1,1,28,33,0.199742,"\text{Not used}","int(x^2*(A + B*x^3)*(a + b*x^3),x)","\frac{B\,b\,x^9}{9}+\left(\frac{A\,b}{6}+\frac{B\,a}{6}\right)\,x^6+\frac{A\,a\,x^3}{3}","Not used",1,"x^6*((A*b)/6 + (B*a)/6) + (A*a*x^3)/3 + (B*b*x^9)/9","B"
2,1,28,33,2.483497,"\text{Not used}","int(x*(A + B*x^3)*(a + b*x^3),x)","\frac{B\,b\,x^8}{8}+\left(\frac{A\,b}{5}+\frac{B\,a}{5}\right)\,x^5+\frac{A\,a\,x^2}{2}","Not used",1,"x^5*((A*b)/5 + (B*a)/5) + (A*a*x^2)/2 + (B*b*x^8)/8","B"
3,1,25,28,0.033882,"\text{Not used}","int((A + B*x^3)*(a + b*x^3),x)","\frac{B\,b\,x^7}{7}+\left(\frac{A\,b}{4}+\frac{B\,a}{4}\right)\,x^4+A\,a\,x","Not used",1,"x^4*((A*b)/4 + (B*a)/4) + A*a*x + (B*b*x^7)/7","B"
4,1,26,29,0.034777,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3))/x,x)","x^3\,\left(\frac{A\,b}{3}+\frac{B\,a}{3}\right)+\frac{B\,b\,x^6}{6}+A\,a\,\ln\left(x\right)","Not used",1,"x^3*((A*b)/3 + (B*a)/3) + (B*b*x^6)/6 + A*a*log(x)","B"
5,1,28,31,0.039223,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3))/x^2,x)","x^2\,\left(\frac{A\,b}{2}+\frac{B\,a}{2}\right)-\frac{A\,a}{x}+\frac{B\,b\,x^5}{5}","Not used",1,"x^2*((A*b)/2 + (B*a)/2) - (A*a)/x + (B*b*x^5)/5","B"
6,1,24,28,2.337433,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3))/x^3,x)","x\,\left(A\,b+B\,a\right)-\frac{A\,a}{2\,x^2}+\frac{B\,b\,x^4}{4}","Not used",1,"x*(A*b + B*a) - (A*a)/(2*x^2) + (B*b*x^4)/4","B"
7,1,25,29,0.040189,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3))/x^4,x)","\ln\left(x\right)\,\left(A\,b+B\,a\right)-\frac{A\,a}{3\,x^3}+\frac{B\,b\,x^3}{3}","Not used",1,"log(x)*(A*b + B*a) - (A*a)/(3*x^3) + (B*b*x^3)/3","B"
8,1,29,31,0.033246,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3))/x^5,x)","\frac{B\,b\,x^2}{2}-\frac{\left(A\,b+B\,a\right)\,x^3+\frac{A\,a}{4}}{x^4}","Not used",1,"(B*b*x^2)/2 - ((A*a)/4 + x^3*(A*b + B*a))/x^4","B"
9,1,28,28,2.316272,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3))/x^6,x)","B\,b\,x-\frac{\left(\frac{A\,b}{2}+\frac{B\,a}{2}\right)\,x^3+\frac{A\,a}{5}}{x^5}","Not used",1,"B*b*x - ((A*a)/5 + x^3*((A*b)/2 + (B*a)/2))/x^5","B"
10,1,29,29,0.051866,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3))/x^7,x)","B\,b\,\ln\left(x\right)-\frac{\left(\frac{A\,b}{3}+\frac{B\,a}{3}\right)\,x^3+\frac{A\,a}{6}}{x^6}","Not used",1,"B*b*log(x) - ((A*a)/6 + x^3*((A*b)/3 + (B*a)/3))/x^6","B"
11,1,51,42,2.375099,"\text{Not used}","int(x^2*(A + B*x^3)*(a + b*x^3)^2,x)","x^6\,\left(\frac{B\,a^2}{6}+\frac{A\,b\,a}{3}\right)+x^9\,\left(\frac{A\,b^2}{9}+\frac{2\,B\,a\,b}{9}\right)+\frac{A\,a^2\,x^3}{3}+\frac{B\,b^2\,x^{12}}{12}","Not used",1,"x^6*((B*a^2)/6 + (A*a*b)/3) + x^9*((A*b^2)/9 + (2*B*a*b)/9) + (A*a^2*x^3)/3 + (B*b^2*x^12)/12","B"
12,1,51,55,0.043083,"\text{Not used}","int(x*(A + B*x^3)*(a + b*x^3)^2,x)","x^5\,\left(\frac{B\,a^2}{5}+\frac{2\,A\,b\,a}{5}\right)+x^8\,\left(\frac{A\,b^2}{8}+\frac{B\,a\,b}{4}\right)+\frac{A\,a^2\,x^2}{2}+\frac{B\,b^2\,x^{11}}{11}","Not used",1,"x^5*((B*a^2)/5 + (2*A*a*b)/5) + x^8*((A*b^2)/8 + (B*a*b)/4) + (A*a^2*x^2)/2 + (B*b^2*x^11)/11","B"
13,1,48,50,0.043382,"\text{Not used}","int((A + B*x^3)*(a + b*x^3)^2,x)","x^4\,\left(\frac{B\,a^2}{4}+\frac{A\,b\,a}{2}\right)+x^7\,\left(\frac{A\,b^2}{7}+\frac{2\,B\,a\,b}{7}\right)+\frac{B\,b^2\,x^{10}}{10}+A\,a^2\,x","Not used",1,"x^4*((B*a^2)/4 + (A*a*b)/2) + x^7*((A*b^2)/7 + (2*B*a*b)/7) + (B*b^2*x^10)/10 + A*a^2*x","B"
14,1,49,46,0.038072,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^2)/x,x)","x^3\,\left(\frac{B\,a^2}{3}+\frac{2\,A\,b\,a}{3}\right)+x^6\,\left(\frac{A\,b^2}{6}+\frac{B\,a\,b}{3}\right)+\frac{B\,b^2\,x^9}{9}+A\,a^2\,\ln\left(x\right)","Not used",1,"x^3*((B*a^2)/3 + (2*A*a*b)/3) + x^6*((A*b^2)/6 + (B*a*b)/3) + (B*b^2*x^9)/9 + A*a^2*log(x)","B"
15,1,50,53,0.049621,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^2)/x^2,x)","x^2\,\left(\frac{B\,a^2}{2}+A\,b\,a\right)+x^5\,\left(\frac{A\,b^2}{5}+\frac{2\,B\,a\,b}{5}\right)-\frac{A\,a^2}{x}+\frac{B\,b^2\,x^8}{8}","Not used",1,"x^2*((B*a^2)/2 + A*a*b) + x^5*((A*b^2)/5 + (2*B*a*b)/5) - (A*a^2)/x + (B*b^2*x^8)/8","B"
16,1,48,50,0.046122,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^2)/x^3,x)","x^4\,\left(\frac{A\,b^2}{4}+\frac{B\,a\,b}{2}\right)+x\,\left(B\,a^2+2\,A\,b\,a\right)-\frac{A\,a^2}{2\,x^2}+\frac{B\,b^2\,x^7}{7}","Not used",1,"x^4*((A*b^2)/4 + (B*a*b)/2) + x*(B*a^2 + 2*A*a*b) - (A*a^2)/(2*x^2) + (B*b^2*x^7)/7","B"
17,1,49,51,0.043067,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^2)/x^4,x)","x^3\,\left(\frac{A\,b^2}{3}+\frac{2\,B\,a\,b}{3}\right)+\ln\left(x\right)\,\left(B\,a^2+2\,A\,b\,a\right)-\frac{A\,a^2}{3\,x^3}+\frac{B\,b^2\,x^6}{6}","Not used",1,"x^3*((A*b^2)/3 + (2*B*a*b)/3) + log(x)*(B*a^2 + 2*A*a*b) - (A*a^2)/(3*x^3) + (B*b^2*x^6)/6","B"
18,1,52,53,0.048572,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^2)/x^5,x)","x^2\,\left(\frac{A\,b^2}{2}+B\,a\,b\right)-\frac{x^3\,\left(B\,a^2+2\,A\,b\,a\right)+\frac{A\,a^2}{4}}{x^4}+\frac{B\,b^2\,x^5}{5}","Not used",1,"x^2*((A*b^2)/2 + B*a*b) - (x^3*(B*a^2 + 2*A*a*b) + (A*a^2)/4)/x^4 + (B*b^2*x^5)/5","B"
19,1,50,50,2.370871,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^2)/x^6,x)","x\,\left(A\,b^2+2\,B\,a\,b\right)-\frac{x^3\,\left(\frac{B\,a^2}{2}+A\,b\,a\right)+\frac{A\,a^2}{5}}{x^5}+\frac{B\,b^2\,x^4}{4}","Not used",1,"x*(A*b^2 + 2*B*a*b) - (x^3*((B*a^2)/2 + A*a*b) + (A*a^2)/5)/x^5 + (B*b^2*x^4)/4","B"
20,1,52,51,2.358590,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^2)/x^7,x)","\ln\left(x\right)\,\left(A\,b^2+2\,B\,a\,b\right)-\frac{x^3\,\left(\frac{B\,a^2}{3}+\frac{2\,A\,b\,a}{3}\right)+\frac{A\,a^2}{6}}{x^6}+\frac{B\,b^2\,x^3}{3}","Not used",1,"log(x)*(A*b^2 + 2*B*a*b) - (x^3*((B*a^2)/3 + (2*A*a*b)/3) + (A*a^2)/6)/x^6 + (B*b^2*x^3)/3","B"
21,1,53,53,0.045401,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^2)/x^8,x)","\frac{B\,b^2\,x^2}{2}-\frac{x^3\,\left(\frac{B\,a^2}{4}+\frac{A\,b\,a}{2}\right)+x^6\,\left(A\,b^2+2\,B\,a\,b\right)+\frac{A\,a^2}{7}}{x^7}","Not used",1,"(B*b^2*x^2)/2 - (x^3*((B*a^2)/4 + (A*a*b)/2) + x^6*(A*b^2 + 2*B*a*b) + (A*a^2)/7)/x^7","B"
22,1,50,50,2.341652,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^2)/x^9,x)","B\,b^2\,x-\frac{x^3\,\left(\frac{B\,a^2}{5}+\frac{2\,A\,b\,a}{5}\right)+x^6\,\left(\frac{A\,b^2}{2}+B\,a\,b\right)+\frac{A\,a^2}{8}}{x^8}","Not used",1,"B*b^2*x - (x^3*((B*a^2)/5 + (2*A*a*b)/5) + x^6*((A*b^2)/2 + B*a*b) + (A*a^2)/8)/x^8","B"
23,1,107,117,0.049759,"\text{Not used}","int(x^9*(A + B*x^3)*(a + b*x^3)^5,x)","x^{13}\,\left(\frac{B\,a^5}{13}+\frac{5\,A\,b\,a^4}{13}\right)+x^{25}\,\left(\frac{A\,b^5}{25}+\frac{B\,a\,b^4}{5}\right)+\frac{A\,a^5\,x^{10}}{10}+\frac{B\,b^5\,x^{28}}{28}+\frac{10\,a^2\,b^2\,x^{19}\,\left(A\,b+B\,a\right)}{19}+\frac{5\,a^3\,b\,x^{16}\,\left(2\,A\,b+B\,a\right)}{16}+\frac{5\,a\,b^3\,x^{22}\,\left(A\,b+2\,B\,a\right)}{22}","Not used",1,"x^13*((B*a^5)/13 + (5*A*a^4*b)/13) + x^25*((A*b^5)/25 + (B*a*b^4)/5) + (A*a^5*x^10)/10 + (B*b^5*x^28)/28 + (10*a^2*b^2*x^19*(A*b + B*a))/19 + (5*a^3*b*x^16*(2*A*b + B*a))/16 + (5*a*b^3*x^22*(A*b + 2*B*a))/22","B"
24,1,107,95,2.338086,"\text{Not used}","int(x^8*(A + B*x^3)*(a + b*x^3)^5,x)","x^{12}\,\left(\frac{B\,a^5}{12}+\frac{5\,A\,b\,a^4}{12}\right)+x^{24}\,\left(\frac{A\,b^5}{24}+\frac{5\,B\,a\,b^4}{24}\right)+\frac{A\,a^5\,x^9}{9}+\frac{B\,b^5\,x^{27}}{27}+\frac{5\,a^2\,b^2\,x^{18}\,\left(A\,b+B\,a\right)}{9}+\frac{a^3\,b\,x^{15}\,\left(2\,A\,b+B\,a\right)}{3}+\frac{5\,a\,b^3\,x^{21}\,\left(A\,b+2\,B\,a\right)}{21}","Not used",1,"x^12*((B*a^5)/12 + (5*A*a^4*b)/12) + x^24*((A*b^5)/24 + (5*B*a*b^4)/24) + (A*a^5*x^9)/9 + (B*b^5*x^27)/27 + (5*a^2*b^2*x^18*(A*b + B*a))/9 + (a^3*b*x^15*(2*A*b + B*a))/3 + (5*a*b^3*x^21*(A*b + 2*B*a))/21","B"
25,1,107,117,0.041324,"\text{Not used}","int(x^7*(A + B*x^3)*(a + b*x^3)^5,x)","x^{11}\,\left(\frac{B\,a^5}{11}+\frac{5\,A\,b\,a^4}{11}\right)+x^{23}\,\left(\frac{A\,b^5}{23}+\frac{5\,B\,a\,b^4}{23}\right)+\frac{A\,a^5\,x^8}{8}+\frac{B\,b^5\,x^{26}}{26}+\frac{10\,a^2\,b^2\,x^{17}\,\left(A\,b+B\,a\right)}{17}+\frac{5\,a^3\,b\,x^{14}\,\left(2\,A\,b+B\,a\right)}{14}+\frac{a\,b^3\,x^{20}\,\left(A\,b+2\,B\,a\right)}{4}","Not used",1,"x^11*((B*a^5)/11 + (5*A*a^4*b)/11) + x^23*((A*b^5)/23 + (5*B*a*b^4)/23) + (A*a^5*x^8)/8 + (B*b^5*x^26)/26 + (10*a^2*b^2*x^17*(A*b + B*a))/17 + (5*a^3*b*x^14*(2*A*b + B*a))/14 + (a*b^3*x^20*(A*b + 2*B*a))/4","B"
26,1,107,117,0.041427,"\text{Not used}","int(x^6*(A + B*x^3)*(a + b*x^3)^5,x)","x^{10}\,\left(\frac{B\,a^5}{10}+\frac{A\,b\,a^4}{2}\right)+x^{22}\,\left(\frac{A\,b^5}{22}+\frac{5\,B\,a\,b^4}{22}\right)+\frac{A\,a^5\,x^7}{7}+\frac{B\,b^5\,x^{25}}{25}+\frac{5\,a^2\,b^2\,x^{16}\,\left(A\,b+B\,a\right)}{8}+\frac{5\,a^3\,b\,x^{13}\,\left(2\,A\,b+B\,a\right)}{13}+\frac{5\,a\,b^3\,x^{19}\,\left(A\,b+2\,B\,a\right)}{19}","Not used",1,"x^10*((B*a^5)/10 + (A*a^4*b)/2) + x^22*((A*b^5)/22 + (5*B*a*b^4)/22) + (A*a^5*x^7)/7 + (B*b^5*x^25)/25 + (5*a^2*b^2*x^16*(A*b + B*a))/8 + (5*a^3*b*x^13*(2*A*b + B*a))/13 + (5*a*b^3*x^19*(A*b + 2*B*a))/19","B"
27,1,107,67,0.040235,"\text{Not used}","int(x^5*(A + B*x^3)*(a + b*x^3)^5,x)","x^9\,\left(\frac{B\,a^5}{9}+\frac{5\,A\,b\,a^4}{9}\right)+x^{21}\,\left(\frac{A\,b^5}{21}+\frac{5\,B\,a\,b^4}{21}\right)+\frac{A\,a^5\,x^6}{6}+\frac{B\,b^5\,x^{24}}{24}+\frac{2\,a^2\,b^2\,x^{15}\,\left(A\,b+B\,a\right)}{3}+\frac{5\,a^3\,b\,x^{12}\,\left(2\,A\,b+B\,a\right)}{12}+\frac{5\,a\,b^3\,x^{18}\,\left(A\,b+2\,B\,a\right)}{18}","Not used",1,"x^9*((B*a^5)/9 + (5*A*a^4*b)/9) + x^21*((A*b^5)/21 + (5*B*a*b^4)/21) + (A*a^5*x^6)/6 + (B*b^5*x^24)/24 + (2*a^2*b^2*x^15*(A*b + B*a))/3 + (5*a^3*b*x^12*(2*A*b + B*a))/12 + (5*a*b^3*x^18*(A*b + 2*B*a))/18","B"
28,1,107,117,0.040781,"\text{Not used}","int(x^4*(A + B*x^3)*(a + b*x^3)^5,x)","x^8\,\left(\frac{B\,a^5}{8}+\frac{5\,A\,b\,a^4}{8}\right)+x^{20}\,\left(\frac{A\,b^5}{20}+\frac{B\,a\,b^4}{4}\right)+\frac{A\,a^5\,x^5}{5}+\frac{B\,b^5\,x^{23}}{23}+\frac{5\,a^2\,b^2\,x^{14}\,\left(A\,b+B\,a\right)}{7}+\frac{5\,a^3\,b\,x^{11}\,\left(2\,A\,b+B\,a\right)}{11}+\frac{5\,a\,b^3\,x^{17}\,\left(A\,b+2\,B\,a\right)}{17}","Not used",1,"x^8*((B*a^5)/8 + (5*A*a^4*b)/8) + x^20*((A*b^5)/20 + (B*a*b^4)/4) + (A*a^5*x^5)/5 + (B*b^5*x^23)/23 + (5*a^2*b^2*x^14*(A*b + B*a))/7 + (5*a^3*b*x^11*(2*A*b + B*a))/11 + (5*a*b^3*x^17*(A*b + 2*B*a))/17","B"
29,1,107,117,0.040078,"\text{Not used}","int(x^3*(A + B*x^3)*(a + b*x^3)^5,x)","x^7\,\left(\frac{B\,a^5}{7}+\frac{5\,A\,b\,a^4}{7}\right)+x^{19}\,\left(\frac{A\,b^5}{19}+\frac{5\,B\,a\,b^4}{19}\right)+\frac{A\,a^5\,x^4}{4}+\frac{B\,b^5\,x^{22}}{22}+\frac{10\,a^2\,b^2\,x^{13}\,\left(A\,b+B\,a\right)}{13}+\frac{a^3\,b\,x^{10}\,\left(2\,A\,b+B\,a\right)}{2}+\frac{5\,a\,b^3\,x^{16}\,\left(A\,b+2\,B\,a\right)}{16}","Not used",1,"x^7*((B*a^5)/7 + (5*A*a^4*b)/7) + x^19*((A*b^5)/19 + (5*B*a*b^4)/19) + (A*a^5*x^4)/4 + (B*b^5*x^22)/22 + (10*a^2*b^2*x^13*(A*b + B*a))/13 + (a^3*b*x^10*(2*A*b + B*a))/2 + (5*a*b^3*x^16*(A*b + 2*B*a))/16","B"
30,1,107,42,0.041343,"\text{Not used}","int(x^2*(A + B*x^3)*(a + b*x^3)^5,x)","x^6\,\left(\frac{B\,a^5}{6}+\frac{5\,A\,b\,a^4}{6}\right)+x^{18}\,\left(\frac{A\,b^5}{18}+\frac{5\,B\,a\,b^4}{18}\right)+\frac{A\,a^5\,x^3}{3}+\frac{B\,b^5\,x^{21}}{21}+\frac{5\,a^2\,b^2\,x^{12}\,\left(A\,b+B\,a\right)}{6}+\frac{5\,a^3\,b\,x^9\,\left(2\,A\,b+B\,a\right)}{9}+\frac{a\,b^3\,x^{15}\,\left(A\,b+2\,B\,a\right)}{3}","Not used",1,"x^6*((B*a^5)/6 + (5*A*a^4*b)/6) + x^18*((A*b^5)/18 + (5*B*a*b^4)/18) + (A*a^5*x^3)/3 + (B*b^5*x^21)/21 + (5*a^2*b^2*x^12*(A*b + B*a))/6 + (5*a^3*b*x^9*(2*A*b + B*a))/9 + (a*b^3*x^15*(A*b + 2*B*a))/3","B"
31,1,106,117,0.040424,"\text{Not used}","int(x*(A + B*x^3)*(a + b*x^3)^5,x)","x^5\,\left(\frac{B\,a^5}{5}+A\,b\,a^4\right)+x^{17}\,\left(\frac{A\,b^5}{17}+\frac{5\,B\,a\,b^4}{17}\right)+\frac{A\,a^5\,x^2}{2}+\frac{B\,b^5\,x^{20}}{20}+\frac{10\,a^2\,b^2\,x^{11}\,\left(A\,b+B\,a\right)}{11}+\frac{5\,a^3\,b\,x^8\,\left(2\,A\,b+B\,a\right)}{8}+\frac{5\,a\,b^3\,x^{14}\,\left(A\,b+2\,B\,a\right)}{14}","Not used",1,"x^5*((B*a^5)/5 + A*a^4*b) + x^17*((A*b^5)/17 + (5*B*a*b^4)/17) + (A*a^5*x^2)/2 + (B*b^5*x^20)/20 + (10*a^2*b^2*x^11*(A*b + B*a))/11 + (5*a^3*b*x^8*(2*A*b + B*a))/8 + (5*a*b^3*x^14*(A*b + 2*B*a))/14","B"
32,1,103,109,0.041135,"\text{Not used}","int((A + B*x^3)*(a + b*x^3)^5,x)","x^4\,\left(\frac{B\,a^5}{4}+\frac{5\,A\,b\,a^4}{4}\right)+x^{16}\,\left(\frac{A\,b^5}{16}+\frac{5\,B\,a\,b^4}{16}\right)+\frac{B\,b^5\,x^{19}}{19}+A\,a^5\,x+a^2\,b^2\,x^{10}\,\left(A\,b+B\,a\right)+\frac{5\,a^3\,b\,x^7\,\left(2\,A\,b+B\,a\right)}{7}+\frac{5\,a\,b^3\,x^{13}\,\left(A\,b+2\,B\,a\right)}{13}","Not used",1,"x^4*((B*a^5)/4 + (5*A*a^4*b)/4) + x^16*((A*b^5)/16 + (5*B*a*b^4)/16) + (B*b^5*x^19)/19 + A*a^5*x + a^2*b^2*x^10*(A*b + B*a) + (5*a^3*b*x^7*(2*A*b + B*a))/7 + (5*a*b^3*x^13*(A*b + 2*B*a))/13","B"
33,1,105,88,0.045523,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^5)/x,x)","x^3\,\left(\frac{B\,a^5}{3}+\frac{5\,A\,b\,a^4}{3}\right)+x^{15}\,\left(\frac{A\,b^5}{15}+\frac{B\,a\,b^4}{3}\right)+\frac{B\,b^5\,x^{18}}{18}+A\,a^5\,\ln\left(x\right)+\frac{10\,a^2\,b^2\,x^9\,\left(A\,b+B\,a\right)}{9}+\frac{5\,a^3\,b\,x^6\,\left(2\,A\,b+B\,a\right)}{6}+\frac{5\,a\,b^3\,x^{12}\,\left(A\,b+2\,B\,a\right)}{12}","Not used",1,"x^3*((B*a^5)/3 + (5*A*a^4*b)/3) + x^15*((A*b^5)/15 + (B*a*b^4)/3) + (B*b^5*x^18)/18 + A*a^5*log(x) + (10*a^2*b^2*x^9*(A*b + B*a))/9 + (5*a^3*b*x^6*(2*A*b + B*a))/6 + (5*a*b^3*x^12*(A*b + 2*B*a))/12","B"
34,1,106,112,0.042094,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^5)/x^2,x)","x^2\,\left(\frac{B\,a^5}{2}+\frac{5\,A\,b\,a^4}{2}\right)+x^{14}\,\left(\frac{A\,b^5}{14}+\frac{5\,B\,a\,b^4}{14}\right)-\frac{A\,a^5}{x}+\frac{B\,b^5\,x^{17}}{17}+\frac{5\,a^2\,b^2\,x^8\,\left(A\,b+B\,a\right)}{4}+a^3\,b\,x^5\,\left(2\,A\,b+B\,a\right)+\frac{5\,a\,b^3\,x^{11}\,\left(A\,b+2\,B\,a\right)}{11}","Not used",1,"x^2*((B*a^5)/2 + (5*A*a^4*b)/2) + x^14*((A*b^5)/14 + (5*B*a*b^4)/14) - (A*a^5)/x + (B*b^5*x^17)/17 + (5*a^2*b^2*x^8*(A*b + B*a))/4 + a^3*b*x^5*(2*A*b + B*a) + (5*a*b^3*x^11*(A*b + 2*B*a))/11","B"
35,1,104,112,0.042929,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^5)/x^3,x)","x\,\left(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}{2\,x^2}+\frac{B\,b^5\,x^{16}}{16}+\frac{10\,a^2\,b^2\,x^7\,\left(A\,b+B\,a\right)}{7}+\frac{5\,a^3\,b\,x^4\,\left(2\,A\,b+B\,a\right)}{4}+\frac{a\,b^3\,x^{10}\,\left(A\,b+2\,B\,a\right)}{2}","Not used",1,"x*(B*a^5 + 5*A*a^4*b) + x^13*((A*b^5)/13 + (5*B*a*b^4)/13) - (A*a^5)/(2*x^2) + (B*b^5*x^16)/16 + (10*a^2*b^2*x^7*(A*b + B*a))/7 + (5*a^3*b*x^4*(2*A*b + B*a))/4 + (a*b^3*x^10*(A*b + 2*B*a))/2","B"
36,1,105,113,2.347607,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^5)/x^4,x)","x^{12}\,\left(\frac{A\,b^5}{12}+\frac{5\,B\,a\,b^4}{12}\right)+\ln\left(x\right)\,\left(B\,a^5+5\,A\,b\,a^4\right)-\frac{A\,a^5}{3\,x^3}+\frac{B\,b^5\,x^{15}}{15}+\frac{5\,a^2\,b^2\,x^6\,\left(A\,b+B\,a\right)}{3}+\frac{5\,a^3\,b\,x^3\,\left(2\,A\,b+B\,a\right)}{3}+\frac{5\,a\,b^3\,x^9\,\left(A\,b+2\,B\,a\right)}{9}","Not used",1,"x^12*((A*b^5)/12 + (5*B*a*b^4)/12) + log(x)*(B*a^5 + 5*A*a^4*b) - (A*a^5)/(3*x^3) + (B*b^5*x^15)/15 + (5*a^2*b^2*x^6*(A*b + B*a))/3 + (5*a^3*b*x^3*(2*A*b + B*a))/3 + (5*a*b^3*x^9*(A*b + 2*B*a))/9","B"
37,1,109,113,0.042257,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^5)/x^5,x)","x^{11}\,\left(\frac{A\,b^5}{11}+\frac{5\,B\,a\,b^4}{11}\right)-\frac{\frac{A\,a^5}{4}+x^3\,\left(B\,a^5+5\,A\,b\,a^4\right)}{x^4}+\frac{B\,b^5\,x^{14}}{14}+2\,a^2\,b^2\,x^5\,\left(A\,b+B\,a\right)+\frac{5\,a^3\,b\,x^2\,\left(2\,A\,b+B\,a\right)}{2}+\frac{5\,a\,b^3\,x^8\,\left(A\,b+2\,B\,a\right)}{8}","Not used",1,"x^11*((A*b^5)/11 + (5*B*a*b^4)/11) - ((A*a^5)/4 + x^3*(B*a^5 + 5*A*a^4*b))/x^4 + (B*b^5*x^14)/14 + 2*a^2*b^2*x^5*(A*b + B*a) + (5*a^3*b*x^2*(2*A*b + B*a))/2 + (5*a*b^3*x^8*(A*b + 2*B*a))/8","B"
38,1,108,113,0.043259,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^5)/x^6,x)","x^{10}\,\left(\frac{A\,b^5}{10}+\frac{B\,a\,b^4}{2}\right)-\frac{\frac{A\,a^5}{5}+x^3\,\left(\frac{B\,a^5}{2}+\frac{5\,A\,b\,a^4}{2}\right)}{x^5}+\frac{B\,b^5\,x^{13}}{13}+\frac{5\,a^2\,b^2\,x^4\,\left(A\,b+B\,a\right)}{2}+5\,a^3\,b\,x\,\left(2\,A\,b+B\,a\right)+\frac{5\,a\,b^3\,x^7\,\left(A\,b+2\,B\,a\right)}{7}","Not used",1,"x^10*((A*b^5)/10 + (B*a*b^4)/2) - ((A*a^5)/5 + x^3*((B*a^5)/2 + (5*A*a^4*b)/2))/x^5 + (B*b^5*x^13)/13 + (5*a^2*b^2*x^4*(A*b + B*a))/2 + 5*a^3*b*x*(2*A*b + B*a) + (5*a*b^3*x^7*(A*b + 2*B*a))/7","B"
39,1,113,114,0.049103,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^5)/x^7,x)","\ln\left(x\right)\,\left(5\,B\,a^4\,b+10\,A\,a^3\,b^2\right)-\frac{\frac{A\,a^5}{6}+x^3\,\left(\frac{B\,a^5}{3}+\frac{5\,A\,b\,a^4}{3}\right)}{x^6}+x^9\,\left(\frac{A\,b^5}{9}+\frac{5\,B\,a\,b^4}{9}\right)+\frac{B\,b^5\,x^{12}}{12}+\frac{10\,a^2\,b^2\,x^3\,\left(A\,b+B\,a\right)}{3}+\frac{5\,a\,b^3\,x^6\,\left(A\,b+2\,B\,a\right)}{6}","Not used",1,"log(x)*(10*A*a^3*b^2 + 5*B*a^4*b) - ((A*a^5)/6 + x^3*((B*a^5)/3 + (5*A*a^4*b)/3))/x^6 + x^9*((A*b^5)/9 + (5*B*a*b^4)/9) + (B*b^5*x^12)/12 + (10*a^2*b^2*x^3*(A*b + B*a))/3 + (5*a*b^3*x^6*(A*b + 2*B*a))/6","B"
40,1,113,110,2.340695,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^5)/x^8,x)","x^8\,\left(\frac{A\,b^5}{8}+\frac{5\,B\,a\,b^4}{8}\right)-\frac{\frac{A\,a^5}{7}+x^6\,\left(5\,B\,a^4\,b+10\,A\,a^3\,b^2\right)+x^3\,\left(\frac{B\,a^5}{4}+\frac{5\,A\,b\,a^4}{4}\right)}{x^7}+\frac{B\,b^5\,x^{11}}{11}+5\,a^2\,b^2\,x^2\,\left(A\,b+B\,a\right)+a\,b^3\,x^5\,\left(A\,b+2\,B\,a\right)","Not used",1,"x^8*((A*b^5)/8 + (5*B*a*b^4)/8) - ((A*a^5)/7 + x^6*(10*A*a^3*b^2 + 5*B*a^4*b) + x^3*((B*a^5)/4 + (5*A*a^4*b)/4))/x^7 + (B*b^5*x^11)/11 + 5*a^2*b^2*x^2*(A*b + B*a) + a*b^3*x^5*(A*b + 2*B*a)","B"
41,1,111,113,0.044167,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^5)/x^9,x)","x^7\,\left(\frac{A\,b^5}{7}+\frac{5\,B\,a\,b^4}{7}\right)-\frac{\frac{A\,a^5}{8}+x^6\,\left(\frac{5\,B\,a^4\,b}{2}+5\,A\,a^3\,b^2\right)+x^3\,\left(\frac{B\,a^5}{5}+A\,b\,a^4\right)}{x^8}+\frac{B\,b^5\,x^{10}}{10}+10\,a^2\,b^2\,x\,\left(A\,b+B\,a\right)+\frac{5\,a\,b^3\,x^4\,\left(A\,b+2\,B\,a\right)}{4}","Not used",1,"x^7*((A*b^5)/7 + (5*B*a*b^4)/7) - ((A*a^5)/8 + x^6*(5*A*a^3*b^2 + (5*B*a^4*b)/2) + x^3*((B*a^5)/5 + A*a^4*b))/x^8 + (B*b^5*x^10)/10 + 10*a^2*b^2*x*(A*b + B*a) + (5*a*b^3*x^4*(A*b + 2*B*a))/4","B"
42,1,118,114,0.050171,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^5)/x^10,x)","x^6\,\left(\frac{A\,b^5}{6}+\frac{5\,B\,a\,b^4}{6}\right)-\frac{\frac{A\,a^5}{9}+x^6\,\left(\frac{5\,B\,a^4\,b}{3}+\frac{10\,A\,a^3\,b^2}{3}\right)+x^3\,\left(\frac{B\,a^5}{6}+\frac{5\,A\,b\,a^4}{6}\right)}{x^9}+\ln\left(x\right)\,\left(10\,B\,a^3\,b^2+10\,A\,a^2\,b^3\right)+\frac{B\,b^5\,x^9}{9}+\frac{5\,a\,b^3\,x^3\,\left(A\,b+2\,B\,a\right)}{3}","Not used",1,"x^6*((A*b^5)/6 + (5*B*a*b^4)/6) - ((A*a^5)/9 + x^6*((10*A*a^3*b^2)/3 + (5*B*a^4*b)/3) + x^3*((B*a^5)/6 + (5*A*a^4*b)/6))/x^9 + log(x)*(10*A*a^2*b^3 + 10*B*a^3*b^2) + (B*b^5*x^9)/9 + (5*a*b^3*x^3*(A*b + 2*B*a))/3","B"
43,1,118,115,2.364118,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^5)/x^11,x)","x^5\,\left(\frac{A\,b^5}{5}+B\,a\,b^4\right)-\frac{\frac{A\,a^5}{10}+x^6\,\left(\frac{5\,B\,a^4\,b}{4}+\frac{5\,A\,a^3\,b^2}{2}\right)+x^3\,\left(\frac{B\,a^5}{7}+\frac{5\,A\,b\,a^4}{7}\right)+x^9\,\left(10\,B\,a^3\,b^2+10\,A\,a^2\,b^3\right)}{x^{10}}+\frac{B\,b^5\,x^8}{8}+\frac{5\,a\,b^3\,x^2\,\left(A\,b+2\,B\,a\right)}{2}","Not used",1,"x^5*((A*b^5)/5 + B*a*b^4) - ((A*a^5)/10 + x^6*((5*A*a^3*b^2)/2 + (5*B*a^4*b)/4) + x^3*((B*a^5)/7 + (5*A*a^4*b)/7) + x^9*(10*A*a^2*b^3 + 10*B*a^3*b^2))/x^10 + (B*b^5*x^8)/8 + (5*a*b^3*x^2*(A*b + 2*B*a))/2","B"
44,1,116,109,0.067399,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^5)/x^12,x)","x^4\,\left(\frac{A\,b^5}{4}+\frac{5\,B\,a\,b^4}{4}\right)-\frac{\frac{A\,a^5}{11}+x^6\,\left(B\,a^4\,b+2\,A\,a^3\,b^2\right)+x^3\,\left(\frac{B\,a^5}{8}+\frac{5\,A\,b\,a^4}{8}\right)+x^9\,\left(5\,B\,a^3\,b^2+5\,A\,a^2\,b^3\right)}{x^{11}}+\frac{B\,b^5\,x^7}{7}+5\,a\,b^3\,x\,\left(A\,b+2\,B\,a\right)","Not used",1,"x^4*((A*b^5)/4 + (5*B*a*b^4)/4) - ((A*a^5)/11 + x^6*(2*A*a^3*b^2 + B*a^4*b) + x^3*((B*a^5)/8 + (5*A*a^4*b)/8) + x^9*(5*A*a^2*b^3 + 5*B*a^3*b^2))/x^11 + (B*b^5*x^7)/7 + 5*a*b^3*x*(A*b + 2*B*a)","B"
45,1,122,114,0.064206,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^5)/x^13,x)","\ln\left(x\right)\,\left(10\,B\,a^2\,b^3+5\,A\,a\,b^4\right)-\frac{\frac{A\,a^5}{12}+x^6\,\left(\frac{5\,B\,a^4\,b}{6}+\frac{5\,A\,a^3\,b^2}{3}\right)+x^3\,\left(\frac{B\,a^5}{9}+\frac{5\,A\,b\,a^4}{9}\right)+x^9\,\left(\frac{10\,B\,a^3\,b^2}{3}+\frac{10\,A\,a^2\,b^3}{3}\right)}{x^{12}}+x^3\,\left(\frac{A\,b^5}{3}+\frac{5\,B\,a\,b^4}{3}\right)+\frac{B\,b^5\,x^6}{6}","Not used",1,"log(x)*(10*B*a^2*b^3 + 5*A*a*b^4) - ((A*a^5)/12 + x^6*((5*A*a^3*b^2)/3 + (5*B*a^4*b)/6) + x^3*((B*a^5)/9 + (5*A*a^4*b)/9) + x^9*((10*A*a^2*b^3)/3 + (10*B*a^3*b^2)/3))/x^12 + x^3*((A*b^5)/3 + (5*B*a*b^4)/3) + (B*b^5*x^6)/6","B"
46,1,123,115,2.374619,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^5)/x^14,x)","x^2\,\left(\frac{A\,b^5}{2}+\frac{5\,B\,a\,b^4}{2}\right)-\frac{\frac{A\,a^5}{13}+x^{12}\,\left(10\,B\,a^2\,b^3+5\,A\,a\,b^4\right)+x^6\,\left(\frac{5\,B\,a^4\,b}{7}+\frac{10\,A\,a^3\,b^2}{7}\right)+x^3\,\left(\frac{B\,a^5}{10}+\frac{A\,b\,a^4}{2}\right)+x^9\,\left(\frac{5\,B\,a^3\,b^2}{2}+\frac{5\,A\,a^2\,b^3}{2}\right)}{x^{13}}+\frac{B\,b^5\,x^5}{5}","Not used",1,"x^2*((A*b^5)/2 + (5*B*a*b^4)/2) - ((A*a^5)/13 + x^12*(10*B*a^2*b^3 + 5*A*a*b^4) + x^6*((10*A*a^3*b^2)/7 + (5*B*a^4*b)/7) + x^3*((B*a^5)/10 + (A*a^4*b)/2) + x^9*((5*A*a^2*b^3)/2 + (5*B*a^3*b^2)/2))/x^13 + (B*b^5*x^5)/5","B"
47,1,120,110,2.392342,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^5)/x^15,x)","x\,\left(A\,b^5+5\,B\,a\,b^4\right)-\frac{\frac{A\,a^5}{14}+x^{12}\,\left(5\,B\,a^2\,b^3+\frac{5\,A\,a\,b^4}{2}\right)+x^6\,\left(\frac{5\,B\,a^4\,b}{8}+\frac{5\,A\,a^3\,b^2}{4}\right)+x^3\,\left(\frac{B\,a^5}{11}+\frac{5\,A\,b\,a^4}{11}\right)+x^9\,\left(2\,B\,a^3\,b^2+2\,A\,a^2\,b^3\right)}{x^{14}}+\frac{B\,b^5\,x^4}{4}","Not used",1,"x*(A*b^5 + 5*B*a*b^4) - ((A*a^5)/14 + x^12*(5*B*a^2*b^3 + (5*A*a*b^4)/2) + x^6*((5*A*a^3*b^2)/4 + (5*B*a^4*b)/8) + x^3*((B*a^5)/11 + (5*A*a^4*b)/11) + x^9*(2*A*a^2*b^3 + 2*B*a^3*b^2))/x^14 + (B*b^5*x^4)/4","B"
48,1,121,113,0.078969,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^5)/x^16,x)","\ln\left(x\right)\,\left(A\,b^5+5\,B\,a\,b^4\right)-\frac{\frac{A\,a^5}{15}+x^{12}\,\left(\frac{10\,B\,a^2\,b^3}{3}+\frac{5\,A\,a\,b^4}{3}\right)+x^6\,\left(\frac{5\,B\,a^4\,b}{9}+\frac{10\,A\,a^3\,b^2}{9}\right)+x^3\,\left(\frac{B\,a^5}{12}+\frac{5\,A\,b\,a^4}{12}\right)+x^9\,\left(\frac{5\,B\,a^3\,b^2}{3}+\frac{5\,A\,a^2\,b^3}{3}\right)}{x^{15}}+\frac{B\,b^5\,x^3}{3}","Not used",1,"log(x)*(A*b^5 + 5*B*a*b^4) - ((A*a^5)/15 + x^12*((10*B*a^2*b^3)/3 + (5*A*a*b^4)/3) + x^6*((10*A*a^3*b^2)/9 + (5*B*a^4*b)/9) + x^3*((B*a^5)/12 + (5*A*a^4*b)/12) + x^9*((5*A*a^2*b^3)/3 + (5*B*a^3*b^2)/3))/x^15 + (B*b^5*x^3)/3","B"
49,1,121,115,2.362665,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^5)/x^17,x)","\frac{B\,b^5\,x^2}{2}-\frac{\frac{A\,a^5}{16}+x^6\,\left(\frac{B\,a^4\,b}{2}+A\,a^3\,b^2\right)+x^{12}\,\left(\frac{5\,B\,a^2\,b^3}{2}+\frac{5\,A\,a\,b^4}{4}\right)+x^3\,\left(\frac{B\,a^5}{13}+\frac{5\,A\,b\,a^4}{13}\right)+x^{15}\,\left(A\,b^5+5\,B\,a\,b^4\right)+x^9\,\left(\frac{10\,B\,a^3\,b^2}{7}+\frac{10\,A\,a^2\,b^3}{7}\right)}{x^{16}}","Not used",1,"(B*b^5*x^2)/2 - ((A*a^5)/16 + x^6*(A*a^3*b^2 + (B*a^4*b)/2) + x^12*((5*B*a^2*b^3)/2 + (5*A*a*b^4)/4) + x^3*((B*a^5)/13 + (5*A*a^4*b)/13) + x^15*(A*b^5 + 5*B*a*b^4) + x^9*((10*A*a^2*b^3)/7 + (10*B*a^3*b^2)/7))/x^16","B"
50,1,119,110,0.076776,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^5)/x^18,x)","B\,b^5\,x-\frac{\frac{A\,a^5}{17}+x^{12}\,\left(2\,B\,a^2\,b^3+A\,a\,b^4\right)+x^6\,\left(\frac{5\,B\,a^4\,b}{11}+\frac{10\,A\,a^3\,b^2}{11}\right)+x^3\,\left(\frac{B\,a^5}{14}+\frac{5\,A\,b\,a^4}{14}\right)+x^{15}\,\left(\frac{A\,b^5}{2}+\frac{5\,B\,a\,b^4}{2}\right)+x^9\,\left(\frac{5\,B\,a^3\,b^2}{4}+\frac{5\,A\,a^2\,b^3}{4}\right)}{x^{17}}","Not used",1,"B*b^5*x - ((A*a^5)/17 + x^12*(2*B*a^2*b^3 + A*a*b^4) + x^6*((10*A*a^3*b^2)/11 + (5*B*a^4*b)/11) + x^3*((B*a^5)/14 + (5*A*a^4*b)/14) + x^15*((A*b^5)/2 + (5*B*a*b^4)/2) + x^9*((5*A*a^2*b^3)/4 + (5*B*a^3*b^2)/4))/x^17","B"
51,1,121,91,0.093357,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^5)/x^19,x)","B\,b^5\,\ln\left(x\right)-\frac{\frac{A\,a^5}{18}+x^{12}\,\left(\frac{5\,B\,a^2\,b^3}{3}+\frac{5\,A\,a\,b^4}{6}\right)+x^6\,\left(\frac{5\,B\,a^4\,b}{12}+\frac{5\,A\,a^3\,b^2}{6}\right)+x^3\,\left(\frac{B\,a^5}{15}+\frac{A\,b\,a^4}{3}\right)+x^{15}\,\left(\frac{A\,b^5}{3}+\frac{5\,B\,a\,b^4}{3}\right)+x^9\,\left(\frac{10\,B\,a^3\,b^2}{9}+\frac{10\,A\,a^2\,b^3}{9}\right)}{x^{18}}","Not used",1,"B*b^5*log(x) - ((A*a^5)/18 + x^12*((5*B*a^2*b^3)/3 + (5*A*a*b^4)/6) + x^6*((5*A*a^3*b^2)/6 + (5*B*a^4*b)/12) + x^3*((B*a^5)/15 + (A*a^4*b)/3) + x^15*((A*b^5)/3 + (5*B*a*b^4)/3) + x^9*((10*A*a^2*b^3)/9 + (10*B*a^3*b^2)/9))/x^18","B"
52,1,119,113,2.369006,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^5)/x^20,x)","-\frac{\frac{A\,a^5}{19}+x^{12}\,\left(\frac{10\,B\,a^2\,b^3}{7}+\frac{5\,A\,a\,b^4}{7}\right)+x^6\,\left(\frac{5\,B\,a^4\,b}{13}+\frac{10\,A\,a^3\,b^2}{13}\right)+x^3\,\left(\frac{B\,a^5}{16}+\frac{5\,A\,b\,a^4}{16}\right)+x^{15}\,\left(\frac{A\,b^5}{4}+\frac{5\,B\,a\,b^4}{4}\right)+x^9\,\left(B\,a^3\,b^2+A\,a^2\,b^3\right)+B\,b^5\,x^{18}}{x^{19}}","Not used",1,"-((A*a^5)/19 + x^12*((10*B*a^2*b^3)/7 + (5*A*a*b^4)/7) + x^6*((10*A*a^3*b^2)/13 + (5*B*a^4*b)/13) + x^3*((B*a^5)/16 + (5*A*a^4*b)/16) + x^15*((A*b^5)/4 + (5*B*a*b^4)/4) + x^9*(A*a^2*b^3 + B*a^3*b^2) + B*b^5*x^18)/x^19","B"
53,1,121,117,2.346717,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^5)/x^21,x)","-\frac{\frac{A\,a^5}{20}+x^{12}\,\left(\frac{5\,B\,a^2\,b^3}{4}+\frac{5\,A\,a\,b^4}{8}\right)+x^6\,\left(\frac{5\,B\,a^4\,b}{14}+\frac{5\,A\,a^3\,b^2}{7}\right)+x^3\,\left(\frac{B\,a^5}{17}+\frac{5\,A\,b\,a^4}{17}\right)+x^{15}\,\left(\frac{A\,b^5}{5}+B\,a\,b^4\right)+x^9\,\left(\frac{10\,B\,a^3\,b^2}{11}+\frac{10\,A\,a^2\,b^3}{11}\right)+\frac{B\,b^5\,x^{18}}{2}}{x^{20}}","Not used",1,"-((A*a^5)/20 + x^12*((5*B*a^2*b^3)/4 + (5*A*a*b^4)/8) + x^6*((5*A*a^3*b^2)/7 + (5*B*a^4*b)/14) + x^3*((B*a^5)/17 + (5*A*a^4*b)/17) + x^15*((A*b^5)/5 + B*a*b^4) + x^9*((10*A*a^2*b^3)/11 + (10*B*a^3*b^2)/11) + (B*b^5*x^18)/2)/x^20","B"
54,1,122,48,2.370371,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^5)/x^22,x)","-\frac{\frac{A\,a^5}{21}+x^6\,\left(\frac{B\,a^4\,b}{3}+\frac{2\,A\,a^3\,b^2}{3}\right)+x^{12}\,\left(\frac{10\,B\,a^2\,b^3}{9}+\frac{5\,A\,a\,b^4}{9}\right)+x^3\,\left(\frac{B\,a^5}{18}+\frac{5\,A\,b\,a^4}{18}\right)+x^{15}\,\left(\frac{A\,b^5}{6}+\frac{5\,B\,a\,b^4}{6}\right)+x^9\,\left(\frac{5\,B\,a^3\,b^2}{6}+\frac{5\,A\,a^2\,b^3}{6}\right)+\frac{B\,b^5\,x^{18}}{3}}{x^{21}}","Not used",1,"-((A*a^5)/21 + x^6*((2*A*a^3*b^2)/3 + (B*a^4*b)/3) + x^12*((10*B*a^2*b^3)/9 + (5*A*a*b^4)/9) + x^3*((B*a^5)/18 + (5*A*a^4*b)/18) + x^15*((A*b^5)/6 + (5*B*a*b^4)/6) + x^9*((5*A*a^2*b^3)/6 + (5*B*a^3*b^2)/6) + (B*b^5*x^18)/3)/x^21","B"
55,1,121,117,0.063900,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^5)/x^23,x)","-\frac{\frac{A\,a^5}{22}+x^{12}\,\left(B\,a^2\,b^3+\frac{A\,a\,b^4}{2}\right)+x^6\,\left(\frac{5\,B\,a^4\,b}{16}+\frac{5\,A\,a^3\,b^2}{8}\right)+x^3\,\left(\frac{B\,a^5}{19}+\frac{5\,A\,b\,a^4}{19}\right)+x^{15}\,\left(\frac{A\,b^5}{7}+\frac{5\,B\,a\,b^4}{7}\right)+x^9\,\left(\frac{10\,B\,a^3\,b^2}{13}+\frac{10\,A\,a^2\,b^3}{13}\right)+\frac{B\,b^5\,x^{18}}{4}}{x^{22}}","Not used",1,"-((A*a^5)/22 + x^12*(B*a^2*b^3 + (A*a*b^4)/2) + x^6*((5*A*a^3*b^2)/8 + (5*B*a^4*b)/16) + x^3*((B*a^5)/19 + (5*A*a^4*b)/19) + x^15*((A*b^5)/7 + (5*B*a*b^4)/7) + x^9*((10*A*a^2*b^3)/13 + (10*B*a^3*b^2)/13) + (B*b^5*x^18)/4)/x^22","B"
56,1,164,183,0.268455,"\text{Not used}","int((x^6*(A + B*x^3))/(a + b*x^3),x)","x^4\,\left(\frac{A}{4\,b}-\frac{B\,a}{4\,b^2}\right)+\frac{B\,x^7}{7\,b}+\frac{a^{4/3}\,\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(A\,b-B\,a\right)}{3\,b^{10/3}}-\frac{a\,x\,\left(\frac{A}{b}-\frac{B\,a}{b^2}\right)}{b}-\frac{a^{4/3}\,\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)}{3\,b^{10/3}}+\frac{a^{4/3}\,\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)}{3\,b^{10/3}}","Not used",1,"x^4*(A/(4*b) - (B*a)/(4*b^2)) + (B*x^7)/(7*b) + (a^(4/3)*log(b^(1/3)*x + a^(1/3))*(A*b - B*a))/(3*b^(10/3)) - (a*x*(A/b - (B*a)/b^2))/b - (a^(4/3)*log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(A*b - B*a))/(3*b^(10/3)) + (a^(4/3)*log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(A*b - B*a))/(3*b^(10/3))","B"
57,1,52,54,0.078887,"\text{Not used}","int((x^5*(A + B*x^3))/(a + b*x^3),x)","x^3\,\left(\frac{A}{3\,b}-\frac{B\,a}{3\,b^2}\right)+\frac{\ln\left(b\,x^3+a\right)\,\left(B\,a^2-A\,a\,b\right)}{3\,b^3}+\frac{B\,x^6}{6\,b}","Not used",1,"x^3*(A/(3*b) - (B*a)/(3*b^2)) + (log(a + b*x^3)*(B*a^2 - A*a*b))/(3*b^3) + (B*x^6)/(6*b)","B"
58,1,144,167,2.545007,"\text{Not used}","int((x^4*(A + B*x^3))/(a + b*x^3),x)","x^2\,\left(\frac{A}{2\,b}-\frac{B\,a}{2\,b^2}\right)+\frac{B\,x^5}{5\,b}+\frac{a^{2/3}\,\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(A\,b-B\,a\right)}{3\,b^{8/3}}+\frac{a^{2/3}\,\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)}{3\,b^{8/3}}-\frac{a^{2/3}\,\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)}{3\,b^{8/3}}","Not used",1,"x^2*(A/(2*b) - (B*a)/(2*b^2)) + (B*x^5)/(5*b) + (a^(2/3)*log(b^(1/3)*x + a^(1/3))*(A*b - B*a))/(3*b^(8/3)) + (a^(2/3)*log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(A*b - B*a))/(3*b^(8/3)) - (a^(2/3)*log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(A*b - B*a))/(3*b^(8/3))","B"
59,1,162,162,2.609901,"\text{Not used}","int((x^3*(A + B*x^3))/(a + b*x^3),x)","x\,\left(\frac{A}{b}-\frac{B\,a}{b^2}\right)+\frac{B\,x^4}{4\,b}+\frac{{\left(-a\right)}^{1/3}\,\ln\left({\left(-a\right)}^{4/3}+a\,b^{1/3}\,x\right)\,\left(A\,b-B\,a\right)}{3\,b^{7/3}}-\frac{{\left(-a\right)}^{1/3}\,\ln\left(2\,a\,b^{1/3}\,x-{\left(-a\right)}^{4/3}-\sqrt{3}\,{\left(-a\right)}^{4/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)}{3\,b^{7/3}}+\frac{{\left(-a\right)}^{1/3}\,\ln\left(2\,a\,b^{1/3}\,x-{\left(-a\right)}^{4/3}+\sqrt{3}\,{\left(-a\right)}^{4/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)}{3\,b^{7/3}}","Not used",1,"x*(A/b - (B*a)/b^2) + (B*x^4)/(4*b) + ((-a)^(1/3)*log((-a)^(4/3) + a*b^(1/3)*x)*(A*b - B*a))/(3*b^(7/3)) - ((-a)^(1/3)*log(2*a*b^(1/3)*x - 3^(1/2)*(-a)^(4/3)*1i - (-a)^(4/3))*((3^(1/2)*1i)/2 + 1/2)*(A*b - B*a))/(3*b^(7/3)) + ((-a)^(1/3)*log(3^(1/2)*(-a)^(4/3)*1i - (-a)^(4/3) + 2*a*b^(1/3)*x)*((3^(1/2)*1i)/2 - 1/2)*(A*b - B*a))/(3*b^(7/3))","B"
60,1,31,35,0.062501,"\text{Not used}","int((x^2*(A + B*x^3))/(a + b*x^3),x)","\frac{B\,x^3}{3\,b}+\frac{\ln\left(b\,x^3+a\right)\,\left(A\,b-B\,a\right)}{3\,b^2}","Not used",1,"(B*x^3)/(3*b) + (log(a + b*x^3)*(A*b - B*a))/(3*b^2)","B"
61,1,126,150,2.565907,"\text{Not used}","int((x*(A + B*x^3))/(a + b*x^3),x)","\frac{B\,x^2}{2\,b}-\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(A\,b-B\,a\right)}{3\,a^{1/3}\,b^{5/3}}-\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)}{3\,a^{1/3}\,b^{5/3}}+\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)}{3\,a^{1/3}\,b^{5/3}}","Not used",1,"(B*x^2)/(2*b) - (log(b^(1/3)*x + a^(1/3))*(A*b - B*a))/(3*a^(1/3)*b^(5/3)) - (log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(A*b - B*a))/(3*a^(1/3)*b^(5/3)) + (log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(A*b - B*a))/(3*a^(1/3)*b^(5/3))","B"
62,1,123,145,2.540535,"\text{Not used}","int((A + B*x^3)/(a + b*x^3),x)","\frac{B\,x}{b}+\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(A\,b-B\,a\right)}{3\,a^{2/3}\,b^{4/3}}-\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)}{3\,a^{2/3}\,b^{4/3}}+\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)}{3\,a^{2/3}\,b^{4/3}}","Not used",1,"(B*x)/b + (log(b^(1/3)*x + a^(1/3))*(A*b - B*a))/(3*a^(2/3)*b^(4/3)) - (log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(A*b - B*a))/(3*a^(2/3)*b^(4/3)) + (log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(A*b - B*a))/(3*a^(2/3)*b^(4/3))","B"
63,1,36,34,0.104759,"\text{Not used}","int((A + B*x^3)/(x*(a + b*x^3)),x)","\frac{B\,\ln\left(b\,x^3+a\right)}{3\,b}-\frac{A\,\ln\left(b\,x^3+a\right)}{3\,a}+\frac{A\,\ln\left(x\right)}{a}","Not used",1,"(B*log(a + b*x^3))/(3*b) - (A*log(a + b*x^3))/(3*a) + (A*log(x))/a","B"
64,1,126,147,2.544825,"\text{Not used}","int((A + B*x^3)/(x^2*(a + b*x^3)),x)","\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(A\,b-B\,a\right)}{3\,a^{4/3}\,b^{2/3}}-\frac{A}{a\,x}+\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)}{3\,a^{4/3}\,b^{2/3}}-\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)}{3\,a^{4/3}\,b^{2/3}}","Not used",1,"(log(b^(1/3)*x + a^(1/3))*(A*b - B*a))/(3*a^(4/3)*b^(2/3)) - A/(a*x) + (log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(A*b - B*a))/(3*a^(4/3)*b^(2/3)) - (log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(A*b - B*a))/(3*a^(4/3)*b^(2/3))","B"
65,1,126,149,0.244014,"\text{Not used}","int((A + B*x^3)/(x^3*(a + b*x^3)),x)","-\frac{A}{2\,a\,x^2}-\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(A\,b-B\,a\right)}{3\,a^{5/3}\,b^{1/3}}+\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)}{3\,a^{5/3}\,b^{1/3}}-\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)}{3\,a^{5/3}\,b^{1/3}}","Not used",1,"(log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(A*b - B*a))/(3*a^(5/3)*b^(1/3)) - (log(b^(1/3)*x + a^(1/3))*(A*b - B*a))/(3*a^(5/3)*b^(1/3)) - A/(2*a*x^2) - (log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(A*b - B*a))/(3*a^(5/3)*b^(1/3))","B"
66,1,46,50,2.404918,"\text{Not used}","int((A + B*x^3)/(x^4*(a + b*x^3)),x)","\frac{\ln\left(b\,x^3+a\right)\,\left(A\,b-B\,a\right)}{3\,a^2}-\frac{A}{3\,a\,x^3}-\frac{\ln\left(x\right)\,\left(A\,b-B\,a\right)}{a^2}","Not used",1,"(log(a + b*x^3)*(A*b - B*a))/(3*a^2) - A/(3*a*x^3) - (log(x)*(A*b - B*a))/a^2","B"
67,1,178,165,2.591465,"\text{Not used}","int((A + B*x^3)/(x^5*(a + b*x^3)),x)","\frac{{\left(-b\right)}^{1/3}\,\ln\left(a^{1/3}\,{\left(-b\right)}^{8/3}+b^3\,x\right)\,\left(A\,b-B\,a\right)}{3\,a^{7/3}}-\frac{\frac{A}{4\,a}-\frac{x^3\,\left(A\,b-B\,a\right)}{a^2}}{x^4}+\frac{{\left(-b\right)}^{1/3}\,\ln\left(a^{1/3}\,{\left(-b\right)}^{8/3}-2\,b^3\,x+\sqrt{3}\,a^{1/3}\,{\left(-b\right)}^{8/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)}{3\,a^{7/3}}-\frac{{\left(-b\right)}^{1/3}\,\ln\left(2\,b^3\,x-a^{1/3}\,{\left(-b\right)}^{8/3}+\sqrt{3}\,a^{1/3}\,{\left(-b\right)}^{8/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)}{3\,a^{7/3}}","Not used",1,"((-b)^(1/3)*log(a^(1/3)*(-b)^(8/3) + b^3*x)*(A*b - B*a))/(3*a^(7/3)) - (A/(4*a) - (x^3*(A*b - B*a))/a^2)/x^4 + ((-b)^(1/3)*log(a^(1/3)*(-b)^(8/3) - 2*b^3*x + 3^(1/2)*a^(1/3)*(-b)^(8/3)*1i)*((3^(1/2)*1i)/2 - 1/2)*(A*b - B*a))/(3*a^(7/3)) - ((-b)^(1/3)*log(2*b^3*x - a^(1/3)*(-b)^(8/3) + 3^(1/2)*a^(1/3)*(-b)^(8/3)*1i)*((3^(1/2)*1i)/2 + 1/2)*(A*b - B*a))/(3*a^(7/3))","B"
68,1,145,168,2.563937,"\text{Not used}","int((A + B*x^3)/(x^6*(a + b*x^3)),x)","\frac{b^{2/3}\,\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(A\,b-B\,a\right)}{3\,a^{8/3}}-\frac{\frac{A}{5\,a}-\frac{x^3\,\left(A\,b-B\,a\right)}{2\,a^2}}{x^5}-\frac{b^{2/3}\,\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)}{3\,a^{8/3}}+\frac{b^{2/3}\,\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)}{3\,a^{8/3}}","Not used",1,"(b^(2/3)*log(b^(1/3)*x + a^(1/3))*(A*b - B*a))/(3*a^(8/3)) - (A/(5*a) - (x^3*(A*b - B*a))/(2*a^2))/x^5 - (b^(2/3)*log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(A*b - B*a))/(3*a^(8/3)) + (b^(2/3)*log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(A*b - B*a))/(3*a^(8/3))","B"
69,1,70,69,0.126630,"\text{Not used}","int((A + B*x^3)/(x^7*(a + b*x^3)),x)","\frac{\ln\left(x\right)\,\left(A\,b^2-B\,a\,b\right)}{a^3}-\frac{\ln\left(b\,x^3+a\right)\,\left(A\,b^2-B\,a\,b\right)}{3\,a^3}-\frac{\frac{A}{6\,a}-\frac{x^3\,\left(A\,b-B\,a\right)}{3\,a^2}}{x^6}","Not used",1,"(log(x)*(A*b^2 - B*a*b))/a^3 - (log(a + b*x^3)*(A*b^2 - B*a*b))/(3*a^3) - (A/(6*a) - (x^3*(A*b - B*a))/(3*a^2))/x^6","B"
70,1,161,184,2.580503,"\text{Not used}","int((A + B*x^3)/(x^8*(a + b*x^3)),x)","\frac{b^{4/3}\,\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(A\,b-B\,a\right)}{3\,a^{10/3}}-\frac{\frac{A}{7\,a}-\frac{x^3\,\left(A\,b-B\,a\right)}{4\,a^2}+\frac{b\,x^6\,\left(A\,b-B\,a\right)}{a^3}}{x^7}+\frac{b^{4/3}\,\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)}{3\,a^{10/3}}-\frac{b^{4/3}\,\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)}{3\,a^{10/3}}","Not used",1,"(b^(4/3)*log(b^(1/3)*x + a^(1/3))*(A*b - B*a))/(3*a^(10/3)) - (A/(7*a) - (x^3*(A*b - B*a))/(4*a^2) + (b*x^6*(A*b - B*a))/a^3)/x^7 + (b^(4/3)*log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(A*b - B*a))/(3*a^(10/3)) - (b^(4/3)*log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(A*b - B*a))/(3*a^(10/3))","B"
71,1,209,233,2.619895,"\text{Not used}","int((x^9*(A + B*x^3))/(a + b*x^3)^2,x)","x^4\,\left(\frac{A}{4\,b^2}-\frac{B\,a}{2\,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^7}{7\,b^2}+\frac{x\,\left(\frac{B\,a^3}{3}-\frac{A\,a^2\,b}{3}\right)}{b^5\,x^3+a\,b^4}+\frac{a^{4/3}\,\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(7\,A\,b-10\,B\,a\right)}{9\,b^{13/3}}-\frac{a^{4/3}\,\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(7\,A\,b-10\,B\,a\right)}{9\,b^{13/3}}+\frac{a^{4/3}\,\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(7\,A\,b-10\,B\,a\right)}{9\,b^{13/3}}","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)/b^4) + (B*x^7)/(7*b^2) + (x*((B*a^3)/3 - (A*a^2*b)/3))/(a*b^4 + b^5*x^3) + (a^(4/3)*log(b^(1/3)*x + a^(1/3))*(7*A*b - 10*B*a))/(9*b^(13/3)) - (a^(4/3)*log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(7*A*b - 10*B*a))/(9*b^(13/3)) + (a^(4/3)*log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(7*A*b - 10*B*a))/(9*b^(13/3))","B"
72,1,86,82,0.083382,"\text{Not used}","int((x^8*(A + B*x^3))/(a + b*x^3)^2,x)","x^3\,\left(\frac{A}{3\,b^2}-\frac{2\,B\,a}{3\,b^3}\right)+\frac{\ln\left(b\,x^3+a\right)\,\left(3\,B\,a^2-2\,A\,a\,b\right)}{3\,b^4}+\frac{B\,x^6}{6\,b^2}+\frac{B\,a^3-A\,a^2\,b}{3\,b\,\left(b^4\,x^3+a\,b^3\right)}","Not used",1,"x^3*(A/(3*b^2) - (2*B*a)/(3*b^3)) + (log(a + b*x^3)*(3*B*a^2 - 2*A*a*b))/(3*b^4) + (B*x^6)/(6*b^2) + (B*a^3 - A*a^2*b)/(3*b*(a*b^3 + b^4*x^3))","B"
73,1,179,215,0.267819,"\text{Not used}","int((x^7*(A + B*x^3))/(a + b*x^3)^2,x)","x^2\,\left(\frac{A}{2\,b^2}-\frac{B\,a}{b^3}\right)+\frac{B\,x^5}{5\,b^2}-\frac{x^2\,\left(\frac{B\,a^2}{3}-\frac{A\,a\,b}{3}\right)}{b^4\,x^3+a\,b^3}+\frac{a^{2/3}\,\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(5\,A\,b-8\,B\,a\right)}{9\,b^{11/3}}+\frac{a^{2/3}\,\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(5\,A\,b-8\,B\,a\right)}{9\,b^{11/3}}-\frac{a^{2/3}\,\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(5\,A\,b-8\,B\,a\right)}{9\,b^{11/3}}","Not used",1,"x^2*(A/(2*b^2) - (B*a)/b^3) + (B*x^5)/(5*b^2) - (x^2*((B*a^2)/3 - (A*a*b)/3))/(a*b^3 + b^4*x^3) + (a^(2/3)*log(b^(1/3)*x + a^(1/3))*(5*A*b - 8*B*a))/(9*b^(11/3)) + (a^(2/3)*log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(5*A*b - 8*B*a))/(9*b^(11/3)) - (a^(2/3)*log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(5*A*b - 8*B*a))/(9*b^(11/3))","B"
74,1,193,213,2.621221,"\text{Not used}","int((x^6*(A + B*x^3))/(a + b*x^3)^2,x)","x\,\left(\frac{A}{b^2}-\frac{2\,B\,a}{b^3}\right)-\frac{x\,\left(\frac{B\,a^2}{3}-\frac{A\,a\,b}{3}\right)}{b^4\,x^3+a\,b^3}+\frac{B\,x^4}{4\,b^2}+\frac{{\left(-a\right)}^{1/3}\,\ln\left({\left(-a\right)}^{4/3}+a\,b^{1/3}\,x\right)\,\left(4\,A\,b-7\,B\,a\right)}{9\,b^{10/3}}-\frac{{\left(-a\right)}^{1/3}\,\ln\left({\left(-a\right)}^{4/3}-2\,a\,b^{1/3}\,x+\sqrt{3}\,{\left(-a\right)}^{4/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(4\,A\,b-7\,B\,a\right)}{9\,b^{10/3}}+\frac{{\left(-a\right)}^{1/3}\,\ln\left(2\,a\,b^{1/3}\,x-{\left(-a\right)}^{4/3}+\sqrt{3}\,{\left(-a\right)}^{4/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(4\,A\,b-7\,B\,a\right)}{9\,b^{10/3}}","Not used",1,"x*(A/b^2 - (2*B*a)/b^3) - (x*((B*a^2)/3 - (A*a*b)/3))/(a*b^3 + b^4*x^3) + (B*x^4)/(4*b^2) + ((-a)^(1/3)*log((-a)^(4/3) + a*b^(1/3)*x)*(4*A*b - 7*B*a))/(9*b^(10/3)) - ((-a)^(1/3)*log((-a)^(4/3) + 3^(1/2)*(-a)^(4/3)*1i - 2*a*b^(1/3)*x)*((3^(1/2)*1i)/2 + 1/2)*(4*A*b - 7*B*a))/(9*b^(10/3)) + ((-a)^(1/3)*log(3^(1/2)*(-a)^(4/3)*1i - (-a)^(4/3) + 2*a*b^(1/3)*x)*((3^(1/2)*1i)/2 - 1/2)*(4*A*b - 7*B*a))/(9*b^(10/3))","B"
75,1,62,60,0.080722,"\text{Not used}","int((x^5*(A + B*x^3))/(a + b*x^3)^2,x)","\frac{B\,x^3}{3\,b^2}+\frac{\ln\left(b\,x^3+a\right)\,\left(A\,b-2\,B\,a\right)}{3\,b^3}-\frac{B\,a^2-A\,a\,b}{3\,b\,\left(b^3\,x^3+a\,b^2\right)}","Not used",1,"(B*x^3)/(3*b^2) + (log(a + b*x^3)*(A*b - 2*B*a))/(3*b^3) - (B*a^2 - A*a*b)/(3*b*(a*b^2 + b^3*x^3))","B"
76,1,158,196,2.577872,"\text{Not used}","int((x^4*(A + B*x^3))/(a + b*x^3)^2,x)","\frac{B\,x^2}{2\,b^2}-\frac{x^2\,\left(\frac{A\,b}{3}-\frac{B\,a}{3}\right)}{b^3\,x^3+a\,b^2}-\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(2\,A\,b-5\,B\,a\right)}{9\,a^{1/3}\,b^{8/3}}-\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(2\,A\,b-5\,B\,a\right)}{9\,a^{1/3}\,b^{8/3}}+\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(2\,A\,b-5\,B\,a\right)}{9\,a^{1/3}\,b^{8/3}}","Not used",1,"(B*x^2)/(2*b^2) - (x^2*((A*b)/3 - (B*a)/3))/(a*b^2 + b^3*x^3) - (log(b^(1/3)*x + a^(1/3))*(2*A*b - 5*B*a))/(9*a^(1/3)*b^(8/3)) - (log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(2*A*b - 5*B*a))/(9*a^(1/3)*b^(8/3)) + (log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(2*A*b - 5*B*a))/(9*a^(1/3)*b^(8/3))","B"
77,1,150,190,2.576542,"\text{Not used}","int((x^3*(A + B*x^3))/(a + b*x^3)^2,x)","\frac{B\,x}{b^2}-\frac{x\,\left(\frac{A\,b}{3}-\frac{B\,a}{3}\right)}{b^3\,x^3+a\,b^2}+\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(A\,b-4\,B\,a\right)}{9\,a^{2/3}\,b^{7/3}}-\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-4\,B\,a\right)}{9\,a^{2/3}\,b^{7/3}}+\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-4\,B\,a\right)}{9\,a^{2/3}\,b^{7/3}}","Not used",1,"(B*x)/b^2 - (x*((A*b)/3 - (B*a)/3))/(a*b^2 + b^3*x^3) + (log(b^(1/3)*x + a^(1/3))*(A*b - 4*B*a))/(9*a^(2/3)*b^(7/3)) - (log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(A*b - 4*B*a))/(9*a^(2/3)*b^(7/3)) + (log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(A*b - 4*B*a))/(9*a^(2/3)*b^(7/3))","B"
78,1,37,41,2.348389,"\text{Not used}","int((x^2*(A + B*x^3))/(a + b*x^3)^2,x)","\frac{B\,\ln\left(b\,x^3+a\right)}{3\,b^2}-\frac{A\,b-B\,a}{3\,b^2\,\left(b\,x^3+a\right)}","Not used",1,"(B*log(a + b*x^3))/(3*b^2) - (A*b - B*a)/(3*b^2*(a + b*x^3))","B"
79,1,145,171,0.250500,"\text{Not used}","int((x*(A + B*x^3))/(a + b*x^3)^2,x)","\frac{x^2\,\left(A\,b-B\,a\right)}{3\,a\,b\,\left(b\,x^3+a\right)}-\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b+2\,B\,a\right)}{9\,a^{4/3}\,b^{5/3}}+\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b+2\,B\,a\right)}{9\,a^{4/3}\,b^{5/3}}-\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(A\,b+2\,B\,a\right)}{9\,a^{4/3}\,b^{5/3}}","Not used",1,"(log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(A*b + 2*B*a))/(9*a^(4/3)*b^(5/3)) - (log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(A*b + 2*B*a))/(9*a^(4/3)*b^(5/3)) - (log(b^(1/3)*x + a^(1/3))*(A*b + 2*B*a))/(9*a^(4/3)*b^(5/3)) + (x^2*(A*b - B*a))/(3*a*b*(a + b*x^3))","B"
80,1,143,169,2.550380,"\text{Not used}","int((A + B*x^3)/(a + b*x^3)^2,x)","\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(2\,A\,b+B\,a\right)}{9\,a^{5/3}\,b^{4/3}}-\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(2\,A\,b+B\,a\right)}{9\,a^{5/3}\,b^{4/3}}+\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(2\,A\,b+B\,a\right)}{9\,a^{5/3}\,b^{4/3}}+\frac{x\,\left(A\,b-B\,a\right)}{3\,a\,b\,\left(b\,x^3+a\right)}","Not used",1,"(log(b^(1/3)*x + a^(1/3))*(2*A*b + B*a))/(9*a^(5/3)*b^(4/3)) - (log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(2*A*b + B*a))/(9*a^(5/3)*b^(4/3)) + (log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(2*A*b + B*a))/(9*a^(5/3)*b^(4/3)) + (x*(A*b - B*a))/(3*a*b*(a + b*x^3))","B"
81,1,47,51,0.140919,"\text{Not used}","int((A + B*x^3)/(x*(a + b*x^3)^2),x)","\frac{A\,\ln\left(x\right)}{a^2}-\frac{A\,\ln\left(b\,x^3+a\right)}{3\,a^2}+\frac{A\,b-B\,a}{3\,a\,b\,\left(b\,x^3+a\right)}","Not used",1,"(A*log(x))/a^2 - (A*log(a + b*x^3))/(3*a^2) + (A*b - B*a)/(3*a*b*(a + b*x^3))","B"
82,1,156,195,2.569178,"\text{Not used}","int((A + B*x^3)/(x^2*(a + b*x^3)^2),x)","\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(4\,A\,b-B\,a\right)}{9\,a^{7/3}\,b^{2/3}}-\frac{\frac{A}{a}+\frac{x^3\,\left(4\,A\,b-B\,a\right)}{3\,a^2}}{b\,x^4+a\,x}+\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(4\,A\,b-B\,a\right)}{9\,a^{7/3}\,b^{2/3}}-\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(4\,A\,b-B\,a\right)}{9\,a^{7/3}\,b^{2/3}}","Not used",1,"(log(b^(1/3)*x + a^(1/3))*(4*A*b - B*a))/(9*a^(7/3)*b^(2/3)) - (A/a + (x^3*(4*A*b - B*a))/(3*a^2))/(a*x + b*x^4) + (log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(4*A*b - B*a))/(9*a^(7/3)*b^(2/3)) - (log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(4*A*b - B*a))/(9*a^(7/3)*b^(2/3))","B"
83,1,159,196,2.565343,"\text{Not used}","int((A + B*x^3)/(x^3*(a + b*x^3)^2),x)","-\frac{\frac{A}{2\,a}+\frac{x^3\,\left(5\,A\,b-2\,B\,a\right)}{6\,a^2}}{b\,x^5+a\,x^2}-\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(5\,A\,b-2\,B\,a\right)}{9\,a^{8/3}\,b^{1/3}}+\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(5\,A\,b-2\,B\,a\right)}{9\,a^{8/3}\,b^{1/3}}-\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(5\,A\,b-2\,B\,a\right)}{9\,a^{8/3}\,b^{1/3}}","Not used",1,"(log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(5*A*b - 2*B*a))/(9*a^(8/3)*b^(1/3)) - (log(b^(1/3)*x + a^(1/3))*(5*A*b - 2*B*a))/(9*a^(8/3)*b^(1/3)) - (A/(2*a) + (x^3*(5*A*b - 2*B*a))/(6*a^2))/(a*x^2 + b*x^5) - (log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(5*A*b - 2*B*a))/(9*a^(8/3)*b^(1/3))","B"
84,1,78,76,2.432249,"\text{Not used}","int((A + B*x^3)/(x^4*(a + b*x^3)^2),x)","\frac{\ln\left(b\,x^3+a\right)\,\left(2\,A\,b-B\,a\right)}{3\,a^3}-\frac{\frac{A}{3\,a}+\frac{x^3\,\left(2\,A\,b-B\,a\right)}{3\,a^2}}{b\,x^6+a\,x^3}-\frac{\ln\left(x\right)\,\left(2\,A\,b-B\,a\right)}{a^3}","Not used",1,"(log(a + b*x^3)*(2*A*b - B*a))/(3*a^3) - (A/(3*a) + (x^3*(2*A*b - B*a))/(3*a^2))/(a*x^3 + b*x^6) - (log(x)*(2*A*b - B*a))/a^3","B"
85,1,209,215,2.615305,"\text{Not used}","int((A + B*x^3)/(x^5*(a + b*x^3)^2),x)","\frac{\frac{x^3\,\left(7\,A\,b-4\,B\,a\right)}{4\,a^2}-\frac{A}{4\,a}+\frac{b\,x^6\,\left(7\,A\,b-4\,B\,a\right)}{3\,a^3}}{b\,x^7+a\,x^4}+\frac{{\left(-b\right)}^{1/3}\,\ln\left(a^{1/3}\,{\left(-b\right)}^{8/3}+b^3\,x\right)\,\left(7\,A\,b-4\,B\,a\right)}{9\,a^{10/3}}+\frac{{\left(-b\right)}^{1/3}\,\ln\left(a^{1/3}\,{\left(-b\right)}^{8/3}-2\,b^3\,x+\sqrt{3}\,a^{1/3}\,{\left(-b\right)}^{8/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(7\,A\,b-4\,B\,a\right)}{9\,a^{10/3}}-\frac{{\left(-b\right)}^{1/3}\,\ln\left(2\,b^3\,x-a^{1/3}\,{\left(-b\right)}^{8/3}+\sqrt{3}\,a^{1/3}\,{\left(-b\right)}^{8/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(7\,A\,b-4\,B\,a\right)}{9\,a^{10/3}}","Not used",1,"((x^3*(7*A*b - 4*B*a))/(4*a^2) - A/(4*a) + (b*x^6*(7*A*b - 4*B*a))/(3*a^3))/(a*x^4 + b*x^7) + ((-b)^(1/3)*log(a^(1/3)*(-b)^(8/3) + b^3*x)*(7*A*b - 4*B*a))/(9*a^(10/3)) + ((-b)^(1/3)*log(a^(1/3)*(-b)^(8/3) - 2*b^3*x + 3^(1/2)*a^(1/3)*(-b)^(8/3)*1i)*((3^(1/2)*1i)/2 - 1/2)*(7*A*b - 4*B*a))/(9*a^(10/3)) - ((-b)^(1/3)*log(2*b^3*x - a^(1/3)*(-b)^(8/3) + 3^(1/2)*a^(1/3)*(-b)^(8/3)*1i)*((3^(1/2)*1i)/2 + 1/2)*(7*A*b - 4*B*a))/(9*a^(10/3))","B"
86,1,176,215,2.574085,"\text{Not used}","int((A + B*x^3)/(x^6*(a + b*x^3)^2),x)","\frac{\frac{x^3\,\left(8\,A\,b-5\,B\,a\right)}{10\,a^2}-\frac{A}{5\,a}+\frac{b\,x^6\,\left(8\,A\,b-5\,B\,a\right)}{6\,a^3}}{b\,x^8+a\,x^5}+\frac{b^{2/3}\,\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(8\,A\,b-5\,B\,a\right)}{9\,a^{11/3}}-\frac{b^{2/3}\,\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(8\,A\,b-5\,B\,a\right)}{9\,a^{11/3}}+\frac{b^{2/3}\,\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(8\,A\,b-5\,B\,a\right)}{9\,a^{11/3}}","Not used",1,"((x^3*(8*A*b - 5*B*a))/(10*a^2) - A/(5*a) + (b*x^6*(8*A*b - 5*B*a))/(6*a^3))/(a*x^5 + b*x^8) + (b^(2/3)*log(b^(1/3)*x + a^(1/3))*(8*A*b - 5*B*a))/(9*a^(11/3)) - (b^(2/3)*log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(8*A*b - 5*B*a))/(9*a^(11/3)) + (b^(2/3)*log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(8*A*b - 5*B*a))/(9*a^(11/3))","B"
87,1,100,97,0.144142,"\text{Not used}","int((A + B*x^3)/(x^7*(a + b*x^3)^2),x)","\frac{\frac{x^3\,\left(3\,A\,b-2\,B\,a\right)}{6\,a^2}-\frac{A}{6\,a}+\frac{b\,x^6\,\left(3\,A\,b-2\,B\,a\right)}{3\,a^3}}{b\,x^9+a\,x^6}-\frac{\ln\left(b\,x^3+a\right)\,\left(3\,A\,b^2-2\,B\,a\,b\right)}{3\,a^4}+\frac{\ln\left(x\right)\,\left(3\,A\,b^2-2\,B\,a\,b\right)}{a^4}","Not used",1,"((x^3*(3*A*b - 2*B*a))/(6*a^2) - A/(6*a) + (b*x^6*(3*A*b - 2*B*a))/(3*a^3))/(a*x^6 + b*x^9) - (log(a + b*x^3)*(3*A*b^2 - 2*B*a*b))/(3*a^4) + (log(x)*(3*A*b^2 - 2*B*a*b))/a^4","B"
88,1,117,107,0.096813,"\text{Not used}","int((x^11*(A + B*x^3))/(a + b*x^3)^3,x)","\frac{\frac{7\,B\,a^4-5\,A\,a^3\,b}{6\,b}+x^3\,\left(\frac{4\,B\,a^3}{3}-A\,a^2\,b\right)}{a^2\,b^4+2\,a\,b^5\,x^3+b^6\,x^6}+x^3\,\left(\frac{A}{3\,b^3}-\frac{B\,a}{b^4}\right)+\frac{\ln\left(b\,x^3+a\right)\,\left(2\,B\,a^2-A\,a\,b\right)}{b^5}+\frac{B\,x^6}{6\,b^3}","Not used",1,"((7*B*a^4 - 5*A*a^3*b)/(6*b) + x^3*((4*B*a^3)/3 - A*a^2*b))/(a^2*b^4 + b^6*x^6 + 2*a*b^5*x^3) + x^3*(A/(3*b^3) - (B*a)/b^4) + (log(a + b*x^3)*(2*B*a^2 - A*a*b))/b^5 + (B*x^6)/(6*b^3)","B"
89,1,94,88,2.402108,"\text{Not used}","int((x^8*(A + B*x^3))/(a + b*x^3)^3,x)","\frac{B\,x^3}{3\,b^3}-\frac{x^3\,\left(B\,a^2-\frac{2\,A\,a\,b}{3}\right)+\frac{5\,B\,a^3-3\,A\,a^2\,b}{6\,b}}{a^2\,b^3+2\,a\,b^4\,x^3+b^5\,x^6}+\frac{\ln\left(b\,x^3+a\right)\,\left(A\,b-3\,B\,a\right)}{3\,b^4}","Not used",1,"(B*x^3)/(3*b^3) - (x^3*(B*a^2 - (2*A*a*b)/3) + (5*B*a^3 - 3*A*a^2*b)/(6*b))/(a^2*b^3 + b^5*x^6 + 2*a*b^4*x^3) + (log(a + b*x^3)*(A*b - 3*B*a))/(3*b^4)","B"
90,1,70,66,2.384642,"\text{Not used}","int((x^5*(A + B*x^3))/(a + b*x^3)^3,x)","\frac{\frac{3\,B\,a^2-A\,a\,b}{6\,b^3}-\frac{x^3\,\left(A\,b-2\,B\,a\right)}{3\,b^2}}{a^2+2\,a\,b\,x^3+b^2\,x^6}+\frac{B\,\ln\left(b\,x^3+a\right)}{3\,b^3}","Not used",1,"((3*B*a^2 - A*a*b)/(6*b^3) - (x^3*(A*b - 2*B*a))/(3*b^2))/(a^2 + b^2*x^6 + 2*a*b*x^3) + (B*log(a + b*x^3))/(3*b^3)","B"
91,1,44,32,2.331979,"\text{Not used}","int((x^2*(A + B*x^3))/(a + b*x^3)^3,x)","-\frac{\frac{A\,b+B\,a}{6\,b^2}+\frac{B\,x^3}{3\,b}}{a^2+2\,a\,b\,x^3+b^2\,x^6}","Not used",1,"-((A*b + B*a)/(6*b^2) + (B*x^3)/(3*b))/(a^2 + b^2*x^6 + 2*a*b*x^3)","B"
92,1,71,68,0.160657,"\text{Not used}","int((A + B*x^3)/(x*(a + b*x^3)^3),x)","\frac{\frac{3\,A\,b-B\,a}{6\,a\,b}+\frac{A\,b\,x^3}{3\,a^2}}{a^2+2\,a\,b\,x^3+b^2\,x^6}-\frac{A\,\ln\left(b\,x^3+a\right)}{3\,a^3}+\frac{A\,\ln\left(x\right)}{a^3}","Not used",1,"((3*A*b - B*a)/(6*a*b) + (A*b*x^3)/(3*a^2))/(a^2 + b^2*x^6 + 2*a*b*x^3) - (A*log(a + b*x^3))/(3*a^3) + (A*log(x))/a^3","B"
93,1,107,101,2.458100,"\text{Not used}","int((A + B*x^3)/(x^4*(a + b*x^3)^3),x)","\frac{\ln\left(b\,x^3+a\right)\,\left(3\,A\,b-B\,a\right)}{3\,a^4}-\frac{\frac{A}{3\,a}+\frac{x^3\,\left(3\,A\,b-B\,a\right)}{2\,a^2}+\frac{b\,x^6\,\left(3\,A\,b-B\,a\right)}{3\,a^3}}{a^2\,x^3+2\,a\,b\,x^6+b^2\,x^9}-\frac{\ln\left(x\right)\,\left(3\,A\,b-B\,a\right)}{a^4}","Not used",1,"(log(a + b*x^3)*(3*A*b - B*a))/(3*a^4) - (A/(3*a) + (x^3*(3*A*b - B*a))/(2*a^2) + (b*x^6*(3*A*b - B*a))/(3*a^3))/(a^2*x^3 + b^2*x^9 + 2*a*b*x^6) - (log(x)*(3*A*b - B*a))/a^4","B"
94,1,130,122,0.153411,"\text{Not used}","int((A + B*x^3)/(x^7*(a + b*x^3)^3),x)","\frac{\frac{x^3\,\left(2\,A\,b-B\,a\right)}{3\,a^2}-\frac{A}{6\,a}+\frac{b^2\,x^9\,\left(2\,A\,b-B\,a\right)}{a^4}+\frac{3\,b\,x^6\,\left(2\,A\,b-B\,a\right)}{2\,a^3}}{a^2\,x^6+2\,a\,b\,x^9+b^2\,x^{12}}-\frac{\ln\left(b\,x^3+a\right)\,\left(2\,A\,b^2-B\,a\,b\right)}{a^5}+\frac{\ln\left(x\right)\,\left(6\,A\,b^2-3\,B\,a\,b\right)}{a^5}","Not used",1,"((x^3*(2*A*b - B*a))/(3*a^2) - A/(6*a) + (b^2*x^9*(2*A*b - B*a))/a^4 + (3*b*x^6*(2*A*b - B*a))/(2*a^3))/(a^2*x^6 + b^2*x^12 + 2*a*b*x^9) - (log(a + b*x^3)*(2*A*b^2 - B*a*b))/a^5 + (log(x)*(6*A*b^2 - 3*B*a*b))/a^5","B"
95,1,213,246,2.582353,"\text{Not used}","int((x^10*(A + B*x^3))/(a + b*x^3)^3,x)","\frac{x^5\,\left(\frac{7\,A\,a\,b^2}{9}-\frac{10\,B\,a^2\,b}{9}\right)-x^2\,\left(\frac{17\,B\,a^3}{18}-\frac{11\,A\,a^2\,b}{18}\right)}{a^2\,b^4+2\,a\,b^5\,x^3+b^6\,x^6}+x^2\,\left(\frac{A}{2\,b^3}-\frac{3\,B\,a}{2\,b^4}\right)+\frac{B\,x^5}{5\,b^3}+\frac{4\,a^{2/3}\,\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(5\,A\,b-11\,B\,a\right)}{27\,b^{14/3}}+\frac{4\,a^{2/3}\,\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(5\,A\,b-11\,B\,a\right)}{27\,b^{14/3}}-\frac{4\,a^{2/3}\,\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(5\,A\,b-11\,B\,a\right)}{27\,b^{14/3}}","Not used",1,"(x^5*((7*A*a*b^2)/9 - (10*B*a^2*b)/9) - x^2*((17*B*a^3)/18 - (11*A*a^2*b)/18))/(a^2*b^4 + b^6*x^6 + 2*a*b^5*x^3) + x^2*(A/(2*b^3) - (3*B*a)/(2*b^4)) + (B*x^5)/(5*b^3) + (4*a^(2/3)*log(b^(1/3)*x + a^(1/3))*(5*A*b - 11*B*a))/(27*b^(14/3)) + (4*a^(2/3)*log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(5*A*b - 11*B*a))/(27*b^(14/3)) - (4*a^(2/3)*log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(5*A*b - 11*B*a))/(27*b^(14/3))","B"
96,1,227,244,0.320242,"\text{Not used}","int((x^9*(A + B*x^3))/(a + b*x^3)^3,x)","\frac{x^4\,\left(\frac{13\,A\,a\,b^2}{18}-\frac{19\,B\,a^2\,b}{18}\right)-x\,\left(\frac{8\,B\,a^3}{9}-\frac{5\,A\,a^2\,b}{9}\right)}{a^2\,b^4+2\,a\,b^5\,x^3+b^6\,x^6}+x\,\left(\frac{A}{b^3}-\frac{3\,B\,a}{b^4}\right)+\frac{B\,x^4}{4\,b^3}+\frac{7\,{\left(-a\right)}^{1/3}\,\ln\left({\left(-a\right)}^{4/3}+a\,b^{1/3}\,x\right)\,\left(2\,A\,b-5\,B\,a\right)}{27\,b^{13/3}}-\frac{7\,{\left(-a\right)}^{1/3}\,\ln\left({\left(-a\right)}^{4/3}-2\,a\,b^{1/3}\,x+\sqrt{3}\,{\left(-a\right)}^{4/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(2\,A\,b-5\,B\,a\right)}{27\,b^{13/3}}+\frac{7\,{\left(-a\right)}^{1/3}\,\ln\left(2\,a\,b^{1/3}\,x-{\left(-a\right)}^{4/3}+\sqrt{3}\,{\left(-a\right)}^{4/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(2\,A\,b-5\,B\,a\right)}{27\,b^{13/3}}","Not used",1,"(x^4*((13*A*a*b^2)/18 - (19*B*a^2*b)/18) - x*((8*B*a^3)/9 - (5*A*a^2*b)/9))/(a^2*b^4 + b^6*x^6 + 2*a*b^5*x^3) + x*(A/b^3 - (3*B*a)/b^4) + (B*x^4)/(4*b^3) + (7*(-a)^(1/3)*log((-a)^(4/3) + a*b^(1/3)*x)*(2*A*b - 5*B*a))/(27*b^(13/3)) - (7*(-a)^(1/3)*log((-a)^(4/3) + 3^(1/2)*(-a)^(4/3)*1i - 2*a*b^(1/3)*x)*((3^(1/2)*1i)/2 + 1/2)*(2*A*b - 5*B*a))/(27*b^(13/3)) + (7*(-a)^(1/3)*log(3^(1/2)*(-a)^(4/3)*1i - (-a)^(4/3) + 2*a*b^(1/3)*x)*((3^(1/2)*1i)/2 - 1/2)*(2*A*b - 5*B*a))/(27*b^(13/3))","B"
97,1,187,222,2.558159,"\text{Not used}","int((x^7*(A + B*x^3))/(a + b*x^3)^3,x)","\frac{x^2\,\left(\frac{11\,B\,a^2}{18}-\frac{5\,A\,a\,b}{18}\right)-x^5\,\left(\frac{4\,A\,b^2}{9}-\frac{7\,B\,a\,b}{9}\right)}{a^2\,b^3+2\,a\,b^4\,x^3+b^5\,x^6}+\frac{B\,x^2}{2\,b^3}-\frac{5\,\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(A\,b-4\,B\,a\right)}{27\,a^{1/3}\,b^{11/3}}-\frac{5\,\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-4\,B\,a\right)}{27\,a^{1/3}\,b^{11/3}}+\frac{5\,\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-4\,B\,a\right)}{27\,a^{1/3}\,b^{11/3}}","Not used",1,"(x^2*((11*B*a^2)/18 - (5*A*a*b)/18) - x^5*((4*A*b^2)/9 - (7*B*a*b)/9))/(a^2*b^3 + b^5*x^6 + 2*a*b^4*x^3) + (B*x^2)/(2*b^3) - (5*log(b^(1/3)*x + a^(1/3))*(A*b - 4*B*a))/(27*a^(1/3)*b^(11/3)) - (5*log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(A*b - 4*B*a))/(27*a^(1/3)*b^(11/3)) + (5*log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(A*b - 4*B*a))/(27*a^(1/3)*b^(11/3))","B"
98,1,183,220,2.603154,"\text{Not used}","int((x^6*(A + B*x^3))/(a + b*x^3)^3,x)","\frac{B\,x}{b^3}-\frac{x^4\,\left(\frac{7\,A\,b^2}{18}-\frac{13\,B\,a\,b}{18}\right)-x\,\left(\frac{5\,B\,a^2}{9}-\frac{2\,A\,a\,b}{9}\right)}{a^2\,b^3+2\,a\,b^4\,x^3+b^5\,x^6}+\frac{2\,\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(A\,b-7\,B\,a\right)}{27\,a^{2/3}\,b^{10/3}}-\frac{2\,\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-7\,B\,a\right)}{27\,a^{2/3}\,b^{10/3}}+\frac{2\,\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-7\,B\,a\right)}{27\,a^{2/3}\,b^{10/3}}","Not used",1,"(B*x)/b^3 - (x^4*((7*A*b^2)/18 - (13*B*a*b)/18) - x*((5*B*a^2)/9 - (2*A*a*b)/9))/(a^2*b^3 + b^5*x^6 + 2*a*b^4*x^3) + (2*log(b^(1/3)*x + a^(1/3))*(A*b - 7*B*a))/(27*a^(2/3)*b^(10/3)) - (2*log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(A*b - 7*B*a))/(27*a^(2/3)*b^(10/3)) + (2*log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(A*b - 7*B*a))/(27*a^(2/3)*b^(10/3))","B"
99,1,175,201,0.266590,"\text{Not used}","int((x^4*(A + B*x^3))/(a + b*x^3)^3,x)","-\frac{\frac{x^2\,\left(A\,b+5\,B\,a\right)}{18\,b^2}-\frac{x^5\,\left(A\,b-4\,B\,a\right)}{9\,a\,b}}{a^2+2\,a\,b\,x^3+b^2\,x^6}-\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(A\,b+5\,B\,a\right)}{27\,a^{4/3}\,b^{8/3}}-\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b+5\,B\,a\right)}{27\,a^{4/3}\,b^{8/3}}+\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b+5\,B\,a\right)}{27\,a^{4/3}\,b^{8/3}}","Not used",1,"(log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(A*b + 5*B*a))/(27*a^(4/3)*b^(8/3)) - (log(b^(1/3)*x + a^(1/3))*(A*b + 5*B*a))/(27*a^(4/3)*b^(8/3)) - (log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(A*b + 5*B*a))/(27*a^(4/3)*b^(8/3)) - ((x^2*(A*b + 5*B*a))/(18*b^2) - (x^5*(A*b - 4*B*a))/(9*a*b))/(a^2 + b^2*x^6 + 2*a*b*x^3)","B"
100,1,173,199,2.559271,"\text{Not used}","int((x^3*(A + B*x^3))/(a + b*x^3)^3,x)","\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(A\,b+2\,B\,a\right)}{27\,a^{5/3}\,b^{7/3}}-\frac{\frac{x\,\left(A\,b+2\,B\,a\right)}{9\,b^2}-\frac{x^4\,\left(A\,b-7\,B\,a\right)}{18\,a\,b}}{a^2+2\,a\,b\,x^3+b^2\,x^6}-\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b+2\,B\,a\right)}{27\,a^{5/3}\,b^{7/3}}+\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b+2\,B\,a\right)}{27\,a^{5/3}\,b^{7/3}}","Not used",1,"(log(b^(1/3)*x + a^(1/3))*(A*b + 2*B*a))/(27*a^(5/3)*b^(7/3)) - ((x*(A*b + 2*B*a))/(9*b^2) - (x^4*(A*b - 7*B*a))/(18*a*b))/(a^2 + b^2*x^6 + 2*a*b*x^3) - (log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(A*b + 2*B*a))/(27*a^(5/3)*b^(7/3)) + (log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(A*b + 2*B*a))/(27*a^(5/3)*b^(7/3))","B"
101,1,175,201,0.268165,"\text{Not used}","int((x*(A + B*x^3))/(a + b*x^3)^3,x)","\frac{\frac{x^5\,\left(2\,A\,b+B\,a\right)}{9\,a^2}+\frac{x^2\,\left(7\,A\,b-B\,a\right)}{18\,a\,b}}{a^2+2\,a\,b\,x^3+b^2\,x^6}-\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(2\,A\,b+B\,a\right)}{27\,a^{7/3}\,b^{5/3}}-\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(2\,A\,b+B\,a\right)}{27\,a^{7/3}\,b^{5/3}}+\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(2\,A\,b+B\,a\right)}{27\,a^{7/3}\,b^{5/3}}","Not used",1,"((x^5*(2*A*b + B*a))/(9*a^2) + (x^2*(7*A*b - B*a))/(18*a*b))/(a^2 + b^2*x^6 + 2*a*b*x^3) - (log(b^(1/3)*x + a^(1/3))*(2*A*b + B*a))/(27*a^(7/3)*b^(5/3)) - (log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(2*A*b + B*a))/(27*a^(7/3)*b^(5/3)) + (log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(2*A*b + B*a))/(27*a^(7/3)*b^(5/3))","B"
102,1,173,197,0.256428,"\text{Not used}","int((A + B*x^3)/(a + b*x^3)^3,x)","\frac{\frac{x^4\,\left(5\,A\,b+B\,a\right)}{18\,a^2}+\frac{x\,\left(4\,A\,b-B\,a\right)}{9\,a\,b}}{a^2+2\,a\,b\,x^3+b^2\,x^6}+\frac{\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(5\,A\,b+B\,a\right)}{27\,a^{8/3}\,b^{4/3}}-\frac{\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(5\,A\,b+B\,a\right)}{27\,a^{8/3}\,b^{4/3}}+\frac{\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(5\,A\,b+B\,a\right)}{27\,a^{8/3}\,b^{4/3}}","Not used",1,"((x^4*(5*A*b + B*a))/(18*a^2) + (x*(4*A*b - B*a))/(9*a*b))/(a^2 + b^2*x^6 + 2*a*b*x^3) + (log(b^(1/3)*x + a^(1/3))*(5*A*b + B*a))/(27*a^(8/3)*b^(4/3)) - (log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(5*A*b + B*a))/(27*a^(8/3)*b^(4/3)) + (log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(5*A*b + B*a))/(27*a^(8/3)*b^(4/3))","B"
103,1,185,227,2.597596,"\text{Not used}","int((A + B*x^3)/(x^2*(a + b*x^3)^3),x)","\frac{2\,\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(7\,A\,b-B\,a\right)}{27\,a^{10/3}\,b^{2/3}}-\frac{\frac{A}{a}+\frac{7\,x^3\,\left(7\,A\,b-B\,a\right)}{18\,a^2}+\frac{2\,b\,x^6\,\left(7\,A\,b-B\,a\right)}{9\,a^3}}{a^2\,x+2\,a\,b\,x^4+b^2\,x^7}+\frac{2\,\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(7\,A\,b-B\,a\right)}{27\,a^{10/3}\,b^{2/3}}-\frac{2\,\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(7\,A\,b-B\,a\right)}{27\,a^{10/3}\,b^{2/3}}","Not used",1,"(2*log(b^(1/3)*x + a^(1/3))*(7*A*b - B*a))/(27*a^(10/3)*b^(2/3)) - (A/a + (7*x^3*(7*A*b - B*a))/(18*a^2) + (2*b*x^6*(7*A*b - B*a))/(9*a^3))/(a^2*x + b^2*x^7 + 2*a*b*x^4) + (2*log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(7*A*b - B*a))/(27*a^(10/3)*b^(2/3)) - (2*log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(7*A*b - B*a))/(27*a^(10/3)*b^(2/3))","B"
104,1,188,227,2.582839,"\text{Not used}","int((A + B*x^3)/(x^3*(a + b*x^3)^3),x)","-\frac{\frac{A}{2\,a}+\frac{4\,x^3\,\left(4\,A\,b-B\,a\right)}{9\,a^2}+\frac{5\,b\,x^6\,\left(4\,A\,b-B\,a\right)}{18\,a^3}}{a^2\,x^2+2\,a\,b\,x^5+b^2\,x^8}-\frac{5\,\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(4\,A\,b-B\,a\right)}{27\,a^{11/3}\,b^{1/3}}+\frac{5\,\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(4\,A\,b-B\,a\right)}{27\,a^{11/3}\,b^{1/3}}-\frac{5\,\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(4\,A\,b-B\,a\right)}{27\,a^{11/3}\,b^{1/3}}","Not used",1,"(5*log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(4*A*b - B*a))/(27*a^(11/3)*b^(1/3)) - (5*log(b^(1/3)*x + a^(1/3))*(4*A*b - B*a))/(27*a^(11/3)*b^(1/3)) - (A/(2*a) + (4*x^3*(4*A*b - B*a))/(9*a^2) + (5*b*x^6*(4*A*b - B*a))/(18*a^3))/(a^2*x^2 + b^2*x^8 + 2*a*b*x^5) - (5*log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(4*A*b - B*a))/(27*a^(11/3)*b^(1/3))","B"
105,1,240,246,2.637485,"\text{Not used}","int((A + B*x^3)/(x^5*(a + b*x^3)^3),x)","\frac{\frac{x^3\,\left(5\,A\,b-2\,B\,a\right)}{2\,a^2}-\frac{A}{4\,a}+\frac{7\,b^2\,x^9\,\left(5\,A\,b-2\,B\,a\right)}{9\,a^4}+\frac{49\,b\,x^6\,\left(5\,A\,b-2\,B\,a\right)}{36\,a^3}}{a^2\,x^4+2\,a\,b\,x^7+b^2\,x^{10}}+\frac{7\,{\left(-b\right)}^{1/3}\,\ln\left(a^{1/3}\,{\left(-b\right)}^{8/3}+b^3\,x\right)\,\left(5\,A\,b-2\,B\,a\right)}{27\,a^{13/3}}+\frac{7\,{\left(-b\right)}^{1/3}\,\ln\left(a^{1/3}\,{\left(-b\right)}^{8/3}-2\,b^3\,x+\sqrt{3}\,a^{1/3}\,{\left(-b\right)}^{8/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(5\,A\,b-2\,B\,a\right)}{27\,a^{13/3}}-\frac{7\,{\left(-b\right)}^{1/3}\,\ln\left(2\,b^3\,x-a^{1/3}\,{\left(-b\right)}^{8/3}+\sqrt{3}\,a^{1/3}\,{\left(-b\right)}^{8/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(5\,A\,b-2\,B\,a\right)}{27\,a^{13/3}}","Not used",1,"((x^3*(5*A*b - 2*B*a))/(2*a^2) - A/(4*a) + (7*b^2*x^9*(5*A*b - 2*B*a))/(9*a^4) + (49*b*x^6*(5*A*b - 2*B*a))/(36*a^3))/(a^2*x^4 + b^2*x^10 + 2*a*b*x^7) + (7*(-b)^(1/3)*log(a^(1/3)*(-b)^(8/3) + b^3*x)*(5*A*b - 2*B*a))/(27*a^(13/3)) + (7*(-b)^(1/3)*log(a^(1/3)*(-b)^(8/3) - 2*b^3*x + 3^(1/2)*a^(1/3)*(-b)^(8/3)*1i)*((3^(1/2)*1i)/2 - 1/2)*(5*A*b - 2*B*a))/(27*a^(13/3)) - (7*(-b)^(1/3)*log(2*b^3*x - a^(1/3)*(-b)^(8/3) + 3^(1/2)*a^(1/3)*(-b)^(8/3)*1i)*((3^(1/2)*1i)/2 + 1/2)*(5*A*b - 2*B*a))/(27*a^(13/3))","B"
106,1,207,246,2.583527,"\text{Not used}","int((A + B*x^3)/(x^6*(a + b*x^3)^3),x)","\frac{\frac{x^3\,\left(11\,A\,b-5\,B\,a\right)}{10\,a^2}-\frac{A}{5\,a}+\frac{2\,b^2\,x^9\,\left(11\,A\,b-5\,B\,a\right)}{9\,a^4}+\frac{16\,b\,x^6\,\left(11\,A\,b-5\,B\,a\right)}{45\,a^3}}{a^2\,x^5+2\,a\,b\,x^8+b^2\,x^{11}}+\frac{4\,b^{2/3}\,\ln\left(b^{1/3}\,x+a^{1/3}\right)\,\left(11\,A\,b-5\,B\,a\right)}{27\,a^{14/3}}-\frac{4\,b^{2/3}\,\ln\left(a^{1/3}-2\,b^{1/3}\,x+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(11\,A\,b-5\,B\,a\right)}{27\,a^{14/3}}+\frac{4\,b^{2/3}\,\ln\left(2\,b^{1/3}\,x-a^{1/3}+\sqrt{3}\,a^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(11\,A\,b-5\,B\,a\right)}{27\,a^{14/3}}","Not used",1,"((x^3*(11*A*b - 5*B*a))/(10*a^2) - A/(5*a) + (2*b^2*x^9*(11*A*b - 5*B*a))/(9*a^4) + (16*b*x^6*(11*A*b - 5*B*a))/(45*a^3))/(a^2*x^5 + b^2*x^11 + 2*a*b*x^8) + (4*b^(2/3)*log(b^(1/3)*x + a^(1/3))*(11*A*b - 5*B*a))/(27*a^(14/3)) - (4*b^(2/3)*log(3^(1/2)*a^(1/3)*1i - 2*b^(1/3)*x + a^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(11*A*b - 5*B*a))/(27*a^(14/3)) + (4*b^(2/3)*log(3^(1/2)*a^(1/3)*1i + 2*b^(1/3)*x - a^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(11*A*b - 5*B*a))/(27*a^(14/3))","B"
107,1,68,70,2.843979,"\text{Not used}","int(x^8/((a + b*x^3)*(c + d*x^3)),x)","\frac{a^2\,\ln\left(b\,x^3+a\right)}{3\,b^3\,c-3\,a\,b^2\,d}+\frac{c^2\,\ln\left(d\,x^3+c\right)}{3\,a\,d^3-3\,b\,c\,d^2}+\frac{x^3}{3\,b\,d}","Not used",1,"(a^2*log(a + b*x^3))/(3*b^3*c - 3*a*b^2*d) + (c^2*log(c + d*x^3))/(3*a*d^3 - 3*b*c*d^2) + x^3/(3*b*d)","B"
108,1,1751,301,11.360268,"\text{Not used}","int(x^7/((a + b*x^3)*(c + d*x^3)),x)","\ln\left(\frac{\left(\frac{\left(27\,a^2\,b\,c^2\,d\,x\,\left(a^2\,d^2+b^2\,c^2\right)\,{\left(a\,d-b\,c\right)}^2+27\,a\,b^3\,c\,d^3\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(\frac{a^5}{b^5\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}\right)\,{\left(\frac{a^5}{b^5\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}}{3}-\frac{9\,\left(a^8\,c\,d^7-a^7\,b\,c^2\,d^6-a^2\,b^6\,c^7\,d+a\,b^7\,c^8\right)}{b^2\,d^2}\right)\,{\left(\frac{a^5}{b^5\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}}{9}-\frac{a^4\,c^4\,x\,\left(a^2\,d^2+a\,b\,c\,d+b^2\,c^2\right)}{b^2\,d^2}\right)\,{\left(-\frac{a^5}{-27\,a^3\,b^5\,d^3+81\,a^2\,b^6\,c\,d^2-81\,a\,b^7\,c^2\,d+27\,b^8\,c^3}\right)}^{1/3}+\ln\left(\frac{\left(\frac{\left(27\,a^2\,b\,c^2\,d\,x\,\left(a^2\,d^2+b^2\,c^2\right)\,{\left(a\,d-b\,c\right)}^2+27\,a\,b^3\,c\,d^3\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(-\frac{c^5}{d^5\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}\right)\,{\left(-\frac{c^5}{d^5\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}}{3}-\frac{9\,\left(a^8\,c\,d^7-a^7\,b\,c^2\,d^6-a^2\,b^6\,c^7\,d+a\,b^7\,c^8\right)}{b^2\,d^2}\right)\,{\left(-\frac{c^5}{d^5\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}}{9}-\frac{a^4\,c^4\,x\,\left(a^2\,d^2+a\,b\,c\,d+b^2\,c^2\right)}{b^2\,d^2}\right)\,{\left(-\frac{c^5}{27\,a^3\,d^8-81\,a^2\,b\,c\,d^7+81\,a\,b^2\,c^2\,d^6-27\,b^3\,c^3\,d^5}\right)}^{1/3}-\frac{\ln\left(\frac{{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(\frac{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(27\,a^2\,b\,c^2\,d\,x\,\left(a^2\,d^2+b^2\,c^2\right)\,{\left(a\,d-b\,c\right)}^2+\frac{27\,a\,b^3\,c\,d^3\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(\frac{a^5}{b^5\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}}{4}\right)\,{\left(\frac{a^5}{b^5\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}}{6}+\frac{9\,\left(a^8\,c\,d^7-a^7\,b\,c^2\,d^6-a^2\,b^6\,c^7\,d+a\,b^7\,c^8\right)}{b^2\,d^2}\right)\,{\left(\frac{a^5}{b^5\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}}{36}+\frac{a^4\,c^4\,x\,\left(a^2\,d^2+a\,b\,c\,d+b^2\,c^2\right)}{b^2\,d^2}\right)\,{\left(-\frac{a^5}{-27\,a^3\,b^5\,d^3+81\,a^2\,b^6\,c\,d^2-81\,a\,b^7\,c^2\,d+27\,b^8\,c^3}\right)}^{1/3}\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}+\frac{\ln\left(\frac{{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(\frac{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(27\,a^2\,b\,c^2\,d\,x\,\left(a^2\,d^2+b^2\,c^2\right)\,{\left(a\,d-b\,c\right)}^2+\frac{27\,a\,b^3\,c\,d^3\,{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(\frac{a^5}{b^5\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}}{4}\right)\,{\left(\frac{a^5}{b^5\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}}{6}-\frac{9\,\left(a^8\,c\,d^7-a^7\,b\,c^2\,d^6-a^2\,b^6\,c^7\,d+a\,b^7\,c^8\right)}{b^2\,d^2}\right)\,{\left(\frac{a^5}{b^5\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}}{36}-\frac{a^4\,c^4\,x\,\left(a^2\,d^2+a\,b\,c\,d+b^2\,c^2\right)}{b^2\,d^2}\right)\,{\left(-\frac{a^5}{-27\,a^3\,b^5\,d^3+81\,a^2\,b^6\,c\,d^2-81\,a\,b^7\,c^2\,d+27\,b^8\,c^3}\right)}^{1/3}\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}-\frac{\ln\left(\frac{{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(\frac{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(27\,a^2\,b\,c^2\,d\,x\,\left(a^2\,d^2+b^2\,c^2\right)\,{\left(a\,d-b\,c\right)}^2+\frac{27\,a\,b^3\,c\,d^3\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(-\frac{c^5}{d^5\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}}{4}\right)\,{\left(-\frac{c^5}{d^5\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}}{6}+\frac{9\,\left(a^8\,c\,d^7-a^7\,b\,c^2\,d^6-a^2\,b^6\,c^7\,d+a\,b^7\,c^8\right)}{b^2\,d^2}\right)\,{\left(-\frac{c^5}{d^5\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}}{36}+\frac{a^4\,c^4\,x\,\left(a^2\,d^2+a\,b\,c\,d+b^2\,c^2\right)}{b^2\,d^2}\right)\,{\left(-\frac{c^5}{27\,a^3\,d^8-81\,a^2\,b\,c\,d^7+81\,a\,b^2\,c^2\,d^6-27\,b^3\,c^3\,d^5}\right)}^{1/3}\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}+\frac{\ln\left(\frac{{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(\frac{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(27\,a^2\,b\,c^2\,d\,x\,\left(a^2\,d^2+b^2\,c^2\right)\,{\left(a\,d-b\,c\right)}^2+\frac{27\,a\,b^3\,c\,d^3\,{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(-\frac{c^5}{d^5\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}}{4}\right)\,{\left(-\frac{c^5}{d^5\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}}{6}-\frac{9\,\left(a^8\,c\,d^7-a^7\,b\,c^2\,d^6-a^2\,b^6\,c^7\,d+a\,b^7\,c^8\right)}{b^2\,d^2}\right)\,{\left(-\frac{c^5}{d^5\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}}{36}-\frac{a^4\,c^4\,x\,\left(a^2\,d^2+a\,b\,c\,d+b^2\,c^2\right)}{b^2\,d^2}\right)\,{\left(-\frac{c^5}{27\,a^3\,d^8-81\,a^2\,b\,c\,d^7+81\,a\,b^2\,c^2\,d^6-27\,b^3\,c^3\,d^5}\right)}^{1/3}\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}+\frac{x^2}{2\,b\,d}","Not used",1,"log(((((27*a^2*b*c^2*d*x*(a^2*d^2 + b^2*c^2)*(a*d - b*c)^2 + 27*a*b^3*c*d^3*(a*d + b*c)*(a*d - b*c)^4*(a^5/(b^5*(a*d - b*c)^3))^(2/3))*(a^5/(b^5*(a*d - b*c)^3))^(1/3))/3 - (9*(a*b^7*c^8 + a^8*c*d^7 - a^2*b^6*c^7*d - a^7*b*c^2*d^6))/(b^2*d^2))*(a^5/(b^5*(a*d - b*c)^3))^(2/3))/9 - (a^4*c^4*x*(a^2*d^2 + b^2*c^2 + a*b*c*d))/(b^2*d^2))*(-a^5/(27*b^8*c^3 - 27*a^3*b^5*d^3 + 81*a^2*b^6*c*d^2 - 81*a*b^7*c^2*d))^(1/3) + log(((((27*a^2*b*c^2*d*x*(a^2*d^2 + b^2*c^2)*(a*d - b*c)^2 + 27*a*b^3*c*d^3*(a*d + b*c)*(a*d - b*c)^4*(-c^5/(d^5*(a*d - b*c)^3))^(2/3))*(-c^5/(d^5*(a*d - b*c)^3))^(1/3))/3 - (9*(a*b^7*c^8 + a^8*c*d^7 - a^2*b^6*c^7*d - a^7*b*c^2*d^6))/(b^2*d^2))*(-c^5/(d^5*(a*d - b*c)^3))^(2/3))/9 - (a^4*c^4*x*(a^2*d^2 + b^2*c^2 + a*b*c*d))/(b^2*d^2))*(-c^5/(27*a^3*d^8 - 27*b^3*c^3*d^5 + 81*a*b^2*c^2*d^6 - 81*a^2*b*c*d^7))^(1/3) - (log(((3^(1/2)*1i + 1)^2*(((3^(1/2)*1i + 1)*(27*a^2*b*c^2*d*x*(a^2*d^2 + b^2*c^2)*(a*d - b*c)^2 + (27*a*b^3*c*d^3*(3^(1/2)*1i + 1)^2*(a*d + b*c)*(a*d - b*c)^4*(a^5/(b^5*(a*d - b*c)^3))^(2/3))/4)*(a^5/(b^5*(a*d - b*c)^3))^(1/3))/6 + (9*(a*b^7*c^8 + a^8*c*d^7 - a^2*b^6*c^7*d - a^7*b*c^2*d^6))/(b^2*d^2))*(a^5/(b^5*(a*d - b*c)^3))^(2/3))/36 + (a^4*c^4*x*(a^2*d^2 + b^2*c^2 + a*b*c*d))/(b^2*d^2))*(-a^5/(27*b^8*c^3 - 27*a^3*b^5*d^3 + 81*a^2*b^6*c*d^2 - 81*a*b^7*c^2*d))^(1/3)*(3^(1/2)*1i + 1))/2 + (log(((3^(1/2)*1i - 1)^2*(((3^(1/2)*1i - 1)*(27*a^2*b*c^2*d*x*(a^2*d^2 + b^2*c^2)*(a*d - b*c)^2 + (27*a*b^3*c*d^3*(3^(1/2)*1i - 1)^2*(a*d + b*c)*(a*d - b*c)^4*(a^5/(b^5*(a*d - b*c)^3))^(2/3))/4)*(a^5/(b^5*(a*d - b*c)^3))^(1/3))/6 - (9*(a*b^7*c^8 + a^8*c*d^7 - a^2*b^6*c^7*d - a^7*b*c^2*d^6))/(b^2*d^2))*(a^5/(b^5*(a*d - b*c)^3))^(2/3))/36 - (a^4*c^4*x*(a^2*d^2 + b^2*c^2 + a*b*c*d))/(b^2*d^2))*(-a^5/(27*b^8*c^3 - 27*a^3*b^5*d^3 + 81*a^2*b^6*c*d^2 - 81*a*b^7*c^2*d))^(1/3)*(3^(1/2)*1i - 1))/2 - (log(((3^(1/2)*1i + 1)^2*(((3^(1/2)*1i + 1)*(27*a^2*b*c^2*d*x*(a^2*d^2 + b^2*c^2)*(a*d - b*c)^2 + (27*a*b^3*c*d^3*(3^(1/2)*1i + 1)^2*(a*d + b*c)*(a*d - b*c)^4*(-c^5/(d^5*(a*d - b*c)^3))^(2/3))/4)*(-c^5/(d^5*(a*d - b*c)^3))^(1/3))/6 + (9*(a*b^7*c^8 + a^8*c*d^7 - a^2*b^6*c^7*d - a^7*b*c^2*d^6))/(b^2*d^2))*(-c^5/(d^5*(a*d - b*c)^3))^(2/3))/36 + (a^4*c^4*x*(a^2*d^2 + b^2*c^2 + a*b*c*d))/(b^2*d^2))*(-c^5/(27*a^3*d^8 - 27*b^3*c^3*d^5 + 81*a*b^2*c^2*d^6 - 81*a^2*b*c*d^7))^(1/3)*(3^(1/2)*1i + 1))/2 + (log(((3^(1/2)*1i - 1)^2*(((3^(1/2)*1i - 1)*(27*a^2*b*c^2*d*x*(a^2*d^2 + b^2*c^2)*(a*d - b*c)^2 + (27*a*b^3*c*d^3*(3^(1/2)*1i - 1)^2*(a*d + b*c)*(a*d - b*c)^4*(-c^5/(d^5*(a*d - b*c)^3))^(2/3))/4)*(-c^5/(d^5*(a*d - b*c)^3))^(1/3))/6 - (9*(a*b^7*c^8 + a^8*c*d^7 - a^2*b^6*c^7*d - a^7*b*c^2*d^6))/(b^2*d^2))*(-c^5/(d^5*(a*d - b*c)^3))^(2/3))/36 - (a^4*c^4*x*(a^2*d^2 + b^2*c^2 + a*b*c*d))/(b^2*d^2))*(-c^5/(27*a^3*d^8 - 27*b^3*c^3*d^5 + 81*a*b^2*c^2*d^6 - 81*a^2*b*c*d^7))^(1/3)*(3^(1/2)*1i - 1))/2 + x^2/(2*b*d)","B"
109,1,873,296,1.829414,"\text{Not used}","int(x^6/((a + b*x^3)*(c + d*x^3)),x)","\ln\left(a\,x+b^2\,c\,{\left(-\frac{a^4}{b^4\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}-a\,b\,d\,{\left(-\frac{a^4}{b^4\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}\right)\,{\left(\frac{a^4}{-27\,a^3\,b^4\,d^3+81\,a^2\,b^5\,c\,d^2-81\,a\,b^6\,c^2\,d+27\,b^7\,c^3}\right)}^{1/3}+\ln\left(c\,x+a\,d^2\,{\left(\frac{c^4}{d^4\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}-b\,c\,d\,{\left(\frac{c^4}{d^4\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}\right)\,{\left(\frac{c^4}{27\,a^3\,d^7-81\,a^2\,b\,c\,d^6+81\,a\,b^2\,c^2\,d^5-27\,b^3\,c^3\,d^4}\right)}^{1/3}+\frac{x}{b\,d}+\frac{\ln\left(\frac{3\,x\,\left(a^6\,c^2\,d^4+a^2\,b^4\,c^6\right)}{b\,d}-\frac{3\,a\,c^2\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(-\frac{a^4}{b^4\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}\,\left(a^5\,d^5-a^4\,b\,c\,d^4+a\,b^4\,c^4\,d-b^5\,c^5\right)}{2\,d}\right)\,{\left(\frac{a^4}{-27\,a^3\,b^4\,d^3+81\,a^2\,b^5\,c\,d^2-81\,a\,b^6\,c^2\,d+27\,b^7\,c^3}\right)}^{1/3}\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}-\frac{\ln\left(\frac{3\,x\,\left(a^6\,c^2\,d^4+a^2\,b^4\,c^6\right)}{b\,d}+\frac{3\,a\,c^2\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(-\frac{a^4}{b^4\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}\,\left(a^5\,d^5-a^4\,b\,c\,d^4+a\,b^4\,c^4\,d-b^5\,c^5\right)}{2\,d}\right)\,{\left(\frac{a^4}{-27\,a^3\,b^4\,d^3+81\,a^2\,b^5\,c\,d^2-81\,a\,b^6\,c^2\,d+27\,b^7\,c^3}\right)}^{1/3}\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}+\frac{\ln\left(\frac{3\,x\,\left(a^6\,c^2\,d^4+a^2\,b^4\,c^6\right)}{b\,d}+\frac{3\,a^2\,c\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(\frac{c^4}{d^4\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}\,\left(a^5\,d^5-a^4\,b\,c\,d^4+a\,b^4\,c^4\,d-b^5\,c^5\right)}{2\,b}\right)\,{\left(\frac{c^4}{27\,a^3\,d^7-81\,a^2\,b\,c\,d^6+81\,a\,b^2\,c^2\,d^5-27\,b^3\,c^3\,d^4}\right)}^{1/3}\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}-\frac{\ln\left(\frac{3\,x\,\left(a^6\,c^2\,d^4+a^2\,b^4\,c^6\right)}{b\,d}-\frac{3\,a^2\,c\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(\frac{c^4}{d^4\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}\,\left(a^5\,d^5-a^4\,b\,c\,d^4+a\,b^4\,c^4\,d-b^5\,c^5\right)}{2\,b}\right)\,{\left(\frac{c^4}{27\,a^3\,d^7-81\,a^2\,b\,c\,d^6+81\,a\,b^2\,c^2\,d^5-27\,b^3\,c^3\,d^4}\right)}^{1/3}\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}","Not used",1,"log(a*x + b^2*c*(-a^4/(b^4*(a*d - b*c)^3))^(1/3) - a*b*d*(-a^4/(b^4*(a*d - b*c)^3))^(1/3))*(a^4/(27*b^7*c^3 - 27*a^3*b^4*d^3 + 81*a^2*b^5*c*d^2 - 81*a*b^6*c^2*d))^(1/3) + log(c*x + a*d^2*(c^4/(d^4*(a*d - b*c)^3))^(1/3) - b*c*d*(c^4/(d^4*(a*d - b*c)^3))^(1/3))*(c^4/(27*a^3*d^7 - 27*b^3*c^3*d^4 + 81*a*b^2*c^2*d^5 - 81*a^2*b*c*d^6))^(1/3) + x/(b*d) + (log((3*x*(a^2*b^4*c^6 + a^6*c^2*d^4))/(b*d) - (3*a*c^2*(3^(1/2)*1i - 1)*(-a^4/(b^4*(a*d - b*c)^3))^(1/3)*(a^5*d^5 - b^5*c^5 + a*b^4*c^4*d - a^4*b*c*d^4))/(2*d))*(a^4/(27*b^7*c^3 - 27*a^3*b^4*d^3 + 81*a^2*b^5*c*d^2 - 81*a*b^6*c^2*d))^(1/3)*(3^(1/2)*1i - 1))/2 - (log((3*x*(a^2*b^4*c^6 + a^6*c^2*d^4))/(b*d) + (3*a*c^2*(3^(1/2)*1i + 1)*(-a^4/(b^4*(a*d - b*c)^3))^(1/3)*(a^5*d^5 - b^5*c^5 + a*b^4*c^4*d - a^4*b*c*d^4))/(2*d))*(a^4/(27*b^7*c^3 - 27*a^3*b^4*d^3 + 81*a^2*b^5*c*d^2 - 81*a*b^6*c^2*d))^(1/3)*(3^(1/2)*1i + 1))/2 + (log((3*x*(a^2*b^4*c^6 + a^6*c^2*d^4))/(b*d) + (3*a^2*c*(3^(1/2)*1i - 1)*(c^4/(d^4*(a*d - b*c)^3))^(1/3)*(a^5*d^5 - b^5*c^5 + a*b^4*c^4*d - a^4*b*c*d^4))/(2*b))*(c^4/(27*a^3*d^7 - 27*b^3*c^3*d^4 + 81*a*b^2*c^2*d^5 - 81*a^2*b*c*d^6))^(1/3)*(3^(1/2)*1i - 1))/2 - (log((3*x*(a^2*b^4*c^6 + a^6*c^2*d^4))/(b*d) - (3*a^2*c*(3^(1/2)*1i + 1)*(c^4/(d^4*(a*d - b*c)^3))^(1/3)*(a^5*d^5 - b^5*c^5 + a*b^4*c^4*d - a^4*b*c*d^4))/(2*b))*(c^4/(27*a^3*d^7 - 27*b^3*c^3*d^4 + 81*a*b^2*c^2*d^5 - 81*a^2*b*c*d^6))^(1/3)*(3^(1/2)*1i + 1))/2","B"
110,1,51,53,0.312953,"\text{Not used}","int(x^5/((a + b*x^3)*(c + d*x^3)),x)","-\frac{a\,\ln\left(b\,x^3+a\right)}{3\,b^2\,c-3\,a\,b\,d}-\frac{c\,\ln\left(d\,x^3+c\right)}{3\,a\,d^2-3\,b\,c\,d}","Not used",1,"- (a*log(a + b*x^3))/(3*b^2*c - 3*a*b*d) - (c*log(c + d*x^3))/(3*a*d^2 - 3*b*c*d)","B"
111,1,1364,288,9.046244,"\text{Not used}","int(x^4/((a + b*x^3)*(c + d*x^3)),x)","\ln\left(a\,x+b^3\,c^2\,{\left(-\frac{a^2}{b^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}+a^2\,b\,d^2\,{\left(-\frac{a^2}{b^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}-2\,a\,b^2\,c\,d\,{\left(-\frac{a^2}{b^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}\right)\,{\left(\frac{a^2}{-27\,a^3\,b^2\,d^3+81\,a^2\,b^3\,c\,d^2-81\,a\,b^4\,c^2\,d+27\,b^5\,c^3}\right)}^{1/3}+\ln\left(c\,x+a^2\,d^3\,{\left(\frac{c^2}{d^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}+b^2\,c^2\,d\,{\left(\frac{c^2}{d^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}-2\,a\,b\,c\,d^2\,{\left(\frac{c^2}{d^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}\right)\,{\left(\frac{c^2}{27\,a^3\,d^5-81\,a^2\,b\,c\,d^4+81\,a\,b^2\,c^2\,d^3-27\,b^3\,c^3\,d^2}\right)}^{1/3}+\frac{\ln\left(\frac{{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,{\left(-\frac{a^2}{b^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}\,\left(\frac{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(54\,a^2\,b^3\,c^2\,d^3\,x\,{\left(a\,d-b\,c\right)}^2+\frac{27\,a\,b^3\,c\,d^3\,{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(-\frac{a^2}{b^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}}{4}\right)\,{\left(-\frac{a^2}{b^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}}{6}-9\,a^2\,b^4\,c^4\,d^2-9\,a^4\,b^2\,c^2\,d^4+9\,a\,b^5\,c^5\,d+9\,a^5\,b\,c\,d^5\right)}{36}+a^2\,b\,c^2\,d\,x\,\left(a\,d+b\,c\right)\right)\,{\left(\frac{a^2}{-27\,a^3\,b^2\,d^3+81\,a^2\,b^3\,c\,d^2-81\,a\,b^4\,c^2\,d+27\,b^5\,c^3}\right)}^{1/3}\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}-\frac{\ln\left(\frac{{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,{\left(-\frac{a^2}{b^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}\,\left(\frac{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(54\,a^2\,b^3\,c^2\,d^3\,x\,{\left(a\,d-b\,c\right)}^2+\frac{27\,a\,b^3\,c\,d^3\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(-\frac{a^2}{b^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}}{4}\right)\,{\left(-\frac{a^2}{b^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}}{6}+9\,a^2\,b^4\,c^4\,d^2+9\,a^4\,b^2\,c^2\,d^4-9\,a\,b^5\,c^5\,d-9\,a^5\,b\,c\,d^5\right)}{36}-a^2\,b\,c^2\,d\,x\,\left(a\,d+b\,c\right)\right)\,{\left(\frac{a^2}{-27\,a^3\,b^2\,d^3+81\,a^2\,b^3\,c\,d^2-81\,a\,b^4\,c^2\,d+27\,b^5\,c^3}\right)}^{1/3}\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}+\frac{\ln\left(\frac{{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,{\left(\frac{c^2}{d^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}\,\left(\frac{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(54\,a^2\,b^3\,c^2\,d^3\,x\,{\left(a\,d-b\,c\right)}^2+\frac{27\,a\,b^3\,c\,d^3\,{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(\frac{c^2}{d^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}}{4}\right)\,{\left(\frac{c^2}{d^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}}{6}-9\,a^2\,b^4\,c^4\,d^2-9\,a^4\,b^2\,c^2\,d^4+9\,a\,b^5\,c^5\,d+9\,a^5\,b\,c\,d^5\right)}{36}+a^2\,b\,c^2\,d\,x\,\left(a\,d+b\,c\right)\right)\,{\left(\frac{c^2}{27\,a^3\,d^5-81\,a^2\,b\,c\,d^4+81\,a\,b^2\,c^2\,d^3-27\,b^3\,c^3\,d^2}\right)}^{1/3}\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}-\frac{\ln\left(\frac{{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,{\left(\frac{c^2}{d^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}\,\left(\frac{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(54\,a^2\,b^3\,c^2\,d^3\,x\,{\left(a\,d-b\,c\right)}^2+\frac{27\,a\,b^3\,c\,d^3\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(\frac{c^2}{d^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}}{4}\right)\,{\left(\frac{c^2}{d^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}}{6}+9\,a^2\,b^4\,c^4\,d^2+9\,a^4\,b^2\,c^2\,d^4-9\,a\,b^5\,c^5\,d-9\,a^5\,b\,c\,d^5\right)}{36}-a^2\,b\,c^2\,d\,x\,\left(a\,d+b\,c\right)\right)\,{\left(\frac{c^2}{27\,a^3\,d^5-81\,a^2\,b\,c\,d^4+81\,a\,b^2\,c^2\,d^3-27\,b^3\,c^3\,d^2}\right)}^{1/3}\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}","Not used",1,"log(a*x + b^3*c^2*(-a^2/(b^2*(a*d - b*c)^3))^(2/3) + a^2*b*d^2*(-a^2/(b^2*(a*d - b*c)^3))^(2/3) - 2*a*b^2*c*d*(-a^2/(b^2*(a*d - b*c)^3))^(2/3))*(a^2/(27*b^5*c^3 - 27*a^3*b^2*d^3 + 81*a^2*b^3*c*d^2 - 81*a*b^4*c^2*d))^(1/3) + log(c*x + a^2*d^3*(c^2/(d^2*(a*d - b*c)^3))^(2/3) + b^2*c^2*d*(c^2/(d^2*(a*d - b*c)^3))^(2/3) - 2*a*b*c*d^2*(c^2/(d^2*(a*d - b*c)^3))^(2/3))*(c^2/(27*a^3*d^5 - 27*b^3*c^3*d^2 + 81*a*b^2*c^2*d^3 - 81*a^2*b*c*d^4))^(1/3) + (log(((3^(1/2)*1i - 1)^2*(-a^2/(b^2*(a*d - b*c)^3))^(2/3)*(((3^(1/2)*1i - 1)*(54*a^2*b^3*c^2*d^3*x*(a*d - b*c)^2 + (27*a*b^3*c*d^3*(3^(1/2)*1i - 1)^2*(a*d + b*c)*(a*d - b*c)^4*(-a^2/(b^2*(a*d - b*c)^3))^(2/3))/4)*(-a^2/(b^2*(a*d - b*c)^3))^(1/3))/6 - 9*a^2*b^4*c^4*d^2 - 9*a^4*b^2*c^2*d^4 + 9*a*b^5*c^5*d + 9*a^5*b*c*d^5))/36 + a^2*b*c^2*d*x*(a*d + b*c))*(a^2/(27*b^5*c^3 - 27*a^3*b^2*d^3 + 81*a^2*b^3*c*d^2 - 81*a*b^4*c^2*d))^(1/3)*(3^(1/2)*1i - 1))/2 - (log(((3^(1/2)*1i + 1)^2*(-a^2/(b^2*(a*d - b*c)^3))^(2/3)*(((3^(1/2)*1i + 1)*(54*a^2*b^3*c^2*d^3*x*(a*d - b*c)^2 + (27*a*b^3*c*d^3*(3^(1/2)*1i + 1)^2*(a*d + b*c)*(a*d - b*c)^4*(-a^2/(b^2*(a*d - b*c)^3))^(2/3))/4)*(-a^2/(b^2*(a*d - b*c)^3))^(1/3))/6 + 9*a^2*b^4*c^4*d^2 + 9*a^4*b^2*c^2*d^4 - 9*a*b^5*c^5*d - 9*a^5*b*c*d^5))/36 - a^2*b*c^2*d*x*(a*d + b*c))*(a^2/(27*b^5*c^3 - 27*a^3*b^2*d^3 + 81*a^2*b^3*c*d^2 - 81*a*b^4*c^2*d))^(1/3)*(3^(1/2)*1i + 1))/2 + (log(((3^(1/2)*1i - 1)^2*(c^2/(d^2*(a*d - b*c)^3))^(2/3)*(((3^(1/2)*1i - 1)*(54*a^2*b^3*c^2*d^3*x*(a*d - b*c)^2 + (27*a*b^3*c*d^3*(3^(1/2)*1i - 1)^2*(a*d + b*c)*(a*d - b*c)^4*(c^2/(d^2*(a*d - b*c)^3))^(2/3))/4)*(c^2/(d^2*(a*d - b*c)^3))^(1/3))/6 - 9*a^2*b^4*c^4*d^2 - 9*a^4*b^2*c^2*d^4 + 9*a*b^5*c^5*d + 9*a^5*b*c*d^5))/36 + a^2*b*c^2*d*x*(a*d + b*c))*(c^2/(27*a^3*d^5 - 27*b^3*c^3*d^2 + 81*a*b^2*c^2*d^3 - 81*a^2*b*c*d^4))^(1/3)*(3^(1/2)*1i - 1))/2 - (log(((3^(1/2)*1i + 1)^2*(c^2/(d^2*(a*d - b*c)^3))^(2/3)*(((3^(1/2)*1i + 1)*(54*a^2*b^3*c^2*d^3*x*(a*d - b*c)^2 + (27*a*b^3*c*d^3*(3^(1/2)*1i + 1)^2*(a*d + b*c)*(a*d - b*c)^4*(c^2/(d^2*(a*d - b*c)^3))^(2/3))/4)*(c^2/(d^2*(a*d - b*c)^3))^(1/3))/6 + 9*a^2*b^4*c^4*d^2 + 9*a^4*b^2*c^2*d^4 - 9*a*b^5*c^5*d - 9*a^5*b*c*d^5))/36 - a^2*b*c^2*d*x*(a*d + b*c))*(c^2/(27*a^3*d^5 - 27*b^3*c^3*d^2 + 81*a*b^2*c^2*d^3 - 81*a^2*b*c*d^4))^(1/3)*(3^(1/2)*1i + 1))/2","B"
112,1,1265,288,8.116513,"\text{Not used}","int(x^3/((a + b*x^3)*(c + d*x^3)),x)","\ln\left(x+a\,d\,{\left(\frac{a}{b\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}-b\,c\,{\left(\frac{a}{b\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}\right)\,{\left(-\frac{a}{-27\,a^3\,b\,d^3+81\,a^2\,b^2\,c\,d^2-81\,a\,b^3\,c^2\,d+27\,b^4\,c^3}\right)}^{1/3}+\ln\left(x-a\,d\,{\left(-\frac{c}{d\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}+b\,c\,{\left(-\frac{c}{d\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}\right)\,{\left(-\frac{c}{27\,a^3\,d^4-81\,a^2\,b\,c\,d^3+81\,a\,b^2\,c^2\,d^2-27\,b^3\,c^3\,d}\right)}^{1/3}+\frac{\ln\left(\frac{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(\frac{a}{b\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}\,\left(\frac{{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(81\,a\,b^3\,c\,d^3\,x\,{\left(a\,d-b\,c\right)}^4-\frac{81\,a\,b^3\,c\,d^3\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(\frac{a}{b\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}}{2}\right)\,{\left(\frac{a}{b\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}}{36}+9\,a\,b^5\,c^4\,d^2+9\,a^4\,b^2\,c\,d^5-9\,a^2\,b^4\,c^3\,d^3-9\,a^3\,b^3\,c^2\,d^4\right)}{6}-3\,a\,b^2\,c\,d^2\,x\,\left(a^2\,d^2+b^2\,c^2\right)\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(-\frac{a}{-27\,a^3\,b\,d^3+81\,a^2\,b^2\,c\,d^2-81\,a\,b^3\,c^2\,d+27\,b^4\,c^3}\right)}^{1/3}}{2}-\frac{\ln\left(\frac{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(\frac{a}{b\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}\,\left(\frac{{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(81\,a\,b^3\,c\,d^3\,x\,{\left(a\,d-b\,c\right)}^4+\frac{81\,a\,b^3\,c\,d^3\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(\frac{a}{b\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}}{2}\right)\,{\left(\frac{a}{b\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}}{36}+9\,a\,b^5\,c^4\,d^2+9\,a^4\,b^2\,c\,d^5-9\,a^2\,b^4\,c^3\,d^3-9\,a^3\,b^3\,c^2\,d^4\right)}{6}+3\,a\,b^2\,c\,d^2\,x\,\left(a^2\,d^2+b^2\,c^2\right)\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(-\frac{a}{-27\,a^3\,b\,d^3+81\,a^2\,b^2\,c\,d^2-81\,a\,b^3\,c^2\,d+27\,b^4\,c^3}\right)}^{1/3}}{2}+\frac{\ln\left(\frac{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(-\frac{c}{d\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}\,\left(\frac{{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(81\,a\,b^3\,c\,d^3\,x\,{\left(a\,d-b\,c\right)}^4-\frac{81\,a\,b^3\,c\,d^3\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(-\frac{c}{d\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}}{2}\right)\,{\left(-\frac{c}{d\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}}{36}+9\,a\,b^5\,c^4\,d^2+9\,a^4\,b^2\,c\,d^5-9\,a^2\,b^4\,c^3\,d^3-9\,a^3\,b^3\,c^2\,d^4\right)}{6}-3\,a\,b^2\,c\,d^2\,x\,\left(a^2\,d^2+b^2\,c^2\right)\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(-\frac{c}{27\,a^3\,d^4-81\,a^2\,b\,c\,d^3+81\,a\,b^2\,c^2\,d^2-27\,b^3\,c^3\,d}\right)}^{1/3}}{2}-\frac{\ln\left(\frac{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(-\frac{c}{d\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}\,\left(\frac{{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(81\,a\,b^3\,c\,d^3\,x\,{\left(a\,d-b\,c\right)}^4+\frac{81\,a\,b^3\,c\,d^3\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(-\frac{c}{d\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}}{2}\right)\,{\left(-\frac{c}{d\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}}{36}+9\,a\,b^5\,c^4\,d^2+9\,a^4\,b^2\,c\,d^5-9\,a^2\,b^4\,c^3\,d^3-9\,a^3\,b^3\,c^2\,d^4\right)}{6}+3\,a\,b^2\,c\,d^2\,x\,\left(a^2\,d^2+b^2\,c^2\right)\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(-\frac{c}{27\,a^3\,d^4-81\,a^2\,b\,c\,d^3+81\,a\,b^2\,c^2\,d^2-27\,b^3\,c^3\,d}\right)}^{1/3}}{2}","Not used",1,"log(x + a*d*(a/(b*(a*d - b*c)^3))^(1/3) - b*c*(a/(b*(a*d - b*c)^3))^(1/3))*(-a/(27*b^4*c^3 - 27*a^3*b*d^3 + 81*a^2*b^2*c*d^2 - 81*a*b^3*c^2*d))^(1/3) + log(x - a*d*(-c/(d*(a*d - b*c)^3))^(1/3) + b*c*(-c/(d*(a*d - b*c)^3))^(1/3))*(-c/(27*a^3*d^4 - 27*b^3*c^3*d + 81*a*b^2*c^2*d^2 - 81*a^2*b*c*d^3))^(1/3) + (log(((3^(1/2)*1i - 1)*(a/(b*(a*d - b*c)^3))^(1/3)*(((3^(1/2)*1i - 1)^2*(81*a*b^3*c*d^3*x*(a*d - b*c)^4 - (81*a*b^3*c*d^3*(3^(1/2)*1i - 1)*(a*d + b*c)*(a*d - b*c)^4*(a/(b*(a*d - b*c)^3))^(1/3))/2)*(a/(b*(a*d - b*c)^3))^(2/3))/36 + 9*a*b^5*c^4*d^2 + 9*a^4*b^2*c*d^5 - 9*a^2*b^4*c^3*d^3 - 9*a^3*b^3*c^2*d^4))/6 - 3*a*b^2*c*d^2*x*(a^2*d^2 + b^2*c^2))*(3^(1/2)*1i - 1)*(-a/(27*b^4*c^3 - 27*a^3*b*d^3 + 81*a^2*b^2*c*d^2 - 81*a*b^3*c^2*d))^(1/3))/2 - (log(((3^(1/2)*1i + 1)*(a/(b*(a*d - b*c)^3))^(1/3)*(((3^(1/2)*1i + 1)^2*(81*a*b^3*c*d^3*x*(a*d - b*c)^4 + (81*a*b^3*c*d^3*(3^(1/2)*1i + 1)*(a*d + b*c)*(a*d - b*c)^4*(a/(b*(a*d - b*c)^3))^(1/3))/2)*(a/(b*(a*d - b*c)^3))^(2/3))/36 + 9*a*b^5*c^4*d^2 + 9*a^4*b^2*c*d^5 - 9*a^2*b^4*c^3*d^3 - 9*a^3*b^3*c^2*d^4))/6 + 3*a*b^2*c*d^2*x*(a^2*d^2 + b^2*c^2))*(3^(1/2)*1i + 1)*(-a/(27*b^4*c^3 - 27*a^3*b*d^3 + 81*a^2*b^2*c*d^2 - 81*a*b^3*c^2*d))^(1/3))/2 + (log(((3^(1/2)*1i - 1)*(-c/(d*(a*d - b*c)^3))^(1/3)*(((3^(1/2)*1i - 1)^2*(81*a*b^3*c*d^3*x*(a*d - b*c)^4 - (81*a*b^3*c*d^3*(3^(1/2)*1i - 1)*(a*d + b*c)*(a*d - b*c)^4*(-c/(d*(a*d - b*c)^3))^(1/3))/2)*(-c/(d*(a*d - b*c)^3))^(2/3))/36 + 9*a*b^5*c^4*d^2 + 9*a^4*b^2*c*d^5 - 9*a^2*b^4*c^3*d^3 - 9*a^3*b^3*c^2*d^4))/6 - 3*a*b^2*c*d^2*x*(a^2*d^2 + b^2*c^2))*(3^(1/2)*1i - 1)*(-c/(27*a^3*d^4 - 27*b^3*c^3*d + 81*a*b^2*c^2*d^2 - 81*a^2*b*c*d^3))^(1/3))/2 - (log(((3^(1/2)*1i + 1)*(-c/(d*(a*d - b*c)^3))^(1/3)*(((3^(1/2)*1i + 1)^2*(81*a*b^3*c*d^3*x*(a*d - b*c)^4 + (81*a*b^3*c*d^3*(3^(1/2)*1i + 1)*(a*d + b*c)*(a*d - b*c)^4*(-c/(d*(a*d - b*c)^3))^(1/3))/2)*(-c/(d*(a*d - b*c)^3))^(2/3))/36 + 9*a*b^5*c^4*d^2 + 9*a^4*b^2*c*d^5 - 9*a^2*b^4*c^3*d^3 - 9*a^3*b^3*c^2*d^4))/6 + 3*a*b^2*c*d^2*x*(a^2*d^2 + b^2*c^2))*(3^(1/2)*1i + 1)*(-c/(27*a^3*d^4 - 27*b^3*c^3*d + 81*a*b^2*c^2*d^2 - 81*a^2*b*c*d^3))^(1/3))/2","B"
113,1,602,45,0.257496,"\text{Not used}","int(x^2/((a + b*x^3)*(c + d*x^3)),x)","-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{x^3\,\left(36\,c\,b^4\,d^3+36\,a\,b^3\,d^4\right)+\frac{x^3\,\left(54\,a^2\,b^3\,d^5+108\,a\,b^4\,c\,d^4+54\,b^5\,c^2\,d^3\right)+108\,a\,b^4\,c^2\,d^3+108\,a^2\,b^3\,c\,d^4}{3\,a\,d-3\,b\,c}+36\,a\,b^3\,c\,d^3}{3\,a\,d-3\,b\,c}+6\,b^3\,d^3\,x^3\right)\,1{}\mathrm{i}}{3\,a\,d-3\,b\,c}-\frac{\left(\frac{x^3\,\left(36\,c\,b^4\,d^3+36\,a\,b^3\,d^4\right)-\frac{x^3\,\left(54\,a^2\,b^3\,d^5+108\,a\,b^4\,c\,d^4+54\,b^5\,c^2\,d^3\right)+108\,a\,b^4\,c^2\,d^3+108\,a^2\,b^3\,c\,d^4}{3\,a\,d-3\,b\,c}+36\,a\,b^3\,c\,d^3}{3\,a\,d-3\,b\,c}-6\,b^3\,d^3\,x^3\right)\,1{}\mathrm{i}}{3\,a\,d-3\,b\,c}}{\frac{\frac{x^3\,\left(36\,c\,b^4\,d^3+36\,a\,b^3\,d^4\right)+\frac{x^3\,\left(54\,a^2\,b^3\,d^5+108\,a\,b^4\,c\,d^4+54\,b^5\,c^2\,d^3\right)+108\,a\,b^4\,c^2\,d^3+108\,a^2\,b^3\,c\,d^4}{3\,a\,d-3\,b\,c}+36\,a\,b^3\,c\,d^3}{3\,a\,d-3\,b\,c}+6\,b^3\,d^3\,x^3}{3\,a\,d-3\,b\,c}+\frac{\frac{x^3\,\left(36\,c\,b^4\,d^3+36\,a\,b^3\,d^4\right)-\frac{x^3\,\left(54\,a^2\,b^3\,d^5+108\,a\,b^4\,c\,d^4+54\,b^5\,c^2\,d^3\right)+108\,a\,b^4\,c^2\,d^3+108\,a^2\,b^3\,c\,d^4}{3\,a\,d-3\,b\,c}+36\,a\,b^3\,c\,d^3}{3\,a\,d-3\,b\,c}-6\,b^3\,d^3\,x^3}{3\,a\,d-3\,b\,c}}\right)\,2{}\mathrm{i}}{3\,a\,d-3\,b\,c}","Not used",1,"-(atan(((((x^3*(36*a*b^3*d^4 + 36*b^4*c*d^3) + (x^3*(54*a^2*b^3*d^5 + 54*b^5*c^2*d^3 + 108*a*b^4*c*d^4) + 108*a*b^4*c^2*d^3 + 108*a^2*b^3*c*d^4)/(3*a*d - 3*b*c) + 36*a*b^3*c*d^3)/(3*a*d - 3*b*c) + 6*b^3*d^3*x^3)*1i)/(3*a*d - 3*b*c) - (((x^3*(36*a*b^3*d^4 + 36*b^4*c*d^3) - (x^3*(54*a^2*b^3*d^5 + 54*b^5*c^2*d^3 + 108*a*b^4*c*d^4) + 108*a*b^4*c^2*d^3 + 108*a^2*b^3*c*d^4)/(3*a*d - 3*b*c) + 36*a*b^3*c*d^3)/(3*a*d - 3*b*c) - 6*b^3*d^3*x^3)*1i)/(3*a*d - 3*b*c))/(((x^3*(36*a*b^3*d^4 + 36*b^4*c*d^3) + (x^3*(54*a^2*b^3*d^5 + 54*b^5*c^2*d^3 + 108*a*b^4*c*d^4) + 108*a*b^4*c^2*d^3 + 108*a^2*b^3*c*d^4)/(3*a*d - 3*b*c) + 36*a*b^3*c*d^3)/(3*a*d - 3*b*c) + 6*b^3*d^3*x^3)/(3*a*d - 3*b*c) + ((x^3*(36*a*b^3*d^4 + 36*b^4*c*d^3) - (x^3*(54*a^2*b^3*d^5 + 54*b^5*c^2*d^3 + 108*a*b^4*c*d^4) + 108*a*b^4*c^2*d^3 + 108*a^2*b^3*c*d^4)/(3*a*d - 3*b*c) + 36*a*b^3*c*d^3)/(3*a*d - 3*b*c) - 6*b^3*d^3*x^3)/(3*a*d - 3*b*c)))*2i)/(3*a*d - 3*b*c)","B"
114,1,982,288,5.415144,"\text{Not used}","int(x/((a + b*x^3)*(c + d*x^3)),x)","\ln\left(b\,x+a^3\,d^2\,{\left(\frac{b}{a\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}+a\,b^2\,c^2\,{\left(\frac{b}{a\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}-2\,a^2\,b\,c\,d\,{\left(\frac{b}{a\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}\right)\,{\left(\frac{b}{27\,a^4\,d^3-81\,a^3\,b\,c\,d^2+81\,a^2\,b^2\,c^2\,d-27\,a\,b^3\,c^3}\right)}^{1/3}+\ln\left(d\,x+b^2\,c^3\,{\left(-\frac{d}{c\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}+a^2\,c\,d^2\,{\left(-\frac{d}{c\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}-2\,a\,b\,c^2\,d\,{\left(-\frac{d}{c\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}\right)\,{\left(\frac{d}{-27\,a^3\,c\,d^3+81\,a^2\,b\,c^2\,d^2-81\,a\,b^2\,c^3\,d+27\,b^3\,c^4}\right)}^{1/3}+\frac{\ln\left(b^4\,d^4\,x-\frac{b\,{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^3\,\left(27\,b^3\,d^3\,x\,\left(a^2\,d^2+b^2\,c^2\right)\,{\left(a\,d-b\,c\right)}^2+\frac{27\,a\,b^3\,c\,d^3\,{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(\frac{b}{a\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}}{4}\right)}{216\,a\,{\left(a\,d-b\,c\right)}^3}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(\frac{b}{27\,a^4\,d^3-81\,a^3\,b\,c\,d^2+81\,a^2\,b^2\,c^2\,d-27\,a\,b^3\,c^3}\right)}^{1/3}}{2}-\frac{\ln\left(b^4\,d^4\,x+\frac{b\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^3\,\left(27\,b^3\,d^3\,x\,\left(a^2\,d^2+b^2\,c^2\right)\,{\left(a\,d-b\,c\right)}^2+\frac{27\,a\,b^3\,c\,d^3\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(\frac{b}{a\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}}{4}\right)}{216\,a\,{\left(a\,d-b\,c\right)}^3}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(\frac{b}{27\,a^4\,d^3-81\,a^3\,b\,c\,d^2+81\,a^2\,b^2\,c^2\,d-27\,a\,b^3\,c^3}\right)}^{1/3}}{2}+\frac{\ln\left(b^4\,d^4\,x+\frac{d\,{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^3\,\left(27\,b^3\,d^3\,x\,\left(a^2\,d^2+b^2\,c^2\right)\,{\left(a\,d-b\,c\right)}^2+\frac{27\,a\,b^3\,c\,d^3\,{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(-\frac{d}{c\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}}{4}\right)}{216\,c\,{\left(a\,d-b\,c\right)}^3}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(\frac{d}{-27\,a^3\,c\,d^3+81\,a^2\,b\,c^2\,d^2-81\,a\,b^2\,c^3\,d+27\,b^3\,c^4}\right)}^{1/3}}{2}-\frac{\ln\left(b^4\,d^4\,x-\frac{d\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^3\,\left(27\,b^3\,d^3\,x\,\left(a^2\,d^2+b^2\,c^2\right)\,{\left(a\,d-b\,c\right)}^2+\frac{27\,a\,b^3\,c\,d^3\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(-\frac{d}{c\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}}{4}\right)}{216\,c\,{\left(a\,d-b\,c\right)}^3}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(\frac{d}{-27\,a^3\,c\,d^3+81\,a^2\,b\,c^2\,d^2-81\,a\,b^2\,c^3\,d+27\,b^3\,c^4}\right)}^{1/3}}{2}","Not used",1,"log(b*x + a^3*d^2*(b/(a*(a*d - b*c)^3))^(2/3) + a*b^2*c^2*(b/(a*(a*d - b*c)^3))^(2/3) - 2*a^2*b*c*d*(b/(a*(a*d - b*c)^3))^(2/3))*(b/(27*a^4*d^3 - 27*a*b^3*c^3 + 81*a^2*b^2*c^2*d - 81*a^3*b*c*d^2))^(1/3) + log(d*x + b^2*c^3*(-d/(c*(a*d - b*c)^3))^(2/3) + a^2*c*d^2*(-d/(c*(a*d - b*c)^3))^(2/3) - 2*a*b*c^2*d*(-d/(c*(a*d - b*c)^3))^(2/3))*(d/(27*b^3*c^4 - 27*a^3*c*d^3 + 81*a^2*b*c^2*d^2 - 81*a*b^2*c^3*d))^(1/3) + (log(b^4*d^4*x - (b*(3^(1/2)*1i - 1)^3*(27*b^3*d^3*x*(a^2*d^2 + b^2*c^2)*(a*d - b*c)^2 + (27*a*b^3*c*d^3*(3^(1/2)*1i - 1)^2*(a*d + b*c)*(a*d - b*c)^4*(b/(a*(a*d - b*c)^3))^(2/3))/4))/(216*a*(a*d - b*c)^3))*(3^(1/2)*1i - 1)*(b/(27*a^4*d^3 - 27*a*b^3*c^3 + 81*a^2*b^2*c^2*d - 81*a^3*b*c*d^2))^(1/3))/2 - (log(b^4*d^4*x + (b*(3^(1/2)*1i + 1)^3*(27*b^3*d^3*x*(a^2*d^2 + b^2*c^2)*(a*d - b*c)^2 + (27*a*b^3*c*d^3*(3^(1/2)*1i + 1)^2*(a*d + b*c)*(a*d - b*c)^4*(b/(a*(a*d - b*c)^3))^(2/3))/4))/(216*a*(a*d - b*c)^3))*(3^(1/2)*1i + 1)*(b/(27*a^4*d^3 - 27*a*b^3*c^3 + 81*a^2*b^2*c^2*d - 81*a^3*b*c*d^2))^(1/3))/2 + (log(b^4*d^4*x + (d*(3^(1/2)*1i - 1)^3*(27*b^3*d^3*x*(a^2*d^2 + b^2*c^2)*(a*d - b*c)^2 + (27*a*b^3*c*d^3*(3^(1/2)*1i - 1)^2*(a*d + b*c)*(a*d - b*c)^4*(-d/(c*(a*d - b*c)^3))^(2/3))/4))/(216*c*(a*d - b*c)^3))*(3^(1/2)*1i - 1)*(d/(27*b^3*c^4 - 27*a^3*c*d^3 + 81*a^2*b*c^2*d^2 - 81*a*b^2*c^3*d))^(1/3))/2 - (log(b^4*d^4*x - (d*(3^(1/2)*1i + 1)^3*(27*b^3*d^3*x*(a^2*d^2 + b^2*c^2)*(a*d - b*c)^2 + (27*a*b^3*c*d^3*(3^(1/2)*1i + 1)^2*(a*d + b*c)*(a*d - b*c)^4*(-d/(c*(a*d - b*c)^3))^(2/3))/4))/(216*c*(a*d - b*c)^3))*(3^(1/2)*1i + 1)*(d/(27*b^3*c^4 - 27*a^3*c*d^3 + 81*a^2*b*c^2*d^2 - 81*a*b^2*c^3*d))^(1/3))/2","B"
115,1,1364,288,9.007166,"\text{Not used}","int(1/((a + b*x^3)*(c + d*x^3)),x)","\ln\left(\frac{{\left(-\frac{b^2}{a^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}\,\left(9\,a^2\,b^4\,d^6+9\,b^6\,c^2\,d^4-18\,a\,b^5\,c\,d^5-9\,b^3\,d^3\,\left(x+a\,c\,{\left(-\frac{b^2}{a^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}\right)\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(-\frac{b^2}{a^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}\right)}{3}-6\,b^5\,d^5\,x\right)\,{\left(-\frac{b^2}{27\,a^5\,d^3-81\,a^4\,b\,c\,d^2+81\,a^3\,b^2\,c^2\,d-27\,a^2\,b^3\,c^3}\right)}^{1/3}+\ln\left(\frac{{\left(\frac{d^2}{c^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}\,\left(9\,a^2\,b^4\,d^6+9\,b^6\,c^2\,d^4-18\,a\,b^5\,c\,d^5-9\,b^3\,d^3\,\left(x+a\,c\,{\left(\frac{d^2}{c^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}\right)\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(\frac{d^2}{c^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}\right)}{3}-6\,b^5\,d^5\,x\right)\,{\left(-\frac{d^2}{-27\,a^3\,c^2\,d^3+81\,a^2\,b\,c^3\,d^2-81\,a\,b^2\,c^4\,d+27\,b^3\,c^5}\right)}^{1/3}+\frac{\ln\left(6\,b^5\,d^5\,x+\frac{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(-\frac{b^2}{a^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}\,\left(\frac{{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(81\,b^3\,d^3\,x\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4+\frac{81\,a\,b^3\,c\,d^3\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(-\frac{b^2}{a^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}}{2}\right)\,{\left(-\frac{b^2}{a^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}}{36}-9\,a^2\,b^4\,d^6-9\,b^6\,c^2\,d^4+18\,a\,b^5\,c\,d^5\right)}{6}\right)\,{\left(-\frac{b^2}{27\,a^5\,d^3-81\,a^4\,b\,c\,d^2+81\,a^3\,b^2\,c^2\,d-27\,a^2\,b^3\,c^3}\right)}^{1/3}\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}-\frac{\ln\left(6\,b^5\,d^5\,x-\frac{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(-\frac{b^2}{a^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}\,\left(\frac{{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(81\,b^3\,d^3\,x\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4-\frac{81\,a\,b^3\,c\,d^3\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(-\frac{b^2}{a^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}}{2}\right)\,{\left(-\frac{b^2}{a^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}}{36}-9\,a^2\,b^4\,d^6-9\,b^6\,c^2\,d^4+18\,a\,b^5\,c\,d^5\right)}{6}\right)\,{\left(-\frac{b^2}{27\,a^5\,d^3-81\,a^4\,b\,c\,d^2+81\,a^3\,b^2\,c^2\,d-27\,a^2\,b^3\,c^3}\right)}^{1/3}\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}+\frac{\ln\left(6\,b^5\,d^5\,x+\frac{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(\frac{d^2}{c^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}\,\left(\frac{{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(81\,b^3\,d^3\,x\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4+\frac{81\,a\,b^3\,c\,d^3\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(\frac{d^2}{c^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}}{2}\right)\,{\left(\frac{d^2}{c^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}}{36}-9\,a^2\,b^4\,d^6-9\,b^6\,c^2\,d^4+18\,a\,b^5\,c\,d^5\right)}{6}\right)\,{\left(-\frac{d^2}{-27\,a^3\,c^2\,d^3+81\,a^2\,b\,c^3\,d^2-81\,a\,b^2\,c^4\,d+27\,b^3\,c^5}\right)}^{1/3}\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}-\frac{\ln\left(6\,b^5\,d^5\,x-\frac{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(\frac{d^2}{c^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}\,\left(\frac{{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(81\,b^3\,d^3\,x\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4-\frac{81\,a\,b^3\,c\,d^3\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(\frac{d^2}{c^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}}{2}\right)\,{\left(\frac{d^2}{c^2\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}}{36}-9\,a^2\,b^4\,d^6-9\,b^6\,c^2\,d^4+18\,a\,b^5\,c\,d^5\right)}{6}\right)\,{\left(-\frac{d^2}{-27\,a^3\,c^2\,d^3+81\,a^2\,b\,c^3\,d^2-81\,a\,b^2\,c^4\,d+27\,b^3\,c^5}\right)}^{1/3}\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}","Not used",1,"log(((-b^2/(a^2*(a*d - b*c)^3))^(1/3)*(9*a^2*b^4*d^6 + 9*b^6*c^2*d^4 - 18*a*b^5*c*d^5 - 9*b^3*d^3*(x + a*c*(-b^2/(a^2*(a*d - b*c)^3))^(1/3))*(a*d + b*c)*(a*d - b*c)^4*(-b^2/(a^2*(a*d - b*c)^3))^(2/3)))/3 - 6*b^5*d^5*x)*(-b^2/(27*a^5*d^3 - 27*a^2*b^3*c^3 + 81*a^3*b^2*c^2*d - 81*a^4*b*c*d^2))^(1/3) + log(((d^2/(c^2*(a*d - b*c)^3))^(1/3)*(9*a^2*b^4*d^6 + 9*b^6*c^2*d^4 - 18*a*b^5*c*d^5 - 9*b^3*d^3*(x + a*c*(d^2/(c^2*(a*d - b*c)^3))^(1/3))*(a*d + b*c)*(a*d - b*c)^4*(d^2/(c^2*(a*d - b*c)^3))^(2/3)))/3 - 6*b^5*d^5*x)*(-d^2/(27*b^3*c^5 - 27*a^3*c^2*d^3 + 81*a^2*b*c^3*d^2 - 81*a*b^2*c^4*d))^(1/3) + (log(6*b^5*d^5*x + ((3^(1/2)*1i - 1)*(-b^2/(a^2*(a*d - b*c)^3))^(1/3)*(((3^(1/2)*1i - 1)^2*(81*b^3*d^3*x*(a*d + b*c)*(a*d - b*c)^4 + (81*a*b^3*c*d^3*(3^(1/2)*1i - 1)*(a*d + b*c)*(a*d - b*c)^4*(-b^2/(a^2*(a*d - b*c)^3))^(1/3))/2)*(-b^2/(a^2*(a*d - b*c)^3))^(2/3))/36 - 9*a^2*b^4*d^6 - 9*b^6*c^2*d^4 + 18*a*b^5*c*d^5))/6)*(-b^2/(27*a^5*d^3 - 27*a^2*b^3*c^3 + 81*a^3*b^2*c^2*d - 81*a^4*b*c*d^2))^(1/3)*(3^(1/2)*1i - 1))/2 - (log(6*b^5*d^5*x - ((3^(1/2)*1i + 1)*(-b^2/(a^2*(a*d - b*c)^3))^(1/3)*(((3^(1/2)*1i + 1)^2*(81*b^3*d^3*x*(a*d + b*c)*(a*d - b*c)^4 - (81*a*b^3*c*d^3*(3^(1/2)*1i + 1)*(a*d + b*c)*(a*d - b*c)^4*(-b^2/(a^2*(a*d - b*c)^3))^(1/3))/2)*(-b^2/(a^2*(a*d - b*c)^3))^(2/3))/36 - 9*a^2*b^4*d^6 - 9*b^6*c^2*d^4 + 18*a*b^5*c*d^5))/6)*(-b^2/(27*a^5*d^3 - 27*a^2*b^3*c^3 + 81*a^3*b^2*c^2*d - 81*a^4*b*c*d^2))^(1/3)*(3^(1/2)*1i + 1))/2 + (log(6*b^5*d^5*x + ((3^(1/2)*1i - 1)*(d^2/(c^2*(a*d - b*c)^3))^(1/3)*(((3^(1/2)*1i - 1)^2*(81*b^3*d^3*x*(a*d + b*c)*(a*d - b*c)^4 + (81*a*b^3*c*d^3*(3^(1/2)*1i - 1)*(a*d + b*c)*(a*d - b*c)^4*(d^2/(c^2*(a*d - b*c)^3))^(1/3))/2)*(d^2/(c^2*(a*d - b*c)^3))^(2/3))/36 - 9*a^2*b^4*d^6 - 9*b^6*c^2*d^4 + 18*a*b^5*c*d^5))/6)*(-d^2/(27*b^3*c^5 - 27*a^3*c^2*d^3 + 81*a^2*b*c^3*d^2 - 81*a*b^2*c^4*d))^(1/3)*(3^(1/2)*1i - 1))/2 - (log(6*b^5*d^5*x - ((3^(1/2)*1i + 1)*(d^2/(c^2*(a*d - b*c)^3))^(1/3)*(((3^(1/2)*1i + 1)^2*(81*b^3*d^3*x*(a*d + b*c)*(a*d - b*c)^4 - (81*a*b^3*c*d^3*(3^(1/2)*1i + 1)*(a*d + b*c)*(a*d - b*c)^4*(d^2/(c^2*(a*d - b*c)^3))^(1/3))/2)*(d^2/(c^2*(a*d - b*c)^3))^(2/3))/36 - 9*a^2*b^4*d^6 - 9*b^6*c^2*d^4 + 18*a*b^5*c*d^5))/6)*(-d^2/(27*b^3*c^5 - 27*a^3*c^2*d^3 + 81*a^2*b*c^3*d^2 - 81*a*b^2*c^4*d))^(1/3)*(3^(1/2)*1i + 1))/2","B"
116,1,58,62,2.840462,"\text{Not used}","int(1/(x*(a + b*x^3)*(c + d*x^3)),x)","\frac{b\,\ln\left(b\,x^3+a\right)}{3\,a^2\,d-3\,a\,b\,c}+\frac{d\,\ln\left(d\,x^3+c\right)}{3\,b\,c^2-3\,a\,c\,d}+\frac{\ln\left(x\right)}{a\,c}","Not used",1,"(b*log(a + b*x^3))/(3*a^2*d - 3*a*b*c) + (d*log(c + d*x^3))/(3*b*c^2 - 3*a*c*d) + log(x)/(a*c)","B"
117,1,716,299,3.854122,"\text{Not used}","int(1/(x^2*(a + b*x^3)*(c + d*x^3)),x)","\ln\left(b-a^2\,d\,x\,{\left(-\frac{b^4}{a^4\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}+a\,b\,c\,x\,{\left(-\frac{b^4}{a^4\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}\right)\,{\left(-\frac{b^4}{27\,a^7\,d^3-81\,a^6\,b\,c\,d^2+81\,a^5\,b^2\,c^2\,d-27\,a^4\,b^3\,c^3}\right)}^{1/3}+\ln\left(d-b\,c^2\,x\,{\left(\frac{d^4}{c^4\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}+a\,c\,d\,x\,{\left(\frac{d^4}{c^4\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}\right)\,{\left(-\frac{d^4}{-27\,a^3\,c^4\,d^3+81\,a^2\,b\,c^5\,d^2-81\,a\,b^2\,c^6\,d+27\,b^3\,c^7}\right)}^{1/3}-\frac{1}{a\,c\,x}-\frac{\ln\left(b+2\,a^2\,d\,x\,{\left(-\frac{b^4}{a^4\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}-2\,a\,b\,c\,x\,{\left(-\frac{b^4}{a^4\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}-\sqrt{3}\,b\,1{}\mathrm{i}\right)\,{\left(-\frac{b^4}{27\,a^7\,d^3-81\,a^6\,b\,c\,d^2+81\,a^5\,b^2\,c^2\,d-27\,a^4\,b^3\,c^3}\right)}^{1/3}\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}+\frac{\ln\left(b+2\,a^2\,d\,x\,{\left(-\frac{b^4}{a^4\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}-2\,a\,b\,c\,x\,{\left(-\frac{b^4}{a^4\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}+\sqrt{3}\,b\,1{}\mathrm{i}\right)\,{\left(-\frac{b^4}{27\,a^7\,d^3-81\,a^6\,b\,c\,d^2+81\,a^5\,b^2\,c^2\,d-27\,a^4\,b^3\,c^3}\right)}^{1/3}\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}-\frac{\ln\left(d+2\,b\,c^2\,x\,{\left(\frac{d^4}{c^4\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}-2\,a\,c\,d\,x\,{\left(\frac{d^4}{c^4\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}-\sqrt{3}\,d\,1{}\mathrm{i}\right)\,{\left(-\frac{d^4}{-27\,a^3\,c^4\,d^3+81\,a^2\,b\,c^5\,d^2-81\,a\,b^2\,c^6\,d+27\,b^3\,c^7}\right)}^{1/3}\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}+\frac{\ln\left(d+2\,b\,c^2\,x\,{\left(\frac{d^4}{c^4\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}-2\,a\,c\,d\,x\,{\left(\frac{d^4}{c^4\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}+\sqrt{3}\,d\,1{}\mathrm{i}\right)\,{\left(-\frac{d^4}{-27\,a^3\,c^4\,d^3+81\,a^2\,b\,c^5\,d^2-81\,a\,b^2\,c^6\,d+27\,b^3\,c^7}\right)}^{1/3}\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}","Not used",1,"log(b - a^2*d*x*(-b^4/(a^4*(a*d - b*c)^3))^(1/3) + a*b*c*x*(-b^4/(a^4*(a*d - b*c)^3))^(1/3))*(-b^4/(27*a^7*d^3 - 27*a^4*b^3*c^3 + 81*a^5*b^2*c^2*d - 81*a^6*b*c*d^2))^(1/3) + log(d - b*c^2*x*(d^4/(c^4*(a*d - b*c)^3))^(1/3) + a*c*d*x*(d^4/(c^4*(a*d - b*c)^3))^(1/3))*(-d^4/(27*b^3*c^7 - 27*a^3*c^4*d^3 + 81*a^2*b*c^5*d^2 - 81*a*b^2*c^6*d))^(1/3) - 1/(a*c*x) - (log(b - 3^(1/2)*b*1i + 2*a^2*d*x*(-b^4/(a^4*(a*d - b*c)^3))^(1/3) - 2*a*b*c*x*(-b^4/(a^4*(a*d - b*c)^3))^(1/3))*(-b^4/(27*a^7*d^3 - 27*a^4*b^3*c^3 + 81*a^5*b^2*c^2*d - 81*a^6*b*c*d^2))^(1/3)*(3^(1/2)*1i + 1))/2 + (log(b + 3^(1/2)*b*1i + 2*a^2*d*x*(-b^4/(a^4*(a*d - b*c)^3))^(1/3) - 2*a*b*c*x*(-b^4/(a^4*(a*d - b*c)^3))^(1/3))*(-b^4/(27*a^7*d^3 - 27*a^4*b^3*c^3 + 81*a^5*b^2*c^2*d - 81*a^6*b*c*d^2))^(1/3)*(3^(1/2)*1i - 1))/2 - (log(d - 3^(1/2)*d*1i + 2*b*c^2*x*(d^4/(c^4*(a*d - b*c)^3))^(1/3) - 2*a*c*d*x*(d^4/(c^4*(a*d - b*c)^3))^(1/3))*(-d^4/(27*b^3*c^7 - 27*a^3*c^4*d^3 + 81*a^2*b*c^5*d^2 - 81*a*b^2*c^6*d))^(1/3)*(3^(1/2)*1i + 1))/2 + (log(d + 3^(1/2)*d*1i + 2*b*c^2*x*(d^4/(c^4*(a*d - b*c)^3))^(1/3) - 2*a*c*d*x*(d^4/(c^4*(a*d - b*c)^3))^(1/3))*(-d^4/(27*b^3*c^7 - 27*a^3*c^4*d^3 + 81*a^2*b*c^5*d^2 - 81*a*b^2*c^6*d))^(1/3)*(3^(1/2)*1i - 1))/2","B"
118,1,1829,301,11.834160,"\text{Not used}","int(1/(x^3*(a + b*x^3)*(c + d*x^3)),x)","\ln\left(\frac{{\left(\frac{b^5}{a^5\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}\,\left(\frac{\left(81\,a^{10}\,b^3\,c^{10}\,d^3\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(\frac{b^5}{a^5\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}-81\,a^8\,b^3\,c^8\,d^3\,x\,{\left(a\,d-b\,c\right)}^4\,\left(a^2\,d^2+a\,b\,c\,d+b^2\,c^2\right)\right)\,{\left(\frac{b^5}{a^5\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}}{9}+9\,a^6\,b^9\,c^{11}\,d^4-9\,a^7\,b^8\,c^{10}\,d^5-9\,a^{10}\,b^5\,c^7\,d^8+9\,a^{11}\,b^4\,c^6\,d^9\right)}{3}+3\,a^6\,b^6\,c^6\,d^6\,x\,\left(a^2\,d^2+b^2\,c^2\right)\right)\,{\left(\frac{b^5}{27\,a^8\,d^3-81\,a^7\,b\,c\,d^2+81\,a^6\,b^2\,c^2\,d-27\,a^5\,b^3\,c^3}\right)}^{1/3}+\ln\left(\frac{{\left(-\frac{d^5}{c^5\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}\,\left(\frac{\left(81\,a^{10}\,b^3\,c^{10}\,d^3\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(-\frac{d^5}{c^5\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}-81\,a^8\,b^3\,c^8\,d^3\,x\,{\left(a\,d-b\,c\right)}^4\,\left(a^2\,d^2+a\,b\,c\,d+b^2\,c^2\right)\right)\,{\left(-\frac{d^5}{c^5\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}}{9}+9\,a^6\,b^9\,c^{11}\,d^4-9\,a^7\,b^8\,c^{10}\,d^5-9\,a^{10}\,b^5\,c^7\,d^8+9\,a^{11}\,b^4\,c^6\,d^9\right)}{3}+3\,a^6\,b^6\,c^6\,d^6\,x\,\left(a^2\,d^2+b^2\,c^2\right)\right)\,{\left(\frac{d^5}{-27\,a^3\,c^5\,d^3+81\,a^2\,b\,c^6\,d^2-81\,a\,b^2\,c^7\,d+27\,b^3\,c^8}\right)}^{1/3}+\frac{\ln\left(\frac{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(\frac{b^5}{a^5\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}\,\left(\frac{{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(81\,a^8\,b^3\,c^8\,d^3\,x\,{\left(a\,d-b\,c\right)}^4\,\left(a^2\,d^2+a\,b\,c\,d+b^2\,c^2\right)-\frac{81\,a^{10}\,b^3\,c^{10}\,d^3\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(\frac{b^5}{a^5\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}}{2}\right)\,{\left(\frac{b^5}{a^5\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}}{36}-9\,a^6\,b^9\,c^{11}\,d^4+9\,a^7\,b^8\,c^{10}\,d^5+9\,a^{10}\,b^5\,c^7\,d^8-9\,a^{11}\,b^4\,c^6\,d^9\right)}{6}-3\,a^6\,b^6\,c^6\,d^6\,x\,\left(a^2\,d^2+b^2\,c^2\right)\right)\,{\left(\frac{b^5}{27\,a^8\,d^3-81\,a^7\,b\,c\,d^2+81\,a^6\,b^2\,c^2\,d-27\,a^5\,b^3\,c^3}\right)}^{1/3}\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}-\frac{\ln\left(\frac{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(\frac{b^5}{a^5\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}\,\left(\frac{{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(81\,a^8\,b^3\,c^8\,d^3\,x\,{\left(a\,d-b\,c\right)}^4\,\left(a^2\,d^2+a\,b\,c\,d+b^2\,c^2\right)+\frac{81\,a^{10}\,b^3\,c^{10}\,d^3\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(\frac{b^5}{a^5\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}}{2}\right)\,{\left(\frac{b^5}{a^5\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}}{36}-9\,a^6\,b^9\,c^{11}\,d^4+9\,a^7\,b^8\,c^{10}\,d^5+9\,a^{10}\,b^5\,c^7\,d^8-9\,a^{11}\,b^4\,c^6\,d^9\right)}{6}+3\,a^6\,b^6\,c^6\,d^6\,x\,\left(a^2\,d^2+b^2\,c^2\right)\right)\,{\left(\frac{b^5}{27\,a^8\,d^3-81\,a^7\,b\,c\,d^2+81\,a^6\,b^2\,c^2\,d-27\,a^5\,b^3\,c^3}\right)}^{1/3}\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}+\frac{\ln\left(\frac{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(-\frac{d^5}{c^5\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}\,\left(\frac{{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(81\,a^8\,b^3\,c^8\,d^3\,x\,{\left(a\,d-b\,c\right)}^4\,\left(a^2\,d^2+a\,b\,c\,d+b^2\,c^2\right)-\frac{81\,a^{10}\,b^3\,c^{10}\,d^3\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(-\frac{d^5}{c^5\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}}{2}\right)\,{\left(-\frac{d^5}{c^5\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}}{36}-9\,a^6\,b^9\,c^{11}\,d^4+9\,a^7\,b^8\,c^{10}\,d^5+9\,a^{10}\,b^5\,c^7\,d^8-9\,a^{11}\,b^4\,c^6\,d^9\right)}{6}-3\,a^6\,b^6\,c^6\,d^6\,x\,\left(a^2\,d^2+b^2\,c^2\right)\right)\,{\left(\frac{d^5}{-27\,a^3\,c^5\,d^3+81\,a^2\,b\,c^6\,d^2-81\,a\,b^2\,c^7\,d+27\,b^3\,c^8}\right)}^{1/3}\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}-\frac{\ln\left(\frac{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(-\frac{d^5}{c^5\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}\,\left(\frac{{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(81\,a^8\,b^3\,c^8\,d^3\,x\,{\left(a\,d-b\,c\right)}^4\,\left(a^2\,d^2+a\,b\,c\,d+b^2\,c^2\right)+\frac{81\,a^{10}\,b^3\,c^{10}\,d^3\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(-\frac{d^5}{c^5\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}}{2}\right)\,{\left(-\frac{d^5}{c^5\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}}{36}-9\,a^6\,b^9\,c^{11}\,d^4+9\,a^7\,b^8\,c^{10}\,d^5+9\,a^{10}\,b^5\,c^7\,d^8-9\,a^{11}\,b^4\,c^6\,d^9\right)}{6}+3\,a^6\,b^6\,c^6\,d^6\,x\,\left(a^2\,d^2+b^2\,c^2\right)\right)\,{\left(\frac{d^5}{-27\,a^3\,c^5\,d^3+81\,a^2\,b\,c^6\,d^2-81\,a\,b^2\,c^7\,d+27\,b^3\,c^8}\right)}^{1/3}\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}-\frac{1}{2\,a\,c\,x^2}","Not used",1,"log(((b^5/(a^5*(a*d - b*c)^3))^(1/3)*(((81*a^10*b^3*c^10*d^3*(a*d + b*c)*(a*d - b*c)^4*(b^5/(a^5*(a*d - b*c)^3))^(1/3) - 81*a^8*b^3*c^8*d^3*x*(a*d - b*c)^4*(a^2*d^2 + b^2*c^2 + a*b*c*d))*(b^5/(a^5*(a*d - b*c)^3))^(2/3))/9 + 9*a^6*b^9*c^11*d^4 - 9*a^7*b^8*c^10*d^5 - 9*a^10*b^5*c^7*d^8 + 9*a^11*b^4*c^6*d^9))/3 + 3*a^6*b^6*c^6*d^6*x*(a^2*d^2 + b^2*c^2))*(b^5/(27*a^8*d^3 - 27*a^5*b^3*c^3 + 81*a^6*b^2*c^2*d - 81*a^7*b*c*d^2))^(1/3) + log(((-d^5/(c^5*(a*d - b*c)^3))^(1/3)*(((81*a^10*b^3*c^10*d^3*(a*d + b*c)*(a*d - b*c)^4*(-d^5/(c^5*(a*d - b*c)^3))^(1/3) - 81*a^8*b^3*c^8*d^3*x*(a*d - b*c)^4*(a^2*d^2 + b^2*c^2 + a*b*c*d))*(-d^5/(c^5*(a*d - b*c)^3))^(2/3))/9 + 9*a^6*b^9*c^11*d^4 - 9*a^7*b^8*c^10*d^5 - 9*a^10*b^5*c^7*d^8 + 9*a^11*b^4*c^6*d^9))/3 + 3*a^6*b^6*c^6*d^6*x*(a^2*d^2 + b^2*c^2))*(d^5/(27*b^3*c^8 - 27*a^3*c^5*d^3 + 81*a^2*b*c^6*d^2 - 81*a*b^2*c^7*d))^(1/3) + (log(((3^(1/2)*1i - 1)*(b^5/(a^5*(a*d - b*c)^3))^(1/3)*(((3^(1/2)*1i - 1)^2*(81*a^8*b^3*c^8*d^3*x*(a*d - b*c)^4*(a^2*d^2 + b^2*c^2 + a*b*c*d) - (81*a^10*b^3*c^10*d^3*(3^(1/2)*1i - 1)*(a*d + b*c)*(a*d - b*c)^4*(b^5/(a^5*(a*d - b*c)^3))^(1/3))/2)*(b^5/(a^5*(a*d - b*c)^3))^(2/3))/36 - 9*a^6*b^9*c^11*d^4 + 9*a^7*b^8*c^10*d^5 + 9*a^10*b^5*c^7*d^8 - 9*a^11*b^4*c^6*d^9))/6 - 3*a^6*b^6*c^6*d^6*x*(a^2*d^2 + b^2*c^2))*(b^5/(27*a^8*d^3 - 27*a^5*b^3*c^3 + 81*a^6*b^2*c^2*d - 81*a^7*b*c*d^2))^(1/3)*(3^(1/2)*1i - 1))/2 - (log(((3^(1/2)*1i + 1)*(b^5/(a^5*(a*d - b*c)^3))^(1/3)*(((3^(1/2)*1i + 1)^2*(81*a^8*b^3*c^8*d^3*x*(a*d - b*c)^4*(a^2*d^2 + b^2*c^2 + a*b*c*d) + (81*a^10*b^3*c^10*d^3*(3^(1/2)*1i + 1)*(a*d + b*c)*(a*d - b*c)^4*(b^5/(a^5*(a*d - b*c)^3))^(1/3))/2)*(b^5/(a^5*(a*d - b*c)^3))^(2/3))/36 - 9*a^6*b^9*c^11*d^4 + 9*a^7*b^8*c^10*d^5 + 9*a^10*b^5*c^7*d^8 - 9*a^11*b^4*c^6*d^9))/6 + 3*a^6*b^6*c^6*d^6*x*(a^2*d^2 + b^2*c^2))*(b^5/(27*a^8*d^3 - 27*a^5*b^3*c^3 + 81*a^6*b^2*c^2*d - 81*a^7*b*c*d^2))^(1/3)*(3^(1/2)*1i + 1))/2 + (log(((3^(1/2)*1i - 1)*(-d^5/(c^5*(a*d - b*c)^3))^(1/3)*(((3^(1/2)*1i - 1)^2*(81*a^8*b^3*c^8*d^3*x*(a*d - b*c)^4*(a^2*d^2 + b^2*c^2 + a*b*c*d) - (81*a^10*b^3*c^10*d^3*(3^(1/2)*1i - 1)*(a*d + b*c)*(a*d - b*c)^4*(-d^5/(c^5*(a*d - b*c)^3))^(1/3))/2)*(-d^5/(c^5*(a*d - b*c)^3))^(2/3))/36 - 9*a^6*b^9*c^11*d^4 + 9*a^7*b^8*c^10*d^5 + 9*a^10*b^5*c^7*d^8 - 9*a^11*b^4*c^6*d^9))/6 - 3*a^6*b^6*c^6*d^6*x*(a^2*d^2 + b^2*c^2))*(d^5/(27*b^3*c^8 - 27*a^3*c^5*d^3 + 81*a^2*b*c^6*d^2 - 81*a*b^2*c^7*d))^(1/3)*(3^(1/2)*1i - 1))/2 - (log(((3^(1/2)*1i + 1)*(-d^5/(c^5*(a*d - b*c)^3))^(1/3)*(((3^(1/2)*1i + 1)^2*(81*a^8*b^3*c^8*d^3*x*(a*d - b*c)^4*(a^2*d^2 + b^2*c^2 + a*b*c*d) + (81*a^10*b^3*c^10*d^3*(3^(1/2)*1i + 1)*(a*d + b*c)*(a*d - b*c)^4*(-d^5/(c^5*(a*d - b*c)^3))^(1/3))/2)*(-d^5/(c^5*(a*d - b*c)^3))^(2/3))/36 - 9*a^6*b^9*c^11*d^4 + 9*a^7*b^8*c^10*d^5 + 9*a^10*b^5*c^7*d^8 - 9*a^11*b^4*c^6*d^9))/6 + 3*a^6*b^6*c^6*d^6*x*(a^2*d^2 + b^2*c^2))*(d^5/(27*b^3*c^8 - 27*a^3*c^5*d^3 + 81*a^2*b*c^6*d^2 - 81*a*b^2*c^7*d))^(1/3)*(3^(1/2)*1i + 1))/2 - 1/(2*a*c*x^2)","B"
119,1,87,87,3.222969,"\text{Not used}","int(1/(x^4*(a + b*x^3)*(c + d*x^3)),x)","-\frac{b^2\,\ln\left(b\,x^3+a\right)}{3\,\left(a^3\,d-a^2\,b\,c\right)}-\frac{d^2\,\ln\left(d\,x^3+c\right)}{3\,\left(b\,c^3-a\,c^2\,d\right)}-\frac{1}{3\,a\,c\,x^3}-\frac{\ln\left(x\right)\,\left(a\,d+b\,c\right)}{a^2\,c^2}","Not used",1,"- (b^2*log(a + b*x^3))/(3*(a^3*d - a^2*b*c)) - (d^2*log(c + d*x^3))/(3*(b*c^3 - a*c^2*d)) - 1/(3*a*c*x^3) - (log(x)*(a*d + b*c))/(a^2*c^2)","B"
120,1,1734,318,11.370090,"\text{Not used}","int(1/(x^5*(a + b*x^3)*(c + d*x^3)),x)","\ln\left(\frac{{\left(\frac{b^7}{a^7\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}\,\left(\frac{\left(27\,a^{14}\,b^3\,c^{14}\,d^3\,x\,\left(a^6\,d^6+b^6\,c^6\right)\,{\left(a\,d-b\,c\right)}^2+27\,a^{19}\,b^3\,c^{19}\,d^3\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(\frac{b^7}{a^7\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}\right)\,{\left(\frac{b^7}{a^7\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}}{3}+9\,a^{13}\,b^{11}\,c^{20}\,d^4-9\,a^{14}\,b^{10}\,c^{19}\,d^5-9\,a^{19}\,b^5\,c^{14}\,d^{10}+9\,a^{20}\,b^4\,c^{13}\,d^{11}\right)}{9}+a^{13}\,b^9\,c^{13}\,d^9\,x\right)\,{\left(\frac{b^7}{27\,a^{10}\,d^3-81\,a^9\,b\,c\,d^2+81\,a^8\,b^2\,c^2\,d-27\,a^7\,b^3\,c^3}\right)}^{1/3}+\ln\left(\frac{{\left(-\frac{d^7}{c^7\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}\,\left(\frac{\left(27\,a^{14}\,b^3\,c^{14}\,d^3\,x\,\left(a^6\,d^6+b^6\,c^6\right)\,{\left(a\,d-b\,c\right)}^2+27\,a^{19}\,b^3\,c^{19}\,d^3\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(-\frac{d^7}{c^7\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}\right)\,{\left(-\frac{d^7}{c^7\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}}{3}+9\,a^{13}\,b^{11}\,c^{20}\,d^4-9\,a^{14}\,b^{10}\,c^{19}\,d^5-9\,a^{19}\,b^5\,c^{14}\,d^{10}+9\,a^{20}\,b^4\,c^{13}\,d^{11}\right)}{9}+a^{13}\,b^9\,c^{13}\,d^9\,x\right)\,{\left(\frac{d^7}{-27\,a^3\,c^7\,d^3+81\,a^2\,b\,c^8\,d^2-81\,a\,b^2\,c^9\,d+27\,b^3\,c^{10}}\right)}^{1/3}-\frac{\frac{1}{4\,a\,c}-\frac{x^3\,\left(a\,d+b\,c\right)}{a^2\,c^2}}{x^4}+\frac{\ln\left(\frac{{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,{\left(\frac{b^7}{a^7\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}\,\left(\frac{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(27\,a^{14}\,b^3\,c^{14}\,d^3\,x\,\left(a^6\,d^6+b^6\,c^6\right)\,{\left(a\,d-b\,c\right)}^2+\frac{27\,a^{19}\,b^3\,c^{19}\,d^3\,{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(\frac{b^7}{a^7\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}}{4}\right)\,{\left(\frac{b^7}{a^7\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}}{6}+9\,a^{13}\,b^{11}\,c^{20}\,d^4-9\,a^{14}\,b^{10}\,c^{19}\,d^5-9\,a^{19}\,b^5\,c^{14}\,d^{10}+9\,a^{20}\,b^4\,c^{13}\,d^{11}\right)}{36}+a^{13}\,b^9\,c^{13}\,d^9\,x\right)\,{\left(\frac{b^7}{27\,a^{10}\,d^3-81\,a^9\,b\,c\,d^2+81\,a^8\,b^2\,c^2\,d-27\,a^7\,b^3\,c^3}\right)}^{1/3}\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}-\frac{\ln\left(\frac{{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,{\left(\frac{b^7}{a^7\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}\,\left(\frac{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(27\,a^{14}\,b^3\,c^{14}\,d^3\,x\,\left(a^6\,d^6+b^6\,c^6\right)\,{\left(a\,d-b\,c\right)}^2+\frac{27\,a^{19}\,b^3\,c^{19}\,d^3\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(\frac{b^7}{a^7\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}}{4}\right)\,{\left(\frac{b^7}{a^7\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}}{6}-9\,a^{13}\,b^{11}\,c^{20}\,d^4+9\,a^{14}\,b^{10}\,c^{19}\,d^5+9\,a^{19}\,b^5\,c^{14}\,d^{10}-9\,a^{20}\,b^4\,c^{13}\,d^{11}\right)}{36}-a^{13}\,b^9\,c^{13}\,d^9\,x\right)\,{\left(\frac{b^7}{27\,a^{10}\,d^3-81\,a^9\,b\,c\,d^2+81\,a^8\,b^2\,c^2\,d-27\,a^7\,b^3\,c^3}\right)}^{1/3}\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}+\frac{\ln\left(\frac{{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,{\left(-\frac{d^7}{c^7\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}\,\left(\frac{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(27\,a^{14}\,b^3\,c^{14}\,d^3\,x\,\left(a^6\,d^6+b^6\,c^6\right)\,{\left(a\,d-b\,c\right)}^2+\frac{27\,a^{19}\,b^3\,c^{19}\,d^3\,{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(-\frac{d^7}{c^7\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}}{4}\right)\,{\left(-\frac{d^7}{c^7\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}}{6}+9\,a^{13}\,b^{11}\,c^{20}\,d^4-9\,a^{14}\,b^{10}\,c^{19}\,d^5-9\,a^{19}\,b^5\,c^{14}\,d^{10}+9\,a^{20}\,b^4\,c^{13}\,d^{11}\right)}{36}+a^{13}\,b^9\,c^{13}\,d^9\,x\right)\,{\left(\frac{d^7}{-27\,a^3\,c^7\,d^3+81\,a^2\,b\,c^8\,d^2-81\,a\,b^2\,c^9\,d+27\,b^3\,c^{10}}\right)}^{1/3}\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}-\frac{\ln\left(\frac{{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,{\left(-\frac{d^7}{c^7\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}\,\left(\frac{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(27\,a^{14}\,b^3\,c^{14}\,d^3\,x\,\left(a^6\,d^6+b^6\,c^6\right)\,{\left(a\,d-b\,c\right)}^2+\frac{27\,a^{19}\,b^3\,c^{19}\,d^3\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(-\frac{d^7}{c^7\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}}{4}\right)\,{\left(-\frac{d^7}{c^7\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}}{6}-9\,a^{13}\,b^{11}\,c^{20}\,d^4+9\,a^{14}\,b^{10}\,c^{19}\,d^5+9\,a^{19}\,b^5\,c^{14}\,d^{10}-9\,a^{20}\,b^4\,c^{13}\,d^{11}\right)}{36}-a^{13}\,b^9\,c^{13}\,d^9\,x\right)\,{\left(\frac{d^7}{-27\,a^3\,c^7\,d^3+81\,a^2\,b\,c^8\,d^2-81\,a\,b^2\,c^9\,d+27\,b^3\,c^{10}}\right)}^{1/3}\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}","Not used",1,"log(((b^7/(a^7*(a*d - b*c)^3))^(2/3)*(((27*a^14*b^3*c^14*d^3*x*(a^6*d^6 + b^6*c^6)*(a*d - b*c)^2 + 27*a^19*b^3*c^19*d^3*(a*d + b*c)*(a*d - b*c)^4*(b^7/(a^7*(a*d - b*c)^3))^(2/3))*(b^7/(a^7*(a*d - b*c)^3))^(1/3))/3 + 9*a^13*b^11*c^20*d^4 - 9*a^14*b^10*c^19*d^5 - 9*a^19*b^5*c^14*d^10 + 9*a^20*b^4*c^13*d^11))/9 + a^13*b^9*c^13*d^9*x)*(b^7/(27*a^10*d^3 - 27*a^7*b^3*c^3 + 81*a^8*b^2*c^2*d - 81*a^9*b*c*d^2))^(1/3) + log(((-d^7/(c^7*(a*d - b*c)^3))^(2/3)*(((27*a^14*b^3*c^14*d^3*x*(a^6*d^6 + b^6*c^6)*(a*d - b*c)^2 + 27*a^19*b^3*c^19*d^3*(a*d + b*c)*(a*d - b*c)^4*(-d^7/(c^7*(a*d - b*c)^3))^(2/3))*(-d^7/(c^7*(a*d - b*c)^3))^(1/3))/3 + 9*a^13*b^11*c^20*d^4 - 9*a^14*b^10*c^19*d^5 - 9*a^19*b^5*c^14*d^10 + 9*a^20*b^4*c^13*d^11))/9 + a^13*b^9*c^13*d^9*x)*(d^7/(27*b^3*c^10 - 27*a^3*c^7*d^3 + 81*a^2*b*c^8*d^2 - 81*a*b^2*c^9*d))^(1/3) - (1/(4*a*c) - (x^3*(a*d + b*c))/(a^2*c^2))/x^4 + (log(((3^(1/2)*1i - 1)^2*(b^7/(a^7*(a*d - b*c)^3))^(2/3)*(((3^(1/2)*1i - 1)*(27*a^14*b^3*c^14*d^3*x*(a^6*d^6 + b^6*c^6)*(a*d - b*c)^2 + (27*a^19*b^3*c^19*d^3*(3^(1/2)*1i - 1)^2*(a*d + b*c)*(a*d - b*c)^4*(b^7/(a^7*(a*d - b*c)^3))^(2/3))/4)*(b^7/(a^7*(a*d - b*c)^3))^(1/3))/6 + 9*a^13*b^11*c^20*d^4 - 9*a^14*b^10*c^19*d^5 - 9*a^19*b^5*c^14*d^10 + 9*a^20*b^4*c^13*d^11))/36 + a^13*b^9*c^13*d^9*x)*(b^7/(27*a^10*d^3 - 27*a^7*b^3*c^3 + 81*a^8*b^2*c^2*d - 81*a^9*b*c*d^2))^(1/3)*(3^(1/2)*1i - 1))/2 - (log(((3^(1/2)*1i + 1)^2*(b^7/(a^7*(a*d - b*c)^3))^(2/3)*(((3^(1/2)*1i + 1)*(27*a^14*b^3*c^14*d^3*x*(a^6*d^6 + b^6*c^6)*(a*d - b*c)^2 + (27*a^19*b^3*c^19*d^3*(3^(1/2)*1i + 1)^2*(a*d + b*c)*(a*d - b*c)^4*(b^7/(a^7*(a*d - b*c)^3))^(2/3))/4)*(b^7/(a^7*(a*d - b*c)^3))^(1/3))/6 - 9*a^13*b^11*c^20*d^4 + 9*a^14*b^10*c^19*d^5 + 9*a^19*b^5*c^14*d^10 - 9*a^20*b^4*c^13*d^11))/36 - a^13*b^9*c^13*d^9*x)*(b^7/(27*a^10*d^3 - 27*a^7*b^3*c^3 + 81*a^8*b^2*c^2*d - 81*a^9*b*c*d^2))^(1/3)*(3^(1/2)*1i + 1))/2 + (log(((3^(1/2)*1i - 1)^2*(-d^7/(c^7*(a*d - b*c)^3))^(2/3)*(((3^(1/2)*1i - 1)*(27*a^14*b^3*c^14*d^3*x*(a^6*d^6 + b^6*c^6)*(a*d - b*c)^2 + (27*a^19*b^3*c^19*d^3*(3^(1/2)*1i - 1)^2*(a*d + b*c)*(a*d - b*c)^4*(-d^7/(c^7*(a*d - b*c)^3))^(2/3))/4)*(-d^7/(c^7*(a*d - b*c)^3))^(1/3))/6 + 9*a^13*b^11*c^20*d^4 - 9*a^14*b^10*c^19*d^5 - 9*a^19*b^5*c^14*d^10 + 9*a^20*b^4*c^13*d^11))/36 + a^13*b^9*c^13*d^9*x)*(d^7/(27*b^3*c^10 - 27*a^3*c^7*d^3 + 81*a^2*b*c^8*d^2 - 81*a*b^2*c^9*d))^(1/3)*(3^(1/2)*1i - 1))/2 - (log(((3^(1/2)*1i + 1)^2*(-d^7/(c^7*(a*d - b*c)^3))^(2/3)*(((3^(1/2)*1i + 1)*(27*a^14*b^3*c^14*d^3*x*(a^6*d^6 + b^6*c^6)*(a*d - b*c)^2 + (27*a^19*b^3*c^19*d^3*(3^(1/2)*1i + 1)^2*(a*d + b*c)*(a*d - b*c)^4*(-d^7/(c^7*(a*d - b*c)^3))^(2/3))/4)*(-d^7/(c^7*(a*d - b*c)^3))^(1/3))/6 - 9*a^13*b^11*c^20*d^4 + 9*a^14*b^10*c^19*d^5 + 9*a^19*b^5*c^14*d^10 - 9*a^20*b^4*c^13*d^11))/36 - a^13*b^9*c^13*d^9*x)*(d^7/(27*b^3*c^10 - 27*a^3*c^7*d^3 + 81*a^2*b*c^8*d^2 - 81*a*b^2*c^9*d))^(1/3)*(3^(1/2)*1i + 1))/2","B"
121,1,1860,321,11.572565,"\text{Not used}","int(1/(x^6*(a + b*x^3)*(c + d*x^3)),x)","\ln\left(\frac{{\left(-\frac{b^8}{a^8\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}\,\left(9\,a^{13}\,b^{11}\,c^{19}\,d^5-9\,a^{12}\,b^{12}\,c^{20}\,d^4+9\,a^{19}\,b^5\,c^{13}\,d^{11}-9\,a^{20}\,b^4\,c^{12}\,d^{12}+9\,a^{16}\,b^3\,c^{16}\,d^3\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,\left(a^3\,c^3\,{\left(-\frac{b^8}{a^8\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}+a^2\,d^2\,x+b^2\,c^2\,x\right)\,{\left(-\frac{b^8}{a^8\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}\right)}{3}+3\,a^{12}\,b^7\,c^{12}\,d^7\,x\,\left(a^4\,d^4+b^4\,c^4\right)\right)\,{\left(-\frac{b^8}{27\,a^{11}\,d^3-81\,a^{10}\,b\,c\,d^2+81\,a^9\,b^2\,c^2\,d-27\,a^8\,b^3\,c^3}\right)}^{1/3}-\frac{\frac{1}{5\,a\,c}-\frac{x^3\,\left(a\,d+b\,c\right)}{2\,a^2\,c^2}}{x^5}+\ln\left(\frac{{\left(\frac{d^8}{c^8\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}\,\left(9\,a^{13}\,b^{11}\,c^{19}\,d^5-9\,a^{12}\,b^{12}\,c^{20}\,d^4+9\,a^{19}\,b^5\,c^{13}\,d^{11}-9\,a^{20}\,b^4\,c^{12}\,d^{12}+9\,a^{16}\,b^3\,c^{16}\,d^3\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,\left(a^3\,c^3\,{\left(\frac{d^8}{c^8\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}+a^2\,d^2\,x+b^2\,c^2\,x\right)\,{\left(\frac{d^8}{c^8\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}\right)}{3}+3\,a^{12}\,b^7\,c^{12}\,d^7\,x\,\left(a^4\,d^4+b^4\,c^4\right)\right)\,{\left(-\frac{d^8}{-27\,a^3\,c^8\,d^3+81\,a^2\,b\,c^9\,d^2-81\,a\,b^2\,c^{10}\,d+27\,b^3\,c^{11}}\right)}^{1/3}+\frac{\ln\left(\frac{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(-\frac{b^8}{a^8\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}\,\left(\frac{{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(81\,a^{16}\,b^3\,c^{16}\,d^3\,x\,{\left(a\,d-b\,c\right)}^4\,\left(a^3\,d^3+a^2\,b\,c\,d^2+a\,b^2\,c^2\,d+b^3\,c^3\right)+\frac{81\,a^{19}\,b^3\,c^{19}\,d^3\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(-\frac{b^8}{a^8\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}}{2}\right)\,{\left(-\frac{b^8}{a^8\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}}{36}-9\,a^{12}\,b^{12}\,c^{20}\,d^4+9\,a^{13}\,b^{11}\,c^{19}\,d^5+9\,a^{19}\,b^5\,c^{13}\,d^{11}-9\,a^{20}\,b^4\,c^{12}\,d^{12}\right)}{6}+3\,a^{12}\,b^7\,c^{12}\,d^7\,x\,\left(a^4\,d^4+b^4\,c^4\right)\right)\,{\left(-\frac{b^8}{27\,a^{11}\,d^3-81\,a^{10}\,b\,c\,d^2+81\,a^9\,b^2\,c^2\,d-27\,a^8\,b^3\,c^3}\right)}^{1/3}\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}-\frac{\ln\left(\frac{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(-\frac{b^8}{a^8\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}\,\left(\frac{{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(81\,a^{16}\,b^3\,c^{16}\,d^3\,x\,{\left(a\,d-b\,c\right)}^4\,\left(a^3\,d^3+a^2\,b\,c\,d^2+a\,b^2\,c^2\,d+b^3\,c^3\right)-\frac{81\,a^{19}\,b^3\,c^{19}\,d^3\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(-\frac{b^8}{a^8\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}}{2}\right)\,{\left(-\frac{b^8}{a^8\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}}{36}-9\,a^{12}\,b^{12}\,c^{20}\,d^4+9\,a^{13}\,b^{11}\,c^{19}\,d^5+9\,a^{19}\,b^5\,c^{13}\,d^{11}-9\,a^{20}\,b^4\,c^{12}\,d^{12}\right)}{6}-3\,a^{12}\,b^7\,c^{12}\,d^7\,x\,\left(a^4\,d^4+b^4\,c^4\right)\right)\,{\left(-\frac{b^8}{27\,a^{11}\,d^3-81\,a^{10}\,b\,c\,d^2+81\,a^9\,b^2\,c^2\,d-27\,a^8\,b^3\,c^3}\right)}^{1/3}\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}+\frac{\ln\left(\frac{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(\frac{d^8}{c^8\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}\,\left(\frac{{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(81\,a^{16}\,b^3\,c^{16}\,d^3\,x\,{\left(a\,d-b\,c\right)}^4\,\left(a^3\,d^3+a^2\,b\,c\,d^2+a\,b^2\,c^2\,d+b^3\,c^3\right)+\frac{81\,a^{19}\,b^3\,c^{19}\,d^3\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(\frac{d^8}{c^8\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}}{2}\right)\,{\left(\frac{d^8}{c^8\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}}{36}-9\,a^{12}\,b^{12}\,c^{20}\,d^4+9\,a^{13}\,b^{11}\,c^{19}\,d^5+9\,a^{19}\,b^5\,c^{13}\,d^{11}-9\,a^{20}\,b^4\,c^{12}\,d^{12}\right)}{6}+3\,a^{12}\,b^7\,c^{12}\,d^7\,x\,\left(a^4\,d^4+b^4\,c^4\right)\right)\,{\left(-\frac{d^8}{-27\,a^3\,c^8\,d^3+81\,a^2\,b\,c^9\,d^2-81\,a\,b^2\,c^{10}\,d+27\,b^3\,c^{11}}\right)}^{1/3}\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}-\frac{\ln\left(\frac{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(\frac{d^8}{c^8\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}\,\left(\frac{{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(81\,a^{16}\,b^3\,c^{16}\,d^3\,x\,{\left(a\,d-b\,c\right)}^4\,\left(a^3\,d^3+a^2\,b\,c\,d^2+a\,b^2\,c^2\,d+b^3\,c^3\right)-\frac{81\,a^{19}\,b^3\,c^{19}\,d^3\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(\frac{d^8}{c^8\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}}{2}\right)\,{\left(\frac{d^8}{c^8\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}}{36}-9\,a^{12}\,b^{12}\,c^{20}\,d^4+9\,a^{13}\,b^{11}\,c^{19}\,d^5+9\,a^{19}\,b^5\,c^{13}\,d^{11}-9\,a^{20}\,b^4\,c^{12}\,d^{12}\right)}{6}-3\,a^{12}\,b^7\,c^{12}\,d^7\,x\,\left(a^4\,d^4+b^4\,c^4\right)\right)\,{\left(-\frac{d^8}{-27\,a^3\,c^8\,d^3+81\,a^2\,b\,c^9\,d^2-81\,a\,b^2\,c^{10}\,d+27\,b^3\,c^{11}}\right)}^{1/3}\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}","Not used",1,"log(((-b^8/(a^8*(a*d - b*c)^3))^(1/3)*(9*a^13*b^11*c^19*d^5 - 9*a^12*b^12*c^20*d^4 + 9*a^19*b^5*c^13*d^11 - 9*a^20*b^4*c^12*d^12 + 9*a^16*b^3*c^16*d^3*(a*d + b*c)*(a*d - b*c)^4*(a^3*c^3*(-b^8/(a^8*(a*d - b*c)^3))^(1/3) + a^2*d^2*x + b^2*c^2*x)*(-b^8/(a^8*(a*d - b*c)^3))^(2/3)))/3 + 3*a^12*b^7*c^12*d^7*x*(a^4*d^4 + b^4*c^4))*(-b^8/(27*a^11*d^3 - 27*a^8*b^3*c^3 + 81*a^9*b^2*c^2*d - 81*a^10*b*c*d^2))^(1/3) - (1/(5*a*c) - (x^3*(a*d + b*c))/(2*a^2*c^2))/x^5 + log(((d^8/(c^8*(a*d - b*c)^3))^(1/3)*(9*a^13*b^11*c^19*d^5 - 9*a^12*b^12*c^20*d^4 + 9*a^19*b^5*c^13*d^11 - 9*a^20*b^4*c^12*d^12 + 9*a^16*b^3*c^16*d^3*(a*d + b*c)*(a*d - b*c)^4*(a^3*c^3*(d^8/(c^8*(a*d - b*c)^3))^(1/3) + a^2*d^2*x + b^2*c^2*x)*(d^8/(c^8*(a*d - b*c)^3))^(2/3)))/3 + 3*a^12*b^7*c^12*d^7*x*(a^4*d^4 + b^4*c^4))*(-d^8/(27*b^3*c^11 - 27*a^3*c^8*d^3 + 81*a^2*b*c^9*d^2 - 81*a*b^2*c^10*d))^(1/3) + (log(((3^(1/2)*1i - 1)*(-b^8/(a^8*(a*d - b*c)^3))^(1/3)*(((3^(1/2)*1i - 1)^2*(81*a^16*b^3*c^16*d^3*x*(a*d - b*c)^4*(a^3*d^3 + b^3*c^3 + a*b^2*c^2*d + a^2*b*c*d^2) + (81*a^19*b^3*c^19*d^3*(3^(1/2)*1i - 1)*(a*d + b*c)*(a*d - b*c)^4*(-b^8/(a^8*(a*d - b*c)^3))^(1/3))/2)*(-b^8/(a^8*(a*d - b*c)^3))^(2/3))/36 - 9*a^12*b^12*c^20*d^4 + 9*a^13*b^11*c^19*d^5 + 9*a^19*b^5*c^13*d^11 - 9*a^20*b^4*c^12*d^12))/6 + 3*a^12*b^7*c^12*d^7*x*(a^4*d^4 + b^4*c^4))*(-b^8/(27*a^11*d^3 - 27*a^8*b^3*c^3 + 81*a^9*b^2*c^2*d - 81*a^10*b*c*d^2))^(1/3)*(3^(1/2)*1i - 1))/2 - (log(((3^(1/2)*1i + 1)*(-b^8/(a^8*(a*d - b*c)^3))^(1/3)*(((3^(1/2)*1i + 1)^2*(81*a^16*b^3*c^16*d^3*x*(a*d - b*c)^4*(a^3*d^3 + b^3*c^3 + a*b^2*c^2*d + a^2*b*c*d^2) - (81*a^19*b^3*c^19*d^3*(3^(1/2)*1i + 1)*(a*d + b*c)*(a*d - b*c)^4*(-b^8/(a^8*(a*d - b*c)^3))^(1/3))/2)*(-b^8/(a^8*(a*d - b*c)^3))^(2/3))/36 - 9*a^12*b^12*c^20*d^4 + 9*a^13*b^11*c^19*d^5 + 9*a^19*b^5*c^13*d^11 - 9*a^20*b^4*c^12*d^12))/6 - 3*a^12*b^7*c^12*d^7*x*(a^4*d^4 + b^4*c^4))*(-b^8/(27*a^11*d^3 - 27*a^8*b^3*c^3 + 81*a^9*b^2*c^2*d - 81*a^10*b*c*d^2))^(1/3)*(3^(1/2)*1i + 1))/2 + (log(((3^(1/2)*1i - 1)*(d^8/(c^8*(a*d - b*c)^3))^(1/3)*(((3^(1/2)*1i - 1)^2*(81*a^16*b^3*c^16*d^3*x*(a*d - b*c)^4*(a^3*d^3 + b^3*c^3 + a*b^2*c^2*d + a^2*b*c*d^2) + (81*a^19*b^3*c^19*d^3*(3^(1/2)*1i - 1)*(a*d + b*c)*(a*d - b*c)^4*(d^8/(c^8*(a*d - b*c)^3))^(1/3))/2)*(d^8/(c^8*(a*d - b*c)^3))^(2/3))/36 - 9*a^12*b^12*c^20*d^4 + 9*a^13*b^11*c^19*d^5 + 9*a^19*b^5*c^13*d^11 - 9*a^20*b^4*c^12*d^12))/6 + 3*a^12*b^7*c^12*d^7*x*(a^4*d^4 + b^4*c^4))*(-d^8/(27*b^3*c^11 - 27*a^3*c^8*d^3 + 81*a^2*b*c^9*d^2 - 81*a*b^2*c^10*d))^(1/3)*(3^(1/2)*1i - 1))/2 - (log(((3^(1/2)*1i + 1)*(d^8/(c^8*(a*d - b*c)^3))^(1/3)*(((3^(1/2)*1i + 1)^2*(81*a^16*b^3*c^16*d^3*x*(a*d - b*c)^4*(a^3*d^3 + b^3*c^3 + a*b^2*c^2*d + a^2*b*c*d^2) - (81*a^19*b^3*c^19*d^3*(3^(1/2)*1i + 1)*(a*d + b*c)*(a*d - b*c)^4*(d^8/(c^8*(a*d - b*c)^3))^(1/3))/2)*(d^8/(c^8*(a*d - b*c)^3))^(2/3))/36 - 9*a^12*b^12*c^20*d^4 + 9*a^13*b^11*c^19*d^5 + 9*a^19*b^5*c^13*d^11 - 9*a^20*b^4*c^12*d^12))/6 - 3*a^12*b^7*c^12*d^7*x*(a^4*d^4 + b^4*c^4))*(-d^8/(27*b^3*c^11 - 27*a^3*c^8*d^3 + 81*a^2*b*c^9*d^2 - 81*a*b^2*c^10*d))^(1/3)*(3^(1/2)*1i + 1))/2","B"
122,1,118,119,3.212365,"\text{Not used}","int(1/(x^7*(a + b*x^3)*(c + d*x^3)),x)","\frac{b^3\,\ln\left(b\,x^3+a\right)}{3\,a^4\,d-3\,a^3\,b\,c}-\frac{\frac{1}{6\,a\,c}-\frac{x^3\,\left(a\,d+b\,c\right)}{3\,a^2\,c^2}}{x^6}+\frac{d^3\,\ln\left(d\,x^3+c\right)}{3\,b\,c^4-3\,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^3))/(3*a^4*d - 3*a^3*b*c) - (1/(6*a*c) - (x^3*(a*d + b*c))/(3*a^2*c^2))/x^6 + (d^3*log(c + d*x^3))/(3*b*c^4 - 3*a*c^3*d) + (log(x)*(a^2*d^2 + b^2*c^2 + a*b*c*d))/(a^3*c^3)","B"
123,1,1814,352,11.908518,"\text{Not used}","int(1/(x^8*(a + b*x^3)*(c + d*x^3)),x)","\ln\left(\frac{{\left(-\frac{b^{10}}{a^{10}\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}\,\left(\frac{\left(27\,a^{21}\,b^3\,c^{21}\,d^3\,x\,\left(a^8\,d^8+b^8\,c^8\right)\,{\left(a\,d-b\,c\right)}^2+27\,a^{28}\,b^3\,c^{28}\,d^3\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(-\frac{b^{10}}{a^{10}\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}\right)\,{\left(-\frac{b^{10}}{a^{10}\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}}{3}-9\,a^{19}\,b^{14}\,c^{29}\,d^4+9\,a^{20}\,b^{13}\,c^{28}\,d^5+9\,a^{28}\,b^5\,c^{20}\,d^{13}-9\,a^{29}\,b^4\,c^{19}\,d^{14}\right)}{9}-a^{19}\,b^{11}\,c^{19}\,d^{11}\,x\,\left(a\,d+b\,c\right)\right)\,{\left(-\frac{b^{10}}{27\,a^{13}\,d^3-81\,a^{12}\,b\,c\,d^2+81\,a^{11}\,b^2\,c^2\,d-27\,a^{10}\,b^3\,c^3}\right)}^{1/3}+\ln\left(\frac{{\left(\frac{d^{10}}{c^{10}\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}\,\left(\frac{\left(27\,a^{21}\,b^3\,c^{21}\,d^3\,x\,\left(a^8\,d^8+b^8\,c^8\right)\,{\left(a\,d-b\,c\right)}^2+27\,a^{28}\,b^3\,c^{28}\,d^3\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(\frac{d^{10}}{c^{10}\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}\right)\,{\left(\frac{d^{10}}{c^{10}\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}}{3}-9\,a^{19}\,b^{14}\,c^{29}\,d^4+9\,a^{20}\,b^{13}\,c^{28}\,d^5+9\,a^{28}\,b^5\,c^{20}\,d^{13}-9\,a^{29}\,b^4\,c^{19}\,d^{14}\right)}{9}-a^{19}\,b^{11}\,c^{19}\,d^{11}\,x\,\left(a\,d+b\,c\right)\right)\,{\left(-\frac{d^{10}}{-27\,a^3\,c^{10}\,d^3+81\,a^2\,b\,c^{11}\,d^2-81\,a\,b^2\,c^{12}\,d+27\,b^3\,c^{13}}\right)}^{1/3}-\frac{\frac{1}{7\,a\,c}-\frac{x^3\,\left(a\,d+b\,c\right)}{4\,a^2\,c^2}+\frac{x^6\,\left(a^2\,d^2+a\,b\,c\,d+b^2\,c^2\right)}{a^3\,c^3}}{x^7}-\frac{\ln\left(\frac{{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,{\left(-\frac{b^{10}}{a^{10}\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}\,\left(\frac{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(27\,a^{21}\,b^3\,c^{21}\,d^3\,x\,\left(a^8\,d^8+b^8\,c^8\right)\,{\left(a\,d-b\,c\right)}^2+\frac{27\,a^{28}\,b^3\,c^{28}\,d^3\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(-\frac{b^{10}}{a^{10}\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}}{4}\right)\,{\left(-\frac{b^{10}}{a^{10}\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}}{6}+9\,a^{19}\,b^{14}\,c^{29}\,d^4-9\,a^{20}\,b^{13}\,c^{28}\,d^5-9\,a^{28}\,b^5\,c^{20}\,d^{13}+9\,a^{29}\,b^4\,c^{19}\,d^{14}\right)}{36}+a^{19}\,b^{11}\,c^{19}\,d^{11}\,x\,\left(a\,d+b\,c\right)\right)\,{\left(-\frac{b^{10}}{27\,a^{13}\,d^3-81\,a^{12}\,b\,c\,d^2+81\,a^{11}\,b^2\,c^2\,d-27\,a^{10}\,b^3\,c^3}\right)}^{1/3}\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}+\frac{\ln\left(\frac{{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,{\left(-\frac{b^{10}}{a^{10}\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}\,\left(\frac{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(27\,a^{21}\,b^3\,c^{21}\,d^3\,x\,\left(a^8\,d^8+b^8\,c^8\right)\,{\left(a\,d-b\,c\right)}^2+\frac{27\,a^{28}\,b^3\,c^{28}\,d^3\,{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(-\frac{b^{10}}{a^{10}\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}}{4}\right)\,{\left(-\frac{b^{10}}{a^{10}\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}}{6}-9\,a^{19}\,b^{14}\,c^{29}\,d^4+9\,a^{20}\,b^{13}\,c^{28}\,d^5+9\,a^{28}\,b^5\,c^{20}\,d^{13}-9\,a^{29}\,b^4\,c^{19}\,d^{14}\right)}{36}-a^{19}\,b^{11}\,c^{19}\,d^{11}\,x\,\left(a\,d+b\,c\right)\right)\,{\left(-\frac{b^{10}}{27\,a^{13}\,d^3-81\,a^{12}\,b\,c\,d^2+81\,a^{11}\,b^2\,c^2\,d-27\,a^{10}\,b^3\,c^3}\right)}^{1/3}\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}-\frac{\ln\left(\frac{{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,{\left(\frac{d^{10}}{c^{10}\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}\,\left(\frac{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(27\,a^{21}\,b^3\,c^{21}\,d^3\,x\,\left(a^8\,d^8+b^8\,c^8\right)\,{\left(a\,d-b\,c\right)}^2+\frac{27\,a^{28}\,b^3\,c^{28}\,d^3\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(\frac{d^{10}}{c^{10}\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}}{4}\right)\,{\left(\frac{d^{10}}{c^{10}\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}}{6}+9\,a^{19}\,b^{14}\,c^{29}\,d^4-9\,a^{20}\,b^{13}\,c^{28}\,d^5-9\,a^{28}\,b^5\,c^{20}\,d^{13}+9\,a^{29}\,b^4\,c^{19}\,d^{14}\right)}{36}+a^{19}\,b^{11}\,c^{19}\,d^{11}\,x\,\left(a\,d+b\,c\right)\right)\,{\left(-\frac{d^{10}}{-27\,a^3\,c^{10}\,d^3+81\,a^2\,b\,c^{11}\,d^2-81\,a\,b^2\,c^{12}\,d+27\,b^3\,c^{13}}\right)}^{1/3}\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}+\frac{\ln\left(\frac{{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,{\left(\frac{d^{10}}{c^{10}\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}\,\left(\frac{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(27\,a^{21}\,b^3\,c^{21}\,d^3\,x\,\left(a^8\,d^8+b^8\,c^8\right)\,{\left(a\,d-b\,c\right)}^2+\frac{27\,a^{28}\,b^3\,c^{28}\,d^3\,{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(a\,d+b\,c\right)\,{\left(a\,d-b\,c\right)}^4\,{\left(\frac{d^{10}}{c^{10}\,{\left(a\,d-b\,c\right)}^3}\right)}^{2/3}}{4}\right)\,{\left(\frac{d^{10}}{c^{10}\,{\left(a\,d-b\,c\right)}^3}\right)}^{1/3}}{6}-9\,a^{19}\,b^{14}\,c^{29}\,d^4+9\,a^{20}\,b^{13}\,c^{28}\,d^5+9\,a^{28}\,b^5\,c^{20}\,d^{13}-9\,a^{29}\,b^4\,c^{19}\,d^{14}\right)}{36}-a^{19}\,b^{11}\,c^{19}\,d^{11}\,x\,\left(a\,d+b\,c\right)\right)\,{\left(-\frac{d^{10}}{-27\,a^3\,c^{10}\,d^3+81\,a^2\,b\,c^{11}\,d^2-81\,a\,b^2\,c^{12}\,d+27\,b^3\,c^{13}}\right)}^{1/3}\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}","Not used",1,"log(((-b^10/(a^10*(a*d - b*c)^3))^(2/3)*(((27*a^21*b^3*c^21*d^3*x*(a^8*d^8 + b^8*c^8)*(a*d - b*c)^2 + 27*a^28*b^3*c^28*d^3*(a*d + b*c)*(a*d - b*c)^4*(-b^10/(a^10*(a*d - b*c)^3))^(2/3))*(-b^10/(a^10*(a*d - b*c)^3))^(1/3))/3 - 9*a^19*b^14*c^29*d^4 + 9*a^20*b^13*c^28*d^5 + 9*a^28*b^5*c^20*d^13 - 9*a^29*b^4*c^19*d^14))/9 - a^19*b^11*c^19*d^11*x*(a*d + b*c))*(-b^10/(27*a^13*d^3 - 27*a^10*b^3*c^3 + 81*a^11*b^2*c^2*d - 81*a^12*b*c*d^2))^(1/3) + log(((d^10/(c^10*(a*d - b*c)^3))^(2/3)*(((27*a^21*b^3*c^21*d^3*x*(a^8*d^8 + b^8*c^8)*(a*d - b*c)^2 + 27*a^28*b^3*c^28*d^3*(a*d + b*c)*(a*d - b*c)^4*(d^10/(c^10*(a*d - b*c)^3))^(2/3))*(d^10/(c^10*(a*d - b*c)^3))^(1/3))/3 - 9*a^19*b^14*c^29*d^4 + 9*a^20*b^13*c^28*d^5 + 9*a^28*b^5*c^20*d^13 - 9*a^29*b^4*c^19*d^14))/9 - a^19*b^11*c^19*d^11*x*(a*d + b*c))*(-d^10/(27*b^3*c^13 - 27*a^3*c^10*d^3 + 81*a^2*b*c^11*d^2 - 81*a*b^2*c^12*d))^(1/3) - (1/(7*a*c) - (x^3*(a*d + b*c))/(4*a^2*c^2) + (x^6*(a^2*d^2 + b^2*c^2 + a*b*c*d))/(a^3*c^3))/x^7 - (log(((3^(1/2)*1i + 1)^2*(-b^10/(a^10*(a*d - b*c)^3))^(2/3)*(((3^(1/2)*1i + 1)*(27*a^21*b^3*c^21*d^3*x*(a^8*d^8 + b^8*c^8)*(a*d - b*c)^2 + (27*a^28*b^3*c^28*d^3*(3^(1/2)*1i + 1)^2*(a*d + b*c)*(a*d - b*c)^4*(-b^10/(a^10*(a*d - b*c)^3))^(2/3))/4)*(-b^10/(a^10*(a*d - b*c)^3))^(1/3))/6 + 9*a^19*b^14*c^29*d^4 - 9*a^20*b^13*c^28*d^5 - 9*a^28*b^5*c^20*d^13 + 9*a^29*b^4*c^19*d^14))/36 + a^19*b^11*c^19*d^11*x*(a*d + b*c))*(-b^10/(27*a^13*d^3 - 27*a^10*b^3*c^3 + 81*a^11*b^2*c^2*d - 81*a^12*b*c*d^2))^(1/3)*(3^(1/2)*1i + 1))/2 + (log(((3^(1/2)*1i - 1)^2*(-b^10/(a^10*(a*d - b*c)^3))^(2/3)*(((3^(1/2)*1i - 1)*(27*a^21*b^3*c^21*d^3*x*(a^8*d^8 + b^8*c^8)*(a*d - b*c)^2 + (27*a^28*b^3*c^28*d^3*(3^(1/2)*1i - 1)^2*(a*d + b*c)*(a*d - b*c)^4*(-b^10/(a^10*(a*d - b*c)^3))^(2/3))/4)*(-b^10/(a^10*(a*d - b*c)^3))^(1/3))/6 - 9*a^19*b^14*c^29*d^4 + 9*a^20*b^13*c^28*d^5 + 9*a^28*b^5*c^20*d^13 - 9*a^29*b^4*c^19*d^14))/36 - a^19*b^11*c^19*d^11*x*(a*d + b*c))*(-b^10/(27*a^13*d^3 - 27*a^10*b^3*c^3 + 81*a^11*b^2*c^2*d - 81*a^12*b*c*d^2))^(1/3)*(3^(1/2)*1i - 1))/2 - (log(((3^(1/2)*1i + 1)^2*(d^10/(c^10*(a*d - b*c)^3))^(2/3)*(((3^(1/2)*1i + 1)*(27*a^21*b^3*c^21*d^3*x*(a^8*d^8 + b^8*c^8)*(a*d - b*c)^2 + (27*a^28*b^3*c^28*d^3*(3^(1/2)*1i + 1)^2*(a*d + b*c)*(a*d - b*c)^4*(d^10/(c^10*(a*d - b*c)^3))^(2/3))/4)*(d^10/(c^10*(a*d - b*c)^3))^(1/3))/6 + 9*a^19*b^14*c^29*d^4 - 9*a^20*b^13*c^28*d^5 - 9*a^28*b^5*c^20*d^13 + 9*a^29*b^4*c^19*d^14))/36 + a^19*b^11*c^19*d^11*x*(a*d + b*c))*(-d^10/(27*b^3*c^13 - 27*a^3*c^10*d^3 + 81*a^2*b*c^11*d^2 - 81*a*b^2*c^12*d))^(1/3)*(3^(1/2)*1i + 1))/2 + (log(((3^(1/2)*1i - 1)^2*(d^10/(c^10*(a*d - b*c)^3))^(2/3)*(((3^(1/2)*1i - 1)*(27*a^21*b^3*c^21*d^3*x*(a^8*d^8 + b^8*c^8)*(a*d - b*c)^2 + (27*a^28*b^3*c^28*d^3*(3^(1/2)*1i - 1)^2*(a*d + b*c)*(a*d - b*c)^4*(d^10/(c^10*(a*d - b*c)^3))^(2/3))/4)*(d^10/(c^10*(a*d - b*c)^3))^(1/3))/6 - 9*a^19*b^14*c^29*d^4 + 9*a^20*b^13*c^28*d^5 + 9*a^28*b^5*c^20*d^13 - 9*a^29*b^4*c^19*d^14))/36 - a^19*b^11*c^19*d^11*x*(a*d + b*c))*(-d^10/(27*b^3*c^13 - 27*a^3*c^10*d^3 + 81*a^2*b*c^11*d^2 - 81*a*b^2*c^12*d))^(1/3)*(3^(1/2)*1i - 1))/2","B"
124,1,559,148,3.212525,"\text{Not used}","int(x^m*(A + B*x^3)*(a + b*x^3)^5,x)","\frac{B\,b^5\,x^m\,x^{19}\,\left(m^6+51\,m^5+1005\,m^4+9605\,m^3+45474\,m^2+95064\,m+58240\right)}{m^7+70\,m^6+1974\,m^5+28700\,m^4+227969\,m^3+959070\,m^2+1864456\,m+1106560}+\frac{a^4\,x^m\,x^4\,\left(5\,A\,b+B\,a\right)\,\left(m^6+66\,m^5+1710\,m^4+21860\,m^3+140529\,m^2+396954\,m+276640\right)}{m^7+70\,m^6+1974\,m^5+28700\,m^4+227969\,m^3+959070\,m^2+1864456\,m+1106560}+\frac{b^4\,x^m\,x^{16}\,\left(A\,b+5\,B\,a\right)\,\left(m^6+54\,m^5+1110\,m^4+10940\,m^3+52929\,m^2+112206\,m+69160\right)}{m^7+70\,m^6+1974\,m^5+28700\,m^4+227969\,m^3+959070\,m^2+1864456\,m+1106560}+\frac{A\,a^5\,x\,x^m\,\left(m^6+69\,m^5+1905\,m^4+26795\,m^3+201174\,m^2+757896\,m+1106560\right)}{m^7+70\,m^6+1974\,m^5+28700\,m^4+227969\,m^3+959070\,m^2+1864456\,m+1106560}+\frac{10\,a^2\,b^2\,x^m\,x^{10}\,\left(A\,b+B\,a\right)\,\left(m^6+60\,m^5+1374\,m^4+14960\,m^3+78369\,m^2+175380\,m+110656\right)}{m^7+70\,m^6+1974\,m^5+28700\,m^4+227969\,m^3+959070\,m^2+1864456\,m+1106560}+\frac{5\,a\,b^3\,x^m\,x^{13}\,\left(A\,b+2\,B\,a\right)\,\left(m^6+57\,m^5+1233\,m^4+12671\,m^3+63246\,m^2+136872\,m+85120\right)}{m^7+70\,m^6+1974\,m^5+28700\,m^4+227969\,m^3+959070\,m^2+1864456\,m+1106560}+\frac{5\,a^3\,b\,x^m\,x^7\,\left(2\,A\,b+B\,a\right)\,\left(m^6+63\,m^5+1533\,m^4+17969\,m^3+102186\,m^2+243768\,m+158080\right)}{m^7+70\,m^6+1974\,m^5+28700\,m^4+227969\,m^3+959070\,m^2+1864456\,m+1106560}","Not used",1,"(B*b^5*x^m*x^19*(95064*m + 45474*m^2 + 9605*m^3 + 1005*m^4 + 51*m^5 + m^6 + 58240))/(1864456*m + 959070*m^2 + 227969*m^3 + 28700*m^4 + 1974*m^5 + 70*m^6 + m^7 + 1106560) + (a^4*x^m*x^4*(5*A*b + B*a)*(396954*m + 140529*m^2 + 21860*m^3 + 1710*m^4 + 66*m^5 + m^6 + 276640))/(1864456*m + 959070*m^2 + 227969*m^3 + 28700*m^4 + 1974*m^5 + 70*m^6 + m^7 + 1106560) + (b^4*x^m*x^16*(A*b + 5*B*a)*(112206*m + 52929*m^2 + 10940*m^3 + 1110*m^4 + 54*m^5 + m^6 + 69160))/(1864456*m + 959070*m^2 + 227969*m^3 + 28700*m^4 + 1974*m^5 + 70*m^6 + m^7 + 1106560) + (A*a^5*x*x^m*(757896*m + 201174*m^2 + 26795*m^3 + 1905*m^4 + 69*m^5 + m^6 + 1106560))/(1864456*m + 959070*m^2 + 227969*m^3 + 28700*m^4 + 1974*m^5 + 70*m^6 + m^7 + 1106560) + (10*a^2*b^2*x^m*x^10*(A*b + B*a)*(175380*m + 78369*m^2 + 14960*m^3 + 1374*m^4 + 60*m^5 + m^6 + 110656))/(1864456*m + 959070*m^2 + 227969*m^3 + 28700*m^4 + 1974*m^5 + 70*m^6 + m^7 + 1106560) + (5*a*b^3*x^m*x^13*(A*b + 2*B*a)*(136872*m + 63246*m^2 + 12671*m^3 + 1233*m^4 + 57*m^5 + m^6 + 85120))/(1864456*m + 959070*m^2 + 227969*m^3 + 28700*m^4 + 1974*m^5 + 70*m^6 + m^7 + 1106560) + (5*a^3*b*x^m*x^7*(2*A*b + B*a)*(243768*m + 102186*m^2 + 17969*m^3 + 1533*m^4 + 63*m^5 + m^6 + 158080))/(1864456*m + 959070*m^2 + 227969*m^3 + 28700*m^4 + 1974*m^5 + 70*m^6 + m^7 + 1106560)","B"
125,1,177,71,2.717512,"\text{Not used}","int(x^m*(A + B*x^3)*(a + b*x^3)^2,x)","x^m\,\left(\frac{B\,b^2\,x^{10}\,\left(m^3+12\,m^2+39\,m+28\right)}{m^4+22\,m^3+159\,m^2+418\,m+280}+\frac{A\,a^2\,x\,\left(m^3+21\,m^2+138\,m+280\right)}{m^4+22\,m^3+159\,m^2+418\,m+280}+\frac{a\,x^4\,\left(2\,A\,b+B\,a\right)\,\left(m^3+18\,m^2+87\,m+70\right)}{m^4+22\,m^3+159\,m^2+418\,m+280}+\frac{b\,x^7\,\left(A\,b+2\,B\,a\right)\,\left(m^3+15\,m^2+54\,m+40\right)}{m^4+22\,m^3+159\,m^2+418\,m+280}\right)","Not used",1,"x^m*((B*b^2*x^10*(39*m + 12*m^2 + m^3 + 28))/(418*m + 159*m^2 + 22*m^3 + m^4 + 280) + (A*a^2*x*(138*m + 21*m^2 + m^3 + 280))/(418*m + 159*m^2 + 22*m^3 + m^4 + 280) + (a*x^4*(2*A*b + B*a)*(87*m + 18*m^2 + m^3 + 70))/(418*m + 159*m^2 + 22*m^3 + m^4 + 280) + (b*x^7*(A*b + 2*B*a)*(54*m + 15*m^2 + m^3 + 40))/(418*m + 159*m^2 + 22*m^3 + m^4 + 280))","B"
126,1,95,45,2.654767,"\text{Not used}","int(x^m*(A + B*x^3)*(a + b*x^3),x)","x^m\,\left(\frac{x^4\,\left(A\,b+B\,a\right)\,\left(m^2+8\,m+7\right)}{m^3+12\,m^2+39\,m+28}+\frac{B\,b\,x^7\,\left(m^2+5\,m+4\right)}{m^3+12\,m^2+39\,m+28}+\frac{A\,a\,x\,\left(m^2+11\,m+28\right)}{m^3+12\,m^2+39\,m+28}\right)","Not used",1,"x^m*((x^4*(A*b + B*a)*(8*m + m^2 + 7))/(39*m + 12*m^2 + m^3 + 28) + (B*b*x^7*(5*m + m^2 + 4))/(39*m + 12*m^2 + m^3 + 28) + (A*a*x*(11*m + m^2 + 28))/(39*m + 12*m^2 + m^3 + 28))","B"
127,0,-1,66,0.000000,"\text{Not used}","int((x^m*(A + B*x^3))/(a + b*x^3),x)","\int \frac{x^m\,\left(B\,x^3+A\right)}{b\,x^3+a} \,d x","Not used",1,"int((x^m*(A + B*x^3))/(a + b*x^3), x)","F"
128,0,-1,93,0.000000,"\text{Not used}","int((x^m*(A + B*x^3))/(a + b*x^3)^2,x)","\int \frac{x^m\,\left(B\,x^3+A\right)}{{\left(b\,x^3+a\right)}^2} \,d x","Not used",1,"int((x^m*(A + B*x^3))/(a + b*x^3)^2, x)","F"
129,0,-1,93,0.000000,"\text{Not used}","int((x^m*(A + B*x^3))/(a + b*x^3)^3,x)","\int \frac{x^m\,\left(B\,x^3+A\right)}{{\left(b\,x^3+a\right)}^3} \,d x","Not used",1,"int((x^m*(A + B*x^3))/(a + b*x^3)^3, x)","F"
130,0,-1,112,0.000000,"\text{Not used}","int((e*x)^m/((a + b*x^3)*(c + d*x^3)),x)","\int \frac{{\left(e\,x\right)}^m}{\left(b\,x^3+a\right)\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int((e*x)^m/((a + b*x^3)*(c + d*x^3)), x)","F"
131,1,31,39,0.053004,"\text{Not used}","int(x^(7/2)*(A + B*x^3)*(a + b*x^3),x)","\frac{2\,x^{9/2}\,\left(35\,A\,a+21\,A\,b\,x^3+21\,B\,a\,x^3+15\,B\,b\,x^6\right)}{315}","Not used",1,"(2*x^(9/2)*(35*A*a + 21*A*b*x^3 + 21*B*a*x^3 + 15*B*b*x^6))/315","B"
132,1,31,39,2.559684,"\text{Not used}","int(x^(5/2)*(A + B*x^3)*(a + b*x^3),x)","\frac{2\,x^{7/2}\,\left(247\,A\,a+133\,A\,b\,x^3+133\,B\,a\,x^3+91\,B\,b\,x^6\right)}{1729}","Not used",1,"(2*x^(7/2)*(247*A*a + 133*A*b*x^3 + 133*B*a*x^3 + 91*B*b*x^6))/1729","B"
133,1,31,39,0.043581,"\text{Not used}","int(x^(3/2)*(A + B*x^3)*(a + b*x^3),x)","\frac{2\,x^{5/2}\,\left(187\,A\,a+85\,A\,b\,x^3+85\,B\,a\,x^3+55\,B\,b\,x^6\right)}{935}","Not used",1,"(2*x^(5/2)*(187*A*a + 85*A*b*x^3 + 85*B*a*x^3 + 55*B*b*x^6))/935","B"
134,1,31,39,0.040656,"\text{Not used}","int(x^(1/2)*(A + B*x^3)*(a + b*x^3),x)","\frac{2\,x^{3/2}\,\left(15\,A\,a+5\,A\,b\,x^3+5\,B\,a\,x^3+3\,B\,b\,x^6\right)}{45}","Not used",1,"(2*x^(3/2)*(15*A*a + 5*A*b*x^3 + 5*B*a*x^3 + 3*B*b*x^6))/45","B"
135,1,31,37,2.590043,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3))/x^(1/2),x)","\frac{2\,\sqrt{x}\,\left(91\,A\,a+13\,A\,b\,x^3+13\,B\,a\,x^3+7\,B\,b\,x^6\right)}{91}","Not used",1,"(2*x^(1/2)*(91*A*a + 13*A*b*x^3 + 13*B*a*x^3 + 7*B*b*x^6))/91","B"
136,1,31,37,2.599444,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3))/x^(3/2),x)","\frac{22\,A\,b\,x^3-110\,A\,a+22\,B\,a\,x^3+10\,B\,b\,x^6}{55\,\sqrt{x}}","Not used",1,"(22*A*b*x^3 - 110*A*a + 22*B*a*x^3 + 10*B*b*x^6)/(55*x^(1/2))","B"
137,1,31,39,0.040259,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3))/x^(5/2),x)","\frac{6\,A\,b\,x^3-6\,A\,a+6\,B\,a\,x^3+2\,B\,b\,x^6}{9\,x^{3/2}}","Not used",1,"(6*A*b*x^3 - 6*A*a + 6*B*a*x^3 + 2*B*b*x^6)/(9*x^(3/2))","B"
