{a^8\,c^2\,d^2-2\,a^7\,b\,c^3\,d+a^6\,b^2\,c^4}+\frac{\sqrt{d\,x^2+c}\,\left(a\,d+4\,b\,c\right)\,\left(-16\,a^9\,b^2\,c^2\,d^5+64\,a^8\,b^3\,c^3\,d^4-80\,a^7\,b^4\,c^4\,d^3+32\,a^6\,b^5\,c^5\,d^2\right)}{8\,a^3\,\sqrt{c^3}\,\left(a^6\,c^2\,d^2-2\,a^5\,b\,c^3\,d+a^4\,b^2\,c^4\right)}\right)\,\left(a\,d+4\,b\,c\right)}{4\,a^3\,\sqrt{c^3}}\right)\,\left(a\,d+4\,b\,c\right)}{4\,a^3\,\sqrt{c^3}}}\right)\,\left(a\,d+4\,b\,c\right)\,1{}\mathrm{i}}{2\,a^3\,\sqrt{c^3}}","Not used",1,"(((c + d*x^2)^(1/2)*(a^2*d^3 + 2*b^2*c^2*d - 2*a*b*c*d^2))/(2*a^2*(b*c^2 - a*c*d)) + (b*(c + d*x^2)^(3/2)*(a*d^2 - 2*b*c*d))/(2*a^2*(b*c^2 - a*c*d)))/((c + d*x^2)*(a*d - 2*b*c) + b*(c + d*x^2)^2 + b*c^2 - a*c*d) + (atan((((-b^3*(a*d - b*c)^3)^(1/2)*(5*a*d - 4*b*c)*(((c + d*x^2)^(1/2)*(a^4*b^3*d^6 + 32*b^7*c^4*d^2 - 64*a*b^6*c^3*d^3 + 6*a^3*b^4*c*d^5 + 26*a^2*b^5*c^2*d^4))/(2*(a^4*b^2*c^4 + a^6*c^2*d^2 - 2*a^5*b*c^3*d)) + ((-b^3*(a*d - b*c)^3)^(1/2)*(5*a*d - 4*b*c)*((2*a^9*b^2*c*d^6 + 4*a^6*b^5*c^4*d^3 - 8*a^7*b^4*c^3*d^4 + 2*a^8*b^3*c^2*d^5)/(a^6*b^2*c^4 + a^8*c^2*d^2 - 2*a^7*b*c^3*d) - ((-b^3*(a*d - b*c)^3)^(1/2)*(c + d*x^2)^(1/2)*(5*a*d - 4*b*c)*(32*a^6*b^5*c^5*d^2 - 80*a^7*b^4*c^4*d^3 + 64*a^8*b^3*c^3*d^4 - 16*a^9*b^2*c^2*d^5))/(8*(a^4*b^2*c^4 + a^6*c^2*d^2 - 2*a^5*b*c^3*d)*(a^6*d^3 - a^3*b^3*c^3 + 3*a^4*b^2*c^2*d - 3*a^5*b*c*d^2))))/(4*(a^6*d^3 - a^3*b^3*c^3 + 3*a^4*b^2*c^2*d - 3*a^5*b*c*d^2)))*1i)/(4*(a^6*d^3 - a^3*b^3*c^3 + 3*a^4*b^2*c^2*d - 3*a^5*b*c*d^2)) + ((-b^3*(a*d - b*c)^3)^(1/2)*(5*a*d - 4*b*c)*(((c + d*x^2)^(1/2)*(a^4*b^3*d^6 + 32*b^7*c^4*d^2 - 64*a*b^6*c^3*d^3 + 6*a^3*b^4*c*d^5 + 26*a^2*b^5*c^2*d^4))/(2*(a^4*b^2*c^4 + a^6*c^2*d^2 - 2*a^5*b*c^3*d)) - ((-b^3*(a*d - b*c)^3)^(1/2)*(5*a*d - 4*b*c)*((2*a^9*b^2*c*d^6 + 4*a^6*b^5*c^4*d^3 - 8*a^7*b^4*c^3*d^4 + 2*a^8*b^3*c^2*d^5)/(a^6*b^2*c^4 + a^8*c^2*d^2 - 2*a^7*b*c^3*d) + ((-b^3*(a*d - b*c)^3)^(1/2)*(c + d*x^2)^(1/2)*(5*a*d - 4*b*c)*(32*a^6*b^5*c^5*d^2 - 80*a^7*b^4*c^4*d^3 + 64*a^8*b^3*c^3*d^4 - 16*a^9*b^2*c^2*d^5))/(8*(a^4*b^2*c^4 + a^6*c^2*d^2 - 2*a^5*b*c^3*d)*(a^6*d^3 - a^3*b^3*c^3 + 3*a^4*b^2*c^2*d - 3*a^5*b*c*d^2))))/(4*(a^6*d^3 - a^3*b^3*c^3 + 3*a^4*b^2*c^2*d - 3*a^5*b*c*d^2)))*1i)/(4*(a^6*d^3 - a^3*b^3*c^3 + 3*a^4*b^2*c^2*d - 3*a^5*b*c*d^2)))/(((5*a^3*b^4*d^6)/4 + 8*b^7*c^3*d^3 - 12*a*b^6*c^2*d^4 + (3*a^2*b^5*c*d^5)/2)/(a^6*b^2*c^4 + a^8*c^2*d^2 - 2*a^7*b*c^3*d) - ((-b^3*(a*d - b*c)^3)^(1/2)*(5*a*d - 4*b*c)*(((c + d*x^2)^(1/2)*(a^4*b^3*d^6 + 32*b^7*c^4*d^2 - 64*a*b^6*c^3*d^3 + 6*a^3*b^4*c*d^5 + 26*a^2*b^5*c^2*d^4))/(2*(a^4*b^2*c^4 + a^6*c^2*d^2 - 2*a^5*b*c^3*d)) + ((-b^3*(a*d - b*c)^3)^(1/2)*(5*a*d - 4*b*c)*((2*a^9*b^2*c*d^6 + 4*a^6*b^5*c^4*d^3 - 8*a^7*b^4*c^3*d^4 + 2*a^8*b^3*c^2*d^5)/(a^6*b^2*c^4 + a^8*c^2*d^2 - 2*a^7*b*c^3*d) - ((-b^3*(a*d - b*c)^3)^(1/2)*(c + d*x^2)^(1/2)*(5*a*d - 4*b*c)*(32*a^6*b^5*c^5*d^2 - 80*a^7*b^4*c^4*d^3 + 64*a^8*b^3*c^3*d^4 - 16*a^9*b^2*c^2*d^5))/(8*(a^4*b^2*c^4 + a^6*c^2*d^2 - 2*a^5*b*c^3*d)*(a^6*d^3 - a^3*b^3*c^3 + 3*a^4*b^2*c^2*d - 3*a^5*b*c*d^2))))/(4*(a^6*d^3 - a^3*b^3*c^3 + 3*a^4*b^2*c^2*d - 3*a^5*b*c*d^2))))/(4*(a^6*d^3 - a^3*b^3*c^3 + 3*a^4*b^2*c^2*d - 3*a^5*b*c*d^2)) + ((-b^3*(a*d - b*c)^3)^(1/2)*(5*a*d - 4*b*c)*(((c + d*x^2)^(1/2)*(a^4*b^3*d^6 + 32*b^7*c^4*d^2 - 64*a*b^6*c^3*d^3 + 6*a^3*b^4*c*d^5 + 26*a^2*b^5*c^2*d^4))/(2*(a^4*b^2*c^4 + a^6*c^2*d^2 - 2*a^5*b*c^3*d)) - ((-b^3*(a*d - b*c)^3)^(1/2)*(5*a*d - 4*b*c)*((2*a^9*b^2*c*d^6 + 4*a^6*b^5*c^4*d^3 - 8*a^7*b^4*c^3*d^4 + 2*a^8*b^3*c^2*d^5)/(a^6*b^2*c^4 + a^8*c^2*d^2 - 2*a^7*b*c^3*d) + ((-b^3*(a*d - b*c)^3)^(1/2)*(c + d*x^2)^(1/2)*(5*a*d - 4*b*c)*(32*a^6*b^5*c^5*d^2 - 80*a^7*b^4*c^4*d^3 + 64*a^8*b^3*c^3*d^4 - 16*a^9*b^2*c^2*d^5))/(8*(a^4*b^2*c^4 + a^6*c^2*d^2 - 2*a^5*b*c^3*d)*(a^6*d^3 - a^3*b^3*c^3 + 3*a^4*b^2*c^2*d - 3*a^5*b*c*d^2))))/(4*(a^6*d^3 - a^3*b^3*c^3 + 3*a^4*b^2*c^2*d - 3*a^5*b*c*d^2))))/(4*(a^6*d^3 - a^3*b^3*c^3 + 3*a^4*b^2*c^2*d - 3*a^5*b*c*d^2))))*(-b^3*(a*d - b*c)^3)^(1/2)*(5*a*d - 4*b*c)*1i)/(2*(a^6*d^3 - a^3*b^3*c^3 + 3*a^4*b^2*c^2*d - 3*a^5*b*c*d^2)) + (atan((((((c + d*x^2)^(1/2)*(a^4*b^3*d^6 + 32*b^7*c^4*d^2 - 64*a*b^6*c^3*d^3 + 6*a^3*b^4*c*d^5 + 26*a^2*b^5*c^2*d^4))/(2*(a^4*b^2*c^4 + a^6*c^2*d^2 - 2*a^5*b*c^3*d)) + (((2*a^9*b^2*c*d^6 + 4*a^6*b^5*c^4*d^3 - 8*a^7*b^4*c^3*d^4 + 2*a^8*b^3*c^2*d^5)/(a^6*b^2*c^4 + a^8*c^2*d^2 - 2*a^7*b*c^3*d) - ((c + d*x^2)^(1/2)*(a*d + 4*b*c)*(32*a^6*b^5*c^5*d^2 - 80*a^7*b^4*c^4*d^3 + 64*a^8*b^3*c^3*d^4 - 16*a^9*b^2*c^2*d^5))/(8*a^3*(c^3)^(1/2)*(a^4*b^2*c^4 + a^6*c^2*d^2 - 2*a^5*b*c^3*d)))*(a*d + 4*b*c))/(4*a^3*(c^3)^(1/2)))*(a*d + 4*b*c)*1i)/(4*a^3*(c^3)^(1/2)) + ((((c + d*x^2)^(1/2)*(a^4*b^3*d^6 + 32*b^7*c^4*d^2 - 64*a*b^6*c^3*d^3 + 6*a^3*b^4*c*d^5 + 26*a^2*b^5*c^2*d^4))/(2*(a^4*b^2*c^4 + a^6*c^2*d^2 - 2*a^5*b*c^3*d)) - (((2*a^9*b^2*c*d^6 + 4*a^6*b^5*c^4*d^3 - 8*a^7*b^4*c^3*d^4 + 2*a^8*b^3*c^2*d^5)/(a^6*b^2*c^4 + a^8*c^2*d^2 - 2*a^7*b*c^3*d) + ((c + d*x^2)^(1/2)*(a*d + 4*b*c)*(32*a^6*b^5*c^5*d^2 - 80*a^7*b^4*c^4*d^3 + 64*a^8*b^3*c^3*d^4 - 16*a^9*b^2*c^2*d^5))/(8*a^3*(c^3)^(1/2)*(a^4*b^2*c^4 + a^6*c^2*d^2 - 2*a^5*b*c^3*d)))*(a*d + 4*b*c))/(4*a^3*(c^3)^(1/2)))*(a*d + 4*b*c)*1i)/(4*a^3*(c^3)^(1/2)))/(((5*a^3*b^4*d^6)/4 + 8*b^7*c^3*d^3 - 12*a*b^6*c^2*d^4 + (3*a^2*b^5*c*d^5)/2)/(a^6*b^2*c^4 + a^8*c^2*d^2 - 2*a^7*b*c^3*d) - ((((c + d*x^2)^(1/2)*(a^4*b^3*d^6 + 32*b^7*c^4*d^2 - 64*a*b^6*c^3*d^3 + 6*a^3*b^4*c*d^5 + 26*a^2*b^5*c^2*d^4))/(2*(a^4*b^2*c^4 + a^6*c^2*d^2 - 2*a^5*b*c^3*d)) + (((2*a^9*b^2*c*d^6 + 4*a^6*b^5*c^4*d^3 - 8*a^7*b^4*c^3*d^4 + 2*a^8*b^3*c^2*d^5)/(a^6*b^2*c^4 + a^8*c^2*d^2 - 2*a^7*b*c^3*d) - ((c + d*x^2)^(1/2)*(a*d + 4*b*c)*(32*a^6*b^5*c^5*d^2 - 80*a^7*b^4*c^4*d^3 + 64*a^8*b^3*c^3*d^4 - 16*a^9*b^2*c^2*d^5))/(8*a^3*(c^3)^(1/2)*(a^4*b^2*c^4 + a^6*c^2*d^2 - 2*a^5*b*c^3*d)))*(a*d + 4*b*c))/(4*a^3*(c^3)^(1/2)))*(a*d + 4*b*c))/(4*a^3*(c^3)^(1/2)) + ((((c + d*x^2)^(1/2)*(a^4*b^3*d^6 + 32*b^7*c^4*d^2 - 64*a*b^6*c^3*d^3 + 6*a^3*b^4*c*d^5 + 26*a^2*b^5*c^2*d^4))/(2*(a^4*b^2*c^4 + a^6*c^2*d^2 - 2*a^5*b*c^3*d)) - (((2*a^9*b^2*c*d^6 + 4*a^6*b^5*c^4*d^3 - 8*a^7*b^4*c^3*d^4 + 2*a^8*b^3*c^2*d^5)/(a^6*b^2*c^4 + a^8*c^2*d^2 - 2*a^7*b*c^3*d) + ((c + d*x^2)^(1/2)*(a*d + 4*b*c)*(32*a^6*b^5*c^5*d^2 - 80*a^7*b^4*c^4*d^3 + 64*a^8*b^3*c^3*d^4 - 16*a^9*b^2*c^2*d^5))/(8*a^3*(c^3)^(1/2)*(a^4*b^2*c^4 + a^6*c^2*d^2 - 2*a^5*b*c^3*d)))*(a*d + 4*b*c))/(4*a^3*(c^3)^(1/2)))*(a*d + 4*b*c))/(4*a^3*(c^3)^(1/2))))*(a*d + 4*b*c)*1i)/(2*a^3*(c^3)^(1/2))","B"
766,0,-1,206,0.000000,"\text{Not used}","int(1/(x^4*(a + b*x^2)^2*(c + d*x^2)^(1/2)),x)","\int \frac{1}{x^4\,{\left(b\,x^2+a\right)}^2\,\sqrt{d\,x^2+c}} \,d x","Not used",1,"int(1/(x^4*(a + b*x^2)^2*(c + d*x^2)^(1/2)), x)","F"
767,0,-1,130,0.000000,"\text{Not used}","int(x^4/((a + b*x^2)^2*(c + d*x^2)^(3/2)),x)","\int \frac{x^4}{{\left(b\,x^2+a\right)}^2\,{\left(d\,x^2+c\right)}^{3/2}} \,d x","Not used",1,"int(x^4/((a + b*x^2)^2*(c + d*x^2)^(3/2)), x)","F"
768,1,142,134,1.100897,"\text{Not used}","int(x^3/((a + b*x^2)^2*(c + d*x^2)^(3/2)),x)","\frac{\frac{c}{a\,d-b\,c}+\frac{\left(d\,x^2+c\right)\,\left(a\,d+2\,b\,c\right)}{2\,{\left(a\,d-b\,c\right)}^2}}{b\,{\left(d\,x^2+c\right)}^{3/2}+\sqrt{d\,x^2+c}\,\left(a\,d-b\,c\right)}+\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d\,x^2+c}\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}{{\left(a\,d-b\,c\right)}^{5/2}}\right)\,\left(a\,d+2\,b\,c\right)}{2\,\sqrt{b}\,{\left(a\,d-b\,c\right)}^{5/2}}","Not used",1,"(c/(a*d - b*c) + ((c + d*x^2)*(a*d + 2*b*c))/(2*(a*d - b*c)^2))/(b*(c + d*x^2)^(3/2) + (c + d*x^2)^(1/2)*(a*d - b*c)) + (atan((b^(1/2)*(c + d*x^2)^(1/2)*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/(a*d - b*c)^(5/2))*(a*d + 2*b*c))/(2*b^(1/2)*(a*d - b*c)^(5/2))","B"
769,0,-1,123,0.000000,"\text{Not used}","int(x^2/((a + b*x^2)^2*(c + d*x^2)^(3/2)),x)","\int \frac{x^2}{{\left(b\,x^2+a\right)}^2\,{\left(d\,x^2+c\right)}^{3/2}} \,d x","Not used",1,"int(x^2/((a + b*x^2)^2*(c + d*x^2)^(3/2)), x)","F"
770,1,130,113,0.985856,"\text{Not used}","int(x/((a + b*x^2)^2*(c + d*x^2)^(3/2)),x)","-\frac{\frac{d}{a\,d-b\,c}+\frac{3\,b\,d\,\left(d\,x^2+c\right)}{2\,{\left(a\,d-b\,c\right)}^2}}{b\,{\left(d\,x^2+c\right)}^{3/2}+\sqrt{d\,x^2+c}\,\left(a\,d-b\,c\right)}-\frac{3\,\sqrt{b}\,d\,\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d\,x^2+c}\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}{{\left(a\,d-b\,c\right)}^{5/2}}\right)}{2\,{\left(a\,d-b\,c\right)}^{5/2}}","Not used",1,"- (d/(a*d - b*c) + (3*b*d*(c + d*x^2))/(2*(a*d - b*c)^2))/(b*(c + d*x^2)^(3/2) + (c + d*x^2)^(1/2)*(a*d - b*c)) - (3*b^(1/2)*d*atan((b^(1/2)*(c + d*x^2)^(1/2)*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/(a*d - b*c)^(5/2)))/(2*(a*d - b*c)^(5/2))","B"
771,0,-1,142,0.000000,"\text{Not used}","int(1/((a + b*x^2)^2*(c + d*x^2)^(3/2)),x)","\int \frac{1}{{\left(b\,x^2+a\right)}^2\,{\left(d\,x^2+c\right)}^{3/2}} \,d x","Not used",1,"int(1/((a + b*x^2)^2*(c + d*x^2)^(3/2)), x)","F"
772,1,5227,170,3.405059,"\text{Not used}","int(1/(x*(a + b*x^2)^2*(c + d*x^2)^(3/2)),x)","\frac{\mathrm{atanh}\left(\frac{240\,a^3\,b^{11}\,c^{11}\,d^4\,\sqrt{d\,x^2+c}}{\sqrt{c^3}\,\left(64\,a^{12}\,b^2\,c\,d^{13}-704\,a^{11}\,b^3\,c^2\,d^{12}+3520\,a^{10}\,b^4\,c^3\,d^{11}-10160\,a^9\,b^5\,c^4\,d^{10}+18400\,a^8\,b^6\,c^5\,d^9-21584\,a^7\,b^7\,c^6\,d^8+16384\,a^6\,b^8\,c^7\,d^7-7760\,a^5\,b^9\,c^8\,d^6+2080\,a^4\,b^{10}\,c^9\,d^5-240\,a^3\,b^{11}\,c^{10}\,d^4\right)}-\frac{2080\,a^4\,b^{10}\,c^{10}\,d^5\,\sqrt{d\,x^2+c}}{\sqrt{c^3}\,\left(64\,a^{12}\,b^2\,c\,d^{13}-704\,a^{11}\,b^3\,c^2\,d^{12}+3520\,a^{10}\,b^4\,c^3\,d^{11}-10160\,a^9\,b^5\,c^4\,d^{10}+18400\,a^8\,b^6\,c^5\,d^9-21584\,a^7\,b^7\,c^6\,d^8+16384\,a^6\,b^8\,c^7\,d^7-7760\,a^5\,b^9\,c^8\,d^6+2080\,a^4\,b^{10}\,c^9\,d^5-240\,a^3\,b^{11}\,c^{10}\,d^4\right)}+\frac{7760\,a^5\,b^9\,c^9\,d^6\,\sqrt{d\,x^2+c}}{\sqrt{c^3}\,\left(64\,a^{12}\,b^2\,c\,d^{13}-704\,a^{11}\,b^3\,c^2\,d^{12}+3520\,a^{10}\,b^4\,c^3\,d^{11}-10160\,a^9\,b^5\,c^4\,d^{10}+18400\,a^8\,b^6\,c^5\,d^9-21584\,a^7\,b^7\,c^6\,d^8+16384\,a^6\,b^8\,c^7\,d^7-7760\,a^5\,b^9\,c^8\,d^6+2080\,a^4\,b^{10}\,c^9\,d^5-240\,a^3\,b^{11}\,c^{10}\,d^4\right)}-\frac{16384\,a^6\,b^8\,c^8\,d^7\,\sqrt{d\,x^2+c}}{\sqrt{c^3}\,\left(64\,a^{12}\,b^2\,c\,d^{13}-704\,a^{11}\,b^3\,c^2\,d^{12}+3520\,a^{10}\,b^4\,c^3\,d^{11}-10160\,a^9\,b^5\,c^4\,d^{10}+18400\,a^8\,b^6\,c^5\,d^9-21584\,a^7\,b^7\,c^6\,d^8+16384\,a^6\,b^8\,c^7\,d^7-7760\,a^5\,b^9\,c^8\,d^6+2080\,a^4\,b^{10}\,c^9\,d^5-240\,a^3\,b^{11}\,c^{10}\,d^4\right)}+\frac{21584\,a^7\,b^7\,c^7\,d^8\,\sqrt{d\,x^2+c}}{\sqrt{c^3}\,\left(64\,a^{12}\,b^2\,c\,d^{13}-704\,a^{11}\,b^3\,c^2\,d^{12}+3520\,a^{10}\,b^4\,c^3\,d^{11}-10160\,a^9\,b^5\,c^4\,d^{10}+18400\,a^8\,b^6\,c^5\,d^9-21584\,a^7\,b^7\,c^6\,d^8+16384\,a^6\,b^8\,c^7\,d^7-7760\,a^5\,b^9\,c^8\,d^6+2080\,a^4\,b^{10}\,c^9\,d^5-240\,a^3\,b^{11}\,c^{10}\,d^4\right)}-\frac{18400\,a^8\,b^6\,c^6\,d^9\,\sqrt{d\,x^2+c}}{\sqrt{c^3}\,\left(64\,a^{12}\,b^2\,c\,d^{13}-704\,a^{11}\,b^3\,c^2\,d^{12}+3520\,a^{10}\,b^4\,c^3\,d^{11}-10160\,a^9\,b^5\,c^4\,d^{10}+18400\,a^8\,b^6\,c^5\,d^9-21584\,a^7\,b^7\,c^6\,d^8+16384\,a^6\,b^8\,c^7\,d^7-7760\,a^5\,b^9\,c^8\,d^6+2080\,a^4\,b^{10}\,c^9\,d^5-240\,a^3\,b^{11}\,c^{10}\,d^4\right)}+\frac{10160\,a^9\,b^5\,c^5\,d^{10}\,\sqrt{d\,x^2+c}}{\sqrt{c^3}\,\left(64\,a^{12}\,b^2\,c\,d^{13}-704\,a^{11}\,b^3\,c^2\,d^{12}+3520\,a^{10}\,b^4\,c^3\,d^{11}-10160\,a^9\,b^5\,c^4\,d^{10}+18400\,a^8\,b^6\,c^5\,d^9-21584\,a^7\,b^7\,c^6\,d^8+16384\,a^6\,b^8\,c^7\,d^7-7760\,a^5\,b^9\,c^8\,d^6+2080\,a^4\,b^{10}\,c^9\,d^5-240\,a^3\,b^{11}\,c^{10}\,d^4\right)}-\frac{3520\,a^{10}\,b^4\,c^4\,d^{11}\,\sqrt{d\,x^2+c}}{\sqrt{c^3}\,\left(64\,a^{12}\,b^2\,c\,d^{13}-704\,a^{11}\,b^3\,c^2\,d^{12}+3520\,a^{10}\,b^4\,c^3\,d^{11}-10160\,a^9\,b^5\,c^4\,d^{10}+18400\,a^8\,b^6\,c^5\,d^9-21584\,a^7\,b^7\,c^6\,d^8+16384\,a^6\,b^8\,c^7\,d^7-7760\,a^5\,b^9\,c^8\,d^6+2080\,a^4\,b^{10}\,c^9\,d^5-240\,a^3\,b^{11}\,c^{10}\,d^4\right)}+\frac{704\,a^{11}\,b^3\,c^3\,d^{12}\,\sqrt{d\,x^2+c}}{\sqrt{c^3}\,\left(64\,a^{12}\,b^2\,c\,d^{13}-704\,a^{11}\,b^3\,c^2\,d^{12}+3520\,a^{10}\,b^4\,c^3\,d^{11}-10160\,a^9\,b^5\,c^4\,d^{10}+18400\,a^8\,b^6\,c^5\,d^9-21584\,a^7\,b^7\,c^6\,d^8+16384\,a^6\,b^8\,c^7\,d^7-7760\,a^5\,b^9\,c^8\,d^6+2080\,a^4\,b^{10}\,c^9\,d^5-240\,a^3\,b^{11}\,c^{10}\,d^4\right)}-\frac{64\,a^{12}\,b^2\,c^2\,d^{13}\,\sqrt{d\,x^2+c}}{\sqrt{c^3}\,\left(64\,a^{12}\,b^2\,c\,d^{13}-704\,a^{11}\,b^3\,c^2\,d^{12}+3520\,a^{10}\,b^4\,c^3\,d^{11}-10160\,a^9\,b^5\,c^4\,d^{10}+18400\,a^8\,b^6\,c^5\,d^9-21584\,a^7\,b^7\,c^6\,d^8+16384\,a^6\,b^8\,c^7\,d^7-7760\,a^5\,b^9\,c^8\,d^6+2080\,a^4\,b^{10}\,c^9\,d^5-240\,a^3\,b^{11}\,c^{10}\,d^4\right)}\right)}{a^2\,\sqrt{c^3}}-\frac{\frac{d^2}{b\,c^2-a\,c\,d}+\frac{d\,\left(d\,x^2+c\right)\,\left(c\,b^2+2\,a\,d\,b\right)}{2\,a\,\left(b\,c^2-a\,c\,d\right)\,\left(a\,d-b\,c\right)}}{b\,{\left(d\,x^2+c\right)}^{3/2}+\sqrt{d\,x^2+c}\,\left(a\,d-b\,c\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-b^3\,{\left(a\,d-b\,c\right)}^5}\,\left(5\,a\,d-2\,b\,c\right)\,\left(\sqrt{d\,x^2+c}\,\left(64\,a^{13}\,b^3\,c^3\,d^{12}-640\,a^{12}\,b^4\,c^4\,d^{11}+3280\,a^{11}\,b^5\,c^5\,d^{10}-10400\,a^{10}\,b^6\,c^6\,d^9+21424\,a^9\,b^7\,c^7\,d^8-29312\,a^8\,b^8\,c^8\,d^7+26800\,a^7\,b^9\,c^9\,d^6-16160\,a^6\,b^{10}\,c^{10}\,d^5+6160\,a^5\,b^{11}\,c^{11}\,d^4-1344\,a^4\,b^{12}\,c^{12}\,d^3+128\,a^3\,b^{13}\,c^{13}\,d^2\right)+\frac{\sqrt{-b^3\,{\left(a\,d-b\,c\right)}^5}\,\left(5\,a\,d-2\,b\,c\right)\,\left(64\,a^6\,b^{12}\,c^{14}\,d^3-896\,a^7\,b^{11}\,c^{13}\,d^4+4992\,a^8\,b^{10}\,c^{12}\,d^5-15360\,a^9\,b^9\,c^{11}\,d^6+29568\,a^{10}\,b^8\,c^{10}\,d^7-37632\,a^{11}\,b^7\,c^9\,d^8+32256\,a^{12}\,b^6\,c^8\,d^9-18432\,a^{13}\,b^5\,c^7\,d^{10}+6720\,a^{14}\,b^4\,c^6\,d^{11}-1408\,a^{15}\,b^3\,c^5\,d^{12}+128\,a^{16}\,b^2\,c^4\,d^{13}-\frac{\sqrt{-b^3\,{\left(a\,d-b\,c\right)}^5}\,\sqrt{d\,x^2+c}\,\left(5\,a\,d-2\,b\,c\right)\,\left(-256\,a^{18}\,b^2\,c^5\,d^{13}+3072\,a^{17}\,b^3\,c^6\,d^{12}-16640\,a^{16}\,b^4\,c^7\,d^{11}+53760\,a^{15}\,b^5\,c^8\,d^{10}-115200\,a^{14}\,b^6\,c^9\,d^9+172032\,a^{13}\,b^7\,c^{10}\,d^8-182784\,a^{12}\,b^8\,c^{11}\,d^7+138240\,a^{11}\,b^9\,c^{12}\,d^6-72960\,a^{10}\,b^{10}\,c^{13}\,d^5+25600\,a^9\,b^{11}\,c^{14}\,d^4-5376\,a^8\,b^{12}\,c^{15}\,d^3+512\,a^7\,b^{13}\,c^{16}\,d^2\right)}{4\,\left(a^7\,d^5-5\,a^6\,b\,c\,d^4+10\,a^5\,b^2\,c^2\,d^3-10\,a^4\,b^3\,c^3\,d^2+5\,a^3\,b^4\,c^4\,d-a^2\,b^5\,c^5\right)}\right)}{4\,\left(a^7\,d^5-5\,a^6\,b\,c\,d^4+10\,a^5\,b^2\,c^2\,d^3-10\,a^4\,b^3\,c^3\,d^2+5\,a^3\,b^4\,c^4\,d-a^2\,b^5\,c^5\right)}\right)\,1{}\mathrm{i}}{4\,\left(a^7\,d^5-5\,a^6\,b\,c\,d^4+10\,a^5\,b^2\,c^2\,d^3-10\,a^4\,b^3\,c^3\,d^2+5\,a^3\,b^4\,c^4\,d-a^2\,b^5\,c^5\right)}+\frac{\sqrt{-b^3\,{\left(a\,d-b\,c\right)}^5}\,\left(5\,a\,d-2\,b\,c\right)\,\left(\sqrt{d\,x^2+c}\,\left(64\,a^{13}\,b^3\,c^3\,d^{12}-640\,a^{12}\,b^4\,c^4\,d^{11}+3280\,a^{11}\,b^5\,c^5\,d^{10}-10400\,a^{10}\,b^6\,c^6\,d^9+21424\,a^9\,b^7\,c^7\,d^8-29312\,a^8\,b^8\,c^8\,d^7+26800\,a^7\,b^9\,c^9\,d^6-16160\,a^6\,b^{10}\,c^{10}\,d^5+6160\,a^5\,b^{11}\,c^{11}\,d^4-1344\,a^4\,b^{12}\,c^{12}\,d^3+128\,a^3\,b^{13}\,c^{13}\,d^2\right)-\frac{\sqrt{-b^3\,{\left(a\,d-b\,c\right)}^5}\,\left(5\,a\,d-2\,b\,c\right)\,\left(64\,a^6\,b^{12}\,c^{14}\,d^3-896\,a^7\,b^{11}\,c^{13}\,d^4+4992\,a^8\,b^{10}\,c^{12}\,d^5-15360\,a^9\,b^9\,c^{11}\,d^6+29568\,a^{10}\,b^8\,c^{10}\,d^7-37632\,a^{11}\,b^7\,c^9\,d^8+32256\,a^{12}\,b^6\,c^8\,d^9-18432\,a^{13}\,b^5\,c^7\,d^{10}+6720\,a^{14}\,b^4\,c^6\,d^{11}-1408\,a^{15}\,b^3\,c^5\,d^{12}+128\,a^{16}\,b^2\,c^4\,d^{13}+\frac{\sqrt{-b^3\,{\left(a\,d-b\,c\right)}^5}\,\sqrt{d\,x^2+c}\,\left(5\,a\,d-2\,b\,c\right)\,\left(-256\,a^{18}\,b^2\,c^5\,d^{13}+3072\,a^{17}\,b^3\,c^6\,d^{12}-16640\,a^{16}\,b^4\,c^7\,d^{11}+53760\,a^{15}\,b^5\,c^8\,d^{10}-115200\,a^{14}\,b^6\,c^9\,d^9+172032\,a^{13}\,b^7\,c^{10}\,d^8-182784\,a^{12}\,b^8\,c^{11}\,d^7+138240\,a^{11}\,b^9\,c^{12}\,d^6-72960\,a^{10}\,b^{10}\,c^{13}\,d^5+25600\,a^9\,b^{11}\,c^{14}\,d^4-5376\,a^8\,b^{12}\,c^{15}\,d^3+512\,a^7\,b^{13}\,c^{16}\,d^2\right)}{4\,\left(a^7\,d^5-5\,a^6\,b\,c\,d^4+10\,a^5\,b^2\,c^2\,d^3-10\,a^4\,b^3\,c^3\,d^2+5\,a^3\,b^4\,c^4\,d-a^2\,b^5\,c^5\right)}\right)}{4\,\left(a^7\,d^5-5\,a^6\,b\,c\,d^4+10\,a^5\,b^2\,c^2\,d^3-10\,a^4\,b^3\,c^3\,d^2+5\,a^3\,b^4\,c^4\,d-a^2\,b^5\,c^5\right)}\right)\,1{}\mathrm{i}}{4\,\left(a^7\,d^5-5\,a^6\,b\,c\,d^4+10\,a^5\,b^2\,c^2\,d^3-10\,a^4\,b^3\,c^3\,d^2+5\,a^3\,b^4\,c^4\,d-a^2\,b^5\,c^5\right)}}{\frac{\sqrt{-b^3\,{\left(a\,d-b\,c\right)}^5}\,\left(5\,a\,d-2\,b\,c\right)\,\left(\sqrt{d\,x^2+c}\,\left(64\,a^{13}\,b^3\,c^3\,d^{12}-640\,a^{12}\,b^4\,c^4\,d^{11}+3280\,a^{11}\,b^5\,c^5\,d^{10}-10400\,a^{10}\,b^6\,c^6\,d^9+21424\,a^9\,b^7\,c^7\,d^8-29312\,a^8\,b^8\,c^8\,d^7+26800\,a^7\,b^9\,c^9\,d^6-16160\,a^6\,b^{10}\,c^{10}\,d^5+6160\,a^5\,b^{11}\,c^{11}\,d^4-1344\,a^4\,b^{12}\,c^{12}\,d^3+128\,a^3\,b^{13}\,c^{13}\,d^2\right)-\frac{\sqrt{-b^3\,{\left(a\,d-b\,c\right)}^5}\,\left(5\,a\,d-2\,b\,c\right)\,\left(64\,a^6\,b^{12}\,c^{14}\,d^3-896\,a^7\,b^{11}\,c^{13}\,d^4+4992\,a^8\,b^{10}\,c^{12}\,d^5-15360\,a^9\,b^9\,c^{11}\,d^6+29568\,a^{10}\,b^8\,c^{10}\,d^7-37632\,a^{11}\,b^7\,c^9\,d^8+32256\,a^{12}\,b^6\,c^8\,d^9-18432\,a^{13}\,b^5\,c^7\,d^{10}+6720\,a^{14}\,b^4\,c^6\,d^{11}-1408\,a^{15}\,b^3\,c^5\,d^{12}+128\,a^{16}\,b^2\,c^4\,d^{13}+\frac{\sqrt{-b^3\,{\left(a\,d-b\,c\right)}^5}\,\sqrt{d\,x^2+c}\,\left(5\,a\,d-2\,b\,c\right)\,\left(-256\,a^{18}\,b^2\,c^5\,d^{13}+3072\,a^{17}\,b^3\,c^6\,d^{12}-16640\,a^{16}\,b^4\,c^7\,d^{11}+53760\,a^{15}\,b^5\,c^8\,d^{10}-115200\,a^{14}\,b^6\,c^9\,d^9+172032\,a^{13}\,b^7\,c^{10}\,d^8-182784\,a^{12}\,b^8\,c^{11}\,d^7+138240\,a^{11}\,b^9\,c^{12}\,d^6-72960\,a^{10}\,b^{10}\,c^{13}\,d^5+25600\,a^9\,b^{11}\,c^{14}\,d^4-5376\,a^8\,b^{12}\,c^{15}\,d^3+512\,a^7\,b^{13}\,c^{16}\,d^2\right)}{4\,\left(a^7\,d^5-5\,a^6\,b\,c\,d^4+10\,a^5\,b^2\,c^2\,d^3-10\,a^4\,b^3\,c^3\,d^2+5\,a^3\,b^4\,c^4\,d-a^2\,b^5\,c^5\right)}\right)}{4\,\left(a^7\,d^5-5\,a^6\,b\,c\,d^4+10\,a^5\,b^2\,c^2\,d^3-10\,a^4\,b^3\,c^3\,d^2+5\,a^3\,b^4\,c^4\,d-a^2\,b^5\,c^5\right)}\right)}{4\,\left(a^7\,d^5-5\,a^6\,b\,c\,d^4+10\,a^5\,b^2\,c^2\,d^3-10\,a^4\,b^3\,c^3\,d^2+5\,a^3\,b^4\,c^4\,d-a^2\,b^5\,c^5\right)}-\frac{\sqrt{-b^3\,{\left(a\,d-b\,c\right)}^5}\,\left(5\,a\,d-2\,b\,c\right)\,\left(\sqrt{d\,x^2+c}\,\left(64\,a^{13}\,b^3\,c^3\,d^{12}-640\,a^{12}\,b^4\,c^4\,d^{11}+3280\,a^{11}\,b^5\,c^5\,d^{10}-10400\,a^{10}\,b^6\,c^6\,d^9+21424\,a^9\,b^7\,c^7\,d^8-29312\,a^8\,b^8\,c^8\,d^7+26800\,a^7\,b^9\,c^9\,d^6-16160\,a^6\,b^{10}\,c^{10}\,d^5+6160\,a^5\,b^{11}\,c^{11}\,d^4-1344\,a^4\,b^{12}\,c^{12}\,d^3+128\,a^3\,b^{13}\,c^{13}\,d^2\right)+\frac{\sqrt{-b^3\,{\left(a\,d-b\,c\right)}^5}\,\left(5\,a\,d-2\,b\,c\right)\,\left(64\,a^6\,b^{12}\,c^{14}\,d^3-896\,a^7\,b^{11}\,c^{13}\,d^4+4992\,a^8\,b^{10}\,c^{12}\,d^5-15360\,a^9\,b^9\,c^{11}\,d^6+29568\,a^{10}\,b^8\,c^{10}\,d^7-37632\,a^{11}\,b^7\,c^9\,d^8+32256\,a^{12}\,b^6\,c^8\,d^9-18432\,a^{13}\,b^5\,c^7\,d^{10}+6720\,a^{14}\,b^4\,c^6\,d^{11}-1408\,a^{15}\,b^3\,c^5\,d^{12}+128\,a^{16}\,b^2\,c^4\,d^{13}-\frac{\sqrt{-b^3\,{\left(a\,d-b\,c\right)}^5}\,\sqrt{d\,x^2+c}\,\left(5\,a\,d-2\,b\,c\right)\,\left(-256\,a^{18}\,b^2\,c^5\,d^{13}+3072\,a^{17}\,b^3\,c^6\,d^{12}-16640\,a^{16}\,b^4\,c^7\,d^{11}+53760\,a^{15}\,b^5\,c^8\,d^{10}-115200\,a^{14}\,b^6\,c^9\,d^9+172032\,a^{13}\,b^7\,c^{10}\,d^8-182784\,a^{12}\,b^8\,c^{11}\,d^7+138240\,a^{11}\,b^9\,c^{12}\,d^6-72960\,a^{10}\,b^{10}\,c^{13}\,d^5+25600\,a^9\,b^{11}\,c^{14}\,d^4-5376\,a^8\,b^{12}\,c^{15}\,d^3+512\,a^7\,b^{13}\,c^{16}\,d^2\right)}{4\,\left(a^7\,d^5-5\,a^6\,b\,c\,d^4+10\,a^5\,b^2\,c^2\,d^3-10\,a^4\,b^3\,c^3\,d^2+5\,a^3\,b^4\,c^4\,d-a^2\,b^5\,c^5\right)}\right)}{4\,\left(a^7\,d^5-5\,a^6\,b\,c\,d^4+10\,a^5\,b^2\,c^2\,d^3-10\,a^4\,b^3\,c^3\,d^2+5\,a^3\,b^4\,c^4\,d-a^2\,b^5\,c^5\right)}\right)}{4\,\left(a^7\,d^5-5\,a^6\,b\,c\,d^4+10\,a^5\,b^2\,c^2\,d^3-10\,a^4\,b^3\,c^3\,d^2+5\,a^3\,b^4\,c^4\,d-a^2\,b^5\,c^5\right)}+32\,a^2\,b^{12}\,c^{11}\,d^3-208\,a^3\,b^{11}\,c^{10}\,d^4+416\,a^4\,b^{10}\,c^9\,d^5+80\,a^5\,b^9\,c^8\,d^6-1600\,a^6\,b^8\,c^7\,d^7+2768\,a^7\,b^7\,c^6\,d^8-2272\,a^8\,b^6\,c^5\,d^9+944\,a^9\,b^5\,c^4\,d^{10}-160\,a^{10}\,b^4\,c^3\,d^{11}}\right)\,\sqrt{-b^3\,{\left(a\,d-b\,c\right)}^5}\,\left(5\,a\,d-2\,b\,c\right)\,1{}\mathrm{i}}{2\,\left(a^7\,d^5-5\,a^6\,b\,c\,d^4+10\,a^5\,b^2\,c^2\,d^3-10\,a^4\,b^3\,c^3\,d^2+5\,a^3\,b^4\,c^4\,d-a^2\,b^5\,c^5\right)}","Not used",1,"atanh((240*a^3*b^11*c^11*d^4*(c + d*x^2)^(1/2))/((c^3)^(1/2)*(64*a^12*b^2*c*d^13 - 240*a^3*b^11*c^10*d^4 + 2080*a^4*b^10*c^9*d^5 - 7760*a^5*b^9*c^8*d^6 + 16384*a^6*b^8*c^7*d^7 - 21584*a^7*b^7*c^6*d^8 + 18400*a^8*b^6*c^5*d^9 - 10160*a^9*b^5*c^4*d^10 + 3520*a^10*b^4*c^3*d^11 - 704*a^11*b^3*c^2*d^12)) - (2080*a^4*b^10*c^10*d^5*(c + d*x^2)^(1/2))/((c^3)^(1/2)*(64*a^12*b^2*c*d^13 - 240*a^3*b^11*c^10*d^4 + 2080*a^4*b^10*c^9*d^5 - 7760*a^5*b^9*c^8*d^6 + 16384*a^6*b^8*c^7*d^7 - 21584*a^7*b^7*c^6*d^8 + 18400*a^8*b^6*c^5*d^9 - 10160*a^9*b^5*c^4*d^10 + 3520*a^10*b^4*c^3*d^11 - 704*a^11*b^3*c^2*d^12)) + (7760*a^5*b^9*c^9*d^6*(c + d*x^2)^(1/2))/((c^3)^(1/2)*(64*a^12*b^2*c*d^13 - 240*a^3*b^11*c^10*d^4 + 2080*a^4*b^10*c^9*d^5 - 7760*a^5*b^9*c^8*d^6 + 16384*a^6*b^8*c^7*d^7 - 21584*a^7*b^7*c^6*d^8 + 18400*a^8*b^6*c^5*d^9 - 10160*a^9*b^5*c^4*d^10 + 3520*a^10*b^4*c^3*d^11 - 704*a^11*b^3*c^2*d^12)) - (16384*a^6*b^8*c^8*d^7*(c + d*x^2)^(1/2))/((c^3)^(1/2)*(64*a^12*b^2*c*d^13 - 240*a^3*b^11*c^10*d^4 + 2080*a^4*b^10*c^9*d^5 - 7760*a^5*b^9*c^8*d^6 + 16384*a^6*b^8*c^7*d^7 - 21584*a^7*b^7*c^6*d^8 + 18400*a^8*b^6*c^5*d^9 - 10160*a^9*b^5*c^4*d^10 + 3520*a^10*b^4*c^3*d^11 - 704*a^11*b^3*c^2*d^12)) + (21584*a^7*b^7*c^7*d^8*(c + d*x^2)^(1/2))/((c^3)^(1/2)*(64*a^12*b^2*c*d^13 - 240*a^3*b^11*c^10*d^4 + 2080*a^4*b^10*c^9*d^5 - 7760*a^5*b^9*c^8*d^6 + 16384*a^6*b^8*c^7*d^7 - 21584*a^7*b^7*c^6*d^8 + 18400*a^8*b^6*c^5*d^9 - 10160*a^9*b^5*c^4*d^10 + 3520*a^10*b^4*c^3*d^11 - 704*a^11*b^3*c^2*d^12)) - (18400*a^8*b^6*c^6*d^9*(c + d*x^2)^(1/2))/((c^3)^(1/2)*(64*a^12*b^2*c*d^13 - 240*a^3*b^11*c^10*d^4 + 2080*a^4*b^10*c^9*d^5 - 7760*a^5*b^9*c^8*d^6 + 16384*a^6*b^8*c^7*d^7 - 21584*a^7*b^7*c^6*d^8 + 18400*a^8*b^6*c^5*d^9 - 10160*a^9*b^5*c^4*d^10 + 3520*a^10*b^4*c^3*d^11 - 704*a^11*b^3*c^2*d^12)) + (10160*a^9*b^5*c^5*d^10*(c + d*x^2)^(1/2))/((c^3)^(1/2)*(64*a^12*b^2*c*d^13 - 240*a^3*b^11*c^10*d^4 + 2080*a^4*b^10*c^9*d^5 - 7760*a^5*b^9*c^8*d^6 + 16384*a^6*b^8*c^7*d^7 - 21584*a^7*b^7*c^6*d^8 + 18400*a^8*b^6*c^5*d^9 - 10160*a^9*b^5*c^4*d^10 + 3520*a^10*b^4*c^3*d^11 - 704*a^11*b^3*c^2*d^12)) - (3520*a^10*b^4*c^4*d^11*(c + d*x^2)^(1/2))/((c^3)^(1/2)*(64*a^12*b^2*c*d^13 - 240*a^3*b^11*c^10*d^4 + 2080*a^4*b^10*c^9*d^5 - 7760*a^5*b^9*c^8*d^6 + 16384*a^6*b^8*c^7*d^7 - 21584*a^7*b^7*c^6*d^8 + 18400*a^8*b^6*c^5*d^9 - 10160*a^9*b^5*c^4*d^10 + 3520*a^10*b^4*c^3*d^11 - 704*a^11*b^3*c^2*d^12)) + (704*a^11*b^3*c^3*d^12*(c + d*x^2)^(1/2))/((c^3)^(1/2)*(64*a^12*b^2*c*d^13 - 240*a^3*b^11*c^10*d^4 + 2080*a^4*b^10*c^9*d^5 - 7760*a^5*b^9*c^8*d^6 + 16384*a^6*b^8*c^7*d^7 - 21584*a^7*b^7*c^6*d^8 + 18400*a^8*b^6*c^5*d^9 - 10160*a^9*b^5*c^4*d^10 + 3520*a^10*b^4*c^3*d^11 - 704*a^11*b^3*c^2*d^12)) - (64*a^12*b^2*c^2*d^13*(c + d*x^2)^(1/2))/((c^3)^(1/2)*(64*a^12*b^2*c*d^13 - 240*a^3*b^11*c^10*d^4 + 2080*a^4*b^10*c^9*d^5 - 7760*a^5*b^9*c^8*d^6 + 16384*a^6*b^8*c^7*d^7 - 21584*a^7*b^7*c^6*d^8 + 18400*a^8*b^6*c^5*d^9 - 10160*a^9*b^5*c^4*d^10 + 3520*a^10*b^4*c^3*d^11 - 704*a^11*b^3*c^2*d^12)))/(a^2*(c^3)^(1/2)) - (d^2/(b*c^2 - a*c*d) + (d*(c + d*x^2)*(b^2*c + 2*a*b*d))/(2*a*(b*c^2 - a*c*d)*(a*d - b*c)))/(b*(c + d*x^2)^(3/2) + (c + d*x^2)^(1/2)*(a*d - b*c)) - (atan((((-b^3*(a*d - b*c)^5)^(1/2)*(5*a*d - 2*b*c)*((c + d*x^2)^(1/2)*(128*a^3*b^13*c^13*d^2 - 1344*a^4*b^12*c^12*d^3 + 6160*a^5*b^11*c^11*d^4 - 16160*a^6*b^10*c^10*d^5 + 26800*a^7*b^9*c^9*d^6 - 29312*a^8*b^8*c^8*d^7 + 21424*a^9*b^7*c^7*d^8 - 10400*a^10*b^6*c^6*d^9 + 3280*a^11*b^5*c^5*d^10 - 640*a^12*b^4*c^4*d^11 + 64*a^13*b^3*c^3*d^12) + ((-b^3*(a*d - b*c)^5)^(1/2)*(5*a*d - 2*b*c)*(64*a^6*b^12*c^14*d^3 - 896*a^7*b^11*c^13*d^4 + 4992*a^8*b^10*c^12*d^5 - 15360*a^9*b^9*c^11*d^6 + 29568*a^10*b^8*c^10*d^7 - 37632*a^11*b^7*c^9*d^8 + 32256*a^12*b^6*c^8*d^9 - 18432*a^13*b^5*c^7*d^10 + 6720*a^14*b^4*c^6*d^11 - 1408*a^15*b^3*c^5*d^12 + 128*a^16*b^2*c^4*d^13 - ((-b^3*(a*d - b*c)^5)^(1/2)*(c + d*x^2)^(1/2)*(5*a*d - 2*b*c)*(512*a^7*b^13*c^16*d^2 - 5376*a^8*b^12*c^15*d^3 + 25600*a^9*b^11*c^14*d^4 - 72960*a^10*b^10*c^13*d^5 + 138240*a^11*b^9*c^12*d^6 - 182784*a^12*b^8*c^11*d^7 + 172032*a^13*b^7*c^10*d^8 - 115200*a^14*b^6*c^9*d^9 + 53760*a^15*b^5*c^8*d^10 - 16640*a^16*b^4*c^7*d^11 + 3072*a^17*b^3*c^6*d^12 - 256*a^18*b^2*c^5*d^13))/(4*(a^7*d^5 - a^2*b^5*c^5 + 5*a^3*b^4*c^4*d - 10*a^4*b^3*c^3*d^2 + 10*a^5*b^2*c^2*d^3 - 5*a^6*b*c*d^4))))/(4*(a^7*d^5 - a^2*b^5*c^5 + 5*a^3*b^4*c^4*d - 10*a^4*b^3*c^3*d^2 + 10*a^5*b^2*c^2*d^3 - 5*a^6*b*c*d^4)))*1i)/(4*(a^7*d^5 - a^2*b^5*c^5 + 5*a^3*b^4*c^4*d - 10*a^4*b^3*c^3*d^2 + 10*a^5*b^2*c^2*d^3 - 5*a^6*b*c*d^4)) + ((-b^3*(a*d - b*c)^5)^(1/2)*(5*a*d - 2*b*c)*((c + d*x^2)^(1/2)*(128*a^3*b^13*c^13*d^2 - 1344*a^4*b^12*c^12*d^3 + 6160*a^5*b^11*c^11*d^4 - 16160*a^6*b^10*c^10*d^5 + 26800*a^7*b^9*c^9*d^6 - 29312*a^8*b^8*c^8*d^7 + 21424*a^9*b^7*c^7*d^8 - 10400*a^10*b^6*c^6*d^9 + 3280*a^11*b^5*c^5*d^10 - 640*a^12*b^4*c^4*d^11 + 64*a^13*b^3*c^3*d^12) - ((-b^3*(a*d - b*c)^5)^(1/2)*(5*a*d - 2*b*c)*(64*a^6*b^12*c^14*d^3 - 896*a^7*b^11*c^13*d^4 + 4992*a^8*b^10*c^12*d^5 - 15360*a^9*b^9*c^11*d^6 + 29568*a^10*b^8*c^10*d^7 - 37632*a^11*b^7*c^9*d^8 + 32256*a^12*b^6*c^8*d^9 - 18432*a^13*b^5*c^7*d^10 + 6720*a^14*b^4*c^6*d^11 - 1408*a^15*b^3*c^5*d^12 + 128*a^16*b^2*c^4*d^13 + ((-b^3*(a*d - b*c)^5)^(1/2)*(c + d*x^2)^(1/2)*(5*a*d - 2*b*c)*(512*a^7*b^13*c^16*d^2 - 5376*a^8*b^12*c^15*d^3 + 25600*a^9*b^11*c^14*d^4 - 72960*a^10*b^10*c^13*d^5 + 138240*a^11*b^9*c^12*d^6 - 182784*a^12*b^8*c^11*d^7 + 172032*a^13*b^7*c^10*d^8 - 115200*a^14*b^6*c^9*d^9 + 53760*a^15*b^5*c^8*d^10 - 16640*a^16*b^4*c^7*d^11 + 3072*a^17*b^3*c^6*d^12 - 256*a^18*b^2*c^5*d^13))/(4*(a^7*d^5 - a^2*b^5*c^5 + 5*a^3*b^4*c^4*d - 10*a^4*b^3*c^3*d^2 + 10*a^5*b^2*c^2*d^3 - 5*a^6*b*c*d^4))))/(4*(a^7*d^5 - a^2*b^5*c^5 + 5*a^3*b^4*c^4*d - 10*a^4*b^3*c^3*d^2 + 10*a^5*b^2*c^2*d^3 - 5*a^6*b*c*d^4)))*1i)/(4*(a^7*d^5 - a^2*b^5*c^5 + 5*a^3*b^4*c^4*d - 10*a^4*b^3*c^3*d^2 + 10*a^5*b^2*c^2*d^3 - 5*a^6*b*c*d^4)))/(((-b^3*(a*d - b*c)^5)^(1/2)*(5*a*d - 2*b*c)*((c + d*x^2)^(1/2)*(128*a^3*b^13*c^13*d^2 - 1344*a^4*b^12*c^12*d^3 + 6160*a^5*b^11*c^11*d^4 - 16160*a^6*b^10*c^10*d^5 + 26800*a^7*b^9*c^9*d^6 - 29312*a^8*b^8*c^8*d^7 + 21424*a^9*b^7*c^7*d^8 - 10400*a^10*b^6*c^6*d^9 + 3280*a^11*b^5*c^5*d^10 - 640*a^12*b^4*c^4*d^11 + 64*a^13*b^3*c^3*d^12) - ((-b^3*(a*d - b*c)^5)^(1/2)*(5*a*d - 2*b*c)*(64*a^6*b^12*c^14*d^3 - 896*a^7*b^11*c^13*d^4 + 4992*a^8*b^10*c^12*d^5 - 15360*a^9*b^9*c^11*d^6 + 29568*a^10*b^8*c^10*d^7 - 37632*a^11*b^7*c^9*d^8 + 32256*a^12*b^6*c^8*d^9 - 18432*a^13*b^5*c^7*d^10 + 6720*a^14*b^4*c^6*d^11 - 1408*a^15*b^3*c^5*d^12 + 128*a^16*b^2*c^4*d^13 + ((-b^3*(a*d - b*c)^5)^(1/2)*(c + d*x^2)^(1/2)*(5*a*d - 2*b*c)*(512*a^7*b^13*c^16*d^2 - 5376*a^8*b^12*c^15*d^3 + 25600*a^9*b^11*c^14*d^4 - 72960*a^10*b^10*c^13*d^5 + 138240*a^11*b^9*c^12*d^6 - 182784*a^12*b^8*c^11*d^7 + 172032*a^13*b^7*c^10*d^8 - 115200*a^14*b^6*c^9*d^9 + 53760*a^15*b^5*c^8*d^10 - 16640*a^16*b^4*c^7*d^11 + 3072*a^17*b^3*c^6*d^12 - 256*a^18*b^2*c^5*d^13))/(4*(a^7*d^5 - a^2*b^5*c^5 + 5*a^3*b^4*c^4*d - 10*a^4*b^3*c^3*d^2 + 10*a^5*b^2*c^2*d^3 - 5*a^6*b*c*d^4))))/(4*(a^7*d^5 - a^2*b^5*c^5 + 5*a^3*b^4*c^4*d - 10*a^4*b^3*c^3*d^2 + 10*a^5*b^2*c^2*d^3 - 5*a^6*b*c*d^4))))/(4*(a^7*d^5 - a^2*b^5*c^5 + 5*a^3*b^4*c^4*d - 10*a^4*b^3*c^3*d^2 + 10*a^5*b^2*c^2*d^3 - 5*a^6*b*c*d^4)) - ((-b^3*(a*d - b*c)^5)^(1/2)*(5*a*d - 2*b*c)*((c + d*x^2)^(1/2)*(128*a^3*b^13*c^13*d^2 - 1344*a^4*b^12*c^12*d^3 + 6160*a^5*b^11*c^11*d^4 - 16160*a^6*b^10*c^10*d^5 + 26800*a^7*b^9*c^9*d^6 - 29312*a^8*b^8*c^8*d^7 + 21424*a^9*b^7*c^7*d^8 - 10400*a^10*b^6*c^6*d^9 + 3280*a^11*b^5*c^5*d^10 - 640*a^12*b^4*c^4*d^11 + 64*a^13*b^3*c^3*d^12) + ((-b^3*(a*d - b*c)^5)^(1/2)*(5*a*d - 2*b*c)*(64*a^6*b^12*c^14*d^3 - 896*a^7*b^11*c^13*d^4 + 4992*a^8*b^10*c^12*d^5 - 15360*a^9*b^9*c^11*d^6 + 29568*a^10*b^8*c^10*d^7 - 37632*a^11*b^7*c^9*d^8 + 32256*a^12*b^6*c^8*d^9 - 18432*a^13*b^5*c^7*d^10 + 6720*a^14*b^4*c^6*d^11 - 1408*a^15*b^3*c^5*d^12 + 128*a^16*b^2*c^4*d^13 - ((-b^3*(a*d - b*c)^5)^(1/2)*(c + d*x^2)^(1/2)*(5*a*d - 2*b*c)*(512*a^7*b^13*c^16*d^2 - 5376*a^8*b^12*c^15*d^3 + 25600*a^9*b^11*c^14*d^4 - 72960*a^10*b^10*c^13*d^5 + 138240*a^11*b^9*c^12*d^6 - 182784*a^12*b^8*c^11*d^7 + 172032*a^13*b^7*c^10*d^8 - 115200*a^14*b^6*c^9*d^9 + 53760*a^15*b^5*c^8*d^10 - 16640*a^16*b^4*c^7*d^11 + 3072*a^17*b^3*c^6*d^12 - 256*a^18*b^2*c^5*d^13))/(4*(a^7*d^5 - a^2*b^5*c^5 + 5*a^3*b^4*c^4*d - 10*a^4*b^3*c^3*d^2 + 10*a^5*b^2*c^2*d^3 - 5*a^6*b*c*d^4))))/(4*(a^7*d^5 - a^2*b^5*c^5 + 5*a^3*b^4*c^4*d - 10*a^4*b^3*c^3*d^2 + 10*a^5*b^2*c^2*d^3 - 5*a^6*b*c*d^4))))/(4*(a^7*d^5 - a^2*b^5*c^5 + 5*a^3*b^4*c^4*d - 10*a^4*b^3*c^3*d^2 + 10*a^5*b^2*c^2*d^3 - 5*a^6*b*c*d^4)) + 32*a^2*b^12*c^11*d^3 - 208*a^3*b^11*c^10*d^4 + 416*a^4*b^10*c^9*d^5 + 80*a^5*b^9*c^8*d^6 - 1600*a^6*b^8*c^7*d^7 + 2768*a^7*b^7*c^6*d^8 - 2272*a^8*b^6*c^5*d^9 + 944*a^9*b^5*c^4*d^10 - 160*a^10*b^4*c^3*d^11))*(-b^3*(a*d - b*c)^5)^(1/2)*(5*a*d - 2*b*c)*1i)/(2*(a^7*d^5 - a^2*b^5*c^5 + 5*a^3*b^4*c^4*d - 10*a^4*b^3*c^3*d^2 + 10*a^5*b^2*c^2*d^3 - 5*a^6*b*c*d^4))","B"
773,0,-1,205,0.000000,"\text{Not used}","int(1/(x^2*(a + b*x^2)^2*(c + d*x^2)^(3/2)),x)","\int \frac{1}{x^2\,{\left(b\,x^2+a\right)}^2\,{\left(d\,x^2+c\right)}^{3/2}} \,d x","Not used",1,"int(1/(x^2*(a + b*x^2)^2*(c + d*x^2)^(3/2)), x)","F"
774,1,4286,241,4.901023,"\text{Not used}","int(1/(x^3*(a + b*x^2)^2*(c + d*x^2)^(3/2)),x)","-\frac{\frac{d^3}{b\,c^2-a\,c\,d}+\frac{d\,{\left(d\,x^2+c\right)}^2\,\left(3\,a^2\,b\,d^2-2\,a\,b^2\,c\,d+2\,b^3\,c^2\right)}{2\,a^2\,{\left(b\,c^2-a\,c\,d\right)}^2}+\frac{d\,\left(d\,x^2+c\right)\,\left(a\,d-2\,b\,c\right)\,\left(3\,a^2\,d^2-a\,b\,c\,d+b^2\,c^2\right)}{2\,a^2\,{\left(b\,c^2-a\,c\,d\right)}^2}}{b\,{\left(d\,x^2+c\right)}^{5/2}+\sqrt{d\,x^2+c}\,\left(b\,c^2-a\,c\,d\right)+{\left(d\,x^2+c\right)}^{3/2}\,\left(a\,d-2\,b\,c\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^5}\,\left(7\,a\,d-4\,b\,c\right)\,\left(\sqrt{d\,x^2+c}\,\left(144\,a^{18}\,b^3\,c^6\,d^{14}-1056\,a^{17}\,b^4\,c^7\,d^{13}+2896\,a^{16}\,b^5\,c^8\,d^{12}-2560\,a^{15}\,b^6\,c^9\,d^{11}-3536\,a^{14}\,b^7\,c^{10}\,d^{10}+8032\,a^{13}\,b^8\,c^{11}\,d^9+4624\,a^{12}\,b^9\,c^{12}\,d^8-31808\,a^{11}\,b^{10}\,c^{13}\,d^7+47680\,a^{10}\,b^{11}\,c^{14}\,d^6-38144\,a^9\,b^{12}\,c^{15}\,d^5+17824\,a^8\,b^{13}\,c^{16}\,d^4-4608\,a^7\,b^{14}\,c^{17}\,d^3+512\,a^6\,b^{15}\,c^{18}\,d^2\right)+\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^5}\,\left(7\,a\,d-4\,b\,c\right)\,\left(128\,a^{10}\,b^{13}\,c^{19}\,d^3-1216\,a^{11}\,b^{12}\,c^{18}\,d^4+4800\,a^{12}\,b^{11}\,c^{17}\,d^5-9792\,a^{13}\,b^{10}\,c^{16}\,d^6+9216\,a^{14}\,b^9\,c^{15}\,d^7+2688\,a^{15}\,b^8\,c^{14}\,d^8-18816\,a^{16}\,b^7\,c^{13}\,d^9+24960\,a^{17}\,b^6\,c^{12}\,d^{10}-18048\,a^{18}\,b^5\,c^{11}\,d^{11}+7744\,a^{19}\,b^4\,c^{10}\,d^{12}-1856\,a^{20}\,b^3\,c^9\,d^{13}+192\,a^{21}\,b^2\,c^8\,d^{14}-\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^5}\,\sqrt{d\,x^2+c}\,\left(7\,a\,d-4\,b\,c\right)\,\left(-256\,a^{23}\,b^2\,c^{10}\,d^{13}+3072\,a^{22}\,b^3\,c^{11}\,d^{12}-16640\,a^{21}\,b^4\,c^{12}\,d^{11}+53760\,a^{20}\,b^5\,c^{13}\,d^{10}-115200\,a^{19}\,b^6\,c^{14}\,d^9+172032\,a^{18}\,b^7\,c^{15}\,d^8-182784\,a^{17}\,b^8\,c^{16}\,d^7+138240\,a^{16}\,b^9\,c^{17}\,d^6-72960\,a^{15}\,b^{10}\,c^{18}\,d^5+25600\,a^{14}\,b^{11}\,c^{19}\,d^4-5376\,a^{13}\,b^{12}\,c^{20}\,d^3+512\,a^{12}\,b^{13}\,c^{21}\,d^2\right)}{4\,\left(a^8\,d^5-5\,a^7\,b\,c\,d^4+10\,a^6\,b^2\,c^2\,d^3-10\,a^5\,b^3\,c^3\,d^2+5\,a^4\,b^4\,c^4\,d-a^3\,b^5\,c^5\right)}\right)}{4\,\left(a^8\,d^5-5\,a^7\,b\,c\,d^4+10\,a^6\,b^2\,c^2\,d^3-10\,a^5\,b^3\,c^3\,d^2+5\,a^4\,b^4\,c^4\,d-a^3\,b^5\,c^5\right)}\right)\,1{}\mathrm{i}}{4\,\left(a^8\,d^5-5\,a^7\,b\,c\,d^4+10\,a^6\,b^2\,c^2\,d^3-10\,a^5\,b^3\,c^3\,d^2+5\,a^4\,b^4\,c^4\,d-a^3\,b^5\,c^5\right)}+\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^5}\,\left(7\,a\,d-4\,b\,c\right)\,\left(\sqrt{d\,x^2+c}\,\left(144\,a^{18}\,b^3\,c^6\,d^{14}-1056\,a^{17}\,b^4\,c^7\,d^{13}+2896\,a^{16}\,b^5\,c^8\,d^{12}-2560\,a^{15}\,b^6\,c^9\,d^{11}-3536\,a^{14}\,b^7\,c^{10}\,d^{10}+8032\,a^{13}\,b^8\,c^{11}\,d^9+4624\,a^{12}\,b^9\,c^{12}\,d^8-31808\,a^{11}\,b^{10}\,c^{13}\,d^7+47680\,a^{10}\,b^{11}\,c^{14}\,d^6-38144\,a^9\,b^{12}\,c^{15}\,d^5+17824\,a^8\,b^{13}\,c^{16}\,d^4-4608\,a^7\,b^{14}\,c^{17}\,d^3+512\,a^6\,b^{15}\,c^{18}\,d^2\right)-\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^5}\,\left(7\,a\,d-4\,b\,c\right)\,\left(128\,a^{10}\,b^{13}\,c^{19}\,d^3-1216\,a^{11}\,b^{12}\,c^{18}\,d^4+4800\,a^{12}\,b^{11}\,c^{17}\,d^5-9792\,a^{13}\,b^{10}\,c^{16}\,d^6+9216\,a^{14}\,b^9\,c^{15}\,d^7+2688\,a^{15}\,b^8\,c^{14}\,d^8-18816\,a^{16}\,b^7\,c^{13}\,d^9+24960\,a^{17}\,b^6\,c^{12}\,d^{10}-18048\,a^{18}\,b^5\,c^{11}\,d^{11}+7744\,a^{19}\,b^4\,c^{10}\,d^{12}-1856\,a^{20}\,b^3\,c^9\,d^{13}+192\,a^{21}\,b^2\,c^8\,d^{14}+\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^5}\,\sqrt{d\,x^2+c}\,\left(7\,a\,d-4\,b\,c\right)\,\left(-256\,a^{23}\,b^2\,c^{10}\,d^{13}+3072\,a^{22}\,b^3\,c^{11}\,d^{12}-16640\,a^{21}\,b^4\,c^{12}\,d^{11}+53760\,a^{20}\,b^5\,c^{13}\,d^{10}-115200\,a^{19}\,b^6\,c^{14}\,d^9+172032\,a^{18}\,b^7\,c^{15}\,d^8-182784\,a^{17}\,b^8\,c^{16}\,d^7+138240\,a^{16}\,b^9\,c^{17}\,d^6-72960\,a^{15}\,b^{10}\,c^{18}\,d^5+25600\,a^{14}\,b^{11}\,c^{19}\,d^4-5376\,a^{13}\,b^{12}\,c^{20}\,d^3+512\,a^{12}\,b^{13}\,c^{21}\,d^2\right)}{4\,\left(a^8\,d^5-5\,a^7\,b\,c\,d^4+10\,a^6\,b^2\,c^2\,d^3-10\,a^5\,b^3\,c^3\,d^2+5\,a^4\,b^4\,c^4\,d-a^3\,b^5\,c^5\right)}\right)}{4\,\left(a^8\,d^5-5\,a^7\,b\,c\,d^4+10\,a^6\,b^2\,c^2\,d^3-10\,a^5\,b^3\,c^3\,d^2+5\,a^4\,b^4\,c^4\,d-a^3\,b^5\,c^5\right)}\right)\,1{}\mathrm{i}}{4\,\left(a^8\,d^5-5\,a^7\,b\,c\,d^4+10\,a^6\,b^2\,c^2\,d^3-10\,a^5\,b^3\,c^3\,d^2+5\,a^4\,b^4\,c^4\,d-a^3\,b^5\,c^5\right)}}{\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^5}\,\left(7\,a\,d-4\,b\,c\right)\,\left(\sqrt{d\,x^2+c}\,\left(144\,a^{18}\,b^3\,c^6\,d^{14}-1056\,a^{17}\,b^4\,c^7\,d^{13}+2896\,a^{16}\,b^5\,c^8\,d^{12}-2560\,a^{15}\,b^6\,c^9\,d^{11}-3536\,a^{14}\,b^7\,c^{10}\,d^{10}+8032\,a^{13}\,b^8\,c^{11}\,d^9+4624\,a^{12}\,b^9\,c^{12}\,d^8-31808\,a^{11}\,b^{10}\,c^{13}\,d^7+47680\,a^{10}\,b^{11}\,c^{14}\,d^6-38144\,a^9\,b^{12}\,c^{15}\,d^5+17824\,a^8\,b^{13}\,c^{16}\,d^4-4608\,a^7\,b^{14}\,c^{17}\,d^3+512\,a^6\,b^{15}\,c^{18}\,d^2\right)-\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^5}\,\left(7\,a\,d-4\,b\,c\right)\,\left(128\,a^{10}\,b^{13}\,c^{19}\,d^3-1216\,a^{11}\,b^{12}\,c^{18}\,d^4+4800\,a^{12}\,b^{11}\,c^{17}\,d^5-9792\,a^{13}\,b^{10}\,c^{16}\,d^6+9216\,a^{14}\,b^9\,c^{15}\,d^7+2688\,a^{15}\,b^8\,c^{14}\,d^8-18816\,a^{16}\,b^7\,c^{13}\,d^9+24960\,a^{17}\,b^6\,c^{12}\,d^{10}-18048\,a^{18}\,b^5\,c^{11}\,d^{11}+7744\,a^{19}\,b^4\,c^{10}\,d^{12}-1856\,a^{20}\,b^3\,c^9\,d^{13}+192\,a^{21}\,b^2\,c^8\,d^{14}+\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^5}\,\sqrt{d\,x^2+c}\,\left(7\,a\,d-4\,b\,c\right)\,\left(-256\,a^{23}\,b^2\,c^{10}\,d^{13}+3072\,a^{22}\,b^3\,c^{11}\,d^{12}-16640\,a^{21}\,b^4\,c^{12}\,d^{11}+53760\,a^{20}\,b^5\,c^{13}\,d^{10}-115200\,a^{19}\,b^6\,c^{14}\,d^9+172032\,a^{18}\,b^7\,c^{15}\,d^8-182784\,a^{17}\,b^8\,c^{16}\,d^7+138240\,a^{16}\,b^9\,c^{17}\,d^6-72960\,a^{15}\,b^{10}\,c^{18}\,d^5+25600\,a^{14}\,b^{11}\,c^{19}\,d^4-5376\,a^{13}\,b^{12}\,c^{20}\,d^3+512\,a^{12}\,b^{13}\,c^{21}\,d^2\right)}{4\,\left(a^8\,d^5-5\,a^7\,b\,c\,d^4+10\,a^6\,b^2\,c^2\,d^3-10\,a^5\,b^3\,c^3\,d^2+5\,a^4\,b^4\,c^4\,d-a^3\,b^5\,c^5\right)}\right)}{4\,\left(a^8\,d^5-5\,a^7\,b\,c\,d^4+10\,a^6\,b^2\,c^2\,d^3-10\,a^5\,b^3\,c^3\,d^2+5\,a^4\,b^4\,c^4\,d-a^3\,b^5\,c^5\right)}\right)}{4\,\left(a^8\,d^5-5\,a^7\,b\,c\,d^4+10\,a^6\,b^2\,c^2\,d^3-10\,a^5\,b^3\,c^3\,d^2+5\,a^4\,b^4\,c^4\,d-a^3\,b^5\,c^5\right)}-\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^5}\,\left(7\,a\,d-4\,b\,c\right)\,\left(\sqrt{d\,x^2+c}\,\left(144\,a^{18}\,b^3\,c^6\,d^{14}-1056\,a^{17}\,b^4\,c^7\,d^{13}+2896\,a^{16}\,b^5\,c^8\,d^{12}-2560\,a^{15}\,b^6\,c^9\,d^{11}-3536\,a^{14}\,b^7\,c^{10}\,d^{10}+8032\,a^{13}\,b^8\,c^{11}\,d^9+4624\,a^{12}\,b^9\,c^{12}\,d^8-31808\,a^{11}\,b^{10}\,c^{13}\,d^7+47680\,a^{10}\,b^{11}\,c^{14}\,d^6-38144\,a^9\,b^{12}\,c^{15}\,d^5+17824\,a^8\,b^{13}\,c^{16}\,d^4-4608\,a^7\,b^{14}\,c^{17}\,d^3+512\,a^6\,b^{15}\,c^{18}\,d^2\right)+\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^5}\,\left(7\,a\,d-4\,b\,c\right)\,\left(128\,a^{10}\,b^{13}\,c^{19}\,d^3-1216\,a^{11}\,b^{12}\,c^{18}\,d^4+4800\,a^{12}\,b^{11}\,c^{17}\,d^5-9792\,a^{13}\,b^{10}\,c^{16}\,d^6+9216\,a^{14}\,b^9\,c^{15}\,d^7+2688\,a^{15}\,b^8\,c^{14}\,d^8-18816\,a^{16}\,b^7\,c^{13}\,d^9+24960\,a^{17}\,b^6\,c^{12}\,d^{10}-18048\,a^{18}\,b^5\,c^{11}\,d^{11}+7744\,a^{19}\,b^4\,c^{10}\,d^{12}-1856\,a^{20}\,b^3\,c^9\,d^{13}+192\,a^{21}\,b^2\,c^8\,d^{14}-\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^5}\,\sqrt{d\,x^2+c}\,\left(7\,a\,d-4\,b\,c\right)\,\left(-256\,a^{23}\,b^2\,c^{10}\,d^{13}+3072\,a^{22}\,b^3\,c^{11}\,d^{12}-16640\,a^{21}\,b^4\,c^{12}\,d^{11}+53760\,a^{20}\,b^5\,c^{13}\,d^{10}-115200\,a^{19}\,b^6\,c^{14}\,d^9+172032\,a^{18}\,b^7\,c^{15}\,d^8-182784\,a^{17}\,b^8\,c^{16}\,d^7+138240\,a^{16}\,b^9\,c^{17}\,d^6-72960\,a^{15}\,b^{10}\,c^{18}\,d^5+25600\,a^{14}\,b^{11}\,c^{19}\,d^4-5376\,a^{13}\,b^{12}\,c^{20}\,d^3+512\,a^{12}\,b^{13}\,c^{21}\,d^2\right)}{4\,\left(a^8\,d^5-5\,a^7\,b\,c\,d^4+10\,a^6\,b^2\,c^2\,d^3-10\,a^5\,b^3\,c^3\,d^2+5\,a^4\,b^4\,c^4\,d-a^3\,b^5\,c^5\right)}\right)}{4\,\left(a^8\,d^5-5\,a^7\,b\,c\,d^4+10\,a^6\,b^2\,c^2\,d^3-10\,a^5\,b^3\,c^3\,d^2+5\,a^4\,b^4\,c^4\,d-a^3\,b^5\,c^5\right)}\right)}{4\,\left(a^8\,d^5-5\,a^7\,b\,c\,d^4+10\,a^6\,b^2\,c^2\,d^3-10\,a^5\,b^3\,c^3\,d^2+5\,a^4\,b^4\,c^4\,d-a^3\,b^5\,c^5\right)}+256\,a^4\,b^{15}\,c^{16}\,d^3-2048\,a^5\,b^{14}\,c^{15}\,d^4+7216\,a^6\,b^{13}\,c^{14}\,d^5-14672\,a^7\,b^{12}\,c^{13}\,d^6+18424\,a^8\,b^{11}\,c^{12}\,d^7-12992\,a^9\,b^{10}\,c^{11}\,d^8+1288\,a^{10}\,b^9\,c^{10}\,d^9+7024\,a^{11}\,b^8\,c^9\,d^{10}-6968\,a^{12}\,b^7\,c^8\,d^{11}+2976\,a^{13}\,b^6\,c^7\,d^{12}-504\,a^{14}\,b^5\,c^6\,d^{13}}\right)\,\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^5}\,\left(7\,a\,d-4\,b\,c\right)\,1{}\mathrm{i}}{2\,\left(a^8\,d^5-5\,a^7\,b\,c\,d^4+10\,a^6\,b^2\,c^2\,d^3-10\,a^5\,b^3\,c^3\,d^2+5\,a^4\,b^4\,c^4\,d-a^3\,b^5\,c^5\right)}-\frac{\mathrm{atan}\left(\frac{-a^{14}\,c^{10}\,d^{14}\,\sqrt{d\,x^2+c}\,27{}\mathrm{i}+a^3\,b^{11}\,c^{21}\,d^3\,\sqrt{d\,x^2+c}\,140{}\mathrm{i}-a^4\,b^{10}\,c^{20}\,d^4\,\sqrt{d\,x^2+c}\,1015{}\mathrm{i}+a^5\,b^9\,c^{19}\,d^5\,\sqrt{d\,x^2+c}\,2996{}\mathrm{i}-a^6\,b^8\,c^{18}\,d^6\,\sqrt{d\,x^2+c}\,4375{}\mathrm{i}+a^7\,b^7\,c^{17}\,d^7\,\sqrt{d\,x^2+c}\,2561{}\mathrm{i}+a^8\,b^6\,c^{16}\,d^8\,\sqrt{d\,x^2+c}\,1316{}\mathrm{i}-a^9\,b^5\,c^{15}\,d^9\,\sqrt{d\,x^2+c}\,3073{}\mathrm{i}+a^{10}\,b^4\,c^{14}\,d^{10}\,\sqrt{d\,x^2+c}\,1694{}\mathrm{i}+a^{11}\,b^3\,c^{13}\,d^{11}\,\sqrt{d\,x^2+c}\,35{}\mathrm{i}-a^{12}\,b^2\,c^{12}\,d^{12}\,\sqrt{d\,x^2+c}\,441{}\mathrm{i}+a^{13}\,b\,c^{11}\,d^{13}\,\sqrt{d\,x^2+c}\,189{}\mathrm{i}}{c^5\,\sqrt{c^5}\,\left(c^5\,\left(c^5\,\left(2561\,a^7\,b^7\,d^7-4375\,a^6\,b^8\,c\,d^6+2996\,a^5\,b^9\,c^2\,d^5-1015\,a^4\,b^{10}\,c^3\,d^4+140\,a^3\,b^{11}\,c^4\,d^3\right)-441\,a^{12}\,b^2\,d^{12}+35\,a^{11}\,b^3\,c\,d^{11}+1316\,a^8\,b^6\,c^4\,d^8-3073\,a^9\,b^5\,c^3\,d^9+1694\,a^{10}\,b^4\,c^2\,d^{10}\right)-27\,a^{14}\,c^3\,d^{14}+189\,a^{13}\,b\,c^4\,d^{13}\right)}\right)\,\left(3\,a\,d+4\,b\,c\right)\,1{}\mathrm{i}}{2\,a^3\,\sqrt{c^5}}","Not