138,1,30,37,0.042128,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3))/x^(7/2),x)","\frac{2\,A\,b\,x^3-\frac{2\,A\,a}{5}+2\,B\,a\,x^3+\frac{2\,B\,b\,x^6}{7}}{x^{5/2}}","Not used",1,"(2*A*b*x^3 - (2*A*a)/5 + 2*B*a*x^3 + (2*B*b*x^6)/7)/x^(5/2)","B"
139,1,51,63,2.566511,"\text{Not used}","int(x^(7/2)*(A + B*x^3)*(a + b*x^3)^2,x)","x^{15/2}\,\left(\frac{2\,B\,a^2}{15}+\frac{4\,A\,b\,a}{15}\right)+x^{21/2}\,\left(\frac{2\,A\,b^2}{21}+\frac{4\,B\,a\,b}{21}\right)+\frac{2\,A\,a^2\,x^{9/2}}{9}+\frac{2\,B\,b^2\,x^{27/2}}{27}","Not used",1,"x^(15/2)*((2*B*a^2)/15 + (4*A*a*b)/15) + x^(21/2)*((2*A*b^2)/21 + (4*B*a*b)/21) + (2*A*a^2*x^(9/2))/9 + (2*B*b^2*x^(27/2))/27","B"
140,1,51,63,0.046946,"\text{Not used}","int(x^(5/2)*(A + B*x^3)*(a + b*x^3)^2,x)","x^{13/2}\,\left(\frac{2\,B\,a^2}{13}+\frac{4\,A\,b\,a}{13}\right)+x^{19/2}\,\left(\frac{2\,A\,b^2}{19}+\frac{4\,B\,a\,b}{19}\right)+\frac{2\,A\,a^2\,x^{7/2}}{7}+\frac{2\,B\,b^2\,x^{25/2}}{25}","Not used",1,"x^(13/2)*((2*B*a^2)/13 + (4*A*a*b)/13) + x^(19/2)*((2*A*b^2)/19 + (4*B*a*b)/19) + (2*A*a^2*x^(7/2))/7 + (2*B*b^2*x^(25/2))/25","B"
141,1,51,63,0.047471,"\text{Not used}","int(x^(3/2)*(A + B*x^3)*(a + b*x^3)^2,x)","x^{11/2}\,\left(\frac{2\,B\,a^2}{11}+\frac{4\,A\,b\,a}{11}\right)+x^{17/2}\,\left(\frac{2\,A\,b^2}{17}+\frac{4\,B\,a\,b}{17}\right)+\frac{2\,A\,a^2\,x^{5/2}}{5}+\frac{2\,B\,b^2\,x^{23/2}}{23}","Not used",1,"x^(11/2)*((2*B*a^2)/11 + (4*A*a*b)/11) + x^(17/2)*((2*A*b^2)/17 + (4*B*a*b)/17) + (2*A*a^2*x^(5/2))/5 + (2*B*b^2*x^(23/2))/23","B"
142,1,51,63,0.049146,"\text{Not used}","int(x^(1/2)*(A + B*x^3)*(a + b*x^3)^2,x)","x^{9/2}\,\left(\frac{2\,B\,a^2}{9}+\frac{4\,A\,b\,a}{9}\right)+x^{15/2}\,\left(\frac{2\,A\,b^2}{15}+\frac{4\,B\,a\,b}{15}\right)+\frac{2\,A\,a^2\,x^{3/2}}{3}+\frac{2\,B\,b^2\,x^{21/2}}{21}","Not used",1,"x^(9/2)*((2*B*a^2)/9 + (4*A*a*b)/9) + x^(15/2)*((2*A*b^2)/15 + (4*B*a*b)/15) + (2*A*a^2*x^(3/2))/3 + (2*B*b^2*x^(21/2))/21","B"
143,1,51,61,0.045106,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^2)/x^(1/2),x)","x^{7/2}\,\left(\frac{2\,B\,a^2}{7}+\frac{4\,A\,b\,a}{7}\right)+x^{13/2}\,\left(\frac{2\,A\,b^2}{13}+\frac{4\,B\,a\,b}{13}\right)+2\,A\,a^2\,\sqrt{x}+\frac{2\,B\,b^2\,x^{19/2}}{19}","Not used",1,"x^(7/2)*((2*B*a^2)/7 + (4*A*a*b)/7) + x^(13/2)*((2*A*b^2)/13 + (4*B*a*b)/13) + 2*A*a^2*x^(1/2) + (2*B*b^2*x^(19/2))/19","B"
144,1,51,61,0.049970,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^2)/x^(3/2),x)","x^{5/2}\,\left(\frac{2\,B\,a^2}{5}+\frac{4\,A\,b\,a}{5}\right)+x^{11/2}\,\left(\frac{2\,A\,b^2}{11}+\frac{4\,B\,a\,b}{11}\right)-\frac{2\,A\,a^2}{\sqrt{x}}+\frac{2\,B\,b^2\,x^{17/2}}{17}","Not used",1,"x^(5/2)*((2*B*a^2)/5 + (4*A*a*b)/5) + x^(11/2)*((2*A*b^2)/11 + (4*B*a*b)/11) - (2*A*a^2)/x^(1/2) + (2*B*b^2*x^(17/2))/17","B"
145,1,51,63,0.048356,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^2)/x^(5/2),x)","x^{3/2}\,\left(\frac{2\,B\,a^2}{3}+\frac{4\,A\,b\,a}{3}\right)+x^{9/2}\,\left(\frac{2\,A\,b^2}{9}+\frac{4\,B\,a\,b}{9}\right)-\frac{2\,A\,a^2}{3\,x^{3/2}}+\frac{2\,B\,b^2\,x^{15/2}}{15}","Not used",1,"x^(3/2)*((2*B*a^2)/3 + (4*A*a*b)/3) + x^(9/2)*((2*A*b^2)/9 + (4*B*a*b)/9) - (2*A*a^2)/(3*x^(3/2)) + (2*B*b^2*x^(15/2))/15","B"
146,1,51,61,0.047586,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^2)/x^(7/2),x)","\sqrt{x}\,\left(2\,B\,a^2+4\,A\,b\,a\right)+x^{7/2}\,\left(\frac{2\,A\,b^2}{7}+\frac{4\,B\,a\,b}{7}\right)-\frac{2\,A\,a^2}{5\,x^{5/2}}+\frac{2\,B\,b^2\,x^{13/2}}{13}","Not used",1,"x^(1/2)*(2*B*a^2 + 4*A*a*b) + x^(7/2)*((2*A*b^2)/7 + (4*B*a*b)/7) - (2*A*a^2)/(5*x^(5/2)) + (2*B*b^2*x^(13/2))/13","B"
147,1,69,85,2.518907,"\text{Not used}","int(x^(7/2)*(A + B*x^3)*(a + b*x^3)^3,x)","x^{15/2}\,\left(\frac{2\,B\,a^3}{15}+\frac{2\,A\,b\,a^2}{5}\right)+x^{27/2}\,\left(\frac{2\,A\,b^3}{27}+\frac{2\,B\,a\,b^2}{9}\right)+\frac{2\,A\,a^3\,x^{9/2}}{9}+\frac{2\,B\,b^3\,x^{33/2}}{33}+\frac{2\,a\,b\,x^{21/2}\,\left(A\,b+B\,a\right)}{7}","Not used",1,"x^(15/2)*((2*B*a^3)/15 + (2*A*a^2*b)/5) + x^(27/2)*((2*A*b^3)/27 + (2*B*a*b^2)/9) + (2*A*a^3*x^(9/2))/9 + (2*B*b^3*x^(33/2))/33 + (2*a*b*x^(21/2)*(A*b + B*a))/7","B"
148,1,69,85,0.030015,"\text{Not used}","int(x^(5/2)*(A + B*x^3)*(a + b*x^3)^3,x)","x^{13/2}\,\left(\frac{2\,B\,a^3}{13}+\frac{6\,A\,b\,a^2}{13}\right)+x^{25/2}\,\left(\frac{2\,A\,b^3}{25}+\frac{6\,B\,a\,b^2}{25}\right)+\frac{2\,A\,a^3\,x^{7/2}}{7}+\frac{2\,B\,b^3\,x^{31/2}}{31}+\frac{6\,a\,b\,x^{19/2}\,\left(A\,b+B\,a\right)}{19}","Not used",1,"x^(13/2)*((2*B*a^3)/13 + (6*A*a^2*b)/13) + x^(25/2)*((2*A*b^3)/25 + (6*B*a*b^2)/25) + (2*A*a^3*x^(7/2))/7 + (2*B*b^3*x^(31/2))/31 + (6*a*b*x^(19/2)*(A*b + B*a))/19","B"
149,1,69,85,0.031693,"\text{Not used}","int(x^(3/2)*(A + B*x^3)*(a + b*x^3)^3,x)","x^{11/2}\,\left(\frac{2\,B\,a^3}{11}+\frac{6\,A\,b\,a^2}{11}\right)+x^{23/2}\,\left(\frac{2\,A\,b^3}{23}+\frac{6\,B\,a\,b^2}{23}\right)+\frac{2\,A\,a^3\,x^{5/2}}{5}+\frac{2\,B\,b^3\,x^{29/2}}{29}+\frac{6\,a\,b\,x^{17/2}\,\left(A\,b+B\,a\right)}{17}","Not used",1,"x^(11/2)*((2*B*a^3)/11 + (6*A*a^2*b)/11) + x^(23/2)*((2*A*b^3)/23 + (6*B*a*b^2)/23) + (2*A*a^3*x^(5/2))/5 + (2*B*b^3*x^(29/2))/29 + (6*a*b*x^(17/2)*(A*b + B*a))/17","B"
150,1,69,85,0.033054,"\text{Not used}","int(x^(1/2)*(A + B*x^3)*(a + b*x^3)^3,x)","x^{9/2}\,\left(\frac{2\,B\,a^3}{9}+\frac{2\,A\,b\,a^2}{3}\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^{3/2}}{3}+\frac{2\,B\,b^3\,x^{27/2}}{27}+\frac{2\,a\,b\,x^{15/2}\,\left(A\,b+B\,a\right)}{5}","Not used",1,"x^(9/2)*((2*B*a^3)/9 + (2*A*a^2*b)/3) + x^(21/2)*((2*A*b^3)/21 + (2*B*a*b^2)/7) + (2*A*a^3*x^(3/2))/3 + (2*B*b^3*x^(27/2))/27 + (2*a*b*x^(15/2)*(A*b + B*a))/5","B"
151,1,69,83,0.030022,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^3)/x^(1/2),x)","x^{7/2}\,\left(\frac{2\,B\,a^3}{7}+\frac{6\,A\,b\,a^2}{7}\right)+x^{19/2}\,\left(\frac{2\,A\,b^3}{19}+\frac{6\,B\,a\,b^2}{19}\right)+2\,A\,a^3\,\sqrt{x}+\frac{2\,B\,b^3\,x^{25/2}}{25}+\frac{6\,a\,b\,x^{13/2}\,\left(A\,b+B\,a\right)}{13}","Not used",1,"x^(7/2)*((2*B*a^3)/7 + (6*A*a^2*b)/7) + x^(19/2)*((2*A*b^3)/19 + (6*B*a*b^2)/19) + 2*A*a^3*x^(1/2) + (2*B*b^3*x^(25/2))/25 + (6*a*b*x^(13/2)*(A*b + B*a))/13","B"
152,1,69,83,0.032620,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^3)/x^(3/2),x)","x^{5/2}\,\left(\frac{2\,B\,a^3}{5}+\frac{6\,A\,b\,a^2}{5}\right)+x^{17/2}\,\left(\frac{2\,A\,b^3}{17}+\frac{6\,B\,a\,b^2}{17}\right)-\frac{2\,A\,a^3}{\sqrt{x}}+\frac{2\,B\,b^3\,x^{23/2}}{23}+\frac{6\,a\,b\,x^{11/2}\,\left(A\,b+B\,a\right)}{11}","Not used",1,"x^(5/2)*((2*B*a^3)/5 + (6*A*a^2*b)/5) + x^(17/2)*((2*A*b^3)/17 + (6*B*a*b^2)/17) - (2*A*a^3)/x^(1/2) + (2*B*b^3*x^(23/2))/23 + (6*a*b*x^(11/2)*(A*b + B*a))/11","B"
153,1,69,85,0.033622,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^3)/x^(5/2),x)","x^{3/2}\,\left(\frac{2\,B\,a^3}{3}+2\,A\,b\,a^2\right)+x^{15/2}\,\left(\frac{2\,A\,b^3}{15}+\frac{2\,B\,a\,b^2}{5}\right)-\frac{2\,A\,a^3}{3\,x^{3/2}}+\frac{2\,B\,b^3\,x^{21/2}}{21}+\frac{2\,a\,b\,x^{9/2}\,\left(A\,b+B\,a\right)}{3}","Not used",1,"x^(3/2)*((2*B*a^3)/3 + 2*A*a^2*b) + x^(15/2)*((2*A*b^3)/15 + (2*B*a*b^2)/5) - (2*A*a^3)/(3*x^(3/2)) + (2*B*b^3*x^(21/2))/21 + (2*a*b*x^(9/2)*(A*b + B*a))/3","B"
154,1,69,83,0.032126,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^3)/x^(7/2),x)","\sqrt{x}\,\left(2\,B\,a^3+6\,A\,b\,a^2\right)+x^{13/2}\,\left(\frac{2\,A\,b^3}{13}+\frac{6\,B\,a\,b^2}{13}\right)-\frac{2\,A\,a^3}{5\,x^{5/2}}+\frac{2\,B\,b^3\,x^{19/2}}{19}+\frac{6\,a\,b\,x^{7/2}\,\left(A\,b+B\,a\right)}{7}","Not used",1,"x^(1/2)*(2*B*a^3 + 6*A*a^2*b) + x^(13/2)*((2*A*b^3)/13 + (6*B*a*b^2)/13) - (2*A*a^3)/(5*x^(5/2)) + (2*B*b^3*x^(19/2))/19 + (6*a*b*x^(7/2)*(A*b + B*a))/7","B"
155,1,111,73,2.607039,"\text{Not used}","int((x^(7/2)*(A + B*x^3))/(a + b*x^3),x)","x^{3/2}\,\left(\frac{2\,A}{3\,b}-\frac{2\,B\,a}{3\,b^2}\right)+\frac{2\,B\,x^{9/2}}{9\,b}-\frac{2\,\sqrt{a}\,\mathrm{atan}\left(\frac{72\,b^{3/2}\,x^{3/2}\,\left(A^2\,a^2\,b^2-2\,A\,B\,a^3\,b+B^2\,a^4\right)}{\sqrt{a}\,\left(72\,A\,a^2\,b^2-72\,B\,a^3\,b\right)\,\left(A\,b-B\,a\right)}\right)\,\left(A\,b-B\,a\right)}{3\,b^{5/2}}","Not used",1,"x^(3/2)*((2*A)/(3*b) - (2*B*a)/(3*b^2)) + (2*B*x^(9/2))/(9*b) - (2*a^(1/2)*atan((72*b^(3/2)*x^(3/2)*(B^2*a^4 + A^2*a^2*b^2 - 2*A*B*a^3*b))/(a^(1/2)*(72*A*a^2*b^2 - 72*B*a^3*b)*(A*b - B*a)))*(A*b - B*a))/(3*b^(5/2))","B"
156,1,1933,288,2.888807,"\text{Not used}","int((x^(5/2)*(A + B*x^3))/(a + b*x^3),x)","\sqrt{x}\,\left(\frac{2\,A}{b}-\frac{2\,B\,a}{b^2}\right)+\frac{2\,B\,x^{7/2}}{7\,b}+\frac{{\left(-a\right)}^{1/6}\,\mathrm{atan}\left(\frac{\frac{{\left(-a\right)}^{1/6}\,\left(A\,b-B\,a\right)\,\left(\frac{96\,\sqrt{x}\,\left(A^4\,a^4\,b^4-4\,A^3\,B\,a^5\,b^3+6\,A^2\,B^2\,a^6\,b^2-4\,A\,B^3\,a^7\,b+B^4\,a^8\right)}{b^3}-\frac{96\,{\left(-a\right)}^{1/6}\,\left(A\,b-B\,a\right)\,\left(-A^3\,a^4\,b^3+3\,A^2\,B\,a^5\,b^2-3\,A\,B^2\,a^6\,b+B^3\,a^7\right)}{b^{19/6}}\right)\,1{}\mathrm{i}}{3\,b^{13/6}}+\frac{{\left(-a\right)}^{1/6}\,\left(A\,b-B\,a\right)\,\left(\frac{96\,\sqrt{x}\,\left(A^4\,a^4\,b^4-4\,A^3\,B\,a^5\,b^3+6\,A^2\,B^2\,a^6\,b^2-4\,A\,B^3\,a^7\,b+B^4\,a^8\right)}{b^3}+\frac{96\,{\left(-a\right)}^{1/6}\,\left(A\,b-B\,a\right)\,\left(-A^3\,a^4\,b^3+3\,A^2\,B\,a^5\,b^2-3\,A\,B^2\,a^6\,b+B^3\,a^7\right)}{b^{19/6}}\right)\,1{}\mathrm{i}}{3\,b^{13/6}}}{\frac{{\left(-a\right)}^{1/6}\,\left(A\,b-B\,a\right)\,\left(\frac{96\,\sqrt{x}\,\left(A^4\,a^4\,b^4-4\,A^3\,B\,a^5\,b^3+6\,A^2\,B^2\,a^6\,b^2-4\,A\,B^3\,a^7\,b+B^4\,a^8\right)}{b^3}-\frac{96\,{\left(-a\right)}^{1/6}\,\left(A\,b-B\,a\right)\,\left(-A^3\,a^4\,b^3+3\,A^2\,B\,a^5\,b^2-3\,A\,B^2\,a^6\,b+B^3\,a^7\right)}{b^{19/6}}\right)}{3\,b^{13/6}}-\frac{{\left(-a\right)}^{1/6}\,\left(A\,b-B\,a\right)\,\left(\frac{96\,\sqrt{x}\,\left(A^4\,a^4\,b^4-4\,A^3\,B\,a^5\,b^3+6\,A^2\,B^2\,a^6\,b^2-4\,A\,B^3\,a^7\,b+B^4\,a^8\right)}{b^3}+\frac{96\,{\left(-a\right)}^{1/6}\,\left(A\,b-B\,a\right)\,\left(-A^3\,a^4\,b^3+3\,A^2\,B\,a^5\,b^2-3\,A\,B^2\,a^6\,b+B^3\,a^7\right)}{b^{19/6}}\right)}{3\,b^{13/6}}}\right)\,\left(A\,b-B\,a\right)\,2{}\mathrm{i}}{3\,b^{13/6}}+\frac{{\left(-a\right)}^{1/6}\,\mathrm{atan}\left(\frac{\frac{{\left(-a\right)}^{1/6}\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(\frac{96\,\sqrt{x}\,\left(A^4\,a^4\,b^4-4\,A^3\,B\,a^5\,b^3+6\,A^2\,B^2\,a^6\,b^2-4\,A\,B^3\,a^7\,b+B^4\,a^8\right)}{b^3}-\frac{96\,{\left(-a\right)}^{1/6}\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(-A^3\,a^4\,b^3+3\,A^2\,B\,a^5\,b^2-3\,A\,B^2\,a^6\,b+B^3\,a^7\right)}{b^{19/6}}\right)\,1{}\mathrm{i}}{3\,b^{13/6}}+\frac{{\left(-a\right)}^{1/6}\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(\frac{96\,\sqrt{x}\,\left(A^4\,a^4\,b^4-4\,A^3\,B\,a^5\,b^3+6\,A^2\,B^2\,a^6\,b^2-4\,A\,B^3\,a^7\,b+B^4\,a^8\right)}{b^3}+\frac{96\,{\left(-a\right)}^{1/6}\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(-A^3\,a^4\,b^3+3\,A^2\,B\,a^5\,b^2-3\,A\,B^2\,a^6\,b+B^3\,a^7\right)}{b^{19/6}}\right)\,1{}\mathrm{i}}{3\,b^{13/6}}}{\frac{{\left(-a\right)}^{1/6}\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(\frac{96\,\sqrt{x}\,\left(A^4\,a^4\,b^4-4\,A^3\,B\,a^5\,b^3+6\,A^2\,B^2\,a^6\,b^2-4\,A\,B^3\,a^7\,b+B^4\,a^8\right)}{b^3}-\frac{96\,{\left(-a\right)}^{1/6}\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(-A^3\,a^4\,b^3+3\,A^2\,B\,a^5\,b^2-3\,A\,B^2\,a^6\,b+B^3\,a^7\right)}{b^{19/6}}\right)}{3\,b^{13/6}}-\frac{{\left(-a\right)}^{1/6}\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(\frac{96\,\sqrt{x}\,\left(A^4\,a^4\,b^4-4\,A^3\,B\,a^5\,b^3+6\,A^2\,B^2\,a^6\,b^2-4\,A\,B^3\,a^7\,b+B^4\,a^8\right)}{b^3}+\frac{96\,{\left(-a\right)}^{1/6}\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(-A^3\,a^4\,b^3+3\,A^2\,B\,a^5\,b^2-3\,A\,B^2\,a^6\,b+B^3\,a^7\right)}{b^{19/6}}\right)}{3\,b^{13/6}}}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,2{}\mathrm{i}}{3\,b^{13/6}}+\frac{{\left(-a\right)}^{1/6}\,\mathrm{atan}\left(\frac{\frac{{\left(-a\right)}^{1/6}\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(\frac{96\,\sqrt{x}\,\left(A^4\,a^4\,b^4-4\,A^3\,B\,a^5\,b^3+6\,A^2\,B^2\,a^6\,b^2-4\,A\,B^3\,a^7\,b+B^4\,a^8\right)}{b^3}-\frac{96\,{\left(-a\right)}^{1/6}\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(-A^3\,a^4\,b^3+3\,A^2\,B\,a^5\,b^2-3\,A\,B^2\,a^6\,b+B^3\,a^7\right)}{b^{19/6}}\right)\,1{}\mathrm{i}}{3\,b^{13/6}}+\frac{{\left(-a\right)}^{1/6}\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(\frac{96\,\sqrt{x}\,\left(A^4\,a^4\,b^4-4\,A^3\,B\,a^5\,b^3+6\,A^2\,B^2\,a^6\,b^2-4\,A\,B^3\,a^7\,b+B^4\,a^8\right)}{b^3}+\frac{96\,{\left(-a\right)}^{1/6}\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(-A^3\,a^4\,b^3+3\,A^2\,B\,a^5\,b^2-3\,A\,B^2\,a^6\,b+B^3\,a^7\right)}{b^{19/6}}\right)\,1{}\mathrm{i}}{3\,b^{13/6}}}{\frac{{\left(-a\right)}^{1/6}\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(\frac{96\,\sqrt{x}\,\left(A^4\,a^4\,b^4-4\,A^3\,B\,a^5\,b^3+6\,A^2\,B^2\,a^6\,b^2-4\,A\,B^3\,a^7\,b+B^4\,a^8\right)}{b^3}-\frac{96\,{\left(-a\right)}^{1/6}\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(-A^3\,a^4\,b^3+3\,A^2\,B\,a^5\,b^2-3\,A\,B^2\,a^6\,b+B^3\,a^7\right)}{b^{19/6}}\right)}{3\,b^{13/6}}-\frac{{\left(-a\right)}^{1/6}\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(\frac{96\,\sqrt{x}\,\left(A^4\,a^4\,b^4-4\,A^3\,B\,a^5\,b^3+6\,A^2\,B^2\,a^6\,b^2-4\,A\,B^3\,a^7\,b+B^4\,a^8\right)}{b^3}+\frac{96\,{\left(-a\right)}^{1/6}\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(-A^3\,a^4\,b^3+3\,A^2\,B\,a^5\,b^2-3\,A\,B^2\,a^6\,b+B^3\,a^7\right)}{b^{19/6}}\right)}{3\,b^{13/6}}}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,2{}\mathrm{i}}{3\,b^{13/6}}","Not used",1,"x^(1/2)*((2*A)/b - (2*B*a)/b^2) + (2*B*x^(7/2))/(7*b) + ((-a)^(1/6)*atan((((-a)^(1/6)*(A*b - B*a)*((96*x^(1/2)*(B^4*a^8 + A^4*a^4*b^4 + 6*A^2*B^2*a^6*b^2 - 4*A*B^3*a^7*b - 4*A^3*B*a^5*b^3))/b^3 - (96*(-a)^(1/6)*(A*b - B*a)*(B^3*a^7 - A^3*a^4*b^3 - 3*A*B^2*a^6*b + 3*A^2*B*a^5*b^2))/b^(19/6))*1i)/(3*b^(13/6)) + ((-a)^(1/6)*(A*b - B*a)*((96*x^(1/2)*(B^4*a^8 + A^4*a^4*b^4 + 6*A^2*B^2*a^6*b^2 - 4*A*B^3*a^7*b - 4*A^3*B*a^5*b^3))/b^3 + (96*(-a)^(1/6)*(A*b - B*a)*(B^3*a^7 - A^3*a^4*b^3 - 3*A*B^2*a^6*b + 3*A^2*B*a^5*b^2))/b^(19/6))*1i)/(3*b^(13/6)))/(((-a)^(1/6)*(A*b - B*a)*((96*x^(1/2)*(B^4*a^8 + A^4*a^4*b^4 + 6*A^2*B^2*a^6*b^2 - 4*A*B^3*a^7*b - 4*A^3*B*a^5*b^3))/b^3 - (96*(-a)^(1/6)*(A*b - B*a)*(B^3*a^7 - A^3*a^4*b^3 - 3*A*B^2*a^6*b + 3*A^2*B*a^5*b^2))/b^(19/6)))/(3*b^(13/6)) - ((-a)^(1/6)*(A*b - B*a)*((96*x^(1/2)*(B^4*a^8 + A^4*a^4*b^4 + 6*A^2*B^2*a^6*b^2 - 4*A*B^3*a^7*b - 4*A^3*B*a^5*b^3))/b^3 + (96*(-a)^(1/6)*(A*b - B*a)*(B^3*a^7 - A^3*a^4*b^3 - 3*A*B^2*a^6*b + 3*A^2*B*a^5*b^2))/b^(19/6)))/(3*b^(13/6))))*(A*b - B*a)*2i)/(3*b^(13/6)) + ((-a)^(1/6)*atan((((-a)^(1/6)*((3^(1/2)*1i)/2 - 1/2)*(A*b - B*a)*((96*x^(1/2)*(B^4*a^8 + A^4*a^4*b^4 + 6*A^2*B^2*a^6*b^2 - 4*A*B^3*a^7*b - 4*A^3*B*a^5*b^3))/b^3 - (96*(-a)^(1/6)*((3^(1/2)*1i)/2 - 1/2)*(A*b - B*a)*(B^3*a^7 - A^3*a^4*b^3 - 3*A*B^2*a^6*b + 3*A^2*B*a^5*b^2))/b^(19/6))*1i)/(3*b^(13/6)) + ((-a)^(1/6)*((3^(1/2)*1i)/2 - 1/2)*(A*b - B*a)*((96*x^(1/2)*(B^4*a^8 + A^4*a^4*b^4 + 6*A^2*B^2*a^6*b^2 - 4*A*B^3*a^7*b - 4*A^3*B*a^5*b^3))/b^3 + (96*(-a)^(1/6)*((3^(1/2)*1i)/2 - 1/2)*(A*b - B*a)*(B^3*a^7 - A^3*a^4*b^3 - 3*A*B^2*a^6*b + 3*A^2*B*a^5*b^2))/b^(19/6))*1i)/(3*b^(13/6)))/(((-a)^(1/6)*((3^(1/2)*1i)/2 - 1/2)*(A*b - B*a)*((96*x^(1/2)*(B^4*a^8 + A^4*a^4*b^4 + 6*A^2*B^2*a^6*b^2 - 4*A*B^3*a^7*b - 4*A^3*B*a^5*b^3))/b^3 - (96*(-a)^(1/6)*((3^(1/2)*1i)/2 - 1/2)*(A*b - B*a)*(B^3*a^7 - A^3*a^4*b^3 - 3*A*B^2*a^6*b + 3*A^2*B*a^5*b^2))/b^(19/6)))/(3*b^(13/6)) - ((-a)^(1/6)*((3^(1/2)*1i)/2 - 1/2)*(A*b - B*a)*((96*x^(1/2)*(B^4*a^8 + A^4*a^4*b^4 + 6*A^2*B^2*a^6*b^2 - 4*A*B^3*a^7*b - 4*A^3*B*a^5*b^3))/b^3 + (96*(-a)^(1/6)*((3^(1/2)*1i)/2 - 1/2)*(A*b - B*a)*(B^3*a^7 - A^3*a^4*b^3 - 3*A*B^2*a^6*b + 3*A^2*B*a^5*b^2))/b^(19/6)))/(3*b^(13/6))))*((3^(1/2)*1i)/2 - 1/2)*(A*b - B*a)*2i)/(3*b^(13/6)) + ((-a)^(1/6)*atan((((-a)^(1/6)*((3^(1/2)*1i)/2 + 1/2)*(A*b - B*a)*((96*x^(1/2)*(B^4*a^8 + A^4*a^4*b^4 + 6*A^2*B^2*a^6*b^2 - 4*A*B^3*a^7*b - 4*A^3*B*a^5*b^3))/b^3 - (96*(-a)^(1/6)*((3^(1/2)*1i)/2 + 1/2)*(A*b - B*a)*(B^3*a^7 - A^3*a^4*b^3 - 3*A*B^2*a^6*b + 3*A^2*B*a^5*b^2))/b^(19/6))*1i)/(3*b^(13/6)) + ((-a)^(1/6)*((3^(1/2)*1i)/2 + 1/2)*(A*b - B*a)*((96*x^(1/2)*(B^4*a^8 + A^4*a^4*b^4 + 6*A^2*B^2*a^6*b^2 - 4*A*B^3*a^7*b - 4*A^3*B*a^5*b^3))/b^3 + (96*(-a)^(1/6)*((3^(1/2)*1i)/2 + 1/2)*(A*b - B*a)*(B^3*a^7 - A^3*a^4*b^3 - 3*A*B^2*a^6*b + 3*A^2*B*a^5*b^2))/b^(19/6))*1i)/(3*b^(13/6)))/(((-a)^(1/6)*((3^(1/2)*1i)/2 + 1/2)*(A*b - B*a)*((96*x^(1/2)*(B^4*a^8 + A^4*a^4*b^4 + 6*A^2*B^2*a^6*b^2 - 4*A*B^3*a^7*b - 4*A^3*B*a^5*b^3))/b^3 - (96*(-a)^(1/6)*((3^(1/2)*1i)/2 + 1/2)*(A*b - B*a)*(B^3*a^7 - A^3*a^4*b^3 - 3*A*B^2*a^6*b + 3*A^2*B*a^5*b^2))/b^(19/6)))/(3*b^(13/6)) - ((-a)^(1/6)*((3^(1/2)*1i)/2 + 1/2)*(A*b - B*a)*((96*x^(1/2)*(B^4*a^8 + A^4*a^4*b^4 + 6*A^2*B^2*a^6*b^2 - 4*A*B^3*a^7*b - 4*A^3*B*a^5*b^3))/b^3 + (96*(-a)^(1/6)*((3^(1/2)*1i)/2 + 1/2)*(A*b - B*a)*(B^3*a^7 - A^3*a^4*b^3 - 3*A*B^2*a^6*b + 3*A^2*B*a^5*b^2))/b^(19/6)))/(3*b^(13/6))))*((3^(1/2)*1i)/2 + 1/2)*(A*b - B*a)*2i)/(3*b^(13/6))","B"
157,1,1640,270,2.852762,"\text{Not used}","int((x^(3/2)*(A + B*x^3))/(a + b*x^3),x)","\frac{2\,B\,x^{5/2}}{5\,b}+\frac{\mathrm{atan}\left(\frac{\frac{{\left(A\,b-B\,a\right)}^2\,\left(32\,A^3\,a^3\,b^3-32\,B^3\,a^6+96\,A\,B^2\,a^5\,b-96\,A^2\,B\,a^4\,b^2+\frac{\sqrt{x}\,\left(A\,b-B\,a\right)\,\left(864\,A^2\,a^3\,b^4-1728\,A\,B\,a^4\,b^3+864\,B^2\,a^5\,b^2\right)}{27\,{\left(-a\right)}^{1/6}\,b^{11/6}}\right)\,1{}\mathrm{i}}{{\left(-a\right)}^{1/3}\,b^{11/3}}+\frac{{\left(A\,b-B\,a\right)}^2\,\left(32\,B^3\,a^6-32\,A^3\,a^3\,b^3-96\,A\,B^2\,a^5\,b+96\,A^2\,B\,a^4\,b^2+\frac{\sqrt{x}\,\left(A\,b-B\,a\right)\,\left(864\,A^2\,a^3\,b^4-1728\,A\,B\,a^4\,b^3+864\,B^2\,a^5\,b^2\right)}{27\,{\left(-a\right)}^{1/6}\,b^{11/6}}\right)\,1{}\mathrm{i}}{{\left(-a\right)}^{1/3}\,b^{11/3}}}{\frac{{\left(A\,b-B\,a\right)}^2\,\left(32\,A^3\,a^3\,b^3-32\,B^3\,a^6+96\,A\,B^2\,a^5\,b-96\,A^2\,B\,a^4\,b^2+\frac{\sqrt{x}\,\left(A\,b-B\,a\right)\,\left(864\,A^2\,a^3\,b^4-1728\,A\,B\,a^4\,b^3+864\,B^2\,a^5\,b^2\right)}{27\,{\left(-a\right)}^{1/6}\,b^{11/6}}\right)}{{\left(-a\right)}^{1/3}\,b^{11/3}}-\frac{{\left(A\,b-B\,a\right)}^2\,\left(32\,B^3\,a^6-32\,A^3\,a^3\,b^3-96\,A\,B^2\,a^5\,b+96\,A^2\,B\,a^4\,b^2+\frac{\sqrt{x}\,\left(A\,b-B\,a\right)\,\left(864\,A^2\,a^3\,b^4-1728\,A\,B\,a^4\,b^3+864\,B^2\,a^5\,b^2\right)}{27\,{\left(-a\right)}^{1/6}\,b^{11/6}}\right)}{{\left(-a\right)}^{1/3}\,b^{11/3}}}\right)\,\left(A\,b-B\,a\right)\,2{}\mathrm{i}}{3\,{\left(-a\right)}^{1/6}\,b^{11/6}}+\frac{\mathrm{atan}\left(\frac{\frac{{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(A\,b-B\,a\right)}^2\,\left(32\,A^3\,a^3\,b^3-32\,B^3\,a^6+96\,A\,B^2\,a^5\,b-96\,A^2\,B\,a^4\,b^2+\frac{\sqrt{x}\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(864\,A^2\,a^3\,b^4-1728\,A\,B\,a^4\,b^3+864\,B^2\,a^5\,b^2\right)}{27\,{\left(-a\right)}^{1/6}\,b^{11/6}}\right)\,1{}\mathrm{i}}{{\left(-a\right)}^{1/3}\,b^{11/3}}+\frac{{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(A\,b-B\,a\right)}^2\,\left(32\,B^3\,a^6-32\,A^3\,a^3\,b^3-96\,A\,B^2\,a^5\,b+96\,A^2\,B\,a^4\,b^2+\frac{\sqrt{x}\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(864\,A^2\,a^3\,b^4-1728\,A\,B\,a^4\,b^3+864\,B^2\,a^5\,b^2\right)}{27\,{\left(-a\right)}^{1/6}\,b^{11/6}}\right)\,1{}\mathrm{i}}{{\left(-a\right)}^{1/3}\,b^{11/3}}}{\frac{{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(A\,b-B\,a\right)}^2\,\left(32\,A^3\,a^3\,b^3-32\,B^3\,a^6+96\,A\,B^2\,a^5\,b-96\,A^2\,B\,a^4\,b^2+\frac{\sqrt{x}\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(864\,A^2\,a^3\,b^4-1728\,A\,B\,a^4\,b^3+864\,B^2\,a^5\,b^2\right)}{27\,{\left(-a\right)}^{1/6}\,b^{11/6}}\right)}{{\left(-a\right)}^{1/3}\,b^{11/3}}-\frac{{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(A\,b-B\,a\right)}^2\,\left(32\,B^3\,a^6-32\,A^3\,a^3\,b^3-96\,A\,B^2\,a^5\,b+96\,A^2\,B\,a^4\,b^2+\frac{\sqrt{x}\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(864\,A^2\,a^3\,b^4-1728\,A\,B\,a^4\,b^3+864\,B^2\,a^5\,b^2\right)}{27\,{\left(-a\right)}^{1/6}\,b^{11/6}}\right)}{{\left(-a\right)}^{1/3}\,b^{11/3}}}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,2{}\mathrm{i}}{3\,{\left(-a\right)}^{1/6}\,b^{11/6}}+\frac{\mathrm{atan}\left(\frac{\frac{{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(A\,b-B\,a\right)}^2\,\left(32\,A^3\,a^3\,b^3-32\,B^3\,a^6+96\,A\,B^2\,a^5\,b-96\,A^2\,B\,a^4\,b^2+\frac{\sqrt{x}\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(864\,A^2\,a^3\,b^4-1728\,A\,B\,a^4\,b^3+864\,B^2\,a^5\,b^2\right)}{27\,{\left(-a\right)}^{1/6}\,b^{11/6}}\right)\,1{}\mathrm{i}}{{\left(-a\right)}^{1/3}\,b^{11/3}}+\frac{{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(A\,b-B\,a\right)}^2\,\left(32\,B^3\,a^6-32\,A^3\,a^3\,b^3-96\,A\,B^2\,a^5\,b+96\,A^2\,B\,a^4\,b^2+\frac{\sqrt{x}\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(864\,A^2\,a^3\,b^4-1728\,A\,B\,a^4\,b^3+864\,B^2\,a^5\,b^2\right)}{27\,{\left(-a\right)}^{1/6}\,b^{11/6}}\right)\,1{}\mathrm{i}}{{\left(-a\right)}^{1/3}\,b^{11/3}}}{\frac{{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(A\,b-B\,a\right)}^2\,\left(32\,A^3\,a^3\,b^3-32\,B^3\,a^6+96\,A\,B^2\,a^5\,b-96\,A^2\,B\,a^4\,b^2+\frac{\sqrt{x}\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(864\,A^2\,a^3\,b^4-1728\,A\,B\,a^4\,b^3+864\,B^2\,a^5\,b^2\right)}{27\,{\left(-a\right)}^{1/6}\,b^{11/6}}\right)}{{\left(-a\right)}^{1/3}\,b^{11/3}}-\frac{{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(A\,b-B\,a\right)}^2\,\left(32\,B^3\,a^6-32\,A^3\,a^3\,b^3-96\,A\,B^2\,a^5\,b+96\,A^2\,B\,a^4\,b^2+\frac{\sqrt{x}\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(864\,A^2\,a^3\,b^4-1728\,A\,B\,a^4\,b^3+864\,B^2\,a^5\,b^2\right)}{27\,{\left(-a\right)}^{1/6}\,b^{11/6}}\right)}{{\left(-a\right)}^{1/3}\,b^{11/3}}}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,2{}\mathrm{i}}{3\,{\left(-a\right)}^{1/6}\,b^{11/6}}","Not used",1,"(2*B*x^(5/2))/(5*b) + (atan((((A*b - B*a)^2*(32*A^3*a^3*b^3 - 32*B^3*a^6 + 96*A*B^2*a^5*b - 96*A^2*B*a^4*b^2 + (x^(1/2)*(A*b - B*a)*(864*A^2*a^3*b^4 + 864*B^2*a^5*b^2 - 1728*A*B*a^4*b^3))/(27*(-a)^(1/6)*b^(11/6)))*1i)/((-a)^(1/3)*b^(11/3)) + ((A*b - B*a)^2*(32*B^3*a^6 - 32*A^3*a^3*b^3 - 96*A*B^2*a^5*b + 96*A^2*B*a^4*b^2 + (x^(1/2)*(A*b - B*a)*(864*A^2*a^3*b^4 + 864*B^2*a^5*b^2 - 1728*A*B*a^4*b^3))/(27*(-a)^(1/6)*b^(11/6)))*1i)/((-a)^(1/3)*b^(11/3)))/(((A*b - B*a)^2*(32*A^3*a^3*b^3 - 32*B^3*a^6 + 96*A*B^2*a^5*b - 96*A^2*B*a^4*b^2 + (x^(1/2)*(A*b - B*a)*(864*A^2*a^3*b^4 + 864*B^2*a^5*b^2 - 1728*A*B*a^4*b^3))/(27*(-a)^(1/6)*b^(11/6))))/((-a)^(1/3)*b^(11/3)) - ((A*b - B*a)^2*(32*B^3*a^6 - 32*A^3*a^3*b^3 - 96*A*B^2*a^5*b + 96*A^2*B*a^4*b^2 + (x^(1/2)*(A*b - B*a)*(864*A^2*a^3*b^4 + 864*B^2*a^5*b^2 - 1728*A*B*a^4*b^3))/(27*(-a)^(1/6)*b^(11/6))))/((-a)^(1/3)*b^(11/3))))*(A*b - B*a)*2i)/(3*(-a)^(1/6)*b^(11/6)) + (atan(((((3^(1/2)*1i)/2 - 1/2)^2*(A*b - B*a)^2*(32*A^3*a^3*b^3 - 32*B^3*a^6 + 96*A*B^2*a^5*b - 96*A^2*B*a^4*b^2 + (x^(1/2)*((3^(1/2)*1i)/2 - 1/2)*(A*b - B*a)*(864*A^2*a^3*b^4 + 864*B^2*a^5*b^2 - 1728*A*B*a^4*b^3))/(27*(-a)^(1/6)*b^(11/6)))*1i)/((-a)^(1/3)*b^(11/3)) + (((3^(1/2)*1i)/2 - 1/2)^2*(A*b - B*a)^2*(32*B^3*a^6 - 32*A^3*a^3*b^3 - 96*A*B^2*a^5*b + 96*A^2*B*a^4*b^2 + (x^(1/2)*((3^(1/2)*1i)/2 - 1/2)*(A*b - B*a)*(864*A^2*a^3*b^4 + 864*B^2*a^5*b^2 - 1728*A*B*a^4*b^3))/(27*(-a)^(1/6)*b^(11/6)))*1i)/((-a)^(1/3)*b^(11/3)))/((((3^(1/2)*1i)/2 - 1/2)^2*(A*b - B*a)^2*(32*A^3*a^3*b^3 - 32*B^3*a^6 + 96*A*B^2*a^5*b - 96*A^2*B*a^4*b^2 + (x^(1/2)*((3^(1/2)*1i)/2 - 1/2)*(A*b - B*a)*(864*A^2*a^3*b^4 + 864*B^2*a^5*b^2 - 1728*A*B*a^4*b^3))/(27*(-a)^(1/6)*b^(11/6))))/((-a)^(1/3)*b^(11/3)) - (((3^(1/2)*1i)/2 - 1/2)^2*(A*b - B*a)^2*(32*B^3*a^6 - 32*A^3*a^3*b^3 - 96*A*B^2*a^5*b + 96*A^2*B*a^4*b^2 + (x^(1/2)*((3^(1/2)*1i)/2 - 1/2)*(A*b - B*a)*(864*A^2*a^3*b^4 + 864*B^2*a^5*b^2 - 1728*A*B*a^4*b^3))/(27*(-a)^(1/6)*b^(11/6))))/((-a)^(1/3)*b^(11/3))))*((3^(1/2)*1i)/2 - 1/2)*(A*b - B*a)*2i)/(3*(-a)^(1/6)*b^(11/6)) + (atan(((((3^(1/2)*1i)/2 + 1/2)^2*(A*b - B*a)^2*(32*A^3*a^3*b^3 - 32*B^3*a^6 + 96*A*B^2*a^5*b - 96*A^2*B*a^4*b^2 + (x^(1/2)*((3^(1/2)*1i)/2 + 1/2)*(A*b - B*a)*(864*A^2*a^3*b^4 + 864*B^2*a^5*b^2 - 1728*A*B*a^4*b^3))/(27*(-a)^(1/6)*b^(11/6)))*1i)/((-a)^(1/3)*b^(11/3)) + (((3^(1/2)*1i)/2 + 1/2)^2*(A*b - B*a)^2*(32*B^3*a^6 - 32*A^3*a^3*b^3 - 96*A*B^2*a^5*b + 96*A^2*B*a^4*b^2 + (x^(1/2)*((3^(1/2)*1i)/2 + 1/2)*(A*b - B*a)*(864*A^2*a^3*b^4 + 864*B^2*a^5*b^2 - 1728*A*B*a^4*b^3))/(27*(-a)^(1/6)*b^(11/6)))*1i)/((-a)^(1/3)*b^(11/3)))/((((3^(1/2)*1i)/2 + 1/2)^2*(A*b - B*a)^2*(32*A^3*a^3*b^3 - 32*B^3*a^6 + 96*A*B^2*a^5*b - 96*A^2*B*a^4*b^2 + (x^(1/2)*((3^(1/2)*1i)/2 + 1/2)*(A*b - B*a)*(864*A^2*a^3*b^4 + 864*B^2*a^5*b^2 - 1728*A*B*a^4*b^3))/(27*(-a)^(1/6)*b^(11/6))))/((-a)^(1/3)*b^(11/3)) - (((3^(1/2)*1i)/2 + 1/2)^2*(A*b - B*a)^2*(32*B^3*a^6 - 32*A^3*a^3*b^3 - 96*A*B^2*a^5*b + 96*A^2*B*a^4*b^2 + (x^(1/2)*((3^(1/2)*1i)/2 + 1/2)*(A*b - B*a)*(864*A^2*a^3*b^4 + 864*B^2*a^5*b^2 - 1728*A*B*a^4*b^3))/(27*(-a)^(1/6)*b^(11/6))))/((-a)^(1/3)*b^(11/3))))*((3^(1/2)*1i)/2 + 1/2)*(A*b - B*a)*2i)/(3*(-a)^(1/6)*b^(11/6))","B"
158,1,93,53,2.599565,"\text{Not used}","int((x^(1/2)*(A + B*x^3))/(a + b*x^3),x)","\frac{2\,B\,x^{3/2}}{3\,b}-\frac{2\,\mathrm{atan}\left(\frac{3\,\sqrt{a}\,b^{3/2}\,x^{3/2}\,\left(24\,A^2\,b^3-48\,A\,B\,a\,b^2+24\,B^2\,a^2\,b\right)}{\left(72\,B\,a^2\,b^2-72\,A\,a\,b^3\right)\,\left(A\,b-B\,a\right)}\right)\,\left(A\,b-B\,a\right)}{3\,\sqrt{a}\,b^{3/2}}","Not used",1,"(2*B*x^(3/2))/(3*b) - (2*atan((3*a^(1/2)*b^(3/2)*x^(3/2)*(24*A^2*b^3 + 24*B^2*a^2*b - 48*A*B*a*b^2))/((72*B*a^2*b^2 - 72*A*a*b^3)*(A*b - B*a)))*(A*b - B*a))/(3*a^(1/2)*b^(3/2))","B"
159,1,1915,268,2.884833,"\text{Not used}","int((A + B*x^3)/(x^(1/2)*(a + b*x^3)),x)","\frac{2\,B\,\sqrt{x}}{b}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\sqrt{x}\,\left(96\,A^4\,b^5-384\,A^3\,B\,a\,b^4+576\,A^2\,B^2\,a^2\,b^3-384\,A\,B^3\,a^3\,b^2+96\,B^4\,a^4\,b\right)-\frac{\left(A\,b-B\,a\right)\,\left(288\,A^3\,a\,b^5-864\,A^2\,B\,a^2\,b^4+864\,A\,B^2\,a^3\,b^3-288\,B^3\,a^4\,b^2\right)}{3\,{\left(-a\right)}^{5/6}\,b^{7/6}}\right)\,\left(A\,b-B\,a\right)\,1{}\mathrm{i}}{3\,{\left(-a\right)}^{5/6}\,b^{7/6}}+\frac{\left(\sqrt{x}\,\left(96\,A^4\,b^5-384\,A^3\,B\,a\,b^4+576\,A^2\,B^2\,a^2\,b^3-384\,A\,B^3\,a^3\,b^2+96\,B^4\,a^4\,b\right)+\frac{\left(A\,b-B\,a\right)\,\left(288\,A^3\,a\,b^5-864\,A^2\,B\,a^2\,b^4+864\,A\,B^2\,a^3\,b^3-288\,B^3\,a^4\,b^2\right)}{3\,{\left(-a\right)}^{5/6}\,b^{7/6}}\right)\,\left(A\,b-B\,a\right)\,1{}\mathrm{i}}{3\,{\left(-a\right)}^{5/6}\,b^{7/6}}}{\frac{\left(\sqrt{x}\,\left(96\,A^4\,b^5-384\,A^3\,B\,a\,b^4+576\,A^2\,B^2\,a^2\,b^3-384\,A\,B^3\,a^3\,b^2+96\,B^4\,a^4\,b\right)-\frac{\left(A\,b-B\,a\right)\,\left(288\,A^3\,a\,b^5-864\,A^2\,B\,a^2\,b^4+864\,A\,B^2\,a^3\,b^3-288\,B^3\,a^4\,b^2\right)}{3\,{\left(-a\right)}^{5/6}\,b^{7/6}}\right)\,\left(A\,b-B\,a\right)}{3\,{\left(-a\right)}^{5/6}\,b^{7/6}}-\frac{\left(\sqrt{x}\,\left(96\,A^4\,b^5-384\,A^3\,B\,a\,b^4+576\,A^2\,B^2\,a^2\,b^3-384\,A\,B^3\,a^3\,b^2+96\,B^4\,a^4\,b\right)+\frac{\left(A\,b-B\,a\right)\,\left(288\,A^3\,a\,b^5-864\,A^2\,B\,a^2\,b^4+864\,A\,B^2\,a^3\,b^3-288\,B^3\,a^4\,b^2\right)}{3\,{\left(-a\right)}^{5/6}\,b^{7/6}}\right)\,\left(A\,b-B\,a\right)}{3\,{\left(-a\right)}^{5/6}\,b^{7/6}}}\right)\,\left(A\,b-B\,a\right)\,2{}\mathrm{i}}{3\,{\left(-a\right)}^{5/6}\,b^{7/6}}+\frac{\mathrm{atan}\left(\frac{\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(\sqrt{x}\,\left(96\,A^4\,b^5-384\,A^3\,B\,a\,b^4+576\,A^2\,B^2\,a^2\,b^3-384\,A\,B^3\,a^3\,b^2+96\,B^4\,a^4\,b\right)-\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(288\,A^3\,a\,b^5-864\,A^2\,B\,a^2\,b^4+864\,A\,B^2\,a^3\,b^3-288\,B^3\,a^4\,b^2\right)}{3\,{\left(-a\right)}^{5/6}\,b^{7/6}}\right)\,1{}\mathrm{i}}{3\,{\left(-a\right)}^{5/6}\,b^{7/6}}+\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(\sqrt{x}\,\left(96\,A^4\,b^5-384\,A^3\,B\,a\,b^4+576\,A^2\,B^2\,a^2\,b^3-384\,A\,B^3\,a^3\,b^2+96\,B^4\,a^4\,b\right)+\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(288\,A^3\,a\,b^5-864\,A^2\,B\,a^2\,b^4+864\,A\,B^2\,a^3\,b^3-288\,B^3\,a^4\,b^2\right)}{3\,{\left(-a\right)}^{5/6}\,b^{7/6}}\right)\,1{}\mathrm{i}}{3\,{\left(-a\right)}^{5/6}\,b^{7/6}}}{\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(\sqrt{x}\,\left(96\,A^4\,b^5-384\,A^3\,B\,a\,b^4+576\,A^2\,B^2\,a^2\,b^3-384\,A\,B^3\,a^3\,b^2+96\,B^4\,a^4\,b\right)-\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(288\,A^3\,a\,b^5-864\,A^2\,B\,a^2\,b^4+864\,A\,B^2\,a^3\,b^3-288\,B^3\,a^4\,b^2\right)}{3\,{\left(-a\right)}^{5/6}\,b^{7/6}}\right)}{3\,{\left(-a\right)}^{5/6}\,b^{7/6}}-\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(\sqrt{x}\,\left(96\,A^4\,b^5-384\,A^3\,B\,a\,b^4+576\,A^2\,B^2\,a^2\,b^3-384\,A\,B^3\,a^3\,b^2+96\,B^4\,a^4\,b\right)+\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(288\,A^3\,a\,b^5-864\,A^2\,B\,a^2\,b^4+864\,A\,B^2\,a^3\,b^3-288\,B^3\,a^4\,b^2\right)}{3\,{\left(-a\right)}^{5/6}\,b^{7/6}}\right)}{3\,{\left(-a\right)}^{5/6}\,b^{7/6}}}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,2{}\mathrm{i}}{3\,{\left(-a\right)}^{5/6}\,b^{7/6}}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(\sqrt{x}\,\left(96\,A^4\,b^5-384\,A^3\,B\,a\,b^4+576\,A^2\,B^2\,a^2\,b^3-384\,A\,B^3\,a^3\,b^2+96\,B^4\,a^4\,b\right)-\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(288\,A^3\,a\,b^5-864\,A^2\,B\,a^2\,b^4+864\,A\,B^2\,a^3\,b^3-288\,B^3\,a^4\,b^2\right)}{3\,{\left(-a\right)}^{5/6}\,b^{7/6}}\right)\,1{}\mathrm{i}}{3\,{\left(-a\right)}^{5/6}\,b^{7/6}}+\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(\sqrt{x}\,\left(96\,A^4\,b^5-384\,A^3\,B\,a\,b^4+576\,A^2\,B^2\,a^2\,b^3-384\,A\,B^3\,a^3\,b^2+96\,B^4\,a^4\,b\right)+\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(288\,A^3\,a\,b^5-864\,A^2\,B\,a^2\,b^4+864\,A\,B^2\,a^3\,b^3-288\,B^3\,a^4\,b^2\right)}{3\,{\left(-a\right)}^{5/6}\,b^{7/6}}\right)\,1{}\mathrm{i}}{3\,{\left(-a\right)}^{5/6}\,b^{7/6}}}{\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(\sqrt{x}\,\left(96\,A^4\,b^5-384\,A^3\,B\,a\,b^4+576\,A^2\,B^2\,a^2\,b^3-384\,A\,B^3\,a^3\,b^2+96\,B^4\,a^4\,b\right)-\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(288\,A^3\,a\,b^5-864\,A^2\,B\,a^2\,b^4+864\,A\,B^2\,a^3\,b^3-288\,B^3\,a^4\,b^2\right)}{3\,{\left(-a\right)}^{5/6}\,b^{7/6}}\right)}{3\,{\left(-a\right)}^{5/6}\,b^{7/6}}-\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(\sqrt{x}\,\left(96\,A^4\,b^5-384\,A^3\,B\,a\,b^4+576\,A^2\,B^2\,a^2\,b^3-384\,A\,B^3\,a^3\,b^2+96\,B^4\,a^4\,b\right)+\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(288\,A^3\,a\,b^5-864\,A^2\,B\,a^2\,b^4+864\,A\,B^2\,a^3\,b^3-288\,B^3\,a^4\,b^2\right)}{3\,{\left(-a\right)}^{5/6}\,b^{7/6}}\right)}{3\,{\left(-a\right)}^{5/6}\,b^{7/6}}}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,2{}\mathrm{i}}{3\,{\left(-a\right)}^{5/6}\,b^{7/6}}","Not used",1,"(2*B*x^(1/2))/b + (atan((((x^(1/2)*(96*A^4*b^5 + 96*B^4*a^4*b + 576*A^2*B^2*a^2*b^3 - 384*A^3*B*a*b^4 - 384*A*B^3*a^3*b^2) - ((A*b - B*a)*(288*A^3*a*b^5 - 288*B^3*a^4*b^2 + 864*A*B^2*a^3*b^3 - 864*A^2*B*a^2*b^4))/(3*(-a)^(5/6)*b^(7/6)))*(A*b - B*a)*1i)/(3*(-a)^(5/6)*b^(7/6)) + ((x^(1/2)*(96*A^4*b^5 + 96*B^4*a^4*b + 576*A^2*B^2*a^2*b^3 - 384*A^3*B*a*b^4 - 384*A*B^3*a^3*b^2) + ((A*b - B*a)*(288*A^3*a*b^5 - 288*B^3*a^4*b^2 + 864*A*B^2*a^3*b^3 - 864*A^2*B*a^2*b^4))/(3*(-a)^(5/6)*b^(7/6)))*(A*b - B*a)*1i)/(3*(-a)^(5/6)*b^(7/6)))/(((x^(1/2)*(96*A^4*b^5 + 96*B^4*a^4*b + 576*A^2*B^2*a^2*b^3 - 384*A^3*B*a*b^4 - 384*A*B^3*a^3*b^2) - ((A*b - B*a)*(288*A^3*a*b^5 - 288*B^3*a^4*b^2 + 864*A*B^2*a^3*b^3 - 864*A^2*B*a^2*b^4))/(3*(-a)^(5/6)*b^(7/6)))*(A*b - B*a))/(3*(-a)^(5/6)*b^(7/6)) - ((x^(1/2)*(96*A^4*b^5 + 96*B^4*a^4*b + 576*A^2*B^2*a^2*b^3 - 384*A^3*B*a*b^4 - 384*A*B^3*a^3*b^2) + ((A*b - B*a)*(288*A^3*a*b^5 - 288*B^3*a^4*b^2 + 864*A*B^2*a^3*b^3 - 864*A^2*B*a^2*b^4))/(3*(-a)^(5/6)*b^(7/6)))*(A*b - B*a))/(3*(-a)^(5/6)*b^(7/6))))*(A*b - B*a)*2i)/(3*(-a)^(5/6)*b^(7/6)) + (atan(((((3^(1/2)*1i)/2 - 1/2)*(A*b - B*a)*(x^(1/2)*(96*A^4*b^5 + 96*B^4*a^4*b + 576*A^2*B^2*a^2*b^3 - 384*A^3*B*a*b^4 - 384*A*B^3*a^3*b^2) - (((3^(1/2)*1i)/2 - 1/2)*(A*b - B*a)*(288*A^3*a*b^5 - 288*B^3*a^4*b^2 + 864*A*B^2*a^3*b^3 - 864*A^2*B*a^2*b^4))/(3*(-a)^(5/6)*b^(7/6)))*1i)/(3*(-a)^(5/6)*b^(7/6)) + (((3^(1/2)*1i)/2 - 1/2)*(A*b - B*a)*(x^(1/2)*(96*A^4*b^5 + 96*B^4*a^4*b + 576*A^2*B^2*a^2*b^3 - 384*A^3*B*a*b^4 - 384*A*B^3*a^3*b^2) + (((3^(1/2)*1i)/2 - 1/2)*(A*b - B*a)*(288*A^3*a*b^5 - 288*B^3*a^4*b^2 + 864*A*B^2*a^3*b^3 - 864*A^2*B*a^2*b^4))/(3*(-a)^(5/6)*b^(7/6)))*1i)/(3*(-a)^(5/6)*b^(7/6)))/((((3^(1/2)*1i)/2 - 1/2)*(A*b - B*a)*(x^(1/2)*(96*A^4*b^5 + 96*B^4*a^4*b + 576*A^2*B^2*a^2*b^3 - 384*A^3*B*a*b^4 - 384*A*B^3*a^3*b^2) - (((3^(1/2)*1i)/2 - 1/2)*(A*b - B*a)*(288*A^3*a*b^5 - 288*B^3*a^4*b^2 + 864*A*B^2*a^3*b^3 - 864*A^2*B*a^2*b^4))/(3*(-a)^(5/6)*b^(7/6))))/(3*(-a)^(5/6)*b^(7/6)) - (((3^(1/2)*1i)/2 - 1/2)*(A*b - B*a)*(x^(1/2)*(96*A^4*b^5 + 96*B^4*a^4*b + 576*A^2*B^2*a^2*b^3 - 384*A^3*B*a*b^4 - 384*A*B^3*a^3*b^2) + (((3^(1/2)*1i)/2 - 1/2)*(A*b - B*a)*(288*A^3*a*b^5 - 288*B^3*a^4*b^2 + 864*A*B^2*a^3*b^3 - 864*A^2*B*a^2*b^4))/(3*(-a)^(5/6)*b^(7/6))))/(3*(-a)^(5/6)*b^(7/6))))*((3^(1/2)*1i)/2 - 1/2)*(A*b - B*a)*2i)/(3*(-a)^(5/6)*b^(7/6)) + (atan(((((3^(1/2)*1i)/2 + 1/2)*(A*b - B*a)*(x^(1/2)*(96*A^4*b^5 + 96*B^4*a^4*b + 576*A^2*B^2*a^2*b^3 - 384*A^3*B*a*b^4 - 384*A*B^3*a^3*b^2) - (((3^(1/2)*1i)/2 + 1/2)*(A*b - B*a)*(288*A^3*a*b^5 - 288*B^3*a^4*b^2 + 864*A*B^2*a^3*b^3 - 864*A^2*B*a^2*b^4))/(3*(-a)^(5/6)*b^(7/6)))*1i)/(3*(-a)^(5/6)*b^(7/6)) + (((3^(1/2)*1i)/2 + 1/2)*(A*b - B*a)*(x^(1/2)*(96*A^4*b^5 + 96*B^4*a^4*b + 576*A^2*B^2*a^2*b^3 - 384*A^3*B*a*b^4 - 384*A*B^3*a^3*b^2) + (((3^(1/2)*1i)/2 + 1/2)*(A*b - B*a)*(288*A^3*a*b^5 - 288*B^3*a^4*b^2 + 864*A*B^2*a^3*b^3 - 864*A^2*B*a^2*b^4))/(3*(-a)^(5/6)*b^(7/6)))*1i)/(3*(-a)^(5/6)*b^(7/6)))/((((3^(1/2)*1i)/2 + 1/2)*(A*b - B*a)*(x^(1/2)*(96*A^4*b^5 + 96*B^4*a^4*b + 576*A^2*B^2*a^2*b^3 - 384*A^3*B*a*b^4 - 384*A*B^3*a^3*b^2) - (((3^(1/2)*1i)/2 + 1/2)*(A*b - B*a)*(288*A^3*a*b^5 - 288*B^3*a^4*b^2 + 864*A*B^2*a^3*b^3 - 864*A^2*B*a^2*b^4))/(3*(-a)^(5/6)*b^(7/6))))/(3*(-a)^(5/6)*b^(7/6)) - (((3^(1/2)*1i)/2 + 1/2)*(A*b - B*a)*(x^(1/2)*(96*A^4*b^5 + 96*B^4*a^4*b + 576*A^2*B^2*a^2*b^3 - 384*A^3*B*a*b^4 - 384*A*B^3*a^3*b^2) + (((3^(1/2)*1i)/2 + 1/2)*(A*b - B*a)*(288*A^3*a*b^5 - 288*B^3*a^4*b^2 + 864*A*B^2*a^3*b^3 - 864*A^2*B*a^2*b^4))/(3*(-a)^(5/6)*b^(7/6))))/(3*(-a)^(5/6)*b^(7/6))))*((3^(1/2)*1i)/2 + 1/2)*(A*b - B*a)*2i)/(3*(-a)^(5/6)*b^(7/6))","B"
160,1,1700,268,2.855849,"\text{Not used}","int((A + B*x^3)/(x^(3/2)*(a + b*x^3)),x)","-\frac{2\,A}{a\,\sqrt{x}}+\frac{\mathrm{atan}\left(\frac{\frac{{\left(A\,b-B\,a\right)}^2\,\left(32\,B^3\,a^{12}\,b^3-32\,A^3\,a^9\,b^6-96\,A\,B^2\,a^{11}\,b^4+96\,A^2\,B\,a^{10}\,b^5+\frac{\sqrt{x}\,\left(A\,b-B\,a\right)\,\left(864\,A^2\,a^{10}\,b^6-1728\,A\,B\,a^{11}\,b^5+864\,B^2\,a^{12}\,b^4\right)}{27\,{\left(-a\right)}^{7/6}\,b^{5/6}}\right)\,1{}\mathrm{i}}{{\left(-a\right)}^{7/3}\,b^{5/3}}+\frac{{\left(A\,b-B\,a\right)}^2\,\left(32\,A^3\,a^9\,b^6-32\,B^3\,a^{12}\,b^3+96\,A\,B^2\,a^{11}\,b^4-96\,A^2\,B\,a^{10}\,b^5+\frac{\sqrt{x}\,\left(A\,b-B\,a\right)\,\left(864\,A^2\,a^{10}\,b^6-1728\,A\,B\,a^{11}\,b^5+864\,B^2\,a^{12}\,b^4\right)}{27\,{\left(-a\right)}^{7/6}\,b^{5/6}}\right)\,1{}\mathrm{i}}{{\left(-a\right)}^{7/3}\,b^{5/3}}}{\frac{{\left(A\,b-B\,a\right)}^2\,\left(32\,B^3\,a^{12}\,b^3-32\,A^3\,a^9\,b^6-96\,A\,B^2\,a^{11}\,b^4+96\,A^2\,B\,a^{10}\,b^5+\frac{\sqrt{x}\,\left(A\,b-B\,a\right)\,\left(864\,A^2\,a^{10}\,b^6-1728\,A\,B\,a^{11}\,b^5+864\,B^2\,a^{12}\,b^4\right)}{27\,{\left(-a\right)}^{7/6}\,b^{5/6}}\right)}{{\left(-a\right)}^{7/3}\,b^{5/3}}-\frac{{\left(A\,b-B\,a\right)}^2\,\left(32\,A^3\,a^9\,b^6-32\,B^3\,a^{12}\,b^3+96\,A\,B^2\,a^{11}\,b^4-96\,A^2\,B\,a^{10}\,b^5+\frac{\sqrt{x}\,\left(A\,b-B\,a\right)\,\left(864\,A^2\,a^{10}\,b^6-1728\,A\,B\,a^{11}\,b^5+864\,B^2\,a^{12}\,b^4\right)}{27\,{\left(-a\right)}^{7/6}\,b^{5/6}}\right)}{{\left(-a\right)}^{7/3}\,b^{5/3}}}\right)\,\left(A\,b-B\,a\right)\,2{}\mathrm{i}}{3\,{\left(-a\right)}^{7/6}\,b^{5/6}}+\frac{\mathrm{atan}\left(\frac{\frac{{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(A\,b-B\,a\right)}^2\,\left(32\,B^3\,a^{12}\,b^3-32\,A^3\,a^9\,b^6-96\,A\,B^2\,a^{11}\,b^4+96\,A^2\,B\,a^{10}\,b^5+\frac{\sqrt{x}\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(864\,A^2\,a^{10}\,b^6-1728\,A\,B\,a^{11}\,b^5+864\,B^2\,a^{12}\,b^4\right)}{27\,{\left(-a\right)}^{7/6}\,b^{5/6}}\right)\,1{}\mathrm{i}}{{\left(-a\right)}^{7/3}\,b^{5/3}}+\frac{{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(A\,b-B\,a\right)}^2\,\left(32\,A^3\,a^9\,b^6-32\,B^3\,a^{12}\,b^3+96\,A\,B^2\,a^{11}\,b^4-96\,A^2\,B\,a^{10}\,b^5+\frac{\sqrt{x}\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(864\,A^2\,a^{10}\,b^6-1728\,A\,B\,a^{11}\,b^5+864\,B^2\,a^{12}\,b^4\right)}{27\,{\left(-a\right)}^{7/6}\,b^{5/6}}\right)\,1{}\mathrm{i}}{{\left(-a\right)}^{7/3}\,b^{5/3}}}{\frac{{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(A\,b-B\,a\right)}^2\,\left(32\,B^3\,a^{12}\,b^3-32\,A^3\,a^9\,b^6-96\,A\,B^2\,a^{11}\,b^4+96\,A^2\,B\,a^{10}\,b^5+\frac{\sqrt{x}\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(864\,A^2\,a^{10}\,b^6-1728\,A\,B\,a^{11}\,b^5+864\,B^2\,a^{12}\,b^4\right)}{27\,{\left(-a\right)}^{7/6}\,b^{5/6}}\right)}{{\left(-a\right)}^{7/3}\,b^{5/3}}-\frac{{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(A\,b-B\,a\right)}^2\,\left(32\,A^3\,a^9\,b^6-32\,B^3\,a^{12}\,b^3+96\,A\,B^2\,a^{11}\,b^4-96\,A^2\,B\,a^{10}\,b^5+\frac{\sqrt{x}\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(864\,A^2\,a^{10}\,b^6-1728\,A\,B\,a^{11}\,b^5+864\,B^2\,a^{12}\,b^4\right)}{27\,{\left(-a\right)}^{7/6}\,b^{5/6}}\right)}{{\left(-a\right)}^{7/3}\,b^{5/3}}}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,2{}\mathrm{i}}{3\,{\left(-a\right)}^{7/6}\,b^{5/6}}+\frac{\mathrm{atan}\left(\frac{\frac{{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(A\,b-B\,a\right)}^2\,\left(32\,B^3\,a^{12}\,b^3-32\,A^3\,a^9\,b^6-96\,A\,B^2\,a^{11}\,b^4+96\,A^2\,B\,a^{10}\,b^5+\frac{\sqrt{x}\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(864\,A^2\,a^{10}\,b^6-1728\,A\,B\,a^{11}\,b^5+864\,B^2\,a^{12}\,b^4\right)}{27\,{\left(-a\right)}^{7/6}\,b^{5/6}}\right)\,1{}\mathrm{i}}{{\left(-a\right)}^{7/3}\,b^{5/3}}+\frac{{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(A\,b-B\,a\right)}^2\,\left(32\,A^3\,a^9\,b^6-32\,B^3\,a^{12}\,b^3+96\,A\,B^2\,a^{11}\,b^4-96\,A^2\,B\,a^{10}\,b^5+\frac{\sqrt{x}\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(864\,A^2\,a^{10}\,b^6-1728\,A\,B\,a^{11}\,b^5+864\,B^2\,a^{12}\,b^4\right)}{27\,{\left(-a\right)}^{7/6}\,b^{5/6}}\right)\,1{}\mathrm{i}}{{\left(-a\right)}^{7/3}\,b^{5/3}}}{\frac{{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(A\,b-B\,a\right)}^2\,\left(32\,B^3\,a^{12}\,b^3-32\,A^3\,a^9\,b^6-96\,A\,B^2\,a^{11}\,b^4+96\,A^2\,B\,a^{10}\,b^5+\frac{\sqrt{x}\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(864\,A^2\,a^{10}\,b^6-1728\,A\,B\,a^{11}\,b^5+864\,B^2\,a^{12}\,b^4\right)}{27\,{\left(-a\right)}^{7/6}\,b^{5/6}}\right)}{{\left(-a\right)}^{7/3}\,b^{5/3}}-\frac{{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(A\,b-B\,a\right)}^2\,\left(32\,A^3\,a^9\,b^6-32\,B^3\,a^{12}\,b^3+96\,A\,B^2\,a^{11}\,b^4-96\,A^2\,B\,a^{10}\,b^5+\frac{\sqrt{x}\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(864\,A^2\,a^{10}\,b^6-1728\,A\,B\,a^{11}\,b^5+864\,B^2\,a^{12}\,b^4\right)}{27\,{\left(-a\right)}^{7/6}\,b^{5/6}}\right)}{{\left(-a\right)}^{7/3}\,b^{5/3}}}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,2{}\mathrm{i}}{3\,{\left(-a\right)}^{7/6}\,b^{5/6}}","Not used",1,"(atan((((A*b - B*a)^2*(32*B^3*a^12*b^3 - 32*A^3*a^9*b^6 - 96*A*B^2*a^11*b^4 + 96*A^2*B*a^10*b^5 + (x^(1/2)*(A*b - B*a)*(864*A^2*a^10*b^6 + 864*B^2*a^12*b^4 - 1728*A*B*a^11*b^5))/(27*(-a)^(7/6)*b^(5/6)))*1i)/((-a)^(7/3)*b^(5/3)) + ((A*b - B*a)^2*(32*A^3*a^9*b^6 - 32*B^3*a^12*b^3 + 96*A*B^2*a^11*b^4 - 96*A^2*B*a^10*b^5 + (x^(1/2)*(A*b - B*a)*(864*A^2*a^10*b^6 + 864*B^2*a^12*b^4 - 1728*A*B*a^11*b^5))/(27*(-a)^(7/6)*b^(5/6)))*1i)/((-a)^(7/3)*b^(5/3)))/(((A*b - B*a)^2*(32*B^3*a^12*b^3 - 32*A^3*a^9*b^6 - 96*A*B^2*a^11*b^4 + 96*A^2*B*a^10*b^5 + (x^(1/2)*(A*b - B*a)*(864*A^2*a^10*b^6 + 864*B^2*a^12*b^4 - 1728*A*B*a^11*b^5))/(27*(-a)^(7/6)*b^(5/6))))/((-a)^(7/3)*b^(5/3)) - ((A*b - B*a)^2*(32*A^3*a^9*b^6 - 32*B^3*a^12*b^3 + 96*A*B^2*a^11*b^4 - 96*A^2*B*a^10*b^5 + (x^(1/2)*(A*b - B*a)*(864*A^2*a^10*b^6 + 864*B^2*a^12*b^4 - 1728*A*B*a^11*b^5))/(27*(-a)^(7/6)*b^(5/6))))/((-a)^(7/3)*b^(5/3))))*(A*b - B*a)*2i)/(3*(-a)^(7/6)*b^(5/6)) - (2*A)/(a*x^(1/2)) + (atan(((((3^(1/2)*1i)/2 - 1/2)^2*(A*b - B*a)^2*(32*B^3*a^12*b^3 - 32*A^3*a^9*b^6 - 96*A*B^2*a^11*b^4 + 96*A^2*B*a^10*b^5 + (x^(1/2)*((3^(1/2)*1i)/2 - 1/2)*(A*b - B*a)*(864*A^2*a^10*b^6 + 864*B^2*a^12*b^4 - 1728*A*B*a^11*b^5))/(27*(-a)^(7/6)*b^(5/6)))*1i)/((-a)^(7/3)*b^(5/3)) + (((3^(1/2)*1i)/2 - 1/2)^2*(A*b - B*a)^2*(32*A^3*a^9*b^6 - 32*B^3*a^12*b^3 + 96*A*B^2*a^11*b^4 - 96*A^2*B*a^10*b^5 + (x^(1/2)*((3^(1/2)*1i)/2 - 1/2)*(A*b - B*a)*(864*A^2*a^10*b^6 + 864*B^2*a^12*b^4 - 1728*A*B*a^11*b^5))/(27*(-a)^(7/6)*b^(5/6)))*1i)/((-a)^(7/3)*b^(5/3)))/((((3^(1/2)*1i)/2 - 1/2)^2*(A*b - B*a)^2*(32*B^3*a^12*b^3 - 32*A^3*a^9*b^6 - 96*A*B^2*a^11*b^4 + 96*A^2*B*a^10*b^5 + (x^(1/2)*((3^(1/2)*1i)/2 - 1/2)*(A*b - B*a)*(864*A^2*a^10*b^6 + 864*B^2*a^12*b^4 - 1728*A*B*a^11*b^5))/(27*(-a)^(7/6)*b^(5/6))))/((-a)^(7/3)*b^(5/3)) - (((3^(1/2)*1i)/2 - 1/2)^2*(A*b - B*a)^2*(32*A^3*a^9*b^6 - 32*B^3*a^12*b^3 + 96*A*B^2*a^11*b^4 - 96*A^2*B*a^10*b^5 + (x^(1/2)*((3^(1/2)*1i)/2 - 1/2)*(A*b - B*a)*(864*A^2*a^10*b^6 + 864*B^2*a^12*b^4 - 1728*A*B*a^11*b^5))/(27*(-a)^(7/6)*b^(5/6))))/((-a)^(7/3)*b^(5/3))))*((3^(1/2)*1i)/2 - 1/2)*(A*b - B*a)*2i)/(3*(-a)^(7/6)*b^(5/6)) + (atan(((((3^(1/2)*1i)/2 + 1/2)^2*(A*b - B*a)^2*(32*B^3*a^12*b^3 - 32*A^3*a^9*b^6 - 96*A*B^2*a^11*b^4 + 96*A^2*B*a^10*b^5 + (x^(1/2)*((3^(1/2)*1i)/2 + 1/2)*(A*b - B*a)*(864*A^2*a^10*b^6 + 864*B^2*a^12*b^4 - 1728*A*B*a^11*b^5))/(27*(-a)^(7/6)*b^(5/6)))*1i)/((-a)^(7/3)*b^(5/3)) + (((3^(1/2)*1i)/2 + 1/2)^2*(A*b - B*a)^2*(32*A^3*a^9*b^6 - 32*B^3*a^12*b^3 + 96*A*B^2*a^11*b^4 - 96*A^2*B*a^10*b^5 + (x^(1/2)*((3^(1/2)*1i)/2 + 1/2)*(A*b - B*a)*(864*A^2*a^10*b^6 + 864*B^2*a^12*b^4 - 1728*A*B*a^11*b^5))/(27*(-a)^(7/6)*b^(5/6)))*1i)/((-a)^(7/3)*b^(5/3)))/((((3^(1/2)*1i)/2 + 1/2)^2*(A*b - B*a)^2*(32*B^3*a^12*b^3 - 32*A^3*a^9*b^6 - 96*A*B^2*a^11*b^4 + 96*A^2*B*a^10*b^5 + (x^(1/2)*((3^(1/2)*1i)/2 + 1/2)*(A*b - B*a)*(864*A^2*a^10*b^6 + 864*B^2*a^12*b^4 - 1728*A*B*a^11*b^5))/(27*(-a)^(7/6)*b^(5/6))))/((-a)^(7/3)*b^(5/3)) - (((3^(1/2)*1i)/2 + 1/2)^2*(A*b - B*a)^2*(32*A^3*a^9*b^6 - 32*B^3*a^12*b^3 + 96*A*B^2*a^11*b^4 - 96*A^2*B*a^10*b^5 + (x^(1/2)*((3^(1/2)*1i)/2 + 1/2)*(A*b - B*a)*(864*A^2*a^10*b^6 + 864*B^2*a^12*b^4 - 1728*A*B*a^11*b^5))/(27*(-a)^(7/6)*b^(5/6))))/((-a)^(7/3)*b^(5/3))))*((3^(1/2)*1i)/2 + 1/2)*(A*b - B*a)*2i)/(3*(-a)^(7/6)*b^(5/6))","B"
161,1,102,53,0.100729,"\text{Not used}","int((A + B*x^3)/(x^(5/2)*(a + b*x^3)),x)","-\frac{2\,A}{3\,a\,x^{3/2}}-\frac{2\,\mathrm{atan}\left(\frac{3\,a^{3/2}\,\sqrt{b}\,x^{3/2}\,\left(24\,A^2\,a^3\,b^5-48\,A\,B\,a^4\,b^4+24\,B^2\,a^5\,b^3\right)}{\left(A\,b-B\,a\right)\,\left(72\,A\,a^5\,b^4-72\,B\,a^6\,b^3\right)}\right)\,\left(A\,b-B\,a\right)}{3\,a^{3/2}\,\sqrt{b}}","Not used",1,"- (2*A)/(3*a*x^(3/2)) - (2*atan((3*a^(3/2)*b^(1/2)*x^(3/2)*(24*A^2*a^3*b^5 + 24*B^2*a^5*b^3 - 48*A*B*a^4*b^4))/((A*b - B*a)*(72*A*a^5*b^4 - 72*B*a^6*b^3)))*(A*b - B*a))/(3*a^(3/2)*b^(1/2))","B"
162,1,2023,270,2.912536,"\text{Not used}","int((A + B*x^3)/(x^(7/2)*(a + b*x^3)),x)","-\frac{2\,A}{5\,a\,x^{5/2}}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\sqrt{x}\,\left(96\,A^4\,a^5\,b^9-384\,A^3\,B\,a^6\,b^8+576\,A^2\,B^2\,a^7\,b^7-384\,A\,B^3\,a^8\,b^6+96\,B^4\,a^9\,b^5\right)-\frac{\left(A\,b-B\,a\right)\,\left(288\,A^3\,a^7\,b^8-864\,A^2\,B\,a^8\,b^7+864\,A\,B^2\,a^9\,b^6-288\,B^3\,a^{10}\,b^5\right)}{3\,{\left(-a\right)}^{11/6}\,b^{1/6}}\right)\,\left(A\,b-B\,a\right)\,1{}\mathrm{i}}{3\,{\left(-a\right)}^{11/6}\,b^{1/6}}+\frac{\left(\sqrt{x}\,\left(96\,A^4\,a^5\,b^9-384\,A^3\,B\,a^6\,b^8+576\,A^2\,B^2\,a^7\,b^7-384\,A\,B^3\,a^8\,b^6+96\,B^4\,a^9\,b^5\right)+\frac{\left(A\,b-B\,a\right)\,\left(288\,A^3\,a^7\,b^8-864\,A^2\,B\,a^8\,b^7+864\,A\,B^2\,a^9\,b^6-288\,B^3\,a^{10}\,b^5\right)}{3\,{\left(-a\right)}^{11/6}\,b^{1/6}}\right)\,\left(A\,b-B\,a\right)\,1{}\mathrm{i}}{3\,{\left(-a\right)}^{11/6}\,b^{1/6}}}{\frac{\left(\sqrt{x}\,\left(96\,A^4\,a^5\,b^9-384\,A^3\,B\,a^6\,b^8+576\,A^2\,B^2\,a^7\,b^7-384\,A\,B^3\,a^8\,b^6+96\,B^4\,a^9\,b^5\right)-\frac{\left(A\,b-B\,a\right)\,\left(288\,A^3\,a^7\,b^8-864\,A^2\,B\,a^8\,b^7+864\,A\,B^2\,a^9\,b^6-288\,B^3\,a^{10}\,b^5\right)}{3\,{\left(-a\right)}^{11/6}\,b^{1/6}}\right)\,\left(A\,b-B\,a\right)}{3\,{\left(-a\right)}^{11/6}\,b^{1/6}}-\frac{\left(\sqrt{x}\,\left(96\,A^4\,a^5\,b^9-384\,A^3\,B\,a^6\,b^8+576\,A^2\,B^2\,a^7\,b^7-384\,A\,B^3\,a^8\,b^6+96\,B^4\,a^9\,b^5\right)+\frac{\left(A\,b-B\,a\right)\,\left(288\,A^3\,a^7\,b^8-864\,A^2\,B\,a^8\,b^7+864\,A\,B^2\,a^9\,b^6-288\,B^3\,a^{10}\,b^5\right)}{3\,{\left(-a\right)}^{11/6}\,b^{1/6}}\right)\,\left(A\,b-B\,a\right)}{3\,{\left(-a\right)}^{11/6}\,b^{1/6}}}\right)\,\left(A\,b-B\,a\right)\,2{}\mathrm{i}}{3\,{\left(-a\right)}^{11/6}\,b^{1/6}}-\frac{\mathrm{atan}\left(\frac{\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\sqrt{x}\,\left(96\,A^4\,a^5\,b^9-384\,A^3\,B\,a^6\,b^8+576\,A^2\,B^2\,a^7\,b^7-384\,A\,B^3\,a^8\,b^6+96\,B^4\,a^9\,b^5\right)-\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(288\,A^3\,a^7\,b^8-864\,A^2\,B\,a^8\,b^7+864\,A\,B^2\,a^9\,b^6-288\,B^3\,a^{10}\,b^5\right)}{3\,{\left(-a\right)}^{11/6}\,b^{1/6}}\right)\,\left(A\,b-B\,a\right)\,1{}\mathrm{i}}{3\,{\left(-a\right)}^{11/6}\,b^{1/6}}+\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\sqrt{x}\,\left(96\,A^4\,a^5\,b^9-384\,A^3\,B\,a^6\,b^8+576\,A^2\,B^2\,a^7\,b^7-384\,A\,B^3\,a^8\,b^6+96\,B^4\,a^9\,b^5\right)+\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(288\,A^3\,a^7\,b^8-864\,A^2\,B\,a^8\,b^7+864\,A\,B^2\,a^9\,b^6-288\,B^3\,a^{10}\,b^5\right)}{3\,{\left(-a\right)}^{11/6}\,b^{1/6}}\right)\,\left(A\,b-B\,a\right)\,1{}\mathrm{i}}{3\,{\left(-a\right)}^{11/6}\,b^{1/6}}}{\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\sqrt{x}\,\left(96\,A^4\,a^5\,b^9-384\,A^3\,B\,a^6\,b^8+576\,A^2\,B^2\,a^7\,b^7-384\,A\,B^3\,a^8\,b^6+96\,B^4\,a^9\,b^5\right)-\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(288\,A^3\,a^7\,b^8-864\,A^2\,B\,a^8\,b^7+864\,A\,B^2\,a^9\,b^6-288\,B^3\,a^{10}\,b^5\right)}{3\,{\left(-a\right)}^{11/6}\,b^{1/6}}\right)\,\left(A\,b-B\,a\right)}{3\,{\left(-a\right)}^{11/6}\,b^{1/6}}-\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\sqrt{x}\,\left(96\,A^4\,a^5\,b^9-384\,A^3\,B\,a^6\,b^8+576\,A^2\,B^2\,a^7\,b^7-384\,A\,B^3\,a^8\,b^6+96\,B^4\,a^9\,b^5\right)+\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(288\,A^3\,a^7\,b^8-864\,A^2\,B\,a^8\,b^7+864\,A\,B^2\,a^9\,b^6-288\,B^3\,a^{10}\,b^5\right)}{3\,{\left(-a\right)}^{11/6}\,b^{1/6}}\right)\,\left(A\,b-B\,a\right)}{3\,{\left(-a\right)}^{11/6}\,b^{1/6}}}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,2{}\mathrm{i}}{3\,{\left(-a\right)}^{11/6}\,b^{1/6}}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\sqrt{x}\,\left(96\,A^4\,a^5\,b^9-384\,A^3\,B\,a^6\,b^8+576\,A^2\,B^2\,a^7\,b^7-384\,A\,B^3\,a^8\,b^6+96\,B^4\,a^9\,b^5\right)-\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(288\,A^3\,a^7\,b^8-864\,A^2\,B\,a^8\,b^7+864\,A\,B^2\,a^9\,b^6-288\,B^3\,a^{10}\,b^5\right)}{3\,{\left(-a\right)}^{11/6}\,b^{1/6}}\right)\,\left(A\,b-B\,a\right)\,1{}\mathrm{i}}{3\,{\left(-a\right)}^{11/6}\,b^{1/6}}+\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\sqrt{x}\,\left(96\,A^4\,a^5\,b^9-384\,A^3\,B\,a^6\,b^8+576\,A^2\,B^2\,a^7\,b^7-384\,A\,B^3\,a^8\,b^6+96\,B^4\,a^9\,b^5\right)+\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(288\,A^3\,a^7\,b^8-864\,A^2\,B\,a^8\,b^7+864\,A\,B^2\,a^9\,b^6-288\,B^3\,a^{10}\,b^5\right)}{3\,{\left(-a\right)}^{11/6}\,b^{1/6}}\right)\,\left(A\,b-B\,a\right)\,1{}\mathrm{i}}{3\,{\left(-a\right)}^{11/6}\,b^{1/6}}}{\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\sqrt{x}\,\left(96\,A^4\,a^5\,b^9-384\,A^3\,B\,a^6\,b^8+576\,A^2\,B^2\,a^7\,b^7-384\,A\,B^3\,a^8\,b^6+96\,B^4\,a^9\,b^5\right)-\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(288\,A^3\,a^7\,b^8-864\,A^2\,B\,a^8\,b^7+864\,A\,B^2\,a^9\,b^6-288\,B^3\,a^{10}\,b^5\right)}{3\,{\left(-a\right)}^{11/6}\,b^{1/6}}\right)\,\left(A\,b-B\,a\right)}{3\,{\left(-a\right)}^{11/6}\,b^{1/6}}-\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\sqrt{x}\,\left(96\,A^4\,a^5\,b^9-384\,A^3\,B\,a^6\,b^8+576\,A^2\,B^2\,a^7\,b^7-384\,A\,B^3\,a^8\,b^6+96\,B^4\,a^9\,b^5\right)+\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,\left(288\,A^3\,a^7\,b^8-864\,A^2\,B\,a^8\,b^7+864\,A\,B^2\,a^9\,b^6-288\,B^3\,a^{10}\,b^5\right)}{3\,{\left(-a\right)}^{11/6}\,b^{1/6}}\right)\,\left(A\,b-B\,a\right)}{3\,{\left(-a\right)}^{11/6}\,b^{1/6}}}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-B\,a\right)\,2{}\mathrm{i}}{3\,{\left(-a\right)}^{11/6}\,b^{1/6}}","Not used",1,"- (2*A)/(5*a*x^(5/2)) - (atan((((x^(1/2)*(96*A^4*a^5*b^9 + 96*B^4*a^9*b^5 + 576*A^2*B^2*a^7*b^7 - 384*A*B^3*a^8*b^6 - 384*A^3*B*a^6*b^8) - ((A*b - B*a)*(288*A^3*a^7*b^8 - 288*B^3*a^10*b^5 + 864*A*B^2*a^9*b^6 - 864*A^2*B*a^8*b^7))/(3*(-a)^(11/6)*b^(1/6)))*(A*b - B*a)*1i)/(3*(-a)^(11/6)*b^(1/6)) + ((x^(1/2)*(96*A^4*a^5*b^9 + 96*B^4*a^9*b^5 + 576*A^2*B^2*a^7*b^7 - 384*A*B^3*a^8*b^6 - 384*A^3*B*a^6*b^8) + ((A*b - B*a)*(288*A^3*a^7*b^8 - 288*B^3*a^10*b^5 + 864*A*B^2*a^9*b^6 - 864*A^2*B*a^8*b^7))/(3*(-a)^(11/6)*b^(1/6)))*(A*b - B*a)*1i)/(3*(-a)^(11/6)*b^(1/6)))/(((x^(1/2)*(96*A^4*a^5*b^9 + 96*B^4*a^9*b^5 + 576*A^2*B^2*a^7*b^7 - 384*A*B^3*a^8*b^6 - 384*A^3*B*a^6*b^8) - ((A*b - B*a)*(288*A^3*a^7*b^8 - 288*B^3*a^10*b^5 + 864*A*B^2*a^9*b^6 - 864*A^2*B*a^8*b^7))/(3*(-a)^(11/6)*b^(1/6)))*(A*b - B*a))/(3*(-a)^(11/6)*b^(1/6)) - ((x^(1/2)*(96*A^4*a^5*b^9 + 96*B^4*a^9*b^5 + 576*A^2*B^2*a^7*b^7 - 384*A*B^3*a^8*b^6 - 384*A^3*B*a^6*b^8) + ((A*b - B*a)*(288*A^3*a^7*b^8 - 288*B^3*a^10*b^5 + 864*A*B^2*a^9*b^6 - 864*A^2*B*a^8*b^7))/(3*(-a)^(11/6)*b^(1/6)))*(A*b - B*a))/(3*(-a)^(11/6)*b^(1/6))))*(A*b - B*a)*2i)/(3*(-a)^(11/6)*b^(1/6)) - (atan(((((3^(1/2)*1i)/2 - 1/2)*(x^(1/2)*(96*A^4*a^5*b^9 + 96*B^4*a^9*b^5 + 576*A^2*B^2*a^7*b^7 - 384*A*B^3*a^8*b^6 - 384*A^3*B*a^6*b^8) - (((3^(1/2)*1i)/2 - 1/2)*(A*b - B*a)*(288*A^3*a^7*b^8 - 288*B^3*a^10*b^5 + 864*A*B^2*a^9*b^6 - 864*A^2*B*a^8*b^7))/(3*(-a)^(11/6)*b^(1/6)))*(A*b - B*a)*1i)/(3*(-a)^(11/6)*b^(1/6)) + (((3^(1/2)*1i)/2 - 1/2)*(x^(1/2)*(96*A^4*a^5*b^9 + 96*B^4*a^9*b^5 + 576*A^2*B^2*a^7*b^7 - 384*A*B^3*a^8*b^6 - 384*A^3*B*a^6*b^8) + (((3^(1/2)*1i)/2 - 1/2)*(A*b - B*a)*(288*A^3*a^7*b^8 - 288*B^3*a^10*b^5 + 864*A*B^2*a^9*b^6 - 864*A^2*B*a^8*b^7))/(3*(-a)^(11/6)*b^(1/6)))*(A*b - B*a)*1i)/(3*(-a)^(11/6)*b^(1/6)))/((((3^(1/2)*1i)/2 - 1/2)*(x^(1/2)*(96*A^4*a^5*b^9 + 96*B^4*a^9*b^5 + 576*A^2*B^2*a^7*b^7 - 384*A*B^3*a^8*b^6 - 384*A^3*B*a^6*b^8) - (((3^(1/2)*1i)/2 - 1/2)*(A*b - B*a)*(288*A^3*a^7*b^8 - 288*B^3*a^10*b^5 + 864*A*B^2*a^9*b^6 - 864*A^2*B*a^8*b^7))/(3*(-a)^(11/6)*b^(1/6)))*(A*b - B*a))/(3*(-a)^(11/6)*b^(1/6)) - (((3^(1/2)*1i)/2 - 1/2)*(x^(1/2)*(96*A^4*a^5*b^9 + 96*B^4*a^9*b^5 + 576*A^2*B^2*a^7*b^7 - 384*A*B^3*a^8*b^6 - 384*A^3*B*a^6*b^8) + (((3^(1/2)*1i)/2 - 1/2)*(A*b - B*a)*(288*A^3*a^7*b^8 - 288*B^3*a^10*b^5 + 864*A*B^2*a^9*b^6 - 864*A^2*B*a^8*b^7))/(3*(-a)^(11/6)*b^(1/6)))*(A*b - B*a))/(3*(-a)^(11/6)*b^(1/6))))*((3^(1/2)*1i)/2 - 1/2)*(A*b - B*a)*2i)/(3*(-a)^(11/6)*b^(1/6)) - (atan(((((3^(1/2)*1i)/2 + 1/2)*(x^(1/2)*(96*A^4*a^5*b^9 + 96*B^4*a^9*b^5 + 576*A^2*B^2*a^7*b^7 - 384*A*B^3*a^8*b^6 - 384*A^3*B*a^6*b^8) - (((3^(1/2)*1i)/2 + 1/2)*(A*b - B*a)*(288*A^3*a^7*b^8 - 288*B^3*a^10*b^5 + 864*A*B^2*a^9*b^6 - 864*A^2*B*a^8*b^7))/(3*(-a)^(11/6)*b^(1/6)))*(A*b - B*a)*1i)/(3*(-a)^(11/6)*b^(1/6)) + (((3^(1/2)*1i)/2 + 1/2)*(x^(1/2)*(96*A^4*a^5*b^9 + 96*B^4*a^9*b^5 + 576*A^2*B^2*a^7*b^7 - 384*A*B^3*a^8*b^6 - 384*A^3*B*a^6*b^8) + (((3^(1/2)*1i)/2 + 1/2)*(A*b - B*a)*(288*A^3*a^7*b^8 - 288*B^3*a^10*b^5 + 864*A*B^2*a^9*b^6 - 864*A^2*B*a^8*b^7))/(3*(-a)^(11/6)*b^(1/6)))*(A*b - B*a)*1i)/(3*(-a)^(11/6)*b^(1/6)))/((((3^(1/2)*1i)/2 + 1/2)*(x^(1/2)*(96*A^4*a^5*b^9 + 96*B^4*a^9*b^5 + 576*A^2*B^2*a^7*b^7 - 384*A*B^3*a^8*b^6 - 384*A^3*B*a^6*b^8) - (((3^(1/2)*1i)/2 + 1/2)*(A*b - B*a)*(288*A^3*a^7*b^8 - 288*B^3*a^10*b^5 + 864*A*B^2*a^9*b^6 - 864*A^2*B*a^8*b^7))/(3*(-a)^(11/6)*b^(1/6)))*(A*b - B*a))/(3*(-a)^(11/6)*b^(1/6)) - (((3^(1/2)*1i)/2 + 1/2)*(x^(1/2)*(96*A^4*a^5*b^9 + 96*B^4*a^9*b^5 + 576*A^2*B^2*a^7*b^7 - 384*A*B^3*a^8*b^6 - 384*A^3*B*a^6*b^8) + (((3^(1/2)*1i)/2 + 1/2)*(A*b - B*a)*(288*A^3*a^7*b^8 - 288*B^3*a^10*b^5 + 864*A*B^2*a^9*b^6 - 864*A^2*B*a^8*b^7))/(3*(-a)^(11/6)*b^(1/6)))*(A*b - B*a))/(3*(-a)^(11/6)*b^(1/6))))*((3^(1/2)*1i)/2 + 1/2)*(A*b - B*a)*2i)/(3*(-a)^(11/6)*b^(1/6))","B"
163,1,116,95,2.649772,"\text{Not used}","int((x^(7/2)*(A + B*x^3))/(a + b*x^3)^2,x)","\frac{2\,B\,x^{3/2}}{3\,b^2}-\frac{x^{3/2}\,\left(\frac{A\,b}{3}-\frac{B\,a}{3}\right)}{b^3\,x^3+a\,b^2}+\frac{\mathrm{atan}\left(\frac{36\,\sqrt{a}\,b^{3/2}\,x^{3/2}\,\left(A^2\,b^2-6\,A\,B\,a\,b+9\,B^2\,a^2\right)}{\left(A\,b-3\,B\,a\right)\,\left(36\,A\,a\,b^2-108\,B\,a^2\,b\right)}\right)\,\left(A\,b-3\,B\,a\right)}{3\,\sqrt{a}\,b^{5/2}}","Not used",1,"(2*B*x^(3/2))/(3*b^2) - (x^(3/2)*((A*b)/3 - (B*a)/3))/(a*b^2 + b^3*x^3) + (atan((36*a^(1/2)*b^(3/2)*x^(3/2)*(A^2*b^2 + 9*B^2*a^2 - 6*A*B*a*b))/((A*b - 3*B*a)*(36*A*a*b^2 - 108*B*a^2*b)))*(A*b - 3*B*a))/(3*a^(1/2)*b^(5/2))","B"
164,1,1884,312,2.888224,"\text{Not used}","int((x^(5/2)*(A + B*x^3))/(a + b*x^3)^2,x)","\frac{2\,B\,\sqrt{x}}{b^2}-\frac{\sqrt{x}\,\left(\frac{A\,b}{3}-\frac{B\,a}{3}\right)}{b^3\,x^3+a\,b^2}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{2\,\sqrt{x}\,\left(A^4\,b^4-28\,A^3\,B\,a\,b^3+294\,A^2\,B^2\,a^2\,b^2-1372\,A\,B^3\,a^3\,b+2401\,B^4\,a^4\right)}{27\,b^3}-\frac{2\,\left(A\,b-7\,B\,a\right)\,\left(-A^3\,a\,b^3+21\,A^2\,B\,a^2\,b^2-147\,A\,B^2\,a^3\,b+343\,B^3\,a^4\right)}{27\,{\left(-a\right)}^{5/6}\,b^{19/6}}\right)\,\left(A\,b-7\,B\,a\right)\,1{}\mathrm{i}}{18\,{\left(-a\right)}^{5/6}\,b^{13/6}}+\frac{\left(\frac{2\,\sqrt{x}\,\left(A^4\,b^4-28\,A^3\,B\,a\,b^3+294\,A^2\,B^2\,a^2\,b^2-1372\,A\,B^3\,a^3\,b+2401\,B^4\,a^4\right)}{27\,b^3}+\frac{2\,\left(A\,b-7\,B\,a\right)\,\left(-A^3\,a\,b^3+21\,A^2\,B\,a^2\,b^2-147\,A\,B^2\,a^3\,b+343\,B^3\,a^4\right)}{27\,{\left(-a\right)}^{5/6}\,b^{19/6}}\right)\,\left(A\,b-7\,B\,a\right)\,1{}\mathrm{i}}{18\,{\left(-a\right)}^{5/6}\,b^{13/6}}}{\frac{\left(\frac{2\,\sqrt{x}\,\left(A^4\,b^4-28\,A^3\,B\,a\,b^3+294\,A^2\,B^2\,a^2\,b^2-1372\,A\,B^3\,a^3\,b+2401\,B^4\,a^4\right)}{27\,b^3}-\frac{2\,\left(A\,b-7\,B\,a\right)\,\left(-A^3\,a\,b^3+21\,A^2\,B\,a^2\,b^2-147\,A\,B^2\,a^3\,b+343\,B^3\,a^4\right)}{27\,{\left(-a\right)}^{5/6}\,b^{19/6}}\right)\,\left(A\,b-7\,B\,a\right)}{18\,{\left(-a\right)}^{5/6}\,b^{13/6}}-\frac{\left(\frac{2\,\sqrt{x}\,\left(A^4\,b^4-28\,A^3\,B\,a\,b^3+294\,A^2\,B^2\,a^2\,b^2-1372\,A\,B^3\,a^3\,b+2401\,B^4\,a^4\right)}{27\,b^3}+\frac{2\,\left(A\,b-7\,B\,a\right)\,\left(-A^3\,a\,b^3+21\,A^2\,B\,a^2\,b^2-147\,A\,B^2\,a^3\,b+343\,B^3\,a^4\right)}{27\,{\left(-a\right)}^{5/6}\,b^{19/6}}\right)\,\left(A\,b-7\,B\,a\right)}{18\,{\left(-a\right)}^{5/6}\,b^{13/6}}}\right)\,\left(A\,b-7\,B\,a\right)\,1{}\mathrm{i}}{9\,{\left(-a\right)}^{5/6}\,b^{13/6}}-\frac{\mathrm{atan}\left(\frac{\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{2\,\sqrt{x}\,\left(A^4\,b^4-28\,A^3\,B\,a\,b^3+294\,A^2\,B^2\,a^2\,b^2-1372\,A\,B^3\,a^3\,b+2401\,B^4\,a^4\right)}{27\,b^3}-\frac{2\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-7\,B\,a\right)\,\left(-A^3\,a\,b^3+21\,A^2\,B\,a^2\,b^2-147\,A\,B^2\,a^3\,b+343\,B^3\,a^4\right)}{27\,{\left(-a\right)}^{5/6}\,b^{19/6}}\right)\,\left(A\,b-7\,B\,a\right)\,1{}\mathrm{i}}{18\,{\left(-a\right)}^{5/6}\,b^{13/6}}+\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{2\,\sqrt{x}\,\left(A^4\,b^4-28\,A^3\,B\,a\,b^3+294\,A^2\,B^2\,a^2\,b^2-1372\,A\,B^3\,a^3\,b+2401\,B^4\,a^4\right)}{27\,b^3}+\frac{2\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-7\,B\,a\right)\,\left(-A^3\,a\,b^3+21\,A^2\,B\,a^2\,b^2-147\,A\,B^2\,a^3\,b+343\,B^3\,a^4\right)}{27\,{\left(-a\right)}^{5/6}\,b^{19/6}}\right)\,\left(A\,b-7\,B\,a\right)\,1{}\mathrm{i}}{18\,{\left(-a\right)}^{5/6}\,b^{13/6}}}{\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{2\,\sqrt{x}\,\left(A^4\,b^4-28\,A^3\,B\,a\,b^3+294\,A^2\,B^2\,a^2\,b^2-1372\,A\,B^3\,a^3\,b+2401\,B^4\,a^4\right)}{27\,b^3}-\frac{2\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-7\,B\,a\right)\,\left(-A^3\,a\,b^3+21\,A^2\,B\,a^2\,b^2-147\,A\,B^2\,a^3\,b+343\,B^3\,a^4\right)}{27\,{\left(-a\right)}^{5/6}\,b^{19/6}}\right)\,\left(A\,b-7\,B\,a\right)}{18\,{\left(-a\right)}^{5/6}\,b^{13/6}}-\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{2\,\sqrt{x}\,\left(A^4\,b^4-28\,A^3\,B\,a\,b^3+294\,A^2\,B^2\,a^2\,b^2-1372\,A\,B^3\,a^3\,b+2401\,B^4\,a^4\right)}{27\,b^3}+\frac{2\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-7\,B\,a\right)\,\left(-A^3\,a\,b^3+21\,A^2\,B\,a^2\,b^2-147\,A\,B^2\,a^3\,b+343\,B^3\,a^4\right)}{27\,{\left(-a\right)}^{5/6}\,b^{19/6}}\right)\,\left(A\,b-7\,B\,a\right)}{18\,{\left(-a\right)}^{5/6}\,b^{13/6}}}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-7\,B\,a\right)\,1{}\mathrm{i}}{9\,{\left(-a\right)}^{5/6}\,b^{13/6}}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{2\,\sqrt{x}\,\left(A^4\,b^4-28\,A^3\,B\,a\,b^3+294\,A^2\,B^2\,a^2\,b^2-1372\,A\,B^3\,a^3\,b+2401\,B^4\,a^4\right)}{27\,b^3}-\frac{2\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-7\,B\,a\right)\,\left(-A^3\,a\,b^3+21\,A^2\,B\,a^2\,b^2-147\,A\,B^2\,a^3\,b+343\,B^3\,a^4\right)}{27\,{\left(-a\right)}^{5/6}\,b^{19/6}}\right)\,\left(A\,b-7\,B\,a\right)\,1{}\mathrm{i}}{18\,{\left(-a\right)}^{5/6}\,b^{13/6}}+\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{2\,\sqrt{x}\,\left(A^4\,b^4-28\,A^3\,B\,a\,b^3+294\,A^2\,B^2\,a^2\,b^2-1372\,A\,B^3\,a^3\,b+2401\,B^4\,a^4\right)}{27\,b^3}+\frac{2\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-7\,B\,a\right)\,\left(-A^3\,a\,b^3+21\,A^2\,B\,a^2\,b^2-147\,A\,B^2\,a^3\,b+343\,B^3\,a^4\right)}{27\,{\left(-a\right)}^{5/6}\,b^{19/6}}\right)\,\left(A\,b-7\,B\,a\right)\,1{}\mathrm{i}}{18\,{\left(-a\right)}^{5/6}\,b^{13/6}}}{\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{2\,\sqrt{x}\,\left(A^4\,b^4-28\,A^3\,B\,a\,b^3+294\,A^2\,B^2\,a^2\,b^2-1372\,A\,B^3\,a^3\,b+2401\,B^4\,a^4\right)}{27\,b^3}-\frac{2\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-7\,B\,a\right)\,\left(-A^3\,a\,b^3+21\,A^2\,B\,a^2\,b^2-147\,A\,B^2\,a^3\,b+343\,B^3\,a^4\right)}{27\,{\left(-a\right)}^{5/6}\,b^{19/6}}\right)\,\left(A\,b-7\,B\,a\right)}{18\,{\left(-a\right)}^{5/6}\,b^{13/6}}-\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{2\,\sqrt{x}\,\left(A^4\,b^4-28\,A^3\,B\,a\,b^3+294\,A^2\,B^2\,a^2\,b^2-1372\,A\,B^3\,a^3\,b+2401\,B^4\,a^4\right)}{27\,b^3}+\frac{2\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-7\,B\,a\right)\,\left(-A^3\,a\,b^3+21\,A^2\,B\,a^2\,b^2-147\,A\,B^2\,a^3\,b+343\,B^3\,a^4\right)}{27\,{\left(-a\right)}^{5/6}\,b^{19/6}}\right)\,\left(A\,b-7\,B\,a\right)}{18\,{\left(-a\right)}^{5/6}\,b^{13/6}}}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b-7\,B\,a\right)\,1{}\mathrm{i}}{9\,{\left(-a\right)}^{5/6}\,b^{13/6}}","Not used",1,"(2*B*x^(1/2))/b^2 - (x^(1/2)*((A*b)/3 - (B*a)/3))/(a*b^2 + b^3*x^3) - (atan(((((2*x^(1/2)*(A^4*b^4 + 2401*B^4*a^4 + 294*A^2*B^2*a^2*b^2 - 1372*A*B^3*a^3*b - 28*A^3*B*a*b^3))/(27*b^3) - (2*(A*b - 7*B*a)*(343*B^3*a^4 - A^3*a*b^3 - 147*A*B^2*a^3*b + 21*A^2*B*a^2*b^2))/(27*(-a)^(5/6)*b^(19/6)))*(A*b - 7*B*a)*1i)/(18*(-a)^(5/6)*b^(13/6)) + (((2*x^(1/2)*(A^4*b^4 + 2401*B^4*a^4 + 294*A^2*B^2*a^2*b^2 - 1372*A*B^3*a^3*b - 28*A^3*B*a*b^3))/(27*b^3) + (2*(A*b - 7*B*a)*(343*B^3*a^4 - A^3*a*b^3 - 147*A*B^2*a^3*b + 21*A^2*B*a^2*b^2))/(27*(-a)^(5/6)*b^(19/6)))*(A*b - 7*B*a)*1i)/(18*(-a)^(5/6)*b^(13/6)))/((((2*x^(1/2)*(A^4*b^4 + 2401*B^4*a^4 + 294*A^2*B^2*a^2*b^2 - 1372*A*B^3*a^3*b - 28*A^3*B*a*b^3))/(27*b^3) - (2*(A*b - 7*B*a)*(343*B^3*a^4 - A^3*a*b^3 - 147*A*B^2*a^3*b + 21*A^2*B*a^2*b^2))/(27*(-a)^(5/6)*b^(19/6)))*(A*b - 7*B*a))/(18*(-a)^(5/6)*b^(13/6)) - (((2*x^(1/2)*(A^4*b^4 + 2401*B^4*a^4 + 294*A^2*B^2*a^2*b^2 - 1372*A*B^3*a^3*b - 28*A^3*B*a*b^3))/(27*b^3) + (2*(A*b - 7*B*a)*(343*B^3*a^4 - A^3*a*b^3 - 147*A*B^2*a^3*b + 21*A^2*B*a^2*b^2))/(27*(-a)^(5/6)*b^(19/6)))*(A*b - 7*B*a))/(18*(-a)^(5/6)*b^(13/6))))*(A*b - 7*B*a)*1i)/(9*(-a)^(5/6)*b^(13/6)) - (atan(((((3^(1/2)*1i)/2 - 1/2)*((2*x^(1/2)*(A^4*b^4 + 2401*B^4*a^4 + 294*A^2*B^2*a^2*b^2 - 1372*A*B^3*a^3*b - 28*A^3*B*a*b^3))/(27*b^3) - (2*((3^(1/2)*1i)/2 - 1/2)*(A*b - 7*B*a)*(343*B^3*a^4 - A^3*a*b^3 - 147*A*B^2*a^3*b + 21*A^2*B*a^2*b^2))/(27*(-a)^(5/6)*b^(19/6)))*(A*b - 7*B*a)*1i)/(18*(-a)^(5/6)*b^(13/6)) + (((3^(1/2)*1i)/2 - 1/2)*((2*x^(1/2)*(A^4*b^4 + 2401*B^4*a^4 + 294*A^2*B^2*a^2*b^2 - 1372*A*B^3*a^3*b - 28*A^3*B*a*b^3))/(27*b^3) + (2*((3^(1/2)*1i)/2 - 1/2)*(A*b - 7*B*a)*(343*B^3*a^4 - A^3*a*b^3 - 147*A*B^2*a^3*b + 21*A^2*B*a^2*b^2))/(27*(-a)^(5/6)*b^(19/6)))*(A*b - 7*B*a)*1i)/(18*(-a)^(5/6)*b^(13/6)))/((((3^(1/2)*1i)/2 - 1/2)*((2*x^(1/2)*(A^4*b^4 + 2401*B^4*a^4 + 294*A^2*B^2*a^2*b^2 - 1372*A*B^3*a^3*b - 28*A^3*B*a*b^3))/(27*b^3) - (2*((3^(1/2)*1i)/2 - 1/2)*(A*b - 7*B*a)*(343*B^3*a^4 - A^3*a*b^3 - 147*A*B^2*a^3*b + 21*A^2*B*a^2*b^2))/(27*(-a)^(5/6)*b^(19/6)))*(A*b - 7*B*a))/(18*(-a)^(5/6)*b^(13/6)) - (((3^(1/2)*1i)/2 - 1/2)*((2*x^(1/2)*(A^4*b^4 + 2401*B^4*a^4 + 294*A^2*B^2*a^2*b^2 - 1372*A*B^3*a^3*b - 28*A^3*B*a*b^3))/(27*b^3) + (2*((3^(1/2)*1i)/2 - 1/2)*(A*b - 7*B*a)*(343*B^3*a^4 - A^3*a*b^3 - 147*A*B^2*a^3*b + 21*A^2*B*a^2*b^2))/(27*(-a)^(5/6)*b^(19/6)))*(A*b - 7*B*a))/(18*(-a)^(5/6)*b^(13/6))))*((3^(1/2)*1i)/2 - 1/2)*(A*b - 7*B*a)*1i)/(9*(-a)^(5/6)*b^(13/6)) - (atan(((((3^(1/2)*1i)/2 + 1/2)*((2*x^(1/2)*(A^4*b^4 + 2401*B^4*a^4 + 294*A^2*B^2*a^2*b^2 - 1372*A*B^3*a^3*b - 28*A^3*B*a*b^3))/(27*b^3) - (2*((3^(1/2)*1i)/2 + 1/2)*(A*b - 7*B*a)*(343*B^3*a^4 - A^3*a*b^3 - 147*A*B^2*a^3*b + 21*A^2*B*a^2*b^2))/(27*(-a)^(5/6)*b^(19/6)))*(A*b - 7*B*a)*1i)/(18*(-a)^(5/6)*b^(13/6)) + (((3^(1/2)*1i)/2 + 1/2)*((2*x^(1/2)*(A^4*b^4 + 2401*B^4*a^4 + 294*A^2*B^2*a^2*b^2 - 1372*A*B^3*a^3*b - 28*A^3*B*a*b^3))/(27*b^3) + (2*((3^(1/2)*1i)/2 + 1/2)*(A*b - 7*B*a)*(343*B^3*a^4 - A^3*a*b^3 - 147*A*B^2*a^3*b + 21*A^2*B*a^2*b^2))/(27*(-a)^(5/6)*b^(19/6)))*(A*b - 7*B*a)*1i)/(18*(-a)^(5/6)*b^(13/6)))/((((3^(1/2)*1i)/2 + 1/2)*((2*x^(1/2)*(A^4*b^4 + 2401*B^4*a^4 + 294*A^2*B^2*a^2*b^2 - 1372*A*B^3*a^3*b - 28*A^3*B*a*b^3))/(27*b^3) - (2*((3^(1/2)*1i)/2 + 1/2)*(A*b - 7*B*a)*(343*B^3*a^4 - A^3*a*b^3 - 147*A*B^2*a^3*b + 21*A^2*B*a^2*b^2))/(27*(-a)^(5/6)*b^(19/6)))*(A*b - 7*B*a))/(18*(-a)^(5/6)*b^(13/6)) - (((3^(1/2)*1i)/2 + 1/2)*((2*x^(1/2)*(A^4*b^4 + 2401*B^4*a^4 + 294*A^2*B^2*a^2*b^2 - 1372*A*B^3*a^3*b - 28*A^3*B*a*b^3))/(27*b^3) + (2*((3^(1/2)*1i)/2 + 1/2)*(A*b - 7*B*a)*(343*B^3*a^4 - A^3*a*b^3 - 147*A*B^2*a^3*b + 21*A^2*B*a^2*b^2))/(27*(-a)^(5/6)*b^(19/6)))*(A*b - 7*B*a))/(18*(-a)^(5/6)*b^(13/6))))*((3^(1/2)*1i)/2 + 1/2)*(A*b - 7*B*a)*1i)/(9*(-a)^(5/6)*b^(13/6))","B"
165,1,1578,289,2.868862,"\text{Not used}","int((x^(3/2)*(A + B*x^3))/(a + b*x^3)^2,x)","\frac{x^{5/2}\,\left(A\,b-B\,a\right)}{3\,a\,b\,\left(b\,x^3+a\right)}-\frac{\mathrm{atan}\left(\frac{\frac{{\left(A\,b+5\,B\,a\right)}^2\,\left(\frac{4\,A^3\,b^3}{3}+\frac{500\,B^3\,a^3}{3}+100\,A\,B^2\,a^2\,b+20\,A^2\,B\,a\,b^2-\frac{\sqrt{x}\,\left(A\,b+5\,B\,a\right)\,\left(24\,A^2\,a\,b^4+240\,A\,B\,a^2\,b^3+600\,B^2\,a^3\,b^2\right)}{18\,{\left(-a\right)}^{7/6}\,b^{11/6}}\right)\,1{}\mathrm{i}}{324\,{\left(-a\right)}^{7/3}\,b^{11/3}}-\frac{{\left(A\,b+5\,B\,a\right)}^2\,\left(\frac{4\,A^3\,b^3}{3}+\frac{500\,B^3\,a^3}{3}+100\,A\,B^2\,a^2\,b+20\,A^2\,B\,a\,b^2+\frac{\sqrt{x}\,\left(A\,b+5\,B\,a\right)\,\left(24\,A^2\,a\,b^4+240\,A\,B\,a^2\,b^3+600\,B^2\,a^3\,b^2\right)}{18\,{\left(-a\right)}^{7/6}\,b^{11/6}}\right)\,1{}\mathrm{i}}{324\,{\left(-a\right)}^{7/3}\,b^{11/3}}}{\frac{{\left(A\,b+5\,B\,a\right)}^2\,\left(\frac{4\,A^3\,b^3}{3}+\frac{500\,B^3\,a^3}{3}+100\,A\,B^2\,a^2\,b+20\,A^2\,B\,a\,b^2-\frac{\sqrt{x}\,\left(A\,b+5\,B\,a\right)\,\left(24\,A^2\,a\,b^4+240\,A\,B\,a^2\,b^3+600\,B^2\,a^3\,b^2\right)}{18\,{\left(-a\right)}^{7/6}\,b^{11/6}}\right)}{324\,{\left(-a\right)}^{7/3}\,b^{11/3}}+\frac{{\left(A\,b+5\,B\,a\right)}^2\,\left(\frac{4\,A^3\,b^3}{3}+\frac{500\,B^3\,a^3}{3}+100\,A\,B^2\,a^2\,b+20\,A^2\,B\,a\,b^2+\frac{\sqrt{x}\,\left(A\,b+5\,B\,a\right)\,\left(24\,A^2\,a\,b^4+240\,A\,B\,a^2\,b^3+600\,B^2\,a^3\,b^2\right)}{18\,{\left(-a\right)}^{7/6}\,b^{11/6}}\right)}{324\,{\left(-a\right)}^{7/3}\,b^{11/3}}}\right)\,\left(A\,b+5\,B\,a\right)\,1{}\mathrm{i}}{9\,{\left(-a\right)}^{7/6}\,b^{11/6}}-\frac{\mathrm{atan}\left(\frac{\frac{{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(A\,b+5\,B\,a\right)}^2\,\left(\frac{4\,A^3\,b^3}{3}+\frac{500\,B^3\,a^3}{3}+100\,A\,B^2\,a^2\,b+20\,A^2\,B\,a\,b^2-\frac{\sqrt{x}\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b+5\,B\,a\right)\,\left(24\,A^2\,a\,b^4+240\,A\,B\,a^2\,b^3+600\,B^2\,a^3\,b^2\right)}{18\,{\left(-a\right)}^{7/6}\,b^{11/6}}\right)\,1{}\mathrm{i}}{324\,{\left(-a\right)}^{7/3}\,b^{11/3}}-\frac{{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(A\,b+5\,B\,a\right)}^2\,\left(\frac{4\,A^3\,b^3}{3}+\frac{500\,B^3\,a^3}{3}+100\,A\,B^2\,a^2\,b+20\,A^2\,B\,a\,b^2+\frac{\sqrt{x}\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b+5\,B\,a\right)\,\left(24\,A^2\,a\,b^4+240\,A\,B\,a^2\,b^3+600\,B^2\,a^3\,b^2\right)}{18\,{\left(-a\right)}^{7/6}\,b^{11/6}}\right)\,1{}\mathrm{i}}{324\,{\left(-a\right)}^{7/3}\,b^{11/3}}}{\frac{{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(A\,b+5\,B\,a\right)}^2\,\left(\frac{4\,A^3\,b^3}{3}+\frac{500\,B^3\,a^3}{3}+100\,A\,B^2\,a^2\,b+20\,A^2\,B\,a\,b^2-\frac{\sqrt{x}\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b+5\,B\,a\right)\,\left(24\,A^2\,a\,b^4+240\,A\,B\,a^2\,b^3+600\,B^2\,a^3\,b^2\right)}{18\,{\left(-a\right)}^{7/6}\,b^{11/6}}\right)}{324\,{\left(-a\right)}^{7/3}\,b^{11/3}}+\frac{{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(A\,b+5\,B\,a\right)}^2\,\left(\frac{4\,A^3\,b^3}{3}+\frac{500\,B^3\,a^3}{3}+100\,A\,B^2\,a^2\,b+20\,A^2\,B\,a\,b^2+\frac{\sqrt{x}\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b+5\,B\,a\right)\,\left(24\,A^2\,a\,b^4+240\,A\,B\,a^2\,b^3+600\,B^2\,a^3\,b^2\right)}{18\,{\left(-a\right)}^{7/6}\,b^{11/6}}\right)}{324\,{\left(-a\right)}^{7/3}\,b^{11/3}}}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b+5\,B\,a\right)\,1{}\mathrm{i}}{9\,{\left(-a\right)}^{7/6}\,b^{11/6}}-\frac{\mathrm{atan}\left(\frac{\frac{{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(A\,b+5\,B\,a\right)}^2\,\left(\frac{4\,A^3\,b^3}{3}+\frac{500\,B^3\,a^3}{3}+100\,A\,B^2\,a^2\,b+20\,A^2\,B\,a\,b^2-\frac{\sqrt{x}\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b+5\,B\,a\right)\,\left(24\,A^2\,a\,b^4+240\,A\,B\,a^2\,b^3+600\,B^2\,a^3\,b^2\right)}{18\,{\left(-a\right)}^{7/6}\,b^{11/6}}\right)\,1{}\mathrm{i}}{324\,{\left(-a\right)}^{7/3}\,b^{11/3}}-\frac{{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(A\,b+5\,B\,a\right)}^2\,\left(\frac{4\,A^3\,b^3}{3}+\frac{500\,B^3\,a^3}{3}+100\,A\,B^2\,a^2\,b+20\,A^2\,B\,a\,b^2+\frac{\sqrt{x}\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b+5\,B\,a\right)\,\left(24\,A^2\,a\,b^4+240\,A\,B\,a^2\,b^3+600\,B^2\,a^3\,b^2\right)}{18\,{\left(-a\right)}^{7/6}\,b^{11/6}}\right)\,1{}\mathrm{i}}{324\,{\left(-a\right)}^{7/3}\,b^{11/3}}}{\frac{{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(A\,b+5\,B\,a\right)}^2\,\left(\frac{4\,A^3\,b^3}{3}+\frac{500\,B^3\,a^3}{3}+100\,A\,B^2\,a^2\,b+20\,A^2\,B\,a\,b^2-\frac{\sqrt{x}\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b+5\,B\,a\right)\,\left(24\,A^2\,a\,b^4+240\,A\,B\,a^2\,b^3+600\,B^2\,a^3\,b^2\right)}{18\,{\left(-a\right)}^{7/6}\,b^{11/6}}\right)}{324\,{\left(-a\right)}^{7/3}\,b^{11/3}}+\frac{{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(A\,b+5\,B\,a\right)}^2\,\left(\frac{4\,A^3\,b^3}{3}+\frac{500\,B^3\,a^3}{3}+100\,A\,B^2\,a^2\,b+20\,A^2\,B\,a\,b^2+\frac{\sqrt{x}\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b+5\,B\,a\right)\,\left(24\,A^2\,a\,b^4+240\,A\,B\,a^2\,b^3+600\,B^2\,a^3\,b^2\right)}{18\,{\left(-a\right)}^{7/6}\,b^{11/6}}\right)}{324\,{\left(-a\right)}^{7/3}\,b^{11/3}}}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(A\,b+5\,B\,a\right)\,1{}\mathrm{i}}{9\,{\left(-a\right)}^{7/6}\,b^{11/6}}","Not used",1,"(x^(5/2)*(A*b - B*a))/(3*a*b*(a + b*x^3)) - (atan(((((3^(1/2)*1i)/2 - 1/2)^2*(A*b + 5*B*a)^2*((4*A^3*b^3)/3 + (500*B^3*a^3)/3 + 100*A*B^2*a^2*b + 20*A^2*B*a*b^2 - (x^(1/2)*((3^(1/2)*1i)/2 - 1/2)*(A*b + 5*B*a)*(24*A^2*a*b^4 + 600*B^2*a^3*b^2 + 240*A*B*a^2*b^3))/(18*(-a)^(7/6)*b^(11/6)))*1i)/(324*(-a)^(7/3)*b^(11/3)) - (((3^(1/2)*1i)/2 - 1/2)^2*(A*b + 5*B*a)^2*((4*A^3*b^3)/3 + (500*B^3*a^3)/3 + 100*A*B^2*a^2*b + 20*A^2*B*a*b^2 + (x^(1/2)*((3^(1/2)*1i)/2 - 1/2)*(A*b + 5*B*a)*(24*A^2*a*b^4 + 600*B^2*a^3*b^2 + 240*A*B*a^2*b^3))/(18*(-a)^(7/6)*b^(11/6)))*1i)/(324*(-a)^(7/3)*b^(11/3)))/((((3^(1/2)*1i)/2 - 1/2)^2*(A*b + 5*B*a)^2*((4*A^3*b^3)/3 + (500*B^3*a^3)/3 + 100*A*B^2*a^2*b + 20*A^2*B*a*b^2 - (x^(1/2)*((3^(1/2)*1i)/2 - 1/2)*(A*b + 5*B*a)*(24*A^2*a*b^4 + 600*B^2*a^3*b^2 + 240*A*B*a^2*b^3))/(18*(-a)^(7/6)*b^(11/6))))/(324*(-a)^(7/3)*b^(11/3)) + (((3^(1/2)*1i)/2 - 1/2)^2*(A*b + 5*B*a)^2*((4*A^3*b^3)/3 + (500*B^3*a^3)/3 + 100*A*B^2*a^2*b + 20*A^2*B*a*b^2 + (x^(1/2)*((3^(1/2)*1i)/2 - 1/2)*(A*b + 5*B*a)*(24*A^2*a*b^4 + 600*B^2*a^3*b^2 + 240*A*B*a^2*b^3))/(18*(-a)^(7/6)*b^(11/6))))/(324*(-a)^(7/3)*b^(11/3))))*((3^(1/2)*1i)/2 - 1/2)*(A*b + 5*B*a)*1i)/(9*(-a)^(7/6)*b^(11/6)) - (atan(((((3^(1/2)*1i)/2 + 1/2)^2*(A*b + 5*B*a)^2*((4*A^3*b^3)/3 + (500*B^3*a^3)/3 + 100*A*B^2*a^2*b + 20*A^2*B*a*b^2 - (x^(1/2)*((3^(1/2)*1i)/2 + 1/2)*(A*b + 5*B*a)*(24*A^2*a*b^4 + 600*B^2*a^3*b^2 + 240*A*B*a^2*b^3))/(18*(-a)^(7/6)*b^(11/6)))*1i)/(324*(-a)^(7/3)*b^(11/3)) - (((3^(1/2)*1i)/2 + 1/2)^2*(A*b + 5*B*a)^2*((4*A^3*b^3)/3 + (500*B^3*a^3)/3 + 100*A*B^2*a^2*b + 20*A^2*B*a*b^2 + (x^(1/2)*((3^(1/2)*1i)/2 + 1/2)*(A*b + 5*B*a)*(24*A^2*a*b^4 + 600*B^2*a^3*b^2 + 240*A*B*a^2*b^3))/(18*(-a)^(7/6)*b^(11/6)))*1i)/(324*(-a)^(7/3)*b^(11/3)))/((((3^(1/2)*1i)/2 + 1/2)^2*(A*b + 5*B*a)^2*((4*A^3*b^3)/3 + (500*B^3*a^3)/3 + 100*A*B^2*a^2*b + 20*A^2*B*a*b^2 - (x^(1/2)*((3^(1/2)*1i)/2 + 1/2)*(A*b + 5*B*a)*(24*A^2*a*b^4 + 600*B^2*a^3*b^2 + 240*A*B*a^2*b^3))/(18*(-a)^(7/6)*b^(11/6))))/(324*(-a)^(7/3)*b^(11/3)) + (((3^(1/2)*1i)/2 + 1/2)^2*(A*b + 5*B*a)^2*((4*A^3*b^3)/3 + (500*B^3*a^3)/3 + 100*A*B^2*a^2*b + 20*A^2*B*a*b^2 + (x^(1/2)*((3^(1/2)*1i)/2 + 1/2)*(A*b + 5*B*a)*(24*A^2*a*b^4 + 600*B^2*a^3*b^2 + 240*A*B*a^2*b^3))/(18*(-a)^(7/6)*b^(11/6))))/(324*(-a)^(7/3)*b^(11/3))))*((3^(1/2)*1i)/2 + 1/2)*(A*b + 5*B*a)*1i)/(9*(-a)^(7/6)*b^(11/6)) - (atan((((A*b + 5*B*a)^2*((4*A^3*b^3)/3 + (500*B^3*a^3)/3 + 100*A*B^2*a^2*b + 20*A^2*B*a*b^2 - (x^(1/2)*(A*b + 5*B*a)*(24*A^2*a*b^4 + 600*B^2*a^3*b^2 + 240*A*B*a^2*b^3))/(18*(-a)^(7/6)*b^(11/6)))*1i)/(324*(-a)^(7/3)*b^(11/3)) - ((A*b + 5*B*a)^2*((4*A^3*b^3)/3 + (500*B^3*a^3)/3 + 100*A*B^2*a^2*b + 20*A^2*B*a*b^2 + (x^(1/2)*(A*b + 5*B*a)*(24*A^2*a*b^4 + 600*B^2*a^3*b^2 + 240*A*B*a^2*b^3))/(18*(-a)^(7/6)*b^(11/6)))*1i)/(324*(-a)^(7/3)*b^(11/3)))/(((A*b + 5*B*a)^2*((4*A^3*b^3)/3 + (500*B^3*a^3)/3 + 100*A*B^2*a^2*b + 20*A^2*B*a*b^2 - (x^(1/2)*(A*b + 5*B*a)*(24*A^2*a*b^4 + 600*B^2*a^3*b^2 + 240*A*B*a^2*b^3))/(18*(-a)^(7/6)*b^(11/6))))/(324*(-a)^(7/3)*b^(11/3)) + ((A*b + 5*B*a)^2*((4*A^3*b^3)/3 + (500*B^3*a^3)/3 + 100*A*B^2*a^2*b + 20*A^2*B*a*b^2 + (x^(1/2)*(A*b + 5*B*a)*(24*A^2*a*b^4 + 600*B^2*a^3*b^2 + 240*A*B*a^2*b^3))/(18*(-a)^(7/6)*b^(11/6))))/(324*(-a)^(7/3)*b^(11/3))))*(A*b + 5*B*a)*1i)/(9*(-a)^(7/6)*b^(11/6))","B"
166,1,115,71,0.140893,"\text{Not used}","int((x^(1/2)*(A + B*x^3))/(a + b*x^3)^2,x)","\frac{B\,a^2\,\mathrm{atan}\left(\frac{\sqrt{b}\,x^{3/2}}{\sqrt{a}}\right)+A\,b^2\,x^3\,\mathrm{atan}\left(\frac{\sqrt{b}\,x^{3/2}}{\sqrt{a}}\right)+A\,a\,b\,\mathrm{atan}\left(\frac{\sqrt{b}\,x^{3/2}}{\sqrt{a}}\right)+A\,\sqrt{a}\,b^{3/2}\,x^{3/2}-B\,a^{3/2}\,\sqrt{b}\,x^{3/2}+B\,a\,b\,x^3\,\mathrm{atan}\left(\frac{\sqrt{b}\,x^{3/2}}{\sqrt{a}}\right)}{3\,a^{5/2}\,b^{3/2}+3\,a^{3/2}\,b^{5/2}\,x^3}","Not used",1,"(B*a^2*atan((b^(1/2)*x^(3/2))/a^(1/2)) + A*b^2*x^3*atan((b^(1/2)*x^(3/2))/a^(1/2)) + A*a*b*atan((b^(1/2)*x^(3/2))/a^(1/2)) + A*a^(1/2)*b^(3/2)*x^(3/2) - B*a^(3/2)*b^(1/2)*x^(3/2) + B*a*b*x^3*atan((b^(1/2)*x^(3/2))/a^(1/2)))/(3*a^(5/2)*b^(3/2) + 3*a^(3/2)*b^(5/2)*x^3)","B"
167,1,1922,289,2.916799,"\text{Not used}","int((A + B*x^3)/(x^(1/2)*(a + b*x^3)^2),x)","\frac{\sqrt{x}\,\left(A\,b-B\,a\right)}{3\,a\,b\,\left(b\,x^3+a\right)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{2\,\sqrt{x}\,\left(625\,A^4\,b^5+500\,A^3\,B\,a\,b^4+150\,A^2\,B^2\,a^2\,b^3+20\,A\,B^3\,a^3\,b^2+B^4\,a^4\,b\right)}{27\,a^4}-\frac{2\,\left(5\,A\,b+B\,a\right)\,\left(125\,A^3\,b^5+75\,A^2\,B\,a\,b^4+15\,A\,B^2\,a^2\,b^3+B^3\,a^3\,b^2\right)}{27\,{\left(-a\right)}^{23/6}\,b^{7/6}}\right)\,\left(5\,A\,b+B\,a\right)\,1{}\mathrm{i}}{18\,{\left(-a\right)}^{11/6}\,b^{7/6}}+\frac{\left(\frac{2\,\sqrt{x}\,\left(625\,A^4\,b^5+500\,A^3\,B\,a\,b^4+150\,A^2\,B^2\,a^2\,b^3+20\,A\,B^3\,a^3\,b^2+B^4\,a^4\,b\right)}{27\,a^4}+\frac{2\,\left(5\,A\,b+B\,a\right)\,\left(125\,A^3\,b^5+75\,A^2\,B\,a\,b^4+15\,A\,B^2\,a^2\,b^3+B^3\,a^3\,b^2\right)}{27\,{\left(-a\right)}^{23/6}\,b^{7/6}}\right)\,\left(5\,A\,b+B\,a\right)\,1{}\mathrm{i}}{18\,{\left(-a\right)}^{11/6}\,b^{7/6}}}{\frac{\left(\frac{2\,\sqrt{x}\,\left(625\,A^4\,b^5+500\,A^3\,B\,a\,b^4+150\,A^2\,B^2\,a^2\,b^3+20\,A\,B^3\,a^3\,b^2+B^4\,a^4\,b\right)}{27\,a^4}-\frac{2\,\left(5\,A\,b+B\,a\right)\,\left(125\,A^3\,b^5+75\,A^2\,B\,a\,b^4+15\,A\,B^2\,a^2\,b^3+B^3\,a^3\,b^2\right)}{27\,{\left(-a\right)}^{23/6}\,b^{7/6}}\right)\,\left(5\,A\,b+B\,a\right)}{18\,{\left(-a\right)}^{11/6}\,b^{7/6}}-\frac{\left(\frac{2\,\sqrt{x}\,\left(625\,A^4\,b^5+500\,A^3\,B\,a\,b^4+150\,A^2\,B^2\,a^2\,b^3+20\,A\,B^3\,a^3\,b^2+B^4\,a^4\,b\right)}{27\,a^4}+\frac{2\,\left(5\,A\,b+B\,a\right)\,\left(125\,A^3\,b^5+75\,A^2\,B\,a\,b^4+15\,A\,B^2\,a^2\,b^3+B^3\,a^3\,b^2\right)}{27\,{\left(-a\right)}^{23/6}\,b^{7/6}}\right)\,\left(5\,A\,b+B\,a\right)}{18\,{\left(-a\right)}^{11/6}\,b^{7/6}}}\right)\,\left(5\,A\,b+B\,a\right)\,1{}\mathrm{i}}{9\,{\left(-a\right)}^{11/6}\,b^{7/6}}+\frac{\mathrm{atan}\left(\frac{\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(5\,A\,b+B\,a\right)\,\left(\frac{2\,\sqrt{x}\,\left(625\,A^4\,b^5+500\,A^3\,B\,a\,b^4+150\,A^2\,B^2\,a^2\,b^3+20\,A\,B^3\,a^3\,b^2+B^4\,a^4\,b\right)}{27\,a^4}-\frac{2\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(5\,A\,b+B\,a\right)\,\left(125\,A^3\,b^5+75\,A^2\,B\,a\,b^4+15\,A\,B^2\,a^2\,b^3+B^3\,a^3\,b^2\right)}{27\,{\left(-a\right)}^{23/6}\,b^{7/6}}\right)\,1{}\mathrm{i}}{18\,{\left(-a\right)}^{11/6}\,b^{7/6}}+\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(5\,A\,b+B\,a\right)\,\left(\frac{2\,\sqrt{x}\,\left(625\,A^4\,b^5+500\,A^3\,B\,a\,b^4+150\,A^2\,B^2\,a^2\,b^3+20\,A\,B^3\,a^3\,b^2+B^4\,a^4\,b\right)}{27\,a^4}+\frac{2\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(5\,A\,b+B\,a\right)\,\left(125\,A^3\,b^5+75\,A^2\,B\,a\,b^4+15\,A\,B^2\,a^2\,b^3+B^3\,a^3\,b^2\right)}{27\,{\left(-a\right)}^{23/6}\,b^{7/6}}\right)\,1{}\mathrm{i}}{18\,{\left(-a\right)}^{11/6}\,b^{7/6}}}{\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(5\,A\,b+B\,a\right)\,\left(\frac{2\,\sqrt{x}\,\left(625\,A^4\,b^5+500\,A^3\,B\,a\,b^4+150\,A^2\,B^2\,a^2\,b^3+20\,A\,B^3\,a^3\,b^2+B^4\,a^4\,b\right)}{27\,a^4}-\frac{2\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(5\,A\,b+B\,a\right)\,\left(125\,A^3\,b^5+75\,A^2\,B\,a\,b^4+15\,A\,B^2\,a^2\,b^3+B^3\,a^3\,b^2\right)}{27\,{\left(-a\right)}^{23/6}\,b^{7/6}}\right)}{18\,{\left(-a\right)}^{11/6}\,b^{7/6}}-\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(5\,A\,b+B\,a\right)\,\left(\frac{2\,\sqrt{x}\,\left(625\,A^4\,b^5+500\,A^3\,B\,a\,b^4+150\,A^2\,B^2\,a^2\,b^3+20\,A\,B^3\,a^3\,b^2+B^4\,a^4\,b\right)}{27\,a^4}+\frac{2\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(5\,A\,b+B\,a\right)\,\left(125\,A^3\,b^5+75\,A^2\,B\,a\,b^4+15\,A\,B^2\,a^2\,b^3+B^3\,a^3\,b^2\right)}{27\,{\left(-a\right)}^{23/6}\,b^{7/6}}\right)}{18\,{\left(-a\right)}^{11/6}\,b^{7/6}}}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(5\,A\,b+B\,a\right)\,1{}\mathrm{i}}{9\,{\left(-a\right)}^{11/6}\,b^{7/6}}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(5\,A\,b+B\,a\right)\,\left(\frac{2\,\sqrt{x}\,\left(625\,A^4\,b^5+500\,A^3\,B\,a\,b^4+150\,A^2\,B^2\,a^2\,b^3+20\,A\,B^3\,a^3\,b^2+B^4\,a^4\,b\right)}{27\,a^4}-\frac{2\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(5\,A\,b+B\,a\right)\,\left(125\,A^3\,b^5+75\,A^2\,B\,a\,b^4+15\,A\,B^2\,a^2\,b^3+B^3\,a^3\,b^2\right)}{27\,{\left(-a\right)}^{23/6}\,b^{7/6}}\right)\,1{}\mathrm{i}}{18\,{\left(-a\right)}^{11/6}\,b^{7/6}}+\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(5\,A\,b+B\,a\right)\,\left(\frac{2\,\sqrt{x}\,\left(625\,A^4\,b^5+500\,A^3\,B\,a\,b^4+150\,A^2\,B^2\,a^2\,b^3+20\,A\,B^3\,a^3\,b^2+B^4\,a^4\,b\right)}{27\,a^4}+\frac{2\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(5\,A\,b+B\,a\right)\,\left(125\,A^3\,b^5+75\,A^2\,B\,a\,b^4+15\,A\,B^2\,a^2\,b^3+B^3\,a^3\,b^2\right)}{27\,{\left(-a\right)}^{23/6}\,b^{7/6}}\right)\,1{}\mathrm{i}}{18\,{\left(-a\right)}^{11/6}\,b^{7/6}}}{\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(5\,A\,b+B\,a\right)\,\left(\frac{2\,\sqrt{x}\,\left(625\,A^4\,b^5+500\,A^3\,B\,a\,b^4+150\,A^2\,B^2\,a^2\,b^3+20\,A\,B^3\,a^3\,b^2+B^4\,a^4\,b\right)}{27\,a^4}-\frac{2\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(5\,A\,b+B\,a\right)\,\left(125\,A^3\,b^5+75\,A^2\,B\,a\,b^4+15\,A\,B^2\,a^2\,b^3+B^3\,a^3\,b^2\right)}{27\,{\left(-a\right)}^{23/6}\,b^{7/6}}\right)}{18\,{\left(-a\right)}^{11/6}\,b^{7/6}}-\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(5\,A\,b+B\,a\right)\,\left(\frac{2\,\sqrt{x}\,\left(625\,A^4\,b^5+500\,A^3\,B\,a\,b^4+150\,A^2\,B^2\,a^2\,b^3+20\,A\,B^3\,a^3\,b^2+B^4\,a^4\,b\right)}{27\,a^4}+\frac{2\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(5\,A\,b+B\,a\right)\,\left(125\,A^3\,b^5+75\,A^2\,B\,a\,b^4+15\,A\,B^2\,a^2\,b^3+B^3\,a^3\,b^2\right)}{27\,{\left(-a\right)}^{23/6}\,b^{7/6}}\right)}{18\,{\left(-a\right)}^{11/6}\,b^{7/6}}}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(5\,A\,b+B\,a\right)\,1{}\mathrm{i}}{9\,{\left(-a\right)}^{11/6}\,b^{7/6}}","Not used",1,"(atan(((((2*x^(1/2)*(625*A^4*b^5 + B^4*a^4*b + 150*A^2*B^2*a^2*b^3 + 500*A^3*B*a*b^4 + 20*A*B^3*a^3*b^2))/(27*a^4) - (2*(5*A*b + B*a)*(125*A^3*b^5 + B^3*a^3*b^2 + 75*A^2*B*a*b^4 + 15*A*B^2*a^2*b^3))/(27*(-a)^(23/6)*b^(7/6)))*(5*A*b + B*a)*1i)/(18*(-a)^(11/6)*b^(7/6)) + (((2*x^(1/2)*(625*A^4*b^5 + B^4*a^4*b + 150*A^2*B^2*a^2*b^3 + 500*A^3*B*a*b^4 + 20*A*B^3*a^3*b^2))/(27*a^4) + (2*(5*A*b + B*a)*(125*A^3*b^5 + B^3*a^3*b^2 + 75*A^2*B*a*b^4 + 15*A*B^2*a^2*b^3))/(27*(-a)^(23/6)*b^(7/6)))*(5*A*b + B*a)*1i)/(18*(-a)^(11/6)*b^(7/6)))/((((2*x^(1/2)*(625*A^4*b^5 + B^4*a^4*b + 150*A^2*B^2*a^2*b^3 + 500*A^3*B*a*b^4 + 20*A*B^3*a^3*b^2))/(27*a^4) - (2*(5*A*b + B*a)*(125*A^3*b^5 + B^3*a^3*b^2 + 75*A^2*B*a*b^4 + 15*A*B^2*a^2*b^3))/(27*(-a)^(23/6)*b^(7/6)))*(5*A*b + B*a))/(18*(-a)^(11/6)*b^(7/6)) - (((2*x^(1/2)*(625*A^4*b^5 + B^4*a^4*b + 150*A^2*B^2*a^2*b^3 + 500*A^3*B*a*b^4 + 20*A*B^3*a^3*b^2))/(27*a^4) + (2*(5*A*b + B*a)*(125*A^3*b^5 + B^3*a^3*b^2 + 75*A^2*B*a*b^4 + 15*A*B^2*a^2*b^3))/(27*(-a)^(23/6)*b^(7/6)))*(5*A*b + B*a))/(18*(-a)^(11/6)*b^(7/6))))*(5*A*b + B*a)*1i)/(9*(-a)^(11/6)*b^(7/6)) + (atan(((((3^(1/2)*1i)/2 - 1/2)*(5*A*b + B*a)*((2*x^(1/2)*(625*A^4*b^5 + B^4*a^4*b + 150*A^2*B^2*a^2*b^3 + 500*A^3*B*a*b^4 + 20*A*B^3*a^3*b^2))/(27*a^4) - (2*((3^(1/2)*1i)/2 - 1/2)*(5*A*b + B*a)*(125*A^3*b^5 + B^3*a^3*b^2 + 75*A^2*B*a*b^4 + 15*A*B^2*a^2*b^3))/(27*(-a)^(23/6)*b^(7/6)))*1i)/(18*(-a)^(11/6)*b^(7/6)) + (((3^(1/2)*1i)/2 - 1/2)*(5*A*b + B*a)*((2*x^(1/2)*(625*A^4*b^5 + B^4*a^4*b + 150*A^2*B^2*a^2*b^3 + 500*A^3*B*a*b^4 + 20*A*B^3*a^3*b^2))/(27*a^4) + (2*((3^(1/2)*1i)/2 - 1/2)*(5*A*b + B*a)*(125*A^3*b^5 + B^3*a^3*b^2 + 75*A^2*B*a*b^4 + 15*A*B^2*a^2*b^3))/(27*(-a)^(23/6)*b^(7/6)))*1i)/(18*(-a)^(11/6)*b^(7/6)))/((((3^(1/2)*1i)/2 - 1/2)*(5*A*b + B*a)*((2*x^(1/2)*(625*A^4*b^5 + B^4*a^4*b + 150*A^2*B^2*a^2*b^3 + 500*A^3*B*a*b^4 + 20*A*B^3*a^3*b^2))/(27*a^4) - (2*((3^(1/2)*1i)/2 - 1/2)*(5*A*b + B*a)*(125*A^3*b^5 + B^3*a^3*b^2 + 75*A^2*B*a*b^4 + 15*A*B^2*a^2*b^3))/(27*(-a)^(23/6)*b^(7/6))))/(18*(-a)^(11/6)*b^(7/6)) - (((3^(1/2)*1i)/2 - 1/2)*(5*A*b + B*a)*((2*x^(1/2)*(625*A^4*b^5 + B^4*a^4*b + 150*A^2*B^2*a^2*b^3 + 500*A^3*B*a*b^4 + 20*A*B^3*a^3*b^2))/(27*a^4) + (2*((3^(1/2)*1i)/2 - 1/2)*(5*A*b + B*a)*(125*A^3*b^5 + B^3*a^3*b^2 + 75*A^2*B*a*b^4 + 15*A*B^2*a^2*b^3))/(27*(-a)^(23/6)*b^(7/6))))/(18*(-a)^(11/6)*b^(7/6))))*((3^(1/2)*1i)/2 - 1/2)*(5*A*b + B*a)*1i)/(9*(-a)^(11/6)*b^(7/6)) + (atan(((((3^(1/2)*1i)/2 + 1/2)*(5*A*b + B*a)*((2*x^(1/2)*(625*A^4*b^5 + B^4*a^4*b + 150*A^2*B^2*a^2*b^3 + 500*A^3*B*a*b^4 + 20*A*B^3*a^3*b^2))/(27*a^4) - (2*((3^(1/2)*1i)/2 + 1/2)*(5*A*b + B*a)*(125*A^3*b^5 + B^3*a^3*b^2 + 75*A^2*B*a*b^4 + 15*A*B^2*a^2*b^3))/(27*(-a)^(23/6)*b^(7/6)))*1i)/(18*(-a)^(11/6)*b^(7/6)) + (((3^(1/2)*1i)/2 + 1/2)*(5*A*b + B*a)*((2*x^(1/2)*(625*A^4*b^5 + B^4*a^4*b + 150*A^2*B^2*a^2*b^3 + 500*A^3*B*a*b^4 + 20*A*B^3*a^3*b^2))/(27*a^4) + (2*((3^(1/2)*1i)/2 + 1/2)*(5*A*b + B*a)*(125*A^3*b^5 + B^3*a^3*b^2 + 75*A^2*B*a*b^4 + 15*A*B^2*a^2*b^3))/(27*(-a)^(23/6)*b^(7/6)))*1i)/(18*(-a)^(11/6)*b^(7/6)))/((((3^(1/2)*1i)/2 + 1/2)*(5*A*b + B*a)*((2*x^(1/2)*(625*A^4*b^5 + B^4*a^4*b + 150*A^2*B^2*a^2*b^3 + 500*A^3*B*a*b^4 + 20*A*B^3*a^3*b^2))/(27*a^4) - (2*((3^(1/2)*1i)/2 + 1/2)*(5*A*b + B*a)*(125*A^3*b^5 + B^3*a^3*b^2 + 75*A^2*B*a*b^4 + 15*A*B^2*a^2*b^3))/(27*(-a)^(23/6)*b^(7/6))))/(18*(-a)^(11/6)*b^(7/6)) - (((3^(1/2)*1i)/2 + 1/2)*(5*A*b + B*a)*((2*x^(1/2)*(625*A^4*b^5 + B^4*a^4*b + 150*A^2*B^2*a^2*b^3 + 500*A^3*B*a*b^4 + 20*A*B^3*a^3*b^2))/(27*a^4) + (2*((3^(1/2)*1i)/2 + 1/2)*(5*A*b + B*a)*(125*A^3*b^5 + B^3*a^3*b^2 + 75*A^2*B*a*b^4 + 15*A*B^2*a^2*b^3))/(27*(-a)^(23/6)*b^(7/6))))/(18*(-a)^(11/6)*b^(7/6))))*((3^(1/2)*1i)/2 + 1/2)*(5*A*b + B*a)*1i)/(9*(-a)^(11/6)*b^(7/6)) + (x^(1/2)*(A*b - B*a))/(3*a*b*(a + b*x^3))","B"
168,1,1757,318,2.911652,"\text{Not used}","int((A + B*x^3)/(x^(3/2)*(a + b*x^3)^2),x)","-\frac{\frac{2\,A}{a}+\frac{x^3\,\left(7\,A\,b-B\,a\right)}{3\,a^2}}{a\,\sqrt{x}+b\,x^{7/2}}+\frac{\mathrm{atan}\left(\frac{\frac{{\left(7\,A\,b-B\,a\right)}^2\,\left(81\,B^3\,a^{18}\,b^3-27783\,A^3\,a^{15}\,b^6-1701\,A\,B^2\,a^{17}\,b^4+11907\,A^2\,B\,a^{16}\,b^5+\frac{\sqrt{x}\,\left(7\,A\,b-B\,a\right)\,\left(23147208\,A^2\,a^{17}\,b^6-6613488\,A\,B\,a^{18}\,b^5+472392\,B^2\,a^{19}\,b^4\right)}{5832\,{\left(-a\right)}^{13/6}\,b^{5/6}}\right)\,1{}\mathrm{i}}{{\left(-a\right)}^{13/3}\,b^{5/3}}+\frac{{\left(7\,A\,b-B\,a\right)}^2\,\left(27783\,A^3\,a^{15}\,b^6-81\,B^3\,a^{18}\,b^3+1701\,A\,B^2\,a^{17}\,b^4-11907\,A^2\,B\,a^{16}\,b^5+\frac{\sqrt{x}\,\left(7\,A\,b-B\,a\right)\,\left(23147208\,A^2\,a^{17}\,b^6-6613488\,A\,B\,a^{18}\,b^5+472392\,B^2\,a^{19}\,b^4\right)}{5832\,{\left(-a\right)}^{13/6}\,b^{5/6}}\right)\,1{}\mathrm{i}}{{\left(-a\right)}^{13/3}\,b^{5/3}}}{\frac{{\left(7\,A\,b-B\,a\right)}^2\,\left(81\,B^3\,a^{18}\,b^3-27783\,A^3\,a^{15}\,b^6-1701\,A\,B^2\,a^{17}\,b^4+11907\,A^2\,B\,a^{16}\,b^5+\frac{\sqrt{x}\,\left(7\,A\,b-B\,a\right)\,\left(23147208\,A^2\,a^{17}\,b^6-6613488\,A\,B\,a^{18}\,b^5+472392\,B^2\,a^{19}\,b^4\right)}{5832\,{\left(-a\right)}^{13/6}\,b^{5/6}}\right)}{{\left(-a\right)}^{13/3}\,b^{5/3}}-\frac{{\left(7\,A\,b-B\,a\right)}^2\,\left(27783\,A^3\,a^{15}\,b^6-81\,B^3\,a^{18}\,b^3+1701\,A\,B^2\,a^{17}\,b^4-11907\,A^2\,B\,a^{16}\,b^5+\frac{\sqrt{x}\,\left(7\,A\,b-B\,a\right)\,\left(23147208\,A^2\,a^{17}\,b^6-6613488\,A\,B\,a^{18}\,b^5+472392\,B^2\,a^{19}\,b^4\right)}{5832\,{\left(-a\right)}^{13/6}\,b^{5/6}}\right)}{{\left(-a\right)}^{13/3}\,b^{5/3}}}\right)\,\left(7\,A\,b-B\,a\right)\,1{}\mathrm{i}}{9\,{\left(-a\right)}^{13/6}\,b^{5/6}}+\frac{\mathrm{atan}\left(\frac{\frac{{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(7\,A\,b-B\,a\right)}^2\,\left(81\,B^3\,a^{18}\,b^3-27783\,A^3\,a^{15}\,b^6-1701\,A\,B^2\,a^{17}\,b^4+11907\,A^2\,B\,a^{16}\,b^5+\frac{\sqrt{x}\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(7\,A\,b-B\,a\right)\,\left(23147208\,A^2\,a^{17}\,b^6-6613488\,A\,B\,a^{18}\,b^5+472392\,B^2\,a^{19}\,b^4\right)}{5832\,{\left(-a\right)}^{13/6}\,b^{5/6}}\right)\,1{}\mathrm{i}}{{\left(-a\right)}^{13/3}\,b^{5/3}}+\frac{{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(7\,A\,b-B\,a\right)}^2\,\left(27783\,A^3\,a^{15}\,b^6-81\,B^3\,a^{18}\,b^3+1701\,A\,B^2\,a^{17}\,b^4-11907\,A^2\,B\,a^{16}\,b^5+\frac{\sqrt{x}\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(7\,A\,b-B\,a\right)\,\left(23147208\,A^2\,a^{17}\,b^6-6613488\,A\,B\,a^{18}\,b^5+472392\,B^2\,a^{19}\,b^4\right)}{5832\,{\left(-a\right)}^{13/6}\,b^{5/6}}\right)\,1{}\mathrm{i}}{{\left(-a\right)}^{13/3}\,b^{5/3}}}{\frac{{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(7\,A\,b-B\,a\right)}^2\,\left(81\,B^3\,a^{18}\,b^3-27783\,A^3\,a^{15}\,b^6-1701\,A\,B^2\,a^{17}\,b^4+11907\,A^2\,B\,a^{16}\,b^5+\frac{\sqrt{x}\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(7\,A\,b-B\,a\right)\,\left(23147208\,A^2\,a^{17}\,b^6-6613488\,A\,B\,a^{18}\,b^5+472392\,B^2\,a^{19}\,b^4\right)}{5832\,{\left(-a\right)}^{13/6}\,b^{5/6}}\right)}{{\left(-a\right)}^{13/3}\,b^{5/3}}-\frac{{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(7\,A\,b-B\,a\right)}^2\,\left(27783\,A^3\,a^{15}\,b^6-81\,B^3\,a^{18}\,b^3+1701\,A\,B^2\,a^{17}\,b^4-11907\,A^2\,B\,a^{16}\,b^5+\frac{\sqrt{x}\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(7\,A\,b-B\,a\right)\,\left(23147208\,A^2\,a^{17}\,b^6-6613488\,A\,B\,a^{18}\,b^5+472392\,B^2\,a^{19}\,b^4\right)}{5832\,{\left(-a\right)}^{13/6}\,b^{5/6}}\right)}{{\left(-a\right)}^{13/3}\,b^{5/3}}}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(7\,A\,b-B\,a\right)\,1{}\mathrm{i}}{9\,{\left(-a\right)}^{13/6}\,b^{5/6}}+\frac{\mathrm{atan}\left(\frac{\frac{{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(7\,A\,b-B\,a\right)}^2\,\left(81\,B^3\,a^{18}\,b^3-27783\,A^3\,a^{15}\,b^6-1701\,A\,B^2\,a^{17}\,b^4+11907\,A^2\,B\,a^{16}\,b^5+\frac{\sqrt{x}\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(7\,A\,b-B\,a\right)\,\left(23147208\,A^2\,a^{17}\,b^6-6613488\,A\,B\,a^{18}\,b^5+472392\,B^2\,a^{19}\,b^4\right)}{5832\,{\left(-a\right)}^{13/6}\,b^{5/6}}\right)\,1{}\mathrm{i}}{{\left(-a\right)}^{13/3}\,b^{5/3}}+\frac{{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(7\,A\,b-B\,a\right)}^2\,\left(27783\,A^3\,a^{15}\,b^6-81\,B^3\,a^{18}\,b^3+1701\,A\,B^2\,a^{17}\,b^4-11907\,A^2\,B\,a^{16}\,b^5+\frac{\sqrt{x}\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(7\,A\,b-B\,a\right)\,\left(23147208\,A^2\,a^{17}\,b^6-6613488\,A\,B\,a^{18}\,b^5+472392\,B^2\,a^{19}\,b^4\right)}{5832\,{\left(-a\right)}^{13/6}\,b^{5/6}}\right)\,1{}\mathrm{i}}{{\left(-a\right)}^{13/3}\,b^{5/3}}}{\frac{{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(7\,A\,b-B\,a\right)}^2\,\left(81\,B^3\,a^{18}\,b^3-27783\,A^3\,a^{15}\,b^6-1701\,A\,B^2\,a^{17}\,b^4+11907\,A^2\,B\,a^{16}\,b^5+\frac{\sqrt{x}\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(7\,A\,b-B\,a\right)\,\left(23147208\,A^2\,a^{17}\,b^6-6613488\,A\,B\,a^{18}\,b^5+472392\,B^2\,a^{19}\,b^4\right)}{5832\,{\left(-a\right)}^{13/6}\,b^{5/6}}\right)}{{\left(-a\right)}^{13/3}\,b^{5/3}}-\frac{{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(7\,A\,b-B\,a\right)}^2\,\left(27783\,A^3\,a^{15}\,b^6-81\,B^3\,a^{18}\,b^3+1701\,A\,B^2\,a^{17}\,b^4-11907\,A^2\,B\,a^{16}\,b^5+\frac{\sqrt{x}\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(7\,A\,b-B\,a\right)\,\left(23147208\,A^2\,a^{17}\,b^6-6613488\,A\,B\,a^{18}\,b^5+472392\,B^2\,a^{19}\,b^4\right)}{5832\,{\left(-a\right)}^{13/6}\,b^{5/6}}\right)}{{\left(-a\right)}^{13/3}\,b^{5/3}}}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(7\,A\,b-B\,a\right)\,1{}\mathrm{i}}{9\,{\left(-a\right)}^{13/6}\,b^{5/6}}","Not used",1,"(atan((((7*A*b - B*a)^2*(81*B^3*a^18*b^3 - 27783*A^3*a^15*b^6 - 1701*A*B^2*a^17*b^4 + 11907*A^2*B*a^16*b^5 + (x^(1/2)*(7*A*b - B*a)*(23147208*A^2*a^17*b^6 + 472392*B^2*a^19*b^4 - 6613488*A*B*a^18*b^5))/(5832*(-a)^(13/6)*b^(5/6)))*1i)/((-a)^(13/3)*b^(5/3)) + ((7*A*b - B*a)^2*(27783*A^3*a^15*b^6 - 81*B^3*a^18*b^3 + 1701*A*B^2*a^17*b^4 - 11907*A^2*B*a^16*b^5 + (x^(1/2)*(7*A*b - B*a)*(23147208*A^2*a^17*b^6 + 472392*B^2*a^19*b^4 - 6613488*A*B*a^18*b^5))/(5832*(-a)^(13/6)*b^(5/6)))*1i)/((-a)^(13/3)*b^(5/3)))/(((7*A*b - B*a)^2*(81*B^3*a^18*b^3 - 27783*A^3*a^15*b^6 - 1701*A*B^2*a^17*b^4 + 11907*A^2*B*a^16*b^5 + (x^(1/2)*(7*A*b - B*a)*(23147208*A^2*a^17*b^6 + 472392*B^2*a^19*b^4 - 6613488*A*B*a^18*b^5))/(5832*(-a)^(13/6)*b^(5/6))))/((-a)^(13/3)*b^(5/3)) - ((7*A*b - B*a)^2*(27783*A^3*a^15*b^6 - 81*B^3*a^18*b^3 + 1701*A*B^2*a^17*b^4 - 11907*A^2*B*a^16*b^5 + (x^(1/2)*(7*A*b - B*a)*(23147208*A^2*a^17*b^6 + 472392*B^2*a^19*b^4 - 6613488*A*B*a^18*b^5))/(5832*(-a)^(13/6)*b^(5/6))))/((-a)^(13/3)*b^(5/3))))*(7*A*b - B*a)*1i)/(9*(-a)^(13/6)*b^(5/6)) - ((2*A)/a + (x^3*(7*A*b - B*a))/(3*a^2))/(a*x^(1/2) + b*x^(7/2)) + (atan(((((3^(1/2)*1i)/2 - 1/2)^2*(7*A*b - B*a)^2*(81*B^3*a^18*b^3 - 27783*A^3*a^15*b^6 - 1701*A*B^2*a^17*b^4 + 11907*A^2*B*a^16*b^5 + (x^(1/2)*((3^(1/2)*1i)/2 - 1/2)*(7*A*b - B*a)*(23147208*A^2*a^17*b^6 + 472392*B^2*a^19*b^4 - 6613488*A*B*a^18*b^5))/(5832*(-a)^(13/6)*b^(5/6)))*1i)/((-a)^(13/3)*b^(5/3)) + (((3^(1/2)*1i)/2 - 1/2)^2*(7*A*b - B*a)^2*(27783*A^3*a^15*b^6 - 81*B^3*a^18*b^3 + 1701*A*B^2*a^17*b^4 - 11907*A^2*B*a^16*b^5 + (x^(1/2)*((3^(1/2)*1i)/2 - 1/2)*(7*A*b - B*a)*(23147208*A^2*a^17*b^6 + 472392*B^2*a^19*b^4 - 6613488*A*B*a^18*b^5))/(5832*(-a)^(13/6)*b^(5/6)))*1i)/((-a)^(13/3)*b^(5/3)))/((((3^(1/2)*1i)/2 - 1/2)^2*(7*A*b - B*a)^2*(81*B^3*a^18*b^3 - 27783*A^3*a^15*b^6 - 1701*A*B^2*a^17*b^4 + 11907*A^2*B*a^16*b^5 + (x^(1/2)*((3^(1/2)*1i)/2 - 1/2)*(7*A*b - B*a)*(23147208*A^2*a^17*b^6 + 472392*B^2*a^19*b^4 - 6613488*A*B*a^18*b^5))/(5832*(-a)^(13/6)*b^(5/6))))/((-a)^(13/3)*b^(5/3)) - (((3^(1/2)*1i)/2 - 1/2)^2*(7*A*b - B*a)^2*(27783*A^3*a^15*b^6 - 81*B^3*a^18*b^3 + 1701*A*B^2*a^17*b^4 - 11907*A^2*B*a^16*b^5 + (x^(1/2)*((3^(1/2)*1i)/2 - 1/2)*(7*A*b - B*a)*(23147208*A^2*a^17*b^6 + 472392*B^2*a^19*b^4 - 6613488*A*B*a^18*b^5))/(5832*(-a)^(13/6)*b^(5/6))))/((-a)^(13/3)*b^(5/3))))*((3^(1/2)*1i)/2 - 1/2)*(7*A*b - B*a)*1i)/(9*(-a)^(13/6)*b^(5/6)) + (atan(((((3^(1/2)*1i)/2 + 1/2)^2*(7*A*b - B*a)^2*(81*B^3*a^18*b^3 - 27783*A^3*a^15*b^6 - 1701*A*B^2*a^17*b^4 + 11907*A^2*B*a^16*b^5 + (x^(1/2)*((3^(1/2)*1i)/2 + 1/2)*(7*A*b - B*a)*(23147208*A^2*a^17*b^6 + 472392*B^2*a^19*b^4 - 6613488*A*B*a^18*b^5))/(5832*(-a)^(13/6)*b^(5/6)))*1i)/((-a)^(13/3)*b^(5/3)) + (((3^(1/2)*1i)/2 + 1/2)^2*(7*A*b - B*a)^2*(27783*A^3*a^15*b^6 - 81*B^3*a^18*b^3 + 1701*A*B^2*a^17*b^4 - 11907*A^2*B*a^16*b^5 + (x^(1/2)*((3^(1/2)*1i)/2 + 1/2)*(7*A*b - B*a)*(23147208*A^2*a^17*b^6 + 472392*B^2*a^19*b^4 - 6613488*A*B*a^18*b^5))/(5832*(-a)^(13/6)*b^(5/6)))*1i)/((-a)^(13/3)*b^(5/3)))/((((3^(1/2)*1i)/2 + 1/2)^2*(7*A*b - B*a)^2*(81*B^3*a^18*b^3 - 27783*A^3*a^15*b^6 - 1701*A*B^2*a^17*b^4 + 11907*A^2*B*a^16*b^5 + (x^(1/2)*((3^(1/2)*1i)/2 + 1/2)*(7*A*b - B*a)*(23147208*A^2*a^17*b^6 + 472392*B^2*a^19*b^4 - 6613488*A*B*a^18*b^5))/(5832*(-a)^(13/6)*b^(5/6))))/((-a)^(13/3)*b^(5/3)) - (((3^(1/2)*1i)/2 + 1/2)^2*(7*A*b - B*a)^2*(27783*A^3*a^15*b^6 - 81*B^3*a^18*b^3 + 1701*A*B^2*a^17*b^4 - 11907*A^2*B*a^16*b^5 + (x^(1/2)*((3^(1/2)*1i)/2 + 1/2)*(7*A*b - B*a)*(23147208*A^2*a^17*b^6 + 472392*B^2*a^19*b^4 - 6613488*A*B*a^18*b^5))/(5832*(-a)^(13/6)*b^(5/6))))/((-a)^(13/3)*b^(5/3))))*((3^(1/2)*1i)/2 + 1/2)*(7*A*b - B*a)*1i)/(9*(-a)^(13/6)*b^(5/6))","B"
169,1,139,96,0.152075,"\text{Not used}","int((A + B*x^3)/(x^(5/2)*(a + b*x^3)^2),x)","-\frac{2\,A\,a^{3/2}\,\sqrt{b}-B\,a^2\,x^{3/2}\,\mathrm{atan}\left(\frac{\sqrt{b}\,x^{3/2}}{\sqrt{a}}\right)+3\,A\,b^2\,x^{9/2}\,\mathrm{atan}\left(\frac{\sqrt{b}\,x^{3/2}}{\sqrt{a}}\right)+3\,A\,\sqrt{a}\,b^{3/2}\,x^3-B\,a^{3/2}\,\sqrt{b}\,x^3+3\,A\,a\,b\,x^{3/2}\,\mathrm{atan}\left(\frac{\sqrt{b}\,x^{3/2}}{\sqrt{a}}\right)-B\,a\,b\,x^{9/2}\,\mathrm{atan}\left(\frac{\sqrt{b}\,x^{3/2}}{\sqrt{a}}\right)}{3\,a^{7/2}\,\sqrt{b}\,x^{3/2}+3\,a^{5/2}\,b^{3/2}\,x^{9/2}}","Not used",1,"-(2*A*a^(3/2)*b^(1/2) - B*a^2*x^(3/2)*atan((b^(1/2)*x^(3/2))/a^(1/2)) + 3*A*b^2*x^(9/2)*atan((b^(1/2)*x^(3/2))/a^(1/2)) + 3*A*a^(1/2)*b^(3/2)*x^3 - B*a^(3/2)*b^(1/2)*x^3 + 3*A*a*b*x^(3/2)*atan((b^(1/2)*x^(3/2))/a^(1/2)) - B*a*b*x^(9/2)*atan((b^(1/2)*x^(3/2))/a^(1/2)))/(3*a^(7/2)*b^(1/2)*x^(3/2) + 3*a^(5/2)*b^(3/2)*x^(9/2))","B"
170,1,2080,318,2.957255,"\text{Not used}","int((A + B*x^3)/(x^(7/2)*(a + b*x^3)^2),x)","-\frac{\frac{2\,A}{5\,a}+\frac{x^3\,\left(11\,A\,b-5\,B\,a\right)}{15\,a^2}}{a\,x^{5/2}+b\,x^{11/2}}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\sqrt{x}\,\left(21346578\,A^4\,a^{10}\,b^9-38811960\,A^3\,B\,a^{11}\,b^8+26462700\,A^2\,B^2\,a^{12}\,b^7-8019000\,A\,B^3\,a^{13}\,b^6+911250\,B^4\,a^{14}\,b^5\right)-\frac{\left(11\,A\,b-5\,B\,a\right)\,\left(34930764\,A^3\,a^{13}\,b^8-47632860\,A^2\,B\,a^{14}\,b^7+21651300\,A\,B^2\,a^{15}\,b^6-3280500\,B^3\,a^{16}\,b^5\right)}{18\,{\left(-a\right)}^{17/6}\,b^{1/6}}\right)\,\left(11\,A\,b-5\,B\,a\right)\,1{}\mathrm{i}}{18\,{\left(-a\right)}^{17/6}\,b^{1/6}}+\frac{\left(\sqrt{x}\,\left(21346578\,A^4\,a^{10}\,b^9-38811960\,A^3\,B\,a^{11}\,b^8+26462700\,A^2\,B^2\,a^{12}\,b^7-8019000\,A\,B^3\,a^{13}\,b^6+911250\,B^4\,a^{14}\,b^5\right)+\frac{\left(11\,A\,b-5\,B\,a\right)\,\left(34930764\,A^3\,a^{13}\,b^8-47632860\,A^2\,B\,a^{14}\,b^7+21651300\,A\,B^2\,a^{15}\,b^6-3280500\,B^3\,a^{16}\,b^5\right)}{18\,{\left(-a\right)}^{17/6}\,b^{1/6}}\right)\,\left(11\,A\,b-5\,B\,a\right)\,1{}\mathrm{i}}{18\,{\left(-a\right)}^{17/6}\,b^{1/6}}}{\frac{\left(\sqrt{x}\,\left(21346578\,A^4\,a^{10}\,b^9-38811960\,A^3\,B\,a^{11}\,b^8+26462700\,A^2\,B^2\,a^{12}\,b^7-8019000\,A\,B^3\,a^{13}\,b^6+911250\,B^4\,a^{14}\,b^5\right)-\frac{\left(11\,A\,b-5\,B\,a\right)\,\left(34930764\,A^3\,a^{13}\,b^8-47632860\,A^2\,B\,a^{14}\,b^7+21651300\,A\,B^2\,a^{15}\,b^6-3280500\,B^3\,a^{16}\,b^5\right)}{18\,{\left(-a\right)}^{17/6}\,b^{1/6}}\right)\,\left(11\,A\,b-5\,B\,a\right)}{18\,{\left(-a\right)}^{17/6}\,b^{1/6}}-\frac{\left(\sqrt{x}\,\left(21346578\,A^4\,a^{10}\,b^9-38811960\,A^3\,B\,a^{11}\,b^8+26462700\,A^2\,B^2\,a^{12}\,b^7-8019000\,A\,B^3\,a^{13}\,b^6+911250\,B^4\,a^{14}\,b^5\right)+\frac{\left(11\,A\,b-5\,B\,a\right)\,\left(34930764\,A^3\,a^{13}\,b^8-47632860\,A^2\,B\,a^{14}\,b^7+21651300\,A\,B^2\,a^{15}\,b^6-3280500\,B^3\,a^{16}\,b^5\right)}{18\,{\left(-a\right)}^{17/6}\,b^{1/6}}\right)\,\left(11\,A\,b-5\,B\,a\right)}{18\,{\left(-a\right)}^{17/6}\,b^{1/6}}}\right)\,\left(11\,A\,b-5\,B\,a\right)\,1{}\mathrm{i}}{9\,{\left(-a\right)}^{17/6}\,b^{1/6}}-\frac{\mathrm{atan}\left(\frac{\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\sqrt{x}\,\left(21346578\,A^4\,a^{10}\,b^9-38811960\,A^3\,B\,a^{11}\,b^8+26462700\,A^2\,B^2\,a^{12}\,b^7-8019000\,A\,B^3\,a^{13}\,b^6+911250\,B^4\,a^{14}\,b^5\right)-\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(11\,A\,b-5\,B\,a\right)\,\left(34930764\,A^3\,a^{13}\,b^8-47632860\,A^2\,B\,a^{14}\,b^7+21651300\,A\,B^2\,a^{15}\,b^6-3280500\,B^3\,a^{16}\,b^5\right)}{18\,{\left(-a\right)}^{17/6}\,b^{1/6}}\right)\,\left(11\,A\,b-5\,B\,a\right)\,1{}\mathrm{i}}{18\,{\left(-a\right)}^{17/6}\,b^{1/6}}+\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\sqrt{x}\,\left(21346578\,A^4\,a^{10}\,b^9-38811960\,A^3\,B\,a^{11}\,b^8+26462700\,A^2\,B^2\,a^{12}\,b^7-8019000\,A\,B^3\,a^{13}\,b^6+911250\,B^4\,a^{14}\,b^5\right)+\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(11\,A\,b-5\,B\,a\right)\,\left(34930764\,A^3\,a^{13}\,b^8-47632860\,A^2\,B\,a^{14}\,b^7+21651300\,A\,B^2\,a^{15}\,b^6-3280500\,B^3\,a^{16}\,b^5\right)}{18\,{\left(-a\right)}^{17/6}\,b^{1/6}}\right)\,\left(11\,A\,b-5\,B\,a\right)\,1{}\mathrm{i}}{18\,{\left(-a\right)}^{17/6}\,b^{1/6}}}{\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\sqrt{x}\,\left(21346578\,A^4\,a^{10}\,b^9-38811960\,A^3\,B\,a^{11}\,b^8+26462700\,A^2\,B^2\,a^{12}\,b^7-8019000\,A\,B^3\,a^{13}\,b^6+911250\,B^4\,a^{14}\,b^5\right)-\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(11\,A\,b-5\,B\,a\right)\,\left(34930764\,A^3\,a^{13}\,b^8-47632860\,A^2\,B\,a^{14}\,b^7+21651300\,A\,B^2\,a^{15}\,b^6-3280500\,B^3\,a^{16}\,b^5\right)}{18\,{\left(-a\right)}^{17/6}\,b^{1/6}}\right)\,\left(11\,A\,b-5\,B\,a\right)}{18\,{\left(-a\right)}^{17/6}\,b^{1/6}}-\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\sqrt{x}\,\left(21346578\,A^4\,a^{10}\,b^9-38811960\,A^3\,B\,a^{11}\,b^8+26462700\,A^2\,B^2\,a^{12}\,b^7-8019000\,A\,B^3\,a^{13}\,b^6+911250\,B^4\,a^{14}\,b^5\right)+\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(11\,A\,b-5\,B\,a\right)\,\left(34930764\,A^3\,a^{13}\,b^8-47632860\,A^2\,B\,a^{14}\,b^7+21651300\,A\,B^2\,a^{15}\,b^6-3280500\,B^3\,a^{16}\,b^5\right)}{18\,{\left(-a\right)}^{17/6}\,b^{1/6}}\right)\,\left(11\,A\,b-5\,B\,a\right)}{18\,{\left(-a\right)}^{17/6}\,b^{1/6}}}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(11\,A\,b-5\,B\,a\right)\,1{}\mathrm{i}}{9\,{\left(-a\right)}^{17/6}\,b^{1/6}}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\sqrt{x}\,\left(21346578\,A^4\,a^{10}\,b^9-38811960\,A^3\,B\,a^{11}\,b^8+26462700\,A^2\,B^2\,a^{12}\,b^7-8019000\,A\,B^3\,a^{13}\,b^6+911250\,B^4\,a^{14}\,b^5\right)-\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(11\,A\,b-5\,B\,a\right)\,\left(34930764\,A^3\,a^{13}\,b^8-47632860\,A^2\,B\,a^{14}\,b^7+21651300\,A\,B^2\,a^{15}\,b^6-3280500\,B^3\,a^{16}\,b^5\right)}{18\,{\left(-a\right)}^{17/6}\,b^{1/6}}\right)\,\left(11\,A\,b-5\,B\,a\right)\,1{}\mathrm{i}}{18\,{\left(-a\right)}^{17/6}\,b^{1/6}}+\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\sqrt{x}\,\left(21346578\,A^4\,a^{10}\,b^9-38811960\,A^3\,B\,a^{11}\,b^8+26462700\,A^2\,B^2\,a^{12}\,b^7-8019000\,A\,B^3\,a^{13}\,b^6+911250\,B^4\,a^{14}\,b^5\right)+\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(11\,A\,b-5\,B\,a\right)\,\left(34930764\,A^3\,a^{13}\,b^8-47632860\,A^2\,B\,a^{14}\,b^7+21651300\,A\,B^2\,a^{15}\,b^6-3280500\,B^3\,a^{16}\,b^5\right)}{18\,{\left(-a\right)}^{17/6}\,b^{1/6}}\right)\,\left(11\,A\,b-5\,B\,a\right)\,1{}\mathrm{i}}{18\,{\left(-a\right)}^{17/6}\,b^{1/6}}}{\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\sqrt{x}\,\left(21346578\,A^4\,a^{10}\,b^9-38811960\,A^3\,B\,a^{11}\,b^8+26462700\,A^2\,B^2\,a^{12}\,b^7-8019000\,A\,B^3\,a^{13}\,b^6+911250\,B^4\,a^{14}\,b^5\right)-\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(11\,A\,b-5\,B\,a\right)\,\left(34930764\,A^3\,a^{13}\,b^8-47632860\,A^2\,B\,a^{14}\,b^7+21651300\,A\,B^2\,a^{15}\,b^6-3280500\,B^3\,a^{16}\,b^5\right)}{18\,{\left(-a\right)}^{17/6}\,b^{1/6}}\right)\,\left(11\,A\,b-5\,B\,a\right)}{18\,{\left(-a\right)}^{17/6}\,b^{1/6}}-\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\sqrt{x}\,\left(21346578\,A^4\,a^{10}\,b^9-38811960\,A^3\,B\,a^{11}\,b^8+26462700\,A^2\,B^2\,a^{12}\,b^7-8019000\,A\,B^3\,a^{13}\,b^6+911250\,B^4\,a^{14}\,b^5\right)+\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(11\,A\,b-5\,B\,a\right)\,\left(34930764\,A^3\,a^{13}\,b^8-47632860\,A^2\,B\,a^{14}\,b^7+21651300\,A\,B^2\,a^{15}\,b^6-3280500\,B^3\,a^{16}\,b^5\right)}{18\,{\left(-a\right)}^{17/6}\,b^{1/6}}\right)\,\left(11\,A\,b-5\,B\,a\right)}{18\,{\left(-a\right)}^{17/6}\,b^{1/6}}}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(11\,A\,b-5\,B\,a\right)\,1{}\mathrm{i}}{9\,{\left(-a\right)}^{17/6}\,b^{1/6}}","Not used",1,"- ((2*A)/(5*a) + (x^3*(11*A*b - 5*B*a))/(15*a^2))/(a*x^(5/2) + b*x^(11/2)) - (atan((((x^(1/2)*(21346578*A^4*a^10*b^9 + 911250*B^4*a^14*b^5 + 26462700*A^2*B^2*a^12*b^7 - 8019000*A*B^3*a^13*b^6 - 38811960*A^3*B*a^11*b^8) - ((11*A*b - 5*B*a)*(34930764*A^3*a^13*b^8 - 3280500*B^3*a^16*b^5 + 21651300*A*B^2*a^15*b^6 - 47632860*A^2*B*a^14*b^7))/(18*(-a)^(17/6)*b^(1/6)))*(11*A*b - 5*B*a)*1i)/(18*(-a)^(17/6)*b^(1/6)) + ((x^(1/2)*(21346578*A^4*a^10*b^9 + 911250*B^4*a^14*b^5 + 26462700*A^2*B^2*a^12*b^7 - 8019000*A*B^3*a^13*b^6 - 38811960*A^3*B*a^11*b^8) + ((11*A*b - 5*B*a)*(34930764*A^3*a^13*b^8 - 3280500*B^3*a^16*b^5 + 21651300*A*B^2*a^15*b^6 - 47632860*A^2*B*a^14*b^7))/(18*(-a)^(17/6)*b^(1/6)))*(11*A*b - 5*B*a)*1i)/(18*(-a)^(17/6)*b^(1/6)))/(((x^(1/2)*(21346578*A^4*a^10*b^9 + 911250*B^4*a^14*b^5 + 26462700*A^2*B^2*a^12*b^7 - 8019000*A*B^3*a^13*b^6 - 38811960*A^3*B*a^11*b^8) - ((11*A*b - 5*B*a)*(34930764*A^3*a^13*b^8 - 3280500*B^3*a^16*b^5 + 21651300*A*B^2*a^15*b^6 - 47632860*A^2*B*a^14*b^7))/(18*(-a)^(17/6)*b^(1/6)))*(11*A*b - 5*B*a))/(18*(-a)^(17/6)*b^(1/6)) - ((x^(1/2)*(21346578*A^4*a^10*b^9 + 911250*B^4*a^14*b^5 + 26462700*A^2*B^2*a^12*b^7 - 8019000*A*B^3*a^13*b^6 - 38811960*A^3*B*a^11*b^8) + ((11*A*b - 5*B*a)*(34930764*A^3*a^13*b^8 - 3280500*B^3*a^16*b^5 + 21651300*A*B^2*a^15*b^6 - 47632860*A^2*B*a^14*b^7))/(18*(-a)^(17/6)*b^(1/6)))*(11*A*b - 5*B*a))/(18*(-a)^(17/6)*b^(1/6))))*(11*A*b - 5*B*a)*1i)/(9*(-a)^(17/6)*b^(1/6)) - (atan(((((3^(1/2)*1i)/2 - 1/2)*(x^(1/2)*(21346578*A^4*a^10*b^9 + 911250*B^4*a^14*b^5 + 26462700*A^2*B^2*a^12*b^7 - 8019000*A*B^3*a^13*b^6 - 38811960*A^3*B*a^11*b^8) - (((3^(1/2)*1i)/2 - 1/2)*(11*A*b - 5*B*a)*(34930764*A^3*a^13*b^8 - 3280500*B^3*a^16*b^5 + 21651300*A*B^2*a^15*b^6 - 47632860*A^2*B*a^14*b^7))/(18*(-a)^(17/6)*b^(1/6)))*(11*A*b - 5*B*a)*1i)/(18*(-a)^(17/6)*b^(1/6)) + (((3^(1/2)*1i)/2 - 1/2)*(x^(1/2)*(21346578*A^4*a^10*b^9 + 911250*B^4*a^14*b^5 + 26462700*A^2*B^2*a^12*b^7 - 8019000*A*B^3*a^13*b^6 - 38811960*A^3*B*a^11*b^8) + (((3^(1/2)*1i)/2 - 1/2)*(11*A*b - 5*B*a)*(34930764*A^3*a^13*b^8 - 3280500*B^3*a^16*b^5 + 21651300*A*B^2*a^15*b^6 - 47632860*A^2*B*a^14*b^7))/(18*(-a)^(17/6)*b^(1/6)))*(11*A*b - 5*B*a)*1i)/(18*(-a)^(17/6)*b^(1/6)))/((((3^(1/2)*1i)/2 - 1/2)*(x^(1/2)*(21346578*A^4*a^10*b^9 + 911250*B^4*a^14*b^5 + 26462700*A^2*B^2*a^12*b^7 - 8019000*A*B^3*a^13*b^6 - 38811960*A^3*B*a^11*b^8) - (((3^(1/2)*1i)/2 - 1/2)*(11*A*b - 5*B*a)*(34930764*A^3*a^13*b^8 - 3280500*B^3*a^16*b^5 + 21651300*A*B^2*a^15*b^6 - 47632860*A^2*B*a^14*b^7))/(18*(-a)^(17/6)*b^(1/6)))*(11*A*b - 5*B*a))/(18*(-a)^(17/6)*b^(1/6)) - (((3^(1/2)*1i)/2 - 1/2)*(x^(1/2)*(21346578*A^4*a^10*b^9 + 911250*B^4*a^14*b^5 + 26462700*A^2*B^2*a^12*b^7 - 8019000*A*B^3*a^13*b^6 - 38811960*A^3*B*a^11*b^8) + (((3^(1/2)*1i)/2 - 1/2)*(11*A*b - 5*B*a)*(34930764*A^3*a^13*b^8 - 3280500*B^3*a^16*b^5 + 21651300*A*B^2*a^15*b^6 - 47632860*A^2*B*a^14*b^7))/(18*(-a)^(17/6)*b^(1/6)))*(11*A*b - 5*B*a))/(18*(-a)^(17/6)*b^(1/6))))*((3^(1/2)*1i)/2 - 1/2)*(11*A*b - 5*B*a)*1i)/(9*(-a)^(17/6)*b^(1/6)) - (atan(((((3^(1/2)*1i)/2 + 1/2)*(x^(1/2)*(21346578*A^4*a^10*b^9 + 911250*B^4*a^14*b^5 + 26462700*A^2*B^2*a^12*b^7 - 8019000*A*B^3*a^13*b^6 - 38811960*A^3*B*a^11*b^8) - (((3^(1/2)*1i)/2 + 1/2)*(11*A*b - 5*B*a)*(34930764*A^3*a^13*b^8 - 3280500*B^3*a^16*b^5 + 21651300*A*B^2*a^15*b^6 - 47632860*A^2*B*a^14*b^7))/(18*(-a)^(17/6)*b^(1/6)))*(11*A*b - 5*B*a)*1i)/(18*(-a)^(17/6)*b^(1/6)) + (((3^(1/2)*1i)/2 + 1/2)*(x^(1/2)*(21346578*A^4*a^10*b^9 + 911250*B^4*a^14*b^5 + 26462700*A^2*B^2*a^12*b^7 - 8019000*A*B^3*a^13*b^6 - 38811960*A^3*B*a^11*b^8) + (((3^(1/2)*1i)/2 + 1/2)*(11*A*b - 5*B*a)*(34930764*A^3*a^13*b^8 - 3280500*B^3*a^16*b^5 + 21651300*A*B^2*a^15*b^6 - 47632860*A^2*B*a^14*b^7))/(18*(-a)^(17/6)*b^(1/6)))*(11*A*b - 5*B*a)*1i)/(18*(-a)^(17/6)*b^(1/6)))/((((3^(1/2)*1i)/2 + 1/2)*(x^(1/2)*(21346578*A^4*a^10*b^9 + 911250*B^4*a^14*b^5 + 26462700*A^2*B^2*a^12*b^7 - 8019000*A*B^3*a^13*b^6 - 38811960*A^3*B*a^11*b^8) - (((3^(1/2)*1i)/2 + 1/2)*(11*A*b - 5*B*a)*(34930764*A^3*a^13*b^8 - 3280500*B^3*a^16*b^5 + 21651300*A*B^2*a^15*b^6 - 47632860*A^2*B*a^14*b^7))/(18*(-a)^(17/6)*b^(1/6)))*(11*A*b - 5*B*a))/(18*(-a)^(17/6)*b^(1/6)) - (((3^(1/2)*1i)/2 + 1/2)*(x^(1/2)*(21346578*A^4*a^10*b^9 + 911250*B^4*a^14*b^5 + 26462700*A^2*B^2*a^12*b^7 - 8019000*A*B^3*a^13*b^6 - 38811960*A^3*B*a^11*b^8) + (((3^(1/2)*1i)/2 + 1/2)*(11*A*b - 5*B*a)*(34930764*A^3*a^13*b^8 - 3280500*B^3*a^16*b^5 + 21651300*A*B^2*a^15*b^6 - 47632860*A^2*B*a^14*b^7))/(18*(-a)^(17/6)*b^(1/6)))*(11*A*b - 5*B*a))/(18*(-a)^(17/6)*b^(1/6))))*((3^(1/2)*1i)/2 + 1/2)*(11*A*b - 5*B*a)*1i)/(9*(-a)^(17/6)*b^(1/6))","B"
171,1,133,104,2.760640,"\text{Not used}","int((x^(7/2)*(A + B*x^3))/(a + b*x^3)^3,x)","\frac{\mathrm{atan}\left(\frac{9\,b^{3/2}\,x^{3/2}\,\left(A^2\,b^2+6\,A\,B\,a\,b+9\,B^2\,a^2\right)}{\sqrt{a}\,\left(9\,A\,b^2+27\,B\,a\,b\right)\,\left(A\,b+3\,B\,a\right)}\right)\,\left(A\,b+3\,B\,a\right)}{12\,a^{3/2}\,b^{5/2}}-\frac{\frac{x^{3/2}\,\left(A\,b+3\,B\,a\right)}{12\,b^2}-\frac{x^{9/2}\,\left(A\,b-5\,B\,a\right)}{12\,a\,b}}{a^2+2\,a\,b\,x^3+b^2\,x^6}","Not used",1,"(atan((9*b^(3/2)*x^(3/2)*(A^2*b^2 + 9*B^2*a^2 + 6*A*B*a*b))/(a^(1/2)*(9*A*b^2 + 27*B*a*b)*(A*b + 3*B*a)))*(A*b + 3*B*a))/(12*a^(3/2)*b^(5/2)) - ((x^(3/2)*(A*b + 3*B*a))/(12*b^2) - (x^(9/2)*(A*b - 5*B*a))/(12*a*b))/(a^2 + b^2*x^6 + 2*a*b*x^3)","B"
172,1,1944,327,2.984222,"\text{Not used}","int((x^(5/2)*(A + B*x^3))/(a + b*x^3)^3,x)","-\frac{\frac{\sqrt{x}\,\left(5\,A\,b+7\,B\,a\right)}{36\,b^2}-\frac{x^{7/2}\,\left(A\,b-13\,B\,a\right)}{36\,a\,b}}{a^2+2\,a\,b\,x^3+b^2\,x^6}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\left(5\,A\,b+7\,B\,a\right)\,\left(125\,A^3\,b^3+525\,A^2\,B\,a\,b^2+735\,A\,B^2\,a^2\,b+343\,B^3\,a^3\right)}{279936\,{\left(-a\right)}^{23/6}\,b^{19/6}}-\frac{\sqrt{x}\,\left(625\,A^4\,b^4+3500\,A^3\,B\,a\,b^3+7350\,A^2\,B^2\,a^2\,b^2+6860\,A\,B^3\,a^3\,b+2401\,B^4\,a^4\right)}{279936\,a^4\,b^3}\right)\,\left(5\,A\,b+7\,B\,a\right)\,1{}\mathrm{i}}{216\,{\left(-a\right)}^{11/6}\,b^{13/6}}-\frac{\left(\frac{\left(5\,A\,b+7\,B\,a\right)\,\left(125\,A^3\,b^3+525\,A^2\,B\,a\,b^2+735\,A\,B^2\,a^2\,b+343\,B^3\,a^3\right)}{279936\,{\left(-a\right)}^{23/6}\,b^{19/6}}+\frac{\sqrt{x}\,\left(625\,A^4\,b^4+3500\,A^3\,B\,a\,b^3+7350\,A^2\,B^2\,a^2\,b^2+6860\,A\,B^3\,a^3\,b+2401\,B^4\,a^4\right)}{279936\,a^4\,b^3}\right)\,\left(5\,A\,b+7\,B\,a\right)\,1{}\mathrm{i}}{216\,{\left(-a\right)}^{11/6}\,b^{13/6}}}{\frac{\left(\frac{\left(5\,A\,b+7\,B\,a\right)\,\left(125\,A^3\,b^3+525\,A^2\,B\,a\,b^2+735\,A\,B^2\,a^2\,b+343\,B^3\,a^3\right)}{279936\,{\left(-a\right)}^{23/6}\,b^{19/6}}-\frac{\sqrt{x}\,\left(625\,A^4\,b^4+3500\,A^3\,B\,a\,b^3+7350\,A^2\,B^2\,a^2\,b^2+6860\,A\,B^3\,a^3\,b+2401\,B^4\,a^4\right)}{279936\,a^4\,b^3}\right)\,\left(5\,A\,b+7\,B\,a\right)}{216\,{\left(-a\right)}^{11/6}\,b^{13/6}}+\frac{\left(\frac{\left(5\,A\,b+7\,B\,a\right)\,\left(125\,A^3\,b^3+525\,A^2\,B\,a\,b^2+735\,A\,B^2\,a^2\,b+343\,B^3\,a^3\right)}{279936\,{\left(-a\right)}^{23/6}\,b^{19/6}}+\frac{\sqrt{x}\,\left(625\,A^4\,b^4+3500\,A^3\,B\,a\,b^3+7350\,A^2\,B^2\,a^2\,b^2+6860\,A\,B^3\,a^3\,b+2401\,B^4\,a^4\right)}{279936\,a^4\,b^3}\right)\,\left(5\,A\,b+7\,B\,a\right)}{216\,{\left(-a\right)}^{11/6}\,b^{13/6}}}\right)\,\left(5\,A\,b+7\,B\,a\right)\,1{}\mathrm{i}}{108\,{\left(-a\right)}^{11/6}\,b^{13/6}}+\frac{\mathrm{atan}\left(\frac{\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{\sqrt{x}\,\left(625\,A^4\,b^4+3500\,A^3\,B\,a\,b^3+7350\,A^2\,B^2\,a^2\,b^2+6860\,A\,B^3\,a^3\,b+2401\,B^4\,a^4\right)}{279936\,a^4\,b^3}-\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(5\,A\,b+7\,B\,a\right)\,\left(125\,A^3\,b^3+525\,A^2\,B\,a\,b^2+735\,A\,B^2\,a^2\,b+343\,B^3\,a^3\right)}{279936\,{\left(-a\right)}^{23/6}\,b^{19/6}}\right)\,\left(5\,A\,b+7\,B\,a\right)\,1{}\mathrm{i}}{216\,{\left(-a\right)}^{11/6}\,b^{13/6}}+\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{\sqrt{x}\,\left(625\,A^4\,b^4+3500\,A^3\,B\,a\,b^3+7350\,A^2\,B^2\,a^2\,b^2+6860\,A\,B^3\,a^3\,b+2401\,B^4\,a^4\right)}{279936\,a^4\,b^3}+\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(5\,A\,b+7\,B\,a\right)\,\left(125\,A^3\,b^3+525\,A^2\,B\,a\,b^2+735\,A\,B^2\,a^2\,b+343\,B^3\,a^3\right)}{279936\,{\left(-a\right)}^{23/6}\,b^{19/6}}\right)\,\left(5\,A\,b+7\,B\,a\right)\,1{}\mathrm{i}}{216\,{\left(-a\right)}^{11/6}\,b^{13/6}}}{\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{\sqrt{x}\,\left(625\,A^4\,b^4+3500\,A^3\,B\,a\,b^3+7350\,A^2\,B^2\,a^2\,b^2+6860\,A\,B^3\,a^3\,b+2401\,B^4\,a^4\right)}{279936\,a^4\,b^3}-\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(5\,A\,b+7\,B\,a\right)\,\left(125\,A^3\,b^3+525\,A^2\,B\,a\,b^2+735\,A\,B^2\,a^2\,b+343\,B^3\,a^3\right)}{279936\,{\left(-a\right)}^{23/6}\,b^{19/6}}\right)\,\left(5\,A\,b+7\,B\,a\right)}{216\,{\left(-a\right)}^{11/6}\,b^{13/6}}-\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{\sqrt{x}\,\left(625\,A^4\,b^4+3500\,A^3\,B\,a\,b^3+7350\,A^2\,B^2\,a^2\,b^2+6860\,A\,B^3\,a^3\,b+2401\,B^4\,a^4\right)}{279936\,a^4\,b^3}+\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(5\,A\,b+7\,B\,a\right)\,\left(125\,A^3\,b^3+525\,A^2\,B\,a\,b^2+735\,A\,B^2\,a^2\,b+343\,B^3\,a^3\right)}{279936\,{\left(-a\right)}^{23/6}\,b^{19/6}}\right)\,\left(5\,A\,b+7\,B\,a\right)}{216\,{\left(-a\right)}^{11/6}\,b^{13/6}}}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(5\,A\,b+7\,B\,a\right)\,1{}\mathrm{i}}{108\,{\left(-a\right)}^{11/6}\,b^{13/6}}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{\sqrt{x}\,\left(625\,A^4\,b^4+3500\,A^3\,B\,a\,b^3+7350\,A^2\,B^2\,a^2\,b^2+6860\,A\,B^3\,a^3\,b+2401\,B^4\,a^4\right)}{279936\,a^4\,b^3}-\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(5\,A\,b+7\,B\,a\right)\,\left(125\,A^3\,b^3+525\,A^2\,B\,a\,b^2+735\,A\,B^2\,a^2\,b+343\,B^3\,a^3\right)}{279936\,{\left(-a\right)}^{23/6}\,b^{19/6}}\right)\,\left(5\,A\,b+7\,B\,a\right)\,1{}\mathrm{i}}{216\,{\left(-a\right)}^{11/6}\,b^{13/6}}+\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{\sqrt{x}\,\left(625\,A^4\,b^4+3500\,A^3\,B\,a\,b^3+7350\,A^2\,B^2\,a^2\,b^2+6860\,A\,B^3\,a^3\,b+2401\,B^4\,a^4\right)}{279936\,a^4\,b^3}+\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(5\,A\,b+7\,B\,a\right)\,\left(125\,A^3\,b^3+525\,A^2\,B\,a\,b^2+735\,A\,B^2\,a^2\,b+343\,B^3\,a^3\right)}{279936\,{\left(-a\right)}^{23/6}\,b^{19/6}}\right)\,\left(5\,A\,b+7\,B\,a\right)\,1{}\mathrm{i}}{216\,{\left(-a\right)}^{11/6}\,b^{13/6}}}{\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{\sqrt{x}\,\left(625\,A^4\,b^4+3500\,A^3\,B\,a\,b^3+7350\,A^2\,B^2\,a^2\,b^2+6860\,A\,B^3\,a^3\,b+2401\,B^4\,a^4\right)}{279936\,a^4\,b^3}-\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(5\,A\,b+7\,B\,a\right)\,\left(125\,A^3\,b^3+525\,A^2\,B\,a\,b^2+735\,A\,B^2\,a^2\,b+343\,B^3\,a^3\right)}{279936\,{\left(-a\right)}^{23/6}\,b^{19/6}}\right)\,\left(5\,A\,b+7\,B\,a\right)}{216\,{\left(-a\right)}^{11/6}\,b^{13/6}}-\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{\sqrt{x}\,\left(625\,A^4\,b^4+3500\,A^3\,B\,a\,b^3+7350\,A^2\,B^2\,a^2\,b^2+6860\,A\,B^3\,a^3\,b+2401\,B^4\,a^4\right)}{279936\,a^4\,b^3}+\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(5\,A\,b+7\,B\,a\right)\,\left(125\,A^3\,b^3+525\,A^2\,B\,a\,b^2+735\,A\,B^2\,a^2\,b+343\,B^3\,a^3\right)}{279936\,{\left(-a\right)}^{23/6}\,b^{19/6}}\right)\,\left(5\,A\,b+7\,B\,a\right)}{216\,{\left(-a\right)}^{11/6}\,b^{13/6}}}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(5\,A\,b+7\,B\,a\right)\,1{}\mathrm{i}}{108\,{\left(-a\right)}^{11/6}\,b^{13/6}}","Not used",1,"(atan((((((5*A*b + 7*B*a)*(125*A^3*b^3 + 343*B^3*a^3 + 735*A*B^2*a^2*b + 525*A^2*B*a*b^2))/(279936*(-a)^(23/6)*b^(19/6)) - (x^(1/2)*(625*A^4*b^4 + 2401*B^4*a^4 + 7350*A^2*B^2*a^2*b^2 + 6860*A*B^3*a^3*b + 3500*A^3*B*a*b^3))/(279936*a^4*b^3))*(5*A*b + 7*B*a)*1i)/(216*(-a)^(11/6)*b^(13/6)) - ((((5*A*b + 7*B*a)*(125*A^3*b^3 + 343*B^3*a^3 + 735*A*B^2*a^2*b + 525*A^2*B*a*b^2))/(279936*(-a)^(23/6)*b^(19/6)) + (x^(1/2)*(625*A^4*b^4 + 2401*B^4*a^4 + 7350*A^2*B^2*a^2*b^2 + 6860*A*B^3*a^3*b + 3500*A^3*B*a*b^3))/(279936*a^4*b^3))*(5*A*b + 7*B*a)*1i)/(216*(-a)^(11/6)*b^(13/6)))/(((((5*A*b + 7*B*a)*(125*A^3*b^3 + 343*B^3*a^3 + 735*A*B^2*a^2*b + 525*A^2*B*a*b^2))/(279936*(-a)^(23/6)*b^(19/6)) - (x^(1/2)*(625*A^4*b^4 + 2401*B^4*a^4 + 7350*A^2*B^2*a^2*b^2 + 6860*A*B^3*a^3*b + 3500*A^3*B*a*b^3))/(279936*a^4*b^3))*(5*A*b + 7*B*a))/(216*(-a)^(11/6)*b^(13/6)) + ((((5*A*b + 7*B*a)*(125*A^3*b^3 + 343*B^3*a^3 + 735*A*B^2*a^2*b + 525*A^2*B*a*b^2))/(279936*(-a)^(23/6)*b^(19/6)) + (x^(1/2)*(625*A^4*b^4 + 2401*B^4*a^4 + 7350*A^2*B^2*a^2*b^2 + 6860*A*B^3*a^3*b + 3500*A^3*B*a*b^3))/(279936*a^4*b^3))*(5*A*b + 7*B*a))/(216*(-a)^(11/6)*b^(13/6))))*(5*A*b + 7*B*a)*1i)/(108*(-a)^(11/6)*b^(13/6)) - ((x^(1/2)*(5*A*b + 7*B*a))/(36*b^2) - (x^(7/2)*(A*b - 13*B*a))/(36*a*b))/(a^2 + b^2*x^6 + 2*a*b*x^3) + (atan(((((3^(1/2)*1i)/2 - 1/2)*((x^(1/2)*(625*A^4*b^4 + 2401*B^4*a^4 + 7350*A^2*B^2*a^2*b^2 + 6860*A*B^3*a^3*b + 3500*A^3*B*a*b^3))/(279936*a^4*b^3) - (((3^(1/2)*1i)/2 - 1/2)*(5*A*b + 7*B*a)*(125*A^3*b^3 + 343*B^3*a^3 + 735*A*B^2*a^2*b + 525*A^2*B*a*b^2))/(279936*(-a)^(23/6)*b^(19/6)))*(5*A*b + 7*B*a)*1i)/(216*(-a)^(11/6)*b^(13/6)) + (((3^(1/2)*1i)/2 - 1/2)*((x^(1/2)*(625*A^4*b^4 + 2401*B^4*a^4 + 7350*A^2*B^2*a^2*b^2 + 6860*A*B^3*a^3*b + 3500*A^3*B*a*b^3))/(279936*a^4*b^3) + (((3^(1/2)*1i)/2 - 1/2)*(5*A*b + 7*B*a)*(125*A^3*b^3 + 343*B^3*a^3 + 735*A*B^2*a^2*b + 525*A^2*B*a*b^2))/(279936*(-a)^(23/6)*b^(19/6)))*(5*A*b + 7*B*a)*1i)/(216*(-a)^(11/6)*b^(13/6)))/((((3^(1/2)*1i)/2 - 1/2)*((x^(1/2)*(625*A^4*b^4 + 2401*B^4*a^4 + 7350*A^2*B^2*a^2*b^2 + 6860*A*B^3*a^3*b + 3500*A^3*B*a*b^3))/(279936*a^4*b^3) - (((3^(1/2)*1i)/2 - 1/2)*(5*A*b + 7*B*a)*(125*A^3*b^3 + 343*B^3*a^3 + 735*A*B^2*a^2*b + 525*A^2*B*a*b^2))/(279936*(-a)^(23/6)*b^(19/6)))*(5*A*b + 7*B*a))/(216*(-a)^(11/6)*b^(13/6)) - (((3^(1/2)*1i)/2 - 1/2)*((x^(1/2)*(625*A^4*b^4 + 2401*B^4*a^4 + 7350*A^2*B^2*a^2*b^2 + 6860*A*B^3*a^3*b + 3500*A^3*B*a*b^3))/(279936*a^4*b^3) + (((3^(1/2)*1i)/2 - 1/2)*(5*A*b + 7*B*a)*(125*A^3*b^3 + 343*B^3*a^3 + 735*A*B^2*a^2*b + 525*A^2*B*a*b^2))/(279936*(-a)^(23/6)*b^(19/6)))*(5*A*b + 7*B*a))/(216*(-a)^(11/6)*b^(13/6))))*((3^(1/2)*1i)/2 - 1/2)*(5*A*b + 7*B*a)*1i)/(108*(-a)^(11/6)*b^(13/6)) + (atan(((((3^(1/2)*1i)/2 + 1/2)*((x^(1/2)*(625*A^4*b^4 + 2401*B^4*a^4 + 7350*A^2*B^2*a^2*b^2 + 6860*A*B^3*a^3*b + 3500*A^3*B*a*b^3))/(279936*a^4*b^3) - (((3^(1/2)*1i)/2 + 1/2)*(5*A*b + 7*B*a)*(125*A^3*b^3 + 343*B^3*a^3 + 735*A*B^2*a^2*b + 525*A^2*B*a*b^2))/(279936*(-a)^(23/6)*b^(19/6)))*(5*A*b + 7*B*a)*1i)/(216*(-a)^(11/6)*b^(13/6)) + (((3^(1/2)*1i)/2 + 1/2)*((x^(1/2)*(625*A^4*b^4 + 2401*B^4*a^4 + 7350*A^2*B^2*a^2*b^2 + 6860*A*B^3*a^3*b + 3500*A^3*B*a*b^3))/(279936*a^4*b^3) + (((3^(1/2)*1i)/2 + 1/2)*(5*A*b + 7*B*a)*(125*A^3*b^3 + 343*B^3*a^3 + 735*A*B^2*a^2*b + 525*A^2*B*a*b^2))/(279936*(-a)^(23/6)*b^(19/6)))*(5*A*b + 7*B*a)*1i)/(216*(-a)^(11/6)*b^(13/6)))/((((3^(1/2)*1i)/2 + 1/2)*((x^(1/2)*(625*A^4*b^4 + 2401*B^4*a^4 + 7350*A^2*B^2*a^2*b^2 + 6860*A*B^3*a^3*b + 3500*A^3*B*a*b^3))/(279936*a^4*b^3) - (((3^(1/2)*1i)/2 + 1/2)*(5*A*b + 7*B*a)*(125*A^3*b^3 + 343*B^3*a^3 + 735*A*B^2*a^2*b + 525*A^2*B*a*b^2))/(279936*(-a)^(23/6)*b^(19/6)))*(5*A*b + 7*B*a))/(216*(-a)^(11/6)*b^(13/6)) - (((3^(1/2)*1i)/2 + 1/2)*((x^(1/2)*(625*A^4*b^4 + 2401*B^4*a^4 + 7350*A^2*B^2*a^2*b^2 + 6860*A*B^3*a^3*b + 3500*A^3*B*a*b^3))/(279936*a^4*b^3) + (((3^(1/2)*1i)/2 + 1/2)*(5*A*b + 7*B*a)*(125*A^3*b^3 + 343*B^3*a^3 + 735*A*B^2*a^2*b + 525*A^2*B*a*b^2))/(279936*(-a)^(23/6)*b^(19/6)))*(5*A*b + 7*B*a))/(216*(-a)^(11/6)*b^(13/6))))*((3^(1/2)*1i)/2 + 1/2)*(5*A*b + 7*B*a)*1i)/(108*(-a)^(11/6)*b^(13/6))","B"
173,1,1672,327,2.893350,"\text{Not used}","int((x^(3/2)*(A + B*x^3))/(a + b*x^3)^3,x)","\frac{\frac{x^{11/2}\,\left(7\,A\,b+5\,B\,a\right)}{36\,a^2}+\frac{x^{5/2}\,\left(13\,A\,b-B\,a\right)}{36\,a\,b}}{a^2+2\,a\,b\,x^3+b^2\,x^6}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{343\,A^3\,b^3+735\,A^2\,B\,a\,b^2+525\,A\,B^2\,a^2\,b+125\,B^3\,a^3}{1296\,a^3}-\frac{\sqrt{x}\,\left(7\,A\,b+5\,B\,a\right)\,\left(49\,A^2\,b^4+70\,A\,B\,a\,b^3+25\,B^2\,a^2\,b^2\right)}{1296\,{\left(-a\right)}^{19/6}\,b^{11/6}}\right)\,{\left(7\,A\,b+5\,B\,a\right)}^2\,1{}\mathrm{i}}{46656\,{\left(-a\right)}^{13/3}\,b^{11/3}}-\frac{\left(\frac{343\,A^3\,b^3+735\,A^2\,B\,a\,b^2+525\,A\,B^2\,a^2\,b+125\,B^3\,a^3}{1296\,a^3}+\frac{\sqrt{x}\,\left(7\,A\,b+5\,B\,a\right)\,\left(49\,A^2\,b^4+70\,A\,B\,a\,b^3+25\,B^2\,a^2\,b^2\right)}{1296\,{\left(-a\right)}^{19/6}\,b^{11/6}}\right)\,{\left(7\,A\,b+5\,B\,a\right)}^2\,1{}\mathrm{i}}{46656\,{\left(-a\right)}^{13/3}\,b^{11/3}}}{\frac{\left(\frac{343\,A^3\,b^3+735\,A^2\,B\,a\,b^2+525\,A\,B^2\,a^2\,b+125\,B^3\,a^3}{1296\,a^3}-\frac{\sqrt{x}\,\left(7\,A\,b+5\,B\,a\right)\,\left(49\,A^2\,b^4+70\,A\,B\,a\,b^3+25\,B^2\,a^2\,b^2\right)}{1296\,{\left(-a\right)}^{19/6}\,b^{11/6}}\right)\,{\left(7\,A\,b+5\,B\,a\right)}^2}{46656\,{\left(-a\right)}^{13/3}\,b^{11/3}}+\frac{\left(\frac{343\,A^3\,b^3+735\,A^2\,B\,a\,b^2+525\,A\,B^2\,a^2\,b+125\,B^3\,a^3}{1296\,a^3}+\frac{\sqrt{x}\,\left(7\,A\,b+5\,B\,a\right)\,\left(49\,A^2\,b^4+70\,A\,B\,a\,b^3+25\,B^2\,a^2\,b^2\right)}{1296\,{\left(-a\right)}^{19/6}\,b^{11/6}}\right)\,{\left(7\,A\,b+5\,B\,a\right)}^2}{46656\,{\left(-a\right)}^{13/3}\,b^{11/3}}}\right)\,\left(7\,A\,b+5\,B\,a\right)\,1{}\mathrm{i}}{108\,{\left(-a\right)}^{13/6}\,b^{11/6}}+\frac{\mathrm{atan}\left(\frac{\frac{{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(7\,A\,b+5\,B\,a\right)}^2\,\left(\frac{343\,A^3\,b^3+735\,A^2\,B\,a\,b^2+525\,A\,B^2\,a^2\,b+125\,B^3\,a^3}{1296\,a^3}-\frac{\sqrt{x}\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(7\,A\,b+5\,B\,a\right)\,\left(49\,A^2\,b^4+70\,A\,B\,a\,b^3+25\,B^2\,a^2\,b^2\right)}{1296\,{\left(-a\right)}^{19/6}\,b^{11/6}}\right)\,1{}\mathrm{i}}{46656\,{\left(-a\right)}^{13/3}\,b^{11/3}}-\frac{{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(7\,A\,b+5\,B\,a\right)}^2\,\left(\frac{343\,A^3\,b^3+735\,A^2\,B\,a\,b^2+525\,A\,B^2\,a^2\,b+125\,B^3\,a^3}{1296\,a^3}+\frac{\sqrt{x}\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(7\,A\,b+5\,B\,a\right)\,\left(49\,A^2\,b^4+70\,A\,B\,a\,b^3+25\,B^2\,a^2\,b^2\right)}{1296\,{\left(-a\right)}^{19/6}\,b^{11/6}}\right)\,1{}\mathrm{i}}{46656\,{\left(-a\right)}^{13/3}\,b^{11/3}}}{\frac{{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(7\,A\,b+5\,B\,a\right)}^2\,\left(\frac{343\,A^3\,b^3+735\,A^2\,B\,a\,b^2+525\,A\,B^2\,a^2\,b+125\,B^3\,a^3}{1296\,a^3}-\frac{\sqrt{x}\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(7\,A\,b+5\,B\,a\right)\,\left(49\,A^2\,b^4+70\,A\,B\,a\,b^3+25\,B^2\,a^2\,b^2\right)}{1296\,{\left(-a\right)}^{19/6}\,b^{11/6}}\right)}{46656\,{\left(-a\right)}^{13/3}\,b^{11/3}}+\frac{{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(7\,A\,b+5\,B\,a\right)}^2\,\left(\frac{343\,A^3\,b^3+735\,A^2\,B\,a\,b^2+525\,A\,B^2\,a^2\,b+125\,B^3\,a^3}{1296\,a^3}+\frac{\sqrt{x}\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(7\,A\,b+5\,B\,a\right)\,\left(49\,A^2\,b^4+70\,A\,B\,a\,b^3+25\,B^2\,a^2\,b^2\right)}{1296\,{\left(-a\right)}^{19/6}\,b^{11/6}}\right)}{46656\,{\left(-a\right)}^{13/3}\,b^{11/3}}}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(7\,A\,b+5\,B\,a\right)\,1{}\mathrm{i}}{108\,{\left(-a\right)}^{13/6}\,b^{11/6}}+\frac{\mathrm{atan}\left(\frac{\frac{{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(7\,A\,b+5\,B\,a\right)}^2\,\left(\frac{343\,A^3\,b^3+735\,A^2\,B\,a\,b^2+525\,A\,B^2\,a^2\,b+125\,B^3\,a^3}{1296\,a^3}-\frac{\sqrt{x}\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(7\,A\,b+5\,B\,a\right)\,\left(49\,A^2\,b^4+70\,A\,B\,a\,b^3+25\,B^2\,a^2\,b^2\right)}{1296\,{\left(-a\right)}^{19/6}\,b^{11/6}}\right)\,1{}\mathrm{i}}{46656\,{\left(-a\right)}^{13/3}\,b^{11/3}}-\frac{{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(7\,A\,b+5\,B\,a\right)}^2\,\left(\frac{343\,A^3\,b^3+735\,A^2\,B\,a\,b^2+525\,A\,B^2\,a^2\,b+125\,B^3\,a^3}{1296\,a^3}+\frac{\sqrt{x}\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(7\,A\,b+5\,B\,a\right)\,\left(49\,A^2\,b^4+70\,A\,B\,a\,b^3+25\,B^2\,a^2\,b^2\right)}{1296\,{\left(-a\right)}^{19/6}\,b^{11/6}}\right)\,1{}\mathrm{i}}{46656\,{\left(-a\right)}^{13/3}\,b^{11/3}}}{\frac{{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(7\,A\,b+5\,B\,a\right)}^2\,\left(\frac{343\,A^3\,b^3+735\,A^2\,B\,a\,b^2+525\,A\,B^2\,a^2\,b+125\,B^3\,a^3}{1296\,a^3}-\frac{\sqrt{x}\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(7\,A\,b+5\,B\,a\right)\,\left(49\,A^2\,b^4+70\,A\,B\,a\,b^3+25\,B^2\,a^2\,b^2\right)}{1296\,{\left(-a\right)}^{19/6}\,b^{11/6}}\right)}{46656\,{\left(-a\right)}^{13/3}\,b^{11/3}}+\frac{{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(7\,A\,b+5\,B\,a\right)}^2\,\left(\frac{343\,A^3\,b^3+735\,A^2\,B\,a\,b^2+525\,A\,B^2\,a^2\,b+125\,B^3\,a^3}{1296\,a^3}+\frac{\sqrt{x}\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(7\,A\,b+5\,B\,a\right)\,\left(49\,A^2\,b^4+70\,A\,B\,a\,b^3+25\,B^2\,a^2\,b^2\right)}{1296\,{\left(-a\right)}^{19/6}\,b^{11/6}}\right)}{46656\,{\left(-a\right)}^{13/3}\,b^{11/3}}}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(7\,A\,b+5\,B\,a\right)\,1{}\mathrm{i}}{108\,{\left(-a\right)}^{13/6}\,b^{11/6}}","Not used",1,"((x^(11/2)*(7*A*b + 5*B*a))/(36*a^2) + (x^(5/2)*(13*A*b - B*a))/(36*a*b))/(a^2 + b^2*x^6 + 2*a*b*x^3) + (atan(((((343*A^3*b^3 + 125*B^3*a^3 + 525*A*B^2*a^2*b + 735*A^2*B*a*b^2)/(1296*a^3) - (x^(1/2)*(7*A*b + 5*B*a)*(49*A^2*b^4 + 25*B^2*a^2*b^2 + 70*A*B*a*b^3))/(1296*(-a)^(19/6)*b^(11/6)))*(7*A*b + 5*B*a)^2*1i)/(46656*(-a)^(13/3)*b^(11/3)) - (((343*A^3*b^3 + 125*B^3*a^3 + 525*A*B^2*a^2*b + 735*A^2*B*a*b^2)/(1296*a^3) + (x^(1/2)*(7*A*b + 5*B*a)*(49*A^2*b^4 + 25*B^2*a^2*b^2 + 70*A*B*a*b^3))/(1296*(-a)^(19/6)*b^(11/6)))*(7*A*b + 5*B*a)^2*1i)/(46656*(-a)^(13/3)*b^(11/3)))/((((343*A^3*b^3 + 125*B^3*a^3 + 525*A*B^2*a^2*b + 735*A^2*B*a*b^2)/(1296*a^3) - (x^(1/2)*(7*A*b + 5*B*a)*(49*A^2*b^4 + 25*B^2*a^2*b^2 + 70*A*B*a*b^3))/(1296*(-a)^(19/6)*b^(11/6)))*(7*A*b + 5*B*a)^2)/(46656*(-a)^(13/3)*b^(11/3)) + (((343*A^3*b^3 + 125*B^3*a^3 + 525*A*B^2*a^2*b + 735*A^2*B*a*b^2)/(1296*a^3) + (x^(1/2)*(7*A*b + 5*B*a)*(49*A^2*b^4 + 25*B^2*a^2*b^2 + 70*A*B*a*b^3))/(1296*(-a)^(19/6)*b^(11/6)))*(7*A*b + 5*B*a)^2)/(46656*(-a)^(13/3)*b^(11/3))))*(7*A*b + 5*B*a)*1i)/(108*(-a)^(13/6)*b^(11/6)) + (atan(((((3^(1/2)*1i)/2 - 1/2)^2*(7*A*b + 5*B*a)^2*((343*A^3*b^3 + 125*B^3*a^3 + 525*A*B^2*a^2*b + 735*A^2*B*a*b^2)/(1296*a^3) - (x^(1/2)*((3^(1/2)*1i)/2 - 1/2)*(7*A*b + 5*B*a)*(49*A^2*b^4 + 25*B^2*a^2*b^2 + 70*A*B*a*b^3))/(1296*(-a)^(19/6)*b^(11/6)))*1i)/(46656*(-a)^(13/3)*b^(11/3)) - (((3^(1/2)*1i)/2 - 1/2)^2*(7*A*b + 5*B*a)^2*((343*A^3*b^3 + 125*B^3*a^3 + 525*A*B^2*a^2*b + 735*A^2*B*a*b^2)/(1296*a^3) + (x^(1/2)*((3^(1/2)*1i)/2 - 1/2)*(7*A*b + 5*B*a)*(49*A^2*b^4 + 25*B^2*a^2*b^2 + 70*A*B*a*b^3))/(1296*(-a)^(19/6)*b^(11/6)))*1i)/(46656*(-a)^(13/3)*b^(11/3)))/((((3^(1/2)*1i)/2 - 1/2)^2*(7*A*b + 5*B*a)^2*((343*A^3*b^3 + 125*B^3*a^3 + 525*A*B^2*a^2*b + 735*A^2*B*a*b^2)/(1296*a^3) - (x^(1/2)*((3^(1/2)*1i)/2 - 1/2)*(7*A*b + 5*B*a)*(49*A^2*b^4 + 25*B^2*a^2*b^2 + 70*A*B*a*b^3))/(1296*(-a)^(19/6)*b^(11/6))))/(46656*(-a)^(13/3)*b^(11/3)) + (((3^(1/2)*1i)/2 - 1/2)^2*(7*A*b + 5*B*a)^2*((343*A^3*b^3 + 125*B^3*a^3 + 525*A*B^2*a^2*b + 735*A^2*B*a*b^2)/(1296*a^3) + (x^(1/2)*((3^(1/2)*1i)/2 - 1/2)*(7*A*b + 5*B*a)*(49*A^2*b^4 + 25*B^2*a^2*b^2 + 70*A*B*a*b^3))/(1296*(-a)^(19/6)*b^(11/6))))/(46656*(-a)^(13/3)*b^(11/3))))*((3^(1/2)*1i)/2 - 1/2)*(7*A*b + 5*B*a)*1i)/(108*(-a)^(13/6)*b^(11/6)) + (atan(((((3^(1/2)*1i)/2 + 1/2)^2*(7*A*b + 5*B*a)^2*((343*A^3*b^3 + 125*B^3*a^3 + 525*A*B^2*a^2*b + 735*A^2*B*a*b^2)/(1296*a^3) - (x^(1/2)*((3^(1/2)*1i)/2 + 1/2)*(7*A*b + 5*B*a)*(49*A^2*b^4 + 25*B^2*a^2*b^2 + 70*A*B*a*b^3))/(1296*(-a)^(19/6)*b^(11/6)))*1i)/(46656*(-a)^(13/3)*b^(11/3)) - (((3^(1/2)*1i)/2 + 1/2)^2*(7*A*b + 5*B*a)^2*((343*A^3*b^3 + 125*B^3*a^3 + 525*A*B^2*a^2*b + 735*A^2*B*a*b^2)/(1296*a^3) + (x^(1/2)*((3^(1/2)*1i)/2 + 1/2)*(7*A*b + 5*B*a)*(49*A^2*b^4 + 25*B^2*a^2*b^2 + 70*A*B*a*b^3))/(1296*(-a)^(19/6)*b^(11/6)))*1i)/(46656*(-a)^(13/3)*b^(11/3)))/((((3^(1/2)*1i)/2 + 1/2)^2*(7*A*b + 5*B*a)^2*((343*A^3*b^3 + 125*B^3*a^3 + 525*A*B^2*a^2*b + 735*A^2*B*a*b^2)/(1296*a^3) - (x^(1/2)*((3^(1/2)*1i)/2 + 1/2)*(7*A*b + 5*B*a)*(49*A^2*b^4 + 25*B^2*a^2*b^2 + 70*A*B*a*b^3))/(1296*(-a)^(19/6)*b^(11/6))))/(46656*(-a)^(13/3)*b^(11/3)) + (((3^(1/2)*1i)/2 + 1/2)^2*(7*A*b + 5*B*a)^2*((343*A^3*b^3 + 125*B^3*a^3 + 525*A*B^2*a^2*b + 735*A^2*B*a*b^2)/(1296*a^3) + (x^(1/2)*((3^(1/2)*1i)/2 + 1/2)*(7*A*b + 5*B*a)*(49*A^2*b^4 + 25*B^2*a^2*b^2 + 70*A*B*a*b^3))/(1296*(-a)^(19/6)*b^(11/6))))/(46656*(-a)^(13/3)*b^(11/3))))*((3^(1/2)*1i)/2 + 1/2)*(7*A*b + 5*B*a)*1i)/(108*(-a)^(13/6)*b^(11/6))","B"
174,1,136,104,2.706278,"\text{Not used}","int((x^(1/2)*(A + B*x^3))/(a + b*x^3)^3,x)","\frac{\frac{x^{9/2}\,\left(3\,A\,b+B\,a\right)}{12\,a^2}+\frac{x^{3/2}\,\left(5\,A\,b-B\,a\right)}{12\,a\,b}}{a^2+2\,a\,b\,x^3+b^2\,x^6}+\frac{\mathrm{atan}\left(\frac{b^{3/2}\,x^{3/2}\,\left(9\,A^2\,b^3+6\,A\,B\,a\,b^2+B^2\,a^2\,b\right)}{\sqrt{a}\,\left(3\,A\,b+B\,a\right)\,\left(3\,A\,b^3+B\,a\,b^2\right)}\right)\,\left(3\,A\,b+B\,a\right)}{12\,a^{5/2}\,b^{3/2}}","Not used",1,"((x^(9/2)*(3*A*b + B*a))/(12*a^2) + (x^(3/2)*(5*A*b - B*a))/(12*a*b))/(a^2 + b^2*x^6 + 2*a*b*x^3) + (atan((b^(3/2)*x^(3/2)*(9*A^2*b^3 + B^2*a^2*b + 6*A*B*a*b^2))/(a^(1/2)*(3*A*b + B*a)*(3*A*b^3 + B*a*b^2)))*(3*A*b + B*a))/(12*a^(5/2)*b^(3/2))","B"
175,1,1952,321,2.949810,"\text{Not used}","int((A + B*x^3)/(x^(1/2)*(a + b*x^3)^3),x)","\frac{\frac{x^{7/2}\,\left(11\,A\,b+B\,a\right)}{36\,a^2}+\frac{\sqrt{x}\,\left(17\,A\,b-5\,B\,a\right)}{36\,a\,b}}{a^2+2\,a\,b\,x^3+b^2\,x^6}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{625\,\sqrt{x}\,\left(14641\,A^4\,b^5+5324\,A^3\,B\,a\,b^4+726\,A^2\,B^2\,a^2\,b^3+44\,A\,B^3\,a^3\,b^2+B^4\,a^4\,b\right)}{279936\,a^8}-\frac{625\,\left(11\,A\,b+B\,a\right)\,\left(1331\,A^3\,b^5+363\,A^2\,B\,a\,b^4+33\,A\,B^2\,a^2\,b^3+B^3\,a^3\,b^2\right)}{279936\,{\left(-a\right)}^{47/6}\,b^{7/6}}\right)\,\left(11\,A\,b+B\,a\right)\,5{}\mathrm{i}}{216\,{\left(-a\right)}^{17/6}\,b^{7/6}}+\frac{\left(\frac{625\,\sqrt{x}\,\left(14641\,A^4\,b^5+5324\,A^3\,B\,a\,b^4+726\,A^2\,B^2\,a^2\,b^3+44\,A\,B^3\,a^3\,b^2+B^4\,a^4\,b\right)}{279936\,a^8}+\frac{625\,\left(11\,A\,b+B\,a\right)\,\left(1331\,A^3\,b^5+363\,A^2\,B\,a\,b^4+33\,A\,B^2\,a^2\,b^3+B^3\,a^3\,b^2\right)}{279936\,{\left(-a\right)}^{47/6}\,b^{7/6}}\right)\,\left(11\,A\,b+B\,a\right)\,5{}\mathrm{i}}{216\,{\left(-a\right)}^{17/6}\,b^{7/6}}}{\frac{5\,\left(\frac{625\,\sqrt{x}\,\left(14641\,A^4\,b^5+5324\,A^3\,B\,a\,b^4+726\,A^2\,B^2\,a^2\,b^3+44\,A\,B^3\,a^3\,b^2+B^4\,a^4\,b\right)}{279936\,a^8}-\frac{625\,\left(11\,A\,b+B\,a\right)\,\left(1331\,A^3\,b^5+363\,A^2\,B\,a\,b^4+33\,A\,B^2\,a^2\,b^3+B^3\,a^3\,b^2\right)}{279936\,{\left(-a\right)}^{47/6}\,b^{7/6}}\right)\,\left(11\,A\,b+B\,a\right)}{216\,{\left(-a\right)}^{17/6}\,b^{7/6}}-\frac{5\,\left(\frac{625\,\sqrt{x}\,\left(14641\,A^4\,b^5+5324\,A^3\,B\,a\,b^4+726\,A^2\,B^2\,a^2\,b^3+44\,A\,B^3\,a^3\,b^2+B^4\,a^4\,b\right)}{279936\,a^8}+\frac{625\,\left(11\,A\,b+B\,a\right)\,\left(1331\,A^3\,b^5+363\,A^2\,B\,a\,b^4+33\,A\,B^2\,a^2\,b^3+B^3\,a^3\,b^2\right)}{279936\,{\left(-a\right)}^{47/6}\,b^{7/6}}\right)\,\left(11\,A\,b+B\,a\right)}{216\,{\left(-a\right)}^{17/6}\,b^{7/6}}}\right)\,\left(11\,A\,b+B\,a\right)\,5{}\mathrm{i}}{108\,{\left(-a\right)}^{17/6}\,b^{7/6}}-\frac{\mathrm{atan}\left(\frac{\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(11\,A\,b+B\,a\right)\,\left(\frac{625\,\sqrt{x}\,\left(14641\,A^4\,b^5+5324\,A^3\,B\,a\,b^4+726\,A^2\,B^2\,a^2\,b^3+44\,A\,B^3\,a^3\,b^2+B^4\,a^4\,b\right)}{279936\,a^8}-\frac{625\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(11\,A\,b+B\,a\right)\,\left(1331\,A^3\,b^5+363\,A^2\,B\,a\,b^4+33\,A\,B^2\,a^2\,b^3+B^3\,a^3\,b^2\right)}{279936\,{\left(-a\right)}^{47/6}\,b^{7/6}}\right)\,5{}\mathrm{i}}{216\,{\left(-a\right)}^{17/6}\,b^{7/6}}+\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(11\,A\,b+B\,a\right)\,\left(\frac{625\,\sqrt{x}\,\left(14641\,A^4\,b^5+5324\,A^3\,B\,a\,b^4+726\,A^2\,B^2\,a^2\,b^3+44\,A\,B^3\,a^3\,b^2+B^4\,a^4\,b\right)}{279936\,a^8}+\frac{625\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(11\,A\,b+B\,a\right)\,\left(1331\,A^3\,b^5+363\,A^2\,B\,a\,b^4+33\,A\,B^2\,a^2\,b^3+B^3\,a^3\,b^2\right)}{279936\,{\left(-a\right)}^{47/6}\,b^{7/6}}\right)\,5{}\mathrm{i}}{216\,{\left(-a\right)}^{17/6}\,b^{7/6}}}{\frac{5\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(11\,A\,b+B\,a\right)\,\left(\frac{625\,\sqrt{x}\,\left(14641\,A^4\,b^5+5324\,A^3\,B\,a\,b^4+726\,A^2\,B^2\,a^2\,b^3+44\,A\,B^3\,a^3\,b^2+B^4\,a^4\,b\right)}{279936\,a^8}-\frac{625\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(11\,A\,b+B\,a\right)\,\left(1331\,A^3\,b^5+363\,A^2\,B\,a\,b^4+33\,A\,B^2\,a^2\,b^3+B^3\,a^3\,b^2\right)}{279936\,{\left(-a\right)}^{47/6}\,b^{7/6}}\right)}{216\,{\left(-a\right)}^{17/6}\,b^{7/6}}-\frac{5\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(11\,A\,b+B\,a\right)\,\left(\frac{625\,\sqrt{x}\,\left(14641\,A^4\,b^5+5324\,A^3\,B\,a\,b^4+726\,A^2\,B^2\,a^2\,b^3+44\,A\,B^3\,a^3\,b^2+B^4\,a^4\,b\right)}{279936\,a^8}+\frac{625\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(11\,A\,b+B\,a\right)\,\left(1331\,A^3\,b^5+363\,A^2\,B\,a\,b^4+33\,A\,B^2\,a^2\,b^3+B^3\,a^3\,b^2\right)}{279936\,{\left(-a\right)}^{47/6}\,b^{7/6}}\right)}{216\,{\left(-a\right)}^{17/6}\,b^{7/6}}}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(11\,A\,b+B\,a\right)\,5{}\mathrm{i}}{108\,{\left(-a\right)}^{17/6}\,b^{7/6}}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(11\,A\,b+B\,a\right)\,\left(\frac{625\,\sqrt{x}\,\left(14641\,A^4\,b^5+5324\,A^3\,B\,a\,b^4+726\,A^2\,B^2\,a^2\,b^3+44\,A\,B^3\,a^3\,b^2+B^4\,a^4\,b\right)}{279936\,a^8}-\frac{625\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(11\,A\,b+B\,a\right)\,\left(1331\,A^3\,b^5+363\,A^2\,B\,a\,b^4+33\,A\,B^2\,a^2\,b^3+B^3\,a^3\,b^2\right)}{279936\,{\left(-a\right)}^{47/6}\,b^{7/6}}\right)\,5{}\mathrm{i}}{216\,{\left(-a\right)}^{17/6}\,b^{7/6}}+\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(11\,A\,b+B\,a\right)\,\left(\frac{625\,\sqrt{x}\,\left(14641\,A^4\,b^5+5324\,A^3\,B\,a\,b^4+726\,A^2\,B^2\,a^2\,b^3+44\,A\,B^3\,a^3\,b^2+B^4\,a^4\,b\right)}{279936\,a^8}+\frac{625\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(11\,A\,b+B\,a\right)\,\left(1331\,A^3\,b^5+363\,A^2\,B\,a\,b^4+33\,A\,B^2\,a^2\,b^3+B^3\,a^3\,b^2\right)}{279936\,{\left(-a\right)}^{47/6}\,b^{7/6}}\right)\,5{}\mathrm{i}}{216\,{\left(-a\right)}^{17/6}\,b^{7/6}}}{\frac{5\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(11\,A\,b+B\,a\right)\,\left(\frac{625\,\sqrt{x}\,\left(14641\,A^4\,b^5+5324\,A^3\,B\,a\,b^4+726\,A^2\,B^2\,a^2\,b^3+44\,A\,B^3\,a^3\,b^2+B^4\,a^4\,b\right)}{279936\,a^8}-\frac{625\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(11\,A\,b+B\,a\right)\,\left(1331\,A^3\,b^5+363\,A^2\,B\,a\,b^4+33\,A\,B^2\,a^2\,b^3+B^3\,a^3\,b^2\right)}{279936\,{\left(-a\right)}^{47/6}\,b^{7/6}}\right)}{216\,{\left(-a\right)}^{17/6}\,b^{7/6}}-\frac{5\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(11\,A\,b+B\,a\right)\,\left(\frac{625\,\sqrt{x}\,\left(14641\,A^4\,b^5+5324\,A^3\,B\,a\,b^4+726\,A^2\,B^2\,a^2\,b^3+44\,A\,B^3\,a^3\,b^2+B^4\,a^4\,b\right)}{279936\,a^8}+\frac{625\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(11\,A\,b+B\,a\right)\,\left(1331\,A^3\,b^5+363\,A^2\,B\,a\,b^4+33\,A\,B^2\,a^2\,b^3+B^3\,a^3\,b^2\right)}{279936\,{\left(-a\right)}^{47/6}\,b^{7/6}}\right)}{216\,{\left(-a\right)}^{17/6}\,b^{7/6}}}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(11\,A\,b+B\,a\right)\,5{}\mathrm{i}}{108\,{\left(-a\right)}^{17/6}\,b^{7/6}}","Not used",1,"((x^(7/2)*(11*A*b + B*a))/(36*a^2) + (x^(1/2)*(17*A*b - 5*B*a))/(36*a*b))/(a^2 + b^2*x^6 + 2*a*b*x^3) - (atan(((((625*x^(1/2)*(14641*A^4*b^5 + B^4*a^4*b + 726*A^2*B^2*a^2*b^3 + 5324*A^3*B*a*b^4 + 44*A*B^3*a^3*b^2))/(279936*a^8) - (625*(11*A*b + B*a)*(1331*A^3*b^5 + B^3*a^3*b^2 + 363*A^2*B*a*b^4 + 33*A*B^2*a^2*b^3))/(279936*(-a)^(47/6)*b^(7/6)))*(11*A*b + B*a)*5i)/(216*(-a)^(17/6)*b^(7/6)) + (((625*x^(1/2)*(14641*A^4*b^5 + B^4*a^4*b + 726*A^2*B^2*a^2*b^3 + 5324*A^3*B*a*b^4 + 44*A*B^3*a^3*b^2))/(279936*a^8) + (625*(11*A*b + B*a)*(1331*A^3*b^5 + B^3*a^3*b^2 + 363*A^2*B*a*b^4 + 33*A*B^2*a^2*b^3))/(279936*(-a)^(47/6)*b^(7/6)))*(11*A*b + B*a)*5i)/(216*(-a)^(17/6)*b^(7/6)))/((5*((625*x^(1/2)*(14641*A^4*b^5 + B^4*a^4*b + 726*A^2*B^2*a^2*b^3 + 5324*A^3*B*a*b^4 + 44*A*B^3*a^3*b^2))/(279936*a^8) - (625*(11*A*b + B*a)*(1331*A^3*b^5 + B^3*a^3*b^2 + 363*A^2*B*a*b^4 + 33*A*B^2*a^2*b^3))/(279936*(-a)^(47/6)*b^(7/6)))*(11*A*b + B*a))/(216*(-a)^(17/6)*b^(7/6)) - (5*((625*x^(1/2)*(14641*A^4*b^5 + B^4*a^4*b + 726*A^2*B^2*a^2*b^3 + 5324*A^3*B*a*b^4 + 44*A*B^3*a^3*b^2))/(279936*a^8) + (625*(11*A*b + B*a)*(1331*A^3*b^5 + B^3*a^3*b^2 + 363*A^2*B*a*b^4 + 33*A*B^2*a^2*b^3))/(279936*(-a)^(47/6)*b^(7/6)))*(11*A*b + B*a))/(216*(-a)^(17/6)*b^(7/6))))*(11*A*b + B*a)*5i)/(108*(-a)^(17/6)*b^(7/6)) - (atan(((((3^(1/2)*1i)/2 - 1/2)*(11*A*b + B*a)*((625*x^(1/2)*(14641*A^4*b^5 + B^4*a^4*b + 726*A^2*B^2*a^2*b^3 + 5324*A^3*B*a*b^4 + 44*A*B^3*a^3*b^2))/(279936*a^8) - (625*((3^(1/2)*1i)/2 - 1/2)*(11*A*b + B*a)*(1331*A^3*b^5 + B^3*a^3*b^2 + 363*A^2*B*a*b^4 + 33*A*B^2*a^2*b^3))/(279936*(-a)^(47/6)*b^(7/6)))*5i)/(216*(-a)^(17/6)*b^(7/6)) + (((3^(1/2)*1i)/2 - 1/2)*(11*A*b + B*a)*((625*x^(1/2)*(14641*A^4*b^5 + B^4*a^4*b + 726*A^2*B^2*a^2*b^3 + 5324*A^3*B*a*b^4 + 44*A*B^3*a^3*b^2))/(279936*a^8) + (625*((3^(1/2)*1i)/2 - 1/2)*(11*A*b + B*a)*(1331*A^3*b^5 + B^3*a^3*b^2 + 363*A^2*B*a*b^4 + 33*A*B^2*a^2*b^3))/(279936*(-a)^(47/6)*b^(7/6)))*5i)/(216*(-a)^(17/6)*b^(7/6)))/((5*((3^(1/2)*1i)/2 - 1/2)*(11*A*b + B*a)*((625*x^(1/2)*(14641*A^4*b^5 + B^4*a^4*b + 726*A^2*B^2*a^2*b^3 + 5324*A^3*B*a*b^4 + 44*A*B^3*a^3*b^2))/(279936*a^8) - (625*((3^(1/2)*1i)/2 - 1/2)*(11*A*b + B*a)*(1331*A^3*b^5 + B^3*a^3*b^2 + 363*A^2*B*a*b^4 + 33*A*B^2*a^2*b^3))/(279936*(-a)^(47/6)*b^(7/6))))/(216*(-a)^(17/6)*b^(7/6)) - (5*((3^(1/2)*1i)/2 - 1/2)*(11*A*b + B*a)*((625*x^(1/2)*(14641*A^4*b^5 + B^4*a^4*b + 726*A^2*B^2*a^2*b^3 + 5324*A^3*B*a*b^4 + 44*A*B^3*a^3*b^2))/(279936*a^8) + (625*((3^(1/2)*1i)/2 - 1/2)*(11*A*b + B*a)*(1331*A^3*b^5 + B^3*a^3*b^2 + 363*A^2*B*a*b^4 + 33*A*B^2*a^2*b^3))/(279936*(-a)^(47/6)*b^(7/6))))/(216*(-a)^(17/6)*b^(7/6))))*((3^(1/2)*1i)/2 - 1/2)*(11*A*b + B*a)*5i)/(108*(-a)^(17/6)*b^(7/6)) - (atan(((((3^(1/2)*1i)/2 + 1/2)*(11*A*b + B*a)*((625*x^(1/2)*(14641*A^4*b^5 + B^4*a^4*b + 726*A^2*B^2*a^2*b^3 + 5324*A^3*B*a*b^4 + 44*A*B^3*a^3*b^2))/(279936*a^8) - (625*((3^(1/2)*1i)/2 + 1/2)*(11*A*b + B*a)*(1331*A^3*b^5 + B^3*a^3*b^2 + 363*A^2*B*a*b^4 + 33*A*B^2*a^2*b^3))/(279936*(-a)^(47/6)*b^(7/6)))*5i)/(216*(-a)^(17/6)*b^(7/6)) + (((3^(1/2)*1i)/2 + 1/2)*(11*A*b + B*a)*((625*x^(1/2)*(14641*A^4*b^5 + B^4*a^4*b + 726*A^2*B^2*a^2*b^3 + 5324*A^3*B*a*b^4 + 44*A*B^3*a^3*b^2))/(279936*a^8) + (625*((3^(1/2)*1i)/2 + 1/2)*(11*A*b + B*a)*(1331*A^3*b^5 + B^3*a^3*b^2 + 363*A^2*B*a*b^4 + 33*A*B^2*a^2*b^3))/(279936*(-a)^(47/6)*b^(7/6)))*5i)/(216*(-a)^(17/6)*b^(7/6)))/((5*((3^(1/2)*1i)/2 + 1/2)*(11*A*b + B*a)*((625*x^(1/2)*(14641*A^4*b^5 + B^4*a^4*b + 726*A^2*B^2*a^2*b^3 + 5324*A^3*B*a*b^4 + 44*A*B^3*a^3*b^2))/(279936*a^8) - (625*((3^(1/2)*1i)/2 + 1/2)*(11*A*b + B*a)*(1331*A^3*b^5 + B^3*a^3*b^2 + 363*A^2*B*a*b^4 + 33*A*B^2*a^2*b^3))/(279936*(-a)^(47/6)*b^(7/6))))/(216*(-a)^(17/6)*b^(7/6)) - (5*((3^(1/2)*1i)/2 + 1/2)*(11*A*b + B*a)*((625*x^(1/2)*(14641*A^4*b^5 + B^4*a^4*b + 726*A^2*B^2*a^2*b^3 + 5324*A^3*B*a*b^4 + 44*A*B^3*a^3*b^2))/(279936*a^8) + (625*((3^(1/2)*1i)/2 + 1/2)*(11*A*b + B*a)*(1331*A^3*b^5 + B^3*a^3*b^2 + 363*A^2*B*a*b^4 + 33*A*B^2*a^2*b^3))/(279936*(-a)^(47/6)*b^(7/6))))/(216*(-a)^(17/6)*b^(7/6))))*((3^(1/2)*1i)/2 + 1/2)*(11*A*b + B*a)*5i)/(108*(-a)^(17/6)*b^(7/6))","B"
176,1,1786,351,2.910794,"\text{Not used}","int((A + B*x^3)/(x^(3/2)*(a + b*x^3)^3),x)","-\frac{\frac{2\,A}{a}+\frac{13\,x^3\,\left(13\,A\,b-B\,a\right)}{36\,a^2}+\frac{7\,b\,x^6\,\left(13\,A\,b-B\,a\right)}{36\,a^3}}{a^2\,\sqrt{x}+b^2\,x^{13/2}+2\,a\,b\,x^{7/2}}+\frac{\mathrm{atan}\left(\frac{\frac{{\left(13\,A\,b-B\,a\right)}^2\,\left(28229306112\,B^3\,a^{24}\,b^3-62019785528064\,A^3\,a^{21}\,b^6-1100942938368\,A\,B^2\,a^{23}\,b^4+14312258198784\,A^2\,B\,a^{22}\,b^5+\frac{343\,\sqrt{x}\,\left(13\,A\,b-B\,a\right)\,\left(140169666861858816\,A^2\,a^{24}\,b^6-21564564132593664\,A\,B\,a^{25}\,b^5+829406312792064\,B^2\,a^{26}\,b^4\right)}{10077696\,{\left(-a\right)}^{19/6}\,b^{5/6}}\right)\,1{}\mathrm{i}}{{\left(-a\right)}^{19/3}\,b^{5/3}}+\frac{{\left(13\,A\,b-B\,a\right)}^2\,\left(62019785528064\,A^3\,a^{21}\,b^6-28229306112\,B^3\,a^{24}\,b^3+1100942938368\,A\,B^2\,a^{23}\,b^4-14312258198784\,A^2\,B\,a^{22}\,b^5+\frac{343\,\sqrt{x}\,\left(13\,A\,b-B\,a\right)\,\left(140169666861858816\,A^2\,a^{24}\,b^6-21564564132593664\,A\,B\,a^{25}\,b^5+829406312792064\,B^2\,a^{26}\,b^4\right)}{10077696\,{\left(-a\right)}^{19/6}\,b^{5/6}}\right)\,1{}\mathrm{i}}{{\left(-a\right)}^{19/3}\,b^{5/3}}}{\frac{{\left(13\,A\,b-B\,a\right)}^2\,\left(28229306112\,B^3\,a^{24}\,b^3-62019785528064\,A^3\,a^{21}\,b^6-1100942938368\,A\,B^2\,a^{23}\,b^4+14312258198784\,A^2\,B\,a^{22}\,b^5+\frac{343\,\sqrt{x}\,\left(13\,A\,b-B\,a\right)\,\left(140169666861858816\,A^2\,a^{24}\,b^6-21564564132593664\,A\,B\,a^{25}\,b^5+829406312792064\,B^2\,a^{26}\,b^4\right)}{10077696\,{\left(-a\right)}^{19/6}\,b^{5/6}}\right)}{{\left(-a\right)}^{19/3}\,b^{5/3}}-\frac{{\left(13\,A\,b-B\,a\right)}^2\,\left(62019785528064\,A^3\,a^{21}\,b^6-28229306112\,B^3\,a^{24}\,b^3+1100942938368\,A\,B^2\,a^{23}\,b^4-14312258198784\,A^2\,B\,a^{22}\,b^5+\frac{343\,\sqrt{x}\,\left(13\,A\,b-B\,a\right)\,\left(140169666861858816\,A^2\,a^{24}\,b^6-21564564132593664\,A\,B\,a^{25}\,b^5+829406312792064\,B^2\,a^{26}\,b^4\right)}{10077696\,{\left(-a\right)}^{19/6}\,b^{5/6}}\right)}{{\left(-a\right)}^{19/3}\,b^{5/3}}}\right)\,\left(13\,A\,b-B\,a\right)\,7{}\mathrm{i}}{108\,{\left(-a\right)}^{19/6}\,b^{5/6}}+\frac{\mathrm{atan}\left(\frac{\frac{{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(13\,A\,b-B\,a\right)}^2\,\left(28229306112\,B^3\,a^{24}\,b^3-62019785528064\,A^3\,a^{21}\,b^6-1100942938368\,A\,B^2\,a^{23}\,b^4+14312258198784\,A^2\,B\,a^{22}\,b^5+\frac{343\,\sqrt{x}\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(13\,A\,b-B\,a\right)\,\left(140169666861858816\,A^2\,a^{24}\,b^6-21564564132593664\,A\,B\,a^{25}\,b^5+829406312792064\,B^2\,a^{26}\,b^4\right)}{10077696\,{\left(-a\right)}^{19/6}\,b^{5/6}}\right)\,1{}\mathrm{i}}{{\left(-a\right)}^{19/3}\,b^{5/3}}+\frac{{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(13\,A\,b-B\,a\right)}^2\,\left(62019785528064\,A^3\,a^{21}\,b^6-28229306112\,B^3\,a^{24}\,b^3+1100942938368\,A\,B^2\,a^{23}\,b^4-14312258198784\,A^2\,B\,a^{22}\,b^5+\frac{343\,\sqrt{x}\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(13\,A\,b-B\,a\right)\,\left(140169666861858816\,A^2\,a^{24}\,b^6-21564564132593664\,A\,B\,a^{25}\,b^5+829406312792064\,B^2\,a^{26}\,b^4\right)}{10077696\,{\left(-a\right)}^{19/6}\,b^{5/6}}\right)\,1{}\mathrm{i}}{{\left(-a\right)}^{19/3}\,b^{5/3}}}{\frac{{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(13\,A\,b-B\,a\right)}^2\,\left(28229306112\,B^3\,a^{24}\,b^3-62019785528064\,A^3\,a^{21}\,b^6-1100942938368\,A\,B^2\,a^{23}\,b^4+14312258198784\,A^2\,B\,a^{22}\,b^5+\frac{343\,\sqrt{x}\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(13\,A\,b-B\,a\right)\,\left(140169666861858816\,A^2\,a^{24}\,b^6-21564564132593664\,A\,B\,a^{25}\,b^5+829406312792064\,B^2\,a^{26}\,b^4\right)}{10077696\,{\left(-a\right)}^{19/6}\,b^{5/6}}\right)}{{\left(-a\right)}^{19/3}\,b^{5/3}}-\frac{{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(13\,A\,b-B\,a\right)}^2\,\left(62019785528064\,A^3\,a^{21}\,b^6-28229306112\,B^3\,a^{24}\,b^3+1100942938368\,A\,B^2\,a^{23}\,b^4-14312258198784\,A^2\,B\,a^{22}\,b^5+\frac{343\,\sqrt{x}\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(13\,A\,b-B\,a\right)\,\left(140169666861858816\,A^2\,a^{24}\,b^6-21564564132593664\,A\,B\,a^{25}\,b^5+829406312792064\,B^2\,a^{26}\,b^4\right)}{10077696\,{\left(-a\right)}^{19/6}\,b^{5/6}}\right)}{{\left(-a\right)}^{19/3}\,b^{5/3}}}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(13\,A\,b-B\,a\right)\,7{}\mathrm{i}}{108\,{\left(-a\right)}^{19/6}\,b^{5/6}}+\frac{\mathrm{atan}\left(\frac{\frac{{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(13\,A\,b-B\,a\right)}^2\,\left(28229306112\,B^3\,a^{24}\,b^3-62019785528064\,A^3\,a^{21}\,b^6-1100942938368\,A\,B^2\,a^{23}\,b^4+14312258198784\,A^2\,B\,a^{22}\,b^5+\frac{343\,\sqrt{x}\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(13\,A\,b-B\,a\right)\,\left(140169666861858816\,A^2\,a^{24}\,b^6-21564564132593664\,A\,B\,a^{25}\,b^5+829406312792064\,B^2\,a^{26}\,b^4\right)}{10077696\,{\left(-a\right)}^{19/6}\,b^{5/6}}\right)\,1{}\mathrm{i}}{{\left(-a\right)}^{19/3}\,b^{5/3}}+\frac{{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(13\,A\,b-B\,a\right)}^2\,\left(62019785528064\,A^3\,a^{21}\,b^6-28229306112\,B^3\,a^{24}\,b^3+1100942938368\,A\,B^2\,a^{23}\,b^4-14312258198784\,A^2\,B\,a^{22}\,b^5+\frac{343\,\sqrt{x}\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(13\,A\,b-B\,a\right)\,\left(140169666861858816\,A^2\,a^{24}\,b^6-21564564132593664\,A\,B\,a^{25}\,b^5+829406312792064\,B^2\,a^{26}\,b^4\right)}{10077696\,{\left(-a\right)}^{19/6}\,b^{5/6}}\right)\,1{}\mathrm{i}}{{\left(-a\right)}^{19/3}\,b^{5/3}}}{\frac{{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(13\,A\,b-B\,a\right)}^2\,\left(28229306112\,B^3\,a^{24}\,b^3-62019785528064\,A^3\,a^{21}\,b^6-1100942938368\,A\,B^2\,a^{23}\,b^4+14312258198784\,A^2\,B\,a^{22}\,b^5+\frac{343\,\sqrt{x}\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(13\,A\,b-B\,a\right)\,\left(140169666861858816\,A^2\,a^{24}\,b^6-21564564132593664\,A\,B\,a^{25}\,b^5+829406312792064\,B^2\,a^{26}\,b^4\right)}{10077696\,{\left(-a\right)}^{19/6}\,b^{5/6}}\right)}{{\left(-a\right)}^{19/3}\,b^{5/3}}-\frac{{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(13\,A\,b-B\,a\right)}^2\,\left(62019785528064\,A^3\,a^{21}\,b^6-28229306112\,B^3\,a^{24}\,b^3+1100942938368\,A\,B^2\,a^{23}\,b^4-14312258198784\,A^2\,B\,a^{22}\,b^5+\frac{343\,\sqrt{x}\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(13\,A\,b-B\,a\right)\,\left(140169666861858816\,A^2\,a^{24}\,b^6-21564564132593664\,A\,B\,a^{25}\,b^5+829406312792064\,B^2\,a^{26}\,b^4\right)}{10077696\,{\left(-a\right)}^{19/6}\,b^{5/6}}\right)}{{\left(-a\right)}^{19/3}\,b^{5/3}}}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(13\,A\,b-B\,a\right)\,7{}\mathrm{i}}{108\,{\left(-a\right)}^{19/6}\,b^{5/6}}","Not used",1,"(atan((((13*A*b - B*a)^2*(28229306112*B^3*a^24*b^3 - 62019785528064*A^3*a^21*b^6 - 1100942938368*A*B^2*a^23*b^4 + 14312258198784*A^2*B*a^22*b^5 + (343*x^(1/2)*(13*A*b - B*a)*(140169666861858816*A^2*a^24*b^6 + 829406312792064*B^2*a^26*b^4 - 21564564132593664*A*B*a^25*b^5))/(10077696*(-a)^(19/6)*b^(5/6)))*1i)/((-a)^(19/3)*b^(5/3)) + ((13*A*b - B*a)^2*(62019785528064*A^3*a^21*b^6 - 28229306112*B^3*a^24*b^3 + 1100942938368*A*B^2*a^23*b^4 - 14312258198784*A^2*B*a^22*b^5 + (343*x^(1/2)*(13*A*b - B*a)*(140169666861858816*A^2*a^24*b^6 + 829406312792064*B^2*a^26*b^4 - 21564564132593664*A*B*a^25*b^5))/(10077696*(-a)^(19/6)*b^(5/6)))*1i)/((-a)^(19/3)*b^(5/3)))/(((13*A*b - B*a)^2*(28229306112*B^3*a^24*b^3 - 62019785528064*A^3*a^21*b^6 - 1100942938368*A*B^2*a^23*b^4 + 14312258198784*A^2*B*a^22*b^5 + (343*x^(1/2)*(13*A*b - B*a)*(140169666861858816*A^2*a^24*b^6 + 829406312792064*B^2*a^26*b^4 - 21564564132593664*A*B*a^25*b^5))/(10077696*(-a)^(19/6)*b^(5/6))))/((-a)^(19/3)*b^(5/3)) - ((13*A*b - B*a)^2*(62019785528064*A^3*a^21*b^6 - 28229306112*B^3*a^24*b^3 + 1100942938368*A*B^2*a^23*b^4 - 14312258198784*A^2*B*a^22*b^5 + (343*x^(1/2)*(13*A*b - B*a)*(140169666861858816*A^2*a^24*b^6 + 829406312792064*B^2*a^26*b^4 - 21564564132593664*A*B*a^25*b^5))/(10077696*(-a)^(19/6)*b^(5/6))))/((-a)^(19/3)*b^(5/3))))*(13*A*b - B*a)*7i)/(108*(-a)^(19/6)*b^(5/6)) - ((2*A)/a + (13*x^3*(13*A*b - B*a))/(36*a^2) + (7*b*x^6*(13*A*b - B*a))/(36*a^3))/(a^2*x^(1/2) + b^2*x^(13/2) + 2*a*b*x^(7/2)) + (atan(((((3^(1/2)*1i)/2 - 1/2)^2*(13*A*b - B*a)^2*(28229306112*B^3*a^24*b^3 - 62019785528064*A^3*a^21*b^6 - 1100942938368*A*B^2*a^23*b^4 + 14312258198784*A^2*B*a^22*b^5 + (343*x^(1/2)*((3^(1/2)*1i)/2 - 1/2)*(13*A*b - B*a)*(140169666861858816*A^2*a^24*b^6 + 829406312792064*B^2*a^26*b^4 - 21564564132593664*A*B*a^25*b^5))/(10077696*(-a)^(19/6)*b^(5/6)))*1i)/((-a)^(19/3)*b^(5/3)) + (((3^(1/2)*1i)/2 - 1/2)^2*(13*A*b - B*a)^2*(62019785528064*A^3*a^21*b^6 - 28229306112*B^3*a^24*b^3 + 1100942938368*A*B^2*a^23*b^4 - 14312258198784*A^2*B*a^22*b^5 + (343*x^(1/2)*((3^(1/2)*1i)/2 - 1/2)*(13*A*b - B*a)*(140169666861858816*A^2*a^24*b^6 + 829406312792064*B^2*a^26*b^4 - 21564564132593664*A*B*a^25*b^5))/(10077696*(-a)^(19/6)*b^(5/6)))*1i)/((-a)^(19/3)*b^(5/3)))/((((3^(1/2)*1i)/2 - 1/2)^2*(13*A*b - B*a)^2*(28229306112*B^3*a^24*b^3 - 62019785528064*A^3*a^21*b^6 - 1100942938368*A*B^2*a^23*b^4 + 14312258198784*A^2*B*a^22*b^5 + (343*x^(1/2)*((3^(1/2)*1i)/2 - 1/2)*(13*A*b - B*a)*(140169666861858816*A^2*a^24*b^6 + 829406312792064*B^2*a^26*b^4 - 21564564132593664*A*B*a^25*b^5))/(10077696*(-a)^(19/6)*b^(5/6))))/((-a)^(19/3)*b^(5/3)) - (((3^(1/2)*1i)/2 - 1/2)^2*(13*A*b - B*a)^2*(62019785528064*A^3*a^21*b^6 - 28229306112*B^3*a^24*b^3 + 1100942938368*A*B^2*a^23*b^4 - 14312258198784*A^2*B*a^22*b^5 + (343*x^(1/2)*((3^(1/2)*1i)/2 - 1/2)*(13*A*b - B*a)*(140169666861858816*A^2*a^24*b^6 + 829406312792064*B^2*a^26*b^4 - 21564564132593664*A*B*a^25*b^5))/(10077696*(-a)^(19/6)*b^(5/6))))/((-a)^(19/3)*b^(5/3))))*((3^(1/2)*1i)/2 - 1/2)*(13*A*b - B*a)*7i)/(108*(-a)^(19/6)*b^(5/6)) + (atan(((((3^(1/2)*1i)/2 + 1/2)^2*(13*A*b - B*a)^2*(28229306112*B^3*a^24*b^3 - 62019785528064*A^3*a^21*b^6 - 1100942938368*A*B^2*a^23*b^4 + 14312258198784*A^2*B*a^22*b^5 + (343*x^(1/2)*((3^(1/2)*1i)/2 + 1/2)*(13*A*b - B*a)*(140169666861858816*A^2*a^24*b^6 + 829406312792064*B^2*a^26*b^4 - 21564564132593664*A*B*a^25*b^5))/(10077696*(-a)^(19/6)*b^(5/6)))*1i)/((-a)^(19/3)*b^(5/3)) + (((3^(1/2)*1i)/2 + 1/2)^2*(13*A*b - B*a)^2*(62019785528064*A^3*a^21*b^6 - 28229306112*B^3*a^24*b^3 + 1100942938368*A*B^2*a^23*b^4 - 14312258198784*A^2*B*a^22*b^5 + (343*x^(1/2)*((3^(1/2)*1i)/2 + 1/2)*(13*A*b - B*a)*(140169666861858816*A^2*a^24*b^6 + 829406312792064*B^2*a^26*b^4 - 21564564132593664*A*B*a^25*b^5))/(10077696*(-a)^(19/6)*b^(5/6)))*1i)/((-a)^(19/3)*b^(5/3)))/((((3^(1/2)*1i)/2 + 1/2)^2*(13*A*b - B*a)^2*(28229306112*B^3*a^24*b^3 - 62019785528064*A^3*a^21*b^6 - 1100942938368*A*B^2*a^23*b^4 + 14312258198784*A^2*B*a^22*b^5 + (343*x^(1/2)*((3^(1/2)*1i)/2 + 1/2)*(13*A*b - B*a)*(140169666861858816*A^2*a^24*b^6 + 829406312792064*B^2*a^26*b^4 - 21564564132593664*A*B*a^25*b^5))/(10077696*(-a)^(19/6)*b^(5/6))))/((-a)^(19/3)*b^(5/3)) - (((3^(1/2)*1i)/2 + 1/2)^2*(13*A*b - B*a)^2*(62019785528064*A^3*a^21*b^6 - 28229306112*B^3*a^24*b^3 + 1100942938368*A*B^2*a^23*b^4 - 14312258198784*A^2*B*a^22*b^5 + (343*x^(1/2)*((3^(1/2)*1i)/2 + 1/2)*(13*A*b - B*a)*(140169666861858816*A^2*a^24*b^6 + 829406312792064*B^2*a^26*b^4 - 21564564132593664*A*B*a^25*b^5))/(10077696*(-a)^(19/6)*b^(5/6))))/((-a)^(19/3)*b^(5/3))))*((3^(1/2)*1i)/2 + 1/2)*(13*A*b - B*a)*7i)/(108*(-a)^(19/6)*b^(5/6))","B"
177,1,163,129,2.728401,"\text{Not used}","int((A + B*x^3)/(x^(5/2)*(a + b*x^3)^3),x)","-\frac{\frac{2\,A}{3\,a}+\frac{5\,x^3\,\left(5\,A\,b-B\,a\right)}{12\,a^2}+\frac{b\,x^6\,\left(5\,A\,b-B\,a\right)}{4\,a^3}}{a^2\,x^{3/2}+b^2\,x^{15/2}+2\,a\,b\,x^{9/2}}-\frac{\mathrm{atan}\left(\frac{8\,a^{7/2}\,\sqrt{b}\,x^{3/2}\,\left(86400\,A^2\,a^9\,b^5-34560\,A\,B\,a^{10}\,b^4+3456\,B^2\,a^{11}\,b^3\right)}{\left(5\,A\,b-B\,a\right)\,\left(138240\,A\,a^{13}\,b^4-27648\,B\,a^{14}\,b^3\right)}\right)\,\left(5\,A\,b-B\,a\right)}{4\,a^{7/2}\,\sqrt{b}}","Not used",1,"- ((2*A)/(3*a) + (5*x^3*(5*A*b - B*a))/(12*a^2) + (b*x^6*(5*A*b - B*a))/(4*a^3))/(a^2*x^(3/2) + b^2*x^(15/2) + 2*a*b*x^(9/2)) - (atan((8*a^(7/2)*b^(1/2)*x^(3/2)*(86400*A^2*a^9*b^5 + 3456*B^2*a^11*b^3 - 34560*A*B*a^10*b^4))/((5*A*b - B*a)*(138240*A*a^13*b^4 - 27648*B*a^14*b^3)))*(5*A*b - B*a))/(4*a^(7/2)*b^(1/2))","B"
178,1,2109,351,2.959342,"\text{Not used}","int((A + B*x^3)/(x^(7/2)*(a + b*x^3)^3),x)","-\frac{\frac{2\,A}{5\,a}+\frac{17\,x^3\,\left(17\,A\,b-5\,B\,a\right)}{180\,a^2}+\frac{11\,b\,x^6\,\left(17\,A\,b-5\,B\,a\right)}{180\,a^3}}{a^2\,x^{5/2}+b^2\,x^{17/2}+2\,a\,b\,x^{11/2}}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\sqrt{x}\,\left(443639472636450816\,A^4\,a^{15}\,b^9-521928791337000960\,A^3\,B\,a^{16}\,b^8+230262702060441600\,A^2\,B^2\,a^{17}\,b^7-45149549423616000\,A\,B^3\,a^{18}\,b^6+3319819810560000\,B^4\,a^{19}\,b^5\right)-\frac{11\,\left(17\,A\,b-5\,B\,a\right)\,\left(512439176949055488\,A^3\,a^{19}\,b^8-452152214955048960\,A^2\,B\,a^{20}\,b^7+132985945575014400\,A\,B^2\,a^{21}\,b^6-13037837801472000\,B^3\,a^{22}\,b^5\right)}{216\,{\left(-a\right)}^{23/6}\,b^{1/6}}\right)\,\left(17\,A\,b-5\,B\,a\right)\,11{}\mathrm{i}}{216\,{\left(-a\right)}^{23/6}\,b^{1/6}}+\frac{\left(\sqrt{x}\,\left(443639472636450816\,A^4\,a^{15}\,b^9-521928791337000960\,A^3\,B\,a^{16}\,b^8+230262702060441600\,A^2\,B^2\,a^{17}\,b^7-45149549423616000\,A\,B^3\,a^{18}\,b^6+3319819810560000\,B^4\,a^{19}\,b^5\right)+\frac{11\,\left(17\,A\,b-5\,B\,a\right)\,\left(512439176949055488\,A^3\,a^{19}\,b^8-452152214955048960\,A^2\,B\,a^{20}\,b^7+132985945575014400\,A\,B^2\,a^{21}\,b^6-13037837801472000\,B^3\,a^{22}\,b^5\right)}{216\,{\left(-a\right)}^{23/6}\,b^{1/6}}\right)\,\left(17\,A\,b-5\,B\,a\right)\,11{}\mathrm{i}}{216\,{\left(-a\right)}^{23/6}\,b^{1/6}}}{\frac{11\,\left(\sqrt{x}\,\left(443639472636450816\,A^4\,a^{15}\,b^9-521928791337000960\,A^3\,B\,a^{16}\,b^8+230262702060441600\,A^2\,B^2\,a^{17}\,b^7-45149549423616000\,A\,B^3\,a^{18}\,b^6+3319819810560000\,B^4\,a^{19}\,b^5\right)-\frac{11\,\left(17\,A\,b-5\,B\,a\right)\,\left(512439176949055488\,A^3\,a^{19}\,b^8-452152214955048960\,A^2\,B\,a^{20}\,b^7+132985945575014400\,A\,B^2\,a^{21}\,b^6-13037837801472000\,B^3\,a^{22}\,b^5\right)}{216\,{\left(-a\right)}^{23/6}\,b^{1/6}}\right)\,\left(17\,A\,b-5\,B\,a\right)}{216\,{\left(-a\right)}^{23/6}\,b^{1/6}}-\frac{11\,\left(\sqrt{x}\,\left(443639472636450816\,A^4\,a^{15}\,b^9-521928791337000960\,A^3\,B\,a^{16}\,b^8+230262702060441600\,A^2\,B^2\,a^{17}\,b^7-45149549423616000\,A\,B^3\,a^{18}\,b^6+3319819810560000\,B^4\,a^{19}\,b^5\right)+\frac{11\,\left(17\,A\,b-5\,B\,a\right)\,\left(512439176949055488\,A^3\,a^{19}\,b^8-452152214955048960\,A^2\,B\,a^{20}\,b^7+132985945575014400\,A\,B^2\,a^{21}\,b^6-13037837801472000\,B^3\,a^{22}\,b^5\right)}{216\,{\left(-a\right)}^{23/6}\,b^{1/6}}\right)\,\left(17\,A\,b-5\,B\,a\right)}{216\,{\left(-a\right)}^{23/6}\,b^{1/6}}}\right)\,\left(17\,A\,b-5\,B\,a\right)\,11{}\mathrm{i}}{108\,{\left(-a\right)}^{23/6}\,b^{1/6}}-\frac{\mathrm{atan}\left(\frac{\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(17\,A\,b-5\,B\,a\right)\,\left(\sqrt{x}\,\left(443639472636450816\,A^4\,a^{15}\,b^9-521928791337000960\,A^3\,B\,a^{16}\,b^8+230262702060441600\,A^2\,B^2\,a^{17}\,b^7-45149549423616000\,A\,B^3\,a^{18}\,b^6+3319819810560000\,B^4\,a^{19}\,b^5\right)-\frac{11\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(17\,A\,b-5\,B\,a\right)\,\left(512439176949055488\,A^3\,a^{19}\,b^8-452152214955048960\,A^2\,B\,a^{20}\,b^7+132985945575014400\,A\,B^2\,a^{21}\,b^6-13037837801472000\,B^3\,a^{22}\,b^5\right)}{216\,{\left(-a\right)}^{23/6}\,b^{1/6}}\right)\,11{}\mathrm{i}}{216\,{\left(-a\right)}^{23/6}\,b^{1/6}}+\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(17\,A\,b-5\,B\,a\right)\,\left(\sqrt{x}\,\left(443639472636450816\,A^4\,a^{15}\,b^9-521928791337000960\,A^3\,B\,a^{16}\,b^8+230262702060441600\,A^2\,B^2\,a^{17}\,b^7-45149549423616000\,A\,B^3\,a^{18}\,b^6+3319819810560000\,B^4\,a^{19}\,b^5\right)+\frac{11\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(17\,A\,b-5\,B\,a\right)\,\left(512439176949055488\,A^3\,a^{19}\,b^8-452152214955048960\,A^2\,B\,a^{20}\,b^7+132985945575014400\,A\,B^2\,a^{21}\,b^6-13037837801472000\,B^3\,a^{22}\,b^5\right)}{216\,{\left(-a\right)}^{23/6}\,b^{1/6}}\right)\,11{}\mathrm{i}}{216\,{\left(-a\right)}^{23/6}\,b^{1/6}}}{\frac{11\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(17\,A\,b-5\,B\,a\right)\,\left(\sqrt{x}\,\left(443639472636450816\,A^4\,a^{15}\,b^9-521928791337000960\,A^3\,B\,a^{16}\,b^8+230262702060441600\,A^2\,B^2\,a^{17}\,b^7-45149549423616000\,A\,B^3\,a^{18}\,b^6+3319819810560000\,B^4\,a^{19}\,b^5\right)-\frac{11\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(17\,A\,b-5\,B\,a\right)\,\left(512439176949055488\,A^3\,a^{19}\,b^8-452152214955048960\,A^2\,B\,a^{20}\,b^7+132985945575014400\,A\,B^2\,a^{21}\,b^6-13037837801472000\,B^3\,a^{22}\,b^5\right)}{216\,{\left(-a\right)}^{23/6}\,b^{1/6}}\right)}{216\,{\left(-a\right)}^{23/6}\,b^{1/6}}-\frac{11\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(17\,A\,b-5\,B\,a\right)\,\left(\sqrt{x}\,\left(443639472636450816\,A^4\,a^{15}\,b^9-521928791337000960\,A^3\,B\,a^{16}\,b^8+230262702060441600\,A^2\,B^2\,a^{17}\,b^7-45149549423616000\,A\,B^3\,a^{18}\,b^6+3319819810560000\,B^4\,a^{19}\,b^5\right)+\frac{11\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(17\,A\,b-5\,B\,a\right)\,\left(512439176949055488\,A^3\,a^{19}\,b^8-452152214955048960\,A^2\,B\,a^{20}\,b^7+132985945575014400\,A\,B^2\,a^{21}\,b^6-13037837801472000\,B^3\,a^{22}\,b^5\right)}{216\,{\left(-a\right)}^{23/6}\,b^{1/6}}\right)}{216\,{\left(-a\right)}^{23/6}\,b^{1/6}}}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(17\,A\,b-5\,B\,a\right)\,11{}\mathrm{i}}{108\,{\left(-a\right)}^{23/6}\,b^{1/6}}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(17\,A\,b-5\,B\,a\right)\,\left(\sqrt{x}\,\left(443639472636450816\,A^4\,a^{15}\,b^9-521928791337000960\,A^3\,B\,a^{16}\,b^8+230262702060441600\,A^2\,B^2\,a^{17}\,b^7-45149549423616000\,A\,B^3\,a^{18}\,b^6+3319819810560000\,B^4\,a^{19}\,b^5\right)-\frac{11\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(17\,A\,b-5\,B\,a\right)\,\left(512439176949055488\,A^3\,a^{19}\,b^8-452152214955048960\,A^2\,B\,a^{20}\,b^7+132985945575014400\,A\,B^2\,a^{21}\,b^6-13037837801472000\,B^3\,a^{22}\,b^5\right)}{216\,{\left(-a\right)}^{23/6}\,b^{1/6}}\right)\,11{}\mathrm{i}}{216\,{\left(-a\right)}^{23/6}\,b^{1/6}}+\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(17\,A\,b-5\,B\,a\right)\,\left(\sqrt{x}\,\left(443639472636450816\,A^4\,a^{15}\,b^9-521928791337000960\,A^3\,B\,a^{16}\,b^8+230262702060441600\,A^2\,B^2\,a^{17}\,b^7-45149549423616000\,A\,B^3\,a^{18}\,b^6+3319819810560000\,B^4\,a^{19}\,b^5\right)+\frac{11\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(17\,A\,b-5\,B\,a\right)\,\left(512439176949055488\,A^3\,a^{19}\,b^8-452152214955048960\,A^2\,B\,a^{20}\,b^7+132985945575014400\,A\,B^2\,a^{21}\,b^6-13037837801472000\,B^3\,a^{22}\,b^5\right)}{216\,{\left(-a\right)}^{23/6}\,b^{1/6}}\right)\,11{}\mathrm{i}}{216\,{\left(-a\right)}^{23/6}\,b^{1/6}}}{\frac{11\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(17\,A\,b-5\,B\,a\right)\,\left(\sqrt{x}\,\left(443639472636450816\,A^4\,a^{15}\,b^9-521928791337000960\,A^3\,B\,a^{16}\,b^8+230262702060441600\,A^2\,B^2\,a^{17}\,b^7-45149549423616000\,A\,B^3\,a^{18}\,b^6+3319819810560000\,B^4\,a^{19}\,b^5\right)-\frac{11\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(17\,A\,b-5\,B\,a\right)\,\left(512439176949055488\,A^3\,a^{19}\,b^8-452152214955048960\,A^2\,B\,a^{20}\,b^7+132985945575014400\,A\,B^2\,a^{21}\,b^6-13037837801472000\,B^3\,a^{22}\,b^5\right)}{216\,{\left(-a\right)}^{23/6}\,b^{1/6}}\right)}{216\,{\left(-a\right)}^{23/6}\,b^{1/6}}-\frac{11\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(17\,A\,b-5\,B\,a\right)\,\left(\sqrt{x}\,\left(443639472636450816\,A^4\,a^{15}\,b^9-521928791337000960\,A^3\,B\,a^{16}\,b^8+230262702060441600\,A^2\,B^2\,a^{17}\,b^7-45149549423616000\,A\,B^3\,a^{18}\,b^6+3319819810560000\,B^4\,a^{19}\,b^5\right)+\frac{11\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(17\,A\,b-5\,B\,a\right)\,\left(512439176949055488\,A^3\,a^{19}\,b^8-452152214955048960\,A^2\,B\,a^{20}\,b^7+132985945575014400\,A\,B^2\,a^{21}\,b^6-13037837801472000\,B^3\,a^{22}\,b^5\right)}{216\,{\left(-a\right)}^{23/6}\,b^{1/6}}\right)}{216\,{\left(-a\right)}^{23/6}\,b^{1/6}}}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(17\,A\,b-5\,B\,a\right)\,11{}\mathrm{i}}{108\,{\left(-a\right)}^{23/6}\,b^{1/6}}","Not used",1,"- ((2*A)/(5*a) + (17*x^3*(17*A*b - 5*B*a))/(180*a^2) + (11*b*x^6*(17*A*b - 5*B*a))/(180*a^3))/(a^2*x^(5/2) + b^2*x^(17/2) + 2*a*b*x^(11/2)) - (atan((((x^(1/2)*(443639472636450816*A^4*a^15*b^9 + 3319819810560000*B^4*a^19*b^5 + 230262702060441600*A^2*B^2*a^17*b^7 - 45149549423616000*A*B^3*a^18*b^6 - 521928791337000960*A^3*B*a^16*b^8) - (11*(17*A*b - 5*B*a)*(512439176949055488*A^3*a^19*b^8 - 13037837801472000*B^3*a^22*b^5 + 132985945575014400*A*B^2*a^21*b^6 - 452152214955048960*A^2*B*a^20*b^7))/(216*(-a)^(23/6)*b^(1/6)))*(17*A*b - 5*B*a)*11i)/(216*(-a)^(23/6)*b^(1/6)) + ((x^(1/2)*(443639472636450816*A^4*a^15*b^9 + 3319819810560000*B^4*a^19*b^5 + 230262702060441600*A^2*B^2*a^17*b^7 - 45149549423616000*A*B^3*a^18*b^6 - 521928791337000960*A^3*B*a^16*b^8) + (11*(17*A*b - 5*B*a)*(512439176949055488*A^3*a^19*b^8 - 13037837801472000*B^3*a^22*b^5 + 132985945575014400*A*B^2*a^21*b^6 - 452152214955048960*A^2*B*a^20*b^7))/(216*(-a)^(23/6)*b^(1/6)))*(17*A*b - 5*B*a)*11i)/(216*(-a)^(23/6)*b^(1/6)))/((11*(x^(1/2)*(443639472636450816*A^4*a^15*b^9 + 3319819810560000*B^4*a^19*b^5 + 230262702060441600*A^2*B^2*a^17*b^7 - 45149549423616000*A*B^3*a^18*b^6 - 521928791337000960*A^3*B*a^16*b^8) - (11*(17*A*b - 5*B*a)*(512439176949055488*A^3*a^19*b^8 - 13037837801472000*B^3*a^22*b^5 + 132985945575014400*A*B^2*a^21*b^6 - 452152214955048960*A^2*B*a^20*b^7))/(216*(-a)^(23/6)*b^(1/6)))*(17*A*b - 5*B*a))/(216*(-a)^(23/6)*b^(1/6)) - (11*(x^(1/2)*(443639472636450816*A^4*a^15*b^9 + 3319819810560000*B^4*a^19*b^5 + 230262702060441600*A^2*B^2*a^17*b^7 - 45149549423616000*A*B^3*a^18*b^6 - 521928791337000960*A^3*B*a^16*b^8) + (11*(17*A*b - 5*B*a)*(512439176949055488*A^3*a^19*b^8 - 13037837801472000*B^3*a^22*b^5 + 132985945575014400*A*B^2*a^21*b^6 - 452152214955048960*A^2*B*a^20*b^7))/(216*(-a)^(23/6)*b^(1/6)))*(17*A*b - 5*B*a))/(216*(-a)^(23/6)*b^(1/6))))*(17*A*b - 5*B*a)*11i)/(108*(-a)^(23/6)*b^(1/6)) - (atan(((((3^(1/2)*1i)/2 - 1/2)*(17*A*b - 5*B*a)*(x^(1/2)*(443639472636450816*A^4*a^15*b^9 + 3319819810560000*B^4*a^19*b^5 + 230262702060441600*A^2*B^2*a^17*b^7 - 45149549423616000*A*B^3*a^18*b^6 - 521928791337000960*A^3*B*a^16*b^8) - (11*((3^(1/2)*1i)/2 - 1/2)*(17*A*b - 5*B*a)*(512439176949055488*A^3*a^19*b^8 - 13037837801472000*B^3*a^22*b^5 + 132985945575014400*A*B^2*a^21*b^6 - 452152214955048960*A^2*B*a^20*b^7))/(216*(-a)^(23/6)*b^(1/6)))*11i)/(216*(-a)^(23/6)*b^(1/6)) + (((3^(1/2)*1i)/2 - 1/2)*(17*A*b - 5*B*a)*(x^(1/2)*(443639472636450816*A^4*a^15*b^9 + 3319819810560000*B^4*a^19*b^5 + 230262702060441600*A^2*B^2*a^17*b^7 - 45149549423616000*A*B^3*a^18*b^6 - 521928791337000960*A^3*B*a^16*b^8) + (11*((3^(1/2)*1i)/2 - 1/2)*(17*A*b - 5*B*a)*(512439176949055488*A^3*a^19*b^8 - 13037837801472000*B^3*a^22*b^5 + 132985945575014400*A*B^2*a^21*b^6 - 452152214955048960*A^2*B*a^20*b^7))/(216*(-a)^(23/6)*b^(1/6)))*11i)/(216*(-a)^(23/6)*b^(1/6)))/((11*((3^(1/2)*1i)/2 - 1/2)*(17*A*b - 5*B*a)*(x^(1/2)*(443639472636450816*A^4*a^15*b^9 + 3319819810560000*B^4*a^19*b^5 + 230262702060441600*A^2*B^2*a^17*b^7 - 45149549423616000*A*B^3*a^18*b^6 - 521928791337000960*A^3*B*a^16*b^8) - (11*((3^(1/2)*1i)/2 - 1/2)*(17*A*b - 5*B*a)*(512439176949055488*A^3*a^19*b^8 - 13037837801472000*B^3*a^22*b^5 + 132985945575014400*A*B^2*a^21*b^6 - 452152214955048960*A^2*B*a^20*b^7))/(216*(-a)^(23/6)*b^(1/6))))/(216*(-a)^(23/6)*b^(1/6)) - (11*((3^(1/2)*1i)/2 - 1/2)*(17*A*b - 5*B*a)*(x^(1/2)*(443639472636450816*A^4*a^15*b^9 + 3319819810560000*B^4*a^19*b^5 + 230262702060441600*A^2*B^2*a^17*b^7 - 45149549423616000*A*B^3*a^18*b^6 - 521928791337000960*A^3*B*a^16*b^8) + (11*((3^(1/2)*1i)/2 - 1/2)*(17*A*b - 5*B*a)*(512439176949055488*A^3*a^19*b^8 - 13037837801472000*B^3*a^22*b^5 + 132985945575014400*A*B^2*a^21*b^6 - 452152214955048960*A^2*B*a^20*b^7))/(216*(-a)^(23/6)*b^(1/6))))/(216*(-a)^(23/6)*b^(1/6))))*((3^(1/2)*1i)/2 - 1/2)*(17*A*b - 5*B*a)*11i)/(108*(-a)^(23/6)*b^(1/6)) - (atan(((((3^(1/2)*1i)/2 + 1/2)*(17*A*b - 5*B*a)*(x^(1/2)*(443639472636450816*A^4*a^15*b^9 + 3319819810560000*B^4*a^19*b^5 + 230262702060441600*A^2*B^2*a^17*b^7 - 45149549423616000*A*B^3*a^18*b^6 - 521928791337000960*A^3*B*a^16*b^8) - (11*((3^(1/2)*1i)/2 + 1/2)*(17*A*b - 5*B*a)*(512439176949055488*A^3*a^19*b^8 - 13037837801472000*B^3*a^22*b^5 + 132985945575014400*A*B^2*a^21*b^6 - 452152214955048960*A^2*B*a^20*b^7))/(216*(-a)^(23/6)*b^(1/6)))*11i)/(216*(-a)^(23/6)*b^(1/6)) + (((3^(1/2)*1i)/2 + 1/2)*(17*A*b - 5*B*a)*(x^(1/2)*(443639472636450816*A^4*a^15*b^9 + 3319819810560000*B^4*a^19*b^5 + 230262702060441600*A^2*B^2*a^17*b^7 - 45149549423616000*A*B^3*a^18*b^6 - 521928791337000960*A^3*B*a^16*b^8) + (11*((3^(1/2)*1i)/2 + 1/2)*(17*A*b - 5*B*a)*(512439176949055488*A^3*a^19*b^8 - 13037837801472000*B^3*a^22*b^5 + 132985945575014400*A*B^2*a^21*b^6 - 452152214955048960*A^2*B*a^20*b^7))/(216*(-a)^(23/6)*b^(1/6)))*11i)/(216*(-a)^(23/6)*b^(1/6)))/((11*((3^(1/2)*1i)/2 + 1/2)*(17*A*b - 5*B*a)*(x^(1/2)*(443639472636450816*A^4*a^15*b^9 + 3319819810560000*B^4*a^19*b^5 + 230262702060441600*A^2*B^2*a^17*b^7 - 45149549423616000*A*B^3*a^18*b^6 - 521928791337000960*A^3*B*a^16*b^8) - (11*((3^(1/2)*1i)/2 + 1/2)*(17*A*b - 5*B*a)*(512439176949055488*A^3*a^19*b^8 - 13037837801472000*B^3*a^22*b^5 + 132985945575014400*A*B^2*a^21*b^6 - 452152214955048960*A^2*B*a^20*b^7))/(216*(-a)^(23/6)*b^(1/6))))/(216*(-a)^(23/6)*b^(1/6)) - (11*((3^(1/2)*1i)/2 + 1/2)*(17*A*b - 5*B*a)*(x^(1/2)*(443639472636450816*A^4*a^15*b^9 + 3319819810560000*B^4*a^19*b^5 + 230262702060441600*A^2*B^2*a^17*b^7 - 45149549423616000*A*B^3*a^18*b^6 - 521928791337000960*A^3*B*a^16*b^8) + (11*((3^(1/2)*1i)/2 + 1/2)*(17*A*b - 5*B*a)*(512439176949055488*A^3*a^19*b^8 - 13037837801472000*B^3*a^22*b^5 + 132985945575014400*A*B^2*a^21*b^6 - 452152214955048960*A^2*B*a^20*b^7))/(216*(-a)^(23/6)*b^(1/6))))/(216*(-a)^(23/6)*b^(1/6))))*((3^(1/2)*1i)/2 + 1/2)*(17*A*b - 5*B*a)*11i)/(108*(-a)^(23/6)*b^(1/6))","B"
179,1,154,103,2.716913,"\text{Not used}","int(x^8*(A + B*x^3)*(a + b*x^3)^(1/2),x)","\frac{2\,B\,x^{12}\,\sqrt{b\,x^3+a}}{27}+\frac{x^9\,\sqrt{b\,x^3+a}\,\left(2\,A\,b+\frac{2\,B\,a}{9}\right)}{21\,b}+\frac{8\,a^2\,\left(2\,A\,a-\frac{6\,a\,\left(2\,A\,b+\frac{2\,B\,a}{9}\right)}{7\,b}\right)\,\sqrt{b\,x^3+a}}{45\,b^3}+\frac{x^6\,\left(2\,A\,a-\frac{6\,a\,\left(2\,A\,b+\frac{2\,B\,a}{9}\right)}{7\,b}\right)\,\sqrt{b\,x^3+a}}{15\,b}-\frac{4\,a\,x^3\,\left(2\,A\,a-\frac{6\,a\,\left(2\,A\,b+\frac{2\,B\,a}{9}\right)}{7\,b}\right)\,\sqrt{b\,x^3+a}}{45\,b^2}","Not used",1,"(2*B*x^12*(a + b*x^3)^(1/2))/27 + (x^9*(a + b*x^3)^(1/2)*(2*A*b + (2*B*a)/9))/(21*b) + (8*a^2*(2*A*a - (6*a*(2*A*b + (2*B*a)/9))/(7*b))*(a + b*x^3)^(1/2))/(45*b^3) + (x^6*(2*A*a - (6*a*(2*A*b + (2*B*a)/9))/(7*b))*(a + b*x^3)^(1/2))/(15*b) - (4*a*x^3*(2*A*a - (6*a*(2*A*b + (2*B*a)/9))/(7*b))*(a + b*x^3)^(1/2))/(45*b^2)","B"
180,1,114,73,2.662291,"\text{Not used}","int(x^5*(A + B*x^3)*(a + b*x^3)^(1/2),x)","\frac{2\,B\,x^9\,\sqrt{b\,x^3+a}}{21}+\frac{x^6\,\sqrt{b\,x^3+a}\,\left(2\,A\,b+\frac{2\,B\,a}{7}\right)}{15\,b}-\frac{2\,a\,\left(2\,A\,a-\frac{4\,a\,\left(2\,A\,b+\frac{2\,B\,a}{7}\right)}{5\,b}\right)\,\sqrt{b\,x^3+a}}{9\,b^2}+\frac{x^3\,\left(2\,A\,a-\frac{4\,a\,\left(2\,A\,b+\frac{2\,B\,a}{7}\right)}{5\,b}\right)\,\sqrt{b\,x^3+a}}{9\,b}","Not used",1,"(2*B*x^9*(a + b*x^3)^(1/2))/21 + (x^6*(a + b*x^3)^(1/2)*(2*A*b + (2*B*a)/7))/(15*b) - (2*a*(2*A*a - (4*a*(2*A*b + (2*B*a)/7))/(5*b))*(a + b*x^3)^(1/2))/(9*b^2) + (x^3*(2*A*a - (4*a*(2*A*b + (2*B*a)/7))/(5*b))*(a + b*x^3)^(1/2))/(9*b)","B"
181,1,44,46,2.598390,"\text{Not used}","int(x^2*(A + B*x^3)*(a + b*x^3)^(1/2),x)","\frac{6\,B\,{\left(b\,x^3+a\right)}^{5/2}+10\,A\,b\,{\left(b\,x^3+a\right)}^{3/2}-10\,B\,a\,{\left(b\,x^3+a\right)}^{3/2}}{45\,b^2}","Not used",1,"(6*B*(a + b*x^3)^(5/2) + 10*A*b*(a + b*x^3)^(3/2) - 10*B*a*(a + b*x^3)^(3/2))/(45*b^2)","B"
182,1,80,64,2.714417,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^(1/2))/x,x)","\frac{2\,B\,x^3\,\sqrt{b\,x^3+a}}{9}+\frac{\sqrt{b\,x^3+a}\,\left(2\,A\,b+\frac{2\,B\,a}{3}\right)}{3\,b}+\frac{A\,\sqrt{a}\,\ln\left(\frac{{\left(\sqrt{b\,x^3+a}-\sqrt{a}\right)}^3\,\left(\sqrt{b\,x^3+a}+\sqrt{a}\right)}{x^6}\right)}{3}","Not used",1,"(2*B*x^3*(a + b*x^3)^(1/2))/9 + ((a + b*x^3)^(1/2)*(2*A*b + (2*B*a)/3))/(3*b) + (A*a^(1/2)*log((((a + b*x^3)^(1/2) - a^(1/2))^3*((a + b*x^3)^(1/2) + a^(1/2)))/x^6))/3","B"
183,1,76,84,2.933143,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^(1/2))/x^4,x)","\frac{2\,B\,\sqrt{b\,x^3+a}}{3}-\frac{A\,\sqrt{b\,x^3+a}}{3\,x^3}+\frac{\ln\left(\frac{{\left(\sqrt{b\,x^3+a}-\sqrt{a}\right)}^3\,\left(\sqrt{b\,x^3+a}+\sqrt{a}\right)}{x^6}\right)\,\left(\frac{A\,b}{2}+B\,a\right)}{3\,\sqrt{a}}","Not used",1,"(2*B*(a + b*x^3)^(1/2))/3 - (A*(a + b*x^3)^(1/2))/(3*x^3) + (log((((a + b*x^3)^(1/2) - a^(1/2))^3*((a + b*x^3)^(1/2) + a^(1/2)))/x^6)*((A*b)/2 + B*a))/(3*a^(1/2))","B"
184,1,93,88,3.118991,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^(1/2))/x^7,x)","\frac{b\,\ln\left(\frac{\left(\sqrt{b\,x^3+a}-\sqrt{a}\right)\,{\left(\sqrt{b\,x^3+a}+\sqrt{a}\right)}^3}{x^6}\right)\,\left(A\,b-4\,B\,a\right)}{24\,a^{3/2}}-\frac{\left(4\,B\,a^2+A\,b\,a\right)\,\sqrt{b\,x^3+a}}{12\,a^2\,x^3}-\frac{A\,\sqrt{b\,x^3+a}}{6\,x^6}","Not used",1,"(b*log((((a + b*x^3)^(1/2) - a^(1/2))*((a + b*x^3)^(1/2) + a^(1/2))^3)/x^6)*(A*b - 4*B*a))/(24*a^(3/2)) - ((4*B*a^2 + A*a*b)*(a + b*x^3)^(1/2))/(12*a^2*x^3) - (A*(a + b*x^3)^(1/2))/(6*x^6)","B"
185,0,-1,303,0.000000,"\text{Not used}","int(x^3*(A + B*x^3)*(a + b*x^3)^(1/2),x)","\int x^3\,\left(B\,x^3+A\right)\,\sqrt{b\,x^3+a} \,d x","Not used",1,"int(x^3*(A + B*x^3)*(a + b*x^3)^(1/2), x)","F"
186,0,-1,268,0.000000,"\text{Not used}","int((A + B*x^3)*(a + b*x^3)^(1/2),x)","\int \left(B\,x^3+A\right)\,\sqrt{b\,x^3+a} \,d x","Not used",1,"int((A + B*x^3)*(a + b*x^3)^(1/2), x)","F"
187,0,-1,269,0.000000,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^(1/2))/x^3,x)","\int \frac{\left(B\,x^3+A\right)\,\sqrt{b\,x^3+a}}{x^3} \,d x","Not used",1,"int(((A + B*x^3)*(a + b*x^3)^(1/2))/x^3, x)","F"
188,0,-1,272,0.000000,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^(1/2))/x^6,x)","\int \frac{\left(B\,x^3+A\right)\,\sqrt{b\,x^3+a}}{x^6} \,d x","Not used",1,"int(((A + B*x^3)*(a + b*x^3)^(1/2))/x^6, x)","F"
189,0,-1,305,0.000000,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^(1/2))/x^9,x)","\int \frac{\left(B\,x^3+A\right)\,\sqrt{b\,x^3+a}}{x^9} \,d x","Not used",1,"int(((A + B*x^3)*(a + b*x^3)^(1/2))/x^9, x)","F"
190,0,-1,581,0.000000,"\text{Not used}","int(x^4*(A + B*x^3)*(a + b*x^3)^(1/2),x)","\int x^4\,\left(B\,x^3+A\right)\,\sqrt{b\,x^3+a} \,d x","Not used",1,"int(x^4*(A + B*x^3)*(a + b*x^3)^(1/2), x)","F"
191,0,-1,548,0.000000,"\text{Not used}","int(x*(A + B*x^3)*(a + b*x^3)^(1/2),x)","\int x\,\left(B\,x^3+A\right)\,\sqrt{b\,x^3+a} \,d x","Not used",1,"int(x*(A + B*x^3)*(a + b*x^3)^(1/2), x)","F"
192,0,-1,545,0.000000,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^(1/2))/x^2,x)","\int \frac{\left(B\,x^3+A\right)\,\sqrt{b\,x^3+a}}{x^2} \,d x","Not used",1,"int(((A + B*x^3)*(a + b*x^3)^(1/2))/x^2, x)","F"
193,0,-1,546,0.000000,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^(1/2))/x^5,x)","\int \frac{\left(B\,x^3+A\right)\,\sqrt{b\,x^3+a}}{x^5} \,d x","Not used",1,"int(((A + B*x^3)*(a + b*x^3)^(1/2))/x^5, x)","F"
194,0,-1,581,0.000000,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^(1/2))/x^8,x)","\int \frac{\left(B\,x^3+A\right)\,\sqrt{b\,x^3+a}}{x^8} \,d x","Not used",1,"int(((A + B*x^3)*(a + b*x^3)^(1/2))/x^8, x)","F"
195,0,-1,614,0.000000,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^(1/2))/x^11,x)","\int \frac{\left(B\,x^3+A\right)\,\sqrt{b\,x^3+a}}{x^{11}} \,d x","Not used",1,"int(((A + B*x^3)*(a + b*x^3)^(1/2))/x^11, x)","F"
196,1,206,103,2.654743,"\text{Not used}","int(x^8*(A + B*x^3)*(a + b*x^3)^(3/2),x)","\frac{20\,A\,a\,x^9\,\sqrt{b\,x^3+a}}{189}+\frac{2\,A\,b\,x^{12}\,\sqrt{b\,x^3+a}}{27}+\frac{8\,B\,a\,x^{12}\,\sqrt{b\,x^3+a}}{99}+\frac{2\,B\,b\,x^{15}\,\sqrt{b\,x^3+a}}{33}+\frac{16\,A\,a^4\,\sqrt{b\,x^3+a}}{945\,b^3}-\frac{32\,B\,a^5\,\sqrt{b\,x^3+a}}{3465\,b^4}-\frac{8\,A\,a^3\,x^3\,\sqrt{b\,x^3+a}}{945\,b^2}+\frac{2\,A\,a^2\,x^6\,\sqrt{b\,x^3+a}}{315\,b}+\frac{16\,B\,a^4\,x^3\,\sqrt{b\,x^3+a}}{3465\,b^3}-\frac{4\,B\,a^3\,x^6\,\sqrt{b\,x^3+a}}{1155\,b^2}+\frac{2\,B\,a^2\,x^9\,\sqrt{b\,x^3+a}}{693\,b}","Not used",1,"(20*A*a*x^9*(a + b*x^3)^(1/2))/189 + (2*A*b*x^12*(a + b*x^3)^(1/2))/27 + (8*B*a*x^12*(a + b*x^3)^(1/2))/99 + (2*B*b*x^15*(a + b*x^3)^(1/2))/33 + (16*A*a^4*(a + b*x^3)^(1/2))/(945*b^3) - (32*B*a^5*(a + b*x^3)^(1/2))/(3465*b^4) - (8*A*a^3*x^3*(a + b*x^3)^(1/2))/(945*b^2) + (2*A*a^2*x^6*(a + b*x^3)^(1/2))/(315*b) + (16*B*a^4*x^3*(a + b*x^3)^(1/2))/(3465*b^3) - (4*B*a^3*x^6*(a + b*x^3)^(1/2))/(1155*b^2) + (2*B*a^2*x^9*(a + b*x^3)^(1/2))/(693*b)","B"
197,1,211,73,2.715406,"\text{Not used}","int(x^5*(A + B*x^3)*(a + b*x^3)^(3/2),x)","\frac{x^6\,\sqrt{b\,x^3+a}\,\left(2\,B\,a^2+4\,A\,a\,b-\frac{6\,a\,\left(2\,A\,b^2+\frac{20\,B\,a\,b}{9}\right)}{7\,b}\right)}{15\,b}-\frac{2\,a\,\left(2\,A\,a^2-\frac{4\,a\,\left(2\,B\,a^2+4\,A\,a\,b-\frac{6\,a\,\left(2\,A\,b^2+\frac{20\,B\,a\,b}{9}\right)}{7\,b}\right)}{5\,b}\right)\,\sqrt{b\,x^3+a}}{9\,b^2}+\frac{2\,B\,b\,x^{12}\,\sqrt{b\,x^3+a}}{27}+\frac{x^3\,\left(2\,A\,a^2-\frac{4\,a\,\left(2\,B\,a^2+4\,A\,a\,b-\frac{6\,a\,\left(2\,A\,b^2+\frac{20\,B\,a\,b}{9}\right)}{7\,b}\right)}{5\,b}\right)\,\sqrt{b\,x^3+a}}{9\,b}+\frac{x^9\,\left(2\,A\,b^2+\frac{20\,B\,a\,b}{9}\right)\,\sqrt{b\,x^3+a}}{21\,b}","Not used",1,"(x^6*(a + b*x^3)^(1/2)*(2*B*a^2 + 4*A*a*b - (6*a*(2*A*b^2 + (20*B*a*b)/9))/(7*b)))/(15*b) - (2*a*(2*A*a^2 - (4*a*(2*B*a^2 + 4*A*a*b - (6*a*(2*A*b^2 + (20*B*a*b)/9))/(7*b)))/(5*b))*(a + b*x^3)^(1/2))/(9*b^2) + (2*B*b*x^12*(a + b*x^3)^(1/2))/27 + (x^3*(2*A*a^2 - (4*a*(2*B*a^2 + 4*A*a*b - (6*a*(2*A*b^2 + (20*B*a*b)/9))/(7*b)))/(5*b))*(a + b*x^3)^(1/2))/(9*b) + (x^9*(2*A*b^2 + (20*B*a*b)/9)*(a + b*x^3)^(1/2))/(21*b)","B"
198,1,150,46,3.346145,"\text{Not used}","int(x^2*(A + B*x^3)*(a + b*x^3)^(3/2),x)","\frac{\left(2\,A\,a^2-\frac{2\,a\,\left(2\,B\,a^2+4\,A\,a\,b-\frac{4\,a\,\left(2\,A\,b^2+\frac{16\,B\,a\,b}{7}\right)}{5\,b}\right)}{3\,b}\right)\,\sqrt{b\,x^3+a}}{3\,b}+\frac{x^3\,\sqrt{b\,x^3+a}\,\left(2\,B\,a^2+4\,A\,a\,b-\frac{4\,a\,\left(2\,A\,b^2+\frac{16\,B\,a\,b}{7}\right)}{5\,b}\right)}{9\,b}+\frac{2\,B\,b\,x^9\,\sqrt{b\,x^3+a}}{21}+\frac{x^6\,\left(2\,A\,b^2+\frac{16\,B\,a\,b}{7}\right)\,\sqrt{b\,x^3+a}}{15\,b}","Not used",1,"((2*A*a^2 - (2*a*(2*B*a^2 + 4*A*a*b - (4*a*(2*A*b^2 + (16*B*a*b)/7))/(5*b)))/(3*b))*(a + b*x^3)^(1/2))/(3*b) + (x^3*(a + b*x^3)^(1/2)*(2*B*a^2 + 4*A*a*b - (4*a*(2*A*b^2 + (16*B*a*b)/7))/(5*b)))/(9*b) + (2*B*b*x^9*(a + b*x^3)^(1/2))/21 + (x^6*(2*A*b^2 + (16*B*a*b)/7)*(a + b*x^3)^(1/2))/(15*b)","B"
199,1,131,81,2.792565,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^(3/2))/x,x)","\frac{A\,a^{3/2}\,\ln\left(\frac{{\left(\sqrt{b\,x^3+a}-\sqrt{a}\right)}^3\,\left(\sqrt{b\,x^3+a}+\sqrt{a}\right)}{x^6}\right)}{3}+\frac{\sqrt{b\,x^3+a}\,\left(2\,B\,a^2+4\,A\,a\,b-\frac{2\,a\,\left(2\,A\,b^2+\frac{12\,B\,a\,b}{5}\right)}{3\,b}\right)}{3\,b}+\frac{2\,B\,b\,x^6\,\sqrt{b\,x^3+a}}{15}+\frac{x^3\,\left(2\,A\,b^2+\frac{12\,B\,a\,b}{5}\right)\,\sqrt{b\,x^3+a}}{9\,b}","Not used",1,"(A*a^(3/2)*log((((a + b*x^3)^(1/2) - a^(1/2))^3*((a + b*x^3)^(1/2) + a^(1/2)))/x^6))/3 + ((a + b*x^3)^(1/2)*(2*B*a^2 + 4*A*a*b - (2*a*(2*A*b^2 + (12*B*a*b)/5))/(3*b)))/(3*b) + (2*B*b*x^6*(a + b*x^3)^(1/2))/15 + (x^3*(2*A*b^2 + (12*B*a*b)/5)*(a + b*x^3)^(1/2))/(9*b)","B"
200,1,111,110,3.378865,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^(3/2))/x^4,x)","\frac{\ln\left(\frac{{\left(\sqrt{b\,x^3+a}-\sqrt{a}\right)}^3\,\left(\sqrt{b\,x^3+a}+\sqrt{a}\right)}{x^6}\right)\,\left(3\,A\,b+2\,B\,a\right)\,\sqrt{\frac{a}{4}}}{3}+\frac{\left(2\,A\,b^2+\frac{8\,B\,a\,b}{3}\right)\,\sqrt{b\,x^3+a}}{3\,b}-\frac{A\,a\,\sqrt{b\,x^3+a}}{3\,x^3}+\frac{2\,B\,b\,x^3\,\sqrt{b\,x^3+a}}{9}","Not used",1,"(log((((a + b*x^3)^(1/2) - a^(1/2))^3*((a + b*x^3)^(1/2) + a^(1/2)))/x^6)*(3*A*b + 2*B*a)*(a/4)^(1/2))/3 + ((2*A*b^2 + (8*B*a*b)/3)*(a + b*x^3)^(1/2))/(3*b) - (A*a*(a + b*x^3)^(1/2))/(3*x^3) + (2*B*b*x^3*(a + b*x^3)^(1/2))/9","B"
201,1,110,115,3.472478,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^(3/2))/x^7,x)","\frac{2\,B\,b\,\sqrt{b\,x^3+a}}{3}-\frac{\sqrt{b\,x^3+a}\,\left(4\,B\,a^3+5\,A\,b\,a^2\right)}{12\,a^2\,x^3}-\frac{A\,a\,\sqrt{b\,x^3+a}}{6\,x^6}+\frac{b\,\ln\left(\frac{{\left(\sqrt{b\,x^3+a}-\sqrt{a}\right)}^3\,\left(\sqrt{b\,x^3+a}+\sqrt{a}\right)}{x^6}\right)\,\left(A\,b+4\,B\,a\right)}{8\,\sqrt{a}}","Not used",1,"(2*B*b*(a + b*x^3)^(1/2))/3 - ((a + b*x^3)^(1/2)*(4*B*a^3 + 5*A*a^2*b))/(12*a^2*x^3) - (A*a*(a + b*x^3)^(1/2))/(6*x^6) + (b*log((((a + b*x^3)^(1/2) - a^(1/2))^3*((a + b*x^3)^(1/2) + a^(1/2)))/x^6)*(A*b + 4*B*a))/(8*a^(1/2))","B"
202,0,-1,336,0.000000,"\text{Not used}","int(x^3*(A + B*x^3)*(a + b*x^3)^(3/2),x)","\int x^3\,\left(B\,x^3+A\right)\,{\left(b\,x^3+a\right)}^{3/2} \,d x","Not used",1,"int(x^3*(A + B*x^3)*(a + b*x^3)^(3/2), x)","F"
203,0,-1,299,0.000000,"\text{Not used}","int((A + B*x^3)*(a + b*x^3)^(3/2),x)","\int \left(B\,x^3+A\right)\,{\left(b\,x^3+a\right)}^{3/2} \,d x","Not used",1,"int((A + B*x^3)*(a + b*x^3)^(3/2), x)","F"
204,0,-1,295,0.000000,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^(3/2))/x^3,x)","\int \frac{\left(B\,x^3+A\right)\,{\left(b\,x^3+a\right)}^{3/2}}{x^3} \,d x","Not used",1,"int(((A + B*x^3)*(a + b*x^3)^(3/2))/x^3, x)","F"
205,0,-1,297,0.000000,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^(3/2))/x^6,x)","\int \frac{\left(B\,x^3+A\right)\,{\left(b\,x^3+a\right)}^{3/2}}{x^6} \,d x","Not used",1,"int(((A + B*x^3)*(a + b*x^3)^(3/2))/x^6, x)","F"
206,0,-1,302,0.000000,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^(3/2))/x^9,x)","\int \frac{\left(B\,x^3+A\right)\,{\left(b\,x^3+a\right)}^{3/2}}{x^9} \,d x","Not used",1,"int(((A + B*x^3)*(a + b*x^3)^(3/2))/x^9, x)","F"
207,0,-1,614,0.000000,"\text{Not used}","int(x^4*(A + B*x^3)*(a + b*x^3)^(3/2),x)","\int x^4\,\left(B\,x^3+A\right)\,{\left(b\,x^3+a\right)}^{3/2} \,d x","Not used",1,"int(x^4*(A + B*x^3)*(a + b*x^3)^(3/2), x)","F"
208,0,-1,581,0.000000,"\text{Not used}","int(x*(A + B*x^3)*(a + b*x^3)^(3/2),x)","\int x\,\left(B\,x^3+A\right)\,{\left(b\,x^3+a\right)}^{3/2} \,d x","Not used",1,"int(x*(A + B*x^3)*(a + b*x^3)^(3/2), x)","F"
209,0,-1,573,0.000000,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^(3/2))/x^2,x)","\int \frac{\left(B\,x^3+A\right)\,{\left(b\,x^3+a\right)}^{3/2}}{x^2} \,d x","Not used",1,"int(((A + B*x^3)*(a + b*x^3)^(3/2))/x^2, x)","F"
210,0,-1,578,0.000000,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^(3/2))/x^5,x)","\int \frac{\left(B\,x^3+A\right)\,{\left(b\,x^3+a\right)}^{3/2}}{x^5} \,d x","Not used",1,"int(((A + B*x^3)*(a + b*x^3)^(3/2))/x^5, x)","F"
211,0,-1,576,0.000000,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^(3/2))/x^8,x)","\int \frac{\left(B\,x^3+A\right)\,{\left(b\,x^3+a\right)}^{3/2}}{x^8} \,d x","Not used",1,"int(((A + B*x^3)*(a + b*x^3)^(3/2))/x^8, x)","F"
212,0,-1,608,0.000000,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^(3/2))/x^11,x)","\int \frac{\left(B\,x^3+A\right)\,{\left(b\,x^3+a\right)}^{3/2}}{x^{11}} \,d x","Not used",1,"int(((A + B*x^3)*(a + b*x^3)^(3/2))/x^11, x)","F"
213,1,104,103,2.675766,"\text{Not used}","int((x^8*(A + B*x^3))/(a + b*x^3)^(1/2),x)","\frac{8\,a^2\,\sqrt{b\,x^3+a}\,\left(2\,A-\frac{12\,B\,a}{7\,b}\right)}{45\,b^3}+\frac{x^6\,\sqrt{b\,x^3+a}\,\left(2\,A-\frac{12\,B\,a}{7\,b}\right)}{15\,b}+\frac{2\,B\,x^9\,\sqrt{b\,x^3+a}}{21\,b}-\frac{4\,a\,x^3\,\sqrt{b\,x^3+a}\,\left(2\,A-\frac{12\,B\,a}{7\,b}\right)}{45\,b^2}","Not used",1,"(8*a^2*(a + b*x^3)^(1/2)*(2*A - (12*B*a)/(7*b)))/(45*b^3) + (x^6*(a + b*x^3)^(1/2)*(2*A - (12*B*a)/(7*b)))/(15*b) + (2*B*x^9*(a + b*x^3)^(1/2))/(21*b) - (4*a*x^3*(a + b*x^3)^(1/2)*(2*A - (12*B*a)/(7*b)))/(45*b^2)","B"
214,1,52,73,2.649350,"\text{Not used}","int((x^5*(A + B*x^3))/(a + b*x^3)^(1/2),x)","\frac{2\,\sqrt{b\,x^3+a}\,\left(8\,B\,a^2-4\,B\,a\,b\,x^3-10\,A\,a\,b+3\,B\,b^2\,x^6+5\,A\,b^2\,x^3\right)}{45\,b^3}","Not used",1,"(2*(a + b*x^3)^(1/2)*(8*B*a^2 + 5*A*b^2*x^3 + 3*B*b^2*x^6 - 10*A*a*b - 4*B*a*b*x^3))/(45*b^3)","B"
215,1,29,46,2.604423,"\text{Not used}","int((x^2*(A + B*x^3))/(a + b*x^3)^(1/2),x)","\frac{2\,\sqrt{b\,x^3+a}\,\left(B\,b\,x^3+3\,A\,b-2\,B\,a\right)}{9\,b^2}","Not used",1,"(2*(a + b*x^3)^(1/2)*(3*A*b - 2*B*a + B*b*x^3))/(9*b^2)","B"
216,1,57,48,2.715430,"\text{Not used}","int((A + B*x^3)/(x*(a + b*x^3)^(1/2)),x)","\frac{2\,B\,\sqrt{b\,x^3+a}}{3\,b}+\frac{A\,\ln\left(\frac{{\left(\sqrt{b\,x^3+a}-\sqrt{a}\right)}^3\,\left(\sqrt{b\,x^3+a}+\sqrt{a}\right)}{x^6}\right)}{3\,\sqrt{a}}","Not used",1,"(2*B*(a + b*x^3)^(1/2))/(3*b) + (A*log((((a + b*x^3)^(1/2) - a^(1/2))^3*((a + b*x^3)^(1/2) + a^(1/2)))/x^6))/(3*a^(1/2))","B"
217,1,67,58,2.893950,"\text{Not used}","int((A + B*x^3)/(x^4*(a + b*x^3)^(1/2)),x)","\frac{\ln\left(\frac{\left(\sqrt{b\,x^3+a}-\sqrt{a}\right)\,{\left(\sqrt{b\,x^3+a}+\sqrt{a}\right)}^3}{x^6}\right)\,\left(A\,b-2\,B\,a\right)}{6\,a^{3/2}}-\frac{A\,\sqrt{b\,x^3+a}}{3\,a\,x^3}","Not used",1,"(log((((a + b*x^3)^(1/2) - a^(1/2))*((a + b*x^3)^(1/2) + a^(1/2))^3)/x^6)*(A*b - 2*B*a))/(6*a^(3/2)) - (A*(a + b*x^3)^(1/2))/(3*a*x^3)","B"
218,1,95,90,2.994663,"\text{Not used}","int((A + B*x^3)/(x^7*(a + b*x^3)^(1/2)),x)","\frac{\sqrt{b\,x^3+a}\,\left(3\,A\,b-4\,B\,a\right)}{12\,a^2\,x^3}-\frac{A\,\sqrt{b\,x^3+a}}{6\,a\,x^6}+\frac{b\,\ln\left(\frac{{\left(\sqrt{b\,x^3+a}-\sqrt{a}\right)}^3\,\left(\sqrt{b\,x^3+a}+\sqrt{a}\right)}{x^6}\right)\,\left(3\,A\,b-4\,B\,a\right)}{24\,a^{5/2}}","Not used",1,"((a + b*x^3)^(1/2)*(3*A*b - 4*B*a))/(12*a^2*x^3) - (A*(a + b*x^3)^(1/2))/(6*a*x^6) + (b*log((((a + b*x^3)^(1/2) - a^(1/2))^3*((a + b*x^3)^(1/2) + a^(1/2)))/x^6)*(3*A*b - 4*B*a))/(24*a^(5/2))","B"
219,0,-1,270,0.000000,"\text{Not used}","int((x^3*(A + B*x^3))/(a + b*x^3)^(1/2),x)","\int \frac{x^3\,\left(B\,x^3+A\right)}{\sqrt{b\,x^3+a}} \,d x","Not used",1,"int((x^3*(A + B*x^3))/(a + b*x^3)^(1/2), x)","F"
220,0,-1,239,0.000000,"\text{Not used}","int((A + B*x^3)/(a + b*x^3)^(1/2),x)","\int \frac{B\,x^3+A}{\sqrt{b\,x^3+a}} \,d x","Not used",1,"int((A + B*x^3)/(a + b*x^3)^(1/2), x)","F"
221,0,-1,243,0.000000,"\text{Not used}","int((A + B*x^3)/(x^3*(a + b*x^3)^(1/2)),x)","\int \frac{B\,x^3+A}{x^3\,\sqrt{b\,x^3+a}} \,d x","Not used",1,"int((A + B*x^3)/(x^3*(a + b*x^3)^(1/2)), x)","F"
222,0,-1,274,0.000000,"\text{Not used}","int((A + B*x^3)/(x^6*(a + b*x^3)^(1/2)),x)","\int \frac{B\,x^3+A}{x^6\,\sqrt{b\,x^3+a}} \,d x","Not used",1,"int((A + B*x^3)/(x^6*(a + b*x^3)^(1/2)), x)","F"
223,0,-1,548,0.000000,"\text{Not used}","int((x^4*(A + B*x^3))/(a + b*x^3)^(1/2),x)","\int \frac{x^4\,\left(B\,x^3+A\right)}{\sqrt{b\,x^3+a}} \,d x","Not used",1,"int((x^4*(A + B*x^3))/(a + b*x^3)^(1/2), x)","F"
224,0,-1,517,0.000000,"\text{Not used}","int((x*(A + B*x^3))/(a + b*x^3)^(1/2),x)","\int \frac{x\,\left(B\,x^3+A\right)}{\sqrt{b\,x^3+a}} \,d x","Not used",1,"int((x*(A + B*x^3))/(a + b*x^3)^(1/2), x)","F"
225,0,-1,509,0.000000,"\text{Not used}","int((A + B*x^3)/(x^2*(a + b*x^3)^(1/2)),x)","\int \frac{B\,x^3+A}{x^2\,\sqrt{b\,x^3+a}} \,d x","Not used",1,"int((A + B*x^3)/(x^2*(a + b*x^3)^(1/2)), x)","F"
226,0,-1,550,0.000000,"\text{Not used}","int((A + B*x^3)/(x^5*(a + b*x^3)^(1/2)),x)","\int \frac{B\,x^3+A}{x^5\,\sqrt{b\,x^3+a}} \,d x","Not used",1,"int((A + B*x^3)/(x^5*(a + b*x^3)^(1/2)), x)","F"
227,0,-1,581,0.000000,"\text{Not used}","int((A + B*x^3)/(x^8*(a + b*x^3)^(1/2)),x)","\int \frac{B\,x^3+A}{x^8\,\sqrt{b\,x^3+a}} \,d x","Not used",1,"int((A + B*x^3)/(x^8*(a + b*x^3)^(1/2)), x)","F"
228,1,152,103,2.770925,"\text{Not used}","int((x^8*(A + B*x^3))/(a + b*x^3)^(3/2),x)","\frac{\sqrt{b\,x^3+a}\,\left(\frac{2\,\left(B\,a^2-A\,a\,b\right)}{b^3}-\frac{2\,a\,\left(\frac{2\,\left(A\,b^2-B\,a\,b\right)}{b^3}-\frac{8\,B\,a}{5\,b^2}\right)}{3\,b}\right)}{3\,b}+\frac{x^3\,\sqrt{b\,x^3+a}\,\left(\frac{2\,\left(A\,b^2-B\,a\,b\right)}{b^3}-\frac{8\,B\,a}{5\,b^2}\right)}{9\,b}-\frac{a^2\,\left(\frac{2\,A}{3\,b}-\frac{2\,B\,a}{3\,b^2}\right)}{b^2\,\sqrt{b\,x^3+a}}+\frac{2\,B\,x^6\,\sqrt{b\,x^3+a}}{15\,b^2}","Not used",1,"((a + b*x^3)^(1/2)*((2*(B*a^2 - A*a*b))/b^3 - (2*a*((2*(A*b^2 - B*a*b))/b^3 - (8*B*a)/(5*b^2)))/(3*b)))/(3*b) + (x^3*(a + b*x^3)^(1/2)*((2*(A*b^2 - B*a*b))/b^3 - (8*B*a)/(5*b^2)))/(9*b) - (a^2*((2*A)/(3*b) - (2*B*a)/(3*b^2)))/(b^2*(a + b*x^3)^(1/2)) + (2*B*x^6*(a + b*x^3)^(1/2))/(15*b^2)","B"
229,1,60,73,2.680267,"\text{Not used}","int((x^5*(A + B*x^3))/(a + b*x^3)^(3/2),x)","\frac{2\,B\,{\left(b\,x^3+a\right)}^2-6\,B\,a^2+6\,A\,b\,\left(b\,x^3+a\right)-12\,B\,a\,\left(b\,x^3+a\right)+6\,A\,a\,b}{9\,b^3\,\sqrt{b\,x^3+a}}","Not used",1,"(2*B*(a + b*x^3)^2 - 6*B*a^2 + 6*A*b*(a + b*x^3) - 12*B*a*(a + b*x^3) + 6*A*a*b)/(9*b^3*(a + b*x^3)^(1/2))","B"
230,1,33,46,2.614558,"\text{Not used}","int((x^2*(A + B*x^3))/(a + b*x^3)^(3/2),x)","\frac{2\,B\,a-2\,A\,b+2\,B\,\left(b\,x^3+a\right)}{3\,b^2\,\sqrt{b\,x^3+a}}","Not used",1,"(2*B*a - 2*A*b + 2*B*(a + b*x^3))/(3*b^2*(a + b*x^3)^(1/2))","B"
231,1,65,58,2.768948,"\text{Not used}","int((A + B*x^3)/(x*(a + b*x^3)^(3/2)),x)","\frac{\frac{2\,A}{3\,a}-\frac{2\,B}{3\,b}}{\sqrt{b\,x^3+a}}+\frac{A\,\ln\left(\frac{{\left(\sqrt{b\,x^3+a}-\sqrt{a}\right)}^3\,\left(\sqrt{b\,x^3+a}+\sqrt{a}\right)}{x^6}\right)}{3\,a^{3/2}}","Not used",1,"((2*A)/(3*a) - (2*B)/(3*b))/(a + b*x^3)^(1/2) + (A*log((((a + b*x^3)^(1/2) - a^(1/2))^3*((a + b*x^3)^(1/2) + a^(1/2)))/x^6))/(3*a^(3/2))","B"
232,1,131,86,2.929259,"\text{Not used}","int((A + B*x^3)/(x^4*(a + b*x^3)^(3/2)),x)","\frac{\ln\left(\frac{\left(\sqrt{b\,x^3+a}-\sqrt{a}\right)\,{\left(\sqrt{b\,x^3+a}+\sqrt{a}\right)}^3}{x^6}\right)\,\left(3\,A\,b-2\,B\,a\right)}{6\,a^{5/2}}-\frac{\frac{2\,B\,a^2-3\,A\,a\,b}{2\,a^3}-\frac{a\,\left(\frac{A\,b^2}{3\,a^3}+\frac{5\,b\,\left(2\,B\,a^2-3\,A\,a\,b\right)}{6\,a^4}\right)}{b}}{\sqrt{b\,x^3+a}}-\frac{A\,\sqrt{b\,x^3+a}}{3\,a^2\,x^3}","Not used",1,"(log((((a + b*x^3)^(1/2) - a^(1/2))*((a + b*x^3)^(1/2) + a^(1/2))^3)/x^6)*(3*A*b - 2*B*a))/(6*a^(5/2)) - ((2*B*a^2 - 3*A*a*b)/(2*a^3) - (a*((A*b^2)/(3*a^3) + (5*b*(2*B*a^2 - 3*A*a*b))/(6*a^4)))/b)/(a + b*x^3)^(1/2) - (A*(a + b*x^3)^(1/2))/(3*a^2*x^3)","B"
233,1,167,118,3.179765,"\text{Not used}","int((A + B*x^3)/(x^7*(a + b*x^3)^(3/2)),x)","\frac{b\,\ln\left(\frac{{\left(\sqrt{b\,x^3+a}-\sqrt{a}\right)}^3\,\left(\sqrt{b\,x^3+a}+\sqrt{a}\right)}{x^6}\right)\,\left(5\,A\,b-4\,B\,a\right)}{8\,a^{7/2}}-\frac{\left(4\,B\,a^2-7\,A\,a\,b\right)\,\sqrt{b\,x^3+a}}{12\,a^4\,x^3}-\frac{A\,\sqrt{b\,x^3+a}}{6\,a^2\,x^6}-\frac{\frac{a\,\left(\frac{7\,A\,b^3-4\,B\,a\,b^2}{12\,a^4}-\frac{5\,b^2\,\left(5\,A\,b-4\,B\,a\right)}{8\,a^4}\right)}{b}+\frac{3\,b\,\left(5\,A\,b-4\,B\,a\right)}{8\,a^3}}{\sqrt{b\,x^3+a}}","Not used",1,"(b*log((((a + b*x^3)^(1/2) - a^(1/2))^3*((a + b*x^3)^(1/2) + a^(1/2)))/x^6)*(5*A*b - 4*B*a))/(8*a^(7/2)) - ((4*B*a^2 - 7*A*a*b)*(a + b*x^3)^(1/2))/(12*a^4*x^3) - (A*(a + b*x^3)^(1/2))/(6*a^2*x^6) - ((a*((7*A*b^3 - 4*B*a*b^2)/(12*a^4) - (5*b^2*(5*A*b - 4*B*a))/(8*a^4)))/b + (3*b*(5*A*b - 4*B*a))/(8*a^3))/(a + b*x^3)^(1/2)","B"
234,0,-1,300,0.000000,"\text{Not used}","int((x^6*(A + B*x^3))/(a + b*x^3)^(3/2),x)","\int \frac{x^6\,\left(B\,x^3+A\right)}{{\left(b\,x^3+a\right)}^{3/2}} \,d x","Not used",1,"int((x^6*(A + B*x^3))/(a + b*x^3)^(3/2), x)","F"
235,0,-1,269,0.000000,"\text{Not used}","int((x^3*(A + B*x^3))/(a + b*x^3)^(3/2),x)","\int \frac{x^3\,\left(B\,x^3+A\right)}{{\left(b\,x^3+a\right)}^{3/2}} \,d x","Not used",1,"int((x^3*(A + B*x^3))/(a + b*x^3)^(3/2), x)","F"
236,0,-1,251,0.000000,"\text{Not used}","int((A + B*x^3)/(a + b*x^3)^(3/2),x)","\int \frac{B\,x^3+A}{{\left(b\,x^3+a\right)}^{3/2}} \,d x","Not used",1,"int((A + B*x^3)/(a + b*x^3)^(3/2), x)","F"
237,0,-1,272,0.000000,"\text{Not used}","int((A + B*x^3)/(x^3*(a + b*x^3)^(3/2)),x)","\int \frac{B\,x^3+A}{x^3\,{\left(b\,x^3+a\right)}^{3/2}} \,d x","Not used",1,"int((A + B*x^3)/(x^3*(a + b*x^3)^(3/2)), x)","F"
238,0,-1,304,0.000000,"\text{Not used}","int((A + B*x^3)/(x^6*(a + b*x^3)^(3/2)),x)","\int \frac{B\,x^3+A}{x^6\,{\left(b\,x^3+a\right)}^{3/2}} \,d x","Not used",1,"int((A + B*x^3)/(x^6*(a + b*x^3)^(3/2)), x)","F"
239,0,-1,547,0.000000,"\text{Not used}","int((x^4*(A + B*x^3))/(a + b*x^3)^(3/2),x)","\int \frac{x^4\,\left(B\,x^3+A\right)}{{\left(b\,x^3+a\right)}^{3/2}} \,d x","Not used",1,"int((x^4*(A + B*x^3))/(a + b*x^3)^(3/2), x)","F"
240,0,-1,524,0.000000,"\text{Not used}","int((x*(A + B*x^3))/(a + b*x^3)^(3/2),x)","\int \frac{x\,\left(B\,x^3+A\right)}{{\left(b\,x^3+a\right)}^{3/2}} \,d x","Not used",1,"int((x*(A + B*x^3))/(a + b*x^3)^(3/2), x)","F"
241,0,-1,548,0.000000,"\text{Not used}","int((A + B*x^3)/(x^2*(a + b*x^3)^(3/2)),x)","\int \frac{B\,x^3+A}{x^2\,{\left(b\,x^3+a\right)}^{3/2}} \,d x","Not used",1,"int((A + B*x^3)/(x^2*(a + b*x^3)^(3/2)), x)","F"
242,0,-1,580,0.000000,"\text{Not used}","int((A + B*x^3)/(x^5*(a + b*x^3)^(3/2)),x)","\int \frac{B\,x^3+A}{x^5\,{\left(b\,x^3+a\right)}^{3/2}} \,d x","Not used",1,"int((A + B*x^3)/(x^5*(a + b*x^3)^(3/2)), x)","F"
243,0,-1,611,0.000000,"\text{Not used}","int((A + B*x^3)/(x^8*(a + b*x^3)^(3/2)),x)","\int \frac{B\,x^3+A}{x^8\,{\left(b\,x^3+a\right)}^{3/2}} \,d x","Not used",1,"int((A + B*x^3)/(x^8*(a + b*x^3)^(3/2)), x)","F"
244,1,145,103,2.796593,"\text{Not used}","int((x^8*(A + B*x^3))/(a + b*x^3)^(5/2),x)","\frac{\sqrt{b\,x^3+a}\,\left(\frac{2\,\left(A\,b-2\,B\,a\right)}{b^3}-\frac{4\,B\,a}{3\,b^3}\right)}{3\,b}-\frac{\frac{2\,B\,a^2-2\,A\,a\,b}{3\,b^4}-\frac{a\,\left(\frac{2\,A\,b^2-2\,B\,a\,b}{3\,b^4}-\frac{2\,B\,a}{3\,b^3}\right)}{b}}{\sqrt{b\,x^3+a}}-\frac{a^2\,\left(\frac{2\,A}{9\,b}-\frac{2\,B\,a}{9\,b^2}\right)}{b^2\,{\left(b\,x^3+a\right)}^{3/2}}+\frac{2\,B\,x^3\,\sqrt{b\,x^3+a}}{9\,b^3}","Not used",1,"((a + b*x^3)^(1/2)*((2*(A*b - 2*B*a))/b^3 - (4*B*a)/(3*b^3)))/(3*b) - ((2*B*a^2 - 2*A*a*b)/(3*b^4) - (a*((2*A*b^2 - 2*B*a*b)/(3*b^4) - (2*B*a)/(3*b^3)))/b)/(a + b*x^3)^(1/2) - (a^2*((2*A)/(9*b) - (2*B*a)/(9*b^2)))/(b^2*(a + b*x^3)^(3/2)) + (2*B*x^3*(a + b*x^3)^(1/2))/(9*b^3)","B"
245,1,60,73,2.760914,"\text{Not used}","int((x^5*(A + B*x^3))/(a + b*x^3)^(5/2),x)","\frac{6\,B\,{\left(b\,x^3+a\right)}^2-2\,B\,a^2-6\,A\,b\,\left(b\,x^3+a\right)+12\,B\,a\,\left(b\,x^3+a\right)+2\,A\,a\,b}{9\,b^3\,{\left(b\,x^3+a\right)}^{3/2}}","Not used",1,"(6*B*(a + b*x^3)^2 - 2*B*a^2 - 6*A*b*(a + b*x^3) + 12*B*a*(a + b*x^3) + 2*A*a*b)/(9*b^3*(a + b*x^3)^(3/2))","B"
246,1,33,46,2.677505,"\text{Not used}","int((x^2*(A + B*x^3))/(a + b*x^3)^(5/2),x)","-\frac{2\,A\,b-2\,B\,a+6\,B\,\left(b\,x^3+a\right)}{9\,b^2\,{\left(b\,x^3+a\right)}^{3/2}}","Not used",1,"-(2*A*b - 2*B*a + 6*B*(a + b*x^3))/(9*b^2*(a + b*x^3)^(3/2))","B"
247,1,80,77,2.781843,"\text{Not used}","int((A + B*x^3)/(x*(a + b*x^3)^(5/2)),x)","\frac{\frac{2\,A}{9\,a}-\frac{2\,B}{9\,b}}{{\left(b\,x^3+a\right)}^{3/2}}+\frac{2\,A}{3\,a^2\,\sqrt{b\,x^3+a}}+\frac{A\,\ln\left(\frac{{\left(\sqrt{b\,x^3+a}-\sqrt{a}\right)}^3\,\left(\sqrt{b\,x^3+a}+\sqrt{a}\right)}{x^6}\right)}{3\,a^{5/2}}","Not used",1,"((2*A)/(9*a) - (2*B)/(9*b))/(a + b*x^3)^(3/2) + (2*A)/(3*a^2*(a + b*x^3)^(1/2)) + (A*log((((a + b*x^3)^(1/2) - a^(1/2))^3*((a + b*x^3)^(1/2) + a^(1/2)))/x^6))/(3*a^(5/2))","B"
248,1,198,113,2.971124,"\text{Not used}","int((A + B*x^3)/(x^4*(a + b*x^3)^(5/2)),x)","\frac{\ln\left(\frac{\left(\sqrt{b\,x^3+a}-\sqrt{a}\right)\,{\left(\sqrt{b\,x^3+a}+\sqrt{a}\right)}^3}{x^6}\right)\,\left(5\,A\,b-2\,B\,a\right)}{6\,a^{7/2}}-\frac{\frac{2\,B\,a^2-5\,A\,a\,b}{2\,a^4}-\frac{a\,\left(\frac{A\,b^2}{3\,a^4}+\frac{5\,b\,\left(2\,B\,a^2-5\,A\,a\,b\right)}{6\,a^5}\right)}{b}}{\sqrt{b\,x^3+a}}-\frac{\frac{2\,B\,a^3-5\,A\,a^2\,b}{4\,a^4}-\frac{a\,\left(\frac{13\,b\,\left(2\,B\,a^3-5\,A\,a^2\,b\right)}{36\,a^5}+\frac{A\,b^2}{3\,a^3}\right)}{b}}{{\left(b\,x^3+a\right)}^{3/2}}-\frac{A\,\sqrt{b\,x^3+a}}{3\,a^3\,x^3}","Not used",1,"(log((((a + b*x^3)^(1/2) - a^(1/2))*((a + b*x^3)^(1/2) + a^(1/2))^3)/x^6)*(5*A*b - 2*B*a))/(6*a^(7/2)) - ((2*B*a^2 - 5*A*a*b)/(2*a^4) - (a*((A*b^2)/(3*a^4) + (5*b*(2*B*a^2 - 5*A*a*b))/(6*a^5)))/b)/(a + b*x^3)^(1/2) - ((2*B*a^3 - 5*A*a^2*b)/(4*a^4) - (a*((13*b*(2*B*a^3 - 5*A*a^2*b))/(36*a^5) + (A*b^2)/(3*a^3)))/b)/(a + b*x^3)^(3/2) - (A*(a + b*x^3)^(1/2))/(3*a^3*x^3)","B"
249,0,-1,299,0.000000,"\text{Not used}","int((x^6*(A + B*x^3))/(a + b*x^3)^(5/2),x)","\int \frac{x^6\,\left(B\,x^3+A\right)}{{\left(b\,x^3+a\right)}^{5/2}} \,d x","Not used",1,"int((x^6*(A + B*x^3))/(a + b*x^3)^(5/2), x)","F"
250,0,-1,283,0.000000,"\text{Not used}","int((x^3*(A + B*x^3))/(a + b*x^3)^(5/2),x)","\int \frac{x^3\,\left(B\,x^3+A\right)}{{\left(b\,x^3+a\right)}^{5/2}} \,d x","Not used",1,"int((x^3*(A + B*x^3))/(a + b*x^3)^(5/2), x)","F"
251,0,-1,283,0.000000,"\text{Not used}","int((A + B*x^3)/(a + b*x^3)^(5/2),x)","\int \frac{B\,x^3+A}{{\left(b\,x^3+a\right)}^{5/2}} \,d x","Not used",1,"int((A + B*x^3)/(a + b*x^3)^(5/2), x)","F"
252,0,-1,300,0.000000,"\text{Not used}","int((A + B*x^3)/(x^3*(a + b*x^3)^(5/2)),x)","\int \frac{B\,x^3+A}{x^3\,{\left(b\,x^3+a\right)}^{5/2}} \,d x","Not used",1,"int((A + B*x^3)/(x^3*(a + b*x^3)^(5/2)), x)","F"
253,0,-1,334,0.000000,"\text{Not used}","int((A + B*x^3)/(x^6*(a + b*x^3)^(5/2)),x)","\int \frac{B\,x^3+A}{x^6\,{\left(b\,x^3+a\right)}^{5/2}} \,d x","Not used",1,"int((A + B*x^3)/(x^6*(a + b*x^3)^(5/2)), x)","F"
254,0,-1,577,0.000000,"\text{Not used}","int((x^7*(A + B*x^3))/(a + b*x^3)^(5/2),x)","\int \frac{x^7\,\left(B\,x^3+A\right)}{{\left(b\,x^3+a\right)}^{5/2}} \,d x","Not used",1,"int((x^7*(A + B*x^3))/(a + b*x^3)^(5/2), x)","F"
255,0,-1,559,0.000000,"\text{Not used}","int((x^4*(A + B*x^3))/(a + b*x^3)^(5/2),x)","\int \frac{x^4\,\left(B\,x^3+A\right)}{{\left(b\,x^3+a\right)}^{5/2}} \,d x","Not used",1,"int((x^4*(A + B*x^3))/(a + b*x^3)^(5/2), x)","F"
256,0,-1,563,0.000000,"\text{Not used}","int((x*(A + B*x^3))/(a + b*x^3)^(5/2),x)","\int \frac{x\,\left(B\,x^3+A\right)}{{\left(b\,x^3+a\right)}^{5/2}} \,d x","Not used",1,"int((x*(A + B*x^3))/(a + b*x^3)^(5/2), x)","F"
257,0,-1,578,0.000000,"\text{Not used}","int((A + B*x^3)/(x^2*(a + b*x^3)^(5/2)),x)","\int \frac{B\,x^3+A}{x^2\,{\left(b\,x^3+a\right)}^{5/2}} \,d x","Not used",1,"int((A + B*x^3)/(x^2*(a + b*x^3)^(5/2)), x)","F"
258,0,-1,610,0.000000,"\text{Not used}","int((A + B*x^3)/(x^5*(a + b*x^3)^(5/2)),x)","\int \frac{B\,x^3+A}{x^5\,{\left(b\,x^3+a\right)}^{5/2}} \,d x","Not used",1,"int((A + B*x^3)/(x^5*(a + b*x^3)^(5/2)), x)","F"
259,1,109,97,4.539088,"\text{Not used}","int((x^8*(c + d*x^3)^(1/2))/(4*c + d*x^3),x)","\frac{436\,c^2\,\sqrt{d\,x^3+c}}{45\,d^3}+\frac{2\,x^6\,\sqrt{d\,x^3+c}}{15\,d}-\frac{38\,c\,x^3\,\sqrt{d\,x^3+c}}{45\,d^2}+\frac{\sqrt{3}\,c^{5/2}\,\ln\left(\frac{2\,\sqrt{3}\,c-\sqrt{3}\,d\,x^3+\sqrt{c}\,\sqrt{d\,x^3+c}\,6{}\mathrm{i}}{d\,x^3+4\,c}\right)\,16{}\mathrm{i}}{3\,d^3}","Not used",1,"(436*c^2*(c + d*x^3)^(1/2))/(45*d^3) + (2*x^6*(c + d*x^3)^(1/2))/(15*d) - (38*c*x^3*(c + d*x^3)^(1/2))/(45*d^2) + (3^(1/2)*c^(5/2)*log((2*3^(1/2)*c + c^(1/2)*(c + d*x^3)^(1/2)*6i - 3^(1/2)*d*x^3)/(4*c + d*x^3))*16i)/(3*d^3)","B"
260,1,88,76,4.278268,"\text{Not used}","int((x^5*(c + d*x^3)^(1/2))/(4*c + d*x^3),x)","\frac{2\,x^3\,\sqrt{d\,x^3+c}}{9\,d}-\frac{22\,c\,\sqrt{d\,x^3+c}}{9\,d^2}+\frac{\sqrt{3}\,c^{3/2}\,\ln\left(\frac{\sqrt{3}\,d\,x^3-2\,\sqrt{3}\,c+\sqrt{c}\,\sqrt{d\,x^3+c}\,6{}\mathrm{i}}{d\,x^3+4\,c}\right)\,4{}\mathrm{i}}{3\,d^2}","Not used",1,"(2*x^3*(c + d*x^3)^(1/2))/(9*d) - (22*c*(c + d*x^3)^(1/2))/(9*d^2) + (3^(1/2)*c^(3/2)*log((c^(1/2)*(c + d*x^3)^(1/2)*6i - 2*3^(1/2)*c + 3^(1/2)*d*x^3)/(4*c + d*x^3))*4i)/(3*d^2)","B"
261,1,71,57,3.865730,"\text{Not used}","int((x^2*(c + d*x^3)^(1/2))/(4*c + d*x^3),x)","\frac{2\,\sqrt{d\,x^3+c}}{3\,d}+\frac{\sqrt{3}\,\sqrt{c}\,\ln\left(\frac{2\,\sqrt{3}\,c-\sqrt{3}\,d\,x^3+\sqrt{c}\,\sqrt{d\,x^3+c}\,6{}\mathrm{i}}{d\,x^3+4\,c}\right)\,1{}\mathrm{i}}{3\,d}","Not used",1,"(2*(c + d*x^3)^(1/2))/(3*d) + (3^(1/2)*c^(1/2)*log((2*3^(1/2)*c + c^(1/2)*(c + d*x^3)^(1/2)*6i - 3^(1/2)*d*x^3)/(4*c + d*x^3))*1i)/(3*d)","B"
262,1,93,65,4.658495,"\text{Not used}","int((c + d*x^3)^(1/2)/(x*(4*c + d*x^3)),x)","\frac{\ln\left(\frac{{\left(\sqrt{d\,x^3+c}-\sqrt{c}\right)}^3\,\left(\sqrt{d\,x^3+c}+\sqrt{c}\right)}{x^6}\right)}{12\,\sqrt{c}}+\frac{\sqrt{3}\,\ln\left(\frac{\sqrt{3}\,d\,x^3-2\,\sqrt{3}\,c+\sqrt{c}\,\sqrt{d\,x^3+c}\,6{}\mathrm{i}}{d\,x^3+4\,c}\right)\,1{}\mathrm{i}}{12\,\sqrt{c}}","Not used",1,"log((((c + d*x^3)^(1/2) - c^(1/2))^3*((c + d*x^3)^(1/2) + c^(1/2)))/x^6)/(12*c^(1/2)) + (3^(1/2)*log((c^(1/2)*(c + d*x^3)^(1/2)*6i - 2*3^(1/2)*c + 3^(1/2)*d*x^3)/(4*c + d*x^3))*1i)/(12*c^(1/2))","B"
263,1,113,88,4.858108,"\text{Not used}","int((c + d*x^3)^(1/2)/(x^4*(4*c + d*x^3)),x)","\frac{d\,\ln\left(\frac{{\left(\sqrt{d\,x^3+c}-\sqrt{c}\right)}^3\,\left(\sqrt{d\,x^3+c}+\sqrt{c}\right)}{x^6}\right)}{48\,c^{3/2}}-\frac{\sqrt{d\,x^3+c}}{12\,c\,x^3}+\frac{\sqrt{3}\,d\,\ln\left(\frac{2\,\sqrt{3}\,c-\sqrt{3}\,d\,x^3+\sqrt{c}\,\sqrt{d\,x^3+c}\,6{}\mathrm{i}}{d\,x^3+4\,c}\right)\,1{}\mathrm{i}}{48\,c^{3/2}}","Not used",1,"(d*log((((c + d*x^3)^(1/2) - c^(1/2))^3*((c + d*x^3)^(1/2) + c^(1/2)))/x^6))/(48*c^(3/2)) - (c + d*x^3)^(1/2)/(12*c*x^3) + (3^(1/2)*d*log((2*3^(1/2)*c + c^(1/2)*(c + d*x^3)^(1/2)*6i - 3^(1/2)*d*x^3)/(4*c + d*x^3))*1i)/(48*c^(3/2))","B"
264,0,-1,689,0.000000,"\text{Not used}","int((x^4*(c + d*x^3)^(1/2))/(4*c + d*x^3),x)","\int \frac{x^4\,\sqrt{d\,x^3+c}}{d\,x^3+4\,c} \,d x","Not used",1,"int((x^4*(c + d*x^3)^(1/2))/(4*c + d*x^3), x)","F"
265,0,-1,659,0.000000,"\text{Not used}","int((x*(c + d*x^3)^(1/2))/(4*c + d*x^3),x)","\int \frac{x\,\sqrt{d\,x^3+c}}{d\,x^3+4\,c} \,d x","Not used",1,"int((x*(c + d*x^3)^(1/2))/(4*c + d*x^3), x)","F"
266,0,-1,697,0.000000,"\text{Not used}","int((c + d*x^3)^(1/2)/(x^2*(4*c + d*x^3)),x)","\int \frac{\sqrt{d\,x^3+c}}{x^2\,\left(d\,x^3+4\,c\right)} \,d x","Not used",1,"int((c + d*x^3)^(1/2)/(x^2*(4*c + d*x^3)), x)","F"
267,0,-1,66,0.000000,"\text{Not used}","int((x^3*(c + d*x^3)^(1/2))/(4*c + d*x^3),x)","\int \frac{x^3\,\sqrt{d\,x^3+c}}{d\,x^3+4\,c} \,d x","Not used",1,"int((x^3*(c + d*x^3)^(1/2))/(4*c + d*x^3), x)","F"
268,0,-1,64,0.000000,"\text{Not used}","int((c + d*x^3)^(1/2)/(4*c + d*x^3),x)","\int \frac{\sqrt{d\,x^3+c}}{d\,x^3+4\,c} \,d x","Not used",1,"int((c + d*x^3)^(1/2)/(4*c + d*x^3), x)","F"
269,0,-1,66,0.000000,"\text{Not used}","int((c + d*x^3)^(1/2)/(x^3*(4*c + d*x^3)),x)","\int \frac{\sqrt{d\,x^3+c}}{x^3\,\left(d\,x^3+4\,c\right)} \,d x","Not used",1,"int((c + d*x^3)^(1/2)/(x^3*(4*c + d*x^3)), x)","F"
270,1,88,78,5.383091,"\text{Not used}","int(x^8/((c + d*x^3)^(1/2)*(4*c + d*x^3)),x)","\frac{2\,x^3\,\sqrt{d\,x^3+c}}{9\,d^2}-\frac{28\,c\,\sqrt{d\,x^3+c}}{9\,d^3}+\frac{\sqrt{3}\,c^{3/2}\,\ln\left(\frac{\sqrt{3}\,d\,x^3-2\,\sqrt{3}\,c+\sqrt{c}\,\sqrt{d\,x^3+c}\,6{}\mathrm{i}}{d\,x^3+4\,c}\right)\,16{}\mathrm{i}}{9\,d^3}","Not used",1,"(2*x^3*(c + d*x^3)^(1/2))/(9*d^2) - (28*c*(c + d*x^3)^(1/2))/(9*d^3) + (3^(1/2)*c^(3/2)*log((c^(1/2)*(c + d*x^3)^(1/2)*6i - 2*3^(1/2)*c + 3^(1/2)*d*x^3)/(4*c + d*x^3))*16i)/(9*d^3)","B"
271,1,71,59,4.859422,"\text{Not used}","int(x^5/((c + d*x^3)^(1/2)*(4*c + d*x^3)),x)","\frac{2\,\sqrt{d\,x^3+c}}{3\,d^2}+\frac{\sqrt{3}\,\sqrt{c}\,\ln\left(\frac{2\,\sqrt{3}\,c-\sqrt{3}\,d\,x^3+\sqrt{c}\,\sqrt{d\,x^3+c}\,6{}\mathrm{i}}{d\,x^3+4\,c}\right)\,4{}\mathrm{i}}{9\,d^2}","Not used",1,"(2*(c + d*x^3)^(1/2))/(3*d^2) + (3^(1/2)*c^(1/2)*log((2*3^(1/2)*c + c^(1/2)*(c + d*x^3)^(1/2)*6i - 3^(1/2)*d*x^3)/(4*c + d*x^3))*4i)/(9*d^2)","B"
272,1,56,40,5.210458,"\text{Not used}","int(x^2/((c + d*x^3)^(1/2)*(4*c + d*x^3)),x)","\frac{\sqrt{3}\,\ln\left(\frac{\sqrt{3}\,d\,x^3-2\,\sqrt{3}\,c+\sqrt{c}\,\sqrt{d\,x^3+c}\,6{}\mathrm{i}}{2\,d\,x^3+8\,c}\right)\,1{}\mathrm{i}}{9\,\sqrt{c}\,d}","Not used",1,"(3^(1/2)*log((c^(1/2)*(c + d*x^3)^(1/2)*6i - 2*3^(1/2)*c + 3^(1/2)*d*x^3)/(8*c + 2*d*x^3))*1i)/(9*c^(1/2)*d)","B"
273,1,94,65,5.506726,"\text{Not used}","int(1/(x*(c + d*x^3)^(1/2)*(4*c + d*x^3)),x)","\frac{\ln\left(\frac{{\left(\sqrt{d\,x^3+c}-\sqrt{c}\right)}^3\,\left(\sqrt{d\,x^3+c}+\sqrt{c}\right)}{x^6}\right)}{12\,c^{3/2}}+\frac{\sqrt{3}\,\ln\left(\frac{2\,\sqrt{3}\,c-\sqrt{3}\,d\,x^3+\sqrt{c}\,\sqrt{d\,x^3+c}\,6{}\mathrm{i}}{d\,x^3+4\,c}\right)\,1{}\mathrm{i}}{36\,c^{3/2}}","Not used",1,"log((((c + d*x^3)^(1/2) - c^(1/2))^3*((c + d*x^3)^(1/2) + c^(1/2)))/x^6)/(12*c^(3/2)) + (3^(1/2)*log((2*3^(1/2)*c + c^(1/2)*(c + d*x^3)^(1/2)*6i - 3^(1/2)*d*x^3)/(4*c + d*x^3))*1i)/(36*c^(3/2))","B"
274,1,112,88,5.719245,"\text{Not used}","int(1/(x^4*(c + d*x^3)^(1/2)*(4*c + d*x^3)),x)","\frac{d\,\ln\left(\frac{\left(\sqrt{d\,x^3+c}-\sqrt{c}\right)\,{\left(\sqrt{d\,x^3+c}+\sqrt{c}\right)}^3}{x^6}\right)}{16\,c^{5/2}}-\frac{\sqrt{d\,x^3+c}}{12\,c^2\,x^3}+\frac{\sqrt{3}\,d\,\ln\left(\frac{\sqrt{3}\,d\,x^3-2\,\sqrt{3}\,c+\sqrt{c}\,\sqrt{d\,x^3+c}\,6{}\mathrm{i}}{d\,x^3+4\,c}\right)\,1{}\mathrm{i}}{144\,c^{5/2}}","Not used",1,"(d*log((((c + d*x^3)^(1/2) - c^(1/2))*((c + d*x^3)^(1/2) + c^(1/2))^3)/x^6))/(16*c^(5/2)) - (c + d*x^3)^(1/2)/(12*c^2*x^3) + (3^(1/2)*d*log((c^(1/2)*(c + d*x^3)^(1/2)*6i - 2*3^(1/2)*c + 3^(1/2)*d*x^3)/(4*c + d*x^3))*1i)/(144*c^(5/2))","B"
275,0,-1,667,0.000000,"\text{Not used}","int(x^4/((c + d*x^3)^(1/2)*(4*c + d*x^3)),x)","\int \frac{x^4}{\sqrt{d\,x^3+c}\,\left(d\,x^3+4\,c\right)} \,d x","Not used",1,"int(x^4/((c + d*x^3)^(1/2)*(4*c + d*x^3)), x)","F"
276,1,453,206,25.803849,"\text{Not used}","int(x/((c + d*x^3)^(1/2)*(4*c + d*x^3)),x)","\frac{\sqrt{3}\,{314928}^{1/3}\,\ln\left(\frac{{\left(\sqrt{d\,x^3+c}+\sqrt{3}\,\sqrt{-c}-2^{1/3}\,\sqrt{3}\,{\left(-c\right)}^{1/6}\,d^{1/3}\,x\right)}^3\,\left(54\,\sqrt{d\,x^3+c}-54\,\sqrt{3}\,\sqrt{-c}+54\,2^{1/3}\,\sqrt{3}\,{\left(-c\right)}^{1/6}\,d^{1/3}\,x\right)}{{\left(d^{1/3}\,x-2^{2/3}\,{\left(-c\right)}^{1/3}\right)}^6}\right)}{2916\,{\left(-c\right)}^{5/6}\,d^{2/3}}+\frac{\sqrt{3}\,{314928}^{1/3}\,\ln\left(\frac{{\left(2\,\sqrt{3}\,\sqrt{-c}-2\,\sqrt{d\,x^3+c}+2^{1/3}\,\sqrt{3}\,{\left(-c\right)}^{1/6}\,d^{1/3}\,x+2^{1/3}\,{\left(-c\right)}^{1/6}\,d^{1/3}\,x\,3{}\mathrm{i}\right)}^3\,\left(108\,\sqrt{d\,x^3+c}+108\,\sqrt{3}\,\sqrt{-c}+54\,2^{1/3}\,\sqrt{3}\,{\left(-c\right)}^{1/6}\,d^{1/3}\,x+2^{1/3}\,{\left(-c\right)}^{1/6}\,d^{1/3}\,x\,162{}\mathrm{i}\right)}{{\left(2\,d^{1/3}\,x+2^{2/3}\,{\left(-c\right)}^{1/3}-2^{2/3}\,\sqrt{3}\,{\left(-c\right)}^{1/3}\,1{}\mathrm{i}\right)}^6}\right)\,\sqrt{-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}{2916\,{\left(-c\right)}^{5/6}\,d^{2/3}}+\frac{\sqrt{3}\,{314928}^{1/3}\,\ln\left(\frac{{\left(2\,\sqrt{d\,x^3+c}+2\,\sqrt{3}\,\sqrt{-c}+2^{1/3}\,\sqrt{3}\,{\left(-c\right)}^{1/6}\,d^{1/3}\,x-2^{1/3}\,{\left(-c\right)}^{1/6}\,d^{1/3}\,x\,3{}\mathrm{i}\right)}^3\,\left(108\,\sqrt{d\,x^3+c}-108\,\sqrt{3}\,\sqrt{-c}-54\,2^{1/3}\,\sqrt{3}\,{\left(-c\right)}^{1/6}\,d^{1/3}\,x+2^{1/3}\,{\left(-c\right)}^{1/6}\,d^{1/3}\,x\,162{}\mathrm{i}\right)}{{\left(2\,d^{1/3}\,x+2^{2/3}\,{\left(-c\right)}^{1/3}+2^{2/3}\,\sqrt{3}\,{\left(-c\right)}^{1/3}\,1{}\mathrm{i}\right)}^6}\right)\,\sqrt{\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\,1{}\mathrm{i}}{2916\,{\left(-c\right)}^{5/6}\,d^{2/3}}","Not used",1,"(3^(1/2)*314928^(1/3)*log((((c + d*x^3)^(1/2) + 3^(1/2)*(-c)^(1/2) - 2^(1/3)*3^(1/2)*(-c)^(1/6)*d^(1/3)*x)^3*(54*(c + d*x^3)^(1/2) - 54*3^(1/2)*(-c)^(1/2) + 54*2^(1/3)*3^(1/2)*(-c)^(1/6)*d^(1/3)*x))/(d^(1/3)*x - 2^(2/3)*(-c)^(1/3))^6))/(2916*(-c)^(5/6)*d^(2/3)) + (3^(1/2)*314928^(1/3)*log(((2*3^(1/2)*(-c)^(1/2) - 2*(c + d*x^3)^(1/2) + 2^(1/3)*(-c)^(1/6)*d^(1/3)*x*3i + 2^(1/3)*3^(1/2)*(-c)^(1/6)*d^(1/3)*x)^3*(108*(c + d*x^3)^(1/2) + 108*3^(1/2)*(-c)^(1/2) + 2^(1/3)*(-c)^(1/6)*d^(1/3)*x*162i + 54*2^(1/3)*3^(1/2)*(-c)^(1/6)*d^(1/3)*x))/(2*d^(1/3)*x + 2^(2/3)*(-c)^(1/3) - 2^(2/3)*3^(1/2)*(-c)^(1/3)*1i)^6)*((3^(1/2)*1i)/2 - 1/2)^(1/2))/(2916*(-c)^(5/6)*d^(2/3)) + (3^(1/2)*314928^(1/3)*log(((2*(c + d*x^3)^(1/2) + 2*3^(1/2)*(-c)^(1/2) - 2^(1/3)*(-c)^(1/6)*d^(1/3)*x*3i + 2^(1/3)*3^(1/2)*(-c)^(1/6)*d^(1/3)*x)^3*(108*(c + d*x^3)^(1/2) - 108*3^(1/2)*(-c)^(1/2) + 2^(1/3)*(-c)^(1/6)*d^(1/3)*x*162i - 54*2^(1/3)*3^(1/2)*(-c)^(1/6)*d^(1/3)*x))/(2*d^(1/3)*x + 2^(2/3)*(-c)^(1/3) + 2^(2/3)*3^(1/2)*(-c)^(1/3)*1i)^6)*((3^(1/2)*1i)/2 + 1/2)^(1/2)*1i)/(2916*(-c)^(5/6)*d^(2/3))","B"
277,0,-1,697,0.000000,"\text{Not used}","int(1/(x^2*(c + d*x^3)^(1/2)*(4*c + d*x^3)),x)","\int \frac{1}{x^2\,\sqrt{d\,x^3+c}\,\left(d\,x^3+4\,c\right)} \,d x","Not used",1,"int(1/(x^2*(c + d*x^3)^(1/2)*(4*c + d*x^3)), x)","F"
278,0,-1,66,0.000000,"\text{Not used}","int(x^3/((c + d*x^3)^(1/2)*(4*c + d*x^3)),x)","\int \frac{x^3}{\sqrt{d\,x^3+c}\,\left(d\,x^3+4\,c\right)} \,d x","Not used",1,"int(x^3/((c + d*x^3)^(1/2)*(4*c + d*x^3)), x)","F"
279,0,-1,64,0.000000,"\text{Not used}","int(1/((c + d*x^3)^(1/2)*(4*c + d*x^3)),x)","\int \frac{1}{\sqrt{d\,x^3+c}\,\left(d\,x^3+4\,c\right)} \,d x","Not used",1,"int(1/((c + d*x^3)^(1/2)*(4*c + d*x^3)), x)","F"
280,0,-1,66,0.000000,"\text{Not used}","int(1/(x^3*(c + d*x^3)^(1/2)*(4*c + d*x^3)),x)","\int \frac{1}{x^3\,\sqrt{d\,x^3+c}\,\left(d\,x^3+4\,c\right)} \,d x","Not used",1,"int(1/(x^3*(c + d*x^3)^(1/2)*(4*c + d*x^3)), x)","F"
281,1,653,127,3.419131,"\text{Not used}","int(-x/((1 - x^3)^(1/2)*(x^3 - 4)),x)","-\frac{2^{1/3}\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{x^3-1}\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\Pi \left(-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{2^{2/3}-1};\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{3\,\sqrt{1-x^3}\,\left(2^{2/3}-1\right)\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}-\frac{2^{1/3}\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{x^3-1}\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\Pi \left(\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{2^{2/3}\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)+1};\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{3\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{1-x^3}\,\left(2^{2/3}\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)+1\right)\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}-\frac{2^{1/3}\,\left(\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{x^3-1}\,\sqrt{-\frac{x+\frac{1}{2}-\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{\frac{x+\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\,\Pi \left(-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{2^{2/3}\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1};\mathrm{asin}\left(\sqrt{-\frac{x-1}{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}}\right)\middle|-\frac{\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}{-\frac{3}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}}\right)}{3\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\sqrt{1-x^3}\,\left(2^{2/3}\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,\sqrt{x^3+\left(-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)-1\right)\,x+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}}","Not used",1,"- (2^(1/3)*((3^(1/2)*1i)/2 + 3/2)*(x^3 - 1)^(1/2)*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticPi(-((3^(1/2)*1i)/2 + 3/2)/(2^(2/3) - 1), asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(3*(1 - x^3)^(1/2)*(2^(2/3) - 1)*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2)) - (2^(1/3)*((3^(1/2)*1i)/2 + 3/2)*(x^3 - 1)^(1/2)*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticPi(((3^(1/2)*1i)/2 + 3/2)/(2^(2/3)*((3^(1/2)*1i)/2 + 1/2) + 1), asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(3*((3^(1/2)*1i)/2 + 1/2)*(1 - x^3)^(1/2)*(2^(2/3)*((3^(1/2)*1i)/2 + 1/2) + 1)*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2)) - (2^(1/3)*((3^(1/2)*1i)/2 + 3/2)*(x^3 - 1)^(1/2)*(-(x - (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 - 3/2))^(1/2)*((x + (3^(1/2)*1i)/2 + 1/2)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*(-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)*ellipticPi(-((3^(1/2)*1i)/2 + 3/2)/(2^(2/3)*((3^(1/2)*1i)/2 - 1/2) - 1), asin((-(x - 1)/((3^(1/2)*1i)/2 + 3/2))^(1/2)), -((3^(1/2)*1i)/2 + 3/2)/((3^(1/2)*1i)/2 - 3/2)))/(3*((3^(1/2)*1i)/2 - 1/2)*(1 - x^3)^(1/2)*(2^(2/3)*((3^(1/2)*1i)/2 - 1/2) - 1)*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) - x*(((3^(1/2)*1i)/2 - 1/2)*((3^(1/2)*1i)/2 + 1/2) + 1) + x^3)^(1/2))","B"
282,1,118,111,3.509517,"\text{Not used}","int((x^11*(c + d*x^3)^(1/2))/(8*c - d*x^3),x)","\frac{512\,c^{7/2}\,\ln\left(\frac{10\,c+d\,x^3+6\,\sqrt{c}\,\sqrt{d\,x^3+c}}{8\,c-d\,x^3}\right)}{d^4}-\frac{37264\,c^3\,\sqrt{d\,x^3+c}}{105\,d^4}-\frac{2\,x^9\,\sqrt{d\,x^3+c}}{21\,d}-\frac{38\,c\,x^6\,\sqrt{d\,x^3+c}}{35\,d^2}-\frac{1528\,c^2\,x^3\,\sqrt{d\,x^3+c}}{105\,d^3}","Not used",1,"(512*c^(7/2)*log((10*c + d*x^3 + 6*c^(1/2)*(c + d*x^3)^(1/2))/(8*c - d*x^3)))/d^4 - (37264*c^3*(c + d*x^3)^(1/2))/(105*d^4) - (2*x^9*(c + d*x^3)^(1/2))/(21*d) - (38*c*x^6*(c + d*x^3)^(1/2))/(35*d^2) - (1528*c^2*x^3*(c + d*x^3)^(1/2))/(105*d^3)","B"
283,1,98,90,3.404101,"\text{Not used}","int((x^8*(c + d*x^3)^(1/2))/(8*c - d*x^3),x)","\frac{64\,c^{5/2}\,\ln\left(\frac{10\,c+d\,x^3+6\,\sqrt{c}\,\sqrt{d\,x^3+c}}{8\,c-d\,x^3}\right)}{d^3}-\frac{1996\,c^2\,\sqrt{d\,x^3+c}}{45\,d^3}-\frac{2\,x^6\,\sqrt{d\,x^3+c}}{15\,d}-\frac{82\,c\,x^3\,\sqrt{d\,x^3+c}}{45\,d^2}","Not used",1,"(64*c^(5/2)*log((10*c + d*x^3 + 6*c^(1/2)*(c + d*x^3)^(1/2))/(8*c - d*x^3)))/d^3 - (1996*c^2*(c + d*x^3)^(1/2))/(45*d^3) - (2*x^6*(c + d*x^3)^(1/2))/(15*d) - (82*c*x^3*(c + d*x^3)^(1/2))/(45*d^2)","B"
284,1,78,69,3.508188,"\text{Not used}","int((x^5*(c + d*x^3)^(1/2))/(8*c - d*x^3),x)","\frac{8\,c^{3/2}\,\ln\left(\frac{10\,c+d\,x^3+6\,\sqrt{c}\,\sqrt{d\,x^3+c}}{8\,c-d\,x^3}\right)}{d^2}-\frac{50\,c\,\sqrt{d\,x^3+c}}{9\,d^2}-\frac{2\,x^3\,\sqrt{d\,x^3+c}}{9\,d}","Not used",1,"(8*c^(3/2)*log((10*c + d*x^3 + 6*c^(1/2)*(c + d*x^3)^(1/2))/(8*c - d*x^3)))/d^2 - (50*c*(c + d*x^3)^(1/2))/(9*d^2) - (2*x^3*(c + d*x^3)^(1/2))/(9*d)","B"
285,1,59,50,3.496152,"\text{Not used}","int((x^2*(c + d*x^3)^(1/2))/(8*c - d*x^3),x)","\frac{\sqrt{c}\,\ln\left(\frac{10\,c+d\,x^3+6\,\sqrt{c}\,\sqrt{d\,x^3+c}}{8\,c-d\,x^3}\right)}{d}-\frac{2\,\sqrt{d\,x^3+c}}{3\,d}","Not used",1,"(c^(1/2)*log((10*c + d*x^3 + 6*c^(1/2)*(c + d*x^3)^(1/2))/(8*c - d*x^3)))/d - (2*(c + d*x^3)^(1/2))/(3*d)","B"
286,1,125,58,4.687416,"\text{Not used}","int((c + d*x^3)^(1/2)/(x*(8*c - d*x^3)),x)","\frac{\ln\left(\frac{{\left(\sqrt{d\,x^3+c}-\sqrt{c}\right)}^3\,\left(\sqrt{d\,x^3+c}+\sqrt{c}\right)\,{\left(6\,c+d\,x^3+6\,\sqrt{c}\,\sqrt{d\,x^3+c}\right)}^3\,{\left(24\,c^2-24\,c^{3/2}\,\sqrt{d\,x^3+c}+d^2\,x^6-20\,c\,d\,x^3\right)}^3}{x^{15}\,{\left(8\,c-d\,x^3\right)}^3\,{\left(24\,c-d\,x^3\right)}^3}\right)}{24\,\sqrt{c}}","Not used",1,"log((((c + d*x^3)^(1/2) - c^(1/2))^3*((c + d*x^3)^(1/2) + c^(1/2))*(6*c + d*x^3 + 6*c^(1/2)*(c + d*x^3)^(1/2))^3*(24*c^2 - 24*c^(3/2)*(c + d*x^3)^(1/2) + d^2*x^6 - 20*c*d*x^3)^3)/(x^15*(8*c - d*x^3)^3*(24*c - d*x^3)^3))/(24*c^(1/2))","B"
287,1,69,81,3.748169,"\text{Not used}","int((c + d*x^3)^(1/2)/(x^4*(8*c - d*x^3)),x)","\frac{d\,\mathrm{atanh}\left(\frac{c\,\sqrt{d\,x^3+c}}{3\,\sqrt{c^3}}\right)}{32\,\sqrt{c^3}}-\frac{5\,d\,\mathrm{atanh}\left(\frac{c\,\sqrt{d\,x^3+c}}{\sqrt{c^3}}\right)}{96\,\sqrt{c^3}}-\frac{\sqrt{d\,x^3+c}}{24\,c\,x^3}","Not used",1,"(d*atanh((c*(c + d*x^3)^(1/2))/(3*(c^3)^(1/2))))/(32*(c^3)^(1/2)) - (5*d*atanh((c*(c + d*x^3)^(1/2))/(c^3)^(1/2)))/(96*(c^3)^(1/2)) - (c + d*x^3)^(1/2)/(24*c*x^3)","B"
288,1,83,107,3.909636,"\text{Not used}","int((c + d*x^3)^(1/2)/(x^7*(8*c - d*x^3)),x)","\frac{d^2\,\mathrm{atanh}\left(\frac{d^4\,\sqrt{d\,x^3+c}}{2048\,c^{7/2}\,\left(\frac{d^4}{2048\,c^3}+\frac{d^5\,x^3}{8192\,c^4}\right)}\right)}{256\,c^{5/2}}-\frac{\sqrt{d\,x^3+c}}{192\,c\,x^6}-\frac{{\left(d\,x^3+c\right)}^{3/2}}{64\,c^2\,x^6}","Not used",1,"(d^2*atanh((d^4*(c + d*x^3)^(1/2))/(2048*c^(7/2)*(d^4/(2048*c^3) + (d^5*x^3)/(8192*c^4)))))/(256*c^(5/2)) - (c + d*x^3)^(1/2)/(192*c*x^6) - (c + d*x^3)^(3/2)/(64*c^2*x^6)","B"
289,0,-1,648,0.000000,"\text{Not used}","int((x^7*(c + d*x^3)^(1/2))/(8*c - d*x^3),x)","\int \frac{x^7\,\sqrt{d\,x^3+c}}{8\,c-d\,x^3} \,d x","Not used",1,"int((x^7*(c + d*x^3)^(1/2))/(8*c - d*x^3), x)","F"
290,0,-1,624,0.000000,"\text{Not used}","int((x^4*(c + d*x^3)^(1/2))/(8*c - d*x^3),x)","\int \frac{x^4\,\sqrt{d\,x^3+c}}{8\,c-d\,x^3} \,d x","Not used",1,"int((x^4*(c + d*x^3)^(1/2))/(8*c - d*x^3), x)","F"
291,0,-1,601,0.000000,"\text{Not used}","int((x*(c + d*x^3)^(1/2))/(8*c - d*x^3),x)","\int \frac{x\,\sqrt{d\,x^3+c}}{8\,c-d\,x^3} \,d x","Not used",1,"int((x*(c + d*x^3)^(1/2))/(8*c - d*x^3), x)","F"
292,0,-1,632,0.000000,"\text{Not used}","int((c + d*x^3)^(1/2)/(x^2*(8*c - d*x^3)),x)","\int \frac{\sqrt{d\,x^3+c}}{x^2\,\left(8\,c-d\,x^3\right)} \,d x","Not used",1,"int((c + d*x^3)^(1/2)/(x^2*(8*c - d*x^3)), x)","F"
293,0,-1,654,0.000000,"\text{Not used}","int((c + d*x^3)^(1/2)/(x^5*(8*c - d*x^3)),x)","\int \frac{\sqrt{d\,x^3+c}}{x^5\,\left(8\,c-d\,x^3\right)} \,d x","Not used",1,"int((c + d*x^3)^(1/2)/(x^5*(8*c - d*x^3)), x)","F"
294,0,-1,678,0.000000,"\text{Not used}","int((c + d*x^3)^(1/2)/(x^8*(8*c - d*x^3)),x)","\int \frac{\sqrt{d\,x^3+c}}{x^8\,\left(8\,c-d\,x^3\right)} \,d x","Not used",1,"int((c + d*x^3)^(1/2)/(x^8*(8*c - d*x^3)), x)","F"
295,1,135,130,3.525304,"\text{Not used}","int((x^11*(c + d*x^3)^(3/2))/(8*c - d*x^3),x)","\frac{4608\,c^{9/2}\,\ln\left(\frac{10\,c+d\,x^3+6\,\sqrt{c}\,\sqrt{d\,x^3+c}}{8\,c-d\,x^3}\right)}{d^4}-\frac{2\,x^{12}\,\sqrt{d\,x^3+c}}{27}-\frac{3018352\,c^4\,\sqrt{d\,x^3+c}}{945\,d^4}-\frac{164\,c\,x^9\,\sqrt{d\,x^3+c}}{189\,d}-\frac{123784\,c^3\,x^3\,\sqrt{d\,x^3+c}}{945\,d^3}-\frac{3074\,c^2\,x^6\,\sqrt{d\,x^3+c}}{315\,d^2}","Not used",1,"(4608*c^(9/2)*log((10*c + d*x^3 + 6*c^(1/2)*(c + d*x^3)^(1/2))/(8*c - d*x^3)))/d^4 - (2*x^12*(c + d*x^3)^(1/2))/27 - (3018352*c^4*(c + d*x^3)^(1/2))/(945*d^4) - (164*c*x^9*(c + d*x^3)^(1/2))/(189*d) - (123784*c^3*x^3*(c + d*x^3)^(1/2))/(945*d^3) - (3074*c^2*x^6*(c + d*x^3)^(1/2))/(315*d^2)","B"
296,1,115,109,3.495063,"\text{Not used}","int((x^8*(c + d*x^3)^(3/2))/(8*c - d*x^3),x)","\frac{576\,c^{7/2}\,\ln\left(\frac{10\,c+d\,x^3+6\,\sqrt{c}\,\sqrt{d\,x^3+c}}{8\,c-d\,x^3}\right)}{d^3}-\frac{2\,x^9\,\sqrt{d\,x^3+c}}{21}-\frac{125764\,c^3\,\sqrt{d\,x^3+c}}{315\,d^3}-\frac{128\,c\,x^6\,\sqrt{d\,x^3+c}}{105\,d}-\frac{5158\,c^2\,x^3\,\sqrt{d\,x^3+c}}{315\,d^2}","Not used",1,"(576*c^(7/2)*log((10*c + d*x^3 + 6*c^(1/2)*(c + d*x^3)^(1/2))/(8*c - d*x^3)))/d^3 - (2*x^9*(c + d*x^3)^(1/2))/21 - (125764*c^3*(c + d*x^3)^(1/2))/(315*d^3) - (128*c*x^6*(c + d*x^3)^(1/2))/(105*d) - (5158*c^2*x^3*(c + d*x^3)^(1/2))/(315*d^2)","B"
297,1,95,88,3.521071,"\text{Not used}","int((x^5*(c + d*x^3)^(3/2))/(8*c - d*x^3),x)","\frac{72\,c^{5/2}\,\ln\left(\frac{10\,c+d\,x^3+6\,\sqrt{c}\,\sqrt{d\,x^3+c}}{8\,c-d\,x^3}\right)}{d^2}-\frac{2\,x^6\,\sqrt{d\,x^3+c}}{15}-\frac{2246\,c^2\,\sqrt{d\,x^3+c}}{45\,d^2}-\frac{92\,c\,x^3\,\sqrt{d\,x^3+c}}{45\,d}","Not used",1,"(72*c^(5/2)*log((10*c + d*x^3 + 6*c^(1/2)*(c + d*x^3)^(1/2))/(8*c - d*x^3)))/d^2 - (2*x^6*(c + d*x^3)^(1/2))/15 - (2246*c^2*(c + d*x^3)^(1/2))/(45*d^2) - (92*c*x^3*(c + d*x^3)^(1/2))/(45*d)","B"
298,1,75,67,3.449073,"\text{Not used}","int((x^2*(c + d*x^3)^(3/2))/(8*c - d*x^3),x)","\frac{9\,c^{3/2}\,\ln\left(\frac{10\,c+d\,x^3+6\,\sqrt{c}\,\sqrt{d\,x^3+c}}{8\,c-d\,x^3}\right)}{d}-\frac{56\,c\,\sqrt{d\,x^3+c}}{9\,d}-\frac{2\,x^3\,\sqrt{d\,x^3+c}}{9}","Not used",1,"(9*c^(3/2)*log((10*c + d*x^3 + 6*c^(1/2)*(c + d*x^3)^(1/2))/(8*c - d*x^3)))/d - (56*c*(c + d*x^3)^(1/2))/(9*d) - (2*x^3*(c + d*x^3)^(1/2))/9","B"
299,1,89,73,5.893384,"\text{Not used}","int((c + d*x^3)^(3/2)/(x*(8*c - d*x^3)),x)","\frac{\sqrt{c}\,\ln\left(\frac{{\left(\sqrt{d\,x^3+c}-\sqrt{c}\right)}^3\,\left(\sqrt{d\,x^3+c}+\sqrt{c}\right)\,{\left(10\,c+d\,x^3+6\,\sqrt{c}\,\sqrt{d\,x^3+c}\right)}^{27}}{x^6\,{\left(8\,c-d\,x^3\right)}^{27}}\right)}{24}-\frac{2\,\sqrt{d\,x^3+c}}{3}","Not used",1,"(c^(1/2)*log((((c + d*x^3)^(1/2) - c^(1/2))^3*((c + d*x^3)^(1/2) + c^(1/2))*(10*c + d*x^3 + 6*c^(1/2)*(c + d*x^3)^(1/2))^27)/(x^6*(8*c - d*x^3)^27)))/24 - (2*(c + d*x^3)^(1/2))/3","B"
300,1,56,78,3.523913,"\text{Not used}","int((c + d*x^3)^(3/2)/(x^4*(8*c - d*x^3)),x)","\frac{9\,d\,\mathrm{atanh}\left(\frac{\sqrt{d\,x^3+c}}{3\,\sqrt{c}}\right)}{32\,\sqrt{c}}-\frac{13\,d\,\mathrm{atanh}\left(\frac{\sqrt{d\,x^3+c}}{\sqrt{c}}\right)}{96\,\sqrt{c}}-\frac{\sqrt{d\,x^3+c}}{24\,x^3}","Not used",1,"(9*d*atanh((c + d*x^3)^(1/2)/(3*c^(1/2))))/(32*c^(1/2)) - (13*d*atanh((c + d*x^3)^(1/2)/c^(1/2)))/(96*c^(1/2)) - (c + d*x^3)^(1/2)/(24*x^3)","B"
301,1,87,104,3.736515,"\text{Not used}","int((c + d*x^3)^(3/2)/(x^7*(8*c - d*x^3)),x)","\frac{7\,\sqrt{d\,x^3+c}}{192\,x^6}-\frac{37\,d^2\,\mathrm{atanh}\left(\frac{c\,\sqrt{d\,x^3+c}}{\sqrt{c^3}}\right)}{768\,\sqrt{c^3}}+\frac{9\,d^2\,\mathrm{atanh}\left(\frac{c\,\sqrt{d\,x^3+c}}{3\,\sqrt{c^3}}\right)}{256\,\sqrt{c^3}}-\frac{11\,{\left(d\,x^3+c\right)}^{3/2}}{192\,c\,x^6}","Not used",1,"(7*(c + d*x^3)^(1/2))/(192*x^6) - (37*d^2*atanh((c*(c + d*x^3)^(1/2))/(c^3)^(1/2)))/(768*(c^3)^(1/2)) + (9*d^2*atanh((c*(c + d*x^3)^(1/2))/(3*(c^3)^(1/2))))/(256*(c^3)^(1/2)) - (11*(c + d*x^3)^(3/2))/(192*c*x^6)","B"
302,0,-1,669,0.000000,"\text{Not used}","int((x^7*(c + d*x^3)^(3/2))/(8*c - d*x^3),x)","\int \frac{x^7\,{\left(d\,x^3+c\right)}^{3/2}}{8\,c-d\,x^3} \,d x","Not used",1,"int((x^7*(c + d*x^3)^(3/2))/(8*c - d*x^3), x)","F"
303,0,-1,645,0.000000,"\text{Not used}","int((x^4*(c + d*x^3)^(3/2))/(8*c - d*x^3),x)","\int \frac{x^4\,{\left(d\,x^3+c\right)}^{3/2}}{8\,c-d\,x^3} \,d x","Not used",1,"int((x^4*(c + d*x^3)^(3/2))/(8*c - d*x^3), x)","F"
304,0,-1,627,0.000000,"\text{Not used}","int((x*(c + d*x^3)^(3/2))/(8*c - d*x^3),x)","\int \frac{x\,{\left(d\,x^3+c\right)}^{3/2}}{8\,c-d\,x^3} \,d x","Not used",1,"int((x*(c + d*x^3)^(3/2))/(8*c - d*x^3), x)","F"
305,0,-1,626,0.000000,"\text{Not used}","int((c + d*x^3)^(3/2)/(x^2*(8*c - d*x^3)),x)","\int \frac{{\left(d\,x^3+c\right)}^{3/2}}{x^2\,\left(8\,c-d\,x^3\right)} \,d x","Not used",1,"int((c + d*x^3)^(3/2)/(x^2*(8*c - d*x^3)), x)","F"
306,0,-1,651,0.000000,"\text{Not used}","int((c + d*x^3)^(3/2)/(x^5*(8*c - d*x^3)),x)","\int \frac{{\left(d\,x^3+c\right)}^{3/2}}{x^5\,\left(8\,c-d\,x^3\right)} \,d x","Not used",1,"int((c + d*x^3)^(3/2)/(x^5*(8*c - d*x^3)), x)","F"
307,0,-1,675,0.000000,"\text{Not used}","int((c + d*x^3)^(3/2)/(x^8*(8*c - d*x^3)),x)","\int \frac{{\left(d\,x^3+c\right)}^{3/2}}{x^8\,\left(8\,c-d\,x^3\right)} \,d x","Not used",1,"int((c + d*x^3)^(3/2)/(x^8*(8*c - d*x^3)), x)","F"
308,1,98,90,3.221137,"\text{Not used}","int(x^11/((c + d*x^3)^(1/2)*(8*c - d*x^3)),x)","\frac{512\,c^{5/2}\,\ln\left(\frac{10\,c+d\,x^3+6\,\sqrt{c}\,\sqrt{d\,x^3+c}}{8\,c-d\,x^3}\right)}{9\,d^4}-\frac{592\,c^2\,\sqrt{d\,x^3+c}}{15\,d^4}-\frac{2\,x^6\,\sqrt{d\,x^3+c}}{15\,d^2}-\frac{8\,c\,x^3\,\sqrt{d\,x^3+c}}{5\,d^3}","Not used",1,"(512*c^(5/2)*log((10*c + d*x^3 + 6*c^(1/2)*(c + d*x^3)^(1/2))/(8*c - d*x^3)))/(9*d^4) - (592*c^2*(c + d*x^3)^(1/2))/(15*d^4) - (2*x^6*(c + d*x^3)^(1/2))/(15*d^2) - (8*c*x^3*(c + d*x^3)^(1/2))/(5*d^3)","B"
309,1,78,71,3.392865,"\text{Not used}","int(x^8/((c + d*x^3)^(1/2)*(8*c - d*x^3)),x)","\frac{64\,c^{3/2}\,\ln\left(\frac{10\,c+d\,x^3+6\,\sqrt{c}\,\sqrt{d\,x^3+c}}{8\,c-d\,x^3}\right)}{9\,d^3}-\frac{44\,c\,\sqrt{d\,x^3+c}}{9\,d^3}-\frac{2\,x^3\,\sqrt{d\,x^3+c}}{9\,d^2}","Not used",1,"(64*c^(3/2)*log((10*c + d*x^3 + 6*c^(1/2)*(c + d*x^3)^(1/2))/(8*c - d*x^3)))/(9*d^3) - (44*c*(c + d*x^3)^(1/2))/(9*d^3) - (2*x^3*(c + d*x^3)^(1/2))/(9*d^2)","B"
310,1,60,52,3.270838,"\text{Not used}","int(x^5/((c + d*x^3)^(1/2)*(8*c - d*x^3)),x)","\frac{8\,\sqrt{c}\,\ln\left(\frac{10\,c+d\,x^3+6\,\sqrt{c}\,\sqrt{d\,x^3+c}}{8\,c-d\,x^3}\right)}{9\,d^2}-\frac{2\,\sqrt{d\,x^3+c}}{3\,d^2}","Not used",1,"(8*c^(1/2)*log((10*c + d*x^3 + 6*c^(1/2)*(c + d*x^3)^(1/2))/(8*c - d*x^3)))/(9*d^2) - (2*(c + d*x^3)^(1/2))/(3*d^2)","B"
311,1,45,33,3.232890,"\text{Not used}","int(x^2/((c + d*x^3)^(1/2)*(8*c - d*x^3)),x)","\frac{\ln\left(\frac{10\,c+d\,x^3+6\,\sqrt{c}\,\sqrt{d\,x^3+c}}{8\,c-d\,x^3}\right)}{9\,\sqrt{c}\,d}","Not used",1,"log((10*c + d*x^3 + 6*c^(1/2)*(c + d*x^3)^(1/2))/(8*c - d*x^3))/(9*c^(1/2)*d)","B"
312,1,47,58,3.283467,"\text{Not used}","int(1/(x*(c + d*x^3)^(1/2)*(8*c - d*x^3)),x)","-\frac{3\,\mathrm{atanh}\left(\frac{c\,\sqrt{d\,x^3+c}}{\sqrt{c^3}}\right)-\mathrm{atanh}\left(\frac{c\,\sqrt{d\,x^3+c}}{3\,\sqrt{c^3}}\right)}{36\,\sqrt{c^3}}","Not used",1,"-(3*atanh((c*(c + d*x^3)^(1/2))/(c^3)^(1/2)) - atanh((c*(c + d*x^3)^(1/2))/(3*(c^3)^(1/2))))/(36*(c^3)^(1/2))","B"
313,1,73,81,3.416697,"\text{Not used}","int(1/(x^4*(c + d*x^3)^(1/2)*(8*c - d*x^3)),x)","\frac{d\,\mathrm{atanh}\left(\frac{c^2\,\sqrt{d\,x^3+c}}{\sqrt{c^5}}\right)}{32\,\sqrt{c^5}}+\frac{d\,\mathrm{atanh}\left(\frac{c^2\,\sqrt{d\,x^3+c}}{3\,\sqrt{c^5}}\right)}{288\,\sqrt{c^5}}-\frac{\sqrt{d\,x^3+c}}{24\,c^2\,x^3}","Not used",1,"(d*atanh((c^2*(c + d*x^3)^(1/2))/(c^5)^(1/2)))/(32*(c^5)^(1/2)) + (d*atanh((c^2*(c + d*x^3)^(1/2))/(3*(c^5)^(1/2))))/(288*(c^5)^(1/2)) - (c + d*x^3)^(1/2)/(24*c^2*x^3)","B"
314,1,94,107,3.500632,"\text{Not used}","int(1/(x^7*(c + d*x^3)^(1/2)*(8*c - d*x^3)),x)","\frac{d^2\,\mathrm{atanh}\left(\frac{c^3\,\sqrt{d\,x^3+c}}{3\,\sqrt{c^7}}\right)}{2304\,\sqrt{c^7}}-\frac{7\,d^2\,\mathrm{atanh}\left(\frac{c^3\,\sqrt{d\,x^3+c}}{\sqrt{c^7}}\right)}{256\,\sqrt{c^7}}-\frac{3\,\sqrt{d\,x^3+c}}{64\,c^2\,x^6}+\frac{5\,{\left(d\,x^3+c\right)}^{3/2}}{192\,c^3\,x^6}","Not used",1,"(d^2*atanh((c^3*(c + d*x^3)^(1/2))/(3*(c^7)^(1/2))))/(2304*(c^7)^(1/2)) - (7*d^2*atanh((c^3*(c + d*x^3)^(1/2))/(c^7)^(1/2)))/(256*(c^7)^(1/2)) - (3*(c + d*x^3)^(1/2))/(64*c^2*x^6) + (5*(c + d*x^3)^(3/2))/(192*c^3*x^6)","B"
315,0,-1,630,0.000000,"\text{Not used}","int(x^7/((c + d*x^3)^(1/2)*(8*c - d*x^3)),x)","\int \frac{x^7}{\sqrt{d\,x^3+c}\,\left(8\,c-d\,x^3\right)} \,d x","Not used",1,"int(x^7/((c + d*x^3)^(1/2)*(8*c - d*x^3)), x)","F"
316,0,-1,601,0.000000,"\text{Not used}","int(x^4/((c + d*x^3)^(1/2)*(8*c - d*x^3)),x)","\int \frac{x^4}{\sqrt{d\,x^3+c}\,\left(8\,c-d\,x^3\right)} \,d x","Not used",1,"int(x^4/((c + d*x^3)^(1/2)*(8*c - d*x^3)), x)","F"
317,1,272,141,40.219380,"\text{Not used}","int(x/((c + d*x^3)^(1/2)*(8*c - d*x^3)),x)","\frac{\ln\left(\frac{\left(\sqrt{d\,x^3+c}+\sqrt{c}\right)\,{\left(\sqrt{d\,x^3+c}-\sqrt{c}+2\,c^{1/6}\,d^{1/3}\,x\right)}^3}{x^3\,{\left(d^{1/3}\,x-2\,c^{1/3}\right)}^3}\right)}{54\,c^{5/6}\,d^{2/3}}+\frac{\sqrt{2}\,\ln\left(\frac{\left(\sqrt{d\,x^3+c}-\sqrt{c}\right)\,{\left(-\sqrt{3}\,c^{1/6}\,d^{1/3}\,x+\sqrt{d\,x^3+c}\,1{}\mathrm{i}+\sqrt{c}\,1{}\mathrm{i}+c^{1/6}\,d^{1/3}\,x\,1{}\mathrm{i}\right)}^3}{x^3\,{\left(d^{1/3}\,x+c^{1/3}-\sqrt{3}\,c^{1/3}\,1{}\mathrm{i}\right)}^3}\right)\,\sqrt{-1+\sqrt{3}\,1{}\mathrm{i}}}{108\,c^{5/6}\,d^{2/3}}+\frac{\sqrt{2}\,\ln\left(\frac{\left(\sqrt{d\,x^3+c}+\sqrt{c}\right)\,{\left(\sqrt{3}\,c^{1/6}\,d^{1/3}\,x-\sqrt{d\,x^3+c}\,1{}\mathrm{i}+\sqrt{c}\,1{}\mathrm{i}+c^{1/6}\,d^{1/3}\,x\,1{}\mathrm{i}\right)}^3}{x^3\,{\left(d^{1/3}\,x+c^{1/3}+\sqrt{3}\,c^{1/3}\,1{}\mathrm{i}\right)}^3}\right)\,\sqrt{1+\sqrt{3}\,1{}\mathrm{i}}\,1{}\mathrm{i}}{108\,c^{5/6}\,d^{2/3}}","Not used",1,"log((((c + d*x^3)^(1/2) + c^(1/2))*((c + d*x^3)^(1/2) - c^(1/2) + 2*c^(1/6)*d^(1/3)*x)^3)/(x^3*(d^(1/3)*x - 2*c^(1/3))^3))/(54*c^(5/6)*d^(2/3)) + (2^(1/2)*log((((c + d*x^3)^(1/2) - c^(1/2))*((c + d*x^3)^(1/2)*1i + c^(1/2)*1i + c^(1/6)*d^(1/3)*x*1i - 3^(1/2)*c^(1/6)*d^(1/3)*x)^3)/(x^3*(d^(1/3)*x - 3^(1/2)*c^(1/3)*1i + c^(1/3))^3))*(3^(1/2)*1i - 1)^(1/2))/(108*c^(5/6)*d^(2/3)) + (2^(1/2)*log((((c + d*x^3)^(1/2) + c^(1/2))*(c^(1/2)*1i - (c + d*x^3)^(1/2)*1i + c^(1/6)*d^(1/3)*x*1i + 3^(1/2)*c^(1/6)*d^(1/3)*x)^3)/(x^3*(3^(1/2)*c^(1/3)*1i + d^(1/3)*x + c^(1/3))^3))*(3^(1/2)*1i + 1)^(1/2)*1i)/(108*c^(5/6)*d^(2/3))","B"
318,0,-1,632,0.000000,"\text{Not used}","int(1/(x^2*(c + d*x^3)^(1/2)*(8*c - d*x^3)),x)","\int \frac{1}{x^2\,\sqrt{d\,x^3+c}\,\left(8\,c-d\,x^3\right)} \,d x","Not used",1,"int(1/(x^2*(c + d*x^3)^(1/2)*(8*c - d*x^3)), x)","F"
319,0,-1,654,0.000000,"\text{Not used}","int(1/(x^5*(c + d*x^3)^(1/2)*(8*c - d*x^3)),x)","\int \frac{1}{x^5\,\sqrt{d\,x^3+c}\,\left(8\,c-d\,x^3\right)} \,d x","Not used",1,"int(1/(x^5*(c + d*x^3)^(1/2)*(8*c - d*x^3)), x)","F"
320,0,-1,678,0.000000,"\text{Not used}","int(1/(x^8*(c + d*x^3)^(1/2)*(8*c - d*x^3)),x)","\int \frac{1}{x^8\,\sqrt{d\,x^3+c}\,\left(8\,c-d\,x^3\right)} \,d x","Not used",1,"int(1/(x^8*(c + d*x^3)^(1/2)*(8*c - d*x^3)), x)","F"
321,0,-1,66,0.000000,"\text{Not used}","int(x^3/((c + d*x^3)^(1/2)*(8*c - d*x^3)),x)","\int \frac{x^3}{\sqrt{d\,x^3+c}\,\left(8\,c-d\,x^3\right)} \,d x","Not used",1,"int(x^3/((c + d*x^3)^(1/2)*(8*c - d*x^3)), x)","F"
322,0,-1,64,0.000000,"\text{Not used}","int(1/((c + d*x^3)^(1/2)*(8*c - d*x^3)),x)","\int \frac{1}{\sqrt{d\,x^3+c}\,\left(8\,c-d\,x^3\right)} \,d x","Not used",1,"int(1/((c + d*x^3)^(1/2)*(8*c - d*x^3)), x)","F"
323,0,-1,66,0.000000,"\text{Not used}","int(1/(x^3*(c + d*x^3)^(1/2)*(8*c - d*x^3)),x)","\int \frac{1}{x^3\,\sqrt{d\,x^3+c}\,\left(8\,c-d\,x^3\right)} \,d x","Not used",1,"int(1/(x^3*(c + d*x^3)^(1/2)*(8*c - d*x^3)), x)","F"
324,0,-1,66,0.000000,"\text{Not used}","int(1/(x^6*(c + d*x^3)^(1/2)*(8*c - d*x^3)),x)","\int \frac{1}{x^6\,\sqrt{d\,x^3+c}\,\left(8\,c-d\,x^3\right)} \,d x","Not used",1,"int(1/(x^6*(c + d*x^3)^(1/2)*(8*c - d*x^3)), x)","F"
325,1,95,90,3.781706,"\text{Not used}","int(x^11/((c + d*x^3)^(3/2)*(8*c - d*x^3)),x)","\frac{512\,c^{3/2}\,\ln\left(\frac{10\,c+d\,x^3+6\,\sqrt{c}\,\sqrt{d\,x^3+c}}{8\,c-d\,x^3}\right)}{81\,d^4}-\frac{38\,c\,\sqrt{d\,x^3+c}}{9\,d^4}+\frac{2\,c^2}{27\,d^4\,\sqrt{d\,x^3+c}}-\frac{2\,x^3\,\sqrt{d\,x^3+c}}{9\,d^3}","Not used",1,"(512*c^(3/2)*log((10*c + d*x^3 + 6*c^(1/2)*(c + d*x^3)^(1/2))/(8*c - d*x^3)))/(81*d^4) - (38*c*(c + d*x^3)^(1/2))/(9*d^4) + (2*c^2)/(27*d^4*(c + d*x^3)^(1/2)) - (2*x^3*(c + d*x^3)^(1/2))/(9*d^3)","B"
326,1,75,71,3.711745,"\text{Not used}","int(x^8/((c + d*x^3)^(3/2)*(8*c - d*x^3)),x)","\frac{64\,\sqrt{c}\,\ln\left(\frac{10\,c+d\,x^3+6\,\sqrt{c}\,\sqrt{d\,x^3+c}}{8\,c-d\,x^3}\right)}{81\,d^3}-\frac{2\,c}{27\,d^3\,\sqrt{d\,x^3+c}}-\frac{2\,\sqrt{d\,x^3+c}}{3\,d^3}","Not used",1,"(64*c^(1/2)*log((10*c + d*x^3 + 6*c^(1/2)*(c + d*x^3)^(1/2))/(8*c - d*x^3)))/(81*d^3) - (2*c)/(27*d^3*(c + d*x^3)^(1/2)) - (2*(c + d*x^3)^(1/2))/(3*d^3)","B"
327,1,60,52,3.677041,"\text{Not used}","int(x^5/((c + d*x^3)^(3/2)*(8*c - d*x^3)),x)","\frac{2}{27\,d^2\,\sqrt{d\,x^3+c}}+\frac{8\,\ln\left(\frac{10\,c+d\,x^3+6\,\sqrt{c}\,\sqrt{d\,x^3+c}}{8\,c-d\,x^3}\right)}{81\,\sqrt{c}\,d^2}","Not used",1,"2/(27*d^2*(c + d*x^3)^(1/2)) + (8*log((10*c + d*x^3 + 6*c^(1/2)*(c + d*x^3)^(1/2))/(8*c - d*x^3)))/(81*c^(1/2)*d^2)","B"
328,1,63,55,3.629794,"\text{Not used}","int(x^2/((c + d*x^3)^(3/2)*(8*c - d*x^3)),x)","\frac{\ln\left(\frac{10\,c+d\,x^3+6\,\sqrt{c}\,\sqrt{d\,x^3+c}}{8\,c-d\,x^3}\right)}{81\,c^{3/2}\,d}-\frac{2}{27\,c\,d\,\sqrt{d\,x^3+c}}","Not used",1,"log((10*c + d*x^3 + 6*c^(1/2)*(c + d*x^3)^(1/2))/(8*c - d*x^3))/(81*c^(3/2)*d) - 2/(27*c*d*(c + d*x^3)^(1/2))","B"
329,1,68,76,3.661939,"\text{Not used}","int(1/(x*(c + d*x^3)^(3/2)*(8*c - d*x^3)),x)","\frac{2}{27\,c^2\,\sqrt{d\,x^3+c}}-\frac{\mathrm{atanh}\left(\frac{c^2\,\sqrt{d\,x^3+c}}{\sqrt{c^5}}\right)}{12\,\sqrt{c^5}}+\frac{\mathrm{atanh}\left(\frac{c^2\,\sqrt{d\,x^3+c}}{3\,\sqrt{c^5}}\right)}{324\,\sqrt{c^5}}","Not used",1,"2/(27*c^2*(c + d*x^3)^(1/2)) - atanh((c^2*(c + d*x^3)^(1/2))/(c^5)^(1/2))/(12*(c^5)^(1/2)) + atanh((c^2*(c + d*x^3)^(1/2))/(3*(c^5)^(1/2)))/(324*(c^5)^(1/2))","B"
330,1,88,100,3.800982,"\text{Not used}","int(1/(x^4*(c + d*x^3)^(3/2)*(8*c - d*x^3)),x)","\frac{11\,d\,\mathrm{atanh}\left(\frac{c^3\,\sqrt{d\,x^3+c}}{\sqrt{c^7}}\right)}{96\,\sqrt{c^7}}-\frac{25\,d}{216\,c^3\,\sqrt{d\,x^3+c}}+\frac{d\,\mathrm{atanh}\left(\frac{c^3\,\sqrt{d\,x^3+c}}{3\,\sqrt{c^7}}\right)}{2592\,\sqrt{c^7}}-\frac{1}{24\,c^2\,x^3\,\sqrt{d\,x^3+c}}","Not used",1,"(11*d*atanh((c^3*(c + d*x^3)^(1/2))/(c^7)^(1/2)))/(96*(c^7)^(1/2)) - (25*d)/(216*c^3*(c + d*x^3)^(1/2)) + (d*atanh((c^3*(c + d*x^3)^(1/2))/(3*(c^7)^(1/2))))/(2592*(c^7)^(1/2)) - 1/(24*c^2*x^3*(c + d*x^3)^(1/2))","B"
331,1,112,128,4.025218,"\text{Not used}","int(1/(x^7*(c + d*x^3)^(3/2)*(8*c - d*x^3)),x)","\frac{245\,d^2}{1728\,c^4\,\sqrt{d\,x^3+c}}-\frac{109\,d^2\,\mathrm{atanh}\left(\frac{c^4\,\sqrt{d\,x^3+c}}{\sqrt{c^9}}\right)}{768\,\sqrt{c^9}}+\frac{d^2\,\mathrm{atanh}\left(\frac{c^4\,\sqrt{d\,x^3+c}}{3\,\sqrt{c^9}}\right)}{20736\,\sqrt{c^9}}-\frac{1}{48\,c^2\,x^6\,\sqrt{d\,x^3+c}}+\frac{3\,d}{64\,c^3\,x^3\,\sqrt{d\,x^3+c}}","Not used",1,"(245*d^2)/(1728*c^4*(c + d*x^3)^(1/2)) - (109*d^2*atanh((c^4*(c + d*x^3)^(1/2))/(c^9)^(1/2)))/(768*(c^9)^(1/2)) + (d^2*atanh((c^4*(c + d*x^3)^(1/2))/(3*(c^9)^(1/2))))/(20736*(c^9)^(1/2)) - 1/(48*c^2*x^6*(c + d*x^3)^(1/2)) + (3*d)/(64*c^3*x^3*(c + d*x^3)^(1/2))","B"
332,0,-1,629,0.000000,"\text{Not used}","int(x^7/((c + d*x^3)^(3/2)*(8*c - d*x^3)),x)","\int \frac{x^7}{{\left(d\,x^3+c\right)}^{3/2}\,\left(8\,c-d\,x^3\right)} \,d x","Not used",1,"int(x^7/((c + d*x^3)^(3/2)*(8*c - d*x^3)), x)","F"
333,0,-1,635,0.000000,"\text{Not used}","int(x^4/((c + d*x^3)^(3/2)*(8*c - d*x^3)),x)","\int \frac{x^4}{{\left(d\,x^3+c\right)}^{3/2}\,\left(8\,c-d\,x^3\right)} \,d x","Not used",1,"int(x^4/((c + d*x^3)^(3/2)*(8*c - d*x^3)), x)","F"
334,0,-1,632,0.000000,"\text{Not used}","int(x/((c + d*x^3)^(3/2)*(8*c - d*x^3)),x)","\int \frac{x}{{\left(d\,x^3+c\right)}^{3/2}\,\left(8\,c-d\,x^3\right)} \,d x","Not used",1,"int(x/((c + d*x^3)^(3/2)*(8*c - d*x^3)), x)","F"
335,0,-1,653,0.000000,"\text{Not used}","int(1/(x^2*(c + d*x^3)^(3/2)*(8*c - d*x^3)),x)","\int \frac{1}{x^2\,{\left(d\,x^3+c\right)}^{3/2}\,\left(8\,c-d\,x^3\right)} \,d x","Not used",1,"int(1/(x^2*(c + d*x^3)^(3/2)*(8*c - d*x^3)), x)","F"
336,0,-1,675,0.000000,"\text{Not used}","int(1/(x^5*(c + d*x^3)^(3/2)*(8*c - d*x^3)),x)","\int \frac{1}{x^5\,{\left(d\,x^3+c\right)}^{3/2}\,\left(8\,c-d\,x^3\right)} \,d x","Not used",1,"int(1/(x^5*(c + d*x^3)^(3/2)*(8*c - d*x^3)), x)","F"
337,0,-1,699,0.000000,"\text{Not used}","int(1/(x^8*(c + d*x^3)^(3/2)*(8*c - d*x^3)),x)","\int \frac{1}{x^8\,{\left(d\,x^3+c\right)}^{3/2}\,\left(8\,c-d\,x^3\right)} \,d x","Not used",1,"int(1/(x^8*(c + d*x^3)^(3/2)*(8*c - d*x^3)), x)","F"
338,0,-1,66,0.000000,"\text{Not used}","int(x^3/((c + d*x^3)^(3/2)*(8*c - d*x^3)),x)","\int \frac{x^3}{{\left(d\,x^3+c\right)}^{3/2}\,\left(8\,c-d\,x^3\right)} \,d x","Not used",1,"int(x^3/((c + d*x^3)^(3/2)*(8*c - d*x^3)), x)","F"
339,0,-1,64,0.000000,"\text{Not used}","int(1/((c + d*x^3)^(3/2)*(8*c - d*x^3)),x)","\int \frac{1}{{\left(d\,x^3+c\right)}^{3/2}\,\left(8\,c-d\,x^3\right)} \,d x","Not used",1,"int(1/((c + d*x^3)^(3/2)*(8*c - d*x^3)), x)","F"
340,0,-1,66,0.000000,"\text{Not used}","int(1/(x^3*(c + d*x^3)^(3/2)*(8*c - d*x^3)),x)","\int \frac{1}{x^3\,{\left(d\,x^3+c\right)}^{3/2}\,\left(8\,c-d\,x^3\right)} \,d x","Not used",1,"int(1/(x^3*(c + d*x^3)^(3/2)*(8*c - d*x^3)), x)","F"
341,0,-1,66,0.000000,"\text{Not used}","int(1/(x^6*(c + d*x^3)^(3/2)*(8*c - d*x^3)),x)","\int \frac{1}{x^6\,{\left(d\,x^3+c\right)}^{3/2}\,\left(8\,c-d\,x^3\right)} \,d x","Not used",1,"int(1/(x^6*(c + d*x^3)^(3/2)*(8*c - d*x^3)), x)","F"
342,0,-1,737,0.000000,"\text{Not used}","int((x*(a + b*x^3)^(1/2))/(b*x^3 + 2*a*(3*3^(1/2) + 5)),x)","\int \frac{x\,\sqrt{b\,x^3+a}}{b\,x^3+2\,a\,\left(3\,\sqrt{3}+5\right)} \,d x","Not used",1,"int((x*(a + b*x^3)^(1/2))/(b*x^3 + 2*a*(3*3^(1/2) + 5)), x)","F"
343,0,-1,757,0.000000,"\text{Not used}","int(-(x*(a - b*x^3)^(1/2))/(b*x^3 - 2*a*(3*3^(1/2) + 5)),x)","-\int \frac{x\,\sqrt{a-b\,x^3}}{b\,x^3-2\,a\,\left(3\,\sqrt{3}+5\right)} \,d x","Not used",1,"-int((x*(a - b*x^3)^(1/2))/(b*x^3 - 2*a*(3*3^(1/2) + 5)), x)","F"
344,0,-1,774,0.000000,"\text{Not used}","int((x*(b*x^3 - a)^(1/2))/(b*x^3 - 2*a*(3*3^(1/2) + 5)),x)","\int \frac{x\,\sqrt{b\,x^3-a}}{b\,x^3-2\,a\,\left(3\,\sqrt{3}+5\right)} \,d x","Not used",1,"int((x*(b*x^3 - a)^(1/2))/(b*x^3 - 2*a*(3*3^(1/2) + 5)), x)","F"
345,0,-1,768,0.000000,"\text{Not used}","int(-(x*(- a - b*x^3)^(1/2))/(b*x^3 + 2*a*(3*3^(1/2) + 5)),x)","\int -\frac{x\,\sqrt{-b\,x^3-a}}{b\,x^3+2\,a\,\left(3\,\sqrt{3}+5\right)} \,d x","Not used",1,"int(-(x*(- a - b*x^3)^(1/2))/(b*x^3 + 2*a*(3*3^(1/2) + 5)), x)","F"
346,0,-1,738,0.000000,"\text{Not used}","int((x*(a + b*x^3)^(1/2))/(b*x^3 - 2*a*(3*3^(1/2) - 5)),x)","\int \frac{x\,\sqrt{b\,x^3+a}}{b\,x^3-2\,a\,\left(3\,\sqrt{3}-5\right)} \,d x","Not used",1,"int((x*(a + b*x^3)^(1/2))/(b*x^3 - 2*a*(3*3^(1/2) - 5)), x)","F"
347,0,-1,758,0.000000,"\text{Not used}","int(-(x*(a - b*x^3)^(1/2))/(b*x^3 + 2*a*(3*3^(1/2) - 5)),x)","\int -\frac{x\,\sqrt{a-b\,x^3}}{b\,x^3+2\,a\,\left(3\,\sqrt{3}-5\right)} \,d x","Not used",1,"int(-(x*(a - b*x^3)^(1/2))/(b*x^3 + 2*a*(3*3^(1/2) - 5)), x)","F"
348,0,-1,774,0.000000,"\text{Not used}","int(-(x*(b*x^3 - a)^(1/2))/(b*x^3 + 2*a*(3*3^(1/2) - 5)),x)","\int -\frac{x\,\sqrt{b\,x^3-a}}{b\,x^3+2\,a\,\left(3\,\sqrt{3}-5\right)} \,d x","Not used",1,"int(-(x*(b*x^3 - a)^(1/2))/(b*x^3 + 2*a*(3*3^(1/2) - 5)), x)","F"
349,0,-1,768,0.000000,"\text{Not used}","int((x*(- a - b*x^3)^(1/2))/(b*x^3 - 2*a*(3*3^(1/2) - 5)),x)","\int \frac{x\,\sqrt{-b\,x^3-a}}{b\,x^3-2\,a\,\left(3\,\sqrt{3}-5\right)} \,d x","Not used",1,"int((x*(- a - b*x^3)^(1/2))/(b*x^3 - 2*a*(3*3^(1/2) - 5)), x)","F"
350,0,-1,318,0.000000,"\text{Not used}","int(x/((a + b*x^3)^(1/2)*(b*x^3 + 2*a*(3*3^(1/2) + 5))),x)","\int \frac{x}{\sqrt{b\,x^3+a}\,\left(b\,x^3+2\,a\,\left(3\,\sqrt{3}+5\right)\right)} \,d x","Not used",1,"int(x/((a + b*x^3)^(1/2)*(b*x^3 + 2*a*(3*3^(1/2) + 5))), x)","F"
351,0,-1,324,0.000000,"\text{Not used}","int(-x/((a - b*x^3)^(1/2)*(b*x^3 - 2*a*(3*3^(1/2) + 5))),x)","-\int \frac{x}{\sqrt{a-b\,x^3}\,\left(b\,x^3-2\,a\,\left(3\,\sqrt{3}+5\right)\right)} \,d x","Not used",1,"-int(x/((a - b*x^3)^(1/2)*(b*x^3 - 2*a*(3*3^(1/2) + 5))), x)","F"
352,0,-1,328,0.000000,"\text{Not used}","int(x/((b*x^3 - a)^(1/2)*(b*x^3 - 2*a*(3*3^(1/2) + 5))),x)","\int \frac{x}{\sqrt{b\,x^3-a}\,\left(b\,x^3-2\,a\,\left(3\,\sqrt{3}+5\right)\right)} \,d x","Not used",1,"int(x/((b*x^3 - a)^(1/2)*(b*x^3 - 2*a*(3*3^(1/2) + 5))), x)","F"
353,0,-1,330,0.000000,"\text{Not used}","int(-x/((- a - b*x^3)^(1/2)*(b*x^3 + 2*a*(3*3^(1/2) + 5))),x)","\int -\frac{x}{\sqrt{-b\,x^3-a}\,\left(b\,x^3+2\,a\,\left(3\,\sqrt{3}+5\right)\right)} \,d x","Not used",1,"int(-x/((- a - b*x^3)^(1/2)*(b*x^3 + 2*a*(3*3^(1/2) + 5))), x)","F"
354,0,-1,310,0.000000,"\text{Not used}","int(x/((a + b*x^3)^(1/2)*(b*x^3 - 2*a*(3*3^(1/2) - 5))),x)","\int \frac{x}{\sqrt{b\,x^3+a}\,\left(b\,x^3-2\,a\,\left(3\,\sqrt{3}-5\right)\right)} \,d x","Not used",1,"int(x/((a + b*x^3)^(1/2)*(b*x^3 - 2*a*(3*3^(1/2) - 5))), x)","F"
355,0,-1,316,0.000000,"\text{Not used}","int(-x/((a - b*x^3)^(1/2)*(b*x^3 + 2*a*(3*3^(1/2) - 5))),x)","\int -\frac{x}{\sqrt{a-b\,x^3}\,\left(b\,x^3+2\,a\,\left(3\,\sqrt{3}-5\right)\right)} \,d x","Not used",1,"int(-x/((a - b*x^3)^(1/2)*(b*x^3 + 2*a*(3*3^(1/2) - 5))), x)","F"
356,0,-1,320,0.000000,"\text{Not used}","int(-x/((b*x^3 - a)^(1/2)*(b*x^3 + 2*a*(3*3^(1/2) - 5))),x)","\int -\frac{x}{\sqrt{b\,x^3-a}\,\left(b\,x^3+2\,a\,\left(3\,\sqrt{3}-5\right)\right)} \,d x","Not used",1,"int(-x/((b*x^3 - a)^(1/2)*(b*x^3 + 2*a*(3*3^(1/2) - 5))), x)","F"
357,0,-1,322,0.000000,"\text{Not used}","int(x/((- a - b*x^3)^(1/2)*(b*x^3 - 2*a*(3*3^(1/2) - 5))),x)","\int \frac{x}{\sqrt{-b\,x^3-a}\,\left(b\,x^3-2\,a\,\left(3\,\sqrt{3}-5\right)\right)} \,d x","Not used",1,"int(x/((- a - b*x^3)^(1/2)*(b*x^3 - 2*a*(3*3^(1/2) - 5))), x)","F"
358,1,176,125,6.170765,"\text{Not used}","int((x^8*(c + d*x^3)^(1/2))/(a + b*x^3),x)","\frac{2\,a^2\,\sqrt{d\,x^3+c}}{3\,b^3}+\frac{2\,{\left(d\,x^3+c\right)}^{5/2}}{15\,b\,d^2}-\frac{2\,a\,{\left(d\,x^3+c\right)}^{3/2}}{9\,b^2\,d}-\frac{2\,c\,{\left(d\,x^3+c\right)}^{3/2}}{9\,b\,d^2}+\frac{a^2\,\ln\left(\frac{a^2\,d^2\,1{}\mathrm{i}+b^2\,c^2\,2{}\mathrm{i}-2\,\sqrt{b}\,\sqrt{d\,x^3+c}\,{\left(a\,d-b\,c\right)}^{3/2}-a\,b\,d^2\,x^3\,1{}\mathrm{i}+b^2\,c\,d\,x^3\,1{}\mathrm{i}-a\,b\,c\,d\,3{}\mathrm{i}}{2\,b\,x^3+2\,a}\right)\,\sqrt{a\,d-b\,c}\,1{}\mathrm{i}}{3\,b^{7/2}}","Not used",1,"(2*a^2*(c + d*x^3)^(1/2))/(3*b^3) + (2*(c + d*x^3)^(5/2))/(15*b*d^2) - (2*a*(c + d*x^3)^(3/2))/(9*b^2*d) - (2*c*(c + d*x^3)^(3/2))/(9*b*d^2) + (a^2*log((a^2*d^2*1i + b^2*c^2*2i - 2*b^(1/2)*(c + d*x^3)^(1/2)*(a*d - b*c)^(3/2) - a*b*d^2*x^3*1i + b^2*c*d*x^3*1i - a*b*c*d*3i)/(2*a + 2*b*x^3))*(a*d - b*c)^(1/2)*1i)/(3*b^(7/2))","B"
359,1,136,93,6.057867,"\text{Not used}","int((x^5*(c + d*x^3)^(1/2))/(a + b*x^3),x)","\frac{2\,{\left(d\,x^3+c\right)}^{3/2}}{9\,b\,d}-\frac{2\,a\,\sqrt{d\,x^3+c}}{3\,b^2}+\frac{a\,\ln\left(\frac{a^2\,d^2\,1{}\mathrm{i}+b^2\,c^2\,2{}\mathrm{i}+2\,\sqrt{b}\,\sqrt{d\,x^3+c}\,{\left(a\,d-b\,c\right)}^{3/2}-a\,b\,d^2\,x^3\,1{}\mathrm{i}+b^2\,c\,d\,x^3\,1{}\mathrm{i}-a\,b\,c\,d\,3{}\mathrm{i}}{2\,b\,x^3+2\,a}\right)\,\sqrt{a\,d-b\,c}\,1{}\mathrm{i}}{3\,b^{5/2}}","Not used",1,"(2*(c + d*x^3)^(3/2))/(9*b*d) - (2*a*(c + d*x^3)^(1/2))/(3*b^2) + (a*log((a^2*d^2*1i + b^2*c^2*2i + 2*b^(1/2)*(c + d*x^3)^(1/2)*(a*d - b*c)^(3/2) - a*b*d^2*x^3*1i + b^2*c*d*x^3*1i - a*b*c*d*3i)/(2*a + 2*b*x^3))*(a*d - b*c)^(1/2)*1i)/(3*b^(5/2))","B"
360,1,82,70,6.155521,"\text{Not used}","int((x^2*(c + d*x^3)^(1/2))/(a + b*x^3),x)","\frac{2\,\sqrt{d\,x^3+c}}{3\,b}+\frac{\ln\left(\frac{a\,d-2\,b\,c-b\,d\,x^3+\sqrt{b}\,\sqrt{d\,x^3+c}\,\sqrt{a\,d-b\,c}\,2{}\mathrm{i}}{b\,x^3+a}\right)\,\sqrt{a\,d-b\,c}\,1{}\mathrm{i}}{3\,b^{3/2}}","Not used",1,"(2*(c + d*x^3)^(1/2))/(3*b) + (log((a*d - 2*b*c + b^(1/2)*(c + d*x^3)^(1/2)*(a*d - b*c)^(1/2)*2i - b*d*x^3)/(a + b*x^3))*(a*d - b*c)^(1/2)*1i)/(3*b^(3/2))","B"
361,1,114,85,7.937779,"\text{Not used}","int((c + d*x^3)^(1/2)/(x*(a + b*x^3)),x)","\frac{\sqrt{c}\,\ln\left(\frac{{\left(\sqrt{d\,x^3+c}-\sqrt{c}\right)}^3\,\left(\sqrt{d\,x^3+c}+\sqrt{c}\right)}{x^6}\right)}{3\,a}+\frac{\ln\left(\frac{2\,b\,c-a\,d+b\,d\,x^3+\sqrt{b}\,\sqrt{d\,x^3+c}\,\sqrt{a\,d-b\,c}\,2{}\mathrm{i}}{b\,x^3+a}\right)\,\sqrt{a\,d-b\,c}\,1{}\mathrm{i}}{3\,a\,\sqrt{b}}","Not used",1,"(c^(1/2)*log((((c + d*x^3)^(1/2) - c^(1/2))^3*((c + d*x^3)^(1/2) + c^(1/2)))/x^6))/(3*a) + (log((2*b*c - a*d + b^(1/2)*(c + d*x^3)^(1/2)*(a*d - b*c)^(1/2)*2i + b*d*x^3)/(a + b*x^3))*(a*d - b*c)^(1/2)*1i)/(3*a*b^(1/2))","B"
362,1,137,115,5.130121,"\text{Not used}","int((c + d*x^3)^(1/2)/(x^4*(a + b*x^3)),x)","\frac{\ln\left(\frac{a\,d-2\,b\,c+2\,\sqrt{d\,x^3+c}\,\sqrt{b^2\,c-a\,b\,d}-b\,d\,x^3}{b\,x^3+a}\right)\,\sqrt{b^2\,c-a\,b\,d}}{3\,a^2}-\frac{\sqrt{d\,x^3+c}}{3\,a\,x^3}+\frac{\ln\left(\frac{{\left(\sqrt{d\,x^3+c}-\sqrt{c}\right)}^3\,\left(\sqrt{d\,x^3+c}+\sqrt{c}\right)}{x^6}\right)\,\left(a\,d-2\,b\,c\right)}{6\,a^2\,\sqrt{c}}","Not used",1,"(log((a*d - 2*b*c + 2*(c + d*x^3)^(1/2)*(b^2*c - a*b*d)^(1/2) - b*d*x^3)/(a + b*x^3))*(b^2*c - a*b*d)^(1/2))/(3*a^2) - (c + d*x^3)^(1/2)/(3*a*x^3) + (log((((c + d*x^3)^(1/2) - c^(1/2))^3*((c + d*x^3)^(1/2) + c^(1/2)))/x^6)*(a*d - 2*b*c))/(6*a^2*c^(1/2))","B"
363,0,-1,64,0.000000,"\text{Not used}","int((x^3*(c + d*x^3)^(1/2))/(a + b*x^3),x)","\int \frac{x^3\,\sqrt{d\,x^3+c}}{b\,x^3+a} \,d x","Not used",1,"int((x^3*(c + d*x^3)^(1/2))/(a + b*x^3), x)","F"
364,0,-1,64,0.000000,"\text{Not used}","int((x*(c + d*x^3)^(1/2))/(a + b*x^3),x)","\int \frac{x\,\sqrt{d\,x^3+c}}{b\,x^3+a} \,d x","Not used",1,"int((x*(c + d*x^3)^(1/2))/(a + b*x^3), x)","F"
365,0,-1,59,0.000000,"\text{Not used}","int((c + d*x^3)^(1/2)/(a + b*x^3),x)","\int \frac{\sqrt{d\,x^3+c}}{b\,x^3+a} \,d x","Not used",1,"int((c + d*x^3)^(1/2)/(a + b*x^3), x)","F"
366,0,-1,62,0.000000,"\text{Not used}","int((c + d*x^3)^(1/2)/(x^2*(a + b*x^3)),x)","\int \frac{\sqrt{d\,x^3+c}}{x^2\,\left(b\,x^3+a\right)} \,d x","Not used",1,"int((c + d*x^3)^(1/2)/(x^2*(a + b*x^3)), x)","F"
367,0,-1,64,0.000000,"\text{Not used}","int((c + d*x^3)^(1/2)/(x^3*(a + b*x^3)),x)","\int \frac{\sqrt{d\,x^3+c}}{x^3\,\left(b\,x^3+a\right)} \,d x","Not used",1,"int((c + d*x^3)^(1/2)/(x^3*(a + b*x^3)), x)","F"
368,1,330,154,6.122159,"\text{Not used}","int((x^8*(c + d*x^3)^(3/2))/(a + b*x^3),x)","\frac{2\,d\,x^9\,\sqrt{d\,x^3+c}}{21\,b}-\frac{\left(\frac{2\,a\,\left(\frac{c^2}{b}+\frac{a\,\left(\frac{a\,d^2}{b^2}-\frac{2\,c\,d}{b}\right)}{b}\right)}{b}+\frac{2\,c\,\left(\frac{2\,c^2}{b}+\frac{2\,a\,\left(\frac{a\,d^2}{b^2}-\frac{2\,c\,d}{b}\right)}{b}+\frac{4\,c\,\left(\frac{2\,a\,d^2}{b^2}-\frac{16\,c\,d}{7\,b}\right)}{5\,d}\right)}{3\,d}\right)\,\sqrt{d\,x^3+c}}{3\,d}+\frac{x^3\,\sqrt{d\,x^3+c}\,\left(\frac{2\,c^2}{b}+\frac{2\,a\,\left(\frac{a\,d^2}{b^2}-\frac{2\,c\,d}{b}\right)}{b}+\frac{4\,c\,\left(\frac{2\,a\,d^2}{b^2}-\frac{16\,c\,d}{7\,b}\right)}{5\,d}\right)}{9\,d}-\frac{x^6\,\sqrt{d\,x^3+c}\,\left(\frac{2\,a\,d^2}{b^2}-\frac{16\,c\,d}{7\,b}\right)}{15\,d}+\frac{a^2\,\ln\left(\frac{a^2\,d^2+2\,b^2\,c^2-a\,b\,d^2\,x^3+b^2\,c\,d\,x^3-3\,a\,b\,c\,d-\sqrt{b}\,\sqrt{d\,x^3+c}\,{\left(a\,d-b\,c\right)}^{3/2}\,2{}\mathrm{i}}{b\,x^3+a}\right)\,{\left(a\,d-b\,c\right)}^{3/2}\,1{}\mathrm{i}}{3\,b^{9/2}}","Not used",1,"(2*d*x^9*(c + d*x^3)^(1/2))/(21*b) - (((2*a*(c^2/b + (a*((a*d^2)/b^2 - (2*c*d)/b))/b))/b + (2*c*((2*c^2)/b + (2*a*((a*d^2)/b^2 - (2*c*d)/b))/b + (4*c*((2*a*d^2)/b^2 - (16*c*d)/(7*b)))/(5*d)))/(3*d))*(c + d*x^3)^(1/2))/(3*d) + (x^3*(c + d*x^3)^(1/2)*((2*c^2)/b + (2*a*((a*d^2)/b^2 - (2*c*d)/b))/b + (4*c*((2*a*d^2)/b^2 - (16*c*d)/(7*b)))/(5*d)))/(9*d) - (x^6*(c + d*x^3)^(1/2)*((2*a*d^2)/b^2 - (16*c*d)/(7*b)))/(15*d) + (a^2*log((a^2*d^2 + 2*b^2*c^2 - b^(1/2)*(c + d*x^3)^(1/2)*(a*d - b*c)^(3/2)*2i - a*b*d^2*x^3 + b^2*c*d*x^3 - 3*a*b*c*d)/(a + b*x^3))*(a*d - b*c)^(3/2)*1i)/(3*b^(9/2))","B"
369,1,215,120,6.133787,"\text{Not used}","int((x^5*(c + d*x^3)^(3/2))/(a + b*x^3),x)","\frac{\sqrt{d\,x^3+c}\,\left(\frac{2\,c^2}{b}+\frac{2\,a\,\left(\frac{a\,d^2}{b^2}-\frac{2\,c\,d}{b}\right)}{b}+\frac{2\,c\,\left(\frac{2\,a\,d^2}{b^2}-\frac{12\,c\,d}{5\,b}\right)}{3\,d}\right)}{3\,d}+\frac{2\,d\,x^6\,\sqrt{d\,x^3+c}}{15\,b}-\frac{x^3\,\sqrt{d\,x^3+c}\,\left(\frac{2\,a\,d^2}{b^2}-\frac{12\,c\,d}{5\,b}\right)}{9\,d}+\frac{a\,\ln\left(\frac{a^2\,d^2+2\,b^2\,c^2-a\,b\,d^2\,x^3+b^2\,c\,d\,x^3-3\,a\,b\,c\,d+\sqrt{b}\,\sqrt{d\,x^3+c}\,{\left(a\,d-b\,c\right)}^{3/2}\,2{}\mathrm{i}}{b\,x^3+a}\right)\,{\left(a\,d-b\,c\right)}^{3/2}\,1{}\mathrm{i}}{3\,b^{7/2}}","Not used",1,"((c + d*x^3)^(1/2)*((2*c^2)/b + (2*a*((a*d^2)/b^2 - (2*c*d)/b))/b + (2*c*((2*a*d^2)/b^2 - (12*c*d)/(5*b)))/(3*d)))/(3*d) + (2*d*x^6*(c + d*x^3)^(1/2))/(15*b) - (x^3*(c + d*x^3)^(1/2)*((2*a*d^2)/b^2 - (12*c*d)/(5*b)))/(9*d) + (a*log((a^2*d^2 + 2*b^2*c^2 + b^(1/2)*(c + d*x^3)^(1/2)*(a*d - b*c)^(3/2)*2i - a*b*d^2*x^3 + b^2*c*d*x^3 - 3*a*b*c*d)/(a + b*x^3))*(a*d - b*c)^(3/2)*1i)/(3*b^(7/2))","B"
370,1,143,96,5.908074,"\text{Not used}","int((x^2*(c + d*x^3)^(3/2))/(a + b*x^3),x)","\frac{2\,d\,x^3\,\sqrt{d\,x^3+c}}{9\,b}-\frac{\sqrt{d\,x^3+c}\,\left(\frac{2\,a\,d^2}{b^2}-\frac{8\,c\,d}{3\,b}\right)}{3\,d}+\frac{\ln\left(\frac{a^2\,d^2+2\,b^2\,c^2-a\,b\,d^2\,x^3+b^2\,c\,d\,x^3-3\,a\,b\,c\,d-\sqrt{b}\,\sqrt{d\,x^3+c}\,{\left(a\,d-b\,c\right)}^{3/2}\,2{}\mathrm{i}}{b\,x^3+a}\right)\,{\left(a\,d-b\,c\right)}^{3/2}\,1{}\mathrm{i}}{3\,b^{5/2}}","Not used",1,"(log((a^2*d^2 + 2*b^2*c^2 - b^(1/2)*(c + d*x^3)^(1/2)*(a*d - b*c)^(3/2)*2i - a*b*d^2*x^3 + b^2*c*d*x^3 - 3*a*b*c*d)/(a + b*x^3))*(a*d - b*c)^(3/2)*1i)/(3*b^(5/2)) - ((c + d*x^3)^(1/2)*((2*a*d^2)/b^2 - (8*c*d)/(3*b)))/(3*d) + (2*d*x^3*(c + d*x^3)^(1/2))/(9*b)","B"
371,1,155,104,7.878998,"\text{Not used}","int((c + d*x^3)^(3/2)/(x*(a + b*x^3)),x)","\frac{c^{3/2}\,\ln\left(\frac{{\left(\sqrt{d\,x^3+c}-\sqrt{c}\right)}^3\,\left(\sqrt{d\,x^3+c}+\sqrt{c}\right)}{x^6}\right)}{3\,a}+\frac{2\,d\,\sqrt{d\,x^3+c}}{3\,b}+\frac{\ln\left(\frac{a^2\,d^2+2\,b^2\,c^2-a\,b\,d^2\,x^3+b^2\,c\,d\,x^3-3\,a\,b\,c\,d+\sqrt{b}\,\sqrt{d\,x^3+c}\,{\left(a\,d-b\,c\right)}^{3/2}\,2{}\mathrm{i}}{b\,x^3+a}\right)\,{\left(a\,d-b\,c\right)}^{3/2}\,1{}\mathrm{i}}{3\,a\,b^{3/2}}","Not used",1,"(c^(3/2)*log((((c + d*x^3)^(1/2) - c^(1/2))^3*((c + d*x^3)^(1/2) + c^(1/2)))/x^6))/(3*a) + (2*d*(c + d*x^3)^(1/2))/(3*b) + (log((a^2*d^2 + 2*b^2*c^2 + b^(1/2)*(c + d*x^3)^(1/2)*(a*d - b*c)^(3/2)*2i - a*b*d^2*x^3 + b^2*c*d*x^3 - 3*a*b*c*d)/(a + b*x^3))*(a*d - b*c)^(3/2)*1i)/(3*a*b^(3/2))","B"
372,1,167,116,9.517041,"\text{Not used}","int((c + d*x^3)^(3/2)/(x^4*(a + b*x^3)),x)","\frac{\sqrt{c}\,\ln\left(\frac{{\left(\sqrt{d\,x^3+c}-\sqrt{c}\right)}^3\,\left(\sqrt{d\,x^3+c}+\sqrt{c}\right)}{x^6}\right)\,\left(3\,a\,d-2\,b\,c\right)}{6\,a^2}-\frac{c\,\sqrt{d\,x^3+c}}{3\,a\,x^3}+\frac{\ln\left(\frac{a^2\,d^2+2\,b^2\,c^2-a\,b\,d^2\,x^3+b^2\,c\,d\,x^3-3\,a\,b\,c\,d-\sqrt{b}\,\sqrt{d\,x^3+c}\,{\left(a\,d-b\,c\right)}^{3/2}\,2{}\mathrm{i}}{b\,x^3+a}\right)\,{\left(a\,d-b\,c\right)}^{3/2}\,1{}\mathrm{i}}{3\,a^2\,\sqrt{b}}","Not used",1,"(c^(1/2)*log((((c + d*x^3)^(1/2) - c^(1/2))^3*((c + d*x^3)^(1/2) + c^(1/2)))/x^6)*(3*a*d - 2*b*c))/(6*a^2) - (c*(c + d*x^3)^(1/2))/(3*a*x^3) + (log((a^2*d^2 + 2*b^2*c^2 - b^(1/2)*(c + d*x^3)^(1/2)*(a*d - b*c)^(3/2)*2i - a*b*d^2*x^3 + b^2*c*d*x^3 - 3*a*b*c*d)/(a + b*x^3))*(a*d - b*c)^(3/2)*1i)/(3*a^2*b^(1/2))","B"
373,0,-1,65,0.000000,"\text{Not used}","int((x^3*(c + d*x^3)^(3/2))/(a + b*x^3),x)","\int \frac{x^3\,{\left(d\,x^3+c\right)}^{3/2}}{b\,x^3+a} \,d x","Not used",1,"int((x^3*(c + d*x^3)^(3/2))/(a + b*x^3), x)","F"
374,0,-1,65,0.000000,"\text{Not used}","int((x*(c + d*x^3)^(3/2))/(a + b*x^3),x)","\int \frac{x\,{\left(d\,x^3+c\right)}^{3/2}}{b\,x^3+a} \,d x","Not used",1,"int((x*(c + d*x^3)^(3/2))/(a + b*x^3), x)","F"
375,0,-1,60,0.000000,"\text{Not used}","int((c + d*x^3)^(3/2)/(a + b*x^3),x)","\int \frac{{\left(d\,x^3+c\right)}^{3/2}}{b\,x^3+a} \,d x","Not used",1,"int((c + d*x^3)^(3/2)/(a + b*x^3), x)","F"
376,0,-1,63,0.000000,"\text{Not used}","int((c + d*x^3)^(3/2)/(x^2*(a + b*x^3)),x)","\int \frac{{\left(d\,x^3+c\right)}^{3/2}}{x^2\,\left(b\,x^3+a\right)} \,d x","Not used",1,"int((c + d*x^3)^(3/2)/(x^2*(a + b*x^3)), x)","F"
377,0,-1,65,0.000000,"\text{Not used}","int((c + d*x^3)^(3/2)/(x^3*(a + b*x^3)),x)","\int \frac{{\left(d\,x^3+c\right)}^{3/2}}{x^3\,\left(b\,x^3+a\right)} \,d x","Not used",1,"int((c + d*x^3)^(3/2)/(x^3*(a + b*x^3)), x)","F"
378,1,121,104,5.425746,"\text{Not used}","int(x^8/((a + b*x^3)*(c + d*x^3)^(1/2)),x)","\frac{2\,x^3\,\sqrt{d\,x^3+c}}{9\,b\,d}-\frac{\left(\frac{2\,a}{b^2}+\frac{4\,c}{3\,b\,d}\right)\,\sqrt{d\,x^3+c}}{3\,d}+\frac{a^2\,\ln\left(\frac{2\,b\,c-a\,d+b\,d\,x^3+\sqrt{b}\,\sqrt{d\,x^3+c}\,\sqrt{a\,d-b\,c}\,2{}\mathrm{i}}{b\,x^3+a}\right)\,1{}\mathrm{i}}{3\,b^{5/2}\,\sqrt{a\,d-b\,c}}","Not used",1,"(2*x^3*(c + d*x^3)^(1/2))/(9*b*d) - (((2*a)/b^2 + (4*c)/(3*b*d))*(c + d*x^3)^(1/2))/(3*d) + (a^2*log((2*b*c - a*d + b^(1/2)*(c + d*x^3)^(1/2)*(a*d - b*c)^(1/2)*2i + b*d*x^3)/(a + b*x^3))*1i)/(3*b^(5/2)*(a*d - b*c)^(1/2))","B"
379,1,86,74,5.098485,"\text{Not used}","int(x^5/((a + b*x^3)*(c + d*x^3)^(1/2)),x)","\frac{2\,\sqrt{d\,x^3+c}}{3\,b\,d}+\frac{a\,\ln\left(\frac{a\,d-2\,b\,c-b\,d\,x^3+\sqrt{b}\,\sqrt{d\,x^3+c}\,\sqrt{a\,d-b\,c}\,2{}\mathrm{i}}{b\,x^3+a}\right)\,1{}\mathrm{i}}{3\,b^{3/2}\,\sqrt{a\,d-b\,c}}","Not used",1,"(2*(c + d*x^3)^(1/2))/(3*b*d) + (a*log((a*d - 2*b*c + b^(1/2)*(c + d*x^3)^(1/2)*(a*d - b*c)^(1/2)*2i - b*d*x^3)/(a + b*x^3))*1i)/(3*b^(3/2)*(a*d - b*c)^(1/2))","B"
380,1,70,51,5.887536,"\text{Not used}","int(x^2/((a + b*x^3)*(c + d*x^3)^(1/2)),x)","\frac{\ln\left(\frac{a\,d\,1{}\mathrm{i}-b\,c\,2{}\mathrm{i}+2\,\sqrt{d\,x^3+c}\,\sqrt{a\,b\,d-b^2\,c}-b\,d\,x^3\,1{}\mathrm{i}}{b\,x^3+a}\right)\,1{}\mathrm{i}}{3\,\sqrt{a\,b\,d-b^2\,c}}","Not used",1,"(log((a*d*1i - b*c*2i + 2*(c + d*x^3)^(1/2)*(a*b*d - b^2*c)^(1/2) - b*d*x^3*1i)/(a + b*x^3))*1i)/(3*(a*b*d - b^2*c)^(1/2))","B"
381,1,114,85,7.313435,"\text{Not used}","int(1/(x*(a + b*x^3)*(c + d*x^3)^(1/2)),x)","\frac{\ln\left(\frac{{\left(\sqrt{d\,x^3+c}-\sqrt{c}\right)}^3\,\left(\sqrt{d\,x^3+c}+\sqrt{c}\right)}{x^6}\right)}{3\,a\,\sqrt{c}}+\frac{\sqrt{b}\,\ln\left(\frac{a\,d-2\,b\,c-b\,d\,x^3+\sqrt{b}\,\sqrt{d\,x^3+c}\,\sqrt{a\,d-b\,c}\,2{}\mathrm{i}}{b\,x^3+a}\right)\,1{}\mathrm{i}}{3\,a\,\sqrt{a\,d-b\,c}}","Not used",1,"log((((c + d*x^3)^(1/2) - c^(1/2))^3*((c + d*x^3)^(1/2) + c^(1/2)))/x^6)/(3*a*c^(1/2)) + (b^(1/2)*log((a*d - 2*b*c + b^(1/2)*(c + d*x^3)^(1/2)*(a*d - b*c)^(1/2)*2i - b*d*x^3)/(a + b*x^3))*1i)/(3*a*(a*d - b*c)^(1/2))","B"
382,1,142,117,8.424488,"\text{Not used}","int(1/(x^4*(a + b*x^3)*(c + d*x^3)^(1/2)),x)","\frac{\ln\left(\frac{\left(\sqrt{d\,x^3+c}-\sqrt{c}\right)\,{\left(\sqrt{d\,x^3+c}+\sqrt{c}\right)}^3}{x^6}\right)\,\left(a\,d+2\,b\,c\right)}{6\,a^2\,c^{3/2}}-\frac{\sqrt{d\,x^3+c}}{3\,a\,c\,x^3}+\frac{b^{3/2}\,\ln\left(\frac{2\,b\,c-a\,d+b\,d\,x^3+\sqrt{b}\,\sqrt{d\,x^3+c}\,\sqrt{a\,d-b\,c}\,2{}\mathrm{i}}{b\,x^3+a}\right)\,1{}\mathrm{i}}{3\,a^2\,\sqrt{a\,d-b\,c}}","Not used",1,"(log((((c + d*x^3)^(1/2) - c^(1/2))*((c + d*x^3)^(1/2) + c^(1/2))^3)/x^6)*(a*d + 2*b*c))/(6*a^2*c^(3/2)) - (c + d*x^3)^(1/2)/(3*a*c*x^3) + (b^(3/2)*log((2*b*c - a*d + b^(1/2)*(c + d*x^3)^(1/2)*(a*d - b*c)^(1/2)*2i + b*d*x^3)/(a + b*x^3))*1i)/(3*a^2*(a*d - b*c)^(1/2))","B"
383,0,-1,64,0.000000,"\text{Not used}","int(x^3/((a + b*x^3)*(c + d*x^3)^(1/2)),x)","\int \frac{x^3}{\left(b\,x^3+a\right)\,\sqrt{d\,x^3+c}} \,d x","Not used",1,"int(x^3/((a + b*x^3)*(c + d*x^3)^(1/2)), x)","F"
384,0,-1,64,0.000000,"\text{Not used}","int(x/((a + b*x^3)*(c + d*x^3)^(1/2)),x)","\int \frac{x}{\left(b\,x^3+a\right)\,\sqrt{d\,x^3+c}} \,d x","Not used",1,"int(x/((a + b*x^3)*(c + d*x^3)^(1/2)), x)","F"
385,0,-1,59,0.000000,"\text{Not used}","int(1/((a + b*x^3)*(c + d*x^3)^(1/2)),x)","\int \frac{1}{\left(b\,x^3+a\right)\,\sqrt{d\,x^3+c}} \,d x","Not used",1,"int(1/((a + b*x^3)*(c + d*x^3)^(1/2)), x)","F"
386,0,-1,62,0.000000,"\text{Not used}","int(1/(x^2*(a + b*x^3)*(c + d*x^3)^(1/2)),x)","\int \frac{1}{x^2\,\left(b\,x^3+a\right)\,\sqrt{d\,x^3+c}} \,d x","Not used",1,"int(1/(x^2*(a + b*x^3)*(c + d*x^3)^(1/2)), x)","F"
387,0,-1,64,0.000000,"\text{Not used}","int(1/(x^3*(a + b*x^3)*(c + d*x^3)^(1/2)),x)","\int \frac{1}{x^3\,\left(b\,x^3+a\right)\,\sqrt{d\,x^3+c}} \,d x","Not used",1,"int(1/(x^3*(a + b*x^3)*(c + d*x^3)^(1/2)), x)","F"
388,1,115,107,6.456521,"\text{Not used}","int(x^8/((a + b*x^3)*(c + d*x^3)^(3/2)),x)","\frac{2\,\sqrt{d\,x^3+c}}{3\,b\,d^2}-\frac{2\,c^2}{3\,d^2\,\sqrt{d\,x^3+c}\,\left(a\,d-b\,c\right)}+\frac{a^2\,\ln\left(\frac{a\,d-2\,b\,c-b\,d\,x^3+\sqrt{b}\,\sqrt{d\,x^3+c}\,\sqrt{a\,d-b\,c}\,2{}\mathrm{i}}{b\,x^3+a}\right)\,1{}\mathrm{i}}{3\,b^{3/2}\,{\left(a\,d-b\,c\right)}^{3/2}}","Not used",1,"(2*(c + d*x^3)^(1/2))/(3*b*d^2) - (2*c^2)/(3*d^2*(c + d*x^3)^(1/2)*(a*d - b*c)) + (a^2*log((a*d - 2*b*c + b^(1/2)*(c + d*x^3)^(1/2)*(a*d - b*c)^(1/2)*2i - b*d*x^3)/(a + b*x^3))*1i)/(3*b^(3/2)*(a*d - b*c)^(3/2))","B"
389,1,94,82,5.990141,"\text{Not used}","int(x^5/((a + b*x^3)*(c + d*x^3)^(3/2)),x)","\frac{2\,c}{3\,d\,\sqrt{d\,x^3+c}\,\left(a\,d-b\,c\right)}+\frac{a\,\ln\left(\frac{2\,b\,c-a\,d+b\,d\,x^3+\sqrt{b}\,\sqrt{d\,x^3+c}\,\sqrt{a\,d-b\,c}\,2{}\mathrm{i}}{b\,x^3+a}\right)\,1{}\mathrm{i}}{3\,\sqrt{b}\,{\left(a\,d-b\,c\right)}^{3/2}}","Not used",1,"(2*c)/(3*d*(c + d*x^3)^(1/2)*(a*d - b*c)) + (a*log((2*b*c - a*d + b^(1/2)*(c + d*x^3)^(1/2)*(a*d - b*c)^(1/2)*2i + b*d*x^3)/(a + b*x^3))*1i)/(3*b^(1/2)*(a*d - b*c)^(3/2))","B"
390,1,89,77,5.848342,"\text{Not used}","int(x^2/((a + b*x^3)*(c + d*x^3)^(3/2)),x)","-\frac{2}{3\,\sqrt{d\,x^3+c}\,\left(a\,d-b\,c\right)}+\frac{\sqrt{b}\,\ln\left(\frac{a\,d-2\,b\,c-b\,d\,x^3+\sqrt{b}\,\sqrt{d\,x^3+c}\,\sqrt{a\,d-b\,c}\,2{}\mathrm{i}}{b\,x^3+a}\right)\,1{}\mathrm{i}}{3\,{\left(a\,d-b\,c\right)}^{3/2}}","Not used",1,"(b^(1/2)*log((a*d - 2*b*c + b^(1/2)*(c + d*x^3)^(1/2)*(a*d - b*c)^(1/2)*2i - b*d*x^3)/(a + b*x^3))*1i)/(3*(a*d - b*c)^(3/2)) - 2/(3*(c + d*x^3)^(1/2)*(a*d - b*c))","B"
391,1,139,114,8.443711,"\text{Not used}","int(1/(x*(a + b*x^3)*(c + d*x^3)^(3/2)),x)","\frac{\ln\left(\frac{{\left(\sqrt{d\,x^3+c}-\sqrt{c}\right)}^3\,\left(\sqrt{d\,x^3+c}+\sqrt{c}\right)}{x^6}\right)}{3\,a\,c^{3/2}}+\frac{2\,d}{3\,c\,\sqrt{d\,x^3+c}\,\left(a\,d-b\,c\right)}+\frac{b^{3/2}\,\ln\left(\frac{2\,b\,c-a\,d+b\,d\,x^3+\sqrt{b}\,\sqrt{d\,x^3+c}\,\sqrt{a\,d-b\,c}\,2{}\mathrm{i}}{b\,x^3+a}\right)\,1{}\mathrm{i}}{3\,a\,{\left(a\,d-b\,c\right)}^{3/2}}","Not used",1,"log((((c + d*x^3)^(1/2) - c^(1/2))^3*((c + d*x^3)^(1/2) + c^(1/2)))/x^6)/(3*a*c^(3/2)) + (2*d)/(3*c*(c + d*x^3)^(1/2)*(a*d - b*c)) + (b^(3/2)*log((2*b*c - a*d + b^(1/2)*(c + d*x^3)^(1/2)*(a*d - b*c)^(1/2)*2i + b*d*x^3)/(a + b*x^3))*1i)/(3*a*(a*d - b*c)^(3/2))","B"
392,1,597,158,10.471690,"\text{Not used}","int(1/(x^4*(a + b*x^3)*(c + d*x^3)^(3/2)),x)","\frac{\ln\left(\frac{\left(\sqrt{d\,x^3+c}-\sqrt{c}\right)\,{\left(\sqrt{d\,x^3+c}+\sqrt{c}\right)}^3}{x^6}\right)\,\left(3\,a\,d+2\,b\,c\right)}{6\,a^2\,c^{5/2}}-\frac{\sqrt{d\,x^3+c}}{3\,a\,c^2\,x^3}-\frac{\frac{c\,\left(\frac{c\,\left(\frac{c\,\left(\frac{3\,a^2\,d^4+24\,a\,b\,c\,d^3+15\,b^2\,c^2\,d^2}{8\,a^3\,c^5}+\frac{c\,\left(\frac{c\,\left(\frac{3\,b^2\,d^4}{8\,a^3\,c^5}+\frac{b^2\,d^4\,\left(5\,a\,d-3\,b\,c\right)}{8\,a^3\,c^4\,\left(b\,c^2-a\,c\,d\right)}-\frac{b\,d^4\,\left(a\,d+2\,b\,c\right)\,\left(5\,a\,d-3\,b\,c\right)}{4\,a^3\,c^5\,\left(b\,c^2-a\,c\,d\right)}\right)}{d}-\frac{3\,b\,d^3\,\left(a\,d+2\,b\,c\right)}{4\,a^3\,c^5}+\frac{d\,\left(5\,a\,d-3\,b\,c\right)\,\left(3\,a^2\,d^4+24\,a\,b\,c\,d^3+15\,b^2\,c^2\,d^2\right)}{24\,a^3\,c^5\,\left(b\,c^2-a\,c\,d\right)}\right)}{d}-\frac{d^2\,\left(5\,a\,d-3\,b\,c\right)\,\left(6\,a^2\,d^2+14\,a\,b\,c\,d+3\,b^2\,c^2\right)}{12\,a^3\,c^4\,\left(b\,c^2-a\,c\,d\right)}\right)}{d}-\frac{d\,\left(6\,a^2\,d^2+14\,a\,b\,c\,d+3\,b^2\,c^2\right)}{4\,a^3\,c^4}+\frac{d^2\,\left(5\,a\,d-3\,b\,c\right)\,\left(13\,a\,d+18\,b\,c\right)}{24\,a^2\,c^3\,\left(b\,c^2-a\,c\,d\right)}\right)}{d}+\frac{d\,\left(13\,a\,d+18\,b\,c\right)}{8\,a^2\,c^3}-\frac{d\,\left(3\,a\,d+2\,b\,c\right)\,\left(5\,a\,d-3\,b\,c\right)}{6\,a^2\,c^2\,\left(b\,c^2-a\,c\,d\right)}\right)}{d}-\frac{3\,a\,d+2\,b\,c}{2\,a^2\,c^2}}{\sqrt{d\,x^3+c}}+\frac{b^{5/2}\,\ln\left(\frac{a\,d-2\,b\,c-b\,d\,x^3+\sqrt{b}\,\sqrt{d\,x^3+c}\,\sqrt{a\,d-b\,c}\,2{}\mathrm{i}}{b\,x^3+a}\right)\,1{}\mathrm{i}}{3\,a^2\,{\left(a\,d-b\,c\right)}^{3/2}}","Not used",1,"(log((((c + d*x^3)^(1/2) - c^(1/2))*((c + d*x^3)^(1/2) + c^(1/2))^3)/x^6)*(3*a*d + 2*b*c))/(6*a^2*c^(5/2)) - (c + d*x^3)^(1/2)/(3*a*c^2*x^3) - ((c*((c*((c*((3*a^2*d^4 + 15*b^2*c^2*d^2 + 24*a*b*c*d^3)/(8*a^3*c^5) + (c*((c*((3*b^2*d^4)/(8*a^3*c^5) + (b^2*d^4*(5*a*d - 3*b*c))/(8*a^3*c^4*(b*c^2 - a*c*d)) - (b*d^4*(a*d + 2*b*c)*(5*a*d - 3*b*c))/(4*a^3*c^5*(b*c^2 - a*c*d))))/d - (3*b*d^3*(a*d + 2*b*c))/(4*a^3*c^5) + (d*(5*a*d - 3*b*c)*(3*a^2*d^4 + 15*b^2*c^2*d^2 + 24*a*b*c*d^3))/(24*a^3*c^5*(b*c^2 - a*c*d))))/d - (d^2*(5*a*d - 3*b*c)*(6*a^2*d^2 + 3*b^2*c^2 + 14*a*b*c*d))/(12*a^3*c^4*(b*c^2 - a*c*d))))/d - (d*(6*a^2*d^2 + 3*b^2*c^2 + 14*a*b*c*d))/(4*a^3*c^4) + (d^2*(5*a*d - 3*b*c)*(13*a*d + 18*b*c))/(24*a^2*c^3*(b*c^2 - a*c*d))))/d + (d*(13*a*d + 18*b*c))/(8*a^2*c^3) - (d*(3*a*d + 2*b*c)*(5*a*d - 3*b*c))/(6*a^2*c^2*(b*c^2 - a*c*d))))/d - (3*a*d + 2*b*c)/(2*a^2*c^2))/(c + d*x^3)^(1/2) + (b^(5/2)*log((a*d - 2*b*c + b^(1/2)*(c + d*x^3)^(1/2)*(a*d - b*c)^(1/2)*2i - b*d*x^3)/(a + b*x^3))*1i)/(3*a^2*(a*d - b*c)^(3/2))","B"
393,0,-1,67,0.000000,"\text{Not used}","int(x^3/((a + b*x^3)*(c + d*x^3)^(3/2)),x)","\int \frac{x^3}{\left(b\,x^3+a\right)\,{\left(d\,x^3+c\right)}^{3/2}} \,d x","Not used",1,"int(x^3/((a + b*x^3)*(c + d*x^3)^(3/2)), x)","F"
394,0,-1,67,0.000000,"\text{Not used}","int(x/((a + b*x^3)*(c + d*x^3)^(3/2)),x)","\int \frac{x}{\left(b\,x^3+a\right)\,{\left(d\,x^3+c\right)}^{3/2}} \,d x","Not used",1,"int(x/((a + b*x^3)*(c + d*x^3)^(3/2)), x)","F"
395,0,-1,62,0.000000,"\text{Not used}","int(1/((a + b*x^3)*(c + d*x^3)^(3/2)),x)","\int \frac{1}{\left(b\,x^3+a\right)\,{\left(d\,x^3+c\right)}^{3/2}} \,d x","Not used",1,"int(1/((a + b*x^3)*(c + d*x^3)^(3/2)), x)","F"
396,0,-1,65,0.000000,"\text{Not used}","int(1/(x^2*(a + b*x^3)*(c + d*x^3)^(3/2)),x)","\int \frac{1}{x^2\,\left(b\,x^3+a\right)\,{\left(d\,x^3+c\right)}^{3/2}} \,d x","Not used",1,"int(1/(x^2*(a + b*x^3)*(c + d*x^3)^(3/2)), x)","F"
397,0,-1,67,0.000000,"\text{Not used}","int(1/(x^3*(a + b*x^3)*(c + d*x^3)^(3/2)),x)","\int \frac{1}{x^3\,\left(b\,x^3+a\right)\,{\left(d\,x^3+c\right)}^{3/2}} \,d x","Not used",1,"int(1/(x^3*(a + b*x^3)*(c + d*x^3)^(3/2)), x)","F"
398,1,127,117,4.087125,"\text{Not used}","int((x^11*(c + d*x^3)^(1/2))/(8*c - d*x^3)^2,x)","\frac{1984\,c^{5/2}\,\ln\left(\frac{10\,c+d\,x^3-6\,\sqrt{c}\,\sqrt{d\,x^3+c}}{8\,c-d\,x^3}\right)}{9\,d^4}+\frac{1972\,c^2\,\sqrt{d\,x^3+c}}{15\,d^4}+\frac{2\,x^6\,\sqrt{d\,x^3+c}}{15\,d^2}+\frac{18\,c\,x^3\,\sqrt{d\,x^3+c}}{5\,d^3}+\frac{512\,c^3\,\sqrt{d\,x^3+c}}{3\,d^4\,\left(8\,c-d\,x^3\right)}","Not used",1,"(1984*c^(5/2)*log((10*c + d*x^3 - 6*c^(1/2)*(c + d*x^3)^(1/2))/(8*c - d*x^3)))/(9*d^4) + (1972*c^2*(c + d*x^3)^(1/2))/(15*d^4) + (2*x^6*(c + d*x^3)^(1/2))/(15*d^2) + (18*c*x^3*(c + d*x^3)^(1/2))/(5*d^3) + (512*c^3*(c + d*x^3)^(1/2))/(3*d^4*(8*c - d*x^3))","B"
399,1,107,102,4.012685,"\text{Not used}","int((x^8*(c + d*x^3)^(1/2))/(8*c - d*x^3)^2,x)","\frac{98\,c\,\sqrt{d\,x^3+c}}{9\,d^3}+\frac{176\,c^{3/2}\,\ln\left(\frac{10\,c+d\,x^3-6\,\sqrt{c}\,\sqrt{d\,x^3+c}}{8\,c-d\,x^3}\right)}{9\,d^3}+\frac{2\,x^3\,\sqrt{d\,x^3+c}}{9\,d^2}+\frac{64\,c^2\,\sqrt{d\,x^3+c}}{3\,d^3\,\left(8\,c-d\,x^3\right)}","Not used",1,"(98*c*(c + d*x^3)^(1/2))/(9*d^3) + (176*c^(3/2)*log((10*c + d*x^3 - 6*c^(1/2)*(c + d*x^3)^(1/2))/(8*c - d*x^3)))/(9*d^3) + (2*x^3*(c + d*x^3)^(1/2))/(9*d^2) + (64*c^2*(c + d*x^3)^(1/2))/(3*d^3*(8*c - d*x^3))","B"
400,1,87,82,3.985437,"\text{Not used}","int((x^5*(c + d*x^3)^(1/2))/(8*c - d*x^3)^2,x)","\frac{2\,\sqrt{d\,x^3+c}}{3\,d^2}+\frac{13\,\sqrt{c}\,\ln\left(\frac{10\,c+d\,x^3-6\,\sqrt{c}\,\sqrt{d\,x^3+c}}{8\,c-d\,x^3}\right)}{9\,d^2}+\frac{8\,c\,\sqrt{d\,x^3+c}}{3\,d^2\,\left(8\,c-d\,x^3\right)}","Not used",1,"(2*(c + d*x^3)^(1/2))/(3*d^2) + (13*c^(1/2)*log((10*c + d*x^3 - 6*c^(1/2)*(c + d*x^3)^(1/2))/(8*c - d*x^3)))/(9*d^2) + (8*c*(c + d*x^3)^(1/2))/(3*d^2*(8*c - d*x^3))","B"
401,1,72,64,3.925726,"\text{Not used}","int((x^2*(c + d*x^3)^(1/2))/(8*c - d*x^3)^2,x)","\frac{\ln\left(\frac{10\,c+d\,x^3-6\,\sqrt{c}\,\sqrt{d\,x^3+c}}{8\,c-d\,x^3}\right)}{18\,\sqrt{c}\,d}+\frac{\sqrt{d\,x^3+c}}{3\,d\,\left(8\,c-d\,x^3\right)}","Not used",1,"log((10*c + d*x^3 - 6*c^(1/2)*(c + d*x^3)^(1/2))/(8*c - d*x^3))/(18*c^(1/2)*d) + (c + d*x^3)^(1/2)/(3*d*(8*c - d*x^3))","B"
402,1,76,88,3.981133,"\text{Not used}","int((c + d*x^3)^(1/2)/(x*(8*c - d*x^3)^2),x)","\frac{5\,\mathrm{atanh}\left(\frac{c\,\sqrt{d\,x^3+c}}{3\,\sqrt{c^3}}\right)}{288\,\sqrt{c^3}}-\frac{\mathrm{atanh}\left(\frac{c\,\sqrt{d\,x^3+c}}{\sqrt{c^3}}\right)}{96\,\sqrt{c^3}}+\frac{\sqrt{d\,x^3+c}}{8\,c\,\left(24\,c-3\,d\,x^3\right)}","Not used",1,"(5*atanh((c*(c + d*x^3)^(1/2))/(3*(c^3)^(1/2))))/(288*(c^3)^(1/2)) - atanh((c*(c + d*x^3)^(1/2))/(c^3)^(1/2))/(96*(c^3)^(1/2)) + (c + d*x^3)^(1/2)/(8*c*(24*c - 3*d*x^3))","B"
403,1,117,124,4.211900,"\text{Not used}","int((c + d*x^3)^(1/2)/(x^4*(8*c - d*x^3)^2),x)","\frac{\frac{5\,d\,\sqrt{d\,x^3+c}}{32\,c}-\frac{d\,{\left(d\,x^3+c\right)}^{3/2}}{32\,c^2}}{3\,{\left(d\,x^3+c\right)}^2-30\,c\,\left(d\,x^3+c\right)+27\,c^2}+\frac{d\,\left(\mathrm{atanh}\left(\frac{c^2\,\sqrt{d\,x^3+c}}{\sqrt{c^5}}\right)\,1{}\mathrm{i}-\frac{\mathrm{atanh}\left(\frac{c^2\,\sqrt{d\,x^3+c}}{3\,\sqrt{c^5}}\right)\,7{}\mathrm{i}}{9}\right)\,1{}\mathrm{i}}{128\,\sqrt{c^5}}","Not used",1,"((5*d*(c + d*x^3)^(1/2))/(32*c) - (d*(c + d*x^3)^(3/2))/(32*c^2))/(3*(c + d*x^3)^2 - 30*c*(c + d*x^3) + 27*c^2) + (d*(atanh((c^2*(c + d*x^3)^(1/2))/(c^5)^(1/2))*1i - (atanh((c^2*(c + d*x^3)^(1/2))/(3*(c^5)^(1/2)))*7i)/9)*1i)/(128*(c^5)^(1/2))","B"
404,1,154,164,4.452791,"\text{Not used}","int((c + d*x^3)^(1/2)/(x^7*(8*c - d*x^3)^2),x)","\frac{\frac{d^2\,\sqrt{d\,x^3+c}}{512\,c}-\frac{19\,d^2\,{\left(d\,x^3+c\right)}^{3/2}}{256\,c^2}+\frac{5\,d^2\,{\left(d\,x^3+c\right)}^{5/2}}{512\,c^3}}{33\,c\,{\left(d\,x^3+c\right)}^2-57\,c^2\,\left(d\,x^3+c\right)-3\,{\left(d\,x^3+c\right)}^3+27\,c^3}+\frac{d^2\,\left(\mathrm{atanh}\left(\frac{c^3\,\sqrt{d\,x^3+c}}{\sqrt{c^7}}\right)\,1{}\mathrm{i}-\frac{\mathrm{atanh}\left(\frac{c^3\,\sqrt{d\,x^3+c}}{3\,\sqrt{c^7}}\right)\,23{}\mathrm{i}}{9}\right)\,1{}\mathrm{i}}{2048\,\sqrt{c^7}}","Not used",1,"((d^2*(c + d*x^3)^(1/2))/(512*c) - (19*d^2*(c + d*x^3)^(3/2))/(256*c^2) + (5*d^2*(c + d*x^3)^(5/2))/(512*c^3))/(33*c*(c + d*x^3)^2 - 57*c^2*(c + d*x^3) - 3*(c + d*x^3)^3 + 27*c^3) + (d^2*(atanh((c^3*(c + d*x^3)^(1/2))/(c^7)^(1/2))*1i - (atanh((c^3*(c + d*x^3)^(1/2))/(3*(c^7)^(1/2)))*23i)/9)*1i)/(2048*(c^7)^(1/2))","B"
405,0,-1,663,0.000000,"\text{Not used}","int((x^7*(c + d*x^3)^(1/2))/(8*c - d*x^3)^2,x)","\int \frac{x^7\,\sqrt{d\,x^3+c}}{{\left(8\,c-d\,x^3\right)}^2} \,d x","Not used",1,"int((x^7*(c + d*x^3)^(1/2))/(8*c - d*x^3)^2, x)","F"
406,0,-1,641,0.000000,"\text{Not used}","int((x^4*(c + d*x^3)^(1/2))/(8*c - d*x^3)^2,x)","\int \frac{x^4\,\sqrt{d\,x^3+c}}{{\left(8\,c-d\,x^3\right)}^2} \,d x","Not used",1,"int((x^4*(c + d*x^3)^(1/2))/(8*c - d*x^3)^2, x)","F"
407,0,-1,644,0.000000,"\text{Not used}","int((x*(c + d*x^3)^(1/2))/(8*c - d*x^3)^2,x)","\int \frac{x\,\sqrt{d\,x^3+c}}{{\left(8\,c-d\,x^3\right)}^2} \,d x","Not used",1,"int((x*(c + d*x^3)^(1/2))/(8*c - d*x^3)^2, x)","F"
408,0,-1,665,0.000000,"\text{Not used}","int((c + d*x^3)^(1/2)/(x^2*(8*c - d*x^3)^2),x)","\int \frac{\sqrt{d\,x^3+c}}{x^2\,{\left(8\,c-d\,x^3\right)}^2} \,d x","Not used",1,"int((c + d*x^3)^(1/2)/(x^2*(8*c - d*x^3)^2), x)","F"
409,0,-1,687,0.000000,"\text{Not used}","int((c + d*x^3)^(1/2)/(x^5*(8*c - d*x^3)^2),x)","\int \frac{\sqrt{d\,x^3+c}}{x^5\,{\left(8\,c-d\,x^3\right)}^2} \,d x","Not used",1,"int((c + d*x^3)^(1/2)/(x^5*(8*c - d*x^3)^2), x)","F"
410,0,-1,711,0.000000,"\text{Not used}","int((c + d*x^3)^(1/2)/(x^8*(8*c - d*x^3)^2),x)","\int \frac{\sqrt{d\,x^3+c}}{x^8\,{\left(8\,c-d\,x^3\right)}^2} \,d x","Not used",1,"int((c + d*x^3)^(1/2)/(x^8*(8*c - d*x^3)^2), x)","F"
411,1,147,134,4.104477,"\text{Not used}","int((x^11*(c + d*x^3)^(3/2))/(8*c - d*x^3)^2,x)","\frac{2496\,c^{7/2}\,\ln\left(\frac{10\,c+d\,x^3-6\,\sqrt{c}\,\sqrt{d\,x^3+c}}{8\,c-d\,x^3}\right)}{d^4}+\frac{32300\,c^3\,\sqrt{d\,x^3+c}}{21\,d^4}+\frac{2\,x^9\,\sqrt{d\,x^3+c}}{21\,d}+\frac{16\,c\,x^6\,\sqrt{d\,x^3+c}}{7\,d^2}+\frac{986\,c^2\,x^3\,\sqrt{d\,x^3+c}}{21\,d^3}+\frac{1536\,c^4\,\sqrt{d\,x^3+c}}{d^4\,\left(8\,c-d\,x^3\right)}","Not used",1,"(2496*c^(7/2)*log((10*c + d*x^3 - 6*c^(1/2)*(c + d*x^3)^(1/2))/(8*c - d*x^3)))/d^4 + (32300*c^3*(c + d*x^3)^(1/2))/(21*d^4) + (2*x^9*(c + d*x^3)^(1/2))/(21*d) + (16*c*x^6*(c + d*x^3)^(1/2))/(7*d^2) + (986*c^2*x^3*(c + d*x^3)^(1/2))/(21*d^3) + (1536*c^4*(c + d*x^3)^(1/2))/(d^4*(8*c - d*x^3))","B"
412,1,127,119,4.052486,"\text{Not used}","int((x^8*(c + d*x^3)^(3/2))/(8*c - d*x^3)^2,x)","\frac{240\,c^{5/2}\,\ln\left(\frac{10\,c+d\,x^3-6\,\sqrt{c}\,\sqrt{d\,x^3+c}}{8\,c-d\,x^3}\right)}{d^3}+\frac{6406\,c^2\,\sqrt{d\,x^3+c}}{45\,d^3}+\frac{2\,x^6\,\sqrt{d\,x^3+c}}{15\,d}+\frac{172\,c\,x^3\,\sqrt{d\,x^3+c}}{45\,d^2}+\frac{192\,c^3\,\sqrt{d\,x^3+c}}{d^3\,\left(8\,c-d\,x^3\right)}","Not used",1,"(240*c^(5/2)*log((10*c + d*x^3 - 6*c^(1/2)*(c + d*x^3)^(1/2))/(8*c - d*x^3)))/d^3 + (6406*c^2*(c + d*x^3)^(1/2))/(45*d^3) + (2*x^6*(c + d*x^3)^(1/2))/(15*d) + (172*c*x^3*(c + d*x^3)^(1/2))/(45*d^2) + (192*c^3*(c + d*x^3)^(1/2))/(d^3*(8*c - d*x^3))","B"
413,1,107,97,4.043780,"\text{Not used}","int((x^5*(c + d*x^3)^(3/2))/(8*c - d*x^3)^2,x)","\frac{104\,c\,\sqrt{d\,x^3+c}}{9\,d^2}+\frac{21\,c^{3/2}\,\ln\left(\frac{10\,c+d\,x^3-6\,\sqrt{c}\,\sqrt{d\,x^3+c}}{8\,c-d\,x^3}\right)}{d^2}+\frac{2\,x^3\,\sqrt{d\,x^3+c}}{9\,d}+\frac{24\,c^2\,\sqrt{d\,x^3+c}}{d^2\,\left(8\,c-d\,x^3\right)}","Not used",1,"(104*c*(c + d*x^3)^(1/2))/(9*d^2) + (21*c^(3/2)*log((10*c + d*x^3 - 6*c^(1/2)*(c + d*x^3)^(1/2))/(8*c - d*x^3)))/d^2 + (2*x^3*(c + d*x^3)^(1/2))/(9*d) + (24*c^2*(c + d*x^3)^(1/2))/(d^2*(8*c - d*x^3))","B"
414,1,87,77,3.986768,"\text{Not used}","int((x^2*(c + d*x^3)^(3/2))/(8*c - d*x^3)^2,x)","\frac{2\,\sqrt{d\,x^3+c}}{3\,d}+\frac{3\,\sqrt{c}\,\ln\left(\frac{10\,c+d\,x^3-6\,\sqrt{c}\,\sqrt{d\,x^3+c}}{8\,c-d\,x^3}\right)}{2\,d}+\frac{3\,c\,\sqrt{d\,x^3+c}}{d\,\left(8\,c-d\,x^3\right)}","Not used",1,"(2*(c + d*x^3)^(1/2))/(3*d) + (3*c^(1/2)*log((10*c + d*x^3 - 6*c^(1/2)*(c + d*x^3)^(1/2))/(8*c - d*x^3)))/(2*d) + (3*c*(c + d*x^3)^(1/2))/(d*(8*c - d*x^3))","B"
415,1,101,85,4.721504,"\text{Not used}","int((c + d*x^3)^(3/2)/(x*(8*c - d*x^3)^2),x)","\frac{3\,\sqrt{d\,x^3+c}}{8\,\left(8\,c-d\,x^3\right)}+\frac{\ln\left(\frac{{\left(\sqrt{d\,x^3+c}-\sqrt{c}\right)}^3\,\left(\sqrt{d\,x^3+c}+\sqrt{c}\right)\,{\left(10\,c+d\,x^3-6\,\sqrt{c}\,\sqrt{d\,x^3+c}\right)}^9}{x^6\,{\left(8\,c-d\,x^3\right)}^9}\right)}{192\,\sqrt{c}}","Not used",1,"(3*(c + d*x^3)^(1/2))/(8*(8*c - d*x^3)) + log((((c + d*x^3)^(1/2) - c^(1/2))^3*((c + d*x^3)^(1/2) + c^(1/2))*(10*c + d*x^3 - 6*c^(1/2)*(c + d*x^3)^(1/2))^9)/(x^6*(8*c - d*x^3)^9))/(192*c^(1/2))","B"
416,1,110,121,4.235047,"\text{Not used}","int((c + d*x^3)^(3/2)/(x^4*(8*c - d*x^3)^2),x)","\frac{\frac{9\,d\,\sqrt{d\,x^3+c}}{32}-\frac{5\,d\,{\left(d\,x^3+c\right)}^{3/2}}{32\,c}}{3\,{\left(d\,x^3+c\right)}^2-30\,c\,\left(d\,x^3+c\right)+27\,c^2}+\frac{d\,\left(\mathrm{atanh}\left(\frac{c\,\sqrt{d\,x^3+c}}{\sqrt{c^3}}\right)\,1{}\mathrm{i}-\frac{\mathrm{atanh}\left(\frac{c\,\sqrt{d\,x^3+c}}{3\,\sqrt{c^3}}\right)\,9{}\mathrm{i}}{7}\right)\,7{}\mathrm{i}}{384\,\sqrt{c^3}}","Not used",1,"((9*d*(c + d*x^3)^(1/2))/32 - (5*d*(c + d*x^3)^(3/2))/(32*c))/(3*(c + d*x^3)^2 - 30*c*(c + d*x^3) + 27*c^2) + (d*(atanh((c*(c + d*x^3)^(1/2))/(c^3)^(1/2))*1i - (atanh((c*(c + d*x^3)^(1/2))/(3*(c^3)^(1/2)))*9i)/7)*7i)/(384*(c^3)^(1/2))","B"
417,1,151,161,4.617681,"\text{Not used}","int((c + d*x^3)^(3/2)/(x^7*(8*c - d*x^3)^2),x)","\frac{\frac{81\,d^2\,\sqrt{d\,x^3+c}}{512}-\frac{67\,d^2\,{\left(d\,x^3+c\right)}^{3/2}}{256\,c}+\frac{21\,d^2\,{\left(d\,x^3+c\right)}^{5/2}}{512\,c^2}}{33\,c\,{\left(d\,x^3+c\right)}^2-57\,c^2\,\left(d\,x^3+c\right)-3\,{\left(d\,x^3+c\right)}^3+27\,c^3}+\frac{d^2\,\left(\mathrm{atanh}\left(\frac{c^2\,\sqrt{d\,x^3+c}}{\sqrt{c^5}}\right)\,1{}\mathrm{i}-\frac{\mathrm{atanh}\left(\frac{c^2\,\sqrt{d\,x^3+c}}{3\,\sqrt{c^5}}\right)\,15{}\mathrm{i}}{17}\right)\,17{}\mathrm{i}}{2048\,\sqrt{c^5}}","Not used",1,"((81*d^2*(c + d*x^3)^(1/2))/512 - (67*d^2*(c + d*x^3)^(3/2))/(256*c) + (21*d^2*(c + d*x^3)^(5/2))/(512*c^2))/(33*c*(c + d*x^3)^2 - 57*c^2*(c + d*x^3) - 3*(c + d*x^3)^3 + 27*c^3) + (d^2*(atanh((c^2*(c + d*x^3)^(1/2))/(c^5)^(1/2))*1i - (atanh((c^2*(c + d*x^3)^(1/2))/(3*(c^5)^(1/2)))*15i)/17)*17i)/(2048*(c^5)^(1/2))","B"
418,0,-1,681,0.000000,"\text{Not used}","int((x^7*(c + d*x^3)^(3/2))/(8*c - d*x^3)^2,x)","\int \frac{x^7\,{\left(d\,x^3+c\right)}^{3/2}}{{\left(8\,c-d\,x^3\right)}^2} \,d x","Not used",1,"int((x^7*(c + d*x^3)^(3/2))/(8*c - d*x^3)^2, x)","F"
419,0,-1,657,0.000000,"\text{Not used}","int((x^4*(c + d*x^3)^(3/2))/(8*c - d*x^3)^2,x)","\int \frac{x^4\,{\left(d\,x^3+c\right)}^{3/2}}{{\left(8\,c-d\,x^3\right)}^2} \,d x","Not used",1,"int((x^4*(c + d*x^3)^(3/2))/(8*c - d*x^3)^2, x)","F"
420,0,-1,638,0.000000,"\text{Not used}","int((x*(c + d*x^3)^(3/2))/(8*c - d*x^3)^2,x)","\int \frac{x\,{\left(d\,x^3+c\right)}^{3/2}}{{\left(8\,c-d\,x^3\right)}^2} \,d x","Not used",1,"int((x*(c + d*x^3)^(3/2))/(8*c - d*x^3)^2, x)","F"
421,0,-1,522,0.000000,"\text{Not used}","int((c + d*x^3)^(3/2)/(x^2*(8*c - d*x^3)^2),x)","\int \frac{{\left(d\,x^3+c\right)}^{3/2}}{x^2\,{\left(8\,c-d\,x^3\right)}^2} \,d x","Not used",1,"int((c + d*x^3)^(3/2)/(x^2*(8*c - d*x^3)^2), x)","F"
422,0,-1,684,0.000000,"\text{Not used}","int((c + d*x^3)^(3/2)/(x^5*(8*c - d*x^3)^2),x)","\int \frac{{\left(d\,x^3+c\right)}^{3/2}}{x^5\,{\left(8\,c-d\,x^3\right)}^2} \,d x","Not used",1,"int((c + d*x^3)^(3/2)/(x^5*(8*c - d*x^3)^2), x)","F"
423,0,-1,708,0.000000,"\text{Not used}","int((c + d*x^3)^(3/2)/(x^8*(8*c - d*x^3)^2),x)","\int \frac{{\left(d\,x^3+c\right)}^{3/2}}{x^8\,{\left(8\,c-d\,x^3\right)}^2} \,d x","Not used",1,"int((c + d*x^3)^(3/2)/(x^8*(8*c - d*x^3)^2), x)","F"
424,1,107,95,4.061389,"\text{Not used}","int(x^11/((c + d*x^3)^(1/2)*(8*c - d*x^3)^2),x)","\frac{92\,c\,\sqrt{d\,x^3+c}}{9\,d^4}+\frac{1472\,c^{3/2}\,\ln\left(\frac{10\,c+d\,x^3-6\,\sqrt{c}\,\sqrt{d\,x^3+c}}{8\,c-d\,x^3}\right)}{81\,d^4}+\frac{2\,x^3\,\sqrt{d\,x^3+c}}{9\,d^3}+\frac{512\,c^2\,\sqrt{d\,x^3+c}}{27\,d^4\,\left(8\,c-d\,x^3\right)}","Not used",1,"(92*c*(c + d*x^3)^(1/2))/(9*d^4) + (1472*c^(3/2)*log((10*c + d*x^3 - 6*c^(1/2)*(c + d*x^3)^(1/2))/(8*c - d*x^3)))/(81*d^4) + (2*x^3*(c + d*x^3)^(1/2))/(9*d^3) + (512*c^2*(c + d*x^3)^(1/2))/(27*d^4*(8*c - d*x^3))","B"
425,1,87,83,3.996976,"\text{Not used}","int(x^8/((c + d*x^3)^(1/2)*(8*c - d*x^3)^2),x)","\frac{2\,\sqrt{d\,x^3+c}}{3\,d^3}+\frac{112\,\sqrt{c}\,\ln\left(\frac{10\,c+d\,x^3-6\,\sqrt{c}\,\sqrt{d\,x^3+c}}{8\,c-d\,x^3}\right)}{81\,d^3}+\frac{64\,c\,\sqrt{d\,x^3+c}}{27\,d^3\,\left(8\,c-d\,x^3\right)}","Not used",1,"(2*(c + d*x^3)^(1/2))/(3*d^3) + (112*c^(1/2)*log((10*c + d*x^3 - 6*c^(1/2)*(c + d*x^3)^(1/2))/(8*c - d*x^3)))/(81*d^3) + (64*c*(c + d*x^3)^(1/2))/(27*d^3*(8*c - d*x^3))","B"
426,1,72,64,4.009446,"\text{Not used}","int(x^5/((c + d*x^3)^(1/2)*(8*c - d*x^3)^2),x)","\frac{5\,\ln\left(\frac{10\,c+d\,x^3-6\,\sqrt{c}\,\sqrt{d\,x^3+c}}{8\,c-d\,x^3}\right)}{81\,\sqrt{c}\,d^2}+\frac{8\,\sqrt{d\,x^3+c}}{27\,d^2\,\left(8\,c-d\,x^3\right)}","Not used",1,"(5*log((10*c + d*x^3 - 6*c^(1/2)*(c + d*x^3)^(1/2))/(8*c - d*x^3)))/(81*c^(1/2)*d^2) + (8*(c + d*x^3)^(1/2))/(27*d^2*(8*c - d*x^3))","B"
427,1,75,67,3.976582,"\text{Not used}","int(x^2/((c + d*x^3)^(1/2)*(8*c - d*x^3)^2),x)","\frac{\ln\left(\frac{10\,c+d\,x^3+6\,\sqrt{c}\,\sqrt{d\,x^3+c}}{8\,c-d\,x^3}\right)}{162\,c^{3/2}\,d}+\frac{\sqrt{d\,x^3+c}}{27\,c\,d\,\left(8\,c-d\,x^3\right)}","Not used",1,"log((10*c + d*x^3 + 6*c^(1/2)*(c + d*x^3)^(1/2))/(8*c - d*x^3))/(162*c^(3/2)*d) + (c + d*x^3)^(1/2)/(27*c*d*(8*c - d*x^3))","B"
428,1,80,88,4.008408,"\text{Not used}","int(1/(x*(c + d*x^3)^(1/2)*(8*c - d*x^3)^2),x)","\frac{13\,\mathrm{atanh}\left(\frac{c^2\,\sqrt{d\,x^3+c}}{3\,\sqrt{c^5}}\right)}{2592\,\sqrt{c^5}}-\frac{\mathrm{atanh}\left(\frac{c^2\,\sqrt{d\,x^3+c}}{\sqrt{c^5}}\right)}{96\,\sqrt{c^5}}+\frac{\sqrt{d\,x^3+c}}{72\,c^2\,\left(24\,c-3\,d\,x^3\right)}","Not used",1,"(13*atanh((c^2*(c + d*x^3)^(1/2))/(3*(c^5)^(1/2))))/(2592*(c^5)^(1/2)) - atanh((c^2*(c + d*x^3)^(1/2))/(c^5)^(1/2))/(96*(c^5)^(1/2)) + (c + d*x^3)^(1/2)/(72*c^2*(24*c - 3*d*x^3))","B"
429,1,117,124,4.110793,"\text{Not used}","int(1/(x^4*(c + d*x^3)^(1/2)*(8*c - d*x^3)^2),x)","\frac{\frac{41\,d\,\sqrt{d\,x^3+c}}{288\,c^2}-\frac{5\,d\,{\left(d\,x^3+c\right)}^{3/2}}{288\,c^3}}{3\,{\left(d\,x^3+c\right)}^2-30\,c\,\left(d\,x^3+c\right)+27\,c^2}-\frac{d\,\left(\mathrm{atanh}\left(\frac{c^3\,\sqrt{d\,x^3+c}}{\sqrt{c^7}}\right)\,1{}\mathrm{i}+\frac{\mathrm{atanh}\left(\frac{c^3\,\sqrt{d\,x^3+c}}{3\,\sqrt{c^7}}\right)\,11{}\mathrm{i}}{27}\right)\,1{}\mathrm{i}}{384\,\sqrt{c^7}}","Not used",1,"((41*d*(c + d*x^3)^(1/2))/(288*c^2) - (5*d*(c + d*x^3)^(3/2))/(288*c^3))/(3*(c + d*x^3)^2 - 30*c*(c + d*x^3) + 27*c^2) - (d*(atanh((c^3*(c + d*x^3)^(1/2))/(c^7)^(1/2))*1i + (atanh((c^3*(c + d*x^3)^(1/2))/(3*(c^7)^(1/2)))*11i)/27)*1i)/(384*(c^7)^(1/2))","B"
430,1,155,164,4.368315,"\text{Not used}","int(1/(x^7*(c + d*x^3)^(1/2)*(8*c - d*x^3)^2),x)","-\frac{\frac{647\,d^2\,\sqrt{d\,x^3+c}}{4608\,c^2}-\frac{197\,d^2\,{\left(d\,x^3+c\right)}^{3/2}}{2304\,c^3}+\frac{35\,d^2\,{\left(d\,x^3+c\right)}^{5/2}}{4608\,c^4}}{33\,c\,{\left(d\,x^3+c\right)}^2-57\,c^2\,\left(d\,x^3+c\right)-3\,{\left(d\,x^3+c\right)}^3+27\,c^3}+\frac{d^2\,\left(\mathrm{atanh}\left(\frac{c^4\,\sqrt{d\,x^3+c}}{\sqrt{c^9}}\right)\,1{}\mathrm{i}-\frac{\mathrm{atanh}\left(\frac{c^4\,\sqrt{d\,x^3+c}}{3\,\sqrt{c^9}}\right)\,31{}\mathrm{i}}{513}\right)\,19{}\mathrm{i}}{6144\,\sqrt{c^9}}","Not used",1,"(d^2*(atanh((c^4*(c + d*x^3)^(1/2))/(c^9)^(1/2))*1i - (atanh((c^4*(c + d*x^3)^(1/2))/(3*(c^9)^(1/2)))*31i)/513)*19i)/(6144*(c^9)^(1/2)) - ((647*d^2*(c + d*x^3)^(1/2))/(4608*c^2) - (197*d^2*(c + d*x^3)^(3/2))/(2304*c^3) + (35*d^2*(c + d*x^3)^(5/2))/(4608*c^4))/(33*c*(c + d*x^3)^2 - 57*c^2*(c + d*x^3) - 3*(c + d*x^3)^3 + 27*c^3)","B"
431,0,-1,641,0.000000,"\text{Not used}","int(x^7/((c + d*x^3)^(1/2)*(8*c - d*x^3)^2),x)","\int \frac{x^7}{\sqrt{d\,x^3+c}\,{\left(8\,c-d\,x^3\right)}^2} \,d x","Not used",1,"int(x^7/((c + d*x^3)^(1/2)*(8*c - d*x^3)^2), x)","F"
432,0,-1,647,0.000000,"\text{Not used}","int(x^4/((c + d*x^3)^(1/2)*(8*c - d*x^3)^2),x)","\int \frac{x^4}{\sqrt{d\,x^3+c}\,{\left(8\,c-d\,x^3\right)}^2} \,d x","Not used",1,"int(x^4/((c + d*x^3)^(1/2)*(8*c - d*x^3)^2), x)","F"
433,0,-1,644,0.000000,"\text{Not used}","int(x/((c + d*x^3)^(1/2)*(8*c - d*x^3)^2),x)","\int \frac{x}{\sqrt{d\,x^3+c}\,{\left(8\,c-d\,x^3\right)}^2} \,d x","Not used",1,"int(x/((c + d*x^3)^(1/2)*(8*c - d*x^3)^2), x)","F"
434,0,-1,665,0.000000,"\text{Not used}","int(1/(x^2*(c + d*x^3)^(1/2)*(8*c - d*x^3)^2),x)","\int \frac{1}{x^2\,\sqrt{d\,x^3+c}\,{\left(8\,c-d\,x^3\right)}^2} \,d x","Not used",1,"int(1/(x^2*(c + d*x^3)^(1/2)*(8*c - d*x^3)^2), x)","F"
435,0,-1,687,0.000000,"\text{Not used}","int(1/(x^5*(c + d*x^3)^(1/2)*(8*c - d*x^3)^2),x)","\int \frac{1}{x^5\,\sqrt{d\,x^3+c}\,{\left(8\,c-d\,x^3\right)}^2} \,d x","Not used",1,"int(1/(x^5*(c + d*x^3)^(1/2)*(8*c - d*x^3)^2), x)","F"
436,0,-1,711,0.000000,"\text{Not used}","int(1/(x^8*(c + d*x^3)^(1/2)*(8*c - d*x^3)^2),x)","\int \frac{1}{x^8\,\sqrt{d\,x^3+c}\,{\left(8\,c-d\,x^3\right)}^2} \,d x","Not used",1,"int(1/(x^8*(c + d*x^3)^(1/2)*(8*c - d*x^3)^2), x)","F"
437,0,-1,66,0.000000,"\text{Not used}","int(x^6/((c + d*x^3)^(1/2)*(8*c - d*x^3)^2),x)","\int \frac{x^6}{\sqrt{d\,x^3+c}\,{\left(8\,c-d\,x^3\right)}^2} \,d x","Not used",1,"int(x^6/((c + d*x^3)^(1/2)*(8*c - d*x^3)^2), x)","F"
438,0,-1,66,0.000000,"\text{Not used}","int(x^3/((c + d*x^3)^(1/2)*(8*c - d*x^3)^2),x)","\int \frac{x^3}{\sqrt{d\,x^3+c}\,{\left(8\,c-d\,x^3\right)}^2} \,d x","Not used",1,"int(x^3/((c + d*x^3)^(1/2)*(8*c - d*x^3)^2), x)","F"
439,0,-1,64,0.000000,"\text{Not used}","int(1/((c + d*x^3)^(1/2)*(8*c - d*x^3)^2),x)","\int \frac{1}{\sqrt{d\,x^3+c}\,{\left(8\,c-d\,x^3\right)}^2} \,d x","Not used",1,"int(1/((c + d*x^3)^(1/2)*(8*c - d*x^3)^2), x)","F"
440,0,-1,66,0.000000,"\text{Not used}","int(1/(x^3*(c + d*x^3)^(1/2)*(8*c - d*x^3)^2),x)","\int \frac{1}{x^3\,\sqrt{d\,x^3+c}\,{\left(8\,c-d\,x^3\right)}^2} \,d x","Not used",1,"int(1/(x^3*(c + d*x^3)^(1/2)*(8*c - d*x^3)^2), x)","F"
441,0,-1,66,0.000000,"\text{Not used}","int(1/(x^6*(c + d*x^3)^(1/2)*(8*c - d*x^3)^2),x)","\int \frac{1}{x^6\,\sqrt{d\,x^3+c}\,{\left(8\,c-d\,x^3\right)}^2} \,d x","Not used",1,"int(1/(x^6*(c + d*x^3)^(1/2)*(8*c - d*x^3)^2), x)","F"
442,1,111,95,4.382806,"\text{Not used}","int(x^11/((c + d*x^3)^(3/2)*(8*c - d*x^3)^2),x)","\frac{2\,\sqrt{d\,x^3+c}}{3\,d^4}+\frac{320\,\sqrt{c}\,\ln\left(\frac{10\,c+d\,x^3-6\,\sqrt{c}\,\sqrt{d\,x^3+c}}{8\,c-d\,x^3}\right)}{243\,d^4}+\frac{\sqrt{d\,x^3+c}\,\left(\frac{176\,c^2}{81\,d^4}+\frac{170\,c\,x^3}{81\,d^3}\right)}{8\,c^2+7\,c\,d\,x^3-d^2\,x^6}","Not used",1,"(2*(c + d*x^3)^(1/2))/(3*d^4) + (320*c^(1/2)*log((10*c + d*x^3 - 6*c^(1/2)*(c + d*x^3)^(1/2))/(8*c - d*x^3)))/(243*d^4) + ((c + d*x^3)^(1/2)*((176*c^2)/(81*d^4) + (170*c*x^3)/(81*d^3)))/(8*c^2 - d^2*x^6 + 7*c*d*x^3)","B"
443,1,94,83,4.300262,"\text{Not used}","int(x^8/((c + d*x^3)^(3/2)*(8*c - d*x^3)^2),x)","\frac{16\,\ln\left(\frac{10\,c+d\,x^3-6\,\sqrt{c}\,\sqrt{d\,x^3+c}}{8\,c-d\,x^3}\right)}{243\,\sqrt{c}\,d^3}+\frac{\sqrt{d\,x^3+c}\,\left(\frac{16\,c}{81\,d^3}+\frac{22\,x^3}{81\,d^2}\right)}{8\,c^2+7\,c\,d\,x^3-d^2\,x^6}","Not used",1,"(16*log((10*c + d*x^3 - 6*c^(1/2)*(c + d*x^3)^(1/2))/(8*c - d*x^3)))/(243*c^(1/2)*d^3) + ((c + d*x^3)^(1/2)*((16*c)/(81*d^3) + (22*x^3)/(81*d^2)))/(8*c^2 - d^2*x^6 + 7*c*d*x^3)","B"
444,1,96,85,4.264301,"\text{Not used}","int(x^5/((c + d*x^3)^(3/2)*(8*c - d*x^3)^2),x)","\frac{\left(\frac{8}{81\,d^2}+\frac{2\,x^3}{81\,c\,d}\right)\,\sqrt{d\,x^3+c}}{8\,c^2+7\,c\,d\,x^3-d^2\,x^6}+\frac{\ln\left(\frac{10\,c+d\,x^3+6\,\sqrt{c}\,\sqrt{d\,x^3+c}}{8\,c-d\,x^3}\right)}{243\,c^{3/2}\,d^2}","Not used",1,"((8/(81*d^2) + (2*x^3)/(81*c*d))*(c + d*x^3)^(1/2))/(8*c^2 - d^2*x^6 + 7*c*d*x^3) + log((10*c + d*x^3 + 6*c^(1/2)*(c + d*x^3)^(1/2))/(8*c - d*x^3))/(243*c^(3/2)*d^2)","B"
445,1,97,88,4.261243,"\text{Not used}","int(x^2/((c + d*x^3)^(3/2)*(8*c - d*x^3)^2),x)","\frac{\ln\left(\frac{10\,c+d\,x^3+6\,\sqrt{c}\,\sqrt{d\,x^3+c}}{8\,c-d\,x^3}\right)}{486\,c^{5/2}\,d}-\frac{\left(\frac{5}{81\,c\,d}-\frac{x^3}{81\,c^2}\right)\,\sqrt{d\,x^3+c}}{8\,c^2+7\,c\,d\,x^3-d^2\,x^6}","Not used",1,"log((10*c + d*x^3 + 6*c^(1/2)*(c + d*x^3)^(1/2))/(8*c - d*x^3))/(486*c^(5/2)*d) - ((5/(81*c*d) - x^3/(81*c^2))*(c + d*x^3)^(1/2))/(8*c^2 - d^2*x^6 + 7*c*d*x^3)","B"
446,1,101,106,4.331719,"\text{Not used}","int(1/(x*(c + d*x^3)^(3/2)*(8*c - d*x^3)^2),x)","-\frac{\frac{5\,\left(d\,x^3+c\right)}{216\,c^3}-\frac{2}{9\,c^2}}{27\,c\,\sqrt{d\,x^3+c}-3\,{\left(d\,x^3+c\right)}^{3/2}}+\frac{\left(\mathrm{atanh}\left(\frac{c^3\,\sqrt{d\,x^3+c}}{\sqrt{c^7}}\right)\,1{}\mathrm{i}-\frac{\mathrm{atanh}\left(\frac{c^3\,\sqrt{d\,x^3+c}}{3\,\sqrt{c^7}}\right)\,7{}\mathrm{i}}{81}\right)\,1{}\mathrm{i}}{96\,\sqrt{c^7}}","Not used",1,"((atanh((c^3*(c + d*x^3)^(1/2))/(c^7)^(1/2))*1i - (atanh((c^3*(c + d*x^3)^(1/2))/(3*(c^7)^(1/2)))*7i)/81)*1i)/(96*(c^7)^(1/2)) - ((5*(c + d*x^3))/(216*c^3) - 2/(9*c^2))/(27*c*(c + d*x^3)^(1/2) - 3*(c + d*x^3)^(3/2))","B"
447,1,133,143,4.562415,"\text{Not used}","int(1/(x^4*(c + d*x^3)^(3/2)*(8*c - d*x^3)^2),x)","-\frac{\frac{2\,d}{9\,c^2}+\frac{35\,d\,{\left(d\,x^3+c\right)}^2}{864\,c^4}-\frac{335\,d\,\left(d\,x^3+c\right)}{864\,c^3}}{3\,{\left(d\,x^3+c\right)}^{5/2}-30\,c\,{\left(d\,x^3+c\right)}^{3/2}+27\,c^2\,\sqrt{d\,x^3+c}}-\frac{d\,\left(\mathrm{atanh}\left(\frac{c^4\,\sqrt{d\,x^3+c}}{\sqrt{c^9}}\right)\,1{}\mathrm{i}+\frac{\mathrm{atanh}\left(\frac{c^4\,\sqrt{d\,x^3+c}}{3\,\sqrt{c^9}}\right)\,1{}\mathrm{i}}{81}\right)\,5{}\mathrm{i}}{384\,\sqrt{c^9}}","Not used",1,"- ((2*d)/(9*c^2) + (35*d*(c + d*x^3)^2)/(864*c^4) - (335*d*(c + d*x^3))/(864*c^3))/(3*(c + d*x^3)^(5/2) - 30*c*(c + d*x^3)^(3/2) + 27*c^2*(c + d*x^3)^(1/2)) - (d*(atanh((c^4*(c + d*x^3)^(1/2))/(c^9)^(1/2))*1i + (atanh((c^4*(c + d*x^3)^(1/2))/(3*(c^9)^(1/2)))*1i)/81)*5i)/(384*(c^9)^(1/2))","B"
448,1,171,185,4.763498,"\text{Not used}","int(1/(x^7*(c + d*x^3)^(3/2)*(8*c - d*x^3)^2),x)","\frac{\frac{2\,d^2}{9\,c^2}-\frac{10373\,d^2\,\left(d\,x^3+c\right)}{13824\,c^3}+\frac{3551\,d^2\,{\left(d\,x^3+c\right)}^2}{6912\,c^4}-\frac{665\,d^2\,{\left(d\,x^3+c\right)}^3}{13824\,c^5}}{33\,c\,{\left(d\,x^3+c\right)}^{5/2}-3\,{\left(d\,x^3+c\right)}^{7/2}+27\,c^3\,\sqrt{d\,x^3+c}-57\,c^2\,{\left(d\,x^3+c\right)}^{3/2}}+\frac{d^2\,\left(\mathrm{atanh}\left(\frac{c^5\,\sqrt{d\,x^3+c}}{\sqrt{c^{11}}}\right)\,1{}\mathrm{i}-\frac{\mathrm{atanh}\left(\frac{c^5\,\sqrt{d\,x^3+c}}{3\,\sqrt{c^{11}}}\right)\,13{}\mathrm{i}}{8019}\right)\,33{}\mathrm{i}}{2048\,\sqrt{c^{11}}}","Not used",1,"((2*d^2)/(9*c^2) - (10373*d^2*(c + d*x^3))/(13824*c^3) + (3551*d^2*(c + d*x^3)^2)/(6912*c^4) - (665*d^2*(c + d*x^3)^3)/(13824*c^5))/(33*c*(c + d*x^3)^(5/2) - 3*(c + d*x^3)^(7/2) + 27*c^3*(c + d*x^3)^(1/2) - 57*c^2*(c + d*x^3)^(3/2)) + (d^2*(atanh((c^5*(c + d*x^3)^(1/2))/(c^11)^(1/2))*1i - (atanh((c^5*(c + d*x^3)^(1/2))/(3*(c^11)^(1/2)))*13i)/8019)*33i)/(2048*(c^11)^(1/2))","B"
449,0,-1,668,0.000000,"\text{Not used}","int(x^7/((c + d*x^3)^(3/2)*(8*c - d*x^3)^2),x)","\int \frac{x^7}{{\left(d\,x^3+c\right)}^{3/2}\,{\left(8\,c-d\,x^3\right)}^2} \,d x","Not used",1,"int(x^7/((c + d*x^3)^(3/2)*(8*c - d*x^3)^2), x)","F"
450,0,-1,671,0.000000,"\text{Not used}","int(x^4/((c + d*x^3)^(3/2)*(8*c - d*x^3)^2),x)","\int \frac{x^4}{{\left(d\,x^3+c\right)}^{3/2}\,{\left(8\,c-d\,x^3\right)}^2} \,d x","Not used",1,"int(x^4/((c + d*x^3)^(3/2)*(8*c - d*x^3)^2), x)","F"
451,0,-1,665,0.000000,"\text{Not used}","int(x/((c + d*x^3)^(3/2)*(8*c - d*x^3)^2),x)","\int \frac{x}{{\left(d\,x^3+c\right)}^{3/2}\,{\left(8\,c-d\,x^3\right)}^2} \,d x","Not used",1,"int(x/((c + d*x^3)^(3/2)*(8*c - d*x^3)^2), x)","F"
452,0,-1,686,0.000000,"\text{Not used}","int(1/(x^2*(c + d*x^3)^(3/2)*(8*c - d*x^3)^2),x)","\int \frac{1}{x^2\,{\left(d\,x^3+c\right)}^{3/2}\,{\left(8\,c-d\,x^3\right)}^2} \,d x","Not used",1,"int(1/(x^2*(c + d*x^3)^(3/2)*(8*c - d*x^3)^2), x)","F"
453,0,-1,708,0.000000,"\text{Not used}","int(1/(x^5*(c + d*x^3)^(3/2)*(8*c - d*x^3)^2),x)","\int \frac{1}{x^5\,{\left(d\,x^3+c\right)}^{3/2}\,{\left(8\,c-d\,x^3\right)}^2} \,d x","Not used",1,"int(1/(x^5*(c + d*x^3)^(3/2)*(8*c - d*x^3)^2), x)","F"
454,0,-1,732,0.000000,"\text{Not used}","int(1/(x^8*(c + d*x^3)^(3/2)*(8*c - d*x^3)^2),x)","\int \frac{1}{x^8\,{\left(d\,x^3+c\right)}^{3/2}\,{\left(8\,c-d\,x^3\right)}^2} \,d x","Not used",1,"int(1/(x^8*(c + d*x^3)^(3/2)*(8*c - d*x^3)^2), x)","F"
455,0,-1,256,0.000000,"\text{Not used}","int(x^6/((c + d*x^3)^(3/2)*(8*c - d*x^3)^2),x)","\int \frac{x^6}{{\left(d\,x^3+c\right)}^{3/2}\,{\left(8\,c-d\,x^3\right)}^2} \,d x","Not used",1,"int(x^6/((c + d*x^3)^(3/2)*(8*c - d*x^3)^2), x)","F"
456,0,-1,66,0.000000,"\text{Not used}","int(x^3/((c + d*x^3)^(3/2)*(8*c - d*x^3)^2),x)","\int \frac{x^3}{{\left(d\,x^3+c\right)}^{3/2}\,{\left(8\,c-d\,x^3\right)}^2} \,d x","Not used",1,"int(x^3/((c + d*x^3)^(3/2)*(8*c - d*x^3)^2), x)","F"
457,0,-1,64,0.000000,"\text{Not used}","int(1/((c + d*x^3)^(3/2)*(8*c - d*x^3)^2),x)","\int \frac{1}{{\left(d\,x^3+c\right)}^{3/2}\,{\left(8\,c-d\,x^3\right)}^2} \,d x","Not used",1,"int(1/((c + d*x^3)^(3/2)*(8*c - d*x^3)^2), x)","F"
458,0,-1,66,0.000000,"\text{Not used}","int(1/(x^3*(c + d*x^3)^(3/2)*(8*c - d*x^3)^2),x)","\int \frac{1}{x^3\,{\left(d\,x^3+c\right)}^{3/2}\,{\left(8\,c-d\,x^3\right)}^2} \,d x","Not used",1,"int(1/(x^3*(c + d*x^3)^(3/2)*(8*c - d*x^3)^2), x)","F"
459,0,-1,66,0.000000,"\text{Not used}","int(1/(x^6*(c + d*x^3)^(3/2)*(8*c - d*x^3)^2),x)","\int \frac{1}{x^6\,{\left(d\,x^3+c\right)}^{3/2}\,{\left(8\,c-d\,x^3\right)}^2} \,d x","Not used",1,"int(1/(x^6*(c + d*x^3)^(3/2)*(8*c - d*x^3)^2), x)","F"
460,1,202,161,6.841814,"\text{Not used}","int((x^8*(c + d*x^3)^(1/2))/(a + b*x^3)^2,x)","\frac{2\,x^3\,\sqrt{d\,x^3+c}}{9\,b^2}-\frac{\sqrt{d\,x^3+c}\,\left(\frac{4\,c}{3\,b^2}-\frac{2\,b^2\,c-2\,a\,b\,d}{b^4}+\frac{2\,a\,d}{b^3}\right)}{3\,d}+\frac{a^2\,\left(\frac{2\,a\,d}{3\,\left(2\,b^2\,c-2\,a\,b\,d\right)}-\frac{2\,b\,c}{3\,\left(2\,b^2\,c-2\,a\,b\,d\right)}\right)\,\sqrt{d\,x^3+c}}{b^2\,\left(b\,x^3+a\right)}+\frac{a\,\ln\left(\frac{2\,b\,c-a\,d+b\,d\,x^3+\sqrt{b}\,\sqrt{d\,x^3+c}\,\sqrt{a\,d-b\,c}\,2{}\mathrm{i}}{b\,x^3+a}\right)\,\left(5\,a\,d-4\,b\,c\right)\,1{}\mathrm{i}}{6\,b^{7/2}\,\sqrt{a\,d-b\,c}}","Not used",1,"(2*x^3*(c + d*x^3)^(1/2))/(9*b^2) - ((c + d*x^3)^(1/2)*((4*c)/(3*b^2) - (2*b^2*c - 2*a*b*d)/b^4 + (2*a*d)/b^3))/(3*d) + (a*log((2*b*c - a*d + b^(1/2)*(c + d*x^3)^(1/2)*(a*d - b*c)^(1/2)*2i + b*d*x^3)/(a + b*x^3))*(5*a*d - 4*b*c)*1i)/(6*b^(7/2)*(a*d - b*c)^(1/2)) + (a^2*((2*a*d)/(3*(2*b^2*c - 2*a*b*d)) - (2*b*c)/(3*(2*b^2*c - 2*a*b*d)))*(c + d*x^3)^(1/2))/(b^2*(a + b*x^3))","B"
461,1,152,136,6.087324,"\text{Not used}","int((x^5*(c + d*x^3)^(1/2))/(a + b*x^3)^2,x)","\frac{2\,\sqrt{d\,x^3+c}}{3\,b^2}-\frac{a\,\left(\frac{2\,a\,d}{3\,\left(2\,b^2\,c-2\,a\,b\,d\right)}-\frac{2\,b\,c}{3\,\left(2\,b^2\,c-2\,a\,b\,d\right)}\right)\,\sqrt{d\,x^3+c}}{b\,\left(b\,x^3+a\right)}+\frac{\ln\left(\frac{a\,d-2\,b\,c-b\,d\,x^3+\sqrt{b}\,\sqrt{d\,x^3+c}\,\sqrt{a\,d-b\,c}\,2{}\mathrm{i}}{b\,x^3+a}\right)\,\left(3\,a\,d-2\,b\,c\right)\,1{}\mathrm{i}}{6\,b^{5/2}\,\sqrt{a\,d-b\,c}}","Not used",1,"(2*(c + d*x^3)^(1/2))/(3*b^2) + (log((a*d - 2*b*c + b^(1/2)*(c + d*x^3)^(1/2)*(a*d - b*c)^(1/2)*2i - b*d*x^3)/(a + b*x^3))*(3*a*d - 2*b*c)*1i)/(6*b^(5/2)*(a*d - b*c)^(1/2)) - (a*((2*a*d)/(3*(2*b^2*c - 2*a*b*d)) - (2*b*c)/(3*(2*b^2*c - 2*a*b*d)))*(c + d*x^3)^(1/2))/(b*(a + b*x^3))","B"
462,1,125,80,5.685559,"\text{Not used}","int((x^2*(c + d*x^3)^(1/2))/(a + b*x^3)^2,x)","\frac{\left(\frac{2\,a\,d}{3\,\left(2\,b^2\,c-2\,a\,b\,d\right)}-\frac{2\,b\,c}{3\,\left(2\,b^2\,c-2\,a\,b\,d\right)}\right)\,\sqrt{d\,x^3+c}}{b\,x^3+a}+\frac{d\,\ln\left(\frac{2\,b\,c-a\,d+b\,d\,x^3+\sqrt{b}\,\sqrt{d\,x^3+c}\,\sqrt{a\,d-b\,c}\,2{}\mathrm{i}}{b\,x^3+a}\right)\,1{}\mathrm{i}}{6\,b^{3/2}\,\sqrt{a\,d-b\,c}}","Not used",1,"(((2*a*d)/(3*(2*b^2*c - 2*a*b*d)) - (2*b*c)/(3*(2*b^2*c - 2*a*b*d)))*(c + d*x^3)^(1/2))/(a + b*x^3) + (d*log((2*b*c - a*d + b^(1/2)*(c + d*x^3)^(1/2)*(a*d - b*c)^(1/2)*2i + b*d*x^3)/(a + b*x^3))*1i)/(6*b^(3/2)*(a*d - b*c)^(1/2))","B"
463,1,182,121,8.281322,"\text{Not used}","int((c + d*x^3)^(1/2)/(x*(a + b*x^3)^2),x)","\frac{\sqrt{c}\,\ln\left(\frac{{\left(\sqrt{d\,x^3+c}-\sqrt{c}\right)}^3\,\left(\sqrt{d\,x^3+c}+\sqrt{c}\right)}{x^6}\right)}{3\,a^2}-\frac{\left(\frac{b\,d}{3\,\left(b^2\,c-a\,b\,d\right)}-\frac{b^2\,c}{3\,a\,\left(b^2\,c-a\,b\,d\right)}\right)\,\sqrt{d\,x^3+c}}{b\,x^3+a}+\frac{\ln\left(\frac{2\,b\,c-a\,d+b\,d\,x^3+\sqrt{d\,x^3+c}\,\sqrt{a\,b\,d-b^2\,c}\,2{}\mathrm{i}}{b\,x^3+a}\right)\,\left(a\,d-2\,b\,c\right)\,1{}\mathrm{i}}{6\,a^2\,\sqrt{a\,b\,d-b^2\,c}}","Not used",1,"(c^(1/2)*log((((c + d*x^3)^(1/2) - c^(1/2))^3*((c + d*x^3)^(1/2) + c^(1/2)))/x^6))/(3*a^2) - (((b*d)/(3*(b^2*c - a*b*d)) - (b^2*c)/(3*a*(b^2*c - a*b*d)))*(c + d*x^3)^(1/2))/(a + b*x^3) + (log((2*b*c - a*d + (c + d*x^3)^(1/2)*(a*b*d - b^2*c)^(1/2)*2i + b*d*x^3)/(a + b*x^3))*(a*d - 2*b*c)*1i)/(6*a^2*(a*b*d - b^2*c)^(1/2))","B"
464,1,438,161,9.692044,"\text{Not used}","int((c + d*x^3)^(1/2)/(x^4*(a + b*x^3)^2),x)","\frac{\left(\frac{a\,\left(\frac{a\,\left(\frac{a\,\left(\frac{b^2\,d^2}{2\,a^3\,c^2}-\frac{b^2\,d^2\,\left(3\,a\,d-4\,b\,c\right)}{6\,a^2\,c^2\,\left(a^2\,d-a\,b\,c\right)}+\frac{b^2\,d\,\left(2\,a\,d-b\,c\right)\,\left(3\,a\,d-4\,b\,c\right)}{6\,a^3\,c^2\,\left(a^2\,d-a\,b\,c\right)}\right)}{b}-\frac{b\,d\,\left(2\,a\,d-b\,c\right)}{2\,a^3\,c^2}+\frac{b\,\left(3\,a\,d-4\,b\,c\right)\,\left(-a^2\,d^2+2\,a\,b\,c\,d+2\,b^2\,c^2\right)}{6\,a^3\,c^2\,\left(a^2\,d-a\,b\,c\right)}\right)}{b}-\frac{-a^2\,d^2+2\,a\,b\,c\,d+2\,b^2\,c^2}{2\,a^3\,c^2}+\frac{b\,\left(a\,d-4\,b\,c\right)\,\left(3\,a\,d-4\,b\,c\right)}{6\,a^2\,c\,\left(a^2\,d-a\,b\,c\right)}\right)}{b}-\frac{a\,d-4\,b\,c}{2\,a^2\,c}\right)\,\sqrt{d\,x^3+c}}{b\,x^3+a}-\frac{\sqrt{d\,x^3+c}}{3\,a^2\,x^3}+\frac{\ln\left(\frac{{\left(\sqrt{d\,x^3+c}-\sqrt{c}\right)}^3\,\left(\sqrt{d\,x^3+c}+\sqrt{c}\right)}{x^6}\right)\,\left(a\,d-4\,b\,c\right)}{6\,a^3\,\sqrt{c}}+\frac{\sqrt{b}\,\ln\left(\frac{a\,d-2\,b\,c-b\,d\,x^3+\sqrt{b}\,\sqrt{d\,x^3+c}\,\sqrt{a\,d-b\,c}\,2{}\mathrm{i}}{b\,x^3+a}\right)\,\left(3\,a\,d-4\,b\,c\right)\,1{}\mathrm{i}}{6\,a^3\,\sqrt{a\,d-b\,c}}","Not used",1,"(((a*((a*((a*((b^2*d^2)/(2*a^3*c^2) - (b^2*d^2*(3*a*d - 4*b*c))/(6*a^2*c^2*(a^2*d - a*b*c)) + (b^2*d*(2*a*d - b*c)*(3*a*d - 4*b*c))/(6*a^3*c^2*(a^2*d - a*b*c))))/b - (b*d*(2*a*d - b*c))/(2*a^3*c^2) + (b*(3*a*d - 4*b*c)*(2*b^2*c^2 - a^2*d^2 + 2*a*b*c*d))/(6*a^3*c^2*(a^2*d - a*b*c))))/b - (2*b^2*c^2 - a^2*d^2 + 2*a*b*c*d)/(2*a^3*c^2) + (b*(a*d - 4*b*c)*(3*a*d - 4*b*c))/(6*a^2*c*(a^2*d - a*b*c))))/b - (a*d - 4*b*c)/(2*a^2*c))*(c + d*x^3)^(1/2))/(a + b*x^3) - (c + d*x^3)^(1/2)/(3*a^2*x^3) + (log((((c + d*x^3)^(1/2) - c^(1/2))^3*((c + d*x^3)^(1/2) + c^(1/2)))/x^6)*(a*d - 4*b*c))/(6*a^3*c^(1/2)) + (b^(1/2)*log((a*d - 2*b*c + b^(1/2)*(c + d*x^3)^(1/2)*(a*d - b*c)^(1/2)*2i - b*d*x^3)/(a + b*x^3))*(3*a*d - 4*b*c)*1i)/(6*a^3*(a*d - b*c)^(1/2))","B"
465,0,-1,64,0.000000,"\text{Not used}","int((x^3*(c + d*x^3)^(1/2))/(a + b*x^3)^2,x)","\int \frac{x^3\,\sqrt{d\,x^3+c}}{{\left(b\,x^3+a\right)}^2} \,d x","Not used",1,"int((x^3*(c + d*x^3)^(1/2))/(a + b*x^3)^2, x)","F"
466,0,-1,64,0.000000,"\text{Not used}","int((x*(c + d*x^3)^(1/2))/(a + b*x^3)^2,x)","\int \frac{x\,\sqrt{d\,x^3+c}}{{\left(b\,x^3+a\right)}^2} \,d x","Not used",1,"int((x*(c + d*x^3)^(1/2))/(a + b*x^3)^2, x)","F"
467,0,-1,59,0.000000,"\text{Not used}","int((c + d*x^3)^(1/2)/(a + b*x^3)^2,x)","\int \frac{\sqrt{d\,x^3+c}}{{\left(b\,x^3+a\right)}^2} \,d x","Not used",1,"int((c + d*x^3)^(1/2)/(a + b*x^3)^2, x)","F"
468,0,-1,62,0.000000,"\text{Not used}","int((c + d*x^3)^(1/2)/(x^2*(a + b*x^3)^2),x)","\int \frac{\sqrt{d\,x^3+c}}{x^2\,{\left(b\,x^3+a\right)}^2} \,d x","Not used",1,"int((c + d*x^3)^(1/2)/(x^2*(a + b*x^3)^2), x)","F"
469,0,-1,64,0.000000,"\text{Not used}","int((c + d*x^3)^(1/2)/(x^3*(a + b*x^3)^2),x)","\int \frac{\sqrt{d\,x^3+c}}{x^3\,{\left(b\,x^3+a\right)}^2} \,d x","Not used",1,"int((c + d*x^3)^(1/2)/(x^3*(a + b*x^3)^2), x)","F"
470,1,331,189,7.751964,"\text{Not used}","int((x^8*(c + d*x^3)^(3/2))/(a + b*x^3)^2,x)","\frac{\sqrt{d\,x^3+c}\,\left(\frac{2\,{\left(a\,d-b\,c\right)}^2}{b^4}+\frac{2\,c\,\left(\frac{2\,d\,\left(a\,d-2\,b\,c\right)}{b^3}+\frac{2\,a\,d^2}{b^3}+\frac{8\,c\,d}{5\,b^2}\right)}{3\,d}+\frac{2\,a\,\left(\frac{d\,\left(a\,d-2\,b\,c\right)}{b^3}+\frac{a\,d^2}{b^3}\right)}{b}\right)}{3\,d}+\frac{2\,d\,x^6\,\sqrt{d\,x^3+c}}{15\,b^2}-\frac{x^3\,\sqrt{d\,x^3+c}\,\left(\frac{2\,d\,\left(a\,d-2\,b\,c\right)}{b^3}+\frac{2\,a\,d^2}{b^3}+\frac{8\,c\,d}{5\,b^2}\right)}{9\,d}-\frac{a^2\,\left(\frac{2\,b\,c^2}{3\,\left(2\,b^2\,c-2\,a\,b\,d\right)}+\frac{a\,\left(\frac{2\,a\,d^2}{3\,\left(2\,b^2\,c-2\,a\,b\,d\right)}-\frac{4\,b\,c\,d}{3\,\left(2\,b^2\,c-2\,a\,b\,d\right)}\right)}{b}\right)\,\sqrt{d\,x^3+c}}{b^2\,\left(b\,x^3+a\right)}+\frac{a\,\ln\left(\frac{a\,d-2\,b\,c-b\,d\,x^3+\sqrt{b}\,\sqrt{d\,x^3+c}\,\sqrt{a\,d-b\,c}\,2{}\mathrm{i}}{b\,x^3+a}\right)\,\sqrt{a\,d-b\,c}\,\left(7\,a\,d-4\,b\,c\right)\,1{}\mathrm{i}}{6\,b^{9/2}}","Not used",1,"((c + d*x^3)^(1/2)*((2*(a*d - b*c)^2)/b^4 + (2*c*((2*d*(a*d - 2*b*c))/b^3 + (2*a*d^2)/b^3 + (8*c*d)/(5*b^2)))/(3*d) + (2*a*((d*(a*d - 2*b*c))/b^3 + (a*d^2)/b^3))/b))/(3*d) + (2*d*x^6*(c + d*x^3)^(1/2))/(15*b^2) - (x^3*(c + d*x^3)^(1/2)*((2*d*(a*d - 2*b*c))/b^3 + (2*a*d^2)/b^3 + (8*c*d)/(5*b^2)))/(9*d) + (a*log((a*d - 2*b*c + b^(1/2)*(c + d*x^3)^(1/2)*(a*d - b*c)^(1/2)*2i - b*d*x^3)/(a + b*x^3))*(a*d - b*c)^(1/2)*(7*a*d - 4*b*c)*1i)/(6*b^(9/2)) - (a^2*((2*b*c^2)/(3*(2*b^2*c - 2*a*b*d)) + (a*((2*a*d^2)/(3*(2*b^2*c - 2*a*b*d)) - (4*b*c*d)/(3*(2*b^2*c - 2*a*b*d))))/b)*(c + d*x^3)^(1/2))/(b^2*(a + b*x^3))","B"
471,1,229,163,7.378916,"\text{Not used}","int((x^5*(c + d*x^3)^(3/2))/(a + b*x^3)^2,x)","\frac{2\,d\,x^3\,\sqrt{d\,x^3+c}}{9\,b^2}-\frac{\sqrt{d\,x^3+c}\,\left(\frac{2\,d\,\left(a\,d-2\,b\,c\right)}{b^3}+\frac{2\,a\,d^2}{b^3}+\frac{4\,c\,d}{3\,b^2}\right)}{3\,d}+\frac{a\,\left(\frac{2\,b\,c^2}{3\,\left(2\,b^2\,c-2\,a\,b\,d\right)}+\frac{a\,\left(\frac{2\,a\,d^2}{3\,\left(2\,b^2\,c-2\,a\,b\,d\right)}-\frac{4\,b\,c\,d}{3\,\left(2\,b^2\,c-2\,a\,b\,d\right)}\right)}{b}\right)\,\sqrt{d\,x^3+c}}{b\,\left(b\,x^3+a\right)}+\frac{\ln\left(\frac{2\,b\,c-a\,d+b\,d\,x^3+\sqrt{b}\,\sqrt{d\,x^3+c}\,\sqrt{a\,d-b\,c}\,2{}\mathrm{i}}{b\,x^3+a}\right)\,\sqrt{a\,d-b\,c}\,\left(5\,a\,d-2\,b\,c\right)\,1{}\mathrm{i}}{6\,b^{7/2}}","Not used",1,"(2*d*x^3*(c + d*x^3)^(1/2))/(9*b^2) - ((c + d*x^3)^(1/2)*((2*d*(a*d - 2*b*c))/b^3 + (2*a*d^2)/b^3 + (4*c*d)/(3*b^2)))/(3*d) + (log((2*b*c - a*d + b^(1/2)*(c + d*x^3)^(1/2)*(a*d - b*c)^(1/2)*2i + b*d*x^3)/(a + b*x^3))*(a*d - b*c)^(1/2)*(5*a*d - 2*b*c)*1i)/(6*b^(7/2)) + (a*((2*b*c^2)/(3*(2*b^2*c - 2*a*b*d)) + (a*((2*a*d^2)/(3*(2*b^2*c - 2*a*b*d)) - (4*b*c*d)/(3*(2*b^2*c - 2*a*b*d))))/b)*(c + d*x^3)^(1/2))/(b*(a + b*x^3))","B"
472,1,170,94,7.354285,"\text{Not used}","int((x^2*(c + d*x^3)^(3/2))/(a + b*x^3)^2,x)","\frac{2\,d\,\sqrt{d\,x^3+c}}{3\,b^2}-\frac{\left(\frac{2\,b\,c^2}{3\,\left(2\,b^2\,c-2\,a\,b\,d\right)}+\frac{a\,\left(\frac{2\,a\,d^2}{3\,\left(2\,b^2\,c-2\,a\,b\,d\right)}-\frac{4\,b\,c\,d}{3\,\left(2\,b^2\,c-2\,a\,b\,d\right)}\right)}{b}\right)\,\sqrt{d\,x^3+c}}{b\,x^3+a}+\frac{d\,\ln\left(\frac{a\,d-2\,b\,c-b\,d\,x^3+\sqrt{b}\,\sqrt{d\,x^3+c}\,\sqrt{a\,d-b\,c}\,2{}\mathrm{i}}{b\,x^3+a}\right)\,\sqrt{a\,d-b\,c}\,1{}\mathrm{i}}{2\,b^{5/2}}","Not used",1,"(2*d*(c + d*x^3)^(1/2))/(3*b^2) - (((2*b*c^2)/(3*(2*b^2*c - 2*a*b*d)) + (a*((2*a*d^2)/(3*(2*b^2*c - 2*a*b*d)) - (4*b*c*d)/(3*(2*b^2*c - 2*a*b*d))))/b)*(c + d*x^3)^(1/2))/(a + b*x^3) + (d*log((a*d - 2*b*c + b^(1/2)*(c + d*x^3)^(1/2)*(a*d - b*c)^(1/2)*2i - b*d*x^3)/(a + b*x^3))*(a*d - b*c)^(1/2)*1i)/(2*b^(5/2))","B"
473,1,214,131,9.143290,"\text{Not used}","int((c + d*x^3)^(3/2)/(x*(a + b*x^3)^2),x)","\frac{c^{3/2}\,\ln\left(\frac{{\left(\sqrt{d\,x^3+c}-\sqrt{c}\right)}^3\,\left(\sqrt{d\,x^3+c}+\sqrt{c}\right)}{x^6}\right)}{3\,a^2}+\frac{\sqrt{d\,x^3+c}\,\left(\frac{a\,\left(\frac{b\,d^2}{3\,\left(b^2\,c-a\,b\,d\right)}-\frac{2\,b^2\,c\,d}{3\,a\,\left(b^2\,c-a\,b\,d\right)}\right)}{b}+\frac{b^2\,c^2}{3\,a\,\left(b^2\,c-a\,b\,d\right)}\right)}{b\,x^3+a}+\frac{\ln\left(\frac{2\,b\,c-a\,d+b\,d\,x^3+\sqrt{b}\,\sqrt{d\,x^3+c}\,\sqrt{a\,d-b\,c}\,2{}\mathrm{i}}{b\,x^3+a}\right)\,\sqrt{a\,d-b\,c}\,\left(a\,d+2\,b\,c\right)\,1{}\mathrm{i}}{6\,a^2\,b^{3/2}}","Not used",1,"(c^(3/2)*log((((c + d*x^3)^(1/2) - c^(1/2))^3*((c + d*x^3)^(1/2) + c^(1/2)))/x^6))/(3*a^2) + ((c + d*x^3)^(1/2)*((a*((b*d^2)/(3*(b^2*c - a*b*d)) - (2*b^2*c*d)/(3*a*(b^2*c - a*b*d))))/b + (b^2*c^2)/(3*a*(b^2*c - a*b*d))))/(a + b*x^3) + (log((2*b*c - a*d + b^(1/2)*(c + d*x^3)^(1/2)*(a*d - b*c)^(1/2)*2i + b*d*x^3)/(a + b*x^3))*(a*d - b*c)^(1/2)*(a*d + 2*b*c)*1i)/(6*a^2*b^(3/2))","B"
474,1,531,170,10.816223,"\text{Not used}","int((c + d*x^3)^(3/2)/(x^4*(a + b*x^3)^2),x)","\frac{\sqrt{c}\,\ln\left(\frac{{\left(\sqrt{d\,x^3+c}-\sqrt{c}\right)}^3\,\left(\sqrt{d\,x^3+c}+\sqrt{c}\right)}{x^6}\right)\,\left(3\,a\,d-4\,b\,c\right)}{6\,a^3}-\frac{c\,\sqrt{d\,x^3+c}}{3\,a^2\,x^3}-\frac{\sqrt{d\,x^3+c}\,\left(\frac{3\,a\,d-4\,b\,c}{2\,a^2}-\frac{a\,\left(\frac{a\,\left(\frac{a\,\left(\frac{b\,d^2\,\left(a\,d+b\,c\right)}{a^3\,c^2}-\frac{a\,\left(\frac{b^2\,d^3}{2\,a^3\,c^2}-\frac{b^2\,d^3\,\left(3\,a\,d-4\,b\,c\right)}{6\,a^2\,c^2\,\left(a^2\,d-a\,b\,c\right)}+\frac{b^2\,d^2\,\left(a\,d+b\,c\right)\,\left(3\,a\,d-4\,b\,c\right)}{3\,a^3\,c^2\,\left(a^2\,d-a\,b\,c\right)}\right)}{b}+\frac{b\,\left(3\,a\,d-4\,b\,c\right)\,\left(a^2\,d^3+4\,a\,b\,c\,d^2-b^2\,c^2\,d\right)}{6\,a^3\,c^2\,\left(a^2\,d-a\,b\,c\right)}\right)}{b}-\frac{a^2\,d^3+4\,a\,b\,c\,d^2-b^2\,c^2\,d}{2\,a^3\,c^2}+\frac{b\,\left(3\,a\,d-4\,b\,c\right)\,\left(-4\,a^2\,c\,d^2+2\,a\,b\,c^2\,d+2\,b^2\,c^3\right)}{6\,a^3\,c^2\,\left(a^2\,d-a\,b\,c\right)}\right)}{b}-\frac{-4\,a^2\,c\,d^2+2\,a\,b\,c^2\,d+2\,b^2\,c^3}{2\,a^3\,c^2}+\frac{b\,{\left(3\,a\,d-4\,b\,c\right)}^2}{6\,a^2\,\left(a^2\,d-a\,b\,c\right)}\right)}{b}\right)}{b\,x^3+a}+\frac{\ln\left(\frac{2\,b\,c-a\,d+b\,d\,x^3+\sqrt{b}\,\sqrt{d\,x^3+c}\,\sqrt{a\,d-b\,c}\,2{}\mathrm{i}}{b\,x^3+a}\right)\,\sqrt{a\,d-b\,c}\,\left(a\,d-4\,b\,c\right)\,1{}\mathrm{i}}{6\,a^3\,\sqrt{b}}","Not used",1,"(c^(1/2)*log((((c + d*x^3)^(1/2) - c^(1/2))^3*((c + d*x^3)^(1/2) + c^(1/2)))/x^6)*(3*a*d - 4*b*c))/(6*a^3) - (c*(c + d*x^3)^(1/2))/(3*a^2*x^3) - ((c + d*x^3)^(1/2)*((3*a*d - 4*b*c)/(2*a^2) - (a*((a*((a*((b*d^2*(a*d + b*c))/(a^3*c^2) - (a*((b^2*d^3)/(2*a^3*c^2) - (b^2*d^3*(3*a*d - 4*b*c))/(6*a^2*c^2*(a^2*d - a*b*c)) + (b^2*d^2*(a*d + b*c)*(3*a*d - 4*b*c))/(3*a^3*c^2*(a^2*d - a*b*c))))/b + (b*(3*a*d - 4*b*c)*(a^2*d^3 - b^2*c^2*d + 4*a*b*c*d^2))/(6*a^3*c^2*(a^2*d - a*b*c))))/b - (a^2*d^3 - b^2*c^2*d + 4*a*b*c*d^2)/(2*a^3*c^2) + (b*(3*a*d - 4*b*c)*(2*b^2*c^3 - 4*a^2*c*d^2 + 2*a*b*c^2*d))/(6*a^3*c^2*(a^2*d - a*b*c))))/b - (2*b^2*c^3 - 4*a^2*c*d^2 + 2*a*b*c^2*d)/(2*a^3*c^2) + (b*(3*a*d - 4*b*c)^2)/(6*a^2*(a^2*d - a*b*c))))/b))/(a + b*x^3) + (log((2*b*c - a*d + b^(1/2)*(c + d*x^3)^(1/2)*(a*d - b*c)^(1/2)*2i + b*d*x^3)/(a + b*x^3))*(a*d - b*c)^(1/2)*(a*d - 4*b*c)*1i)/(6*a^3*b^(1/2))","B"
475,0,-1,65,0.000000,"\text{Not used}","int((x^3*(c + d*x^3)^(3/2))/(a + b*x^3)^2,x)","\int \frac{x^3\,{\left(d\,x^3+c\right)}^{3/2}}{{\left(b\,x^3+a\right)}^2} \,d x","Not used",1,"int((x^3*(c + d*x^3)^(3/2))/(a + b*x^3)^2, x)","F"
476,0,-1,65,0.000000,"\text{Not used}","int((x*(c + d*x^3)^(3/2))/(a + b*x^3)^2,x)","\int \frac{x\,{\left(d\,x^3+c\right)}^{3/2}}{{\left(b\,x^3+a\right)}^2} \,d x","Not used",1,"int((x*(c + d*x^3)^(3/2))/(a + b*x^3)^2, x)","F"
477,0,-1,60,0.000000,"\text{Not used}","int((c + d*x^3)^(3/2)/(a + b*x^3)^2,x)","\int \frac{{\left(d\,x^3+c\right)}^{3/2}}{{\left(b\,x^3+a\right)}^2} \,d x","Not used",1,"int((c + d*x^3)^(3/2)/(a + b*x^3)^2, x)","F"
478,0,-1,63,0.000000,"\text{Not used}","int((c + d*x^3)^(3/2)/(x^2*(a + b*x^3)^2),x)","\int \frac{{\left(d\,x^3+c\right)}^{3/2}}{x^2\,{\left(b\,x^3+a\right)}^2} \,d x","Not used",1,"int((c + d*x^3)^(3/2)/(x^2*(a + b*x^3)^2), x)","F"
479,0,-1,65,0.000000,"\text{Not used}","int((c + d*x^3)^(3/2)/(x^3*(a + b*x^3)^2),x)","\int \frac{{\left(d\,x^3+c\right)}^{3/2}}{x^3\,{\left(b\,x^3+a\right)}^2} \,d x","Not used",1,"int((c + d*x^3)^(3/2)/(x^3*(a + b*x^3)^2), x)","F"
480,1,160,123,7.289539,"\text{Not used}","int(x^8/((a + b*x^3)^2*(c + d*x^3)^(1/2)),x)","\frac{2\,\sqrt{d\,x^3+c}\,\left(2\,b^2\,c-2\,a\,b\,d\right)}{3\,d\,\left(2\,b^4\,c-2\,a\,b^3\,d\right)}-\frac{2\,a^2\,\sqrt{d\,x^3+c}}{3\,b\,\left(b\,x^3+a\right)\,\left(2\,b^2\,c-2\,a\,b\,d\right)}+\frac{a\,\ln\left(\frac{a\,d-2\,b\,c-b\,d\,x^3+\sqrt{b}\,\sqrt{d\,x^3+c}\,\sqrt{a\,d-b\,c}\,2{}\mathrm{i}}{b\,x^3+a}\right)\,\left(3\,a\,d-4\,b\,c\right)\,1{}\mathrm{i}}{6\,b^{5/2}\,{\left(a\,d-b\,c\right)}^{3/2}}","Not used",1,"(2*(c + d*x^3)^(1/2)*(2*b^2*c - 2*a*b*d))/(3*d*(2*b^4*c - 2*a*b^3*d)) - (2*a^2*(c + d*x^3)^(1/2))/(3*b*(a + b*x^3)*(2*b^2*c - 2*a*b*d)) + (a*log((a*d - 2*b*c + b^(1/2)*(c + d*x^3)^(1/2)*(a*d - b*c)^(1/2)*2i - b*d*x^3)/(a + b*x^3))*(3*a*d - 4*b*c)*1i)/(6*b^(5/2)*(a*d - b*c)^(3/2))","B"
481,1,111,99,6.846474,"\text{Not used}","int(x^5/((a + b*x^3)^2*(c + d*x^3)^(1/2)),x)","\frac{2\,a\,\sqrt{d\,x^3+c}}{3\,\left(b\,x^3+a\right)\,\left(2\,b^2\,c-2\,a\,b\,d\right)}+\frac{\ln\left(\frac{2\,b\,c-a\,d+b\,d\,x^3+\sqrt{b}\,\sqrt{d\,x^3+c}\,\sqrt{a\,d-b\,c}\,2{}\mathrm{i}}{b\,x^3+a}\right)\,\left(a\,d-2\,b\,c\right)\,1{}\mathrm{i}}{6\,b^{3/2}\,{\left(a\,d-b\,c\right)}^{3/2}}","Not used",1,"(log((2*b*c - a*d + b^(1/2)*(c + d*x^3)^(1/2)*(a*d - b*c)^(1/2)*2i + b*d*x^3)/(a + b*x^3))*(a*d - 2*b*c)*1i)/(6*b^(3/2)*(a*d - b*c)^(3/2)) + (2*a*(c + d*x^3)^(1/2))/(3*(a + b*x^3)*(2*b^2*c - 2*a*b*d))","B"
482,1,104,87,6.372759,"\text{Not used}","int(x^2/((a + b*x^3)^2*(c + d*x^3)^(1/2)),x)","-\frac{2\,b\,\sqrt{d\,x^3+c}}{3\,\left(b\,x^3+a\right)\,\left(2\,b^2\,c-2\,a\,b\,d\right)}+\frac{d\,\ln\left(\frac{2\,b\,c-a\,d+b\,d\,x^3+\sqrt{b}\,\sqrt{d\,x^3+c}\,\sqrt{a\,d-b\,c}\,2{}\mathrm{i}}{b\,x^3+a}\right)\,1{}\mathrm{i}}{6\,\sqrt{b}\,{\left(a\,d-b\,c\right)}^{3/2}}","Not used",1,"(d*log((2*b*c - a*d + b^(1/2)*(c + d*x^3)^(1/2)*(a*d - b*c)^(1/2)*2i + b*d*x^3)/(a + b*x^3))*1i)/(6*b^(1/2)*(a*d - b*c)^(3/2)) - (2*b*(c + d*x^3)^(1/2))/(3*(a + b*x^3)*(2*b^2*c - 2*a*b*d))","B"
483,1,162,132,9.647010,"\text{Not used}","int(1/(x*(a + b*x^3)^2*(c + d*x^3)^(1/2)),x)","\frac{\ln\left(\frac{{\left(\sqrt{d\,x^3+c}-\sqrt{c}\right)}^3\,\left(\sqrt{d\,x^3+c}+\sqrt{c}\right)}{x^6}\right)}{3\,a^2\,\sqrt{c}}+\frac{b^2\,\sqrt{d\,x^3+c}}{3\,a\,\left(b\,x^3+a\right)\,\left(b^2\,c-a\,b\,d\right)}+\frac{\sqrt{b}\,\ln\left(\frac{a\,d-2\,b\,c-b\,d\,x^3+\sqrt{b}\,\sqrt{d\,x^3+c}\,\sqrt{a\,d-b\,c}\,2{}\mathrm{i}}{b\,x^3+a}\right)\,\left(3\,a\,d-2\,b\,c\right)\,1{}\mathrm{i}}{6\,a^2\,{\left(a\,d-b\,c\right)}^{3/2}}","Not used",1,"log((((c + d*x^3)^(1/2) - c^(1/2))^3*((c + d*x^3)^(1/2) + c^(1/2)))/x^6)/(3*a^2*c^(1/2)) + (b^2*(c + d*x^3)^(1/2))/(3*a*(a + b*x^3)*(b^2*c - a*b*d)) + (b^(1/2)*log((a*d - 2*b*c + b^(1/2)*(c + d*x^3)^(1/2)*(a*d - b*c)^(1/2)*2i - b*d*x^3)/(a + b*x^3))*(3*a*d - 2*b*c)*1i)/(6*a^2*(a*d - b*c)^(3/2))","B"
484,1,355,185,11.550686,"\text{Not used}","int(1/(x^4*(a + b*x^3)^2*(c + d*x^3)^(1/2)),x)","\frac{\sqrt{d\,x^3+c}\,\left(\frac{d\,a^2+4\,b\,c\,a}{2\,a^3\,c^2}-\frac{a\,\left(\frac{2\,c\,b^2+2\,a\,d\,b}{2\,a^3\,c^2}-\frac{a\,\left(\frac{b^2\,d}{2\,a^3\,c^2}+\frac{b\,\left(2\,c\,b^2+2\,a\,d\,b\right)\,\left(3\,a\,d-4\,b\,c\right)}{6\,a^3\,c^2\,\left(a^2\,d-a\,b\,c\right)}-\frac{b^2\,d\,\left(3\,a\,d-4\,b\,c\right)}{6\,a^2\,c^2\,\left(a^2\,d-a\,b\,c\right)}\right)}{b}+\frac{b\,\left(d\,a^2+4\,b\,c\,a\right)\,\left(3\,a\,d-4\,b\,c\right)}{6\,a^3\,c^2\,\left(a^2\,d-a\,b\,c\right)}\right)}{b}\right)}{b\,x^3+a}-\frac{\sqrt{d\,x^3+c}}{3\,a^2\,c\,x^3}+\frac{\ln\left(\frac{\left(\sqrt{d\,x^3+c}-\sqrt{c}\right)\,{\left(\sqrt{d\,x^3+c}+\sqrt{c}\right)}^3}{x^6}\right)\,\left(a\,d+4\,b\,c\right)}{6\,a^3\,c^{3/2}}+\frac{b^{3/2}\,\ln\left(\frac{2\,b\,c-a\,d+b\,d\,x^3+\sqrt{b}\,\sqrt{d\,x^3+c}\,\sqrt{a\,d-b\,c}\,2{}\mathrm{i}}{b\,x^3+a}\right)\,\left(5\,a\,d-4\,b\,c\right)\,1{}\mathrm{i}}{6\,a^3\,{\left(a\,d-b\,c\right)}^{3/2}}","Not used",1,"((c + d*x^3)^(1/2)*((a^2*d + 4*a*b*c)/(2*a^3*c^2) - (a*((2*b^2*c + 2*a*b*d)/(2*a^3*c^2) - (a*((b^2*d)/(2*a^3*c^2) + (b*(2*b^2*c + 2*a*b*d)*(3*a*d - 4*b*c))/(6*a^3*c^2*(a^2*d - a*b*c)) - (b^2*d*(3*a*d - 4*b*c))/(6*a^2*c^2*(a^2*d - a*b*c))))/b + (b*(a^2*d + 4*a*b*c)*(3*a*d - 4*b*c))/(6*a^3*c^2*(a^2*d - a*b*c))))/b))/(a + b*x^3) - (c + d*x^3)^(1/2)/(3*a^2*c*x^3) + (log((((c + d*x^3)^(1/2) - c^(1/2))*((c + d*x^3)^(1/2) + c^(1/2))^3)/x^6)*(a*d + 4*b*c))/(6*a^3*c^(3/2)) + (b^(3/2)*log((2*b*c - a*d + b^(1/2)*(c + d*x^3)^(1/2)*(a*d - b*c)^(1/2)*2i + b*d*x^3)/(a + b*x^3))*(5*a*d - 4*b*c)*1i)/(6*a^3*(a*d - b*c)^(3/2))","B"