used",1,"(atan((((-b^5*(a*d - b*c)^5)^(1/2)*(7*a*d - 4*b*c)*((c + d*x^2)^(1/2)*(512*a^6*b^15*c^18*d^2 - 4608*a^7*b^14*c^17*d^3 + 17824*a^8*b^13*c^16*d^4 - 38144*a^9*b^12*c^15*d^5 + 47680*a^10*b^11*c^14*d^6 - 31808*a^11*b^10*c^13*d^7 + 4624*a^12*b^9*c^12*d^8 + 8032*a^13*b^8*c^11*d^9 - 3536*a^14*b^7*c^10*d^10 - 2560*a^15*b^6*c^9*d^11 + 2896*a^16*b^5*c^8*d^12 - 1056*a^17*b^4*c^7*d^13 + 144*a^18*b^3*c^6*d^14) + ((-b^5*(a*d - b*c)^5)^(1/2)*(7*a*d - 4*b*c)*(128*a^10*b^13*c^19*d^3 - 1216*a^11*b^12*c^18*d^4 + 4800*a^12*b^11*c^17*d^5 - 9792*a^13*b^10*c^16*d^6 + 9216*a^14*b^9*c^15*d^7 + 2688*a^15*b^8*c^14*d^8 - 18816*a^16*b^7*c^13*d^9 + 24960*a^17*b^6*c^12*d^10 - 18048*a^18*b^5*c^11*d^11 + 7744*a^19*b^4*c^10*d^12 - 1856*a^20*b^3*c^9*d^13 + 192*a^21*b^2*c^8*d^14 - ((-b^5*(a*d - b*c)^5)^(1/2)*(c + d*x^2)^(1/2)*(7*a*d - 4*b*c)*(512*a^12*b^13*c^21*d^2 - 5376*a^13*b^12*c^20*d^3 + 25600*a^14*b^11*c^19*d^4 - 72960*a^15*b^10*c^18*d^5 + 138240*a^16*b^9*c^17*d^6 - 182784*a^17*b^8*c^16*d^7 + 172032*a^18*b^7*c^15*d^8 - 115200*a^19*b^6*c^14*d^9 + 53760*a^20*b^5*c^13*d^10 - 16640*a^21*b^4*c^12*d^11 + 3072*a^22*b^3*c^11*d^12 - 256*a^23*b^2*c^10*d^13))/(4*(a^8*d^5 - a^3*b^5*c^5 + 5*a^4*b^4*c^4*d - 10*a^5*b^3*c^3*d^2 + 10*a^6*b^2*c^2*d^3 - 5*a^7*b*c*d^4))))/(4*(a^8*d^5 - a^3*b^5*c^5 + 5*a^4*b^4*c^4*d - 10*a^5*b^3*c^3*d^2 + 10*a^6*b^2*c^2*d^3 - 5*a^7*b*c*d^4)))*1i)/(4*(a^8*d^5 - a^3*b^5*c^5 + 5*a^4*b^4*c^4*d - 10*a^5*b^3*c^3*d^2 + 10*a^6*b^2*c^2*d^3 - 5*a^7*b*c*d^4)) + ((-b^5*(a*d - b*c)^5)^(1/2)*(7*a*d - 4*b*c)*((c + d*x^2)^(1/2)*(512*a^6*b^15*c^18*d^2 - 4608*a^7*b^14*c^17*d^3 + 17824*a^8*b^13*c^16*d^4 - 38144*a^9*b^12*c^15*d^5 + 47680*a^10*b^11*c^14*d^6 - 31808*a^11*b^10*c^13*d^7 + 4624*a^12*b^9*c^12*d^8 + 8032*a^13*b^8*c^11*d^9 - 3536*a^14*b^7*c^10*d^10 - 2560*a^15*b^6*c^9*d^11 + 2896*a^16*b^5*c^8*d^12 - 1056*a^17*b^4*c^7*d^13 + 144*a^18*b^3*c^6*d^14) - ((-b^5*(a*d - b*c)^5)^(1/2)*(7*a*d - 4*b*c)*(128*a^10*b^13*c^19*d^3 - 1216*a^11*b^12*c^18*d^4 + 4800*a^12*b^11*c^17*d^5 - 9792*a^13*b^10*c^16*d^6 + 9216*a^14*b^9*c^15*d^7 + 2688*a^15*b^8*c^14*d^8 - 18816*a^16*b^7*c^13*d^9 + 24960*a^17*b^6*c^12*d^10 - 18048*a^18*b^5*c^11*d^11 + 7744*a^19*b^4*c^10*d^12 - 1856*a^20*b^3*c^9*d^13 + 192*a^21*b^2*c^8*d^14 + ((-b^5*(a*d - b*c)^5)^(1/2)*(c + d*x^2)^(1/2)*(7*a*d - 4*b*c)*(512*a^12*b^13*c^21*d^2 - 5376*a^13*b^12*c^20*d^3 + 25600*a^14*b^11*c^19*d^4 - 72960*a^15*b^10*c^18*d^5 + 138240*a^16*b^9*c^17*d^6 - 182784*a^17*b^8*c^16*d^7 + 172032*a^18*b^7*c^15*d^8 - 115200*a^19*b^6*c^14*d^9 + 53760*a^20*b^5*c^13*d^10 - 16640*a^21*b^4*c^12*d^11 + 3072*a^22*b^3*c^11*d^12 - 256*a^23*b^2*c^10*d^13))/(4*(a^8*d^5 - a^3*b^5*c^5 + 5*a^4*b^4*c^4*d - 10*a^5*b^3*c^3*d^2 + 10*a^6*b^2*c^2*d^3 - 5*a^7*b*c*d^4))))/(4*(a^8*d^5 - a^3*b^5*c^5 + 5*a^4*b^4*c^4*d - 10*a^5*b^3*c^3*d^2 + 10*a^6*b^2*c^2*d^3 - 5*a^7*b*c*d^4)))*1i)/(4*(a^8*d^5 - a^3*b^5*c^5 + 5*a^4*b^4*c^4*d - 10*a^5*b^3*c^3*d^2 + 10*a^6*b^2*c^2*d^3 - 5*a^7*b*c*d^4)))/(((-b^5*(a*d - b*c)^5)^(1/2)*(7*a*d - 4*b*c)*((c + d*x^2)^(1/2)*(512*a^6*b^15*c^18*d^2 - 4608*a^7*b^14*c^17*d^3 + 17824*a^8*b^13*c^16*d^4 - 38144*a^9*b^12*c^15*d^5 + 47680*a^10*b^11*c^14*d^6 - 31808*a^11*b^10*c^13*d^7 + 4624*a^12*b^9*c^12*d^8 + 8032*a^13*b^8*c^11*d^9 - 3536*a^14*b^7*c^10*d^10 - 2560*a^15*b^6*c^9*d^11 + 2896*a^16*b^5*c^8*d^12 - 1056*a^17*b^4*c^7*d^13 + 144*a^18*b^3*c^6*d^14) - ((-b^5*(a*d - b*c)^5)^(1/2)*(7*a*d - 4*b*c)*(128*a^10*b^13*c^19*d^3 - 1216*a^11*b^12*c^18*d^4 + 4800*a^12*b^11*c^17*d^5 - 9792*a^13*b^10*c^16*d^6 + 9216*a^14*b^9*c^15*d^7 + 2688*a^15*b^8*c^14*d^8 - 18816*a^16*b^7*c^13*d^9 + 24960*a^17*b^6*c^12*d^10 - 18048*a^18*b^5*c^11*d^11 + 7744*a^19*b^4*c^10*d^12 - 1856*a^20*b^3*c^9*d^13 + 192*a^21*b^2*c^8*d^14 + ((-b^5*(a*d - b*c)^5)^(1/2)*(c + d*x^2)^(1/2)*(7*a*d - 4*b*c)*(512*a^12*b^13*c^21*d^2 - 5376*a^13*b^12*c^20*d^3 + 25600*a^14*b^11*c^19*d^4 - 72960*a^15*b^10*c^18*d^5 + 138240*a^16*b^9*c^17*d^6 - 182784*a^17*b^8*c^16*d^7 + 172032*a^18*b^7*c^15*d^8 - 115200*a^19*b^6*c^14*d^9 + 53760*a^20*b^5*c^13*d^10 - 16640*a^21*b^4*c^12*d^11 + 3072*a^22*b^3*c^11*d^12 - 256*a^23*b^2*c^10*d^13))/(4*(a^8*d^5 - a^3*b^5*c^5 + 5*a^4*b^4*c^4*d - 10*a^5*b^3*c^3*d^2 + 10*a^6*b^2*c^2*d^3 - 5*a^7*b*c*d^4))))/(4*(a^8*d^5 - a^3*b^5*c^5 + 5*a^4*b^4*c^4*d - 10*a^5*b^3*c^3*d^2 + 10*a^6*b^2*c^2*d^3 - 5*a^7*b*c*d^4))))/(4*(a^8*d^5 - a^3*b^5*c^5 + 5*a^4*b^4*c^4*d - 10*a^5*b^3*c^3*d^2 + 10*a^6*b^2*c^2*d^3 - 5*a^7*b*c*d^4)) - ((-b^5*(a*d - b*c)^5)^(1/2)*(7*a*d - 4*b*c)*((c + d*x^2)^(1/2)*(512*a^6*b^15*c^18*d^2 - 4608*a^7*b^14*c^17*d^3 + 17824*a^8*b^13*c^16*d^4 - 38144*a^9*b^12*c^15*d^5 + 47680*a^10*b^11*c^14*d^6 - 31808*a^11*b^10*c^13*d^7 + 4624*a^12*b^9*c^12*d^8 + 8032*a^13*b^8*c^11*d^9 - 3536*a^14*b^7*c^10*d^10 - 2560*a^15*b^6*c^9*d^11 + 2896*a^16*b^5*c^8*d^12 - 1056*a^17*b^4*c^7*d^13 + 144*a^18*b^3*c^6*d^14) + ((-b^5*(a*d - b*c)^5)^(1/2)*(7*a*d - 4*b*c)*(128*a^10*b^13*c^19*d^3 - 1216*a^11*b^12*c^18*d^4 + 4800*a^12*b^11*c^17*d^5 - 9792*a^13*b^10*c^16*d^6 + 9216*a^14*b^9*c^15*d^7 + 2688*a^15*b^8*c^14*d^8 - 18816*a^16*b^7*c^13*d^9 + 24960*a^17*b^6*c^12*d^10 - 18048*a^18*b^5*c^11*d^11 + 7744*a^19*b^4*c^10*d^12 - 1856*a^20*b^3*c^9*d^13 + 192*a^21*b^2*c^8*d^14 - ((-b^5*(a*d - b*c)^5)^(1/2)*(c + d*x^2)^(1/2)*(7*a*d - 4*b*c)*(512*a^12*b^13*c^21*d^2 - 5376*a^13*b^12*c^20*d^3 + 25600*a^14*b^11*c^19*d^4 - 72960*a^15*b^10*c^18*d^5 + 138240*a^16*b^9*c^17*d^6 - 182784*a^17*b^8*c^16*d^7 + 172032*a^18*b^7*c^15*d^8 - 115200*a^19*b^6*c^14*d^9 + 53760*a^20*b^5*c^13*d^10 - 16640*a^21*b^4*c^12*d^11 + 3072*a^22*b^3*c^11*d^12 - 256*a^23*b^2*c^10*d^13))/(4*(a^8*d^5 - a^3*b^5*c^5 + 5*a^4*b^4*c^4*d - 10*a^5*b^3*c^3*d^2 + 10*a^6*b^2*c^2*d^3 - 5*a^7*b*c*d^4))))/(4*(a^8*d^5 - a^3*b^5*c^5 + 5*a^4*b^4*c^4*d - 10*a^5*b^3*c^3*d^2 + 10*a^6*b^2*c^2*d^3 - 5*a^7*b*c*d^4))))/(4*(a^8*d^5 - a^3*b^5*c^5 + 5*a^4*b^4*c^4*d - 10*a^5*b^3*c^3*d^2 + 10*a^6*b^2*c^2*d^3 - 5*a^7*b*c*d^4)) + 256*a^4*b^15*c^16*d^3 - 2048*a^5*b^14*c^15*d^4 + 7216*a^6*b^13*c^14*d^5 - 14672*a^7*b^12*c^13*d^6 + 18424*a^8*b^11*c^12*d^7 - 12992*a^9*b^10*c^11*d^8 + 1288*a^10*b^9*c^10*d^9 + 7024*a^11*b^8*c^9*d^10 - 6968*a^12*b^7*c^8*d^11 + 2976*a^13*b^6*c^7*d^12 - 504*a^14*b^5*c^6*d^13))*(-b^5*(a*d - b*c)^5)^(1/2)*(7*a*d - 4*b*c)*1i)/(2*(a^8*d^5 - a^3*b^5*c^5 + 5*a^4*b^4*c^4*d - 10*a^5*b^3*c^3*d^2 + 10*a^6*b^2*c^2*d^3 - 5*a^7*b*c*d^4)) - (d^3/(b*c^2 - a*c*d) + (d*(c + d*x^2)^2*(2*b^3*c^2 + 3*a^2*b*d^2 - 2*a*b^2*c*d))/(2*a^2*(b*c^2 - a*c*d)^2) + (d*(c + d*x^2)*(a*d - 2*b*c)*(3*a^2*d^2 + b^2*c^2 - a*b*c*d))/(2*a^2*(b*c^2 - a*c*d)^2))/(b*(c + d*x^2)^(5/2) + (c + d*x^2)^(1/2)*(b*c^2 - a*c*d) + (c + d*x^2)^(3/2)*(a*d - 2*b*c)) - (atan((a^3*b^11*c^21*d^3*(c + d*x^2)^(1/2)*140i - a^14*c^10*d^14*(c + d*x^2)^(1/2)*27i - a^4*b^10*c^20*d^4*(c + d*x^2)^(1/2)*1015i + a^5*b^9*c^19*d^5*(c + d*x^2)^(1/2)*2996i - a^6*b^8*c^18*d^6*(c + d*x^2)^(1/2)*4375i + a^7*b^7*c^17*d^7*(c + d*x^2)^(1/2)*2561i + a^8*b^6*c^16*d^8*(c + d*x^2)^(1/2)*1316i - a^9*b^5*c^15*d^9*(c + d*x^2)^(1/2)*3073i + a^10*b^4*c^14*d^10*(c + d*x^2)^(1/2)*1694i + a^11*b^3*c^13*d^11*(c + d*x^2)^(1/2)*35i - a^12*b^2*c^12*d^12*(c + d*x^2)^(1/2)*441i + a^13*b*c^11*d^13*(c + d*x^2)^(1/2)*189i)/(c^5*(c^5)^(1/2)*(c^5*(c^5*(2561*a^7*b^7*d^7 - 4375*a^6*b^8*c*d^6 + 140*a^3*b^11*c^4*d^3 - 1015*a^4*b^10*c^3*d^4 + 2996*a^5*b^9*c^2*d^5) - 441*a^12*b^2*d^12 + 35*a^11*b^3*c*d^11 + 1316*a^8*b^6*c^4*d^8 - 3073*a^9*b^5*c^3*d^9 + 1694*a^10*b^4*c^2*d^10) - 27*a^14*c^3*d^14 + 189*a^13*b*c^4*d^13)))*(3*a*d + 4*b*c)*1i)/(2*a^3*(c^5)^(1/2))","B"
775,0,-1,277,0.000000,"\text{Not used}","int(1/(x^4*(a + b*x^2)^2*(c + d*x^2)^(3/2)),x)","\int \frac{1}{x^4\,{\left(b\,x^2+a\right)}^2\,{\left(d\,x^2+c\right)}^{3/2}} \,d x","Not used",1,"int(1/(x^4*(a + b*x^2)^2*(c + d*x^2)^(3/2)), x)","F"
776,0,-1,174,0.000000,"\text{Not used}","int(x^4/((a + b*x^2)^2*(c + d*x^2)^(5/2)),x)","\int \frac{x^4}{{\left(b\,x^2+a\right)}^2\,{\left(d\,x^2+c\right)}^{5/2}} \,d x","Not used",1,"int(x^4/((a + b*x^2)^2*(c + d*x^2)^(5/2)), x)","F"
777,1,193,170,1.430713,"\text{Not used}","int(x^3/((a + b*x^2)^2*(c + d*x^2)^(5/2)),x)","-\frac{\frac{\left(d\,x^2+c\right)\,\left(3\,a\,d+2\,b\,c\right)}{3\,{\left(a\,d-b\,c\right)}^2}-\frac{c}{3\,\left(a\,d-b\,c\right)}+\frac{b\,{\left(d\,x^2+c\right)}^2\,\left(3\,a\,d+2\,b\,c\right)}{2\,{\left(a\,d-b\,c\right)}^3}}{b\,{\left(d\,x^2+c\right)}^{5/2}+{\left(d\,x^2+c\right)}^{3/2}\,\left(a\,d-b\,c\right)}-\frac{\sqrt{b}\,\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d\,x^2+c}\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)}{{\left(a\,d-b\,c\right)}^{7/2}}\right)\,\left(3\,a\,d+2\,b\,c\right)}{2\,{\left(a\,d-b\,c\right)}^{7/2}}","Not used",1,"- (((c + d*x^2)*(3*a*d + 2*b*c))/(3*(a*d - b*c)^2) - c/(3*(a*d - b*c)) + (b*(c + d*x^2)^2*(3*a*d + 2*b*c))/(2*(a*d - b*c)^3))/(b*(c + d*x^2)^(5/2) + (c + d*x^2)^(3/2)*(a*d - b*c)) - (b^(1/2)*atan((b^(1/2)*(c + d*x^2)^(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*d - b*c)^(7/2))*(3*a*d + 2*b*c))/(2*(a*d - b*c)^(7/2))","B"
778,0,-1,163,0.000000,"\text{Not used}","int(x^2/((a + b*x^2)^2*(c + d*x^2)^(5/2)),x)","\int \frac{x^2}{{\left(b\,x^2+a\right)}^2\,{\left(d\,x^2+c\right)}^{5/2}} \,d x","Not used",1,"int(x^2/((a + b*x^2)^2*(c + d*x^2)^(5/2)), x)","F"
779,1,171,140,1.243110,"\text{Not used}","int(x/((a + b*x^2)^2*(c + d*x^2)^(5/2)),x)","\frac{\frac{5\,b^2\,d\,{\left(d\,x^2+c\right)}^2}{2\,{\left(a\,d-b\,c\right)}^3}-\frac{d}{3\,\left(a\,d-b\,c\right)}+\frac{5\,b\,d\,\left(d\,x^2+c\right)}{3\,{\left(a\,d-b\,c\right)}^2}}{b\,{\left(d\,x^2+c\right)}^{5/2}+{\left(d\,x^2+c\right)}^{3/2}\,\left(a\,d-b\,c\right)}+\frac{5\,b^{3/2}\,d\,\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d\,x^2+c}\,\left(a^3\,d^3-3\,a^2\,b\,c\,d^2+3\,a\,b^2\,c^2\,d-b^3\,c^3\right)}{{\left(a\,d-b\,c\right)}^{7/2}}\right)}{2\,{\left(a\,d-b\,c\right)}^{7/2}}","Not used",1,"((5*b^2*d*(c + d*x^2)^2)/(2*(a*d - b*c)^3) - d/(3*(a*d - b*c)) + (5*b*d*(c + d*x^2))/(3*(a*d - b*c)^2))/(b*(c + d*x^2)^(5/2) + (c + d*x^2)^(3/2)*(a*d - b*c)) + (5*b^(3/2)*d*atan((b^(1/2)*(c + d*x^2)^(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*d - b*c)^(7/2)))/(2*(a*d - b*c)^(7/2))","B"
780,0,-1,201,0.000000,"\text{Not used}","int(1/((a + b*x^2)^2*(c + d*x^2)^(5/2)),x)","\int \frac{1}{{\left(b\,x^2+a\right)}^2\,{\left(d\,x^2+c\right)}^{5/2}} \,d x","Not used",1,"int(1/((a + b*x^2)^2*(c + d*x^2)^(5/2)), x)","F"
781,1,8467,225,5.137471,"\text{Not used}","int(1/(x*(a + b*x^2)^2*(c + d*x^2)^(5/2)),x)","\frac{\frac{d^2\,\left(d\,x^2+c\right)\,\left(3\,a\,d-8\,b\,c\right)}{3\,{\left(b\,c^2-a\,c\,d\right)}^2}-\frac{d^2}{3\,\left(b\,c^2-a\,c\,d\right)}+\frac{d\,{\left(d\,x^2+c\right)}^2\,\left(-2\,a^2\,b\,d^2+6\,a\,b^2\,c\,d+b^3\,c^2\right)}{2\,a\,c\,\left(b\,c^2-a\,c\,d\right)\,{\left(a\,d-b\,c\right)}^2}}{b\,{\left(d\,x^2+c\right)}^{5/2}+{\left(d\,x^2+c\right)}^{3/2}\,\left(a\,d-b\,c\right)}-\frac{\mathrm{atanh}\left(\frac{560\,a^3\,b^{16}\,c^{19}\,d^4\,\sqrt{d\,x^2+c}}{\sqrt{c^5}\,\left(64\,a^{17}\,b^2\,c^3\,d^{18}-1024\,a^{16}\,b^3\,c^4\,d^{17}+7680\,a^{15}\,b^4\,c^5\,d^{16}-35840\,a^{14}\,b^5\,c^6\,d^{15}+116480\,a^{13}\,b^6\,c^7\,d^{14}-278768\,a^{12}\,b^7\,c^8\,d^{13}+505008\,a^{11}\,b^8\,c^9\,d^{12}-699840\,a^{10}\,b^9\,c^{10}\,d^{11}+741120\,a^9\,b^{10}\,c^{11}\,d^{10}-593440\,a^8\,b^{11}\,c^{12}\,d^9+351904\,a^7\,b^{12}\,c^{13}\,d^8-149184\,a^6\,b^{13}\,c^{14}\,d^7+42560\,a^5\,b^{14}\,c^{15}\,d^6-7280\,a^4\,b^{15}\,c^{16}\,d^5+560\,a^3\,b^{16}\,c^{17}\,d^4\right)}-\frac{7280\,a^4\,b^{15}\,c^{18}\,d^5\,\sqrt{d\,x^2+c}}{\sqrt{c^5}\,\left(64\,a^{17}\,b^2\,c^3\,d^{18}-1024\,a^{16}\,b^3\,c^4\,d^{17}+7680\,a^{15}\,b^4\,c^5\,d^{16}-35840\,a^{14}\,b^5\,c^6\,d^{15}+116480\,a^{13}\,b^6\,c^7\,d^{14}-278768\,a^{12}\,b^7\,c^8\,d^{13}+505008\,a^{11}\,b^8\,c^9\,d^{12}-699840\,a^{10}\,b^9\,c^{10}\,d^{11}+741120\,a^9\,b^{10}\,c^{11}\,d^{10}-593440\,a^8\,b^{11}\,c^{12}\,d^9+351904\,a^7\,b^{12}\,c^{13}\,d^8-149184\,a^6\,b^{13}\,c^{14}\,d^7+42560\,a^5\,b^{14}\,c^{15}\,d^6-7280\,a^4\,b^{15}\,c^{16}\,d^5+560\,a^3\,b^{16}\,c^{17}\,d^4\right)}+\frac{42560\,a^5\,b^{14}\,c^{17}\,d^6\,\sqrt{d\,x^2+c}}{\sqrt{c^5}\,\left(64\,a^{17}\,b^2\,c^3\,d^{18}-1024\,a^{16}\,b^3\,c^4\,d^{17}+7680\,a^{15}\,b^4\,c^5\,d^{16}-35840\,a^{14}\,b^5\,c^6\,d^{15}+116480\,a^{13}\,b^6\,c^7\,d^{14}-278768\,a^{12}\,b^7\,c^8\,d^{13}+505008\,a^{11}\,b^8\,c^9\,d^{12}-699840\,a^{10}\,b^9\,c^{10}\,d^{11}+741120\,a^9\,b^{10}\,c^{11}\,d^{10}-593440\,a^8\,b^{11}\,c^{12}\,d^9+351904\,a^7\,b^{12}\,c^{13}\,d^8-149184\,a^6\,b^{13}\,c^{14}\,d^7+42560\,a^5\,b^{14}\,c^{15}\,d^6-7280\,a^4\,b^{15}\,c^{16}\,d^5+560\,a^3\,b^{16}\,c^{17}\,d^4\right)}-\frac{149184\,a^6\,b^{13}\,c^{16}\,d^7\,\sqrt{d\,x^2+c}}{\sqrt{c^5}\,\left(64\,a^{17}\,b^2\,c^3\,d^{18}-1024\,a^{16}\,b^3\,c^4\,d^{17}+7680\,a^{15}\,b^4\,c^5\,d^{16}-35840\,a^{14}\,b^5\,c^6\,d^{15}+116480\,a^{13}\,b^6\,c^7\,d^{14}-278768\,a^{12}\,b^7\,c^8\,d^{13}+505008\,a^{11}\,b^8\,c^9\,d^{12}-699840\,a^{10}\,b^9\,c^{10}\,d^{11}+741120\,a^9\,b^{10}\,c^{11}\,d^{10}-593440\,a^8\,b^{11}\,c^{12}\,d^9+351904\,a^7\,b^{12}\,c^{13}\,d^8-149184\,a^6\,b^{13}\,c^{14}\,d^7+42560\,a^5\,b^{14}\,c^{15}\,d^6-7280\,a^4\,b^{15}\,c^{16}\,d^5+560\,a^3\,b^{16}\,c^{17}\,d^4\right)}+\frac{351904\,a^7\,b^{12}\,c^{15}\,d^8\,\sqrt{d\,x^2+c}}{\sqrt{c^5}\,\left(64\,a^{17}\,b^2\,c^3\,d^{18}-1024\,a^{16}\,b^3\,c^4\,d^{17}+7680\,a^{15}\,b^4\,c^5\,d^{16}-35840\,a^{14}\,b^5\,c^6\,d^{15}+116480\,a^{13}\,b^6\,c^7\,d^{14}-278768\,a^{12}\,b^7\,c^8\,d^{13}+505008\,a^{11}\,b^8\,c^9\,d^{12}-699840\,a^{10}\,b^9\,c^{10}\,d^{11}+741120\,a^9\,b^{10}\,c^{11}\,d^{10}-593440\,a^8\,b^{11}\,c^{12}\,d^9+351904\,a^7\,b^{12}\,c^{13}\,d^8-149184\,a^6\,b^{13}\,c^{14}\,d^7+42560\,a^5\,b^{14}\,c^{15}\,d^6-7280\,a^4\,b^{15}\,c^{16}\,d^5+560\,a^3\,b^{16}\,c^{17}\,d^4\right)}-\frac{593440\,a^8\,b^{11}\,c^{14}\,d^9\,\sqrt{d\,x^2+c}}{\sqrt{c^5}\,\left(64\,a^{17}\,b^2\,c^3\,d^{18}-1024\,a^{16}\,b^3\,c^4\,d^{17}+7680\,a^{15}\,b^4\,c^5\,d^{16}-35840\,a^{14}\,b^5\,c^6\,d^{15}+116480\,a^{13}\,b^6\,c^7\,d^{14}-278768\,a^{12}\,b^7\,c^8\,d^{13}+505008\,a^{11}\,b^8\,c^9\,d^{12}-699840\,a^{10}\,b^9\,c^{10}\,d^{11}+741120\,a^9\,b^{10}\,c^{11}\,d^{10}-593440\,a^8\,b^{11}\,c^{12}\,d^9+351904\,a^7\,b^{12}\,c^{13}\,d^8-149184\,a^6\,b^{13}\,c^{14}\,d^7+42560\,a^5\,b^{14}\,c^{15}\,d^6-7280\,a^4\,b^{15}\,c^{16}\,d^5+560\,a^3\,b^{16}\,c^{17}\,d^4\right)}+\frac{741120\,a^9\,b^{10}\,c^{13}\,d^{10}\,\sqrt{d\,x^2+c}}{\sqrt{c^5}\,\left(64\,a^{17}\,b^2\,c^3\,d^{18}-1024\,a^{16}\,b^3\,c^4\,d^{17}+7680\,a^{15}\,b^4\,c^5\,d^{16}-35840\,a^{14}\,b^5\,c^6\,d^{15}+116480\,a^{13}\,b^6\,c^7\,d^{14}-278768\,a^{12}\,b^7\,c^8\,d^{13}+505008\,a^{11}\,b^8\,c^9\,d^{12}-699840\,a^{10}\,b^9\,c^{10}\,d^{11}+741120\,a^9\,b^{10}\,c^{11}\,d^{10}-593440\,a^8\,b^{11}\,c^{12}\,d^9+351904\,a^7\,b^{12}\,c^{13}\,d^8-149184\,a^6\,b^{13}\,c^{14}\,d^7+42560\,a^5\,b^{14}\,c^{15}\,d^6-7280\,a^4\,b^{15}\,c^{16}\,d^5+560\,a^3\,b^{16}\,c^{17}\,d^4\right)}-\frac{699840\,a^{10}\,b^9\,c^{12}\,d^{11}\,\sqrt{d\,x^2+c}}{\sqrt{c^5}\,\left(64\,a^{17}\,b^2\,c^3\,d^{18}-1024\,a^{16}\,b^3\,c^4\,d^{17}+7680\,a^{15}\,b^4\,c^5\,d^{16}-35840\,a^{14}\,b^5\,c^6\,d^{15}+116480\,a^{13}\,b^6\,c^7\,d^{14}-278768\,a^{12}\,b^7\,c^8\,d^{13}+505008\,a^{11}\,b^8\,c^9\,d^{12}-699840\,a^{10}\,b^9\,c^{10}\,d^{11}+741120\,a^9\,b^{10}\,c^{11}\,d^{10}-593440\,a^8\,b^{11}\,c^{12}\,d^9+351904\,a^7\,b^{12}\,c^{13}\,d^8-149184\,a^6\,b^{13}\,c^{14}\,d^7+42560\,a^5\,b^{14}\,c^{15}\,d^6-7280\,a^4\,b^{15}\,c^{16}\,d^5+560\,a^3\,b^{16}\,c^{17}\,d^4\right)}+\frac{505008\,a^{11}\,b^8\,c^{11}\,d^{12}\,\sqrt{d\,x^2+c}}{\sqrt{c^5}\,\left(64\,a^{17}\,b^2\,c^3\,d^{18}-1024\,a^{16}\,b^3\,c^4\,d^{17}+7680\,a^{15}\,b^4\,c^5\,d^{16}-35840\,a^{14}\,b^5\,c^6\,d^{15}+116480\,a^{13}\,b^6\,c^7\,d^{14}-278768\,a^{12}\,b^7\,c^8\,d^{13}+505008\,a^{11}\,b^8\,c^9\,d^{12}-699840\,a^{10}\,b^9\,c^{10}\,d^{11}+741120\,a^9\,b^{10}\,c^{11}\,d^{10}-593440\,a^8\,b^{11}\,c^{12}\,d^9+351904\,a^7\,b^{12}\,c^{13}\,d^8-149184\,a^6\,b^{13}\,c^{14}\,d^7+42560\,a^5\,b^{14}\,c^{15}\,d^6-7280\,a^4\,b^{15}\,c^{16}\,d^5+560\,a^3\,b^{16}\,c^{17}\,d^4\right)}-\frac{278768\,a^{12}\,b^7\,c^{10}\,d^{13}\,\sqrt{d\,x^2+c}}{\sqrt{c^5}\,\left(64\,a^{17}\,b^2\,c^3\,d^{18}-1024\,a^{16}\,b^3\,c^4\,d^{17}+7680\,a^{15}\,b^4\,c^5\,d^{16}-35840\,a^{14}\,b^5\,c^6\,d^{15}+116480\,a^{13}\,b^6\,c^7\,d^{14}-278768\,a^{12}\,b^7\,c^8\,d^{13}+505008\,a^{11}\,b^8\,c^9\,d^{12}-699840\,a^{10}\,b^9\,c^{10}\,d^{11}+741120\,a^9\,b^{10}\,c^{11}\,d^{10}-593440\,a^8\,b^{11}\,c^{12}\,d^9+351904\,a^7\,b^{12}\,c^{13}\,d^8-149184\,a^6\,b^{13}\,c^{14}\,d^7+42560\,a^5\,b^{14}\,c^{15}\,d^6-7280\,a^4\,b^{15}\,c^{16}\,d^5+560\,a^3\,b^{16}\,c^{17}\,d^4\right)}+\frac{116480\,a^{13}\,b^6\,c^9\,d^{14}\,\sqrt{d\,x^2+c}}{\sqrt{c^5}\,\left(64\,a^{17}\,b^2\,c^3\,d^{18}-1024\,a^{16}\,b^3\,c^4\,d^{17}+7680\,a^{15}\,b^4\,c^5\,d^{16}-35840\,a^{14}\,b^5\,c^6\,d^{15}+116480\,a^{13}\,b^6\,c^7\,d^{14}-278768\,a^{12}\,b^7\,c^8\,d^{13}+505008\,a^{11}\,b^8\,c^9\,d^{12}-699840\,a^{10}\,b^9\,c^{10}\,d^{11}+741120\,a^9\,b^{10}\,c^{11}\,d^{10}-593440\,a^8\,b^{11}\,c^{12}\,d^9+351904\,a^7\,b^{12}\,c^{13}\,d^8-149184\,a^6\,b^{13}\,c^{14}\,d^7+42560\,a^5\,b^{14}\,c^{15}\,d^6-7280\,a^4\,b^{15}\,c^{16}\,d^5+560\,a^3\,b^{16}\,c^{17}\,d^4\right)}-\frac{35840\,a^{14}\,b^5\,c^8\,d^{15}\,\sqrt{d\,x^2+c}}{\sqrt{c^5}\,\left(64\,a^{17}\,b^2\,c^3\,d^{18}-1024\,a^{16}\,b^3\,c^4\,d^{17}+7680\,a^{15}\,b^4\,c^5\,d^{16}-35840\,a^{14}\,b^5\,c^6\,d^{15}+116480\,a^{13}\,b^6\,c^7\,d^{14}-278768\,a^{12}\,b^7\,c^8\,d^{13}+505008\,a^{11}\,b^8\,c^9\,d^{12}-699840\,a^{10}\,b^9\,c^{10}\,d^{11}+741120\,a^9\,b^{10}\,c^{11}\,d^{10}-593440\,a^8\,b^{11}\,c^{12}\,d^9+351904\,a^7\,b^{12}\,c^{13}\,d^8-149184\,a^6\,b^{13}\,c^{14}\,d^7+42560\,a^5\,b^{14}\,c^{15}\,d^6-7280\,a^4\,b^{15}\,c^{16}\,d^5+560\,a^3\,b^{16}\,c^{17}\,d^4\right)}+\frac{7680\,a^{15}\,b^4\,c^7\,d^{16}\,\sqrt{d\,x^2+c}}{\sqrt{c^5}\,\left(64\,a^{17}\,b^2\,c^3\,d^{18}-1024\,a^{16}\,b^3\,c^4\,d^{17}+7680\,a^{15}\,b^4\,c^5\,d^{16}-35840\,a^{14}\,b^5\,c^6\,d^{15}+116480\,a^{13}\,b^6\,c^7\,d^{14}-278768\,a^{12}\,b^7\,c^8\,d^{13}+505008\,a^{11}\,b^8\,c^9\,d^{12}-699840\,a^{10}\,b^9\,c^{10}\,d^{11}+741120\,a^9\,b^{10}\,c^{11}\,d^{10}-593440\,a^8\,b^{11}\,c^{12}\,d^9+351904\,a^7\,b^{12}\,c^{13}\,d^8-149184\,a^6\,b^{13}\,c^{14}\,d^7+42560\,a^5\,b^{14}\,c^{15}\,d^6-7280\,a^4\,b^{15}\,c^{16}\,d^5+560\,a^3\,b^{16}\,c^{17}\,d^4\right)}-\frac{1024\,a^{16}\,b^3\,c^6\,d^{17}\,\sqrt{d\,x^2+c}}{\sqrt{c^5}\,\left(64\,a^{17}\,b^2\,c^3\,d^{18}-1024\,a^{16}\,b^3\,c^4\,d^{17}+7680\,a^{15}\,b^4\,c^5\,d^{16}-35840\,a^{14}\,b^5\,c^6\,d^{15}+116480\,a^{13}\,b^6\,c^7\,d^{14}-278768\,a^{12}\,b^7\,c^8\,d^{13}+505008\,a^{11}\,b^8\,c^9\,d^{12}-699840\,a^{10}\,b^9\,c^{10}\,d^{11}+741120\,a^9\,b^{10}\,c^{11}\,d^{10}-593440\,a^8\,b^{11}\,c^{12}\,d^9+351904\,a^7\,b^{12}\,c^{13}\,d^8-149184\,a^6\,b^{13}\,c^{14}\,d^7+42560\,a^5\,b^{14}\,c^{15}\,d^6-7280\,a^4\,b^{15}\,c^{16}\,d^5+560\,a^3\,b^{16}\,c^{17}\,d^4\right)}+\frac{64\,a^{17}\,b^2\,c^5\,d^{18}\,\sqrt{d\,x^2+c}}{\sqrt{c^5}\,\left(64\,a^{17}\,b^2\,c^3\,d^{18}-1024\,a^{16}\,b^3\,c^4\,d^{17}+7680\,a^{15}\,b^4\,c^5\,d^{16}-35840\,a^{14}\,b^5\,c^6\,d^{15}+116480\,a^{13}\,b^6\,c^7\,d^{14}-278768\,a^{12}\,b^7\,c^8\,d^{13}+505008\,a^{11}\,b^8\,c^9\,d^{12}-699840\,a^{10}\,b^9\,c^{10}\,d^{11}+741120\,a^9\,b^{10}\,c^{11}\,d^{10}-593440\,a^8\,b^{11}\,c^{12}\,d^9+351904\,a^7\,b^{12}\,c^{13}\,d^8-149184\,a^6\,b^{13}\,c^{14}\,d^7+42560\,a^5\,b^{14}\,c^{15}\,d^6-7280\,a^4\,b^{15}\,c^{16}\,d^5+560\,a^3\,b^{16}\,c^{17}\,d^4\right)}\right)}{a^2\,\sqrt{c^5}}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^7}\,\left(\sqrt{d\,x^2+c}\,\left(-64\,a^{18}\,b^3\,c^6\,d^{17}+960\,a^{17}\,b^4\,c^7\,d^{16}-6720\,a^{16}\,b^5\,c^8\,d^{15}+29120\,a^{15}\,b^6\,c^9\,d^{14}-88144\,a^{14}\,b^7\,c^{10}\,d^{13}+199696\,a^{13}\,b^8\,c^{11}\,d^{12}-352640\,a^{12}\,b^9\,c^{12}\,d^{11}+494400\,a^{11}\,b^{10}\,c^{13}\,d^{10}-550560\,a^{10}\,b^{11}\,c^{14}\,d^9+480928\,a^9\,b^{12}\,c^{15}\,d^8-322560\,a^8\,b^{13}\,c^{16}\,d^7+161280\,a^7\,b^{14}\,c^{17}\,d^6-57680\,a^6\,b^{15}\,c^{18}\,d^5+13840\,a^5\,b^{16}\,c^{19}\,d^4-1984\,a^4\,b^{17}\,c^{20}\,d^3+128\,a^3\,b^{18}\,c^{21}\,d^2\right)-\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^7}\,\left(7\,a\,d-2\,b\,c\right)\,\left(1536\,a^7\,b^{16}\,c^{22}\,d^4-64\,a^6\,b^{17}\,c^{23}\,d^3-13952\,a^8\,b^{15}\,c^{21}\,d^5+71040\,a^9\,b^{14}\,c^{20}\,d^6-235968\,a^{10}\,b^{13}\,c^{19}\,d^7+551936\,a^{11}\,b^{12}\,c^{18}\,d^8-948992\,a^{12}\,b^{11}\,c^{17}\,d^9+1229184\,a^{13}\,b^{10}\,c^{16}\,d^{10}-1214400\,a^{14}\,b^9\,c^{15}\,d^{11}+918016\,a^{15}\,b^8\,c^{14}\,d^{12}-528000\,a^{16}\,b^7\,c^{13}\,d^{13}+227456\,a^{17}\,b^6\,c^{12}\,d^{14}-71232\,a^{18}\,b^5\,c^{11}\,d^{15}+15360\,a^{19}\,b^4\,c^{10}\,d^{16}-2048\,a^{20}\,b^3\,c^9\,d^{17}+128\,a^{21}\,b^2\,c^8\,d^{18}+\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^7}\,\sqrt{d\,x^2+c}\,\left(7\,a\,d-2\,b\,c\right)\,\left(256\,a^{23}\,b^2\,c^{10}\,d^{18}-4352\,a^{22}\,b^3\,c^{11}\,d^{17}+34560\,a^{21}\,b^4\,c^{12}\,d^{16}-170240\,a^{20}\,b^5\,c^{13}\,d^{15}+582400\,a^{19}\,b^6\,c^{14}\,d^{14}-1467648\,a^{18}\,b^7\,c^{15}\,d^{13}+2818816\,a^{17}\,b^8\,c^{16}\,d^{12}-4209920\,a^{16}\,b^9\,c^{17}\,d^{11}+4942080\,a^{15}\,b^{10}\,c^{18}\,d^{10}-4576000\,a^{14}\,b^{11}\,c^{19}\,d^9+3331328\,a^{13}\,b^{12}\,c^{20}\,d^8-1886976\,a^{12}\,b^{13}\,c^{21}\,d^7+815360\,a^{11}\,b^{14}\,c^{22}\,d^6-259840\,a^{10}\,b^{15}\,c^{23}\,d^5+57600\,a^9\,b^{16}\,c^{24}\,d^4-7936\,a^8\,b^{17}\,c^{25}\,d^3+512\,a^7\,b^{18}\,c^{26}\,d^2\right)}{4\,\left(a^9\,d^7-7\,a^8\,b\,c\,d^6+21\,a^7\,b^2\,c^2\,d^5-35\,a^6\,b^3\,c^3\,d^4+35\,a^5\,b^4\,c^4\,d^3-21\,a^4\,b^5\,c^5\,d^2+7\,a^3\,b^6\,c^6\,d-a^2\,b^7\,c^7\right)}\right)}{4\,\left(a^9\,d^7-7\,a^8\,b\,c\,d^6+21\,a^7\,b^2\,c^2\,d^5-35\,a^6\,b^3\,c^3\,d^4+35\,a^5\,b^4\,c^4\,d^3-21\,a^4\,b^5\,c^5\,d^2+7\,a^3\,b^6\,c^6\,d-a^2\,b^7\,c^7\right)}\right)\,\left(7\,a\,d-2\,b\,c\right)\,1{}\mathrm{i}}{4\,\left(a^9\,d^7-7\,a^8\,b\,c\,d^6+21\,a^7\,b^2\,c^2\,d^5-35\,a^6\,b^3\,c^3\,d^4+35\,a^5\,b^4\,c^4\,d^3-21\,a^4\,b^5\,c^5\,d^2+7\,a^3\,b^6\,c^6\,d-a^2\,b^7\,c^7\right)}+\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^7}\,\left(\sqrt{d\,x^2+c}\,\left(-64\,a^{18}\,b^3\,c^6\,d^{17}+960\,a^{17}\,b^4\,c^7\,d^{16}-6720\,a^{16}\,b^5\,c^8\,d^{15}+29120\,a^{15}\,b^6\,c^9\,d^{14}-88144\,a^{14}\,b^7\,c^{10}\,d^{13}+199696\,a^{13}\,b^8\,c^{11}\,d^{12}-352640\,a^{12}\,b^9\,c^{12}\,d^{11}+494400\,a^{11}\,b^{10}\,c^{13}\,d^{10}-550560\,a^{10}\,b^{11}\,c^{14}\,d^9+480928\,a^9\,b^{12}\,c^{15}\,d^8-322560\,a^8\,b^{13}\,c^{16}\,d^7+161280\,a^7\,b^{14}\,c^{17}\,d^6-57680\,a^6\,b^{15}\,c^{18}\,d^5+13840\,a^5\,b^{16}\,c^{19}\,d^4-1984\,a^4\,b^{17}\,c^{20}\,d^3+128\,a^3\,b^{18}\,c^{21}\,d^2\right)-\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^7}\,\left(7\,a\,d-2\,b\,c\right)\,\left(64\,a^6\,b^{17}\,c^{23}\,d^3-1536\,a^7\,b^{16}\,c^{22}\,d^4+13952\,a^8\,b^{15}\,c^{21}\,d^5-71040\,a^9\,b^{14}\,c^{20}\,d^6+235968\,a^{10}\,b^{13}\,c^{19}\,d^7-551936\,a^{11}\,b^{12}\,c^{18}\,d^8+948992\,a^{12}\,b^{11}\,c^{17}\,d^9-1229184\,a^{13}\,b^{10}\,c^{16}\,d^{10}+1214400\,a^{14}\,b^9\,c^{15}\,d^{11}-918016\,a^{15}\,b^8\,c^{14}\,d^{12}+528000\,a^{16}\,b^7\,c^{13}\,d^{13}-227456\,a^{17}\,b^6\,c^{12}\,d^{14}+71232\,a^{18}\,b^5\,c^{11}\,d^{15}-15360\,a^{19}\,b^4\,c^{10}\,d^{16}+2048\,a^{20}\,b^3\,c^9\,d^{17}-128\,a^{21}\,b^2\,c^8\,d^{18}+\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^7}\,\sqrt{d\,x^2+c}\,\left(7\,a\,d-2\,b\,c\right)\,\left(256\,a^{23}\,b^2\,c^{10}\,d^{18}-4352\,a^{22}\,b^3\,c^{11}\,d^{17}+34560\,a^{21}\,b^4\,c^{12}\,d^{16}-170240\,a^{20}\,b^5\,c^{13}\,d^{15}+582400\,a^{19}\,b^6\,c^{14}\,d^{14}-1467648\,a^{18}\,b^7\,c^{15}\,d^{13}+2818816\,a^{17}\,b^8\,c^{16}\,d^{12}-4209920\,a^{16}\,b^9\,c^{17}\,d^{11}+4942080\,a^{15}\,b^{10}\,c^{18}\,d^{10}-4576000\,a^{14}\,b^{11}\,c^{19}\,d^9+3331328\,a^{13}\,b^{12}\,c^{20}\,d^8-1886976\,a^{12}\,b^{13}\,c^{21}\,d^7+815360\,a^{11}\,b^{14}\,c^{22}\,d^6-259840\,a^{10}\,b^{15}\,c^{23}\,d^5+57600\,a^9\,b^{16}\,c^{24}\,d^4-7936\,a^8\,b^{17}\,c^{25}\,d^3+512\,a^7\,b^{18}\,c^{26}\,d^2\right)}{4\,\left(a^9\,d^7-7\,a^8\,b\,c\,d^6+21\,a^7\,b^2\,c^2\,d^5-35\,a^6\,b^3\,c^3\,d^4+35\,a^5\,b^4\,c^4\,d^3-21\,a^4\,b^5\,c^5\,d^2+7\,a^3\,b^6\,c^6\,d-a^2\,b^7\,c^7\right)}\right)}{4\,\left(a^9\,d^7-7\,a^8\,b\,c\,d^6+21\,a^7\,b^2\,c^2\,d^5-35\,a^6\,b^3\,c^3\,d^4+35\,a^5\,b^4\,c^4\,d^3-21\,a^4\,b^5\,c^5\,d^2+7\,a^3\,b^6\,c^6\,d-a^2\,b^7\,c^7\right)}\right)\,\left(7\,a\,d-2\,b\,c\right)\,1{}\mathrm{i}}{4\,\left(a^9\,d^7-7\,a^8\,b\,c\,d^6+21\,a^7\,b^2\,c^2\,d^5-35\,a^6\,b^3\,c^3\,d^4+35\,a^5\,b^4\,c^4\,d^3-21\,a^4\,b^5\,c^5\,d^2+7\,a^3\,b^6\,c^6\,d-a^2\,b^7\,c^7\right)}}{208\,a^3\,b^{16}\,c^{17}\,d^4-32\,a^2\,b^{17}\,c^{18}\,d^3+304\,a^4\,b^{15}\,c^{16}\,d^5-7040\,a^5\,b^{14}\,c^{15}\,d^6+31200\,a^6\,b^{13}\,c^{14}\,d^7-75936\,a^7\,b^{12}\,c^{13}\,d^8+118944\,a^8\,b^{11}\,c^{12}\,d^9-126528\,a^9\,b^{10}\,c^{11}\,d^{10}+92640\,a^{10}\,b^9\,c^{10}\,d^{11}-46000\,a^{11}\,b^8\,c^9\,d^{12}+14768\,a^{12}\,b^7\,c^8\,d^{13}-2752\,a^{13}\,b^6\,c^7\,d^{14}+224\,a^{14}\,b^5\,c^6\,d^{15}+\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^7}\,\left(\sqrt{d\,x^2+c}\,\left(-64\,a^{18}\,b^3\,c^6\,d^{17}+960\,a^{17}\,b^4\,c^7\,d^{16}-6720\,a^{16}\,b^5\,c^8\,d^{15}+29120\,a^{15}\,b^6\,c^9\,d^{14}-88144\,a^{14}\,b^7\,c^{10}\,d^{13}+199696\,a^{13}\,b^8\,c^{11}\,d^{12}-352640\,a^{12}\,b^9\,c^{12}\,d^{11}+494400\,a^{11}\,b^{10}\,c^{13}\,d^{10}-550560\,a^{10}\,b^{11}\,c^{14}\,d^9+480928\,a^9\,b^{12}\,c^{15}\,d^8-322560\,a^8\,b^{13}\,c^{16}\,d^7+161280\,a^7\,b^{14}\,c^{17}\,d^6-57680\,a^6\,b^{15}\,c^{18}\,d^5+13840\,a^5\,b^{16}\,c^{19}\,d^4-1984\,a^4\,b^{17}\,c^{20}\,d^3+128\,a^3\,b^{18}\,c^{21}\,d^2\right)-\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^7}\,\left(7\,a\,d-2\,b\,c\right)\,\left(1536\,a^7\,b^{16}\,c^{22}\,d^4-64\,a^6\,b^{17}\,c^{23}\,d^3-13952\,a^8\,b^{15}\,c^{21}\,d^5+71040\,a^9\,b^{14}\,c^{20}\,d^6-235968\,a^{10}\,b^{13}\,c^{19}\,d^7+551936\,a^{11}\,b^{12}\,c^{18}\,d^8-948992\,a^{12}\,b^{11}\,c^{17}\,d^9+1229184\,a^{13}\,b^{10}\,c^{16}\,d^{10}-1214400\,a^{14}\,b^9\,c^{15}\,d^{11}+918016\,a^{15}\,b^8\,c^{14}\,d^{12}-528000\,a^{16}\,b^7\,c^{13}\,d^{13}+227456\,a^{17}\,b^6\,c^{12}\,d^{14}-71232\,a^{18}\,b^5\,c^{11}\,d^{15}+15360\,a^{19}\,b^4\,c^{10}\,d^{16}-2048\,a^{20}\,b^3\,c^9\,d^{17}+128\,a^{21}\,b^2\,c^8\,d^{18}+\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^7}\,\sqrt{d\,x^2+c}\,\left(7\,a\,d-2\,b\,c\right)\,\left(256\,a^{23}\,b^2\,c^{10}\,d^{18}-4352\,a^{22}\,b^3\,c^{11}\,d^{17}+34560\,a^{21}\,b^4\,c^{12}\,d^{16}-170240\,a^{20}\,b^5\,c^{13}\,d^{15}+582400\,a^{19}\,b^6\,c^{14}\,d^{14}-1467648\,a^{18}\,b^7\,c^{15}\,d^{13}+2818816\,a^{17}\,b^8\,c^{16}\,d^{12}-4209920\,a^{16}\,b^9\,c^{17}\,d^{11}+4942080\,a^{15}\,b^{10}\,c^{18}\,d^{10}-4576000\,a^{14}\,b^{11}\,c^{19}\,d^9+3331328\,a^{13}\,b^{12}\,c^{20}\,d^8-1886976\,a^{12}\,b^{13}\,c^{21}\,d^7+815360\,a^{11}\,b^{14}\,c^{22}\,d^6-259840\,a^{10}\,b^{15}\,c^{23}\,d^5+57600\,a^9\,b^{16}\,c^{24}\,d^4-7936\,a^8\,b^{17}\,c^{25}\,d^3+512\,a^7\,b^{18}\,c^{26}\,d^2\right)}{4\,\left(a^9\,d^7-7\,a^8\,b\,c\,d^6+21\,a^7\,b^2\,c^2\,d^5-35\,a^6\,b^3\,c^3\,d^4+35\,a^5\,b^4\,c^4\,d^3-21\,a^4\,b^5\,c^5\,d^2+7\,a^3\,b^6\,c^6\,d-a^2\,b^7\,c^7\right)}\right)}{4\,\left(a^9\,d^7-7\,a^8\,b\,c\,d^6+21\,a^7\,b^2\,c^2\,d^5-35\,a^6\,b^3\,c^3\,d^4+35\,a^5\,b^4\,c^4\,d^3-21\,a^4\,b^5\,c^5\,d^2+7\,a^3\,b^6\,c^6\,d-a^2\,b^7\,c^7\right)}\right)\,\left(7\,a\,d-2\,b\,c\right)}{4\,\left(a^9\,d^7-7\,a^8\,b\,c\,d^6+21\,a^7\,b^2\,c^2\,d^5-35\,a^6\,b^3\,c^3\,d^4+35\,a^5\,b^4\,c^4\,d^3-21\,a^4\,b^5\,c^5\,d^2+7\,a^3\,b^6\,c^6\,d-a^2\,b^7\,c^7\right)}-\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^7}\,\left(\sqrt{d\,x^2+c}\,\left(-64\,a^{18}\,b^3\,c^6\,d^{17}+960\,a^{17}\,b^4\,c^7\,d^{16}-6720\,a^{16}\,b^5\,c^8\,d^{15}+29120\,a^{15}\,b^6\,c^9\,d^{14}-88144\,a^{14}\,b^7\,c^{10}\,d^{13}+199696\,a^{13}\,b^8\,c^{11}\,d^{12}-352640\,a^{12}\,b^9\,c^{12}\,d^{11}+494400\,a^{11}\,b^{10}\,c^{13}\,d^{10}-550560\,a^{10}\,b^{11}\,c^{14}\,d^9+480928\,a^9\,b^{12}\,c^{15}\,d^8-322560\,a^8\,b^{13}\,c^{16}\,d^7+161280\,a^7\,b^{14}\,c^{17}\,d^6-57680\,a^6\,b^{15}\,c^{18}\,d^5+13840\,a^5\,b^{16}\,c^{19}\,d^4-1984\,a^4\,b^{17}\,c^{20}\,d^3+128\,a^3\,b^{18}\,c^{21}\,d^2\right)-\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^7}\,\left(7\,a\,d-2\,b\,c\right)\,\left(64\,a^6\,b^{17}\,c^{23}\,d^3-1536\,a^7\,b^{16}\,c^{22}\,d^4+13952\,a^8\,b^{15}\,c^{21}\,d^5-71040\,a^9\,b^{14}\,c^{20}\,d^6+235968\,a^{10}\,b^{13}\,c^{19}\,d^7-551936\,a^{11}\,b^{12}\,c^{18}\,d^8+948992\,a^{12}\,b^{11}\,c^{17}\,d^9-1229184\,a^{13}\,b^{10}\,c^{16}\,d^{10}+1214400\,a^{14}\,b^9\,c^{15}\,d^{11}-918016\,a^{15}\,b^8\,c^{14}\,d^{12}+528000\,a^{16}\,b^7\,c^{13}\,d^{13}-227456\,a^{17}\,b^6\,c^{12}\,d^{14}+71232\,a^{18}\,b^5\,c^{11}\,d^{15}-15360\,a^{19}\,b^4\,c^{10}\,d^{16}+2048\,a^{20}\,b^3\,c^9\,d^{17}-128\,a^{21}\,b^2\,c^8\,d^{18}+\frac{\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^7}\,\sqrt{d\,x^2+c}\,\left(7\,a\,d-2\,b\,c\right)\,\left(256\,a^{23}\,b^2\,c^{10}\,d^{18}-4352\,a^{22}\,b^3\,c^{11}\,d^{17}+34560\,a^{21}\,b^4\,c^{12}\,d^{16}-170240\,a^{20}\,b^5\,c^{13}\,d^{15}+582400\,a^{19}\,b^6\,c^{14}\,d^{14}-1467648\,a^{18}\,b^7\,c^{15}\,d^{13}+2818816\,a^{17}\,b^8\,c^{16}\,d^{12}-4209920\,a^{16}\,b^9\,c^{17}\,d^{11}+4942080\,a^{15}\,b^{10}\,c^{18}\,d^{10}-4576000\,a^{14}\,b^{11}\,c^{19}\,d^9+3331328\,a^{13}\,b^{12}\,c^{20}\,d^8-1886976\,a^{12}\,b^{13}\,c^{21}\,d^7+815360\,a^{11}\,b^{14}\,c^{22}\,d^6-259840\,a^{10}\,b^{15}\,c^{23}\,d^5+57600\,a^9\,b^{16}\,c^{24}\,d^4-7936\,a^8\,b^{17}\,c^{25}\,d^3+512\,a^7\,b^{18}\,c^{26}\,d^2\right)}{4\,\left(a^9\,d^7-7\,a^8\,b\,c\,d^6+21\,a^7\,b^2\,c^2\,d^5-35\,a^6\,b^3\,c^3\,d^4+35\,a^5\,b^4\,c^4\,d^3-21\,a^4\,b^5\,c^5\,d^2+7\,a^3\,b^6\,c^6\,d-a^2\,b^7\,c^7\right)}\right)}{4\,\left(a^9\,d^7-7\,a^8\,b\,c\,d^6+21\,a^7\,b^2\,c^2\,d^5-35\,a^6\,b^3\,c^3\,d^4+35\,a^5\,b^4\,c^4\,d^3-21\,a^4\,b^5\,c^5\,d^2+7\,a^3\,b^6\,c^6\,d-a^2\,b^7\,c^7\right)}\right)\,\left(7\,a\,d-2\,b\,c\right)}{4\,\left(a^9\,d^7-7\,a^8\,b\,c\,d^6+21\,a^7\,b^2\,c^2\,d^5-35\,a^6\,b^3\,c^3\,d^4+35\,a^5\,b^4\,c^4\,d^3-21\,a^4\,b^5\,c^5\,d^2+7\,a^3\,b^6\,c^6\,d-a^2\,b^7\,c^7\right)}}\right)\,\sqrt{-b^5\,{\left(a\,d-b\,c\right)}^7}\,\left(7\,a\,d-2\,b\,c\right)\,1{}\mathrm{i}}{2\,\left(a^9\,d^7-7\,a^8\,b\,c\,d^6+21\,a^7\,b^2\,c^2\,d^5-35\,a^6\,b^3\,c^3\,d^4+35\,a^5\,b^4\,c^4\,d^3-21\,a^4\,b^5\,c^5\,d^2+7\,a^3\,b^6\,c^6\,d-a^2\,b^7\,c^7\right)}","Not used",1,"((d^2*(c + d*x^2)*(3*a*d - 8*b*c))/(3*(b*c^2 - a*c*d)^2) - d^2/(3*(b*c^2 - a*c*d)) + (d*(c + d*x^2)^2*(b^3*c^2 - 2*a^2*b*d^2 + 6*a*b^2*c*d))/(2*a*c*(b*c^2 - a*c*d)*(a*d - b*c)^2))/(b*(c + d*x^2)^(5/2) + (c + d*x^2)^(3/2)*(a*d - b*c)) - atanh((560*a^3*b^16*c^19*d^4*(c + d*x^2)^(1/2))/((c^5)^(1/2)*(560*a^3*b^16*c^17*d^4 - 7280*a^4*b^15*c^16*d^5 + 42560*a^5*b^14*c^15*d^6 - 149184*a^6*b^13*c^14*d^7 + 351904*a^7*b^12*c^13*d^8 - 593440*a^8*b^11*c^12*d^9 + 741120*a^9*b^10*c^11*d^10 - 699840*a^10*b^9*c^10*d^11 + 505008*a^11*b^8*c^9*d^12 - 278768*a^12*b^7*c^8*d^13 + 116480*a^13*b^6*c^7*d^14 - 35840*a^14*b^5*c^6*d^15 + 7680*a^15*b^4*c^5*d^16 - 1024*a^16*b^3*c^4*d^17 + 64*a^17*b^2*c^3*d^18)) - (7280*a^4*b^15*c^18*d^5*(c + d*x^2)^(1/2))/((c^5)^(1/2)*(560*a^3*b^16*c^17*d^4 - 7280*a^4*b^15*c^16*d^5 + 42560*a^5*b^14*c^15*d^6 - 149184*a^6*b^13*c^14*d^7 + 351904*a^7*b^12*c^13*d^8 - 593440*a^8*b^11*c^12*d^9 + 741120*a^9*b^10*c^11*d^10 - 699840*a^10*b^9*c^10*d^11 + 505008*a^11*b^8*c^9*d^12 - 278768*a^12*b^7*c^8*d^13 + 116480*a^13*b^6*c^7*d^14 - 35840*a^14*b^5*c^6*d^15 + 7680*a^15*b^4*c^5*d^16 - 1024*a^16*b^3*c^4*d^17 + 64*a^17*b^2*c^3*d^18)) + (42560*a^5*b^14*c^17*d^6*(c + d*x^2)^(1/2))/((c^5)^(1/2)*(560*a^3*b^16*c^17*d^4 - 7280*a^4*b^15*c^16*d^5 + 42560*a^5*b^14*c^15*d^6 - 149184*a^6*b^13*c^14*d^7 + 351904*a^7*b^12*c^13*d^8 - 593440*a^8*b^11*c^12*d^9 + 741120*a^9*b^10*c^11*d^10 - 699840*a^10*b^9*c^10*d^11 + 505008*a^11*b^8*c^9*d^12 - 278768*a^12*b^7*c^8*d^13 + 116480*a^13*b^6*c^7*d^14 - 35840*a^14*b^5*c^6*d^15 + 7680*a^15*b^4*c^5*d^16 - 1024*a^16*b^3*c^4*d^17 + 64*a^17*b^2*c^3*d^18)) - (149184*a^6*b^13*c^16*d^7*(c + d*x^2)^(1/2))/((c^5)^(1/2)*(560*a^3*b^16*c^17*d^4 - 7280*a^4*b^15*c^16*d^5 + 42560*a^5*b^14*c^15*d^6 - 149184*a^6*b^13*c^14*d^7 + 351904*a^7*b^12*c^13*d^8 - 593440*a^8*b^11*c^12*d^9 + 741120*a^9*b^10*c^11*d^10 - 699840*a^10*b^9*c^10*d^11 + 505008*a^11*b^8*c^9*d^12 - 278768*a^12*b^7*c^8*d^13 + 116480*a^13*b^6*c^7*d^14 - 35840*a^14*b^5*c^6*d^15 + 7680*a^15*b^4*c^5*d^16 - 1024*a^16*b^3*c^4*d^17 + 64*a^17*b^2*c^3*d^18)) + (351904*a^7*b^12*c^15*d^8*(c + d*x^2)^(1/2))/((c^5)^(1/2)*(560*a^3*b^16*c^17*d^4 - 7280*a^4*b^15*c^16*d^5 + 42560*a^5*b^14*c^15*d^6 - 149184*a^6*b^13*c^14*d^7 + 351904*a^7*b^12*c^13*d^8 - 593440*a^8*b^11*c^12*d^9 + 741120*a^9*b^10*c^11*d^10 - 699840*a^10*b^9*c^10*d^11 + 505008*a^11*b^8*c^9*d^12 - 278768*a^12*b^7*c^8*d^13 + 116480*a^13*b^6*c^7*d^14 - 35840*a^14*b^5*c^6*d^15 + 7680*a^15*b^4*c^5*d^16 - 1024*a^16*b^3*c^4*d^17 + 64*a^17*b^2*c^3*d^18)) - (593440*a^8*b^11*c^14*d^9*(c + d*x^2)^(1/2))/((c^5)^(1/2)*(560*a^3*b^16*c^17*d^4 - 7280*a^4*b^15*c^16*d^5 + 42560*a^5*b^14*c^15*d^6 - 149184*a^6*b^13*c^14*d^7 + 351904*a^7*b^12*c^13*d^8 - 593440*a^8*b^11*c^12*d^9 + 741120*a^9*b^10*c^11*d^10 - 699840*a^10*b^9*c^10*d^11 + 505008*a^11*b^8*c^9*d^12 - 278768*a^12*b^7*c^8*d^13 + 116480*a^13*b^6*c^7*d^14 - 35840*a^14*b^5*c^6*d^15 + 7680*a^15*b^4*c^5*d^16 - 1024*a^16*b^3*c^4*d^17 + 64*a^17*b^2*c^3*d^18)) + (741120*a^9*b^10*c^13*d^10*(c + d*x^2)^(1/2))/((c^5)^(1/2)*(560*a^3*b^16*c^17*d^4 - 7280*a^4*b^15*c^16*d^5 + 42560*a^5*b^14*c^15*d^6 - 149184*a^6*b^13*c^14*d^7 + 351904*a^7*b^12*c^13*d^8 - 593440*a^8*b^11*c^12*d^9 + 741120*a^9*b^10*c^11*d^10 - 699840*a^10*b^9*c^10*d^11 + 505008*a^11*b^8*c^9*d^12 - 278768*a^12*b^7*c^8*d^13 + 116480*a^13*b^6*c^7*d^14 - 35840*a^14*b^5*c^6*d^15 + 7680*a^15*b^4*c^5*d^16 - 1024*a^16*b^3*c^4*d^17 + 64*a^17*b^2*c^3*d^18)) - (699840*a^10*b^9*c^12*d^11*(c + d*x^2)^(1/2))/((c^5)^(1/2)*(560*a^3*b^16*c^17*d^4 - 7280*a^4*b^15*c^16*d^5 + 42560*a^5*b^14*c^15*d^6 - 149184*a^6*b^13*c^14*d^7 + 351904*a^7*b^12*c^13*d^8 - 593440*a^8*b^11*c^12*d^9 + 741120*a^9*b^10*c^11*d^10 - 699840*a^10*b^9*c^10*d^11 + 505008*a^11*b^8*c^9*d^12 - 278768*a^12*b^7*c^8*d^13 + 116480*a^13*b^6*c^7*d^14 - 35840*a^14*b^5*c^6*d^15 + 7680*a^15*b^4*c^5*d^16 - 1024*a^16*b^3*c^4*d^17 + 64*a^17*b^2*c^3*d^18)) + (505008*a^11*b^8*c^11*d^12*(c + d*x^2)^(1/2))/((c^5)^(1/2)*(560*a^3*b^16*c^17*d^4 - 7280*a^4*b^15*c^16*d^5 + 42560*a^5*b^14*c^15*d^6 - 149184*a^6*b^13*c^14*d^7 + 351904*a^7*b^12*c^13*d^8 - 593440*a^8*b^11*c^12*d^9 + 741120*a^9*b^10*c^11*d^10 - 699840*a^10*b^9*c^10*d^11 + 505008*a^11*b^8*c^9*d^12 - 278768*a^12*b^7*c^8*d^13 + 116480*a^13*b^6*c^7*d^14 - 35840*a^14*b^5*c^6*d^15 + 7680*a^15*b^4*c^5*d^16 - 1024*a^16*b^3*c^4*d^17 + 64*a^17*b^2*c^3*d^18)) - (278768*a^12*b^7*c^10*d^13*(c + d*x^2)^(1/2))/((c^5)^(1/2)*(560*a^3*b^16*c^17*d^4 - 7280*a^4*b^15*c^16*d^5 + 42560*a^5*b^14*c^15*d^6 - 149184*a^6*b^13*c^14*d^7 + 351904*a^7*b^12*c^13*d^8 - 593440*a^8*b^11*c^12*d^9 + 741120*a^9*b^10*c^11*d^10 - 699840*a^10*b^9*c^10*d^11 + 505008*a^11*b^8*c^9*d^12 - 278768*a^12*b^7*c^8*d^13 + 116480*a^13*b^6*c^7*d^14 - 35840*a^14*b^5*c^6*d^15 + 7680*a^15*b^4*c^5*d^16 - 1024*a^16*b^3*c^4*d^17 + 64*a^17*b^2*c^3*d^18)) + (116480*a^13*b^6*c^9*d^14*(c + d*x^2)^(1/2))/((c^5)^(1/2)*(560*a^3*b^16*c^17*d^4 - 7280*a^4*b^15*c^16*d^5 + 42560*a^5*b^14*c^15*d^6 - 149184*a^6*b^13*c^14*d^7 + 351904*a^7*b^12*c^13*d^8 - 593440*a^8*b^11*c^12*d^9 + 741120*a^9*b^10*c^11*d^10 - 699840*a^10*b^9*c^10*d^11 + 505008*a^11*b^8*c^9*d^12 - 278768*a^12*b^7*c^8*d^13 + 116480*a^13*b^6*c^7*d^14 - 35840*a^14*b^5*c^6*d^15 + 7680*a^15*b^4*c^5*d^16 - 1024*a^16*b^3*c^4*d^17 + 64*a^17*b^2*c^3*d^18)) - (35840*a^14*b^5*c^8*d^15*(c + d*x^2)^(1/2))/((c^5)^(1/2)*(560*a^3*b^16*c^17*d^4 - 7280*a^4*b^15*c^16*d^5 + 42560*a^5*b^14*c^15*d^6 - 149184*a^6*b^13*c^14*d^7 + 351904*a^7*b^12*c^13*d^8 - 593440*a^8*b^11*c^12*d^9 + 741120*a^9*b^10*c^11*d^10 - 699840*a^10*b^9*c^10*d^11 + 505008*a^11*b^8*c^9*d^12 - 278768*a^12*b^7*c^8*d^13 + 116480*a^13*b^6*c^7*d^14 - 35840*a^14*b^5*c^6*d^15 + 7680*a^15*b^4*c^5*d^16 - 1024*a^16*b^3*c^4*d^17 + 64*a^17*b^2*c^3*d^18)) + (7680*a^15*b^4*c^7*d^16*(c + d*x^2)^(1/2))/((c^5)^(1/2)*(560*a^3*b^16*c^17*d^4 - 7280*a^4*b^15*c^16*d^5 + 42560*a^5*b^14*c^15*d^6 - 149184*a^6*b^13*c^14*d^7 + 351904*a^7*b^12*c^13*d^8 - 593440*a^8*b^11*c^12*d^9 + 741120*a^9*b^10*c^11*d^10 - 699840*a^10*b^9*c^10*d^11 + 505008*a^11*b^8*c^9*d^12 - 278768*a^12*b^7*c^8*d^13 + 116480*a^13*b^6*c^7*d^14 - 35840*a^14*b^5*c^6*d^15 + 7680*a^15*b^4*c^5*d^16 - 1024*a^16*b^3*c^4*d^17 + 64*a^17*b^2*c^3*d^18)) - (1024*a^16*b^3*c^6*d^17*(c + d*x^2)^(1/2))/((c^5)^(1/2)*(560*a^3*b^16*c^17*d^4 - 7280*a^4*b^15*c^16*d^5 + 42560*a^5*b^14*c^15*d^6 - 149184*a^6*b^13*c^14*d^7 + 351904*a^7*b^12*c^13*d^8 - 593440*a^8*b^11*c^12*d^9 + 741120*a^9*b^10*c^11*d^10 - 699840*a^10*b^9*c^10*d^11 + 505008*a^11*b^8*c^9*d^12 - 278768*a^12*b^7*c^8*d^13 + 116480*a^13*b^6*c^7*d^14 - 35840*a^14*b^5*c^6*d^15 + 7680*a^15*b^4*c^5*d^16 - 1024*a^16*b^3*c^4*d^17 + 64*a^17*b^2*c^3*d^18)) + (64*a^17*b^2*c^5*d^18*(c + d*x^2)^(1/2))/((c^5)^(1/2)*(560*a^3*b^16*c^17*d^4 - 7280*a^4*b^15*c^16*d^5 + 42560*a^5*b^14*c^15*d^6 - 149184*a^6*b^13*c^14*d^7 + 351904*a^7*b^12*c^13*d^8 - 593440*a^8*b^11*c^12*d^9 + 741120*a^9*b^10*c^11*d^10 - 699840*a^10*b^9*c^10*d^11 + 505008*a^11*b^8*c^9*d^12 - 278768*a^12*b^7*c^8*d^13 + 116480*a^13*b^6*c^7*d^14 - 35840*a^14*b^5*c^6*d^15 + 7680*a^15*b^4*c^5*d^16 - 1024*a^16*b^3*c^4*d^17 + 64*a^17*b^2*c^3*d^18)))/(a^2*(c^5)^(1/2)) + (atan((((-b^5*(a*d - b*c)^7)^(1/2)*((c + d*x^2)^(1/2)*(128*a^3*b^18*c^21*d^2 - 1984*a^4*b^17*c^20*d^3 + 13840*a^5*b^16*c^19*d^4 - 57680*a^6*b^15*c^18*d^5 + 161280*a^7*b^14*c^17*d^6 - 322560*a^8*b^13*c^16*d^7 + 480928*a^9*b^12*c^15*d^8 - 550560*a^10*b^11*c^14*d^9 + 494400*a^11*b^10*c^13*d^10 - 352640*a^12*b^9*c^12*d^11 + 199696*a^13*b^8*c^11*d^12 - 88144*a^14*b^7*c^10*d^13 + 29120*a^15*b^6*c^9*d^14 - 6720*a^16*b^5*c^8*d^15 + 960*a^17*b^4*c^7*d^16 - 64*a^18*b^3*c^6*d^17) - ((-b^5*(a*d - b*c)^7)^(1/2)*(7*a*d - 2*b*c)*(1536*a^7*b^16*c^22*d^4 - 64*a^6*b^17*c^23*d^3 - 13952*a^8*b^15*c^21*d^5 + 71040*a^9*b^14*c^20*d^6 - 235968*a^10*b^13*c^19*d^7 + 551936*a^11*b^12*c^18*d^8 - 948992*a^12*b^11*c^17*d^9 + 1229184*a^13*b^10*c^16*d^10 - 1214400*a^14*b^9*c^15*d^11 + 918016*a^15*b^8*c^14*d^12 - 528000*a^16*b^7*c^13*d^13 + 227456*a^17*b^6*c^12*d^14 - 71232*a^18*b^5*c^11*d^15 + 15360*a^19*b^4*c^10*d^16 - 2048*a^20*b^3*c^9*d^17 + 128*a^21*b^2*c^8*d^18 + ((-b^5*(a*d - b*c)^7)^(1/2)*(c + d*x^2)^(1/2)*(7*a*d - 2*b*c)*(512*a^7*b^18*c^26*d^2 - 7936*a^8*b^17*c^25*d^3 + 57600*a^9*b^16*c^24*d^4 - 259840*a^10*b^15*c^23*d^5 + 815360*a^11*b^14*c^22*d^6 - 1886976*a^12*b^13*c^21*d^7 + 3331328*a^13*b^12*c^20*d^8 - 4576000*a^14*b^11*c^19*d^9 + 4942080*a^15*b^10*c^18*d^10 - 4209920*a^16*b^9*c^17*d^11 + 2818816*a^17*b^8*c^16*d^12 - 1467648*a^18*b^7*c^15*d^13 + 582400*a^19*b^6*c^14*d^14 - 170240*a^20*b^5*c^13*d^15 + 34560*a^21*b^4*c^12*d^16 - 4352*a^22*b^3*c^11*d^17 + 256*a^23*b^2*c^10*d^18))/(4*(a^9*d^7 - a^2*b^7*c^7 + 7*a^3*b^6*c^6*d - 21*a^4*b^5*c^5*d^2 + 35*a^5*b^4*c^4*d^3 - 35*a^6*b^3*c^3*d^4 + 21*a^7*b^2*c^2*d^5 - 7*a^8*b*c*d^6))))/(4*(a^9*d^7 - a^2*b^7*c^7 + 7*a^3*b^6*c^6*d - 21*a^4*b^5*c^5*d^2 + 35*a^5*b^4*c^4*d^3 - 35*a^6*b^3*c^3*d^4 + 21*a^7*b^2*c^2*d^5 - 7*a^8*b*c*d^6)))*(7*a*d - 2*b*c)*1i)/(4*(a^9*d^7 - a^2*b^7*c^7 + 7*a^3*b^6*c^6*d - 21*a^4*b^5*c^5*d^2 + 35*a^5*b^4*c^4*d^3 - 35*a^6*b^3*c^3*d^4 + 21*a^7*b^2*c^2*d^5 - 7*a^8*b*c*d^6)) + ((-b^5*(a*d - b*c)^7)^(1/2)*((c + d*x^2)^(1/2)*(128*a^3*b^18*c^21*d^2 - 1984*a^4*b^17*c^20*d^3 + 13840*a^5*b^16*c^19*d^4 - 57680*a^6*b^15*c^18*d^5 + 161280*a^7*b^14*c^17*d^6 - 322560*a^8*b^13*c^16*d^7 + 480928*a^9*b^12*c^15*d^8 - 550560*a^10*b^11*c^14*d^9 + 494400*a^11*b^10*c^13*d^10 - 352640*a^12*b^9*c^12*d^11 + 199696*a^13*b^8*c^11*d^12 - 88144*a^14*b^7*c^10*d^13 + 29120*a^15*b^6*c^9*d^14 - 6720*a^16*b^5*c^8*d^15 + 960*a^17*b^4*c^7*d^16 - 64*a^18*b^3*c^6*d^17) - ((-b^5*(a*d - b*c)^7)^(1/2)*(7*a*d - 2*b*c)*(64*a^6*b^17*c^23*d^3 - 1536*a^7*b^16*c^22*d^4 + 13952*a^8*b^15*c^21*d^5 - 71040*a^9*b^14*c^20*d^6 + 235968*a^10*b^13*c^19*d^7 - 551936*a^11*b^12*c^18*d^8 + 948992*a^12*b^11*c^17*d^9 - 1229184*a^13*b^10*c^16*d^10 + 1214400*a^14*b^9*c^15*d^11 - 918016*a^15*b^8*c^14*d^12 + 528000*a^16*b^7*c^13*d^13 - 227456*a^17*b^6*c^12*d^14 + 71232*a^18*b^5*c^11*d^15 - 15360*a^19*b^4*c^10*d^16 + 2048*a^20*b^3*c^9*d^17 - 128*a^21*b^2*c^8*d^18 + ((-b^5*(a*d - b*c)^7)^(1/2)*(c + d*x^2)^(1/2)*(7*a*d - 2*b*c)*(512*a^7*b^18*c^26*d^2 - 7936*a^8*b^17*c^25*d^3 + 57600*a^9*b^16*c^24*d^4 - 259840*a^10*b^15*c^23*d^5 + 815360*a^11*b^14*c^22*d^6 - 1886976*a^12*b^13*c^21*d^7 + 3331328*a^13*b^12*c^20*d^8 - 4576000*a^14*b^11*c^19*d^9 + 4942080*a^15*b^10*c^18*d^10 - 4209920*a^16*b^9*c^17*d^11 + 2818816*a^17*b^8*c^16*d^12 - 1467648*a^18*b^7*c^15*d^13 + 582400*a^19*b^6*c^14*d^14 - 170240*a^20*b^5*c^13*d^15 + 34560*a^21*b^4*c^12*d^16 - 4352*a^22*b^3*c^11*d^17 + 256*a^23*b^2*c^10*d^18))/(4*(a^9*d^7 - a^2*b^7*c^7 + 7*a^3*b^6*c^6*d - 21*a^4*b^5*c^5*d^2 + 35*a^5*b^4*c^4*d^3 - 35*a^6*b^3*c^3*d^4 + 21*a^7*b^2*c^2*d^5 - 7*a^8*b*c*d^6))))/(4*(a^9*d^7 - a^2*b^7*c^7 + 7*a^3*b^6*c^6*d - 21*a^4*b^5*c^5*d^2 + 35*a^5*b^4*c^4*d^3 - 35*a^6*b^3*c^3*d^4 + 21*a^7*b^2*c^2*d^5 - 7*a^8*b*c*d^6)))*(7*a*d - 2*b*c)*1i)/(4*(a^9*d^7 - a^2*b^7*c^7 + 7*a^3*b^6*c^6*d - 21*a^4*b^5*c^5*d^2 + 35*a^5*b^4*c^4*d^3 - 35*a^6*b^3*c^3*d^4 + 21*a^7*b^2*c^2*d^5 - 7*a^8*b*c*d^6)))/(208*a^3*b^16*c^17*d^4 - 32*a^2*b^17*c^18*d^3 + 304*a^4*b^15*c^16*d^5 - 7040*a^5*b^14*c^15*d^6 + 31200*a^6*b^13*c^14*d^7 - 75936*a^7*b^12*c^13*d^8 + 118944*a^8*b^11*c^12*d^9 - 126528*a^9*b^10*c^11*d^10 + 92640*a^10*b^9*c^10*d^11 - 46000*a^11*b^8*c^9*d^12 + 14768*a^12*b^7*c^8*d^13 - 2752*a^13*b^6*c^7*d^14 + 224*a^14*b^5*c^6*d^15 + ((-b^5*(a*d - b*c)^7)^(1/2)*((c + d*x^2)^(1/2)*(128*a^3*b^18*c^21*d^2 - 1984*a^4*b^17*c^20*d^3 + 13840*a^5*b^16*c^19*d^4 - 57680*a^6*b^15*c^18*d^5 + 161280*a^7*b^14*c^17*d^6 - 322560*a^8*b^13*c^16*d^7 + 480928*a^9*b^12*c^15*d^8 - 550560*a^10*b^11*c^14*d^9 + 494400*a^11*b^10*c^13*d^10 - 352640*a^12*b^9*c^12*d^11 + 199696*a^13*b^8*c^11*d^12 - 88144*a^14*b^7*c^10*d^13 + 29120*a^15*b^6*c^9*d^14 - 6720*a^16*b^5*c^8*d^15 + 960*a^17*b^4*c^7*d^16 - 64*a^18*b^3*c^6*d^17) - ((-b^5*(a*d - b*c)^7)^(1/2)*(7*a*d - 2*b*c)*(1536*a^7*b^16*c^22*d^4 - 64*a^6*b^17*c^23*d^3 - 13952*a^8*b^15*c^21*d^5 + 71040*a^9*b^14*c^20*d^6 - 235968*a^10*b^13*c^19*d^7 + 551936*a^11*b^12*c^18*d^8 - 948992*a^12*b^11*c^17*d^9 + 1229184*a^13*b^10*c^16*d^10 - 1214400*a^14*b^9*c^15*d^11 + 918016*a^15*b^8*c^14*d^12 - 528000*a^16*b^7*c^13*d^13 + 227456*a^17*b^6*c^12*d^14 - 71232*a^18*b^5*c^11*d^15 + 15360*a^19*b^4*c^10*d^16 - 2048*a^20*b^3*c^9*d^17 + 128*a^21*b^2*c^8*d^18 + ((-b^5*(a*d - b*c)^7)^(1/2)*(c + d*x^2)^(1/2)*(7*a*d - 2*b*c)*(512*a^7*b^18*c^26*d^2 - 7936*a^8*b^17*c^25*d^3 + 57600*a^9*b^16*c^24*d^4 - 259840*a^10*b^15*c^23*d^5 + 815360*a^11*b^14*c^22*d^6 - 1886976*a^12*b^13*c^21*d^7 + 3331328*a^13*b^12*c^20*d^8 - 4576000*a^14*b^11*c^19*d^9 + 4942080*a^15*b^10*c^18*d^10 - 4209920*a^16*b^9*c^17*d^11 + 2818816*a^17*b^8*c^16*d^12 - 1467648*a^18*b^7*c^15*d^13 + 582400*a^19*b^6*c^14*d^14 - 170240*a^20*b^5*c^13*d^15 + 34560*a^21*b^4*c^12*d^16 - 4352*a^22*b^3*c^11*d^17 + 256*a^23*b^2*c^10*d^18))/(4*(a^9*d^7 - a^2*b^7*c^7 + 7*a^3*b^6*c^6*d - 21*a^4*b^5*c^5*d^2 + 35*a^5*b^4*c^4*d^3 - 35*a^6*b^3*c^3*d^4 + 21*a^7*b^2*c^2*d^5 - 7*a^8*b*c*d^6))))/(4*(a^9*d^7 - a^2*b^7*c^7 + 7*a^3*b^6*c^6*d - 21*a^4*b^5*c^5*d^2 + 35*a^5*b^4*c^4*d^3 - 35*a^6*b^3*c^3*d^4 + 21*a^7*b^2*c^2*d^5 - 7*a^8*b*c*d^6)))*(7*a*d - 2*b*c))/(4*(a^9*d^7 - a^2*b^7*c^7 + 7*a^3*b^6*c^6*d - 21*a^4*b^5*c^5*d^2 + 35*a^5*b^4*c^4*d^3 - 35*a^6*b^3*c^3*d^4 + 21*a^7*b^2*c^2*d^5 - 7*a^8*b*c*d^6)) - ((-b^5*(a*d - b*c)^7)^(1/2)*((c + d*x^2)^(1/2)*(128*a^3*b^18*c^21*d^2 - 1984*a^4*b^17*c^20*d^3 + 13840*a^5*b^16*c^19*d^4 - 57680*a^6*b^15*c^18*d^5 + 161280*a^7*b^14*c^17*d^6 - 322560*a^8*b^13*c^16*d^7 + 480928*a^9*b^12*c^15*d^8 - 550560*a^10*b^11*c^14*d^9 + 494400*a^11*b^10*c^13*d^10 - 352640*a^12*b^9*c^12*d^11 + 199696*a^13*b^8*c^11*d^12 - 88144*a^14*b^7*c^10*d^13 + 29120*a^15*b^6*c^9*d^14 - 6720*a^16*b^5*c^8*d^15 + 960*a^17*b^4*c^7*d^16 - 64*a^18*b^3*c^6*d^17) - ((-b^5*(a*d - b*c)^7)^(1/2)*(7*a*d - 2*b*c)*(64*a^6*b^17*c^23*d^3 - 1536*a^7*b^16*c^22*d^4 + 13952*a^8*b^15*c^21*d^5 - 71040*a^9*b^14*c^20*d^6 + 235968*a^10*b^13*c^19*d^7 - 551936*a^11*b^12*c^18*d^8 + 948992*a^12*b^11*c^17*d^9 - 1229184*a^13*b^10*c^16*d^10 + 1214400*a^14*b^9*c^15*d^11 - 918016*a^15*b^8*c^14*d^12 + 528000*a^16*b^7*c^13*d^13 - 227456*a^17*b^6*c^12*d^14 + 71232*a^18*b^5*c^11*d^15 - 15360*a^19*b^4*c^10*d^16 + 2048*a^20*b^3*c^9*d^17 - 128*a^21*b^2*c^8*d^18 + ((-b^5*(a*d - b*c)^7)^(1/2)*(c + d*x^2)^(1/2)*(7*a*d - 2*b*c)*(512*a^7*b^18*c^26*d^2 - 7936*a^8*b^17*c^25*d^3 + 57600*a^9*b^16*c^24*d^4 - 259840*a^10*b^15*c^23*d^5 + 815360*a^11*b^14*c^22*d^6 - 1886976*a^12*b^13*c^21*d^7 + 3331328*a^13*b^12*c^20*d^8 - 4576000*a^14*b^11*c^19*d^9 + 4942080*a^15*b^10*c^18*d^10 - 4209920*a^16*b^9*c^17*d^11 + 2818816*a^17*b^8*c^16*d^12 - 1467648*a^18*b^7*c^15*d^13 + 582400*a^19*b^6*c^14*d^14 - 170240*a^20*b^5*c^13*d^15 + 34560*a^21*b^4*c^12*d^16 - 4352*a^22*b^3*c^11*d^17 + 256*a^23*b^2*c^10*d^18))/(4*(a^9*d^7 - a^2*b^7*c^7 + 7*a^3*b^6*c^6*d - 21*a^4*b^5*c^5*d^2 + 35*a^5*b^4*c^4*d^3 - 35*a^6*b^3*c^3*d^4 + 21*a^7*b^2*c^2*d^5 - 7*a^8*b*c*d^6))))/(4*(a^9*d^7 - a^2*b^7*c^7 + 7*a^3*b^6*c^6*d - 21*a^4*b^5*c^5*d^2 + 35*a^5*b^4*c^4*d^3 - 35*a^6*b^3*c^3*d^4 + 21*a^7*b^2*c^2*d^5 - 7*a^8*b*c*d^6)))*(7*a*d - 2*b*c))/(4*(a^9*d^7 - a^2*b^7*c^7 + 7*a^3*b^6*c^6*d - 21*a^4*b^5*c^5*d^2 + 35*a^5*b^4*c^4*d^3 - 35*a^6*b^3*c^3*d^4 + 21*a^7*b^2*c^2*d^5 - 7*a^8*b*c*d^6))))*(-b^5*(a*d - b*c)^7)^(1/2)*(7*a*d - 2*b*c)*1i)/(2*(a^9*d^7 - a^2*b^7*c^7 + 7*a^3*b^6*c^6*d - 21*a^4*b^5*c^5*d^2 + 35*a^5*b^4*c^4*d^3 - 35*a^6*b^3*c^3*d^4 + 21*a^7*b^2*c^2*d^5 - 7*a^8*b*c*d^6))","B"
782,0,-1,279,0.000000,"\text{Not used}","int(1/(x^2*(a + b*x^2)^2*(c + d*x^2)^(5/2)),x)","\int \frac{1}{x^2\,{\left(b\,x^2+a\right)}^2\,{\left(d\,x^2+c\right)}^{5/2}} \,d x","Not used",1,"int(1/(x^2*(a + b*x^2)^2*(c + d*x^2)^(5/2)), x)","F"
783,1,5800,304,6.581701,"\text{Not used}","int(1/(x^3*(a + b*x^2)^2*(c + d*x^2)^(5/2)),x)","\frac{\frac{5\,d^3\,\left(d\,x^2+c\right)\,\left(a\,d-2\,b\,c\right)}{3\,{\left(b\,c^2-a\,c\,d\right)}^2}-\frac{d^3}{3\,\left(b\,c^2-a\,c\,d\right)}+\frac{d\,{\left(d\,x^2+c\right)}^2\,\left(15\,a^4\,d^4-58\,a^3\,b\,c\,d^3+64\,a^2\,b^2\,c^2\,d^2-12\,a\,b^3\,c^3\,d+6\,b^4\,c^4\right)}{6\,a^2\,{\left(b\,c^2-a\,c\,d\right)}^3}+\frac{d\,{\left(d\,x^2+c\right)}^3\,\left(a\,d-2\,b\,c\right)\,\left(5\,a^2\,b\,d^2-a\,b^2\,c\,d+b^3\,c^2\right)}{2\,a^2\,{\left(b\,c^2-a\,c\,d\right)}^3}}{b\,{\left(d\,x^2+c\right)}^{7/2}+{\left(d\,x^2+c\right)}^{3/2}\,\left(b\,c^2-a\,c\,d\right)+{\left(d\,x^2+c\right)}^{5/2}\,\left(a\,d-2\,b\,c\right)}-\frac{\mathrm{atan}\left(\frac{a^{19}\,c^{15}\,d^{19}\,\sqrt{d\,x^2+c}\,125{}\mathrm{i}+a^3\,b^{16}\,c^{31}\,d^3\,\sqrt{d\,x^2+c}\,420{}\mathrm{i}-a^4\,b^{15}\,c^{30}\,d^4\,\sqrt{d\,x^2+c}\,4515{}\mathrm{i}+a^5\,b^{14}\,c^{29}\,d^5\,\sqrt{d\,x^2+c}\,20916{}\mathrm{i}-a^6\,b^{13}\,c^{28}\,d^6\,\sqrt{d\,x^2+c}\,52836{}\mathrm{i}+a^7\,b^{12}\,c^{27}\,d^7\,\sqrt{d\,x^2+c}\,71070{}\mathrm{i}-a^8\,b^{11}\,c^{26}\,d^8\,\sqrt{d\,x^2+c}\,19530{}\mathrm{i}-a^9\,b^{10}\,c^{25}\,d^9\,\sqrt{d\,x^2+c}\,107740{}\mathrm{i}+a^{10}\,b^9\,c^{24}\,d^{10}\,\sqrt{d\,x^2+c}\,212608{}\mathrm{i}-a^{11}\,b^8\,c^{23}\,d^{11}\,\sqrt{d\,x^2+c}\,184563{}\mathrm{i}+a^{12}\,b^7\,c^{22}\,d^{12}\,\sqrt{d\,x^2+c}\,40965{}\mathrm{i}+a^{13}\,b^6\,c^{21}\,d^{13}\,\sqrt{d\,x^2+c}\,91560{}\mathrm{i}-a^{14}\,b^5\,c^{20}\,d^{14}\,\sqrt{d\,x^2+c}\,126720{}\mathrm{i}+a^{15}\,b^4\,c^{19}\,d^{15}\,\sqrt{d\,x^2+c}\,87276{}\mathrm{i}-a^{16}\,b^3\,c^{18}\,d^{16}\,\sqrt{d\,x^2+c}\,37776{}\mathrm{i}+a^{17}\,b^2\,c^{17}\,d^{17}\,\sqrt{d\,x^2+c}\,10440{}\mathrm{i}-a^{18}\,b\,c^{16}\,d^{18}\,\sqrt{d\,x^2+c}\,1700{}\mathrm{i}}{c^7\,\sqrt{c^7}\,\left(c^7\,\left(c^7\,\left(212608\,a^{10}\,b^9\,d^{10}-107740\,a^9\,b^{10}\,c\,d^9-19530\,a^8\,b^{11}\,c^2\,d^8+71070\,a^7\,b^{12}\,c^3\,d^7-52836\,a^6\,b^{13}\,c^4\,d^6+20916\,a^5\,b^{14}\,c^5\,d^5-4515\,a^4\,b^{15}\,c^6\,d^4+420\,a^3\,b^{16}\,c^7\,d^3\right)+10440\,a^{17}\,b^2\,d^{17}-37776\,a^{16}\,b^3\,c\,d^{16}-184563\,a^{11}\,b^8\,c^6\,d^{11}+40965\,a^{12}\,b^7\,c^5\,d^{12}+91560\,a^{13}\,b^6\,c^4\,d^{13}-126720\,a^{14}\,b^5\,c^3\,d^{14}+87276\,a^{15}\,b^4\,c^2\,d^{15}\right)+125\,a^{19}\,c^5\,d^{19}-1700\,a^{18}\,b\,c^6\,d^{18}\right)}\right)\,\left(5\,a\,d+4\,b\,c\right)\,1{}\mathrm{i}}{2\,a^3\,\sqrt{c^7}}+\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-b^7\,{\left(a\,d-b\,c\right)}^7}\,\left(\sqrt{d\,x^2+c}\,\left(-400\,a^{23}\,b^3\,c^9\,d^{19}+5360\,a^{22}\,b^4\,c^{10}\,d^{18}-32656\,a^{21}\,b^5\,c^{11}\,d^{17}+118640\,a^{20}\,b^6\,c^{12}\,d^{16}-281680\,a^{19}\,b^7\,c^{13}\,d^{15}+444080\,a^{18}\,b^8\,c^{14}\,d^{14}-430816\,a^{17}\,b^9\,c^{15}\,d^{13}+152384\,a^{16}\,b^{10}\,c^{16}\,d^{12}+205840\,a^{15}\,b^{11}\,c^{17}\,d^{11}-316400\,a^{14}\,b^{12}\,c^{18}\,d^{10}+85360\,a^{13}\,b^{13}\,c^{19}\,d^9+235312\,a^{12}\,b^{14}\,c^{20}\,d^8-363440\,a^{11}\,b^{15}\,c^{21}\,d^7+275920\,a^{10}\,b^{16}\,c^{22}\,d^6-129920\,a^9\,b^{17}\,c^{23}\,d^5+38560\,a^8\,b^{18}\,c^{24}\,d^4-6656\,a^7\,b^{19}\,c^{25}\,d^3+512\,a^6\,b^{20}\,c^{26}\,d^2\right)+\frac{\sqrt{-b^7\,{\left(a\,d-b\,c\right)}^7}\,\left(9\,a\,d-4\,b\,c\right)\,\left(128\,a^{10}\,b^{18}\,c^{28}\,d^3-1792\,a^{11}\,b^{17}\,c^{27}\,d^4+10624\,a^{12}\,b^{16}\,c^{26}\,d^5-33280\,a^{13}\,b^{15}\,c^{25}\,d^6+47936\,a^{14}\,b^{14}\,c^{24}\,d^7+40448\,a^{15}\,b^{13}\,c^{23}\,d^8-368896\,a^{16}\,b^{12}\,c^{22}\,d^9+948992\,a^{17}\,b^{11}\,c^{21}\,d^{10}-1531200\,a^{18}\,b^{10}\,c^{20}\,d^{11}+1754368\,a^{19}\,b^9\,c^{19}\,d^{12}-1485440\,a^{20}\,b^8\,c^{18}\,d^{13}+939008\,a^{21}\,b^7\,c^{17}\,d^{14}-439616\,a^{22}\,b^6\,c^{16}\,d^{15}+148480\,a^{23}\,b^5\,c^{15}\,d^{16}-34304\,a^{24}\,b^4\,c^{14}\,d^{17}+4864\,a^{25}\,b^3\,c^{13}\,d^{18}-320\,a^{26}\,b^2\,c^{12}\,d^{19}-\frac{\sqrt{-b^7\,{\left(a\,d-b\,c\right)}^7}\,\sqrt{d\,x^2+c}\,\left(9\,a\,d-4\,b\,c\right)\,\left(256\,a^{28}\,b^2\,c^{15}\,d^{18}-4352\,a^{27}\,b^3\,c^{16}\,d^{17}+34560\,a^{26}\,b^4\,c^{17}\,d^{16}-170240\,a^{25}\,b^5\,c^{18}\,d^{15}+582400\,a^{24}\,b^6\,c^{19}\,d^{14}-1467648\,a^{23}\,b^7\,c^{20}\,d^{13}+2818816\,a^{22}\,b^8\,c^{21}\,d^{12}-4209920\,a^{21}\,b^9\,c^{22}\,d^{11}+4942080\,a^{20}\,b^{10}\,c^{23}\,d^{10}-4576000\,a^{19}\,b^{11}\,c^{24}\,d^9+3331328\,a^{18}\,b^{12}\,c^{25}\,d^8-1886976\,a^{17}\,b^{13}\,c^{26}\,d^7+815360\,a^{16}\,b^{14}\,c^{27}\,d^6-259840\,a^{15}\,b^{15}\,c^{28}\,d^5+57600\,a^{14}\,b^{16}\,c^{29}\,d^4-7936\,a^{13}\,b^{17}\,c^{30}\,d^3+512\,a^{12}\,b^{18}\,c^{31}\,d^2\right)}{4\,\left(a^{10}\,d^7-7\,a^9\,b\,c\,d^6+21\,a^8\,b^2\,c^2\,d^5-35\,a^7\,b^3\,c^3\,d^4+35\,a^6\,b^4\,c^4\,d^3-21\,a^5\,b^5\,c^5\,d^2+7\,a^4\,b^6\,c^6\,d-a^3\,b^7\,c^7\right)}\right)}{4\,\left(a^{10}\,d^7-7\,a^9\,b\,c\,d^6+21\,a^8\,b^2\,c^2\,d^5-35\,a^7\,b^3\,c^3\,d^4+35\,a^6\,b^4\,c^4\,d^3-21\,a^5\,b^5\,c^5\,d^2+7\,a^4\,b^6\,c^6\,d-a^3\,b^7\,c^7\right)}\right)\,\left(9\,a\,d-4\,b\,c\right)\,1{}\mathrm{i}}{4\,\left(a^{10}\,d^7-7\,a^9\,b\,c\,d^6+21\,a^8\,b^2\,c^2\,d^5-35\,a^7\,b^3\,c^3\,d^4+35\,a^6\,b^4\,c^4\,d^3-21\,a^5\,b^5\,c^5\,d^2+7\,a^4\,b^6\,c^6\,d-a^3\,b^7\,c^7\right)}+\frac{\sqrt{-b^7\,{\left(a\,d-b\,c\right)}^7}\,\left(\sqrt{d\,x^2+c}\,\left(-400\,a^{23}\,b^3\,c^9\,d^{19}+5360\,a^{22}\,b^4\,c^{10}\,d^{18}-32656\,a^{21}\,b^5\,c^{11}\,d^{17}+118640\,a^{20}\,b^6\,c^{12}\,d^{16}-281680\,a^{19}\,b^7\,c^{13}\,d^{15}+444080\,a^{18}\,b^8\,c^{14}\,d^{14}-430816\,a^{17}\,b^9\,c^{15}\,d^{13}+152384\,a^{16}\,b^{10}\,c^{16}\,d^{12}+205840\,a^{15}\,b^{11}\,c^{17}\,d^{11}-316400\,a^{14}\,b^{12}\,c^{18}\,d^{10}+85360\,a^{13}\,b^{13}\,c^{19}\,d^9+235312\,a^{12}\,b^{14}\,c^{20}\,d^8-363440\,a^{11}\,b^{15}\,c^{21}\,d^7+275920\,a^{10}\,b^{16}\,c^{22}\,d^6-129920\,a^9\,b^{17}\,c^{23}\,d^5+38560\,a^8\,b^{18}\,c^{24}\,d^4-6656\,a^7\,b^{19}\,c^{25}\,d^3+512\,a^6\,b^{20}\,c^{26}\,d^2\right)-\frac{\sqrt{-b^7\,{\left(a\,d-b\,c\right)}^7}\,\left(9\,a\,d-4\,b\,c\right)\,\left(128\,a^{10}\,b^{18}\,c^{28}\,d^3-1792\,a^{11}\,b^{17}\,c^{27}\,d^4+10624\,a^{12}\,b^{16}\,c^{26}\,d^5-33280\,a^{13}\,b^{15}\,c^{25}\,d^6+47936\,a^{14}\,b^{14}\,c^{24}\,d^7+40448\,a^{15}\,b^{13}\,c^{23}\,d^8-368896\,a^{16}\,b^{12}\,c^{22}\,d^9+948992\,a^{17}\,b^{11}\,c^{21}\,d^{10}-1531200\,a^{18}\,b^{10}\,c^{20}\,d^{11}+1754368\,a^{19}\,b^9\,c^{19}\,d^{12}-1485440\,a^{20}\,b^8\,c^{18}\,d^{13}+939008\,a^{21}\,b^7\,c^{17}\,d^{14}-439616\,a^{22}\,b^6\,c^{16}\,d^{15}+148480\,a^{23}\,b^5\,c^{15}\,d^{16}-34304\,a^{24}\,b^4\,c^{14}\,d^{17}+4864\,a^{25}\,b^3\,c^{13}\,d^{18}-320\,a^{26}\,b^2\,c^{12}\,d^{19}+\frac{\sqrt{-b^7\,{\left(a\,d-b\,c\right)}^7}\,\sqrt{d\,x^2+c}\,\left(9\,a\,d-4\,b\,c\right)\,\left(256\,a^{28}\,b^2\,c^{15}\,d^{18}-4352\,a^{27}\,b^3\,c^{16}\,d^{17}+34560\,a^{26}\,b^4\,c^{17}\,d^{16}-170240\,a^{25}\,b^5\,c^{18}\,d^{15}+582400\,a^{24}\,b^6\,c^{19}\,d^{14}-1467648\,a^{23}\,b^7\,c^{20}\,d^{13}+2818816\,a^{22}\,b^8\,c^{21}\,d^{12}-4209920\,a^{21}\,b^9\,c^{22}\,d^{11}+4942080\,a^{20}\,b^{10}\,c^{23}\,d^{10}-4576000\,a^{19}\,b^{11}\,c^{24}\,d^9+3331328\,a^{18}\,b^{12}\,c^{25}\,d^8-1886976\,a^{17}\,b^{13}\,c^{26}\,d^7+815360\,a^{16}\,b^{14}\,c^{27}\,d^6-259840\,a^{15}\,b^{15}\,c^{28}\,d^5+57600\,a^{14}\,b^{16}\,c^{29}\,d^4-7936\,a^{13}\,b^{17}\,c^{30}\,d^3+512\,a^{12}\,b^{18}\,c^{31}\,d^2\right)}{4\,\left(a^{10}\,d^7-7\,a^9\,b\,c\,d^6+21\,a^8\,b^2\,c^2\,d^5-35\,a^7\,b^3\,c^3\,d^4+35\,a^6\,b^4\,c^4\,d^3-21\,a^5\,b^5\,c^5\,d^2+7\,a^4\,b^6\,c^6\,d-a^3\,b^7\,c^7\right)}\right)}{4\,\left(a^{10}\,d^7-7\,a^9\,b\,c\,d^6+21\,a^8\,b^2\,c^2\,d^5-35\,a^7\,b^3\,c^3\,d^4+35\,a^6\,b^4\,c^4\,d^3-21\,a^5\,b^5\,c^5\,d^2+7\,a^4\,b^6\,c^6\,d-a^3\,b^7\,c^7\right)}\right)\,\left(9\,a\,d-4\,b\,c\right)\,1{}\mathrm{i}}{4\,\left(a^{10}\,d^7-7\,a^9\,b\,c\,d^6+21\,a^8\,b^2\,c^2\,d^5-35\,a^7\,b^3\,c^3\,d^4+35\,a^6\,b^4\,c^4\,d^3-21\,a^5\,b^5\,c^5\,d^2+7\,a^4\,b^6\,c^6\,d-a^3\,b^7\,c^7\right)}}{256\,a^4\,b^{20}\,c^{23}\,d^3-2944\,a^5\,b^{19}\,c^{22}\,d^4+16048\,a^6\,b^{18}\,c^{21}\,d^5-55160\,a^7\,b^{17}\,c^{20}\,d^6+130000\,a^8\,b^{16}\,c^{19}\,d^7-206112\,a^9\,b^{15}\,c^{18}\,d^8+182808\,a^{10}\,b^{14}\,c^{17}\,d^9+23664\,a^{11}\,b^{13}\,c^{16}\,d^{10}-332160\,a^{12}\,b^{12}\,c^{15}\,d^{11}+519200\,a^{13}\,b^{11}\,c^{14}\,d^{12}-460544\,a^{14}\,b^{10}\,c^{13}\,d^{13}+260936\,a^{15}\,b^9\,c^{12}\,d^{14}-93712\,a^{16}\,b^8\,c^{11}\,d^{15}+19520\,a^{17}\,b^7\,c^{10}\,d^{16}-1800\,a^{18}\,b^6\,c^9\,d^{17}-\frac{\sqrt{-b^7\,{\left(a\,d-b\,c\right)}^7}\,\left(\sqrt{d\,x^2+c}\,\left(-400\,a^{23}\,b^3\,c^9\,d^{19}+5360\,a^{22}\,b^4\,c^{10}\,d^{18}-32656\,a^{21}\,b^5\,c^{11}\,d^{17}+118640\,a^{20}\,b^6\,c^{12}\,d^{16}-281680\,a^{19}\,b^7\,c^{13}\,d^{15}+444080\,a^{18}\,b^8\,c^{14}\,d^{14}-430816\,a^{17}\,b^9\,c^{15}\,d^{13}+152384\,a^{16}\,b^{10}\,c^{16}\,d^{12}+205840\,a^{15}\,b^{11}\,c^{17}\,d^{11}-316400\,a^{14}\,b^{12}\,c^{18}\,d^{10}+85360\,a^{13}\,b^{13}\,c^{19}\,d^9+235312\,a^{12}\,b^{14}\,c^{20}\,d^8-363440\,a^{11}\,b^{15}\,c^{21}\,d^7+275920\,a^{10}\,b^{16}\,c^{22}\,d^6-129920\,a^9\,b^{17}\,c^{23}\,d^5+38560\,a^8\,b^{18}\,c^{24}\,d^4-6656\,a^7\,b^{19}\,c^{25}\,d^3+512\,a^6\,b^{20}\,c^{26}\,d^2\right)+\frac{\sqrt{-b^7\,{\left(a\,d-b\,c\right)}^7}\,\left(9\,a\,d-4\,b\,c\right)\,\left(128\,a^{10}\,b^{18}\,c^{28}\,d^3-1792\,a^{11}\,b^{17}\,c^{27}\,d^4+10624\,a^{12}\,b^{16}\,c^{26}\,d^5-33280\,a^{13}\,b^{15}\,c^{25}\,d^6+47936\,a^{14}\,b^{14}\,c^{24}\,d^7+40448\,a^{15}\,b^{13}\,c^{23}\,d^8-368896\,a^{16}\,b^{12}\,c^{22}\,d^9+948992\,a^{17}\,b^{11}\,c^{21}\,d^{10}-1531200\,a^{18}\,b^{10}\,c^{20}\,d^{11}+1754368\,a^{19}\,b^9\,c^{19}\,d^{12}-1485440\,a^{20}\,b^8\,c^{18}\,d^{13}+939008\,a^{21}\,b^7\,c^{17}\,d^{14}-439616\,a^{22}\,b^6\,c^{16}\,d^{15}+148480\,a^{23}\,b^5\,c^{15}\,d^{16}-34304\,a^{24}\,b^4\,c^{14}\,d^{17}+4864\,a^{25}\,b^3\,c^{13}\,d^{18}-320\,a^{26}\,b^2\,c^{12}\,d^{19}-\frac{\sqrt{-b^7\,{\left(a\,d-b\,c\right)}^7}\,\sqrt{d\,x^2+c}\,\left(9\,a\,d-4\,b\,c\right)\,\left(256\,a^{28}\,b^2\,c^{15}\,d^{18}-4352\,a^{27}\,b^3\,c^{16}\,d^{17}+34560\,a^{26}\,b^4\,c^{17}\,d^{16}-170240\,a^{25}\,b^5\,c^{18}\,d^{15}+582400\,a^{24}\,b^6\,c^{19}\,d^{14}-1467648\,a^{23}\,b^7\,c^{20}\,d^{13}+2818816\,a^{22}\,b^8\,c^{21}\,d^{12}-4209920\,a^{21}\,b^9\,c^{22}\,d^{11}+4942080\,a^{20}\,b^{10}\,c^{23}\,d^{10}-4576000\,a^{19}\,b^{11}\,c^{24}\,d^9+3331328\,a^{18}\,b^{12}\,c^{25}\,d^8-1886976\,a^{17}\,b^{13}\,c^{26}\,d^7+815360\,a^{16}\,b^{14}\,c^{27}\,d^6-259840\,a^{15}\,b^{15}\,c^{28}\,d^5+57600\,a^{14}\,b^{16}\,c^{29}\,d^4-7936\,a^{13}\,b^{17}\,c^{30}\,d^3+512\,a^{12}\,b^{18}\,c^{31}\,d^2\right)}{4\,\left(a^{10}\,d^7-7\,a^9\,b\,c\,d^6+21\,a^8\,b^2\,c^2\,d^5-35\,a^7\,b^3\,c^3\,d^4+35\,a^6\,b^4\,c^4\,d^3-21\,a^5\,b^5\,c^5\,d^2+7\,a^4\,b^6\,c^6\,d-a^3\,b^7\,c^7\right)}\right)}{4\,\left(a^{10}\,d^7-7\,a^9\,b\,c\,d^6+21\,a^8\,b^2\,c^2\,d^5-35\,a^7\,b^3\,c^3\,d^4+35\,a^6\,b^4\,c^4\,d^3-21\,a^5\,b^5\,c^5\,d^2+7\,a^4\,b^6\,c^6\,d-a^3\,b^7\,c^7\right)}\right)\,\left(9\,a\,d-4\,b\,c\right)}{4\,\left(a^{10}\,d^7-7\,a^9\,b\,c\,d^6+21\,a^8\,b^2\,c^2\,d^5-35\,a^7\,b^3\,c^3\,d^4+35\,a^6\,b^4\,c^4\,d^3-21\,a^5\,b^5\,c^5\,d^2+7\,a^4\,b^6\,c^6\,d-a^3\,b^7\,c^7\right)}+\frac{\sqrt{-b^7\,{\left(a\,d-b\,c\right)}^7}\,\left(\sqrt{d\,x^2+c}\,\left(-400\,a^{23}\,b^3\,c^9\,d^{19}+5360\,a^{22}\,b^4\,c^{10}\,d^{18}-32656\,a^{21}\,b^5\,c^{11}\,d^{17}+118640\,a^{20}\,b^6\,c^{12}\,d^{16}-281680\,a^{19}\,b^7\,c^{13}\,d^{15}+444080\,a^{18}\,b^8\,c^{14}\,d^{14}-430816\,a^{17}\,b^9\,c^{15}\,d^{13}+152384\,a^{16}\,b^{10}\,c^{16}\,d^{12}+205840\,a^{15}\,b^{11}\,c^{17}\,d^{11}-316400\,a^{14}\,b^{12}\,c^{18}\,d^{10}+85360\,a^{13}\,b^{13}\,c^{19}\,d^9+235312\,a^{12}\,b^{14}\,c^{20}\,d^8-363440\,a^{11}\,b^{15}\,c^{21}\,d^7+275920\,a^{10}\,b^{16}\,c^{22}\,d^6-129920\,a^9\,b^{17}\,c^{23}\,d^5+38560\,a^8\,b^{18}\,c^{24}\,d^4-6656\,a^7\,b^{19}\,c^{25}\,d^3+512\,a^6\,b^{20}\,c^{26}\,d^2\right)-\frac{\sqrt{-b^7\,{\left(a\,d-b\,c\right)}^7}\,\left(9\,a\,d-4\,b\,c\right)\,\left(128\,a^{10}\,b^{18}\,c^{28}\,d^3-1792\,a^{11}\,b^{17}\,c^{27}\,d^4+10624\,a^{12}\,b^{16}\,c^{26}\,d^5-33280\,a^{13}\,b^{15}\,c^{25}\,d^6+47936\,a^{14}\,b^{14}\,c^{24}\,d^7+40448\,a^{15}\,b^{13}\,c^{23}\,d^8-368896\,a^{16}\,b^{12}\,c^{22}\,d^9+948992\,a^{17}\,b^{11}\,c^{21}\,d^{10}-1531200\,a^{18}\,b^{10}\,c^{20}\,d^{11}+1754368\,a^{19}\,b^9\,c^{19}\,d^{12}-1485440\,a^{20}\,b^8\,c^{18}\,d^{13}+939008\,a^{21}\,b^7\,c^{17}\,d^{14}-439616\,a^{22}\,b^6\,c^{16}\,d^{15}+148480\,a^{23}\,b^5\,c^{15}\,d^{16}-34304\,a^{24}\,b^4\,c^{14}\,d^{17}+4864\,a^{25}\,b^3\,c^{13}\,d^{18}-320\,a^{26}\,b^2\,c^{12}\,d^{19}+\frac{\sqrt{-b^7\,{\left(a\,d-b\,c\right)}^7}\,\sqrt{d\,x^2+c}\,\left(9\,a\,d-4\,b\,c\right)\,\left(256\,a^{28}\,b^2\,c^{15}\,d^{18}-4352\,a^{27}\,b^3\,c^{16}\,d^{17}+34560\,a^{26}\,b^4\,c^{17}\,d^{16}-170240\,a^{25}\,b^5\,c^{18}\,d^{15}+582400\,a^{24}\,b^6\,c^{19}\,d^{14}-1467648\,a^{23}\,b^7\,c^{20}\,d^{13}+2818816\,a^{22}\,b^8\,c^{21}\,d^{12}-4209920\,a^{21}\,b^9\,c^{22}\,d^{11}+4942080\,a^{20}\,b^{10}\,c^{23}\,d^{10}-4576000\,a^{19}\,b^{11}\,c^{24}\,d^9+3331328\,a^{18}\,b^{12}\,c^{25}\,d^8-1886976\,a^{17}\,b^{13}\,c^{26}\,d^7+815360\,a^{16}\,b^{14}\,c^{27}\,d^6-259840\,a^{15}\,b^{15}\,c^{28}\,d^5+57600\,a^{14}\,b^{16}\,c^{29}\,d^4-7936\,a^{13}\,b^{17}\,c^{30}\,d^3+512\,a^{12}\,b^{18}\,c^{31}\,d^2\right)}{4\,\left(a^{10}\,d^7-7\,a^9\,b\,c\,d^6+21\,a^8\,b^2\,c^2\,d^5-35\,a^7\,b^3\,c^3\,d^4+35\,a^6\,b^4\,c^4\,d^3-21\,a^5\,b^5\,c^5\,d^2+7\,a^4\,b^6\,c^6\,d-a^3\,b^7\,c^7\right)}\right)}{4\,\left(a^{10}\,d^7-7\,a^9\,b\,c\,d^6+21\,a^8\,b^2\,c^2\,d^5-35\,a^7\,b^3\,c^3\,d^4+35\,a^6\,b^4\,c^4\,d^3-21\,a^5\,b^5\,c^5\,d^2+7\,a^4\,b^6\,c^6\,d-a^3\,b^7\,c^7\right)}\right)\,\left(9\,a\,d-4\,b\,c\right)}{4\,\left(a^{10}\,d^7-7\,a^9\,b\,c\,d^6+21\,a^8\,b^2\,c^2\,d^5-35\,a^7\,b^3\,c^3\,d^4+35\,a^6\,b^4\,c^4\,d^3-21\,a^5\,b^5\,c^5\,d^2+7\,a^4\,b^6\,c^6\,d-a^3\,b^7\,c^7\right)}}\right)\,\sqrt{-b^7\,{\left(a\,d-b\,c\right)}^7}\,\left(9\,a\,d-4\,b\,c\right)\,1{}\mathrm{i}}{2\,\left(a^{10}\,d^7-7\,a^9\,b\,c\,d^6+21\,a^8\,b^2\,c^2\,d^5-35\,a^7\,b^3\,c^3\,d^4+35\,a^6\,b^4\,c^4\,d^3-21\,a^5\,b^5\,c^5\,d^2+7\,a^4\,b^6\,c^6\,d-a^3\,b^7\,c^7\right)}","Not used",1,"((5*d^3*(c + d*x^2)*(a*d - 2*b*c))/(3*(b*c^2 - a*c*d)^2) - d^3/(3*(b*c^2 - a*c*d)) + (d*(c + d*x^2)^2*(15*a^4*d^4 + 6*b^4*c^4 + 64*a^2*b^2*c^2*d^2 - 12*a*b^3*c^3*d - 58*a^3*b*c*d^3))/(6*a^2*(b*c^2 - a*c*d)^3) + (d*(c + d*x^2)^3*(a*d - 2*b*c)*(b^3*c^2 + 5*a^2*b*d^2 - a*b^2*c*d))/(2*a^2*(b*c^2 - a*c*d)^3))/(b*(c + d*x^2)^(7/2) + (c + d*x^2)^(3/2)*(b*c^2 - a*c*d) + (c + d*x^2)^(5/2)*(a*d - 2*b*c)) - (atan((a^19*c^15*d^19*(c + d*x^2)^(1/2)*125i + a^3*b^16*c^31*d^3*(c + d*x^2)^(1/2)*420i - a^4*b^15*c^30*d^4*(c + d*x^2)^(1/2)*4515i + a^5*b^14*c^29*d^5*(c + d*x^2)^(1/2)*20916i - a^6*b^13*c^28*d^6*(c + d*x^2)^(1/2)*52836i + a^7*b^12*c^27*d^7*(c + d*x^2)^(1/2)*71070i - a^8*b^11*c^26*d^8*(c + d*x^2)^(1/2)*19530i - a^9*b^10*c^25*d^9*(c + d*x^2)^(1/2)*107740i + a^10*b^9*c^24*d^10*(c + d*x^2)^(1/2)*212608i - a^11*b^8*c^23*d^11*(c + d*x^2)^(1/2)*184563i + a^12*b^7*c^22*d^12*(c + d*x^2)^(1/2)*40965i + a^13*b^6*c^21*d^13*(c + d*x^2)^(1/2)*91560i - a^14*b^5*c^20*d^14*(c + d*x^2)^(1/2)*126720i + a^15*b^4*c^19*d^15*(c + d*x^2)^(1/2)*87276i - a^16*b^3*c^18*d^16*(c + d*x^2)^(1/2)*37776i + a^17*b^2*c^17*d^17*(c + d*x^2)^(1/2)*10440i - a^18*b*c^16*d^18*(c + d*x^2)^(1/2)*1700i)/(c^7*(c^7)^(1/2)*(c^7*(c^7*(212608*a^10*b^9*d^10 - 107740*a^9*b^10*c*d^9 + 420*a^3*b^16*c^7*d^3 - 4515*a^4*b^15*c^6*d^4 + 20916*a^5*b^14*c^5*d^5 - 52836*a^6*b^13*c^4*d^6 + 71070*a^7*b^12*c^3*d^7 - 19530*a^8*b^11*c^2*d^8) + 10440*a^17*b^2*d^17 - 37776*a^16*b^3*c*d^16 - 184563*a^11*b^8*c^6*d^11 + 40965*a^12*b^7*c^5*d^12 + 91560*a^13*b^6*c^4*d^13 - 126720*a^14*b^5*c^3*d^14 + 87276*a^15*b^4*c^2*d^15) + 125*a^19*c^5*d^19 - 1700*a^18*b*c^6*d^18)))*(5*a*d + 4*b*c)*1i)/(2*a^3*(c^7)^(1/2)) + (atan((((-b^7*(a*d - b*c)^7)^(1/2)*((c + d*x^2)^(1/2)*(512*a^6*b^20*c^26*d^2 - 6656*a^7*b^19*c^25*d^3 + 38560*a^8*b^18*c^24*d^4 - 129920*a^9*b^17*c^23*d^5 + 275920*a^10*b^16*c^22*d^6 - 363440*a^11*b^15*c^21*d^7 + 235312*a^12*b^14*c^20*d^8 + 85360*a^13*b^13*c^19*d^9 - 316400*a^14*b^12*c^18*d^10 + 205840*a^15*b^11*c^17*d^11 + 152384*a^16*b^10*c^16*d^12 - 430816*a^17*b^9*c^15*d^13 + 444080*a^18*b^8*c^14*d^14 - 281680*a^19*b^7*c^13*d^15 + 118640*a^20*b^6*c^12*d^16 - 32656*a^21*b^5*c^11*d^17 + 5360*a^22*b^4*c^10*d^18 - 400*a^23*b^3*c^9*d^19) + ((-b^7*(a*d - b*c)^7)^(1/2)*(9*a*d - 4*b*c)*(128*a^10*b^18*c^28*d^3 - 1792*a^11*b^17*c^27*d^4 + 10624*a^12*b^16*c^26*d^5 - 33280*a^13*b^15*c^25*d^6 + 47936*a^14*b^14*c^24*d^7 + 40448*a^15*b^13*c^23*d^8 - 368896*a^16*b^12*c^22*d^9 + 948992*a^17*b^11*c^21*d^10 - 1531200*a^18*b^10*c^20*d^11 + 1754368*a^19*b^9*c^19*d^12 - 1485440*a^20*b^8*c^18*d^13 + 939008*a^21*b^7*c^17*d^14 - 439616*a^22*b^6*c^16*d^15 + 148480*a^23*b^5*c^15*d^16 - 34304*a^24*b^4*c^14*d^17 + 4864*a^25*b^3*c^13*d^18 - 320*a^26*b^2*c^12*d^19 - ((-b^7*(a*d - b*c)^7)^(1/2)*(c + d*x^2)^(1/2)*(9*a*d - 4*b*c)*(512*a^12*b^18*c^31*d^2 - 7936*a^13*b^17*c^30*d^3 + 57600*a^14*b^16*c^29*d^4 - 259840*a^15*b^15*c^28*d^5 + 815360*a^16*b^14*c^27*d^6 - 1886976*a^17*b^13*c^26*d^7 + 3331328*a^18*b^12*c^25*d^8 - 4576000*a^19*b^11*c^24*d^9 + 4942080*a^20*b^10*c^23*d^10 - 4209920*a^21*b^9*c^22*d^11 + 2818816*a^22*b^8*c^21*d^12 - 1467648*a^23*b^7*c^20*d^13 + 582400*a^24*b^6*c^19*d^14 - 170240*a^25*b^5*c^18*d^15 + 34560*a^26*b^4*c^17*d^16 - 4352*a^27*b^3*c^16*d^17 + 256*a^28*b^2*c^15*d^18))/(4*(a^10*d^7 - a^3*b^7*c^7 + 7*a^4*b^6*c^6*d - 21*a^5*b^5*c^5*d^2 + 35*a^6*b^4*c^4*d^3 - 35*a^7*b^3*c^3*d^4 + 21*a^8*b^2*c^2*d^5 - 7*a^9*b*c*d^6))))/(4*(a^10*d^7 - a^3*b^7*c^7 + 7*a^4*b^6*c^6*d - 21*a^5*b^5*c^5*d^2 + 35*a^6*b^4*c^4*d^3 - 35*a^7*b^3*c^3*d^4 + 21*a^8*b^2*c^2*d^5 - 7*a^9*b*c*d^6)))*(9*a*d - 4*b*c)*1i)/(4*(a^10*d^7 - a^3*b^7*c^7 + 7*a^4*b^6*c^6*d - 21*a^5*b^5*c^5*d^2 + 35*a^6*b^4*c^4*d^3 - 35*a^7*b^3*c^3*d^4 + 21*a^8*b^2*c^2*d^5 - 7*a^9*b*c*d^6)) + ((-b^7*(a*d - b*c)^7)^(1/2)*((c + d*x^2)^(1/2)*(512*a^6*b^20*c^26*d^2 - 6656*a^7*b^19*c^25*d^3 + 38560*a^8*b^18*c^24*d^4 - 129920*a^9*b^17*c^23*d^5 + 275920*a^10*b^16*c^22*d^6 - 363440*a^11*b^15*c^21*d^7 + 235312*a^12*b^14*c^20*d^8 + 85360*a^13*b^13*c^19*d^9 - 316400*a^14*b^12*c^18*d^10 + 205840*a^15*b^11*c^17*d^11 + 152384*a^16*b^10*c^16*d^12 - 430816*a^17*b^9*c^15*d^13 + 444080*a^18*b^8*c^14*d^14 - 281680*a^19*b^7*c^13*d^15 + 118640*a^20*b^6*c^12*d^16 - 32656*a^21*b^5*c^11*d^17 + 5360*a^22*b^4*c^10*d^18 - 400*a^23*b^3*c^9*d^19) - ((-b^7*(a*d - b*c)^7)^(1/2)*(9*a*d - 4*b*c)*(128*a^10*b^18*c^28*d^3 - 1792*a^11*b^17*c^27*d^4 + 10624*a^12*b^16*c^26*d^5 - 33280*a^13*b^15*c^25*d^6 + 47936*a^14*b^14*c^24*d^7 + 40448*a^15*b^13*c^23*d^8 - 368896*a^16*b^12*c^22*d^9 + 948992*a^17*b^11*c^21*d^10 - 1531200*a^18*b^10*c^20*d^11 + 1754368*a^19*b^9*c^19*d^12 - 1485440*a^20*b^8*c^18*d^13 + 939008*a^21*b^7*c^17*d^14 - 439616*a^22*b^6*c^16*d^15 + 148480*a^23*b^5*c^15*d^16 - 34304*a^24*b^4*c^14*d^17 + 4864*a^25*b^3*c^13*d^18 - 320*a^26*b^2*c^12*d^19 + ((-b^7*(a*d - b*c)^7)^(1/2)*(c + d*x^2)^(1/2)*(9*a*d - 4*b*c)*(512*a^12*b^18*c^31*d^2 - 7936*a^13*b^17*c^30*d^3 + 57600*a^14*b^16*c^29*d^4 - 259840*a^15*b^15*c^28*d^5 + 815360*a^16*b^14*c^27*d^6 - 1886976*a^17*b^13*c^26*d^7 + 3331328*a^18*b^12*c^25*d^8 - 4576000*a^19*b^11*c^24*d^9 + 4942080*a^20*b^10*c^23*d^10 - 4209920*a^21*b^9*c^22*d^11 + 2818816*a^22*b^8*c^21*d^12 - 1467648*a^23*b^7*c^20*d^13 + 582400*a^24*b^6*c^19*d^14 - 170240*a^25*b^5*c^18*d^15 + 34560*a^26*b^4*c^17*d^16 - 4352*a^27*b^3*c^16*d^17 + 256*a^28*b^2*c^15*d^18))/(4*(a^10*d^7 - a^3*b^7*c^7 + 7*a^4*b^6*c^6*d - 21*a^5*b^5*c^5*d^2 + 35*a^6*b^4*c^4*d^3 - 35*a^7*b^3*c^3*d^4 + 21*a^8*b^2*c^2*d^5 - 7*a^9*b*c*d^6))))/(4*(a^10*d^7 - a^3*b^7*c^7 + 7*a^4*b^6*c^6*d - 21*a^5*b^5*c^5*d^2 + 35*a^6*b^4*c^4*d^3 - 35*a^7*b^3*c^3*d^4 + 21*a^8*b^2*c^2*d^5 - 7*a^9*b*c*d^6)))*(9*a*d - 4*b*c)*1i)/(4*(a^10*d^7 - a^3*b^7*c^7 + 7*a^4*b^6*c^6*d - 21*a^5*b^5*c^5*d^2 + 35*a^6*b^4*c^4*d^3 - 35*a^7*b^3*c^3*d^4 + 21*a^8*b^2*c^2*d^5 - 7*a^9*b*c*d^6)))/(256*a^4*b^20*c^23*d^3 - 2944*a^5*b^19*c^22*d^4 + 16048*a^6*b^18*c^21*d^5 - 55160*a^7*b^17*c^20*d^6 + 130000*a^8*b^16*c^19*d^7 - 206112*a^9*b^15*c^18*d^8 + 182808*a^10*b^14*c^17*d^9 + 23664*a^11*b^13*c^16*d^10 - 332160*a^12*b^12*c^15*d^11 + 519200*a^13*b^11*c^14*d^12 - 460544*a^14*b^10*c^13*d^13 + 260936*a^15*b^9*c^12*d^14 - 93712*a^16*b^8*c^11*d^15 + 19520*a^17*b^7*c^10*d^16 - 1800*a^18*b^6*c^9*d^17 - ((-b^7*(a*d - b*c)^7)^(1/2)*((c + d*x^2)^(1/2)*(512*a^6*b^20*c^26*d^2 - 6656*a^7*b^19*c^25*d^3 + 38560*a^8*b^18*c^24*d^4 - 129920*a^9*b^17*c^23*d^5 + 275920*a^10*b^16*c^22*d^6 - 363440*a^11*b^15*c^21*d^7 + 235312*a^12*b^14*c^20*d^8 + 85360*a^13*b^13*c^19*d^9 - 316400*a^14*b^12*c^18*d^10 + 205840*a^15*b^11*c^17*d^11 + 152384*a^16*b^10*c^16*d^12 - 430816*a^17*b^9*c^15*d^13 + 444080*a^18*b^8*c^14*d^14 - 281680*a^19*b^7*c^13*d^15 + 118640*a^20*b^6*c^12*d^16 - 32656*a^21*b^5*c^11*d^17 + 5360*a^22*b^4*c^10*d^18 - 400*a^23*b^3*c^9*d^19) + ((-b^7*(a*d - b*c)^7)^(1/2)*(9*a*d - 4*b*c)*(128*a^10*b^18*c^28*d^3 - 1792*a^11*b^17*c^27*d^4 + 10624*a^12*b^16*c^26*d^5 - 33280*a^13*b^15*c^25*d^6 + 47936*a^14*b^14*c^24*d^7 + 40448*a^15*b^13*c^23*d^8 - 368896*a^16*b^12*c^22*d^9 + 948992*a^17*b^11*c^21*d^10 - 1531200*a^18*b^10*c^20*d^11 + 1754368*a^19*b^9*c^19*d^12 - 1485440*a^20*b^8*c^18*d^13 + 939008*a^21*b^7*c^17*d^14 - 439616*a^22*b^6*c^16*d^15 + 148480*a^23*b^5*c^15*d^16 - 34304*a^24*b^4*c^14*d^17 + 4864*a^25*b^3*c^13*d^18 - 320*a^26*b^2*c^12*d^19 - ((-b^7*(a*d - b*c)^7)^(1/2)*(c + d*x^2)^(1/2)*(9*a*d - 4*b*c)*(512*a^12*b^18*c^31*d^2 - 7936*a^13*b^17*c^30*d^3 + 57600*a^14*b^16*c^29*d^4 - 259840*a^15*b^15*c^28*d^5 + 815360*a^16*b^14*c^27*d^6 - 1886976*a^17*b^13*c^26*d^7 + 3331328*a^18*b^12*c^25*d^8 - 4576000*a^19*b^11*c^24*d^9 + 4942080*a^20*b^10*c^23*d^10 - 4209920*a^21*b^9*c^22*d^11 + 2818816*a^22*b^8*c^21*d^12 - 1467648*a^23*b^7*c^20*d^13 + 582400*a^24*b^6*c^19*d^14 - 170240*a^25*b^5*c^18*d^15 + 34560*a^26*b^4*c^17*d^16 - 4352*a^27*b^3*c^16*d^17 + 256*a^28*b^2*c^15*d^18))/(4*(a^10*d^7 - a^3*b^7*c^7 + 7*a^4*b^6*c^6*d - 21*a^5*b^5*c^5*d^2 + 35*a^6*b^4*c^4*d^3 - 35*a^7*b^3*c^3*d^4 + 21*a^8*b^2*c^2*d^5 - 7*a^9*b*c*d^6))))/(4*(a^10*d^7 - a^3*b^7*c^7 + 7*a^4*b^6*c^6*d - 21*a^5*b^5*c^5*d^2 + 35*a^6*b^4*c^4*d^3 - 35*a^7*b^3*c^3*d^4 + 21*a^8*b^2*c^2*d^5 - 7*a^9*b*c*d^6)))*(9*a*d - 4*b*c))/(4*(a^10*d^7 - a^3*b^7*c^7 + 7*a^4*b^6*c^6*d - 21*a^5*b^5*c^5*d^2 + 35*a^6*b^4*c^4*d^3 - 35*a^7*b^3*c^3*d^4 + 21*a^8*b^2*c^2*d^5 - 7*a^9*b*c*d^6)) + ((-b^7*(a*d - b*c)^7)^(1/2)*((c + d*x^2)^(1/2)*(512*a^6*b^20*c^26*d^2 - 6656*a^7*b^19*c^25*d^3 + 38560*a^8*b^18*c^24*d^4 - 129920*a^9*b^17*c^23*d^5 + 275920*a^10*b^16*c^22*d^6 - 363440*a^11*b^15*c^21*d^7 + 235312*a^12*b^14*c^20*d^8 + 85360*a^13*b^13*c^19*d^9 - 316400*a^14*b^12*c^18*d^10 + 205840*a^15*b^11*c^17*d^11 + 152384*a^16*b^10*c^16*d^12 - 430816*a^17*b^9*c^15*d^13 + 444080*a^18*b^8*c^14*d^14 - 281680*a^19*b^7*c^13*d^15 + 118640*a^20*b^6*c^12*d^16 - 32656*a^21*b^5*c^11*d^17 + 5360*a^22*b^4*c^10*d^18 - 400*a^23*b^3*c^9*d^19) - ((-b^7*(a*d - b*c)^7)^(1/2)*(9*a*d - 4*b*c)*(128*a^10*b^18*c^28*d^3 - 1792*a^11*b^17*c^27*d^4 + 10624*a^12*b^16*c^26*d^5 - 33280*a^13*b^15*c^25*d^6 + 47936*a^14*b^14*c^24*d^7 + 40448*a^15*b^13*c^23*d^8 - 368896*a^16*b^12*c^22*d^9 + 948992*a^17*b^11*c^21*d^10 - 1531200*a^18*b^10*c^20*d^11 + 1754368*a^19*b^9*c^19*d^12 - 1485440*a^20*b^8*c^18*d^13 + 939008*a^21*b^7*c^17*d^14 - 439616*a^22*b^6*c^16*d^15 + 148480*a^23*b^5*c^15*d^16 - 34304*a^24*b^4*c^14*d^17 + 4864*a^25*b^3*c^13*d^18 - 320*a^26*b^2*c^12*d^19 + ((-b^7*(a*d - b*c)^7)^(1/2)*(c + d*x^2)^(1/2)*(9*a*d - 4*b*c)*(512*a^12*b^18*c^31*d^2 - 7936*a^13*b^17*c^30*d^3 + 57600*a^14*b^16*c^29*d^4 - 259840*a^15*b^15*c^28*d^5 + 815360*a^16*b^14*c^27*d^6 - 1886976*a^17*b^13*c^26*d^7 + 3331328*a^18*b^12*c^25*d^8 - 4576000*a^19*b^11*c^24*d^9 + 4942080*a^20*b^10*c^23*d^10 - 4209920*a^21*b^9*c^22*d^11 + 2818816*a^22*b^8*c^21*d^12 - 1467648*a^23*b^7*c^20*d^13 + 582400*a^24*b^6*c^19*d^14 - 170240*a^25*b^5*c^18*d^15 + 34560*a^26*b^4*c^17*d^16 - 4352*a^27*b^3*c^16*d^17 + 256*a^28*b^2*c^15*d^18))/(4*(a^10*d^7 - a^3*b^7*c^7 + 7*a^4*b^6*c^6*d - 21*a^5*b^5*c^5*d^2 + 35*a^6*b^4*c^4*d^3 - 35*a^7*b^3*c^3*d^4 + 21*a^8*b^2*c^2*d^5 - 7*a^9*b*c*d^6))))/(4*(a^10*d^7 - a^3*b^7*c^7 + 7*a^4*b^6*c^6*d - 21*a^5*b^5*c^5*d^2 + 35*a^6*b^4*c^4*d^3 - 35*a^7*b^3*c^3*d^4 + 21*a^8*b^2*c^2*d^5 - 7*a^9*b*c*d^6)))*(9*a*d - 4*b*c))/(4*(a^10*d^7 - a^3*b^7*c^7 + 7*a^4*b^6*c^6*d - 21*a^5*b^5*c^5*d^2 + 35*a^6*b^4*c^4*d^3 - 35*a^7*b^3*c^3*d^4 + 21*a^8*b^2*c^2*d^5 - 7*a^9*b*c*d^6))))*(-b^7*(a*d - b*c)^7)^(1/2)*(9*a*d - 4*b*c)*1i)/(2*(a^10*d^7 - a^3*b^7*c^7 + 7*a^4*b^6*c^6*d - 21*a^5*b^5*c^5*d^2 + 35*a^6*b^4*c^4*d^3 - 35*a^7*b^3*c^3*d^4 + 21*a^8*b^2*c^2*d^5 - 7*a^9*b*c*d^6))","B"
784,0,-1,362,0.000000,"\text{Not used}","int(1/(x^4*(a + b*x^2)^2*(c + d*x^2)^(5/2)),x)","\int \frac{1}{x^4\,{\left(b\,x^2+a\right)}^2\,{\left(d\,x^2+c\right)}^{5/2}} \,d x","Not used",1,"int(1/(x^4*(a + b*x^2)^2*(c + d*x^2)^(5/2)), x)","F"