485,0,-1,64,0.000000,"\text{Not used}","int(x^3/((a + b*x^3)^2*(c + d*x^3)^(1/2)),x)","\int \frac{x^3}{{\left(b\,x^3+a\right)}^2\,\sqrt{d\,x^3+c}} \,d x","Not used",1,"int(x^3/((a + b*x^3)^2*(c + d*x^3)^(1/2)), x)","F"
486,0,-1,64,0.000000,"\text{Not used}","int(x/((a + b*x^3)^2*(c + d*x^3)^(1/2)),x)","\int \frac{x}{{\left(b\,x^3+a\right)}^2\,\sqrt{d\,x^3+c}} \,d x","Not used",1,"int(x/((a + b*x^3)^2*(c + d*x^3)^(1/2)), x)","F"
487,0,-1,59,0.000000,"\text{Not used}","int(1/((a + b*x^3)^2*(c + d*x^3)^(1/2)),x)","\int \frac{1}{{\left(b\,x^3+a\right)}^2\,\sqrt{d\,x^3+c}} \,d x","Not used",1,"int(1/((a + b*x^3)^2*(c + d*x^3)^(1/2)), x)","F"
488,0,-1,62,0.000000,"\text{Not used}","int(1/(x^2*(a + b*x^3)^2*(c + d*x^3)^(1/2)),x)","\int \frac{1}{x^2\,{\left(b\,x^3+a\right)}^2\,\sqrt{d\,x^3+c}} \,d x","Not used",1,"int(1/(x^2*(a + b*x^3)^2*(c + d*x^3)^(1/2)), x)","F"
489,0,-1,64,0.000000,"\text{Not used}","int(1/(x^3*(a + b*x^3)^2*(c + d*x^3)^(1/2)),x)","\int \frac{1}{x^3\,{\left(b\,x^3+a\right)}^2\,\sqrt{d\,x^3+c}} \,d x","Not used",1,"int(1/(x^3*(a + b*x^3)^2*(c + d*x^3)^(1/2)), x)","F"
490,1,367,150,7.898101,"\text{Not used}","int(x^8/((a + b*x^3)^2*(c + d*x^3)^(3/2)),x)","\frac{\sqrt{d\,x^3+c}\,\left(x^3\,\left(\frac{\left(\frac{3\,b\,d\,\left(a\,d+b\,c\right)-b\,d\,\left(a\,d+2\,b\,c\right)}{3\,\left(a^2\,b\,d^3-2\,a\,b^2\,c\,d^2+b^3\,c^2\,d\right)}-\frac{b\,d\,\left(a\,d+b\,c\right)}{a^2\,b\,d^3-2\,a\,b^2\,c\,d^2+b^3\,c^2\,d}\right)\,\left(a\,d+b\,c\right)}{b\,d}+\frac{a\,b\,c\,d}{a^2\,b\,d^3-2\,a\,b^2\,c\,d^2+b^3\,c^2\,d}\right)+\frac{a\,c\,\left(\frac{3\,b\,d\,\left(a\,d+b\,c\right)-b\,d\,\left(a\,d+2\,b\,c\right)}{3\,\left(a^2\,b\,d^3-2\,a\,b^2\,c\,d^2+b^3\,c^2\,d\right)}-\frac{b\,d\,\left(a\,d+b\,c\right)}{a^2\,b\,d^3-2\,a\,b^2\,c\,d^2+b^3\,c^2\,d}\right)}{b\,d}\right)}{b\,d\,x^6+\left(a\,d+b\,c\right)\,x^3+a\,c}+\frac{a\,\ln\left(\frac{2\,b\,c-a\,d+b\,d\,x^3+\sqrt{b}\,\sqrt{d\,x^3+c}\,\sqrt{a\,d-b\,c}\,2{}\mathrm{i}}{b\,x^3+a}\right)\,\left(a\,d-4\,b\,c\right)\,1{}\mathrm{i}}{6\,b^{3/2}\,{\left(a\,d-b\,c\right)}^{5/2}}","Not used",1,"((c + d*x^3)^(1/2)*(x^3*((((3*b*d*(a*d + b*c) - b*d*(a*d + 2*b*c))/(3*(a^2*b*d^3 + b^3*c^2*d - 2*a*b^2*c*d^2)) - (b*d*(a*d + b*c))/(a^2*b*d^3 + b^3*c^2*d - 2*a*b^2*c*d^2))*(a*d + b*c))/(b*d) + (a*b*c*d)/(a^2*b*d^3 + b^3*c^2*d - 2*a*b^2*c*d^2)) + (a*c*((3*b*d*(a*d + b*c) - b*d*(a*d + 2*b*c))/(3*(a^2*b*d^3 + b^3*c^2*d - 2*a*b^2*c*d^2)) - (b*d*(a*d + b*c))/(a^2*b*d^3 + b^3*c^2*d - 2*a*b^2*c*d^2)))/(b*d)))/(a*c + x^3*(a*d + b*c) + b*d*x^6) + (a*log((2*b*c - a*d + b^(1/2)*(c + d*x^3)^(1/2)*(a*d - b*c)^(1/2)*2i + b*d*x^3)/(a + b*x^3))*(a*d - 4*b*c)*1i)/(6*b^(3/2)*(a*d - b*c)^(5/2))","B"
491,1,247,134,7.704075,"\text{Not used}","int(x^5/((a + b*x^3)^2*(c + d*x^3)^(3/2)),x)","-\frac{\sqrt{d\,x^3+c}\,\left(x^3\,\left(\frac{3\,b\,d\,\left(a\,d+b\,c\right)-b\,d\,\left(a\,d+2\,b\,c\right)}{3\,\left(a^2\,b\,d^3-2\,a\,b^2\,c\,d^2+b^3\,c^2\,d\right)}-\frac{b\,d\,\left(a\,d+b\,c\right)}{a^2\,b\,d^3-2\,a\,b^2\,c\,d^2+b^3\,c^2\,d}\right)-\frac{a\,b\,c\,d}{a^2\,b\,d^3-2\,a\,b^2\,c\,d^2+b^3\,c^2\,d}\right)}{b\,d\,x^6+\left(a\,d+b\,c\right)\,x^3+a\,c}+\frac{\ln\left(\frac{2\,b\,c-a\,d+b\,d\,x^3+\sqrt{b}\,\sqrt{d\,x^3+c}\,\sqrt{a\,d-b\,c}\,2{}\mathrm{i}}{b\,x^3+a}\right)\,\left(a\,d+2\,b\,c\right)\,1{}\mathrm{i}}{6\,\sqrt{b}\,{\left(a\,d-b\,c\right)}^{5/2}}","Not used",1,"(log((2*b*c - a*d + b^(1/2)*(c + d*x^3)^(1/2)*(a*d - b*c)^(1/2)*2i + b*d*x^3)/(a + b*x^3))*(a*d + 2*b*c)*1i)/(6*b^(1/2)*(a*d - b*c)^(5/2)) - ((c + d*x^3)^(1/2)*(x^3*((3*b*d*(a*d + b*c) - b*d*(a*d + 2*b*c))/(3*(a^2*b*d^3 + b^3*c^2*d - 2*a*b^2*c*d^2)) - (b*d*(a*d + b*c))/(a^2*b*d^3 + b^3*c^2*d - 2*a*b^2*c*d^2)) - (a*b*c*d)/(a^2*b*d^3 + b^3*c^2*d - 2*a*b^2*c*d^2)))/(a*c + x^3*(a*d + b*c) + b*d*x^6)","B"
492,1,199,108,7.428687,"\text{Not used}","int(x^2/((a + b*x^3)^2*(c + d*x^3)^(3/2)),x)","-\frac{\left(\frac{3\,b\,d\,\left(a\,d+b\,c\right)-b\,d\,\left(a\,d+2\,b\,c\right)}{3\,\left(a^2\,b\,d^3-2\,a\,b^2\,c\,d^2+b^3\,c^2\,d\right)}+\frac{b^2\,d^2\,x^3}{a^2\,b\,d^3-2\,a\,b^2\,c\,d^2+b^3\,c^2\,d}\right)\,\sqrt{d\,x^3+c}}{b\,d\,x^6+\left(a\,d+b\,c\right)\,x^3+a\,c}+\frac{\sqrt{b}\,d\,\ln\left(\frac{a\,d-2\,b\,c-b\,d\,x^3+\sqrt{b}\,\sqrt{d\,x^3+c}\,\sqrt{a\,d-b\,c}\,2{}\mathrm{i}}{b\,x^3+a}\right)\,1{}\mathrm{i}}{2\,{\left(a\,d-b\,c\right)}^{5/2}}","Not used",1,"(b^(1/2)*d*log((a*d - 2*b*c + b^(1/2)*(c + d*x^3)^(1/2)*(a*d - b*c)^(1/2)*2i - b*d*x^3)/(a + b*x^3))*1i)/(2*(a*d - b*c)^(5/2)) - (((3*b*d*(a*d + b*c) - b*d*(a*d + 2*b*c))/(3*(a^2*b*d^3 + b^3*c^2*d - 2*a*b^2*c*d^2)) + (b^2*d^2*x^3)/(a^2*b*d^3 + b^3*c^2*d - 2*a*b^2*c*d^2))*(c + d*x^3)^(1/2))/(a*c + x^3*(a*d + b*c) + b*d*x^6)","B"
493,1,288,172,12.181550,"\text{Not used}","int(1/(x*(a + b*x^3)^2*(c + d*x^3)^(3/2)),x)","\frac{\ln\left(\frac{{\left(\sqrt{d\,x^3+c}-\sqrt{c}\right)}^3\,\left(\sqrt{d\,x^3+c}+\sqrt{c}\right)}{x^6}\right)}{3\,a^2\,c^{3/2}}+\frac{\left(\frac{{\left(2\,a\,d+b\,c\right)}^4+{\left(2\,a\,d+b\,c\right)}^2\,\left(\left(a\,d+2\,b\,c\right)\,\left(2\,a\,d+b\,c\right)-9\,a\,b\,c\,d\right)}{9\,a\,c\,{\left(2\,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\,\left(2\,a\,d+b\,c\right)}{3\,a\,c\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}\right)\,\sqrt{d\,x^3+c}}{b\,d\,x^6+\left(a\,d+b\,c\right)\,x^3+a\,c}+\frac{b^{3/2}\,\ln\left(\frac{2\,b\,c-a\,d+b\,d\,x^3+\sqrt{b}\,\sqrt{d\,x^3+c}\,\sqrt{a\,d-b\,c}\,2{}\mathrm{i}}{b\,x^3+a}\right)\,\left(5\,a\,d-2\,b\,c\right)\,1{}\mathrm{i}}{6\,a^2\,{\left(a\,d-b\,c\right)}^{5/2}}","Not used",1,"log((((c + d*x^3)^(1/2) - c^(1/2))^3*((c + d*x^3)^(1/2) + c^(1/2)))/x^6)/(3*a^2*c^(3/2)) + ((((2*a*d + b*c)^4 + (2*a*d + b*c)^2*((a*d + 2*b*c)*(2*a*d + b*c) - 9*a*b*c*d))/(9*a*c*(2*a*d + b*c)^2*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)) + (b*d*x^3*(2*a*d + b*c))/(3*a*c*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)))*(c + d*x^3)^(1/2))/(a*c + x^3*(a*d + b*c) + b*d*x^6) + (b^(3/2)*log((2*b*c - a*d + b^(1/2)*(c + d*x^3)^(1/2)*(a*d - b*c)^(1/2)*2i + b*d*x^3)/(a + b*x^3))*(5*a*d - 2*b*c)*1i)/(6*a^2*(a*d - b*c)^(5/2))","B"
494,1,18847,241,19.625647,"\text{Not used}","int(1/(x^4*(a + b*x^3)^2*(c + d*x^3)^(3/2)),x)","\frac{2\,b\,\ln\left(\frac{1}{x^6}\right)}{3\,a^3\,c^{3/2}}-\frac{\sqrt{d\,x^3+c}}{3\,a^2\,c^2\,x^3}+\frac{d\,\ln\left(\frac{1}{x^6}\right)}{2\,a^2\,c^{5/2}}+\frac{2\,b\,\ln\left(c^{3/2}\,\sqrt{d\,x^3+c}-\sqrt{c}\,{\left(d\,x^3+c\right)}^{3/2}+d^2\,x^6+2\,c\,d\,x^3+3\,\sqrt{c}\,d\,x^3\,\sqrt{d\,x^3+c}\right)}{3\,a^3\,c^{3/2}}+\frac{d\,\ln\left(c^{3/2}\,\sqrt{d\,x^3+c}-\sqrt{c}\,{\left(d\,x^3+c\right)}^{3/2}+d^2\,x^6+2\,c\,d\,x^3+3\,\sqrt{c}\,d\,x^3\,\sqrt{d\,x^3+c}\right)}{2\,a^2\,c^{5/2}}-\frac{b^7\,c^9\,x^4\,\sqrt{d\,x^3+c}}{2\,\left(2\,a^9\,c^6\,d^5\,x+2\,a^9\,c^5\,d^6\,x^4-3\,a^8\,b\,c^7\,d^4\,x-a^8\,b\,c^6\,d^5\,x^4+2\,a^8\,b\,c^5\,d^6\,x^7-3\,a^7\,b^2\,c^7\,d^4\,x^4-3\,a^7\,b^2\,c^6\,d^5\,x^7+a^6\,b^3\,c^9\,d^2\,x+a^6\,b^3\,c^8\,d^3\,x^4+a^5\,b^4\,c^9\,d^2\,x^4+a^5\,b^4\,c^8\,d^3\,x^7\right)}-\frac{5\,a^9\,d^7\,x^4\,\sqrt{d\,x^3+c}}{4\,\left(2\,a^9\,b^2\,c^6\,d^3\,x+2\,a^9\,b^2\,c^5\,d^4\,x^4-3\,a^8\,b^3\,c^7\,d^2\,x-a^8\,b^3\,c^6\,d^3\,x^4+2\,a^8\,b^3\,c^5\,d^4\,x^7-3\,a^7\,b^4\,c^7\,d^2\,x^4-3\,a^7\,b^4\,c^6\,d^3\,x^7+a^6\,b^5\,c^9\,x+a^6\,b^5\,c^8\,d\,x^4+a^5\,b^6\,c^9\,x^4+a^5\,b^6\,c^8\,d\,x^7\right)}+\frac{3\,a^2\,d^2\,x\,\sqrt{d\,x^3+c}}{2\,a^4\,c^3\,d\,x+2\,a^4\,c^2\,d^2\,x^4+a^3\,b\,c^4\,x+3\,a^3\,b\,c^3\,d\,x^4+2\,a^3\,b\,c^2\,d^2\,x^7+a^2\,b^2\,c^4\,x^4+a^2\,b^2\,c^3\,d\,x^7}+\frac{2\,b^2\,c^2\,x\,\sqrt{d\,x^3+c}}{2\,a^4\,c^3\,d\,x+2\,a^4\,c^2\,d^2\,x^4+a^3\,b\,c^4\,x+3\,a^3\,b\,c^3\,d\,x^4+2\,a^3\,b\,c^2\,d^2\,x^7+a^2\,b^2\,c^4\,x^4+a^2\,b^2\,c^3\,d\,x^7}+\frac{5\,a^4\,d^4\,x^4\,\sqrt{d\,x^3+c}}{2\,\left(2\,a^5\,b\,c^5\,d\,x+2\,a^5\,b\,c^4\,d^2\,x^4+a^4\,b^2\,c^6\,x+3\,a^4\,b^2\,c^5\,d\,x^4+2\,a^4\,b^2\,c^4\,d^2\,x^7+a^3\,b^3\,c^6\,x^4+a^3\,b^3\,c^5\,d\,x^7\right)}-\frac{65\,a^3\,d^3\,x^4\,\sqrt{d\,x^3+c}}{24\,\left(2\,a^5\,c^4\,d\,x+2\,a^5\,c^3\,d^2\,x^4+a^4\,b\,c^5\,x+3\,a^4\,b\,c^4\,d\,x^4+2\,a^4\,b\,c^3\,d^2\,x^7+a^3\,b^2\,c^5\,x^4+a^3\,b^2\,c^4\,d\,x^7\right)}-\frac{8\,b^3\,c^3\,x^4\,\sqrt{d\,x^3+c}}{3\,\left(2\,a^5\,c^4\,d\,x+2\,a^5\,c^3\,d^2\,x^4+a^4\,b\,c^5\,x+3\,a^4\,b\,c^4\,d\,x^4+2\,a^4\,b\,c^3\,d^2\,x^7+a^3\,b^2\,c^5\,x^4+a^3\,b^2\,c^4\,d\,x^7\right)}+\frac{14\,b^3\,c^4\,x^4\,\sqrt{d\,x^3+c}}{2\,a^5\,c^5\,d\,x+2\,a^5\,c^4\,d^2\,x^4+a^4\,b\,c^6\,x+3\,a^4\,b\,c^5\,d\,x^4+2\,a^4\,b\,c^4\,d^2\,x^7+a^3\,b^2\,c^6\,x^4+a^3\,b^2\,c^5\,d\,x^7}-\frac{5\,a^7\,c^2\,d^5\,x\,\sqrt{d\,x^3+c}}{2\,\left(2\,a^8\,b\,c^6\,d^3\,x+2\,a^8\,b\,c^5\,d^4\,x^4-3\,a^7\,b^2\,c^7\,d^2\,x-a^7\,b^2\,c^6\,d^3\,x^4+2\,a^7\,b^2\,c^5\,d^4\,x^7-3\,a^6\,b^3\,c^7\,d^2\,x^4-3\,a^6\,b^3\,c^6\,d^3\,x^7+a^5\,b^4\,c^9\,x+a^5\,b^4\,c^8\,d\,x^4+a^4\,b^5\,c^9\,x^4+a^4\,b^5\,c^8\,d\,x^7\right)}-\frac{5\,a^7\,c\,d^6\,x^4\,\sqrt{d\,x^3+c}}{2\,\left(2\,a^8\,b\,c^6\,d^3\,x+2\,a^8\,b\,c^5\,d^4\,x^4-3\,a^7\,b^2\,c^7\,d^2\,x-a^7\,b^2\,c^6\,d^3\,x^4+2\,a^7\,b^2\,c^5\,d^4\,x^7-3\,a^6\,b^3\,c^7\,d^2\,x^4-3\,a^6\,b^3\,c^6\,d^3\,x^7+a^5\,b^4\,c^9\,x+a^5\,b^4\,c^8\,d\,x^4+a^4\,b^5\,c^9\,x^4+a^4\,b^5\,c^8\,d\,x^7\right)}-\frac{3\,a^8\,c^2\,d^5\,x\,\sqrt{d\,x^3+c}}{8\,\left(2\,a^9\,b\,c^6\,d^3\,x+2\,a^9\,b\,c^5\,d^4\,x^4-3\,a^8\,b^2\,c^7\,d^2\,x-a^8\,b^2\,c^6\,d^3\,x^4+2\,a^8\,b^2\,c^5\,d^4\,x^7-3\,a^7\,b^3\,c^7\,d^2\,x^4-3\,a^7\,b^3\,c^6\,d^3\,x^7+a^6\,b^4\,c^9\,x+a^6\,b^4\,c^8\,d\,x^4+a^5\,b^5\,c^9\,x^4+a^5\,b^5\,c^8\,d\,x^7\right)}-\frac{3\,a^8\,c\,d^6\,x^4\,\sqrt{d\,x^3+c}}{8\,\left(2\,a^9\,b\,c^6\,d^3\,x+2\,a^9\,b\,c^5\,d^4\,x^4-3\,a^8\,b^2\,c^7\,d^2\,x-a^8\,b^2\,c^6\,d^3\,x^4+2\,a^8\,b^2\,c^5\,d^4\,x^7-3\,a^7\,b^3\,c^7\,d^2\,x^4-3\,a^7\,b^3\,c^6\,d^3\,x^7+a^6\,b^4\,c^9\,x+a^6\,b^4\,c^8\,d\,x^4+a^5\,b^5\,c^9\,x^4+a^5\,b^5\,c^8\,d\,x^7\right)}+\frac{23\,a^9\,c^3\,d^5\,x\,\sqrt{d\,x^3+c}}{8\,\left(2\,a^{10}\,b\,c^7\,d^3\,x+2\,a^{10}\,b\,c^6\,d^4\,x^4-3\,a^9\,b^2\,c^8\,d^2\,x-a^9\,b^2\,c^7\,d^3\,x^4+2\,a^9\,b^2\,c^6\,d^4\,x^7-3\,a^8\,b^3\,c^8\,d^2\,x^4-3\,a^8\,b^3\,c^7\,d^3\,x^7+a^7\,b^4\,c^{10}\,x+a^7\,b^4\,c^9\,d\,x^4+a^6\,b^5\,c^{10}\,x^4+a^6\,b^5\,c^9\,d\,x^7\right)}-\frac{a\,b^6\,c^9\,x\,\sqrt{d\,x^3+c}}{2\,\left(2\,a^9\,c^6\,d^5\,x+2\,a^9\,c^5\,d^6\,x^4-3\,a^8\,b\,c^7\,d^4\,x-a^8\,b\,c^6\,d^5\,x^4+2\,a^8\,b\,c^5\,d^6\,x^7-3\,a^7\,b^2\,c^7\,d^4\,x^4-3\,a^7\,b^2\,c^6\,d^5\,x^7+a^6\,b^3\,c^9\,d^2\,x+a^6\,b^3\,c^8\,d^3\,x^4+a^5\,b^4\,c^9\,d^2\,x^4+a^5\,b^4\,c^8\,d^3\,x^7\right)}+\frac{3\,a^2\,b^6\,c^9\,x^4\,\sqrt{d\,x^3+c}}{4\,\left(2\,a^{10}\,c^7\,d^4\,x+2\,a^{10}\,c^6\,d^5\,x^4-3\,a^9\,b\,c^8\,d^3\,x-a^9\,b\,c^7\,d^4\,x^4+2\,a^9\,b\,c^6\,d^5\,x^7-3\,a^8\,b^2\,c^8\,d^3\,x^4-3\,a^8\,b^2\,c^7\,d^4\,x^7+a^7\,b^3\,c^{10}\,d\,x+a^7\,b^3\,c^9\,d^2\,x^4+a^6\,b^4\,c^{10}\,d\,x^4+a^6\,b^4\,c^9\,d^2\,x^7\right)}-\frac{5\,a^6\,c^2\,d^3\,x\,\sqrt{d\,x^3+c}}{2\,\left(2\,a^7\,b\,c^6\,d\,x+2\,a^7\,b\,c^5\,d^2\,x^4+a^6\,b^2\,c^7\,x+3\,a^6\,b^2\,c^6\,d\,x^4+2\,a^6\,b^2\,c^5\,d^2\,x^7+a^5\,b^3\,c^7\,x^4+a^5\,b^3\,c^6\,d\,x^7\right)}-\frac{5\,a^6\,c\,d^4\,x^4\,\sqrt{d\,x^3+c}}{2\,\left(2\,a^7\,b\,c^6\,d\,x+2\,a^7\,b\,c^5\,d^2\,x^4+a^6\,b^2\,c^7\,x+3\,a^6\,b^2\,c^6\,d\,x^4+2\,a^6\,b^2\,c^5\,d^2\,x^7+a^5\,b^3\,c^7\,x^4+a^5\,b^3\,c^6\,d\,x^7\right)}+\frac{4\,a^2\,b^4\,c^6\,x\,\sqrt{d\,x^3+c}}{2\,a^8\,c^5\,d^3\,x+2\,a^8\,c^4\,d^4\,x^4-3\,a^7\,b\,c^6\,d^2\,x-a^7\,b\,c^5\,d^3\,x^4+2\,a^7\,b\,c^4\,d^4\,x^7-3\,a^6\,b^2\,c^6\,d^2\,x^4-3\,a^6\,b^2\,c^5\,d^3\,x^7+a^5\,b^3\,c^8\,x+a^5\,b^3\,c^7\,d\,x^4+a^4\,b^4\,c^8\,x^4+a^4\,b^4\,c^7\,d\,x^7}+\frac{8\,a\,b^5\,c^6\,x^4\,\sqrt{d\,x^3+c}}{3\,\left(2\,a^8\,c^5\,d^3\,x+2\,a^8\,c^4\,d^4\,x^4-3\,a^7\,b\,c^6\,d^2\,x-a^7\,b\,c^5\,d^3\,x^4+2\,a^7\,b\,c^4\,d^4\,x^7-3\,a^6\,b^2\,c^6\,d^2\,x^4-3\,a^6\,b^2\,c^5\,d^3\,x^7+a^5\,b^3\,c^8\,x+a^5\,b^3\,c^7\,d\,x^4+a^4\,b^4\,c^8\,x^4+a^4\,b^4\,c^7\,d\,x^7\right)}-\frac{14\,a^2\,b^4\,c^7\,x\,\sqrt{d\,x^3+c}}{2\,a^8\,c^6\,d^3\,x+2\,a^8\,c^5\,d^4\,x^4-3\,a^7\,b\,c^7\,d^2\,x-a^7\,b\,c^6\,d^3\,x^4+2\,a^7\,b\,c^5\,d^4\,x^7-3\,a^6\,b^2\,c^7\,d^2\,x^4-3\,a^6\,b^2\,c^6\,d^3\,x^7+a^5\,b^3\,c^9\,x+a^5\,b^3\,c^8\,d\,x^4+a^4\,b^4\,c^9\,x^4+a^4\,b^4\,c^8\,d\,x^7}-\frac{14\,a\,b^5\,c^7\,x^4\,\sqrt{d\,x^3+c}}{2\,a^8\,c^6\,d^3\,x+2\,a^8\,c^5\,d^4\,x^4-3\,a^7\,b\,c^7\,d^2\,x-a^7\,b\,c^6\,d^3\,x^4+2\,a^7\,b\,c^5\,d^4\,x^7-3\,a^6\,b^2\,c^7\,d^2\,x^4-3\,a^6\,b^2\,c^6\,d^3\,x^7+a^5\,b^3\,c^9\,x+a^5\,b^3\,c^8\,d\,x^4+a^4\,b^4\,c^9\,x^4+a^4\,b^4\,c^8\,d\,x^7}+\frac{a^3\,b^4\,c^7\,x\,\sqrt{d\,x^3+c}}{8\,\left(2\,a^9\,c^6\,d^3\,x+2\,a^9\,c^5\,d^4\,x^4-3\,a^8\,b\,c^7\,d^2\,x-a^8\,b\,c^6\,d^3\,x^4+2\,a^8\,b\,c^5\,d^4\,x^7-3\,a^7\,b^2\,c^7\,d^2\,x^4-3\,a^7\,b^2\,c^6\,d^3\,x^7+a^6\,b^3\,c^9\,x+a^6\,b^3\,c^8\,d\,x^4+a^5\,b^4\,c^9\,x^4+a^5\,b^4\,c^8\,d\,x^7\right)}+\frac{269\,a^4\,b^4\,c^8\,x\,\sqrt{d\,x^3+c}}{24\,\left(2\,a^{10}\,c^7\,d^3\,x+2\,a^{10}\,c^6\,d^4\,x^4-3\,a^9\,b\,c^8\,d^2\,x-a^9\,b\,c^7\,d^3\,x^4+2\,a^9\,b\,c^6\,d^4\,x^7-3\,a^8\,b^2\,c^8\,d^2\,x^4-3\,a^8\,b^2\,c^7\,d^3\,x^7+a^7\,b^3\,c^{10}\,x+a^7\,b^3\,c^9\,d\,x^4+a^6\,b^4\,c^{10}\,x^4+a^6\,b^4\,c^9\,d\,x^7\right)}+\frac{65\,a^6\,c^2\,d^4\,x\,\sqrt{d\,x^3+c}}{8\,\left(2\,a^8\,c^5\,d^3\,x+2\,a^8\,c^4\,d^4\,x^4-3\,a^7\,b\,c^6\,d^2\,x-a^7\,b\,c^5\,d^3\,x^4+2\,a^7\,b\,c^4\,d^4\,x^7-3\,a^6\,b^2\,c^6\,d^2\,x^4-3\,a^6\,b^2\,c^5\,d^3\,x^7+a^5\,b^3\,c^8\,x+a^5\,b^3\,c^7\,d\,x^4+a^4\,b^4\,c^8\,x^4+a^4\,b^4\,c^7\,d\,x^7\right)}+\frac{65\,a^6\,c\,d^5\,x^4\,\sqrt{d\,x^3+c}}{24\,\left(2\,a^8\,c^5\,d^3\,x+2\,a^8\,c^4\,d^4\,x^4-3\,a^7\,b\,c^6\,d^2\,x-a^7\,b\,c^5\,d^3\,x^4+2\,a^7\,b\,c^4\,d^4\,x^7-3\,a^6\,b^2\,c^6\,d^2\,x^4-3\,a^6\,b^2\,c^5\,d^3\,x^7+a^5\,b^3\,c^8\,x+a^5\,b^3\,c^7\,d\,x^4+a^4\,b^4\,c^8\,x^4+a^4\,b^4\,c^7\,d\,x^7\right)}-\frac{41\,a^6\,c^3\,d^4\,x\,\sqrt{d\,x^3+c}}{3\,\left(2\,a^8\,c^6\,d^3\,x+2\,a^8\,c^5\,d^4\,x^4-3\,a^7\,b\,c^7\,d^2\,x-a^7\,b\,c^6\,d^3\,x^4+2\,a^7\,b\,c^5\,d^4\,x^7-3\,a^6\,b^2\,c^7\,d^2\,x^4-3\,a^6\,b^2\,c^6\,d^3\,x^7+a^5\,b^3\,c^9\,x+a^5\,b^3\,c^8\,d\,x^4+a^4\,b^4\,c^9\,x^4+a^4\,b^4\,c^8\,d\,x^7\right)}-\frac{5\,a^7\,c^3\,d^4\,x\,\sqrt{d\,x^3+c}}{8\,\left(2\,a^9\,c^6\,d^3\,x+2\,a^9\,c^5\,d^4\,x^4-3\,a^8\,b\,c^7\,d^2\,x-a^8\,b\,c^6\,d^3\,x^4+2\,a^8\,b\,c^5\,d^4\,x^7-3\,a^7\,b^2\,c^7\,d^2\,x^4-3\,a^7\,b^2\,c^6\,d^3\,x^7+a^6\,b^3\,c^9\,x+a^6\,b^3\,c^8\,d\,x^4+a^5\,b^4\,c^9\,x^4+a^5\,b^4\,c^8\,d\,x^7\right)}+\frac{47\,a^8\,c^4\,d^4\,x\,\sqrt{d\,x^3+c}}{6\,\left(2\,a^{10}\,c^7\,d^3\,x+2\,a^{10}\,c^6\,d^4\,x^4-3\,a^9\,b\,c^8\,d^2\,x-a^9\,b\,c^7\,d^3\,x^4+2\,a^9\,b\,c^6\,d^4\,x^7-3\,a^8\,b^2\,c^8\,d^2\,x^4-3\,a^8\,b^2\,c^7\,d^3\,x^7+a^7\,b^3\,c^{10}\,x+a^7\,b^3\,c^9\,d\,x^4+a^6\,b^4\,c^{10}\,x^4+a^6\,b^4\,c^9\,d\,x^7\right)}-\frac{34\,a^3\,b^2\,c^5\,x\,\sqrt{d\,x^3+c}}{3\,\left(2\,a^7\,c^6\,d\,x+2\,a^7\,c^5\,d^2\,x^4+a^6\,b\,c^7\,x+3\,a^6\,b\,c^6\,d\,x^4+2\,a^6\,b\,c^5\,d^2\,x^7+a^5\,b^2\,c^7\,x^4+a^5\,b^2\,c^6\,d\,x^7\right)}+\frac{47\,a^3\,c^2\,d^2\,x\,\sqrt{d\,x^3+c}}{3\,\left(2\,a^5\,c^5\,d\,x+2\,a^5\,c^4\,d^2\,x^4+a^4\,b\,c^6\,x+3\,a^4\,b\,c^5\,d\,x^4+2\,a^4\,b\,c^4\,d^2\,x^7+a^3\,b^2\,c^6\,x^4+a^3\,b^2\,c^5\,d\,x^7\right)}+\frac{38\,a^3\,c\,d^3\,x^4\,\sqrt{d\,x^3+c}}{3\,\left(2\,a^5\,c^5\,d\,x+2\,a^5\,c^4\,d^2\,x^4+a^4\,b\,c^6\,x+3\,a^4\,b\,c^5\,d\,x^4+2\,a^4\,b\,c^4\,d^2\,x^7+a^3\,b^2\,c^6\,x^4+a^3\,b^2\,c^5\,d\,x^7\right)}-\frac{257\,a^5\,c^3\,d^2\,x\,\sqrt{d\,x^3+c}}{24\,\left(2\,a^7\,c^6\,d\,x+2\,a^7\,c^5\,d^2\,x^4+a^6\,b\,c^7\,x+3\,a^6\,b\,c^6\,d\,x^4+2\,a^6\,b\,c^5\,d^2\,x^7+a^5\,b^2\,c^7\,x^4+a^5\,b^2\,c^6\,d\,x^7\right)}-\frac{5\,a^9\,c\,d^6\,x\,\sqrt{d\,x^3+c}}{4\,\left(2\,a^9\,b^2\,c^6\,d^3\,x+2\,a^9\,b^2\,c^5\,d^4\,x^4-3\,a^8\,b^3\,c^7\,d^2\,x-a^8\,b^3\,c^6\,d^3\,x^4+2\,a^8\,b^3\,c^5\,d^4\,x^7-3\,a^7\,b^4\,c^7\,d^2\,x^4-3\,a^7\,b^4\,c^6\,d^3\,x^7+a^6\,b^5\,c^9\,x+a^6\,b^5\,c^8\,d\,x^4+a^5\,b^6\,c^9\,x^4+a^5\,b^6\,c^8\,d\,x^7\right)}+\frac{23\,a^9\,c^2\,d^6\,x^4\,\sqrt{d\,x^3+c}}{8\,\left(2\,a^{10}\,b\,c^7\,d^3\,x+2\,a^{10}\,b\,c^6\,d^4\,x^4-3\,a^9\,b^2\,c^8\,d^2\,x-a^9\,b^2\,c^7\,d^3\,x^4+2\,a^9\,b^2\,c^6\,d^4\,x^7-3\,a^8\,b^3\,c^8\,d^2\,x^4-3\,a^8\,b^3\,c^7\,d^3\,x^7+a^7\,b^4\,c^{10}\,x+a^7\,b^4\,c^9\,d\,x^4+a^6\,b^5\,c^{10}\,x^4+a^6\,b^5\,c^9\,d\,x^7\right)}+\frac{a^2\,b^6\,c^{10}\,x\,\sqrt{d\,x^3+c}}{2\,\left(2\,a^{10}\,c^7\,d^5\,x+2\,a^{10}\,c^6\,d^6\,x^4-3\,a^9\,b\,c^8\,d^4\,x-a^9\,b\,c^7\,d^5\,x^4+2\,a^9\,b\,c^6\,d^6\,x^7-3\,a^8\,b^2\,c^8\,d^4\,x^4-3\,a^8\,b^2\,c^7\,d^5\,x^7+a^7\,b^3\,c^{10}\,d^2\,x+a^7\,b^3\,c^9\,d^3\,x^4+a^6\,b^4\,c^{10}\,d^2\,x^4+a^6\,b^4\,c^9\,d^3\,x^7\right)}+\frac{a\,b^7\,c^{10}\,x^4\,\sqrt{d\,x^3+c}}{2\,\left(2\,a^{10}\,c^7\,d^5\,x+2\,a^{10}\,c^6\,d^6\,x^4-3\,a^9\,b\,c^8\,d^4\,x-a^9\,b\,c^7\,d^5\,x^4+2\,a^9\,b\,c^6\,d^6\,x^7-3\,a^8\,b^2\,c^8\,d^4\,x^4-3\,a^8\,b^2\,c^7\,d^5\,x^7+a^7\,b^3\,c^{10}\,d^2\,x+a^7\,b^3\,c^9\,d^3\,x^4+a^6\,b^4\,c^{10}\,d^2\,x^4+a^6\,b^4\,c^9\,d^3\,x^7\right)}+\frac{a^2\,b^5\,c^7\,x^4\,\sqrt{d\,x^3+c}}{8\,\left(2\,a^9\,c^6\,d^3\,x+2\,a^9\,c^5\,d^4\,x^4-3\,a^8\,b\,c^7\,d^2\,x-a^8\,b\,c^6\,d^3\,x^4+2\,a^8\,b\,c^5\,d^4\,x^7-3\,a^7\,b^2\,c^7\,d^2\,x^4-3\,a^7\,b^2\,c^6\,d^3\,x^7+a^6\,b^3\,c^9\,x+a^6\,b^3\,c^8\,d\,x^4+a^5\,b^4\,c^9\,x^4+a^5\,b^4\,c^8\,d\,x^7\right)}+\frac{269\,a^3\,b^5\,c^8\,x^4\,\sqrt{d\,x^3+c}}{24\,\left(2\,a^{10}\,c^7\,d^3\,x+2\,a^{10}\,c^6\,d^4\,x^4-3\,a^9\,b\,c^8\,d^2\,x-a^9\,b\,c^7\,d^3\,x^4+2\,a^9\,b\,c^6\,d^4\,x^7-3\,a^8\,b^2\,c^8\,d^2\,x^4-3\,a^8\,b^2\,c^7\,d^3\,x^7+a^7\,b^3\,c^{10}\,x+a^7\,b^3\,c^9\,d\,x^4+a^6\,b^4\,c^{10}\,x^4+a^6\,b^4\,c^9\,d\,x^7\right)}-\frac{26\,a^6\,c^2\,d^5\,x^4\,\sqrt{d\,x^3+c}}{3\,\left(2\,a^8\,c^6\,d^3\,x+2\,a^8\,c^5\,d^4\,x^4-3\,a^7\,b\,c^7\,d^2\,x-a^7\,b\,c^6\,d^3\,x^4+2\,a^7\,b\,c^5\,d^4\,x^7-3\,a^6\,b^2\,c^7\,d^2\,x^4-3\,a^6\,b^2\,c^6\,d^3\,x^7+a^5\,b^3\,c^9\,x+a^5\,b^3\,c^8\,d\,x^4+a^4\,b^4\,c^9\,x^4+a^4\,b^4\,c^8\,d\,x^7\right)}-\frac{5\,a^7\,c^2\,d^5\,x^4\,\sqrt{d\,x^3+c}}{8\,\left(2\,a^9\,c^6\,d^3\,x+2\,a^9\,c^5\,d^4\,x^4-3\,a^8\,b\,c^7\,d^2\,x-a^8\,b\,c^6\,d^3\,x^4+2\,a^8\,b\,c^5\,d^4\,x^7-3\,a^7\,b^2\,c^7\,d^2\,x^4-3\,a^7\,b^2\,c^6\,d^3\,x^7+a^6\,b^3\,c^9\,x+a^6\,b^3\,c^8\,d\,x^4+a^5\,b^4\,c^9\,x^4+a^5\,b^4\,c^8\,d\,x^7\right)}+\frac{79\,a^8\,c^3\,d^5\,x^4\,\sqrt{d\,x^3+c}}{12\,\left(2\,a^{10}\,c^7\,d^3\,x+2\,a^{10}\,c^6\,d^4\,x^4-3\,a^9\,b\,c^8\,d^2\,x-a^9\,b\,c^7\,d^3\,x^4+2\,a^9\,b\,c^6\,d^4\,x^7-3\,a^8\,b^2\,c^8\,d^2\,x^4-3\,a^8\,b^2\,c^7\,d^3\,x^7+a^7\,b^3\,c^{10}\,x+a^7\,b^3\,c^9\,d\,x^4+a^6\,b^4\,c^{10}\,x^4+a^6\,b^4\,c^9\,d\,x^7\right)}-\frac{34\,a^2\,b^3\,c^5\,x^4\,\sqrt{d\,x^3+c}}{3\,\left(2\,a^7\,c^6\,d\,x+2\,a^7\,c^5\,d^2\,x^4+a^6\,b\,c^7\,x+3\,a^6\,b\,c^6\,d\,x^4+2\,a^6\,b\,c^5\,d^2\,x^7+a^5\,b^2\,c^7\,x^4+a^5\,b^2\,c^6\,d\,x^7\right)}-\frac{239\,a^5\,c^2\,d^3\,x^4\,\sqrt{d\,x^3+c}}{24\,\left(2\,a^7\,c^6\,d\,x+2\,a^7\,c^5\,d^2\,x^4+a^6\,b\,c^7\,x+3\,a^6\,b\,c^6\,d\,x^4+2\,a^6\,b\,c^5\,d^2\,x^7+a^5\,b^2\,c^7\,x^4+a^5\,b^2\,c^6\,d\,x^7\right)}-\frac{3\,a^2\,b^5\,c^8\,x\,\sqrt{d\,x^3+c}}{4\,\left(2\,a^9\,c^6\,d^4\,x+2\,a^9\,c^5\,d^5\,x^4-3\,a^8\,b\,c^7\,d^3\,x-a^8\,b\,c^6\,d^4\,x^4+2\,a^8\,b\,c^5\,d^5\,x^7-3\,a^7\,b^2\,c^7\,d^3\,x^4-3\,a^7\,b^2\,c^6\,d^4\,x^7+a^6\,b^3\,c^9\,d\,x+a^6\,b^3\,c^8\,d^2\,x^4+a^5\,b^4\,c^9\,d\,x^4+a^5\,b^4\,c^8\,d^2\,x^7\right)}-\frac{3\,a\,b^6\,c^8\,x^4\,\sqrt{d\,x^3+c}}{4\,\left(2\,a^9\,c^6\,d^4\,x+2\,a^9\,c^5\,d^5\,x^4-3\,a^8\,b\,c^7\,d^3\,x-a^8\,b\,c^6\,d^4\,x^4+2\,a^8\,b\,c^5\,d^5\,x^7-3\,a^7\,b^2\,c^7\,d^3\,x^4-3\,a^7\,b^2\,c^6\,d^4\,x^7+a^6\,b^3\,c^9\,d\,x+a^6\,b^3\,c^8\,d^2\,x^4+a^5\,b^4\,c^9\,d\,x^4+a^5\,b^4\,c^8\,d^2\,x^7\right)}+\frac{3\,a^3\,b^5\,c^9\,x\,\sqrt{d\,x^3+c}}{4\,\left(2\,a^{10}\,c^7\,d^4\,x+2\,a^{10}\,c^6\,d^5\,x^4-3\,a^9\,b\,c^8\,d^3\,x-a^9\,b\,c^7\,d^4\,x^4+2\,a^9\,b\,c^6\,d^5\,x^7-3\,a^8\,b^2\,c^8\,d^3\,x^4-3\,a^8\,b^2\,c^7\,d^4\,x^7+a^7\,b^3\,c^{10}\,d\,x+a^7\,b^3\,c^9\,d^2\,x^4+a^6\,b^4\,c^{10}\,d\,x^4+a^6\,b^4\,c^9\,d^2\,x^7\right)}+\frac{5\,a^4\,c\,d^3\,x\,\sqrt{d\,x^3+c}}{2\,\left(2\,a^5\,b\,c^5\,d\,x+2\,a^5\,b\,c^4\,d^2\,x^4+a^4\,b^2\,c^6\,x+3\,a^4\,b^2\,c^5\,d\,x^4+2\,a^4\,b^2\,c^4\,d^2\,x^7+a^3\,b^3\,c^6\,x^4+a^3\,b^3\,c^5\,d\,x^7\right)}-\frac{8\,a\,b^4\,c^5\,x\,\sqrt{d\,x^3+c}}{3\,\left(2\,a^7\,c^4\,d^3\,x+2\,a^7\,c^3\,d^4\,x^4-3\,a^6\,b\,c^5\,d^2\,x-a^6\,b\,c^4\,d^3\,x^4+2\,a^6\,b\,c^3\,d^4\,x^7-3\,a^5\,b^2\,c^5\,d^2\,x^4-3\,a^5\,b^2\,c^4\,d^3\,x^7+a^4\,b^3\,c^7\,x+a^4\,b^3\,c^6\,d\,x^4+a^3\,b^4\,c^7\,x^4+a^3\,b^4\,c^6\,d\,x^7\right)}-\frac{5\,a^5\,c\,d^4\,x\,\sqrt{d\,x^3+c}}{2\,a^7\,c^4\,d^3\,x+2\,a^7\,c^3\,d^4\,x^4-3\,a^6\,b\,c^5\,d^2\,x-a^6\,b\,c^4\,d^3\,x^4+2\,a^6\,b\,c^3\,d^4\,x^7-3\,a^5\,b^2\,c^5\,d^2\,x^4-3\,a^5\,b^2\,c^4\,d^3\,x^7+a^4\,b^3\,c^7\,x+a^4\,b^3\,c^6\,d\,x^4+a^3\,b^4\,c^7\,x^4+a^3\,b^4\,c^6\,d\,x^7}+\frac{5\,a^{10}\,c^2\,d^6\,x\,\sqrt{d\,x^3+c}}{4\,\left(2\,a^{10}\,b^2\,c^7\,d^3\,x+2\,a^{10}\,b^2\,c^6\,d^4\,x^4-3\,a^9\,b^3\,c^8\,d^2\,x-a^9\,b^3\,c^7\,d^3\,x^4+2\,a^9\,b^3\,c^6\,d^4\,x^7-3\,a^8\,b^4\,c^8\,d^2\,x^4-3\,a^8\,b^4\,c^7\,d^3\,x^7+a^7\,b^5\,c^{10}\,x+a^7\,b^5\,c^9\,d\,x^4+a^6\,b^6\,c^{10}\,x^4+a^6\,b^6\,c^9\,d\,x^7\right)}+\frac{5\,a^{10}\,c\,d^7\,x^4\,\sqrt{d\,x^3+c}}{4\,\left(2\,a^{10}\,b^2\,c^7\,d^3\,x+2\,a^{10}\,b^2\,c^6\,d^4\,x^4-3\,a^9\,b^3\,c^8\,d^2\,x-a^9\,b^3\,c^7\,d^3\,x^4+2\,a^9\,b^3\,c^6\,d^4\,x^7-3\,a^8\,b^4\,c^8\,d^2\,x^4-3\,a^8\,b^4\,c^7\,d^3\,x^7+a^7\,b^5\,c^{10}\,x+a^7\,b^5\,c^9\,d\,x^4+a^6\,b^6\,c^{10}\,x^4+a^6\,b^6\,c^9\,d\,x^7\right)}-\frac{11\,a\,b^2\,c^3\,x\,\sqrt{d\,x^3+c}}{3\,\left(2\,a^5\,c^4\,d\,x+2\,a^5\,c^3\,d^2\,x^4+a^4\,b\,c^5\,x+3\,a^4\,b\,c^4\,d\,x^4+2\,a^4\,b\,c^3\,d^2\,x^7+a^3\,b^2\,c^5\,x^4+a^3\,b^2\,c^4\,d\,x^7\right)}+\frac{14\,a\,b^2\,c^4\,x\,\sqrt{d\,x^3+c}}{2\,a^5\,c^5\,d\,x+2\,a^5\,c^4\,d^2\,x^4+a^4\,b\,c^6\,x+3\,a^4\,b\,c^5\,d\,x^4+2\,a^4\,b\,c^4\,d^2\,x^7+a^3\,b^2\,c^6\,x^4+a^3\,b^2\,c^5\,d\,x^7}+\frac{11\,a\,b\,d^2\,x^4\,\sqrt{d\,x^3+c}}{2\,\left(2\,a^4\,c^3\,d\,x+2\,a^4\,c^2\,d^2\,x^4+a^3\,b\,c^4\,x+3\,a^3\,b\,c^3\,d\,x^4+2\,a^3\,b\,c^2\,d^2\,x^7+a^2\,b^2\,c^4\,x^4+a^2\,b^2\,c^3\,d\,x^7\right)}-\frac{143\,a^3\,c\,d^2\,x\,\sqrt{d\,x^3+c}}{24\,\left(2\,a^5\,c^4\,d\,x+2\,a^5\,c^3\,d^2\,x^4+a^4\,b\,c^5\,x+3\,a^4\,b\,c^4\,d\,x^4+2\,a^4\,b\,c^3\,d^2\,x^7+a^3\,b^2\,c^5\,x^4+a^3\,b^2\,c^4\,d\,x^7\right)}+\frac{22\,b^2\,c\,d\,x^4\,\sqrt{d\,x^3+c}}{3\,\left(2\,a^4\,c^3\,d\,x+2\,a^4\,c^2\,d^2\,x^4+a^3\,b\,c^4\,x+3\,a^3\,b\,c^3\,d\,x^4+2\,a^3\,b\,c^2\,d^2\,x^7+a^2\,b^2\,c^4\,x^4+a^2\,b^2\,c^3\,d\,x^7\right)}+\frac{11\,a^3\,b^2\,c^3\,d^2\,x\,\sqrt{d\,x^3+c}}{3\,\left(2\,a^7\,c^4\,d^3\,x+2\,a^7\,c^3\,d^4\,x^4-3\,a^6\,b\,c^5\,d^2\,x-a^6\,b\,c^4\,d^3\,x^4+2\,a^6\,b\,c^3\,d^4\,x^7-3\,a^5\,b^2\,c^5\,d^2\,x^4-3\,a^5\,b^2\,c^4\,d^3\,x^7+a^4\,b^3\,c^7\,x+a^4\,b^3\,c^6\,d\,x^4+a^3\,b^4\,c^7\,x^4+a^3\,b^4\,c^6\,d\,x^7\right)}-\frac{31\,a^4\,b^2\,c^4\,d^2\,x\,\sqrt{d\,x^3+c}}{2\,\left(2\,a^8\,c^5\,d^3\,x+2\,a^8\,c^4\,d^4\,x^4-3\,a^7\,b\,c^6\,d^2\,x-a^7\,b\,c^5\,d^3\,x^4+2\,a^7\,b\,c^4\,d^4\,x^7-3\,a^6\,b^2\,c^6\,d^2\,x^4-3\,a^6\,b^2\,c^5\,d^3\,x^7+a^5\,b^3\,c^8\,x+a^5\,b^3\,c^7\,d\,x^4+a^4\,b^4\,c^8\,x^4+a^4\,b^4\,c^7\,d\,x^7\right)}+\frac{28\,a^2\,b^4\,c^5\,d\,x^4\,\sqrt{d\,x^3+c}}{3\,\left(2\,a^8\,c^5\,d^3\,x+2\,a^8\,c^4\,d^4\,x^4-3\,a^7\,b\,c^6\,d^2\,x-a^7\,b\,c^5\,d^3\,x^4+2\,a^7\,b\,c^4\,d^4\,x^7-3\,a^6\,b^2\,c^6\,d^2\,x^4-3\,a^6\,b^2\,c^5\,d^3\,x^7+a^5\,b^3\,c^8\,x+a^5\,b^3\,c^7\,d\,x^4+a^4\,b^4\,c^8\,x^4+a^4\,b^4\,c^7\,d\,x^7\right)}+\frac{29\,a^5\,b\,c^2\,d^4\,x^4\,\sqrt{d\,x^3+c}}{3\,\left(2\,a^8\,c^5\,d^3\,x+2\,a^8\,c^4\,d^4\,x^4-3\,a^7\,b\,c^6\,d^2\,x-a^7\,b\,c^5\,d^3\,x^4+2\,a^7\,b\,c^4\,d^4\,x^7-3\,a^6\,b^2\,c^6\,d^2\,x^4-3\,a^6\,b^2\,c^5\,d^3\,x^7+a^5\,b^3\,c^8\,x+a^5\,b^3\,c^7\,d\,x^4+a^4\,b^4\,c^8\,x^4+a^4\,b^4\,c^7\,d\,x^7\right)}+\frac{23\,a^4\,b^2\,c^5\,d^2\,x\,\sqrt{d\,x^3+c}}{3\,\left(2\,a^8\,c^6\,d^3\,x+2\,a^8\,c^5\,d^4\,x^4-3\,a^7\,b\,c^7\,d^2\,x-a^7\,b\,c^6\,d^3\,x^4+2\,a^7\,b\,c^5\,d^4\,x^7-3\,a^6\,b^2\,c^7\,d^2\,x^4-3\,a^6\,b^2\,c^6\,d^3\,x^7+a^5\,b^3\,c^9\,x+a^5\,b^3\,c^8\,d\,x^4+a^4\,b^4\,c^9\,x^4+a^4\,b^4\,c^8\,d\,x^7\right)}+\frac{7\,a^2\,b^4\,c^6\,d\,x^4\,\sqrt{d\,x^3+c}}{3\,\left(2\,a^8\,c^6\,d^3\,x+2\,a^8\,c^5\,d^4\,x^4-3\,a^7\,b\,c^7\,d^2\,x-a^7\,b\,c^6\,d^3\,x^4+2\,a^7\,b\,c^5\,d^4\,x^7-3\,a^6\,b^2\,c^7\,d^2\,x^4-3\,a^6\,b^2\,c^6\,d^3\,x^7+a^5\,b^3\,c^9\,x+a^5\,b^3\,c^8\,d\,x^4+a^4\,b^4\,c^9\,x^4+a^4\,b^4\,c^8\,d\,x^7\right)}-\frac{7\,a^5\,b\,c^3\,d^4\,x^4\,\sqrt{d\,x^3+c}}{4\,\left(2\,a^8\,c^6\,d^3\,x+2\,a^8\,c^5\,d^4\,x^4-3\,a^7\,b\,c^7\,d^2\,x-a^7\,b\,c^6\,d^3\,x^4+2\,a^7\,b\,c^5\,d^4\,x^7-3\,a^6\,b^2\,c^7\,d^2\,x^4-3\,a^6\,b^2\,c^6\,d^3\,x^7+a^5\,b^3\,c^9\,x+a^5\,b^3\,c^8\,d\,x^4+a^4\,b^4\,c^9\,x^4+a^4\,b^4\,c^8\,d\,x^7\right)}-\frac{9\,a^5\,b^2\,c^5\,d^2\,x\,\sqrt{d\,x^3+c}}{8\,\left(2\,a^9\,c^6\,d^3\,x+2\,a^9\,c^5\,d^4\,x^4-3\,a^8\,b\,c^7\,d^2\,x-a^8\,b\,c^6\,d^3\,x^4+2\,a^8\,b\,c^5\,d^4\,x^7-3\,a^7\,b^2\,c^7\,d^2\,x^4-3\,a^7\,b^2\,c^6\,d^3\,x^7+a^6\,b^3\,c^9\,x+a^6\,b^3\,c^8\,d\,x^4+a^5\,b^4\,c^9\,x^4+a^5\,b^4\,c^8\,d\,x^7\right)}-\frac{9\,a^3\,b^4\,c^6\,d\,x^4\,\sqrt{d\,x^3+c}}{8\,\left(2\,a^9\,c^6\,d^3\,x+2\,a^9\,c^5\,d^4\,x^4-3\,a^8\,b\,c^7\,d^2\,x-a^8\,b\,c^6\,d^3\,x^4+2\,a^8\,b\,c^5\,d^4\,x^7-3\,a^7\,b^2\,c^7\,d^2\,x^4-3\,a^7\,b^2\,c^6\,d^3\,x^7+a^6\,b^3\,c^9\,x+a^6\,b^3\,c^8\,d\,x^4+a^5\,b^4\,c^9\,x^4+a^5\,b^4\,c^8\,d\,x^7\right)}-\frac{9\,a^6\,b\,c^3\,d^4\,x^4\,\sqrt{d\,x^3+c}}{8\,\left(2\,a^9\,c^6\,d^3\,x+2\,a^9\,c^5\,d^4\,x^4-3\,a^8\,b\,c^7\,d^2\,x-a^8\,b\,c^6\,d^3\,x^4+2\,a^8\,b\,c^5\,d^4\,x^7-3\,a^7\,b^2\,c^7\,d^2\,x^4-3\,a^7\,b^2\,c^6\,d^3\,x^7+a^6\,b^3\,c^9\,x+a^6\,b^3\,c^8\,d\,x^4+a^5\,b^4\,c^9\,x^4+a^5\,b^4\,c^8\,d\,x^7\right)}+\frac{23\,a^6\,b^2\,c^6\,d^2\,x\,\sqrt{d\,x^3+c}}{24\,\left(2\,a^{10}\,c^7\,d^3\,x+2\,a^{10}\,c^6\,d^4\,x^4-3\,a^9\,b\,c^8\,d^2\,x-a^9\,b\,c^7\,d^3\,x^4+2\,a^9\,b\,c^6\,d^4\,x^7-3\,a^8\,b^2\,c^8\,d^2\,x^4-3\,a^8\,b^2\,c^7\,d^3\,x^7+a^7\,b^3\,c^{10}\,x+a^7\,b^3\,c^9\,d\,x^4+a^6\,b^4\,c^{10}\,x^4+a^6\,b^4\,c^9\,d\,x^7\right)}-\frac{31\,a^4\,b^4\,c^7\,d\,x^4\,\sqrt{d\,x^3+c}}{8\,\left(2\,a^{10}\,c^7\,d^3\,x+2\,a^{10}\,c^6\,d^4\,x^4-3\,a^9\,b\,c^8\,d^2\,x-a^9\,b\,c^7\,d^3\,x^4+2\,a^9\,b\,c^6\,d^4\,x^7-3\,a^8\,b^2\,c^8\,d^2\,x^4-3\,a^8\,b^2\,c^7\,d^3\,x^7+a^7\,b^3\,c^{10}\,x+a^7\,b^3\,c^9\,d\,x^4+a^6\,b^4\,c^{10}\,x^4+a^6\,b^4\,c^9\,d\,x^7\right)}-\frac{21\,a^7\,b\,c^4\,d^4\,x^4\,\sqrt{d\,x^3+c}}{8\,\left(2\,a^{10}\,c^7\,d^3\,x+2\,a^{10}\,c^6\,d^4\,x^4-3\,a^9\,b\,c^8\,d^2\,x-a^9\,b\,c^7\,d^3\,x^4+2\,a^9\,b\,c^6\,d^4\,x^7-3\,a^8\,b^2\,c^8\,d^2\,x^4-3\,a^8\,b^2\,c^7\,d^3\,x^7+a^7\,b^3\,c^{10}\,x+a^7\,b^3\,c^9\,d\,x^4+a^6\,b^4\,c^{10}\,x^4+a^6\,b^4\,c^9\,d\,x^7\right)}+\frac{209\,a^2\,b\,c^2\,d^2\,x^4\,\sqrt{d\,x^3+c}}{12\,\left(2\,a^5\,c^5\,d\,x+2\,a^5\,c^4\,d^2\,x^4+a^4\,b\,c^6\,x+3\,a^4\,b\,c^5\,d\,x^4+2\,a^4\,b\,c^4\,d^2\,x^7+a^3\,b^2\,c^6\,x^4+a^3\,b^2\,c^5\,d\,x^7\right)}-\frac{89\,a^3\,b^2\,c^4\,d\,x^4\,\sqrt{d\,x^3+c}}{6\,\left(2\,a^7\,c^6\,d\,x+2\,a^7\,c^5\,d^2\,x^4+a^6\,b\,c^7\,x+3\,a^6\,b\,c^6\,d\,x^4+2\,a^6\,b\,c^5\,d^2\,x^7+a^5\,b^2\,c^7\,x^4+a^5\,b^2\,c^6\,d\,x^7\right)}-\frac{109\,a^4\,b\,c^3\,d^2\,x^4\,\sqrt{d\,x^3+c}}{12\,\left(2\,a^7\,c^6\,d\,x+2\,a^7\,c^5\,d^2\,x^4+a^6\,b\,c^7\,x+3\,a^6\,b\,c^6\,d\,x^4+2\,a^6\,b\,c^5\,d^2\,x^7+a^5\,b^2\,c^7\,x^4+a^5\,b^2\,c^6\,d\,x^7\right)}-\frac{33\,a^2\,b\,c^2\,d\,x\,\sqrt{d\,x^3+c}}{2\,\left(2\,a^5\,c^4\,d\,x+2\,a^5\,c^3\,d^2\,x^4+a^4\,b\,c^5\,x+3\,a^4\,b\,c^4\,d\,x^4+2\,a^4\,b\,c^3\,d^2\,x^7+a^3\,b^2\,c^5\,x^4+a^3\,b^2\,c^4\,d\,x^7\right)}+\frac{329\,a^2\,b\,c^3\,d\,x\,\sqrt{d\,x^3+c}}{12\,\left(2\,a^5\,c^5\,d\,x+2\,a^5\,c^4\,d^2\,x^4+a^4\,b\,c^6\,x+3\,a^4\,b\,c^5\,d\,x^4+2\,a^4\,b\,c^4\,d^2\,x^7+a^3\,b^2\,c^6\,x^4+a^3\,b^2\,c^5\,d\,x^7\right)}-\frac{205\,a^4\,b\,c^4\,d\,x\,\sqrt{d\,x^3+c}}{12\,\left(2\,a^7\,c^6\,d\,x+2\,a^7\,c^5\,d^2\,x^4+a^6\,b\,c^7\,x+3\,a^6\,b\,c^6\,d\,x^4+2\,a^6\,b\,c^5\,d^2\,x^7+a^5\,b^2\,c^7\,x^4+a^5\,b^2\,c^6\,d\,x^7\right)}+\frac{6\,a^2\,b^3\,c^3\,d^2\,x^4\,\sqrt{d\,x^3+c}}{2\,a^7\,c^4\,d^3\,x+2\,a^7\,c^3\,d^4\,x^4-3\,a^6\,b\,c^5\,d^2\,x-a^6\,b\,c^4\,d^3\,x^4+2\,a^6\,b\,c^3\,d^4\,x^7-3\,a^5\,b^2\,c^5\,d^2\,x^4-3\,a^5\,b^2\,c^4\,d^3\,x^7+a^4\,b^3\,c^7\,x+a^4\,b^3\,c^6\,d\,x^4+a^3\,b^4\,c^7\,x^4+a^3\,b^4\,c^6\,d\,x^7}-\frac{a^3\,b^2\,c^2\,d^3\,x^4\,\sqrt{d\,x^3+c}}{2\,a^7\,c^4\,d^3\,x+2\,a^7\,c^3\,d^4\,x^4-3\,a^6\,b\,c^5\,d^2\,x-a^6\,b\,c^4\,d^3\,x^4+2\,a^6\,b\,c^3\,d^4\,x^7-3\,a^5\,b^2\,c^5\,d^2\,x^4-3\,a^5\,b^2\,c^4\,d^3\,x^7+a^4\,b^3\,c^7\,x+a^4\,b^3\,c^6\,d\,x^4+a^3\,b^4\,c^7\,x^4+a^3\,b^4\,c^6\,d\,x^7}-\frac{19\,a^3\,b^3\,c^4\,d^2\,x^4\,\sqrt{d\,x^3+c}}{3\,\left(2\,a^8\,c^5\,d^3\,x+2\,a^8\,c^4\,d^4\,x^4-3\,a^7\,b\,c^6\,d^2\,x-a^7\,b\,c^5\,d^3\,x^4+2\,a^7\,b\,c^4\,d^4\,x^7-3\,a^6\,b^2\,c^6\,d^2\,x^4-3\,a^6\,b^2\,c^5\,d^3\,x^7+a^5\,b^3\,c^8\,x+a^5\,b^3\,c^7\,d\,x^4+a^4\,b^4\,c^8\,x^4+a^4\,b^4\,c^7\,d\,x^7\right)}+\frac{10\,a^4\,b^2\,c^3\,d^3\,x^4\,\sqrt{d\,x^3+c}}{3\,\left(2\,a^8\,c^5\,d^3\,x+2\,a^8\,c^4\,d^4\,x^4-3\,a^7\,b\,c^6\,d^2\,x-a^7\,b\,c^5\,d^3\,x^4+2\,a^7\,b\,c^4\,d^4\,x^7-3\,a^6\,b^2\,c^6\,d^2\,x^4-3\,a^6\,b^2\,c^5\,d^3\,x^7+a^5\,b^3\,c^8\,x+a^5\,b^3\,c^7\,d\,x^4+a^4\,b^4\,c^8\,x^4+a^4\,b^4\,c^7\,d\,x^7\right)}-\frac{a^3\,b^3\,c^5\,d^2\,x^4\,\sqrt{d\,x^3+c}}{2\,\left(2\,a^8\,c^6\,d^3\,x+2\,a^8\,c^5\,d^4\,x^4-3\,a^7\,b\,c^7\,d^2\,x-a^7\,b\,c^6\,d^3\,x^4+2\,a^7\,b\,c^5\,d^4\,x^7-3\,a^6\,b^2\,c^7\,d^2\,x^4-3\,a^6\,b^2\,c^6\,d^3\,x^7+a^5\,b^3\,c^9\,x+a^5\,b^3\,c^8\,d\,x^4+a^4\,b^4\,c^9\,x^4+a^4\,b^4\,c^8\,d\,x^7\right)}-\frac{97\,a^4\,b^2\,c^4\,d^3\,x^4\,\sqrt{d\,x^3+c}}{6\,\left(2\,a^8\,c^6\,d^3\,x+2\,a^8\,c^5\,d^4\,x^4-3\,a^7\,b\,c^7\,d^2\,x-a^7\,b\,c^6\,d^3\,x^4+2\,a^7\,b\,c^5\,d^4\,x^7-3\,a^6\,b^2\,c^7\,d^2\,x^4-3\,a^6\,b^2\,c^6\,d^3\,x^7+a^5\,b^3\,c^9\,x+a^5\,b^3\,c^8\,d\,x^4+a^4\,b^4\,c^9\,x^4+a^4\,b^4\,c^8\,d\,x^7\right)}-\frac{9\,a^4\,b^3\,c^5\,d^2\,x^4\,\sqrt{d\,x^3+c}}{8\,\left(2\,a^9\,c^6\,d^3\,x+2\,a^9\,c^5\,d^4\,x^4-3\,a^8\,b\,c^7\,d^2\,x-a^8\,b\,c^6\,d^3\,x^4+2\,a^8\,b\,c^5\,d^4\,x^7-3\,a^7\,b^2\,c^7\,d^2\,x^4-3\,a^7\,b^2\,c^6\,d^3\,x^7+a^6\,b^3\,c^9\,x+a^6\,b^3\,c^8\,d\,x^4+a^5\,b^4\,c^9\,x^4+a^5\,b^4\,c^8\,d\,x^7\right)}-\frac{9\,a^5\,b^2\,c^4\,d^3\,x^4\,\sqrt{d\,x^3+c}}{8\,\left(2\,a^9\,c^6\,d^3\,x+2\,a^9\,c^5\,d^4\,x^4-3\,a^8\,b\,c^7\,d^2\,x-a^8\,b\,c^6\,d^3\,x^4+2\,a^8\,b\,c^5\,d^4\,x^7-3\,a^7\,b^2\,c^7\,d^2\,x^4-3\,a^7\,b^2\,c^6\,d^3\,x^7+a^6\,b^3\,c^9\,x+a^6\,b^3\,c^8\,d\,x^4+a^5\,b^4\,c^9\,x^4+a^5\,b^4\,c^8\,d\,x^7\right)}+\frac{31\,a^5\,b^3\,c^6\,d^2\,x^4\,\sqrt{d\,x^3+c}}{24\,\left(2\,a^{10}\,c^7\,d^3\,x+2\,a^{10}\,c^6\,d^4\,x^4-3\,a^9\,b\,c^8\,d^2\,x-a^9\,b\,c^7\,d^3\,x^4+2\,a^9\,b\,c^6\,d^4\,x^7-3\,a^8\,b^2\,c^8\,d^2\,x^4-3\,a^8\,b^2\,c^7\,d^3\,x^7+a^7\,b^3\,c^{10}\,x+a^7\,b^3\,c^9\,d\,x^4+a^6\,b^4\,c^{10}\,x^4+a^6\,b^4\,c^9\,d\,x^7\right)}+\frac{415\,a^6\,b^2\,c^5\,d^3\,x^4\,\sqrt{d\,x^3+c}}{24\,\left(2\,a^{10}\,c^7\,d^3\,x+2\,a^{10}\,c^6\,d^4\,x^4-3\,a^9\,b\,c^8\,d^2\,x-a^9\,b\,c^7\,d^3\,x^4+2\,a^9\,b\,c^6\,d^4\,x^7-3\,a^8\,b^2\,c^8\,d^2\,x^4-3\,a^8\,b^2\,c^7\,d^3\,x^7+a^7\,b^3\,c^{10}\,x+a^7\,b^3\,c^9\,d\,x^4+a^6\,b^4\,c^{10}\,x^4+a^6\,b^4\,c^9\,d\,x^7\right)}+\frac{11\,a\,b\,c\,d\,x\,\sqrt{d\,x^3+c}}{2\,\left(2\,a^4\,c^3\,d\,x+2\,a^4\,c^2\,d^2\,x^4+a^3\,b\,c^4\,x+3\,a^3\,b\,c^3\,d\,x^4+2\,a^3\,b\,c^2\,d^2\,x^7+a^2\,b^2\,c^4\,x^4+a^2\,b^2\,c^3\,d\,x^7\right)}-\frac{10\,a^2\,b^3\,c^4\,d\,x\,\sqrt{d\,x^3+c}}{3\,\left(2\,a^7\,c^4\,d^3\,x+2\,a^7\,c^3\,d^4\,x^4-3\,a^6\,b\,c^5\,d^2\,x-a^6\,b\,c^4\,d^3\,x^4+2\,a^6\,b\,c^3\,d^4\,x^7-3\,a^5\,b^2\,c^5\,d^2\,x^4-3\,a^5\,b^2\,c^4\,d^3\,x^7+a^4\,b^3\,c^7\,x+a^4\,b^3\,c^6\,d\,x^4+a^3\,b^4\,c^7\,x^4+a^3\,b^4\,c^6\,d\,x^7\right)}-\frac{19\,a^4\,b\,c^2\,d^3\,x\,\sqrt{d\,x^3+c}}{6\,\left(2\,a^7\,c^4\,d^3\,x+2\,a^7\,c^3\,d^4\,x^4-3\,a^6\,b\,c^5\,d^2\,x-a^6\,b\,c^4\,d^3\,x^4+2\,a^6\,b\,c^3\,d^4\,x^7-3\,a^5\,b^2\,c^5\,d^2\,x^4-3\,a^5\,b^2\,c^4\,d^3\,x^7+a^4\,b^3\,c^7\,x+a^4\,b^3\,c^6\,d\,x^4+a^3\,b^4\,c^7\,x^4+a^3\,b^4\,c^6\,d\,x^7\right)}-\frac{8\,a\,b^4\,c^4\,d\,x^4\,\sqrt{d\,x^3+c}}{2\,a^7\,c^4\,d^3\,x+2\,a^7\,c^3\,d^4\,x^4-3\,a^6\,b\,c^5\,d^2\,x-a^6\,b\,c^4\,d^3\,x^4+2\,a^6\,b\,c^3\,d^4\,x^7-3\,a^5\,b^2\,c^5\,d^2\,x^4-3\,a^5\,b^2\,c^4\,d^3\,x^7+a^4\,b^3\,c^7\,x+a^4\,b^3\,c^6\,d\,x^4+a^3\,b^4\,c^7\,x^4+a^3\,b^4\,c^6\,d\,x^7}-\frac{15\,a^4\,b\,c\,d^4\,x^4\,\sqrt{d\,x^3+c}}{2\,\left(2\,a^7\,c^4\,d^3\,x+2\,a^7\,c^3\,d^4\,x^4-3\,a^6\,b\,c^5\,d^2\,x-a^6\,b\,c^4\,d^3\,x^4+2\,a^6\,b\,c^3\,d^4\,x^7-3\,a^5\,b^2\,c^5\,d^2\,x^4-3\,a^5\,b^2\,c^4\,d^3\,x^7+a^4\,b^3\,c^7\,x+a^4\,b^3\,c^6\,d\,x^4+a^3\,b^4\,c^7\,x^4+a^3\,b^4\,c^6\,d\,x^7\right)}+\frac{12\,a^3\,b^3\,c^5\,d\,x\,\sqrt{d\,x^3+c}}{2\,a^8\,c^5\,d^3\,x+2\,a^8\,c^4\,d^4\,x^4-3\,a^7\,b\,c^6\,d^2\,x-a^7\,b\,c^5\,d^3\,x^4+2\,a^7\,b\,c^4\,d^4\,x^7-3\,a^6\,b^2\,c^6\,d^2\,x^4-3\,a^6\,b^2\,c^5\,d^3\,x^7+a^5\,b^3\,c^8\,x+a^5\,b^3\,c^7\,d\,x^4+a^4\,b^4\,c^8\,x^4+a^4\,b^4\,c^7\,d\,x^7}+\frac{51\,a^5\,b\,c^3\,d^3\,x\,\sqrt{d\,x^3+c}}{4\,\left(2\,a^8\,c^5\,d^3\,x+2\,a^8\,c^4\,d^4\,x^4-3\,a^7\,b\,c^6\,d^2\,x-a^7\,b\,c^5\,d^3\,x^4+2\,a^7\,b\,c^4\,d^4\,x^7-3\,a^6\,b^2\,c^6\,d^2\,x^4-3\,a^6\,b^2\,c^5\,d^3\,x^7+a^5\,b^3\,c^8\,x+a^5\,b^3\,c^7\,d\,x^4+a^4\,b^4\,c^8\,x^4+a^4\,b^4\,c^7\,d\,x^7\right)}-\frac{14\,a^3\,b^3\,c^6\,d\,x\,\sqrt{d\,x^3+c}}{3\,\left(2\,a^8\,c^6\,d^3\,x+2\,a^8\,c^5\,d^4\,x^4-3\,a^7\,b\,c^7\,d^2\,x-a^7\,b\,c^6\,d^3\,x^4+2\,a^7\,b\,c^5\,d^4\,x^7-3\,a^6\,b^2\,c^7\,d^2\,x^4-3\,a^6\,b^2\,c^6\,d^3\,x^7+a^5\,b^3\,c^9\,x+a^5\,b^3\,c^8\,d\,x^4+a^4\,b^4\,c^9\,x^4+a^4\,b^4\,c^8\,d\,x^7\right)}-\frac{169\,a^5\,b\,c^4\,d^3\,x\,\sqrt{d\,x^3+c}}{12\,\left(2\,a^8\,c^6\,d^3\,x+2\,a^8\,c^5\,d^4\,x^4-3\,a^7\,b\,c^7\,d^2\,x-a^7\,b\,c^6\,d^3\,x^4+2\,a^7\,b\,c^5\,d^4\,x^7-3\,a^6\,b^2\,c^7\,d^2\,x^4-3\,a^6\,b^2\,c^6\,d^3\,x^7+a^5\,b^3\,c^9\,x+a^5\,b^3\,c^8\,d\,x^4+a^4\,b^4\,c^9\,x^4+a^4\,b^4\,c^8\,d\,x^7\right)}-\frac{9\,a^4\,b^3\,c^6\,d\,x\,\sqrt{d\,x^3+c}}{8\,\left(2\,a^9\,c^6\,d^3\,x+2\,a^9\,c^5\,d^4\,x^4-3\,a^8\,b\,c^7\,d^2\,x-a^8\,b\,c^6\,d^3\,x^4+2\,a^8\,b\,c^5\,d^4\,x^7-3\,a^7\,b^2\,c^7\,d^2\,x^4-3\,a^7\,b^2\,c^6\,d^3\,x^7+a^6\,b^3\,c^9\,x+a^6\,b^3\,c^8\,d\,x^4+a^5\,b^4\,c^9\,x^4+a^5\,b^4\,c^8\,d\,x^7\right)}-\frac{9\,a^6\,b\,c^4\,d^3\,x\,\sqrt{d\,x^3+c}}{8\,\left(2\,a^9\,c^6\,d^3\,x+2\,a^9\,c^5\,d^4\,x^4-3\,a^8\,b\,c^7\,d^2\,x-a^8\,b\,c^6\,d^3\,x^4+2\,a^8\,b\,c^5\,d^4\,x^7-3\,a^7\,b^2\,c^7\,d^2\,x^4-3\,a^7\,b^2\,c^6\,d^3\,x^7+a^6\,b^3\,c^9\,x+a^6\,b^3\,c^8\,d\,x^4+a^5\,b^4\,c^9\,x^4+a^5\,b^4\,c^8\,d\,x^7\right)}-\frac{7\,a^5\,b^3\,c^7\,d\,x\,\sqrt{d\,x^3+c}}{8\,\left(2\,a^{10}\,c^7\,d^3\,x+2\,a^{10}\,c^6\,d^4\,x^4-3\,a^9\,b\,c^8\,d^2\,x-a^9\,b\,c^7\,d^3\,x^4+2\,a^9\,b\,c^6\,d^4\,x^7-3\,a^8\,b^2\,c^8\,d^2\,x^4-3\,a^8\,b^2\,c^7\,d^3\,x^7+a^7\,b^3\,c^{10}\,x+a^7\,b^3\,c^9\,d\,x^4+a^6\,b^4\,c^{10}\,x^4+a^6\,b^4\,c^9\,d\,x^7\right)}+\frac{77\,a^7\,b\,c^5\,d^3\,x\,\sqrt{d\,x^3+c}}{8\,\left(2\,a^{10}\,c^7\,d^3\,x+2\,a^{10}\,c^6\,d^4\,x^4-3\,a^9\,b\,c^8\,d^2\,x-a^9\,b\,c^7\,d^3\,x^4+2\,a^9\,b\,c^6\,d^4\,x^7-3\,a^8\,b^2\,c^8\,d^2\,x^4-3\,a^8\,b^2\,c^7\,d^3\,x^7+a^7\,b^3\,c^{10}\,x+a^7\,b^3\,c^9\,d\,x^4+a^6\,b^4\,c^{10}\,x^4+a^6\,b^4\,c^9\,d\,x^7\right)}-\frac{41\,a\,b^2\,c^2\,d\,x^4\,\sqrt{d\,x^3+c}}{3\,\left(2\,a^5\,c^4\,d\,x+2\,a^5\,c^3\,d^2\,x^4+a^4\,b\,c^5\,x+3\,a^4\,b\,c^4\,d\,x^4+2\,a^4\,b\,c^3\,d^2\,x^7+a^3\,b^2\,c^5\,x^4+a^3\,b^2\,c^4\,d\,x^7\right)}-\frac{71\,a^2\,b\,c\,d^2\,x^4\,\sqrt{d\,x^3+c}}{6\,\left(2\,a^5\,c^4\,d\,x+2\,a^5\,c^3\,d^2\,x^4+a^4\,b\,c^5\,x+3\,a^4\,b\,c^4\,d\,x^4+2\,a^4\,b\,c^3\,d^2\,x^7+a^3\,b^2\,c^5\,x^4+a^3\,b^2\,c^4\,d\,x^7\right)}+\frac{133\,a\,b^2\,c^3\,d\,x^4\,\sqrt{d\,x^3+c}}{6\,\left(2\,a^5\,c^5\,d\,x+2\,a^5\,c^4\,d^2\,x^4+a^4\,b\,c^6\,x+3\,a^4\,b\,c^5\,d\,x^4+2\,a^4\,b\,c^4\,d^2\,x^7+a^3\,b^2\,c^6\,x^4+a^3\,b^2\,c^5\,d\,x^7\right)}-\frac{b^{7/2}\,c\,\ln\left(\frac{36\,a^6\,b^7\,c^9\,\sqrt{d\,x^3+c}\,\sqrt{a\,d-b\,c}}{a\,\sqrt{a\,d-b\,c}+b\,x^3\,\sqrt{a\,d-b\,c}}+\frac{360\,a^8\,b^5\,c^7\,d^2\,\sqrt{d\,x^3+c}\,\sqrt{a\,d-b\,c}}{a\,\sqrt{a\,d-b\,c}+b\,x^3\,\sqrt{a\,d-b\,c}}-\frac{360\,a^9\,b^4\,c^6\,d^3\,\sqrt{d\,x^3+c}\,\sqrt{a\,d-b\,c}}{a\,\sqrt{a\,d-b\,c}+b\,x^3\,\sqrt{a\,d-b\,c}}+\frac{180\,a^{10}\,b^3\,c^5\,d^4\,\sqrt{d\,x^3+c}\,\sqrt{a\,d-b\,c}}{a\,\sqrt{a\,d-b\,c}+b\,x^3\,\sqrt{a\,d-b\,c}}-\frac{36\,a^{11}\,b^2\,c^4\,d^5\,\sqrt{d\,x^3+c}\,\sqrt{a\,d-b\,c}}{a\,\sqrt{a\,d-b\,c}+b\,x^3\,\sqrt{a\,d-b\,c}}-\frac{180\,a^7\,b^6\,c^8\,d\,\sqrt{d\,x^3+c}\,\sqrt{a\,d-b\,c}}{a\,\sqrt{a\,d-b\,c}+b\,x^3\,\sqrt{a\,d-b\,c}}+\frac{a^6\,b^{15/2}\,c^{10}\,36{}\mathrm{i}}{a\,\sqrt{a\,d-b\,c}+b\,x^3\,\sqrt{a\,d-b\,c}}-\frac{a^7\,b^{13/2}\,c^9\,d\,198{}\mathrm{i}}{a\,\sqrt{a\,d-b\,c}+b\,x^3\,\sqrt{a\,d-b\,c}}+\frac{a^{12}\,b^{3/2}\,c^4\,d^6\,18{}\mathrm{i}}{a\,\sqrt{a\,d-b\,c}+b\,x^3\,\sqrt{a\,d-b\,c}}-\frac{a^{11}\,b^{5/2}\,c^5\,d^5\,126{}\mathrm{i}}{a\,\sqrt{a\,d-b\,c}+b\,x^3\,\sqrt{a\,d-b\,c}}+\frac{a^{10}\,b^{7/2}\,c^6\,d^4\,360{}\mathrm{i}}{a\,\sqrt{a\,d-b\,c}+b\,x^3\,\sqrt{a\,d-b\,c}}-\frac{a^9\,b^{9/2}\,c^7\,d^3\,540{}\mathrm{i}}{a\,\sqrt{a\,d-b\,c}+b\,x^3\,\sqrt{a\,d-b\,c}}+\frac{a^8\,b^{11/2}\,c^8\,d^2\,450{}\mathrm{i}}{a\,\sqrt{a\,d-b\,c}+b\,x^3\,\sqrt{a\,d-b\,c}}+\frac{a^6\,b^{15/2}\,c^9\,d\,x^3\,18{}\mathrm{i}}{a\,\sqrt{a\,d-b\,c}+b\,x^3\,\sqrt{a\,d-b\,c}}-\frac{a^{11}\,b^{5/2}\,c^4\,d^6\,x^3\,18{}\mathrm{i}}{a\,\sqrt{a\,d-b\,c}+b\,x^3\,\sqrt{a\,d-b\,c}}+\frac{a^{10}\,b^{7/2}\,c^5\,d^5\,x^3\,90{}\mathrm{i}}{a\,\sqrt{a\,d-b\,c}+b\,x^3\,\sqrt{a\,d-b\,c}}-\frac{a^9\,b^{9/2}\,c^6\,d^4\,x^3\,180{}\mathrm{i}}{a\,\sqrt{a\,d-b\,c}+b\,x^3\,\sqrt{a\,d-b\,c}}+\frac{a^8\,b^{11/2}\,c^7\,d^3\,x^3\,180{}\mathrm{i}}{a\,\sqrt{a\,d-b\,c}+b\,x^3\,\sqrt{a\,d-b\,c}}-\frac{a^7\,b^{13/2}\,c^8\,d^2\,x^3\,90{}\mathrm{i}}{a\,\sqrt{a\,d-b\,c}+b\,x^3\,\sqrt{a\,d-b\,c}}\right)\,2{}\mathrm{i}}{3\,a^3\,{\left(a\,d-b\,c\right)}^{5/2}}+\frac{b^{5/2}\,d\,\ln\left(\frac{36\,a^6\,b^7\,c^9\,\sqrt{d\,x^3+c}\,\sqrt{a\,d-b\,c}}{a\,\sqrt{a\,d-b\,c}+b\,x^3\,\sqrt{a\,d-b\,c}}+\frac{360\,a^8\,b^5\,c^7\,d^2\,\sqrt{d\,x^3+c}\,\sqrt{a\,d-b\,c}}{a\,\sqrt{a\,d-b\,c}+b\,x^3\,\sqrt{a\,d-b\,c}}-\frac{360\,a^9\,b^4\,c^6\,d^3\,\sqrt{d\,x^3+c}\,\sqrt{a\,d-b\,c}}{a\,\sqrt{a\,d-b\,c}+b\,x^3\,\sqrt{a\,d-b\,c}}+\frac{180\,a^{10}\,b^3\,c^5\,d^4\,\sqrt{d\,x^3+c}\,\sqrt{a\,d-b\,c}}{a\,\sqrt{a\,d-b\,c}+b\,x^3\,\sqrt{a\,d-b\,c}}-\frac{36\,a^{11}\,b^2\,c^4\,d^5\,\sqrt{d\,x^3+c}\,\sqrt{a\,d-b\,c}}{a\,\sqrt{a\,d-b\,c}+b\,x^3\,\sqrt{a\,d-b\,c}}-\frac{180\,a^7\,b^6\,c^8\,d\,\sqrt{d\,x^3+c}\,\sqrt{a\,d-b\,c}}{a\,\sqrt{a\,d-b\,c}+b\,x^3\,\sqrt{a\,d-b\,c}}+\frac{a^6\,b^{15/2}\,c^{10}\,36{}\mathrm{i}}{a\,\sqrt{a\,d-b\,c}+b\,x^3\,\sqrt{a\,d-b\,c}}-\frac{a^7\,b^{13/2}\,c^9\,d\,198{}\mathrm{i}}{a\,\sqrt{a\,d-b\,c}+b\,x^3\,\sqrt{a\,d-b\,c}}+\frac{a^{12}\,b^{3/2}\,c^4\,d^6\,18{}\mathrm{i}}{a\,\sqrt{a\,d-b\,c}+b\,x^3\,\sqrt{a\,d-b\,c}}-\frac{a^{11}\,b^{5/2}\,c^5\,d^5\,126{}\mathrm{i}}{a\,\sqrt{a\,d-b\,c}+b\,x^3\,\sqrt{a\,d-b\,c}}+\frac{a^{10}\,b^{7/2}\,c^6\,d^4\,360{}\mathrm{i}}{a\,\sqrt{a\,d-b\,c}+b\,x^3\,\sqrt{a\,d-b\,c}}-\frac{a^9\,b^{9/2}\,c^7\,d^3\,540{}\mathrm{i}}{a\,\sqrt{a\,d-b\,c}+b\,x^3\,\sqrt{a\,d-b\,c}}+\frac{a^8\,b^{11/2}\,c^8\,d^2\,450{}\mathrm{i}}{a\,\sqrt{a\,d-b\,c}+b\,x^3\,\sqrt{a\,d-b\,c}}+\frac{a^6\,b^{15/2}\,c^9\,d\,x^3\,18{}\mathrm{i}}{a\,\sqrt{a\,d-b\,c}+b\,x^3\,\sqrt{a\,d-b\,c}}-\frac{a^{11}\,b^{5/2}\,c^4\,d^6\,x^3\,18{}\mathrm{i}}{a\,\sqrt{a\,d-b\,c}+b\,x^3\,\sqrt{a\,d-b\,c}}+\frac{a^{10}\,b^{7/2}\,c^5\,d^5\,x^3\,90{}\mathrm{i}}{a\,\sqrt{a\,d-b\,c}+b\,x^3\,\sqrt{a\,d-b\,c}}-\frac{a^9\,b^{9/2}\,c^6\,d^4\,x^3\,180{}\mathrm{i}}{a\,\sqrt{a\,d-b\,c}+b\,x^3\,\sqrt{a\,d-b\,c}}+\frac{a^8\,b^{11/2}\,c^7\,d^3\,x^3\,180{}\mathrm{i}}{a\,\sqrt{a\,d-b\,c}+b\,x^3\,\sqrt{a\,d-b\,c}}-\frac{a^7\,b^{13/2}\,c^8\,d^2\,x^3\,90{}\mathrm{i}}{a\,\sqrt{a\,d-b\,c}+b\,x^3\,\sqrt{a\,d-b\,c}}\right)\,7{}\mathrm{i}}{6\,a^2\,{\left(a\,d-b\,c\right)}^{5/2}}","Not used",1,"(2*b*log(1/x^6))/(3*a^3*c^(3/2)) - (c + d*x^3)^(1/2)/(3*a^2*c^2*x^3) + (d*log(1/x^6))/(2*a^2*c^(5/2)) + (2*b*log(c^(3/2)*(c + d*x^3)^(1/2) - c^(1/2)*(c + d*x^3)^(3/2) + d^2*x^6 + 2*c*d*x^3 + 3*c^(1/2)*d*x^3*(c + d*x^3)^(1/2)))/(3*a^3*c^(3/2)) + (d*log(c^(3/2)*(c + d*x^3)^(1/2) - c^(1/2)*(c + d*x^3)^(3/2) + d^2*x^6 + 2*c*d*x^3 + 3*c^(1/2)*d*x^3*(c + d*x^3)^(1/2)))/(2*a^2*c^(5/2)) - (b^7*c^9*x^4*(c + d*x^3)^(1/2))/(2*(2*a^9*c^6*d^5*x + 2*a^9*c^5*d^6*x^4 + a^5*b^4*c^9*d^2*x^4 + a^6*b^3*c^8*d^3*x^4 - 3*a^7*b^2*c^7*d^4*x^4 + a^5*b^4*c^8*d^3*x^7 - 3*a^7*b^2*c^6*d^5*x^7 - 3*a^8*b*c^7*d^4*x + a^6*b^3*c^9*d^2*x - a^8*b*c^6*d^5*x^4 + 2*a^8*b*c^5*d^6*x^7)) - (5*a^9*d^7*x^4*(c + d*x^3)^(1/2))/(4*(a^6*b^5*c^9*x + a^5*b^6*c^9*x^4 - 3*a^7*b^4*c^7*d^2*x^4 - a^8*b^3*c^6*d^3*x^4 + 2*a^9*b^2*c^5*d^4*x^4 - 3*a^7*b^4*c^6*d^3*x^7 + 2*a^8*b^3*c^5*d^4*x^7 - 3*a^8*b^3*c^7*d^2*x + 2*a^9*b^2*c^6*d^3*x + a^6*b^5*c^8*d*x^4 + a^5*b^6*c^8*d*x^7)) + (3*a^2*d^2*x*(c + d*x^3)^(1/2))/(a^2*b^2*c^4*x^4 + 2*a^4*c^2*d^2*x^4 + a^3*b*c^4*x + 2*a^4*c^3*d*x + 3*a^3*b*c^3*d*x^4 + a^2*b^2*c^3*d*x^7 + 2*a^3*b*c^2*d^2*x^7) + (2*b^2*c^2*x*(c + d*x^3)^(1/2))/(a^2*b^2*c^4*x^4 + 2*a^4*c^2*d^2*x^4 + a^3*b*c^4*x + 2*a^4*c^3*d*x + 3*a^3*b*c^3*d*x^4 + a^2*b^2*c^3*d*x^7 + 2*a^3*b*c^2*d^2*x^7) - (b^(7/2)*c*log((a^6*b^(15/2)*c^10*36i)/(a*(a*d - b*c)^(1/2) + b*x^3*(a*d - b*c)^(1/2)) - (a^7*b^(13/2)*c^9*d*198i)/(a*(a*d - b*c)^(1/2) + b*x^3*(a*d - b*c)^(1/2)) + (a^12*b^(3/2)*c^4*d^6*18i)/(a*(a*d - b*c)^(1/2) + b*x^3*(a*d - b*c)^(1/2)) - (a^11*b^(5/2)*c^5*d^5*126i)/(a*(a*d - b*c)^(1/2) + b*x^3*(a*d - b*c)^(1/2)) + (a^10*b^(7/2)*c^6*d^4*360i)/(a*(a*d - b*c)^(1/2) + b*x^3*(a*d - b*c)^(1/2)) - (a^9*b^(9/2)*c^7*d^3*540i)/(a*(a*d - b*c)^(1/2) + b*x^3*(a*d - b*c)^(1/2)) + (a^8*b^(11/2)*c^8*d^2*450i)/(a*(a*d - b*c)^(1/2) + b*x^3*(a*d - b*c)^(1/2)) + (a^6*b^(15/2)*c^9*d*x^3*18i)/(a*(a*d - b*c)^(1/2) + b*x^3*(a*d - b*c)^(1/2)) - (a^11*b^(5/2)*c^4*d^6*x^3*18i)/(a*(a*d - b*c)^(1/2) + b*x^3*(a*d - b*c)^(1/2)) + (a^10*b^(7/2)*c^5*d^5*x^3*90i)/(a*(a*d - b*c)^(1/2) + b*x^3*(a*d - b*c)^(1/2)) - (a^9*b^(9/2)*c^6*d^4*x^3*180i)/(a*(a*d - b*c)^(1/2) + b*x^3*(a*d - b*c)^(1/2)) + (a^8*b^(11/2)*c^7*d^3*x^3*180i)/(a*(a*d - b*c)^(1/2) + b*x^3*(a*d - b*c)^(1/2)) - (a^7*b^(13/2)*c^8*d^2*x^3*90i)/(a*(a*d - b*c)^(1/2) + b*x^3*(a*d - b*c)^(1/2)) + (36*a^6*b^7*c^9*(c + d*x^3)^(1/2)*(a*d - b*c)^(1/2))/(a*(a*d - b*c)^(1/2) + b*x^3*(a*d - b*c)^(1/2)) + (360*a^8*b^5*c^7*d^2*(c + d*x^3)^(1/2)*(a*d - b*c)^(1/2))/(a*(a*d - b*c)^(1/2) + b*x^3*(a*d - b*c)^(1/2)) - (360*a^9*b^4*c^6*d^3*(c + d*x^3)^(1/2)*(a*d - b*c)^(1/2))/(a*(a*d - b*c)^(1/2) + b*x^3*(a*d - b*c)^(1/2)) + (180*a^10*b^3*c^5*d^4*(c + d*x^3)^(1/2)*(a*d - b*c)^(1/2))/(a*(a*d - b*c)^(1/2) + b*x^3*(a*d - b*c)^(1/2)) - (36*a^11*b^2*c^4*d^5*(c + d*x^3)^(1/2)*(a*d - b*c)^(1/2))/(a*(a*d - b*c)^(1/2) + b*x^3*(a*d - b*c)^(1/2)) - (180*a^7*b^6*c^8*d*(c + d*x^3)^(1/2)*(a*d - b*c)^(1/2))/(a*(a*d - b*c)^(1/2) + b*x^3*(a*d - b*c)^(1/2)))*2i)/(3*a^3*(a*d - b*c)^(5/2)) + (b^(5/2)*d*log((a^6*b^(15/2)*c^10*36i)/(a*(a*d - b*c)^(1/2) + b*x^3*(a*d - b*c)^(1/2)) - (a^7*b^(13/2)*c^9*d*198i)/(a*(a*d - b*c)^(1/2) + b*x^3*(a*d - b*c)^(1/2)) + (a^12*b^(3/2)*c^4*d^6*18i)/(a*(a*d - b*c)^(1/2) + b*x^3*(a*d - b*c)^(1/2)) - (a^11*b^(5/2)*c^5*d^5*126i)/(a*(a*d - b*c)^(1/2) + b*x^3*(a*d - b*c)^(1/2)) + (a^10*b^(7/2)*c^6*d^4*360i)/(a*(a*d - b*c)^(1/2) + b*x^3*(a*d - b*c)^(1/2)) - (a^9*b^(9/2)*c^7*d^3*540i)/(a*(a*d - b*c)^(1/2) + b*x^3*(a*d - b*c)^(1/2)) + (a^8*b^(11/2)*c^8*d^2*450i)/(a*(a*d - b*c)^(1/2) + b*x^3*(a*d - b*c)^(1/2)) + (a^6*b^(15/2)*c^9*d*x^3*18i)/(a*(a*d - b*c)^(1/2) + b*x^3*(a*d - b*c)^(1/2)) - (a^11*b^(5/2)*c^4*d^6*x^3*18i)/(a*(a*d - b*c)^(1/2) + b*x^3*(a*d - b*c)^(1/2)) + (a^10*b^(7/2)*c^5*d^5*x^3*90i)/(a*(a*d - b*c)^(1/2) + b*x^3*(a*d - b*c)^(1/2)) - (a^9*b^(9/2)*c^6*d^4*x^3*180i)/(a*(a*d - b*c)^(1/2) + b*x^3*(a*d - b*c)^(1/2)) + (a^8*b^(11/2)*c^7*d^3*x^3*180i)/(a*(a*d - b*c)^(1/2) + b*x^3*(a*d - b*c)^(1/2)) - (a^7*b^(13/2)*c^8*d^2*x^3*90i)/(a*(a*d - b*c)^(1/2) + b*x^3*(a*d - b*c)^(1/2)) + (36*a^6*b^7*c^9*(c + d*x^3)^(1/2)*(a*d - b*c)^(1/2))/(a*(a*d - b*c)^(1/2) + b*x^3*(a*d - b*c)^(1/2)) + (360*a^8*b^5*c^7*d^2*(c + d*x^3)^(1/2)*(a*d - b*c)^(1/2))/(a*(a*d - b*c)^(1/2) + b*x^3*(a*d - b*c)^(1/2)) - (360*a^9*b^4*c^6*d^3*(c + d*x^3)^(1/2)*(a*d - b*c)^(1/2))/(a*(a*d - b*c)^(1/2) + b*x^3*(a*d - b*c)^(1/2)) + (180*a^10*b^3*c^5*d^4*(c + d*x^3)^(1/2)*(a*d - b*c)^(1/2))/(a*(a*d - b*c)^(1/2) + b*x^3*(a*d - b*c)^(1/2)) - (36*a^11*b^2*c^4*d^5*(c + d*x^3)^(1/2)*(a*d - b*c)^(1/2))/(a*(a*d - b*c)^(1/2) + b*x^3*(a*d - b*c)^(1/2)) - (180*a^7*b^6*c^8*d*(c + d*x^3)^(1/2)*(a*d - b*c)^(1/2))/(a*(a*d - b*c)^(1/2) + b*x^3*(a*d - b*c)^(1/2)))*7i)/(6*a^2*(a*d - b*c)^(5/2)) + (5*a^4*d^4*x^4*(c + d*x^3)^(1/2))/(2*(a^4*b^2*c^6*x + a^3*b^3*c^6*x^4 + 2*a^5*b*c^5*d*x + 2*a^4*b^2*c^4*d^2*x^7 + 3*a^4*b^2*c^5*d*x^4 + 2*a^5*b*c^4*d^2*x^4 + a^3*b^3*c^5*d*x^7)) - (65*a^3*d^3*x^4*(c + d*x^3)^(1/2))/(24*(a^3*b^2*c^5*x^4 + 2*a^5*c^3*d^2*x^4 + a^4*b*c^5*x + 2*a^5*c^4*d*x + 3*a^4*b*c^4*d*x^4 + a^3*b^2*c^4*d*x^7 + 2*a^4*b*c^3*d^2*x^7)) - (8*b^3*c^3*x^4*(c + d*x^3)^(1/2))/(3*(a^3*b^2*c^5*x^4 + 2*a^5*c^3*d^2*x^4 + a^4*b*c^5*x + 2*a^5*c^4*d*x + 3*a^4*b*c^4*d*x^4 + a^3*b^2*c^4*d*x^7 + 2*a^4*b*c^3*d^2*x^7)) + (14*b^3*c^4*x^4*(c + d*x^3)^(1/2))/(a^3*b^2*c^6*x^4 + 2*a^5*c^4*d^2*x^4 + a^4*b*c^6*x + 2*a^5*c^5*d*x + 3*a^4*b*c^5*d*x^4 + a^3*b^2*c^5*d*x^7 + 2*a^4*b*c^4*d^2*x^7) - (5*a^7*c^2*d^5*x*(c + d*x^3)^(1/2))/(2*(a^5*b^4*c^9*x + a^4*b^5*c^9*x^4 - 3*a^6*b^3*c^7*d^2*x^4 - a^7*b^2*c^6*d^3*x^4 - 3*a^6*b^3*c^6*d^3*x^7 + 2*a^7*b^2*c^5*d^4*x^7 + 2*a^8*b*c^6*d^3*x - 3*a^7*b^2*c^7*d^2*x + a^5*b^4*c^8*d*x^4 + 2*a^8*b*c^5*d^4*x^4 + a^4*b^5*c^8*d*x^7)) - (5*a^7*c*d^6*x^4*(c + d*x^3)^(1/2))/(2*(a^5*b^4*c^9*x + a^4*b^5*c^9*x^4 - 3*a^6*b^3*c^7*d^2*x^4 - a^7*b^2*c^6*d^3*x^4 - 3*a^6*b^3*c^6*d^3*x^7 + 2*a^7*b^2*c^5*d^4*x^7 + 2*a^8*b*c^6*d^3*x - 3*a^7*b^2*c^7*d^2*x + a^5*b^4*c^8*d*x^4 + 2*a^8*b*c^5*d^4*x^4 + a^4*b^5*c^8*d*x^7)) - (3*a^8*c^2*d^5*x*(c + d*x^3)^(1/2))/(8*(a^6*b^4*c^9*x + a^5*b^5*c^9*x^4 - 3*a^7*b^3*c^7*d^2*x^4 - a^8*b^2*c^6*d^3*x^4 - 3*a^7*b^3*c^6*d^3*x^7 + 2*a^8*b^2*c^5*d^4*x^7 + 2*a^9*b*c^6*d^3*x - 3*a^8*b^2*c^7*d^2*x + a^6*b^4*c^8*d*x^4 + 2*a^9*b*c^5*d^4*x^4 + a^5*b^5*c^8*d*x^7)) - (3*a^8*c*d^6*x^4*(c + d*x^3)^(1/2))/(8*(a^6*b^4*c^9*x + a^5*b^5*c^9*x^4 - 3*a^7*b^3*c^7*d^2*x^4 - a^8*b^2*c^6*d^3*x^4 - 3*a^7*b^3*c^6*d^3*x^7 + 2*a^8*b^2*c^5*d^4*x^7 + 2*a^9*b*c^6*d^3*x - 3*a^8*b^2*c^7*d^2*x + a^6*b^4*c^8*d*x^4 + 2*a^9*b*c^5*d^4*x^4 + a^5*b^5*c^8*d*x^7)) + (23*a^9*c^3*d^5*x*(c + d*x^3)^(1/2))/(8*(a^7*b^4*c^10*x + a^6*b^5*c^10*x^4 - 3*a^8*b^3*c^8*d^2*x^4 - a^9*b^2*c^7*d^3*x^4 - 3*a^8*b^3*c^7*d^3*x^7 + 2*a^9*b^2*c^6*d^4*x^7 + 2*a^10*b*c^7*d^3*x - 3*a^9*b^2*c^8*d^2*x + a^7*b^4*c^9*d*x^4 + 2*a^10*b*c^6*d^4*x^4 + a^6*b^5*c^9*d*x^7)) - (a*b^6*c^9*x*(c + d*x^3)^(1/2))/(2*(2*a^9*c^6*d^5*x + 2*a^9*c^5*d^6*x^4 + a^5*b^4*c^9*d^2*x^4 + a^6*b^3*c^8*d^3*x^4 - 3*a^7*b^2*c^7*d^4*x^4 + a^5*b^4*c^8*d^3*x^7 - 3*a^7*b^2*c^6*d^5*x^7 - 3*a^8*b*c^7*d^4*x + a^6*b^3*c^9*d^2*x - a^8*b*c^6*d^5*x^4 + 2*a^8*b*c^5*d^6*x^7)) + (3*a^2*b^6*c^9*x^4*(c + d*x^3)^(1/2))/(4*(2*a^10*c^7*d^4*x + 2*a^10*c^6*d^5*x^4 + a^7*b^3*c^9*d^2*x^4 - 3*a^8*b^2*c^8*d^3*x^4 + a^6*b^4*c^9*d^2*x^7 - 3*a^8*b^2*c^7*d^4*x^7 + a^7*b^3*c^10*d*x - 3*a^9*b*c^8*d^3*x + a^6*b^4*c^10*d*x^4 - a^9*b*c^7*d^4*x^4 + 2*a^9*b*c^6*d^5*x^7)) - (5*a^6*c^2*d^3*x*(c + d*x^3)^(1/2))/(2*(a^6*b^2*c^7*x + a^5*b^3*c^7*x^4 + 2*a^7*b*c^6*d*x + 2*a^6*b^2*c^5*d^2*x^7 + 3*a^6*b^2*c^6*d*x^4 + 2*a^7*b*c^5*d^2*x^4 + a^5*b^3*c^6*d*x^7)) - (5*a^6*c*d^4*x^4*(c + d*x^3)^(1/2))/(2*(a^6*b^2*c^7*x + a^5*b^3*c^7*x^4 + 2*a^7*b*c^6*d*x + 2*a^6*b^2*c^5*d^2*x^7 + 3*a^6*b^2*c^6*d*x^4 + 2*a^7*b*c^5*d^2*x^4 + a^5*b^3*c^6*d*x^7)) + (4*a^2*b^4*c^6*x*(c + d*x^3)^(1/2))/(a^5*b^3*c^8*x + 2*a^8*c^5*d^3*x + a^4*b^4*c^8*x^4 + 2*a^8*c^4*d^4*x^4 - 3*a^6*b^2*c^6*d^2*x^4 - 3*a^6*b^2*c^5*d^3*x^7 - 3*a^7*b*c^6*d^2*x + a^5*b^3*c^7*d*x^4 - a^7*b*c^5*d^3*x^4 + a^4*b^4*c^7*d*x^7 + 2*a^7*b*c^4*d^4*x^7) + (8*a*b^5*c^6*x^4*(c + d*x^3)^(1/2))/(3*(a^5*b^3*c^8*x + 2*a^8*c^5*d^3*x + a^4*b^4*c^8*x^4 + 2*a^8*c^4*d^4*x^4 - 3*a^6*b^2*c^6*d^2*x^4 - 3*a^6*b^2*c^5*d^3*x^7 - 3*a^7*b*c^6*d^2*x + a^5*b^3*c^7*d*x^4 - a^7*b*c^5*d^3*x^4 + a^4*b^4*c^7*d*x^7 + 2*a^7*b*c^4*d^4*x^7)) - (14*a^2*b^4*c^7*x*(c + d*x^3)^(1/2))/(a^5*b^3*c^9*x + 2*a^8*c^6*d^3*x + a^4*b^4*c^9*x^4 + 2*a^8*c^5*d^4*x^4 - 3*a^6*b^2*c^7*d^2*x^4 - 3*a^6*b^2*c^6*d^3*x^7 - 3*a^7*b*c^7*d^2*x + a^5*b^3*c^8*d*x^4 - a^7*b*c^6*d^3*x^4 + a^4*b^4*c^8*d*x^7 + 2*a^7*b*c^5*d^4*x^7) - (14*a*b^5*c^7*x^4*(c + d*x^3)^(1/2))/(a^5*b^3*c^9*x + 2*a^8*c^6*d^3*x + a^4*b^4*c^9*x^4 + 2*a^8*c^5*d^4*x^4 - 3*a^6*b^2*c^7*d^2*x^4 - 3*a^6*b^2*c^6*d^3*x^7 - 3*a^7*b*c^7*d^2*x + a^5*b^3*c^8*d*x^4 - a^7*b*c^6*d^3*x^4 + a^4*b^4*c^8*d*x^7 + 2*a^7*b*c^5*d^4*x^7) + (a^3*b^4*c^7*x*(c + d*x^3)^(1/2))/(8*(a^6*b^3*c^9*x + 2*a^9*c^6*d^3*x + a^5*b^4*c^9*x^4 + 2*a^9*c^5*d^4*x^4 - 3*a^7*b^2*c^7*d^2*x^4 - 3*a^7*b^2*c^6*d^3*x^7 - 3*a^8*b*c^7*d^2*x + a^6*b^3*c^8*d*x^4 - a^8*b*c^6*d^3*x^4 + a^5*b^4*c^8*d*x^7 + 2*a^8*b*c^5*d^4*x^7)) + (269*a^4*b^4*c^8*x*(c + d*x^3)^(1/2))/(24*(a^7*b^3*c^10*x + 2*a^10*c^7*d^3*x + a^6*b^4*c^10*x^4 + 2*a^10*c^6*d^4*x^4 - 3*a^8*b^2*c^8*d^2*x^4 - 3*a^8*b^2*c^7*d^3*x^7 - 3*a^9*b*c^8*d^2*x + a^7*b^3*c^9*d*x^4 - a^9*b*c^7*d^3*x^4 + a^6*b^4*c^9*d*x^7 + 2*a^9*b*c^6*d^4*x^7)) + (65*a^6*c^2*d^4*x*(c + d*x^3)^(1/2))/(8*(a^5*b^3*c^8*x + 2*a^8*c^5*d^3*x + a^4*b^4*c^8*x^4 + 2*a^8*c^4*d^4*x^4 - 3*a^6*b^2*c^6*d^2*x^4 - 3*a^6*b^2*c^5*d^3*x^7 - 3*a^7*b*c^6*d^2*x + a^5*b^3*c^7*d*x^4 - a^7*b*c^5*d^3*x^4 + a^4*b^4*c^7*d*x^7 + 2*a^7*b*c^4*d^4*x^7)) + (65*a^6*c*d^5*x^4*(c + d*x^3)^(1/2))/(24*(a^5*b^3*c^8*x + 2*a^8*c^5*d^3*x + a^4*b^4*c^8*x^4 + 2*a^8*c^4*d^4*x^4 - 3*a^6*b^2*c^6*d^2*x^4 - 3*a^6*b^2*c^5*d^3*x^7 - 3*a^7*b*c^6*d^2*x + a^5*b^3*c^7*d*x^4 - a^7*b*c^5*d^3*x^4 + a^4*b^4*c^7*d*x^7 + 2*a^7*b*c^4*d^4*x^7)) - (41*a^6*c^3*d^4*x*(c + d*x^3)^(1/2))/(3*(a^5*b^3*c^9*x + 2*a^8*c^6*d^3*x + a^4*b^4*c^9*x^4 + 2*a^8*c^5*d^4*x^4 - 3*a^6*b^2*c^7*d^2*x^4 - 3*a^6*b^2*c^6*d^3*x^7 - 3*a^7*b*c^7*d^2*x + a^5*b^3*c^8*d*x^4 - a^7*b*c^6*d^3*x^4 + a^4*b^4*c^8*d*x^7 + 2*a^7*b*c^5*d^4*x^7)) - (5*a^7*c^3*d^4*x*(c + d*x^3)^(1/2))/(8*(a^6*b^3*c^9*x + 2*a^9*c^6*d^3*x + a^5*b^4*c^9*x^4 + 2*a^9*c^5*d^4*x^4 - 3*a^7*b^2*c^7*d^2*x^4 - 3*a^7*b^2*c^6*d^3*x^7 - 3*a^8*b*c^7*d^2*x + a^6*b^3*c^8*d*x^4 - a^8*b*c^6*d^3*x^4 + a^5*b^4*c^8*d*x^7 + 2*a^8*b*c^5*d^4*x^7)) + (47*a^8*c^4*d^4*x*(c + d*x^3)^(1/2))/(6*(a^7*b^3*c^10*x + 2*a^10*c^7*d^3*x + a^6*b^4*c^10*x^4 + 2*a^10*c^6*d^4*x^4 - 3*a^8*b^2*c^8*d^2*x^4 - 3*a^8*b^2*c^7*d^3*x^7 - 3*a^9*b*c^8*d^2*x + a^7*b^3*c^9*d*x^4 - a^9*b*c^7*d^3*x^4 + a^6*b^4*c^9*d*x^7 + 2*a^9*b*c^6*d^4*x^7)) - (34*a^3*b^2*c^5*x*(c + d*x^3)^(1/2))/(3*(a^5*b^2*c^7*x^4 + 2*a^7*c^5*d^2*x^4 + a^6*b*c^7*x + 2*a^7*c^6*d*x + 3*a^6*b*c^6*d*x^4 + a^5*b^2*c^6*d*x^7 + 2*a^6*b*c^5*d^2*x^7)) + (47*a^3*c^2*d^2*x*(c + d*x^3)^(1/2))/(3*(a^3*b^2*c^6*x^4 + 2*a^5*c^4*d^2*x^4 + a^4*b*c^6*x + 2*a^5*c^5*d*x + 3*a^4*b*c^5*d*x^4 + a^3*b^2*c^5*d*x^7 + 2*a^4*b*c^4*d^2*x^7)) + (38*a^3*c*d^3*x^4*(c + d*x^3)^(1/2))/(3*(a^3*b^2*c^6*x^4 + 2*a^5*c^4*d^2*x^4 + a^4*b*c^6*x + 2*a^5*c^5*d*x + 3*a^4*b*c^5*d*x^4 + a^3*b^2*c^5*d*x^7 + 2*a^4*b*c^4*d^2*x^7)) - (257*a^5*c^3*d^2*x*(c + d*x^3)^(1/2))/(24*(a^5*b^2*c^7*x^4 + 2*a^7*c^5*d^2*x^4 + a^6*b*c^7*x + 2*a^7*c^6*d*x + 3*a^6*b*c^6*d*x^4 + a^5*b^2*c^6*d*x^7 + 2*a^6*b*c^5*d^2*x^7)) - (5*a^9*c*d^6*x*(c + d*x^3)^(1/2))/(4*(a^6*b^5*c^9*x + a^5*b^6*c^9*x^4 - 3*a^7*b^4*c^7*d^2*x^4 - a^8*b^3*c^6*d^3*x^4 + 2*a^9*b^2*c^5*d^4*x^4 - 3*a^7*b^4*c^6*d^3*x^7 + 2*a^8*b^3*c^5*d^4*x^7 - 3*a^8*b^3*c^7*d^2*x + 2*a^9*b^2*c^6*d^3*x + a^6*b^5*c^8*d*x^4 + a^5*b^6*c^8*d*x^7)) + (23*a^9*c^2*d^6*x^4*(c + d*x^3)^(1/2))/(8*(a^7*b^4*c^10*x + a^6*b^5*c^10*x^4 - 3*a^8*b^3*c^8*d^2*x^4 - a^9*b^2*c^7*d^3*x^4 - 3*a^8*b^3*c^7*d^3*x^7 + 2*a^9*b^2*c^6*d^4*x^7 + 2*a^10*b*c^7*d^3*x - 3*a^9*b^2*c^8*d^2*x + a^7*b^4*c^9*d*x^4 + 2*a^10*b*c^6*d^4*x^4 + a^6*b^5*c^9*d*x^7)) + (a^2*b^6*c^10*x*(c + d*x^3)^(1/2))/(2*(2*a^10*c^7*d^5*x + 2*a^10*c^6*d^6*x^4 + a^6*b^4*c^10*d^2*x^4 + a^7*b^3*c^9*d^3*x^4 - 3*a^8*b^2*c^8*d^4*x^4 + a^6*b^4*c^9*d^3*x^7 - 3*a^8*b^2*c^7*d^5*x^7 - 3*a^9*b*c^8*d^4*x + a^7*b^3*c^10*d^2*x - a^9*b*c^7*d^5*x^4 + 2*a^9*b*c^6*d^6*x^7)) + (a*b^7*c^10*x^4*(c + d*x^3)^(1/2))/(2*(2*a^10*c^7*d^5*x + 2*a^10*c^6*d^6*x^4 + a^6*b^4*c^10*d^2*x^4 + a^7*b^3*c^9*d^3*x^4 - 3*a^8*b^2*c^8*d^4*x^4 + a^6*b^4*c^9*d^3*x^7 - 3*a^8*b^2*c^7*d^5*x^7 - 3*a^9*b*c^8*d^4*x + a^7*b^3*c^10*d^2*x - a^9*b*c^7*d^5*x^4 + 2*a^9*b*c^6*d^6*x^7)) + (a^2*b^5*c^7*x^4*(c + d*x^3)^(1/2))/(8*(a^6*b^3*c^9*x + 2*a^9*c^6*d^3*x + a^5*b^4*c^9*x^4 + 2*a^9*c^5*d^4*x^4 - 3*a^7*b^2*c^7*d^2*x^4 - 3*a^7*b^2*c^6*d^3*x^7 - 3*a^8*b*c^7*d^2*x + a^6*b^3*c^8*d*x^4 - a^8*b*c^6*d^3*x^4 + a^5*b^4*c^8*d*x^7 + 2*a^8*b*c^5*d^4*x^7)) + (269*a^3*b^5*c^8*x^4*(c + d*x^3)^(1/2))/(24*(a^7*b^3*c^10*x + 2*a^10*c^7*d^3*x + a^6*b^4*c^10*x^4 + 2*a^10*c^6*d^4*x^4 - 3*a^8*b^2*c^8*d^2*x^4 - 3*a^8*b^2*c^7*d^3*x^7 - 3*a^9*b*c^8*d^2*x + a^7*b^3*c^9*d*x^4 - a^9*b*c^7*d^3*x^4 + a^6*b^4*c^9*d*x^7 + 2*a^9*b*c^6*d^4*x^7)) - (26*a^6*c^2*d^5*x^4*(c + d*x^3)^(1/2))/(3*(a^5*b^3*c^9*x + 2*a^8*c^6*d^3*x + a^4*b^4*c^9*x^4 + 2*a^8*c^5*d^4*x^4 - 3*a^6*b^2*c^7*d^2*x^4 - 3*a^6*b^2*c^6*d^3*x^7 - 3*a^7*b*c^7*d^2*x + a^5*b^3*c^8*d*x^4 - a^7*b*c^6*d^3*x^4 + a^4*b^4*c^8*d*x^7 + 2*a^7*b*c^5*d^4*x^7)) - (5*a^7*c^2*d^5*x^4*(c + d*x^3)^(1/2))/(8*(a^6*b^3*c^9*x + 2*a^9*c^6*d^3*x + a^5*b^4*c^9*x^4 + 2*a^9*c^5*d^4*x^4 - 3*a^7*b^2*c^7*d^2*x^4 - 3*a^7*b^2*c^6*d^3*x^7 - 3*a^8*b*c^7*d^2*x + a^6*b^3*c^8*d*x^4 - a^8*b*c^6*d^3*x^4 + a^5*b^4*c^8*d*x^7 + 2*a^8*b*c^5*d^4*x^7)) + (79*a^8*c^3*d^5*x^4*(c + d*x^3)^(1/2))/(12*(a^7*b^3*c^10*x + 2*a^10*c^7*d^3*x + a^6*b^4*c^10*x^4 + 2*a^10*c^6*d^4*x^4 - 3*a^8*b^2*c^8*d^2*x^4 - 3*a^8*b^2*c^7*d^3*x^7 - 3*a^9*b*c^8*d^2*x + a^7*b^3*c^9*d*x^4 - a^9*b*c^7*d^3*x^4 + a^6*b^4*c^9*d*x^7 + 2*a^9*b*c^6*d^4*x^7)) - (34*a^2*b^3*c^5*x^4*(c + d*x^3)^(1/2))/(3*(a^5*b^2*c^7*x^4 + 2*a^7*c^5*d^2*x^4 + a^6*b*c^7*x + 2*a^7*c^6*d*x + 3*a^6*b*c^6*d*x^4 + a^5*b^2*c^6*d*x^7 + 2*a^6*b*c^5*d^2*x^7)) - (239*a^5*c^2*d^3*x^4*(c + d*x^3)^(1/2))/(24*(a^5*b^2*c^7*x^4 + 2*a^7*c^5*d^2*x^4 + a^6*b*c^7*x + 2*a^7*c^6*d*x + 3*a^6*b*c^6*d*x^4 + a^5*b^2*c^6*d*x^7 + 2*a^6*b*c^5*d^2*x^7)) - (3*a^2*b^5*c^8*x*(c + d*x^3)^(1/2))/(4*(2*a^9*c^6*d^4*x + 2*a^9*c^5*d^5*x^4 + a^6*b^3*c^8*d^2*x^4 - 3*a^7*b^2*c^7*d^3*x^4 + a^5*b^4*c^8*d^2*x^7 - 3*a^7*b^2*c^6*d^4*x^7 + a^6*b^3*c^9*d*x - 3*a^8*b*c^7*d^3*x + a^5*b^4*c^9*d*x^4 - a^8*b*c^6*d^4*x^4 + 2*a^8*b*c^5*d^5*x^7)) - (3*a*b^6*c^8*x^4*(c + d*x^3)^(1/2))/(4*(2*a^9*c^6*d^4*x + 2*a^9*c^5*d^5*x^4 + a^6*b^3*c^8*d^2*x^4 - 3*a^7*b^2*c^7*d^3*x^4 + a^5*b^4*c^8*d^2*x^7 - 3*a^7*b^2*c^6*d^4*x^7 + a^6*b^3*c^9*d*x - 3*a^8*b*c^7*d^3*x + a^5*b^4*c^9*d*x^4 - a^8*b*c^6*d^4*x^4 + 2*a^8*b*c^5*d^5*x^7)) + (3*a^3*b^5*c^9*x*(c + d*x^3)^(1/2))/(4*(2*a^10*c^7*d^4*x + 2*a^10*c^6*d^5*x^4 + a^7*b^3*c^9*d^2*x^4 - 3*a^8*b^2*c^8*d^3*x^4 + a^6*b^4*c^9*d^2*x^7 - 3*a^8*b^2*c^7*d^4*x^7 + a^7*b^3*c^10*d*x - 3*a^9*b*c^8*d^3*x + a^6*b^4*c^10*d*x^4 - a^9*b*c^7*d^4*x^4 + 2*a^9*b*c^6*d^5*x^7)) + (5*a^4*c*d^3*x*(c + d*x^3)^(1/2))/(2*(a^4*b^2*c^6*x + a^3*b^3*c^6*x^4 + 2*a^5*b*c^5*d*x + 2*a^4*b^2*c^4*d^2*x^7 + 3*a^4*b^2*c^5*d*x^4 + 2*a^5*b*c^4*d^2*x^4 + a^3*b^3*c^5*d*x^7)) - (8*a*b^4*c^5*x*(c + d*x^3)^(1/2))/(3*(a^4*b^3*c^7*x + 2*a^7*c^4*d^3*x + a^3*b^4*c^7*x^4 + 2*a^7*c^3*d^4*x^4 - 3*a^5*b^2*c^5*d^2*x^4 - 3*a^5*b^2*c^4*d^3*x^7 - 3*a^6*b*c^5*d^2*x + a^4*b^3*c^6*d*x^4 - a^6*b*c^4*d^3*x^4 + a^3*b^4*c^6*d*x^7 + 2*a^6*b*c^3*d^4*x^7)) - (5*a^5*c*d^4*x*(c + d*x^3)^(1/2))/(a^4*b^3*c^7*x + 2*a^7*c^4*d^3*x + a^3*b^4*c^7*x^4 + 2*a^7*c^3*d^4*x^4 - 3*a^5*b^2*c^5*d^2*x^4 - 3*a^5*b^2*c^4*d^3*x^7 - 3*a^6*b*c^5*d^2*x + a^4*b^3*c^6*d*x^4 - a^6*b*c^4*d^3*x^4 + a^3*b^4*c^6*d*x^7 + 2*a^6*b*c^3*d^4*x^7) + (5*a^10*c^2*d^6*x*(c + d*x^3)^(1/2))/(4*(a^7*b^5*c^10*x + a^6*b^6*c^10*x^4 - 3*a^8*b^4*c^8*d^2*x^4 - a^9*b^3*c^7*d^3*x^4 + 2*a^10*b^2*c^6*d^4*x^4 - 3*a^8*b^4*c^7*d^3*x^7 + 2*a^9*b^3*c^6*d^4*x^7 - 3*a^9*b^3*c^8*d^2*x + 2*a^10*b^2*c^7*d^3*x + a^7*b^5*c^9*d*x^4 + a^6*b^6*c^9*d*x^7)) + (5*a^10*c*d^7*x^4*(c + d*x^3)^(1/2))/(4*(a^7*b^5*c^10*x + a^6*b^6*c^10*x^4 - 3*a^8*b^4*c^8*d^2*x^4 - a^9*b^3*c^7*d^3*x^4 + 2*a^10*b^2*c^6*d^4*x^4 - 3*a^8*b^4*c^7*d^3*x^7 + 2*a^9*b^3*c^6*d^4*x^7 - 3*a^9*b^3*c^8*d^2*x + 2*a^10*b^2*c^7*d^3*x + a^7*b^5*c^9*d*x^4 + a^6*b^6*c^9*d*x^7)) - (11*a*b^2*c^3*x*(c + d*x^3)^(1/2))/(3*(a^3*b^2*c^5*x^4 + 2*a^5*c^3*d^2*x^4 + a^4*b*c^5*x + 2*a^5*c^4*d*x + 3*a^4*b*c^4*d*x^4 + a^3*b^2*c^4*d*x^7 + 2*a^4*b*c^3*d^2*x^7)) + (14*a*b^2*c^4*x*(c + d*x^3)^(1/2))/(a^3*b^2*c^6*x^4 + 2*a^5*c^4*d^2*x^4 + a^4*b*c^6*x + 2*a^5*c^5*d*x + 3*a^4*b*c^5*d*x^4 + a^3*b^2*c^5*d*x^7 + 2*a^4*b*c^4*d^2*x^7) + (11*a*b*d^2*x^4*(c + d*x^3)^(1/2))/(2*(a^2*b^2*c^4*x^4 + 2*a^4*c^2*d^2*x^4 + a^3*b*c^4*x + 2*a^4*c^3*d*x + 3*a^3*b*c^3*d*x^4 + a^2*b^2*c^3*d*x^7 + 2*a^3*b*c^2*d^2*x^7)) - (143*a^3*c*d^2*x*(c + d*x^3)^(1/2))/(24*(a^3*b^2*c^5*x^4 + 2*a^5*c^3*d^2*x^4 + a^4*b*c^5*x + 2*a^5*c^4*d*x + 3*a^4*b*c^4*d*x^4 + a^3*b^2*c^4*d*x^7 + 2*a^4*b*c^3*d^2*x^7)) + (22*b^2*c*d*x^4*(c + d*x^3)^(1/2))/(3*(a^2*b^2*c^4*x^4 + 2*a^4*c^2*d^2*x^4 + a^3*b*c^4*x + 2*a^4*c^3*d*x + 3*a^3*b*c^3*d*x^4 + a^2*b^2*c^3*d*x^7 + 2*a^3*b*c^2*d^2*x^7)) + (11*a^3*b^2*c^3*d^2*x*(c + d*x^3)^(1/2))/(3*(a^4*b^3*c^7*x + 2*a^7*c^4*d^3*x + a^3*b^4*c^7*x^4 + 2*a^7*c^3*d^4*x^4 - 3*a^5*b^2*c^5*d^2*x^4 - 3*a^5*b^2*c^4*d^3*x^7 - 3*a^6*b*c^5*d^2*x + a^4*b^3*c^6*d*x^4 - a^6*b*c^4*d^3*x^4 + a^3*b^4*c^6*d*x^7 + 2*a^6*b*c^3*d^4*x^7)) - (31*a^4*b^2*c^4*d^2*x*(c + d*x^3)^(1/2))/(2*(a^5*b^3*c^8*x + 2*a^8*c^5*d^3*x + a^4*b^4*c^8*x^4 + 2*a^8*c^4*d^4*x^4 - 3*a^6*b^2*c^6*d^2*x^4 - 3*a^6*b^2*c^5*d^3*x^7 - 3*a^7*b*c^6*d^2*x + a^5*b^3*c^7*d*x^4 - a^7*b*c^5*d^3*x^4 + a^4*b^4*c^7*d*x^7 + 2*a^7*b*c^4*d^4*x^7)) + (28*a^2*b^4*c^5*d*x^4*(c + d*x^3)^(1/2))/(3*(a^5*b^3*c^8*x + 2*a^8*c^5*d^3*x + a^4*b^4*c^8*x^4 + 2*a^8*c^4*d^4*x^4 - 3*a^6*b^2*c^6*d^2*x^4 - 3*a^6*b^2*c^5*d^3*x^7 - 3*a^7*b*c^6*d^2*x + a^5*b^3*c^7*d*x^4 - a^7*b*c^5*d^3*x^4 + a^4*b^4*c^7*d*x^7 + 2*a^7*b*c^4*d^4*x^7)) + (29*a^5*b*c^2*d^4*x^4*(c + d*x^3)^(1/2))/(3*(a^5*b^3*c^8*x + 2*a^8*c^5*d^3*x + a^4*b^4*c^8*x^4 + 2*a^8*c^4*d^4*x^4 - 3*a^6*b^2*c^6*d^2*x^4 - 3*a^6*b^2*c^5*d^3*x^7 - 3*a^7*b*c^6*d^2*x + a^5*b^3*c^7*d*x^4 - a^7*b*c^5*d^3*x^4 + a^4*b^4*c^7*d*x^7 + 2*a^7*b*c^4*d^4*x^7)) + (23*a^4*b^2*c^5*d^2*x*(c + d*x^3)^(1/2))/(3*(a^5*b^3*c^9*x + 2*a^8*c^6*d^3*x + a^4*b^4*c^9*x^4 + 2*a^8*c^5*d^4*x^4 - 3*a^6*b^2*c^7*d^2*x^4 - 3*a^6*b^2*c^6*d^3*x^7 - 3*a^7*b*c^7*d^2*x + a^5*b^3*c^8*d*x^4 - a^7*b*c^6*d^3*x^4 + a^4*b^4*c^8*d*x^7 + 2*a^7*b*c^5*d^4*x^7)) + (7*a^2*b^4*c^6*d*x^4*(c + d*x^3)^(1/2))/(3*(a^5*b^3*c^9*x + 2*a^8*c^6*d^3*x + a^4*b^4*c^9*x^4 + 2*a^8*c^5*d^4*x^4 - 3*a^6*b^2*c^7*d^2*x^4 - 3*a^6*b^2*c^6*d^3*x^7 - 3*a^7*b*c^7*d^2*x + a^5*b^3*c^8*d*x^4 - a^7*b*c^6*d^3*x^4 + a^4*b^4*c^8*d*x^7 + 2*a^7*b*c^5*d^4*x^7)) - (7*a^5*b*c^3*d^4*x^4*(c + d*x^3)^(1/2))/(4*(a^5*b^3*c^9*x + 2*a^8*c^6*d^3*x + a^4*b^4*c^9*x^4 + 2*a^8*c^5*d^4*x^4 - 3*a^6*b^2*c^7*d^2*x^4 - 3*a^6*b^2*c^6*d^3*x^7 - 3*a^7*b*c^7*d^2*x + a^5*b^3*c^8*d*x^4 - a^7*b*c^6*d^3*x^4 + a^4*b^4*c^8*d*x^7 + 2*a^7*b*c^5*d^4*x^7)) - (9*a^5*b^2*c^5*d^2*x*(c + d*x^3)^(1/2))/(8*(a^6*b^3*c^9*x + 2*a^9*c^6*d^3*x + a^5*b^4*c^9*x^4 + 2*a^9*c^5*d^4*x^4 - 3*a^7*b^2*c^7*d^2*x^4 - 3*a^7*b^2*c^6*d^3*x^7 - 3*a^8*b*c^7*d^2*x + a^6*b^3*c^8*d*x^4 - a^8*b*c^6*d^3*x^4 + a^5*b^4*c^8*d*x^7 + 2*a^8*b*c^5*d^4*x^7)) - (9*a^3*b^4*c^6*d*x^4*(c + d*x^3)^(1/2))/(8*(a^6*b^3*c^9*x + 2*a^9*c^6*d^3*x + a^5*b^4*c^9*x^4 + 2*a^9*c^5*d^4*x^4 - 3*a^7*b^2*c^7*d^2*x^4 - 3*a^7*b^2*c^6*d^3*x^7 - 3*a^8*b*c^7*d^2*x + a^6*b^3*c^8*d*x^4 - a^8*b*c^6*d^3*x^4 + a^5*b^4*c^8*d*x^7 + 2*a^8*b*c^5*d^4*x^7)) - (9*a^6*b*c^3*d^4*x^4*(c + d*x^3)^(1/2))/(8*(a^6*b^3*c^9*x + 2*a^9*c^6*d^3*x + a^5*b^4*c^9*x^4 + 2*a^9*c^5*d^4*x^4 - 3*a^7*b^2*c^7*d^2*x^4 - 3*a^7*b^2*c^6*d^3*x^7 - 3*a^8*b*c^7*d^2*x + a^6*b^3*c^8*d*x^4 - a^8*b*c^6*d^3*x^4 + a^5*b^4*c^8*d*x^7 + 2*a^8*b*c^5*d^4*x^7)) + (23*a^6*b^2*c^6*d^2*x*(c + d*x^3)^(1/2))/(24*(a^7*b^3*c^10*x + 2*a^10*c^7*d^3*x + a^6*b^4*c^10*x^4 + 2*a^10*c^6*d^4*x^4 - 3*a^8*b^2*c^8*d^2*x^4 - 3*a^8*b^2*c^7*d^3*x^7 - 3*a^9*b*c^8*d^2*x + a^7*b^3*c^9*d*x^4 - a^9*b*c^7*d^3*x^4 + a^6*b^4*c^9*d*x^7 + 2*a^9*b*c^6*d^4*x^7)) - (31*a^4*b^4*c^7*d*x^4*(c + d*x^3)^(1/2))/(8*(a^7*b^3*c^10*x + 2*a^10*c^7*d^3*x + a^6*b^4*c^10*x^4 + 2*a^10*c^6*d^4*x^4 - 3*a^8*b^2*c^8*d^2*x^4 - 3*a^8*b^2*c^7*d^3*x^7 - 3*a^9*b*c^8*d^2*x + a^7*b^3*c^9*d*x^4 - a^9*b*c^7*d^3*x^4 + a^6*b^4*c^9*d*x^7 + 2*a^9*b*c^6*d^4*x^7)) - (21*a^7*b*c^4*d^4*x^4*(c + d*x^3)^(1/2))/(8*(a^7*b^3*c^10*x + 2*a^10*c^7*d^3*x + a^6*b^4*c^10*x^4 + 2*a^10*c^6*d^4*x^4 - 3*a^8*b^2*c^8*d^2*x^4 - 3*a^8*b^2*c^7*d^3*x^7 - 3*a^9*b*c^8*d^2*x + a^7*b^3*c^9*d*x^4 - a^9*b*c^7*d^3*x^4 + a^6*b^4*c^9*d*x^7 + 2*a^9*b*c^6*d^4*x^7)) + (209*a^2*b*c^2*d^2*x^4*(c + d*x^3)^(1/2))/(12*(a^3*b^2*c^6*x^4 + 2*a^5*c^4*d^2*x^4 + a^4*b*c^6*x + 2*a^5*c^5*d*x + 3*a^4*b*c^5*d*x^4 + a^3*b^2*c^5*d*x^7 + 2*a^4*b*c^4*d^2*x^7)) - (89*a^3*b^2*c^4*d*x^4*(c + d*x^3)^(1/2))/(6*(a^5*b^2*c^7*x^4 + 2*a^7*c^5*d^2*x^4 + a^6*b*c^7*x + 2*a^7*c^6*d*x + 3*a^6*b*c^6*d*x^4 + a^5*b^2*c^6*d*x^7 + 2*a^6*b*c^5*d^2*x^7)) - (109*a^4*b*c^3*d^2*x^4*(c + d*x^3)^(1/2))/(12*(a^5*b^2*c^7*x^4 + 2*a^7*c^5*d^2*x^4 + a^6*b*c^7*x + 2*a^7*c^6*d*x + 3*a^6*b*c^6*d*x^4 + a^5*b^2*c^6*d*x^7 + 2*a^6*b*c^5*d^2*x^7)) - (33*a^2*b*c^2*d*x*(c + d*x^3)^(1/2))/(2*(a^3*b^2*c^5*x^4 + 2*a^5*c^3*d^2*x^4 + a^4*b*c^5*x + 2*a^5*c^4*d*x + 3*a^4*b*c^4*d*x^4 + a^3*b^2*c^4*d*x^7 + 2*a^4*b*c^3*d^2*x^7)) + (329*a^2*b*c^3*d*x*(c + d*x^3)^(1/2))/(12*(a^3*b^2*c^6*x^4 + 2*a^5*c^4*d^2*x^4 + a^4*b*c^6*x + 2*a^5*c^5*d*x + 3*a^4*b*c^5*d*x^4 + a^3*b^2*c^5*d*x^7 + 2*a^4*b*c^4*d^2*x^7)) - (205*a^4*b*c^4*d*x*(c + d*x^3)^(1/2))/(12*(a^5*b^2*c^7*x^4 + 2*a^7*c^5*d^2*x^4 + a^6*b*c^7*x + 2*a^7*c^6*d*x + 3*a^6*b*c^6*d*x^4 + a^5*b^2*c^6*d*x^7 + 2*a^6*b*c^5*d^2*x^7)) + (6*a^2*b^3*c^3*d^2*x^4*(c + d*x^3)^(1/2))/(a^4*b^3*c^7*x + 2*a^7*c^4*d^3*x + a^3*b^4*c^7*x^4 + 2*a^7*c^3*d^4*x^4 - 3*a^5*b^2*c^5*d^2*x^4 - 3*a^5*b^2*c^4*d^3*x^7 - 3*a^6*b*c^5*d^2*x + a^4*b^3*c^6*d*x^4 - a^6*b*c^4*d^3*x^4 + a^3*b^4*c^6*d*x^7 + 2*a^6*b*c^3*d^4*x^7) - (a^3*b^2*c^2*d^3*x^4*(c + d*x^3)^(1/2))/(a^4*b^3*c^7*x + 2*a^7*c^4*d^3*x + a^3*b^4*c^7*x^4 + 2*a^7*c^3*d^4*x^4 - 3*a^5*b^2*c^5*d^2*x^4 - 3*a^5*b^2*c^4*d^3*x^7 - 3*a^6*b*c^5*d^2*x + a^4*b^3*c^6*d*x^4 - a^6*b*c^4*d^3*x^4 + a^3*b^4*c^6*d*x^7 + 2*a^6*b*c^3*d^4*x^7) - (19*a^3*b^3*c^4*d^2*x^4*(c + d*x^3)^(1/2))/(3*(a^5*b^3*c^8*x + 2*a^8*c^5*d^3*x + a^4*b^4*c^8*x^4 + 2*a^8*c^4*d^4*x^4 - 3*a^6*b^2*c^6*d^2*x^4 - 3*a^6*b^2*c^5*d^3*x^7 - 3*a^7*b*c^6*d^2*x + a^5*b^3*c^7*d*x^4 - a^7*b*c^5*d^3*x^4 + a^4*b^4*c^7*d*x^7 + 2*a^7*b*c^4*d^4*x^7)) + (10*a^4*b^2*c^3*d^3*x^4*(c + d*x^3)^(1/2))/(3*(a^5*b^3*c^8*x + 2*a^8*c^5*d^3*x + a^4*b^4*c^8*x^4 + 2*a^8*c^4*d^4*x^4 - 3*a^6*b^2*c^6*d^2*x^4 - 3*a^6*b^2*c^5*d^3*x^7 - 3*a^7*b*c^6*d^2*x + a^5*b^3*c^7*d*x^4 - a^7*b*c^5*d^3*x^4 + a^4*b^4*c^7*d*x^7 + 2*a^7*b*c^4*d^4*x^7)) - (a^3*b^3*c^5*d^2*x^4*(c + d*x^3)^(1/2))/(2*(a^5*b^3*c^9*x + 2*a^8*c^6*d^3*x + a^4*b^4*c^9*x^4 + 2*a^8*c^5*d^4*x^4 - 3*a^6*b^2*c^7*d^2*x^4 - 3*a^6*b^2*c^6*d^3*x^7 - 3*a^7*b*c^7*d^2*x + a^5*b^3*c^8*d*x^4 - a^7*b*c^6*d^3*x^4 + a^4*b^4*c^8*d*x^7 + 2*a^7*b*c^5*d^4*x^7)) - (97*a^4*b^2*c^4*d^3*x^4*(c + d*x^3)^(1/2))/(6*(a^5*b^3*c^9*x + 2*a^8*c^6*d^3*x + a^4*b^4*c^9*x^4 + 2*a^8*c^5*d^4*x^4 - 3*a^6*b^2*c^7*d^2*x^4 - 3*a^6*b^2*c^6*d^3*x^7 - 3*a^7*b*c^7*d^2*x + a^5*b^3*c^8*d*x^4 - a^7*b*c^6*d^3*x^4 + a^4*b^4*c^8*d*x^7 + 2*a^7*b*c^5*d^4*x^7)) - (9*a^4*b^3*c^5*d^2*x^4*(c + d*x^3)^(1/2))/(8*(a^6*b^3*c^9*x + 2*a^9*c^6*d^3*x + a^5*b^4*c^9*x^4 + 2*a^9*c^5*d^4*x^4 - 3*a^7*b^2*c^7*d^2*x^4 - 3*a^7*b^2*c^6*d^3*x^7 - 3*a^8*b*c^7*d^2*x + a^6*b^3*c^8*d*x^4 - a^8*b*c^6*d^3*x^4 + a^5*b^4*c^8*d*x^7 + 2*a^8*b*c^5*d^4*x^7)) - (9*a^5*b^2*c^4*d^3*x^4*(c + d*x^3)^(1/2))/(8*(a^6*b^3*c^9*x + 2*a^9*c^6*d^3*x + a^5*b^4*c^9*x^4 + 2*a^9*c^5*d^4*x^4 - 3*a^7*b^2*c^7*d^2*x^4 - 3*a^7*b^2*c^6*d^3*x^7 - 3*a^8*b*c^7*d^2*x + a^6*b^3*c^8*d*x^4 - a^8*b*c^6*d^3*x^4 + a^5*b^4*c^8*d*x^7 + 2*a^8*b*c^5*d^4*x^7)) + (31*a^5*b^3*c^6*d^2*x^4*(c + d*x^3)^(1/2))/(24*(a^7*b^3*c^10*x + 2*a^10*c^7*d^3*x + a^6*b^4*c^10*x^4 + 2*a^10*c^6*d^4*x^4 - 3*a^8*b^2*c^8*d^2*x^4 - 3*a^8*b^2*c^7*d^3*x^7 - 3*a^9*b*c^8*d^2*x + a^7*b^3*c^9*d*x^4 - a^9*b*c^7*d^3*x^4 + a^6*b^4*c^9*d*x^7 + 2*a^9*b*c^6*d^4*x^7)) + (415*a^6*b^2*c^5*d^3*x^4*(c + d*x^3)^(1/2))/(24*(a^7*b^3*c^10*x + 2*a^10*c^7*d^3*x + a^6*b^4*c^10*x^4 + 2*a^10*c^6*d^4*x^4 - 3*a^8*b^2*c^8*d^2*x^4 - 3*a^8*b^2*c^7*d^3*x^7 - 3*a^9*b*c^8*d^2*x + a^7*b^3*c^9*d*x^4 - a^9*b*c^7*d^3*x^4 + a^6*b^4*c^9*d*x^7 + 2*a^9*b*c^6*d^4*x^7)) + (11*a*b*c*d*x*(c + d*x^3)^(1/2))/(2*(a^2*b^2*c^4*x^4 + 2*a^4*c^2*d^2*x^4 + a^3*b*c^4*x + 2*a^4*c^3*d*x + 3*a^3*b*c^3*d*x^4 + a^2*b^2*c^3*d*x^7 + 2*a^3*b*c^2*d^2*x^7)) - (10*a^2*b^3*c^4*d*x*(c + d*x^3)^(1/2))/(3*(a^4*b^3*c^7*x + 2*a^7*c^4*d^3*x + a^3*b^4*c^7*x^4 + 2*a^7*c^3*d^4*x^4 - 3*a^5*b^2*c^5*d^2*x^4 - 3*a^5*b^2*c^4*d^3*x^7 - 3*a^6*b*c^5*d^2*x + a^4*b^3*c^6*d*x^4 - a^6*b*c^4*d^3*x^4 + a^3*b^4*c^6*d*x^7 + 2*a^6*b*c^3*d^4*x^7)) - (19*a^4*b*c^2*d^3*x*(c + d*x^3)^(1/2))/(6*(a^4*b^3*c^7*x + 2*a^7*c^4*d^3*x + a^3*b^4*c^7*x^4 + 2*a^7*c^3*d^4*x^4 - 3*a^5*b^2*c^5*d^2*x^4 - 3*a^5*b^2*c^4*d^3*x^7 - 3*a^6*b*c^5*d^2*x + a^4*b^3*c^6*d*x^4 - a^6*b*c^4*d^3*x^4 + a^3*b^4*c^6*d*x^7 + 2*a^6*b*c^3*d^4*x^7)) - (8*a*b^4*c^4*d*x^4*(c + d*x^3)^(1/2))/(a^4*b^3*c^7*x + 2*a^7*c^4*d^3*x + a^3*b^4*c^7*x^4 + 2*a^7*c^3*d^4*x^4 - 3*a^5*b^2*c^5*d^2*x^4 - 3*a^5*b^2*c^4*d^3*x^7 - 3*a^6*b*c^5*d^2*x + a^4*b^3*c^6*d*x^4 - a^6*b*c^4*d^3*x^4 + a^3*b^4*c^6*d*x^7 + 2*a^6*b*c^3*d^4*x^7) - (15*a^4*b*c*d^4*x^4*(c + d*x^3)^(1/2))/(2*(a^4*b^3*c^7*x + 2*a^7*c^4*d^3*x + a^3*b^4*c^7*x^4 + 2*a^7*c^3*d^4*x^4 - 3*a^5*b^2*c^5*d^2*x^4 - 3*a^5*b^2*c^4*d^3*x^7 - 3*a^6*b*c^5*d^2*x + a^4*b^3*c^6*d*x^4 - a^6*b*c^4*d^3*x^4 + a^3*b^4*c^6*d*x^7 + 2*a^6*b*c^3*d^4*x^7)) + (12*a^3*b^3*c^5*d*x*(c + d*x^3)^(1/2))/(a^5*b^3*c^8*x + 2*a^8*c^5*d^3*x + a^4*b^4*c^8*x^4 + 2*a^8*c^4*d^4*x^4 - 3*a^6*b^2*c^6*d^2*x^4 - 3*a^6*b^2*c^5*d^3*x^7 - 3*a^7*b*c^6*d^2*x + a^5*b^3*c^7*d*x^4 - a^7*b*c^5*d^3*x^4 + a^4*b^4*c^7*d*x^7 + 2*a^7*b*c^4*d^4*x^7) + (51*a^5*b*c^3*d^3*x*(c + d*x^3)^(1/2))/(4*(a^5*b^3*c^8*x + 2*a^8*c^5*d^3*x + a^4*b^4*c^8*x^4 + 2*a^8*c^4*d^4*x^4 - 3*a^6*b^2*c^6*d^2*x^4 - 3*a^6*b^2*c^5*d^3*x^7 - 3*a^7*b*c^6*d^2*x + a^5*b^3*c^7*d*x^4 - a^7*b*c^5*d^3*x^4 + a^4*b^4*c^7*d*x^7 + 2*a^7*b*c^4*d^4*x^7)) - (14*a^3*b^3*c^6*d*x*(c + d*x^3)^(1/2))/(3*(a^5*b^3*c^9*x + 2*a^8*c^6*d^3*x + a^4*b^4*c^9*x^4 + 2*a^8*c^5*d^4*x^4 - 3*a^6*b^2*c^7*d^2*x^4 - 3*a^6*b^2*c^6*d^3*x^7 - 3*a^7*b*c^7*d^2*x + a^5*b^3*c^8*d*x^4 - a^7*b*c^6*d^3*x^4 + a^4*b^4*c^8*d*x^7 + 2*a^7*b*c^5*d^4*x^7)) - (169*a^5*b*c^4*d^3*x*(c + d*x^3)^(1/2))/(12*(a^5*b^3*c^9*x + 2*a^8*c^6*d^3*x + a^4*b^4*c^9*x^4 + 2*a^8*c^5*d^4*x^4 - 3*a^6*b^2*c^7*d^2*x^4 - 3*a^6*b^2*c^6*d^3*x^7 - 3*a^7*b*c^7*d^2*x + a^5*b^3*c^8*d*x^4 - a^7*b*c^6*d^3*x^4 + a^4*b^4*c^8*d*x^7 + 2*a^7*b*c^5*d^4*x^7)) - (9*a^4*b^3*c^6*d*x*(c + d*x^3)^(1/2))/(8*(a^6*b^3*c^9*x + 2*a^9*c^6*d^3*x + a^5*b^4*c^9*x^4 + 2*a^9*c^5*d^4*x^4 - 3*a^7*b^2*c^7*d^2*x^4 - 3*a^7*b^2*c^6*d^3*x^7 - 3*a^8*b*c^7*d^2*x + a^6*b^3*c^8*d*x^4 - a^8*b*c^6*d^3*x^4 + a^5*b^4*c^8*d*x^7 + 2*a^8*b*c^5*d^4*x^7)) - (9*a^6*b*c^4*d^3*x*(c + d*x^3)^(1/2))/(8*(a^6*b^3*c^9*x + 2*a^9*c^6*d^3*x + a^5*b^4*c^9*x^4 + 2*a^9*c^5*d^4*x^4 - 3*a^7*b^2*c^7*d^2*x^4 - 3*a^7*b^2*c^6*d^3*x^7 - 3*a^8*b*c^7*d^2*x + a^6*b^3*c^8*d*x^4 - a^8*b*c^6*d^3*x^4 + a^5*b^4*c^8*d*x^7 + 2*a^8*b*c^5*d^4*x^7)) - (7*a^5*b^3*c^7*d*x*(c + d*x^3)^(1/2))/(8*(a^7*b^3*c^10*x + 2*a^10*c^7*d^3*x + a^6*b^4*c^10*x^4 + 2*a^10*c^6*d^4*x^4 - 3*a^8*b^2*c^8*d^2*x^4 - 3*a^8*b^2*c^7*d^3*x^7 - 3*a^9*b*c^8*d^2*x + a^7*b^3*c^9*d*x^4 - a^9*b*c^7*d^3*x^4 + a^6*b^4*c^9*d*x^7 + 2*a^9*b*c^6*d^4*x^7)) + (77*a^7*b*c^5*d^3*x*(c + d*x^3)^(1/2))/(8*(a^7*b^3*c^10*x + 2*a^10*c^7*d^3*x + a^6*b^4*c^10*x^4 + 2*a^10*c^6*d^4*x^4 - 3*a^8*b^2*c^8*d^2*x^4 - 3*a^8*b^2*c^7*d^3*x^7 - 3*a^9*b*c^8*d^2*x + a^7*b^3*c^9*d*x^4 - a^9*b*c^7*d^3*x^4 + a^6*b^4*c^9*d*x^7 + 2*a^9*b*c^6*d^4*x^7)) - (41*a*b^2*c^2*d*x^4*(c + d*x^3)^(1/2))/(3*(a^3*b^2*c^5*x^4 + 2*a^5*c^3*d^2*x^4 + a^4*b*c^5*x + 2*a^5*c^4*d*x + 3*a^4*b*c^4*d*x^4 + a^3*b^2*c^4*d*x^7 + 2*a^4*b*c^3*d^2*x^7)) - (71*a^2*b*c*d^2*x^4*(c + d*x^3)^(1/2))/(6*(a^3*b^2*c^5*x^4 + 2*a^5*c^3*d^2*x^4 + a^4*b*c^5*x + 2*a^5*c^4*d*x + 3*a^4*b*c^4*d*x^4 + a^3*b^2*c^4*d*x^7 + 2*a^4*b*c^3*d^2*x^7)) + (133*a*b^2*c^3*d*x^4*(c + d*x^3)^(1/2))/(6*(a^3*b^2*c^6*x^4 + 2*a^5*c^4*d^2*x^4 + a^4*b*c^6*x + 2*a^5*c^5*d*x + 3*a^4*b*c^5*d*x^4 + a^3*b^2*c^5*d*x^7 + 2*a^4*b*c^4*d^2*x^7))","B"
495,0,-1,67,0.000000,"\text{Not used}","int(x^3/((a + b*x^3)^2*(c + d*x^3)^(3/2)),x)","\int \frac{x^3}{{\left(b\,x^3+a\right)}^2\,{\left(d\,x^3+c\right)}^{3/2}} \,d x","Not used",1,"int(x^3/((a + b*x^3)^2*(c + d*x^3)^(3/2)), x)","F"
496,0,-1,67,0.000000,"\text{Not used}","int(x/((a + b*x^3)^2*(c + d*x^3)^(3/2)),x)","\int \frac{x}{{\left(b\,x^3+a\right)}^2\,{\left(d\,x^3+c\right)}^{3/2}} \,d x","Not used",1,"int(x/((a + b*x^3)^2*(c + d*x^3)^(3/2)), x)","F"
497,0,-1,62,0.000000,"\text{Not used}","int(1/((a + b*x^3)^2*(c + d*x^3)^(3/2)),x)","\int \frac{1}{{\left(b\,x^3+a\right)}^2\,{\left(d\,x^3+c\right)}^{3/2}} \,d x","Not used",1,"int(1/((a + b*x^3)^2*(c + d*x^3)^(3/2)), x)","F"
498,0,-1,65,0.000000,"\text{Not used}","int(1/(x^2*(a + b*x^3)^2*(c + d*x^3)^(3/2)),x)","\int \frac{1}{x^2\,{\left(b\,x^3+a\right)}^2\,{\left(d\,x^3+c\right)}^{3/2}} \,d x","Not used",1,"int(1/(x^2*(a + b*x^3)^2*(c + d*x^3)^(3/2)), x)","F"
499,0,-1,67,0.000000,"\text{Not used}","int(1/(x^3*(a + b*x^3)^2*(c + d*x^3)^(3/2)),x)","\int \frac{1}{x^3\,{\left(b\,x^3+a\right)}^2\,{\left(d\,x^3+c\right)}^{3/2}} \,d x","Not used",1,"int(1/(x^3*(a + b*x^3)^2*(c + d*x^3)^(3/2)), x)","F"
500,0,-1,134,0.000000,"\text{Not used}","int((A + B*x^3)*(e*x)^m*(a + b*x^3)^(5/2),x)","\int \left(B\,x^3+A\right)\,{\left(e\,x\right)}^m\,{\left(b\,x^3+a\right)}^{5/2} \,d x","Not used",1,"int((A + B*x^3)*(e*x)^m*(a + b*x^3)^(5/2), x)","F"
501,0,-1,132,0.000000,"\text{Not used}","int((A + B*x^3)*(e*x)^m*(a + b*x^3)^(3/2),x)","\int \left(B\,x^3+A\right)\,{\left(e\,x\right)}^m\,{\left(b\,x^3+a\right)}^{3/2} \,d x","Not used",1,"int((A + B*x^3)*(e*x)^m*(a + b*x^3)^(3/2), x)","F"
502,0,-1,131,0.000000,"\text{Not used}","int((A + B*x^3)*(e*x)^m*(a + b*x^3)^(1/2),x)","\int \left(B\,x^3+A\right)\,{\left(e\,x\right)}^m\,\sqrt{b\,x^3+a} \,d x","Not used",1,"int((A + B*x^3)*(e*x)^m*(a + b*x^3)^(1/2), x)","F"
503,0,-1,131,0.000000,"\text{Not used}","int(((A + B*x^3)*(e*x)^m)/(a + b*x^3)^(1/2),x)","\int \frac{\left(B\,x^3+A\right)\,{\left(e\,x\right)}^m}{\sqrt{b\,x^3+a}} \,d x","Not used",1,"int(((A + B*x^3)*(e*x)^m)/(a + b*x^3)^(1/2), x)","F"
504,0,-1,133,0.000000,"\text{Not used}","int(((A + B*x^3)*(e*x)^m)/(a + b*x^3)^(3/2),x)","\int \frac{\left(B\,x^3+A\right)\,{\left(e\,x\right)}^m}{{\left(b\,x^3+a\right)}^{3/2}} \,d x","Not used",1,"int(((A + B*x^3)*(e*x)^m)/(a + b*x^3)^(3/2), x)","F"
505,0,-1,133,0.000000,"\text{Not used}","int(((A + B*x^3)*(e*x)^m)/(a + b*x^3)^(5/2),x)","\int \frac{\left(B\,x^3+A\right)\,{\left(e\,x\right)}^m}{{\left(b\,x^3+a\right)}^{5/2}} \,d x","Not used",1,"int(((A + B*x^3)*(e*x)^m)/(a + b*x^3)^(5/2), x)","F"
506,1,283,88,9.251184,"\text{Not used}","int(x^5/((a + b*x^3)^(1/2)*(c + d*x^3)^(1/2)),x)","\frac{\frac{\left(\sqrt{b\,x^3+a}-\sqrt{a}\right)\,\left(\frac{2\,a\,d}{3}+\frac{2\,b\,c}{3}\right)}{d^3\,\left(\sqrt{d\,x^3+c}-\sqrt{c}\right)}+\frac{{\left(\sqrt{b\,x^3+a}-\sqrt{a}\right)}^3\,\left(\frac{2\,a\,d}{3}+\frac{2\,b\,c}{3}\right)}{b\,d^2\,{\left(\sqrt{d\,x^3+c}-\sqrt{c}\right)}^3}-\frac{8\,\sqrt{a}\,\sqrt{c}\,{\left(\sqrt{b\,x^3+a}-\sqrt{a}\right)}^2}{3\,d^2\,{\left(\sqrt{d\,x^3+c}-\sqrt{c}\right)}^2}}{\frac{{\left(\sqrt{b\,x^3+a}-\sqrt{a}\right)}^4}{{\left(\sqrt{d\,x^3+c}-\sqrt{c}\right)}^4}+\frac{b^2}{d^2}-\frac{2\,b\,{\left(\sqrt{b\,x^3+a}-\sqrt{a}\right)}^2}{d\,{\left(\sqrt{d\,x^3+c}-\sqrt{c}\right)}^2}}-\frac{2\,\mathrm{atanh}\left(\frac{\sqrt{d}\,\left(\sqrt{b\,x^3+a}-\sqrt{a}\right)}{\sqrt{b}\,\left(\sqrt{d\,x^3+c}-\sqrt{c}\right)}\right)\,\left(a\,d+b\,c\right)}{3\,b^{3/2}\,d^{3/2}}","Not used",1,"((((a + b*x^3)^(1/2) - a^(1/2))*((2*a*d)/3 + (2*b*c)/3))/(d^3*((c + d*x^3)^(1/2) - c^(1/2))) + (((a + b*x^3)^(1/2) - a^(1/2))^3*((2*a*d)/3 + (2*b*c)/3))/(b*d^2*((c + d*x^3)^(1/2) - c^(1/2))^3) - (8*a^(1/2)*c^(1/2)*((a + b*x^3)^(1/2) - a^(1/2))^2)/(3*d^2*((c + d*x^3)^(1/2) - c^(1/2))^2))/(((a + b*x^3)^(1/2) - a^(1/2))^4/((c + d*x^3)^(1/2) - c^(1/2))^4 + b^2/d^2 - (2*b*((a + b*x^3)^(1/2) - a^(1/2))^2)/(d*((c + d*x^3)^(1/2) - c^(1/2))^2)) - (2*atanh((d^(1/2)*((a + b*x^3)^(1/2) - a^(1/2)))/(b^(1/2)*((c + d*x^3)^(1/2) - c^(1/2))))*(a*d + b*c))/(3*b^(3/2)*d^(3/2))","B"
507,1,49,48,5.043032,"\text{Not used}","int(x^2/((a + b*x^3)^(1/2)*(c + d*x^3)^(1/2)),x)","-\frac{4\,\mathrm{atan}\left(\frac{b\,\left(\sqrt{d\,x^3+c}-\sqrt{c}\right)}{\sqrt{-b\,d}\,\left(\sqrt{b\,x^3+a}-\sqrt{a}\right)}\right)}{3\,\sqrt{-b\,d}}","Not used",1,"-(4*atan((b*((c + d*x^3)^(1/2) - c^(1/2)))/((-b*d)^(1/2)*((a + b*x^3)^(1/2) - a^(1/2)))))/(3*(-b*d)^(1/2))","B"
508,1,136,48,7.572066,"\text{Not used}","int(1/(x*(a + b*x^3)^(1/2)*(c + d*x^3)^(1/2)),x)","-\frac{\ln\left(\frac{\sqrt{b\,x^3+a}-\sqrt{a}}{\sqrt{d\,x^3+c}-\sqrt{c}}\right)-\ln\left(\frac{\left(\sqrt{c}\,\sqrt{b\,x^3+a}-\sqrt{a}\,\sqrt{d\,x^3+c}\right)\,\left(b\,\sqrt{c}-\frac{\sqrt{a}\,d\,\left(\sqrt{b\,x^3+a}-\sqrt{a}\right)}{\sqrt{d\,x^3+c}-\sqrt{c}}\right)}{\sqrt{d\,x^3+c}-\sqrt{c}}\right)}{3\,\sqrt{a}\,\sqrt{c}}","Not used",1,"-(log(((a + b*x^3)^(1/2) - a^(1/2))/((c + d*x^3)^(1/2) - c^(1/2))) - log(((c^(1/2)*(a + b*x^3)^(1/2) - a^(1/2)*(c + d*x^3)^(1/2))*(b*c^(1/2) - (a^(1/2)*d*((a + b*x^3)^(1/2) - a^(1/2)))/((c + d*x^3)^(1/2) - c^(1/2))))/((c + d*x^3)^(1/2) - c^(1/2))))/(3*a^(1/2)*c^(1/2))","B"
509,1,481,91,10.774560,"\text{Not used}","int(1/(x^4*(a + b*x^3)^(1/2)*(c + d*x^3)^(1/2)),x)","\frac{\frac{\left(\sqrt{b\,x^3+a}-\sqrt{a}\right)\,\left(\frac{c\,b^2}{12}+\frac{a\,d\,b}{12}\right)}{a^{3/2}\,c^{3/2}\,d\,\left(\sqrt{d\,x^3+c}-\sqrt{c}\right)}-\frac{b^2}{12\,a\,c\,d}+\frac{{\left(\sqrt{b\,x^3+a}-\sqrt{a}\right)}^2\,\left(\frac{a^2\,d^2}{12}-\frac{a\,b\,c\,d}{4}+\frac{b^2\,c^2}{12}\right)}{a^2\,c^2\,d\,{\left(\sqrt{d\,x^3+c}-\sqrt{c}\right)}^2}}{\frac{{\left(\sqrt{b\,x^3+a}-\sqrt{a}\right)}^3}{{\left(\sqrt{d\,x^3+c}-\sqrt{c}\right)}^3}+\frac{b\,\left(\sqrt{b\,x^3+a}-\sqrt{a}\right)}{d\,\left(\sqrt{d\,x^3+c}-\sqrt{c}\right)}-\frac{{\left(\sqrt{b\,x^3+a}-\sqrt{a}\right)}^2\,\left(a\,d+b\,c\right)}{\sqrt{a}\,\sqrt{c}\,d\,{\left(\sqrt{d\,x^3+c}-\sqrt{c}\right)}^2}}+\frac{\ln\left(\frac{\sqrt{b\,x^3+a}-\sqrt{a}}{\sqrt{d\,x^3+c}-\sqrt{c}}\right)\,\left(\sqrt{a}\,b\,c^{3/2}+a^{3/2}\,\sqrt{c}\,d\right)}{6\,a^2\,c^2}-\frac{\ln\left(\frac{\left(\sqrt{c}\,\sqrt{b\,x^3+a}-\sqrt{a}\,\sqrt{d\,x^3+c}\right)\,\left(b\,\sqrt{c}-\frac{\sqrt{a}\,d\,\left(\sqrt{b\,x^3+a}-\sqrt{a}\right)}{\sqrt{d\,x^3+c}-\sqrt{c}}\right)}{\sqrt{d\,x^3+c}-\sqrt{c}}\right)\,\left(\sqrt{a}\,b\,c^{3/2}+a^{3/2}\,\sqrt{c}\,d\right)}{6\,a^2\,c^2}-\frac{d\,\left(\sqrt{b\,x^3+a}-\sqrt{a}\right)}{12\,a\,c\,\left(\sqrt{d\,x^3+c}-\sqrt{c}\right)}","Not used",1,"((((a + b*x^3)^(1/2) - a^(1/2))*((b^2*c)/12 + (a*b*d)/12))/(a^(3/2)*c^(3/2)*d*((c + d*x^3)^(1/2) - c^(1/2))) - b^2/(12*a*c*d) + (((a + b*x^3)^(1/2) - a^(1/2))^2*((a^2*d^2)/12 + (b^2*c^2)/12 - (a*b*c*d)/4))/(a^2*c^2*d*((c + d*x^3)^(1/2) - c^(1/2))^2))/(((a + b*x^3)^(1/2) - a^(1/2))^3/((c + d*x^3)^(1/2) - c^(1/2))^3 + (b*((a + b*x^3)^(1/2) - a^(1/2)))/(d*((c + d*x^3)^(1/2) - c^(1/2))) - (((a + b*x^3)^(1/2) - a^(1/2))^2*(a*d + b*c))/(a^(1/2)*c^(1/2)*d*((c + d*x^3)^(1/2) - c^(1/2))^2)) + (log(((a + b*x^3)^(1/2) - a^(1/2))/((c + d*x^3)^(1/2) - c^(1/2)))*(a^(1/2)*b*c^(3/2) + a^(3/2)*c^(1/2)*d))/(6*a^2*c^2) - (log(((c^(1/2)*(a + b*x^3)^(1/2) - a^(1/2)*(c + d*x^3)^(1/2))*(b*c^(1/2) - (a^(1/2)*d*((a + b*x^3)^(1/2) - a^(1/2)))/((c + d*x^3)^(1/2) - c^(1/2))))/((c + d*x^3)^(1/2) - c^(1/2)))*(a^(1/2)*b*c^(3/2) + a^(3/2)*c^(1/2)*d))/(6*a^2*c^2) - (d*((a + b*x^3)^(1/2) - a^(1/2)))/(12*a*c*((c + d*x^3)^(1/2) - c^(1/2)))","B"
510,0,-1,88,0.000000,"\text{Not used}","int(x^4/((a + b*x^3)^(1/2)*(c + d*x^3)^(1/2)),x)","\int \frac{x^4}{\sqrt{b\,x^3+a}\,\sqrt{d\,x^3+c}} \,d x","Not used",1,"int(x^4/((a + b*x^3)^(1/2)*(c + d*x^3)^(1/2)), x)","F"
511,0,-1,88,0.000000,"\text{Not used}","int(x^3/((a + b*x^3)^(1/2)*(c + d*x^3)^(1/2)),x)","\int \frac{x^3}{\sqrt{b\,x^3+a}\,\sqrt{d\,x^3+c}} \,d x","Not used",1,"int(x^3/((a + b*x^3)^(1/2)*(c + d*x^3)^(1/2)), x)","F"
512,0,-1,88,0.000000,"\text{Not used}","int(x/((a + b*x^3)^(1/2)*(c + d*x^3)^(1/2)),x)","\int \frac{x}{\sqrt{b\,x^3+a}\,\sqrt{d\,x^3+c}} \,d x","Not used",1,"int(x/((a + b*x^3)^(1/2)*(c + d*x^3)^(1/2)), x)","F"
513,0,-1,83,0.000000,"\text{Not used}","int(1/((a + b*x^3)^(1/2)*(c + d*x^3)^(1/2)),x)","\int \frac{1}{\sqrt{b\,x^3+a}\,\sqrt{d\,x^3+c}} \,d x","Not used",1,"int(1/((a + b*x^3)^(1/2)*(c + d*x^3)^(1/2)), x)","F"
514,0,-1,86,0.000000,"\text{Not used}","int(1/(x^2*(a + b*x^3)^(1/2)*(c + d*x^3)^(1/2)),x)","\int \frac{1}{x^2\,\sqrt{b\,x^3+a}\,\sqrt{d\,x^3+c}} \,d x","Not used",1,"int(1/(x^2*(a + b*x^3)^(1/2)*(c + d*x^3)^(1/2)), x)","F"
515,0,-1,88,0.000000,"\text{Not used}","int(1/(x^3*(a + b*x^3)^(1/2)*(c + d*x^3)^(1/2)),x)","\int \frac{1}{x^3\,\sqrt{b\,x^3+a}\,\sqrt{d\,x^3+c}} \,d x","Not used",1,"int(1/(x^3*(a + b*x^3)^(1/2)*(c + d*x^3)^(1/2)), x)","F"
516,0,-1,161,0.000000,"\text{Not used}","int((A + B*x^3)*(e*x)^(7/2)*(a + b*x^3)^(1/2),x)","\int \left(B\,x^3+A\right)\,{\left(e\,x\right)}^{7/2}\,\sqrt{b\,x^3+a} \,d x","Not used",1,"int((A + B*x^3)*(e*x)^(7/2)*(a + b*x^3)^(1/2), x)","F"
517,0,-1,324,0.000000,"\text{Not used}","int((A + B*x^3)*(e*x)^(5/2)*(a + b*x^3)^(1/2),x)","\int \left(B\,x^3+A\right)\,{\left(e\,x\right)}^{5/2}\,\sqrt{b\,x^3+a} \,d x","Not used",1,"int((A + B*x^3)*(e*x)^(5/2)*(a + b*x^3)^(1/2), x)","F"
518,0,-1,581,0.000000,"\text{Not used}","int((A + B*x^3)*(e*x)^(3/2)*(a + b*x^3)^(1/2),x)","\int \left(B\,x^3+A\right)\,{\left(e\,x\right)}^{3/2}\,\sqrt{b\,x^3+a} \,d x","Not used",1,"int((A + B*x^3)*(e*x)^(3/2)*(a + b*x^3)^(1/2), x)","F"
519,0,-1,121,0.000000,"\text{Not used}","int((A + B*x^3)*(e*x)^(1/2)*(a + b*x^3)^(1/2),x)","\int \left(B\,x^3+A\right)\,\sqrt{e\,x}\,\sqrt{b\,x^3+a} \,d x","Not used",1,"int((A + B*x^3)*(e*x)^(1/2)*(a + b*x^3)^(1/2), x)","F"
520,0,-1,286,0.000000,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^(1/2))/(e*x)^(1/2),x)","\int \frac{\left(B\,x^3+A\right)\,\sqrt{b\,x^3+a}}{\sqrt{e\,x}} \,d x","Not used",1,"int(((A + B*x^3)*(a + b*x^3)^(1/2))/(e*x)^(1/2), x)","F"
521,0,-1,580,0.000000,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^(1/2))/(e*x)^(3/2),x)","\int \frac{\left(B\,x^3+A\right)\,\sqrt{b\,x^3+a}}{{\left(e\,x\right)}^{3/2}} \,d x","Not used",1,"int(((A + B*x^3)*(a + b*x^3)^(1/2))/(e*x)^(3/2), x)","F"
522,0,-1,118,0.000000,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^(1/2))/(e*x)^(5/2),x)","\int \frac{\left(B\,x^3+A\right)\,\sqrt{b\,x^3+a}}{{\left(e\,x\right)}^{5/2}} \,d x","Not used",1,"int(((A + B*x^3)*(a + b*x^3)^(1/2))/(e*x)^(5/2), x)","F"
523,0,-1,283,0.000000,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^(1/2))/(e*x)^(7/2),x)","\int \frac{\left(B\,x^3+A\right)\,\sqrt{b\,x^3+a}}{{\left(e\,x\right)}^{7/2}} \,d x","Not used",1,"int(((A + B*x^3)*(a + b*x^3)^(1/2))/(e*x)^(7/2), x)","F"
524,0,-1,564,0.000000,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^(1/2))/x^(9/2),x)","\int \frac{\left(B\,x^3+A\right)\,\sqrt{b\,x^3+a}}{x^{9/2}} \,d x","Not used",1,"int(((A + B*x^3)*(a + b*x^3)^(1/2))/x^(9/2), x)","F"
525,0,-1,79,0.000000,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^(1/2))/x^(11/2),x)","\int \frac{\left(B\,x^3+A\right)\,\sqrt{b\,x^3+a}}{x^{11/2}} \,d x","Not used",1,"int(((A + B*x^3)*(a + b*x^3)^(1/2))/x^(11/2), x)","F"
526,0,-1,269,0.000000,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^(1/2))/x^(13/2),x)","\int \frac{\left(B\,x^3+A\right)\,\sqrt{b\,x^3+a}}{x^{13/2}} \,d x","Not used",1,"int(((A + B*x^3)*(a + b*x^3)^(1/2))/x^(13/2), x)","F"
527,0,-1,201,0.000000,"\text{Not used}","int((A + B*x^3)*(e*x)^(7/2)*(a + b*x^3)^(3/2),x)","\int \left(B\,x^3+A\right)\,{\left(e\,x\right)}^{7/2}\,{\left(b\,x^3+a\right)}^{3/2} \,d x","Not used",1,"int((A + B*x^3)*(e*x)^(7/2)*(a + b*x^3)^(3/2), x)","F"
528,0,-1,364,0.000000,"\text{Not used}","int((A + B*x^3)*(e*x)^(5/2)*(a + b*x^3)^(3/2),x)","\int \left(B\,x^3+A\right)\,{\left(e\,x\right)}^{5/2}\,{\left(b\,x^3+a\right)}^{3/2} \,d x","Not used",1,"int((A + B*x^3)*(e*x)^(5/2)*(a + b*x^3)^(3/2), x)","F"
529,0,-1,621,0.000000,"\text{Not used}","int((A + B*x^3)*(e*x)^(3/2)*(a + b*x^3)^(3/2),x)","\int \left(B\,x^3+A\right)\,{\left(e\,x\right)}^{3/2}\,{\left(b\,x^3+a\right)}^{3/2} \,d x","Not used",1,"int((A + B*x^3)*(e*x)^(3/2)*(a + b*x^3)^(3/2), x)","F"
530,0,-1,161,0.000000,"\text{Not used}","int((A + B*x^3)*(e*x)^(1/2)*(a + b*x^3)^(3/2),x)","\int \left(B\,x^3+A\right)\,\sqrt{e\,x}\,{\left(b\,x^3+a\right)}^{3/2} \,d x","Not used",1,"int((A + B*x^3)*(e*x)^(1/2)*(a + b*x^3)^(3/2), x)","F"
531,0,-1,324,0.000000,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^(3/2))/(e*x)^(1/2),x)","\int \frac{\left(B\,x^3+A\right)\,{\left(b\,x^3+a\right)}^{3/2}}{\sqrt{e\,x}} \,d x","Not used",1,"int(((A + B*x^3)*(a + b*x^3)^(3/2))/(e*x)^(1/2), x)","F"
532,0,-1,614,0.000000,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^(3/2))/(e*x)^(3/2),x)","\int \frac{\left(B\,x^3+A\right)\,{\left(b\,x^3+a\right)}^{3/2}}{{\left(e\,x\right)}^{3/2}} \,d x","Not used",1,"int(((A + B*x^3)*(a + b*x^3)^(3/2))/(e*x)^(3/2), x)","F"
533,0,-1,152,0.000000,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^(3/2))/(e*x)^(5/2),x)","\int \frac{\left(B\,x^3+A\right)\,{\left(b\,x^3+a\right)}^{3/2}}{{\left(e\,x\right)}^{5/2}} \,d x","Not used",1,"int(((A + B*x^3)*(a + b*x^3)^(3/2))/(e*x)^(5/2), x)","F"
534,0,-1,314,0.000000,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^(3/2))/(e*x)^(7/2),x)","\int \frac{\left(B\,x^3+A\right)\,{\left(b\,x^3+a\right)}^{3/2}}{{\left(e\,x\right)}^{7/2}} \,d x","Not used",1,"int(((A + B*x^3)*(a + b*x^3)^(3/2))/(e*x)^(7/2), x)","F"
535,0,-1,241,0.000000,"\text{Not used}","int((A + B*x^3)*(e*x)^(7/2)*(a + b*x^3)^(5/2),x)","\int \left(B\,x^3+A\right)\,{\left(e\,x\right)}^{7/2}\,{\left(b\,x^3+a\right)}^{5/2} \,d x","Not used",1,"int((A + B*x^3)*(e*x)^(7/2)*(a + b*x^3)^(5/2), x)","F"
536,0,-1,404,0.000000,"\text{Not used}","int((A + B*x^3)*(e*x)^(5/2)*(a + b*x^3)^(5/2),x)","\int \left(B\,x^3+A\right)\,{\left(e\,x\right)}^{5/2}\,{\left(b\,x^3+a\right)}^{5/2} \,d x","Not used",1,"int((A + B*x^3)*(e*x)^(5/2)*(a + b*x^3)^(5/2), x)","F"
537,0,-1,661,0.000000,"\text{Not used}","int((A + B*x^3)*(e*x)^(3/2)*(a + b*x^3)^(5/2),x)","\int \left(B\,x^3+A\right)\,{\left(e\,x\right)}^{3/2}\,{\left(b\,x^3+a\right)}^{5/2} \,d x","Not used",1,"int((A + B*x^3)*(e*x)^(3/2)*(a + b*x^3)^(5/2), x)","F"
538,0,-1,201,0.000000,"\text{Not used}","int((A + B*x^3)*(e*x)^(1/2)*(a + b*x^3)^(5/2),x)","\int \left(B\,x^3+A\right)\,\sqrt{e\,x}\,{\left(b\,x^3+a\right)}^{5/2} \,d x","Not used",1,"int((A + B*x^3)*(e*x)^(1/2)*(a + b*x^3)^(5/2), x)","F"
539,0,-1,364,0.000000,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^(5/2))/(e*x)^(1/2),x)","\int \frac{\left(B\,x^3+A\right)\,{\left(b\,x^3+a\right)}^{5/2}}{\sqrt{e\,x}} \,d x","Not used",1,"int(((A + B*x^3)*(a + b*x^3)^(5/2))/(e*x)^(1/2), x)","F"
540,0,-1,650,0.000000,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^(5/2))/(e*x)^(3/2),x)","\int \frac{\left(B\,x^3+A\right)\,{\left(b\,x^3+a\right)}^{5/2}}{{\left(e\,x\right)}^{3/2}} \,d x","Not used",1,"int(((A + B*x^3)*(a + b*x^3)^(5/2))/(e*x)^(3/2), x)","F"
541,0,-1,188,0.000000,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^(5/2))/(e*x)^(5/2),x)","\int \frac{\left(B\,x^3+A\right)\,{\left(b\,x^3+a\right)}^{5/2}}{{\left(e\,x\right)}^{5/2}} \,d x","Not used",1,"int(((A + B*x^3)*(a + b*x^3)^(5/2))/(e*x)^(5/2), x)","F"
542,0,-1,352,0.000000,"\text{Not used}","int(((A + B*x^3)*(a + b*x^3)^(5/2))/(e*x)^(7/2),x)","\int \frac{\left(B\,x^3+A\right)\,{\left(b\,x^3+a\right)}^{5/2}}{{\left(e\,x\right)}^{7/2}} \,d x","Not used",1,"int(((A + B*x^3)*(a + b*x^3)^(5/2))/(e*x)^(7/2), x)","F"
543,0,-1,121,0.000000,"\text{Not used}","int(((A + B*x^3)*(e*x)^(7/2))/(a + b*x^3)^(1/2),x)","\int \frac{\left(B\,x^3+A\right)\,{\left(e\,x\right)}^{7/2}}{\sqrt{b\,x^3+a}} \,d x","Not used",1,"int(((A + B*x^3)*(e*x)^(7/2))/(a + b*x^3)^(1/2), x)","F"
544,0,-1,286,0.000000,"\text{Not used}","int(((A + B*x^3)*(e*x)^(5/2))/(a + b*x^3)^(1/2),x)","\int \frac{\left(B\,x^3+A\right)\,{\left(e\,x\right)}^{5/2}}{\sqrt{b\,x^3+a}} \,d x","Not used",1,"int(((A + B*x^3)*(e*x)^(5/2))/(a + b*x^3)^(1/2), x)","F"
545,0,-1,543,0.000000,"\text{Not used}","int(((A + B*x^3)*(e*x)^(3/2))/(a + b*x^3)^(1/2),x)","\int \frac{\left(B\,x^3+A\right)\,{\left(e\,x\right)}^{3/2}}{\sqrt{b\,x^3+a}} \,d x","Not used",1,"int(((A + B*x^3)*(e*x)^(3/2))/(a + b*x^3)^(1/2), x)","F"
546,0,-1,83,0.000000,"\text{Not used}","int(((A + B*x^3)*(e*x)^(1/2))/(a + b*x^3)^(1/2),x)","\int \frac{\left(B\,x^3+A\right)\,\sqrt{e\,x}}{\sqrt{b\,x^3+a}} \,d x","Not used",1,"int(((A + B*x^3)*(e*x)^(1/2))/(a + b*x^3)^(1/2), x)","F"
547,0,-1,249,0.000000,"\text{Not used}","int((A + B*x^3)/((e*x)^(1/2)*(a + b*x^3)^(1/2)),x)","\int \frac{B\,x^3+A}{\sqrt{e\,x}\,\sqrt{b\,x^3+a}} \,d x","Not used",1,"int((A + B*x^3)/((e*x)^(1/2)*(a + b*x^3)^(1/2)), x)","F"
548,0,-1,542,0.000000,"\text{Not used}","int((A + B*x^3)/((e*x)^(3/2)*(a + b*x^3)^(1/2)),x)","\int \frac{B\,x^3+A}{{\left(e\,x\right)}^{3/2}\,\sqrt{b\,x^3+a}} \,d x","Not used",1,"int((A + B*x^3)/((e*x)^(3/2)*(a + b*x^3)^(1/2)), x)","F"
549,0,-1,75,0.000000,"\text{Not used}","int((A + B*x^3)/((e*x)^(5/2)*(a + b*x^3)^(1/2)),x)","\int \frac{B\,x^3+A}{{\left(e\,x\right)}^{5/2}\,\sqrt{b\,x^3+a}} \,d x","Not used",1,"int((A + B*x^3)/((e*x)^(5/2)*(a + b*x^3)^(1/2)), x)","F"
550,0,-1,246,0.000000,"\text{Not used}","int((A + B*x^3)/((e*x)^(7/2)*(a + b*x^3)^(1/2)),x)","\int \frac{B\,x^3+A}{{\left(e\,x\right)}^{7/2}\,\sqrt{b\,x^3+a}} \,d x","Not used",1,"int((A + B*x^3)/((e*x)^(7/2)*(a + b*x^3)^(1/2)), x)","F"
551,0,-1,120,0.000000,"\text{Not used}","int(((A + B*x^3)*(e*x)^(7/2))/(a + b*x^3)^(3/2),x)","\int \frac{\left(B\,x^3+A\right)\,{\left(e\,x\right)}^{7/2}}{{\left(b\,x^3+a\right)}^{3/2}} \,d x","Not used",1,"int(((A + B*x^3)*(e*x)^(7/2))/(a + b*x^3)^(3/2), x)","F"
552,0,-1,286,0.000000,"\text{Not used}","int(((A + B*x^3)*(e*x)^(5/2))/(a + b*x^3)^(3/2),x)","\int \frac{\left(B\,x^3+A\right)\,{\left(e\,x\right)}^{5/2}}{{\left(b\,x^3+a\right)}^{3/2}} \,d x","Not used",1,"int(((A + B*x^3)*(e*x)^(5/2))/(a + b*x^3)^(3/2), x)","F"
553,0,-1,553,0.000000,"\text{Not used}","int(((A + B*x^3)*(e*x)^(3/2))/(a + b*x^3)^(3/2),x)","\int \frac{\left(B\,x^3+A\right)\,{\left(e\,x\right)}^{3/2}}{{\left(b\,x^3+a\right)}^{3/2}} \,d x","Not used",1,"int(((A + B*x^3)*(e*x)^(3/2))/(a + b*x^3)^(3/2), x)","F"
554,0,-1,85,0.000000,"\text{Not used}","int(((A + B*x^3)*(e*x)^(1/2))/(a + b*x^3)^(3/2),x)","\int \frac{\left(B\,x^3+A\right)\,\sqrt{e\,x}}{{\left(b\,x^3+a\right)}^{3/2}} \,d x","Not used",1,"int(((A + B*x^3)*(e*x)^(1/2))/(a + b*x^3)^(3/2), x)","F"
555,0,-1,258,0.000000,"\text{Not used}","int((A + B*x^3)/((e*x)^(1/2)*(a + b*x^3)^(3/2)),x)","\int \frac{B\,x^3+A}{\sqrt{e\,x}\,{\left(b\,x^3+a\right)}^{3/2}} \,d x","Not used",1,"int((A + B*x^3)/((e*x)^(1/2)*(a + b*x^3)^(3/2)), x)","F"
556,0,-1,585,0.000000,"\text{Not used}","int((A + B*x^3)/((e*x)^(3/2)*(a + b*x^3)^(3/2)),x)","\int \frac{B\,x^3+A}{{\left(e\,x\right)}^{3/2}\,{\left(b\,x^3+a\right)}^{3/2}} \,d x","Not used",1,"int((A + B*x^3)/((e*x)^(3/2)*(a + b*x^3)^(3/2)), x)","F"
557,1,70,67,4.747370,"\text{Not used}","int((A + B*x^3)/((e*x)^(5/2)*(a + b*x^3)^(3/2)),x)","-\frac{\left(\frac{2\,A}{3\,a\,b\,e^2}+\frac{x^3\,\left(4\,A\,b-2\,B\,a\right)}{3\,a^2\,b\,e^2}\right)\,\sqrt{b\,x^3+a}}{x^4\,\sqrt{e\,x}+\frac{a\,x\,\sqrt{e\,x}}{b}}","Not used",1,"-(((2*A)/(3*a*b*e^2) + (x^3*(4*A*b - 2*B*a))/(3*a^2*b*e^2))*(a + b*x^3)^(1/2))/(x^4*(e*x)^(1/2) + (a*x*(e*x)^(1/2))/b)","B"
558,0,-1,283,0.000000,"\text{Not used}","int((A + B*x^3)/((e*x)^(7/2)*(a + b*x^3)^(3/2)),x)","\int \frac{B\,x^3+A}{{\left(e\,x\right)}^{7/2}\,{\left(b\,x^3+a\right)}^{3/2}} \,d x","Not used",1,"int((A + B*x^3)/((e*x)^(7/2)*(a + b*x^3)^(3/2)), x)","F"
559,0,-1,114,0.000000,"\text{Not used}","int(((A + B*x^3)*(e*x)^(7/2))/(a + b*x^3)^(5/2),x)","\int \frac{\left(B\,x^3+A\right)\,{\left(e\,x\right)}^{7/2}}{{\left(b\,x^3+a\right)}^{5/2}} \,d x","Not used",1,"int(((A + B*x^3)*(e*x)^(7/2))/(a + b*x^3)^(5/2), x)","F"
560,0,-1,299,0.000000,"\text{Not used}","int(((A + B*x^3)*(e*x)^(5/2))/(a + b*x^3)^(5/2),x)","\int \frac{\left(B\,x^3+A\right)\,{\left(e\,x\right)}^{5/2}}{{\left(b\,x^3+a\right)}^{5/2}} \,d x","Not used",1,"int(((A + B*x^3)*(e*x)^(5/2))/(a + b*x^3)^(5/2), x)","F"
561,0,-1,596,0.000000,"\text{Not used}","int(((A + B*x^3)*(e*x)^(3/2))/(a + b*x^3)^(5/2),x)","\int \frac{\left(B\,x^3+A\right)\,{\left(e\,x\right)}^{3/2}}{{\left(b\,x^3+a\right)}^{5/2}} \,d x","Not used",1,"int(((A + B*x^3)*(e*x)^(3/2))/(a + b*x^3)^(5/2), x)","F"
562,1,73,79,4.628272,"\text{Not used}","int(((A + B*x^3)*(e*x)^(1/2))/(a + b*x^3)^(5/2),x)","\frac{\left(\frac{2\,A\,x\,\sqrt{e\,x}}{3\,a\,b^2}+\frac{x^4\,\sqrt{e\,x}\,\left(4\,A\,b+2\,B\,a\right)}{9\,a^2\,b^2}\right)\,\sqrt{b\,x^3+a}}{x^6+\frac{a^2}{b^2}+\frac{2\,a\,x^3}{b}}","Not used",1,"(((2*A*x*(e*x)^(1/2))/(3*a*b^2) + (x^4*(e*x)^(1/2)*(4*A*b + 2*B*a))/(9*a^2*b^2))*(a + b*x^3)^(1/2))/(x^6 + a^2/b^2 + (2*a*x^3)/b)","B"
563,0,-1,297,0.000000,"\text{Not used}","int((A + B*x^3)/((e*x)^(1/2)*(a + b*x^3)^(5/2)),x)","\int \frac{B\,x^3+A}{\sqrt{e\,x}\,{\left(b\,x^3+a\right)}^{5/2}} \,d x","Not used",1,"int((A + B*x^3)/((e*x)^(1/2)*(a + b*x^3)^(5/2)), x)","F"
564,0,-1,624,0.000000,"\text{Not used}","int((A + B*x^3)/((e*x)^(3/2)*(a + b*x^3)^(5/2)),x)","\int \frac{B\,x^3+A}{{\left(e\,x\right)}^{3/2}\,{\left(b\,x^3+a\right)}^{5/2}} \,d x","Not used",1,"int((A + B*x^3)/((e*x)^(3/2)*(a + b*x^3)^(5/2)), x)","F"
565,1,115,104,4.804353,"\text{Not used}","int((A + B*x^3)/((e*x)^(5/2)*(a + b*x^3)^(5/2)),x)","-\frac{\sqrt{b\,x^3+a}\,\left(\frac{2\,A}{3\,a\,b^2\,e^2}-\frac{x^3\,\left(6\,B\,a^2-24\,A\,a\,b\right)}{9\,a^3\,b^2\,e^2}+\frac{x^6\,\left(16\,A\,b^2-4\,B\,a\,b\right)}{9\,a^3\,b^2\,e^2}\right)}{x^7\,\sqrt{e\,x}+\frac{a^2\,x\,\sqrt{e\,x}}{b^2}+\frac{2\,a\,x^4\,\sqrt{e\,x}}{b}}","Not used",1,"-((a + b*x^3)^(1/2)*((2*A)/(3*a*b^2*e^2) - (x^3*(6*B*a^2 - 24*A*a*b))/(9*a^3*b^2*e^2) + (x^6*(16*A*b^2 - 4*B*a*b))/(9*a^3*b^2*e^2)))/(x^7*(e*x)^(1/2) + (a^2*x*(e*x)^(1/2))/b^2 + (2*a*x^4*(e*x)^(1/2))/b)","B"
566,0,-1,320,0.000000,"\text{Not used}","int((A + B*x^3)/((e*x)^(7/2)*(a + b*x^3)^(5/2)),x)","\int \frac{B\,x^3+A}{{\left(e\,x\right)}^{7/2}\,{\left(b\,x^3+a\right)}^{5/2}} \,d x","Not used",1,"int((A + B*x^3)/((e*x)^(7/2)*(a + b*x^3)^(5/2)), x)","F"
567,1,240,220,4.808756,"\text{Not used}","int((x^11*(a + b*x^3)^(1/3))/(a*d - b*d*x^3),x)","\frac{a\,{\left(b\,x^3+a\right)}^{7/3}}{7\,b^4\,d}-\frac{a^3\,{\left(b\,x^3+a\right)}^{1/3}}{b^4\,d}-\frac{a^2\,{\left(b\,x^3+a\right)}^{4/3}}{4\,b^4\,d}-\frac{{\left(b\,x^3+a\right)}^{10/3}}{10\,b^4\,d}-\frac{2^{1/3}\,a^{10/3}\,\ln\left({\left(b\,x^3+a\right)}^{1/3}-2^{1/3}\,a^{1/3}\right)}{3\,b^4\,d}-\frac{2^{1/3}\,a^{10/3}\,\ln\left(\frac{6\,a^4\,{\left(b\,x^3+a\right)}^{1/3}}{b^4\,d}-\frac{6\,2^{1/3}\,a^{13/3}\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}{b^4\,d}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}{3\,b^4\,d}+\frac{2^{1/3}\,a^{10/3}\,\ln\left(\frac{6\,a^4\,{\left(b\,x^3+a\right)}^{1/3}}{b^4\,d}+\frac{18\,2^{1/3}\,a^{13/3}\,\left(\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)}{b^4\,d}\right)\,\left(\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)}{b^4\,d}","Not used",1,"(a*(a + b*x^3)^(7/3))/(7*b^4*d) - (a^3*(a + b*x^3)^(1/3))/(b^4*d) - (a^2*(a + b*x^3)^(4/3))/(4*b^4*d) - (a + b*x^3)^(10/3)/(10*b^4*d) - (2^(1/3)*a^(10/3)*log((a + b*x^3)^(1/3) - 2^(1/3)*a^(1/3)))/(3*b^4*d) - (2^(1/3)*a^(10/3)*log((6*a^4*(a + b*x^3)^(1/3))/(b^4*d) - (6*2^(1/3)*a^(13/3)*((3^(1/2)*1i)/2 - 1/2))/(b^4*d))*((3^(1/2)*1i)/2 - 1/2))/(3*b^4*d) + (2^(1/3)*a^(10/3)*log((6*a^4*(a + b*x^3)^(1/3))/(b^4*d) + (18*2^(1/3)*a^(13/3)*((3^(1/2)*1i)/6 + 1/6))/(b^4*d))*((3^(1/2)*1i)/6 + 1/6))/(b^4*d)","B"
568,1,219,174,4.650493,"\text{Not used}","int((x^8*(a + b*x^3)^(1/3))/(a*d - b*d*x^3),x)","\frac{2^{1/3}\,{\left(-a\right)}^{7/3}\,\ln\left(6\,a^3\,{\left(b\,x^3+a\right)}^{1/3}-6\,2^{1/3}\,{\left(-a\right)}^{10/3}\right)}{3\,b^3\,d}-\frac{a^2\,{\left(b\,x^3+a\right)}^{1/3}}{b^3\,d}-\frac{{\left(b\,x^3+a\right)}^{7/3}}{7\,b^3\,d}-\frac{2^{1/3}\,{\left(-a\right)}^{7/3}\,\ln\left(\frac{6\,a^3\,{\left(b\,x^3+a\right)}^{1/3}}{b^3\,d}+\frac{6\,2^{1/3}\,{\left(-a\right)}^{10/3}\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}{b^3\,d}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}{3\,b^3\,d}+\frac{2^{1/3}\,{\left(-a\right)}^{7/3}\,\ln\left(\frac{6\,a^3\,{\left(b\,x^3+a\right)}^{1/3}}{b^3\,d}-\frac{18\,2^{1/3}\,{\left(-a\right)}^{10/3}\,\left(-\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)}{b^3\,d}\right)\,\left(-\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)}{b^3\,d}","Not used",1,"(2^(1/3)*(-a)^(7/3)*log(6*a^3*(a + b*x^3)^(1/3) - 6*2^(1/3)*(-a)^(10/3)))/(3*b^3*d) - (a^2*(a + b*x^3)^(1/3))/(b^3*d) - (a + b*x^3)^(7/3)/(7*b^3*d) - (2^(1/3)*(-a)^(7/3)*log((6*a^3*(a + b*x^3)^(1/3))/(b^3*d) + (6*2^(1/3)*(-a)^(10/3)*((3^(1/2)*1i)/2 + 1/2))/(b^3*d))*((3^(1/2)*1i)/2 + 1/2))/(3*b^3*d) + (2^(1/3)*(-a)^(7/3)*log((6*a^3*(a + b*x^3)^(1/3))/(b^3*d) - (18*2^(1/3)*(-a)^(10/3)*((3^(1/2)*1i)/6 - 1/6))/(b^3*d))*((3^(1/2)*1i)/6 - 1/6))/(b^3*d)","B"
569,1,200,172,4.660580,"\text{Not used}","int((x^5*(a + b*x^3)^(1/3))/(a*d - b*d*x^3),x)","-\frac{{\left(b\,x^3+a\right)}^{4/3}}{4\,b^2\,d}-\frac{a\,{\left(b\,x^3+a\right)}^{1/3}}{b^2\,d}-\frac{2^{1/3}\,a^{4/3}\,\ln\left({\left(b\,x^3+a\right)}^{1/3}-2^{1/3}\,a^{1/3}\right)}{3\,b^2\,d}-\frac{2^{1/3}\,a^{4/3}\,\ln\left(\frac{6\,a^2\,{\left(b\,x^3+a\right)}^{1/3}}{b^2\,d}-\frac{6\,2^{1/3}\,a^{7/3}\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}{b^2\,d}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}{3\,b^2\,d}+\frac{2^{1/3}\,a^{4/3}\,\ln\left(\frac{6\,a^2\,{\left(b\,x^3+a\right)}^{1/3}}{b^2\,d}+\frac{18\,2^{1/3}\,a^{7/3}\,\left(\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)}{b^2\,d}\right)\,\left(\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)}{b^2\,d}","Not used",1,"(2^(1/3)*a^(4/3)*log((6*a^2*(a + b*x^3)^(1/3))/(b^2*d) + (18*2^(1/3)*a^(7/3)*((3^(1/2)*1i)/6 + 1/6))/(b^2*d))*((3^(1/2)*1i)/6 + 1/6))/(b^2*d) - (a*(a + b*x^3)^(1/3))/(b^2*d) - (2^(1/3)*a^(4/3)*log((a + b*x^3)^(1/3) - 2^(1/3)*a^(1/3)))/(3*b^2*d) - (2^(1/3)*a^(4/3)*log((6*a^2*(a + b*x^3)^(1/3))/(b^2*d) - (6*2^(1/3)*a^(7/3)*((3^(1/2)*1i)/2 - 1/2))/(b^2*d))*((3^(1/2)*1i)/2 - 1/2))/(3*b^2*d) - (a + b*x^3)^(4/3)/(4*b^2*d)","B"
570,1,194,150,4.637997,"\text{Not used}","int((x^2*(a + b*x^3)^(1/3))/(a*d - b*d*x^3),x)","\frac{2^{1/3}\,{\left(-a\right)}^{1/3}\,\ln\left(6\,a\,{\left(b\,x^3+a\right)}^{1/3}-6\,2^{1/3}\,{\left(-a\right)}^{4/3}\right)}{3\,b\,d}-\frac{{\left(b\,x^3+a\right)}^{1/3}}{b\,d}+\frac{2^{1/3}\,{\left(-a\right)}^{1/3}\,\ln\left(\frac{6\,a\,{\left(b\,x^3+a\right)}^{1/3}}{b\,d}-\frac{6\,2^{1/3}\,{\left(-a\right)}^{4/3}\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}{b\,d}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}{3\,b\,d}-\frac{2^{1/3}\,{\left(-a\right)}^{1/3}\,\ln\left(\frac{6\,a\,{\left(b\,x^3+a\right)}^{1/3}}{b\,d}+\frac{6\,2^{1/3}\,{\left(-a\right)}^{4/3}\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}{b\,d}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}{3\,b\,d}","Not used",1,"(2^(1/3)*(-a)^(1/3)*log(6*a*(a + b*x^3)^(1/3) - 6*2^(1/3)*(-a)^(4/3)))/(3*b*d) - (a + b*x^3)^(1/3)/(b*d) + (2^(1/3)*(-a)^(1/3)*log((6*a*(a + b*x^3)^(1/3))/(b*d) - (6*2^(1/3)*(-a)^(4/3)*((3^(1/2)*1i)/2 - 1/2))/(b*d))*((3^(1/2)*1i)/2 - 1/2))/(3*b*d) - (2^(1/3)*(-a)^(1/3)*log((6*a*(a + b*x^3)^(1/3))/(b*d) + (6*2^(1/3)*(-a)^(4/3)*((3^(1/2)*1i)/2 + 1/2))/(b*d))*((3^(1/2)*1i)/2 + 1/2))/(3*b*d)","B"
571,1,345,214,5.097339,"\text{Not used}","int((a + b*x^3)^(1/3)/(x*(a*d - b*d*x^3)),x)","\ln\left({\left(b\,x^3+a\right)}^{1/3}-a\,d\,{\left(\frac{1}{a^2\,d^3}\right)}^{1/3}\right)\,{\left(\frac{1}{27\,a^2\,d^3}\right)}^{1/3}+\ln\left({\left(b\,x^3+a\right)}^{1/3}+2^{1/3}\,a\,d\,{\left(-\frac{1}{a^2\,d^3}\right)}^{1/3}\right)\,{\left(-\frac{2}{27\,a^2\,d^3}\right)}^{1/3}-\ln\left(2^{1/3}\,a\,d\,{\left(-\frac{1}{a^2\,d^3}\right)}^{1/3}-2\,{\left(b\,x^3+a\right)}^{1/3}+2^{1/3}\,\sqrt{3}\,a\,d\,{\left(-\frac{1}{a^2\,d^3}\right)}^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{2}{27\,a^2\,d^3}\right)}^{1/3}+\ln\left(2\,{\left(b\,x^3+a\right)}^{1/3}-2^{1/3}\,a\,d\,{\left(-\frac{1}{a^2\,d^3}\right)}^{1/3}+2^{1/3}\,\sqrt{3}\,a\,d\,{\left(-\frac{1}{a^2\,d^3}\right)}^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{2}{27\,a^2\,d^3}\right)}^{1/3}+\ln\left(2\,{\left(b\,x^3+a\right)}^{1/3}+a\,d\,{\left(\frac{1}{a^2\,d^3}\right)}^{1/3}-\sqrt{3}\,a\,d\,{\left(\frac{1}{a^2\,d^3}\right)}^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(\frac{1}{27\,a^2\,d^3}\right)}^{1/3}-\ln\left(2\,{\left(b\,x^3+a\right)}^{1/3}+a\,d\,{\left(\frac{1}{a^2\,d^3}\right)}^{1/3}+\sqrt{3}\,a\,d\,{\left(\frac{1}{a^2\,d^3}\right)}^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(\frac{1}{27\,a^2\,d^3}\right)}^{1/3}","Not used",1,"log((a + b*x^3)^(1/3) - a*d*(1/(a^2*d^3))^(1/3))*(1/(27*a^2*d^3))^(1/3) + log((a + b*x^3)^(1/3) + 2^(1/3)*a*d*(-1/(a^2*d^3))^(1/3))*(-2/(27*a^2*d^3))^(1/3) - log(2^(1/3)*a*d*(-1/(a^2*d^3))^(1/3) - 2*(a + b*x^3)^(1/3) + 2^(1/3)*3^(1/2)*a*d*(-1/(a^2*d^3))^(1/3)*1i)*((3^(1/2)*1i)/2 + 1/2)*(-2/(27*a^2*d^3))^(1/3) + log(2*(a + b*x^3)^(1/3) - 2^(1/3)*a*d*(-1/(a^2*d^3))^(1/3) + 2^(1/3)*3^(1/2)*a*d*(-1/(a^2*d^3))^(1/3)*1i)*((3^(1/2)*1i)/2 - 1/2)*(-2/(27*a^2*d^3))^(1/3) + log(2*(a + b*x^3)^(1/3) + a*d*(1/(a^2*d^3))^(1/3) - 3^(1/2)*a*d*(1/(a^2*d^3))^(1/3)*1i)*((3^(1/2)*1i)/2 - 1/2)*(1/(27*a^2*d^3))^(1/3) - log(2*(a + b*x^3)^(1/3) + a*d*(1/(a^2*d^3))^(1/3) + 3^(1/2)*a*d*(1/(a^2*d^3))^(1/3)*1i)*((3^(1/2)*1i)/2 + 1/2)*(1/(27*a^2*d^3))^(1/3)","B"
572,1,455,268,5.345474,"\text{Not used}","int((a + b*x^3)^(1/3)/(x^4*(a*d - b*d*x^3)),x)","\frac{4\,\ln\left(b\,{\left(b\,x^3+a\right)}^{1/3}-a^2\,d\,{\left(\frac{b^3}{a^5\,d^3}\right)}^{1/3}\right)\,{\left(\frac{b^3}{a^5\,d^3}\right)}^{1/3}}{9}+\ln\left(b\,{\left(b\,x^3+a\right)}^{1/3}+2^{1/3}\,a^2\,d\,{\left(-\frac{b^3}{a^5\,d^3}\right)}^{1/3}\right)\,{\left(-\frac{2\,b^3}{27\,a^5\,d^3}\right)}^{1/3}+\ln\left(2\,b\,{\left(b\,x^3+a\right)}^{1/3}+a^2\,d\,{\left(\frac{b^3}{a^5\,d^3}\right)}^{1/3}-\sqrt{3}\,a^2\,d\,{\left(\frac{b^3}{a^5\,d^3}\right)}^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(\frac{64\,b^3}{729\,a^5\,d^3}\right)}^{1/3}-\ln\left(2\,b\,{\left(b\,x^3+a\right)}^{1/3}+a^2\,d\,{\left(\frac{b^3}{a^5\,d^3}\right)}^{1/3}+\sqrt{3}\,a^2\,d\,{\left(\frac{b^3}{a^5\,d^3}\right)}^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(\frac{64\,b^3}{729\,a^5\,d^3}\right)}^{1/3}-\ln\left(2^{1/3}\,a^2\,d\,{\left(-\frac{b^3}{a^5\,d^3}\right)}^{1/3}-2\,b\,{\left(b\,x^3+a\right)}^{1/3}+2^{1/3}\,\sqrt{3}\,a^2\,d\,{\left(-\frac{b^3}{a^5\,d^3}\right)}^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{2\,b^3}{27\,a^5\,d^3}\right)}^{1/3}+\ln\left(2\,b\,{\left(b\,x^3+a\right)}^{1/3}-2^{1/3}\,a^2\,d\,{\left(-\frac{b^3}{a^5\,d^3}\right)}^{1/3}+2^{1/3}\,\sqrt{3}\,a^2\,d\,{\left(-\frac{b^3}{a^5\,d^3}\right)}^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{2\,b^3}{27\,a^5\,d^3}\right)}^{1/3}-\frac{b\,{\left(b\,x^3+a\right)}^{1/3}}{3\,a\,\left(d\,\left(b\,x^3+a\right)-a\,d\right)}","Not used",1,"(4*log(b*(a + b*x^3)^(1/3) - a^2*d*(b^3/(a^5*d^3))^(1/3))*(b^3/(a^5*d^3))^(1/3))/9 + log(b*(a + b*x^3)^(1/3) + 2^(1/3)*a^2*d*(-b^3/(a^5*d^3))^(1/3))*(-(2*b^3)/(27*a^5*d^3))^(1/3) + log(2*b*(a + b*x^3)^(1/3) + a^2*d*(b^3/(a^5*d^3))^(1/3) - 3^(1/2)*a^2*d*(b^3/(a^5*d^3))^(1/3)*1i)*((3^(1/2)*1i)/2 - 1/2)*((64*b^3)/(729*a^5*d^3))^(1/3) - log(2*b*(a + b*x^3)^(1/3) + a^2*d*(b^3/(a^5*d^3))^(1/3) + 3^(1/2)*a^2*d*(b^3/(a^5*d^3))^(1/3)*1i)*((3^(1/2)*1i)/2 + 1/2)*((64*b^3)/(729*a^5*d^3))^(1/3) - log(2^(1/3)*a^2*d*(-b^3/(a^5*d^3))^(1/3) - 2*b*(a + b*x^3)^(1/3) + 2^(1/3)*3^(1/2)*a^2*d*(-b^3/(a^5*d^3))^(1/3)*1i)*((3^(1/2)*1i)/2 + 1/2)*(-(2*b^3)/(27*a^5*d^3))^(1/3) + log(2*b*(a + b*x^3)^(1/3) - 2^(1/3)*a^2*d*(-b^3/(a^5*d^3))^(1/3) + 2^(1/3)*3^(1/2)*a^2*d*(-b^3/(a^5*d^3))^(1/3)*1i)*((3^(1/2)*1i)/2 - 1/2)*(-(2*b^3)/(27*a^5*d^3))^(1/3) - (b*(a + b*x^3)^(1/3))/(3*a*(d*(a + b*x^3) - a*d))","B"
573,1,490,283,5.441808,"\text{Not used}","int((a + b*x^3)^(1/3)/(x^7*(a*d - b*d*x^3)),x)","\frac{\frac{2\,b^2\,{\left(b\,x^3+a\right)}^{1/3}}{9\,a}-\frac{7\,b^2\,{\left(b\,x^3+a\right)}^{4/3}}{18\,a^2}}{d\,{\left(b\,x^3+a\right)}^2+a^2\,d-2\,a\,d\,\left(b\,x^3+a\right)}+\frac{11\,\ln\left(b^2\,{\left(b\,x^3+a\right)}^{1/3}-a^3\,d\,{\left(\frac{b^6}{a^8\,d^3}\right)}^{1/3}\right)\,{\left(\frac{b^6}{a^8\,d^3}\right)}^{1/3}}{27}+\ln\left(b^2\,{\left(b\,x^3+a\right)}^{1/3}+2^{1/3}\,a^3\,d\,{\left(-\frac{b^6}{a^8\,d^3}\right)}^{1/3}\right)\,{\left(-\frac{2\,b^6}{27\,a^8\,d^3}\right)}^{1/3}-\ln\left(2^{1/3}\,a^3\,d\,{\left(-\frac{b^6}{a^8\,d^3}\right)}^{1/3}-2\,b^2\,{\left(b\,x^3+a\right)}^{1/3}+2^{1/3}\,\sqrt{3}\,a^3\,d\,{\left(-\frac{b^6}{a^8\,d^3}\right)}^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{2\,b^6}{27\,a^8\,d^3}\right)}^{1/3}+\ln\left(2\,b^2\,{\left(b\,x^3+a\right)}^{1/3}-2^{1/3}\,a^3\,d\,{\left(-\frac{b^6}{a^8\,d^3}\right)}^{1/3}+2^{1/3}\,\sqrt{3}\,a^3\,d\,{\left(-\frac{b^6}{a^8\,d^3}\right)}^{1/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{2\,b^6}{27\,a^8\,d^3}\right)}^{1/3}+\frac{11\,\ln\left(2\,b^2\,{\left(b\,x^3+a\right)}^{1/3}+a^3\,d\,{\left(\frac{b^6}{a^8\,d^3}\right)}^{1/3}-\sqrt{3}\,a^3\,d\,{\left(\frac{b^6}{a^8\,d^3}\right)}^{1/3}\,1{}\mathrm{i}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(\frac{b^6}{a^8\,d^3}\right)}^{1/3}}{54}-\frac{11\,\ln\left(2\,b^2\,{\left(b\,x^3+a\right)}^{1/3}+a^3\,d\,{\left(\frac{b^6}{a^8\,d^3}\right)}^{1/3}+\sqrt{3}\,a^3\,d\,{\left(\frac{b^6}{a^8\,d^3}\right)}^{1/3}\,1{}\mathrm{i}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(\frac{b^6}{a^8\,d^3}\right)}^{1/3}}{54}","Not used",1,"((2*b^2*(a + b*x^3)^(1/3))/(9*a) - (7*b^2*(a + b*x^3)^(4/3))/(18*a^2))/(d*(a + b*x^3)^2 + a^2*d - 2*a*d*(a + b*x^3)) + (11*log(b^2*(a + b*x^3)^(1/3) - a^3*d*(b^6/(a^8*d^3))^(1/3))*(b^6/(a^8*d^3))^(1/3))/27 + log(b^2*(a + b*x^3)^(1/3) + 2^(1/3)*a^3*d*(-b^6/(a^8*d^3))^(1/3))*(-(2*b^6)/(27*a^8*d^3))^(1/3) - log(2^(1/3)*a^3*d*(-b^6/(a^8*d^3))^(1/3) - 2*b^2*(a + b*x^3)^(1/3) + 2^(1/3)*3^(1/2)*a^3*d*(-b^6/(a^8*d^3))^(1/3)*1i)*((3^(1/2)*1i)/2 + 1/2)*(-(2*b^6)/(27*a^8*d^3))^(1/3) + log(2*b^2*(a + b*x^3)^(1/3) - 2^(1/3)*a^3*d*(-b^6/(a^8*d^3))^(1/3) + 2^(1/3)*3^(1/2)*a^3*d*(-b^6/(a^8*d^3))^(1/3)*1i)*((3^(1/2)*1i)/2 - 1/2)*(-(2*b^6)/(27*a^8*d^3))^(1/3) + (11*log(2*b^2*(a + b*x^3)^(1/3) + a^3*d*(b^6/(a^8*d^3))^(1/3) - 3^(1/2)*a^3*d*(b^6/(a^8*d^3))^(1/3)*1i)*(3^(1/2)*1i - 1)*(b^6/(a^8*d^3))^(1/3))/54 - (11*log(2*b^2*(a + b*x^3)^(1/3) + a^3*d*(b^6/(a^8*d^3))^(1/3) + 3^(1/2)*a^3*d*(b^6/(a^8*d^3))^(1/3)*1i)*(3^(1/2)*1i + 1)*(b^6/(a^8*d^3))^(1/3))/54","B"
574,0,-1,268,0.000000,"\text{Not used}","int((x^7*(a + b*x^3)^(1/3))/(a*d - b*d*x^3),x)","\int \frac{x^7\,{\left(b\,x^3+a\right)}^{1/3}}{a\,d-b\,d\,x^3} \,d x","Not used",1,"int((x^7*(a + b*x^3)^(1/3))/(a*d - b*d*x^3), x)","F"
575,0,-1,233,0.000000,"\text{Not used}","int((x^4*(a + b*x^3)^(1/3))/(a*d - b*d*x^3),x)","\int \frac{x^4\,{\left(b\,x^3+a\right)}^{1/3}}{a\,d-b\,d\,x^3} \,d x","Not used",1,"int((x^4*(a + b*x^3)^(1/3))/(a*d - b*d*x^3), x)","F"
576,0,-1,201,0.000000,"\text{Not used}","int((x*(a + b*x^3)^(1/3))/(a*d - b*d*x^3),x)","\int \frac{x\,{\left(b\,x^3+a\right)}^{1/3}}{a\,d-b\,d\,x^3} \,d x","Not used",1,"int((x*(a + b*x^3)^(1/3))/(a*d - b*d*x^3), x)","F"
577,0,-1,156,0.000000,"\text{Not used}","int((a + b*x^3)^(1/3)/(x^2*(a*d - b*d*x^3)),x)","\int \frac{{\left(b\,x^3+a\right)}^{1/3}}{x^2\,\left(a\,d-b\,d\,x^3\right)} \,d x","Not used",1,"int((a + b*x^3)^(1/3)/(x^2*(a*d - b*d*x^3)), x)","F"
578,0,-1,183,0.000000,"\text{Not used}","int((a + b*x^3)^(1/3)/(x^5*(a*d - b*d*x^3)),x)","\int \frac{{\left(b\,x^3+a\right)}^{1/3}}{x^5\,\left(a\,d-b\,d\,x^3\right)} \,d x","Not used",1,"int((a + b*x^3)^(1/3)/(x^5*(a*d - b*d*x^3)), x)","F"
579,0,-1,210,0.000000,"\text{Not used}","int((a + b*x^3)^(1/3)/(x^8*(a*d - b*d*x^3)),x)","\int \frac{{\left(b\,x^3+a\right)}^{1/3}}{x^8\,\left(a\,d-b\,d\,x^3\right)} \,d x","Not used",1,"int((a + b*x^3)^(1/3)/(x^8*(a*d - b*d*x^3)), x)","F"
580,0,-1,237,0.000000,"\text{Not used}","int((a + b*x^3)^(1/3)/(x^11*(a*d - b*d*x^3)),x)","\int \frac{{\left(b\,x^3+a\right)}^{1/3}}{x^{11}\,\left(a\,d-b\,d\,x^3\right)} \,d x","Not used",1,"int((a + b*x^3)^(1/3)/(x^11*(a*d - b*d*x^3)), x)","F"
581,0,-1,521,0.000000,"\text{Not used}","int((x^6*(a + b*x^3)^(1/3))/(a*d - b*d*x^3),x)","\int \frac{x^6\,{\left(b\,x^3+a\right)}^{1/3}}{a\,d-b\,d\,x^3} \,d x","Not used",1,"int((x^6*(a + b*x^3)^(1/3))/(a*d - b*d*x^3), x)","F"
582,0,-1,494,0.000000,"\text{Not used}","int((x^3*(a + b*x^3)^(1/3))/(a*d - b*d*x^3),x)","\int \frac{x^3\,{\left(b\,x^3+a\right)}^{1/3}}{a\,d-b\,d\,x^3} \,d x","Not used",1,"int((x^3*(a + b*x^3)^(1/3))/(a*d - b*d*x^3), x)","F"
583,0,-1,416,0.000000,"\text{Not used}","int((a + b*x^3)^(1/3)/(a*d - b*d*x^3),x)","\int \frac{{\left(b\,x^3+a\right)}^{1/3}}{a\,d-b\,d\,x^3} \,d x","Not used",1,"int((a + b*x^3)^(1/3)/(a*d - b*d*x^3), x)","F"
584,0,-1,496,0.000000,"\text{Not used}","int((a + b*x^3)^(1/3)/(x^3*(a*d - b*d*x^3)),x)","\int \frac{{\left(b\,x^3+a\right)}^{1/3}}{x^3\,\left(a\,d-b\,d\,x^3\right)} \,d x","Not used",1,"int((a + b*x^3)^(1/3)/(x^3*(a*d - b*d*x^3)), x)","F"
585,0,-1,523,0.000000,"\text{Not used}","int((a + b*x^3)^(1/3)/(x^6*(a*d - b*d*x^3)),x)","\int \frac{{\left(b\,x^3+a\right)}^{1/3}}{x^6\,\left(a\,d-b\,d\,x^3\right)} \,d x","Not used",1,"int((a + b*x^3)^(1/3)/(x^6*(a*d - b*d*x^3)), x)","F"
586,1,261,223,4.846121,"\text{Not used}","int((x^11*(a + b*x^3)^(2/3))/(a*d - b*d*x^3),x)","\frac{a\,{\left(b\,x^3+a\right)}^{8/3}}{8\,b^4\,d}-\frac{a^3\,{\left(b\,x^3+a\right)}^{2/3}}{2\,b^4\,d}-\frac{a^2\,{\left(b\,x^3+a\right)}^{5/3}}{5\,b^4\,d}-\frac{{\left(b\,x^3+a\right)}^{11/3}}{11\,b^4\,d}+\frac{4^{1/3}\,{\left(-a\right)}^{11/3}\,\ln\left(4\,a^8\,{\left(b\,x^3+a\right)}^{1/3}+4\,2^{1/3}\,{\left(-a\right)}^{25/3}\right)}{3\,b^4\,d}-\frac{4^{1/3}\,{\left(-a\right)}^{11/3}\,\ln\left(\frac{4\,a^8\,{\left(b\,x^3+a\right)}^{1/3}}{b^8\,d^2}+\frac{2\,4^{2/3}\,{\left(-a\right)}^{25/3}\,{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2}{b^8\,d^2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}{3\,b^4\,d}+\frac{4^{1/3}\,{\left(-a\right)}^{11/3}\,\ln\left(\frac{4\,a^8\,{\left(b\,x^3+a\right)}^{1/3}}{b^8\,d^2}+\frac{18\,4^{2/3}\,{\left(-a\right)}^{25/3}\,{\left(-\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)}^2}{b^8\,d^2}\right)\,\left(-\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)}{b^4\,d}","Not used",1,"(a*(a + b*x^3)^(8/3))/(8*b^4*d) - (a^3*(a + b*x^3)^(2/3))/(2*b^4*d) - (a^2*(a + b*x^3)^(5/3))/(5*b^4*d) - (a + b*x^3)^(11/3)/(11*b^4*d) + (4^(1/3)*(-a)^(11/3)*log(4*a^8*(a + b*x^3)^(1/3) + 4*2^(1/3)*(-a)^(25/3)))/(3*b^4*d) - (4^(1/3)*(-a)^(11/3)*log((4*a^8*(a + b*x^3)^(1/3))/(b^8*d^2) + (2*4^(2/3)*(-a)^(25/3)*((3^(1/2)*1i)/2 + 1/2)^2)/(b^8*d^2))*((3^(1/2)*1i)/2 + 1/2))/(3*b^4*d) + (4^(1/3)*(-a)^(11/3)*log((4*a^8*(a + b*x^3)^(1/3))/(b^8*d^2) + (18*4^(2/3)*(-a)^(25/3)*((3^(1/2)*1i)/6 - 1/6)^2)/(b^8*d^2))*((3^(1/2)*1i)/6 - 1/6))/(b^4*d)","B"
587,1,206,177,4.914846,"\text{Not used}","int((x^8*(a + b*x^3)^(2/3))/(a*d - b*d*x^3),x)","-\frac{{\left(b\,x^3+a\right)}^{8/3}}{8\,b^3\,d}-\frac{a^2\,{\left(b\,x^3+a\right)}^{2/3}}{2\,b^3\,d}-\frac{4^{1/3}\,a^{8/3}\,\ln\left({\left(b\,x^3+a\right)}^{1/3}-2^{1/3}\,a^{1/3}\right)}{3\,b^3\,d}-\frac{4^{1/3}\,a^{8/3}\,\ln\left(\frac{4\,a^6\,{\left(b\,x^3+a\right)}^{1/3}}{b^6\,d^2}-\frac{2\,4^{2/3}\,a^{19/3}\,{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2}{b^6\,d^2}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}{3\,b^3\,d}+\frac{4^{1/3}\,a^{8/3}\,\ln\left(\frac{4\,a^6\,{\left(b\,x^3+a\right)}^{1/3}}{b^6\,d^2}-\frac{18\,4^{2/3}\,a^{19/3}\,{\left(\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)}^2}{b^6\,d^2}\right)\,\left(\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)}{b^3\,d}","Not used",1,"(4^(1/3)*a^(8/3)*log((4*a^6*(a + b*x^3)^(1/3))/(b^6*d^2) - (18*4^(2/3)*a^(19/3)*((3^(1/2)*1i)/6 + 1/6)^2)/(b^6*d^2))*((3^(1/2)*1i)/6 + 1/6))/(b^3*d) - (a^2*(a + b*x^3)^(2/3))/(2*b^3*d) - (4^(1/3)*a^(8/3)*log((a + b*x^3)^(1/3) - 2^(1/3)*a^(1/3)))/(3*b^3*d) - (4^(1/3)*a^(8/3)*log((4*a^6*(a + b*x^3)^(1/3))/(b^6*d^2) - (2*4^(2/3)*a^(19/3)*((3^(1/2)*1i)/2 - 1/2)^2)/(b^6*d^2))*((3^(1/2)*1i)/2 - 1/2))/(3*b^3*d) - (a + b*x^3)^(8/3)/(8*b^3*d)","B"
588,1,221,175,4.838538,"\text{Not used}","int((x^5*(a + b*x^3)^(2/3))/(a*d - b*d*x^3),x)","\frac{4^{1/3}\,{\left(-a\right)}^{5/3}\,\ln\left(4\,a^4\,{\left(b\,x^3+a\right)}^{1/3}+4\,2^{1/3}\,{\left(-a\right)}^{13/3}\right)}{3\,b^2\,d}-\frac{a\,{\left(b\,x^3+a\right)}^{2/3}}{2\,b^2\,d}-\frac{{\left(b\,x^3+a\right)}^{5/3}}{5\,b^2\,d}-\frac{4^{1/3}\,{\left(-a\right)}^{5/3}\,\ln\left(\frac{4\,a^4\,{\left(b\,x^3+a\right)}^{1/3}}{b^4\,d^2}+\frac{2\,4^{2/3}\,{\left(-a\right)}^{13/3}\,{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2}{b^4\,d^2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}{3\,b^2\,d}+\frac{4^{1/3}\,{\left(-a\right)}^{5/3}\,\ln\left(\frac{4\,a^4\,{\left(b\,x^3+a\right)}^{1/3}}{b^4\,d^2}+\frac{18\,4^{2/3}\,{\left(-a\right)}^{13/3}\,{\left(-\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)}^2}{b^4\,d^2}\right)\,\left(-\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)}{b^2\,d}","Not used",1,"(4^(1/3)*(-a)^(5/3)*log(4*a^4*(a + b*x^3)^(1/3) + 4*2^(1/3)*(-a)^(13/3)))/(3*b^2*d) - (a*(a + b*x^3)^(2/3))/(2*b^2*d) - (a + b*x^3)^(5/3)/(5*b^2*d) - (4^(1/3)*(-a)^(5/3)*log((4*a^4*(a + b*x^3)^(1/3))/(b^4*d^2) + (2*4^(2/3)*(-a)^(13/3)*((3^(1/2)*1i)/2 + 1/2)^2)/(b^4*d^2))*((3^(1/2)*1i)/2 + 1/2))/(3*b^2*d) + (4^(1/3)*(-a)^(5/3)*log((4*a^4*(a + b*x^3)^(1/3))/(b^4*d^2) + (18*4^(2/3)*(-a)^(13/3)*((3^(1/2)*1i)/6 - 1/6)^2)/(b^4*d^2))*((3^(1/2)*1i)/6 - 1/6))/(b^2*d)","B"
589,1,186,153,4.829912,"\text{Not used}","int((x^2*(a + b*x^3)^(2/3))/(a*d - b*d*x^3),x)","-\frac{{\left(b\,x^3+a\right)}^{2/3}}{2\,b\,d}-\frac{4^{1/3}\,a^{2/3}\,\ln\left({\left(b\,x^3+a\right)}^{1/3}-2^{1/3}\,a^{1/3}\right)}{3\,b\,d}-\frac{4^{1/3}\,a^{2/3}\,\ln\left(\frac{4\,a^2\,{\left(b\,x^3+a\right)}^{1/3}}{b^2\,d^2}-\frac{2\,4^{2/3}\,a^{7/3}\,{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2}{b^2\,d^2}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}{3\,b\,d}+\frac{4^{1/3}\,a^{2/3}\,\ln\left(\frac{4\,a^2\,{\left(b\,x^3+a\right)}^{1/3}}{b^2\,d^2}-\frac{18\,4^{2/3}\,a^{7/3}\,{\left(\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)}^2}{b^2\,d^2}\right)\,\left(\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)}{b\,d}","Not used",1,"(4^(1/3)*a^(2/3)*log((4*a^2*(a + b*x^3)^(1/3))/(b^2*d^2) - (18*4^(2/3)*a^(7/3)*((3^(1/2)*1i)/6 + 1/6)^2)/(b^2*d^2))*((3^(1/2)*1i)/6 + 1/6))/(b*d) - (4^(1/3)*a^(2/3)*log((a + b*x^3)^(1/3) - 2^(1/3)*a^(1/3)))/(3*b*d) - (4^(1/3)*a^(2/3)*log((4*a^2*(a + b*x^3)^(1/3))/(b^2*d^2) - (2*4^(2/3)*a^(7/3)*((3^(1/2)*1i)/2 - 1/2)^2)/(b^2*d^2))*((3^(1/2)*1i)/2 - 1/2))/(3*b*d) - (a + b*x^3)^(2/3)/(2*b*d)","B"
590,1,369,214,5.855346,"\text{Not used}","int((a + b*x^3)^(2/3)/(x*(a*d - b*d*x^3)),x)","\ln\left(2\,{\left(b\,x^3+a\right)}^{1/3}-2\,2^{1/3}\,a\,d^2\,{\left(-\frac{1}{a\,d^3}\right)}^{2/3}\right)\,{\left(-\frac{4}{27\,a\,d^3}\right)}^{1/3}+\ln\left({\left(b\,x^3+a\right)}^{1/3}-a\,d^2\,{\left(\frac{1}{a\,d^3}\right)}^{2/3}\right)\,{\left(\frac{1}{27\,a\,d^3}\right)}^{1/3}-\ln\left(4\,{\left(b\,x^3+a\right)}^{1/3}+2\,2^{1/3}\,a\,d^2\,{\left(-\frac{1}{a\,d^3}\right)}^{2/3}-2^{1/3}\,\sqrt{3}\,a\,d^2\,{\left(-\frac{1}{a\,d^3}\right)}^{2/3}\,2{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{4}{27\,a\,d^3}\right)}^{1/3}+\ln\left(4\,{\left(b\,x^3+a\right)}^{1/3}+2\,2^{1/3}\,a\,d^2\,{\left(-\frac{1}{a\,d^3}\right)}^{2/3}+2^{1/3}\,\sqrt{3}\,a\,d^2\,{\left(-\frac{1}{a\,d^3}\right)}^{2/3}\,2{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{4}{27\,a\,d^3}\right)}^{1/3}-\ln\left(2\,{\left(b\,x^3+a\right)}^{1/3}+a\,d^2\,{\left(\frac{1}{a\,d^3}\right)}^{2/3}-\sqrt{3}\,a\,d^2\,{\left(\frac{1}{a\,d^3}\right)}^{2/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(\frac{1}{27\,a\,d^3}\right)}^{1/3}+\ln\left(2\,{\left(b\,x^3+a\right)}^{1/3}+a\,d^2\,{\left(\frac{1}{a\,d^3}\right)}^{2/3}+\sqrt{3}\,a\,d^2\,{\left(\frac{1}{a\,d^3}\right)}^{2/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(\frac{1}{27\,a\,d^3}\right)}^{1/3}","Not used",1,"log(2*(a + b*x^3)^(1/3) - 2*2^(1/3)*a*d^2*(-1/(a*d^3))^(2/3))*(-4/(27*a*d^3))^(1/3) + log((a + b*x^3)^(1/3) - a*d^2*(1/(a*d^3))^(2/3))*(1/(27*a*d^3))^(1/3) - log(4*(a + b*x^3)^(1/3) + 2*2^(1/3)*a*d^2*(-1/(a*d^3))^(2/3) - 2^(1/3)*3^(1/2)*a*d^2*(-1/(a*d^3))^(2/3)*2i)*((3^(1/2)*1i)/2 + 1/2)*(-4/(27*a*d^3))^(1/3) + log(4*(a + b*x^3)^(1/3) + 2*2^(1/3)*a*d^2*(-1/(a*d^3))^(2/3) + 2^(1/3)*3^(1/2)*a*d^2*(-1/(a*d^3))^(2/3)*2i)*((3^(1/2)*1i)/2 - 1/2)*(-4/(27*a*d^3))^(1/3) - log(2*(a + b*x^3)^(1/3) + a*d^2*(1/(a*d^3))^(2/3) - 3^(1/2)*a*d^2*(1/(a*d^3))^(2/3)*1i)*((3^(1/2)*1i)/2 + 1/2)*(1/(27*a*d^3))^(1/3) + log(2*(a + b*x^3)^(1/3) + a*d^2*(1/(a*d^3))^(2/3) + 3^(1/2)*a*d^2*(1/(a*d^3))^(2/3)*1i)*((3^(1/2)*1i)/2 - 1/2)*(1/(27*a*d^3))^(1/3)","B"
591,1,490,269,5.560901,"\text{Not used}","int((a + b*x^3)^(2/3)/(x^4*(a*d - b*d*x^3)),x)","\ln\left(2\,b^2\,{\left(b\,x^3+a\right)}^{1/3}-2\,2^{1/3}\,a^3\,d^2\,{\left(-\frac{b^3}{a^4\,d^3}\right)}^{2/3}\right)\,{\left(-\frac{4\,b^3}{27\,a^4\,d^3}\right)}^{1/3}+\frac{5\,\ln\left(b^2\,{\left(b\,x^3+a\right)}^{1/3}-a^3\,d^2\,{\left(\frac{b^3}{a^4\,d^3}\right)}^{2/3}\right)\,{\left(\frac{b^3}{a^4\,d^3}\right)}^{1/3}}{9}-\ln\left(4\,b^2\,{\left(b\,x^3+a\right)}^{1/3}+2\,2^{1/3}\,a^3\,d^2\,{\left(-\frac{b^3}{a^4\,d^3}\right)}^{2/3}-2^{1/3}\,\sqrt{3}\,a^3\,d^2\,{\left(-\frac{b^3}{a^4\,d^3}\right)}^{2/3}\,2{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{4\,b^3}{27\,a^4\,d^3}\right)}^{1/3}+\ln\left(4\,b^2\,{\left(b\,x^3+a\right)}^{1/3}+2\,2^{1/3}\,a^3\,d^2\,{\left(-\frac{b^3}{a^4\,d^3}\right)}^{2/3}+2^{1/3}\,\sqrt{3}\,a^3\,d^2\,{\left(-\frac{b^3}{a^4\,d^3}\right)}^{2/3}\,2{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{4\,b^3}{27\,a^4\,d^3}\right)}^{1/3}-\ln\left(2\,b^2\,{\left(b\,x^3+a\right)}^{1/3}+a^3\,d^2\,{\left(\frac{b^3}{a^4\,d^3}\right)}^{2/3}-\sqrt{3}\,a^3\,d^2\,{\left(\frac{b^3}{a^4\,d^3}\right)}^{2/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(\frac{125\,b^3}{729\,a^4\,d^3}\right)}^{1/3}+\ln\left(2\,b^2\,{\left(b\,x^3+a\right)}^{1/3}+a^3\,d^2\,{\left(\frac{b^3}{a^4\,d^3}\right)}^{2/3}+\sqrt{3}\,a^3\,d^2\,{\left(\frac{b^3}{a^4\,d^3}\right)}^{2/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(\frac{125\,b^3}{729\,a^4\,d^3}\right)}^{1/3}-\frac{b\,{\left(b\,x^3+a\right)}^{2/3}}{3\,a\,\left(d\,\left(b\,x^3+a\right)-a\,d\right)}","Not used",1,"log(2*b^2*(a + b*x^3)^(1/3) - 2*2^(1/3)*a^3*d^2*(-b^3/(a^4*d^3))^(2/3))*(-(4*b^3)/(27*a^4*d^3))^(1/3) + (5*log(b^2*(a + b*x^3)^(1/3) - a^3*d^2*(b^3/(a^4*d^3))^(2/3))*(b^3/(a^4*d^3))^(1/3))/9 - log(4*b^2*(a + b*x^3)^(1/3) + 2*2^(1/3)*a^3*d^2*(-b^3/(a^4*d^3))^(2/3) - 2^(1/3)*3^(1/2)*a^3*d^2*(-b^3/(a^4*d^3))^(2/3)*2i)*((3^(1/2)*1i)/2 + 1/2)*(-(4*b^3)/(27*a^4*d^3))^(1/3) + log(4*b^2*(a + b*x^3)^(1/3) + 2*2^(1/3)*a^3*d^2*(-b^3/(a^4*d^3))^(2/3) + 2^(1/3)*3^(1/2)*a^3*d^2*(-b^3/(a^4*d^3))^(2/3)*2i)*((3^(1/2)*1i)/2 - 1/2)*(-(4*b^3)/(27*a^4*d^3))^(1/3) - log(2*b^2*(a + b*x^3)^(1/3) + a^3*d^2*(b^3/(a^4*d^3))^(2/3) - 3^(1/2)*a^3*d^2*(b^3/(a^4*d^3))^(2/3)*1i)*((3^(1/2)*1i)/2 + 1/2)*((125*b^3)/(729*a^4*d^3))^(1/3) + log(2*b^2*(a + b*x^3)^(1/3) + a^3*d^2*(b^3/(a^4*d^3))^(2/3) + 3^(1/2)*a^3*d^2*(b^3/(a^4*d^3))^(2/3)*1i)*((3^(1/2)*1i)/2 - 1/2)*((125*b^3)/(729*a^4*d^3))^(1/3) - (b*(a + b*x^3)^(2/3))/(3*a*(d*(a + b*x^3) - a*d))","B"
592,1,513,284,5.454691,"\text{Not used}","int((a + b*x^3)^(2/3)/(x^7*(a*d - b*d*x^3)),x)","\frac{\frac{5\,b^2\,{\left(b\,x^3+a\right)}^{2/3}}{18\,a}-\frac{4\,b^2\,{\left(b\,x^3+a\right)}^{5/3}}{9\,a^2}}{d\,{\left(b\,x^3+a\right)}^2+a^2\,d-2\,a\,d\,\left(b\,x^3+a\right)}+\ln\left(2\,b^4\,{\left(b\,x^3+a\right)}^{1/3}-2\,2^{1/3}\,a^5\,d^2\,{\left(-\frac{b^6}{a^7\,d^3}\right)}^{2/3}\right)\,{\left(-\frac{4\,b^6}{27\,a^7\,d^3}\right)}^{1/3}+\frac{14\,\ln\left(b^4\,{\left(b\,x^3+a\right)}^{1/3}-a^5\,d^2\,{\left(\frac{b^6}{a^7\,d^3}\right)}^{2/3}\right)\,{\left(\frac{b^6}{a^7\,d^3}\right)}^{1/3}}{27}-\ln\left(4\,b^4\,{\left(b\,x^3+a\right)}^{1/3}+2\,2^{1/3}\,a^5\,d^2\,{\left(-\frac{b^6}{a^7\,d^3}\right)}^{2/3}-2^{1/3}\,\sqrt{3}\,a^5\,d^2\,{\left(-\frac{b^6}{a^7\,d^3}\right)}^{2/3}\,2{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{4\,b^6}{27\,a^7\,d^3}\right)}^{1/3}+\ln\left(4\,b^4\,{\left(b\,x^3+a\right)}^{1/3}+2\,2^{1/3}\,a^5\,d^2\,{\left(-\frac{b^6}{a^7\,d^3}\right)}^{2/3}+2^{1/3}\,\sqrt{3}\,a^5\,d^2\,{\left(-\frac{b^6}{a^7\,d^3}\right)}^{2/3}\,2{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{4\,b^6}{27\,a^7\,d^3}\right)}^{1/3}-\frac{7\,\ln\left(2\,b^4\,{\left(b\,x^3+a\right)}^{1/3}+a^5\,d^2\,{\left(\frac{b^6}{a^7\,d^3}\right)}^{2/3}-\sqrt{3}\,a^5\,d^2\,{\left(\frac{b^6}{a^7\,d^3}\right)}^{2/3}\,1{}\mathrm{i}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(\frac{b^6}{a^7\,d^3}\right)}^{1/3}}{27}+\frac{7\,\ln\left(2\,b^4\,{\left(b\,x^3+a\right)}^{1/3}+a^5\,d^2\,{\left(\frac{b^6}{a^7\,d^3}\right)}^{2/3}+\sqrt{3}\,a^5\,d^2\,{\left(\frac{b^6}{a^7\,d^3}\right)}^{2/3}\,1{}\mathrm{i}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(\frac{b^6}{a^7\,d^3}\right)}^{1/3}}{27}","Not used",1,"((5*b^2*(a + b*x^3)^(2/3))/(18*a) - (4*b^2*(a + b*x^3)^(5/3))/(9*a^2))/(d*(a + b*x^3)^2 + a^2*d - 2*a*d*(a + b*x^3)) + log(2*b^4*(a + b*x^3)^(1/3) - 2*2^(1/3)*a^5*d^2*(-b^6/(a^7*d^3))^(2/3))*(-(4*b^6)/(27*a^7*d^3))^(1/3) + (14*log(b^4*(a + b*x^3)^(1/3) - a^5*d^2*(b^6/(a^7*d^3))^(2/3))*(b^6/(a^7*d^3))^(1/3))/27 - log(4*b^4*(a + b*x^3)^(1/3) + 2*2^(1/3)*a^5*d^2*(-b^6/(a^7*d^3))^(2/3) - 2^(1/3)*3^(1/2)*a^5*d^2*(-b^6/(a^7*d^3))^(2/3)*2i)*((3^(1/2)*1i)/2 + 1/2)*(-(4*b^6)/(27*a^7*d^3))^(1/3) + log(4*b^4*(a + b*x^3)^(1/3) + 2*2^(1/3)*a^5*d^2*(-b^6/(a^7*d^3))^(2/3) + 2^(1/3)*3^(1/2)*a^5*d^2*(-b^6/(a^7*d^3))^(2/3)*2i)*((3^(1/2)*1i)/2 - 1/2)*(-(4*b^6)/(27*a^7*d^3))^(1/3) - (7*log(2*b^4*(a + b*x^3)^(1/3) + a^5*d^2*(b^6/(a^7*d^3))^(2/3) - 3^(1/2)*a^5*d^2*(b^6/(a^7*d^3))^(2/3)*1i)*(3^(1/2)*1i + 1)*(b^6/(a^7*d^3))^(1/3))/27 + (7*log(2*b^4*(a + b*x^3)^(1/3) + a^5*d^2*(b^6/(a^7*d^3))^(2/3) + 3^(1/2)*a^5*d^2*(b^6/(a^7*d^3))^(2/3)*1i)*(3^(1/2)*1i - 1)*(b^6/(a^7*d^3))^(1/3))/27","B"
593,0,-1,264,0.000000,"\text{Not used}","int((x^6*(a + b*x^3)^(2/3))/(a*d - b*d*x^3),x)","\int \frac{x^6\,{\left(b\,x^3+a\right)}^{2/3}}{a\,d-b\,d\,x^3} \,d x","Not used",1,"int((x^6*(a + b*x^3)^(2/3))/(a*d - b*d*x^3), x)","F"
594,0,-1,229,0.000000,"\text{Not used}","int((x^3*(a + b*x^3)^(2/3))/(a*d - b*d*x^3),x)","\int \frac{x^3\,{\left(b\,x^3+a\right)}^{2/3}}{a\,d-b\,d\,x^3} \,d x","Not used",1,"int((x^3*(a + b*x^3)^(2/3))/(a*d - b*d*x^3), x)","F"
595,0,-1,200,0.000000,"\text{Not used}","int((a + b*x^3)^(2/3)/(a*d - b*d*x^3),x)","\int \frac{{\left(b\,x^3+a\right)}^{2/3}}{a\,d-b\,d\,x^3} \,d x","Not used",1,"int((a + b*x^3)^(2/3)/(a*d - b*d*x^3), x)","F"
596,0,-1,157,0.000000,"\text{Not used}","int((a + b*x^3)^(2/3)/(x^3*(a*d - b*d*x^3)),x)","\int \frac{{\left(b\,x^3+a\right)}^{2/3}}{x^3\,\left(a\,d-b\,d\,x^3\right)} \,d x","Not used",1,"int((a + b*x^3)^(2/3)/(x^3*(a*d - b*d*x^3)), x)","F"
597,0,-1,182,0.000000,"\text{Not used}","int((a + b*x^3)^(2/3)/(x^6*(a*d - b*d*x^3)),x)","\int \frac{{\left(b\,x^3+a\right)}^{2/3}}{x^6\,\left(a\,d-b\,d\,x^3\right)} \,d x","Not used",1,"int((a + b*x^3)^(2/3)/(x^6*(a*d - b*d*x^3)), x)","F"
598,0,-1,209,0.000000,"\text{Not used}","int((a + b*x^3)^(2/3)/(x^9*(a*d - b*d*x^3)),x)","\int \frac{{\left(b\,x^3+a\right)}^{2/3}}{x^9\,\left(a\,d-b\,d\,x^3\right)} \,d x","Not used",1,"int((a + b*x^3)^(2/3)/(x^9*(a*d - b*d*x^3)), x)","F"
599,0,-1,236,0.000000,"\text{Not used}","int((a + b*x^3)^(2/3)/(x^12*(a*d - b*d*x^3)),x)","\int \frac{{\left(b\,x^3+a\right)}^{2/3}}{x^{12}\,\left(a\,d-b\,d\,x^3\right)} \,d x","Not used",1,"int((a + b*x^3)^(2/3)/(x^12*(a*d - b*d*x^3)), x)","F"
600,0,-1,512,0.000000,"\text{Not used}","int((x^7*(a + b*x^3)^(2/3))/(a*d - b*d*x^3),x)","\int \frac{x^7\,{\left(b\,x^3+a\right)}^{2/3}}{a\,d-b\,d\,x^3} \,d x","Not used",1,"int((x^7*(a + b*x^3)^(2/3))/(a*d - b*d*x^3), x)","F"
601,0,-1,485,0.000000,"\text{Not used}","int((x^4*(a + b*x^3)^(2/3))/(a*d - b*d*x^3),x)","\int \frac{x^4\,{\left(b\,x^3+a\right)}^{2/3}}{a\,d-b\,d\,x^3} \,d x","Not used",1,"int((x^4*(a + b*x^3)^(2/3))/(a*d - b*d*x^3), x)","F"
602,0,-1,457,0.000000,"\text{Not used}","int((x*(a + b*x^3)^(2/3))/(a*d - b*d*x^3),x)","\int \frac{x\,{\left(b\,x^3+a\right)}^{2/3}}{a\,d-b\,d\,x^3} \,d x","Not used",1,"int((x*(a + b*x^3)^(2/3))/(a*d - b*d*x^3), x)","F"
603,0,-1,483,0.000000,"\text{Not used}","int((a + b*x^3)^(2/3)/(x^2*(a*d - b*d*x^3)),x)","\int \frac{{\left(b\,x^3+a\right)}^{2/3}}{x^2\,\left(a\,d-b\,d\,x^3\right)} \,d x","Not used",1,"int((a + b*x^3)^(2/3)/(x^2*(a*d - b*d*x^3)), x)","F"
604,0,-1,512,0.000000,"\text{Not used}","int((a + b*x^3)^(2/3)/(x^5*(a*d - b*d*x^3)),x)","\int \frac{{\left(b\,x^3+a\right)}^{2/3}}{x^5\,\left(a\,d-b\,d\,x^3\right)} \,d x","Not used",1,"int((a + b*x^3)^(2/3)/(x^5*(a*d - b*d*x^3)), x)","F"
605,1,133,127,5.034046,"\text{Not used}","int(x^14/((1 - x^3)^(1/3)*(x^3 + 1)),x)","\frac{2^{2/3}\,\ln\left({\left(1-x^3\right)}^{1/3}-2^{1/3}\right)}{6}+\frac{2\,{\left(1-x^3\right)}^{5/3}}{5}-\frac{{\left(1-x^3\right)}^{8/3}}{4}+\frac{{\left(1-x^3\right)}^{11/3}}{11}+\frac{2^{2/3}\,\ln\left({\left(1-x^3\right)}^{1/3}-\frac{2^{1/3}\,{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2}{4}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{12}-\frac{2^{2/3}\,\ln\left({\left(1-x^3\right)}^{1/3}-\frac{2^{1/3}\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2}{4}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{12}","Not used",1,"(2^(2/3)*log((1 - x^3)^(1/3) - 2^(1/3)))/6 + (2*(1 - x^3)^(5/3))/5 - (1 - x^3)^(8/3)/4 + (1 - x^3)^(11/3)/11 + (2^(2/3)*log((1 - x^3)^(1/3) - (2^(1/3)*(3^(1/2)*1i - 1)^2)/4)*(3^(1/2)*1i - 1))/12 - (2^(2/3)*log((1 - x^3)^(1/3) - (2^(1/3)*(3^(1/2)*1i + 1)^2)/4)*(3^(1/2)*1i + 1))/12","B"
606,1,133,128,4.729585,"\text{Not used}","int(x^11/((1 - x^3)^(1/3)*(x^3 + 1)),x)","\frac{{\left(1-x^3\right)}^{5/3}}{5}-\frac{{\left(1-x^3\right)}^{2/3}}{2}-\frac{2^{2/3}\,\ln\left({\left(1-x^3\right)}^{1/3}-2^{1/3}\right)}{6}-\frac{{\left(1-x^3\right)}^{8/3}}{8}-\frac{2^{2/3}\,\ln\left({\left(1-x^3\right)}^{1/3}-\frac{2^{1/3}\,{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2}{4}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{12}+\frac{2^{2/3}\,\ln\left({\left(1-x^3\right)}^{1/3}-\frac{2^{1/3}\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2}{4}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{12}","Not used",1,"(1 - x^3)^(5/3)/5 - (1 - x^3)^(2/3)/2 - (2^(2/3)*log((1 - x^3)^(1/3) - 2^(1/3)))/6 - (1 - x^3)^(8/3)/8 - (2^(2/3)*log((1 - x^3)^(1/3) - (2^(1/3)*(3^(1/2)*1i - 1)^2)/4)*(3^(1/2)*1i - 1))/12 + (2^(2/3)*log((1 - x^3)^(1/3) - (2^(1/3)*(3^(1/2)*1i + 1)^2)/4)*(3^(1/2)*1i + 1))/12","B"
607,1,111,97,4.649407,"\text{Not used}","int(x^8/((1 - x^3)^(1/3)*(x^3 + 1)),x)","\frac{2^{2/3}\,\ln\left({\left(1-x^3\right)}^{1/3}-2^{1/3}\right)}{6}+\frac{{\left(1-x^3\right)}^{5/3}}{5}+\frac{2^{2/3}\,\ln\left({\left(1-x^3\right)}^{1/3}-\frac{2^{1/3}\,{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2}{4}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{12}-\frac{2^{2/3}\,\ln\left({\left(1-x^3\right)}^{1/3}-\frac{2^{1/3}\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2}{4}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{12}","Not used",1,"(2^(2/3)*log((1 - x^3)^(1/3) - 2^(1/3)))/6 + (1 - x^3)^(5/3)/5 + (2^(2/3)*log((1 - x^3)^(1/3) - (2^(1/3)*(3^(1/2)*1i - 1)^2)/4)*(3^(1/2)*1i - 1))/12 - (2^(2/3)*log((1 - x^3)^(1/3) - (2^(1/3)*(3^(1/2)*1i + 1)^2)/4)*(3^(1/2)*1i + 1))/12","B"
608,1,111,98,4.685276,"\text{Not used}","int(x^5/((1 - x^3)^(1/3)*(x^3 + 1)),x)","-\frac{2^{2/3}\,\ln\left({\left(1-x^3\right)}^{1/3}-2^{1/3}\right)}{6}-\frac{{\left(1-x^3\right)}^{2/3}}{2}-\frac{2^{2/3}\,\ln\left({\left(1-x^3\right)}^{1/3}-\frac{2^{1/3}\,{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2}{4}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{12}+\frac{2^{2/3}\,\ln\left({\left(1-x^3\right)}^{1/3}-\frac{2^{1/3}\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2}{4}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{12}","Not used",1,"(2^(2/3)*log((1 - x^3)^(1/3) - (2^(1/3)*(3^(1/2)*1i + 1)^2)/4)*(3^(1/2)*1i + 1))/12 - (1 - x^3)^(2/3)/2 - (2^(2/3)*log((1 - x^3)^(1/3) - (2^(1/3)*(3^(1/2)*1i - 1)^2)/4)*(3^(1/2)*1i - 1))/12 - (2^(2/3)*log((1 - x^3)^(1/3) - 2^(1/3)))/6","B"
609,1,100,82,4.894106,"\text{Not used}","int(x^2/((1 - x^3)^(1/3)*(x^3 + 1)),x)","\frac{2^{2/3}\,\ln\left({\left(1-x^3\right)}^{1/3}-2^{1/3}\right)}{6}+\frac{2^{2/3}\,\ln\left({\left(1-x^3\right)}^{1/3}-\frac{2^{1/3}\,{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2}{4}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{12}-\frac{2^{2/3}\,\ln\left({\left(1-x^3\right)}^{1/3}-\frac{2^{1/3}\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2}{4}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{12}","Not used",1,"(2^(2/3)*log((1 - x^3)^(1/3) - 2^(1/3)))/6 + (2^(2/3)*log((1 - x^3)^(1/3) - (2^(1/3)*(3^(1/2)*1i - 1)^2)/4)*(3^(1/2)*1i - 1))/12 - (2^(2/3)*log((1 - x^3)^(1/3) - (2^(1/3)*(3^(1/2)*1i + 1)^2)/4)*(3^(1/2)*1i + 1))/12","B"
610,1,256,137,4.797586,"\text{Not used}","int(1/(x*(1 - x^3)^(1/3)*(x^3 + 1)),x)","\frac{\ln\left(6-6\,{\left(1-x^3\right)}^{1/3}\right)}{3}+\ln\left({\left(-\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)}^3\,\left(1458\,{\left(-\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)}^2-135\,{\left(1-x^3\right)}^{1/3}\right)-{\left(1-x^3\right)}^{1/3}\right)\,\left(-\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)-\ln\left(-{\left(\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)}^3\,\left(1458\,{\left(\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)}^2-135\,{\left(1-x^3\right)}^{1/3}\right)-{\left(1-x^3\right)}^{1/3}\right)\,\left(\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)-\frac{2^{2/3}\,\ln\left(\frac{3\,{\left(1-x^3\right)}^{1/3}}{2}-\frac{3\,2^{1/3}}{2}\right)}{6}+\frac{{\left(-1\right)}^{1/3}\,2^{2/3}\,\ln\left(\frac{3\,{\left(1-x^3\right)}^{1/3}}{2}-\frac{3\,{\left(-1\right)}^{2/3}\,2^{1/3}}{2}\right)}{6}-\frac{{\left(-1\right)}^{1/3}\,2^{2/3}\,\ln\left(-\frac{{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^3\,\left(135\,{\left(1-x^3\right)}^{1/3}-\frac{81\,{\left(-1\right)}^{2/3}\,2^{1/3}\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2}{4}\right)}{432}-{\left(1-x^3\right)}^{1/3}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{12}","Not used",1,"log(6 - 6*(1 - x^3)^(1/3))/3 + log(((3^(1/2)*1i)/6 - 1/6)^3*(1458*((3^(1/2)*1i)/6 - 1/6)^2 - 135*(1 - x^3)^(1/3)) - (1 - x^3)^(1/3))*((3^(1/2)*1i)/6 - 1/6) - log(- ((3^(1/2)*1i)/6 + 1/6)^3*(1458*((3^(1/2)*1i)/6 + 1/6)^2 - 135*(1 - x^3)^(1/3)) - (1 - x^3)^(1/3))*((3^(1/2)*1i)/6 + 1/6) - (2^(2/3)*log((3*(1 - x^3)^(1/3))/2 - (3*2^(1/3))/2))/6 + ((-1)^(1/3)*2^(2/3)*log((3*(1 - x^3)^(1/3))/2 - (3*(-1)^(2/3)*2^(1/3))/2))/6 - ((-1)^(1/3)*2^(2/3)*log(- ((3^(1/2)*1i + 1)^3*(135*(1 - x^3)^(1/3) - (81*(-1)^(2/3)*2^(1/3)*(3^(1/2)*1i + 1)^2)/4))/432 - (1 - x^3)^(1/3))*(3^(1/2)*1i + 1))/12","B"
611,1,382,157,4.859998,"\text{Not used}","int(1/(x^4*(1 - x^3)^(1/3)*(x^3 + 1)),x)","\frac{2^{2/3}\,\ln\left(\frac{2^{1/3}\,\left(\frac{2^{2/3}\,\left(81\,2^{1/3}-75\,{\left(1-x^3\right)}^{1/3}\right)}{6}-\frac{38}{3}\right)}{18}+\frac{16\,{\left(1-x^3\right)}^{1/3}}{27}\right)}{6}-\frac{{\left(1-x^3\right)}^{2/3}}{3\,x^3}-\frac{2\,\ln\left(\frac{344\,{\left(1-x^3\right)}^{1/3}}{243}-\frac{344}{243}\right)}{9}+\ln\left({\left(\frac{1}{9}+\frac{\sqrt{3}\,1{}\mathrm{i}}{9}\right)}^2\,\left(\left(\frac{1}{9}+\frac{\sqrt{3}\,1{}\mathrm{i}}{9}\right)\,\left(1458\,{\left(\frac{1}{9}+\frac{\sqrt{3}\,1{}\mathrm{i}}{9}\right)}^2-75\,{\left(1-x^3\right)}^{1/3}\right)-\frac{38}{3}\right)+\frac{16\,{\left(1-x^3\right)}^{1/3}}{27}\right)\,\left(\frac{1}{9}+\frac{\sqrt{3}\,1{}\mathrm{i}}{9}\right)-\ln\left(\frac{16\,{\left(1-x^3\right)}^{1/3}}{27}-{\left(-\frac{1}{9}+\frac{\sqrt{3}\,1{}\mathrm{i}}{9}\right)}^2\,\left(\left(-\frac{1}{9}+\frac{\sqrt{3}\,1{}\mathrm{i}}{9}\right)\,\left(1458\,{\left(-\frac{1}{9}+\frac{\sqrt{3}\,1{}\mathrm{i}}{9}\right)}^2-75\,{\left(1-x^3\right)}^{1/3}\right)+\frac{38}{3}\right)\right)\,\left(-\frac{1}{9}+\frac{\sqrt{3}\,1{}\mathrm{i}}{9}\right)+\frac{2^{2/3}\,\ln\left(\frac{16\,{\left(1-x^3\right)}^{1/3}}{27}+\frac{2^{1/3}\,{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(\frac{2^{2/3}\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(\frac{81\,2^{1/3}\,{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2}{4}-75\,{\left(1-x^3\right)}^{1/3}\right)}{12}-\frac{38}{3}\right)}{72}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{12}-\frac{2^{2/3}\,\ln\left(\frac{16\,{\left(1-x^3\right)}^{1/3}}{27}-\frac{2^{1/3}\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(\frac{2^{2/3}\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(\frac{81\,2^{1/3}\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2}{4}-75\,{\left(1-x^3\right)}^{1/3}\right)}{12}+\frac{38}{3}\right)}{72}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{12}","Not used",1,"(2^(2/3)*log((2^(1/3)*((2^(2/3)*(81*2^(1/3) - 75*(1 - x^3)^(1/3)))/6 - 38/3))/18 + (16*(1 - x^3)^(1/3))/27))/6 - (1 - x^3)^(2/3)/(3*x^3) - (2*log((344*(1 - x^3)^(1/3))/243 - 344/243))/9 + log(((3^(1/2)*1i)/9 + 1/9)^2*(((3^(1/2)*1i)/9 + 1/9)*(1458*((3^(1/2)*1i)/9 + 1/9)^2 - 75*(1 - x^3)^(1/3)) - 38/3) + (16*(1 - x^3)^(1/3))/27)*((3^(1/2)*1i)/9 + 1/9) - log((16*(1 - x^3)^(1/3))/27 - ((3^(1/2)*1i)/9 - 1/9)^2*(((3^(1/2)*1i)/9 - 1/9)*(1458*((3^(1/2)*1i)/9 - 1/9)^2 - 75*(1 - x^3)^(1/3)) + 38/3))*((3^(1/2)*1i)/9 - 1/9) + (2^(2/3)*log((16*(1 - x^3)^(1/3))/27 + (2^(1/3)*(3^(1/2)*1i - 1)^2*((2^(2/3)*(3^(1/2)*1i - 1)*((81*2^(1/3)*(3^(1/2)*1i - 1)^2)/4 - 75*(1 - x^3)^(1/3)))/12 - 38/3))/72)*(3^(1/2)*1i - 1))/12 - (2^(2/3)*log((16*(1 - x^3)^(1/3))/27 - (2^(1/3)*(3^(1/2)*1i + 1)^2*((2^(2/3)*(3^(1/2)*1i + 1)*((81*2^(1/3)*(3^(1/2)*1i + 1)^2)/4 - 75*(1 - x^3)^(1/3)))/12 + 38/3))/72)*(3^(1/2)*1i + 1))/12","B"
612,0,-1,154,0.000000,"\text{Not used}","int(x^6/((1 - x^3)^(1/3)*(x^3 + 1)),x)","\int \frac{x^6}{{\left(1-x^3\right)}^{1/3}\,\left(x^3+1\right)} \,d x","Not used",1,"int(x^6/((1 - x^3)^(1/3)*(x^3 + 1)), x)","F"
613,0,-1,135,0.000000,"\text{Not used}","int(x^3/((1 - x^3)^(1/3)*(x^3 + 1)),x)","\int \frac{x^3}{{\left(1-x^3\right)}^{1/3}\,\left(x^3+1\right)} \,d x","Not used",1,"int(x^3/((1 - x^3)^(1/3)*(x^3 + 1)), x)","F"
614,0,-1,88,0.000000,"\text{Not used}","int(1/((1 - x^3)^(1/3)*(x^3 + 1)),x)","\int \frac{1}{{\left(1-x^3\right)}^{1/3}\,\left(x^3+1\right)} \,d x","Not used",1,"int(1/((1 - x^3)^(1/3)*(x^3 + 1)), x)","F"
615,0,-1,105,0.000000,"\text{Not used}","int(1/(x^3*(1 - x^3)^(1/3)*(x^3 + 1)),x)","\int \frac{1}{x^3\,{\left(1-x^3\right)}^{1/3}\,\left(x^3+1\right)} \,d x","Not used",1,"int(1/(x^3*(1 - x^3)^(1/3)*(x^3 + 1)), x)","F"
616,0,-1,124,0.000000,"\text{Not used}","int(1/(x^6*(1 - x^3)^(1/3)*(x^3 + 1)),x)","\int \frac{1}{x^6\,{\left(1-x^3\right)}^{1/3}\,\left(x^3+1\right)} \,d x","Not used",1,"int(1/(x^6*(1 - x^3)^(1/3)*(x^3 + 1)), x)","F"
617,0,-1,141,0.000000,"\text{Not used}","int(1/(x^9*(1 - x^3)^(1/3)*(x^3 + 1)),x)","\int \frac{1}{x^9\,{\left(1-x^3\right)}^{1/3}\,\left(x^3+1\right)} \,d x","Not used",1,"int(1/(x^9*(1 - x^3)^(1/3)*(x^3 + 1)), x)","F"
618,0,-1,271,0.000000,"\text{Not used}","int(x^7/((1 - x^3)^(1/3)*(x^3 + 1)),x)","\int \frac{x^7}{{\left(1-x^3\right)}^{1/3}\,\left(x^3+1\right)} \,d x","Not used",1,"int(x^7/((1 - x^3)^(1/3)*(x^3 + 1)), x)","F"
619,0,-1,254,0.000000,"\text{Not used}","int(x^4/((1 - x^3)^(1/3)*(x^3 + 1)),x)","\int \frac{x^4}{{\left(1-x^3\right)}^{1/3}\,\left(x^3+1\right)} \,d x","Not used",1,"int(x^4/((1 - x^3)^(1/3)*(x^3 + 1)), x)","F"
620,0,-1,233,0.000000,"\text{Not used}","int(x/((1 - x^3)^(1/3)*(x^3 + 1)),x)","\int \frac{x}{{\left(1-x^3\right)}^{1/3}\,\left(x^3+1\right)} \,d x","Not used",1,"int(x/((1 - x^3)^(1/3)*(x^3 + 1)), x)","F"
621,0,-1,270,0.000000,"\text{Not used}","int(1/(x^2*(1 - x^3)^(1/3)*(x^3 + 1)),x)","\int \frac{1}{x^2\,{\left(1-x^3\right)}^{1/3}\,\left(x^3+1\right)} \,d x","Not used",1,"int(1/(x^2*(1 - x^3)^(1/3)*(x^3 + 1)), x)","F"
622,0,-1,289,0.000000,"\text{Not used}","int(1/(x^5*(1 - x^3)^(1/3)*(x^3 + 1)),x)","\int \frac{1}{x^5\,{\left(1-x^3\right)}^{1/3}\,\left(x^3+1\right)} \,d x","Not used",1,"int(1/(x^5*(1 - x^3)^(1/3)*(x^3 + 1)), x)","F"
623,1,135,125,5.184693,"\text{Not used}","int(x^11/((1 - x^3)^(2/3)*(x^3 + 1)),x)","\frac{{\left(1-x^3\right)}^{4/3}}{4}-{\left(1-x^3\right)}^{1/3}-\frac{2^{1/3}\,\ln\left(3\,2^{1/3}-3\,{\left(1-x^3\right)}^{1/3}\right)}{6}-\frac{{\left(1-x^3\right)}^{7/3}}{7}-\frac{2^{1/3}\,\ln\left(3\,{\left(1-x^3\right)}^{1/3}-\frac{3\,2^{1/3}\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{12}+\frac{2^{1/3}\,\ln\left(\frac{3\,2^{1/3}\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}+3\,{\left(1-x^3\right)}^{1/3}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{12}","Not used",1,"(1 - x^3)^(4/3)/4 - (1 - x^3)^(1/3) - (2^(1/3)*log(3*2^(1/3) - 3*(1 - x^3)^(1/3)))/6 - (1 - x^3)^(7/3)/7 - (2^(1/3)*log(3*(1 - x^3)^(1/3) - (3*2^(1/3)*(3^(1/2)*1i - 1))/2)*(3^(1/2)*1i - 1))/12 + (2^(1/3)*log((3*2^(1/3)*(3^(1/2)*1i + 1))/2 + 3*(1 - x^3)^(1/3))*(3^(1/2)*1i + 1))/12","B"
624,1,113,98,4.976231,"\text{Not used}","int(x^8/((1 - x^3)^(2/3)*(x^3 + 1)),x)","\frac{2^{1/3}\,\ln\left(\frac{{\left(1-x^3\right)}^{1/3}}{2}-\frac{2^{1/3}}{2}\right)}{6}+\frac{{\left(1-x^3\right)}^{4/3}}{4}+\frac{2^{1/3}\,\ln\left(3\,{\left(1-x^3\right)}^{1/3}-\frac{3\,2^{1/3}\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{12}-\frac{2^{1/3}\,\ln\left(\frac{3\,2^{1/3}\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}+3\,{\left(1-x^3\right)}^{1/3}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{12}","Not used",1,"(2^(1/3)*log((1 - x^3)^(1/3)/2 - 2^(1/3)/2))/6 + (1 - x^3)^(4/3)/4 + (2^(1/3)*log(3*(1 - x^3)^(1/3) - (3*2^(1/3)*(3^(1/2)*1i - 1))/2)*(3^(1/2)*1i - 1))/12 - (2^(1/3)*log((3*2^(1/3)*(3^(1/2)*1i + 1))/2 + 3*(1 - x^3)^(1/3))*(3^(1/2)*1i + 1))/12","B"
625,1,113,95,4.891564,"\text{Not used}","int(x^5/((1 - x^3)^(2/3)*(x^3 + 1)),x)","-\frac{2^{1/3}\,\ln\left(\frac{{\left(1-x^3\right)}^{1/3}}{2}-\frac{2^{1/3}}{2}\right)}{6}-{\left(1-x^3\right)}^{1/3}-\frac{2^{1/3}\,\ln\left(3\,{\left(1-x^3\right)}^{1/3}-\frac{3\,2^{1/3}\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{12}+\frac{2^{1/3}\,\ln\left(\frac{3\,2^{1/3}\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}+3\,{\left(1-x^3\right)}^{1/3}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{12}","Not used",1,"(2^(1/3)*log((3*2^(1/3)*(3^(1/2)*1i + 1))/2 + 3*(1 - x^3)^(1/3))*(3^(1/2)*1i + 1))/12 - (1 - x^3)^(1/3) - (2^(1/3)*log(3*(1 - x^3)^(1/3) - (3*2^(1/3)*(3^(1/2)*1i - 1))/2)*(3^(1/2)*1i - 1))/12 - (2^(1/3)*log((1 - x^3)^(1/3)/2 - 2^(1/3)/2))/6","B"
626,1,102,83,5.052397,"\text{Not used}","int(x^2/((1 - x^3)^(2/3)*(x^3 + 1)),x)","\frac{2^{1/3}\,\ln\left(3\,2^{1/3}-3\,{\left(1-x^3\right)}^{1/3}\right)}{6}+\frac{2^{1/3}\,\ln\left(3\,{\left(1-x^3\right)}^{1/3}-\frac{3\,2^{1/3}\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{12}-\frac{2^{1/3}\,\ln\left(\frac{3\,2^{1/3}\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}+3\,{\left(1-x^3\right)}^{1/3}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{12}","Not used",1,"(2^(1/3)*log(3*2^(1/3) - 3*(1 - x^3)^(1/3)))/6 + (2^(1/3)*log(3*(1 - x^3)^(1/3) - (3*2^(1/3)*(3^(1/2)*1i - 1))/2)*(3^(1/2)*1i - 1))/12 - (2^(1/3)*log((3*2^(1/3)*(3^(1/2)*1i + 1))/2 + 3*(1 - x^3)^(1/3))*(3^(1/2)*1i + 1))/12","B"
627,1,344,137,4.920723,"\text{Not used}","int(1/(x*(1 - x^3)^(2/3)*(x^3 + 1)),x)","\frac{\ln\left(5-5\,{\left(1-x^3\right)}^{1/3}\right)}{3}-\frac{2^{1/3}\,\ln\left(6\,{\left(1-x^3\right)}^{1/3}-\frac{2^{1/3}\,\left(\frac{2^{2/3}\,\left(243\,2^{1/3}+243\,{\left(1-x^3\right)}^{1/3}\right)}{36}+9\right)}{6}\right)}{6}+\ln\left(\left(-\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)\,\left({\left(-\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)}^2\,\left(243\,{\left(1-x^3\right)}^{1/3}+243-\sqrt{3}\,243{}\mathrm{i}\right)+9\right)+6\,{\left(1-x^3\right)}^{1/3}\right)\,\left(-\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)-\ln\left(6\,{\left(1-x^3\right)}^{1/3}-\left(\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)\,\left({\left(\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)}^2\,\left(243\,{\left(1-x^3\right)}^{1/3}+243+\sqrt{3}\,243{}\mathrm{i}\right)+9\right)\right)\,\left(\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)+\frac{{\left(-1\right)}^{1/3}\,2^{1/3}\,\ln\left(6\,{\left(1-x^3\right)}^{1/3}-\frac{{\left(-1\right)}^{1/3}\,2^{1/3}\,\left(\frac{{\left(-1\right)}^{2/3}\,2^{2/3}\,\left(243\,{\left(-1\right)}^{1/3}\,2^{1/3}-243\,{\left(1-x^3\right)}^{1/3}\right)}{36}-9\right)}{6}\right)}{6}-\frac{{\left(-1\right)}^{1/3}\,2^{1/3}\,\ln\left(6\,{\left(1-x^3\right)}^{1/3}-\frac{{\left(-1\right)}^{1/3}\,2^{1/3}\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(\frac{{\left(-1\right)}^{2/3}\,2^{2/3}\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(243\,{\left(1-x^3\right)}^{1/3}+\frac{243\,{\left(-1\right)}^{1/3}\,2^{1/3}\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}\right)}{144}+9\right)}{12}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{12}","Not used",1,"log(5 - 5*(1 - x^3)^(1/3))/3 - (2^(1/3)*log(6*(1 - x^3)^(1/3) - (2^(1/3)*((2^(2/3)*(243*2^(1/3) + 243*(1 - x^3)^(1/3)))/36 + 9))/6))/6 + log(((3^(1/2)*1i)/6 - 1/6)*(((3^(1/2)*1i)/6 - 1/6)^2*(243*(1 - x^3)^(1/3) - 3^(1/2)*243i + 243) + 9) + 6*(1 - x^3)^(1/3))*((3^(1/2)*1i)/6 - 1/6) - log(6*(1 - x^3)^(1/3) - ((3^(1/2)*1i)/6 + 1/6)*(((3^(1/2)*1i)/6 + 1/6)^2*(3^(1/2)*243i + 243*(1 - x^3)^(1/3) + 243) + 9))*((3^(1/2)*1i)/6 + 1/6) + ((-1)^(1/3)*2^(1/3)*log(6*(1 - x^3)^(1/3) - ((-1)^(1/3)*2^(1/3)*(((-1)^(2/3)*2^(2/3)*(243*(-1)^(1/3)*2^(1/3) - 243*(1 - x^3)^(1/3)))/36 - 9))/6))/6 - ((-1)^(1/3)*2^(1/3)*log(6*(1 - x^3)^(1/3) - ((-1)^(1/3)*2^(1/3)*(3^(1/2)*1i + 1)*(((-1)^(2/3)*2^(2/3)*(3^(1/2)*1i + 1)^2*(243*(1 - x^3)^(1/3) + (243*(-1)^(1/3)*2^(1/3)*(3^(1/2)*1i + 1))/2))/144 + 9))/12)*(3^(1/2)*1i + 1))/12","B"
628,1,368,158,5.072973,"\text{Not used}","int(1/(x^4*(1 - x^3)^(2/3)*(x^3 + 1)),x)","\frac{2^{1/3}\,\ln\left(\frac{10\,{\left(1-x^3\right)}^{1/3}}{9}-\frac{2^{1/3}\,\left(\frac{2^{2/3}\,\left(243\,2^{1/3}+27\,{\left(1-x^3\right)}^{1/3}\right)}{36}-\frac{25}{3}\right)}{6}\right)}{6}-\frac{{\left(1-x^3\right)}^{1/3}}{3\,x^3}-\frac{\ln\left(\frac{31\,{\left(1-x^3\right)}^{1/3}}{243}-\frac{31}{243}\right)}{9}-\ln\left(\left(-\frac{1}{18}+\frac{\sqrt{3}\,1{}\mathrm{i}}{18}\right)\,\left({\left(-\frac{1}{18}+\frac{\sqrt{3}\,1{}\mathrm{i}}{18}\right)}^2\,\left(27\,{\left(1-x^3\right)}^{1/3}+81-\sqrt{3}\,81{}\mathrm{i}\right)-\frac{25}{3}\right)+\frac{10\,{\left(1-x^3\right)}^{1/3}}{9}\right)\,\left(-\frac{1}{18}+\frac{\sqrt{3}\,1{}\mathrm{i}}{18}\right)+\ln\left(\frac{10\,{\left(1-x^3\right)}^{1/3}}{9}-\left(\frac{1}{18}+\frac{\sqrt{3}\,1{}\mathrm{i}}{18}\right)\,\left({\left(\frac{1}{18}+\frac{\sqrt{3}\,1{}\mathrm{i}}{18}\right)}^2\,\left(27\,{\left(1-x^3\right)}^{1/3}+81+\sqrt{3}\,81{}\mathrm{i}\right)-\frac{25}{3}\right)\right)\,\left(\frac{1}{18}+\frac{\sqrt{3}\,1{}\mathrm{i}}{18}\right)+\frac{2^{1/3}\,\ln\left(\frac{10\,{\left(1-x^3\right)}^{1/3}}{9}-\frac{2^{1/3}\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(\frac{2^{2/3}\,{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(\frac{243\,2^{1/3}\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}+27\,{\left(1-x^3\right)}^{1/3}\right)}{144}-\frac{25}{3}\right)}{12}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{12}-\frac{2^{1/3}\,\ln\left(\frac{10\,{\left(1-x^3\right)}^{1/3}}{9}-\frac{2^{1/3}\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(\frac{2^{2/3}\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(\frac{243\,2^{1/3}\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{2}-27\,{\left(1-x^3\right)}^{1/3}\right)}{144}+\frac{25}{3}\right)}{12}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{12}","Not used",1,"(2^(1/3)*log((10*(1 - x^3)^(1/3))/9 - (2^(1/3)*((2^(2/3)*(243*2^(1/3) + 27*(1 - x^3)^(1/3)))/36 - 25/3))/6))/6 - (1 - x^3)^(1/3)/(3*x^3) - log((31*(1 - x^3)^(1/3))/243 - 31/243)/9 - log(((3^(1/2)*1i)/18 - 1/18)*(((3^(1/2)*1i)/18 - 1/18)^2*(27*(1 - x^3)^(1/3) - 3^(1/2)*81i + 81) - 25/3) + (10*(1 - x^3)^(1/3))/9)*((3^(1/2)*1i)/18 - 1/18) + log((10*(1 - x^3)^(1/3))/9 - ((3^(1/2)*1i)/18 + 1/18)*(((3^(1/2)*1i)/18 + 1/18)^2*(3^(1/2)*81i + 27*(1 - x^3)^(1/3) + 81) - 25/3))*((3^(1/2)*1i)/18 + 1/18) + (2^(1/3)*log((10*(1 - x^3)^(1/3))/9 - (2^(1/3)*(3^(1/2)*1i - 1)*((2^(2/3)*(3^(1/2)*1i - 1)^2*((243*2^(1/3)*(3^(1/2)*1i - 1))/2 + 27*(1 - x^3)^(1/3)))/144 - 25/3))/12)*(3^(1/2)*1i - 1))/12 - (2^(1/3)*log((10*(1 - x^3)^(1/3))/9 - (2^(1/3)*(3^(1/2)*1i + 1)*((2^(2/3)*(3^(1/2)*1i + 1)^2*((243*2^(1/3)*(3^(1/2)*1i + 1))/2 - 27*(1 - x^3)^(1/3)))/144 + 25/3))/12)*(3^(1/2)*1i + 1))/12","B"
629,0,-1,160,0.000000,"\text{Not used}","int(x^7/((1 - x^3)^(2/3)*(x^3 + 1)),x)","\int \frac{x^7}{{\left(1-x^3\right)}^{2/3}\,\left(x^3+1\right)} \,d x","Not used",1,"int(x^7/((1 - x^3)^(2/3)*(x^3 + 1)), x)","F"
630,0,-1,139,0.000000,"\text{Not used}","int(x^4/((1 - x^3)^(2/3)*(x^3 + 1)),x)","\int \frac{x^4}{{\left(1-x^3\right)}^{2/3}\,\left(x^3+1\right)} \,d x","Not used",1,"int(x^4/((1 - x^3)^(2/3)*(x^3 + 1)), x)","F"
631,0,-1,88,0.000000,"\text{Not used}","int(x/((1 - x^3)^(2/3)*(x^3 + 1)),x)","\int \frac{x}{{\left(1-x^3\right)}^{2/3}\,\left(x^3+1\right)} \,d x","Not used",1,"int(x/((1 - x^3)^(2/3)*(x^3 + 1)), x)","F"
632,0,-1,103,0.000000,"\text{Not used}","int(1/(x^2*(1 - x^3)^(2/3)*(x^3 + 1)),x)","\int \frac{1}{x^2\,{\left(1-x^3\right)}^{2/3}\,\left(x^3+1\right)} \,d x","Not used",1,"int(1/(x^2*(1 - x^3)^(2/3)*(x^3 + 1)), x)","F"
633,0,-1,124,0.000000,"\text{Not used}","int(1/(x^5*(1 - x^3)^(2/3)*(x^3 + 1)),x)","\int \frac{1}{x^5\,{\left(1-x^3\right)}^{2/3}\,\left(x^3+1\right)} \,d x","Not used",1,"int(1/(x^5*(1 - x^3)^(2/3)*(x^3 + 1)), x)","F"
634,0,-1,291,0.000000,"\text{Not used}","int(x^6/((1 - x^3)^(2/3)*(x^3 + 1)),x)","\int \frac{x^6}{{\left(1-x^3\right)}^{2/3}\,\left(x^3+1\right)} \,d x","Not used",1,"int(x^6/((1 - x^3)^(2/3)*(x^3 + 1)), x)","F"
635,0,-1,294,0.000000,"\text{Not used}","int(x^3/((1 - x^3)^(2/3)*(x^3 + 1)),x)","\int \frac{x^3}{{\left(1-x^3\right)}^{2/3}\,\left(x^3+1\right)} \,d x","Not used",1,"int(x^3/((1 - x^3)^(2/3)*(x^3 + 1)), x)","F"
636,0,-1,293,0.000000,"\text{Not used}","int(1/((1 - x^3)^(2/3)*(x^3 + 1)),x)","\int \frac{1}{{\left(1-x^3\right)}^{2/3}\,\left(x^3+1\right)} \,d x","Not used",1,"int(1/((1 - x^3)^(2/3)*(x^3 + 1)), x)","F"
637,0,-1,294,0.000000,"\text{Not used}","int(1/(x^3*(1 - x^3)^(2/3)*(x^3 + 1)),x)","\int \frac{1}{x^3\,{\left(1-x^3\right)}^{2/3}\,\left(x^3+1\right)} \,d x","Not used",1,"int(1/(x^3*(1 - x^3)^(2/3)*(x^3 + 1)), x)","F"
638,1,148,141,4.861448,"\text{Not used}","int(x^14/((1 - x^3)^(4/3)*(x^3 + 1)),x)","\frac{2^{2/3}\,\ln\left(\frac{{\left(1-x^3\right)}^{1/3}}{4}-\frac{2^{1/3}}{4}\right)}{12}+\frac{1}{2\,{\left(1-x^3\right)}^{1/3}}+{\left(1-x^3\right)}^{2/3}-\frac{2\,{\left(1-x^3\right)}^{5/3}}{5}+\frac{{\left(1-x^3\right)}^{8/3}}{8}+\frac{2^{2/3}\,\ln\left(\frac{{\left(1-x^3\right)}^{1/3}}{4}-\frac{2^{1/3}\,{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2}{16}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{24}-\frac{2^{2/3}\,\ln\left(\frac{{\left(1-x^3\right)}^{1/3}}{4}-\frac{2^{1/3}\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2}{16}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{24}","Not used",1,"(2^(2/3)*log((1 - x^3)^(1/3)/4 - 2^(1/3)/4))/12 + 1/(2*(1 - x^3)^(1/3)) + (1 - x^3)^(2/3) - (2*(1 - x^3)^(5/3))/5 + (1 - x^3)^(8/3)/8 + (2^(2/3)*log((1 - x^3)^(1/3)/4 - (2^(1/3)*(3^(1/2)*1i - 1)^2)/16)*(3^(1/2)*1i - 1))/24 - (2^(2/3)*log((1 - x^3)^(1/3)/4 - (2^(1/3)*(3^(1/2)*1i + 1)^2)/16)*(3^(1/2)*1i + 1))/24","B"
639,1,139,130,5.149760,"\text{Not used}","int(x^11/((1 - x^3)^(4/3)*(x^3 + 1)),x)","\frac{1}{2\,{\left(1-x^3\right)}^{1/3}}-\frac{2^{2/3}\,\ln\left(\frac{{\left(1-x^3\right)}^{1/3}}{4}-\frac{2^{1/3}}{4}\right)}{12}+\frac{{\left(1-x^3\right)}^{2/3}}{2}-\frac{{\left(1-x^3\right)}^{5/3}}{5}-\frac{2^{2/3}\,\ln\left(\frac{{\left(1-x^3\right)}^{1/3}}{4}-\frac{2^{1/3}\,{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2}{16}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{24}+\frac{2^{2/3}\,\ln\left(\frac{{\left(1-x^3\right)}^{1/3}}{4}-\frac{2^{1/3}\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2}{16}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{24}","Not used",1,"1/(2*(1 - x^3)^(1/3)) - (2^(2/3)*log((1 - x^3)^(1/3)/4 - 2^(1/3)/4))/12 + (1 - x^3)^(2/3)/2 - (1 - x^3)^(5/3)/5 - (2^(2/3)*log((1 - x^3)^(1/3)/4 - (2^(1/3)*(3^(1/2)*1i - 1)^2)/16)*(3^(1/2)*1i - 1))/24 + (2^(2/3)*log((1 - x^3)^(1/3)/4 - (2^(1/3)*(3^(1/2)*1i + 1)^2)/16)*(3^(1/2)*1i + 1))/24","B"
640,1,128,115,4.889656,"\text{Not used}","int(x^8/((1 - x^3)^(4/3)*(x^3 + 1)),x)","\frac{2^{2/3}\,\ln\left(\frac{{\left(1-x^3\right)}^{1/3}}{4}-\frac{2^{1/3}}{4}\right)}{12}+\frac{1}{2\,{\left(1-x^3\right)}^{1/3}}+\frac{{\left(1-x^3\right)}^{2/3}}{2}+\frac{2^{2/3}\,\ln\left(\frac{{\left(1-x^3\right)}^{1/3}}{4}-\frac{2^{1/3}\,{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2}{16}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{24}-\frac{2^{2/3}\,\ln\left(\frac{{\left(1-x^3\right)}^{1/3}}{4}-\frac{2^{1/3}\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2}{16}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{24}","Not used",1,"(2^(2/3)*log((1 - x^3)^(1/3)/4 - 2^(1/3)/4))/12 + 1/(2*(1 - x^3)^(1/3)) + (1 - x^3)^(2/3)/2 + (2^(2/3)*log((1 - x^3)^(1/3)/4 - (2^(1/3)*(3^(1/2)*1i - 1)^2)/16)*(3^(1/2)*1i - 1))/24 - (2^(2/3)*log((1 - x^3)^(1/3)/4 - (2^(1/3)*(3^(1/2)*1i + 1)^2)/16)*(3^(1/2)*1i + 1))/24","B"
641,1,117,100,4.845757,"\text{Not used}","int(x^5/((1 - x^3)^(4/3)*(x^3 + 1)),x)","\frac{1}{2\,{\left(1-x^3\right)}^{1/3}}-\frac{2^{2/3}\,\ln\left(\frac{{\left(1-x^3\right)}^{1/3}}{4}-\frac{2^{1/3}}{4}\right)}{12}-\frac{2^{2/3}\,\ln\left(\frac{{\left(1-x^3\right)}^{1/3}}{4}-\frac{2^{1/3}\,{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2}{16}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{24}+\frac{2^{2/3}\,\ln\left(\frac{{\left(1-x^3\right)}^{1/3}}{4}-\frac{2^{1/3}\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2}{16}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{24}","Not used",1,"1/(2*(1 - x^3)^(1/3)) - (2^(2/3)*log((1 - x^3)^(1/3)/4 - 2^(1/3)/4))/12 - (2^(2/3)*log((1 - x^3)^(1/3)/4 - (2^(1/3)*(3^(1/2)*1i - 1)^2)/16)*(3^(1/2)*1i - 1))/24 + (2^(2/3)*log((1 - x^3)^(1/3)/4 - (2^(1/3)*(3^(1/2)*1i + 1)^2)/16)*(3^(1/2)*1i + 1))/24","B"
642,1,117,100,4.902768,"\text{Not used}","int(x^2/((1 - x^3)^(4/3)*(x^3 + 1)),x)","\frac{2^{2/3}\,\ln\left(\frac{{\left(1-x^3\right)}^{1/3}}{4}-\frac{2^{1/3}}{4}\right)}{12}+\frac{1}{2\,{\left(1-x^3\right)}^{1/3}}+\frac{2^{2/3}\,\ln\left(\frac{{\left(1-x^3\right)}^{1/3}}{4}-\frac{2^{1/3}\,{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2}{16}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{24}-\frac{2^{2/3}\,\ln\left(\frac{{\left(1-x^3\right)}^{1/3}}{4}-\frac{2^{1/3}\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2}{16}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{24}","Not used",1,"(2^(2/3)*log((1 - x^3)^(1/3)/4 - 2^(1/3)/4))/12 + 1/(2*(1 - x^3)^(1/3)) + (2^(2/3)*log((1 - x^3)^(1/3)/4 - (2^(1/3)*(3^(1/2)*1i - 1)^2)/16)*(3^(1/2)*1i - 1))/24 - (2^(2/3)*log((1 - x^3)^(1/3)/4 - (2^(1/3)*(3^(1/2)*1i + 1)^2)/16)*(3^(1/2)*1i + 1))/24","B"