785,0,-1,212,0.000000,"\text{Not used}","int((A + B*x^2)*(e*x)^(3/2)*(a + b*x^2)^(1/2),x)","\int \left(B\,x^2+A\right)\,{\left(e\,x\right)}^{3/2}\,\sqrt{b\,x^2+a} \,d x","Not used",1,"int((A + B*x^2)*(e*x)^(3/2)*(a + b*x^2)^(1/2), x)","F"
786,0,-1,337,0.000000,"\text{Not used}","int((A + B*x^2)*(e*x)^(1/2)*(a + b*x^2)^(1/2),x)","\int \left(B\,x^2+A\right)\,\sqrt{e\,x}\,\sqrt{b\,x^2+a} \,d x","Not used",1,"int((A + B*x^2)*(e*x)^(1/2)*(a + b*x^2)^(1/2), x)","F"
787,0,-1,176,0.000000,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^(1/2))/(e*x)^(1/2),x)","\int \frac{\left(B\,x^2+A\right)\,\sqrt{b\,x^2+a}}{\sqrt{e\,x}} \,d x","Not used",1,"int(((A + B*x^2)*(a + b*x^2)^(1/2))/(e*x)^(1/2), x)","F"
788,0,-1,333,0.000000,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^(1/2))/(e*x)^(3/2),x)","\int \frac{\left(B\,x^2+A\right)\,\sqrt{b\,x^2+a}}{{\left(e\,x\right)}^{3/2}} \,d x","Not used",1,"int(((A + B*x^2)*(a + b*x^2)^(1/2))/(e*x)^(3/2), x)","F"
789,0,-1,172,0.000000,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^(1/2))/(e*x)^(5/2),x)","\int \frac{\left(B\,x^2+A\right)\,\sqrt{b\,x^2+a}}{{\left(e\,x\right)}^{5/2}} \,d x","Not used",1,"int(((A + B*x^2)*(a + b*x^2)^(1/2))/(e*x)^(5/2), x)","F"
790,0,-1,338,0.000000,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^(1/2))/(e*x)^(7/2),x)","\int \frac{\left(B\,x^2+A\right)\,\sqrt{b\,x^2+a}}{{\left(e\,x\right)}^{7/2}} \,d x","Not used",1,"int(((A + B*x^2)*(a + b*x^2)^(1/2))/(e*x)^(7/2), x)","F"
791,0,-1,152,0.000000,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^(1/2))/x^(9/2),x)","\int \frac{\left(B\,x^2+A\right)\,\sqrt{b\,x^2+a}}{x^{9/2}} \,d x","Not used",1,"int(((A + B*x^2)*(a + b*x^2)^(1/2))/x^(9/2), x)","F"
792,0,-1,331,0.000000,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^(1/2))/x^(11/2),x)","\int \frac{\left(B\,x^2+A\right)\,\sqrt{b\,x^2+a}}{x^{11/2}} \,d x","Not used",1,"int(((A + B*x^2)*(a + b*x^2)^(1/2))/x^(11/2), x)","F"
793,0,-1,187,0.000000,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^(1/2))/x^(13/2),x)","\int \frac{\left(B\,x^2+A\right)\,\sqrt{b\,x^2+a}}{x^{13/2}} \,d x","Not used",1,"int(((A + B*x^2)*(a + b*x^2)^(1/2))/x^(13/2), x)","F"
794,0,-1,252,0.000000,"\text{Not used}","int((A + B*x^2)*(e*x)^(3/2)*(a + b*x^2)^(3/2),x)","\int \left(B\,x^2+A\right)\,{\left(e\,x\right)}^{3/2}\,{\left(b\,x^2+a\right)}^{3/2} \,d x","Not used",1,"int((A + B*x^2)*(e*x)^(3/2)*(a + b*x^2)^(3/2), x)","F"
795,0,-1,377,0.000000,"\text{Not used}","int((A + B*x^2)*(e*x)^(1/2)*(a + b*x^2)^(3/2),x)","\int \left(B\,x^2+A\right)\,\sqrt{e\,x}\,{\left(b\,x^2+a\right)}^{3/2} \,d x","Not used",1,"int((A + B*x^2)*(e*x)^(1/2)*(a + b*x^2)^(3/2), x)","F"
796,0,-1,214,0.000000,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^(3/2))/(e*x)^(1/2),x)","\int \frac{\left(B\,x^2+A\right)\,{\left(b\,x^2+a\right)}^{3/2}}{\sqrt{e\,x}} \,d x","Not used",1,"int(((A + B*x^2)*(a + b*x^2)^(3/2))/(e*x)^(1/2), x)","F"
797,0,-1,367,0.000000,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^(3/2))/(e*x)^(3/2),x)","\int \frac{\left(B\,x^2+A\right)\,{\left(b\,x^2+a\right)}^{3/2}}{{\left(e\,x\right)}^{3/2}} \,d x","Not used",1,"int(((A + B*x^2)*(a + b*x^2)^(3/2))/(e*x)^(3/2), x)","F"
798,0,-1,210,0.000000,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^(3/2))/(e*x)^(5/2),x)","\int \frac{\left(B\,x^2+A\right)\,{\left(b\,x^2+a\right)}^{3/2}}{{\left(e\,x\right)}^{5/2}} \,d x","Not used",1,"int(((A + B*x^2)*(a + b*x^2)^(3/2))/(e*x)^(5/2), x)","F"
799,0,-1,365,0.000000,"\text{Not used}","int(((A + B*x^2)*(a + b*x^2)^(3/2))/(e*x)^(7/2),x)","\int \frac{\left(B\,x^2+A\right)\,{\left(b\,x^2+a\right)}^{3/2}}{{\left(e\,x\right)}^{7/2}} \,d x","Not used",1,"int(((A + B*x^2)*(a + b*x^2)^(3/2))/(e*x)^(7/2), x)","F"
800,0,-1,338,0.000000,"\text{Not used}","int(((A + B*x^2)*(e*x)^(5/2))/(a + b*x^2)^(1/2),x)","\int \frac{\left(B\,x^2+A\right)\,{\left(e\,x\right)}^{5/2}}{\sqrt{b\,x^2+a}} \,d x","Not used",1,"int(((A + B*x^2)*(e*x)^(5/2))/(a + b*x^2)^(1/2), x)","F"
801,0,-1,174,0.000000,"\text{Not used}","int(((A + B*x^2)*(e*x)^(3/2))/(a + b*x^2)^(1/2),x)","\int \frac{\left(B\,x^2+A\right)\,{\left(e\,x\right)}^{3/2}}{\sqrt{b\,x^2+a}} \,d x","Not used",1,"int(((A + B*x^2)*(e*x)^(3/2))/(a + b*x^2)^(1/2), x)","F"
802,0,-1,299,0.000000,"\text{Not used}","int(((A + B*x^2)*(e*x)^(1/2))/(a + b*x^2)^(1/2),x)","\int \frac{\left(B\,x^2+A\right)\,\sqrt{e\,x}}{\sqrt{b\,x^2+a}} \,d x","Not used",1,"int(((A + B*x^2)*(e*x)^(1/2))/(a + b*x^2)^(1/2), x)","F"
803,0,-1,139,0.000000,"\text{Not used}","int((A + B*x^2)/((e*x)^(1/2)*(a + b*x^2)^(1/2)),x)","\int \frac{B\,x^2+A}{\sqrt{e\,x}\,\sqrt{b\,x^2+a}} \,d x","Not used",1,"int((A + B*x^2)/((e*x)^(1/2)*(a + b*x^2)^(1/2)), x)","F"
804,0,-1,290,0.000000,"\text{Not used}","int((A + B*x^2)/((e*x)^(3/2)*(a + b*x^2)^(1/2)),x)","\int \frac{B\,x^2+A}{{\left(e\,x\right)}^{3/2}\,\sqrt{b\,x^2+a}} \,d x","Not used",1,"int((A + B*x^2)/((e*x)^(3/2)*(a + b*x^2)^(1/2)), x)","F"
805,0,-1,138,0.000000,"\text{Not used}","int((A + B*x^2)/((e*x)^(5/2)*(a + b*x^2)^(1/2)),x)","\int \frac{B\,x^2+A}{{\left(e\,x\right)}^{5/2}\,\sqrt{b\,x^2+a}} \,d x","Not used",1,"int((A + B*x^2)/((e*x)^(5/2)*(a + b*x^2)^(1/2)), x)","F"
806,0,-1,342,0.000000,"\text{Not used}","int((A + B*x^2)/((e*x)^(7/2)*(a + b*x^2)^(1/2)),x)","\int \frac{B\,x^2+A}{{\left(e\,x\right)}^{7/2}\,\sqrt{b\,x^2+a}} \,d x","Not used",1,"int((A + B*x^2)/((e*x)^(7/2)*(a + b*x^2)^(1/2)), x)","F"
807,0,-1,211,0.000000,"\text{Not used}","int(((A + B*x^2)*(e*x)^(7/2))/(a + b*x^2)^(3/2),x)","\int \frac{\left(B\,x^2+A\right)\,{\left(e\,x\right)}^{7/2}}{{\left(b\,x^2+a\right)}^{3/2}} \,d x","Not used",1,"int(((A + B*x^2)*(e*x)^(7/2))/(a + b*x^2)^(3/2), x)","F"
808,0,-1,337,0.000000,"\text{Not used}","int(((A + B*x^2)*(e*x)^(5/2))/(a + b*x^2)^(3/2),x)","\int \frac{\left(B\,x^2+A\right)\,{\left(e\,x\right)}^{5/2}}{{\left(b\,x^2+a\right)}^{3/2}} \,d x","Not used",1,"int(((A + B*x^2)*(e*x)^(5/2))/(a + b*x^2)^(3/2), x)","F"
809,0,-1,174,0.000000,"\text{Not used}","int(((A + B*x^2)*(e*x)^(3/2))/(a + b*x^2)^(3/2),x)","\int \frac{\left(B\,x^2+A\right)\,{\left(e\,x\right)}^{3/2}}{{\left(b\,x^2+a\right)}^{3/2}} \,d x","Not used",1,"int(((A + B*x^2)*(e*x)^(3/2))/(a + b*x^2)^(3/2), x)","F"
810,0,-1,301,0.000000,"\text{Not used}","int(((A + B*x^2)*(e*x)^(1/2))/(a + b*x^2)^(3/2),x)","\int \frac{\left(B\,x^2+A\right)\,\sqrt{e\,x}}{{\left(b\,x^2+a\right)}^{3/2}} \,d x","Not used",1,"int(((A + B*x^2)*(e*x)^(1/2))/(a + b*x^2)^(3/2), x)","F"
811,0,-1,144,0.000000,"\text{Not used}","int((A + B*x^2)/((e*x)^(1/2)*(a + b*x^2)^(3/2)),x)","\int \frac{B\,x^2+A}{\sqrt{e\,x}\,{\left(b\,x^2+a\right)}^{3/2}} \,d x","Not used",1,"int((A + B*x^2)/((e*x)^(1/2)*(a + b*x^2)^(3/2)), x)","F"
812,0,-1,333,0.000000,"\text{Not used}","int((A + B*x^2)/((e*x)^(3/2)*(a + b*x^2)^(3/2)),x)","\int \frac{B\,x^2+A}{{\left(e\,x\right)}^{3/2}\,{\left(b\,x^2+a\right)}^{3/2}} \,d x","Not used",1,"int((A + B*x^2)/((e*x)^(3/2)*(a + b*x^2)^(3/2)), x)","F"
813,0,-1,176,0.000000,"\text{Not used}","int((A + B*x^2)/((e*x)^(5/2)*(a + b*x^2)^(3/2)),x)","\int \frac{B\,x^2+A}{{\left(e\,x\right)}^{5/2}\,{\left(b\,x^2+a\right)}^{3/2}} \,d x","Not used",1,"int((A + B*x^2)/((e*x)^(5/2)*(a + b*x^2)^(3/2)), x)","F"
814,0,-1,379,0.000000,"\text{Not used}","int((A + B*x^2)/((e*x)^(7/2)*(a + b*x^2)^(3/2)),x)","\int \frac{B\,x^2+A}{{\left(e\,x\right)}^{7/2}\,{\left(b\,x^2+a\right)}^{3/2}} \,d x","Not used",1,"int((A + B*x^2)/((e*x)^(7/2)*(a + b*x^2)^(3/2)), x)","F"
815,0,-1,208,0.000000,"\text{Not used}","int(((A + B*x^2)*(e*x)^(7/2))/(a + b*x^2)^(5/2),x)","\int \frac{\left(B\,x^2+A\right)\,{\left(e\,x\right)}^{7/2}}{{\left(b\,x^2+a\right)}^{5/2}} \,d x","Not used",1,"int(((A + B*x^2)*(e*x)^(7/2))/(a + b*x^2)^(5/2), x)","F"
816,0,-1,349,0.000000,"\text{Not used}","int(((A + B*x^2)*(e*x)^(5/2))/(a + b*x^2)^(5/2),x)","\int \frac{\left(B\,x^2+A\right)\,{\left(e\,x\right)}^{5/2}}{{\left(b\,x^2+a\right)}^{5/2}} \,d x","Not used",1,"int(((A + B*x^2)*(e*x)^(5/2))/(a + b*x^2)^(5/2), x)","F"
817,0,-1,185,0.000000,"\text{Not used}","int(((A + B*x^2)*(e*x)^(3/2))/(a + b*x^2)^(5/2),x)","\int \frac{\left(B\,x^2+A\right)\,{\left(e\,x\right)}^{3/2}}{{\left(b\,x^2+a\right)}^{5/2}} \,d x","Not used",1,"int(((A + B*x^2)*(e*x)^(3/2))/(a + b*x^2)^(5/2), x)","F"
818,0,-1,344,0.000000,"\text{Not used}","int(((A + B*x^2)*(e*x)^(1/2))/(a + b*x^2)^(5/2),x)","\int \frac{\left(B\,x^2+A\right)\,\sqrt{e\,x}}{{\left(b\,x^2+a\right)}^{5/2}} \,d x","Not used",1,"int(((A + B*x^2)*(e*x)^(1/2))/(a + b*x^2)^(5/2), x)","F"
819,0,-1,187,0.000000,"\text{Not used}","int((A + B*x^2)/((e*x)^(1/2)*(a + b*x^2)^(5/2)),x)","\int \frac{B\,x^2+A}{\sqrt{e\,x}\,{\left(b\,x^2+a\right)}^{5/2}} \,d x","Not used",1,"int((A + B*x^2)/((e*x)^(1/2)*(a + b*x^2)^(5/2)), x)","F"
820,0,-1,377,0.000000,"\text{Not used}","int((A + B*x^2)/((e*x)^(3/2)*(a + b*x^2)^(5/2)),x)","\int \frac{B\,x^2+A}{{\left(e\,x\right)}^{3/2}\,{\left(b\,x^2+a\right)}^{5/2}} \,d x","Not used",1,"int((A + B*x^2)/((e*x)^(3/2)*(a + b*x^2)^(5/2)), x)","F"
821,0,-1,213,0.000000,"\text{Not used}","int((A + B*x^2)/((e*x)^(5/2)*(a + b*x^2)^(5/2)),x)","\int \frac{B\,x^2+A}{{\left(e\,x\right)}^{5/2}\,{\left(b\,x^2+a\right)}^{5/2}} \,d x","Not used",1,"int((A + B*x^2)/((e*x)^(5/2)*(a + b*x^2)^(5/2)), x)","F"
822,0,-1,288,0.000000,"\text{Not used}","int((e*x)^(3/2)*(a + b*x^2)^2*(c + d*x^2)^(1/2),x)","\int {\left(e\,x\right)}^{3/2}\,{\left(b\,x^2+a\right)}^2\,\sqrt{d\,x^2+c} \,d x","Not used",1,"int((e*x)^(3/2)*(a + b*x^2)^2*(c + d*x^2)^(1/2), x)","F"
823,0,-1,425,0.000000,"\text{Not used}","int((e*x)^(1/2)*(a + b*x^2)^2*(c + d*x^2)^(1/2),x)","\int \sqrt{e\,x}\,{\left(b\,x^2+a\right)}^2\,\sqrt{d\,x^2+c} \,d x","Not used",1,"int((e*x)^(1/2)*(a + b*x^2)^2*(c + d*x^2)^(1/2), x)","F"
824,0,-1,244,0.000000,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^(1/2))/(e*x)^(1/2),x)","\int \frac{{\left(b\,x^2+a\right)}^2\,\sqrt{d\,x^2+c}}{\sqrt{e\,x}} \,d x","Not used",1,"int(((a + b*x^2)^2*(c + d*x^2)^(1/2))/(e*x)^(1/2), x)","F"
825,0,-1,421,0.000000,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^(1/2))/(e*x)^(3/2),x)","\int \frac{{\left(b\,x^2+a\right)}^2\,\sqrt{d\,x^2+c}}{{\left(e\,x\right)}^{3/2}} \,d x","Not used",1,"int(((a + b*x^2)^2*(c + d*x^2)^(1/2))/(e*x)^(3/2), x)","F"
826,0,-1,234,0.000000,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^(1/2))/(e*x)^(5/2),x)","\int \frac{{\left(b\,x^2+a\right)}^2\,\sqrt{d\,x^2+c}}{{\left(e\,x\right)}^{5/2}} \,d x","Not used",1,"int(((a + b*x^2)^2*(c + d*x^2)^(1/2))/(e*x)^(5/2), x)","F"
827,0,-1,421,0.000000,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^(1/2))/(e*x)^(7/2),x)","\int \frac{{\left(b\,x^2+a\right)}^2\,\sqrt{d\,x^2+c}}{{\left(e\,x\right)}^{7/2}} \,d x","Not used",1,"int(((a + b*x^2)^2*(c + d*x^2)^(1/2))/(e*x)^(7/2), x)","F"
828,0,-1,213,0.000000,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^(1/2))/x^(9/2),x)","\int \frac{{\left(b\,x^2+a\right)}^2\,\sqrt{d\,x^2+c}}{x^{9/2}} \,d x","Not used",1,"int(((a + b*x^2)^2*(c + d*x^2)^(1/2))/x^(9/2), x)","F"
829,0,-1,386,0.000000,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^(1/2))/x^(11/2),x)","\int \frac{{\left(b\,x^2+a\right)}^2\,\sqrt{d\,x^2+c}}{x^{11/2}} \,d x","Not used",1,"int(((a + b*x^2)^2*(c + d*x^2)^(1/2))/x^(11/2), x)","F"
830,0,-1,217,0.000000,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^(1/2))/x^(13/2),x)","\int \frac{{\left(b\,x^2+a\right)}^2\,\sqrt{d\,x^2+c}}{x^{13/2}} \,d x","Not used",1,"int(((a + b*x^2)^2*(c + d*x^2)^(1/2))/x^(13/2), x)","F"
831,0,-1,441,0.000000,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^(1/2))/x^(15/2),x)","\int \frac{{\left(b\,x^2+a\right)}^2\,\sqrt{d\,x^2+c}}{x^{15/2}} \,d x","Not used",1,"int(((a + b*x^2)^2*(c + d*x^2)^(1/2))/x^(15/2), x)","F"
832,0,-1,530,0.000000,"\text{Not used}","int((e*x)^(5/2)*(a + b*x^2)^2*(c + d*x^2)^(3/2),x)","\int {\left(e\,x\right)}^{5/2}\,{\left(b\,x^2+a\right)}^2\,{\left(d\,x^2+c\right)}^{3/2} \,d x","Not used",1,"int((e*x)^(5/2)*(a + b*x^2)^2*(c + d*x^2)^(3/2), x)","F"
833,0,-1,340,0.000000,"\text{Not used}","int((e*x)^(3/2)*(a + b*x^2)^2*(c + d*x^2)^(3/2),x)","\int {\left(e\,x\right)}^{3/2}\,{\left(b\,x^2+a\right)}^2\,{\left(d\,x^2+c\right)}^{3/2} \,d x","Not used",1,"int((e*x)^(3/2)*(a + b*x^2)^2*(c + d*x^2)^(3/2), x)","F"
834,0,-1,482,0.000000,"\text{Not used}","int((e*x)^(1/2)*(a + b*x^2)^2*(c + d*x^2)^(3/2),x)","\int \sqrt{e\,x}\,{\left(b\,x^2+a\right)}^2\,{\left(d\,x^2+c\right)}^{3/2} \,d x","Not used",1,"int((e*x)^(1/2)*(a + b*x^2)^2*(c + d*x^2)^(3/2), x)","F"
835,0,-1,286,0.000000,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^(3/2))/(e*x)^(1/2),x)","\int \frac{{\left(b\,x^2+a\right)}^2\,{\left(d\,x^2+c\right)}^{3/2}}{\sqrt{e\,x}} \,d x","Not used",1,"int(((a + b*x^2)^2*(c + d*x^2)^(3/2))/(e*x)^(1/2), x)","F"
836,0,-1,476,0.000000,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^(3/2))/(e*x)^(3/2),x)","\int \frac{{\left(b\,x^2+a\right)}^2\,{\left(d\,x^2+c\right)}^{3/2}}{{\left(e\,x\right)}^{3/2}} \,d x","Not used",1,"int(((a + b*x^2)^2*(c + d*x^2)^(3/2))/(e*x)^(3/2), x)","F"
837,0,-1,288,0.000000,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^(3/2))/(e*x)^(5/2),x)","\int \frac{{\left(b\,x^2+a\right)}^2\,{\left(d\,x^2+c\right)}^{3/2}}{{\left(e\,x\right)}^{5/2}} \,d x","Not used",1,"int(((a + b*x^2)^2*(c + d*x^2)^(3/2))/(e*x)^(5/2), x)","F"
838,0,-1,468,0.000000,"\text{Not used}","int(((a + b*x^2)^2*(c + d*x^2)^(3/2))/(e*x)^(7/2),x)","\int \frac{{\left(b\,x^2+a\right)}^2\,{\left(d\,x^2+c\right)}^{3/2}}{{\left(e\,x\right)}^{7/2}} \,d x","Not used",1,"int(((a + b*x^2)^2*(c + d*x^2)^(3/2))/(e*x)^(7/2), x)","F"
839,0,-1,430,0.000000,"\text{Not used}","int(((e*x)^(5/2)*(a + b*x^2)^2)/(c + d*x^2)^(1/2),x)","\int \frac{{\left(e\,x\right)}^{5/2}\,{\left(b\,x^2+a\right)}^2}{\sqrt{d\,x^2+c}} \,d x","Not used",1,"int(((e*x)^(5/2)*(a + b*x^2)^2)/(c + d*x^2)^(1/2), x)","F"
840,0,-1,240,0.000000,"\text{Not used}","int(((e*x)^(3/2)*(a + b*x^2)^2)/(c + d*x^2)^(1/2),x)","\int \frac{{\left(e\,x\right)}^{3/2}\,{\left(b\,x^2+a\right)}^2}{\sqrt{d\,x^2+c}} \,d x","Not used",1,"int(((e*x)^(3/2)*(a + b*x^2)^2)/(c + d*x^2)^(1/2), x)","F"
841,0,-1,375,0.000000,"\text{Not used}","int(((e*x)^(1/2)*(a + b*x^2)^2)/(c + d*x^2)^(1/2),x)","\int \frac{\sqrt{e\,x}\,{\left(b\,x^2+a\right)}^2}{\sqrt{d\,x^2+c}} \,d x","Not used",1,"int(((e*x)^(1/2)*(a + b*x^2)^2)/(c + d*x^2)^(1/2), x)","F"
842,0,-1,193,0.000000,"\text{Not used}","int((a + b*x^2)^2/((e*x)^(1/2)*(c + d*x^2)^(1/2)),x)","\int \frac{{\left(b\,x^2+a\right)}^2}{\sqrt{e\,x}\,\sqrt{d\,x^2+c}} \,d x","Not used",1,"int((a + b*x^2)^2/((e*x)^(1/2)*(c + d*x^2)^(1/2)), x)","F"
843,0,-1,372,0.000000,"\text{Not used}","int((a + b*x^2)^2/((e*x)^(3/2)*(c + d*x^2)^(1/2)),x)","\int \frac{{\left(b\,x^2+a\right)}^2}{{\left(e\,x\right)}^{3/2}\,\sqrt{d\,x^2+c}} \,d x","Not used",1,"int((a + b*x^2)^2/((e*x)^(3/2)*(c + d*x^2)^(1/2)), x)","F"
844,0,-1,184,0.000000,"\text{Not used}","int((a + b*x^2)^2/((e*x)^(5/2)*(c + d*x^2)^(1/2)),x)","\int \frac{{\left(b\,x^2+a\right)}^2}{{\left(e\,x\right)}^{5/2}\,\sqrt{d\,x^2+c}} \,d x","Not used",1,"int((a + b*x^2)^2/((e*x)^(5/2)*(c + d*x^2)^(1/2)), x)","F"
845,0,-1,387,0.000000,"\text{Not used}","int((a + b*x^2)^2/((e*x)^(7/2)*(c + d*x^2)^(1/2)),x)","\int \frac{{\left(b\,x^2+a\right)}^2}{{\left(e\,x\right)}^{7/2}\,\sqrt{d\,x^2+c}} \,d x","Not used",1,"int((a + b*x^2)^2/((e*x)^(7/2)*(c + d*x^2)^(1/2)), x)","F"
846,0,-1,193,0.000000,"\text{Not used}","int((a + b*x^2)^2/((e*x)^(9/2)*(c + d*x^2)^(1/2)),x)","\int \frac{{\left(b\,x^2+a\right)}^2}{{\left(e\,x\right)}^{9/2}\,\sqrt{d\,x^2+c}} \,d x","Not used",1,"int((a + b*x^2)^2/((e*x)^(9/2)*(c + d*x^2)^(1/2)), x)","F"
847,0,-1,438,0.000000,"\text{Not used}","int((a + b*x^2)^2/((e*x)^(11/2)*(c + d*x^2)^(1/2)),x)","\int \frac{{\left(b\,x^2+a\right)}^2}{{\left(e\,x\right)}^{11/2}\,\sqrt{d\,x^2+c}} \,d x","Not used",1,"int((a + b*x^2)^2/((e*x)^(11/2)*(c + d*x^2)^(1/2)), x)","F"
848,0,-1,242,0.000000,"\text{Not used}","int((a + b*x^2)^2/((e*x)^(13/2)*(c + d*x^2)^(1/2)),x)","\int \frac{{\left(b\,x^2+a\right)}^2}{{\left(e\,x\right)}^{13/2}\,\sqrt{d\,x^2+c}} \,d x","Not used",1,"int((a + b*x^2)^2/((e*x)^(13/2)*(c + d*x^2)^(1/2)), x)","F"
849,0,-1,296,0.000000,"\text{Not used}","int(((e*x)^(7/2)*(a + b*x^2)^2)/(c + d*x^2)^(3/2),x)","\int \frac{{\left(e\,x\right)}^{7/2}\,{\left(b\,x^2+a\right)}^2}{{\left(d\,x^2+c\right)}^{3/2}} \,d x","Not used",1,"int(((e*x)^(7/2)*(a + b*x^2)^2)/(c + d*x^2)^(3/2), x)","F"
850,0,-1,436,0.000000,"\text{Not used}","int(((e*x)^(5/2)*(a + b*x^2)^2)/(c + d*x^2)^(3/2),x)","\int \frac{{\left(e\,x\right)}^{5/2}\,{\left(b\,x^2+a\right)}^2}{{\left(d\,x^2+c\right)}^{3/2}} \,d x","Not used",1,"int(((e*x)^(5/2)*(a + b*x^2)^2)/(c + d*x^2)^(3/2), x)","F"
851,0,-1,245,0.000000,"\text{Not used}","int(((e*x)^(3/2)*(a + b*x^2)^2)/(c + d*x^2)^(3/2),x)","\int \frac{{\left(e\,x\right)}^{3/2}\,{\left(b\,x^2+a\right)}^2}{{\left(d\,x^2+c\right)}^{3/2}} \,d x","Not used",1,"int(((e*x)^(3/2)*(a + b*x^2)^2)/(c + d*x^2)^(3/2), x)","F"
852,0,-1,384,0.000000,"\text{Not used}","int(((e*x)^(1/2)*(a + b*x^2)^2)/(c + d*x^2)^(3/2),x)","\int \frac{\sqrt{e\,x}\,{\left(b\,x^2+a\right)}^2}{{\left(d\,x^2+c\right)}^{3/2}} \,d x","Not used",1,"int(((e*x)^(1/2)*(a + b*x^2)^2)/(c + d*x^2)^(3/2), x)","F"
853,0,-1,193,0.000000,"\text{Not used}","int((a + b*x^2)^2/((e*x)^(1/2)*(c + d*x^2)^(3/2)),x)","\int \frac{{\left(b\,x^2+a\right)}^2}{\sqrt{e\,x}\,{\left(d\,x^2+c\right)}^{3/2}} \,d x","Not used",1,"int((a + b*x^2)^2/((e*x)^(1/2)*(c + d*x^2)^(3/2)), x)","F"
854,0,-1,393,0.000000,"\text{Not used}","int((a + b*x^2)^2/((e*x)^(3/2)*(c + d*x^2)^(3/2)),x)","\int \frac{{\left(b\,x^2+a\right)}^2}{{\left(e\,x\right)}^{3/2}\,{\left(d\,x^2+c\right)}^{3/2}} \,d x","Not used",1,"int((a + b*x^2)^2/((e*x)^(3/2)*(c + d*x^2)^(3/2)), x)","F"
855,0,-1,207,0.000000,"\text{Not used}","int((a + b*x^2)^2/((e*x)^(5/2)*(c + d*x^2)^(3/2)),x)","\int \frac{{\left(b\,x^2+a\right)}^2}{{\left(e\,x\right)}^{5/2}\,{\left(d\,x^2+c\right)}^{3/2}} \,d x","Not used",1,"int((a + b*x^2)^2/((e*x)^(5/2)*(c + d*x^2)^(3/2)), x)","F"
856,0,-1,434,0.000000,"\text{Not used}","int((a + b*x^2)^2/((e*x)^(7/2)*(c + d*x^2)^(3/2)),x)","\int \frac{{\left(b\,x^2+a\right)}^2}{{\left(e\,x\right)}^{7/2}\,{\left(d\,x^2+c\right)}^{3/2}} \,d x","Not used",1,"int((a + b*x^2)^2/((e*x)^(7/2)*(c + d*x^2)^(3/2)), x)","F"
857,0,-1,302,0.000000,"\text{Not used}","int(((e*x)^(7/2)*(a + b*x^2)^2)/(c + d*x^2)^(5/2),x)","\int \frac{{\left(e\,x\right)}^{7/2}\,{\left(b\,x^2+a\right)}^2}{{\left(d\,x^2+c\right)}^{5/2}} \,d x","Not used",1,"int(((e*x)^(7/2)*(a + b*x^2)^2)/(c + d*x^2)^(5/2), x)","F"
858,0,-1,442,0.000000,"\text{Not used}","int(((e*x)^(5/2)*(a + b*x^2)^2)/(c + d*x^2)^(5/2),x)","\int \frac{{\left(e\,x\right)}^{5/2}\,{\left(b\,x^2+a\right)}^2}{{\left(d\,x^2+c\right)}^{5/2}} \,d x","Not used",1,"int(((e*x)^(5/2)*(a + b*x^2)^2)/(c + d*x^2)^(5/2), x)","F"
859,0,-1,248,0.000000,"\text{Not used}","int(((e*x)^(3/2)*(a + b*x^2)^2)/(c + d*x^2)^(5/2),x)","\int \frac{{\left(e\,x\right)}^{3/2}\,{\left(b\,x^2+a\right)}^2}{{\left(d\,x^2+c\right)}^{5/2}} \,d x","Not used",1,"int(((e*x)^(3/2)*(a + b*x^2)^2)/(c + d*x^2)^(5/2), x)","F"
860,0,-1,403,0.000000,"\text{Not used}","int(((e*x)^(1/2)*(a + b*x^2)^2)/(c + d*x^2)^(5/2),x)","\int \frac{\sqrt{e\,x}\,{\left(b\,x^2+a\right)}^2}{{\left(d\,x^2+c\right)}^{5/2}} \,d x","Not used",1,"int(((e*x)^(1/2)*(a + b*x^2)^2)/(c + d*x^2)^(5/2), x)","F"
861,0,-1,213,0.000000,"\text{Not used}","int((a + b*x^2)^2/((e*x)^(1/2)*(c + d*x^2)^(5/2)),x)","\int \frac{{\left(b\,x^2+a\right)}^2}{\sqrt{e\,x}\,{\left(d\,x^2+c\right)}^{5/2}} \,d x","Not used",1,"int((a + b*x^2)^2/((e*x)^(1/2)*(c + d*x^2)^(5/2)), x)","F"
862,0,-1,442,0.000000,"\text{Not used}","int((a + b*x^2)^2/((e*x)^(3/2)*(c + d*x^2)^(5/2)),x)","\int \frac{{\left(b\,x^2+a\right)}^2}{{\left(e\,x\right)}^{3/2}\,{\left(d\,x^2+c\right)}^{5/2}} \,d x","Not used",1,"int((a + b*x^2)^2/((e*x)^(3/2)*(c + d*x^2)^(5/2)), x)","F"
863,0,-1,258,0.000000,"\text{Not used}","int((a + b*x^2)^2/((e*x)^(5/2)*(c + d*x^2)^(5/2)),x)","\int \frac{{\left(b\,x^2+a\right)}^2}{{\left(e\,x\right)}^{5/2}\,{\left(d\,x^2+c\right)}^{5/2}} \,d x","Not used",1,"int((a + b*x^2)^2/((e*x)^(5/2)*(c + d*x^2)^(5/2)), x)","F"
864,0,-1,489,0.000000,"\text{Not used}","int((a + b*x^2)^2/((e*x)^(7/2)*(c + d*x^2)^(5/2)),x)","\int \frac{{\left(b\,x^2+a\right)}^2}{{\left(e\,x\right)}^{7/2}\,{\left(d\,x^2+c\right)}^{5/2}} \,d x","Not used",1,"int((a + b*x^2)^2/((e*x)^(7/2)*(c + d*x^2)^(5/2)), x)","F"
865,0,-1,372,0.000000,"\text{Not used}","int(((e*x)^(7/2)*(c - d*x^2)^(1/2))/(a - b*x^2),x)","\int \frac{{\left(e\,x\right)}^{7/2}\,\sqrt{c-d\,x^2}}{a-b\,x^2} \,d x","Not used",1,"int(((e*x)^(7/2)*(c - d*x^2)^(1/2))/(a - b*x^2), x)","F"
866,0,-1,414,0.000000,"\text{Not used}","int(((e*x)^(5/2)*(c - d*x^2)^(1/2))/(a - b*x^2),x)","\int \frac{{\left(e\,x\right)}^{5/2}\,\sqrt{c-d\,x^2}}{a-b\,x^2} \,d x","Not used",1,"int(((e*x)^(5/2)*(c - d*x^2)^(1/2))/(a - b*x^2), x)","F"
867,0,-1,315,0.000000,"\text{Not used}","int(((e*x)^(3/2)*(c - d*x^2)^(1/2))/(a - b*x^2),x)","\int \frac{{\left(e\,x\right)}^{3/2}\,\sqrt{c-d\,x^2}}{a-b\,x^2} \,d x","Not used",1,"int(((e*x)^(3/2)*(c - d*x^2)^(1/2))/(a - b*x^2), x)","F"
868,0,-1,365,0.000000,"\text{Not used}","int(((e*x)^(1/2)*(c - d*x^2)^(1/2))/(a - b*x^2),x)","\int \frac{\sqrt{e\,x}\,\sqrt{c-d\,x^2}}{a-b\,x^2} \,d x","Not used",1,"int(((e*x)^(1/2)*(c - d*x^2)^(1/2))/(a - b*x^2), x)","F"
869,0,-1,283,0.000000,"\text{Not used}","int((c - d*x^2)^(1/2)/((e*x)^(1/2)*(a - b*x^2)),x)","\int \frac{\sqrt{c-d\,x^2}}{\sqrt{e\,x}\,\left(a-b\,x^2\right)} \,d x","Not used",1,"int((c - d*x^2)^(1/2)/((e*x)^(1/2)*(a - b*x^2)), x)","F"
870,0,-1,392,0.000000,"\text{Not used}","int((c - d*x^2)^(1/2)/((e*x)^(3/2)*(a - b*x^2)),x)","\int \frac{\sqrt{c-d\,x^2}}{{\left(e\,x\right)}^{3/2}\,\left(a-b\,x^2\right)} \,d x","Not used",1,"int((c - d*x^2)^(1/2)/((e*x)^(3/2)*(a - b*x^2)), x)","F"
871,0,-1,308,0.000000,"\text{Not used}","int((c - d*x^2)^(1/2)/((e*x)^(5/2)*(a - b*x^2)),x)","\int \frac{\sqrt{c-d\,x^2}}{{\left(e\,x\right)}^{5/2}\,\left(a-b\,x^2\right)} \,d x","Not used",1,"int((c - d*x^2)^(1/2)/((e*x)^(5/2)*(a - b*x^2)), x)","F"
872,0,-1,457,0.000000,"\text{Not used}","int((c - d*x^2)^(1/2)/((e*x)^(7/2)*(a - b*x^2)),x)","\int \frac{\sqrt{c-d\,x^2}}{{\left(e\,x\right)}^{7/2}\,\left(a-b\,x^2\right)} \,d x","Not used",1,"int((c - d*x^2)^(1/2)/((e*x)^(7/2)*(a - b*x^2)), x)","F"
873,0,-1,485,0.000000,"\text{Not used}","int(((e*x)^(5/2)*(c - d*x^2)^(3/2))/(a - b*x^2),x)","\int \frac{{\left(e\,x\right)}^{5/2}\,{\left(c-d\,x^2\right)}^{3/2}}{a-b\,x^2} \,d x","Not used",1,"int(((e*x)^(5/2)*(c - d*x^2)^(3/2))/(a - b*x^2), x)","F"
874,0,-1,372,0.000000,"\text{Not used}","int(((e*x)^(3/2)*(c - d*x^2)^(3/2))/(a - b*x^2),x)","\int \frac{{\left(e\,x\right)}^{3/2}\,{\left(c-d\,x^2\right)}^{3/2}}{a-b\,x^2} \,d x","Not used",1,"int(((e*x)^(3/2)*(c - d*x^2)^(3/2))/(a - b*x^2), x)","F"
875,0,-1,421,0.000000,"\text{Not used}","int(((e*x)^(1/2)*(c - d*x^2)^(3/2))/(a - b*x^2),x)","\int \frac{\sqrt{e\,x}\,{\left(c-d\,x^2\right)}^{3/2}}{a-b\,x^2} \,d x","Not used",1,"int(((e*x)^(1/2)*(c - d*x^2)^(3/2))/(a - b*x^2), x)","F"
876,0,-1,328,0.000000,"\text{Not used}","int((c - d*x^2)^(3/2)/((e*x)^(1/2)*(a - b*x^2)),x)","\int \frac{{\left(c-d\,x^2\right)}^{3/2}}{\sqrt{e\,x}\,\left(a-b\,x^2\right)} \,d x","Not used",1,"int((c - d*x^2)^(3/2)/((e*x)^(1/2)*(a - b*x^2)), x)","F"
877,0,-1,417,0.000000,"\text{Not used}","int((c - d*x^2)^(3/2)/((e*x)^(3/2)*(a - b*x^2)),x)","\int \frac{{\left(c-d\,x^2\right)}^{3/2}}{{\left(e\,x\right)}^{3/2}\,\left(a-b\,x^2\right)} \,d x","Not used",1,"int((c - d*x^2)^(3/2)/((e*x)^(3/2)*(a - b*x^2)), x)","F"
878,0,-1,330,0.000000,"\text{Not used}","int((c - d*x^2)^(3/2)/((e*x)^(5/2)*(a - b*x^2)),x)","\int \frac{{\left(c-d\,x^2\right)}^{3/2}}{{\left(e\,x\right)}^{5/2}\,\left(a-b\,x^2\right)} \,d x","Not used",1,"int((c - d*x^2)^(3/2)/((e*x)^(5/2)*(a - b*x^2)), x)","F"
879,0,-1,459,0.000000,"\text{Not used}","int((c - d*x^2)^(3/2)/((e*x)^(7/2)*(a - b*x^2)),x)","\int \frac{{\left(c-d\,x^2\right)}^{3/2}}{{\left(e\,x\right)}^{7/2}\,\left(a-b\,x^2\right)} \,d x","Not used",1,"int((c - d*x^2)^(3/2)/((e*x)^(7/2)*(a - b*x^2)), x)","F"
880,0,-1,305,0.000000,"\text{Not used}","int((e*x)^(7/2)/((a - b*x^2)*(c - d*x^2)^(1/2)),x)","\int \frac{{\left(e\,x\right)}^{7/2}}{\left(a-b\,x^2\right)\,\sqrt{c-d\,x^2}} \,d x","Not used",1,"int((e*x)^(7/2)/((a - b*x^2)*(c - d*x^2)^(1/2)), x)","F"
881,0,-1,349,0.000000,"\text{Not used}","int((e*x)^(5/2)/((a - b*x^2)*(c - d*x^2)^(1/2)),x)","\int \frac{{\left(e\,x\right)}^{5/2}}{\left(a-b\,x^2\right)\,\sqrt{c-d\,x^2}} \,d x","Not used",1,"int((e*x)^(5/2)/((a - b*x^2)*(c - d*x^2)^(1/2)), x)","F"
882,0,-1,261,0.000000,"\text{Not used}","int((e*x)^(3/2)/((a - b*x^2)*(c - d*x^2)^(1/2)),x)","\int \frac{{\left(e\,x\right)}^{3/2}}{\left(a-b\,x^2\right)\,\sqrt{c-d\,x^2}} \,d x","Not used",1,"int((e*x)^(3/2)/((a - b*x^2)*(c - d*x^2)^(1/2)), x)","F"
883,0,-1,203,0.000000,"\text{Not used}","int((e*x)^(1/2)/((a - b*x^2)*(c - d*x^2)^(1/2)),x)","\int \frac{\sqrt{e\,x}}{\left(a-b\,x^2\right)\,\sqrt{c-d\,x^2}} \,d x","Not used",1,"int((e*x)^(1/2)/((a - b*x^2)*(c - d*x^2)^(1/2)), x)","F"
884,0,-1,188,0.000000,"\text{Not used}","int(1/((e*x)^(1/2)*(a - b*x^2)*(c - d*x^2)^(1/2)),x)","\int \frac{1}{\sqrt{e\,x}\,\left(a-b\,x^2\right)\,\sqrt{c-d\,x^2}} \,d x","Not used",1,"int(1/((e*x)^(1/2)*(a - b*x^2)*(c - d*x^2)^(1/2)), x)","F"
885,0,-1,379,0.000000,"\text{Not used}","int(1/((e*x)^(3/2)*(a - b*x^2)*(c - d*x^2)^(1/2)),x)","\int \frac{1}{{\left(e\,x\right)}^{3/2}\,\left(a-b\,x^2\right)\,\sqrt{c-d\,x^2}} \,d x","Not used",1,"int(1/((e*x)^(3/2)*(a - b*x^2)*(c - d*x^2)^(1/2)), x)","F"
886,0,-1,297,0.000000,"\text{Not used}","int(1/((e*x)^(5/2)*(a - b*x^2)*(c - d*x^2)^(1/2)),x)","\int \frac{1}{{\left(e\,x\right)}^{5/2}\,\left(a-b\,x^2\right)\,\sqrt{c-d\,x^2}} \,d x","Not used",1,"int(1/((e*x)^(5/2)*(a - b*x^2)*(c - d*x^2)^(1/2)), x)","F"
887,0,-1,444,0.000000,"\text{Not used}","int(1/((e*x)^(7/2)*(a - b*x^2)*(c - d*x^2)^(1/2)),x)","\int \frac{1}{{\left(e\,x\right)}^{7/2}\,\left(a-b\,x^2\right)\,\sqrt{c-d\,x^2}} \,d x","Not used",1,"int(1/((e*x)^(7/2)*(a - b*x^2)*(c - d*x^2)^(1/2)), x)","F"
888,0,-1,444,0.000000,"\text{Not used}","int((e*x)^(9/2)/((a - b*x^2)*(c - d*x^2)^(3/2)),x)","\int \frac{{\left(e\,x\right)}^{9/2}}{\left(a-b\,x^2\right)\,{\left(c-d\,x^2\right)}^{3/2}} \,d x","Not used",1,"int((e*x)^(9/2)/((a - b*x^2)*(c - d*x^2)^(3/2)), x)","F"
889,0,-1,338,0.000000,"\text{Not used}","int((e*x)^(7/2)/((a - b*x^2)*(c - d*x^2)^(3/2)),x)","\int \frac{{\left(e\,x\right)}^{7/2}}{\left(a-b\,x^2\right)\,{\left(c-d\,x^2\right)}^{3/2}} \,d x","Not used",1,"int((e*x)^(7/2)/((a - b*x^2)*(c - d*x^2)^(3/2)), x)","F"
890,0,-1,414,0.000000,"\text{Not used}","int((e*x)^(5/2)/((a - b*x^2)*(c - d*x^2)^(3/2)),x)","\int \frac{{\left(e\,x\right)}^{5/2}}{\left(a-b\,x^2\right)\,{\left(c-d\,x^2\right)}^{3/2}} \,d x","Not used",1,"int((e*x)^(5/2)/((a - b*x^2)*(c - d*x^2)^(3/2)), x)","F"
891,0,-1,314,0.000000,"\text{Not used}","int((e*x)^(3/2)/((a - b*x^2)*(c - d*x^2)^(3/2)),x)","\int \frac{{\left(e\,x\right)}^{3/2}}{\left(a-b\,x^2\right)\,{\left(c-d\,x^2\right)}^{3/2}} \,d x","Not used",1,"int((e*x)^(3/2)/((a - b*x^2)*(c - d*x^2)^(3/2)), x)","F"
892,0,-1,420,0.000000,"\text{Not used}","int((e*x)^(1/2)/((a - b*x^2)*(c - d*x^2)^(3/2)),x)","\int \frac{\sqrt{e\,x}}{\left(a-b\,x^2\right)\,{\left(c-d\,x^2\right)}^{3/2}} \,d x","Not used",1,"int((e*x)^(1/2)/((a - b*x^2)*(c - d*x^2)^(3/2)), x)","F"
893,0,-1,328,0.000000,"\text{Not used}","int(1/((e*x)^(1/2)*(a - b*x^2)*(c - d*x^2)^(3/2)),x)","\int \frac{1}{\sqrt{e\,x}\,\left(a-b\,x^2\right)\,{\left(c-d\,x^2\right)}^{3/2}} \,d x","Not used",1,"int(1/((e*x)^(1/2)*(a - b*x^2)*(c - d*x^2)^(3/2)), x)","F"
894,0,-1,493,0.000000,"\text{Not used}","int(1/((e*x)^(3/2)*(a - b*x^2)*(c - d*x^2)^(3/2)),x)","\int \frac{1}{{\left(e\,x\right)}^{3/2}\,\left(a-b\,x^2\right)\,{\left(c-d\,x^2\right)}^{3/2}} \,d x","Not used",1,"int(1/((e*x)^(3/2)*(a - b*x^2)*(c - d*x^2)^(3/2)), x)","F"
895,0,-1,397,0.000000,"\text{Not used}","int(1/((e*x)^(5/2)*(a - b*x^2)*(c - d*x^2)^(3/2)),x)","\int \frac{1}{{\left(e\,x\right)}^{5/2}\,\left(a-b\,x^2\right)\,{\left(c-d\,x^2\right)}^{3/2}} \,d x","Not used",1,"int(1/((e*x)^(5/2)*(a - b*x^2)*(c - d*x^2)^(3/2)), x)","F"
896,0,-1,362,0.000000,"\text{Not used}","int(((e*x)^(7/2)*(c - d*x^2)^(1/2))/(a - b*x^2)^2,x)","\int \frac{{\left(e\,x\right)}^{7/2}\,\sqrt{c-d\,x^2}}{{\left(a-b\,x^2\right)}^2} \,d x","Not used",1,"int(((e*x)^(7/2)*(c - d*x^2)^(1/2))/(a - b*x^2)^2, x)","F"
897,0,-1,413,0.000000,"\text{Not used}","int(((e*x)^(5/2)*(c - d*x^2)^(1/2))/(a - b*x^2)^2,x)","\int \frac{{\left(e\,x\right)}^{5/2}\,\sqrt{c-d\,x^2}}{{\left(a-b\,x^2\right)}^2} \,d x","Not used",1,"int(((e*x)^(5/2)*(c - d*x^2)^(1/2))/(a - b*x^2)^2, x)","F"
898,0,-1,328,0.000000,"\text{Not used}","int(((e*x)^(3/2)*(c - d*x^2)^(1/2))/(a - b*x^2)^2,x)","\int \frac{{\left(e\,x\right)}^{3/2}\,\sqrt{c-d\,x^2}}{{\left(a-b\,x^2\right)}^2} \,d x","Not used",1,"int(((e*x)^(3/2)*(c - d*x^2)^(1/2))/(a - b*x^2)^2, x)","F"
899,0,-1,417,0.000000,"\text{Not used}","int(((e*x)^(1/2)*(c - d*x^2)^(1/2))/(a - b*x^2)^2,x)","\int \frac{\sqrt{e\,x}\,\sqrt{c-d\,x^2}}{{\left(a-b\,x^2\right)}^2} \,d x","Not used",1,"int(((e*x)^(1/2)*(c - d*x^2)^(1/2))/(a - b*x^2)^2, x)","F"
900,0,-1,335,0.000000,"\text{Not used}","int((c - d*x^2)^(1/2)/((e*x)^(1/2)*(a - b*x^2)^2),x)","\int \frac{\sqrt{c-d\,x^2}}{\sqrt{e\,x}\,{\left(a-b\,x^2\right)}^2} \,d x","Not used",1,"int((c - d*x^2)^(1/2)/((e*x)^(1/2)*(a - b*x^2)^2), x)","F"
901,0,-1,444,0.000000,"\text{Not used}","int((c - d*x^2)^(1/2)/((e*x)^(3/2)*(a - b*x^2)^2),x)","\int \frac{\sqrt{c-d\,x^2}}{{\left(e\,x\right)}^{3/2}\,{\left(a-b\,x^2\right)}^2} \,d x","Not used",1,"int((c - d*x^2)^(1/2)/((e*x)^(3/2)*(a - b*x^2)^2), x)","F"
902,0,-1,355,0.000000,"\text{Not used}","int((c - d*x^2)^(1/2)/((e*x)^(5/2)*(a - b*x^2)^2),x)","\int \frac{\sqrt{c-d\,x^2}}{{\left(e\,x\right)}^{5/2}\,{\left(a-b\,x^2\right)}^2} \,d x","Not used",1,"int((c - d*x^2)^(1/2)/((e*x)^(5/2)*(a - b*x^2)^2), x)","F"
903,0,-1,429,0.000000,"\text{Not used}","int(((e*x)^(7/2)*(c - d*x^2)^(3/2))/(a - b*x^2)^2,x)","\int \frac{{\left(e\,x\right)}^{7/2}\,{\left(c-d\,x^2\right)}^{3/2}}{{\left(a-b\,x^2\right)}^2} \,d x","Not used",1,"int(((e*x)^(7/2)*(c - d*x^2)^(3/2))/(a - b*x^2)^2, x)","F"
904,0,-1,485,0.000000,"\text{Not used}","int(((e*x)^(5/2)*(c - d*x^2)^(3/2))/(a - b*x^2)^2,x)","\int \frac{{\left(e\,x\right)}^{5/2}\,{\left(c-d\,x^2\right)}^{3/2}}{{\left(a-b\,x^2\right)}^2} \,d x","Not used",1,"int(((e*x)^(5/2)*(c - d*x^2)^(3/2))/(a - b*x^2)^2, x)","F"
905,0,-1,381,0.000000,"\text{Not used}","int(((e*x)^(3/2)*(c - d*x^2)^(3/2))/(a - b*x^2)^2,x)","\int \frac{{\left(e\,x\right)}^{3/2}\,{\left(c-d\,x^2\right)}^{3/2}}{{\left(a-b\,x^2\right)}^2} \,d x","Not used",1,"int(((e*x)^(3/2)*(c - d*x^2)^(3/2))/(a - b*x^2)^2, x)","F"
906,0,-1,474,0.000000,"\text{Not used}","int(((e*x)^(1/2)*(c - d*x^2)^(3/2))/(a - b*x^2)^2,x)","\int \frac{\sqrt{e\,x}\,{\left(c-d\,x^2\right)}^{3/2}}{{\left(a-b\,x^2\right)}^2} \,d x","Not used",1,"int(((e*x)^(1/2)*(c - d*x^2)^(3/2))/(a - b*x^2)^2, x)","F"
907,0,-1,366,0.000000,"\text{Not used}","int((c - d*x^2)^(3/2)/((e*x)^(1/2)*(a - b*x^2)^2),x)","\int \frac{{\left(c-d\,x^2\right)}^{3/2}}{\sqrt{e\,x}\,{\left(a-b\,x^2\right)}^2} \,d x","Not used",1,"int((c - d*x^2)^(3/2)/((e*x)^(1/2)*(a - b*x^2)^2), x)","F"
908,0,-1,519,0.000000,"\text{Not used}","int((c - d*x^2)^(3/2)/((e*x)^(3/2)*(a - b*x^2)^2),x)","\int \frac{{\left(c-d\,x^2\right)}^{3/2}}{{\left(e\,x\right)}^{3/2}\,{\left(a-b\,x^2\right)}^2} \,d x","Not used",1,"int((c - d*x^2)^(3/2)/((e*x)^(3/2)*(a - b*x^2)^2), x)","F"
909,0,-1,412,0.000000,"\text{Not used}","int((c - d*x^2)^(3/2)/((e*x)^(5/2)*(a - b*x^2)^2),x)","\int \frac{{\left(c-d\,x^2\right)}^{3/2}}{{\left(e\,x\right)}^{5/2}\,{\left(a-b\,x^2\right)}^2} \,d x","Not used",1,"int((c - d*x^2)^(3/2)/((e*x)^(5/2)*(a - b*x^2)^2), x)","F"
910,0,-1,484,0.000000,"\text{Not used}","int((e*x)^(9/2)/((a - b*x^2)^2*(c - d*x^2)^(1/2)),x)","\int \frac{{\left(e\,x\right)}^{9/2}}{{\left(a-b\,x^2\right)}^2\,\sqrt{c-d\,x^2}} \,d x","Not used",1,"int((e*x)^(9/2)/((a - b*x^2)^2*(c - d*x^2)^(1/2)), x)","F"
911,0,-1,376,0.000000,"\text{Not used}","int((e*x)^(7/2)/((a - b*x^2)^2*(c - d*x^2)^(1/2)),x)","\int \frac{{\left(e\,x\right)}^{7/2}}{{\left(a-b\,x^2\right)}^2\,\sqrt{c-d\,x^2}} \,d x","Not used",1,"int((e*x)^(7/2)/((a - b*x^2)^2*(c - d*x^2)^(1/2)), x)","F"
912,0,-1,460,0.000000,"\text{Not used}","int((e*x)^(5/2)/((a - b*x^2)^2*(c - d*x^2)^(1/2)),x)","\int \frac{{\left(e\,x\right)}^{5/2}}{{\left(a-b\,x^2\right)}^2\,\sqrt{c-d\,x^2}} \,d x","Not used",1,"int((e*x)^(5/2)/((a - b*x^2)^2*(c - d*x^2)^(1/2)), x)","F"
913,0,-1,363,0.000000,"\text{Not used}","int((e*x)^(3/2)/((a - b*x^2)^2*(c - d*x^2)^(1/2)),x)","\int \frac{{\left(e\,x\right)}^{3/2}}{{\left(a-b\,x^2\right)}^2\,\sqrt{c-d\,x^2}} \,d x","Not used",1,"int((e*x)^(3/2)/((a - b*x^2)^2*(c - d*x^2)^(1/2)), x)","F"
914,0,-1,464,0.000000,"\text{Not used}","int((e*x)^(1/2)/((a - b*x^2)^2*(c - d*x^2)^(1/2)),x)","\int \frac{\sqrt{e\,x}}{{\left(a-b\,x^2\right)}^2\,\sqrt{c-d\,x^2}} \,d x","Not used",1,"int((e*x)^(1/2)/((a - b*x^2)^2*(c - d*x^2)^(1/2)), x)","F"
915,0,-1,367,0.000000,"\text{Not used}","int(1/((e*x)^(1/2)*(a - b*x^2)^2*(c - d*x^2)^(1/2)),x)","\int \frac{1}{\sqrt{e\,x}\,{\left(a-b\,x^2\right)}^2\,\sqrt{c-d\,x^2}} \,d x","Not used",1,"int(1/((e*x)^(1/2)*(a - b*x^2)^2*(c - d*x^2)^(1/2)), x)","F"
916,0,-1,535,0.000000,"\text{Not used}","int(1/((e*x)^(3/2)*(a - b*x^2)^2*(c - d*x^2)^(1/2)),x)","\int \frac{1}{{\left(e\,x\right)}^{3/2}\,{\left(a-b\,x^2\right)}^2\,\sqrt{c-d\,x^2}} \,d x","Not used",1,"int(1/((e*x)^(3/2)*(a - b*x^2)^2*(c - d*x^2)^(1/2)), x)","F"
917,0,-1,429,0.000000,"\text{Not used}","int(1/((e*x)^(5/2)*(a - b*x^2)^2*(c - d*x^2)^(1/2)),x)","\int \frac{1}{{\left(e\,x\right)}^{5/2}\,{\left(a-b\,x^2\right)}^2\,\sqrt{c-d\,x^2}} \,d x","Not used",1,"int(1/((e*x)^(5/2)*(a - b*x^2)^2*(c - d*x^2)^(1/2)), x)","F"
918,0,-1,529,0.000000,"\text{Not used}","int((e*x)^(9/2)/((a - b*x^2)^2*(c - d*x^2)^(3/2)),x)","\int \frac{{\left(e\,x\right)}^{9/2}}{{\left(a-b\,x^2\right)}^2\,{\left(c-d\,x^2\right)}^{3/2}} \,d x","Not used",1,"int((e*x)^(9/2)/((a - b*x^2)^2*(c - d*x^2)^(3/2)), x)","F"
919,0,-1,420,0.000000,"\text{Not used}","int((e*x)^(7/2)/((a - b*x^2)^2*(c - d*x^2)^(3/2)),x)","\int \frac{{\left(e\,x\right)}^{7/2}}{{\left(a-b\,x^2\right)}^2\,{\left(c-d\,x^2\right)}^{3/2}} \,d x","Not used",1,"int((e*x)^(7/2)/((a - b*x^2)^2*(c - d*x^2)^(3/2)), x)","F"
920,0,-1,485,0.000000,"\text{Not used}","int((e*x)^(5/2)/((a - b*x^2)^2*(c - d*x^2)^(3/2)),x)","\int \frac{{\left(e\,x\right)}^{5/2}}{{\left(a-b\,x^2\right)}^2\,{\left(c-d\,x^2\right)}^{3/2}} \,d x","Not used",1,"int((e*x)^(5/2)/((a - b*x^2)^2*(c - d*x^2)^(3/2)), x)","F"
921,0,-1,391,0.000000,"\text{Not used}","int((e*x)^(3/2)/((a - b*x^2)^2*(c - d*x^2)^(3/2)),x)","\int \frac{{\left(e\,x\right)}^{3/2}}{{\left(a-b\,x^2\right)}^2\,{\left(c-d\,x^2\right)}^{3/2}} \,d x","Not used",1,"int((e*x)^(3/2)/((a - b*x^2)^2*(c - d*x^2)^(3/2)), x)","F"
922,0,-1,531,0.000000,"\text{Not used}","int((e*x)^(1/2)/((a - b*x^2)^2*(c - d*x^2)^(3/2)),x)","\int \frac{\sqrt{e\,x}}{{\left(a-b\,x^2\right)}^2\,{\left(c-d\,x^2\right)}^{3/2}} \,d x","Not used",1,"int((e*x)^(1/2)/((a - b*x^2)^2*(c - d*x^2)^(3/2)), x)","F"
923,0,-1,426,0.000000,"\text{Not used}","int(1/((e*x)^(1/2)*(a - b*x^2)^2*(c - d*x^2)^(3/2)),x)","\int \frac{1}{\sqrt{e\,x}\,{\left(a-b\,x^2\right)}^2\,{\left(c-d\,x^2\right)}^{3/2}} \,d x","Not used",1,"int(1/((e*x)^(1/2)*(a - b*x^2)^2*(c - d*x^2)^(3/2)), x)","F"
924,0,-1,628,0.000000,"\text{Not used}","int(1/((e*x)^(3/2)*(a - b*x^2)^2*(c - d*x^2)^(3/2)),x)","\int \frac{1}{{\left(e\,x\right)}^{3/2}\,{\left(a-b\,x^2\right)}^2\,{\left(c-d\,x^2\right)}^{3/2}} \,d x","Not used",1,"int(1/((e*x)^(3/2)*(a - b*x^2)^2*(c - d*x^2)^(3/2)), x)","F"
925,0,-1,512,0.000000,"\text{Not used}","int(1/((e*x)^(5/2)*(a - b*x^2)^2*(c - d*x^2)^(3/2)),x)","\int \frac{1}{{\left(e\,x\right)}^{5/2}\,{\left(a-b\,x^2\right)}^2\,{\left(c-d\,x^2\right)}^{3/2}} \,d x","Not used",1,"int(1/((e*x)^(5/2)*(a - b*x^2)^2*(c - d*x^2)^(3/2)), x)","F"
926,0,-1,568,0.000000,"\text{Not used}","int((e*x)^(9/2)/((a - b*x^2)^2*(c - d*x^2)^(5/2)),x)","\int \frac{{\left(e\,x\right)}^{9/2}}{{\left(a-b\,x^2\right)}^2\,{\left(c-d\,x^2\right)}^{5/2}} \,d x","Not used",1,"int((e*x)^(9/2)/((a - b*x^2)^2*(c - d*x^2)^(5/2)), x)","F"
927,0,-1,454,0.000000,"\text{Not used}","int((e*x)^(7/2)/((a - b*x^2)^2*(c - d*x^2)^(5/2)),x)","\int \frac{{\left(e\,x\right)}^{7/2}}{{\left(a-b\,x^2\right)}^2\,{\left(c-d\,x^2\right)}^{5/2}} \,d x","Not used",1,"int((e*x)^(7/2)/((a - b*x^2)^2*(c - d*x^2)^(5/2)), x)","F"