643,1,253,154,5.399154,"\text{Not used}","int(1/(x*(1 - x^3)^(4/3)*(x^3 + 1)),x)","\frac{\ln\left(\frac{17}{4}-\frac{17\,{\left(1-x^3\right)}^{1/3}}{4}\right)}{3}+\ln\left(\left(-\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)\,\left(1458\,{\left(-\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)}^2-\frac{459\,{\left(1-x^3\right)}^{1/3}}{4}\right)-\frac{63}{4}\right)\,\left(-\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)-\ln\left(\left(\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)\,\left(1458\,{\left(\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)}^2-\frac{459\,{\left(1-x^3\right)}^{1/3}}{4}\right)+\frac{63}{4}\right)\,\left(\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)-\frac{2^{2/3}\,\ln\left(\frac{2^{2/3}\,\left(\frac{81\,2^{1/3}}{4}-\frac{459\,{\left(1-x^3\right)}^{1/3}}{4}\right)}{12}+\frac{63}{4}\right)}{12}+\frac{1}{2\,{\left(1-x^3\right)}^{1/3}}+\frac{{\left(-1\right)}^{1/3}\,2^{2/3}\,\ln\left(\frac{{\left(-1\right)}^{1/3}\,2^{2/3}\,\left(\frac{81\,{\left(-1\right)}^{2/3}\,2^{1/3}}{4}-\frac{459\,{\left(1-x^3\right)}^{1/3}}{4}\right)}{12}-\frac{63}{4}\right)}{12}-\frac{{\left(-1\right)}^{1/3}\,2^{2/3}\,\ln\left(\frac{{\left(-1\right)}^{1/3}\,2^{2/3}\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(\frac{459\,{\left(1-x^3\right)}^{1/3}}{4}-\frac{81\,{\left(-1\right)}^{2/3}\,2^{1/3}\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2}{16}\right)}{24}-\frac{63}{4}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{24}","Not used",1,"log(17/4 - (17*(1 - x^3)^(1/3))/4)/3 + log(((3^(1/2)*1i)/6 - 1/6)*(1458*((3^(1/2)*1i)/6 - 1/6)^2 - (459*(1 - x^3)^(1/3))/4) - 63/4)*((3^(1/2)*1i)/6 - 1/6) - log(((3^(1/2)*1i)/6 + 1/6)*(1458*((3^(1/2)*1i)/6 + 1/6)^2 - (459*(1 - x^3)^(1/3))/4) + 63/4)*((3^(1/2)*1i)/6 + 1/6) - (2^(2/3)*log((2^(2/3)*((81*2^(1/3))/4 - (459*(1 - x^3)^(1/3))/4))/12 + 63/4))/12 + 1/(2*(1 - x^3)^(1/3)) + ((-1)^(1/3)*2^(2/3)*log(((-1)^(1/3)*2^(2/3)*((81*(-1)^(2/3)*2^(1/3))/4 - (459*(1 - x^3)^(1/3))/4))/12 - 63/4))/12 - ((-1)^(1/3)*2^(2/3)*log(((-1)^(1/3)*2^(2/3)*(3^(1/2)*1i + 1)*((459*(1 - x^3)^(1/3))/4 - (81*(-1)^(2/3)*2^(1/3)*(3^(1/2)*1i + 1)^2)/16))/24 - 63/4)*(3^(1/2)*1i + 1))/24","B"
644,1,399,175,5.024252,"\text{Not used}","int(1/(x^4*(1 - x^3)^(4/3)*(x^3 + 1)),x)","\frac{\ln\left(\frac{11\,{\left(1-x^3\right)}^{1/3}}{972}-\frac{11}{972}\right)}{9}+\frac{2^{2/3}\,\ln\left(\frac{2^{1/3}\,\left(\frac{2^{2/3}\,\left(\frac{81\,2^{1/3}}{4}-\frac{75\,{\left(1-x^3\right)}^{1/3}}{4}\right)}{12}-\frac{35}{12}\right)}{72}+\frac{{\left(1-x^3\right)}^{1/3}}{27}\right)}{12}+\ln\left({\left(-\frac{1}{18}+\frac{\sqrt{3}\,1{}\mathrm{i}}{18}\right)}^2\,\left(\left(-\frac{1}{18}+\frac{\sqrt{3}\,1{}\mathrm{i}}{18}\right)\,\left(1458\,{\left(-\frac{1}{18}+\frac{\sqrt{3}\,1{}\mathrm{i}}{18}\right)}^2-\frac{75\,{\left(1-x^3\right)}^{1/3}}{4}\right)-\frac{35}{12}\right)+\frac{{\left(1-x^3\right)}^{1/3}}{27}\right)\,\left(-\frac{1}{18}+\frac{\sqrt{3}\,1{}\mathrm{i}}{18}\right)-\ln\left(\frac{{\left(1-x^3\right)}^{1/3}}{27}-{\left(\frac{1}{18}+\frac{\sqrt{3}\,1{}\mathrm{i}}{18}\right)}^2\,\left(\left(\frac{1}{18}+\frac{\sqrt{3}\,1{}\mathrm{i}}{18}\right)\,\left(1458\,{\left(\frac{1}{18}+\frac{\sqrt{3}\,1{}\mathrm{i}}{18}\right)}^2-\frac{75\,{\left(1-x^3\right)}^{1/3}}{4}\right)+\frac{35}{12}\right)\right)\,\left(\frac{1}{18}+\frac{\sqrt{3}\,1{}\mathrm{i}}{18}\right)+\frac{\frac{5\,x^3}{6}-\frac{1}{3}}{{\left(1-x^3\right)}^{1/3}-{\left(1-x^3\right)}^{4/3}}+\frac{2^{2/3}\,\ln\left(\frac{{\left(1-x^3\right)}^{1/3}}{27}+\frac{2^{1/3}\,{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(\frac{2^{2/3}\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(\frac{81\,2^{1/3}\,{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2}{16}-\frac{75\,{\left(1-x^3\right)}^{1/3}}{4}\right)}{24}-\frac{35}{12}\right)}{288}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{24}-\frac{2^{2/3}\,\ln\left(\frac{{\left(1-x^3\right)}^{1/3}}{27}-\frac{2^{1/3}\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(\frac{2^{2/3}\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(\frac{81\,2^{1/3}\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2}{16}-\frac{75\,{\left(1-x^3\right)}^{1/3}}{4}\right)}{24}+\frac{35}{12}\right)}{288}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{24}","Not used",1,"log((11*(1 - x^3)^(1/3))/972 - 11/972)/9 + (2^(2/3)*log((2^(1/3)*((2^(2/3)*((81*2^(1/3))/4 - (75*(1 - x^3)^(1/3))/4))/12 - 35/12))/72 + (1 - x^3)^(1/3)/27))/12 + log(((3^(1/2)*1i)/18 - 1/18)^2*(((3^(1/2)*1i)/18 - 1/18)*(1458*((3^(1/2)*1i)/18 - 1/18)^2 - (75*(1 - x^3)^(1/3))/4) - 35/12) + (1 - x^3)^(1/3)/27)*((3^(1/2)*1i)/18 - 1/18) - log((1 - x^3)^(1/3)/27 - ((3^(1/2)*1i)/18 + 1/18)^2*(((3^(1/2)*1i)/18 + 1/18)*(1458*((3^(1/2)*1i)/18 + 1/18)^2 - (75*(1 - x^3)^(1/3))/4) + 35/12))*((3^(1/2)*1i)/18 + 1/18) + ((5*x^3)/6 - 1/3)/((1 - x^3)^(1/3) - (1 - x^3)^(4/3)) + (2^(2/3)*log((1 - x^3)^(1/3)/27 + (2^(1/3)*(3^(1/2)*1i - 1)^2*((2^(2/3)*(3^(1/2)*1i - 1)*((81*2^(1/3)*(3^(1/2)*1i - 1)^2)/16 - (75*(1 - x^3)^(1/3))/4))/24 - 35/12))/288)*(3^(1/2)*1i - 1))/24 - (2^(2/3)*log((1 - x^3)^(1/3)/27 - (2^(1/3)*(3^(1/2)*1i + 1)^2*((2^(2/3)*(3^(1/2)*1i + 1)*((81*2^(1/3)*(3^(1/2)*1i + 1)^2)/16 - (75*(1 - x^3)^(1/3))/4))/24 + 35/12))/288)*(3^(1/2)*1i + 1))/24","B"
645,0,-1,174,0.000000,"\text{Not used}","int(x^9/((1 - x^3)^(4/3)*(x^3 + 1)),x)","\int \frac{x^9}{{\left(1-x^3\right)}^{4/3}\,\left(x^3+1\right)} \,d x","Not used",1,"int(x^9/((1 - x^3)^(4/3)*(x^3 + 1)), x)","F"
646,0,-1,153,0.000000,"\text{Not used}","int(x^6/((1 - x^3)^(4/3)*(x^3 + 1)),x)","\int \frac{x^6}{{\left(1-x^3\right)}^{4/3}\,\left(x^3+1\right)} \,d x","Not used",1,"int(x^6/((1 - x^3)^(4/3)*(x^3 + 1)), x)","F"
647,0,-1,106,0.000000,"\text{Not used}","int(x^3/((1 - x^3)^(4/3)*(x^3 + 1)),x)","\int \frac{x^3}{{\left(1-x^3\right)}^{4/3}\,\left(x^3+1\right)} \,d x","Not used",1,"int(x^3/((1 - x^3)^(4/3)*(x^3 + 1)), x)","F"
648,0,-1,106,0.000000,"\text{Not used}","int(1/((1 - x^3)^(4/3)*(x^3 + 1)),x)","\int \frac{1}{{\left(1-x^3\right)}^{4/3}\,\left(x^3+1\right)} \,d x","Not used",1,"int(1/((1 - x^3)^(4/3)*(x^3 + 1)), x)","F"
649,0,-1,124,0.000000,"\text{Not used}","int(1/(x^3*(1 - x^3)^(4/3)*(x^3 + 1)),x)","\int \frac{1}{x^3\,{\left(1-x^3\right)}^{4/3}\,\left(x^3+1\right)} \,d x","Not used",1,"int(1/(x^3*(1 - x^3)^(4/3)*(x^3 + 1)), x)","F"
650,0,-1,144,0.000000,"\text{Not used}","int(1/(x^6*(1 - x^3)^(4/3)*(x^3 + 1)),x)","\int \frac{1}{x^6\,{\left(1-x^3\right)}^{4/3}\,\left(x^3+1\right)} \,d x","Not used",1,"int(1/(x^6*(1 - x^3)^(4/3)*(x^3 + 1)), x)","F"
651,0,-1,162,0.000000,"\text{Not used}","int(1/(x^9*(1 - x^3)^(4/3)*(x^3 + 1)),x)","\int \frac{1}{x^9\,{\left(1-x^3\right)}^{4/3}\,\left(x^3+1\right)} \,d x","Not used",1,"int(1/(x^9*(1 - x^3)^(4/3)*(x^3 + 1)), x)","F"
652,0,-1,292,0.000000,"\text{Not used}","int(x^10/((1 - x^3)^(4/3)*(x^3 + 1)),x)","\int \frac{x^{10}}{{\left(1-x^3\right)}^{4/3}\,\left(x^3+1\right)} \,d x","Not used",1,"int(x^10/((1 - x^3)^(4/3)*(x^3 + 1)), x)","F"
653,0,-1,274,0.000000,"\text{Not used}","int(x^7/((1 - x^3)^(4/3)*(x^3 + 1)),x)","\int \frac{x^7}{{\left(1-x^3\right)}^{4/3}\,\left(x^3+1\right)} \,d x","Not used",1,"int(x^7/((1 - x^3)^(4/3)*(x^3 + 1)), x)","F"
654,0,-1,274,0.000000,"\text{Not used}","int(x^4/((1 - x^3)^(4/3)*(x^3 + 1)),x)","\int \frac{x^4}{{\left(1-x^3\right)}^{4/3}\,\left(x^3+1\right)} \,d x","Not used",1,"int(x^4/((1 - x^3)^(4/3)*(x^3 + 1)), x)","F"
655,0,-1,274,0.000000,"\text{Not used}","int(x/((1 - x^3)^(4/3)*(x^3 + 1)),x)","\int \frac{x}{{\left(1-x^3\right)}^{4/3}\,\left(x^3+1\right)} \,d x","Not used",1,"int(x/((1 - x^3)^(4/3)*(x^3 + 1)), x)","F"
656,0,-1,292,0.000000,"\text{Not used}","int(1/(x^2*(1 - x^3)^(4/3)*(x^3 + 1)),x)","\int \frac{1}{x^2\,{\left(1-x^3\right)}^{4/3}\,\left(x^3+1\right)} \,d x","Not used",1,"int(1/(x^2*(1 - x^3)^(4/3)*(x^3 + 1)), x)","F"
657,0,-1,308,0.000000,"\text{Not used}","int(1/(x^5*(1 - x^3)^(4/3)*(x^3 + 1)),x)","\int \frac{1}{x^5\,{\left(1-x^3\right)}^{4/3}\,\left(x^3+1\right)} \,d x","Not used",1,"int(1/(x^5*(1 - x^3)^(4/3)*(x^3 + 1)), x)","F"
658,1,442,264,4.983829,"\text{Not used}","int((x^11*(a + b*x^3)^(1/3))/(c + d*x^3),x)","\left(\frac{3\,a^2}{4\,b^3\,d}+\frac{\left(\frac{3\,a}{b^3\,d}+\frac{b^4\,c-a\,b^3\,d}{b^6\,d^2}\right)\,\left(b^4\,c-a\,b^3\,d\right)}{4\,b^3\,d}\right)\,{\left(b\,x^3+a\right)}^{4/3}-\left(\frac{3\,a}{7\,b^3\,d}+\frac{b^4\,c-a\,b^3\,d}{7\,b^6\,d^2}\right)\,{\left(b\,x^3+a\right)}^{7/3}-{\left(b\,x^3+a\right)}^{1/3}\,\left(\frac{a^3}{b^3\,d}+\frac{\left(\frac{3\,a^2}{b^3\,d}+\frac{\left(\frac{3\,a}{b^3\,d}+\frac{b^4\,c-a\,b^3\,d}{b^6\,d^2}\right)\,\left(b^4\,c-a\,b^3\,d\right)}{b^3\,d}\right)\,\left(b^4\,c-a\,b^3\,d\right)}{b^3\,d}\right)+\frac{{\left(b\,x^3+a\right)}^{10/3}}{10\,b^3\,d}-\frac{c^3\,\ln\left({\left(a\,d-b\,c\right)}^{1/3}-d^{1/3}\,{\left(b\,x^3+a\right)}^{1/3}\right)\,{\left(a\,d-b\,c\right)}^{1/3}}{3\,d^{13/3}}-\frac{c^3\,\ln\left(\frac{3\,{\left(b\,x^3+a\right)}^{1/3}\,\left(b\,c^4-a\,c^3\,d\right)}{d^2}+\frac{3\,c^3\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(a\,d-b\,c\right)}^{4/3}}{d^{7/3}}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(a\,d-b\,c\right)}^{1/3}}{3\,d^{13/3}}+\frac{c^3\,\ln\left(\frac{3\,{\left(b\,x^3+a\right)}^{1/3}\,\left(b\,c^4-a\,c^3\,d\right)}{d^2}-\frac{9\,c^3\,\left(\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)\,{\left(a\,d-b\,c\right)}^{4/3}}{d^{7/3}}\right)\,\left(\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)\,{\left(a\,d-b\,c\right)}^{1/3}}{d^{13/3}}","Not used",1,"((3*a^2)/(4*b^3*d) + (((3*a)/(b^3*d) + (b^4*c - a*b^3*d)/(b^6*d^2))*(b^4*c - a*b^3*d))/(4*b^3*d))*(a + b*x^3)^(4/3) - ((3*a)/(7*b^3*d) + (b^4*c - a*b^3*d)/(7*b^6*d^2))*(a + b*x^3)^(7/3) - (a + b*x^3)^(1/3)*(a^3/(b^3*d) + (((3*a^2)/(b^3*d) + (((3*a)/(b^3*d) + (b^4*c - a*b^3*d)/(b^6*d^2))*(b^4*c - a*b^3*d))/(b^3*d))*(b^4*c - a*b^3*d))/(b^3*d)) + (a + b*x^3)^(10/3)/(10*b^3*d) - (c^3*log((a*d - b*c)^(1/3) - d^(1/3)*(a + b*x^3)^(1/3))*(a*d - b*c)^(1/3))/(3*d^(13/3)) - (c^3*log((3*(a + b*x^3)^(1/3)*(b*c^4 - a*c^3*d))/d^2 + (3*c^3*((3^(1/2)*1i)/2 - 1/2)*(a*d - b*c)^(4/3))/d^(7/3))*((3^(1/2)*1i)/2 - 1/2)*(a*d - b*c)^(1/3))/(3*d^(13/3)) + (c^3*log((3*(a + b*x^3)^(1/3)*(b*c^4 - a*c^3*d))/d^2 - (9*c^3*((3^(1/2)*1i)/6 + 1/6)*(a*d - b*c)^(4/3))/d^(7/3))*((3^(1/2)*1i)/6 + 1/6)*(a*d - b*c)^(1/3))/d^(13/3)","B"
659,1,336,220,4.932922,"\text{Not used}","int((x^8*(a + b*x^3)^(1/3))/(c + d*x^3),x)","\left(\frac{a^2}{b^2\,d}+\frac{\left(\frac{2\,a}{b^2\,d}+\frac{b^3\,c-a\,b^2\,d}{b^4\,d^2}\right)\,\left(b^3\,c-a\,b^2\,d\right)}{b^2\,d}\right)\,{\left(b\,x^3+a\right)}^{1/3}-\left(\frac{a}{2\,b^2\,d}+\frac{b^3\,c-a\,b^2\,d}{4\,b^4\,d^2}\right)\,{\left(b\,x^3+a\right)}^{4/3}+\frac{{\left(b\,x^3+a\right)}^{7/3}}{7\,b^2\,d}+\frac{c^2\,\ln\left({\left(a\,d-b\,c\right)}^{1/3}-d^{1/3}\,{\left(b\,x^3+a\right)}^{1/3}\right)\,{\left(a\,d-b\,c\right)}^{1/3}}{3\,d^{10/3}}-\frac{c^2\,\ln\left(\frac{3\,{\left(b\,x^3+a\right)}^{1/3}\,\left(b\,c^3-a\,c^2\,d\right)}{d}-\frac{3\,c^2\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(a\,d-b\,c\right)}^{4/3}}{d^{4/3}}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(a\,d-b\,c\right)}^{1/3}}{3\,d^{10/3}}+\frac{c^2\,\ln\left(\frac{3\,{\left(b\,x^3+a\right)}^{1/3}\,\left(b\,c^3-a\,c^2\,d\right)}{d}+\frac{9\,c^2\,\left(-\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)\,{\left(a\,d-b\,c\right)}^{4/3}}{d^{4/3}}\right)\,\left(-\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)\,{\left(a\,d-b\,c\right)}^{1/3}}{d^{10/3}}","Not used",1,"(a^2/(b^2*d) + (((2*a)/(b^2*d) + (b^3*c - a*b^2*d)/(b^4*d^2))*(b^3*c - a*b^2*d))/(b^2*d))*(a + b*x^3)^(1/3) - (a/(2*b^2*d) + (b^3*c - a*b^2*d)/(4*b^4*d^2))*(a + b*x^3)^(4/3) + (a + b*x^3)^(7/3)/(7*b^2*d) + (c^2*log((a*d - b*c)^(1/3) - d^(1/3)*(a + b*x^3)^(1/3))*(a*d - b*c)^(1/3))/(3*d^(10/3)) - (c^2*log((3*(a + b*x^3)^(1/3)*(b*c^3 - a*c^2*d))/d - (3*c^2*((3^(1/2)*1i)/2 + 1/2)*(a*d - b*c)^(4/3))/d^(4/3))*((3^(1/2)*1i)/2 + 1/2)*(a*d - b*c)^(1/3))/(3*d^(10/3)) + (c^2*log((3*(a + b*x^3)^(1/3)*(b*c^3 - a*c^2*d))/d + (9*c^2*((3^(1/2)*1i)/6 - 1/6)*(a*d - b*c)^(4/3))/d^(4/3))*((3^(1/2)*1i)/6 - 1/6)*(a*d - b*c)^(1/3))/d^(10/3)","B"
660,1,298,186,4.616960,"\text{Not used}","int((x^5*(a + b*x^3)^(1/3))/(c + d*x^3),x)","\frac{{\left(b\,x^3+a\right)}^{4/3}}{4\,b\,d}-{\left(b\,x^3+a\right)}^{1/3}\,\left(\frac{a}{b\,d}+\frac{b^2\,c-a\,b\,d}{b^2\,d^2}\right)-\frac{c\,\ln\left({\left(b\,x^3+a\right)}^{1/3}\,\left(3\,b\,c^2-3\,a\,c\,d\right)+\frac{c\,{\left(a\,d-b\,c\right)}^{1/3}\,\left(9\,a\,d^3-9\,b\,c\,d^2\right)}{3\,d^{7/3}}\right)\,{\left(a\,d-b\,c\right)}^{1/3}}{3\,d^{7/3}}-\frac{c\,\ln\left({\left(b\,x^3+a\right)}^{1/3}\,\left(3\,b\,c^2-3\,a\,c\,d\right)+\frac{c\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(a\,d-b\,c\right)}^{1/3}\,\left(9\,a\,d^3-9\,b\,c\,d^2\right)}{3\,d^{7/3}}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(a\,d-b\,c\right)}^{1/3}}{3\,d^{7/3}}+\frac{c\,\ln\left({\left(b\,x^3+a\right)}^{1/3}\,\left(3\,b\,c^2-3\,a\,c\,d\right)-\frac{c\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(a\,d-b\,c\right)}^{1/3}\,\left(9\,a\,d^3-9\,b\,c\,d^2\right)}{3\,d^{7/3}}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(a\,d-b\,c\right)}^{1/3}}{3\,d^{7/3}}","Not used",1,"(a + b*x^3)^(4/3)/(4*b*d) - (a + b*x^3)^(1/3)*(a/(b*d) + (b^2*c - a*b*d)/(b^2*d^2)) - (c*log((a + b*x^3)^(1/3)*(3*b*c^2 - 3*a*c*d) + (c*(a*d - b*c)^(1/3)*(9*a*d^3 - 9*b*c*d^2))/(3*d^(7/3)))*(a*d - b*c)^(1/3))/(3*d^(7/3)) - (c*log((a + b*x^3)^(1/3)*(3*b*c^2 - 3*a*c*d) + (c*((3^(1/2)*1i)/2 - 1/2)*(a*d - b*c)^(1/3)*(9*a*d^3 - 9*b*c*d^2))/(3*d^(7/3)))*((3^(1/2)*1i)/2 - 1/2)*(a*d - b*c)^(1/3))/(3*d^(7/3)) + (c*log((a + b*x^3)^(1/3)*(3*b*c^2 - 3*a*c*d) - (c*((3^(1/2)*1i)/2 + 1/2)*(a*d - b*c)^(1/3)*(9*a*d^3 - 9*b*c*d^2))/(3*d^(7/3)))*((3^(1/2)*1i)/2 + 1/2)*(a*d - b*c)^(1/3))/(3*d^(7/3))","B"
661,1,249,159,4.620635,"\text{Not used}","int((x^2*(a + b*x^3)^(1/3))/(c + d*x^3),x)","\frac{{\left(b\,x^3+a\right)}^{1/3}}{d}+\frac{\ln\left({\left(b\,x^3+a\right)}^{1/3}\,\left(3\,a\,d^2-3\,b\,c\,d\right)-\frac{{\left(a\,d-b\,c\right)}^{1/3}\,\left(9\,a\,d^3-9\,b\,c\,d^2\right)}{3\,d^{4/3}}\right)\,{\left(a\,d-b\,c\right)}^{1/3}}{3\,d^{4/3}}-\frac{\ln\left({\left(b\,x^3+a\right)}^{1/3}\,\left(3\,a\,d^2-3\,b\,c\,d\right)+\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(a\,d-b\,c\right)}^{1/3}\,\left(9\,a\,d^3-9\,b\,c\,d^2\right)}{3\,d^{4/3}}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(a\,d-b\,c\right)}^{1/3}}{3\,d^{4/3}}+\frac{\ln\left({\left(b\,x^3+a\right)}^{1/3}\,\left(3\,a\,d^2-3\,b\,c\,d\right)-\frac{\left(-\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)\,{\left(a\,d-b\,c\right)}^{1/3}\,\left(9\,a\,d^3-9\,b\,c\,d^2\right)}{d^{4/3}}\right)\,\left(-\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)\,{\left(a\,d-b\,c\right)}^{1/3}}{d^{4/3}}","Not used",1,"(a + b*x^3)^(1/3)/d + (log((a + b*x^3)^(1/3)*(3*a*d^2 - 3*b*c*d) - ((a*d - b*c)^(1/3)*(9*a*d^3 - 9*b*c*d^2))/(3*d^(4/3)))*(a*d - b*c)^(1/3))/(3*d^(4/3)) - (log((a + b*x^3)^(1/3)*(3*a*d^2 - 3*b*c*d) + (((3^(1/2)*1i)/2 + 1/2)*(a*d - b*c)^(1/3)*(9*a*d^3 - 9*b*c*d^2))/(3*d^(4/3)))*((3^(1/2)*1i)/2 + 1/2)*(a*d - b*c)^(1/3))/(3*d^(4/3)) + (log((a + b*x^3)^(1/3)*(3*a*d^2 - 3*b*c*d) - (((3^(1/2)*1i)/6 - 1/6)*(a*d - b*c)^(1/3)*(9*a*d^3 - 9*b*c*d^2))/d^(4/3))*((3^(1/2)*1i)/6 - 1/6)*(a*d - b*c)^(1/3))/d^(4/3)","B"
662,1,1607,246,4.744135,"\text{Not used}","int((a + b*x^3)^(1/3)/(x*(c + d*x^3)),x)","\ln\left({\left(b\,x^3+a\right)}^{1/3}\,\left(6\,a^4\,b^4\,d^5-12\,a^3\,b^5\,c\,d^4+9\,a^2\,b^6\,c^2\,d^3-3\,a\,b^7\,c^3\,d^2\right)-{\left(\frac{a}{27\,c^3}\right)}^{1/3}\,\left(\left(\left(486\,a^3\,b^4\,c^4\,d^5-729\,a^2\,b^5\,c^5\,d^4+243\,a\,b^6\,c^6\,d^3\right)\,{\left(\frac{a}{27\,c^3}\right)}^{1/3}-{\left(b\,x^3+a\right)}^{1/3}\,\left(81\,a\,b^6\,c^5\,d^3-81\,a^2\,b^5\,c^4\,d^4\right)\right)\,{\left(\frac{a}{27\,c^3}\right)}^{2/3}-9\,a\,b^7\,c^4\,d^2+27\,a^2\,b^6\,c^3\,d^3-18\,a^3\,b^5\,c^2\,d^4\right)\right)\,{\left(\frac{a}{27\,c^3}\right)}^{1/3}+\ln\left({\left(b\,x^3+a\right)}^{1/3}\,\left(6\,a^4\,b^4\,d^5-12\,a^3\,b^5\,c\,d^4+9\,a^2\,b^6\,c^2\,d^3-3\,a\,b^7\,c^3\,d^2\right)-\left(\left(\left(486\,a^3\,b^4\,c^4\,d^5-729\,a^2\,b^5\,c^5\,d^4+243\,a\,b^6\,c^6\,d^3\right)\,{\left(-\frac{a\,d-b\,c}{27\,c^3\,d}\right)}^{1/3}-{\left(b\,x^3+a\right)}^{1/3}\,\left(81\,a\,b^6\,c^5\,d^3-81\,a^2\,b^5\,c^4\,d^4\right)\right)\,{\left(-\frac{a\,d-b\,c}{27\,c^3\,d}\right)}^{2/3}-9\,a\,b^7\,c^4\,d^2+27\,a^2\,b^6\,c^3\,d^3-18\,a^3\,b^5\,c^2\,d^4\right)\,{\left(-\frac{a\,d-b\,c}{27\,c^3\,d}\right)}^{1/3}\right)\,{\left(-\frac{a\,d-b\,c}{27\,c^3\,d}\right)}^{1/3}+\ln\left({\left(b\,x^3+a\right)}^{1/3}\,\left(6\,a^4\,b^4\,d^5-12\,a^3\,b^5\,c\,d^4+9\,a^2\,b^6\,c^2\,d^3-3\,a\,b^7\,c^3\,d^2\right)+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{a\,d-b\,c}{27\,c^3\,d}\right)}^{1/3}\,\left({\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,\left({\left(b\,x^3+a\right)}^{1/3}\,\left(81\,a\,b^6\,c^5\,d^3-81\,a^2\,b^5\,c^4\,d^4\right)-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(486\,a^3\,b^4\,c^4\,d^5-729\,a^2\,b^5\,c^5\,d^4+243\,a\,b^6\,c^6\,d^3\right)\,{\left(-\frac{a\,d-b\,c}{27\,c^3\,d}\right)}^{1/3}\right)\,{\left(-\frac{a\,d-b\,c}{27\,c^3\,d}\right)}^{2/3}+9\,a\,b^7\,c^4\,d^2-27\,a^2\,b^6\,c^3\,d^3+18\,a^3\,b^5\,c^2\,d^4\right)\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{a\,d-b\,c}{27\,c^3\,d}\right)}^{1/3}-\ln\left({\left(b\,x^3+a\right)}^{1/3}\,\left(6\,a^4\,b^4\,d^5-12\,a^3\,b^5\,c\,d^4+9\,a^2\,b^6\,c^2\,d^3-3\,a\,b^7\,c^3\,d^2\right)-\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{a\,d-b\,c}{27\,c^3\,d}\right)}^{1/3}\,\left({\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,\left({\left(b\,x^3+a\right)}^{1/3}\,\left(81\,a\,b^6\,c^5\,d^3-81\,a^2\,b^5\,c^4\,d^4\right)+\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(486\,a^3\,b^4\,c^4\,d^5-729\,a^2\,b^5\,c^5\,d^4+243\,a\,b^6\,c^6\,d^3\right)\,{\left(-\frac{a\,d-b\,c}{27\,c^3\,d}\right)}^{1/3}\right)\,{\left(-\frac{a\,d-b\,c}{27\,c^3\,d}\right)}^{2/3}+9\,a\,b^7\,c^4\,d^2-27\,a^2\,b^6\,c^3\,d^3+18\,a^3\,b^5\,c^2\,d^4\right)\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{a\,d-b\,c}{27\,c^3\,d}\right)}^{1/3}+\ln\left({\left(b\,x^3+a\right)}^{1/3}\,\left(6\,a^4\,b^4\,d^5-12\,a^3\,b^5\,c\,d^4+9\,a^2\,b^6\,c^2\,d^3-3\,a\,b^7\,c^3\,d^2\right)+\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(\frac{a}{27\,c^3}\right)}^{1/3}\,\left({\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,\left({\left(b\,x^3+a\right)}^{1/3}\,\left(81\,a\,b^6\,c^5\,d^3-81\,a^2\,b^5\,c^4\,d^4\right)-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(486\,a^3\,b^4\,c^4\,d^5-729\,a^2\,b^5\,c^5\,d^4+243\,a\,b^6\,c^6\,d^3\right)\,{\left(\frac{a}{27\,c^3}\right)}^{1/3}\right)\,{\left(\frac{a}{27\,c^3}\right)}^{2/3}+9\,a\,b^7\,c^4\,d^2-27\,a^2\,b^6\,c^3\,d^3+18\,a^3\,b^5\,c^2\,d^4\right)\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(\frac{a}{27\,c^3}\right)}^{1/3}-\ln\left({\left(b\,x^3+a\right)}^{1/3}\,\left(6\,a^4\,b^4\,d^5-12\,a^3\,b^5\,c\,d^4+9\,a^2\,b^6\,c^2\,d^3-3\,a\,b^7\,c^3\,d^2\right)-\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(\frac{a}{27\,c^3}\right)}^{1/3}\,\left({\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,\left({\left(b\,x^3+a\right)}^{1/3}\,\left(81\,a\,b^6\,c^5\,d^3-81\,a^2\,b^5\,c^4\,d^4\right)+\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(486\,a^3\,b^4\,c^4\,d^5-729\,a^2\,b^5\,c^5\,d^4+243\,a\,b^6\,c^6\,d^3\right)\,{\left(\frac{a}{27\,c^3}\right)}^{1/3}\right)\,{\left(\frac{a}{27\,c^3}\right)}^{2/3}+9\,a\,b^7\,c^4\,d^2-27\,a^2\,b^6\,c^3\,d^3+18\,a^3\,b^5\,c^2\,d^4\right)\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(\frac{a}{27\,c^3}\right)}^{1/3}","Not used",1,"log((a + b*x^3)^(1/3)*(6*a^4*b^4*d^5 - 3*a*b^7*c^3*d^2 - 12*a^3*b^5*c*d^4 + 9*a^2*b^6*c^2*d^3) - (a/(27*c^3))^(1/3)*(((243*a*b^6*c^6*d^3 - 729*a^2*b^5*c^5*d^4 + 486*a^3*b^4*c^4*d^5)*(a/(27*c^3))^(1/3) - (a + b*x^3)^(1/3)*(81*a*b^6*c^5*d^3 - 81*a^2*b^5*c^4*d^4))*(a/(27*c^3))^(2/3) - 9*a*b^7*c^4*d^2 + 27*a^2*b^6*c^3*d^3 - 18*a^3*b^5*c^2*d^4))*(a/(27*c^3))^(1/3) + log((a + b*x^3)^(1/3)*(6*a^4*b^4*d^5 - 3*a*b^7*c^3*d^2 - 12*a^3*b^5*c*d^4 + 9*a^2*b^6*c^2*d^3) - (((243*a*b^6*c^6*d^3 - 729*a^2*b^5*c^5*d^4 + 486*a^3*b^4*c^4*d^5)*(-(a*d - b*c)/(27*c^3*d))^(1/3) - (a + b*x^3)^(1/3)*(81*a*b^6*c^5*d^3 - 81*a^2*b^5*c^4*d^4))*(-(a*d - b*c)/(27*c^3*d))^(2/3) - 9*a*b^7*c^4*d^2 + 27*a^2*b^6*c^3*d^3 - 18*a^3*b^5*c^2*d^4)*(-(a*d - b*c)/(27*c^3*d))^(1/3))*(-(a*d - b*c)/(27*c^3*d))^(1/3) + log((a + b*x^3)^(1/3)*(6*a^4*b^4*d^5 - 3*a*b^7*c^3*d^2 - 12*a^3*b^5*c*d^4 + 9*a^2*b^6*c^2*d^3) + ((3^(1/2)*1i)/2 - 1/2)*(-(a*d - b*c)/(27*c^3*d))^(1/3)*(((3^(1/2)*1i)/2 - 1/2)^2*((a + b*x^3)^(1/3)*(81*a*b^6*c^5*d^3 - 81*a^2*b^5*c^4*d^4) - ((3^(1/2)*1i)/2 - 1/2)*(243*a*b^6*c^6*d^3 - 729*a^2*b^5*c^5*d^4 + 486*a^3*b^4*c^4*d^5)*(-(a*d - b*c)/(27*c^3*d))^(1/3))*(-(a*d - b*c)/(27*c^3*d))^(2/3) + 9*a*b^7*c^4*d^2 - 27*a^2*b^6*c^3*d^3 + 18*a^3*b^5*c^2*d^4))*((3^(1/2)*1i)/2 - 1/2)*(-(a*d - b*c)/(27*c^3*d))^(1/3) - log((a + b*x^3)^(1/3)*(6*a^4*b^4*d^5 - 3*a*b^7*c^3*d^2 - 12*a^3*b^5*c*d^4 + 9*a^2*b^6*c^2*d^3) - ((3^(1/2)*1i)/2 + 1/2)*(-(a*d - b*c)/(27*c^3*d))^(1/3)*(((3^(1/2)*1i)/2 + 1/2)^2*((a + b*x^3)^(1/3)*(81*a*b^6*c^5*d^3 - 81*a^2*b^5*c^4*d^4) + ((3^(1/2)*1i)/2 + 1/2)*(243*a*b^6*c^6*d^3 - 729*a^2*b^5*c^5*d^4 + 486*a^3*b^4*c^4*d^5)*(-(a*d - b*c)/(27*c^3*d))^(1/3))*(-(a*d - b*c)/(27*c^3*d))^(2/3) + 9*a*b^7*c^4*d^2 - 27*a^2*b^6*c^3*d^3 + 18*a^3*b^5*c^2*d^4))*((3^(1/2)*1i)/2 + 1/2)*(-(a*d - b*c)/(27*c^3*d))^(1/3) + log((a + b*x^3)^(1/3)*(6*a^4*b^4*d^5 - 3*a*b^7*c^3*d^2 - 12*a^3*b^5*c*d^4 + 9*a^2*b^6*c^2*d^3) + ((3^(1/2)*1i)/2 - 1/2)*(a/(27*c^3))^(1/3)*(((3^(1/2)*1i)/2 - 1/2)^2*((a + b*x^3)^(1/3)*(81*a*b^6*c^5*d^3 - 81*a^2*b^5*c^4*d^4) - ((3^(1/2)*1i)/2 - 1/2)*(243*a*b^6*c^6*d^3 - 729*a^2*b^5*c^5*d^4 + 486*a^3*b^4*c^4*d^5)*(a/(27*c^3))^(1/3))*(a/(27*c^3))^(2/3) + 9*a*b^7*c^4*d^2 - 27*a^2*b^6*c^3*d^3 + 18*a^3*b^5*c^2*d^4))*((3^(1/2)*1i)/2 - 1/2)*(a/(27*c^3))^(1/3) - log((a + b*x^3)^(1/3)*(6*a^4*b^4*d^5 - 3*a*b^7*c^3*d^2 - 12*a^3*b^5*c*d^4 + 9*a^2*b^6*c^2*d^3) - ((3^(1/2)*1i)/2 + 1/2)*(a/(27*c^3))^(1/3)*(((3^(1/2)*1i)/2 + 1/2)^2*((a + b*x^3)^(1/3)*(81*a*b^6*c^5*d^3 - 81*a^2*b^5*c^4*d^4) + ((3^(1/2)*1i)/2 + 1/2)*(243*a*b^6*c^6*d^3 - 729*a^2*b^5*c^5*d^4 + 486*a^3*b^4*c^4*d^5)*(a/(27*c^3))^(1/3))*(a/(27*c^3))^(2/3) + 9*a*b^7*c^4*d^2 - 27*a^2*b^6*c^3*d^3 + 18*a^3*b^5*c^2*d^4))*((3^(1/2)*1i)/2 + 1/2)*(a/(27*c^3))^(1/3)","B"
663,1,1917,340,9.989981,"\text{Not used}","int((a + b*x^3)^(1/3)/(x^4*(c + d*x^3)),x)","\ln\left(-\frac{\left(\frac{\left(27\,b^5\,c^3\,d^3\,{\left(b\,x^3+a\right)}^{1/3}\,\left(4\,a^2\,d^2-5\,a\,b\,c\,d+b^2\,c^2\right)-27\,a\,b^4\,c^4\,d^3\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)\,{\left(-\frac{{\left(3\,a\,d-b\,c\right)}^3}{a^2\,c^6}\right)}^{1/3}\right)\,{\left(-\frac{{\left(3\,a\,d-b\,c\right)}^3}{a^2\,c^6}\right)}^{2/3}}{81}-\frac{b^5\,d^4\,\left(27\,a^3\,d^3-45\,a^2\,b\,c\,d^2+17\,a\,b^2\,c^2\,d+b^3\,c^3\right)}{3\,c}\right)\,{\left(-\frac{{\left(3\,a\,d-b\,c\right)}^3}{a^2\,c^6}\right)}^{1/3}}{9}-\frac{2\,b^4\,d^5\,{\left(b\,x^3+a\right)}^{1/3}\,\left(27\,a^4\,d^4-72\,a^3\,b\,c\,d^3+72\,a^2\,b^2\,c^2\,d^2-32\,a\,b^3\,c^3\,d+5\,b^4\,c^4\right)}{9\,c^4}\right)\,{\left(-\frac{27\,a^3\,d^3-27\,a^2\,b\,c\,d^2+9\,a\,b^2\,c^2\,d-b^3\,c^3}{729\,a^2\,c^6}\right)}^{1/3}+\ln\left(-\frac{\left(\frac{\left(27\,b^5\,c^3\,d^3\,{\left(b\,x^3+a\right)}^{1/3}\,\left(4\,a^2\,d^2-5\,a\,b\,c\,d+b^2\,c^2\right)-81\,a\,b^4\,c^4\,d^3\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)\,{\left(\frac{d^2\,\left(a\,d-b\,c\right)}{c^6}\right)}^{1/3}\right)\,{\left(\frac{d^2\,\left(a\,d-b\,c\right)}{c^6}\right)}^{2/3}}{9}-\frac{b^5\,d^4\,\left(27\,a^3\,d^3-45\,a^2\,b\,c\,d^2+17\,a\,b^2\,c^2\,d+b^3\,c^3\right)}{3\,c}\right)\,{\left(\frac{d^2\,\left(a\,d-b\,c\right)}{c^6}\right)}^{1/3}}{3}-\frac{2\,b^4\,d^5\,{\left(b\,x^3+a\right)}^{1/3}\,\left(27\,a^4\,d^4-72\,a^3\,b\,c\,d^3+72\,a^2\,b^2\,c^2\,d^2-32\,a\,b^3\,c^3\,d+5\,b^4\,c^4\right)}{9\,c^4}\right)\,{\left(\frac{a\,d^3-b\,c\,d^2}{27\,c^6}\right)}^{1/3}+\ln\left(\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(27\,b^5\,c^3\,d^3\,{\left(b\,x^3+a\right)}^{1/3}\,\left(4\,a^2\,d^2-5\,a\,b\,c\,d+b^2\,c^2\right)-81\,a\,b^4\,c^4\,d^3\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)\,{\left(\frac{d^2\,\left(a\,d-b\,c\right)}{c^6}\right)}^{1/3}\right)\,{\left(\frac{d^2\,\left(a\,d-b\,c\right)}{c^6}\right)}^{2/3}}{9}+\frac{b^5\,d^4\,\left(27\,a^3\,d^3-45\,a^2\,b\,c\,d^2+17\,a\,b^2\,c^2\,d+b^3\,c^3\right)}{3\,c}\right)\,{\left(\frac{d^2\,\left(a\,d-b\,c\right)}{c^6}\right)}^{1/3}}{3}-\frac{2\,b^4\,d^5\,{\left(b\,x^3+a\right)}^{1/3}\,\left(27\,a^4\,d^4-72\,a^3\,b\,c\,d^3+72\,a^2\,b^2\,c^2\,d^2-32\,a\,b^3\,c^3\,d+5\,b^4\,c^4\right)}{9\,c^4}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(\frac{a\,d^3-b\,c\,d^2}{27\,c^6}\right)}^{1/3}-\ln\left(\frac{2\,b^4\,d^5\,{\left(b\,x^3+a\right)}^{1/3}\,\left(27\,a^4\,d^4-72\,a^3\,b\,c\,d^3+72\,a^2\,b^2\,c^2\,d^2-32\,a\,b^3\,c^3\,d+5\,b^4\,c^4\right)}{9\,c^4}-\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(27\,b^5\,c^3\,d^3\,{\left(b\,x^3+a\right)}^{1/3}\,\left(4\,a^2\,d^2-5\,a\,b\,c\,d+b^2\,c^2\right)+81\,a\,b^4\,c^4\,d^3\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)\,{\left(\frac{d^2\,\left(a\,d-b\,c\right)}{c^6}\right)}^{1/3}\right)\,{\left(\frac{d^2\,\left(a\,d-b\,c\right)}{c^6}\right)}^{2/3}}{9}-\frac{b^5\,d^4\,\left(27\,a^3\,d^3-45\,a^2\,b\,c\,d^2+17\,a\,b^2\,c^2\,d+b^3\,c^3\right)}{3\,c}\right)\,{\left(\frac{d^2\,\left(a\,d-b\,c\right)}{c^6}\right)}^{1/3}}{3}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(\frac{a\,d^3-b\,c\,d^2}{27\,c^6}\right)}^{1/3}+\ln\left(\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(27\,b^5\,c^3\,d^3\,{\left(b\,x^3+a\right)}^{1/3}\,\left(4\,a^2\,d^2-5\,a\,b\,c\,d+b^2\,c^2\right)-27\,a\,b^4\,c^4\,d^3\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)\,{\left(-\frac{{\left(3\,a\,d-b\,c\right)}^3}{a^2\,c^6}\right)}^{1/3}\right)\,{\left(-\frac{{\left(3\,a\,d-b\,c\right)}^3}{a^2\,c^6}\right)}^{2/3}}{81}+\frac{b^5\,d^4\,\left(27\,a^3\,d^3-45\,a^2\,b\,c\,d^2+17\,a\,b^2\,c^2\,d+b^3\,c^3\right)}{3\,c}\right)\,{\left(-\frac{{\left(3\,a\,d-b\,c\right)}^3}{a^2\,c^6}\right)}^{1/3}}{9}-\frac{2\,b^4\,d^5\,{\left(b\,x^3+a\right)}^{1/3}\,\left(27\,a^4\,d^4-72\,a^3\,b\,c\,d^3+72\,a^2\,b^2\,c^2\,d^2-32\,a\,b^3\,c^3\,d+5\,b^4\,c^4\right)}{9\,c^4}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{27\,a^3\,d^3-27\,a^2\,b\,c\,d^2+9\,a\,b^2\,c^2\,d-b^3\,c^3}{729\,a^2\,c^6}\right)}^{1/3}-\ln\left(\frac{2\,b^4\,d^5\,{\left(b\,x^3+a\right)}^{1/3}\,\left(27\,a^4\,d^4-72\,a^3\,b\,c\,d^3+72\,a^2\,b^2\,c^2\,d^2-32\,a\,b^3\,c^3\,d+5\,b^4\,c^4\right)}{9\,c^4}-\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(27\,b^5\,c^3\,d^3\,{\left(b\,x^3+a\right)}^{1/3}\,\left(4\,a^2\,d^2-5\,a\,b\,c\,d+b^2\,c^2\right)+27\,a\,b^4\,c^4\,d^3\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)\,{\left(-\frac{{\left(3\,a\,d-b\,c\right)}^3}{a^2\,c^6}\right)}^{1/3}\right)\,{\left(-\frac{{\left(3\,a\,d-b\,c\right)}^3}{a^2\,c^6}\right)}^{2/3}}{81}-\frac{b^5\,d^4\,\left(27\,a^3\,d^3-45\,a^2\,b\,c\,d^2+17\,a\,b^2\,c^2\,d+b^3\,c^3\right)}{3\,c}\right)\,{\left(-\frac{{\left(3\,a\,d-b\,c\right)}^3}{a^2\,c^6}\right)}^{1/3}}{9}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{27\,a^3\,d^3-27\,a^2\,b\,c\,d^2+9\,a\,b^2\,c^2\,d-b^3\,c^3}{729\,a^2\,c^6}\right)}^{1/3}-\frac{{\left(b\,x^3+a\right)}^{1/3}}{3\,c\,x^3}","Not used",1,"log(- ((((27*b^5*c^3*d^3*(a + b*x^3)^(1/3)*(4*a^2*d^2 + b^2*c^2 - 5*a*b*c*d) - 27*a*b^4*c^4*d^3*(2*a^2*d^2 + b^2*c^2 - 3*a*b*c*d)*(-(3*a*d - b*c)^3/(a^2*c^6))^(1/3))*(-(3*a*d - b*c)^3/(a^2*c^6))^(2/3))/81 - (b^5*d^4*(27*a^3*d^3 + b^3*c^3 + 17*a*b^2*c^2*d - 45*a^2*b*c*d^2))/(3*c))*(-(3*a*d - b*c)^3/(a^2*c^6))^(1/3))/9 - (2*b^4*d^5*(a + b*x^3)^(1/3)*(27*a^4*d^4 + 5*b^4*c^4 + 72*a^2*b^2*c^2*d^2 - 32*a*b^3*c^3*d - 72*a^3*b*c*d^3))/(9*c^4))*(-(27*a^3*d^3 - b^3*c^3 + 9*a*b^2*c^2*d - 27*a^2*b*c*d^2)/(729*a^2*c^6))^(1/3) + log(- ((((27*b^5*c^3*d^3*(a + b*x^3)^(1/3)*(4*a^2*d^2 + b^2*c^2 - 5*a*b*c*d) - 81*a*b^4*c^4*d^3*(2*a^2*d^2 + b^2*c^2 - 3*a*b*c*d)*((d^2*(a*d - b*c))/c^6)^(1/3))*((d^2*(a*d - b*c))/c^6)^(2/3))/9 - (b^5*d^4*(27*a^3*d^3 + b^3*c^3 + 17*a*b^2*c^2*d - 45*a^2*b*c*d^2))/(3*c))*((d^2*(a*d - b*c))/c^6)^(1/3))/3 - (2*b^4*d^5*(a + b*x^3)^(1/3)*(27*a^4*d^4 + 5*b^4*c^4 + 72*a^2*b^2*c^2*d^2 - 32*a*b^3*c^3*d - 72*a^3*b*c*d^3))/(9*c^4))*((a*d^3 - b*c*d^2)/(27*c^6))^(1/3) + log((((3^(1/2)*1i)/2 - 1/2)*((((3^(1/2)*1i)/2 + 1/2)*(27*b^5*c^3*d^3*(a + b*x^3)^(1/3)*(4*a^2*d^2 + b^2*c^2 - 5*a*b*c*d) - 81*a*b^4*c^4*d^3*((3^(1/2)*1i)/2 - 1/2)*(2*a^2*d^2 + b^2*c^2 - 3*a*b*c*d)*((d^2*(a*d - b*c))/c^6)^(1/3))*((d^2*(a*d - b*c))/c^6)^(2/3))/9 + (b^5*d^4*(27*a^3*d^3 + b^3*c^3 + 17*a*b^2*c^2*d - 45*a^2*b*c*d^2))/(3*c))*((d^2*(a*d - b*c))/c^6)^(1/3))/3 - (2*b^4*d^5*(a + b*x^3)^(1/3)*(27*a^4*d^4 + 5*b^4*c^4 + 72*a^2*b^2*c^2*d^2 - 32*a*b^3*c^3*d - 72*a^3*b*c*d^3))/(9*c^4))*((3^(1/2)*1i)/2 - 1/2)*((a*d^3 - b*c*d^2)/(27*c^6))^(1/3) - log((2*b^4*d^5*(a + b*x^3)^(1/3)*(27*a^4*d^4 + 5*b^4*c^4 + 72*a^2*b^2*c^2*d^2 - 32*a*b^3*c^3*d - 72*a^3*b*c*d^3))/(9*c^4) - (((3^(1/2)*1i)/2 + 1/2)*((((3^(1/2)*1i)/2 - 1/2)*(27*b^5*c^3*d^3*(a + b*x^3)^(1/3)*(4*a^2*d^2 + b^2*c^2 - 5*a*b*c*d) + 81*a*b^4*c^4*d^3*((3^(1/2)*1i)/2 + 1/2)*(2*a^2*d^2 + b^2*c^2 - 3*a*b*c*d)*((d^2*(a*d - b*c))/c^6)^(1/3))*((d^2*(a*d - b*c))/c^6)^(2/3))/9 - (b^5*d^4*(27*a^3*d^3 + b^3*c^3 + 17*a*b^2*c^2*d - 45*a^2*b*c*d^2))/(3*c))*((d^2*(a*d - b*c))/c^6)^(1/3))/3)*((3^(1/2)*1i)/2 + 1/2)*((a*d^3 - b*c*d^2)/(27*c^6))^(1/3) + log((((3^(1/2)*1i)/2 - 1/2)*((((3^(1/2)*1i)/2 + 1/2)*(27*b^5*c^3*d^3*(a + b*x^3)^(1/3)*(4*a^2*d^2 + b^2*c^2 - 5*a*b*c*d) - 27*a*b^4*c^4*d^3*((3^(1/2)*1i)/2 - 1/2)*(2*a^2*d^2 + b^2*c^2 - 3*a*b*c*d)*(-(3*a*d - b*c)^3/(a^2*c^6))^(1/3))*(-(3*a*d - b*c)^3/(a^2*c^6))^(2/3))/81 + (b^5*d^4*(27*a^3*d^3 + b^3*c^3 + 17*a*b^2*c^2*d - 45*a^2*b*c*d^2))/(3*c))*(-(3*a*d - b*c)^3/(a^2*c^6))^(1/3))/9 - (2*b^4*d^5*(a + b*x^3)^(1/3)*(27*a^4*d^4 + 5*b^4*c^4 + 72*a^2*b^2*c^2*d^2 - 32*a*b^3*c^3*d - 72*a^3*b*c*d^3))/(9*c^4))*((3^(1/2)*1i)/2 - 1/2)*(-(27*a^3*d^3 - b^3*c^3 + 9*a*b^2*c^2*d - 27*a^2*b*c*d^2)/(729*a^2*c^6))^(1/3) - log((2*b^4*d^5*(a + b*x^3)^(1/3)*(27*a^4*d^4 + 5*b^4*c^4 + 72*a^2*b^2*c^2*d^2 - 32*a*b^3*c^3*d - 72*a^3*b*c*d^3))/(9*c^4) - (((3^(1/2)*1i)/2 + 1/2)*((((3^(1/2)*1i)/2 - 1/2)*(27*b^5*c^3*d^3*(a + b*x^3)^(1/3)*(4*a^2*d^2 + b^2*c^2 - 5*a*b*c*d) + 27*a*b^4*c^4*d^3*((3^(1/2)*1i)/2 + 1/2)*(2*a^2*d^2 + b^2*c^2 - 3*a*b*c*d)*(-(3*a*d - b*c)^3/(a^2*c^6))^(1/3))*(-(3*a*d - b*c)^3/(a^2*c^6))^(2/3))/81 - (b^5*d^4*(27*a^3*d^3 + b^3*c^3 + 17*a*b^2*c^2*d - 45*a^2*b*c*d^2))/(3*c))*(-(3*a*d - b*c)^3/(a^2*c^6))^(1/3))/9)*((3^(1/2)*1i)/2 + 1/2)*(-(27*a^3*d^3 - b^3*c^3 + 9*a*b^2*c^2*d - 27*a^2*b*c*d^2)/(729*a^2*c^6))^(1/3) - (a + b*x^3)^(1/3)/(3*c*x^3)","B"
664,1,2767,370,12.554403,"\text{Not used}","int((a + b*x^3)^(1/3)/(x^7*(c + d*x^3)),x)","\ln\left(\frac{\left(\frac{\left(81\,a\,b^4\,c^4\,d^3\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)\,{\left(-\frac{d^5\,\left(a\,d-b\,c\right)}{c^9}\right)}^{1/3}+\frac{9\,b^5\,c^2\,d^3\,{\left(b\,x^3+a\right)}^{1/3}\,\left(12\,a^3\,d^3-14\,a^2\,b\,c\,d^2+a\,b^2\,c^2\,d+b^3\,c^3\right)}{a}\right)\,{\left(-\frac{d^5\,\left(a\,d-b\,c\right)}{c^9}\right)}^{2/3}}{9}-\frac{b^5\,d^4\,\left(729\,a^6\,d^6-1458\,a^5\,b\,c\,d^5+864\,a^4\,b^2\,c^2\,d^4-135\,a^3\,b^3\,c^3\,d^3-9\,a^2\,b^4\,c^4\,d^2+8\,a\,b^5\,c^5\,d+b^6\,c^6\right)}{81\,a^3\,c^4}\right)\,{\left(-\frac{d^5\,\left(a\,d-b\,c\right)}{c^9}\right)}^{1/3}}{3}-\frac{b^4\,d^6\,{\left(b\,x^3+a\right)}^{1/3}\,\left(1458\,a^7\,d^7-3888\,a^6\,b\,c\,d^6+3564\,a^5\,b^2\,c^2\,d^5-1080\,a^4\,b^3\,c^3\,d^4-135\,a^3\,b^4\,c^4\,d^3+72\,a^2\,b^5\,c^5\,d^2+8\,a\,b^6\,c^6\,d+b^7\,c^7\right)}{243\,a^3\,c^8}\right)\,{\left(-\frac{a\,d^6-b\,c\,d^5}{27\,c^9}\right)}^{1/3}+\ln\left(\frac{\left(\frac{\left(\frac{9\,b^5\,c^2\,d^3\,{\left(b\,x^3+a\right)}^{1/3}\,\left(12\,a^3\,d^3-14\,a^2\,b\,c\,d^2+a\,b^2\,c^2\,d+b^3\,c^3\right)}{a}+9\,a\,b^4\,c^4\,d^3\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)\,{\left(-\frac{{\left(-9\,a^2\,d^2+3\,a\,b\,c\,d+b^2\,c^2\right)}^3}{a^5\,c^9}\right)}^{1/3}\right)\,{\left(-\frac{{\left(-9\,a^2\,d^2+3\,a\,b\,c\,d+b^2\,c^2\right)}^3}{a^5\,c^9}\right)}^{2/3}}{729}-\frac{b^5\,d^4\,\left(729\,a^6\,d^6-1458\,a^5\,b\,c\,d^5+864\,a^4\,b^2\,c^2\,d^4-135\,a^3\,b^3\,c^3\,d^3-9\,a^2\,b^4\,c^4\,d^2+8\,a\,b^5\,c^5\,d+b^6\,c^6\right)}{81\,a^3\,c^4}\right)\,{\left(-\frac{{\left(-9\,a^2\,d^2+3\,a\,b\,c\,d+b^2\,c^2\right)}^3}{a^5\,c^9}\right)}^{1/3}}{27}-\frac{b^4\,d^6\,{\left(b\,x^3+a\right)}^{1/3}\,\left(1458\,a^7\,d^7-3888\,a^6\,b\,c\,d^6+3564\,a^5\,b^2\,c^2\,d^5-1080\,a^4\,b^3\,c^3\,d^4-135\,a^3\,b^4\,c^4\,d^3+72\,a^2\,b^5\,c^5\,d^2+8\,a\,b^6\,c^6\,d+b^7\,c^7\right)}{243\,a^3\,c^8}\right)\,{\left(-\frac{-729\,a^6\,d^6+729\,a^5\,b\,c\,d^5-135\,a^3\,b^3\,c^3\,d^3+9\,a\,b^5\,c^5\,d+b^6\,c^6}{19683\,a^5\,c^9}\right)}^{1/3}-\frac{\frac{{\left(b\,x^3+a\right)}^{1/3}\,\left(c\,b^2+3\,a\,d\,b\right)}{9\,c^2}-\frac{b\,{\left(b\,x^3+a\right)}^{4/3}\,\left(6\,a\,d-b\,c\right)}{18\,a\,c^2}}{{\left(b\,x^3+a\right)}^2-2\,a\,\left(b\,x^3+a\right)+a^2}+\ln\left(-\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{\left(\frac{9\,b^5\,c^2\,d^3\,{\left(b\,x^3+a\right)}^{1/3}\,\left(12\,a^3\,d^3-14\,a^2\,b\,c\,d^2+a\,b^2\,c^2\,d+b^3\,c^3\right)}{a}+81\,a\,b^4\,c^4\,d^3\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)\,{\left(-\frac{d^5\,\left(a\,d-b\,c\right)}{c^9}\right)}^{1/3}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{d^5\,\left(a\,d-b\,c\right)}{c^9}\right)}^{2/3}}{9}+\frac{b^5\,d^4\,\left(729\,a^6\,d^6-1458\,a^5\,b\,c\,d^5+864\,a^4\,b^2\,c^2\,d^4-135\,a^3\,b^3\,c^3\,d^3-9\,a^2\,b^4\,c^4\,d^2+8\,a\,b^5\,c^5\,d+b^6\,c^6\right)}{81\,a^3\,c^4}\right)\,{\left(-\frac{d^5\,\left(a\,d-b\,c\right)}{c^9}\right)}^{1/3}}{3}-\frac{b^4\,d^6\,{\left(b\,x^3+a\right)}^{1/3}\,\left(1458\,a^7\,d^7-3888\,a^6\,b\,c\,d^6+3564\,a^5\,b^2\,c^2\,d^5-1080\,a^4\,b^3\,c^3\,d^4-135\,a^3\,b^4\,c^4\,d^3+72\,a^2\,b^5\,c^5\,d^2+8\,a\,b^6\,c^6\,d+b^7\,c^7\right)}{243\,a^3\,c^8}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{a\,d^6-b\,c\,d^5}{27\,c^9}\right)}^{1/3}-\ln\left(\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{\left(\frac{9\,b^5\,c^2\,d^3\,{\left(b\,x^3+a\right)}^{1/3}\,\left(12\,a^3\,d^3-14\,a^2\,b\,c\,d^2+a\,b^2\,c^2\,d+b^3\,c^3\right)}{a}-81\,a\,b^4\,c^4\,d^3\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)\,{\left(-\frac{d^5\,\left(a\,d-b\,c\right)}{c^9}\right)}^{1/3}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{d^5\,\left(a\,d-b\,c\right)}{c^9}\right)}^{2/3}}{9}-\frac{b^5\,d^4\,\left(729\,a^6\,d^6-1458\,a^5\,b\,c\,d^5+864\,a^4\,b^2\,c^2\,d^4-135\,a^3\,b^3\,c^3\,d^3-9\,a^2\,b^4\,c^4\,d^2+8\,a\,b^5\,c^5\,d+b^6\,c^6\right)}{81\,a^3\,c^4}\right)\,{\left(-\frac{d^5\,\left(a\,d-b\,c\right)}{c^9}\right)}^{1/3}}{3}+\frac{b^4\,d^6\,{\left(b\,x^3+a\right)}^{1/3}\,\left(1458\,a^7\,d^7-3888\,a^6\,b\,c\,d^6+3564\,a^5\,b^2\,c^2\,d^5-1080\,a^4\,b^3\,c^3\,d^4-135\,a^3\,b^4\,c^4\,d^3+72\,a^2\,b^5\,c^5\,d^2+8\,a\,b^6\,c^6\,d+b^7\,c^7\right)}{243\,a^3\,c^8}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{a\,d^6-b\,c\,d^5}{27\,c^9}\right)}^{1/3}+\ln\left(-\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{9\,b^5\,c^2\,d^3\,{\left(b\,x^3+a\right)}^{1/3}\,\left(12\,a^3\,d^3-14\,a^2\,b\,c\,d^2+a\,b^2\,c^2\,d+b^3\,c^3\right)}{a}+9\,a\,b^4\,c^4\,d^3\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)\,{\left(-\frac{{\left(-9\,a^2\,d^2+3\,a\,b\,c\,d+b^2\,c^2\right)}^3}{a^5\,c^9}\right)}^{1/3}\right)\,{\left(-\frac{{\left(-9\,a^2\,d^2+3\,a\,b\,c\,d+b^2\,c^2\right)}^3}{a^5\,c^9}\right)}^{2/3}}{729}+\frac{b^5\,d^4\,\left(729\,a^6\,d^6-1458\,a^5\,b\,c\,d^5+864\,a^4\,b^2\,c^2\,d^4-135\,a^3\,b^3\,c^3\,d^3-9\,a^2\,b^4\,c^4\,d^2+8\,a\,b^5\,c^5\,d+b^6\,c^6\right)}{81\,a^3\,c^4}\right)\,{\left(-\frac{{\left(-9\,a^2\,d^2+3\,a\,b\,c\,d+b^2\,c^2\right)}^3}{a^5\,c^9}\right)}^{1/3}}{27}-\frac{b^4\,d^6\,{\left(b\,x^3+a\right)}^{1/3}\,\left(1458\,a^7\,d^7-3888\,a^6\,b\,c\,d^6+3564\,a^5\,b^2\,c^2\,d^5-1080\,a^4\,b^3\,c^3\,d^4-135\,a^3\,b^4\,c^4\,d^3+72\,a^2\,b^5\,c^5\,d^2+8\,a\,b^6\,c^6\,d+b^7\,c^7\right)}{243\,a^3\,c^8}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{-729\,a^6\,d^6+729\,a^5\,b\,c\,d^5-135\,a^3\,b^3\,c^3\,d^3+9\,a\,b^5\,c^5\,d+b^6\,c^6}{19683\,a^5\,c^9}\right)}^{1/3}-\ln\left(\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{9\,b^5\,c^2\,d^3\,{\left(b\,x^3+a\right)}^{1/3}\,\left(12\,a^3\,d^3-14\,a^2\,b\,c\,d^2+a\,b^2\,c^2\,d+b^3\,c^3\right)}{a}-9\,a\,b^4\,c^4\,d^3\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)\,{\left(-\frac{{\left(-9\,a^2\,d^2+3\,a\,b\,c\,d+b^2\,c^2\right)}^3}{a^5\,c^9}\right)}^{1/3}\right)\,{\left(-\frac{{\left(-9\,a^2\,d^2+3\,a\,b\,c\,d+b^2\,c^2\right)}^3}{a^5\,c^9}\right)}^{2/3}}{729}-\frac{b^5\,d^4\,\left(729\,a^6\,d^6-1458\,a^5\,b\,c\,d^5+864\,a^4\,b^2\,c^2\,d^4-135\,a^3\,b^3\,c^3\,d^3-9\,a^2\,b^4\,c^4\,d^2+8\,a\,b^5\,c^5\,d+b^6\,c^6\right)}{81\,a^3\,c^4}\right)\,{\left(-\frac{{\left(-9\,a^2\,d^2+3\,a\,b\,c\,d+b^2\,c^2\right)}^3}{a^5\,c^9}\right)}^{1/3}}{27}+\frac{b^4\,d^6\,{\left(b\,x^3+a\right)}^{1/3}\,\left(1458\,a^7\,d^7-3888\,a^6\,b\,c\,d^6+3564\,a^5\,b^2\,c^2\,d^5-1080\,a^4\,b^3\,c^3\,d^4-135\,a^3\,b^4\,c^4\,d^3+72\,a^2\,b^5\,c^5\,d^2+8\,a\,b^6\,c^6\,d+b^7\,c^7\right)}{243\,a^3\,c^8}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{-729\,a^6\,d^6+729\,a^5\,b\,c\,d^5-135\,a^3\,b^3\,c^3\,d^3+9\,a\,b^5\,c^5\,d+b^6\,c^6}{19683\,a^5\,c^9}\right)}^{1/3}","Not used",1,"log(((((81*a*b^4*c^4*d^3*(2*a^2*d^2 + b^2*c^2 - 3*a*b*c*d)*(-(d^5*(a*d - b*c))/c^9)^(1/3) + (9*b^5*c^2*d^3*(a + b*x^3)^(1/3)*(12*a^3*d^3 + b^3*c^3 + a*b^2*c^2*d - 14*a^2*b*c*d^2))/a)*(-(d^5*(a*d - b*c))/c^9)^(2/3))/9 - (b^5*d^4*(729*a^6*d^6 + b^6*c^6 - 9*a^2*b^4*c^4*d^2 - 135*a^3*b^3*c^3*d^3 + 864*a^4*b^2*c^2*d^4 + 8*a*b^5*c^5*d - 1458*a^5*b*c*d^5))/(81*a^3*c^4))*(-(d^5*(a*d - b*c))/c^9)^(1/3))/3 - (b^4*d^6*(a + b*x^3)^(1/3)*(1458*a^7*d^7 + b^7*c^7 + 72*a^2*b^5*c^5*d^2 - 135*a^3*b^4*c^4*d^3 - 1080*a^4*b^3*c^3*d^4 + 3564*a^5*b^2*c^2*d^5 + 8*a*b^6*c^6*d - 3888*a^6*b*c*d^6))/(243*a^3*c^8))*(-(a*d^6 - b*c*d^5)/(27*c^9))^(1/3) + log((((((9*b^5*c^2*d^3*(a + b*x^3)^(1/3)*(12*a^3*d^3 + b^3*c^3 + a*b^2*c^2*d - 14*a^2*b*c*d^2))/a + 9*a*b^4*c^4*d^3*(2*a^2*d^2 + b^2*c^2 - 3*a*b*c*d)*(-(b^2*c^2 - 9*a^2*d^2 + 3*a*b*c*d)^3/(a^5*c^9))^(1/3))*(-(b^2*c^2 - 9*a^2*d^2 + 3*a*b*c*d)^3/(a^5*c^9))^(2/3))/729 - (b^5*d^4*(729*a^6*d^6 + b^6*c^6 - 9*a^2*b^4*c^4*d^2 - 135*a^3*b^3*c^3*d^3 + 864*a^4*b^2*c^2*d^4 + 8*a*b^5*c^5*d - 1458*a^5*b*c*d^5))/(81*a^3*c^4))*(-(b^2*c^2 - 9*a^2*d^2 + 3*a*b*c*d)^3/(a^5*c^9))^(1/3))/27 - (b^4*d^6*(a + b*x^3)^(1/3)*(1458*a^7*d^7 + b^7*c^7 + 72*a^2*b^5*c^5*d^2 - 135*a^3*b^4*c^4*d^3 - 1080*a^4*b^3*c^3*d^4 + 3564*a^5*b^2*c^2*d^5 + 8*a*b^6*c^6*d - 3888*a^6*b*c*d^6))/(243*a^3*c^8))*(-(b^6*c^6 - 729*a^6*d^6 - 135*a^3*b^3*c^3*d^3 + 9*a*b^5*c^5*d + 729*a^5*b*c*d^5)/(19683*a^5*c^9))^(1/3) - (((a + b*x^3)^(1/3)*(b^2*c + 3*a*b*d))/(9*c^2) - (b*(a + b*x^3)^(4/3)*(6*a*d - b*c))/(18*a*c^2))/((a + b*x^3)^2 - 2*a*(a + b*x^3) + a^2) + log(- (((3^(1/2)*1i)/2 - 1/2)*((((9*b^5*c^2*d^3*(a + b*x^3)^(1/3)*(12*a^3*d^3 + b^3*c^3 + a*b^2*c^2*d - 14*a^2*b*c*d^2))/a + 81*a*b^4*c^4*d^3*((3^(1/2)*1i)/2 - 1/2)*(2*a^2*d^2 + b^2*c^2 - 3*a*b*c*d)*(-(d^5*(a*d - b*c))/c^9)^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(-(d^5*(a*d - b*c))/c^9)^(2/3))/9 + (b^5*d^4*(729*a^6*d^6 + b^6*c^6 - 9*a^2*b^4*c^4*d^2 - 135*a^3*b^3*c^3*d^3 + 864*a^4*b^2*c^2*d^4 + 8*a*b^5*c^5*d - 1458*a^5*b*c*d^5))/(81*a^3*c^4))*(-(d^5*(a*d - b*c))/c^9)^(1/3))/3 - (b^4*d^6*(a + b*x^3)^(1/3)*(1458*a^7*d^7 + b^7*c^7 + 72*a^2*b^5*c^5*d^2 - 135*a^3*b^4*c^4*d^3 - 1080*a^4*b^3*c^3*d^4 + 3564*a^5*b^2*c^2*d^5 + 8*a*b^6*c^6*d - 3888*a^6*b*c*d^6))/(243*a^3*c^8))*((3^(1/2)*1i)/2 - 1/2)*(-(a*d^6 - b*c*d^5)/(27*c^9))^(1/3) - log((((3^(1/2)*1i)/2 + 1/2)*((((9*b^5*c^2*d^3*(a + b*x^3)^(1/3)*(12*a^3*d^3 + b^3*c^3 + a*b^2*c^2*d - 14*a^2*b*c*d^2))/a - 81*a*b^4*c^4*d^3*((3^(1/2)*1i)/2 + 1/2)*(2*a^2*d^2 + b^2*c^2 - 3*a*b*c*d)*(-(d^5*(a*d - b*c))/c^9)^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(-(d^5*(a*d - b*c))/c^9)^(2/3))/9 - (b^5*d^4*(729*a^6*d^6 + b^6*c^6 - 9*a^2*b^4*c^4*d^2 - 135*a^3*b^3*c^3*d^3 + 864*a^4*b^2*c^2*d^4 + 8*a*b^5*c^5*d - 1458*a^5*b*c*d^5))/(81*a^3*c^4))*(-(d^5*(a*d - b*c))/c^9)^(1/3))/3 + (b^4*d^6*(a + b*x^3)^(1/3)*(1458*a^7*d^7 + b^7*c^7 + 72*a^2*b^5*c^5*d^2 - 135*a^3*b^4*c^4*d^3 - 1080*a^4*b^3*c^3*d^4 + 3564*a^5*b^2*c^2*d^5 + 8*a*b^6*c^6*d - 3888*a^6*b*c*d^6))/(243*a^3*c^8))*((3^(1/2)*1i)/2 + 1/2)*(-(a*d^6 - b*c*d^5)/(27*c^9))^(1/3) + log(- (((3^(1/2)*1i)/2 - 1/2)*((((3^(1/2)*1i)/2 + 1/2)*((9*b^5*c^2*d^3*(a + b*x^3)^(1/3)*(12*a^3*d^3 + b^3*c^3 + a*b^2*c^2*d - 14*a^2*b*c*d^2))/a + 9*a*b^4*c^4*d^3*((3^(1/2)*1i)/2 - 1/2)*(2*a^2*d^2 + b^2*c^2 - 3*a*b*c*d)*(-(b^2*c^2 - 9*a^2*d^2 + 3*a*b*c*d)^3/(a^5*c^9))^(1/3))*(-(b^2*c^2 - 9*a^2*d^2 + 3*a*b*c*d)^3/(a^5*c^9))^(2/3))/729 + (b^5*d^4*(729*a^6*d^6 + b^6*c^6 - 9*a^2*b^4*c^4*d^2 - 135*a^3*b^3*c^3*d^3 + 864*a^4*b^2*c^2*d^4 + 8*a*b^5*c^5*d - 1458*a^5*b*c*d^5))/(81*a^3*c^4))*(-(b^2*c^2 - 9*a^2*d^2 + 3*a*b*c*d)^3/(a^5*c^9))^(1/3))/27 - (b^4*d^6*(a + b*x^3)^(1/3)*(1458*a^7*d^7 + b^7*c^7 + 72*a^2*b^5*c^5*d^2 - 135*a^3*b^4*c^4*d^3 - 1080*a^4*b^3*c^3*d^4 + 3564*a^5*b^2*c^2*d^5 + 8*a*b^6*c^6*d - 3888*a^6*b*c*d^6))/(243*a^3*c^8))*((3^(1/2)*1i)/2 - 1/2)*(-(b^6*c^6 - 729*a^6*d^6 - 135*a^3*b^3*c^3*d^3 + 9*a*b^5*c^5*d + 729*a^5*b*c*d^5)/(19683*a^5*c^9))^(1/3) - log((((3^(1/2)*1i)/2 + 1/2)*((((3^(1/2)*1i)/2 - 1/2)*((9*b^5*c^2*d^3*(a + b*x^3)^(1/3)*(12*a^3*d^3 + b^3*c^3 + a*b^2*c^2*d - 14*a^2*b*c*d^2))/a - 9*a*b^4*c^4*d^3*((3^(1/2)*1i)/2 + 1/2)*(2*a^2*d^2 + b^2*c^2 - 3*a*b*c*d)*(-(b^2*c^2 - 9*a^2*d^2 + 3*a*b*c*d)^3/(a^5*c^9))^(1/3))*(-(b^2*c^2 - 9*a^2*d^2 + 3*a*b*c*d)^3/(a^5*c^9))^(2/3))/729 - (b^5*d^4*(729*a^6*d^6 + b^6*c^6 - 9*a^2*b^4*c^4*d^2 - 135*a^3*b^3*c^3*d^3 + 864*a^4*b^2*c^2*d^4 + 8*a*b^5*c^5*d - 1458*a^5*b*c*d^5))/(81*a^3*c^4))*(-(b^2*c^2 - 9*a^2*d^2 + 3*a*b*c*d)^3/(a^5*c^9))^(1/3))/27 + (b^4*d^6*(a + b*x^3)^(1/3)*(1458*a^7*d^7 + b^7*c^7 + 72*a^2*b^5*c^5*d^2 - 135*a^3*b^4*c^4*d^3 - 1080*a^4*b^3*c^3*d^4 + 3564*a^5*b^2*c^2*d^5 + 8*a*b^6*c^6*d - 3888*a^6*b*c*d^6))/(243*a^3*c^8))*((3^(1/2)*1i)/2 + 1/2)*(-(b^6*c^6 - 729*a^6*d^6 - 135*a^3*b^3*c^3*d^3 + 9*a*b^5*c^5*d + 729*a^5*b*c*d^5)/(19683*a^5*c^9))^(1/3)","B"
665,0,-1,336,0.000000,"\text{Not used}","int((x^7*(a + b*x^3)^(1/3))/(c + d*x^3),x)","\int \frac{x^7\,{\left(b\,x^3+a\right)}^{1/3}}{d\,x^3+c} \,d x","Not used",1,"int((x^7*(a + b*x^3)^(1/3))/(c + d*x^3), x)","F"
666,0,-1,276,0.000000,"\text{Not used}","int((x^4*(a + b*x^3)^(1/3))/(c + d*x^3),x)","\int \frac{x^4\,{\left(b\,x^3+a\right)}^{1/3}}{d\,x^3+c} \,d x","Not used",1,"int((x^4*(a + b*x^3)^(1/3))/(c + d*x^3), x)","F"
667,0,-1,234,0.000000,"\text{Not used}","int((x*(a + b*x^3)^(1/3))/(c + d*x^3),x)","\int \frac{x\,{\left(b\,x^3+a\right)}^{1/3}}{d\,x^3+c} \,d x","Not used",1,"int((x*(a + b*x^3)^(1/3))/(c + d*x^3), x)","F"
668,0,-1,168,0.000000,"\text{Not used}","int((a + b*x^3)^(1/3)/(x^2*(c + d*x^3)),x)","\int \frac{{\left(b\,x^3+a\right)}^{1/3}}{x^2\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int((a + b*x^3)^(1/3)/(x^2*(c + d*x^3)), x)","F"
669,0,-1,204,0.000000,"\text{Not used}","int((a + b*x^3)^(1/3)/(x^5*(c + d*x^3)),x)","\int \frac{{\left(b\,x^3+a\right)}^{1/3}}{x^5\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int((a + b*x^3)^(1/3)/(x^5*(c + d*x^3)), x)","F"
670,0,-1,258,0.000000,"\text{Not used}","int((a + b*x^3)^(1/3)/(x^8*(c + d*x^3)),x)","\int \frac{{\left(b\,x^3+a\right)}^{1/3}}{x^8\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int((a + b*x^3)^(1/3)/(x^8*(c + d*x^3)), x)","F"
671,0,-1,318,0.000000,"\text{Not used}","int((a + b*x^3)^(1/3)/(x^11*(c + d*x^3)),x)","\int \frac{{\left(b\,x^3+a\right)}^{1/3}}{x^{11}\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int((a + b*x^3)^(1/3)/(x^11*(c + d*x^3)), x)","F"
672,0,-1,64,0.000000,"\text{Not used}","int((x^6*(a + b*x^3)^(1/3))/(c + d*x^3),x)","\int \frac{x^6\,{\left(b\,x^3+a\right)}^{1/3}}{d\,x^3+c} \,d x","Not used",1,"int((x^6*(a + b*x^3)^(1/3))/(c + d*x^3), x)","F"
673,0,-1,64,0.000000,"\text{Not used}","int((x^3*(a + b*x^3)^(1/3))/(c + d*x^3),x)","\int \frac{x^3\,{\left(b\,x^3+a\right)}^{1/3}}{d\,x^3+c} \,d x","Not used",1,"int((x^3*(a + b*x^3)^(1/3))/(c + d*x^3), x)","F"
674,0,-1,59,0.000000,"\text{Not used}","int((a + b*x^3)^(1/3)/(c + d*x^3),x)","\int \frac{{\left(b\,x^3+a\right)}^{1/3}}{d\,x^3+c} \,d x","Not used",1,"int((a + b*x^3)^(1/3)/(c + d*x^3), x)","F"
675,0,-1,64,0.000000,"\text{Not used}","int((a + b*x^3)^(1/3)/(x^3*(c + d*x^3)),x)","\int \frac{{\left(b\,x^3+a\right)}^{1/3}}{x^3\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int((a + b*x^3)^(1/3)/(x^3*(c + d*x^3)), x)","F"
676,0,-1,64,0.000000,"\text{Not used}","int((a + b*x^3)^(1/3)/(x^6*(c + d*x^3)),x)","\int \frac{{\left(b\,x^3+a\right)}^{1/3}}{x^6\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int((a + b*x^3)^(1/3)/(x^6*(c + d*x^3)), x)","F"
677,1,490,266,5.127414,"\text{Not used}","int((x^11*(a + b*x^3)^(2/3))/(c + d*x^3),x)","\left(\frac{3\,a^2}{5\,b^3\,d}+\frac{\left(\frac{3\,a}{b^3\,d}+\frac{b^4\,c-a\,b^3\,d}{b^6\,d^2}\right)\,\left(b^4\,c-a\,b^3\,d\right)}{5\,b^3\,d}\right)\,{\left(b\,x^3+a\right)}^{5/3}-\left(\frac{3\,a}{8\,b^3\,d}+\frac{b^4\,c-a\,b^3\,d}{8\,b^6\,d^2}\right)\,{\left(b\,x^3+a\right)}^{8/3}-{\left(b\,x^3+a\right)}^{2/3}\,\left(\frac{a^3}{2\,b^3\,d}+\frac{\left(\frac{3\,a^2}{b^3\,d}+\frac{\left(\frac{3\,a}{b^3\,d}+\frac{b^4\,c-a\,b^3\,d}{b^6\,d^2}\right)\,\left(b^4\,c-a\,b^3\,d\right)}{b^3\,d}\right)\,\left(b^4\,c-a\,b^3\,d\right)}{2\,b^3\,d}\right)+\frac{{\left(b\,x^3+a\right)}^{11/3}}{11\,b^3\,d}-\frac{c^3\,\ln\left(\frac{{\left(b\,x^3+a\right)}^{1/3}\,\left(a^2\,c^6\,d^2-2\,a\,b\,c^7\,d+b^2\,c^8\right)}{d^7}-\frac{c^6\,{\left(a\,d-b\,c\right)}^{4/3}\,\left(9\,a\,d^3-9\,b\,c\,d^2\right)}{9\,d^{28/3}}\right)\,{\left(a\,d-b\,c\right)}^{2/3}}{3\,d^{14/3}}-\frac{c^3\,\ln\left(\frac{c^6\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(a\,d-b\,c\right)}^{7/3}}{d^{22/3}}+\frac{c^6\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(a\,d-b\,c\right)}^2}{d^7}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(a\,d-b\,c\right)}^{2/3}}{3\,d^{14/3}}+\frac{c^3\,\ln\left(\frac{c^6\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(a\,d-b\,c\right)}^2}{d^7}-\frac{c^6\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,{\left(a\,d-b\,c\right)}^{7/3}}{4\,d^{22/3}}\right)\,\left(\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)\,{\left(a\,d-b\,c\right)}^{2/3}}{d^{14/3}}","Not used",1,"((3*a^2)/(5*b^3*d) + (((3*a)/(b^3*d) + (b^4*c - a*b^3*d)/(b^6*d^2))*(b^4*c - a*b^3*d))/(5*b^3*d))*(a + b*x^3)^(5/3) - ((3*a)/(8*b^3*d) + (b^4*c - a*b^3*d)/(8*b^6*d^2))*(a + b*x^3)^(8/3) - (a + b*x^3)^(2/3)*(a^3/(2*b^3*d) + (((3*a^2)/(b^3*d) + (((3*a)/(b^3*d) + (b^4*c - a*b^3*d)/(b^6*d^2))*(b^4*c - a*b^3*d))/(b^3*d))*(b^4*c - a*b^3*d))/(2*b^3*d)) + (a + b*x^3)^(11/3)/(11*b^3*d) - (c^3*log(((a + b*x^3)^(1/3)*(b^2*c^8 + a^2*c^6*d^2 - 2*a*b*c^7*d))/d^7 - (c^6*(a*d - b*c)^(4/3)*(9*a*d^3 - 9*b*c*d^2))/(9*d^(28/3)))*(a*d - b*c)^(2/3))/(3*d^(14/3)) - (c^3*log((c^6*((3^(1/2)*1i)/2 + 1/2)*(a*d - b*c)^(7/3))/d^(22/3) + (c^6*(a + b*x^3)^(1/3)*(a*d - b*c)^2)/d^7)*((3^(1/2)*1i)/2 - 1/2)*(a*d - b*c)^(2/3))/(3*d^(14/3)) + (c^3*log((c^6*(a + b*x^3)^(1/3)*(a*d - b*c)^2)/d^7 - (c^6*(3^(1/2)*1i + 1)^2*(a*d - b*c)^(7/3))/(4*d^(22/3)))*((3^(1/2)*1i)/6 + 1/6)*(a*d - b*c)^(2/3))/d^(14/3)","B"
678,1,385,223,5.105212,"\text{Not used}","int((x^8*(a + b*x^3)^(2/3))/(c + d*x^3),x)","\left(\frac{a^2}{2\,b^2\,d}+\frac{\left(\frac{2\,a}{b^2\,d}+\frac{b^3\,c-a\,b^2\,d}{b^4\,d^2}\right)\,\left(b^3\,c-a\,b^2\,d\right)}{2\,b^2\,d}\right)\,{\left(b\,x^3+a\right)}^{2/3}-\left(\frac{2\,a}{5\,b^2\,d}+\frac{b^3\,c-a\,b^2\,d}{5\,b^4\,d^2}\right)\,{\left(b\,x^3+a\right)}^{5/3}+\frac{{\left(b\,x^3+a\right)}^{8/3}}{8\,b^2\,d}+\frac{c^2\,\ln\left(\frac{{\left(b\,x^3+a\right)}^{1/3}\,\left(a^2\,c^4\,d^2-2\,a\,b\,c^5\,d+b^2\,c^6\right)}{d^5}-\frac{c^4\,{\left(a\,d-b\,c\right)}^{4/3}\,\left(9\,a\,d^3-9\,b\,c\,d^2\right)}{9\,d^{22/3}}\right)\,{\left(a\,d-b\,c\right)}^{2/3}}{3\,d^{11/3}}-\frac{c^2\,\ln\left(\frac{c^4\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(a\,d-b\,c\right)}^2}{d^5}-\frac{c^4\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(a\,d-b\,c\right)}^{7/3}}{d^{16/3}}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(a\,d-b\,c\right)}^{2/3}}{3\,d^{11/3}}+\frac{c^2\,\ln\left(\frac{c^4\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(a\,d-b\,c\right)}^2}{d^5}-\frac{c^4\,{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,{\left(a\,d-b\,c\right)}^{7/3}}{4\,d^{16/3}}\right)\,\left(-\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)\,{\left(a\,d-b\,c\right)}^{2/3}}{d^{11/3}}","Not used",1,"(a^2/(2*b^2*d) + (((2*a)/(b^2*d) + (b^3*c - a*b^2*d)/(b^4*d^2))*(b^3*c - a*b^2*d))/(2*b^2*d))*(a + b*x^3)^(2/3) - ((2*a)/(5*b^2*d) + (b^3*c - a*b^2*d)/(5*b^4*d^2))*(a + b*x^3)^(5/3) + (a + b*x^3)^(8/3)/(8*b^2*d) + (c^2*log(((a + b*x^3)^(1/3)*(b^2*c^6 + a^2*c^4*d^2 - 2*a*b*c^5*d))/d^5 - (c^4*(a*d - b*c)^(4/3)*(9*a*d^3 - 9*b*c*d^2))/(9*d^(22/3)))*(a*d - b*c)^(2/3))/(3*d^(11/3)) - (c^2*log((c^4*(a + b*x^3)^(1/3)*(a*d - b*c)^2)/d^5 - (c^4*((3^(1/2)*1i)/2 - 1/2)*(a*d - b*c)^(7/3))/d^(16/3))*((3^(1/2)*1i)/2 + 1/2)*(a*d - b*c)^(2/3))/(3*d^(11/3)) + (c^2*log((c^4*(a + b*x^3)^(1/3)*(a*d - b*c)^2)/d^5 - (c^4*(3^(1/2)*1i - 1)^2*(a*d - b*c)^(7/3))/(4*d^(16/3)))*((3^(1/2)*1i)/6 - 1/6)*(a*d - b*c)^(2/3))/d^(11/3)","B"
679,1,302,188,5.057615,"\text{Not used}","int((x^5*(a + b*x^3)^(2/3))/(c + d*x^3),x)","\frac{{\left(b\,x^3+a\right)}^{5/3}}{5\,b\,d}-{\left(b\,x^3+a\right)}^{2/3}\,\left(\frac{a}{2\,b\,d}+\frac{b^2\,c-a\,b\,d}{2\,b^2\,d^2}\right)-\frac{c\,\ln\left(\frac{{\left(b\,x^3+a\right)}^{1/3}\,\left(a^2\,c^2\,d^2-2\,a\,b\,c^3\,d+b^2\,c^4\right)}{d^3}-\frac{c^2\,{\left(a\,d-b\,c\right)}^{4/3}\,\left(9\,a\,d^3-9\,b\,c\,d^2\right)}{9\,d^{16/3}}\right)\,{\left(a\,d-b\,c\right)}^{2/3}}{3\,d^{8/3}}-\frac{c\,\ln\left(\frac{c^2\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(a\,d-b\,c\right)}^{7/3}}{d^{10/3}}+\frac{c^2\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(a\,d-b\,c\right)}^2}{d^3}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(a\,d-b\,c\right)}^{2/3}}{3\,d^{8/3}}+\frac{c\,\ln\left(\frac{c^2\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(a\,d-b\,c\right)}^2}{d^3}-\frac{c^2\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(a\,d-b\,c\right)}^{7/3}}{d^{10/3}}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(a\,d-b\,c\right)}^{2/3}}{3\,d^{8/3}}","Not used",1,"(a + b*x^3)^(5/3)/(5*b*d) - (a + b*x^3)^(2/3)*(a/(2*b*d) + (b^2*c - a*b*d)/(2*b^2*d^2)) - (c*log(((a + b*x^3)^(1/3)*(b^2*c^4 + a^2*c^2*d^2 - 2*a*b*c^3*d))/d^3 - (c^2*(a*d - b*c)^(4/3)*(9*a*d^3 - 9*b*c*d^2))/(9*d^(16/3)))*(a*d - b*c)^(2/3))/(3*d^(8/3)) - (c*log((c^2*((3^(1/2)*1i)/2 + 1/2)*(a*d - b*c)^(7/3))/d^(10/3) + (c^2*(a + b*x^3)^(1/3)*(a*d - b*c)^2)/d^3)*((3^(1/2)*1i)/2 - 1/2)*(a*d - b*c)^(2/3))/(3*d^(8/3)) + (c*log((c^2*(a + b*x^3)^(1/3)*(a*d - b*c)^2)/d^3 - (c^2*((3^(1/2)*1i)/2 - 1/2)*(a*d - b*c)^(7/3))/d^(10/3))*((3^(1/2)*1i)/2 + 1/2)*(a*d - b*c)^(2/3))/(3*d^(8/3))","B"
680,1,238,162,5.049228,"\text{Not used}","int((x^2*(a + b*x^3)^(2/3))/(c + d*x^3),x)","\frac{{\left(b\,x^3+a\right)}^{2/3}}{2\,d}+\frac{\ln\left(\frac{{\left(b\,x^3+a\right)}^{1/3}\,\left(a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)}{d}-\frac{{\left(a\,d-b\,c\right)}^{4/3}\,\left(9\,a\,d^3-9\,b\,c\,d^2\right)}{9\,d^{10/3}}\right)\,{\left(a\,d-b\,c\right)}^{2/3}}{3\,d^{5/3}}-\frac{\ln\left(\frac{{\left(b\,x^3+a\right)}^{1/3}\,{\left(a\,d-b\,c\right)}^2}{d}-\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(a\,d-b\,c\right)}^{7/3}}{d^{4/3}}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(a\,d-b\,c\right)}^{2/3}}{3\,d^{5/3}}+\frac{\ln\left(\frac{{\left(b\,x^3+a\right)}^{1/3}\,{\left(a\,d-b\,c\right)}^2}{d}-\frac{{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,{\left(a\,d-b\,c\right)}^{7/3}}{4\,d^{4/3}}\right)\,\left(-\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)\,{\left(a\,d-b\,c\right)}^{2/3}}{d^{5/3}}","Not used",1,"(a + b*x^3)^(2/3)/(2*d) + (log(((a + b*x^3)^(1/3)*(a^2*d^2 + b^2*c^2 - 2*a*b*c*d))/d - ((a*d - b*c)^(4/3)*(9*a*d^3 - 9*b*c*d^2))/(9*d^(10/3)))*(a*d - b*c)^(2/3))/(3*d^(5/3)) - (log(((a + b*x^3)^(1/3)*(a*d - b*c)^2)/d - (((3^(1/2)*1i)/2 - 1/2)*(a*d - b*c)^(7/3))/d^(4/3))*((3^(1/2)*1i)/2 + 1/2)*(a*d - b*c)^(2/3))/(3*d^(5/3)) + (log(((a + b*x^3)^(1/3)*(a*d - b*c)^2)/d - ((3^(1/2)*1i - 1)^2*(a*d - b*c)^(7/3))/(4*d^(4/3)))*((3^(1/2)*1i)/6 - 1/6)*(a*d - b*c)^(2/3))/d^(5/3)","B"
681,1,1963,245,4.770477,"\text{Not used}","int((a + b*x^3)^(2/3)/(x*(c + d*x^3)),x)","\ln\left({\left(b\,x^3+a\right)}^{1/3}\,\left(2\,a^5\,b^5\,d^4-5\,a^4\,b^6\,c\,d^3+4\,a^3\,b^7\,c^2\,d^2-a^2\,b^8\,c^3\,d\right)-{\left(\frac{a^2}{27\,c^3}\right)}^{2/3}\,\left(\left({\left(b\,x^3+a\right)}^{1/3}\,\left(54\,a^4\,b^4\,c^2\,d^5-108\,a^3\,b^5\,c^3\,d^4+54\,a^2\,b^6\,c^4\,d^3\right)-\left(486\,a^3\,b^4\,c^4\,d^5-729\,a^2\,b^5\,c^5\,d^4+243\,a\,b^6\,c^6\,d^3\right)\,{\left(\frac{a^2}{27\,c^3}\right)}^{2/3}\right)\,{\left(\frac{a^2}{27\,c^3}\right)}^{1/3}+36\,a^2\,b^7\,c^4\,d^2-54\,a^3\,b^6\,c^3\,d^3+27\,a^4\,b^5\,c^2\,d^4-9\,a\,b^8\,c^5\,d\right)\right)\,{\left(\frac{a^2}{27\,c^3}\right)}^{1/3}+\ln\left({\left(b\,x^3+a\right)}^{1/3}\,\left(2\,a^5\,b^5\,d^4-5\,a^4\,b^6\,c\,d^3+4\,a^3\,b^7\,c^2\,d^2-a^2\,b^8\,c^3\,d\right)-{\left(-\frac{a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2}{27\,c^3\,d^2}\right)}^{2/3}\,\left(\left({\left(b\,x^3+a\right)}^{1/3}\,\left(54\,a^4\,b^4\,c^2\,d^5-108\,a^3\,b^5\,c^3\,d^4+54\,a^2\,b^6\,c^4\,d^3\right)-\left(486\,a^3\,b^4\,c^4\,d^5-729\,a^2\,b^5\,c^5\,d^4+243\,a\,b^6\,c^6\,d^3\right)\,{\left(-\frac{a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2}{27\,c^3\,d^2}\right)}^{2/3}\right)\,{\left(-\frac{a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2}{27\,c^3\,d^2}\right)}^{1/3}+36\,a^2\,b^7\,c^4\,d^2-54\,a^3\,b^6\,c^3\,d^3+27\,a^4\,b^5\,c^2\,d^4-9\,a\,b^8\,c^5\,d\right)\right)\,{\left(-\frac{a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2}{27\,c^3\,d^2}\right)}^{1/3}-\ln\left({\left(b\,x^3+a\right)}^{1/3}\,\left(2\,a^5\,b^5\,d^4-5\,a^4\,b^6\,c\,d^3+4\,a^3\,b^7\,c^2\,d^2-a^2\,b^8\,c^3\,d\right)+{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(\frac{a^2}{27\,c^3}\right)}^{2/3}\,\left(\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left({\left(b\,x^3+a\right)}^{1/3}\,\left(54\,a^4\,b^4\,c^2\,d^5-108\,a^3\,b^5\,c^3\,d^4+54\,a^2\,b^6\,c^4\,d^3\right)-{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,\left(486\,a^3\,b^4\,c^4\,d^5-729\,a^2\,b^5\,c^5\,d^4+243\,a\,b^6\,c^6\,d^3\right)\,{\left(\frac{a^2}{27\,c^3}\right)}^{2/3}\right)\,{\left(\frac{a^2}{27\,c^3}\right)}^{1/3}-36\,a^2\,b^7\,c^4\,d^2+54\,a^3\,b^6\,c^3\,d^3-27\,a^4\,b^5\,c^2\,d^4+9\,a\,b^8\,c^5\,d\right)\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(\frac{a^2}{27\,c^3}\right)}^{1/3}+\ln\left({\left(b\,x^3+a\right)}^{1/3}\,\left(2\,a^5\,b^5\,d^4-5\,a^4\,b^6\,c\,d^3+4\,a^3\,b^7\,c^2\,d^2-a^2\,b^8\,c^3\,d\right)-{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(\frac{a^2}{27\,c^3}\right)}^{2/3}\,\left(\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left({\left(b\,x^3+a\right)}^{1/3}\,\left(54\,a^4\,b^4\,c^2\,d^5-108\,a^3\,b^5\,c^3\,d^4+54\,a^2\,b^6\,c^4\,d^3\right)-{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,\left(486\,a^3\,b^4\,c^4\,d^5-729\,a^2\,b^5\,c^5\,d^4+243\,a\,b^6\,c^6\,d^3\right)\,{\left(\frac{a^2}{27\,c^3}\right)}^{2/3}\right)\,{\left(\frac{a^2}{27\,c^3}\right)}^{1/3}+36\,a^2\,b^7\,c^4\,d^2-54\,a^3\,b^6\,c^3\,d^3+27\,a^4\,b^5\,c^2\,d^4-9\,a\,b^8\,c^5\,d\right)\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(\frac{a^2}{27\,c^3}\right)}^{1/3}-\ln\left({\left(b\,x^3+a\right)}^{1/3}\,\left(2\,a^5\,b^5\,d^4-5\,a^4\,b^6\,c\,d^3+4\,a^3\,b^7\,c^2\,d^2-a^2\,b^8\,c^3\,d\right)+{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(-\frac{a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2}{27\,c^3\,d^2}\right)}^{2/3}\,\left(\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left({\left(b\,x^3+a\right)}^{1/3}\,\left(54\,a^4\,b^4\,c^2\,d^5-108\,a^3\,b^5\,c^3\,d^4+54\,a^2\,b^6\,c^4\,d^3\right)-{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,\left(486\,a^3\,b^4\,c^4\,d^5-729\,a^2\,b^5\,c^5\,d^4+243\,a\,b^6\,c^6\,d^3\right)\,{\left(-\frac{a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2}{27\,c^3\,d^2}\right)}^{2/3}\right)\,{\left(-\frac{a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2}{27\,c^3\,d^2}\right)}^{1/3}-36\,a^2\,b^7\,c^4\,d^2+54\,a^3\,b^6\,c^3\,d^3-27\,a^4\,b^5\,c^2\,d^4+9\,a\,b^8\,c^5\,d\right)\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2}{27\,c^3\,d^2}\right)}^{1/3}+\ln\left({\left(b\,x^3+a\right)}^{1/3}\,\left(2\,a^5\,b^5\,d^4-5\,a^4\,b^6\,c\,d^3+4\,a^3\,b^7\,c^2\,d^2-a^2\,b^8\,c^3\,d\right)-{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(-\frac{a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2}{27\,c^3\,d^2}\right)}^{2/3}\,\left(\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left({\left(b\,x^3+a\right)}^{1/3}\,\left(54\,a^4\,b^4\,c^2\,d^5-108\,a^3\,b^5\,c^3\,d^4+54\,a^2\,b^6\,c^4\,d^3\right)-{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,\left(486\,a^3\,b^4\,c^4\,d^5-729\,a^2\,b^5\,c^5\,d^4+243\,a\,b^6\,c^6\,d^3\right)\,{\left(-\frac{a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2}{27\,c^3\,d^2}\right)}^{2/3}\right)\,{\left(-\frac{a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2}{27\,c^3\,d^2}\right)}^{1/3}+36\,a^2\,b^7\,c^4\,d^2-54\,a^3\,b^6\,c^3\,d^3+27\,a^4\,b^5\,c^2\,d^4-9\,a\,b^8\,c^5\,d\right)\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2}{27\,c^3\,d^2}\right)}^{1/3}","Not used",1,"log((a + b*x^3)^(1/3)*(2*a^5*b^5*d^4 - a^2*b^8*c^3*d - 5*a^4*b^6*c*d^3 + 4*a^3*b^7*c^2*d^2) - (a^2/(27*c^3))^(2/3)*(((a + b*x^3)^(1/3)*(54*a^2*b^6*c^4*d^3 - 108*a^3*b^5*c^3*d^4 + 54*a^4*b^4*c^2*d^5) - (243*a*b^6*c^6*d^3 - 729*a^2*b^5*c^5*d^4 + 486*a^3*b^4*c^4*d^5)*(a^2/(27*c^3))^(2/3))*(a^2/(27*c^3))^(1/3) + 36*a^2*b^7*c^4*d^2 - 54*a^3*b^6*c^3*d^3 + 27*a^4*b^5*c^2*d^4 - 9*a*b^8*c^5*d))*(a^2/(27*c^3))^(1/3) + log((a + b*x^3)^(1/3)*(2*a^5*b^5*d^4 - a^2*b^8*c^3*d - 5*a^4*b^6*c*d^3 + 4*a^3*b^7*c^2*d^2) - (-(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)/(27*c^3*d^2))^(2/3)*(((a + b*x^3)^(1/3)*(54*a^2*b^6*c^4*d^3 - 108*a^3*b^5*c^3*d^4 + 54*a^4*b^4*c^2*d^5) - (243*a*b^6*c^6*d^3 - 729*a^2*b^5*c^5*d^4 + 486*a^3*b^4*c^4*d^5)*(-(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)/(27*c^3*d^2))^(2/3))*(-(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)/(27*c^3*d^2))^(1/3) + 36*a^2*b^7*c^4*d^2 - 54*a^3*b^6*c^3*d^3 + 27*a^4*b^5*c^2*d^4 - 9*a*b^8*c^5*d))*(-(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)/(27*c^3*d^2))^(1/3) - log((a + b*x^3)^(1/3)*(2*a^5*b^5*d^4 - a^2*b^8*c^3*d - 5*a^4*b^6*c*d^3 + 4*a^3*b^7*c^2*d^2) + ((3^(1/2)*1i)/2 + 1/2)^2*(a^2/(27*c^3))^(2/3)*(((3^(1/2)*1i)/2 + 1/2)*((a + b*x^3)^(1/3)*(54*a^2*b^6*c^4*d^3 - 108*a^3*b^5*c^3*d^4 + 54*a^4*b^4*c^2*d^5) - ((3^(1/2)*1i)/2 + 1/2)^2*(243*a*b^6*c^6*d^3 - 729*a^2*b^5*c^5*d^4 + 486*a^3*b^4*c^4*d^5)*(a^2/(27*c^3))^(2/3))*(a^2/(27*c^3))^(1/3) - 36*a^2*b^7*c^4*d^2 + 54*a^3*b^6*c^3*d^3 - 27*a^4*b^5*c^2*d^4 + 9*a*b^8*c^5*d))*((3^(1/2)*1i)/2 + 1/2)*(a^2/(27*c^3))^(1/3) + log((a + b*x^3)^(1/3)*(2*a^5*b^5*d^4 - a^2*b^8*c^3*d - 5*a^4*b^6*c*d^3 + 4*a^3*b^7*c^2*d^2) - ((3^(1/2)*1i)/2 - 1/2)^2*(a^2/(27*c^3))^(2/3)*(((3^(1/2)*1i)/2 - 1/2)*((a + b*x^3)^(1/3)*(54*a^2*b^6*c^4*d^3 - 108*a^3*b^5*c^3*d^4 + 54*a^4*b^4*c^2*d^5) - ((3^(1/2)*1i)/2 - 1/2)^2*(243*a*b^6*c^6*d^3 - 729*a^2*b^5*c^5*d^4 + 486*a^3*b^4*c^4*d^5)*(a^2/(27*c^3))^(2/3))*(a^2/(27*c^3))^(1/3) + 36*a^2*b^7*c^4*d^2 - 54*a^3*b^6*c^3*d^3 + 27*a^4*b^5*c^2*d^4 - 9*a*b^8*c^5*d))*((3^(1/2)*1i)/2 - 1/2)*(a^2/(27*c^3))^(1/3) - log((a + b*x^3)^(1/3)*(2*a^5*b^5*d^4 - a^2*b^8*c^3*d - 5*a^4*b^6*c*d^3 + 4*a^3*b^7*c^2*d^2) + ((3^(1/2)*1i)/2 + 1/2)^2*(-(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)/(27*c^3*d^2))^(2/3)*(((3^(1/2)*1i)/2 + 1/2)*((a + b*x^3)^(1/3)*(54*a^2*b^6*c^4*d^3 - 108*a^3*b^5*c^3*d^4 + 54*a^4*b^4*c^2*d^5) - ((3^(1/2)*1i)/2 + 1/2)^2*(243*a*b^6*c^6*d^3 - 729*a^2*b^5*c^5*d^4 + 486*a^3*b^4*c^4*d^5)*(-(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)/(27*c^3*d^2))^(2/3))*(-(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)/(27*c^3*d^2))^(1/3) - 36*a^2*b^7*c^4*d^2 + 54*a^3*b^6*c^3*d^3 - 27*a^4*b^5*c^2*d^4 + 9*a*b^8*c^5*d))*((3^(1/2)*1i)/2 + 1/2)*(-(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)/(27*c^3*d^2))^(1/3) + log((a + b*x^3)^(1/3)*(2*a^5*b^5*d^4 - a^2*b^8*c^3*d - 5*a^4*b^6*c*d^3 + 4*a^3*b^7*c^2*d^2) - ((3^(1/2)*1i)/2 - 1/2)^2*(-(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)/(27*c^3*d^2))^(2/3)*(((3^(1/2)*1i)/2 - 1/2)*((a + b*x^3)^(1/3)*(54*a^2*b^6*c^4*d^3 - 108*a^3*b^5*c^3*d^4 + 54*a^4*b^4*c^2*d^5) - ((3^(1/2)*1i)/2 - 1/2)^2*(243*a*b^6*c^6*d^3 - 729*a^2*b^5*c^5*d^4 + 486*a^3*b^4*c^4*d^5)*(-(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)/(27*c^3*d^2))^(2/3))*(-(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)/(27*c^3*d^2))^(1/3) + 36*a^2*b^7*c^4*d^2 - 54*a^3*b^6*c^3*d^3 + 27*a^4*b^5*c^2*d^4 - 9*a*b^8*c^5*d))*((3^(1/2)*1i)/2 - 1/2)*(-(a^2*d^2 + b^2*c^2 - 2*a*b*c*d)/(27*c^3*d^2))^(1/3)","B"
682,1,1908,347,10.570893,"\text{Not used}","int((a + b*x^3)^(2/3)/(x^4*(c + d*x^3)),x)","\ln\left(-\frac{\left(\frac{\left(6\,b^4\,d^3\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(a\,d-b\,c\right)}^2\,\left(9\,a^2\,d^2-6\,a\,b\,c\,d+2\,b^2\,c^2\right)-27\,a\,b^4\,c^4\,d^3\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)\,{\left(\frac{d\,{\left(a\,d-b\,c\right)}^2}{c^6}\right)}^{2/3}\right)\,{\left(\frac{d\,{\left(a\,d-b\,c\right)}^2}{c^6}\right)}^{1/3}}{3}-\frac{a\,b^5\,d^4\,\left(27\,a^3\,d^3-72\,a^2\,b\,c\,d^2+64\,a\,b^2\,c^2\,d-19\,b^3\,c^3\right)}{3\,c}\right)\,{\left(\frac{d\,{\left(a\,d-b\,c\right)}^2}{c^6}\right)}^{2/3}}{9}-\frac{b^5\,d^4\,{\left(b\,x^3+a\right)}^{1/3}\,\left(4\,a\,d-3\,b\,c\right)\,{\left(3\,a^2\,d^2-5\,a\,b\,c\,d+2\,b^2\,c^2\right)}^2}{27\,c^5}\right)\,{\left(\frac{a^2\,d^3-2\,a\,b\,c\,d^2+b^2\,c^2\,d}{27\,c^6}\right)}^{1/3}+\ln\left(-\frac{\left(\frac{\left(6\,b^4\,d^3\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(a\,d-b\,c\right)}^2\,\left(9\,a^2\,d^2-6\,a\,b\,c\,d+2\,b^2\,c^2\right)-3\,a\,b^4\,c^4\,d^3\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)\,{\left(-\frac{{\left(3\,a\,d-2\,b\,c\right)}^3}{a\,c^6}\right)}^{2/3}\right)\,{\left(-\frac{{\left(3\,a\,d-2\,b\,c\right)}^3}{a\,c^6}\right)}^{1/3}}{9}-\frac{a\,b^5\,d^4\,\left(27\,a^3\,d^3-72\,a^2\,b\,c\,d^2+64\,a\,b^2\,c^2\,d-19\,b^3\,c^3\right)}{3\,c}\right)\,{\left(-\frac{{\left(3\,a\,d-2\,b\,c\right)}^3}{a\,c^6}\right)}^{2/3}}{81}-\frac{b^5\,d^4\,{\left(b\,x^3+a\right)}^{1/3}\,\left(4\,a\,d-3\,b\,c\right)\,{\left(3\,a^2\,d^2-5\,a\,b\,c\,d+2\,b^2\,c^2\right)}^2}{27\,c^5}\right)\,{\left(-\frac{27\,a^3\,d^3-54\,a^2\,b\,c\,d^2+36\,a\,b^2\,c^2\,d-8\,b^3\,c^3}{729\,a\,c^6}\right)}^{1/3}-\ln\left(\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(6\,b^4\,d^3\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(a\,d-b\,c\right)}^2\,\left(9\,a^2\,d^2-6\,a\,b\,c\,d+2\,b^2\,c^2\right)-3\,a\,b^4\,c^4\,d^3\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)\,{\left(-\frac{{\left(3\,a\,d-2\,b\,c\right)}^3}{a\,c^6}\right)}^{2/3}\right)\,{\left(-\frac{{\left(3\,a\,d-2\,b\,c\right)}^3}{a\,c^6}\right)}^{1/3}}{9}+\frac{a\,b^5\,d^4\,\left(27\,a^3\,d^3-72\,a^2\,b\,c\,d^2+64\,a\,b^2\,c^2\,d-19\,b^3\,c^3\right)}{3\,c}\right)\,{\left(-\frac{{\left(3\,a\,d-2\,b\,c\right)}^3}{a\,c^6}\right)}^{2/3}}{81}-\frac{b^5\,d^4\,{\left(b\,x^3+a\right)}^{1/3}\,\left(4\,a\,d-3\,b\,c\right)\,{\left(3\,a^2\,d^2-5\,a\,b\,c\,d+2\,b^2\,c^2\right)}^2}{27\,c^5}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{27\,a^3\,d^3-54\,a^2\,b\,c\,d^2+36\,a\,b^2\,c^2\,d-8\,b^3\,c^3}{729\,a\,c^6}\right)}^{1/3}+\ln\left(\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(6\,b^4\,d^3\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(a\,d-b\,c\right)}^2\,\left(9\,a^2\,d^2-6\,a\,b\,c\,d+2\,b^2\,c^2\right)+3\,a\,b^4\,c^4\,d^3\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)\,{\left(-\frac{{\left(3\,a\,d-2\,b\,c\right)}^3}{a\,c^6}\right)}^{2/3}\right)\,{\left(-\frac{{\left(3\,a\,d-2\,b\,c\right)}^3}{a\,c^6}\right)}^{1/3}}{9}-\frac{a\,b^5\,d^4\,\left(27\,a^3\,d^3-72\,a^2\,b\,c\,d^2+64\,a\,b^2\,c^2\,d-19\,b^3\,c^3\right)}{3\,c}\right)\,{\left(-\frac{{\left(3\,a\,d-2\,b\,c\right)}^3}{a\,c^6}\right)}^{2/3}}{81}-\frac{b^5\,d^4\,{\left(b\,x^3+a\right)}^{1/3}\,\left(4\,a\,d-3\,b\,c\right)\,{\left(3\,a^2\,d^2-5\,a\,b\,c\,d+2\,b^2\,c^2\right)}^2}{27\,c^5}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{27\,a^3\,d^3-54\,a^2\,b\,c\,d^2+36\,a\,b^2\,c^2\,d-8\,b^3\,c^3}{729\,a\,c^6}\right)}^{1/3}-\frac{{\left(b\,x^3+a\right)}^{2/3}}{3\,c\,x^3}-\ln\left(\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(6\,b^4\,d^3\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(a\,d-b\,c\right)}^2\,\left(9\,a^2\,d^2-6\,a\,b\,c\,d+2\,b^2\,c^2\right)-27\,a\,b^4\,c^4\,d^3\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)\,{\left(\frac{d\,{\left(a\,d-b\,c\right)}^2}{c^6}\right)}^{2/3}\right)\,{\left(\frac{d\,{\left(a\,d-b\,c\right)}^2}{c^6}\right)}^{1/3}}{3}+\frac{a\,b^5\,d^4\,\left(27\,a^3\,d^3-72\,a^2\,b\,c\,d^2+64\,a\,b^2\,c^2\,d-19\,b^3\,c^3\right)}{3\,c}\right)\,{\left(\frac{d\,{\left(a\,d-b\,c\right)}^2}{c^6}\right)}^{2/3}}{9}-\frac{b^5\,d^4\,{\left(b\,x^3+a\right)}^{1/3}\,\left(4\,a\,d-3\,b\,c\right)\,{\left(3\,a^2\,d^2-5\,a\,b\,c\,d+2\,b^2\,c^2\right)}^2}{27\,c^5}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(\frac{a^2\,d^3-2\,a\,b\,c\,d^2+b^2\,c^2\,d}{27\,c^6}\right)}^{1/3}+\ln\left(\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(6\,b^4\,d^3\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(a\,d-b\,c\right)}^2\,\left(9\,a^2\,d^2-6\,a\,b\,c\,d+2\,b^2\,c^2\right)+27\,a\,b^4\,c^4\,d^3\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)\,{\left(\frac{d\,{\left(a\,d-b\,c\right)}^2}{c^6}\right)}^{2/3}\right)\,{\left(\frac{d\,{\left(a\,d-b\,c\right)}^2}{c^6}\right)}^{1/3}}{3}-\frac{a\,b^5\,d^4\,\left(27\,a^3\,d^3-72\,a^2\,b\,c\,d^2+64\,a\,b^2\,c^2\,d-19\,b^3\,c^3\right)}{3\,c}\right)\,{\left(\frac{d\,{\left(a\,d-b\,c\right)}^2}{c^6}\right)}^{2/3}}{9}-\frac{b^5\,d^4\,{\left(b\,x^3+a\right)}^{1/3}\,\left(4\,a\,d-3\,b\,c\right)\,{\left(3\,a^2\,d^2-5\,a\,b\,c\,d+2\,b^2\,c^2\right)}^2}{27\,c^5}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(\frac{a^2\,d^3-2\,a\,b\,c\,d^2+b^2\,c^2\,d}{27\,c^6}\right)}^{1/3}","Not used",1,"log(- ((((6*b^4*d^3*(a + b*x^3)^(1/3)*(a*d - b*c)^2*(9*a^2*d^2 + 2*b^2*c^2 - 6*a*b*c*d) - 27*a*b^4*c^4*d^3*(2*a^2*d^2 + b^2*c^2 - 3*a*b*c*d)*((d*(a*d - b*c)^2)/c^6)^(2/3))*((d*(a*d - b*c)^2)/c^6)^(1/3))/3 - (a*b^5*d^4*(27*a^3*d^3 - 19*b^3*c^3 + 64*a*b^2*c^2*d - 72*a^2*b*c*d^2))/(3*c))*((d*(a*d - b*c)^2)/c^6)^(2/3))/9 - (b^5*d^4*(a + b*x^3)^(1/3)*(4*a*d - 3*b*c)*(3*a^2*d^2 + 2*b^2*c^2 - 5*a*b*c*d)^2)/(27*c^5))*((a^2*d^3 + b^2*c^2*d - 2*a*b*c*d^2)/(27*c^6))^(1/3) + log(- ((((6*b^4*d^3*(a + b*x^3)^(1/3)*(a*d - b*c)^2*(9*a^2*d^2 + 2*b^2*c^2 - 6*a*b*c*d) - 3*a*b^4*c^4*d^3*(2*a^2*d^2 + b^2*c^2 - 3*a*b*c*d)*(-(3*a*d - 2*b*c)^3/(a*c^6))^(2/3))*(-(3*a*d - 2*b*c)^3/(a*c^6))^(1/3))/9 - (a*b^5*d^4*(27*a^3*d^3 - 19*b^3*c^3 + 64*a*b^2*c^2*d - 72*a^2*b*c*d^2))/(3*c))*(-(3*a*d - 2*b*c)^3/(a*c^6))^(2/3))/81 - (b^5*d^4*(a + b*x^3)^(1/3)*(4*a*d - 3*b*c)*(3*a^2*d^2 + 2*b^2*c^2 - 5*a*b*c*d)^2)/(27*c^5))*(-(27*a^3*d^3 - 8*b^3*c^3 + 36*a*b^2*c^2*d - 54*a^2*b*c*d^2)/(729*a*c^6))^(1/3) - log((((3^(1/2)*1i)/2 - 1/2)*((((3^(1/2)*1i)/2 + 1/2)*(6*b^4*d^3*(a + b*x^3)^(1/3)*(a*d - b*c)^2*(9*a^2*d^2 + 2*b^2*c^2 - 6*a*b*c*d) - 3*a*b^4*c^4*d^3*((3^(1/2)*1i)/2 - 1/2)*(2*a^2*d^2 + b^2*c^2 - 3*a*b*c*d)*(-(3*a*d - 2*b*c)^3/(a*c^6))^(2/3))*(-(3*a*d - 2*b*c)^3/(a*c^6))^(1/3))/9 + (a*b^5*d^4*(27*a^3*d^3 - 19*b^3*c^3 + 64*a*b^2*c^2*d - 72*a^2*b*c*d^2))/(3*c))*(-(3*a*d - 2*b*c)^3/(a*c^6))^(2/3))/81 - (b^5*d^4*(a + b*x^3)^(1/3)*(4*a*d - 3*b*c)*(3*a^2*d^2 + 2*b^2*c^2 - 5*a*b*c*d)^2)/(27*c^5))*((3^(1/2)*1i)/2 + 1/2)*(-(27*a^3*d^3 - 8*b^3*c^3 + 36*a*b^2*c^2*d - 54*a^2*b*c*d^2)/(729*a*c^6))^(1/3) + log((((3^(1/2)*1i)/2 + 1/2)*((((3^(1/2)*1i)/2 - 1/2)*(6*b^4*d^3*(a + b*x^3)^(1/3)*(a*d - b*c)^2*(9*a^2*d^2 + 2*b^2*c^2 - 6*a*b*c*d) + 3*a*b^4*c^4*d^3*((3^(1/2)*1i)/2 + 1/2)*(2*a^2*d^2 + b^2*c^2 - 3*a*b*c*d)*(-(3*a*d - 2*b*c)^3/(a*c^6))^(2/3))*(-(3*a*d - 2*b*c)^3/(a*c^6))^(1/3))/9 - (a*b^5*d^4*(27*a^3*d^3 - 19*b^3*c^3 + 64*a*b^2*c^2*d - 72*a^2*b*c*d^2))/(3*c))*(-(3*a*d - 2*b*c)^3/(a*c^6))^(2/3))/81 - (b^5*d^4*(a + b*x^3)^(1/3)*(4*a*d - 3*b*c)*(3*a^2*d^2 + 2*b^2*c^2 - 5*a*b*c*d)^2)/(27*c^5))*((3^(1/2)*1i)/2 - 1/2)*(-(27*a^3*d^3 - 8*b^3*c^3 + 36*a*b^2*c^2*d - 54*a^2*b*c*d^2)/(729*a*c^6))^(1/3) - (a + b*x^3)^(2/3)/(3*c*x^3) - log((((3^(1/2)*1i)/2 - 1/2)*((((3^(1/2)*1i)/2 + 1/2)*(6*b^4*d^3*(a + b*x^3)^(1/3)*(a*d - b*c)^2*(9*a^2*d^2 + 2*b^2*c^2 - 6*a*b*c*d) - 27*a*b^4*c^4*d^3*((3^(1/2)*1i)/2 - 1/2)*(2*a^2*d^2 + b^2*c^2 - 3*a*b*c*d)*((d*(a*d - b*c)^2)/c^6)^(2/3))*((d*(a*d - b*c)^2)/c^6)^(1/3))/3 + (a*b^5*d^4*(27*a^3*d^3 - 19*b^3*c^3 + 64*a*b^2*c^2*d - 72*a^2*b*c*d^2))/(3*c))*((d*(a*d - b*c)^2)/c^6)^(2/3))/9 - (b^5*d^4*(a + b*x^3)^(1/3)*(4*a*d - 3*b*c)*(3*a^2*d^2 + 2*b^2*c^2 - 5*a*b*c*d)^2)/(27*c^5))*((3^(1/2)*1i)/2 + 1/2)*((a^2*d^3 + b^2*c^2*d - 2*a*b*c*d^2)/(27*c^6))^(1/3) + log((((3^(1/2)*1i)/2 + 1/2)*((((3^(1/2)*1i)/2 - 1/2)*(6*b^4*d^3*(a + b*x^3)^(1/3)*(a*d - b*c)^2*(9*a^2*d^2 + 2*b^2*c^2 - 6*a*b*c*d) + 27*a*b^4*c^4*d^3*((3^(1/2)*1i)/2 + 1/2)*(2*a^2*d^2 + b^2*c^2 - 3*a*b*c*d)*((d*(a*d - b*c)^2)/c^6)^(2/3))*((d*(a*d - b*c)^2)/c^6)^(1/3))/3 - (a*b^5*d^4*(27*a^3*d^3 - 19*b^3*c^3 + 64*a*b^2*c^2*d - 72*a^2*b*c*d^2))/(3*c))*((d*(a*d - b*c)^2)/c^6)^(2/3))/9 - (b^5*d^4*(a + b*x^3)^(1/3)*(4*a*d - 3*b*c)*(3*a^2*d^2 + 2*b^2*c^2 - 5*a*b*c*d)^2)/(27*c^5))*((3^(1/2)*1i)/2 - 1/2)*((a^2*d^3 + b^2*c^2*d - 2*a*b*c*d^2)/(27*c^6))^(1/3)","B"
683,1,2788,370,15.187000,"\text{Not used}","int((a + b*x^3)^(2/3)/(x^7*(c + d*x^3)),x)","\ln\left(\frac{\left(\frac{\left(27\,a\,b^4\,c^4\,d^3\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)\,{\left(-\frac{d^4\,{\left(a\,d-b\,c\right)}^2}{c^9}\right)}^{2/3}-\frac{b^4\,d^3\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(a\,d-b\,c\right)}^2\,\left(162\,a^4\,d^4-108\,a^3\,b\,c\,d^3+18\,a^2\,b^2\,c^2\,d^2+12\,a\,b^3\,c^3\,d+b^4\,c^4\right)}{3\,a^2\,c^2}\right)\,{\left(-\frac{d^4\,{\left(a\,d-b\,c\right)}^2}{c^9}\right)}^{1/3}}{3}-\frac{b^5\,d^4\,\left(729\,a^6\,d^6-2187\,a^5\,b\,c\,d^5+2295\,a^4\,b^2\,c^2\,d^4-918\,a^3\,b^3\,c^3\,d^3+63\,a^2\,b^4\,c^4\,d^2+17\,a\,b^5\,c^5\,d+b^6\,c^6\right)}{81\,a^2\,c^4}\right)\,{\left(-\frac{d^4\,{\left(a\,d-b\,c\right)}^2}{c^9}\right)}^{2/3}}{9}+\frac{2\,b^5\,d^7\,{\left(b\,x^3+a\right)}^{1/3}\,\left(6\,a\,d-5\,b\,c\right)\,{\left(9\,a^3\,d^3-15\,a^2\,b\,c\,d^2+5\,a\,b^2\,c^2\,d+b^3\,c^3\right)}^2}{729\,a^2\,c^{10}}\right)\,{\left(-\frac{a^2\,d^6-2\,a\,b\,c\,d^5+b^2\,c^2\,d^4}{27\,c^9}\right)}^{1/3}+\ln\left(\frac{\left(\frac{\left(\frac{a\,b^4\,c^4\,d^3\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)\,{\left(-\frac{{\left(-9\,a^2\,d^2+6\,a\,b\,c\,d+b^2\,c^2\right)}^3}{a^4\,c^9}\right)}^{2/3}}{3}-\frac{b^4\,d^3\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(a\,d-b\,c\right)}^2\,\left(162\,a^4\,d^4-108\,a^3\,b\,c\,d^3+18\,a^2\,b^2\,c^2\,d^2+12\,a\,b^3\,c^3\,d+b^4\,c^4\right)}{3\,a^2\,c^2}\right)\,{\left(-\frac{{\left(-9\,a^2\,d^2+6\,a\,b\,c\,d+b^2\,c^2\right)}^3}{a^4\,c^9}\right)}^{1/3}}{27}-\frac{b^5\,d^4\,\left(729\,a^6\,d^6-2187\,a^5\,b\,c\,d^5+2295\,a^4\,b^2\,c^2\,d^4-918\,a^3\,b^3\,c^3\,d^3+63\,a^2\,b^4\,c^4\,d^2+17\,a\,b^5\,c^5\,d+b^6\,c^6\right)}{81\,a^2\,c^4}\right)\,{\left(-\frac{{\left(-9\,a^2\,d^2+6\,a\,b\,c\,d+b^2\,c^2\right)}^3}{a^4\,c^9}\right)}^{2/3}}{729}+\frac{2\,b^5\,d^7\,{\left(b\,x^3+a\right)}^{1/3}\,\left(6\,a\,d-5\,b\,c\right)\,{\left(9\,a^3\,d^3-15\,a^2\,b\,c\,d^2+5\,a\,b^2\,c^2\,d+b^3\,c^3\right)}^2}{729\,a^2\,c^{10}}\right)\,{\left(-\frac{-729\,a^6\,d^6+1458\,a^5\,b\,c\,d^5-729\,a^4\,b^2\,c^2\,d^4-108\,a^3\,b^3\,c^3\,d^3+81\,a^2\,b^4\,c^4\,d^2+18\,a\,b^5\,c^5\,d+b^6\,c^6}{19683\,a^4\,c^9}\right)}^{1/3}-\frac{\frac{{\left(b\,x^3+a\right)}^{2/3}\,\left(c\,b^2+6\,a\,d\,b\right)}{18\,c^2}-\frac{b\,{\left(b\,x^3+a\right)}^{5/3}\,\left(3\,a\,d-b\,c\right)}{9\,a\,c^2}}{{\left(b\,x^3+a\right)}^2-2\,a\,\left(b\,x^3+a\right)+a^2}-\ln\left(\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{b^4\,d^3\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(a\,d-b\,c\right)}^2\,\left(162\,a^4\,d^4-108\,a^3\,b\,c\,d^3+18\,a^2\,b^2\,c^2\,d^2+12\,a\,b^3\,c^3\,d+b^4\,c^4\right)}{3\,a^2\,c^2}-27\,a\,b^4\,c^4\,d^3\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)\,{\left(-\frac{d^4\,{\left(a\,d-b\,c\right)}^2}{c^9}\right)}^{2/3}\right)\,{\left(-\frac{d^4\,{\left(a\,d-b\,c\right)}^2}{c^9}\right)}^{1/3}}{3}-\frac{b^5\,d^4\,\left(729\,a^6\,d^6-2187\,a^5\,b\,c\,d^5+2295\,a^4\,b^2\,c^2\,d^4-918\,a^3\,b^3\,c^3\,d^3+63\,a^2\,b^4\,c^4\,d^2+17\,a\,b^5\,c^5\,d+b^6\,c^6\right)}{81\,a^2\,c^4}\right)\,{\left(-\frac{d^4\,{\left(a\,d-b\,c\right)}^2}{c^9}\right)}^{2/3}}{9}+\frac{2\,b^5\,d^7\,{\left(b\,x^3+a\right)}^{1/3}\,\left(6\,a\,d-5\,b\,c\right)\,{\left(9\,a^3\,d^3-15\,a^2\,b\,c\,d^2+5\,a\,b^2\,c^2\,d+b^3\,c^3\right)}^2}{729\,a^2\,c^{10}}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{a^2\,d^6-2\,a\,b\,c\,d^5+b^2\,c^2\,d^4}{27\,c^9}\right)}^{1/3}+\ln\left(\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{b^4\,d^3\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(a\,d-b\,c\right)}^2\,\left(162\,a^4\,d^4-108\,a^3\,b\,c\,d^3+18\,a^2\,b^2\,c^2\,d^2+12\,a\,b^3\,c^3\,d+b^4\,c^4\right)}{3\,a^2\,c^2}+27\,a\,b^4\,c^4\,d^3\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)\,{\left(-\frac{d^4\,{\left(a\,d-b\,c\right)}^2}{c^9}\right)}^{2/3}\right)\,{\left(-\frac{d^4\,{\left(a\,d-b\,c\right)}^2}{c^9}\right)}^{1/3}}{3}+\frac{b^5\,d^4\,\left(729\,a^6\,d^6-2187\,a^5\,b\,c\,d^5+2295\,a^4\,b^2\,c^2\,d^4-918\,a^3\,b^3\,c^3\,d^3+63\,a^2\,b^4\,c^4\,d^2+17\,a\,b^5\,c^5\,d+b^6\,c^6\right)}{81\,a^2\,c^4}\right)\,{\left(-\frac{d^4\,{\left(a\,d-b\,c\right)}^2}{c^9}\right)}^{2/3}}{9}+\frac{2\,b^5\,d^7\,{\left(b\,x^3+a\right)}^{1/3}\,\left(6\,a\,d-5\,b\,c\right)\,{\left(9\,a^3\,d^3-15\,a^2\,b\,c\,d^2+5\,a\,b^2\,c^2\,d+b^3\,c^3\right)}^2}{729\,a^2\,c^{10}}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{a^2\,d^6-2\,a\,b\,c\,d^5+b^2\,c^2\,d^4}{27\,c^9}\right)}^{1/3}-\ln\left(\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{b^4\,d^3\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(a\,d-b\,c\right)}^2\,\left(162\,a^4\,d^4-108\,a^3\,b\,c\,d^3+18\,a^2\,b^2\,c^2\,d^2+12\,a\,b^3\,c^3\,d+b^4\,c^4\right)}{3\,a^2\,c^2}-\frac{a\,b^4\,c^4\,d^3\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)\,{\left(-\frac{{\left(-9\,a^2\,d^2+6\,a\,b\,c\,d+b^2\,c^2\right)}^3}{a^4\,c^9}\right)}^{2/3}}{3}\right)\,{\left(-\frac{{\left(-9\,a^2\,d^2+6\,a\,b\,c\,d+b^2\,c^2\right)}^3}{a^4\,c^9}\right)}^{1/3}}{27}-\frac{b^5\,d^4\,\left(729\,a^6\,d^6-2187\,a^5\,b\,c\,d^5+2295\,a^4\,b^2\,c^2\,d^4-918\,a^3\,b^3\,c^3\,d^3+63\,a^2\,b^4\,c^4\,d^2+17\,a\,b^5\,c^5\,d+b^6\,c^6\right)}{81\,a^2\,c^4}\right)\,{\left(-\frac{{\left(-9\,a^2\,d^2+6\,a\,b\,c\,d+b^2\,c^2\right)}^3}{a^4\,c^9}\right)}^{2/3}}{729}+\frac{2\,b^5\,d^7\,{\left(b\,x^3+a\right)}^{1/3}\,\left(6\,a\,d-5\,b\,c\right)\,{\left(9\,a^3\,d^3-15\,a^2\,b\,c\,d^2+5\,a\,b^2\,c^2\,d+b^3\,c^3\right)}^2}{729\,a^2\,c^{10}}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{-729\,a^6\,d^6+1458\,a^5\,b\,c\,d^5-729\,a^4\,b^2\,c^2\,d^4-108\,a^3\,b^3\,c^3\,d^3+81\,a^2\,b^4\,c^4\,d^2+18\,a\,b^5\,c^5\,d+b^6\,c^6}{19683\,a^4\,c^9}\right)}^{1/3}+\ln\left(\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{b^4\,d^3\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(a\,d-b\,c\right)}^2\,\left(162\,a^4\,d^4-108\,a^3\,b\,c\,d^3+18\,a^2\,b^2\,c^2\,d^2+12\,a\,b^3\,c^3\,d+b^4\,c^4\right)}{3\,a^2\,c^2}+\frac{a\,b^4\,c^4\,d^3\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)\,{\left(-\frac{{\left(-9\,a^2\,d^2+6\,a\,b\,c\,d+b^2\,c^2\right)}^3}{a^4\,c^9}\right)}^{2/3}}{3}\right)\,{\left(-\frac{{\left(-9\,a^2\,d^2+6\,a\,b\,c\,d+b^2\,c^2\right)}^3}{a^4\,c^9}\right)}^{1/3}}{27}+\frac{b^5\,d^4\,\left(729\,a^6\,d^6-2187\,a^5\,b\,c\,d^5+2295\,a^4\,b^2\,c^2\,d^4-918\,a^3\,b^3\,c^3\,d^3+63\,a^2\,b^4\,c^4\,d^2+17\,a\,b^5\,c^5\,d+b^6\,c^6\right)}{81\,a^2\,c^4}\right)\,{\left(-\frac{{\left(-9\,a^2\,d^2+6\,a\,b\,c\,d+b^2\,c^2\right)}^3}{a^4\,c^9}\right)}^{2/3}}{729}+\frac{2\,b^5\,d^7\,{\left(b\,x^3+a\right)}^{1/3}\,\left(6\,a\,d-5\,b\,c\right)\,{\left(9\,a^3\,d^3-15\,a^2\,b\,c\,d^2+5\,a\,b^2\,c^2\,d+b^3\,c^3\right)}^2}{729\,a^2\,c^{10}}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{-729\,a^6\,d^6+1458\,a^5\,b\,c\,d^5-729\,a^4\,b^2\,c^2\,d^4-108\,a^3\,b^3\,c^3\,d^3+81\,a^2\,b^4\,c^4\,d^2+18\,a\,b^5\,c^5\,d+b^6\,c^6}{19683\,a^4\,c^9}\right)}^{1/3}","Not used",1,"log(((((27*a*b^4*c^4*d^3*(2*a^2*d^2 + b^2*c^2 - 3*a*b*c*d)*(-(d^4*(a*d - b*c)^2)/c^9)^(2/3) - (b^4*d^3*(a + b*x^3)^(1/3)*(a*d - b*c)^2*(162*a^4*d^4 + b^4*c^4 + 18*a^2*b^2*c^2*d^2 + 12*a*b^3*c^3*d - 108*a^3*b*c*d^3))/(3*a^2*c^2))*(-(d^4*(a*d - b*c)^2)/c^9)^(1/3))/3 - (b^5*d^4*(729*a^6*d^6 + b^6*c^6 + 63*a^2*b^4*c^4*d^2 - 918*a^3*b^3*c^3*d^3 + 2295*a^4*b^2*c^2*d^4 + 17*a*b^5*c^5*d - 2187*a^5*b*c*d^5))/(81*a^2*c^4))*(-(d^4*(a*d - b*c)^2)/c^9)^(2/3))/9 + (2*b^5*d^7*(a + b*x^3)^(1/3)*(6*a*d - 5*b*c)*(9*a^3*d^3 + b^3*c^3 + 5*a*b^2*c^2*d - 15*a^2*b*c*d^2)^2)/(729*a^2*c^10))*(-(a^2*d^6 + b^2*c^2*d^4 - 2*a*b*c*d^5)/(27*c^9))^(1/3) + log((((((a*b^4*c^4*d^3*(2*a^2*d^2 + b^2*c^2 - 3*a*b*c*d)*(-(b^2*c^2 - 9*a^2*d^2 + 6*a*b*c*d)^3/(a^4*c^9))^(2/3))/3 - (b^4*d^3*(a + b*x^3)^(1/3)*(a*d - b*c)^2*(162*a^4*d^4 + b^4*c^4 + 18*a^2*b^2*c^2*d^2 + 12*a*b^3*c^3*d - 108*a^3*b*c*d^3))/(3*a^2*c^2))*(-(b^2*c^2 - 9*a^2*d^2 + 6*a*b*c*d)^3/(a^4*c^9))^(1/3))/27 - (b^5*d^4*(729*a^6*d^6 + b^6*c^6 + 63*a^2*b^4*c^4*d^2 - 918*a^3*b^3*c^3*d^3 + 2295*a^4*b^2*c^2*d^4 + 17*a*b^5*c^5*d - 2187*a^5*b*c*d^5))/(81*a^2*c^4))*(-(b^2*c^2 - 9*a^2*d^2 + 6*a*b*c*d)^3/(a^4*c^9))^(2/3))/729 + (2*b^5*d^7*(a + b*x^3)^(1/3)*(6*a*d - 5*b*c)*(9*a^3*d^3 + b^3*c^3 + 5*a*b^2*c^2*d - 15*a^2*b*c*d^2)^2)/(729*a^2*c^10))*(-(b^6*c^6 - 729*a^6*d^6 + 81*a^2*b^4*c^4*d^2 - 108*a^3*b^3*c^3*d^3 - 729*a^4*b^2*c^2*d^4 + 18*a*b^5*c^5*d + 1458*a^5*b*c*d^5)/(19683*a^4*c^9))^(1/3) - (((a + b*x^3)^(2/3)*(b^2*c + 6*a*b*d))/(18*c^2) - (b*(a + b*x^3)^(5/3)*(3*a*d - b*c))/(9*a*c^2))/((a + b*x^3)^2 - 2*a*(a + b*x^3) + a^2) - log((((3^(1/2)*1i)/2 - 1/2)*((((3^(1/2)*1i)/2 + 1/2)*((b^4*d^3*(a + b*x^3)^(1/3)*(a*d - b*c)^2*(162*a^4*d^4 + b^4*c^4 + 18*a^2*b^2*c^2*d^2 + 12*a*b^3*c^3*d - 108*a^3*b*c*d^3))/(3*a^2*c^2) - 27*a*b^4*c^4*d^3*((3^(1/2)*1i)/2 - 1/2)*(2*a^2*d^2 + b^2*c^2 - 3*a*b*c*d)*(-(d^4*(a*d - b*c)^2)/c^9)^(2/3))*(-(d^4*(a*d - b*c)^2)/c^9)^(1/3))/3 - (b^5*d^4*(729*a^6*d^6 + b^6*c^6 + 63*a^2*b^4*c^4*d^2 - 918*a^3*b^3*c^3*d^3 + 2295*a^4*b^2*c^2*d^4 + 17*a*b^5*c^5*d - 2187*a^5*b*c*d^5))/(81*a^2*c^4))*(-(d^4*(a*d - b*c)^2)/c^9)^(2/3))/9 + (2*b^5*d^7*(a + b*x^3)^(1/3)*(6*a*d - 5*b*c)*(9*a^3*d^3 + b^3*c^3 + 5*a*b^2*c^2*d - 15*a^2*b*c*d^2)^2)/(729*a^2*c^10))*((3^(1/2)*1i)/2 + 1/2)*(-(a^2*d^6 + b^2*c^2*d^4 - 2*a*b*c*d^5)/(27*c^9))^(1/3) + log((((3^(1/2)*1i)/2 + 1/2)*((((3^(1/2)*1i)/2 - 1/2)*((b^4*d^3*(a + b*x^3)^(1/3)*(a*d - b*c)^2*(162*a^4*d^4 + b^4*c^4 + 18*a^2*b^2*c^2*d^2 + 12*a*b^3*c^3*d - 108*a^3*b*c*d^3))/(3*a^2*c^2) + 27*a*b^4*c^4*d^3*((3^(1/2)*1i)/2 + 1/2)*(2*a^2*d^2 + b^2*c^2 - 3*a*b*c*d)*(-(d^4*(a*d - b*c)^2)/c^9)^(2/3))*(-(d^4*(a*d - b*c)^2)/c^9)^(1/3))/3 + (b^5*d^4*(729*a^6*d^6 + b^6*c^6 + 63*a^2*b^4*c^4*d^2 - 918*a^3*b^3*c^3*d^3 + 2295*a^4*b^2*c^2*d^4 + 17*a*b^5*c^5*d - 2187*a^5*b*c*d^5))/(81*a^2*c^4))*(-(d^4*(a*d - b*c)^2)/c^9)^(2/3))/9 + (2*b^5*d^7*(a + b*x^3)^(1/3)*(6*a*d - 5*b*c)*(9*a^3*d^3 + b^3*c^3 + 5*a*b^2*c^2*d - 15*a^2*b*c*d^2)^2)/(729*a^2*c^10))*((3^(1/2)*1i)/2 - 1/2)*(-(a^2*d^6 + b^2*c^2*d^4 - 2*a*b*c*d^5)/(27*c^9))^(1/3) - log((((3^(1/2)*1i)/2 - 1/2)*((((3^(1/2)*1i)/2 + 1/2)*((b^4*d^3*(a + b*x^3)^(1/3)*(a*d - b*c)^2*(162*a^4*d^4 + b^4*c^4 + 18*a^2*b^2*c^2*d^2 + 12*a*b^3*c^3*d - 108*a^3*b*c*d^3))/(3*a^2*c^2) - (a*b^4*c^4*d^3*((3^(1/2)*1i)/2 - 1/2)*(2*a^2*d^2 + b^2*c^2 - 3*a*b*c*d)*(-(b^2*c^2 - 9*a^2*d^2 + 6*a*b*c*d)^3/(a^4*c^9))^(2/3))/3)*(-(b^2*c^2 - 9*a^2*d^2 + 6*a*b*c*d)^3/(a^4*c^9))^(1/3))/27 - (b^5*d^4*(729*a^6*d^6 + b^6*c^6 + 63*a^2*b^4*c^4*d^2 - 918*a^3*b^3*c^3*d^3 + 2295*a^4*b^2*c^2*d^4 + 17*a*b^5*c^5*d - 2187*a^5*b*c*d^5))/(81*a^2*c^4))*(-(b^2*c^2 - 9*a^2*d^2 + 6*a*b*c*d)^3/(a^4*c^9))^(2/3))/729 + (2*b^5*d^7*(a + b*x^3)^(1/3)*(6*a*d - 5*b*c)*(9*a^3*d^3 + b^3*c^3 + 5*a*b^2*c^2*d - 15*a^2*b*c*d^2)^2)/(729*a^2*c^10))*((3^(1/2)*1i)/2 + 1/2)*(-(b^6*c^6 - 729*a^6*d^6 + 81*a^2*b^4*c^4*d^2 - 108*a^3*b^3*c^3*d^3 - 729*a^4*b^2*c^2*d^4 + 18*a*b^5*c^5*d + 1458*a^5*b*c*d^5)/(19683*a^4*c^9))^(1/3) + log((((3^(1/2)*1i)/2 + 1/2)*((((3^(1/2)*1i)/2 - 1/2)*((b^4*d^3*(a + b*x^3)^(1/3)*(a*d - b*c)^2*(162*a^4*d^4 + b^4*c^4 + 18*a^2*b^2*c^2*d^2 + 12*a*b^3*c^3*d - 108*a^3*b*c*d^3))/(3*a^2*c^2) + (a*b^4*c^4*d^3*((3^(1/2)*1i)/2 + 1/2)*(2*a^2*d^2 + b^2*c^2 - 3*a*b*c*d)*(-(b^2*c^2 - 9*a^2*d^2 + 6*a*b*c*d)^3/(a^4*c^9))^(2/3))/3)*(-(b^2*c^2 - 9*a^2*d^2 + 6*a*b*c*d)^3/(a^4*c^9))^(1/3))/27 + (b^5*d^4*(729*a^6*d^6 + b^6*c^6 + 63*a^2*b^4*c^4*d^2 - 918*a^3*b^3*c^3*d^3 + 2295*a^4*b^2*c^2*d^4 + 17*a*b^5*c^5*d - 2187*a^5*b*c*d^5))/(81*a^2*c^4))*(-(b^2*c^2 - 9*a^2*d^2 + 6*a*b*c*d)^3/(a^4*c^9))^(2/3))/729 + (2*b^5*d^7*(a + b*x^3)^(1/3)*(6*a*d - 5*b*c)*(9*a^3*d^3 + b^3*c^3 + 5*a*b^2*c^2*d - 15*a^2*b*c*d^2)^2)/(729*a^2*c^10))*((3^(1/2)*1i)/2 - 1/2)*(-(b^6*c^6 - 729*a^6*d^6 + 81*a^2*b^4*c^4*d^2 - 108*a^3*b^3*c^3*d^3 - 729*a^4*b^2*c^2*d^4 + 18*a*b^5*c^5*d + 1458*a^5*b*c*d^5)/(19683*a^4*c^9))^(1/3)","B"
684,0,-1,334,0.000000,"\text{Not used}","int((x^6*(a + b*x^3)^(2/3))/(c + d*x^3),x)","\int \frac{x^6\,{\left(b\,x^3+a\right)}^{2/3}}{d\,x^3+c} \,d x","Not used",1,"int((x^6*(a + b*x^3)^(2/3))/(c + d*x^3), x)","F"
685,0,-1,272,0.000000,"\text{Not used}","int((x^3*(a + b*x^3)^(2/3))/(c + d*x^3),x)","\int \frac{x^3\,{\left(b\,x^3+a\right)}^{2/3}}{d\,x^3+c} \,d x","Not used",1,"int((x^3*(a + b*x^3)^(2/3))/(c + d*x^3), x)","F"
686,0,-1,233,0.000000,"\text{Not used}","int((a + b*x^3)^(2/3)/(c + d*x^3),x)","\int \frac{{\left(b\,x^3+a\right)}^{2/3}}{d\,x^3+c} \,d x","Not used",1,"int((a + b*x^3)^(2/3)/(c + d*x^3), x)","F"
687,0,-1,169,0.000000,"\text{Not used}","int((a + b*x^3)^(2/3)/(x^3*(c + d*x^3)),x)","\int \frac{{\left(b\,x^3+a\right)}^{2/3}}{x^3\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int((a + b*x^3)^(2/3)/(x^3*(c + d*x^3)), x)","F"
688,0,-1,206,0.000000,"\text{Not used}","int((a + b*x^3)^(2/3)/(x^6*(c + d*x^3)),x)","\int \frac{{\left(b\,x^3+a\right)}^{2/3}}{x^6\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int((a + b*x^3)^(2/3)/(x^6*(c + d*x^3)), x)","F"
689,0,-1,257,0.000000,"\text{Not used}","int((a + b*x^3)^(2/3)/(x^9*(c + d*x^3)),x)","\int \frac{{\left(b\,x^3+a\right)}^{2/3}}{x^9\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int((a + b*x^3)^(2/3)/(x^9*(c + d*x^3)), x)","F"
690,0,-1,320,0.000000,"\text{Not used}","int((a + b*x^3)^(2/3)/(x^12*(c + d*x^3)),x)","\int \frac{{\left(b\,x^3+a\right)}^{2/3}}{x^{12}\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int((a + b*x^3)^(2/3)/(x^12*(c + d*x^3)), x)","F"
691,0,-1,64,0.000000,"\text{Not used}","int((x^7*(a + b*x^3)^(2/3))/(c + d*x^3),x)","\int \frac{x^7\,{\left(b\,x^3+a\right)}^{2/3}}{d\,x^3+c} \,d x","Not used",1,"int((x^7*(a + b*x^3)^(2/3))/(c + d*x^3), x)","F"
692,0,-1,64,0.000000,"\text{Not used}","int((x^4*(a + b*x^3)^(2/3))/(c + d*x^3),x)","\int \frac{x^4\,{\left(b\,x^3+a\right)}^{2/3}}{d\,x^3+c} \,d x","Not used",1,"int((x^4*(a + b*x^3)^(2/3))/(c + d*x^3), x)","F"
693,0,-1,64,0.000000,"\text{Not used}","int((x*(a + b*x^3)^(2/3))/(c + d*x^3),x)","\int \frac{x\,{\left(b\,x^3+a\right)}^{2/3}}{d\,x^3+c} \,d x","Not used",1,"int((x*(a + b*x^3)^(2/3))/(c + d*x^3), x)","F"
694,0,-1,62,0.000000,"\text{Not used}","int((a + b*x^3)^(2/3)/(x^2*(c + d*x^3)),x)","\int \frac{{\left(b\,x^3+a\right)}^{2/3}}{x^2\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int((a + b*x^3)^(2/3)/(x^2*(c + d*x^3)), x)","F"
695,0,-1,64,0.000000,"\text{Not used}","int((a + b*x^3)^(2/3)/(x^5*(c + d*x^3)),x)","\int \frac{{\left(b\,x^3+a\right)}^{2/3}}{x^5\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int((a + b*x^3)^(2/3)/(x^5*(c + d*x^3)), x)","F"
696,1,477,251,5.123087,"\text{Not used}","int((x^8*(a + b*x^3)^(4/3))/(c + d*x^3),x)","\left(\frac{a^2}{4\,b^2\,d}+\frac{\left(\frac{2\,a}{b^2\,d}+\frac{b^3\,c-a\,b^2\,d}{b^4\,d^2}\right)\,\left(b^3\,c-a\,b^2\,d\right)}{4\,b^2\,d}\right)\,{\left(b\,x^3+a\right)}^{4/3}-\left(\frac{2\,a}{7\,b^2\,d}+\frac{b^3\,c-a\,b^2\,d}{7\,b^4\,d^2}\right)\,{\left(b\,x^3+a\right)}^{7/3}+\frac{{\left(b\,x^3+a\right)}^{10/3}}{10\,b^2\,d}+\frac{c^2\,\ln\left(\frac{3\,{\left(b\,x^3+a\right)}^{1/3}\,\left(a^2\,c^2\,d^2-2\,a\,b\,c^3\,d+b^2\,c^4\right)}{d^2}-\frac{c^2\,{\left(a\,d-b\,c\right)}^{4/3}\,\left(9\,a\,d^3-9\,b\,c\,d^2\right)}{3\,d^{13/3}}\right)\,{\left(a\,d-b\,c\right)}^{4/3}}{3\,d^{13/3}}-\frac{\left(\frac{a^2}{b^2\,d}+\frac{\left(\frac{2\,a}{b^2\,d}+\frac{b^3\,c-a\,b^2\,d}{b^4\,d^2}\right)\,\left(b^3\,c-a\,b^2\,d\right)}{b^2\,d}\right)\,{\left(b\,x^3+a\right)}^{1/3}\,\left(b^3\,c-a\,b^2\,d\right)}{b^2\,d}-\frac{c^2\,\ln\left(\frac{3\,c^2\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(a\,d-b\,c\right)}^{7/3}}{d^{7/3}}+\frac{3\,c^2\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(a\,d-b\,c\right)}^2}{d^2}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(a\,d-b\,c\right)}^{4/3}}{3\,d^{13/3}}+\frac{c^2\,\ln\left(\frac{3\,c^2\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(a\,d-b\,c\right)}^2}{d^2}-\frac{9\,c^2\,\left(-\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)\,{\left(a\,d-b\,c\right)}^{7/3}}{d^{7/3}}\right)\,\left(-\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)\,{\left(a\,d-b\,c\right)}^{4/3}}{d^{13/3}}","Not used",1,"(a^2/(4*b^2*d) + (((2*a)/(b^2*d) + (b^3*c - a*b^2*d)/(b^4*d^2))*(b^3*c - a*b^2*d))/(4*b^2*d))*(a + b*x^3)^(4/3) - ((2*a)/(7*b^2*d) + (b^3*c - a*b^2*d)/(7*b^4*d^2))*(a + b*x^3)^(7/3) + (a + b*x^3)^(10/3)/(10*b^2*d) + (c^2*log((3*(a + b*x^3)^(1/3)*(b^2*c^4 + a^2*c^2*d^2 - 2*a*b*c^3*d))/d^2 - (c^2*(a*d - b*c)^(4/3)*(9*a*d^3 - 9*b*c*d^2))/(3*d^(13/3)))*(a*d - b*c)^(4/3))/(3*d^(13/3)) - ((a^2/(b^2*d) + (((2*a)/(b^2*d) + (b^3*c - a*b^2*d)/(b^4*d^2))*(b^3*c - a*b^2*d))/(b^2*d))*(a + b*x^3)^(1/3)*(b^3*c - a*b^2*d))/(b^2*d) - (c^2*log((3*c^2*((3^(1/2)*1i)/2 + 1/2)*(a*d - b*c)^(7/3))/d^(7/3) + (3*c^2*(a + b*x^3)^(1/3)*(a*d - b*c)^2)/d^2)*((3^(1/2)*1i)/2 + 1/2)*(a*d - b*c)^(4/3))/(3*d^(13/3)) + (c^2*log((3*c^2*(a + b*x^3)^(1/3)*(a*d - b*c)^2)/d^2 - (9*c^2*((3^(1/2)*1i)/6 - 1/6)*(a*d - b*c)^(7/3))/d^(7/3))*((3^(1/2)*1i)/6 - 1/6)*(a*d - b*c)^(4/3))/d^(13/3)","B"
697,1,348,211,5.056783,"\text{Not used}","int((x^5*(a + b*x^3)^(4/3))/(c + d*x^3),x)","\frac{{\left(b\,x^3+a\right)}^{7/3}}{7\,b\,d}-{\left(b\,x^3+a\right)}^{4/3}\,\left(\frac{a}{4\,b\,d}+\frac{b^2\,c-a\,b\,d}{4\,b^2\,d^2}\right)-\frac{c\,\ln\left(\frac{3\,{\left(b\,x^3+a\right)}^{1/3}\,\left(a^2\,c\,d^2-2\,a\,b\,c^2\,d+b^2\,c^3\right)}{d}-\frac{c\,{\left(a\,d-b\,c\right)}^{4/3}\,\left(9\,a\,d^3-9\,b\,c\,d^2\right)}{3\,d^{10/3}}\right)\,{\left(a\,d-b\,c\right)}^{4/3}}{3\,d^{10/3}}-\frac{c\,\ln\left(\frac{3\,c\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(a\,d-b\,c\right)}^2}{d}-\frac{3\,c\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(a\,d-b\,c\right)}^{7/3}}{d^{4/3}}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(a\,d-b\,c\right)}^{4/3}}{3\,d^{10/3}}+\frac{c\,\ln\left(\frac{3\,c\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(a\,d-b\,c\right)}^2}{d}+\frac{3\,c\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(a\,d-b\,c\right)}^{7/3}}{d^{4/3}}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(a\,d-b\,c\right)}^{4/3}}{3\,d^{10/3}}+\frac{{\left(b\,x^3+a\right)}^{1/3}\,\left(b^2\,c-a\,b\,d\right)\,\left(\frac{a}{b\,d}+\frac{b^2\,c-a\,b\,d}{b^2\,d^2}\right)}{b\,d}","Not used",1,"(a + b*x^3)^(7/3)/(7*b*d) - (a + b*x^3)^(4/3)*(a/(4*b*d) + (b^2*c - a*b*d)/(4*b^2*d^2)) - (c*log((3*(a + b*x^3)^(1/3)*(b^2*c^3 + a^2*c*d^2 - 2*a*b*c^2*d))/d - (c*(a*d - b*c)^(4/3)*(9*a*d^3 - 9*b*c*d^2))/(3*d^(10/3)))*(a*d - b*c)^(4/3))/(3*d^(10/3)) - (c*log((3*c*(a + b*x^3)^(1/3)*(a*d - b*c)^2)/d - (3*c*((3^(1/2)*1i)/2 - 1/2)*(a*d - b*c)^(7/3))/d^(4/3))*((3^(1/2)*1i)/2 - 1/2)*(a*d - b*c)^(4/3))/(3*d^(10/3)) + (c*log((3*c*(a + b*x^3)^(1/3)*(a*d - b*c)^2)/d + (3*c*((3^(1/2)*1i)/2 + 1/2)*(a*d - b*c)^(7/3))/d^(4/3))*((3^(1/2)*1i)/2 + 1/2)*(a*d - b*c)^(4/3))/(3*d^(10/3)) + ((a + b*x^3)^(1/3)*(b^2*c - a*b*d)*(a/(b*d) + (b^2*c - a*b*d)/(b^2*d^2)))/(b*d)","B"
698,1,304,187,4.724916,"\text{Not used}","int((x^2*(a + b*x^3)^(4/3))/(c + d*x^3),x)","\frac{{\left(b\,x^3+a\right)}^{4/3}}{4\,d}+\frac{\ln\left({\left(b\,x^3+a\right)}^{1/3}\,\left(3\,a^2\,d^2-6\,a\,b\,c\,d+3\,b^2\,c^2\right)-\frac{{\left(a\,d-b\,c\right)}^{4/3}\,\left(9\,a\,d^3-9\,b\,c\,d^2\right)}{3\,d^{7/3}}\right)\,{\left(a\,d-b\,c\right)}^{4/3}}{3\,d^{7/3}}+\frac{{\left(b\,x^3+a\right)}^{1/3}\,\left(a\,d-b\,c\right)}{d^2}-\frac{\ln\left({\left(b\,x^3+a\right)}^{1/3}\,\left(3\,a^2\,d^2-6\,a\,b\,c\,d+3\,b^2\,c^2\right)+\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(a\,d-b\,c\right)}^{4/3}\,\left(9\,a\,d^3-9\,b\,c\,d^2\right)}{3\,d^{7/3}}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(a\,d-b\,c\right)}^{4/3}}{3\,d^{7/3}}+\frac{\ln\left({\left(b\,x^3+a\right)}^{1/3}\,\left(3\,a^2\,d^2-6\,a\,b\,c\,d+3\,b^2\,c^2\right)-\frac{\left(-\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)\,{\left(a\,d-b\,c\right)}^{4/3}\,\left(9\,a\,d^3-9\,b\,c\,d^2\right)}{d^{7/3}}\right)\,\left(-\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)\,{\left(a\,d-b\,c\right)}^{4/3}}{d^{7/3}}","Not used",1,"(a + b*x^3)^(4/3)/(4*d) + (log((a + b*x^3)^(1/3)*(3*a^2*d^2 + 3*b^2*c^2 - 6*a*b*c*d) - ((a*d - b*c)^(4/3)*(9*a*d^3 - 9*b*c*d^2))/(3*d^(7/3)))*(a*d - b*c)^(4/3))/(3*d^(7/3)) + ((a + b*x^3)^(1/3)*(a*d - b*c))/d^2 - (log((a + b*x^3)^(1/3)*(3*a^2*d^2 + 3*b^2*c^2 - 6*a*b*c*d) + (((3^(1/2)*1i)/2 + 1/2)*(a*d - b*c)^(4/3)*(9*a*d^3 - 9*b*c*d^2))/(3*d^(7/3)))*((3^(1/2)*1i)/2 + 1/2)*(a*d - b*c)^(4/3))/(3*d^(7/3)) + (log((a + b*x^3)^(1/3)*(3*a^2*d^2 + 3*b^2*c^2 - 6*a*b*c*d) - (((3^(1/2)*1i)/6 - 1/6)*(a*d - b*c)^(4/3)*(9*a*d^3 - 9*b*c*d^2))/d^(7/3))*((3^(1/2)*1i)/6 - 1/6)*(a*d - b*c)^(4/3))/d^(7/3)","B"
699,1,796,261,6.080019,"\text{Not used}","int((a + b*x^3)^(4/3)/(x*(c + d*x^3)),x)","\ln\left(c\,d\,{\left(-\frac{{\left(a\,d-b\,c\right)}^4}{c^3\,d^4}\right)}^{1/3}+a\,d\,{\left(b\,x^3+a\right)}^{1/3}-b\,c\,{\left(b\,x^3+a\right)}^{1/3}\right)\,{\left(-\frac{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}{27\,c^3\,d^4}\right)}^{1/3}+\ln\left(c\,{\left(\frac{a^4}{c^3}\right)}^{1/3}-a\,{\left(b\,x^3+a\right)}^{1/3}\right)\,{\left(\frac{a^4}{27\,c^3}\right)}^{1/3}+\frac{b\,{\left(b\,x^3+a\right)}^{1/3}}{d}-\ln\left(c\,{\left(\frac{a^4}{c^3}\right)}^{1/3}+2\,a\,{\left(b\,x^3+a\right)}^{1/3}+\sqrt{3}\,c\,{\left(\frac{a^4}{c^3}\right)}^{1/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(\frac{a^4}{27\,c^3}\right)}^{1/3}+\ln\left(\sqrt{3}\,c\,{\left(\frac{a^4}{c^3}\right)}^{1/3}+c\,{\left(\frac{a^4}{c^3}\right)}^{1/3}\,1{}\mathrm{i}+a\,{\left(b\,x^3+a\right)}^{1/3}\,2{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(\frac{a^4}{27\,c^3}\right)}^{1/3}+\ln\left(\frac{3\,a^2\,b^4\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(a\,d-b\,c\right)}^2\,\left(2\,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}+3\,a^2\,b^4\,c\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{{\left(a\,d-b\,c\right)}^4}{c^3\,d^4}\right)}^{1/3}\,\left(2\,a^5\,d^5-6\,a^4\,b\,c\,d^4+10\,a^3\,b^2\,c^2\,d^3-10\,a^2\,b^3\,c^3\,d^2+5\,a\,b^4\,c^4\,d-b^5\,c^5\right)\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{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}{27\,c^3\,d^4}\right)}^{1/3}-\ln\left(\frac{3\,a^2\,b^4\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(a\,d-b\,c\right)}^2\,\left(2\,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}-3\,a^2\,b^4\,c\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{{\left(a\,d-b\,c\right)}^4}{c^3\,d^4}\right)}^{1/3}\,\left(2\,a^5\,d^5-6\,a^4\,b\,c\,d^4+10\,a^3\,b^2\,c^2\,d^3-10\,a^2\,b^3\,c^3\,d^2+5\,a\,b^4\,c^4\,d-b^5\,c^5\right)\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{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}{27\,c^3\,d^4}\right)}^{1/3}","Not used",1,"log(c*d*(-(a*d - b*c)^4/(c^3*d^4))^(1/3) + a*d*(a + b*x^3)^(1/3) - b*c*(a + b*x^3)^(1/3))*(-(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)/(27*c^3*d^4))^(1/3) + log(c*(a^4/c^3)^(1/3) - a*(a + b*x^3)^(1/3))*(a^4/(27*c^3))^(1/3) + (b*(a + b*x^3)^(1/3))/d - log(c*(a^4/c^3)^(1/3) + 2*a*(a + b*x^3)^(1/3) + 3^(1/2)*c*(a^4/c^3)^(1/3)*1i)*((3^(1/2)*1i)/2 + 1/2)*(a^4/(27*c^3))^(1/3) + log(c*(a^4/c^3)^(1/3)*1i + a*(a + b*x^3)^(1/3)*2i + 3^(1/2)*c*(a^4/c^3)^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(a^4/(27*c^3))^(1/3) + log((3*a^2*b^4*(a + b*x^3)^(1/3)*(a*d - b*c)^2*(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 + 3*a^2*b^4*c*((3^(1/2)*1i)/2 - 1/2)*(-(a*d - b*c)^4/(c^3*d^4))^(1/3)*(2*a^5*d^5 - b^5*c^5 - 10*a^2*b^3*c^3*d^2 + 10*a^3*b^2*c^2*d^3 + 5*a*b^4*c^4*d - 6*a^4*b*c*d^4))*((3^(1/2)*1i)/2 - 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)/(27*c^3*d^4))^(1/3) - log((3*a^2*b^4*(a + b*x^3)^(1/3)*(a*d - b*c)^2*(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 - 3*a^2*b^4*c*((3^(1/2)*1i)/2 + 1/2)*(-(a*d - b*c)^4/(c^3*d^4))^(1/3)*(2*a^5*d^5 - b^5*c^5 - 10*a^2*b^3*c^3*d^2 + 10*a^3*b^2*c^2*d^3 + 5*a*b^4*c^4*d - 6*a^4*b*c*d^4))*((3^(1/2)*1i)/2 + 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)/(27*c^3*d^4))^(1/3)","B"
700,1,2047,399,10.881316,"\text{Not used}","int((a + b*x^3)^(4/3)/(x^4*(c + d*x^3)),x)","\ln\left(c^2\,{\left(-\frac{a\,{\left(3\,a\,d-4\,b\,c\right)}^3}{c^6}\right)}^{1/3}+3\,a\,d\,{\left(b\,x^3+a\right)}^{1/3}-4\,b\,c\,{\left(b\,x^3+a\right)}^{1/3}\right)\,{\left(-\frac{27\,a^4\,d^3-108\,a^3\,b\,c\,d^2+144\,a^2\,b^2\,c^2\,d-64\,a\,b^3\,c^3}{729\,c^6}\right)}^{1/3}+\ln\left(\frac{\left(\frac{\left(81\,a\,b^4\,c^4\,d^3\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)\,{\left(\frac{{\left(a\,d-b\,c\right)}^4}{c^6\,d}\right)}^{1/3}-108\,a\,b^5\,c^3\,d^3\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(a\,d-b\,c\right)}^2\right)\,{\left(\frac{{\left(a\,d-b\,c\right)}^4}{c^6\,d}\right)}^{2/3}}{9}+\frac{a\,b^5\,d^2\,\left(27\,a^5\,d^5-153\,a^4\,b\,c\,d^4+332\,a^3\,b^2\,c^2\,d^3-341\,a^2\,b^3\,c^3\,d^2+162\,a\,b^4\,c^4\,d-27\,b^5\,c^5\right)}{3\,c}\right)\,{\left(\frac{{\left(a\,d-b\,c\right)}^4}{c^6\,d}\right)}^{1/3}}{3}-\frac{a\,b^4\,d^2\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(a\,d-b\,c\right)}^2\,\left(54\,a^5\,d^5-252\,a^4\,b\,c\,d^4+450\,a^3\,b^2\,c^2\,d^3-388\,a^2\,b^3\,c^3\,d^2+171\,a\,b^4\,c^4\,d-36\,b^5\,c^5\right)}{9\,c^4}\right)\,{\left(\frac{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}{27\,c^6\,d}\right)}^{1/3}+\ln\left(\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(108\,a\,b^5\,c^3\,d^3\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(a\,d-b\,c\right)}^2-81\,a\,b^4\,c^4\,d^3\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)\,{\left(\frac{{\left(a\,d-b\,c\right)}^4}{c^6\,d}\right)}^{1/3}\right)\,{\left(\frac{{\left(a\,d-b\,c\right)}^4}{c^6\,d}\right)}^{2/3}}{9}+\frac{a\,b^5\,d^2\,\left(27\,a^5\,d^5-153\,a^4\,b\,c\,d^4+332\,a^3\,b^2\,c^2\,d^3-341\,a^2\,b^3\,c^3\,d^2+162\,a\,b^4\,c^4\,d-27\,b^5\,c^5\right)}{3\,c}\right)\,{\left(\frac{{\left(a\,d-b\,c\right)}^4}{c^6\,d}\right)}^{1/3}}{3}-\frac{a\,b^4\,d^2\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(a\,d-b\,c\right)}^2\,\left(54\,a^5\,d^5-252\,a^4\,b\,c\,d^4+450\,a^3\,b^2\,c^2\,d^3-388\,a^2\,b^3\,c^3\,d^2+171\,a\,b^4\,c^4\,d-36\,b^5\,c^5\right)}{9\,c^4}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(\frac{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}{27\,c^6\,d}\right)}^{1/3}-\ln\left(\frac{a\,b^4\,d^2\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(a\,d-b\,c\right)}^2\,\left(54\,a^5\,d^5-252\,a^4\,b\,c\,d^4+450\,a^3\,b^2\,c^2\,d^3-388\,a^2\,b^3\,c^3\,d^2+171\,a\,b^4\,c^4\,d-36\,b^5\,c^5\right)}{9\,c^4}-\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(108\,a\,b^5\,c^3\,d^3\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(a\,d-b\,c\right)}^2+81\,a\,b^4\,c^4\,d^3\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)\,{\left(\frac{{\left(a\,d-b\,c\right)}^4}{c^6\,d}\right)}^{1/3}\right)\,{\left(\frac{{\left(a\,d-b\,c\right)}^4}{c^6\,d}\right)}^{2/3}}{9}-\frac{a\,b^5\,d^2\,\left(27\,a^5\,d^5-153\,a^4\,b\,c\,d^4+332\,a^3\,b^2\,c^2\,d^3-341\,a^2\,b^3\,c^3\,d^2+162\,a\,b^4\,c^4\,d-27\,b^5\,c^5\right)}{3\,c}\right)\,{\left(\frac{{\left(a\,d-b\,c\right)}^4}{c^6\,d}\right)}^{1/3}}{3}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(\frac{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}{27\,c^6\,d}\right)}^{1/3}+\ln\left(\frac{a\,b^4\,d^2\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(a\,d-b\,c\right)}^2\,\left(54\,a^5\,d^5-252\,a^4\,b\,c\,d^4+450\,a^3\,b^2\,c^2\,d^3-388\,a^2\,b^3\,c^3\,d^2+171\,a\,b^4\,c^4\,d-36\,b^5\,c^5\right)}{9\,c^4}-\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(108\,a\,b^5\,c^3\,d^3\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(a\,d-b\,c\right)}^2-27\,a\,b^4\,c^4\,d^3\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)\,{\left(-\frac{a\,{\left(3\,a\,d-4\,b\,c\right)}^3}{c^6}\right)}^{1/3}\right)\,{\left(-\frac{a\,{\left(3\,a\,d-4\,b\,c\right)}^3}{c^6}\right)}^{2/3}}{81}+\frac{a\,b^5\,d^2\,\left(27\,a^5\,d^5-153\,a^4\,b\,c\,d^4+332\,a^3\,b^2\,c^2\,d^3-341\,a^2\,b^3\,c^3\,d^2+162\,a\,b^4\,c^4\,d-27\,b^5\,c^5\right)}{3\,c}\right)\,{\left(-\frac{a\,{\left(3\,a\,d-4\,b\,c\right)}^3}{c^6}\right)}^{1/3}}{9}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{27\,a^4\,d^3-108\,a^3\,b\,c\,d^2+144\,a^2\,b^2\,c^2\,d-64\,a\,b^3\,c^3}{729\,c^6}\right)}^{1/3}-\ln\left(\frac{a\,b^4\,d^2\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(a\,d-b\,c\right)}^2\,\left(54\,a^5\,d^5-252\,a^4\,b\,c\,d^4+450\,a^3\,b^2\,c^2\,d^3-388\,a^2\,b^3\,c^3\,d^2+171\,a\,b^4\,c^4\,d-36\,b^5\,c^5\right)}{9\,c^4}-\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(108\,a\,b^5\,c^3\,d^3\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(a\,d-b\,c\right)}^2+27\,a\,b^4\,c^4\,d^3\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)\,{\left(-\frac{a\,{\left(3\,a\,d-4\,b\,c\right)}^3}{c^6}\right)}^{1/3}\right)\,{\left(-\frac{a\,{\left(3\,a\,d-4\,b\,c\right)}^3}{c^6}\right)}^{2/3}}{81}-\frac{a\,b^5\,d^2\,\left(27\,a^5\,d^5-153\,a^4\,b\,c\,d^4+332\,a^3\,b^2\,c^2\,d^3-341\,a^2\,b^3\,c^3\,d^2+162\,a\,b^4\,c^4\,d-27\,b^5\,c^5\right)}{3\,c}\right)\,{\left(-\frac{a\,{\left(3\,a\,d-4\,b\,c\right)}^3}{c^6}\right)}^{1/3}}{9}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{27\,a^4\,d^3-108\,a^3\,b\,c\,d^2+144\,a^2\,b^2\,c^2\,d-64\,a\,b^3\,c^3}{729\,c^6}\right)}^{1/3}-\frac{a\,{\left(b\,x^3+a\right)}^{1/3}}{3\,c\,x^3}","Not used",1,"log(c^2*(-(a*(3*a*d - 4*b*c)^3)/c^6)^(1/3) + 3*a*d*(a + b*x^3)^(1/3) - 4*b*c*(a + b*x^3)^(1/3))*(-(27*a^4*d^3 - 64*a*b^3*c^3 + 144*a^2*b^2*c^2*d - 108*a^3*b*c*d^2)/(729*c^6))^(1/3) + log(((((81*a*b^4*c^4*d^3*(2*a^2*d^2 + b^2*c^2 - 3*a*b*c*d)*((a*d - b*c)^4/(c^6*d))^(1/3) - 108*a*b^5*c^3*d^3*(a + b*x^3)^(1/3)*(a*d - b*c)^2)*((a*d - b*c)^4/(c^6*d))^(2/3))/9 + (a*b^5*d^2*(27*a^5*d^5 - 27*b^5*c^5 - 341*a^2*b^3*c^3*d^2 + 332*a^3*b^2*c^2*d^3 + 162*a*b^4*c^4*d - 153*a^4*b*c*d^4))/(3*c))*((a*d - b*c)^4/(c^6*d))^(1/3))/3 - (a*b^4*d^2*(a + b*x^3)^(1/3)*(a*d - b*c)^2*(54*a^5*d^5 - 36*b^5*c^5 - 388*a^2*b^3*c^3*d^2 + 450*a^3*b^2*c^2*d^3 + 171*a*b^4*c^4*d - 252*a^4*b*c*d^4))/(9*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)/(27*c^6*d))^(1/3) + log((((3^(1/2)*1i)/2 - 1/2)*((((3^(1/2)*1i)/2 + 1/2)*(108*a*b^5*c^3*d^3*(a + b*x^3)^(1/3)*(a*d - b*c)^2 - 81*a*b^4*c^4*d^3*((3^(1/2)*1i)/2 - 1/2)*(2*a^2*d^2 + b^2*c^2 - 3*a*b*c*d)*((a*d - b*c)^4/(c^6*d))^(1/3))*((a*d - b*c)^4/(c^6*d))^(2/3))/9 + (a*b^5*d^2*(27*a^5*d^5 - 27*b^5*c^5 - 341*a^2*b^3*c^3*d^2 + 332*a^3*b^2*c^2*d^3 + 162*a*b^4*c^4*d - 153*a^4*b*c*d^4))/(3*c))*((a*d - b*c)^4/(c^6*d))^(1/3))/3 - (a*b^4*d^2*(a + b*x^3)^(1/3)*(a*d - b*c)^2*(54*a^5*d^5 - 36*b^5*c^5 - 388*a^2*b^3*c^3*d^2 + 450*a^3*b^2*c^2*d^3 + 171*a*b^4*c^4*d - 252*a^4*b*c*d^4))/(9*c^4))*((3^(1/2)*1i)/2 - 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)/(27*c^6*d))^(1/3) - log((a*b^4*d^2*(a + b*x^3)^(1/3)*(a*d - b*c)^2*(54*a^5*d^5 - 36*b^5*c^5 - 388*a^2*b^3*c^3*d^2 + 450*a^3*b^2*c^2*d^3 + 171*a*b^4*c^4*d - 252*a^4*b*c*d^4))/(9*c^4) - (((3^(1/2)*1i)/2 + 1/2)*((((3^(1/2)*1i)/2 - 1/2)*(108*a*b^5*c^3*d^3*(a + b*x^3)^(1/3)*(a*d - b*c)^2 + 81*a*b^4*c^4*d^3*((3^(1/2)*1i)/2 + 1/2)*(2*a^2*d^2 + b^2*c^2 - 3*a*b*c*d)*((a*d - b*c)^4/(c^6*d))^(1/3))*((a*d - b*c)^4/(c^6*d))^(2/3))/9 - (a*b^5*d^2*(27*a^5*d^5 - 27*b^5*c^5 - 341*a^2*b^3*c^3*d^2 + 332*a^3*b^2*c^2*d^3 + 162*a*b^4*c^4*d - 153*a^4*b*c*d^4))/(3*c))*((a*d - b*c)^4/(c^6*d))^(1/3))/3)*((3^(1/2)*1i)/2 + 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)/(27*c^6*d))^(1/3) + log((a*b^4*d^2*(a + b*x^3)^(1/3)*(a*d - b*c)^2*(54*a^5*d^5 - 36*b^5*c^5 - 388*a^2*b^3*c^3*d^2 + 450*a^3*b^2*c^2*d^3 + 171*a*b^4*c^4*d - 252*a^4*b*c*d^4))/(9*c^4) - (((3^(1/2)*1i)/2 - 1/2)*((((3^(1/2)*1i)/2 + 1/2)*(108*a*b^5*c^3*d^3*(a + b*x^3)^(1/3)*(a*d - b*c)^2 - 27*a*b^4*c^4*d^3*((3^(1/2)*1i)/2 - 1/2)*(2*a^2*d^2 + b^2*c^2 - 3*a*b*c*d)*(-(a*(3*a*d - 4*b*c)^3)/c^6)^(1/3))*(-(a*(3*a*d - 4*b*c)^3)/c^6)^(2/3))/81 + (a*b^5*d^2*(27*a^5*d^5 - 27*b^5*c^5 - 341*a^2*b^3*c^3*d^2 + 332*a^3*b^2*c^2*d^3 + 162*a*b^4*c^4*d - 153*a^4*b*c*d^4))/(3*c))*(-(a*(3*a*d - 4*b*c)^3)/c^6)^(1/3))/9)*((3^(1/2)*1i)/2 - 1/2)*(-(27*a^4*d^3 - 64*a*b^3*c^3 + 144*a^2*b^2*c^2*d - 108*a^3*b*c*d^2)/(729*c^6))^(1/3) - log((a*b^4*d^2*(a + b*x^3)^(1/3)*(a*d - b*c)^2*(54*a^5*d^5 - 36*b^5*c^5 - 388*a^2*b^3*c^3*d^2 + 450*a^3*b^2*c^2*d^3 + 171*a*b^4*c^4*d - 252*a^4*b*c*d^4))/(9*c^4) - (((3^(1/2)*1i)/2 + 1/2)*((((3^(1/2)*1i)/2 - 1/2)*(108*a*b^5*c^3*d^3*(a + b*x^3)^(1/3)*(a*d - b*c)^2 + 27*a*b^4*c^4*d^3*((3^(1/2)*1i)/2 + 1/2)*(2*a^2*d^2 + b^2*c^2 - 3*a*b*c*d)*(-(a*(3*a*d - 4*b*c)^3)/c^6)^(1/3))*(-(a*(3*a*d - 4*b*c)^3)/c^6)^(2/3))/81 - (a*b^5*d^2*(27*a^5*d^5 - 27*b^5*c^5 - 341*a^2*b^3*c^3*d^2 + 332*a^3*b^2*c^2*d^3 + 162*a*b^4*c^4*d - 153*a^4*b*c*d^4))/(3*c))*(-(a*(3*a*d - 4*b*c)^3)/c^6)^(1/3))/9)*((3^(1/2)*1i)/2 + 1/2)*(-(27*a^4*d^3 - 64*a*b^3*c^3 + 144*a^2*b^2*c^2*d - 108*a^3*b*c*d^2)/(729*c^6))^(1/3) - (a*(a + b*x^3)^(1/3))/(3*c*x^3)","B"
701,1,2841,440,13.254005,"\text{Not used}","int((a + b*x^3)^(4/3)/(x^7*(c + d*x^3)),x)","\ln\left(\frac{\left(\frac{\left(18\,b^5\,c^2\,d^3\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(a\,d-b\,c\right)}^2\,\left(6\,a\,d-b\,c\right)+9\,a\,b^4\,c^4\,d^3\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)\,{\left(\frac{{\left(9\,a^2\,d^2-12\,a\,b\,c\,d+2\,b^2\,c^2\right)}^3}{a^2\,c^9}\right)}^{1/3}\right)\,{\left(\frac{{\left(9\,a^2\,d^2-12\,a\,b\,c\,d+2\,b^2\,c^2\right)}^3}{a^2\,c^9}\right)}^{2/3}}{729}+\frac{b^5\,d^4\,\left(-729\,a^6\,d^6+3645\,a^5\,b\,c\,d^5-7182\,a^4\,b^2\,c^2\,d^4+6939\,a^3\,b^3\,c^3\,d^3-3258\,a^2\,b^4\,c^4\,d^2+577\,a\,b^5\,c^5\,d+8\,b^6\,c^6\right)}{81\,c^4}\right)\,{\left(\frac{{\left(9\,a^2\,d^2-12\,a\,b\,c\,d+2\,b^2\,c^2\right)}^3}{a^2\,c^9}\right)}^{1/3}}{27}-\frac{b^4\,d^5\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(a\,d-b\,c\right)}^2\,\left(1458\,a^6\,d^6-6804\,a^5\,b\,c\,d^5+12798\,a^4\,b^2\,c^2\,d^4-12420\,a^3\,b^3\,c^3\,d^3+6561\,a^2\,b^4\,c^4\,d^2-1764\,a\,b^5\,c^5\,d+170\,b^6\,c^6\right)}{243\,c^8}\right)\,{\left(\frac{729\,a^6\,d^6-2916\,a^5\,b\,c\,d^5+4374\,a^4\,b^2\,c^2\,d^4-3024\,a^3\,b^3\,c^3\,d^3+972\,a^2\,b^4\,c^4\,d^2-144\,a\,b^5\,c^5\,d+8\,b^6\,c^6}{19683\,a^2\,c^9}\right)}^{1/3}+\ln\left(\frac{\left(\frac{\left(18\,b^5\,c^2\,d^3\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(a\,d-b\,c\right)}^2\,\left(6\,a\,d-b\,c\right)+81\,a\,b^4\,c^4\,d^3\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)\,{\left(-\frac{d^2\,{\left(a\,d-b\,c\right)}^4}{c^9}\right)}^{1/3}\right)\,{\left(-\frac{d^2\,{\left(a\,d-b\,c\right)}^4}{c^9}\right)}^{2/3}}{9}+\frac{b^5\,d^4\,\left(-729\,a^6\,d^6+3645\,a^5\,b\,c\,d^5-7182\,a^4\,b^2\,c^2\,d^4+6939\,a^3\,b^3\,c^3\,d^3-3258\,a^2\,b^4\,c^4\,d^2+577\,a\,b^5\,c^5\,d+8\,b^6\,c^6\right)}{81\,c^4}\right)\,{\left(-\frac{d^2\,{\left(a\,d-b\,c\right)}^4}{c^9}\right)}^{1/3}}{3}-\frac{b^4\,d^5\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(a\,d-b\,c\right)}^2\,\left(1458\,a^6\,d^6-6804\,a^5\,b\,c\,d^5+12798\,a^4\,b^2\,c^2\,d^4-12420\,a^3\,b^3\,c^3\,d^3+6561\,a^2\,b^4\,c^4\,d^2-1764\,a\,b^5\,c^5\,d+170\,b^6\,c^6\right)}{243\,c^8}\right)\,{\left(-\frac{a^4\,d^6-4\,a^3\,b\,c\,d^5+6\,a^2\,b^2\,c^2\,d^4-4\,a\,b^3\,c^3\,d^3+b^4\,c^4\,d^2}{27\,c^9}\right)}^{1/3}+\frac{\frac{\left(2\,a\,b^2\,c-3\,a^2\,b\,d\right)\,{\left(b\,x^3+a\right)}^{1/3}}{9\,c^2}+\frac{b\,{\left(b\,x^3+a\right)}^{4/3}\,\left(6\,a\,d-7\,b\,c\right)}{18\,c^2}}{{\left(b\,x^3+a\right)}^2-2\,a\,\left(b\,x^3+a\right)+a^2}+\ln\left(\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(18\,b^5\,c^2\,d^3\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(a\,d-b\,c\right)}^2\,\left(6\,a\,d-b\,c\right)+81\,a\,b^4\,c^4\,d^3\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)\,{\left(-\frac{d^2\,{\left(a\,d-b\,c\right)}^4}{c^9}\right)}^{1/3}\right)\,{\left(-\frac{d^2\,{\left(a\,d-b\,c\right)}^4}{c^9}\right)}^{2/3}}{9}-\frac{b^5\,d^4\,\left(-729\,a^6\,d^6+3645\,a^5\,b\,c\,d^5-7182\,a^4\,b^2\,c^2\,d^4+6939\,a^3\,b^3\,c^3\,d^3-3258\,a^2\,b^4\,c^4\,d^2+577\,a\,b^5\,c^5\,d+8\,b^6\,c^6\right)}{81\,c^4}\right)\,{\left(-\frac{d^2\,{\left(a\,d-b\,c\right)}^4}{c^9}\right)}^{1/3}}{3}+\frac{b^4\,d^5\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(a\,d-b\,c\right)}^2\,\left(1458\,a^6\,d^6-6804\,a^5\,b\,c\,d^5+12798\,a^4\,b^2\,c^2\,d^4-12420\,a^3\,b^3\,c^3\,d^3+6561\,a^2\,b^4\,c^4\,d^2-1764\,a\,b^5\,c^5\,d+170\,b^6\,c^6\right)}{243\,c^8}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{a^4\,d^6-4\,a^3\,b\,c\,d^5+6\,a^2\,b^2\,c^2\,d^4-4\,a\,b^3\,c^3\,d^3+b^4\,c^4\,d^2}{27\,c^9}\right)}^{1/3}-\ln\left(\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(18\,b^5\,c^2\,d^3\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(a\,d-b\,c\right)}^2\,\left(6\,a\,d-b\,c\right)-81\,a\,b^4\,c^4\,d^3\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)\,{\left(-\frac{d^2\,{\left(a\,d-b\,c\right)}^4}{c^9}\right)}^{1/3}\right)\,{\left(-\frac{d^2\,{\left(a\,d-b\,c\right)}^4}{c^9}\right)}^{2/3}}{9}+\frac{b^5\,d^4\,\left(-729\,a^6\,d^6+3645\,a^5\,b\,c\,d^5-7182\,a^4\,b^2\,c^2\,d^4+6939\,a^3\,b^3\,c^3\,d^3-3258\,a^2\,b^4\,c^4\,d^2+577\,a\,b^5\,c^5\,d+8\,b^6\,c^6\right)}{81\,c^4}\right)\,{\left(-\frac{d^2\,{\left(a\,d-b\,c\right)}^4}{c^9}\right)}^{1/3}}{3}+\frac{b^4\,d^5\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(a\,d-b\,c\right)}^2\,\left(1458\,a^6\,d^6-6804\,a^5\,b\,c\,d^5+12798\,a^4\,b^2\,c^2\,d^4-12420\,a^3\,b^3\,c^3\,d^3+6561\,a^2\,b^4\,c^4\,d^2-1764\,a\,b^5\,c^5\,d+170\,b^6\,c^6\right)}{243\,c^8}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{a^4\,d^6-4\,a^3\,b\,c\,d^5+6\,a^2\,b^2\,c^2\,d^4-4\,a\,b^3\,c^3\,d^3+b^4\,c^4\,d^2}{27\,c^9}\right)}^{1/3}+\ln\left(\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(18\,b^5\,c^2\,d^3\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(a\,d-b\,c\right)}^2\,\left(6\,a\,d-b\,c\right)+9\,a\,b^4\,c^4\,d^3\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)\,{\left(\frac{{\left(9\,a^2\,d^2-12\,a\,b\,c\,d+2\,b^2\,c^2\right)}^3}{a^2\,c^9}\right)}^{1/3}\right)\,{\left(\frac{{\left(9\,a^2\,d^2-12\,a\,b\,c\,d+2\,b^2\,c^2\right)}^3}{a^2\,c^9}\right)}^{2/3}}{729}-\frac{b^5\,d^4\,\left(-729\,a^6\,d^6+3645\,a^5\,b\,c\,d^5-7182\,a^4\,b^2\,c^2\,d^4+6939\,a^3\,b^3\,c^3\,d^3-3258\,a^2\,b^4\,c^4\,d^2+577\,a\,b^5\,c^5\,d+8\,b^6\,c^6\right)}{81\,c^4}\right)\,{\left(\frac{{\left(9\,a^2\,d^2-12\,a\,b\,c\,d+2\,b^2\,c^2\right)}^3}{a^2\,c^9}\right)}^{1/3}}{27}+\frac{b^4\,d^5\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(a\,d-b\,c\right)}^2\,\left(1458\,a^6\,d^6-6804\,a^5\,b\,c\,d^5+12798\,a^4\,b^2\,c^2\,d^4-12420\,a^3\,b^3\,c^3\,d^3+6561\,a^2\,b^4\,c^4\,d^2-1764\,a\,b^5\,c^5\,d+170\,b^6\,c^6\right)}{243\,c^8}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(\frac{729\,a^6\,d^6-2916\,a^5\,b\,c\,d^5+4374\,a^4\,b^2\,c^2\,d^4-3024\,a^3\,b^3\,c^3\,d^3+972\,a^2\,b^4\,c^4\,d^2-144\,a\,b^5\,c^5\,d+8\,b^6\,c^6}{19683\,a^2\,c^9}\right)}^{1/3}-\ln\left(\frac{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(\frac{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(18\,b^5\,c^2\,d^3\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(a\,d-b\,c\right)}^2\,\left(6\,a\,d-b\,c\right)-9\,a\,b^4\,c^4\,d^3\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)\,{\left(\frac{{\left(9\,a^2\,d^2-12\,a\,b\,c\,d+2\,b^2\,c^2\right)}^3}{a^2\,c^9}\right)}^{1/3}\right)\,{\left(\frac{{\left(9\,a^2\,d^2-12\,a\,b\,c\,d+2\,b^2\,c^2\right)}^3}{a^2\,c^9}\right)}^{2/3}}{729}+\frac{b^5\,d^4\,\left(-729\,a^6\,d^6+3645\,a^5\,b\,c\,d^5-7182\,a^4\,b^2\,c^2\,d^4+6939\,a^3\,b^3\,c^3\,d^3-3258\,a^2\,b^4\,c^4\,d^2+577\,a\,b^5\,c^5\,d+8\,b^6\,c^6\right)}{81\,c^4}\right)\,{\left(\frac{{\left(9\,a^2\,d^2-12\,a\,b\,c\,d+2\,b^2\,c^2\right)}^3}{a^2\,c^9}\right)}^{1/3}}{27}+\frac{b^4\,d^5\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(a\,d-b\,c\right)}^2\,\left(1458\,a^6\,d^6-6804\,a^5\,b\,c\,d^5+12798\,a^4\,b^2\,c^2\,d^4-12420\,a^3\,b^3\,c^3\,d^3+6561\,a^2\,b^4\,c^4\,d^2-1764\,a\,b^5\,c^5\,d+170\,b^6\,c^6\right)}{243\,c^8}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(\frac{729\,a^6\,d^6-2916\,a^5\,b\,c\,d^5+4374\,a^4\,b^2\,c^2\,d^4-3024\,a^3\,b^3\,c^3\,d^3+972\,a^2\,b^4\,c^4\,d^2-144\,a\,b^5\,c^5\,d+8\,b^6\,c^6}{19683\,a^2\,c^9}\right)}^{1/3}","Not used",1,"log(((((18*b^5*c^2*d^3*(a + b*x^3)^(1/3)*(a*d - b*c)^2*(6*a*d - b*c) + 9*a*b^4*c^4*d^3*(2*a^2*d^2 + b^2*c^2 - 3*a*b*c*d)*((9*a^2*d^2 + 2*b^2*c^2 - 12*a*b*c*d)^3/(a^2*c^9))^(1/3))*((9*a^2*d^2 + 2*b^2*c^2 - 12*a*b*c*d)^3/(a^2*c^9))^(2/3))/729 + (b^5*d^4*(8*b^6*c^6 - 729*a^6*d^6 - 3258*a^2*b^4*c^4*d^2 + 6939*a^3*b^3*c^3*d^3 - 7182*a^4*b^2*c^2*d^4 + 577*a*b^5*c^5*d + 3645*a^5*b*c*d^5))/(81*c^4))*((9*a^2*d^2 + 2*b^2*c^2 - 12*a*b*c*d)^3/(a^2*c^9))^(1/3))/27 - (b^4*d^5*(a + b*x^3)^(1/3)*(a*d - b*c)^2*(1458*a^6*d^6 + 170*b^6*c^6 + 6561*a^2*b^4*c^4*d^2 - 12420*a^3*b^3*c^3*d^3 + 12798*a^4*b^2*c^2*d^4 - 1764*a*b^5*c^5*d - 6804*a^5*b*c*d^5))/(243*c^8))*((729*a^6*d^6 + 8*b^6*c^6 + 972*a^2*b^4*c^4*d^2 - 3024*a^3*b^3*c^3*d^3 + 4374*a^4*b^2*c^2*d^4 - 144*a*b^5*c^5*d - 2916*a^5*b*c*d^5)/(19683*a^2*c^9))^(1/3) + log(((((18*b^5*c^2*d^3*(a + b*x^3)^(1/3)*(a*d - b*c)^2*(6*a*d - b*c) + 81*a*b^4*c^4*d^3*(2*a^2*d^2 + b^2*c^2 - 3*a*b*c*d)*(-(d^2*(a*d - b*c)^4)/c^9)^(1/3))*(-(d^2*(a*d - b*c)^4)/c^9)^(2/3))/9 + (b^5*d^4*(8*b^6*c^6 - 729*a^6*d^6 - 3258*a^2*b^4*c^4*d^2 + 6939*a^3*b^3*c^3*d^3 - 7182*a^4*b^2*c^2*d^4 + 577*a*b^5*c^5*d + 3645*a^5*b*c*d^5))/(81*c^4))*(-(d^2*(a*d - b*c)^4)/c^9)^(1/3))/3 - (b^4*d^5*(a + b*x^3)^(1/3)*(a*d - b*c)^2*(1458*a^6*d^6 + 170*b^6*c^6 + 6561*a^2*b^4*c^4*d^2 - 12420*a^3*b^3*c^3*d^3 + 12798*a^4*b^2*c^2*d^4 - 1764*a*b^5*c^5*d - 6804*a^5*b*c*d^5))/(243*c^8))*(-(a^4*d^6 + b^4*c^4*d^2 - 4*a*b^3*c^3*d^3 + 6*a^2*b^2*c^2*d^4 - 4*a^3*b*c*d^5)/(27*c^9))^(1/3) + (((2*a*b^2*c - 3*a^2*b*d)*(a + b*x^3)^(1/3))/(9*c^2) + (b*(a + b*x^3)^(4/3)*(6*a*d - 7*b*c))/(18*c^2))/((a + b*x^3)^2 - 2*a*(a + b*x^3) + a^2) + log((((3^(1/2)*1i)/2 - 1/2)*((((3^(1/2)*1i)/2 + 1/2)*(18*b^5*c^2*d^3*(a + b*x^3)^(1/3)*(a*d - b*c)^2*(6*a*d - b*c) + 81*a*b^4*c^4*d^3*((3^(1/2)*1i)/2 - 1/2)*(2*a^2*d^2 + b^2*c^2 - 3*a*b*c*d)*(-(d^2*(a*d - b*c)^4)/c^9)^(1/3))*(-(d^2*(a*d - b*c)^4)/c^9)^(2/3))/9 - (b^5*d^4*(8*b^6*c^6 - 729*a^6*d^6 - 3258*a^2*b^4*c^4*d^2 + 6939*a^3*b^3*c^3*d^3 - 7182*a^4*b^2*c^2*d^4 + 577*a*b^5*c^5*d + 3645*a^5*b*c*d^5))/(81*c^4))*(-(d^2*(a*d - b*c)^4)/c^9)^(1/3))/3 + (b^4*d^5*(a + b*x^3)^(1/3)*(a*d - b*c)^2*(1458*a^6*d^6 + 170*b^6*c^6 + 6561*a^2*b^4*c^4*d^2 - 12420*a^3*b^3*c^3*d^3 + 12798*a^4*b^2*c^2*d^4 - 1764*a*b^5*c^5*d - 6804*a^5*b*c*d^5))/(243*c^8))*((3^(1/2)*1i)/2 - 1/2)*(-(a^4*d^6 + b^4*c^4*d^2 - 4*a*b^3*c^3*d^3 + 6*a^2*b^2*c^2*d^4 - 4*a^3*b*c*d^5)/(27*c^9))^(1/3) - log((((3^(1/2)*1i)/2 + 1/2)*((((3^(1/2)*1i)/2 - 1/2)*(18*b^5*c^2*d^3*(a + b*x^3)^(1/3)*(a*d - b*c)^2*(6*a*d - b*c) - 81*a*b^4*c^4*d^3*((3^(1/2)*1i)/2 + 1/2)*(2*a^2*d^2 + b^2*c^2 - 3*a*b*c*d)*(-(d^2*(a*d - b*c)^4)/c^9)^(1/3))*(-(d^2*(a*d - b*c)^4)/c^9)^(2/3))/9 + (b^5*d^4*(8*b^6*c^6 - 729*a^6*d^6 - 3258*a^2*b^4*c^4*d^2 + 6939*a^3*b^3*c^3*d^3 - 7182*a^4*b^2*c^2*d^4 + 577*a*b^5*c^5*d + 3645*a^5*b*c*d^5))/(81*c^4))*(-(d^2*(a*d - b*c)^4)/c^9)^(1/3))/3 + (b^4*d^5*(a + b*x^3)^(1/3)*(a*d - b*c)^2*(1458*a^6*d^6 + 170*b^6*c^6 + 6561*a^2*b^4*c^4*d^2 - 12420*a^3*b^3*c^3*d^3 + 12798*a^4*b^2*c^2*d^4 - 1764*a*b^5*c^5*d - 6804*a^5*b*c*d^5))/(243*c^8))*((3^(1/2)*1i)/2 + 1/2)*(-(a^4*d^6 + b^4*c^4*d^2 - 4*a*b^3*c^3*d^3 + 6*a^2*b^2*c^2*d^4 - 4*a^3*b*c*d^5)/(27*c^9))^(1/3) + log((((3^(1/2)*1i)/2 - 1/2)*((((3^(1/2)*1i)/2 + 1/2)*(18*b^5*c^2*d^3*(a + b*x^3)^(1/3)*(a*d - b*c)^2*(6*a*d - b*c) + 9*a*b^4*c^4*d^3*((3^(1/2)*1i)/2 - 1/2)*(2*a^2*d^2 + b^2*c^2 - 3*a*b*c*d)*((9*a^2*d^2 + 2*b^2*c^2 - 12*a*b*c*d)^3/(a^2*c^9))^(1/3))*((9*a^2*d^2 + 2*b^2*c^2 - 12*a*b*c*d)^3/(a^2*c^9))^(2/3))/729 - (b^5*d^4*(8*b^6*c^6 - 729*a^6*d^6 - 3258*a^2*b^4*c^4*d^2 + 6939*a^3*b^3*c^3*d^3 - 7182*a^4*b^2*c^2*d^4 + 577*a*b^5*c^5*d + 3645*a^5*b*c*d^5))/(81*c^4))*((9*a^2*d^2 + 2*b^2*c^2 - 12*a*b*c*d)^3/(a^2*c^9))^(1/3))/27 + (b^4*d^5*(a + b*x^3)^(1/3)*(a*d - b*c)^2*(1458*a^6*d^6 + 170*b^6*c^6 + 6561*a^2*b^4*c^4*d^2 - 12420*a^3*b^3*c^3*d^3 + 12798*a^4*b^2*c^2*d^4 - 1764*a*b^5*c^5*d - 6804*a^5*b*c*d^5))/(243*c^8))*((3^(1/2)*1i)/2 - 1/2)*((729*a^6*d^6 + 8*b^6*c^6 + 972*a^2*b^4*c^4*d^2 - 3024*a^3*b^3*c^3*d^3 + 4374*a^4*b^2*c^2*d^4 - 144*a*b^5*c^5*d - 2916*a^5*b*c*d^5)/(19683*a^2*c^9))^(1/3) - log((((3^(1/2)*1i)/2 + 1/2)*((((3^(1/2)*1i)/2 - 1/2)*(18*b^5*c^2*d^3*(a + b*x^3)^(1/3)*(a*d - b*c)^2*(6*a*d - b*c) - 9*a*b^4*c^4*d^3*((3^(1/2)*1i)/2 + 1/2)*(2*a^2*d^2 + b^2*c^2 - 3*a*b*c*d)*((9*a^2*d^2 + 2*b^2*c^2 - 12*a*b*c*d)^3/(a^2*c^9))^(1/3))*((9*a^2*d^2 + 2*b^2*c^2 - 12*a*b*c*d)^3/(a^2*c^9))^(2/3))/729 + (b^5*d^4*(8*b^6*c^6 - 729*a^6*d^6 - 3258*a^2*b^4*c^4*d^2 + 6939*a^3*b^3*c^3*d^3 - 7182*a^4*b^2*c^2*d^4 + 577*a*b^5*c^5*d + 3645*a^5*b*c*d^5))/(81*c^4))*((9*a^2*d^2 + 2*b^2*c^2 - 12*a*b*c*d)^3/(a^2*c^9))^(1/3))/27 + (b^4*d^5*(a + b*x^3)^(1/3)*(a*d - b*c)^2*(1458*a^6*d^6 + 170*b^6*c^6 + 6561*a^2*b^4*c^4*d^2 - 12420*a^3*b^3*c^3*d^3 + 12798*a^4*b^2*c^2*d^4 - 1764*a*b^5*c^5*d - 6804*a^5*b*c*d^5))/(243*c^8))*((3^(1/2)*1i)/2 + 1/2)*((729*a^6*d^6 + 8*b^6*c^6 + 972*a^2*b^4*c^4*d^2 - 3024*a^3*b^3*c^3*d^3 + 4374*a^4*b^2*c^2*d^4 - 144*a*b^5*c^5*d - 2916*a^5*b*c*d^5)/(19683*a^2*c^9))^(1/3)","B"
702,0,-1,334,0.000000,"\text{Not used}","int((x^4*(a + b*x^3)^(4/3))/(c + d*x^3),x)","\int \frac{x^4\,{\left(b\,x^3+a\right)}^{4/3}}{d\,x^3+c} \,d x","Not used",1,"int((x^4*(a + b*x^3)^(4/3))/(c + d*x^3), x)","F"
703,0,-1,277,0.000000,"\text{Not used}","int((x*(a + b*x^3)^(4/3))/(c + d*x^3),x)","\int \frac{x\,{\left(b\,x^3+a\right)}^{4/3}}{d\,x^3+c} \,d x","Not used",1,"int((x*(a + b*x^3)^(4/3))/(c + d*x^3), x)","F"
704,0,-1,254,0.000000,"\text{Not used}","int((a + b*x^3)^(4/3)/(x^2*(c + d*x^3)),x)","\int \frac{{\left(b\,x^3+a\right)}^{4/3}}{x^2\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int((a + b*x^3)^(4/3)/(x^2*(c + d*x^3)), x)","F"
705,0,-1,201,0.000000,"\text{Not used}","int((a + b*x^3)^(4/3)/(x^5*(c + d*x^3)),x)","\int \frac{{\left(b\,x^3+a\right)}^{4/3}}{x^5\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int((a + b*x^3)^(4/3)/(x^5*(c + d*x^3)), x)","F"
706,0,-1,250,0.000000,"\text{Not used}","int((a + b*x^3)^(4/3)/(x^8*(c + d*x^3)),x)","\int \frac{{\left(b\,x^3+a\right)}^{4/3}}{x^8\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int((a + b*x^3)^(4/3)/(x^8*(c + d*x^3)), x)","F"
707,0,-1,318,0.000000,"\text{Not used}","int((a + b*x^3)^(4/3)/(x^11*(c + d*x^3)),x)","\int \frac{{\left(b\,x^3+a\right)}^{4/3}}{x^{11}\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int((a + b*x^3)^(4/3)/(x^11*(c + d*x^3)), x)","F"
708,0,-1,392,0.000000,"\text{Not used}","int((a + b*x^3)^(4/3)/(x^14*(c + d*x^3)),x)","\int \frac{{\left(b\,x^3+a\right)}^{4/3}}{x^{14}\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int((a + b*x^3)^(4/3)/(x^14*(c + d*x^3)), x)","F"
709,0,-1,65,0.000000,"\text{Not used}","int((x^6*(a + b*x^3)^(4/3))/(c + d*x^3),x)","\int \frac{x^6\,{\left(b\,x^3+a\right)}^{4/3}}{d\,x^3+c} \,d x","Not used",1,"int((x^6*(a + b*x^3)^(4/3))/(c + d*x^3), x)","F"
710,0,-1,65,0.000000,"\text{Not used}","int((x^3*(a + b*x^3)^(4/3))/(c + d*x^3),x)","\int \frac{x^3\,{\left(b\,x^3+a\right)}^{4/3}}{d\,x^3+c} \,d x","Not used",1,"int((x^3*(a + b*x^3)^(4/3))/(c + d*x^3), x)","F"
711,0,-1,60,0.000000,"\text{Not used}","int((a + b*x^3)^(4/3)/(c + d*x^3),x)","\int \frac{{\left(b\,x^3+a\right)}^{4/3}}{d\,x^3+c} \,d x","Not used",1,"int((a + b*x^3)^(4/3)/(c + d*x^3), x)","F"
712,0,-1,65,0.000000,"\text{Not used}","int((a + b*x^3)^(4/3)/(x^3*(c + d*x^3)),x)","\int \frac{{\left(b\,x^3+a\right)}^{4/3}}{x^3\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int((a + b*x^3)^(4/3)/(x^3*(c + d*x^3)), x)","F"
713,0,-1,65,0.000000,"\text{Not used}","int((a + b*x^3)^(4/3)/(x^6*(c + d*x^3)),x)","\int \frac{{\left(b\,x^3+a\right)}^{4/3}}{x^6\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int((a + b*x^3)^(4/3)/(x^6*(c + d*x^3)), x)","F"
714,1,438,290,5.114652,"\text{Not used}","int(x^14/((a + b*x^3)^(1/3)*(c + d*x^3)),x)","\left(\frac{6\,a^2}{5\,b^4\,d}+\frac{\left(\frac{4\,a}{b^4\,d}+\frac{b^5\,c-a\,b^4\,d}{b^8\,d^2}\right)\,\left(b^5\,c-a\,b^4\,d\right)}{5\,b^4\,d}\right)\,{\left(b\,x^3+a\right)}^{5/3}-\left(\frac{a}{2\,b^4\,d}+\frac{b^5\,c-a\,b^4\,d}{8\,b^8\,d^2}\right)\,{\left(b\,x^3+a\right)}^{8/3}-{\left(b\,x^3+a\right)}^{2/3}\,\left(\frac{2\,a^3}{b^4\,d}+\frac{\left(\frac{6\,a^2}{b^4\,d}+\frac{\left(\frac{4\,a}{b^4\,d}+\frac{b^5\,c-a\,b^4\,d}{b^8\,d^2}\right)\,\left(b^5\,c-a\,b^4\,d\right)}{b^4\,d}\right)\,\left(b^5\,c-a\,b^4\,d\right)}{2\,b^4\,d}\right)+\frac{{\left(b\,x^3+a\right)}^{11/3}}{11\,b^4\,d}+\frac{c^4\,\ln\left(\frac{c^8\,{\left(b\,x^3+a\right)}^{1/3}}{d^7}-\frac{c^8\,{\left(a\,d-b\,c\right)}^{1/3}}{d^{22/3}}\right)}{3\,d^{14/3}\,{\left(a\,d-b\,c\right)}^{1/3}}-\frac{\ln\left(\frac{c^8\,{\left(b\,x^3+a\right)}^{1/3}}{d^7}-\frac{c^8\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,{\left(a\,d-b\,c\right)}^{1/3}}{4\,d^{22/3}}\right)\,\left(c^4+\sqrt{3}\,c^4\,1{}\mathrm{i}\right)}{6\,d^{14/3}\,{\left(a\,d-b\,c\right)}^{1/3}}+\frac{c^4\,\ln\left(\frac{c^8\,{\left(b\,x^3+a\right)}^{1/3}}{d^7}-\frac{c^8\,{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,{\left(a\,d-b\,c\right)}^{1/3}}{4\,d^{22/3}}\right)\,\left(-\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)}{d^{14/3}\,{\left(a\,d-b\,c\right)}^{1/3}}","Not used",1,"((6*a^2)/(5*b^4*d) + (((4*a)/(b^4*d) + (b^5*c - a*b^4*d)/(b^8*d^2))*(b^5*c - a*b^4*d))/(5*b^4*d))*(a + b*x^3)^(5/3) - (a/(2*b^4*d) + (b^5*c - a*b^4*d)/(8*b^8*d^2))*(a + b*x^3)^(8/3) - (a + b*x^3)^(2/3)*((2*a^3)/(b^4*d) + (((6*a^2)/(b^4*d) + (((4*a)/(b^4*d) + (b^5*c - a*b^4*d)/(b^8*d^2))*(b^5*c - a*b^4*d))/(b^4*d))*(b^5*c - a*b^4*d))/(2*b^4*d)) + (a + b*x^3)^(11/3)/(11*b^4*d) + (c^4*log((c^8*(a + b*x^3)^(1/3))/d^7 - (c^8*(a*d - b*c)^(1/3))/d^(22/3)))/(3*d^(14/3)*(a*d - b*c)^(1/3)) - (log((c^8*(a + b*x^3)^(1/3))/d^7 - (c^8*(3^(1/2)*1i + 1)^2*(a*d - b*c)^(1/3))/(4*d^(22/3)))*(3^(1/2)*c^4*1i + c^4))/(6*d^(14/3)*(a*d - b*c)^(1/3)) + (c^4*log((c^8*(a + b*x^3)^(1/3))/d^7 - (c^8*(3^(1/2)*1i - 1)^2*(a*d - b*c)^(1/3))/(4*d^(22/3)))*((3^(1/2)*1i)/6 - 1/6))/(d^(14/3)*(a*d - b*c)^(1/3))","B"
715,1,339,244,5.090034,"\text{Not used}","int(x^11/((a + b*x^3)^(1/3)*(c + d*x^3)),x)","\left(\frac{3\,a^2}{2\,b^3\,d}+\frac{\left(\frac{3\,a}{b^3\,d}+\frac{b^4\,c-a\,b^3\,d}{b^6\,d^2}\right)\,\left(b^4\,c-a\,b^3\,d\right)}{2\,b^3\,d}\right)\,{\left(b\,x^3+a\right)}^{2/3}-\left(\frac{3\,a}{5\,b^3\,d}+\frac{b^4\,c-a\,b^3\,d}{5\,b^6\,d^2}\right)\,{\left(b\,x^3+a\right)}^{5/3}+\frac{{\left(b\,x^3+a\right)}^{8/3}}{8\,b^3\,d}-\frac{c^3\,\ln\left(\frac{c^6\,{\left(b\,x^3+a\right)}^{1/3}}{d^5}+\frac{b\,c^7-a\,c^6\,d}{d^{16/3}\,{\left(a\,d-b\,c\right)}^{2/3}}\right)}{3\,d^{11/3}\,{\left(a\,d-b\,c\right)}^{1/3}}+\frac{\ln\left(\frac{c^6\,{\left(b\,x^3+a\right)}^{1/3}}{d^5}-\frac{c^6\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,{\left(a\,d-b\,c\right)}^{1/3}}{4\,d^{16/3}}\right)\,\left(c^3+\sqrt{3}\,c^3\,1{}\mathrm{i}\right)}{6\,d^{11/3}\,{\left(a\,d-b\,c\right)}^{1/3}}-\frac{c^3\,\ln\left(\frac{c^6\,{\left(b\,x^3+a\right)}^{1/3}}{d^5}+\frac{c^6\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(a\,d-b\,c\right)}^{1/3}}{d^{16/3}}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}{3\,d^{11/3}\,{\left(a\,d-b\,c\right)}^{1/3}}","Not used",1,"((3*a^2)/(2*b^3*d) + (((3*a)/(b^3*d) + (b^4*c - a*b^3*d)/(b^6*d^2))*(b^4*c - a*b^3*d))/(2*b^3*d))*(a + b*x^3)^(2/3) - ((3*a)/(5*b^3*d) + (b^4*c - a*b^3*d)/(5*b^6*d^2))*(a + b*x^3)^(5/3) + (a + b*x^3)^(8/3)/(8*b^3*d) - (c^3*log((c^6*(a + b*x^3)^(1/3))/d^5 + (b*c^7 - a*c^6*d)/(d^(16/3)*(a*d - b*c)^(2/3))))/(3*d^(11/3)*(a*d - b*c)^(1/3)) + (log((c^6*(a + b*x^3)^(1/3))/d^5 - (c^6*(3^(1/2)*1i + 1)^2*(a*d - b*c)^(1/3))/(4*d^(16/3)))*(3^(1/2)*c^3*1i + c^3))/(6*d^(11/3)*(a*d - b*c)^(1/3)) - (c^3*log((c^6*(a + b*x^3)^(1/3))/d^5 + (c^6*((3^(1/2)*1i)/2 + 1/2)*(a*d - b*c)^(1/3))/d^(16/3))*((3^(1/2)*1i)/2 - 1/2))/(3*d^(11/3)*(a*d - b*c)^(1/3))","B"
716,1,267,203,5.112549,"\text{Not used}","int(x^8/((a + b*x^3)^(1/3)*(c + d*x^3)),x)","\frac{{\left(b\,x^3+a\right)}^{5/3}}{5\,b^2\,d}-\left(\frac{a}{b^2\,d}+\frac{b^3\,c-a\,b^2\,d}{2\,b^4\,d^2}\right)\,{\left(b\,x^3+a\right)}^{2/3}+\frac{c^2\,\ln\left(\frac{c^4\,{\left(b\,x^3+a\right)}^{1/3}}{d^3}+\frac{b\,c^5-a\,c^4\,d}{d^{10/3}\,{\left(a\,d-b\,c\right)}^{2/3}}\right)}{3\,d^{8/3}\,{\left(a\,d-b\,c\right)}^{1/3}}-\frac{\ln\left(\frac{c^4\,{\left(b\,x^3+a\right)}^{1/3}}{d^3}-\frac{c^4\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,{\left(a\,d-b\,c\right)}^{1/3}}{4\,d^{10/3}}\right)\,\left(c^2+\sqrt{3}\,c^2\,1{}\mathrm{i}\right)}{6\,d^{8/3}\,{\left(a\,d-b\,c\right)}^{1/3}}+\frac{c^2\,\ln\left(\frac{c^4\,{\left(b\,x^3+a\right)}^{1/3}}{d^3}-\frac{c^4\,{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,{\left(a\,d-b\,c\right)}^{1/3}}{4\,d^{10/3}}\right)\,\left(-\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)}{d^{8/3}\,{\left(a\,d-b\,c\right)}^{1/3}}","Not used",1,"(a + b*x^3)^(5/3)/(5*b^2*d) - (a/(b^2*d) + (b^3*c - a*b^2*d)/(2*b^4*d^2))*(a + b*x^3)^(2/3) + (c^2*log((c^4*(a + b*x^3)^(1/3))/d^3 + (b*c^5 - a*c^4*d)/(d^(10/3)*(a*d - b*c)^(2/3))))/(3*d^(8/3)*(a*d - b*c)^(1/3)) - (log((c^4*(a + b*x^3)^(1/3))/d^3 - (c^4*(3^(1/2)*1i + 1)^2*(a*d - b*c)^(1/3))/(4*d^(10/3)))*(3^(1/2)*c^2*1i + c^2))/(6*d^(8/3)*(a*d - b*c)^(1/3)) + (c^2*log((c^4*(a + b*x^3)^(1/3))/d^3 - (c^4*(3^(1/2)*1i - 1)^2*(a*d - b*c)^(1/3))/(4*d^(10/3)))*((3^(1/2)*1i)/6 - 1/6))/(d^(8/3)*(a*d - b*c)^(1/3))","B"
717,1,219,168,5.096803,"\text{Not used}","int(x^5/((a + b*x^3)^(1/3)*(c + d*x^3)),x)","\frac{{\left(b\,x^3+a\right)}^{2/3}}{2\,b\,d}+\frac{\ln\left(\frac{c^2\,{\left(b\,x^3+a\right)}^{1/3}}{d}-\frac{c^2\,{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,{\left(a\,d-b\,c\right)}^{1/3}}{4\,d^{4/3}}\right)\,\left(c-\sqrt{3}\,c\,1{}\mathrm{i}\right)}{6\,d^{5/3}\,{\left(a\,d-b\,c\right)}^{1/3}}+\frac{\ln\left(\frac{c^2\,{\left(b\,x^3+a\right)}^{1/3}}{d}-\frac{c^2\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,{\left(a\,d-b\,c\right)}^{1/3}}{4\,d^{4/3}}\right)\,\left(c+\sqrt{3}\,c\,1{}\mathrm{i}\right)}{6\,d^{5/3}\,{\left(a\,d-b\,c\right)}^{1/3}}-\frac{c\,\ln\left(\frac{c^2\,{\left(b\,x^3+a\right)}^{1/3}}{d}+\frac{b\,c^3-a\,c^2\,d}{d^{4/3}\,{\left(a\,d-b\,c\right)}^{2/3}}\right)}{3\,d^{5/3}\,{\left(a\,d-b\,c\right)}^{1/3}}","Not used",1,"(a + b*x^3)^(2/3)/(2*b*d) + (log((c^2*(a + b*x^3)^(1/3))/d - (c^2*(3^(1/2)*1i - 1)^2*(a*d - b*c)^(1/3))/(4*d^(4/3)))*(c - 3^(1/2)*c*1i))/(6*d^(5/3)*(a*d - b*c)^(1/3)) + (log((c^2*(a + b*x^3)^(1/3))/d - (c^2*(3^(1/2)*1i + 1)^2*(a*d - b*c)^(1/3))/(4*d^(4/3)))*(c + 3^(1/2)*c*1i))/(6*d^(5/3)*(a*d - b*c)^(1/3)) - (c*log((c^2*(a + b*x^3)^(1/3))/d + (b*c^3 - a*c^2*d)/(d^(4/3)*(a*d - b*c)^(2/3))))/(3*d^(5/3)*(a*d - b*c)^(1/3))","B"
718,1,208,145,4.933858,"\text{Not used}","int(x^2/((a + b*x^3)^(1/3)*(c + d*x^3)),x)","\frac{\ln\left(d\,{\left(b\,x^3+a\right)}^{1/3}-\frac{9\,a\,d^3-9\,b\,c\,d^2}{9\,d^{4/3}\,{\left(a\,d-b\,c\right)}^{2/3}}\right)}{3\,d^{2/3}\,{\left(a\,d-b\,c\right)}^{1/3}}+\frac{\ln\left(d\,{\left(b\,x^3+a\right)}^{1/3}-\frac{{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(9\,a\,d^3-9\,b\,c\,d^2\right)}{36\,d^{4/3}\,{\left(a\,d-b\,c\right)}^{2/3}}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{6\,d^{2/3}\,{\left(a\,d-b\,c\right)}^{1/3}}-\frac{\ln\left(d\,{\left(b\,x^3+a\right)}^{1/3}-\frac{{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(9\,a\,d^3-9\,b\,c\,d^2\right)}{36\,d^{4/3}\,{\left(a\,d-b\,c\right)}^{2/3}}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{6\,d^{2/3}\,{\left(a\,d-b\,c\right)}^{1/3}}","Not used",1,"log(d*(a + b*x^3)^(1/3) - (9*a*d^3 - 9*b*c*d^2)/(9*d^(4/3)*(a*d - b*c)^(2/3)))/(3*d^(2/3)*(a*d - b*c)^(1/3)) + (log(d*(a + b*x^3)^(1/3) - ((3^(1/2)*1i - 1)^2*(9*a*d^3 - 9*b*c*d^2))/(36*d^(4/3)*(a*d - b*c)^(2/3)))*(3^(1/2)*1i - 1))/(6*d^(2/3)*(a*d - b*c)^(1/3)) - (log(d*(a + b*x^3)^(1/3) - ((3^(1/2)*1i + 1)^2*(9*a*d^3 - 9*b*c*d^2))/(36*d^(4/3)*(a*d - b*c)^(2/3)))*(3^(1/2)*1i + 1))/(6*d^(2/3)*(a*d - b*c)^(1/3))","B"
719,1,702,244,6.435831,"\text{Not used}","int(1/(x*(a + b*x^3)^(1/3)*(c + d*x^3)),x)","\ln\left(b^5\,d^4\,{\left(b\,x^3+a\right)}^{1/3}-\frac{d\,\left(27\,b^4\,c^2\,d^3\,{\left(b\,x^3+a\right)}^{1/3}\,\left(2\,a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)-243\,a\,b^4\,c^4\,d^3\,{\left(\frac{d}{27\,b\,c^4-27\,a\,c^3\,d}\right)}^{2/3}\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)\right)}{27\,b\,c^4-27\,a\,c^3\,d}\right)\,{\left(\frac{d}{27\,b\,c^4-27\,a\,c^3\,d}\right)}^{1/3}+\ln\left({\left(b\,x^3+a\right)}^{1/3}-a\,c^2\,{\left(\frac{1}{a\,c^3}\right)}^{2/3}\right)\,{\left(\frac{1}{27\,a\,c^3}\right)}^{1/3}+\frac{\ln\left(b^5\,d^4\,{\left(b\,x^3+a\right)}^{1/3}-\frac{d\,{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^3\,\left(27\,b^4\,c^2\,d^3\,{\left(b\,x^3+a\right)}^{1/3}\,\left(2\,a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)-\frac{243\,a\,b^4\,c^4\,d^3\,{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,{\left(\frac{d}{27\,b\,c^4-27\,a\,c^3\,d}\right)}^{2/3}\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)}{4}\right)}{8\,\left(27\,b\,c^4-27\,a\,c^3\,d\right)}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(\frac{d}{27\,b\,c^4-27\,a\,c^3\,d}\right)}^{1/3}}{2}-\frac{\ln\left(b^5\,d^4\,{\left(b\,x^3+a\right)}^{1/3}+\frac{d\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^3\,\left(27\,b^4\,c^2\,d^3\,{\left(b\,x^3+a\right)}^{1/3}\,\left(2\,a^2\,d^2-2\,a\,b\,c\,d+b^2\,c^2\right)-\frac{243\,a\,b^4\,c^4\,d^3\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,{\left(\frac{d}{27\,b\,c^4-27\,a\,c^3\,d}\right)}^{2/3}\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)}{4}\right)}{8\,\left(27\,b\,c^4-27\,a\,c^3\,d\right)}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(\frac{d}{27\,b\,c^4-27\,a\,c^3\,d}\right)}^{1/3}}{2}-\ln\left(\sqrt{3}\,a\,c^2\,{\left(\frac{1}{a\,c^3}\right)}^{2/3}+{\left(b\,x^3+a\right)}^{1/3}\,2{}\mathrm{i}+a\,c^2\,{\left(\frac{1}{a\,c^3}\right)}^{2/3}\,1{}\mathrm{i}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(\frac{1}{27\,a\,c^3}\right)}^{1/3}+\ln\left(-\sqrt{3}\,a\,c^2\,{\left(\frac{1}{a\,c^3}\right)}^{2/3}+{\left(b\,x^3+a\right)}^{1/3}\,2{}\mathrm{i}+a\,c^2\,{\left(\frac{1}{a\,c^3}\right)}^{2/3}\,1{}\mathrm{i}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(\frac{1}{27\,a\,c^3}\right)}^{1/3}","Not used",1,"log(b^5*d^4*(a + b*x^3)^(1/3) - (d*(27*b^4*c^2*d^3*(a + b*x^3)^(1/3)*(2*a^2*d^2 + b^2*c^2 - 2*a*b*c*d) - 243*a*b^4*c^4*d^3*(d/(27*b*c^4 - 27*a*c^3*d))^(2/3)*(2*a^2*d^2 + b^2*c^2 - 3*a*b*c*d)))/(27*b*c^4 - 27*a*c^3*d))*(d/(27*b*c^4 - 27*a*c^3*d))^(1/3) + log((a + b*x^3)^(1/3) - a*c^2*(1/(a*c^3))^(2/3))*(1/(27*a*c^3))^(1/3) + (log(b^5*d^4*(a + b*x^3)^(1/3) - (d*(3^(1/2)*1i - 1)^3*(27*b^4*c^2*d^3*(a + b*x^3)^(1/3)*(2*a^2*d^2 + b^2*c^2 - 2*a*b*c*d) - (243*a*b^4*c^4*d^3*(3^(1/2)*1i - 1)^2*(d/(27*b*c^4 - 27*a*c^3*d))^(2/3)*(2*a^2*d^2 + b^2*c^2 - 3*a*b*c*d))/4))/(8*(27*b*c^4 - 27*a*c^3*d)))*(3^(1/2)*1i - 1)*(d/(27*b*c^4 - 27*a*c^3*d))^(1/3))/2 - (log(b^5*d^4*(a + b*x^3)^(1/3) + (d*(3^(1/2)*1i + 1)^3*(27*b^4*c^2*d^3*(a + b*x^3)^(1/3)*(2*a^2*d^2 + b^2*c^2 - 2*a*b*c*d) - (243*a*b^4*c^4*d^3*(3^(1/2)*1i + 1)^2*(d/(27*b*c^4 - 27*a*c^3*d))^(2/3)*(2*a^2*d^2 + b^2*c^2 - 3*a*b*c*d))/4))/(8*(27*b*c^4 - 27*a*c^3*d)))*(3^(1/2)*1i + 1)*(d/(27*b*c^4 - 27*a*c^3*d))^(1/3))/2 - log((a + b*x^3)^(1/3)*2i + a*c^2*(1/(a*c^3))^(2/3)*1i + 3^(1/2)*a*c^2*(1/(a*c^3))^(2/3))*((3^(1/2)*1i)/2 + 1/2)*(1/(27*a*c^3))^(1/3) + log((a + b*x^3)^(1/3)*2i + a*c^2*(1/(a*c^3))^(2/3)*1i - 3^(1/2)*a*c^2*(1/(a*c^3))^(2/3))*((3^(1/2)*1i)/2 - 1/2)*(1/(27*a*c^3))^(1/3)","B"
720,1,1929,296,11.355053,"\text{Not used}","int(1/(x^4*(a + b*x^3)^(1/3)*(c + d*x^3)),x)","\ln\left(-\frac{\left(\frac{\left(\frac{3\,b^4\,d^3\,{\left(b\,x^3+a\right)}^{1/3}\,\left(18\,a^4\,d^4-12\,a^3\,b\,c\,d^3-2\,a^2\,b^2\,c^2\,d^2+4\,a\,b^3\,c^3\,d+b^4\,c^4\right)}{a^2}-3\,a\,b^4\,c^4\,d^3\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)\,{\left(-\frac{{\left(3\,a\,d+b\,c\right)}^3}{a^4\,c^6}\right)}^{2/3}\right)\,{\left(-\frac{{\left(3\,a\,d+b\,c\right)}^3}{a^4\,c^6}\right)}^{1/3}}{9}+\frac{b^5\,d^4\,\left(-27\,a^3\,d^3+18\,a^2\,b\,c\,d^2+8\,a\,b^2\,c^2\,d+b^3\,c^3\right)}{3\,a^2\,c}\right)\,{\left(-\frac{{\left(3\,a\,d+b\,c\right)}^3}{a^4\,c^6}\right)}^{2/3}}{81}-\frac{4\,b^5\,d^7\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(3\,a\,d+b\,c\right)}^2}{27\,a^2\,c^5}\right)\,{\left(-\frac{27\,a^3\,d^3+27\,a^2\,b\,c\,d^2+9\,a\,b^2\,c^2\,d+b^3\,c^3}{729\,a^4\,c^6}\right)}^{1/3}+\ln\left(-{\left(-\frac{d^4}{27\,b\,c^7-27\,a\,c^6\,d}\right)}^{2/3}\,\left({\left(-\frac{d^4}{27\,b\,c^7-27\,a\,c^6\,d}\right)}^{1/3}\,\left(\frac{3\,b^4\,d^3\,{\left(b\,x^3+a\right)}^{1/3}\,\left(18\,a^4\,d^4-12\,a^3\,b\,c\,d^3-2\,a^2\,b^2\,c^2\,d^2+4\,a\,b^3\,c^3\,d+b^4\,c^4\right)}{a^2}-243\,a\,b^4\,c^4\,d^3\,{\left(-\frac{d^4}{27\,b\,c^7-27\,a\,c^6\,d}\right)}^{2/3}\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)\right)+\frac{b^5\,d^4\,\left(-27\,a^3\,d^3+18\,a^2\,b\,c\,d^2+8\,a\,b^2\,c^2\,d+b^3\,c^3\right)}{3\,a^2\,c}\right)-\frac{4\,b^5\,d^7\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(3\,a\,d+b\,c\right)}^2}{27\,a^2\,c^5}\right)\,{\left(-\frac{d^4}{27\,b\,c^7-27\,a\,c^6\,d}\right)}^{1/3}-\ln\left(\frac{\left(\frac{\left(\frac{3\,b^4\,d^3\,{\left(b\,x^3+a\right)}^{1/3}\,\left(18\,a^4\,d^4-12\,a^3\,b\,c\,d^3-2\,a^2\,b^2\,c^2\,d^2+4\,a\,b^3\,c^3\,d+b^4\,c^4\right)}{a^2}-3\,a\,b^4\,c^4\,d^3\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)\,{\left(-\frac{{\left(3\,a\,d+b\,c\right)}^3}{a^4\,c^6}\right)}^{2/3}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{{\left(3\,a\,d+b\,c\right)}^3}{a^4\,c^6}\right)}^{1/3}}{9}-\frac{b^5\,d^4\,\left(-27\,a^3\,d^3+18\,a^2\,b\,c\,d^2+8\,a\,b^2\,c^2\,d+b^3\,c^3\right)}{3\,a^2\,c}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{{\left(3\,a\,d+b\,c\right)}^3}{a^4\,c^6}\right)}^{2/3}}{81}-\frac{4\,b^5\,d^7\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(3\,a\,d+b\,c\right)}^2}{27\,a^2\,c^5}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{27\,a^3\,d^3+27\,a^2\,b\,c\,d^2+9\,a\,b^2\,c^2\,d+b^3\,c^3}{729\,a^4\,c^6}\right)}^{1/3}+\ln\left(\frac{\left(\frac{\left(\frac{3\,b^4\,d^3\,{\left(b\,x^3+a\right)}^{1/3}\,\left(18\,a^4\,d^4-12\,a^3\,b\,c\,d^3-2\,a^2\,b^2\,c^2\,d^2+4\,a\,b^3\,c^3\,d+b^4\,c^4\right)}{a^2}+3\,a\,b^4\,c^4\,d^3\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)\,{\left(-\frac{{\left(3\,a\,d+b\,c\right)}^3}{a^4\,c^6}\right)}^{2/3}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{{\left(3\,a\,d+b\,c\right)}^3}{a^4\,c^6}\right)}^{1/3}}{9}+\frac{b^5\,d^4\,\left(-27\,a^3\,d^3+18\,a^2\,b\,c\,d^2+8\,a\,b^2\,c^2\,d+b^3\,c^3\right)}{3\,a^2\,c}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{{\left(3\,a\,d+b\,c\right)}^3}{a^4\,c^6}\right)}^{2/3}}{81}-\frac{4\,b^5\,d^7\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(3\,a\,d+b\,c\right)}^2}{27\,a^2\,c^5}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{27\,a^3\,d^3+27\,a^2\,b\,c\,d^2+9\,a\,b^2\,c^2\,d+b^3\,c^3}{729\,a^4\,c^6}\right)}^{1/3}+\frac{\ln\left(-\frac{{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(\frac{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(-\frac{d^4}{27\,b\,c^7-27\,a\,c^6\,d}\right)}^{1/3}\,\left(\frac{3\,b^4\,d^3\,{\left(b\,x^3+a\right)}^{1/3}\,\left(18\,a^4\,d^4-12\,a^3\,b\,c\,d^3-2\,a^2\,b^2\,c^2\,d^2+4\,a\,b^3\,c^3\,d+b^4\,c^4\right)}{a^2}-\frac{243\,a\,b^4\,c^4\,d^3\,{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,{\left(-\frac{d^4}{27\,b\,c^7-27\,a\,c^6\,d}\right)}^{2/3}\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)}{4}\right)}{2}+\frac{b^5\,d^4\,\left(-27\,a^3\,d^3+18\,a^2\,b\,c\,d^2+8\,a\,b^2\,c^2\,d+b^3\,c^3\right)}{3\,a^2\,c}\right)\,{\left(-\frac{d^4}{27\,b\,c^7-27\,a\,c^6\,d}\right)}^{2/3}}{4}-\frac{4\,b^5\,d^7\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(3\,a\,d+b\,c\right)}^2}{27\,a^2\,c^5}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(-\frac{d^4}{27\,b\,c^7-27\,a\,c^6\,d}\right)}^{1/3}}{2}-\frac{\ln\left(\frac{{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(\frac{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(-\frac{d^4}{27\,b\,c^7-27\,a\,c^6\,d}\right)}^{1/3}\,\left(\frac{3\,b^4\,d^3\,{\left(b\,x^3+a\right)}^{1/3}\,\left(18\,a^4\,d^4-12\,a^3\,b\,c\,d^3-2\,a^2\,b^2\,c^2\,d^2+4\,a\,b^3\,c^3\,d+b^4\,c^4\right)}{a^2}-\frac{243\,a\,b^4\,c^4\,d^3\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,{\left(-\frac{d^4}{27\,b\,c^7-27\,a\,c^6\,d}\right)}^{2/3}\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)}{4}\right)}{2}-\frac{b^5\,d^4\,\left(-27\,a^3\,d^3+18\,a^2\,b\,c\,d^2+8\,a\,b^2\,c^2\,d+b^3\,c^3\right)}{3\,a^2\,c}\right)\,{\left(-\frac{d^4}{27\,b\,c^7-27\,a\,c^6\,d}\right)}^{2/3}}{4}-\frac{4\,b^5\,d^7\,{\left(b\,x^3+a\right)}^{1/3}\,{\left(3\,a\,d+b\,c\right)}^2}{27\,a^2\,c^5}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(-\frac{d^4}{27\,b\,c^7-27\,a\,c^6\,d}\right)}^{1/3}}{2}-\frac{{\left(b\,x^3+a\right)}^{2/3}}{3\,a\,c\,x^3}","Not used",1,"log(- (((((3*b^4*d^3*(a + b*x^3)^(1/3)*(18*a^4*d^4 + b^4*c^4 - 2*a^2*b^2*c^2*d^2 + 4*a*b^3*c^3*d - 12*a^3*b*c*d^3))/a^2 - 3*a*b^4*c^4*d^3*(2*a^2*d^2 + b^2*c^2 - 3*a*b*c*d)*(-(3*a*d + b*c)^3/(a^4*c^6))^(2/3))*(-(3*a*d + b*c)^3/(a^4*c^6))^(1/3))/9 + (b^5*d^4*(b^3*c^3 - 27*a^3*d^3 + 8*a*b^2*c^2*d + 18*a^2*b*c*d^2))/(3*a^2*c))*(-(3*a*d + b*c)^3/(a^4*c^6))^(2/3))/81 - (4*b^5*d^7*(a + b*x^3)^(1/3)*(3*a*d + b*c)^2)/(27*a^2*c^5))*(-(27*a^3*d^3 + b^3*c^3 + 9*a*b^2*c^2*d + 27*a^2*b*c*d^2)/(729*a^4*c^6))^(1/3) + log(- (-d^4/(27*b*c^7 - 27*a*c^6*d))^(2/3)*((-d^4/(27*b*c^7 - 27*a*c^6*d))^(1/3)*((3*b^4*d^3*(a + b*x^3)^(1/3)*(18*a^4*d^4 + b^4*c^4 - 2*a^2*b^2*c^2*d^2 + 4*a*b^3*c^3*d - 12*a^3*b*c*d^3))/a^2 - 243*a*b^4*c^4*d^3*(-d^4/(27*b*c^7 - 27*a*c^6*d))^(2/3)*(2*a^2*d^2 + b^2*c^2 - 3*a*b*c*d)) + (b^5*d^4*(b^3*c^3 - 27*a^3*d^3 + 8*a*b^2*c^2*d + 18*a^2*b*c*d^2))/(3*a^2*c)) - (4*b^5*d^7*(a + b*x^3)^(1/3)*(3*a*d + b*c)^2)/(27*a^2*c^5))*(-d^4/(27*b*c^7 - 27*a*c^6*d))^(1/3) - log((((((3*b^4*d^3*(a + b*x^3)^(1/3)*(18*a^4*d^4 + b^4*c^4 - 2*a^2*b^2*c^2*d^2 + 4*a*b^3*c^3*d - 12*a^3*b*c*d^3))/a^2 - 3*a*b^4*c^4*d^3*((3^(1/2)*1i)/2 - 1/2)*(2*a^2*d^2 + b^2*c^2 - 3*a*b*c*d)*(-(3*a*d + b*c)^3/(a^4*c^6))^(2/3))*((3^(1/2)*1i)/2 + 1/2)*(-(3*a*d + b*c)^3/(a^4*c^6))^(1/3))/9 - (b^5*d^4*(b^3*c^3 - 27*a^3*d^3 + 8*a*b^2*c^2*d + 18*a^2*b*c*d^2))/(3*a^2*c))*((3^(1/2)*1i)/2 - 1/2)*(-(3*a*d + b*c)^3/(a^4*c^6))^(2/3))/81 - (4*b^5*d^7*(a + b*x^3)^(1/3)*(3*a*d + b*c)^2)/(27*a^2*c^5))*((3^(1/2)*1i)/2 + 1/2)*(-(27*a^3*d^3 + b^3*c^3 + 9*a*b^2*c^2*d + 27*a^2*b*c*d^2)/(729*a^4*c^6))^(1/3) + log((((((3*b^4*d^3*(a + b*x^3)^(1/3)*(18*a^4*d^4 + b^4*c^4 - 2*a^2*b^2*c^2*d^2 + 4*a*b^3*c^3*d - 12*a^3*b*c*d^3))/a^2 + 3*a*b^4*c^4*d^3*((3^(1/2)*1i)/2 + 1/2)*(2*a^2*d^2 + b^2*c^2 - 3*a*b*c*d)*(-(3*a*d + b*c)^3/(a^4*c^6))^(2/3))*((3^(1/2)*1i)/2 - 1/2)*(-(3*a*d + b*c)^3/(a^4*c^6))^(1/3))/9 + (b^5*d^4*(b^3*c^3 - 27*a^3*d^3 + 8*a*b^2*c^2*d + 18*a^2*b*c*d^2))/(3*a^2*c))*((3^(1/2)*1i)/2 + 1/2)*(-(3*a*d + b*c)^3/(a^4*c^6))^(2/3))/81 - (4*b^5*d^7*(a + b*x^3)^(1/3)*(3*a*d + b*c)^2)/(27*a^2*c^5))*((3^(1/2)*1i)/2 - 1/2)*(-(27*a^3*d^3 + b^3*c^3 + 9*a*b^2*c^2*d + 27*a^2*b*c*d^2)/(729*a^4*c^6))^(1/3) + (log(- ((3^(1/2)*1i - 1)^2*(((3^(1/2)*1i - 1)*(-d^4/(27*b*c^7 - 27*a*c^6*d))^(1/3)*((3*b^4*d^3*(a + b*x^3)^(1/3)*(18*a^4*d^4 + b^4*c^4 - 2*a^2*b^2*c^2*d^2 + 4*a*b^3*c^3*d - 12*a^3*b*c*d^3))/a^2 - (243*a*b^4*c^4*d^3*(3^(1/2)*1i - 1)^2*(-d^4/(27*b*c^7 - 27*a*c^6*d))^(2/3)*(2*a^2*d^2 + b^2*c^2 - 3*a*b*c*d))/4))/2 + (b^5*d^4*(b^3*c^3 - 27*a^3*d^3 + 8*a*b^2*c^2*d + 18*a^2*b*c*d^2))/(3*a^2*c))*(-d^4/(27*b*c^7 - 27*a*c^6*d))^(2/3))/4 - (4*b^5*d^7*(a + b*x^3)^(1/3)*(3*a*d + b*c)^2)/(27*a^2*c^5))*(3^(1/2)*1i - 1)*(-d^4/(27*b*c^7 - 27*a*c^6*d))^(1/3))/2 - (log(((3^(1/2)*1i + 1)^2*(((3^(1/2)*1i + 1)*(-d^4/(27*b*c^7 - 27*a*c^6*d))^(1/3)*((3*b^4*d^3*(a + b*x^3)^(1/3)*(18*a^4*d^4 + b^4*c^4 - 2*a^2*b^2*c^2*d^2 + 4*a*b^3*c^3*d - 12*a^3*b*c*d^3))/a^2 - (243*a*b^4*c^4*d^3*(3^(1/2)*1i + 1)^2*(-d^4/(27*b*c^7 - 27*a*c^6*d))^(2/3)*(2*a^2*d^2 + b^2*c^2 - 3*a*b*c*d))/4))/2 - (b^5*d^4*(b^3*c^3 - 27*a^3*d^3 + 8*a*b^2*c^2*d + 18*a^2*b*c*d^2))/(3*a^2*c))*(-d^4/(27*b*c^7 - 27*a*c^6*d))^(2/3))/4 - (4*b^5*d^7*(a + b*x^3)^(1/3)*(3*a*d + b*c)^2)/(27*a^2*c^5))*(3^(1/2)*1i + 1)*(-d^4/(27*b*c^7 - 27*a*c^6*d))^(1/3))/2 - (a + b*x^3)^(2/3)/(3*a*c*x^3)","B"
721,0,-1,273,0.000000,"\text{Not used}","int(x^6/((a + b*x^3)^(1/3)*(c + d*x^3)),x)","\int \frac{x^6}{{\left(b\,x^3+a\right)}^{1/3}\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int(x^6/((a + b*x^3)^(1/3)*(c + d*x^3)), x)","F"
722,0,-1,233,0.000000,"\text{Not used}","int(x^3/((a + b*x^3)^(1/3)*(c + d*x^3)),x)","\int \frac{x^3}{{\left(b\,x^3+a\right)}^{1/3}\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int(x^3/((a + b*x^3)^(1/3)*(c + d*x^3)), x)","F"
723,0,-1,148,0.000000,"\text{Not used}","int(1/((a + b*x^3)^(1/3)*(c + d*x^3)),x)","\int \frac{1}{{\left(b\,x^3+a\right)}^{1/3}\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int(1/((a + b*x^3)^(1/3)*(c + d*x^3)), x)","F"
724,0,-1,176,0.000000,"\text{Not used}","int(1/(x^3*(a + b*x^3)^(1/3)*(c + d*x^3)),x)","\int \frac{1}{x^3\,{\left(b\,x^3+a\right)}^{1/3}\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int(1/(x^3*(a + b*x^3)^(1/3)*(c + d*x^3)), x)","F"
725,0,-1,214,0.000000,"\text{Not used}","int(1/(x^6*(a + b*x^3)^(1/3)*(c + d*x^3)),x)","\int \frac{1}{x^6\,{\left(b\,x^3+a\right)}^{1/3}\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int(1/(x^6*(a + b*x^3)^(1/3)*(c + d*x^3)), x)","F"
726,0,-1,262,0.000000,"\text{Not used}","int(1/(x^9*(a + b*x^3)^(1/3)*(c + d*x^3)),x)","\int \frac{1}{x^9\,{\left(b\,x^3+a\right)}^{1/3}\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int(1/(x^9*(a + b*x^3)^(1/3)*(c + d*x^3)), x)","F"
727,0,-1,64,0.000000,"\text{Not used}","int(x^7/((a + b*x^3)^(1/3)*(c + d*x^3)),x)","\int \frac{x^7}{{\left(b\,x^3+a\right)}^{1/3}\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int(x^7/((a + b*x^3)^(1/3)*(c + d*x^3)), x)","F"
728,0,-1,64,0.000000,"\text{Not used}","int(x^4/((a + b*x^3)^(1/3)*(c + d*x^3)),x)","\int \frac{x^4}{{\left(b\,x^3+a\right)}^{1/3}\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int(x^4/((a + b*x^3)^(1/3)*(c + d*x^3)), x)","F"
729,0,-1,64,0.000000,"\text{Not used}","int(x/((a + b*x^3)^(1/3)*(c + d*x^3)),x)","\int \frac{x}{{\left(b\,x^3+a\right)}^{1/3}\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int(x/((a + b*x^3)^(1/3)*(c + d*x^3)), x)","F"
730,0,-1,62,0.000000,"\text{Not used}","int(1/(x^2*(a + b*x^3)^(1/3)*(c + d*x^3)),x)","\int \frac{1}{x^2\,{\left(b\,x^3+a\right)}^{1/3}\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int(1/(x^2*(a + b*x^3)^(1/3)*(c + d*x^3)), x)","F"
731,0,-1,64,0.000000,"\text{Not used}","int(1/(x^5*(a + b*x^3)^(1/3)*(c + d*x^3)),x)","\int \frac{1}{x^5\,{\left(b\,x^3+a\right)}^{1/3}\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int(1/(x^5*(a + b*x^3)^(1/3)*(c + d*x^3)), x)","F"
732,1,331,241,5.012410,"\text{Not used}","int(x^11/((a + b*x^3)^(2/3)*(c + d*x^3)),x)","\left(\frac{3\,a^2}{b^3\,d}+\frac{\left(\frac{3\,a}{b^3\,d}+\frac{b^4\,c-a\,b^3\,d}{b^6\,d^2}\right)\,\left(b^4\,c-a\,b^3\,d\right)}{b^3\,d}\right)\,{\left(b\,x^3+a\right)}^{1/3}-\left(\frac{3\,a}{4\,b^3\,d}+\frac{b^4\,c-a\,b^3\,d}{4\,b^6\,d^2}\right)\,{\left(b\,x^3+a\right)}^{4/3}+\frac{{\left(b\,x^3+a\right)}^{7/3}}{7\,b^3\,d}+\frac{\ln\left(\frac{3\,c^3\,{\left(b\,x^3+a\right)}^{1/3}}{d}+\frac{3\,c^3\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(a\,d-b\,c\right)}^{1/3}}{2\,d^{4/3}}\right)\,\left(c^3+\sqrt{3}\,c^3\,1{}\mathrm{i}\right)}{6\,d^{10/3}\,{\left(a\,d-b\,c\right)}^{2/3}}-\frac{c^3\,\ln\left(\frac{3\,c^3\,{\left(b\,x^3+a\right)}^{1/3}}{d}-\frac{3\,c^3\,{\left(a\,d-b\,c\right)}^{1/3}}{d^{4/3}}\right)}{3\,d^{10/3}\,{\left(a\,d-b\,c\right)}^{2/3}}-\frac{c^3\,\ln\left(\frac{3\,c^3\,{\left(b\,x^3+a\right)}^{1/3}}{d}-\frac{3\,c^3\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(a\,d-b\,c\right)}^{1/3}}{d^{4/3}}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}{3\,d^{10/3}\,{\left(a\,d-b\,c\right)}^{2/3}}","Not used",1,"((3*a^2)/(b^3*d) + (((3*a)/(b^3*d) + (b^4*c - a*b^3*d)/(b^6*d^2))*(b^4*c - a*b^3*d))/(b^3*d))*(a + b*x^3)^(1/3) - ((3*a)/(4*b^3*d) + (b^4*c - a*b^3*d)/(4*b^6*d^2))*(a + b*x^3)^(4/3) + (a + b*x^3)^(7/3)/(7*b^3*d) + (log((3*c^3*(a + b*x^3)^(1/3))/d + (3*c^3*(3^(1/2)*1i + 1)*(a*d - b*c)^(1/3))/(2*d^(4/3)))*(3^(1/2)*c^3*1i + c^3))/(6*d^(10/3)*(a*d - b*c)^(2/3)) - (c^3*log((3*c^3*(a + b*x^3)^(1/3))/d - (3*c^3*(a*d - b*c)^(1/3))/d^(4/3)))/(3*d^(10/3)*(a*d - b*c)^(2/3)) - (c^3*log((3*c^3*(a + b*x^3)^(1/3))/d - (3*c^3*((3^(1/2)*1i)/2 - 1/2)*(a*d - b*c)^(1/3))/d^(4/3))*((3^(1/2)*1i)/2 - 1/2))/(3*d^(10/3)*(a*d - b*c)^(2/3))","B"
733,1,292,201,4.687601,"\text{Not used}","int(x^8/((a + b*x^3)^(2/3)*(c + d*x^3)),x)","\frac{{\left(b\,x^3+a\right)}^{4/3}}{4\,b^2\,d}-\left(\frac{2\,a}{b^2\,d}+\frac{b^3\,c-a\,b^2\,d}{b^4\,d^2}\right)\,{\left(b\,x^3+a\right)}^{1/3}-\frac{\ln\left(3\,c^2\,{\left(b\,x^3+a\right)}^{1/3}+\frac{\left(c^2+\sqrt{3}\,c^2\,1{}\mathrm{i}\right)\,\left(9\,a\,d^3-9\,b\,c\,d^2\right)}{6\,d^{7/3}\,{\left(a\,d-b\,c\right)}^{2/3}}\right)\,\left(c^2+\sqrt{3}\,c^2\,1{}\mathrm{i}\right)}{6\,d^{7/3}\,{\left(a\,d-b\,c\right)}^{2/3}}+\frac{c^2\,\ln\left(3\,c^2\,{\left(b\,x^3+a\right)}^{1/3}-\frac{c^2\,\left(9\,a\,d^3-9\,b\,c\,d^2\right)}{3\,d^{7/3}\,{\left(a\,d-b\,c\right)}^{2/3}}\right)}{3\,d^{7/3}\,{\left(a\,d-b\,c\right)}^{2/3}}+\frac{c^2\,\ln\left(3\,c^2\,{\left(b\,x^3+a\right)}^{1/3}-\frac{c^2\,\left(-\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)\,\left(9\,a\,d^3-9\,b\,c\,d^2\right)}{d^{7/3}\,{\left(a\,d-b\,c\right)}^{2/3}}\right)\,\left(-\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)}{d^{7/3}\,{\left(a\,d-b\,c\right)}^{2/3}}","Not used",1,"(a + b*x^3)^(4/3)/(4*b^2*d) - ((2*a)/(b^2*d) + (b^3*c - a*b^2*d)/(b^4*d^2))*(a + b*x^3)^(1/3) - (log(3*c^2*(a + b*x^3)^(1/3) + ((3^(1/2)*c^2*1i + c^2)*(9*a*d^3 - 9*b*c*d^2))/(6*d^(7/3)*(a*d - b*c)^(2/3)))*(3^(1/2)*c^2*1i + c^2))/(6*d^(7/3)*(a*d - b*c)^(2/3)) + (c^2*log(3*c^2*(a + b*x^3)^(1/3) - (c^2*(9*a*d^3 - 9*b*c*d^2))/(3*d^(7/3)*(a*d - b*c)^(2/3))))/(3*d^(7/3)*(a*d - b*c)^(2/3)) + (c^2*log(3*c^2*(a + b*x^3)^(1/3) - (c^2*((3^(1/2)*1i)/6 - 1/6)*(9*a*d^3 - 9*b*c*d^2))/(d^(7/3)*(a*d - b*c)^(2/3)))*((3^(1/2)*1i)/6 - 1/6))/(d^(7/3)*(a*d - b*c)^(2/3))","B"
734,1,232,165,4.683628,"\text{Not used}","int(x^5/((a + b*x^3)^(2/3)*(c + d*x^3)),x)","\frac{{\left(b\,x^3+a\right)}^{1/3}}{b\,d}-\frac{c\,\ln\left(3\,c\,d\,{\left(b\,x^3+a\right)}^{1/3}-\frac{c\,\left(9\,a\,d^3-9\,b\,c\,d^2\right)}{3\,d^{4/3}\,{\left(a\,d-b\,c\right)}^{2/3}}\right)}{3\,d^{4/3}\,{\left(a\,d-b\,c\right)}^{2/3}}+\frac{\ln\left(3\,c\,d\,{\left(b\,x^3+a\right)}^{1/3}+\frac{\left(9\,a\,d^3-9\,b\,c\,d^2\right)\,\left(c-\sqrt{3}\,c\,1{}\mathrm{i}\right)}{6\,d^{4/3}\,{\left(a\,d-b\,c\right)}^{2/3}}\right)\,\left(c-\sqrt{3}\,c\,1{}\mathrm{i}\right)}{6\,d^{4/3}\,{\left(a\,d-b\,c\right)}^{2/3}}+\frac{\ln\left(3\,c\,d\,{\left(b\,x^3+a\right)}^{1/3}+\frac{\left(9\,a\,d^3-9\,b\,c\,d^2\right)\,\left(c+\sqrt{3}\,c\,1{}\mathrm{i}\right)}{6\,d^{4/3}\,{\left(a\,d-b\,c\right)}^{2/3}}\right)\,\left(c+\sqrt{3}\,c\,1{}\mathrm{i}\right)}{6\,d^{4/3}\,{\left(a\,d-b\,c\right)}^{2/3}}","Not used",1,"(a + b*x^3)^(1/3)/(b*d) - (c*log(3*c*d*(a + b*x^3)^(1/3) - (c*(9*a*d^3 - 9*b*c*d^2))/(3*d^(4/3)*(a*d - b*c)^(2/3))))/(3*d^(4/3)*(a*d - b*c)^(2/3)) + (log(3*c*d*(a + b*x^3)^(1/3) + ((9*a*d^3 - 9*b*c*d^2)*(c - 3^(1/2)*c*1i))/(6*d^(4/3)*(a*d - b*c)^(2/3)))*(c - 3^(1/2)*c*1i))/(6*d^(4/3)*(a*d - b*c)^(2/3)) + (log(3*c*d*(a + b*x^3)^(1/3) + ((9*a*d^3 - 9*b*c*d^2)*(c + 3^(1/2)*c*1i))/(6*d^(4/3)*(a*d - b*c)^(2/3)))*(c + 3^(1/2)*c*1i))/(6*d^(4/3)*(a*d - b*c)^(2/3))","B"
735,1,213,145,4.847086,"\text{Not used}","int(x^2/((a + b*x^3)^(2/3)*(c + d*x^3)),x)","\frac{\ln\left(3\,d^2\,{\left(b\,x^3+a\right)}^{1/3}-\frac{9\,a\,d^3-9\,b\,c\,d^2}{3\,d^{1/3}\,{\left(a\,d-b\,c\right)}^{2/3}}\right)}{3\,d^{1/3}\,{\left(a\,d-b\,c\right)}^{2/3}}+\frac{\ln\left(3\,d^2\,{\left(b\,x^3+a\right)}^{1/3}-\frac{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(9\,a\,d^3-9\,b\,c\,d^2\right)}{6\,d^{1/3}\,{\left(a\,d-b\,c\right)}^{2/3}}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}{6\,d^{1/3}\,{\left(a\,d-b\,c\right)}^{2/3}}-\frac{\ln\left(3\,d^2\,{\left(b\,x^3+a\right)}^{1/3}+\frac{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(9\,a\,d^3-9\,b\,c\,d^2\right)}{6\,d^{1/3}\,{\left(a\,d-b\,c\right)}^{2/3}}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}{6\,d^{1/3}\,{\left(a\,d-b\,c\right)}^{2/3}}","Not used",1,"log(3*d^2*(a + b*x^3)^(1/3) - (9*a*d^3 - 9*b*c*d^2)/(3*d^(1/3)*(a*d - b*c)^(2/3)))/(3*d^(1/3)*(a*d - b*c)^(2/3)) + (log(3*d^2*(a + b*x^3)^(1/3) - ((3^(1/2)*1i - 1)*(9*a*d^3 - 9*b*c*d^2))/(6*d^(1/3)*(a*d - b*c)^(2/3)))*(3^(1/2)*1i - 1))/(6*d^(1/3)*(a*d - b*c)^(2/3)) - (log(3*d^2*(a + b*x^3)^(1/3) + ((3^(1/2)*1i + 1)*(9*a*d^3 - 9*b*c*d^2))/(6*d^(1/3)*(a*d - b*c)^(2/3)))*(3^(1/2)*1i + 1))/(6*d^(1/3)*(a*d - b*c)^(2/3))","B"