928,0,-1,551,0.000000,"\text{Not used}","int((e*x)^(5/2)/((a - b*x^2)^2*(c - d*x^2)^(5/2)),x)","\int \frac{{\left(e\,x\right)}^{5/2}}{{\left(a-b\,x^2\right)}^2\,{\left(c-d\,x^2\right)}^{5/2}} \,d x","Not used",1,"int((e*x)^(5/2)/((a - b*x^2)^2*(c - d*x^2)^(5/2)), x)","F"
929,0,-1,447,0.000000,"\text{Not used}","int((e*x)^(3/2)/((a - b*x^2)^2*(c - d*x^2)^(5/2)),x)","\int \frac{{\left(e\,x\right)}^{3/2}}{{\left(a-b\,x^2\right)}^2\,{\left(c-d\,x^2\right)}^{5/2}} \,d x","Not used",1,"int((e*x)^(3/2)/((a - b*x^2)^2*(c - d*x^2)^(5/2)), x)","F"
930,0,-1,625,0.000000,"\text{Not used}","int((e*x)^(1/2)/((a - b*x^2)^2*(c - d*x^2)^(5/2)),x)","\int \frac{\sqrt{e\,x}}{{\left(a-b\,x^2\right)}^2\,{\left(c-d\,x^2\right)}^{5/2}} \,d x","Not used",1,"int((e*x)^(1/2)/((a - b*x^2)^2*(c - d*x^2)^(5/2)), x)","F"
931,0,-1,514,0.000000,"\text{Not used}","int(1/((e*x)^(1/2)*(a - b*x^2)^2*(c - d*x^2)^(5/2)),x)","\int \frac{1}{\sqrt{e\,x}\,{\left(a-b\,x^2\right)}^2\,{\left(c-d\,x^2\right)}^{5/2}} \,d x","Not used",1,"int(1/((e*x)^(1/2)*(a - b*x^2)^2*(c - d*x^2)^(5/2)), x)","F"
932,0,-1,735,0.000000,"\text{Not used}","int(1/((e*x)^(3/2)*(a - b*x^2)^2*(c - d*x^2)^(5/2)),x)","\int \frac{1}{{\left(e\,x\right)}^{3/2}\,{\left(a-b\,x^2\right)}^2\,{\left(c-d\,x^2\right)}^{5/2}} \,d x","Not used",1,"int(1/((e*x)^(3/2)*(a - b*x^2)^2*(c - d*x^2)^(5/2)), x)","F"
933,0,-1,606,0.000000,"\text{Not used}","int(1/((e*x)^(5/2)*(a - b*x^2)^2*(c - d*x^2)^(5/2)),x)","\int \frac{1}{{\left(e\,x\right)}^{5/2}\,{\left(a-b\,x^2\right)}^2\,{\left(c-d\,x^2\right)}^{5/2}} \,d x","Not used",1,"int(1/((e*x)^(5/2)*(a - b*x^2)^2*(c - d*x^2)^(5/2)), x)","F"
934,1,993,209,54.784979,"\text{Not used}","int((x^5*(a + b*x^2)^(1/2))/(c + d*x^2)^(1/2),x)","\frac{\mathrm{atanh}\left(\frac{\sqrt{d}\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{\sqrt{b}\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}\right)\,\left(a\,d-b\,c\right)\,\left(a^2\,d^2+2\,a\,b\,c\,d+5\,b^2\,c^2\right)}{8\,b^{5/2}\,d^{7/2}}-\frac{\frac{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)\,\left(\frac{a^3\,b^3\,d^3}{8}+\frac{a^2\,b^4\,c\,d^2}{8}+\frac{3\,a\,b^5\,c^2\,d}{8}-\frac{5\,b^6\,c^3}{8}\right)}{d^9\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}-\frac{{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^5\,\left(\frac{19\,a^3\,b\,d^3}{4}+\frac{275\,a^2\,b^2\,c\,d^2}{4}+\frac{313\,a\,b^3\,c^2\,d}{4}+\frac{33\,b^4\,c^3}{4}\right)}{d^7\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^5}-\frac{{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^7\,\left(\frac{19\,a^3\,d^3}{4}+\frac{275\,a^2\,b\,c\,d^2}{4}+\frac{313\,a\,b^2\,c^2\,d}{4}+\frac{33\,b^3\,c^3}{4}\right)}{d^6\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^7}-\frac{{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^3\,\left(\frac{17\,a^3\,b^2\,d^3}{24}+\frac{91\,a^2\,b^3\,c\,d^2}{8}+\frac{17\,a\,b^4\,c^2\,d}{8}-\frac{85\,b^5\,c^3}{24}\right)}{d^8\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^3}+\frac{{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^{11}\,\left(\frac{a^3\,d^3}{8}+\frac{a^2\,b\,c\,d^2}{8}+\frac{3\,a\,b^2\,c^2\,d}{8}-\frac{5\,b^3\,c^3}{8}\right)}{b^2\,d^4\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^{11}}-\frac{{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^9\,\left(\frac{17\,a^3\,d^3}{24}+\frac{91\,a^2\,b\,c\,d^2}{8}+\frac{17\,a\,b^2\,c^2\,d}{8}-\frac{85\,b^3\,c^3}{24}\right)}{b\,d^5\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^9}+\frac{\sqrt{a}\,\sqrt{c}\,{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^8\,\left(16\,d\,a^2+48\,b\,c\,a\right)}{d^4\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^8}+\frac{\sqrt{a}\,\sqrt{c}\,{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^4\,\left(16\,d\,a^2\,b^2+48\,c\,a\,b^3\right)}{d^6\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^4}+\frac{\sqrt{a}\,\sqrt{c}\,{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^6\,\left(32\,a^2\,b\,d^2+\frac{352\,a\,b^2\,c\,d}{3}+64\,b^3\,c^2\right)}{d^6\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^6}}{\frac{{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^{12}}{{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^{12}}+\frac{b^6}{d^6}-\frac{6\,b^5\,{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^2}{d^5\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^2}+\frac{15\,b^4\,{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^4}{d^4\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^4}-\frac{20\,b^3\,{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^6}{d^3\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^6}+\frac{15\,b^2\,{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^8}{d^2\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^8}-\frac{6\,b\,{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^{10}}{d\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^{10}}}","Not used",1,"(atanh((d^(1/2)*((a + b*x^2)^(1/2) - a^(1/2)))/(b^(1/2)*((c + d*x^2)^(1/2) - c^(1/2))))*(a*d - b*c)*(a^2*d^2 + 5*b^2*c^2 + 2*a*b*c*d))/(8*b^(5/2)*d^(7/2)) - ((((a + b*x^2)^(1/2) - a^(1/2))*((a^3*b^3*d^3)/8 - (5*b^6*c^3)/8 + (a^2*b^4*c*d^2)/8 + (3*a*b^5*c^2*d)/8))/(d^9*((c + d*x^2)^(1/2) - c^(1/2))) - (((a + b*x^2)^(1/2) - a^(1/2))^5*((33*b^4*c^3)/4 + (19*a^3*b*d^3)/4 + (275*a^2*b^2*c*d^2)/4 + (313*a*b^3*c^2*d)/4))/(d^7*((c + d*x^2)^(1/2) - c^(1/2))^5) - (((a + b*x^2)^(1/2) - a^(1/2))^7*((19*a^3*d^3)/4 + (33*b^3*c^3)/4 + (313*a*b^2*c^2*d)/4 + (275*a^2*b*c*d^2)/4))/(d^6*((c + d*x^2)^(1/2) - c^(1/2))^7) - (((a + b*x^2)^(1/2) - a^(1/2))^3*((17*a^3*b^2*d^3)/24 - (85*b^5*c^3)/24 + (91*a^2*b^3*c*d^2)/8 + (17*a*b^4*c^2*d)/8))/(d^8*((c + d*x^2)^(1/2) - c^(1/2))^3) + (((a + b*x^2)^(1/2) - a^(1/2))^11*((a^3*d^3)/8 - (5*b^3*c^3)/8 + (3*a*b^2*c^2*d)/8 + (a^2*b*c*d^2)/8))/(b^2*d^4*((c + d*x^2)^(1/2) - c^(1/2))^11) - (((a + b*x^2)^(1/2) - a^(1/2))^9*((17*a^3*d^3)/24 - (85*b^3*c^3)/24 + (17*a*b^2*c^2*d)/8 + (91*a^2*b*c*d^2)/8))/(b*d^5*((c + d*x^2)^(1/2) - c^(1/2))^9) + (a^(1/2)*c^(1/2)*((a + b*x^2)^(1/2) - a^(1/2))^8*(16*a^2*d + 48*a*b*c))/(d^4*((c + d*x^2)^(1/2) - c^(1/2))^8) + (a^(1/2)*c^(1/2)*((a + b*x^2)^(1/2) - a^(1/2))^4*(16*a^2*b^2*d + 48*a*b^3*c))/(d^6*((c + d*x^2)^(1/2) - c^(1/2))^4) + (a^(1/2)*c^(1/2)*((a + b*x^2)^(1/2) - a^(1/2))^6*(64*b^3*c^2 + 32*a^2*b*d^2 + (352*a*b^2*c*d)/3))/(d^6*((c + d*x^2)^(1/2) - c^(1/2))^6))/(((a + b*x^2)^(1/2) - a^(1/2))^12/((c + d*x^2)^(1/2) - c^(1/2))^12 + b^6/d^6 - (6*b^5*((a + b*x^2)^(1/2) - a^(1/2))^2)/(d^5*((c + d*x^2)^(1/2) - c^(1/2))^2) + (15*b^4*((a + b*x^2)^(1/2) - a^(1/2))^4)/(d^4*((c + d*x^2)^(1/2) - c^(1/2))^4) - (20*b^3*((a + b*x^2)^(1/2) - a^(1/2))^6)/(d^3*((c + d*x^2)^(1/2) - c^(1/2))^6) + (15*b^2*((a + b*x^2)^(1/2) - a^(1/2))^8)/(d^2*((c + d*x^2)^(1/2) - c^(1/2))^8) - (6*b*((a + b*x^2)^(1/2) - a^(1/2))^10)/(d*((c + d*x^2)^(1/2) - c^(1/2))^10))","B"
935,1,639,137,25.181239,"\text{Not used}","int((x^3*(a + b*x^2)^(1/2))/(c + d*x^2)^(1/2),x)","\frac{\frac{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)\,\left(\frac{a^2\,b^2\,d^2}{4}+\frac{a\,b^3\,c\,d}{2}-\frac{3\,b^4\,c^2}{4}\right)}{d^6\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}+\frac{{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^3\,\left(\frac{7\,a^2\,b\,d^2}{4}+\frac{23\,a\,b^2\,c\,d}{2}+\frac{11\,b^3\,c^2}{4}\right)}{d^5\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^3}+\frac{{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^5\,\left(\frac{7\,a^2\,d^2}{4}+\frac{23\,a\,b\,c\,d}{2}+\frac{11\,b^2\,c^2}{4}\right)}{d^4\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^5}+\frac{{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^7\,\left(\frac{a^2\,d^2}{4}+\frac{a\,b\,c\,d}{2}-\frac{3\,b^2\,c^2}{4}\right)}{b\,d^3\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^7}-\frac{4\,a^{3/2}\,\sqrt{c}\,{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^6}{d^2\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^6}-\frac{\sqrt{a}\,\sqrt{c}\,{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^4\,\left(16\,c\,b^2+8\,a\,d\,b\right)}{d^4\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^4}-\frac{4\,a^{3/2}\,b^2\,\sqrt{c}\,{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^2}{d^4\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^2}}{\frac{{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^8}{{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^8}+\frac{b^4}{d^4}-\frac{4\,b^3\,{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^2}{d^3\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^2}+\frac{6\,b^2\,{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^4}{d^2\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^4}-\frac{4\,b\,{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^6}{d\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^6}}-\frac{\mathrm{atanh}\left(\frac{\sqrt{d}\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{\sqrt{b}\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}\right)\,\left(a\,d-b\,c\right)\,\left(a\,d+3\,b\,c\right)}{4\,b^{3/2}\,d^{5/2}}","Not used",1,"((((a + b*x^2)^(1/2) - a^(1/2))*((a^2*b^2*d^2)/4 - (3*b^4*c^2)/4 + (a*b^3*c*d)/2))/(d^6*((c + d*x^2)^(1/2) - c^(1/2))) + (((a + b*x^2)^(1/2) - a^(1/2))^3*((11*b^3*c^2)/4 + (7*a^2*b*d^2)/4 + (23*a*b^2*c*d)/2))/(d^5*((c + d*x^2)^(1/2) - c^(1/2))^3) + (((a + b*x^2)^(1/2) - a^(1/2))^5*((7*a^2*d^2)/4 + (11*b^2*c^2)/4 + (23*a*b*c*d)/2))/(d^4*((c + d*x^2)^(1/2) - c^(1/2))^5) + (((a + b*x^2)^(1/2) - a^(1/2))^7*((a^2*d^2)/4 - (3*b^2*c^2)/4 + (a*b*c*d)/2))/(b*d^3*((c + d*x^2)^(1/2) - c^(1/2))^7) - (4*a^(3/2)*c^(1/2)*((a + b*x^2)^(1/2) - a^(1/2))^6)/(d^2*((c + d*x^2)^(1/2) - c^(1/2))^6) - (a^(1/2)*c^(1/2)*((a + b*x^2)^(1/2) - a^(1/2))^4*(16*b^2*c + 8*a*b*d))/(d^4*((c + d*x^2)^(1/2) - c^(1/2))^4) - (4*a^(3/2)*b^2*c^(1/2)*((a + b*x^2)^(1/2) - a^(1/2))^2)/(d^4*((c + d*x^2)^(1/2) - c^(1/2))^2))/(((a + b*x^2)^(1/2) - a^(1/2))^8/((c + d*x^2)^(1/2) - c^(1/2))^8 + b^4/d^4 - (4*b^3*((a + b*x^2)^(1/2) - a^(1/2))^2)/(d^3*((c + d*x^2)^(1/2) - c^(1/2))^2) + (6*b^2*((a + b*x^2)^(1/2) - a^(1/2))^4)/(d^2*((c + d*x^2)^(1/2) - c^(1/2))^4) - (4*b*((a + b*x^2)^(1/2) - a^(1/2))^6)/(d*((c + d*x^2)^(1/2) - c^(1/2))^6)) - (atanh((d^(1/2)*((a + b*x^2)^(1/2) - a^(1/2)))/(b^(1/2)*((c + d*x^2)^(1/2) - c^(1/2))))*(a*d - b*c)*(a*d + 3*b*c))/(4*b^(3/2)*d^(5/2))","B"
936,1,280,86,4.997870,"\text{Not used}","int((x*(a + b*x^2)^(1/2))/(c + d*x^2)^(1/2),x)","\frac{\frac{{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^3\,\left(a\,d+b\,c\right)}{d^2\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^3}+\frac{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)\,\left(c\,b^2+a\,d\,b\right)}{d^3\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}-\frac{4\,\sqrt{a}\,b\,\sqrt{c}\,{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^2}{d^2\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^2}}{\frac{{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^4}{{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^4}+\frac{b^2}{d^2}-\frac{2\,b\,{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^2}{d\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^2}}+\frac{\mathrm{atanh}\left(\frac{\sqrt{d}\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{\sqrt{b}\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}\right)\,\left(a\,d-b\,c\right)}{\sqrt{b}\,d^{3/2}}","Not used",1,"((((a + b*x^2)^(1/2) - a^(1/2))^3*(a*d + b*c))/(d^2*((c + d*x^2)^(1/2) - c^(1/2))^3) + (((a + b*x^2)^(1/2) - a^(1/2))*(b^2*c + a*b*d))/(d^3*((c + d*x^2)^(1/2) - c^(1/2))) - (4*a^(1/2)*b*c^(1/2)*((a + b*x^2)^(1/2) - a^(1/2))^2)/(d^2*((c + d*x^2)^(1/2) - c^(1/2))^2))/(((a + b*x^2)^(1/2) - a^(1/2))^4/((c + d*x^2)^(1/2) - c^(1/2))^4 + b^2/d^2 - (2*b*((a + b*x^2)^(1/2) - a^(1/2))^2)/(d*((c + d*x^2)^(1/2) - c^(1/2))^2)) + (atanh((d^(1/2)*((a + b*x^2)^(1/2) - a^(1/2)))/(b^(1/2)*((c + d*x^2)^(1/2) - c^(1/2))))*(a*d - b*c))/(b^(1/2)*d^(3/2))","B"
937,1,4638,92,19.830835,"\text{Not used}","int((a + b*x^2)^(1/2)/(x*(c + d*x^2)^(1/2)),x)","\frac{2\,\mathrm{atanh}\left(\frac{20\,a\,b^7\,\sqrt{b\,d}}{34\,\sqrt{a}\,b^8\,\sqrt{c}-\frac{33\,a^{3/2}\,b^7\,d}{\sqrt{c}}-\frac{54\,b^8\,c\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{\sqrt{d\,x^2+c}-\sqrt{c}}+\frac{25\,b^9\,c^{3/2}}{2\,\sqrt{a}\,d}+\frac{4\,a^{5/2}\,b^6\,d^2}{c^{3/2}}-\frac{18\,b^{10}\,c^{5/2}}{a^{3/2}\,d^2}+\frac{a^{7/2}\,b^5\,d^3}{2\,c^{5/2}}+\frac{20\,a\,b^7\,d\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{\sqrt{d\,x^2+c}-\sqrt{c}}+\frac{10\,a^2\,b^6\,d^2\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{c\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}+\frac{23\,b^9\,c^2\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{a\,d\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}-\frac{3\,a^3\,b^5\,d^3\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{c^2\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}+\frac{4\,b^{10}\,c^3\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{a^2\,d^2\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}}-\frac{54\,b^8\,\sqrt{b\,d}}{\frac{25\,b^9\,\sqrt{c}}{2\,\sqrt{a}}+\frac{34\,\sqrt{a}\,b^8\,d}{\sqrt{c}}-\frac{54\,b^8\,d\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{\sqrt{d\,x^2+c}-\sqrt{c}}-\frac{33\,a^{3/2}\,b^7\,d^2}{c^{3/2}}-\frac{18\,b^{10}\,c^{3/2}}{a^{3/2}\,d}+\frac{4\,a^{5/2}\,b^6\,d^3}{c^{5/2}}+\frac{a^{7/2}\,b^5\,d^4}{2\,c^{7/2}}+\frac{23\,b^9\,c\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{a\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}+\frac{10\,a^2\,b^6\,d^3\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{c^2\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}+\frac{4\,b^{10}\,c^2\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{a^2\,d\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}-\frac{3\,a^3\,b^5\,d^4\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{c^3\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}+\frac{20\,a\,b^7\,d^2\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{c\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}}+\frac{23\,b^9\,c\,\sqrt{b\,d}}{\frac{25\,\sqrt{a}\,b^9\,\sqrt{c}\,d}{2}-\frac{18\,b^{10}\,c^{3/2}}{\sqrt{a}}+\frac{34\,a^{3/2}\,b^8\,d^2}{\sqrt{c}}-\frac{33\,a^{5/2}\,b^7\,d^3}{c^{3/2}}+\frac{4\,a^{7/2}\,b^6\,d^4}{c^{5/2}}+\frac{a^{9/2}\,b^5\,d^5}{2\,c^{7/2}}-\frac{54\,a\,b^8\,d^2\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{\sqrt{d\,x^2+c}-\sqrt{c}}+\frac{4\,b^{10}\,c^2\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{a\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}+\frac{23\,b^9\,c\,d\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{\sqrt{d\,x^2+c}-\sqrt{c}}+\frac{20\,a^2\,b^7\,d^3\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{c\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}+\frac{10\,a^3\,b^6\,d^4\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{c^2\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}-\frac{3\,a^4\,b^5\,d^5\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{c^3\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}}+\frac{10\,a^2\,b^6\,\sqrt{b\,d}}{\frac{4\,a^{5/2}\,b^6\,d}{\sqrt{c}}-33\,a^{3/2}\,b^7\,\sqrt{c}+\frac{34\,\sqrt{a}\,b^8\,c^{3/2}}{d}+\frac{25\,b^9\,c^{5/2}}{2\,\sqrt{a}\,d^2}+\frac{a^{7/2}\,b^5\,d^2}{2\,c^{3/2}}-\frac{18\,b^{10}\,c^{7/2}}{a^{3/2}\,d^3}+\frac{10\,a^2\,b^6\,d\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{\sqrt{d\,x^2+c}-\sqrt{c}}-\frac{54\,b^8\,c^2\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{d\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}+\frac{20\,a\,b^7\,c\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{\sqrt{d\,x^2+c}-\sqrt{c}}-\frac{3\,a^3\,b^5\,d^2\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{c\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}+\frac{23\,b^9\,c^3\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{a\,d^2\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}+\frac{4\,b^{10}\,c^4\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{a^2\,d^3\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}}-\frac{3\,a^3\,b^5\,\sqrt{b\,d}}{4\,a^{5/2}\,b^6\,\sqrt{c}+\frac{a^{7/2}\,b^5\,d}{2\,\sqrt{c}}-\frac{33\,a^{3/2}\,b^7\,c^{3/2}}{d}+\frac{34\,\sqrt{a}\,b^8\,c^{5/2}}{d^2}+\frac{25\,b^9\,c^{7/2}}{2\,\sqrt{a}\,d^3}-\frac{18\,b^{10}\,c^{9/2}}{a^{3/2}\,d^4}+\frac{10\,a^2\,b^6\,c\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{\sqrt{d\,x^2+c}-\sqrt{c}}-\frac{3\,a^3\,b^5\,d\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{\sqrt{d\,x^2+c}-\sqrt{c}}-\frac{54\,b^8\,c^3\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{d^2\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}+\frac{23\,b^9\,c^4\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{a\,d^3\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}+\frac{4\,b^{10}\,c^5\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{a^2\,d^4\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}+\frac{20\,a\,b^7\,c^2\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{d\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}}+\frac{4\,b^{10}\,c^2\,\sqrt{b\,d}}{\frac{25\,a^{3/2}\,b^9\,\sqrt{c}\,d^2}{2}-18\,\sqrt{a}\,b^{10}\,c^{3/2}\,d+\frac{34\,a^{5/2}\,b^8\,d^3}{\sqrt{c}}-\frac{33\,a^{7/2}\,b^7\,d^4}{c^{3/2}}+\frac{4\,a^{9/2}\,b^6\,d^5}{c^{5/2}}+\frac{a^{11/2}\,b^5\,d^6}{2\,c^{7/2}}+\frac{4\,b^{10}\,c^2\,d\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{\sqrt{d\,x^2+c}-\sqrt{c}}-\frac{54\,a^2\,b^8\,d^3\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{\sqrt{d\,x^2+c}-\sqrt{c}}+\frac{20\,a^3\,b^7\,d^4\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{c\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}+\frac{10\,a^4\,b^6\,d^5\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{c^2\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}-\frac{3\,a^5\,b^5\,d^6\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{c^3\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}+\frac{23\,a\,b^9\,c\,d^2\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{\sqrt{d\,x^2+c}-\sqrt{c}}}+\frac{34\,\sqrt{a}\,b^7\,\sqrt{b\,d}\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{\sqrt{c}\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)\,\left(\frac{34\,\sqrt{a}\,b^8}{\sqrt{c}}-\frac{54\,b^8\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{\sqrt{d\,x^2+c}-\sqrt{c}}-\frac{33\,a^{3/2}\,b^7\,d}{c^{3/2}}+\frac{25\,b^9\,\sqrt{c}}{2\,\sqrt{a}\,d}-\frac{18\,b^{10}\,c^{3/2}}{a^{3/2}\,d^2}+\frac{4\,a^{5/2}\,b^6\,d^2}{c^{5/2}}+\frac{a^{7/2}\,b^5\,d^3}{2\,c^{7/2}}+\frac{10\,a^2\,b^6\,d^2\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{c^2\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}-\frac{3\,a^3\,b^5\,d^3\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{c^3\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}+\frac{4\,b^{10}\,c^2\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{a^2\,d^2\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}+\frac{20\,a\,b^7\,d\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{c\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}+\frac{23\,b^9\,c\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{a\,d\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}\right)}-\frac{33\,a^{3/2}\,b^6\,\sqrt{b\,d}\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{c^{3/2}\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)\,\left(\frac{4\,a^{5/2}\,b^6\,d}{c^{5/2}}-\frac{33\,a^{3/2}\,b^7}{c^{3/2}}+\frac{34\,\sqrt{a}\,b^8}{\sqrt{c}\,d}+\frac{25\,b^9\,\sqrt{c}}{2\,\sqrt{a}\,d^2}-\frac{18\,b^{10}\,c^{3/2}}{a^{3/2}\,d^3}+\frac{a^{7/2}\,b^5\,d^2}{2\,c^{7/2}}-\frac{54\,b^8\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{d\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}+\frac{20\,a\,b^7\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{c\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}-\frac{3\,a^3\,b^5\,d^2\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{c^3\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}+\frac{4\,b^{10}\,c^2\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{a^2\,d^3\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}+\frac{10\,a^2\,b^6\,d\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{c^2\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}+\frac{23\,b^9\,c\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{a\,d^2\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}\right)}+\frac{25\,b^8\,\sqrt{c}\,\sqrt{b\,d}\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{2\,\sqrt{a}\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)\,\left(\frac{25\,b^9\,\sqrt{c}}{2\,\sqrt{a}}+\frac{34\,\sqrt{a}\,b^8\,d}{\sqrt{c}}-\frac{54\,b^8\,d\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{\sqrt{d\,x^2+c}-\sqrt{c}}-\frac{33\,a^{3/2}\,b^7\,d^2}{c^{3/2}}-\frac{18\,b^{10}\,c^{3/2}}{a^{3/2}\,d}+\frac{4\,a^{5/2}\,b^6\,d^3}{c^{5/2}}+\frac{a^{7/2}\,b^5\,d^4}{2\,c^{7/2}}+\frac{23\,b^9\,c\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{a\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}+\frac{10\,a^2\,b^6\,d^3\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{c^2\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}+\frac{4\,b^{10}\,c^2\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{a^2\,d\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}-\frac{3\,a^3\,b^5\,d^4\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{c^3\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}+\frac{20\,a\,b^7\,d^2\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{c\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}\right)}+\frac{4\,a^{5/2}\,b^5\,\sqrt{b\,d}\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{c^{5/2}\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)\,\left(\frac{4\,a^{5/2}\,b^6}{c^{5/2}}+\frac{a^{7/2}\,b^5\,d}{2\,c^{7/2}}+\frac{34\,\sqrt{a}\,b^8}{\sqrt{c}\,d^2}+\frac{25\,b^9\,\sqrt{c}}{2\,\sqrt{a}\,d^3}-\frac{33\,a^{3/2}\,b^7}{c^{3/2}\,d}-\frac{18\,b^{10}\,c^{3/2}}{a^{3/2}\,d^4}-\frac{54\,b^8\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{d^2\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}+\frac{10\,a^2\,b^6\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{c^2\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}+\frac{4\,b^{10}\,c^2\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{a^2\,d^4\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}+\frac{20\,a\,b^7\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{c\,d\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}-\frac{3\,a^3\,b^5\,d\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{c^3\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}+\frac{23\,b^9\,c\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{a\,d^3\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}\right)}-\frac{18\,b^9\,c^{3/2}\,\sqrt{b\,d}\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{a^{3/2}\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)\,\left(\frac{25\,b^9\,\sqrt{c}\,d}{2\,\sqrt{a}}-\frac{18\,b^{10}\,c^{3/2}}{a^{3/2}}+\frac{34\,\sqrt{a}\,b^8\,d^2}{\sqrt{c}}-\frac{33\,a^{3/2}\,b^7\,d^3}{c^{3/2}}+\frac{4\,a^{5/2}\,b^6\,d^4}{c^{5/2}}+\frac{a^{7/2}\,b^5\,d^5}{2\,c^{7/2}}-\frac{54\,b^8\,d^2\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{\sqrt{d\,x^2+c}-\sqrt{c}}+\frac{4\,b^{10}\,c^2\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{a^2\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}+\frac{10\,a^2\,b^6\,d^4\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{c^2\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}-\frac{3\,a^3\,b^5\,d^5\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{c^3\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}+\frac{23\,b^9\,c\,d\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{a\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}+\frac{20\,a\,b^7\,d^3\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{c\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}\right)}+\frac{a^{7/2}\,b^4\,\sqrt{b\,d}\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{2\,c^{7/2}\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)\,\left(\frac{a^{7/2}\,b^5}{2\,c^{7/2}}+\frac{34\,\sqrt{a}\,b^8}{\sqrt{c}\,d^3}+\frac{25\,b^9\,\sqrt{c}}{2\,\sqrt{a}\,d^4}-\frac{33\,a^{3/2}\,b^7}{c^{3/2}\,d^2}+\frac{4\,a^{5/2}\,b^6}{c^{5/2}\,d}-\frac{18\,b^{10}\,c^{3/2}}{a^{3/2}\,d^5}-\frac{54\,b^8\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{d^3\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}-\frac{3\,a^3\,b^5\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{c^3\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}+\frac{10\,a^2\,b^6\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{c^2\,d\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}+\frac{4\,b^{10}\,c^2\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{a^2\,d^5\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}+\frac{20\,a\,b^7\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{c\,d^2\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}+\frac{23\,b^9\,c\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{a\,d^4\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}\right)}\right)\,\sqrt{b\,d}}{d}-\frac{\sqrt{a}\,\ln\left(\frac{\sqrt{b\,x^2+a}-\sqrt{a}}{\sqrt{d\,x^2+c}-\sqrt{c}}\right)-\sqrt{a}\,\ln\left(\frac{\left(\sqrt{c}\,\sqrt{b\,x^2+a}-\sqrt{a}\,\sqrt{d\,x^2+c}\right)\,\left(b\,\sqrt{c}-\frac{\sqrt{a}\,d\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{\sqrt{d\,x^2+c}-\sqrt{c}}\right)}{\sqrt{d\,x^2+c}-\sqrt{c}}\right)}{2\,\sqrt{c}}","Not used",1,"(2*atanh((20*a*b^7*(b*d)^(1/2))/(34*a^(1/2)*b^8*c^(1/2) - (33*a^(3/2)*b^7*d)/c^(1/2) - (54*b^8*c*((a + b*x^2)^(1/2) - a^(1/2)))/((c + d*x^2)^(1/2) - c^(1/2)) + (25*b^9*c^(3/2))/(2*a^(1/2)*d) + (4*a^(5/2)*b^6*d^2)/c^(3/2) - (18*b^10*c^(5/2))/(a^(3/2)*d^2) + (a^(7/2)*b^5*d^3)/(2*c^(5/2)) + (20*a*b^7*d*((a + b*x^2)^(1/2) - a^(1/2)))/((c + d*x^2)^(1/2) - c^(1/2)) + (10*a^2*b^6*d^2*((a + b*x^2)^(1/2) - a^(1/2)))/(c*((c + d*x^2)^(1/2) - c^(1/2))) + (23*b^9*c^2*((a + b*x^2)^(1/2) - a^(1/2)))/(a*d*((c + d*x^2)^(1/2) - c^(1/2))) - (3*a^3*b^5*d^3*((a + b*x^2)^(1/2) - a^(1/2)))/(c^2*((c + d*x^2)^(1/2) - c^(1/2))) + (4*b^10*c^3*((a + b*x^2)^(1/2) - a^(1/2)))/(a^2*d^2*((c + d*x^2)^(1/2) - c^(1/2)))) - (54*b^8*(b*d)^(1/2))/((25*b^9*c^(1/2))/(2*a^(1/2)) + (34*a^(1/2)*b^8*d)/c^(1/2) - (54*b^8*d*((a + b*x^2)^(1/2) - a^(1/2)))/((c + d*x^2)^(1/2) - c^(1/2)) - (33*a^(3/2)*b^7*d^2)/c^(3/2) - (18*b^10*c^(3/2))/(a^(3/2)*d) + (4*a^(5/2)*b^6*d^3)/c^(5/2) + (a^(7/2)*b^5*d^4)/(2*c^(7/2)) + (23*b^9*c*((a + b*x^2)^(1/2) - a^(1/2)))/(a*((c + d*x^2)^(1/2) - c^(1/2))) + (10*a^2*b^6*d^3*((a + b*x^2)^(1/2) - a^(1/2)))/(c^2*((c + d*x^2)^(1/2) - c^(1/2))) + (4*b^10*c^2*((a + b*x^2)^(1/2) - a^(1/2)))/(a^2*d*((c + d*x^2)^(1/2) - c^(1/2))) - (3*a^3*b^5*d^4*((a + b*x^2)^(1/2) - a^(1/2)))/(c^3*((c + d*x^2)^(1/2) - c^(1/2))) + (20*a*b^7*d^2*((a + b*x^2)^(1/2) - a^(1/2)))/(c*((c + d*x^2)^(1/2) - c^(1/2)))) + (23*b^9*c*(b*d)^(1/2))/((25*a^(1/2)*b^9*c^(1/2)*d)/2 - (18*b^10*c^(3/2))/a^(1/2) + (34*a^(3/2)*b^8*d^2)/c^(1/2) - (33*a^(5/2)*b^7*d^3)/c^(3/2) + (4*a^(7/2)*b^6*d^4)/c^(5/2) + (a^(9/2)*b^5*d^5)/(2*c^(7/2)) - (54*a*b^8*d^2*((a + b*x^2)^(1/2) - a^(1/2)))/((c + d*x^2)^(1/2) - c^(1/2)) + (4*b^10*c^2*((a + b*x^2)^(1/2) - a^(1/2)))/(a*((c + d*x^2)^(1/2) - c^(1/2))) + (23*b^9*c*d*((a + b*x^2)^(1/2) - a^(1/2)))/((c + d*x^2)^(1/2) - c^(1/2)) + (20*a^2*b^7*d^3*((a + b*x^2)^(1/2) - a^(1/2)))/(c*((c + d*x^2)^(1/2) - c^(1/2))) + (10*a^3*b^6*d^4*((a + b*x^2)^(1/2) - a^(1/2)))/(c^2*((c + d*x^2)^(1/2) - c^(1/2))) - (3*a^4*b^5*d^5*((a + b*x^2)^(1/2) - a^(1/2)))/(c^3*((c + d*x^2)^(1/2) - c^(1/2)))) + (10*a^2*b^6*(b*d)^(1/2))/((4*a^(5/2)*b^6*d)/c^(1/2) - 33*a^(3/2)*b^7*c^(1/2) + (34*a^(1/2)*b^8*c^(3/2))/d + (25*b^9*c^(5/2))/(2*a^(1/2)*d^2) + (a^(7/2)*b^5*d^2)/(2*c^(3/2)) - (18*b^10*c^(7/2))/(a^(3/2)*d^3) + (10*a^2*b^6*d*((a + b*x^2)^(1/2) - a^(1/2)))/((c + d*x^2)^(1/2) - c^(1/2)) - (54*b^8*c^2*((a + b*x^2)^(1/2) - a^(1/2)))/(d*((c + d*x^2)^(1/2) - c^(1/2))) + (20*a*b^7*c*((a + b*x^2)^(1/2) - a^(1/2)))/((c + d*x^2)^(1/2) - c^(1/2)) - (3*a^3*b^5*d^2*((a + b*x^2)^(1/2) - a^(1/2)))/(c*((c + d*x^2)^(1/2) - c^(1/2))) + (23*b^9*c^3*((a + b*x^2)^(1/2) - a^(1/2)))/(a*d^2*((c + d*x^2)^(1/2) - c^(1/2))) + (4*b^10*c^4*((a + b*x^2)^(1/2) - a^(1/2)))/(a^2*d^3*((c + d*x^2)^(1/2) - c^(1/2)))) - (3*a^3*b^5*(b*d)^(1/2))/(4*a^(5/2)*b^6*c^(1/2) + (a^(7/2)*b^5*d)/(2*c^(1/2)) - (33*a^(3/2)*b^7*c^(3/2))/d + (34*a^(1/2)*b^8*c^(5/2))/d^2 + (25*b^9*c^(7/2))/(2*a^(1/2)*d^3) - (18*b^10*c^(9/2))/(a^(3/2)*d^4) + (10*a^2*b^6*c*((a + b*x^2)^(1/2) - a^(1/2)))/((c + d*x^2)^(1/2) - c^(1/2)) - (3*a^3*b^5*d*((a + b*x^2)^(1/2) - a^(1/2)))/((c + d*x^2)^(1/2) - c^(1/2)) - (54*b^8*c^3*((a + b*x^2)^(1/2) - a^(1/2)))/(d^2*((c + d*x^2)^(1/2) - c^(1/2))) + (23*b^9*c^4*((a + b*x^2)^(1/2) - a^(1/2)))/(a*d^3*((c + d*x^2)^(1/2) - c^(1/2))) + (4*b^10*c^5*((a + b*x^2)^(1/2) - a^(1/2)))/(a^2*d^4*((c + d*x^2)^(1/2) - c^(1/2))) + (20*a*b^7*c^2*((a + b*x^2)^(1/2) - a^(1/2)))/(d*((c + d*x^2)^(1/2) - c^(1/2)))) + (4*b^10*c^2*(b*d)^(1/2))/((25*a^(3/2)*b^9*c^(1/2)*d^2)/2 - 18*a^(1/2)*b^10*c^(3/2)*d + (34*a^(5/2)*b^8*d^3)/c^(1/2) - (33*a^(7/2)*b^7*d^4)/c^(3/2) + (4*a^(9/2)*b^6*d^5)/c^(5/2) + (a^(11/2)*b^5*d^6)/(2*c^(7/2)) + (4*b^10*c^2*d*((a + b*x^2)^(1/2) - a^(1/2)))/((c + d*x^2)^(1/2) - c^(1/2)) - (54*a^2*b^8*d^3*((a + b*x^2)^(1/2) - a^(1/2)))/((c + d*x^2)^(1/2) - c^(1/2)) + (20*a^3*b^7*d^4*((a + b*x^2)^(1/2) - a^(1/2)))/(c*((c + d*x^2)^(1/2) - c^(1/2))) + (10*a^4*b^6*d^5*((a + b*x^2)^(1/2) - a^(1/2)))/(c^2*((c + d*x^2)^(1/2) - c^(1/2))) - (3*a^5*b^5*d^6*((a + b*x^2)^(1/2) - a^(1/2)))/(c^3*((c + d*x^2)^(1/2) - c^(1/2))) + (23*a*b^9*c*d^2*((a + b*x^2)^(1/2) - a^(1/2)))/((c + d*x^2)^(1/2) - c^(1/2))) + (34*a^(1/2)*b^7*(b*d)^(1/2)*((a + b*x^2)^(1/2) - a^(1/2)))/(c^(1/2)*((c + d*x^2)^(1/2) - c^(1/2))*((34*a^(1/2)*b^8)/c^(1/2) - (54*b^8*((a + b*x^2)^(1/2) - a^(1/2)))/((c + d*x^2)^(1/2) - c^(1/2)) - (33*a^(3/2)*b^7*d)/c^(3/2) + (25*b^9*c^(1/2))/(2*a^(1/2)*d) - (18*b^10*c^(3/2))/(a^(3/2)*d^2) + (4*a^(5/2)*b^6*d^2)/c^(5/2) + (a^(7/2)*b^5*d^3)/(2*c^(7/2)) + (10*a^2*b^6*d^2*((a + b*x^2)^(1/2) - a^(1/2)))/(c^2*((c + d*x^2)^(1/2) - c^(1/2))) - (3*a^3*b^5*d^3*((a + b*x^2)^(1/2) - a^(1/2)))/(c^3*((c + d*x^2)^(1/2) - c^(1/2))) + (4*b^10*c^2*((a + b*x^2)^(1/2) - a^(1/2)))/(a^2*d^2*((c + d*x^2)^(1/2) - c^(1/2))) + (20*a*b^7*d*((a + b*x^2)^(1/2) - a^(1/2)))/(c*((c + d*x^2)^(1/2) - c^(1/2))) + (23*b^9*c*((a + b*x^2)^(1/2) - a^(1/2)))/(a*d*((c + d*x^2)^(1/2) - c^(1/2))))) - (33*a^(3/2)*b^6*(b*d)^(1/2)*((a + b*x^2)^(1/2) - a^(1/2)))/(c^(3/2)*((c + d*x^2)^(1/2) - c^(1/2))*((4*a^(5/2)*b^6*d)/c^(5/2) - (33*a^(3/2)*b^7)/c^(3/2) + (34*a^(1/2)*b^8)/(c^(1/2)*d) + (25*b^9*c^(1/2))/(2*a^(1/2)*d^2) - (18*b^10*c^(3/2))/(a^(3/2)*d^3) + (a^(7/2)*b^5*d^2)/(2*c^(7/2)) - (54*b^8*((a + b*x^2)^(1/2) - a^(1/2)))/(d*((c + d*x^2)^(1/2) - c^(1/2))) + (20*a*b^7*((a + b*x^2)^(1/2) - a^(1/2)))/(c*((c + d*x^2)^(1/2) - c^(1/2))) - (3*a^3*b^5*d^2*((a + b*x^2)^(1/2) - a^(1/2)))/(c^3*((c + d*x^2)^(1/2) - c^(1/2))) + (4*b^10*c^2*((a + b*x^2)^(1/2) - a^(1/2)))/(a^2*d^3*((c + d*x^2)^(1/2) - c^(1/2))) + (10*a^2*b^6*d*((a + b*x^2)^(1/2) - a^(1/2)))/(c^2*((c + d*x^2)^(1/2) - c^(1/2))) + (23*b^9*c*((a + b*x^2)^(1/2) - a^(1/2)))/(a*d^2*((c + d*x^2)^(1/2) - c^(1/2))))) + (25*b^8*c^(1/2)*(b*d)^(1/2)*((a + b*x^2)^(1/2) - a^(1/2)))/(2*a^(1/2)*((c + d*x^2)^(1/2) - c^(1/2))*((25*b^9*c^(1/2))/(2*a^(1/2)) + (34*a^(1/2)*b^8*d)/c^(1/2) - (54*b^8*d*((a + b*x^2)^(1/2) - a^(1/2)))/((c + d*x^2)^(1/2) - c^(1/2)) - (33*a^(3/2)*b^7*d^2)/c^(3/2) - (18*b^10*c^(3/2))/(a^(3/2)*d) + (4*a^(5/2)*b^6*d^3)/c^(5/2) + (a^(7/2)*b^5*d^4)/(2*c^(7/2)) + (23*b^9*c*((a + b*x^2)^(1/2) - a^(1/2)))/(a*((c + d*x^2)^(1/2) - c^(1/2))) + (10*a^2*b^6*d^3*((a + b*x^2)^(1/2) - a^(1/2)))/(c^2*((c + d*x^2)^(1/2) - c^(1/2))) + (4*b^10*c^2*((a + b*x^2)^(1/2) - a^(1/2)))/(a^2*d*((c + d*x^2)^(1/2) - c^(1/2))) - (3*a^3*b^5*d^4*((a + b*x^2)^(1/2) - a^(1/2)))/(c^3*((c + d*x^2)^(1/2) - c^(1/2))) + (20*a*b^7*d^2*((a + b*x^2)^(1/2) - a^(1/2)))/(c*((c + d*x^2)^(1/2) - c^(1/2))))) + (4*a^(5/2)*b^5*(b*d)^(1/2)*((a + b*x^2)^(1/2) - a^(1/2)))/(c^(5/2)*((c + d*x^2)^(1/2) - c^(1/2))*((4*a^(5/2)*b^6)/c^(5/2) + (a^(7/2)*b^5*d)/(2*c^(7/2)) + (34*a^(1/2)*b^8)/(c^(1/2)*d^2) + (25*b^9*c^(1/2))/(2*a^(1/2)*d^3) - (33*a^(3/2)*b^7)/(c^(3/2)*d) - (18*b^10*c^(3/2))/(a^(3/2)*d^4) - (54*b^8*((a + b*x^2)^(1/2) - a^(1/2)))/(d^2*((c + d*x^2)^(1/2) - c^(1/2))) + (10*a^2*b^6*((a + b*x^2)^(1/2) - a^(1/2)))/(c^2*((c + d*x^2)^(1/2) - c^(1/2))) + (4*b^10*c^2*((a + b*x^2)^(1/2) - a^(1/2)))/(a^2*d^4*((c + d*x^2)^(1/2) - c^(1/2))) + (20*a*b^7*((a + b*x^2)^(1/2) - a^(1/2)))/(c*d*((c + d*x^2)^(1/2) - c^(1/2))) - (3*a^3*b^5*d*((a + b*x^2)^(1/2) - a^(1/2)))/(c^3*((c + d*x^2)^(1/2) - c^(1/2))) + (23*b^9*c*((a + b*x^2)^(1/2) - a^(1/2)))/(a*d^3*((c + d*x^2)^(1/2) - c^(1/2))))) - (18*b^9*c^(3/2)*(b*d)^(1/2)*((a + b*x^2)^(1/2) - a^(1/2)))/(a^(3/2)*((c + d*x^2)^(1/2) - c^(1/2))*((25*b^9*c^(1/2)*d)/(2*a^(1/2)) - (18*b^10*c^(3/2))/a^(3/2) + (34*a^(1/2)*b^8*d^2)/c^(1/2) - (33*a^(3/2)*b^7*d^3)/c^(3/2) + (4*a^(5/2)*b^6*d^4)/c^(5/2) + (a^(7/2)*b^5*d^5)/(2*c^(7/2)) - (54*b^8*d^2*((a + b*x^2)^(1/2) - a^(1/2)))/((c + d*x^2)^(1/2) - c^(1/2)) + (4*b^10*c^2*((a + b*x^2)^(1/2) - a^(1/2)))/(a^2*((c + d*x^2)^(1/2) - c^(1/2))) + (10*a^2*b^6*d^4*((a + b*x^2)^(1/2) - a^(1/2)))/(c^2*((c + d*x^2)^(1/2) - c^(1/2))) - (3*a^3*b^5*d^5*((a + b*x^2)^(1/2) - a^(1/2)))/(c^3*((c + d*x^2)^(1/2) - c^(1/2))) + (23*b^9*c*d*((a + b*x^2)^(1/2) - a^(1/2)))/(a*((c + d*x^2)^(1/2) - c^(1/2))) + (20*a*b^7*d^3*((a + b*x^2)^(1/2) - a^(1/2)))/(c*((c + d*x^2)^(1/2) - c^(1/2))))) + (a^(7/2)*b^4*(b*d)^(1/2)*((a + b*x^2)^(1/2) - a^(1/2)))/(2*c^(7/2)*((c + d*x^2)^(1/2) - c^(1/2))*((a^(7/2)*b^5)/(2*c^(7/2)) + (34*a^(1/2)*b^8)/(c^(1/2)*d^3) + (25*b^9*c^(1/2))/(2*a^(1/2)*d^4) - (33*a^(3/2)*b^7)/(c^(3/2)*d^2) + (4*a^(5/2)*b^6)/(c^(5/2)*d) - (18*b^10*c^(3/2))/(a^(3/2)*d^5) - (54*b^8*((a + b*x^2)^(1/2) - a^(1/2)))/(d^3*((c + d*x^2)^(1/2) - c^(1/2))) - (3*a^3*b^5*((a + b*x^2)^(1/2) - a^(1/2)))/(c^3*((c + d*x^2)^(1/2) - c^(1/2))) + (10*a^2*b^6*((a + b*x^2)^(1/2) - a^(1/2)))/(c^2*d*((c + d*x^2)^(1/2) - c^(1/2))) + (4*b^10*c^2*((a + b*x^2)^(1/2) - a^(1/2)))/(a^2*d^5*((c + d*x^2)^(1/2) - c^(1/2))) + (20*a*b^7*((a + b*x^2)^(1/2) - a^(1/2)))/(c*d^2*((c + d*x^2)^(1/2) - c^(1/2))) + (23*b^9*c*((a + b*x^2)^(1/2) - a^(1/2)))/(a*d^4*((c + d*x^2)^(1/2) - c^(1/2))))))*(b*d)^(1/2))/d - (a^(1/2)*log(((a + b*x^2)^(1/2) - a^(1/2))/((c + d*x^2)^(1/2) - c^(1/2))) - a^(1/2)*log(((c^(1/2)*(a + b*x^2)^(1/2) - a^(1/2)*(c + d*x^2)^(1/2))*(b*c^(1/2) - (a^(1/2)*d*((a + b*x^2)^(1/2) - a^(1/2)))/((c + d*x^2)^(1/2) - c^(1/2))))/((c + d*x^2)^(1/2) - c^(1/2))))/(2*c^(1/2))","B"
938,1,477,89,6.405429,"\text{Not used}","int((a + b*x^2)^(1/2)/(x^3*(c + d*x^2)^(1/2)),x)","\frac{\frac{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)\,\left(\frac{c\,b^2}{8}+\frac{a\,d\,b}{8}\right)}{\sqrt{a}\,c^{3/2}\,d\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}-\frac{b^2}{8\,c\,d}+\frac{{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^2\,\left(\frac{a^2\,d^2}{8}-\frac{3\,a\,b\,c\,d}{8}+\frac{b^2\,c^2}{8}\right)}{a\,c^2\,d\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^2}}{\frac{{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^3}{{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^3}+\frac{b\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{d\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}-\frac{{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^2\,\left(a\,d+b\,c\right)}{\sqrt{a}\,\sqrt{c}\,d\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^2}}-\frac{d\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{8\,c\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}-\frac{\ln\left(\frac{\sqrt{b\,x^2+a}-\sqrt{a}}{\sqrt{d\,x^2+c}-\sqrt{c}}\right)\,\left(\sqrt{a}\,b\,c^{3/2}-a^{3/2}\,\sqrt{c}\,d\right)}{4\,a\,c^2}+\frac{\ln\left(\frac{\left(\sqrt{c}\,\sqrt{b\,x^2+a}-\sqrt{a}\,\sqrt{d\,x^2+c}\right)\,\left(b\,\sqrt{c}-\frac{\sqrt{a}\,d\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{\sqrt{d\,x^2+c}-\sqrt{c}}\right)}{\sqrt{d\,x^2+c}-\sqrt{c}}\right)\,\left(\sqrt{a}\,b\,c^{3/2}-a^{3/2}\,\sqrt{c}\,d\right)}{4\,a\,c^2}","Not used",1,"((((a + b*x^2)^(1/2) - a^(1/2))*((b^2*c)/8 + (a*b*d)/8))/(a^(1/2)*c^(3/2)*d*((c + d*x^2)^(1/2) - c^(1/2))) - b^2/(8*c*d) + (((a + b*x^2)^(1/2) - a^(1/2))^2*((a^2*d^2)/8 + (b^2*c^2)/8 - (3*a*b*c*d)/8))/(a*c^2*d*((c + d*x^2)^(1/2) - c^(1/2))^2))/(((a + b*x^2)^(1/2) - a^(1/2))^3/((c + d*x^2)^(1/2) - c^(1/2))^3 + (b*((a + b*x^2)^(1/2) - a^(1/2)))/(d*((c + d*x^2)^(1/2) - c^(1/2))) - (((a + b*x^2)^(1/2) - a^(1/2))^2*(a*d + b*c))/(a^(1/2)*c^(1/2)*d*((c + d*x^2)^(1/2) - c^(1/2))^2)) - (d*((a + b*x^2)^(1/2) - a^(1/2)))/(8*c*((c + d*x^2)^(1/2) - c^(1/2))) - (log(((a + b*x^2)^(1/2) - a^(1/2))/((c + d*x^2)^(1/2) - c^(1/2)))*(a^(1/2)*b*c^(3/2) - a^(3/2)*c^(1/2)*d))/(4*a*c^2) + (log(((c^(1/2)*(a + b*x^2)^(1/2) - a^(1/2)*(c + d*x^2)^(1/2))*(b*c^(1/2) - (a^(1/2)*d*((a + b*x^2)^(1/2) - a^(1/2)))/((c + d*x^2)^(1/2) - c^(1/2))))/((c + d*x^2)^(1/2) - c^(1/2)))*(a^(1/2)*b*c^(3/2) - a^(3/2)*c^(1/2)*d))/(4*a*c^2)","B"
939,1,955,143,21.518359,"\text{Not used}","int((a + b*x^2)^(1/2)/(x^5*(c + d*x^2)^(1/2)),x)","\frac{\ln\left(\frac{\sqrt{b\,x^2+a}-\sqrt{a}}{\sqrt{d\,x^2+c}-\sqrt{c}}\right)\,\left(\sqrt{a}\,b^2\,c^{5/2}-3\,a^{5/2}\,\sqrt{c}\,d^2+2\,a^{3/2}\,b\,c^{3/2}\,d\right)}{16\,a^2\,c^3}-\frac{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)\,\left(\frac{b\,d}{8\,a\,c}-\frac{3\,d\,\left(a\,d+b\,c\right)}{32\,a\,c^2}\right)}{\sqrt{d\,x^2+c}-\sqrt{c}}-\frac{\frac{{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^5\,\left(\frac{a^2\,d^2}{8}-\frac{11\,a\,b\,c\,d}{32}+\frac{5\,b^2\,c^2}{32}\right)}{a\,c^3\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^5}-\frac{b^4}{64\,\sqrt{a}\,c^{3/2}\,d^2}+\frac{{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^2\,\left(\frac{11\,a^2\,b^2\,d^2}{64}+\frac{a\,b^3\,c\,d}{16}-\frac{5\,b^4\,c^2}{64}\right)}{a^{3/2}\,c^{5/2}\,d^2\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^2}+\frac{{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^3\,\left(\frac{a^3\,b\,d^3}{32}-\frac{9\,a^2\,b^2\,c\,d^2}{16}+\frac{3\,a\,b^3\,c^2\,d}{16}+\frac{b^4\,c^3}{32}\right)}{a^2\,c^3\,d^2\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^3}+\frac{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)\,\left(\frac{b^4\,c}{16}-\frac{a\,b^3\,d}{16}\right)}{a\,c^2\,d^2\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}+\frac{{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^4\,\left(-\frac{7\,a^4\,d^4}{64}+\frac{a^3\,b\,c\,d^3}{4}+\frac{21\,a^2\,b^2\,c^2\,d^2}{64}-\frac{a\,b^3\,c^3\,d}{4}+\frac{b^4\,c^4}{64}\right)}{a^{5/2}\,c^{7/2}\,d^2\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^4}}{\frac{{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^6}{{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^6}+\frac{b^2\,{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^2}{d^2\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^2}-\frac{{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^3\,\left(2\,c\,b^2+2\,a\,d\,b\right)}{\sqrt{a}\,\sqrt{c}\,d^2\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^3}-\frac{{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^5\,\left(2\,a\,d+2\,b\,c\right)}{\sqrt{a}\,\sqrt{c}\,d\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^5}+\frac{{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^4\,\left(a^2\,d^2+4\,a\,b\,c\,d+b^2\,c^2\right)}{a\,c\,d^2\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^4}}-\frac{\ln\left(\frac{\left(\sqrt{c}\,\sqrt{b\,x^2+a}-\sqrt{a}\,\sqrt{d\,x^2+c}\right)\,\left(b\,\sqrt{c}-\frac{\sqrt{a}\,d\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{\sqrt{d\,x^2+c}-\sqrt{c}}\right)}{\sqrt{d\,x^2+c}-\sqrt{c}}\right)\,\left(\sqrt{a}\,b^2\,c^{5/2}-3\,a^{5/2}\,\sqrt{c}\,d^2+2\,a^{3/2}\,b\,c^{3/2}\,d\right)}{16\,a^2\,c^3}+\frac{d^2\,{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^2}{64\,\sqrt{a}\,c^{3/2}\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^2}","Not used",1,"(log(((a + b*x^2)^(1/2) - a^(1/2))/((c + d*x^2)^(1/2) - c^(1/2)))*(a^(1/2)*b^2*c^(5/2) - 3*a^(5/2)*c^(1/2)*d^2 + 2*a^(3/2)*b*c^(3/2)*d))/(16*a^2*c^3) - (((a + b*x^2)^(1/2) - a^(1/2))*((b*d)/(8*a*c) - (3*d*(a*d + b*c))/(32*a*c^2)))/((c + d*x^2)^(1/2) - c^(1/2)) - ((((a + b*x^2)^(1/2) - a^(1/2))^5*((a^2*d^2)/8 + (5*b^2*c^2)/32 - (11*a*b*c*d)/32))/(a*c^3*((c + d*x^2)^(1/2) - c^(1/2))^5) - b^4/(64*a^(1/2)*c^(3/2)*d^2) + (((a + b*x^2)^(1/2) - a^(1/2))^2*((11*a^2*b^2*d^2)/64 - (5*b^4*c^2)/64 + (a*b^3*c*d)/16))/(a^(3/2)*c^(5/2)*d^2*((c + d*x^2)^(1/2) - c^(1/2))^2) + (((a + b*x^2)^(1/2) - a^(1/2))^3*((b^4*c^3)/32 + (a^3*b*d^3)/32 - (9*a^2*b^2*c*d^2)/16 + (3*a*b^3*c^2*d)/16))/(a^2*c^3*d^2*((c + d*x^2)^(1/2) - c^(1/2))^3) + (((a + b*x^2)^(1/2) - a^(1/2))*((b^4*c)/16 - (a*b^3*d)/16))/(a*c^2*d^2*((c + d*x^2)^(1/2) - c^(1/2))) + (((a + b*x^2)^(1/2) - a^(1/2))^4*((b^4*c^4)/64 - (7*a^4*d^4)/64 + (21*a^2*b^2*c^2*d^2)/64 - (a*b^3*c^3*d)/4 + (a^3*b*c*d^3)/4))/(a^(5/2)*c^(7/2)*d^2*((c + d*x^2)^(1/2) - c^(1/2))^4))/(((a + b*x^2)^(1/2) - a^(1/2))^6/((c + d*x^2)^(1/2) - c^(1/2))^6 + (b^2*((a + b*x^2)^(1/2) - a^(1/2))^2)/(d^2*((c + d*x^2)^(1/2) - c^(1/2))^2) - (((a + b*x^2)^(1/2) - a^(1/2))^3*(2*b^2*c + 2*a*b*d))/(a^(1/2)*c^(1/2)*d^2*((c + d*x^2)^(1/2) - c^(1/2))^3) - (((a + b*x^2)^(1/2) - a^(1/2))^5*(2*a*d + 2*b*c))/(a^(1/2)*c^(1/2)*d*((c + d*x^2)^(1/2) - c^(1/2))^5) + (((a + b*x^2)^(1/2) - a^(1/2))^4*(a^2*d^2 + b^2*c^2 + 4*a*b*c*d))/(a*c*d^2*((c + d*x^2)^(1/2) - c^(1/2))^4)) - (log(((c^(1/2)*(a + b*x^2)^(1/2) - a^(1/2)*(c + d*x^2)^(1/2))*(b*c^(1/2) - (a^(1/2)*d*((a + b*x^2)^(1/2) - a^(1/2)))/((c + d*x^2)^(1/2) - c^(1/2))))/((c + d*x^2)^(1/2) - c^(1/2)))*(a^(1/2)*b^2*c^(5/2) - 3*a^(5/2)*c^(1/2)*d^2 + 2*a^(3/2)*b*c^(3/2)*d))/(16*a^2*c^3) + (d^2*((a + b*x^2)^(1/2) - a^(1/2))^2)/(64*a^(1/2)*c^(3/2)*((c + d*x^2)^(1/2) - c^(1/2))^2)","B"
940,0,-1,343,0.000000,"\text{Not used}","int((x^4*(a + b*x^2)^(1/2))/(c + d*x^2)^(1/2),x)","\int \frac{x^4\,\sqrt{b\,x^2+a}}{\sqrt{d\,x^2+c}} \,d x","Not used",1,"int((x^4*(a + b*x^2)^(1/2))/(c + d*x^2)^(1/2), x)","F"
941,0,-1,259,0.000000,"\text{Not used}","int((x^2*(a + b*x^2)^(1/2))/(c + d*x^2)^(1/2),x)","\int \frac{x^2\,\sqrt{b\,x^2+a}}{\sqrt{d\,x^2+c}} \,d x","Not used",1,"int((x^2*(a + b*x^2)^(1/2))/(c + d*x^2)^(1/2), x)","F"
942,0,-1,232,0.000000,"\text{Not used}","int((a + b*x^2)^(1/2)/(x^2*(c + d*x^2)^(1/2)),x)","\int \frac{\sqrt{b\,x^2+a}}{x^2\,\sqrt{d\,x^2+c}} \,d x","Not used",1,"int((a + b*x^2)^(1/2)/(x^2*(c + d*x^2)^(1/2)), x)","F"
943,0,-1,307,0.000000,"\text{Not used}","int((a + b*x^2)^(1/2)/(x^4*(c + d*x^2)^(1/2)),x)","\int \frac{\sqrt{b\,x^2+a}}{x^4\,\sqrt{d\,x^2+c}} \,d x","Not used",1,"int((a + b*x^2)^(1/2)/(x^4*(c + d*x^2)^(1/2)), x)","F"
944,0,-1,276,0.000000,"\text{Not used}","int((x^5*(a + b*x^2)^(3/2))/(c + d*x^2)^(1/2),x)","\int \frac{x^5\,{\left(b\,x^2+a\right)}^{3/2}}{\sqrt{d\,x^2+c}} \,d x","Not used",1,"int((x^5*(a + b*x^2)^(3/2))/(c + d*x^2)^(1/2), x)","F"
945,0,-1,187,0.000000,"\text{Not used}","int((x^3*(a + b*x^2)^(3/2))/(c + d*x^2)^(1/2),x)","\int \frac{x^3\,{\left(b\,x^2+a\right)}^{3/2}}{\sqrt{d\,x^2+c}} \,d x","Not used",1,"int((x^3*(a + b*x^2)^(3/2))/(c + d*x^2)^(1/2), x)","F"
946,0,-1,125,0.000000,"\text{Not used}","int((x*(a + b*x^2)^(3/2))/(c + d*x^2)^(1/2),x)","\int \frac{x\,{\left(b\,x^2+a\right)}^{3/2}}{\sqrt{d\,x^2+c}} \,d x","Not used",1,"int((x*(a + b*x^2)^(3/2))/(c + d*x^2)^(1/2), x)","F"
947,0,-1,133,0.000000,"\text{Not used}","int((a + b*x^2)^(3/2)/(x*(c + d*x^2)^(1/2)),x)","\int \frac{{\left(b\,x^2+a\right)}^{3/2}}{x\,\sqrt{d\,x^2+c}} \,d x","Not used",1,"int((a + b*x^2)^(3/2)/(x*(c + d*x^2)^(1/2)), x)","F"
948,0,-1,136,0.000000,"\text{Not used}","int((a + b*x^2)^(3/2)/(x^3*(c + d*x^2)^(1/2)),x)","\int \frac{{\left(b\,x^2+a\right)}^{3/2}}{x^3\,\sqrt{d\,x^2+c}} \,d x","Not used",1,"int((a + b*x^2)^(3/2)/(x^3*(c + d*x^2)^(1/2)), x)","F"
949,0,-1,131,0.000000,"\text{Not used}","int((a + b*x^2)^(3/2)/(x^5*(c + d*x^2)^(1/2)),x)","\int \frac{{\left(b\,x^2+a\right)}^{3/2}}{x^5\,\sqrt{d\,x^2+c}} \,d x","Not used",1,"int((a + b*x^2)^(3/2)/(x^5*(c + d*x^2)^(1/2)), x)","F"
950,0,-1,429,0.000000,"\text{Not used}","int((x^4*(a + b*x^2)^(3/2))/(c + d*x^2)^(1/2),x)","\int \frac{x^4\,{\left(b\,x^2+a\right)}^{3/2}}{\sqrt{d\,x^2+c}} \,d x","Not used",1,"int((x^4*(a + b*x^2)^(3/2))/(c + d*x^2)^(1/2), x)","F"
951,0,-1,335,0.000000,"\text{Not used}","int((x^2*(a + b*x^2)^(3/2))/(c + d*x^2)^(1/2),x)","\int \frac{x^2\,{\left(b\,x^2+a\right)}^{3/2}}{\sqrt{d\,x^2+c}} \,d x","Not used",1,"int((x^2*(a + b*x^2)^(3/2))/(c + d*x^2)^(1/2), x)","F"
952,0,-1,244,0.000000,"\text{Not used}","int((a + b*x^2)^(3/2)/(x^2*(c + d*x^2)^(1/2)),x)","\int \frac{{\left(b\,x^2+a\right)}^{3/2}}{x^2\,\sqrt{d\,x^2+c}} \,d x","Not used",1,"int((a + b*x^2)^(3/2)/(x^2*(c + d*x^2)^(1/2)), x)","F"
953,0,-1,311,0.000000,"\text{Not used}","int((a + b*x^2)^(3/2)/(x^4*(c + d*x^2)^(1/2)),x)","\int \frac{{\left(b\,x^2+a\right)}^{3/2}}{x^4\,\sqrt{d\,x^2+c}} \,d x","Not used",1,"int((a + b*x^2)^(3/2)/(x^4*(c + d*x^2)^(1/2)), x)","F"
954,0,-1,340,0.000000,"\text{Not used}","int((x^5*(a + b*x^2)^(5/2))/(c + d*x^2)^(1/2),x)","\int \frac{x^5\,{\left(b\,x^2+a\right)}^{5/2}}{\sqrt{d\,x^2+c}} \,d x","Not used",1,"int((x^5*(a + b*x^2)^(5/2))/(c + d*x^2)^(1/2), x)","F"
955,0,-1,237,0.000000,"\text{Not used}","int((x^3*(a + b*x^2)^(5/2))/(c + d*x^2)^(1/2),x)","\int \frac{x^3\,{\left(b\,x^2+a\right)}^{5/2}}{\sqrt{d\,x^2+c}} \,d x","Not used",1,"int((x^3*(a + b*x^2)^(5/2))/(c + d*x^2)^(1/2), x)","F"
956,0,-1,164,0.000000,"\text{Not used}","int((x*(a + b*x^2)^(5/2))/(c + d*x^2)^(1/2),x)","\int \frac{x\,{\left(b\,x^2+a\right)}^{5/2}}{\sqrt{d\,x^2+c}} \,d x","Not used",1,"int((x*(a + b*x^2)^(5/2))/(c + d*x^2)^(1/2), x)","F"
957,0,-1,187,0.000000,"\text{Not used}","int((a + b*x^2)^(5/2)/(x*(c + d*x^2)^(1/2)),x)","\int \frac{{\left(b\,x^2+a\right)}^{5/2}}{x\,\sqrt{d\,x^2+c}} \,d x","Not used",1,"int((a + b*x^2)^(5/2)/(x*(c + d*x^2)^(1/2)), x)","F"
958,0,-1,187,0.000000,"\text{Not used}","int((a + b*x^2)^(5/2)/(x^3*(c + d*x^2)^(1/2)),x)","\int \frac{{\left(b\,x^2+a\right)}^{5/2}}{x^3\,\sqrt{d\,x^2+c}} \,d x","Not used",1,"int((a + b*x^2)^(5/2)/(x^3*(c + d*x^2)^(1/2)), x)","F"
959,0,-1,192,0.000000,"\text{Not used}","int((a + b*x^2)^(5/2)/(x^5*(c + d*x^2)^(1/2)),x)","\int \frac{{\left(b\,x^2+a\right)}^{5/2}}{x^5\,\sqrt{d\,x^2+c}} \,d x","Not used",1,"int((a + b*x^2)^(5/2)/(x^5*(c + d*x^2)^(1/2)), x)","F"
960,0,-1,553,0.000000,"\text{Not used}","int((x^4*(a + b*x^2)^(5/2))/(c + d*x^2)^(1/2),x)","\int \frac{x^4\,{\left(b\,x^2+a\right)}^{5/2}}{\sqrt{d\,x^2+c}} \,d x","Not used",1,"int((x^4*(a + b*x^2)^(5/2))/(c + d*x^2)^(1/2), x)","F"
961,0,-1,436,0.000000,"\text{Not used}","int((x^2*(a + b*x^2)^(5/2))/(c + d*x^2)^(1/2),x)","\int \frac{x^2\,{\left(b\,x^2+a\right)}^{5/2}}{\sqrt{d\,x^2+c}} \,d x","Not used",1,"int((x^2*(a + b*x^2)^(5/2))/(c + d*x^2)^(1/2), x)","F"
962,0,-1,330,0.000000,"\text{Not used}","int((a + b*x^2)^(5/2)/(x^2*(c + d*x^2)^(1/2)),x)","\int \frac{{\left(b\,x^2+a\right)}^{5/2}}{x^2\,\sqrt{d\,x^2+c}} \,d x","Not used",1,"int((a + b*x^2)^(5/2)/(x^2*(c + d*x^2)^(1/2)), x)","F"
963,0,-1,336,0.000000,"\text{Not used}","int((a + b*x^2)^(5/2)/(x^4*(c + d*x^2)^(1/2)),x)","\int \frac{{\left(b\,x^2+a\right)}^{5/2}}{x^4\,\sqrt{d\,x^2+c}} \,d x","Not used",1,"int((a + b*x^2)^(5/2)/(x^4*(c + d*x^2)^(1/2)), x)","F"
964,0,-1,99,0.000000,"\text{Not used}","int((x^4*(3*x^2 - 1)^(1/2))/(2 - 3*x^2)^(1/2),x)","\int \frac{x^4\,\sqrt{3\,x^2-1}}{\sqrt{2-3\,x^2}} \,d x","Not used",1,"int((x^4*(3*x^2 - 1)^(1/2))/(2 - 3*x^2)^(1/2), x)","F"
965,1,414,65,12.038267,"\text{Not used}","int((x^3*(3*x^2 - 1)^(1/2))/(2 - 3*x^2)^(1/2),x)","-\frac{7\,\mathrm{atan}\left(\frac{\sqrt{3\,x^2-1}-\mathrm{i}}{\sqrt{2}-\sqrt{2-3\,x^2}}\right)}{36}+\frac{\frac{7\,\left(\sqrt{3\,x^2-1}-\mathrm{i}\right)}{36\,\left(\sqrt{2}-\sqrt{2-3\,x^2}\right)}+\frac{143\,{\left(\sqrt{3\,x^2-1}-\mathrm{i}\right)}^3}{36\,{\left(\sqrt{2}-\sqrt{2-3\,x^2}\right)}^3}-\frac{143\,{\left(\sqrt{3\,x^2-1}-\mathrm{i}\right)}^5}{36\,{\left(\sqrt{2}-\sqrt{2-3\,x^2}\right)}^5}-\frac{7\,{\left(\sqrt{3\,x^2-1}-\mathrm{i}\right)}^7}{36\,{\left(\sqrt{2}-\sqrt{2-3\,x^2}\right)}^7}+\frac{\sqrt{2}\,{\left(\sqrt{3\,x^2-1}-\mathrm{i}\right)}^2\,4{}\mathrm{i}}{9\,{\left(\sqrt{2}-\sqrt{2-3\,x^2}\right)}^2}-\frac{\sqrt{2}\,{\left(\sqrt{3\,x^2-1}-\mathrm{i}\right)}^4\,40{}\mathrm{i}}{9\,{\left(\sqrt{2}-\sqrt{2-3\,x^2}\right)}^4}+\frac{\sqrt{2}\,{\left(\sqrt{3\,x^2-1}-\mathrm{i}\right)}^6\,4{}\mathrm{i}}{9\,{\left(\sqrt{2}-\sqrt{2-3\,x^2}\right)}^6}}{\frac{4\,{\left(\sqrt{3\,x^2-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{2}-\sqrt{2-3\,x^2}\right)}^2}+\frac{6\,{\left(\sqrt{3\,x^2-1}-\mathrm{i}\right)}^4}{{\left(\sqrt{2}-\sqrt{2-3\,x^2}\right)}^4}+\frac{4\,{\left(\sqrt{3\,x^2-1}-\mathrm{i}\right)}^6}{{\left(\sqrt{2}-\sqrt{2-3\,x^2}\right)}^6}+\frac{{\left(\sqrt{3\,x^2-1}-\mathrm{i}\right)}^8}{{\left(\sqrt{2}-\sqrt{2-3\,x^2}\right)}^8}+1}","Not used",1,"((7*((3*x^2 - 1)^(1/2) - 1i))/(36*(2^(1/2) - (2 - 3*x^2)^(1/2))) + (143*((3*x^2 - 1)^(1/2) - 1i)^3)/(36*(2^(1/2) - (2 - 3*x^2)^(1/2))^3) - (143*((3*x^2 - 1)^(1/2) - 1i)^5)/(36*(2^(1/2) - (2 - 3*x^2)^(1/2))^5) - (7*((3*x^2 - 1)^(1/2) - 1i)^7)/(36*(2^(1/2) - (2 - 3*x^2)^(1/2))^7) + (2^(1/2)*((3*x^2 - 1)^(1/2) - 1i)^2*4i)/(9*(2^(1/2) - (2 - 3*x^2)^(1/2))^2) - (2^(1/2)*((3*x^2 - 1)^(1/2) - 1i)^4*40i)/(9*(2^(1/2) - (2 - 3*x^2)^(1/2))^4) + (2^(1/2)*((3*x^2 - 1)^(1/2) - 1i)^6*4i)/(9*(2^(1/2) - (2 - 3*x^2)^(1/2))^6))/((4*((3*x^2 - 1)^(1/2) - 1i)^2)/(2^(1/2) - (2 - 3*x^2)^(1/2))^2 + (6*((3*x^2 - 1)^(1/2) - 1i)^4)/(2^(1/2) - (2 - 3*x^2)^(1/2))^4 + (4*((3*x^2 - 1)^(1/2) - 1i)^6)/(2^(1/2) - (2 - 3*x^2)^(1/2))^6 + ((3*x^2 - 1)^(1/2) - 1i)^8/(2^(1/2) - (2 - 3*x^2)^(1/2))^8 + 1) - (7*atan(((3*x^2 - 1)^(1/2) - 1i)/(2^(1/2) - (2 - 3*x^2)^(1/2))))/36","B"
966,0,-1,70,0.000000,"\text{Not used}","int((x^2*(3*x^2 - 1)^(1/2))/(2 - 3*x^2)^(1/2),x)","\int \frac{x^2\,\sqrt{3\,x^2-1}}{\sqrt{2-3\,x^2}} \,d x","Not used",1,"int((x^2*(3*x^2 - 1)^(1/2))/(2 - 3*x^2)^(1/2), x)","F"
967,1,206,39,2.741226,"\text{Not used}","int((x*(3*x^2 - 1)^(1/2))/(2 - 3*x^2)^(1/2),x)","-\frac{\mathrm{atan}\left(\frac{\sqrt{3\,x^2-1}-\mathrm{i}}{\sqrt{2}-\sqrt{2-3\,x^2}}\right)}{3}-\frac{-\frac{\sqrt{3\,x^2-1}-\mathrm{i}}{\sqrt{2}-\sqrt{2-3\,x^2}}+\frac{{\left(\sqrt{3\,x^2-1}-\mathrm{i}\right)}^3}{{\left(\sqrt{2}-\sqrt{2-3\,x^2}\right)}^3}+\frac{\sqrt{2}\,{\left(\sqrt{3\,x^2-1}-\mathrm{i}\right)}^2\,4{}\mathrm{i}}{3\,{\left(\sqrt{2}-\sqrt{2-3\,x^2}\right)}^2}}{\frac{2\,{\left(\sqrt{3\,x^2-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{2}-\sqrt{2-3\,x^2}\right)}^2}+\frac{{\left(\sqrt{3\,x^2-1}-\mathrm{i}\right)}^4}{{\left(\sqrt{2}-\sqrt{2-3\,x^2}\right)}^4}+1}","Not used",1,"- atan(((3*x^2 - 1)^(1/2) - 1i)/(2^(1/2) - (2 - 3*x^2)^(1/2)))/3 - (((3*x^2 - 1)^(1/2) - 1i)^3/(2^(1/2) - (2 - 3*x^2)^(1/2))^3 - ((3*x^2 - 1)^(1/2) - 1i)/(2^(1/2) - (2 - 3*x^2)^(1/2)) + (2^(1/2)*((3*x^2 - 1)^(1/2) - 1i)^2*4i)/(3*(2^(1/2) - (2 - 3*x^2)^(1/2))^2))/((2*((3*x^2 - 1)^(1/2) - 1i)^2)/(2^(1/2) - (2 - 3*x^2)^(1/2))^2 + ((3*x^2 - 1)^(1/2) - 1i)^4/(2^(1/2) - (2 - 3*x^2)^(1/2))^4 + 1)","B"
968,0,-1,241,0.000000,"\text{Not used}","int((x^2*(b*x^2 + 2)^(1/2))/(d*x^2 + 3)^(1/2),x)","\int \frac{x^2\,\sqrt{b\,x^2+2}}{\sqrt{d\,x^2+3}} \,d x","Not used",1,"int((x^2*(b*x^2 + 2)^(1/2))/(d*x^2 + 3)^(1/2), x)","F"
969,1,550,141,22.537696,"\text{Not used}","int(x^5/((a + b*x^2)^(1/2)*(c + d*x^2)^(1/2)),x)","\frac{\mathrm{atanh}\left(\frac{\sqrt{d}\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{\sqrt{b}\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}\right)\,\left(3\,a^2\,d^2+2\,a\,b\,c\,d+3\,b^2\,c^2\right)}{4\,b^{5/2}\,d^{5/2}}-\frac{\frac{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)\,\left(\frac{3\,a^2\,b\,d^2}{4}+\frac{a\,b^2\,c\,d}{2}+\frac{3\,b^3\,c^2}{4}\right)}{d^6\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}-\frac{{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^3\,\left(\frac{11\,a^2\,d^2}{4}+\frac{25\,a\,b\,c\,d}{2}+\frac{11\,b^2\,c^2}{4}\right)}{d^5\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^3}+\frac{{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^7\,\left(\frac{3\,a^2\,d^2}{4}+\frac{a\,b\,c\,d}{2}+\frac{3\,b^2\,c^2}{4}\right)}{b^2\,d^3\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^7}-\frac{{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^5\,\left(\frac{11\,a^2\,d^2}{4}+\frac{25\,a\,b\,c\,d}{2}+\frac{11\,b^2\,c^2}{4}\right)}{b\,d^4\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^5}+\frac{\sqrt{a}\,\sqrt{c}\,{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^4\,\left(16\,a\,d+16\,b\,c\right)}{d^4\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^4}}{\frac{{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^8}{{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^8}+\frac{b^4}{d^4}-\frac{4\,b^3\,{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^2}{d^3\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^2}+\frac{6\,b^2\,{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^4}{d^2\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^4}-\frac{4\,b\,{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^6}{d\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^6}}","Not used",1,"(atanh((d^(1/2)*((a + b*x^2)^(1/2) - a^(1/2)))/(b^(1/2)*((c + d*x^2)^(1/2) - c^(1/2))))*(3*a^2*d^2 + 3*b^2*c^2 + 2*a*b*c*d))/(4*b^(5/2)*d^(5/2)) - ((((a + b*x^2)^(1/2) - a^(1/2))*((3*b^3*c^2)/4 + (3*a^2*b*d^2)/4 + (a*b^2*c*d)/2))/(d^6*((c + d*x^2)^(1/2) - c^(1/2))) - (((a + b*x^2)^(1/2) - a^(1/2))^3*((11*a^2*d^2)/4 + (11*b^2*c^2)/4 + (25*a*b*c*d)/2))/(d^5*((c + d*x^2)^(1/2) - c^(1/2))^3) + (((a + b*x^2)^(1/2) - a^(1/2))^7*((3*a^2*d^2)/4 + (3*b^2*c^2)/4 + (a*b*c*d)/2))/(b^2*d^3*((c + d*x^2)^(1/2) - c^(1/2))^7) - (((a + b*x^2)^(1/2) - a^(1/2))^5*((11*a^2*d^2)/4 + (11*b^2*c^2)/4 + (25*a*b*c*d)/2))/(b*d^4*((c + d*x^2)^(1/2) - c^(1/2))^5) + (a^(1/2)*c^(1/2)*((a + b*x^2)^(1/2) - a^(1/2))^4*(16*a*d + 16*b*c))/(d^4*((c + d*x^2)^(1/2) - c^(1/2))^4))/(((a + b*x^2)^(1/2) - a^(1/2))^8/((c + d*x^2)^(1/2) - c^(1/2))^8 + b^4/d^4 - (4*b^3*((a + b*x^2)^(1/2) - a^(1/2))^2)/(d^3*((c + d*x^2)^(1/2) - c^(1/2))^2) + (6*b^2*((a + b*x^2)^(1/2) - a^(1/2))^4)/(d^2*((c + d*x^2)^(1/2) - c^(1/2))^4) - (4*b*((a + b*x^2)^(1/2) - a^(1/2))^6)/(d*((c + d*x^2)^(1/2) - c^(1/2))^6))","B"
970,1,279,88,5.145758,"\text{Not used}","int(x^3/((a + b*x^2)^(1/2)*(c + d*x^2)^(1/2)),x)","\frac{\frac{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)\,\left(a\,d+b\,c\right)}{d^3\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}+\frac{{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^3\,\left(a\,d+b\,c\right)}{b\,d^2\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^3}-\frac{4\,\sqrt{a}\,\sqrt{c}\,{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^2}{d^2\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^2}}{\frac{{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^4}{{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^4}+\frac{b^2}{d^2}-\frac{2\,b\,{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^2}{d\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^2}}-\frac{\mathrm{atanh}\left(\frac{\sqrt{d}\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{\sqrt{b}\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}\right)\,\left(a\,d+b\,c\right)}{b^{3/2}\,d^{3/2}}","Not used",1,"((((a + b*x^2)^(1/2) - a^(1/2))*(a*d + b*c))/(d^3*((c + d*x^2)^(1/2) - c^(1/2))) + (((a + b*x^2)^(1/2) - a^(1/2))^3*(a*d + b*c))/(b*d^2*((c + d*x^2)^(1/2) - c^(1/2))^3) - (4*a^(1/2)*c^(1/2)*((a + b*x^2)^(1/2) - a^(1/2))^2)/(d^2*((c + d*x^2)^(1/2) - c^(1/2))^2))/(((a + b*x^2)^(1/2) - a^(1/2))^4/((c + d*x^2)^(1/2) - c^(1/2))^4 + b^2/d^2 - (2*b*((a + b*x^2)^(1/2) - a^(1/2))^2)/(d*((c + d*x^2)^(1/2) - c^(1/2))^2)) - (atanh((d^(1/2)*((a + b*x^2)^(1/2) - a^(1/2)))/(b^(1/2)*((c + d*x^2)^(1/2) - c^(1/2))))*(a*d + b*c))/(b^(3/2)*d^(3/2))","B"
971,1,49,45,1.224354,"\text{Not used}","int(x/((a + b*x^2)^(1/2)*(c + d*x^2)^(1/2)),x)","-\frac{2\,\mathrm{atan}\left(\frac{b\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}{\sqrt{-b\,d}\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}\right)}{\sqrt{-b\,d}}","Not used",1,"-(2*atan((b*((c + d*x^2)^(1/2) - c^(1/2)))/((-b*d)^(1/2)*((a + b*x^2)^(1/2) - a^(1/2)))))/(-b*d)^(1/2)","B"
972,1,136,46,3.450603,"\text{Not used}","int(1/(x*(a + b*x^2)^(1/2)*(c + d*x^2)^(1/2)),x)","-\frac{\ln\left(\frac{\sqrt{b\,x^2+a}-\sqrt{a}}{\sqrt{d\,x^2+c}-\sqrt{c}}\right)-\ln\left(\frac{\left(\sqrt{c}\,\sqrt{b\,x^2+a}-\sqrt{a}\,\sqrt{d\,x^2+c}\right)\,\left(b\,\sqrt{c}-\frac{\sqrt{a}\,d\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{\sqrt{d\,x^2+c}-\sqrt{c}}\right)}{\sqrt{d\,x^2+c}-\sqrt{c}}\right)}{2\,\sqrt{a}\,\sqrt{c}}","Not used",1,"-(log(((a + b*x^2)^(1/2) - a^(1/2))/((c + d*x^2)^(1/2) - c^(1/2))) - log(((c^(1/2)*(a + b*x^2)^(1/2) - a^(1/2)*(c + d*x^2)^(1/2))*(b*c^(1/2) - (a^(1/2)*d*((a + b*x^2)^(1/2) - a^(1/2)))/((c + d*x^2)^(1/2) - c^(1/2))))/((c + d*x^2)^(1/2) - c^(1/2))))/(2*a^(1/2)*c^(1/2))","B"
973,1,481,91,6.695752,"\text{Not used}","int(1/(x^3*(a + b*x^2)^(1/2)*(c + d*x^2)^(1/2)),x)","\frac{\frac{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)\,\left(\frac{c\,b^2}{8}+\frac{a\,d\,b}{8}\right)}{a^{3/2}\,c^{3/2}\,d\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}-\frac{b^2}{8\,a\,c\,d}+\frac{{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^2\,\left(\frac{a^2\,d^2}{8}-\frac{3\,a\,b\,c\,d}{8}+\frac{b^2\,c^2}{8}\right)}{a^2\,c^2\,d\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^2}}{\frac{{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^3}{{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^3}+\frac{b\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{d\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}-\frac{{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^2\,\left(a\,d+b\,c\right)}{\sqrt{a}\,\sqrt{c}\,d\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^2}}+\frac{\ln\left(\frac{\sqrt{b\,x^2+a}-\sqrt{a}}{\sqrt{d\,x^2+c}-\sqrt{c}}\right)\,\left(\sqrt{a}\,b\,c^{3/2}+a^{3/2}\,\sqrt{c}\,d\right)}{4\,a^2\,c^2}-\frac{\ln\left(\frac{\left(\sqrt{c}\,\sqrt{b\,x^2+a}-\sqrt{a}\,\sqrt{d\,x^2+c}\right)\,\left(b\,\sqrt{c}-\frac{\sqrt{a}\,d\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{\sqrt{d\,x^2+c}-\sqrt{c}}\right)}{\sqrt{d\,x^2+c}-\sqrt{c}}\right)\,\left(\sqrt{a}\,b\,c^{3/2}+a^{3/2}\,\sqrt{c}\,d\right)}{4\,a^2\,c^2}-\frac{d\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{8\,a\,c\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}","Not used",1,"((((a + b*x^2)^(1/2) - a^(1/2))*((b^2*c)/8 + (a*b*d)/8))/(a^(3/2)*c^(3/2)*d*((c + d*x^2)^(1/2) - c^(1/2))) - b^2/(8*a*c*d) + (((a + b*x^2)^(1/2) - a^(1/2))^2*((a^2*d^2)/8 + (b^2*c^2)/8 - (3*a*b*c*d)/8))/(a^2*c^2*d*((c + d*x^2)^(1/2) - c^(1/2))^2))/(((a + b*x^2)^(1/2) - a^(1/2))^3/((c + d*x^2)^(1/2) - c^(1/2))^3 + (b*((a + b*x^2)^(1/2) - a^(1/2)))/(d*((c + d*x^2)^(1/2) - c^(1/2))) - (((a + b*x^2)^(1/2) - a^(1/2))^2*(a*d + b*c))/(a^(1/2)*c^(1/2)*d*((c + d*x^2)^(1/2) - c^(1/2))^2)) + (log(((a + b*x^2)^(1/2) - a^(1/2))/((c + d*x^2)^(1/2) - c^(1/2)))*(a^(1/2)*b*c^(3/2) + a^(3/2)*c^(1/2)*d))/(4*a^2*c^2) - (log(((c^(1/2)*(a + b*x^2)^(1/2) - a^(1/2)*(c + d*x^2)^(1/2))*(b*c^(1/2) - (a^(1/2)*d*((a + b*x^2)^(1/2) - a^(1/2)))/((c + d*x^2)^(1/2) - c^(1/2))))/((c + d*x^2)^(1/2) - c^(1/2)))*(a^(1/2)*b*c^(3/2) + a^(3/2)*c^(1/2)*d))/(4*a^2*c^2) - (d*((a + b*x^2)^(1/2) - a^(1/2)))/(8*a*c*((c + d*x^2)^(1/2) - c^(1/2)))","B"
974,1,962,149,21.575270,"\text{Not used}","int(1/(x^5*(a + b*x^2)^(1/2)*(c + d*x^2)^(1/2)),x)","\frac{\ln\left(\frac{\left(\sqrt{c}\,\sqrt{b\,x^2+a}-\sqrt{a}\,\sqrt{d\,x^2+c}\right)\,\left(b\,\sqrt{c}-\frac{\sqrt{a}\,d\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}{\sqrt{d\,x^2+c}-\sqrt{c}}\right)}{\sqrt{d\,x^2+c}-\sqrt{c}}\right)\,\left(3\,\sqrt{a}\,b^2\,c^{5/2}+3\,a^{5/2}\,\sqrt{c}\,d^2+2\,a^{3/2}\,b\,c^{3/2}\,d\right)}{16\,a^3\,c^3}-\frac{\ln\left(\frac{\sqrt{b\,x^2+a}-\sqrt{a}}{\sqrt{d\,x^2+c}-\sqrt{c}}\right)\,\left(3\,\sqrt{a}\,b^2\,c^{5/2}+3\,a^{5/2}\,\sqrt{c}\,d^2+2\,a^{3/2}\,b\,c^{3/2}\,d\right)}{16\,a^3\,c^3}-\frac{\frac{{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^2\,\left(\frac{11\,a^2\,b^2\,d^2}{64}+\frac{5\,a\,b^3\,c\,d}{16}+\frac{11\,b^4\,c^2}{64}\right)}{a^{5/2}\,c^{5/2}\,d^2\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^2}-\frac{b^4}{64\,a^{3/2}\,c^{3/2}\,d^2}+\frac{{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^3\,\left(\frac{a^3\,b\,d^3}{32}-\frac{9\,a^2\,b^2\,c\,d^2}{16}-\frac{9\,a\,b^3\,c^2\,d}{16}+\frac{b^4\,c^3}{32}\right)}{a^3\,c^3\,d^2\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^3}-\frac{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)\,\left(\frac{c\,b^4}{16}+\frac{a\,d\,b^3}{16}\right)}{a^2\,c^2\,d^2\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}+\frac{{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^5\,\left(\frac{a^3\,d^3}{8}-\frac{7\,a^2\,b\,c\,d^2}{32}-\frac{7\,a\,b^2\,c^2\,d}{32}+\frac{b^3\,c^3}{8}\right)}{a^3\,c^3\,d\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^5}+\frac{{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^4\,\left(-\frac{7\,a^4\,d^4}{64}+\frac{a^3\,b\,c\,d^3}{8}+\frac{45\,a^2\,b^2\,c^2\,d^2}{64}+\frac{a\,b^3\,c^3\,d}{8}-\frac{7\,b^4\,c^4}{64}\right)}{a^{7/2}\,c^{7/2}\,d^2\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^4}}{\frac{{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^6}{{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^6}+\frac{b^2\,{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^2}{d^2\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^2}-\frac{{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^3\,\left(2\,c\,b^2+2\,a\,d\,b\right)}{\sqrt{a}\,\sqrt{c}\,d^2\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^3}-\frac{{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^5\,\left(2\,a\,d+2\,b\,c\right)}{\sqrt{a}\,\sqrt{c}\,d\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^5}+\frac{{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^4\,\left(a^2\,d^2+4\,a\,b\,c\,d+b^2\,c^2\right)}{a\,c\,d^2\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^4}}+\frac{d^2\,{\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)}^2}{64\,a^{3/2}\,c^{3/2}\,{\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}^2}+\frac{3\,d\,\left(\sqrt{b\,x^2+a}-\sqrt{a}\right)\,\left(a\,d+b\,c\right)}{32\,a^2\,c^2\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}","Not used",1,"(log(((c^(1/2)*(a + b*x^2)^(1/2) - a^(1/2)*(c + d*x^2)^(1/2))*(b*c^(1/2) - (a^(1/2)*d*((a + b*x^2)^(1/2) - a^(1/2)))/((c + d*x^2)^(1/2) - c^(1/2))))/((c + d*x^2)^(1/2) - c^(1/2)))*(3*a^(1/2)*b^2*c^(5/2) + 3*a^(5/2)*c^(1/2)*d^2 + 2*a^(3/2)*b*c^(3/2)*d))/(16*a^3*c^3) - (log(((a + b*x^2)^(1/2) - a^(1/2))/((c + d*x^2)^(1/2) - c^(1/2)))*(3*a^(1/2)*b^2*c^(5/2) + 3*a^(5/2)*c^(1/2)*d^2 + 2*a^(3/2)*b*c^(3/2)*d))/(16*a^3*c^3) - ((((a + b*x^2)^(1/2) - a^(1/2))^2*((11*b^4*c^2)/64 + (11*a^2*b^2*d^2)/64 + (5*a*b^3*c*d)/16))/(a^(5/2)*c^(5/2)*d^2*((c + d*x^2)^(1/2) - c^(1/2))^2) - b^4/(64*a^(3/2)*c^(3/2)*d^2) + (((a + b*x^2)^(1/2) - a^(1/2))^3*((b^4*c^3)/32 + (a^3*b*d^3)/32 - (9*a^2*b^2*c*d^2)/16 - (9*a*b^3*c^2*d)/16))/(a^3*c^3*d^2*((c + d*x^2)^(1/2) - c^(1/2))^3) - (((a + b*x^2)^(1/2) - a^(1/2))*((b^4*c)/16 + (a*b^3*d)/16))/(a^2*c^2*d^2*((c + d*x^2)^(1/2) - c^(1/2))) + (((a + b*x^2)^(1/2) - a^(1/2))^5*((a^3*d^3)/8 + (b^3*c^3)/8 - (7*a*b^2*c^2*d)/32 - (7*a^2*b*c*d^2)/32))/(a^3*c^3*d*((c + d*x^2)^(1/2) - c^(1/2))^5) + (((a + b*x^2)^(1/2) - a^(1/2))^4*((45*a^2*b^2*c^2*d^2)/64 - (7*b^4*c^4)/64 - (7*a^4*d^4)/64 + (a*b^3*c^3*d)/8 + (a^3*b*c*d^3)/8))/(a^(7/2)*c^(7/2)*d^2*((c + d*x^2)^(1/2) - c^(1/2))^4))/(((a + b*x^2)^(1/2) - a^(1/2))^6/((c + d*x^2)^(1/2) - c^(1/2))^6 + (b^2*((a + b*x^2)^(1/2) - a^(1/2))^2)/(d^2*((c + d*x^2)^(1/2) - c^(1/2))^2) - (((a + b*x^2)^(1/2) - a^(1/2))^3*(2*b^2*c + 2*a*b*d))/(a^(1/2)*c^(1/2)*d^2*((c + d*x^2)^(1/2) - c^(1/2))^3) - (((a + b*x^2)^(1/2) - a^(1/2))^5*(2*a*d + 2*b*c))/(a^(1/2)*c^(1/2)*d*((c + d*x^2)^(1/2) - c^(1/2))^5) + (((a + b*x^2)^(1/2) - a^(1/2))^4*(a^2*d^2 + b^2*c^2 + 4*a*b*c*d))/(a*c*d^2*((c + d*x^2)^(1/2) - c^(1/2))^4)) + (d^2*((a + b*x^2)^(1/2) - a^(1/2))^2)/(64*a^(3/2)*c^(3/2)*((c + d*x^2)^(1/2) - c^(1/2))^2) + (3*d*((a + b*x^2)^(1/2) - a^(1/2))*(a*d + b*c))/(32*a^2*c^2*((c + d*x^2)^(1/2) - c^(1/2)))","B"
975,0,-1,342,0.000000,"\text{Not used}","int(x^6/((a + b*x^2)^(1/2)*(c + d*x^2)^(1/2)),x)","\int \frac{x^6}{\sqrt{b\,x^2+a}\,\sqrt{d\,x^2+c}} \,d x","Not used",1,"int(x^6/((a + b*x^2)^(1/2)*(c + d*x^2)^(1/2)), x)","F"
976,0,-1,261,0.000000,"\text{Not used}","int(x^4/((a + b*x^2)^(1/2)*(c + d*x^2)^(1/2)),x)","\int \frac{x^4}{\sqrt{b\,x^2+a}\,\sqrt{d\,x^2+c}} \,d x","Not used",1,"int(x^4/((a + b*x^2)^(1/2)*(c + d*x^2)^(1/2)), x)","F"
977,0,-1,116,0.000000,"\text{Not used}","int(x^2/((a + b*x^2)^(1/2)*(c + d*x^2)^(1/2)),x)","\int \frac{x^2}{\sqrt{b\,x^2+a}\,\sqrt{d\,x^2+c}} \,d x","Not used",1,"int(x^2/((a + b*x^2)^(1/2)*(c + d*x^2)^(1/2)), x)","F"
978,0,-1,153,0.000000,"\text{Not used}","int(1/(x^2*(a + b*x^2)^(1/2)*(c + d*x^2)^(1/2)),x)","\int \frac{1}{x^2\,\sqrt{b\,x^2+a}\,\sqrt{d\,x^2+c}} \,d x","Not used",1,"int(1/(x^2*(a + b*x^2)^(1/2)*(c + d*x^2)^(1/2)), x)","F"
979,0,-1,307,0.000000,"\text{Not used}","int(1/(x^4*(a + b*x^2)^(1/2)*(c + d*x^2)^(1/2)),x)","\int \frac{1}{x^4\,\sqrt{b\,x^2+a}\,\sqrt{d\,x^2+c}} \,d x","Not used",1,"int(1/(x^4*(a + b*x^2)^(1/2)*(c + d*x^2)^(1/2)), x)","F"
980,0,-1,129,0.000000,"\text{Not used}","int(x^5/((a + b*x^2)^(3/2)*(c + d*x^2)^(1/2)),x)","\int \frac{x^5}{{\left(b\,x^2+a\right)}^{3/2}\,\sqrt{d\,x^2+c}} \,d x","Not used",1,"int(x^5/((a + b*x^2)^(3/2)*(c + d*x^2)^(1/2)), x)","F"
981,0,-1,83,0.000000,"\text{Not used}","int(x^3/((a + b*x^2)^(3/2)*(c + d*x^2)^(1/2)),x)","\int \frac{x^3}{{\left(b\,x^2+a\right)}^{3/2}\,\sqrt{d\,x^2+c}} \,d x","Not used",1,"int(x^3/((a + b*x^2)^(3/2)*(c + d*x^2)^(1/2)), x)","F"
982,1,45,34,1.211624,"\text{Not used}","int(x/((a + b*x^2)^(3/2)*(c + d*x^2)^(1/2)),x)","\frac{d\,x^2+c}{\left(a\,d\,\sqrt{d\,x^2+c}-b\,c\,\sqrt{d\,x^2+c}\right)\,\sqrt{b\,x^2+a}}","Not used",1,"(c + d*x^2)/((a*d*(c + d*x^2)^(1/2) - b*c*(c + d*x^2)^(1/2))*(a + b*x^2)^(1/2))","B"
983,0,-1,137,0.000000,"\text{Not used}","int(x^5/((a + b*x^2)^(5/2)*(c + d*x^2)^(1/2)),x)","\int \frac{x^5}{{\left(b\,x^2+a\right)}^{5/2}\,\sqrt{d\,x^2+c}} \,d x","Not used",1,"int(x^5/((a + b*x^2)^(5/2)*(c + d*x^2)^(1/2)), x)","F"
984,1,139,89,1.405736,"\text{Not used}","int(x^3/((a + b*x^2)^(5/2)*(c + d*x^2)^(1/2)),x)","-\frac{\sqrt{b\,x^2+a}\,\left(\frac{2\,a\,c^2}{3\,b^2\,{\left(a\,d-b\,c\right)}^2}+\frac{x^2\,\left(3\,b\,c^2+a\,d\,c\right)}{3\,b^2\,{\left(a\,d-b\,c\right)}^2}-\frac{x^4\,\left(a\,d^2-3\,b\,c\,d\right)}{3\,b^2\,{\left(a\,d-b\,c\right)}^2}\right)}{x^4\,\sqrt{d\,x^2+c}+\frac{a^2\,\sqrt{d\,x^2+c}}{b^2}+\frac{2\,a\,x^2\,\sqrt{d\,x^2+c}}{b}}","Not used",1,"-((a + b*x^2)^(1/2)*((2*a*c^2)/(3*b^2*(a*d - b*c)^2) + (x^2*(3*b*c^2 + a*c*d))/(3*b^2*(a*d - b*c)^2) - (x^4*(a*d^2 - 3*b*c*d))/(3*b^2*(a*d - b*c)^2)))/(x^4*(c + d*x^2)^(1/2) + (a^2*(c + d*x^2)^(1/2))/b^2 + (2*a*x^2*(c + d*x^2)^(1/2))/b)","B"
985,1,137,74,1.337291,"\text{Not used}","int(x/((a + b*x^2)^(5/2)*(c + d*x^2)^(1/2)),x)","\frac{\sqrt{b\,x^2+a}\,\left(\frac{x^2\,\left(3\,a\,d^2+b\,c\,d\right)}{3\,b^2\,{\left(a\,d-b\,c\right)}^2}-\frac{b\,c^2-3\,a\,c\,d}{3\,b^2\,{\left(a\,d-b\,c\right)}^2}+\frac{2\,d^2\,x^4}{3\,b\,{\left(a\,d-b\,c\right)}^2}\right)}{x^4\,\sqrt{d\,x^2+c}+\frac{a^2\,\sqrt{d\,x^2+c}}{b^2}+\frac{2\,a\,x^2\,\sqrt{d\,x^2+c}}{b}}","Not used",1,"((a + b*x^2)^(1/2)*((x^2*(3*a*d^2 + b*c*d))/(3*b^2*(a*d - b*c)^2) - (b*c^2 - 3*a*c*d)/(3*b^2*(a*d - b*c)^2) + (2*d^2*x^4)/(3*b*(a*d - b*c)^2)))/(x^4*(c + d*x^2)^(1/2) + (a^2*(c + d*x^2)^(1/2))/b^2 + (2*a*x^2*(c + d*x^2)^(1/2))/b)","B"
986,1,220,154,1.598882,"\text{Not used}","int(x^5/((a + b*x^2)^(7/2)*(c + d*x^2)^(1/2)),x)","\frac{\sqrt{b\,x^2+a}\,\left(\frac{8\,a^2\,c^3}{15\,b^3\,{\left(a\,d-b\,c\right)}^3}+\frac{x^4\,\left(-a^2\,c\,d^2+10\,a\,b\,c^2\,d+15\,b^2\,c^3\right)}{15\,b^3\,{\left(a\,d-b\,c\right)}^3}+\frac{x^6\,\left(3\,a^2\,d^3-10\,a\,b\,c\,d^2+15\,b^2\,c^2\,d\right)}{15\,b^3\,{\left(a\,d-b\,c\right)}^3}+\frac{4\,a\,c^2\,x^2\,\left(a\,d+5\,b\,c\right)}{15\,b^3\,{\left(a\,d-b\,c\right)}^3}\right)}{x^6\,\sqrt{d\,x^2+c}+\frac{a^3\,\sqrt{d\,x^2+c}}{b^3}+\frac{3\,a\,x^4\,\sqrt{d\,x^2+c}}{b}+\frac{3\,a^2\,x^2\,\sqrt{d\,x^2+c}}{b^2}}","Not used",1,"((a + b*x^2)^(1/2)*((8*a^2*c^3)/(15*b^3*(a*d - b*c)^3) + (x^4*(15*b^2*c^3 - a^2*c*d^2 + 10*a*b*c^2*d))/(15*b^3*(a*d - b*c)^3) + (x^6*(3*a^2*d^3 + 15*b^2*c^2*d - 10*a*b*c*d^2))/(15*b^3*(a*d - b*c)^3) + (4*a*c^2*x^2*(a*d + 5*b*c))/(15*b^3*(a*d - b*c)^3)))/(x^6*(c + d*x^2)^(1/2) + (a^3*(c + d*x^2)^(1/2))/b^3 + (3*a*x^4*(c + d*x^2)^(1/2))/b + (3*a^2*x^2*(c + d*x^2)^(1/2))/b^2)","B"
987,1,227,138,1.544359,"\text{Not used}","int(x^3/((a + b*x^2)^(7/2)*(c + d*x^2)^(1/2)),x)","-\frac{\sqrt{b\,x^2+a}\,\left(\frac{x^2\,\left(5\,a^2\,c\,d^2+24\,a\,b\,c^2\,d-5\,b^2\,c^3\right)}{15\,b^3\,{\left(a\,d-b\,c\right)}^3}+\frac{x^4\,\left(-5\,a^2\,d^3+24\,a\,b\,c\,d^2+5\,b^2\,c^2\,d\right)}{15\,b^3\,{\left(a\,d-b\,c\right)}^3}-\frac{2\,d^2\,x^6\,\left(a\,d-5\,b\,c\right)}{15\,b^2\,{\left(a\,d-b\,c\right)}^3}+\frac{2\,a\,c^2\,\left(5\,a\,d-b\,c\right)}{15\,b^3\,{\left(a\,d-b\,c\right)}^3}\right)}{x^6\,\sqrt{d\,x^2+c}+\frac{a^3\,\sqrt{d\,x^2+c}}{b^3}+\frac{3\,a\,x^4\,\sqrt{d\,x^2+c}}{b}+\frac{3\,a^2\,x^2\,\sqrt{d\,x^2+c}}{b^2}}","Not used",1,"-((a + b*x^2)^(1/2)*((x^2*(5*a^2*c*d^2 - 5*b^2*c^3 + 24*a*b*c^2*d))/(15*b^3*(a*d - b*c)^3) + (x^4*(5*b^2*c^2*d - 5*a^2*d^3 + 24*a*b*c*d^2))/(15*b^3*(a*d - b*c)^3) - (2*d^2*x^6*(a*d - 5*b*c))/(15*b^2*(a*d - b*c)^3) + (2*a*c^2*(5*a*d - b*c))/(15*b^3*(a*d - b*c)^3)))/(x^6*(c + d*x^2)^(1/2) + (a^3*(c + d*x^2)^(1/2))/b^3 + (3*a*x^4*(c + d*x^2)^(1/2))/b + (3*a^2*x^2*(c + d*x^2)^(1/2))/b^2)","B"
988,1,216,113,1.469529,"\text{Not used}","int(x/((a + b*x^2)^(7/2)*(c + d*x^2)^(1/2)),x)","\frac{\sqrt{b\,x^2+a}\,\left(\frac{15\,a^2\,c\,d^2-10\,a\,b\,c^2\,d+3\,b^2\,c^3}{15\,b^3\,{\left(a\,d-b\,c\right)}^3}+\frac{8\,d^3\,x^6}{15\,b\,{\left(a\,d-b\,c\right)}^3}+\frac{x^2\,\left(15\,a^2\,d^3+10\,a\,b\,c\,d^2-b^2\,c^2\,d\right)}{15\,b^3\,{\left(a\,d-b\,c\right)}^3}+\frac{4\,d^2\,x^4\,\left(5\,a\,d+b\,c\right)}{15\,b^2\,{\left(a\,d-b\,c\right)}^3}\right)}{x^6\,\sqrt{d\,x^2+c}+\frac{a^3\,\sqrt{d\,x^2+c}}{b^3}+\frac{3\,a\,x^4\,\sqrt{d\,x^2+c}}{b}+\frac{3\,a^2\,x^2\,\sqrt{d\,x^2+c}}{b^2}}","Not used",1,"((a + b*x^2)^(1/2)*((3*b^2*c^3 + 15*a^2*c*d^2 - 10*a*b*c^2*d)/(15*b^3*(a*d - b*c)^3) + (8*d^3*x^6)/(15*b*(a*d - b*c)^3) + (x^2*(15*a^2*d^3 - b^2*c^2*d + 10*a*b*c*d^2))/(15*b^3*(a*d - b*c)^3) + (4*d^2*x^4*(5*a*d + b*c))/(15*b^2*(a*d - b*c)^3)))/(x^6*(c + d*x^2)^(1/2) + (a^3*(c + d*x^2)^(1/2))/b^3 + (3*a*x^4*(c + d*x^2)^(1/2))/b + (3*a^2*x^2*(c + d*x^2)^(1/2))/b^2)","B"
989,1,336,217,1.860734,"\text{Not used}","int(x^5/((a + b*x^2)^(9/2)*(c + d*x^2)^(1/2)),x)","\frac{\sqrt{b\,x^2+a}\,\left(\frac{x^6\,\left(21\,a^3\,d^4-95\,a^2\,b\,c\,d^3+231\,a\,b^2\,c^2\,d^2+35\,b^3\,c^3\,d\right)}{105\,b^4\,{\left(a\,d-b\,c\right)}^4}-\frac{x^4\,\left(7\,a^3\,c\,d^3-99\,a^2\,b\,c^2\,d^2-231\,a\,b^2\,c^3\,d+35\,b^3\,c^4\right)}{105\,b^4\,{\left(a\,d-b\,c\right)}^4}+\frac{8\,a^2\,c^3\,\left(7\,a\,d-b\,c\right)}{105\,b^4\,{\left(a\,d-b\,c\right)}^4}+\frac{2\,d^2\,x^8\,\left(3\,a^2\,d^2-14\,a\,b\,c\,d+35\,b^2\,c^2\right)}{105\,b^3\,{\left(a\,d-b\,c\right)}^4}+\frac{4\,a\,c^2\,x^2\,\left(7\,a^2\,d^2+48\,a\,b\,c\,d-7\,b^2\,c^2\right)}{105\,b^4\,{\left(a\,d-b\,c\right)}^4}\right)}{x^8\,\sqrt{d\,x^2+c}+\frac{a^4\,\sqrt{d\,x^2+c}}{b^4}+\frac{4\,a\,x^6\,\sqrt{d\,x^2+c}}{b}+\frac{6\,a^2\,x^4\,\sqrt{d\,x^2+c}}{b^2}+\frac{4\,a^3\,x^2\,\sqrt{d\,x^2+c}}{b^3}}","Not used",1,"((a + b*x^2)^(1/2)*((x^6*(21*a^3*d^4 + 35*b^3*c^3*d + 231*a*b^2*c^2*d^2 - 95*a^2*b*c*d^3))/(105*b^4*(a*d - b*c)^4) - (x^4*(35*b^3*c^4 + 7*a^3*c*d^3 - 99*a^2*b*c^2*d^2 - 231*a*b^2*c^3*d))/(105*b^4*(a*d - b*c)^4) + (8*a^2*c^3*(7*a*d - b*c))/(105*b^4*(a*d - b*c)^4) + (2*d^2*x^8*(3*a^2*d^2 + 35*b^2*c^2 - 14*a*b*c*d))/(105*b^3*(a*d - b*c)^4) + (4*a*c^2*x^2*(7*a^2*d^2 - 7*b^2*c^2 + 48*a*b*c*d))/(105*b^4*(a*d - b*c)^4)))/(x^8*(c + d*x^2)^(1/2) + (a^4*(c + d*x^2)^(1/2))/b^4 + (4*a*x^6*(c + d*x^2)^(1/2))/b + (6*a^2*x^4*(c + d*x^2)^(1/2))/b^2 + (4*a^3*x^2*(c + d*x^2)^(1/2))/b^3)","B"
990,1,48,47,1.270984,"\text{Not used}","int(x/((a - b*x^2)^(1/2)*(c + d*x^2)^(1/2)),x)","-\frac{2\,\mathrm{atan}\left(\frac{d\,\left(\sqrt{a-b\,x^2}-\sqrt{a}\right)}{\sqrt{b\,d}\,\left(\sqrt{d\,x^2+c}-\sqrt{c}\right)}\right)}{\sqrt{b\,d}}","Not used",1,"-(2*atan((d*((a - b*x^2)^(1/2) - a^(1/2)))/((b*d)^(1/2)*((c + d*x^2)^(1/2) - c^(1/2)))))/(b*d)^(1/2)","B"
991,1,51,48,1.249263,"\text{Not used}","int(x/((a - b*x^2)^(1/2)*(c - d*x^2)^(1/2)),x)","\frac{2\,\mathrm{atan}\left(\frac{b\,\left(\sqrt{c-d\,x^2}-\sqrt{c}\right)}{\sqrt{-b\,d}\,\left(\sqrt{a-b\,x^2}-\sqrt{a}\right)}\right)}{\sqrt{-b\,d}}","Not used",1,"(2*atan((b*((c - d*x^2)^(1/2) - c^(1/2)))/((-b*d)^(1/2)*((a - b*x^2)^(1/2) - a^(1/2)))))/(-b*d)^(1/2)","B"
992,0,-1,110,0.000000,"\text{Not used}","int(x^2/((b*x^2 + 2)^(1/2)*(d*x^2 + 3)^(1/2)),x)","\int \frac{x^2}{\sqrt{b\,x^2+2}\,\sqrt{d\,x^2+3}} \,d x","Not used",1,"int(x^2/((b*x^2 + 2)^(1/2)*(d*x^2 + 3)^(1/2)), x)","F"
993,0,-1,87,0.000000,"\text{Not used}","int(x^2/((4 - x^2)^(1/2)*(c + d*x^2)^(1/2)),x)","\int \frac{x^2}{\sqrt{4-x^2}\,\sqrt{d\,x^2+c}} \,d x","Not used",1,"int(x^2/((4 - x^2)^(1/2)*(c + d*x^2)^(1/2)), x)","F"
994,0,-1,88,0.000000,"\text{Not used}","int(x^2/((x^2 + 4)^(1/2)*(c + d*x^2)^(1/2)),x)","\int \frac{x^2}{\sqrt{x^2+4}\,\sqrt{d\,x^2+c}} \,d x","Not used",1,"int(x^2/((x^2 + 4)^(1/2)*(c + d*x^2)^(1/2)), x)","F"