736,1,1413,245,4.942351,"\text{Not used}","int(1/(x*(a + b*x^3)^(2/3)*(c + d*x^3)),x)","\ln\left(\left(\left(\left(81\,b^6\,c^5\,d^3-162\,a\,b^5\,c^4\,d^4\right)\,{\left(b\,x^3+a\right)}^{1/3}-\left(486\,a^3\,b^4\,c^4\,d^5-729\,a^2\,b^5\,c^5\,d^4+243\,a\,b^6\,c^6\,d^3\right)\,{\left(\frac{1}{27\,a^2\,c^3}\right)}^{1/3}\right)\,{\left(\frac{1}{27\,a^2\,c^3}\right)}^{2/3}-9\,b^5\,c^2\,d^4\right)\,{\left(\frac{1}{27\,a^2\,c^3}\right)}^{1/3}+6\,b^4\,d^5\,{\left(b\,x^3+a\right)}^{1/3}\right)\,{\left(\frac{1}{27\,a^2\,c^3}\right)}^{1/3}+\ln\left(-\left(\left(\left(81\,b^6\,c^5\,d^3-162\,a\,b^5\,c^4\,d^4\right)\,{\left(b\,x^3+a\right)}^{1/3}-{\left(-\frac{d^2}{27\,a^2\,c^3\,d^2-54\,a\,b\,c^4\,d+27\,b^2\,c^5}\right)}^{1/3}\,\left(486\,a^3\,b^4\,c^4\,d^5-729\,a^2\,b^5\,c^5\,d^4+243\,a\,b^6\,c^6\,d^3\right)\right)\,{\left(-\frac{d^2}{27\,a^2\,c^3\,d^2-54\,a\,b\,c^4\,d+27\,b^2\,c^5}\right)}^{2/3}-9\,b^5\,c^2\,d^4\right)\,{\left(-\frac{d^2}{27\,a^2\,c^3\,d^2-54\,a\,b\,c^4\,d+27\,b^2\,c^5}\right)}^{1/3}-6\,b^4\,d^5\,{\left(b\,x^3+a\right)}^{1/3}\right)\,{\left(-\frac{d^2}{27\,a^2\,c^3\,d^2-54\,a\,b\,c^4\,d+27\,b^2\,c^5}\right)}^{1/3}+\ln\left(\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left({\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,\left(\left(81\,b^6\,c^5\,d^3-162\,a\,b^5\,c^4\,d^4\right)\,{\left(b\,x^3+a\right)}^{1/3}-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(486\,a^3\,b^4\,c^4\,d^5-729\,a^2\,b^5\,c^5\,d^4+243\,a\,b^6\,c^6\,d^3\right)\,{\left(\frac{1}{27\,a^2\,c^3}\right)}^{1/3}\right)\,{\left(\frac{1}{27\,a^2\,c^3}\right)}^{2/3}-9\,b^5\,c^2\,d^4\right)\,{\left(\frac{1}{27\,a^2\,c^3}\right)}^{1/3}+6\,b^4\,d^5\,{\left(b\,x^3+a\right)}^{1/3}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(\frac{1}{27\,a^2\,c^3}\right)}^{1/3}-\ln\left(6\,b^4\,d^5\,{\left(b\,x^3+a\right)}^{1/3}-\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left({\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,\left(\left(81\,b^6\,c^5\,d^3-162\,a\,b^5\,c^4\,d^4\right)\,{\left(b\,x^3+a\right)}^{1/3}+\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(486\,a^3\,b^4\,c^4\,d^5-729\,a^2\,b^5\,c^5\,d^4+243\,a\,b^6\,c^6\,d^3\right)\,{\left(\frac{1}{27\,a^2\,c^3}\right)}^{1/3}\right)\,{\left(\frac{1}{27\,a^2\,c^3}\right)}^{2/3}-9\,b^5\,c^2\,d^4\right)\,{\left(\frac{1}{27\,a^2\,c^3}\right)}^{1/3}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(\frac{1}{27\,a^2\,c^3}\right)}^{1/3}+\frac{\ln\left(6\,b^4\,d^5\,{\left(b\,x^3+a\right)}^{1/3}+\frac{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(\frac{{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(\left(81\,b^6\,c^5\,d^3-162\,a\,b^5\,c^4\,d^4\right)\,{\left(b\,x^3+a\right)}^{1/3}-\frac{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(-\frac{d^2}{27\,a^2\,c^3\,d^2-54\,a\,b\,c^4\,d+27\,b^2\,c^5}\right)}^{1/3}\,\left(486\,a^3\,b^4\,c^4\,d^5-729\,a^2\,b^5\,c^5\,d^4+243\,a\,b^6\,c^6\,d^3\right)}{2}\right)\,{\left(-\frac{d^2}{27\,a^2\,c^3\,d^2-54\,a\,b\,c^4\,d+27\,b^2\,c^5}\right)}^{2/3}}{4}-9\,b^5\,c^2\,d^4\right)\,{\left(-\frac{d^2}{27\,a^2\,c^3\,d^2-54\,a\,b\,c^4\,d+27\,b^2\,c^5}\right)}^{1/3}}{2}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(-\frac{d^2}{27\,a^2\,c^3\,d^2-54\,a\,b\,c^4\,d+27\,b^2\,c^5}\right)}^{1/3}}{2}-\frac{\ln\left(6\,b^4\,d^5\,{\left(b\,x^3+a\right)}^{1/3}-\frac{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(\frac{{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,\left(\left(81\,b^6\,c^5\,d^3-162\,a\,b^5\,c^4\,d^4\right)\,{\left(b\,x^3+a\right)}^{1/3}+\frac{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(-\frac{d^2}{27\,a^2\,c^3\,d^2-54\,a\,b\,c^4\,d+27\,b^2\,c^5}\right)}^{1/3}\,\left(486\,a^3\,b^4\,c^4\,d^5-729\,a^2\,b^5\,c^5\,d^4+243\,a\,b^6\,c^6\,d^3\right)}{2}\right)\,{\left(-\frac{d^2}{27\,a^2\,c^3\,d^2-54\,a\,b\,c^4\,d+27\,b^2\,c^5}\right)}^{2/3}}{4}-9\,b^5\,c^2\,d^4\right)\,{\left(-\frac{d^2}{27\,a^2\,c^3\,d^2-54\,a\,b\,c^4\,d+27\,b^2\,c^5}\right)}^{1/3}}{2}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(-\frac{d^2}{27\,a^2\,c^3\,d^2-54\,a\,b\,c^4\,d+27\,b^2\,c^5}\right)}^{1/3}}{2}","Not used",1,"log((((81*b^6*c^5*d^3 - 162*a*b^5*c^4*d^4)*(a + b*x^3)^(1/3) - (243*a*b^6*c^6*d^3 - 729*a^2*b^5*c^5*d^4 + 486*a^3*b^4*c^4*d^5)*(1/(27*a^2*c^3))^(1/3))*(1/(27*a^2*c^3))^(2/3) - 9*b^5*c^2*d^4)*(1/(27*a^2*c^3))^(1/3) + 6*b^4*d^5*(a + b*x^3)^(1/3))*(1/(27*a^2*c^3))^(1/3) + log(- (((81*b^6*c^5*d^3 - 162*a*b^5*c^4*d^4)*(a + b*x^3)^(1/3) - (-d^2/(27*b^2*c^5 + 27*a^2*c^3*d^2 - 54*a*b*c^4*d))^(1/3)*(243*a*b^6*c^6*d^3 - 729*a^2*b^5*c^5*d^4 + 486*a^3*b^4*c^4*d^5))*(-d^2/(27*b^2*c^5 + 27*a^2*c^3*d^2 - 54*a*b*c^4*d))^(2/3) - 9*b^5*c^2*d^4)*(-d^2/(27*b^2*c^5 + 27*a^2*c^3*d^2 - 54*a*b*c^4*d))^(1/3) - 6*b^4*d^5*(a + b*x^3)^(1/3))*(-d^2/(27*b^2*c^5 + 27*a^2*c^3*d^2 - 54*a*b*c^4*d))^(1/3) + log(((3^(1/2)*1i)/2 - 1/2)*(((3^(1/2)*1i)/2 - 1/2)^2*((81*b^6*c^5*d^3 - 162*a*b^5*c^4*d^4)*(a + b*x^3)^(1/3) - ((3^(1/2)*1i)/2 - 1/2)*(243*a*b^6*c^6*d^3 - 729*a^2*b^5*c^5*d^4 + 486*a^3*b^4*c^4*d^5)*(1/(27*a^2*c^3))^(1/3))*(1/(27*a^2*c^3))^(2/3) - 9*b^5*c^2*d^4)*(1/(27*a^2*c^3))^(1/3) + 6*b^4*d^5*(a + b*x^3)^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(1/(27*a^2*c^3))^(1/3) - log(6*b^4*d^5*(a + b*x^3)^(1/3) - ((3^(1/2)*1i)/2 + 1/2)*(((3^(1/2)*1i)/2 + 1/2)^2*((81*b^6*c^5*d^3 - 162*a*b^5*c^4*d^4)*(a + b*x^3)^(1/3) + ((3^(1/2)*1i)/2 + 1/2)*(243*a*b^6*c^6*d^3 - 729*a^2*b^5*c^5*d^4 + 486*a^3*b^4*c^4*d^5)*(1/(27*a^2*c^3))^(1/3))*(1/(27*a^2*c^3))^(2/3) - 9*b^5*c^2*d^4)*(1/(27*a^2*c^3))^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(1/(27*a^2*c^3))^(1/3) + (log(6*b^4*d^5*(a + b*x^3)^(1/3) + ((3^(1/2)*1i - 1)*(((3^(1/2)*1i - 1)^2*((81*b^6*c^5*d^3 - 162*a*b^5*c^4*d^4)*(a + b*x^3)^(1/3) - ((3^(1/2)*1i - 1)*(-d^2/(27*b^2*c^5 + 27*a^2*c^3*d^2 - 54*a*b*c^4*d))^(1/3)*(243*a*b^6*c^6*d^3 - 729*a^2*b^5*c^5*d^4 + 486*a^3*b^4*c^4*d^5))/2)*(-d^2/(27*b^2*c^5 + 27*a^2*c^3*d^2 - 54*a*b*c^4*d))^(2/3))/4 - 9*b^5*c^2*d^4)*(-d^2/(27*b^2*c^5 + 27*a^2*c^3*d^2 - 54*a*b*c^4*d))^(1/3))/2)*(3^(1/2)*1i - 1)*(-d^2/(27*b^2*c^5 + 27*a^2*c^3*d^2 - 54*a*b*c^4*d))^(1/3))/2 - (log(6*b^4*d^5*(a + b*x^3)^(1/3) - ((3^(1/2)*1i + 1)*(((3^(1/2)*1i + 1)^2*((81*b^6*c^5*d^3 - 162*a*b^5*c^4*d^4)*(a + b*x^3)^(1/3) + ((3^(1/2)*1i + 1)*(-d^2/(27*b^2*c^5 + 27*a^2*c^3*d^2 - 54*a*b*c^4*d))^(1/3)*(243*a*b^6*c^6*d^3 - 729*a^2*b^5*c^5*d^4 + 486*a^3*b^4*c^4*d^5))/2)*(-d^2/(27*b^2*c^5 + 27*a^2*c^3*d^2 - 54*a*b*c^4*d))^(2/3))/4 - 9*b^5*c^2*d^4)*(-d^2/(27*b^2*c^5 + 27*a^2*c^3*d^2 - 54*a*b*c^4*d))^(1/3))/2)*(3^(1/2)*1i + 1)*(-d^2/(27*b^2*c^5 + 27*a^2*c^3*d^2 - 54*a*b*c^4*d))^(1/3))/2","B"
737,1,1959,299,11.141071,"\text{Not used}","int(1/(x^4*(a + b*x^3)^(2/3)*(c + d*x^3)),x)","\ln\left(-\frac{\left(\frac{\left(\frac{27\,b^5\,c^3\,d^3\,{\left(b\,x^3+a\right)}^{1/3}\,\left(4\,a^2\,d^2+a\,b\,c\,d-2\,b^2\,c^2\right)}{a}-81\,a\,b^4\,c^4\,d^3\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)\,{\left(\frac{d^5}{c^6\,{\left(a\,d-b\,c\right)}^2}\right)}^{1/3}\right)\,{\left(\frac{d^5}{c^6\,{\left(a\,d-b\,c\right)}^2}\right)}^{2/3}}{9}+\frac{b^5\,d^4\,\left(-27\,a^3\,d^3+18\,a^2\,b\,c\,d^2+28\,a\,b^2\,c^2\,d+8\,b^3\,c^3\right)}{3\,a^3\,c}\right)\,{\left(\frac{d^5}{c^6\,{\left(a\,d-b\,c\right)}^2}\right)}^{1/3}}{3}-\frac{2\,b^4\,d^6\,{\left(b\,x^3+a\right)}^{1/3}\,\left(27\,a^3\,d^3+36\,a^2\,b\,c\,d^2+18\,a\,b^2\,c^2\,d+4\,b^3\,c^3\right)}{9\,a^3\,c^4}\right)\,{\left(\frac{d^5}{27\,a^2\,c^6\,d^2-54\,a\,b\,c^7\,d+27\,b^2\,c^8}\right)}^{1/3}+\ln\left(-\frac{\left(\frac{\left(\frac{27\,b^5\,c^3\,d^3\,{\left(b\,x^3+a\right)}^{1/3}\,\left(4\,a^2\,d^2+a\,b\,c\,d-2\,b^2\,c^2\right)}{a}-27\,a\,b^4\,c^4\,d^3\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)\,{\left(-\frac{{\left(3\,a\,d+2\,b\,c\right)}^3}{a^5\,c^6}\right)}^{1/3}\right)\,{\left(-\frac{{\left(3\,a\,d+2\,b\,c\right)}^3}{a^5\,c^6}\right)}^{2/3}}{81}+\frac{b^5\,d^4\,\left(-27\,a^3\,d^3+18\,a^2\,b\,c\,d^2+28\,a\,b^2\,c^2\,d+8\,b^3\,c^3\right)}{3\,a^3\,c}\right)\,{\left(-\frac{{\left(3\,a\,d+2\,b\,c\right)}^3}{a^5\,c^6}\right)}^{1/3}}{9}-\frac{2\,b^4\,d^6\,{\left(b\,x^3+a\right)}^{1/3}\,\left(27\,a^3\,d^3+36\,a^2\,b\,c\,d^2+18\,a\,b^2\,c^2\,d+4\,b^3\,c^3\right)}{9\,a^3\,c^4}\right)\,{\left(-\frac{27\,a^3\,d^3+54\,a^2\,b\,c\,d^2+36\,a\,b^2\,c^2\,d+8\,b^3\,c^3}{729\,a^5\,c^6}\right)}^{1/3}+\frac{\ln\left(\frac{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(\frac{\left(\frac{27\,b^5\,c^3\,d^3\,{\left(b\,x^3+a\right)}^{1/3}\,\left(4\,a^2\,d^2+a\,b\,c\,d-2\,b^2\,c^2\right)}{a}-\frac{81\,a\,b^4\,c^4\,d^3\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)\,{\left(\frac{d^5}{c^6\,{\left(a\,d-b\,c\right)}^2}\right)}^{1/3}}{2}\right)\,{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,{\left(\frac{d^5}{c^6\,{\left(a\,d-b\,c\right)}^2}\right)}^{2/3}}{36}+\frac{b^5\,d^4\,\left(-27\,a^3\,d^3+18\,a^2\,b\,c\,d^2+28\,a\,b^2\,c^2\,d+8\,b^3\,c^3\right)}{3\,a^3\,c}\right)\,{\left(\frac{d^5}{c^6\,{\left(a\,d-b\,c\right)}^2}\right)}^{1/3}}{6}+\frac{2\,b^4\,d^6\,{\left(b\,x^3+a\right)}^{1/3}\,\left(27\,a^3\,d^3+36\,a^2\,b\,c\,d^2+18\,a\,b^2\,c^2\,d+4\,b^3\,c^3\right)}{9\,a^3\,c^4}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(\frac{d^5}{27\,a^2\,c^6\,d^2-54\,a\,b\,c^7\,d+27\,b^2\,c^8}\right)}^{1/3}}{2}-\frac{\ln\left(\frac{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(\frac{\left(\frac{27\,b^5\,c^3\,d^3\,{\left(b\,x^3+a\right)}^{1/3}\,\left(4\,a^2\,d^2+a\,b\,c\,d-2\,b^2\,c^2\right)}{a}+\frac{81\,a\,b^4\,c^4\,d^3\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)\,{\left(\frac{d^5}{c^6\,{\left(a\,d-b\,c\right)}^2}\right)}^{1/3}}{2}\right)\,{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,{\left(\frac{d^5}{c^6\,{\left(a\,d-b\,c\right)}^2}\right)}^{2/3}}{36}+\frac{b^5\,d^4\,\left(-27\,a^3\,d^3+18\,a^2\,b\,c\,d^2+28\,a\,b^2\,c^2\,d+8\,b^3\,c^3\right)}{3\,a^3\,c}\right)\,{\left(\frac{d^5}{c^6\,{\left(a\,d-b\,c\right)}^2}\right)}^{1/3}}{6}-\frac{2\,b^4\,d^6\,{\left(b\,x^3+a\right)}^{1/3}\,\left(27\,a^3\,d^3+36\,a^2\,b\,c\,d^2+18\,a\,b^2\,c^2\,d+4\,b^3\,c^3\right)}{9\,a^3\,c^4}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(\frac{d^5}{27\,a^2\,c^6\,d^2-54\,a\,b\,c^7\,d+27\,b^2\,c^8}\right)}^{1/3}}{2}+\ln\left(\frac{2\,b^4\,d^6\,{\left(b\,x^3+a\right)}^{1/3}\,\left(27\,a^3\,d^3+36\,a^2\,b\,c\,d^2+18\,a\,b^2\,c^2\,d+4\,b^3\,c^3\right)}{9\,a^3\,c^4}-\frac{\left(\frac{\left(\frac{27\,b^5\,c^3\,d^3\,{\left(b\,x^3+a\right)}^{1/3}\,\left(4\,a^2\,d^2+a\,b\,c\,d-2\,b^2\,c^2\right)}{a}-27\,a\,b^4\,c^4\,d^3\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)\,{\left(-\frac{{\left(3\,a\,d+2\,b\,c\right)}^3}{a^5\,c^6}\right)}^{1/3}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{{\left(3\,a\,d+2\,b\,c\right)}^3}{a^5\,c^6}\right)}^{2/3}}{81}-\frac{b^5\,d^4\,\left(-27\,a^3\,d^3+18\,a^2\,b\,c\,d^2+28\,a\,b^2\,c^2\,d+8\,b^3\,c^3\right)}{3\,a^3\,c}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{{\left(3\,a\,d+2\,b\,c\right)}^3}{a^5\,c^6}\right)}^{1/3}}{9}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{27\,a^3\,d^3+54\,a^2\,b\,c\,d^2+36\,a\,b^2\,c^2\,d+8\,b^3\,c^3}{729\,a^5\,c^6}\right)}^{1/3}-\ln\left(\frac{\left(\frac{\left(\frac{27\,b^5\,c^3\,d^3\,{\left(b\,x^3+a\right)}^{1/3}\,\left(4\,a^2\,d^2+a\,b\,c\,d-2\,b^2\,c^2\right)}{a}+27\,a\,b^4\,c^4\,d^3\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left(2\,a^2\,d^2-3\,a\,b\,c\,d+b^2\,c^2\right)\,{\left(-\frac{{\left(3\,a\,d+2\,b\,c\right)}^3}{a^5\,c^6}\right)}^{1/3}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{{\left(3\,a\,d+2\,b\,c\right)}^3}{a^5\,c^6}\right)}^{2/3}}{81}+\frac{b^5\,d^4\,\left(-27\,a^3\,d^3+18\,a^2\,b\,c\,d^2+28\,a\,b^2\,c^2\,d+8\,b^3\,c^3\right)}{3\,a^3\,c}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{{\left(3\,a\,d+2\,b\,c\right)}^3}{a^5\,c^6}\right)}^{1/3}}{9}-\frac{2\,b^4\,d^6\,{\left(b\,x^3+a\right)}^{1/3}\,\left(27\,a^3\,d^3+36\,a^2\,b\,c\,d^2+18\,a\,b^2\,c^2\,d+4\,b^3\,c^3\right)}{9\,a^3\,c^4}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{27\,a^3\,d^3+54\,a^2\,b\,c\,d^2+36\,a\,b^2\,c^2\,d+8\,b^3\,c^3}{729\,a^5\,c^6}\right)}^{1/3}-\frac{{\left(b\,x^3+a\right)}^{1/3}}{3\,a\,c\,x^3}","Not used",1,"log(- (((((27*b^5*c^3*d^3*(a + b*x^3)^(1/3)*(4*a^2*d^2 - 2*b^2*c^2 + a*b*c*d))/a - 81*a*b^4*c^4*d^3*(2*a^2*d^2 + b^2*c^2 - 3*a*b*c*d)*(d^5/(c^6*(a*d - b*c)^2))^(1/3))*(d^5/(c^6*(a*d - b*c)^2))^(2/3))/9 + (b^5*d^4*(8*b^3*c^3 - 27*a^3*d^3 + 28*a*b^2*c^2*d + 18*a^2*b*c*d^2))/(3*a^3*c))*(d^5/(c^6*(a*d - b*c)^2))^(1/3))/3 - (2*b^4*d^6*(a + b*x^3)^(1/3)*(27*a^3*d^3 + 4*b^3*c^3 + 18*a*b^2*c^2*d + 36*a^2*b*c*d^2))/(9*a^3*c^4))*(d^5/(27*b^2*c^8 + 27*a^2*c^6*d^2 - 54*a*b*c^7*d))^(1/3) + log(- (((((27*b^5*c^3*d^3*(a + b*x^3)^(1/3)*(4*a^2*d^2 - 2*b^2*c^2 + a*b*c*d))/a - 27*a*b^4*c^4*d^3*(2*a^2*d^2 + b^2*c^2 - 3*a*b*c*d)*(-(3*a*d + 2*b*c)^3/(a^5*c^6))^(1/3))*(-(3*a*d + 2*b*c)^3/(a^5*c^6))^(2/3))/81 + (b^5*d^4*(8*b^3*c^3 - 27*a^3*d^3 + 28*a*b^2*c^2*d + 18*a^2*b*c*d^2))/(3*a^3*c))*(-(3*a*d + 2*b*c)^3/(a^5*c^6))^(1/3))/9 - (2*b^4*d^6*(a + b*x^3)^(1/3)*(27*a^3*d^3 + 4*b^3*c^3 + 18*a*b^2*c^2*d + 36*a^2*b*c*d^2))/(9*a^3*c^4))*(-(27*a^3*d^3 + 8*b^3*c^3 + 36*a*b^2*c^2*d + 54*a^2*b*c*d^2)/(729*a^5*c^6))^(1/3) + (log(((3^(1/2)*1i - 1)*((((27*b^5*c^3*d^3*(a + b*x^3)^(1/3)*(4*a^2*d^2 - 2*b^2*c^2 + a*b*c*d))/a - (81*a*b^4*c^4*d^3*(3^(1/2)*1i - 1)*(2*a^2*d^2 + b^2*c^2 - 3*a*b*c*d)*(d^5/(c^6*(a*d - b*c)^2))^(1/3))/2)*(3^(1/2)*1i - 1)^2*(d^5/(c^6*(a*d - b*c)^2))^(2/3))/36 + (b^5*d^4*(8*b^3*c^3 - 27*a^3*d^3 + 28*a*b^2*c^2*d + 18*a^2*b*c*d^2))/(3*a^3*c))*(d^5/(c^6*(a*d - b*c)^2))^(1/3))/6 + (2*b^4*d^6*(a + b*x^3)^(1/3)*(27*a^3*d^3 + 4*b^3*c^3 + 18*a*b^2*c^2*d + 36*a^2*b*c*d^2))/(9*a^3*c^4))*(3^(1/2)*1i - 1)*(d^5/(27*b^2*c^8 + 27*a^2*c^6*d^2 - 54*a*b*c^7*d))^(1/3))/2 - (log(((3^(1/2)*1i + 1)*((((27*b^5*c^3*d^3*(a + b*x^3)^(1/3)*(4*a^2*d^2 - 2*b^2*c^2 + a*b*c*d))/a + (81*a*b^4*c^4*d^3*(3^(1/2)*1i + 1)*(2*a^2*d^2 + b^2*c^2 - 3*a*b*c*d)*(d^5/(c^6*(a*d - b*c)^2))^(1/3))/2)*(3^(1/2)*1i + 1)^2*(d^5/(c^6*(a*d - b*c)^2))^(2/3))/36 + (b^5*d^4*(8*b^3*c^3 - 27*a^3*d^3 + 28*a*b^2*c^2*d + 18*a^2*b*c*d^2))/(3*a^3*c))*(d^5/(c^6*(a*d - b*c)^2))^(1/3))/6 - (2*b^4*d^6*(a + b*x^3)^(1/3)*(27*a^3*d^3 + 4*b^3*c^3 + 18*a*b^2*c^2*d + 36*a^2*b*c*d^2))/(9*a^3*c^4))*(3^(1/2)*1i + 1)*(d^5/(27*b^2*c^8 + 27*a^2*c^6*d^2 - 54*a*b*c^7*d))^(1/3))/2 + log((2*b^4*d^6*(a + b*x^3)^(1/3)*(27*a^3*d^3 + 4*b^3*c^3 + 18*a*b^2*c^2*d + 36*a^2*b*c*d^2))/(9*a^3*c^4) - (((((27*b^5*c^3*d^3*(a + b*x^3)^(1/3)*(4*a^2*d^2 - 2*b^2*c^2 + a*b*c*d))/a - 27*a*b^4*c^4*d^3*((3^(1/2)*1i)/2 - 1/2)*(2*a^2*d^2 + b^2*c^2 - 3*a*b*c*d)*(-(3*a*d + 2*b*c)^3/(a^5*c^6))^(1/3))*((3^(1/2)*1i)/2 + 1/2)*(-(3*a*d + 2*b*c)^3/(a^5*c^6))^(2/3))/81 - (b^5*d^4*(8*b^3*c^3 - 27*a^3*d^3 + 28*a*b^2*c^2*d + 18*a^2*b*c*d^2))/(3*a^3*c))*((3^(1/2)*1i)/2 - 1/2)*(-(3*a*d + 2*b*c)^3/(a^5*c^6))^(1/3))/9)*((3^(1/2)*1i)/2 - 1/2)*(-(27*a^3*d^3 + 8*b^3*c^3 + 36*a*b^2*c^2*d + 54*a^2*b*c*d^2)/(729*a^5*c^6))^(1/3) - log((((((27*b^5*c^3*d^3*(a + b*x^3)^(1/3)*(4*a^2*d^2 - 2*b^2*c^2 + a*b*c*d))/a + 27*a*b^4*c^4*d^3*((3^(1/2)*1i)/2 + 1/2)*(2*a^2*d^2 + b^2*c^2 - 3*a*b*c*d)*(-(3*a*d + 2*b*c)^3/(a^5*c^6))^(1/3))*((3^(1/2)*1i)/2 - 1/2)*(-(3*a*d + 2*b*c)^3/(a^5*c^6))^(2/3))/81 + (b^5*d^4*(8*b^3*c^3 - 27*a^3*d^3 + 28*a*b^2*c^2*d + 18*a^2*b*c*d^2))/(3*a^3*c))*((3^(1/2)*1i)/2 + 1/2)*(-(3*a*d + 2*b*c)^3/(a^5*c^6))^(1/3))/9 - (2*b^4*d^6*(a + b*x^3)^(1/3)*(27*a^3*d^3 + 4*b^3*c^3 + 18*a*b^2*c^2*d + 36*a^2*b*c*d^2))/(9*a^3*c^4))*((3^(1/2)*1i)/2 + 1/2)*(-(27*a^3*d^3 + 8*b^3*c^3 + 36*a*b^2*c^2*d + 54*a^2*b*c*d^2)/(729*a^5*c^6))^(1/3) - (a + b*x^3)^(1/3)/(3*a*c*x^3)","B"
738,0,-1,279,0.000000,"\text{Not used}","int(x^7/((a + b*x^3)^(2/3)*(c + d*x^3)),x)","\int \frac{x^7}{{\left(b\,x^3+a\right)}^{2/3}\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int(x^7/((a + b*x^3)^(2/3)*(c + d*x^3)), x)","F"
739,0,-1,234,0.000000,"\text{Not used}","int(x^4/((a + b*x^3)^(2/3)*(c + d*x^3)),x)","\int \frac{x^4}{{\left(b\,x^3+a\right)}^{2/3}\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int(x^4/((a + b*x^3)^(2/3)*(c + d*x^3)), x)","F"
740,0,-1,149,0.000000,"\text{Not used}","int(x/((a + b*x^3)^(2/3)*(c + d*x^3)),x)","\int \frac{x}{{\left(b\,x^3+a\right)}^{2/3}\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int(x/((a + b*x^3)^(2/3)*(c + d*x^3)), x)","F"
741,0,-1,173,0.000000,"\text{Not used}","int(1/(x^2*(a + b*x^3)^(2/3)*(c + d*x^3)),x)","\int \frac{1}{x^2\,{\left(b\,x^3+a\right)}^{2/3}\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int(1/(x^2*(a + b*x^3)^(2/3)*(c + d*x^3)), x)","F"
742,0,-1,215,0.000000,"\text{Not used}","int(1/(x^5*(a + b*x^3)^(2/3)*(c + d*x^3)),x)","\int \frac{1}{x^5\,{\left(b\,x^3+a\right)}^{2/3}\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int(1/(x^5*(a + b*x^3)^(2/3)*(c + d*x^3)), x)","F"
743,0,-1,64,0.000000,"\text{Not used}","int(x^6/((a + b*x^3)^(2/3)*(c + d*x^3)),x)","\int \frac{x^6}{{\left(b\,x^3+a\right)}^{2/3}\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int(x^6/((a + b*x^3)^(2/3)*(c + d*x^3)), x)","F"
744,0,-1,64,0.000000,"\text{Not used}","int(x^3/((a + b*x^3)^(2/3)*(c + d*x^3)),x)","\int \frac{x^3}{{\left(b\,x^3+a\right)}^{2/3}\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int(x^3/((a + b*x^3)^(2/3)*(c + d*x^3)), x)","F"
745,0,-1,59,0.000000,"\text{Not used}","int(1/((a + b*x^3)^(2/3)*(c + d*x^3)),x)","\int \frac{1}{{\left(b\,x^3+a\right)}^{2/3}\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int(1/((a + b*x^3)^(2/3)*(c + d*x^3)), x)","F"
746,0,-1,64,0.000000,"\text{Not used}","int(1/(x^3*(a + b*x^3)^(2/3)*(c + d*x^3)),x)","\int \frac{1}{x^3\,{\left(b\,x^3+a\right)}^{2/3}\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int(1/(x^3*(a + b*x^3)^(2/3)*(c + d*x^3)), x)","F"
747,1,564,347,5.189428,"\text{Not used}","int(x^14/((a + b*x^3)^(4/3)*(c + d*x^3)),x)","\left(\frac{3\,a^2}{b^4\,d}+\frac{\left(\frac{4\,a}{b^4\,d}+\frac{b^5\,c-a\,b^4\,d}{b^8\,d^2}\right)\,\left(b^5\,c-a\,b^4\,d\right)}{2\,b^4\,d}\right)\,{\left(b\,x^3+a\right)}^{2/3}-\left(\frac{4\,a}{5\,b^4\,d}+\frac{b^5\,c-a\,b^4\,d}{5\,b^8\,d^2}\right)\,{\left(b\,x^3+a\right)}^{5/3}+\frac{{\left(b\,x^3+a\right)}^{8/3}}{8\,b^4\,d}+\frac{a^4}{b^4\,{\left(b\,x^3+a\right)}^{1/3}\,\left(a\,d-b\,c\right)}+\frac{c^4\,\ln\left({\left(b\,x^3+a\right)}^{1/3}\,\left(a\,c^8\,d^5-b\,c^9\,d^4\right)-\frac{c^8\,\left(9\,a^4\,d^{15}-36\,a^3\,b\,c\,d^{14}+54\,a^2\,b^2\,c^2\,d^{13}-36\,a\,b^3\,c^3\,d^{12}+9\,b^4\,c^4\,d^{11}\right)}{9\,d^{22/3}\,{\left(a\,d-b\,c\right)}^{8/3}}\right)}{3\,d^{11/3}\,{\left(a\,d-b\,c\right)}^{4/3}}-\frac{\ln\left({\left(b\,x^3+a\right)}^{1/3}\,\left(a\,c^8\,d^5-b\,c^9\,d^4\right)-\frac{{\left(c^4+\sqrt{3}\,c^4\,1{}\mathrm{i}\right)}^2\,\left(9\,a^4\,d^{15}-36\,a^3\,b\,c\,d^{14}+54\,a^2\,b^2\,c^2\,d^{13}-36\,a\,b^3\,c^3\,d^{12}+9\,b^4\,c^4\,d^{11}\right)}{36\,d^{22/3}\,{\left(a\,d-b\,c\right)}^{8/3}}\right)\,\left(c^4+\sqrt{3}\,c^4\,1{}\mathrm{i}\right)}{6\,d^{11/3}\,{\left(a\,d-b\,c\right)}^{4/3}}+\frac{c^4\,\ln\left({\left(b\,x^3+a\right)}^{1/3}\,\left(a\,c^8\,d^5-b\,c^9\,d^4\right)-\frac{c^8\,{\left(-\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)}^2\,\left(9\,a^4\,d^{15}-36\,a^3\,b\,c\,d^{14}+54\,a^2\,b^2\,c^2\,d^{13}-36\,a\,b^3\,c^3\,d^{12}+9\,b^4\,c^4\,d^{11}\right)}{d^{22/3}\,{\left(a\,d-b\,c\right)}^{8/3}}\right)\,\left(-\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)}{d^{11/3}\,{\left(a\,d-b\,c\right)}^{4/3}}","Not used",1,"((3*a^2)/(b^4*d) + (((4*a)/(b^4*d) + (b^5*c - a*b^4*d)/(b^8*d^2))*(b^5*c - a*b^4*d))/(2*b^4*d))*(a + b*x^3)^(2/3) - ((4*a)/(5*b^4*d) + (b^5*c - a*b^4*d)/(5*b^8*d^2))*(a + b*x^3)^(5/3) + (a + b*x^3)^(8/3)/(8*b^4*d) + a^4/(b^4*(a + b*x^3)^(1/3)*(a*d - b*c)) + (c^4*log((a + b*x^3)^(1/3)*(a*c^8*d^5 - b*c^9*d^4) - (c^8*(9*a^4*d^15 + 9*b^4*c^4*d^11 - 36*a*b^3*c^3*d^12 + 54*a^2*b^2*c^2*d^13 - 36*a^3*b*c*d^14))/(9*d^(22/3)*(a*d - b*c)^(8/3))))/(3*d^(11/3)*(a*d - b*c)^(4/3)) - (log((a + b*x^3)^(1/3)*(a*c^8*d^5 - b*c^9*d^4) - ((3^(1/2)*c^4*1i + c^4)^2*(9*a^4*d^15 + 9*b^4*c^4*d^11 - 36*a*b^3*c^3*d^12 + 54*a^2*b^2*c^2*d^13 - 36*a^3*b*c*d^14))/(36*d^(22/3)*(a*d - b*c)^(8/3)))*(3^(1/2)*c^4*1i + c^4))/(6*d^(11/3)*(a*d - b*c)^(4/3)) + (c^4*log((a + b*x^3)^(1/3)*(a*c^8*d^5 - b*c^9*d^4) - (c^8*((3^(1/2)*1i)/6 - 1/6)^2*(9*a^4*d^15 + 9*b^4*c^4*d^11 - 36*a*b^3*c^3*d^12 + 54*a^2*b^2*c^2*d^13 - 36*a^3*b*c*d^14))/(d^(22/3)*(a*d - b*c)^(8/3)))*((3^(1/2)*1i)/6 - 1/6))/(d^(11/3)*(a*d - b*c)^(4/3))","B"
748,1,493,253,5.160284,"\text{Not used}","int(x^11/((a + b*x^3)^(4/3)*(c + d*x^3)),x)","\frac{{\left(b\,x^3+a\right)}^{5/3}}{5\,b^3\,d}-\left(\frac{3\,a}{2\,b^3\,d}+\frac{b^4\,c-a\,b^3\,d}{2\,b^6\,d^2}\right)\,{\left(b\,x^3+a\right)}^{2/3}-\frac{a^3}{b^3\,{\left(b\,x^3+a\right)}^{1/3}\,\left(a\,d-b\,c\right)}-\frac{c^3\,\ln\left({\left(b\,x^3+a\right)}^{1/3}\,\left(a\,c^6\,d^4-b\,c^7\,d^3\right)-\frac{c^6\,\left(9\,a^4\,d^{12}-36\,a^3\,b\,c\,d^{11}+54\,a^2\,b^2\,c^2\,d^{10}-36\,a\,b^3\,c^3\,d^9+9\,b^4\,c^4\,d^8\right)}{9\,d^{16/3}\,{\left(a\,d-b\,c\right)}^{8/3}}\right)}{3\,d^{8/3}\,{\left(a\,d-b\,c\right)}^{4/3}}+\frac{\ln\left({\left(b\,x^3+a\right)}^{1/3}\,\left(a\,c^6\,d^4-b\,c^7\,d^3\right)-\frac{{\left(c^3+\sqrt{3}\,c^3\,1{}\mathrm{i}\right)}^2\,\left(9\,a^4\,d^{12}-36\,a^3\,b\,c\,d^{11}+54\,a^2\,b^2\,c^2\,d^{10}-36\,a\,b^3\,c^3\,d^9+9\,b^4\,c^4\,d^8\right)}{36\,d^{16/3}\,{\left(a\,d-b\,c\right)}^{8/3}}\right)\,\left(c^3+\sqrt{3}\,c^3\,1{}\mathrm{i}\right)}{6\,d^{8/3}\,{\left(a\,d-b\,c\right)}^{4/3}}-\frac{c^3\,\ln\left({\left(b\,x^3+a\right)}^{1/3}\,\left(a\,c^6\,d^4-b\,c^7\,d^3\right)-\frac{c^6\,{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,\left(9\,a^4\,d^{12}-36\,a^3\,b\,c\,d^{11}+54\,a^2\,b^2\,c^2\,d^{10}-36\,a\,b^3\,c^3\,d^9+9\,b^4\,c^4\,d^8\right)}{9\,d^{16/3}\,{\left(a\,d-b\,c\right)}^{8/3}}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}{3\,d^{8/3}\,{\left(a\,d-b\,c\right)}^{4/3}}","Not used",1,"(a + b*x^3)^(5/3)/(5*b^3*d) - ((3*a)/(2*b^3*d) + (b^4*c - a*b^3*d)/(2*b^6*d^2))*(a + b*x^3)^(2/3) - a^3/(b^3*(a + b*x^3)^(1/3)*(a*d - b*c)) - (c^3*log((a + b*x^3)^(1/3)*(a*c^6*d^4 - b*c^7*d^3) - (c^6*(9*a^4*d^12 + 9*b^4*c^4*d^8 - 36*a*b^3*c^3*d^9 + 54*a^2*b^2*c^2*d^10 - 36*a^3*b*c*d^11))/(9*d^(16/3)*(a*d - b*c)^(8/3))))/(3*d^(8/3)*(a*d - b*c)^(4/3)) + (log((a + b*x^3)^(1/3)*(a*c^6*d^4 - b*c^7*d^3) - ((3^(1/2)*c^3*1i + c^3)^2*(9*a^4*d^12 + 9*b^4*c^4*d^8 - 36*a*b^3*c^3*d^9 + 54*a^2*b^2*c^2*d^10 - 36*a^3*b*c*d^11))/(36*d^(16/3)*(a*d - b*c)^(8/3)))*(3^(1/2)*c^3*1i + c^3))/(6*d^(8/3)*(a*d - b*c)^(4/3)) - (c^3*log((a + b*x^3)^(1/3)*(a*c^6*d^4 - b*c^7*d^3) - (c^6*((3^(1/2)*1i)/2 - 1/2)^2*(9*a^4*d^12 + 9*b^4*c^4*d^8 - 36*a*b^3*c^3*d^9 + 54*a^2*b^2*c^2*d^10 - 36*a^3*b*c*d^11))/(9*d^(16/3)*(a*d - b*c)^(8/3)))*((3^(1/2)*1i)/2 - 1/2))/(3*d^(8/3)*(a*d - b*c)^(4/3))","B"
749,1,449,203,4.986110,"\text{Not used}","int(x^8/((a + b*x^3)^(4/3)*(c + d*x^3)),x)","\frac{{\left(b\,x^3+a\right)}^{2/3}}{2\,b^2\,d}+\frac{a^2}{b^2\,{\left(b\,x^3+a\right)}^{1/3}\,\left(a\,d-b\,c\right)}+\frac{c^2\,\ln\left({\left(b\,x^3+a\right)}^{1/3}\,\left(a\,c^4\,d^3-b\,c^5\,d^2\right)-\frac{c^4\,\left(9\,a^4\,d^9-36\,a^3\,b\,c\,d^8+54\,a^2\,b^2\,c^2\,d^7-36\,a\,b^3\,c^3\,d^6+9\,b^4\,c^4\,d^5\right)}{9\,d^{10/3}\,{\left(a\,d-b\,c\right)}^{8/3}}\right)}{3\,d^{5/3}\,{\left(a\,d-b\,c\right)}^{4/3}}-\frac{\ln\left({\left(b\,x^3+a\right)}^{1/3}\,\left(a\,c^4\,d^3-b\,c^5\,d^2\right)-\frac{{\left(c^2+\sqrt{3}\,c^2\,1{}\mathrm{i}\right)}^2\,\left(9\,a^4\,d^9-36\,a^3\,b\,c\,d^8+54\,a^2\,b^2\,c^2\,d^7-36\,a\,b^3\,c^3\,d^6+9\,b^4\,c^4\,d^5\right)}{36\,d^{10/3}\,{\left(a\,d-b\,c\right)}^{8/3}}\right)\,\left(c^2+\sqrt{3}\,c^2\,1{}\mathrm{i}\right)}{6\,d^{5/3}\,{\left(a\,d-b\,c\right)}^{4/3}}+\frac{c^2\,\ln\left({\left(b\,x^3+a\right)}^{1/3}\,\left(a\,c^4\,d^3-b\,c^5\,d^2\right)-\frac{c^4\,{\left(-\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)}^2\,\left(9\,a^4\,d^9-36\,a^3\,b\,c\,d^8+54\,a^2\,b^2\,c^2\,d^7-36\,a\,b^3\,c^3\,d^6+9\,b^4\,c^4\,d^5\right)}{d^{10/3}\,{\left(a\,d-b\,c\right)}^{8/3}}\right)\,\left(-\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)}{d^{5/3}\,{\left(a\,d-b\,c\right)}^{4/3}}","Not used",1,"(a + b*x^3)^(2/3)/(2*b^2*d) + a^2/(b^2*(a + b*x^3)^(1/3)*(a*d - b*c)) + (c^2*log((a + b*x^3)^(1/3)*(a*c^4*d^3 - b*c^5*d^2) - (c^4*(9*a^4*d^9 + 9*b^4*c^4*d^5 - 36*a*b^3*c^3*d^6 + 54*a^2*b^2*c^2*d^7 - 36*a^3*b*c*d^8))/(9*d^(10/3)*(a*d - b*c)^(8/3))))/(3*d^(5/3)*(a*d - b*c)^(4/3)) - (log((a + b*x^3)^(1/3)*(a*c^4*d^3 - b*c^5*d^2) - ((3^(1/2)*c^2*1i + c^2)^2*(9*a^4*d^9 + 9*b^4*c^4*d^5 - 36*a*b^3*c^3*d^6 + 54*a^2*b^2*c^2*d^7 - 36*a^3*b*c*d^8))/(36*d^(10/3)*(a*d - b*c)^(8/3)))*(3^(1/2)*c^2*1i + c^2))/(6*d^(5/3)*(a*d - b*c)^(4/3)) + (c^2*log((a + b*x^3)^(1/3)*(a*c^4*d^3 - b*c^5*d^2) - (c^4*((3^(1/2)*1i)/6 - 1/6)^2*(9*a^4*d^9 + 9*b^4*c^4*d^5 - 36*a*b^3*c^3*d^6 + 54*a^2*b^2*c^2*d^7 - 36*a^3*b*c*d^8))/(d^(10/3)*(a*d - b*c)^(8/3)))*((3^(1/2)*1i)/6 - 1/6))/(d^(5/3)*(a*d - b*c)^(4/3))","B"
750,1,412,174,4.978107,"\text{Not used}","int(x^5/((a + b*x^3)^(4/3)*(c + d*x^3)),x)","-\frac{a}{b\,{\left(b\,x^3+a\right)}^{1/3}\,\left(a\,d-b\,c\right)}-\frac{c\,\ln\left({\left(b\,x^3+a\right)}^{1/3}\,\left(a\,c^2\,d^2-b\,c^3\,d\right)-\frac{c^2\,\left(9\,a^4\,d^6-36\,a^3\,b\,c\,d^5+54\,a^2\,b^2\,c^2\,d^4-36\,a\,b^3\,c^3\,d^3+9\,b^4\,c^4\,d^2\right)}{9\,d^{4/3}\,{\left(a\,d-b\,c\right)}^{8/3}}\right)}{3\,d^{2/3}\,{\left(a\,d-b\,c\right)}^{4/3}}+\frac{\ln\left({\left(b\,x^3+a\right)}^{1/3}\,\left(a\,c^2\,d^2-b\,c^3\,d\right)-\frac{{\left(c-\sqrt{3}\,c\,1{}\mathrm{i}\right)}^2\,\left(9\,a^4\,d^6-36\,a^3\,b\,c\,d^5+54\,a^2\,b^2\,c^2\,d^4-36\,a\,b^3\,c^3\,d^3+9\,b^4\,c^4\,d^2\right)}{36\,d^{4/3}\,{\left(a\,d-b\,c\right)}^{8/3}}\right)\,\left(c-\sqrt{3}\,c\,1{}\mathrm{i}\right)}{6\,d^{2/3}\,{\left(a\,d-b\,c\right)}^{4/3}}+\frac{\ln\left({\left(b\,x^3+a\right)}^{1/3}\,\left(a\,c^2\,d^2-b\,c^3\,d\right)-\frac{{\left(c+\sqrt{3}\,c\,1{}\mathrm{i}\right)}^2\,\left(9\,a^4\,d^6-36\,a^3\,b\,c\,d^5+54\,a^2\,b^2\,c^2\,d^4-36\,a\,b^3\,c^3\,d^3+9\,b^4\,c^4\,d^2\right)}{36\,d^{4/3}\,{\left(a\,d-b\,c\right)}^{8/3}}\right)\,\left(c+\sqrt{3}\,c\,1{}\mathrm{i}\right)}{6\,d^{2/3}\,{\left(a\,d-b\,c\right)}^{4/3}}","Not used",1,"(log((a + b*x^3)^(1/3)*(a*c^2*d^2 - b*c^3*d) - ((c - 3^(1/2)*c*1i)^2*(9*a^4*d^6 + 9*b^4*c^4*d^2 - 36*a*b^3*c^3*d^3 + 54*a^2*b^2*c^2*d^4 - 36*a^3*b*c*d^5))/(36*d^(4/3)*(a*d - b*c)^(8/3)))*(c - 3^(1/2)*c*1i))/(6*d^(2/3)*(a*d - b*c)^(4/3)) - (c*log((a + b*x^3)^(1/3)*(a*c^2*d^2 - b*c^3*d) - (c^2*(9*a^4*d^6 + 9*b^4*c^4*d^2 - 36*a*b^3*c^3*d^3 + 54*a^2*b^2*c^2*d^4 - 36*a^3*b*c*d^5))/(9*d^(4/3)*(a*d - b*c)^(8/3))))/(3*d^(2/3)*(a*d - b*c)^(4/3)) - a/(b*(a + b*x^3)^(1/3)*(a*d - b*c)) + (log((a + b*x^3)^(1/3)*(a*c^2*d^2 - b*c^3*d) - ((c + 3^(1/2)*c*1i)^2*(9*a^4*d^6 + 9*b^4*c^4*d^2 - 36*a*b^3*c^3*d^3 + 54*a^2*b^2*c^2*d^4 - 36*a^3*b*c*d^5))/(36*d^(4/3)*(a*d - b*c)^(8/3)))*(c + 3^(1/2)*c*1i))/(6*d^(2/3)*(a*d - b*c)^(4/3))","B"
751,1,389,167,4.923478,"\text{Not used}","int(x^2/((a + b*x^3)^(4/3)*(c + d*x^3)),x)","\frac{1}{{\left(b\,x^3+a\right)}^{1/3}\,\left(a\,d-b\,c\right)}+\frac{d^{1/3}\,\ln\left({\left(b\,x^3+a\right)}^{1/3}\,\left(a\,d^4-b\,c\,d^3\right)-\frac{d^{2/3}\,\left(9\,a^4\,d^6-36\,a^3\,b\,c\,d^5+54\,a^2\,b^2\,c^2\,d^4-36\,a\,b^3\,c^3\,d^3+9\,b^4\,c^4\,d^2\right)}{9\,{\left(a\,d-b\,c\right)}^{8/3}}\right)}{3\,{\left(a\,d-b\,c\right)}^{4/3}}-\frac{d^{1/3}\,\ln\left({\left(b\,x^3+a\right)}^{1/3}\,\left(a\,d^4-b\,c\,d^3\right)-\frac{d^{2/3}\,{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,\left(9\,a^4\,d^6-36\,a^3\,b\,c\,d^5+54\,a^2\,b^2\,c^2\,d^4-36\,a\,b^3\,c^3\,d^3+9\,b^4\,c^4\,d^2\right)}{9\,{\left(a\,d-b\,c\right)}^{8/3}}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}{3\,{\left(a\,d-b\,c\right)}^{4/3}}+\frac{d^{1/3}\,\ln\left({\left(b\,x^3+a\right)}^{1/3}\,\left(a\,d^4-b\,c\,d^3\right)-\frac{d^{2/3}\,{\left(-\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)}^2\,\left(9\,a^4\,d^6-36\,a^3\,b\,c\,d^5+54\,a^2\,b^2\,c^2\,d^4-36\,a\,b^3\,c^3\,d^3+9\,b^4\,c^4\,d^2\right)}{{\left(a\,d-b\,c\right)}^{8/3}}\right)\,\left(-\frac{1}{6}+\frac{\sqrt{3}\,1{}\mathrm{i}}{6}\right)}{{\left(a\,d-b\,c\right)}^{4/3}}","Not used",1,"1/((a + b*x^3)^(1/3)*(a*d - b*c)) + (d^(1/3)*log((a + b*x^3)^(1/3)*(a*d^4 - b*c*d^3) - (d^(2/3)*(9*a^4*d^6 + 9*b^4*c^4*d^2 - 36*a*b^3*c^3*d^3 + 54*a^2*b^2*c^2*d^4 - 36*a^3*b*c*d^5))/(9*(a*d - b*c)^(8/3))))/(3*(a*d - b*c)^(4/3)) - (d^(1/3)*log((a + b*x^3)^(1/3)*(a*d^4 - b*c*d^3) - (d^(2/3)*((3^(1/2)*1i)/2 + 1/2)^2*(9*a^4*d^6 + 9*b^4*c^4*d^2 - 36*a*b^3*c^3*d^3 + 54*a^2*b^2*c^2*d^4 - 36*a^3*b*c*d^5))/(9*(a*d - b*c)^(8/3)))*((3^(1/2)*1i)/2 + 1/2))/(3*(a*d - b*c)^(4/3)) + (d^(1/3)*log((a + b*x^3)^(1/3)*(a*d^4 - b*c*d^3) - (d^(2/3)*((3^(1/2)*1i)/6 - 1/6)^2*(9*a^4*d^6 + 9*b^4*c^4*d^2 - 36*a*b^3*c^3*d^3 + 54*a^2*b^2*c^2*d^4 - 36*a^3*b*c*d^5))/(a*d - b*c)^(8/3))*((3^(1/2)*1i)/6 - 1/6))/(a*d - b*c)^(4/3)","B"
752,1,3804,271,5.341570,"\text{Not used}","int(1/(x*(a + b*x^3)^(4/3)*(c + d*x^3)),x)","\ln\left(9\,a^7\,b^{14}\,c^{11}\,d^4-\left({\left(b\,x^3+a\right)}^{1/3}\,\left(-54\,a^{18}\,b^4\,c^2\,d^{14}+486\,a^{17}\,b^5\,c^3\,d^{13}-2052\,a^{16}\,b^6\,c^4\,d^{12}+5400\,a^{15}\,b^7\,c^5\,d^{11}-9855\,a^{14}\,b^8\,c^6\,d^{10}+13041\,a^{13}\,b^9\,c^7\,d^9-12663\,a^{12}\,b^{10}\,c^8\,d^8+8937\,a^{11}\,b^{11}\,c^9\,d^7-4455\,a^{10}\,b^{12}\,c^{10}\,d^6+1485\,a^9\,b^{13}\,c^{11}\,d^5-297\,a^8\,b^{14}\,c^{12}\,d^4+27\,a^7\,b^{15}\,c^{13}\,d^3\right)-{\left(-\frac{d^4}{27\,a^4\,c^3\,d^4-108\,a^3\,b\,c^4\,d^3+162\,a^2\,b^2\,c^5\,d^2-108\,a\,b^3\,c^6\,d+27\,b^4\,c^7}\right)}^{2/3}\,\left(-486\,a^{21}\,b^4\,c^4\,d^{14}+5103\,a^{20}\,b^5\,c^5\,d^{13}-24300\,a^{19}\,b^6\,c^6\,d^{12}+69255\,a^{18}\,b^7\,c^7\,d^{11}-131220\,a^{17}\,b^8\,c^8\,d^{10}+173502\,a^{16}\,b^9\,c^9\,d^9-163296\,a^{15}\,b^{10}\,c^{10}\,d^8+109350\,a^{14}\,b^{11}\,c^{11}\,d^7-51030\,a^{13}\,b^{12}\,c^{12}\,d^6+15795\,a^{12}\,b^{13}\,c^{13}\,d^5-2916\,a^{11}\,b^{14}\,c^{14}\,d^4+243\,a^{10}\,b^{15}\,c^{15}\,d^3\right)\right)\,{\left(-\frac{d^4}{27\,a^4\,c^3\,d^4-108\,a^3\,b\,c^4\,d^3+162\,a^2\,b^2\,c^5\,d^2-108\,a\,b^3\,c^6\,d+27\,b^4\,c^7}\right)}^{1/3}-90\,a^8\,b^{13}\,c^{10}\,d^5+405\,a^9\,b^{12}\,c^9\,d^6-1071\,a^{10}\,b^{11}\,c^8\,d^7+1827\,a^{11}\,b^{10}\,c^7\,d^8-2079\,a^{12}\,b^9\,c^6\,d^9+1575\,a^{13}\,b^8\,c^5\,d^{10}-765\,a^{14}\,b^7\,c^4\,d^{11}+216\,a^{15}\,b^6\,c^3\,d^{12}-27\,a^{16}\,b^5\,c^2\,d^{13}\right)\,{\left(-\frac{d^4}{27\,a^4\,c^3\,d^4-108\,a^3\,b\,c^4\,d^3+162\,a^2\,b^2\,c^5\,d^2-108\,a\,b^3\,c^6\,d+27\,b^4\,c^7}\right)}^{1/3}+\ln\left(9\,a^7\,b^{14}\,c^{11}\,d^4-\left({\left(b\,x^3+a\right)}^{1/3}\,\left(-54\,a^{18}\,b^4\,c^2\,d^{14}+486\,a^{17}\,b^5\,c^3\,d^{13}-2052\,a^{16}\,b^6\,c^4\,d^{12}+5400\,a^{15}\,b^7\,c^5\,d^{11}-9855\,a^{14}\,b^8\,c^6\,d^{10}+13041\,a^{13}\,b^9\,c^7\,d^9-12663\,a^{12}\,b^{10}\,c^8\,d^8+8937\,a^{11}\,b^{11}\,c^9\,d^7-4455\,a^{10}\,b^{12}\,c^{10}\,d^6+1485\,a^9\,b^{13}\,c^{11}\,d^5-297\,a^8\,b^{14}\,c^{12}\,d^4+27\,a^7\,b^{15}\,c^{13}\,d^3\right)-{\left(\frac{1}{27\,a^4\,c^3}\right)}^{2/3}\,\left(-486\,a^{21}\,b^4\,c^4\,d^{14}+5103\,a^{20}\,b^5\,c^5\,d^{13}-24300\,a^{19}\,b^6\,c^6\,d^{12}+69255\,a^{18}\,b^7\,c^7\,d^{11}-131220\,a^{17}\,b^8\,c^8\,d^{10}+173502\,a^{16}\,b^9\,c^9\,d^9-163296\,a^{15}\,b^{10}\,c^{10}\,d^8+109350\,a^{14}\,b^{11}\,c^{11}\,d^7-51030\,a^{13}\,b^{12}\,c^{12}\,d^6+15795\,a^{12}\,b^{13}\,c^{13}\,d^5-2916\,a^{11}\,b^{14}\,c^{14}\,d^4+243\,a^{10}\,b^{15}\,c^{15}\,d^3\right)\right)\,{\left(\frac{1}{27\,a^4\,c^3}\right)}^{1/3}-90\,a^8\,b^{13}\,c^{10}\,d^5+405\,a^9\,b^{12}\,c^9\,d^6-1071\,a^{10}\,b^{11}\,c^8\,d^7+1827\,a^{11}\,b^{10}\,c^7\,d^8-2079\,a^{12}\,b^9\,c^6\,d^9+1575\,a^{13}\,b^8\,c^5\,d^{10}-765\,a^{14}\,b^7\,c^4\,d^{11}+216\,a^{15}\,b^6\,c^3\,d^{12}-27\,a^{16}\,b^5\,c^2\,d^{13}\right)\,{\left(\frac{1}{27\,a^4\,c^3}\right)}^{1/3}+\frac{\ln\left(\frac{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(-\frac{d^4}{27\,a^4\,c^3\,d^4-108\,a^3\,b\,c^4\,d^3+162\,a^2\,b^2\,c^5\,d^2-108\,a\,b^3\,c^6\,d+27\,b^4\,c^7}\right)}^{1/3}\,\left({\left(b\,x^3+a\right)}^{1/3}\,\left(-54\,a^{18}\,b^4\,c^2\,d^{14}+486\,a^{17}\,b^5\,c^3\,d^{13}-2052\,a^{16}\,b^6\,c^4\,d^{12}+5400\,a^{15}\,b^7\,c^5\,d^{11}-9855\,a^{14}\,b^8\,c^6\,d^{10}+13041\,a^{13}\,b^9\,c^7\,d^9-12663\,a^{12}\,b^{10}\,c^8\,d^8+8937\,a^{11}\,b^{11}\,c^9\,d^7-4455\,a^{10}\,b^{12}\,c^{10}\,d^6+1485\,a^9\,b^{13}\,c^{11}\,d^5-297\,a^8\,b^{14}\,c^{12}\,d^4+27\,a^7\,b^{15}\,c^{13}\,d^3\right)-\frac{{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,{\left(-\frac{d^4}{27\,a^4\,c^3\,d^4-108\,a^3\,b\,c^4\,d^3+162\,a^2\,b^2\,c^5\,d^2-108\,a\,b^3\,c^6\,d+27\,b^4\,c^7}\right)}^{2/3}\,\left(-486\,a^{21}\,b^4\,c^4\,d^{14}+5103\,a^{20}\,b^5\,c^5\,d^{13}-24300\,a^{19}\,b^6\,c^6\,d^{12}+69255\,a^{18}\,b^7\,c^7\,d^{11}-131220\,a^{17}\,b^8\,c^8\,d^{10}+173502\,a^{16}\,b^9\,c^9\,d^9-163296\,a^{15}\,b^{10}\,c^{10}\,d^8+109350\,a^{14}\,b^{11}\,c^{11}\,d^7-51030\,a^{13}\,b^{12}\,c^{12}\,d^6+15795\,a^{12}\,b^{13}\,c^{13}\,d^5-2916\,a^{11}\,b^{14}\,c^{14}\,d^4+243\,a^{10}\,b^{15}\,c^{15}\,d^3\right)}{4}\right)}{2}-9\,a^7\,b^{14}\,c^{11}\,d^4+90\,a^8\,b^{13}\,c^{10}\,d^5-405\,a^9\,b^{12}\,c^9\,d^6+1071\,a^{10}\,b^{11}\,c^8\,d^7-1827\,a^{11}\,b^{10}\,c^7\,d^8+2079\,a^{12}\,b^9\,c^6\,d^9-1575\,a^{13}\,b^8\,c^5\,d^{10}+765\,a^{14}\,b^7\,c^4\,d^{11}-216\,a^{15}\,b^6\,c^3\,d^{12}+27\,a^{16}\,b^5\,c^2\,d^{13}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(-\frac{d^4}{27\,a^4\,c^3\,d^4-108\,a^3\,b\,c^4\,d^3+162\,a^2\,b^2\,c^5\,d^2-108\,a\,b^3\,c^6\,d+27\,b^4\,c^7}\right)}^{1/3}}{2}-\frac{\ln\left(\frac{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(-\frac{d^4}{27\,a^4\,c^3\,d^4-108\,a^3\,b\,c^4\,d^3+162\,a^2\,b^2\,c^5\,d^2-108\,a\,b^3\,c^6\,d+27\,b^4\,c^7}\right)}^{1/3}\,\left({\left(b\,x^3+a\right)}^{1/3}\,\left(-54\,a^{18}\,b^4\,c^2\,d^{14}+486\,a^{17}\,b^5\,c^3\,d^{13}-2052\,a^{16}\,b^6\,c^4\,d^{12}+5400\,a^{15}\,b^7\,c^5\,d^{11}-9855\,a^{14}\,b^8\,c^6\,d^{10}+13041\,a^{13}\,b^9\,c^7\,d^9-12663\,a^{12}\,b^{10}\,c^8\,d^8+8937\,a^{11}\,b^{11}\,c^9\,d^7-4455\,a^{10}\,b^{12}\,c^{10}\,d^6+1485\,a^9\,b^{13}\,c^{11}\,d^5-297\,a^8\,b^{14}\,c^{12}\,d^4+27\,a^7\,b^{15}\,c^{13}\,d^3\right)-\frac{{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,{\left(-\frac{d^4}{27\,a^4\,c^3\,d^4-108\,a^3\,b\,c^4\,d^3+162\,a^2\,b^2\,c^5\,d^2-108\,a\,b^3\,c^6\,d+27\,b^4\,c^7}\right)}^{2/3}\,\left(-486\,a^{21}\,b^4\,c^4\,d^{14}+5103\,a^{20}\,b^5\,c^5\,d^{13}-24300\,a^{19}\,b^6\,c^6\,d^{12}+69255\,a^{18}\,b^7\,c^7\,d^{11}-131220\,a^{17}\,b^8\,c^8\,d^{10}+173502\,a^{16}\,b^9\,c^9\,d^9-163296\,a^{15}\,b^{10}\,c^{10}\,d^8+109350\,a^{14}\,b^{11}\,c^{11}\,d^7-51030\,a^{13}\,b^{12}\,c^{12}\,d^6+15795\,a^{12}\,b^{13}\,c^{13}\,d^5-2916\,a^{11}\,b^{14}\,c^{14}\,d^4+243\,a^{10}\,b^{15}\,c^{15}\,d^3\right)}{4}\right)}{2}+9\,a^7\,b^{14}\,c^{11}\,d^4-90\,a^8\,b^{13}\,c^{10}\,d^5+405\,a^9\,b^{12}\,c^9\,d^6-1071\,a^{10}\,b^{11}\,c^8\,d^7+1827\,a^{11}\,b^{10}\,c^7\,d^8-2079\,a^{12}\,b^9\,c^6\,d^9+1575\,a^{13}\,b^8\,c^5\,d^{10}-765\,a^{14}\,b^7\,c^4\,d^{11}+216\,a^{15}\,b^6\,c^3\,d^{12}-27\,a^{16}\,b^5\,c^2\,d^{13}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(-\frac{d^4}{27\,a^4\,c^3\,d^4-108\,a^3\,b\,c^4\,d^3+162\,a^2\,b^2\,c^5\,d^2-108\,a\,b^3\,c^6\,d+27\,b^4\,c^7}\right)}^{1/3}}{2}-\frac{b}{{\left(b\,x^3+a\right)}^{1/3}\,\left(a^2\,d-a\,b\,c\right)}+\ln\left(\left({\left(b\,x^3+a\right)}^{1/3}\,\left(-54\,a^{18}\,b^4\,c^2\,d^{14}+486\,a^{17}\,b^5\,c^3\,d^{13}-2052\,a^{16}\,b^6\,c^4\,d^{12}+5400\,a^{15}\,b^7\,c^5\,d^{11}-9855\,a^{14}\,b^8\,c^6\,d^{10}+13041\,a^{13}\,b^9\,c^7\,d^9-12663\,a^{12}\,b^{10}\,c^8\,d^8+8937\,a^{11}\,b^{11}\,c^9\,d^7-4455\,a^{10}\,b^{12}\,c^{10}\,d^6+1485\,a^9\,b^{13}\,c^{11}\,d^5-297\,a^8\,b^{14}\,c^{12}\,d^4+27\,a^7\,b^{15}\,c^{13}\,d^3\right)-{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(\frac{1}{27\,a^4\,c^3}\right)}^{2/3}\,\left(-486\,a^{21}\,b^4\,c^4\,d^{14}+5103\,a^{20}\,b^5\,c^5\,d^{13}-24300\,a^{19}\,b^6\,c^6\,d^{12}+69255\,a^{18}\,b^7\,c^7\,d^{11}-131220\,a^{17}\,b^8\,c^8\,d^{10}+173502\,a^{16}\,b^9\,c^9\,d^9-163296\,a^{15}\,b^{10}\,c^{10}\,d^8+109350\,a^{14}\,b^{11}\,c^{11}\,d^7-51030\,a^{13}\,b^{12}\,c^{12}\,d^6+15795\,a^{12}\,b^{13}\,c^{13}\,d^5-2916\,a^{11}\,b^{14}\,c^{14}\,d^4+243\,a^{10}\,b^{15}\,c^{15}\,d^3\right)\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(\frac{1}{27\,a^4\,c^3}\right)}^{1/3}-9\,a^7\,b^{14}\,c^{11}\,d^4+90\,a^8\,b^{13}\,c^{10}\,d^5-405\,a^9\,b^{12}\,c^9\,d^6+1071\,a^{10}\,b^{11}\,c^8\,d^7-1827\,a^{11}\,b^{10}\,c^7\,d^8+2079\,a^{12}\,b^9\,c^6\,d^9-1575\,a^{13}\,b^8\,c^5\,d^{10}+765\,a^{14}\,b^7\,c^4\,d^{11}-216\,a^{15}\,b^6\,c^3\,d^{12}+27\,a^{16}\,b^5\,c^2\,d^{13}\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(\frac{1}{27\,a^4\,c^3}\right)}^{1/3}-\ln\left(\left({\left(b\,x^3+a\right)}^{1/3}\,\left(-54\,a^{18}\,b^4\,c^2\,d^{14}+486\,a^{17}\,b^5\,c^3\,d^{13}-2052\,a^{16}\,b^6\,c^4\,d^{12}+5400\,a^{15}\,b^7\,c^5\,d^{11}-9855\,a^{14}\,b^8\,c^6\,d^{10}+13041\,a^{13}\,b^9\,c^7\,d^9-12663\,a^{12}\,b^{10}\,c^8\,d^8+8937\,a^{11}\,b^{11}\,c^9\,d^7-4455\,a^{10}\,b^{12}\,c^{10}\,d^6+1485\,a^9\,b^{13}\,c^{11}\,d^5-297\,a^8\,b^{14}\,c^{12}\,d^4+27\,a^7\,b^{15}\,c^{13}\,d^3\right)-{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(\frac{1}{27\,a^4\,c^3}\right)}^{2/3}\,\left(-486\,a^{21}\,b^4\,c^4\,d^{14}+5103\,a^{20}\,b^5\,c^5\,d^{13}-24300\,a^{19}\,b^6\,c^6\,d^{12}+69255\,a^{18}\,b^7\,c^7\,d^{11}-131220\,a^{17}\,b^8\,c^8\,d^{10}+173502\,a^{16}\,b^9\,c^9\,d^9-163296\,a^{15}\,b^{10}\,c^{10}\,d^8+109350\,a^{14}\,b^{11}\,c^{11}\,d^7-51030\,a^{13}\,b^{12}\,c^{12}\,d^6+15795\,a^{12}\,b^{13}\,c^{13}\,d^5-2916\,a^{11}\,b^{14}\,c^{14}\,d^4+243\,a^{10}\,b^{15}\,c^{15}\,d^3\right)\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(\frac{1}{27\,a^4\,c^3}\right)}^{1/3}+9\,a^7\,b^{14}\,c^{11}\,d^4-90\,a^8\,b^{13}\,c^{10}\,d^5+405\,a^9\,b^{12}\,c^9\,d^6-1071\,a^{10}\,b^{11}\,c^8\,d^7+1827\,a^{11}\,b^{10}\,c^7\,d^8-2079\,a^{12}\,b^9\,c^6\,d^9+1575\,a^{13}\,b^8\,c^5\,d^{10}-765\,a^{14}\,b^7\,c^4\,d^{11}+216\,a^{15}\,b^6\,c^3\,d^{12}-27\,a^{16}\,b^5\,c^2\,d^{13}\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(\frac{1}{27\,a^4\,c^3}\right)}^{1/3}","Not used",1,"log(9*a^7*b^14*c^11*d^4 - ((a + b*x^3)^(1/3)*(27*a^7*b^15*c^13*d^3 - 297*a^8*b^14*c^12*d^4 + 1485*a^9*b^13*c^11*d^5 - 4455*a^10*b^12*c^10*d^6 + 8937*a^11*b^11*c^9*d^7 - 12663*a^12*b^10*c^8*d^8 + 13041*a^13*b^9*c^7*d^9 - 9855*a^14*b^8*c^6*d^10 + 5400*a^15*b^7*c^5*d^11 - 2052*a^16*b^6*c^4*d^12 + 486*a^17*b^5*c^3*d^13 - 54*a^18*b^4*c^2*d^14) - (-d^4/(27*b^4*c^7 + 27*a^4*c^3*d^4 - 108*a^3*b*c^4*d^3 + 162*a^2*b^2*c^5*d^2 - 108*a*b^3*c^6*d))^(2/3)*(243*a^10*b^15*c^15*d^3 - 2916*a^11*b^14*c^14*d^4 + 15795*a^12*b^13*c^13*d^5 - 51030*a^13*b^12*c^12*d^6 + 109350*a^14*b^11*c^11*d^7 - 163296*a^15*b^10*c^10*d^8 + 173502*a^16*b^9*c^9*d^9 - 131220*a^17*b^8*c^8*d^10 + 69255*a^18*b^7*c^7*d^11 - 24300*a^19*b^6*c^6*d^12 + 5103*a^20*b^5*c^5*d^13 - 486*a^21*b^4*c^4*d^14))*(-d^4/(27*b^4*c^7 + 27*a^4*c^3*d^4 - 108*a^3*b*c^4*d^3 + 162*a^2*b^2*c^5*d^2 - 108*a*b^3*c^6*d))^(1/3) - 90*a^8*b^13*c^10*d^5 + 405*a^9*b^12*c^9*d^6 - 1071*a^10*b^11*c^8*d^7 + 1827*a^11*b^10*c^7*d^8 - 2079*a^12*b^9*c^6*d^9 + 1575*a^13*b^8*c^5*d^10 - 765*a^14*b^7*c^4*d^11 + 216*a^15*b^6*c^3*d^12 - 27*a^16*b^5*c^2*d^13)*(-d^4/(27*b^4*c^7 + 27*a^4*c^3*d^4 - 108*a^3*b*c^4*d^3 + 162*a^2*b^2*c^5*d^2 - 108*a*b^3*c^6*d))^(1/3) + log(9*a^7*b^14*c^11*d^4 - ((a + b*x^3)^(1/3)*(27*a^7*b^15*c^13*d^3 - 297*a^8*b^14*c^12*d^4 + 1485*a^9*b^13*c^11*d^5 - 4455*a^10*b^12*c^10*d^6 + 8937*a^11*b^11*c^9*d^7 - 12663*a^12*b^10*c^8*d^8 + 13041*a^13*b^9*c^7*d^9 - 9855*a^14*b^8*c^6*d^10 + 5400*a^15*b^7*c^5*d^11 - 2052*a^16*b^6*c^4*d^12 + 486*a^17*b^5*c^3*d^13 - 54*a^18*b^4*c^2*d^14) - (1/(27*a^4*c^3))^(2/3)*(243*a^10*b^15*c^15*d^3 - 2916*a^11*b^14*c^14*d^4 + 15795*a^12*b^13*c^13*d^5 - 51030*a^13*b^12*c^12*d^6 + 109350*a^14*b^11*c^11*d^7 - 163296*a^15*b^10*c^10*d^8 + 173502*a^16*b^9*c^9*d^9 - 131220*a^17*b^8*c^8*d^10 + 69255*a^18*b^7*c^7*d^11 - 24300*a^19*b^6*c^6*d^12 + 5103*a^20*b^5*c^5*d^13 - 486*a^21*b^4*c^4*d^14))*(1/(27*a^4*c^3))^(1/3) - 90*a^8*b^13*c^10*d^5 + 405*a^9*b^12*c^9*d^6 - 1071*a^10*b^11*c^8*d^7 + 1827*a^11*b^10*c^7*d^8 - 2079*a^12*b^9*c^6*d^9 + 1575*a^13*b^8*c^5*d^10 - 765*a^14*b^7*c^4*d^11 + 216*a^15*b^6*c^3*d^12 - 27*a^16*b^5*c^2*d^13)*(1/(27*a^4*c^3))^(1/3) + (log(((3^(1/2)*1i - 1)*(-d^4/(27*b^4*c^7 + 27*a^4*c^3*d^4 - 108*a^3*b*c^4*d^3 + 162*a^2*b^2*c^5*d^2 - 108*a*b^3*c^6*d))^(1/3)*((a + b*x^3)^(1/3)*(27*a^7*b^15*c^13*d^3 - 297*a^8*b^14*c^12*d^4 + 1485*a^9*b^13*c^11*d^5 - 4455*a^10*b^12*c^10*d^6 + 8937*a^11*b^11*c^9*d^7 - 12663*a^12*b^10*c^8*d^8 + 13041*a^13*b^9*c^7*d^9 - 9855*a^14*b^8*c^6*d^10 + 5400*a^15*b^7*c^5*d^11 - 2052*a^16*b^6*c^4*d^12 + 486*a^17*b^5*c^3*d^13 - 54*a^18*b^4*c^2*d^14) - ((3^(1/2)*1i - 1)^2*(-d^4/(27*b^4*c^7 + 27*a^4*c^3*d^4 - 108*a^3*b*c^4*d^3 + 162*a^2*b^2*c^5*d^2 - 108*a*b^3*c^6*d))^(2/3)*(243*a^10*b^15*c^15*d^3 - 2916*a^11*b^14*c^14*d^4 + 15795*a^12*b^13*c^13*d^5 - 51030*a^13*b^12*c^12*d^6 + 109350*a^14*b^11*c^11*d^7 - 163296*a^15*b^10*c^10*d^8 + 173502*a^16*b^9*c^9*d^9 - 131220*a^17*b^8*c^8*d^10 + 69255*a^18*b^7*c^7*d^11 - 24300*a^19*b^6*c^6*d^12 + 5103*a^20*b^5*c^5*d^13 - 486*a^21*b^4*c^4*d^14))/4))/2 - 9*a^7*b^14*c^11*d^4 + 90*a^8*b^13*c^10*d^5 - 405*a^9*b^12*c^9*d^6 + 1071*a^10*b^11*c^8*d^7 - 1827*a^11*b^10*c^7*d^8 + 2079*a^12*b^9*c^6*d^9 - 1575*a^13*b^8*c^5*d^10 + 765*a^14*b^7*c^4*d^11 - 216*a^15*b^6*c^3*d^12 + 27*a^16*b^5*c^2*d^13)*(3^(1/2)*1i - 1)*(-d^4/(27*b^4*c^7 + 27*a^4*c^3*d^4 - 108*a^3*b*c^4*d^3 + 162*a^2*b^2*c^5*d^2 - 108*a*b^3*c^6*d))^(1/3))/2 - (log(((3^(1/2)*1i + 1)*(-d^4/(27*b^4*c^7 + 27*a^4*c^3*d^4 - 108*a^3*b*c^4*d^3 + 162*a^2*b^2*c^5*d^2 - 108*a*b^3*c^6*d))^(1/3)*((a + b*x^3)^(1/3)*(27*a^7*b^15*c^13*d^3 - 297*a^8*b^14*c^12*d^4 + 1485*a^9*b^13*c^11*d^5 - 4455*a^10*b^12*c^10*d^6 + 8937*a^11*b^11*c^9*d^7 - 12663*a^12*b^10*c^8*d^8 + 13041*a^13*b^9*c^7*d^9 - 9855*a^14*b^8*c^6*d^10 + 5400*a^15*b^7*c^5*d^11 - 2052*a^16*b^6*c^4*d^12 + 486*a^17*b^5*c^3*d^13 - 54*a^18*b^4*c^2*d^14) - ((3^(1/2)*1i + 1)^2*(-d^4/(27*b^4*c^7 + 27*a^4*c^3*d^4 - 108*a^3*b*c^4*d^3 + 162*a^2*b^2*c^5*d^2 - 108*a*b^3*c^6*d))^(2/3)*(243*a^10*b^15*c^15*d^3 - 2916*a^11*b^14*c^14*d^4 + 15795*a^12*b^13*c^13*d^5 - 51030*a^13*b^12*c^12*d^6 + 109350*a^14*b^11*c^11*d^7 - 163296*a^15*b^10*c^10*d^8 + 173502*a^16*b^9*c^9*d^9 - 131220*a^17*b^8*c^8*d^10 + 69255*a^18*b^7*c^7*d^11 - 24300*a^19*b^6*c^6*d^12 + 5103*a^20*b^5*c^5*d^13 - 486*a^21*b^4*c^4*d^14))/4))/2 + 9*a^7*b^14*c^11*d^4 - 90*a^8*b^13*c^10*d^5 + 405*a^9*b^12*c^9*d^6 - 1071*a^10*b^11*c^8*d^7 + 1827*a^11*b^10*c^7*d^8 - 2079*a^12*b^9*c^6*d^9 + 1575*a^13*b^8*c^5*d^10 - 765*a^14*b^7*c^4*d^11 + 216*a^15*b^6*c^3*d^12 - 27*a^16*b^5*c^2*d^13)*(3^(1/2)*1i + 1)*(-d^4/(27*b^4*c^7 + 27*a^4*c^3*d^4 - 108*a^3*b*c^4*d^3 + 162*a^2*b^2*c^5*d^2 - 108*a*b^3*c^6*d))^(1/3))/2 - b/((a + b*x^3)^(1/3)*(a^2*d - a*b*c)) + log(((a + b*x^3)^(1/3)*(27*a^7*b^15*c^13*d^3 - 297*a^8*b^14*c^12*d^4 + 1485*a^9*b^13*c^11*d^5 - 4455*a^10*b^12*c^10*d^6 + 8937*a^11*b^11*c^9*d^7 - 12663*a^12*b^10*c^8*d^8 + 13041*a^13*b^9*c^7*d^9 - 9855*a^14*b^8*c^6*d^10 + 5400*a^15*b^7*c^5*d^11 - 2052*a^16*b^6*c^4*d^12 + 486*a^17*b^5*c^3*d^13 - 54*a^18*b^4*c^2*d^14) - ((3^(1/2)*1i)/2 - 1/2)^2*(1/(27*a^4*c^3))^(2/3)*(243*a^10*b^15*c^15*d^3 - 2916*a^11*b^14*c^14*d^4 + 15795*a^12*b^13*c^13*d^5 - 51030*a^13*b^12*c^12*d^6 + 109350*a^14*b^11*c^11*d^7 - 163296*a^15*b^10*c^10*d^8 + 173502*a^16*b^9*c^9*d^9 - 131220*a^17*b^8*c^8*d^10 + 69255*a^18*b^7*c^7*d^11 - 24300*a^19*b^6*c^6*d^12 + 5103*a^20*b^5*c^5*d^13 - 486*a^21*b^4*c^4*d^14))*((3^(1/2)*1i)/2 - 1/2)*(1/(27*a^4*c^3))^(1/3) - 9*a^7*b^14*c^11*d^4 + 90*a^8*b^13*c^10*d^5 - 405*a^9*b^12*c^9*d^6 + 1071*a^10*b^11*c^8*d^7 - 1827*a^11*b^10*c^7*d^8 + 2079*a^12*b^9*c^6*d^9 - 1575*a^13*b^8*c^5*d^10 + 765*a^14*b^7*c^4*d^11 - 216*a^15*b^6*c^3*d^12 + 27*a^16*b^5*c^2*d^13)*((3^(1/2)*1i)/2 - 1/2)*(1/(27*a^4*c^3))^(1/3) - log(((a + b*x^3)^(1/3)*(27*a^7*b^15*c^13*d^3 - 297*a^8*b^14*c^12*d^4 + 1485*a^9*b^13*c^11*d^5 - 4455*a^10*b^12*c^10*d^6 + 8937*a^11*b^11*c^9*d^7 - 12663*a^12*b^10*c^8*d^8 + 13041*a^13*b^9*c^7*d^9 - 9855*a^14*b^8*c^6*d^10 + 5400*a^15*b^7*c^5*d^11 - 2052*a^16*b^6*c^4*d^12 + 486*a^17*b^5*c^3*d^13 - 54*a^18*b^4*c^2*d^14) - ((3^(1/2)*1i)/2 + 1/2)^2*(1/(27*a^4*c^3))^(2/3)*(243*a^10*b^15*c^15*d^3 - 2916*a^11*b^14*c^14*d^4 + 15795*a^12*b^13*c^13*d^5 - 51030*a^13*b^12*c^12*d^6 + 109350*a^14*b^11*c^11*d^7 - 163296*a^15*b^10*c^10*d^8 + 173502*a^16*b^9*c^9*d^9 - 131220*a^17*b^8*c^8*d^10 + 69255*a^18*b^7*c^7*d^11 - 24300*a^19*b^6*c^6*d^12 + 5103*a^20*b^5*c^5*d^13 - 486*a^21*b^4*c^4*d^14))*((3^(1/2)*1i)/2 + 1/2)*(1/(27*a^4*c^3))^(1/3) + 9*a^7*b^14*c^11*d^4 - 90*a^8*b^13*c^10*d^5 + 405*a^9*b^12*c^9*d^6 - 1071*a^10*b^11*c^8*d^7 + 1827*a^11*b^10*c^7*d^8 - 2079*a^12*b^9*c^6*d^9 + 1575*a^13*b^8*c^5*d^10 - 765*a^14*b^7*c^4*d^11 + 216*a^15*b^6*c^3*d^12 - 27*a^16*b^5*c^2*d^13)*((3^(1/2)*1i)/2 + 1/2)*(1/(27*a^4*c^3))^(1/3)","B"
753,1,5875,357,6.390038,"\text{Not used}","int(1/(x^4*(a + b*x^3)^(4/3)*(c + d*x^3)),x)","\ln\left({\left(\frac{d^7}{27\,a^4\,c^6\,d^4-108\,a^3\,b\,c^7\,d^3+162\,a^2\,b^2\,c^8\,d^2-108\,a\,b^3\,c^9\,d+27\,b^4\,c^{10}}\right)}^{2/3}\,\left(419904\,a^{13}\,b^{17}\,c^{20}\,d^4-\left({\left(b\,x^3+a\right)}^{1/3}\,\left(1062882\,a^{27}\,b^4\,c^9\,d^{16}-8148762\,a^{26}\,b^5\,c^{10}\,d^{15}+25745364\,a^{25}\,b^6\,c^{11}\,d^{14}-38736144\,a^{24}\,b^7\,c^{12}\,d^{13}+12105045\,a^{23}\,b^8\,c^{13}\,d^{12}+55092717\,a^{22}\,b^9\,c^{14}\,d^{11}-93710763\,a^{21}\,b^{10}\,c^{15}\,d^{10}+42338133\,a^{20}\,b^{11}\,c^{16}\,d^9+56509893\,a^{19}\,b^{12}\,c^{17}\,d^8-107173935\,a^{18}\,b^{13}\,c^{18}\,d^7+83790531\,a^{17}\,b^{14}\,c^{19}\,d^6-36905625\,a^{16}\,b^{15}\,c^{20}\,d^5+8975448\,a^{15}\,b^{16}\,c^{21}\,d^4-944784\,a^{14}\,b^{17}\,c^{22}\,d^3\right)+{\left(\frac{d^7}{27\,a^4\,c^6\,d^4-108\,a^3\,b\,c^7\,d^3+162\,a^2\,b^2\,c^8\,d^2-108\,a\,b^3\,c^9\,d+27\,b^4\,c^{10}}\right)}^{2/3}\,\left(-9565938\,a^{30}\,b^4\,c^{13}\,d^{14}+100442349\,a^{29}\,b^5\,c^{14}\,d^{13}-478296900\,a^{28}\,b^6\,c^{15}\,d^{12}+1363146165\,a^{27}\,b^7\,c^{16}\,d^{11}-2582803260\,a^{26}\,b^8\,c^{17}\,d^{10}+3415039866\,a^{25}\,b^9\,c^{18}\,d^9-3214155168\,a^{24}\,b^{10}\,c^{19}\,d^8+2152336050\,a^{23}\,b^{11}\,c^{20}\,d^7-1004423490\,a^{22}\,b^{12}\,c^{21}\,d^6+310892985\,a^{21}\,b^{13}\,c^{22}\,d^5-57395628\,a^{20}\,b^{14}\,c^{23}\,d^4+4782969\,a^{19}\,b^{15}\,c^{24}\,d^3\right)\right)\,{\left(\frac{d^7}{27\,a^4\,c^6\,d^4-108\,a^3\,b\,c^7\,d^3+162\,a^2\,b^2\,c^8\,d^2-108\,a\,b^3\,c^9\,d+27\,b^4\,c^{10}}\right)}^{1/3}-3254256\,a^{14}\,b^{16}\,c^{19}\,d^5+10156428\,a^{15}\,b^{15}\,c^{18}\,d^6-14781933\,a^{16}\,b^{14}\,c^{17}\,d^7+4920750\,a^{17}\,b^{13}\,c^{16}\,d^8+15529887\,a^{18}\,b^{12}\,c^{15}\,d^9-22182741\,a^{19}\,b^{11}\,c^{14}\,d^{10}+5412825\,a^{20}\,b^{10}\,c^{13}\,d^{11}+13404123\,a^{21}\,b^9\,c^{12}\,d^{12}-15713595\,a^{22}\,b^8\,c^{11}\,d^{13}+7801029\,a^{23}\,b^7\,c^{10}\,d^{14}-1889568\,a^{24}\,b^6\,c^9\,d^{15}+177147\,a^{25}\,b^5\,c^8\,d^{16}\right)-{\left(b\,x^3+a\right)}^{1/3}\,\left(26244\,a^{22}\,b^5\,c^4\,d^{18}-113724\,a^{21}\,b^6\,c^5\,d^{17}+107892\,a^{20}\,b^7\,c^6\,d^{16}+224532\,a^{19}\,b^8\,c^7\,d^{15}-551124\,a^{18}\,b^9\,c^8\,d^{14}+265356\,a^{17}\,b^{10}\,c^9\,d^{13}+347004\,a^{16}\,b^{11}\,c^{10}\,d^{12}-516132\,a^{15}\,b^{12}\,c^{11}\,d^{11}+256608\,a^{14}\,b^{13}\,c^{12}\,d^{10}-46656\,a^{13}\,b^{14}\,c^{13}\,d^9\right)\right)\,{\left(\frac{d^7}{27\,a^4\,c^6\,d^4-108\,a^3\,b\,c^7\,d^3+162\,a^2\,b^2\,c^8\,d^2-108\,a\,b^3\,c^9\,d+27\,b^4\,c^{10}}\right)}^{1/3}+\frac{\frac{b^2}{a^2\,d-a\,b\,c}+\frac{b\,\left(b\,x^3+a\right)\,\left(a\,d-4\,b\,c\right)}{3\,a^2\,c\,\left(a\,d-b\,c\right)}}{a\,{\left(b\,x^3+a\right)}^{1/3}-{\left(b\,x^3+a\right)}^{4/3}}+\ln\left({\left(-\frac{27\,a^3\,d^3+108\,a^2\,b\,c\,d^2+144\,a\,b^2\,c^2\,d+64\,b^3\,c^3}{729\,a^7\,c^6}\right)}^{2/3}\,\left(419904\,a^{13}\,b^{17}\,c^{20}\,d^4-\left({\left(b\,x^3+a\right)}^{1/3}\,\left(1062882\,a^{27}\,b^4\,c^9\,d^{16}-8148762\,a^{26}\,b^5\,c^{10}\,d^{15}+25745364\,a^{25}\,b^6\,c^{11}\,d^{14}-38736144\,a^{24}\,b^7\,c^{12}\,d^{13}+12105045\,a^{23}\,b^8\,c^{13}\,d^{12}+55092717\,a^{22}\,b^9\,c^{14}\,d^{11}-93710763\,a^{21}\,b^{10}\,c^{15}\,d^{10}+42338133\,a^{20}\,b^{11}\,c^{16}\,d^9+56509893\,a^{19}\,b^{12}\,c^{17}\,d^8-107173935\,a^{18}\,b^{13}\,c^{18}\,d^7+83790531\,a^{17}\,b^{14}\,c^{19}\,d^6-36905625\,a^{16}\,b^{15}\,c^{20}\,d^5+8975448\,a^{15}\,b^{16}\,c^{21}\,d^4-944784\,a^{14}\,b^{17}\,c^{22}\,d^3\right)+{\left(-\frac{27\,a^3\,d^3+108\,a^2\,b\,c\,d^2+144\,a\,b^2\,c^2\,d+64\,b^3\,c^3}{729\,a^7\,c^6}\right)}^{2/3}\,\left(-9565938\,a^{30}\,b^4\,c^{13}\,d^{14}+100442349\,a^{29}\,b^5\,c^{14}\,d^{13}-478296900\,a^{28}\,b^6\,c^{15}\,d^{12}+1363146165\,a^{27}\,b^7\,c^{16}\,d^{11}-2582803260\,a^{26}\,b^8\,c^{17}\,d^{10}+3415039866\,a^{25}\,b^9\,c^{18}\,d^9-3214155168\,a^{24}\,b^{10}\,c^{19}\,d^8+2152336050\,a^{23}\,b^{11}\,c^{20}\,d^7-1004423490\,a^{22}\,b^{12}\,c^{21}\,d^6+310892985\,a^{21}\,b^{13}\,c^{22}\,d^5-57395628\,a^{20}\,b^{14}\,c^{23}\,d^4+4782969\,a^{19}\,b^{15}\,c^{24}\,d^3\right)\right)\,{\left(-\frac{27\,a^3\,d^3+108\,a^2\,b\,c\,d^2+144\,a\,b^2\,c^2\,d+64\,b^3\,c^3}{729\,a^7\,c^6}\right)}^{1/3}-3254256\,a^{14}\,b^{16}\,c^{19}\,d^5+10156428\,a^{15}\,b^{15}\,c^{18}\,d^6-14781933\,a^{16}\,b^{14}\,c^{17}\,d^7+4920750\,a^{17}\,b^{13}\,c^{16}\,d^8+15529887\,a^{18}\,b^{12}\,c^{15}\,d^9-22182741\,a^{19}\,b^{11}\,c^{14}\,d^{10}+5412825\,a^{20}\,b^{10}\,c^{13}\,d^{11}+13404123\,a^{21}\,b^9\,c^{12}\,d^{12}-15713595\,a^{22}\,b^8\,c^{11}\,d^{13}+7801029\,a^{23}\,b^7\,c^{10}\,d^{14}-1889568\,a^{24}\,b^6\,c^9\,d^{15}+177147\,a^{25}\,b^5\,c^8\,d^{16}\right)-{\left(b\,x^3+a\right)}^{1/3}\,\left(26244\,a^{22}\,b^5\,c^4\,d^{18}-113724\,a^{21}\,b^6\,c^5\,d^{17}+107892\,a^{20}\,b^7\,c^6\,d^{16}+224532\,a^{19}\,b^8\,c^7\,d^{15}-551124\,a^{18}\,b^9\,c^8\,d^{14}+265356\,a^{17}\,b^{10}\,c^9\,d^{13}+347004\,a^{16}\,b^{11}\,c^{10}\,d^{12}-516132\,a^{15}\,b^{12}\,c^{11}\,d^{11}+256608\,a^{14}\,b^{13}\,c^{12}\,d^{10}-46656\,a^{13}\,b^{14}\,c^{13}\,d^9\right)\right)\,{\left(-\frac{27\,a^3\,d^3+108\,a^2\,b\,c\,d^2+144\,a\,b^2\,c^2\,d+64\,b^3\,c^3}{729\,a^7\,c^6}\right)}^{1/3}+\frac{\ln\left(-{\left(b\,x^3+a\right)}^{1/3}\,\left(26244\,a^{22}\,b^5\,c^4\,d^{18}-113724\,a^{21}\,b^6\,c^5\,d^{17}+107892\,a^{20}\,b^7\,c^6\,d^{16}+224532\,a^{19}\,b^8\,c^7\,d^{15}-551124\,a^{18}\,b^9\,c^8\,d^{14}+265356\,a^{17}\,b^{10}\,c^9\,d^{13}+347004\,a^{16}\,b^{11}\,c^{10}\,d^{12}-516132\,a^{15}\,b^{12}\,c^{11}\,d^{11}+256608\,a^{14}\,b^{13}\,c^{12}\,d^{10}-46656\,a^{13}\,b^{14}\,c^{13}\,d^9\right)+\frac{{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,{\left(\frac{d^7}{27\,a^4\,c^6\,d^4-108\,a^3\,b\,c^7\,d^3+162\,a^2\,b^2\,c^8\,d^2-108\,a\,b^3\,c^9\,d+27\,b^4\,c^{10}}\right)}^{2/3}\,\left(419904\,a^{13}\,b^{17}\,c^{20}\,d^4-\frac{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(\frac{d^7}{27\,a^4\,c^6\,d^4-108\,a^3\,b\,c^7\,d^3+162\,a^2\,b^2\,c^8\,d^2-108\,a\,b^3\,c^9\,d+27\,b^4\,c^{10}}\right)}^{1/3}\,\left({\left(b\,x^3+a\right)}^{1/3}\,\left(1062882\,a^{27}\,b^4\,c^9\,d^{16}-8148762\,a^{26}\,b^5\,c^{10}\,d^{15}+25745364\,a^{25}\,b^6\,c^{11}\,d^{14}-38736144\,a^{24}\,b^7\,c^{12}\,d^{13}+12105045\,a^{23}\,b^8\,c^{13}\,d^{12}+55092717\,a^{22}\,b^9\,c^{14}\,d^{11}-93710763\,a^{21}\,b^{10}\,c^{15}\,d^{10}+42338133\,a^{20}\,b^{11}\,c^{16}\,d^9+56509893\,a^{19}\,b^{12}\,c^{17}\,d^8-107173935\,a^{18}\,b^{13}\,c^{18}\,d^7+83790531\,a^{17}\,b^{14}\,c^{19}\,d^6-36905625\,a^{16}\,b^{15}\,c^{20}\,d^5+8975448\,a^{15}\,b^{16}\,c^{21}\,d^4-944784\,a^{14}\,b^{17}\,c^{22}\,d^3\right)+\frac{{\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,{\left(\frac{d^7}{27\,a^4\,c^6\,d^4-108\,a^3\,b\,c^7\,d^3+162\,a^2\,b^2\,c^8\,d^2-108\,a\,b^3\,c^9\,d+27\,b^4\,c^{10}}\right)}^{2/3}\,\left(-9565938\,a^{30}\,b^4\,c^{13}\,d^{14}+100442349\,a^{29}\,b^5\,c^{14}\,d^{13}-478296900\,a^{28}\,b^6\,c^{15}\,d^{12}+1363146165\,a^{27}\,b^7\,c^{16}\,d^{11}-2582803260\,a^{26}\,b^8\,c^{17}\,d^{10}+3415039866\,a^{25}\,b^9\,c^{18}\,d^9-3214155168\,a^{24}\,b^{10}\,c^{19}\,d^8+2152336050\,a^{23}\,b^{11}\,c^{20}\,d^7-1004423490\,a^{22}\,b^{12}\,c^{21}\,d^6+310892985\,a^{21}\,b^{13}\,c^{22}\,d^5-57395628\,a^{20}\,b^{14}\,c^{23}\,d^4+4782969\,a^{19}\,b^{15}\,c^{24}\,d^3\right)}{4}\right)}{2}-3254256\,a^{14}\,b^{16}\,c^{19}\,d^5+10156428\,a^{15}\,b^{15}\,c^{18}\,d^6-14781933\,a^{16}\,b^{14}\,c^{17}\,d^7+4920750\,a^{17}\,b^{13}\,c^{16}\,d^8+15529887\,a^{18}\,b^{12}\,c^{15}\,d^9-22182741\,a^{19}\,b^{11}\,c^{14}\,d^{10}+5412825\,a^{20}\,b^{10}\,c^{13}\,d^{11}+13404123\,a^{21}\,b^9\,c^{12}\,d^{12}-15713595\,a^{22}\,b^8\,c^{11}\,d^{13}+7801029\,a^{23}\,b^7\,c^{10}\,d^{14}-1889568\,a^{24}\,b^6\,c^9\,d^{15}+177147\,a^{25}\,b^5\,c^8\,d^{16}\right)}{4}\right)\,\left(-1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(\frac{d^7}{27\,a^4\,c^6\,d^4-108\,a^3\,b\,c^7\,d^3+162\,a^2\,b^2\,c^8\,d^2-108\,a\,b^3\,c^9\,d+27\,b^4\,c^{10}}\right)}^{1/3}}{2}-\frac{\ln\left(-{\left(b\,x^3+a\right)}^{1/3}\,\left(26244\,a^{22}\,b^5\,c^4\,d^{18}-113724\,a^{21}\,b^6\,c^5\,d^{17}+107892\,a^{20}\,b^7\,c^6\,d^{16}+224532\,a^{19}\,b^8\,c^7\,d^{15}-551124\,a^{18}\,b^9\,c^8\,d^{14}+265356\,a^{17}\,b^{10}\,c^9\,d^{13}+347004\,a^{16}\,b^{11}\,c^{10}\,d^{12}-516132\,a^{15}\,b^{12}\,c^{11}\,d^{11}+256608\,a^{14}\,b^{13}\,c^{12}\,d^{10}-46656\,a^{13}\,b^{14}\,c^{13}\,d^9\right)+\frac{{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,{\left(\frac{d^7}{27\,a^4\,c^6\,d^4-108\,a^3\,b\,c^7\,d^3+162\,a^2\,b^2\,c^8\,d^2-108\,a\,b^3\,c^9\,d+27\,b^4\,c^{10}}\right)}^{2/3}\,\left(\frac{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(\frac{d^7}{27\,a^4\,c^6\,d^4-108\,a^3\,b\,c^7\,d^3+162\,a^2\,b^2\,c^8\,d^2-108\,a\,b^3\,c^9\,d+27\,b^4\,c^{10}}\right)}^{1/3}\,\left({\left(b\,x^3+a\right)}^{1/3}\,\left(1062882\,a^{27}\,b^4\,c^9\,d^{16}-8148762\,a^{26}\,b^5\,c^{10}\,d^{15}+25745364\,a^{25}\,b^6\,c^{11}\,d^{14}-38736144\,a^{24}\,b^7\,c^{12}\,d^{13}+12105045\,a^{23}\,b^8\,c^{13}\,d^{12}+55092717\,a^{22}\,b^9\,c^{14}\,d^{11}-93710763\,a^{21}\,b^{10}\,c^{15}\,d^{10}+42338133\,a^{20}\,b^{11}\,c^{16}\,d^9+56509893\,a^{19}\,b^{12}\,c^{17}\,d^8-107173935\,a^{18}\,b^{13}\,c^{18}\,d^7+83790531\,a^{17}\,b^{14}\,c^{19}\,d^6-36905625\,a^{16}\,b^{15}\,c^{20}\,d^5+8975448\,a^{15}\,b^{16}\,c^{21}\,d^4-944784\,a^{14}\,b^{17}\,c^{22}\,d^3\right)+\frac{{\left(1+\sqrt{3}\,1{}\mathrm{i}\right)}^2\,{\left(\frac{d^7}{27\,a^4\,c^6\,d^4-108\,a^3\,b\,c^7\,d^3+162\,a^2\,b^2\,c^8\,d^2-108\,a\,b^3\,c^9\,d+27\,b^4\,c^{10}}\right)}^{2/3}\,\left(-9565938\,a^{30}\,b^4\,c^{13}\,d^{14}+100442349\,a^{29}\,b^5\,c^{14}\,d^{13}-478296900\,a^{28}\,b^6\,c^{15}\,d^{12}+1363146165\,a^{27}\,b^7\,c^{16}\,d^{11}-2582803260\,a^{26}\,b^8\,c^{17}\,d^{10}+3415039866\,a^{25}\,b^9\,c^{18}\,d^9-3214155168\,a^{24}\,b^{10}\,c^{19}\,d^8+2152336050\,a^{23}\,b^{11}\,c^{20}\,d^7-1004423490\,a^{22}\,b^{12}\,c^{21}\,d^6+310892985\,a^{21}\,b^{13}\,c^{22}\,d^5-57395628\,a^{20}\,b^{14}\,c^{23}\,d^4+4782969\,a^{19}\,b^{15}\,c^{24}\,d^3\right)}{4}\right)}{2}+419904\,a^{13}\,b^{17}\,c^{20}\,d^4-3254256\,a^{14}\,b^{16}\,c^{19}\,d^5+10156428\,a^{15}\,b^{15}\,c^{18}\,d^6-14781933\,a^{16}\,b^{14}\,c^{17}\,d^7+4920750\,a^{17}\,b^{13}\,c^{16}\,d^8+15529887\,a^{18}\,b^{12}\,c^{15}\,d^9-22182741\,a^{19}\,b^{11}\,c^{14}\,d^{10}+5412825\,a^{20}\,b^{10}\,c^{13}\,d^{11}+13404123\,a^{21}\,b^9\,c^{12}\,d^{12}-15713595\,a^{22}\,b^8\,c^{11}\,d^{13}+7801029\,a^{23}\,b^7\,c^{10}\,d^{14}-1889568\,a^{24}\,b^6\,c^9\,d^{15}+177147\,a^{25}\,b^5\,c^8\,d^{16}\right)}{4}\right)\,\left(1+\sqrt{3}\,1{}\mathrm{i}\right)\,{\left(\frac{d^7}{27\,a^4\,c^6\,d^4-108\,a^3\,b\,c^7\,d^3+162\,a^2\,b^2\,c^8\,d^2-108\,a\,b^3\,c^9\,d+27\,b^4\,c^{10}}\right)}^{1/3}}{2}-\ln\left(-{\left(b\,x^3+a\right)}^{1/3}\,\left(26244\,a^{22}\,b^5\,c^4\,d^{18}-113724\,a^{21}\,b^6\,c^5\,d^{17}+107892\,a^{20}\,b^7\,c^6\,d^{16}+224532\,a^{19}\,b^8\,c^7\,d^{15}-551124\,a^{18}\,b^9\,c^8\,d^{14}+265356\,a^{17}\,b^{10}\,c^9\,d^{13}+347004\,a^{16}\,b^{11}\,c^{10}\,d^{12}-516132\,a^{15}\,b^{12}\,c^{11}\,d^{11}+256608\,a^{14}\,b^{13}\,c^{12}\,d^{10}-46656\,a^{13}\,b^{14}\,c^{13}\,d^9\right)+{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(-\frac{27\,a^3\,d^3+108\,a^2\,b\,c\,d^2+144\,a\,b^2\,c^2\,d+64\,b^3\,c^3}{729\,a^7\,c^6}\right)}^{2/3}\,\left(\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left({\left(b\,x^3+a\right)}^{1/3}\,\left(1062882\,a^{27}\,b^4\,c^9\,d^{16}-8148762\,a^{26}\,b^5\,c^{10}\,d^{15}+25745364\,a^{25}\,b^6\,c^{11}\,d^{14}-38736144\,a^{24}\,b^7\,c^{12}\,d^{13}+12105045\,a^{23}\,b^8\,c^{13}\,d^{12}+55092717\,a^{22}\,b^9\,c^{14}\,d^{11}-93710763\,a^{21}\,b^{10}\,c^{15}\,d^{10}+42338133\,a^{20}\,b^{11}\,c^{16}\,d^9+56509893\,a^{19}\,b^{12}\,c^{17}\,d^8-107173935\,a^{18}\,b^{13}\,c^{18}\,d^7+83790531\,a^{17}\,b^{14}\,c^{19}\,d^6-36905625\,a^{16}\,b^{15}\,c^{20}\,d^5+8975448\,a^{15}\,b^{16}\,c^{21}\,d^4-944784\,a^{14}\,b^{17}\,c^{22}\,d^3\right)+{\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(-\frac{27\,a^3\,d^3+108\,a^2\,b\,c\,d^2+144\,a\,b^2\,c^2\,d+64\,b^3\,c^3}{729\,a^7\,c^6}\right)}^{2/3}\,\left(-9565938\,a^{30}\,b^4\,c^{13}\,d^{14}+100442349\,a^{29}\,b^5\,c^{14}\,d^{13}-478296900\,a^{28}\,b^6\,c^{15}\,d^{12}+1363146165\,a^{27}\,b^7\,c^{16}\,d^{11}-2582803260\,a^{26}\,b^8\,c^{17}\,d^{10}+3415039866\,a^{25}\,b^9\,c^{18}\,d^9-3214155168\,a^{24}\,b^{10}\,c^{19}\,d^8+2152336050\,a^{23}\,b^{11}\,c^{20}\,d^7-1004423490\,a^{22}\,b^{12}\,c^{21}\,d^6+310892985\,a^{21}\,b^{13}\,c^{22}\,d^5-57395628\,a^{20}\,b^{14}\,c^{23}\,d^4+4782969\,a^{19}\,b^{15}\,c^{24}\,d^3\right)\right)\,{\left(-\frac{27\,a^3\,d^3+108\,a^2\,b\,c\,d^2+144\,a\,b^2\,c^2\,d+64\,b^3\,c^3}{729\,a^7\,c^6}\right)}^{1/3}+419904\,a^{13}\,b^{17}\,c^{20}\,d^4-3254256\,a^{14}\,b^{16}\,c^{19}\,d^5+10156428\,a^{15}\,b^{15}\,c^{18}\,d^6-14781933\,a^{16}\,b^{14}\,c^{17}\,d^7+4920750\,a^{17}\,b^{13}\,c^{16}\,d^8+15529887\,a^{18}\,b^{12}\,c^{15}\,d^9-22182741\,a^{19}\,b^{11}\,c^{14}\,d^{10}+5412825\,a^{20}\,b^{10}\,c^{13}\,d^{11}+13404123\,a^{21}\,b^9\,c^{12}\,d^{12}-15713595\,a^{22}\,b^8\,c^{11}\,d^{13}+7801029\,a^{23}\,b^7\,c^{10}\,d^{14}-1889568\,a^{24}\,b^6\,c^9\,d^{15}+177147\,a^{25}\,b^5\,c^8\,d^{16}\right)\right)\,\left(\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{27\,a^3\,d^3+108\,a^2\,b\,c\,d^2+144\,a\,b^2\,c^2\,d+64\,b^3\,c^3}{729\,a^7\,c^6}\right)}^{1/3}+\ln\left(-{\left(b\,x^3+a\right)}^{1/3}\,\left(26244\,a^{22}\,b^5\,c^4\,d^{18}-113724\,a^{21}\,b^6\,c^5\,d^{17}+107892\,a^{20}\,b^7\,c^6\,d^{16}+224532\,a^{19}\,b^8\,c^7\,d^{15}-551124\,a^{18}\,b^9\,c^8\,d^{14}+265356\,a^{17}\,b^{10}\,c^9\,d^{13}+347004\,a^{16}\,b^{11}\,c^{10}\,d^{12}-516132\,a^{15}\,b^{12}\,c^{11}\,d^{11}+256608\,a^{14}\,b^{13}\,c^{12}\,d^{10}-46656\,a^{13}\,b^{14}\,c^{13}\,d^9\right)+{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(-\frac{27\,a^3\,d^3+108\,a^2\,b\,c\,d^2+144\,a\,b^2\,c^2\,d+64\,b^3\,c^3}{729\,a^7\,c^6}\right)}^{2/3}\,\left(419904\,a^{13}\,b^{17}\,c^{20}\,d^4-\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,\left({\left(b\,x^3+a\right)}^{1/3}\,\left(1062882\,a^{27}\,b^4\,c^9\,d^{16}-8148762\,a^{26}\,b^5\,c^{10}\,d^{15}+25745364\,a^{25}\,b^6\,c^{11}\,d^{14}-38736144\,a^{24}\,b^7\,c^{12}\,d^{13}+12105045\,a^{23}\,b^8\,c^{13}\,d^{12}+55092717\,a^{22}\,b^9\,c^{14}\,d^{11}-93710763\,a^{21}\,b^{10}\,c^{15}\,d^{10}+42338133\,a^{20}\,b^{11}\,c^{16}\,d^9+56509893\,a^{19}\,b^{12}\,c^{17}\,d^8-107173935\,a^{18}\,b^{13}\,c^{18}\,d^7+83790531\,a^{17}\,b^{14}\,c^{19}\,d^6-36905625\,a^{16}\,b^{15}\,c^{20}\,d^5+8975448\,a^{15}\,b^{16}\,c^{21}\,d^4-944784\,a^{14}\,b^{17}\,c^{22}\,d^3\right)+{\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)}^2\,{\left(-\frac{27\,a^3\,d^3+108\,a^2\,b\,c\,d^2+144\,a\,b^2\,c^2\,d+64\,b^3\,c^3}{729\,a^7\,c^6}\right)}^{2/3}\,\left(-9565938\,a^{30}\,b^4\,c^{13}\,d^{14}+100442349\,a^{29}\,b^5\,c^{14}\,d^{13}-478296900\,a^{28}\,b^6\,c^{15}\,d^{12}+1363146165\,a^{27}\,b^7\,c^{16}\,d^{11}-2582803260\,a^{26}\,b^8\,c^{17}\,d^{10}+3415039866\,a^{25}\,b^9\,c^{18}\,d^9-3214155168\,a^{24}\,b^{10}\,c^{19}\,d^8+2152336050\,a^{23}\,b^{11}\,c^{20}\,d^7-1004423490\,a^{22}\,b^{12}\,c^{21}\,d^6+310892985\,a^{21}\,b^{13}\,c^{22}\,d^5-57395628\,a^{20}\,b^{14}\,c^{23}\,d^4+4782969\,a^{19}\,b^{15}\,c^{24}\,d^3\right)\right)\,{\left(-\frac{27\,a^3\,d^3+108\,a^2\,b\,c\,d^2+144\,a\,b^2\,c^2\,d+64\,b^3\,c^3}{729\,a^7\,c^6}\right)}^{1/3}-3254256\,a^{14}\,b^{16}\,c^{19}\,d^5+10156428\,a^{15}\,b^{15}\,c^{18}\,d^6-14781933\,a^{16}\,b^{14}\,c^{17}\,d^7+4920750\,a^{17}\,b^{13}\,c^{16}\,d^8+15529887\,a^{18}\,b^{12}\,c^{15}\,d^9-22182741\,a^{19}\,b^{11}\,c^{14}\,d^{10}+5412825\,a^{20}\,b^{10}\,c^{13}\,d^{11}+13404123\,a^{21}\,b^9\,c^{12}\,d^{12}-15713595\,a^{22}\,b^8\,c^{11}\,d^{13}+7801029\,a^{23}\,b^7\,c^{10}\,d^{14}-1889568\,a^{24}\,b^6\,c^9\,d^{15}+177147\,a^{25}\,b^5\,c^8\,d^{16}\right)\right)\,\left(-\frac{1}{2}+\frac{\sqrt{3}\,1{}\mathrm{i}}{2}\right)\,{\left(-\frac{27\,a^3\,d^3+108\,a^2\,b\,c\,d^2+144\,a\,b^2\,c^2\,d+64\,b^3\,c^3}{729\,a^7\,c^6}\right)}^{1/3}","Not used",1,"log((d^7/(27*b^4*c^10 + 27*a^4*c^6*d^4 - 108*a^3*b*c^7*d^3 + 162*a^2*b^2*c^8*d^2 - 108*a*b^3*c^9*d))^(2/3)*(419904*a^13*b^17*c^20*d^4 - ((a + b*x^3)^(1/3)*(8975448*a^15*b^16*c^21*d^4 - 944784*a^14*b^17*c^22*d^3 - 36905625*a^16*b^15*c^20*d^5 + 83790531*a^17*b^14*c^19*d^6 - 107173935*a^18*b^13*c^18*d^7 + 56509893*a^19*b^12*c^17*d^8 + 42338133*a^20*b^11*c^16*d^9 - 93710763*a^21*b^10*c^15*d^10 + 55092717*a^22*b^9*c^14*d^11 + 12105045*a^23*b^8*c^13*d^12 - 38736144*a^24*b^7*c^12*d^13 + 25745364*a^25*b^6*c^11*d^14 - 8148762*a^26*b^5*c^10*d^15 + 1062882*a^27*b^4*c^9*d^16) + (d^7/(27*b^4*c^10 + 27*a^4*c^6*d^4 - 108*a^3*b*c^7*d^3 + 162*a^2*b^2*c^8*d^2 - 108*a*b^3*c^9*d))^(2/3)*(4782969*a^19*b^15*c^24*d^3 - 57395628*a^20*b^14*c^23*d^4 + 310892985*a^21*b^13*c^22*d^5 - 1004423490*a^22*b^12*c^21*d^6 + 2152336050*a^23*b^11*c^20*d^7 - 3214155168*a^24*b^10*c^19*d^8 + 3415039866*a^25*b^9*c^18*d^9 - 2582803260*a^26*b^8*c^17*d^10 + 1363146165*a^27*b^7*c^16*d^11 - 478296900*a^28*b^6*c^15*d^12 + 100442349*a^29*b^5*c^14*d^13 - 9565938*a^30*b^4*c^13*d^14))*(d^7/(27*b^4*c^10 + 27*a^4*c^6*d^4 - 108*a^3*b*c^7*d^3 + 162*a^2*b^2*c^8*d^2 - 108*a*b^3*c^9*d))^(1/3) - 3254256*a^14*b^16*c^19*d^5 + 10156428*a^15*b^15*c^18*d^6 - 14781933*a^16*b^14*c^17*d^7 + 4920750*a^17*b^13*c^16*d^8 + 15529887*a^18*b^12*c^15*d^9 - 22182741*a^19*b^11*c^14*d^10 + 5412825*a^20*b^10*c^13*d^11 + 13404123*a^21*b^9*c^12*d^12 - 15713595*a^22*b^8*c^11*d^13 + 7801029*a^23*b^7*c^10*d^14 - 1889568*a^24*b^6*c^9*d^15 + 177147*a^25*b^5*c^8*d^16) - (a + b*x^3)^(1/3)*(256608*a^14*b^13*c^12*d^10 - 46656*a^13*b^14*c^13*d^9 - 516132*a^15*b^12*c^11*d^11 + 347004*a^16*b^11*c^10*d^12 + 265356*a^17*b^10*c^9*d^13 - 551124*a^18*b^9*c^8*d^14 + 224532*a^19*b^8*c^7*d^15 + 107892*a^20*b^7*c^6*d^16 - 113724*a^21*b^6*c^5*d^17 + 26244*a^22*b^5*c^4*d^18))*(d^7/(27*b^4*c^10 + 27*a^4*c^6*d^4 - 108*a^3*b*c^7*d^3 + 162*a^2*b^2*c^8*d^2 - 108*a*b^3*c^9*d))^(1/3) + (b^2/(a^2*d - a*b*c) + (b*(a + b*x^3)*(a*d - 4*b*c))/(3*a^2*c*(a*d - b*c)))/(a*(a + b*x^3)^(1/3) - (a + b*x^3)^(4/3)) + log((-(27*a^3*d^3 + 64*b^3*c^3 + 144*a*b^2*c^2*d + 108*a^2*b*c*d^2)/(729*a^7*c^6))^(2/3)*(419904*a^13*b^17*c^20*d^4 - ((a + b*x^3)^(1/3)*(8975448*a^15*b^16*c^21*d^4 - 944784*a^14*b^17*c^22*d^3 - 36905625*a^16*b^15*c^20*d^5 + 83790531*a^17*b^14*c^19*d^6 - 107173935*a^18*b^13*c^18*d^7 + 56509893*a^19*b^12*c^17*d^8 + 42338133*a^20*b^11*c^16*d^9 - 93710763*a^21*b^10*c^15*d^10 + 55092717*a^22*b^9*c^14*d^11 + 12105045*a^23*b^8*c^13*d^12 - 38736144*a^24*b^7*c^12*d^13 + 25745364*a^25*b^6*c^11*d^14 - 8148762*a^26*b^5*c^10*d^15 + 1062882*a^27*b^4*c^9*d^16) + (-(27*a^3*d^3 + 64*b^3*c^3 + 144*a*b^2*c^2*d + 108*a^2*b*c*d^2)/(729*a^7*c^6))^(2/3)*(4782969*a^19*b^15*c^24*d^3 - 57395628*a^20*b^14*c^23*d^4 + 310892985*a^21*b^13*c^22*d^5 - 1004423490*a^22*b^12*c^21*d^6 + 2152336050*a^23*b^11*c^20*d^7 - 3214155168*a^24*b^10*c^19*d^8 + 3415039866*a^25*b^9*c^18*d^9 - 2582803260*a^26*b^8*c^17*d^10 + 1363146165*a^27*b^7*c^16*d^11 - 478296900*a^28*b^6*c^15*d^12 + 100442349*a^29*b^5*c^14*d^13 - 9565938*a^30*b^4*c^13*d^14))*(-(27*a^3*d^3 + 64*b^3*c^3 + 144*a*b^2*c^2*d + 108*a^2*b*c*d^2)/(729*a^7*c^6))^(1/3) - 3254256*a^14*b^16*c^19*d^5 + 10156428*a^15*b^15*c^18*d^6 - 14781933*a^16*b^14*c^17*d^7 + 4920750*a^17*b^13*c^16*d^8 + 15529887*a^18*b^12*c^15*d^9 - 22182741*a^19*b^11*c^14*d^10 + 5412825*a^20*b^10*c^13*d^11 + 13404123*a^21*b^9*c^12*d^12 - 15713595*a^22*b^8*c^11*d^13 + 7801029*a^23*b^7*c^10*d^14 - 1889568*a^24*b^6*c^9*d^15 + 177147*a^25*b^5*c^8*d^16) - (a + b*x^3)^(1/3)*(256608*a^14*b^13*c^12*d^10 - 46656*a^13*b^14*c^13*d^9 - 516132*a^15*b^12*c^11*d^11 + 347004*a^16*b^11*c^10*d^12 + 265356*a^17*b^10*c^9*d^13 - 551124*a^18*b^9*c^8*d^14 + 224532*a^19*b^8*c^7*d^15 + 107892*a^20*b^7*c^6*d^16 - 113724*a^21*b^6*c^5*d^17 + 26244*a^22*b^5*c^4*d^18))*(-(27*a^3*d^3 + 64*b^3*c^3 + 144*a*b^2*c^2*d + 108*a^2*b*c*d^2)/(729*a^7*c^6))^(1/3) + (log(((3^(1/2)*1i - 1)^2*(d^7/(27*b^4*c^10 + 27*a^4*c^6*d^4 - 108*a^3*b*c^7*d^3 + 162*a^2*b^2*c^8*d^2 - 108*a*b^3*c^9*d))^(2/3)*(419904*a^13*b^17*c^20*d^4 - ((3^(1/2)*1i - 1)*(d^7/(27*b^4*c^10 + 27*a^4*c^6*d^4 - 108*a^3*b*c^7*d^3 + 162*a^2*b^2*c^8*d^2 - 108*a*b^3*c^9*d))^(1/3)*((a + b*x^3)^(1/3)*(8975448*a^15*b^16*c^21*d^4 - 944784*a^14*b^17*c^22*d^3 - 36905625*a^16*b^15*c^20*d^5 + 83790531*a^17*b^14*c^19*d^6 - 107173935*a^18*b^13*c^18*d^7 + 56509893*a^19*b^12*c^17*d^8 + 42338133*a^20*b^11*c^16*d^9 - 93710763*a^21*b^10*c^15*d^10 + 55092717*a^22*b^9*c^14*d^11 + 12105045*a^23*b^8*c^13*d^12 - 38736144*a^24*b^7*c^12*d^13 + 25745364*a^25*b^6*c^11*d^14 - 8148762*a^26*b^5*c^10*d^15 + 1062882*a^27*b^4*c^9*d^16) + ((3^(1/2)*1i - 1)^2*(d^7/(27*b^4*c^10 + 27*a^4*c^6*d^4 - 108*a^3*b*c^7*d^3 + 162*a^2*b^2*c^8*d^2 - 108*a*b^3*c^9*d))^(2/3)*(4782969*a^19*b^15*c^24*d^3 - 57395628*a^20*b^14*c^23*d^4 + 310892985*a^21*b^13*c^22*d^5 - 1004423490*a^22*b^12*c^21*d^6 + 2152336050*a^23*b^11*c^20*d^7 - 3214155168*a^24*b^10*c^19*d^8 + 3415039866*a^25*b^9*c^18*d^9 - 2582803260*a^26*b^8*c^17*d^10 + 1363146165*a^27*b^7*c^16*d^11 - 478296900*a^28*b^6*c^15*d^12 + 100442349*a^29*b^5*c^14*d^13 - 9565938*a^30*b^4*c^13*d^14))/4))/2 - 3254256*a^14*b^16*c^19*d^5 + 10156428*a^15*b^15*c^18*d^6 - 14781933*a^16*b^14*c^17*d^7 + 4920750*a^17*b^13*c^16*d^8 + 15529887*a^18*b^12*c^15*d^9 - 22182741*a^19*b^11*c^14*d^10 + 5412825*a^20*b^10*c^13*d^11 + 13404123*a^21*b^9*c^12*d^12 - 15713595*a^22*b^8*c^11*d^13 + 7801029*a^23*b^7*c^10*d^14 - 1889568*a^24*b^6*c^9*d^15 + 177147*a^25*b^5*c^8*d^16))/4 - (a + b*x^3)^(1/3)*(256608*a^14*b^13*c^12*d^10 - 46656*a^13*b^14*c^13*d^9 - 516132*a^15*b^12*c^11*d^11 + 347004*a^16*b^11*c^10*d^12 + 265356*a^17*b^10*c^9*d^13 - 551124*a^18*b^9*c^8*d^14 + 224532*a^19*b^8*c^7*d^15 + 107892*a^20*b^7*c^6*d^16 - 113724*a^21*b^6*c^5*d^17 + 26244*a^22*b^5*c^4*d^18))*(3^(1/2)*1i - 1)*(d^7/(27*b^4*c^10 + 27*a^4*c^6*d^4 - 108*a^3*b*c^7*d^3 + 162*a^2*b^2*c^8*d^2 - 108*a*b^3*c^9*d))^(1/3))/2 - (log(((3^(1/2)*1i + 1)^2*(d^7/(27*b^4*c^10 + 27*a^4*c^6*d^4 - 108*a^3*b*c^7*d^3 + 162*a^2*b^2*c^8*d^2 - 108*a*b^3*c^9*d))^(2/3)*(((3^(1/2)*1i + 1)*(d^7/(27*b^4*c^10 + 27*a^4*c^6*d^4 - 108*a^3*b*c^7*d^3 + 162*a^2*b^2*c^8*d^2 - 108*a*b^3*c^9*d))^(1/3)*((a + b*x^3)^(1/3)*(8975448*a^15*b^16*c^21*d^4 - 944784*a^14*b^17*c^22*d^3 - 36905625*a^16*b^15*c^20*d^5 + 83790531*a^17*b^14*c^19*d^6 - 107173935*a^18*b^13*c^18*d^7 + 56509893*a^19*b^12*c^17*d^8 + 42338133*a^20*b^11*c^16*d^9 - 93710763*a^21*b^10*c^15*d^10 + 55092717*a^22*b^9*c^14*d^11 + 12105045*a^23*b^8*c^13*d^12 - 38736144*a^24*b^7*c^12*d^13 + 25745364*a^25*b^6*c^11*d^14 - 8148762*a^26*b^5*c^10*d^15 + 1062882*a^27*b^4*c^9*d^16) + ((3^(1/2)*1i + 1)^2*(d^7/(27*b^4*c^10 + 27*a^4*c^6*d^4 - 108*a^3*b*c^7*d^3 + 162*a^2*b^2*c^8*d^2 - 108*a*b^3*c^9*d))^(2/3)*(4782969*a^19*b^15*c^24*d^3 - 57395628*a^20*b^14*c^23*d^4 + 310892985*a^21*b^13*c^22*d^5 - 1004423490*a^22*b^12*c^21*d^6 + 2152336050*a^23*b^11*c^20*d^7 - 3214155168*a^24*b^10*c^19*d^8 + 3415039866*a^25*b^9*c^18*d^9 - 2582803260*a^26*b^8*c^17*d^10 + 1363146165*a^27*b^7*c^16*d^11 - 478296900*a^28*b^6*c^15*d^12 + 100442349*a^29*b^5*c^14*d^13 - 9565938*a^30*b^4*c^13*d^14))/4))/2 + 419904*a^13*b^17*c^20*d^4 - 3254256*a^14*b^16*c^19*d^5 + 10156428*a^15*b^15*c^18*d^6 - 14781933*a^16*b^14*c^17*d^7 + 4920750*a^17*b^13*c^16*d^8 + 15529887*a^18*b^12*c^15*d^9 - 22182741*a^19*b^11*c^14*d^10 + 5412825*a^20*b^10*c^13*d^11 + 13404123*a^21*b^9*c^12*d^12 - 15713595*a^22*b^8*c^11*d^13 + 7801029*a^23*b^7*c^10*d^14 - 1889568*a^24*b^6*c^9*d^15 + 177147*a^25*b^5*c^8*d^16))/4 - (a + b*x^3)^(1/3)*(256608*a^14*b^13*c^12*d^10 - 46656*a^13*b^14*c^13*d^9 - 516132*a^15*b^12*c^11*d^11 + 347004*a^16*b^11*c^10*d^12 + 265356*a^17*b^10*c^9*d^13 - 551124*a^18*b^9*c^8*d^14 + 224532*a^19*b^8*c^7*d^15 + 107892*a^20*b^7*c^6*d^16 - 113724*a^21*b^6*c^5*d^17 + 26244*a^22*b^5*c^4*d^18))*(3^(1/2)*1i + 1)*(d^7/(27*b^4*c^10 + 27*a^4*c^6*d^4 - 108*a^3*b*c^7*d^3 + 162*a^2*b^2*c^8*d^2 - 108*a*b^3*c^9*d))^(1/3))/2 - log(((3^(1/2)*1i)/2 + 1/2)^2*(-(27*a^3*d^3 + 64*b^3*c^3 + 144*a*b^2*c^2*d + 108*a^2*b*c*d^2)/(729*a^7*c^6))^(2/3)*(((3^(1/2)*1i)/2 + 1/2)*((a + b*x^3)^(1/3)*(8975448*a^15*b^16*c^21*d^4 - 944784*a^14*b^17*c^22*d^3 - 36905625*a^16*b^15*c^20*d^5 + 83790531*a^17*b^14*c^19*d^6 - 107173935*a^18*b^13*c^18*d^7 + 56509893*a^19*b^12*c^17*d^8 + 42338133*a^20*b^11*c^16*d^9 - 93710763*a^21*b^10*c^15*d^10 + 55092717*a^22*b^9*c^14*d^11 + 12105045*a^23*b^8*c^13*d^12 - 38736144*a^24*b^7*c^12*d^13 + 25745364*a^25*b^6*c^11*d^14 - 8148762*a^26*b^5*c^10*d^15 + 1062882*a^27*b^4*c^9*d^16) + ((3^(1/2)*1i)/2 + 1/2)^2*(-(27*a^3*d^3 + 64*b^3*c^3 + 144*a*b^2*c^2*d + 108*a^2*b*c*d^2)/(729*a^7*c^6))^(2/3)*(4782969*a^19*b^15*c^24*d^3 - 57395628*a^20*b^14*c^23*d^4 + 310892985*a^21*b^13*c^22*d^5 - 1004423490*a^22*b^12*c^21*d^6 + 2152336050*a^23*b^11*c^20*d^7 - 3214155168*a^24*b^10*c^19*d^8 + 3415039866*a^25*b^9*c^18*d^9 - 2582803260*a^26*b^8*c^17*d^10 + 1363146165*a^27*b^7*c^16*d^11 - 478296900*a^28*b^6*c^15*d^12 + 100442349*a^29*b^5*c^14*d^13 - 9565938*a^30*b^4*c^13*d^14))*(-(27*a^3*d^3 + 64*b^3*c^3 + 144*a*b^2*c^2*d + 108*a^2*b*c*d^2)/(729*a^7*c^6))^(1/3) + 419904*a^13*b^17*c^20*d^4 - 3254256*a^14*b^16*c^19*d^5 + 10156428*a^15*b^15*c^18*d^6 - 14781933*a^16*b^14*c^17*d^7 + 4920750*a^17*b^13*c^16*d^8 + 15529887*a^18*b^12*c^15*d^9 - 22182741*a^19*b^11*c^14*d^10 + 5412825*a^20*b^10*c^13*d^11 + 13404123*a^21*b^9*c^12*d^12 - 15713595*a^22*b^8*c^11*d^13 + 7801029*a^23*b^7*c^10*d^14 - 1889568*a^24*b^6*c^9*d^15 + 177147*a^25*b^5*c^8*d^16) - (a + b*x^3)^(1/3)*(256608*a^14*b^13*c^12*d^10 - 46656*a^13*b^14*c^13*d^9 - 516132*a^15*b^12*c^11*d^11 + 347004*a^16*b^11*c^10*d^12 + 265356*a^17*b^10*c^9*d^13 - 551124*a^18*b^9*c^8*d^14 + 224532*a^19*b^8*c^7*d^15 + 107892*a^20*b^7*c^6*d^16 - 113724*a^21*b^6*c^5*d^17 + 26244*a^22*b^5*c^4*d^18))*((3^(1/2)*1i)/2 + 1/2)*(-(27*a^3*d^3 + 64*b^3*c^3 + 144*a*b^2*c^2*d + 108*a^2*b*c*d^2)/(729*a^7*c^6))^(1/3) + log(((3^(1/2)*1i)/2 - 1/2)^2*(-(27*a^3*d^3 + 64*b^3*c^3 + 144*a*b^2*c^2*d + 108*a^2*b*c*d^2)/(729*a^7*c^6))^(2/3)*(419904*a^13*b^17*c^20*d^4 - ((3^(1/2)*1i)/2 - 1/2)*((a + b*x^3)^(1/3)*(8975448*a^15*b^16*c^21*d^4 - 944784*a^14*b^17*c^22*d^3 - 36905625*a^16*b^15*c^20*d^5 + 83790531*a^17*b^14*c^19*d^6 - 107173935*a^18*b^13*c^18*d^7 + 56509893*a^19*b^12*c^17*d^8 + 42338133*a^20*b^11*c^16*d^9 - 93710763*a^21*b^10*c^15*d^10 + 55092717*a^22*b^9*c^14*d^11 + 12105045*a^23*b^8*c^13*d^12 - 38736144*a^24*b^7*c^12*d^13 + 25745364*a^25*b^6*c^11*d^14 - 8148762*a^26*b^5*c^10*d^15 + 1062882*a^27*b^4*c^9*d^16) + ((3^(1/2)*1i)/2 - 1/2)^2*(-(27*a^3*d^3 + 64*b^3*c^3 + 144*a*b^2*c^2*d + 108*a^2*b*c*d^2)/(729*a^7*c^6))^(2/3)*(4782969*a^19*b^15*c^24*d^3 - 57395628*a^20*b^14*c^23*d^4 + 310892985*a^21*b^13*c^22*d^5 - 1004423490*a^22*b^12*c^21*d^6 + 2152336050*a^23*b^11*c^20*d^7 - 3214155168*a^24*b^10*c^19*d^8 + 3415039866*a^25*b^9*c^18*d^9 - 2582803260*a^26*b^8*c^17*d^10 + 1363146165*a^27*b^7*c^16*d^11 - 478296900*a^28*b^6*c^15*d^12 + 100442349*a^29*b^5*c^14*d^13 - 9565938*a^30*b^4*c^13*d^14))*(-(27*a^3*d^3 + 64*b^3*c^3 + 144*a*b^2*c^2*d + 108*a^2*b*c*d^2)/(729*a^7*c^6))^(1/3) - 3254256*a^14*b^16*c^19*d^5 + 10156428*a^15*b^15*c^18*d^6 - 14781933*a^16*b^14*c^17*d^7 + 4920750*a^17*b^13*c^16*d^8 + 15529887*a^18*b^12*c^15*d^9 - 22182741*a^19*b^11*c^14*d^10 + 5412825*a^20*b^10*c^13*d^11 + 13404123*a^21*b^9*c^12*d^12 - 15713595*a^22*b^8*c^11*d^13 + 7801029*a^23*b^7*c^10*d^14 - 1889568*a^24*b^6*c^9*d^15 + 177147*a^25*b^5*c^8*d^16) - (a + b*x^3)^(1/3)*(256608*a^14*b^13*c^12*d^10 - 46656*a^13*b^14*c^13*d^9 - 516132*a^15*b^12*c^11*d^11 + 347004*a^16*b^11*c^10*d^12 + 265356*a^17*b^10*c^9*d^13 - 551124*a^18*b^9*c^8*d^14 + 224532*a^19*b^8*c^7*d^15 + 107892*a^20*b^7*c^6*d^16 - 113724*a^21*b^6*c^5*d^17 + 26244*a^22*b^5*c^4*d^18))*((3^(1/2)*1i)/2 - 1/2)*(-(27*a^3*d^3 + 64*b^3*c^3 + 144*a*b^2*c^2*d + 108*a^2*b*c*d^2)/(729*a^7*c^6))^(1/3)","B"
754,0,-1,322,0.000000,"\text{Not used}","int(x^9/((a + b*x^3)^(4/3)*(c + d*x^3)),x)","\int \frac{x^9}{{\left(b\,x^3+a\right)}^{4/3}\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int(x^9/((a + b*x^3)^(4/3)*(c + d*x^3)), x)","F"
755,0,-1,260,0.000000,"\text{Not used}","int(x^6/((a + b*x^3)^(4/3)*(c + d*x^3)),x)","\int \frac{x^6}{{\left(b\,x^3+a\right)}^{4/3}\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int(x^6/((a + b*x^3)^(4/3)*(c + d*x^3)), x)","F"
756,0,-1,172,0.000000,"\text{Not used}","int(x^3/((a + b*x^3)^(4/3)*(c + d*x^3)),x)","\int \frac{x^3}{{\left(b\,x^3+a\right)}^{4/3}\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int(x^3/((a + b*x^3)^(4/3)*(c + d*x^3)), x)","F"
757,0,-1,179,0.000000,"\text{Not used}","int(1/((a + b*x^3)^(4/3)*(c + d*x^3)),x)","\int \frac{1}{{\left(b\,x^3+a\right)}^{4/3}\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int(1/((a + b*x^3)^(4/3)*(c + d*x^3)), x)","F"
758,0,-1,229,0.000000,"\text{Not used}","int(1/(x^3*(a + b*x^3)^(4/3)*(c + d*x^3)),x)","\int \frac{1}{x^3\,{\left(b\,x^3+a\right)}^{4/3}\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int(1/(x^3*(a + b*x^3)^(4/3)*(c + d*x^3)), x)","F"
759,0,-1,287,0.000000,"\text{Not used}","int(1/(x^6*(a + b*x^3)^(4/3)*(c + d*x^3)),x)","\int \frac{1}{x^6\,{\left(b\,x^3+a\right)}^{4/3}\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int(1/(x^6*(a + b*x^3)^(4/3)*(c + d*x^3)), x)","F"
760,0,-1,351,0.000000,"\text{Not used}","int(1/(x^9*(a + b*x^3)^(4/3)*(c + d*x^3)),x)","\int \frac{1}{x^9\,{\left(b\,x^3+a\right)}^{4/3}\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int(1/(x^9*(a + b*x^3)^(4/3)*(c + d*x^3)), x)","F"
761,0,-1,67,0.000000,"\text{Not used}","int(x^10/((a + b*x^3)^(4/3)*(c + d*x^3)),x)","\int \frac{x^{10}}{{\left(b\,x^3+a\right)}^{4/3}\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int(x^10/((a + b*x^3)^(4/3)*(c + d*x^3)), x)","F"
762,0,-1,67,0.000000,"\text{Not used}","int(x^7/((a + b*x^3)^(4/3)*(c + d*x^3)),x)","\int \frac{x^7}{{\left(b\,x^3+a\right)}^{4/3}\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int(x^7/((a + b*x^3)^(4/3)*(c + d*x^3)), x)","F"
763,0,-1,67,0.000000,"\text{Not used}","int(x^4/((a + b*x^3)^(4/3)*(c + d*x^3)),x)","\int \frac{x^4}{{\left(b\,x^3+a\right)}^{4/3}\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int(x^4/((a + b*x^3)^(4/3)*(c + d*x^3)), x)","F"
764,0,-1,67,0.000000,"\text{Not used}","int(x/((a + b*x^3)^(4/3)*(c + d*x^3)),x)","\int \frac{x}{{\left(b\,x^3+a\right)}^{4/3}\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int(x/((a + b*x^3)^(4/3)*(c + d*x^3)), x)","F"
765,0,-1,65,0.000000,"\text{Not used}","int(1/(x^2*(a + b*x^3)^(4/3)*(c + d*x^3)),x)","\int \frac{1}{x^2\,{\left(b\,x^3+a\right)}^{4/3}\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int(1/(x^2*(a + b*x^3)^(4/3)*(c + d*x^3)), x)","F"
766,0,-1,67,0.000000,"\text{Not used}","int(1/(x^5*(a + b*x^3)^(4/3)*(c + d*x^3)),x)","\int \frac{1}{x^5\,{\left(b\,x^3+a\right)}^{4/3}\,\left(d\,x^3+c\right)} \,d x","Not used",1,"int(1/(x^5*(a + b*x^3)^(4/3)*(c + d*x^3)), x)","F"
767,1,88,90,5.879921,"\text{Not used}","int(x^15/((a + b*x^4)*(c + d*x^4)),x)","\frac{x^8}{8\,b\,d}-\frac{c^3\,\ln\left(d\,x^4+c\right)}{4\,\left(a\,d^4-b\,c\,d^3\right)}-\frac{a^3\,\ln\left(b\,x^4+a\right)}{4\,\left(b^4\,c-a\,b^3\,d\right)}-\frac{x^4\,\left(a\,d+b\,c\right)}{4\,b^2\,d^2}","Not used",1,"x^8/(8*b*d) - (c^3*log(c + d*x^4))/(4*(a*d^4 - b*c*d^3)) - (a^3*log(a + b*x^4))/(4*(b^4*c - a*b^3*d)) - (x^4*(a*d + b*c))/(4*b^2*d^2)","B"
768,1,68,70,5.632676,"\text{Not used}","int(x^11/((a + b*x^4)*(c + d*x^4)),x)","\frac{a^2\,\ln\left(b\,x^4+a\right)}{4\,b^3\,c-4\,a\,b^2\,d}+\frac{c^2\,\ln\left(d\,x^4+c\right)}{4\,a\,d^3-4\,b\,c\,d^2}+\frac{x^4}{4\,b\,d}","Not used",1,"(a^2*log(a + b*x^4))/(4*b^3*c - 4*a*b^2*d) + (c^2*log(c + d*x^4))/(4*a*d^3 - 4*b*c*d^2) + x^4/(4*b*d)","B"
769,1,51,53,5.095624,"\text{Not used}","int(x^7/((a + b*x^4)*(c + d*x^4)),x)","-\frac{a\,\ln\left(b\,x^4+a\right)}{4\,b^2\,c-4\,a\,b\,d}-\frac{c\,\ln\left(d\,x^4+c\right)}{4\,a\,d^2-4\,b\,c\,d}","Not used",1,"- (a*log(a + b*x^4))/(4*b^2*c - 4*a*b*d) - (c*log(c + d*x^4))/(4*a*d^2 - 4*b*c*d)","B"
770,1,1012,45,4.986599,"\text{Not used}","int(x^3/((a + b*x^4)*(c + d*x^4)),x)","-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{x^4\,\left(96\,c\,b^5\,d^4+96\,a\,b^4\,d^5\right)+\frac{\frac{x^4\,\left(512\,a^3\,b^4\,d^7+1536\,a^2\,b^5\,c\,d^6+1536\,a\,b^6\,c^2\,d^5+512\,b^7\,c^3\,d^4\right)+1024\,a\,b^6\,c^3\,d^4+1024\,a^3\,b^4\,c\,d^6+2048\,a^2\,b^5\,c^2\,d^5}{4\,a\,d-4\,b\,c}+x^4\,\left(384\,a^2\,b^4\,d^6+768\,a\,b^5\,c\,d^5+384\,b^6\,c^2\,d^4\right)+512\,a\,b^5\,c^2\,d^4+512\,a^2\,b^4\,c\,d^5}{4\,a\,d-4\,b\,c}+64\,a\,b^4\,c\,d^4}{4\,a\,d-4\,b\,c}+8\,b^4\,d^4\,x^4\right)\,1{}\mathrm{i}}{4\,a\,d-4\,b\,c}-\frac{\left(\frac{x^4\,\left(96\,c\,b^5\,d^4+96\,a\,b^4\,d^5\right)-\frac{x^4\,\left(384\,a^2\,b^4\,d^6+768\,a\,b^5\,c\,d^5+384\,b^6\,c^2\,d^4\right)-\frac{x^4\,\left(512\,a^3\,b^4\,d^7+1536\,a^2\,b^5\,c\,d^6+1536\,a\,b^6\,c^2\,d^5+512\,b^7\,c^3\,d^4\right)+1024\,a\,b^6\,c^3\,d^4+1024\,a^3\,b^4\,c\,d^6+2048\,a^2\,b^5\,c^2\,d^5}{4\,a\,d-4\,b\,c}+512\,a\,b^5\,c^2\,d^4+512\,a^2\,b^4\,c\,d^5}{4\,a\,d-4\,b\,c}+64\,a\,b^4\,c\,d^4}{4\,a\,d-4\,b\,c}-8\,b^4\,d^4\,x^4\right)\,1{}\mathrm{i}}{4\,a\,d-4\,b\,c}}{\frac{\frac{x^4\,\left(96\,c\,b^5\,d^4+96\,a\,b^4\,d^5\right)+\frac{\frac{x^4\,\left(512\,a^3\,b^4\,d^7+1536\,a^2\,b^5\,c\,d^6+1536\,a\,b^6\,c^2\,d^5+512\,b^7\,c^3\,d^4\right)+1024\,a\,b^6\,c^3\,d^4+1024\,a^3\,b^4\,c\,d^6+2048\,a^2\,b^5\,c^2\,d^5}{4\,a\,d-4\,b\,c}+x^4\,\left(384\,a^2\,b^4\,d^6+768\,a\,b^5\,c\,d^5+384\,b^6\,c^2\,d^4\right)+512\,a\,b^5\,c^2\,d^4+512\,a^2\,b^4\,c\,d^5}{4\,a\,d-4\,b\,c}+64\,a\,b^4\,c\,d^4}{4\,a\,d-4\,b\,c}+8\,b^4\,d^4\,x^4}{4\,a\,d-4\,b\,c}+\frac{\frac{x^4\,\left(96\,c\,b^5\,d^4+96\,a\,b^4\,d^5\right)-\frac{x^4\,\left(384\,a^2\,b^4\,d^6+768\,a\,b^5\,c\,d^5+384\,b^6\,c^2\,d^4\right)-\frac{x^4\,\left(512\,a^3\,b^4\,d^7+1536\,a^2\,b^5\,c\,d^6+1536\,a\,b^6\,c^2\,d^5+512\,b^7\,c^3\,d^4\right)+1024\,a\,b^6\,c^3\,d^4+1024\,a^3\,b^4\,c\,d^6+2048\,a^2\,b^5\,c^2\,d^5}{4\,a\,d-4\,b\,c}+512\,a\,b^5\,c^2\,d^4+512\,a^2\,b^4\,c\,d^5}{4\,a\,d-4\,b\,c}+64\,a\,b^4\,c\,d^4}{4\,a\,d-4\,b\,c}-8\,b^4\,d^4\,x^4}{4\,a\,d-4\,b\,c}}\right)\,2{}\mathrm{i}}{4\,a\,d-4\,b\,c}","Not used",1,"-(atan(((((x^4*(96*a*b^4*d^5 + 96*b^5*c*d^4) + ((x^4*(512*a^3*b^4*d^7 + 512*b^7*c^3*d^4 + 1536*a*b^6*c^2*d^5 + 1536*a^2*b^5*c*d^6) + 1024*a*b^6*c^3*d^4 + 1024*a^3*b^4*c*d^6 + 2048*a^2*b^5*c^2*d^5)/(4*a*d - 4*b*c) + x^4*(384*a^2*b^4*d^6 + 384*b^6*c^2*d^4 + 768*a*b^5*c*d^5) + 512*a*b^5*c^2*d^4 + 512*a^2*b^4*c*d^5)/(4*a*d - 4*b*c) + 64*a*b^4*c*d^4)/(4*a*d - 4*b*c) + 8*b^4*d^4*x^4)*1i)/(4*a*d - 4*b*c) - (((x^4*(96*a*b^4*d^5 + 96*b^5*c*d^4) - (x^4*(384*a^2*b^4*d^6 + 384*b^6*c^2*d^4 + 768*a*b^5*c*d^5) - (x^4*(512*a^3*b^4*d^7 + 512*b^7*c^3*d^4 + 1536*a*b^6*c^2*d^5 + 1536*a^2*b^5*c*d^6) + 1024*a*b^6*c^3*d^4 + 1024*a^3*b^4*c*d^6 + 2048*a^2*b^5*c^2*d^5)/(4*a*d - 4*b*c) + 512*a*b^5*c^2*d^4 + 512*a^2*b^4*c*d^5)/(4*a*d - 4*b*c) + 64*a*b^4*c*d^4)/(4*a*d - 4*b*c) - 8*b^4*d^4*x^4)*1i)/(4*a*d - 4*b*c))/(((x^4*(96*a*b^4*d^5 + 96*b^5*c*d^4) + ((x^4*(512*a^3*b^4*d^7 + 512*b^7*c^3*d^4 + 1536*a*b^6*c^2*d^5 + 1536*a^2*b^5*c*d^6) + 1024*a*b^6*c^3*d^4 + 1024*a^3*b^4*c*d^6 + 2048*a^2*b^5*c^2*d^5)/(4*a*d - 4*b*c) + x^4*(384*a^2*b^4*d^6 + 384*b^6*c^2*d^4 + 768*a*b^5*c*d^5) + 512*a*b^5*c^2*d^4 + 512*a^2*b^4*c*d^5)/(4*a*d - 4*b*c) + 64*a*b^4*c*d^4)/(4*a*d - 4*b*c) + 8*b^4*d^4*x^4)/(4*a*d - 4*b*c) + ((x^4*(96*a*b^4*d^5 + 96*b^5*c*d^4) - (x^4*(384*a^2*b^4*d^6 + 384*b^6*c^2*d^4 + 768*a*b^5*c*d^5) - (x^4*(512*a^3*b^4*d^7 + 512*b^7*c^3*d^4 + 1536*a*b^6*c^2*d^5 + 1536*a^2*b^5*c*d^6) + 1024*a*b^6*c^3*d^4 + 1024*a^3*b^4*c*d^6 + 2048*a^2*b^5*c^2*d^5)/(4*a*d - 4*b*c) + 512*a*b^5*c^2*d^4 + 512*a^2*b^4*c*d^5)/(4*a*d - 4*b*c) + 64*a*b^4*c*d^4)/(4*a*d - 4*b*c) - 8*b^4*d^4*x^4)/(4*a*d - 4*b*c)))*2i)/(4*a*d - 4*b*c)","B"
771,1,58,62,5.491663,"\text{Not used}","int(1/(x*(a + b*x^4)*(c + d*x^4)),x)","\frac{b\,\ln\left(b\,x^4+a\right)}{4\,a^2\,d-4\,a\,b\,c}+\frac{d\,\ln\left(d\,x^4+c\right)}{4\,b\,c^2-4\,a\,c\,d}+\frac{\ln\left(x\right)}{a\,c}","Not used",1,"(b*log(a + b*x^4))/(4*a^2*d - 4*a*b*c) + (d*log(c + d*x^4))/(4*b*c^2 - 4*a*c*d) + log(x)/(a*c)","B"
772,1,87,87,6.214464,"\text{Not used}","int(1/(x^5*(a + b*x^4)*(c + d*x^4)),x)","-\frac{b^2\,\ln\left(b\,x^4+a\right)}{4\,\left(a^3\,d-a^2\,b\,c\right)}-\frac{d^2\,\ln\left(d\,x^4+c\right)}{4\,\left(b\,c^3-a\,c^2\,d\right)}-\frac{1}{4\,a\,c\,x^4}-\frac{\ln\left(x\right)\,\left(a\,d+b\,c\right)}{a^2\,c^2}","Not used",1,"- (b^2*log(a + b*x^4))/(4*(a^3*d - a^2*b*c)) - (d^2*log(c + d*x^4))/(4*(b*c^3 - a*c^2*d)) - 1/(4*a*c*x^4) - (log(x)*(a*d + b*c))/(a^2*c^2)","B"
773,1,532,112,5.704763,"\text{Not used}","int(x^13/((a + b*x^4)*(c + d*x^4)),x)","\frac{\ln\left(d^{10}\,{\left(-a^5\,b^5\right)}^{5/2}+b^{20}\,c^{10}\,\sqrt{-a^5\,b^5}-a^2\,b^{23}\,c^{10}\,x^2-a^{12}\,b^{13}\,d^{10}\,x^2+2\,b^{10}\,c^5\,d^5\,{\left(-a^5\,b^5\right)}^{3/2}+2\,a^7\,b^{18}\,c^5\,d^5\,x^2\right)\,\sqrt{-a^5\,b^5}}{4\,b^6\,c-4\,a\,b^5\,d}-\frac{\ln\left(d^{10}\,{\left(-a^5\,b^5\right)}^{5/2}+b^{20}\,c^{10}\,\sqrt{-a^5\,b^5}+a^2\,b^{23}\,c^{10}\,x^2+a^{12}\,b^{13}\,d^{10}\,x^2+2\,b^{10}\,c^5\,d^5\,{\left(-a^5\,b^5\right)}^{3/2}-2\,a^7\,b^{18}\,c^5\,d^5\,x^2\right)\,\sqrt{-a^5\,b^5}}{4\,\left(b^6\,c-a\,b^5\,d\right)}-\frac{\ln\left(b^{10}\,{\left(-c^5\,d^5\right)}^{5/2}+a^{10}\,d^{20}\,\sqrt{-c^5\,d^5}+a^{10}\,c^2\,d^{23}\,x^2+b^{10}\,c^{12}\,d^{13}\,x^2+2\,a^5\,b^5\,d^{10}\,{\left(-c^5\,d^5\right)}^{3/2}-2\,a^5\,b^5\,c^7\,d^{18}\,x^2\right)\,\sqrt{-c^5\,d^5}}{4\,\left(a\,d^6-b\,c\,d^5\right)}+\frac{\ln\left(b^{10}\,{\left(-c^5\,d^5\right)}^{5/2}+a^{10}\,d^{20}\,\sqrt{-c^5\,d^5}-a^{10}\,c^2\,d^{23}\,x^2-b^{10}\,c^{12}\,d^{13}\,x^2+2\,a^5\,b^5\,d^{10}\,{\left(-c^5\,d^5\right)}^{3/2}+2\,a^5\,b^5\,c^7\,d^{18}\,x^2\right)\,\sqrt{-c^5\,d^5}}{4\,a\,d^6-4\,b\,c\,d^5}+\frac{x^6}{6\,b\,d}-\frac{x^2\,\left(a\,d+b\,c\right)}{2\,b^2\,d^2}","Not used",1,"(log(d^10*(-a^5*b^5)^(5/2) + b^20*c^10*(-a^5*b^5)^(1/2) - a^2*b^23*c^10*x^2 - a^12*b^13*d^10*x^2 + 2*b^10*c^5*d^5*(-a^5*b^5)^(3/2) + 2*a^7*b^18*c^5*d^5*x^2)*(-a^5*b^5)^(1/2))/(4*b^6*c - 4*a*b^5*d) - (log(d^10*(-a^5*b^5)^(5/2) + b^20*c^10*(-a^5*b^5)^(1/2) + a^2*b^23*c^10*x^2 + a^12*b^13*d^10*x^2 + 2*b^10*c^5*d^5*(-a^5*b^5)^(3/2) - 2*a^7*b^18*c^5*d^5*x^2)*(-a^5*b^5)^(1/2))/(4*(b^6*c - a*b^5*d)) - (log(b^10*(-c^5*d^5)^(5/2) + a^10*d^20*(-c^5*d^5)^(1/2) + a^10*c^2*d^23*x^2 + b^10*c^12*d^13*x^2 + 2*a^5*b^5*d^10*(-c^5*d^5)^(3/2) - 2*a^5*b^5*c^7*d^18*x^2)*(-c^5*d^5)^(1/2))/(4*(a*d^6 - b*c*d^5)) + (log(b^10*(-c^5*d^5)^(5/2) + a^10*d^20*(-c^5*d^5)^(1/2) - a^10*c^2*d^23*x^2 - b^10*c^12*d^13*x^2 + 2*a^5*b^5*d^10*(-c^5*d^5)^(3/2) + 2*a^5*b^5*c^7*d^18*x^2)*(-c^5*d^5)^(1/2))/(4*a*d^6 - 4*b*c*d^5) + x^6/(6*b*d) - (x^2*(a*d + b*c))/(2*b^2*d^2)","B"
774,1,518,92,5.724346,"\text{Not used}","int(x^9/((a + b*x^4)*(c + d*x^4)),x)","\frac{\ln\left(b^9\,c^6\,\sqrt{-a^3\,b^3}-a^3\,d^6\,{\left(-a^3\,b^3\right)}^{3/2}+a\,b^{11}\,c^6\,x^2+a^7\,b^5\,d^6\,x^2+2\,b^3\,c^3\,d^3\,{\left(-a^3\,b^3\right)}^{3/2}-2\,a^4\,b^8\,c^3\,d^3\,x^2\right)\,\sqrt{-a^3\,b^3}}{4\,b^4\,c-4\,a\,b^3\,d}-\frac{\ln\left(a^3\,d^6\,{\left(-a^3\,b^3\right)}^{3/2}-b^9\,c^6\,\sqrt{-a^3\,b^3}+a\,b^{11}\,c^6\,x^2+a^7\,b^5\,d^6\,x^2-2\,b^3\,c^3\,d^3\,{\left(-a^3\,b^3\right)}^{3/2}-2\,a^4\,b^8\,c^3\,d^3\,x^2\right)\,\sqrt{-a^3\,b^3}}{4\,\left(b^4\,c-a\,b^3\,d\right)}-\frac{\ln\left(b^6\,c^3\,{\left(-c^3\,d^3\right)}^{3/2}-a^6\,d^9\,\sqrt{-c^3\,d^3}+a^6\,c\,d^{11}\,x^2+b^6\,c^7\,d^5\,x^2-2\,a^3\,b^3\,d^3\,{\left(-c^3\,d^3\right)}^{3/2}-2\,a^3\,b^3\,c^4\,d^8\,x^2\right)\,\sqrt{-c^3\,d^3}}{4\,\left(a\,d^4-b\,c\,d^3\right)}+\frac{\ln\left(a^6\,d^9\,\sqrt{-c^3\,d^3}-b^6\,c^3\,{\left(-c^3\,d^3\right)}^{3/2}+a^6\,c\,d^{11}\,x^2+b^6\,c^7\,d^5\,x^2+2\,a^3\,b^3\,d^3\,{\left(-c^3\,d^3\right)}^{3/2}-2\,a^3\,b^3\,c^4\,d^8\,x^2\right)\,\sqrt{-c^3\,d^3}}{4\,a\,d^4-4\,b\,c\,d^3}+\frac{x^2}{2\,b\,d}","Not used",1,"(log(b^9*c^6*(-a^3*b^3)^(1/2) - a^3*d^6*(-a^3*b^3)^(3/2) + a*b^11*c^6*x^2 + a^7*b^5*d^6*x^2 + 2*b^3*c^3*d^3*(-a^3*b^3)^(3/2) - 2*a^4*b^8*c^3*d^3*x^2)*(-a^3*b^3)^(1/2))/(4*b^4*c - 4*a*b^3*d) - (log(a^3*d^6*(-a^3*b^3)^(3/2) - b^9*c^6*(-a^3*b^3)^(1/2) + a*b^11*c^6*x^2 + a^7*b^5*d^6*x^2 - 2*b^3*c^3*d^3*(-a^3*b^3)^(3/2) - 2*a^4*b^8*c^3*d^3*x^2)*(-a^3*b^3)^(1/2))/(4*(b^4*c - a*b^3*d)) - (log(b^6*c^3*(-c^3*d^3)^(3/2) - a^6*d^9*(-c^3*d^3)^(1/2) + a^6*c*d^11*x^2 + b^6*c^7*d^5*x^2 - 2*a^3*b^3*d^3*(-c^3*d^3)^(3/2) - 2*a^3*b^3*c^4*d^8*x^2)*(-c^3*d^3)^(1/2))/(4*(a*d^4 - b*c*d^3)) + (log(a^6*d^9*(-c^3*d^3)^(1/2) - b^6*c^3*(-c^3*d^3)^(3/2) + a^6*c*d^11*x^2 + b^6*c^7*d^5*x^2 + 2*a^3*b^3*d^3*(-c^3*d^3)^(3/2) - 2*a^3*b^3*c^4*d^8*x^2)*(-c^3*d^3)^(1/2))/(4*a*d^4 - 4*b*c*d^3) + x^2/(2*b*d)","B"
775,1,379,79,5.344912,"\text{Not used}","int(x^5/((a + b*x^4)*(c + d*x^4)),x)","\frac{\ln\left(d^2\,{\left(-a\,b\right)}^{5/2}+b^4\,c^2\,\sqrt{-a\,b}-b^5\,c^2\,x^2+2\,b^2\,c\,d\,{\left(-a\,b\right)}^{3/2}-a^2\,b^3\,d^2\,x^2+2\,a\,b^4\,c\,d\,x^2\right)\,\sqrt{-a\,b}}{4\,b^2\,c-4\,a\,b\,d}-\frac{\ln\left(d^2\,{\left(-a\,b\right)}^{5/2}+b^4\,c^2\,\sqrt{-a\,b}+b^5\,c^2\,x^2+2\,b^2\,c\,d\,{\left(-a\,b\right)}^{3/2}+a^2\,b^3\,d^2\,x^2-2\,a\,b^4\,c\,d\,x^2\right)\,\sqrt{-a\,b}}{4\,\left(b^2\,c-a\,b\,d\right)}-\frac{\ln\left(b^2\,{\left(-c\,d\right)}^{5/2}+a^2\,d^4\,\sqrt{-c\,d}+a^2\,d^5\,x^2+2\,a\,b\,d^2\,{\left(-c\,d\right)}^{3/2}+b^2\,c^2\,d^3\,x^2-2\,a\,b\,c\,d^4\,x^2\right)\,\sqrt{-c\,d}}{4\,\left(a\,d^2-b\,c\,d\right)}+\frac{\ln\left(b^2\,{\left(-c\,d\right)}^{5/2}+a^2\,d^4\,\sqrt{-c\,d}-a^2\,d^5\,x^2+2\,a\,b\,d^2\,{\left(-c\,d\right)}^{3/2}-b^2\,c^2\,d^3\,x^2+2\,a\,b\,c\,d^4\,x^2\right)\,\sqrt{-c\,d}}{4\,a\,d^2-4\,b\,c\,d}","Not used",1,"(log(d^2*(-a*b)^(5/2) + b^4*c^2*(-a*b)^(1/2) - b^5*c^2*x^2 + 2*b^2*c*d*(-a*b)^(3/2) - a^2*b^3*d^2*x^2 + 2*a*b^4*c*d*x^2)*(-a*b)^(1/2))/(4*b^2*c - 4*a*b*d) - (log(d^2*(-a*b)^(5/2) + b^4*c^2*(-a*b)^(1/2) + b^5*c^2*x^2 + 2*b^2*c*d*(-a*b)^(3/2) + a^2*b^3*d^2*x^2 - 2*a*b^4*c*d*x^2)*(-a*b)^(1/2))/(4*(b^2*c - a*b*d)) - (log(b^2*(-c*d)^(5/2) + a^2*d^4*(-c*d)^(1/2) + a^2*d^5*x^2 + 2*a*b*d^2*(-c*d)^(3/2) + b^2*c^2*d^3*x^2 - 2*a*b*c*d^4*x^2)*(-c*d)^(1/2))/(4*(a*d^2 - b*c*d)) + (log(b^2*(-c*d)^(5/2) + a^2*d^4*(-c*d)^(1/2) - a^2*d^5*x^2 + 2*a*b*d^2*(-c*d)^(3/2) - b^2*c^2*d^3*x^2 + 2*a*b*c*d^4*x^2)*(-c*d)^(1/2))/(4*a*d^2 - 4*b*c*d)","B"
776,1,399,79,5.294839,"\text{Not used}","int(x/((a + b*x^4)*(c + d*x^4)),x)","\frac{\ln\left(a^2\,d^2\,{\left(-a\,b\right)}^{5/2}+b^2\,c^2\,{\left(-a\,b\right)}^{5/2}+2\,c\,d\,{\left(-a\,b\right)}^{7/2}-a^2\,b^5\,c^2\,x^2-a^4\,b^3\,d^2\,x^2+2\,a^3\,b^4\,c\,d\,x^2\right)\,\sqrt{-a\,b}}{4\,a^2\,d-4\,a\,b\,c}-\frac{\ln\left(a^2\,d^2\,{\left(-a\,b\right)}^{5/2}+b^2\,c^2\,{\left(-a\,b\right)}^{5/2}+2\,c\,d\,{\left(-a\,b\right)}^{7/2}+a^2\,b^5\,c^2\,x^2+a^4\,b^3\,d^2\,x^2-2\,a^3\,b^4\,c\,d\,x^2\right)\,\sqrt{-a\,b}}{4\,\left(a^2\,d-a\,b\,c\right)}-\frac{\ln\left(a^2\,d^2\,{\left(-c\,d\right)}^{5/2}+b^2\,c^2\,{\left(-c\,d\right)}^{5/2}+2\,a\,b\,{\left(-c\,d\right)}^{7/2}+a^2\,c^2\,d^5\,x^2+b^2\,c^4\,d^3\,x^2-2\,a\,b\,c^3\,d^4\,x^2\right)\,\sqrt{-c\,d}}{4\,\left(b\,c^2-a\,c\,d\right)}+\frac{\ln\left(a^2\,d^2\,{\left(-c\,d\right)}^{5/2}+b^2\,c^2\,{\left(-c\,d\right)}^{5/2}+2\,a\,b\,{\left(-c\,d\right)}^{7/2}-a^2\,c^2\,d^5\,x^2-b^2\,c^4\,d^3\,x^2+2\,a\,b\,c^3\,d^4\,x^2\right)\,\sqrt{-c\,d}}{4\,b\,c^2-4\,a\,c\,d}","Not used",1,"(log(a^2*d^2*(-a*b)^(5/2) + b^2*c^2*(-a*b)^(5/2) + 2*c*d*(-a*b)^(7/2) - a^2*b^5*c^2*x^2 - a^4*b^3*d^2*x^2 + 2*a^3*b^4*c*d*x^2)*(-a*b)^(1/2))/(4*a^2*d - 4*a*b*c) - (log(a^2*d^2*(-a*b)^(5/2) + b^2*c^2*(-a*b)^(5/2) + 2*c*d*(-a*b)^(7/2) + a^2*b^5*c^2*x^2 + a^4*b^3*d^2*x^2 - 2*a^3*b^4*c*d*x^2)*(-a*b)^(1/2))/(4*(a^2*d - a*b*c)) - (log(a^2*d^2*(-c*d)^(5/2) + b^2*c^2*(-c*d)^(5/2) + 2*a*b*(-c*d)^(7/2) + a^2*c^2*d^5*x^2 + b^2*c^4*d^3*x^2 - 2*a*b*c^3*d^4*x^2)*(-c*d)^(1/2))/(4*(b*c^2 - a*c*d)) + (log(a^2*d^2*(-c*d)^(5/2) + b^2*c^2*(-c*d)^(5/2) + 2*a*b*(-c*d)^(7/2) - a^2*c^2*d^5*x^2 - b^2*c^4*d^3*x^2 + 2*a*b*c^3*d^4*x^2)*(-c*d)^(1/2))/(4*b*c^2 - 4*a*c*d)","B"
777,1,354,92,5.348488,"\text{Not used}","int(1/(x^3*(a + b*x^4)*(c + d*x^4)),x)","\frac{\ln\left(c^3\,x^2\,{\left(-a^3\,b^3\right)}^{3/2}-a^8\,b\,d^3+a^5\,b^4\,c^3+a^6\,d^3\,x^2\,\sqrt{-a^3\,b^3}\right)\,\sqrt{-a^3\,b^3}}{4\,a^4\,d-4\,a^3\,b\,c}-\frac{\ln\left(c^3\,x^2\,{\left(-a^3\,b^3\right)}^{3/2}+a^8\,b\,d^3-a^5\,b^4\,c^3+a^6\,d^3\,x^2\,\sqrt{-a^3\,b^3}\right)\,\sqrt{-a^3\,b^3}}{4\,\left(a^4\,d-a^3\,b\,c\right)}-\frac{1}{2\,a\,c\,x^2}-\frac{\ln\left(a^3\,x^2\,{\left(-c^3\,d^3\right)}^{3/2}+b^3\,c^8\,d-a^3\,c^5\,d^4+b^3\,c^6\,x^2\,\sqrt{-c^3\,d^3}\right)\,\sqrt{-c^3\,d^3}}{4\,\left(b\,c^4-a\,c^3\,d\right)}+\frac{\ln\left(a^3\,x^2\,{\left(-c^3\,d^3\right)}^{3/2}-b^3\,c^8\,d+a^3\,c^5\,d^4+b^3\,c^6\,x^2\,\sqrt{-c^3\,d^3}\right)\,\sqrt{-c^3\,d^3}}{4\,b\,c^4-4\,a\,c^3\,d}","Not used",1,"(log(c^3*x^2*(-a^3*b^3)^(3/2) - a^8*b*d^3 + a^5*b^4*c^3 + a^6*d^3*x^2*(-a^3*b^3)^(1/2))*(-a^3*b^3)^(1/2))/(4*a^4*d - 4*a^3*b*c) - (log(c^3*x^2*(-a^3*b^3)^(3/2) + a^8*b*d^3 - a^5*b^4*c^3 + a^6*d^3*x^2*(-a^3*b^3)^(1/2))*(-a^3*b^3)^(1/2))/(4*(a^4*d - a^3*b*c)) - 1/(2*a*c*x^2) - (log(a^3*x^2*(-c^3*d^3)^(3/2) + b^3*c^8*d - a^3*c^5*d^4 + b^3*c^6*x^2*(-c^3*d^3)^(1/2))*(-c^3*d^3)^(1/2))/(4*(b*c^4 - a*c^3*d)) + (log(a^3*x^2*(-c^3*d^3)^(3/2) - b^3*c^8*d + a^3*c^5*d^4 + b^3*c^6*x^2*(-c^3*d^3)^(1/2))*(-c^3*d^3)^(1/2))/(4*b*c^4 - 4*a*c^3*d)","B"
778,1,535,112,5.530120,"\text{Not used}","int(1/(x^7*(a + b*x^4)*(c + d*x^4)),x)","\frac{\ln\left(c^{10}\,{\left(-a^5\,b^5\right)}^{5/2}+a^{20}\,d^{10}\,\sqrt{-a^5\,b^5}-a^{12}\,b^{13}\,c^{10}\,x^2-a^{22}\,b^3\,d^{10}\,x^2+2\,a^{10}\,c^5\,d^5\,{\left(-a^5\,b^5\right)}^{3/2}+2\,a^{17}\,b^8\,c^5\,d^5\,x^2\right)\,\sqrt{-a^5\,b^5}}{4\,a^6\,d-4\,a^5\,b\,c}-\frac{\ln\left(c^{10}\,{\left(-a^5\,b^5\right)}^{5/2}+a^{20}\,d^{10}\,\sqrt{-a^5\,b^5}+a^{12}\,b^{13}\,c^{10}\,x^2+a^{22}\,b^3\,d^{10}\,x^2+2\,a^{10}\,c^5\,d^5\,{\left(-a^5\,b^5\right)}^{3/2}-2\,a^{17}\,b^8\,c^5\,d^5\,x^2\right)\,\sqrt{-a^5\,b^5}}{4\,\left(a^6\,d-a^5\,b\,c\right)}-\frac{\frac{1}{6\,a\,c}-\frac{x^4\,\left(a\,d+b\,c\right)}{2\,a^2\,c^2}}{x^6}-\frac{\ln\left(a^{10}\,{\left(-c^5\,d^5\right)}^{5/2}+b^{10}\,c^{20}\,\sqrt{-c^5\,d^5}+a^{10}\,c^{12}\,d^{13}\,x^2+b^{10}\,c^{22}\,d^3\,x^2+2\,a^5\,b^5\,c^{10}\,{\left(-c^5\,d^5\right)}^{3/2}-2\,a^5\,b^5\,c^{17}\,d^8\,x^2\right)\,\sqrt{-c^5\,d^5}}{4\,\left(b\,c^6-a\,c^5\,d\right)}+\frac{\ln\left(a^{10}\,{\left(-c^5\,d^5\right)}^{5/2}+b^{10}\,c^{20}\,\sqrt{-c^5\,d^5}-a^{10}\,c^{12}\,d^{13}\,x^2-b^{10}\,c^{22}\,d^3\,x^2+2\,a^5\,b^5\,c^{10}\,{\left(-c^5\,d^5\right)}^{3/2}+2\,a^5\,b^5\,c^{17}\,d^8\,x^2\right)\,\sqrt{-c^5\,d^5}}{4\,b\,c^6-4\,a\,c^5\,d}","Not used",1,"(log(c^10*(-a^5*b^5)^(5/2) + a^20*d^10*(-a^5*b^5)^(1/2) - a^12*b^13*c^10*x^2 - a^22*b^3*d^10*x^2 + 2*a^10*c^5*d^5*(-a^5*b^5)^(3/2) + 2*a^17*b^8*c^5*d^5*x^2)*(-a^5*b^5)^(1/2))/(4*a^6*d - 4*a^5*b*c) - (log(c^10*(-a^5*b^5)^(5/2) + a^20*d^10*(-a^5*b^5)^(1/2) + a^12*b^13*c^10*x^2 + a^22*b^3*d^10*x^2 + 2*a^10*c^5*d^5*(-a^5*b^5)^(3/2) - 2*a^17*b^8*c^5*d^5*x^2)*(-a^5*b^5)^(1/2))/(4*(a^6*d - a^5*b*c)) - (1/(6*a*c) - (x^4*(a*d + b*c))/(2*a^2*c^2))/x^6 - (log(a^10*(-c^5*d^5)^(5/2) + b^10*c^20*(-c^5*d^5)^(1/2) + a^10*c^12*d^13*x^2 + b^10*c^22*d^3*x^2 + 2*a^5*b^5*c^10*(-c^5*d^5)^(3/2) - 2*a^5*b^5*c^17*d^8*x^2)*(-c^5*d^5)^(1/2))/(4*(b*c^6 - a*c^5*d)) + (log(a^10*(-c^5*d^5)^(5/2) + b^10*c^20*(-c^5*d^5)^(1/2) - a^10*c^12*d^13*x^2 - b^10*c^22*d^3*x^2 + 2*a^5*b^5*c^10*(-c^5*d^5)^(3/2) + 2*a^5*b^5*c^17*d^8*x^2)*(-c^5*d^5)^(1/2))/(4*b*c^6 - 4*a*c^5*d)","B"
779,1,6361,457,5.632839,"\text{Not used}","int(x^8/((a + b*x^4)*(c + d*x^4)),x)","\frac{x}{b\,d}-2\,\mathrm{atan}\left(\frac{{\left(-\frac{c^5}{256\,a^4\,d^9-1024\,a^3\,b\,c\,d^8+1536\,a^2\,b^2\,c^2\,d^7-1024\,a\,b^3\,c^3\,d^6+256\,b^4\,c^4\,d^5}\right)}^{1/4}\,\left(\frac{4\,x\,\left(a^8\,c^4\,d^4+a^4\,b^4\,c^8\right)}{b\,d}+\left(\frac{16\,\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{x\,{\left(-\frac{c^5}{256\,a^4\,d^9-1024\,a^3\,b\,c\,d^8+1536\,a^2\,b^2\,c^2\,d^7-1024\,a\,b^3\,c^3\,d^6+256\,b^4\,c^4\,d^5}\right)}^{3/4}\,\left(256\,a^8\,b^4\,c^3\,d^9-768\,a^7\,b^5\,c^4\,d^8+512\,a^6\,b^6\,c^5\,d^7+512\,a^5\,b^7\,c^6\,d^6-768\,a^4\,b^8\,c^7\,d^5+256\,a^3\,b^9\,c^8\,d^4\right)\,4{}\mathrm{i}}{b\,d}\right)\,{\left(-\frac{c^5}{256\,a^4\,d^9-1024\,a^3\,b\,c\,d^8+1536\,a^2\,b^2\,c^2\,d^7-1024\,a\,b^3\,c^3\,d^6+256\,b^4\,c^4\,d^5}\right)}^{1/4}\,1{}\mathrm{i}\right)-{\left(-\frac{c^5}{256\,a^4\,d^9-1024\,a^3\,b\,c\,d^8+1536\,a^2\,b^2\,c^2\,d^7-1024\,a\,b^3\,c^3\,d^6+256\,b^4\,c^4\,d^5}\right)}^{1/4}\,\left(-\frac{4\,x\,\left(a^8\,c^4\,d^4+a^4\,b^4\,c^8\right)}{b\,d}+\left(\frac{16\,\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{x\,{\left(-\frac{c^5}{256\,a^4\,d^9-1024\,a^3\,b\,c\,d^8+1536\,a^2\,b^2\,c^2\,d^7-1024\,a\,b^3\,c^3\,d^6+256\,b^4\,c^4\,d^5}\right)}^{3/4}\,\left(256\,a^8\,b^4\,c^3\,d^9-768\,a^7\,b^5\,c^4\,d^8+512\,a^6\,b^6\,c^5\,d^7+512\,a^5\,b^7\,c^6\,d^6-768\,a^4\,b^8\,c^7\,d^5+256\,a^3\,b^9\,c^8\,d^4\right)\,4{}\mathrm{i}}{b\,d}\right)\,{\left(-\frac{c^5}{256\,a^4\,d^9-1024\,a^3\,b\,c\,d^8+1536\,a^2\,b^2\,c^2\,d^7-1024\,a\,b^3\,c^3\,d^6+256\,b^4\,c^4\,d^5}\right)}^{1/4}\,1{}\mathrm{i}\right)}{{\left(-\frac{c^5}{256\,a^4\,d^9-1024\,a^3\,b\,c\,d^8+1536\,a^2\,b^2\,c^2\,d^7-1024\,a\,b^3\,c^3\,d^6+256\,b^4\,c^4\,d^5}\right)}^{1/4}\,\left(\frac{4\,x\,\left(a^8\,c^4\,d^4+a^4\,b^4\,c^8\right)}{b\,d}+\left(\frac{16\,\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{x\,{\left(-\frac{c^5}{256\,a^4\,d^9-1024\,a^3\,b\,c\,d^8+1536\,a^2\,b^2\,c^2\,d^7-1024\,a\,b^3\,c^3\,d^6+256\,b^4\,c^4\,d^5}\right)}^{3/4}\,\left(256\,a^8\,b^4\,c^3\,d^9-768\,a^7\,b^5\,c^4\,d^8+512\,a^6\,b^6\,c^5\,d^7+512\,a^5\,b^7\,c^6\,d^6-768\,a^4\,b^8\,c^7\,d^5+256\,a^3\,b^9\,c^8\,d^4\right)\,4{}\mathrm{i}}{b\,d}\right)\,{\left(-\frac{c^5}{256\,a^4\,d^9-1024\,a^3\,b\,c\,d^8+1536\,a^2\,b^2\,c^2\,d^7-1024\,a\,b^3\,c^3\,d^6+256\,b^4\,c^4\,d^5}\right)}^{1/4}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}+{\left(-\frac{c^5}{256\,a^4\,d^9-1024\,a^3\,b\,c\,d^8+1536\,a^2\,b^2\,c^2\,d^7-1024\,a\,b^3\,c^3\,d^6+256\,b^4\,c^4\,d^5}\right)}^{1/4}\,\left(-\frac{4\,x\,\left(a^8\,c^4\,d^4+a^4\,b^4\,c^8\right)}{b\,d}+\left(\frac{16\,\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{x\,{\left(-\frac{c^5}{256\,a^4\,d^9-1024\,a^3\,b\,c\,d^8+1536\,a^2\,b^2\,c^2\,d^7-1024\,a\,b^3\,c^3\,d^6+256\,b^4\,c^4\,d^5}\right)}^{3/4}\,\left(256\,a^8\,b^4\,c^3\,d^9-768\,a^7\,b^5\,c^4\,d^8+512\,a^6\,b^6\,c^5\,d^7+512\,a^5\,b^7\,c^6\,d^6-768\,a^4\,b^8\,c^7\,d^5+256\,a^3\,b^9\,c^8\,d^4\right)\,4{}\mathrm{i}}{b\,d}\right)\,{\left(-\frac{c^5}{256\,a^4\,d^9-1024\,a^3\,b\,c\,d^8+1536\,a^2\,b^2\,c^2\,d^7-1024\,a\,b^3\,c^3\,d^6+256\,b^4\,c^4\,d^5}\right)}^{1/4}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}\right)\,{\left(-\frac{c^5}{256\,a^4\,d^9-1024\,a^3\,b\,c\,d^8+1536\,a^2\,b^2\,c^2\,d^7-1024\,a\,b^3\,c^3\,d^6+256\,b^4\,c^4\,d^5}\right)}^{1/4}-2\,\mathrm{atan}\left(\frac{{\left(-\frac{a^5}{256\,a^4\,b^5\,d^4-1024\,a^3\,b^6\,c\,d^3+1536\,a^2\,b^7\,c^2\,d^2-1024\,a\,b^8\,c^3\,d+256\,b^9\,c^4}\right)}^{1/4}\,\left(\frac{4\,x\,\left(a^8\,c^4\,d^4+a^4\,b^4\,c^8\right)}{b\,d}+\left(\frac{16\,\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{x\,{\left(-\frac{a^5}{256\,a^4\,b^5\,d^4-1024\,a^3\,b^6\,c\,d^3+1536\,a^2\,b^7\,c^2\,d^2-1024\,a\,b^8\,c^3\,d+256\,b^9\,c^4}\right)}^{3/4}\,\left(256\,a^8\,b^4\,c^3\,d^9-768\,a^7\,b^5\,c^4\,d^8+512\,a^6\,b^6\,c^5\,d^7+512\,a^5\,b^7\,c^6\,d^6-768\,a^4\,b^8\,c^7\,d^5+256\,a^3\,b^9\,c^8\,d^4\right)\,4{}\mathrm{i}}{b\,d}\right)\,{\left(-\frac{a^5}{256\,a^4\,b^5\,d^4-1024\,a^3\,b^6\,c\,d^3+1536\,a^2\,b^7\,c^2\,d^2-1024\,a\,b^8\,c^3\,d+256\,b^9\,c^4}\right)}^{1/4}\,1{}\mathrm{i}\right)-{\left(-\frac{a^5}{256\,a^4\,b^5\,d^4-1024\,a^3\,b^6\,c\,d^3+1536\,a^2\,b^7\,c^2\,d^2-1024\,a\,b^8\,c^3\,d+256\,b^9\,c^4}\right)}^{1/4}\,\left(-\frac{4\,x\,\left(a^8\,c^4\,d^4+a^4\,b^4\,c^8\right)}{b\,d}+\left(\frac{16\,\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{x\,{\left(-\frac{a^5}{256\,a^4\,b^5\,d^4-1024\,a^3\,b^6\,c\,d^3+1536\,a^2\,b^7\,c^2\,d^2-1024\,a\,b^8\,c^3\,d+256\,b^9\,c^4}\right)}^{3/4}\,\left(256\,a^8\,b^4\,c^3\,d^9-768\,a^7\,b^5\,c^4\,d^8+512\,a^6\,b^6\,c^5\,d^7+512\,a^5\,b^7\,c^6\,d^6-768\,a^4\,b^8\,c^7\,d^5+256\,a^3\,b^9\,c^8\,d^4\right)\,4{}\mathrm{i}}{b\,d}\right)\,{\left(-\frac{a^5}{256\,a^4\,b^5\,d^4-1024\,a^3\,b^6\,c\,d^3+1536\,a^2\,b^7\,c^2\,d^2-1024\,a\,b^8\,c^3\,d+256\,b^9\,c^4}\right)}^{1/4}\,1{}\mathrm{i}\right)}{{\left(-\frac{a^5}{256\,a^4\,b^5\,d^4-1024\,a^3\,b^6\,c\,d^3+1536\,a^2\,b^7\,c^2\,d^2-1024\,a\,b^8\,c^3\,d+256\,b^9\,c^4}\right)}^{1/4}\,\left(\frac{4\,x\,\left(a^8\,c^4\,d^4+a^4\,b^4\,c^8\right)}{b\,d}+\left(\frac{16\,\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{x\,{\left(-\frac{a^5}{256\,a^4\,b^5\,d^4-1024\,a^3\,b^6\,c\,d^3+1536\,a^2\,b^7\,c^2\,d^2-1024\,a\,b^8\,c^3\,d+256\,b^9\,c^4}\right)}^{3/4}\,\left(256\,a^8\,b^4\,c^3\,d^9-768\,a^7\,b^5\,c^4\,d^8+512\,a^6\,b^6\,c^5\,d^7+512\,a^5\,b^7\,c^6\,d^6-768\,a^4\,b^8\,c^7\,d^5+256\,a^3\,b^9\,c^8\,d^4\right)\,4{}\mathrm{i}}{b\,d}\right)\,{\left(-\frac{a^5}{256\,a^4\,b^5\,d^4-1024\,a^3\,b^6\,c\,d^3+1536\,a^2\,b^7\,c^2\,d^2-1024\,a\,b^8\,c^3\,d+256\,b^9\,c^4}\right)}^{1/4}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}+{\left(-\frac{a^5}{256\,a^4\,b^5\,d^4-1024\,a^3\,b^6\,c\,d^3+1536\,a^2\,b^7\,c^2\,d^2-1024\,a\,b^8\,c^3\,d+256\,b^9\,c^4}\right)}^{1/4}\,\left(-\frac{4\,x\,\left(a^8\,c^4\,d^4+a^4\,b^4\,c^8\right)}{b\,d}+\left(\frac{16\,\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{x\,{\left(-\frac{a^5}{256\,a^4\,b^5\,d^4-1024\,a^3\,b^6\,c\,d^3+1536\,a^2\,b^7\,c^2\,d^2-1024\,a\,b^8\,c^3\,d+256\,b^9\,c^4}\right)}^{3/4}\,\left(256\,a^8\,b^4\,c^3\,d^9-768\,a^7\,b^5\,c^4\,d^8+512\,a^6\,b^6\,c^5\,d^7+512\,a^5\,b^7\,c^6\,d^6-768\,a^4\,b^8\,c^7\,d^5+256\,a^3\,b^9\,c^8\,d^4\right)\,4{}\mathrm{i}}{b\,d}\right)\,{\left(-\frac{a^5}{256\,a^4\,b^5\,d^4-1024\,a^3\,b^6\,c\,d^3+1536\,a^2\,b^7\,c^2\,d^2-1024\,a\,b^8\,c^3\,d+256\,b^9\,c^4}\right)}^{1/4}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}\right)\,{\left(-\frac{a^5}{256\,a^4\,b^5\,d^4-1024\,a^3\,b^6\,c\,d^3+1536\,a^2\,b^7\,c^2\,d^2-1024\,a\,b^8\,c^3\,d+256\,b^9\,c^4}\right)}^{1/4}+\mathrm{atan}\left(\frac{{\left(-\frac{a^5}{256\,a^4\,b^5\,d^4-1024\,a^3\,b^6\,c\,d^3+1536\,a^2\,b^7\,c^2\,d^2-1024\,a\,b^8\,c^3\,d+256\,b^9\,c^4}\right)}^{1/4}\,\left(\left(\frac{16\,\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{4\,x\,{\left(-\frac{a^5}{256\,a^4\,b^5\,d^4-1024\,a^3\,b^6\,c\,d^3+1536\,a^2\,b^7\,c^2\,d^2-1024\,a\,b^8\,c^3\,d+256\,b^9\,c^4}\right)}^{3/4}\,\left(256\,a^8\,b^4\,c^3\,d^9-768\,a^7\,b^5\,c^4\,d^8+512\,a^6\,b^6\,c^5\,d^7+512\,a^5\,b^7\,c^6\,d^6-768\,a^4\,b^8\,c^7\,d^5+256\,a^3\,b^9\,c^8\,d^4\right)}{b\,d}\right)\,{\left(-\frac{a^5}{256\,a^4\,b^5\,d^4-1024\,a^3\,b^6\,c\,d^3+1536\,a^2\,b^7\,c^2\,d^2-1024\,a\,b^8\,c^3\,d+256\,b^9\,c^4}\right)}^{1/4}-\frac{4\,x\,\left(a^8\,c^4\,d^4+a^4\,b^4\,c^8\right)}{b\,d}\right)\,1{}\mathrm{i}-{\left(-\frac{a^5}{256\,a^4\,b^5\,d^4-1024\,a^3\,b^6\,c\,d^3+1536\,a^2\,b^7\,c^2\,d^2-1024\,a\,b^8\,c^3\,d+256\,b^9\,c^4}\right)}^{1/4}\,\left(\left(\frac{16\,\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{4\,x\,{\left(-\frac{a^5}{256\,a^4\,b^5\,d^4-1024\,a^3\,b^6\,c\,d^3+1536\,a^2\,b^7\,c^2\,d^2-1024\,a\,b^8\,c^3\,d+256\,b^9\,c^4}\right)}^{3/4}\,\left(256\,a^8\,b^4\,c^3\,d^9-768\,a^7\,b^5\,c^4\,d^8+512\,a^6\,b^6\,c^5\,d^7+512\,a^5\,b^7\,c^6\,d^6-768\,a^4\,b^8\,c^7\,d^5+256\,a^3\,b^9\,c^8\,d^4\right)}{b\,d}\right)\,{\left(-\frac{a^5}{256\,a^4\,b^5\,d^4-1024\,a^3\,b^6\,c\,d^3+1536\,a^2\,b^7\,c^2\,d^2-1024\,a\,b^8\,c^3\,d+256\,b^9\,c^4}\right)}^{1/4}+\frac{4\,x\,\left(a^8\,c^4\,d^4+a^4\,b^4\,c^8\right)}{b\,d}\right)\,1{}\mathrm{i}}{{\left(-\frac{a^5}{256\,a^4\,b^5\,d^4-1024\,a^3\,b^6\,c\,d^3+1536\,a^2\,b^7\,c^2\,d^2-1024\,a\,b^8\,c^3\,d+256\,b^9\,c^4}\right)}^{1/4}\,\left(\left(\frac{16\,\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{4\,x\,{\left(-\frac{a^5}{256\,a^4\,b^5\,d^4-1024\,a^3\,b^6\,c\,d^3+1536\,a^2\,b^7\,c^2\,d^2-1024\,a\,b^8\,c^3\,d+256\,b^9\,c^4}\right)}^{3/4}\,\left(256\,a^8\,b^4\,c^3\,d^9-768\,a^7\,b^5\,c^4\,d^8+512\,a^6\,b^6\,c^5\,d^7+512\,a^5\,b^7\,c^6\,d^6-768\,a^4\,b^8\,c^7\,d^5+256\,a^3\,b^9\,c^8\,d^4\right)}{b\,d}\right)\,{\left(-\frac{a^5}{256\,a^4\,b^5\,d^4-1024\,a^3\,b^6\,c\,d^3+1536\,a^2\,b^7\,c^2\,d^2-1024\,a\,b^8\,c^3\,d+256\,b^9\,c^4}\right)}^{1/4}-\frac{4\,x\,\left(a^8\,c^4\,d^4+a^4\,b^4\,c^8\right)}{b\,d}\right)+{\left(-\frac{a^5}{256\,a^4\,b^5\,d^4-1024\,a^3\,b^6\,c\,d^3+1536\,a^2\,b^7\,c^2\,d^2-1024\,a\,b^8\,c^3\,d+256\,b^9\,c^4}\right)}^{1/4}\,\left(\left(\frac{16\,\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{4\,x\,{\left(-\frac{a^5}{256\,a^4\,b^5\,d^4-1024\,a^3\,b^6\,c\,d^3+1536\,a^2\,b^7\,c^2\,d^2-1024\,a\,b^8\,c^3\,d+256\,b^9\,c^4}\right)}^{3/4}\,\left(256\,a^8\,b^4\,c^3\,d^9-768\,a^7\,b^5\,c^4\,d^8+512\,a^6\,b^6\,c^5\,d^7+512\,a^5\,b^7\,c^6\,d^6-768\,a^4\,b^8\,c^7\,d^5+256\,a^3\,b^9\,c^8\,d^4\right)}{b\,d}\right)\,{\left(-\frac{a^5}{256\,a^4\,b^5\,d^4-1024\,a^3\,b^6\,c\,d^3+1536\,a^2\,b^7\,c^2\,d^2-1024\,a\,b^8\,c^3\,d+256\,b^9\,c^4}\right)}^{1/4}+\frac{4\,x\,\left(a^8\,c^4\,d^4+a^4\,b^4\,c^8\right)}{b\,d}\right)}\right)\,{\left(-\frac{a^5}{256\,a^4\,b^5\,d^4-1024\,a^3\,b^6\,c\,d^3+1536\,a^2\,b^7\,c^2\,d^2-1024\,a\,b^8\,c^3\,d+256\,b^9\,c^4}\right)}^{1/4}\,2{}\mathrm{i}+\mathrm{atan}\left(\frac{{\left(-\frac{c^5}{256\,a^4\,d^9-1024\,a^3\,b\,c\,d^8+1536\,a^2\,b^2\,c^2\,d^7-1024\,a\,b^3\,c^3\,d^6+256\,b^4\,c^4\,d^5}\right)}^{1/4}\,\left(\left(\frac{16\,\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{4\,x\,{\left(-\frac{c^5}{256\,a^4\,d^9-1024\,a^3\,b\,c\,d^8+1536\,a^2\,b^2\,c^2\,d^7-1024\,a\,b^3\,c^3\,d^6+256\,b^4\,c^4\,d^5}\right)}^{3/4}\,\left(256\,a^8\,b^4\,c^3\,d^9-768\,a^7\,b^5\,c^4\,d^8+512\,a^6\,b^6\,c^5\,d^7+512\,a^5\,b^7\,c^6\,d^6-768\,a^4\,b^8\,c^7\,d^5+256\,a^3\,b^9\,c^8\,d^4\right)}{b\,d}\right)\,{\left(-\frac{c^5}{256\,a^4\,d^9-1024\,a^3\,b\,c\,d^8+1536\,a^2\,b^2\,c^2\,d^7-1024\,a\,b^3\,c^3\,d^6+256\,b^4\,c^4\,d^5}\right)}^{1/4}-\frac{4\,x\,\left(a^8\,c^4\,d^4+a^4\,b^4\,c^8\right)}{b\,d}\right)\,1{}\mathrm{i}-{\left(-\frac{c^5}{256\,a^4\,d^9-1024\,a^3\,b\,c\,d^8+1536\,a^2\,b^2\,c^2\,d^7-1024\,a\,b^3\,c^3\,d^6+256\,b^4\,c^4\,d^5}\right)}^{1/4}\,\left(\left(\frac{16\,\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{4\,x\,{\left(-\frac{c^5}{256\,a^4\,d^9-1024\,a^3\,b\,c\,d^8+1536\,a^2\,b^2\,c^2\,d^7-1024\,a\,b^3\,c^3\,d^6+256\,b^4\,c^4\,d^5}\right)}^{3/4}\,\left(256\,a^8\,b^4\,c^3\,d^9-768\,a^7\,b^5\,c^4\,d^8+512\,a^6\,b^6\,c^5\,d^7+512\,a^5\,b^7\,c^6\,d^6-768\,a^4\,b^8\,c^7\,d^5+256\,a^3\,b^9\,c^8\,d^4\right)}{b\,d}\right)\,{\left(-\frac{c^5}{256\,a^4\,d^9-1024\,a^3\,b\,c\,d^8+1536\,a^2\,b^2\,c^2\,d^7-1024\,a\,b^3\,c^3\,d^6+256\,b^4\,c^4\,d^5}\right)}^{1/4}+\frac{4\,x\,\left(a^8\,c^4\,d^4+a^4\,b^4\,c^8\right)}{b\,d}\right)\,1{}\mathrm{i}}{{\left(-\frac{c^5}{256\,a^4\,d^9-1024\,a^3\,b\,c\,d^8+1536\,a^2\,b^2\,c^2\,d^7-1024\,a\,b^3\,c^3\,d^6+256\,b^4\,c^4\,d^5}\right)}^{1/4}\,\left(\left(\frac{16\,\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{4\,x\,{\left(-\frac{c^5}{256\,a^4\,d^9-1024\,a^3\,b\,c\,d^8+1536\,a^2\,b^2\,c^2\,d^7-1024\,a\,b^3\,c^3\,d^6+256\,b^4\,c^4\,d^5}\right)}^{3/4}\,\left(256\,a^8\,b^4\,c^3\,d^9-768\,a^7\,b^5\,c^4\,d^8+512\,a^6\,b^6\,c^5\,d^7+512\,a^5\,b^7\,c^6\,d^6-768\,a^4\,b^8\,c^7\,d^5+256\,a^3\,b^9\,c^8\,d^4\right)}{b\,d}\right)\,{\left(-\frac{c^5}{256\,a^4\,d^9-1024\,a^3\,b\,c\,d^8+1536\,a^2\,b^2\,c^2\,d^7-1024\,a\,b^3\,c^3\,d^6+256\,b^4\,c^4\,d^5}\right)}^{1/4}-\frac{4\,x\,\left(a^8\,c^4\,d^4+a^4\,b^4\,c^8\right)}{b\,d}\right)+{\left(-\frac{c^5}{256\,a^4\,d^9-1024\,a^3\,b\,c\,d^8+1536\,a^2\,b^2\,c^2\,d^7-1024\,a\,b^3\,c^3\,d^6+256\,b^4\,c^4\,d^5}\right)}^{1/4}\,\left(\left(\frac{16\,\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{4\,x\,{\left(-\frac{c^5}{256\,a^4\,d^9-1024\,a^3\,b\,c\,d^8+1536\,a^2\,b^2\,c^2\,d^7-1024\,a\,b^3\,c^3\,d^6+256\,b^4\,c^4\,d^5}\right)}^{3/4}\,\left(256\,a^8\,b^4\,c^3\,d^9-768\,a^7\,b^5\,c^4\,d^8+512\,a^6\,b^6\,c^5\,d^7+512\,a^5\,b^7\,c^6\,d^6-768\,a^4\,b^8\,c^7\,d^5+256\,a^3\,b^9\,c^8\,d^4\right)}{b\,d}\right)\,{\left(-\frac{c^5}{256\,a^4\,d^9-1024\,a^3\,b\,c\,d^8+1536\,a^2\,b^2\,c^2\,d^7-1024\,a\,b^3\,c^3\,d^6+256\,b^4\,c^4\,d^5}\right)}^{1/4}+\frac{4\,x\,\left(a^8\,c^4\,d^4+a^4\,b^4\,c^8\right)}{b\,d}\right)}\right)\,{\left(-\frac{c^5}{256\,a^4\,d^9-1024\,a^3\,b\,c\,d^8+1536\,a^2\,b^2\,c^2\,d^7-1024\,a\,b^3\,c^3\,d^6+256\,b^4\,c^4\,d^5}\right)}^{1/4}\,2{}\mathrm{i}","Not used",1,"atan(((-a^5/(256*b^9*c^4 + 256*a^4*b^5*d^4 - 1024*a^3*b^6*c*d^3 + 1536*a^2*b^7*c^2*d^2 - 1024*a*b^8*c^3*d))^(1/4)*(((16*(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) - (4*x*(-a^5/(256*b^9*c^4 + 256*a^4*b^5*d^4 - 1024*a^3*b^6*c*d^3 + 1536*a^2*b^7*c^2*d^2 - 1024*a*b^8*c^3*d))^(3/4)*(256*a^3*b^9*c^8*d^4 - 768*a^4*b^8*c^7*d^5 + 512*a^5*b^7*c^6*d^6 + 512*a^6*b^6*c^5*d^7 - 768*a^7*b^5*c^4*d^8 + 256*a^8*b^4*c^3*d^9))/(b*d))*(-a^5/(256*b^9*c^4 + 256*a^4*b^5*d^4 - 1024*a^3*b^6*c*d^3 + 1536*a^2*b^7*c^2*d^2 - 1024*a*b^8*c^3*d))^(1/4) - (4*x*(a^4*b^4*c^8 + a^8*c^4*d^4))/(b*d))*1i - (-a^5/(256*b^9*c^4 + 256*a^4*b^5*d^4 - 1024*a^3*b^6*c*d^3 + 1536*a^2*b^7*c^2*d^2 - 1024*a*b^8*c^3*d))^(1/4)*(((16*(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) + (4*x*(-a^5/(256*b^9*c^4 + 256*a^4*b^5*d^4 - 1024*a^3*b^6*c*d^3 + 1536*a^2*b^7*c^2*d^2 - 1024*a*b^8*c^3*d))^(3/4)*(256*a^3*b^9*c^8*d^4 - 768*a^4*b^8*c^7*d^5 + 512*a^5*b^7*c^6*d^6 + 512*a^6*b^6*c^5*d^7 - 768*a^7*b^5*c^4*d^8 + 256*a^8*b^4*c^3*d^9))/(b*d))*(-a^5/(256*b^9*c^4 + 256*a^4*b^5*d^4 - 1024*a^3*b^6*c*d^3 + 1536*a^2*b^7*c^2*d^2 - 1024*a*b^8*c^3*d))^(1/4) + (4*x*(a^4*b^4*c^8 + a^8*c^4*d^4))/(b*d))*1i)/((-a^5/(256*b^9*c^4 + 256*a^4*b^5*d^4 - 1024*a^3*b^6*c*d^3 + 1536*a^2*b^7*c^2*d^2 - 1024*a*b^8*c^3*d))^(1/4)*(((16*(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) - (4*x*(-a^5/(256*b^9*c^4 + 256*a^4*b^5*d^4 - 1024*a^3*b^6*c*d^3 + 1536*a^2*b^7*c^2*d^2 - 1024*a*b^8*c^3*d))^(3/4)*(256*a^3*b^9*c^8*d^4 - 768*a^4*b^8*c^7*d^5 + 512*a^5*b^7*c^6*d^6 + 512*a^6*b^6*c^5*d^7 - 768*a^7*b^5*c^4*d^8 + 256*a^8*b^4*c^3*d^9))/(b*d))*(-a^5/(256*b^9*c^4 + 256*a^4*b^5*d^4 - 1024*a^3*b^6*c*d^3 + 1536*a^2*b^7*c^2*d^2 - 1024*a*b^8*c^3*d))^(1/4) - (4*x*(a^4*b^4*c^8 + a^8*c^4*d^4))/(b*d)) + (-a^5/(256*b^9*c^4 + 256*a^4*b^5*d^4 - 1024*a^3*b^6*c*d^3 + 1536*a^2*b^7*c^2*d^2 - 1024*a*b^8*c^3*d))^(1/4)*(((16*(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) + (4*x*(-a^5/(256*b^9*c^4 + 256*a^4*b^5*d^4 - 1024*a^3*b^6*c*d^3 + 1536*a^2*b^7*c^2*d^2 - 1024*a*b^8*c^3*d))^(3/4)*(256*a^3*b^9*c^8*d^4 - 768*a^4*b^8*c^7*d^5 + 512*a^5*b^7*c^6*d^6 + 512*a^6*b^6*c^5*d^7 - 768*a^7*b^5*c^4*d^8 + 256*a^8*b^4*c^3*d^9))/(b*d))*(-a^5/(256*b^9*c^4 + 256*a^4*b^5*d^4 - 1024*a^3*b^6*c*d^3 + 1536*a^2*b^7*c^2*d^2 - 1024*a*b^8*c^3*d))^(1/4) + (4*x*(a^4*b^4*c^8 + a^8*c^4*d^4))/(b*d))))*(-a^5/(256*b^9*c^4 + 256*a^4*b^5*d^4 - 1024*a^3*b^6*c*d^3 + 1536*a^2*b^7*c^2*d^2 - 1024*a*b^8*c^3*d))^(1/4)*2i - 2*atan(((-a^5/(256*b^9*c^4 + 256*a^4*b^5*d^4 - 1024*a^3*b^6*c*d^3 + 1536*a^2*b^7*c^2*d^2 - 1024*a*b^8*c^3*d))^(1/4)*(((16*(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*(-a^5/(256*b^9*c^4 + 256*a^4*b^5*d^4 - 1024*a^3*b^6*c*d^3 + 1536*a^2*b^7*c^2*d^2 - 1024*a*b^8*c^3*d))^(3/4)*(256*a^3*b^9*c^8*d^4 - 768*a^4*b^8*c^7*d^5 + 512*a^5*b^7*c^6*d^6 + 512*a^6*b^6*c^5*d^7 - 768*a^7*b^5*c^4*d^8 + 256*a^8*b^4*c^3*d^9)*4i)/(b*d))*(-a^5/(256*b^9*c^4 + 256*a^4*b^5*d^4 - 1024*a^3*b^6*c*d^3 + 1536*a^2*b^7*c^2*d^2 - 1024*a*b^8*c^3*d))^(1/4)*1i + (4*x*(a^4*b^4*c^8 + a^8*c^4*d^4))/(b*d)) - (-a^5/(256*b^9*c^4 + 256*a^4*b^5*d^4 - 1024*a^3*b^6*c*d^3 + 1536*a^2*b^7*c^2*d^2 - 1024*a*b^8*c^3*d))^(1/4)*(((16*(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*(-a^5/(256*b^9*c^4 + 256*a^4*b^5*d^4 - 1024*a^3*b^6*c*d^3 + 1536*a^2*b^7*c^2*d^2 - 1024*a*b^8*c^3*d))^(3/4)*(256*a^3*b^9*c^8*d^4 - 768*a^4*b^8*c^7*d^5 + 512*a^5*b^7*c^6*d^6 + 512*a^6*b^6*c^5*d^7 - 768*a^7*b^5*c^4*d^8 + 256*a^8*b^4*c^3*d^9)*4i)/(b*d))*(-a^5/(256*b^9*c^4 + 256*a^4*b^5*d^4 - 1024*a^3*b^6*c*d^3 + 1536*a^2*b^7*c^2*d^2 - 1024*a*b^8*c^3*d))^(1/4)*1i - (4*x*(a^4*b^4*c^8 + a^8*c^4*d^4))/(b*d)))/((-a^5/(256*b^9*c^4 + 256*a^4*b^5*d^4 - 1024*a^3*b^6*c*d^3 + 1536*a^2*b^7*c^2*d^2 - 1024*a*b^8*c^3*d))^(1/4)*(((16*(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*(-a^5/(256*b^9*c^4 + 256*a^4*b^5*d^4 - 1024*a^3*b^6*c*d^3 + 1536*a^2*b^7*c^2*d^2 - 1024*a*b^8*c^3*d))^(3/4)*(256*a^3*b^9*c^8*d^4 - 768*a^4*b^8*c^7*d^5 + 512*a^5*b^7*c^6*d^6 + 512*a^6*b^6*c^5*d^7 - 768*a^7*b^5*c^4*d^8 + 256*a^8*b^4*c^3*d^9)*4i)/(b*d))*(-a^5/(256*b^9*c^4 + 256*a^4*b^5*d^4 - 1024*a^3*b^6*c*d^3 + 1536*a^2*b^7*c^2*d^2 - 1024*a*b^8*c^3*d))^(1/4)*1i + (4*x*(a^4*b^4*c^8 + a^8*c^4*d^4))/(b*d))*1i + (-a^5/(256*b^9*c^4 + 256*a^4*b^5*d^4 - 1024*a^3*b^6*c*d^3 + 1536*a^2*b^7*c^2*d^2 - 1024*a*b^8*c^3*d))^(1/4)*(((16*(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*(-a^5/(256*b^9*c^4 + 256*a^4*b^5*d^4 - 1024*a^3*b^6*c*d^3 + 1536*a^2*b^7*c^2*d^2 - 1024*a*b^8*c^3*d))^(3/4)*(256*a^3*b^9*c^8*d^4 - 768*a^4*b^8*c^7*d^5 + 512*a^5*b^7*c^6*d^6 + 512*a^6*b^6*c^5*d^7 - 768*a^7*b^5*c^4*d^8 + 256*a^8*b^4*c^3*d^9)*4i)/(b*d))*(-a^5/(256*b^9*c^4 + 256*a^4*b^5*d^4 - 1024*a^3*b^6*c*d^3 + 1536*a^2*b^7*c^2*d^2 - 1024*a*b^8*c^3*d))^(1/4)*1i - (4*x*(a^4*b^4*c^8 + a^8*c^4*d^4))/(b*d))*1i))*(-a^5/(256*b^9*c^4 + 256*a^4*b^5*d^4 - 1024*a^3*b^6*c*d^3 + 1536*a^2*b^7*c^2*d^2 - 1024*a*b^8*c^3*d))^(1/4) + atan(((-c^5/(256*a^4*d^9 + 256*b^4*c^4*d^5 - 1024*a*b^3*c^3*d^6 + 1536*a^2*b^2*c^2*d^7 - 1024*a^3*b*c*d^8))^(1/4)*(((16*(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) - (4*x*(-c^5/(256*a^4*d^9 + 256*b^4*c^4*d^5 - 1024*a*b^3*c^3*d^6 + 1536*a^2*b^2*c^2*d^7 - 1024*a^3*b*c*d^8))^(3/4)*(256*a^3*b^9*c^8*d^4 - 768*a^4*b^8*c^7*d^5 + 512*a^5*b^7*c^6*d^6 + 512*a^6*b^6*c^5*d^7 - 768*a^7*b^5*c^4*d^8 + 256*a^8*b^4*c^3*d^9))/(b*d))*(-c^5/(256*a^4*d^9 + 256*b^4*c^4*d^5 - 1024*a*b^3*c^3*d^6 + 1536*a^2*b^2*c^2*d^7 - 1024*a^3*b*c*d^8))^(1/4) - (4*x*(a^4*b^4*c^8 + a^8*c^4*d^4))/(b*d))*1i - (-c^5/(256*a^4*d^9 + 256*b^4*c^4*d^5 - 1024*a*b^3*c^3*d^6 + 1536*a^2*b^2*c^2*d^7 - 1024*a^3*b*c*d^8))^(1/4)*(((16*(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) + (4*x*(-c^5/(256*a^4*d^9 + 256*b^4*c^4*d^5 - 1024*a*b^3*c^3*d^6 + 1536*a^2*b^2*c^2*d^7 - 1024*a^3*b*c*d^8))^(3/4)*(256*a^3*b^9*c^8*d^4 - 768*a^4*b^8*c^7*d^5 + 512*a^5*b^7*c^6*d^6 + 512*a^6*b^6*c^5*d^7 - 768*a^7*b^5*c^4*d^8 + 256*a^8*b^4*c^3*d^9))/(b*d))*(-c^5/(256*a^4*d^9 + 256*b^4*c^4*d^5 - 1024*a*b^3*c^3*d^6 + 1536*a^2*b^2*c^2*d^7 - 1024*a^3*b*c*d^8))^(1/4) + (4*x*(a^4*b^4*c^8 + a^8*c^4*d^4))/(b*d))*1i)/((-c^5/(256*a^4*d^9 + 256*b^4*c^4*d^5 - 1024*a*b^3*c^3*d^6 + 1536*a^2*b^2*c^2*d^7 - 1024*a^3*b*c*d^8))^(1/4)*(((16*(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) - (4*x*(-c^5/(256*a^4*d^9 + 256*b^4*c^4*d^5 - 1024*a*b^3*c^3*d^6 + 1536*a^2*b^2*c^2*d^7 - 1024*a^3*b*c*d^8))^(3/4)*(256*a^3*b^9*c^8*d^4 - 768*a^4*b^8*c^7*d^5 + 512*a^5*b^7*c^6*d^6 + 512*a^6*b^6*c^5*d^7 - 768*a^7*b^5*c^4*d^8 + 256*a^8*b^4*c^3*d^9))/(b*d))*(-c^5/(256*a^4*d^9 + 256*b^4*c^4*d^5 - 1024*a*b^3*c^3*d^6 + 1536*a^2*b^2*c^2*d^7 - 1024*a^3*b*c*d^8))^(1/4) - (4*x*(a^4*b^4*c^8 + a^8*c^4*d^4))/(b*d)) + (-c^5/(256*a^4*d^9 + 256*b^4*c^4*d^5 - 1024*a*b^3*c^3*d^6 + 1536*a^2*b^2*c^2*d^7 - 1024*a^3*b*c*d^8))^(1/4)*(((16*(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) + (4*x*(-c^5/(256*a^4*d^9 + 256*b^4*c^4*d^5 - 1024*a*b^3*c^3*d^6 + 1536*a^2*b^2*c^2*d^7 - 1024*a^3*b*c*d^8))^(3/4)*(256*a^3*b^9*c^8*d^4 - 768*a^4*b^8*c^7*d^5 + 512*a^5*b^7*c^6*d^6 + 512*a^6*b^6*c^5*d^7 - 768*a^7*b^5*c^4*d^8 + 256*a^8*b^4*c^3*d^9))/(b*d))*(-c^5/(256*a^4*d^9 + 256*b^4*c^4*d^5 - 1024*a*b^3*c^3*d^6 + 1536*a^2*b^2*c^2*d^7 - 1024*a^3*b*c*d^8))^(1/4) + (4*x*(a^4*b^4*c^8 + a^8*c^4*d^4))/(b*d))))*(-c^5/(256*a^4*d^9 + 256*b^4*c^4*d^5 - 1024*a*b^3*c^3*d^6 + 1536*a^2*b^2*c^2*d^7 - 1024*a^3*b*c*d^8))^(1/4)*2i - 2*atan(((-c^5/(256*a^4*d^9 + 256*b^4*c^4*d^5 - 1024*a*b^3*c^3*d^6 + 1536*a^2*b^2*c^2*d^7 - 1024*a^3*b*c*d^8))^(1/4)*(((16*(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*(-c^5/(256*a^4*d^9 + 256*b^4*c^4*d^5 - 1024*a*b^3*c^3*d^6 + 1536*a^2*b^2*c^2*d^7 - 1024*a^3*b*c*d^8))^(3/4)*(256*a^3*b^9*c^8*d^4 - 768*a^4*b^8*c^7*d^5 + 512*a^5*b^7*c^6*d^6 + 512*a^6*b^6*c^5*d^7 - 768*a^7*b^5*c^4*d^8 + 256*a^8*b^4*c^3*d^9)*4i)/(b*d))*(-c^5/(256*a^4*d^9 + 256*b^4*c^4*d^5 - 1024*a*b^3*c^3*d^6 + 1536*a^2*b^2*c^2*d^7 - 1024*a^3*b*c*d^8))^(1/4)*1i + (4*x*(a^4*b^4*c^8 + a^8*c^4*d^4))/(b*d)) - (-c^5/(256*a^4*d^9 + 256*b^4*c^4*d^5 - 1024*a*b^3*c^3*d^6 + 1536*a^2*b^2*c^2*d^7 - 1024*a^3*b*c*d^8))^(1/4)*(((16*(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*(-c^5/(256*a^4*d^9 + 256*b^4*c^4*d^5 - 1024*a*b^3*c^3*d^6 + 1536*a^2*b^2*c^2*d^7 - 1024*a^3*b*c*d^8))^(3/4)*(256*a^3*b^9*c^8*d^4 - 768*a^4*b^8*c^7*d^5 + 512*a^5*b^7*c^6*d^6 + 512*a^6*b^6*c^5*d^7 - 768*a^7*b^5*c^4*d^8 + 256*a^8*b^4*c^3*d^9)*4i)/(b*d))*(-c^5/(256*a^4*d^9 + 256*b^4*c^4*d^5 - 1024*a*b^3*c^3*d^6 + 1536*a^2*b^2*c^2*d^7 - 1024*a^3*b*c*d^8))^(1/4)*1i - (4*x*(a^4*b^4*c^8 + a^8*c^4*d^4))/(b*d)))/((-c^5/(256*a^4*d^9 + 256*b^4*c^4*d^5 - 1024*a*b^3*c^3*d^6 + 1536*a^2*b^2*c^2*d^7 - 1024*a^3*b*c*d^8))^(1/4)*(((16*(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*(-c^5/(256*a^4*d^9 + 256*b^4*c^4*d^5 - 1024*a*b^3*c^3*d^6 + 1536*a^2*b^2*c^2*d^7 - 1024*a^3*b*c*d^8))^(3/4)*(256*a^3*b^9*c^8*d^4 - 768*a^4*b^8*c^7*d^5 + 512*a^5*b^7*c^6*d^6 + 512*a^6*b^6*c^5*d^7 - 768*a^7*b^5*c^4*d^8 + 256*a^8*b^4*c^3*d^9)*4i)/(b*d))*(-c^5/(256*a^4*d^9 + 256*b^4*c^4*d^5 - 1024*a*b^3*c^3*d^6 + 1536*a^2*b^2*c^2*d^7 - 1024*a^3*b*c*d^8))^(1/4)*1i + (4*x*(a^4*b^4*c^8 + a^8*c^4*d^4))/(b*d))*1i + (-c^5/(256*a^4*d^9 + 256*b^4*c^4*d^5 - 1024*a*b^3*c^3*d^6 + 1536*a^2*b^2*c^2*d^7 - 1024*a^3*b*c*d^8))^(1/4)*(((16*(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*(-c^5/(256*a^4*d^9 + 256*b^4*c^4*d^5 - 1024*a*b^3*c^3*d^6 + 1536*a^2*b^2*c^2*d^7 - 1024*a^3*b*c*d^8))^(3/4)*(256*a^3*b^9*c^8*d^4 - 768*a^4*b^8*c^7*d^5 + 512*a^5*b^7*c^6*d^6 + 512*a^6*b^6*c^5*d^7 - 768*a^7*b^5*c^4*d^8 + 256*a^8*b^4*c^3*d^9)*4i)/(b*d))*(-c^5/(256*a^4*d^9 + 256*b^4*c^4*d^5 - 1024*a*b^3*c^3*d^6 + 1536*a^2*b^2*c^2*d^7 - 1024*a^3*b*c*d^8))^(1/4)*1i - (4*x*(a^4*b^4*c^8 + a^8*c^4*d^4))/(b*d))*1i))*(-c^5/(256*a^4*d^9 + 256*b^4*c^4*d^5 - 1024*a*b^3*c^3*d^6 + 1536*a^2*b^2*c^2*d^7 - 1024*a^3*b*c*d^8))^(1/4) + x/(b*d)","B"
780,1,2553,449,5.724899,"\text{Not used}","int(x^6/((a + b*x^4)*(c + d*x^4)),x)","-2\,\mathrm{atan}\left(\frac{4\,b^4\,c^3\,x\,{\left(-\frac{a^3}{256\,a^4\,b^3\,d^4-1024\,a^3\,b^4\,c\,d^3+1536\,a^2\,b^5\,c^2\,d^2-1024\,a\,b^6\,c^3\,d+256\,b^7\,c^4}\right)}^{1/4}+4\,a^3\,b\,d^3\,x\,{\left(-\frac{a^3}{256\,a^4\,b^3\,d^4-1024\,a^3\,b^4\,c\,d^3+1536\,a^2\,b^5\,c^2\,d^2-1024\,a\,b^6\,c^3\,d+256\,b^7\,c^4}\right)}^{1/4}+2048\,a^4\,b^4\,d^7\,x\,{\left(-\frac{a^3}{256\,a^4\,b^3\,d^4-1024\,a^3\,b^4\,c\,d^3+1536\,a^2\,b^5\,c^2\,d^2-1024\,a\,b^6\,c^3\,d+256\,b^7\,c^4}\right)}^{5/4}+2048\,b^8\,c^4\,d^3\,x\,{\left(-\frac{a^3}{256\,a^4\,b^3\,d^4-1024\,a^3\,b^4\,c\,d^3+1536\,a^2\,b^5\,c^2\,d^2-1024\,a\,b^6\,c^3\,d+256\,b^7\,c^4}\right)}^{5/4}-8192\,a\,b^7\,c^3\,d^4\,x\,{\left(-\frac{a^3}{256\,a^4\,b^3\,d^4-1024\,a^3\,b^4\,c\,d^3+1536\,a^2\,b^5\,c^2\,d^2-1024\,a\,b^6\,c^3\,d+256\,b^7\,c^4}\right)}^{5/4}-8192\,a^3\,b^5\,c\,d^6\,x\,{\left(-\frac{a^3}{256\,a^4\,b^3\,d^4-1024\,a^3\,b^4\,c\,d^3+1536\,a^2\,b^5\,c^2\,d^2-1024\,a\,b^6\,c^3\,d+256\,b^7\,c^4}\right)}^{5/4}+12288\,a^2\,b^6\,c^2\,d^5\,x\,{\left(-\frac{a^3}{256\,a^4\,b^3\,d^4-1024\,a^3\,b^4\,c\,d^3+1536\,a^2\,b^5\,c^2\,d^2-1024\,a\,b^6\,c^3\,d+256\,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}{256\,a^4\,b^3\,d^4-1024\,a^3\,b^4\,c\,d^3+1536\,a^2\,b^5\,c^2\,d^2-1024\,a\,b^6\,c^3\,d+256\,b^7\,c^4}\right)}^{1/4}-\mathrm{atan}\left(\frac{b^4\,c^3\,x\,{\left(-\frac{a^3}{256\,a^4\,b^3\,d^4-1024\,a^3\,b^4\,c\,d^3+1536\,a^2\,b^5\,c^2\,d^2-1024\,a\,b^6\,c^3\,d+256\,b^7\,c^4}\right)}^{1/4}\,4{}\mathrm{i}+a^3\,b\,d^3\,x\,{\left(-\frac{a^3}{256\,a^4\,b^3\,d^4-1024\,a^3\,b^4\,c\,d^3+1536\,a^2\,b^5\,c^2\,d^2-1024\,a\,b^6\,c^3\,d+256\,b^7\,c^4}\right)}^{1/4}\,4{}\mathrm{i}+a^4\,b^4\,d^7\,x\,{\left(-\frac{a^3}{256\,a^4\,b^3\,d^4-1024\,a^3\,b^4\,c\,d^3+1536\,a^2\,b^5\,c^2\,d^2-1024\,a\,b^6\,c^3\,d+256\,b^7\,c^4}\right)}^{5/4}\,2048{}\mathrm{i}+b^8\,c^4\,d^3\,x\,{\left(-\frac{a^3}{256\,a^4\,b^3\,d^4-1024\,a^3\,b^4\,c\,d^3+1536\,a^2\,b^5\,c^2\,d^2-1024\,a\,b^6\,c^3\,d+256\,b^7\,c^4}\right)}^{5/4}\,2048{}\mathrm{i}-a\,b^7\,c^3\,d^4\,x\,{\left(-\frac{a^3}{256\,a^4\,b^3\,d^4-1024\,a^3\,b^4\,c\,d^3+1536\,a^2\,b^5\,c^2\,d^2-1024\,a\,b^6\,c^3\,d+256\,b^7\,c^4}\right)}^{5/4}\,8192{}\mathrm{i}-a^3\,b^5\,c\,d^6\,x\,{\left(-\frac{a^3}{256\,a^4\,b^3\,d^4-1024\,a^3\,b^4\,c\,d^3+1536\,a^2\,b^5\,c^2\,d^2-1024\,a\,b^6\,c^3\,d+256\,b^7\,c^4}\right)}^{5/4}\,8192{}\mathrm{i}+a^2\,b^6\,c^2\,d^5\,x\,{\left(-\frac{a^3}{256\,a^4\,b^3\,d^4-1024\,a^3\,b^4\,c\,d^3+1536\,a^2\,b^5\,c^2\,d^2-1024\,a\,b^6\,c^3\,d+256\,b^7\,c^4}\right)}^{5/4}\,12288{}\mathrm{i}}{a^3\,d^2+a^2\,b\,c\,d+a\,b^2\,c^2}\right)\,{\left(-\frac{a^3}{256\,a^4\,b^3\,d^4-1024\,a^3\,b^4\,c\,d^3+1536\,a^2\,b^5\,c^2\,d^2-1024\,a\,b^6\,c^3\,d+256\,b^7\,c^4}\right)}^{1/4}\,2{}\mathrm{i}-2\,\mathrm{atan}\left(\frac{4\,a^3\,d^4\,x\,{\left(-\frac{c^3}{256\,a^4\,d^7-1024\,a^3\,b\,c\,d^6+1536\,a^2\,b^2\,c^2\,d^5-1024\,a\,b^3\,c^3\,d^4+256\,b^4\,c^4\,d^3}\right)}^{1/4}+2048\,b^7\,c^4\,d^4\,x\,{\left(-\frac{c^3}{256\,a^4\,d^7-1024\,a^3\,b\,c\,d^6+1536\,a^2\,b^2\,c^2\,d^5-1024\,a\,b^3\,c^3\,d^4+256\,b^4\,c^4\,d^3}\right)}^{5/4}+4\,b^3\,c^3\,d\,x\,{\left(-\frac{c^3}{256\,a^4\,d^7-1024\,a^3\,b\,c\,d^6+1536\,a^2\,b^2\,c^2\,d^5-1024\,a\,b^3\,c^3\,d^4+256\,b^4\,c^4\,d^3}\right)}^{1/4}+2048\,a^4\,b^3\,d^8\,x\,{\left(-\frac{c^3}{256\,a^4\,d^7-1024\,a^3\,b\,c\,d^6+1536\,a^2\,b^2\,c^2\,d^5-1024\,a\,b^3\,c^3\,d^4+256\,b^4\,c^4\,d^3}\right)}^{5/4}-8192\,a\,b^6\,c^3\,d^5\,x\,{\left(-\frac{c^3}{256\,a^4\,d^7-1024\,a^3\,b\,c\,d^6+1536\,a^2\,b^2\,c^2\,d^5-1024\,a\,b^3\,c^3\,d^4+256\,b^4\,c^4\,d^3}\right)}^{5/4}-8192\,a^3\,b^4\,c\,d^7\,x\,{\left(-\frac{c^3}{256\,a^4\,d^7-1024\,a^3\,b\,c\,d^6+1536\,a^2\,b^2\,c^2\,d^5-1024\,a\,b^3\,c^3\,d^4+256\,b^4\,c^4\,d^3}\right)}^{5/4}+12288\,a^2\,b^5\,c^2\,d^6\,x\,{\left(-\frac{c^3}{256\,a^4\,d^7-1024\,a^3\,b\,c\,d^6+1536\,a^2\,b^2\,c^2\,d^5-1024\,a\,b^3\,c^3\,d^4+256\,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}{256\,a^4\,d^7-1024\,a^3\,b\,c\,d^6+1536\,a^2\,b^2\,c^2\,d^5-1024\,a\,b^3\,c^3\,d^4+256\,b^4\,c^4\,d^3}\right)}^{1/4}-\mathrm{atan}\left(\frac{a^3\,d^4\,x\,{\left(-\frac{c^3}{256\,a^4\,d^7-1024\,a^3\,b\,c\,d^6+1536\,a^2\,b^2\,c^2\,d^5-1024\,a\,b^3\,c^3\,d^4+256\,b^4\,c^4\,d^3}\right)}^{1/4}\,4{}\mathrm{i}+b^7\,c^4\,d^4\,x\,{\left(-\frac{c^3}{256\,a^4\,d^7-1024\,a^3\,b\,c\,d^6+1536\,a^2\,b^2\,c^2\,d^5-1024\,a\,b^3\,c^3\,d^4+256\,b^4\,c^4\,d^3}\right)}^{5/4}\,2048{}\mathrm{i}+b^3\,c^3\,d\,x\,{\left(-\frac{c^3}{256\,a^4\,d^7-1024\,a^3\,b\,c\,d^6+1536\,a^2\,b^2\,c^2\,d^5-1024\,a\,b^3\,c^3\,d^4+256\,b^4\,c^4\,d^3}\right)}^{1/4}\,4{}\mathrm{i}+a^4\,b^3\,d^8\,x\,{\left(-\frac{c^3}{256\,a^4\,d^7-1024\,a^3\,b\,c\,d^6+1536\,a^2\,b^2\,c^2\,d^5-1024\,a\,b^3\,c^3\,d^4+256\,b^4\,c^4\,d^3}\right)}^{5/4}\,2048{}\mathrm{i}-a\,b^6\,c^3\,d^5\,x\,{\left(-\frac{c^3}{256\,a^4\,d^7-1024\,a^3\,b\,c\,d^6+1536\,a^2\,b^2\,c^2\,d^5-1024\,a\,b^3\,c^3\,d^4+256\,b^4\,c^4\,d^3}\right)}^{5/4}\,8192{}\mathrm{i}-a^3\,b^4\,c\,d^7\,x\,{\left(-\frac{c^3}{256\,a^4\,d^7-1024\,a^3\,b\,c\,d^6+1536\,a^2\,b^2\,c^2\,d^5-1024\,a\,b^3\,c^3\,d^4+256\,b^4\,c^4\,d^3}\right)}^{5/4}\,8192{}\mathrm{i}+a^2\,b^5\,c^2\,d^6\,x\,{\left(-\frac{c^3}{256\,a^4\,d^7-1024\,a^3\,b\,c\,d^6+1536\,a^2\,b^2\,c^2\,d^5-1024\,a\,b^3\,c^3\,d^4+256\,b^4\,c^4\,d^3}\right)}^{5/4}\,12288{}\mathrm{i}}{a^2\,c\,d^2+a\,b\,c^2\,d+b^2\,c^3}\right)\,{\left(-\frac{c^3}{256\,a^4\,d^7-1024\,a^3\,b\,c\,d^6+1536\,a^2\,b^2\,c^2\,d^5-1024\,a\,b^3\,c^3\,d^4+256\,b^4\,c^4\,d^3}\right)}^{1/4}\,2{}\mathrm{i}","Not used",1,"- 2*atan((4*b^4*c^3*x*(-a^3/(256*b^7*c^4 + 256*a^4*b^3*d^4 - 1024*a^3*b^4*c*d^3 + 1536*a^2*b^5*c^2*d^2 - 1024*a*b^6*c^3*d))^(1/4) + 4*a^3*b*d^3*x*(-a^3/(256*b^7*c^4 + 256*a^4*b^3*d^4 - 1024*a^3*b^4*c*d^3 + 1536*a^2*b^5*c^2*d^2 - 1024*a*b^6*c^3*d))^(1/4) + 2048*a^4*b^4*d^7*x*(-a^3/(256*b^7*c^4 + 256*a^4*b^3*d^4 - 1024*a^3*b^4*c*d^3 + 1536*a^2*b^5*c^2*d^2 - 1024*a*b^6*c^3*d))^(5/4) + 2048*b^8*c^4*d^3*x*(-a^3/(256*b^7*c^4 + 256*a^4*b^3*d^4 - 1024*a^3*b^4*c*d^3 + 1536*a^2*b^5*c^2*d^2 - 1024*a*b^6*c^3*d))^(5/4) - 8192*a*b^7*c^3*d^4*x*(-a^3/(256*b^7*c^4 + 256*a^4*b^3*d^4 - 1024*a^3*b^4*c*d^3 + 1536*a^2*b^5*c^2*d^2 - 1024*a*b^6*c^3*d))^(5/4) - 8192*a^3*b^5*c*d^6*x*(-a^3/(256*b^7*c^4 + 256*a^4*b^3*d^4 - 1024*a^3*b^4*c*d^3 + 1536*a^2*b^5*c^2*d^2 - 1024*a*b^6*c^3*d))^(5/4) + 12288*a^2*b^6*c^2*d^5*x*(-a^3/(256*b^7*c^4 + 256*a^4*b^3*d^4 - 1024*a^3*b^4*c*d^3 + 1536*a^2*b^5*c^2*d^2 - 1024*a*b^6*c^3*d))^(5/4))/(a^3*d^2 + a*b^2*c^2 + a^2*b*c*d))*(-a^3/(256*b^7*c^4 + 256*a^4*b^3*d^4 - 1024*a^3*b^4*c*d^3 + 1536*a^2*b^5*c^2*d^2 - 1024*a*b^6*c^3*d))^(1/4) - atan((b^4*c^3*x*(-a^3/(256*b^7*c^4 + 256*a^4*b^3*d^4 - 1024*a^3*b^4*c*d^3 + 1536*a^2*b^5*c^2*d^2 - 1024*a*b^6*c^3*d))^(1/4)*4i + a^3*b*d^3*x*(-a^3/(256*b^7*c^4 + 256*a^4*b^3*d^4 - 1024*a^3*b^4*c*d^3 + 1536*a^2*b^5*c^2*d^2 - 1024*a*b^6*c^3*d))^(1/4)*4i + a^4*b^4*d^7*x*(-a^3/(256*b^7*c^4 + 256*a^4*b^3*d^4 - 1024*a^3*b^4*c*d^3 + 1536*a^2*b^5*c^2*d^2 - 1024*a*b^6*c^3*d))^(5/4)*2048i + b^8*c^4*d^3*x*(-a^3/(256*b^7*c^4 + 256*a^4*b^3*d^4 - 1024*a^3*b^4*c*d^3 + 1536*a^2*b^5*c^2*d^2 - 1024*a*b^6*c^3*d))^(5/4)*2048i - a*b^7*c^3*d^4*x*(-a^3/(256*b^7*c^4 + 256*a^4*b^3*d^4 - 1024*a^3*b^4*c*d^3 + 1536*a^2*b^5*c^2*d^2 - 1024*a*b^6*c^3*d))^(5/4)*8192i - a^3*b^5*c*d^6*x*(-a^3/(256*b^7*c^4 + 256*a^4*b^3*d^4 - 1024*a^3*b^4*c*d^3 + 1536*a^2*b^5*c^2*d^2 - 1024*a*b^6*c^3*d))^(5/4)*8192i + a^2*b^6*c^2*d^5*x*(-a^3/(256*b^7*c^4 + 256*a^4*b^3*d^4 - 1024*a^3*b^4*c*d^3 + 1536*a^2*b^5*c^2*d^2 - 1024*a*b^6*c^3*d))^(5/4)*12288i)/(a^3*d^2 + a*b^2*c^2 + a^2*b*c*d))*(-a^3/(256*b^7*c^4 + 256*a^4*b^3*d^4 - 1024*a^3*b^4*c*d^3 + 1536*a^2*b^5*c^2*d^2 - 1024*a*b^6*c^3*d))^(1/4)*2i - 2*atan((4*a^3*d^4*x*(-c^3/(256*a^4*d^7 + 256*b^4*c^4*d^3 - 1024*a*b^3*c^3*d^4 + 1536*a^2*b^2*c^2*d^5 - 1024*a^3*b*c*d^6))^(1/4) + 2048*b^7*c^4*d^4*x*(-c^3/(256*a^4*d^7 + 256*b^4*c^4*d^3 - 1024*a*b^3*c^3*d^4 + 1536*a^2*b^2*c^2*d^5 - 1024*a^3*b*c*d^6))^(5/4) + 4*b^3*c^3*d*x*(-c^3/(256*a^4*d^7 + 256*b^4*c^4*d^3 - 1024*a*b^3*c^3*d^4 + 1536*a^2*b^2*c^2*d^5 - 1024*a^3*b*c*d^6))^(1/4) + 2048*a^4*b^3*d^8*x*(-c^3/(256*a^4*d^7 + 256*b^4*c^4*d^3 - 1024*a*b^3*c^3*d^4 + 1536*a^2*b^2*c^2*d^5 - 1024*a^3*b*c*d^6))^(5/4) - 8192*a*b^6*c^3*d^5*x*(-c^3/(256*a^4*d^7 + 256*b^4*c^4*d^3 - 1024*a*b^3*c^3*d^4 + 1536*a^2*b^2*c^2*d^5 - 1024*a^3*b*c*d^6))^(5/4) - 8192*a^3*b^4*c*d^7*x*(-c^3/(256*a^4*d^7 + 256*b^4*c^4*d^3 - 1024*a*b^3*c^3*d^4 + 1536*a^2*b^2*c^2*d^5 - 1024*a^3*b*c*d^6))^(5/4) + 12288*a^2*b^5*c^2*d^6*x*(-c^3/(256*a^4*d^7 + 256*b^4*c^4*d^3 - 1024*a*b^3*c^3*d^4 + 1536*a^2*b^2*c^2*d^5 - 1024*a^3*b*c*d^6))^(5/4))/(b^2*c^3 + a^2*c*d^2 + a*b*c^2*d))*(-c^3/(256*a^4*d^7 + 256*b^4*c^4*d^3 - 1024*a*b^3*c^3*d^4 + 1536*a^2*b^2*c^2*d^5 - 1024*a^3*b*c*d^6))^(1/4) - atan((a^3*d^4*x*(-c^3/(256*a^4*d^7 + 256*b^4*c^4*d^3 - 1024*a*b^3*c^3*d^4 + 1536*a^2*b^2*c^2*d^5 - 1024*a^3*b*c*d^6))^(1/4)*4i + b^7*c^4*d^4*x*(-c^3/(256*a^4*d^7 + 256*b^4*c^4*d^3 - 1024*a*b^3*c^3*d^4 + 1536*a^2*b^2*c^2*d^5 - 1024*a^3*b*c*d^6))^(5/4)*2048i + b^3*c^3*d*x*(-c^3/(256*a^4*d^7 + 256*b^4*c^4*d^3 - 1024*a*b^3*c^3*d^4 + 1536*a^2*b^2*c^2*d^5 - 1024*a^3*b*c*d^6))^(1/4)*4i + a^4*b^3*d^8*x*(-c^3/(256*a^4*d^7 + 256*b^4*c^4*d^3 - 1024*a*b^3*c^3*d^4 + 1536*a^2*b^2*c^2*d^5 - 1024*a^3*b*c*d^6))^(5/4)*2048i - a*b^6*c^3*d^5*x*(-c^3/(256*a^4*d^7 + 256*b^4*c^4*d^3 - 1024*a*b^3*c^3*d^4 + 1536*a^2*b^2*c^2*d^5 - 1024*a^3*b*c*d^6))^(5/4)*8192i - a^3*b^4*c*d^7*x*(-c^3/(256*a^4*d^7 + 256*b^4*c^4*d^3 - 1024*a*b^3*c^3*d^4 + 1536*a^2*b^2*c^2*d^5 - 1024*a^3*b*c*d^6))^(5/4)*8192i + a^2*b^5*c^2*d^6*x*(-c^3/(256*a^4*d^7 + 256*b^4*c^4*d^3 - 1024*a*b^3*c^3*d^4 + 1536*a^2*b^2*c^2*d^5 - 1024*a^3*b*c*d^6))^(5/4)*12288i)/(b^2*c^3 + a^2*c*d^2 + a*b*c^2*d))*(-c^3/(256*a^4*d^7 + 256*b^4*c^4*d^3 - 1024*a*b^3*c^3*d^4 + 1536*a^2*b^2*c^2*d^5 - 1024*a^3*b*c*d^6))^(1/4)*2i","B"
781,1,5889,449,5.858523,"\text{Not used}","int(x^4/((a + b*x^4)*(c + d*x^4)),x)","-\mathrm{atan}\left(\frac{a^2\,d^2\,x\,1{}\mathrm{i}+b^2\,c^2\,x\,1{}\mathrm{i}-\frac{a^6\,b\,d^6\,x\,256{}\mathrm{i}}{256\,a^4\,b\,d^4-1024\,a^3\,b^2\,c\,d^3+1536\,a^2\,b^3\,c^2\,d^2-1024\,a\,b^4\,c^3\,d+256\,b^5\,c^4}-\frac{a\,b^6\,c^5\,d\,x\,256{}\mathrm{i}}{256\,a^4\,b\,d^4-1024\,a^3\,b^2\,c\,d^3+1536\,a^2\,b^3\,c^2\,d^2-1024\,a\,b^4\,c^3\,d+256\,b^5\,c^4}+\frac{a^5\,b^2\,c\,d^5\,x\,768{}\mathrm{i}}{256\,a^4\,b\,d^4-1024\,a^3\,b^2\,c\,d^3+1536\,a^2\,b^3\,c^2\,d^2-1024\,a\,b^4\,c^3\,d+256\,b^5\,c^4}+\frac{a^2\,b^5\,c^4\,d^2\,x\,768{}\mathrm{i}}{256\,a^4\,b\,d^4-1024\,a^3\,b^2\,c\,d^3+1536\,a^2\,b^3\,c^2\,d^2-1024\,a\,b^4\,c^3\,d+256\,b^5\,c^4}-\frac{a^3\,b^4\,c^3\,d^3\,x\,512{}\mathrm{i}}{256\,a^4\,b\,d^4-1024\,a^3\,b^2\,c\,d^3+1536\,a^2\,b^3\,c^2\,d^2-1024\,a\,b^4\,c^3\,d+256\,b^5\,c^4}-\frac{a^4\,b^3\,c^2\,d^4\,x\,512{}\mathrm{i}}{256\,a^4\,b\,d^4-1024\,a^3\,b^2\,c\,d^3+1536\,a^2\,b^3\,c^2\,d^2-1024\,a\,b^4\,c^3\,d+256\,b^5\,c^4}}{{\left(-\frac{a}{256\,a^4\,b\,d^4-1024\,a^3\,b^2\,c\,d^3+1536\,a^2\,b^3\,c^2\,d^2-1024\,a\,b^4\,c^3\,d+256\,b^5\,c^4}\right)}^{1/4}\,\left(\frac{a\,\left(1024\,a^6\,b\,d^7-6144\,a^5\,b^2\,c\,d^6+15360\,a^4\,b^3\,c^2\,d^5-20480\,a^3\,b^4\,c^3\,d^4+15360\,a^2\,b^5\,c^4\,d^3-6144\,a\,b^6\,c^5\,d^2+1024\,b^7\,c^6\,d\right)}{256\,a^4\,b\,d^4-1024\,a^3\,b^2\,c\,d^3+1536\,a^2\,b^3\,c^2\,d^2-1024\,a\,b^4\,c^3\,d+256\,b^5\,c^4}-4\,b^3\,c^3-4\,a^3\,d^3+4\,a\,b^2\,c^2\,d+4\,a^2\,b\,c\,d^2\right)}\right)\,{\left(-\frac{a}{256\,a^4\,b\,d^4-1024\,a^3\,b^2\,c\,d^3+1536\,a^2\,b^3\,c^2\,d^2-1024\,a\,b^4\,c^3\,d+256\,b^5\,c^4}\right)}^{1/4}\,2{}\mathrm{i}-\mathrm{atan}\left(\frac{a^2\,d^2\,x\,1{}\mathrm{i}+b^2\,c^2\,x\,1{}\mathrm{i}-\frac{b^6\,c^6\,d\,x\,256{}\mathrm{i}}{256\,a^4\,d^5-1024\,a^3\,b\,c\,d^4+1536\,a^2\,b^2\,c^2\,d^3-1024\,a\,b^3\,c^3\,d^2+256\,b^4\,c^4\,d}-\frac{a^5\,b\,c\,d^6\,x\,256{}\mathrm{i}}{256\,a^4\,d^5-1024\,a^3\,b\,c\,d^4+1536\,a^2\,b^2\,c^2\,d^3-1024\,a\,b^3\,c^3\,d^2+256\,b^4\,c^4\,d}+\frac{a\,b^5\,c^5\,d^2\,x\,768{}\mathrm{i}}{256\,a^4\,d^5-1024\,a^3\,b\,c\,d^4+1536\,a^2\,b^2\,c^2\,d^3-1024\,a\,b^3\,c^3\,d^2+256\,b^4\,c^4\,d}-\frac{a^2\,b^4\,c^4\,d^3\,x\,512{}\mathrm{i}}{256\,a^4\,d^5-1024\,a^3\,b\,c\,d^4+1536\,a^2\,b^2\,c^2\,d^3-1024\,a\,b^3\,c^3\,d^2+256\,b^4\,c^4\,d}-\frac{a^3\,b^3\,c^3\,d^4\,x\,512{}\mathrm{i}}{256\,a^4\,d^5-1024\,a^3\,b\,c\,d^4+1536\,a^2\,b^2\,c^2\,d^3-1024\,a\,b^3\,c^3\,d^2+256\,b^4\,c^4\,d}+\frac{a^4\,b^2\,c^2\,d^5\,x\,768{}\mathrm{i}}{256\,a^4\,d^5-1024\,a^3\,b\,c\,d^4+1536\,a^2\,b^2\,c^2\,d^3-1024\,a\,b^3\,c^3\,d^2+256\,b^4\,c^4\,d}}{{\left(-\frac{c}{256\,a^4\,d^5-1024\,a^3\,b\,c\,d^4+1536\,a^2\,b^2\,c^2\,d^3-1024\,a\,b^3\,c^3\,d^2+256\,b^4\,c^4\,d}\right)}^{1/4}\,\left(\frac{c\,\left(1024\,a^6\,b\,d^7-6144\,a^5\,b^2\,c\,d^6+15360\,a^4\,b^3\,c^2\,d^5-20480\,a^3\,b^4\,c^3\,d^4+15360\,a^2\,b^5\,c^4\,d^3-6144\,a\,b^6\,c^5\,d^2+1024\,b^7\,c^6\,d\right)}{256\,a^4\,d^5-1024\,a^3\,b\,c\,d^4+1536\,a^2\,b^2\,c^2\,d^3-1024\,a\,b^3\,c^3\,d^2+256\,b^4\,c^4\,d}-4\,b^3\,c^3-4\,a^3\,d^3+4\,a\,b^2\,c^2\,d+4\,a^2\,b\,c\,d^2\right)}\right)\,{\left(-\frac{c}{256\,a^4\,d^5-1024\,a^3\,b\,c\,d^4+1536\,a^2\,b^2\,c^2\,d^3-1024\,a\,b^3\,c^3\,d^2+256\,b^4\,c^4\,d}\right)}^{1/4}\,2{}\mathrm{i}-2\,\mathrm{atan}\left(\frac{\left(x\,\left(4\,a^4\,b^3\,c^2\,d^5+4\,a^2\,b^5\,c^4\,d^3\right)-{\left(-\frac{a}{256\,a^4\,b\,d^4-1024\,a^3\,b^2\,c\,d^3+1536\,a^2\,b^3\,c^2\,d^2-1024\,a\,b^4\,c^3\,d+256\,b^5\,c^4}\right)}^{1/4}\,\left(16\,a^2\,b^6\,c^5\,d^3-16\,a^3\,b^5\,c^4\,d^4-16\,a^4\,b^4\,c^3\,d^5+16\,a^5\,b^3\,c^2\,d^6+\left(x\,\left(1024\,a^7\,b^4\,c^2\,d^9-3072\,a^6\,b^5\,c^3\,d^8+2048\,a^5\,b^6\,c^4\,d^7+2048\,a^4\,b^7\,c^5\,d^6-3072\,a^3\,b^8\,c^6\,d^5+1024\,a^2\,b^9\,c^7\,d^4\right)-{\left(-\frac{a}{256\,a^4\,b\,d^4-1024\,a^3\,b^2\,c\,d^3+1536\,a^2\,b^3\,c^2\,d^2-1024\,a\,b^4\,c^3\,d+256\,b^5\,c^4}\right)}^{1/4}\,\left(4096\,a^8\,b^4\,c^2\,d^{10}-24576\,a^7\,b^5\,c^3\,d^9+61440\,a^6\,b^6\,c^4\,d^8-81920\,a^5\,b^7\,c^5\,d^7+61440\,a^4\,b^8\,c^6\,d^6-24576\,a^3\,b^9\,c^7\,d^5+4096\,a^2\,b^{10}\,c^8\,d^4\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{a}{256\,a^4\,b\,d^4-1024\,a^3\,b^2\,c\,d^3+1536\,a^2\,b^3\,c^2\,d^2-1024\,a\,b^4\,c^3\,d+256\,b^5\,c^4}\right)}^{3/4}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{a}{256\,a^4\,b\,d^4-1024\,a^3\,b^2\,c\,d^3+1536\,a^2\,b^3\,c^2\,d^2-1024\,a\,b^4\,c^3\,d+256\,b^5\,c^4}\right)}^{1/4}+\left(x\,\left(4\,a^4\,b^3\,c^2\,d^5+4\,a^2\,b^5\,c^4\,d^3\right)-{\left(-\frac{a}{256\,a^4\,b\,d^4-1024\,a^3\,b^2\,c\,d^3+1536\,a^2\,b^3\,c^2\,d^2-1024\,a\,b^4\,c^3\,d+256\,b^5\,c^4}\right)}^{1/4}\,\left(16\,a^3\,b^5\,c^4\,d^4-16\,a^2\,b^6\,c^5\,d^3+16\,a^4\,b^4\,c^3\,d^5-16\,a^5\,b^3\,c^2\,d^6+\left(x\,\left(1024\,a^7\,b^4\,c^2\,d^9-3072\,a^6\,b^5\,c^3\,d^8+2048\,a^5\,b^6\,c^4\,d^7+2048\,a^4\,b^7\,c^5\,d^6-3072\,a^3\,b^8\,c^6\,d^5+1024\,a^2\,b^9\,c^7\,d^4\right)+{\left(-\frac{a}{256\,a^4\,b\,d^4-1024\,a^3\,b^2\,c\,d^3+1536\,a^2\,b^3\,c^2\,d^2-1024\,a\,b^4\,c^3\,d+256\,b^5\,c^4}\right)}^{1/4}\,\left(4096\,a^8\,b^4\,c^2\,d^{10}-24576\,a^7\,b^5\,c^3\,d^9+61440\,a^6\,b^6\,c^4\,d^8-81920\,a^5\,b^7\,c^5\,d^7+61440\,a^4\,b^8\,c^6\,d^6-24576\,a^3\,b^9\,c^7\,d^5+4096\,a^2\,b^{10}\,c^8\,d^4\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{a}{256\,a^4\,b\,d^4-1024\,a^3\,b^2\,c\,d^3+1536\,a^2\,b^3\,c^2\,d^2-1024\,a\,b^4\,c^3\,d+256\,b^5\,c^4}\right)}^{3/4}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{a}{256\,a^4\,b\,d^4-1024\,a^3\,b^2\,c\,d^3+1536\,a^2\,b^3\,c^2\,d^2-1024\,a\,b^4\,c^3\,d+256\,b^5\,c^4}\right)}^{1/4}}{\left(x\,\left(4\,a^4\,b^3\,c^2\,d^5+4\,a^2\,b^5\,c^4\,d^3\right)-{\left(-\frac{a}{256\,a^4\,b\,d^4-1024\,a^3\,b^2\,c\,d^3+1536\,a^2\,b^3\,c^2\,d^2-1024\,a\,b^4\,c^3\,d+256\,b^5\,c^4}\right)}^{1/4}\,\left(16\,a^2\,b^6\,c^5\,d^3-16\,a^3\,b^5\,c^4\,d^4-16\,a^4\,b^4\,c^3\,d^5+16\,a^5\,b^3\,c^2\,d^6+\left(x\,\left(1024\,a^7\,b^4\,c^2\,d^9-3072\,a^6\,b^5\,c^3\,d^8+2048\,a^5\,b^6\,c^4\,d^7+2048\,a^4\,b^7\,c^5\,d^6-3072\,a^3\,b^8\,c^6\,d^5+1024\,a^2\,b^9\,c^7\,d^4\right)-{\left(-\frac{a}{256\,a^4\,b\,d^4-1024\,a^3\,b^2\,c\,d^3+1536\,a^2\,b^3\,c^2\,d^2-1024\,a\,b^4\,c^3\,d+256\,b^5\,c^4}\right)}^{1/4}\,\left(4096\,a^8\,b^4\,c^2\,d^{10}-24576\,a^7\,b^5\,c^3\,d^9+61440\,a^6\,b^6\,c^4\,d^8-81920\,a^5\,b^7\,c^5\,d^7+61440\,a^4\,b^8\,c^6\,d^6-24576\,a^3\,b^9\,c^7\,d^5+4096\,a^2\,b^{10}\,c^8\,d^4\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{a}{256\,a^4\,b\,d^4-1024\,a^3\,b^2\,c\,d^3+1536\,a^2\,b^3\,c^2\,d^2-1024\,a\,b^4\,c^3\,d+256\,b^5\,c^4}\right)}^{3/4}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{a}{256\,a^4\,b\,d^4-1024\,a^3\,b^2\,c\,d^3+1536\,a^2\,b^3\,c^2\,d^2-1024\,a\,b^4\,c^3\,d+256\,b^5\,c^4}\right)}^{1/4}\,1{}\mathrm{i}-\left(x\,\left(4\,a^4\,b^3\,c^2\,d^5+4\,a^2\,b^5\,c^4\,d^3\right)-{\left(-\frac{a}{256\,a^4\,b\,d^4-1024\,a^3\,b^2\,c\,d^3+1536\,a^2\,b^3\,c^2\,d^2-1024\,a\,b^4\,c^3\,d+256\,b^5\,c^4}\right)}^{1/4}\,\left(16\,a^3\,b^5\,c^4\,d^4-16\,a^2\,b^6\,c^5\,d^3+16\,a^4\,b^4\,c^3\,d^5-16\,a^5\,b^3\,c^2\,d^6+\left(x\,\left(1024\,a^7\,b^4\,c^2\,d^9-3072\,a^6\,b^5\,c^3\,d^8+2048\,a^5\,b^6\,c^4\,d^7+2048\,a^4\,b^7\,c^5\,d^6-3072\,a^3\,b^8\,c^6\,d^5+1024\,a^2\,b^9\,c^7\,d^4\right)+{\left(-\frac{a}{256\,a^4\,b\,d^4-1024\,a^3\,b^2\,c\,d^3+1536\,a^2\,b^3\,c^2\,d^2-1024\,a\,b^4\,c^3\,d+256\,b^5\,c^4}\right)}^{1/4}\,\left(4096\,a^8\,b^4\,c^2\,d^{10}-24576\,a^7\,b^5\,c^3\,d^9+61440\,a^6\,b^6\,c^4\,d^8-81920\,a^5\,b^7\,c^5\,d^7+61440\,a^4\,b^8\,c^6\,d^6-24576\,a^3\,b^9\,c^7\,d^5+4096\,a^2\,b^{10}\,c^8\,d^4\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{a}{256\,a^4\,b\,d^4-1024\,a^3\,b^2\,c\,d^3+1536\,a^2\,b^3\,c^2\,d^2-1024\,a\,b^4\,c^3\,d+256\,b^5\,c^4}\right)}^{3/4}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{a}{256\,a^4\,b\,d^4-1024\,a^3\,b^2\,c\,d^3+1536\,a^2\,b^3\,c^2\,d^2-1024\,a\,b^4\,c^3\,d+256\,b^5\,c^4}\right)}^{1/4}\,1{}\mathrm{i}}\right)\,{\left(-\frac{a}{256\,a^4\,b\,d^4-1024\,a^3\,b^2\,c\,d^3+1536\,a^2\,b^3\,c^2\,d^2-1024\,a\,b^4\,c^3\,d+256\,b^5\,c^4}\right)}^{1/4}-2\,\mathrm{atan}\left(\frac{\left(x\,\left(4\,a^4\,b^3\,c^2\,d^5+4\,a^2\,b^5\,c^4\,d^3\right)-{\left(-\frac{c}{256\,a^4\,d^5-1024\,a^3\,b\,c\,d^4+1536\,a^2\,b^2\,c^2\,d^3-1024\,a\,b^3\,c^3\,d^2+256\,b^4\,c^4\,d}\right)}^{1/4}\,\left(16\,a^2\,b^6\,c^5\,d^3-16\,a^3\,b^5\,c^4\,d^4-16\,a^4\,b^4\,c^3\,d^5+16\,a^5\,b^3\,c^2\,d^6+\left(x\,\left(1024\,a^7\,b^4\,c^2\,d^9-3072\,a^6\,b^5\,c^3\,d^8+2048\,a^5\,b^6\,c^4\,d^7+2048\,a^4\,b^7\,c^5\,d^6-3072\,a^3\,b^8\,c^6\,d^5+1024\,a^2\,b^9\,c^7\,d^4\right)-{\left(-\frac{c}{256\,a^4\,d^5-1024\,a^3\,b\,c\,d^4+1536\,a^2\,b^2\,c^2\,d^3-1024\,a\,b^3\,c^3\,d^2+256\,b^4\,c^4\,d}\right)}^{1/4}\,\left(4096\,a^8\,b^4\,c^2\,d^{10}-24576\,a^7\,b^5\,c^3\,d^9+61440\,a^6\,b^6\,c^4\,d^8-81920\,a^5\,b^7\,c^5\,d^7+61440\,a^4\,b^8\,c^6\,d^6-24576\,a^3\,b^9\,c^7\,d^5+4096\,a^2\,b^{10}\,c^8\,d^4\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{c}{256\,a^4\,d^5-1024\,a^3\,b\,c\,d^4+1536\,a^2\,b^2\,c^2\,d^3-1024\,a\,b^3\,c^3\,d^2+256\,b^4\,c^4\,d}\right)}^{3/4}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{c}{256\,a^4\,d^5-1024\,a^3\,b\,c\,d^4+1536\,a^2\,b^2\,c^2\,d^3-1024\,a\,b^3\,c^3\,d^2+256\,b^4\,c^4\,d}\right)}^{1/4}+\left(x\,\left(4\,a^4\,b^3\,c^2\,d^5+4\,a^2\,b^5\,c^4\,d^3\right)-{\left(-\frac{c}{256\,a^4\,d^5-1024\,a^3\,b\,c\,d^4+1536\,a^2\,b^2\,c^2\,d^3-1024\,a\,b^3\,c^3\,d^2+256\,b^4\,c^4\,d}\right)}^{1/4}\,\left(16\,a^3\,b^5\,c^4\,d^4-16\,a^2\,b^6\,c^5\,d^3+16\,a^4\,b^4\,c^3\,d^5-16\,a^5\,b^3\,c^2\,d^6+\left(x\,\left(1024\,a^7\,b^4\,c^2\,d^9-3072\,a^6\,b^5\,c^3\,d^8+2048\,a^5\,b^6\,c^4\,d^7+2048\,a^4\,b^7\,c^5\,d^6-3072\,a^3\,b^8\,c^6\,d^5+1024\,a^2\,b^9\,c^7\,d^4\right)+{\left(-\frac{c}{256\,a^4\,d^5-1024\,a^3\,b\,c\,d^4+1536\,a^2\,b^2\,c^2\,d^3-1024\,a\,b^3\,c^3\,d^2+256\,b^4\,c^4\,d}\right)}^{1/4}\,\left(4096\,a^8\,b^4\,c^2\,d^{10}-24576\,a^7\,b^5\,c^3\,d^9+61440\,a^6\,b^6\,c^4\,d^8-81920\,a^5\,b^7\,c^5\,d^7+61440\,a^4\,b^8\,c^6\,d^6-24576\,a^3\,b^9\,c^7\,d^5+4096\,a^2\,b^{10}\,c^8\,d^4\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{c}{256\,a^4\,d^5-1024\,a^3\,b\,c\,d^4+1536\,a^2\,b^2\,c^2\,d^3-1024\,a\,b^3\,c^3\,d^2+256\,b^4\,c^4\,d}\right)}^{3/4}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{c}{256\,a^4\,d^5-1024\,a^3\,b\,c\,d^4+1536\,a^2\,b^2\,c^2\,d^3-1024\,a\,b^3\,c^3\,d^2+256\,b^4\,c^4\,d}\right)}^{1/4}}{\left(x\,\left(4\,a^4\,b^3\,c^2\,d^5+4\,a^2\,b^5\,c^4\,d^3\right)-{\left(-\frac{c}{256\,a^4\,d^5-1024\,a^3\,b\,c\,d^4+1536\,a^2\,b^2\,c^2\,d^3-1024\,a\,b^3\,c^3\,d^2+256\,b^4\,c^4\,d}\right)}^{1/4}\,\left(16\,a^2\,b^6\,c^5\,d^3-16\,a^3\,b^5\,c^4\,d^4-16\,a^4\,b^4\,c^3\,d^5+16\,a^5\,b^3\,c^2\,d^6+\left(x\,\left(1024\,a^7\,b^4\,c^2\,d^9-3072\,a^6\,b^5\,c^3\,d^8+2048\,a^5\,b^6\,c^4\,d^7+2048\,a^4\,b^7\,c^5\,d^6-3072\,a^3\,b^8\,c^6\,d^5+1024\,a^2\,b^9\,c^7\,d^4\right)-{\left(-\frac{c}{256\,a^4\,d^5-1024\,a^3\,b\,c\,d^4+1536\,a^2\,b^2\,c^2\,d^3-1024\,a\,b^3\,c^3\,d^2+256\,b^4\,c^4\,d}\right)}^{1/4}\,\left(4096\,a^8\,b^4\,c^2\,d^{10}-24576\,a^7\,b^5\,c^3\,d^9+61440\,a^6\,b^6\,c^4\,d^8-81920\,a^5\,b^7\,c^5\,d^7+61440\,a^4\,b^8\,c^6\,d^6-24576\,a^3\,b^9\,c^7\,d^5+4096\,a^2\,b^{10}\,c^8\,d^4\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{c}{256\,a^4\,d^5-1024\,a^3\,b\,c\,d^4+1536\,a^2\,b^2\,c^2\,d^3-1024\,a\,b^3\,c^3\,d^2+256\,b^4\,c^4\,d}\right)}^{3/4}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{c}{256\,a^4\,d^5-1024\,a^3\,b\,c\,d^4+1536\,a^2\,b^2\,c^2\,d^3-1024\,a\,b^3\,c^3\,d^2+256\,b^4\,c^4\,d}\right)}^{1/4}\,1{}\mathrm{i}-\left(x\,\left(4\,a^4\,b^3\,c^2\,d^5+4\,a^2\,b^5\,c^4\,d^3\right)-{\left(-\frac{c}{256\,a^4\,d^5-1024\,a^3\,b\,c\,d^4+1536\,a^2\,b^2\,c^2\,d^3-1024\,a\,b^3\,c^3\,d^2+256\,b^4\,c^4\,d}\right)}^{1/4}\,\left(16\,a^3\,b^5\,c^4\,d^4-16\,a^2\,b^6\,c^5\,d^3+16\,a^4\,b^4\,c^3\,d^5-16\,a^5\,b^3\,c^2\,d^6+\left(x\,\left(1024\,a^7\,b^4\,c^2\,d^9-3072\,a^6\,b^5\,c^3\,d^8+2048\,a^5\,b^6\,c^4\,d^7+2048\,a^4\,b^7\,c^5\,d^6-3072\,a^3\,b^8\,c^6\,d^5+1024\,a^2\,b^9\,c^7\,d^4\right)+{\left(-\frac{c}{256\,a^4\,d^5-1024\,a^3\,b\,c\,d^4+1536\,a^2\,b^2\,c^2\,d^3-1024\,a\,b^3\,c^3\,d^2+256\,b^4\,c^4\,d}\right)}^{1/4}\,\left(4096\,a^8\,b^4\,c^2\,d^{10}-24576\,a^7\,b^5\,c^3\,d^9+61440\,a^6\,b^6\,c^4\,d^8-81920\,a^5\,b^7\,c^5\,d^7+61440\,a^4\,b^8\,c^6\,d^6-24576\,a^3\,b^9\,c^7\,d^5+4096\,a^2\,b^{10}\,c^8\,d^4\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{c}{256\,a^4\,d^5-1024\,a^3\,b\,c\,d^4+1536\,a^2\,b^2\,c^2\,d^3-1024\,a\,b^3\,c^3\,d^2+256\,b^4\,c^4\,d}\right)}^{3/4}\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{c}{256\,a^4\,d^5-1024\,a^3\,b\,c\,d^4+1536\,a^2\,b^2\,c^2\,d^3-1024\,a\,b^3\,c^3\,d^2+256\,b^4\,c^4\,d}\right)}^{1/4}\,1{}\mathrm{i}}\right)\,{\left(-\frac{c}{256\,a^4\,d^5-1024\,a^3\,b\,c\,d^4+1536\,a^2\,b^2\,c^2\,d^3-1024\,a\,b^3\,c^3\,d^2+256\,b^4\,c^4\,d}\right)}^{1/4}","Not used",1,"- atan((a^2*d^2*x*1i + b^2*c^2*x*1i - (a^6*b*d^6*x*256i)/(256*b^5*c^4 + 256*a^4*b*d^4 - 1024*a^3*b^2*c*d^3 + 1536*a^2*b^3*c^2*d^2 - 1024*a*b^4*c^3*d) - (a*b^6*c^5*d*x*256i)/(256*b^5*c^4 + 256*a^4*b*d^4 - 1024*a^3*b^2*c*d^3 + 1536*a^2*b^3*c^2*d^2 - 1024*a*b^4*c^3*d) + (a^5*b^2*c*d^5*x*768i)/(256*b^5*c^4 + 256*a^4*b*d^4 - 1024*a^3*b^2*c*d^3 + 1536*a^2*b^3*c^2*d^2 - 1024*a*b^4*c^3*d) + (a^2*b^5*c^4*d^2*x*768i)/(256*b^5*c^4 + 256*a^4*b*d^4 - 1024*a^3*b^2*c*d^3 + 1536*a^2*b^3*c^2*d^2 - 1024*a*b^4*c^3*d) - (a^3*b^4*c^3*d^3*x*512i)/(256*b^5*c^4 + 256*a^4*b*d^4 - 1024*a^3*b^2*c*d^3 + 1536*a^2*b^3*c^2*d^2 - 1024*a*b^4*c^3*d) - (a^4*b^3*c^2*d^4*x*512i)/(256*b^5*c^4 + 256*a^4*b*d^4 - 1024*a^3*b^2*c*d^3 + 1536*a^2*b^3*c^2*d^2 - 1024*a*b^4*c^3*d))/((-a/(256*b^5*c^4 + 256*a^4*b*d^4 - 1024*a^3*b^2*c*d^3 + 1536*a^2*b^3*c^2*d^2 - 1024*a*b^4*c^3*d))^(1/4)*((a*(1024*a^6*b*d^7 + 1024*b^7*c^6*d - 6144*a*b^6*c^5*d^2 - 6144*a^5*b^2*c*d^6 + 15360*a^2*b^5*c^4*d^3 - 20480*a^3*b^4*c^3*d^4 + 15360*a^4*b^3*c^2*d^5))/(256*b^5*c^4 + 256*a^4*b*d^4 - 1024*a^3*b^2*c*d^3 + 1536*a^2*b^3*c^2*d^2 - 1024*a*b^4*c^3*d) - 4*b^3*c^3 - 4*a^3*d^3 + 4*a*b^2*c^2*d + 4*a^2*b*c*d^2)))*(-a/(256*b^5*c^4 + 256*a^4*b*d^4 - 1024*a^3*b^2*c*d^3 + 1536*a^2*b^3*c^2*d^2 - 1024*a*b^4*c^3*d))^(1/4)*2i - atan((a^2*d^2*x*1i + b^2*c^2*x*1i - (b^6*c^6*d*x*256i)/(256*a^4*d^5 + 256*b^4*c^4*d - 1024*a*b^3*c^3*d^2 + 1536*a^2*b^2*c^2*d^3 - 1024*a^3*b*c*d^4) - (a^5*b*c*d^6*x*256i)/(256*a^4*d^5 + 256*b^4*c^4*d - 1024*a*b^3*c^3*d^2 + 1536*a^2*b^2*c^2*d^3 - 1024*a^3*b*c*d^4) + (a*b^5*c^5*d^2*x*768i)/(256*a^4*d^5 + 256*b^4*c^4*d - 1024*a*b^3*c^3*d^2 + 1536*a^2*b^2*c^2*d^3 - 1024*a^3*b*c*d^4) - (a^2*b^4*c^4*d^3*x*512i)/(256*a^4*d^5 + 256*b^4*c^4*d - 1024*a*b^3*c^3*d^2 + 1536*a^2*b^2*c^2*d^3 - 1024*a^3*b*c*d^4) - (a^3*b^3*c^3*d^4*x*512i)/(256*a^4*d^5 + 256*b^4*c^4*d - 1024*a*b^3*c^3*d^2 + 1536*a^2*b^2*c^2*d^3 - 1024*a^3*b*c*d^4) + (a^4*b^2*c^2*d^5*x*768i)/(256*a^4*d^5 + 256*b^4*c^4*d - 1024*a*b^3*c^3*d^2 + 1536*a^2*b^2*c^2*d^3 - 1024*a^3*b*c*d^4))/((-c/(256*a^4*d^5 + 256*b^4*c^4*d - 1024*a*b^3*c^3*d^2 + 1536*a^2*b^2*c^2*d^3 - 1024*a^3*b*c*d^4))^(1/4)*((c*(1024*a^6*b*d^7 + 1024*b^7*c^6*d - 6144*a*b^6*c^5*d^2 - 6144*a^5*b^2*c*d^6 + 15360*a^2*b^5*c^4*d^3 - 20480*a^3*b^4*c^3*d^4 + 15360*a^4*b^3*c^2*d^5))/(256*a^4*d^5 + 256*b^4*c^4*d - 1024*a*b^3*c^3*d^2 + 1536*a^2*b^2*c^2*d^3 - 1024*a^3*b*c*d^4) - 4*b^3*c^3 - 4*a^3*d^3 + 4*a*b^2*c^2*d + 4*a^2*b*c*d^2)))*(-c/(256*a^4*d^5 + 256*b^4*c^4*d - 1024*a*b^3*c^3*d^2 + 1536*a^2*b^2*c^2*d^3 - 1024*a^3*b*c*d^4))^(1/4)*2i - 2*atan(((x*(4*a^2*b^5*c^4*d^3 + 4*a^4*b^3*c^2*d^5) - (-a/(256*b^5*c^4 + 256*a^4*b*d^4 - 1024*a^3*b^2*c*d^3 + 1536*a^2*b^3*c^2*d^2 - 1024*a*b^4*c^3*d))^(1/4)*((x*(1024*a^2*b^9*c^7*d^4 - 3072*a^3*b^8*c^6*d^5 + 2048*a^4*b^7*c^5*d^6 + 2048*a^5*b^6*c^4*d^7 - 3072*a^6*b^5*c^3*d^8 + 1024*a^7*b^4*c^2*d^9) - (-a/(256*b^5*c^4 + 256*a^4*b*d^4 - 1024*a^3*b^2*c*d^3 + 1536*a^2*b^3*c^2*d^2 - 1024*a*b^4*c^3*d))^(1/4)*(4096*a^2*b^10*c^8*d^4 - 24576*a^3*b^9*c^7*d^5 + 61440*a^4*b^8*c^6*d^6 - 81920*a^5*b^7*c^5*d^7 + 61440*a^6*b^6*c^4*d^8 - 24576*a^7*b^5*c^3*d^9 + 4096*a^8*b^4*c^2*d^10)*1i)*(-a/(256*b^5*c^4 + 256*a^4*b*d^4 - 1024*a^3*b^2*c*d^3 + 1536*a^2*b^3*c^2*d^2 - 1024*a*b^4*c^3*d))^(3/4)*1i + 16*a^2*b^6*c^5*d^3 - 16*a^3*b^5*c^4*d^4 - 16*a^4*b^4*c^3*d^5 + 16*a^5*b^3*c^2*d^6)*1i)*(-a/(256*b^5*c^4 + 256*a^4*b*d^4 - 1024*a^3*b^2*c*d^3 + 1536*a^2*b^3*c^2*d^2 - 1024*a*b^4*c^3*d))^(1/4) + (x*(4*a^2*b^5*c^4*d^3 + 4*a^4*b^3*c^2*d^5) - (-a/(256*b^5*c^4 + 256*a^4*b*d^4 - 1024*a^3*b^2*c*d^3 + 1536*a^2*b^3*c^2*d^2 - 1024*a*b^4*c^3*d))^(1/4)*((x*(1024*a^2*b^9*c^7*d^4 - 3072*a^3*b^8*c^6*d^5 + 2048*a^4*b^7*c^5*d^6 + 2048*a^5*b^6*c^4*d^7 - 3072*a^6*b^5*c^3*d^8 + 1024*a^7*b^4*c^2*d^9) + (-a/(256*b^5*c^4 + 256*a^4*b*d^4 - 1024*a^3*b^2*c*d^3 + 1536*a^2*b^3*c^2*d^2 - 1024*a*b^4*c^3*d))^(1/4)*(4096*a^2*b^10*c^8*d^4 - 24576*a^3*b^9*c^7*d^5 + 61440*a^4*b^8*c^6*d^6 - 81920*a^5*b^7*c^5*d^7 + 61440*a^6*b^6*c^4*d^8 - 24576*a^7*b^5*c^3*d^9 + 4096*a^8*b^4*c^2*d^10)*1i)*(-a/(256*b^5*c^4 + 256*a^4*b*d^4 - 1024*a^3*b^2*c*d^3 + 1536*a^2*b^3*c^2*d^2 - 1024*a*b^4*c^3*d))^(3/4)*1i - 16*a^2*b^6*c^5*d^3 + 16*a^3*b^5*c^4*d^4 + 16*a^4*b^4*c^3*d^5 - 16*a^5*b^3*c^2*d^6)*1i)*(-a/(256*b^5*c^4 + 256*a^4*b*d^4 - 1024*a^3*b^2*c*d^3 + 1536*a^2*b^3*c^2*d^2 - 1024*a*b^4*c^3*d))^(1/4))/((x*(4*a^2*b^5*c^4*d^3 + 4*a^4*b^3*c^2*d^5) - (-a/(256*b^5*c^4 + 256*a^4*b*d^4 - 1024*a^3*b^2*c*d^3 + 1536*a^2*b^3*c^2*d^2 - 1024*a*b^4*c^3*d))^(1/4)*((x*(1024*a^2*b^9*c^7*d^4 - 3072*a^3*b^8*c^6*d^5 + 2048*a^4*b^7*c^5*d^6 + 2048*a^5*b^6*c^4*d^7 - 3072*a^6*b^5*c^3*d^8 + 1024*a^7*b^4*c^2*d^9) - (-a/(256*b^5*c^4 + 256*a^4*b*d^4 - 1024*a^3*b^2*c*d^3 + 1536*a^2*b^3*c^2*d^2 - 1024*a*b^4*c^3*d))^(1/4)*(4096*a^2*b^10*c^8*d^4 - 24576*a^3*b^9*c^7*d^5 + 61440*a^4*b^8*c^6*d^6 - 81920*a^5*b^7*c^5*d^7 + 61440*a^6*b^6*c^4*d^8 - 24576*a^7*b^5*c^3*d^9 + 4096*a^8*b^4*c^2*d^10)*1i)*(-a/(256*b^5*c^4 + 256*a^4*b*d^4 - 1024*a^3*b^2*c*d^3 + 1536*a^2*b^3*c^2*d^2 - 1024*a*b^4*c^3*d))^(3/4)*1i + 16*a^2*b^6*c^5*d^3 - 16*a^3*b^5*c^4*d^4 - 16*a^4*b^4*c^3*d^5 + 16*a^5*b^3*c^2*d^6)*1i)*(-a/(256*b^5*c^4 + 256*a^4*b*d^4 - 1024*a^3*b^2*c*d^3 + 1536*a^2*b^3*c^2*d^2 - 1024*a*b^4*c^3*d))^(1/4)*1i - (x*(4*a^2*b^5*c^4*d^3 + 4*a^4*b^3*c^2*d^5) - (-a/(256*b^5*c^4 + 256*a^4*b*d^4 - 1024*a^3*b^2*c*d^3 + 1536*a^2*b^3*c^2*d^2 - 1024*a*b^4*c^3*d))^(1/4)*((x*(1024*a^2*b^9*c^7*d^4 - 3072*a^3*b^8*c^6*d^5 + 2048*a^4*b^7*c^5*d^6 + 2048*a^5*b^6*c^4*d^7 - 3072*a^6*b^5*c^3*d^8 + 1024*a^7*b^4*c^2*d^9) + (-a/(256*b^5*c^4 + 256*a^4*b*d^4 - 1024*a^3*b^2*c*d^3 + 1536*a^2*b^3*c^2*d^2 - 1024*a*b^4*c^3*d))^(1/4)*(4096*a^2*b^10*c^8*d^4 - 24576*a^3*b^9*c^7*d^5 + 61440*a^4*b^8*c^6*d^6 - 81920*a^5*b^7*c^5*d^7 + 61440*a^6*b^6*c^4*d^8 - 24576*a^7*b^5*c^3*d^9 + 4096*a^8*b^4*c^2*d^10)*1i)*(-a/(256*b^5*c^4 + 256*a^4*b*d^4 - 1024*a^3*b^2*c*d^3 + 1536*a^2*b^3*c^2*d^2 - 1024*a*b^4*c^3*d))^(3/4)*1i - 16*a^2*b^6*c^5*d^3 + 16*a^3*b^5*c^4*d^4 + 16*a^4*b^4*c^3*d^5 - 16*a^5*b^3*c^2*d^6)*1i)*(-a/(256*b^5*c^4 + 256*a^4*b*d^4 - 1024*a^3*b^2*c*d^3 + 1536*a^2*b^3*c^2*d^2 - 1024*a*b^4*c^3*d))^(1/4)*1i))*(-a/(256*b^5*c^4 + 256*a^4*b*d^4 - 1024*a^3*b^2*c*d^3 + 1536*a^2*b^3*c^2*d^2 - 1024*a*b^4*c^3*d))^(1/4) - 2*atan(((x*(4*a^2*b^5*c^4*d^3 + 4*a^4*b^3*c^2*d^5) - (-c/(256*a^4*d^5 + 256*b^4*c^4*d - 1024*a*b^3*c^3*d^2 + 1536*a^2*b^2*c^2*d^3 - 1024*a^3*b*c*d^4))^(1/4)*((x*(1024*a^2*b^9*c^7*d^4 - 3072*a^3*b^8*c^6*d^5 + 2048*a^4*b^7*c^5*d^6 + 2048*a^5*b^6*c^4*d^7 - 3072*a^6*b^5*c^3*d^8 + 1024*a^7*b^4*c^2*d^9) - (-c/(256*a^4*d^5 + 256*b^4*c^4*d - 1024*a*b^3*c^3*d^2 + 1536*a^2*b^2*c^2*d^3 - 1024*a^3*b*c*d^4))^(1/4)*(4096*a^2*b^10*c^8*d^4 - 24576*a^3*b^9*c^7*d^5 + 61440*a^4*b^8*c^6*d^6 - 81920*a^5*b^7*c^5*d^7 + 61440*a^6*b^6*c^4*d^8 - 24576*a^7*b^5*c^3*d^9 + 4096*a^8*b^4*c^2*d^10)*1i)*(-c/(256*a^4*d^5 + 256*b^4*c^4*d - 1024*a*b^3*c^3*d^2 + 1536*a^2*b^2*c^2*d^3 - 1024*a^3*b*c*d^4))^(3/4)*1i + 16*a^2*b^6*c^5*d^3 - 16*a^3*b^5*c^4*d^4 - 16*a^4*b^4*c^3*d^5 + 16*a^5*b^3*c^2*d^6)*1i)*(-c/(256*a^4*d^5 + 256*b^4*c^4*d - 1024*a*b^3*c^3*d^2 + 1536*a^2*b^2*c^2*d^3 - 1024*a^3*b*c*d^4))^(1/4) + (x*(4*a^2*b^5*c^4*d^3 + 4*a^4*b^3*c^2*d^5) - (-c/(256*a^4*d^5 + 256*b^4*c^4*d - 1024*a*b^3*c^3*d^2 + 1536*a^2*b^2*c^2*d^3 - 1024*a^3*b*c*d^4))^(1/4)*((x*(1024*a^2*b^9*c^7*d^4 - 3072*a^3*b^8*c^6*d^5 + 2048*a^4*b^7*c^5*d^6 + 2048*a^5*b^6*c^4*d^7 - 3072*a^6*b^5*c^3*d^8 + 1024*a^7*b^4*c^2*d^9) + (-c/(256*a^4*d^5 + 256*b^4*c^4*d - 1024*a*b^3*c^3*d^2 + 1536*a^2*b^2*c^2*d^3 - 1024*a^3*b*c*d^4))^(1/4)*(4096*a^2*b^10*c^8*d^4 - 24576*a^3*b^9*c^7*d^5 + 61440*a^4*b^8*c^6*d^6 - 81920*a^5*b^7*c^5*d^7 + 61440*a^6*b^6*c^4*d^8 - 24576*a^7*b^5*c^3*d^9 + 4096*a^8*b^4*c^2*d^10)*1i)*(-c/(256*a^4*d^5 + 256*b^4*c^4*d - 1024*a*b^3*c^3*d^2 + 1536*a^2*b^2*c^2*d^3 - 1024*a^3*b*c*d^4))^(3/4)*1i - 16*a^2*b^6*c^5*d^3 + 16*a^3*b^5*c^4*d^4 + 16*a^4*b^4*c^3*d^5 - 16*a^5*b^3*c^2*d^6)*1i)*(-c/(256*a^4*d^5 + 256*b^4*c^4*d - 1024*a*b^3*c^3*d^2 + 1536*a^2*b^2*c^2*d^3 - 1024*a^3*b*c*d^4))^(1/4))/((x*(4*a^2*b^5*c^4*d^3 + 4*a^4*b^3*c^2*d^5) - (-c/(256*a^4*d^5 + 256*b^4*c^4*d - 1024*a*b^3*c^3*d^2 + 1536*a^2*b^2*c^2*d^3 - 1024*a^3*b*c*d^4))^(1/4)*((x*(1024*a^2*b^9*c^7*d^4 - 3072*a^3*b^8*c^6*d^5 + 2048*a^4*b^7*c^5*d^6 + 2048*a^5*b^6*c^4*d^7 - 3072*a^6*b^5*c^3*d^8 + 1024*a^7*b^4*c^2*d^9) - (-c/(256*a^4*d^5 + 256*b^4*c^4*d - 1024*a*b^3*c^3*d^2 + 1536*a^2*b^2*c^2*d^3 - 1024*a^3*b*c*d^4))^(1/4)*(4096*a^2*b^10*c^8*d^4 - 24576*a^3*b^9*c^7*d^5 + 61440*a^4*b^8*c^6*d^6 - 81920*a^5*b^7*c^5*d^7 + 61440*a^6*b^6*c^4*d^8 - 24576*a^7*b^5*c^3*d^9 + 4096*a^8*b^4*c^2*d^10)*1i)*(-c/(256*a^4*d^5 + 256*b^4*c^4*d - 1024*a*b^3*c^3*d^2 + 1536*a^2*b^2*c^2*d^3 - 1024*a^3*b*c*d^4))^(3/4)*1i + 16*a^2*b^6*c^5*d^3 - 16*a^3*b^5*c^4*d^4 - 16*a^4*b^4*c^3*d^5 + 16*a^5*b^3*c^2*d^6)*1i)*(-c/(256*a^4*d^5 + 256*b^4*c^4*d - 1024*a*b^3*c^3*d^2 + 1536*a^2*b^2*c^2*d^3 - 1024*a^3*b*c*d^4))^(1/4)*1i - (x*(4*a^2*b^5*c^4*d^3 + 4*a^4*b^3*c^2*d^5) - (-c/(256*a^4*d^5 + 256*b^4*c^4*d - 1024*a*b^3*c^3*d^2 + 1536*a^2*b^2*c^2*d^3 - 1024*a^3*b*c*d^4))^(1/4)*((x*(1024*a^2*b^9*c^7*d^4 - 3072*a^3*b^8*c^6*d^5 + 2048*a^4*b^7*c^5*d^6 + 2048*a^5*b^6*c^4*d^7 - 3072*a^6*b^5*c^3*d^8 + 1024*a^7*b^4*c^2*d^9) + (-c/(256*a^4*d^5 + 256*b^4*c^4*d - 1024*a*b^3*c^3*d^2 + 1536*a^2*b^2*c^2*d^3 - 1024*a^3*b*c*d^4))^(1/4)*(4096*a^2*b^10*c^8*d^4 - 24576*a^3*b^9*c^7*d^5 + 61440*a^4*b^8*c^6*d^6 - 81920*a^5*b^7*c^5*d^7 + 61440*a^6*b^6*c^4*d^8 - 24576*a^7*b^5*c^3*d^9 + 4096*a^8*b^4*c^2*d^10)*1i)*(-c/(256*a^4*d^5 + 256*b^4*c^4*d - 1024*a*b^3*c^3*d^2 + 1536*a^2*b^2*c^2*d^3 - 1024*a^3*b*c*d^4))^(3/4)*1i - 16*a^2*b^6*c^5*d^3 + 16*a^3*b^5*c^4*d^4 + 16*a^4*b^4*c^3*d^5 - 16*a^5*b^3*c^2*d^6)*1i)*(-c/(256*a^4*d^5 + 256*b^4*c^4*d - 1024*a*b^3*c^3*d^2 + 1536*a^2*b^2*c^2*d^3 - 1024*a^3*b*c*d^4))^(1/4)*1i))*(-c/(256*a^4*d^5 + 256*b^4*c^4*d - 1024*a*b^3*c^3*d^2 + 1536*a^2*b^2*c^2*d^3 - 1024*a^3*b*c*d^4))^(1/4)","B"