995,0,-1,31,0.000000,"\text{Not used}","int(x^2/((1 - x^2)^(1/2)*(3*x^2 + 2)^(1/2)),x)","\int \frac{x^2}{\sqrt{1-x^2}\,\sqrt{3\,x^2+2}} \,d x","Not used",1,"int(x^2/((1 - x^2)^(1/2)*(3*x^2 + 2)^(1/2)), x)","F"
996,0,-1,31,0.000000,"\text{Not used}","int(x^2/((1 - x^2)^(1/2)*(2 - 3*x^2)^(1/2)),x)","\int \frac{x^2}{\sqrt{1-x^2}\,\sqrt{2-3\,x^2}} \,d x","Not used",1,"int(x^2/((1 - x^2)^(1/2)*(2 - 3*x^2)^(1/2)), x)","F"
997,0,-1,35,0.000000,"\text{Not used}","int(x^2/((4 - x^2)^(1/2)*(3*x^2 + 2)^(1/2)),x)","\int \frac{x^2}{\sqrt{4-x^2}\,\sqrt{3\,x^2+2}} \,d x","Not used",1,"int(x^2/((4 - x^2)^(1/2)*(3*x^2 + 2)^(1/2)), x)","F"
998,0,-1,35,0.000000,"\text{Not used}","int(x^2/((4 - x^2)^(1/2)*(2 - 3*x^2)^(1/2)),x)","\int \frac{x^2}{\sqrt{4-x^2}\,\sqrt{2-3\,x^2}} \,d x","Not used",1,"int(x^2/((4 - x^2)^(1/2)*(2 - 3*x^2)^(1/2)), x)","F"
999,0,-1,35,0.000000,"\text{Not used}","int(x^2/((3*x^2 + 2)^(1/2)*(1 - 4*x^2)^(1/2)),x)","\int \frac{x^2}{\sqrt{3\,x^2+2}\,\sqrt{1-4\,x^2}} \,d x","Not used",1,"int(x^2/((3*x^2 + 2)^(1/2)*(1 - 4*x^2)^(1/2)), x)","F"
1000,0,-1,35,0.000000,"\text{Not used}","int(x^2/((2 - 3*x^2)^(1/2)*(1 - 4*x^2)^(1/2)),x)","\int \frac{x^2}{\sqrt{2-3\,x^2}\,\sqrt{1-4\,x^2}} \,d x","Not used",1,"int(x^2/((2 - 3*x^2)^(1/2)*(1 - 4*x^2)^(1/2)), x)","F"
1001,0,-1,42,0.000000,"\text{Not used}","int(x^2/((x^2 + 1)^(1/2)*(2 - 3*x^2)^(1/2)),x)","\int \frac{x^2}{\sqrt{x^2+1}\,\sqrt{2-3\,x^2}} \,d x","Not used",1,"int(x^2/((x^2 + 1)^(1/2)*(2 - 3*x^2)^(1/2)), x)","F"
1002,0,-1,43,0.000000,"\text{Not used}","int(x^2/((x^2 + 4)^(1/2)*(2 - 3*x^2)^(1/2)),x)","\int \frac{x^2}{\sqrt{x^2+4}\,\sqrt{2-3\,x^2}} \,d x","Not used",1,"int(x^2/((x^2 + 4)^(1/2)*(2 - 3*x^2)^(1/2)), x)","F"
1003,0,-1,47,0.000000,"\text{Not used}","int(x^2/((2 - 3*x^2)^(1/2)*(4*x^2 + 1)^(1/2)),x)","\int \frac{x^2}{\sqrt{2-3\,x^2}\,\sqrt{4\,x^2+1}} \,d x","Not used",1,"int(x^2/((2 - 3*x^2)^(1/2)*(4*x^2 + 1)^(1/2)), x)","F"
1004,0,-1,80,0.000000,"\text{Not used}","int(x^2/((x^2 + 1)^(1/2)*(3*x^2 + 2)^(1/2)),x)","\int \frac{x^2}{\sqrt{x^2+1}\,\sqrt{3\,x^2+2}} \,d x","Not used",1,"int(x^2/((x^2 + 1)^(1/2)*(3*x^2 + 2)^(1/2)), x)","F"
1005,0,-1,82,0.000000,"\text{Not used}","int(x^2/((x^2 + 4)^(1/2)*(3*x^2 + 2)^(1/2)),x)","\int \frac{x^2}{\sqrt{x^2+4}\,\sqrt{3\,x^2+2}} \,d x","Not used",1,"int(x^2/((x^2 + 4)^(1/2)*(3*x^2 + 2)^(1/2)), x)","F"
1006,0,-1,88,0.000000,"\text{Not used}","int(x^2/((3*x^2 + 2)^(1/2)*(4*x^2 + 1)^(1/2)),x)","\int \frac{x^2}{\sqrt{3\,x^2+2}\,\sqrt{4\,x^2+1}} \,d x","Not used",1,"int(x^2/((3*x^2 + 2)^(1/2)*(4*x^2 + 1)^(1/2)), x)","F"
1007,0,-1,17,0.000000,"\text{Not used}","int(x^2/((1 - x^2)^(1/2)*(2*x^2 - 1)^(1/2)),x)","\int \frac{x^2}{\sqrt{1-x^2}\,\sqrt{2\,x^2-1}} \,d x","Not used",1,"int(x^2/((1 - x^2)^(1/2)*(2*x^2 - 1)^(1/2)), x)","F"
1008,1,128,109,0.888822,"\text{Not used}","int(x^5/((1 - x^2)^(1/3)*(x^2 + 3)),x)","\frac{9\,2^{1/3}\,\ln\left(\frac{729\,{\left(1-x^2\right)}^{1/3}}{4}-\frac{729\,2^{2/3}}{4}\right)}{4}+\frac{3\,{\left(1-x^2\right)}^{2/3}}{2}+\frac{3\,{\left(1-x^2\right)}^{5/3}}{10}+\frac{9\,2^{1/3}\,\ln\left(\frac{729\,{\left(1-x^2\right)}^{1/3}}{4}-\frac{729\,2^{2/3}\,{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2}{16}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{8}-\frac{9\,2^{1/3}\,\ln\left(\frac{729\,{\left(1-x^2\right)}^{1/3}}{4}-\frac{729\,2^{2/3}\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2}{16}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{8}","Not used",1,"(9*2^(1/3)*log((729*(1 - x^2)^(1/3))/4 - (729*2^(2/3))/4))/4 + (3*(1 - x^2)^(2/3))/2 + (3*(1 - x^2)^(5/3))/10 + (9*2^(1/3)*log((729*(1 - x^2)^(1/3))/4 - (729*2^(2/3)*(3^(1/2)*1i - 1)^2)/16)*(3^(1/2)*1i - 1))/8 - (9*2^(1/3)*log((729*(1 - x^2)^(1/3))/4 - (729*2^(2/3)*(3^(1/2)*1i + 1)^2)/16)*(3^(1/2)*1i + 1))/8","B"
1009,1,117,94,0.861910,"\text{Not used}","int(x^3/((1 - x^2)^(1/3)*(x^2 + 3)),x)","-\frac{3\,2^{1/3}\,\ln\left(\frac{81\,{\left(1-x^2\right)}^{1/3}}{4}-\frac{81\,2^{2/3}}{4}\right)}{4}-\frac{3\,{\left(1-x^2\right)}^{2/3}}{4}-\frac{3\,2^{1/3}\,\ln\left(\frac{81\,{\left(1-x^2\right)}^{1/3}}{4}-\frac{81\,2^{2/3}\,{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2}{16}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{8}+\frac{3\,2^{1/3}\,\ln\left(\frac{81\,{\left(1-x^2\right)}^{1/3}}{4}-\frac{81\,2^{2/3}\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2}{16}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{8}","Not used",1,"(3*2^(1/3)*log((81*(1 - x^2)^(1/3))/4 - (81*2^(2/3)*(3^(1/2)*1i + 1)^2)/16)*(3^(1/2)*1i + 1))/8 - (3*(1 - x^2)^(2/3))/4 - (3*2^(1/3)*log((81*(1 - x^2)^(1/3))/4 - (81*2^(2/3)*(3^(1/2)*1i - 1)^2)/16)*(3^(1/2)*1i - 1))/8 - (3*2^(1/3)*log((81*(1 - x^2)^(1/3))/4 - (81*2^(2/3))/4))/4","B"
1010,1,106,79,1.051305,"\text{Not used}","int(x/((1 - x^2)^(1/3)*(x^2 + 3)),x)","\frac{2^{1/3}\,\ln\left(\frac{9\,{\left(1-x^2\right)}^{1/3}}{4}-\frac{9\,2^{2/3}}{4}\right)}{4}+\frac{2^{1/3}\,\ln\left(\frac{9\,{\left(1-x^2\right)}^{1/3}}{4}-\frac{9\,2^{2/3}\,{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2}{16}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{8}-\frac{2^{1/3}\,\ln\left(\frac{9\,{\left(1-x^2\right)}^{1/3}}{4}-\frac{9\,2^{2/3}\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2}{16}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{8}","Not used",1,"(2^(1/3)*log((9*(1 - x^2)^(1/3))/4 - (9*2^(2/3))/4))/4 + (2^(1/3)*log((9*(1 - x^2)^(1/3))/4 - (9*2^(2/3)*(3^(1/2)*1i - 1)^2)/16)*(3^(1/2)*1i - 1))/8 - (2^(1/3)*log((9*(1 - x^2)^(1/3))/4 - (9*2^(2/3)*(3^(1/2)*1i + 1)^2)/16)*(3^(1/2)*1i + 1))/8","B"
1011,1,256,136,0.954475,"\text{Not used}","int(1/(x*(1 - x^2)^(1/3)*(x^2 + 3)),x)","\frac{\ln\left(\frac{405}{8}-\frac{405\,{\left(1-x^2\right)}^{1/3}}{8}\right)}{6}+\ln\left({\left(-\frac{1}{12}+\frac{\sqrt{3}\,1{}\mathrm{i}}{12}\right)}^3\,\left(393660\,{\left(-\frac{1}{12}+\frac{\sqrt{3}\,1{}\mathrm{i}}{12}\right)}^2-\frac{37179\,{\left(1-x^2\right)}^{1/3}}{4}\right)-\frac{243\,{\left(1-x^2\right)}^{1/3}}{32}\right)\,\left(-\frac{1}{12}+\frac{\sqrt{3}\,1{}\mathrm{i}}{12}\right)-\ln\left(-{\left(\frac{1}{12}+\frac{\sqrt{3}\,1{}\mathrm{i}}{12}\right)}^3\,\left(393660\,{\left(\frac{1}{12}+\frac{\sqrt{3}\,1{}\mathrm{i}}{12}\right)}^2-\frac{37179\,{\left(1-x^2\right)}^{1/3}}{4}\right)-\frac{243\,{\left(1-x^2\right)}^{1/3}}{32}\right)\,\left(\frac{1}{12}+\frac{\sqrt{3}\,1{}\mathrm{i}}{12}\right)-\frac{2^{1/3}\,\ln\left(\frac{405\,{\left(1-x^2\right)}^{1/3}}{128}-\frac{405\,2^{2/3}}{128}\right)}{12}+\frac{{\left(-1\right)}^{1/3}\,2^{1/3}\,\ln\left(\frac{405\,{\left(1-x^2\right)}^{1/3}}{128}-\frac{405\,{\left(-1\right)}^{2/3}\,2^{2/3}}{128}\right)}{12}-\frac{{\left(-1\right)}^{1/3}\,2^{1/3}\,\ln\left(-\frac{{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^3\,\left(\frac{37179\,{\left(1-x^2\right)}^{1/3}}{4}-\frac{10935\,{\left(-1\right)}^{2/3}\,2^{2/3}\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2}{16}\right)}{6912}-\frac{243\,{\left(1-x^2\right)}^{1/3}}{32}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{24}","Not used",1,"log(405/8 - (405*(1 - x^2)^(1/3))/8)/6 + log(((3^(1/2)*1i)/12 - 1/12)^3*(393660*((3^(1/2)*1i)/12 - 1/12)^2 - (37179*(1 - x^2)^(1/3))/4) - (243*(1 - x^2)^(1/3))/32)*((3^(1/2)*1i)/12 - 1/12) - log(- ((3^(1/2)*1i)/12 + 1/12)^3*(393660*((3^(1/2)*1i)/12 + 1/12)^2 - (37179*(1 - x^2)^(1/3))/4) - (243*(1 - x^2)^(1/3))/32)*((3^(1/2)*1i)/12 + 1/12) - (2^(1/3)*log((405*(1 - x^2)^(1/3))/128 - (405*2^(2/3))/128))/12 + ((-1)^(1/3)*2^(1/3)*log((405*(1 - x^2)^(1/3))/128 - (405*(-1)^(2/3)*2^(2/3))/128))/12 - ((-1)^(1/3)*2^(1/3)*log(- ((3^(1/2)*1i + 1)^3*((37179*(1 - x^2)^(1/3))/4 - (10935*(-1)^(2/3)*2^(2/3)*(3^(1/2)*1i + 1)^2)/16))/6912 - (243*(1 - x^2)^(1/3))/32)*(3^(1/2)*1i + 1))/24","B"
1012,1,120,97,0.886312,"\text{Not used}","int(1/(x^3*(1 - x^2)^(1/3)*(x^2 + 3)),x)","\frac{2^{1/3}\,\ln\left(\frac{{\left(1-x^2\right)}^{1/3}}{36}-\frac{2^{2/3}}{36}\right)}{36}-\frac{{\left(1-x^2\right)}^{2/3}}{6\,x^2}+\frac{2^{1/3}\,\ln\left(\frac{{\left(1-x^2\right)}^{1/3}}{36}-\frac{2^{2/3}\,{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2}{144}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{72}-\frac{2^{1/3}\,\ln\left(\frac{{\left(1-x^2\right)}^{1/3}}{36}-\frac{2^{2/3}\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2}{144}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{72}","Not used",1,"(2^(1/3)*log((1 - x^2)^(1/3)/36 - 2^(2/3)/36))/36 - (1 - x^2)^(2/3)/(6*x^2) + (2^(1/3)*log((1 - x^2)^(1/3)/36 - (2^(2/3)*(3^(1/2)*1i - 1)^2)/144)*(3^(1/2)*1i - 1))/72 - (2^(1/3)*log((1 - x^2)^(1/3)/36 - (2^(2/3)*(3^(1/2)*1i + 1)^2)/144)*(3^(1/2)*1i + 1))/72","B"
1013,1,397,172,0.982461,"\text{Not used}","int(1/(x^5*(1 - x^2)^(1/3)*(x^2 + 3)),x)","\frac{\ln\left(\frac{11}{486}-\frac{11\,{\left(1-x^2\right)}^{1/3}}{486}\right)}{27}-\frac{2^{1/3}\,\ln\left(-\frac{2^{2/3}\,\left(\frac{2^{1/3}\,\left(\frac{135\,2^{2/3}}{4}-\frac{1755\,{\left(1-x^2\right)}^{1/3}}{4}\right)}{108}+\frac{7}{2}\right)}{11664}-\frac{{\left(1-x^2\right)}^{1/3}}{2916}\right)}{108}+\ln\left({\left(-\frac{1}{54}+\frac{\sqrt{3}\,1{}\mathrm{i}}{54}\right)}^2\,\left(\left(-\frac{1}{54}+\frac{\sqrt{3}\,1{}\mathrm{i}}{54}\right)\,\left(393660\,{\left(-\frac{1}{54}+\frac{\sqrt{3}\,1{}\mathrm{i}}{54}\right)}^2-\frac{1755\,{\left(1-x^2\right)}^{1/3}}{4}\right)-\frac{7}{2}\right)-\frac{{\left(1-x^2\right)}^{1/3}}{2916}\right)\,\left(-\frac{1}{54}+\frac{\sqrt{3}\,1{}\mathrm{i}}{54}\right)-\ln\left(-{\left(\frac{1}{54}+\frac{\sqrt{3}\,1{}\mathrm{i}}{54}\right)}^2\,\left(\left(\frac{1}{54}+\frac{\sqrt{3}\,1{}\mathrm{i}}{54}\right)\,\left(393660\,{\left(\frac{1}{54}+\frac{\sqrt{3}\,1{}\mathrm{i}}{54}\right)}^2-\frac{1755\,{\left(1-x^2\right)}^{1/3}}{4}\right)+\frac{7}{2}\right)-\frac{{\left(1-x^2\right)}^{1/3}}{2916}\right)\,\left(\frac{1}{54}+\frac{\sqrt{3}\,1{}\mathrm{i}}{54}\right)-\frac{\frac{5\,{\left(1-x^2\right)}^{2/3}}{36}-\frac{{\left(1-x^2\right)}^{5/3}}{18}}{{\left(x^2-1\right)}^2+2\,x^2-1}+\frac{{\left(-1\right)}^{1/3}\,2^{1/3}\,\ln\left(\frac{{\left(-1\right)}^{2/3}\,2^{2/3}\,\left(\frac{{\left(-1\right)}^{1/3}\,2^{1/3}\,\left(\frac{135\,{\left(-1\right)}^{2/3}\,2^{2/3}}{4}-\frac{1755\,{\left(1-x^2\right)}^{1/3}}{4}\right)}{108}-\frac{7}{2}\right)}{11664}-\frac{{\left(1-x^2\right)}^{1/3}}{2916}\right)}{108}-\frac{{\left(-1\right)}^{1/3}\,2^{1/3}\,\ln\left(-\frac{{\left(1-x^2\right)}^{1/3}}{2916}+\frac{{\left(-1\right)}^{2/3}\,2^{2/3}\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(\frac{{\left(-1\right)}^{1/3}\,2^{1/3}\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(\frac{1755\,{\left(1-x^2\right)}^{1/3}}{4}-\frac{135\,{\left(-1\right)}^{2/3}\,2^{2/3}\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2}{16}\right)}{216}-\frac{7}{2}\right)}{46656}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{216}","Not used",1,"log(11/486 - (11*(1 - x^2)^(1/3))/486)/27 - (2^(1/3)*log(- (2^(2/3)*((2^(1/3)*((135*2^(2/3))/4 - (1755*(1 - x^2)^(1/3))/4))/108 + 7/2))/11664 - (1 - x^2)^(1/3)/2916))/108 + log(((3^(1/2)*1i)/54 - 1/54)^2*(((3^(1/2)*1i)/54 - 1/54)*(393660*((3^(1/2)*1i)/54 - 1/54)^2 - (1755*(1 - x^2)^(1/3))/4) - 7/2) - (1 - x^2)^(1/3)/2916)*((3^(1/2)*1i)/54 - 1/54) - log(- ((3^(1/2)*1i)/54 + 1/54)^2*(((3^(1/2)*1i)/54 + 1/54)*(393660*((3^(1/2)*1i)/54 + 1/54)^2 - (1755*(1 - x^2)^(1/3))/4) + 7/2) - (1 - x^2)^(1/3)/2916)*((3^(1/2)*1i)/54 + 1/54) - ((5*(1 - x^2)^(2/3))/36 - (1 - x^2)^(5/3)/18)/((x^2 - 1)^2 + 2*x^2 - 1) + ((-1)^(1/3)*2^(1/3)*log(((-1)^(2/3)*2^(2/3)*(((-1)^(1/3)*2^(1/3)*((135*(-1)^(2/3)*2^(2/3))/4 - (1755*(1 - x^2)^(1/3))/4))/108 - 7/2))/11664 - (1 - x^2)^(1/3)/2916))/108 - ((-1)^(1/3)*2^(1/3)*log(((-1)^(2/3)*2^(2/3)*(3^(1/2)*1i + 1)^2*(((-1)^(1/3)*2^(1/3)*(3^(1/2)*1i + 1)*((1755*(1 - x^2)^(1/3))/4 - (135*(-1)^(2/3)*2^(2/3)*(3^(1/2)*1i + 1)^2)/16))/216 - 7/2))/46656 - (1 - x^2)^(1/3)/2916)*(3^(1/2)*1i + 1))/216","B"
1014,0,-1,536,0.000000,"\text{Not used}","int(x^4/((1 - x^2)^(1/3)*(x^2 + 3)),x)","\int \frac{x^4}{{\left(1-x^2\right)}^{1/3}\,\left(x^2+3\right)} \,d x","Not used",1,"int(x^4/((1 - x^2)^(1/3)*(x^2 + 3)), x)","F"
1015,0,-1,515,0.000000,"\text{Not used}","int(x^2/((1 - x^2)^(1/3)*(x^2 + 3)),x)","\int \frac{x^2}{{\left(1-x^2\right)}^{1/3}\,\left(x^2+3\right)} \,d x","Not used",1,"int(x^2/((1 - x^2)^(1/3)*(x^2 + 3)), x)","F"
1016,0,-1,113,0.000000,"\text{Not used}","int(1/((1 - x^2)^(1/3)*(x^2 + 3)),x)","\int \frac{1}{{\left(1-x^2\right)}^{1/3}\,\left(x^2+3\right)} \,d x","Not used",1,"int(1/((1 - x^2)^(1/3)*(x^2 + 3)), x)","F"
1017,0,-1,538,0.000000,"\text{Not used}","int(1/(x^2*(1 - x^2)^(1/3)*(x^2 + 3)),x)","\int \frac{1}{x^2\,{\left(1-x^2\right)}^{1/3}\,\left(x^2+3\right)} \,d x","Not used",1,"int(1/(x^2*(1 - x^2)^(1/3)*(x^2 + 3)), x)","F"
1018,0,-1,556,0.000000,"\text{Not used}","int(1/(x^4*(1 - x^2)^(1/3)*(x^2 + 3)),x)","\int \frac{1}{x^4\,{\left(1-x^2\right)}^{1/3}\,\left(x^2+3\right)} \,d x","Not used",1,"int(1/(x^4*(1 - x^2)^(1/3)*(x^2 + 3)), x)","F"
1019,1,148,133,0.923914,"\text{Not used}","int(x^7/((1 - x^2)^(1/3)*(x^2 + 3)^2),x)","\frac{99\,2^{1/3}\,\ln\left(\frac{88209\,{\left(1-x^2\right)}^{1/3}}{64}-\frac{88209\,2^{2/3}}{64}\right)}{16}+\frac{27\,{\left(1-x^2\right)}^{2/3}}{8\,\left(x^2+3\right)}+\frac{15\,{\left(1-x^2\right)}^{2/3}}{4}+\frac{3\,{\left(1-x^2\right)}^{5/3}}{10}+\frac{99\,2^{1/3}\,\ln\left(\frac{88209\,{\left(1-x^2\right)}^{1/3}}{64}-\frac{88209\,2^{2/3}\,{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2}{256}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{32}-\frac{99\,2^{1/3}\,\ln\left(\frac{88209\,{\left(1-x^2\right)}^{1/3}}{64}-\frac{88209\,2^{2/3}\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2}{256}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{32}","Not used",1,"(99*2^(1/3)*log((88209*(1 - x^2)^(1/3))/64 - (88209*2^(2/3))/64))/16 + (27*(1 - x^2)^(2/3))/(8*(x^2 + 3)) + (15*(1 - x^2)^(2/3))/4 + (3*(1 - x^2)^(5/3))/10 + (99*2^(1/3)*log((88209*(1 - x^2)^(1/3))/64 - (88209*2^(2/3)*(3^(1/2)*1i - 1)^2)/256)*(3^(1/2)*1i - 1))/32 - (99*2^(1/3)*log((88209*(1 - x^2)^(1/3))/64 - (88209*2^(2/3)*(3^(1/2)*1i + 1)^2)/256)*(3^(1/2)*1i + 1))/32","B"
1020,1,137,116,0.888454,"\text{Not used}","int(x^5/((1 - x^2)^(1/3)*(x^2 + 3)^2),x)","-\frac{21\,2^{1/3}\,\ln\left(\frac{3969\,{\left(1-x^2\right)}^{1/3}}{64}-\frac{3969\,2^{2/3}}{64}\right)}{16}-\frac{9\,{\left(1-x^2\right)}^{2/3}}{8\,\left(x^2+3\right)}-\frac{3\,{\left(1-x^2\right)}^{2/3}}{4}-\frac{21\,2^{1/3}\,\ln\left(\frac{3969\,{\left(1-x^2\right)}^{1/3}}{64}-\frac{3969\,2^{2/3}\,{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2}{256}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{32}+\frac{21\,2^{1/3}\,\ln\left(\frac{3969\,{\left(1-x^2\right)}^{1/3}}{64}-\frac{3969\,2^{2/3}\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2}{256}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{32}","Not used",1,"(21*2^(1/3)*log((3969*(1 - x^2)^(1/3))/64 - (3969*2^(2/3)*(3^(1/2)*1i + 1)^2)/256)*(3^(1/2)*1i + 1))/32 - (9*(1 - x^2)^(2/3))/(8*(x^2 + 3)) - (3*(1 - x^2)^(2/3))/4 - (21*2^(1/3)*log((3969*(1 - x^2)^(1/3))/64 - (3969*2^(2/3)*(3^(1/2)*1i - 1)^2)/256)*(3^(1/2)*1i - 1))/32 - (21*2^(1/3)*log((3969*(1 - x^2)^(1/3))/64 - (3969*2^(2/3))/64))/16","B"
1021,1,126,101,0.861576,"\text{Not used}","int(x^3/((1 - x^2)^(1/3)*(x^2 + 3)^2),x)","\frac{3\,2^{1/3}\,\ln\left(\frac{81\,{\left(1-x^2\right)}^{1/3}}{64}-\frac{81\,2^{2/3}}{64}\right)}{16}+\frac{3\,{\left(1-x^2\right)}^{2/3}}{8\,\left(x^2+3\right)}+\frac{3\,2^{1/3}\,\ln\left(\frac{81\,{\left(1-x^2\right)}^{1/3}}{64}-\frac{81\,2^{2/3}\,{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2}{256}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{32}-\frac{3\,2^{1/3}\,\ln\left(\frac{81\,{\left(1-x^2\right)}^{1/3}}{64}-\frac{81\,2^{2/3}\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2}{256}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{32}","Not used",1,"(3*2^(1/3)*log((81*(1 - x^2)^(1/3))/64 - (81*2^(2/3))/64))/16 + (3*(1 - x^2)^(2/3))/(8*(x^2 + 3)) + (3*2^(1/3)*log((81*(1 - x^2)^(1/3))/64 - (81*2^(2/3)*(3^(1/2)*1i - 1)^2)/256)*(3^(1/2)*1i - 1))/32 - (3*2^(1/3)*log((81*(1 - x^2)^(1/3))/64 - (81*2^(2/3)*(3^(1/2)*1i + 1)^2)/256)*(3^(1/2)*1i + 1))/32","B"
1022,1,126,101,0.859704,"\text{Not used}","int(x/((1 - x^2)^(1/3)*(x^2 + 3)^2),x)","\frac{2^{1/3}\,\ln\left(\frac{{\left(1-x^2\right)}^{1/3}}{64}-\frac{2^{2/3}}{64}\right)}{48}-\frac{{\left(1-x^2\right)}^{2/3}}{8\,\left(x^2+3\right)}+\frac{2^{1/3}\,\ln\left(\frac{{\left(1-x^2\right)}^{1/3}}{64}-\frac{2^{2/3}\,{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2}{256}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{96}-\frac{2^{1/3}\,\ln\left(\frac{{\left(1-x^2\right)}^{1/3}}{64}-\frac{2^{2/3}\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2}{256}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{96}","Not used",1,"(2^(1/3)*log((1 - x^2)^(1/3)/64 - 2^(2/3)/64))/48 - (1 - x^2)^(2/3)/(8*(x^2 + 3)) + (2^(1/3)*log((1 - x^2)^(1/3)/64 - (2^(2/3)*(3^(1/2)*1i - 1)^2)/256)*(3^(1/2)*1i - 1))/96 - (2^(1/3)*log((1 - x^2)^(1/3)/64 - (2^(2/3)*(3^(1/2)*1i + 1)^2)/256)*(3^(1/2)*1i + 1))/96","B"
1023,1,375,158,0.933491,"\text{Not used}","int(1/(x*(1 - x^2)^(1/3)*(x^2 + 3)^2),x)","\frac{\ln\left(\frac{127}{512}-\frac{127\,{\left(1-x^2\right)}^{1/3}}{512}\right)}{18}-\frac{5\,2^{1/3}\,\ln\left(-\frac{25\,2^{2/3}\,\left(\frac{5\,2^{1/3}\,\left(\frac{30375\,2^{2/3}}{64}-\frac{68283\,{\left(1-x^2\right)}^{1/3}}{64}\right)}{144}-\frac{1647}{128}\right)}{20736}-\frac{25\,{\left(1-x^2\right)}^{1/3}}{384}\right)}{144}+\ln\left({\left(-\frac{1}{36}+\frac{\sqrt{3}\,1{}\mathrm{i}}{36}\right)}^2\,\left(\left(-\frac{1}{36}+\frac{\sqrt{3}\,1{}\mathrm{i}}{36}\right)\,\left(393660\,{\left(-\frac{1}{36}+\frac{\sqrt{3}\,1{}\mathrm{i}}{36}\right)}^2-\frac{68283\,{\left(1-x^2\right)}^{1/3}}{64}\right)+\frac{1647}{128}\right)-\frac{25\,{\left(1-x^2\right)}^{1/3}}{384}\right)\,\left(-\frac{1}{36}+\frac{\sqrt{3}\,1{}\mathrm{i}}{36}\right)-\ln\left(-{\left(\frac{1}{36}+\frac{\sqrt{3}\,1{}\mathrm{i}}{36}\right)}^2\,\left(\left(\frac{1}{36}+\frac{\sqrt{3}\,1{}\mathrm{i}}{36}\right)\,\left(393660\,{\left(\frac{1}{36}+\frac{\sqrt{3}\,1{}\mathrm{i}}{36}\right)}^2-\frac{68283\,{\left(1-x^2\right)}^{1/3}}{64}\right)-\frac{1647}{128}\right)-\frac{25\,{\left(1-x^2\right)}^{1/3}}{384}\right)\,\left(\frac{1}{36}+\frac{\sqrt{3}\,1{}\mathrm{i}}{36}\right)+\frac{{\left(1-x^2\right)}^{2/3}}{24\,\left(x^2+3\right)}+\frac{5\,{\left(-1\right)}^{1/3}\,2^{1/3}\,\ln\left(\frac{25\,{\left(-1\right)}^{2/3}\,2^{2/3}\,\left(\frac{5\,{\left(-1\right)}^{1/3}\,2^{1/3}\,\left(\frac{30375\,{\left(-1\right)}^{2/3}\,2^{2/3}}{64}-\frac{68283\,{\left(1-x^2\right)}^{1/3}}{64}\right)}{144}+\frac{1647}{128}\right)}{20736}-\frac{25\,{\left(1-x^2\right)}^{1/3}}{384}\right)}{144}-\frac{5\,{\left(-1\right)}^{1/3}\,2^{1/3}\,\ln\left(-\frac{25\,{\left(1-x^2\right)}^{1/3}}{384}+\frac{25\,{\left(-1\right)}^{2/3}\,2^{2/3}\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(\frac{5\,{\left(-1\right)}^{1/3}\,2^{1/3}\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(\frac{68283\,{\left(1-x^2\right)}^{1/3}}{64}-\frac{30375\,{\left(-1\right)}^{2/3}\,2^{2/3}\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2}{256}\right)}{288}+\frac{1647}{128}\right)}{82944}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{288}","Not used",1,"log(127/512 - (127*(1 - x^2)^(1/3))/512)/18 - (5*2^(1/3)*log(- (25*2^(2/3)*((5*2^(1/3)*((30375*2^(2/3))/64 - (68283*(1 - x^2)^(1/3))/64))/144 - 1647/128))/20736 - (25*(1 - x^2)^(1/3))/384))/144 + log(((3^(1/2)*1i)/36 - 1/36)^2*(((3^(1/2)*1i)/36 - 1/36)*(393660*((3^(1/2)*1i)/36 - 1/36)^2 - (68283*(1 - x^2)^(1/3))/64) + 1647/128) - (25*(1 - x^2)^(1/3))/384)*((3^(1/2)*1i)/36 - 1/36) - log(- ((3^(1/2)*1i)/36 + 1/36)^2*(((3^(1/2)*1i)/36 + 1/36)*(393660*((3^(1/2)*1i)/36 + 1/36)^2 - (68283*(1 - x^2)^(1/3))/64) - 1647/128) - (25*(1 - x^2)^(1/3))/384)*((3^(1/2)*1i)/36 + 1/36) + (1 - x^2)^(2/3)/(24*(x^2 + 3)) + (5*(-1)^(1/3)*2^(1/3)*log((25*(-1)^(2/3)*2^(2/3)*((5*(-1)^(1/3)*2^(1/3)*((30375*(-1)^(2/3)*2^(2/3))/64 - (68283*(1 - x^2)^(1/3))/64))/144 + 1647/128))/20736 - (25*(1 - x^2)^(1/3))/384))/144 - (5*(-1)^(1/3)*2^(1/3)*log((25*(-1)^(2/3)*2^(2/3)*(3^(1/2)*1i + 1)^2*((5*(-1)^(1/3)*2^(1/3)*(3^(1/2)*1i + 1)*((68283*(1 - x^2)^(1/3))/64 - (30375*(-1)^(2/3)*2^(2/3)*(3^(1/2)*1i + 1)^2)/256))/288 + 1647/128))/82944 - (25*(1 - x^2)^(1/3))/384)*(3^(1/2)*1i + 1))/288","B"
1024,1,409,183,0.987517,"\text{Not used}","int(1/(x^3*(1 - x^2)^(1/3)*(x^2 + 3)^2),x)","\frac{2^{1/3}\,\ln\left(\frac{2^{2/3}\,\left(\frac{2^{1/3}\,\left(\frac{10935\,2^{2/3}}{64}-\frac{9099\,{\left(1-x^2\right)}^{1/3}}{64}\right)}{48}-\frac{665}{128}\right)}{2304}+\frac{{\left(1-x^2\right)}^{1/3}}{576}\right)}{48}-\frac{\ln\left(\frac{985\,{\left(1-x^2\right)}^{1/3}}{373248}-\frac{985}{373248}\right)}{54}+\ln\left({\left(\frac{1}{108}+\frac{\sqrt{3}\,1{}\mathrm{i}}{108}\right)}^2\,\left(\left(\frac{1}{108}+\frac{\sqrt{3}\,1{}\mathrm{i}}{108}\right)\,\left(393660\,{\left(\frac{1}{108}+\frac{\sqrt{3}\,1{}\mathrm{i}}{108}\right)}^2-\frac{9099\,{\left(1-x^2\right)}^{1/3}}{64}\right)-\frac{665}{128}\right)+\frac{{\left(1-x^2\right)}^{1/3}}{576}\right)\,\left(\frac{1}{108}+\frac{\sqrt{3}\,1{}\mathrm{i}}{108}\right)-\ln\left(\frac{{\left(1-x^2\right)}^{1/3}}{576}-{\left(-\frac{1}{108}+\frac{\sqrt{3}\,1{}\mathrm{i}}{108}\right)}^2\,\left(\left(-\frac{1}{108}+\frac{\sqrt{3}\,1{}\mathrm{i}}{108}\right)\,\left(393660\,{\left(-\frac{1}{108}+\frac{\sqrt{3}\,1{}\mathrm{i}}{108}\right)}^2-\frac{9099\,{\left(1-x^2\right)}^{1/3}}{64}\right)+\frac{665}{128}\right)\right)\,\left(-\frac{1}{108}+\frac{\sqrt{3}\,1{}\mathrm{i}}{108}\right)-\frac{\frac{17\,{\left(1-x^2\right)}^{2/3}}{72}-\frac{5\,{\left(1-x^2\right)}^{5/3}}{72}}{{\left(x^2-1\right)}^2+5\,x^2-1}+\frac{2^{1/3}\,\ln\left(\frac{{\left(1-x^2\right)}^{1/3}}{576}+\frac{2^{2/3}\,{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(\frac{2^{1/3}\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(\frac{10935\,2^{2/3}\,{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2}{256}-\frac{9099\,{\left(1-x^2\right)}^{1/3}}{64}\right)}{96}-\frac{665}{128}\right)}{9216}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{96}-\frac{2^{1/3}\,\ln\left(\frac{{\left(1-x^2\right)}^{1/3}}{576}-\frac{2^{2/3}\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(\frac{2^{1/3}\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(\frac{10935\,2^{2/3}\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2}{256}-\frac{9099\,{\left(1-x^2\right)}^{1/3}}{64}\right)}{96}+\frac{665}{128}\right)}{9216}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{96}","Not used",1,"(2^(1/3)*log((2^(2/3)*((2^(1/3)*((10935*2^(2/3))/64 - (9099*(1 - x^2)^(1/3))/64))/48 - 665/128))/2304 + (1 - x^2)^(1/3)/576))/48 - log((985*(1 - x^2)^(1/3))/373248 - 985/373248)/54 + log(((3^(1/2)*1i)/108 + 1/108)^2*(((3^(1/2)*1i)/108 + 1/108)*(393660*((3^(1/2)*1i)/108 + 1/108)^2 - (9099*(1 - x^2)^(1/3))/64) - 665/128) + (1 - x^2)^(1/3)/576)*((3^(1/2)*1i)/108 + 1/108) - log((1 - x^2)^(1/3)/576 - ((3^(1/2)*1i)/108 - 1/108)^2*(((3^(1/2)*1i)/108 - 1/108)*(393660*((3^(1/2)*1i)/108 - 1/108)^2 - (9099*(1 - x^2)^(1/3))/64) + 665/128))*((3^(1/2)*1i)/108 - 1/108) - ((17*(1 - x^2)^(2/3))/72 - (5*(1 - x^2)^(5/3))/72)/((x^2 - 1)^2 + 5*x^2 - 1) + (2^(1/3)*log((1 - x^2)^(1/3)/576 + (2^(2/3)*(3^(1/2)*1i - 1)^2*((2^(1/3)*(3^(1/2)*1i - 1)*((10935*2^(2/3)*(3^(1/2)*1i - 1)^2)/256 - (9099*(1 - x^2)^(1/3))/64))/96 - 665/128))/9216)*(3^(1/2)*1i - 1))/96 - (2^(1/3)*log((1 - x^2)^(1/3)/576 - (2^(2/3)*(3^(1/2)*1i + 1)^2*((2^(1/3)*(3^(1/2)*1i + 1)*((10935*2^(2/3)*(3^(1/2)*1i + 1)^2)/256 - (9099*(1 - x^2)^(1/3))/64))/96 + 665/128))/9216)*(3^(1/2)*1i + 1))/96","B"
1025,1,416,208,1.013498,"\text{Not used}","int(1/(x^5*(1 - x^2)^(1/3)*(x^2 + 3)^2),x)","\frac{\ln\left(\frac{9109}{10077696}-\frac{9109\,{\left(1-x^2\right)}^{1/3}}{10077696}\right)}{54}-\frac{13\,2^{1/3}\,\ln\left(-\frac{169\,2^{2/3}\,\left(\frac{13\,2^{1/3}\,\left(\frac{2535\,2^{2/3}}{64}-\frac{7419\,{\left(1-x^2\right)}^{1/3}}{64}\right)}{1296}-\frac{469}{3456}\right)}{1679616}-\frac{845\,{\left(1-x^2\right)}^{1/3}}{5038848}\right)}{1296}+\frac{\frac{{\left(1-x^2\right)}^{5/3}}{54}-\frac{23\,{\left(1-x^2\right)}^{2/3}}{216}+\frac{{\left(1-x^2\right)}^{8/3}}{216}}{6\,{\left(x^2-1\right)}^2+{\left(x^2-1\right)}^3+9\,x^2-5}+\ln\left({\left(-\frac{1}{108}+\frac{\sqrt{3}\,1{}\mathrm{i}}{108}\right)}^2\,\left(\left(-\frac{1}{108}+\frac{\sqrt{3}\,1{}\mathrm{i}}{108}\right)\,\left(393660\,{\left(-\frac{1}{108}+\frac{\sqrt{3}\,1{}\mathrm{i}}{108}\right)}^2-\frac{7419\,{\left(1-x^2\right)}^{1/3}}{64}\right)+\frac{469}{3456}\right)-\frac{845\,{\left(1-x^2\right)}^{1/3}}{5038848}\right)\,\left(-\frac{1}{108}+\frac{\sqrt{3}\,1{}\mathrm{i}}{108}\right)-\ln\left(-{\left(\frac{1}{108}+\frac{\sqrt{3}\,1{}\mathrm{i}}{108}\right)}^2\,\left(\left(\frac{1}{108}+\frac{\sqrt{3}\,1{}\mathrm{i}}{108}\right)\,\left(393660\,{\left(\frac{1}{108}+\frac{\sqrt{3}\,1{}\mathrm{i}}{108}\right)}^2-\frac{7419\,{\left(1-x^2\right)}^{1/3}}{64}\right)-\frac{469}{3456}\right)-\frac{845\,{\left(1-x^2\right)}^{1/3}}{5038848}\right)\,\left(\frac{1}{108}+\frac{\sqrt{3}\,1{}\mathrm{i}}{108}\right)+\frac{13\,{\left(-1\right)}^{1/3}\,2^{1/3}\,\ln\left(\frac{169\,{\left(-1\right)}^{2/3}\,2^{2/3}\,\left(\frac{13\,{\left(-1\right)}^{1/3}\,2^{1/3}\,\left(\frac{2535\,{\left(-1\right)}^{2/3}\,2^{2/3}}{64}-\frac{7419\,{\left(1-x^2\right)}^{1/3}}{64}\right)}{1296}+\frac{469}{3456}\right)}{1679616}-\frac{845\,{\left(1-x^2\right)}^{1/3}}{5038848}\right)}{1296}-\frac{13\,{\left(-1\right)}^{1/3}\,2^{1/3}\,\ln\left(-\frac{845\,{\left(1-x^2\right)}^{1/3}}{5038848}+\frac{169\,{\left(-1\right)}^{2/3}\,2^{2/3}\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(\frac{13\,{\left(-1\right)}^{1/3}\,2^{1/3}\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(\frac{7419\,{\left(1-x^2\right)}^{1/3}}{64}-\frac{2535\,{\left(-1\right)}^{2/3}\,2^{2/3}\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2}{256}\right)}{2592}+\frac{469}{3456}\right)}{6718464}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{2592}","Not used",1,"log(9109/10077696 - (9109*(1 - x^2)^(1/3))/10077696)/54 - (13*2^(1/3)*log(- (169*2^(2/3)*((13*2^(1/3)*((2535*2^(2/3))/64 - (7419*(1 - x^2)^(1/3))/64))/1296 - 469/3456))/1679616 - (845*(1 - x^2)^(1/3))/5038848))/1296 + ((1 - x^2)^(5/3)/54 - (23*(1 - x^2)^(2/3))/216 + (1 - x^2)^(8/3)/216)/(6*(x^2 - 1)^2 + (x^2 - 1)^3 + 9*x^2 - 5) + log(((3^(1/2)*1i)/108 - 1/108)^2*(((3^(1/2)*1i)/108 - 1/108)*(393660*((3^(1/2)*1i)/108 - 1/108)^2 - (7419*(1 - x^2)^(1/3))/64) + 469/3456) - (845*(1 - x^2)^(1/3))/5038848)*((3^(1/2)*1i)/108 - 1/108) - log(- ((3^(1/2)*1i)/108 + 1/108)^2*(((3^(1/2)*1i)/108 + 1/108)*(393660*((3^(1/2)*1i)/108 + 1/108)^2 - (7419*(1 - x^2)^(1/3))/64) - 469/3456) - (845*(1 - x^2)^(1/3))/5038848)*((3^(1/2)*1i)/108 + 1/108) + (13*(-1)^(1/3)*2^(1/3)*log((169*(-1)^(2/3)*2^(2/3)*((13*(-1)^(1/3)*2^(1/3)*((2535*(-1)^(2/3)*2^(2/3))/64 - (7419*(1 - x^2)^(1/3))/64))/1296 + 469/3456))/1679616 - (845*(1 - x^2)^(1/3))/5038848))/1296 - (13*(-1)^(1/3)*2^(1/3)*log((169*(-1)^(2/3)*2^(2/3)*(3^(1/2)*1i + 1)^2*((13*(-1)^(1/3)*2^(1/3)*(3^(1/2)*1i + 1)*((7419*(1 - x^2)^(1/3))/64 - (2535*(-1)^(2/3)*2^(2/3)*(3^(1/2)*1i + 1)^2)/256))/2592 + 469/3456))/6718464 - (845*(1 - x^2)^(1/3))/5038848)*(3^(1/2)*1i + 1))/2592","B"
1026,0,-1,543,0.000000,"\text{Not used}","int(x^4/((1 - x^2)^(1/3)*(x^2 + 3)^2),x)","\int \frac{x^4}{{\left(1-x^2\right)}^{1/3}\,{\left(x^2+3\right)}^2} \,d x","Not used",1,"int(x^4/((1 - x^2)^(1/3)*(x^2 + 3)^2), x)","F"
1027,0,-1,543,0.000000,"\text{Not used}","int(x^2/((1 - x^2)^(1/3)*(x^2 + 3)^2),x)","\int \frac{x^2}{{\left(1-x^2\right)}^{1/3}\,{\left(x^2+3\right)}^2} \,d x","Not used",1,"int(x^2/((1 - x^2)^(1/3)*(x^2 + 3)^2), x)","F"
1028,0,-1,543,0.000000,"\text{Not used}","int(1/((1 - x^2)^(1/3)*(x^2 + 3)^2),x)","\int \frac{1}{{\left(1-x^2\right)}^{1/3}\,{\left(x^2+3\right)}^2} \,d x","Not used",1,"int(1/((1 - x^2)^(1/3)*(x^2 + 3)^2), x)","F"
1029,0,-1,563,0.000000,"\text{Not used}","int(1/(x^2*(1 - x^2)^(1/3)*(x^2 + 3)^2),x)","\int \frac{1}{x^2\,{\left(1-x^2\right)}^{1/3}\,{\left(x^2+3\right)}^2} \,d x","Not used",1,"int(1/(x^2*(1 - x^2)^(1/3)*(x^2 + 3)^2), x)","F"
1030,0,-1,581,0.000000,"\text{Not used}","int(1/(x^4*(1 - x^2)^(1/3)*(x^2 + 3)^2),x)","\int \frac{1}{x^4\,{\left(1-x^2\right)}^{1/3}\,{\left(x^2+3\right)}^2} \,d x","Not used",1,"int(1/(x^4*(1 - x^2)^(1/3)*(x^2 + 3)^2), x)","F"
1031,1,82,136,0.908580,"\text{Not used}","int(-x^7/((2 - 3*x^2)^(1/4)*(3*x^2 - 4)),x)","\frac{56\,{\left(2-3\,x^2\right)}^{3/4}}{243}-\frac{16\,{\left(2-3\,x^2\right)}^{7/4}}{567}+\frac{2\,{\left(2-3\,x^2\right)}^{11/4}}{891}+2^{1/4}\,\mathrm{atan}\left(2^{1/4}\,{\left(2-3\,x^2\right)}^{1/4}\,\left(\frac{1}{2}-\frac{1}{2}{}\mathrm{i}\right)\right)\,\left(-\frac{32}{81}+\frac{32}{81}{}\mathrm{i}\right)+2^{1/4}\,\mathrm{atan}\left(2^{1/4}\,{\left(2-3\,x^2\right)}^{1/4}\,\left(\frac{1}{2}+\frac{1}{2}{}\mathrm{i}\right)\right)\,\left(-\frac{32}{81}-\frac{32}{81}{}\mathrm{i}\right)","Not used",1,"(56*(2 - 3*x^2)^(3/4))/243 - 2^(1/4)*atan(2^(1/4)*(2 - 3*x^2)^(1/4)*(1/2 + 1i/2))*(32/81 + 32i/81) - 2^(1/4)*atan(2^(1/4)*(2 - 3*x^2)^(1/4)*(1/2 - 1i/2))*(32/81 - 32i/81) - (16*(2 - 3*x^2)^(7/4))/567 + (2*(2 - 3*x^2)^(11/4))/891","B"
1032,1,71,121,0.169914,"\text{Not used}","int(-x^5/((2 - 3*x^2)^(1/4)*(3*x^2 - 4)),x)","\frac{4\,{\left(2-3\,x^2\right)}^{3/4}}{27}-\frac{2\,{\left(2-3\,x^2\right)}^{7/4}}{189}+2^{1/4}\,\mathrm{atan}\left(2^{1/4}\,{\left(2-3\,x^2\right)}^{1/4}\,\left(\frac{1}{2}-\frac{1}{2}{}\mathrm{i}\right)\right)\,\left(-\frac{8}{27}+\frac{8}{27}{}\mathrm{i}\right)+2^{1/4}\,\mathrm{atan}\left(2^{1/4}\,{\left(2-3\,x^2\right)}^{1/4}\,\left(\frac{1}{2}+\frac{1}{2}{}\mathrm{i}\right)\right)\,\left(-\frac{8}{27}-\frac{8}{27}{}\mathrm{i}\right)","Not used",1,"(4*(2 - 3*x^2)^(3/4))/27 - 2^(1/4)*atan(2^(1/4)*(2 - 3*x^2)^(1/4)*(1/2 + 1i/2))*(8/27 + 8i/27) - 2^(1/4)*atan(2^(1/4)*(2 - 3*x^2)^(1/4)*(1/2 - 1i/2))*(8/27 - 8i/27) - (2*(2 - 3*x^2)^(7/4))/189","B"
1033,1,60,106,0.153167,"\text{Not used}","int(-x^3/((2 - 3*x^2)^(1/4)*(3*x^2 - 4)),x)","\frac{2\,{\left(2-3\,x^2\right)}^{3/4}}{27}+2^{1/4}\,\mathrm{atan}\left(2^{1/4}\,{\left(2-3\,x^2\right)}^{1/4}\,\left(\frac{1}{2}-\frac{1}{2}{}\mathrm{i}\right)\right)\,\left(-\frac{2}{9}+\frac{2}{9}{}\mathrm{i}\right)+2^{1/4}\,\mathrm{atan}\left(2^{1/4}\,{\left(2-3\,x^2\right)}^{1/4}\,\left(\frac{1}{2}+\frac{1}{2}{}\mathrm{i}\right)\right)\,\left(-\frac{2}{9}-\frac{2}{9}{}\mathrm{i}\right)","Not used",1,"(2*(2 - 3*x^2)^(3/4))/27 - 2^(1/4)*atan(2^(1/4)*(2 - 3*x^2)^(1/4)*(1/2 + 1i/2))*(2/9 + 2i/9) - 2^(1/4)*atan(2^(1/4)*(2 - 3*x^2)^(1/4)*(1/2 - 1i/2))*(2/9 - 2i/9)","B"
1034,1,49,91,0.146887,"\text{Not used}","int(-x/((2 - 3*x^2)^(1/4)*(3*x^2 - 4)),x)","2^{1/4}\,\mathrm{atan}\left(2^{1/4}\,{\left(2-3\,x^2\right)}^{1/4}\,\left(\frac{1}{2}-\frac{1}{2}{}\mathrm{i}\right)\right)\,\left(-\frac{1}{6}+\frac{1}{6}{}\mathrm{i}\right)+2^{1/4}\,\mathrm{atan}\left(2^{1/4}\,{\left(2-3\,x^2\right)}^{1/4}\,\left(\frac{1}{2}+\frac{1}{2}{}\mathrm{i}\right)\right)\,\left(-\frac{1}{6}-\frac{1}{6}{}\mathrm{i}\right)","Not used",1,"- 2^(1/4)*atan(2^(1/4)*(2 - 3*x^2)^(1/4)*(1/2 - 1i/2))*(1/6 - 1i/6) - 2^(1/4)*atan(2^(1/4)*(2 - 3*x^2)^(1/4)*(1/2 + 1i/2))*(1/6 + 1i/6)","B"
1035,1,91,145,0.971219,"\text{Not used}","int(-1/(x*(2 - 3*x^2)^(1/4)*(3*x^2 - 4)),x)","\frac{2^{3/4}\,\mathrm{atan}\left(\frac{2^{3/4}\,{\left(2-3\,x^2\right)}^{1/4}}{2}\right)}{8}+2^{1/4}\,\mathrm{atan}\left(2^{1/4}\,{\left(2-3\,x^2\right)}^{1/4}\,\left(\frac{1}{2}-\frac{1}{2}{}\mathrm{i}\right)\right)\,\left(-\frac{1}{8}+\frac{1}{8}{}\mathrm{i}\right)+2^{1/4}\,\mathrm{atan}\left(2^{1/4}\,{\left(2-3\,x^2\right)}^{1/4}\,\left(\frac{1}{2}+\frac{1}{2}{}\mathrm{i}\right)\right)\,\left(-\frac{1}{8}-\frac{1}{8}{}\mathrm{i}\right)+\frac{2^{3/4}\,\mathrm{atan}\left(\frac{2^{3/4}\,{\left(2-3\,x^2\right)}^{1/4}\,1{}\mathrm{i}}{2}\right)\,1{}\mathrm{i}}{8}","Not used",1,"(2^(3/4)*atan((2^(3/4)*(2 - 3*x^2)^(1/4))/2))/8 - 2^(1/4)*atan(2^(1/4)*(2 - 3*x^2)^(1/4)*(1/2 - 1i/2))*(1/8 - 1i/8) - 2^(1/4)*atan(2^(1/4)*(2 - 3*x^2)^(1/4)*(1/2 + 1i/2))*(1/8 + 1i/8) + (2^(3/4)*atan((2^(3/4)*(2 - 3*x^2)^(1/4)*1i)/2)*1i)/8","B"
1036,1,109,163,1.009375,"\text{Not used}","int(-1/(x^3*(2 - 3*x^2)^(1/4)*(3*x^2 - 4)),x)","\frac{9\,2^{3/4}\,\mathrm{atan}\left(\frac{2^{3/4}\,{\left(2-3\,x^2\right)}^{1/4}}{2}\right)}{64}-\frac{{\left(2-3\,x^2\right)}^{3/4}}{16\,x^2}+\frac{2^{3/4}\,\mathrm{atan}\left(\frac{2^{3/4}\,{\left(2-3\,x^2\right)}^{1/4}\,1{}\mathrm{i}}{2}\right)\,9{}\mathrm{i}}{64}-\frac{{\left(-1\right)}^{1/4}\,2^{3/4}\,\mathrm{atan}\left(\frac{{\left(-1\right)}^{1/4}\,2^{3/4}\,{\left(2-3\,x^2\right)}^{1/4}\,1{}\mathrm{i}}{2}\right)\,3{}\mathrm{i}}{32}-\frac{{\left(-1\right)}^{3/4}\,2^{3/4}\,\mathrm{atan}\left(\frac{{\left(-1\right)}^{3/4}\,2^{3/4}\,{\left(2-3\,x^2\right)}^{1/4}\,1{}\mathrm{i}}{2}\right)\,3{}\mathrm{i}}{32}","Not used",1,"(9*2^(3/4)*atan((2^(3/4)*(2 - 3*x^2)^(1/4))/2))/64 - (2 - 3*x^2)^(3/4)/(16*x^2) + (2^(3/4)*atan((2^(3/4)*(2 - 3*x^2)^(1/4)*1i)/2)*9i)/64 - ((-1)^(1/4)*2^(3/4)*atan(((-1)^(1/4)*2^(3/4)*(2 - 3*x^2)^(1/4)*1i)/2)*3i)/32 - ((-1)^(3/4)*2^(3/4)*atan(((-1)^(3/4)*2^(3/4)*(2 - 3*x^2)^(1/4)*1i)/2)*3i)/32","B"
1037,0,-1,164,0.000000,"\text{Not used}","int(-x^4/((2 - 3*x^2)^(1/4)*(3*x^2 - 4)),x)","-\int \frac{x^4}{{\left(2-3\,x^2\right)}^{1/4}\,\left(3\,x^2-4\right)} \,d x","Not used",1,"-int(x^4/((2 - 3*x^2)^(1/4)*(3*x^2 - 4)), x)","F"
1038,0,-1,148,0.000000,"\text{Not used}","int(-x^2/((2 - 3*x^2)^(1/4)*(3*x^2 - 4)),x)","-\int \frac{x^2}{{\left(2-3\,x^2\right)}^{1/4}\,\left(3\,x^2-4\right)} \,d x","Not used",1,"-int(x^2/((2 - 3*x^2)^(1/4)*(3*x^2 - 4)), x)","F"
1039,0,-1,120,0.000000,"\text{Not used}","int(-1/((2 - 3*x^2)^(1/4)*(3*x^2 - 4)),x)","-\int \frac{1}{{\left(2-3\,x^2\right)}^{1/4}\,\left(3\,x^2-4\right)} \,d x","Not used",1,"-int(1/((2 - 3*x^2)^(1/4)*(3*x^2 - 4)), x)","F"
1040,0,-1,166,0.000000,"\text{Not used}","int(-1/(x^2*(2 - 3*x^2)^(1/4)*(3*x^2 - 4)),x)","-\int \frac{1}{x^2\,{\left(2-3\,x^2\right)}^{1/4}\,\left(3\,x^2-4\right)} \,d x","Not used",1,"-int(1/(x^2*(2 - 3*x^2)^(1/4)*(3*x^2 - 4)), x)","F"
1041,0,-1,184,0.000000,"\text{Not used}","int(-1/(x^4*(2 - 3*x^2)^(1/4)*(3*x^2 - 4)),x)","-\int \frac{1}{x^4\,{\left(2-3\,x^2\right)}^{1/4}\,\left(3\,x^2-4\right)} \,d x","Not used",1,"-int(1/(x^4*(2 - 3*x^2)^(1/4)*(3*x^2 - 4)), x)","F"
1042,1,62,78,0.126100,"\text{Not used}","int(x^7/((3*x^2 - 1)^(1/4)*(3*x^2 - 2)),x)","\frac{8\,\mathrm{atan}\left({\left(3\,x^2-1\right)}^{1/4}\right)}{81}+\frac{14\,{\left(3\,x^2-1\right)}^{3/4}}{243}+\frac{8\,{\left(3\,x^2-1\right)}^{7/4}}{567}+\frac{2\,{\left(3\,x^2-1\right)}^{11/4}}{891}+\frac{\mathrm{atan}\left({\left(3\,x^2-1\right)}^{1/4}\,1{}\mathrm{i}\right)\,8{}\mathrm{i}}{81}","Not used",1,"(8*atan((3*x^2 - 1)^(1/4)))/81 + (atan((3*x^2 - 1)^(1/4)*1i)*8i)/81 + (14*(3*x^2 - 1)^(3/4))/243 + (8*(3*x^2 - 1)^(7/4))/567 + (2*(3*x^2 - 1)^(11/4))/891","B"
1043,1,51,63,0.851195,"\text{Not used}","int(x^5/((3*x^2 - 1)^(1/4)*(3*x^2 - 2)),x)","\frac{4\,\mathrm{atan}\left({\left(3\,x^2-1\right)}^{1/4}\right)}{27}+\frac{2\,{\left(3\,x^2-1\right)}^{3/4}}{27}+\frac{2\,{\left(3\,x^2-1\right)}^{7/4}}{189}+\frac{\mathrm{atan}\left({\left(3\,x^2-1\right)}^{1/4}\,1{}\mathrm{i}\right)\,4{}\mathrm{i}}{27}","Not used",1,"(4*atan((3*x^2 - 1)^(1/4)))/27 + (atan((3*x^2 - 1)^(1/4)*1i)*4i)/27 + (2*(3*x^2 - 1)^(3/4))/27 + (2*(3*x^2 - 1)^(7/4))/189","B"
1044,1,36,48,0.864765,"\text{Not used}","int(x^3/((3*x^2 - 1)^(1/4)*(3*x^2 - 2)),x)","\frac{2\,\mathrm{atan}\left({\left(3\,x^2-1\right)}^{1/4}\right)}{9}-\frac{2\,\mathrm{atanh}\left({\left(3\,x^2-1\right)}^{1/4}\right)}{9}+\frac{2\,{\left(3\,x^2-1\right)}^{3/4}}{27}","Not used",1,"(2*atan((3*x^2 - 1)^(1/4)))/9 - (2*atanh((3*x^2 - 1)^(1/4)))/9 + (2*(3*x^2 - 1)^(3/4))/27","B"
1045,1,25,33,0.163731,"\text{Not used}","int(x/((3*x^2 - 1)^(1/4)*(3*x^2 - 2)),x)","\frac{\mathrm{atan}\left({\left(3\,x^2-1\right)}^{1/4}\right)}{3}-\frac{\mathrm{atanh}\left({\left(3\,x^2-1\right)}^{1/4}\right)}{3}","Not used",1,"atan((3*x^2 - 1)^(1/4))/3 - atanh((3*x^2 - 1)^(1/4))/3","B"
1046,1,77,173,0.193033,"\text{Not used}","int(1/(x*(3*x^2 - 1)^(1/4)*(3*x^2 - 2)),x)","\frac{\mathrm{atan}\left({\left(3\,x^2-1\right)}^{1/4}\right)}{2}+\frac{\mathrm{atan}\left({\left(3\,x^2-1\right)}^{1/4}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{2}+\sqrt{2}\,\mathrm{atan}\left(\sqrt{2}\,{\left(3\,x^2-1\right)}^{1/4}\,\left(\frac{1}{2}-\frac{1}{2}{}\mathrm{i}\right)\right)\,\left(-\frac{1}{4}+\frac{1}{4}{}\mathrm{i}\right)+\sqrt{2}\,\mathrm{atan}\left(\sqrt{2}\,{\left(3\,x^2-1\right)}^{1/4}\,\left(\frac{1}{2}+\frac{1}{2}{}\mathrm{i}\right)\right)\,\left(-\frac{1}{4}-\frac{1}{4}{}\mathrm{i}\right)","Not used",1,"atan((3*x^2 - 1)^(1/4))/2 + (atan((3*x^2 - 1)^(1/4)*1i)*1i)/2 - 2^(1/2)*atan(2^(1/2)*(3*x^2 - 1)^(1/4)*(1/2 - 1i/2))*(1/4 - 1i/4) - 2^(1/2)*atan(2^(1/2)*(3*x^2 - 1)^(1/4)*(1/2 + 1i/2))*(1/4 + 1i/4)","B"
1047,1,82,191,0.226432,"\text{Not used}","int(1/(x^3*(3*x^2 - 1)^(1/4)*(3*x^2 - 2)),x)","\frac{3\,\mathrm{atan}\left({\left(3\,x^2-1\right)}^{1/4}\right)}{4}+\frac{\mathrm{atan}\left({\left(3\,x^2-1\right)}^{1/4}\,1{}\mathrm{i}\right)\,3{}\mathrm{i}}{4}-\frac{{\left(3\,x^2-1\right)}^{3/4}}{4\,x^2}-\frac{{\left(-1\right)}^{1/4}\,\mathrm{atan}\left({\left(-1\right)}^{1/4}\,{\left(3\,x^2-1\right)}^{1/4}\,1{}\mathrm{i}\right)\,9{}\mathrm{i}}{8}-\frac{{\left(-1\right)}^{3/4}\,\mathrm{atan}\left({\left(-1\right)}^{3/4}\,{\left(3\,x^2-1\right)}^{1/4}\,1{}\mathrm{i}\right)\,9{}\mathrm{i}}{8}","Not used",1,"(3*atan((3*x^2 - 1)^(1/4)))/4 + (atan((3*x^2 - 1)^(1/4)*1i)*3i)/4 - (3*x^2 - 1)^(3/4)/(4*x^2) - ((-1)^(1/4)*atan((-1)^(1/4)*(3*x^2 - 1)^(1/4)*1i)*9i)/8 - ((-1)^(3/4)*atan((-1)^(3/4)*(3*x^2 - 1)^(1/4)*1i)*9i)/8","B"
1048,0,-1,244,0.000000,"\text{Not used}","int(x^4/((3*x^2 - 1)^(1/4)*(3*x^2 - 2)),x)","\int \frac{x^4}{{\left(3\,x^2-1\right)}^{1/4}\,\left(3\,x^2-2\right)} \,d x","Not used",1,"int(x^4/((3*x^2 - 1)^(1/4)*(3*x^2 - 2)), x)","F"
1049,0,-1,224,0.000000,"\text{Not used}","int(x^2/((3*x^2 - 1)^(1/4)*(3*x^2 - 2)),x)","\int \frac{x^2}{{\left(3\,x^2-1\right)}^{1/4}\,\left(3\,x^2-2\right)} \,d x","Not used",1,"int(x^2/((3*x^2 - 1)^(1/4)*(3*x^2 - 2)), x)","F"
1050,0,-1,61,0.000000,"\text{Not used}","int(1/((3*x^2 - 1)^(1/4)*(3*x^2 - 2)),x)","\int \frac{1}{{\left(3\,x^2-1\right)}^{1/4}\,\left(3\,x^2-2\right)} \,d x","Not used",1,"int(1/((3*x^2 - 1)^(1/4)*(3*x^2 - 2)), x)","F"
1051,0,-1,246,0.000000,"\text{Not used}","int(1/(x^2*(3*x^2 - 1)^(1/4)*(3*x^2 - 2)),x)","\int \frac{1}{x^2\,{\left(3\,x^2-1\right)}^{1/4}\,\left(3\,x^2-2\right)} \,d x","Not used",1,"int(1/(x^2*(3*x^2 - 1)^(1/4)*(3*x^2 - 2)), x)","F"
1052,0,-1,264,0.000000,"\text{Not used}","int(1/(x^4*(3*x^2 - 1)^(1/4)*(3*x^2 - 2)),x)","\int \frac{1}{x^4\,{\left(3\,x^2-1\right)}^{1/4}\,\left(3\,x^2-2\right)} \,d x","Not used",1,"int(1/(x^4*(3*x^2 - 1)^(1/4)*(3*x^2 - 2)), x)","F"
1053,0,-1,129,0.000000,"\text{Not used}","int(x^2/((3*x^2 + 2)^(3/4)*(3*x^2 + 4)),x)","\int \frac{x^2}{{\left(3\,x^2+2\right)}^{3/4}\,\left(3\,x^2+4\right)} \,d x","Not used",1,"int(x^2/((3*x^2 + 2)^(3/4)*(3*x^2 + 4)), x)","F"
1054,0,-1,120,0.000000,"\text{Not used}","int(-x^2/((2 - 3*x^2)^(3/4)*(3*x^2 - 4)),x)","-\int \frac{x^2}{{\left(2-3\,x^2\right)}^{3/4}\,\left(3\,x^2-4\right)} \,d x","Not used",1,"-int(x^2/((2 - 3*x^2)^(3/4)*(3*x^2 - 4)), x)","F"
1055,0,-1,124,0.000000,"\text{Not used}","int(x^2/((b*x^2 + 2)^(3/4)*(b*x^2 + 4)),x)","\int \frac{x^2}{{\left(b\,x^2+2\right)}^{3/4}\,\left(b\,x^2+4\right)} \,d x","Not used",1,"int(x^2/((b*x^2 + 2)^(3/4)*(b*x^2 + 4)), x)","F"
1056,0,-1,119,0.000000,"\text{Not used}","int(-x^2/((2 - b*x^2)^(3/4)*(b*x^2 - 4)),x)","-\int \frac{x^2}{{\left(2-b\,x^2\right)}^{3/4}\,\left(b\,x^2-4\right)} \,d x","Not used",1,"-int(x^2/((2 - b*x^2)^(3/4)*(b*x^2 - 4)), x)","F"
1057,0,-1,120,0.000000,"\text{Not used}","int(x^2/((2*a + 3*x^2)*(a + 3*x^2)^(3/4)),x)","\int \frac{x^2}{\left(3\,x^2+2\,a\right)\,{\left(3\,x^2+a\right)}^{3/4}} \,d x","Not used",1,"int(x^2/((2*a + 3*x^2)*(a + 3*x^2)^(3/4)), x)","F"
1058,0,-1,120,0.000000,"\text{Not used}","int(x^2/((2*a - 3*x^2)*(a - 3*x^2)^(3/4)),x)","\int \frac{x^2}{\left(2\,a-3\,x^2\right)\,{\left(a-3\,x^2\right)}^{3/4}} \,d x","Not used",1,"int(x^2/((2*a - 3*x^2)*(a - 3*x^2)^(3/4)), x)","F"
1059,0,-1,115,0.000000,"\text{Not used}","int(x^2/((a + b*x^2)^(3/4)*(2*a + b*x^2)),x)","\int \frac{x^2}{{\left(b\,x^2+a\right)}^{3/4}\,\left(b\,x^2+2\,a\right)} \,d x","Not used",1,"int(x^2/((a + b*x^2)^(3/4)*(2*a + b*x^2)), x)","F"
1060,0,-1,119,0.000000,"\text{Not used}","int(x^2/((a - b*x^2)^(3/4)*(2*a - b*x^2)),x)","\int \frac{x^2}{{\left(a-b\,x^2\right)}^{3/4}\,\left(2\,a-b\,x^2\right)} \,d x","Not used",1,"int(x^2/((a - b*x^2)^(3/4)*(2*a - b*x^2)), x)","F"
1061,1,82,188,0.882621,"\text{Not used}","int(-x^7/((2 - 3*x^2)^(3/4)*(3*x^2 - 4)),x)","\frac{56\,{\left(2-3\,x^2\right)}^{1/4}}{81}-\frac{16\,{\left(2-3\,x^2\right)}^{5/4}}{405}+\frac{2\,{\left(2-3\,x^2\right)}^{9/4}}{729}+2^{3/4}\,\mathrm{atan}\left(2^{1/4}\,{\left(2-3\,x^2\right)}^{1/4}\,\left(\frac{1}{2}-\frac{1}{2}{}\mathrm{i}\right)\right)\,\left(-\frac{16}{81}-\frac{16}{81}{}\mathrm{i}\right)+2^{3/4}\,\mathrm{atan}\left(2^{1/4}\,{\left(2-3\,x^2\right)}^{1/4}\,\left(\frac{1}{2}+\frac{1}{2}{}\mathrm{i}\right)\right)\,\left(-\frac{16}{81}+\frac{16}{81}{}\mathrm{i}\right)","Not used",1,"(56*(2 - 3*x^2)^(1/4))/81 - 2^(3/4)*atan(2^(1/4)*(2 - 3*x^2)^(1/4)*(1/2 + 1i/2))*(16/81 - 16i/81) - 2^(3/4)*atan(2^(1/4)*(2 - 3*x^2)^(1/4)*(1/2 - 1i/2))*(16/81 + 16i/81) - (16*(2 - 3*x^2)^(5/4))/405 + (2*(2 - 3*x^2)^(9/4))/729","B"
1062,1,71,173,0.216916,"\text{Not used}","int(-x^5/((2 - 3*x^2)^(3/4)*(3*x^2 - 4)),x)","\frac{4\,{\left(2-3\,x^2\right)}^{1/4}}{9}-\frac{2\,{\left(2-3\,x^2\right)}^{5/4}}{135}+2^{3/4}\,\mathrm{atan}\left(2^{1/4}\,{\left(2-3\,x^2\right)}^{1/4}\,\left(\frac{1}{2}-\frac{1}{2}{}\mathrm{i}\right)\right)\,\left(-\frac{4}{27}-\frac{4}{27}{}\mathrm{i}\right)+2^{3/4}\,\mathrm{atan}\left(2^{1/4}\,{\left(2-3\,x^2\right)}^{1/4}\,\left(\frac{1}{2}+\frac{1}{2}{}\mathrm{i}\right)\right)\,\left(-\frac{4}{27}+\frac{4}{27}{}\mathrm{i}\right)","Not used",1,"(4*(2 - 3*x^2)^(1/4))/9 - 2^(3/4)*atan(2^(1/4)*(2 - 3*x^2)^(1/4)*(1/2 + 1i/2))*(4/27 - 4i/27) - 2^(3/4)*atan(2^(1/4)*(2 - 3*x^2)^(1/4)*(1/2 - 1i/2))*(4/27 + 4i/27) - (2*(2 - 3*x^2)^(5/4))/135","B"
1063,1,60,158,0.165887,"\text{Not used}","int(-x^3/((2 - 3*x^2)^(3/4)*(3*x^2 - 4)),x)","\frac{2\,{\left(2-3\,x^2\right)}^{1/4}}{9}+2^{3/4}\,\mathrm{atan}\left(2^{1/4}\,{\left(2-3\,x^2\right)}^{1/4}\,\left(\frac{1}{2}-\frac{1}{2}{}\mathrm{i}\right)\right)\,\left(-\frac{1}{9}-\frac{1}{9}{}\mathrm{i}\right)+2^{3/4}\,\mathrm{atan}\left(2^{1/4}\,{\left(2-3\,x^2\right)}^{1/4}\,\left(\frac{1}{2}+\frac{1}{2}{}\mathrm{i}\right)\right)\,\left(-\frac{1}{9}+\frac{1}{9}{}\mathrm{i}\right)","Not used",1,"(2*(2 - 3*x^2)^(1/4))/9 - 2^(3/4)*atan(2^(1/4)*(2 - 3*x^2)^(1/4)*(1/2 + 1i/2))*(1/9 - 1i/9) - 2^(3/4)*atan(2^(1/4)*(2 - 3*x^2)^(1/4)*(1/2 - 1i/2))*(1/9 + 1i/9)","B"
1064,1,49,143,0.955170,"\text{Not used}","int(-x/((2 - 3*x^2)^(3/4)*(3*x^2 - 4)),x)","2^{3/4}\,\mathrm{atan}\left(2^{1/4}\,{\left(2-3\,x^2\right)}^{1/4}\,\left(\frac{1}{2}-\frac{1}{2}{}\mathrm{i}\right)\right)\,\left(-\frac{1}{12}-\frac{1}{12}{}\mathrm{i}\right)+2^{3/4}\,\mathrm{atan}\left(2^{1/4}\,{\left(2-3\,x^2\right)}^{1/4}\,\left(\frac{1}{2}+\frac{1}{2}{}\mathrm{i}\right)\right)\,\left(-\frac{1}{12}+\frac{1}{12}{}\mathrm{i}\right)","Not used",1,"- 2^(3/4)*atan(2^(1/4)*(2 - 3*x^2)^(1/4)*(1/2 - 1i/2))*(1/12 + 1i/12) - 2^(3/4)*atan(2^(1/4)*(2 - 3*x^2)^(1/4)*(1/2 + 1i/2))*(1/12 - 1i/12)","B"
1065,1,91,197,0.241321,"\text{Not used}","int(-1/(x*(2 - 3*x^2)^(3/4)*(3*x^2 - 4)),x)","-\frac{2^{1/4}\,\mathrm{atan}\left(\frac{2^{3/4}\,{\left(2-3\,x^2\right)}^{1/4}}{2}\right)}{8}+\frac{2^{1/4}\,\mathrm{atan}\left(\frac{2^{3/4}\,{\left(2-3\,x^2\right)}^{1/4}\,1{}\mathrm{i}}{2}\right)\,1{}\mathrm{i}}{8}+2^{3/4}\,\mathrm{atan}\left(2^{1/4}\,{\left(2-3\,x^2\right)}^{1/4}\,\left(\frac{1}{2}-\frac{1}{2}{}\mathrm{i}\right)\right)\,\left(-\frac{1}{16}-\frac{1}{16}{}\mathrm{i}\right)+2^{3/4}\,\mathrm{atan}\left(2^{1/4}\,{\left(2-3\,x^2\right)}^{1/4}\,\left(\frac{1}{2}+\frac{1}{2}{}\mathrm{i}\right)\right)\,\left(-\frac{1}{16}+\frac{1}{16}{}\mathrm{i}\right)","Not used",1,"(2^(1/4)*atan((2^(3/4)*(2 - 3*x^2)^(1/4)*1i)/2)*1i)/8 - (2^(1/4)*atan((2^(3/4)*(2 - 3*x^2)^(1/4))/2))/8 - 2^(3/4)*atan(2^(1/4)*(2 - 3*x^2)^(1/4)*(1/2 - 1i/2))*(1/16 + 1i/16) - 2^(3/4)*atan(2^(1/4)*(2 - 3*x^2)^(1/4)*(1/2 + 1i/2))*(1/16 - 1i/16)","B"
1066,1,107,215,1.006796,"\text{Not used}","int(-1/(x^3*(2 - 3*x^2)^(3/4)*(3*x^2 - 4)),x)","-\frac{{\left(2-3\,x^2\right)}^{1/4}}{16\,x^2}-\frac{15\,2^{1/4}\,\mathrm{atan}\left(\frac{2^{3/4}\,{\left(2-3\,x^2\right)}^{1/4}}{2}\right)}{64}+\frac{2^{1/4}\,\mathrm{atan}\left(\frac{2^{3/4}\,{\left(2-3\,x^2\right)}^{1/4}\,1{}\mathrm{i}}{2}\right)\,15{}\mathrm{i}}{64}+2^{3/4}\,\mathrm{atan}\left(2^{1/4}\,{\left(2-3\,x^2\right)}^{1/4}\,\left(\frac{1}{2}-\frac{1}{2}{}\mathrm{i}\right)\right)\,\left(-\frac{3}{64}-\frac{3}{64}{}\mathrm{i}\right)+\frac{{\left(-1\right)}^{1/4}\,2^{1/4}\,\mathrm{atan}\left(\frac{{\left(-1\right)}^{1/4}\,2^{3/4}\,{\left(2-3\,x^2\right)}^{1/4}}{2}\right)\,3{}\mathrm{i}}{32}","Not used",1,"(2^(1/4)*atan((2^(3/4)*(2 - 3*x^2)^(1/4)*1i)/2)*15i)/64 - (15*2^(1/4)*atan((2^(3/4)*(2 - 3*x^2)^(1/4))/2))/64 - (2 - 3*x^2)^(1/4)/(16*x^2) - 2^(3/4)*atan(2^(1/4)*(2 - 3*x^2)^(1/4)*(1/2 - 1i/2))*(3/64 + 3i/64) + ((-1)^(1/4)*2^(1/4)*atan(((-1)^(1/4)*2^(3/4)*(2 - 3*x^2)^(1/4))/2)*3i)/32","B"
1067,0,-1,182,0.000000,"\text{Not used}","int(-x^6/((2 - 3*x^2)^(3/4)*(3*x^2 - 4)),x)","-\int \frac{x^6}{{\left(2-3\,x^2\right)}^{3/4}\,\left(3\,x^2-4\right)} \,d x","Not used",1,"-int(x^6/((2 - 3*x^2)^(3/4)*(3*x^2 - 4)), x)","F"
1068,0,-1,164,0.000000,"\text{Not used}","int(-x^4/((2 - 3*x^2)^(3/4)*(3*x^2 - 4)),x)","-\int \frac{x^4}{{\left(2-3\,x^2\right)}^{3/4}\,\left(3\,x^2-4\right)} \,d x","Not used",1,"-int(x^4/((2 - 3*x^2)^(3/4)*(3*x^2 - 4)), x)","F"
1069,0,-1,120,0.000000,"\text{Not used}","int(-x^2/((2 - 3*x^2)^(3/4)*(3*x^2 - 4)),x)","-\int \frac{x^2}{{\left(2-3\,x^2\right)}^{3/4}\,\left(3\,x^2-4\right)} \,d x","Not used",1,"-int(x^2/((2 - 3*x^2)^(3/4)*(3*x^2 - 4)), x)","F"
1070,0,-1,148,0.000000,"\text{Not used}","int(-1/((2 - 3*x^2)^(3/4)*(3*x^2 - 4)),x)","-\int \frac{1}{{\left(2-3\,x^2\right)}^{3/4}\,\left(3\,x^2-4\right)} \,d x","Not used",1,"-int(1/((2 - 3*x^2)^(3/4)*(3*x^2 - 4)), x)","F"
1071,0,-1,166,0.000000,"\text{Not used}","int(-1/(x^2*(2 - 3*x^2)^(3/4)*(3*x^2 - 4)),x)","-\int \frac{1}{x^2\,{\left(2-3\,x^2\right)}^{3/4}\,\left(3\,x^2-4\right)} \,d x","Not used",1,"-int(1/(x^2*(2 - 3*x^2)^(3/4)*(3*x^2 - 4)), x)","F"
1072,0,-1,184,0.000000,"\text{Not used}","int(-1/(x^4*(2 - 3*x^2)^(3/4)*(3*x^2 - 4)),x)","-\int \frac{1}{x^4\,{\left(2-3\,x^2\right)}^{3/4}\,\left(3\,x^2-4\right)} \,d x","Not used",1,"-int(1/(x^4*(2 - 3*x^2)^(3/4)*(3*x^2 - 4)), x)","F"
1073,0,-1,61,0.000000,"\text{Not used}","int(x^2/((3*x^2 - 1)^(3/4)*(3*x^2 - 2)),x)","\int \frac{x^2}{{\left(3\,x^2-1\right)}^{3/4}\,\left(3\,x^2-2\right)} \,d x","Not used",1,"int(x^2/((3*x^2 - 1)^(3/4)*(3*x^2 - 2)), x)","F"
1074,0,-1,61,0.000000,"\text{Not used}","int(-x^2/((- 3*x^2 - 1)^(3/4)*(3*x^2 + 2)),x)","-\int \frac{x^2}{{\left(-3\,x^2-1\right)}^{3/4}\,\left(3\,x^2+2\right)} \,d x","Not used",1,"-int(x^2/((- 3*x^2 - 1)^(3/4)*(3*x^2 + 2)), x)","F"
1075,0,-1,72,0.000000,"\text{Not used}","int(x^2/((b*x^2 - 1)^(3/4)*(b*x^2 - 2)),x)","\int \frac{x^2}{{\left(b\,x^2-1\right)}^{3/4}\,\left(b\,x^2-2\right)} \,d x","Not used",1,"int(x^2/((b*x^2 - 1)^(3/4)*(b*x^2 - 2)), x)","F"
1076,0,-1,74,0.000000,"\text{Not used}","int(-x^2/((- b*x^2 - 1)^(3/4)*(b*x^2 + 2)),x)","-\int \frac{x^2}{{\left(-b\,x^2-1\right)}^{3/4}\,\left(b\,x^2+2\right)} \,d x","Not used",1,"-int(x^2/((- b*x^2 - 1)^(3/4)*(b*x^2 + 2)), x)","F"
1077,0,-1,85,0.000000,"\text{Not used}","int(-x^2/((2*a - 3*x^2)*(3*x^2 - a)^(3/4)),x)","-\int \frac{x^2}{\left(2\,a-3\,x^2\right)\,{\left(3\,x^2-a\right)}^{3/4}} \,d x","Not used",1,"-int(x^2/((2*a - 3*x^2)*(3*x^2 - a)^(3/4)), x)","F"
1078,0,-1,85,0.000000,"\text{Not used}","int(-x^2/((2*a + 3*x^2)*(- a - 3*x^2)^(3/4)),x)","-\int \frac{x^2}{\left(3\,x^2+2\,a\right)\,{\left(-3\,x^2-a\right)}^{3/4}} \,d x","Not used",1,"-int(x^2/((2*a + 3*x^2)*(- a - 3*x^2)^(3/4)), x)","F"
1079,0,-1,96,0.000000,"\text{Not used}","int(-x^2/((b*x^2 - a)^(3/4)*(2*a - b*x^2)),x)","-\int \frac{x^2}{{\left(b\,x^2-a\right)}^{3/4}\,\left(2\,a-b\,x^2\right)} \,d x","Not used",1,"-int(x^2/((b*x^2 - a)^(3/4)*(2*a - b*x^2)), x)","F"
1080,0,-1,98,0.000000,"\text{Not used}","int(-x^2/((- a - b*x^2)^(3/4)*(2*a + b*x^2)),x)","-\int \frac{x^2}{{\left(-b\,x^2-a\right)}^{3/4}\,\left(b\,x^2+2\,a\right)} \,d x","Not used",1,"-int(x^2/((- a - b*x^2)^(3/4)*(2*a + b*x^2)), x)","F"
1081,1,62,78,0.105217,"\text{Not used}","int(x^7/((3*x^2 - 1)^(3/4)*(3*x^2 - 2)),x)","\frac{14\,{\left(3\,x^2-1\right)}^{1/4}}{81}-\frac{8\,\mathrm{atan}\left({\left(3\,x^2-1\right)}^{1/4}\right)}{81}+\frac{8\,{\left(3\,x^2-1\right)}^{5/4}}{405}+\frac{2\,{\left(3\,x^2-1\right)}^{9/4}}{729}+\frac{\mathrm{atan}\left({\left(3\,x^2-1\right)}^{1/4}\,1{}\mathrm{i}\right)\,8{}\mathrm{i}}{81}","Not used",1,"(atan((3*x^2 - 1)^(1/4)*1i)*8i)/81 - (8*atan((3*x^2 - 1)^(1/4)))/81 + (14*(3*x^2 - 1)^(1/4))/81 + (8*(3*x^2 - 1)^(5/4))/405 + (2*(3*x^2 - 1)^(9/4))/729","B"
1082,1,51,63,0.122847,"\text{Not used}","int(x^5/((3*x^2 - 1)^(3/4)*(3*x^2 - 2)),x)","\frac{2\,{\left(3\,x^2-1\right)}^{1/4}}{9}-\frac{4\,\mathrm{atan}\left({\left(3\,x^2-1\right)}^{1/4}\right)}{27}+\frac{2\,{\left(3\,x^2-1\right)}^{5/4}}{135}+\frac{\mathrm{atan}\left({\left(3\,x^2-1\right)}^{1/4}\,1{}\mathrm{i}\right)\,4{}\mathrm{i}}{27}","Not used",1,"(atan((3*x^2 - 1)^(1/4)*1i)*4i)/27 - (4*atan((3*x^2 - 1)^(1/4)))/27 + (2*(3*x^2 - 1)^(1/4))/9 + (2*(3*x^2 - 1)^(5/4))/135","B"
1083,1,36,48,0.116050,"\text{Not used}","int(x^3/((3*x^2 - 1)^(3/4)*(3*x^2 - 2)),x)","\frac{2\,{\left(3\,x^2-1\right)}^{1/4}}{9}-\frac{2\,\mathrm{atanh}\left({\left(3\,x^2-1\right)}^{1/4}\right)}{9}-\frac{2\,\mathrm{atan}\left({\left(3\,x^2-1\right)}^{1/4}\right)}{9}","Not used",1,"(2*(3*x^2 - 1)^(1/4))/9 - (2*atanh((3*x^2 - 1)^(1/4)))/9 - (2*atan((3*x^2 - 1)^(1/4)))/9","B"
1084,1,25,33,0.868379,"\text{Not used}","int(x/((3*x^2 - 1)^(3/4)*(3*x^2 - 2)),x)","-\frac{\mathrm{atan}\left({\left(3\,x^2-1\right)}^{1/4}\right)}{3}-\frac{\mathrm{atanh}\left({\left(3\,x^2-1\right)}^{1/4}\right)}{3}","Not used",1,"- atan((3*x^2 - 1)^(1/4))/3 - atanh((3*x^2 - 1)^(1/4))/3","B"
1085,1,77,173,0.912131,"\text{Not used}","int(1/(x*(3*x^2 - 1)^(3/4)*(3*x^2 - 2)),x)","-\frac{\mathrm{atan}\left({\left(3\,x^2-1\right)}^{1/4}\right)}{2}+\frac{\mathrm{atan}\left({\left(3\,x^2-1\right)}^{1/4}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{2}+\sqrt{2}\,\mathrm{atan}\left(\sqrt{2}\,{\left(3\,x^2-1\right)}^{1/4}\,\left(\frac{1}{2}-\frac{1}{2}{}\mathrm{i}\right)\right)\,\left(-\frac{1}{4}-\frac{1}{4}{}\mathrm{i}\right)+\sqrt{2}\,\mathrm{atan}\left(\sqrt{2}\,{\left(3\,x^2-1\right)}^{1/4}\,\left(\frac{1}{2}+\frac{1}{2}{}\mathrm{i}\right)\right)\,\left(-\frac{1}{4}+\frac{1}{4}{}\mathrm{i}\right)","Not used",1,"(atan((3*x^2 - 1)^(1/4)*1i)*1i)/2 - atan((3*x^2 - 1)^(1/4))/2 - 2^(1/2)*atan(2^(1/2)*(3*x^2 - 1)^(1/4)*(1/2 - 1i/2))*(1/4 + 1i/4) - 2^(1/2)*atan(2^(1/2)*(3*x^2 - 1)^(1/4)*(1/2 + 1i/2))*(1/4 - 1i/4)","B"
1086,1,81,191,0.213724,"\text{Not used}","int(1/(x^3*(3*x^2 - 1)^(3/4)*(3*x^2 - 2)),x)","-\frac{3\,\mathrm{atan}\left({\left(3\,x^2-1\right)}^{1/4}\right)}{4}+\frac{\mathrm{atan}\left({\left(3\,x^2-1\right)}^{1/4}\,1{}\mathrm{i}\right)\,3{}\mathrm{i}}{4}-\frac{{\left(3\,x^2-1\right)}^{1/4}}{4\,x^2}+\frac{{\left(-1\right)}^{1/4}\,\mathrm{atan}\left({\left(-1\right)}^{1/4}\,{\left(3\,x^2-1\right)}^{1/4}\right)\,15{}\mathrm{i}}{8}-\frac{{\left(-1\right)}^{3/4}\,\mathrm{atan}\left({\left(-1\right)}^{3/4}\,{\left(3\,x^2-1\right)}^{1/4}\right)\,15{}\mathrm{i}}{8}","Not used",1,"(atan((3*x^2 - 1)^(1/4)*1i)*3i)/4 - (3*atan((3*x^2 - 1)^(1/4)))/4 - (3*x^2 - 1)^(1/4)/(4*x^2) + ((-1)^(1/4)*atan((-1)^(1/4)*(3*x^2 - 1)^(1/4))*15i)/8 - ((-1)^(3/4)*atan((-1)^(3/4)*(3*x^2 - 1)^(1/4))*15i)/8","B"
1087,0,-1,165,0.000000,"\text{Not used}","int(x^6/((3*x^2 - 1)^(3/4)*(3*x^2 - 2)),x)","\int \frac{x^6}{{\left(3\,x^2-1\right)}^{3/4}\,\left(3\,x^2-2\right)} \,d x","Not used",1,"int(x^6/((3*x^2 - 1)^(3/4)*(3*x^2 - 2)), x)","F"
1088,0,-1,147,0.000000,"\text{Not used}","int(x^4/((3*x^2 - 1)^(3/4)*(3*x^2 - 2)),x)","\int \frac{x^4}{{\left(3\,x^2-1\right)}^{3/4}\,\left(3\,x^2-2\right)} \,d x","Not used",1,"int(x^4/((3*x^2 - 1)^(3/4)*(3*x^2 - 2)), x)","F"
1089,0,-1,61,0.000000,"\text{Not used}","int(x^2/((3*x^2 - 1)^(3/4)*(3*x^2 - 2)),x)","\int \frac{x^2}{{\left(3\,x^2-1\right)}^{3/4}\,\left(3\,x^2-2\right)} \,d x","Not used",1,"int(x^2/((3*x^2 - 1)^(3/4)*(3*x^2 - 2)), x)","F"
1090,0,-1,127,0.000000,"\text{Not used}","int(1/((3*x^2 - 1)^(3/4)*(3*x^2 - 2)),x)","\int \frac{1}{{\left(3\,x^2-1\right)}^{3/4}\,\left(3\,x^2-2\right)} \,d x","Not used",1,"int(1/((3*x^2 - 1)^(3/4)*(3*x^2 - 2)), x)","F"
1091,0,-1,149,0.000000,"\text{Not used}","int(1/(x^2*(3*x^2 - 1)^(3/4)*(3*x^2 - 2)),x)","\int \frac{1}{x^2\,{\left(3\,x^2-1\right)}^{3/4}\,\left(3\,x^2-2\right)} \,d x","Not used",1,"int(1/(x^2*(3*x^2 - 1)^(3/4)*(3*x^2 - 2)), x)","F"
1092,0,-1,165,0.000000,"\text{Not used}","int(1/(x^4*(3*x^2 - 1)^(3/4)*(3*x^2 - 2)),x)","\int \frac{1}{x^4\,{\left(3\,x^2-1\right)}^{3/4}\,\left(3\,x^2-2\right)} \,d x","Not used",1,"int(1/(x^4*(3*x^2 - 1)^(3/4)*(3*x^2 - 2)), x)","F"
1093,0,-1,173,0.000000,"\text{Not used}","int(((e*x)^(5/2)*(c + d*x^2))/(a + b*x^2)^(3/4),x)","\int \frac{{\left(e\,x\right)}^{5/2}\,\left(d\,x^2+c\right)}{{\left(b\,x^2+a\right)}^{3/4}} \,d x","Not used",1,"int(((e*x)^(5/2)*(c + d*x^2))/(a + b*x^2)^(3/4), x)","F"
1094,0,-1,136,0.000000,"\text{Not used}","int(((e*x)^(1/2)*(c + d*x^2))/(a + b*x^2)^(3/4),x)","\int \frac{\sqrt{e\,x}\,\left(d\,x^2+c\right)}{{\left(b\,x^2+a\right)}^{3/4}} \,d x","Not used",1,"int(((e*x)^(1/2)*(c + d*x^2))/(a + b*x^2)^(3/4), x)","F"
1095,0,-1,113,0.000000,"\text{Not used}","int((c + d*x^2)/((e*x)^(3/2)*(a + b*x^2)^(3/4)),x)","\int \frac{d\,x^2+c}{{\left(e\,x\right)}^{3/2}\,{\left(b\,x^2+a\right)}^{3/4}} \,d x","Not used",1,"int((c + d*x^2)/((e*x)^(3/2)*(a + b*x^2)^(3/4)), x)","F"
1096,1,49,67,1.166707,"\text{Not used}","int((c + d*x^2)/((e*x)^(7/2)*(a + b*x^2)^(3/4)),x)","-\frac{\left(\frac{2\,c}{5\,a\,e^3}+\frac{x^2\,\left(10\,a\,d-8\,b\,c\right)}{5\,a^2\,e^3}\right)\,{\left(b\,x^2+a\right)}^{1/4}}{x^2\,\sqrt{e\,x}}","Not used",1,"-(((2*c)/(5*a*e^3) + (x^2*(10*a*d - 8*b*c))/(5*a^2*e^3))*(a + b*x^2)^(1/4))/(x^2*(e*x)^(1/2))","B"
1097,1,75,104,1.211704,"\text{Not used}","int((c + d*x^2)/((e*x)^(11/2)*(a + b*x^2)^(3/4)),x)","-\frac{{\left(b\,x^2+a\right)}^{1/4}\,\left(\frac{2\,c}{9\,a\,e^5}+\frac{x^2\,\left(18\,a^2\,d-16\,a\,b\,c\right)}{45\,a^3\,e^5}+\frac{x^4\,\left(64\,b^2\,c-72\,a\,b\,d\right)}{45\,a^3\,e^5}\right)}{x^4\,\sqrt{e\,x}}","Not used",1,"-((a + b*x^2)^(1/4)*((2*c)/(9*a*e^5) + (x^2*(18*a^2*d - 16*a*b*c))/(45*a^3*e^5) + (x^4*(64*b^2*c - 72*a*b*d))/(45*a^3*e^5)))/(x^4*(e*x)^(1/2))","B"
1098,1,100,141,1.258905,"\text{Not used}","int((c + d*x^2)/((e*x)^(15/2)*(a + b*x^2)^(3/4)),x)","-\frac{{\left(b\,x^2+a\right)}^{1/4}\,\left(\frac{2\,c}{13\,a\,e^7}+\frac{x^2\,\left(130\,a^3\,d-120\,a^2\,b\,c\right)}{585\,a^4\,e^7}-\frac{x^6\,\left(768\,b^3\,c-832\,a\,b^2\,d\right)}{585\,a^4\,e^7}-\frac{16\,b\,x^4\,\left(13\,a\,d-12\,b\,c\right)}{585\,a^3\,e^7}\right)}{x^6\,\sqrt{e\,x}}","Not used",1,"-((a + b*x^2)^(1/4)*((2*c)/(13*a*e^7) + (x^2*(130*a^3*d - 120*a^2*b*c))/(585*a^4*e^7) - (x^6*(768*b^3*c - 832*a*b^2*d))/(585*a^4*e^7) - (16*b*x^4*(13*a*d - 12*b*c))/(585*a^3*e^7)))/(x^6*(e*x)^(1/2))","B"
1099,0,-1,180,0.000000,"\text{Not used}","int(((e*x)^(7/2)*(c + d*x^2))/(a + b*x^2)^(3/4),x)","\int \frac{{\left(e\,x\right)}^{7/2}\,\left(d\,x^2+c\right)}{{\left(b\,x^2+a\right)}^{3/4}} \,d x","Not used",1,"int(((e*x)^(7/2)*(c + d*x^2))/(a + b*x^2)^(3/4), x)","F"
1100,0,-1,139,0.000000,"\text{Not used}","int(((e*x)^(3/2)*(c + d*x^2))/(a + b*x^2)^(3/4),x)","\int \frac{{\left(e\,x\right)}^{3/2}\,\left(d\,x^2+c\right)}{{\left(b\,x^2+a\right)}^{3/4}} \,d x","Not used",1,"int(((e*x)^(3/2)*(c + d*x^2))/(a + b*x^2)^(3/4), x)","F"
1101,0,-1,102,0.000000,"\text{Not used}","int((c + d*x^2)/((e*x)^(1/2)*(a + b*x^2)^(3/4)),x)","\int \frac{d\,x^2+c}{\sqrt{e\,x}\,{\left(b\,x^2+a\right)}^{3/4}} \,d x","Not used",1,"int((c + d*x^2)/((e*x)^(1/2)*(a + b*x^2)^(3/4)), x)","F"
1102,0,-1,107,0.000000,"\text{Not used}","int((c + d*x^2)/((e*x)^(5/2)*(a + b*x^2)^(3/4)),x)","\int \frac{d\,x^2+c}{{\left(e\,x\right)}^{5/2}\,{\left(b\,x^2+a\right)}^{3/4}} \,d x","Not used",1,"int((c + d*x^2)/((e*x)^(5/2)*(a + b*x^2)^(3/4)), x)","F"
1103,0,-1,144,0.000000,"\text{Not used}","int((c + d*x^2)/((e*x)^(9/2)*(a + b*x^2)^(3/4)),x)","\int \frac{d\,x^2+c}{{\left(e\,x\right)}^{9/2}\,{\left(b\,x^2+a\right)}^{3/4}} \,d x","Not used",1,"int((c + d*x^2)/((e*x)^(9/2)*(a + b*x^2)^(3/4)), x)","F"
1104,0,-1,182,0.000000,"\text{Not used}","int((c + d*x^2)/((e*x)^(13/2)*(a + b*x^2)^(3/4)),x)","\int \frac{d\,x^2+c}{{\left(e\,x\right)}^{13/2}\,{\left(b\,x^2+a\right)}^{3/4}} \,d x","Not used",1,"int((c + d*x^2)/((e*x)^(13/2)*(a + b*x^2)^(3/4)), x)","F"
1105,0,-1,171,0.000000,"\text{Not used}","int(((e*x)^(3/2)*(c + d*x^2))/(a + b*x^2)^(5/4),x)","\int \frac{{\left(e\,x\right)}^{3/2}\,\left(d\,x^2+c\right)}{{\left(b\,x^2+a\right)}^{5/4}} \,d x","Not used",1,"int(((e*x)^(3/2)*(c + d*x^2))/(a + b*x^2)^(5/4), x)","F"
1106,0,-1,122,0.000000,"\text{Not used}","int((c + d*x^2)/((e*x)^(1/2)*(a + b*x^2)^(5/4)),x)","\int \frac{d\,x^2+c}{\sqrt{e\,x}\,{\left(b\,x^2+a\right)}^{5/4}} \,d x","Not used",1,"int((c + d*x^2)/((e*x)^(1/2)*(a + b*x^2)^(5/4)), x)","F"
1107,1,70,67,1.201142,"\text{Not used}","int((c + d*x^2)/((e*x)^(5/2)*(a + b*x^2)^(5/4)),x)","-\frac{{\left(b\,x^2+a\right)}^{3/4}\,\left(\frac{2\,c}{3\,a\,b\,e^2}-\frac{x^2\,\left(6\,a\,d-8\,b\,c\right)}{3\,a^2\,b\,e^2}\right)}{x^3\,\sqrt{e\,x}+\frac{a\,x\,\sqrt{e\,x}}{b}}","Not used",1,"-((a + b*x^2)^(3/4)*((2*c)/(3*a*b*e^2) - (x^2*(6*a*d - 8*b*c))/(3*a^2*b*e^2)))/(x^3*(e*x)^(1/2) + (a*x*(e*x)^(1/2))/b)","B"
1108,1,101,104,1.231966,"\text{Not used}","int((c + d*x^2)/((e*x)^(9/2)*(a + b*x^2)^(5/4)),x)","-\frac{{\left(b\,x^2+a\right)}^{3/4}\,\left(\frac{2\,c}{7\,a\,b\,e^4}+\frac{x^2\,\left(14\,a^2\,d-16\,a\,b\,c\right)}{21\,a^3\,b\,e^4}-\frac{x^4\,\left(64\,b^2\,c-56\,a\,b\,d\right)}{21\,a^3\,b\,e^4}\right)}{x^5\,\sqrt{e\,x}+\frac{a\,x^3\,\sqrt{e\,x}}{b}}","Not used",1,"-((a + b*x^2)^(3/4)*((2*c)/(7*a*b*e^4) + (x^2*(14*a^2*d - 16*a*b*c))/(21*a^3*b*e^4) - (x^4*(64*b^2*c - 56*a*b*d))/(21*a^3*b*e^4)))/(x^5*(e*x)^(1/2) + (a*x^3*(e*x)^(1/2))/b)","B"
1109,1,125,141,1.271367,"\text{Not used}","int((c + d*x^2)/((e*x)^(13/2)*(a + b*x^2)^(5/4)),x)","-\frac{{\left(b\,x^2+a\right)}^{3/4}\,\left(\frac{2\,c}{11\,a\,b\,e^6}-\frac{16\,x^4\,\left(11\,a\,d-12\,b\,c\right)}{231\,a^3\,e^6}+\frac{x^2\,\left(66\,a^3\,d-72\,a^2\,b\,c\right)}{231\,a^4\,b\,e^6}+\frac{x^6\,\left(768\,b^3\,c-704\,a\,b^2\,d\right)}{231\,a^4\,b\,e^6}\right)}{x^7\,\sqrt{e\,x}+\frac{a\,x^5\,\sqrt{e\,x}}{b}}","Not used",1,"-((a + b*x^2)^(3/4)*((2*c)/(11*a*b*e^6) - (16*x^4*(11*a*d - 12*b*c))/(231*a^3*e^6) + (x^2*(66*a^3*d - 72*a^2*b*c))/(231*a^4*b*e^6) + (x^6*(768*b^3*c - 704*a*b^2*d))/(231*a^4*b*e^6)))/(x^7*(e*x)^(1/2) + (a*x^5*(e*x)^(1/2))/b)","B"
1110,0,-1,180,0.000000,"\text{Not used}","int(((e*x)^(9/2)*(c + d*x^2))/(a + b*x^2)^(5/4),x)","\int \frac{{\left(e\,x\right)}^{9/2}\,\left(d\,x^2+c\right)}{{\left(b\,x^2+a\right)}^{5/4}} \,d x","Not used",1,"int(((e*x)^(9/2)*(c + d*x^2))/(a + b*x^2)^(5/4), x)","F"
1111,0,-1,142,0.000000,"\text{Not used}","int(((e*x)^(5/2)*(c + d*x^2))/(a + b*x^2)^(5/4),x)","\int \frac{{\left(e\,x\right)}^{5/2}\,\left(d\,x^2+c\right)}{{\left(b\,x^2+a\right)}^{5/4}} \,d x","Not used",1,"int(((e*x)^(5/2)*(c + d*x^2))/(a + b*x^2)^(5/4), x)","F"
1112,0,-1,99,0.000000,"\text{Not used}","int(((e*x)^(1/2)*(c + d*x^2))/(a + b*x^2)^(5/4),x)","\int \frac{\sqrt{e\,x}\,\left(d\,x^2+c\right)}{{\left(b\,x^2+a\right)}^{5/4}} \,d x","Not used",1,"int(((e*x)^(1/2)*(c + d*x^2))/(a + b*x^2)^(5/4), x)","F"
1113,0,-1,103,0.000000,"\text{Not used}","int((c + d*x^2)/((e*x)^(3/2)*(a + b*x^2)^(5/4)),x)","\int \frac{d\,x^2+c}{{\left(e\,x\right)}^{3/2}\,{\left(b\,x^2+a\right)}^{5/4}} \,d x","Not used",1,"int((c + d*x^2)/((e*x)^(3/2)*(a + b*x^2)^(5/4)), x)","F"
1114,0,-1,144,0.000000,"\text{Not used}","int((c + d*x^2)/((e*x)^(7/2)*(a + b*x^2)^(5/4)),x)","\int \frac{d\,x^2+c}{{\left(e\,x\right)}^{7/2}\,{\left(b\,x^2+a\right)}^{5/4}} \,d x","Not used",1,"int((c + d*x^2)/((e*x)^(7/2)*(a + b*x^2)^(5/4)), x)","F"
1115,0,-1,182,0.000000,"\text{Not used}","int((c + d*x^2)/((e*x)^(11/2)*(a + b*x^2)^(5/4)),x)","\int \frac{d\,x^2+c}{{\left(e\,x\right)}^{11/2}\,{\left(b\,x^2+a\right)}^{5/4}} \,d x","Not used",1,"int((c + d*x^2)/((e*x)^(11/2)*(a + b*x^2)^(5/4)), x)","F"
1116,0,-1,184,0.000000,"\text{Not used}","int(((e*x)^(5/2)*(c + d*x^2))/(a + b*x^2)^(7/4),x)","\int \frac{{\left(e\,x\right)}^{5/2}\,\left(d\,x^2+c\right)}{{\left(b\,x^2+a\right)}^{7/4}} \,d x","Not used",1,"int(((e*x)^(5/2)*(c + d*x^2))/(a + b*x^2)^(7/4), x)","F"
1117,0,-1,125,0.000000,"\text{Not used}","int(((e*x)^(1/2)*(c + d*x^2))/(a + b*x^2)^(7/4),x)","\int \frac{\sqrt{e\,x}\,\left(d\,x^2+c\right)}{{\left(b\,x^2+a\right)}^{7/4}} \,d x","Not used",1,"int(((e*x)^(1/2)*(c + d*x^2))/(a + b*x^2)^(7/4), x)","F"
1118,1,69,65,1.177218,"\text{Not used}","int((c + d*x^2)/((e*x)^(3/2)*(a + b*x^2)^(7/4)),x)","-\frac{{\left(b\,x^2+a\right)}^{1/4}\,\left(\frac{2\,c}{a\,b\,e}-\frac{x^2\,\left(2\,a\,d-8\,b\,c\right)}{3\,a^2\,b\,e}\right)}{x^2\,\sqrt{e\,x}+\frac{a\,\sqrt{e\,x}}{b}}","Not used",1,"-((a + b*x^2)^(1/4)*((2*c)/(a*b*e) - (x^2*(2*a*d - 8*b*c))/(3*a^2*b*e)))/(x^2*(e*x)^(1/2) + (a*(e*x)^(1/2))/b)","B"
1119,1,101,104,1.209158,"\text{Not used}","int((c + d*x^2)/((e*x)^(7/2)*(a + b*x^2)^(7/4)),x)","-\frac{{\left(b\,x^2+a\right)}^{1/4}\,\left(\frac{2\,c}{5\,a\,b\,e^3}+\frac{x^2\,\left(30\,a^2\,d-48\,a\,b\,c\right)}{15\,a^3\,b\,e^3}-\frac{x^4\,\left(64\,b^2\,c-40\,a\,b\,d\right)}{15\,a^3\,b\,e^3}\right)}{x^4\,\sqrt{e\,x}+\frac{a\,x^2\,\sqrt{e\,x}}{b}}","Not used",1,"-((a + b*x^2)^(1/4)*((2*c)/(5*a*b*e^3) + (x^2*(30*a^2*d - 48*a*b*c))/(15*a^3*b*e^3) - (x^4*(64*b^2*c - 40*a*b*d))/(15*a^3*b*e^3)))/(x^4*(e*x)^(1/2) + (a*x^2*(e*x)^(1/2))/b)","B"
1120,1,125,141,1.261839,"\text{Not used}","int((c + d*x^2)/((e*x)^(11/2)*(a + b*x^2)^(7/4)),x)","-\frac{{\left(b\,x^2+a\right)}^{1/4}\,\left(\frac{2\,c}{9\,a\,b\,e^5}-\frac{16\,x^4\,\left(3\,a\,d-4\,b\,c\right)}{15\,a^3\,e^5}+\frac{x^2\,\left(18\,a^3\,d-24\,a^2\,b\,c\right)}{45\,a^4\,b\,e^5}+\frac{x^6\,\left(256\,b^3\,c-192\,a\,b^2\,d\right)}{45\,a^4\,b\,e^5}\right)}{x^6\,\sqrt{e\,x}+\frac{a\,x^4\,\sqrt{e\,x}}{b}}","Not used",1,"-((a + b*x^2)^(1/4)*((2*c)/(9*a*b*e^5) - (16*x^4*(3*a*d - 4*b*c))/(15*a^3*e^5) + (x^2*(18*a^3*d - 24*a^2*b*c))/(45*a^4*b*e^5) + (x^6*(256*b^3*c - 192*a*b^2*d))/(45*a^4*b*e^5)))/(x^6*(e*x)^(1/2) + (a*x^4*(e*x)^(1/2))/b)","B"
1121,0,-1,192,0.000000,"\text{Not used}","int(((e*x)^(7/2)*(c + d*x^2))/(a + b*x^2)^(7/4),x)","\int \frac{{\left(e\,x\right)}^{7/2}\,\left(d\,x^2+c\right)}{{\left(b\,x^2+a\right)}^{7/4}} \,d x","Not used",1,"int(((e*x)^(7/2)*(c + d*x^2))/(a + b*x^2)^(7/4), x)","F"
1122,0,-1,152,0.000000,"\text{Not used}","int(((e*x)^(3/2)*(c + d*x^2))/(a + b*x^2)^(7/4),x)","\int \frac{{\left(e\,x\right)}^{3/2}\,\left(d\,x^2+c\right)}{{\left(b\,x^2+a\right)}^{7/4}} \,d x","Not used",1,"int(((e*x)^(3/2)*(c + d*x^2))/(a + b*x^2)^(7/4), x)","F"
1123,0,-1,116,0.000000,"\text{Not used}","int((c + d*x^2)/((e*x)^(1/2)*(a + b*x^2)^(7/4)),x)","\int \frac{d\,x^2+c}{\sqrt{e\,x}\,{\left(b\,x^2+a\right)}^{7/4}} \,d x","Not used",1,"int((c + d*x^2)/((e*x)^(1/2)*(a + b*x^2)^(7/4)), x)","F"
1124,0,-1,144,0.000000,"\text{Not used}","int((c + d*x^2)/((e*x)^(5/2)*(a + b*x^2)^(7/4)),x)","\int \frac{d\,x^2+c}{{\left(e\,x\right)}^{5/2}\,{\left(b\,x^2+a\right)}^{7/4}} \,d x","Not used",1,"int((c + d*x^2)/((e*x)^(5/2)*(a + b*x^2)^(7/4)), x)","F"
1125,0,-1,181,0.000000,"\text{Not used}","int((c + d*x^2)/((e*x)^(9/2)*(a + b*x^2)^(7/4)),x)","\int \frac{d\,x^2+c}{{\left(e\,x\right)}^{9/2}\,{\left(b\,x^2+a\right)}^{7/4}} \,d x","Not used",1,"int((c + d*x^2)/((e*x)^(9/2)*(a + b*x^2)^(7/4)), x)","F"
1126,0,-1,221,0.000000,"\text{Not used}","int(((e*x)^(7/2)*(c + d*x^2))/(a + b*x^2)^(9/4),x)","\int \frac{{\left(e\,x\right)}^{7/2}\,\left(d\,x^2+c\right)}{{\left(b\,x^2+a\right)}^{9/4}} \,d x","Not used",1,"int(((e*x)^(7/2)*(c + d*x^2))/(a + b*x^2)^(9/4), x)","F"
1127,0,-1,149,0.000000,"\text{Not used}","int(((e*x)^(3/2)*(c + d*x^2))/(a + b*x^2)^(9/4),x)","\int \frac{{\left(e\,x\right)}^{3/2}\,\left(d\,x^2+c\right)}{{\left(b\,x^2+a\right)}^{9/4}} \,d x","Not used",1,"int(((e*x)^(3/2)*(c + d*x^2))/(a + b*x^2)^(9/4), x)","F"
1128,1,79,79,1.214632,"\text{Not used}","int((c + d*x^2)/((e*x)^(1/2)*(a + b*x^2)^(9/4)),x)","\frac{{\left(b\,x^2+a\right)}^{3/4}\,\left(\frac{x^3\,\left(2\,a\,d+8\,b\,c\right)}{5\,a^2\,b^2}+\frac{2\,c\,x}{a\,b^2}\right)}{x^4\,\sqrt{e\,x}+\frac{a^2\,\sqrt{e\,x}}{b^2}+\frac{2\,a\,x^2\,\sqrt{e\,x}}{b}}","Not used",1,"((a + b*x^2)^(3/4)*((x^3*(2*a*d + 8*b*c))/(5*a^2*b^2) + (2*c*x)/(a*b^2)))/(x^4*(e*x)^(1/2) + (a^2*(e*x)^(1/2))/b^2 + (2*a*x^2*(e*x)^(1/2))/b)","B"
1129,1,115,104,1.309603,"\text{Not used}","int((c + d*x^2)/((e*x)^(5/2)*(a + b*x^2)^(9/4)),x)","-\frac{{\left(b\,x^2+a\right)}^{3/4}\,\left(\frac{2\,c}{3\,a\,b^2\,e^2}-\frac{x^2\,\left(30\,a^2\,d-80\,a\,b\,c\right)}{15\,a^3\,b^2\,e^2}+\frac{x^4\,\left(64\,b^2\,c-24\,a\,b\,d\right)}{15\,a^3\,b^2\,e^2}\right)}{x^5\,\sqrt{e\,x}+\frac{2\,a\,x^3\,\sqrt{e\,x}}{b}+\frac{a^2\,x\,\sqrt{e\,x}}{b^2}}","Not used",1,"-((a + b*x^2)^(3/4)*((2*c)/(3*a*b^2*e^2) - (x^2*(30*a^2*d - 80*a*b*c))/(15*a^3*b^2*e^2) + (x^4*(64*b^2*c - 24*a*b*d))/(15*a^3*b^2*e^2)))/(x^5*(e*x)^(1/2) + (2*a*x^3*(e*x)^(1/2))/b + (a^2*x*(e*x)^(1/2))/b^2)","B"
1130,1,144,141,1.338385,"\text{Not used}","int((c + d*x^2)/((e*x)^(9/2)*(a + b*x^2)^(9/4)),x)","-\frac{{\left(b\,x^2+a\right)}^{3/4}\,\left(\frac{2\,c}{7\,a\,b^2\,e^4}+\frac{16\,x^4\,\left(7\,a\,d-12\,b\,c\right)}{21\,a^3\,b\,e^4}+\frac{x^2\,\left(70\,a^3\,d-120\,a^2\,b\,c\right)}{105\,a^4\,b^2\,e^4}-\frac{x^6\,\left(768\,b^3\,c-448\,a\,b^2\,d\right)}{105\,a^4\,b^2\,e^4}\right)}{x^7\,\sqrt{e\,x}+\frac{a^2\,x^3\,\sqrt{e\,x}}{b^2}+\frac{2\,a\,x^5\,\sqrt{e\,x}}{b}}","Not used",1,"-((a + b*x^2)^(3/4)*((2*c)/(7*a*b^2*e^4) + (16*x^4*(7*a*d - 12*b*c))/(21*a^3*b*e^4) + (x^2*(70*a^3*d - 120*a^2*b*c))/(105*a^4*b^2*e^4) - (x^6*(768*b^3*c - 448*a*b^2*d))/(105*a^4*b^2*e^4)))/(x^7*(e*x)^(1/2) + (a^2*x^3*(e*x)^(1/2))/b^2 + (2*a*x^5*(e*x)^(1/2))/b)","B"
1131,1,156,178,1.406262,"\text{Not used}","int((c + d*x^2)/((e*x)^(13/2)*(a + b*x^2)^(9/4)),x)","\frac{{\left(b\,x^2+a\right)}^{3/4}\,\left(\frac{64\,x^6\,\left(11\,a\,d-16\,b\,c\right)}{77\,a^4\,e^6}-\frac{2\,c}{11\,a\,b^2\,e^6}+\frac{8\,x^4\,\left(11\,a\,d-16\,b\,c\right)}{77\,a^3\,b\,e^6}-\frac{x^2\,\left(110\,a^4\,d-160\,a^3\,b\,c\right)}{385\,a^5\,b^2\,e^6}+\frac{256\,b\,x^8\,\left(11\,a\,d-16\,b\,c\right)}{385\,a^5\,e^6}\right)}{x^9\,\sqrt{e\,x}+\frac{a^2\,x^5\,\sqrt{e\,x}}{b^2}+\frac{2\,a\,x^7\,\sqrt{e\,x}}{b}}","Not used",1,"((a + b*x^2)^(3/4)*((64*x^6*(11*a*d - 16*b*c))/(77*a^4*e^6) - (2*c)/(11*a*b^2*e^6) + (8*x^4*(11*a*d - 16*b*c))/(77*a^3*b*e^6) - (x^2*(110*a^4*d - 160*a^3*b*c))/(385*a^5*b^2*e^6) + (256*b*x^8*(11*a*d - 16*b*c))/(385*a^5*e^6)))/(x^9*(e*x)^(1/2) + (a^2*x^5*(e*x)^(1/2))/b^2 + (2*a*x^7*(e*x)^(1/2))/b)","B"
1132,0,-1,230,0.000000,"\text{Not used}","int(((e*x)^(13/2)*(c + d*x^2))/(a + b*x^2)^(9/4),x)","\int \frac{{\left(e\,x\right)}^{13/2}\,\left(d\,x^2+c\right)}{{\left(b\,x^2+a\right)}^{9/4}} \,d x","Not used",1,"int(((e*x)^(13/2)*(c + d*x^2))/(a + b*x^2)^(9/4), x)","F"
1133,0,-1,192,0.000000,"\text{Not used}","int(((e*x)^(9/2)*(c + d*x^2))/(a + b*x^2)^(9/4),x)","\int \frac{{\left(e\,x\right)}^{9/2}\,\left(d\,x^2+c\right)}{{\left(b\,x^2+a\right)}^{9/4}} \,d x","Not used",1,"int(((e*x)^(9/2)*(c + d*x^2))/(a + b*x^2)^(9/4), x)","F"
1134,0,-1,155,0.000000,"\text{Not used}","int(((e*x)^(5/2)*(c + d*x^2))/(a + b*x^2)^(9/4),x)","\int \frac{{\left(e\,x\right)}^{5/2}\,\left(d\,x^2+c\right)}{{\left(b\,x^2+a\right)}^{9/4}} \,d x","Not used",1,"int(((e*x)^(5/2)*(c + d*x^2))/(a + b*x^2)^(9/4), x)","F"
1135,0,-1,114,0.000000,"\text{Not used}","int(((e*x)^(1/2)*(c + d*x^2))/(a + b*x^2)^(9/4),x)","\int \frac{\sqrt{e\,x}\,\left(d\,x^2+c\right)}{{\left(b\,x^2+a\right)}^{9/4}} \,d x","Not used",1,"int(((e*x)^(1/2)*(c + d*x^2))/(a + b*x^2)^(9/4), x)","F"
1136,0,-1,142,0.000000,"\text{Not used}","int((c + d*x^2)/((e*x)^(3/2)*(a + b*x^2)^(9/4)),x)","\int \frac{d\,x^2+c}{{\left(e\,x\right)}^{3/2}\,{\left(b\,x^2+a\right)}^{9/4}} \,d x","Not used",1,"int((c + d*x^2)/((e*x)^(3/2)*(a + b*x^2)^(9/4)), x)","F"
1137,0,-1,181,0.000000,"\text{Not used}","int((c + d*x^2)/((e*x)^(7/2)*(a + b*x^2)^(9/4)),x)","\int \frac{d\,x^2+c}{{\left(e\,x\right)}^{7/2}\,{\left(b\,x^2+a\right)}^{9/4}} \,d x","Not used",1,"int((c + d*x^2)/((e*x)^(7/2)*(a + b*x^2)^(9/4)), x)","F"
1138,0,-1,219,0.000000,"\text{Not used}","int((c + d*x^2)/((e*x)^(11/2)*(a + b*x^2)^(9/4)),x)","\int \frac{d\,x^2+c}{{\left(e\,x\right)}^{11/2}\,{\left(b\,x^2+a\right)}^{9/4}} \,d x","Not used",1,"int((c + d*x^2)/((e*x)^(11/2)*(a + b*x^2)^(9/4)), x)","F"
1139,0,-1,101,0.000000,"\text{Not used}","int((e*x)^m*(a + b*x^2)^p*(c + d*x^2)^q,x)","\int {\left(e\,x\right)}^m\,{\left(b\,x^2+a\right)}^p\,{\left(d\,x^2+c\right)}^q \,d x","Not used",1,"int((e*x)^m*(a + b*x^2)^p*(c + d*x^2)^q, x)","F"
1140,0,-1,84,0.000000,"\text{Not used}","int(x^4*(a + b*x^2)^p*(c + d*x^2)^q,x)","\int x^4\,{\left(b\,x^2+a\right)}^p\,{\left(d\,x^2+c\right)}^q \,d x","Not used",1,"int(x^4*(a + b*x^2)^p*(c + d*x^2)^q, x)","F"
1141,0,-1,84,0.000000,"\text{Not used}","int(x^2*(a + b*x^2)^p*(c + d*x^2)^q,x)","\int x^2\,{\left(b\,x^2+a\right)}^p\,{\left(d\,x^2+c\right)}^q \,d x","Not used",1,"int(x^2*(a + b*x^2)^p*(c + d*x^2)^q, x)","F"
1142,0,-1,79,0.000000,"\text{Not used}","int((a + b*x^2)^p*(c + d*x^2)^q,x)","\int {\left(b\,x^2+a\right)}^p\,{\left(d\,x^2+c\right)}^q \,d x","Not used",1,"int((a + b*x^2)^p*(c + d*x^2)^q, x)","F"
1143,0,-1,82,0.000000,"\text{Not used}","int(((a + b*x^2)^p*(c + d*x^2)^q)/x^2,x)","\int \frac{{\left(b\,x^2+a\right)}^p\,{\left(d\,x^2+c\right)}^q}{x^2} \,d x","Not used",1,"int(((a + b*x^2)^p*(c + d*x^2)^q)/x^2, x)","F"
1144,0,-1,84,0.000000,"\text{Not used}","int(((a + b*x^2)^p*(c + d*x^2)^q)/x^4,x)","\int \frac{{\left(b\,x^2+a\right)}^p\,{\left(d\,x^2+c\right)}^q}{x^4} \,d x","Not used",1,"int(((a + b*x^2)^p*(c + d*x^2)^q)/x^4, x)","F"
1145,0,-1,242,0.000000,"\text{Not used}","int(x^5*(a + b*x^2)^p*(c + d*x^2)^q,x)","\int x^5\,{\left(b\,x^2+a\right)}^p\,{\left(d\,x^2+c\right)}^q \,d x","Not used",1,"int(x^5*(a + b*x^2)^p*(c + d*x^2)^q, x)","F"
1146,0,-1,146,0.000000,"\text{Not used}","int(x^3*(a + b*x^2)^p*(c + d*x^2)^q,x)","\int x^3\,{\left(b\,x^2+a\right)}^p\,{\left(d\,x^2+c\right)}^q \,d x","Not used",1,"int(x^3*(a + b*x^2)^p*(c + d*x^2)^q, x)","F"
1147,0,-1,85,0.000000,"\text{Not used}","int(x*(a + b*x^2)^p*(c + d*x^2)^q,x)","\int x\,{\left(b\,x^2+a\right)}^p\,{\left(d\,x^2+c\right)}^q \,d x","Not used",1,"int(x*(a + b*x^2)^p*(c + d*x^2)^q, x)","F"
1148,0,-1,97,0.000000,"\text{Not used}","int(((a + b*x^2)^p*(c + d*x^2)^q)/x,x)","\int \frac{{\left(b\,x^2+a\right)}^p\,{\left(d\,x^2+c\right)}^q}{x} \,d x","Not used",1,"int(((a + b*x^2)^p*(c + d*x^2)^q)/x, x)","F"
1149,0,-1,98,0.000000,"\text{Not used}","int(((a + b*x^2)^p*(c + d*x^2)^q)/x^3,x)","\int \frac{{\left(b\,x^2+a\right)}^p\,{\left(d\,x^2+c\right)}^q}{x^3} \,d x","Not used",1,"int(((a + b*x^2)^p*(c + d*x^2)^q)/x^3, x)","F"
1150,0,-1,100,0.000000,"\text{Not used}","int(((a + b*x^2)^p*(c + d*x^2)^q)/x^5,x)","\int \frac{{\left(b\,x^2+a\right)}^p\,{\left(d\,x^2+c\right)}^q}{x^5} \,d x","Not used",1,"int(((a + b*x^2)^p*(c + d*x^2)^q)/x^5, x)","F"
1151,0,-1,91,0.000000,"\text{Not used}","int((e*x)^(5/2)*(a + b*x^2)^p*(c + d*x^2)^q,x)","\int {\left(e\,x\right)}^{5/2}\,{\left(b\,x^2+a\right)}^p\,{\left(d\,x^2+c\right)}^q \,d x","Not used",1,"int((e*x)^(5/2)*(a + b*x^2)^p*(c + d*x^2)^q, x)","F"
1152,0,-1,91,0.000000,"\text{Not used}","int((e*x)^(3/2)*(a + b*x^2)^p*(c + d*x^2)^q,x)","\int {\left(e\,x\right)}^{3/2}\,{\left(b\,x^2+a\right)}^p\,{\left(d\,x^2+c\right)}^q \,d x","Not used",1,"int((e*x)^(3/2)*(a + b*x^2)^p*(c + d*x^2)^q, x)","F"
1153,0,-1,91,0.000000,"\text{Not used}","int((e*x)^(1/2)*(a + b*x^2)^p*(c + d*x^2)^q,x)","\int \sqrt{e\,x}\,{\left(b\,x^2+a\right)}^p\,{\left(d\,x^2+c\right)}^q \,d x","Not used",1,"int((e*x)^(1/2)*(a + b*x^2)^p*(c + d*x^2)^q, x)","F"
1154,0,-1,89,0.000000,"\text{Not used}","int(((a + b*x^2)^p*(c + d*x^2)^q)/(e*x)^(1/2),x)","\int \frac{{\left(b\,x^2+a\right)}^p\,{\left(d\,x^2+c\right)}^q}{\sqrt{e\,x}} \,d x","Not used",1,"int(((a + b*x^2)^p*(c + d*x^2)^q)/(e*x)^(1/2), x)","F"
1155,0,-1,89,0.000000,"\text{Not used}","int(((a + b*x^2)^p*(c + d*x^2)^q)/(e*x)^(3/2),x)","\int \frac{{\left(b\,x^2+a\right)}^p\,{\left(d\,x^2+c\right)}^q}{{\left(e\,x\right)}^{3/2}} \,d x","Not used",1,"int(((a + b*x^2)^p*(c + d*x^2)^q)/(e*x)^(3/2), x)","F"
1156,0,-1,91,0.000000,"\text{Not used}","int(((a + b*x^2)^p*(c + d*x^2)^q)/(e*x)^(5/2),x)","\int \frac{{\left(b\,x^2+a\right)}^p\,{\left(d\,x^2+c\right)}^q}{{\left(e\,x\right)}^{5/2}} \,d x","Not used",1,"int(((a + b*x^2)^p*(c + d*x^2)^q)/(e*x)^(5/2), x)","F"