782,1,6633,449,5.497387,"\text{Not used}","int(x^2/((a + b*x^4)*(c + d*x^4)),x)","\mathrm{atan}\left(\frac{\left(x\,\left(4\,a^2\,b^5\,c\,d^6+4\,a\,b^6\,c^2\,d^5\right)+{\left(-\frac{b}{256\,a^5\,d^4-1024\,a^4\,b\,c\,d^3+1536\,a^3\,b^2\,c^2\,d^2-1024\,a^2\,b^3\,c^3\,d+256\,a\,b^4\,c^4}\right)}^{3/4}\,\left(x\,{\left(-\frac{b}{256\,a^5\,d^4-1024\,a^4\,b\,c\,d^3+1536\,a^3\,b^2\,c^2\,d^2-1024\,a^2\,b^3\,c^3\,d+256\,a\,b^4\,c^4}\right)}^{1/4}\,\left(1024\,a^7\,b^4\,c\,d^{10}-4096\,a^6\,b^5\,c^2\,d^9+7168\,a^5\,b^6\,c^3\,d^8-8192\,a^4\,b^7\,c^4\,d^7+7168\,a^3\,b^8\,c^5\,d^6-4096\,a^2\,b^9\,c^6\,d^5+1024\,a\,b^{10}\,c^7\,d^4\right)+256\,a\,b^9\,c^6\,d^4+256\,a^6\,b^4\,c\,d^9-768\,a^2\,b^8\,c^5\,d^5+512\,a^3\,b^7\,c^4\,d^6+512\,a^4\,b^6\,c^3\,d^7-768\,a^5\,b^5\,c^2\,d^8\right)\right)\,{\left(-\frac{b}{256\,a^5\,d^4-1024\,a^4\,b\,c\,d^3+1536\,a^3\,b^2\,c^2\,d^2-1024\,a^2\,b^3\,c^3\,d+256\,a\,b^4\,c^4}\right)}^{1/4}\,1{}\mathrm{i}+\left(x\,\left(4\,a^2\,b^5\,c\,d^6+4\,a\,b^6\,c^2\,d^5\right)-{\left(-\frac{b}{256\,a^5\,d^4-1024\,a^4\,b\,c\,d^3+1536\,a^3\,b^2\,c^2\,d^2-1024\,a^2\,b^3\,c^3\,d+256\,a\,b^4\,c^4}\right)}^{3/4}\,\left(256\,a\,b^9\,c^6\,d^4-x\,{\left(-\frac{b}{256\,a^5\,d^4-1024\,a^4\,b\,c\,d^3+1536\,a^3\,b^2\,c^2\,d^2-1024\,a^2\,b^3\,c^3\,d+256\,a\,b^4\,c^4}\right)}^{1/4}\,\left(1024\,a^7\,b^4\,c\,d^{10}-4096\,a^6\,b^5\,c^2\,d^9+7168\,a^5\,b^6\,c^3\,d^8-8192\,a^4\,b^7\,c^4\,d^7+7168\,a^3\,b^8\,c^5\,d^6-4096\,a^2\,b^9\,c^6\,d^5+1024\,a\,b^{10}\,c^7\,d^4\right)+256\,a^6\,b^4\,c\,d^9-768\,a^2\,b^8\,c^5\,d^5+512\,a^3\,b^7\,c^4\,d^6+512\,a^4\,b^6\,c^3\,d^7-768\,a^5\,b^5\,c^2\,d^8\right)\right)\,{\left(-\frac{b}{256\,a^5\,d^4-1024\,a^4\,b\,c\,d^3+1536\,a^3\,b^2\,c^2\,d^2-1024\,a^2\,b^3\,c^3\,d+256\,a\,b^4\,c^4}\right)}^{1/4}\,1{}\mathrm{i}}{\left(x\,\left(4\,a^2\,b^5\,c\,d^6+4\,a\,b^6\,c^2\,d^5\right)+{\left(-\frac{b}{256\,a^5\,d^4-1024\,a^4\,b\,c\,d^3+1536\,a^3\,b^2\,c^2\,d^2-1024\,a^2\,b^3\,c^3\,d+256\,a\,b^4\,c^4}\right)}^{3/4}\,\left(x\,{\left(-\frac{b}{256\,a^5\,d^4-1024\,a^4\,b\,c\,d^3+1536\,a^3\,b^2\,c^2\,d^2-1024\,a^2\,b^3\,c^3\,d+256\,a\,b^4\,c^4}\right)}^{1/4}\,\left(1024\,a^7\,b^4\,c\,d^{10}-4096\,a^6\,b^5\,c^2\,d^9+7168\,a^5\,b^6\,c^3\,d^8-8192\,a^4\,b^7\,c^4\,d^7+7168\,a^3\,b^8\,c^5\,d^6-4096\,a^2\,b^9\,c^6\,d^5+1024\,a\,b^{10}\,c^7\,d^4\right)+256\,a\,b^9\,c^6\,d^4+256\,a^6\,b^4\,c\,d^9-768\,a^2\,b^8\,c^5\,d^5+512\,a^3\,b^7\,c^4\,d^6+512\,a^4\,b^6\,c^3\,d^7-768\,a^5\,b^5\,c^2\,d^8\right)\right)\,{\left(-\frac{b}{256\,a^5\,d^4-1024\,a^4\,b\,c\,d^3+1536\,a^3\,b^2\,c^2\,d^2-1024\,a^2\,b^3\,c^3\,d+256\,a\,b^4\,c^4}\right)}^{1/4}-\left(x\,\left(4\,a^2\,b^5\,c\,d^6+4\,a\,b^6\,c^2\,d^5\right)-{\left(-\frac{b}{256\,a^5\,d^4-1024\,a^4\,b\,c\,d^3+1536\,a^3\,b^2\,c^2\,d^2-1024\,a^2\,b^3\,c^3\,d+256\,a\,b^4\,c^4}\right)}^{3/4}\,\left(256\,a\,b^9\,c^6\,d^4-x\,{\left(-\frac{b}{256\,a^5\,d^4-1024\,a^4\,b\,c\,d^3+1536\,a^3\,b^2\,c^2\,d^2-1024\,a^2\,b^3\,c^3\,d+256\,a\,b^4\,c^4}\right)}^{1/4}\,\left(1024\,a^7\,b^4\,c\,d^{10}-4096\,a^6\,b^5\,c^2\,d^9+7168\,a^5\,b^6\,c^3\,d^8-8192\,a^4\,b^7\,c^4\,d^7+7168\,a^3\,b^8\,c^5\,d^6-4096\,a^2\,b^9\,c^6\,d^5+1024\,a\,b^{10}\,c^7\,d^4\right)+256\,a^6\,b^4\,c\,d^9-768\,a^2\,b^8\,c^5\,d^5+512\,a^3\,b^7\,c^4\,d^6+512\,a^4\,b^6\,c^3\,d^7-768\,a^5\,b^5\,c^2\,d^8\right)\right)\,{\left(-\frac{b}{256\,a^5\,d^4-1024\,a^4\,b\,c\,d^3+1536\,a^3\,b^2\,c^2\,d^2-1024\,a^2\,b^3\,c^3\,d+256\,a\,b^4\,c^4}\right)}^{1/4}+2\,a\,b^5\,c\,d^5}\right)\,{\left(-\frac{b}{256\,a^5\,d^4-1024\,a^4\,b\,c\,d^3+1536\,a^3\,b^2\,c^2\,d^2-1024\,a^2\,b^3\,c^3\,d+256\,a\,b^4\,c^4}\right)}^{1/4}\,2{}\mathrm{i}+2\,\mathrm{atan}\left(\frac{\left(x\,\left(4\,a^2\,b^5\,c\,d^6+4\,a\,b^6\,c^2\,d^5\right)+{\left(-\frac{b}{256\,a^5\,d^4-1024\,a^4\,b\,c\,d^3+1536\,a^3\,b^2\,c^2\,d^2-1024\,a^2\,b^3\,c^3\,d+256\,a\,b^4\,c^4}\right)}^{3/4}\,\left(256\,a\,b^9\,c^6\,d^4+256\,a^6\,b^4\,c\,d^9-768\,a^2\,b^8\,c^5\,d^5+512\,a^3\,b^7\,c^4\,d^6+512\,a^4\,b^6\,c^3\,d^7-768\,a^5\,b^5\,c^2\,d^8-x\,{\left(-\frac{b}{256\,a^5\,d^4-1024\,a^4\,b\,c\,d^3+1536\,a^3\,b^2\,c^2\,d^2-1024\,a^2\,b^3\,c^3\,d+256\,a\,b^4\,c^4}\right)}^{1/4}\,\left(1024\,a^7\,b^4\,c\,d^{10}-4096\,a^6\,b^5\,c^2\,d^9+7168\,a^5\,b^6\,c^3\,d^8-8192\,a^4\,b^7\,c^4\,d^7+7168\,a^3\,b^8\,c^5\,d^6-4096\,a^2\,b^9\,c^6\,d^5+1024\,a\,b^{10}\,c^7\,d^4\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{b}{256\,a^5\,d^4-1024\,a^4\,b\,c\,d^3+1536\,a^3\,b^2\,c^2\,d^2-1024\,a^2\,b^3\,c^3\,d+256\,a\,b^4\,c^4}\right)}^{1/4}+\left(x\,\left(4\,a^2\,b^5\,c\,d^6+4\,a\,b^6\,c^2\,d^5\right)-{\left(-\frac{b}{256\,a^5\,d^4-1024\,a^4\,b\,c\,d^3+1536\,a^3\,b^2\,c^2\,d^2-1024\,a^2\,b^3\,c^3\,d+256\,a\,b^4\,c^4}\right)}^{3/4}\,\left(256\,a\,b^9\,c^6\,d^4+256\,a^6\,b^4\,c\,d^9-768\,a^2\,b^8\,c^5\,d^5+512\,a^3\,b^7\,c^4\,d^6+512\,a^4\,b^6\,c^3\,d^7-768\,a^5\,b^5\,c^2\,d^8+x\,{\left(-\frac{b}{256\,a^5\,d^4-1024\,a^4\,b\,c\,d^3+1536\,a^3\,b^2\,c^2\,d^2-1024\,a^2\,b^3\,c^3\,d+256\,a\,b^4\,c^4}\right)}^{1/4}\,\left(1024\,a^7\,b^4\,c\,d^{10}-4096\,a^6\,b^5\,c^2\,d^9+7168\,a^5\,b^6\,c^3\,d^8-8192\,a^4\,b^7\,c^4\,d^7+7168\,a^3\,b^8\,c^5\,d^6-4096\,a^2\,b^9\,c^6\,d^5+1024\,a\,b^{10}\,c^7\,d^4\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{b}{256\,a^5\,d^4-1024\,a^4\,b\,c\,d^3+1536\,a^3\,b^2\,c^2\,d^2-1024\,a^2\,b^3\,c^3\,d+256\,a\,b^4\,c^4}\right)}^{1/4}}{2\,a\,b^5\,c\,d^5-\left(x\,\left(4\,a^2\,b^5\,c\,d^6+4\,a\,b^6\,c^2\,d^5\right)+{\left(-\frac{b}{256\,a^5\,d^4-1024\,a^4\,b\,c\,d^3+1536\,a^3\,b^2\,c^2\,d^2-1024\,a^2\,b^3\,c^3\,d+256\,a\,b^4\,c^4}\right)}^{3/4}\,\left(256\,a\,b^9\,c^6\,d^4+256\,a^6\,b^4\,c\,d^9-768\,a^2\,b^8\,c^5\,d^5+512\,a^3\,b^7\,c^4\,d^6+512\,a^4\,b^6\,c^3\,d^7-768\,a^5\,b^5\,c^2\,d^8-x\,{\left(-\frac{b}{256\,a^5\,d^4-1024\,a^4\,b\,c\,d^3+1536\,a^3\,b^2\,c^2\,d^2-1024\,a^2\,b^3\,c^3\,d+256\,a\,b^4\,c^4}\right)}^{1/4}\,\left(1024\,a^7\,b^4\,c\,d^{10}-4096\,a^6\,b^5\,c^2\,d^9+7168\,a^5\,b^6\,c^3\,d^8-8192\,a^4\,b^7\,c^4\,d^7+7168\,a^3\,b^8\,c^5\,d^6-4096\,a^2\,b^9\,c^6\,d^5+1024\,a\,b^{10}\,c^7\,d^4\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{b}{256\,a^5\,d^4-1024\,a^4\,b\,c\,d^3+1536\,a^3\,b^2\,c^2\,d^2-1024\,a^2\,b^3\,c^3\,d+256\,a\,b^4\,c^4}\right)}^{1/4}\,1{}\mathrm{i}+\left(x\,\left(4\,a^2\,b^5\,c\,d^6+4\,a\,b^6\,c^2\,d^5\right)-{\left(-\frac{b}{256\,a^5\,d^4-1024\,a^4\,b\,c\,d^3+1536\,a^3\,b^2\,c^2\,d^2-1024\,a^2\,b^3\,c^3\,d+256\,a\,b^4\,c^4}\right)}^{3/4}\,\left(256\,a\,b^9\,c^6\,d^4+256\,a^6\,b^4\,c\,d^9-768\,a^2\,b^8\,c^5\,d^5+512\,a^3\,b^7\,c^4\,d^6+512\,a^4\,b^6\,c^3\,d^7-768\,a^5\,b^5\,c^2\,d^8+x\,{\left(-\frac{b}{256\,a^5\,d^4-1024\,a^4\,b\,c\,d^3+1536\,a^3\,b^2\,c^2\,d^2-1024\,a^2\,b^3\,c^3\,d+256\,a\,b^4\,c^4}\right)}^{1/4}\,\left(1024\,a^7\,b^4\,c\,d^{10}-4096\,a^6\,b^5\,c^2\,d^9+7168\,a^5\,b^6\,c^3\,d^8-8192\,a^4\,b^7\,c^4\,d^7+7168\,a^3\,b^8\,c^5\,d^6-4096\,a^2\,b^9\,c^6\,d^5+1024\,a\,b^{10}\,c^7\,d^4\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{b}{256\,a^5\,d^4-1024\,a^4\,b\,c\,d^3+1536\,a^3\,b^2\,c^2\,d^2-1024\,a^2\,b^3\,c^3\,d+256\,a\,b^4\,c^4}\right)}^{1/4}\,1{}\mathrm{i}}\right)\,{\left(-\frac{b}{256\,a^5\,d^4-1024\,a^4\,b\,c\,d^3+1536\,a^3\,b^2\,c^2\,d^2-1024\,a^2\,b^3\,c^3\,d+256\,a\,b^4\,c^4}\right)}^{1/4}+\mathrm{atan}\left(\frac{\left(x\,\left(4\,a^2\,b^5\,c\,d^6+4\,a\,b^6\,c^2\,d^5\right)+{\left(-\frac{d}{256\,a^4\,c\,d^4-1024\,a^3\,b\,c^2\,d^3+1536\,a^2\,b^2\,c^3\,d^2-1024\,a\,b^3\,c^4\,d+256\,b^4\,c^5}\right)}^{3/4}\,\left(x\,{\left(-\frac{d}{256\,a^4\,c\,d^4-1024\,a^3\,b\,c^2\,d^3+1536\,a^2\,b^2\,c^3\,d^2-1024\,a\,b^3\,c^4\,d+256\,b^4\,c^5}\right)}^{1/4}\,\left(1024\,a^7\,b^4\,c\,d^{10}-4096\,a^6\,b^5\,c^2\,d^9+7168\,a^5\,b^6\,c^3\,d^8-8192\,a^4\,b^7\,c^4\,d^7+7168\,a^3\,b^8\,c^5\,d^6-4096\,a^2\,b^9\,c^6\,d^5+1024\,a\,b^{10}\,c^7\,d^4\right)+256\,a\,b^9\,c^6\,d^4+256\,a^6\,b^4\,c\,d^9-768\,a^2\,b^8\,c^5\,d^5+512\,a^3\,b^7\,c^4\,d^6+512\,a^4\,b^6\,c^3\,d^7-768\,a^5\,b^5\,c^2\,d^8\right)\right)\,{\left(-\frac{d}{256\,a^4\,c\,d^4-1024\,a^3\,b\,c^2\,d^3+1536\,a^2\,b^2\,c^3\,d^2-1024\,a\,b^3\,c^4\,d+256\,b^4\,c^5}\right)}^{1/4}\,1{}\mathrm{i}+\left(x\,\left(4\,a^2\,b^5\,c\,d^6+4\,a\,b^6\,c^2\,d^5\right)-{\left(-\frac{d}{256\,a^4\,c\,d^4-1024\,a^3\,b\,c^2\,d^3+1536\,a^2\,b^2\,c^3\,d^2-1024\,a\,b^3\,c^4\,d+256\,b^4\,c^5}\right)}^{3/4}\,\left(256\,a\,b^9\,c^6\,d^4-x\,{\left(-\frac{d}{256\,a^4\,c\,d^4-1024\,a^3\,b\,c^2\,d^3+1536\,a^2\,b^2\,c^3\,d^2-1024\,a\,b^3\,c^4\,d+256\,b^4\,c^5}\right)}^{1/4}\,\left(1024\,a^7\,b^4\,c\,d^{10}-4096\,a^6\,b^5\,c^2\,d^9+7168\,a^5\,b^6\,c^3\,d^8-8192\,a^4\,b^7\,c^4\,d^7+7168\,a^3\,b^8\,c^5\,d^6-4096\,a^2\,b^9\,c^6\,d^5+1024\,a\,b^{10}\,c^7\,d^4\right)+256\,a^6\,b^4\,c\,d^9-768\,a^2\,b^8\,c^5\,d^5+512\,a^3\,b^7\,c^4\,d^6+512\,a^4\,b^6\,c^3\,d^7-768\,a^5\,b^5\,c^2\,d^8\right)\right)\,{\left(-\frac{d}{256\,a^4\,c\,d^4-1024\,a^3\,b\,c^2\,d^3+1536\,a^2\,b^2\,c^3\,d^2-1024\,a\,b^3\,c^4\,d+256\,b^4\,c^5}\right)}^{1/4}\,1{}\mathrm{i}}{\left(x\,\left(4\,a^2\,b^5\,c\,d^6+4\,a\,b^6\,c^2\,d^5\right)+{\left(-\frac{d}{256\,a^4\,c\,d^4-1024\,a^3\,b\,c^2\,d^3+1536\,a^2\,b^2\,c^3\,d^2-1024\,a\,b^3\,c^4\,d+256\,b^4\,c^5}\right)}^{3/4}\,\left(x\,{\left(-\frac{d}{256\,a^4\,c\,d^4-1024\,a^3\,b\,c^2\,d^3+1536\,a^2\,b^2\,c^3\,d^2-1024\,a\,b^3\,c^4\,d+256\,b^4\,c^5}\right)}^{1/4}\,\left(1024\,a^7\,b^4\,c\,d^{10}-4096\,a^6\,b^5\,c^2\,d^9+7168\,a^5\,b^6\,c^3\,d^8-8192\,a^4\,b^7\,c^4\,d^7+7168\,a^3\,b^8\,c^5\,d^6-4096\,a^2\,b^9\,c^6\,d^5+1024\,a\,b^{10}\,c^7\,d^4\right)+256\,a\,b^9\,c^6\,d^4+256\,a^6\,b^4\,c\,d^9-768\,a^2\,b^8\,c^5\,d^5+512\,a^3\,b^7\,c^4\,d^6+512\,a^4\,b^6\,c^3\,d^7-768\,a^5\,b^5\,c^2\,d^8\right)\right)\,{\left(-\frac{d}{256\,a^4\,c\,d^4-1024\,a^3\,b\,c^2\,d^3+1536\,a^2\,b^2\,c^3\,d^2-1024\,a\,b^3\,c^4\,d+256\,b^4\,c^5}\right)}^{1/4}-\left(x\,\left(4\,a^2\,b^5\,c\,d^6+4\,a\,b^6\,c^2\,d^5\right)-{\left(-\frac{d}{256\,a^4\,c\,d^4-1024\,a^3\,b\,c^2\,d^3+1536\,a^2\,b^2\,c^3\,d^2-1024\,a\,b^3\,c^4\,d+256\,b^4\,c^5}\right)}^{3/4}\,\left(256\,a\,b^9\,c^6\,d^4-x\,{\left(-\frac{d}{256\,a^4\,c\,d^4-1024\,a^3\,b\,c^2\,d^3+1536\,a^2\,b^2\,c^3\,d^2-1024\,a\,b^3\,c^4\,d+256\,b^4\,c^5}\right)}^{1/4}\,\left(1024\,a^7\,b^4\,c\,d^{10}-4096\,a^6\,b^5\,c^2\,d^9+7168\,a^5\,b^6\,c^3\,d^8-8192\,a^4\,b^7\,c^4\,d^7+7168\,a^3\,b^8\,c^5\,d^6-4096\,a^2\,b^9\,c^6\,d^5+1024\,a\,b^{10}\,c^7\,d^4\right)+256\,a^6\,b^4\,c\,d^9-768\,a^2\,b^8\,c^5\,d^5+512\,a^3\,b^7\,c^4\,d^6+512\,a^4\,b^6\,c^3\,d^7-768\,a^5\,b^5\,c^2\,d^8\right)\right)\,{\left(-\frac{d}{256\,a^4\,c\,d^4-1024\,a^3\,b\,c^2\,d^3+1536\,a^2\,b^2\,c^3\,d^2-1024\,a\,b^3\,c^4\,d+256\,b^4\,c^5}\right)}^{1/4}+2\,a\,b^5\,c\,d^5}\right)\,{\left(-\frac{d}{256\,a^4\,c\,d^4-1024\,a^3\,b\,c^2\,d^3+1536\,a^2\,b^2\,c^3\,d^2-1024\,a\,b^3\,c^4\,d+256\,b^4\,c^5}\right)}^{1/4}\,2{}\mathrm{i}+2\,\mathrm{atan}\left(\frac{\left(x\,\left(4\,a^2\,b^5\,c\,d^6+4\,a\,b^6\,c^2\,d^5\right)+{\left(-\frac{d}{256\,a^4\,c\,d^4-1024\,a^3\,b\,c^2\,d^3+1536\,a^2\,b^2\,c^3\,d^2-1024\,a\,b^3\,c^4\,d+256\,b^4\,c^5}\right)}^{3/4}\,\left(256\,a\,b^9\,c^6\,d^4+256\,a^6\,b^4\,c\,d^9-768\,a^2\,b^8\,c^5\,d^5+512\,a^3\,b^7\,c^4\,d^6+512\,a^4\,b^6\,c^3\,d^7-768\,a^5\,b^5\,c^2\,d^8-x\,{\left(-\frac{d}{256\,a^4\,c\,d^4-1024\,a^3\,b\,c^2\,d^3+1536\,a^2\,b^2\,c^3\,d^2-1024\,a\,b^3\,c^4\,d+256\,b^4\,c^5}\right)}^{1/4}\,\left(1024\,a^7\,b^4\,c\,d^{10}-4096\,a^6\,b^5\,c^2\,d^9+7168\,a^5\,b^6\,c^3\,d^8-8192\,a^4\,b^7\,c^4\,d^7+7168\,a^3\,b^8\,c^5\,d^6-4096\,a^2\,b^9\,c^6\,d^5+1024\,a\,b^{10}\,c^7\,d^4\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{d}{256\,a^4\,c\,d^4-1024\,a^3\,b\,c^2\,d^3+1536\,a^2\,b^2\,c^3\,d^2-1024\,a\,b^3\,c^4\,d+256\,b^4\,c^5}\right)}^{1/4}+\left(x\,\left(4\,a^2\,b^5\,c\,d^6+4\,a\,b^6\,c^2\,d^5\right)-{\left(-\frac{d}{256\,a^4\,c\,d^4-1024\,a^3\,b\,c^2\,d^3+1536\,a^2\,b^2\,c^3\,d^2-1024\,a\,b^3\,c^4\,d+256\,b^4\,c^5}\right)}^{3/4}\,\left(256\,a\,b^9\,c^6\,d^4+256\,a^6\,b^4\,c\,d^9-768\,a^2\,b^8\,c^5\,d^5+512\,a^3\,b^7\,c^4\,d^6+512\,a^4\,b^6\,c^3\,d^7-768\,a^5\,b^5\,c^2\,d^8+x\,{\left(-\frac{d}{256\,a^4\,c\,d^4-1024\,a^3\,b\,c^2\,d^3+1536\,a^2\,b^2\,c^3\,d^2-1024\,a\,b^3\,c^4\,d+256\,b^4\,c^5}\right)}^{1/4}\,\left(1024\,a^7\,b^4\,c\,d^{10}-4096\,a^6\,b^5\,c^2\,d^9+7168\,a^5\,b^6\,c^3\,d^8-8192\,a^4\,b^7\,c^4\,d^7+7168\,a^3\,b^8\,c^5\,d^6-4096\,a^2\,b^9\,c^6\,d^5+1024\,a\,b^{10}\,c^7\,d^4\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{d}{256\,a^4\,c\,d^4-1024\,a^3\,b\,c^2\,d^3+1536\,a^2\,b^2\,c^3\,d^2-1024\,a\,b^3\,c^4\,d+256\,b^4\,c^5}\right)}^{1/4}}{2\,a\,b^5\,c\,d^5-\left(x\,\left(4\,a^2\,b^5\,c\,d^6+4\,a\,b^6\,c^2\,d^5\right)+{\left(-\frac{d}{256\,a^4\,c\,d^4-1024\,a^3\,b\,c^2\,d^3+1536\,a^2\,b^2\,c^3\,d^2-1024\,a\,b^3\,c^4\,d+256\,b^4\,c^5}\right)}^{3/4}\,\left(256\,a\,b^9\,c^6\,d^4+256\,a^6\,b^4\,c\,d^9-768\,a^2\,b^8\,c^5\,d^5+512\,a^3\,b^7\,c^4\,d^6+512\,a^4\,b^6\,c^3\,d^7-768\,a^5\,b^5\,c^2\,d^8-x\,{\left(-\frac{d}{256\,a^4\,c\,d^4-1024\,a^3\,b\,c^2\,d^3+1536\,a^2\,b^2\,c^3\,d^2-1024\,a\,b^3\,c^4\,d+256\,b^4\,c^5}\right)}^{1/4}\,\left(1024\,a^7\,b^4\,c\,d^{10}-4096\,a^6\,b^5\,c^2\,d^9+7168\,a^5\,b^6\,c^3\,d^8-8192\,a^4\,b^7\,c^4\,d^7+7168\,a^3\,b^8\,c^5\,d^6-4096\,a^2\,b^9\,c^6\,d^5+1024\,a\,b^{10}\,c^7\,d^4\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{d}{256\,a^4\,c\,d^4-1024\,a^3\,b\,c^2\,d^3+1536\,a^2\,b^2\,c^3\,d^2-1024\,a\,b^3\,c^4\,d+256\,b^4\,c^5}\right)}^{1/4}\,1{}\mathrm{i}+\left(x\,\left(4\,a^2\,b^5\,c\,d^6+4\,a\,b^6\,c^2\,d^5\right)-{\left(-\frac{d}{256\,a^4\,c\,d^4-1024\,a^3\,b\,c^2\,d^3+1536\,a^2\,b^2\,c^3\,d^2-1024\,a\,b^3\,c^4\,d+256\,b^4\,c^5}\right)}^{3/4}\,\left(256\,a\,b^9\,c^6\,d^4+256\,a^6\,b^4\,c\,d^9-768\,a^2\,b^8\,c^5\,d^5+512\,a^3\,b^7\,c^4\,d^6+512\,a^4\,b^6\,c^3\,d^7-768\,a^5\,b^5\,c^2\,d^8+x\,{\left(-\frac{d}{256\,a^4\,c\,d^4-1024\,a^3\,b\,c^2\,d^3+1536\,a^2\,b^2\,c^3\,d^2-1024\,a\,b^3\,c^4\,d+256\,b^4\,c^5}\right)}^{1/4}\,\left(1024\,a^7\,b^4\,c\,d^{10}-4096\,a^6\,b^5\,c^2\,d^9+7168\,a^5\,b^6\,c^3\,d^8-8192\,a^4\,b^7\,c^4\,d^7+7168\,a^3\,b^8\,c^5\,d^6-4096\,a^2\,b^9\,c^6\,d^5+1024\,a\,b^{10}\,c^7\,d^4\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,{\left(-\frac{d}{256\,a^4\,c\,d^4-1024\,a^3\,b\,c^2\,d^3+1536\,a^2\,b^2\,c^3\,d^2-1024\,a\,b^3\,c^4\,d+256\,b^4\,c^5}\right)}^{1/4}\,1{}\mathrm{i}}\right)\,{\left(-\frac{d}{256\,a^4\,c\,d^4-1024\,a^3\,b\,c^2\,d^3+1536\,a^2\,b^2\,c^3\,d^2-1024\,a\,b^3\,c^4\,d+256\,b^4\,c^5}\right)}^{1/4}","Not used",1,"atan(((x*(4*a*b^6*c^2*d^5 + 4*a^2*b^5*c*d^6) + (-b/(256*a^5*d^4 + 256*a*b^4*c^4 - 1024*a^2*b^3*c^3*d + 1536*a^3*b^2*c^2*d^2 - 1024*a^4*b*c*d^3))^(3/4)*(x*(-b/(256*a^5*d^4 + 256*a*b^4*c^4 - 1024*a^2*b^3*c^3*d + 1536*a^3*b^2*c^2*d^2 - 1024*a^4*b*c*d^3))^(1/4)*(1024*a*b^10*c^7*d^4 + 1024*a^7*b^4*c*d^10 - 4096*a^2*b^9*c^6*d^5 + 7168*a^3*b^8*c^5*d^6 - 8192*a^4*b^7*c^4*d^7 + 7168*a^5*b^6*c^3*d^8 - 4096*a^6*b^5*c^2*d^9) + 256*a*b^9*c^6*d^4 + 256*a^6*b^4*c*d^9 - 768*a^2*b^8*c^5*d^5 + 512*a^3*b^7*c^4*d^6 + 512*a^4*b^6*c^3*d^7 - 768*a^5*b^5*c^2*d^8))*(-b/(256*a^5*d^4 + 256*a*b^4*c^4 - 1024*a^2*b^3*c^3*d + 1536*a^3*b^2*c^2*d^2 - 1024*a^4*b*c*d^3))^(1/4)*1i + (x*(4*a*b^6*c^2*d^5 + 4*a^2*b^5*c*d^6) - (-b/(256*a^5*d^4 + 256*a*b^4*c^4 - 1024*a^2*b^3*c^3*d + 1536*a^3*b^2*c^2*d^2 - 1024*a^4*b*c*d^3))^(3/4)*(256*a*b^9*c^6*d^4 - x*(-b/(256*a^5*d^4 + 256*a*b^4*c^4 - 1024*a^2*b^3*c^3*d + 1536*a^3*b^2*c^2*d^2 - 1024*a^4*b*c*d^3))^(1/4)*(1024*a*b^10*c^7*d^4 + 1024*a^7*b^4*c*d^10 - 4096*a^2*b^9*c^6*d^5 + 7168*a^3*b^8*c^5*d^6 - 8192*a^4*b^7*c^4*d^7 + 7168*a^5*b^6*c^3*d^8 - 4096*a^6*b^5*c^2*d^9) + 256*a^6*b^4*c*d^9 - 768*a^2*b^8*c^5*d^5 + 512*a^3*b^7*c^4*d^6 + 512*a^4*b^6*c^3*d^7 - 768*a^5*b^5*c^2*d^8))*(-b/(256*a^5*d^4 + 256*a*b^4*c^4 - 1024*a^2*b^3*c^3*d + 1536*a^3*b^2*c^2*d^2 - 1024*a^4*b*c*d^3))^(1/4)*1i)/((x*(4*a*b^6*c^2*d^5 + 4*a^2*b^5*c*d^6) + (-b/(256*a^5*d^4 + 256*a*b^4*c^4 - 1024*a^2*b^3*c^3*d + 1536*a^3*b^2*c^2*d^2 - 1024*a^4*b*c*d^3))^(3/4)*(x*(-b/(256*a^5*d^4 + 256*a*b^4*c^4 - 1024*a^2*b^3*c^3*d + 1536*a^3*b^2*c^2*d^2 - 1024*a^4*b*c*d^3))^(1/4)*(1024*a*b^10*c^7*d^4 + 1024*a^7*b^4*c*d^10 - 4096*a^2*b^9*c^6*d^5 + 7168*a^3*b^8*c^5*d^6 - 8192*a^4*b^7*c^4*d^7 + 7168*a^5*b^6*c^3*d^8 - 4096*a^6*b^5*c^2*d^9) + 256*a*b^9*c^6*d^4 + 256*a^6*b^4*c*d^9 - 768*a^2*b^8*c^5*d^5 + 512*a^3*b^7*c^4*d^6 + 512*a^4*b^6*c^3*d^7 - 768*a^5*b^5*c^2*d^8))*(-b/(256*a^5*d^4 + 256*a*b^4*c^4 - 1024*a^2*b^3*c^3*d + 1536*a^3*b^2*c^2*d^2 - 1024*a^4*b*c*d^3))^(1/4) - (x*(4*a*b^6*c^2*d^5 + 4*a^2*b^5*c*d^6) - (-b/(256*a^5*d^4 + 256*a*b^4*c^4 - 1024*a^2*b^3*c^3*d + 1536*a^3*b^2*c^2*d^2 - 1024*a^4*b*c*d^3))^(3/4)*(256*a*b^9*c^6*d^4 - x*(-b/(256*a^5*d^4 + 256*a*b^4*c^4 - 1024*a^2*b^3*c^3*d + 1536*a^3*b^2*c^2*d^2 - 1024*a^4*b*c*d^3))^(1/4)*(1024*a*b^10*c^7*d^4 + 1024*a^7*b^4*c*d^10 - 4096*a^2*b^9*c^6*d^5 + 7168*a^3*b^8*c^5*d^6 - 8192*a^4*b^7*c^4*d^7 + 7168*a^5*b^6*c^3*d^8 - 4096*a^6*b^5*c^2*d^9) + 256*a^6*b^4*c*d^9 - 768*a^2*b^8*c^5*d^5 + 512*a^3*b^7*c^4*d^6 + 512*a^4*b^6*c^3*d^7 - 768*a^5*b^5*c^2*d^8))*(-b/(256*a^5*d^4 + 256*a*b^4*c^4 - 1024*a^2*b^3*c^3*d + 1536*a^3*b^2*c^2*d^2 - 1024*a^4*b*c*d^3))^(1/4) + 2*a*b^5*c*d^5))*(-b/(256*a^5*d^4 + 256*a*b^4*c^4 - 1024*a^2*b^3*c^3*d + 1536*a^3*b^2*c^2*d^2 - 1024*a^4*b*c*d^3))^(1/4)*2i + 2*atan(((x*(4*a*b^6*c^2*d^5 + 4*a^2*b^5*c*d^6) + (-b/(256*a^5*d^4 + 256*a*b^4*c^4 - 1024*a^2*b^3*c^3*d + 1536*a^3*b^2*c^2*d^2 - 1024*a^4*b*c*d^3))^(3/4)*(256*a*b^9*c^6*d^4 - x*(-b/(256*a^5*d^4 + 256*a*b^4*c^4 - 1024*a^2*b^3*c^3*d + 1536*a^3*b^2*c^2*d^2 - 1024*a^4*b*c*d^3))^(1/4)*(1024*a*b^10*c^7*d^4 + 1024*a^7*b^4*c*d^10 - 4096*a^2*b^9*c^6*d^5 + 7168*a^3*b^8*c^5*d^6 - 8192*a^4*b^7*c^4*d^7 + 7168*a^5*b^6*c^3*d^8 - 4096*a^6*b^5*c^2*d^9)*1i + 256*a^6*b^4*c*d^9 - 768*a^2*b^8*c^5*d^5 + 512*a^3*b^7*c^4*d^6 + 512*a^4*b^6*c^3*d^7 - 768*a^5*b^5*c^2*d^8)*1i)*(-b/(256*a^5*d^4 + 256*a*b^4*c^4 - 1024*a^2*b^3*c^3*d + 1536*a^3*b^2*c^2*d^2 - 1024*a^4*b*c*d^3))^(1/4) + (x*(4*a*b^6*c^2*d^5 + 4*a^2*b^5*c*d^6) - (-b/(256*a^5*d^4 + 256*a*b^4*c^4 - 1024*a^2*b^3*c^3*d + 1536*a^3*b^2*c^2*d^2 - 1024*a^4*b*c*d^3))^(3/4)*(x*(-b/(256*a^5*d^4 + 256*a*b^4*c^4 - 1024*a^2*b^3*c^3*d + 1536*a^3*b^2*c^2*d^2 - 1024*a^4*b*c*d^3))^(1/4)*(1024*a*b^10*c^7*d^4 + 1024*a^7*b^4*c*d^10 - 4096*a^2*b^9*c^6*d^5 + 7168*a^3*b^8*c^5*d^6 - 8192*a^4*b^7*c^4*d^7 + 7168*a^5*b^6*c^3*d^8 - 4096*a^6*b^5*c^2*d^9)*1i + 256*a*b^9*c^6*d^4 + 256*a^6*b^4*c*d^9 - 768*a^2*b^8*c^5*d^5 + 512*a^3*b^7*c^4*d^6 + 512*a^4*b^6*c^3*d^7 - 768*a^5*b^5*c^2*d^8)*1i)*(-b/(256*a^5*d^4 + 256*a*b^4*c^4 - 1024*a^2*b^3*c^3*d + 1536*a^3*b^2*c^2*d^2 - 1024*a^4*b*c*d^3))^(1/4))/((x*(4*a*b^6*c^2*d^5 + 4*a^2*b^5*c*d^6) - (-b/(256*a^5*d^4 + 256*a*b^4*c^4 - 1024*a^2*b^3*c^3*d + 1536*a^3*b^2*c^2*d^2 - 1024*a^4*b*c*d^3))^(3/4)*(x*(-b/(256*a^5*d^4 + 256*a*b^4*c^4 - 1024*a^2*b^3*c^3*d + 1536*a^3*b^2*c^2*d^2 - 1024*a^4*b*c*d^3))^(1/4)*(1024*a*b^10*c^7*d^4 + 1024*a^7*b^4*c*d^10 - 4096*a^2*b^9*c^6*d^5 + 7168*a^3*b^8*c^5*d^6 - 8192*a^4*b^7*c^4*d^7 + 7168*a^5*b^6*c^3*d^8 - 4096*a^6*b^5*c^2*d^9)*1i + 256*a*b^9*c^6*d^4 + 256*a^6*b^4*c*d^9 - 768*a^2*b^8*c^5*d^5 + 512*a^3*b^7*c^4*d^6 + 512*a^4*b^6*c^3*d^7 - 768*a^5*b^5*c^2*d^8)*1i)*(-b/(256*a^5*d^4 + 256*a*b^4*c^4 - 1024*a^2*b^3*c^3*d + 1536*a^3*b^2*c^2*d^2 - 1024*a^4*b*c*d^3))^(1/4)*1i - (x*(4*a*b^6*c^2*d^5 + 4*a^2*b^5*c*d^6) + (-b/(256*a^5*d^4 + 256*a*b^4*c^4 - 1024*a^2*b^3*c^3*d + 1536*a^3*b^2*c^2*d^2 - 1024*a^4*b*c*d^3))^(3/4)*(256*a*b^9*c^6*d^4 - x*(-b/(256*a^5*d^4 + 256*a*b^4*c^4 - 1024*a^2*b^3*c^3*d + 1536*a^3*b^2*c^2*d^2 - 1024*a^4*b*c*d^3))^(1/4)*(1024*a*b^10*c^7*d^4 + 1024*a^7*b^4*c*d^10 - 4096*a^2*b^9*c^6*d^5 + 7168*a^3*b^8*c^5*d^6 - 8192*a^4*b^7*c^4*d^7 + 7168*a^5*b^6*c^3*d^8 - 4096*a^6*b^5*c^2*d^9)*1i + 256*a^6*b^4*c*d^9 - 768*a^2*b^8*c^5*d^5 + 512*a^3*b^7*c^4*d^6 + 512*a^4*b^6*c^3*d^7 - 768*a^5*b^5*c^2*d^8)*1i)*(-b/(256*a^5*d^4 + 256*a*b^4*c^4 - 1024*a^2*b^3*c^3*d + 1536*a^3*b^2*c^2*d^2 - 1024*a^4*b*c*d^3))^(1/4)*1i + 2*a*b^5*c*d^5))*(-b/(256*a^5*d^4 + 256*a*b^4*c^4 - 1024*a^2*b^3*c^3*d + 1536*a^3*b^2*c^2*d^2 - 1024*a^4*b*c*d^3))^(1/4) + atan(((x*(4*a*b^6*c^2*d^5 + 4*a^2*b^5*c*d^6) + (-d/(256*b^4*c^5 + 256*a^4*c*d^4 - 1024*a^3*b*c^2*d^3 + 1536*a^2*b^2*c^3*d^2 - 1024*a*b^3*c^4*d))^(3/4)*(x*(-d/(256*b^4*c^5 + 256*a^4*c*d^4 - 1024*a^3*b*c^2*d^3 + 1536*a^2*b^2*c^3*d^2 - 1024*a*b^3*c^4*d))^(1/4)*(1024*a*b^10*c^7*d^4 + 1024*a^7*b^4*c*d^10 - 4096*a^2*b^9*c^6*d^5 + 7168*a^3*b^8*c^5*d^6 - 8192*a^4*b^7*c^4*d^7 + 7168*a^5*b^6*c^3*d^8 - 4096*a^6*b^5*c^2*d^9) + 256*a*b^9*c^6*d^4 + 256*a^6*b^4*c*d^9 - 768*a^2*b^8*c^5*d^5 + 512*a^3*b^7*c^4*d^6 + 512*a^4*b^6*c^3*d^7 - 768*a^5*b^5*c^2*d^8))*(-d/(256*b^4*c^5 + 256*a^4*c*d^4 - 1024*a^3*b*c^2*d^3 + 1536*a^2*b^2*c^3*d^2 - 1024*a*b^3*c^4*d))^(1/4)*1i + (x*(4*a*b^6*c^2*d^5 + 4*a^2*b^5*c*d^6) - (-d/(256*b^4*c^5 + 256*a^4*c*d^4 - 1024*a^3*b*c^2*d^3 + 1536*a^2*b^2*c^3*d^2 - 1024*a*b^3*c^4*d))^(3/4)*(256*a*b^9*c^6*d^4 - x*(-d/(256*b^4*c^5 + 256*a^4*c*d^4 - 1024*a^3*b*c^2*d^3 + 1536*a^2*b^2*c^3*d^2 - 1024*a*b^3*c^4*d))^(1/4)*(1024*a*b^10*c^7*d^4 + 1024*a^7*b^4*c*d^10 - 4096*a^2*b^9*c^6*d^5 + 7168*a^3*b^8*c^5*d^6 - 8192*a^4*b^7*c^4*d^7 + 7168*a^5*b^6*c^3*d^8 - 4096*a^6*b^5*c^2*d^9) + 256*a^6*b^4*c*d^9 - 768*a^2*b^8*c^5*d^5 + 512*a^3*b^7*c^4*d^6 + 512*a^4*b^6*c^3*d^7 - 768*a^5*b^5*c^2*d^8))*(-d/(256*b^4*c^5 + 256*a^4*c*d^4 - 1024*a^3*b*c^2*d^3 + 1536*a^2*b^2*c^3*d^2 - 1024*a*b^3*c^4*d))^(1/4)*1i)/((x*(4*a*b^6*c^2*d^5 + 4*a^2*b^5*c*d^6) + (-d/(256*b^4*c^5 + 256*a^4*c*d^4 - 1024*a^3*b*c^2*d^3 + 1536*a^2*b^2*c^3*d^2 - 1024*a*b^3*c^4*d))^(3/4)*(x*(-d/(256*b^4*c^5 + 256*a^4*c*d^4 - 1024*a^3*b*c^2*d^3 + 1536*a^2*b^2*c^3*d^2 - 1024*a*b^3*c^4*d))^(1/4)*(1024*a*b^10*c^7*d^4 + 1024*a^7*b^4*c*d^10 - 4096*a^2*b^9*c^6*d^5 + 7168*a^3*b^8*c^5*d^6 - 8192*a^4*b^7*c^4*d^7 + 7168*a^5*b^6*c^3*d^8 - 4096*a^6*b^5*c^2*d^9) + 256*a*b^9*c^6*d^4 + 256*a^6*b^4*c*d^9 - 768*a^2*b^8*c^5*d^5 + 512*a^3*b^7*c^4*d^6 + 512*a^4*b^6*c^3*d^7 - 768*a^5*b^5*c^2*d^8))*(-d/(256*b^4*c^5 + 256*a^4*c*d^4 - 1024*a^3*b*c^2*d^3 + 1536*a^2*b^2*c^3*d^2 - 1024*a*b^3*c^4*d))^(1/4) - (x*(4*a*b^6*c^2*d^5 + 4*a^2*b^5*c*d^6) - (-d/(256*b^4*c^5 + 256*a^4*c*d^4 - 1024*a^3*b*c^2*d^3 + 1536*a^2*b^2*c^3*d^2 - 1024*a*b^3*c^4*d))^(3/4)*(256*a*b^9*c^6*d^4 - x*(-d/(256*b^4*c^5 + 256*a^4*c*d^4 - 1024*a^3*b*c^2*d^3 + 1536*a^2*b^2*c^3*d^2 - 1024*a*b^3*c^4*d))^(1/4)*(1024*a*b^10*c^7*d^4 + 1024*a^7*b^4*c*d^10 - 4096*a^2*b^9*c^6*d^5 + 7168*a^3*b^8*c^5*d^6 - 8192*a^4*b^7*c^4*d^7 + 7168*a^5*b^6*c^3*d^8 - 4096*a^6*b^5*c^2*d^9) + 256*a^6*b^4*c*d^9 - 768*a^2*b^8*c^5*d^5 + 512*a^3*b^7*c^4*d^6 + 512*a^4*b^6*c^3*d^7 - 768*a^5*b^5*c^2*d^8))*(-d/(256*b^4*c^5 + 256*a^4*c*d^4 - 1024*a^3*b*c^2*d^3 + 1536*a^2*b^2*c^3*d^2 - 1024*a*b^3*c^4*d))^(1/4) + 2*a*b^5*c*d^5))*(-d/(256*b^4*c^5 + 256*a^4*c*d^4 - 1024*a^3*b*c^2*d^3 + 1536*a^2*b^2*c^3*d^2 - 1024*a*b^3*c^4*d))^(1/4)*2i + 2*atan(((x*(4*a*b^6*c^2*d^5 + 4*a^2*b^5*c*d^6) + (-d/(256*b^4*c^5 + 256*a^4*c*d^4 - 1024*a^3*b*c^2*d^3 + 1536*a^2*b^2*c^3*d^2 - 1024*a*b^3*c^4*d))^(3/4)*(256*a*b^9*c^6*d^4 - x*(-d/(256*b^4*c^5 + 256*a^4*c*d^4 - 1024*a^3*b*c^2*d^3 + 1536*a^2*b^2*c^3*d^2 - 1024*a*b^3*c^4*d))^(1/4)*(1024*a*b^10*c^7*d^4 + 1024*a^7*b^4*c*d^10 - 4096*a^2*b^9*c^6*d^5 + 7168*a^3*b^8*c^5*d^6 - 8192*a^4*b^7*c^4*d^7 + 7168*a^5*b^6*c^3*d^8 - 4096*a^6*b^5*c^2*d^9)*1i + 256*a^6*b^4*c*d^9 - 768*a^2*b^8*c^5*d^5 + 512*a^3*b^7*c^4*d^6 + 512*a^4*b^6*c^3*d^7 - 768*a^5*b^5*c^2*d^8)*1i)*(-d/(256*b^4*c^5 + 256*a^4*c*d^4 - 1024*a^3*b*c^2*d^3 + 1536*a^2*b^2*c^3*d^2 - 1024*a*b^3*c^4*d))^(1/4) + (x*(4*a*b^6*c^2*d^5 + 4*a^2*b^5*c*d^6) - (-d/(256*b^4*c^5 + 256*a^4*c*d^4 - 1024*a^3*b*c^2*d^3 + 1536*a^2*b^2*c^3*d^2 - 1024*a*b^3*c^4*d))^(3/4)*(x*(-d/(256*b^4*c^5 + 256*a^4*c*d^4 - 1024*a^3*b*c^2*d^3 + 1536*a^2*b^2*c^3*d^2 - 1024*a*b^3*c^4*d))^(1/4)*(1024*a*b^10*c^7*d^4 + 1024*a^7*b^4*c*d^10 - 4096*a^2*b^9*c^6*d^5 + 7168*a^3*b^8*c^5*d^6 - 8192*a^4*b^7*c^4*d^7 + 7168*a^5*b^6*c^3*d^8 - 4096*a^6*b^5*c^2*d^9)*1i + 256*a*b^9*c^6*d^4 + 256*a^6*b^4*c*d^9 - 768*a^2*b^8*c^5*d^5 + 512*a^3*b^7*c^4*d^6 + 512*a^4*b^6*c^3*d^7 - 768*a^5*b^5*c^2*d^8)*1i)*(-d/(256*b^4*c^5 + 256*a^4*c*d^4 - 1024*a^3*b*c^2*d^3 + 1536*a^2*b^2*c^3*d^2 - 1024*a*b^3*c^4*d))^(1/4))/((x*(4*a*b^6*c^2*d^5 + 4*a^2*b^5*c*d^6) - (-d/(256*b^4*c^5 + 256*a^4*c*d^4 - 1024*a^3*b*c^2*d^3 + 1536*a^2*b^2*c^3*d^2 - 1024*a*b^3*c^4*d))^(3/4)*(x*(-d/(256*b^4*c^5 + 256*a^4*c*d^4 - 1024*a^3*b*c^2*d^3 + 1536*a^2*b^2*c^3*d^2 - 1024*a*b^3*c^4*d))^(1/4)*(1024*a*b^10*c^7*d^4 + 1024*a^7*b^4*c*d^10 - 4096*a^2*b^9*c^6*d^5 + 7168*a^3*b^8*c^5*d^6 - 8192*a^4*b^7*c^4*d^7 + 7168*a^5*b^6*c^3*d^8 - 4096*a^6*b^5*c^2*d^9)*1i + 256*a*b^9*c^6*d^4 + 256*a^6*b^4*c*d^9 - 768*a^2*b^8*c^5*d^5 + 512*a^3*b^7*c^4*d^6 + 512*a^4*b^6*c^3*d^7 - 768*a^5*b^5*c^2*d^8)*1i)*(-d/(256*b^4*c^5 + 256*a^4*c*d^4 - 1024*a^3*b*c^2*d^3 + 1536*a^2*b^2*c^3*d^2 - 1024*a*b^3*c^4*d))^(1/4)*1i - (x*(4*a*b^6*c^2*d^5 + 4*a^2*b^5*c*d^6) + (-d/(256*b^4*c^5 + 256*a^4*c*d^4 - 1024*a^3*b*c^2*d^3 + 1536*a^2*b^2*c^3*d^2 - 1024*a*b^3*c^4*d))^(3/4)*(256*a*b^9*c^6*d^4 - x*(-d/(256*b^4*c^5 + 256*a^4*c*d^4 - 1024*a^3*b*c^2*d^3 + 1536*a^2*b^2*c^3*d^2 - 1024*a*b^3*c^4*d))^(1/4)*(1024*a*b^10*c^7*d^4 + 1024*a^7*b^4*c*d^10 - 4096*a^2*b^9*c^6*d^5 + 7168*a^3*b^8*c^5*d^6 - 8192*a^4*b^7*c^4*d^7 + 7168*a^5*b^6*c^3*d^8 - 4096*a^6*b^5*c^2*d^9)*1i + 256*a^6*b^4*c*d^9 - 768*a^2*b^8*c^5*d^5 + 512*a^3*b^7*c^4*d^6 + 512*a^4*b^6*c^3*d^7 - 768*a^5*b^5*c^2*d^8)*1i)*(-d/(256*b^4*c^5 + 256*a^4*c*d^4 - 1024*a^3*b*c^2*d^3 + 1536*a^2*b^2*c^3*d^2 - 1024*a*b^3*c^4*d))^(1/4)*1i + 2*a*b^5*c*d^5))*(-d/(256*b^4*c^5 + 256*a^4*c*d^4 - 1024*a^3*b*c^2*d^3 + 1536*a^2*b^2*c^3*d^2 - 1024*a*b^3*c^4*d))^(1/4)","B"
783,1,6153,449,5.852968,"\text{Not used}","int(1/((a + b*x^4)*(c + d*x^4)),x)","-2\,\mathrm{atan}\left(\frac{b^3\,d^3\,x-\frac{128\,b^{10}\,c^7\,x}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}-\frac{128\,a^7\,b^3\,d^7\,x}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}-\frac{768\,a^2\,b^8\,c^5\,d^2\,x}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}+\frac{384\,a^3\,b^7\,c^4\,d^3\,x}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}+\frac{384\,a^4\,b^6\,c^3\,d^4\,x}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}-\frac{768\,a^5\,b^5\,c^2\,d^5\,x}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}+\frac{512\,a\,b^9\,c^6\,d\,x}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}+\frac{512\,a^6\,b^4\,c\,d^6\,x}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}}{{\left(-\frac{b^3}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}\right)}^{1/4}\,\left(\frac{b^3\,\left(512\,a^8\,c\,d^7-2560\,a^7\,b\,c^2\,d^6+4608\,a^6\,b^2\,c^3\,d^5-2560\,a^5\,b^3\,c^4\,d^4-2560\,a^4\,b^4\,c^5\,d^3+4608\,a^3\,b^5\,c^6\,d^2-2560\,a^2\,b^6\,c^7\,d+512\,a\,b^7\,c^8\right)}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}+2\,a^2\,b^2\,d^4+2\,b^4\,c^2\,d^2-4\,a\,b^3\,c\,d^3\right)}\right)\,{\left(-\frac{b^3}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}\right)}^{1/4}-2\,\mathrm{atan}\left(\frac{b^3\,d^3\,x-\frac{128\,a^7\,d^{10}\,x}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}-\frac{128\,b^7\,c^7\,d^3\,x}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}-\frac{768\,a^2\,b^5\,c^5\,d^5\,x}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}+\frac{384\,a^3\,b^4\,c^4\,d^6\,x}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}+\frac{384\,a^4\,b^3\,c^3\,d^7\,x}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}-\frac{768\,a^5\,b^2\,c^2\,d^8\,x}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}+\frac{512\,a^6\,b\,c\,d^9\,x}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}+\frac{512\,a\,b^6\,c^6\,d^4\,x}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}}{{\left(-\frac{d^3}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}\right)}^{1/4}\,\left(\frac{d^3\,\left(512\,a^8\,c\,d^7-2560\,a^7\,b\,c^2\,d^6+4608\,a^6\,b^2\,c^3\,d^5-2560\,a^5\,b^3\,c^4\,d^4-2560\,a^4\,b^4\,c^5\,d^3+4608\,a^3\,b^5\,c^6\,d^2-2560\,a^2\,b^6\,c^7\,d+512\,a\,b^7\,c^8\right)}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}+2\,a^2\,b^2\,d^4+2\,b^4\,c^2\,d^2-4\,a\,b^3\,c\,d^3\right)}\right)\,{\left(-\frac{d^3}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}\right)}^{1/4}-\mathrm{atan}\left(\frac{\left({\left(-\frac{d^3}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}\right)}^{1/4}\,\left({\left(-\frac{d^3}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}\right)}^{3/4}\,\left({\left(-\frac{d^3}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}\right)}^{1/4}\,\left(4096\,a^8\,b^4\,c\,d^{11}-20480\,a^7\,b^5\,c^2\,d^{10}+36864\,a^6\,b^6\,c^3\,d^9-20480\,a^5\,b^7\,c^4\,d^8-20480\,a^4\,b^8\,c^5\,d^7+36864\,a^3\,b^9\,c^6\,d^6-20480\,a^2\,b^{10}\,c^7\,d^5+4096\,a\,b^{11}\,c^8\,d^4\right)+x\,\left(1024\,a^7\,b^4\,d^{11}-4096\,a^6\,b^5\,c\,d^{10}+6144\,a^5\,b^6\,c^2\,d^9-3072\,a^4\,b^7\,c^3\,d^8-3072\,a^3\,b^8\,c^4\,d^7+6144\,a^2\,b^9\,c^5\,d^6-4096\,a\,b^{10}\,c^6\,d^5+1024\,b^{11}\,c^7\,d^4\right)\right)-16\,a^2\,b^6\,d^8-16\,b^8\,c^2\,d^6+32\,a\,b^7\,c\,d^7\right)+8\,b^7\,d^7\,x\right)\,{\left(-\frac{d^3}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}\right)}^{1/4}\,1{}\mathrm{i}-\left({\left(-\frac{d^3}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}\right)}^{1/4}\,\left({\left(-\frac{d^3}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}\right)}^{3/4}\,\left({\left(-\frac{d^3}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}\right)}^{1/4}\,\left(4096\,a^8\,b^4\,c\,d^{11}-20480\,a^7\,b^5\,c^2\,d^{10}+36864\,a^6\,b^6\,c^3\,d^9-20480\,a^5\,b^7\,c^4\,d^8-20480\,a^4\,b^8\,c^5\,d^7+36864\,a^3\,b^9\,c^6\,d^6-20480\,a^2\,b^{10}\,c^7\,d^5+4096\,a\,b^{11}\,c^8\,d^4\right)-x\,\left(1024\,a^7\,b^4\,d^{11}-4096\,a^6\,b^5\,c\,d^{10}+6144\,a^5\,b^6\,c^2\,d^9-3072\,a^4\,b^7\,c^3\,d^8-3072\,a^3\,b^8\,c^4\,d^7+6144\,a^2\,b^9\,c^5\,d^6-4096\,a\,b^{10}\,c^6\,d^5+1024\,b^{11}\,c^7\,d^4\right)\right)-16\,a^2\,b^6\,d^8-16\,b^8\,c^2\,d^6+32\,a\,b^7\,c\,d^7\right)-8\,b^7\,d^7\,x\right)\,{\left(-\frac{d^3}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}\right)}^{1/4}\,1{}\mathrm{i}}{\left({\left(-\frac{d^3}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}\right)}^{1/4}\,\left({\left(-\frac{d^3}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}\right)}^{3/4}\,\left({\left(-\frac{d^3}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}\right)}^{1/4}\,\left(4096\,a^8\,b^4\,c\,d^{11}-20480\,a^7\,b^5\,c^2\,d^{10}+36864\,a^6\,b^6\,c^3\,d^9-20480\,a^5\,b^7\,c^4\,d^8-20480\,a^4\,b^8\,c^5\,d^7+36864\,a^3\,b^9\,c^6\,d^6-20480\,a^2\,b^{10}\,c^7\,d^5+4096\,a\,b^{11}\,c^8\,d^4\right)+x\,\left(1024\,a^7\,b^4\,d^{11}-4096\,a^6\,b^5\,c\,d^{10}+6144\,a^5\,b^6\,c^2\,d^9-3072\,a^4\,b^7\,c^3\,d^8-3072\,a^3\,b^8\,c^4\,d^7+6144\,a^2\,b^9\,c^5\,d^6-4096\,a\,b^{10}\,c^6\,d^5+1024\,b^{11}\,c^7\,d^4\right)\right)-16\,a^2\,b^6\,d^8-16\,b^8\,c^2\,d^6+32\,a\,b^7\,c\,d^7\right)+8\,b^7\,d^7\,x\right)\,{\left(-\frac{d^3}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}\right)}^{1/4}+\left({\left(-\frac{d^3}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}\right)}^{1/4}\,\left({\left(-\frac{d^3}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}\right)}^{3/4}\,\left({\left(-\frac{d^3}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}\right)}^{1/4}\,\left(4096\,a^8\,b^4\,c\,d^{11}-20480\,a^7\,b^5\,c^2\,d^{10}+36864\,a^6\,b^6\,c^3\,d^9-20480\,a^5\,b^7\,c^4\,d^8-20480\,a^4\,b^8\,c^5\,d^7+36864\,a^3\,b^9\,c^6\,d^6-20480\,a^2\,b^{10}\,c^7\,d^5+4096\,a\,b^{11}\,c^8\,d^4\right)-x\,\left(1024\,a^7\,b^4\,d^{11}-4096\,a^6\,b^5\,c\,d^{10}+6144\,a^5\,b^6\,c^2\,d^9-3072\,a^4\,b^7\,c^3\,d^8-3072\,a^3\,b^8\,c^4\,d^7+6144\,a^2\,b^9\,c^5\,d^6-4096\,a\,b^{10}\,c^6\,d^5+1024\,b^{11}\,c^7\,d^4\right)\right)-16\,a^2\,b^6\,d^8-16\,b^8\,c^2\,d^6+32\,a\,b^7\,c\,d^7\right)-8\,b^7\,d^7\,x\right)\,{\left(-\frac{d^3}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}\right)}^{1/4}}\right)\,{\left(-\frac{d^3}{256\,a^4\,c^3\,d^4-1024\,a^3\,b\,c^4\,d^3+1536\,a^2\,b^2\,c^5\,d^2-1024\,a\,b^3\,c^6\,d+256\,b^4\,c^7}\right)}^{1/4}\,2{}\mathrm{i}-\mathrm{atan}\left(\frac{\left({\left(-\frac{b^3}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}\right)}^{1/4}\,\left({\left(-\frac{b^3}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}\right)}^{3/4}\,\left({\left(-\frac{b^3}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}\right)}^{1/4}\,\left(4096\,a^8\,b^4\,c\,d^{11}-20480\,a^7\,b^5\,c^2\,d^{10}+36864\,a^6\,b^6\,c^3\,d^9-20480\,a^5\,b^7\,c^4\,d^8-20480\,a^4\,b^8\,c^5\,d^7+36864\,a^3\,b^9\,c^6\,d^6-20480\,a^2\,b^{10}\,c^7\,d^5+4096\,a\,b^{11}\,c^8\,d^4\right)+x\,\left(1024\,a^7\,b^4\,d^{11}-4096\,a^6\,b^5\,c\,d^{10}+6144\,a^5\,b^6\,c^2\,d^9-3072\,a^4\,b^7\,c^3\,d^8-3072\,a^3\,b^8\,c^4\,d^7+6144\,a^2\,b^9\,c^5\,d^6-4096\,a\,b^{10}\,c^6\,d^5+1024\,b^{11}\,c^7\,d^4\right)\right)-16\,a^2\,b^6\,d^8-16\,b^8\,c^2\,d^6+32\,a\,b^7\,c\,d^7\right)+8\,b^7\,d^7\,x\right)\,{\left(-\frac{b^3}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}\right)}^{1/4}\,1{}\mathrm{i}-\left({\left(-\frac{b^3}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}\right)}^{1/4}\,\left({\left(-\frac{b^3}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}\right)}^{3/4}\,\left({\left(-\frac{b^3}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}\right)}^{1/4}\,\left(4096\,a^8\,b^4\,c\,d^{11}-20480\,a^7\,b^5\,c^2\,d^{10}+36864\,a^6\,b^6\,c^3\,d^9-20480\,a^5\,b^7\,c^4\,d^8-20480\,a^4\,b^8\,c^5\,d^7+36864\,a^3\,b^9\,c^6\,d^6-20480\,a^2\,b^{10}\,c^7\,d^5+4096\,a\,b^{11}\,c^8\,d^4\right)-x\,\left(1024\,a^7\,b^4\,d^{11}-4096\,a^6\,b^5\,c\,d^{10}+6144\,a^5\,b^6\,c^2\,d^9-3072\,a^4\,b^7\,c^3\,d^8-3072\,a^3\,b^8\,c^4\,d^7+6144\,a^2\,b^9\,c^5\,d^6-4096\,a\,b^{10}\,c^6\,d^5+1024\,b^{11}\,c^7\,d^4\right)\right)-16\,a^2\,b^6\,d^8-16\,b^8\,c^2\,d^6+32\,a\,b^7\,c\,d^7\right)-8\,b^7\,d^7\,x\right)\,{\left(-\frac{b^3}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}\right)}^{1/4}\,1{}\mathrm{i}}{\left({\left(-\frac{b^3}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}\right)}^{1/4}\,\left({\left(-\frac{b^3}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}\right)}^{3/4}\,\left({\left(-\frac{b^3}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}\right)}^{1/4}\,\left(4096\,a^8\,b^4\,c\,d^{11}-20480\,a^7\,b^5\,c^2\,d^{10}+36864\,a^6\,b^6\,c^3\,d^9-20480\,a^5\,b^7\,c^4\,d^8-20480\,a^4\,b^8\,c^5\,d^7+36864\,a^3\,b^9\,c^6\,d^6-20480\,a^2\,b^{10}\,c^7\,d^5+4096\,a\,b^{11}\,c^8\,d^4\right)+x\,\left(1024\,a^7\,b^4\,d^{11}-4096\,a^6\,b^5\,c\,d^{10}+6144\,a^5\,b^6\,c^2\,d^9-3072\,a^4\,b^7\,c^3\,d^8-3072\,a^3\,b^8\,c^4\,d^7+6144\,a^2\,b^9\,c^5\,d^6-4096\,a\,b^{10}\,c^6\,d^5+1024\,b^{11}\,c^7\,d^4\right)\right)-16\,a^2\,b^6\,d^8-16\,b^8\,c^2\,d^6+32\,a\,b^7\,c\,d^7\right)+8\,b^7\,d^7\,x\right)\,{\left(-\frac{b^3}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}\right)}^{1/4}+\left({\left(-\frac{b^3}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}\right)}^{1/4}\,\left({\left(-\frac{b^3}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}\right)}^{3/4}\,\left({\left(-\frac{b^3}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}\right)}^{1/4}\,\left(4096\,a^8\,b^4\,c\,d^{11}-20480\,a^7\,b^5\,c^2\,d^{10}+36864\,a^6\,b^6\,c^3\,d^9-20480\,a^5\,b^7\,c^4\,d^8-20480\,a^4\,b^8\,c^5\,d^7+36864\,a^3\,b^9\,c^6\,d^6-20480\,a^2\,b^{10}\,c^7\,d^5+4096\,a\,b^{11}\,c^8\,d^4\right)-x\,\left(1024\,a^7\,b^4\,d^{11}-4096\,a^6\,b^5\,c\,d^{10}+6144\,a^5\,b^6\,c^2\,d^9-3072\,a^4\,b^7\,c^3\,d^8-3072\,a^3\,b^8\,c^4\,d^7+6144\,a^2\,b^9\,c^5\,d^6-4096\,a\,b^{10}\,c^6\,d^5+1024\,b^{11}\,c^7\,d^4\right)\right)-16\,a^2\,b^6\,d^8-16\,b^8\,c^2\,d^6+32\,a\,b^7\,c\,d^7\right)-8\,b^7\,d^7\,x\right)\,{\left(-\frac{b^3}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}\right)}^{1/4}}\right)\,{\left(-\frac{b^3}{256\,a^7\,d^4-1024\,a^6\,b\,c\,d^3+1536\,a^5\,b^2\,c^2\,d^2-1024\,a^4\,b^3\,c^3\,d+256\,a^3\,b^4\,c^4}\right)}^{1/4}\,2{}\mathrm{i}","Not used",1,"- atan((((-d^3/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d))^(1/4)*((-d^3/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d))^(3/4)*((-d^3/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d))^(1/4)*(4096*a*b^11*c^8*d^4 + 4096*a^8*b^4*c*d^11 - 20480*a^2*b^10*c^7*d^5 + 36864*a^3*b^9*c^6*d^6 - 20480*a^4*b^8*c^5*d^7 - 20480*a^5*b^7*c^4*d^8 + 36864*a^6*b^6*c^3*d^9 - 20480*a^7*b^5*c^2*d^10) + x*(1024*a^7*b^4*d^11 + 1024*b^11*c^7*d^4 - 4096*a*b^10*c^6*d^5 - 4096*a^6*b^5*c*d^10 + 6144*a^2*b^9*c^5*d^6 - 3072*a^3*b^8*c^4*d^7 - 3072*a^4*b^7*c^3*d^8 + 6144*a^5*b^6*c^2*d^9)) - 16*a^2*b^6*d^8 - 16*b^8*c^2*d^6 + 32*a*b^7*c*d^7) + 8*b^7*d^7*x)*(-d^3/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d))^(1/4)*1i - ((-d^3/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d))^(1/4)*((-d^3/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d))^(3/4)*((-d^3/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d))^(1/4)*(4096*a*b^11*c^8*d^4 + 4096*a^8*b^4*c*d^11 - 20480*a^2*b^10*c^7*d^5 + 36864*a^3*b^9*c^6*d^6 - 20480*a^4*b^8*c^5*d^7 - 20480*a^5*b^7*c^4*d^8 + 36864*a^6*b^6*c^3*d^9 - 20480*a^7*b^5*c^2*d^10) - x*(1024*a^7*b^4*d^11 + 1024*b^11*c^7*d^4 - 4096*a*b^10*c^6*d^5 - 4096*a^6*b^5*c*d^10 + 6144*a^2*b^9*c^5*d^6 - 3072*a^3*b^8*c^4*d^7 - 3072*a^4*b^7*c^3*d^8 + 6144*a^5*b^6*c^2*d^9)) - 16*a^2*b^6*d^8 - 16*b^8*c^2*d^6 + 32*a*b^7*c*d^7) - 8*b^7*d^7*x)*(-d^3/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d))^(1/4)*1i)/(((-d^3/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d))^(1/4)*((-d^3/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d))^(3/4)*((-d^3/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d))^(1/4)*(4096*a*b^11*c^8*d^4 + 4096*a^8*b^4*c*d^11 - 20480*a^2*b^10*c^7*d^5 + 36864*a^3*b^9*c^6*d^6 - 20480*a^4*b^8*c^5*d^7 - 20480*a^5*b^7*c^4*d^8 + 36864*a^6*b^6*c^3*d^9 - 20480*a^7*b^5*c^2*d^10) + x*(1024*a^7*b^4*d^11 + 1024*b^11*c^7*d^4 - 4096*a*b^10*c^6*d^5 - 4096*a^6*b^5*c*d^10 + 6144*a^2*b^9*c^5*d^6 - 3072*a^3*b^8*c^4*d^7 - 3072*a^4*b^7*c^3*d^8 + 6144*a^5*b^6*c^2*d^9)) - 16*a^2*b^6*d^8 - 16*b^8*c^2*d^6 + 32*a*b^7*c*d^7) + 8*b^7*d^7*x)*(-d^3/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d))^(1/4) + ((-d^3/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d))^(1/4)*((-d^3/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d))^(3/4)*((-d^3/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d))^(1/4)*(4096*a*b^11*c^8*d^4 + 4096*a^8*b^4*c*d^11 - 20480*a^2*b^10*c^7*d^5 + 36864*a^3*b^9*c^6*d^6 - 20480*a^4*b^8*c^5*d^7 - 20480*a^5*b^7*c^4*d^8 + 36864*a^6*b^6*c^3*d^9 - 20480*a^7*b^5*c^2*d^10) - x*(1024*a^7*b^4*d^11 + 1024*b^11*c^7*d^4 - 4096*a*b^10*c^6*d^5 - 4096*a^6*b^5*c*d^10 + 6144*a^2*b^9*c^5*d^6 - 3072*a^3*b^8*c^4*d^7 - 3072*a^4*b^7*c^3*d^8 + 6144*a^5*b^6*c^2*d^9)) - 16*a^2*b^6*d^8 - 16*b^8*c^2*d^6 + 32*a*b^7*c*d^7) - 8*b^7*d^7*x)*(-d^3/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d))^(1/4)))*(-d^3/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d))^(1/4)*2i - atan((((-b^3/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3))^(1/4)*((-b^3/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3))^(3/4)*((-b^3/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3))^(1/4)*(4096*a*b^11*c^8*d^4 + 4096*a^8*b^4*c*d^11 - 20480*a^2*b^10*c^7*d^5 + 36864*a^3*b^9*c^6*d^6 - 20480*a^4*b^8*c^5*d^7 - 20480*a^5*b^7*c^4*d^8 + 36864*a^6*b^6*c^3*d^9 - 20480*a^7*b^5*c^2*d^10) + x*(1024*a^7*b^4*d^11 + 1024*b^11*c^7*d^4 - 4096*a*b^10*c^6*d^5 - 4096*a^6*b^5*c*d^10 + 6144*a^2*b^9*c^5*d^6 - 3072*a^3*b^8*c^4*d^7 - 3072*a^4*b^7*c^3*d^8 + 6144*a^5*b^6*c^2*d^9)) - 16*a^2*b^6*d^8 - 16*b^8*c^2*d^6 + 32*a*b^7*c*d^7) + 8*b^7*d^7*x)*(-b^3/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3))^(1/4)*1i - ((-b^3/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3))^(1/4)*((-b^3/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3))^(3/4)*((-b^3/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3))^(1/4)*(4096*a*b^11*c^8*d^4 + 4096*a^8*b^4*c*d^11 - 20480*a^2*b^10*c^7*d^5 + 36864*a^3*b^9*c^6*d^6 - 20480*a^4*b^8*c^5*d^7 - 20480*a^5*b^7*c^4*d^8 + 36864*a^6*b^6*c^3*d^9 - 20480*a^7*b^5*c^2*d^10) - x*(1024*a^7*b^4*d^11 + 1024*b^11*c^7*d^4 - 4096*a*b^10*c^6*d^5 - 4096*a^6*b^5*c*d^10 + 6144*a^2*b^9*c^5*d^6 - 3072*a^3*b^8*c^4*d^7 - 3072*a^4*b^7*c^3*d^8 + 6144*a^5*b^6*c^2*d^9)) - 16*a^2*b^6*d^8 - 16*b^8*c^2*d^6 + 32*a*b^7*c*d^7) - 8*b^7*d^7*x)*(-b^3/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3))^(1/4)*1i)/(((-b^3/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3))^(1/4)*((-b^3/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3))^(3/4)*((-b^3/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3))^(1/4)*(4096*a*b^11*c^8*d^4 + 4096*a^8*b^4*c*d^11 - 20480*a^2*b^10*c^7*d^5 + 36864*a^3*b^9*c^6*d^6 - 20480*a^4*b^8*c^5*d^7 - 20480*a^5*b^7*c^4*d^8 + 36864*a^6*b^6*c^3*d^9 - 20480*a^7*b^5*c^2*d^10) + x*(1024*a^7*b^4*d^11 + 1024*b^11*c^7*d^4 - 4096*a*b^10*c^6*d^5 - 4096*a^6*b^5*c*d^10 + 6144*a^2*b^9*c^5*d^6 - 3072*a^3*b^8*c^4*d^7 - 3072*a^4*b^7*c^3*d^8 + 6144*a^5*b^6*c^2*d^9)) - 16*a^2*b^6*d^8 - 16*b^8*c^2*d^6 + 32*a*b^7*c*d^7) + 8*b^7*d^7*x)*(-b^3/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3))^(1/4) + ((-b^3/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3))^(1/4)*((-b^3/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3))^(3/4)*((-b^3/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3))^(1/4)*(4096*a*b^11*c^8*d^4 + 4096*a^8*b^4*c*d^11 - 20480*a^2*b^10*c^7*d^5 + 36864*a^3*b^9*c^6*d^6 - 20480*a^4*b^8*c^5*d^7 - 20480*a^5*b^7*c^4*d^8 + 36864*a^6*b^6*c^3*d^9 - 20480*a^7*b^5*c^2*d^10) - x*(1024*a^7*b^4*d^11 + 1024*b^11*c^7*d^4 - 4096*a*b^10*c^6*d^5 - 4096*a^6*b^5*c*d^10 + 6144*a^2*b^9*c^5*d^6 - 3072*a^3*b^8*c^4*d^7 - 3072*a^4*b^7*c^3*d^8 + 6144*a^5*b^6*c^2*d^9)) - 16*a^2*b^6*d^8 - 16*b^8*c^2*d^6 + 32*a*b^7*c*d^7) - 8*b^7*d^7*x)*(-b^3/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3))^(1/4)))*(-b^3/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3))^(1/4)*2i - 2*atan((b^3*d^3*x - (128*b^10*c^7*x)/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3) - (128*a^7*b^3*d^7*x)/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3) - (768*a^2*b^8*c^5*d^2*x)/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3) + (384*a^3*b^7*c^4*d^3*x)/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3) + (384*a^4*b^6*c^3*d^4*x)/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3) - (768*a^5*b^5*c^2*d^5*x)/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3) + (512*a*b^9*c^6*d*x)/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3) + (512*a^6*b^4*c*d^6*x)/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3))/((-b^3/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3))^(1/4)*((b^3*(512*a*b^7*c^8 + 512*a^8*c*d^7 - 2560*a^2*b^6*c^7*d - 2560*a^7*b*c^2*d^6 + 4608*a^3*b^5*c^6*d^2 - 2560*a^4*b^4*c^5*d^3 - 2560*a^5*b^3*c^4*d^4 + 4608*a^6*b^2*c^3*d^5))/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3) + 2*a^2*b^2*d^4 + 2*b^4*c^2*d^2 - 4*a*b^3*c*d^3)))*(-b^3/(256*a^7*d^4 + 256*a^3*b^4*c^4 - 1024*a^4*b^3*c^3*d + 1536*a^5*b^2*c^2*d^2 - 1024*a^6*b*c*d^3))^(1/4) - 2*atan((b^3*d^3*x - (128*a^7*d^10*x)/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d) - (128*b^7*c^7*d^3*x)/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d) - (768*a^2*b^5*c^5*d^5*x)/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d) + (384*a^3*b^4*c^4*d^6*x)/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d) + (384*a^4*b^3*c^3*d^7*x)/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d) - (768*a^5*b^2*c^2*d^8*x)/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d) + (512*a^6*b*c*d^9*x)/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d) + (512*a*b^6*c^6*d^4*x)/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d))/((-d^3/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d))^(1/4)*((d^3*(512*a*b^7*c^8 + 512*a^8*c*d^7 - 2560*a^2*b^6*c^7*d - 2560*a^7*b*c^2*d^6 + 4608*a^3*b^5*c^6*d^2 - 2560*a^4*b^4*c^5*d^3 - 2560*a^5*b^3*c^4*d^4 + 4608*a^6*b^2*c^3*d^5))/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d) + 2*a^2*b^2*d^4 + 2*b^4*c^2*d^2 - 4*a*b^3*c*d^3)))*(-d^3/(256*b^4*c^7 + 256*a^4*c^3*d^4 - 1024*a^3*b*c^4*d^3 + 1536*a^2*b^2*c^5*d^2 - 1024*a*b^3*c^6*d))^(1/4)","B"
784,1,5962,460,6.083975,"\text{Not used}","int(1/(x^2*(a + b*x^4)*(c + d*x^4)),x)","2\,\mathrm{atan}\left(\frac{{\left(-\frac{d^5}{256\,a^4\,c^5\,d^4-1024\,a^3\,b\,c^6\,d^3+1536\,a^2\,b^2\,c^7\,d^2-1024\,a\,b^3\,c^8\,d+256\,b^4\,c^9}\right)}^{1/4}\,\left(x\,\left(4\,a^{12}\,b^8\,c^{11}\,d^9+4\,a^{11}\,b^9\,c^{12}\,d^8\right)-{\left(-\frac{d^5}{256\,a^4\,c^5\,d^4-1024\,a^3\,b\,c^6\,d^3+1536\,a^2\,b^2\,c^7\,d^2-1024\,a\,b^3\,c^8\,d+256\,b^4\,c^9}\right)}^{3/4}\,\left(768\,a^{12}\,b^{11}\,c^{18}\,d^5-256\,a^{11}\,b^{12}\,c^{19}\,d^4-768\,a^{13}\,b^{10}\,c^{17}\,d^6+256\,a^{14}\,b^9\,c^{16}\,d^7+256\,a^{16}\,b^7\,c^{14}\,d^9-768\,a^{17}\,b^6\,c^{13}\,d^{10}+768\,a^{18}\,b^5\,c^{12}\,d^{11}-256\,a^{19}\,b^4\,c^{11}\,d^{12}+x\,{\left(-\frac{d^5}{256\,a^4\,c^5\,d^4-1024\,a^3\,b\,c^6\,d^3+1536\,a^2\,b^2\,c^7\,d^2-1024\,a\,b^3\,c^8\,d+256\,b^4\,c^9}\right)}^{1/4}\,\left(1024\,a^{20}\,b^4\,c^{12}\,d^{12}-4096\,a^{19}\,b^5\,c^{13}\,d^{11}+6144\,a^{18}\,b^6\,c^{14}\,d^{10}-4096\,a^{17}\,b^7\,c^{15}\,d^9+2048\,a^{16}\,b^8\,c^{16}\,d^8-4096\,a^{15}\,b^9\,c^{17}\,d^7+6144\,a^{14}\,b^{10}\,c^{18}\,d^6-4096\,a^{13}\,b^{11}\,c^{19}\,d^5+1024\,a^{12}\,b^{12}\,c^{20}\,d^4\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)+{\left(-\frac{d^5}{256\,a^4\,c^5\,d^4-1024\,a^3\,b\,c^6\,d^3+1536\,a^2\,b^2\,c^7\,d^2-1024\,a\,b^3\,c^8\,d+256\,b^4\,c^9}\right)}^{1/4}\,\left(x\,\left(4\,a^{12}\,b^8\,c^{11}\,d^9+4\,a^{11}\,b^9\,c^{12}\,d^8\right)-{\left(-\frac{d^5}{256\,a^4\,c^5\,d^4-1024\,a^3\,b\,c^6\,d^3+1536\,a^2\,b^2\,c^7\,d^2-1024\,a\,b^3\,c^8\,d+256\,b^4\,c^9}\right)}^{3/4}\,\left(256\,a^{11}\,b^{12}\,c^{19}\,d^4-768\,a^{12}\,b^{11}\,c^{18}\,d^5+768\,a^{13}\,b^{10}\,c^{17}\,d^6-256\,a^{14}\,b^9\,c^{16}\,d^7-256\,a^{16}\,b^7\,c^{14}\,d^9+768\,a^{17}\,b^6\,c^{13}\,d^{10}-768\,a^{18}\,b^5\,c^{12}\,d^{11}+256\,a^{19}\,b^4\,c^{11}\,d^{12}+x\,{\left(-\frac{d^5}{256\,a^4\,c^5\,d^4-1024\,a^3\,b\,c^6\,d^3+1536\,a^2\,b^2\,c^7\,d^2-1024\,a\,b^3\,c^8\,d+256\,b^4\,c^9}\right)}^{1/4}\,\left(1024\,a^{20}\,b^4\,c^{12}\,d^{12}-4096\,a^{19}\,b^5\,c^{13}\,d^{11}+6144\,a^{18}\,b^6\,c^{14}\,d^{10}-4096\,a^{17}\,b^7\,c^{15}\,d^9+2048\,a^{16}\,b^8\,c^{16}\,d^8-4096\,a^{15}\,b^9\,c^{17}\,d^7+6144\,a^{14}\,b^{10}\,c^{18}\,d^6-4096\,a^{13}\,b^{11}\,c^{19}\,d^5+1024\,a^{12}\,b^{12}\,c^{20}\,d^4\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)}{{\left(-\frac{d^5}{256\,a^4\,c^5\,d^4-1024\,a^3\,b\,c^6\,d^3+1536\,a^2\,b^2\,c^7\,d^2-1024\,a\,b^3\,c^8\,d+256\,b^4\,c^9}\right)}^{1/4}\,\left(x\,\left(4\,a^{12}\,b^8\,c^{11}\,d^9+4\,a^{11}\,b^9\,c^{12}\,d^8\right)-{\left(-\frac{d^5}{256\,a^4\,c^5\,d^4-1024\,a^3\,b\,c^6\,d^3+1536\,a^2\,b^2\,c^7\,d^2-1024\,a\,b^3\,c^8\,d+256\,b^4\,c^9}\right)}^{3/4}\,\left(768\,a^{12}\,b^{11}\,c^{18}\,d^5-256\,a^{11}\,b^{12}\,c^{19}\,d^4-768\,a^{13}\,b^{10}\,c^{17}\,d^6+256\,a^{14}\,b^9\,c^{16}\,d^7+256\,a^{16}\,b^7\,c^{14}\,d^9-768\,a^{17}\,b^6\,c^{13}\,d^{10}+768\,a^{18}\,b^5\,c^{12}\,d^{11}-256\,a^{19}\,b^4\,c^{11}\,d^{12}+x\,{\left(-\frac{d^5}{256\,a^4\,c^5\,d^4-1024\,a^3\,b\,c^6\,d^3+1536\,a^2\,b^2\,c^7\,d^2-1024\,a\,b^3\,c^8\,d+256\,b^4\,c^9}\right)}^{1/4}\,\left(1024\,a^{20}\,b^4\,c^{12}\,d^{12}-4096\,a^{19}\,b^5\,c^{13}\,d^{11}+6144\,a^{18}\,b^6\,c^{14}\,d^{10}-4096\,a^{17}\,b^7\,c^{15}\,d^9+2048\,a^{16}\,b^8\,c^{16}\,d^8-4096\,a^{15}\,b^9\,c^{17}\,d^7+6144\,a^{14}\,b^{10}\,c^{18}\,d^6-4096\,a^{13}\,b^{11}\,c^{19}\,d^5+1024\,a^{12}\,b^{12}\,c^{20}\,d^4\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}-{\left(-\frac{d^5}{256\,a^4\,c^5\,d^4-1024\,a^3\,b\,c^6\,d^3+1536\,a^2\,b^2\,c^7\,d^2-1024\,a\,b^3\,c^8\,d+256\,b^4\,c^9}\right)}^{1/4}\,\left(x\,\left(4\,a^{12}\,b^8\,c^{11}\,d^9+4\,a^{11}\,b^9\,c^{12}\,d^8\right)-{\left(-\frac{d^5}{256\,a^4\,c^5\,d^4-1024\,a^3\,b\,c^6\,d^3+1536\,a^2\,b^2\,c^7\,d^2-1024\,a\,b^3\,c^8\,d+256\,b^4\,c^9}\right)}^{3/4}\,\left(256\,a^{11}\,b^{12}\,c^{19}\,d^4-768\,a^{12}\,b^{11}\,c^{18}\,d^5+768\,a^{13}\,b^{10}\,c^{17}\,d^6-256\,a^{14}\,b^9\,c^{16}\,d^7-256\,a^{16}\,b^7\,c^{14}\,d^9+768\,a^{17}\,b^6\,c^{13}\,d^{10}-768\,a^{18}\,b^5\,c^{12}\,d^{11}+256\,a^{19}\,b^4\,c^{11}\,d^{12}+x\,{\left(-\frac{d^5}{256\,a^4\,c^5\,d^4-1024\,a^3\,b\,c^6\,d^3+1536\,a^2\,b^2\,c^7\,d^2-1024\,a\,b^3\,c^8\,d+256\,b^4\,c^9}\right)}^{1/4}\,\left(1024\,a^{20}\,b^4\,c^{12}\,d^{12}-4096\,a^{19}\,b^5\,c^{13}\,d^{11}+6144\,a^{18}\,b^6\,c^{14}\,d^{10}-4096\,a^{17}\,b^7\,c^{15}\,d^9+2048\,a^{16}\,b^8\,c^{16}\,d^8-4096\,a^{15}\,b^9\,c^{17}\,d^7+6144\,a^{14}\,b^{10}\,c^{18}\,d^6-4096\,a^{13}\,b^{11}\,c^{19}\,d^5+1024\,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}{256\,a^4\,c^5\,d^4-1024\,a^3\,b\,c^6\,d^3+1536\,a^2\,b^2\,c^7\,d^2-1024\,a\,b^3\,c^8\,d+256\,b^4\,c^9}\right)}^{1/4}+2\,\mathrm{atan}\left(\frac{{\left(-\frac{b^5}{256\,a^9\,d^4-1024\,a^8\,b\,c\,d^3+1536\,a^7\,b^2\,c^2\,d^2-1024\,a^6\,b^3\,c^3\,d+256\,a^5\,b^4\,c^4}\right)}^{1/4}\,\left(x\,\left(4\,a^{12}\,b^8\,c^{11}\,d^9+4\,a^{11}\,b^9\,c^{12}\,d^8\right)-{\left(-\frac{b^5}{256\,a^9\,d^4-1024\,a^8\,b\,c\,d^3+1536\,a^7\,b^2\,c^2\,d^2-1024\,a^6\,b^3\,c^3\,d+256\,a^5\,b^4\,c^4}\right)}^{3/4}\,\left(768\,a^{12}\,b^{11}\,c^{18}\,d^5-256\,a^{11}\,b^{12}\,c^{19}\,d^4-768\,a^{13}\,b^{10}\,c^{17}\,d^6+256\,a^{14}\,b^9\,c^{16}\,d^7+256\,a^{16}\,b^7\,c^{14}\,d^9-768\,a^{17}\,b^6\,c^{13}\,d^{10}+768\,a^{18}\,b^5\,c^{12}\,d^{11}-256\,a^{19}\,b^4\,c^{11}\,d^{12}+x\,{\left(-\frac{b^5}{256\,a^9\,d^4-1024\,a^8\,b\,c\,d^3+1536\,a^7\,b^2\,c^2\,d^2-1024\,a^6\,b^3\,c^3\,d+256\,a^5\,b^4\,c^4}\right)}^{1/4}\,\left(1024\,a^{20}\,b^4\,c^{12}\,d^{12}-4096\,a^{19}\,b^5\,c^{13}\,d^{11}+6144\,a^{18}\,b^6\,c^{14}\,d^{10}-4096\,a^{17}\,b^7\,c^{15}\,d^9+2048\,a^{16}\,b^8\,c^{16}\,d^8-4096\,a^{15}\,b^9\,c^{17}\,d^7+6144\,a^{14}\,b^{10}\,c^{18}\,d^6-4096\,a^{13}\,b^{11}\,c^{19}\,d^5+1024\,a^{12}\,b^{12}\,c^{20}\,d^4\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)+{\left(-\frac{b^5}{256\,a^9\,d^4-1024\,a^8\,b\,c\,d^3+1536\,a^7\,b^2\,c^2\,d^2-1024\,a^6\,b^3\,c^3\,d+256\,a^5\,b^4\,c^4}\right)}^{1/4}\,\left(x\,\left(4\,a^{12}\,b^8\,c^{11}\,d^9+4\,a^{11}\,b^9\,c^{12}\,d^8\right)-{\left(-\frac{b^5}{256\,a^9\,d^4-1024\,a^8\,b\,c\,d^3+1536\,a^7\,b^2\,c^2\,d^2-1024\,a^6\,b^3\,c^3\,d+256\,a^5\,b^4\,c^4}\right)}^{3/4}\,\left(256\,a^{11}\,b^{12}\,c^{19}\,d^4-768\,a^{12}\,b^{11}\,c^{18}\,d^5+768\,a^{13}\,b^{10}\,c^{17}\,d^6-256\,a^{14}\,b^9\,c^{16}\,d^7-256\,a^{16}\,b^7\,c^{14}\,d^9+768\,a^{17}\,b^6\,c^{13}\,d^{10}-768\,a^{18}\,b^5\,c^{12}\,d^{11}+256\,a^{19}\,b^4\,c^{11}\,d^{12}+x\,{\left(-\frac{b^5}{256\,a^9\,d^4-1024\,a^8\,b\,c\,d^3+1536\,a^7\,b^2\,c^2\,d^2-1024\,a^6\,b^3\,c^3\,d+256\,a^5\,b^4\,c^4}\right)}^{1/4}\,\left(1024\,a^{20}\,b^4\,c^{12}\,d^{12}-4096\,a^{19}\,b^5\,c^{13}\,d^{11}+6144\,a^{18}\,b^6\,c^{14}\,d^{10}-4096\,a^{17}\,b^7\,c^{15}\,d^9+2048\,a^{16}\,b^8\,c^{16}\,d^8-4096\,a^{15}\,b^9\,c^{17}\,d^7+6144\,a^{14}\,b^{10}\,c^{18}\,d^6-4096\,a^{13}\,b^{11}\,c^{19}\,d^5+1024\,a^{12}\,b^{12}\,c^{20}\,d^4\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)}{{\left(-\frac{b^5}{256\,a^9\,d^4-1024\,a^8\,b\,c\,d^3+1536\,a^7\,b^2\,c^2\,d^2-1024\,a^6\,b^3\,c^3\,d+256\,a^5\,b^4\,c^4}\right)}^{1/4}\,\left(x\,\left(4\,a^{12}\,b^8\,c^{11}\,d^9+4\,a^{11}\,b^9\,c^{12}\,d^8\right)-{\left(-\frac{b^5}{256\,a^9\,d^4-1024\,a^8\,b\,c\,d^3+1536\,a^7\,b^2\,c^2\,d^2-1024\,a^6\,b^3\,c^3\,d+256\,a^5\,b^4\,c^4}\right)}^{3/4}\,\left(768\,a^{12}\,b^{11}\,c^{18}\,d^5-256\,a^{11}\,b^{12}\,c^{19}\,d^4-768\,a^{13}\,b^{10}\,c^{17}\,d^6+256\,a^{14}\,b^9\,c^{16}\,d^7+256\,a^{16}\,b^7\,c^{14}\,d^9-768\,a^{17}\,b^6\,c^{13}\,d^{10}+768\,a^{18}\,b^5\,c^{12}\,d^{11}-256\,a^{19}\,b^4\,c^{11}\,d^{12}+x\,{\left(-\frac{b^5}{256\,a^9\,d^4-1024\,a^8\,b\,c\,d^3+1536\,a^7\,b^2\,c^2\,d^2-1024\,a^6\,b^3\,c^3\,d+256\,a^5\,b^4\,c^4}\right)}^{1/4}\,\left(1024\,a^{20}\,b^4\,c^{12}\,d^{12}-4096\,a^{19}\,b^5\,c^{13}\,d^{11}+6144\,a^{18}\,b^6\,c^{14}\,d^{10}-4096\,a^{17}\,b^7\,c^{15}\,d^9+2048\,a^{16}\,b^8\,c^{16}\,d^8-4096\,a^{15}\,b^9\,c^{17}\,d^7+6144\,a^{14}\,b^{10}\,c^{18}\,d^6-4096\,a^{13}\,b^{11}\,c^{19}\,d^5+1024\,a^{12}\,b^{12}\,c^{20}\,d^4\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}-{\left(-\frac{b^5}{256\,a^9\,d^4-1024\,a^8\,b\,c\,d^3+1536\,a^7\,b^2\,c^2\,d^2-1024\,a^6\,b^3\,c^3\,d+256\,a^5\,b^4\,c^4}\right)}^{1/4}\,\left(x\,\left(4\,a^{12}\,b^8\,c^{11}\,d^9+4\,a^{11}\,b^9\,c^{12}\,d^8\right)-{\left(-\frac{b^5}{256\,a^9\,d^4-1024\,a^8\,b\,c\,d^3+1536\,a^7\,b^2\,c^2\,d^2-1024\,a^6\,b^3\,c^3\,d+256\,a^5\,b^4\,c^4}\right)}^{3/4}\,\left(256\,a^{11}\,b^{12}\,c^{19}\,d^4-768\,a^{12}\,b^{11}\,c^{18}\,d^5+768\,a^{13}\,b^{10}\,c^{17}\,d^6-256\,a^{14}\,b^9\,c^{16}\,d^7-256\,a^{16}\,b^7\,c^{14}\,d^9+768\,a^{17}\,b^6\,c^{13}\,d^{10}-768\,a^{18}\,b^5\,c^{12}\,d^{11}+256\,a^{19}\,b^4\,c^{11}\,d^{12}+x\,{\left(-\frac{b^5}{256\,a^9\,d^4-1024\,a^8\,b\,c\,d^3+1536\,a^7\,b^2\,c^2\,d^2-1024\,a^6\,b^3\,c^3\,d+256\,a^5\,b^4\,c^4}\right)}^{1/4}\,\left(1024\,a^{20}\,b^4\,c^{12}\,d^{12}-4096\,a^{19}\,b^5\,c^{13}\,d^{11}+6144\,a^{18}\,b^6\,c^{14}\,d^{10}-4096\,a^{17}\,b^7\,c^{15}\,d^9+2048\,a^{16}\,b^8\,c^{16}\,d^8-4096\,a^{15}\,b^9\,c^{17}\,d^7+6144\,a^{14}\,b^{10}\,c^{18}\,d^6-4096\,a^{13}\,b^{11}\,c^{19}\,d^5+1024\,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}{256\,a^9\,d^4-1024\,a^8\,b\,c\,d^3+1536\,a^7\,b^2\,c^2\,d^2-1024\,a^6\,b^3\,c^3\,d+256\,a^5\,b^4\,c^4}\right)}^{1/4}-\frac{1}{a\,c\,x}+\mathrm{atan}\left(\frac{a^{14}\,c\,d^8\,x\,{\left(-\frac{b^5}{256\,a^9\,d^4-1024\,a^8\,b\,c\,d^3+1536\,a^7\,b^2\,c^2\,d^2-1024\,a^6\,b^3\,c^3\,d+256\,a^5\,b^4\,c^4}\right)}^{5/4}\,1024{}\mathrm{i}+a^6\,b^8\,c^9\,x\,{\left(-\frac{b^5}{256\,a^9\,d^4-1024\,a^8\,b\,c\,d^3+1536\,a^7\,b^2\,c^2\,d^2-1024\,a^6\,b^3\,c^3\,d+256\,a^5\,b^4\,c^4}\right)}^{5/4}\,1024{}\mathrm{i}+a^6\,b^4\,d^5\,x\,{\left(-\frac{b^5}{256\,a^9\,d^4-1024\,a^8\,b\,c\,d^3+1536\,a^7\,b^2\,c^2\,d^2-1024\,a^6\,b^3\,c^3\,d+256\,a^5\,b^4\,c^4}\right)}^{1/4}\,4{}\mathrm{i}+a^5\,b^5\,c\,d^4\,x\,{\left(-\frac{b^5}{256\,a^9\,d^4-1024\,a^8\,b\,c\,d^3+1536\,a^7\,b^2\,c^2\,d^2-1024\,a^6\,b^3\,c^3\,d+256\,a^5\,b^4\,c^4}\right)}^{1/4}\,4{}\mathrm{i}-a^7\,b^7\,c^8\,d\,x\,{\left(-\frac{b^5}{256\,a^9\,d^4-1024\,a^8\,b\,c\,d^3+1536\,a^7\,b^2\,c^2\,d^2-1024\,a^6\,b^3\,c^3\,d+256\,a^5\,b^4\,c^4}\right)}^{5/4}\,4096{}\mathrm{i}-a^{13}\,b\,c^2\,d^7\,x\,{\left(-\frac{b^5}{256\,a^9\,d^4-1024\,a^8\,b\,c\,d^3+1536\,a^7\,b^2\,c^2\,d^2-1024\,a^6\,b^3\,c^3\,d+256\,a^5\,b^4\,c^4}\right)}^{5/4}\,4096{}\mathrm{i}+a^8\,b^6\,c^7\,d^2\,x\,{\left(-\frac{b^5}{256\,a^9\,d^4-1024\,a^8\,b\,c\,d^3+1536\,a^7\,b^2\,c^2\,d^2-1024\,a^6\,b^3\,c^3\,d+256\,a^5\,b^4\,c^4}\right)}^{5/4}\,6144{}\mathrm{i}-a^9\,b^5\,c^6\,d^3\,x\,{\left(-\frac{b^5}{256\,a^9\,d^4-1024\,a^8\,b\,c\,d^3+1536\,a^7\,b^2\,c^2\,d^2-1024\,a^6\,b^3\,c^3\,d+256\,a^5\,b^4\,c^4}\right)}^{5/4}\,4096{}\mathrm{i}+a^{10}\,b^4\,c^5\,d^4\,x\,{\left(-\frac{b^5}{256\,a^9\,d^4-1024\,a^8\,b\,c\,d^3+1536\,a^7\,b^2\,c^2\,d^2-1024\,a^6\,b^3\,c^3\,d+256\,a^5\,b^4\,c^4}\right)}^{5/4}\,2048{}\mathrm{i}-a^{11}\,b^3\,c^4\,d^5\,x\,{\left(-\frac{b^5}{256\,a^9\,d^4-1024\,a^8\,b\,c\,d^3+1536\,a^7\,b^2\,c^2\,d^2-1024\,a^6\,b^3\,c^3\,d+256\,a^5\,b^4\,c^4}\right)}^{5/4}\,4096{}\mathrm{i}+a^{12}\,b^2\,c^3\,d^6\,x\,{\left(-\frac{b^5}{256\,a^9\,d^4-1024\,a^8\,b\,c\,d^3+1536\,a^7\,b^2\,c^2\,d^2-1024\,a^6\,b^3\,c^3\,d+256\,a^5\,b^4\,c^4}\right)}^{5/4}\,6144{}\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}{256\,a^9\,d^4-1024\,a^8\,b\,c\,d^3+1536\,a^7\,b^2\,c^2\,d^2-1024\,a^6\,b^3\,c^3\,d+256\,a^5\,b^4\,c^4}\right)}^{1/4}\,2{}\mathrm{i}+\mathrm{atan}\left(\frac{b^5\,c^6\,d^4\,x\,{\left(-\frac{d^5}{256\,a^4\,c^5\,d^4-1024\,a^3\,b\,c^6\,d^3+1536\,a^2\,b^2\,c^7\,d^2-1024\,a\,b^3\,c^8\,d+256\,b^4\,c^9}\right)}^{1/4}\,4{}\mathrm{i}+a\,b^8\,c^{14}\,x\,{\left(-\frac{d^5}{256\,a^4\,c^5\,d^4-1024\,a^3\,b\,c^6\,d^3+1536\,a^2\,b^2\,c^7\,d^2-1024\,a\,b^3\,c^8\,d+256\,b^4\,c^9}\right)}^{5/4}\,1024{}\mathrm{i}+a^9\,c^6\,d^8\,x\,{\left(-\frac{d^5}{256\,a^4\,c^5\,d^4-1024\,a^3\,b\,c^6\,d^3+1536\,a^2\,b^2\,c^7\,d^2-1024\,a\,b^3\,c^8\,d+256\,b^4\,c^9}\right)}^{5/4}\,1024{}\mathrm{i}+a\,b^4\,c^5\,d^5\,x\,{\left(-\frac{d^5}{256\,a^4\,c^5\,d^4-1024\,a^3\,b\,c^6\,d^3+1536\,a^2\,b^2\,c^7\,d^2-1024\,a\,b^3\,c^8\,d+256\,b^4\,c^9}\right)}^{1/4}\,4{}\mathrm{i}-a^2\,b^7\,c^{13}\,d\,x\,{\left(-\frac{d^5}{256\,a^4\,c^5\,d^4-1024\,a^3\,b\,c^6\,d^3+1536\,a^2\,b^2\,c^7\,d^2-1024\,a\,b^3\,c^8\,d+256\,b^4\,c^9}\right)}^{5/4}\,4096{}\mathrm{i}-a^8\,b\,c^7\,d^7\,x\,{\left(-\frac{d^5}{256\,a^4\,c^5\,d^4-1024\,a^3\,b\,c^6\,d^3+1536\,a^2\,b^2\,c^7\,d^2-1024\,a\,b^3\,c^8\,d+256\,b^4\,c^9}\right)}^{5/4}\,4096{}\mathrm{i}+a^3\,b^6\,c^{12}\,d^2\,x\,{\left(-\frac{d^5}{256\,a^4\,c^5\,d^4-1024\,a^3\,b\,c^6\,d^3+1536\,a^2\,b^2\,c^7\,d^2-1024\,a\,b^3\,c^8\,d+256\,b^4\,c^9}\right)}^{5/4}\,6144{}\mathrm{i}-a^4\,b^5\,c^{11}\,d^3\,x\,{\left(-\frac{d^5}{256\,a^4\,c^5\,d^4-1024\,a^3\,b\,c^6\,d^3+1536\,a^2\,b^2\,c^7\,d^2-1024\,a\,b^3\,c^8\,d+256\,b^4\,c^9}\right)}^{5/4}\,4096{}\mathrm{i}+a^5\,b^4\,c^{10}\,d^4\,x\,{\left(-\frac{d^5}{256\,a^4\,c^5\,d^4-1024\,a^3\,b\,c^6\,d^3+1536\,a^2\,b^2\,c^7\,d^2-1024\,a\,b^3\,c^8\,d+256\,b^4\,c^9}\right)}^{5/4}\,2048{}\mathrm{i}-a^6\,b^3\,c^9\,d^5\,x\,{\left(-\frac{d^5}{256\,a^4\,c^5\,d^4-1024\,a^3\,b\,c^6\,d^3+1536\,a^2\,b^2\,c^7\,d^2-1024\,a\,b^3\,c^8\,d+256\,b^4\,c^9}\right)}^{5/4}\,4096{}\mathrm{i}+a^7\,b^2\,c^8\,d^6\,x\,{\left(-\frac{d^5}{256\,a^4\,c^5\,d^4-1024\,a^3\,b\,c^6\,d^3+1536\,a^2\,b^2\,c^7\,d^2-1024\,a\,b^3\,c^8\,d+256\,b^4\,c^9}\right)}^{5/4}\,6144{}\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}{256\,a^4\,c^5\,d^4-1024\,a^3\,b\,c^6\,d^3+1536\,a^2\,b^2\,c^7\,d^2-1024\,a\,b^3\,c^8\,d+256\,b^4\,c^9}\right)}^{1/4}\,2{}\mathrm{i}","Not used",1,"2*atan(((-d^5/(256*b^4*c^9 + 256*a^4*c^5*d^4 - 1024*a^3*b*c^6*d^3 + 1536*a^2*b^2*c^7*d^2 - 1024*a*b^3*c^8*d))^(1/4)*(x*(4*a^11*b^9*c^12*d^8 + 4*a^12*b^8*c^11*d^9) - (-d^5/(256*b^4*c^9 + 256*a^4*c^5*d^4 - 1024*a^3*b*c^6*d^3 + 1536*a^2*b^2*c^7*d^2 - 1024*a*b^3*c^8*d))^(3/4)*(x*(-d^5/(256*b^4*c^9 + 256*a^4*c^5*d^4 - 1024*a^3*b*c^6*d^3 + 1536*a^2*b^2*c^7*d^2 - 1024*a*b^3*c^8*d))^(1/4)*(1024*a^12*b^12*c^20*d^4 - 4096*a^13*b^11*c^19*d^5 + 6144*a^14*b^10*c^18*d^6 - 4096*a^15*b^9*c^17*d^7 + 2048*a^16*b^8*c^16*d^8 - 4096*a^17*b^7*c^15*d^9 + 6144*a^18*b^6*c^14*d^10 - 4096*a^19*b^5*c^13*d^11 + 1024*a^20*b^4*c^12*d^12)*1i - 256*a^11*b^12*c^19*d^4 + 768*a^12*b^11*c^18*d^5 - 768*a^13*b^10*c^17*d^6 + 256*a^14*b^9*c^16*d^7 + 256*a^16*b^7*c^14*d^9 - 768*a^17*b^6*c^13*d^10 + 768*a^18*b^5*c^12*d^11 - 256*a^19*b^4*c^11*d^12)*1i) + (-d^5/(256*b^4*c^9 + 256*a^4*c^5*d^4 - 1024*a^3*b*c^6*d^3 + 1536*a^2*b^2*c^7*d^2 - 1024*a*b^3*c^8*d))^(1/4)*(x*(4*a^11*b^9*c^12*d^8 + 4*a^12*b^8*c^11*d^9) - (-d^5/(256*b^4*c^9 + 256*a^4*c^5*d^4 - 1024*a^3*b*c^6*d^3 + 1536*a^2*b^2*c^7*d^2 - 1024*a*b^3*c^8*d))^(3/4)*(x*(-d^5/(256*b^4*c^9 + 256*a^4*c^5*d^4 - 1024*a^3*b*c^6*d^3 + 1536*a^2*b^2*c^7*d^2 - 1024*a*b^3*c^8*d))^(1/4)*(1024*a^12*b^12*c^20*d^4 - 4096*a^13*b^11*c^19*d^5 + 6144*a^14*b^10*c^18*d^6 - 4096*a^15*b^9*c^17*d^7 + 2048*a^16*b^8*c^16*d^8 - 4096*a^17*b^7*c^15*d^9 + 6144*a^18*b^6*c^14*d^10 - 4096*a^19*b^5*c^13*d^11 + 1024*a^20*b^4*c^12*d^12)*1i + 256*a^11*b^12*c^19*d^4 - 768*a^12*b^11*c^18*d^5 + 768*a^13*b^10*c^17*d^6 - 256*a^14*b^9*c^16*d^7 - 256*a^16*b^7*c^14*d^9 + 768*a^17*b^6*c^13*d^10 - 768*a^18*b^5*c^12*d^11 + 256*a^19*b^4*c^11*d^12)*1i))/((-d^5/(256*b^4*c^9 + 256*a^4*c^5*d^4 - 1024*a^3*b*c^6*d^3 + 1536*a^2*b^2*c^7*d^2 - 1024*a*b^3*c^8*d))^(1/4)*(x*(4*a^11*b^9*c^12*d^8 + 4*a^12*b^8*c^11*d^9) - (-d^5/(256*b^4*c^9 + 256*a^4*c^5*d^4 - 1024*a^3*b*c^6*d^3 + 1536*a^2*b^2*c^7*d^2 - 1024*a*b^3*c^8*d))^(3/4)*(x*(-d^5/(256*b^4*c^9 + 256*a^4*c^5*d^4 - 1024*a^3*b*c^6*d^3 + 1536*a^2*b^2*c^7*d^2 - 1024*a*b^3*c^8*d))^(1/4)*(1024*a^12*b^12*c^20*d^4 - 4096*a^13*b^11*c^19*d^5 + 6144*a^14*b^10*c^18*d^6 - 4096*a^15*b^9*c^17*d^7 + 2048*a^16*b^8*c^16*d^8 - 4096*a^17*b^7*c^15*d^9 + 6144*a^18*b^6*c^14*d^10 - 4096*a^19*b^5*c^13*d^11 + 1024*a^20*b^4*c^12*d^12)*1i - 256*a^11*b^12*c^19*d^4 + 768*a^12*b^11*c^18*d^5 - 768*a^13*b^10*c^17*d^6 + 256*a^14*b^9*c^16*d^7 + 256*a^16*b^7*c^14*d^9 - 768*a^17*b^6*c^13*d^10 + 768*a^18*b^5*c^12*d^11 - 256*a^19*b^4*c^11*d^12)*1i)*1i - (-d^5/(256*b^4*c^9 + 256*a^4*c^5*d^4 - 1024*a^3*b*c^6*d^3 + 1536*a^2*b^2*c^7*d^2 - 1024*a*b^3*c^8*d))^(1/4)*(x*(4*a^11*b^9*c^12*d^8 + 4*a^12*b^8*c^11*d^9) - (-d^5/(256*b^4*c^9 + 256*a^4*c^5*d^4 - 1024*a^3*b*c^6*d^3 + 1536*a^2*b^2*c^7*d^2 - 1024*a*b^3*c^8*d))^(3/4)*(x*(-d^5/(256*b^4*c^9 + 256*a^4*c^5*d^4 - 1024*a^3*b*c^6*d^3 + 1536*a^2*b^2*c^7*d^2 - 1024*a*b^3*c^8*d))^(1/4)*(1024*a^12*b^12*c^20*d^4 - 4096*a^13*b^11*c^19*d^5 + 6144*a^14*b^10*c^18*d^6 - 4096*a^15*b^9*c^17*d^7 + 2048*a^16*b^8*c^16*d^8 - 4096*a^17*b^7*c^15*d^9 + 6144*a^18*b^6*c^14*d^10 - 4096*a^19*b^5*c^13*d^11 + 1024*a^20*b^4*c^12*d^12)*1i + 256*a^11*b^12*c^19*d^4 - 768*a^12*b^11*c^18*d^5 + 768*a^13*b^10*c^17*d^6 - 256*a^14*b^9*c^16*d^7 - 256*a^16*b^7*c^14*d^9 + 768*a^17*b^6*c^13*d^10 - 768*a^18*b^5*c^12*d^11 + 256*a^19*b^4*c^11*d^12)*1i)*1i))*(-d^5/(256*b^4*c^9 + 256*a^4*c^5*d^4 - 1024*a^3*b*c^6*d^3 + 1536*a^2*b^2*c^7*d^2 - 1024*a*b^3*c^8*d))^(1/4) + atan((a^14*c*d^8*x*(-b^5/(256*a^9*d^4 + 256*a^5*b^4*c^4 - 1024*a^6*b^3*c^3*d + 1536*a^7*b^2*c^2*d^2 - 1024*a^8*b*c*d^3))^(5/4)*1024i + a^6*b^8*c^9*x*(-b^5/(256*a^9*d^4 + 256*a^5*b^4*c^4 - 1024*a^6*b^3*c^3*d + 1536*a^7*b^2*c^2*d^2 - 1024*a^8*b*c*d^3))^(5/4)*1024i + a^6*b^4*d^5*x*(-b^5/(256*a^9*d^4 + 256*a^5*b^4*c^4 - 1024*a^6*b^3*c^3*d + 1536*a^7*b^2*c^2*d^2 - 1024*a^8*b*c*d^3))^(1/4)*4i + a^5*b^5*c*d^4*x*(-b^5/(256*a^9*d^4 + 256*a^5*b^4*c^4 - 1024*a^6*b^3*c^3*d + 1536*a^7*b^2*c^2*d^2 - 1024*a^8*b*c*d^3))^(1/4)*4i - a^7*b^7*c^8*d*x*(-b^5/(256*a^9*d^4 + 256*a^5*b^4*c^4 - 1024*a^6*b^3*c^3*d + 1536*a^7*b^2*c^2*d^2 - 1024*a^8*b*c*d^3))^(5/4)*4096i - a^13*b*c^2*d^7*x*(-b^5/(256*a^9*d^4 + 256*a^5*b^4*c^4 - 1024*a^6*b^3*c^3*d + 1536*a^7*b^2*c^2*d^2 - 1024*a^8*b*c*d^3))^(5/4)*4096i + a^8*b^6*c^7*d^2*x*(-b^5/(256*a^9*d^4 + 256*a^5*b^4*c^4 - 1024*a^6*b^3*c^3*d + 1536*a^7*b^2*c^2*d^2 - 1024*a^8*b*c*d^3))^(5/4)*6144i - a^9*b^5*c^6*d^3*x*(-b^5/(256*a^9*d^4 + 256*a^5*b^4*c^4 - 1024*a^6*b^3*c^3*d + 1536*a^7*b^2*c^2*d^2 - 1024*a^8*b*c*d^3))^(5/4)*4096i + a^10*b^4*c^5*d^4*x*(-b^5/(256*a^9*d^4 + 256*a^5*b^4*c^4 - 1024*a^6*b^3*c^3*d + 1536*a^7*b^2*c^2*d^2 - 1024*a^8*b*c*d^3))^(5/4)*2048i - a^11*b^3*c^4*d^5*x*(-b^5/(256*a^9*d^4 + 256*a^5*b^4*c^4 - 1024*a^6*b^3*c^3*d + 1536*a^7*b^2*c^2*d^2 - 1024*a^8*b*c*d^3))^(5/4)*4096i + a^12*b^2*c^3*d^6*x*(-b^5/(256*a^9*d^4 + 256*a^5*b^4*c^4 - 1024*a^6*b^3*c^3*d + 1536*a^7*b^2*c^2*d^2 - 1024*a^8*b*c*d^3))^(5/4)*6144i)/(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/(256*a^9*d^4 + 256*a^5*b^4*c^4 - 1024*a^6*b^3*c^3*d + 1536*a^7*b^2*c^2*d^2 - 1024*a^8*b*c*d^3))^(1/4)*2i + atan((b^5*c^6*d^4*x*(-d^5/(256*b^4*c^9 + 256*a^4*c^5*d^4 - 1024*a^3*b*c^6*d^3 + 1536*a^2*b^2*c^7*d^2 - 1024*a*b^3*c^8*d))^(1/4)*4i + a*b^8*c^14*x*(-d^5/(256*b^4*c^9 + 256*a^4*c^5*d^4 - 1024*a^3*b*c^6*d^3 + 1536*a^2*b^2*c^7*d^2 - 1024*a*b^3*c^8*d))^(5/4)*1024i + a^9*c^6*d^8*x*(-d^5/(256*b^4*c^9 + 256*a^4*c^5*d^4 - 1024*a^3*b*c^6*d^3 + 1536*a^2*b^2*c^7*d^2 - 1024*a*b^3*c^8*d))^(5/4)*1024i + a*b^4*c^5*d^5*x*(-d^5/(256*b^4*c^9 + 256*a^4*c^5*d^4 - 1024*a^3*b*c^6*d^3 + 1536*a^2*b^2*c^7*d^2 - 1024*a*b^3*c^8*d))^(1/4)*4i - a^2*b^7*c^13*d*x*(-d^5/(256*b^4*c^9 + 256*a^4*c^5*d^4 - 1024*a^3*b*c^6*d^3 + 1536*a^2*b^2*c^7*d^2 - 1024*a*b^3*c^8*d))^(5/4)*4096i - a^8*b*c^7*d^7*x*(-d^5/(256*b^4*c^9 + 256*a^4*c^5*d^4 - 1024*a^3*b*c^6*d^3 + 1536*a^2*b^2*c^7*d^2 - 1024*a*b^3*c^8*d))^(5/4)*4096i + a^3*b^6*c^12*d^2*x*(-d^5/(256*b^4*c^9 + 256*a^4*c^5*d^4 - 1024*a^3*b*c^6*d^3 + 1536*a^2*b^2*c^7*d^2 - 1024*a*b^3*c^8*d))^(5/4)*6144i - a^4*b^5*c^11*d^3*x*(-d^5/(256*b^4*c^9 + 256*a^4*c^5*d^4 - 1024*a^3*b*c^6*d^3 + 1536*a^2*b^2*c^7*d^2 - 1024*a*b^3*c^8*d))^(5/4)*4096i + a^5*b^4*c^10*d^4*x*(-d^5/(256*b^4*c^9 + 256*a^4*c^5*d^4 - 1024*a^3*b*c^6*d^3 + 1536*a^2*b^2*c^7*d^2 - 1024*a*b^3*c^8*d))^(5/4)*2048i - a^6*b^3*c^9*d^5*x*(-d^5/(256*b^4*c^9 + 256*a^4*c^5*d^4 - 1024*a^3*b*c^6*d^3 + 1536*a^2*b^2*c^7*d^2 - 1024*a*b^3*c^8*d))^(5/4)*4096i + a^7*b^2*c^8*d^6*x*(-d^5/(256*b^4*c^9 + 256*a^4*c^5*d^4 - 1024*a^3*b*c^6*d^3 + 1536*a^2*b^2*c^7*d^2 - 1024*a*b^3*c^8*d))^(5/4)*6144i)/(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/(256*b^4*c^9 + 256*a^4*c^5*d^4 - 1024*a^3*b*c^6*d^3 + 1536*a^2*b^2*c^7*d^2 - 1024*a*b^3*c^8*d))^(1/4)*2i + 2*atan(((-b^5/(256*a^9*d^4 + 256*a^5*b^4*c^4 - 1024*a^6*b^3*c^3*d + 1536*a^7*b^2*c^2*d^2 - 1024*a^8*b*c*d^3))^(1/4)*(x*(4*a^11*b^9*c^12*d^8 + 4*a^12*b^8*c^11*d^9) - (-b^5/(256*a^9*d^4 + 256*a^5*b^4*c^4 - 1024*a^6*b^3*c^3*d + 1536*a^7*b^2*c^2*d^2 - 1024*a^8*b*c*d^3))^(3/4)*(x*(-b^5/(256*a^9*d^4 + 256*a^5*b^4*c^4 - 1024*a^6*b^3*c^3*d + 1536*a^7*b^2*c^2*d^2 - 1024*a^8*b*c*d^3))^(1/4)*(1024*a^12*b^12*c^20*d^4 - 4096*a^13*b^11*c^19*d^5 + 6144*a^14*b^10*c^18*d^6 - 4096*a^15*b^9*c^17*d^7 + 2048*a^16*b^8*c^16*d^8 - 4096*a^17*b^7*c^15*d^9 + 6144*a^18*b^6*c^14*d^10 - 4096*a^19*b^5*c^13*d^11 + 1024*a^20*b^4*c^12*d^12)*1i - 256*a^11*b^12*c^19*d^4 + 768*a^12*b^11*c^18*d^5 - 768*a^13*b^10*c^17*d^6 + 256*a^14*b^9*c^16*d^7 + 256*a^16*b^7*c^14*d^9 - 768*a^17*b^6*c^13*d^10 + 768*a^18*b^5*c^12*d^11 - 256*a^19*b^4*c^11*d^12)*1i) + (-b^5/(256*a^9*d^4 + 256*a^5*b^4*c^4 - 1024*a^6*b^3*c^3*d + 1536*a^7*b^2*c^2*d^2 - 1024*a^8*b*c*d^3))^(1/4)*(x*(4*a^11*b^9*c^12*d^8 + 4*a^12*b^8*c^11*d^9) - (-b^5/(256*a^9*d^4 + 256*a^5*b^4*c^4 - 1024*a^6*b^3*c^3*d + 1536*a^7*b^2*c^2*d^2 - 1024*a^8*b*c*d^3))^(3/4)*(x*(-b^5/(256*a^9*d^4 + 256*a^5*b^4*c^4 - 1024*a^6*b^3*c^3*d + 1536*a^7*b^2*c^2*d^2 - 1024*a^8*b*c*d^3))^(1/4)*(1024*a^12*b^12*c^20*d^4 - 4096*a^13*b^11*c^19*d^5 + 6144*a^14*b^10*c^18*d^6 - 4096*a^15*b^9*c^17*d^7 + 2048*a^16*b^8*c^16*d^8 - 4096*a^17*b^7*c^15*d^9 + 6144*a^18*b^6*c^14*d^10 - 4096*a^19*b^5*c^13*d^11 + 1024*a^20*b^4*c^12*d^12)*1i + 256*a^11*b^12*c^19*d^4 - 768*a^12*b^11*c^18*d^5 + 768*a^13*b^10*c^17*d^6 - 256*a^14*b^9*c^16*d^7 - 256*a^16*b^7*c^14*d^9 + 768*a^17*b^6*c^13*d^10 - 768*a^18*b^5*c^12*d^11 + 256*a^19*b^4*c^11*d^12)*1i))/((-b^5/(256*a^9*d^4 + 256*a^5*b^4*c^4 - 1024*a^6*b^3*c^3*d + 1536*a^7*b^2*c^2*d^2 - 1024*a^8*b*c*d^3))^(1/4)*(x*(4*a^11*b^9*c^12*d^8 + 4*a^12*b^8*c^11*d^9) - (-b^5/(256*a^9*d^4 + 256*a^5*b^4*c^4 - 1024*a^6*b^3*c^3*d + 1536*a^7*b^2*c^2*d^2 - 1024*a^8*b*c*d^3))^(3/4)*(x*(-b^5/(256*a^9*d^4 + 256*a^5*b^4*c^4 - 1024*a^6*b^3*c^3*d + 1536*a^7*b^2*c^2*d^2 - 1024*a^8*b*c*d^3))^(1/4)*(1024*a^12*b^12*c^20*d^4 - 4096*a^13*b^11*c^19*d^5 + 6144*a^14*b^10*c^18*d^6 - 4096*a^15*b^9*c^17*d^7 + 2048*a^16*b^8*c^16*d^8 - 4096*a^17*b^7*c^15*d^9 + 6144*a^18*b^6*c^14*d^10 - 4096*a^19*b^5*c^13*d^11 + 1024*a^20*b^4*c^12*d^12)*1i - 256*a^11*b^12*c^19*d^4 + 768*a^12*b^11*c^18*d^5 - 768*a^13*b^10*c^17*d^6 + 256*a^14*b^9*c^16*d^7 + 256*a^16*b^7*c^14*d^9 - 768*a^17*b^6*c^13*d^10 + 768*a^18*b^5*c^12*d^11 - 256*a^19*b^4*c^11*d^12)*1i)*1i - (-b^5/(256*a^9*d^4 + 256*a^5*b^4*c^4 - 1024*a^6*b^3*c^3*d + 1536*a^7*b^2*c^2*d^2 - 1024*a^8*b*c*d^3))^(1/4)*(x*(4*a^11*b^9*c^12*d^8 + 4*a^12*b^8*c^11*d^9) - (-b^5/(256*a^9*d^4 + 256*a^5*b^4*c^4 - 1024*a^6*b^3*c^3*d + 1536*a^7*b^2*c^2*d^2 - 1024*a^8*b*c*d^3))^(3/4)*(x*(-b^5/(256*a^9*d^4 + 256*a^5*b^4*c^4 - 1024*a^6*b^3*c^3*d + 1536*a^7*b^2*c^2*d^2 - 1024*a^8*b*c*d^3))^(1/4)*(1024*a^12*b^12*c^20*d^4 - 4096*a^13*b^11*c^19*d^5 + 6144*a^14*b^10*c^18*d^6 - 4096*a^15*b^9*c^17*d^7 + 2048*a^16*b^8*c^16*d^8 - 4096*a^17*b^7*c^15*d^9 + 6144*a^18*b^6*c^14*d^10 - 4096*a^19*b^5*c^13*d^11 + 1024*a^20*b^4*c^12*d^12)*1i + 256*a^11*b^12*c^19*d^4 - 768*a^12*b^11*c^18*d^5 + 768*a^13*b^10*c^17*d^6 - 256*a^14*b^9*c^16*d^7 - 256*a^16*b^7*c^14*d^9 + 768*a^17*b^6*c^13*d^10 - 768*a^18*b^5*c^12*d^11 + 256*a^19*b^4*c^11*d^12)*1i)*1i))*(-b^5/(256*a^9*d^4 + 256*a^5*b^4*c^4 - 1024*a^6*b^3*c^3*d + 1536*a^7*b^2*c^2*d^2 - 1024*a^8*b*c*d^3))^(1/4) - 1/(a*c*x)","B"
785,1,7459,462,6.190150,"\text{Not used}","int(1/(x^4*(a + b*x^4)*(c + d*x^4)),x)","-2\,\mathrm{atan}\left(\frac{{\left(-\frac{d^7}{256\,a^4\,c^7\,d^4-1024\,a^3\,b\,c^8\,d^3+1536\,a^2\,b^2\,c^9\,d^2-1024\,a\,b^3\,c^{10}\,d+256\,b^4\,c^{11}}\right)}^{1/4}\,\left(x\,\left(4\,a^{11}\,b^9\,c^9\,d^{11}+4\,a^9\,b^{11}\,c^{11}\,d^9\right)-{\left(-\frac{d^7}{256\,a^4\,c^7\,d^4-1024\,a^3\,b\,c^8\,d^3+1536\,a^2\,b^2\,c^9\,d^2-1024\,a\,b^3\,c^{10}\,d+256\,b^4\,c^{11}}\right)}^{1/4}\,\left(16\,a^{10}\,b^{11}\,c^{13}\,d^8-16\,a^9\,b^{12}\,c^{14}\,d^7+16\,a^{13}\,b^8\,c^{10}\,d^{11}-16\,a^{14}\,b^7\,c^9\,d^{12}+{\left(-\frac{d^7}{256\,a^4\,c^7\,d^4-1024\,a^3\,b\,c^8\,d^3+1536\,a^2\,b^2\,c^9\,d^2-1024\,a\,b^3\,c^{10}\,d+256\,b^4\,c^{11}}\right)}^{3/4}\,\left(x\,\left(1024\,a^{20}\,b^4\,c^{11}\,d^{13}-4096\,a^{19}\,b^5\,c^{12}\,d^{12}+6144\,a^{18}\,b^6\,c^{13}\,d^{11}-4096\,a^{17}\,b^7\,c^{14}\,d^{10}+1024\,a^{16}\,b^8\,c^{15}\,d^9+1024\,a^{15}\,b^9\,c^{16}\,d^8-4096\,a^{14}\,b^{10}\,c^{17}\,d^7+6144\,a^{13}\,b^{11}\,c^{18}\,d^6-4096\,a^{12}\,b^{12}\,c^{19}\,d^5+1024\,a^{11}\,b^{13}\,c^{20}\,d^4\right)-{\left(-\frac{d^7}{256\,a^4\,c^7\,d^4-1024\,a^3\,b\,c^8\,d^3+1536\,a^2\,b^2\,c^9\,d^2-1024\,a\,b^3\,c^{10}\,d+256\,b^4\,c^{11}}\right)}^{1/4}\,\left(4096\,a^{21}\,b^4\,c^{13}\,d^{12}-20480\,a^{20}\,b^5\,c^{14}\,d^{11}+40960\,a^{19}\,b^6\,c^{15}\,d^{10}-45056\,a^{18}\,b^7\,c^{16}\,d^9+40960\,a^{17}\,b^8\,c^{17}\,d^8-45056\,a^{16}\,b^9\,c^{18}\,d^7+40960\,a^{15}\,b^{10}\,c^{19}\,d^6-20480\,a^{14}\,b^{11}\,c^{20}\,d^5+4096\,a^{13}\,b^{12}\,c^{21}\,d^4\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)+{\left(-\frac{d^7}{256\,a^4\,c^7\,d^4-1024\,a^3\,b\,c^8\,d^3+1536\,a^2\,b^2\,c^9\,d^2-1024\,a\,b^3\,c^{10}\,d+256\,b^4\,c^{11}}\right)}^{1/4}\,\left(x\,\left(4\,a^{11}\,b^9\,c^9\,d^{11}+4\,a^9\,b^{11}\,c^{11}\,d^9\right)-{\left(-\frac{d^7}{256\,a^4\,c^7\,d^4-1024\,a^3\,b\,c^8\,d^3+1536\,a^2\,b^2\,c^9\,d^2-1024\,a\,b^3\,c^{10}\,d+256\,b^4\,c^{11}}\right)}^{1/4}\,\left(16\,a^9\,b^{12}\,c^{14}\,d^7-16\,a^{10}\,b^{11}\,c^{13}\,d^8-16\,a^{13}\,b^8\,c^{10}\,d^{11}+16\,a^{14}\,b^7\,c^9\,d^{12}+{\left(-\frac{d^7}{256\,a^4\,c^7\,d^4-1024\,a^3\,b\,c^8\,d^3+1536\,a^2\,b^2\,c^9\,d^2-1024\,a\,b^3\,c^{10}\,d+256\,b^4\,c^{11}}\right)}^{3/4}\,\left(x\,\left(1024\,a^{20}\,b^4\,c^{11}\,d^{13}-4096\,a^{19}\,b^5\,c^{12}\,d^{12}+6144\,a^{18}\,b^6\,c^{13}\,d^{11}-4096\,a^{17}\,b^7\,c^{14}\,d^{10}+1024\,a^{16}\,b^8\,c^{15}\,d^9+1024\,a^{15}\,b^9\,c^{16}\,d^8-4096\,a^{14}\,b^{10}\,c^{17}\,d^7+6144\,a^{13}\,b^{11}\,c^{18}\,d^6-4096\,a^{12}\,b^{12}\,c^{19}\,d^5+1024\,a^{11}\,b^{13}\,c^{20}\,d^4\right)+{\left(-\frac{d^7}{256\,a^4\,c^7\,d^4-1024\,a^3\,b\,c^8\,d^3+1536\,a^2\,b^2\,c^9\,d^2-1024\,a\,b^3\,c^{10}\,d+256\,b^4\,c^{11}}\right)}^{1/4}\,\left(4096\,a^{21}\,b^4\,c^{13}\,d^{12}-20480\,a^{20}\,b^5\,c^{14}\,d^{11}+40960\,a^{19}\,b^6\,c^{15}\,d^{10}-45056\,a^{18}\,b^7\,c^{16}\,d^9+40960\,a^{17}\,b^8\,c^{17}\,d^8-45056\,a^{16}\,b^9\,c^{18}\,d^7+40960\,a^{15}\,b^{10}\,c^{19}\,d^6-20480\,a^{14}\,b^{11}\,c^{20}\,d^5+4096\,a^{13}\,b^{12}\,c^{21}\,d^4\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)}{{\left(-\frac{d^7}{256\,a^4\,c^7\,d^4-1024\,a^3\,b\,c^8\,d^3+1536\,a^2\,b^2\,c^9\,d^2-1024\,a\,b^3\,c^{10}\,d+256\,b^4\,c^{11}}\right)}^{1/4}\,\left(x\,\left(4\,a^{11}\,b^9\,c^9\,d^{11}+4\,a^9\,b^{11}\,c^{11}\,d^9\right)-{\left(-\frac{d^7}{256\,a^4\,c^7\,d^4-1024\,a^3\,b\,c^8\,d^3+1536\,a^2\,b^2\,c^9\,d^2-1024\,a\,b^3\,c^{10}\,d+256\,b^4\,c^{11}}\right)}^{1/4}\,\left(16\,a^{10}\,b^{11}\,c^{13}\,d^8-16\,a^9\,b^{12}\,c^{14}\,d^7+16\,a^{13}\,b^8\,c^{10}\,d^{11}-16\,a^{14}\,b^7\,c^9\,d^{12}+{\left(-\frac{d^7}{256\,a^4\,c^7\,d^4-1024\,a^3\,b\,c^8\,d^3+1536\,a^2\,b^2\,c^9\,d^2-1024\,a\,b^3\,c^{10}\,d+256\,b^4\,c^{11}}\right)}^{3/4}\,\left(x\,\left(1024\,a^{20}\,b^4\,c^{11}\,d^{13}-4096\,a^{19}\,b^5\,c^{12}\,d^{12}+6144\,a^{18}\,b^6\,c^{13}\,d^{11}-4096\,a^{17}\,b^7\,c^{14}\,d^{10}+1024\,a^{16}\,b^8\,c^{15}\,d^9+1024\,a^{15}\,b^9\,c^{16}\,d^8-4096\,a^{14}\,b^{10}\,c^{17}\,d^7+6144\,a^{13}\,b^{11}\,c^{18}\,d^6-4096\,a^{12}\,b^{12}\,c^{19}\,d^5+1024\,a^{11}\,b^{13}\,c^{20}\,d^4\right)-{\left(-\frac{d^7}{256\,a^4\,c^7\,d^4-1024\,a^3\,b\,c^8\,d^3+1536\,a^2\,b^2\,c^9\,d^2-1024\,a\,b^3\,c^{10}\,d+256\,b^4\,c^{11}}\right)}^{1/4}\,\left(4096\,a^{21}\,b^4\,c^{13}\,d^{12}-20480\,a^{20}\,b^5\,c^{14}\,d^{11}+40960\,a^{19}\,b^6\,c^{15}\,d^{10}-45056\,a^{18}\,b^7\,c^{16}\,d^9+40960\,a^{17}\,b^8\,c^{17}\,d^8-45056\,a^{16}\,b^9\,c^{18}\,d^7+40960\,a^{15}\,b^{10}\,c^{19}\,d^6-20480\,a^{14}\,b^{11}\,c^{20}\,d^5+4096\,a^{13}\,b^{12}\,c^{21}\,d^4\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}-{\left(-\frac{d^7}{256\,a^4\,c^7\,d^4-1024\,a^3\,b\,c^8\,d^3+1536\,a^2\,b^2\,c^9\,d^2-1024\,a\,b^3\,c^{10}\,d+256\,b^4\,c^{11}}\right)}^{1/4}\,\left(x\,\left(4\,a^{11}\,b^9\,c^9\,d^{11}+4\,a^9\,b^{11}\,c^{11}\,d^9\right)-{\left(-\frac{d^7}{256\,a^4\,c^7\,d^4-1024\,a^3\,b\,c^8\,d^3+1536\,a^2\,b^2\,c^9\,d^2-1024\,a\,b^3\,c^{10}\,d+256\,b^4\,c^{11}}\right)}^{1/4}\,\left(16\,a^9\,b^{12}\,c^{14}\,d^7-16\,a^{10}\,b^{11}\,c^{13}\,d^8-16\,a^{13}\,b^8\,c^{10}\,d^{11}+16\,a^{14}\,b^7\,c^9\,d^{12}+{\left(-\frac{d^7}{256\,a^4\,c^7\,d^4-1024\,a^3\,b\,c^8\,d^3+1536\,a^2\,b^2\,c^9\,d^2-1024\,a\,b^3\,c^{10}\,d+256\,b^4\,c^{11}}\right)}^{3/4}\,\left(x\,\left(1024\,a^{20}\,b^4\,c^{11}\,d^{13}-4096\,a^{19}\,b^5\,c^{12}\,d^{12}+6144\,a^{18}\,b^6\,c^{13}\,d^{11}-4096\,a^{17}\,b^7\,c^{14}\,d^{10}+1024\,a^{16}\,b^8\,c^{15}\,d^9+1024\,a^{15}\,b^9\,c^{16}\,d^8-4096\,a^{14}\,b^{10}\,c^{17}\,d^7+6144\,a^{13}\,b^{11}\,c^{18}\,d^6-4096\,a^{12}\,b^{12}\,c^{19}\,d^5+1024\,a^{11}\,b^{13}\,c^{20}\,d^4\right)+{\left(-\frac{d^7}{256\,a^4\,c^7\,d^4-1024\,a^3\,b\,c^8\,d^3+1536\,a^2\,b^2\,c^9\,d^2-1024\,a\,b^3\,c^{10}\,d+256\,b^4\,c^{11}}\right)}^{1/4}\,\left(4096\,a^{21}\,b^4\,c^{13}\,d^{12}-20480\,a^{20}\,b^5\,c^{14}\,d^{11}+40960\,a^{19}\,b^6\,c^{15}\,d^{10}-45056\,a^{18}\,b^7\,c^{16}\,d^9+40960\,a^{17}\,b^8\,c^{17}\,d^8-45056\,a^{16}\,b^9\,c^{18}\,d^7+40960\,a^{15}\,b^{10}\,c^{19}\,d^6-20480\,a^{14}\,b^{11}\,c^{20}\,d^5+4096\,a^{13}\,b^{12}\,c^{21}\,d^4\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}\right)\,{\left(-\frac{d^7}{256\,a^4\,c^7\,d^4-1024\,a^3\,b\,c^8\,d^3+1536\,a^2\,b^2\,c^9\,d^2-1024\,a\,b^3\,c^{10}\,d+256\,b^4\,c^{11}}\right)}^{1/4}-2\,\mathrm{atan}\left(-\frac{{\left(-\frac{b^7}{256\,a^{11}\,d^4-1024\,a^{10}\,b\,c\,d^3+1536\,a^9\,b^2\,c^2\,d^2-1024\,a^8\,b^3\,c^3\,d+256\,a^7\,b^4\,c^4}\right)}^{1/4}\,\left(x\,\left(4\,a^{11}\,b^9\,c^9\,d^{11}+4\,a^9\,b^{11}\,c^{11}\,d^9\right)-{\left(-\frac{b^7}{256\,a^{11}\,d^4-1024\,a^{10}\,b\,c\,d^3+1536\,a^9\,b^2\,c^2\,d^2-1024\,a^8\,b^3\,c^3\,d+256\,a^7\,b^4\,c^4}\right)}^{1/4}\,\left(16\,a^9\,b^{12}\,c^{14}\,d^7-16\,a^{10}\,b^{11}\,c^{13}\,d^8-16\,a^{13}\,b^8\,c^{10}\,d^{11}+16\,a^{14}\,b^7\,c^9\,d^{12}+{\left(-\frac{b^7}{256\,a^{11}\,d^4-1024\,a^{10}\,b\,c\,d^3+1536\,a^9\,b^2\,c^2\,d^2-1024\,a^8\,b^3\,c^3\,d+256\,a^7\,b^4\,c^4}\right)}^{3/4}\,\left(x\,\left(1024\,a^{20}\,b^4\,c^{11}\,d^{13}-4096\,a^{19}\,b^5\,c^{12}\,d^{12}+6144\,a^{18}\,b^6\,c^{13}\,d^{11}-4096\,a^{17}\,b^7\,c^{14}\,d^{10}+1024\,a^{16}\,b^8\,c^{15}\,d^9+1024\,a^{15}\,b^9\,c^{16}\,d^8-4096\,a^{14}\,b^{10}\,c^{17}\,d^7+6144\,a^{13}\,b^{11}\,c^{18}\,d^6-4096\,a^{12}\,b^{12}\,c^{19}\,d^5+1024\,a^{11}\,b^{13}\,c^{20}\,d^4\right)+{\left(-\frac{b^7}{256\,a^{11}\,d^4-1024\,a^{10}\,b\,c\,d^3+1536\,a^9\,b^2\,c^2\,d^2-1024\,a^8\,b^3\,c^3\,d+256\,a^7\,b^4\,c^4}\right)}^{1/4}\,\left(4096\,a^{21}\,b^4\,c^{13}\,d^{12}-20480\,a^{20}\,b^5\,c^{14}\,d^{11}+40960\,a^{19}\,b^6\,c^{15}\,d^{10}-45056\,a^{18}\,b^7\,c^{16}\,d^9+40960\,a^{17}\,b^8\,c^{17}\,d^8-45056\,a^{16}\,b^9\,c^{18}\,d^7+40960\,a^{15}\,b^{10}\,c^{19}\,d^6-20480\,a^{14}\,b^{11}\,c^{20}\,d^5+4096\,a^{13}\,b^{12}\,c^{21}\,d^4\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)+{\left(-\frac{b^7}{256\,a^{11}\,d^4-1024\,a^{10}\,b\,c\,d^3+1536\,a^9\,b^2\,c^2\,d^2-1024\,a^8\,b^3\,c^3\,d+256\,a^7\,b^4\,c^4}\right)}^{1/4}\,\left(x\,\left(4\,a^{11}\,b^9\,c^9\,d^{11}+4\,a^9\,b^{11}\,c^{11}\,d^9\right)+{\left(-\frac{b^7}{256\,a^{11}\,d^4-1024\,a^{10}\,b\,c\,d^3+1536\,a^9\,b^2\,c^2\,d^2-1024\,a^8\,b^3\,c^3\,d+256\,a^7\,b^4\,c^4}\right)}^{1/4}\,\left(16\,a^9\,b^{12}\,c^{14}\,d^7-16\,a^{10}\,b^{11}\,c^{13}\,d^8-16\,a^{13}\,b^8\,c^{10}\,d^{11}+16\,a^{14}\,b^7\,c^9\,d^{12}+{\left(-\frac{b^7}{256\,a^{11}\,d^4-1024\,a^{10}\,b\,c\,d^3+1536\,a^9\,b^2\,c^2\,d^2-1024\,a^8\,b^3\,c^3\,d+256\,a^7\,b^4\,c^4}\right)}^{3/4}\,\left(-x\,\left(1024\,a^{20}\,b^4\,c^{11}\,d^{13}-4096\,a^{19}\,b^5\,c^{12}\,d^{12}+6144\,a^{18}\,b^6\,c^{13}\,d^{11}-4096\,a^{17}\,b^7\,c^{14}\,d^{10}+1024\,a^{16}\,b^8\,c^{15}\,d^9+1024\,a^{15}\,b^9\,c^{16}\,d^8-4096\,a^{14}\,b^{10}\,c^{17}\,d^7+6144\,a^{13}\,b^{11}\,c^{18}\,d^6-4096\,a^{12}\,b^{12}\,c^{19}\,d^5+1024\,a^{11}\,b^{13}\,c^{20}\,d^4\right)+{\left(-\frac{b^7}{256\,a^{11}\,d^4-1024\,a^{10}\,b\,c\,d^3+1536\,a^9\,b^2\,c^2\,d^2-1024\,a^8\,b^3\,c^3\,d+256\,a^7\,b^4\,c^4}\right)}^{1/4}\,\left(4096\,a^{21}\,b^4\,c^{13}\,d^{12}-20480\,a^{20}\,b^5\,c^{14}\,d^{11}+40960\,a^{19}\,b^6\,c^{15}\,d^{10}-45056\,a^{18}\,b^7\,c^{16}\,d^9+40960\,a^{17}\,b^8\,c^{17}\,d^8-45056\,a^{16}\,b^9\,c^{18}\,d^7+40960\,a^{15}\,b^{10}\,c^{19}\,d^6-20480\,a^{14}\,b^{11}\,c^{20}\,d^5+4096\,a^{13}\,b^{12}\,c^{21}\,d^4\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)}{{\left(-\frac{b^7}{256\,a^{11}\,d^4-1024\,a^{10}\,b\,c\,d^3+1536\,a^9\,b^2\,c^2\,d^2-1024\,a^8\,b^3\,c^3\,d+256\,a^7\,b^4\,c^4}\right)}^{1/4}\,\left(x\,\left(4\,a^{11}\,b^9\,c^9\,d^{11}+4\,a^9\,b^{11}\,c^{11}\,d^9\right)-{\left(-\frac{b^7}{256\,a^{11}\,d^4-1024\,a^{10}\,b\,c\,d^3+1536\,a^9\,b^2\,c^2\,d^2-1024\,a^8\,b^3\,c^3\,d+256\,a^7\,b^4\,c^4}\right)}^{1/4}\,\left(16\,a^9\,b^{12}\,c^{14}\,d^7-16\,a^{10}\,b^{11}\,c^{13}\,d^8-16\,a^{13}\,b^8\,c^{10}\,d^{11}+16\,a^{14}\,b^7\,c^9\,d^{12}+{\left(-\frac{b^7}{256\,a^{11}\,d^4-1024\,a^{10}\,b\,c\,d^3+1536\,a^9\,b^2\,c^2\,d^2-1024\,a^8\,b^3\,c^3\,d+256\,a^7\,b^4\,c^4}\right)}^{3/4}\,\left(x\,\left(1024\,a^{20}\,b^4\,c^{11}\,d^{13}-4096\,a^{19}\,b^5\,c^{12}\,d^{12}+6144\,a^{18}\,b^6\,c^{13}\,d^{11}-4096\,a^{17}\,b^7\,c^{14}\,d^{10}+1024\,a^{16}\,b^8\,c^{15}\,d^9+1024\,a^{15}\,b^9\,c^{16}\,d^8-4096\,a^{14}\,b^{10}\,c^{17}\,d^7+6144\,a^{13}\,b^{11}\,c^{18}\,d^6-4096\,a^{12}\,b^{12}\,c^{19}\,d^5+1024\,a^{11}\,b^{13}\,c^{20}\,d^4\right)+{\left(-\frac{b^7}{256\,a^{11}\,d^4-1024\,a^{10}\,b\,c\,d^3+1536\,a^9\,b^2\,c^2\,d^2-1024\,a^8\,b^3\,c^3\,d+256\,a^7\,b^4\,c^4}\right)}^{1/4}\,\left(4096\,a^{21}\,b^4\,c^{13}\,d^{12}-20480\,a^{20}\,b^5\,c^{14}\,d^{11}+40960\,a^{19}\,b^6\,c^{15}\,d^{10}-45056\,a^{18}\,b^7\,c^{16}\,d^9+40960\,a^{17}\,b^8\,c^{17}\,d^8-45056\,a^{16}\,b^9\,c^{18}\,d^7+40960\,a^{15}\,b^{10}\,c^{19}\,d^6-20480\,a^{14}\,b^{11}\,c^{20}\,d^5+4096\,a^{13}\,b^{12}\,c^{21}\,d^4\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}-{\left(-\frac{b^7}{256\,a^{11}\,d^4-1024\,a^{10}\,b\,c\,d^3+1536\,a^9\,b^2\,c^2\,d^2-1024\,a^8\,b^3\,c^3\,d+256\,a^7\,b^4\,c^4}\right)}^{1/4}\,\left(x\,\left(4\,a^{11}\,b^9\,c^9\,d^{11}+4\,a^9\,b^{11}\,c^{11}\,d^9\right)+{\left(-\frac{b^7}{256\,a^{11}\,d^4-1024\,a^{10}\,b\,c\,d^3+1536\,a^9\,b^2\,c^2\,d^2-1024\,a^8\,b^3\,c^3\,d+256\,a^7\,b^4\,c^4}\right)}^{1/4}\,\left(16\,a^9\,b^{12}\,c^{14}\,d^7-16\,a^{10}\,b^{11}\,c^{13}\,d^8-16\,a^{13}\,b^8\,c^{10}\,d^{11}+16\,a^{14}\,b^7\,c^9\,d^{12}+{\left(-\frac{b^7}{256\,a^{11}\,d^4-1024\,a^{10}\,b\,c\,d^3+1536\,a^9\,b^2\,c^2\,d^2-1024\,a^8\,b^3\,c^3\,d+256\,a^7\,b^4\,c^4}\right)}^{3/4}\,\left(-x\,\left(1024\,a^{20}\,b^4\,c^{11}\,d^{13}-4096\,a^{19}\,b^5\,c^{12}\,d^{12}+6144\,a^{18}\,b^6\,c^{13}\,d^{11}-4096\,a^{17}\,b^7\,c^{14}\,d^{10}+1024\,a^{16}\,b^8\,c^{15}\,d^9+1024\,a^{15}\,b^9\,c^{16}\,d^8-4096\,a^{14}\,b^{10}\,c^{17}\,d^7+6144\,a^{13}\,b^{11}\,c^{18}\,d^6-4096\,a^{12}\,b^{12}\,c^{19}\,d^5+1024\,a^{11}\,b^{13}\,c^{20}\,d^4\right)+{\left(-\frac{b^7}{256\,a^{11}\,d^4-1024\,a^{10}\,b\,c\,d^3+1536\,a^9\,b^2\,c^2\,d^2-1024\,a^8\,b^3\,c^3\,d+256\,a^7\,b^4\,c^4}\right)}^{1/4}\,\left(4096\,a^{21}\,b^4\,c^{13}\,d^{12}-20480\,a^{20}\,b^5\,c^{14}\,d^{11}+40960\,a^{19}\,b^6\,c^{15}\,d^{10}-45056\,a^{18}\,b^7\,c^{16}\,d^9+40960\,a^{17}\,b^8\,c^{17}\,d^8-45056\,a^{16}\,b^9\,c^{18}\,d^7+40960\,a^{15}\,b^{10}\,c^{19}\,d^6-20480\,a^{14}\,b^{11}\,c^{20}\,d^5+4096\,a^{13}\,b^{12}\,c^{21}\,d^4\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}\right)\,{\left(-\frac{b^7}{256\,a^{11}\,d^4-1024\,a^{10}\,b\,c\,d^3+1536\,a^9\,b^2\,c^2\,d^2-1024\,a^8\,b^3\,c^3\,d+256\,a^7\,b^4\,c^4}\right)}^{1/4}-\frac{1}{3\,a\,c\,x^3}-\mathrm{atan}\left(\frac{a^2\,b^5\,d^7\,x\,1{}\mathrm{i}+b^7\,c^2\,d^5\,x\,1{}\mathrm{i}-\frac{a^2\,b^{16}\,c^{11}\,x\,256{}\mathrm{i}}{256\,a^{11}\,d^4-1024\,a^{10}\,b\,c\,d^3+1536\,a^9\,b^2\,c^2\,d^2-1024\,a^8\,b^3\,c^3\,d+256\,a^7\,b^4\,c^4}-\frac{a^4\,b^{14}\,c^9\,d^2\,x\,1536{}\mathrm{i}}{256\,a^{11}\,d^4-1024\,a^{10}\,b\,c\,d^3+1536\,a^9\,b^2\,c^2\,d^2-1024\,a^8\,b^3\,c^3\,d+256\,a^7\,b^4\,c^4}+\frac{a^5\,b^{13}\,c^8\,d^3\,x\,1024{}\mathrm{i}}{256\,a^{11}\,d^4-1024\,a^{10}\,b\,c\,d^3+1536\,a^9\,b^2\,c^2\,d^2-1024\,a^8\,b^3\,c^3\,d+256\,a^7\,b^4\,c^4}-\frac{a^6\,b^{12}\,c^7\,d^4\,x\,256{}\mathrm{i}}{256\,a^{11}\,d^4-1024\,a^{10}\,b\,c\,d^3+1536\,a^9\,b^2\,c^2\,d^2-1024\,a^8\,b^3\,c^3\,d+256\,a^7\,b^4\,c^4}-\frac{a^7\,b^{11}\,c^6\,d^5\,x\,256{}\mathrm{i}}{256\,a^{11}\,d^4-1024\,a^{10}\,b\,c\,d^3+1536\,a^9\,b^2\,c^2\,d^2-1024\,a^8\,b^3\,c^3\,d+256\,a^7\,b^4\,c^4}+\frac{a^8\,b^{10}\,c^5\,d^6\,x\,1024{}\mathrm{i}}{256\,a^{11}\,d^4-1024\,a^{10}\,b\,c\,d^3+1536\,a^9\,b^2\,c^2\,d^2-1024\,a^8\,b^3\,c^3\,d+256\,a^7\,b^4\,c^4}-\frac{a^9\,b^9\,c^4\,d^7\,x\,1536{}\mathrm{i}}{256\,a^{11}\,d^4-1024\,a^{10}\,b\,c\,d^3+1536\,a^9\,b^2\,c^2\,d^2-1024\,a^8\,b^3\,c^3\,d+256\,a^7\,b^4\,c^4}+\frac{a^{10}\,b^8\,c^3\,d^8\,x\,1024{}\mathrm{i}}{256\,a^{11}\,d^4-1024\,a^{10}\,b\,c\,d^3+1536\,a^9\,b^2\,c^2\,d^2-1024\,a^8\,b^3\,c^3\,d+256\,a^7\,b^4\,c^4}-\frac{a^{11}\,b^7\,c^2\,d^9\,x\,256{}\mathrm{i}}{256\,a^{11}\,d^4-1024\,a^{10}\,b\,c\,d^3+1536\,a^9\,b^2\,c^2\,d^2-1024\,a^8\,b^3\,c^3\,d+256\,a^7\,b^4\,c^4}+\frac{a^3\,b^{15}\,c^{10}\,d\,x\,1024{}\mathrm{i}}{256\,a^{11}\,d^4-1024\,a^{10}\,b\,c\,d^3+1536\,a^9\,b^2\,c^2\,d^2-1024\,a^8\,b^3\,c^3\,d+256\,a^7\,b^4\,c^4}}{{\left(-\frac{b^7}{256\,a^{11}\,d^4-1024\,a^{10}\,b\,c\,d^3+1536\,a^9\,b^2\,c^2\,d^2-1024\,a^8\,b^3\,c^3\,d+256\,a^7\,b^4\,c^4}\right)}^{1/4}\,\left(\frac{b^7\,\left(1024\,a^{12}\,c^4\,d^8-5120\,a^{11}\,b\,c^5\,d^7+10240\,a^{10}\,b^2\,c^6\,d^6-11264\,a^9\,b^3\,c^7\,d^5+10240\,a^8\,b^4\,c^8\,d^4-11264\,a^7\,b^5\,c^9\,d^3+10240\,a^6\,b^6\,c^{10}\,d^2-5120\,a^5\,b^7\,c^{11}\,d+1024\,a^4\,b^8\,c^{12}\right)}{256\,a^{11}\,d^4-1024\,a^{10}\,b\,c\,d^3+1536\,a^9\,b^2\,c^2\,d^2-1024\,a^8\,b^3\,c^3\,d+256\,a^7\,b^4\,c^4}+4\,a^5\,b^3\,d^8+4\,b^8\,c^5\,d^3-4\,a\,b^7\,c^4\,d^4-4\,a^4\,b^4\,c\,d^7\right)}\right)\,{\left(-\frac{b^7}{256\,a^{11}\,d^4-1024\,a^{10}\,b\,c\,d^3+1536\,a^9\,b^2\,c^2\,d^2-1024\,a^8\,b^3\,c^3\,d+256\,a^7\,b^4\,c^4}\right)}^{1/4}\,2{}\mathrm{i}-\mathrm{atan}\left(\frac{a^2\,b^5\,d^7\,x\,1{}\mathrm{i}+b^7\,c^2\,d^5\,x\,1{}\mathrm{i}-\frac{a^{11}\,c^2\,d^{16}\,x\,256{}\mathrm{i}}{256\,a^4\,c^7\,d^4-1024\,a^3\,b\,c^8\,d^3+1536\,a^2\,b^2\,c^9\,d^2-1024\,a\,b^3\,c^{10}\,d+256\,b^4\,c^{11}}-\frac{a^2\,b^9\,c^{11}\,d^7\,x\,256{}\mathrm{i}}{256\,a^4\,c^7\,d^4-1024\,a^3\,b\,c^8\,d^3+1536\,a^2\,b^2\,c^9\,d^2-1024\,a\,b^3\,c^{10}\,d+256\,b^4\,c^{11}}+\frac{a^3\,b^8\,c^{10}\,d^8\,x\,1024{}\mathrm{i}}{256\,a^4\,c^7\,d^4-1024\,a^3\,b\,c^8\,d^3+1536\,a^2\,b^2\,c^9\,d^2-1024\,a\,b^3\,c^{10}\,d+256\,b^4\,c^{11}}-\frac{a^4\,b^7\,c^9\,d^9\,x\,1536{}\mathrm{i}}{256\,a^4\,c^7\,d^4-1024\,a^3\,b\,c^8\,d^3+1536\,a^2\,b^2\,c^9\,d^2-1024\,a\,b^3\,c^{10}\,d+256\,b^4\,c^{11}}+\frac{a^5\,b^6\,c^8\,d^{10}\,x\,1024{}\mathrm{i}}{256\,a^4\,c^7\,d^4-1024\,a^3\,b\,c^8\,d^3+1536\,a^2\,b^2\,c^9\,d^2-1024\,a\,b^3\,c^{10}\,d+256\,b^4\,c^{11}}-\frac{a^6\,b^5\,c^7\,d^{11}\,x\,256{}\mathrm{i}}{256\,a^4\,c^7\,d^4-1024\,a^3\,b\,c^8\,d^3+1536\,a^2\,b^2\,c^9\,d^2-1024\,a\,b^3\,c^{10}\,d+256\,b^4\,c^{11}}-\frac{a^7\,b^4\,c^6\,d^{12}\,x\,256{}\mathrm{i}}{256\,a^4\,c^7\,d^4-1024\,a^3\,b\,c^8\,d^3+1536\,a^2\,b^2\,c^9\,d^2-1024\,a\,b^3\,c^{10}\,d+256\,b^4\,c^{11}}+\frac{a^8\,b^3\,c^5\,d^{13}\,x\,1024{}\mathrm{i}}{256\,a^4\,c^7\,d^4-1024\,a^3\,b\,c^8\,d^3+1536\,a^2\,b^2\,c^9\,d^2-1024\,a\,b^3\,c^{10}\,d+256\,b^4\,c^{11}}-\frac{a^9\,b^2\,c^4\,d^{14}\,x\,1536{}\mathrm{i}}{256\,a^4\,c^7\,d^4-1024\,a^3\,b\,c^8\,d^3+1536\,a^2\,b^2\,c^9\,d^2-1024\,a\,b^3\,c^{10}\,d+256\,b^4\,c^{11}}+\frac{a^{10}\,b\,c^3\,d^{15}\,x\,1024{}\mathrm{i}}{256\,a^4\,c^7\,d^4-1024\,a^3\,b\,c^8\,d^3+1536\,a^2\,b^2\,c^9\,d^2-1024\,a\,b^3\,c^{10}\,d+256\,b^4\,c^{11}}}{{\left(-\frac{d^7}{256\,a^4\,c^7\,d^4-1024\,a^3\,b\,c^8\,d^3+1536\,a^2\,b^2\,c^9\,d^2-1024\,a\,b^3\,c^{10}\,d+256\,b^4\,c^{11}}\right)}^{1/4}\,\left(\frac{d^7\,\left(1024\,a^{12}\,c^4\,d^8-5120\,a^{11}\,b\,c^5\,d^7+10240\,a^{10}\,b^2\,c^6\,d^6-11264\,a^9\,b^3\,c^7\,d^5+10240\,a^8\,b^4\,c^8\,d^4-11264\,a^7\,b^5\,c^9\,d^3+10240\,a^6\,b^6\,c^{10}\,d^2-5120\,a^5\,b^7\,c^{11}\,d+1024\,a^4\,b^8\,c^{12}\right)}{256\,a^4\,c^7\,d^4-1024\,a^3\,b\,c^8\,d^3+1536\,a^2\,b^2\,c^9\,d^2-1024\,a\,b^3\,c^{10}\,d+256\,b^4\,c^{11}}+4\,a^5\,b^3\,d^8+4\,b^8\,c^5\,d^3-4\,a\,b^7\,c^4\,d^4-4\,a^4\,b^4\,c\,d^7\right)}\right)\,{\left(-\frac{d^7}{256\,a^4\,c^7\,d^4-1024\,a^3\,b\,c^8\,d^3+1536\,a^2\,b^2\,c^9\,d^2-1024\,a\,b^3\,c^{10}\,d+256\,b^4\,c^{11}}\right)}^{1/4}\,2{}\mathrm{i}","Not used",1,"- atan((a^2*b^5*d^7*x*1i + b^7*c^2*d^5*x*1i - (a^2*b^16*c^11*x*256i)/(256*a^11*d^4 + 256*a^7*b^4*c^4 - 1024*a^8*b^3*c^3*d + 1536*a^9*b^2*c^2*d^2 - 1024*a^10*b*c*d^3) - (a^4*b^14*c^9*d^2*x*1536i)/(256*a^11*d^4 + 256*a^7*b^4*c^4 - 1024*a^8*b^3*c^3*d + 1536*a^9*b^2*c^2*d^2 - 1024*a^10*b*c*d^3) + (a^5*b^13*c^8*d^3*x*1024i)/(256*a^11*d^4 + 256*a^7*b^4*c^4 - 1024*a^8*b^3*c^3*d + 1536*a^9*b^2*c^2*d^2 - 1024*a^10*b*c*d^3) - (a^6*b^12*c^7*d^4*x*256i)/(256*a^11*d^4 + 256*a^7*b^4*c^4 - 1024*a^8*b^3*c^3*d + 1536*a^9*b^2*c^2*d^2 - 1024*a^10*b*c*d^3) - (a^7*b^11*c^6*d^5*x*256i)/(256*a^11*d^4 + 256*a^7*b^4*c^4 - 1024*a^8*b^3*c^3*d + 1536*a^9*b^2*c^2*d^2 - 1024*a^10*b*c*d^3) + (a^8*b^10*c^5*d^6*x*1024i)/(256*a^11*d^4 + 256*a^7*b^4*c^4 - 1024*a^8*b^3*c^3*d + 1536*a^9*b^2*c^2*d^2 - 1024*a^10*b*c*d^3) - (a^9*b^9*c^4*d^7*x*1536i)/(256*a^11*d^4 + 256*a^7*b^4*c^4 - 1024*a^8*b^3*c^3*d + 1536*a^9*b^2*c^2*d^2 - 1024*a^10*b*c*d^3) + (a^10*b^8*c^3*d^8*x*1024i)/(256*a^11*d^4 + 256*a^7*b^4*c^4 - 1024*a^8*b^3*c^3*d + 1536*a^9*b^2*c^2*d^2 - 1024*a^10*b*c*d^3) - (a^11*b^7*c^2*d^9*x*256i)/(256*a^11*d^4 + 256*a^7*b^4*c^4 - 1024*a^8*b^3*c^3*d + 1536*a^9*b^2*c^2*d^2 - 1024*a^10*b*c*d^3) + (a^3*b^15*c^10*d*x*1024i)/(256*a^11*d^4 + 256*a^7*b^4*c^4 - 1024*a^8*b^3*c^3*d + 1536*a^9*b^2*c^2*d^2 - 1024*a^10*b*c*d^3))/((-b^7/(256*a^11*d^4 + 256*a^7*b^4*c^4 - 1024*a^8*b^3*c^3*d + 1536*a^9*b^2*c^2*d^2 - 1024*a^10*b*c*d^3))^(1/4)*((b^7*(1024*a^4*b^8*c^12 + 1024*a^12*c^4*d^8 - 5120*a^5*b^7*c^11*d - 5120*a^11*b*c^5*d^7 + 10240*a^6*b^6*c^10*d^2 - 11264*a^7*b^5*c^9*d^3 + 10240*a^8*b^4*c^8*d^4 - 11264*a^9*b^3*c^7*d^5 + 10240*a^10*b^2*c^6*d^6))/(256*a^11*d^4 + 256*a^7*b^4*c^4 - 1024*a^8*b^3*c^3*d + 1536*a^9*b^2*c^2*d^2 - 1024*a^10*b*c*d^3) + 4*a^5*b^3*d^8 + 4*b^8*c^5*d^3 - 4*a*b^7*c^4*d^4 - 4*a^4*b^4*c*d^7)))*(-b^7/(256*a^11*d^4 + 256*a^7*b^4*c^4 - 1024*a^8*b^3*c^3*d + 1536*a^9*b^2*c^2*d^2 - 1024*a^10*b*c*d^3))^(1/4)*2i - atan((a^2*b^5*d^7*x*1i + b^7*c^2*d^5*x*1i - (a^11*c^2*d^16*x*256i)/(256*b^4*c^11 + 256*a^4*c^7*d^4 - 1024*a^3*b*c^8*d^3 + 1536*a^2*b^2*c^9*d^2 - 1024*a*b^3*c^10*d) - (a^2*b^9*c^11*d^7*x*256i)/(256*b^4*c^11 + 256*a^4*c^7*d^4 - 1024*a^3*b*c^8*d^3 + 1536*a^2*b^2*c^9*d^2 - 1024*a*b^3*c^10*d) + (a^3*b^8*c^10*d^8*x*1024i)/(256*b^4*c^11 + 256*a^4*c^7*d^4 - 1024*a^3*b*c^8*d^3 + 1536*a^2*b^2*c^9*d^2 - 1024*a*b^3*c^10*d) - (a^4*b^7*c^9*d^9*x*1536i)/(256*b^4*c^11 + 256*a^4*c^7*d^4 - 1024*a^3*b*c^8*d^3 + 1536*a^2*b^2*c^9*d^2 - 1024*a*b^3*c^10*d) + (a^5*b^6*c^8*d^10*x*1024i)/(256*b^4*c^11 + 256*a^4*c^7*d^4 - 1024*a^3*b*c^8*d^3 + 1536*a^2*b^2*c^9*d^2 - 1024*a*b^3*c^10*d) - (a^6*b^5*c^7*d^11*x*256i)/(256*b^4*c^11 + 256*a^4*c^7*d^4 - 1024*a^3*b*c^8*d^3 + 1536*a^2*b^2*c^9*d^2 - 1024*a*b^3*c^10*d) - (a^7*b^4*c^6*d^12*x*256i)/(256*b^4*c^11 + 256*a^4*c^7*d^4 - 1024*a^3*b*c^8*d^3 + 1536*a^2*b^2*c^9*d^2 - 1024*a*b^3*c^10*d) + (a^8*b^3*c^5*d^13*x*1024i)/(256*b^4*c^11 + 256*a^4*c^7*d^4 - 1024*a^3*b*c^8*d^3 + 1536*a^2*b^2*c^9*d^2 - 1024*a*b^3*c^10*d) - (a^9*b^2*c^4*d^14*x*1536i)/(256*b^4*c^11 + 256*a^4*c^7*d^4 - 1024*a^3*b*c^8*d^3 + 1536*a^2*b^2*c^9*d^2 - 1024*a*b^3*c^10*d) + (a^10*b*c^3*d^15*x*1024i)/(256*b^4*c^11 + 256*a^4*c^7*d^4 - 1024*a^3*b*c^8*d^3 + 1536*a^2*b^2*c^9*d^2 - 1024*a*b^3*c^10*d))/((-d^7/(256*b^4*c^11 + 256*a^4*c^7*d^4 - 1024*a^3*b*c^8*d^3 + 1536*a^2*b^2*c^9*d^2 - 1024*a*b^3*c^10*d))^(1/4)*((d^7*(1024*a^4*b^8*c^12 + 1024*a^12*c^4*d^8 - 5120*a^5*b^7*c^11*d - 5120*a^11*b*c^5*d^7 + 10240*a^6*b^6*c^10*d^2 - 11264*a^7*b^5*c^9*d^3 + 10240*a^8*b^4*c^8*d^4 - 11264*a^9*b^3*c^7*d^5 + 10240*a^10*b^2*c^6*d^6))/(256*b^4*c^11 + 256*a^4*c^7*d^4 - 1024*a^3*b*c^8*d^3 + 1536*a^2*b^2*c^9*d^2 - 1024*a*b^3*c^10*d) + 4*a^5*b^3*d^8 + 4*b^8*c^5*d^3 - 4*a*b^7*c^4*d^4 - 4*a^4*b^4*c*d^7)))*(-d^7/(256*b^4*c^11 + 256*a^4*c^7*d^4 - 1024*a^3*b*c^8*d^3 + 1536*a^2*b^2*c^9*d^2 - 1024*a*b^3*c^10*d))^(1/4)*2i - 2*atan(((-d^7/(256*b^4*c^11 + 256*a^4*c^7*d^4 - 1024*a^3*b*c^8*d^3 + 1536*a^2*b^2*c^9*d^2 - 1024*a*b^3*c^10*d))^(1/4)*(x*(4*a^9*b^11*c^11*d^9 + 4*a^11*b^9*c^9*d^11) - (-d^7/(256*b^4*c^11 + 256*a^4*c^7*d^4 - 1024*a^3*b*c^8*d^3 + 1536*a^2*b^2*c^9*d^2 - 1024*a*b^3*c^10*d))^(1/4)*((-d^7/(256*b^4*c^11 + 256*a^4*c^7*d^4 - 1024*a^3*b*c^8*d^3 + 1536*a^2*b^2*c^9*d^2 - 1024*a*b^3*c^10*d))^(3/4)*(x*(1024*a^11*b^13*c^20*d^4 - 4096*a^12*b^12*c^19*d^5 + 6144*a^13*b^11*c^18*d^6 - 4096*a^14*b^10*c^17*d^7 + 1024*a^15*b^9*c^16*d^8 + 1024*a^16*b^8*c^15*d^9 - 4096*a^17*b^7*c^14*d^10 + 6144*a^18*b^6*c^13*d^11 - 4096*a^19*b^5*c^12*d^12 + 1024*a^20*b^4*c^11*d^13) - (-d^7/(256*b^4*c^11 + 256*a^4*c^7*d^4 - 1024*a^3*b*c^8*d^3 + 1536*a^2*b^2*c^9*d^2 - 1024*a*b^3*c^10*d))^(1/4)*(4096*a^13*b^12*c^21*d^4 - 20480*a^14*b^11*c^20*d^5 + 40960*a^15*b^10*c^19*d^6 - 45056*a^16*b^9*c^18*d^7 + 40960*a^17*b^8*c^17*d^8 - 45056*a^18*b^7*c^16*d^9 + 40960*a^19*b^6*c^15*d^10 - 20480*a^20*b^5*c^14*d^11 + 4096*a^21*b^4*c^13*d^12)*1i)*1i - 16*a^9*b^12*c^14*d^7 + 16*a^10*b^11*c^13*d^8 + 16*a^13*b^8*c^10*d^11 - 16*a^14*b^7*c^9*d^12)*1i) + (-d^7/(256*b^4*c^11 + 256*a^4*c^7*d^4 - 1024*a^3*b*c^8*d^3 + 1536*a^2*b^2*c^9*d^2 - 1024*a*b^3*c^10*d))^(1/4)*(x*(4*a^9*b^11*c^11*d^9 + 4*a^11*b^9*c^9*d^11) - (-d^7/(256*b^4*c^11 + 256*a^4*c^7*d^4 - 1024*a^3*b*c^8*d^3 + 1536*a^2*b^2*c^9*d^2 - 1024*a*b^3*c^10*d))^(1/4)*((-d^7/(256*b^4*c^11 + 256*a^4*c^7*d^4 - 1024*a^3*b*c^8*d^3 + 1536*a^2*b^2*c^9*d^2 - 1024*a*b^3*c^10*d))^(3/4)*(x*(1024*a^11*b^13*c^20*d^4 - 4096*a^12*b^12*c^19*d^5 + 6144*a^13*b^11*c^18*d^6 - 4096*a^14*b^10*c^17*d^7 + 1024*a^15*b^9*c^16*d^8 + 1024*a^16*b^8*c^15*d^9 - 4096*a^17*b^7*c^14*d^10 + 6144*a^18*b^6*c^13*d^11 - 4096*a^19*b^5*c^12*d^12 + 1024*a^20*b^4*c^11*d^13) + (-d^7/(256*b^4*c^11 + 256*a^4*c^7*d^4 - 1024*a^3*b*c^8*d^3 + 1536*a^2*b^2*c^9*d^2 - 1024*a*b^3*c^10*d))^(1/4)*(4096*a^13*b^12*c^21*d^4 - 20480*a^14*b^11*c^20*d^5 + 40960*a^15*b^10*c^19*d^6 - 45056*a^16*b^9*c^18*d^7 + 40960*a^17*b^8*c^17*d^8 - 45056*a^18*b^7*c^16*d^9 + 40960*a^19*b^6*c^15*d^10 - 20480*a^20*b^5*c^14*d^11 + 4096*a^21*b^4*c^13*d^12)*1i)*1i + 16*a^9*b^12*c^14*d^7 - 16*a^10*b^11*c^13*d^8 - 16*a^13*b^8*c^10*d^11 + 16*a^14*b^7*c^9*d^12)*1i))/((-d^7/(256*b^4*c^11 + 256*a^4*c^7*d^4 - 1024*a^3*b*c^8*d^3 + 1536*a^2*b^2*c^9*d^2 - 1024*a*b^3*c^10*d))^(1/4)*(x*(4*a^9*b^11*c^11*d^9 + 4*a^11*b^9*c^9*d^11) - (-d^7/(256*b^4*c^11 + 256*a^4*c^7*d^4 - 1024*a^3*b*c^8*d^3 + 1536*a^2*b^2*c^9*d^2 - 1024*a*b^3*c^10*d))^(1/4)*((-d^7/(256*b^4*c^11 + 256*a^4*c^7*d^4 - 1024*a^3*b*c^8*d^3 + 1536*a^2*b^2*c^9*d^2 - 1024*a*b^3*c^10*d))^(3/4)*(x*(1024*a^11*b^13*c^20*d^4 - 4096*a^12*b^12*c^19*d^5 + 6144*a^13*b^11*c^18*d^6 - 4096*a^14*b^10*c^17*d^7 + 1024*a^15*b^9*c^16*d^8 + 1024*a^16*b^8*c^15*d^9 - 4096*a^17*b^7*c^14*d^10 + 6144*a^18*b^6*c^13*d^11 - 4096*a^19*b^5*c^12*d^12 + 1024*a^20*b^4*c^11*d^13) - (-d^7/(256*b^4*c^11 + 256*a^4*c^7*d^4 - 1024*a^3*b*c^8*d^3 + 1536*a^2*b^2*c^9*d^2 - 1024*a*b^3*c^10*d))^(1/4)*(4096*a^13*b^12*c^21*d^4 - 20480*a^14*b^11*c^20*d^5 + 40960*a^15*b^10*c^19*d^6 - 45056*a^16*b^9*c^18*d^7 + 40960*a^17*b^8*c^17*d^8 - 45056*a^18*b^7*c^16*d^9 + 40960*a^19*b^6*c^15*d^10 - 20480*a^20*b^5*c^14*d^11 + 4096*a^21*b^4*c^13*d^12)*1i)*1i - 16*a^9*b^12*c^14*d^7 + 16*a^10*b^11*c^13*d^8 + 16*a^13*b^8*c^10*d^11 - 16*a^14*b^7*c^9*d^12)*1i)*1i - (-d^7/(256*b^4*c^11 + 256*a^4*c^7*d^4 - 1024*a^3*b*c^8*d^3 + 1536*a^2*b^2*c^9*d^2 - 1024*a*b^3*c^10*d))^(1/4)*(x*(4*a^9*b^11*c^11*d^9 + 4*a^11*b^9*c^9*d^11) - (-d^7/(256*b^4*c^11 + 256*a^4*c^7*d^4 - 1024*a^3*b*c^8*d^3 + 1536*a^2*b^2*c^9*d^2 - 1024*a*b^3*c^10*d))^(1/4)*((-d^7/(256*b^4*c^11 + 256*a^4*c^7*d^4 - 1024*a^3*b*c^8*d^3 + 1536*a^2*b^2*c^9*d^2 - 1024*a*b^3*c^10*d))^(3/4)*(x*(1024*a^11*b^13*c^20*d^4 - 4096*a^12*b^12*c^19*d^5 + 6144*a^13*b^11*c^18*d^6 - 4096*a^14*b^10*c^17*d^7 + 1024*a^15*b^9*c^16*d^8 + 1024*a^16*b^8*c^15*d^9 - 4096*a^17*b^7*c^14*d^10 + 6144*a^18*b^6*c^13*d^11 - 4096*a^19*b^5*c^12*d^12 + 1024*a^20*b^4*c^11*d^13) + (-d^7/(256*b^4*c^11 + 256*a^4*c^7*d^4 - 1024*a^3*b*c^8*d^3 + 1536*a^2*b^2*c^9*d^2 - 1024*a*b^3*c^10*d))^(1/4)*(4096*a^13*b^12*c^21*d^4 - 20480*a^14*b^11*c^20*d^5 + 40960*a^15*b^10*c^19*d^6 - 45056*a^16*b^9*c^18*d^7 + 40960*a^17*b^8*c^17*d^8 - 45056*a^18*b^7*c^16*d^9 + 40960*a^19*b^6*c^15*d^10 - 20480*a^20*b^5*c^14*d^11 + 4096*a^21*b^4*c^13*d^12)*1i)*1i + 16*a^9*b^12*c^14*d^7 - 16*a^10*b^11*c^13*d^8 - 16*a^13*b^8*c^10*d^11 + 16*a^14*b^7*c^9*d^12)*1i)*1i))*(-d^7/(256*b^4*c^11 + 256*a^4*c^7*d^4 - 1024*a^3*b*c^8*d^3 + 1536*a^2*b^2*c^9*d^2 - 1024*a*b^3*c^10*d))^(1/4) - 2*atan(-((-b^7/(256*a^11*d^4 + 256*a^7*b^4*c^4 - 1024*a^8*b^3*c^3*d + 1536*a^9*b^2*c^2*d^2 - 1024*a^10*b*c*d^3))^(1/4)*(x*(4*a^9*b^11*c^11*d^9 + 4*a^11*b^9*c^9*d^11) - (-b^7/(256*a^11*d^4 + 256*a^7*b^4*c^4 - 1024*a^8*b^3*c^3*d + 1536*a^9*b^2*c^2*d^2 - 1024*a^10*b*c*d^3))^(1/4)*((-b^7/(256*a^11*d^4 + 256*a^7*b^4*c^4 - 1024*a^8*b^3*c^3*d + 1536*a^9*b^2*c^2*d^2 - 1024*a^10*b*c*d^3))^(3/4)*((-b^7/(256*a^11*d^4 + 256*a^7*b^4*c^4 - 1024*a^8*b^3*c^3*d + 1536*a^9*b^2*c^2*d^2 - 1024*a^10*b*c*d^3))^(1/4)*(4096*a^13*b^12*c^21*d^4 - 20480*a^14*b^11*c^20*d^5 + 40960*a^15*b^10*c^19*d^6 - 45056*a^16*b^9*c^18*d^7 + 40960*a^17*b^8*c^17*d^8 - 45056*a^18*b^7*c^16*d^9 + 40960*a^19*b^6*c^15*d^10 - 20480*a^20*b^5*c^14*d^11 + 4096*a^21*b^4*c^13*d^12)*1i + x*(1024*a^11*b^13*c^20*d^4 - 4096*a^12*b^12*c^19*d^5 + 6144*a^13*b^11*c^18*d^6 - 4096*a^14*b^10*c^17*d^7 + 1024*a^15*b^9*c^16*d^8 + 1024*a^16*b^8*c^15*d^9 - 4096*a^17*b^7*c^14*d^10 + 6144*a^18*b^6*c^13*d^11 - 4096*a^19*b^5*c^12*d^12 + 1024*a^20*b^4*c^11*d^13))*1i + 16*a^9*b^12*c^14*d^7 - 16*a^10*b^11*c^13*d^8 - 16*a^13*b^8*c^10*d^11 + 16*a^14*b^7*c^9*d^12)*1i) + (-b^7/(256*a^11*d^4 + 256*a^7*b^4*c^4 - 1024*a^8*b^3*c^3*d + 1536*a^9*b^2*c^2*d^2 - 1024*a^10*b*c*d^3))^(1/4)*(x*(4*a^9*b^11*c^11*d^9 + 4*a^11*b^9*c^9*d^11) + (-b^7/(256*a^11*d^4 + 256*a^7*b^4*c^4 - 1024*a^8*b^3*c^3*d + 1536*a^9*b^2*c^2*d^2 - 1024*a^10*b*c*d^3))^(1/4)*((-b^7/(256*a^11*d^4 + 256*a^7*b^4*c^4 - 1024*a^8*b^3*c^3*d + 1536*a^9*b^2*c^2*d^2 - 1024*a^10*b*c*d^3))^(3/4)*((-b^7/(256*a^11*d^4 + 256*a^7*b^4*c^4 - 1024*a^8*b^3*c^3*d + 1536*a^9*b^2*c^2*d^2 - 1024*a^10*b*c*d^3))^(1/4)*(4096*a^13*b^12*c^21*d^4 - 20480*a^14*b^11*c^20*d^5 + 40960*a^15*b^10*c^19*d^6 - 45056*a^16*b^9*c^18*d^7 + 40960*a^17*b^8*c^17*d^8 - 45056*a^18*b^7*c^16*d^9 + 40960*a^19*b^6*c^15*d^10 - 20480*a^20*b^5*c^14*d^11 + 4096*a^21*b^4*c^13*d^12)*1i - x*(1024*a^11*b^13*c^20*d^4 - 4096*a^12*b^12*c^19*d^5 + 6144*a^13*b^11*c^18*d^6 - 4096*a^14*b^10*c^17*d^7 + 1024*a^15*b^9*c^16*d^8 + 1024*a^16*b^8*c^15*d^9 - 4096*a^17*b^7*c^14*d^10 + 6144*a^18*b^6*c^13*d^11 - 4096*a^19*b^5*c^12*d^12 + 1024*a^20*b^4*c^11*d^13))*1i + 16*a^9*b^12*c^14*d^7 - 16*a^10*b^11*c^13*d^8 - 16*a^13*b^8*c^10*d^11 + 16*a^14*b^7*c^9*d^12)*1i))/((-b^7/(256*a^11*d^4 + 256*a^7*b^4*c^4 - 1024*a^8*b^3*c^3*d + 1536*a^9*b^2*c^2*d^2 - 1024*a^10*b*c*d^3))^(1/4)*(x*(4*a^9*b^11*c^11*d^9 + 4*a^11*b^9*c^9*d^11) - (-b^7/(256*a^11*d^4 + 256*a^7*b^4*c^4 - 1024*a^8*b^3*c^3*d + 1536*a^9*b^2*c^2*d^2 - 1024*a^10*b*c*d^3))^(1/4)*((-b^7/(256*a^11*d^4 + 256*a^7*b^4*c^4 - 1024*a^8*b^3*c^3*d + 1536*a^9*b^2*c^2*d^2 - 1024*a^10*b*c*d^3))^(3/4)*((-b^7/(256*a^11*d^4 + 256*a^7*b^4*c^4 - 1024*a^8*b^3*c^3*d + 1536*a^9*b^2*c^2*d^2 - 1024*a^10*b*c*d^3))^(1/4)*(4096*a^13*b^12*c^21*d^4 - 20480*a^14*b^11*c^20*d^5 + 40960*a^15*b^10*c^19*d^6 - 45056*a^16*b^9*c^18*d^7 + 40960*a^17*b^8*c^17*d^8 - 45056*a^18*b^7*c^16*d^9 + 40960*a^19*b^6*c^15*d^10 - 20480*a^20*b^5*c^14*d^11 + 4096*a^21*b^4*c^13*d^12)*1i + x*(1024*a^11*b^13*c^20*d^4 - 4096*a^12*b^12*c^19*d^5 + 6144*a^13*b^11*c^18*d^6 - 4096*a^14*b^10*c^17*d^7 + 1024*a^15*b^9*c^16*d^8 + 1024*a^16*b^8*c^15*d^9 - 4096*a^17*b^7*c^14*d^10 + 6144*a^18*b^6*c^13*d^11 - 4096*a^19*b^5*c^12*d^12 + 1024*a^20*b^4*c^11*d^13))*1i + 16*a^9*b^12*c^14*d^7 - 16*a^10*b^11*c^13*d^8 - 16*a^13*b^8*c^10*d^11 + 16*a^14*b^7*c^9*d^12)*1i)*1i - (-b^7/(256*a^11*d^4 + 256*a^7*b^4*c^4 - 1024*a^8*b^3*c^3*d + 1536*a^9*b^2*c^2*d^2 - 1024*a^10*b*c*d^3))^(1/4)*(x*(4*a^9*b^11*c^11*d^9 + 4*a^11*b^9*c^9*d^11) + (-b^7/(256*a^11*d^4 + 256*a^7*b^4*c^4 - 1024*a^8*b^3*c^3*d + 1536*a^9*b^2*c^2*d^2 - 1024*a^10*b*c*d^3))^(1/4)*((-b^7/(256*a^11*d^4 + 256*a^7*b^4*c^4 - 1024*a^8*b^3*c^3*d + 1536*a^9*b^2*c^2*d^2 - 1024*a^10*b*c*d^3))^(3/4)*((-b^7/(256*a^11*d^4 + 256*a^7*b^4*c^4 - 1024*a^8*b^3*c^3*d + 1536*a^9*b^2*c^2*d^2 - 1024*a^10*b*c*d^3))^(1/4)*(4096*a^13*b^12*c^21*d^4 - 20480*a^14*b^11*c^20*d^5 + 40960*a^15*b^10*c^19*d^6 - 45056*a^16*b^9*c^18*d^7 + 40960*a^17*b^8*c^17*d^8 - 45056*a^18*b^7*c^16*d^9 + 40960*a^19*b^6*c^15*d^10 - 20480*a^20*b^5*c^14*d^11 + 4096*a^21*b^4*c^13*d^12)*1i - x*(1024*a^11*b^13*c^20*d^4 - 4096*a^12*b^12*c^19*d^5 + 6144*a^13*b^11*c^18*d^6 - 4096*a^14*b^10*c^17*d^7 + 1024*a^15*b^9*c^16*d^8 + 1024*a^16*b^8*c^15*d^9 - 4096*a^17*b^7*c^14*d^10 + 6144*a^18*b^6*c^13*d^11 - 4096*a^19*b^5*c^12*d^12 + 1024*a^20*b^4*c^11*d^13))*1i + 16*a^9*b^12*c^14*d^7 - 16*a^10*b^11*c^13*d^8 - 16*a^13*b^8*c^10*d^11 + 16*a^14*b^7*c^9*d^12)*1i)*1i))*(-b^7/(256*a^11*d^4 + 256*a^7*b^4*c^4 - 1024*a^8*b^3*c^3*d + 1536*a^9*b^2*c^2*d^2 - 1024*a^10*b*c*d^3))^(1/4) - 1/(3*a*c*x^3)","B"
786,1,4547,479,6.011945,"\text{Not used}","int(1/(x^6*(a + b*x^4)*(c + d*x^4)),x)","-2\,\mathrm{atan}\left(\frac{1024\,a^{11}\,b^{10}\,c^{13}\,x\,{\left(-\frac{b^9}{256\,a^{13}\,d^4-1024\,a^{12}\,b\,c\,d^3+1536\,a^{11}\,b^2\,c^2\,d^2-1024\,a^{10}\,b^3\,c^3\,d+256\,a^9\,b^4\,c^4}\right)}^{5/4}+4\,a^{11}\,b^6\,d^9\,x\,{\left(-\frac{b^9}{256\,a^{13}\,d^4-1024\,a^{12}\,b\,c\,d^3+1536\,a^{11}\,b^2\,c^2\,d^2-1024\,a^{10}\,b^3\,c^3\,d+256\,a^9\,b^4\,c^4}\right)}^{1/4}+1024\,a^{21}\,c^3\,d^{10}\,x\,{\left(-\frac{b^9}{256\,a^{13}\,d^4-1024\,a^{12}\,b\,c\,d^3+1536\,a^{11}\,b^2\,c^2\,d^2-1024\,a^{10}\,b^3\,c^3\,d+256\,a^9\,b^4\,c^4}\right)}^{5/4}-4096\,a^{12}\,b^9\,c^{12}\,d\,x\,{\left(-\frac{b^9}{256\,a^{13}\,d^4-1024\,a^{12}\,b\,c\,d^3+1536\,a^{11}\,b^2\,c^2\,d^2-1024\,a^{10}\,b^3\,c^3\,d+256\,a^9\,b^4\,c^4}\right)}^{5/4}-4096\,a^{20}\,b\,c^4\,d^9\,x\,{\left(-\frac{b^9}{256\,a^{13}\,d^4-1024\,a^{12}\,b\,c\,d^3+1536\,a^{11}\,b^2\,c^2\,d^2-1024\,a^{10}\,b^3\,c^3\,d+256\,a^9\,b^4\,c^4}\right)}^{5/4}+4\,a^8\,b^9\,c^3\,d^6\,x\,{\left(-\frac{b^9}{256\,a^{13}\,d^4-1024\,a^{12}\,b\,c\,d^3+1536\,a^{11}\,b^2\,c^2\,d^2-1024\,a^{10}\,b^3\,c^3\,d+256\,a^9\,b^4\,c^4}\right)}^{1/4}+6144\,a^{13}\,b^8\,c^{11}\,d^2\,x\,{\left(-\frac{b^9}{256\,a^{13}\,d^4-1024\,a^{12}\,b\,c\,d^3+1536\,a^{11}\,b^2\,c^2\,d^2-1024\,a^{10}\,b^3\,c^3\,d+256\,a^9\,b^4\,c^4}\right)}^{5/4}-4096\,a^{14}\,b^7\,c^{10}\,d^3\,x\,{\left(-\frac{b^9}{256\,a^{13}\,d^4-1024\,a^{12}\,b\,c\,d^3+1536\,a^{11}\,b^2\,c^2\,d^2-1024\,a^{10}\,b^3\,c^3\,d+256\,a^9\,b^4\,c^4}\right)}^{5/4}+1024\,a^{15}\,b^6\,c^9\,d^4\,x\,{\left(-\frac{b^9}{256\,a^{13}\,d^4-1024\,a^{12}\,b\,c\,d^3+1536\,a^{11}\,b^2\,c^2\,d^2-1024\,a^{10}\,b^3\,c^3\,d+256\,a^9\,b^4\,c^4}\right)}^{5/4}+1024\,a^{17}\,b^4\,c^7\,d^6\,x\,{\left(-\frac{b^9}{256\,a^{13}\,d^4-1024\,a^{12}\,b\,c\,d^3+1536\,a^{11}\,b^2\,c^2\,d^2-1024\,a^{10}\,b^3\,c^3\,d+256\,a^9\,b^4\,c^4}\right)}^{5/4}-4096\,a^{18}\,b^3\,c^6\,d^7\,x\,{\left(-\frac{b^9}{256\,a^{13}\,d^4-1024\,a^{12}\,b\,c\,d^3+1536\,a^{11}\,b^2\,c^2\,d^2-1024\,a^{10}\,b^3\,c^3\,d+256\,a^9\,b^4\,c^4}\right)}^{5/4}+6144\,a^{19}\,b^2\,c^5\,d^8\,x\,{\left(-\frac{b^9}{256\,a^{13}\,d^4-1024\,a^{12}\,b\,c\,d^3+1536\,a^{11}\,b^2\,c^2\,d^2-1024\,a^{10}\,b^3\,c^3\,d+256\,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}{256\,a^{13}\,d^4-1024\,a^{12}\,b\,c\,d^3+1536\,a^{11}\,b^2\,c^2\,d^2-1024\,a^{10}\,b^3\,c^3\,d+256\,a^9\,b^4\,c^4}\right)}^{1/4}-2\,\mathrm{atan}\left(\frac{4\,b^9\,c^{11}\,d^6\,x\,{\left(-\frac{d^9}{256\,a^4\,c^9\,d^4-1024\,a^3\,b\,c^{10}\,d^3+1536\,a^2\,b^2\,c^{11}\,d^2-1024\,a\,b^3\,c^{12}\,d+256\,b^4\,c^{13}}\right)}^{1/4}+1024\,a^3\,b^{10}\,c^{21}\,x\,{\left(-\frac{d^9}{256\,a^4\,c^9\,d^4-1024\,a^3\,b\,c^{10}\,d^3+1536\,a^2\,b^2\,c^{11}\,d^2-1024\,a\,b^3\,c^{12}\,d+256\,b^4\,c^{13}}\right)}^{5/4}+1024\,a^{13}\,c^{11}\,d^{10}\,x\,{\left(-\frac{d^9}{256\,a^4\,c^9\,d^4-1024\,a^3\,b\,c^{10}\,d^3+1536\,a^2\,b^2\,c^{11}\,d^2-1024\,a\,b^3\,c^{12}\,d+256\,b^4\,c^{13}}\right)}^{5/4}-4096\,a^4\,b^9\,c^{20}\,d\,x\,{\left(-\frac{d^9}{256\,a^4\,c^9\,d^4-1024\,a^3\,b\,c^{10}\,d^3+1536\,a^2\,b^2\,c^{11}\,d^2-1024\,a\,b^3\,c^{12}\,d+256\,b^4\,c^{13}}\right)}^{5/4}-4096\,a^{12}\,b\,c^{12}\,d^9\,x\,{\left(-\frac{d^9}{256\,a^4\,c^9\,d^4-1024\,a^3\,b\,c^{10}\,d^3+1536\,a^2\,b^2\,c^{11}\,d^2-1024\,a\,b^3\,c^{12}\,d+256\,b^4\,c^{13}}\right)}^{5/4}+4\,a^3\,b^6\,c^8\,d^9\,x\,{\left(-\frac{d^9}{256\,a^4\,c^9\,d^4-1024\,a^3\,b\,c^{10}\,d^3+1536\,a^2\,b^2\,c^{11}\,d^2-1024\,a\,b^3\,c^{12}\,d+256\,b^4\,c^{13}}\right)}^{1/4}+6144\,a^5\,b^8\,c^{19}\,d^2\,x\,{\left(-\frac{d^9}{256\,a^4\,c^9\,d^4-1024\,a^3\,b\,c^{10}\,d^3+1536\,a^2\,b^2\,c^{11}\,d^2-1024\,a\,b^3\,c^{12}\,d+256\,b^4\,c^{13}}\right)}^{5/4}-4096\,a^6\,b^7\,c^{18}\,d^3\,x\,{\left(-\frac{d^9}{256\,a^4\,c^9\,d^4-1024\,a^3\,b\,c^{10}\,d^3+1536\,a^2\,b^2\,c^{11}\,d^2-1024\,a\,b^3\,c^{12}\,d+256\,b^4\,c^{13}}\right)}^{5/4}+1024\,a^7\,b^6\,c^{17}\,d^4\,x\,{\left(-\frac{d^9}{256\,a^4\,c^9\,d^4-1024\,a^3\,b\,c^{10}\,d^3+1536\,a^2\,b^2\,c^{11}\,d^2-1024\,a\,b^3\,c^{12}\,d+256\,b^4\,c^{13}}\right)}^{5/4}+1024\,a^9\,b^4\,c^{15}\,d^6\,x\,{\left(-\frac{d^9}{256\,a^4\,c^9\,d^4-1024\,a^3\,b\,c^{10}\,d^3+1536\,a^2\,b^2\,c^{11}\,d^2-1024\,a\,b^3\,c^{12}\,d+256\,b^4\,c^{13}}\right)}^{5/4}-4096\,a^{10}\,b^3\,c^{14}\,d^7\,x\,{\left(-\frac{d^9}{256\,a^4\,c^9\,d^4-1024\,a^3\,b\,c^{10}\,d^3+1536\,a^2\,b^2\,c^{11}\,d^2-1024\,a\,b^3\,c^{12}\,d+256\,b^4\,c^{13}}\right)}^{5/4}+6144\,a^{11}\,b^2\,c^{13}\,d^8\,x\,{\left(-\frac{d^9}{256\,a^4\,c^9\,d^4-1024\,a^3\,b\,c^{10}\,d^3+1536\,a^2\,b^2\,c^{11}\,d^2-1024\,a\,b^3\,c^{12}\,d+256\,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}{256\,a^4\,c^9\,d^4-1024\,a^3\,b\,c^{10}\,d^3+1536\,a^2\,b^2\,c^{11}\,d^2-1024\,a\,b^3\,c^{12}\,d+256\,b^4\,c^{13}}\right)}^{1/4}-\frac{\frac{1}{5\,a\,c}-\frac{x^4\,\left(a\,d+b\,c\right)}{a^2\,c^2}}{x^5}-\mathrm{atan}\left(\frac{a^{11}\,b^{10}\,c^{13}\,x\,{\left(-\frac{b^9}{256\,a^{13}\,d^4-1024\,a^{12}\,b\,c\,d^3+1536\,a^{11}\,b^2\,c^2\,d^2-1024\,a^{10}\,b^3\,c^3\,d+256\,a^9\,b^4\,c^4}\right)}^{5/4}\,1024{}\mathrm{i}+a^{11}\,b^6\,d^9\,x\,{\left(-\frac{b^9}{256\,a^{13}\,d^4-1024\,a^{12}\,b\,c\,d^3+1536\,a^{11}\,b^2\,c^2\,d^2-1024\,a^{10}\,b^3\,c^3\,d+256\,a^9\,b^4\,c^4}\right)}^{1/4}\,4{}\mathrm{i}+a^{21}\,c^3\,d^{10}\,x\,{\left(-\frac{b^9}{256\,a^{13}\,d^4-1024\,a^{12}\,b\,c\,d^3+1536\,a^{11}\,b^2\,c^2\,d^2-1024\,a^{10}\,b^3\,c^3\,d+256\,a^9\,b^4\,c^4}\right)}^{5/4}\,1024{}\mathrm{i}-a^{12}\,b^9\,c^{12}\,d\,x\,{\left(-\frac{b^9}{256\,a^{13}\,d^4-1024\,a^{12}\,b\,c\,d^3+1536\,a^{11}\,b^2\,c^2\,d^2-1024\,a^{10}\,b^3\,c^3\,d+256\,a^9\,b^4\,c^4}\right)}^{5/4}\,4096{}\mathrm{i}-a^{20}\,b\,c^4\,d^9\,x\,{\left(-\frac{b^9}{256\,a^{13}\,d^4-1024\,a^{12}\,b\,c\,d^3+1536\,a^{11}\,b^2\,c^2\,d^2-1024\,a^{10}\,b^3\,c^3\,d+256\,a^9\,b^4\,c^4}\right)}^{5/4}\,4096{}\mathrm{i}+a^8\,b^9\,c^3\,d^6\,x\,{\left(-\frac{b^9}{256\,a^{13}\,d^4-1024\,a^{12}\,b\,c\,d^3+1536\,a^{11}\,b^2\,c^2\,d^2-1024\,a^{10}\,b^3\,c^3\,d+256\,a^9\,b^4\,c^4}\right)}^{1/4}\,4{}\mathrm{i}+a^{13}\,b^8\,c^{11}\,d^2\,x\,{\left(-\frac{b^9}{256\,a^{13}\,d^4-1024\,a^{12}\,b\,c\,d^3+1536\,a^{11}\,b^2\,c^2\,d^2-1024\,a^{10}\,b^3\,c^3\,d+256\,a^9\,b^4\,c^4}\right)}^{5/4}\,6144{}\mathrm{i}-a^{14}\,b^7\,c^{10}\,d^3\,x\,{\left(-\frac{b^9}{256\,a^{13}\,d^4-1024\,a^{12}\,b\,c\,d^3+1536\,a^{11}\,b^2\,c^2\,d^2-1024\,a^{10}\,b^3\,c^3\,d+256\,a^9\,b^4\,c^4}\right)}^{5/4}\,4096{}\mathrm{i}+a^{15}\,b^6\,c^9\,d^4\,x\,{\left(-\frac{b^9}{256\,a^{13}\,d^4-1024\,a^{12}\,b\,c\,d^3+1536\,a^{11}\,b^2\,c^2\,d^2-1024\,a^{10}\,b^3\,c^3\,d+256\,a^9\,b^4\,c^4}\right)}^{5/4}\,1024{}\mathrm{i}+a^{17}\,b^4\,c^7\,d^6\,x\,{\left(-\frac{b^9}{256\,a^{13}\,d^4-1024\,a^{12}\,b\,c\,d^3+1536\,a^{11}\,b^2\,c^2\,d^2-1024\,a^{10}\,b^3\,c^3\,d+256\,a^9\,b^4\,c^4}\right)}^{5/4}\,1024{}\mathrm{i}-a^{18}\,b^3\,c^6\,d^7\,x\,{\left(-\frac{b^9}{256\,a^{13}\,d^4-1024\,a^{12}\,b\,c\,d^3+1536\,a^{11}\,b^2\,c^2\,d^2-1024\,a^{10}\,b^3\,c^3\,d+256\,a^9\,b^4\,c^4}\right)}^{5/4}\,4096{}\mathrm{i}+a^{19}\,b^2\,c^5\,d^8\,x\,{\left(-\frac{b^9}{256\,a^{13}\,d^4-1024\,a^{12}\,b\,c\,d^3+1536\,a^{11}\,b^2\,c^2\,d^2-1024\,a^{10}\,b^3\,c^3\,d+256\,a^9\,b^4\,c^4}\right)}^{5/4}\,6144{}\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}{256\,a^{13}\,d^4-1024\,a^{12}\,b\,c\,d^3+1536\,a^{11}\,b^2\,c^2\,d^2-1024\,a^{10}\,b^3\,c^3\,d+256\,a^9\,b^4\,c^4}\right)}^{1/4}\,2{}\mathrm{i}-\mathrm{atan}\left(\frac{b^9\,c^{11}\,d^6\,x\,{\left(-\frac{d^9}{256\,a^4\,c^9\,d^4-1024\,a^3\,b\,c^{10}\,d^3+1536\,a^2\,b^2\,c^{11}\,d^2-1024\,a\,b^3\,c^{12}\,d+256\,b^4\,c^{13}}\right)}^{1/4}\,4{}\mathrm{i}+a^3\,b^{10}\,c^{21}\,x\,{\left(-\frac{d^9}{256\,a^4\,c^9\,d^4-1024\,a^3\,b\,c^{10}\,d^3+1536\,a^2\,b^2\,c^{11}\,d^2-1024\,a\,b^3\,c^{12}\,d+256\,b^4\,c^{13}}\right)}^{5/4}\,1024{}\mathrm{i}+a^{13}\,c^{11}\,d^{10}\,x\,{\left(-\frac{d^9}{256\,a^4\,c^9\,d^4-1024\,a^3\,b\,c^{10}\,d^3+1536\,a^2\,b^2\,c^{11}\,d^2-1024\,a\,b^3\,c^{12}\,d+256\,b^4\,c^{13}}\right)}^{5/4}\,1024{}\mathrm{i}-a^4\,b^9\,c^{20}\,d\,x\,{\left(-\frac{d^9}{256\,a^4\,c^9\,d^4-1024\,a^3\,b\,c^{10}\,d^3+1536\,a^2\,b^2\,c^{11}\,d^2-1024\,a\,b^3\,c^{12}\,d+256\,b^4\,c^{13}}\right)}^{5/4}\,4096{}\mathrm{i}-a^{12}\,b\,c^{12}\,d^9\,x\,{\left(-\frac{d^9}{256\,a^4\,c^9\,d^4-1024\,a^3\,b\,c^{10}\,d^3+1536\,a^2\,b^2\,c^{11}\,d^2-1024\,a\,b^3\,c^{12}\,d+256\,b^4\,c^{13}}\right)}^{5/4}\,4096{}\mathrm{i}+a^3\,b^6\,c^8\,d^9\,x\,{\left(-\frac{d^9}{256\,a^4\,c^9\,d^4-1024\,a^3\,b\,c^{10}\,d^3+1536\,a^2\,b^2\,c^{11}\,d^2-1024\,a\,b^3\,c^{12}\,d+256\,b^4\,c^{13}}\right)}^{1/4}\,4{}\mathrm{i}+a^5\,b^8\,c^{19}\,d^2\,x\,{\left(-\frac{d^9}{256\,a^4\,c^9\,d^4-1024\,a^3\,b\,c^{10}\,d^3+1536\,a^2\,b^2\,c^{11}\,d^2-1024\,a\,b^3\,c^{12}\,d+256\,b^4\,c^{13}}\right)}^{5/4}\,6144{}\mathrm{i}-a^6\,b^7\,c^{18}\,d^3\,x\,{\left(-\frac{d^9}{256\,a^4\,c^9\,d^4-1024\,a^3\,b\,c^{10}\,d^3+1536\,a^2\,b^2\,c^{11}\,d^2-1024\,a\,b^3\,c^{12}\,d+256\,b^4\,c^{13}}\right)}^{5/4}\,4096{}\mathrm{i}+a^7\,b^6\,c^{17}\,d^4\,x\,{\left(-\frac{d^9}{256\,a^4\,c^9\,d^4-1024\,a^3\,b\,c^{10}\,d^3+1536\,a^2\,b^2\,c^{11}\,d^2-1024\,a\,b^3\,c^{12}\,d+256\,b^4\,c^{13}}\right)}^{5/4}\,1024{}\mathrm{i}+a^9\,b^4\,c^{15}\,d^6\,x\,{\left(-\frac{d^9}{256\,a^4\,c^9\,d^4-1024\,a^3\,b\,c^{10}\,d^3+1536\,a^2\,b^2\,c^{11}\,d^2-1024\,a\,b^3\,c^{12}\,d+256\,b^4\,c^{13}}\right)}^{5/4}\,1024{}\mathrm{i}-a^{10}\,b^3\,c^{14}\,d^7\,x\,{\left(-\frac{d^9}{256\,a^4\,c^9\,d^4-1024\,a^3\,b\,c^{10}\,d^3+1536\,a^2\,b^2\,c^{11}\,d^2-1024\,a\,b^3\,c^{12}\,d+256\,b^4\,c^{13}}\right)}^{5/4}\,4096{}\mathrm{i}+a^{11}\,b^2\,c^{13}\,d^8\,x\,{\left(-\frac{d^9}{256\,a^4\,c^9\,d^4-1024\,a^3\,b\,c^{10}\,d^3+1536\,a^2\,b^2\,c^{11}\,d^2-1024\,a\,b^3\,c^{12}\,d+256\,b^4\,c^{13}}\right)}^{5/4}\,6144{}\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}{256\,a^4\,c^9\,d^4-1024\,a^3\,b\,c^{10}\,d^3+1536\,a^2\,b^2\,c^{11}\,d^2-1024\,a\,b^3\,c^{12}\,d+256\,b^4\,c^{13}}\right)}^{1/4}\,2{}\mathrm{i}","Not used",1,"- 2*atan((1024*a^11*b^10*c^13*x*(-b^9/(256*a^13*d^4 + 256*a^9*b^4*c^4 - 1024*a^10*b^3*c^3*d + 1536*a^11*b^2*c^2*d^2 - 1024*a^12*b*c*d^3))^(5/4) + 4*a^11*b^6*d^9*x*(-b^9/(256*a^13*d^4 + 256*a^9*b^4*c^4 - 1024*a^10*b^3*c^3*d + 1536*a^11*b^2*c^2*d^2 - 1024*a^12*b*c*d^3))^(1/4) + 1024*a^21*c^3*d^10*x*(-b^9/(256*a^13*d^4 + 256*a^9*b^4*c^4 - 1024*a^10*b^3*c^3*d + 1536*a^11*b^2*c^2*d^2 - 1024*a^12*b*c*d^3))^(5/4) - 4096*a^12*b^9*c^12*d*x*(-b^9/(256*a^13*d^4 + 256*a^9*b^4*c^4 - 1024*a^10*b^3*c^3*d + 1536*a^11*b^2*c^2*d^2 - 1024*a^12*b*c*d^3))^(5/4) - 4096*a^20*b*c^4*d^9*x*(-b^9/(256*a^13*d^4 + 256*a^9*b^4*c^4 - 1024*a^10*b^3*c^3*d + 1536*a^11*b^2*c^2*d^2 - 1024*a^12*b*c*d^3))^(5/4) + 4*a^8*b^9*c^3*d^6*x*(-b^9/(256*a^13*d^4 + 256*a^9*b^4*c^4 - 1024*a^10*b^3*c^3*d + 1536*a^11*b^2*c^2*d^2 - 1024*a^12*b*c*d^3))^(1/4) + 6144*a^13*b^8*c^11*d^2*x*(-b^9/(256*a^13*d^4 + 256*a^9*b^4*c^4 - 1024*a^10*b^3*c^3*d + 1536*a^11*b^2*c^2*d^2 - 1024*a^12*b*c*d^3))^(5/4) - 4096*a^14*b^7*c^10*d^3*x*(-b^9/(256*a^13*d^4 + 256*a^9*b^4*c^4 - 1024*a^10*b^3*c^3*d + 1536*a^11*b^2*c^2*d^2 - 1024*a^12*b*c*d^3))^(5/4) + 1024*a^15*b^6*c^9*d^4*x*(-b^9/(256*a^13*d^4 + 256*a^9*b^4*c^4 - 1024*a^10*b^3*c^3*d + 1536*a^11*b^2*c^2*d^2 - 1024*a^12*b*c*d^3))^(5/4) + 1024*a^17*b^4*c^7*d^6*x*(-b^9/(256*a^13*d^4 + 256*a^9*b^4*c^4 - 1024*a^10*b^3*c^3*d + 1536*a^11*b^2*c^2*d^2 - 1024*a^12*b*c*d^3))^(5/4) - 4096*a^18*b^3*c^6*d^7*x*(-b^9/(256*a^13*d^4 + 256*a^9*b^4*c^4 - 1024*a^10*b^3*c^3*d + 1536*a^11*b^2*c^2*d^2 - 1024*a^12*b*c*d^3))^(5/4) + 6144*a^19*b^2*c^5*d^8*x*(-b^9/(256*a^13*d^4 + 256*a^9*b^4*c^4 - 1024*a^10*b^3*c^3*d + 1536*a^11*b^2*c^2*d^2 - 1024*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/(256*a^13*d^4 + 256*a^9*b^4*c^4 - 1024*a^10*b^3*c^3*d + 1536*a^11*b^2*c^2*d^2 - 1024*a^12*b*c*d^3))^(1/4) - atan((a^11*b^10*c^13*x*(-b^9/(256*a^13*d^4 + 256*a^9*b^4*c^4 - 1024*a^10*b^3*c^3*d + 1536*a^11*b^2*c^2*d^2 - 1024*a^12*b*c*d^3))^(5/4)*1024i + a^11*b^6*d^9*x*(-b^9/(256*a^13*d^4 + 256*a^9*b^4*c^4 - 1024*a^10*b^3*c^3*d + 1536*a^11*b^2*c^2*d^2 - 1024*a^12*b*c*d^3))^(1/4)*4i + a^21*c^3*d^10*x*(-b^9/(256*a^13*d^4 + 256*a^9*b^4*c^4 - 1024*a^10*b^3*c^3*d + 1536*a^11*b^2*c^2*d^2 - 1024*a^12*b*c*d^3))^(5/4)*1024i - a^12*b^9*c^12*d*x*(-b^9/(256*a^13*d^4 + 256*a^9*b^4*c^4 - 1024*a^10*b^3*c^3*d + 1536*a^11*b^2*c^2*d^2 - 1024*a^12*b*c*d^3))^(5/4)*4096i - a^20*b*c^4*d^9*x*(-b^9/(256*a^13*d^4 + 256*a^9*b^4*c^4 - 1024*a^10*b^3*c^3*d + 1536*a^11*b^2*c^2*d^2 - 1024*a^12*b*c*d^3))^(5/4)*4096i + a^8*b^9*c^3*d^6*x*(-b^9/(256*a^13*d^4 + 256*a^9*b^4*c^4 - 1024*a^10*b^3*c^3*d + 1536*a^11*b^2*c^2*d^2 - 1024*a^12*b*c*d^3))^(1/4)*4i + a^13*b^8*c^11*d^2*x*(-b^9/(256*a^13*d^4 + 256*a^9*b^4*c^4 - 1024*a^10*b^3*c^3*d + 1536*a^11*b^2*c^2*d^2 - 1024*a^12*b*c*d^3))^(5/4)*6144i - a^14*b^7*c^10*d^3*x*(-b^9/(256*a^13*d^4 + 256*a^9*b^4*c^4 - 1024*a^10*b^3*c^3*d + 1536*a^11*b^2*c^2*d^2 - 1024*a^12*b*c*d^3))^(5/4)*4096i + a^15*b^6*c^9*d^4*x*(-b^9/(256*a^13*d^4 + 256*a^9*b^4*c^4 - 1024*a^10*b^3*c^3*d + 1536*a^11*b^2*c^2*d^2 - 1024*a^12*b*c*d^3))^(5/4)*1024i + a^17*b^4*c^7*d^6*x*(-b^9/(256*a^13*d^4 + 256*a^9*b^4*c^4 - 1024*a^10*b^3*c^3*d + 1536*a^11*b^2*c^2*d^2 - 1024*a^12*b*c*d^3))^(5/4)*1024i - a^18*b^3*c^6*d^7*x*(-b^9/(256*a^13*d^4 + 256*a^9*b^4*c^4 - 1024*a^10*b^3*c^3*d + 1536*a^11*b^2*c^2*d^2 - 1024*a^12*b*c*d^3))^(5/4)*4096i + a^19*b^2*c^5*d^8*x*(-b^9/(256*a^13*d^4 + 256*a^9*b^4*c^4 - 1024*a^10*b^3*c^3*d + 1536*a^11*b^2*c^2*d^2 - 1024*a^12*b*c*d^3))^(5/4)*6144i)/(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/(256*a^13*d^4 + 256*a^9*b^4*c^4 - 1024*a^10*b^3*c^3*d + 1536*a^11*b^2*c^2*d^2 - 1024*a^12*b*c*d^3))^(1/4)*2i - 2*atan((4*b^9*c^11*d^6*x*(-d^9/(256*b^4*c^13 + 256*a^4*c^9*d^4 - 1024*a^3*b*c^10*d^3 + 1536*a^2*b^2*c^11*d^2 - 1024*a*b^3*c^12*d))^(1/4) + 1024*a^3*b^10*c^21*x*(-d^9/(256*b^4*c^13 + 256*a^4*c^9*d^4 - 1024*a^3*b*c^10*d^3 + 1536*a^2*b^2*c^11*d^2 - 1024*a*b^3*c^12*d))^(5/4) + 1024*a^13*c^11*d^10*x*(-d^9/(256*b^4*c^13 + 256*a^4*c^9*d^4 - 1024*a^3*b*c^10*d^3 + 1536*a^2*b^2*c^11*d^2 - 1024*a*b^3*c^12*d))^(5/4) - 4096*a^4*b^9*c^20*d*x*(-d^9/(256*b^4*c^13 + 256*a^4*c^9*d^4 - 1024*a^3*b*c^10*d^3 + 1536*a^2*b^2*c^11*d^2 - 1024*a*b^3*c^12*d))^(5/4) - 4096*a^12*b*c^12*d^9*x*(-d^9/(256*b^4*c^13 + 256*a^4*c^9*d^4 - 1024*a^3*b*c^10*d^3 + 1536*a^2*b^2*c^11*d^2 - 1024*a*b^3*c^12*d))^(5/4) + 4*a^3*b^6*c^8*d^9*x*(-d^9/(256*b^4*c^13 + 256*a^4*c^9*d^4 - 1024*a^3*b*c^10*d^3 + 1536*a^2*b^2*c^11*d^2 - 1024*a*b^3*c^12*d))^(1/4) + 6144*a^5*b^8*c^19*d^2*x*(-d^9/(256*b^4*c^13 + 256*a^4*c^9*d^4 - 1024*a^3*b*c^10*d^3 + 1536*a^2*b^2*c^11*d^2 - 1024*a*b^3*c^12*d))^(5/4) - 4096*a^6*b^7*c^18*d^3*x*(-d^9/(256*b^4*c^13 + 256*a^4*c^9*d^4 - 1024*a^3*b*c^10*d^3 + 1536*a^2*b^2*c^11*d^2 - 1024*a*b^3*c^12*d))^(5/4) + 1024*a^7*b^6*c^17*d^4*x*(-d^9/(256*b^4*c^13 + 256*a^4*c^9*d^4 - 1024*a^3*b*c^10*d^3 + 1536*a^2*b^2*c^11*d^2 - 1024*a*b^3*c^12*d))^(5/4) + 1024*a^9*b^4*c^15*d^6*x*(-d^9/(256*b^4*c^13 + 256*a^4*c^9*d^4 - 1024*a^3*b*c^10*d^3 + 1536*a^2*b^2*c^11*d^2 - 1024*a*b^3*c^12*d))^(5/4) - 4096*a^10*b^3*c^14*d^7*x*(-d^9/(256*b^4*c^13 + 256*a^4*c^9*d^4 - 1024*a^3*b*c^10*d^3 + 1536*a^2*b^2*c^11*d^2 - 1024*a*b^3*c^12*d))^(5/4) + 6144*a^11*b^2*c^13*d^8*x*(-d^9/(256*b^4*c^13 + 256*a^4*c^9*d^4 - 1024*a^3*b*c^10*d^3 + 1536*a^2*b^2*c^11*d^2 - 1024*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/(256*b^4*c^13 + 256*a^4*c^9*d^4 - 1024*a^3*b*c^10*d^3 + 1536*a^2*b^2*c^11*d^2 - 1024*a*b^3*c^12*d))^(1/4) - atan((b^9*c^11*d^6*x*(-d^9/(256*b^4*c^13 + 256*a^4*c^9*d^4 - 1024*a^3*b*c^10*d^3 + 1536*a^2*b^2*c^11*d^2 - 1024*a*b^3*c^12*d))^(1/4)*4i + a^3*b^10*c^21*x*(-d^9/(256*b^4*c^13 + 256*a^4*c^9*d^4 - 1024*a^3*b*c^10*d^3 + 1536*a^2*b^2*c^11*d^2 - 1024*a*b^3*c^12*d))^(5/4)*1024i + a^13*c^11*d^10*x*(-d^9/(256*b^4*c^13 + 256*a^4*c^9*d^4 - 1024*a^3*b*c^10*d^3 + 1536*a^2*b^2*c^11*d^2 - 1024*a*b^3*c^12*d))^(5/4)*1024i - a^4*b^9*c^20*d*x*(-d^9/(256*b^4*c^13 + 256*a^4*c^9*d^4 - 1024*a^3*b*c^10*d^3 + 1536*a^2*b^2*c^11*d^2 - 1024*a*b^3*c^12*d))^(5/4)*4096i - a^12*b*c^12*d^9*x*(-d^9/(256*b^4*c^13 + 256*a^4*c^9*d^4 - 1024*a^3*b*c^10*d^3 + 1536*a^2*b^2*c^11*d^2 - 1024*a*b^3*c^12*d))^(5/4)*4096i + a^3*b^6*c^8*d^9*x*(-d^9/(256*b^4*c^13 + 256*a^4*c^9*d^4 - 1024*a^3*b*c^10*d^3 + 1536*a^2*b^2*c^11*d^2 - 1024*a*b^3*c^12*d))^(1/4)*4i + a^5*b^8*c^19*d^2*x*(-d^9/(256*b^4*c^13 + 256*a^4*c^9*d^4 - 1024*a^3*b*c^10*d^3 + 1536*a^2*b^2*c^11*d^2 - 1024*a*b^3*c^12*d))^(5/4)*6144i - a^6*b^7*c^18*d^3*x*(-d^9/(256*b^4*c^13 + 256*a^4*c^9*d^4 - 1024*a^3*b*c^10*d^3 + 1536*a^2*b^2*c^11*d^2 - 1024*a*b^3*c^12*d))^(5/4)*4096i + a^7*b^6*c^17*d^4*x*(-d^9/(256*b^4*c^13 + 256*a^4*c^9*d^4 - 1024*a^3*b*c^10*d^3 + 1536*a^2*b^2*c^11*d^2 - 1024*a*b^3*c^12*d))^(5/4)*1024i + a^9*b^4*c^15*d^6*x*(-d^9/(256*b^4*c^13 + 256*a^4*c^9*d^4 - 1024*a^3*b*c^10*d^3 + 1536*a^2*b^2*c^11*d^2 - 1024*a*b^3*c^12*d))^(5/4)*1024i - a^10*b^3*c^14*d^7*x*(-d^9/(256*b^4*c^13 + 256*a^4*c^9*d^4 - 1024*a^3*b*c^10*d^3 + 1536*a^2*b^2*c^11*d^2 - 1024*a*b^3*c^12*d))^(5/4)*4096i + a^11*b^2*c^13*d^8*x*(-d^9/(256*b^4*c^13 + 256*a^4*c^9*d^4 - 1024*a^3*b*c^10*d^3 + 1536*a^2*b^2*c^11*d^2 - 1024*a*b^3*c^12*d))^(5/4)*6144i)/(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/(256*b^4*c^13 + 256*a^4*c^9*d^4 - 1024*a^3*b*c^10*d^3 + 1536*a^2*b^2*c^11*d^2 - 1024*a*b^3*c^12*d))^(1/4)*2i - (1/(5*a*c) - (x^4*(a*d + b*c))/(a^2*c^2))/x^5","B"
787,1,87,93,4.688285,"\text{Not used}","int((x^7*(c + d*x^4)^(1/2))/(a + b*x^4),x)","\frac{{\left(d\,x^4+c\right)}^{3/2}}{6\,b\,d}-\frac{a\,\sqrt{d\,x^4+c}}{2\,b^2}+\frac{a\,\mathrm{atan}\left(\frac{a\,\sqrt{b}\,\sqrt{d\,x^4+c}\,\sqrt{a\,d-b\,c}}{a^2\,d-a\,b\,c}\right)\,\sqrt{a\,d-b\,c}}{2\,b^{5/2}}","Not used",1,"(c + d*x^4)^(3/2)/(6*b*d) - (a*(c + d*x^4)^(1/2))/(2*b^2) + (a*atan((a*b^(1/2)*(c + d*x^4)^(1/2)*(a*d - b*c)^(1/2))/(a^2*d - a*b*c))*(a*d - b*c)^(1/2))/(2*b^(5/2))","B"
788,0,-1,120,0.000000,"\text{Not used}","int((x^5*(c + d*x^4)^(1/2))/(a + b*x^4),x)","\int \frac{x^5\,\sqrt{d\,x^4+c}}{b\,x^4+a} \,d x","Not used",1,"int((x^5*(c + d*x^4)^(1/2))/(a + b*x^4), x)","F"
789,1,54,70,4.660039,"\text{Not used}","int((x^3*(c + d*x^4)^(1/2))/(a + b*x^4),x)","\frac{\sqrt{d\,x^4+c}}{2\,b}-\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d\,x^4+c}}{\sqrt{a\,d-b\,c}}\right)\,\sqrt{a\,d-b\,c}}{2\,b^{3/2}}","Not used",1,"(c + d*x^4)^(1/2)/(2*b) - (atan((b^(1/2)*(c + d*x^4)^(1/2))/(a*d - b*c)^(1/2))*(a*d - b*c)^(1/2))/(2*b^(3/2))","B"
790,0,-1,91,0.000000,"\text{Not used}","int((x*(c + d*x^4)^(1/2))/(a + b*x^4),x)","\int \frac{x\,\sqrt{d\,x^4+c}}{b\,x^4+a} \,d x","Not used",1,"int((x*(c + d*x^4)^(1/2))/(a + b*x^4), x)","F"
791,1,199,85,4.868570,"\text{Not used}","int((c + d*x^4)^(1/2)/(x*(a + b*x^4)),x)","\frac{\sqrt{c}\,\mathrm{atanh}\left(\frac{\sqrt{c}\,\left(\sqrt{d\,x^4+c}\,\left(\frac{a^2\,b\,d^4}{2}-a\,b^2\,c\,d^3+b^3\,c^2\,d^2\right)+\frac{c\,\left(8\,a^3\,b^2\,d^3-16\,a^2\,b^3\,c\,d^2\right)\,\sqrt{d\,x^4+c}}{16\,a^2}\right)}{2\,a\,\left(\frac{b^2\,c^2\,d^3}{4}-\frac{a\,b\,c\,d^4}{4}\right)}\right)}{2\,a}+\frac{\mathrm{atanh}\left(\frac{a\,b^2\,c\,d^3\,\sqrt{d\,x^4+c}\,\sqrt{b^2\,c-a\,b\,d}}{4\,\left(\frac{a\,b^3\,c^2\,d^3}{4}-\frac{a^2\,b^2\,c\,d^4}{4}\right)}\right)\,\sqrt{b^2\,c-a\,b\,d}}{2\,a\,b}","Not used",1,"(c^(1/2)*atanh((c^(1/2)*((c + d*x^4)^(1/2)*((a^2*b*d^4)/2 + b^3*c^2*d^2 - a*b^2*c*d^3) + (c*(8*a^3*b^2*d^3 - 16*a^2*b^3*c*d^2)*(c + d*x^4)^(1/2))/(16*a^2)))/(2*a*((b^2*c^2*d^3)/4 - (a*b*c*d^4)/4))))/(2*a) + (atanh((a*b^2*c*d^3*(c + d*x^4)^(1/2)*(b^2*c - a*b*d)^(1/2))/(4*((a*b^3*c^2*d^3)/4 - (a^2*b^2*c*d^4)/4)))*(b^2*c - a*b*d)^(1/2))/(2*a*b)","B"
792,0,-1,76,0.000000,"\text{Not used}","int((c + d*x^4)^(1/2)/(x^3*(a + b*x^4)),x)","\int \frac{\sqrt{d\,x^4+c}}{x^3\,\left(b\,x^4+a\right)} \,d x","Not used",1,"int((c + d*x^4)^(1/2)/(x^3*(a + b*x^4)), x)","F"
793,1,269,115,5.386811,"\text{Not used}","int((c + d*x^4)^(1/2)/(x^5*(a + b*x^4)),x)","\frac{\mathrm{atanh}\left(\frac{b^3\,d^4\,\sqrt{d\,x^4+c}\,\sqrt{b^2\,c-a\,b\,d}}{16\,\left(\frac{a\,b^3\,d^5}{16}-\frac{b^4\,c\,d^4}{16}\right)}\right)\,\sqrt{b^2\,c-a\,b\,d}}{2\,a^2}-\frac{\sqrt{d\,x^4+c}}{4\,a\,x^4}-\frac{\mathrm{atanh}\left(\frac{b^4\,\sqrt{c}\,d^4\,\sqrt{d\,x^4+c}}{16\,\left(\frac{b^4\,c\,d^4}{16}-\frac{3\,a\,b^3\,d^5}{32}+\frac{a^2\,b^2\,d^6}{32\,c}\right)}-\frac{3\,b^3\,d^5\,\sqrt{d\,x^4+c}}{32\,\sqrt{c}\,\left(\frac{a\,b^2\,d^6}{32\,c}-\frac{3\,b^3\,d^5}{32}+\frac{b^4\,c\,d^4}{16\,a}\right)}+\frac{b^2\,d^6\,\sqrt{d\,x^4+c}}{32\,c^{3/2}\,\left(\frac{b^2\,d^6}{32\,c}-\frac{3\,b^3\,d^5}{32\,a}+\frac{b^4\,c\,d^4}{16\,a^2}\right)}\right)\,\left(a\,d-2\,b\,c\right)}{4\,a^2\,\sqrt{c}}","Not used",1,"(atanh((b^3*d^4*(c + d*x^4)^(1/2)*(b^2*c - a*b*d)^(1/2))/(16*((a*b^3*d^5)/16 - (b^4*c*d^4)/16)))*(b^2*c - a*b*d)^(1/2))/(2*a^2) - (c + d*x^4)^(1/2)/(4*a*x^4) - (atanh((b^4*c^(1/2)*d^4*(c + d*x^4)^(1/2))/(16*((b^4*c*d^4)/16 - (3*a*b^3*d^5)/32 + (a^2*b^2*d^6)/(32*c))) - (3*b^3*d^5*(c + d*x^4)^(1/2))/(32*c^(1/2)*((a*b^2*d^6)/(32*c) - (3*b^3*d^5)/32 + (b^4*c*d^4)/(16*a))) + (b^2*d^6*(c + d*x^4)^(1/2))/(32*c^(3/2)*((b^2*d^6)/(32*c) - (3*b^3*d^5)/(32*a) + (b^4*c*d^4)/(16*a^2))))*(a*d - 2*b*c))/(4*a^2*c^(1/2))","B"
794,0,-1,110,0.000000,"\text{Not used}","int((c + d*x^4)^(1/2)/(x^7*(a + b*x^4)),x)","\int \frac{\sqrt{d\,x^4+c}}{x^7\,\left(b\,x^4+a\right)} \,d x","Not used",1,"int((c + d*x^4)^(1/2)/(x^7*(a + b*x^4)), x)","F"
795,0,-1,857,0.000000,"\text{Not used}","int((x^6*(c + d*x^4)^(1/2))/(a + b*x^4),x)","\int \frac{x^6\,\sqrt{d\,x^4+c}}{b\,x^4+a} \,d x","Not used",1,"int((x^6*(c + d*x^4)^(1/2))/(a + b*x^4), x)","F"
796,0,-1,700,0.000000,"\text{Not used}","int((x^4*(c + d*x^4)^(1/2))/(a + b*x^4),x)","\int \frac{x^4\,\sqrt{d\,x^4+c}}{b\,x^4+a} \,d x","Not used",1,"int((x^4*(c + d*x^4)^(1/2))/(a + b*x^4), x)","F"
797,0,-1,786,0.000000,"\text{Not used}","int((x^2*(c + d*x^4)^(1/2))/(a + b*x^4),x)","\int \frac{x^2\,\sqrt{d\,x^4+c}}{b\,x^4+a} \,d x","Not used",1,"int((x^2*(c + d*x^4)^(1/2))/(a + b*x^4), x)","F"
798,0,-1,679,0.000000,"\text{Not used}","int((c + d*x^4)^(1/2)/(a + b*x^4),x)","\int \frac{\sqrt{d\,x^4+c}}{b\,x^4+a} \,d x","Not used",1,"int((c + d*x^4)^(1/2)/(a + b*x^4), x)","F"
799,0,-1,809,0.000000,"\text{Not used}","int((c + d*x^4)^(1/2)/(x^2*(a + b*x^4)),x)","\int \frac{\sqrt{d\,x^4+c}}{x^2\,\left(b\,x^4+a\right)} \,d x","Not used",1,"int((c + d*x^4)^(1/2)/(x^2*(a + b*x^4)), x)","F"
800,0,-1,703,0.000000,"\text{Not used}","int((c + d*x^4)^(1/2)/(x^4*(a + b*x^4)),x)","\int \frac{\sqrt{d\,x^4+c}}{x^4\,\left(b\,x^4+a\right)} \,d x","Not used",1,"int((c + d*x^4)^(1/2)/(x^4*(a + b*x^4)), x)","F"
801,0,-1,71,0.000000,"\text{Not used}","int(((e*x)^(3/2)*(c + d*x^4)^(1/2))/(a + b*x^4),x)","\int \frac{{\left(e\,x\right)}^{3/2}\,\sqrt{d\,x^4+c}}{b\,x^4+a} \,d x","Not used",1,"int(((e*x)^(3/2)*(c + d*x^4)^(1/2))/(a + b*x^4), x)","F"
802,0,-1,71,0.000000,"\text{Not used}","int(((e*x)^(1/2)*(c + d*x^4)^(1/2))/(a + b*x^4),x)","\int \frac{\sqrt{e\,x}\,\sqrt{d\,x^4+c}}{b\,x^4+a} \,d x","Not used",1,"int(((e*x)^(1/2)*(c + d*x^4)^(1/2))/(a + b*x^4), x)","F"
803,0,-1,69,0.000000,"\text{Not used}","int((c + d*x^4)^(1/2)/((e*x)^(1/2)*(a + b*x^4)),x)","\int \frac{\sqrt{d\,x^4+c}}{\sqrt{e\,x}\,\left(b\,x^4+a\right)} \,d x","Not used",1,"int((c + d*x^4)^(1/2)/((e*x)^(1/2)*(a + b*x^4)), x)","F"
804,0,-1,69,0.000000,"\text{Not used}","int((c + d*x^4)^(1/2)/((e*x)^(3/2)*(a + b*x^4)),x)","\int \frac{\sqrt{d\,x^4+c}}{{\left(e\,x\right)}^{3/2}\,\left(b\,x^4+a\right)} \,d x","Not used",1,"int((c + d*x^4)^(1/2)/((e*x)^(3/2)*(a + b*x^4)), x)","F"
805,1,102,104,4.824740,"\text{Not used}","int(x^11/((a + b*x^4)*(c + d*x^4)^(1/2)),x)","\frac{{\left(d\,x^4+c\right)}^{3/2}}{6\,b\,d^2}-\left(\frac{c}{b\,d^2}+\frac{2\,a\,d^3-2\,b\,c\,d^2}{4\,b^2\,d^4}\right)\,\sqrt{d\,x^4+c}+\frac{a^2\,\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d\,x^4+c}}{\sqrt{a\,d-b\,c}}\right)}{2\,b^{5/2}\,\sqrt{a\,d-b\,c}}","Not used",1,"(c + d*x^4)^(3/2)/(6*b*d^2) - (c/(b*d^2) + (2*a*d^3 - 2*b*c*d^2)/(4*b^2*d^4))*(c + d*x^4)^(1/2) + (a^2*atan((b^(1/2)*(c + d*x^4)^(1/2))/(a*d - b*c)^(1/2)))/(2*b^(5/2)*(a*d - b*c)^(1/2))","B"
806,1,58,74,4.728680,"\text{Not used}","int(x^7/((a + b*x^4)*(c + d*x^4)^(1/2)),x)","\frac{\sqrt{d\,x^4+c}}{2\,b\,d}-\frac{a\,\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d\,x^4+c}}{\sqrt{a\,d-b\,c}}\right)}{2\,b^{3/2}\,\sqrt{a\,d-b\,c}}","Not used",1,"(c + d*x^4)^(1/2)/(2*b*d) - (a*atan((b^(1/2)*(c + d*x^4)^(1/2))/(a*d - b*c)^(1/2)))/(2*b^(3/2)*(a*d - b*c)^(1/2))","B"
807,1,40,51,4.796976,"\text{Not used}","int(x^3/((a + b*x^4)*(c + d*x^4)^(1/2)),x)","\frac{\mathrm{atan}\left(\frac{b\,\sqrt{d\,x^4+c}}{\sqrt{a\,b\,d-b^2\,c}}\right)}{2\,\sqrt{a\,b\,d-b^2\,c}}","Not used",1,"atan((b*(c + d*x^4)^(1/2))/(a*b*d - b^2*c)^(1/2))/(2*(a*b*d - b^2*c)^(1/2))","B"
808,1,652,85,5.027632,"\text{Not used}","int(1/(x*(a + b*x^4)*(c + d*x^4)^(1/2)),x)","-\frac{\mathrm{atanh}\left(\frac{\sqrt{d\,x^4+c}}{\sqrt{c}}\right)}{2\,a\,\sqrt{c}}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{b^2\,c-a\,b\,d}\,\left(b^3\,d^2\,\sqrt{d\,x^4+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^4+c}\,\sqrt{b^2\,c-a\,b\,d}}{4\,\left(a^2\,d-a\,b\,c\right)}\right)}{4\,\left(a^2\,d-a\,b\,c\right)}\right)\,1{}\mathrm{i}}{4\,\left(a^2\,d-a\,b\,c\right)}+\frac{\sqrt{b^2\,c-a\,b\,d}\,\left(b^3\,d^2\,\sqrt{d\,x^4+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^4+c}\,\sqrt{b^2\,c-a\,b\,d}}{4\,\left(a^2\,d-a\,b\,c\right)}\right)}{4\,\left(a^2\,d-a\,b\,c\right)}\right)\,1{}\mathrm{i}}{4\,\left(a^2\,d-a\,b\,c\right)}}{\frac{\sqrt{b^2\,c-a\,b\,d}\,\left(b^3\,d^2\,\sqrt{d\,x^4+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^4+c}\,\sqrt{b^2\,c-a\,b\,d}}{4\,\left(a^2\,d-a\,b\,c\right)}\right)}{4\,\left(a^2\,d-a\,b\,c\right)}\right)}{4\,\left(a^2\,d-a\,b\,c\right)}-\frac{\sqrt{b^2\,c-a\,b\,d}\,\left(b^3\,d^2\,\sqrt{d\,x^4+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^4+c}\,\sqrt{b^2\,c-a\,b\,d}}{4\,\left(a^2\,d-a\,b\,c\right)}\right)}{4\,\left(a^2\,d-a\,b\,c\right)}\right)}{4\,\left(a^2\,d-a\,b\,c\right)}}\right)\,\sqrt{b^2\,c-a\,b\,d}\,1{}\mathrm{i}}{2\,\left(a^2\,d-a\,b\,c\right)}","Not used",1,"- atanh((c + d*x^4)^(1/2)/c^(1/2))/(2*a*c^(1/2)) - (atan((((b^2*c - a*b*d)^(1/2)*(b^3*d^2*(c + d*x^4)^(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^4)^(1/2)*(b^2*c - a*b*d)^(1/2))/(4*(a^2*d - a*b*c))))/(4*(a^2*d - a*b*c)))*1i)/(4*(a^2*d - a*b*c)) + ((b^2*c - a*b*d)^(1/2)*(b^3*d^2*(c + d*x^4)^(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^4)^(1/2)*(b^2*c - a*b*d)^(1/2))/(4*(a^2*d - a*b*c))))/(4*(a^2*d - a*b*c)))*1i)/(4*(a^2*d - a*b*c)))/(((b^2*c - a*b*d)^(1/2)*(b^3*d^2*(c + d*x^4)^(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^4)^(1/2)*(b^2*c - a*b*d)^(1/2))/(4*(a^2*d - a*b*c))))/(4*(a^2*d - a*b*c))))/(4*(a^2*d - a*b*c)) - ((b^2*c - a*b*d)^(1/2)*(b^3*d^2*(c + d*x^4)^(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^4)^(1/2)*(b^2*c - a*b*d)^(1/2))/(4*(a^2*d - a*b*c))))/(4*(a^2*d - a*b*c))))/(4*(a^2*d - a*b*c))))*(b^2*c - a*b*d)^(1/2)*1i)/(2*(a^2*d - a*b*c))","B"
809,1,396,117,5.351087,"\text{Not used}","int(1/(x^5*(a + b*x^4)*(c + d*x^4)^(1/2)),x)","\frac{\ln\left(\sqrt{d\,x^4+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}}{4\,a^3\,d-4\,a^2\,b\,c}-\frac{\ln\left(\sqrt{d\,x^4+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}}{4\,\left(a^3\,d-a^2\,b\,c\right)}-\frac{\sqrt{d\,x^4+c}}{4\,a\,c\,x^4}-\frac{\mathrm{atan}\left(\frac{b^4\,d^4\,\sqrt{d\,x^4+c}\,3{}\mathrm{i}}{16\,\sqrt{c^3}\,\left(\frac{3\,b^4\,d^4}{16\,c}+\frac{5\,a\,b^3\,d^5}{32\,c^2}+\frac{a^2\,b^2\,d^6}{32\,c^3}\right)}+\frac{b^2\,d^6\,\sqrt{d\,x^4+c}\,1{}\mathrm{i}}{32\,\sqrt{c^3}\,\left(\frac{5\,b^3\,d^5}{32\,a}+\frac{b^2\,d^6}{32\,c}+\frac{3\,b^4\,c\,d^4}{16\,a^2}\right)}+\frac{b^3\,d^5\,\sqrt{d\,x^4+c}\,5{}\mathrm{i}}{32\,\sqrt{c^3}\,\left(\frac{3\,b^4\,d^4}{16\,a}+\frac{5\,b^3\,d^5}{32\,c}+\frac{a\,b^2\,d^6}{32\,c^2}\right)}\right)\,\left(a\,d+2\,b\,c\right)\,1{}\mathrm{i}}{4\,a^2\,\sqrt{c^3}}","Not used",1,"(log((c + d*x^4)^(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))/(4*a^3*d - 4*a^2*b*c) - (log((c + d*x^4)^(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))/(4*(a^3*d - a^2*b*c)) - (c + d*x^4)^(1/2)/(4*a*c*x^4) - (atan((b^4*d^4*(c + d*x^4)^(1/2)*3i)/(16*(c^3)^(1/2)*((3*b^4*d^4)/(16*c) + (5*a*b^3*d^5)/(32*c^2) + (a^2*b^2*d^6)/(32*c^3))) + (b^2*d^6*(c + d*x^4)^(1/2)*1i)/(32*(c^3)^(1/2)*((5*b^3*d^5)/(32*a) + (b^2*d^6)/(32*c) + (3*b^4*c*d^4)/(16*a^2))) + (b^3*d^5*(c + d*x^4)^(1/2)*5i)/(32*(c^3)^(1/2)*((3*b^4*d^4)/(16*a) + (5*b^3*d^5)/(32*c) + (a*b^2*d^6)/(32*c^2))))*(a*d + 2*b*c)*1i)/(4*a^2*(c^3)^(1/2))","B"
810,0,-1,123,0.000000,"\text{Not used}","int(x^9/((a + b*x^4)*(c + d*x^4)^(1/2)),x)","\int \frac{x^9}{\left(b\,x^4+a\right)\,\sqrt{d\,x^4+c}} \,d x","Not used",1,"int(x^9/((a + b*x^4)*(c + d*x^4)^(1/2)), x)","F"
811,0,-1,91,0.000000,"\text{Not used}","int(x^5/((a + b*x^4)*(c + d*x^4)^(1/2)),x)","\int \frac{x^5}{\left(b\,x^4+a\right)\,\sqrt{d\,x^4+c}} \,d x","Not used",1,"int(x^5/((a + b*x^4)*(c + d*x^4)^(1/2)), x)","F"
812,0,-1,54,0.000000,"\text{Not used}","int(x/((a + b*x^4)*(c + d*x^4)^(1/2)),x)","\int \frac{x}{\left(b\,x^4+a\right)\,\sqrt{d\,x^4+c}} \,d x","Not used",1,"int(x/((a + b*x^4)*(c + d*x^4)^(1/2)), x)","F"
813,0,-1,80,0.000000,"\text{Not used}","int(1/(x^3*(a + b*x^4)*(c + d*x^4)^(1/2)),x)","\int \frac{1}{x^3\,\left(b\,x^4+a\right)\,\sqrt{d\,x^4+c}} \,d x","Not used",1,"int(1/(x^3*(a + b*x^4)*(c + d*x^4)^(1/2)), x)","F"
814,0,-1,115,0.000000,"\text{Not used}","int(1/(x^7*(a + b*x^4)*(c + d*x^4)^(1/2)),x)","\int \frac{1}{x^7\,\left(b\,x^4+a\right)\,\sqrt{d\,x^4+c}} \,d x","Not used",1,"int(1/(x^7*(a + b*x^4)*(c + d*x^4)^(1/2)), x)","F"
815,0,-1,872,0.000000,"\text{Not used}","int(x^8/((a + b*x^4)*(c + d*x^4)^(1/2)),x)","\int \frac{x^8}{\left(b\,x^4+a\right)\,\sqrt{d\,x^4+c}} \,d x","Not used",1,"int(x^8/((a + b*x^4)*(c + d*x^4)^(1/2)), x)","F"
816,0,-1,638,0.000000,"\text{Not used}","int(x^4/((a + b*x^4)*(c + d*x^4)^(1/2)),x)","\int \frac{x^4}{\left(b\,x^4+a\right)\,\sqrt{d\,x^4+c}} \,d x","Not used",1,"int(x^4/((a + b*x^4)*(c + d*x^4)^(1/2)), x)","F"
817,0,-1,638,0.000000,"\text{Not used}","int(1/((a + b*x^4)*(c + d*x^4)^(1/2)),x)","\int \frac{1}{\left(b\,x^4+a\right)\,\sqrt{d\,x^4+c}} \,d x","Not used",1,"int(1/((a + b*x^4)*(c + d*x^4)^(1/2)), x)","F"
818,0,-1,677,0.000000,"\text{Not used}","int(1/(x^4*(a + b*x^4)*(c + d*x^4)^(1/2)),x)","\int \frac{1}{x^4\,\left(b\,x^4+a\right)\,\sqrt{d\,x^4+c}} \,d x","Not used",1,"int(1/(x^4*(a + b*x^4)*(c + d*x^4)^(1/2)), x)","F"
819,0,-1,804,0.000000,"\text{Not used}","int(x^6/((a + b*x^4)*(c + d*x^4)^(1/2)),x)","\int \frac{x^6}{\left(b\,x^4+a\right)\,\sqrt{d\,x^4+c}} \,d x","Not used",1,"int(x^6/((a + b*x^4)*(c + d*x^4)^(1/2)), x)","F"
820,0,-1,656,0.000000,"\text{Not used}","int(x^2/((a + b*x^4)*(c + d*x^4)^(1/2)),x)","\int \frac{x^2}{\left(b\,x^4+a\right)\,\sqrt{d\,x^4+c}} \,d x","Not used",1,"int(x^2/((a + b*x^4)*(c + d*x^4)^(1/2)), x)","F"
821,0,-1,833,0.000000,"\text{Not used}","int(1/(x^2*(a + b*x^4)*(c + d*x^4)^(1/2)),x)","\int \frac{1}{x^2\,\left(b\,x^4+a\right)\,\sqrt{d\,x^4+c}} \,d x","Not used",1,"int(1/(x^2*(a + b*x^4)*(c + d*x^4)^(1/2)), x)","F"
822,1,186,175,5.191379,"\text{Not used}","int(x^15/((a + b*x^4)^2*(c + d*x^4)^(1/2)),x)","\frac{{\left(d\,x^4+c\right)}^{3/2}}{6\,b^2\,d^2}-\left(\frac{3\,c}{2\,b^2\,d^2}+\frac{a\,d-b\,c}{b^3\,d^2}\right)\,\sqrt{d\,x^4+c}+\frac{a^2\,\mathrm{atan}\left(\frac{a^2\,\sqrt{b}\,\sqrt{d\,x^4+c}\,\left(5\,a\,d-6\,b\,c\right)}{\sqrt{a\,d-b\,c}\,\left(5\,a^3\,d-6\,a^2\,b\,c\right)}\right)\,\left(5\,a\,d-6\,b\,c\right)}{4\,b^{7/2}\,{\left(a\,d-b\,c\right)}^{3/2}}-\frac{a^3\,d\,\sqrt{d\,x^4+c}}{2\,\left(a\,d-b\,c\right)\,\left(2\,b^4\,\left(d\,x^4+c\right)-2\,b^4\,c+2\,a\,b^3\,d\right)}","Not used",1,"(c + d*x^4)^(3/2)/(6*b^2*d^2) - ((3*c)/(2*b^2*d^2) + (a*d - b*c)/(b^3*d^2))*(c + d*x^4)^(1/2) + (a^2*atan((a^2*b^(1/2)*(c + d*x^4)^(1/2)*(5*a*d - 6*b*c))/((a*d - b*c)^(1/2)*(5*a^3*d - 6*a^2*b*c)))*(5*a*d - 6*b*c))/(4*b^(7/2)*(a*d - b*c)^(3/2)) - (a^3*d*(c + d*x^4)^(1/2))/(2*(a*d - b*c)*(2*b^4*(c + d*x^4) - 2*b^4*c + 2*a*b^3*d))","B"
823,1,144,123,5.117192,"\text{Not used}","int(x^11/((a + b*x^4)^2*(c + d*x^4)^(1/2)),x)","\frac{\sqrt{d\,x^4+c}}{2\,b^2\,d}-\frac{a\,\mathrm{atan}\left(\frac{a\,\sqrt{b}\,\sqrt{d\,x^4+c}\,\left(3\,a\,d-4\,b\,c\right)}{\left(3\,a^2\,d-4\,a\,b\,c\right)\,\sqrt{a\,d-b\,c}}\right)\,\left(3\,a\,d-4\,b\,c\right)}{4\,b^{5/2}\,{\left(a\,d-b\,c\right)}^{3/2}}+\frac{a^2\,d\,\sqrt{d\,x^4+c}}{2\,\left(a\,d-b\,c\right)\,\left(2\,b^3\,\left(d\,x^4+c\right)-2\,b^3\,c+2\,a\,b^2\,d\right)}","Not used",1,"(c + d*x^4)^(1/2)/(2*b^2*d) - (a*atan((a*b^(1/2)*(c + d*x^4)^(1/2)*(3*a*d - 4*b*c))/((3*a^2*d - 4*a*b*c)*(a*d - b*c)^(1/2)))*(3*a*d - 4*b*c))/(4*b^(5/2)*(a*d - b*c)^(3/2)) + (a^2*d*(c + d*x^4)^(1/2))/(2*(a*d - b*c)*(2*b^3*(c + d*x^4) - 2*b^3*c + 2*a*b^2*d))","B"
824,1,95,99,4.932218,"\text{Not used}","int(x^7/((a + b*x^4)^2*(c + d*x^4)^(1/2)),x)","\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d\,x^4+c}}{\sqrt{a\,d-b\,c}}\right)\,\left(a\,d-2\,b\,c\right)}{4\,b^{3/2}\,{\left(a\,d-b\,c\right)}^{3/2}}-\frac{a\,d\,\sqrt{d\,x^4+c}}{2\,b\,\left(a\,d-b\,c\right)\,\left(2\,b\,\left(d\,x^4+c\right)+2\,a\,d-2\,b\,c\right)}","Not used",1,"(atan((b^(1/2)*(c + d*x^4)^(1/2))/(a*d - b*c)^(1/2))*(a*d - 2*b*c))/(4*b^(3/2)*(a*d - b*c)^(3/2)) - (a*d*(c + d*x^4)^(1/2))/(2*b*(a*d - b*c)*(2*b*(c + d*x^4) + 2*a*d - 2*b*c))","B"
825,1,84,87,4.852287,"\text{Not used}","int(x^3/((a + b*x^4)^2*(c + d*x^4)^(1/2)),x)","\frac{d\,\sqrt{d\,x^4+c}}{2\,\left(a\,d-b\,c\right)\,\left(2\,b\,\left(d\,x^4+c\right)+2\,a\,d-2\,b\,c\right)}+\frac{d\,\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d\,x^4+c}}{\sqrt{a\,d-b\,c}}\right)}{4\,\sqrt{b}\,{\left(a\,d-b\,c\right)}^{3/2}}","Not used",1,"(d*(c + d*x^4)^(1/2))/(2*(a*d - b*c)*(2*b*(c + d*x^4) + 2*a*d - 2*b*c)) + (d*atan((b^(1/2)*(c + d*x^4)^(1/2))/(a*d - b*c)^(1/2)))/(4*b^(1/2)*(a*d - b*c)^(3/2))","B"
826,1,3017,132,5.868696,"\text{Not used}","int(1/(x*(a + b*x^4)^2*(c + d*x^4)^(1/2)),x)","-\frac{b\,d\,\sqrt{d\,x^4+c}}{2\,\left(a^2\,d-a\,b\,c\right)\,\left(2\,b\,\left(d\,x^4+c\right)+2\,a\,d-2\,b\,c\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\frac{2\,a^6\,b^2\,d^5-3\,a^5\,b^3\,c\,d^4+a^4\,b^4\,c^2\,d^3}{4\,\left(a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2\right)}-\frac{\sqrt{d\,x^4+c}\,\left(64\,a^7\,b^2\,d^5-256\,a^6\,b^3\,c\,d^4+320\,a^5\,b^4\,c^2\,d^3-128\,a^4\,b^5\,c^3\,d^2\right)}{128\,a^2\,\sqrt{c}\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}}{4\,a^2\,\sqrt{c}}-\frac{\sqrt{d\,x^4+c}\,\left(13\,a^2\,b^3\,d^4-20\,a\,b^4\,c\,d^3+8\,b^5\,c^2\,d^2\right)}{32\,\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{2\,a^6\,b^2\,d^5-3\,a^5\,b^3\,c\,d^4+a^4\,b^4\,c^2\,d^3}{4\,\left(a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2\right)}+\frac{\sqrt{d\,x^4+c}\,\left(64\,a^7\,b^2\,d^5-256\,a^6\,b^3\,c\,d^4+320\,a^5\,b^4\,c^2\,d^3-128\,a^4\,b^5\,c^3\,d^2\right)}{128\,a^2\,\sqrt{c}\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}}{4\,a^2\,\sqrt{c}}+\frac{\sqrt{d\,x^4+c}\,\left(13\,a^2\,b^3\,d^4-20\,a\,b^4\,c\,d^3+8\,b^5\,c^2\,d^2\right)}{32\,\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}{16}-\frac{b^4\,c\,d^3}{8}}{a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2}+\frac{\frac{\frac{2\,a^6\,b^2\,d^5-3\,a^5\,b^3\,c\,d^4+a^4\,b^4\,c^2\,d^3}{4\,\left(a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2\right)}-\frac{\sqrt{d\,x^4+c}\,\left(64\,a^7\,b^2\,d^5-256\,a^6\,b^3\,c\,d^4+320\,a^5\,b^4\,c^2\,d^3-128\,a^4\,b^5\,c^3\,d^2\right)}{128\,a^2\,\sqrt{c}\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}}{4\,a^2\,\sqrt{c}}-\frac{\sqrt{d\,x^4+c}\,\left(13\,a^2\,b^3\,d^4-20\,a\,b^4\,c\,d^3+8\,b^5\,c^2\,d^2\right)}{32\,\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{2\,a^6\,b^2\,d^5-3\,a^5\,b^3\,c\,d^4+a^4\,b^4\,c^2\,d^3}{4\,\left(a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2\right)}+\frac{\sqrt{d\,x^4+c}\,\left(64\,a^7\,b^2\,d^5-256\,a^6\,b^3\,c\,d^4+320\,a^5\,b^4\,c^2\,d^3-128\,a^4\,b^5\,c^3\,d^2\right)}{128\,a^2\,\sqrt{c}\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}}{4\,a^2\,\sqrt{c}}+\frac{\sqrt{d\,x^4+c}\,\left(13\,a^2\,b^3\,d^4-20\,a\,b^4\,c\,d^3+8\,b^5\,c^2\,d^2\right)}{32\,\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}}{2\,a^2\,\sqrt{c}}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\sqrt{d\,x^4+c}\,\left(13\,a^2\,b^3\,d^4-20\,a\,b^4\,c\,d^3+8\,b^5\,c^2\,d^2\right)}{8\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}-\frac{\left(\frac{2\,a^6\,b^2\,d^5-3\,a^5\,b^3\,c\,d^4+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^4+c}\,\left(3\,a\,d-2\,b\,c\right)\,\sqrt{-b\,{\left(a\,d-b\,c\right)}^3}\,\left(64\,a^7\,b^2\,d^5-256\,a^6\,b^3\,c\,d^4+320\,a^5\,b^4\,c^2\,d^3-128\,a^4\,b^5\,c^3\,d^2\right)}{64\,\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}}{8\,\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}}{8\,\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^4+c}\,\left(13\,a^2\,b^3\,d^4-20\,a\,b^4\,c\,d^3+8\,b^5\,c^2\,d^2\right)}{8\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}+\frac{\left(\frac{2\,a^6\,b^2\,d^5-3\,a^5\,b^3\,c\,d^4+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^4+c}\,\left(3\,a\,d-2\,b\,c\right)\,\sqrt{-b\,{\left(a\,d-b\,c\right)}^3}\,\left(64\,a^7\,b^2\,d^5-256\,a^6\,b^3\,c\,d^4+320\,a^5\,b^4\,c^2\,d^3-128\,a^4\,b^5\,c^3\,d^2\right)}{64\,\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}}{8\,\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}}{8\,\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}{16}-\frac{b^4\,c\,d^3}{8}}{a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2}-\frac{\left(\frac{\sqrt{d\,x^4+c}\,\left(13\,a^2\,b^3\,d^4-20\,a\,b^4\,c\,d^3+8\,b^5\,c^2\,d^2\right)}{8\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}-\frac{\left(\frac{2\,a^6\,b^2\,d^5-3\,a^5\,b^3\,c\,d^4+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^4+c}\,\left(3\,a\,d-2\,b\,c\right)\,\sqrt{-b\,{\left(a\,d-b\,c\right)}^3}\,\left(64\,a^7\,b^2\,d^5-256\,a^6\,b^3\,c\,d^4+320\,a^5\,b^4\,c^2\,d^3-128\,a^4\,b^5\,c^3\,d^2\right)}{64\,\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}}{8\,\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}}{8\,\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^4+c}\,\left(13\,a^2\,b^3\,d^4-20\,a\,b^4\,c\,d^3+8\,b^5\,c^2\,d^2\right)}{8\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}+\frac{\left(\frac{2\,a^6\,b^2\,d^5-3\,a^5\,b^3\,c\,d^4+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^4+c}\,\left(3\,a\,d-2\,b\,c\right)\,\sqrt{-b\,{\left(a\,d-b\,c\right)}^3}\,\left(64\,a^7\,b^2\,d^5-256\,a^6\,b^3\,c\,d^4+320\,a^5\,b^4\,c^2\,d^3-128\,a^4\,b^5\,c^3\,d^2\right)}{64\,\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}}{8\,\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}}{8\,\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)}","Not used",1,"(atan((((((c + d*x^4)^(1/2)*(13*a^2*b^3*d^4 + 8*b^5*c^2*d^2 - 20*a*b^4*c*d^3))/(8*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)) - (((2*a^6*b^2*d^5 - 3*a^5*b^3*c*d^4 + 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^4)^(1/2)*(3*a*d - 2*b*c)*(-b*(a*d - b*c)^3)^(1/2)*(64*a^7*b^2*d^5 - 256*a^6*b^3*c*d^4 - 128*a^4*b^5*c^3*d^2 + 320*a^5*b^4*c^2*d^3))/(64*(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))/(8*(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)/(8*(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^4)^(1/2)*(13*a^2*b^3*d^4 + 8*b^5*c^2*d^2 - 20*a*b^4*c*d^3))/(8*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)) + (((2*a^6*b^2*d^5 - 3*a^5*b^3*c*d^4 + 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^4)^(1/2)*(3*a*d - 2*b*c)*(-b*(a*d - b*c)^3)^(1/2)*(64*a^7*b^2*d^5 - 256*a^6*b^3*c*d^4 - 128*a^4*b^5*c^3*d^2 + 320*a^5*b^4*c^2*d^3))/(64*(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))/(8*(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)/(8*(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)/16 - (b^4*c*d^3)/8)/(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d) - ((((c + d*x^4)^(1/2)*(13*a^2*b^3*d^4 + 8*b^5*c^2*d^2 - 20*a*b^4*c*d^3))/(8*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)) - (((2*a^6*b^2*d^5 - 3*a^5*b^3*c*d^4 + 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^4)^(1/2)*(3*a*d - 2*b*c)*(-b*(a*d - b*c)^3)^(1/2)*(64*a^7*b^2*d^5 - 256*a^6*b^3*c*d^4 - 128*a^4*b^5*c^3*d^2 + 320*a^5*b^4*c^2*d^3))/(64*(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))/(8*(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))/(8*(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^4)^(1/2)*(13*a^2*b^3*d^4 + 8*b^5*c^2*d^2 - 20*a*b^4*c*d^3))/(8*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)) + (((2*a^6*b^2*d^5 - 3*a^5*b^3*c*d^4 + 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^4)^(1/2)*(3*a*d - 2*b*c)*(-b*(a*d - b*c)^3)^(1/2)*(64*a^7*b^2*d^5 - 256*a^6*b^3*c*d^4 - 128*a^4*b^5*c^3*d^2 + 320*a^5*b^4*c^2*d^3))/(64*(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))/(8*(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))/(8*(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)) - (atan((((((2*a^6*b^2*d^5 - 3*a^5*b^3*c*d^4 + a^4*b^4*c^2*d^3)/(4*(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d)) - ((c + d*x^4)^(1/2)*(64*a^7*b^2*d^5 - 256*a^6*b^3*c*d^4 - 128*a^4*b^5*c^3*d^2 + 320*a^5*b^4*c^2*d^3))/(128*a^2*c^(1/2)*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)))/(4*a^2*c^(1/2)) - ((c + d*x^4)^(1/2)*(13*a^2*b^3*d^4 + 8*b^5*c^2*d^2 - 20*a*b^4*c*d^3))/(32*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)))*1i)/(a^2*c^(1/2)) - ((((2*a^6*b^2*d^5 - 3*a^5*b^3*c*d^4 + a^4*b^4*c^2*d^3)/(4*(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d)) + ((c + d*x^4)^(1/2)*(64*a^7*b^2*d^5 - 256*a^6*b^3*c*d^4 - 128*a^4*b^5*c^3*d^2 + 320*a^5*b^4*c^2*d^3))/(128*a^2*c^(1/2)*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)))/(4*a^2*c^(1/2)) + ((c + d*x^4)^(1/2)*(13*a^2*b^3*d^4 + 8*b^5*c^2*d^2 - 20*a*b^4*c*d^3))/(32*(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)/16 - (b^4*c*d^3)/8)/(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d) + (((2*a^6*b^2*d^5 - 3*a^5*b^3*c*d^4 + a^4*b^4*c^2*d^3)/(4*(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d)) - ((c + d*x^4)^(1/2)*(64*a^7*b^2*d^5 - 256*a^6*b^3*c*d^4 - 128*a^4*b^5*c^3*d^2 + 320*a^5*b^4*c^2*d^3))/(128*a^2*c^(1/2)*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)))/(4*a^2*c^(1/2)) - ((c + d*x^4)^(1/2)*(13*a^2*b^3*d^4 + 8*b^5*c^2*d^2 - 20*a*b^4*c*d^3))/(32*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)))/(a^2*c^(1/2)) + (((2*a^6*b^2*d^5 - 3*a^5*b^3*c*d^4 + a^4*b^4*c^2*d^3)/(4*(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d)) + ((c + d*x^4)^(1/2)*(64*a^7*b^2*d^5 - 256*a^6*b^3*c*d^4 - 128*a^4*b^5*c^3*d^2 + 320*a^5*b^4*c^2*d^3))/(128*a^2*c^(1/2)*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)))/(4*a^2*c^(1/2)) + ((c + d*x^4)^(1/2)*(13*a^2*b^3*d^4 + 8*b^5*c^2*d^2 - 20*a*b^4*c*d^3))/(32*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)))/(a^2*c^(1/2))))*1i)/(2*a^2*c^(1/2)) - (b*d*(c + d*x^4)^(1/2))/(2*(a^2*d - a*b*c)*(2*b*(c + d*x^4) + 2*a*d - 2*b*c))","B"
827,1,3822,185,7.047019,"\text{Not used}","int(1/(x^5*(a + b*x^4)^2*(c + d*x^4)^(1/2)),x)","\frac{\frac{\sqrt{d\,x^4+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^4+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^4+c\right)\,\left(2\,a\,d-4\,b\,c\right)+2\,b\,{\left(d\,x^4+c\right)}^2+2\,b\,c^2-2\,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^4+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)}{8\,\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{a^9\,b^2\,c\,d^6+a^8\,b^3\,c^2\,d^5-4\,a^7\,b^4\,c^3\,d^4+2\,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^4+c}\,\left(5\,a\,d-4\,b\,c\right)\,\left(-64\,a^9\,b^2\,c^2\,d^5+256\,a^8\,b^3\,c^3\,d^4-320\,a^7\,b^4\,c^4\,d^3+128\,a^6\,b^5\,c^5\,d^2\right)}{64\,\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)}{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)}\right)\,1{}\mathrm{i}}{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)}+\frac{\sqrt{-b^3\,{\left(a\,d-b\,c\right)}^3}\,\left(5\,a\,d-4\,b\,c\right)\,\left(\frac{\sqrt{d\,x^4+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)}{8\,\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{a^9\,b^2\,c\,d^6+a^8\,b^3\,c^2\,d^5-4\,a^7\,b^4\,c^3\,d^4+2\,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^4+c}\,\left(5\,a\,d-4\,b\,c\right)\,\left(-64\,a^9\,b^2\,c^2\,d^5+256\,a^8\,b^3\,c^3\,d^4-320\,a^7\,b^4\,c^4\,d^3+128\,a^6\,b^5\,c^5\,d^2\right)}{64\,\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)}{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)}\right)\,1{}\mathrm{i}}{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)}}{\frac{\frac{5\,a^3\,b^4\,d^6}{32}+\frac{3\,a^2\,b^5\,c\,d^5}{16}-\frac{3\,a\,b^6\,c^2\,d^4}{2}+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^4+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)}{8\,\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{a^9\,b^2\,c\,d^6+a^8\,b^3\,c^2\,d^5-4\,a^7\,b^4\,c^3\,d^4+2\,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^4+c}\,\left(5\,a\,d-4\,b\,c\right)\,\left(-64\,a^9\,b^2\,c^2\,d^5+256\,a^8\,b^3\,c^3\,d^4-320\,a^7\,b^4\,c^4\,d^3+128\,a^6\,b^5\,c^5\,d^2\right)}{64\,\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)}{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)}\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)}+\frac{\sqrt{-b^3\,{\left(a\,d-b\,c\right)}^3}\,\left(5\,a\,d-4\,b\,c\right)\,\left(\frac{\sqrt{d\,x^4+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)}{8\,\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{a^9\,b^2\,c\,d^6+a^8\,b^3\,c^2\,d^5-4\,a^7\,b^4\,c^3\,d^4+2\,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^4+c}\,\left(5\,a\,d-4\,b\,c\right)\,\left(-64\,a^9\,b^2\,c^2\,d^5+256\,a^8\,b^3\,c^3\,d^4-320\,a^7\,b^4\,c^4\,d^3+128\,a^6\,b^5\,c^5\,d^2\right)}{64\,\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)}{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)}\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)}}\right)\,\sqrt{-b^3\,{\left(a\,d-b\,c\right)}^3}\,\left(5\,a\,d-4\,b\,c\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{\mathrm{atan}\left(\frac{\frac{\left(\frac{\sqrt{d\,x^4+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)}{8\,\left(a^6\,c^2\,d^2-2\,a^5\,b\,c^3\,d+a^4\,b^2\,c^4\right)}+\frac{\left(\frac{a^9\,b^2\,c\,d^6+a^8\,b^3\,c^2\,d^5-4\,a^7\,b^4\,c^3\,d^4+2\,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^4+c}\,\left(a\,d+4\,b\,c\right)\,\left(-64\,a^9\,b^2\,c^2\,d^5+256\,a^8\,b^3\,c^3\,d^4-320\,a^7\,b^4\,c^4\,d^3+128\,a^6\,b^5\,c^5\,d^2\right)}{64\,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)}{8\,a^3\,\sqrt{c^3}}\right)\,\left(a\,d+4\,b\,c\right)\,1{}\mathrm{i}}{8\,a^3\,\sqrt{c^3}}+\frac{\left(\frac{\sqrt{d\,x^4+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)}{8\,\left(a^6\,c^2\,d^2-2\,a^5\,b\,c^3\,d+a^4\,b^2\,c^4\right)}-\frac{\left(\frac{a^9\,b^2\,c\,d^6+a^8\,b^3\,c^2\,d^5-4\,a^7\,b^4\,c^3\,d^4+2\,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^4+c}\,\left(a\,d+4\,b\,c\right)\,\left(-64\,a^9\,b^2\,c^2\,d^5+256\,a^8\,b^3\,c^3\,d^4-320\,a^7\,b^4\,c^4\,d^3+128\,a^6\,b^5\,c^5\,d^2\right)}{64\,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)}{8\,a^3\,\sqrt{c^3}}\right)\,\left(a\,d+4\,b\,c\right)\,1{}\mathrm{i}}{8\,a^3\,\sqrt{c^3}}}{\frac{\frac{5\,a^3\,b^4\,d^6}{32}+\frac{3\,a^2\,b^5\,c\,d^5}{16}-\frac{3\,a\,b^6\,c^2\,d^4}{2}+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^4+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)}{8\,\left(a^6\,c^2\,d^2-2\,a^5\,b\,c^3\,d+a^4\,b^2\,c^4\right)}+\frac{\left(\frac{a^9\,b^2\,c\,d^6+a^8\,b^3\,c^2\,d^5-4\,a^7\,b^4\,c^3\,d^4+2\,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^4+c}\,\left(a\,d+4\,b\,c\right)\,\left(-64\,a^9\,b^2\,c^2\,d^5+256\,a^8\,b^3\,c^3\,d^4-320\,a^7\,b^4\,c^4\,d^3+128\,a^6\,b^5\,c^5\,d^2\right)}{64\,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)}{8\,a^3\,\sqrt{c^3}}\right)\,\left(a\,d+4\,b\,c\right)}{8\,a^3\,\sqrt{c^3}}+\frac{\left(\frac{\sqrt{d\,x^4+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)}{8\,\left(a^6\,c^2\,d^2-2\,a^5\,b\,c^3\,d+a^4\,b^2\,c^4\right)}-\frac{\left(\frac{a^9\,b^2\,c\,d^6+a^8\,b^3\,c^2\,d^5-4\,a^7\,b^4\,c^3\,d^4+2\,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^4+c}\,\left(a\,d+4\,b\,c\right)\,\left(-64\,a^9\,b^2\,c^2\,d^5+256\,a^8\,b^3\,c^3\,d^4-320\,a^7\,b^4\,c^4\,d^3+128\,a^6\,b^5\,c^5\,d^2\right)}{64\,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)}{8\,a^3\,\sqrt{c^3}}\right)\,\left(a\,d+4\,b\,c\right)}{8\,a^3\,\sqrt{c^3}}}\right)\,\left(a\,d+4\,b\,c\right)\,1{}\mathrm{i}}{4\,a^3\,\sqrt{c^3}}","Not used",1,"(((c + d*x^4)^(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^4)^(3/2)*(a*d^2 - 2*b*c*d))/(2*a^2*(b*c^2 - a*c*d)))/((c + d*x^4)*(2*a*d - 4*b*c) + 2*b*(c + d*x^4)^2 + 2*b*c^2 - 2*a*c*d) + (atan((((-b^3*(a*d - b*c)^3)^(1/2)*(5*a*d - 4*b*c)*(((c + d*x^4)^(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))/(8*(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)*((a^9*b^2*c*d^6 + 2*a^6*b^5*c^4*d^3 - 4*a^7*b^4*c^3*d^4 + 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^4)^(1/2)*(5*a*d - 4*b*c)*(128*a^6*b^5*c^5*d^2 - 320*a^7*b^4*c^4*d^3 + 256*a^8*b^3*c^3*d^4 - 64*a^9*b^2*c^2*d^5))/(64*(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))))/(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)))*1i)/(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)) + ((-b^3*(a*d - b*c)^3)^(1/2)*(5*a*d - 4*b*c)*(((c + d*x^4)^(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))/(8*(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)*((a^9*b^2*c*d^6 + 2*a^6*b^5*c^4*d^3 - 4*a^7*b^4*c^3*d^4 + 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^4)^(1/2)*(5*a*d - 4*b*c)*(128*a^6*b^5*c^5*d^2 - 320*a^7*b^4*c^4*d^3 + 256*a^8*b^3*c^3*d^4 - 64*a^9*b^2*c^2*d^5))/(64*(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))))/(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)))*1i)/(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)))/(((5*a^3*b^4*d^6)/32 + b^7*c^3*d^3 - (3*a*b^6*c^2*d^4)/2 + (3*a^2*b^5*c*d^5)/16)/(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^4)^(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))/(8*(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)*((a^9*b^2*c*d^6 + 2*a^6*b^5*c^4*d^3 - 4*a^7*b^4*c^3*d^4 + 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^4)^(1/2)*(5*a*d - 4*b*c)*(128*a^6*b^5*c^5*d^2 - 320*a^7*b^4*c^4*d^3 + 256*a^8*b^3*c^3*d^4 - 64*a^9*b^2*c^2*d^5))/(64*(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))))/(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))))/(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)) + ((-b^3*(a*d - b*c)^3)^(1/2)*(5*a*d - 4*b*c)*(((c + d*x^4)^(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))/(8*(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)*((a^9*b^2*c*d^6 + 2*a^6*b^5*c^4*d^3 - 4*a^7*b^4*c^3*d^4 + 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^4)^(1/2)*(5*a*d - 4*b*c)*(128*a^6*b^5*c^5*d^2 - 320*a^7*b^4*c^4*d^3 + 256*a^8*b^3*c^3*d^4 - 64*a^9*b^2*c^2*d^5))/(64*(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))))/(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))))/(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))))*(-b^3*(a*d - b*c)^3)^(1/2)*(5*a*d - 4*b*c)*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)) + (atan((((((c + d*x^4)^(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))/(8*(a^4*b^2*c^4 + a^6*c^2*d^2 - 2*a^5*b*c^3*d)) + (((a^9*b^2*c*d^6 + 2*a^6*b^5*c^4*d^3 - 4*a^7*b^4*c^3*d^4 + 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^4)^(1/2)*(a*d + 4*b*c)*(128*a^6*b^5*c^5*d^2 - 320*a^7*b^4*c^4*d^3 + 256*a^8*b^3*c^3*d^4 - 64*a^9*b^2*c^2*d^5))/(64*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))/(8*a^3*(c^3)^(1/2)))*(a*d + 4*b*c)*1i)/(8*a^3*(c^3)^(1/2)) + ((((c + d*x^4)^(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))/(8*(a^4*b^2*c^4 + a^6*c^2*d^2 - 2*a^5*b*c^3*d)) - (((a^9*b^2*c*d^6 + 2*a^6*b^5*c^4*d^3 - 4*a^7*b^4*c^3*d^4 + 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^4)^(1/2)*(a*d + 4*b*c)*(128*a^6*b^5*c^5*d^2 - 320*a^7*b^4*c^4*d^3 + 256*a^8*b^3*c^3*d^4 - 64*a^9*b^2*c^2*d^5))/(64*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))/(8*a^3*(c^3)^(1/2)))*(a*d + 4*b*c)*1i)/(8*a^3*(c^3)^(1/2)))/(((5*a^3*b^4*d^6)/32 + b^7*c^3*d^3 - (3*a*b^6*c^2*d^4)/2 + (3*a^2*b^5*c*d^5)/16)/(a^6*b^2*c^4 + a^8*c^2*d^2 - 2*a^7*b*c^3*d) - ((((c + d*x^4)^(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))/(8*(a^4*b^2*c^4 + a^6*c^2*d^2 - 2*a^5*b*c^3*d)) + (((a^9*b^2*c*d^6 + 2*a^6*b^5*c^4*d^3 - 4*a^7*b^4*c^3*d^4 + 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^4)^(1/2)*(a*d + 4*b*c)*(128*a^6*b^5*c^5*d^2 - 320*a^7*b^4*c^4*d^3 + 256*a^8*b^3*c^3*d^4 - 64*a^9*b^2*c^2*d^5))/(64*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))/(8*a^3*(c^3)^(1/2)))*(a*d + 4*b*c))/(8*a^3*(c^3)^(1/2)) + ((((c + d*x^4)^(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))/(8*(a^4*b^2*c^4 + a^6*c^2*d^2 - 2*a^5*b*c^3*d)) - (((a^9*b^2*c*d^6 + 2*a^6*b^5*c^4*d^3 - 4*a^7*b^4*c^3*d^4 + 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^4)^(1/2)*(a*d + 4*b*c)*(128*a^6*b^5*c^5*d^2 - 320*a^7*b^4*c^4*d^3 + 256*a^8*b^3*c^3*d^4 - 64*a^9*b^2*c^2*d^5))/(64*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))/(8*a^3*(c^3)^(1/2)))*(a*d + 4*b*c))/(8*a^3*(c^3)^(1/2))))*(a*d + 4*b*c)*1i)/(4*a^3*(c^3)^(1/2))","B"
828,0,-1,191,0.000000,"\text{Not used}","int(x^13/((a + b*x^4)^2*(c + d*x^4)^(1/2)),x)","\int \frac{x^{13}}{{\left(b\,x^4+a\right)}^2\,\sqrt{d\,x^4+c}} \,d x","Not used",1,"int(x^13/((a + b*x^4)^2*(c + d*x^4)^(1/2)), x)","F"
829,0,-1,141,0.000000,"\text{Not used}","int(x^9/((a + b*x^4)^2*(c + d*x^4)^(1/2)),x)","\int \frac{x^9}{{\left(b\,x^4+a\right)}^2\,\sqrt{d\,x^4+c}} \,d x","Not used",1,"int(x^9/((a + b*x^4)^2*(c + d*x^4)^(1/2)), x)","F"
830,0,-1,93,0.000000,"\text{Not used}","int(x^5/((a + b*x^4)^2*(c + d*x^4)^(1/2)),x)","\int \frac{x^5}{{\left(b\,x^4+a\right)}^2\,\sqrt{d\,x^4+c}} \,d x","Not used",1,"int(x^5/((a + b*x^4)^2*(c + d*x^4)^(1/2)), x)","F"
831,0,-1,104,0.000000,"\text{Not used}","int(x/((a + b*x^4)^2*(c + d*x^4)^(1/2)),x)","\int \frac{x}{{\left(b\,x^4+a\right)}^2\,\sqrt{d\,x^4+c}} \,d x","Not used",1,"int(x/((a + b*x^4)^2*(c + d*x^4)^(1/2)), x)","F"
832,0,-1,149,0.000000,"\text{Not used}","int(1/(x^3*(a + b*x^4)^2*(c + d*x^4)^(1/2)),x)","\int \frac{1}{x^3\,{\left(b\,x^4+a\right)}^2\,\sqrt{d\,x^4+c}} \,d x","Not used",1,"int(1/(x^3*(a + b*x^4)^2*(c + d*x^4)^(1/2)), x)","F"
833,0,-1,208,0.000000,"\text{Not used}","int(1/(x^7*(a + b*x^4)^2*(c + d*x^4)^(1/2)),x)","\int \frac{1}{x^7\,{\left(b\,x^4+a\right)}^2\,\sqrt{d\,x^4+c}} \,d x","Not used",1,"int(1/(x^7*(a + b*x^4)^2*(c + d*x^4)^(1/2)), x)","F"
834,0,-1,996,0.000000,"\text{Not used}","int(x^8/((a + b*x^4)^2*(c + d*x^4)^(1/2)),x)","\int \frac{x^8}{{\left(b\,x^4+a\right)}^2\,\sqrt{d\,x^4+c}} \,d x","Not used",1,"int(x^8/((a + b*x^4)^2*(c + d*x^4)^(1/2)), x)","F"
835,0,-1,908,0.000000,"\text{Not used}","int(x^4/((a + b*x^4)^2*(c + d*x^4)^(1/2)),x)","\int \frac{x^4}{{\left(b\,x^4+a\right)}^2\,\sqrt{d\,x^4+c}} \,d x","Not used",1,"int(x^4/((a + b*x^4)^2*(c + d*x^4)^(1/2)), x)","F"
836,0,-1,983,0.000000,"\text{Not used}","int(1/((a + b*x^4)^2*(c + d*x^4)^(1/2)),x)","\int \frac{1}{{\left(b\,x^4+a\right)}^2\,\sqrt{d\,x^4+c}} \,d x","Not used",1,"int(1/((a + b*x^4)^2*(c + d*x^4)^(1/2)), x)","F"
837,0,-1,1046,0.000000,"\text{Not used}","int(1/(x^4*(a + b*x^4)^2*(c + d*x^4)^(1/2)),x)","\int \frac{1}{x^4\,{\left(b\,x^4+a\right)}^2\,\sqrt{d\,x^4+c}} \,d x","Not used",1,"int(1/(x^4*(a + b*x^4)^2*(c + d*x^4)^(1/2)), x)","F"
838,0,-1,1146,0.000000,"\text{Not used}","int(x^6/((a + b*x^4)^2*(c + d*x^4)^(1/2)),x)","\int \frac{x^6}{{\left(b\,x^4+a\right)}^2\,\sqrt{d\,x^4+c}} \,d x","Not used",1,"int(x^6/((a + b*x^4)^2*(c + d*x^4)^(1/2)), x)","F"
839,0,-1,1144,0.000000,"\text{Not used}","int(x^2/((a + b*x^4)^2*(c + d*x^4)^(1/2)),x)","\int \frac{x^2}{{\left(b\,x^4+a\right)}^2\,\sqrt{d\,x^4+c}} \,d x","Not used",1,"int(x^2/((a + b*x^4)^2*(c + d*x^4)^(1/2)), x)","F"
840,0,-1,1225,0.000000,"\text{Not used}","int(1/(x^2*(a + b*x^4)^2*(c + d*x^4)^(1/2)),x)","\int \frac{1}{x^2\,{\left(b\,x^4+a\right)}^2\,\sqrt{d\,x^4+c}} \,d x","Not used",1,"int(1/(x^2*(a + b*x^4)^2*(c + d*x^4)^(1/2)), x)","F"
841,0,-1,200,0.000000,"\text{Not used}","int(((e*x)^m*(a + b*x^4)^2)/(c + d*x^4)^(1/2),x)","\int \frac{{\left(e\,x\right)}^m\,{\left(b\,x^4+a\right)}^2}{\sqrt{d\,x^4+c}} \,d x","Not used",1,"int(((e*x)^m*(a + b*x^4)^2)/(c + d*x^4)^(1/2), x)","F"
842,0,-1,123,0.000000,"\text{Not used}","int(((e*x)^m*(a + b*x^4))/(c + d*x^4)^(1/2),x)","\int \frac{{\left(e\,x\right)}^m\,\left(b\,x^4+a\right)}{\sqrt{d\,x^4+c}} \,d x","Not used",1,"int(((e*x)^m*(a + b*x^4))/(c + d*x^4)^(1/2), x)","F"
843,0,-1,68,0.000000,"\text{Not used}","int((e*x)^m/(c + d*x^4)^(1/2),x)","\int \frac{{\left(e\,x\right)}^m}{\sqrt{d\,x^4+c}} \,d x","Not used",1,"int((e*x)^m/(c + d*x^4)^(1/2), x)","F"
844,0,-1,81,0.000000,"\text{Not used}","int((e*x)^m/((a + b*x^4)*(c + d*x^4)^(1/2)),x)","\int \frac{{\left(e\,x\right)}^m}{\left(b\,x^4+a\right)\,\sqrt{d\,x^4+c}} \,d x","Not used",1,"int((e*x)^m/((a + b*x^4)*(c + d*x^4)^(1/2)), x)","F"
845,0,-1,81,0.000000,"\text{Not used}","int((e*x)^m/((a + b*x^4)^2*(c + d*x^4)^(1/2)),x)","\int \frac{{\left(e\,x\right)}^m}{{\left(b\,x^4+a\right)}^2\,\sqrt{d\,x^4+c}} \,d x","Not used",1,"int((e*x)^m/((a + b*x^4)^2*(c + d*x^4)^(1/2)), x)","F"
846,0,-1,81,0.000000,"\text{Not used}","int((e*x)^m/((a + b*x^4)^3*(c + d*x^4)^(1/2)),x)","\int \frac{{\left(e\,x\right)}^m}{{\left(b\,x^4+a\right)}^3\,\sqrt{d\,x^4+c}} \,d x","Not used",1,"int((e*x)^m/((a + b*x^4)^3*(c + d*x^4)^(1/2)), x)","F"
847,0,-1,198,0.000000,"\text{Not used}","int(((e*x)^m*(a + b*x^4)^2)/(c + d*x^4)^(3/2),x)","\int \frac{{\left(e\,x\right)}^m\,{\left(b\,x^4+a\right)}^2}{{\left(d\,x^4+c\right)}^{3/2}} \,d x","Not used",1,"int(((e*x)^m*(a + b*x^4)^2)/(c + d*x^4)^(3/2), x)","F"
848,0,-1,132,0.000000,"\text{Not used}","int(((e*x)^m*(a + b*x^4))/(c + d*x^4)^(3/2),x)","\int \frac{{\left(e\,x\right)}^m\,\left(b\,x^4+a\right)}{{\left(d\,x^4+c\right)}^{3/2}} \,d x","Not used",1,"int(((e*x)^m*(a + b*x^4))/(c + d*x^4)^(3/2), x)","F"
849,0,-1,71,0.000000,"\text{Not used}","int((e*x)^m/(c + d*x^4)^(3/2),x)","\int \frac{{\left(e\,x\right)}^m}{{\left(d\,x^4+c\right)}^{3/2}} \,d x","Not used",1,"int((e*x)^m/(c + d*x^4)^(3/2), x)","F"
850,0,-1,84,0.000000,"\text{Not used}","int((e*x)^m/((a + b*x^4)*(c + d*x^4)^(3/2)),x)","\int \frac{{\left(e\,x\right)}^m}{\left(b\,x^4+a\right)\,{\left(d\,x^4+c\right)}^{3/2}} \,d x","Not used",1,"int((e*x)^m/((a + b*x^4)*(c + d*x^4)^(3/2)), x)","F"
851,0,-1,84,0.000000,"\text{Not used}","int((e*x)^m/((a + b*x^4)^2*(c + d*x^4)^(3/2)),x)","\int \frac{{\left(e\,x\right)}^m}{{\left(b\,x^4+a\right)}^2\,{\left(d\,x^4+c\right)}^{3/2}} \,d x","Not used",1,"int((e*x)^m/((a + b*x^4)^2*(c + d*x^4)^(3/2)), x)","F"
852,0,-1,84,0.000000,"\text{Not used}","int((e*x)^m/((a + b*x^4)^3*(c + d*x^4)^(3/2)),x)","\int \frac{{\left(e\,x\right)}^m}{{\left(b\,x^4+a\right)}^3\,{\left(d\,x^4+c\right)}^{3/2}} \,d x","Not used",1,"int((e*x)^m/((a + b*x^4)^3*(c + d*x^4)^(3/2)), x)","F"
853,1,103,104,4.865654,"\text{Not used}","int(x^17/((a + b*x^6)*(c + d*x^6)^(1/2)),x)","\frac{{\left(d\,x^6+c\right)}^{3/2}}{9\,b\,d^2}-\left(\frac{2\,c}{3\,b\,d^2}+\frac{3\,a\,d^3-3\,b\,c\,d^2}{9\,b^2\,d^4}\right)\,\sqrt{d\,x^6+c}+\frac{a^2\,\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d\,x^6+c}}{\sqrt{a\,d-b\,c}}\right)}{3\,b^{5/2}\,\sqrt{a\,d-b\,c}}","Not used",1,"(c + d*x^6)^(3/2)/(9*b*d^2) - ((2*c)/(3*b*d^2) + (3*a*d^3 - 3*b*c*d^2)/(9*b^2*d^4))*(c + d*x^6)^(1/2) + (a^2*atan((b^(1/2)*(c + d*x^6)^(1/2))/(a*d - b*c)^(1/2)))/(3*b^(5/2)*(a*d - b*c)^(1/2))","B"
854,1,58,74,4.745344,"\text{Not used}","int(x^11/((a + b*x^6)*(c + d*x^6)^(1/2)),x)","\frac{\sqrt{d\,x^6+c}}{3\,b\,d}-\frac{a\,\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d\,x^6+c}}{\sqrt{a\,d-b\,c}}\right)}{3\,b^{3/2}\,\sqrt{a\,d-b\,c}}","Not used",1,"(c + d*x^6)^(1/2)/(3*b*d) - (a*atan((b^(1/2)*(c + d*x^6)^(1/2))/(a*d - b*c)^(1/2)))/(3*b^(3/2)*(a*d - b*c)^(1/2))","B"
855,1,40,51,4.724993,"\text{Not used}","int(x^5/((a + b*x^6)*(c + d*x^6)^(1/2)),x)","\frac{\mathrm{atan}\left(\frac{b\,\sqrt{d\,x^6+c}}{\sqrt{a\,b\,d-b^2\,c}}\right)}{3\,\sqrt{a\,b\,d-b^2\,c}}","Not used",1,"atan((b*(c + d*x^6)^(1/2))/(a*b*d - b^2*c)^(1/2))/(3*(a*b*d - b^2*c)^(1/2))","B"
856,1,652,85,5.191390,"\text{Not used}","int(1/(x*(a + b*x^6)*(c + d*x^6)^(1/2)),x)","-\frac{\mathrm{atanh}\left(\frac{\sqrt{d\,x^6+c}}{\sqrt{c}}\right)}{3\,a\,\sqrt{c}}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{b^2\,c-a\,b\,d}\,\left(\frac{2\,b^3\,d^2\,\sqrt{d\,x^6+c}}{27}-\frac{\sqrt{b^2\,c-a\,b\,d}\,\left(\frac{2\,a^2\,b^2\,d^3}{9}-\frac{\left(8\,a^3\,b^2\,d^3-16\,a^2\,b^3\,c\,d^2\right)\,\sqrt{d\,x^6+c}\,\sqrt{b^2\,c-a\,b\,d}}{36\,\left(a^2\,d-a\,b\,c\right)}\right)}{6\,\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(\frac{2\,b^3\,d^2\,\sqrt{d\,x^6+c}}{27}+\frac{\sqrt{b^2\,c-a\,b\,d}\,\left(\frac{2\,a^2\,b^2\,d^3}{9}+\frac{\left(8\,a^3\,b^2\,d^3-16\,a^2\,b^3\,c\,d^2\right)\,\sqrt{d\,x^6+c}\,\sqrt{b^2\,c-a\,b\,d}}{36\,\left(a^2\,d-a\,b\,c\right)}\right)}{6\,\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(\frac{2\,b^3\,d^2\,\sqrt{d\,x^6+c}}{27}-\frac{\sqrt{b^2\,c-a\,b\,d}\,\left(\frac{2\,a^2\,b^2\,d^3}{9}-\frac{\left(8\,a^3\,b^2\,d^3-16\,a^2\,b^3\,c\,d^2\right)\,\sqrt{d\,x^6+c}\,\sqrt{b^2\,c-a\,b\,d}}{36\,\left(a^2\,d-a\,b\,c\right)}\right)}{6\,\left(a^2\,d-a\,b\,c\right)}\right)}{a^2\,d-a\,b\,c}-\frac{\sqrt{b^2\,c-a\,b\,d}\,\left(\frac{2\,b^3\,d^2\,\sqrt{d\,x^6+c}}{27}+\frac{\sqrt{b^2\,c-a\,b\,d}\,\left(\frac{2\,a^2\,b^2\,d^3}{9}+\frac{\left(8\,a^3\,b^2\,d^3-16\,a^2\,b^3\,c\,d^2\right)\,\sqrt{d\,x^6+c}\,\sqrt{b^2\,c-a\,b\,d}}{36\,\left(a^2\,d-a\,b\,c\right)}\right)}{6\,\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}}{3\,\left(a^2\,d-a\,b\,c\right)}","Not used",1,"- atanh((c + d*x^6)^(1/2)/c^(1/2))/(3*a*c^(1/2)) - (atan((((b^2*c - a*b*d)^(1/2)*((2*b^3*d^2*(c + d*x^6)^(1/2))/27 - ((b^2*c - a*b*d)^(1/2)*((2*a^2*b^2*d^3)/9 - ((8*a^3*b^2*d^3 - 16*a^2*b^3*c*d^2)*(c + d*x^6)^(1/2)*(b^2*c - a*b*d)^(1/2))/(36*(a^2*d - a*b*c))))/(6*(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^6)^(1/2))/27 + ((b^2*c - a*b*d)^(1/2)*((2*a^2*b^2*d^3)/9 + ((8*a^3*b^2*d^3 - 16*a^2*b^3*c*d^2)*(c + d*x^6)^(1/2)*(b^2*c - a*b*d)^(1/2))/(36*(a^2*d - a*b*c))))/(6*(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^6)^(1/2))/27 - ((b^2*c - a*b*d)^(1/2)*((2*a^2*b^2*d^3)/9 - ((8*a^3*b^2*d^3 - 16*a^2*b^3*c*d^2)*(c + d*x^6)^(1/2)*(b^2*c - a*b*d)^(1/2))/(36*(a^2*d - a*b*c))))/(6*(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^6)^(1/2))/27 + ((b^2*c - a*b*d)^(1/2)*((2*a^2*b^2*d^3)/9 + ((8*a^3*b^2*d^3 - 16*a^2*b^3*c*d^2)*(c + d*x^6)^(1/2)*(b^2*c - a*b*d)^(1/2))/(36*(a^2*d - a*b*c))))/(6*(a^2*d - a*b*c))))/(a^2*d - a*b*c)))*(b^2*c - a*b*d)^(1/2)*1i)/(3*(a^2*d - a*b*c))","B"
857,1,396,117,5.615002,"\text{Not used}","int(1/(x^7*(a + b*x^6)*(c + d*x^6)^(1/2)),x)","\frac{\ln\left(\sqrt{d\,x^6+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}}{6\,a^3\,d-6\,a^2\,b\,c}-\frac{\ln\left(\sqrt{d\,x^6+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}}{6\,\left(a^3\,d-a^2\,b\,c\right)}-\frac{\sqrt{d\,x^6+c}}{6\,a\,c\,x^6}-\frac{\mathrm{atan}\left(\frac{b^4\,d^4\,\sqrt{d\,x^6+c}\,1{}\mathrm{i}}{18\,\sqrt{c^3}\,\left(\frac{b^4\,d^4}{18\,c}+\frac{5\,a\,b^3\,d^5}{108\,c^2}+\frac{a^2\,b^2\,d^6}{108\,c^3}\right)}+\frac{b^2\,d^6\,\sqrt{d\,x^6+c}\,1{}\mathrm{i}}{108\,\sqrt{c^3}\,\left(\frac{5\,b^3\,d^5}{108\,a}+\frac{b^2\,d^6}{108\,c}+\frac{b^4\,c\,d^4}{18\,a^2}\right)}+\frac{b^3\,d^5\,\sqrt{d\,x^6+c}\,5{}\mathrm{i}}{108\,\sqrt{c^3}\,\left(\frac{b^4\,d^4}{18\,a}+\frac{5\,b^3\,d^5}{108\,c}+\frac{a\,b^2\,d^6}{108\,c^2}\right)}\right)\,\left(a\,d+2\,b\,c\right)\,1{}\mathrm{i}}{6\,a^2\,\sqrt{c^3}}","Not used",1,"(log((c + d*x^6)^(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))/(6*a^3*d - 6*a^2*b*c) - (log((c + d*x^6)^(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))/(6*(a^3*d - a^2*b*c)) - (c + d*x^6)^(1/2)/(6*a*c*x^6) - (atan((b^4*d^4*(c + d*x^6)^(1/2)*1i)/(18*(c^3)^(1/2)*((b^4*d^4)/(18*c) + (5*a*b^3*d^5)/(108*c^2) + (a^2*b^2*d^6)/(108*c^3))) + (b^2*d^6*(c + d*x^6)^(1/2)*1i)/(108*(c^3)^(1/2)*((5*b^3*d^5)/(108*a) + (b^2*d^6)/(108*c) + (b^4*c*d^4)/(18*a^2))) + (b^3*d^5*(c + d*x^6)^(1/2)*5i)/(108*(c^3)^(1/2)*((b^4*d^4)/(18*a) + (5*b^3*d^5)/(108*c) + (a*b^2*d^6)/(108*c^2))))*(a*d + 2*b*c)*1i)/(6*a^2*(c^3)^(1/2))","B"
858,0,-1,123,0.000000,"\text{Not used}","int(x^14/((a + b*x^6)*(c + d*x^6)^(1/2)),x)","\int \frac{x^{14}}{\left(b\,x^6+a\right)\,\sqrt{d\,x^6+c}} \,d x","Not used",1,"int(x^14/((a + b*x^6)*(c + d*x^6)^(1/2)), x)","F"
859,0,-1,91,0.000000,"\text{Not used}","int(x^8/((a + b*x^6)*(c + d*x^6)^(1/2)),x)","\int \frac{x^8}{\left(b\,x^6+a\right)\,\sqrt{d\,x^6+c}} \,d x","Not used",1,"int(x^8/((a + b*x^6)*(c + d*x^6)^(1/2)), x)","F"
860,0,-1,54,0.000000,"\text{Not used}","int(x^2/((a + b*x^6)*(c + d*x^6)^(1/2)),x)","\int \frac{x^2}{\left(b\,x^6+a\right)\,\sqrt{d\,x^6+c}} \,d x","Not used",1,"int(x^2/((a + b*x^6)*(c + d*x^6)^(1/2)), x)","F"
861,0,-1,80,0.000000,"\text{Not used}","int(1/(x^4*(a + b*x^6)*(c + d*x^6)^(1/2)),x)","\int \frac{1}{x^4\,\left(b\,x^6+a\right)\,\sqrt{d\,x^6+c}} \,d x","Not used",1,"int(1/(x^4*(a + b*x^6)*(c + d*x^6)^(1/2)), x)","F"
862,0,-1,115,0.000000,"\text{Not used}","int(1/(x^10*(a + b*x^6)*(c + d*x^6)^(1/2)),x)","\int \frac{1}{x^{10}\,\left(b\,x^6+a\right)\,\sqrt{d\,x^6+c}} \,d x","Not used",1,"int(1/(x^10*(a + b*x^6)*(c + d*x^6)^(1/2)), x)","F"
863,0,-1,64,0.000000,"\text{Not used}","int(x^4/((a + b*x^6)*(c + d*x^6)^(1/2)),x)","\int \frac{x^4}{\left(b\,x^6+a\right)\,\sqrt{d\,x^6+c}} \,d x","Not used",1,"int(x^4/((a + b*x^6)*(c + d*x^6)^(1/2)), x)","F"
864,0,-1,64,0.000000,"\text{Not used}","int(x^3/((a + b*x^6)*(c + d*x^6)^(1/2)),x)","\int \frac{x^3}{\left(b\,x^6+a\right)\,\sqrt{d\,x^6+c}} \,d x","Not used",1,"int(x^3/((a + b*x^6)*(c + d*x^6)^(1/2)), x)","F"
865,0,-1,64,0.000000,"\text{Not used}","int(x/((a + b*x^6)*(c + d*x^6)^(1/2)),x)","\int \frac{x}{\left(b\,x^6+a\right)\,\sqrt{d\,x^6+c}} \,d x","Not used",1,"int(x/((a + b*x^6)*(c + d*x^6)^(1/2)), x)","F"
866,0,-1,59,0.000000,"\text{Not used}","int(1/((a + b*x^6)*(c + d*x^6)^(1/2)),x)","\int \frac{1}{\left(b\,x^6+a\right)\,\sqrt{d\,x^6+c}} \,d x","Not used",1,"int(1/((a + b*x^6)*(c + d*x^6)^(1/2)), x)","F"
867,0,-1,62,0.000000,"\text{Not used}","int(1/(x^2*(a + b*x^6)*(c + d*x^6)^(1/2)),x)","\int \frac{1}{x^2\,\left(b\,x^6+a\right)\,\sqrt{d\,x^6+c}} \,d x","Not used",1,"int(1/(x^2*(a + b*x^6)*(c + d*x^6)^(1/2)), x)","F"
868,0,-1,64,0.000000,"\text{Not used}","int(1/(x^3*(a + b*x^6)*(c + d*x^6)^(1/2)),x)","\int \frac{1}{x^3\,\left(b\,x^6+a\right)\,\sqrt{d\,x^6+c}} \,d x","Not used",1,"int(1/(x^3*(a + b*x^6)*(c + d*x^6)^(1/2)), x)","F"
869,0,-1,64,0.000000,"\text{Not used}","int(1/(x^5*(a + b*x^6)*(c + d*x^6)^(1/2)),x)","\int \frac{1}{x^5\,\left(b\,x^6+a\right)\,\sqrt{d\,x^6+c}} \,d x","Not used",1,"int(1/(x^5*(a + b*x^6)*(c + d*x^6)^(1/2)), x)","F"
870,1,144,123,5.093108,"\text{Not used}","int(x^17/((a + b*x^6)^2*(c + d*x^6)^(1/2)),x)","\frac{\sqrt{d\,x^6+c}}{3\,b^2\,d}-\frac{a\,\mathrm{atan}\left(\frac{a\,\sqrt{b}\,\sqrt{d\,x^6+c}\,\left(3\,a\,d-4\,b\,c\right)}{\left(3\,a^2\,d-4\,a\,b\,c\right)\,\sqrt{a\,d-b\,c}}\right)\,\left(3\,a\,d-4\,b\,c\right)}{6\,b^{5/2}\,{\left(a\,d-b\,c\right)}^{3/2}}+\frac{a^2\,d\,\sqrt{d\,x^6+c}}{2\,\left(a\,d-b\,c\right)\,\left(3\,b^3\,\left(d\,x^6+c\right)-3\,b^3\,c+3\,a\,b^2\,d\right)}","Not used",1,"(c + d*x^6)^(1/2)/(3*b^2*d) - (a*atan((a*b^(1/2)*(c + d*x^6)^(1/2)*(3*a*d - 4*b*c))/((3*a^2*d - 4*a*b*c)*(a*d - b*c)^(1/2)))*(3*a*d - 4*b*c))/(6*b^(5/2)*(a*d - b*c)^(3/2)) + (a^2*d*(c + d*x^6)^(1/2))/(2*(a*d - b*c)*(3*b^3*(c + d*x^6) - 3*b^3*c + 3*a*b^2*d))","B"
871,1,95,99,4.988508,"\text{Not used}","int(x^11/((a + b*x^6)^2*(c + d*x^6)^(1/2)),x)","\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d\,x^6+c}}{\sqrt{a\,d-b\,c}}\right)\,\left(a\,d-2\,b\,c\right)}{6\,b^{3/2}\,{\left(a\,d-b\,c\right)}^{3/2}}-\frac{a\,d\,\sqrt{d\,x^6+c}}{2\,b\,\left(a\,d-b\,c\right)\,\left(3\,b\,\left(d\,x^6+c\right)+3\,a\,d-3\,b\,c\right)}","Not used",1,"(atan((b^(1/2)*(c + d*x^6)^(1/2))/(a*d - b*c)^(1/2))*(a*d - 2*b*c))/(6*b^(3/2)*(a*d - b*c)^(3/2)) - (a*d*(c + d*x^6)^(1/2))/(2*b*(a*d - b*c)*(3*b*(c + d*x^6) + 3*a*d - 3*b*c))","B"
872,1,84,87,4.929448,"\text{Not used}","int(x^5/((a + b*x^6)^2*(c + d*x^6)^(1/2)),x)","\frac{d\,\sqrt{d\,x^6+c}}{2\,\left(a\,d-b\,c\right)\,\left(3\,b\,\left(d\,x^6+c\right)+3\,a\,d-3\,b\,c\right)}+\frac{d\,\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d\,x^6+c}}{\sqrt{a\,d-b\,c}}\right)}{6\,\sqrt{b}\,{\left(a\,d-b\,c\right)}^{3/2}}","Not used",1,"(d*(c + d*x^6)^(1/2))/(2*(a*d - b*c)*(3*b*(c + d*x^6) + 3*a*d - 3*b*c)) + (d*atan((b^(1/2)*(c + d*x^6)^(1/2))/(a*d - b*c)^(1/2)))/(6*b^(1/2)*(a*d - b*c)^(3/2))","B"
873,1,3025,132,6.225909,"\text{Not used}","int(1/(x*(a + b*x^6)^2*(c + d*x^6)^(1/2)),x)","-\frac{b\,d\,\sqrt{d\,x^6+c}}{2\,\left(a^2\,d-a\,b\,c\right)\,\left(3\,b\,\left(d\,x^6+c\right)+3\,a\,d-3\,b\,c\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\frac{\frac{4\,a^6\,b^2\,d^5}{3}-2\,a^5\,b^3\,c\,d^4+\frac{2\,a^4\,b^4\,c^2\,d^3}{3}}{6\,\left(a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2\right)}-\frac{\sqrt{d\,x^6+c}\,\left(144\,a^7\,b^2\,d^5-576\,a^6\,b^3\,c\,d^4+720\,a^5\,b^4\,c^2\,d^3-288\,a^4\,b^5\,c^3\,d^2\right)}{648\,a^2\,\sqrt{c}\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}}{6\,a^2\,\sqrt{c}}-\frac{\sqrt{d\,x^6+c}\,\left(13\,a^2\,b^3\,d^4-20\,a\,b^4\,c\,d^3+8\,b^5\,c^2\,d^2\right)}{108\,\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{\frac{4\,a^6\,b^2\,d^5}{3}-2\,a^5\,b^3\,c\,d^4+\frac{2\,a^4\,b^4\,c^2\,d^3}{3}}{6\,\left(a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2\right)}+\frac{\sqrt{d\,x^6+c}\,\left(144\,a^7\,b^2\,d^5-576\,a^6\,b^3\,c\,d^4+720\,a^5\,b^4\,c^2\,d^3-288\,a^4\,b^5\,c^3\,d^2\right)}{648\,a^2\,\sqrt{c}\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}}{6\,a^2\,\sqrt{c}}+\frac{\sqrt{d\,x^6+c}\,\left(13\,a^2\,b^3\,d^4-20\,a\,b^4\,c\,d^3+8\,b^5\,c^2\,d^2\right)}{108\,\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{a\,b^3\,d^4}{18}-\frac{b^4\,c\,d^3}{27}}{a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2}+\frac{\frac{\frac{\frac{4\,a^6\,b^2\,d^5}{3}-2\,a^5\,b^3\,c\,d^4+\frac{2\,a^4\,b^4\,c^2\,d^3}{3}}{6\,\left(a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2\right)}-\frac{\sqrt{d\,x^6+c}\,\left(144\,a^7\,b^2\,d^5-576\,a^6\,b^3\,c\,d^4+720\,a^5\,b^4\,c^2\,d^3-288\,a^4\,b^5\,c^3\,d^2\right)}{648\,a^2\,\sqrt{c}\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}}{6\,a^2\,\sqrt{c}}-\frac{\sqrt{d\,x^6+c}\,\left(13\,a^2\,b^3\,d^4-20\,a\,b^4\,c\,d^3+8\,b^5\,c^2\,d^2\right)}{108\,\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{\frac{4\,a^6\,b^2\,d^5}{3}-2\,a^5\,b^3\,c\,d^4+\frac{2\,a^4\,b^4\,c^2\,d^3}{3}}{6\,\left(a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2\right)}+\frac{\sqrt{d\,x^6+c}\,\left(144\,a^7\,b^2\,d^5-576\,a^6\,b^3\,c\,d^4+720\,a^5\,b^4\,c^2\,d^3-288\,a^4\,b^5\,c^3\,d^2\right)}{648\,a^2\,\sqrt{c}\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}}{6\,a^2\,\sqrt{c}}+\frac{\sqrt{d\,x^6+c}\,\left(13\,a^2\,b^3\,d^4-20\,a\,b^4\,c\,d^3+8\,b^5\,c^2\,d^2\right)}{108\,\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}}{3\,a^2\,\sqrt{c}}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\sqrt{d\,x^6+c}\,\left(13\,a^2\,b^3\,d^4-20\,a\,b^4\,c\,d^3+8\,b^5\,c^2\,d^2\right)}{18\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}-\frac{\left(\frac{\frac{4\,a^6\,b^2\,d^5}{3}-2\,a^5\,b^3\,c\,d^4+\frac{2\,a^4\,b^4\,c^2\,d^3}{3}}{a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2}-\frac{\sqrt{d\,x^6+c}\,\left(3\,a\,d-2\,b\,c\right)\,\sqrt{-b\,{\left(a\,d-b\,c\right)}^3}\,\left(144\,a^7\,b^2\,d^5-576\,a^6\,b^3\,c\,d^4+720\,a^5\,b^4\,c^2\,d^3-288\,a^4\,b^5\,c^3\,d^2\right)}{216\,\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}}{12\,\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}}{12\,\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^6+c}\,\left(13\,a^2\,b^3\,d^4-20\,a\,b^4\,c\,d^3+8\,b^5\,c^2\,d^2\right)}{18\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}+\frac{\left(\frac{\frac{4\,a^6\,b^2\,d^5}{3}-2\,a^5\,b^3\,c\,d^4+\frac{2\,a^4\,b^4\,c^2\,d^3}{3}}{a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2}+\frac{\sqrt{d\,x^6+c}\,\left(3\,a\,d-2\,b\,c\right)\,\sqrt{-b\,{\left(a\,d-b\,c\right)}^3}\,\left(144\,a^7\,b^2\,d^5-576\,a^6\,b^3\,c\,d^4+720\,a^5\,b^4\,c^2\,d^3-288\,a^4\,b^5\,c^3\,d^2\right)}{216\,\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}}{12\,\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}}{12\,\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{a\,b^3\,d^4}{18}-\frac{b^4\,c\,d^3}{27}}{a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2}-\frac{\left(\frac{\sqrt{d\,x^6+c}\,\left(13\,a^2\,b^3\,d^4-20\,a\,b^4\,c\,d^3+8\,b^5\,c^2\,d^2\right)}{18\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}-\frac{\left(\frac{\frac{4\,a^6\,b^2\,d^5}{3}-2\,a^5\,b^3\,c\,d^4+\frac{2\,a^4\,b^4\,c^2\,d^3}{3}}{a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2}-\frac{\sqrt{d\,x^6+c}\,\left(3\,a\,d-2\,b\,c\right)\,\sqrt{-b\,{\left(a\,d-b\,c\right)}^3}\,\left(144\,a^7\,b^2\,d^5-576\,a^6\,b^3\,c\,d^4+720\,a^5\,b^4\,c^2\,d^3-288\,a^4\,b^5\,c^3\,d^2\right)}{216\,\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}}{12\,\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}}{12\,\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^6+c}\,\left(13\,a^2\,b^3\,d^4-20\,a\,b^4\,c\,d^3+8\,b^5\,c^2\,d^2\right)}{18\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}+\frac{\left(\frac{\frac{4\,a^6\,b^2\,d^5}{3}-2\,a^5\,b^3\,c\,d^4+\frac{2\,a^4\,b^4\,c^2\,d^3}{3}}{a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2}+\frac{\sqrt{d\,x^6+c}\,\left(3\,a\,d-2\,b\,c\right)\,\sqrt{-b\,{\left(a\,d-b\,c\right)}^3}\,\left(144\,a^7\,b^2\,d^5-576\,a^6\,b^3\,c\,d^4+720\,a^5\,b^4\,c^2\,d^3-288\,a^4\,b^5\,c^3\,d^2\right)}{216\,\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}}{12\,\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}}{12\,\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}}{6\,\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^6)^(1/2)*(13*a^2*b^3*d^4 + 8*b^5*c^2*d^2 - 20*a*b^4*c*d^3))/(18*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)) - ((((4*a^6*b^2*d^5)/3 - 2*a^5*b^3*c*d^4 + (2*a^4*b^4*c^2*d^3)/3)/(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d) - ((c + d*x^6)^(1/2)*(3*a*d - 2*b*c)*(-b*(a*d - b*c)^3)^(1/2)*(144*a^7*b^2*d^5 - 576*a^6*b^3*c*d^4 - 288*a^4*b^5*c^3*d^2 + 720*a^5*b^4*c^2*d^3))/(216*(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))/(12*(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)/(12*(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^6)^(1/2)*(13*a^2*b^3*d^4 + 8*b^5*c^2*d^2 - 20*a*b^4*c*d^3))/(18*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)) + ((((4*a^6*b^2*d^5)/3 - 2*a^5*b^3*c*d^4 + (2*a^4*b^4*c^2*d^3)/3)/(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d) + ((c + d*x^6)^(1/2)*(3*a*d - 2*b*c)*(-b*(a*d - b*c)^3)^(1/2)*(144*a^7*b^2*d^5 - 576*a^6*b^3*c*d^4 - 288*a^4*b^5*c^3*d^2 + 720*a^5*b^4*c^2*d^3))/(216*(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))/(12*(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)/(12*(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*b^3*d^4)/18 - (b^4*c*d^3)/27)/(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d) - ((((c + d*x^6)^(1/2)*(13*a^2*b^3*d^4 + 8*b^5*c^2*d^2 - 20*a*b^4*c*d^3))/(18*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)) - ((((4*a^6*b^2*d^5)/3 - 2*a^5*b^3*c*d^4 + (2*a^4*b^4*c^2*d^3)/3)/(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d) - ((c + d*x^6)^(1/2)*(3*a*d - 2*b*c)*(-b*(a*d - b*c)^3)^(1/2)*(144*a^7*b^2*d^5 - 576*a^6*b^3*c*d^4 - 288*a^4*b^5*c^3*d^2 + 720*a^5*b^4*c^2*d^3))/(216*(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))/(12*(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))/(12*(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^6)^(1/2)*(13*a^2*b^3*d^4 + 8*b^5*c^2*d^2 - 20*a*b^4*c*d^3))/(18*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)) + ((((4*a^6*b^2*d^5)/3 - 2*a^5*b^3*c*d^4 + (2*a^4*b^4*c^2*d^3)/3)/(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d) + ((c + d*x^6)^(1/2)*(3*a*d - 2*b*c)*(-b*(a*d - b*c)^3)^(1/2)*(144*a^7*b^2*d^5 - 576*a^6*b^3*c*d^4 - 288*a^4*b^5*c^3*d^2 + 720*a^5*b^4*c^2*d^3))/(216*(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))/(12*(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))/(12*(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)/(6*(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)/3 - 2*a^5*b^3*c*d^4 + (2*a^4*b^4*c^2*d^3)/3)/(6*(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d)) - ((c + d*x^6)^(1/2)*(144*a^7*b^2*d^5 - 576*a^6*b^3*c*d^4 - 288*a^4*b^5*c^3*d^2 + 720*a^5*b^4*c^2*d^3))/(648*a^2*c^(1/2)*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)))/(6*a^2*c^(1/2)) - ((c + d*x^6)^(1/2)*(13*a^2*b^3*d^4 + 8*b^5*c^2*d^2 - 20*a*b^4*c*d^3))/(108*(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)/3 - 2*a^5*b^3*c*d^4 + (2*a^4*b^4*c^2*d^3)/3)/(6*(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d)) + ((c + d*x^6)^(1/2)*(144*a^7*b^2*d^5 - 576*a^6*b^3*c*d^4 - 288*a^4*b^5*c^3*d^2 + 720*a^5*b^4*c^2*d^3))/(648*a^2*c^(1/2)*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)))/(6*a^2*c^(1/2)) + ((c + d*x^6)^(1/2)*(13*a^2*b^3*d^4 + 8*b^5*c^2*d^2 - 20*a*b^4*c*d^3))/(108*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)))*1i)/(a^2*c^(1/2)))/(((a*b^3*d^4)/18 - (b^4*c*d^3)/27)/(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d) + ((((4*a^6*b^2*d^5)/3 - 2*a^5*b^3*c*d^4 + (2*a^4*b^4*c^2*d^3)/3)/(6*(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d)) - ((c + d*x^6)^(1/2)*(144*a^7*b^2*d^5 - 576*a^6*b^3*c*d^4 - 288*a^4*b^5*c^3*d^2 + 720*a^5*b^4*c^2*d^3))/(648*a^2*c^(1/2)*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)))/(6*a^2*c^(1/2)) - ((c + d*x^6)^(1/2)*(13*a^2*b^3*d^4 + 8*b^5*c^2*d^2 - 20*a*b^4*c*d^3))/(108*(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)/3 - 2*a^5*b^3*c*d^4 + (2*a^4*b^4*c^2*d^3)/3)/(6*(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d)) + ((c + d*x^6)^(1/2)*(144*a^7*b^2*d^5 - 576*a^6*b^3*c*d^4 - 288*a^4*b^5*c^3*d^2 + 720*a^5*b^4*c^2*d^3))/(648*a^2*c^(1/2)*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)))/(6*a^2*c^(1/2)) + ((c + d*x^6)^(1/2)*(13*a^2*b^3*d^4 + 8*b^5*c^2*d^2 - 20*a*b^4*c*d^3))/(108*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)))/(a^2*c^(1/2))))*1i)/(3*a^2*c^(1/2)) - (b*d*(c + d*x^6)^(1/2))/(2*(a^2*d - a*b*c)*(3*b*(c + d*x^6) + 3*a*d - 3*b*c))","B"
874,1,3860,185,7.289696,"\text{Not used}","int(1/(x^7*(a + b*x^6)^2*(c + d*x^6)^(1/2)),x)","\frac{\frac{\sqrt{d\,x^6+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^6+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^6+c\right)\,\left(3\,a\,d-6\,b\,c\right)+3\,b\,{\left(d\,x^6+c\right)}^2+3\,b\,c^2-3\,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^6+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)}{18\,\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{144\,a^9\,b^2\,c\,d^6+144\,a^8\,b^3\,c^2\,d^5-576\,a^7\,b^4\,c^3\,d^4+288\,a^6\,b^5\,c^4\,d^3}{216\,\left(a^8\,c^2\,d^2-2\,a^7\,b\,c^3\,d+a^6\,b^2\,c^4\right)}-\frac{\sqrt{-b^3\,{\left(a\,d-b\,c\right)}^3}\,\sqrt{d\,x^6+c}\,\left(5\,a\,d-4\,b\,c\right)\,\left(-144\,a^9\,b^2\,c^2\,d^5+576\,a^8\,b^3\,c^3\,d^4-720\,a^7\,b^4\,c^4\,d^3+288\,a^6\,b^5\,c^5\,d^2\right)}{216\,\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)}{12\,\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}}{12\,\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^6+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)}{18\,\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{144\,a^9\,b^2\,c\,d^6+144\,a^8\,b^3\,c^2\,d^5-576\,a^7\,b^4\,c^3\,d^4+288\,a^6\,b^5\,c^4\,d^3}{216\,\left(a^8\,c^2\,d^2-2\,a^7\,b\,c^3\,d+a^6\,b^2\,c^4\right)}+\frac{\sqrt{-b^3\,{\left(a\,d-b\,c\right)}^3}\,\sqrt{d\,x^6+c}\,\left(5\,a\,d-4\,b\,c\right)\,\left(-144\,a^9\,b^2\,c^2\,d^5+576\,a^8\,b^3\,c^3\,d^4-720\,a^7\,b^4\,c^4\,d^3+288\,a^6\,b^5\,c^5\,d^2\right)}{216\,\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)}{12\,\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}}{12\,\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{5\,a^3\,b^4\,d^6+6\,a^2\,b^5\,c\,d^5-48\,a\,b^6\,c^2\,d^4+32\,b^7\,c^3\,d^3}{108\,\left(a^8\,c^2\,d^2-2\,a^7\,b\,c^3\,d+a^6\,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{\sqrt{d\,x^6+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)}{18\,\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{144\,a^9\,b^2\,c\,d^6+144\,a^8\,b^3\,c^2\,d^5-576\,a^7\,b^4\,c^3\,d^4+288\,a^6\,b^5\,c^4\,d^3}{216\,\left(a^8\,c^2\,d^2-2\,a^7\,b\,c^3\,d+a^6\,b^2\,c^4\right)}-\frac{\sqrt{-b^3\,{\left(a\,d-b\,c\right)}^3}\,\sqrt{d\,x^6+c}\,\left(5\,a\,d-4\,b\,c\right)\,\left(-144\,a^9\,b^2\,c^2\,d^5+576\,a^8\,b^3\,c^3\,d^4-720\,a^7\,b^4\,c^4\,d^3+288\,a^6\,b^5\,c^5\,d^2\right)}{216\,\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)}{12\,\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)}{12\,\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^6+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)}{18\,\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{144\,a^9\,b^2\,c\,d^6+144\,a^8\,b^3\,c^2\,d^5-576\,a^7\,b^4\,c^3\,d^4+288\,a^6\,b^5\,c^4\,d^3}{216\,\left(a^8\,c^2\,d^2-2\,a^7\,b\,c^3\,d+a^6\,b^2\,c^4\right)}+\frac{\sqrt{-b^3\,{\left(a\,d-b\,c\right)}^3}\,\sqrt{d\,x^6+c}\,\left(5\,a\,d-4\,b\,c\right)\,\left(-144\,a^9\,b^2\,c^2\,d^5+576\,a^8\,b^3\,c^3\,d^4-720\,a^7\,b^4\,c^4\,d^3+288\,a^6\,b^5\,c^5\,d^2\right)}{216\,\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)}{12\,\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)}{12\,\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}}{6\,\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^6+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)}{18\,\left(a^6\,c^2\,d^2-2\,a^5\,b\,c^3\,d+a^4\,b^2\,c^4\right)}+\frac{\left(\frac{144\,a^9\,b^2\,c\,d^6+144\,a^8\,b^3\,c^2\,d^5-576\,a^7\,b^4\,c^3\,d^4+288\,a^6\,b^5\,c^4\,d^3}{216\,\left(a^8\,c^2\,d^2-2\,a^7\,b\,c^3\,d+a^6\,b^2\,c^4\right)}-\frac{\sqrt{d\,x^6+c}\,\left(a\,d+4\,b\,c\right)\,\left(-144\,a^9\,b^2\,c^2\,d^5+576\,a^8\,b^3\,c^3\,d^4-720\,a^7\,b^4\,c^4\,d^3+288\,a^6\,b^5\,c^5\,d^2\right)}{216\,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)}{12\,a^3\,\sqrt{c^3}}\right)\,\left(a\,d+4\,b\,c\right)\,1{}\mathrm{i}}{12\,a^3\,\sqrt{c^3}}+\frac{\left(\frac{\sqrt{d\,x^6+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)}{18\,\left(a^6\,c^2\,d^2-2\,a^5\,b\,c^3\,d+a^4\,b^2\,c^4\right)}-\frac{\left(\frac{144\,a^9\,b^2\,c\,d^6+144\,a^8\,b^3\,c^2\,d^5-576\,a^7\,b^4\,c^3\,d^4+288\,a^6\,b^5\,c^4\,d^3}{216\,\left(a^8\,c^2\,d^2-2\,a^7\,b\,c^3\,d+a^6\,b^2\,c^4\right)}+\frac{\sqrt{d\,x^6+c}\,\left(a\,d+4\,b\,c\right)\,\left(-144\,a^9\,b^2\,c^2\,d^5+576\,a^8\,b^3\,c^3\,d^4-720\,a^7\,b^4\,c^4\,d^3+288\,a^6\,b^5\,c^5\,d^2\right)}{216\,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)}{12\,a^3\,\sqrt{c^3}}\right)\,\left(a\,d+4\,b\,c\right)\,1{}\mathrm{i}}{12\,a^3\,\sqrt{c^3}}}{\frac{5\,a^3\,b^4\,d^6+6\,a^2\,b^5\,c\,d^5-48\,a\,b^6\,c^2\,d^4+32\,b^7\,c^3\,d^3}{108\,\left(a^8\,c^2\,d^2-2\,a^7\,b\,c^3\,d+a^6\,b^2\,c^4\right)}-\frac{\left(\frac{\sqrt{d\,x^6+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)}{18\,\left(a^6\,c^2\,d^2-2\,a^5\,b\,c^3\,d+a^4\,b^2\,c^4\right)}+\frac{\left(\frac{144\,a^9\,b^2\,c\,d^6+144\,a^8\,b^3\,c^2\,d^5-576\,a^7\,b^4\,c^3\,d^4+288\,a^6\,b^5\,c^4\,d^3}{216\,\left(a^8\,c^2\,d^2-2\,a^7\,b\,c^3\,d+a^6\,b^2\,c^4\right)}-\frac{\sqrt{d\,x^6+c}\,\left(a\,d+4\,b\,c\right)\,\left(-144\,a^9\,b^2\,c^2\,d^5+576\,a^8\,b^3\,c^3\,d^4-720\,a^7\,b^4\,c^4\,d^3+288\,a^6\,b^5\,c^5\,d^2\right)}{216\,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)}{12\,a^3\,\sqrt{c^3}}\right)\,\left(a\,d+4\,b\,c\right)}{12\,a^3\,\sqrt{c^3}}+\frac{\left(\frac{\sqrt{d\,x^6+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)}{18\,\left(a^6\,c^2\,d^2-2\,a^5\,b\,c^3\,d+a^4\,b^2\,c^4\right)}-\frac{\left(\frac{144\,a^9\,b^2\,c\,d^6+144\,a^8\,b^3\,c^2\,d^5-576\,a^7\,b^4\,c^3\,d^4+288\,a^6\,b^5\,c^4\,d^3}{216\,\left(a^8\,c^2\,d^2-2\,a^7\,b\,c^3\,d+a^6\,b^2\,c^4\right)}+\frac{\sqrt{d\,x^6+c}\,\left(a\,d+4\,b\,c\right)\,\left(-144\,a^9\,b^2\,c^2\,d^5+576\,a^8\,b^3\,c^3\,d^4-720\,a^7\,b^4\,c^4\,d^3+288\,a^6\,b^5\,c^5\,d^2\right)}{216\,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)}{12\,a^3\,\sqrt{c^3}}\right)\,\left(a\,d+4\,b\,c\right)}{12\,a^3\,\sqrt{c^3}}}\right)\,\left(a\,d+4\,b\,c\right)\,1{}\mathrm{i}}{6\,a^3\,\sqrt{c^3}}","Not used",1,"(((c + d*x^6)^(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^6)^(3/2)*(a*d^2 - 2*b*c*d))/(2*a^2*(b*c^2 - a*c*d)))/((c + d*x^6)*(3*a*d - 6*b*c) + 3*b*(c + d*x^6)^2 + 3*b*c^2 - 3*a*c*d) + (atan((((-b^3*(a*d - b*c)^3)^(1/2)*(5*a*d - 4*b*c)*(((c + d*x^6)^(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))/(18*(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)*((144*a^9*b^2*c*d^6 + 288*a^6*b^5*c^4*d^3 - 576*a^7*b^4*c^3*d^4 + 144*a^8*b^3*c^2*d^5)/(216*(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^6)^(1/2)*(5*a*d - 4*b*c)*(288*a^6*b^5*c^5*d^2 - 720*a^7*b^4*c^4*d^3 + 576*a^8*b^3*c^3*d^4 - 144*a^9*b^2*c^2*d^5))/(216*(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))))/(12*(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)/(12*(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^6)^(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))/(18*(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)*((144*a^9*b^2*c*d^6 + 288*a^6*b^5*c^4*d^3 - 576*a^7*b^4*c^3*d^4 + 144*a^8*b^3*c^2*d^5)/(216*(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^6)^(1/2)*(5*a*d - 4*b*c)*(288*a^6*b^5*c^5*d^2 - 720*a^7*b^4*c^4*d^3 + 576*a^8*b^3*c^3*d^4 - 144*a^9*b^2*c^2*d^5))/(216*(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))))/(12*(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)/(12*(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 + 32*b^7*c^3*d^3 - 48*a*b^6*c^2*d^4 + 6*a^2*b^5*c*d^5)/(108*(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^6)^(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))/(18*(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)*((144*a^9*b^2*c*d^6 + 288*a^6*b^5*c^4*d^3 - 576*a^7*b^4*c^3*d^4 + 144*a^8*b^3*c^2*d^5)/(216*(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^6)^(1/2)*(5*a*d - 4*b*c)*(288*a^6*b^5*c^5*d^2 - 720*a^7*b^4*c^4*d^3 + 576*a^8*b^3*c^3*d^4 - 144*a^9*b^2*c^2*d^5))/(216*(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))))/(12*(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))))/(12*(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^6)^(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))/(18*(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)*((144*a^9*b^2*c*d^6 + 288*a^6*b^5*c^4*d^3 - 576*a^7*b^4*c^3*d^4 + 144*a^8*b^3*c^2*d^5)/(216*(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^6)^(1/2)*(5*a*d - 4*b*c)*(288*a^6*b^5*c^5*d^2 - 720*a^7*b^4*c^4*d^3 + 576*a^8*b^3*c^3*d^4 - 144*a^9*b^2*c^2*d^5))/(216*(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))))/(12*(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))))/(12*(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)/(6*(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^6)^(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))/(18*(a^4*b^2*c^4 + a^6*c^2*d^2 - 2*a^5*b*c^3*d)) + (((144*a^9*b^2*c*d^6 + 288*a^6*b^5*c^4*d^3 - 576*a^7*b^4*c^3*d^4 + 144*a^8*b^3*c^2*d^5)/(216*(a^6*b^2*c^4 + a^8*c^2*d^2 - 2*a^7*b*c^3*d)) - ((c + d*x^6)^(1/2)*(a*d + 4*b*c)*(288*a^6*b^5*c^5*d^2 - 720*a^7*b^4*c^4*d^3 + 576*a^8*b^3*c^3*d^4 - 144*a^9*b^2*c^2*d^5))/(216*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))/(12*a^3*(c^3)^(1/2)))*(a*d + 4*b*c)*1i)/(12*a^3*(c^3)^(1/2)) + ((((c + d*x^6)^(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))/(18*(a^4*b^2*c^4 + a^6*c^2*d^2 - 2*a^5*b*c^3*d)) - (((144*a^9*b^2*c*d^6 + 288*a^6*b^5*c^4*d^3 - 576*a^7*b^4*c^3*d^4 + 144*a^8*b^3*c^2*d^5)/(216*(a^6*b^2*c^4 + a^8*c^2*d^2 - 2*a^7*b*c^3*d)) + ((c + d*x^6)^(1/2)*(a*d + 4*b*c)*(288*a^6*b^5*c^5*d^2 - 720*a^7*b^4*c^4*d^3 + 576*a^8*b^3*c^3*d^4 - 144*a^9*b^2*c^2*d^5))/(216*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))/(12*a^3*(c^3)^(1/2)))*(a*d + 4*b*c)*1i)/(12*a^3*(c^3)^(1/2)))/((5*a^3*b^4*d^6 + 32*b^7*c^3*d^3 - 48*a*b^6*c^2*d^4 + 6*a^2*b^5*c*d^5)/(108*(a^6*b^2*c^4 + a^8*c^2*d^2 - 2*a^7*b*c^3*d)) - ((((c + d*x^6)^(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))/(18*(a^4*b^2*c^4 + a^6*c^2*d^2 - 2*a^5*b*c^3*d)) + (((144*a^9*b^2*c*d^6 + 288*a^6*b^5*c^4*d^3 - 576*a^7*b^4*c^3*d^4 + 144*a^8*b^3*c^2*d^5)/(216*(a^6*b^2*c^4 + a^8*c^2*d^2 - 2*a^7*b*c^3*d)) - ((c + d*x^6)^(1/2)*(a*d + 4*b*c)*(288*a^6*b^5*c^5*d^2 - 720*a^7*b^4*c^4*d^3 + 576*a^8*b^3*c^3*d^4 - 144*a^9*b^2*c^2*d^5))/(216*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))/(12*a^3*(c^3)^(1/2)))*(a*d + 4*b*c))/(12*a^3*(c^3)^(1/2)) + ((((c + d*x^6)^(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))/(18*(a^4*b^2*c^4 + a^6*c^2*d^2 - 2*a^5*b*c^3*d)) - (((144*a^9*b^2*c*d^6 + 288*a^6*b^5*c^4*d^3 - 576*a^7*b^4*c^3*d^4 + 144*a^8*b^3*c^2*d^5)/(216*(a^6*b^2*c^4 + a^8*c^2*d^2 - 2*a^7*b*c^3*d)) + ((c + d*x^6)^(1/2)*(a*d + 4*b*c)*(288*a^6*b^5*c^5*d^2 - 720*a^7*b^4*c^4*d^3 + 576*a^8*b^3*c^3*d^4 - 144*a^9*b^2*c^2*d^5))/(216*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))/(12*a^3*(c^3)^(1/2)))*(a*d + 4*b*c))/(12*a^3*(c^3)^(1/2))))*(a*d + 4*b*c)*1i)/(6*a^3*(c^3)^(1/2))","B"
875,0,-1,141,0.000000,"\text{Not used}","int(x^14/((a + b*x^6)^2*(c + d*x^6)^(1/2)),x)","\int \frac{x^{14}}{{\left(b\,x^6+a\right)}^2\,\sqrt{d\,x^6+c}} \,d x","Not used",1,"int(x^14/((a + b*x^6)^2*(c + d*x^6)^(1/2)), x)","F"
876,0,-1,93,0.000000,"\text{Not used}","int(x^8/((a + b*x^6)^2*(c + d*x^6)^(1/2)),x)","\int \frac{x^8}{{\left(b\,x^6+a\right)}^2\,\sqrt{d\,x^6+c}} \,d x","Not used",1,"int(x^8/((a + b*x^6)^2*(c + d*x^6)^(1/2)), x)","F"
877,0,-1,104,0.000000,"\text{Not used}","int(x^2/((a + b*x^6)^2*(c + d*x^6)^(1/2)),x)","\int \frac{x^2}{{\left(b\,x^6+a\right)}^2\,\sqrt{d\,x^6+c}} \,d x","Not used",1,"int(x^2/((a + b*x^6)^2*(c + d*x^6)^(1/2)), x)","F"
878,0,-1,149,0.000000,"\text{Not used}","int(1/(x^4*(a + b*x^6)^2*(c + d*x^6)^(1/2)),x)","\int \frac{1}{x^4\,{\left(b\,x^6+a\right)}^2\,\sqrt{d\,x^6+c}} \,d x","Not used",1,"int(1/(x^4*(a + b*x^6)^2*(c + d*x^6)^(1/2)), x)","F"
879,0,-1,208,0.000000,"\text{Not used}","int(1/(x^10*(a + b*x^6)^2*(c + d*x^6)^(1/2)),x)","\int \frac{1}{x^{10}\,{\left(b\,x^6+a\right)}^2\,\sqrt{d\,x^6+c}} \,d x","Not used",1,"int(1/(x^10*(a + b*x^6)^2*(c + d*x^6)^(1/2)), x)","F"
880,0,-1,64,0.000000,"\text{Not used}","int(x^4/((a + b*x^6)^2*(c + d*x^6)^(1/2)),x)","\int \frac{x^4}{{\left(b\,x^6+a\right)}^2\,\sqrt{d\,x^6+c}} \,d x","Not used",1,"int(x^4/((a + b*x^6)^2*(c + d*x^6)^(1/2)), x)","F"
881,0,-1,64,0.000000,"\text{Not used}","int(x^3/((a + b*x^6)^2*(c + d*x^6)^(1/2)),x)","\int \frac{x^3}{{\left(b\,x^6+a\right)}^2\,\sqrt{d\,x^6+c}} \,d x","Not used",1,"int(x^3/((a + b*x^6)^2*(c + d*x^6)^(1/2)), x)","F"
882,0,-1,64,0.000000,"\text{Not used}","int(x/((a + b*x^6)^2*(c + d*x^6)^(1/2)),x)","\int \frac{x}{{\left(b\,x^6+a\right)}^2\,\sqrt{d\,x^6+c}} \,d x","Not used",1,"int(x/((a + b*x^6)^2*(c + d*x^6)^(1/2)), x)","F"
883,0,-1,59,0.000000,"\text{Not used}","int(1/((a + b*x^6)^2*(c + d*x^6)^(1/2)),x)","\int \frac{1}{{\left(b\,x^6+a\right)}^2\,\sqrt{d\,x^6+c}} \,d x","Not used",1,"int(1/((a + b*x^6)^2*(c + d*x^6)^(1/2)), x)","F"
884,0,-1,62,0.000000,"\text{Not used}","int(1/(x^2*(a + b*x^6)^2*(c + d*x^6)^(1/2)),x)","\int \frac{1}{x^2\,{\left(b\,x^6+a\right)}^2\,\sqrt{d\,x^6+c}} \,d x","Not used",1,"int(1/(x^2*(a + b*x^6)^2*(c + d*x^6)^(1/2)), x)","F"
885,0,-1,64,0.000000,"\text{Not used}","int(1/(x^3*(a + b*x^6)^2*(c + d*x^6)^(1/2)),x)","\int \frac{1}{x^3\,{\left(b\,x^6+a\right)}^2\,\sqrt{d\,x^6+c}} \,d x","Not used",1,"int(1/(x^3*(a + b*x^6)^2*(c + d*x^6)^(1/2)), x)","F"
886,0,-1,64,0.000000,"\text{Not used}","int(1/(x^5*(a + b*x^6)^2*(c + d*x^6)^(1/2)),x)","\int \frac{1}{x^5\,{\left(b\,x^6+a\right)}^2\,\sqrt{d\,x^6+c}} \,d x","Not used",1,"int(1/(x^5*(a + b*x^6)^2*(c + d*x^6)^(1/2)), x)","F"
887,1,103,104,4.678147,"\text{Not used}","int(x^23/((a + b*x^8)*(c + d*x^8)^(1/2)),x)","\frac{{\left(d\,x^8+c\right)}^{3/2}}{12\,b\,d^2}-\left(\frac{c}{2\,b\,d^2}+\frac{4\,a\,d^3-4\,b\,c\,d^2}{16\,b^2\,d^4}\right)\,\sqrt{d\,x^8+c}+\frac{a^2\,\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d\,x^8+c}}{\sqrt{a\,d-b\,c}}\right)}{4\,b^{5/2}\,\sqrt{a\,d-b\,c}}","Not used",1,"(c + d*x^8)^(3/2)/(12*b*d^2) - (c/(2*b*d^2) + (4*a*d^3 - 4*b*c*d^2)/(16*b^2*d^4))*(c + d*x^8)^(1/2) + (a^2*atan((b^(1/2)*(c + d*x^8)^(1/2))/(a*d - b*c)^(1/2)))/(4*b^(5/2)*(a*d - b*c)^(1/2))","B"
888,1,58,74,4.730149,"\text{Not used}","int(x^15/((a + b*x^8)*(c + d*x^8)^(1/2)),x)","\frac{\sqrt{d\,x^8+c}}{4\,b\,d}-\frac{a\,\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d\,x^8+c}}{\sqrt{a\,d-b\,c}}\right)}{4\,b^{3/2}\,\sqrt{a\,d-b\,c}}","Not used",1,"(c + d*x^8)^(1/2)/(4*b*d) - (a*atan((b^(1/2)*(c + d*x^8)^(1/2))/(a*d - b*c)^(1/2)))/(4*b^(3/2)*(a*d - b*c)^(1/2))","B"
889,1,40,51,4.585911,"\text{Not used}","int(x^7/((a + b*x^8)*(c + d*x^8)^(1/2)),x)","\frac{\mathrm{atan}\left(\frac{b\,\sqrt{d\,x^8+c}}{\sqrt{a\,b\,d-b^2\,c}}\right)}{4\,\sqrt{a\,b\,d-b^2\,c}}","Not used",1,"atan((b*(c + d*x^8)^(1/2))/(a*b*d - b^2*c)^(1/2))/(4*(a*b*d - b^2*c)^(1/2))","B"
890,1,652,85,4.812593,"\text{Not used}","int(1/(x*(a + b*x^8)*(c + d*x^8)^(1/2)),x)","-\frac{\mathrm{atanh}\left(\frac{\sqrt{d\,x^8+c}}{\sqrt{c}}\right)}{4\,a\,\sqrt{c}}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{b^2\,c-a\,b\,d}\,\left(\frac{b^3\,d^2\,\sqrt{d\,x^8+c}}{4}-\frac{\sqrt{b^2\,c-a\,b\,d}\,\left(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^8+c}\,\sqrt{b^2\,c-a\,b\,d}}{8\,\left(a^2\,d-a\,b\,c\right)}\right)}{8\,\left(a^2\,d-a\,b\,c\right)}\right)\,1{}\mathrm{i}}{8\,\left(a^2\,d-a\,b\,c\right)}+\frac{\sqrt{b^2\,c-a\,b\,d}\,\left(\frac{b^3\,d^2\,\sqrt{d\,x^8+c}}{4}+\frac{\sqrt{b^2\,c-a\,b\,d}\,\left(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^8+c}\,\sqrt{b^2\,c-a\,b\,d}}{8\,\left(a^2\,d-a\,b\,c\right)}\right)}{8\,\left(a^2\,d-a\,b\,c\right)}\right)\,1{}\mathrm{i}}{8\,\left(a^2\,d-a\,b\,c\right)}}{\frac{\sqrt{b^2\,c-a\,b\,d}\,\left(\frac{b^3\,d^2\,\sqrt{d\,x^8+c}}{4}-\frac{\sqrt{b^2\,c-a\,b\,d}\,\left(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^8+c}\,\sqrt{b^2\,c-a\,b\,d}}{8\,\left(a^2\,d-a\,b\,c\right)}\right)}{8\,\left(a^2\,d-a\,b\,c\right)}\right)}{8\,\left(a^2\,d-a\,b\,c\right)}-\frac{\sqrt{b^2\,c-a\,b\,d}\,\left(\frac{b^3\,d^2\,\sqrt{d\,x^8+c}}{4}+\frac{\sqrt{b^2\,c-a\,b\,d}\,\left(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^8+c}\,\sqrt{b^2\,c-a\,b\,d}}{8\,\left(a^2\,d-a\,b\,c\right)}\right)}{8\,\left(a^2\,d-a\,b\,c\right)}\right)}{8\,\left(a^2\,d-a\,b\,c\right)}}\right)\,\sqrt{b^2\,c-a\,b\,d}\,1{}\mathrm{i}}{4\,\left(a^2\,d-a\,b\,c\right)}","Not used",1,"- atanh((c + d*x^8)^(1/2)/c^(1/2))/(4*a*c^(1/2)) - (atan((((b^2*c - a*b*d)^(1/2)*((b^3*d^2*(c + d*x^8)^(1/2))/4 - ((b^2*c - a*b*d)^(1/2)*(a^2*b^2*d^3 - ((8*a^3*b^2*d^3 - 16*a^2*b^3*c*d^2)*(c + d*x^8)^(1/2)*(b^2*c - a*b*d)^(1/2))/(8*(a^2*d - a*b*c))))/(8*(a^2*d - a*b*c)))*1i)/(8*(a^2*d - a*b*c)) + ((b^2*c - a*b*d)^(1/2)*((b^3*d^2*(c + d*x^8)^(1/2))/4 + ((b^2*c - a*b*d)^(1/2)*(a^2*b^2*d^3 + ((8*a^3*b^2*d^3 - 16*a^2*b^3*c*d^2)*(c + d*x^8)^(1/2)*(b^2*c - a*b*d)^(1/2))/(8*(a^2*d - a*b*c))))/(8*(a^2*d - a*b*c)))*1i)/(8*(a^2*d - a*b*c)))/(((b^2*c - a*b*d)^(1/2)*((b^3*d^2*(c + d*x^8)^(1/2))/4 - ((b^2*c - a*b*d)^(1/2)*(a^2*b^2*d^3 - ((8*a^3*b^2*d^3 - 16*a^2*b^3*c*d^2)*(c + d*x^8)^(1/2)*(b^2*c - a*b*d)^(1/2))/(8*(a^2*d - a*b*c))))/(8*(a^2*d - a*b*c))))/(8*(a^2*d - a*b*c)) - ((b^2*c - a*b*d)^(1/2)*((b^3*d^2*(c + d*x^8)^(1/2))/4 + ((b^2*c - a*b*d)^(1/2)*(a^2*b^2*d^3 + ((8*a^3*b^2*d^3 - 16*a^2*b^3*c*d^2)*(c + d*x^8)^(1/2)*(b^2*c - a*b*d)^(1/2))/(8*(a^2*d - a*b*c))))/(8*(a^2*d - a*b*c))))/(8*(a^2*d - a*b*c))))*(b^2*c - a*b*d)^(1/2)*1i)/(4*(a^2*d - a*b*c))","B"
891,1,396,117,5.507174,"\text{Not used}","int(1/(x^9*(a + b*x^8)*(c + d*x^8)^(1/2)),x)","\frac{\ln\left(\sqrt{d\,x^8+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}}{8\,a^3\,d-8\,a^2\,b\,c}-\frac{\ln\left(\sqrt{d\,x^8+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}}{8\,\left(a^3\,d-a^2\,b\,c\right)}-\frac{\sqrt{d\,x^8+c}}{8\,a\,c\,x^8}-\frac{\mathrm{atan}\left(\frac{b^4\,d^4\,\sqrt{d\,x^8+c}\,3{}\mathrm{i}}{128\,\sqrt{c^3}\,\left(\frac{3\,b^4\,d^4}{128\,c}+\frac{5\,a\,b^3\,d^5}{256\,c^2}+\frac{a^2\,b^2\,d^6}{256\,c^3}\right)}+\frac{b^2\,d^6\,\sqrt{d\,x^8+c}\,1{}\mathrm{i}}{256\,\sqrt{c^3}\,\left(\frac{5\,b^3\,d^5}{256\,a}+\frac{b^2\,d^6}{256\,c}+\frac{3\,b^4\,c\,d^4}{128\,a^2}\right)}+\frac{b^3\,d^5\,\sqrt{d\,x^8+c}\,5{}\mathrm{i}}{256\,\sqrt{c^3}\,\left(\frac{3\,b^4\,d^4}{128\,a}+\frac{5\,b^3\,d^5}{256\,c}+\frac{a\,b^2\,d^6}{256\,c^2}\right)}\right)\,\left(a\,d+2\,b\,c\right)\,1{}\mathrm{i}}{8\,a^2\,\sqrt{c^3}}","Not used",1,"(log((c + d*x^8)^(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))/(8*a^3*d - 8*a^2*b*c) - (log((c + d*x^8)^(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))/(8*(a^3*d - a^2*b*c)) - (c + d*x^8)^(1/2)/(8*a*c*x^8) - (atan((b^4*d^4*(c + d*x^8)^(1/2)*3i)/(128*(c^3)^(1/2)*((3*b^4*d^4)/(128*c) + (5*a*b^3*d^5)/(256*c^2) + (a^2*b^2*d^6)/(256*c^3))) + (b^2*d^6*(c + d*x^8)^(1/2)*1i)/(256*(c^3)^(1/2)*((5*b^3*d^5)/(256*a) + (b^2*d^6)/(256*c) + (3*b^4*c*d^4)/(128*a^2))) + (b^3*d^5*(c + d*x^8)^(1/2)*5i)/(256*(c^3)^(1/2)*((3*b^4*d^4)/(128*a) + (5*b^3*d^5)/(256*c) + (a*b^2*d^6)/(256*c^2))))*(a*d + 2*b*c)*1i)/(8*a^2*(c^3)^(1/2))","B"
892,0,-1,123,0.000000,"\text{Not used}","int(x^19/((a + b*x^8)*(c + d*x^8)^(1/2)),x)","\int \frac{x^{19}}{\left(b\,x^8+a\right)\,\sqrt{d\,x^8+c}} \,d x","Not used",1,"int(x^19/((a + b*x^8)*(c + d*x^8)^(1/2)), x)","F"
893,0,-1,91,0.000000,"\text{Not used}","int(x^11/((a + b*x^8)*(c + d*x^8)^(1/2)),x)","\int \frac{x^{11}}{\left(b\,x^8+a\right)\,\sqrt{d\,x^8+c}} \,d x","Not used",1,"int(x^11/((a + b*x^8)*(c + d*x^8)^(1/2)), x)","F"
894,0,-1,54,0.000000,"\text{Not used}","int(x^3/((a + b*x^8)*(c + d*x^8)^(1/2)),x)","\int \frac{x^3}{\left(b\,x^8+a\right)\,\sqrt{d\,x^8+c}} \,d x","Not used",1,"int(x^3/((a + b*x^8)*(c + d*x^8)^(1/2)), x)","F"
895,0,-1,80,0.000000,"\text{Not used}","int(1/(x^5*(a + b*x^8)*(c + d*x^8)^(1/2)),x)","\int \frac{1}{x^5\,\left(b\,x^8+a\right)\,\sqrt{d\,x^8+c}} \,d x","Not used",1,"int(1/(x^5*(a + b*x^8)*(c + d*x^8)^(1/2)), x)","F"
896,0,-1,115,0.000000,"\text{Not used}","int(1/(x^13*(a + b*x^8)*(c + d*x^8)^(1/2)),x)","\int \frac{1}{x^{13}\,\left(b\,x^8+a\right)\,\sqrt{d\,x^8+c}} \,d x","Not used",1,"int(1/(x^13*(a + b*x^8)*(c + d*x^8)^(1/2)), x)","F"
897,0,-1,851,0.000000,"\text{Not used}","int(x^9/((a + b*x^8)*(c + d*x^8)^(1/2)),x)","\int \frac{x^9}{\left(b\,x^8+a\right)\,\sqrt{d\,x^8+c}} \,d x","Not used",1,"int(x^9/((a + b*x^8)*(c + d*x^8)^(1/2)), x)","F"
898,0,-1,754,0.000000,"\text{Not used}","int(x/((a + b*x^8)*(c + d*x^8)^(1/2)),x)","\int \frac{x}{\left(b\,x^8+a\right)\,\sqrt{d\,x^8+c}} \,d x","Not used",1,"int(x/((a + b*x^8)*(c + d*x^8)^(1/2)), x)","F"
899,0,-1,878,0.000000,"\text{Not used}","int(1/(x^7*(a + b*x^8)*(c + d*x^8)^(1/2)),x)","\int \frac{1}{x^7\,\left(b\,x^8+a\right)\,\sqrt{d\,x^8+c}} \,d x","Not used",1,"int(1/(x^7*(a + b*x^8)*(c + d*x^8)^(1/2)), x)","F"
900,0,-1,1005,0.000000,"\text{Not used}","int(x^13/((a + b*x^8)*(c + d*x^8)^(1/2)),x)","\int \frac{x^{13}}{\left(b\,x^8+a\right)\,\sqrt{d\,x^8+c}} \,d x","Not used",1,"int(x^13/((a + b*x^8)*(c + d*x^8)^(1/2)), x)","F"
901,0,-1,768,0.000000,"\text{Not used}","int(x^5/((a + b*x^8)*(c + d*x^8)^(1/2)),x)","\int \frac{x^5}{\left(b\,x^8+a\right)\,\sqrt{d\,x^8+c}} \,d x","Not used",1,"int(x^5/((a + b*x^8)*(c + d*x^8)^(1/2)), x)","F"
902,0,-1,1032,0.000000,"\text{Not used}","int(1/(x^3*(a + b*x^8)*(c + d*x^8)^(1/2)),x)","\int \frac{1}{x^3\,\left(b\,x^8+a\right)\,\sqrt{d\,x^8+c}} \,d x","Not used",1,"int(1/(x^3*(a + b*x^8)*(c + d*x^8)^(1/2)), x)","F"
903,0,-1,64,0.000000,"\text{Not used}","int(x^4/((a + b*x^8)*(c + d*x^8)^(1/2)),x)","\int \frac{x^4}{\left(b\,x^8+a\right)\,\sqrt{d\,x^8+c}} \,d x","Not used",1,"int(x^4/((a + b*x^8)*(c + d*x^8)^(1/2)), x)","F"
904,0,-1,64,0.000000,"\text{Not used}","int(x^2/((a + b*x^8)*(c + d*x^8)^(1/2)),x)","\int \frac{x^2}{\left(b\,x^8+a\right)\,\sqrt{d\,x^8+c}} \,d x","Not used",1,"int(x^2/((a + b*x^8)*(c + d*x^8)^(1/2)), x)","F"
905,0,-1,59,0.000000,"\text{Not used}","int(1/((a + b*x^8)*(c + d*x^8)^(1/2)),x)","\int \frac{1}{\left(b\,x^8+a\right)\,\sqrt{d\,x^8+c}} \,d x","Not used",1,"int(1/((a + b*x^8)*(c + d*x^8)^(1/2)), x)","F"
906,0,-1,62,0.000000,"\text{Not used}","int(1/(x^2*(a + b*x^8)*(c + d*x^8)^(1/2)),x)","\int \frac{1}{x^2\,\left(b\,x^8+a\right)\,\sqrt{d\,x^8+c}} \,d x","Not used",1,"int(1/(x^2*(a + b*x^8)*(c + d*x^8)^(1/2)), x)","F"
907,0,-1,64,0.000000,"\text{Not used}","int(1/(x^4*(a + b*x^8)*(c + d*x^8)^(1/2)),x)","\int \frac{1}{x^4\,\left(b\,x^8+a\right)\,\sqrt{d\,x^8+c}} \,d x","Not used",1,"int(1/(x^4*(a + b*x^8)*(c + d*x^8)^(1/2)), x)","F"
908,1,144,123,5.020946,"\text{Not used}","int(x^23/((a + b*x^8)^2*(c + d*x^8)^(1/2)),x)","\frac{\sqrt{d\,x^8+c}}{4\,b^2\,d}-\frac{a\,\mathrm{atan}\left(\frac{a\,\sqrt{b}\,\sqrt{d\,x^8+c}\,\left(3\,a\,d-4\,b\,c\right)}{\left(3\,a^2\,d-4\,a\,b\,c\right)\,\sqrt{a\,d-b\,c}}\right)\,\left(3\,a\,d-4\,b\,c\right)}{8\,b^{5/2}\,{\left(a\,d-b\,c\right)}^{3/2}}+\frac{a^2\,d\,\sqrt{d\,x^8+c}}{2\,\left(a\,d-b\,c\right)\,\left(4\,b^3\,\left(d\,x^8+c\right)-4\,b^3\,c+4\,a\,b^2\,d\right)}","Not used",1,"(c + d*x^8)^(1/2)/(4*b^2*d) - (a*atan((a*b^(1/2)*(c + d*x^8)^(1/2)*(3*a*d - 4*b*c))/((3*a^2*d - 4*a*b*c)*(a*d - b*c)^(1/2)))*(3*a*d - 4*b*c))/(8*b^(5/2)*(a*d - b*c)^(3/2)) + (a^2*d*(c + d*x^8)^(1/2))/(2*(a*d - b*c)*(4*b^3*(c + d*x^8) - 4*b^3*c + 4*a*b^2*d))","B"
909,1,95,99,4.836812,"\text{Not used}","int(x^15/((a + b*x^8)^2*(c + d*x^8)^(1/2)),x)","\frac{\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d\,x^8+c}}{\sqrt{a\,d-b\,c}}\right)\,\left(a\,d-2\,b\,c\right)}{8\,b^{3/2}\,{\left(a\,d-b\,c\right)}^{3/2}}-\frac{a\,d\,\sqrt{d\,x^8+c}}{2\,b\,\left(a\,d-b\,c\right)\,\left(4\,b\,\left(d\,x^8+c\right)+4\,a\,d-4\,b\,c\right)}","Not used",1,"(atan((b^(1/2)*(c + d*x^8)^(1/2))/(a*d - b*c)^(1/2))*(a*d - 2*b*c))/(8*b^(3/2)*(a*d - b*c)^(3/2)) - (a*d*(c + d*x^8)^(1/2))/(2*b*(a*d - b*c)*(4*b*(c + d*x^8) + 4*a*d - 4*b*c))","B"
910,1,84,87,4.797479,"\text{Not used}","int(x^7/((a + b*x^8)^2*(c + d*x^8)^(1/2)),x)","\frac{d\,\sqrt{d\,x^8+c}}{2\,\left(a\,d-b\,c\right)\,\left(4\,b\,\left(d\,x^8+c\right)+4\,a\,d-4\,b\,c\right)}+\frac{d\,\mathrm{atan}\left(\frac{\sqrt{b}\,\sqrt{d\,x^8+c}}{\sqrt{a\,d-b\,c}}\right)}{8\,\sqrt{b}\,{\left(a\,d-b\,c\right)}^{3/2}}","Not used",1,"(d*(c + d*x^8)^(1/2))/(2*(a*d - b*c)*(4*b*(c + d*x^8) + 4*a*d - 4*b*c)) + (d*atan((b^(1/2)*(c + d*x^8)^(1/2))/(a*d - b*c)^(1/2)))/(8*b^(1/2)*(a*d - b*c)^(3/2))","B"
911,1,3017,132,5.819867,"\text{Not used}","int(1/(x*(a + b*x^8)^2*(c + d*x^8)^(1/2)),x)","-\frac{b\,d\,\sqrt{d\,x^8+c}}{2\,\left(a^2\,d-a\,b\,c\right)\,\left(4\,b\,\left(d\,x^8+c\right)+4\,a\,d-4\,b\,c\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\frac{a^6\,b^2\,d^5-\frac{3\,a^5\,b^3\,c\,d^4}{2}+\frac{a^4\,b^4\,c^2\,d^3}{2}}{8\,\left(a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2\right)}-\frac{\sqrt{d\,x^8+c}\,\left(256\,a^7\,b^2\,d^5-1024\,a^6\,b^3\,c\,d^4+1280\,a^5\,b^4\,c^2\,d^3-512\,a^4\,b^5\,c^3\,d^2\right)}{2048\,a^2\,\sqrt{c}\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}}{8\,a^2\,\sqrt{c}}-\frac{\sqrt{d\,x^8+c}\,\left(13\,a^2\,b^3\,d^4-20\,a\,b^4\,c\,d^3+8\,b^5\,c^2\,d^2\right)}{256\,\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{a^6\,b^2\,d^5-\frac{3\,a^5\,b^3\,c\,d^4}{2}+\frac{a^4\,b^4\,c^2\,d^3}{2}}{8\,\left(a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2\right)}+\frac{\sqrt{d\,x^8+c}\,\left(256\,a^7\,b^2\,d^5-1024\,a^6\,b^3\,c\,d^4+1280\,a^5\,b^4\,c^2\,d^3-512\,a^4\,b^5\,c^3\,d^2\right)}{2048\,a^2\,\sqrt{c}\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}}{8\,a^2\,\sqrt{c}}+\frac{\sqrt{d\,x^8+c}\,\left(13\,a^2\,b^3\,d^4-20\,a\,b^4\,c\,d^3+8\,b^5\,c^2\,d^2\right)}{256\,\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}{128}-\frac{b^4\,c\,d^3}{64}}{a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2}+\frac{\frac{\frac{a^6\,b^2\,d^5-\frac{3\,a^5\,b^3\,c\,d^4}{2}+\frac{a^4\,b^4\,c^2\,d^3}{2}}{8\,\left(a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2\right)}-\frac{\sqrt{d\,x^8+c}\,\left(256\,a^7\,b^2\,d^5-1024\,a^6\,b^3\,c\,d^4+1280\,a^5\,b^4\,c^2\,d^3-512\,a^4\,b^5\,c^3\,d^2\right)}{2048\,a^2\,\sqrt{c}\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}}{8\,a^2\,\sqrt{c}}-\frac{\sqrt{d\,x^8+c}\,\left(13\,a^2\,b^3\,d^4-20\,a\,b^4\,c\,d^3+8\,b^5\,c^2\,d^2\right)}{256\,\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{a^6\,b^2\,d^5-\frac{3\,a^5\,b^3\,c\,d^4}{2}+\frac{a^4\,b^4\,c^2\,d^3}{2}}{8\,\left(a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2\right)}+\frac{\sqrt{d\,x^8+c}\,\left(256\,a^7\,b^2\,d^5-1024\,a^6\,b^3\,c\,d^4+1280\,a^5\,b^4\,c^2\,d^3-512\,a^4\,b^5\,c^3\,d^2\right)}{2048\,a^2\,\sqrt{c}\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}}{8\,a^2\,\sqrt{c}}+\frac{\sqrt{d\,x^8+c}\,\left(13\,a^2\,b^3\,d^4-20\,a\,b^4\,c\,d^3+8\,b^5\,c^2\,d^2\right)}{256\,\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}}{4\,a^2\,\sqrt{c}}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\sqrt{d\,x^8+c}\,\left(13\,a^2\,b^3\,d^4-20\,a\,b^4\,c\,d^3+8\,b^5\,c^2\,d^2\right)}{32\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}-\frac{\left(\frac{a^6\,b^2\,d^5-\frac{3\,a^5\,b^3\,c\,d^4}{2}+\frac{a^4\,b^4\,c^2\,d^3}{2}}{a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2}-\frac{\sqrt{d\,x^8+c}\,\left(3\,a\,d-2\,b\,c\right)\,\sqrt{-b\,{\left(a\,d-b\,c\right)}^3}\,\left(256\,a^7\,b^2\,d^5-1024\,a^6\,b^3\,c\,d^4+1280\,a^5\,b^4\,c^2\,d^3-512\,a^4\,b^5\,c^3\,d^2\right)}{512\,\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}}{16\,\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}}{16\,\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^8+c}\,\left(13\,a^2\,b^3\,d^4-20\,a\,b^4\,c\,d^3+8\,b^5\,c^2\,d^2\right)}{32\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}+\frac{\left(\frac{a^6\,b^2\,d^5-\frac{3\,a^5\,b^3\,c\,d^4}{2}+\frac{a^4\,b^4\,c^2\,d^3}{2}}{a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2}+\frac{\sqrt{d\,x^8+c}\,\left(3\,a\,d-2\,b\,c\right)\,\sqrt{-b\,{\left(a\,d-b\,c\right)}^3}\,\left(256\,a^7\,b^2\,d^5-1024\,a^6\,b^3\,c\,d^4+1280\,a^5\,b^4\,c^2\,d^3-512\,a^4\,b^5\,c^3\,d^2\right)}{512\,\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}}{16\,\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}}{16\,\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}{128}-\frac{b^4\,c\,d^3}{64}}{a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2}-\frac{\left(\frac{\sqrt{d\,x^8+c}\,\left(13\,a^2\,b^3\,d^4-20\,a\,b^4\,c\,d^3+8\,b^5\,c^2\,d^2\right)}{32\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}-\frac{\left(\frac{a^6\,b^2\,d^5-\frac{3\,a^5\,b^3\,c\,d^4}{2}+\frac{a^4\,b^4\,c^2\,d^3}{2}}{a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2}-\frac{\sqrt{d\,x^8+c}\,\left(3\,a\,d-2\,b\,c\right)\,\sqrt{-b\,{\left(a\,d-b\,c\right)}^3}\,\left(256\,a^7\,b^2\,d^5-1024\,a^6\,b^3\,c\,d^4+1280\,a^5\,b^4\,c^2\,d^3-512\,a^4\,b^5\,c^3\,d^2\right)}{512\,\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}}{16\,\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}}{16\,\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^8+c}\,\left(13\,a^2\,b^3\,d^4-20\,a\,b^4\,c\,d^3+8\,b^5\,c^2\,d^2\right)}{32\,\left(a^4\,d^2-2\,a^3\,b\,c\,d+a^2\,b^2\,c^2\right)}+\frac{\left(\frac{a^6\,b^2\,d^5-\frac{3\,a^5\,b^3\,c\,d^4}{2}+\frac{a^4\,b^4\,c^2\,d^3}{2}}{a^5\,d^2-2\,a^4\,b\,c\,d+a^3\,b^2\,c^2}+\frac{\sqrt{d\,x^8+c}\,\left(3\,a\,d-2\,b\,c\right)\,\sqrt{-b\,{\left(a\,d-b\,c\right)}^3}\,\left(256\,a^7\,b^2\,d^5-1024\,a^6\,b^3\,c\,d^4+1280\,a^5\,b^4\,c^2\,d^3-512\,a^4\,b^5\,c^3\,d^2\right)}{512\,\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}}{16\,\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}}{16\,\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}}{8\,\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^8)^(1/2)*(13*a^2*b^3*d^4 + 8*b^5*c^2*d^2 - 20*a*b^4*c*d^3))/(32*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)) - (((a^6*b^2*d^5 - (3*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^8)^(1/2)*(3*a*d - 2*b*c)*(-b*(a*d - b*c)^3)^(1/2)*(256*a^7*b^2*d^5 - 1024*a^6*b^3*c*d^4 - 512*a^4*b^5*c^3*d^2 + 1280*a^5*b^4*c^2*d^3))/(512*(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))/(16*(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)/(16*(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^8)^(1/2)*(13*a^2*b^3*d^4 + 8*b^5*c^2*d^2 - 20*a*b^4*c*d^3))/(32*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)) + (((a^6*b^2*d^5 - (3*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^8)^(1/2)*(3*a*d - 2*b*c)*(-b*(a*d - b*c)^3)^(1/2)*(256*a^7*b^2*d^5 - 1024*a^6*b^3*c*d^4 - 512*a^4*b^5*c^3*d^2 + 1280*a^5*b^4*c^2*d^3))/(512*(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))/(16*(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)/(16*(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)/128 - (b^4*c*d^3)/64)/(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d) - ((((c + d*x^8)^(1/2)*(13*a^2*b^3*d^4 + 8*b^5*c^2*d^2 - 20*a*b^4*c*d^3))/(32*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)) - (((a^6*b^2*d^5 - (3*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^8)^(1/2)*(3*a*d - 2*b*c)*(-b*(a*d - b*c)^3)^(1/2)*(256*a^7*b^2*d^5 - 1024*a^6*b^3*c*d^4 - 512*a^4*b^5*c^3*d^2 + 1280*a^5*b^4*c^2*d^3))/(512*(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))/(16*(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))/(16*(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^8)^(1/2)*(13*a^2*b^3*d^4 + 8*b^5*c^2*d^2 - 20*a*b^4*c*d^3))/(32*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)) + (((a^6*b^2*d^5 - (3*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^8)^(1/2)*(3*a*d - 2*b*c)*(-b*(a*d - b*c)^3)^(1/2)*(256*a^7*b^2*d^5 - 1024*a^6*b^3*c*d^4 - 512*a^4*b^5*c^3*d^2 + 1280*a^5*b^4*c^2*d^3))/(512*(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))/(16*(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))/(16*(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)/(8*(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((((((a^6*b^2*d^5 - (3*a^5*b^3*c*d^4)/2 + (a^4*b^4*c^2*d^3)/2)/(8*(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d)) - ((c + d*x^8)^(1/2)*(256*a^7*b^2*d^5 - 1024*a^6*b^3*c*d^4 - 512*a^4*b^5*c^3*d^2 + 1280*a^5*b^4*c^2*d^3))/(2048*a^2*c^(1/2)*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)))/(8*a^2*c^(1/2)) - ((c + d*x^8)^(1/2)*(13*a^2*b^3*d^4 + 8*b^5*c^2*d^2 - 20*a*b^4*c*d^3))/(256*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)))*1i)/(a^2*c^(1/2)) - ((((a^6*b^2*d^5 - (3*a^5*b^3*c*d^4)/2 + (a^4*b^4*c^2*d^3)/2)/(8*(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d)) + ((c + d*x^8)^(1/2)*(256*a^7*b^2*d^5 - 1024*a^6*b^3*c*d^4 - 512*a^4*b^5*c^3*d^2 + 1280*a^5*b^4*c^2*d^3))/(2048*a^2*c^(1/2)*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)))/(8*a^2*c^(1/2)) + ((c + d*x^8)^(1/2)*(13*a^2*b^3*d^4 + 8*b^5*c^2*d^2 - 20*a*b^4*c*d^3))/(256*(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)/128 - (b^4*c*d^3)/64)/(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d) + (((a^6*b^2*d^5 - (3*a^5*b^3*c*d^4)/2 + (a^4*b^4*c^2*d^3)/2)/(8*(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d)) - ((c + d*x^8)^(1/2)*(256*a^7*b^2*d^5 - 1024*a^6*b^3*c*d^4 - 512*a^4*b^5*c^3*d^2 + 1280*a^5*b^4*c^2*d^3))/(2048*a^2*c^(1/2)*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)))/(8*a^2*c^(1/2)) - ((c + d*x^8)^(1/2)*(13*a^2*b^3*d^4 + 8*b^5*c^2*d^2 - 20*a*b^4*c*d^3))/(256*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)))/(a^2*c^(1/2)) + (((a^6*b^2*d^5 - (3*a^5*b^3*c*d^4)/2 + (a^4*b^4*c^2*d^3)/2)/(8*(a^5*d^2 + a^3*b^2*c^2 - 2*a^4*b*c*d)) + ((c + d*x^8)^(1/2)*(256*a^7*b^2*d^5 - 1024*a^6*b^3*c*d^4 - 512*a^4*b^5*c^3*d^2 + 1280*a^5*b^4*c^2*d^3))/(2048*a^2*c^(1/2)*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)))/(8*a^2*c^(1/2)) + ((c + d*x^8)^(1/2)*(13*a^2*b^3*d^4 + 8*b^5*c^2*d^2 - 20*a*b^4*c*d^3))/(256*(a^4*d^2 + a^2*b^2*c^2 - 2*a^3*b*c*d)))/(a^2*c^(1/2))))*1i)/(4*a^2*c^(1/2)) - (b*d*(c + d*x^8)^(1/2))/(2*(a^2*d - a*b*c)*(4*b*(c + d*x^8) + 4*a*d - 4*b*c))","B"
912,1,3832,185,7.851244,"\text{Not used}","int(1/(x^9*(a + b*x^8)^2*(c + d*x^8)^(1/2)),x)","\frac{\frac{\sqrt{d\,x^8+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^8+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^8+c\right)\,\left(4\,a\,d-8\,b\,c\right)+4\,b\,{\left(d\,x^8+c\right)}^2+4\,b\,c^2-4\,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^8+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)}{32\,\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{\frac{a^9\,b^2\,c\,d^6}{2}+\frac{a^8\,b^3\,c^2\,d^5}{2}-2\,a^7\,b^4\,c^3\,d^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^8+c}\,\left(5\,a\,d-4\,b\,c\right)\,\left(-256\,a^9\,b^2\,c^2\,d^5+1024\,a^8\,b^3\,c^3\,d^4-1280\,a^7\,b^4\,c^4\,d^3+512\,a^6\,b^5\,c^5\,d^2\right)}{512\,\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)}{16\,\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}}{16\,\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^8+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)}{32\,\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{\frac{a^9\,b^2\,c\,d^6}{2}+\frac{a^8\,b^3\,c^2\,d^5}{2}-2\,a^7\,b^4\,c^3\,d^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^8+c}\,\left(5\,a\,d-4\,b\,c\right)\,\left(-256\,a^9\,b^2\,c^2\,d^5+1024\,a^8\,b^3\,c^3\,d^4-1280\,a^7\,b^4\,c^4\,d^3+512\,a^6\,b^5\,c^5\,d^2\right)}{512\,\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)}{16\,\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}}{16\,\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}{256}+\frac{3\,a^2\,b^5\,c\,d^5}{128}-\frac{3\,a\,b^6\,c^2\,d^4}{16}+\frac{b^7\,c^3\,d^3}{8}}{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^8+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)}{32\,\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{\frac{a^9\,b^2\,c\,d^6}{2}+\frac{a^8\,b^3\,c^2\,d^5}{2}-2\,a^7\,b^4\,c^3\,d^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^8+c}\,\left(5\,a\,d-4\,b\,c\right)\,\left(-256\,a^9\,b^2\,c^2\,d^5+1024\,a^8\,b^3\,c^3\,d^4-1280\,a^7\,b^4\,c^4\,d^3+512\,a^6\,b^5\,c^5\,d^2\right)}{512\,\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)}{16\,\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)}{16\,\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^8+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)}{32\,\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{\frac{a^9\,b^2\,c\,d^6}{2}+\frac{a^8\,b^3\,c^2\,d^5}{2}-2\,a^7\,b^4\,c^3\,d^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^8+c}\,\left(5\,a\,d-4\,b\,c\right)\,\left(-256\,a^9\,b^2\,c^2\,d^5+1024\,a^8\,b^3\,c^3\,d^4-1280\,a^7\,b^4\,c^4\,d^3+512\,a^6\,b^5\,c^5\,d^2\right)}{512\,\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)}{16\,\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)}{16\,\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}}{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)}+\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\sqrt{d\,x^8+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)}{32\,\left(a^6\,c^2\,d^2-2\,a^5\,b\,c^3\,d+a^4\,b^2\,c^4\right)}+\frac{\left(\frac{\frac{a^9\,b^2\,c\,d^6}{2}+\frac{a^8\,b^3\,c^2\,d^5}{2}-2\,a^7\,b^4\,c^3\,d^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^8+c}\,\left(a\,d+4\,b\,c\right)\,\left(-256\,a^9\,b^2\,c^2\,d^5+1024\,a^8\,b^3\,c^3\,d^4-1280\,a^7\,b^4\,c^4\,d^3+512\,a^6\,b^5\,c^5\,d^2\right)}{512\,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)}{16\,a^3\,\sqrt{c^3}}\right)\,\left(a\,d+4\,b\,c\right)\,1{}\mathrm{i}}{16\,a^3\,\sqrt{c^3}}+\frac{\left(\frac{\sqrt{d\,x^8+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)}{32\,\left(a^6\,c^2\,d^2-2\,a^5\,b\,c^3\,d+a^4\,b^2\,c^4\right)}-\frac{\left(\frac{\frac{a^9\,b^2\,c\,d^6}{2}+\frac{a^8\,b^3\,c^2\,d^5}{2}-2\,a^7\,b^4\,c^3\,d^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^8+c}\,\left(a\,d+4\,b\,c\right)\,\left(-256\,a^9\,b^2\,c^2\,d^5+1024\,a^8\,b^3\,c^3\,d^4-1280\,a^7\,b^4\,c^4\,d^3+512\,a^6\,b^5\,c^5\,d^2\right)}{512\,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)}{16\,a^3\,\sqrt{c^3}}\right)\,\left(a\,d+4\,b\,c\right)\,1{}\mathrm{i}}{16\,a^3\,\sqrt{c^3}}}{\frac{\frac{5\,a^3\,b^4\,d^6}{256}+\frac{3\,a^2\,b^5\,c\,d^5}{128}-\frac{3\,a\,b^6\,c^2\,d^4}{16}+\frac{b^7\,c^3\,d^3}{8}}{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^8+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)}{32\,\left(a^6\,c^2\,d^2-2\,a^5\,b\,c^3\,d+a^4\,b^2\,c^4\right)}+\frac{\left(\frac{\frac{a^9\,b^2\,c\,d^6}{2}+\frac{a^8\,b^3\,c^2\,d^5}{2}-2\,a^7\,b^4\,c^3\,d^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^8+c}\,\left(a\,d+4\,b\,c\right)\,\left(-256\,a^9\,b^2\,c^2\,d^5+1024\,a^8\,b^3\,c^3\,d^4-1280\,a^7\,b^4\,c^4\,d^3+512\,a^6\,b^5\,c^5\,d^2\right)}{512\,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)}{16\,a^3\,\sqrt{c^3}}\right)\,\left(a\,d+4\,b\,c\right)}{16\,a^3\,\sqrt{c^3}}+\frac{\left(\frac{\sqrt{d\,x^8+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)}{32\,\left(a^6\,c^2\,d^2-2\,a^5\,b\,c^3\,d+a^4\,b^2\,c^4\right)}-\frac{\left(\frac{\frac{a^9\,b^2\,c\,d^6}{2}+\frac{a^8\,b^3\,c^2\,d^5}{2}-2\,a^7\,b^4\,c^3\,d^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^8+c}\,\left(a\,d+4\,b\,c\right)\,\left(-256\,a^9\,b^2\,c^2\,d^5+1024\,a^8\,b^3\,c^3\,d^4-1280\,a^7\,b^4\,c^4\,d^3+512\,a^6\,b^5\,c^5\,d^2\right)}{512\,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)}{16\,a^3\,\sqrt{c^3}}\right)\,\left(a\,d+4\,b\,c\right)}{16\,a^3\,\sqrt{c^3}}}\right)\,\left(a\,d+4\,b\,c\right)\,1{}\mathrm{i}}{8\,a^3\,\sqrt{c^3}}","Not used",1,"(((c + d*x^8)^(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^8)^(3/2)*(a*d^2 - 2*b*c*d))/(2*a^2*(b*c^2 - a*c*d)))/((c + d*x^8)*(4*a*d - 8*b*c) + 4*b*(c + d*x^8)^2 + 4*b*c^2 - 4*a*c*d) + (atan((((-b^3*(a*d - b*c)^3)^(1/2)*(5*a*d - 4*b*c)*(((c + d*x^8)^(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))/(32*(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)*(((a^9*b^2*c*d^6)/2 + a^6*b^5*c^4*d^3 - 2*a^7*b^4*c^3*d^4 + (a^8*b^3*c^2*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)*(c + d*x^8)^(1/2)*(5*a*d - 4*b*c)*(512*a^6*b^5*c^5*d^2 - 1280*a^7*b^4*c^4*d^3 + 1024*a^8*b^3*c^3*d^4 - 256*a^9*b^2*c^2*d^5))/(512*(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))))/(16*(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)/(16*(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^8)^(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))/(32*(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)*(((a^9*b^2*c*d^6)/2 + a^6*b^5*c^4*d^3 - 2*a^7*b^4*c^3*d^4 + (a^8*b^3*c^2*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)*(c + d*x^8)^(1/2)*(5*a*d - 4*b*c)*(512*a^6*b^5*c^5*d^2 - 1280*a^7*b^4*c^4*d^3 + 1024*a^8*b^3*c^3*d^4 - 256*a^9*b^2*c^2*d^5))/(512*(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))))/(16*(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)/(16*(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)/256 + (b^7*c^3*d^3)/8 - (3*a*b^6*c^2*d^4)/16 + (3*a^2*b^5*c*d^5)/128)/(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^8)^(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))/(32*(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)*(((a^9*b^2*c*d^6)/2 + a^6*b^5*c^4*d^3 - 2*a^7*b^4*c^3*d^4 + (a^8*b^3*c^2*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)*(c + d*x^8)^(1/2)*(5*a*d - 4*b*c)*(512*a^6*b^5*c^5*d^2 - 1280*a^7*b^4*c^4*d^3 + 1024*a^8*b^3*c^3*d^4 - 256*a^9*b^2*c^2*d^5))/(512*(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))))/(16*(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))))/(16*(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^8)^(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))/(32*(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)*(((a^9*b^2*c*d^6)/2 + a^6*b^5*c^4*d^3 - 2*a^7*b^4*c^3*d^4 + (a^8*b^3*c^2*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)*(c + d*x^8)^(1/2)*(5*a*d - 4*b*c)*(512*a^6*b^5*c^5*d^2 - 1280*a^7*b^4*c^4*d^3 + 1024*a^8*b^3*c^3*d^4 - 256*a^9*b^2*c^2*d^5))/(512*(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))))/(16*(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))))/(16*(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)/(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)) + (atan((((((c + d*x^8)^(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))/(32*(a^4*b^2*c^4 + a^6*c^2*d^2 - 2*a^5*b*c^3*d)) + ((((a^9*b^2*c*d^6)/2 + a^6*b^5*c^4*d^3 - 2*a^7*b^4*c^3*d^4 + (a^8*b^3*c^2*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^8)^(1/2)*(a*d + 4*b*c)*(512*a^6*b^5*c^5*d^2 - 1280*a^7*b^4*c^4*d^3 + 1024*a^8*b^3*c^3*d^4 - 256*a^9*b^2*c^2*d^5))/(512*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))/(16*a^3*(c^3)^(1/2)))*(a*d + 4*b*c)*1i)/(16*a^3*(c^3)^(1/2)) + ((((c + d*x^8)^(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))/(32*(a^4*b^2*c^4 + a^6*c^2*d^2 - 2*a^5*b*c^3*d)) - ((((a^9*b^2*c*d^6)/2 + a^6*b^5*c^4*d^3 - 2*a^7*b^4*c^3*d^4 + (a^8*b^3*c^2*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^8)^(1/2)*(a*d + 4*b*c)*(512*a^6*b^5*c^5*d^2 - 1280*a^7*b^4*c^4*d^3 + 1024*a^8*b^3*c^3*d^4 - 256*a^9*b^2*c^2*d^5))/(512*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))/(16*a^3*(c^3)^(1/2)))*(a*d + 4*b*c)*1i)/(16*a^3*(c^3)^(1/2)))/(((5*a^3*b^4*d^6)/256 + (b^7*c^3*d^3)/8 - (3*a*b^6*c^2*d^4)/16 + (3*a^2*b^5*c*d^5)/128)/(a^6*b^2*c^4 + a^8*c^2*d^2 - 2*a^7*b*c^3*d) - ((((c + d*x^8)^(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))/(32*(a^4*b^2*c^4 + a^6*c^2*d^2 - 2*a^5*b*c^3*d)) + ((((a^9*b^2*c*d^6)/2 + a^6*b^5*c^4*d^3 - 2*a^7*b^4*c^3*d^4 + (a^8*b^3*c^2*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^8)^(1/2)*(a*d + 4*b*c)*(512*a^6*b^5*c^5*d^2 - 1280*a^7*b^4*c^4*d^3 + 1024*a^8*b^3*c^3*d^4 - 256*a^9*b^2*c^2*d^5))/(512*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))/(16*a^3*(c^3)^(1/2)))*(a*d + 4*b*c))/(16*a^3*(c^3)^(1/2)) + ((((c + d*x^8)^(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))/(32*(a^4*b^2*c^4 + a^6*c^2*d^2 - 2*a^5*b*c^3*d)) - ((((a^9*b^2*c*d^6)/2 + a^6*b^5*c^4*d^3 - 2*a^7*b^4*c^3*d^4 + (a^8*b^3*c^2*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^8)^(1/2)*(a*d + 4*b*c)*(512*a^6*b^5*c^5*d^2 - 1280*a^7*b^4*c^4*d^3 + 1024*a^8*b^3*c^3*d^4 - 256*a^9*b^2*c^2*d^5))/(512*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))/(16*a^3*(c^3)^(1/2)))*(a*d + 4*b*c))/(16*a^3*(c^3)^(1/2))))*(a*d + 4*b*c)*1i)/(8*a^3*(c^3)^(1/2))","B"
913,0,-1,141,0.000000,"\text{Not used}","int(x^19/((a + b*x^8)^2*(c + d*x^8)^(1/2)),x)","\int \frac{x^{19}}{{\left(b\,x^8+a\right)}^2\,\sqrt{d\,x^8+c}} \,d x","Not used",1,"int(x^19/((a + b*x^8)^2*(c + d*x^8)^(1/2)), x)","F"
914,0,-1,93,0.000000,"\text{Not used}","int(x^11/((a + b*x^8)^2*(c + d*x^8)^(1/2)),x)","\int \frac{x^{11}}{{\left(b\,x^8+a\right)}^2\,\sqrt{d\,x^8+c}} \,d x","Not used",1,"int(x^11/((a + b*x^8)^2*(c + d*x^8)^(1/2)), x)","F"
915,0,-1,104,0.000000,"\text{Not used}","int(x^3/((a + b*x^8)^2*(c + d*x^8)^(1/2)),x)","\int \frac{x^3}{{\left(b\,x^8+a\right)}^2\,\sqrt{d\,x^8+c}} \,d x","Not used",1,"int(x^3/((a + b*x^8)^2*(c + d*x^8)^(1/2)), x)","F"
916,0,-1,149,0.000000,"\text{Not used}","int(1/(x^5*(a + b*x^8)^2*(c + d*x^8)^(1/2)),x)","\int \frac{1}{x^5\,{\left(b\,x^8+a\right)}^2\,\sqrt{d\,x^8+c}} \,d x","Not used",1,"int(1/(x^5*(a + b*x^8)^2*(c + d*x^8)^(1/2)), x)","F"
917,0,-1,208,0.000000,"\text{Not used}","int(1/(x^13*(a + b*x^8)^2*(c + d*x^8)^(1/2)),x)","\int \frac{1}{x^{13}\,{\left(b\,x^8+a\right)}^2\,\sqrt{d\,x^8+c}} \,d x","Not used",1,"int(1/(x^13*(a + b*x^8)^2*(c + d*x^8)^(1/2)), x)","F"
918,0,-1,924,0.000000,"\text{Not used}","int(x^9/((a + b*x^8)^2*(c + d*x^8)^(1/2)),x)","\int \frac{x^9}{{\left(b\,x^8+a\right)}^2\,\sqrt{d\,x^8+c}} \,d x","Not used",1,"int(x^9/((a + b*x^8)^2*(c + d*x^8)^(1/2)), x)","F"
919,0,-1,999,0.000000,"\text{Not used}","int(x/((a + b*x^8)^2*(c + d*x^8)^(1/2)),x)","\int \frac{x}{{\left(b\,x^8+a\right)}^2\,\sqrt{d\,x^8+c}} \,d x","Not used",1,"int(x/((a + b*x^8)^2*(c + d*x^8)^(1/2)), x)","F"
920,0,-1,1060,0.000000,"\text{Not used}","int(1/(x^7*(a + b*x^8)^2*(c + d*x^8)^(1/2)),x)","\int \frac{1}{x^7\,{\left(b\,x^8+a\right)}^2\,\sqrt{d\,x^8+c}} \,d x","Not used",1,"int(1/(x^7*(a + b*x^8)^2*(c + d*x^8)^(1/2)), x)","F"
921,0,-1,1164,0.000000,"\text{Not used}","int(x^13/((a + b*x^8)^2*(c + d*x^8)^(1/2)),x)","\int \frac{x^{13}}{{\left(b\,x^8+a\right)}^2\,\sqrt{d\,x^8+c}} \,d x","Not used",1,"int(x^13/((a + b*x^8)^2*(c + d*x^8)^(1/2)), x)","F"
922,0,-1,1162,0.000000,"\text{Not used}","int(x^5/((a + b*x^8)^2*(c + d*x^8)^(1/2)),x)","\int \frac{x^5}{{\left(b\,x^8+a\right)}^2\,\sqrt{d\,x^8+c}} \,d x","Not used",1,"int(x^5/((a + b*x^8)^2*(c + d*x^8)^(1/2)), x)","F"
923,0,-1,1243,0.000000,"\text{Not used}","int(1/(x^3*(a + b*x^8)^2*(c + d*x^8)^(1/2)),x)","\int \frac{1}{x^3\,{\left(b\,x^8+a\right)}^2\,\sqrt{d\,x^8+c}} \,d x","Not used",1,"int(1/(x^3*(a + b*x^8)^2*(c + d*x^8)^(1/2)), x)","F"
924,0,-1,64,0.000000,"\text{Not used}","int(x^4/((a + b*x^8)^2*(c + d*x^8)^(1/2)),x)","\int \frac{x^4}{{\left(b\,x^8+a\right)}^2\,\sqrt{d\,x^8+c}} \,d x","Not used",1,"int(x^4/((a + b*x^8)^2*(c + d*x^8)^(1/2)), x)","F"
925,0,-1,64,0.000000,"\text{Not used}","int(x^2/((a + b*x^8)^2*(c + d*x^8)^(1/2)),x)","\int \frac{x^2}{{\left(b\,x^8+a\right)}^2\,\sqrt{d\,x^8+c}} \,d x","Not used",1,"int(x^2/((a + b*x^8)^2*(c + d*x^8)^(1/2)), x)","F"
926,0,-1,59,0.000000,"\text{Not used}","int(1/((a + b*x^8)^2*(c + d*x^8)^(1/2)),x)","\int \frac{1}{{\left(b\,x^8+a\right)}^2\,\sqrt{d\,x^8+c}} \,d x","Not used",1,"int(1/((a + b*x^8)^2*(c + d*x^8)^(1/2)), x)","F"
927,0,-1,62,0.000000,"\text{Not used}","int(1/(x^2*(a + b*x^8)^2*(c + d*x^8)^(1/2)),x)","\int \frac{1}{x^2\,{\left(b\,x^8+a\right)}^2\,\sqrt{d\,x^8+c}} \,d x","Not used",1,"int(1/(x^2*(a + b*x^8)^2*(c + d*x^8)^(1/2)), x)","F"
928,0,-1,64,0.000000,"\text{Not used}","int(1/(x^4*(a + b*x^8)^2*(c + d*x^8)^(1/2)),x)","\int \frac{1}{x^4\,{\left(b\,x^8+a\right)}^2\,\sqrt{d\,x^8+c}} \,d x","Not used",1,"int(1/(x^4*(a + b*x^8)^2*(c + d*x^8)^(1/2)), x)","F"
929,1,134,123,5.712695,"\text{Not used}","int(x^5*(a + b/x^2)*(c + d/x^2)^(1/2),x)","\frac{a\,x^6\,\sqrt{c+\frac{d}{x^2}}}{16}+\frac{b\,x^4\,\sqrt{c+\frac{d}{x^2}}}{8}+\frac{a\,x^6\,{\left(c+\frac{d}{x^2}\right)}^{3/2}}{6\,c}-\frac{a\,x^6\,{\left(c+\frac{d}{x^2}\right)}^{5/2}}{16\,c^2}+\frac{b\,x^4\,{\left(c+\frac{d}{x^2}\right)}^{3/2}}{8\,c}-\frac{b\,d^2\,\mathrm{atanh}\left(\frac{\sqrt{c+\frac{d}{x^2}}}{\sqrt{c}}\right)}{8\,c^{3/2}}-\frac{a\,d^3\,\mathrm{atan}\left(\frac{\sqrt{c+\frac{d}{x^2}}\,1{}\mathrm{i}}{\sqrt{c}}\right)\,1{}\mathrm{i}}{16\,c^{5/2}}","Not used",1,"(a*x^6*(c + d/x^2)^(1/2))/16 + (b*x^4*(c + d/x^2)^(1/2))/8 + (a*x^6*(c + d/x^2)^(3/2))/(6*c) - (a*x^6*(c + d/x^2)^(5/2))/(16*c^2) + (b*x^4*(c + d/x^2)^(3/2))/(8*c) - (a*d^3*atan(((c + d/x^2)^(1/2)*1i)/c^(1/2))*1i)/(16*c^(5/2)) - (b*d^2*atanh((c + d/x^2)^(1/2)/c^(1/2)))/(8*c^(3/2))","B"
930,1,93,90,5.305245,"\text{Not used}","int(x^3*(a + b/x^2)*(c + d/x^2)^(1/2),x)","\frac{a\,x^4\,\sqrt{c+\frac{d}{x^2}}}{8}+\frac{b\,x^2\,\sqrt{c+\frac{d}{x^2}}}{2}+\frac{a\,x^4\,{\left(c+\frac{d}{x^2}\right)}^{3/2}}{8\,c}+\frac{b\,d\,\mathrm{atanh}\left(\frac{\sqrt{c+\frac{d}{x^2}}}{\sqrt{c}}\right)}{2\,\sqrt{c}}-\frac{a\,d^2\,\mathrm{atanh}\left(\frac{\sqrt{c+\frac{d}{x^2}}}{\sqrt{c}}\right)}{8\,c^{3/2}}","Not used",1,"(a*x^4*(c + d/x^2)^(1/2))/8 + (b*x^2*(c + d/x^2)^(1/2))/2 + (a*x^4*(c + d/x^2)^(3/2))/(8*c) + (b*d*atanh((c + d/x^2)^(1/2)/c^(1/2)))/(2*c^(1/2)) - (a*d^2*atanh((c + d/x^2)^(1/2)/c^(1/2)))/(8*c^(3/2))","B"
931,1,68,84,5.103649,"\text{Not used}","int(x*(a + b/x^2)*(c + d/x^2)^(1/2),x)","\frac{a\,x^2\,\sqrt{c+\frac{d}{x^2}}}{2}-b\,\sqrt{c+\frac{d}{x^2}}+b\,\sqrt{c}\,\mathrm{atanh}\left(\frac{\sqrt{c+\frac{d}{x^2}}}{\sqrt{c}}\right)+\frac{a\,d\,\mathrm{atanh}\left(\frac{\sqrt{c+\frac{d}{x^2}}}{\sqrt{c}}\right)}{2\,\sqrt{c}}","Not used",1,"(a*x^2*(c + d/x^2)^(1/2))/2 - b*(c + d/x^2)^(1/2) + b*c^(1/2)*atanh((c + d/x^2)^(1/2)/c^(1/2)) + (a*d*atanh((c + d/x^2)^(1/2)/c^(1/2)))/(2*c^(1/2))","B"
932,1,57,59,5.206138,"\text{Not used}","int(((a + b/x^2)*(c + d/x^2)^(1/2))/x,x)","a\,\sqrt{c}\,\mathrm{atanh}\left(\frac{\sqrt{c+\frac{d}{x^2}}}{\sqrt{c}}\right)-a\,\sqrt{c+\frac{d}{x^2}}-\frac{b\,\sqrt{c+\frac{d}{x^2}}\,\left(c\,x^2+d\right)}{3\,d\,x^2}","Not used",1,"a*c^(1/2)*atanh((c + d/x^2)^(1/2)/c^(1/2)) - a*(c + d/x^2)^(1/2) - (b*(c + d/x^2)^(1/2)*(d + c*x^2))/(3*d*x^2)","B"
933,1,91,46,4.816720,"\text{Not used}","int(((a + b/x^2)*(c + d/x^2)^(1/2))/x^3,x)","\frac{\sqrt{c+\frac{d}{x^2}}\,\left(b\,c^2+a\,d\,c\right)}{5\,d^2}-\frac{b\,\sqrt{c+\frac{d}{x^2}}}{5\,x^4}-\frac{\sqrt{c+\frac{d}{x^2}}\,\left(5\,a\,d^2+b\,c\,d\right)}{15\,d^2\,x^2}-\frac{c\,\sqrt{c+\frac{d}{x^2}}\,\left(8\,a\,d+b\,c\right)}{15\,d^2}","Not used",1,"((c + d/x^2)^(1/2)*(b*c^2 + a*c*d))/(5*d^2) - (b*(c + d/x^2)^(1/2))/(5*x^4) - ((c + d/x^2)^(1/2)*(5*a*d^2 + b*c*d))/(15*d^2*x^2) - (c*(c + d/x^2)^(1/2)*(8*a*d + b*c))/(15*d^2)","B"
934,1,126,74,4.923838,"\text{Not used}","int(((a + b/x^2)*(c + d/x^2)^(1/2))/x^5,x)","\frac{2\,a\,c^2\,\sqrt{c+\frac{d}{x^2}}}{15\,d^2}-\frac{b\,\sqrt{c+\frac{d}{x^2}}}{7\,x^6}-\frac{a\,\sqrt{c+\frac{d}{x^2}}}{5\,x^4}-\frac{8\,b\,c^3\,\sqrt{c+\frac{d}{x^2}}}{105\,d^3}-\frac{a\,c\,\sqrt{c+\frac{d}{x^2}}}{15\,d\,x^2}-\frac{b\,c\,\sqrt{c+\frac{d}{x^2}}}{35\,d\,x^4}+\frac{4\,b\,c^2\,\sqrt{c+\frac{d}{x^2}}}{105\,d^2\,x^2}","Not used",1,"(2*a*c^2*(c + d/x^2)^(1/2))/(15*d^2) - (b*(c + d/x^2)^(1/2))/(7*x^6) - (a*(c + d/x^2)^(1/2))/(5*x^4) - (8*b*c^3*(c + d/x^2)^(1/2))/(105*d^3) - (a*c*(c + d/x^2)^(1/2))/(15*d*x^2) - (b*c*(c + d/x^2)^(1/2))/(35*d*x^4) + (4*b*c^2*(c + d/x^2)^(1/2))/(105*d^2*x^2)","B"
935,1,168,104,5.223568,"\text{Not used}","int(((a + b/x^2)*(c + d/x^2)^(1/2))/x^7,x)","\frac{16\,b\,c^4\,\sqrt{c+\frac{d}{x^2}}}{315\,d^4}-\frac{b\,\sqrt{c+\frac{d}{x^2}}}{9\,x^8}-\frac{8\,a\,c^3\,\sqrt{c+\frac{d}{x^2}}}{105\,d^3}-\frac{a\,\sqrt{c+\frac{d}{x^2}}}{7\,x^6}-\frac{a\,c\,\sqrt{c+\frac{d}{x^2}}}{35\,d\,x^4}-\frac{b\,c\,\sqrt{c+\frac{d}{x^2}}}{63\,d\,x^6}+\frac{4\,a\,c^2\,\sqrt{c+\frac{d}{x^2}}}{105\,d^2\,x^2}+\frac{2\,b\,c^2\,\sqrt{c+\frac{d}{x^2}}}{105\,d^2\,x^4}-\frac{8\,b\,c^3\,\sqrt{c+\frac{d}{x^2}}}{315\,d^3\,x^2}","Not used",1,"(16*b*c^4*(c + d/x^2)^(1/2))/(315*d^4) - (b*(c + d/x^2)^(1/2))/(9*x^8) - (8*a*c^3*(c + d/x^2)^(1/2))/(105*d^3) - (a*(c + d/x^2)^(1/2))/(7*x^6) - (a*c*(c + d/x^2)^(1/2))/(35*d*x^4) - (b*c*(c + d/x^2)^(1/2))/(63*d*x^6) + (4*a*c^2*(c + d/x^2)^(1/2))/(105*d^2*x^2) + (2*b*c^2*(c + d/x^2)^(1/2))/(105*d^2*x^4) - (8*b*c^3*(c + d/x^2)^(1/2))/(315*d^3*x^2)","B"
936,1,210,134,5.607173,"\text{Not used}","int(((a + b/x^2)*(c + d/x^2)^(1/2))/x^9,x)","\frac{16\,a\,c^4\,\sqrt{c+\frac{d}{x^2}}}{315\,d^4}-\frac{b\,\sqrt{c+\frac{d}{x^2}}}{11\,x^{10}}-\frac{a\,\sqrt{c+\frac{d}{x^2}}}{9\,x^8}-\frac{128\,b\,c^5\,\sqrt{c+\frac{d}{x^2}}}{3465\,d^5}-\frac{a\,c\,\sqrt{c+\frac{d}{x^2}}}{63\,d\,x^6}-\frac{b\,c\,\sqrt{c+\frac{d}{x^2}}}{99\,d\,x^8}+\frac{2\,a\,c^2\,\sqrt{c+\frac{d}{x^2}}}{105\,d^2\,x^4}-\frac{8\,a\,c^3\,\sqrt{c+\frac{d}{x^2}}}{315\,d^3\,x^2}+\frac{8\,b\,c^2\,\sqrt{c+\frac{d}{x^2}}}{693\,d^2\,x^6}-\frac{16\,b\,c^3\,\sqrt{c+\frac{d}{x^2}}}{1155\,d^3\,x^4}+\frac{64\,b\,c^4\,\sqrt{c+\frac{d}{x^2}}}{3465\,d^4\,x^2}","Not used",1,"(16*a*c^4*(c + d/x^2)^(1/2))/(315*d^4) - (b*(c + d/x^2)^(1/2))/(11*x^10) - (a*(c + d/x^2)^(1/2))/(9*x^8) - (128*b*c^5*(c + d/x^2)^(1/2))/(3465*d^5) - (a*c*(c + d/x^2)^(1/2))/(63*d*x^6) - (b*c*(c + d/x^2)^(1/2))/(99*d*x^8) + (2*a*c^2*(c + d/x^2)^(1/2))/(105*d^2*x^4) - (8*a*c^3*(c + d/x^2)^(1/2))/(315*d^3*x^2) + (8*b*c^2*(c + d/x^2)^(1/2))/(693*d^2*x^6) - (16*b*c^3*(c + d/x^2)^(1/2))/(1155*d^3*x^4) + (64*b*c^4*(c + d/x^2)^(1/2))/(3465*d^4*x^2)","B"
937,1,117,150,4.591260,"\text{Not used}","int(x^10*(a + b/x^2)*(c + d/x^2)^(1/2),x)","\sqrt{c+\frac{d}{x^2}}\,\left(\frac{a\,x^{11}}{11}+\frac{x\,\left(128\,a\,d^5-176\,b\,c\,d^4\right)}{3465\,c^5}+\frac{x^9\,\left(385\,b\,c^5+35\,a\,d\,c^4\right)}{3465\,c^5}-\frac{d\,x^7\,\left(8\,a\,d-11\,b\,c\right)}{693\,c^2}+\frac{2\,d^2\,x^5\,\left(8\,a\,d-11\,b\,c\right)}{1155\,c^3}-\frac{8\,d^3\,x^3\,\left(8\,a\,d-11\,b\,c\right)}{3465\,c^4}\right)","Not used",1,"(c + d/x^2)^(1/2)*((a*x^11)/11 + (x*(128*a*d^5 - 176*b*c*d^4))/(3465*c^5) + (x^9*(385*b*c^5 + 35*a*c^4*d))/(3465*c^5) - (d*x^7*(8*a*d - 11*b*c))/(693*c^2) + (2*d^2*x^5*(8*a*d - 11*b*c))/(1155*c^3) - (8*d^3*x^3*(8*a*d - 11*b*c))/(3465*c^4))","B"
938,1,97,117,4.518375,"\text{Not used}","int(x^8*(a + b/x^2)*(c + d/x^2)^(1/2),x)","\sqrt{c+\frac{d}{x^2}}\,\left(\frac{a\,x^9}{9}-\frac{x\,\left(16\,a\,d^4-24\,b\,c\,d^3\right)}{315\,c^4}+\frac{x^7\,\left(45\,b\,c^4+5\,a\,d\,c^3\right)}{315\,c^4}-\frac{d\,x^5\,\left(2\,a\,d-3\,b\,c\right)}{105\,c^2}+\frac{4\,d^2\,x^3\,\left(2\,a\,d-3\,b\,c\right)}{315\,c^3}\right)","Not used",1,"(c + d/x^2)^(1/2)*((a*x^9)/9 - (x*(16*a*d^4 - 24*b*c*d^3))/(315*c^4) + (x^7*(45*b*c^4 + 5*a*c^3*d))/(315*c^4) - (d*x^5*(2*a*d - 3*b*c))/(105*c^2) + (4*d^2*x^3*(2*a*d - 3*b*c))/(315*c^3))","B"
939,1,77,84,4.487672,"\text{Not used}","int(x^6*(a + b/x^2)*(c + d/x^2)^(1/2),x)","\sqrt{c+\frac{d}{x^2}}\,\left(\frac{a\,x^7}{7}+\frac{x\,\left(8\,a\,d^3-14\,b\,c\,d^2\right)}{105\,c^3}+\frac{x^5\,\left(21\,b\,c^3+3\,a\,d\,c^2\right)}{105\,c^3}-\frac{d\,x^3\,\left(4\,a\,d-7\,b\,c\right)}{105\,c^2}\right)","Not used",1,"(c + d/x^2)^(1/2)*((a*x^7)/7 + (x*(8*a*d^3 - 14*b*c*d^2))/(105*c^3) + (x^5*(21*b*c^3 + 3*a*c^2*d))/(105*c^3) - (d*x^3*(4*a*d - 7*b*c))/(105*c^2))","B"
940,1,54,53,4.442356,"\text{Not used}","int(x^4*(a + b/x^2)*(c + d/x^2)^(1/2),x)","\sqrt{c+\frac{d}{x^2}}\,\left(\frac{a\,x^5}{5}-\frac{x\,\left(2\,a\,d^2-5\,b\,c\,d\right)}{15\,c^2}+\frac{x^3\,\left(5\,b\,c^2+a\,d\,c\right)}{15\,c^2}\right)","Not used",1,"(c + d/x^2)^(1/2)*((a*x^5)/5 - (x*(2*a*d^2 - 5*b*c*d))/(15*c^2) + (x^3*(5*b*c^2 + a*c*d))/(15*c^2))","B"
941,1,80,66,4.720216,"\text{Not used}","int(x^2*(a + b/x^2)*(c + d/x^2)^(1/2),x)","b\,x\,\sqrt{c+\frac{d}{x^2}}+\frac{a\,x\,\sqrt{c+\frac{d}{x^2}}\,\left(c\,x^2+d\right)}{3\,c}+\frac{b\,\sqrt{d}\,\mathrm{asin}\left(\frac{\sqrt{d}\,1{}\mathrm{i}}{\sqrt{c}\,x}\right)\,\sqrt{c+\frac{d}{x^2}}\,1{}\mathrm{i}}{\sqrt{c}\,\sqrt{\frac{d}{c\,x^2}+1}}","Not used",1,"b*x*(c + d/x^2)^(1/2) + (a*x*(c + d/x^2)^(1/2)*(d + c*x^2))/(3*c) + (b*d^(1/2)*asin((d^(1/2)*1i)/(c^(1/2)*x))*(c + d/x^2)^(1/2)*1i)/(c^(1/2)*(d/(c*x^2) + 1)^(1/2))","B"
942,1,97,85,5.108385,"\text{Not used}","int((a + b/x^2)*(c + d/x^2)^(1/2),x)","a\,x\,\sqrt{c+\frac{d}{x^2}}-\frac{b\,\sqrt{c+\frac{d}{x^2}}}{2\,x}-\frac{b\,c\,\ln\left(\sqrt{c+\frac{d}{x^2}}+\frac{\sqrt{d}}{x}\right)}{2\,\sqrt{d}}+\frac{a\,\sqrt{d}\,\mathrm{asin}\left(\frac{\sqrt{d}\,1{}\mathrm{i}}{\sqrt{c}\,x}\right)\,\sqrt{c+\frac{d}{x^2}}\,1{}\mathrm{i}}{\sqrt{c}\,\sqrt{\frac{d}{c\,x^2}+1}}","Not used",1,"a*x*(c + d/x^2)^(1/2) - (b*(c + d/x^2)^(1/2))/(2*x) - (b*c*log((c + d/x^2)^(1/2) + d^(1/2)/x))/(2*d^(1/2)) + (a*d^(1/2)*asin((d^(1/2)*1i)/(c^(1/2)*x))*(c + d/x^2)^(1/2)*1i)/(c^(1/2)*(d/(c*x^2) + 1)^(1/2))","B"
943,0,-1,91,0.000000,"\text{Not used}","int(((a + b/x^2)*(c + d/x^2)^(1/2))/x^2,x)","\int \frac{\left(a+\frac{b}{x^2}\right)\,\sqrt{c+\frac{d}{x^2}}}{x^2} \,d x","Not used",1,"int(((a + b/x^2)*(c + d/x^2)^(1/2))/x^2, x)","F"
944,0,-1,123,0.000000,"\text{Not used}","int(((a + b/x^2)*(c + d/x^2)^(1/2))/x^4,x)","\int \frac{\left(a+\frac{b}{x^2}\right)\,\sqrt{c+\frac{d}{x^2}}}{x^4} \,d x","Not used",1,"int(((a + b/x^2)*(c + d/x^2)^(1/2))/x^4, x)","F"
945,1,130,123,5.783391,"\text{Not used}","int(x^5*(a + b/x^2)*(c + d/x^2)^(3/2),x)","\frac{a\,x^6\,{\left(c+\frac{d}{x^2}\right)}^{3/2}}{6}+\frac{5\,b\,x^4\,{\left(c+\frac{d}{x^2}\right)}^{3/2}}{8}+\frac{a\,x^6\,{\left(c+\frac{d}{x^2}\right)}^{5/2}}{16\,c}+\frac{3\,b\,d^2\,\mathrm{atanh}\left(\frac{\sqrt{c+\frac{d}{x^2}}}{\sqrt{c}}\right)}{8\,\sqrt{c}}-\frac{a\,c\,x^6\,\sqrt{c+\frac{d}{x^2}}}{16}-\frac{3\,b\,c\,x^4\,\sqrt{c+\frac{d}{x^2}}}{8}+\frac{a\,d^3\,\mathrm{atan}\left(\frac{\sqrt{c+\frac{d}{x^2}}\,1{}\mathrm{i}}{\sqrt{c}}\right)\,1{}\mathrm{i}}{16\,c^{3/2}}","Not used",1,"(a*x^6*(c + d/x^2)^(3/2))/6 + (5*b*x^4*(c + d/x^2)^(3/2))/8 + (a*x^6*(c + d/x^2)^(5/2))/(16*c) + (a*d^3*atan(((c + d/x^2)^(1/2)*1i)/c^(1/2))*1i)/(16*c^(3/2)) + (3*b*d^2*atanh((c + d/x^2)^(1/2)/c^(1/2)))/(8*c^(1/2)) - (a*c*x^6*(c + d/x^2)^(1/2))/16 - (3*b*c*x^4*(c + d/x^2)^(1/2))/8","B"
946,1,105,115,5.703100,"\text{Not used}","int(x^3*(a + b/x^2)*(c + d/x^2)^(3/2),x)","\frac{5\,a\,x^4\,{\left(c+\frac{d}{x^2}\right)}^{3/2}}{8}-b\,d\,\sqrt{c+\frac{d}{x^2}}+\frac{3\,b\,\sqrt{c}\,d\,\mathrm{atanh}\left(\frac{\sqrt{c+\frac{d}{x^2}}}{\sqrt{c}}\right)}{2}+\frac{3\,a\,d^2\,\mathrm{atanh}\left(\frac{\sqrt{c+\frac{d}{x^2}}}{\sqrt{c}}\right)}{8\,\sqrt{c}}-\frac{3\,a\,c\,x^4\,\sqrt{c+\frac{d}{x^2}}}{8}+\frac{b\,c\,x^2\,\sqrt{c+\frac{d}{x^2}}}{2}","Not used",1,"(5*a*x^4*(c + d/x^2)^(3/2))/8 - b*d*(c + d/x^2)^(1/2) + (3*b*c^(1/2)*d*atanh((c + d/x^2)^(1/2)/c^(1/2)))/2 + (3*a*d^2*atanh((c + d/x^2)^(1/2)/c^(1/2)))/(8*c^(1/2)) - (3*a*c*x^4*(c + d/x^2)^(1/2))/8 + (b*c*x^2*(c + d/x^2)^(1/2))/2","B"
947,1,95,110,5.650938,"\text{Not used}","int(x*(a + b/x^2)*(c + d/x^2)^(3/2),x)","b\,c^{3/2}\,\mathrm{atanh}\left(\frac{\sqrt{c+\frac{d}{x^2}}}{\sqrt{c}}\right)-\frac{b\,{\left(c+\frac{d}{x^2}\right)}^{3/2}}{3}-a\,d\,\sqrt{c+\frac{d}{x^2}}-b\,c\,\sqrt{c+\frac{d}{x^2}}+\frac{3\,a\,\sqrt{c}\,d\,\mathrm{atanh}\left(\frac{\sqrt{c+\frac{d}{x^2}}}{\sqrt{c}}\right)}{2}+\frac{a\,c\,x^2\,\sqrt{c+\frac{d}{x^2}}}{2}","Not used",1,"b*c^(3/2)*atanh((c + d/x^2)^(1/2)/c^(1/2)) - (b*(c + d/x^2)^(3/2))/3 - a*d*(c + d/x^2)^(1/2) - b*c*(c + d/x^2)^(1/2) + (3*a*c^(1/2)*d*atanh((c + d/x^2)^(1/2)/c^(1/2)))/2 + (a*c*x^2*(c + d/x^2)^(1/2))/2","B"
948,1,72,76,5.831297,"\text{Not used}","int(((a + b/x^2)*(c + d/x^2)^(3/2))/x,x)","a\,c^{3/2}\,\mathrm{atanh}\left(\frac{\sqrt{c+\frac{d}{x^2}}}{\sqrt{c}}\right)-\frac{a\,{\left(c+\frac{d}{x^2}\right)}^{3/2}}{3}-a\,c\,\sqrt{c+\frac{d}{x^2}}-\frac{b\,\sqrt{c+\frac{d}{x^2}}\,{\left(c\,x^2+d\right)}^2}{5\,d\,x^4}","Not used",1,"a*c^(3/2)*atanh((c + d/x^2)^(1/2)/c^(1/2)) - (a*(c + d/x^2)^(3/2))/3 - a*c*(c + d/x^2)^(1/2) - (b*(c + d/x^2)^(1/2)*(d + c*x^2)^2)/(5*d*x^4)","B"
949,1,122,46,5.333204,"\text{Not used}","int(((a + b/x^2)*(c + d/x^2)^(3/2))/x^3,x)","\frac{2\,b\,c^3\,\sqrt{c+\frac{d}{x^2}}}{35\,d^2}-\frac{a\,c^2\,\sqrt{c+\frac{d}{x^2}}}{5\,d}-\frac{2\,a\,c\,\sqrt{c+\frac{d}{x^2}}}{5\,x^2}-\frac{a\,d\,\sqrt{c+\frac{d}{x^2}}}{5\,x^4}-\frac{8\,b\,c\,\sqrt{c+\frac{d}{x^2}}}{35\,x^4}-\frac{b\,d\,\sqrt{c+\frac{d}{x^2}}}{7\,x^6}-\frac{b\,c^2\,\sqrt{c+\frac{d}{x^2}}}{35\,d\,x^2}","Not used",1,"(2*b*c^3*(c + d/x^2)^(1/2))/(35*d^2) - (a*c^2*(c + d/x^2)^(1/2))/(5*d) - (2*a*c*(c + d/x^2)^(1/2))/(5*x^2) - (a*d*(c + d/x^2)^(1/2))/(5*x^4) - (8*b*c*(c + d/x^2)^(1/2))/(35*x^4) - (b*d*(c + d/x^2)^(1/2))/(7*x^6) - (b*c^2*(c + d/x^2)^(1/2))/(35*d*x^2)","B"
950,1,164,74,5.759451,"\text{Not used}","int(((a + b/x^2)*(c + d/x^2)^(3/2))/x^5,x)","\frac{2\,a\,c^3\,\sqrt{c+\frac{d}{x^2}}}{35\,d^2}-\frac{8\,b\,c^4\,\sqrt{c+\frac{d}{x^2}}}{315\,d^3}-\frac{8\,a\,c\,\sqrt{c+\frac{d}{x^2}}}{35\,x^4}-\frac{a\,d\,\sqrt{c+\frac{d}{x^2}}}{7\,x^6}-\frac{10\,b\,c\,\sqrt{c+\frac{d}{x^2}}}{63\,x^6}-\frac{b\,d\,\sqrt{c+\frac{d}{x^2}}}{9\,x^8}-\frac{a\,c^2\,\sqrt{c+\frac{d}{x^2}}}{35\,d\,x^2}-\frac{b\,c^2\,\sqrt{c+\frac{d}{x^2}}}{105\,d\,x^4}+\frac{4\,b\,c^3\,\sqrt{c+\frac{d}{x^2}}}{315\,d^2\,x^2}","Not used",1,"(2*a*c^3*(c + d/x^2)^(1/2))/(35*d^2) - (8*b*c^4*(c + d/x^2)^(1/2))/(315*d^3) - (8*a*c*(c + d/x^2)^(1/2))/(35*x^4) - (a*d*(c + d/x^2)^(1/2))/(7*x^6) - (10*b*c*(c + d/x^2)^(1/2))/(63*x^6) - (b*d*(c + d/x^2)^(1/2))/(9*x^8) - (a*c^2*(c + d/x^2)^(1/2))/(35*d*x^2) - (b*c^2*(c + d/x^2)^(1/2))/(105*d*x^4) + (4*b*c^3*(c + d/x^2)^(1/2))/(315*d^2*x^2)","B"
951,1,206,104,6.314990,"\text{Not used}","int(((a + b/x^2)*(c + d/x^2)^(3/2))/x^7,x)","\frac{16\,b\,c^5\,\sqrt{c+\frac{d}{x^2}}}{1155\,d^4}-\frac{8\,a\,c^4\,\sqrt{c+\frac{d}{x^2}}}{315\,d^3}-\frac{10\,a\,c\,\sqrt{c+\frac{d}{x^2}}}{63\,x^6}-\frac{a\,d\,\sqrt{c+\frac{d}{x^2}}}{9\,x^8}-\frac{4\,b\,c\,\sqrt{c+\frac{d}{x^2}}}{33\,x^8}-\frac{b\,d\,\sqrt{c+\frac{d}{x^2}}}{11\,x^{10}}-\frac{a\,c^2\,\sqrt{c+\frac{d}{x^2}}}{105\,d\,x^4}+\frac{4\,a\,c^3\,\sqrt{c+\frac{d}{x^2}}}{315\,d^2\,x^2}-\frac{b\,c^2\,\sqrt{c+\frac{d}{x^2}}}{231\,d\,x^6}+\frac{2\,b\,c^3\,\sqrt{c+\frac{d}{x^2}}}{385\,d^2\,x^4}-\frac{8\,b\,c^4\,\sqrt{c+\frac{d}{x^2}}}{1155\,d^3\,x^2}","Not used",1,"(16*b*c^5*(c + d/x^2)^(1/2))/(1155*d^4) - (8*a*c^4*(c + d/x^2)^(1/2))/(315*d^3) - (10*a*c*(c + d/x^2)^(1/2))/(63*x^6) - (a*d*(c + d/x^2)^(1/2))/(9*x^8) - (4*b*c*(c + d/x^2)^(1/2))/(33*x^8) - (b*d*(c + d/x^2)^(1/2))/(11*x^10) - (a*c^2*(c + d/x^2)^(1/2))/(105*d*x^4) + (4*a*c^3*(c + d/x^2)^(1/2))/(315*d^2*x^2) - (b*c^2*(c + d/x^2)^(1/2))/(231*d*x^6) + (2*b*c^3*(c + d/x^2)^(1/2))/(385*d^2*x^4) - (8*b*c^4*(c + d/x^2)^(1/2))/(1155*d^3*x^2)","B"
952,1,248,134,6.812097,"\text{Not used}","int(((a + b/x^2)*(c + d/x^2)^(3/2))/x^9,x)","\frac{16\,a\,c^5\,\sqrt{c+\frac{d}{x^2}}}{1155\,d^4}-\frac{128\,b\,c^6\,\sqrt{c+\frac{d}{x^2}}}{15015\,d^5}-\frac{4\,a\,c\,\sqrt{c+\frac{d}{x^2}}}{33\,x^8}-\frac{a\,d\,\sqrt{c+\frac{d}{x^2}}}{11\,x^{10}}-\frac{14\,b\,c\,\sqrt{c+\frac{d}{x^2}}}{143\,x^{10}}-\frac{b\,d\,\sqrt{c+\frac{d}{x^2}}}{13\,x^{12}}-\frac{a\,c^2\,\sqrt{c+\frac{d}{x^2}}}{231\,d\,x^6}+\frac{2\,a\,c^3\,\sqrt{c+\frac{d}{x^2}}}{385\,d^2\,x^4}-\frac{8\,a\,c^4\,\sqrt{c+\frac{d}{x^2}}}{1155\,d^3\,x^2}-\frac{b\,c^2\,\sqrt{c+\frac{d}{x^2}}}{429\,d\,x^8}+\frac{8\,b\,c^3\,\sqrt{c+\frac{d}{x^2}}}{3003\,d^2\,x^6}-\frac{16\,b\,c^4\,\sqrt{c+\frac{d}{x^2}}}{5005\,d^3\,x^4}+\frac{64\,b\,c^5\,\sqrt{c+\frac{d}{x^2}}}{15015\,d^4\,x^2}","Not used",1,"(16*a*c^5*(c + d/x^2)^(1/2))/(1155*d^4) - (128*b*c^6*(c + d/x^2)^(1/2))/(15015*d^5) - (4*a*c*(c + d/x^2)^(1/2))/(33*x^8) - (a*d*(c + d/x^2)^(1/2))/(11*x^10) - (14*b*c*(c + d/x^2)^(1/2))/(143*x^10) - (b*d*(c + d/x^2)^(1/2))/(13*x^12) - (a*c^2*(c + d/x^2)^(1/2))/(231*d*x^6) + (2*a*c^3*(c + d/x^2)^(1/2))/(385*d^2*x^4) - (8*a*c^4*(c + d/x^2)^(1/2))/(1155*d^3*x^2) - (b*c^2*(c + d/x^2)^(1/2))/(429*d*x^8) + (8*b*c^3*(c + d/x^2)^(1/2))/(3003*d^2*x^6) - (16*b*c^4*(c + d/x^2)^(1/2))/(5005*d^3*x^4) + (64*b*c^5*(c + d/x^2)^(1/2))/(15015*d^4*x^2)","B"
953,1,137,150,4.662204,"\text{Not used}","int(x^12*(a + b/x^2)*(c + d/x^2)^(3/2),x)","\sqrt{c+\frac{d}{x^2}}\,\left(\frac{x\,\left(128\,a\,d^6-208\,b\,c\,d^5\right)}{15015\,c^5}+\frac{x^{11}\,\left(1365\,b\,c^6+1470\,a\,d\,c^5\right)}{15015\,c^5}+\frac{a\,c\,x^{13}}{13}+\frac{d\,x^9\,\left(a\,d+52\,b\,c\right)}{429\,c}-\frac{d^2\,x^7\,\left(8\,a\,d-13\,b\,c\right)}{3003\,c^2}+\frac{2\,d^3\,x^5\,\left(8\,a\,d-13\,b\,c\right)}{5005\,c^3}-\frac{8\,d^4\,x^3\,\left(8\,a\,d-13\,b\,c\right)}{15015\,c^4}\right)","Not used",1,"(c + d/x^2)^(1/2)*((x*(128*a*d^6 - 208*b*c*d^5))/(15015*c^5) + (x^11*(1365*b*c^6 + 1470*a*c^5*d))/(15015*c^5) + (a*c*x^13)/13 + (d*x^9*(a*d + 52*b*c))/(429*c) - (d^2*x^7*(8*a*d - 13*b*c))/(3003*c^2) + (2*d^3*x^5*(8*a*d - 13*b*c))/(5005*c^3) - (8*d^4*x^3*(8*a*d - 13*b*c))/(15015*c^4))","B"
954,1,118,117,4.569136,"\text{Not used}","int(x^10*(a + b/x^2)*(c + d/x^2)^(3/2),x)","\sqrt{c+\frac{d}{x^2}}\,\left(\frac{x^9\,\left(385\,b\,c^5+420\,a\,d\,c^4\right)}{3465\,c^4}-\frac{x\,\left(48\,a\,d^5-88\,b\,c\,d^4\right)}{3465\,c^4}+\frac{a\,c\,x^{11}}{11}+\frac{d\,x^7\,\left(3\,a\,d+110\,b\,c\right)}{693\,c}-\frac{d^2\,x^5\,\left(6\,a\,d-11\,b\,c\right)}{1155\,c^2}+\frac{4\,d^3\,x^3\,\left(6\,a\,d-11\,b\,c\right)}{3465\,c^3}\right)","Not used",1,"(c + d/x^2)^(1/2)*((x^9*(385*b*c^5 + 420*a*c^4*d))/(3465*c^4) - (x*(48*a*d^5 - 88*b*c*d^4))/(3465*c^4) + (a*c*x^11)/11 + (d*x^7*(3*a*d + 110*b*c))/(693*c) - (d^2*x^5*(6*a*d - 11*b*c))/(1155*c^2) + (4*d^3*x^3*(6*a*d - 11*b*c))/(3465*c^3))","B"
955,1,97,84,4.551048,"\text{Not used}","int(x^8*(a + b/x^2)*(c + d/x^2)^(3/2),x)","\sqrt{c+\frac{d}{x^2}}\,\left(\frac{x\,\left(8\,a\,d^4-18\,b\,c\,d^3\right)}{315\,c^3}+\frac{x^7\,\left(45\,b\,c^4+50\,a\,d\,c^3\right)}{315\,c^3}+\frac{a\,c\,x^9}{9}+\frac{d\,x^5\,\left(a\,d+24\,b\,c\right)}{105\,c}-\frac{d^2\,x^3\,\left(4\,a\,d-9\,b\,c\right)}{315\,c^2}\right)","Not used",1,"(c + d/x^2)^(1/2)*((x*(8*a*d^4 - 18*b*c*d^3))/(315*c^3) + (x^7*(45*b*c^4 + 50*a*c^3*d))/(315*c^3) + (a*c*x^9)/9 + (d*x^5*(a*d + 24*b*c))/(105*c) - (d^2*x^3*(4*a*d - 9*b*c))/(315*c^2))","B"
956,1,77,53,4.625951,"\text{Not used}","int(x^6*(a + b/x^2)*(c + d/x^2)^(3/2),x)","\sqrt{c+\frac{d}{x^2}}\,\left(\frac{x^5\,\left(7\,b\,c^3+8\,a\,d\,c^2\right)}{35\,c^2}-\frac{x\,\left(2\,a\,d^3-7\,b\,c\,d^2\right)}{35\,c^2}+\frac{a\,c\,x^7}{7}+\frac{d\,x^3\,\left(a\,d+14\,b\,c\right)}{35\,c}\right)","Not used",1,"(c + d/x^2)^(1/2)*((x^5*(7*b*c^3 + 8*a*c^2*d))/(35*c^2) - (x*(2*a*d^3 - 7*b*c*d^2))/(35*c^2) + (a*c*x^7)/7 + (d*x^3*(a*d + 14*b*c))/(35*c))","B"
957,0,-1,86,0.000000,"\text{Not used}","int(x^4*(a + b/x^2)*(c + d/x^2)^(3/2),x)","\int x^4\,\left(a+\frac{b}{x^2}\right)\,{\left(c+\frac{d}{x^2}\right)}^{3/2} \,d x","Not used",1,"int(x^4*(a + b/x^2)*(c + d/x^2)^(3/2), x)","F"
958,0,-1,121,0.000000,"\text{Not used}","int(x^2*(a + b/x^2)*(c + d/x^2)^(3/2),x)","\int x^2\,\left(a+\frac{b}{x^2}\right)\,{\left(c+\frac{d}{x^2}\right)}^{3/2} \,d x","Not used",1,"int(x^2*(a + b/x^2)*(c + d/x^2)^(3/2), x)","F"
959,1,78,112,5.858306,"\text{Not used}","int((a + b/x^2)*(c + d/x^2)^(3/2),x)","\frac{a\,x\,{\left(c\,x^2+d\right)}^{3/2}\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{2},-\frac{1}{2};\ \frac{1}{2};\ -\frac{d}{c\,x^2}\right)}{{\left(\frac{d}{c}+x^2\right)}^{3/2}}-\frac{b\,{\left(c\,x^2+d\right)}^{3/2}\,{{}}_2{\mathrm{F}}_1\left(-\frac{3}{2},\frac{1}{2};\ \frac{3}{2};\ -\frac{d}{c\,x^2}\right)}{x\,{\left(\frac{d}{c}+x^2\right)}^{3/2}}","Not used",1,"(a*x*(d + c*x^2)^(3/2)*hypergeom([-3/2, -1/2], 1/2, -d/(c*x^2)))/(d/c + x^2)^(3/2) - (b*(d + c*x^2)^(3/2)*hypergeom([-3/2, 1/2], 3/2, -d/(c*x^2)))/(x*(d/c + x^2)^(3/2))","B"
960,0,-1,123,0.000000,"\text{Not used}","int(((a + b/x^2)*(c + d/x^2)^(3/2))/x^2,x)","\int \frac{\left(a+\frac{b}{x^2}\right)\,{\left(c+\frac{d}{x^2}\right)}^{3/2}}{x^2} \,d x","Not used",1,"int(((a + b/x^2)*(c + d/x^2)^(3/2))/x^2, x)","F"
961,0,-1,159,0.000000,"\text{Not used}","int(((a + b/x^2)*(c + d/x^2)^(3/2))/x^4,x)","\int \frac{\left(a+\frac{b}{x^2}\right)\,{\left(c+\frac{d}{x^2}\right)}^{3/2}}{x^4} \,d x","Not used",1,"int(((a + b/x^2)*(c + d/x^2)^(3/2))/x^4, x)","F"
962,1,99,90,5.347667,"\text{Not used}","int((x^3*(a + b/x^2))/(c + d/x^2)^(1/2),x)","\frac{5\,a\,x^4\,\sqrt{c+\frac{d}{x^2}}}{8\,c}-\frac{3\,a\,x^4\,{\left(c+\frac{d}{x^2}\right)}^{3/2}}{8\,c^2}+\frac{b\,x^2\,\sqrt{c+\frac{d}{x^2}}}{2\,c}-\frac{b\,d\,\mathrm{atanh}\left(\frac{\sqrt{c+\frac{d}{x^2}}}{\sqrt{c}}\right)}{2\,c^{3/2}}+\frac{3\,a\,d^2\,\mathrm{atanh}\left(\frac{\sqrt{c+\frac{d}{x^2}}}{\sqrt{c}}\right)}{8\,c^{5/2}}","Not used",1,"(5*a*x^4*(c + d/x^2)^(1/2))/(8*c) - (3*a*x^4*(c + d/x^2)^(3/2))/(8*c^2) + (b*x^2*(c + d/x^2)^(1/2))/(2*c) - (b*d*atanh((c + d/x^2)^(1/2)/c^(1/2)))/(2*c^(3/2)) + (3*a*d^2*atanh((c + d/x^2)^(1/2)/c^(1/2)))/(8*c^(5/2))","B"
963,1,59,59,5.076982,"\text{Not used}","int((x*(a + b/x^2))/(c + d/x^2)^(1/2),x)","\frac{b\,\mathrm{atanh}\left(\frac{\sqrt{c+\frac{d}{x^2}}}{\sqrt{c}}\right)}{\sqrt{c}}+\frac{a\,x^2\,\sqrt{c+\frac{d}{x^2}}}{2\,c}-\frac{a\,d\,\mathrm{atanh}\left(\frac{\sqrt{c+\frac{d}{x^2}}}{\sqrt{c}}\right)}{2\,c^{3/2}}","Not used",1,"(b*atanh((c + d/x^2)^(1/2)/c^(1/2)))/c^(1/2) + (a*x^2*(c + d/x^2)^(1/2))/(2*c) - (a*d*atanh((c + d/x^2)^(1/2)/c^(1/2)))/(2*c^(3/2))","B"
964,1,35,43,4.851271,"\text{Not used}","int((a + b/x^2)/(x*(c + d/x^2)^(1/2)),x)","\frac{a\,\mathrm{atanh}\left(\frac{\sqrt{c+\frac{d}{x^2}}}{\sqrt{c}}\right)}{\sqrt{c}}-\frac{b\,\sqrt{c+\frac{d}{x^2}}}{d}","Not used",1,"(a*atanh((c + d/x^2)^(1/2)/c^(1/2)))/c^(1/2) - (b*(c + d/x^2)^(1/2))/d","B"
965,1,35,43,4.564642,"\text{Not used}","int((a + b/x^2)/(x^3*(c + d/x^2)^(1/2)),x)","-\frac{\sqrt{c+\frac{d}{x^2}}\,\left(b\,d+3\,a\,d\,x^2-2\,b\,c\,x^2\right)}{3\,d^2\,x^2}","Not used",1,"-((c + d/x^2)^(1/2)*(b*d + 3*a*d*x^2 - 2*b*c*x^2))/(3*d^2*x^2)","B"
966,1,58,72,4.676381,"\text{Not used}","int((a + b/x^2)/(x^5*(c + d/x^2)^(1/2)),x)","-\frac{\sqrt{c+\frac{d}{x^2}}\,\left(8\,b\,c^2\,x^4-10\,a\,c\,d\,x^4-4\,b\,c\,d\,x^2+5\,a\,d^2\,x^2+3\,b\,d^2\right)}{15\,d^3\,x^4}","Not used",1,"-((c + d/x^2)^(1/2)*(3*b*d^2 + 5*a*d^2*x^2 + 8*b*c^2*x^4 - 10*a*c*d*x^4 - 4*b*c*d*x^2))/(15*d^3*x^4)","B"
967,1,102,101,4.715833,"\text{Not used}","int((a + b/x^2)/(x^7*(c + d/x^2)^(1/2)),x)","\frac{\sqrt{c+\frac{d}{x^2}}\,\left(48\,b\,c^3-56\,a\,c^2\,d\right)}{105\,d^4}-\frac{b\,\sqrt{c+\frac{d}{x^2}}}{7\,d\,x^6}-\frac{\sqrt{c+\frac{d}{x^2}}\,\left(24\,b\,c^2-28\,a\,c\,d\right)}{105\,d^3\,x^2}-\frac{\sqrt{c+\frac{d}{x^2}}\,\left(7\,a\,d-6\,b\,c\right)}{35\,d^2\,x^4}","Not used",1,"((c + d/x^2)^(1/2)*(48*b*c^3 - 56*a*c^2*d))/(105*d^4) - (b*(c + d/x^2)^(1/2))/(7*d*x^6) - ((c + d/x^2)^(1/2)*(24*b*c^2 - 28*a*c*d))/(105*d^3*x^2) - ((c + d/x^2)^(1/2)*(7*a*d - 6*b*c))/(35*d^2*x^4)","B"
968,1,53,82,5.314093,"\text{Not used}","int((x^4*(a + b/x^2))/(c + d/x^2)^(1/2),x)","\frac{x\,\sqrt{c+\frac{d}{x^2}}\,\left(3\,a\,c^2\,x^4+5\,b\,c^2\,x^2-4\,a\,c\,d\,x^2-10\,b\,c\,d+8\,a\,d^2\right)}{15\,c^3}","Not used",1,"(x*(c + d/x^2)^(1/2)*(8*a*d^2 + 3*a*c^2*x^4 + 5*b*c^2*x^2 - 10*b*c*d - 4*a*c*d*x^2))/(15*c^3)","B"
969,1,67,51,4.917028,"\text{Not used}","int((x^2*(a + b/x^2))/(c + d/x^2)^(1/2),x)","\frac{a\,x^3\,\sqrt{c+\frac{d}{x^2}}\,\left(c-\frac{2\,d}{x^2}\right)}{3\,c^2}+\frac{b\,x\,\sqrt{\frac{c\,x^2}{d}+1}}{\sqrt{c+\frac{d}{x^2}}\,\left(\sqrt{\frac{c\,x^2}{d}+1}+1\right)}","Not used",1,"(a*x^3*(c + d/x^2)^(1/2)*(c - (2*d)/x^2))/(3*c^2) + (b*x*((c*x^2)/d + 1)^(1/2))/((c + d/x^2)^(1/2)*(((c*x^2)/d + 1)^(1/2) + 1))","B"
970,1,65,47,4.997519,"\text{Not used}","int((a + b/x^2)/(c + d/x^2)^(1/2),x)","\frac{a\,x\,\sqrt{\frac{c\,x^2}{d}+1}}{\sqrt{c+\frac{d}{x^2}}\,\left(\sqrt{\frac{c\,x^2}{d}+1}+1\right)}-\frac{b\,\ln\left(\sqrt{c+\frac{d}{x^2}}+\frac{\sqrt{d}}{x}\right)}{\sqrt{d}}","Not used",1,"(a*x*((c*x^2)/d + 1)^(1/2))/((c + d/x^2)^(1/2)*(((c*x^2)/d + 1)^(1/2) + 1)) - (b*log((c + d/x^2)^(1/2) + d^(1/2)/x))/d^(1/2)","B"
971,1,94,61,5.528911,"\text{Not used}","int((a + b/x^2)/(x^2*(c + d/x^2)^(1/2)),x)","\left\{\begin{array}{cl} -\frac{3\,a\,x^2+b}{3\,\sqrt{c}\,x^3} & \text{\ if\ \ }d=0\\ \frac{b\,c\,\ln\left(2\,\sqrt{c+\frac{d}{x^2}}+\frac{2\,\sqrt{d}}{x}\right)}{2\,d^{3/2}}-\frac{b\,\sqrt{c+\frac{d}{x^2}}}{2\,d\,x}-\frac{a\,\ln\left(\sqrt{c+\frac{d}{x^2}}+\frac{\sqrt{d}}{x}\right)}{\sqrt{d}} & \text{\ if\ \ }d\neq 0 \end{array}\right.","Not used",1,"piecewise(d == 0, -(b + 3*a*x^2)/(3*c^(1/2)*x^3), d ~= 0, - (a*log((c + d/x^2)^(1/2) + d^(1/2)/x))/d^(1/2) - (b*(c + d/x^2)^(1/2))/(2*d*x) + (b*c*log(2*(c + d/x^2)^(1/2) + (2*d^(1/2))/x))/(2*d^(3/2)))","B"
972,0,-1,93,0.000000,"\text{Not used}","int((a + b/x^2)/(x^4*(c + d/x^2)^(1/2)),x)","\int \frac{a+\frac{b}{x^2}}{x^4\,\sqrt{c+\frac{d}{x^2}}} \,d x","Not used",1,"int((a + b/x^2)/(x^4*(c + d/x^2)^(1/2)), x)","F"
973,1,134,118,6.339375,"\text{Not used}","int((x^3*(a + b/x^2))/(c + d/x^2)^(3/2),x)","\frac{a\,x^4}{4\,c\,\sqrt{c+\frac{d}{x^2}}}-\frac{15\,a\,d^2}{8\,c^3\,\sqrt{c+\frac{d}{x^2}}}+\frac{b\,x^2}{2\,c\,\sqrt{c+\frac{d}{x^2}}}-\frac{3\,b\,d\,\mathrm{atanh}\left(\frac{\sqrt{c+\frac{d}{x^2}}}{\sqrt{c}}\right)}{2\,c^{5/2}}+\frac{15\,a\,d^2\,\mathrm{atanh}\left(\frac{\sqrt{c+\frac{d}{x^2}}}{\sqrt{c}}\right)}{8\,c^{7/2}}+\frac{3\,b\,d}{2\,c^2\,\sqrt{c+\frac{d}{x^2}}}-\frac{5\,a\,d\,x^2}{8\,c^2\,\sqrt{c+\frac{d}{x^2}}}","Not used",1,"(a*x^4)/(4*c*(c + d/x^2)^(1/2)) - (15*a*d^2)/(8*c^3*(c + d/x^2)^(1/2)) + (b*x^2)/(2*c*(c + d/x^2)^(1/2)) - (3*b*d*atanh((c + d/x^2)^(1/2)/c^(1/2)))/(2*c^(5/2)) + (15*a*d^2*atanh((c + d/x^2)^(1/2)/c^(1/2)))/(8*c^(7/2)) + (3*b*d)/(2*c^2*(c + d/x^2)^(1/2)) - (5*a*d*x^2)/(8*c^2*(c + d/x^2)^(1/2))","B"
974,1,90,86,5.609332,"\text{Not used}","int((x*(a + b/x^2))/(c + d/x^2)^(3/2),x)","\frac{b\,\mathrm{atanh}\left(\frac{\sqrt{c+\frac{d}{x^2}}}{\sqrt{c}}\right)}{c^{3/2}}-\frac{b}{c\,\sqrt{c+\frac{d}{x^2}}}+\frac{a\,x^2}{2\,c\,\sqrt{c+\frac{d}{x^2}}}-\frac{3\,a\,d\,\mathrm{atanh}\left(\frac{\sqrt{c+\frac{d}{x^2}}}{\sqrt{c}}\right)}{2\,c^{5/2}}+\frac{3\,a\,d}{2\,c^2\,\sqrt{c+\frac{d}{x^2}}}","Not used",1,"(b*atanh((c + d/x^2)^(1/2)/c^(1/2)))/c^(3/2) - b/(c*(c + d/x^2)^(1/2)) + (a*x^2)/(2*c*(c + d/x^2)^(1/2)) - (3*a*d*atanh((c + d/x^2)^(1/2)/c^(1/2)))/(2*c^(5/2)) + (3*a*d)/(2*c^2*(c + d/x^2)^(1/2))","B"
975,1,54,52,5.057773,"\text{Not used}","int((a + b/x^2)/(x*(c + d/x^2)^(3/2)),x)","\frac{a\,\mathrm{atanh}\left(\frac{\sqrt{c+\frac{d}{x^2}}}{\sqrt{c}}\right)}{c^{3/2}}-\frac{a}{c\,\sqrt{c+\frac{d}{x^2}}}+\frac{b\,\sqrt{x^2}}{d\,\sqrt{c\,x^2+d}}","Not used",1,"(a*atanh((c + d/x^2)^(1/2)/c^(1/2)))/c^(3/2) - a/(c*(c + d/x^2)^(1/2)) + (b*(x^2)^(1/2))/(d*(d + c*x^2)^(1/2))","B"
976,1,46,42,4.519266,"\text{Not used}","int((a + b/x^2)/(x^3*(c + d/x^2)^(3/2)),x)","\frac{x\,\sqrt{c+\frac{d}{x^2}}\,\left(x^2\,\left(\frac{a}{d}-\frac{2\,b\,c}{d^2}\right)-\frac{b}{d}\right)}{c\,x^3+d\,x}","Not used",1,"(x*(c + d/x^2)^(1/2)*(x^2*(a/d - (2*b*c)/d^2) - b/d))/(d*x + c*x^3)","B"
977,1,66,68,4.641653,"\text{Not used}","int((a + b/x^2)/(x^5*(c + d/x^2)^(3/2)),x)","-\frac{\sqrt{c+\frac{d}{x^2}}\,\left(-8\,b\,c^2\,x^4+6\,a\,c\,d\,x^4-4\,b\,c\,d\,x^2+3\,a\,d^2\,x^2+b\,d^2\right)}{3\,d^3\,x^2\,\left(c\,x^2+d\right)}","Not used",1,"-((c + d/x^2)^(1/2)*(b*d^2 + 3*a*d^2*x^2 - 8*b*c^2*x^4 + 6*a*c*d*x^4 - 4*b*c*d*x^2))/(3*d^3*x^2*(d + c*x^2))","B"
978,1,91,100,4.836690,"\text{Not used}","int((a + b/x^2)/(x^7*(c + d/x^2)^(3/2)),x)","-\frac{\sqrt{c+\frac{d}{x^2}}\,\left(48\,b\,c^3\,x^6-40\,a\,c^2\,d\,x^6+24\,b\,c^2\,d\,x^4-20\,a\,c\,d^2\,x^4-6\,b\,c\,d^2\,x^2+5\,a\,d^3\,x^2+3\,b\,d^3\right)}{15\,d^4\,x^4\,\left(c\,x^2+d\right)}","Not used",1,"-((c + d/x^2)^(1/2)*(3*b*d^3 + 5*a*d^3*x^2 + 48*b*c^3*x^6 - 20*a*c*d^2*x^4 - 40*a*c^2*d*x^6 - 6*b*c*d^2*x^2 + 24*b*c^2*d*x^4))/(15*d^4*x^4*(d + c*x^2))","B"
979,1,154,126,4.920468,"\text{Not used}","int((a + b/x^2)/(x^9*(c + d/x^2)^(3/2)),x)","\frac{c\,\sqrt{c+\frac{d}{x^2}}\,\left(21\,a\,d-29\,b\,c\right)}{35\,d^4\,x^2}-\frac{b\,\sqrt{c+\frac{d}{x^2}}}{7\,d^2\,x^6}-\frac{\sqrt{c+\frac{d}{x^2}}\,\left(7\,a\,d^2-13\,b\,c\,d\right)}{35\,d^4\,x^4}-\frac{\sqrt{c+\frac{d}{x^2}}\,\left(x^2\,\left(\frac{58\,b\,c^4-42\,a\,c^3\,d}{35\,d^5}+\frac{2\,c^3\,\left(77\,a\,d-93\,b\,c\right)}{35\,d^5}\right)+\frac{c^2\,\left(77\,a\,d-93\,b\,c\right)}{35\,d^4}\right)}{c\,x^2+d}","Not used",1,"(c*(c + d/x^2)^(1/2)*(21*a*d - 29*b*c))/(35*d^4*x^2) - (b*(c + d/x^2)^(1/2))/(7*d^2*x^6) - ((c + d/x^2)^(1/2)*(7*a*d^2 - 13*b*c*d))/(35*d^4*x^4) - ((c + d/x^2)^(1/2)*(x^2*((58*b*c^4 - 42*a*c^3*d)/(35*d^5) + (2*c^3*(77*a*d - 93*b*c))/(35*d^5)) + (c^2*(77*a*d - 93*b*c))/(35*d^4)))/(d + c*x^2)","B"
980,1,79,111,5.768061,"\text{Not used}","int((x^4*(a + b/x^2))/(c + d/x^2)^(3/2),x)","\frac{3\,a\,c^3\,x^6+5\,b\,c^3\,x^4-6\,a\,c^2\,d\,x^4-20\,b\,c^2\,d\,x^2+24\,a\,c\,d^2\,x^2-40\,b\,c\,d^2+48\,a\,d^3}{15\,c^4\,x\,\sqrt{c+\frac{d}{x^2}}}","Not used",1,"(48*a*d^3 + 3*a*c^3*x^6 + 5*b*c^3*x^4 - 40*b*c*d^2 + 24*a*c*d^2*x^2 - 6*a*c^2*d*x^4 - 20*b*c^2*d*x^2)/(15*c^4*x*(c + d/x^2)^(1/2))","B"
981,1,81,79,5.195122,"\text{Not used}","int((x^2*(a + b/x^2))/(c + d/x^2)^(3/2),x)","\frac{b\,c^2\,x^4+3\,b\,c\,d\,x^2+2\,b\,d^2}{c^2\,x^3\,{\left(c+\frac{d}{x^2}\right)}^{3/2}}-\frac{-a\,c^2\,x^4+4\,a\,c\,d\,x^2+8\,a\,d^2}{3\,c^3\,x\,\sqrt{c+\frac{d}{x^2}}}","Not used",1,"(2*b*d^2 + b*c^2*x^4 + 3*b*c*d*x^2)/(c^2*x^3*(c + d/x^2)^(3/2)) - (8*a*d^2 - a*c^2*x^4 + 4*a*c*d*x^2)/(3*c^3*x*(c + d/x^2)^(1/2))","B"
982,1,38,45,4.897679,"\text{Not used}","int((a + b/x^2)/(c + d/x^2)^(3/2),x)","\frac{\left(c\,x^2+d\right)\,\left(a\,c\,x^2+2\,a\,d-b\,c\right)}{c^2\,x^3\,{\left(c+\frac{d}{x^2}\right)}^{3/2}}","Not used",1,"((d + c*x^2)*(2*a*d - b*c + a*c*x^2))/(c^2*x^3*(c + d/x^2)^(3/2))","B"
983,1,60,59,5.106010,"\text{Not used}","int((a + b/x^2)/(x^2*(c + d/x^2)^(3/2)),x)","\frac{b}{d\,x\,\sqrt{c+\frac{d}{x^2}}}-\frac{a}{c\,x\,\sqrt{c+\frac{d}{x^2}}}-\frac{b\,\ln\left(\sqrt{c+\frac{d}{x^2}}+\frac{\sqrt{d}}{x}\right)}{d^{3/2}}","Not used",1,"b/(d*x*(c + d/x^2)^(1/2)) - a/(c*x*(c + d/x^2)^(1/2)) - (b*log((c + d/x^2)^(1/2) + d^(1/2)/x))/d^(3/2)","B"
984,0,-1,92,0.000000,"\text{Not used}","int((a + b/x^2)/(x^4*(c + d/x^2)^(3/2)),x)","\int \frac{a+\frac{b}{x^2}}{x^4\,{\left(c+\frac{d}{x^2}\right)}^{3/2}} \,d x","Not used",1,"int((a + b/x^2)/(x^4*(c + d/x^2)^(3/2)), x)","F"
985,0,-1,123,0.000000,"\text{Not used}","int((a + b/x^2)/(x^6*(c + d/x^2)^(3/2)),x)","\int \frac{a+\frac{b}{x^2}}{x^6\,{\left(c+\frac{d}{x^2}\right)}^{3/2}} \,d x","Not used",1,"int((a + b/x^2)/(x^6*(c + d/x^2)^(3/2)), x)","F"
986,0,-1,105,0.000000,"\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(a+\frac{b}{x^2}\right)}^p\,{\left(c+\frac{d}{x^2}\right)}^q \,d x","Not used",1,"int((e*x)^m*(a + b/x^2)^p*(c + d/x^2)^q, x)","F"
987,0,-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(a+\frac{b}{x^2}\right)}^p\,{\left(c+\frac{d}{x^2}\right)}^q \,d x","Not used",1,"int(x^4*(a + b/x^2)^p*(c + d/x^2)^q, x)","F"
988,0,-1,100,0.000000,"\text{Not used}","int(x^3*(a + b/x^2)^p*(c + d/x^2)^q,x)","\int x^3\,{\left(a+\frac{b}{x^2}\right)}^p\,{\left(c+\frac{d}{x^2}\right)}^q \,d x","Not used",1,"int(x^3*(a + b/x^2)^p*(c + d/x^2)^q, x)","F"
989,0,-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(a+\frac{b}{x^2}\right)}^p\,{\left(c+\frac{d}{x^2}\right)}^q \,d x","Not used",1,"int(x^2*(a + b/x^2)^p*(c + d/x^2)^q, x)","F"
990,0,-1,98,0.000000,"\text{Not used}","int(x*(a + b/x^2)^p*(c + d/x^2)^q,x)","\int x\,{\left(a+\frac{b}{x^2}\right)}^p\,{\left(c+\frac{d}{x^2}\right)}^q \,d x","Not used",1,"int(x*(a + b/x^2)^p*(c + d/x^2)^q, x)","F"
991,0,-1,79,0.000000,"\text{Not used}","int((a + b/x^2)^p*(c + d/x^2)^q,x)","\int {\left(a+\frac{b}{x^2}\right)}^p\,{\left(c+\frac{d}{x^2}\right)}^q \,d x","Not used",1,"int((a + b/x^2)^p*(c + d/x^2)^q, x)","F"
992,0,-1,97,0.000000,"\text{Not used}","int(((a + b/x^2)^p*(c + d/x^2)^q)/x,x)","\int \frac{{\left(a+\frac{b}{x^2}\right)}^p\,{\left(c+\frac{d}{x^2}\right)}^q}{x} \,d x","Not used",1,"int(((a + b/x^2)^p*(c + d/x^2)^q)/x, x)","F"
993,0,-1,82,0.000000,"\text{Not used}","int(((a + b/x^2)^p*(c + d/x^2)^q)/x^2,x)","\int \frac{{\left(a+\frac{b}{x^2}\right)}^p\,{\left(c+\frac{d}{x^2}\right)}^q}{x^2} \,d x","Not used",1,"int(((a + b/x^2)^p*(c + d/x^2)^q)/x^2, x)","F"
994,0,-1,85,0.000000,"\text{Not used}","int(((a + b/x^2)^p*(c + d/x^2)^q)/x^3,x)","\int \frac{{\left(a+\frac{b}{x^2}\right)}^p\,{\left(c+\frac{d}{x^2}\right)}^q}{x^3} \,d x","Not used",1,"int(((a + b/x^2)^p*(c + d/x^2)^q)/x^3, x)","F"
995,0,-1,84,0.000000,"\text{Not used}","int(((a + b/x^2)^p*(c + d/x^2)^q)/x^4,x)","\int \frac{{\left(a+\frac{b}{x^2}\right)}^p\,{\left(c+\frac{d}{x^2}\right)}^q}{x^4} \,d x","Not used",1,"int(((a + b/x^2)^p*(c + d/x^2)^q)/x^4, x)","F"
996,0,-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(a+\frac{b}{x^2}\right)}^p\,{\left(c+\frac{d}{x^2}\right)}^q \,d x","Not used",1,"int((e*x)^(5/2)*(a + b/x^2)^p*(c + d/x^2)^q, x)","F"
997,0,-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(a+\frac{b}{x^2}\right)}^p\,{\left(c+\frac{d}{x^2}\right)}^q \,d x","Not used",1,"int((e*x)^(3/2)*(a + b/x^2)^p*(c + d/x^2)^q, x)","F"
998,0,-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(a+\frac{b}{x^2}\right)}^p\,{\left(c+\frac{d}{x^2}\right)}^q \,d x","Not used",1,"int((e*x)^(1/2)*(a + b/x^2)^p*(c + d/x^2)^q, x)","F"
999,0,-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(a+\frac{b}{x^2}\right)}^p\,{\left(c+\frac{d}{x^2}\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"
1000,0,-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(a+\frac{b}{x^2}\right)}^p\,{\left(c+\frac{d}{x^2}\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"
1001,0,-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(a+\frac{b}{x^2}\right)}^p\,{\left(c+\frac{d}{x^2}\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"
1002,1,831,135,52.027657,"\text{Not used}","int(x^(5/2)*(x^(1/2) - 1)^(1/2)*(x^(1/2) + 1)^(1/2),x)","-\frac{5\,\mathrm{atanh}\left(\frac{\sqrt{\sqrt{x}-1}-\mathrm{i}}{\sqrt{\sqrt{x}+1}-1}\right)}{16}+\frac{-\frac{235\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^3}{48\,{\left(\sqrt{\sqrt{x}+1}-1\right)}^3}+\frac{1723\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^5}{48\,{\left(\sqrt{\sqrt{x}+1}-1\right)}^5}+\frac{72283\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^7}{16\,{\left(\sqrt{\sqrt{x}+1}-1\right)}^7}+\frac{848801\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^9}{16\,{\left(\sqrt{\sqrt{x}+1}-1\right)}^9}+\frac{4181067\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{11}}{16\,{\left(\sqrt{\sqrt{x}+1}-1\right)}^{11}}+\frac{10994181\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{13}}{16\,{\left(\sqrt{\sqrt{x}+1}-1\right)}^{13}}+\frac{17457599\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{15}}{16\,{\left(\sqrt{\sqrt{x}+1}-1\right)}^{15}}+\frac{17457599\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{17}}{16\,{\left(\sqrt{\sqrt{x}+1}-1\right)}^{17}}+\frac{10994181\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{19}}{16\,{\left(\sqrt{\sqrt{x}+1}-1\right)}^{19}}+\frac{4181067\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{21}}{16\,{\left(\sqrt{\sqrt{x}+1}-1\right)}^{21}}+\frac{848801\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{23}}{16\,{\left(\sqrt{\sqrt{x}+1}-1\right)}^{23}}+\frac{72283\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{25}}{16\,{\left(\sqrt{\sqrt{x}+1}-1\right)}^{25}}+\frac{1723\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{27}}{48\,{\left(\sqrt{\sqrt{x}+1}-1\right)}^{27}}-\frac{235\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{29}}{48\,{\left(\sqrt{\sqrt{x}+1}-1\right)}^{29}}+\frac{5\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{31}}{16\,{\left(\sqrt{\sqrt{x}+1}-1\right)}^{31}}+\frac{5\,\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}{16\,\left(\sqrt{\sqrt{x}+1}-1\right)}}{1+\frac{120\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^4}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^4}-\frac{560\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^6}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^6}+\frac{1820\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^8}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^8}-\frac{4368\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{10}}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^{10}}+\frac{8008\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{12}}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^{12}}-\frac{11440\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{14}}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^{14}}+\frac{12870\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{16}}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^{16}}-\frac{11440\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{18}}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^{18}}+\frac{8008\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{20}}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^{20}}-\frac{4368\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{22}}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^{22}}+\frac{1820\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{24}}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^{24}}-\frac{560\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{26}}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^{26}}+\frac{120\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{28}}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^{28}}-\frac{16\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{30}}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^{30}}+\frac{{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{32}}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^{32}}-\frac{16\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^2}}","Not used",1,"((1723*((x^(1/2) - 1)^(1/2) - 1i)^5)/(48*((x^(1/2) + 1)^(1/2) - 1)^5) - (235*((x^(1/2) - 1)^(1/2) - 1i)^3)/(48*((x^(1/2) + 1)^(1/2) - 1)^3) + (72283*((x^(1/2) - 1)^(1/2) - 1i)^7)/(16*((x^(1/2) + 1)^(1/2) - 1)^7) + (848801*((x^(1/2) - 1)^(1/2) - 1i)^9)/(16*((x^(1/2) + 1)^(1/2) - 1)^9) + (4181067*((x^(1/2) - 1)^(1/2) - 1i)^11)/(16*((x^(1/2) + 1)^(1/2) - 1)^11) + (10994181*((x^(1/2) - 1)^(1/2) - 1i)^13)/(16*((x^(1/2) + 1)^(1/2) - 1)^13) + (17457599*((x^(1/2) - 1)^(1/2) - 1i)^15)/(16*((x^(1/2) + 1)^(1/2) - 1)^15) + (17457599*((x^(1/2) - 1)^(1/2) - 1i)^17)/(16*((x^(1/2) + 1)^(1/2) - 1)^17) + (10994181*((x^(1/2) - 1)^(1/2) - 1i)^19)/(16*((x^(1/2) + 1)^(1/2) - 1)^19) + (4181067*((x^(1/2) - 1)^(1/2) - 1i)^21)/(16*((x^(1/2) + 1)^(1/2) - 1)^21) + (848801*((x^(1/2) - 1)^(1/2) - 1i)^23)/(16*((x^(1/2) + 1)^(1/2) - 1)^23) + (72283*((x^(1/2) - 1)^(1/2) - 1i)^25)/(16*((x^(1/2) + 1)^(1/2) - 1)^25) + (1723*((x^(1/2) - 1)^(1/2) - 1i)^27)/(48*((x^(1/2) + 1)^(1/2) - 1)^27) - (235*((x^(1/2) - 1)^(1/2) - 1i)^29)/(48*((x^(1/2) + 1)^(1/2) - 1)^29) + (5*((x^(1/2) - 1)^(1/2) - 1i)^31)/(16*((x^(1/2) + 1)^(1/2) - 1)^31) + (5*((x^(1/2) - 1)^(1/2) - 1i))/(16*((x^(1/2) + 1)^(1/2) - 1)))/((120*((x^(1/2) - 1)^(1/2) - 1i)^4)/((x^(1/2) + 1)^(1/2) - 1)^4 - (16*((x^(1/2) - 1)^(1/2) - 1i)^2)/((x^(1/2) + 1)^(1/2) - 1)^2 - (560*((x^(1/2) - 1)^(1/2) - 1i)^6)/((x^(1/2) + 1)^(1/2) - 1)^6 + (1820*((x^(1/2) - 1)^(1/2) - 1i)^8)/((x^(1/2) + 1)^(1/2) - 1)^8 - (4368*((x^(1/2) - 1)^(1/2) - 1i)^10)/((x^(1/2) + 1)^(1/2) - 1)^10 + (8008*((x^(1/2) - 1)^(1/2) - 1i)^12)/((x^(1/2) + 1)^(1/2) - 1)^12 - (11440*((x^(1/2) - 1)^(1/2) - 1i)^14)/((x^(1/2) + 1)^(1/2) - 1)^14 + (12870*((x^(1/2) - 1)^(1/2) - 1i)^16)/((x^(1/2) + 1)^(1/2) - 1)^16 - (11440*((x^(1/2) - 1)^(1/2) - 1i)^18)/((x^(1/2) + 1)^(1/2) - 1)^18 + (8008*((x^(1/2) - 1)^(1/2) - 1i)^20)/((x^(1/2) + 1)^(1/2) - 1)^20 - (4368*((x^(1/2) - 1)^(1/2) - 1i)^22)/((x^(1/2) + 1)^(1/2) - 1)^22 + (1820*((x^(1/2) - 1)^(1/2) - 1i)^24)/((x^(1/2) + 1)^(1/2) - 1)^24 - (560*((x^(1/2) - 1)^(1/2) - 1i)^26)/((x^(1/2) + 1)^(1/2) - 1)^26 + (120*((x^(1/2) - 1)^(1/2) - 1i)^28)/((x^(1/2) + 1)^(1/2) - 1)^28 - (16*((x^(1/2) - 1)^(1/2) - 1i)^30)/((x^(1/2) + 1)^(1/2) - 1)^30 + ((x^(1/2) - 1)^(1/2) - 1i)^32/((x^(1/2) + 1)^(1/2) - 1)^32 + 1) - (5*atanh(((x^(1/2) - 1)^(1/2) - 1i)/((x^(1/2) + 1)^(1/2) - 1)))/16","B"
1003,1,632,104,31.389733,"\text{Not used}","int(x^(3/2)*(x^(1/2) - 1)^(1/2)*(x^(1/2) + 1)^(1/2),x)","-\frac{\mathrm{atanh}\left(\frac{\sqrt{\sqrt{x}-1}-\mathrm{i}}{\sqrt{\sqrt{x}+1}-1}\right)}{2}-\frac{\frac{35\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^3}{6\,{\left(\sqrt{\sqrt{x}+1}-1\right)}^3}+\frac{757\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^5}{2\,{\left(\sqrt{\sqrt{x}+1}-1\right)}^5}+\frac{7339\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^7}{2\,{\left(\sqrt{\sqrt{x}+1}-1\right)}^7}+\frac{41929\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^9}{3\,{\left(\sqrt{\sqrt{x}+1}-1\right)}^9}+\frac{25661\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{11}}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^{11}}+\frac{25661\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{13}}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^{13}}+\frac{41929\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{15}}{3\,{\left(\sqrt{\sqrt{x}+1}-1\right)}^{15}}+\frac{7339\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{17}}{2\,{\left(\sqrt{\sqrt{x}+1}-1\right)}^{17}}+\frac{757\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{19}}{2\,{\left(\sqrt{\sqrt{x}+1}-1\right)}^{19}}+\frac{35\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{21}}{6\,{\left(\sqrt{\sqrt{x}+1}-1\right)}^{21}}-\frac{{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{23}}{2\,{\left(\sqrt{\sqrt{x}+1}-1\right)}^{23}}-\frac{\sqrt{\sqrt{x}-1}-\mathrm{i}}{2\,\left(\sqrt{\sqrt{x}+1}-1\right)}}{1+\frac{66\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^4}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^4}-\frac{220\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^6}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^6}+\frac{495\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^8}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^8}-\frac{792\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{10}}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^{10}}+\frac{924\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{12}}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^{12}}-\frac{792\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{14}}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^{14}}+\frac{495\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{16}}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^{16}}-\frac{220\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{18}}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^{18}}+\frac{66\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{20}}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^{20}}-\frac{12\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{22}}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^{22}}+\frac{{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{24}}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^{24}}-\frac{12\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^2}}","Not used",1,"- atanh(((x^(1/2) - 1)^(1/2) - 1i)/((x^(1/2) + 1)^(1/2) - 1))/2 - ((35*((x^(1/2) - 1)^(1/2) - 1i)^3)/(6*((x^(1/2) + 1)^(1/2) - 1)^3) + (757*((x^(1/2) - 1)^(1/2) - 1i)^5)/(2*((x^(1/2) + 1)^(1/2) - 1)^5) + (7339*((x^(1/2) - 1)^(1/2) - 1i)^7)/(2*((x^(1/2) + 1)^(1/2) - 1)^7) + (41929*((x^(1/2) - 1)^(1/2) - 1i)^9)/(3*((x^(1/2) + 1)^(1/2) - 1)^9) + (25661*((x^(1/2) - 1)^(1/2) - 1i)^11)/((x^(1/2) + 1)^(1/2) - 1)^11 + (25661*((x^(1/2) - 1)^(1/2) - 1i)^13)/((x^(1/2) + 1)^(1/2) - 1)^13 + (41929*((x^(1/2) - 1)^(1/2) - 1i)^15)/(3*((x^(1/2) + 1)^(1/2) - 1)^15) + (7339*((x^(1/2) - 1)^(1/2) - 1i)^17)/(2*((x^(1/2) + 1)^(1/2) - 1)^17) + (757*((x^(1/2) - 1)^(1/2) - 1i)^19)/(2*((x^(1/2) + 1)^(1/2) - 1)^19) + (35*((x^(1/2) - 1)^(1/2) - 1i)^21)/(6*((x^(1/2) + 1)^(1/2) - 1)^21) - ((x^(1/2) - 1)^(1/2) - 1i)^23/(2*((x^(1/2) + 1)^(1/2) - 1)^23) - ((x^(1/2) - 1)^(1/2) - 1i)/(2*((x^(1/2) + 1)^(1/2) - 1)))/((66*((x^(1/2) - 1)^(1/2) - 1i)^4)/((x^(1/2) + 1)^(1/2) - 1)^4 - (12*((x^(1/2) - 1)^(1/2) - 1i)^2)/((x^(1/2) + 1)^(1/2) - 1)^2 - (220*((x^(1/2) - 1)^(1/2) - 1i)^6)/((x^(1/2) + 1)^(1/2) - 1)^6 + (495*((x^(1/2) - 1)^(1/2) - 1i)^8)/((x^(1/2) + 1)^(1/2) - 1)^8 - (792*((x^(1/2) - 1)^(1/2) - 1i)^10)/((x^(1/2) + 1)^(1/2) - 1)^10 + (924*((x^(1/2) - 1)^(1/2) - 1i)^12)/((x^(1/2) + 1)^(1/2) - 1)^12 - (792*((x^(1/2) - 1)^(1/2) - 1i)^14)/((x^(1/2) + 1)^(1/2) - 1)^14 + (495*((x^(1/2) - 1)^(1/2) - 1i)^16)/((x^(1/2) + 1)^(1/2) - 1)^16 - (220*((x^(1/2) - 1)^(1/2) - 1i)^18)/((x^(1/2) + 1)^(1/2) - 1)^18 + (66*((x^(1/2) - 1)^(1/2) - 1i)^20)/((x^(1/2) + 1)^(1/2) - 1)^20 - (12*((x^(1/2) - 1)^(1/2) - 1i)^22)/((x^(1/2) + 1)^(1/2) - 1)^22 + ((x^(1/2) - 1)^(1/2) - 1i)^24/((x^(1/2) + 1)^(1/2) - 1)^24 + 1)","B"
1004,0,-1,73,0.000000,"\text{Not used}","int(x^(1/2)*(x^(1/2) - 1)^(1/2)*(x^(1/2) + 1)^(1/2),x)","\int \sqrt{x}\,\sqrt{\sqrt{x}-1}\,\sqrt{\sqrt{x}+1} \,d x","Not used",1,"int(x^(1/2)*(x^(1/2) - 1)^(1/2)*(x^(1/2) + 1)^(1/2), x)","F"
1005,1,41,37,5.069236,"\text{Not used}","int(((x^(1/2) - 1)^(1/2)*(x^(1/2) + 1)^(1/2))/x^(1/2),x)","\sqrt{x}\,\sqrt{\sqrt{x}-1}\,\sqrt{\sqrt{x}+1}-\ln\left(\sqrt{\sqrt{x}-1}\,\sqrt{\sqrt{x}+1}+\sqrt{x}\right)","Not used",1,"x^(1/2)*(x^(1/2) - 1)^(1/2)*(x^(1/2) + 1)^(1/2) - log((x^(1/2) - 1)^(1/2)*(x^(1/2) + 1)^(1/2) + x^(1/2))","B"
1006,1,129,67,6.248752,"\text{Not used}","int(((x^(1/2) - 1)^(1/2)*(x^(1/2) + 1)^(1/2))/x^(3/2),x)","8\,\mathrm{atanh}\left(\frac{\sqrt{\sqrt{x}-1}-\mathrm{i}}{\sqrt{\sqrt{x}+1}-1}\right)-\frac{\frac{5\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^2}{2\,{\left(\sqrt{\sqrt{x}+1}-1\right)}^2}+\frac{1}{2}}{\frac{{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^3}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^3}+\frac{\sqrt{\sqrt{x}-1}-\mathrm{i}}{\sqrt{\sqrt{x}+1}-1}}-\frac{\sqrt{\sqrt{x}-1}-\mathrm{i}}{2\,\left(\sqrt{\sqrt{x}+1}-1\right)}","Not used",1,"8*atanh(((x^(1/2) - 1)^(1/2) - 1i)/((x^(1/2) + 1)^(1/2) - 1)) - ((5*((x^(1/2) - 1)^(1/2) - 1i)^2)/(2*((x^(1/2) + 1)^(1/2) - 1)^2) + 1/2)/(((x^(1/2) - 1)^(1/2) - 1i)^3/((x^(1/2) + 1)^(1/2) - 1)^3 + ((x^(1/2) - 1)^(1/2) - 1i)/((x^(1/2) + 1)^(1/2) - 1)) - ((x^(1/2) - 1)^(1/2) - 1i)/(2*((x^(1/2) + 1)^(1/2) - 1))","B"
1007,1,31,31,5.256835,"\text{Not used}","int(((x^(1/2) - 1)^(1/2)*(x^(1/2) + 1)^(1/2))/x^(5/2),x)","\frac{\sqrt{\sqrt{x}-1}\,\left(\frac{2\,x\,\sqrt{\sqrt{x}+1}}{3}-\frac{2\,\sqrt{\sqrt{x}+1}}{3}\right)}{x^{3/2}}","Not used",1,"((x^(1/2) - 1)^(1/2)*((2*x*(x^(1/2) + 1)^(1/2))/3 - (2*(x^(1/2) + 1)^(1/2))/3))/x^(3/2)","B"
1008,1,43,63,5.074792,"\text{Not used}","int(((x^(1/2) - 1)^(1/2)*(x^(1/2) + 1)^(1/2))/x^(7/2),x)","\frac{\sqrt{\sqrt{x}-1}\,\left(\frac{2\,x\,\sqrt{\sqrt{x}+1}}{15}-\frac{2\,\sqrt{\sqrt{x}+1}}{5}+\frac{4\,x^2\,\sqrt{\sqrt{x}+1}}{15}\right)}{x^{5/2}}","Not used",1,"((x^(1/2) - 1)^(1/2)*((2*x*(x^(1/2) + 1)^(1/2))/15 - (2*(x^(1/2) + 1)^(1/2))/5 + (4*x^2*(x^(1/2) + 1)^(1/2))/15))/x^(5/2)","B"
1009,1,55,94,5.038418,"\text{Not used}","int(((x^(1/2) - 1)^(1/2)*(x^(1/2) + 1)^(1/2))/x^(9/2),x)","\frac{\sqrt{\sqrt{x}-1}\,\left(\frac{2\,x\,\sqrt{\sqrt{x}+1}}{35}-\frac{2\,\sqrt{\sqrt{x}+1}}{7}+\frac{8\,x^2\,\sqrt{\sqrt{x}+1}}{105}+\frac{16\,x^3\,\sqrt{\sqrt{x}+1}}{105}\right)}{x^{7/2}}","Not used",1,"((x^(1/2) - 1)^(1/2)*((2*x*(x^(1/2) + 1)^(1/2))/35 - (2*(x^(1/2) + 1)^(1/2))/7 + (8*x^2*(x^(1/2) + 1)^(1/2))/105 + (16*x^3*(x^(1/2) + 1)^(1/2))/105))/x^(7/2)","B"
1010,1,67,125,5.023377,"\text{Not used}","int(((x^(1/2) - 1)^(1/2)*(x^(1/2) + 1)^(1/2))/x^(11/2),x)","\frac{\sqrt{\sqrt{x}-1}\,\left(\frac{2\,x\,\sqrt{\sqrt{x}+1}}{63}-\frac{2\,\sqrt{\sqrt{x}+1}}{9}+\frac{4\,x^2\,\sqrt{\sqrt{x}+1}}{105}+\frac{16\,x^3\,\sqrt{\sqrt{x}+1}}{315}+\frac{32\,x^4\,\sqrt{\sqrt{x}+1}}{315}\right)}{x^{9/2}}","Not used",1,"((x^(1/2) - 1)^(1/2)*((2*x*(x^(1/2) + 1)^(1/2))/63 - (2*(x^(1/2) + 1)^(1/2))/9 + (4*x^2*(x^(1/2) + 1)^(1/2))/105 + (16*x^3*(x^(1/2) + 1)^(1/2))/315 + (32*x^4*(x^(1/2) + 1)^(1/2))/315))/x^(9/2)","B"
1011,1,632,104,27.092009,"\text{Not used}","int(x^(5/2)/((x^(1/2) - 1)^(1/2)*(x^(1/2) + 1)^(1/2)),x)","\frac{5\,\mathrm{atanh}\left(\frac{\sqrt{\sqrt{x}-1}-\mathrm{i}}{\sqrt{\sqrt{x}+1}-1}\right)}{2}-\frac{-\frac{175\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^3}{6\,{\left(\sqrt{\sqrt{x}+1}-1\right)}^3}+\frac{311\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^5}{2\,{\left(\sqrt{\sqrt{x}+1}-1\right)}^5}+\frac{8361\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^7}{2\,{\left(\sqrt{\sqrt{x}+1}-1\right)}^7}+\frac{42259\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^9}{3\,{\left(\sqrt{\sqrt{x}+1}-1\right)}^9}+\frac{25295\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{11}}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^{11}}+\frac{25295\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{13}}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^{13}}+\frac{42259\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{15}}{3\,{\left(\sqrt{\sqrt{x}+1}-1\right)}^{15}}+\frac{8361\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{17}}{2\,{\left(\sqrt{\sqrt{x}+1}-1\right)}^{17}}+\frac{311\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{19}}{2\,{\left(\sqrt{\sqrt{x}+1}-1\right)}^{19}}-\frac{175\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{21}}{6\,{\left(\sqrt{\sqrt{x}+1}-1\right)}^{21}}+\frac{5\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{23}}{2\,{\left(\sqrt{\sqrt{x}+1}-1\right)}^{23}}+\frac{5\,\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}{2\,\left(\sqrt{\sqrt{x}+1}-1\right)}}{1+\frac{66\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^4}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^4}-\frac{220\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^6}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^6}+\frac{495\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^8}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^8}-\frac{792\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{10}}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^{10}}+\frac{924\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{12}}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^{12}}-\frac{792\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{14}}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^{14}}+\frac{495\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{16}}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^{16}}-\frac{220\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{18}}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^{18}}+\frac{66\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{20}}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^{20}}-\frac{12\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{22}}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^{22}}+\frac{{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{24}}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^{24}}-\frac{12\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^2}}","Not used",1,"(5*atanh(((x^(1/2) - 1)^(1/2) - 1i)/((x^(1/2) + 1)^(1/2) - 1)))/2 - ((311*((x^(1/2) - 1)^(1/2) - 1i)^5)/(2*((x^(1/2) + 1)^(1/2) - 1)^5) - (175*((x^(1/2) - 1)^(1/2) - 1i)^3)/(6*((x^(1/2) + 1)^(1/2) - 1)^3) + (8361*((x^(1/2) - 1)^(1/2) - 1i)^7)/(2*((x^(1/2) + 1)^(1/2) - 1)^7) + (42259*((x^(1/2) - 1)^(1/2) - 1i)^9)/(3*((x^(1/2) + 1)^(1/2) - 1)^9) + (25295*((x^(1/2) - 1)^(1/2) - 1i)^11)/((x^(1/2) + 1)^(1/2) - 1)^11 + (25295*((x^(1/2) - 1)^(1/2) - 1i)^13)/((x^(1/2) + 1)^(1/2) - 1)^13 + (42259*((x^(1/2) - 1)^(1/2) - 1i)^15)/(3*((x^(1/2) + 1)^(1/2) - 1)^15) + (8361*((x^(1/2) - 1)^(1/2) - 1i)^17)/(2*((x^(1/2) + 1)^(1/2) - 1)^17) + (311*((x^(1/2) - 1)^(1/2) - 1i)^19)/(2*((x^(1/2) + 1)^(1/2) - 1)^19) - (175*((x^(1/2) - 1)^(1/2) - 1i)^21)/(6*((x^(1/2) + 1)^(1/2) - 1)^21) + (5*((x^(1/2) - 1)^(1/2) - 1i)^23)/(2*((x^(1/2) + 1)^(1/2) - 1)^23) + (5*((x^(1/2) - 1)^(1/2) - 1i))/(2*((x^(1/2) + 1)^(1/2) - 1)))/((66*((x^(1/2) - 1)^(1/2) - 1i)^4)/((x^(1/2) + 1)^(1/2) - 1)^4 - (12*((x^(1/2) - 1)^(1/2) - 1i)^2)/((x^(1/2) + 1)^(1/2) - 1)^2 - (220*((x^(1/2) - 1)^(1/2) - 1i)^6)/((x^(1/2) + 1)^(1/2) - 1)^6 + (495*((x^(1/2) - 1)^(1/2) - 1i)^8)/((x^(1/2) + 1)^(1/2) - 1)^8 - (792*((x^(1/2) - 1)^(1/2) - 1i)^10)/((x^(1/2) + 1)^(1/2) - 1)^10 + (924*((x^(1/2) - 1)^(1/2) - 1i)^12)/((x^(1/2) + 1)^(1/2) - 1)^12 - (792*((x^(1/2) - 1)^(1/2) - 1i)^14)/((x^(1/2) + 1)^(1/2) - 1)^14 + (495*((x^(1/2) - 1)^(1/2) - 1i)^16)/((x^(1/2) + 1)^(1/2) - 1)^16 - (220*((x^(1/2) - 1)^(1/2) - 1i)^18)/((x^(1/2) + 1)^(1/2) - 1)^18 + (66*((x^(1/2) - 1)^(1/2) - 1i)^20)/((x^(1/2) + 1)^(1/2) - 1)^20 - (12*((x^(1/2) - 1)^(1/2) - 1i)^22)/((x^(1/2) + 1)^(1/2) - 1)^22 + ((x^(1/2) - 1)^(1/2) - 1i)^24/((x^(1/2) + 1)^(1/2) - 1)^24 + 1)","B"
1012,1,429,73,18.764583,"\text{Not used}","int(x^(3/2)/((x^(1/2) - 1)^(1/2)*(x^(1/2) + 1)^(1/2)),x)","3\,\mathrm{atanh}\left(\frac{\sqrt{\sqrt{x}-1}-\mathrm{i}}{\sqrt{\sqrt{x}+1}-1}\right)+\frac{\frac{23\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^3}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^3}+\frac{333\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^5}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^5}+\frac{671\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^7}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^7}+\frac{671\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^9}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^9}+\frac{333\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{11}}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^{11}}+\frac{23\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{13}}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^{13}}-\frac{3\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{15}}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^{15}}-\frac{3\,\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}{\sqrt{\sqrt{x}+1}-1}}{1+\frac{28\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^4}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^4}-\frac{56\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^6}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^6}+\frac{70\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^8}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^8}-\frac{56\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{10}}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^{10}}+\frac{28\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{12}}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^{12}}-\frac{8\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{14}}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^{14}}+\frac{{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^{16}}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^{16}}-\frac{8\,{\left(\sqrt{\sqrt{x}-1}-\mathrm{i}\right)}^2}{{\left(\sqrt{\sqrt{x}+1}-1\right)}^2}}","Not used",1,"3*atanh(((x^(1/2) - 1)^(1/2) - 1i)/((x^(1/2) + 1)^(1/2) - 1)) + ((23*((x^(1/2) - 1)^(1/2) - 1i)^3)/((x^(1/2) + 1)^(1/2) - 1)^3 + (333*((x^(1/2) - 1)^(1/2) - 1i)^5)/((x^(1/2) + 1)^(1/2) - 1)^5 + (671*((x^(1/2) - 1)^(1/2) - 1i)^7)/((x^(1/2) + 1)^(1/2) - 1)^7 + (671*((x^(1/2) - 1)^(1/2) - 1i)^9)/((x^(1/2) + 1)^(1/2) - 1)^9 + (333*((x^(1/2) - 1)^(1/2) - 1i)^11)/((x^(1/2) + 1)^(1/2) - 1)^11 + (23*((x^(1/2) - 1)^(1/2) - 1i)^13)/((x^(1/2) + 1)^(1/2) - 1)^13 - (3*((x^(1/2) - 1)^(1/2) - 1i)^15)/((x^(1/2) + 1)^(1/2) - 1)^15 - (3*((x^(1/2) - 1)^(1/2) - 1i))/((x^(1/2) + 1)^(1/2) - 1))/((28*((x^(1/2) - 1)^(1/2) - 1i)^4)/((x^(1/2) + 1)^(1/2) - 1)^4 - (8*((x^(1/2) - 1)^(1/2) - 1i)^2)/((x^(1/2) + 1)^(1/2) - 1)^2 - (56*((x^(1/2) - 1)^(1/2) - 1i)^6)/((x^(1/2) + 1)^(1/2) - 1)^6 + (70*((x^(1/2) - 1)^(1/2) - 1i)^8)/((x^(1/2) + 1)^(1/2) - 1)^8 - (56*((x^(1/2) - 1)^(1/2) - 1i)^10)/((x^(1/2) + 1)^(1/2) - 1)^10 + (28*((x^(1/2) - 1)^(1/2) - 1i)^12)/((x^(1/2) + 1)^(1/2) - 1)^12 - (8*((x^(1/2) - 1)^(1/2) - 1i)^14)/((x^(1/2) + 1)^(1/2) - 1)^14 + ((x^(1/2) - 1)^(1/2) - 1i)^16/((x^(1/2) + 1)^(1/2) - 1)^16 + 1)","B"
1013,0,-1,35,0.000000,"\text{Not used}","int(x^(1/2)/((x^(1/2) - 1)^(1/2)*(x^(1/2) + 1)^(1/2)),x)","\int \frac{\sqrt{x}}{\sqrt{\sqrt{x}-1}\,\sqrt{\sqrt{x}+1}} \,d x","Not used",1,"int(x^(1/2)/((x^(1/2) - 1)^(1/2)*(x^(1/2) + 1)^(1/2)), x)","F"
1014,1,6,8,5.287194,"\text{Not used}","int(1/(x^(1/2)*(x^(1/2) - 1)^(1/2)*(x^(1/2) + 1)^(1/2)),x)","2\,\mathrm{acosh}\left(\sqrt{x}\right)","Not used",1,"2*acosh(x^(1/2))","B"
1015,1,19,29,5.561270,"\text{Not used}","int(1/(x^(3/2)*(x^(1/2) - 1)^(1/2)*(x^(1/2) + 1)^(1/2)),x)","\frac{2\,\sqrt{\sqrt{x}-1}\,\sqrt{\sqrt{x}+1}}{\sqrt{x}}","Not used",1,"(2*(x^(1/2) - 1)^(1/2)*(x^(1/2) + 1)^(1/2))/x^(1/2)","B"
1016,1,33,63,5.503835,"\text{Not used}","int(1/(x^(5/2)*(x^(1/2) - 1)^(1/2)*(x^(1/2) + 1)^(1/2)),x)","\frac{\sqrt{\sqrt{x}-1}\,\left(\frac{4\,x}{3}+\frac{2\,\sqrt{x}}{3}+\frac{4\,x^{3/2}}{3}+\frac{2}{3}\right)}{x^{3/2}\,\sqrt{\sqrt{x}+1}}","Not used",1,"((x^(1/2) - 1)^(1/2)*((4*x)/3 + (2*x^(1/2))/3 + (4*x^(3/2))/3 + 2/3))/(x^(3/2)*(x^(1/2) + 1)^(1/2))","B"
1017,1,43,94,5.657830,"\text{Not used}","int(1/(x^(7/2)*(x^(1/2) - 1)^(1/2)*(x^(1/2) + 1)^(1/2)),x)","\frac{\sqrt{\sqrt{x}-1}\,\left(\frac{8\,x}{15}+\frac{16\,x^2}{15}+\frac{2\,\sqrt{x}}{5}+\frac{8\,x^{3/2}}{15}+\frac{16\,x^{5/2}}{15}+\frac{2}{5}\right)}{x^{5/2}\,\sqrt{\sqrt{x}+1}}","Not used",1,"((x^(1/2) - 1)^(1/2)*((8*x)/15 + (16*x^2)/15 + (2*x^(1/2))/5 + (8*x^(3/2))/15 + (16*x^(5/2))/15 + 2/5))/(x^(5/2)*(x^(1/2) + 1)^(1/2))","B"
1018,0,-1,78,0.000000,"\text{Not used}","int(x^2*(a + b*x^n)^p*(b*x^n - a)^p,x)","\int x^2\,{\left(a+b\,x^n\right)}^p\,{\left(b\,x^n-a\right)}^p \,d x","Not used",1,"int(x^2*(a + b*x^n)^p*(b*x^n - a)^p, x)","F"
1019,0,-1,70,0.000000,"\text{Not used}","int(x*(a + b*x^n)^p*(b*x^n - a)^p,x)","\int x\,{\left(a+b\,x^n\right)}^p\,{\left(b\,x^n-a\right)}^p \,d x","Not used",1,"int(x*(a + b*x^n)^p*(b*x^n - a)^p, x)","F"
1020,0,-1,73,0.000000,"\text{Not used}","int((a + b*x^n)^p*(b*x^n - a)^p,x)","\int {\left(a+b\,x^n\right)}^p\,{\left(b\,x^n-a\right)}^p \,d x","Not used",1,"int((a + b*x^n)^p*(b*x^n - a)^p, x)","F"
1021,0,-1,72,0.000000,"\text{Not used}","int(((a + b*x^n)^p*(b*x^n - a)^p)/x,x)","\int \frac{{\left(a+b\,x^n\right)}^p\,{\left(b\,x^n-a\right)}^p}{x} \,d x","Not used",1,"int(((a + b*x^n)^p*(b*x^n - a)^p)/x, x)","F"
1022,0,-1,76,0.000000,"\text{Not used}","int(((a + b*x^n)^p*(b*x^n - a)^p)/x^2,x)","\int \frac{{\left(a+b\,x^n\right)}^p\,{\left(b\,x^n-a\right)}^p}{x^2} \,d x","Not used",1,"int(((a + b*x^n)^p*(b*x^n - a)^p)/x^2, x)","F"
1023,1,11,15,0.087178,"\text{Not used}","int(-(x^6 + 1)/(x*(x^6 - 1)),x)","\ln\left(x\right)-\frac{\ln\left(x^6-1\right)}{3}","Not used",1,"log(x) - log(x^6 - 1)/3","B"
1024,1,31,22,4.942285,"\text{Not used}","int((e*x)^m*(a*(m + 1) + b*x^n*(m + n + n*p + 1))*(a + b*x^n)^p,x)","\left(a\,x\,{\left(e\,x\right)}^m+b\,x^{n+1}\,{\left(e\,x\right)}^m\right)\,{\left(a+b\,x^n\right)}^p","Not used",1,"(a*x*(e*x)^m + b*x^(n + 1)*(e*x)^m)*(a + b*x^n)^p","B"
1025,0,-1,114,0.000000,"\text{Not used}","int((e*x)^m/((a + b*x^n)*(c + d*x^n)),x)","\int \frac{{\left(e\,x\right)}^m}{\left(a+b\,x^n\right)\,\left(c+d\,x^n\right)} \,d x","Not used",1,"int((e*x)^m/((a + b*x^n)*(c + d*x^n)), x)","F"
1026,0,-1,89,0.000000,"\text{Not used}","int(x^2/((a + b*x^n)*(c + d*x^n)),x)","\int \frac{x^2}{\left(a+b\,x^n\right)\,\left(c+d\,x^n\right)} \,d x","Not used",1,"int(x^2/((a + b*x^n)*(c + d*x^n)), x)","F"
1027,0,-1,89,0.000000,"\text{Not used}","int(x/((a + b*x^n)*(c + d*x^n)),x)","\int \frac{x}{\left(a+b\,x^n\right)\,\left(c+d\,x^n\right)} \,d x","Not used",1,"int(x/((a + b*x^n)*(c + d*x^n)), x)","F"
1028,0,-1,72,0.000000,"\text{Not used}","int(1/((a + b*x^n)*(c + d*x^n)),x)","\int \frac{1}{\left(a+b\,x^n\right)\,\left(c+d\,x^n\right)} \,d x","Not used",1,"int(1/((a + b*x^n)*(c + d*x^n)), x)","F"
1029,1,162,63,5.724464,"\text{Not used}","int(1/(x*(a + b*x^n)*(c + d*x^n)),x)","\frac{b\,\ln\left(-\frac{1}{b\,d\,x}-\frac{2\,a\,c\,n+a\,d\,n\,x^n+b\,c\,n\,x^n}{d\,x\,\left(a^2\,d\,n-a\,b\,c\,n\right)}\right)}{a^2\,d\,n-a\,b\,c\,n}+\frac{d\,\ln\left(-\frac{1}{b\,d\,x}-\frac{2\,a\,c\,n+a\,d\,n\,x^n+b\,c\,n\,x^n}{b\,x\,\left(b\,c^2\,n-a\,c\,d\,n\right)}\right)}{b\,c^2\,n-a\,c\,d\,n}+\frac{\ln\left(x\right)\,\left(n-1\right)}{a\,c\,n}","Not used",1,"(b*log(- 1/(b*d*x) - (2*a*c*n + a*d*n*x^n + b*c*n*x^n)/(d*x*(a^2*d*n - a*b*c*n))))/(a^2*d*n - a*b*c*n) + (d*log(- 1/(b*d*x) - (2*a*c*n + a*d*n*x^n + b*c*n*x^n)/(b*x*(b*c^2*n - a*c*d*n))))/(b*c^2*n - a*c*d*n) + (log(x)*(n - 1))/(a*c*n)","B"
1030,0,-1,90,0.000000,"\text{Not used}","int(1/(x^2*(a + b*x^n)*(c + d*x^n)),x)","\int \frac{1}{x^2\,\left(a+b\,x^n\right)\,\left(c+d\,x^n\right)} \,d x","Not used",1,"int(1/(x^2*(a + b*x^n)*(c + d*x^n)), x)","F"
1031,0,-1,95,0.000000,"\text{Not used}","int(1/(x^3*(a + b*x^n)*(c + d*x^n)),x)","\int \frac{1}{x^3\,\left(a+b\,x^n\right)\,\left(c+d\,x^n\right)} \,d x","Not used",1,"int(1/(x^3*(a + b*x^n)*(c + d*x^n)), x)","F"
1032,0,-1,175,0.000000,"\text{Not used}","int((e*x)^m/((a + b*x^n)^2*(c + d*x^n)),x)","\int \frac{{\left(e\,x\right)}^m}{{\left(a+b\,x^n\right)}^2\,\left(c+d\,x^n\right)} \,d x","Not used",1,"int((e*x)^m/((a + b*x^n)^2*(c + d*x^n)), x)","F"
1033,0,-1,142,0.000000,"\text{Not used}","int(x^2/((a + b*x^n)^2*(c + d*x^n)),x)","\int \frac{x^2}{{\left(a+b\,x^n\right)}^2\,\left(c+d\,x^n\right)} \,d x","Not used",1,"int(x^2/((a + b*x^n)^2*(c + d*x^n)), x)","F"
1034,0,-1,143,0.000000,"\text{Not used}","int(x/((a + b*x^n)^2*(c + d*x^n)),x)","\int \frac{x}{{\left(a+b\,x^n\right)}^2\,\left(c+d\,x^n\right)} \,d x","Not used",1,"int(x/((a + b*x^n)^2*(c + d*x^n)), x)","F"
1035,0,-1,122,0.000000,"\text{Not used}","int(1/((a + b*x^n)^2*(c + d*x^n)),x)","\int \frac{1}{{\left(a+b\,x^n\right)}^2\,\left(c+d\,x^n\right)} \,d x","Not used",1,"int(1/((a + b*x^n)^2*(c + d*x^n)), x)","F"
1036,0,-1,101,0.000000,"\text{Not used}","int(1/(x*(a + b*x^n)^2*(c + d*x^n)),x)","\int \frac{1}{x\,{\left(a+b\,x^n\right)}^2\,\left(c+d\,x^n\right)} \,d x","Not used",1,"int(1/(x*(a + b*x^n)^2*(c + d*x^n)), x)","F"
1037,0,-1,142,0.000000,"\text{Not used}","int(1/(x^2*(a + b*x^n)^2*(c + d*x^n)),x)","\int \frac{1}{x^2\,{\left(a+b\,x^n\right)}^2\,\left(c+d\,x^n\right)} \,d x","Not used",1,"int(1/(x^2*(a + b*x^n)^2*(c + d*x^n)), x)","F"
1038,0,-1,145,0.000000,"\text{Not used}","int(1/(x^3*(a + b*x^n)^2*(c + d*x^n)),x)","\int \frac{1}{x^3\,{\left(a+b\,x^n\right)}^2\,\left(c+d\,x^n\right)} \,d x","Not used",1,"int(1/(x^3*(a + b*x^n)^2*(c + d*x^n)), x)","F"
1039,0,-1,130,0.000000,"\text{Not used}","int((x^(2*n - 1)*(a + b*x^n)^3)/(c + d*x^n),x)","\int \frac{x^{2\,n-1}\,{\left(a+b\,x^n\right)}^3}{c+d\,x^n} \,d x","Not used",1,"int((x^(2*n - 1)*(a + b*x^n)^3)/(c + d*x^n), x)","F"
1040,0,-1,90,0.000000,"\text{Not used}","int((x^(2*n - 1)*(a + b*x^n)^2)/(c + d*x^n),x)","\int \frac{x^{2\,n-1}\,{\left(a+b\,x^n\right)}^2}{c+d\,x^n} \,d x","Not used",1,"int((x^(2*n - 1)*(a + b*x^n)^2)/(c + d*x^n), x)","F"
1041,0,-1,60,0.000000,"\text{Not used}","int((x^(2*n - 1)*(a + b*x^n))/(c + d*x^n),x)","\int \frac{x^{2\,n-1}\,\left(a+b\,x^n\right)}{c+d\,x^n} \,d x","Not used",1,"int((x^(2*n - 1)*(a + b*x^n))/(c + d*x^n), x)","F"
1042,0,-1,54,0.000000,"\text{Not used}","int(x^(2*n - 1)/((a + b*x^n)*(c + d*x^n)),x)","\int \frac{x^{2\,n-1}}{\left(a+b\,x^n\right)\,\left(c+d\,x^n\right)} \,d x","Not used",1,"int(x^(2*n - 1)/((a + b*x^n)*(c + d*x^n)), x)","F"
1043,0,-1,75,0.000000,"\text{Not used}","int(x^(2*n - 1)/((a + b*x^n)^2*(c + d*x^n)),x)","\int \frac{x^{2\,n-1}}{{\left(a+b\,x^n\right)}^2\,\left(c+d\,x^n\right)} \,d x","Not used",1,"int(x^(2*n - 1)/((a + b*x^n)^2*(c + d*x^n)), x)","F"
1044,0,-1,105,0.000000,"\text{Not used}","int(x^(2*n - 1)/((a + b*x^n)^3*(c + d*x^n)),x)","\int \frac{x^{2\,n-1}}{{\left(a+b\,x^n\right)}^3\,\left(c+d\,x^n\right)} \,d x","Not used",1,"int(x^(2*n - 1)/((a + b*x^n)^3*(c + d*x^n)), x)","F"
1045,0,-1,158,0.000000,"\text{Not used}","int((x^(3*n - 1)*(a + b*x^n)^3)/(c + d*x^n),x)","\int \frac{x^{3\,n-1}\,{\left(a+b\,x^n\right)}^3}{c+d\,x^n} \,d x","Not used",1,"int((x^(3*n - 1)*(a + b*x^n)^3)/(c + d*x^n), x)","F"
1046,0,-1,118,0.000000,"\text{Not used}","int((x^(3*n - 1)*(a + b*x^n)^2)/(c + d*x^n),x)","\int \frac{x^{3\,n-1}\,{\left(a+b\,x^n\right)}^2}{c+d\,x^n} \,d x","Not used",1,"int((x^(3*n - 1)*(a + b*x^n)^2)/(c + d*x^n), x)","F"
1047,0,-1,86,0.000000,"\text{Not used}","int((x^(3*n - 1)*(a + b*x^n))/(c + d*x^n),x)","\int \frac{x^{3\,n-1}\,\left(a+b\,x^n\right)}{c+d\,x^n} \,d x","Not used",1,"int((x^(3*n - 1)*(a + b*x^n))/(c + d*x^n), x)","F"
1048,0,-1,71,0.000000,"\text{Not used}","int(x^(3*n - 1)/((a + b*x^n)*(c + d*x^n)),x)","\int \frac{x^{3\,n-1}}{\left(a+b\,x^n\right)\,\left(c+d\,x^n\right)} \,d x","Not used",1,"int(x^(3*n - 1)/((a + b*x^n)*(c + d*x^n)), x)","F"
1049,0,-1,95,0.000000,"\text{Not used}","int(x^(3*n - 1)/((a + b*x^n)^2*(c + d*x^n)),x)","\int \frac{x^{3\,n-1}}{{\left(a+b\,x^n\right)}^2\,\left(c+d\,x^n\right)} \,d x","Not used",1,"int(x^(3*n - 1)/((a + b*x^n)^2*(c + d*x^n)), x)","F"
1050,0,-1,120,0.000000,"\text{Not used}","int(x^(3*n - 1)/((a + b*x^n)^3*(c + d*x^n)),x)","\int \frac{x^{3\,n-1}}{{\left(a+b\,x^n\right)}^3\,\left(c+d\,x^n\right)} \,d x","Not used",1,"int(x^(3*n - 1)/((a + b*x^n)^3*(c + d*x^n)), x)","F"
1051,1,154,14,0.155922,"\text{Not used}","int(x^13*(b + c*x)^13*(b + 2*c*x),x)","\frac{b^{14}\,x^{14}}{14}+b^{13}\,c\,x^{15}+\frac{13\,b^{12}\,c^2\,x^{16}}{2}+26\,b^{11}\,c^3\,x^{17}+\frac{143\,b^{10}\,c^4\,x^{18}}{2}+143\,b^9\,c^5\,x^{19}+\frac{429\,b^8\,c^6\,x^{20}}{2}+\frac{1716\,b^7\,c^7\,x^{21}}{7}+\frac{429\,b^6\,c^8\,x^{22}}{2}+143\,b^5\,c^9\,x^{23}+\frac{143\,b^4\,c^{10}\,x^{24}}{2}+26\,b^3\,c^{11}\,x^{25}+\frac{13\,b^2\,c^{12}\,x^{26}}{2}+b\,c^{13}\,x^{27}+\frac{c^{14}\,x^{28}}{14}","Not used",1,"(b^14*x^14)/14 + (c^14*x^28)/14 + b^13*c*x^15 + b*c^13*x^27 + (13*b^12*c^2*x^16)/2 + 26*b^11*c^3*x^17 + (143*b^10*c^4*x^18)/2 + 143*b^9*c^5*x^19 + (429*b^8*c^6*x^20)/2 + (1716*b^7*c^7*x^21)/7 + (429*b^6*c^8*x^22)/2 + 143*b^5*c^9*x^23 + (143*b^4*c^10*x^24)/2 + 26*b^3*c^11*x^25 + (13*b^2*c^12*x^26)/2","B"
1052,1,156,16,4.925499,"\text{Not used}","int(x^27*(b + c*x^2)^13*(b + 2*c*x^2),x)","\frac{b^{14}\,x^{28}}{28}+\frac{b^{13}\,c\,x^{30}}{2}+\frac{13\,b^{12}\,c^2\,x^{32}}{4}+13\,b^{11}\,c^3\,x^{34}+\frac{143\,b^{10}\,c^4\,x^{36}}{4}+\frac{143\,b^9\,c^5\,x^{38}}{2}+\frac{429\,b^8\,c^6\,x^{40}}{4}+\frac{858\,b^7\,c^7\,x^{42}}{7}+\frac{429\,b^6\,c^8\,x^{44}}{4}+\frac{143\,b^5\,c^9\,x^{46}}{2}+\frac{143\,b^4\,c^{10}\,x^{48}}{4}+13\,b^3\,c^{11}\,x^{50}+\frac{13\,b^2\,c^{12}\,x^{52}}{4}+\frac{b\,c^{13}\,x^{54}}{2}+\frac{c^{14}\,x^{56}}{28}","Not used",1,"(b^14*x^28)/28 + (c^14*x^56)/28 + (b^13*c*x^30)/2 + (b*c^13*x^54)/2 + (13*b^12*c^2*x^32)/4 + 13*b^11*c^3*x^34 + (143*b^10*c^4*x^36)/4 + (143*b^9*c^5*x^38)/2 + (429*b^8*c^6*x^40)/4 + (858*b^7*c^7*x^42)/7 + (429*b^6*c^8*x^44)/4 + (143*b^5*c^9*x^46)/2 + (143*b^4*c^10*x^48)/4 + 13*b^3*c^11*x^50 + (13*b^2*c^12*x^52)/4","B"
1053,1,156,16,4.771522,"\text{Not used}","int(x^41*(b + c*x^3)^13*(b + 2*c*x^3),x)","\frac{b^{14}\,x^{42}}{42}+\frac{b^{13}\,c\,x^{45}}{3}+\frac{13\,b^{12}\,c^2\,x^{48}}{6}+\frac{26\,b^{11}\,c^3\,x^{51}}{3}+\frac{143\,b^{10}\,c^4\,x^{54}}{6}+\frac{143\,b^9\,c^5\,x^{57}}{3}+\frac{143\,b^8\,c^6\,x^{60}}{2}+\frac{572\,b^7\,c^7\,x^{63}}{7}+\frac{143\,b^6\,c^8\,x^{66}}{2}+\frac{143\,b^5\,c^9\,x^{69}}{3}+\frac{143\,b^4\,c^{10}\,x^{72}}{6}+\frac{26\,b^3\,c^{11}\,x^{75}}{3}+\frac{13\,b^2\,c^{12}\,x^{78}}{6}+\frac{b\,c^{13}\,x^{81}}{3}+\frac{c^{14}\,x^{84}}{42}","Not used",1,"(b^14*x^42)/42 + (c^14*x^84)/42 + (b^13*c*x^45)/3 + (b*c^13*x^81)/3 + (13*b^12*c^2*x^48)/6 + (26*b^11*c^3*x^51)/3 + (143*b^10*c^4*x^54)/6 + (143*b^9*c^5*x^57)/3 + (143*b^8*c^6*x^60)/2 + (572*b^7*c^7*x^63)/7 + (143*b^6*c^8*x^66)/2 + (143*b^5*c^9*x^69)/3 + (143*b^4*c^10*x^72)/6 + (26*b^3*c^11*x^75)/3 + (13*b^2*c^12*x^78)/6","B"
1054,1,229,21,5.209056,"\text{Not used}","int(x^(14*n - 1)*(b + c*x^n)^13*(b + 2*c*x^n),x)","\frac{b^{14}\,x^{14\,n}}{14\,n}+\frac{c^{14}\,x^{28\,n}}{14\,n}+\frac{13\,b^{12}\,c^2\,x^{16\,n}}{2\,n}+\frac{26\,b^{11}\,c^3\,x^{17\,n}}{n}+\frac{143\,b^{10}\,c^4\,x^{18\,n}}{2\,n}+\frac{143\,b^9\,c^5\,x^{19\,n}}{n}+\frac{429\,b^8\,c^6\,x^{20\,n}}{2\,n}+\frac{1716\,b^7\,c^7\,x^{21\,n}}{7\,n}+\frac{429\,b^6\,c^8\,x^{22\,n}}{2\,n}+\frac{143\,b^5\,c^9\,x^{23\,n}}{n}+\frac{143\,b^4\,c^{10}\,x^{24\,n}}{2\,n}+\frac{26\,b^3\,c^{11}\,x^{25\,n}}{n}+\frac{13\,b^2\,c^{12}\,x^{26\,n}}{2\,n}+\frac{b^{13}\,c\,x^{15\,n}}{n}+\frac{b\,c^{13}\,x^{27\,n}}{n}","Not used",1,"(b^14*x^(14*n))/(14*n) + (c^14*x^(28*n))/(14*n) + (13*b^12*c^2*x^(16*n))/(2*n) + (26*b^11*c^3*x^(17*n))/n + (143*b^10*c^4*x^(18*n))/(2*n) + (143*b^9*c^5*x^(19*n))/n + (429*b^8*c^6*x^(20*n))/(2*n) + (1716*b^7*c^7*x^(21*n))/(7*n) + (429*b^6*c^8*x^(22*n))/(2*n) + (143*b^5*c^9*x^(23*n))/n + (143*b^4*c^10*x^(24*n))/(2*n) + (26*b^3*c^11*x^(25*n))/n + (13*b^2*c^12*x^(26*n))/(2*n) + (b^13*c*x^(15*n))/n + (b*c^13*x^(27*n))/n","B"
1055,1,25,13,4.810198,"\text{Not used}","int(x^(m - 1)*(a*m + b*x^n*(m + n*p))*(a + b*x^n)^(p - 1),x)","\left(a\,x^m+b\,x^{m+n}\right)\,{\left(a+b\,x^n\right)}^{p-1}","Not used",1,"(a*x^m + b*x^(m + n))*(a + b*x^n)^(p - 1)","B"
1056,1,8,8,4.661711,"\text{Not used}","int((b + 2*c*x)/(x*(b + c*x)),x)","\ln\left(x\,\left(b+c\,x\right)\right)","Not used",1,"log(x*(b + c*x))","B"
1057,1,13,15,0.060260,"\text{Not used}","int((b + 2*c*x^2)/(x*(b + c*x^2)),x)","\frac{\ln\left(c\,x^2+b\right)}{2}+\ln\left(x\right)","Not used",1,"log(b + c*x^2)/2 + log(x)","B"
1058,1,13,15,4.628049,"\text{Not used}","int((b + 2*c*x^3)/(x*(b + c*x^3)),x)","\frac{\ln\left(c\,x^3+b\right)}{3}+\ln\left(x\right)","Not used",1,"log(b + c*x^3)/3 + log(x)","B"
1059,1,15,15,4.723366,"\text{Not used}","int((b + 2*c*x^n)/(x*(b + c*x^n)),x)","\ln\left(x\right)+\frac{\ln\left(b+c\,x^n\right)}{n}","Not used",1,"log(x) + log(b + c*x^n)/n","B"
1060,1,12,14,7.087465,"\text{Not used}","int((b + 2*c*x)/(x^8*(b + c*x)^8),x)","-\frac{1}{7\,x^7\,{\left(b+c\,x\right)}^7}","Not used",1,"-1/(7*x^7*(b + c*x)^7)","B"
1061,1,14,16,2.315006,"\text{Not used}","int((b + 2*c*x^2)/(x^15*(b + c*x^2)^8),x)","-\frac{1}{14\,x^{14}\,{\left(c\,x^2+b\right)}^7}","Not used",1,"-1/(14*x^14*(b + c*x^2)^7)","B"
1062,1,14,16,9.981414,"\text{Not used}","int((b + 2*c*x^3)/(x^22*(b + c*x^3)^8),x)","-\frac{1}{21\,x^{21}\,{\left(c\,x^3+b\right)}^7}","Not used",1,"-1/(21*x^21*(b + c*x^3)^7)","B"
1063,1,105,21,4.986560,"\text{Not used}","int((b + 2*c*x^n)/(x^(7*n + 1)*(b + c*x^n)^8),x)","-\frac{1}{7\,x^{7\,n}\,\left(b^7\,n+c^7\,n\,x^{7\,n}+7\,b^6\,c\,n\,x^n+7\,b\,c^6\,n\,x^{6\,n}+21\,b^5\,c^2\,n\,x^{2\,n}+35\,b^4\,c^3\,n\,x^{3\,n}+35\,b^3\,c^4\,n\,x^{4\,n}+21\,b^2\,c^5\,n\,x^{5\,n}\right)}","Not used",1,"-1/(7*x^(7*n)*(b^7*n + c^7*n*x^(7*n) + 7*b^6*c*n*x^n + 7*b*c^6*n*x^(6*n) + 21*b^5*c^2*n*x^(2*n) + 35*b^4*c^3*n*x^(3*n) + 35*b^3*c^4*n*x^(4*n) + 21*b^2*c^5*n*x^(5*n)))","B"
1064,1,37,52,4.817204,"\text{Not used}","int(-(x^31*(x^16 + 1)^(1/2))/(x^16 - 1),x)","\frac{\sqrt{2}\,\mathrm{atanh}\left(\frac{\sqrt{2}\,\sqrt{x^{16}+1}}{2}\right)}{8}-\frac{\sqrt{x^{16}+1}}{8}-\frac{{\left(x^{16}+1\right)}^{3/2}}{24}","Not used",1,"(2^(1/2)*atanh((2^(1/2)*(x^16 + 1)^(1/2))/2))/8 - (x^16 + 1)^(1/2)/8 - (x^16 + 1)^(3/2)/24","B"
1065,0,-1,93,0.000000,"\text{Not used}","int((c + d/x)^(1/2)/(x*(a + b/x)^(1/2)),x)","\int \frac{\sqrt{c+\frac{d}{x}}}{x\,\sqrt{a+\frac{b}{x}}} \,d x","Not used",1,"int((c + d/x)^(1/2)/(x*(a + b/x)^(1/2)), x)","F"
1066,0,-1,252,0.000000,"\text{Not used}","int((x^(2*n - 1)*(a + b*x^n)^(5/2))/(c + d*x^n)^(1/2),x)","\int \frac{x^{2\,n-1}\,{\left(a+b\,x^n\right)}^{5/2}}{\sqrt{c+d\,x^n}} \,d x","Not used",1,"int((x^(2*n - 1)*(a + b*x^n)^(5/2))/(c + d*x^n)^(1/2), x)","F"
1067,0,-1,199,0.000000,"\text{Not used}","int((x^(2*n - 1)*(a + b*x^n)^(3/2))/(c + d*x^n)^(1/2),x)","\int \frac{x^{2\,n-1}\,{\left(a+b\,x^n\right)}^{3/2}}{\sqrt{c+d\,x^n}} \,d x","Not used",1,"int((x^(2*n - 1)*(a + b*x^n)^(3/2))/(c + d*x^n)^(1/2), x)","F"
1068,0,-1,146,0.000000,"\text{Not used}","int((x^(2*n - 1)*(a + b*x^n)^(1/2))/(c + d*x^n)^(1/2),x)","\int \frac{x^{2\,n-1}\,\sqrt{a+b\,x^n}}{\sqrt{c+d\,x^n}} \,d x","Not used",1,"int((x^(2*n - 1)*(a + b*x^n)^(1/2))/(c + d*x^n)^(1/2), x)","F"
1069,0,-1,89,0.000000,"\text{Not used}","int(x^(2*n - 1)/((a + b*x^n)^(1/2)*(c + d*x^n)^(1/2)),x)","\int \frac{x^{2\,n-1}}{\sqrt{a+b\,x^n}\,\sqrt{c+d\,x^n}} \,d x","Not used",1,"int(x^(2*n - 1)/((a + b*x^n)^(1/2)*(c + d*x^n)^(1/2)), x)","F"
1070,0,-1,91,0.000000,"\text{Not used}","int(x^(2*n - 1)/((a + b*x^n)^(3/2)*(c + d*x^n)^(1/2)),x)","\int \frac{x^{2\,n-1}}{{\left(a+b\,x^n\right)}^{3/2}\,\sqrt{c+d\,x^n}} \,d x","Not used",1,"int(x^(2*n - 1)/((a + b*x^n)^(3/2)*(c + d*x^n)^(1/2)), x)","F"
1071,0,-1,95,0.000000,"\text{Not used}","int(x^(2*n - 1)/((a + b*x^n)^(5/2)*(c + d*x^n)^(1/2)),x)","\int \frac{x^{2\,n-1}}{{\left(a+b\,x^n\right)}^{5/2}\,\sqrt{c+d\,x^n}} \,d x","Not used",1,"int(x^(2*n - 1)/((a + b*x^n)^(5/2)*(c + d*x^n)^(1/2)), x)","F"
1072,0,-1,358,0.000000,"\text{Not used}","int((x^(3*n - 1)*(a + b*x^n)^(5/2))/(c + d*x^n)^(1/2),x)","\int \frac{x^{3\,n-1}\,{\left(a+b\,x^n\right)}^{5/2}}{\sqrt{c+d\,x^n}} \,d x","Not used",1,"int((x^(3*n - 1)*(a + b*x^n)^(5/2))/(c + d*x^n)^(1/2), x)","F"
1073,0,-1,291,0.000000,"\text{Not used}","int((x^(3*n - 1)*(a + b*x^n)^(3/2))/(c + d*x^n)^(1/2),x)","\int \frac{x^{3\,n-1}\,{\left(a+b\,x^n\right)}^{3/2}}{\sqrt{c+d\,x^n}} \,d x","Not used",1,"int((x^(3*n - 1)*(a + b*x^n)^(3/2))/(c + d*x^n)^(1/2), x)","F"
1074,0,-1,221,0.000000,"\text{Not used}","int((x^(3*n - 1)*(a + b*x^n)^(1/2))/(c + d*x^n)^(1/2),x)","\int \frac{x^{3\,n-1}\,\sqrt{a+b\,x^n}}{\sqrt{c+d\,x^n}} \,d x","Not used",1,"int((x^(3*n - 1)*(a + b*x^n)^(1/2))/(c + d*x^n)^(1/2), x)","F"
1075,0,-1,150,0.000000,"\text{Not used}","int(x^(3*n - 1)/((a + b*x^n)^(1/2)*(c + d*x^n)^(1/2)),x)","\int \frac{x^{3\,n-1}}{\sqrt{a+b\,x^n}\,\sqrt{c+d\,x^n}} \,d x","Not used",1,"int(x^(3*n - 1)/((a + b*x^n)^(1/2)*(c + d*x^n)^(1/2)), x)","F"
1076,0,-1,133,0.000000,"\text{Not used}","int(x^(3*n - 1)/((a + b*x^n)^(3/2)*(c + d*x^n)^(1/2)),x)","\int \frac{x^{3\,n-1}}{{\left(a+b\,x^n\right)}^{3/2}\,\sqrt{c+d\,x^n}} \,d x","Not used",1,"int(x^(3*n - 1)/((a + b*x^n)^(3/2)*(c + d*x^n)^(1/2)), x)","F"
1077,0,-1,147,0.000000,"\text{Not used}","int(x^(3*n - 1)/((a + b*x^n)^(5/2)*(c + d*x^n)^(1/2)),x)","\int \frac{x^{3\,n-1}}{{\left(a+b\,x^n\right)}^{5/2}\,\sqrt{c+d\,x^n}} \,d x","Not used",1,"int(x^(3*n - 1)/((a + b*x^n)^(5/2)*(c + d*x^n)^(1/2)), x)","F"
1078,1,22,20,4.795166,"\text{Not used}","int(x^p*(b + c*x)^p*(b + 2*c*x),x)","\frac{x\,x^p\,{\left(b+c\,x\right)}^p\,\left(b+c\,x\right)}{p+1}","Not used",1,"(x*x^p*(b + c*x)^p*(b + c*x))/(p + 1)","B"
1079,1,47,27,4.881983,"\text{Not used}","int(x^(2*p + 1)*(b + c*x^2)^p*(b + 2*c*x^2),x)","{\left(c\,x^2+b\right)}^p\,\left(\frac{c\,x^{2\,p+1}\,x^3}{2\,p+2}+\frac{b\,x\,x^{2\,p+1}}{2\,p+2}\right)","Not used",1,"(b + c*x^2)^p*((c*x^(2*p + 1)*x^3)/(2*p + 2) + (b*x*x^(2*p + 1))/(2*p + 2))","B"
1080,1,47,27,4.902418,"\text{Not used}","int(x^(3*p + 2)*(b + c*x^3)^p*(b + 2*c*x^3),x)","{\left(c\,x^3+b\right)}^p\,\left(\frac{c\,x^{3\,p+2}\,x^4}{3\,p+3}+\frac{b\,x\,x^{3\,p+2}}{3\,p+3}\right)","Not used",1,"(b + c*x^3)^p*((c*x^(3*p + 2)*x^4)/(3*p + 3) + (b*x*x^(3*p + 2))/(3*p + 3))","B"
1081,1,54,27,4.862705,"\text{Not used}","int(x^(n*(p + 1) - 1)*(b + c*x^n)^p*(b + 2*c*x^n),x)","\left(\frac{b\,x\,x^{n\,\left(p+1\right)-1}}{n\,\left(p+1\right)}+\frac{c\,x\,x^n\,x^{n\,\left(p+1\right)-1}}{n\,\left(p+1\right)}\right)\,{\left(b+c\,x^n\right)}^p","Not used",1,"((b*x*x^(n*(p + 1) - 1))/(n*(p + 1)) + (c*x*x^n*x^(n*(p + 1) - 1))/(n*(p + 1)))*(b + c*x^n)^p","B"